Properties

Label 33.8.f.a.2.7
Level $33$
Weight $8$
Character 33.2
Analytic conductor $10.309$
Analytic rank $0$
Dimension $104$
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] = [33,8,Mod(2,33)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(33, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 1]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("33.2");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 33.f (of order \(10\), degree \(4\), 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: \(10.3087058410\)
Analytic rank: \(0\)
Dimension: \(104\)
Relative dimension: \(26\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 2.7
Character \(\chi\) \(=\) 33.2
Dual form 33.8.f.a.17.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.82493 + 11.7719i) q^{2} +(1.38201 - 46.7449i) q^{3} +(-20.3938 - 14.8170i) q^{4} +(-22.0489 + 7.16411i) q^{5} +(544.992 + 195.065i) q^{6} +(49.3778 - 67.9627i) q^{7} +(-1029.34 + 747.857i) q^{8} +(-2183.18 - 129.204i) q^{9} +O(q^{10})\) \(q+(-3.82493 + 11.7719i) q^{2} +(1.38201 - 46.7449i) q^{3} +(-20.3938 - 14.8170i) q^{4} +(-22.0489 + 7.16411i) q^{5} +(544.992 + 195.065i) q^{6} +(49.3778 - 67.9627i) q^{7} +(-1029.34 + 747.857i) q^{8} +(-2183.18 - 129.204i) q^{9} -286.960i q^{10} +(-4347.42 + 766.243i) q^{11} +(-720.803 + 932.831i) q^{12} +(-2166.72 - 704.010i) q^{13} +(611.185 + 841.224i) q^{14} +(304.414 + 1040.57i) q^{15} +(-5863.66 - 18046.5i) q^{16} +(-2457.83 - 7564.41i) q^{17} +(9871.49 - 25206.0i) q^{18} +(-26304.9 - 36205.6i) q^{19} +(555.811 + 180.594i) q^{20} +(-3108.67 - 2402.09i) q^{21} +(7608.42 - 54108.3i) q^{22} +4847.59i q^{23} +(33536.0 + 49149.8i) q^{24} +(-62769.6 + 45604.8i) q^{25} +(16575.1 - 22813.6i) q^{26} +(-9056.80 + 101874. i) q^{27} +(-2014.00 + 654.390i) q^{28} +(-54996.6 - 39957.4i) q^{29} +(-13413.9 - 396.581i) q^{30} +(-66917.5 + 205951. i) q^{31} +72011.6 q^{32} +(29809.8 + 204279. i) q^{33} +98448.6 q^{34} +(-601.832 + 1852.25i) q^{35} +(42609.0 + 34983.1i) q^{36} +(-27808.6 - 20204.1i) q^{37} +(526824. - 171175. i) q^{38} +(-35903.3 + 100310. i) q^{39} +(17338.0 - 23863.7i) q^{40} +(429481. - 312036. i) q^{41} +(40167.6 - 27407.2i) q^{42} -156862. i q^{43} +(100014. + 48789.0i) q^{44} +(49062.3 - 12791.7i) q^{45} +(-57065.4 - 18541.7i) q^{46} +(-60816.6 - 83706.9i) q^{47} +(-851685. + 249156. i) q^{48} +(252308. + 776524. i) q^{49} +(-296767. - 913354. i) q^{50} +(-356995. + 104437. i) q^{51} +(33756.4 + 46461.7i) q^{52} +(757346. + 246077. i) q^{53} +(-1.16461e6 - 496277. i) q^{54} +(90366.2 - 48040.2i) q^{55} +106884. i q^{56} +(-1.72878e6 + 1.17958e6i) q^{57} +(680733. - 494582. i) q^{58} +(-522927. + 719748. i) q^{59} +(9209.99 - 25731.8i) q^{60} +(1.93678e6 - 629298. i) q^{61} +(-2.16848e6 - 1.57550e6i) q^{62} +(-116582. + 141995. i) q^{63} +(475109. - 1.46223e6i) q^{64} +52817.3 q^{65} +(-2.51877e6 - 430433. i) q^{66} -1.99988e6 q^{67} +(-61957.3 + 190685. i) q^{68} +(226600. + 6699.41i) q^{69} +(-19502.6 - 14169.4i) q^{70} +(5.54290e6 - 1.80100e6i) q^{71} +(2.34385e6 - 1.49971e6i) q^{72} +(-699427. + 962679. i) q^{73} +(344207. - 250081. i) q^{74} +(2.04505e6 + 2.99719e6i) q^{75} +1.12813e6i q^{76} +(-162590. + 333298. i) q^{77} +(-1.04352e6 - 806330. i) q^{78} +(-6.64555e6 - 2.15927e6i) q^{79} +(258574. + 355897. i) q^{80} +(4.74958e6 + 564151. i) q^{81} +(2.03053e6 + 6.24933e6i) q^{82} +(-888068. - 2.73319e6i) q^{83} +(27806.0 + 95048.9i) q^{84} +(108385. + 149179. i) q^{85} +(1.84657e6 + 599987. i) q^{86} +(-1.94381e6 + 2.51559e6i) q^{87} +(3.90192e6 - 4.03997e6i) q^{88} +6.78358e6i q^{89} +(-37076.3 + 626485. i) q^{90} +(-154834. + 112494. i) q^{91} +(71826.6 - 98860.8i) q^{92} +(9.53468e6 + 3.41268e6i) q^{93} +(1.21801e6 - 395755. i) q^{94} +(839374. + 609841. i) q^{95} +(99520.7 - 3.36618e6i) q^{96} +(-2.15812e6 + 6.64202e6i) q^{97} -1.01062e7 q^{98} +(9.59020e6 - 1.11114e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 104 q - 42 q^{3} - 1542 q^{4} - 1725 q^{6} - 10 q^{7} + 550 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 104 q - 42 q^{3} - 1542 q^{4} - 1725 q^{6} - 10 q^{7} + 550 q^{9} + 12942 q^{12} - 10 q^{13} - 21762 q^{15} - 40042 q^{16} + 60435 q^{18} + 10460 q^{19} - 218044 q^{22} + 330875 q^{24} + 462276 q^{25} - 294096 q^{27} - 1044930 q^{28} + 243010 q^{30} + 412 q^{31} + 32138 q^{33} + 720380 q^{34} + 166067 q^{36} - 494526 q^{37} + 1075280 q^{39} + 363510 q^{40} - 1090804 q^{42} - 3105552 q^{45} + 706710 q^{46} + 3640214 q^{48} + 3722248 q^{49} + 53970 q^{51} - 3236270 q^{52} + 1380424 q^{55} - 3039180 q^{57} - 1651930 q^{58} - 12139486 q^{60} + 3921710 q^{61} + 459870 q^{63} + 3705878 q^{64} + 15158784 q^{66} - 15866932 q^{67} + 8740364 q^{69} + 14057584 q^{70} - 28129160 q^{72} - 26920980 q^{73} - 16391598 q^{75} + 43716808 q^{78} + 59786450 q^{79} - 17715062 q^{81} + 23865872 q^{82} + 71482920 q^{84} - 2864030 q^{85} - 108977170 q^{88} - 54544280 q^{90} - 56013610 q^{91} - 71700158 q^{93} + 53266890 q^{94} + 34615450 q^{96} + 71130138 q^{97} + 46642084 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(e\left(\frac{1}{10}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.82493 + 11.7719i −0.338079 + 1.04050i 0.627106 + 0.778934i \(0.284239\pi\)
−0.965185 + 0.261567i \(0.915761\pi\)
\(3\) 1.38201 46.7449i 0.0295520 0.999563i
\(4\) −20.3938 14.8170i −0.159327 0.115758i
\(5\) −22.0489 + 7.16411i −0.0788844 + 0.0256311i −0.348193 0.937423i \(-0.613205\pi\)
0.269309 + 0.963054i \(0.413205\pi\)
\(6\) 544.992 + 195.065i 1.03006 + 0.368680i
\(7\) 49.3778 67.9627i 0.0544112 0.0748907i −0.780944 0.624601i \(-0.785262\pi\)
0.835356 + 0.549710i \(0.185262\pi\)
\(8\) −1029.34 + 747.857i −0.710792 + 0.516420i
\(9\) −2183.18 129.204i −0.998253 0.0590781i
\(10\) 286.960i 0.0907446i
\(11\) −4347.42 + 766.243i −0.984820 + 0.173577i
\(12\) −720.803 + 932.831i −0.120416 + 0.155836i
\(13\) −2166.72 704.010i −0.273527 0.0888744i 0.169042 0.985609i \(-0.445933\pi\)
−0.442569 + 0.896734i \(0.645933\pi\)
\(14\) 611.185 + 841.224i 0.0595285 + 0.0819339i
\(15\) 304.414 + 1040.57i 0.0232887 + 0.0796074i
\(16\) −5863.66 18046.5i −0.357889 1.10147i
\(17\) −2457.83 7564.41i −0.121333 0.373425i 0.871882 0.489716i \(-0.162900\pi\)
−0.993215 + 0.116291i \(0.962900\pi\)
\(18\) 9871.49 25206.0i 0.398959 1.01871i
\(19\) −26304.9 36205.6i −0.879830 1.21098i −0.976468 0.215663i \(-0.930809\pi\)
0.0966373 0.995320i \(-0.469191\pi\)
\(20\) 555.811 + 180.594i 0.0155354 + 0.00504776i
\(21\) −3108.67 2402.09i −0.0732500 0.0566006i
\(22\) 7608.42 54108.3i 0.152340 1.08339i
\(23\) 4847.59i 0.0830765i 0.999137 + 0.0415382i \(0.0132258\pi\)
−0.999137 + 0.0415382i \(0.986774\pi\)
\(24\) 33536.0 + 49149.8i 0.495189 + 0.725742i
\(25\) −62769.6 + 45604.8i −0.803451 + 0.583741i
\(26\) 16575.1 22813.6i 0.184948 0.254559i
\(27\) −9056.80 + 101874.i −0.0885527 + 0.996071i
\(28\) −2014.00 + 654.390i −0.0173383 + 0.00563357i
\(29\) −54996.6 39957.4i −0.418739 0.304231i 0.358392 0.933571i \(-0.383325\pi\)
−0.777130 + 0.629340i \(0.783325\pi\)
\(30\) −13413.9 396.581i −0.0907050 0.00268168i
\(31\) −66917.5 + 205951.i −0.403435 + 1.24165i 0.518759 + 0.854920i \(0.326394\pi\)
−0.922195 + 0.386726i \(0.873606\pi\)
\(32\) 72011.6 0.388488
\(33\) 29809.8 + 204279.i 0.144398 + 0.989520i
\(34\) 98448.6 0.429570
\(35\) −601.832 + 1852.25i −0.00237267 + 0.00730233i
\(36\) 42609.0 + 34983.1i 0.152210 + 0.124968i
\(37\) −27808.6 20204.1i −0.0902553 0.0655743i 0.541742 0.840545i \(-0.317765\pi\)
−0.631998 + 0.774970i \(0.717765\pi\)
\(38\) 526824. 171175.i 1.55748 0.506056i
\(39\) −35903.3 + 100310.i −0.0969189 + 0.270781i
\(40\) 17338.0 23863.7i 0.0428340 0.0589559i
\(41\) 429481. 312036.i 0.973196 0.707068i 0.0170180 0.999855i \(-0.494583\pi\)
0.956178 + 0.292787i \(0.0945827\pi\)
\(42\) 40167.6 27407.2i 0.0836573 0.0570811i
\(43\) 156862.i 0.300870i −0.988620 0.150435i \(-0.951933\pi\)
0.988620 0.150435i \(-0.0480674\pi\)
\(44\) 100014. + 48789.0i 0.177001 + 0.0863450i
\(45\) 49062.3 12791.7i 0.0802609 0.0209260i
\(46\) −57065.4 18541.7i −0.0864411 0.0280864i
\(47\) −60816.6 83706.9i −0.0854436 0.117603i 0.764155 0.645032i \(-0.223156\pi\)
−0.849599 + 0.527429i \(0.823156\pi\)
\(48\) −851685. + 249156.i −1.11157 + 0.325182i
\(49\) 252308. + 776524.i 0.306369 + 0.942907i
\(50\) −296767. 913354.i −0.335753 1.03334i
\(51\) −356995. + 104437.i −0.376848 + 0.110245i
