Properties

Label 11.13.d.a.2.6
Level $11$
Weight $13$
Character 11.2
Analytic conductor $10.054$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [11,13,Mod(2,11)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(11, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 13, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("11.2");
 
S:= CuspForms(chi, 13);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 13 \)
Character orbit: \([\chi]\) \(=\) 11.d (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: \(10.0539319900\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 2.6
Character \(\chi\) \(=\) 11.2
Dual form 11.13.d.a.6.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-8.21322 - 2.66864i) q^{2} +(-83.6942 + 60.8074i) q^{3} +(-3253.40 - 2363.73i) q^{4} +(3579.35 + 11016.1i) q^{5} +(849.672 - 276.075i) q^{6} +(61235.8 - 84283.8i) q^{7} +(41204.4 + 56713.0i) q^{8} +(-160917. + 495252. i) q^{9} +O(q^{10})\) \(q+(-8.21322 - 2.66864i) q^{2} +(-83.6942 + 60.8074i) q^{3} +(-3253.40 - 2363.73i) q^{4} +(3579.35 + 11016.1i) q^{5} +(849.672 - 276.075i) q^{6} +(61235.8 - 84283.8i) q^{7} +(41204.4 + 56713.0i) q^{8} +(-160917. + 495252. i) q^{9} -100030. i q^{10} +(1.75888e6 - 211618. i) q^{11} +416023. q^{12} +(8.42006e6 + 2.73584e6i) q^{13} +(-727866. + 528826. i) q^{14} +(-969432. - 704334. i) q^{15} +(4.90297e6 + 1.50898e7i) q^{16} +(1.10446e7 - 3.58859e6i) q^{17} +(2.64330e6 - 3.63818e6i) q^{18} +(1.20274e7 + 1.65543e7i) q^{19} +(1.43941e7 - 4.43004e7i) q^{20} +1.07777e7i q^{21} +(-1.50108e7 - 2.95574e6i) q^{22} -2.79184e8 q^{23} +(-6.89714e6 - 2.24102e6i) q^{24} +(8.89710e7 - 6.46412e7i) q^{25} +(-6.18548e7 - 4.49402e7i) q^{26} +(-3.36364e7 - 1.03522e8i) q^{27} +(-3.98449e8 + 1.29464e8i) q^{28} +(3.86363e8 - 5.31783e8i) q^{29} +(6.08255e6 + 8.37191e6i) q^{30} +(-3.45867e8 + 1.06447e9i) q^{31} -4.24154e8i q^{32} +(-1.34340e8 + 1.24664e8i) q^{33} -1.00288e8 q^{34} +(1.14766e9 + 3.72899e8i) q^{35} +(1.69417e9 - 1.23089e9i) q^{36} +(2.63099e9 + 1.91153e9i) q^{37} +(-5.46063e7 - 1.68061e8i) q^{38} +(-8.71070e8 + 2.83028e8i) q^{39} +(-4.77272e8 + 6.56908e8i) q^{40} +(3.21175e9 + 4.42059e9i) q^{41} +(2.87617e7 - 8.85193e7i) q^{42} -6.76887e9i q^{43} +(-6.22253e9 - 3.46904e9i) q^{44} -6.03173e9 q^{45} +(2.29300e9 + 7.45041e8i) q^{46} +(-3.26255e9 + 2.37038e9i) q^{47} +(-1.32792e9 - 9.64792e8i) q^{48} +(9.23250e8 + 2.84147e9i) q^{49} +(-9.03242e8 + 2.93481e8i) q^{50} +(-7.06152e8 + 9.71935e8i) q^{51} +(-2.09270e10 - 2.88036e10i) q^{52} +(-1.41164e9 + 4.34459e9i) q^{53} +9.40015e8i q^{54} +(8.62684e9 + 1.86185e10i) q^{55} +7.30318e9 q^{56} +(-2.01325e9 - 6.54144e8i) q^{57} +(-4.59242e9 + 3.33659e9i) q^{58} +(9.97698e9 + 7.24870e9i) q^{59} +(1.48909e9 + 4.58296e9i) q^{60} +(4.88103e10 - 1.58594e10i) q^{61} +(5.68136e9 - 7.81972e9i) q^{62} +(3.18878e10 + 4.38899e10i) q^{63} +(1.89507e10 - 5.83242e10i) q^{64} +1.02549e11i q^{65} +(1.43605e9 - 6.65387e8i) q^{66} +2.92937e10 q^{67} +(-4.44148e10 - 1.44312e10i) q^{68} +(2.33661e10 - 1.69765e10i) q^{69} +(-8.43089e9 - 6.12540e9i) q^{70} +(-2.97774e10 - 9.16454e10i) q^{71} +(-3.47177e10 + 1.12805e10i) q^{72} +(-1.00159e11 + 1.37856e11i) q^{73} +(-1.65077e10 - 2.27210e10i) q^{74} +(-3.51569e9 + 1.08202e10i) q^{75} -8.22874e10i q^{76} +(8.98703e10 - 1.61203e11i) q^{77} +7.90958e9 q^{78} +(4.43236e9 + 1.44016e9i) q^{79} +(-1.48681e11 + 1.08023e11i) q^{80} +(-2.14779e11 - 1.56046e11i) q^{81} +(-1.45818e10 - 4.48783e10i) q^{82} +(-1.76024e11 + 5.71938e10i) q^{83} +(2.54755e10 - 3.50640e10i) q^{84} +(7.90647e10 + 1.08823e11i) q^{85} +(-1.80637e10 + 5.55942e10i) q^{86} +6.80009e10i q^{87} +(8.44750e10 + 9.10316e10i) q^{88} -3.19421e11 q^{89} +(4.95399e10 + 1.60965e10i) q^{90} +(7.46196e11 - 5.42143e11i) q^{91} +(9.08298e11 + 6.59917e11i) q^{92} +(-3.57805e10 - 1.10121e11i) q^{93} +(3.31217e10 - 1.07619e10i) q^{94} +(-1.39314e11 + 1.91749e11i) q^{95} +(2.57917e10 + 3.54993e10i) q^{96} +(1.79652e11 - 5.52911e11i) q^{97} -2.58014e10i q^{98} +(-1.78229e11 + 9.05140e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - 5 q^{2} - 1083 q^{3} + 16247 q^{4} - 723 q^{5} + 147195 q^{6} - 219605 q^{7} + 921595 q^{8} - 3695582 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 44 q - 5 q^{2} - 1083 q^{3} + 16247 q^{4} - 723 q^{5} + 147195 q^{6} - 219605 q^{7} + 921595 q^{8} - 3695582 q^{9} + 2565608 q^{11} + 7500402 q^{12} - 6670805 q^{13} - 249422 q^{14} + 31344279 q^{15} - 182249929 q^{16} - 7887605 q^{17} + 296147970 q^{18} - 59195705 q^{19} - 119854528 q^{20} + 615523885 q^{22} - 407959208 q^{23} + 217767665 q^{24} - 1102003838 q^{25} - 1289107598 q^{26} + 945406779 q^{27} + 5018997220 q^{28} - 541321205 q^{29} - 7192403540 q^{30} + 1789230381 q^{31} + 8868147617 q^{33} + 4668584258 q^{34} - 3628416965 q^{35} - 18485968210 q^{36} - 7637278083 q^{37} - 1555712420 q^{38} + 24275524235 q^{39} + 17352998460 q^{40} - 20307362045 q^{41} - 51939651970 q^{42} + 73504485716 q^{44} + 33796434396 q^{45} - 10698599530 q^{46} - 13177100523 q^{47} - 48055484488 q^{48} - 11538977128 q^{49} + 8631835695 q^{50} + 103295029335 q^{51} - 124762325930 q^{52} + 80932774677 q^{53} - 87742505883 q^{55} - 162644024476 q^{56} + 156654446895 q^{57} + 68439789940 q^{58} + 153452464089 q^{59} + 211654410344 q^{60} - 130004870645 q^{61} - 478111392680 q^{62} + 56162082000 q^{63} + 88053755815 q^{64} - 547107987930 q^{66} + 172356405472 q^{67} + 550428178040 q^{68} + 147718471202 q^{69} + 656066411580 q^{70} - 276485879307 q^{71} - 1923582671435 q^{72} + 401204208595 q^{73} + 668106311350 q^{74} + 545281450749 q^{75} - 431450680685 q^{77} + 349062971320 q^{78} + 454959862075 q^{79} + 732789378812 q^{80} + 681177766216 q^{81} + 455720922385 q^{82} - 1768304661305 q^{83} - 2152859747190 q^{84} - 2586009108005 q^{85} - 686286163053 q^{86} + 2647326267355 q^{88} + 587790027856 q^{89} + 6704158241200 q^{90} - 245650237373 q^{91} + 3006033812992 q^{92} + 794315205079 q^{93} - 1053727188680 q^{94} - 7101305012165 q^{95} - 13699998107060 q^{96} + 647608267617 q^{97} + 6944343091354 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.21322 2.66864i −0.128332 0.0416975i 0.244147 0.969738i \(-0.421492\pi\)
−0.372479 + 0.928041i \(0.621492\pi\)
\(3\) −83.6942 + 60.8074i −0.114807 + 0.0834121i −0.643707 0.765272i \(-0.722605\pi\)
0.528900 + 0.848684i \(0.322605\pi\)
\(4\) −3253.40 2363.73i −0.794287 0.577083i
\(5\) 3579.35 + 11016.1i 0.229078 + 0.705031i 0.997852 + 0.0655099i \(0.0208674\pi\)
−0.768773 + 0.639521i \(0.779133\pi\)
\(6\) 849.672 276.075i 0.0182114 0.00591725i
\(7\) 61235.8 84283.8i 0.520496 0.716401i −0.465149 0.885232i \(-0.653999\pi\)
0.985645 + 0.168831i \(0.0539994\pi\)
\(8\) 41204.4 + 56713.0i 0.157182 + 0.216343i
\(9\) −160917. + 495252.i −0.302794 + 0.931904i
\(10\) 100030.i 0.100030i
\(11\) 1.75888e6 211618.i 0.992840 0.119453i
\(12\) 416023. 0.139325
\(13\) 8.42006e6 + 2.73584e6i 1.74444 + 0.566802i 0.995407 0.0957355i \(-0.0305203\pi\)
0.749029 + 0.662537i \(0.230520\pi\)
\(14\) −727866. + 528826.i −0.0966681 + 0.0702335i
\(15\) −969432. 704334.i −0.0851079 0.0618345i
\(16\) 4.90297e6 + 1.50898e7i 0.292240 + 0.899422i
\(17\) 1.10446e7 3.58859e6i 0.457567 0.148673i −0.0711592 0.997465i \(-0.522670\pi\)
0.528726 + 0.848792i \(0.322670\pi\)
\(18\) 2.64330e6 3.63818e6i 0.0777160 0.106967i
\(19\) 1.20274e7 + 1.65543e7i 0.255653 + 0.351876i 0.917481 0.397780i \(-0.130219\pi\)
−0.661828 + 0.749656i \(0.730219\pi\)
\(20\) 1.43941e7 4.43004e7i 0.224908 0.692194i
\(21\) 1.07777e7i 0.125663i
\(22\) −1.50108e7 2.95574e6i −0.132394 0.0260694i
\(23\) −2.79184e8 −1.88592 −0.942962 0.332902i \(-0.891972\pi\)
−0.942962 + 0.332902i \(0.891972\pi\)
\(24\) −6.89714e6 2.24102e6i −0.0360912 0.0117268i
\(25\) 8.89710e7 6.46412e7i 0.364425 0.264770i
\(26\) −6.18548e7 4.49402e7i −0.200232 0.145477i
\(27\) −3.36364e7 1.03522e8i −0.0868215 0.267209i
\(28\) −3.98449e8 + 1.29464e8i −0.826846 + 0.268658i
\(29\) 3.86363e8 5.31783e8i 0.649543 0.894019i −0.349536 0.936923i \(-0.613661\pi\)
0.999079 + 0.0429039i \(0.0136609\pi\)
\(30\) 6.08255e6 + 8.37191e6i 0.00834369 + 0.0114841i
\(31\) −3.45867e8 + 1.06447e9i −0.389707 + 1.19940i 0.543300 + 0.839539i \(0.317175\pi\)
−0.933007 + 0.359857i \(0.882825\pi\)
\(32\) 4.24154e8i 0.395025i
\(33\) −1.34340e8 + 1.24664e8i −0.104021 + 0.0965288i
\(34\) −1.00288e8 −0.0649195
\(35\) 1.14766e9 + 3.72899e8i 0.624319 + 0.202854i
\(36\) 1.69417e9 1.23089e9i 0.778291 0.565462i
\(37\) 2.63099e9 + 1.91153e9i 1.02544 + 0.745024i 0.967391 0.253290i \(-0.0815125\pi\)
0.0580474 + 0.998314i \(0.481513\pi\)
