Properties

Label 27.9.f.a.14.6
Level $27$
Weight $9$
Character 27.14
Analytic conductor $10.999$
Analytic rank $0$
Dimension $138$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [27,9,Mod(2,27)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(27, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("27.2");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 27.f (of order \(18\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(10.9992224717\)
Analytic rank: \(0\)
Dimension: \(138\)
Relative dimension: \(23\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 14.6
Character \(\chi\) \(=\) 27.14
Dual form 27.9.f.a.2.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-18.2801 + 3.22328i) q^{2} +(61.0463 - 53.2386i) q^{3} +(83.2125 - 30.2869i) q^{4} +(-223.403 + 266.242i) q^{5} +(-944.332 + 1169.98i) q^{6} +(-1438.86 - 523.701i) q^{7} +(2691.76 - 1554.09i) q^{8} +(892.309 - 6500.04i) q^{9} +(3225.67 - 5587.03i) q^{10} +(262.444 + 312.769i) q^{11} +(3467.39 - 6279.02i) q^{12} +(-7243.71 + 41081.1i) q^{13} +(27990.6 + 4935.49i) q^{14} +(536.374 + 28146.7i) q^{15} +(-61562.3 + 51656.9i) q^{16} +(52651.8 + 30398.5i) q^{17} +(4639.91 + 121698. i) q^{18} +(81686.6 + 141485. i) q^{19} +(-10526.3 + 28920.8i) q^{20} +(-115718. + 44632.7i) q^{21} +(-5805.66 - 4871.53i) q^{22} +(88565.0 + 243330. i) q^{23} +(81584.6 - 238177. i) q^{24} +(46855.7 + 265732. i) q^{25} -774316. i q^{26} +(-291581. - 444309. i) q^{27} -135592. q^{28} +(833385. - 146948. i) q^{29} +(-100530. - 512798. i) q^{30} +(-733729. + 267056. i) q^{31} +(447401. - 533192. i) q^{32} +(32672.6 + 5121.24i) q^{33} +(-1.06047e6 - 385978. i) q^{34} +(460877. - 266087. i) q^{35} +(-122615. - 567910. i) q^{36} +(-858362. + 1.48673e6i) q^{37} +(-1.94929e6 - 2.32307e6i) q^{38} +(1.74490e6 + 2.89349e6i) q^{39} +(-187585. + 1.06385e6i) q^{40} +(-24637.0 - 4344.17i) q^{41} +(1.97148e6 - 1.18888e6i) q^{42} +(738972. - 620071. i) q^{43} +(31311.4 + 18077.7i) q^{44} +(1.53124e6 + 1.68970e6i) q^{45} +(-2.40330e6 - 4.16264e6i) q^{46} +(463987. - 1.27479e6i) q^{47} +(-1.00801e6 + 6.43096e6i) q^{48} +(-2.62005e6 - 2.19848e6i) q^{49} +(-1.71306e6 - 4.70659e6i) q^{50} +(4.83258e6 - 947388. i) q^{51} +(641451. + 3.63785e6i) q^{52} -6.06703e6i q^{53} +(6.76226e6 + 7.18218e6i) q^{54} -141903. q^{55} +(-4.68694e6 + 826433. i) q^{56} +(1.25192e7 + 4.28829e6i) q^{57} +(-1.47607e7 + 5.37247e6i) q^{58} +(-1.23794e7 + 1.47532e7i) q^{59} +(897110. + 2.32592e6i) q^{60} +(7.35050e6 + 2.67536e6i) q^{61} +(1.25519e7 - 7.24683e6i) q^{62} +(-4.68799e6 + 8.88533e6i) q^{63} +(3.82665e6 - 6.62796e6i) q^{64} +(-9.31923e6 - 1.11062e7i) q^{65} +(-613767. + 11696.2i) q^{66} +(-3.57529e6 + 2.02765e7i) q^{67} +(5.30197e6 + 934880. i) q^{68} +(1.83611e7 + 1.01394e7i) q^{69} +(-7.56721e6 + 6.34965e6i) q^{70} +(1.86096e7 + 1.07443e7i) q^{71} +(-7.69975e6 - 1.88833e7i) q^{72} +(-2.63704e7 - 4.56749e7i) q^{73} +(1.08988e7 - 2.99443e7i) q^{74} +(1.70076e7 + 1.37274e7i) q^{75} +(1.10825e7 + 9.29932e6i) q^{76} +(-213822. - 587472. i) q^{77} +(-4.12235e7 - 4.72692e7i) q^{78} +(6.77127e6 + 3.84018e7i) q^{79} -2.79308e7i q^{80} +(-4.14543e7 - 1.16001e7i) q^{81} +464371. q^{82} +(-1.82582e7 + 3.21941e6i) q^{83} +(-8.27741e6 + 7.21874e6i) q^{84} +(-1.98560e7 + 7.22697e6i) q^{85} +(-1.15098e7 + 1.37169e7i) q^{86} +(4.30518e7 - 5.33389e7i) q^{87} +(1.19251e6 + 434037. i) q^{88} +(7.85112e7 - 4.53284e7i) q^{89} +(-3.34376e7 - 2.59523e7i) q^{90} +(3.19369e7 - 5.53163e7i) q^{91} +(1.47394e7 + 1.75658e7i) q^{92} +(-3.05738e7 + 5.53655e7i) q^{93} +(-4.37272e6 + 2.47989e7i) q^{94} +(-5.59184e7 - 9.85992e6i) q^{95} +(-1.07418e6 - 5.63684e7i) q^{96} +(5.90263e7 - 4.95290e7i) q^{97} +(5.49811e7 + 3.17433e7i) q^{98} +(2.26719e6 - 1.42681e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 138 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 447 q^{5} - 774 q^{6} - 6 q^{7} - 9 q^{8} - 12960 q^{9} - 3 q^{10} + 28668 q^{11} + 77421 q^{12} - 6 q^{13} - 120975 q^{14} + 105507 q^{15} - 774 q^{16} - 9 q^{17}+ \cdots + 228876057 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −18.2801 + 3.22328i −1.14251 + 0.201455i −0.712703 0.701466i \(-0.752529\pi\)
−0.429806 + 0.902921i \(0.641418\pi\)
\(3\) 61.0463 53.2386i 0.753658 0.657266i
\(4\) 83.2125 30.2869i 0.325049 0.118308i
\(5\) −223.403 + 266.242i −0.357445 + 0.425987i −0.914561 0.404448i \(-0.867464\pi\)
0.557116 + 0.830435i \(0.311908\pi\)
\(6\) −944.332 + 1169.98i −0.728652 + 0.902761i
\(7\) −1438.86 523.701i −0.599274 0.218118i 0.0245293 0.999699i \(-0.492191\pi\)
−0.623804 + 0.781581i \(0.714414\pi\)
\(8\) 2691.76 1554.09i 0.657168 0.379416i
\(9\) 892.309 6500.04i 0.136002 0.990709i
\(10\) 3225.67 5587.03i 0.322567 0.558703i
\(11\) 262.444 + 312.769i 0.0179253 + 0.0213625i 0.774933 0.632044i \(-0.217784\pi\)
−0.757007 + 0.653406i \(0.773339\pi\)
\(12\) 3467.39 6279.02i 0.167216 0.302808i
\(13\) −7243.71 + 41081.1i −0.253622 + 1.43836i 0.545962 + 0.837810i \(0.316164\pi\)
−0.799585 + 0.600554i \(0.794947\pi\)
\(14\) 27990.6 + 4935.49i 0.728617 + 0.128475i
\(15\) 536.374 + 28146.7i 0.0105950 + 0.555985i
\(16\) −61562.3 + 51656.9i −0.939367 + 0.788222i
\(17\) 52651.8 + 30398.5i 0.630402 + 0.363963i 0.780908 0.624646i \(-0.214757\pi\)
−0.150506 + 0.988609i \(0.548090\pi\)
\(18\) 4639.91 + 121698.i 0.0441998 + 1.15929i
\(19\) 81686.6 + 141485.i 0.626811 + 1.08567i 0.988188 + 0.153249i \(0.0489735\pi\)
−0.361377 + 0.932420i \(0.617693\pi\)
\(20\) −10526.3 + 28920.8i −0.0657895 + 0.180755i
\(21\) −115718. + 44632.7i −0.595010 + 0.229496i
\(22\) −5805.66 4871.53i −0.0247834 0.0207957i
\(23\) 88565.0 + 243330.i 0.316483 + 0.869531i 0.991309 + 0.131554i \(0.0419966\pi\)
−0.674826 + 0.737977i \(0.735781\pi\)
\(24\) 81584.6 238177.i 0.245903 0.717884i
\(25\) 46855.7 + 265732.i 0.119951 + 0.680274i
\(26\) 774316.i 1.69444i
\(27\) −291581. 444309.i −0.548660 0.836045i
\(28\) −135592. −0.220599
\(29\) 833385. 146948.i 1.17829 0.207765i 0.449999 0.893029i \(-0.351424\pi\)
0.728295 + 0.685264i \(0.240313\pi\)
\(30\) −100530. 512798.i −0.124111 0.633083i
\(31\) −733729. + 267056.i −0.794491 + 0.289171i −0.707202 0.707012i \(-0.750043\pi\)
−0.0872894 + 0.996183i \(0.527820\pi\)
\(32\) 447401. 533192.i 0.426675 0.508492i
\(33\) 32672.6 + 5121.24i 0.0275504 + 0.00431836i
\(34\) −1.06047e6 385978.i −0.793562 0.288833i
\(35\) 460877. 266087.i 0.307123 0.177318i
\(36\) −122615. 567910.i −0.0730015 0.338119i
\(37\) −858362. + 1.48673e6i −0.457998 + 0.793276i −0.998855 0.0478387i \(-0.984767\pi\)
0.540857 + 0.841115i \(0.318100\pi\)
\(38\) −1.94929e6 2.32307e6i −0.934850 1.11411i
\(39\) 1.74490e6 + 2.89349e6i 0.754243 + 1.25073i
\(40\) −187585. + 1.06385e6i −0.0732754 + 0.415565i
\(41\) −24637.0 4344.17i −0.00871872 0.00153735i 0.169287 0.985567i \(-0.445853\pi\)
−0.178006 + 0.984029i \(0.556965\pi\)
\(42\) 1.97148e6 1.18888e6i 0.633571 0.382069i
\(43\) 738972. 620071.i 0.216150 0.181371i −0.528284 0.849068i \(-0.677164\pi\)
0.744433 + 0.667697i \(0.232720\pi\)
\(44\) 31311.4 + 18077.7i 0.00835396 + 0.00482316i
\(45\) 1.53124e6 + 1.68970e6i 0.373415 + 0.412059i
\(46\) −2.40330e6 4.16264e6i −0.536756 0.929689i
\(47\) 463987. 1.27479e6i 0.0950854 0.261245i −0.883027 0.469322i \(-0.844498\pi\)
0.978112 + 0.208077i \(0.0667205\pi\)
\(48\) −1.00801e6 + 6.43096e6i −0.189890 + 1.21146i
\(49\) −2.62005e6 2.19848e6i −0.454490 0.381362i
\(50\) −1.71306e6 4.70659e6i −0.274089 0.753054i
\(51\) 4.83258e6 947388.i 0.714328 0.140038i
\(52\) 641451. + 3.63785e6i 0.0877304 + 0.497544i
\(53\) 6.06703e6i 0.768905i −0.923145 0.384452i \(-0.874390\pi\)
0.923145 0.384452i \(-0.125610\pi\)
\(54\) 6.76226e6 + 7.18218e6i 0.795275 + 0.844659i
\(55\) −141903. −0.0155075
\(56\) −4.68694e6 + 826433.i −0.476581 + 0.0840341i
\(57\) 1.25192e7 + 4.28829e6i 1.18597 + 0.406242i
\(58\) −1.47607e7 + 5.37247e6i −1.30436 + 0.474747i
\(59\) −1.23794e7 + 1.47532e7i −1.02163 + 1.21753i −0.0458050 + 0.998950i \(0.514585\pi\)
−0.975820 + 0.218575i \(0.929859\pi\)
\(60\) 897110. + 2.32592e6i 0.0692215 + 0.179469i
\(61\) 7.35050e6 + 2.67536e6i 0.530881 + 0.193225i 0.593532 0.804810i \(-0.297733\pi\)
−0.0626504 + 0.998036i \(0.519955\pi\)
\(62\) 1.25519e7 7.24683e6i 0.849458 0.490435i
\(63\) −4.68799e6 + 8.88533e6i −0.297594 + 0.564042i
\(64\) 3.82665e6 6.62796e6i 0.228086 0.395057i
\(65\) −9.31923e6 1.11062e7i −0.522068 0.622176i
\(66\) −613767. + 11696.2i −0.0323465 + 0.000616407i
\(67\) −3.57529e6 + 2.02765e7i −0.177424 + 1.00622i 0.757885 + 0.652388i \(0.226233\pi\)