\(52\) 33756.4 + 46461.7i 0.0332923 + 0.0458230i
\(53\) 757346. + 246077.i 0.698761 + 0.227041i 0.636791 0.771037i \(-0.280262\pi\)
0.0619705 + 0.998078i \(0.480262\pi\)
\(54\) −1.16461e6 496277.i −1.00648 0.428890i
\(55\) 90366.2 48040.2i 0.0732380 0.0389345i
\(56\) 106884.i 0.0813307i
\(57\) −1.72878e6 + 1.17958e6i −1.23645 + 0.843659i
\(58\) 680733. 494582.i 0.458120 0.332843i
\(59\) −522927. + 719748.i −0.331482 + 0.456245i −0.941929 0.335811i \(-0.890990\pi\)
0.610448 + 0.792057i \(0.290990\pi\)
\(60\) 9209.99 25731.8i 0.00550465 0.0153794i
\(61\) 1.93678e6 629298.i 1.09251 0.354978i 0.293295 0.956022i \(-0.405248\pi\)
0.799216 + 0.601044i \(0.205248\pi\)
\(62\) −2.16848e6 1.57550e6i −1.15554 0.839549i
\(63\) −116582. + 141995.i −0.0587406 + 0.0715453i
\(64\) 475109. 1.46223e6i 0.226550 0.697248i
\(65\) 52817.3 0.0238550
\(66\) −2.51877e6 430433.i −1.07841 0.184290i
\(67\) −1.99988e6 −0.812349 −0.406174 0.913796i \(-0.633137\pi\)
−0.406174 + 0.913796i \(0.633137\pi\)
\(68\) −61957.3 + 190685.i −0.0238952 + 0.0735419i
\(69\) 226600. + 6699.41i 0.0830402 + 0.00245507i
\(70\) −19502.6 14169.4i −0.00679592 0.00493753i
\(71\) 5.54290e6 1.80100e6i 1.83795 0.597185i 0.839388 0.543533i \(-0.182914\pi\)
0.998560 0.0536526i \(-0.0170864\pi\)
\(72\) 2.34385e6 1.49971e6i 0.740059 0.473526i
\(73\) −699427. + 962679.i −0.210432 + 0.289635i −0.901166 0.433474i \(-0.857288\pi\)
0.690734 + 0.723109i \(0.257288\pi\)
\(74\) 344207. 250081.i 0.0987436 0.0717414i
\(75\) 2.04505e6 + 2.99719e6i 0.559743 + 0.820351i
\(76\) 1.12813e6i 0.294789i
\(77\) −162590. + 333298.i −0.0405860 + 0.0831984i
\(78\) −1.04352e6 806330.i −0.248982 0.192390i
\(79\) −6.64555e6 2.15927e6i −1.51648 0.492733i −0.571705 0.820459i \(-0.693718\pi\)
−0.944773 + 0.327726i \(0.893718\pi\)
\(80\) 258574. + 355897.i 0.0564638 + 0.0777157i
\(81\) 4.74958e6 + 564151.i 0.993020 + 0.117950i
\(82\) 2.03053e6 + 6.24933e6i 0.406687 + 1.25166i
\(83\) −888068. 2.73319e6i −0.170480 0.524683i 0.828918 0.559369i \(-0.188957\pi\)
−0.999398 + 0.0346867i \(0.988957\pi\)
\(84\) 27806.0 + 95048.9i 0.00511872 + 0.0174972i
\(85\) 108385. + 149179.i 0.0191426 + 0.0263475i
\(86\) 1.84657e6 + 599987.i 0.313056 + 0.101718i
\(87\) −1.94381e6 + 2.51559e6i −0.316473 + 0.409565i
\(88\) 3.90192e6 4.03997e6i 0.610363 0.631958i
\(89\) 6.78358e6i 1.01998i 0.860179 + 0.509992i \(0.170352\pi\)
−0.860179 + 0.509992i \(0.829648\pi\)
\(90\) −37076.3 + 626485.i −0.00536102 + 0.0905861i
\(91\) −154834. + 112494.i −0.0215388 + 0.0156489i
\(92\) 71826.6 98860.8i 0.00961674 0.0132363i
\(93\) 9.53468e6 + 3.41268e6i 1.22918 + 0.439952i
\(94\) 1.21801e6 395755.i 0.151253 0.0491450i
\(95\) 839374. + 609841.i 0.100444 + 0.0729767i
\(96\) 99520.7 3.36618e6i 0.0114806 0.388318i
\(97\) −2.15812e6 + 6.64202e6i −0.240090 + 0.738922i 0.756315 + 0.654208i \(0.226998\pi\)
−0.996405 + 0.0847146i \(0.973002\pi\)
\(98\) −1.01062e7 −1.08467
\(99\) 9.59020e6 1.11114e6i 0.993355 0.115092i
\(100\) 1.95584e6 0.195584
\(101\) −2.69520e6 + 8.29496e6i −0.260295 + 0.801105i 0.732445 + 0.680826i \(0.238379\pi\)
−0.992740 + 0.120279i \(0.961621\pi\)
\(102\) 136057. 4.60198e6i 0.0126946 0.429382i
\(103\) −7.75051e6 5.63107e6i −0.698876 0.507763i 0.180690 0.983540i \(-0.442167\pi\)
−0.879566 + 0.475777i \(0.842167\pi\)
\(104\) 2.75678e6 895732.i 0.240318 0.0780839i
\(105\) 85751.5 + 30692.4i 0.00722902 + 0.00258743i
\(106\) −5.79359e6 + 7.97419e6i −0.472473 + 0.650303i
\(107\) −1.03101e7 + 7.49070e6i −0.813613 + 0.591124i −0.914876 0.403735i \(-0.867712\pi\)
0.101263 + 0.994860i \(0.467712\pi\)
\(108\) 1.69417e6 1.94341e6i 0.129412 0.148450i
\(109\) 1.32232e7i 0.978009i −0.872281 0.489004i \(-0.837360\pi\)
0.872281 0.489004i \(-0.162640\pi\)
\(110\) 219881. + 1.24753e6i 0.0157512 + 0.0893671i
\(111\) −982872. + 1.27199e6i −0.0682129 + 0.0882781i
\(112\) −1.51602e6 492586.i −0.101963 0.0331298i
\(113\) −1.20510e7 1.65868e7i −0.785687 1.08141i −0.994632 0.103478i \(-0.967003\pi\)
0.208945 0.977927i \(-0.432997\pi\)
\(114\) −7.27351e6 2.48629e7i −0.459808 1.57176i
\(115\) −34728.6 106884.i −0.00212934 0.00655344i
\(116\) 529544. + 1.62977e6i 0.0314991 + 0.0969444i
\(117\) 4.63938e6 + 1.81693e6i 0.267799 + 0.104879i
\(118\) −6.47265e6 8.90884e6i −0.362656 0.499154i
\(119\) −635460. 206473.i −0.0345680 0.0112318i
\(120\) −1.09154e6 843442.i −0.0576643 0.0445575i
\(121\) 1.83129e7 6.66235e6i 0.939742 0.341884i
\(122\) 2.52066e7i 1.25677i
\(123\) −1.39926e7 2.05073e7i −0.677999 0.993666i
\(124\) 4.41627e6 3.20861e6i 0.208008 0.151127i
\(125\) 2.12189e6 2.92053e6i 0.0971711 0.133745i
\(126\) −1.22564e6 1.91551e6i −0.0545840 0.0853076i
\(127\) 2.76182e7 8.97371e6i 1.19642 0.388740i 0.357976 0.933731i \(-0.383467\pi\)
0.838442 + 0.544991i \(0.183467\pi\)
\(128\) 2.28532e7 + 1.66038e7i 0.963188 + 0.699797i
\(129\) −7.33252e6 216785.i −0.300739 0.00889131i
\(130\) −202022. + 621761.i −0.00806488 + 0.0248211i
\(131\) −4.64774e7 −1.80631 −0.903155 0.429315i \(-0.858755\pi\)
−0.903155 + 0.429315i \(0.858755\pi\)
\(132\) 2.41886e6 4.60772e6i 0.0915381 0.174372i
\(133\) −3.75951e6 −0.138564
\(134\) 7.64940e6 2.35424e7i 0.274638 0.845249i
\(135\) −530145. 2.31109e6i −0.0185450 0.0808442i
\(136\) 8.18702e6 + 5.94822e6i 0.279087 + 0.202769i
\(137\) −1.63682e7 + 5.31836e6i −0.543851 + 0.176708i −0.568042 0.822999i \(-0.692299\pi\)
0.0241911 + 0.999707i \(0.492299\pi\)
\(138\) −945594. + 2.64189e6i −0.0306287 + 0.0855733i
\(139\) −8.98096e6 + 1.23612e7i −0.283642 + 0.390400i −0.926936 0.375219i \(-0.877567\pi\)
0.643294 + 0.765619i \(0.277567\pi\)
\(140\) 39718.4 28857.1i 0.00122333 0.000888801i
\(141\) −3.99692e6 + 2.72718e6i −0.120077 + 0.0819309i
\(142\) 7.21393e7i 2.11428i
\(143\) 9.95907e6 + 1.40039e6i 0.284802 + 0.0400473i
\(144\) 1.04697e7 + 4.01563e7i 0.292191 + 1.12069i
\(145\) 1.49887e6 + 487013.i 0.0408297 + 0.0132664i
\(146\) −8.65732e6 1.19158e7i −0.230223 0.316874i
\(147\) 3.66473e7 1.07210e7i 0.951549 0.278370i
\(148\) 267759. + 824078.i 0.00678936 + 0.0208955i
\(149\) 1.06258e7 + 3.27028e7i 0.263153 + 0.809903i 0.992113 + 0.125346i \(0.0400042\pi\)
−0.728960 + 0.684557i \(0.759996\pi\)
\(150\) −4.31048e7 + 1.26101e7i −1.04281 + 0.305069i
\(151\) 9.18769e6 + 1.26458e7i 0.217163 + 0.298900i 0.903675 0.428219i \(-0.140859\pi\)
−0.686511 + 0.727119i \(0.740859\pi\)
\(152\) 5.41532e7 + 1.75954e7i 1.25075 + 0.406394i
\(153\) 4.38853e6 + 1.68320e7i 0.0990601 + 0.379941i
\(154\) −3.30166e6 3.18884e6i −0.0728467 0.0703574i
\(155\) 5.02039e6i 0.108287i
\(156\) 2.21850e6 1.51373e6i 0.0467868 0.0319236i
\(157\) −4.59450e7 + 3.33810e7i −0.947523 + 0.688415i −0.950220 0.311581i \(-0.899142\pi\)
0.00269702 + 0.999996i \(0.499142\pi\)
\(158\) 5.08375e7 6.99718e7i 1.02538 1.41131i
\(159\) 1.25495e7 3.50620e7i 0.247592 0.691746i
\(160\) −1.58777e6 + 515899.i −0.0306456 + 0.00995737i
\(161\) 329455. + 239363.i 0.00622165 + 0.00452029i
\(162\) −2.48079e7 + 5.37539e7i −0.458446 + 0.993361i
\(163\) 3.07514e7 9.46429e7i 0.556170 1.71172i −0.136663 0.990618i \(-0.543638\pi\)
0.692833 0.721098i \(-0.256362\pi\)
\(164\) −1.33822e7 −0.236905
\(165\) −2.12075e6 4.29055e6i −0.0367532 0.0743566i
\(166\) 3.55717e7 0.603568
\(167\) 2.40894e7 7.41395e7i 0.400238 1.23180i −0.524569 0.851368i \(-0.675774\pi\)
0.924807 0.380437i \(-0.124226\pi\)
\(168\) 4.99629e6 + 147715.i 0.0812952 + 0.00240348i
\(169\) −4.65656e7 3.38319e7i −0.742098 0.539166i
\(170\) −2.17068e6 + 705297.i −0.0338863 + 0.0110103i
\(171\) 5.27504e7 + 8.24420e7i 0.806751 + 1.26085i
\(172\) −2.32423e6 + 3.19902e6i −0.0348280 + 0.0479367i
\(173\) 4.49966e7 3.26920e7i 0.660722 0.480042i −0.206185 0.978513i \(-0.566105\pi\)
0.866907 + 0.498471i \(0.166105\pi\)
\(174\) −2.21784e7 3.25044e7i −0.319160 0.467756i
\(175\) 6.51786e6i 0.0919331i
\(176\) 3.93198e7 + 7.39626e7i 0.543646 + 1.02263i
\(177\) 3.29219e7 + 2.54389e7i 0.446250 + 0.344820i
\(178\) −7.98557e7 2.59467e7i −1.06129 0.344835i
\(179\) −3.42525e7 4.71445e7i −0.446381 0.614391i 0.525234 0.850958i \(-0.323978\pi\)
−0.971615 + 0.236567i \(0.923978\pi\)
\(180\) −1.19010e6 466082.i −0.0152100 0.00595674i
\(181\) −2.02239e7 6.22427e7i −0.253507 0.780214i −0.994120 0.108282i \(-0.965465\pi\)
0.740613 0.671932i \(-0.234535\pi\)
\(182\) −732036. 2.25298e6i −0.00900083 0.0277017i
\(183\) −2.67399e7 9.14044e7i −0.322538 1.10252i
\(184\) −3.62530e6 4.98980e6i −0.0429024 0.0590501i