\(38\) −5.46063e7 1.68061e8i −0.0181360 0.0558169i
\(39\) −8.71070e8 + 2.83028e8i −0.247551 + 0.0804343i
\(40\) −4.77272e8 + 6.56908e8i −0.116521 + 0.160378i
\(41\) 3.21175e9 + 4.42059e9i 0.676143 + 0.930631i 0.999880 0.0155162i \(-0.00493917\pi\)
−0.323737 + 0.946147i \(0.604939\pi\)
\(42\) 2.87617e7 8.85193e7i 0.00523984 0.0161266i
\(43\) 6.76887e9i 1.07079i −0.844601 0.535396i \(-0.820162\pi\)
0.844601 0.535396i \(-0.179838\pi\)
\(44\) −6.22253e9 3.46904e9i −0.857534 0.478071i
\(45\) −6.03173e9 −0.726385
\(46\) 2.29300e9 + 7.45041e8i 0.242023 + 0.0786382i
\(47\) −3.26255e9 + 2.37038e9i −0.302671 + 0.219903i −0.728745 0.684785i \(-0.759896\pi\)
0.426075 + 0.904688i \(0.359896\pi\)
\(48\) −1.32792e9 9.64792e8i −0.108574 0.0788835i
\(49\) 9.23250e8 + 2.84147e9i 0.0667026 + 0.205290i
\(50\) −9.03242e8 + 2.93481e8i −0.0578075 + 0.0187828i
\(51\) −7.06152e8 + 9.71935e8i −0.0401307 + 0.0552352i
\(52\) −2.09270e10 2.88036e10i −1.05849 1.45689i
\(53\) −1.41164e9 + 4.34459e9i −0.0636898 + 0.196017i −0.977838 0.209363i \(-0.932861\pi\)
0.914148 + 0.405380i \(0.132861\pi\)
\(54\) 9.40015e8i 0.0379116i
\(55\) 8.62684e9 + 1.86185e10i 0.311656 + 0.672619i
\(56\) 7.30318e9 0.236801
\(57\) −2.01325e9 6.54144e8i −0.0587014 0.0190732i
\(58\) −4.59242e9 + 3.33659e9i −0.120635 + 0.0876466i
\(59\) 9.97698e9 + 7.24870e9i 0.236530 + 0.171849i 0.699736 0.714401i \(-0.253301\pi\)
−0.463206 + 0.886251i \(0.653301\pi\)
\(60\) 1.48909e9 + 4.58296e9i 0.0319164 + 0.0982286i
\(61\) 4.88103e10 1.58594e10i 0.947398 0.307828i 0.205740 0.978607i \(-0.434040\pi\)
0.741658 + 0.670778i \(0.234040\pi\)
\(62\) 5.68136e9 7.81972e9i 0.100023 0.137671i
\(63\) 3.18878e10 + 4.38899e10i 0.510014 + 0.701974i
\(64\) 1.89507e10 5.83242e10i 0.275768 0.848728i
\(65\) 1.02549e11i 1.35972i
\(66\) 1.43605e9 6.65387e8i 0.0173742 0.00805028i
\(67\) 2.92937e10 0.323836 0.161918 0.986804i \(-0.448232\pi\)
0.161918 + 0.986804i \(0.448232\pi\)
\(68\) −4.44148e10 1.44312e10i −0.449236 0.145966i
\(69\) 2.33661e10 1.69765e10i 0.216517 0.157309i
\(70\) −8.43089e9 6.12540e9i −0.0716614 0.0520650i
\(71\) −2.97774e10 9.16454e10i −0.232454 0.715419i −0.997449 0.0713832i \(-0.977259\pi\)
0.764995 0.644036i \(-0.222741\pi\)
\(72\) −3.47177e10 + 1.12805e10i −0.249205 + 0.0809716i
\(73\) −1.00159e11 + 1.37856e11i −0.661837 + 0.910940i −0.999540 0.0303125i \(-0.990350\pi\)
0.337704 + 0.941252i \(0.390350\pi\)
\(74\) −1.65077e10 2.27210e10i −0.100530 0.138368i
\(75\) −3.51569e9 + 1.08202e10i −0.0197535 + 0.0607949i
\(76\) 8.22874e10i 0.427023i
\(77\) 8.98703e10 1.61203e11i 0.431193 0.773446i
\(78\) 7.90958e9 0.0351226
\(79\) 4.43236e9 + 1.44016e9i 0.0182336 + 0.00592446i 0.318120 0.948051i \(-0.396949\pi\)
−0.299886 + 0.953975i \(0.596949\pi\)
\(80\) −1.48681e11 + 1.08023e11i −0.567175 + 0.412077i
\(81\) −2.14779e11 1.56046e11i −0.760469 0.552513i
\(82\) −1.45818e10 4.48783e10i −0.0479655 0.147623i
\(83\) −1.76024e11 + 5.71938e10i −0.538399 + 0.174936i −0.565579 0.824694i \(-0.691347\pi\)
0.0271802 + 0.999631i \(0.491347\pi\)
\(84\) 2.54755e10 3.50640e10i 0.0725182 0.0998127i
\(85\) 7.90647e10 + 1.08823e11i 0.209638 + 0.288541i
\(86\) −1.80637e10 + 5.55942e10i −0.0446493 + 0.137417i
\(87\) 6.80009e10i 0.156819i
\(88\) 8.44750e10 + 9.10316e10i 0.181900 + 0.196018i
\(89\) −3.19421e11 −0.642722 −0.321361 0.946957i \(-0.604140\pi\)
−0.321361 + 0.946957i \(0.604140\pi\)
\(90\) 4.95399e10 + 1.60965e10i 0.0932181 + 0.0302884i
\(91\) 7.46196e11 5.42143e11i 1.31403 0.954698i
\(92\) 9.08298e11 + 6.59917e11i 1.49796 + 1.08833i
\(93\) −3.57805e10 1.10121e11i −0.0553030 0.170205i
\(94\) 3.31217e10 1.07619e10i 0.0480116 0.0155999i
\(95\) −1.39314e11 + 1.91749e11i −0.189519 + 0.260850i
\(96\) 2.57917e10 + 3.54993e10i 0.0329498 + 0.0453515i
\(97\) 1.79652e11 5.52911e11i 0.215675 0.663781i −0.783430 0.621481i \(-0.786531\pi\)
0.999105 0.0423000i \(-0.0134685\pi\)
\(98\) 2.58014e10i 0.0291265i
\(99\) −1.78229e11 + 9.05140e11i −0.189308 + 0.961401i
\(100\) −4.42252e11 −0.442252
\(101\) 4.53820e11 + 1.47455e11i 0.427519 + 0.138909i 0.514870 0.857268i \(-0.327840\pi\)
−0.0873508 + 0.996178i \(0.527840\pi\)
\(102\) 8.39352e9 6.09825e9i 0.00745321 0.00541507i
\(103\) 1.25308e11 + 9.10416e10i 0.104944 + 0.0762459i 0.639019 0.769191i \(-0.279340\pi\)
−0.534076 + 0.845437i \(0.679340\pi\)
\(104\) 1.91786e11 + 5.90256e11i 0.151571 + 0.466488i
\(105\) −1.18728e11 + 3.85770e10i −0.0885966 + 0.0287868i
\(106\) 2.31883e10 3.19159e10i 0.0163468 0.0224995i
\(107\) −1.42266e12 1.95812e12i −0.947978 1.30478i −0.952420 0.304790i \(-0.901414\pi\)
0.00444151 0.999990i \(-0.498586\pi\)
\(108\) −1.35266e11 + 4.16307e11i −0.0852407 + 0.262344i
\(109\) 1.65522e12i 0.986953i −0.869759 0.493476i \(-0.835726\pi\)
0.869759 0.493476i \(-0.164274\pi\)
\(110\) −2.11680e10 1.75940e11i −0.0119488 0.0993135i
\(111\) −3.36434e11 −0.179871
\(112\) 1.57206e12 + 5.10795e11i 0.796456 + 0.258784i
\(113\) −1.42821e12 + 1.03765e12i −0.685994 + 0.498404i −0.875341 0.483506i \(-0.839363\pi\)
0.189347 + 0.981910i \(0.439363\pi\)
\(114\) 1.47896e10 + 1.07453e10i 0.00673794 + 0.00489540i
\(115\) −9.99299e11 3.07553e12i −0.432024 1.32963i
\(116\) −2.51399e12 + 8.16844e11i −1.03185 + 0.335267i
\(117\) −2.70986e12 + 3.72981e12i −1.05641 + 1.45402i
\(118\) −6.25990e10 8.61601e10i −0.0231886 0.0319164i
\(119\) 3.73862e11 1.15063e12i 0.131653 0.405185i
\(120\) 8.40011e10i 0.0281318i
\(121\) 3.04886e12 7.44418e11i 0.971462 0.237195i
\(122\) −4.43213e11 −0.134417
\(123\) −5.37610e11 1.74680e11i −0.155252 0.0504443i
\(124\) 3.64136e12 2.64560e12i 1.00169 0.727771i
\(125\) 3.31836e12 + 2.41093e12i 0.869889 + 0.632011i
\(126\) −1.44776e11 4.45574e11i −0.0361803 0.111352i
\(127\) 2.42453e12 7.87777e11i 0.577836 0.187750i −0.00549472 0.999985i \(-0.501749\pi\)
0.583331 + 0.812234i \(0.301749\pi\)
\(128\) −1.33247e12 + 1.83399e12i −0.302969 + 0.417001i
\(129\) 4.11597e11 + 5.66515e11i 0.0893170 + 0.122934i
\(130\) 2.73666e11 8.42256e11i 0.0566970 0.174495i
\(131\) 6.68781e12i 1.32329i 0.749816 + 0.661646i \(0.230142\pi\)
−0.749816 + 0.661646i \(0.769858\pi\)
\(132\) 7.31733e11 8.80378e10i 0.138328 0.0166428i
\(133\) 2.13177e12 0.385150
\(134\) −2.40595e11 7.81741e10i −0.0415583 0.0135031i
\(135\) 1.02002e12 7.41086e11i 0.168502 0.122424i
\(136\) 6.58605e11 + 4.78504e11i 0.104086 + 0.0756227i
\(137\) −2.08497e12 6.41689e12i −0.315339 0.970513i −0.975615 0.219490i \(-0.929561\pi\)
0.660276 0.751023i \(-0.270439\pi\)
\(138\) −2.37215e11 + 7.70758e10i −0.0343453 + 0.0111595i
\(139\) −4.54307e12 + 6.25299e12i −0.629883 + 0.866960i −0.998026 0.0628094i \(-0.979994\pi\)
0.368142 + 0.929770i \(0.379994\pi\)
\(140\) −2.85238e12 3.92596e12i −0.378825 0.521408i
\(141\) 1.28920e11 3.96775e11i 0.0164061 0.0504928i
\(142\) 8.32169e11i 0.101504i
\(143\) 1.53888e13 + 3.03018e12i 1.79965 + 0.354366i
\(144\) −8.26223e12 −0.926664
\(145\) 7.24111e12 + 2.35278e12i 0.779107 + 0.253147i
\(146\) 1.19051e12 8.64958e11i 0.122918 0.0893054i
\(147\) −2.50053e11 1.81674e11i −0.0247815 0.0180048i
\(148\) −4.04133e12 1.24379e13i −0.384551 1.18353i
\(149\) −1.48252e13 + 4.81701e12i −1.35483 + 0.440210i −0.894313 0.447443i \(-0.852335\pi\)
−0.460514 + 0.887653i \(0.652335\pi\)
\(150\) 5.77503e10 7.94865e10i 0.00506999 0.00697824i
\(151\) −8.82320e12 1.21441e13i −0.744328 1.02448i −0.998358 0.0572834i \(-0.981756\pi\)
0.254030 0.967196i \(-0.418244\pi\)
\(152\) −4.43263e11 + 1.36422e12i −0.0359418 + 0.110617i
\(153\) 6.04730e12i 0.471426i
\(154\) −1.16832e12 + 1.08417e12i −0.0875864 + 0.0812779i
\(155\) −1.29643e13 −0.934885
\(156\) 3.50294e12 + 1.13817e12i 0.243044 + 0.0789698i
\(157\) 5.20312e12 3.78029e12i 0.347429 0.252422i −0.400361 0.916358i \(-0.631115\pi\)
0.747790 + 0.663936i \(0.231115\pi\)
\(158\) −3.25607e10 2.36567e10i −0.00209291 0.00152059i
\(159\) −1.46037e11 4.49456e11i −0.00903816 0.0278166i
\(160\) 4.67253e12 1.51820e12i 0.278505 0.0904916i
\(161\) −1.70961e13 + 2.35307e13i −0.981615 + 1.35108i
\(162\) 1.34760e12 + 1.85481e12i 0.0745538 + 0.102614i
\(163\) 7.23713e12 2.22736e13i 0.385870 1.18758i −0.549978 0.835179i \(-0.685364\pi\)
0.935848 0.352405i \(-0.114636\pi\)
\(164\) 2.19737e13i 1.12938i
\(165\) −1.85416e12 1.03369e12i −0.0918848 0.0512254i
\(166\) 1.59836e12 0.0763879
\(167\) 2.23601e13 + 7.26524e12i 1.03080 + 0.334928i 0.775107 0.631830i \(-0.217696\pi\)
0.255695 + 0.966758i \(0.417696\pi\)
\(168\) −6.11234e11 + 4.44087e11i −0.0271864 + 0.0197521i
\(169\) 4.45640e13 + 3.23776e13i 1.91278 + 1.38971i
\(170\) −3.58966e11 1.10478e12i −0.0148717 0.0457703i
