Properties

Label 29.11.f.a.2.18
Level $29$
Weight $11$
Character 29.2
Analytic conductor $18.425$
Analytic rank $0$
Dimension $288$
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] = [29,11,Mod(2,29)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(29, base_ring=CyclotomicField(28))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 11, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("29.2");
 
S:= CuspForms(chi, 11);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 29.f (of order \(28\), degree \(12\), 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: \(18.4253603275\)
Analytic rank: \(0\)
Dimension: \(288\)
Relative dimension: \(24\) over \(\Q(\zeta_{28})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label 2.18
Character \(\chi\) \(=\) 29.2
Dual form 29.11.f.a.15.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(34.3912 + 3.87495i) q^{2} +(-318.343 - 200.028i) q^{3} +(169.411 + 38.6669i) q^{4} +(4257.16 - 3394.97i) q^{5} +(-10173.1 - 8112.76i) q^{6} +(622.677 + 2728.12i) q^{7} +(-27774.2 - 9718.63i) q^{8} +(35710.5 + 74153.6i) q^{9} +O(q^{10})\) \(q+(34.3912 + 3.87495i) q^{2} +(-318.343 - 200.028i) q^{3} +(169.411 + 38.6669i) q^{4} +(4257.16 - 3394.97i) q^{5} +(-10173.1 - 8112.76i) q^{6} +(622.677 + 2728.12i) q^{7} +(-27774.2 - 9718.63i) q^{8} +(35710.5 + 74153.6i) q^{9} +(159564. - 100261. i) q^{10} +(-127349. + 44561.3i) q^{11} +(-46196.2 - 46196.2i) q^{12} +(73775.7 - 153197. i) q^{13} +(10843.2 + 96236.2i) q^{14} +(-2.03432e6 + 229213. i) q^{15} +(-1.07785e6 - 519063. i) q^{16} +(-1.76715e6 + 1.76715e6i) q^{17} +(940784. + 2.68861e6i) q^{18} +(-1.07994e6 - 1.71872e6i) q^{19} +(852481. - 410533. i) q^{20} +(347477. - 993031. i) q^{21} +(-4.55234e6 + 1.03904e6i) q^{22} +(-672709. + 843551. i) q^{23} +(6.89773e6 + 8.64948e6i) q^{24} +(4.42451e6 - 1.93851e7i) q^{25} +(3.13086e6 - 4.98274e6i) q^{26} +(978939. - 8.68833e6i) q^{27} +486251. i q^{28} +(1.20015e7 + 1.66334e7i) q^{29} -7.08510e7 q^{30} +(-2.72154e7 - 3.06643e6i) q^{31} +(-9.54378e6 - 5.99675e6i) q^{32} +(4.94541e7 + 1.12876e7i) q^{33} +(-6.76220e7 + 5.39268e7i) q^{34} +(1.19127e7 + 9.50009e6i) q^{35} +(3.18245e6 + 1.39432e7i) q^{36} +(8.72371e7 + 3.05256e7i) q^{37} +(-3.04806e7 - 6.32936e7i) q^{38} +(-5.41296e7 + 3.40119e7i) q^{39} +(-1.51234e8 + 5.29190e7i) q^{40} +(-1.37470e8 - 1.37470e8i) q^{41} +(1.57981e7 - 3.28051e7i) q^{42} +(-5.14227e6 - 4.56389e7i) q^{43} +(-2.32973e7 + 2.62498e6i) q^{44} +(4.03775e8 + 1.94448e8i) q^{45} +(-2.64040e7 + 2.64040e7i) q^{46} +(-8.02579e7 - 2.29364e8i) q^{47} +(2.39297e8 + 3.80839e8i) q^{48} +(2.47446e8 - 1.19164e8i) q^{49} +(2.27280e8 - 6.49530e8i) q^{50} +(9.16039e8 - 2.09080e8i) q^{51} +(1.84221e7 - 2.31005e7i) q^{52} +(3.88892e7 + 4.87655e7i) q^{53} +(6.73337e7 - 2.95008e8i) q^{54} +(-3.90860e8 + 6.22049e8i) q^{55} +(9.21926e6 - 8.18232e7i) q^{56} +7.63162e8i q^{57} +(3.48292e8 + 6.18548e8i) q^{58} -1.10724e8 q^{59} +(-3.53499e8 - 3.98298e7i) q^{60} +(-8.47655e8 - 5.32617e8i) q^{61} +(-9.24086e8 - 2.10917e8i) q^{62} +(-1.80064e8 + 1.43596e8i) q^{63} +(6.52783e8 + 5.20577e8i) q^{64} +(-2.06024e8 - 9.02650e8i) q^{65} +(1.65704e9 + 5.79825e8i) q^{66} +(-1.09957e9 - 2.28329e9i) q^{67} +(-3.67705e8 + 2.31044e8i) q^{68} +(3.82886e8 - 1.33978e8i) q^{69} +(3.72880e8 + 3.72880e8i) q^{70} +(-6.98018e8 + 1.44945e9i) q^{71} +(-2.71161e8 - 2.40662e9i) q^{72} +(5.90298e8 - 6.65107e7i) q^{73} +(2.88190e9 + 1.38785e9i) q^{74} +(-5.28607e9 + 5.28607e9i) q^{75} +(-1.16497e8 - 3.32928e8i) q^{76} +(-2.00866e8 - 3.19676e8i) q^{77} +(-1.99338e9 + 9.59959e8i) q^{78} +(1.36404e9 - 3.89819e9i) q^{79} +(-6.35076e9 + 1.44952e9i) q^{80} +(9.80606e8 - 1.22964e9i) q^{81} +(-4.19506e9 - 5.26043e9i) q^{82} +(5.86595e8 - 2.57004e9i) q^{83} +(9.72638e7 - 1.54794e8i) q^{84} +(-1.52362e9 + 1.35225e10i) q^{85} -1.58950e9i q^{86} +(-4.93445e8 - 7.69577e9i) q^{87} +3.97009e9 q^{88} +(6.82927e8 + 7.69474e7i) q^{89} +(1.31328e10 + 8.25189e9i) q^{90} +(4.63879e8 + 1.05877e8i) q^{91} +(-1.46582e8 + 1.16895e8i) q^{92} +(8.05044e9 + 6.42001e9i) q^{93} +(-1.87139e9 - 8.19908e9i) q^{94} +(-1.04325e10 - 3.65049e9i) q^{95} +(1.83867e9 + 3.81805e9i) q^{96} +(-9.15356e9 + 5.75156e9i) q^{97} +(8.97173e9 - 3.13934e9i) q^{98} +(-7.85207e9 - 7.85207e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 288 q - 22 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} - 76784 q^{8} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 288 q - 22 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} - 76784 q^{8} - 14 q^{9} - 109580 q^{10} + 263632 q^{11} - 729308 q^{12} - 14 q^{13} - 502630 q^{14} + 721736 q^{15} + 16030218 q^{16} + 4537990 q^{17} - 3653920 q^{18} - 43706 q^{19} - 28125194 q^{20} + 8318690 q^{21} + 24431218 q^{22} - 1804156 q^{23} - 132227942 q^{24} + 76826206 q^{25} + 37018580 q^{26} + 57957318 q^{27} - 4091366 q^{29} - 201956616 q^{30} - 140893664 q^{31} + 121061292 q^{32} + 310830436 q^{33} + 244927186 q^{34} - 14588490 q^{35} - 559552838 q^{36} + 133858412 q^{37} + 21929586 q^{38} + 966545612 q^{39} - 137299672 q^{40} + 408348734 q^{41} - 14 q^{42} - 600101864 q^{43} - 52997658 q^{44} - 1241198886 q^{45} - 102035336 q^{46} + 830850184 q^{47} + 1136468440 q^{48} - 739457742 q^{49} - 3509687658 q^{50} - 2771976830 q^{51} + 70578506 q^{52} - 1225542446 q^{53} + 5404425756 q^{54} + 5929963944 q^{55} + 4468933076 q^{56} - 7683766382 q^{58} - 2316484772 q^{59} - 15584506756 q^{60} - 4735872558 q^{61} + 1072705536 q^{62} + 10136272594 q^{63} + 18488581888 q^{64} + 8688930046 q^{65} + 17014292728 q^{66} - 3314978814 q^{67} - 19937284744 q^{68} - 6050719742 q^{69} - 8553971346 q^{70} - 15734676412 q^{71} + 10135621864 q^{72} + 13472460778 q^{73} - 2860394408 q^{74} - 2553693192 q^{75} + 1533964122 q^{76} - 18826817864 q^{77} - 10732341438 q^{78} - 13300227084 q^{79} - 20977281038 q^{80} + 55998578950 q^{81} + 12348943522 q^{82} + 31177470234 q^{83} + 107438251148 q^{84} + 3272565918 q^{85} - 49229617522 q^{87} - 63399171248 q^{88} - 34988176660 q^{89} - 129126675228 q^{90} - 26793083114 q^{91} + 4799950834 q^{92} + 23488122938 q^{93} - 28591378914 q^{94} + 138203606358 q^{95} + 240366548688 q^{96} - 54535391692 q^{97} - 114107920008 q^{98} - 79431838892 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{28}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 34.3912 + 3.87495i 1.07472 + 0.121092i 0.631544 0.775340i \(-0.282422\pi\)