\(185\) 757892. + 246254.i 0.00880048 + 0.00285945i
\(186\) −7.66433e7 + 9.91883e7i −0.873331 + 1.13023i
\(187\) 1.64814e7 + 3.10024e7i 0.184309 + 0.346696i
\(188\) 2.60822e6i 0.0286281i
\(189\) 6.47643e6 + 5.64584e6i 0.0697782 + 0.0608293i
\(190\) −1.03895e7 + 7.54844e6i −0.109890 + 0.0798399i
\(191\) −5.86275e7 + 8.06939e7i −0.608814 + 0.837961i −0.996479 0.0838393i \(-0.973282\pi\)
0.387665 + 0.921800i \(0.373282\pi\)
\(192\) −6.76955e7 2.42298e7i −0.690248 0.247056i
\(193\) −1.06641e8 + 3.46496e7i −1.06776 + 0.346935i −0.789613 0.613605i \(-0.789719\pi\)
−0.278143 + 0.960540i \(0.589719\pi\)
\(194\) −6.99346e7 5.08105e7i −0.687680 0.499628i
\(195\) 72994.0 2.46894e6i 0.000704962 0.0238446i
\(196\) 6.36022e6 1.95747e7i 0.0603359 0.185695i
\(197\) −1.63981e8 −1.52814 −0.764070 0.645134i \(-0.776802\pi\)
−0.764070 + 0.645134i \(0.776802\pi\)
\(198\) −2.36015e7 + 1.17145e8i −0.216079 + 1.07250i
\(199\) 1.99765e8 1.79694 0.898469 0.439037i \(-0.144680\pi\)
0.898469 + 0.439037i \(0.144680\pi\)
\(200\) 3.05052e7 9.38853e7i 0.269630 0.829837i
\(201\) −2.76386e6 + 9.34844e7i −0.0240065 + 0.811994i
\(202\) −8.73386e7 6.34552e7i −0.745550 0.541674i
\(203\) −5.43122e6 + 1.76471e6i −0.0455682 + 0.0148060i
\(204\) 8.82793e6 + 3.15972e6i 0.0728036 + 0.0260581i
\(205\) −7.23410e6 + 9.95689e6i −0.0586470 + 0.0807207i
\(206\) 9.59337e7 6.96999e7i 0.764603 0.555516i
\(207\) 626327. 1.05832e7i 0.00490800 0.0829314i
\(208\) 4.32297e7i 0.333089i
\(209\) 1.42101e8 + 1.37245e8i 1.07667 + 1.03988i
\(210\) −689302. + 892064.i −0.00513620 + 0.00664704i
\(211\) 1.84966e8 + 6.00991e7i 1.35551 + 0.440432i 0.894542 0.446984i \(-0.147502\pi\)
0.460969 + 0.887416i \(0.347502\pi\)
\(212\) −1.17991e7 1.62400e7i −0.0850496 0.117061i
\(213\) −7.65272e7 2.61592e8i −0.542610 1.85479i
\(214\) −4.87446e7 1.50021e8i −0.340000 1.04641i
\(215\) 1.12378e6 + 3.45864e6i 0.00771163 + 0.0237340i
\(216\) −6.68647e7 1.11636e8i −0.451449 0.753730i
\(217\) 1.06927e7 + 1.47173e7i 0.0710363 + 0.0977730i
\(218\) 1.55662e8 + 5.05777e7i 1.01762 + 0.330644i
\(219\) 4.40337e7 + 3.40251e7i 0.283290 + 0.218900i
\(220\) −2.55472e6 359231.i −0.0161757 0.00227455i
\(221\) 1.81203e7i 0.112925i
\(222\) −1.12143e7 1.64356e7i −0.0687920 0.100821i
\(223\) −1.20937e8 + 8.78660e7i −0.730286 + 0.530584i −0.889654 0.456635i \(-0.849054\pi\)
0.159368 + 0.987219i \(0.449054\pi\)
\(224\) 3.55577e6 4.89410e6i 0.0211381 0.0290941i
\(225\) 1.42930e8 9.14534e7i 0.836534 0.535255i
\(226\) 2.41353e8 7.84203e7i 1.39083 0.451907i
\(227\) −7.62175e7 5.53752e7i −0.432478 0.314214i 0.350161 0.936690i \(-0.386127\pi\)
−0.782639 + 0.622476i \(0.786127\pi\)
\(228\) 5.27344e7 + 1.55909e6i 0.294660 + 0.00871160i
\(229\) −6.60028e7 + 2.03136e8i −0.363193 + 1.11779i 0.587911 + 0.808926i \(0.299950\pi\)
−0.951105 + 0.308869i \(0.900050\pi\)
\(230\) 1.39106e6 0.00753874
\(231\) 1.53553e7 + 8.06088e6i 0.0819626 + 0.0430270i
\(232\) 8.64924e7 0.454747
\(233\) 2.63312e7 8.10392e7i 0.136372 0.419710i −0.859429 0.511255i \(-0.829181\pi\)
0.995801 + 0.0915453i \(0.0291806\pi\)
\(234\) −3.91340e7 + 4.76647e7i −0.199664 + 0.243188i
\(235\) 1.94062e6 + 1.40994e6i 0.00975447 + 0.00708703i
\(236\) 2.13290e7 6.93021e6i 0.105628 0.0343205i
\(237\) −1.10119e8 + 3.07662e8i −0.537333 + 1.50125i
\(238\) 4.86118e6 6.69084e6i 0.0233734 0.0321707i
\(239\) −1.74301e7 + 1.26637e7i −0.0825861 + 0.0600023i −0.628312 0.777961i \(-0.716254\pi\)
0.545726 + 0.837964i \(0.316254\pi\)
\(240\) 1.69937e7 1.15952e7i 0.0793504 0.0541425i
\(241\) 4.01333e8i 1.84691i 0.383707 + 0.923455i \(0.374647\pi\)
−0.383707 + 0.923455i \(0.625353\pi\)
\(242\) 8.38311e6 + 2.41061e8i 0.0380234 + 1.09339i
\(243\) 3.29352e7 2.21239e8i 0.147244 0.989100i
\(244\) −4.88227e7 1.58634e7i −0.215158 0.0699090i
\(245\) −1.11262e7 1.53139e7i −0.0483355 0.0665281i
\(246\) 2.94931e8 8.62804e7i 1.26313 0.369521i
\(247\) 3.15062e7 + 9.69662e7i 0.133032 + 0.409431i
\(248\) −8.51411e7 2.62037e8i −0.354453 1.09089i
\(249\) −1.28990e8 + 3.77354e7i −0.529492 + 0.154900i
\(250\) 2.62641e7 + 3.61495e7i 0.106310 + 0.146323i
\(251\) −1.57070e6 510352.i −0.00626954 0.00203710i 0.305881 0.952070i \(-0.401049\pi\)
−0.312150 + 0.950033i \(0.601049\pi\)
\(252\) 4.48148e6 1.16843e6i 0.0176409 0.00459941i
\(253\) −3.71443e6 2.10745e7i −0.0144202 0.0818154i
\(254\) 3.59444e8i 1.37630i
\(255\) 7.12313e6 4.86026e6i 0.0269017 0.0183556i
\(256\) −1.23657e8 + 8.98422e7i −0.460659 + 0.334688i
\(257\) −2.38482e8 + 3.28243e8i −0.876375 + 1.20623i 0.101037 + 0.994883i \(0.467784\pi\)
−0.977412 + 0.211344i \(0.932216\pi\)
\(258\) 3.05983e7 8.54887e7i 0.110925 0.309913i
\(259\) −2.74625e6 + 892312.i −0.00982181 + 0.00319130i
\(260\) −1.07715e6 782593.i −0.00380074 0.00276140i
\(261\) 1.14905e8 + 9.43399e7i 0.400034 + 0.328438i
\(262\) 1.77773e8 5.47128e8i 0.610676 1.87947i
\(263\) −4.07516e8 −1.38134 −0.690669 0.723171i \(-0.742684\pi\)
−0.690669 + 0.723171i \(0.742684\pi\)
\(264\) −1.83456e8 1.87978e8i −0.613645 0.628772i
\(265\) −1.84615e7 −0.0609407
\(266\) 1.43799e7 4.42566e7i 0.0468456 0.144176i
\(267\) 3.17098e8 + 9.37496e6i 1.01954 + 0.0301426i
\(268\) 4.07852e7 + 2.96322e7i 0.129429 + 0.0940356i
\(269\) −1.47913e8 + 4.80599e7i −0.463313 + 0.150539i −0.531366 0.847142i \(-0.678321\pi\)
0.0680535 + 0.997682i \(0.478321\pi\)
\(270\) 2.92338e7 + 2.59894e6i 0.0903881 + 0.00803568i
\(271\) 7.51288e7 1.03406e8i 0.229305 0.315612i −0.678824 0.734301i \(-0.737510\pi\)
0.908130 + 0.418689i \(0.137510\pi\)
\(272\) −1.22099e8 + 8.87102e7i −0.367893 + 0.267290i
\(273\) 5.04453e6 + 7.39318e6i 0.0150055 + 0.0219919i
\(274\) 2.13028e8i 0.625619i
\(275\) 2.37941e8 2.46360e8i 0.689931 0.714341i
\(276\) −4.52198e6 3.49416e6i −0.0129463 0.0100037i
\(277\) −5.06250e8 1.64491e8i −1.43115 0.465010i −0.512026 0.858970i \(-0.671105\pi\)
−0.919127 + 0.393960i \(0.871105\pi\)
\(278\) −1.11164e8 1.53004e8i −0.310318 0.427116i
\(279\) 1.72703e8 4.40982e8i 0.476085 1.21564i
\(280\) −765729. 2.35667e6i −0.00208460 0.00641573i
\(281\) 9.51532e7 + 2.92852e8i 0.255830 + 0.787364i 0.993665 + 0.112383i \(0.0358482\pi\)
−0.737835 + 0.674981i \(0.764152\pi\)
\(282\) −1.68163e7 5.74827e7i −0.0446537 0.152639i
\(283\) −2.99703e8 4.12506e8i −0.786030 1.08188i −0.994591 0.103868i \(-0.966878\pi\)
0.208561 0.978009i \(-0.433122\pi\)
\(284\) −1.39726e8 4.53998e7i −0.361963 0.117609i
\(285\) 2.96670e7 3.83937e7i 0.0759131 0.0982433i
\(286\) −5.45780e7 + 1.11881e8i −0.137955 + 0.282797i
\(287\) 4.45963e7i 0.111356i
\(288\) −1.57214e8 9.30418e6i −0.387809 0.0229511i
\(289\) 2.80792e8 2.04007e8i 0.684292 0.497167i
\(290\) −1.14662e7 + 1.57818e7i −0.0276074 + 0.0379983i
\(291\) 3.07498e8 + 1.10061e8i 0.731505 + 0.261822i
\(292\) 2.85280e7 9.26930e6i 0.0670550 0.0217875i
\(293\) 3.56249e8 + 2.58830e8i 0.827402 + 0.601143i 0.918823 0.394670i \(-0.129141\pi\)
−0.0914212 + 0.995812i \(0.529141\pi\)
\(294\) −1.39669e7 + 4.72416e8i −0.0320542 + 1.08420i
\(295\) 6.37360e6 1.96159e7i 0.0144547 0.0444869i
\(296\) 4.37342e7 0.0980166
\(297\) −3.86866e7 4.49829e8i −0.0856865 0.996322i
\(298\) −4.25618e8 −0.931671
\(299\) 3.41275e6 1.05034e7i 0.00738337 0.0227237i
\(300\) 2.70299e6 9.14255e7i 0.00577989 0.195498i
\(301\) −1.06608e7 7.74552e6i −0.0225324 0.0163707i
\(302\) −1.84007e8 + 5.97875e7i −0.384424 + 0.124907i
\(303\) 3.84023e8 + 1.37450e8i 0.793063 + 0.283855i
\(304\) −4.99140e8 + 6.87008e8i −1.01898 + 1.40250i
\(305\) −3.81955e7 + 2.77506e7i −0.0770836 + 0.0560045i
\(306\) −2.14931e8 1.27199e7i −0.428819 0.0253782i
\(307\) 7.22073e8i 1.42428i −0.702036 0.712142i \(-0.747725\pi\)
0.702036 0.712142i \(-0.252275\pi\)
\(308\) 8.25430e6 4.38812e6i 0.0160973 0.00855758i
\(309\) −2.73935e8 + 3.54515e8i −0.528194 + 0.683565i
\(310\) 5.90996e7 + 1.92026e7i 0.112673 + 0.0366096i
\(311\) −4.59600e8 6.32585e8i −0.866400 1.19250i −0.980005 0.198971i \(-0.936240\pi\)
0.113606 0.993526i \(-0.463760\pi\)
\(312\) −3.80611e7 1.30103e8i −0.0709479 0.242520i
\(313\) 1.80168e8 + 5.54501e8i 0.332103 + 1.02211i 0.968131 + 0.250443i \(0.0805761\pi\)
−0.636028 + 0.771666i \(0.719424\pi\)
\(314\) −2.17222e8 6.68541e8i −0.395959 1.21864i
\(315\) 1.55323e6 3.96603e6i 0.00279993 0.00714940i
\(316\) 1.03534e8 + 1.42503e8i 0.184578 + 0.254050i
\(317\) 7.53030e8 + 2.44674e8i 1.32771 + 0.431401i 0.885138 0.465330i \(-0.154064\pi\)
0.442577 + 0.896730i \(0.354064\pi\)
\(318\) 3.64746e8 + 2.81841e8i 0.636057 + 0.491484i