\(171\) −1.01340e13 + 3.29273e12i −0.405325 + 0.131698i
\(172\) −1.59998e13 + 2.20218e13i −0.617936 + 0.850516i
\(173\) −1.07740e13 1.48291e13i −0.401883 0.553144i 0.559332 0.828943i \(-0.311058\pi\)
−0.961215 + 0.275799i \(0.911058\pi\)
\(174\) 1.81470e11 5.58506e11i 0.00653896 0.0201249i
\(175\) 1.14572e13i 0.398886i
\(176\) 1.18170e13 + 2.55035e13i 0.397586 + 0.858073i
\(177\) −1.27579e12 −0.0414896
\(178\) 2.62347e12 + 8.52418e11i 0.0824815 + 0.0267999i
\(179\) 2.95743e13 2.14870e13i 0.899076 0.653217i −0.0391524 0.999233i \(-0.512466\pi\)
0.938229 + 0.346016i \(0.112466\pi\)
\(180\) 1.96236e13 + 1.42574e13i 0.576958 + 0.419184i
\(181\) −9.56180e12 2.94282e13i −0.271937 0.836935i −0.990014 0.140972i \(-0.954977\pi\)
0.718077 0.695964i \(-0.245023\pi\)
\(182\) −7.57546e12 + 2.46142e12i −0.208440 + 0.0677262i
\(183\) −3.12077e12 + 4.29537e12i −0.0830912 + 0.114365i
\(184\) −1.15036e13 1.58334e13i −0.296434 0.408006i
\(185\) −1.16404e13 + 3.58253e13i −0.290359 + 0.893635i
\(186\) 9.99934e11i 0.0241487i
\(187\) 1.86666e13 8.64911e12i 0.436531 0.202266i
\(188\) 1.62173e13 0.367310
\(189\) −1.07850e13 3.50426e12i −0.236619 0.0768822i
\(190\) 1.65592e12 1.20310e12i 0.0351981 0.0255729i
\(191\) −2.60381e13 1.89178e13i −0.536302 0.389646i 0.286408 0.958108i \(-0.407539\pi\)
−0.822710 + 0.568462i \(0.807539\pi\)
\(192\) 1.96048e12 + 6.03373e12i 0.0391341 + 0.120442i
\(193\) −3.85185e13 + 1.25154e13i −0.745290 + 0.242159i −0.656953 0.753931i \(-0.728155\pi\)
−0.0883367 + 0.996091i \(0.528155\pi\)
\(194\) −2.95104e12 + 4.06175e12i −0.0553559 + 0.0761909i
\(195\) −6.23573e12 8.58274e12i −0.113417 0.156106i
\(196\) 3.71278e12 1.14268e13i 0.0654881 0.201552i
\(197\) 1.45868e13i 0.249552i −0.992185 0.124776i \(-0.960179\pi\)
0.992185 0.124776i \(-0.0398212\pi\)
\(198\) 3.87933e12 6.95848e12i 0.0643821 0.115484i
\(199\) −1.00343e14 −1.61573 −0.807864 0.589368i \(-0.799377\pi\)
−0.807864 + 0.589368i \(0.799377\pi\)
\(200\) 7.33200e12 + 2.38231e12i 0.114562 + 0.0372236i
\(201\) −2.45171e12 + 1.78127e12i −0.0371786 + 0.0270118i
\(202\) −3.33382e12 2.42216e12i −0.0490721 0.0356529i
\(203\) −2.11615e13 6.51283e13i −0.302392 0.930666i
\(204\) 4.59479e12 1.49294e12i 0.0637506 0.0207138i
\(205\) −3.72018e13 + 5.12039e13i −0.501234 + 0.689889i
\(206\) −7.86225e11 1.08215e12i −0.0102883 0.0141606i
\(207\) 4.49255e13 1.38267e14i 0.571046 1.75750i
\(208\) 1.40471e14i 1.73463i
\(209\) 2.46579e13 + 2.65718e13i 0.295855 + 0.318818i
\(210\) 1.07809e12 0.0125701
\(211\) 8.15535e12 + 2.64983e12i 0.0924161 + 0.0300278i 0.354860 0.934919i \(-0.384528\pi\)
−0.262444 + 0.964947i \(0.584528\pi\)
\(212\) 1.48621e13 1.07979e13i 0.163706 0.118939i
\(213\) 8.06491e12 + 5.85950e12i 0.0863619 + 0.0627456i
\(214\) 6.45910e12 + 1.98791e13i 0.0672495 + 0.206973i
\(215\) 7.45666e13 2.42282e13i 0.754942 0.245296i
\(216\) 4.48509e12 6.17320e12i 0.0441620 0.0607838i
\(217\) 6.85380e13 + 9.43345e13i 0.656407 + 0.903467i
\(218\) −4.41718e12 + 1.35947e13i −0.0411534 + 0.126657i
\(219\) 1.76282e13i 0.159787i
\(220\) 1.59427e13 8.09650e13i 0.140613 0.714104i
\(221\) 1.02814e14 0.882464
\(222\) 2.76321e12 + 8.97820e11i 0.0230832 + 0.00750018i
\(223\) −6.24155e13 + 4.53475e13i −0.507532 + 0.368744i −0.811887 0.583815i \(-0.801559\pi\)
0.304354 + 0.952559i \(0.401559\pi\)
\(224\) −3.57494e13 2.59734e13i −0.282996 0.205609i
\(225\) 1.76967e13 + 5.44649e13i 0.136395 + 0.419780i
\(226\) 1.44993e13 4.71111e12i 0.108817 0.0353567i
\(227\) 6.19377e13 8.52499e13i 0.452689 0.623073i −0.520284 0.853993i \(-0.674174\pi\)
0.972973 + 0.230921i \(0.0741738\pi\)
\(228\) 5.00368e12 + 6.88697e12i 0.0356189 + 0.0490252i
\(229\) −6.21898e13 + 1.91401e14i −0.431228 + 1.32718i 0.465676 + 0.884955i \(0.345811\pi\)
−0.896903 + 0.442227i \(0.854189\pi\)
\(230\) 2.79267e13i 0.188648i
\(231\) 2.28074e12 + 1.89566e13i 0.0150108 + 0.124764i
\(232\) 4.60789e13 0.295511
\(233\) −1.83606e13 5.96571e12i −0.114749 0.0372844i 0.251079 0.967966i \(-0.419214\pi\)
−0.365829 + 0.930682i \(0.619214\pi\)
\(234\) 3.22102e13 2.34021e13i 0.196200 0.142547i
\(235\) −3.77902e13 2.74562e13i −0.224374 0.163017i
\(236\) −1.53251e13 4.71658e13i −0.0887016 0.272995i
\(237\) −4.58535e11 + 1.48987e11i −0.00258751 + 0.000840735i
\(238\) −6.14122e12 + 8.45266e12i −0.0337903 + 0.0465084i
\(239\) −9.48295e13 1.30522e14i −0.508811 0.700318i 0.474908 0.880036i \(-0.342482\pi\)
−0.983718 + 0.179718i \(0.942482\pi\)
\(240\) 5.87515e12 1.80819e13i 0.0307434 0.0946184i
\(241\) 1.22187e14i 0.623622i −0.950144 0.311811i \(-0.899064\pi\)
0.950144 0.311811i \(-0.100936\pi\)
\(242\) −2.70276e13 2.02224e12i −0.134560 0.0100679i
\(243\) 8.53117e13 0.414354
\(244\) −1.96287e14 6.37775e13i −0.930148 0.302223i
\(245\) −2.79973e13 + 2.03412e13i −0.129455 + 0.0940548i
\(246\) 3.94935e12 + 2.86937e12i 0.0178203 + 0.0129472i
\(247\) 5.59815e13 + 1.72293e14i 0.246526 + 0.758729i
\(248\) −7.46204e13 + 2.42457e13i −0.320736 + 0.104213i
\(249\) 1.12544e13 1.54904e13i 0.0472201 0.0649928i
\(250\) −2.08205e13 2.86570e13i −0.0852809 0.117379i
\(251\) −1.93057e13 + 5.94169e13i −0.0772047 + 0.237612i −0.982209 0.187791i \(-0.939867\pi\)
0.905004 + 0.425402i \(0.139867\pi\)
\(252\) 2.18166e14i 0.851889i
\(253\) −4.91051e14 + 5.90803e13i −1.87242 + 0.225278i
\(254\) −2.20155e13 −0.0819834
\(255\) −1.32345e13 4.30015e12i −0.0481356 0.0156402i
\(256\) −1.87379e14 + 1.36139e14i −0.665703 + 0.483661i
\(257\) 2.95784e13 + 2.14900e13i 0.102654 + 0.0745825i 0.637928 0.770096i \(-0.279792\pi\)
−0.535274 + 0.844678i \(0.679792\pi\)
\(258\) −1.86872e12 5.75132e12i −0.00633615 0.0195007i
\(259\) 3.22222e14 1.04696e14i 1.06747 0.346843i
\(260\) 2.42398e14 3.33632e14i 0.784673 1.08001i
\(261\) 2.01194e14 + 2.76920e14i 0.636462 + 0.876015i
\(262\) 1.78473e13 5.49284e13i 0.0551779 0.169820i
\(263\) 3.60964e12i 0.0109076i 0.999985 + 0.00545380i \(0.00173601\pi\)
−0.999985 + 0.00545380i \(0.998264\pi\)
\(264\) −1.26055e13 2.48212e12i −0.0372336 0.00733160i
\(265\) −5.29133e13 −0.152788
\(266\) −1.75087e13 5.68892e12i −0.0494269 0.0160598i
\(267\) 2.67337e13 1.94232e13i 0.0737889 0.0536108i
\(268\) −9.53039e13 6.92424e13i −0.257218 0.186880i
\(269\) 2.04699e14 + 6.29998e14i 0.540258 + 1.66274i 0.732005 + 0.681299i \(0.238585\pi\)
−0.191747 + 0.981444i \(0.561415\pi\)
\(270\) −1.03553e13 + 3.36464e12i −0.0267289 + 0.00868473i
\(271\) 2.99580e14 4.12336e14i 0.756305 1.04096i −0.241208 0.970473i \(-0.577544\pi\)
0.997512 0.0704905i \(-0.0224565\pi\)
\(272\) 1.08302e14 + 1.49065e14i 0.267439 + 0.368098i
\(273\) −2.94860e13 + 9.07485e13i −0.0712262 + 0.219212i
\(274\) 5.82674e13i 0.137696i
\(275\) 1.42810e14 1.32524e14i 0.330188 0.306406i
\(276\) −1.16147e14 −0.262757
\(277\) 5.38575e14 + 1.74994e14i 1.19225 + 0.387386i 0.836905 0.547349i \(-0.184363\pi\)
0.355346 + 0.934735i \(0.384363\pi\)
\(278\) 5.40002e13 3.92334e13i 0.116984 0.0849938i
\(279\) −4.71524e14 3.42582e14i −0.999721 0.726340i
\(280\) 2.61406e13 + 8.04526e13i 0.0542460 + 0.166952i
\(281\) −4.26811e14 + 1.38679e14i −0.866957 + 0.281692i −0.708531 0.705679i \(-0.750642\pi\)
−0.158426 + 0.987371i \(0.550642\pi\)
\(282\) −2.11769e12 + 2.91476e12i −0.00421084 + 0.00579572i
\(283\) 1.44365e14 + 1.98701e14i 0.281023 + 0.386795i 0.926072 0.377346i \(-0.123163\pi\)
−0.645049 + 0.764141i \(0.723163\pi\)
\(284\) −1.19747e14 + 3.68545e14i −0.228221 + 0.702393i
\(285\) 2.45196e13i 0.0457556i
\(286\) −1.18305e14 6.59546e13i −0.216176 0.120517i
\(287\) 5.69259e14 1.01863
\(288\) 2.10063e14 + 6.82537e13i 0.368125 + 0.119611i
\(289\) −3.62247e14 + 2.63188e14i −0.621753 + 0.451730i
\(290\) −5.31941e13 3.86478e13i −0.0894285 0.0649736i
\(291\) 1.85853e13 + 5.71996e13i 0.0306063 + 0.0941965i
\(292\) 6.51711e14 2.11754e14i 1.05138 0.341613i
\(293\) 6.42477e14 8.84293e14i 1.01543 1.39763i 0.100078 0.994980i \(-0.468091\pi\)
0.915356 0.402646i \(-0.131909\pi\)
\(294\) 1.56892e12 + 2.15943e12i 0.00242950 + 0.00334392i
\(295\) −4.41414e13 + 1.35853e14i −0.0669751 + 0.206128i
\(296\) 2.27975e14i 0.338951i
\(297\) −8.10695e13 1.74965e14i −0.118119 0.254925i
\(298\) 1.34618e14 0.192223
\(299\) −2.35075e15 7.63804e14i −3.28987 1.06894i
\(300\) 3.70140e13 2.68922e13i 0.0507736 0.0368892i
\(301\) −5.70506e14 4.14497e14i −0.767117 0.557343i
\(302\) 4.00587e13 + 1.23288e14i 0.0528026 + 0.162510i
\(303\) −4.69485e13 + 1.52545e13i −0.0606689 + 0.0197125i
\(304\) −1.90831e14 + 2.62657e14i −0.241773 + 0.332772i
\(305\) 3.49418e14 + 4.80933e14i 0.434057 + 0.597428i
\(306\) 1.61381e13 4.96678e13i 0.0196572 0.0604988i
\(307\) 2.14416e14i 0.256111i 0.991767 + 0.128055i \(0.0408735\pi\)
