Properties

Label 48.7.i.a.5.10
Level $48$
Weight $7$
Character 48.5
Analytic conductor $11.043$
Analytic rank $0$
Dimension $92$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [48,7,Mod(5,48)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(48, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 2]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("48.5");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 48.i (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(11.0425960138\)
Analytic rank: \(0\)
Dimension: \(92\)
Relative dimension: \(46\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.10
Character \(\chi\) \(=\) 48.5
Dual form 48.7.i.a.29.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-6.62545 + 4.48369i) q^{2} +(17.3541 - 20.6842i) q^{3} +(23.7931 - 59.4129i) q^{4} +(77.8915 - 77.8915i) q^{5} +(-22.2368 + 214.852i) q^{6} -310.530i q^{7} +(108.749 + 500.318i) q^{8} +(-126.674 - 717.910i) q^{9} +O(q^{10})\) \(q+(-6.62545 + 4.48369i) q^{2} +(17.3541 - 20.6842i) q^{3} +(23.7931 - 59.4129i) q^{4} +(77.8915 - 77.8915i) q^{5} +(-22.2368 + 214.852i) q^{6} -310.530i q^{7} +(108.749 + 500.318i) q^{8} +(-126.674 - 717.910i) q^{9} +(-166.825 + 865.307i) q^{10} +(-1027.05 + 1027.05i) q^{11} +(-816.002 - 1523.20i) q^{12} +(-1422.09 + 1422.09i) q^{13} +(1392.32 + 2057.40i) q^{14} +(-259.392 - 2962.86i) q^{15} +(-2963.78 - 2827.23i) q^{16} -6133.59i q^{17} +(4058.15 + 4188.51i) q^{18} +(6349.13 - 6349.13i) q^{19} +(-2774.48 - 6481.04i) q^{20} +(-6423.08 - 5388.96i) q^{21} +(2199.70 - 11409.7i) q^{22} -3000.58 q^{23} +(12235.9 + 6433.15i) q^{24} +3490.83i q^{25} +(3045.77 - 15798.1i) q^{26} +(-17047.7 - 9838.50i) q^{27} +(-18449.5 - 7388.48i) q^{28} +(-17533.8 - 17533.8i) q^{29} +(15003.1 + 18467.2i) q^{30} +11354.1 q^{31} +(32312.8 + 5443.03i) q^{32} +(3420.26 + 39067.3i) q^{33} +(27501.1 + 40637.8i) q^{34} +(-24187.7 - 24187.7i) q^{35} +(-45667.1 - 9555.24i) q^{36} +(-9399.09 - 9399.09i) q^{37} +(-13598.3 + 70533.4i) q^{38} +(4735.79 + 54093.7i) q^{39} +(47441.1 + 30499.9i) q^{40} -81655.3 q^{41} +(66718.2 + 6905.19i) q^{42} +(66104.5 + 66104.5i) q^{43} +(36583.3 + 85456.8i) q^{44} +(-65785.9 - 46052.3i) q^{45} +(19880.2 - 13453.7i) q^{46} -39239.7i q^{47} +(-109913. + 12239.5i) q^{48} +21219.9 q^{49} +(-15651.8 - 23128.3i) q^{50} +(-126869. - 106443. i) q^{51} +(50654.4 + 118326. i) q^{52} +(199357. - 199357. i) q^{53} +(157061. - 11252.2i) q^{54} +159997. i q^{55} +(155364. - 33769.8i) q^{56} +(-21143.7 - 241510. i) q^{57} +(194785. + 37553.1i) q^{58} +(-140266. + 140266. i) q^{59} +(-182204. - 55084.4i) q^{60} +(279820. - 279820. i) q^{61} +(-75225.7 + 50908.0i) q^{62} +(-222933. + 39336.1i) q^{63} +(-238491. + 108818. i) q^{64} +221537. i q^{65} +(-197826. - 243503. i) q^{66} +(-352782. + 352782. i) q^{67} +(-364414. - 145937. i) q^{68} +(-52072.3 + 62064.7i) q^{69} +(268704. + 51804.2i) q^{70} +353151. q^{71} +(345407. - 141449. i) q^{72} -365757. i q^{73} +(104416. + 20130.6i) q^{74} +(72205.0 + 60580.0i) q^{75} +(-226155. - 528286. i) q^{76} +(318931. + 318931. i) q^{77} +(-273916. - 337161. i) q^{78} +469445. q^{79} +(-451070. + 10635.7i) q^{80} +(-499348. + 181881. i) q^{81} +(541003. - 366117. i) q^{82} +(671838. + 671838. i) q^{83} +(-472998. + 253393. i) q^{84} +(-477755. - 477755. i) q^{85} +(-734364. - 141580. i) q^{86} +(-666955. + 58390.4i) q^{87} +(-625543. - 402161. i) q^{88} +289018. q^{89} +(642345. + 10153.4i) q^{90} +(441601. + 441601. i) q^{91} +(-71393.1 + 178273. i) q^{92} +(197039. - 234850. i) q^{93} +(175938. + 259980. i) q^{94} -989087. i q^{95} +(673342. - 573906. i) q^{96} +356725. q^{97} +(-140591. + 95143.5i) q^{98} +(867431. + 607230. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6} + 1496 q^{10} + 4288 q^{12} - 4 q^{13} - 4 q^{15} + 10352 q^{16} + 10020 q^{18} - 3940 q^{19} + 1456 q^{21} - 42088 q^{22} + 66376 q^{24} - 34322 q^{27} + 27000 q^{28} - 127836 q^{30} - 8 q^{31} - 4 q^{33} + 128424 q^{34} + 172420 q^{36} - 4 q^{37} - 164392 q^{40} + 221560 q^{42} - 195268 q^{43} - 31252 q^{45} + 150712 q^{46} - 188048 q^{48} - 1142884 q^{49} + 385056 q^{51} - 122368 q^{52} + 151912 q^{54} - 181960 q^{58} + 242304 q^{60} - 326500 q^{61} + 470592 q^{63} - 251752 q^{64} + 489172 q^{66} + 1207676 q^{67} - 1460 q^{69} + 346392 q^{70} - 903480 q^{72} + 1413778 q^{75} - 359992 q^{76} + 1478252 q^{78} + 860920 q^{79} - 4 q^{81} - 2412800 q^{82} - 730640 q^{84} + 434496 q^{85} + 1259360 q^{88} - 291792 q^{90} + 2320992 q^{91} - 1176260 q^{93} - 1412496 q^{94} + 1956200 q^{96} - 8 q^{97} - 4048228 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.62545 + 4.48369i −0.828181 + 0.560461i
\(3\) 17.3541 20.6842i 0.642743 0.766082i
\(4\) 23.7931 59.4129i 0.371767 0.928326i
\(5\) 77.8915 77.8915i 0.623132 0.623132i −0.323199 0.946331i \(-0.604758\pi\)
0.946331 + 0.323199i \(0.104758\pi\)
\(6\) −22.2368 + 214.852i −0.102948 + 0.994687i
\(7\) 310.530i 0.905336i −0.891679 0.452668i \(-0.850472\pi\)
0.891679 0.452668i \(-0.149528\pi\)
\(8\) 108.749 + 500.318i 0.212400 + 0.977183i
\(9\) −126.674 717.910i −0.173764 0.984787i
\(10\) −166.825 + 865.307i −0.166825 + 0.865307i
\(11\) −1027.05 + 1027.05i −0.771639 + 0.771639i −0.978393 0.206754i \(-0.933710\pi\)
0.206754 + 0.978393i \(0.433710\pi\)
\(12\) −816.002 1523.20i −0.472223 0.881479i
\(13\) −1422.09 + 1422.09i −0.647285 + 0.647285i −0.952336 0.305051i \(-0.901327\pi\)
0.305051 + 0.952336i \(0.401327\pi\)
\(14\) 1392.32 + 2057.40i 0.507406 + 0.749782i
\(15\) −259.392 2962.86i −0.0768569 0.877884i
\(16\) −2963.78 2827.23i −0.723578 0.690242i
\(17\) 6133.59i 1.24844i −0.781248 0.624221i \(-0.785417\pi\)
0.781248 0.624221i \(-0.214583\pi\)
\(18\) 4058.15 + 4188.51i 0.695843 + 0.718194i
\(19\) 6349.13 6349.13i 0.925665 0.925665i −0.0717575 0.997422i \(-0.522861\pi\)
0.997422 + 0.0717575i \(0.0228608\pi\)
\(20\) −2774.48 6481.04i −0.346810 0.810130i
\(21\) −6423.08 5388.96i −0.693562 0.581898i
\(22\) 2199.70 11409.7i 0.206583 1.07153i
\(23\) −3000.58 −0.246616 −0.123308 0.992368i \(-0.539350\pi\)
−0.123308 + 0.992368i \(0.539350\pi\)
\(24\) 12235.9 + 6433.15i 0.885121 + 0.465361i
\(25\) 3490.83i 0.223413i
\(26\) 3045.77 15798.1i 0.173291 0.898847i
\(27\) −17047.7 9838.50i −0.866114 0.499847i
\(28\) −18449.5 7388.48i −0.840447 0.336574i
\(29\) −17533.8 17533.8i −0.718922 0.718922i 0.249463 0.968384i \(-0.419746\pi\)
−0.968384 + 0.249463i \(0.919746\pi\)
\(30\) 15003.1 + 18467.2i 0.555671 + 0.683971i
\(31\) 11354.1 0.381124 0.190562 0.981675i \(-0.438969\pi\)
0.190562 + 0.981675i \(0.438969\pi\)
\(32\) 32312.8 + 5443.03i 0.986108 + 0.166108i
\(33\) 3420.26 + 39067.3i 0.0951737 + 1.08710i
\(34\) 27501.1 + 40637.8i 0.699703 + 1.03394i
\(35\) −24187.7 24187.7i −0.564144 0.564144i
\(36\) −45667.1 9555.24i −0.978803 0.204802i
\(37\) −9399.09 9399.09i −0.185558 0.185558i 0.608214 0.793773i \(-0.291886\pi\)
−0.793773 + 0.608214i \(0.791886\pi\)
\(38\) −13598.3 + 70533.4i −0.247819 + 1.28542i
\(39\) 4735.79 + 54093.7i 0.0798359 + 0.911911i
\(40\) 47441.1 + 30499.9i 0.741267 + 0.476561i
\(41\) −81655.3 −1.18477 −0.592384 0.805656i \(-0.701813\pi\)
−0.592384 + 0.805656i \(0.701813\pi\)
\(42\) 66718.2 + 6905.19i 0.900526 + 0.0932026i
\(43\) 66104.5 + 66104.5i 0.831431 + 0.831431i 0.987712 0.156282i \(-0.0499509\pi\)
−0.156282 + 0.987712i \(0.549951\pi\)
\(44\) 36583.3 + 85456.8i 0.429463 + 1.00320i
\(45\) −65785.9 46052.3i −0.721930 0.505375i
\(46\) 19880.2 13453.7i 0.204243 0.138219i
\(47\) 39239.7i 0.377948i −0.981982 0.188974i \(-0.939484\pi\)
0.981982 0.188974i \(-0.0605161\pi\)
\(48\) −109913. + 12239.5i −0.993857 + 0.110672i
\(49\) 21219.9 0.180366
\(50\) −15651.8 23128.3i −0.125214 0.185026i
\(51\) −126869. 106443.i −0.956409 0.802427i
\(52\) 50654.4 + 118326.i 0.360252 + 0.841531i
\(53\) 199357. 199357.i 1.33907 1.33907i 0.442115 0.896959i \(-0.354228\pi\)
0.896959 0.442115i \(-0.145772\pi\)
\(54\) 157061. 11252.2i 0.997444 0.0714587i
\(55\) 159997.i 0.961666i
\(56\) 155364. 33769.8i 0.884679 0.192293i
\(57\) −21143.7 241510.i −0.114171 1.30410i
\(58\) 194785. + 37553.1i 0.998325 + 0.192470i