\(319\) 2.69710e8 + 1.31571e8i 0.465190 + 0.226930i
\(320\) 3.56444e7i 0.0608087i
\(321\) 3.35904e8 + 4.92295e8i 0.566822 + 0.830727i
\(322\) −4.07791e6 + 2.96277e6i −0.00680678 + 0.00494541i
\(323\) −2.09221e8 + 2.87968e8i −0.345459 + 0.475484i
\(324\) −8.85031e7 8.18796e7i −0.144561 0.133742i
\(325\) 1.68110e8 5.46224e7i 0.271646 0.0882630i
\(326\) 9.96507e8 + 7.24005e8i 1.59301 + 1.15739i
\(327\) −6.18116e8 1.82745e7i −0.977582 0.0289021i
\(328\) −2.08722e8 + 6.42380e8i −0.326595 + 1.00516i
\(329\) −8.69194e6 −0.0134565
\(330\) 5.86198e7 8.55421e6i 0.0897936 0.0131033i
\(331\) 7.12002e8 1.07915 0.539577 0.841936i \(-0.318584\pi\)
0.539577 + 0.841936i \(0.318584\pi\)
\(332\) −2.23865e7 + 6.88987e7i −0.0335741 + 0.103330i
\(333\) 5.81007e7 + 4.77022e7i 0.0862237 + 0.0707919i
\(334\) 7.80624e8 + 5.67156e8i 1.14638 + 0.832895i
\(335\) 4.40951e7 1.43274e7i 0.0640817 0.0208214i
\(336\) −2.51210e7 + 7.01856e7i −0.0361285 + 0.100939i
\(337\) 1.54675e8 2.12892e8i 0.220148 0.303008i −0.684630 0.728891i \(-0.740036\pi\)
0.904778 + 0.425882i \(0.140036\pi\)
\(338\) 5.76376e8 4.18762e8i 0.811891 0.589873i
\(339\) −7.92005e8 + 5.40402e8i −1.10415 + 0.753386i
\(340\) 4.64825e6i 0.00641377i
\(341\) 1.33110e8 9.46630e8i 0.181790 1.29283i
\(342\) −1.17227e9 + 3.05639e8i −1.58466 + 0.413159i
\(343\) 1.31030e8 + 4.25742e7i 0.175324 + 0.0569662i
\(344\) 1.17311e8 + 1.61464e8i 0.155375 + 0.213856i
\(345\) −5.04427e6 + 1.47567e6i −0.00661350 + 0.00193474i
\(346\) 2.12738e8 + 6.54741e8i 0.276108 + 0.849773i
\(347\) −3.09637e8 9.52966e8i −0.397833 1.22440i −0.926734 0.375719i \(-0.877396\pi\)
0.528901 0.848683i \(-0.322604\pi\)
\(348\) 7.69152e7 2.25011e7i 0.0978329 0.0286205i
\(349\) −5.45322e8 7.50571e8i −0.686695 0.945155i 0.313295 0.949656i \(-0.398567\pi\)
−0.999990 + 0.00450133i \(0.998567\pi\)
\(350\) −7.67277e7 2.49303e7i −0.0956564 0.0310807i
\(351\) 9.13439e7 2.14356e8i 0.112747 0.264583i
\(352\) −3.13064e8 + 5.51784e7i −0.382591 + 0.0674325i
\(353\) 1.76805e8i 0.213936i −0.994262 0.106968i \(-0.965886\pi\)
0.994262 0.106968i \(-0.0341142\pi\)
\(354\) −4.25389e8 + 2.90252e8i −0.509653 + 0.347747i
\(355\) −1.09312e8 + 7.94200e7i −0.129679 + 0.0942172i
\(356\) 1.00512e8 1.38343e8i 0.118071 0.162511i
\(357\) −1.05298e7 + 2.94192e7i −0.0122485 + 0.0342209i
\(358\) 6.85994e8 2.22893e8i 0.790187 0.256747i
\(359\) 6.43861e8 + 4.67792e8i 0.734448 + 0.533608i 0.890968 0.454067i \(-0.150027\pi\)
−0.156519 + 0.987675i \(0.550027\pi\)
\(360\) −4.09352e7 + 4.98586e7i −0.0462422 + 0.0563224i
\(361\) −3.42675e8 + 1.05465e9i −0.383361 + 1.17986i
\(362\) 8.10071e8 0.897518
\(363\) −2.86123e8 8.65244e8i −0.313964 0.949435i
\(364\) 4.82448e6 0.00524319
\(365\) 8.52483e6 2.62367e7i 0.00917616 0.0282413i
\(366\) 1.17828e9 + 3.48358e7i 1.25622 + 0.0371400i
\(367\) −4.45239e8 3.23485e8i −0.470177 0.341604i 0.327333 0.944909i \(-0.393850\pi\)
−0.797510 + 0.603305i \(0.793850\pi\)
\(368\) 8.74819e7 2.84246e7i 0.0915062 0.0297322i
\(369\) −9.77950e8 + 6.25740e8i −1.01327 + 0.648338i
\(370\) −5.79777e6 + 7.97994e6i −0.00595052 + 0.00819018i
\(371\) 5.41201e7 3.93206e7i 0.0550237 0.0399771i
\(372\) −1.43883e8 2.10873e8i −0.144914 0.212383i
\(373\) 1.28850e9i 1.28559i −0.766038 0.642796i \(-0.777774\pi\)
0.766038 0.642796i \(-0.222226\pi\)
\(374\) −4.27997e8 + 7.54355e7i −0.423049 + 0.0745634i
\(375\) −1.33587e8 1.03224e8i −0.130815 0.101081i
\(376\) 1.25201e8 + 4.06804e7i 0.121465 + 0.0394664i
\(377\) 9.10318e7 + 1.25295e8i 0.0874981 + 0.120431i
\(378\) −9.12343e7 + 5.46451e7i −0.0868834 + 0.0520391i
\(379\) 7.67116e7 + 2.36094e8i 0.0723809 + 0.222765i 0.980702 0.195508i \(-0.0626355\pi\)
−0.908321 + 0.418273i \(0.862635\pi\)
\(380\) −8.08204e6 2.48740e7i −0.00755577 0.0232543i
\(381\) −3.81307e8 1.30342e9i −0.353214 1.20738i
\(382\) −7.25676e8 9.98807e8i −0.666071 0.916769i
\(383\) −6.09690e8 1.98100e8i −0.554515 0.180173i 0.0183365 0.999832i \(-0.494163\pi\)
−0.572852 + 0.819659i \(0.694163\pi\)
\(384\) 8.07726e8 1.04532e9i 0.727956 0.942087i
\(385\) 1.19714e6 8.51365e6i 0.00106914 0.00760332i
\(386\) 1.38790e9i 1.22829i
\(387\) −2.02672e7 + 3.42459e8i −0.0177748 + 0.300345i
\(388\) 1.42427e8 1.03479e8i 0.123789 0.0899378i
\(389\) −7.88128e8 + 1.08477e9i −0.678849 + 0.934356i −0.999919 0.0126995i \(-0.995957\pi\)
0.321070 + 0.947055i \(0.395957\pi\)
\(390\) 2.87850e7 + 1.03028e7i 0.0245720 + 0.00879487i
\(391\) 3.66691e7 1.19145e7i 0.0310229 0.0100799i
\(392\) −8.40439e8 6.10614e8i −0.704701 0.511995i
\(393\) −6.42322e7 + 2.17258e9i −0.0533800 + 1.80552i
\(394\) 6.27217e8 1.93038e9i 0.516632 1.59003i
\(395\) 1.61996e8 0.132256
\(396\) −2.12045e8 1.19437e8i −0.171591 0.0966511i
\(397\) −1.02794e9 −0.824516 −0.412258 0.911067i \(-0.635260\pi\)
−0.412258 + 0.911067i \(0.635260\pi\)
\(398\) −7.64086e8 + 2.35161e9i −0.607507 + 1.86971i
\(399\) −5.19568e6 + 1.75738e8i −0.00409484 + 0.138503i
\(400\) 1.19107e9 + 8.65360e8i 0.930520 + 0.676062i
\(401\) −5.92566e7 + 1.92536e7i −0.0458914 + 0.0149110i −0.331873 0.943324i \(-0.607680\pi\)
0.285981 + 0.958235i \(0.407680\pi\)
\(402\) −1.08992e9 3.90107e8i −0.836764 0.299497i
\(403\) 2.89983e8 3.99127e8i 0.220701 0.303769i
\(404\) 1.77872e8 1.29231e8i 0.134206 0.0975063i
\(405\) −1.08765e8 + 2.15876e7i −0.0813570 + 0.0161478i
\(406\) 7.06858e7i 0.0524193i
\(407\) 1.36377e8 + 6.65276e7i 0.100267 + 0.0489127i
\(408\) 2.89364e8 3.74481e8i 0.210928 0.272973i
\(409\) 6.60140e8 + 2.14492e8i 0.477094 + 0.155017i 0.537686 0.843145i \(-0.319299\pi\)
−0.0605914 + 0.998163i \(0.519299\pi\)
\(410\) −8.95417e7 1.23244e8i −0.0641626 0.0883123i
\(411\) 2.25986e8 + 7.72483e8i 0.160559 + 0.548836i
\(412\) 7.46270e7 + 2.29678e8i 0.0525721 + 0.161800i
\(413\) 2.30950e7 + 7.10792e7i 0.0161322 + 0.0496497i
\(414\) 1.22188e8 + 4.78529e7i 0.0846308 + 0.0331441i
\(415\) 3.91618e7 + 5.39016e7i 0.0268964 + 0.0370197i
\(416\) −1.56029e8 5.06968e7i −0.106262 0.0345266i
\(417\) 5.65413e8 + 4.36898e8i 0.381847 + 0.295056i
\(418\) −2.15916e9 + 1.14785e9i −1.44600 + 0.768717i
\(419\) 1.30782e9i 0.868557i −0.900779 0.434278i \(-0.857003\pi\)
0.900779 0.434278i \(-0.142997\pi\)
\(420\) −1.29403e6 1.89652e6i −0.000852261 0.00124906i
\(421\) −1.17002e9 + 8.50069e8i −0.764198 + 0.555223i −0.900195 0.435487i \(-0.856576\pi\)
0.135997 + 0.990709i \(0.456576\pi\)
\(422\) −1.41496e9 + 1.94753e9i −0.916540 + 1.26151i
\(423\) 1.21958e8 + 1.90605e8i 0.0783466 + 0.122445i
\(424\) −9.63594e8 + 3.13091e8i −0.613922 + 0.199475i
\(425\) 4.99250e8 + 3.62727e8i 0.315469 + 0.229202i
\(426\) 3.37215e9 + 9.96972e7i 2.11336 + 0.0624812i
\(427\) 5.28652e7 1.62702e8i 0.0328603 0.101134i
\(428\) 3.21251e8 0.198057
\(429\) 7.92248e7 4.63601e8i 0.0484463 0.283494i
\(430\) −4.50132e7 −0.0273023
\(431\) 5.56675e8 1.71327e9i 0.334912 1.03075i −0.631853 0.775088i \(-0.717705\pi\)
0.966765 0.255666i \(-0.0822947\pi\)
\(432\) 1.89157e9 4.33911e8i 1.12883 0.258945i
\(433\) 2.65990e7 + 1.93253e7i 0.0157455 + 0.0114398i 0.595630 0.803259i \(-0.296902\pi\)
−0.579885 + 0.814699i \(0.696902\pi\)
\(434\) −2.14150e8 + 6.95815e7i −0.125749 + 0.0408583i
\(435\) 2.48369e7 6.93916e7i 0.0144672 0.0404199i
\(436\) −1.95927e8 + 2.69671e8i −0.113212 + 0.155823i
\(437\) 1.75510e8 1.27515e8i 0.100604 0.0730932i
\(438\) −5.68967e8 + 3.88218e8i −0.323540 + 0.220758i
\(439\) 1.20890e9i 0.681969i −0.940069 0.340985i \(-0.889240\pi\)
0.940069 0.340985i \(-0.110760\pi\)
\(440\) −5.70900e7 + 1.17030e8i −0.0319504 + 0.0654959i
\(441\) −4.50504e8 1.72789e9i −0.250129 0.959360i
\(442\) −2.13310e8 6.93088e7i −0.117499 0.0381777i
\(443\) 2.05301e9 + 2.82572e9i 1.12196 + 1.54425i 0.802506 + 0.596644i \(0.203500\pi\)
0.319455 + 0.947602i \(0.396500\pi\)
\(444\) 3.88915e7 1.13775e7i 0.0210870 0.00616889i
\(445\) −4.85983e7 1.49570e8i −0.0261433 0.0804609i
\(446\) −5.71776e8 1.75974e9i −0.305178 0.939242i
\(447\) 1.54338e9 4.51506e8i 0.817326 0.239104i
\(448\) −7.59176e7 1.04492e8i −0.0398905 0.0549046i
\(449\) 9.52621e8 + 3.09525e8i 0.496659 + 0.161374i 0.546626 0.837377i \(-0.315912\pi\)
−0.0499677 + 0.998751i \(0.515912\pi\)
\(450\) 5.29886e8 + 2.03236e9i 0.274119 + 1.05137i
\(451\) −1.62804e9 + 1.68564e9i −0.835692 + 0.865259i
\(452\) 5.16829e8i 0.263246i
\(453\) 6.03823e8 4.12001e8i 0.305187 0.208236i
\(454\) 9.43399e8 6.85420e8i 0.473151 0.343764i
\(455\) 2.60800e6 3.58961e6i 0.00129798 0.00178652i
\(456\) 8.97338e8 2.50707e9i 0.443179 1.23820i