−0.991767 + 0.128055i \(0.959127\pi\)
\(308\) −6.73425e14 + 3.12030e14i −0.788833 + 0.365504i
\(309\) −1.60236e13 −0.0184081
\(310\) 1.06478e14 + 3.45969e13i 0.119975 + 0.0389823i
\(311\) −7.59869e13 + 5.52077e13i −0.0839801 + 0.0610151i −0.628983 0.777419i \(-0.716529\pi\)
0.545003 + 0.838434i \(0.316529\pi\)
\(312\) −5.19433e13 3.77390e13i −0.0563121 0.0409131i
\(313\) −2.23396e14 6.87541e14i −0.237579 0.731194i −0.996769 0.0803243i \(-0.974404\pi\)
0.759189 0.650870i \(-0.225596\pi\)
\(314\) −5.28226e13 + 1.71631e13i −0.0551114 + 0.0179068i
\(315\) −3.69358e14 + 5.08377e14i −0.378080 + 0.520383i
\(316\) −1.10161e13 1.51623e13i −0.0110638 0.0152280i
\(317\) 1.74578e14 5.37294e14i 0.172041 0.529489i −0.827445 0.561547i \(-0.810206\pi\)
0.999486 + 0.0320585i \(0.0102063\pi\)
\(318\) 4.08120e12i 0.00394662i
\(319\) 5.67030e14 1.01710e15i 0.538099 0.965207i
\(320\) 7.10336e14 0.661552
\(321\) 2.38137e14 + 7.73753e13i 0.217669 + 0.0707249i
\(322\) 2.03209e14 1.47640e14i 0.182309 0.132455i
\(323\) 1.92244e14 + 1.39674e14i 0.169293 + 0.122998i
\(324\) 3.29910e14 + 1.01536e15i 0.285184 + 0.877707i
\(325\) 9.25989e14 3.00872e14i 0.785789 0.255318i
\(326\) −1.18880e14 + 1.63625e14i −0.0990385 + 0.136315i
\(327\) 1.00650e14 + 1.38532e14i 0.0823238 + 0.113309i
\(328\) −1.18367e14 + 3.64296e14i −0.0950577 + 0.292558i
\(329\) 4.20133e14i 0.331292i
\(330\) 1.24701e13 + 1.34380e13i 0.00965575 + 0.0104052i
\(331\) 4.88114e14 0.371153 0.185577 0.982630i \(-0.440585\pi\)
0.185577 + 0.982630i \(0.440585\pi\)
\(332\) 7.07868e14 + 2.30000e14i 0.528596 + 0.171751i
\(333\) −1.37006e15 + 9.95407e14i −1.00479 + 0.730021i
\(334\) −1.64260e14 1.19342e14i −0.118319 0.0859636i
\(335\) 1.04852e14 + 3.22702e14i 0.0741838 + 0.228314i
\(336\) −1.62633e14 + 5.28426e13i −0.113024 + 0.0367239i
\(337\) 9.15282e14 1.25978e15i 0.624850 0.860032i −0.372845 0.927894i \(-0.621618\pi\)
0.997695 + 0.0678619i \(0.0216177\pi\)
\(338\) −2.79610e14 3.84850e14i −0.187522 0.258102i
\(339\) 5.64356e13 1.73691e14i 0.0371839 0.114440i
\(340\) 5.40933e14i 0.350163i
\(341\) −3.83077e14 + 1.94546e15i −0.243646 + 1.23736i
\(342\) 9.20196e13 0.0575074
\(343\) 1.66744e15 + 5.41785e14i 1.02397 + 0.332707i
\(344\) 3.83883e14 2.78907e14i 0.231659 0.168310i
\(345\) 2.70650e14 + 1.96639e14i 0.160507 + 0.116615i
\(346\) 4.89155e13 + 1.50547e14i 0.0285095 + 0.0877433i
\(347\) 2.03593e14 6.61514e13i 0.116624 0.0378933i −0.250124 0.968214i \(-0.580471\pi\)
0.366747 + 0.930321i \(0.380471\pi\)
\(348\) 1.60736e14 2.21234e14i 0.0904977 0.124559i
\(349\) −7.53008e14 1.03643e15i −0.416722 0.573569i 0.548119 0.836400i \(-0.315344\pi\)
−0.964842 + 0.262831i \(0.915344\pi\)
\(350\) −3.05750e13 + 9.41003e13i −0.0166325 + 0.0511897i
\(351\) 9.63688e14i 0.515340i
\(352\) −8.97585e13 7.46035e14i −0.0471867 0.392196i
\(353\) −1.59907e15 −0.826454 −0.413227 0.910628i \(-0.635598\pi\)
−0.413227 + 0.910628i \(0.635598\pi\)
\(354\) 1.04783e13 + 3.40462e12i 0.00532443 + 0.00173001i
\(355\) 9.02992e14 6.56062e14i 0.451143 0.327774i
\(356\) 1.03920e15 + 7.55025e14i 0.510506 + 0.370904i
\(357\) 3.86766e13 + 1.19034e14i 0.0186827 + 0.0574994i
\(358\) −3.00241e14 + 9.75543e13i −0.142617 + 0.0463392i
\(359\) −2.11764e15 + 2.91468e15i −0.989204 + 1.36152i −0.0574831 + 0.998346i \(0.518308\pi\)
−0.931721 + 0.363176i \(0.881692\pi\)
\(360\) −2.48534e14 3.42078e14i −0.114175 0.157148i
\(361\) 5.54565e14 1.70678e15i 0.250559 0.771140i
\(362\) 2.67217e14i 0.118744i
\(363\) −2.09906e14 + 2.47697e14i −0.0917456 + 0.108263i
\(364\) −3.70916e15 −1.59466
\(365\) −1.87714e15 6.09921e14i −0.793854 0.257939i
\(366\) 3.70943e13 2.69506e13i 0.0154320 0.0112120i
\(367\) 1.65759e15 + 1.20431e15i 0.678390 + 0.492880i 0.872823 0.488036i \(-0.162287\pi\)
−0.194433 + 0.980916i \(0.562287\pi\)
\(368\) −1.36883e15 4.21284e15i −0.551142 1.69624i
\(369\) −2.70613e15 + 8.79276e14i −1.07199 + 0.348311i
\(370\) 1.91210e14 2.63178e14i 0.0745246 0.102574i
\(371\) 2.79736e14 + 3.85023e14i 0.107277 + 0.147653i
\(372\) −1.43888e14 + 4.42843e14i −0.0542961 + 0.167106i
\(373\) 2.51752e13i 0.00934802i −0.999989 0.00467401i \(-0.998512\pi\)
0.999989 0.00467401i \(-0.00148779\pi\)
\(374\) −1.76394e14 + 2.12227e13i −0.0644547 + 0.00775481i
\(375\) −4.24330e14 −0.152587
\(376\) −2.68863e14 8.73589e13i −0.0951490 0.0309158i
\(377\) 4.70808e15 3.42062e15i 1.63982 1.19140i
\(378\) 7.92281e13 + 5.75626e13i 0.0271599 + 0.0197328i
\(379\) 1.43400e14 + 4.41341e14i 0.0483855 + 0.148915i 0.972330 0.233611i \(-0.0750542\pi\)
−0.923945 + 0.382526i \(0.875054\pi\)
\(380\) 9.06487e14 2.94535e14i 0.301065 0.0978218i
\(381\) −1.55016e14 + 2.13362e14i −0.0506789 + 0.0697536i
\(382\) 1.63372e14 + 2.24862e14i 0.0525772 + 0.0723663i
\(383\) −8.81092e14 + 2.71172e15i −0.279144 + 0.859118i 0.708949 + 0.705260i \(0.249170\pi\)
−0.988093 + 0.153858i \(0.950830\pi\)
\(384\) 2.34519e14i 0.0731459i
\(385\) 2.09751e15 + 4.13017e14i 0.644080 + 0.126825i
\(386\) 3.49760e14 0.105742
\(387\) 3.35230e15 + 1.08923e15i 0.997876 + 0.324230i
\(388\) −1.89141e15 + 1.37419e15i −0.554365 + 0.402769i
\(389\) 7.06874e14 + 5.13574e14i 0.204007 + 0.148220i 0.685098 0.728451i \(-0.259759\pi\)
−0.481091 + 0.876671i \(0.659759\pi\)
\(390\) 2.83112e13 + 8.71329e13i 0.00804582 + 0.0247625i
\(391\) −3.08347e15 + 1.00188e15i −0.862936 + 0.280385i
\(392\) −1.23106e14 + 1.69442e14i −0.0339285 + 0.0466985i
\(393\) −4.06668e14 5.59731e14i −0.110379 0.151923i
\(394\) −3.89268e13 + 1.19804e14i −0.0104057 + 0.0320254i
\(395\) 5.39822e13i 0.0142124i
\(396\) 2.71936e15 2.52349e15i 0.705173 0.654382i
\(397\) 4.42682e15 1.13070 0.565352 0.824849i \(-0.308740\pi\)
0.565352 + 0.824849i \(0.308740\pi\)
\(398\) 8.24139e14 + 2.67779e14i 0.207349 + 0.0673718i
\(399\) −1.78417e14 + 1.29627e14i −0.0442179 + 0.0321262i
\(400\) 1.41165e15 + 1.02562e15i 0.344640 + 0.250396i
\(401\) −1.18516e15 3.64754e15i −0.285043 0.877272i −0.986386 0.164448i \(-0.947416\pi\)
0.701343 0.712824i \(-0.252584\pi\)
\(402\) 2.48900e13 8.08725e12i 0.00589751 0.00191622i
\(403\) −5.82444e15 + 8.01665e15i −1.35964 + 1.87138i
\(404\) −1.12791e15 1.55244e15i −0.259411 0.357048i
\(405\) 9.50251e14 2.92457e15i 0.215332 0.662723i
\(406\) 5.91386e14i 0.132043i
\(407\) 5.03210e15 + 2.80538e15i 1.10709 + 0.617199i
\(408\) −8.42180e13 −0.0182576
\(409\) 2.98772e15 + 9.70770e14i 0.638264 + 0.207385i 0.610233 0.792222i \(-0.291076\pi\)
0.0280319 + 0.999607i \(0.491076\pi\)
\(410\) 4.42191e14 3.21270e14i 0.0930908 0.0676344i
\(411\) 5.64695e14 + 4.10275e14i 0.117156 + 0.0851185i
\(412\) −1.92479e14 5.92389e14i −0.0393550 0.121122i
\(413\) 1.22190e15 3.97018e14i 0.246226 0.0800037i
\(414\) −7.37967e14 + 1.01572e15i −0.146566 + 0.201731i
\(415\) −1.26011e15 1.73439e15i −0.246671 0.339514i
\(416\) 1.16042e15 3.57141e15i 0.223901 0.689095i
\(417\) 7.99591e14i 0.152073i
\(418\) −1.31610e14 2.84043e14i −0.0246736 0.0532508i
\(419\) −5.46668e15 −1.01028 −0.505138 0.863039i \(-0.668558\pi\)
−0.505138 + 0.863039i \(0.668558\pi\)
\(420\) 4.77455e14 + 1.55134e14i 0.0869834 + 0.0282626i
\(421\) −2.12998e15 + 1.54752e15i −0.382545 + 0.277935i −0.762394 0.647113i \(-0.775976\pi\)
0.379849 + 0.925049i \(0.375976\pi\)
\(422\) −5.99102e13 4.35273e13i −0.0106078 0.00770703i
\(423\) −6.48936e14 1.99722e15i −0.113282 0.348645i
\(424\) −3.04561e14 + 9.89579e13i −0.0524178 + 0.0170316i
\(425\) 7.50674e14 1.03321e15i 0.127385 0.175330i
\(426\) −5.06020e13 6.96477e13i −0.00846662 0.0116533i
\(427\) 1.65224e15 5.08508e15i 0.272588 0.838940i
\(428\) 9.73334e15i 1.58343i
\(429\) −1.47221e15 + 6.82144e14i −0.236171 + 0.109429i
\(430\) −6.77088e14 −0.107111
\(431\) −5.35157e15 1.73883e15i −0.834868 0.271265i −0.139773 0.990184i \(-0.544637\pi\)
−0.695094 + 0.718919i \(0.744637\pi\)
\(432\) 1.39721e15 1.01513e15i 0.214961 0.156178i
\(433\) −3.58944e15 2.60788e15i −0.544628 0.395695i 0.281173 0.959657i \(-0.409276\pi\)
−0.825801 + 0.563962i \(0.809276\pi\)
\(434\) −3.11173e14 9.57693e14i −0.0465655 0.143314i
\(435\) −7.49106e14 + 2.43399e14i −0.110562 + 0.0359239i
\(436\) −3.91249e15 + 5.38509e15i −0.569554 + 0.783923i
\(437\) −3.35786e15 4.62170e15i −0.482142 0.663611i
\(438\) −4.70432e13 + 1.44784e14i −0.00666272 + 0.0205058i
\(439\) 3.03220e15i 0.423614i −0.977312 0.211807i \(-0.932065\pi\)
0.977312 0.211807i \(-0.0679348\pi\)
\(440\) −7.00449e14 + 1.25642e15i −0.0965296 + 0.173148i
\(441\) −1.55581e15 −0.211507
\(442\) −8.44431e14 2.74372e14i −0.113248 0.0367965i
\(443\) 2.48101e15 1.80256e15i 0.328251 0.238488i −0.411437 0.911438i \(-0.634973\pi\)