0.443180 + 0.896433i \(0.353850\pi\)
\(3\) −318.343 200.028i −1.31005 0.823161i −0.317892 0.948127i \(-0.602975\pi\)
−0.992161 + 0.124966i \(0.960118\pi\)
\(4\) 169.411 + 38.6669i 0.165440 + 0.0377606i
\(5\) 4257.16 3394.97i 1.36229 1.08639i 0.375076 0.926994i \(-0.377617\pi\)
0.987215 0.159396i \(-0.0509547\pi\)
\(6\) −10173.1 8112.76i −1.30827 1.04331i
\(7\) 622.677 + 2728.12i 0.0370486 + 0.162321i 0.990068 0.140588i \(-0.0448994\pi\)
−0.953020 + 0.302909i \(0.902042\pi\)
\(8\) −27774.2 9718.63i −0.847603 0.296589i
\(9\) 35710.5 + 74153.6i 0.604761 + 1.25580i
\(10\) 159564. 100261.i 1.59564 1.00261i
\(11\) −127349. + 44561.3i −0.790736 + 0.276690i −0.695276 0.718743i \(-0.744718\pi\)
−0.0954597 + 0.995433i \(0.530432\pi\)
\(12\) −46196.2 46196.2i −0.185652 0.185652i
\(13\) 73775.7 153197.i 0.198700 0.412604i −0.777682 0.628658i \(-0.783605\pi\)
0.976381 + 0.216054i \(0.0693188\pi\)
\(14\) 10843.2 + 96236.2i 0.0201613 + 0.178936i
\(15\) −2.03432e6 + 229213.i −2.67895 + 0.301845i
\(16\) −1.07785e6 519063.i −1.02791 0.495017i
\(17\) −1.76715e6 + 1.76715e6i −1.24460 + 1.24460i −0.286525 + 0.958073i \(0.592500\pi\)
−0.958073 + 0.286525i \(0.907500\pi\)
\(18\) 940784. + 2.68861e6i 0.497883 + 1.42287i
\(19\) −1.07994e6 1.71872e6i −0.436148 0.694125i 0.554254 0.832348i \(-0.313004\pi\)
−0.990401 + 0.138223i \(0.955861\pi\)
\(20\) 852481. 410533.i 0.266400 0.128292i
\(21\) 347477. 993031.i 0.0850803 0.243146i
\(22\) −4.55234e6 + 1.03904e6i −0.883328 + 0.201614i
\(23\) −672709. + 843551.i −0.104517 + 0.131061i −0.831339 0.555766i \(-0.812425\pi\)
0.726822 + 0.686826i \(0.240997\pi\)
\(24\) 6.89773e6 + 8.64948e6i 0.866264 + 1.08626i
\(25\) 4.42451e6 1.93851e7i 0.453070 1.98503i
\(26\) 3.13086e6 4.98274e6i 0.263510 0.419374i
\(27\) 978939. 8.68833e6i 0.0682240 0.605504i
\(28\) 486251.i 0.0282534i
\(29\) 1.20015e7 + 1.66334e7i 0.585122 + 0.810946i
\(30\) −7.08510e7 −2.91568
\(31\) −2.72154e7 3.06643e6i −0.950617 0.107109i −0.376983 0.926220i \(-0.623038\pi\)
−0.573634 + 0.819111i \(0.694467\pi\)
\(32\) −9.54378e6 5.99675e6i −0.284427 0.178717i
\(33\) 4.94541e7 + 1.12876e7i 1.26367 + 0.288423i
\(34\) −6.76220e7 + 5.39268e7i −1.48831 + 1.18689i
\(35\) 1.19127e7 + 9.50009e6i 0.226815 + 0.180879i
\(36\) 3.18245e6 + 1.39432e7i 0.0526320 + 0.230596i
\(37\) 8.72371e7 + 3.05256e7i 1.25803 + 0.440205i 0.875267 0.483639i \(-0.160685\pi\)
0.382768 + 0.923845i \(0.374971\pi\)
\(38\) −3.04806e7 6.32936e7i −0.384685 0.798807i
\(39\) −5.41296e7 + 3.40119e7i −0.599946 + 0.376971i
\(40\) −1.51234e8 + 5.29190e7i −1.47689 + 0.516787i
\(41\) −1.37470e8 1.37470e8i −1.18655 1.18655i −0.978014 0.208541i \(-0.933128\pi\)
−0.208541 0.978014i \(-0.566872\pi\)
\(42\) 1.57981e7 3.28051e7i 0.120881 0.251012i