\(457\) 7.66775e8 2.49140e8i 0.375804 0.122106i −0.115024 0.993363i \(-0.536694\pi\)
0.490828 + 0.871257i \(0.336694\pi\)
\(458\) −2.13884e9 1.55396e9i −1.04028 0.755806i
\(459\) 7.92877e8 1.81879e8i 0.382703 0.0877888i
\(460\) −875445. + 2.69434e6i −0.000419350 + 0.00129063i
\(461\) 3.76059e9 1.78773 0.893867 0.448332i \(-0.147982\pi\)
0.893867 + 0.448332i \(0.147982\pi\)
\(462\) −1.53625e8 + 1.49929e8i −0.0724794 + 0.0707357i
\(463\) 2.29194e9 1.07318 0.536588 0.843845i \(-0.319713\pi\)
0.536588 + 0.843845i \(0.319713\pi\)
\(464\) −3.98609e8 + 1.22679e9i −0.185240 + 0.570109i
\(465\) −2.34678e8 6.93822e6i −0.108240 0.00320010i
\(466\) 8.53272e8 + 6.19938e8i 0.390604 + 0.283790i
\(467\) −2.17221e9 + 7.05794e8i −0.986944 + 0.320678i −0.757637 0.652676i \(-0.773646\pi\)
−0.229308 + 0.973354i \(0.573646\pi\)
\(468\) −6.76932e7 1.05796e8i −0.0305270 0.0477098i
\(469\) −9.87498e7 + 1.35917e8i −0.0442009 + 0.0608373i
\(470\) −2.40205e7 + 1.74519e7i −0.0106718 + 0.00775355i
\(471\) 1.49690e9 + 2.19383e9i 0.660114 + 0.967453i
\(472\) 1.13194e9i 0.495479i
\(473\) 1.20195e8 + 6.81946e8i 0.0522241 + 0.296303i
\(474\) −3.20057e9 2.47310e9i −1.38039 1.06664i
\(475\) 3.30230e9 + 1.07298e9i 1.41380 + 0.459372i
\(476\) 9.90015e6 + 1.36264e7i 0.00420743 + 0.00579104i
\(477\) −1.62163e9 6.35082e8i −0.684127 0.267926i
\(478\) −8.24072e7 2.53623e8i −0.0345118 0.106216i
\(479\) 8.32601e8 + 2.56248e9i 0.346149 + 1.06534i 0.960966 + 0.276667i \(0.0892298\pi\)
−0.614817 + 0.788670i \(0.710770\pi\)
\(480\) 2.19214e7 + 7.49334e7i 0.00904738 + 0.0309265i
\(481\) 4.60295e7 + 6.33541e7i 0.0188594 + 0.0259578i
\(482\) −4.72446e9 1.53507e9i −1.92171 0.624402i
\(483\) 1.16443e7 1.50696e7i 0.00470218 0.00608535i
\(484\) −4.72186e8 1.35471e8i −0.189302 0.0543111i
\(485\) 1.61910e8i 0.0644432i
\(486\) 2.47844e9 + 1.23393e9i 0.979379 + 0.487602i
\(487\) −4.06454e9 + 2.95306e9i −1.59463 + 1.15857i −0.697710 + 0.716381i \(0.745797\pi\)
−0.896923 + 0.442187i \(0.854203\pi\)
\(488\) −1.52297e9 + 2.09619e9i −0.593230 + 0.816511i
\(489\) −4.38158e9 1.56827e9i −1.69453 0.606512i
\(490\) 2.22831e8 7.24022e7i 0.0855637 0.0278013i
\(491\) −5.71415e8 4.15157e8i −0.217854 0.158280i 0.473506 0.880791i \(-0.342988\pi\)
−0.691360 + 0.722510i \(0.742988\pi\)
\(492\) −1.84943e7 + 6.25549e8i −0.00700100 + 0.236801i
\(493\) −1.67082e8 + 5.14225e8i −0.0628008 + 0.193281i
\(494\) −1.26199e9 −0.470989
\(495\) −2.03493e8 + 9.32047e7i −0.0754103 + 0.0345398i
\(496\) 4.10907e9 1.51202
\(497\) 1.51296e8 4.65640e8i 0.0552814 0.170139i
\(498\) 4.91604e7 1.66280e9i 0.0178366 0.603305i
\(499\) 4.98225e8 + 3.61982e8i 0.179504 + 0.130417i 0.673909 0.738814i \(-0.264614\pi\)
−0.494405 + 0.869232i \(0.664614\pi\)
\(500\) −8.65468e7 + 2.81207e7i −0.0309639 + 0.0100608i
\(501\) −3.43235e9 1.22852e9i −1.21944 0.436465i
\(502\) 1.20156e7 1.65381e7i 0.00423920 0.00583476i
\(503\) −1.93905e9 + 1.40880e9i −0.679361 + 0.493585i −0.873146 0.487459i \(-0.837924\pi\)
0.193784 + 0.981044i \(0.437924\pi\)
\(504\) 1.38098e7 2.33347e8i 0.00480487 0.0811887i
\(505\) 2.02203e8i 0.0698663i
\(506\) 2.62294e8 + 3.68824e7i 0.0900041 + 0.0126559i
\(507\) −1.64582e9 + 2.12995e9i −0.560861 + 0.725841i
\(508\) −6.96205e8 2.26211e8i −0.235621 0.0765579i
\(509\) −9.06159e8 1.24722e9i −0.304573 0.419209i 0.629106 0.777320i \(-0.283421\pi\)
−0.933679 + 0.358110i \(0.883421\pi\)
\(510\) 2.99692e7 + 1.02443e8i 0.0100041 + 0.0341969i
\(511\) 3.08901e7 + 9.50699e7i 0.0102411 + 0.0315188i
\(512\) 5.32693e8 + 1.63946e9i 0.175401 + 0.539829i
\(513\) 3.92665e9 2.35188e9i 1.28414 0.769138i
\(514\) −2.95187e9 4.06290e9i −0.958795 1.31967i
\(515\) 2.11232e8 + 6.86333e7i 0.0681449 + 0.0221416i
\(516\) 1.46326e8 + 1.13067e8i 0.0468865 + 0.0362294i
\(517\) 3.28535e8 + 3.17308e8i 0.104560 + 0.100987i
\(518\) 3.57417e7i 0.0112985i
\(519\) −1.46600e9 2.14855e9i −0.460307 0.674619i
\(520\) −5.43668e7 + 3.94998e7i −0.0169559 + 0.0123192i
\(521\) 3.52050e9 4.84556e9i 1.09062 1.50111i 0.243352 0.969938i \(-0.421753\pi\)
0.847266 0.531168i \(-0.178247\pi\)
\(522\) −1.55006e9 + 9.91807e8i −0.476983 + 0.305197i
\(523\) −1.37872e9 + 4.47974e8i −0.421425 + 0.136929i −0.512050 0.858956i \(-0.671114\pi\)
0.0906246 + 0.995885i \(0.471114\pi\)
\(524\) 9.47852e8 + 6.88655e8i 0.287793 + 0.209094i
\(525\) 3.04677e8 + 9.00774e6i 0.0918929 + 0.00271680i
\(526\) 1.55872e9 4.79725e9i 0.467001 1.43728i
\(527\) 1.72237e9 0.512612
\(528\) 3.51172e9 1.73578e9i 1.03825 0.513188i
\(529\) 3.38133e9 0.993098
\(530\) 7.06141e7 2.17328e8i 0.0206028 0.0634088i
\(531\) 1.23464e9 1.50378e9i 0.357857 0.435865i
\(532\) 7.66708e7 + 5.57046e7i 0.0220769 + 0.0160398i
\(533\) −1.15024e9 + 3.73736e8i −0.329036 + 0.106910i
\(534\) −1.32324e9 + 3.69699e9i −0.376048 + 1.05064i
\(535\) 1.73661e8 2.39024e8i 0.0490302 0.0674843i
\(536\) 2.05855e9 1.49562e9i 0.577411 0.419513i
\(537\) −2.25110e9 + 1.53597e9i −0.627314 + 0.428030i
\(538\) 1.92505e9i 0.532971i
\(539\) −1.69189e9 3.18255e9i −0.465385 0.875415i
\(540\) −2.34317e7 + 5.49871e7i −0.00640363 + 0.0150274i
\(541\) −1.15402e8 3.74964e7i −0.0313346 0.0101812i 0.293308 0.956018i \(-0.405244\pi\)
−0.324642 + 0.945837i \(0.605244\pi\)
\(542\) 9.29924e8 + 1.27993e9i 0.250871 + 0.345294i
\(543\) −2.93748e9 + 8.59345e8i −0.787365 + 0.230339i
\(544\) −1.76992e8 5.44725e8i −0.0471365 0.145071i
\(545\) 9.47322e7 + 2.91556e8i 0.0250674 + 0.0771497i
\(546\) −1.06327e8 + 3.11054e7i −0.0279556 + 0.00817826i
\(547\) −2.21161e9 3.04402e9i −0.577767 0.795229i 0.415681 0.909511i \(-0.363543\pi\)
−0.993448 + 0.114282i \(0.963543\pi\)
\(548\) 4.12613e8 + 1.34066e8i 0.107105 + 0.0348006i
\(549\) −4.30965e9 + 1.12363e9i −1.11157 + 0.289815i
\(550\) 1.99002e9 + 3.74334e9i 0.510021 + 0.959377i
\(551\) 3.04226e9i 0.774757i
\(552\) −2.38258e8 + 1.62568e8i −0.0602921 + 0.0411386i
\(553\) −4.74892e8 + 3.45030e8i −0.119415 + 0.0867598i
\(554\) 3.87274e9 5.33037e9i 0.967686 1.33191i
\(555\) 1.25585e7 3.50873e7i 0.00311827 0.00871214i
\(556\) 3.66312e8 1.19022e8i 0.0903836 0.0293674i
\(557\) 1.51252e8 + 1.09891e8i 0.0370858 + 0.0269444i 0.606174 0.795332i \(-0.292704\pi\)
−0.569088 + 0.822277i \(0.692704\pi\)
\(558\) 4.53063e9 + 3.71977e9i 1.10392 + 0.906350i
\(559\) −1.10433e8 + 3.39877e8i −0.0267397 + 0.0822962i
\(560\) 3.69555e7 0.00889244
\(561\) 1.47198e9 7.27575e8i 0.351992 0.173983i
\(562\) −3.81138e9 −0.905743
\(563\) 9.57946e8 2.94825e9i 0.226236 0.696283i −0.771928 0.635710i \(-0.780707\pi\)
0.998164 0.0605726i \(-0.0192927\pi\)
\(564\) 1.21921e8 + 3.60459e6i 0.0286156 + 0.000846016i
\(565\) 3.84541e8 + 2.79386e8i 0.0896961 + 0.0651680i
\(566\) 6.00233e9 1.95028e9i 1.39143 0.452104i
\(567\) 2.72865e8 2.94938e8i 0.0628648 0.0679501i
\(568\) −4.35862e9 + 5.99913e9i −0.997999 + 1.37363i
\(569\) −3.68369e9 + 2.67636e9i −0.838283 + 0.609048i −0.921890 0.387451i \(-0.873356\pi\)
0.0836077 + 0.996499i \(0.473356\pi\)
\(570\) 3.38493e8 + 4.96091e8i 0.0765575 + 0.112202i
\(571\) 4.33814e9i 0.975162i 0.873078 + 0.487581i \(0.162121\pi\)
−0.873078 + 0.487581i \(0.837879\pi\)
\(572\) −1.82354e8 1.76123e8i −0.0407408 0.0393486i
\(573\) 3.69101e9 + 2.85206e9i 0.819603 + 0.633312i
\(574\) 5.24984e8 + 1.70578e8i 0.115866 + 0.0376470i
\(575\) −2.21073e8 3.04281e8i −0.0484952 0.0667479i
\(576\) −1.22617e9 + 3.13094e9i −0.267346 + 0.682646i
\(577\) 1.44718e9 + 4.45395e9i 0.313622 + 0.965229i 0.976318 + 0.216340i \(0.0694120\pi\)
−0.662696 + 0.748888i \(0.730588\pi\)
\(578\) 1.32755e9 + 4.08577e9i 0.285958 + 0.880088i
\(579\) 1.47232e9 + 5.03280e9i 0.315229 + 1.07754i
\(580\) −2.33517e7 3.21408e7i −0.00496958 0.00684004i
\(581\) −2.29606e8 7.46035e7i −0.0485699 0.0157813i
\(582\) −2.47178e9 + 3.19887e9i −0.519733 + 0.672614i
\(583\) −3.48105e9 4.89487e8i −0.727563 0.102306i
\(584\) 1.51399e9i 0.314542i
\(585\) −1.15310e8 6.82420e6i −0.0238133 0.00140931i
\(586\) −4.40955e9 + 3.20372e9i −0.905216 + 0.657678i
\(587\) 3.45131e9 4.75032e9i 0.704288 0.969369i −0.295613 0.955308i \(-0.595524\pi\)
0.999901 0.0140615i \(-0.00447607\pi\)
\(588\) −9.06230e8 3.24361e8i −0.183831 0.0657972i
\(589\) 9.21683e9 2.99473e9i 1.85857 0.603885i
\(590\) 2.06539e8 + 1.50059e8i 0.0414018 + 0.0300802i
\(591\) −2.26624e8 + 7.66530e9i −0.0451595 + 1.52747i
\(592\) −2.01553e8 + 6.20317e8i −0.0399267 + 0.122882i
\(593\) −9.18277e8 −0.180835 −0.0904175 0.995904i \(-0.528820\pi\)
−0.0904175 + 0.995904i \(0.528820\pi\)