0.739688 + 0.672950i \(0.234973\pi\)
\(444\) 1.09455e15 + 7.95240e14i 0.142869 + 0.103801i
\(445\) −1.14332e15 3.51878e15i −0.147234 0.453139i
\(446\) 6.33649e14 2.05885e14i 0.0805081 0.0261587i
\(447\) 9.47876e14 1.30464e15i 0.118825 0.163548i
\(448\) −3.75532e15 5.16876e15i −0.464493 0.639320i
\(449\) −3.04119e14 + 9.35983e14i −0.0371164 + 0.114233i −0.967898 0.251343i \(-0.919128\pi\)
0.930782 + 0.365576i \(0.119128\pi\)
\(450\) 4.94559e14i 0.0595583i
\(451\) 6.58455e15 + 7.09562e15i 0.782468 + 0.843201i
\(452\) 7.09926e15 0.832496
\(453\) 1.47690e15 + 4.79874e14i 0.170908 + 0.0555314i
\(454\) −7.36209e14 + 5.34887e14i −0.0840748 + 0.0610839i
\(455\) 8.64321e15 + 6.27966e15i 0.974107 + 0.707730i
\(456\) −4.58563e13 1.41131e14i −0.00510047 0.0156976i
\(457\) −8.58679e15 + 2.79002e15i −0.942613 + 0.306274i −0.739710 0.672925i \(-0.765038\pi\)
−0.202903 + 0.979199i \(0.565038\pi\)
\(458\) 1.02156e15 1.40605e15i 0.110680 0.152338i
\(459\) −7.42999e14 1.02265e15i −0.0794533 0.109358i
\(460\) −4.01860e15 + 1.23680e16i −0.424158 + 1.30542i
\(461\) 1.05673e16i 1.10093i −0.834858 0.550465i \(-0.814450\pi\)
0.834858 0.550465i \(-0.185550\pi\)
\(462\) 3.18560e13 1.61781e14i 0.00327596 0.0166370i
\(463\) −4.39564e15 −0.446207 −0.223104 0.974795i \(-0.571619\pi\)
−0.223104 + 0.974795i \(0.571619\pi\)
\(464\) 9.91883e15 + 3.22282e15i 0.993923 + 0.322945i
\(465\) 1.08503e15 7.88324e14i 0.107331 0.0779807i
\(466\) 1.34879e14 + 9.79954e13i 0.0131713 + 0.00956952i
\(467\) 2.81220e15 + 8.65506e15i 0.271110 + 0.834390i 0.990223 + 0.139496i \(0.0445484\pi\)
−0.719113 + 0.694893i \(0.755452\pi\)
\(468\) 1.76325e16 5.72916e15i 1.67818 0.545275i
\(469\) 1.79382e15 2.46898e15i 0.168555 0.231996i
\(470\) 2.37109e14 + 3.26352e14i 0.0219968 + 0.0302761i
\(471\) −2.05601e14 + 6.32776e14i −0.0188322 + 0.0579595i
\(472\) 8.64503e14i 0.0781834i
\(473\) −1.43241e15 1.19056e16i −0.127909 1.06313i
\(474\) 4.16365e12 0.000367116
\(475\) 2.14018e15 + 6.95387e14i 0.186333 + 0.0605431i
\(476\) −3.93610e15 + 2.85974e15i −0.338395 + 0.245858i
\(477\) −1.92451e15 1.39824e15i −0.163384 0.118706i
\(478\) 4.30541e14 + 1.32507e15i 0.0360950 + 0.111089i
\(479\) −1.57757e16 + 5.12584e15i −1.30610 + 0.424377i −0.877699 0.479212i \(-0.840923\pi\)
−0.428400 + 0.903589i \(0.640923\pi\)
\(480\) −2.98746e14 + 4.11189e14i −0.0244261 + 0.0336197i
\(481\) 1.69235e16 + 2.32932e16i 1.36653 + 1.88087i
\(482\) −3.26072e14 + 1.00355e15i −0.0260035 + 0.0800304i
\(483\) 3.00895e15i 0.236991i
\(484\) −1.16788e16 4.78481e15i −0.908500 0.372214i
\(485\) 6.73396e15 0.517393
\(486\) −7.00684e14 2.27666e14i −0.0531746 0.0172775i
\(487\) 1.11704e16 8.11574e15i 0.837323 0.608351i −0.0842983 0.996441i \(-0.526865\pi\)
0.921622 + 0.388090i \(0.126865\pi\)
\(488\) 2.91064e15 + 2.11470e15i 0.215511 + 0.156578i
\(489\) 7.48693e14 + 2.30424e15i 0.0547584 + 0.168529i
\(490\) 2.84232e14 9.23524e13i 0.0205351 0.00667224i
\(491\) 6.03212e15 8.30250e15i 0.430508 0.592543i −0.537562 0.843224i \(-0.680655\pi\)
0.968070 + 0.250681i \(0.0806545\pi\)
\(492\) 1.33616e15 + 1.83907e15i 0.0942038 + 0.129660i
\(493\) 2.35886e15 7.25981e15i 0.164293 0.505643i
\(494\) 1.56448e15i 0.107648i
\(495\) −1.06091e16 + 1.27642e15i −0.721184 + 0.0867686i
\(496\) −1.77584e16 −1.19265
\(497\) −9.54767e15 3.10223e15i −0.633518 0.205842i
\(498\) −1.33773e14 + 9.71918e13i −0.00876986 + 0.00637168i
\(499\) −6.69383e15 4.86335e15i −0.433582 0.315016i 0.349498 0.936937i \(-0.386352\pi\)
−0.783080 + 0.621922i \(0.786352\pi\)
\(500\) −5.09716e15 1.56874e16i −0.326218 1.00400i
\(501\) −2.31319e15 + 7.51602e14i −0.146280 + 0.0475293i
\(502\) 3.17124e14 4.36484e14i 0.0198156 0.0272738i
\(503\) −4.52184e15 6.22378e15i −0.279195 0.384279i 0.646272 0.763107i \(-0.276327\pi\)
−0.925467 + 0.378828i \(0.876327\pi\)
\(504\) −1.17521e15 + 3.61691e15i −0.0717019 + 0.220676i
\(505\) 5.52713e15i 0.333236i
\(506\) 4.19077e15 + 8.25196e14i 0.249684 + 0.0491648i
\(507\) −5.69855e15 −0.335519
\(508\) −9.75005e15 3.16798e15i −0.567315 0.184332i
\(509\) −1.46850e16 + 1.06693e16i −0.844436 + 0.613518i −0.923606 0.383343i \(-0.874773\pi\)
0.0791706 + 0.996861i \(0.474773\pi\)
\(510\) 9.72224e13 + 7.06362e13i 0.00552517 + 0.00401427i
\(511\) 5.48578e15 + 1.68835e16i 0.308115 + 0.948281i
\(512\) 1.07332e16 3.48743e15i 0.595813 0.193591i
\(513\) 1.30918e15 1.80193e15i 0.0718283 0.0988632i
\(514\) −1.85585e14 2.55436e14i −0.0100639 0.0138517i
\(515\) −5.54403e14 + 1.70628e15i −0.0297154 + 0.0914547i
\(516\) 2.81601e15i 0.149188i
\(517\) −5.23681e15 + 4.85962e15i −0.274235 + 0.254483i
\(518\) −2.92588e15 −0.151453
\(519\) 1.80344e15 + 5.85973e14i 0.0922778 + 0.0299829i
\(520\) −5.81586e15 + 4.22547e15i −0.294167 + 0.213725i
\(521\) −2.36450e16 1.71791e16i −1.18226 0.858962i −0.189835 0.981816i \(-0.560795\pi\)
−0.992425 + 0.122854i \(0.960795\pi\)
\(522\) −9.13453e14 2.81132e15i −0.0451506 0.138959i
\(523\) 1.30551e16 4.24185e15i 0.637924 0.207274i 0.0278421 0.999612i \(-0.491136\pi\)
0.610082 + 0.792338i \(0.291136\pi\)
\(524\) 1.58082e16 2.17581e16i 0.763650 1.05107i
\(525\) 6.96681e14 + 9.58899e14i 0.0332719 + 0.0457949i
\(526\) 9.63282e12 2.96468e13i 0.000454819 0.00139979i
\(527\) 1.29978e16i 0.606743i
\(528\) −2.53982e15 1.41594e15i −0.117219 0.0653493i
\(529\) 5.60292e16 2.55671
\(530\) 4.34588e14 + 1.41206e14i 0.0196075 + 0.00637087i
\(531\) −5.19540e15 + 3.77468e15i −0.231767 + 0.168389i
\(532\) −6.93549e15 5.03893e15i −0.305920 0.222264i
\(533\) 1.49491e16 + 4.60085e16i 0.652005 + 2.00667i
\(534\) −2.71403e14 + 8.81841e13i −0.0117049 + 0.00380315i
\(535\) 1.64787e16 2.26810e16i 0.702749 0.967251i
\(536\) 1.20703e15 + 1.66133e15i 0.0509013 + 0.0700596i
\(537\) −1.16863e15 + 3.59667e15i −0.0487339 + 0.149988i
\(538\) 5.72058e15i 0.235910i
\(539\) 2.22519e15 + 4.80242e15i 0.0907474 + 0.195852i
\(540\) −5.07025e15 −0.204487
\(541\) −3.22324e16 1.04730e16i −1.28561 0.417720i −0.415058 0.909795i \(-0.636239\pi\)
−0.870553 + 0.492075i \(0.836239\pi\)
\(542\) −3.56089e15 + 2.58714e15i −0.140463 + 0.102053i
\(543\) 2.58972e15 + 1.88154e15i 0.101031 + 0.0734031i
\(544\) −1.52212e15 4.68460e15i −0.0587293 0.180750i
\(545\) 1.82341e16 5.92461e15i 0.695832 0.226090i
\(546\) 4.84350e14 6.66650e14i 0.0182811 0.0251618i
\(547\) 6.64521e15 + 9.14634e15i 0.248076 + 0.341447i 0.914836 0.403825i \(-0.132320\pi\)
−0.666760 + 0.745272i \(0.732320\pi\)
\(548\) −8.38456e15 + 2.58050e16i −0.309597 + 0.952842i
\(549\) 2.67255e16i 0.976093i
\(550\) −1.52659e15 + 7.07339e14i −0.0551499 + 0.0255536i
\(551\) 1.34503e16 0.480641
\(552\) 1.92557e15 + 6.25657e14i 0.0680653 + 0.0221158i
\(553\) 3.92802e14 2.85387e14i 0.0137348 0.00997892i
\(554\) −3.95644e15 2.87452e15i −0.136850 0.0994276i
\(555\) −1.20422e15 3.70619e15i −0.0412047 0.126815i
\(556\) 2.95608e16 9.60489e15i 1.00062 0.325120i
\(557\) −1.29662e16 + 1.78464e16i −0.434190 + 0.597612i −0.968909 0.247419i \(-0.920418\pi\)
0.534718 + 0.845030i \(0.320418\pi\)
\(558\) 2.95850e15 + 4.07203e15i 0.0980092 + 0.134898i
\(559\) 1.85186e16 5.69943e16i 0.606927 1.86793i
\(560\) 1.91463e16i 0.620809i
\(561\) −1.03636e15 + 1.85895e15i −0.0332454 + 0.0596335i
\(562\) 3.87558e15 0.123004
\(563\) 2.57416e15 + 8.36396e14i 0.0808324 + 0.0262640i 0.349154 0.937065i \(-0.386469\pi\)
−0.268322 + 0.963329i \(0.586469\pi\)
\(564\) −1.35730e15 + 9.86134e14i −0.0421697 + 0.0306381i
\(565\) −1.65430e16 1.20192e16i −0.508537 0.369474i
\(566\) −6.55438e14 2.01723e15i −0.0199358 0.0613560i
\(567\) −2.63043e16 + 8.54679e15i −0.791641 + 0.257220i
\(568\) 3.97053e15 5.46496e15i 0.118238 0.162741i
\(569\) 2.84460e16 + 3.91525e16i 0.838199 + 1.15368i 0.986341 + 0.164716i \(0.0526707\pi\)
−0.148142 + 0.988966i \(0.547329\pi\)
\(570\) −6.54339e13 + 2.01385e14i −0.00190789 + 0.00587188i
\(571\) 5.69972e16i 1.64451i −0.569118 0.822256i \(-0.692715\pi\)
0.569118 0.822256i \(-0.307285\pi\)
\(572\) −4.29034e16 4.62334e16i −1.22494 1.32002i
\(573\) 3.32958e15 0.0940723
\(574\) −4.67545e15 1.51914e15i −0.130723 0.0424745i
\(575\) −2.48393e16 + 1.80468e16i −0.687278 + 0.499336i
\(576\) 2.58357e16 + 1.87707e16i 0.707432 + 0.513979i
\(577\) 1.17029e16 + 3.60179e16i 0.317131 + 0.976030i 0.974868 + 0.222782i \(0.0715139\pi\)
−0.657737 + 0.753248i \(0.728486\pi\)
\(578\) 3.67757e15 1.19491e15i 0.0986265 0.0320457i
\(579\) 2.46274e15 3.38968e15i 0.0653654 0.0899677i
\(580\) −1.79969e16 2.47706e16i −0.472748 0.650681i
\(581\) −5.95848e15 + 1.83383e16i −0.154910 + 0.476763i
\(582\) 5.19390e14i 0.0133646i
\(583\) −1.56351e15 + 7.94033e15i −0.0398190 + 0.202221i
\(584\) −1.19452e16 −0.301105