\(59\) −140266. + 140266.i −0.682960 + 0.682960i −0.960666 0.277706i \(-0.910426\pi\)
0.277706 + 0.960666i \(0.410426\pi\)
\(60\) −182204. 55084.4i −0.843535 0.255020i
\(61\) 279820. 279820.i 1.23279 1.23279i 0.269902 0.962888i \(-0.413009\pi\)
0.962888 0.269902i \(-0.0869912\pi\)
\(62\) −75225.7 + 50908.0i −0.315639 + 0.213605i
\(63\) −222933. + 39336.1i −0.891564 + 0.157315i
\(64\) −238491. + 108818.i −0.909772 + 0.415107i
\(65\) 221537.i 0.806688i
\(66\) −197826. 243503.i −0.688101 0.846978i
\(67\) −352782. + 352782.i −1.17296 + 1.17296i −0.191456 + 0.981501i \(0.561321\pi\)
−0.981501 + 0.191456i \(0.938679\pi\)
\(68\) −364414. 145937.i −1.15896 0.464130i
\(69\) −52072.3 + 62064.7i −0.158511 + 0.188928i
\(70\) 268704. + 51804.2i 0.783394 + 0.151033i
\(71\) 353151. 0.986700 0.493350 0.869831i \(-0.335772\pi\)
0.493350 + 0.869831i \(0.335772\pi\)
\(72\) 345407. 141449.i 0.925410 0.378968i
\(73\) 365757.i 0.940208i −0.882611 0.470104i \(-0.844216\pi\)
0.882611 0.470104i \(-0.155784\pi\)
\(74\) 104416. + 20130.6i 0.257674 + 0.0496777i
\(75\) 72205.0 + 60580.0i 0.171153 + 0.143597i
\(76\) −226155. 528286.i −0.515187 1.20345i
\(77\) 318931. + 318931.i 0.698593 + 0.698593i
\(78\) −273916. 337161.i −0.577209 0.710483i
\(79\) 469445. 0.952146 0.476073 0.879406i \(-0.342060\pi\)
0.476073 + 0.879406i \(0.342060\pi\)
\(80\) −451070. + 10635.7i −0.880997 + 0.0207728i
\(81\) −499348. + 181881.i −0.939612 + 0.342241i
\(82\) 541003. 366117.i 0.981201 0.664016i
\(83\) 671838. + 671838.i 1.17498 + 1.17498i 0.981007 + 0.193973i \(0.0621374\pi\)
0.193973 + 0.981007i \(0.437863\pi\)
\(84\) −472998. + 253393.i −0.798035 + 0.427521i
\(85\) −477755. 477755.i −0.777944 0.777944i
\(86\) −734364. 141580.i −1.15456 0.222591i
\(87\) −666955. + 58390.4i −1.01283 + 0.0886715i
\(88\) −625543. 402161.i −0.917929 0.590136i
\(89\) 289018. 0.409972 0.204986 0.978765i \(-0.434285\pi\)
0.204986 + 0.978765i \(0.434285\pi\)
\(90\) 642345. + 10153.4i 0.881132 + 0.0139279i
\(91\) 441601. + 441601.i 0.586011 + 0.586011i
\(92\) −71393.1 + 178273.i −0.0916839 + 0.228940i
\(93\) 197039. 234850.i 0.244964 0.291972i
\(94\) 175938. + 259980.i 0.211825 + 0.313009i
\(95\) 989087.i 1.15362i
\(96\) 673342. 573906.i 0.761066 0.648675i
\(97\) 356725. 0.390858 0.195429 0.980718i \(-0.437390\pi\)
0.195429 + 0.980718i \(0.437390\pi\)
\(98\) −140591. + 95143.5i −0.149376 + 0.101088i
\(99\) 867431. + 607230.i 0.893983 + 0.625817i
\(100\) 207400. + 83057.5i 0.207400 + 0.0830575i
\(101\) 723463. 723463.i 0.702186 0.702186i −0.262693 0.964879i \(-0.584611\pi\)
0.964879 + 0.262693i \(0.0846106\pi\)
\(102\) 1.31782e6 + 136391.i 1.24181 + 0.128525i
\(103\) 878385.i 0.803847i 0.915673 + 0.401923i \(0.131658\pi\)
−0.915673 + 0.401923i \(0.868342\pi\)
\(104\) −866145. 556844.i −0.769999 0.495033i
\(105\) −920057. + 80549.0i −0.794780 + 0.0695813i
\(106\) −426975. + 2.21469e6i −0.358497 + 1.85949i
\(107\) 952833. 952833.i 0.777796 0.777796i −0.201660 0.979456i \(-0.564634\pi\)
0.979456 + 0.201660i \(0.0646336\pi\)
\(108\) −990151. + 778765.i −0.786014 + 0.618209i
\(109\) −680307. + 680307.i −0.525322 + 0.525322i −0.919174 0.393852i \(-0.871142\pi\)
0.393852 + 0.919174i \(0.371142\pi\)
\(110\) −717377. 1.06005e6i −0.538976 0.796434i
\(111\) −357525. + 31300.6i −0.261419 + 0.0228867i
\(112\) −877941. + 920343.i −0.624901 + 0.655082i
\(113\) 138247.i 0.0958121i 0.998852 + 0.0479060i \(0.0152548\pi\)
−0.998852 + 0.0479060i \(0.984745\pi\)
\(114\) 1.22294e6 + 1.50531e6i 0.825451 + 1.01604i
\(115\) −233720. + 233720.i −0.153675 + 0.153675i
\(116\) −1.45891e6 + 624549.i −0.934665 + 0.400122i
\(117\) 1.20107e6 + 840788.i 0.749913 + 0.524964i
\(118\) 300415. 1.55823e6i 0.182842 0.948387i
\(119\) −1.90467e6 −1.13026
\(120\) 1.45416e6 451986.i 0.841529 0.261566i
\(121\) 338109.i 0.190854i
\(122\) −599307. + 3.10856e6i −0.330042 + 1.71190i
\(123\) −1.41705e6 + 1.68898e6i −0.761500 + 0.907629i
\(124\) 270148. 674577.i 0.141689 0.353807i
\(125\) 1.48896e6 + 1.48896e6i 0.762348 + 0.762348i
\(126\) 1.30066e6 1.26018e6i 0.650207 0.629972i
\(127\) 369091. 0.180187 0.0900934 0.995933i \(-0.471283\pi\)
0.0900934 + 0.995933i \(0.471283\pi\)
\(128\) 1.09221e6 1.79029e6i 0.520805 0.853676i
\(129\) 2.51450e6 220139.i 1.17134 0.102548i
\(130\) −993302. 1.46778e6i −0.452117 0.668084i
\(131\) 2.05595e6 + 2.05595e6i 0.914530 + 0.914530i 0.996625 0.0820941i \(-0.0261608\pi\)
−0.0820941 + 0.996625i \(0.526161\pi\)
\(132\) 2.40248e6 + 726324.i 1.04457 + 0.315798i
\(133\) −1.97160e6 1.97160e6i −0.838038 0.838038i
\(134\) 755575. 3.91911e6i 0.314024 1.62882i
\(135\) −2.09421e6 + 561537.i −0.851174 + 0.228232i
\(136\) 3.06875e6 667021.i 1.21996 0.265169i
\(137\) −3.22146e6 −1.25283 −0.626413 0.779491i \(-0.715478\pi\)
−0.626413 + 0.779491i \(0.715478\pi\)
\(138\) 66723.3 644682.i 0.0253887 0.245306i
\(139\) −1.27858e6 1.27858e6i −0.476083 0.476083i 0.427793 0.903877i \(-0.359291\pi\)
−0.903877 + 0.427793i \(0.859291\pi\)
\(140\) −2.01256e6 + 861559.i −0.733440 + 0.313979i
\(141\) −811642. 680967.i −0.289539 0.242923i
\(142\) −2.33978e6 + 1.58342e6i −0.817166 + 0.553007i
\(143\) 2.92111e6i 0.998941i
\(144\) −1.65427e6 + 2.48586e6i −0.554010 + 0.832510i
\(145\) −2.73146e6 −0.895966
\(146\) 1.63994e6 + 2.42330e6i 0.526950 + 0.778662i
\(147\) 368252. 438918.i 0.115929 0.138175i
\(148\) −782061. + 334794.i −0.241243 + 0.103274i
\(149\) 3.08453e6 3.08453e6i 0.932461 0.932461i −0.0653987 0.997859i \(-0.520832\pi\)
0.997859 + 0.0653987i \(0.0208319\pi\)
\(150\) −750012. 77624.7i −0.222226 0.0229999i
\(151\) 3.73589e6i 1.08508i −0.840028 0.542542i \(-0.817462\pi\)
0.840028 0.542542i \(-0.182538\pi\)
\(152\) 3.86704e6 + 2.48612e6i 1.10115 + 0.707932i
\(153\) −4.40337e6 + 776966.i −1.22945 + 0.216934i
\(154\) −3.54304e6 683073.i −0.970095 0.187027i
\(155\) 884384. 884384.i 0.237490 0.237490i
\(156\) 3.32654e6 + 1.00569e6i 0.876232 + 0.264905i
\(157\) 1.30900e6 1.30900e6i 0.338253 0.338253i −0.517457 0.855710i \(-0.673121\pi\)
0.855710 + 0.517457i \(0.173121\pi\)
\(158\) −3.11028e6 + 2.10484e6i −0.788549 + 0.533640i
\(159\) −663893. 7.58320e6i −0.165161 1.88652i
\(160\) 2.94086e6 2.09293e6i 0.717982 0.510968i
\(161\) 931772.i 0.223271i
\(162\) 2.49291e6 3.44396e6i 0.586356 0.810053i
\(163\) −59111.6 + 59111.6i −0.0136493 + 0.0136493i −0.713898 0.700249i \(-0.753072\pi\)
0.700249 + 0.713898i \(0.253072\pi\)
\(164\) −1.94283e6 + 4.85138e6i −0.440457 + 1.09985i
\(165\) 3.30942e6 + 2.77660e6i 0.736715 + 0.618104i
\(166\) −7.46354e6 1.43892e6i −1.63163 0.314566i
\(167\) −2.28355e6 −0.490300 −0.245150 0.969485i \(-0.578837\pi\)
−0.245150 + 0.969485i \(0.578837\pi\)
\(168\) 1.99769e6 3.79962e6i 0.421308 0.801332i
\(169\) 782154.i 0.162044i
\(170\) 5.30744e6 + 1.02324e6i 1.08029 + 0.208271i
\(171\) −5.36238e6 3.75384e6i −1.07243 0.750736i
\(172\) 5.50029e6 2.35463e6i 1.08094 0.462740i
\(173\) −3.47518e6 3.47518e6i −0.671180 0.671180i 0.286808 0.957988i \(-0.407406\pi\)
−0.957988 + 0.286808i \(0.907406\pi\)
\(174\) 4.15707e6 3.37728e6i 0.789113 0.641090i
\(175\) 1.08401e6 0.202264
\(176\) 5.94767e6 140239.i 1.09096 0.0257235i
\(177\) 467108. + 5.33546e6i 0.0842360 + 0.962171i
\(178\) −1.91487e6 + 1.29586e6i −0.339531 + 0.229773i
\(179\) 2.91510e6 + 2.91510e6i 0.508269 + 0.508269i 0.913995 0.405726i \(-0.132981\pi\)
−0.405726 + 0.913995i \(0.632981\pi\)
\(180\) −4.30135e6 + 2.81280e6i −0.737543 + 0.482305i
\(181\) 5.86054e6 + 5.86054e6i 0.988330 + 0.988330i 0.999933 0.0116025i \(-0.00369326\pi\)
−0.0116025 + 0.999933i \(0.503693\pi\)
\(182\) −4.90580e6 945803.i −0.813759 0.156887i
\(183\) −931847. 1.06439e7i −0.152052 1.73678i
\(184\) −326310. 1.50124e6i −0.0523813 0.240989i
\(185\) −1.46422e6 −0.231255
\(186\) −252478. + 2.43945e6i −0.0392359 + 0.379099i
\(187\) 6.29952e6 + 6.29952e6i 0.963347 + 0.963347i
\(188\) −2.33134e6 933633.i −0.350859 0.140509i
\(189\) −3.05515e6 + 5.29383e6i −0.452530 + 0.784124i
\(190\) 4.43476e6 + 6.55315e6i 0.646560 + 0.955408i
\(191\) 3.40903e6i 0.489250i 0.969618 + 0.244625i \(0.0786649\pi\)
−0.969618 + 0.244625i \(0.921335\pi\)