−0.935309 + 0.353832i \(0.884878\pi\)
\(68\) 5.30197e6 + 934880.i 0.247971 + 0.0437240i
\(69\) 1.83611e7 + 1.01394e7i 0.810034 + 0.447315i
\(70\) −7.56721e6 + 6.34965e6i −0.315169 + 0.264458i
\(71\) 1.86096e7 + 1.07443e7i 0.732325 + 0.422808i 0.819272 0.573405i \(-0.194378\pi\)
−0.0869473 + 0.996213i \(0.527711\pi\)
\(72\) −7.69975e6 1.88833e7i −0.286515 0.702663i
\(73\) −2.63704e7 4.56749e7i −0.928593 1.60837i −0.785678 0.618635i \(-0.787686\pi\)
−0.142914 0.989735i \(-0.545647\pi\)
\(74\) 1.08988e7 2.99443e7i 0.363457 0.998590i
\(75\) 1.70076e7 + 1.37274e7i 0.537523 + 0.433855i
\(76\) 1.10825e7 + 9.29932e6i 0.332188 + 0.278738i
\(77\) −213822. 587472.i −0.00608262 0.0167119i
\(78\) −4.12235e7 4.72692e7i −1.11370 1.27703i
\(79\) 6.77127e6 + 3.84018e7i 0.173845 + 0.985923i 0.939469 + 0.342635i \(0.111319\pi\)
−0.765624 + 0.643289i \(0.777570\pi\)
\(80\) 2.79308e7i 0.681904i
\(81\) −4.14543e7 1.16001e7i −0.963007 0.269477i
\(82\) 464371. 0.0102709
\(83\) −1.82582e7 + 3.21941e6i −0.384721 + 0.0678366i −0.362664 0.931920i \(-0.618133\pi\)
−0.0220569 + 0.999757i \(0.507021\pi\)
\(84\) −8.27741e6 + 7.21874e6i −0.166256 + 0.144992i
\(85\) −1.98560e7 + 7.22697e6i −0.380378 + 0.138446i
\(86\) −1.15098e7 + 1.37169e7i −0.210415 + 0.250762i
\(87\) 4.30518e7 5.33389e7i 0.751474 0.931037i
\(88\) 1.19251e6 + 434037.i 0.0198852 + 0.00723763i
\(89\) 7.85112e7 4.53284e7i 1.25133 0.722455i 0.279955 0.960013i \(-0.409680\pi\)
0.971373 + 0.237558i \(0.0763471\pi\)
\(90\) −3.34376e7 2.59523e7i −0.509642 0.395555i
\(91\) 3.19369e7 5.53163e7i 0.465722 0.806655i
\(92\) 1.47394e7 + 1.75658e7i 0.205745 + 0.245197i
\(93\) −3.05738e7 + 5.53655e7i −0.408712 + 0.740128i
\(94\) −4.37272e6 + 2.47989e7i −0.0560068 + 0.317630i
\(95\) −5.59184e7 9.85992e6i −0.686531 0.121054i
\(96\) −1.07418e6 5.63684e7i −0.0126471 0.663668i
\(97\) 5.90263e7 4.95290e7i 0.666744 0.559464i −0.245356 0.969433i \(-0.578905\pi\)
0.912100 + 0.409969i \(0.134460\pi\)
\(98\) 5.49811e7 + 3.17433e7i 0.596086 + 0.344151i
\(99\) 2.26719e6 1.42681e6i 0.0236019 0.0148534i
\(100\) 1.19472e7 + 2.06931e7i 0.119472 + 0.206931i
\(101\) −6.70812e7 + 1.84304e8i −0.644637 + 1.77113i −0.00799213 + 0.999968i \(0.502544\pi\)
−0.636645 + 0.771157i \(0.719678\pi\)
\(102\) −8.52864e7 + 3.28951e7i −0.787915 + 0.303900i
\(103\) 8.03334e7 + 6.74077e7i 0.713752 + 0.598909i 0.925649 0.378383i \(-0.123520\pi\)
−0.211897 + 0.977292i \(0.567964\pi\)
\(104\) 4.43453e7 + 1.21838e8i 0.379066 + 1.04147i
\(105\) 1.39687e7 4.07801e7i 0.114921 0.335499i
\(106\) 1.95557e7 + 1.10906e8i 0.154900 + 0.878480i
\(107\) 1.09060e8i 0.832017i 0.909361 + 0.416009i \(0.136571\pi\)
−0.909361 + 0.416009i \(0.863429\pi\)
\(108\) −3.77199e7 2.81410e7i −0.277252 0.206845i
\(109\) 7.61337e6 0.0539350 0.0269675 0.999636i \(-0.491415\pi\)
0.0269675 + 0.999636i \(0.491415\pi\)
\(110\) 2.59401e6 457393.i 0.0177174 0.00312406i
\(111\) 2.67513e7 + 1.36457e8i 0.176219 + 0.898886i
\(112\) 1.15632e8 4.20867e7i 0.734864 0.267469i
\(113\) −1.13330e8 + 1.35062e8i −0.695076 + 0.828359i −0.991960 0.126555i \(-0.959608\pi\)
0.296884 + 0.954914i \(0.404053\pi\)
\(114\) −2.42674e8 3.80377e7i −1.43683 0.225214i
\(115\) −8.45704e7 3.07811e7i −0.483534 0.175992i
\(116\) 6.48975e7 3.74686e7i 0.358423 0.206936i
\(117\) 2.60565e8 + 8.37414e7i 1.39051 + 0.446886i
\(118\) 1.78743e8 3.09593e8i 0.921939 1.59684i
\(119\) −5.98387e7 7.13130e7i −0.298397 0.355616i
\(120\) 4.51863e7 + 7.49307e7i 0.217912 + 0.361356i
\(121\) 3.71941e7 2.10938e8i 0.173513 0.984042i
\(122\) −1.42992e8 2.52133e7i −0.645463 0.113812i
\(123\) −1.73528e6 + 1.04644e6i −0.00758138 + 0.00457189i
\(124\) −5.29672e7 + 4.44447e7i −0.224037 + 0.187989i
\(125\) −1.98791e8 1.14772e8i −0.814248 0.470106i
\(126\) 5.70571e7 1.77536e8i 0.226375 0.704374i
\(127\) −9.87685e7 1.71072e8i −0.379668 0.657604i 0.611346 0.791363i \(-0.290628\pi\)
−0.991014 + 0.133759i \(0.957295\pi\)
\(128\) −1.09531e8 + 3.00933e8i −0.408033 + 1.12106i
\(129\) 1.20998e7 7.71949e7i 0.0436939 0.278760i
\(130\) 2.06155e8 + 1.72985e8i 0.721807 + 0.605668i
\(131\) −9.97225e7 2.73985e8i −0.338616 0.930341i −0.985788 0.167996i \(-0.946270\pi\)
0.647171 0.762345i \(-0.275952\pi\)
\(132\) 2.87388e6 563401.i 0.00946613 0.00185576i
\(133\) −4.34394e7 2.46357e8i −0.138828 0.787332i
\(134\) 3.82180e8i 1.18536i
\(135\) 1.83434e8 + 2.16292e7i 0.552260 + 0.0651185i
\(136\) 1.88968e8 0.552373
\(137\) 4.29187e8 7.56772e7i 1.21833 0.214824i 0.472722 0.881212i \(-0.343272\pi\)
0.745605 + 0.666388i \(0.232160\pi\)
\(138\) −3.68326e8 1.26166e8i −1.01558 0.347876i
\(139\) −1.12303e8 + 4.08750e7i −0.300838 + 0.109496i −0.488029 0.872827i \(-0.662284\pi\)
0.187191 + 0.982324i \(0.440062\pi\)
\(140\) 3.02918e7 3.61003e7i 0.0788519 0.0939721i
\(141\) −3.95435e7 1.02523e8i −0.100046 0.259386i
\(142\) −3.74818e8 1.36423e8i −0.921864 0.335531i
\(143\) −1.47500e7 + 8.51589e6i −0.0352733 + 0.0203651i
\(144\) 2.80839e8 + 4.46252e8i 0.653143 + 1.03784i
\(145\) −1.47057e8 + 2.54711e8i −0.332671 + 0.576202i
\(146\) 6.29278e8 + 7.49944e8i 1.38494 + 1.65051i
\(147\) −2.76988e8 + 5.27838e6i −0.593187 + 0.0113040i
\(148\) −2.63981e7 + 1.49711e8i −0.0550208 + 0.312038i
\(149\) −6.60425e8 1.16451e8i −1.33992 0.236264i −0.542686 0.839936i \(-0.682593\pi\)
−0.797233 + 0.603672i \(0.793704\pi\)
\(150\) −3.55148e8 1.96119e8i −0.701527 0.387396i
\(151\) −6.82796e8 + 5.72934e8i −1.31336 + 1.10204i −0.325691 + 0.945476i \(0.605597\pi\)
−0.987668 + 0.156562i \(0.949959\pi\)
\(152\) 4.39762e8 + 2.53896e8i 0.823840 + 0.475644i
\(153\) 2.44573e8 3.15114e8i 0.446317 0.575045i
\(154\) 5.80229e6 + 1.00499e7i 0.0103161 + 0.0178681i
\(155\) 9.28162e7 2.55010e8i 0.160804 0.441805i
\(156\) 2.32832e8 + 1.87927e8i 0.393138 + 0.317316i
\(157\) 9.14157e8 + 7.67068e8i 1.50460 + 1.26251i 0.873511 + 0.486804i \(0.161837\pi\)
0.631092 + 0.775708i \(0.282607\pi\)
\(158\) −2.47560e8 6.80164e8i −0.397239 1.09140i
\(159\) −3.23000e8 3.70370e8i −0.505375 0.579492i
\(160\) 4.20071e7 + 2.38234e8i 0.0640977 + 0.363516i
\(161\) 3.96499e8i 0.590118i
\(162\) 7.95180e8 + 7.84324e7i 1.15453 + 0.113877i
\(163\) −8.51414e8 −1.20612 −0.603060 0.797696i \(-0.706052\pi\)
−0.603060 + 0.797696i \(0.706052\pi\)
\(164\) −2.18168e6 + 384689.i −0.00301589 + 0.000531783i
\(165\) −8.66266e6 + 7.55471e6i −0.0116873 + 0.0101925i
\(166\) 3.23385e8 1.17703e8i 0.425880 0.155008i
\(167\) 9.10357e8 1.08492e9i 1.17043 1.39487i 0.268338 0.963325i \(-0.413526\pi\)
0.902093 0.431541i \(-0.142030\pi\)
\(168\) −2.42122e8 + 2.99977e8i −0.303947 + 0.376574i
\(169\) −8.68649e8 3.16162e8i −1.06487 0.387582i
\(170\) 3.39675e8 1.96111e8i 0.406694 0.234805i
\(171\) 9.92550e8 4.04718e8i 1.16083 0.473334i
\(172\) 4.27117e7 7.39789e7i 0.0488015 0.0845267i
\(173\) 2.97039e8 + 3.53997e8i 0.331611 + 0.395199i 0.905926 0.423436i \(-0.139176\pi\)
−0.574315 + 0.818634i \(0.694732\pi\)
\(174\) −6.15066e8 + 1.11381e9i −0.671004 + 1.21511i
\(175\) 7.17455e7 4.06889e8i 0.0764967 0.433834i
\(176\) −3.23134e7 5.69772e6i −0.0336769 0.00593814i
\(177\) 2.97220e7 + 1.55969e9i 0.0302820 + 1.58908i
\(178\) −1.28909e9 + 1.08167e9i −1.28411 + 1.07750i
\(179\) −6.54667e8 3.77972e8i −0.637688 0.368170i 0.146035 0.989279i \(-0.453349\pi\)
−0.783723 + 0.621110i \(0.786682\pi\)
\(180\) 1.78594e8 + 9.42278e7i 0.170128 + 0.0897613i
\(181\) 1.30127e8 + 2.25387e8i 0.121242 + 0.209997i 0.920258 0.391313i \(-0.127979\pi\)
−0.799016 + 0.601310i \(0.794646\pi\)
\(182\) −4.05511e8 + 1.11413e9i −0.369587 + 1.01543i
\(183\) 5.91154e8 2.28009e8i 0.527104 0.203305i
\(184\) 6.16553e8 + 5.17349e8i 0.537897 + 0.451349i
\(185\) −2.04068e8 5.60671e8i −0.174216 0.478654i
\(186\) 3.80435e8 1.11064e9i 0.317855 0.927940i
\(187\) 4.31045e6 + 2.44458e7i 0.00352498 + 0.0199911i
\(188\) 1.20131e8i 0.0961668i
\(189\) 1.86858e8 + 7.91998e8i 0.146441 + 0.620693i
\(190\) 1.05398e9 0.808754
\(191\) −3.97575e8 + 7.01032e7i −0.298735 + 0.0526750i −0.321007 0.947077i \(-0.604021\pi\)
0.0222719 + 0.999752i \(0.492910\pi\)
\(192\) −1.19260e8 6.08338e8i −0.0877585 0.447651i
\(193\) −1.13999e9 + 4.14921e8i −0.821619 + 0.299045i −0.718414 0.695615i \(-0.755132\pi\)
−0.103204 + 0.994660i \(0.532910\pi\)
\(194\) −9.19364e8 + 1.09566e9i −0.649053 + 0.773512i
\(195\) −1.16018e9 1.81852e8i −0.802396 0.125771i
\(196\) −2.84606e8 1.03588e8i −0.192850 0.0701916i
\(197\) 1.93591e9 1.11770e9i 1.28535 0.742096i 0.307527 0.951539i \(-0.400498\pi\)
0.977821 + 0.209443i \(0.0671651\pi\)