\(585\) −5.07875e16 1.65019e16i −1.26713 0.411716i
\(586\) −7.63666e15 + 5.54836e15i −0.188590 + 0.137018i
\(587\) −5.90831e16 4.29264e16i −1.44422 1.04929i −0.987138 0.159869i \(-0.948893\pi\)
−0.457087 0.889422i \(-0.651107\pi\)
\(588\) 3.84093e14 + 1.18212e15i 0.00929336 + 0.0286020i
\(589\) −2.17814e16 + 7.07721e15i −0.521668 + 0.169500i
\(590\) 7.25085e14 9.97994e14i 0.0171900 0.0236601i
\(591\) 8.86983e14 + 1.22083e15i 0.0208157 + 0.0286503i
\(592\) −1.59449e16 + 4.90733e16i −0.370417 + 1.14003i
\(593\) 5.88056e16i 1.35235i −0.736739 0.676177i \(-0.763635\pi\)
0.736739 0.676177i \(-0.236365\pi\)
\(594\) 1.98924e14 + 1.65337e15i 0.00452864 + 0.0376402i
\(595\) 1.40136e16 0.315827
\(596\) 5.96185e16 + 1.93712e16i 1.33016 + 0.432195i
\(597\) 8.39813e15 6.10160e15i 0.185497 0.134771i
\(598\) 1.72689e16 + 1.25466e16i 0.377622 + 0.274359i
\(599\) −1.24184e16 3.82200e16i −0.268847 0.827426i −0.990782 0.135465i \(-0.956747\pi\)
0.721935 0.691961i \(-0.243253\pi\)
\(600\) −7.58508e14 + 2.46454e14i −0.0162575 + 0.00528237i
\(601\) 3.98531e16 5.48531e16i 0.845699 1.16400i −0.139095 0.990279i \(-0.544419\pi\)
0.984794 0.173725i \(-0.0555805\pi\)
\(602\) 3.57955e15 + 4.92683e15i 0.0752055 + 0.103512i
\(603\) −4.71385e15 + 1.45077e16i −0.0980555 + 0.301784i
\(604\) 6.03652e16i 1.24327i
\(605\) 1.91136e16 + 3.09221e16i 0.389771 + 0.630575i
\(606\) 4.26307e14 0.00860770
\(607\) 2.51227e16 + 8.16287e15i 0.502267 + 0.163196i 0.549182 0.835702i \(-0.314939\pi\)
−0.0469156 + 0.998899i \(0.514939\pi\)
\(608\) 7.02159e15 5.10148e15i 0.139000 0.100989i
\(609\) 5.73138e15 + 4.16409e15i 0.112345 + 0.0816237i
\(610\) −1.58641e15 4.88248e15i −0.0307920 0.0947680i
\(611\) −3.39559e16 + 1.10329e16i −0.652631 + 0.212053i
\(612\) 1.42942e16 1.96743e16i 0.272052 0.374447i
\(613\) −2.42369e15 3.33593e15i −0.0456788 0.0628715i 0.785567 0.618777i \(-0.212372\pi\)
−0.831245 + 0.555906i \(0.812372\pi\)
\(614\) 5.72199e14 1.76105e15i 0.0106792 0.0328671i
\(615\) 6.54761e15i 0.121013i
\(616\) 1.28454e16 1.54548e15i 0.235106 0.0282865i
\(617\) −7.67673e16 −1.39144 −0.695721 0.718312i \(-0.744915\pi\)
−0.695721 + 0.718312i \(0.744915\pi\)
\(618\) 1.31605e14 + 4.27611e13i 0.00236234 + 0.000767569i
\(619\) 7.01421e16 5.09612e16i 1.24691 0.905933i 0.248871 0.968537i \(-0.419940\pi\)
0.998038 + 0.0626038i \(0.0199405\pi\)
\(620\) 4.21780e16 + 3.06441e16i 0.742567 + 0.539506i
\(621\) 9.39077e15 + 2.89018e16i 0.163739 + 0.503936i
\(622\) 7.71427e14 2.50652e14i 0.0133215 0.00432841i
\(623\) −1.95600e16 + 2.69220e16i −0.334534 + 0.460447i
\(624\) −8.54166e15 1.17566e16i −0.144689 0.199147i
\(625\) −6.38465e15 + 1.96499e16i −0.107117 + 0.329671i
\(626\) 6.24309e15i 0.103742i
\(627\) −3.67949e15 7.24520e14i −0.0605594 0.0119246i
\(628\) −2.58634e16 −0.421626
\(629\) 3.59178e16 + 1.16704e16i 0.579971 + 0.188444i
\(630\) 4.39029e15 3.18973e15i 0.0702182 0.0510165i
\(631\) 2.77534e16 + 2.01640e16i 0.439684 + 0.319449i 0.785509 0.618850i \(-0.212401\pi\)
−0.345826 + 0.938299i \(0.612401\pi\)
\(632\) 1.00957e14 + 3.10714e14i 0.00158429 + 0.00487593i
\(633\) −8.43685e14 + 2.74130e14i −0.0131147 + 0.00426122i
\(634\) −2.86769e15 + 3.94703e15i −0.0441567 + 0.0607764i
\(635\) 1.73565e16 + 2.38891e16i 0.264740 + 0.364383i
\(636\) −5.87276e14 + 1.80745e15i −0.00887360 + 0.0273101i
\(637\) 2.64512e16i 0.395922i
\(638\) −7.37142e15 + 6.84049e15i −0.109302 + 0.101429i
\(639\) 5.01793e16 0.737088
\(640\) −2.49728e16 8.11417e15i −0.363403 0.118077i
\(641\) 7.99361e15 5.80770e15i 0.115238 0.0837252i −0.528674 0.848825i \(-0.677310\pi\)
0.643912 + 0.765100i \(0.277310\pi\)
\(642\) −1.74938e15 1.27100e15i −0.0249847 0.0181525i
\(643\) −9.87864e15 3.04033e16i −0.139776 0.430185i 0.856527 0.516103i \(-0.172618\pi\)
−0.996302 + 0.0859179i \(0.972618\pi\)
\(644\) 1.11241e17 3.61443e16i 1.55937 0.506669i
\(645\) −4.76754e15 + 6.56196e15i −0.0662119 + 0.0911329i
\(646\) −1.20621e15 1.66020e15i −0.0165969 0.0228436i
\(647\) 3.70095e16 1.13903e17i 0.504530 1.55278i −0.297029 0.954868i \(-0.595996\pi\)
0.801559 0.597916i \(-0.204004\pi\)
\(648\) 1.86105e16i 0.251367i
\(649\) 1.90822e16 + 1.06383e16i 0.255365 + 0.142365i
\(650\) −8.40827e15 −0.111488
\(651\) −1.14725e16 3.72763e15i −0.150720 0.0489719i
\(652\) −7.61940e16 + 5.53582e16i −0.991826 + 0.720604i
\(653\) 1.37861e16 + 1.00162e16i 0.177812 + 0.129188i 0.673131 0.739523i \(-0.264949\pi\)
−0.495319 + 0.868711i \(0.664949\pi\)
\(654\) −4.56965e14 1.40639e15i −0.00584004 0.0179738i
\(655\) −7.36736e16 + 2.39380e16i −0.932963 + 0.303138i
\(656\) −5.09588e16 + 7.01387e16i −0.639434 + 0.880106i
\(657\) −5.21564e16 7.17872e16i −0.648508 0.892595i
\(658\) 1.12118e15 3.45064e15i 0.0138140 0.0425152i
\(659\) 3.13884e16i 0.383228i −0.981470 0.191614i \(-0.938628\pi\)
0.981470 0.191614i \(-0.0613722\pi\)
\(660\) 3.58896e15 + 7.74573e15i 0.0434216 + 0.0937128i
\(661\) −6.39115e16 −0.766250 −0.383125 0.923697i \(-0.625152\pi\)
−0.383125 + 0.923697i \(0.625152\pi\)
\(662\) −4.00899e15 1.30260e15i −0.0476307 0.0154761i
\(663\) −8.60491e15 + 6.25183e15i −0.101313 + 0.0736082i
\(664\) −1.04966e16 7.62623e15i −0.122473 0.0889819i
\(665\) 7.63035e15 + 2.34838e16i 0.0882297 + 0.271543i
\(666\) 1.39090e16 4.51930e15i 0.159386 0.0517876i
\(667\) −1.07867e17 + 1.48466e17i −1.22499 + 1.68605i
\(668\) −5.55733e16 7.64900e16i −0.625471 0.860887i
\(669\) 2.46635e15 7.59065e15i 0.0275105 0.0846686i
\(670\) 2.93024e15i 0.0323932i
\(671\) 8.24952e16 3.82239e16i 0.903844 0.418793i
\(672\) 4.57139e15 0.0496401
\(673\) 6.41056e16 + 2.08292e16i 0.689931 + 0.224172i 0.632938 0.774202i \(-0.281849\pi\)
0.0569928 + 0.998375i \(0.481849\pi\)
\(674\) −1.08793e16 + 7.90427e15i −0.116049 + 0.0843146i
\(675\) −9.68447e15 7.03618e15i −0.102389 0.0743900i
\(676\) −6.84524e16 2.10675e17i −0.717312 2.20766i
\(677\) −1.68760e17 + 5.48334e16i −1.75282 + 0.569525i −0.996417 0.0845814i \(-0.973045\pi\)
−0.756402 + 0.654107i \(0.773045\pi\)
\(678\) −9.27037e14 + 1.27596e15i −0.00954374 + 0.0131358i
\(679\) −3.56003e16 4.89996e16i −0.363275 0.500005i
\(680\) −2.91388e15 + 8.96800e15i −0.0294726 + 0.0907072i
\(681\) 1.09012e16i 0.109293i
\(682\) 8.33802e15 1.49562e16i 0.0828622 0.148633i
\(683\) 1.54821e17 1.52512 0.762561 0.646916i \(-0.223942\pi\)
0.762561 + 0.646916i \(0.223942\pi\)
\(684\) 4.07530e16 + 1.32414e16i 0.397945 + 0.129300i
\(685\) 6.32263e16 4.59366e16i 0.612004 0.444647i
\(686\) −1.22492e16 8.89960e15i −0.117534 0.0853937i
\(687\) −6.43365e15 1.98007e16i −0.0611951 0.188339i
\(688\) 1.02141e17 3.31876e16i 0.963095 0.312928i
\(689\) −2.37722e16 + 3.27197e16i −0.222206 + 0.305840i
\(690\) −1.69815e15 2.33731e15i −0.0157356 0.0216581i
\(691\) −1.84628e16 + 5.68228e16i −0.169602 + 0.521981i −0.999346 0.0361634i \(-0.988486\pi\)
0.829744 + 0.558144i \(0.188486\pi\)
\(692\) 7.37118e16i 0.671275i
\(693\) 6.53747e16 + 7.04488e16i 0.590215 + 0.636025i
\(694\) −1.84869e15 −0.0165465
\(695\) −8.51449e16 2.76653e16i −0.755527 0.245485i
\(696\) −3.85654e15 + 2.80194e15i −0.0339267 + 0.0246492i
\(697\) 5.13361e16 + 3.72978e16i 0.447740 + 0.325302i
\(698\) 3.41877e15 + 1.05219e16i 0.0295623 + 0.0909833i
\(699\) 1.89943e15 6.17163e14i 0.0162840 0.00529099i
\(700\) −2.70817e16 + 3.72747e16i −0.230190 + 0.316830i
\(701\) 7.72660e16 + 1.06348e17i 0.651149 + 0.896230i 0.999148 0.0412651i \(-0.0131388\pi\)
−0.347999 + 0.937495i \(0.613139\pi\)
\(702\) −2.57173e15 + 7.91498e15i −0.0214884 + 0.0661344i
\(703\) 6.65450e16i 0.551294i
\(704\) 2.09895e16 1.06595e17i 0.172411 0.875592i
\(705\) 4.83236e15 0.0393573
\(706\) 1.31335e16 + 4.26733e15i 0.106060 + 0.0344610i
\(707\) 4.02181e16 2.92202e16i 0.322037 0.233973i
\(708\) 4.15065e15 + 3.01563e15i 0.0329547 + 0.0239430i
\(709\) 2.05738e16 + 6.33197e16i 0.161971 + 0.498496i 0.998800 0.0489682i \(-0.0155933\pi\)
−0.836829 + 0.547464i \(0.815593\pi\)
\(710\) −9.16726e15 + 2.97862e15i −0.0715632 + 0.0232523i
\(711\) −1.42649e15 + 1.96339e15i −0.0110421 + 0.0151981i
\(712\) −1.31616e16 1.81153e16i −0.101025 0.139048i
\(713\) 9.65605e16 2.97183e17i 0.734958 2.26197i
\(714\) 1.08087e15i 0.00815801i
\(715\) 2.17011e16 + 1.80371e17i 0.162423 + 1.34999i
\(716\) −1.47007e17 −1.09108
\(717\) 1.58734e16 + 5.15757e15i 0.116830 + 0.0379603i
\(718\) 2.51709e16 1.82877e16i 0.183718 0.133479i
\(719\) 1.96633e17 + 1.42862e17i 1.42326 + 1.03406i 0.991223 + 0.132198i \(0.0422034\pi\)
0.432032 + 0.901858i \(0.357797\pi\)
\(720\) −2.95734e16 9.10176e16i −0.212279 0.653327i
\(721\) 1.53467e16 4.98644e15i 0.109245 0.0354959i
\(722\) −9.10953e15 + 1.25382e16i −0.0643092 + 0.0885140i