\(43\) −5.14227e6 4.56389e7i −0.0349794 0.310451i −0.999003 0.0446354i \(-0.985787\pi\)
0.964024 0.265815i \(-0.0856412\pi\)
\(44\) −2.32973e7 + 2.62498e6i −0.141267 + 0.0159170i
\(45\) 4.03775e8 + 1.94448e8i 2.18815 + 1.05376i
\(46\) −2.64040e7 + 2.64040e7i −0.128198 + 0.128198i
\(47\) −8.02579e7 2.29364e8i −0.349944 1.00008i −0.975518 0.219918i \(-0.929421\pi\)
0.625575 0.780164i \(-0.284865\pi\)
\(48\) 2.39297e8 + 3.80839e8i 0.939143 + 1.49464i
\(49\) 2.47446e8 1.19164e8i 0.875993 0.421856i
\(50\) 2.27280e8 6.49530e8i 0.727297 2.07850i
\(51\) 9.16039e8 2.09080e8i 2.65499 0.605985i
\(52\) 1.84221e7 2.31005e7i 0.0484531 0.0607582i
\(53\) 3.88892e7 + 4.87655e7i 0.0929928 + 0.116609i 0.826151 0.563449i \(-0.190526\pi\)
−0.733158 + 0.680058i \(0.761954\pi\)
\(54\) 6.73337e7 2.95008e8i 0.146644 0.642489i
\(55\) −3.90860e8 + 6.22049e8i −0.776618 + 1.23598i
\(56\) 9.21926e6 8.18232e7i 0.0167400 0.148572i
\(57\) 7.63162e8i 1.26836i
\(58\) 3.48292e8 + 6.18548e8i 0.530645 + 0.942396i
\(59\) −1.10724e8 −0.154876 −0.0774379 0.996997i \(-0.524674\pi\)
−0.0774379 + 0.996997i \(0.524674\pi\)
\(60\) −3.53499e8 3.98298e7i −0.454603 0.0512215i
\(61\) −8.47655e8 5.32617e8i −1.00362 0.630617i −0.0732801 0.997311i \(-0.523347\pi\)
−0.930342 + 0.366694i \(0.880490\pi\)
\(62\) −9.24086e8 2.10917e8i −1.00868 0.230225i
\(63\) −1.80064e8 + 1.43596e8i −0.181437 + 0.144691i
\(64\) 6.52783e8 + 5.20577e8i 0.607951 + 0.484825i
\(65\) −2.06024e8 9.02650e8i −0.177562 0.777951i
\(66\) 1.65704e9 + 5.79825e8i 1.32317 + 0.462996i
\(67\) −1.09957e9 2.28329e9i −0.814423 1.69117i −0.718232 0.695804i \(-0.755048\pi\)
−0.0961914 0.995363i \(-0.530666\pi\)
\(68\) −3.67705e8 + 2.31044e8i −0.252903 + 0.158910i
\(69\) 3.82886e8 1.33978e8i 0.244807 0.0856617i
\(70\) 3.72880e8 + 3.72880e8i 0.221860 + 0.221860i
\(71\) −6.98018e8 + 1.44945e9i −0.386879 + 0.803362i 0.613033 + 0.790057i \(0.289949\pi\)
−0.999911 + 0.0133043i \(0.995765\pi\)
\(72\) −2.71161e8 2.40662e9i −0.140141 1.24378i
\(73\) 5.90298e8 6.65107e7i 0.284746 0.0320831i 0.0315635 0.999502i \(-0.489951\pi\)
0.253182 + 0.967419i \(0.418523\pi\)
\(74\) 2.88190e9 + 1.38785e9i 1.29873 + 0.625438i
\(75\) −5.28607e9 + 5.28607e9i −2.22754 + 2.22754i
\(76\) −1.16497e8 3.32928e8i −0.0459457 0.131305i
\(77\) −2.00866e8 3.19676e8i −0.0742083 0.118102i
\(78\) −1.99338e9 + 9.59959e8i −0.690425 + 0.332491i
\(79\) 1.36404e9 3.89819e9i 0.443293 1.26686i −0.478128 0.878290i \(-0.658684\pi\)
0.921420 0.388567i \(-0.127030\pi\)
\(80\) −6.35076e9 + 1.44952e9i −1.93810 + 0.442358i
\(81\) 9.80606e8 1.22964e9i 0.281235 0.352658i
\(82\) −4.19506e9 5.26043e9i −1.13154 1.41890i
\(83\) 5.86595e8 2.57004e9i 0.148918 0.652453i −0.844269 0.535920i \(-0.819965\pi\)
0.993187 0.116533i \(-0.0371781\pi\)
\(84\) 9.72638e7 1.54794e8i 0.0232570 0.0370134i
\(85\) −1.52362e9 + 1.35225e10i −0.343385 + 3.04762i
\(86\) 1.58950e9i 0.337885i
\(87\) −4.93445e8 7.69577e9i −0.0990017 1.54403i
\(88\) 3.97009e9 0.752293
\(89\) 6.82927e8 + 7.69474e7i 0.122299 + 0.0137798i 0.172902 0.984939i \(-0.444686\pi\)