\(198\) −3.68456e7 + 3.33901e7i −0.0239731 + 0.0217249i
\(199\) −1.14409e8 + 1.98163e8i −0.0729540 + 0.126360i −0.900195 0.435488i \(-0.856576\pi\)
0.827241 + 0.561848i \(0.189909\pi\)
\(200\) 5.39095e8 + 6.42469e8i 0.336935 + 0.401543i
\(201\) 8.61231e8 + 1.42815e9i 0.527637 + 0.874961i
\(202\) 6.32189e8 3.58532e9i 0.379701 2.15339i
\(203\) −1.27608e9 2.25007e8i −0.751439 0.132499i
\(204\) 3.73437e8 2.25198e8i 0.215624 0.130030i
\(205\) 6.66059e6 5.58890e6i 0.00377135 0.00316454i
\(206\) −1.68578e9 9.73285e8i −0.936121 0.540470i
\(207\) 1.66068e9 3.58550e8i 0.904494 0.195285i
\(208\) −1.67618e9 2.90324e9i −0.895506 1.55106i
\(209\) −2.28140e7 + 6.26811e7i −0.0119569 + 0.0328512i
\(210\) −1.23905e8 + 7.90490e8i −0.0637104 + 0.406461i
\(211\) 2.08099e9 + 1.74615e9i 1.04988 + 0.880953i 0.993081 0.117433i \(-0.0374665\pi\)
0.0567980 + 0.998386i \(0.481911\pi\)
\(212\) −1.83751e8 5.04853e8i −0.0909677 0.249932i
\(213\) 1.70806e9 3.34851e8i 0.829820 0.162680i
\(214\) −3.51533e8 1.99364e9i −0.167614 0.950587i
\(215\) 3.35271e8i 0.156907i
\(216\) −1.47536e9 7.42831e8i −0.677771 0.341252i
\(217\) 1.19559e9 0.539192
\(218\) −1.39173e8 + 2.45400e7i −0.0616212 + 0.0108655i
\(219\) −4.04148e9 1.38436e9i −1.75697 0.601829i
\(220\) −1.18081e7 + 4.29780e6i −0.00504068 + 0.00183466i
\(221\) −1.63020e9 + 1.94280e9i −0.683395 + 0.814438i
\(222\) −9.28858e8 2.40823e9i −0.382417 0.991484i
\(223\) 9.99762e8 + 3.63884e8i 0.404275 + 0.147144i 0.536151 0.844122i \(-0.319878\pi\)
−0.131876 + 0.991266i \(0.542100\pi\)
\(224\) −9.22981e8 + 5.32883e8i −0.366607 + 0.211661i
\(225\) 1.76908e9 6.74488e7i 0.690267 0.0263175i
\(226\) 1.63635e9 2.83424e9i 0.627253 1.08643i
\(227\) −1.55800e9 1.85676e9i −0.586767 0.699281i 0.388214 0.921569i \(-0.373092\pi\)
−0.974981 + 0.222288i \(0.928648\pi\)
\(228\) 1.17163e9 2.23270e7i 0.433561 0.00826210i
\(229\) −5.67440e8 + 3.21811e9i −0.206337 + 1.17020i 0.688984 + 0.724777i \(0.258057\pi\)
−0.895321 + 0.445421i \(0.853054\pi\)
\(230\) 1.64517e9 + 2.90089e8i 0.587896 + 0.103662i
\(231\) −4.43293e7 2.44794e7i −0.0155684 0.00859713i
\(232\) 2.01490e9 1.69070e9i 0.695508 0.583600i
\(233\) 3.12090e9 + 1.80185e9i 1.05890 + 0.611358i 0.925129 0.379653i \(-0.123957\pi\)
0.133775 + 0.991012i \(0.457290\pi\)
\(234\) −5.03309e9 6.90930e8i −1.67869 0.230447i
\(235\) 2.35747e8 + 4.08325e8i 0.0772991 + 0.133886i
\(236\) −5.83293e8 + 1.60258e9i −0.188035 + 0.516622i
\(237\) 2.45782e9 + 1.98380e9i 0.779034 + 0.628787i
\(238\) 1.32372e9 + 1.11073e9i 0.412562 + 0.346180i
\(239\) 7.81125e8 + 2.14612e9i 0.239403 + 0.657754i 0.999964 + 0.00848739i \(0.00270165\pi\)
−0.760561 + 0.649266i \(0.775076\pi\)
\(240\) −1.48700e9 1.70507e9i −0.448193 0.513923i
\(241\) 6.31882e8 + 3.58358e9i 0.187313 + 1.06230i 0.922948 + 0.384926i \(0.125773\pi\)
−0.735635 + 0.677379i \(0.763116\pi\)
\(242\) 3.97586e9i 1.15923i
\(243\) −3.14820e9 + 1.49882e9i −0.902896 + 0.429858i
\(244\) 6.92682e8 0.195422
\(245\) 1.17065e9 2.06418e8i 0.324911 0.0572905i
\(246\) 2.83481e7 2.47224e7i 0.00774076 0.00675073i
\(247\) −6.40409e9 + 2.33090e9i −1.72056 + 0.626232i
\(248\) −1.55999e9 + 1.85913e9i −0.412398 + 0.491477i
\(249\) −9.43199e8 + 1.16857e9i −0.245361 + 0.303989i
\(250\) 4.00387e9 + 1.45729e9i 1.02499 + 0.373066i
\(251\) 3.02697e9 1.74762e9i 0.762629 0.440304i −0.0676098 0.997712i \(-0.521537\pi\)
0.830239 + 0.557408i \(0.188204\pi\)
\(252\) −1.20990e8 + 8.81355e8i −0.0300019 + 0.218549i
\(253\) −5.28628e7 + 9.15610e7i −0.0129023 + 0.0223475i
\(254\) 2.35692e9 + 2.80886e9i 0.566251 + 0.674832i
\(255\) −8.27379e8 + 1.49828e9i −0.195679 + 0.354350i
\(256\) 6.92024e8 3.92466e9i 0.161124 0.913782i
\(257\) 1.73307e9 + 3.05588e8i 0.397269 + 0.0700493i 0.368714 0.929543i \(-0.379798\pi\)
0.0285553 + 0.999592i \(0.490909\pi\)
\(258\) 2.76343e7 + 1.45013e9i 0.00623690 + 0.327288i
\(259\) 2.01366e9 1.68966e9i 0.447494 0.375492i
\(260\) −1.11185e9 6.41927e8i −0.243306 0.140473i
\(261\) −2.11532e8 5.54816e9i −0.0455842 1.19560i
\(262\) 2.70607e9 + 4.68706e9i 0.574294 + 0.994706i
\(263\) 2.40551e9 6.60909e9i 0.502787 1.38140i −0.385755 0.922601i \(-0.626059\pi\)
0.888542 0.458795i \(-0.151719\pi\)
\(264\) 9.59057e7 3.69910e7i 0.0197437 0.00761518i
\(265\) 1.61530e9 + 1.35539e9i 0.327543 + 0.274841i
\(266\) 1.58815e9 + 4.36342e9i 0.317224 + 0.871566i
\(267\) 2.37960e9 6.94696e9i 0.468229 1.36694i
\(268\) 3.16602e8 + 1.79554e9i 0.0613726 + 0.348061i
\(269\) 4.63105e8i 0.0884445i −0.999022 0.0442222i \(-0.985919\pi\)
0.999022 0.0442222i \(-0.0140810\pi\)
\(270\) −3.42291e9 + 1.95874e8i −0.644080 + 0.0368572i
\(271\) −9.95879e9 −1.84642 −0.923208 0.384301i \(-0.874442\pi\)
−0.923208 + 0.384301i \(0.874442\pi\)
\(272\) −4.81167e9 + 8.48426e8i −0.879063 + 0.155002i
\(273\) −9.95332e8 5.07713e9i −0.179191 0.914046i
\(274\) −7.60166e9 + 2.76678e9i −1.34867 + 0.490876i
\(275\) −7.08157e7 + 8.43948e7i −0.0123822 + 0.0147566i
\(276\) 1.83497e9 + 2.87620e8i 0.316222 + 0.0495658i
\(277\) 7.16936e9 + 2.60943e9i 1.21776 + 0.443228i 0.869388 0.494129i \(-0.164513\pi\)
0.348370 + 0.937357i \(0.386735\pi\)
\(278\) 1.92117e9 1.10919e9i 0.321652 0.185706i
\(279\) 1.08116e9 + 5.00756e9i 0.178432 + 0.826437i
\(280\) 8.27046e8 1.43249e9i 0.134554 0.233055i
\(281\) −6.16695e9 7.34949e9i −0.989112 1.17878i −0.983887 0.178791i \(-0.942781\pi\)
−0.00522454 0.999986i \(-0.501663\pi\)
\(282\) 1.05332e9 + 1.74668e9i 0.166558 + 0.276196i
\(283\) 1.71278e9 9.71364e9i 0.267027 1.51439i −0.496174 0.868223i \(-0.665262\pi\)
0.763201 0.646162i \(-0.223627\pi\)
\(284\) 1.87396e9 + 3.30430e8i 0.288063 + 0.0507933i
\(285\) −3.93854e9 + 2.37510e9i −0.596975 + 0.360000i
\(286\) 2.42182e8 2.03215e8i 0.0361974 0.0303733i
\(287\) 3.31741e7 + 1.91531e7i 0.00488958 + 0.00282300i
\(288\) −3.06655e9 3.38390e9i −0.445738 0.491867i
\(289\) −1.63974e9 2.84011e9i −0.235062 0.407139i
\(290\) 1.86722e9 5.13015e9i 0.264000 0.725334i
\(291\) 9.66490e8 6.16604e9i 0.134780 0.859873i
\(292\) −3.57770e9 3.00204e9i −0.492121 0.412939i
\(293\) 6.70230e8 + 1.84144e9i 0.0909396 + 0.249855i 0.976821 0.214057i \(-0.0686678\pi\)
−0.885882 + 0.463911i \(0.846446\pi\)
\(294\) 5.04636e9 9.89300e8i 0.675444 0.132415i
\(295\) −1.16232e9 6.59182e9i −0.153475 0.870397i
\(296\) 5.33588e9i 0.695087i
\(297\) 6.24423e7 2.07804e8i 0.00802515 0.0267071i
\(298\) 1.24480e10 1.57846
\(299\) −1.06378e10 + 1.87573e9i −1.33097 + 0.234686i
\(300\) 1.83100e9 + 6.27188e8i 0.226050 + 0.0774306i
\(301\) −1.38801e9 + 5.05194e8i −0.169093 + 0.0615449i
\(302\) 1.06349e10 1.26742e10i 1.27851 1.52367i
\(303\) 5.71702e9 + 1.48224e10i 0.678265 + 1.75852i
\(304\) −1.23375e10 4.49049e9i −1.44455 0.525775i
\(305\) −2.35442e9 + 1.35932e9i −0.272072 + 0.157081i
\(306\) −3.45513e9 + 6.54866e9i −0.394075 + 0.746907i
\(307\) −2.48105e9 + 4.29730e9i −0.279307 + 0.483773i −0.971213 0.238214i \(-0.923438\pi\)
0.691906 + 0.721988i \(0.256771\pi\)
\(308\) −3.55854e7 4.24090e7i −0.00395429 0.00471254i
\(309\) 8.49275e9 1.61841e8i 0.931568 0.0177523i
\(310\) −8.74722e8 + 4.96080e9i −0.0947160 + 0.537161i
\(311\) −6.42742e9 1.13333e9i −0.687060 0.121147i −0.180790 0.983522i \(-0.557865\pi\)
−0.506271 + 0.862375i \(0.668976\pi\)
\(312\) 9.19359e9 + 5.07687e9i 0.970212 + 0.535769i
\(313\) 6.45751e9 5.41849e9i 0.672802 0.564548i −0.241091 0.970502i \(-0.577505\pi\)
0.913893 + 0.405954i \(0.133061\pi\)
\(314\) −1.91834e10 1.10755e10i −1.97336 1.13932i
\(315\) −1.31833e9 3.23315e9i −0.133901 0.328385i
\(316\) 1.72652e9 + 2.99043e9i 0.173151 + 0.299906i
\(317\) −1.74715e8 + 4.80026e8i −0.0173019 + 0.0475366i −0.948043 0.318142i \(-0.896941\pi\)
0.930741 + 0.365679i \(0.119163\pi\)
\(318\) 7.09829e9 + 5.72929e9i 0.694137 + 0.560264i
\(319\) 2.64678e8 + 2.22091e8i 0.0255597 + 0.0214471i
\(320\) 9.09751e8 + 2.49952e9i 0.0867607 + 0.238373i
\(321\) 5.80622e9 + 6.65774e9i 0.546857 + 0.627057i
\(322\) 1.27803e9 + 7.24806e9i 0.118882 + 0.674215i
\(323\) 9.93262e9i 0.912544i
\(324\) −3.80085e9 + 2.90248e8i −0.344906 + 0.0263384i
\(325\) −1.12560e10 −1.00890
\(326\) 1.55640e10 2.74435e9i 1.37800 0.242979i
\(327\) 4.64768e8 4.05325e8i 0.0406486 0.0354497i
\(328\) −7.30682e7 + 2.65946e7i −0.00631296 + 0.00229773i
\(329\) −1.33522e9 + 1.59125e9i −0.113965 + 0.135818i
\(330\) 1.34004e8 1.66023e8i 0.0112995 0.0139995i
\(331\) −7.92073e9 2.88291e9i −0.659862 0.240170i −0.00968542 0.999953i \(-0.503083\pi\)
−0.650177 + 0.759783i \(0.725305\pi\)
\(332\) −1.42180e9 + 8.20879e8i −0.117027 + 0.0675658i