\(723\) 7.42986e15 + 1.02263e16i 0.0520176 + 0.0715961i
\(724\) −3.84520e16 + 1.18343e17i −0.266985 + 0.821697i
\(725\) 7.22883e16i 0.497783i
\(726\) 2.38502e15 1.47423e15i 0.0162882 0.0100680i
\(727\) −1.06721e17 −0.722840 −0.361420 0.932403i \(-0.617708\pi\)
−0.361420 + 0.932403i \(0.617708\pi\)
\(728\) 6.14932e16 + 1.99803e16i 0.413084 + 0.134219i
\(729\) 1.07002e17 7.77416e16i 0.712898 0.517951i
\(730\) 1.37897e16 + 1.00188e16i 0.0911211 + 0.0662033i
\(731\) −2.42907e16 7.47592e16i −0.159197 0.489959i
\(732\) 2.03062e16 6.59789e15i 0.131996 0.0428883i
\(733\) −6.60750e16 + 9.09444e16i −0.426003 + 0.586343i −0.967030 0.254662i \(-0.918036\pi\)
0.541027 + 0.841005i \(0.318036\pi\)
\(734\) −1.04003e16 1.43147e16i −0.0665071 0.0915391i
\(735\) 1.10632e15 3.40489e15i 0.00701706 0.0215963i
\(736\) 1.18417e17i 0.744986i
\(737\) 5.15239e16 6.19905e15i 0.321517 0.0386830i
\(738\) 2.45725e16 0.152094
\(739\) 3.44750e15 + 1.12016e15i 0.0211660 + 0.00687724i 0.319581 0.947559i \(-0.396458\pi\)
−0.298415 + 0.954436i \(0.596458\pi\)
\(740\) 1.22552e17 8.90394e16i 0.746330 0.542241i
\(741\) −1.51620e16 1.10159e16i −0.0915901 0.0665441i
\(742\) −1.27004e15 3.90879e15i −0.00761019 0.0234218i
\(743\) −2.17749e17 + 7.07510e16i −1.29427 + 0.420533i −0.873583 0.486675i \(-0.838210\pi\)
−0.420683 + 0.907208i \(0.638210\pi\)
\(744\) 4.77098e15 6.56670e15i 0.0281300 0.0387177i
\(745\) −1.06129e17 1.46075e17i −0.620723 0.854352i
\(746\) −6.71834e13 + 2.06769e14i −0.000389789 + 0.00119965i
\(747\) 9.63798e16i 0.554706i
\(748\) −8.11741e16 1.59838e16i −0.463455 0.0912580i
\(749\) −2.52156e17 −1.42816
\(750\) 3.48512e15 + 1.13238e15i 0.0195817 + 0.00636247i
\(751\) −1.40230e17 + 1.01883e17i −0.781630 + 0.567888i −0.905468 0.424415i \(-0.860480\pi\)
0.123838 + 0.992302i \(0.460480\pi\)
\(752\) −5.17648e16 3.76093e16i −0.286238 0.207964i
\(753\) −1.99721e15 6.14678e15i −0.0109560 0.0337192i
\(754\) −4.77969e16 + 1.55301e16i −0.260118 + 0.0845176i
\(755\) 1.02199e17 1.40665e17i 0.551781 0.759461i
\(756\) 2.68048e16 + 3.68936e16i 0.143576 + 0.197615i
\(757\) −3.15983e16 + 9.72496e16i −0.167915 + 0.516788i −0.999239 0.0389991i \(-0.987583\pi\)
0.831325 + 0.555787i \(0.187583\pi\)
\(758\) 4.00752e15i 0.0211281i
\(759\) 3.75056e16 3.48042e16i 0.196176 0.182046i
\(760\) −1.66150e16 −0.0862222
\(761\) 8.39653e16 + 2.72820e16i 0.432307 + 0.140465i 0.517083 0.855935i \(-0.327018\pi\)
−0.0847768 + 0.996400i \(0.527018\pi\)
\(762\) 1.84257e15 1.33870e15i 0.00941225 0.00683840i
\(763\) −1.39508e17 1.01359e17i −0.707054 0.513705i
\(764\) 3.99958e16 + 1.23094e17i 0.201119 + 0.618982i
\(765\) −6.66178e16 + 2.16454e16i −0.332370 + 0.107993i
\(766\) 1.44732e16 1.99207e16i 0.0716460 0.0986123i
\(767\) 6.41754e16 + 8.83299e16i 0.315208 + 0.433846i
\(768\) 7.40428e15 2.27880e16i 0.0360841 0.111055i
\(769\) 4.00581e17i 1.93701i −0.248988 0.968507i \(-0.580098\pi\)
0.248988 0.968507i \(-0.419902\pi\)
\(770\) −1.61251e16 8.98970e15i −0.0773676 0.0431321i
\(771\) −3.78229e15 −0.0180065
\(772\) 1.54899e17 + 5.03297e16i 0.731720 + 0.237750i
\(773\) −7.66908e16 + 5.57191e16i −0.359473 + 0.261172i −0.752832 0.658212i \(-0.771313\pi\)
0.393359 + 0.919385i \(0.371313\pi\)
\(774\) −2.46264e16 1.78921e16i −0.114539 0.0832178i
\(775\) 3.80364e16 + 1.17064e17i 0.175545 + 0.540273i
\(776\) 3.87597e16 1.25938e16i 0.177505 0.0576748i
\(777\) −2.06018e16 + 2.83559e16i −0.0936222 + 0.128860i
\(778\) −4.43517e15 6.10449e15i −0.0200001 0.0275278i
\(779\) −3.45509e16 + 1.06337e17i −0.154609 + 0.475837i
\(780\) 4.26627e16i 0.189444i
\(781\) −7.17685e16 1.54892e17i −0.316248 0.682529i
\(782\) 2.79988e16 0.122433
\(783\) −6.80473e16 2.21099e16i −0.295284 0.0959437i
\(784\) −3.83506e16 + 2.78633e16i −0.165149 + 0.119988i
\(785\) 6.02679e16 + 4.37872e16i 0.257554 + 0.187124i
\(786\) 1.84634e15 + 5.68244e15i 0.00783025 + 0.0240990i
\(787\) 2.21028e17 7.18162e16i 0.930247 0.302255i 0.195583 0.980687i \(-0.437340\pi\)
0.734664 + 0.678432i \(0.237340\pi\)
\(788\) −3.44792e16 + 4.74565e16i −0.144012 + 0.198216i
\(789\) −2.19493e14 3.02106e14i −0.000909826 0.00125227i
\(790\) 1.44059e14 4.43368e14i 0.000592622 0.00182390i
\(791\) 1.83916e17i 0.750864i
\(792\) −5.86771e16 + 2.71878e16i −0.237748 + 0.110160i
\(793\) 4.54375e17 1.82715
\(794\) −3.63585e16 1.18136e16i −0.145105 0.0471475i
\(795\) 4.42853e15 3.21752e15i 0.0175411 0.0127444i
\(796\) 3.26456e17 + 2.37184e17i 1.28335 + 0.932410i
\(797\) −8.23799e16 2.53539e17i −0.321419 0.989226i −0.973031 0.230674i \(-0.925907\pi\)
0.651612 0.758552i \(-0.274093\pi\)
\(798\) 1.81130e15 5.88528e14i 0.00701413 0.00227903i
\(799\) −2.75271e16 + 3.78878e16i −0.105799 + 0.145619i
\(800\) −2.74179e16 3.77374e16i −0.104591 0.143957i
\(801\) 5.14003e16 1.58194e17i 0.194612 0.598955i
\(802\) 3.31208e16i 0.124467i
\(803\) −1.46994e17 + 2.63668e17i −0.548284 + 0.983476i
\(804\) 1.21868e16 0.0451185
\(805\) −3.20410e17 1.04107e17i −1.17742 0.382566i
\(806\) 6.92309e16 5.02992e16i 0.252516 0.183464i
\(807\) −5.54406e16 4.02800e16i −0.200718 0.145830i
\(808\) 1.03368e16 + 3.18133e16i 0.0371464 + 0.114325i
\(809\) 1.40819e17 4.57550e16i 0.502310 0.163210i −0.0468922 0.998900i \(-0.514932\pi\)
0.549202 + 0.835690i \(0.314932\pi\)
\(810\) −1.56092e16 + 2.14843e16i −0.0552677 + 0.0760695i
\(811\) 1.15528e17 + 1.59011e17i 0.406034 + 0.558858i 0.962246 0.272183i \(-0.0877455\pi\)
−0.556211 + 0.831041i \(0.687745\pi\)
\(812\) −8.50992e16 + 2.61909e17i −0.296886 + 0.913721i
\(813\) 5.27268e16i 0.182595i
\(814\) −3.38432e16 3.64700e16i −0.116339 0.125369i
\(815\) 2.71272e17 0.925678
\(816\) −1.81286e16 5.89032e15i −0.0614076 0.0199525i
\(817\) 1.12054e17 8.14120e16i 0.376786 0.273751i
\(818\) −2.19482e16 1.59463e16i −0.0732621 0.0532280i
\(819\) 1.48422e17 + 4.56795e17i 0.491807 + 1.51362i
\(820\) 2.42064e17 7.86515e16i 0.796247 0.258716i
\(821\) 1.65849e17 2.28272e17i 0.541570 0.745407i −0.447268 0.894400i \(-0.647603\pi\)
0.988838 + 0.148993i \(0.0476031\pi\)
\(822\) −3.54309e15 4.87664e15i −0.0114855 0.0158085i
\(823\) 9.51089e16 2.92715e17i 0.306071 0.941989i −0.673205 0.739456i \(-0.735083\pi\)
0.979275 0.202533i \(-0.0649173\pi\)
\(824\) 1.08579e16i 0.0346883i
\(825\) −3.89393e15 + 1.97754e16i −0.0123499 + 0.0627192i
\(826\) −1.10952e16 −0.0349345
\(827\) −1.41527e17 4.59850e16i −0.442391 0.143742i 0.0793472 0.996847i \(-0.474716\pi\)
−0.521739 + 0.853105i \(0.674716\pi\)
\(828\) −4.72986e17 + 3.43644e17i −1.46780 + 1.06642i
\(829\) −4.95024e17 3.59656e17i −1.52510 1.10805i −0.958885 0.283795i \(-0.908407\pi\)
−0.566216 0.824257i \(-0.691593\pi\)
\(830\) 5.72108e15 + 1.76077e16i 0.0174988 + 0.0538559i
\(831\) −5.57165e16 + 1.81034e16i −0.169191 + 0.0549736i
\(832\) 3.19131e17 4.39247e17i 0.962121 1.32425i
\(833\) 2.03938e16 + 2.80696e16i 0.0610418 + 0.0840169i
\(834\) −2.13382e15 + 6.56722e15i −0.00634105 + 0.0195157i
\(835\) 2.72326e17i 0.803472i
\(836\) −1.74135e16 1.44733e17i −0.0510090 0.423966i
\(837\) 1.21830e17 0.354325
\(838\) 4.48991e16 + 1.45886e16i 0.129650 + 0.0421259i
\(839\) −1.04528e17 + 7.59440e16i −0.299682 + 0.217732i −0.727457 0.686154i \(-0.759298\pi\)
0.427775 + 0.903885i \(0.359298\pi\)
\(840\) −7.07993e15 5.14387e15i −0.0201536 0.0146425i
\(841\) −2.41822e16 7.44251e16i −0.0683470 0.210351i
\(842\) 2.16237e16 7.02598e15i 0.0606818 0.0197167i
\(843\) 2.72889e16 3.75599e16i 0.0760362 0.104655i
\(844\) −2.02691e16 2.78980e16i −0.0560764 0.0771825i
\(845\) −1.97166e17 + 6.06813e17i −0.541615 + 1.66692i
\(846\) 1.81354e16i 0.0494657i
\(847\) 1.23957e17 3.02555e17i 0.335715 0.819415i
\(848\) −7.24803e16 −0.194915
\(849\) −2.41650e16 7.85168e15i −0.0645268 0.0209660i
\(850\) −8.92272e15 + 6.48274e15i −0.0236583 + 0.0171888i
\(851\) −7.34532e17 5.33669e17i −1.93390 1.40506i
\(852\) −1.23881e16 3.81266e16i −0.0323867 0.0996760i
\(853\) −1.40740e17 + 4.57292e16i −0.365362 + 0.118713i −0.485944 0.873990i \(-0.661524\pi\)
0.120582 + 0.992703i \(0.461524\pi\)
\(854\) −2.71405e16 + 3.73557e16i −0.0699633 + 0.0962963i
\(855\) −7.25461e16 9.98511e16i −0.185702 0.255597i
\(856\) 5.24312e16 1.61367e17i 0.133275 0.410177i
\(857\) 1.74618e17i 0.440761i 0.975414 + 0.220380i \(0.0707299\pi\)
−0.975414 + 0.220380i \(0.929270\pi\)
\(858\) 1.39120e16 1.67381e15i 0.0348711 0.00419548i
\(859\) −3.52017e17 −0.876203 −0.438102 0.898925i \(-0.644349\pi\)
−0.438102 + 0.898925i \(0.644349\pi\)
\(860\) −2.99864e17 9.74317e16i −0.741196 0.240829i
\(861\) −4.76437e16 + 3.46151e16i −0.116946 + 0.0849664i
\(862\) 3.93133e16 + 2.85628e16i 0.0958288 + 0.0696237i