−0.0506026 + 0.998719i \(0.516114\pi\)
\(90\) 1.31328e10 + 8.25189e9i 2.22405 + 1.39746i
\(91\) 4.63879e8 + 1.05877e8i 0.0743357 + 0.0169666i
\(92\) −1.46582e8 + 1.16895e8i −0.0222403 + 0.0177360i
\(93\) 8.05044e9 + 6.42001e9i 1.15719 + 0.922829i
\(94\) −1.87139e9 8.19908e9i −0.254991 1.11719i
\(95\) −1.04325e10 3.65049e9i −1.34825 0.471773i
\(96\) 1.83867e9 + 3.81805e9i 0.225501 + 0.468258i
\(97\) −9.15356e9 + 5.75156e9i −1.06594 + 0.669772i −0.946380 0.323055i \(-0.895290\pi\)
−0.119556 + 0.992827i \(0.538147\pi\)
\(98\) 8.97173e9 3.13934e9i 0.992535 0.347303i
\(99\) −7.85207e9 7.85207e9i −0.825673 0.825673i
\(100\) 1.49912e9 3.11296e9i 0.149912 0.311296i
\(101\) −3.61955e8 3.21244e9i −0.0344388 0.305653i −0.999109 0.0421940i \(-0.986565\pi\)
0.964671 0.263459i \(-0.0848633\pi\)
\(102\) 3.23138e10 3.64090e9i 2.92676 0.329767i
\(103\) 9.13065e8 + 4.39709e8i 0.0787618 + 0.0379297i 0.472850 0.881143i \(-0.343225\pi\)
−0.394088 + 0.919073i \(0.628940\pi\)
\(104\) −3.53793e9 + 3.53793e9i −0.290792 + 0.290792i
\(105\) −1.89205e9 5.40716e9i −0.148247 0.423665i
\(106\) 1.14848e9 + 1.82779e9i 0.0858211 + 0.136583i
\(107\) −7.26582e9 + 3.49903e9i −0.518043 + 0.249476i −0.674588 0.738195i \(-0.735679\pi\)
0.156545 + 0.987671i \(0.449964\pi\)
\(108\) 5.01794e8 1.43404e9i 0.0341512 0.0975986i
\(109\) 1.60633e10 3.66633e9i 1.04400 0.238286i 0.334063 0.942551i \(-0.391580\pi\)
0.709938 + 0.704264i \(0.248723\pi\)
\(110\) −1.58525e10 + 1.98784e10i −0.984317 + 1.23429i
\(111\) −2.16653e10 2.71675e10i −1.28573 1.61226i
\(112\) 7.44920e8 3.26371e9i 0.0422687 0.185191i
\(113\) 6.35404e9 1.01124e10i 0.344872 0.548860i −0.628582 0.777743i \(-0.716364\pi\)
0.973454 + 0.228883i \(0.0735073\pi\)
\(114\) −2.95722e9 + 2.62460e10i −0.153589 + 1.36314i
\(115\) 5.87495e9i 0.292089i
\(116\) 1.39002e9 + 3.28194e9i 0.0661808 + 0.156258i
\(117\) 1.39947e10 0.638313
\(118\) −3.80794e9 4.29052e8i −0.166449 0.0187543i
\(119\) −5.92137e9 3.72064e9i −0.248135 0.155913i
\(120\) 5.87295e10 + 1.34046e10i 2.36021 + 0.538701i
\(121\) −6.04669e9 + 4.82208e9i −0.233126 + 0.185912i
\(122\) −2.70880e10 2.16019e10i −1.00225 0.799270i
\(123\) 1.62647e10 + 7.12603e10i 0.577724 + 2.53117i
\(124\) −4.49201e9 1.57182e9i −0.153226 0.0536160i
\(125\) −2.39041e10 4.96374e10i −0.783290 1.62652i
\(126\) −6.74905e9 + 4.24071e9i −0.212515 + 0.133532i
\(127\) −1.38828e10 + 4.85780e9i −0.420202 + 0.147035i −0.532094 0.846685i \(-0.678595\pi\)
0.111892 + 0.993720i \(0.464309\pi\)
\(128\) 2.85941e10 + 2.85941e10i 0.832199 + 0.832199i
\(129\) −7.49205e9 + 1.55574e10i −0.209726 + 0.435501i
\(130\) −3.58768e9 3.18415e10i −0.0966265 0.857584i
\(131\) −2.30538e10 + 2.59754e9i −0.597566 + 0.0673296i −0.405567 0.914065i \(-0.632926\pi\)
−0.192000 + 0.981395i \(0.561497\pi\)
\(132\) 7.94159e9 + 3.82447e9i 0.198170 + 0.0954337i
\(133\) 4.01643e9 4.01643e9i 0.0965122 0.0965122i
\(134\) −2.89680e10 8.27857e10i −0.670493 1.91616i
\(135\) −2.53291e10 4.03110e10i −0.564873 0.898991i
\(136\) 6.62556e10 3.19070e10i 1.42406 0.685790i