\(192\) −1.88798e6 + 6.82144e6i −0.266743 + 0.963768i
\(193\) −6.11510e6 −0.850613 −0.425306 0.905049i \(-0.639834\pi\)
−0.425306 + 0.905049i \(0.639834\pi\)
\(194\) −2.36346e6 + 1.59944e6i −0.323701 + 0.219060i
\(195\) 4.58232e6 + 3.84456e6i 0.617990 + 0.518493i
\(196\) 504888. 1.26074e6i 0.0670543 0.167439i
\(197\) 7.02036e6 7.02036e6i 0.918250 0.918250i −0.0786521 0.996902i \(-0.525062\pi\)
0.996902 + 0.0786521i \(0.0250616\pi\)
\(198\) −8.46975e6 133880.i −1.09113 0.0172473i
\(199\) 4.41617e6i 0.560385i 0.959944 + 0.280193i \(0.0903984\pi\)
−0.959944 + 0.280193i \(0.909602\pi\)
\(200\) −1.74652e6 + 379623.i −0.218315 + 0.0474529i
\(201\) 1.17482e6 + 1.34192e7i 0.144672 + 1.65249i
\(202\) −1.54948e6 + 8.03705e6i −0.187989 + 0.975085i
\(203\) −5.44477e6 + 5.44477e6i −0.650866 + 0.650866i
\(204\) −9.34266e6 + 5.00503e6i −1.10048 + 0.589544i
\(205\) −6.36026e6 + 6.36026e6i −0.738266 + 0.738266i
\(206\) −3.93840e6 5.81969e6i −0.450525 0.665730i
\(207\) 380095. + 2.15415e6i 0.0428530 + 0.242865i
\(208\) 8.23531e6 194179.i 0.915145 0.0215780i
\(209\) 1.30418e7i 1.42856i
\(210\) 5.73463e6 4.65892e6i 0.619224 0.503069i
\(211\) 8.74430e6 8.74430e6i 0.930846 0.930846i −0.0669131 0.997759i \(-0.521315\pi\)
0.997759 + 0.0669131i \(0.0213150\pi\)
\(212\) −7.10106e6 1.65877e7i −0.745273 1.74092i
\(213\) 6.12860e6 7.30465e6i 0.634194 0.755894i
\(214\) −2.04074e6 + 1.05851e7i −0.208231 + 1.08008i
\(215\) 1.02980e7 1.03618
\(216\) 3.06845e6 9.59919e6i 0.304480 0.952519i
\(217\) 3.52578e6i 0.345045i
\(218\) 1.45705e6 7.55762e6i 0.140639 0.729484i
\(219\) −7.56540e6 6.34736e6i −0.720277 0.604312i
\(220\) 9.50589e6 + 3.80683e6i 0.892740 + 0.357516i
\(221\) 8.72250e6 + 8.72250e6i 0.808098 + 0.808098i
\(222\) 2.22842e6 1.81041e6i 0.203675 0.165470i
\(223\) 7.67162e6 0.691787 0.345894 0.938274i \(-0.387576\pi\)
0.345894 + 0.938274i \(0.387576\pi\)
\(224\) 1.69022e6 1.00341e7i 0.150384 0.892759i
\(225\) 2.50610e6 442196.i 0.220014 0.0388211i
\(226\) −619856. 915948.i −0.0536989 0.0793497i
\(227\) −3.03062e6 3.03062e6i −0.259092 0.259092i 0.565593 0.824685i \(-0.308647\pi\)
−0.824685 + 0.565593i \(0.808647\pi\)
\(228\) −1.48519e7 4.49007e6i −1.25307 0.378833i
\(229\) −5.57443e6 5.57443e6i −0.464188 0.464188i 0.435837 0.900026i \(-0.356452\pi\)
−0.900026 + 0.435837i \(0.856452\pi\)
\(230\) 500572. 2.59643e6i 0.0411418 0.213399i
\(231\) 1.21316e7 1.06209e6i 0.984195 0.0861642i
\(232\) 6.86568e6 1.06792e7i 0.549819 0.855217i
\(233\) −2.31313e7 −1.82865 −0.914327 0.404976i \(-0.867280\pi\)
−0.914327 + 0.404976i \(0.867280\pi\)
\(234\) −1.17275e7 185374.i −0.915285 0.0144678i
\(235\) −3.05644e6 3.05644e6i −0.235511 0.235511i
\(236\) 4.99623e6 + 1.16709e7i 0.380107 + 0.887911i
\(237\) 8.14677e6 9.71010e6i 0.611984 0.729422i
\(238\) 1.26193e7 8.53993e6i 0.936059 0.633466i
\(239\) 8.10890e6i 0.593975i −0.954881 0.296987i \(-0.904018\pi\)
0.954881 0.296987i \(-0.0959820\pi\)
\(240\) −7.60791e6 + 9.51461e6i −0.550341 + 0.688268i
\(241\) 5.60281e6 0.400272 0.200136 0.979768i \(-0.435862\pi\)
0.200136 + 0.979768i \(0.435862\pi\)
\(242\) 1.51598e6 + 2.24013e6i 0.106966 + 0.158062i
\(243\) −4.90365e6 + 1.34850e7i −0.341744 + 0.939793i
\(244\) −9.96712e6 2.32827e7i −0.686120 1.60274i
\(245\) 1.65285e6 1.65285e6i 0.112392 0.112392i
\(246\) 1.81575e6 1.75438e7i 0.121969 1.17847i
\(247\) 1.80580e7i 1.19834i
\(248\) 1.23474e6 + 5.68063e6i 0.0809507 + 0.372427i
\(249\) 2.55556e7 2.23733e6i 1.65534 0.144922i
\(250\) −1.65411e7 3.18900e6i −1.05863 0.204096i
\(251\) 6.97970e6 6.97970e6i 0.441383 0.441383i −0.451094 0.892477i \(-0.648966\pi\)
0.892477 + 0.451094i \(0.148966\pi\)
\(252\) −2.96719e6 + 1.41810e7i −0.185415 + 0.886146i
\(253\) 3.08175e6 3.08175e6i 0.190299 0.190299i
\(254\) −2.44540e6 + 1.65489e6i −0.149227 + 0.100988i
\(255\) −1.81730e7 + 1.59100e6i −1.09599 + 0.0959513i
\(256\) 790733. + 1.67586e7i 0.0471314 + 0.998889i
\(257\) 1.05065e7i 0.618953i −0.950907 0.309477i \(-0.899846\pi\)
0.950907 0.309477i \(-0.100154\pi\)
\(258\) −1.56727e7 + 1.27328e7i −0.912607 + 0.741419i
\(259\) −2.91870e6 + 2.91870e6i −0.167993 + 0.167993i
\(260\) 1.31621e7 + 5.27105e6i 0.748870 + 0.299900i
\(261\) −1.03666e7 + 1.48087e7i −0.583062 + 0.832907i
\(262\) −2.28398e7 4.40335e6i −1.26996 0.244838i
\(263\) −3.43943e7 −1.89068 −0.945342 0.326080i \(-0.894272\pi\)
−0.945342 + 0.326080i \(0.894272\pi\)
\(264\) −1.91741e7 + 5.95973e6i −1.04208 + 0.323903i
\(265\) 3.10565e7i 1.66884i
\(266\) 2.19028e7 + 4.22269e6i 1.16373 + 0.224359i
\(267\) 5.01563e6 5.97810e6i 0.263507 0.314072i
\(268\) 1.25660e7 + 2.93536e7i 0.652820 + 1.52495i
\(269\) 1.47409e6 + 1.47409e6i 0.0757296 + 0.0757296i 0.743957 0.668227i \(-0.232947\pi\)
−0.668227 + 0.743957i \(0.732947\pi\)
\(270\) 1.13573e7 1.31102e7i 0.577011 0.666067i
\(271\) −2.60363e6 −0.130819 −0.0654096 0.997858i \(-0.520835\pi\)
−0.0654096 + 0.997858i \(0.520835\pi\)
\(272\) −1.73411e7 + 1.81786e7i −0.861727 + 0.903346i
\(273\) 1.67977e7 1.47060e6i 0.825586 0.0722783i
\(274\) 2.13436e7 1.44440e7i 1.03757 0.702160i
\(275\) −3.58526e6 3.58526e6i −0.172394 0.172394i
\(276\) 2.44848e6 + 4.57047e6i 0.116458 + 0.217387i
\(277\) −2.21180e7 2.21180e7i −1.04065 1.04065i −0.999138 0.0415157i \(-0.986781\pi\)
−0.0415157 0.999138i \(-0.513219\pi\)
\(278\) 1.42039e7 + 2.73841e6i 0.661109 + 0.127457i
\(279\) −1.43826e6 8.15119e6i −0.0662255 0.375326i
\(280\) 9.47114e6 1.47319e7i 0.431448 0.671096i
\(281\) 3.37592e6 0.152151 0.0760753 0.997102i \(-0.475761\pi\)
0.0760753 + 0.997102i \(0.475761\pi\)
\(282\) 8.43073e6 + 872564.i 0.375940 + 0.0389090i
\(283\) 2.77260e7 + 2.77260e7i 1.22329 + 1.22329i 0.966456 + 0.256831i \(0.0826782\pi\)
0.256831 + 0.966456i \(0.417322\pi\)
\(284\) 8.40255e6 2.09817e7i 0.366823 0.915980i
\(285\) −2.04585e7 1.71647e7i −0.883770 0.741482i
\(286\) 1.30973e7 + 1.93537e7i 0.559868 + 0.827304i
\(287\) 2.53565e7i 1.07261i
\(288\) −185580. 2.38872e7i −0.00776881 0.999970i
\(289\) −1.34834e7 −0.558607
\(290\) 1.80972e7 1.22470e7i 0.742022 0.502154i
\(291\) 6.19063e6 7.37858e6i 0.251221 0.299429i
\(292\) −2.17307e7 8.70249e6i −0.872820 0.349538i
\(293\) −3.29847e7 + 3.29847e7i −1.31132 + 1.31132i −0.390884 + 0.920440i \(0.627831\pi\)
−0.920440 + 0.390884i \(0.872169\pi\)
\(294\) −471863. + 4.55915e6i −0.0185684 + 0.179408i
\(295\) 2.18510e7i 0.851148i
\(296\) 3.68039e6 5.72467e6i 0.141912 0.220737i
\(297\) 2.76135e7 7.40424e6i 1.05403 0.282625i
\(298\) −6.60633e6 + 3.42665e7i −0.249638 + 1.29485i
\(299\) 4.26708e6 4.26708e6i 0.159631 0.159631i
\(300\) 5.31721e6 2.84852e6i 0.196934 0.105501i
\(301\) 2.05275e7 2.05275e7i 0.752724 0.752724i
\(302\) 1.67506e7 + 2.47520e7i 0.608148 + 0.898646i
\(303\) −2.40926e6 2.75193e7i −0.0866074 0.989258i
\(304\) −3.67679e7 + 866942.i −1.30872 + 0.0308581i
\(305\) 4.35912e7i 1.53638i
\(306\) 2.56906e7 2.48911e7i 0.896624 0.868719i
\(307\) −3.51931e7 + 3.51931e7i −1.21630 + 1.21630i −0.247387 + 0.968917i \(0.579572\pi\)
−0.968917 + 0.247387i \(0.920428\pi\)
\(308\) 2.65369e7 1.13602e7i 0.908236 0.388808i
\(309\) 1.81687e7 + 1.52435e7i 0.615813 + 0.516667i
\(310\) −1.89414e6 + 9.82475e6i −0.0635809 + 0.329789i
\(311\) −1.12861e7 −0.375199 −0.187599 0.982246i \(-0.560071\pi\)
−0.187599 + 0.982246i \(0.560071\pi\)
\(312\) −2.65490e7 + 8.25202e6i −0.874147 + 0.271704i
\(313\) 1.74518e7i 0.569123i 0.958658 + 0.284562i \(0.0918480\pi\)
−0.958658 + 0.284562i \(0.908152\pi\)
\(314\) −2.80357e6 + 1.45419e7i −0.0905571 + 0.469712i
\(315\) −1.43006e7 + 2.04285e7i −0.457534 + 0.653590i
\(316\) 1.11695e7 2.78911e7i 0.353976 0.883901i
\(317\) 1.47576e7 + 1.47576e7i 0.463273 + 0.463273i 0.899727 0.436454i \(-0.143766\pi\)
−0.436454 + 0.899727i \(0.643766\pi\)
\(318\) 3.83993e7 + 4.72654e7i 1.19410 + 1.46981i
\(319\) 3.60162e7 1.10950
\(320\) −1.01005e7 + 2.70524e7i −0.308242 + 0.825575i
\(321\) −3.17309e6 3.62441e7i −0.0959330 1.09578i
\(322\) −4.17777e6 6.17340e6i −0.125135 0.184909i
\(323\) −3.89430e7 3.89430e7i −1.15564 1.15564i
\(324\) −1.07498e6 + 3.39952e7i −0.0316058 + 0.999500i
\(325\) −4.96425e6 4.96425e6i −0.144612 0.144612i
\(326\) 126603. 656679.i 0.00365419 0.0189540i