\(333\) 8.89786e9 + 6.90601e9i 0.723616 + 0.561630i
\(334\) −1.31444e10 + 2.27668e10i −1.05622 + 1.82944i
\(335\) −4.59971e9 5.48172e9i −0.365217 0.435249i
\(336\) 4.81829e9 8.72534e9i 0.378038 0.684581i
\(337\) 2.27225e9 1.28866e10i 0.176172 0.999120i −0.760611 0.649208i \(-0.775101\pi\)
0.936783 0.349912i \(-0.113788\pi\)
\(338\) 1.68981e10 + 2.97959e9i 1.29471 + 0.228292i
\(339\) 2.72097e8 + 1.42786e10i 0.0206028 + 1.08115i
\(340\) −1.43338e9 + 1.20275e9i −0.107262 + 0.0900035i
\(341\) −2.76090e8 1.59400e8i −0.0204189 0.0117889i
\(342\) −1.68394e10 + 1.05976e10i −1.23090 + 0.774643i
\(343\) 7.03206e9 + 1.21799e10i 0.508050 + 0.879968i
\(344\) 1.02549e9 2.81751e9i 0.0732315 0.201202i
\(345\) −6.80146e9 + 2.62333e9i −0.480093 + 0.185173i
\(346\) −6.57095e9 5.51368e9i −0.458483 0.384713i
\(347\) −5.29741e9 1.45545e10i −0.365381 1.00388i −0.977096 0.212798i \(-0.931742\pi\)
0.611715 0.791078i \(-0.290480\pi\)
\(348\) 1.96698e9 5.74237e9i 0.134117 0.391538i
\(349\) −4.91194e8 2.78570e9i −0.0331094 0.187773i 0.963768 0.266744i \(-0.0859477\pi\)
−0.996877 + 0.0789708i \(0.974837\pi\)
\(350\) 7.66924e9i 0.511070i
\(351\) 2.03648e10 8.76001e9i 1.34169 0.577133i
\(352\) 2.84184e8 0.0185110
\(353\) 1.90149e10 3.35285e9i 1.22461 0.215931i 0.476299 0.879284i \(-0.341978\pi\)
0.748307 + 0.663352i \(0.230867\pi\)
\(354\) −5.57064e9 2.84155e10i −0.354725 1.80943i
\(355\) −7.01802e9 + 2.55435e9i −0.441877 + 0.160830i
\(356\) 5.16025e9 6.14975e9i 0.321271 0.382875i
\(357\) −7.44954e9 1.16767e9i −0.458624 0.0718865i
\(358\) 1.31857e10 + 4.79921e9i 0.802734 + 0.292171i
\(359\) −7.35567e9 + 4.24680e9i −0.442838 + 0.255672i −0.704801 0.709405i \(-0.748964\pi\)
0.261963 + 0.965078i \(0.415630\pi\)
\(360\) 6.74766e9 + 2.16859e9i 0.401738 + 0.129112i
\(361\) −4.85363e9 + 8.40674e9i −0.285784 + 0.494993i
\(362\) −3.10523e9 3.70066e9i −0.180825 0.215499i
\(363\) −8.95948e9 1.48572e10i −0.516008 0.855676i
\(364\) 9.82190e8 5.57028e9i 0.0559487 0.317301i
\(365\) 1.80518e10 + 3.18302e9i 1.01707 + 0.179336i
\(366\) −1.00714e10 + 6.07349e9i −0.561264 + 0.338465i
\(367\) 1.46247e10 1.22716e10i 0.806163 0.676451i −0.143526 0.989647i \(-0.545844\pi\)
0.949689 + 0.313195i \(0.101400\pi\)
\(368\) −1.80220e10 1.04050e10i −0.982678 0.567349i
\(369\) −5.02211e7 + 1.56265e8i −0.00270883 + 0.00842863i
\(370\) 5.53759e9 + 9.59138e9i 0.295470 + 0.511769i
\(371\) −3.17731e9 + 8.72959e9i −0.167712 + 0.460785i
\(372\) −8.67277e8 + 5.53308e9i −0.0452883 + 0.288932i
\(373\) 2.34539e9 + 1.96802e9i 0.121166 + 0.101670i 0.701357 0.712810i \(-0.252578\pi\)
−0.580191 + 0.814480i \(0.697022\pi\)
\(374\) −1.57591e8 4.32978e8i −0.00805463 0.0221299i
\(375\) −1.82458e10 + 3.57694e9i −0.922650 + 0.180878i
\(376\) −7.32200e8 4.15251e9i −0.0366335 0.207759i
\(377\) 3.53008e10i 1.74751i
\(378\) −5.96862e9 1.38755e10i −0.292352 0.679646i
\(379\) 9.45638e9 0.458319 0.229160 0.973389i \(-0.426402\pi\)
0.229160 + 0.973389i \(0.426402\pi\)
\(380\) −4.95173e9 + 8.73124e8i −0.237478 + 0.0418737i
\(381\) −1.51371e10 5.18503e9i −0.718361 0.246066i
\(382\) 7.04176e9 2.56299e9i 0.330695 0.120363i
\(383\) 2.14845e9 2.56042e9i 0.0998459 0.118992i −0.713808 0.700342i \(-0.753031\pi\)
0.813653 + 0.581350i \(0.197475\pi\)
\(384\) 9.33480e9 + 2.42021e10i 0.429319 + 1.11308i
\(385\) 2.04178e8 + 7.43148e7i 0.00929323 + 0.00338246i
\(386\) 1.95017e10 1.12593e10i 0.878462 0.507180i
\(387\) −3.37110e9 5.35664e9i −0.150289 0.238808i
\(388\) 3.41165e9 5.90915e9i 0.150535 0.260734i
\(389\) 1.93823e9 + 2.30989e9i 0.0846461 + 0.100877i 0.806705 0.590954i \(-0.201249\pi\)
−0.722059 + 0.691831i \(0.756804\pi\)
\(390\) 2.17945e10 4.15323e8i 0.942081 0.0179526i
\(391\) −2.73378e9 + 1.55040e10i −0.116965 + 0.663342i
\(392\) −1.04692e10 1.84600e9i −0.443371 0.0781783i
\(393\) −2.06743e10 1.14167e10i −0.866683 0.478598i
\(394\) −3.17861e10 + 2.66717e10i −1.31902 + 1.10679i
\(395\) −1.17369e10 6.77629e9i −0.482130 0.278358i
\(396\) 1.45445e8 1.87395e8i 0.00591450 0.00762038i
\(397\) −4.50332e8 7.79998e8i −0.0181289 0.0314001i 0.856819 0.515618i \(-0.172438\pi\)
−0.874948 + 0.484218i \(0.839104\pi\)
\(398\) 1.45268e9 3.99121e9i 0.0578947 0.159064i
\(399\) −1.57675e10 1.27265e10i −0.622116 0.502133i
\(400\) −1.66114e10 1.39387e10i −0.648885 0.544479i
\(401\) 3.39206e9 + 9.31962e9i 0.131186 + 0.360430i 0.987843 0.155457i \(-0.0496849\pi\)
−0.856657 + 0.515886i \(0.827463\pi\)
\(402\) −2.03467e10 2.33307e10i −0.779095 0.893355i
\(403\) −5.65602e9 3.20769e10i −0.214432 1.21611i
\(404\) 1.73681e10i 0.651968i
\(405\) 1.23495e10 8.44536e9i 0.459016 0.313905i
\(406\) 2.40522e10 0.885218
\(407\) −6.90274e8 + 1.21714e8i −0.0251561 + 0.00443570i
\(408\) 1.15358e10 1.00604e10i 0.416301 0.363056i
\(409\) 4.63141e10 1.68570e10i 1.65508 0.602402i 0.665506 0.746393i \(-0.268216\pi\)
0.989579 + 0.143991i \(0.0459937\pi\)
\(410\) −1.03742e8 + 1.23635e8i −0.00367129 + 0.00437527i
\(411\) 2.21713e10 2.74691e10i 0.777006 0.962669i
\(412\) 8.72631e9 + 3.17612e9i 0.302860 + 0.110232i
\(413\) 2.55385e10 1.47446e10i 0.877798 0.506797i
\(414\) −2.92018e10 + 1.19072e10i −0.994051 + 0.405329i
\(415\) 3.22180e9 5.58032e9i 0.108619 0.188134i
\(416\) 1.86633e10 + 2.22420e10i 0.623182 + 0.742679i
\(417\) −4.67957e9 + 8.47414e9i −0.154761 + 0.280254i
\(418\) 2.15005e8 1.21935e9i 0.00704277 0.0399415i
\(419\) −9.07900e9 1.60087e9i −0.294565 0.0519398i 0.0244125 0.999702i \(-0.492228\pi\)
−0.318978 + 0.947762i \(0.603340\pi\)
\(420\) −7.27282e7 3.81648e9i −0.00233725 0.122650i
\(421\) 2.97544e10 2.49669e10i 0.947159 0.794761i −0.0316579 0.999499i \(-0.510079\pi\)
0.978817 + 0.204738i \(0.0656343\pi\)
\(422\) −4.36690e10 2.52123e10i −1.37697 0.794993i
\(423\) −7.87218e9 4.15344e9i −0.245886 0.129732i
\(424\) −9.42870e9 1.63310e10i −0.291735 0.505300i
\(425\) −5.61083e9 + 1.54156e10i −0.171977 + 0.472504i
\(426\) −3.01442e10 + 1.16267e10i −0.915304 + 0.353034i
\(427\) −9.17523e9 7.69893e9i −0.275998 0.231590i
\(428\) 3.30310e9 + 9.07519e9i 0.0984344 + 0.270446i
\(429\) −4.47057e8 + 1.30513e9i −0.0131988 + 0.0385323i
\(430\) −1.08067e9 6.12880e9i −0.0316097 0.179268i
\(431\) 4.74289e10i 1.37447i 0.726436 + 0.687234i \(0.241175\pi\)
−0.726436 + 0.687234i \(0.758825\pi\)
\(432\) 4.09020e10 + 1.22905e10i 1.17438 + 0.352887i
\(433\) −2.37974e10 −0.676984 −0.338492 0.940969i \(-0.609917\pi\)
−0.338492 + 0.940969i \(0.609917\pi\)
\(434\) −2.18555e10 + 3.85372e9i −0.616031 + 0.108623i
\(435\) 4.58312e9 + 2.33783e10i 0.127998 + 0.652913i
\(436\) 6.33527e8 2.30585e8i 0.0175315 0.00638095i
\(437\) −2.71931e10 + 3.24075e10i −0.745647 + 0.888628i
\(438\) 7.83410e10 + 1.22795e10i 2.12859 + 0.333644i
\(439\) 2.94082e10 + 1.07037e10i 0.791789 + 0.288188i 0.706080 0.708132i \(-0.250462\pi\)
0.0857097 + 0.996320i \(0.472684\pi\)
\(440\) −3.81969e8 + 2.20530e8i −0.0101910 + 0.00588378i
\(441\) −1.66281e10 + 1.50687e10i −0.439631 + 0.398401i
\(442\) 2.35381e10 4.07692e10i 0.616712 1.06818i
\(443\) 9.78540e8 + 1.16618e9i 0.0254076 + 0.0302796i 0.778599 0.627522i \(-0.215931\pi\)
−0.753191 + 0.657802i \(0.771486\pi\)
\(444\) 6.35891e9 + 1.05447e10i 0.163625 + 0.271334i
\(445\) −5.47133e9 + 3.10295e10i −0.139525 + 0.791287i
\(446\) −1.94487e10 3.42933e9i −0.491531 0.0866702i
\(447\) −4.65162e10 + 2.80512e10i −1.16513 + 0.702621i
\(448\) −8.97708e9 + 7.53266e9i −0.222855 + 0.186998i
\(449\) 2.91593e10 + 1.68352e10i 0.717451 + 0.414221i 0.813814 0.581126i \(-0.197388\pi\)
−0.0963628 + 0.995346i \(0.530721\pi\)
\(450\) −3.21216e10 + 6.93521e9i −0.783334 + 0.169126i
\(451\) −5.10712e6 8.84580e6i −0.000123444 0.000213811i
\(452\) −5.33990e9 + 1.46712e10i −0.127932 + 0.351490i
\(453\) −1.11800e10 + 7.13266e10i −0.265491 + 1.69379i
\(454\) 3.44654e10 + 2.89199e10i 0.811260 + 0.680728i
\(455\) 7.59270e9 + 2.08608e10i 0.177154 + 0.486726i
\(456\) 4.03629e10 7.91283e9i 0.933519 0.183009i
\(457\) 1.09556e10 + 6.21321e10i 0.251171 + 1.42446i 0.805713 + 0.592307i \(0.201783\pi\)
−0.554541 + 0.832156i \(0.687106\pi\)
\(458\) 6.06566e10i 1.37853i
\(459\) −1.84591e9 3.22573e10i −0.0415871 0.726737i
\(460\) −7.96958e9 −0.177993
\(461\) −3.07188e10 + 5.41656e9i −0.680145 + 0.119928i −0.503039 0.864264i \(-0.667785\pi\)
−0.177106 + 0.984192i \(0.556674\pi\)
\(462\) 8.89249e8 + 3.04602e8i 0.0195189 + 0.00668597i
\(463\) 4.22751e10 1.53869e10i 0.919942 0.334831i 0.161726 0.986836i \(-0.448294\pi\)
0.758215 + 0.652004i \(0.226072\pi\)
\(464\) −4.37142e10 + 5.20966e10i −0.943085 + 1.12393i
\(465\) −7.91030e9 2.05088e10i −0.169193 0.438661i