\(137\) 2.73361e10 7.81221e10i 0.566414 1.61872i −0.202442 0.979294i \(-0.564888\pi\)
0.768855 0.639423i \(-0.220827\pi\)
\(138\) 1.36870e10 3.12398e9i 0.273473 0.0624184i
\(139\) −5.89681e10 + 7.39437e10i −1.13643 + 1.42504i −0.246384 + 0.969172i \(0.579242\pi\)
−0.890048 + 0.455868i \(0.849329\pi\)
\(140\) 1.65081e9 + 2.07005e9i 0.0306942 + 0.0384893i
\(141\) −2.03297e10 + 8.90701e10i −0.364783 + 1.59822i
\(142\) −2.96222e10 + 4.71434e10i −0.513069 + 0.816544i
\(143\) −2.56860e9 + 2.27970e10i −0.0429553 + 0.381239i
\(144\) 9.84622e10i 1.59022i
\(145\) 1.07562e11 + 3.00663e10i 1.67811 + 0.469073i
\(146\) 2.05588e10 0.309908
\(147\) −1.02609e11 1.15612e10i −1.49485 0.168429i
\(148\) 1.35986e10 + 8.54455e9i 0.191507 + 0.120332i
\(149\) 1.08170e11 + 2.46891e10i 1.47291 + 0.336182i 0.882266 0.470751i \(-0.156017\pi\)
0.590643 + 0.806933i \(0.298874\pi\)
\(150\) −2.02277e11 + 1.61311e11i −2.66373 + 2.12426i
\(151\) 1.75615e10 + 1.40048e10i 0.223705 + 0.178399i 0.728929 0.684590i \(-0.240019\pi\)
−0.505224 + 0.862988i \(0.668590\pi\)
\(152\) 1.32910e10 + 5.82318e10i 0.163810 + 0.717699i
\(153\) −1.94147e11 6.79348e10i −2.31565 0.810280i
\(154\) −5.66928e9 1.17724e10i −0.0654522 0.135913i
\(155\) −1.26271e11 + 7.93410e10i −1.41138 + 0.886828i
\(156\) −1.04853e10 + 3.66896e9i −0.113490 + 0.0397118i
\(157\) −3.73466e10 3.73466e10i −0.391519 0.391519i 0.483710 0.875228i \(-0.339289\pi\)
−0.875228 + 0.483710i \(0.839289\pi\)
\(158\) 6.20161e10 1.28778e11i 0.629824 1.30784i
\(159\) −2.62562e9 2.33031e10i −0.0258373 0.229312i
\(160\) −6.09881e10 + 6.87171e9i −0.581628 + 0.0655338i
\(161\) −2.72019e9 1.30997e9i −0.0251461 0.0121097i
\(162\) 3.84890e10 3.84890e10i 0.344954 0.344954i
\(163\) 2.29607e10 + 6.56178e10i 0.199547 + 0.570274i 0.999559 0.0297114i \(-0.00945883\pi\)
−0.800011 + 0.599985i \(0.795173\pi\)
\(164\) −1.79733e10 2.86044e10i −0.151499 0.241109i
\(165\) 2.48855e11 1.19842e11i 2.03482 0.979918i
\(166\) 3.01325e10 8.61136e10i 0.239053 0.683174i
\(167\) 2.30238e11 5.25504e10i 1.77254 0.404570i 0.793552 0.608503i \(-0.208229\pi\)
0.978985 + 0.203933i \(0.0653723\pi\)
\(168\) −1.93018e10 + 2.42037e10i −0.144229 + 0.180857i
\(169\) 6.79269e10 + 8.51777e10i 0.492729 + 0.617863i
\(170\) −1.04798e11 + 4.59149e11i −0.738087 + 3.23377i
\(171\) 8.88841e10 1.41458e11i 0.607916 0.967493i
\(172\) 8.93559e8 7.93056e9i 0.00593582 0.0526819i
\(173\) 1.17501e11i 0.758249i −0.925346 0.379124i \(-0.876225\pi\)
0.925346 0.379124i \(-0.123775\pi\)
\(174\) 1.28506e10 2.66579e11i 0.0805707 1.67139i
\(175\) 5.56399e10 0.338997
\(176\) 1.60392e11 + 1.80719e10i 0.949775 + 0.107014i
\(177\) 3.52483e10 + 2.21480e10i 0.202895 + 0.127488i
\(178\) 2.31885e10 + 5.29262e9i 0.129769 + 0.0296190i
\(179\) 2.81440e10 2.24441e10i 0.153151 0.122134i −0.543916 0.839139i \(-0.683059\pi\)
0.697068 + 0.717005i \(0.254488\pi\)
\(180\) 6.08851e10 + 4.85542e10i 0.322217 + 0.256959i
\(181\) −3.44792e10 1.51063e11i −0.177486 0.777618i −0.982786 0.184750i \(-0.940853\pi\)
0.805299 0.592869i \(-0.202005\pi\)