\(594\) 5.44332e9 + 1.26515e9i 1.06564 + 0.247679i
\(595\) 1.54904e7 0.00301476
\(596\) 2.67856e8 8.24377e8i 0.0518251 0.159501i
\(597\) 2.76077e8 9.33799e9i 0.0531031 1.79615i
\(598\) 1.10591e8 + 8.03491e7i 0.0211478 + 0.0153648i
\(599\) −2.31219e9 + 7.51276e8i −0.439572 + 0.142826i −0.520438 0.853899i \(-0.674231\pi\)
0.0808663 + 0.996725i \(0.474231\pi\)
\(600\) −4.34651e9 1.55571e9i −0.821507 0.294036i
\(601\) 1.01844e9 1.40176e9i 0.191370 0.263398i −0.702541 0.711644i \(-0.747951\pi\)
0.893910 + 0.448246i \(0.147951\pi\)
\(602\) 1.31956e8 9.58719e7i 0.0246515 0.0179103i
\(603\) 4.36610e9 + 2.58393e8i 0.810930 + 0.0479921i
\(604\) 3.94029e8i 0.0727611i
\(605\) −3.56049e8 + 2.78093e8i −0.0653681 + 0.0510560i
\(606\) −3.08691e9 + 3.99494e9i −0.563470 + 0.729217i
\(607\) −8.04951e9 2.61544e9i −1.46086 0.474662i −0.532528 0.846412i \(-0.678758\pi\)
−0.928333 + 0.371750i \(0.878758\pi\)
\(608\) −1.89426e9 2.60722e9i −0.341803 0.470452i
\(609\) 7.49854e7 + 2.56321e8i 0.0134529 + 0.0459858i
\(610\) −1.80583e8 5.55778e8i −0.0322124 0.0991395i
\(611\) 7.28420e7 + 2.24185e8i 0.0129193 + 0.0397614i
\(612\) 1.59901e8 4.08294e8i 0.0281982 0.0720018i
\(613\) −2.65558e9 3.65509e9i −0.465637 0.640894i 0.510029 0.860157i \(-0.329635\pi\)
−0.975666 + 0.219263i \(0.929635\pi\)
\(614\) 8.50018e9 + 2.76188e9i 1.48197 + 0.481521i
\(615\) 4.55437e8 + 3.51918e8i 0.0789523 + 0.0610069i
\(616\) −8.18991e7 4.64669e8i −0.0141171 0.0800962i
\(617\) 1.81137e9i 0.310462i 0.987878 + 0.155231i \(0.0496122\pi\)
−0.987878 + 0.155231i \(0.950388\pi\)
\(618\) −3.12554e9 4.58074e9i −0.532678 0.780685i
\(619\) 2.61871e9 1.90261e9i 0.443783 0.322427i −0.343353 0.939206i \(-0.611563\pi\)
0.787136 + 0.616779i \(0.211563\pi\)
\(620\) −7.43870e7 + 1.02385e8i −0.0125351 + 0.0172530i
\(621\) −4.93843e8 4.39036e7i −0.0827501 0.00735665i
\(622\) 9.20467e9 2.99078e9i 1.53370 0.498331i
\(623\) 4.61030e8 + 3.34958e8i 0.0763873 + 0.0554986i
\(624\) 2.02077e9 + 5.97439e7i 0.332944 + 0.00984345i
\(625\) 1.84725e9 5.68526e9i 0.302654 0.931473i
\(626\) −7.21667e9 −1.17578
\(627\) 6.61189e9 6.45281e9i 1.07125 1.04547i
\(628\) 1.43160e9 0.230655
\(629\) −8.44836e7 + 2.60014e8i −0.0135361 + 0.0416600i
\(630\) 4.07469e7 + 3.34542e7i 0.00649235 + 0.00533039i
\(631\) −3.59821e9 2.61425e9i −0.570143 0.414233i 0.265014 0.964245i \(-0.414623\pi\)
−0.835157 + 0.550011i \(0.814623\pi\)
\(632\) 8.45533e9 2.74730e9i 1.33236 0.432909i
\(633\) 3.06495e9 8.56316e9i 0.480298 1.34190i
\(634\) −5.76057e9 + 7.92875e9i −0.897745 + 1.23564i
\(635\) −5.44662e8 + 3.95720e8i −0.0844149 + 0.0613310i
\(636\) −7.75445e8 + 5.29103e8i −0.119523 + 0.0815531i
\(637\) 1.86014e9i 0.285139i
\(638\) −2.58046e9 + 2.67176e9i −0.393392 + 0.407310i
\(639\) −1.23339e10 + 3.21574e9i −1.87002 + 0.487560i
\(640\) −6.22838e8 2.02372e8i −0.0939171 0.0305155i
\(641\) 2.21117e8 + 3.04341e8i 0.0331603 + 0.0456412i 0.825275 0.564731i \(-0.191020\pi\)
−0.792115 + 0.610372i \(0.791020\pi\)
\(642\) −7.08007e9 + 2.07124e9i −1.05600 + 0.308928i
\(643\) 1.60346e9 + 4.93494e9i 0.237859 + 0.732055i 0.996729 + 0.0808129i \(0.0257516\pi\)
−0.758870 + 0.651242i \(0.774248\pi\)
\(644\) −3.17221e6 9.76306e6i −0.000468017 0.00144041i
\(645\) 1.63227e8 4.77511e7i 0.0239515 0.00700688i
\(646\) −2.58968e9 3.56439e9i −0.377948 0.520201i
\(647\) −4.37115e9 1.42027e9i −0.634499 0.206161i −0.0259322 0.999664i \(-0.508255\pi\)
−0.608567 + 0.793502i \(0.708255\pi\)
\(648\) −5.31082e9 + 2.97130e9i −0.766742 + 0.428978i
\(649\) 1.72188e9 3.52973e9i 0.247256 0.506857i
\(650\) 2.18791e9i 0.312487i
\(651\) 7.02737e8 4.79492e8i 0.0998296 0.0681159i
\(652\) −2.02946e9 + 1.47449e9i −0.286757 + 0.208341i
\(653\) 5.81194e9 7.99945e9i 0.816818 1.12425i −0.173417 0.984848i \(-0.555481\pi\)
0.990235 0.139405i \(-0.0445190\pi\)
\(654\) 2.57938e9 7.20652e9i 0.360573 1.00740i
\(655\) 1.02477e9 3.32969e8i 0.142490 0.0462977i
\(656\) −8.14948e9 5.92094e9i −1.12711 0.818894i
\(657\) 1.65136e9 2.01133e9i 0.227176 0.276697i
\(658\) 3.32460e7 1.02321e8i 0.00454935 0.0140015i
\(659\) −1.08516e10 −1.47705 −0.738526 0.674225i \(-0.764478\pi\)
−0.738526 + 0.674225i \(0.764478\pi\)
\(660\) −2.03229e7 + 1.18924e8i −0.00275158 + 0.0161015i
\(661\) 1.12206e10 1.51116 0.755582 0.655054i \(-0.227354\pi\)
0.755582 + 0.655054i \(0.227354\pi\)
\(662\) −2.72336e9 + 8.38163e9i −0.364839 + 1.12286i
\(663\) 8.47032e8 + 2.50424e7i 0.112876 + 0.00333717i
\(664\) 2.95816e9 + 2.14923e9i 0.392132 + 0.284901i
\(665\) 8.28929e7 2.69335e7i 0.0109305 0.00355155i
\(666\) −7.83777e8 + 5.01499e8i −0.102809 + 0.0657825i
\(667\) 1.93697e8 2.66601e8i 0.0252745 0.0347873i
\(668\) −1.58980e9 + 1.15506e9i −0.206359 + 0.149929i
\(669\) 3.94016e9 + 5.77464e9i 0.508771 + 0.745647i
\(670\) 5.73885e8i 0.0737163i
\(671\) −7.93780e9 + 4.21987e9i −1.01431 + 0.539225i
\(672\) −2.23861e8 1.72978e8i −0.0284567 0.0219887i
\(673\) −1.00907e10 3.27867e9i −1.27605 0.414615i −0.408866 0.912595i \(-0.634076\pi\)
−0.867189 + 0.497979i \(0.834076\pi\)
\(674\) 1.91452e9 + 2.63512e9i 0.240853 + 0.331505i
\(675\) −4.07745e9 6.80763e9i −0.510300 0.851987i
\(676\) 4.48364e8 + 1.37992e9i 0.0558235 + 0.171807i
\(677\) 2.14426e9 + 6.59936e9i 0.265593 + 0.817412i 0.991556 + 0.129678i \(0.0413945\pi\)
−0.725963 + 0.687734i \(0.758606\pi\)
\(678\) −3.33220e9 1.13904e10i −0.410608 1.40357i
\(679\) 3.44846e8 + 4.74640e8i 0.0422748 + 0.0581862i
\(680\) −2.23128e8 7.24988e7i −0.0272128 0.00884198i
\(681\) −2.69385e9 + 3.48625e9i −0.326857 + 0.423003i
\(682\) 1.06345e10 + 5.18775e9i 1.28373 + 0.626230i
\(683\) 5.96763e9i 0.716687i 0.933590 + 0.358344i \(0.116658\pi\)
−0.933590 + 0.358344i \(0.883342\pi\)
\(684\) 1.45759e8 2.46291e9i 0.0174156 0.294274i
\(685\) 3.22800e8 2.34528e8i 0.0383722 0.0278790i
\(686\) −1.00236e9 + 1.37963e9i −0.118547 + 0.163166i
\(687\) 9.40435e9 + 3.36603e9i 1.10657 + 0.396068i
\(688\) −2.83081e9 + 9.19787e8i −0.331399 + 0.107678i
\(689\) −1.46772e9 1.06636e9i −0.170952 0.124204i
\(690\) 1.92246e6 6.50251e7i 0.000222785 0.00753545i
\(691\) −6.99148e8 + 2.15176e9i −0.0806113 + 0.248096i −0.983238 0.182329i \(-0.941636\pi\)
0.902626 + 0.430425i \(0.141636\pi\)
\(692\) −1.40205e9 −0.160839
\(693\) 3.98027e8 7.06642e8i 0.0454303 0.0806553i
\(694\) 1.24026e10 1.40849
\(695\) 1.09463e8 3.36892e8i 0.0123686 0.0380666i
\(696\) 1.19533e8 4.04308e9i 0.0134387 0.454549i
\(697\) −3.41596e9 2.48184e9i −0.382118 0.277625i
\(698\) 1.09215e10 3.54860e9i 1.21559 0.394969i
\(699\) −3.75178e9 1.34285e9i −0.415497 0.148716i
\(700\) 9.65750e7 1.32924e8i 0.0106420 0.0146474i
\(701\) −4.67707e9 + 3.39809e9i −0.512815 + 0.372582i −0.813890 0.581019i \(-0.802654\pi\)
0.301076 + 0.953600i \(0.402654\pi\)
\(702\) 2.17400e9 + 1.89519e9i 0.237181 + 0.206763i
\(703\) 1.53829e9i 0.166992i
\(704\) −9.45070e8 + 6.72099e9i −0.102084 + 0.725988i
\(705\) 6.85897e7 8.87657e7i 0.00737220 0.00954077i
\(706\) 2.08134e9 + 6.76267e8i 0.222600 + 0.0723272i
\(707\) 4.30665e8 + 5.92760e8i 0.0458323 + 0.0630828i
\(708\) −2.94475e8 1.00660e9i −0.0311840 0.106596i
\(709\) 3.47138e9 + 1.06838e10i 0.365797 + 1.12581i 0.949481 + 0.313826i \(0.101611\pi\)
−0.583684 + 0.811981i \(0.698389\pi\)
\(710\) −5.16814e8 1.59059e9i −0.0541914 0.166784i
\(711\) 1.42294e10 + 5.57271e9i 1.48472 + 0.581464i
\(712\) −5.07314e9 6.98258e9i −0.526741 0.724997i
\(713\) −9.98365e8 3.24388e8i −0.103152 0.0335160i
\(714\) −3.06045e8 2.36482e8i −0.0314660 0.0243139i
\(715\) −2.29619e8 + 4.04709e7i −0.0234929 + 0.00414068i
\(716\) 1.46897e9i 0.149561i
\(717\) 5.67875e8 + 8.32270e8i 0.0575355 + 0.0843232i
\(718\) −7.96953e9 + 5.79020e9i −0.803521 + 0.583792i
\(719\) 3.37156e8 4.64056e8i 0.0338283 0.0465607i −0.791768 0.610822i \(-0.790839\pi\)
0.825596 + 0.564262i \(0.190839\pi\)
\(720\) −5.18530e8 8.10395e8i −0.0517738 0.0809157i
\(721\) −7.65406e8 + 2.48696e8i −0.0760534 + 0.0247112i
\(722\) −1.11045e10 8.06789e9i −1.09804 0.797774i
\(723\) 1.87603e10 + 5.54647e8i 1.84610 + 0.0545798i
\(724\) −5.09807e8 + 1.56902e9i −0.0499253 + 0.153654i
\(725\) 5.27437e9 0.514028
\(726\) 1.12800e10 5.87193e7i 1.09403 0.00569512i
\(727\) −2.00789e9 −0.193807 −0.0969034 0.995294i \(-0.530894\pi\)
−0.0969034 + 0.995294i \(0.530894\pi\)
\(728\) 7.52474e7 2.31588e8i 0.00722822 0.0222462i
\(729\) −1.02963e10 1.84531e9i −0.984317 0.176410i
\(730\) 2.76250e8 + 2.00707e8i 0.0262828 + 0.0190956i
\(731\) −1.18657e9 + 3.85540e8i −0.112353 + 0.0365056i