\(327\) 2.26554e6 + 2.58777e7i 0.0647930 + 0.740086i
\(328\) −8.87992e6 4.08536e7i −0.251645 1.15773i
\(329\) −1.21851e7 −0.342170
\(330\) −3.43758e7 3.55782e6i −0.956557 0.0990016i
\(331\) 912322. + 912322.i 0.0251573 + 0.0251573i 0.719574 0.694416i \(-0.244337\pi\)
−0.694416 + 0.719574i \(0.744337\pi\)
\(332\) 5.59009e7 2.39307e7i 1.52758 0.653946i
\(333\) −5.55708e6 + 7.93832e6i −0.150492 + 0.214979i
\(334\) 1.51296e7 1.02387e7i 0.406057 0.274794i
\(335\) 5.49575e7i 1.46181i
\(336\) 3.80073e6 + 3.41312e7i 0.100196 + 0.899775i
\(337\) −2.91976e7 −0.762881 −0.381440 0.924393i \(-0.624572\pi\)
−0.381440 + 0.924393i \(0.624572\pi\)
\(338\) −3.50693e6 5.18212e6i −0.0908192 0.134201i
\(339\) 2.85953e6 + 2.39914e6i 0.0733999 + 0.0615825i
\(340\) −3.97521e7 + 1.70175e7i −1.01140 + 0.432972i
\(341\) −1.16612e7 + 1.16612e7i −0.294090 + 0.294090i
\(342\) 5.23592e7 + 827633.i 1.30892 + 0.0206900i
\(343\) 4.31230e7i 1.06863i
\(344\) −2.58845e7 + 4.02621e7i −0.635864 + 0.989055i
\(345\) 778327. + 8.89030e6i 0.0189542 + 0.216501i
\(346\) 3.86062e7 + 7.44300e6i 0.932029 + 0.179688i
\(347\) 2.35265e7 2.35265e7i 0.563078 0.563078i −0.367103 0.930180i \(-0.619650\pi\)
0.930180 + 0.367103i \(0.119650\pi\)
\(348\) −1.23998e7 + 4.10150e7i −0.294223 + 0.973206i
\(349\) −3.43475e6 + 3.43475e6i −0.0808013 + 0.0808013i −0.746352 0.665551i \(-0.768197\pi\)
0.665551 + 0.746352i \(0.268197\pi\)
\(350\) −7.18203e6 + 4.86035e6i −0.167511 + 0.113361i
\(351\) 3.82345e7 1.02521e7i 0.884166 0.237079i
\(352\) −3.87772e7 + 2.75966e7i −0.889095 + 0.632744i
\(353\) 519893.i 0.0118193i −0.999983 0.00590963i \(-0.998119\pi\)
0.999983 0.00590963i \(-0.00188110\pi\)
\(354\) −2.70173e7 3.32555e7i −0.609022 0.749641i
\(355\) 2.75075e7 2.75075e7i 0.614845 0.614845i
\(356\) 6.87662e6 1.71714e7i 0.152414 0.380588i
\(357\) −3.30537e7 + 3.93966e7i −0.726466 + 0.865872i
\(358\) −3.23842e7 6.24343e6i −0.705804 0.136074i
\(359\) 8.00215e7 1.72951 0.864755 0.502194i \(-0.167474\pi\)
0.864755 + 0.502194i \(0.167474\pi\)
\(360\) 1.58866e7 3.79220e7i 0.340505 0.812800i
\(361\) 3.35771e7i 0.713710i
\(362\) −6.51056e7 1.25519e7i −1.37244 0.264596i
\(363\) −6.99353e6 5.86757e6i −0.146210 0.122670i
\(364\) 3.67438e7 1.57297e7i 0.761869 0.326149i
\(365\) −2.84894e7 2.84894e7i −0.585874 0.585874i
\(366\) 5.38977e7 + 6.63422e7i 1.09933 + 1.35315i
\(367\) −8.64094e7 −1.74809 −0.874043 0.485848i \(-0.838511\pi\)
−0.874043 + 0.485848i \(0.838511\pi\)
\(368\) 8.89306e6 + 8.48334e6i 0.178446 + 0.170225i
\(369\) 1.03436e7 + 5.86212e7i 0.205870 + 1.16674i
\(370\) 9.70111e6 6.56510e6i 0.191521 0.129609i
\(371\) −6.19065e7 6.19065e7i −1.21231 1.21231i
\(372\) −9.26493e6 1.72944e7i −0.179976 0.335952i
\(373\) −3.64362e7 3.64362e7i −0.702112 0.702112i 0.262752 0.964863i \(-0.415370\pi\)
−0.964863 + 0.262752i \(0.915370\pi\)
\(374\) −6.99822e7 1.34921e7i −1.33774 0.257907i
\(375\) 5.66375e7 4.95849e6i 1.07401 0.0940277i
\(376\) 1.96323e7 4.26727e6i 0.369324 0.0802761i
\(377\) 4.98691e7 0.930695
\(378\) −3.49414e6 4.87723e7i −0.0646942 0.903022i
\(379\) −9.14432e6 9.14432e6i −0.167971 0.167971i 0.618116 0.786087i \(-0.287896\pi\)
−0.786087 + 0.618116i \(0.787896\pi\)
\(380\) −5.87645e7 2.35334e7i −1.07094 0.428879i
\(381\) 6.40523e6 7.63437e6i 0.115814 0.138038i
\(382\) −1.52850e7 2.25864e7i −0.274206 0.405188i
\(383\) 1.02744e8i 1.82878i 0.404839 + 0.914388i \(0.367328\pi\)
−0.404839 + 0.914388i \(0.632672\pi\)
\(384\) −1.80765e7 5.36602e7i −0.319242 0.947673i
\(385\) 4.96840e7 0.870631
\(386\) 4.05153e7 2.74182e7i 0.704461 0.476735i
\(387\) 3.90834e7 5.58308e7i 0.674310 0.963255i
\(388\) 8.48760e6 2.11941e7i 0.145308 0.362843i
\(389\) 5.76988e7 5.76988e7i 0.980208 0.980208i −0.0195997 0.999808i \(-0.506239\pi\)
0.999808 + 0.0195997i \(0.00623918\pi\)
\(390\) −4.75977e7 4.92626e6i −0.802402 0.0830470i
\(391\) 1.84044e7i 0.307886i
\(392\) 2.30764e6 + 1.06167e7i 0.0383098 + 0.176251i
\(393\) 7.82047e7 6.84665e6i 1.28841 0.112798i
\(394\) −1.50359e7 + 7.79902e7i −0.245834 + 1.27512i
\(395\) 3.65658e7 3.65658e7i 0.593312 0.593312i
\(396\) 5.67162e7 3.70887e7i 0.913316 0.597250i
\(397\) −3.38251e7 + 3.38251e7i −0.540590 + 0.540590i −0.923702 0.383112i \(-0.874852\pi\)
0.383112 + 0.923702i \(0.374852\pi\)
\(398\) −1.98007e7 2.92591e7i −0.314074 0.464100i
\(399\) −7.49962e7 + 6.56576e6i −1.18065 + 0.103363i
\(400\) 9.86937e6 1.03460e7i 0.154209 0.161657i
\(401\) 1.80656e7i 0.280169i 0.990140 + 0.140084i \(0.0447374\pi\)
−0.990140 + 0.140084i \(0.955263\pi\)
\(402\) −6.79513e7 8.36408e7i −1.04597 1.28748i
\(403\) −1.61464e7 + 1.61464e7i −0.246696 + 0.246696i
\(404\) −2.57696e7 6.01965e7i −0.390808 0.912908i
\(405\) −2.47280e7 + 5.30620e7i −0.372241 + 0.798764i
\(406\) 1.16614e7 6.04867e7i 0.174250 0.903819i
\(407\) 1.93067e7 0.286368
\(408\) 3.94584e7 7.50501e7i 0.580976 1.10502i
\(409\) 8.45299e7i 1.23549i 0.786377 + 0.617746i \(0.211954\pi\)
−0.786377 + 0.617746i \(0.788046\pi\)
\(410\) 1.36221e7 7.06569e7i 0.197649 1.02519i
\(411\) −5.59054e7 + 6.66334e7i −0.805245 + 0.959768i
\(412\) 5.21874e7 + 2.08995e7i 0.746232 + 0.298844i
\(413\) 4.35567e7 + 4.35567e7i 0.618308 + 0.618308i
\(414\) −1.21768e7 1.25680e7i −0.171606 0.177118i
\(415\) 1.04661e8 1.46434
\(416\) −5.36920e7 + 3.82111e7i −0.745812 + 0.530774i
\(417\) −4.86349e7 + 4.25788e6i −0.670718 + 0.0587199i
\(418\) −5.84753e7 8.64076e7i −0.800651 1.18310i
\(419\) 4.87260e7 + 4.87260e7i 0.662397 + 0.662397i 0.955944 0.293548i \(-0.0948359\pi\)
−0.293548 + 0.955944i \(0.594836\pi\)
\(420\) −1.71054e7 + 5.65798e7i −0.230879 + 0.763683i
\(421\) 6.36969e7 + 6.36969e7i 0.853635 + 0.853635i 0.990579 0.136944i \(-0.0437281\pi\)
−0.136944 + 0.990579i \(0.543728\pi\)
\(422\) −1.87282e7 + 9.71416e7i −0.249206 + 1.29261i
\(423\) −2.81705e7 + 4.97064e6i −0.372198 + 0.0656737i
\(424\) 1.21422e8 + 7.80621e7i 1.59294 + 1.02410i
\(425\) 2.14113e7 0.278918
\(426\) −7.85294e6 + 7.58753e7i −0.101579 + 0.981458i
\(427\) −8.68925e7 8.68925e7i −1.11609 1.11609i
\(428\) −3.39397e7 7.92814e7i −0.432889 1.01121i
\(429\) −6.04209e7 5.06931e7i −0.765271 0.642062i
\(430\) −6.82286e7 + 4.61729e7i −0.858146 + 0.580740i
\(431\) 6.42503e7i 0.802497i 0.915969 + 0.401248i \(0.131424\pi\)
−0.915969 + 0.401248i \(0.868576\pi\)
\(432\) 2.27099e7 + 7.73569e7i 0.281685 + 0.959507i
\(433\) 5.28277e7 0.650726 0.325363 0.945589i \(-0.394514\pi\)
0.325363 + 0.945589i \(0.394514\pi\)
\(434\) 1.58085e7 + 2.33599e7i 0.193384 + 0.285760i
\(435\) −4.74020e7 + 5.64982e7i −0.575876 + 0.686384i
\(436\) 2.42324e7 + 5.66056e7i 0.292372 + 0.682967i
\(437\) −1.90511e7 + 1.90511e7i −0.228284 + 0.228284i
\(438\) 7.85837e7 + 8.13325e6i 0.935213 + 0.0967926i
\(439\) 3.37695e6i 0.0399146i −0.999801 0.0199573i \(-0.993647\pi\)
0.999801 0.0199573i \(-0.00635302\pi\)
\(440\) −8.00494e7 + 1.73995e7i −0.939724 + 0.204258i
\(441\) −2.68801e6 1.52340e7i −0.0313412 0.177623i
\(442\) −9.68994e7 1.86815e7i −1.12216 0.216344i
\(443\) 3.55956e7 3.55956e7i 0.409435 0.409435i −0.472106 0.881542i \(-0.656506\pi\)
0.881542 + 0.472106i \(0.156506\pi\)
\(444\) −6.64698e6 + 2.19863e7i −0.0759408 + 0.251191i
\(445\) 2.25120e7 2.25120e7i 0.255467 0.255467i
\(446\) −5.08279e7 + 3.43972e7i −0.572925 + 0.387720i
\(447\) −1.02720e7 1.17330e8i −0.115009 1.31367i
\(448\) 3.37913e7 + 7.40588e7i 0.375812 + 0.823650i
\(449\) 1.40962e7i 0.155726i −0.996964 0.0778631i \(-0.975190\pi\)
0.996964 0.0778631i \(-0.0248097\pi\)
\(450\) −1.46214e7 + 1.41663e7i −0.160454 + 0.155460i
\(451\) 8.38642e7 8.38642e7i 0.914213 0.914213i
\(452\) 8.21365e6 + 3.28932e6i 0.0889448 + 0.0356198i
\(453\) −7.72740e7 6.48329e7i −0.831264 0.697430i
\(454\) 3.36675e7 + 6.49085e6i 0.359785 + 0.0693640i
\(455\) 6.87939e7 0.730324
\(456\) 1.18532e8 3.68425e7i 1.25009 0.388557i
\(457\) 1.53031e8i 1.60336i 0.597756 + 0.801678i \(0.296059\pi\)
−0.597756 + 0.801678i \(0.703941\pi\)
\(458\) 6.19271e7 + 1.19391e7i 0.644591 + 0.124272i
\(459\) −6.03453e7 + 1.04564e8i −0.624030 + 1.08129i
\(460\) 8.32505e6 + 1.94469e7i 0.0855290 + 0.199791i
\(461\) 1.00667e8 + 1.00667e8i 1.02751 + 1.02751i 0.999611 + 0.0278951i \(0.00888042\pi\)