\(182\) 1.55431e10 + 5.43875e9i 0.0778358 + 0.0272359i
\(183\) 1.63307e11 + 3.39110e11i 0.795698 + 1.65228i
\(184\) 2.68821e10 1.68912e10i 0.127460 0.0800886i
\(185\) 4.75016e11 1.66215e11i 2.19204 0.767029i
\(186\) 2.51987e11 + 2.51987e11i 1.13191 + 1.13191i
\(187\) 1.46298e11 3.03791e11i 0.639780 1.32852i
\(188\) −4.72776e9 4.19600e10i −0.0201310 0.178668i
\(189\) 2.43124e10 2.73935e9i 0.100814 0.0113590i
\(190\) −3.44640e11 1.65970e11i −1.39187 0.670289i
\(191\) −2.17880e11 + 2.17880e11i −0.857136 + 0.857136i −0.991000 0.133864i \(-0.957262\pi\)
0.133864 + 0.991000i \(0.457262\pi\)
\(192\) −1.03679e11 2.96297e11i −0.397359 1.13559i
\(193\) −1.88540e11 3.00059e11i −0.704071 1.12052i −0.986897 0.161352i \(-0.948415\pi\)
0.282826 0.959171i \(-0.408728\pi\)
\(194\) −3.37089e11 + 1.62333e11i −1.22669 + 0.590744i
\(195\) −1.14969e11 + 3.28563e11i −0.407763 + 1.16532i
\(196\) 4.65278e10 1.06197e10i 0.160854 0.0367139i
\(197\) −2.00896e11 + 2.51915e11i −0.677080 + 0.849031i −0.995082 0.0990589i \(-0.968417\pi\)
0.318002 + 0.948090i \(0.396988\pi\)
\(198\) −2.39615e11 3.00468e11i −0.787388 0.987353i
\(199\) 1.16961e11 5.12441e11i 0.374780 1.64202i −0.338374 0.941012i \(-0.609877\pi\)
0.713154 0.701007i \(-0.247266\pi\)
\(200\) −3.11284e11 + 4.95405e11i −0.972761 + 1.54814i
\(201\) −1.06680e11 + 9.46813e11i −0.325165 + 2.88592i
\(202\) 1.11882e11i 0.332663i
\(203\) −3.79050e10 + 4.30989e10i −0.109955 + 0.125022i
\(204\) 1.63271e11 0.462125
\(205\) −1.05194e12 1.18525e11i −2.90549 0.327371i
\(206\) 2.96975e10 + 1.86602e10i 0.0800542 + 0.0503014i
\(207\) −8.65751e10 1.97602e10i −0.227794 0.0519924i
\(208\) −1.59038e11 + 1.26828e11i −0.408492 + 0.325762i
\(209\) 2.14118e11 + 1.70753e11i 0.536935 + 0.428191i
\(210\) −4.41172e10 1.93290e11i −0.108022 0.473275i
\(211\) 4.96723e11 + 1.73811e11i 1.18769 + 0.415590i 0.850564 0.525871i \(-0.176261\pi\)
0.337122 + 0.941461i \(0.390546\pi\)
\(212\) 4.70263e9 + 9.76512e9i 0.0109815 + 0.0228033i
\(213\) 5.12139e11 3.21798e11i 1.16813 0.733983i
\(214\) −2.63438e11 + 9.21811e10i −0.586962 + 0.205387i
\(215\) −1.76834e11 1.76834e11i −0.384923 0.384923i
\(216\) −1.11628e11 + 2.31798e11i −0.237413 + 0.492993i
\(217\) −8.58075e9 7.61563e10i −0.0178331 0.158273i
\(218\) 5.66641e11 6.38451e10i 1.15087 0.129672i
\(219\) −2.01221e11 9.69030e10i −0.399442 0.192361i
\(220\) −9.02685e10 + 9.02685e10i −0.175155 + 0.175155i
\(221\) 1.40349e11 + 4.01095e11i 0.266225 + 0.760827i
\(222\) −6.39823e11 1.01827e12i −1.18658 1.88842i
\(223\) −6.92874e11 + 3.33670e11i −1.25641 + 0.605053i −0.939222 0.343311i \(-0.888451\pi\)
−0.317184 + 0.948364i \(0.602737\pi\)
\(224\) 1.04172e10 2.97706e10i 0.0184719 0.0527896i
\(225\) 1.59547e12 3.64157e11i 2.76680 0.631503i
\(226\) 2.57708e11 3.23155e11i 0.437105 0.548112i
\(227\) −7.94578e10 9.96369e10i −0.131828 0.165307i 0.711536 0.702649i \(-0.248000\pi\)
−0.843364 + 0.537342i \(0.819428\pi\)
\(228\) −2.95091e10 + 1.29288e11i −0.0478941 + 0.209838i
\(229\) 2.01768e11 3.21112e11i 0.320387 0.509893i −0.647237 0.762289i \(-0.724076\pi\)