\(466\) −6.28584e10 2.28786e10i −1.33297 0.485161i
\(467\) 6.93681e10 4.00497e10i 1.45845 0.842037i 0.459516 0.888169i \(-0.348023\pi\)
0.998935 + 0.0461320i \(0.0146895\pi\)
\(468\) 2.42185e10 9.23369e8i 0.504853 0.0192483i
\(469\) 1.57631e10 2.73026e10i 0.325800 0.564302i
\(470\) −5.62563e9 6.70437e9i −0.115287 0.137394i
\(471\) 9.66435e10 1.84167e9i 1.96376 0.0374222i
\(472\) −1.03946e10 + 5.89507e10i −0.209431 + 1.18774i
\(473\) 3.87878e8 + 6.83934e7i 0.00774909 + 0.00136637i
\(474\) −5.13236e10 2.83418e10i −1.01673 0.561454i
\(475\) −3.37697e10 + 2.83362e10i −0.663366 + 0.556630i
\(476\) −7.13918e9 4.12181e9i −0.139066 0.0802897i
\(477\) −3.94359e10 5.41367e9i −0.761761 0.104573i
\(478\) −2.11966e10 3.67137e10i −0.406027 0.703260i
\(479\) 5.05947e9 1.39008e10i 0.0961088 0.264057i −0.882317 0.470656i \(-0.844017\pi\)
0.978426 + 0.206599i \(0.0662396\pi\)
\(480\) 1.52476e10 + 1.23069e10i 0.287235 + 0.231838i
\(481\) −5.48586e10 4.60319e10i −1.02486 0.859960i
\(482\) −2.31018e10 6.34716e10i −0.428013 1.17596i
\(483\) −2.11091e10 2.42048e10i −0.387865 0.444748i
\(484\) −3.29364e9 1.86792e10i −0.0600199 0.340390i
\(485\) 2.67802e10i 0.484002i
\(486\) 5.27185e10 3.75463e10i 0.944969 0.673010i
\(487\) −1.00517e10 −0.178699 −0.0893495 0.996000i \(-0.528479\pi\)
−0.0893495 + 0.996000i \(0.528479\pi\)
\(488\) 2.39435e10 4.22189e9i 0.422191 0.0744436i
\(489\) −5.19757e10 + 4.53281e10i −0.909002 + 0.792742i
\(490\) −2.07344e10 + 7.54669e9i −0.359672 + 0.130910i
\(491\) 6.53311e10 7.78585e10i 1.12407 1.33962i 0.190308 0.981724i \(-0.439051\pi\)
0.933763 0.357891i \(-0.116504\pi\)
\(492\) −1.12703e8 + 1.39633e8i −0.00192343 + 0.00238303i
\(493\) 4.83463e10 + 1.75966e10i 0.818418 + 0.297880i
\(494\) 1.09554e11 6.32513e10i 1.83960 1.06209i
\(495\) −1.26621e8 + 9.22375e8i −0.00210905 + 0.0153634i
\(496\) 3.13748e10 5.43428e10i 0.518387 0.897873i
\(497\) −2.11498e10 2.52053e10i −0.346641 0.413111i
\(498\) 1.34752e10 2.44019e10i 0.219087 0.396740i
\(499\) −1.13923e10 + 6.46088e10i −0.183742 + 1.04205i 0.743819 + 0.668381i \(0.233012\pi\)
−0.927561 + 0.373672i \(0.878099\pi\)
\(500\) −2.00180e10 3.52971e9i −0.320288 0.0564754i
\(501\) −2.18570e9 1.14697e11i −0.0346928 1.82054i
\(502\) −4.97004e10 + 4.17036e10i −0.782609 + 0.656687i
\(503\) −9.70501e9 5.60319e9i −0.151609 0.0875313i 0.422277 0.906467i \(-0.361231\pi\)
−0.573885 + 0.818936i \(0.694564\pi\)
\(504\) 1.18965e9 + 3.12027e10i 0.0184373 + 0.483582i
\(505\) −3.40833e10 5.90339e10i −0.524053 0.907687i
\(506\) 6.71212e8 1.84414e9i 0.0102390 0.0281314i
\(507\) −6.98599e10 + 2.69451e10i −1.05729 + 0.407800i
\(508\) −1.34000e10 1.12440e10i −0.201210 0.168836i
\(509\) −9.23104e9 2.53621e10i −0.137524 0.377845i 0.851743 0.523959i \(-0.175546\pi\)
−0.989268 + 0.146114i \(0.953323\pi\)
\(510\) 1.02952e10 3.00557e10i 0.152179 0.444269i
\(511\) 1.40233e10 + 7.95299e10i 0.205667 + 1.16640i
\(512\) 8.00907e9i 0.116547i
\(513\) 3.90450e10 7.75485e10i 0.563762 1.11971i
\(514\) −3.26658e10 −0.467995
\(515\) −3.58935e10 + 6.32899e9i −0.510254 + 0.0899716i
\(516\) −1.33113e9 6.79005e9i −0.0187769 0.0957798i
\(517\) 5.20486e8 1.89441e8i 0.00728529 0.00265163i
\(518\) −3.13638e10 + 3.73779e10i −0.435621 + 0.519153i
\(519\) 3.69795e10 + 5.79631e9i 0.509672 + 0.0798881i
\(520\) −4.23452e10 1.54124e10i −0.579149 0.210793i
\(521\) 1.10388e11 6.37326e10i 1.49820 0.864989i 0.498207 0.867058i \(-0.333992\pi\)
0.999998 + 0.00206969i \(0.000658804\pi\)
\(522\) 2.17501e10 + 1.00739e11i 0.292941 + 1.35680i
\(523\) −4.11516e10 + 7.12766e10i −0.550022 + 0.952666i 0.448251 + 0.893908i \(0.352047\pi\)
−0.998272 + 0.0587576i \(0.981286\pi\)
\(524\) −1.65963e10 1.97787e10i −0.220134 0.262345i
\(525\) −1.72824e10 2.86587e10i −0.227492 0.377241i
\(526\) −2.26701e10 + 1.28569e11i −0.296149 + 1.67955i
\(527\) −4.67503e10 8.24334e9i −0.606096 0.106871i
\(528\) −2.27595e9 + 1.37249e9i −0.0292838 + 0.0176593i
\(529\) 8.62378e9 7.23621e9i 0.110122 0.0924035i
\(530\) −3.38966e10 1.95702e10i −0.429589 0.248023i
\(531\) 8.48501e10 + 9.36310e10i 1.06727 + 1.17772i
\(532\) −1.10761e10 1.91843e10i −0.138274 0.239497i
\(533\) 3.56927e8 9.80648e8i 0.00442252 0.0121508i
\(534\) −2.11074e10 + 1.34661e11i −0.259579 + 1.65607i
\(535\) −2.90364e10 2.43645e10i −0.354428 0.297401i
\(536\) 2.18876e10 + 6.01356e10i 0.265179 + 0.728573i
\(537\) −6.00877e10 + 1.17797e10i −0.722585 + 0.141657i
\(538\) 1.49272e9 + 8.46563e9i 0.0178176 + 0.101049i
\(539\) 1.39645e9i 0.0165451i
\(540\) 1.59190e10 3.75581e9i 0.187216 0.0441702i
\(541\) −2.87855e9 −0.0336035 −0.0168017 0.999859i \(-0.505348\pi\)
−0.0168017 + 0.999859i \(0.505348\pi\)
\(542\) 1.82048e11 3.21000e10i 2.10955 0.371970i
\(543\) 1.99431e10 + 6.83125e9i 0.229399 + 0.0785780i
\(544\) 3.97648e10 1.44732e10i 0.454049 0.165260i
\(545\) −1.70085e9 + 2.02700e9i −0.0192788 + 0.0229756i
\(546\) 3.45598e10 + 8.96024e10i 0.388867 + 1.00821i
\(547\) −3.04941e10 1.10989e10i −0.340617 0.123974i 0.166047 0.986118i \(-0.446899\pi\)
−0.506665 + 0.862143i \(0.669122\pi\)
\(548\) 3.34217e10 1.92960e10i 0.370600 0.213966i
\(549\) 2.39489e10 4.53913e10i 0.263631 0.499670i
\(550\) 1.02249e9 1.77101e9i 0.0111740 0.0193540i
\(551\) 8.88675e10 + 1.05908e11i 0.964132 + 1.14901i
\(552\) 6.51812e10 1.24212e9i 0.702047 0.0133784i
\(553\) 1.03682e10 5.88009e10i 0.110867 0.628757i
\(554\) −1.39468e11 2.45919e10i −1.48059 0.261068i
\(555\) −4.23069e10 2.33627e10i −0.445902 0.246235i
\(556\) −8.10706e9 + 6.80263e9i −0.0848329 + 0.0711832i
\(557\) −1.21822e11 7.03341e10i −1.26563 0.730710i −0.291470 0.956580i \(-0.594144\pi\)
−0.974157 + 0.225870i \(0.927478\pi\)
\(558\) −3.59045e10 8.80541e10i −0.370350 0.908265i
\(559\) 2.01203e10 + 3.48494e10i 0.206057 + 0.356901i
\(560\) −1.46274e10 + 4.01884e10i −0.148736 + 0.408648i
\(561\) 1.56460e9 + 1.26284e9i 0.0157961 + 0.0127496i
\(562\) 1.36422e11 + 1.14472e11i 1.36754 + 1.14750i
\(563\) −1.95156e10 5.36186e10i −0.194244 0.533681i 0.803888 0.594781i \(-0.202761\pi\)
−0.998132 + 0.0611000i \(0.980539\pi\)
\(564\) −6.39562e9 7.33358e9i −0.0632072 0.0724769i
\(565\) −1.06407e10 6.03465e10i −0.104418 0.592186i
\(566\) 1.83087e11i 1.78399i
\(567\) 5.35718e10 + 3.84006e10i 0.518328 + 0.371540i
\(568\) 6.67901e10 0.641680
\(569\) −1.32018e11 + 2.32784e10i −1.25946 + 0.222077i −0.763237 0.646118i \(-0.776391\pi\)
−0.496223 + 0.868195i \(0.665280\pi\)
\(570\) 6.43414e10 5.61122e10i 0.609525 0.531567i
\(571\) 5.91665e10 2.15349e10i 0.556585 0.202580i −0.0483848 0.998829i \(-0.515407\pi\)
0.604970 + 0.796248i \(0.293185\pi\)
\(572\) −9.69461e8 + 1.15536e9i −0.00905621 + 0.0107928i
\(573\) −2.05383e10 + 2.54459e10i −0.190522 + 0.236047i
\(574\) −6.68163e8 2.43192e8i −0.00615510 0.00224027i
\(575\) −6.05109e10 + 3.49360e10i −0.553557 + 0.319596i
\(576\) −3.96674e10 3.07876e10i −0.360366 0.279696i
\(577\) 6.37070e10 1.10344e11i 0.574756 0.995507i −0.421312 0.906916i \(-0.638430\pi\)
0.996068 0.0885910i \(-0.0282364\pi\)
\(578\) 3.91291e10 + 4.66322e10i 0.350581 + 0.417806i
\(579\) −4.75022e10 + 8.60206e10i −0.422668 + 0.765400i
\(580\) −4.52261e9 + 2.56490e10i −0.0399648 + 0.226651i
\(581\) 2.79570e10 + 4.92956e9i 0.245350 + 0.0432617i
\(582\) 2.20732e9 + 1.15831e11i 0.0192386 + 1.00956i
\(583\) 1.89758e9 1.59226e9i 0.0164258 0.0137828i
\(584\) −1.41966e11 8.19639e10i −1.22048 0.704646i
\(585\) −8.05066e10 + 5.06652e10i −0.687397 + 0.432600i
\(586\) −1.81874e10 3.15015e10i −0.154234 0.267141i
\(587\) −1.06263e10 + 2.91956e10i −0.0895015 + 0.245903i −0.976365 0.216128i \(-0.930657\pi\)
0.886863 + 0.462032i \(0.152879\pi\)
\(588\) −2.28890e10 + 8.82833e9i −0.191477 + 0.0738532i
\(589\) −9.77203e10 8.19971e10i −0.811940 0.681298i
\(590\) 4.24946e10 + 1.16753e11i 0.350692 + 0.963518i
\(591\) 5.86756e10 1.71297e11i 0.480959 1.40410i
\(592\) −2.39570e10 1.35867e11i −0.195050 1.10618i
\(593\) 7.72499e10i 0.624711i 0.949965 + 0.312356i \(0.101118\pi\)
−0.949965 + 0.312356i \(0.898882\pi\)
\(594\) −4.71645e8 + 3.99995e9i −0.00378852 + 0.0321298i
\(595\) 3.23547e10 0.258148
\(596\) −5.84825e10 + 1.03120e10i −0.463491 + 0.0817259i
\(597\) 3.56563e9 + 1.81881e10i 0.0280698 + 0.143182i
\(598\) 1.88415e11 6.85774e10i 1.47336 0.536261i
\(599\) 7.99461e10 9.52760e10i 0.620998 0.740076i −0.360244 0.932858i \(-0.617307\pi\)
0.981242 + 0.192782i \(0.0617510\pi\)
\(600\) 6.71139e10 + 1.05197e10i 0.517854 + 0.0811705i
\(601\) −2.16119e11 7.86608e10i −1.65651 0.602921i −0.666703 0.745323i \(-0.732295\pi\)