0.0278951 + 0.999611i \(0.491120\pi\)
\(462\) −7.56150e7 + 6.14310e7i −0.766800 + 0.622962i
\(463\) −2.24428e7 −0.226117 −0.113059 0.993588i \(-0.536065\pi\)
−0.113059 + 0.993588i \(0.536065\pi\)
\(464\) 2.39415e6 + 1.01538e8i 0.0239661 + 1.01643i
\(465\) −2.94515e6 3.36405e7i −0.0292920 0.334582i
\(466\) 1.53255e8 1.03713e8i 1.51446 1.02489i
\(467\) −1.02611e8 1.02611e8i −1.00749 1.00749i −0.999972 0.00752324i \(-0.997605\pi\)
−0.00752324 0.999972i \(-0.502395\pi\)
\(468\) 7.85308e7 5.13541e7i 0.766130 0.501000i
\(469\) 1.09550e8 + 1.09550e8i 1.06192 + 1.06192i
\(470\) 3.39544e7 + 6.54615e6i 0.327041 + 0.0630511i
\(471\) −4.35920e6 4.97922e7i −0.0417200 0.476539i
\(472\) −8.54311e7 5.49236e7i −0.812437 0.522316i
\(473\) −1.35786e8 −1.28313
\(474\) −1.04389e7 + 1.00861e8i −0.0980215 + 0.947087i
\(475\) 2.21637e7 + 2.21637e7i 0.206805 + 0.206805i
\(476\) −4.53179e7 + 1.13162e8i −0.420193 + 1.04925i
\(477\) −1.68374e8 1.17867e8i −1.55138 1.08602i
\(478\) 3.63578e7 + 5.37251e7i 0.332900 + 0.491919i
\(479\) 3.89026e7i 0.353975i −0.984213 0.176987i \(-0.943365\pi\)
0.984213 0.176987i \(-0.0566351\pi\)
\(480\) 7.74525e6 9.71500e7i 0.0700344 0.878455i
\(481\) 2.67326e7 0.240219
\(482\) −3.71211e7 + 2.51213e7i −0.331497 + 0.224337i
\(483\) 1.92730e7 + 1.61700e7i 0.171044 + 0.143506i
\(484\) −2.00881e7 8.04467e6i −0.177175 0.0709532i
\(485\) 2.77859e7 2.77859e7i 0.243556 0.243556i
\(486\) −2.79736e7 1.11331e8i −0.243691 0.969853i
\(487\) 1.47719e8i 1.27894i −0.768816 0.639470i \(-0.779154\pi\)
0.768816 0.639470i \(-0.220846\pi\)
\(488\) 1.70429e8 + 1.09569e8i 1.46651 + 0.942816i
\(489\) 196852. + 2.24850e6i 0.00168350 + 0.0192295i
\(490\) −3.54001e6 + 1.83618e7i −0.0300896 + 0.156072i
\(491\) 1.15929e8 1.15929e8i 0.979371 0.979371i −0.0204209 0.999791i \(-0.506501\pi\)
0.999791 + 0.0204209i \(0.00650064\pi\)
\(492\) 6.66309e7 + 1.24377e8i 0.559475 + 1.04435i
\(493\) −1.07545e8 + 1.07545e8i −0.897532 + 0.897532i
\(494\) −8.09665e7 1.19642e8i −0.671622 0.992441i
\(495\) 1.14864e8 2.02675e7i 0.947037 0.167103i
\(496\) −3.36509e7 3.21005e7i −0.275773 0.263068i
\(497\) 1.09664e8i 0.893295i
\(498\) −1.59286e8 + 1.29407e8i −1.28970 + 1.04778i
\(499\) 1.07143e6 1.07143e6i 0.00862307 0.00862307i −0.702782 0.711405i \(-0.748059\pi\)
0.711405 + 0.702782i \(0.248059\pi\)
\(500\) 1.23890e8 5.30364e7i 0.991123 0.424291i
\(501\) −3.96289e7 + 4.72335e7i −0.315136 + 0.375610i
\(502\) −1.49488e7 + 7.75384e7i −0.118167 + 0.612923i
\(503\) −1.42268e8 −1.11790 −0.558950 0.829201i \(-0.688796\pi\)
−0.558950 + 0.829201i \(0.688796\pi\)
\(504\) −4.39242e7 1.07259e8i −0.343093 0.837807i
\(505\) 1.12703e8i 0.875110i
\(506\) −6.60037e6 + 3.42356e7i −0.0509468 + 0.264257i
\(507\) 1.61782e7 + 1.35735e7i 0.124139 + 0.104152i
\(508\) 8.78183e6 2.19288e7i 0.0669875 0.167272i
\(509\) 4.19418e7 + 4.19418e7i 0.318049 + 0.318049i 0.848017 0.529969i \(-0.177796\pi\)
−0.529969 + 0.848017i \(0.677796\pi\)
\(510\) 1.13270e8 9.20230e7i 0.853899 0.693723i
\(511\) −1.13579e8 −0.851204
\(512\) −8.03792e7 1.07488e8i −0.598871 0.800845i
\(513\) −1.70704e8 + 4.57723e7i −1.26442 + 0.339040i
\(514\) 4.71078e7 + 6.96101e7i 0.346899 + 0.512605i
\(515\) 6.84187e7 + 6.84187e7i 0.500903 + 0.500903i
\(516\) 4.67487e7 1.54632e8i 0.340267 1.12551i
\(517\) 4.03012e7 + 4.03012e7i 0.291639 + 0.291639i
\(518\) 6.25116e6 3.24243e7i 0.0449750 0.233282i
\(519\) −1.32190e8 + 1.15729e7i −0.945575 + 0.0827831i
\(520\) −1.10839e8 + 2.40919e7i −0.788282 + 0.171341i
\(521\) −2.07003e8 −1.46374 −0.731870 0.681444i \(-0.761352\pi\)
−0.731870 + 0.681444i \(0.761352\pi\)
\(522\) 2.28559e6 1.44595e8i 0.0160689 1.01658i
\(523\) 9.02749e6 + 9.02749e6i 0.0631047 + 0.0631047i 0.737955 0.674850i \(-0.235792\pi\)
−0.674850 + 0.737955i \(0.735792\pi\)
\(524\) 1.71067e8 7.32324e7i 1.18897 0.508990i
\(525\) 1.88119e7 2.24218e7i 0.130004 0.154951i
\(526\) 2.27878e8 1.54213e8i 1.56583 1.05965i
\(527\) 6.96412e7i 0.475811i
\(528\) 1.00315e8 1.25457e8i 0.681500 0.852298i
\(529\) −1.39032e8 −0.939180
\(530\) 1.39247e8 + 2.05763e8i 0.935319 + 1.38210i
\(531\) 1.18466e8 + 8.29301e7i 0.791244 + 0.553897i
\(532\) −1.64049e8 + 7.02279e7i −1.08953 + 0.466417i
\(533\) 1.16121e8 1.16121e8i 0.766882 0.766882i
\(534\) −6.42682e6 + 6.20961e7i −0.0422058 + 0.407794i
\(535\) 1.48435e8i 0.969339i
\(536\) −2.14868e8 1.38139e8i −1.39533 0.897058i
\(537\) 1.10885e8 9.70776e6i 0.716062 0.0626897i
\(538\) −1.63758e7 3.15714e6i −0.105161 0.0202743i
\(539\) −2.17940e7 + 2.17940e7i −0.139178 + 0.139178i
\(540\) −1.64652e7 + 1.37784e8i −0.104565 + 0.875016i
\(541\) 1.36157e8 1.36157e8i 0.859900 0.859900i −0.131426 0.991326i \(-0.541956\pi\)
0.991326 + 0.131426i \(0.0419556\pi\)
\(542\) 1.72502e7 1.16739e7i 0.108342 0.0733191i
\(543\) 2.22925e8 1.95166e7i 1.39238 0.121900i
\(544\) 3.33853e7 1.98193e8i 0.207376 1.23110i
\(545\) 1.05980e8i 0.654690i
\(546\) −1.04699e8 + 8.50592e7i −0.643226 + 0.522568i
\(547\) −3.49263e7 + 3.49263e7i −0.213398 + 0.213398i −0.805709 0.592311i \(-0.798216\pi\)
0.592311 + 0.805709i \(0.298216\pi\)
\(548\) −7.66485e7 + 1.91396e8i −0.465760 + 1.16303i
\(549\) −2.36331e8 1.65440e8i −1.42825 0.999821i
\(550\) 3.98291e7 + 7.67876e6i 0.239394 + 0.0461533i
\(551\) −2.22649e8 −1.33096
\(552\) −3.67149e7 1.93032e7i −0.218285 0.114766i
\(553\) 1.45777e8i 0.862012i
\(554\) 2.45712e8 + 4.73714e7i 1.44510 + 0.278604i
\(555\) −2.54101e7 + 3.02862e7i −0.148637 + 0.177160i
\(556\) −1.06385e8 + 4.55426e7i −0.618952 + 0.264968i
\(557\) 6.40563e7 + 6.40563e7i 0.370678 + 0.370678i 0.867724 0.497046i \(-0.165582\pi\)
−0.497046 + 0.867724i \(0.665582\pi\)
\(558\) 4.60765e7 + 4.75566e7i 0.265202 + 0.273721i
\(559\) −1.88013e8 −1.07635
\(560\) 3.30271e6 + 1.40071e8i 0.0188064 + 0.797598i
\(561\) 2.39623e8 2.09785e7i 1.35719 0.118819i
\(562\) −2.23670e7 + 1.51366e7i −0.126008 + 0.0852744i
\(563\) 1.63635e8 + 1.63635e8i 0.916963 + 0.916963i 0.996807 0.0798445i \(-0.0254424\pi\)
−0.0798445 + 0.996807i \(0.525442\pi\)
\(564\) −5.97697e7 + 3.20197e7i −0.333153 + 0.178476i
\(565\) 1.07683e7 + 1.07683e7i 0.0597036 + 0.0597036i
\(566\) −3.08012e8 5.93825e7i −1.69871 0.327498i
\(567\) 5.64795e7 + 1.55063e8i 0.309843 + 0.850665i
\(568\) 3.84047e7 + 1.76688e8i 0.209575 + 0.964187i
\(569\) −2.26122e8 −1.22745 −0.613727 0.789518i \(-0.710330\pi\)
−0.613727 + 0.789518i \(0.710330\pi\)
\(570\) 2.12508e8 + 2.19941e7i 1.14749 + 0.118763i
\(571\) −7.51046e7 7.51046e7i −0.403421 0.403421i 0.476016 0.879437i \(-0.342080\pi\)
−0.879437 + 0.476016i \(0.842080\pi\)
\(572\) −1.73552e8 6.95023e7i −0.927343 0.371374i
\(573\) 7.05132e7 + 5.91605e7i 0.374806 + 0.314462i
\(574\) −1.13690e8 1.67998e8i −0.601157 0.888317i
\(575\) 1.04745e7i 0.0550973i
\(576\) 1.08332e8 + 1.57431e8i 0.566878 + 0.823802i
\(577\) 1.40140e8 0.729513 0.364757 0.931103i \(-0.381152\pi\)
0.364757 + 0.931103i \(0.381152\pi\)
\(578\) 8.93337e7 6.04554e7i 0.462628 0.313077i
\(579\) −1.06122e8 + 1.26486e8i −0.546725 + 0.651639i
\(580\) −6.49900e7 + 1.62284e8i −0.333091 + 0.831749i
\(581\) 2.08626e8 2.08626e8i 1.06375 1.06375i
\(582\) −7.93242e6 + 7.66432e7i −0.0402380 + 0.388781i
\(583\) 4.09500e8i 2.06656i
\(584\) 1.82995e8 3.97756e7i 0.918755 0.199700i
\(585\) 1.59043e8 2.80629e7i 0.794416 0.140173i
\(586\) 7.06453e7 3.66432e8i 0.351068 1.82096i
\(587\) −8.78044e7 + 8.78044e7i −0.434112 + 0.434112i −0.890025 0.455913i \(-0.849313\pi\)
0.455913 + 0.890025i \(0.349313\pi\)
\(588\) −1.73155e7 3.23221e7i −0.0851732 0.158989i
\(589\) 7.20884e7 7.20884e7i 0.352793 0.352793i
\(590\) −9.79731e7 1.44773e8i −0.477035 0.704905i
\(591\) −2.33790e7 2.67043e8i −0.113257 1.29365i
\(592\) 1.28340e6 + 5.44302e7i 0.00618581 + 0.262346i
\(593\) 8.83985e7i 0.423917i −0.977279 0.211959i \(-0.932016\pi\)
0.977279 0.211959i \(-0.0679842\pi\)
\(594\) −1.49754e8 + 1.72867e8i −0.714526 + 0.824807i
\(595\) −1.48357e8 + 1.48357e8i −0.704301 + 0.704301i
\(596\) −1.09870e8 2.56651e8i −0.518969 1.21229i
\(597\) 9.13451e7 + 7.66385e7i 0.429301 + 0.360184i
\(598\) −9.13907e6 + 4.74036e7i −0.0427365 + 0.221671i