\(732\) −8.09009e8 + 2.26029e9i −0.0762368 + 0.212998i
\(733\) −1.47873e9 + 2.03529e9i −0.138683 + 0.190881i −0.872709 0.488240i \(-0.837639\pi\)
0.734026 + 0.679121i \(0.237639\pi\)
\(734\) 5.51104e9 4.00401e9i 0.514396 0.373731i
\(735\) −7.31225e8 + 4.98930e8i −0.0679274 + 0.0463483i
\(736\) 3.49082e8i 0.0322742i
\(737\) 8.69432e9 1.53239e9i 0.800018 0.141005i
\(738\) −3.62557e9 1.39058e10i −0.332032 1.27350i
\(739\) 8.90513e8 + 2.89345e8i 0.0811680 + 0.0263731i 0.349320 0.937004i \(-0.386413\pi\)
−0.268152 + 0.963377i \(0.586413\pi\)
\(740\) −1.18076e7 1.62517e7i −0.00107115 0.00147431i
\(741\) 4.57622e9 1.33875e9i 0.413184 0.120875i
\(742\) 2.55873e8 + 7.87496e8i 0.0229938 + 0.0707676i
\(743\) 1.93958e9 + 5.96941e9i 0.173479 + 0.533913i 0.999561 0.0296369i \(-0.00943508\pi\)
−0.826082 + 0.563550i \(0.809435\pi\)
\(744\) −1.23666e10 + 3.61778e9i −1.10089 + 0.322060i
\(745\) −4.68573e8 6.44935e8i −0.0415174 0.0571438i
\(746\) 1.51681e10 + 4.92841e9i 1.33766 + 0.434631i
\(747\) 1.58567e9 + 6.08179e9i 0.139185 + 0.533838i
\(748\) 1.23243e8 8.76461e8i 0.0107673 0.0765732i
\(749\) 1.07057e9i 0.0930958i
\(750\) 1.72610e9 1.17776e9i 0.149401 0.101939i
\(751\) −1.09516e10 + 7.95681e9i −0.943492 + 0.685487i −0.949259 0.314496i \(-0.898164\pi\)
0.00576642 + 0.999983i \(0.498164\pi\)
\(752\) −1.15401e9 + 1.58835e9i −0.0989569 + 0.136202i
\(753\) −2.60271e7 + 7.27171e7i −0.00222149 + 0.00620660i
\(754\) −1.82315e9 + 5.92376e8i −0.154890 + 0.0503267i
\(755\) −2.93174e8 2.13003e8i −0.0247919 0.0180124i
\(756\) −4.84249e7 2.11102e8i −0.00407608 0.0177691i
\(757\) 2.83725e9 8.73215e9i 0.237718 0.731620i −0.759031 0.651054i \(-0.774327\pi\)
0.996749 0.0805662i \(-0.0256728\pi\)
\(758\) −3.07270e9 −0.256258
\(759\) −9.90259e8 + 1.44506e8i −0.0822058 + 0.0119961i
\(760\) −1.32007e9 −0.109081
\(761\) −1.44458e9 + 4.44597e9i −0.118822 + 0.365696i −0.992725 0.120404i \(-0.961581\pi\)
0.873903 + 0.486100i \(0.161581\pi\)
\(762\) 1.68022e10 + 4.96754e8i 1.37570 + 0.0406724i
\(763\) −8.98682e8 6.52931e8i −0.0732437 0.0532147i
\(764\) 2.39128e9 7.76974e8i 0.194001 0.0630347i
\(765\) −2.17349e8 3.39687e8i −0.0175526 0.0274324i
\(766\) 4.66404e9 6.41950e9i 0.374940 0.516061i
\(767\) 1.63975e9 1.19135e9i 0.131218 0.0953353i
\(768\) 4.02877e9 + 5.90451e9i 0.320929 + 0.470348i
\(769\) 3.28283e9i 0.260319i 0.991493 + 0.130160i \(0.0415489\pi\)
−0.991493 + 0.130160i \(0.958451\pi\)
\(770\) 9.56430e7 + 4.66568e7i 0.00754980 + 0.00368296i
\(771\) 1.50141e10 + 1.16015e10i 1.17980 + 0.911639i
\(772\) 2.68821e9 + 8.73454e8i 0.210283 + 0.0683249i
\(773\) −1.32670e9 1.82604e9i −0.103310 0.142195i 0.754232 0.656608i \(-0.228010\pi\)
−0.857542 + 0.514414i \(0.828010\pi\)
\(774\) −3.95388e9 1.54846e9i −0.306499 0.120035i
\(775\) −5.19196e9 1.59792e10i −0.400660 1.23310i
\(776\) −2.74584e9 8.45083e9i −0.210940 0.649207i
\(777\) 3.79157e7 + 1.29607e8i 0.00289965 + 0.00991183i
\(778\) −9.75524e9 1.34269e10i −0.742693 1.02223i
\(779\) −2.25949e10 7.34153e9i −1.71249 0.556423i
\(780\) −3.80709e7 + 4.92696e7i −0.00287251 + 0.00371747i
\(781\) −2.27173e10 + 1.20769e10i −1.70639 + 0.907146i
\(782\) 4.77238e8i 0.0356871i
\(783\) 4.56871e9 5.24084e9i 0.340117 0.390153i
\(784\) 1.25341e10 9.10654e9i 0.928937 0.674912i
\(785\) 7.73890e8 1.06517e9i 0.0570999 0.0785913i
\(786\) −2.53298e10 9.06611e9i −1.86060 0.665951i
\(787\) 1.77503e10 5.76741e9i 1.29806 0.421764i 0.423151 0.906059i \(-0.360924\pi\)
0.874905 + 0.484295i \(0.160924\pi\)
\(788\) 3.34421e9 + 2.42971e9i 0.243473 + 0.176894i
\(789\) −5.63191e8 + 1.90493e10i −0.0408213 + 1.38073i
\(790\) −6.19623e8 + 1.90700e9i −0.0447129 + 0.137612i
\(791\) −1.72234e9 −0.123737
\(792\) −9.04056e9 + 8.31583e9i −0.646632 + 0.594795i
\(793\) −4.63949e9 −0.330380
\(794\) 3.93178e9 1.21008e10i 0.278752 0.857909i
\(795\) −2.55140e7 + 8.62984e8i −0.00180092 + 0.0609141i
\(796\) −4.07397e9 2.95991e9i −0.286300 0.208009i
\(797\) −1.85602e10 + 6.03059e9i −1.29861 + 0.421945i −0.875098 0.483945i \(-0.839203\pi\)
−0.423514 + 0.905890i \(0.639203\pi\)
\(798\) −2.04890e9 7.33348e8i −0.142729 0.0510858i
\(799\) −4.83716e8 + 6.65779e8i −0.0335488 + 0.0461760i
\(800\) −4.52014e9 + 3.28407e9i −0.312131 + 0.226776i
\(801\) 8.76464e8 1.48098e10i 0.0602588 1.01820i
\(802\) 7.71208e8i 0.0527912i
\(803\) 2.30306e9 4.72110e9i 0.156964 0.321765i
\(804\) 1.44152e9 1.86555e9i 0.0978194 0.126593i
\(805\) −8.97894e6 2.91743e6i −0.000606652 0.000197113i
\(806\) 3.58933e9 + 4.94029e9i 0.241457 + 0.332338i
\(807\) 2.04214e9 + 6.98062e9i 0.136782 + 0.467559i
\(808\) −3.42918e9 1.05539e10i −0.228692 0.703840i
\(809\) 4.79653e9 + 1.47622e10i 0.318498 + 0.980237i 0.974291 + 0.225295i \(0.0723347\pi\)
−0.655792 + 0.754941i \(0.727665\pi\)
\(810\) 1.61889e8 1.36294e9i 0.0107033 0.0901112i
\(811\) 9.93215e9 + 1.36704e10i 0.653838 + 0.899931i 0.999258 0.0385172i \(-0.0122634\pi\)
−0.345420 + 0.938448i \(0.612263\pi\)
\(812\) 1.36911e8 + 4.44851e7i 0.00897414 + 0.00291587i
\(813\) −4.72988e9 3.65480e9i −0.308697 0.238532i
\(814\) −1.30479e9 + 1.35095e9i −0.0847920 + 0.0877920i
\(815\) 2.30708e9i 0.149283i
\(816\) 3.97801e9 + 5.83012e9i 0.256301 + 0.375631i
\(817\) −5.67929e9 + 4.12625e9i −0.364349 + 0.264715i
\(818\) −5.04997e9 + 6.95069e9i −0.322591 + 0.444009i
\(819\) 3.52566e8 2.25589e8i 0.0224257 0.0143491i
\(820\) 2.95062e8 9.58715e7i 0.0186881 0.00607213i
\(821\) 8.07168e9 + 5.86442e9i 0.509053 + 0.369849i 0.812464 0.583011i \(-0.198126\pi\)
−0.303411 + 0.952860i \(0.598126\pi\)
\(822\) −9.95798e9 2.94407e8i −0.625345 0.0184883i
\(823\) 1.18344e9 3.64225e9i 0.0740025 0.227756i −0.907213 0.420672i \(-0.861794\pi\)
0.981215 + 0.192916i \(0.0617944\pi\)
\(824\) 1.21891e10 0.758974
\(825\) −1.11872e10 1.14630e10i −0.693640 0.710740i
\(826\) −9.25075e8 −0.0571145
\(827\) 8.33637e9 2.56567e10i 0.512516 1.57736i −0.275240 0.961376i \(-0.588757\pi\)
0.787756 0.615987i \(-0.211243\pi\)
\(828\) −1.69584e8 + 2.06551e8i −0.0103819 + 0.0126450i
\(829\) 8.50182e9 + 6.17693e9i 0.518288 + 0.376558i 0.815958 0.578111i \(-0.196210\pi\)
−0.297671 + 0.954669i \(0.596210\pi\)
\(830\) −7.84316e8 + 2.54840e8i −0.0476121 + 0.0154701i
\(831\) −8.38875e9 + 2.34373e10i −0.507100 + 1.41679i
\(832\) −2.05885e9 + 2.83377e9i −0.123935 + 0.170582i
\(833\) 5.25382e9 3.81712e9i 0.314933 0.228812i
\(834\) −7.30579e9 + 4.98490e9i −0.436100 + 0.297560i
\(835\) 1.80727e9i 0.107429i
\(836\) −8.64421e8 4.90445e9i −0.0511686 0.290314i
\(837\) −2.03750e10 8.68242e9i −1.20104 0.511801i
\(838\) 1.53955e10 + 5.00231e9i 0.903734 + 0.293641i
\(839\) −1.04462e10 1.43780e10i −0.610650 0.840488i 0.385980 0.922507i \(-0.373863\pi\)
−0.996631 + 0.0820188i \(0.973863\pi\)
\(840\) −1.11221e8 + 3.25370e7i −0.00647453 + 0.00189409i
\(841\) −3.90247e9 1.20106e10i −0.226232 0.696270i
\(842\) −5.53171e9 1.70248e10i −0.319350 0.982858i
\(843\) 1.38208e10 4.04321e9i 0.794580 0.232450i
\(844\) −2.88168e9 3.96629e9i −0.164986 0.227083i
\(845\) 1.26909e9 + 4.12353e8i 0.0723594 + 0.0235110i
\(846\) −2.71027e9 + 7.06634e8i −0.153892 + 0.0401234i
\(847\) 4.51460e8 1.57357e9i 0.0255286 0.0889802i
\(848\) 1.51103e10i 0.850920i
\(849\) −1.96968e10 + 1.34395e10i −1.10463 + 0.753715i
\(850\) −6.17958e9 + 4.48973e9i −0.345138 + 0.250758i
\(851\) 9.79412e7 1.34804e8i 0.00544768 0.00749809i
\(852\) −2.31532e9 + 6.46876e9i −0.128254 + 0.358329i
\(853\) −8.70100e9 + 2.82712e9i −0.480007 + 0.155964i −0.539019 0.842294i \(-0.681205\pi\)
0.0590123 + 0.998257i \(0.481205\pi\)
\(854\) 1.71311e9 + 1.24465e9i 0.0941203 + 0.0683824i
\(855\) −1.75371e9 1.43984e9i −0.0959570 0.0787832i
\(856\) 5.01055e9 1.54209e10i 0.273041 0.840333i
\(857\) 3.07682e10 1.66982 0.834908 0.550389i \(-0.185521\pi\)
0.834908 + 0.550389i \(0.185521\pi\)
\(858\) 5.15444e9 + 2.70587e9i 0.278597 + 0.146252i
\(859\) 1.27141e10 0.684401 0.342200 0.939627i \(-0.388828\pi\)
0.342200 + 0.939627i \(0.388828\pi\)
\(860\) 2.83284e7 8.71858e7i 0.00151872 0.00467414i
\(861\) −2.08465e9 6.16325e7i −0.111307 0.00329078i
\(862\) 1.80392e10 + 1.31063e10i 0.959273 + 0.696953i
\(863\) −2.02983e10 + 6.59531e9i −1.07503 + 0.349299i −0.792446 0.609943i \(-0.791193\pi\)
−0.282587 + 0.959242i \(0.591193\pi\)
\(864\) −6.52195e8 + 7.33611e9i −0.0344017 + 0.386962i
\(865\) −7.57916e8 + 1.04318e9i −0.0398166 + 0.0548029i
\(866\) −3.29235e8 + 2.39203e8i −0.0172263 + 0.0125157i
\(867\) −9.14824e9 1.34075e10i −0.476728 0.698686i