−0.989809 + 0.142402i \(0.954517\pi\)
\(602\) 2.37446e10 1.37090e10i 0.180792 0.104380i
\(603\) 1.28607e11 + 4.13324e10i 0.972740 + 0.312623i
\(604\) −3.94648e10 + 6.83550e10i −0.296526 + 0.513597i
\(605\) 4.78512e10 + 5.70269e10i 0.357167 + 0.425655i
\(606\) −1.52285e11 2.52528e11i −1.12919 1.87249i
\(607\) 4.05256e10 2.29832e11i 0.298521 1.69300i −0.354016 0.935240i \(-0.615184\pi\)
0.652537 0.757757i \(-0.273705\pi\)
\(608\) 1.11986e11 + 1.97461e10i 0.819498 + 0.144500i
\(609\) −8.98791e10 + 5.42008e10i −0.653415 + 0.394036i
\(610\) 3.86576e10 3.24376e10i 0.279200 0.234277i
\(611\) 4.90089e10 + 2.82953e10i 0.351650 + 0.203025i
\(612\) 1.08078e10 3.36288e10i 0.0770424 0.239721i
\(613\) 7.90435e10 + 1.36907e11i 0.559789 + 0.969583i 0.997514 + 0.0704739i \(0.0224512\pi\)
−0.437725 + 0.899109i \(0.644216\pi\)
\(614\) 3.15025e10 8.65523e10i 0.221652 0.608983i
\(615\) 1.09060e8 6.95782e8i 0.000762366 0.00486377i
\(616\) −1.48854e9 1.24904e9i −0.0103380 0.00867465i
\(617\) −6.27486e10 1.72400e11i −0.432976 1.18959i −0.943977 0.330011i \(-0.892948\pi\)
0.511002 0.859580i \(-0.329275\pi\)
\(618\) −1.54727e11 + 3.03330e10i −1.06075 + 0.207951i
\(619\) 3.91904e10 + 2.22260e11i 0.266942 + 1.51391i 0.763447 + 0.645871i \(0.223506\pi\)
−0.496504 + 0.868034i \(0.665383\pi\)
\(620\) 2.40312e10i 0.162633i
\(621\) 8.22900e10 1.10301e11i 0.553325 0.741671i
\(622\) 1.21147e11 0.809378
\(623\) −1.36705e11 + 2.41048e10i −0.907470 + 0.160011i
\(624\) −2.56889e11 8.79943e10i −1.69437 0.580385i
\(625\) −2.40786e10 + 8.76390e9i −0.157802 + 0.0574351i
\(626\) −1.00579e11 + 1.19865e11i −0.654951 + 0.780540i
\(627\) 1.94434e9 + 5.04104e9i 0.0125806 + 0.0326174i
\(628\) 9.93014e10 + 3.61427e10i 0.638435 + 0.232371i
\(629\) −9.03887e10 + 5.21859e10i −0.577446 + 0.333389i
\(630\) 3.45207e10 + 5.48530e10i 0.219138 + 0.348208i
\(631\) −1.16579e11 + 2.01921e11i −0.735368 + 1.27369i 0.219194 + 0.975681i \(0.429657\pi\)
−0.954562 + 0.298013i \(0.903676\pi\)
\(632\) 7.79064e10 + 9.28452e10i 0.488320 + 0.581958i
\(633\) 2.19999e11 4.19238e9i 1.37027 0.0261124i
\(634\) 1.64656e9 9.33810e9i 0.0101911 0.0577965i
\(635\) 6.76118e10 + 1.19218e10i 0.415841 + 0.0733240i
\(636\) −3.80950e10 2.10367e10i −0.232830 0.128573i
\(637\) 1.09295e11 9.17092e10i 0.663807 0.557000i
\(638\) −5.55421e9 3.20673e9i −0.0335228 0.0193544i
\(639\) 8.64436e10 1.11376e11i 0.518477 0.668018i
\(640\) −5.56514e10 9.63910e10i −0.331708 0.574535i
\(641\) −7.15456e10 + 1.96570e11i −0.423790 + 1.16435i 0.525731 + 0.850651i \(0.323792\pi\)
−0.949521 + 0.313703i \(0.898430\pi\)
\(642\) −1.27598e11 1.02989e11i −0.751112 0.606251i
\(643\) 2.36854e9 + 1.98744e9i 0.0138560 + 0.0116265i 0.649689 0.760200i \(-0.274899\pi\)
−0.635833 + 0.771826i \(0.719343\pi\)
\(644\) −1.20087e10 3.29937e10i −0.0698158 0.191817i
\(645\) 1.78494e10 + 2.04671e10i 0.103130 + 0.118254i
\(646\) −3.20156e10 1.81570e11i −0.183837 1.04259i
\(647\) 3.30829e10i 0.188793i −0.995535 0.0943966i \(-0.969908\pi\)
0.995535 0.0943966i \(-0.0300922\pi\)
\(648\) −1.29613e11 + 3.31990e10i −0.735101 + 0.188289i
\(649\) −7.86324e9 −0.0443224
\(650\) 2.05761e11 3.62812e10i 1.15268 0.203249i
\(651\) 7.29863e10 6.36515e10i 0.406366 0.354392i
\(652\) −7.08483e10 + 2.57867e10i −0.392048 + 0.142694i
\(653\) 7.83339e10 9.33547e10i 0.430821 0.513433i −0.506338 0.862335i \(-0.669001\pi\)
0.937159 + 0.348903i \(0.113446\pi\)
\(654\) −7.18955e9 + 8.90747e9i −0.0392998 + 0.0486904i
\(655\) 9.52247e10 + 3.46589e10i 0.517350 + 0.188300i
\(656\) 1.74112e9 1.00524e9i 0.00940185 0.00542816i
\(657\) −3.20419e11 + 1.30653e11i −1.71972 + 0.701223i
\(658\) 1.92790e10 3.33921e10i 0.102844 0.178132i
\(659\) −1.08052e11 1.28771e11i −0.572916 0.682775i 0.399310 0.916816i \(-0.369250\pi\)
−0.972227 + 0.234041i \(0.924805\pi\)
\(660\) −4.92033e8 + 8.91011e8i −0.00259309 + 0.00469578i
\(661\) 3.13825e10 1.77979e11i 0.164392 0.932316i −0.785296 0.619120i \(-0.787489\pi\)
0.949689 0.313196i \(-0.101400\pi\)
\(662\) 1.54084e11 + 2.71693e10i 0.802282 + 0.141464i
\(663\) 3.91398e9 + 2.05390e11i 0.0202565 + 1.06298i
\(664\) −4.41434e10 + 3.70407e10i −0.227088 + 0.190549i
\(665\) 7.52949e10 + 4.34716e10i 0.385016 + 0.222289i
\(666\) −1.84914e11 9.75624e10i −0.939881 0.495890i
\(667\) 1.09566e11 + 1.89773e11i 0.553569 + 0.958809i
\(668\) 4.28942e10 1.17851e11i 0.215423 0.591871i
\(669\) 8.04045e10 3.10121e10i 0.401398 0.154820i
\(670\) 1.01752e11 + 8.53804e10i 0.504946 + 0.423700i
\(671\) 1.09233e9 + 3.00114e9i 0.00538843 + 0.0148046i
\(672\) −2.79746e10 + 8.16687e10i −0.137179 + 0.400478i
\(673\) 1.10197e10 + 6.24957e10i 0.0537166 + 0.304642i 0.999815 0.0192375i \(-0.00612385\pi\)
−0.946098 + 0.323880i \(0.895013\pi\)
\(674\) 2.42892e11i 1.17699i
\(675\) 1.04405e11 9.83007e10i 0.502928 0.473523i
\(676\) −8.18580e10 −0.391990
\(677\) 1.72977e11 3.05005e10i 0.823442 0.145195i 0.253977 0.967210i \(-0.418261\pi\)
0.569465 + 0.822015i \(0.307150\pi\)
\(678\) −5.09978e10 2.60137e11i −0.241342 1.23107i
\(679\) −1.10869e11 + 4.03530e10i −0.521592 + 0.189844i
\(680\) −4.22161e10 + 5.03112e10i −0.197443 + 0.235304i
\(681\) −1.93962e11 3.04023e10i −0.901836 0.141357i
\(682\) 5.56075e9 + 2.02395e9i 0.0257037 + 0.00935538i
\(683\) −2.25895e11 + 1.30420e11i −1.03806 + 0.599325i −0.919284 0.393596i \(-0.871231\pi\)
−0.118778 + 0.992921i \(0.537898\pi\)
\(684\) 7.03350e10 6.37388e10i 0.321327 0.291192i
\(685\) −7.57333e10 + 1.31174e11i −0.343973 + 0.595779i
\(686\) −1.67806e11 1.99984e11i −0.757725 0.903021i
\(687\) 1.36688e11 + 2.26664e11i 0.613624 + 1.01755i
\(688\) −1.34619e10 + 7.63461e10i −0.0600830 + 0.340748i
\(689\) 2.49240e11 + 4.39478e10i 1.10596 + 0.195011i
\(690\) 1.15876e11 6.98779e10i 0.511206 0.308279i
\(691\) −4.63160e10 + 3.88637e10i −0.203151 + 0.170464i −0.738687 0.674048i \(-0.764554\pi\)
0.535536 + 0.844512i \(0.320109\pi\)
\(692\) 3.54388e10 + 2.04606e10i 0.154545 + 0.0892266i
\(693\) −4.00939e9 + 8.65647e8i −0.0173838 + 0.00375325i
\(694\) 1.43751e11 + 2.48984e11i 0.619687 + 1.07333i
\(695\) 1.42063e10 3.90314e10i 0.0608893 0.167292i
\(696\) 3.29917e10 2.10482e11i 0.140594 0.896969i
\(697\) −1.16513e9 9.77658e8i −0.00493676 0.00414244i
\(698\) 1.79582e10 + 4.93397e10i 0.0756556 + 0.207862i
\(699\) 2.86448e11 5.61558e10i 1.19988 0.235226i
\(700\) −6.35327e9 3.60312e10i −0.0264609 0.150067i
\(701\) 2.34678e11i 0.971852i 0.874000 + 0.485926i \(0.161518\pi\)
−0.874000 + 0.485926i \(0.838482\pi\)
\(702\) −3.44036e11 + 2.25776e11i −1.41663 + 0.929670i
\(703\) −2.80467e11 −1.14831
\(704\) 3.07730e9 5.42611e8i 0.0125279 0.00220901i
\(705\) 3.61301e10 + 1.23759e10i 0.146256 + 0.0500982i
\(706\) −3.36789e11 + 1.22581e11i −1.35562 + 0.493406i
\(707\) 1.93041e11 2.30057e11i 0.772629 0.920783i
\(708\) 4.97114e10 + 1.28886e11i 0.197844 + 0.512945i
\(709\) 2.36805e11 + 8.61899e10i 0.937143 + 0.341092i 0.765037 0.643986i \(-0.222721\pi\)
0.172106 + 0.985078i \(0.444943\pi\)
\(710\) 1.20057e11 6.93149e10i 0.472448 0.272768i
\(711\) 2.55655e11 9.74725e9i 1.00041 0.0381420i
\(712\) 1.40889e11 2.44026e11i 0.548222 0.949548i
\(713\) −1.29965e11 1.54887e11i −0.502886 0.599317i
\(714\) 1.39942e11 2.66679e9i 0.538463 0.0102611i
\(715\) 1.02790e9 5.82953e9i 0.00393304 0.0223054i
\(716\) −6.59241e10 1.16242e10i −0.250837 0.0442294i
\(717\) 1.61941e11 + 8.94270e10i 0.612747 + 0.338370i
\(718\) 1.20774e11 1.01341e11i 0.454439 0.381320i
\(719\) −2.59305e11 1.49710e11i −0.970275 0.560189i −0.0709551 0.997480i \(-0.522605\pi\)
−0.899320 + 0.437291i \(0.855938\pi\)
\(720\) −1.81551e11 2.49229e10i −0.675568 0.0927404i
\(721\) −8.02868e10 1.39061e11i −0.297100 0.514593i
\(722\) 6.16278e10 1.69321e11i 0.226792 0.623106i
\(723\) 2.29359e11 + 1.85124e11i 0.839387 + 0.677500i
\(724\) 1.76545e10 + 1.48139e10i 0.0642540 + 0.0539155i
\(725\) 7.80977e10 + 2.14572e11i 0.282674 + 0.776641i
\(726\) 2.11669e11 + 2.42712e11i 0.761924 + 0.873664i
\(727\) 3.23715e10 + 1.83588e11i 0.115885 + 0.657214i 0.986308 + 0.164911i \(0.0527337\pi\)
−0.870424 + 0.492303i \(0.836155\pi\)
\(728\) 1.98531e11i 0.706810i
\(729\) −1.12391e11 + 2.59104e11i −0.397944 + 0.917410i
\(730\) −3.40249e11 −1.19813
\(731\) 5.77575e10 1.01842e10i 0.202273 0.0356663i
\(732\) 4.22857e10 3.68774e10i 0.147282 0.128445i
\(733\) −4.74456e11 + 1.72688e11i −1.64354 + 0.598199i −0.987652 0.156661i \(-0.949927\pi\)
−0.655886 + 0.754860i \(0.727705\pi\)
\(734\) −2.27787e11 + 2.71466e11i −0.784774 + 0.935257i
\(735\) 6.04747e10 7.49250e10i 0.207217 0.256730i