\(599\) −8.79846e7 −0.409380 −0.204690 0.978827i \(-0.565619\pi\)
−0.204690 + 0.978827i \(0.565619\pi\)
\(600\) −2.24570e7 + 4.27134e7i −0.103968 + 0.197747i
\(601\) 1.41134e8i 0.650142i 0.945690 + 0.325071i \(0.105388\pi\)
−0.945690 + 0.325071i \(0.894612\pi\)
\(602\) −4.39649e7 + 2.28042e8i −0.201519 + 1.04526i
\(603\) 2.97954e8 + 2.08578e8i 1.35893 + 0.951296i
\(604\) −2.21960e8 8.88885e7i −1.00731 0.403399i
\(605\) −2.63359e7 2.63359e7i −0.118927 0.118927i
\(606\) 1.39350e8 + 1.71525e8i 0.626167 + 0.770744i
\(607\) −5.90432e7 −0.264000 −0.132000 0.991250i \(-0.542140\pi\)
−0.132000 + 0.991250i \(0.542140\pi\)
\(608\) 2.39717e8 1.70600e8i 1.06657 0.759045i
\(609\) 1.81320e7 + 2.07110e8i 0.0802775 + 0.916956i
\(610\) 1.95449e8 + 2.88811e8i 0.861082 + 1.27240i
\(611\) 5.58022e7 + 5.58022e7i 0.244640 + 0.244640i
\(612\) −5.86080e7 + 2.80103e8i −0.255683 + 1.22198i
\(613\) −1.57380e8 1.57380e8i −0.683234 0.683234i 0.277494 0.960727i \(-0.410496\pi\)
−0.960727 + 0.277494i \(0.910496\pi\)
\(614\) 7.53751e7 3.90964e8i 0.325629 1.68901i
\(615\) 2.11807e7 + 2.41933e8i 0.0910575 + 1.04009i
\(616\) −1.24883e8 + 1.94250e8i −0.534272 + 0.831034i
\(617\) 1.38269e7 0.0588669 0.0294334 0.999567i \(-0.490630\pi\)
0.0294334 + 0.999567i \(0.490630\pi\)
\(618\) −1.88723e8 1.95324e7i −0.799576 0.0827544i
\(619\) −1.34517e7 1.34517e7i −0.0567159 0.0567159i 0.678180 0.734896i \(-0.262769\pi\)
−0.734896 + 0.678180i \(0.762769\pi\)
\(620\) −3.15016e7 7.35861e7i −0.132177 0.308760i
\(621\) 5.11531e7 + 2.95212e7i 0.213598 + 0.123271i
\(622\) 7.47752e7 5.06032e7i 0.310732 0.210284i
\(623\) 8.97487e7i 0.371163i
\(624\) 1.38900e8 1.73711e8i 0.571672 0.714946i
\(625\) 1.77411e8 0.726674
\(626\) −7.82483e7 1.15626e8i −0.318971 0.471337i
\(627\) 2.69759e8 + 2.26328e8i 1.09439 + 0.918195i
\(628\) −4.66264e7 1.08917e8i −0.188258 0.439760i
\(629\) −5.76502e7 + 5.76502e7i −0.231659 + 0.231659i
\(630\) 3.15295e6 1.99468e8i 0.0126094 0.797720i
\(631\) 1.19101e7i 0.0474053i −0.999719 0.0237026i \(-0.992455\pi\)
0.999719 0.0237026i \(-0.00754549\pi\)
\(632\) 5.10516e7 + 2.34872e8i 0.202236 + 0.930420i
\(633\) −2.91200e7 3.32618e8i −0.114810 1.31140i
\(634\) −1.63944e8 3.16071e7i −0.643320 0.124027i
\(635\) 2.87491e7 2.87491e7i 0.112280 0.112280i
\(636\) −4.66336e8 1.40984e8i −1.81271 0.548023i
\(637\) −3.01765e7 + 3.01765e7i −0.116748 + 0.116748i
\(638\) −2.38623e8 + 1.61485e8i −0.918863 + 0.621829i
\(639\) −4.47350e7 2.53531e8i −0.171453 0.971690i
\(640\) −5.43746e7 2.24522e8i −0.207423 0.856483i
\(641\) 2.81769e8i 1.06984i 0.844902 + 0.534921i \(0.179659\pi\)
−0.844902 + 0.534921i \(0.820341\pi\)
\(642\) 1.83530e8 + 2.25906e8i 0.693590 + 0.853735i
\(643\) 3.91150e7 3.91150e7i 0.147133 0.147133i −0.629703 0.776836i \(-0.716823\pi\)
0.776836 + 0.629703i \(0.216823\pi\)
\(644\) 5.53592e7 + 2.21697e7i 0.207268 + 0.0830047i
\(645\) 1.78711e8 2.13005e8i 0.665998 0.793801i
\(646\) 4.32623e8 + 8.34066e7i 1.60477 + 0.309388i
\(647\) 2.11543e8 0.781064 0.390532 0.920589i \(-0.372291\pi\)
0.390532 + 0.920589i \(0.372291\pi\)
\(648\) −1.45302e8 2.30053e8i −0.534006 0.845481i
\(649\) 2.88120e8i 1.05400i
\(650\) 5.51485e7 + 1.06322e7i 0.200814 + 0.0387155i
\(651\) −7.29280e7 6.11865e7i −0.264333 0.221775i
\(652\) 2.10554e6 + 4.91844e6i 0.00759663 + 0.0177453i
\(653\) 1.91048e8 + 1.91048e8i 0.686124 + 0.686124i 0.961373 0.275249i \(-0.0887603\pi\)
−0.275249 + 0.961373i \(0.588760\pi\)
\(654\) −1.31038e8 1.61293e8i −0.468450 0.576611i
\(655\) 3.20282e8 1.13975
\(656\) 2.42008e8 + 2.30859e8i 0.857272 + 0.817776i
\(657\) −2.62581e8 + 4.63318e7i −0.925905 + 0.163374i
\(658\) 8.07318e7 5.46342e7i 0.283378 0.191773i
\(659\) −8.63327e7 8.63327e7i −0.301661 0.301661i 0.540003 0.841663i \(-0.318423\pi\)
−0.841663 + 0.540003i \(0.818423\pi\)
\(660\) 2.43707e8 1.30558e8i 0.847688 0.454121i
\(661\) 7.97831e7 + 7.97831e7i 0.276253 + 0.276253i 0.831611 0.555358i \(-0.187419\pi\)
−0.555358 + 0.831611i \(0.687419\pi\)
\(662\) −1.01351e7 1.95397e6i −0.0349345 0.00673511i
\(663\) 3.31789e8 2.90474e7i 1.13847 0.0996705i
\(664\) −2.63071e8 + 4.09194e8i −0.898604 + 1.39774i
\(665\) −3.07142e8 −1.04442
\(666\) 1.22521e6 7.75112e7i 0.00414750 0.262387i
\(667\) 5.26115e7 + 5.26115e7i 0.177298 + 0.177298i
\(668\) −5.43328e7 + 1.35672e8i −0.182277 + 0.455158i
\(669\) 1.33134e8 1.58681e8i 0.444641 0.529966i
\(670\) −2.46412e8 3.64118e8i −0.819290 1.21065i
\(671\) 5.74779e8i 1.90254i
\(672\) −1.78215e8 2.09093e8i −0.587269 0.689020i
\(673\) −3.42984e8 −1.12520 −0.562598 0.826730i \(-0.690198\pi\)
−0.562598 + 0.826730i \(0.690198\pi\)
\(674\) 1.93447e8 1.30913e8i 0.631803 0.427565i
\(675\) 3.43445e7 5.95106e7i 0.111672 0.193501i
\(676\) 4.64700e7 + 1.86099e7i 0.150429 + 0.0602425i
\(677\) 1.34358e8 1.34358e8i 0.433010 0.433010i −0.456641 0.889651i \(-0.650948\pi\)
0.889651 + 0.456641i \(0.150948\pi\)
\(678\) −2.97027e7 3.07417e6i −0.0953030 0.00986366i
\(679\) 1.10774e8i 0.353858i
\(680\) 1.87074e8 2.90985e8i 0.594958 0.925429i
\(681\) −1.15279e8 + 1.00925e7i −0.365015 + 0.0319563i
\(682\) 2.49755e7 1.29546e8i 0.0787337 0.408386i
\(683\) −1.06305e8 + 1.06305e8i −0.333651 + 0.333651i −0.853971 0.520320i \(-0.825813\pi\)
0.520320 + 0.853971i \(0.325813\pi\)
\(684\) −3.50614e8 + 2.29279e8i −1.09562 + 0.716466i
\(685\) −2.50924e8 + 2.50924e8i −0.780677 + 0.780677i
\(686\) 1.93350e8 + 2.85709e8i 0.598924 + 0.885018i
\(687\) −2.12042e8 + 1.85638e7i −0.653960 + 0.0572528i
\(688\) −9.02624e6 3.82812e8i −0.0277167 1.17549i
\(689\) 5.67006e8i 1.73352i
\(690\) −4.50181e7 5.54124e7i −0.137038 0.168679i
\(691\) 4.39787e7 4.39787e7i 0.133293 0.133293i −0.637312 0.770606i \(-0.719954\pi\)
0.770606 + 0.637312i \(0.219954\pi\)
\(692\) −2.89156e8 + 1.23785e8i −0.872597 + 0.373551i
\(693\) 1.88563e8 2.69364e8i 0.566575 0.809356i
\(694\) −5.03880e7 + 2.61359e8i −0.150747 + 0.781913i
\(695\) −1.99181e8 −0.593325
\(696\) −1.01744e8 3.27339e8i −0.301774 0.970891i
\(697\) 5.00841e8i 1.47911i
\(698\) 7.35640e6 3.81570e7i 0.0216321 0.112204i
\(699\) −4.01421e8 + 4.78452e8i −1.17535 + 1.40090i
\(700\) 2.57919e7 6.44040e7i 0.0751950 0.187767i
\(701\) −2.30678e8 2.30678e8i −0.669657 0.669657i 0.287980 0.957637i \(-0.407016\pi\)
−0.957637 + 0.287980i \(0.907016\pi\)
\(702\) −2.07353e8 + 2.39356e8i −0.599376 + 0.691885i
\(703\) −1.19352e8 −0.343530
\(704\) 1.33181e8 3.56705e8i 0.381703 1.02233i
\(705\) −1.16262e8 + 1.01785e7i −0.331794 + 0.0290479i
\(706\) 2.33104e6 + 3.44453e6i 0.00662423 + 0.00978848i
\(707\) −2.24657e8 2.24657e8i −0.635715 0.635715i
\(708\) 3.28109e8 + 9.91949e7i 0.924524 + 0.279505i
\(709\) 8.22692e6 + 8.22692e6i 0.0230833 + 0.0230833i 0.718554 0.695471i \(-0.244804\pi\)
−0.695471 + 0.718554i \(0.744804\pi\)
\(710\) −5.89144e7 + 3.05584e8i −0.164606 + 0.853799i
\(711\) −5.94664e7 3.37019e8i −0.165448 0.937661i
\(712\) 3.14303e7 + 1.44601e8i 0.0870781 + 0.400618i
\(713\) −3.40688e7 −0.0939913
\(714\) 4.23536e7 4.09222e8i 0.116358 1.12425i
\(715\) −2.27530e8 2.27530e8i −0.622472 0.622472i
\(716\) 2.42553e8 1.03835e8i 0.660797 0.282882i
\(717\) −1.67726e8 1.40722e8i −0.455034 0.381773i
\(718\) −5.30178e8 + 3.58791e8i −1.43235 + 0.969323i
\(719\) 1.76750e8i 0.475525i −0.971323 0.237762i \(-0.923586\pi\)
0.971323 0.237762i \(-0.0764139\pi\)
\(720\) 6.47743e7 + 3.22481e8i 0.173542 + 0.863985i
\(721\) 2.72765e8 0.727751
\(722\) 1.50549e8 + 2.22463e8i 0.400007 + 0.591081i
\(723\) 9.72315e7 1.15890e8i 0.257272 0.306641i
\(724\) 4.87632e8 2.08751e8i 1.28492 0.550064i
\(725\) 6.12074e7 6.12074e7i 0.160616 0.160616i
\(726\) 7.26436e7 + 7.51846e6i 0.189840 + 0.0196480i
\(727\) 4.03065e8i 1.04899i −0.851413 0.524495i \(-0.824254\pi\)
0.851413 0.524495i \(-0.175746\pi\)
\(728\) −1.72917e8 + 2.68964e8i −0.448171 + 0.697108i
\(729\) 1.93828e8 + 3.35448e8i 0.500305 + 0.865849i
\(730\) 3.16492e8 + 6.10174e7i 0.813569 + 0.156850i
\(731\) 4.05459e8 4.05459e8i 1.03799 1.03799i
\(732\) −6.54554e8 1.97887e8i −1.66883 0.504526i
\(733\) 4.11168e8 4.11168e8i 1.04402 1.04402i 0.0450300 0.998986i \(-0.485662\pi\)
0.998986 0.0450300i \(-0.0143384\pi\)
\(734\) 5.72501e8 3.87433e8i 1.44773 0.979734i