\(868\) 4.58576e8i 0.0238009i
\(869\) 3.05455e10 + 4.29514e9i 1.57899 + 0.222028i
\(870\) 7.21874e8 + 5.57795e8i 0.0371658 + 0.0287182i
\(871\) 4.33318e9 + 1.40794e9i 0.222200 + 0.0721970i
\(872\) 9.88903e9 + 1.36111e10i 0.505064 + 0.695160i
\(873\) 5.56974e9 1.42219e10i 0.283325 0.723448i
\(874\) 8.29787e8 + 2.55382e9i 0.0420414 + 0.129390i
\(875\) −9.37128e7 2.88418e8i −0.00472902 0.0145544i
\(876\) −3.93867e8 1.34635e9i −0.0197964 0.0676695i
\(877\) 1.33880e10 + 1.84269e10i 0.670217 + 0.922475i 0.999765 0.0216640i \(-0.00689640\pi\)
−0.329548 + 0.944139i \(0.606896\pi\)
\(878\) 1.42311e10 + 4.62396e9i 0.709589 + 0.230560i
\(879\) 1.25913e10 1.62951e10i 0.625331 0.809276i
\(880\) −1.39683e9 1.34910e9i −0.0690963 0.0667352i
\(881\) 1.59075e10i 0.783764i −0.920016 0.391882i \(-0.871824\pi\)
0.920016 0.391882i \(-0.128176\pi\)
\(882\) 2.20637e10 + 1.30577e9i 1.08278 + 0.0640804i
\(883\) 1.17406e10 8.53005e9i 0.573890 0.416955i −0.262627 0.964898i \(-0.584589\pi\)
0.836516 + 0.547942i \(0.184589\pi\)
\(884\) 2.68488e8 3.69542e8i 0.0130720 0.0179921i
\(885\) −9.08138e8 3.25043e8i −0.0440403 0.0157630i
\(886\) −4.11168e10 + 1.33597e10i −1.98610 + 0.645323i
\(887\) 2.49411e10 + 1.81208e10i 1.20000 + 0.871854i 0.994285 0.106757i \(-0.0340468\pi\)
0.205719 + 0.978611i \(0.434047\pi\)
\(888\) 6.04410e7 2.04435e9i 0.00289659 0.0979738i
\(889\) 7.53851e8 2.32011e9i 0.0359856 0.110752i
\(890\) 1.94661e9 0.0925581
\(891\) −2.10807e10 + 1.18673e9i −0.998419 + 0.0562058i
\(892\) 3.76828e9 0.177773
\(893\) −1.43088e9 + 4.40380e9i −0.0672394 + 0.206941i
\(894\) −5.88208e8 + 1.98955e10i −0.0275327 + 0.931264i
\(895\) 1.09298e9 + 7.94093e8i 0.0509601 + 0.0370247i
\(896\) 2.25688e9 7.33304e8i 0.104817 0.0340570i
\(897\) −4.86262e8 1.74044e8i −0.0224956 0.00805168i
\(898\) −7.28741e9 + 1.00303e10i −0.335820 + 0.462216i
\(899\) 1.19095e10 8.65276e9i 0.546682 0.397187i
\(900\) −4.26995e9 2.52702e8i −0.195242 0.0115547i
\(901\) 6.33369e9i 0.288483i
\(902\) −1.36161e10 2.56126e10i −0.617773 1.16206i
\(903\) −3.76797e8 + 4.87634e8i −0.0170294 + 0.0220387i
\(904\) 2.48091e10 + 8.06097e9i 1.11692 + 0.362909i
\(905\) 8.91828e8 + 1.22750e9i 0.0399955 + 0.0550491i
\(906\) 2.54047e9 + 8.68403e9i 0.113492 + 0.387947i
\(907\) 8.22011e9 + 2.52989e10i 0.365807 + 1.12584i 0.949474 + 0.313845i \(0.101617\pi\)
−0.583667 + 0.811993i \(0.698383\pi\)
\(908\) 7.33872e8 + 2.25863e9i 0.0325327 + 0.100125i
\(909\) 6.95584e9 1.77612e10i 0.307168 0.784328i
\(910\) 3.22811e7 + 4.44312e7i 0.00142005 + 0.00195453i
\(911\) −4.16824e10 1.35434e10i −1.82658 0.593491i −0.999507 0.0313921i \(-0.990006\pi\)
−0.827070 0.562099i \(-0.809994\pi\)
\(912\) 3.14243e10 + 2.42817e10i 1.37178 + 1.05998i
\(913\) 5.95509e9 + 1.12019e10i 0.258965 + 0.487127i
\(914\) 9.97936e9i 0.432306i
\(915\) 1.24441e9 + 1.82380e9i 0.0537021 + 0.0787050i
\(916\) 4.35591e9 3.16475e9i 0.187260 0.136052i
\(917\) −2.29495e9 + 3.15873e9i −0.0982836 + 0.135276i
\(918\) −8.91630e8 + 1.00294e10i −0.0380395 + 0.427882i
\(919\) −5.83126e9 + 1.89469e9i −0.247832 + 0.0805256i −0.430299 0.902686i \(-0.641592\pi\)
0.182467 + 0.983212i \(0.441592\pi\)
\(920\) 1.15681e8 + 8.40473e7i 0.00489785 + 0.00355849i
\(921\) −3.37532e10 9.97911e8i −1.42366 0.0420904i
\(922\) −1.43840e10 + 4.42694e10i −0.604396 + 1.86014i
\(923\) −1.32778e10 −0.555803
\(924\) −1.93715e8 3.91911e8i −0.00807814 0.0163431i
\(925\) 2.66694e9 0.110794
\(926\) −8.76652e9 + 2.69806e10i −0.362818 + 1.11664i
\(927\) 1.61932e10 + 1.32950e10i 0.667657 + 0.548164i
\(928\) −3.96039e9 2.87739e9i −0.162675 0.118190i
\(929\) −1.96421e10 + 6.38211e9i −0.803773 + 0.261162i −0.681958 0.731391i \(-0.738871\pi\)
−0.121815 + 0.992553i \(0.538871\pi\)
\(930\) 9.79302e8 2.73607e9i 0.0399233 0.111542i
\(931\) 2.14776e10 2.95614e10i 0.872291 1.20061i
\(932\) −1.73775e9 + 1.26255e9i −0.0703124 + 0.0510849i
\(933\) −3.02053e10 + 2.06097e10i −1.21758 + 0.830781i
\(934\) 2.82707e10i 1.13533i
\(935\) −5.85500e8 5.65493e8i −0.0234254 0.0226249i
\(936\) −6.13428e9 + 1.59936e9i −0.244511 + 0.0637500i
\(937\) −1.80918e10 5.87839e9i −0.718446 0.233437i −0.0730966 0.997325i \(-0.523288\pi\)
−0.645349 + 0.763888i \(0.723288\pi\)
\(938\) −1.22230e9 1.68235e9i −0.0483579 0.0665589i
\(939\) 2.61691e10 7.65563e9i 1.03148 0.301753i
\(940\) −1.86856e7 5.75083e7i −0.000733769 0.00225831i
\(941\) 8.92235e8 + 2.74602e9i 0.0349072 + 0.107433i 0.966992 0.254807i \(-0.0820119\pi\)
−0.932085 + 0.362240i \(0.882012\pi\)
\(942\) −3.15511e10 + 9.23011e9i −1.22981 + 0.359773i
\(943\) 1.51262e9 + 2.08194e9i 0.0587407 + 0.0808497i
\(944\) 1.60552e10 + 5.21665e9i 0.621174 + 0.201832i
\(945\) −1.83245e8 7.80866e7i −0.00706353 0.00300999i
\(946\) −8.48755e9 1.19347e9i −0.325959 0.0458346i
\(947\) 3.82846e10i 1.46487i −0.680838 0.732434i \(-0.738384\pi\)
0.680838 0.732434i \(-0.261616\pi\)
\(948\) 6.80437e9 4.64276e9i 0.259393 0.176989i
\(949\) 2.19320e9 1.59345e9i 0.0833001 0.0605211i
\(950\) −2.52621e10 + 3.47703e10i −0.955954 + 1.31576i
\(951\) 1.24780e10 3.48622e10i 0.470449 1.31439i
\(952\) 8.08515e8 2.62702e8i 0.0303710 0.00986812i
\(953\) 2.48361e10 + 1.80444e10i 0.929517 + 0.675334i 0.945875 0.324532i \(-0.105207\pi\)
−0.0163574 + 0.999866i \(0.505207\pi\)
\(954\) 1.36787e10 1.66605e10i 0.510067 0.621255i
\(955\) 7.14571e8 2.19922e9i 0.0265481 0.0817067i
\(956\) 5.43104e8 0.0201039
\(957\) 6.52301e9 1.24258e10i 0.240578 0.458280i
\(958\) −3.33500e10 −1.22551
\(959\) −4.46777e8 + 1.37504e9i −0.0163578 + 0.0503443i
\(960\) 1.66619e9 + 4.92608e7i 0.0607822 + 0.00179702i
\(961\) −1.56797e10 1.13919e10i −0.569908 0.414062i
\(962\) −9.21859e8 + 2.99530e8i −0.0333850 + 0.0108475i
\(963\) 2.34765e10 1.50214e10i 0.847114 0.542025i
\(964\) 5.94655e9 8.18472e9i 0.213794 0.294262i
\(965\) 2.10307e9 1.52797e9i 0.0753370 0.0547355i
\(966\) 1.32859e8 + 1.94716e8i 0.00474210 + 0.00694995i
\(967\) 3.11799e10i 1.10887i −0.832226 0.554437i \(-0.812934\pi\)
0.832226 0.554437i \(-0.187066\pi\)
\(968\) −1.38677e10 + 2.05532e10i −0.491405 + 0.728310i
\(969\) 1.31719e10 + 1.01780e10i 0.465067 + 0.359360i
\(970\) 1.90599e9 + 6.19294e8i 0.0670532 + 0.0217869i
\(971\) −5.91639e9 8.14322e9i −0.207391 0.285449i 0.692632 0.721291i \(-0.256451\pi\)
−0.900023 + 0.435842i \(0.856451\pi\)
\(972\) −3.94977e9 + 4.02392e9i −0.137956 + 0.140545i
\(973\) 3.96643e8 + 1.22074e9i 0.0138040 + 0.0424843i
\(974\) −1.92166e10 5.91428e10i −0.666379 2.05090i
\(975\) −2.32099e9 7.93380e9i −0.0801968 0.274135i
\(976\) −2.27132e10 3.12621e10i −0.781996 1.07633i
\(977\) 2.82910e10 + 9.19231e9i 0.970550 + 0.315351i 0.751038 0.660259i \(-0.229554\pi\)
0.219512 + 0.975610i \(0.429554\pi\)
\(978\) 3.52207e10 4.55811e10i 1.20396 1.55811i
\(979\) −5.19787e9 2.94910e10i −0.177046 1.00450i
\(980\) 4.77166e8i 0.0161949i
\(981\) −1.70848e9 + 2.88686e10i −0.0577789 + 0.976301i
\(982\) 7.07281e9 5.13870e9i 0.238343 0.173166i
\(983\) −2.87247e10 + 3.95361e10i −0.964535 + 1.32757i −0.0197753 + 0.999804i \(0.506295\pi\)
−0.944760 + 0.327764i \(0.893705\pi\)
\(984\) 2.97396e10 + 1.06445e10i 0.995065 + 0.356157i
\(985\) 3.61561e9 1.17478e9i 0.120546 0.0391679i
\(986\) −5.41434e9 3.93375e9i −0.179877 0.130689i
\(987\) −1.20123e7 + 4.06304e8i −0.000397665 + 0.0134506i
\(988\) 7.94214e8 2.44434e9i 0.0261992 0.0806329i
\(989\) 7.60404e8 0.0249952
\(990\) −3.18853e8 2.75200e9i −0.0104440 0.0901416i
\(991\) −4.39030e10 −1.43297 −0.716484 0.697604i \(-0.754250\pi\)
−0.716484 + 0.697604i \(0.754250\pi\)
\(992\) −4.81884e9 + 1.48309e10i −0.156730 + 0.482364i
\(993\) 9.83993e8 3.32825e10i 0.0318911 1.07868i
\(994\) 4.90278e9 + 3.56208e9i 0.158340 + 0.115041i
\(995\) −4.40459e9 + 1.43114e9i −0.141750 + 0.0460575i
\(996\) 3.18973e9 + 1.14168e9i 0.102293 + 0.0366130i
\(997\) 7.19929e9 9.90897e9i 0.230068 0.316662i −0.678338 0.734750i \(-0.737300\pi\)
0.908407 + 0.418088i \(0.137300\pi\)
\(998\) −6.16690e9 + 4.48051e9i −0.196386 + 0.142683i
\(999\) 2.31013e9 2.64999e9i 0.0733091 0.0840940i
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 33.8.f.a.2.7 104
3.2 odd 2 inner 33.8.f.a.2.20 yes 104
11.6 odd 10 inner 33.8.f.a.17.20 yes 104
33.17 even 10 inner 33.8.f.a.17.7 yes 104
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.8.f.a.2.7 104 1.1 even 1 trivial
33.8.f.a.2.20 yes 104 3.2 odd 2 inner
33.8.f.a.17.7 yes 104 33.17 even 10 inner
33.8.f.a.17.20 yes 104 11.6 odd 10 inner