\(863\) 1.33757e17 + 4.11662e17i 0.323781 + 0.996496i 0.971988 + 0.235031i \(0.0755193\pi\)
−0.648207 + 0.761464i \(0.724481\pi\)
\(864\) −4.39095e16 + 1.42670e16i −0.105554 + 0.0342966i
\(865\) 1.24795e17 1.71766e17i 0.297921 0.410053i
\(866\) 2.25214e16 + 3.09980e16i 0.0533934 + 0.0734897i
\(867\) 1.43142e16 4.40546e16i 0.0337018 0.103723i
\(868\) 4.68913e17i 1.09641i
\(869\) 8.10074e15 + 1.59510e15i 0.0188107 + 0.00370399i
\(870\) 6.80211e15 0.0156866
\(871\) 2.46654e17 + 8.01429e16i 0.564911 + 0.183551i
\(872\) 9.38725e16 6.82023e16i 0.213520 0.155132i
\(873\) 2.44921e17 + 1.77946e17i 0.553275 + 0.401977i
\(874\) 1.52452e16 + 4.69200e16i 0.0342031 + 0.105266i
\(875\) 4.06405e17 1.32049e17i 0.905546 0.294230i
\(876\) −4.16683e16 + 5.73514e16i −0.0922106 + 0.126917i
\(877\) 4.35819e17 + 5.99854e17i 0.957875 + 1.31840i 0.947939 + 0.318452i \(0.103163\pi\)
0.00993622 + 0.999951i \(0.496837\pi\)
\(878\) −8.09183e15 + 2.49041e16i −0.0176636 + 0.0543630i
\(879\) 1.13078e17i 0.245156i
\(880\) −2.38653e17 + 2.21463e17i −0.513890 + 0.476877i
\(881\) 4.44386e16 0.0950397 0.0475199 0.998870i \(-0.484868\pi\)
0.0475199 + 0.998870i \(0.484868\pi\)
\(882\) 1.27782e16 + 4.15189e15i 0.0271431 + 0.00881931i
\(883\) −3.11052e17 + 2.25993e17i −0.656250 + 0.476793i −0.865394 0.501092i \(-0.832932\pi\)
0.209145 + 0.977885i \(0.432932\pi\)
\(884\) −3.34494e17 2.43024e17i −0.700929 0.509255i
\(885\) −4.56650e15 1.40542e16i −0.00950438 0.0292515i
\(886\) −2.51874e16 + 8.18389e15i −0.0520693 + 0.0169183i
\(887\) 4.99808e17 6.87927e17i 1.02627 1.41254i 0.118557 0.992947i \(-0.462173\pi\)
0.907713 0.419592i \(-0.137827\pi\)
\(888\) −1.38626e16 1.90802e16i −0.0282726 0.0389139i
\(889\) 8.20710e16 2.52589e17i 0.166257 0.511686i
\(890\) 3.19516e16i 0.0642913i
\(891\) −4.10791e17 2.29015e17i −0.821023 0.457717i
\(892\) 3.10252e17 0.615922
\(893\) −7.84801e16 2.54997e16i −0.154757 0.0502837i
\(894\) −1.12667e16 + 8.18575e15i −0.0220685 + 0.0160337i
\(895\) 3.42560e17 + 2.48884e17i 0.666497 + 0.484239i
\(896\) 7.29808e16 + 2.24612e17i 0.141046 + 0.434095i
\(897\) 2.43189e17 7.90169e16i 0.466863 0.151693i
\(898\) 4.99560e15 6.87585e15i 0.00952641 0.0131120i
\(899\) 4.32436e17 + 5.95197e17i 0.819151 + 1.12746i
\(900\) 7.11660e16 2.19026e17i 0.133911 0.412137i
\(901\) 5.30499e16i 0.0991598i
\(902\) −3.51447e16 7.58496e16i −0.0652560 0.140836i
\(903\) 7.29526e16 0.134559
\(904\) −1.17697e17 3.82420e16i −0.215652 0.0700697i
\(905\) 2.89959e17 2.10668e17i 0.527771 0.383448i
\(906\) −1.08495e16 7.88263e15i −0.0196174 0.0142529i
\(907\) 1.65995e17 + 5.10879e17i 0.298161 + 0.917644i 0.982141 + 0.188144i \(0.0602472\pi\)
−0.683981 + 0.729500i \(0.739753\pi\)
\(908\) −4.03016e17 + 1.30948e17i −0.719130 + 0.233659i
\(909\) −1.46055e17 + 2.01027e17i −0.258901 + 0.356346i
\(910\) −5.42305e16 7.46418e16i −0.0954981 0.131442i
\(911\) −2.97700e17 + 9.16227e17i −0.520798 + 1.60285i 0.251681 + 0.967810i \(0.419017\pi\)
−0.772479 + 0.635040i \(0.780983\pi\)
\(912\) 3.35868e16i 0.0583713i
\(913\) −2.97502e17 + 1.37847e17i −0.513647 + 0.237997i
\(914\) 7.79707e16 0.133738
\(915\) −5.84886e16 1.90041e16i −0.0996655 0.0323833i
\(916\) 6.54748e17 4.75702e17i 1.10841 0.805309i
\(917\) 5.63674e17 + 4.09533e17i 0.948008 + 0.688768i
\(918\) 3.37333e15 + 1.03820e16i 0.00563641 + 0.0173471i
\(919\) −2.76851e16 + 8.99544e15i −0.0459572 + 0.0149324i −0.331905 0.943313i \(-0.607691\pi\)
0.285948 + 0.958245i \(0.407691\pi\)
\(920\) 1.33247e17 1.83399e17i 0.219750 0.302461i
\(921\) −1.30381e16 1.79454e16i −0.0213627 0.0294033i
\(922\) −2.82004e16 + 8.67918e16i −0.0459060 + 0.141284i
\(923\) 8.53126e17i 1.37976i
\(924\) 3.73881e16 6.70643e16i 0.0600761 0.107761i
\(925\) 3.57646e17 0.570956
\(926\) 3.61024e16 + 1.17304e16i 0.0572625 + 0.0186057i
\(927\) −6.52527e16 + 4.74089e16i −0.102830 + 0.0747105i
\(928\) −2.25558e17 1.63878e17i −0.353159 0.256585i
\(929\) −2.74426e17 8.44595e17i −0.426904 1.31388i −0.901159 0.433488i \(-0.857283\pi\)
0.474255 0.880387i \(-0.342717\pi\)
\(930\) −1.10154e16 + 3.57911e15i −0.0170256 + 0.00553194i
\(931\) −3.59343e16 + 4.94593e16i −0.0551837 + 0.0759539i
\(932\) 4.56329e16 + 6.28083e16i 0.0696278 + 0.0958344i
\(933\) 3.00263e15 9.24113e15i 0.00455210 0.0140099i
\(934\) 7.85907e16i 0.118383i
\(935\) 1.62094e17 + 1.74675e17i 0.242603 + 0.261434i
\(936\) −3.23187e17 −0.480617
\(937\) 2.41423e17 + 7.84430e16i 0.356731 + 0.115909i 0.481899 0.876227i \(-0.339947\pi\)
−0.125169 + 0.992135i \(0.539947\pi\)
\(938\) −2.13219e16 + 1.54912e16i −0.0313046 + 0.0227441i
\(939\) 6.05045e16 + 4.39591e16i 0.0882662 + 0.0641291i
\(940\) 5.80475e16 + 1.78652e17i 0.0841427 + 0.258965i
\(941\) −8.74347e17 + 2.84093e17i −1.25935 + 0.409187i −0.861263 0.508160i \(-0.830326\pi\)
−0.398087 + 0.917348i \(0.630326\pi\)
\(942\) 3.37730e15 4.64846e15i 0.00483353 0.00665278i
\(943\) −8.96670e17 1.23416e18i −1.27515 1.75510i
\(944\) −6.04646e16 + 1.86091e17i −0.0854415 + 0.262962i
\(945\) 1.31352e17i 0.184436i
\(946\) −2.00070e16 + 1.01606e17i −0.0279149 + 0.141766i
\(947\) −3.74821e17 −0.519666 −0.259833 0.965654i \(-0.583668\pi\)
−0.259833 + 0.965654i \(0.583668\pi\)
\(948\) 1.84396e15 + 5.99140e14i 0.00254040 + 0.000825427i
\(949\) −1.22049e18 + 8.86741e17i −1.67085 + 1.21395i
\(950\) −1.57220e16 1.14227e16i −0.0213879 0.0155392i
\(951\) 1.80603e16 + 5.55840e16i 0.0244142 + 0.0751393i
\(952\) 8.06603e16 2.62081e16i 0.108352 0.0352058i
\(953\) −2.39179e16 + 3.29202e16i −0.0319276 + 0.0439445i −0.824682 0.565596i \(-0.808646\pi\)
0.792755 + 0.609541i \(0.208646\pi\)
\(954\) 1.20750e16 + 1.66199e16i 0.0160176 + 0.0220464i
\(955\) 1.15201e17 3.54552e17i 0.151857 0.467369i
\(956\) 6.48791e17i 0.849879i
\(957\) 1.43902e16 + 1.19605e17i 0.0187325 + 0.155696i
\(958\) 1.43248e17 0.185309
\(959\) −6.68515e17 2.17214e17i −0.859408 0.279239i
\(960\) −5.94510e16 + 4.31937e16i −0.0759508 + 0.0551815i
\(961\) −3.76236e17 2.73351e17i −0.477661 0.347041i
\(962\) −7.68352e16 2.36474e17i −0.0969415 0.298355i
\(963\) 1.19869e18 3.89479e17i 1.50297 0.488345i
\(964\) −2.88817e17 + 3.97522e17i −0.359882 + 0.495335i
\(965\) −2.75742e17 3.79527e17i −0.341460 0.469979i
\(966\) −8.02980e15 + 2.47132e16i −0.00988194 + 0.0304135i
\(967\) 8.30859e17i 1.01618i −0.861305 0.508088i \(-0.830353\pi\)
0.861305 0.508088i \(-0.169647\pi\)
\(968\) 1.67845e17 + 1.42237e17i 0.204012 + 0.172886i
\(969\) −2.45829e16 −0.0296955
\(970\) −5.53075e16 1.79705e16i −0.0663978 0.0215739i
\(971\) 8.56168e17 6.22043e17i 1.02151 0.742173i 0.0549204 0.998491i \(-0.482510\pi\)
0.966592 + 0.256318i \(0.0825095\pi\)
\(972\) −2.77553e17 2.01654e17i −0.329116 0.239116i
\(973\) 2.48828e17 + 7.65814e17i 0.293239 + 0.902498i
\(974\) −1.13403e17 + 3.68467e16i −0.132822 + 0.0431564i
\(975\) −5.92047e16 + 8.14882e16i −0.0689173 + 0.0948565i
\(976\) 4.78631e17 + 6.58779e17i 0.553735 + 0.762151i
\(977\) 3.54188e17 1.09008e18i 0.407255 1.25340i −0.511742 0.859139i \(-0.671000\pi\)
0.918998 0.394263i \(-0.129000\pi\)
\(978\) 2.09232e16i 0.0239109i
\(979\) −5.61822e17 + 6.75951e16i −0.638120 + 0.0767748i
\(980\) 1.39168e17 0.157102
\(981\) 8.19750e17 + 2.66353e17i 0.919745 + 0.298843i
\(982\) −7.16995e16 + 5.20927e16i −0.0799553 + 0.0580909i
\(983\) 1.03692e18 + 7.53369e17i 1.14928 + 0.835000i 0.988385 0.151972i \(-0.0485623\pi\)
0.160894 + 0.986972i \(0.448562\pi\)
\(984\) −1.22453e16 3.76871e16i −0.0134896 0.0415166i
\(985\) 1.60689e17 5.22111e16i 0.175942 0.0571670i
\(986\) −3.87476e16 + 5.33315e16i −0.0421680 + 0.0580393i
\(987\) −2.55472e16 3.51627e16i −0.0276338 0.0380346i
\(988\) 2.25125e17 6.92864e17i 0.242037 0.744915i
\(989\) 1.88976e18i 2.01943i
\(990\) 9.05409e16 + 1.78282e16i 0.0961687 + 0.0189364i
\(991\) −8.64117e17 −0.912285 −0.456143 0.889907i \(-0.650769\pi\)
−0.456143 + 0.889907i \(0.650769\pi\)
\(992\) 4.51499e17 + 1.46701e17i 0.473791 + 0.153944i
\(993\) −4.08523e16 + 2.96809e16i −0.0426109 + 0.0309587i
\(994\) 7.01384e16 + 5.09585e16i 0.0727172 + 0.0528322i
\(995\) −3.59163e17 1.10539e18i −0.370129 1.13914i
\(996\) −7.32301e16 + 2.37939e16i −0.0750125 + 0.0243731i
\(997\) −1.04050e18 + 1.43212e18i −1.05942 + 1.45817i −0.179081 + 0.983834i \(0.557312\pi\)
−0.880343 + 0.474337i \(0.842688\pi\)
\(998\) 4.19993e16 + 5.78071e16i 0.0425069 + 0.0585057i
\(999\) 1.09389e17 3.36664e17i 0.110047 0.338691i
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 11.13.d.a.2.6 44
11.6 odd 10 inner 11.13.d.a.6.6 yes 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
11.13.d.a.2.6 44 1.1 even 1 trivial
11.13.d.a.6.6 yes 44 11.6 odd 10 inner