\(735\) −5.50428e6 6.28716e7i −0.0138624 0.158341i
\(736\) −9.69571e7 1.63322e7i −0.243190 0.0409650i
\(737\) 7.24651e8i 1.81020i
\(738\) −3.31370e8 3.42014e8i −0.824412 0.850893i
\(739\) −1.14783e8 + 1.14783e8i −0.284409 + 0.284409i −0.834865 0.550455i \(-0.814454\pi\)
0.550455 + 0.834865i \(0.314454\pi\)
\(740\) −3.48383e7 + 8.69935e7i −0.0859730 + 0.214680i
\(741\) 3.73516e8 + 3.13380e8i 0.918025 + 0.770223i
\(742\) 6.87727e8 + 1.32589e8i 1.68347 + 0.324560i
\(743\) −2.26310e8 −0.551744 −0.275872 0.961194i \(-0.588967\pi\)
−0.275872 + 0.961194i \(0.588967\pi\)
\(744\) 1.38927e8 + 7.30424e7i 0.337340 + 0.177360i
\(745\) 4.80518e8i 1.16209i
\(746\) 4.04774e8 + 7.80375e7i 0.974981 + 0.187969i
\(747\) 3.97215e8 5.67424e8i 0.952936 1.36127i
\(748\) 5.24158e8 2.24387e8i 1.25244 0.536159i
\(749\) −2.95884e8 2.95884e8i −0.704166 0.704166i
\(750\) −3.53016e8 + 2.86797e8i −0.836779 + 0.679815i
\(751\) 5.05620e8 1.19373 0.596863 0.802343i \(-0.296414\pi\)
0.596863 + 0.802343i \(0.296414\pi\)
\(752\) −1.10940e8 + 1.16298e8i −0.260875 + 0.273475i
\(753\) −2.32436e7 2.65496e8i −0.0544400 0.621831i
\(754\) −3.30405e8 + 2.23597e8i −0.770783 + 0.521618i
\(755\) −2.90994e8 2.90994e8i −0.676151 0.676151i
\(756\) 2.41830e8 + 3.07472e8i 0.559687 + 0.711607i
\(757\) −3.02200e7 3.02200e7i −0.0696637 0.0696637i 0.671416 0.741080i \(-0.265686\pi\)
−0.741080 + 0.671416i \(0.765686\pi\)
\(758\) 1.01586e8 + 1.95849e7i 0.233251 + 0.0449692i
\(759\) −1.02628e7 1.17225e8i −0.0234714 0.268098i
\(760\) 4.94858e8 1.07562e8i 1.12730 0.245029i
\(761\) −1.46101e8 −0.331513 −0.165756 0.986167i \(-0.553007\pi\)
−0.165756 + 0.986167i \(0.553007\pi\)
\(762\) −8.20740e6 + 7.93001e7i −0.0185499 + 0.179229i
\(763\) 2.11256e8 + 2.11256e8i 0.475593 + 0.475593i
\(764\) 2.02540e8 + 8.11114e7i 0.454184 + 0.181887i
\(765\) −2.82466e8 + 4.03504e8i −0.630931 + 0.901288i
\(766\) −4.60672e8 6.80725e8i −1.02496 1.51456i
\(767\) 3.98939e8i 0.884140i
\(768\) 3.60360e8 + 2.74473e8i 0.795524 + 0.605922i
\(769\) −3.00236e8 −0.660213 −0.330107 0.943944i \(-0.607085\pi\)
−0.330107 + 0.943944i \(0.607085\pi\)
\(770\) −3.29179e8 + 2.22767e8i −0.721040 + 0.487955i
\(771\) −2.17318e8 1.82330e8i −0.474169 0.397828i
\(772\) −1.45497e8 + 3.63316e8i −0.316230 + 0.789646i
\(773\) −5.62030e8 + 5.62030e8i −1.21680 + 1.21680i −0.248060 + 0.968745i \(0.579793\pi\)
−0.968745 + 0.248060i \(0.920207\pi\)
\(774\) −8.61697e6 + 5.45142e8i −0.0185837 + 1.17567i
\(775\) 3.96350e7i 0.0851479i
\(776\) 3.87934e7 + 1.78476e8i 0.0830182 + 0.381939i
\(777\) 9.71978e6 + 1.11022e8i 0.0207202 + 0.236672i
\(778\) −1.23577e8 + 6.40984e8i −0.262421 + 1.36116i
\(779\) −5.18441e8 + 5.18441e8i −1.09670 + 1.09670i
\(780\) 3.37444e8 1.80774e8i 0.711079 0.380937i
\(781\) −3.62704e8 + 3.62704e8i −0.761377 + 0.761377i
\(782\) −8.25194e7 1.21937e8i −0.172558 0.254986i
\(783\) 1.26405e8 + 4.71417e8i 0.263317 + 0.982019i
\(784\) −6.28911e7 5.99936e7i −0.130509 0.124496i
\(785\) 2.03920e8i 0.421553i
\(786\) −4.87443e8 + 3.96008e8i −1.00382 + 0.815522i
\(787\) 2.21139e8 2.21139e8i 0.453671 0.453671i −0.442900 0.896571i \(-0.646050\pi\)
0.896571 + 0.442900i \(0.146050\pi\)
\(788\) −2.50064e8 5.84136e8i −0.511060 1.19381i
\(789\) −5.96880e8 + 7.11419e8i −1.21522 + 1.44842i
\(790\) −7.83151e7 + 4.06214e8i −0.158842 + 0.823898i
\(791\) 4.29299e7 0.0867421
\(792\) −2.09476e8 + 5.00027e8i −0.421656 + 1.00651i
\(793\) 7.95855e8i 1.59593i
\(794\) 7.24453e7 3.75768e8i 0.144727 0.750686i
\(795\) −6.42379e8 5.38955e8i −1.27847 1.07263i
\(796\) 2.62377e8 + 1.05074e8i 0.520220 + 0.208333i
\(797\) 2.76872e8 + 2.76872e8i 0.546895 + 0.546895i 0.925541 0.378647i \(-0.123610\pi\)
−0.378647 + 0.925541i \(0.623610\pi\)
\(798\) 4.67445e8 3.79761e8i 0.919859 0.747311i
\(799\) −2.40680e8 −0.471846
\(800\) −1.90007e7 + 1.12798e8i −0.0371107 + 0.220309i
\(801\) −3.66110e7 2.07489e8i −0.0712383 0.403735i
\(802\) −8.10006e7 1.19693e8i −0.157024 0.232030i
\(803\) 3.75651e8 + 3.75651e8i 0.725501 + 0.725501i
\(804\) 8.25227e8 + 2.49485e8i 1.58784 + 0.480039i
\(805\) 7.25771e7 + 7.25771e7i 0.139127 + 0.139127i
\(806\) 3.45818e7 1.79373e8i 0.0660454 0.342572i
\(807\) 5.60716e7 4.90895e6i 0.106690 0.00934046i
\(808\) 4.40637e8 + 2.83286e8i 0.835309 + 0.537020i
\(809\) 6.13120e8 1.15798 0.578988 0.815336i \(-0.303448\pi\)
0.578988 + 0.815336i \(0.303448\pi\)
\(810\) −7.40791e7 4.62432e8i −0.139393 0.870148i
\(811\) 5.50342e8 + 5.50342e8i 1.03174 + 1.03174i 0.999479 + 0.0322606i \(0.0102706\pi\)
0.0322606 + 0.999479i \(0.489729\pi\)
\(812\) 1.93941e8 + 4.53037e8i 0.362245 + 0.846186i
\(813\) −4.51836e7 + 5.38541e7i −0.0840831 + 0.100218i
\(814\) −1.27916e8 + 8.65652e7i −0.237165 + 0.160498i
\(815\) 9.20858e6i 0.0170106i
\(816\) 7.50721e7 + 6.74160e8i 0.138168 + 1.24077i
\(817\) 8.39413e8 1.53925
\(818\) −3.79005e8 5.60048e8i −0.692445 1.02321i
\(819\) 2.61090e8 3.72969e8i 0.475268 0.678923i
\(820\) 2.26551e8 + 5.29211e8i 0.410889 + 0.959815i
\(821\) −2.13638e8 + 2.13638e8i −0.386055 + 0.386055i −0.873278 0.487223i \(-0.838010\pi\)
0.487223 + 0.873278i \(0.338010\pi\)
\(822\) 7.16349e7 6.92138e8i 0.128976 1.24617i
\(823\) 6.57403e8i 1.17932i 0.807651 + 0.589661i \(0.200739\pi\)
−0.807651 + 0.589661i \(0.799261\pi\)
\(824\) −4.39471e8 + 9.55233e7i −0.785505 + 0.170737i
\(825\) −1.36377e8 + 1.19395e7i −0.242873 + 0.0212630i
\(826\) −4.83878e8 9.32880e7i −0.858609 0.165533i
\(827\) 1.81552e8 1.81552e8i 0.320985 0.320985i −0.528160 0.849145i \(-0.677118\pi\)
0.849145 + 0.528160i \(0.177118\pi\)
\(828\) 1.37028e8 + 2.86713e7i 0.241389 + 0.0505075i
\(829\) 7.81081e7 7.81081e7i 0.137098 0.137098i −0.635227 0.772325i \(-0.719093\pi\)
0.772325 + 0.635227i \(0.219093\pi\)
\(830\) −6.93426e8 + 4.69267e8i −1.21273 + 0.820703i
\(831\) −8.41330e8 + 7.36566e7i −1.46610 + 0.128354i
\(832\) 1.84407e8 4.93904e8i 0.320189 0.857575i
\(833\) 1.30154e8i 0.225177i
\(834\) 3.03137e8 2.46274e8i 0.522565 0.424542i
\(835\) −1.77869e8 + 1.77869e8i −0.305521 + 0.305521i
\(836\) 7.74849e8 + 3.10304e8i 1.32617 + 0.531091i
\(837\) −1.93561e8 1.11707e8i −0.330096 0.190504i
\(838\) −5.41303e8 1.04359e8i −0.919832 0.177337i
\(839\) 4.70764e8 0.797109 0.398554 0.917145i \(-0.369512\pi\)
0.398554 + 0.917145i \(0.369512\pi\)
\(840\) −1.40355e8 4.51561e8i −0.236805 0.761866i
\(841\) 2.00434e7i 0.0336965i
\(842\) −7.07617e8 1.36423e8i −1.18539 0.228535i
\(843\) 5.85859e7 6.98283e7i 0.0977936 0.116560i
\(844\) −3.11470e8 7.27578e8i −0.518070 1.21019i
\(845\) 6.09232e7 + 6.09232e7i 0.100975 + 0.100975i
\(846\) 1.64356e8 1.59241e8i 0.271440 0.262992i
\(847\) −1.04993e8 −0.172787
\(848\) −1.15448e9 + 2.72212e7i −1.89321 + 0.0446396i
\(849\) 1.05465e9 9.23324e7i 1.72340 0.150880i
\(850\) −1.41859e8 + 9.60016e7i −0.230994 + 0.156323i
\(851\) 2.82027e7 + 2.82027e7i 0.0457618 + 0.0457618i
\(852\) −2.88172e8 5.37918e8i −0.465943 0.869755i
\(853\) 5.14265e7 + 5.14265e7i 0.0828590 + 0.0828590i 0.747322 0.664463i \(-0.231339\pi\)
−0.664463 + 0.747322i \(0.731339\pi\)
\(854\) 9.65301e8 + 1.86103e8i 1.54985 + 0.298799i
\(855\) −7.10076e8 + 1.25292e8i −1.13607 + 0.200458i
\(856\) 5.80339e8 + 3.73100e8i 0.925252 + 0.594845i
\(857\) 9.46343e8 1.50351 0.751755 0.659443i \(-0.229208\pi\)
0.751755 + 0.659443i \(0.229208\pi\)
\(858\) 6.27608e8 + 6.49561e7i 0.993634 + 0.102839i
\(859\) −6.35758e8 6.35758e8i −1.00303 1.00303i −0.999995 0.00303137i \(-0.999035\pi\)
−0.00303137 0.999995i \(-0.500965\pi\)
\(860\) 2.45020e8 6.11832e8i 0.385218 0.961915i
\(861\) 5.24478e8 + 4.40037e8i 0.821709 + 0.689414i
\(862\) −2.88078e8 4.25687e8i −0.449768 0.664612i
\(863\) 2.56659e7i 0.0399322i −0.999801 0.0199661i \(-0.993644\pi\)
0.999801 0.0199661i \(-0.00635583\pi\)
\(864\) −4.97308e8 4.10700e8i −0.771052 0.636772i
\(865\) −5.41374e8 −0.836468
\(866\) −3.50007e8 + 2.36863e8i −0.538919 + 0.364706i
\(867\) −2.33992e8 + 2.78894e8i −0.359041 + 0.427939i
\(868\) −2.09477e8 8.38892e7i −0.320314 0.128276i
\(869\) −4.82144e8 + 4.82144e8i −0.734713 + 0.734713i
\(870\) 6.07390e7 5.86862e8i 0.0922379 0.891206i
\(871\) 1.00337e9i 1.51848i
\(872\) −4.14352e8 2.66387e8i −0.624914 0.401757i