\(736\) 1.69366e11 + 6.16442e10i 0.577185 + 0.210078i
\(737\) −7.28016e9 + 4.20320e9i −0.0246758 + 0.0142466i
\(738\) 4.14362e8 3.01843e9i 0.00139687 0.0101755i
\(739\) −3.06215e10 + 5.30379e10i −0.102671 + 0.177832i −0.912784 0.408442i \(-0.866072\pi\)
0.810113 + 0.586273i \(0.199406\pi\)
\(740\) −3.39620e10 4.04743e10i −0.113257 0.134975i
\(741\) −2.66853e11 + 4.83237e11i −0.885112 + 1.60283i
\(742\) 2.99438e10 1.69820e11i 0.0987849 0.560237i
\(743\) −3.40134e11 5.99748e10i −1.11608 0.196795i −0.414961 0.909839i \(-0.636205\pi\)
−0.701119 + 0.713044i \(0.747316\pi\)
\(744\) 3.74543e9 + 1.96545e11i 0.0122239 + 0.641461i
\(745\) 1.78545e11 1.49817e11i 0.579593 0.486336i
\(746\) −4.92176e10 2.84158e10i −0.158915 0.0917496i
\(747\) 4.63434e9 + 1.21552e11i 0.0148835 + 0.390372i
\(748\) 1.09907e9 + 1.90364e9i 0.00351090 + 0.00608106i
\(749\) 5.71151e10 1.56923e11i 0.181478 0.498607i
\(750\) 3.22006e11 1.24198e11i 1.01770 0.392527i
\(751\) −2.09990e11 1.76202e11i −0.660143 0.553926i 0.249987 0.968249i \(-0.419574\pi\)
−0.910130 + 0.414324i \(0.864018\pi\)
\(752\) 3.72878e10 + 1.02447e11i 0.116599 + 0.320353i
\(753\) 9.17446e10 2.67838e11i 0.285365 0.833089i
\(754\) −1.13784e11 6.45304e11i −0.352045 1.99654i
\(755\) 3.09784e11i 0.953392i
\(756\) 3.95361e10 + 6.02448e10i 0.121034 + 0.184430i
\(757\) 4.12942e11 1.25749 0.628747 0.777610i \(-0.283568\pi\)
0.628747 + 0.777610i \(0.283568\pi\)
\(758\) −1.72864e11 + 3.04806e10i −0.523634 + 0.0923308i
\(759\) 1.64750e9 + 8.40381e9i 0.00496430 + 0.0253226i
\(760\) −1.65842e11 + 6.03616e10i −0.497096 + 0.180928i
\(761\) 4.01928e10 4.78999e10i 0.119842 0.142822i −0.702788 0.711400i \(-0.748062\pi\)
0.822630 + 0.568577i \(0.192506\pi\)
\(762\) 2.93421e11 + 4.59920e10i 0.870304 + 0.136415i
\(763\) −1.09546e10 3.98713e9i −0.0323219 0.0117642i
\(764\) −3.09600e10 + 1.78748e10i −0.0908715 + 0.0524647i
\(765\) 2.92580e10 + 1.35513e11i 0.0854276 + 0.395672i
\(766\) −3.10210e10 + 5.37300e10i −0.0901033 + 0.156064i
\(767\) −5.16405e11 6.15427e11i −1.49214 1.77826i
\(768\) −1.66698e11 2.76429e11i −0.479165 0.794581i
\(769\) 6.94082e10 3.93633e11i 0.198475 1.12561i −0.708908 0.705301i \(-0.750812\pi\)
0.907383 0.420305i \(-0.138077\pi\)
\(770\) −3.97194e9 7.00361e8i −0.0112990 0.00199232i
\(771\) 1.22067e11 7.36114e10i 0.345446 0.208318i
\(772\) −8.22944e10 + 6.90532e10i −0.231687 + 0.194408i
\(773\) 3.03906e11 + 1.75460e11i 0.851179 + 0.491428i 0.861048 0.508523i \(-0.169808\pi\)
−0.00986956 + 0.999951i \(0.503142\pi\)
\(774\) 7.88901e10 + 8.70542e10i 0.219816 + 0.242564i
\(775\) −1.05345e11 1.82462e11i −0.292015 0.505785i
\(776\) 8.19123e10 2.25052e11i 0.225893 0.620635i
\(777\) 3.29714e10 2.10352e11i 0.0904594 0.577116i
\(778\) −4.28766e10 3.59777e10i −0.117031 0.0982008i
\(779\) −1.39788e9 3.84064e9i −0.00379594 0.0104293i
\(780\) −1.02050e11 + 2.00060e10i −0.275698 + 0.0540483i
\(781\) 1.52351e9 + 8.64027e9i 0.00409489 + 0.0232233i
\(782\) 2.92228e11i 0.781438i
\(783\) −3.08289e11 3.27433e11i −0.820184 0.871115i
\(784\) 2.74863e11 0.727531
\(785\) −4.08451e11 + 7.20210e10i −1.07563 + 0.189662i
\(786\) 4.14728e11 + 1.42060e11i 1.08661 + 0.372205i
\(787\) −4.15833e11 + 1.51351e11i −1.08398 + 0.394535i −0.821386 0.570372i \(-0.806799\pi\)
−0.262590 + 0.964907i \(0.584577\pi\)
\(788\) 1.27240e11 1.51639e11i 0.330005 0.393285i
\(789\) −2.05011e11 5.31526e11i −0.529016 1.37157i
\(790\) 2.36394e11 + 8.60403e10i 0.606915 + 0.220899i
\(791\) 2.33798e11 1.34983e11i 0.597221 0.344806i
\(792\) 3.88534e9 7.36405e9i 0.00987481 0.0187161i
\(793\) −1.63152e11 + 2.82587e11i −0.412571 + 0.714594i
\(794\) 1.07463e10 + 1.28069e10i 0.0270381 + 0.0322228i
\(795\) 1.70767e11 3.25420e9i 0.427500 0.00814658i
\(796\) −3.51855e9 + 1.99547e10i −0.00876419 + 0.0497042i
\(797\) 4.61690e11 + 8.14084e10i 1.14424 + 0.201760i 0.713460 0.700696i \(-0.247127\pi\)
0.430781 + 0.902457i \(0.358238\pi\)
\(798\) 3.29253e11 + 1.81820e11i 0.811930 + 0.448362i
\(799\) 6.31816e10 5.30156e10i 0.155026 0.130082i
\(800\) 1.62650e11 + 9.39058e10i 0.397094 + 0.229262i
\(801\) −2.24580e11 5.50773e11i −0.545559 1.33796i
\(802\) −9.20472e10 1.59430e11i −0.222491 0.385366i
\(803\) 7.36492e9 2.02350e10i 0.0177136 0.0486676i
\(804\) 1.14919e11 + 9.27556e10i 0.275023 + 0.221981i
\(805\) 1.05565e11 + 8.85793e10i 0.251383 + 0.210935i
\(806\) 2.06786e11 + 5.68139e11i 0.489982 + 1.34621i
\(807\) −2.46551e10 2.82709e10i −0.0581316 0.0666569i
\(808\) 1.05858e11 + 6.00352e11i 0.248359 + 1.40851i
\(809\) 2.16664e11i 0.505817i 0.967490 + 0.252908i \(0.0813871\pi\)
−0.967490 + 0.252908i \(0.918613\pi\)
\(810\) −1.98528e11 + 1.94188e11i −0.461192 + 0.451110i
\(811\) −1.65427e11 −0.382405 −0.191203 0.981551i \(-0.561239\pi\)
−0.191203 + 0.981551i \(0.561239\pi\)
\(812\) −1.13001e11 + 1.99250e10i −0.259930 + 0.0458327i
\(813\) −6.07948e11 + 5.30192e11i −1.39157 + 1.21359i
\(814\) 1.22260e10 4.44989e9i 0.0278475 0.0101357i
\(815\) 1.90209e11 2.26682e11i 0.431122 0.513791i
\(816\) −2.48565e11 + 3.07959e11i −0.560635 + 0.694597i
\(817\) 1.48095e11 + 5.39023e10i 0.332394 + 0.120981i
\(818\) −7.92294e11 + 4.57431e11i −1.76959 + 1.02167i
\(819\) −3.31061e11 2.56950e11i −0.735821 0.571102i
\(820\) 3.84974e8 6.66795e8i 0.000851483 0.00147481i
\(821\) 3.93958e11 + 4.69501e11i 0.867116 + 1.03339i 0.999112 + 0.0421384i \(0.0134170\pi\)
−0.131996 + 0.991250i \(0.542139\pi\)
\(822\) −3.16754e11 + 5.73603e11i −0.693801 + 1.25639i
\(823\) −3.55321e10 + 2.01513e11i −0.0774501 + 0.439241i 0.921282 + 0.388896i \(0.127143\pi\)
−0.998732 + 0.0503455i \(0.983968\pi\)
\(824\) 3.20996e11 + 5.66002e10i 0.696290 + 0.122775i
\(825\) 1.70023e8 + 8.92212e9i 0.000367022 + 0.0192598i
\(826\) −4.19321e11 + 3.51852e11i −0.900795 + 0.755857i
\(827\) 3.20967e11 + 1.85311e11i 0.686181 + 0.396167i 0.802180 0.597083i \(-0.203674\pi\)
−0.115999 + 0.993249i \(0.537007\pi\)
\(828\) 1.27330e11 8.01328e10i 0.270901 0.170486i
\(829\) 1.52445e10 + 2.64043e10i 0.0322772 + 0.0559058i 0.881713 0.471787i \(-0.156391\pi\)
−0.849436 + 0.527692i \(0.823057\pi\)
\(830\) −4.09080e10 + 1.12394e11i −0.0861977 + 0.236826i
\(831\) 5.76585e11 2.22390e11i 1.20909 0.466349i
\(832\) 2.44565e11 + 2.05214e11i 0.510388 + 0.428266i
\(833\) −7.11196e10 1.95399e11i −0.147710 0.405829i
\(834\) 5.82287e10 1.69992e11i 0.120357 0.351370i
\(835\) 8.54745e10 + 4.84750e11i 0.175829 + 0.997176i
\(836\) 5.90681e9i 0.0120928i
\(837\) 3.32596e11 + 2.48134e11i 0.677666 + 0.505574i
\(838\) 1.71125e11 0.347007
\(839\) 8.55531e10 1.50853e10i 0.172658 0.0304443i −0.0866505 0.996239i \(-0.527616\pi\)
0.259309 + 0.965794i \(0.416505\pi\)
\(840\) −2.57754e10 1.31479e11i −0.0517711 0.264082i
\(841\) 2.02859e11 7.38346e10i 0.405518 0.147597i
\(842\) −4.63439e11 + 5.52305e11i −0.922028 + 1.09883i
\(843\) −7.67746e11 1.20340e11i −1.52022 0.238286i
\(844\) 2.26050e11 + 8.22753e10i 0.445486 + 0.162144i
\(845\) 2.78235e11 1.60639e11i 0.545738 0.315082i
\(846\) 1.57292e11 + 5.05512e10i 0.307062 + 0.0986847i
\(847\) −1.63986e11 + 2.84031e11i −0.318619 + 0.551865i
\(848\) 3.13404e11 + 3.73501e11i 0.606068 + 0.722284i
\(849\) −4.12582e11 6.84168e11i −0.794107 1.31684i
\(850\) 5.28778e10 2.99885e11i 0.101297 0.574485i
\(851\) −4.37787e11 7.71936e10i −0.834727 0.147185i
\(852\) 1.31990e11 7.95955e10i 0.250486 0.151053i
\(853\) 5.31783e11 4.46219e11i 1.00447 0.842853i 0.0168750 0.999858i \(-0.494628\pi\)
0.987598 + 0.157005i \(0.0501838\pi\)
\(854\) 1.92540e11 + 1.11163e11i 0.361985 + 0.208992i
\(855\) −1.13986e11 + 3.54674e11i −0.213299 + 0.663689i
\(856\) 1.69490e11 + 2.93565e11i 0.315681 + 0.546775i
\(857\) −1.56253e10 + 4.29300e10i −0.0289670 + 0.0795862i −0.953333 0.301920i \(-0.902372\pi\)
0.924366 + 0.381506i \(0.124595\pi\)
\(858\) 3.96546e9 2.52990e10i 0.00731719 0.0466824i
\(859\) 7.59299e11 + 6.37127e11i 1.39457 + 1.17018i 0.963450 + 0.267887i \(0.0863255\pi\)
0.431119 + 0.902295i \(0.358119\pi\)
\(860\) 1.01543e10 + 2.78988e10i 0.0185634 + 0.0510025i
\(861\) 3.04484e9 5.96917e8i 0.00554054 0.00108618i
\(862\) −1.52877e11 8.67008e11i −0.276893 1.57034i
\(863\) 2.70088e11i 0.486926i −0.969910 0.243463i \(-0.921717\pi\)
0.969910 0.243463i \(-0.0782834\pi\)
\(864\) −3.67356e11 4.33159e10i −0.659222 0.0777307i
\(865\) −1.60608e11 −0.286882
\(866\) 4.35020e11 7.67058e10i 0.773460 0.136382i
\(867\) −2.51303e11 8.60808e10i −0.444755 0.152346i
\(868\) 9.94880e10 3.62107e10i 0.175264 0.0637907i
\(869\) −1.02338e10 + 1.21962e10i −0.0179456 + 0.0213867i
\(870\) −1.59135e11 4.12585e11i −0.277772 0.720173i
\(871\) −8.07081e11 2.93753e11i −1.40231 0.510399i
\(872\) 2.04934e10 1.18318e10i 0.0354444 0.0204638i
\(873\) −2.69271e11 4.27869e11i −0.463588 0.736637i
\(874\) 3.92635e11 6.80065e11i 0.672890 1.16548i
\(875\) 2.25926e11 + 2.69248e11i 0.385419 + 0.459325i
\(876\) −3.78230e11 + 7.20768e9i −0.642302 + 0.0122399i
\(877\) 6.08459e10 3.45074e11i 0.102857 0.583330i −0.889198 0.457523i \(-0.848737\pi\)
0.992055 0.125807i \(-0.0401521\pi\)
\(878\) −5.72086e11 1.00874e11i −0.962683 0.169747i
\(879\) 1.38951e11 + 7.67312e10i 0.232758 + 0.128533i
\(880\) 8.73588e9 7.33028e9i 0.0145672 0.0122233i
\(881\) 4.63683e11 + 2.67708e11i 0.769694 + 0.444383i 0.832765 0.553626i \(-0.186756\pi\)
−0.0630716 + 0.998009i \(0.520090\pi\)
\(882\) 2.55393e11 3.29054e11i 0.422022 0.543743i
\(883\) −3.50386e10 6.06887e10i −0.0576374 0.0998309i 0.835767 0.549084i \(-0.185023\pi\)
−0.893404 + 0.449253i \(0.851690\pi\)
\(884\) −7.68118e10 + 2.11039e11i −0.125782 + 0.345583i
\(885\) −4.21894e11 3.40527e11i −0.687750 0.555109i
\(886\) −2.16468e10 1.81638e10i −0.0351284 0.0294762i
\(887\) −2.07018e11 5.68777e11i −0.334436 0.918856i −0.986943 0.161073i \(-0.948505\pi\)
0.652506 0.757783i \(-0.273718\pi\)
\(888\) 2.84075e11 + 3.25736e11i 0.456857 + 0.523858i
\(889\) 5.25232e10 + 2.97874e11i 0.0840899 + 0.476898i
\(890\) 5.84858e11i 0.932161i
\(891\) −7.25129e9 1.60100e10i −0.0115055 0.0254027i
\(892\) 9.42136e10 0.148818
\(893\) 2.18266e11 3.84862e10i 0.343226 0.0605200i
\(894\) 7.59905e11 6.62714e11i 1.18962 1.03747i
\(895\) 2.46887e11 8.98594e10i 0.384774 0.140046i
\(896\) 3.15198e11 3.75638e11i 0.489048 0.582825i
\(897\) −5.49538e11 + 6.80849e11i −0.848845 + 1.05167i
\(898\) −5.87301e11 2.13760e11i −0.903141 0.328716i
\(899\) −5.72236e11 + 3.30380e11i −0.876064 + 0.505796i
\(900\) 1.45167e11 5.91924e10i 0.221257 0.0902186i
\(901\) 1.84429e11 3.19440e11i 0.279853 0.484719i
\(902\) 1.21871e8 + 1.45241e8i 0.000184109 + 0.000219413i
\(903\) −5.78370e10 + 1.04736e11i −0.0869871 + 0.157523i
\(904\) −9.51599e10 + 5.39679e11i −0.142489 + 0.808094i
\(905\) −8.90782e10 1.57069e10i −0.132794 0.0234151i
\(906\) −2.55335e10 1.33990e12i −0.0378964 1.98865i
\(907\) 3.57812e11 3.00240e11i 0.528721 0.443649i −0.338939 0.940808i \(-0.610068\pi\)
0.867659 + 0.497159i \(0.165624\pi\)
\(908\) −1.85881e11 1.07318e11i −0.273458 0.157881i
\(909\) 1.13813e12 + 6.00486e11i 1.66700 + 0.879524i
\(910\) −2.06036e11 3.56864e11i −0.300453 0.520401i
\(911\) −3.31123e11 + 9.09752e11i −0.480746 + 1.32084i 0.428110 + 0.903727i \(0.359180\pi\)
−0.908855 + 0.417111i \(0.863042\pi\)
\(912\) −9.92228e11 + 3.82704e11i −1.43427 + 0.553202i
\(913\) −5.79869e9 4.86568e9i −0.00834539 0.00700261i
\(914\) −4.00538e11 1.10047e12i −0.573930 1.57686i
\(915\) −7.13602e10 + 2.08328e11i −0.101806 + 0.297209i
\(916\) 5.02485e10 + 2.84973e11i 0.0713741 + 0.404783i
\(917\) 4.46451e11i 0.631388i
\(918\) 1.37718e11 + 5.83718e11i 0.193918 + 0.821925i
\(919\) 3.60571e11 0.505509 0.252755 0.967530i \(-0.418663\pi\)
0.252755 + 0.967530i \(0.418663\pi\)
\(920\) −2.75480e11 + 4.85745e10i −0.384537 + 0.0678043i
\(921\) 7.73232e10 + 3.94422e11i 0.107466 + 0.548179i
\(922\) 5.44086e11 1.98031e11i 0.752911 0.274037i
\(923\) −5.76188e11 + 6.86675e11i −0.793885 + 0.946116i
\(924\) −4.43015e9 6.94400e8i −0.00607758 0.000952625i
\(925\) −4.35290e11 1.58433e11i −0.594582 0.216410i
\(926\) −7.23198e11 + 4.17538e11i −0.983588 + 0.567875i
\(927\) 5.09835e11 4.62022e11i 0.690416 0.625667i
\(928\) 2.94506e11 5.10099e11i 0.397102 0.687801i
\(929\) 2.68522e11 + 3.20012e11i 0.360509 + 0.429638i 0.915562 0.402177i \(-0.131746\pi\)
−0.555053 + 0.831815i \(0.687302\pi\)
\(930\) 2.10707e11 + 3.49407e11i 0.281674 + 0.467090i
\(931\) 9.70300e10 5.50285e11i 0.129154 0.732468i
\(932\) 3.14271e11 + 5.54144e10i 0.416524 + 0.0734444i
\(933\) −4.52707e11 + 2.73001e11i −0.597435 + 0.360278i
\(934\) −1.13897e12 + 9.55706e11i −1.49666 + 1.25585i
\(935\) −7.47145e9 4.31365e9i −0.00977594 0.00564414i
\(936\) 8.31520e11 1.79529e11i 1.08335 0.233901i
\(937\) −2.31539e11 4.01037e11i −0.300376 0.520266i 0.675845 0.737044i \(-0.263779\pi\)
−0.976221 + 0.216777i \(0.930445\pi\)
\(938\) −2.00148e11 + 5.49903e11i −0.258548 + 0.710354i
\(939\) 1.05734e11 6.74567e11i 0.136005 0.867687i
\(940\) 3.19840e10 + 2.68377e10i 0.0409658 + 0.0343744i
\(941\) 3.23231e11 + 8.88071e11i 0.412245 + 1.13263i 0.955994 + 0.293386i \(0.0947820\pi\)
−0.543749 + 0.839248i \(0.682996\pi\)
\(942\) −1.76072e12 + 3.45175e11i −2.23608 + 0.438365i
\(943\) −1.12491e9 6.37968e9i −0.00142256 0.00806774i
\(944\) 1.54772e12i 1.94897i
\(945\) −2.52608e11 1.27186e11i −0.316752 0.159482i
\(946\) −7.31091e9 −0.00912866
\(947\) 1.13441e11 2.00028e10i 0.141049 0.0248708i −0.102678 0.994715i \(-0.532741\pi\)
0.243727 + 0.969844i \(0.421630\pi\)
\(948\) 2.64604e11 + 9.06370e10i 0.327615 + 0.112220i
\(949\) 2.06739e12 7.52470e11i 2.54893 0.927736i
\(950\) 5.25980e11 6.26838e11i 0.645765 0.769593i
\(951\) 1.48902e10 + 3.86054e10i 0.0182045 + 0.0471983i
\(952\) −2.71898e11 9.89628e10i −0.331023 0.120483i
\(953\) −7.23371e11 + 4.17638e11i −0.876980 + 0.506324i −0.869661 0.493649i \(-0.835663\pi\)
−0.00731829 + 0.999973i \(0.502330\pi\)
\(954\) 7.38344e11 2.81505e10i 0.891385 0.0339854i
\(955\) 7.01552e10 1.21512e11i 0.0843424 0.146085i
\(956\) 1.29999e11 + 1.54927e11i 0.155635 + 0.185479i
\(957\) 2.79814e10 5.33224e8i 0.0333597 0.000635714i
\(958\) −4.76817e10 + 2.70416e11i −0.0566096 + 0.321049i
\(959\) −6.57171e11 1.15877e11i −0.776969 0.137001i
\(960\) 1.88608e11 + 1.04153e11i 0.222062 + 0.122627i
\(961\) −1.86313e11 + 1.56335e11i −0.218448 + 0.183300i
\(962\) 1.15120e12 + 6.64644e11i 1.34415 + 0.776048i
\(963\) 7.08897e11 + 9.73157e10i 0.824286 + 0.113156i
\(964\) 1.61116e11 + 2.79061e11i 0.186565 + 0.323140i
\(965\) 1.44207e11 3.96206e11i 0.166295 0.456891i
\(966\) 4.63896e11 + 3.74427e11i 0.532736 + 0.429991i
\(967\) −5.96657e11 5.00655e11i −0.682369 0.572575i 0.234329 0.972157i \(-0.424711\pi\)
−0.916697 + 0.399582i \(0.869155\pi\)
\(968\) −2.27699e11 6.25598e11i −0.259334 0.712514i
\(969\) 5.28798e11 + 6.06350e11i 0.599784 + 0.687746i
\(970\) −8.63202e10 4.89546e11i −0.0975046 0.552976i
\(971\) 8.97129e11i 1.00920i −0.863353 0.504601i \(-0.831640\pi\)
0.863353 0.504601i \(-0.168360\pi\)
\(972\) −2.16575e11 + 2.20070e11i −0.242630 + 0.246545i
\(973\) 1.82995e11 0.204168
\(974\) 1.83746e11 3.23993e10i 0.204165 0.0359998i
\(975\) −6.87136e11 + 5.99252e11i −0.760368 + 0.663118i
\(976\) −5.90715e11 + 2.15003e11i −0.650997 + 0.236943i
\(977\) −9.94842e10 + 1.18561e11i −0.109188 + 0.130125i −0.817871 0.575402i \(-0.804846\pi\)
0.708682 + 0.705528i \(0.249290\pi\)
\(978\) 8.04018e11 9.96136e11i 0.878841 1.08884i
\(979\) 3.47821e10 + 1.26597e10i 0.0378639 + 0.0137813i
\(980\) 9.11612e10 5.26320e10i 0.0988339 0.0570618i
\(981\) 6.79348e9 4.94872e10i 0.00733527 0.0534339i
\(982\) −9.43301e11 + 1.63384e12i −1.01439 + 1.75697i
\(983\) 1.17650e11 + 1.40210e11i 0.126002 + 0.150163i 0.825357 0.564611i \(-0.190974\pi\)
−0.699355 + 0.714774i \(0.746529\pi\)
\(984\) −3.04468e9 + 5.51355e9i −0.00324759 + 0.00588100i
\(985\) −1.34911e11 + 7.65118e11i −0.143319 + 0.812800i
\(986\) −9.40495e11 1.65835e11i −0.995059 0.175456i
\(987\) 3.20576e9 + 1.68226e11i 0.00337803 + 0.177265i
\(988\) −4.62305e11 + 3.87920e11i −0.485177 + 0.407112i
\(989\) 2.16329e11 + 1.24898e11i 0.226115 + 0.130548i
\(990\) −6.58418e8 1.72693e10i −0.000685426 0.0179777i
\(991\) 2.68198e11 + 4.64533e11i 0.278075 + 0.481640i 0.970906 0.239460i \(-0.0769703\pi\)
−0.692831 + 0.721100i \(0.743637\pi\)
\(992\) −1.85880e11 + 5.10700e11i −0.191949 + 0.527374i
\(993\) −6.37014e11 + 2.45697e11i −0.655167 + 0.252699i
\(994\) 4.67865e11 + 3.92585e11i 0.479264 + 0.402150i
\(995\) −2.71997e10 7.47307e10i −0.0277506 0.0762442i
\(996\) −4.30935e10 + 1.25806e11i −0.0437899 + 0.127840i
\(997\) −1.28567e11 7.29138e11i −0.130121 0.737953i −0.978134 0.207977i \(-0.933312\pi\)
0.848013 0.529976i \(-0.177799\pi\)
\(998\) 1.21778e12i 1.22757i
\(999\) 9.10847e11 5.21228e10i 0.914500 0.0523318i
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 27.9.f.a.14.6 yes 138
3.2 odd 2 81.9.f.a.71.18 138
27.2 odd 18 inner 27.9.f.a.2.6 138
27.25 even 9 81.9.f.a.8.18 138
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.9.f.a.2.6 138 27.2 odd 18 inner
27.9.f.a.14.6 yes 138 1.1 even 1 trivial
81.9.f.a.8.18 138 27.25 even 9
81.9.f.a.71.18 138 3.2 odd 2