\(873\) −4.51878e7 2.56097e8i −0.0679169 0.384912i
\(874\) 4.08029e7 2.11641e8i 0.0611162 0.317005i
\(875\) 4.62367e8 4.62367e8i 0.690181 0.690181i
\(876\) −5.57119e8 + 2.98458e8i −0.828774 + 0.443988i
\(877\) −6.11052e7 + 6.11052e7i −0.0905898 + 0.0905898i −0.750949 0.660360i \(-0.770404\pi\)
0.660360 + 0.750949i \(0.270404\pi\)
\(878\) 1.51412e7 + 2.23738e7i 0.0223706 + 0.0330565i
\(879\) 1.09845e8 + 1.25468e9i 0.161738 + 1.84743i
\(880\) 4.52349e8 4.74196e8i 0.663783 0.695841i
\(881\) 3.34838e8i 0.489674i −0.969564 0.244837i \(-0.921266\pi\)
0.969564 0.244837i \(-0.0787344\pi\)
\(882\) 8.61137e7 + 8.88798e7i 0.125507 + 0.129538i
\(883\) 4.79823e8 4.79823e8i 0.696945 0.696945i −0.266805 0.963751i \(-0.585968\pi\)
0.963751 + 0.266805i \(0.0859680\pi\)
\(884\) 7.25764e8 3.10693e8i 1.05060 0.449754i
\(885\) 4.51971e8 + 3.79203e8i 0.652050 + 0.547069i
\(886\) −7.62372e7 + 3.95436e8i −0.109614 + 0.568559i
\(887\) 7.22095e8 1.03472 0.517361 0.855767i \(-0.326915\pi\)
0.517361 + 0.855767i \(0.326915\pi\)
\(888\) −5.45407e7 1.75472e8i −0.0778900 0.250593i
\(889\) 1.14614e8i 0.163130i
\(890\) −4.82153e7 + 2.50089e8i −0.0683936 + 0.354752i
\(891\) 3.26056e8 6.99658e8i 0.460955 0.989128i
\(892\) 1.82532e8 4.55793e8i 0.257184 0.642204i
\(893\) −2.49138e8 2.49138e8i −0.349853 0.349853i
\(894\) 5.94129e8 + 7.31309e8i 0.831511 + 1.02350i
\(895\) 4.54122e8 0.633438
\(896\) −5.55939e8 3.39163e8i −0.772864 0.471503i
\(897\) −1.42101e7 1.62313e8i −0.0196888 0.224892i
\(898\) 6.32028e7 + 9.33934e7i 0.0872785 + 0.128970i
\(899\) −1.99079e8 1.99079e8i −0.273998 0.273998i
\(900\) 3.33557e7 1.59416e8i 0.0457554 0.218677i
\(901\) −1.22278e9 1.22278e9i −1.67176 1.67176i
\(902\) −1.79617e8 + 9.31659e8i −0.244753 + 1.26951i
\(903\) −6.83599e7 7.80829e8i −0.0928407 1.06046i
\(904\) −6.91674e7 + 1.50342e7i −0.0936259 + 0.0203505i
\(905\) 9.12973e8 1.23172
\(906\) 8.02665e8 + 8.30742e7i 1.07932 + 0.111707i
\(907\) 3.01488e8 + 3.01488e8i 0.404062 + 0.404062i 0.879662 0.475600i \(-0.157769\pi\)
−0.475600 + 0.879662i \(0.657769\pi\)
\(908\) −2.52165e8 + 1.07950e8i −0.336843 + 0.144200i
\(909\) −6.11026e8 4.27738e8i −0.813519 0.569490i
\(910\) −4.55790e8 + 3.08450e8i −0.604841 + 0.409318i
\(911\) 8.37188e8i 1.10731i 0.832747 + 0.553654i \(0.186767\pi\)
−0.832747 + 0.553654i \(0.813233\pi\)
\(912\) −6.20140e8 + 7.75560e8i −0.817533 + 1.02242i
\(913\) −1.38003e9 −1.81332
\(914\) −6.86142e8 1.01390e9i −0.898619 1.32787i
\(915\) −9.01649e8 7.56483e8i −1.17699 0.987498i
\(916\) −4.63826e8 + 1.98560e8i −0.603488 + 0.258348i
\(917\) 6.38434e8 6.38434e8i 0.827958 0.827958i
\(918\) −6.90163e7 9.63351e8i −0.0892121 1.24525i
\(919\) 1.00319e9i 1.29251i 0.763120 + 0.646257i \(0.223667\pi\)
−0.763120 + 0.646257i \(0.776333\pi\)
\(920\) −1.42351e8 9.15174e7i −0.182809 0.117528i
\(921\) 1.17199e8 + 1.33868e9i 0.150018 + 1.71356i
\(922\) −1.11832e9 2.15605e8i −1.42684 0.275084i
\(923\) −5.02211e8 + 5.02211e8i −0.638676 + 0.638676i
\(924\) 2.25546e8 7.46042e8i 0.285903 0.945687i
\(925\) 3.28106e7 3.28106e7i 0.0414561 0.0414561i
\(926\) 1.48694e8 1.00627e8i 0.187266 0.126730i
\(927\) 6.30601e8 1.11268e8i 0.791618 0.139680i
\(928\) −4.71128e8 6.62002e8i −0.589515 0.828353i
\(929\) 3.39676e8i 0.423660i −0.977307 0.211830i \(-0.932058\pi\)
0.977307 0.211830i \(-0.0679423\pi\)
\(930\) 1.70346e8 + 2.09678e8i 0.211779 + 0.260678i
\(931\) 1.34728e8 1.34728e8i 0.166959 0.166959i
\(932\) −5.50365e8 + 1.37430e9i −0.679834 + 1.69759i
\(933\) −1.95859e8 + 2.33443e8i −0.241156 + 0.287433i
\(934\) 1.13992e9 + 2.19768e8i 1.39905 + 0.269727i
\(935\) 9.81358e8 1.20058
\(936\) −2.90046e8 + 6.92351e8i −0.353704 + 0.844304i
\(937\) 1.22832e9i 1.49311i −0.665324 0.746554i \(-0.731707\pi\)
0.665324 0.746554i \(-0.268293\pi\)
\(938\) −1.21700e9 2.34629e8i −1.47463 0.284297i
\(939\) 3.60976e8 + 3.02859e8i 0.435995 + 0.365800i
\(940\) −2.54314e8 + 1.08870e8i −0.306187 + 0.131076i
\(941\) 2.73475e8 + 2.73475e8i 0.328208 + 0.328208i 0.851905 0.523697i \(-0.175448\pi\)
−0.523697 + 0.851905i \(0.675448\pi\)
\(942\) 2.52134e8 + 3.10350e8i 0.301633 + 0.371278i
\(943\) 2.45014e8 0.292183
\(944\) 8.12279e8 1.91526e7i 0.965583 0.0227673i
\(945\) 1.74374e8 + 6.50315e8i 0.206627 + 0.770599i
\(946\) 8.99640e8 6.08820e8i 1.06266 0.719143i
\(947\) 2.23209e8 + 2.23209e8i 0.262822 + 0.262822i 0.826200 0.563378i \(-0.190498\pi\)
−0.563378 + 0.826200i \(0.690498\pi\)
\(948\) −3.83068e8 7.15056e8i −0.449625 0.839296i
\(949\) 5.20138e8 + 5.20138e8i 0.608583 + 0.608583i
\(950\) −2.46220e8 4.74694e7i −0.287179 0.0553659i
\(951\) 5.61352e8 4.91452e7i 0.652670 0.0571399i
\(952\) −2.07130e8 9.52939e8i −0.240067 1.10447i
\(953\) 1.15460e9 1.33399 0.666995 0.745062i \(-0.267580\pi\)
0.666995 + 0.745062i \(0.267580\pi\)
\(954\) 1.64403e9 + 2.59870e7i 1.89350 + 0.0299302i
\(955\) 2.65535e8 + 2.65535e8i 0.304867 + 0.304867i
\(956\) −4.81773e8 1.92936e8i −0.551402 0.220820i
\(957\) 6.25027e8 7.44967e8i 0.713120 0.849965i
\(958\) 1.74427e8 + 2.57747e8i 0.198389 + 0.293155i
\(959\) 1.00036e9i 1.13423i
\(960\) 3.84275e8 + 6.78390e8i 0.434338 + 0.766771i
\(961\) −7.58589e8 −0.854745
\(962\) −1.77116e8 + 1.19861e8i −0.198944 + 0.134633i
\(963\) −8.04747e8 5.63349e8i −0.901116 0.630810i
\(964\) 1.33308e8 3.32879e8i 0.148808 0.371583i
\(965\) −4.76315e8 + 4.76315e8i −0.530044 + 0.530044i
\(966\) −2.00193e8 2.07196e7i −0.222084 0.0229853i
\(967\) 5.96724e8i 0.659924i 0.943994 + 0.329962i \(0.107036\pi\)
−0.943994 + 0.329962i \(0.892964\pi\)
\(968\) 1.69162e8 3.67690e7i 0.186499 0.0405374i
\(969\) −1.48132e9 + 1.29687e8i −1.62809 + 0.142536i
\(970\) −5.95107e7 + 3.08677e8i −0.0652048 + 0.338212i
\(971\) −3.36566e8 + 3.36566e8i −0.367631 + 0.367631i −0.866613 0.498982i \(-0.833708\pi\)
0.498982 + 0.866613i \(0.333708\pi\)
\(972\) 6.84510e8 + 6.12190e8i 0.745385 + 0.666634i
\(973\) −3.97037e8 + 3.97037e8i −0.431015 + 0.431015i
\(974\) 6.62327e8 + 9.78706e8i 0.716796 + 1.05919i
\(975\) −1.88832e8 + 1.65318e7i −0.203733 + 0.0178364i
\(976\) −1.62044e9 + 3.82080e7i −1.74294 + 0.0410965i
\(977\) 8.45394e8i 0.906516i 0.891379 + 0.453258i \(0.149738\pi\)
−0.891379 + 0.453258i \(0.850262\pi\)
\(978\) −1.13858e7 1.40147e7i −0.0121716 0.0149819i
\(979\) −2.96836e8 + 2.96836e8i −0.316351 + 0.316351i
\(980\) −5.88742e7 1.37527e8i −0.0625528 0.146120i
\(981\) 5.74576e8 + 4.02222e8i 0.608612 + 0.426048i
\(982\) −2.48292e8 + 1.28787e9i −0.262197 + 1.35999i
\(983\) 3.82375e7 0.0402558 0.0201279 0.999797i \(-0.493593\pi\)
0.0201279 + 0.999797i \(0.493593\pi\)
\(984\) −9.99127e8 5.25301e8i −1.04866 0.551345i
\(985\) 1.09365e9i 1.14438i
\(986\) 2.30336e8 1.19473e9i 0.240287 1.24635i
\(987\) −2.11461e8 + 2.52039e8i −0.219927 + 0.262130i
\(988\) 1.07288e9 + 4.29656e8i 1.11245 + 0.445503i
\(989\) −1.98352e8 1.98352e8i −0.205044 0.205044i
\(990\) −6.70150e8 + 6.49293e8i −0.690663 + 0.669168i
\(991\) −1.25057e9 −1.28495 −0.642474 0.766307i \(-0.722092\pi\)
−0.642474 + 0.766307i \(0.722092\pi\)
\(992\) 3.66881e8 + 6.18004e7i 0.375829 + 0.0633077i
\(993\) 3.47031e7 3.03818e6i 0.0354422 0.00310289i
\(994\) 4.91699e8 + 7.26573e8i 0.500657 + 0.739810i
\(995\) 3.43982e8 + 3.43982e8i 0.349194 + 0.349194i
\(996\) 4.75120e8 1.57156e9i 0.480867 1.59057i
\(997\) −3.82791e8 3.82791e8i −0.386257 0.386257i 0.487093 0.873350i \(-0.338057\pi\)
−0.873350 + 0.487093i \(0.838057\pi\)
\(998\) −2.29474e6 + 1.19026e7i −0.00230857 + 0.0119744i
\(999\) 6.77601e7 + 2.52706e8i 0.0679638 + 0.253466i
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 48.7.i.a.5.10 92
3.2 odd 2 inner 48.7.i.a.5.37 yes 92
4.3 odd 2 192.7.i.a.113.14 92
12.11 even 2 192.7.i.a.113.9 92
16.3 odd 4 192.7.i.a.17.9 92
16.13 even 4 inner 48.7.i.a.29.37 yes 92
48.29 odd 4 inner 48.7.i.a.29.10 yes 92
48.35 even 4 192.7.i.a.17.14 92
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
48.7.i.a.5.10 92 1.1 even 1 trivial
48.7.i.a.5.37 yes 92 3.2 odd 2 inner
48.7.i.a.29.10 yes 92 48.29 odd 4 inner
48.7.i.a.29.37 yes 92 16.13 even 4 inner
192.7.i.a.17.9 92 16.3 odd 4
192.7.i.a.17.14 92 48.35 even 4
192.7.i.a.113.9 92 12.11 even 2
192.7.i.a.113.14 92 4.3 odd 2