0.967624 + 0.252396i \(0.0812185\pi\)
\(230\) −2.27652e10 + 2.02047e11i −0.0353697 + 0.313915i
\(231\) 1.41945e11i 0.215805i
\(232\) −1.71679e11 5.78619e11i −0.255433 0.860900i
\(233\) −4.14041e10 −0.0602926 −0.0301463 0.999545i \(-0.509597\pi\)
−0.0301463 + 0.999545i \(0.509597\pi\)
\(234\) 4.81293e11 + 5.42287e10i 0.686010 + 0.0772948i
\(235\) −1.12035e12 7.03965e11i −1.56320 0.982226i
\(236\) −1.87579e10 4.28137e9i −0.0256227 0.00584821i
\(237\) −1.21398e12 + 9.68116e11i −1.62356 + 1.29475i
\(238\) −1.89226e11 1.50902e11i −0.247796 0.197611i
\(239\) −1.20203e11 5.26644e11i −0.154144 0.675347i −0.991654 0.128926i \(-0.958847\pi\)
0.837511 0.546421i \(-0.184010\pi\)
\(240\) 2.31166e12 + 8.08886e11i 2.90314 + 1.01585i
\(241\) 4.99350e11 + 1.03691e12i 0.614214 + 1.27543i 0.943554 + 0.331218i \(0.107460\pi\)
−0.329340 + 0.944211i \(0.606826\pi\)
\(242\) −2.26638e11 + 1.42406e11i −0.273059 + 0.171574i
\(243\) −1.04544e12 + 3.65816e11i −1.23387 + 0.431749i
\(244\) −1.23007e11 1.23007e11i −0.142227 0.142227i
\(245\) 6.48861e11 1.34737e12i 0.735057 1.52636i
\(246\) 2.83232e11 + 2.51375e12i 0.314388 + 2.79027i
\(247\) −3.42977e11 + 3.86442e10i −0.373061 + 0.0420339i
\(248\) 7.26085e11 + 3.49664e11i 0.773978 + 0.372728i
\(249\) −7.00818e11 + 7.00818e11i −0.732164 + 0.732164i
\(250\) −6.29748e11 1.79972e12i −0.644862 1.84291i
\(251\) 9.84546e11 + 1.56690e12i 0.988251 + 1.57279i 0.808008 + 0.589171i \(0.200546\pi\)
0.180243 + 0.983622i \(0.442312\pi\)
\(252\) −3.60573e10 + 1.73643e10i −0.0354805 + 0.0170865i
\(253\) 4.80790e10 1.37402e11i 0.0463824 0.132553i
\(254\) −4.96269e11 + 1.13270e11i −0.469406 + 0.107139i
\(255\) 3.18990e12 4.00001e12i 2.95853 3.70988i
\(256\) 3.39514e11 + 4.25737e11i 0.308786 + 0.387205i
\(257\) 1.48083e11 6.48795e11i 0.132081 0.578684i −0.864962 0.501837i \(-0.832658\pi\)
0.997043 0.0768469i \(-0.0244853\pi\)
\(258\) −3.17945e11 + 5.06006e11i −0.278133 + 0.442647i
\(259\) −2.89571e10 + 2.57001e11i −0.0248460 + 0.220514i
\(260\) 1.60885e11i 0.135409i
\(261\) −8.04849e11 + 1.48394e12i −0.664526 + 1.22522i
\(262\) −8.02913e11 −0.650372
\(263\) 5.45521e11 + 6.14655e10i 0.433544 + 0.0488486i 0.326040 0.945356i \(-0.394286\pi\)
0.107504 + 0.994205i \(0.465714\pi\)
\(264\) −1.26385e12 7.94129e11i −0.985543 0.619258i
\(265\) 3.31114e11 + 7.55747e10i 0.253366 + 0.0578292i
\(266\) 1.53693e11 1.22566e11i 0.115411 0.0920371i
\(267\) −2.02013e11 1.61100e11i −0.148876 0.118724i
\(268\) −9.79919e10 4.29330e11i −0.0708788 0.310540i
\(269\) 6.60613e11 + 2.31159e11i 0.469014 + 0.164115i 0.554430 0.832230i \(-0.312936\pi\)
−0.0854161 + 0.996345i \(0.527222\pi\)
\(270\) −7.14894e11 1.48449e12i −0.498222 1.03457i
\(271\) −6.69690e11 + 4.20794e11i −0.458171 + 0.287888i −0.741275 0.671201i \(-0.765779\pi\)
0.283104 + 0.959089i \(0.408636\pi\)
\(272\) 2.82198e12 9.87453e11i 1.89544 0.663242i
\(273\) −1.26494e11 1.26494e11i −0.0834174 0.0834174i
\(274\) 1.24284e12 2.58078e12i 0.804752 1.67109i
\(275\) 3.00366e11 + 2.66582e12i 0.190980 + 1.69499i
\(276\) 7.00455e10 7.89223e9i 0.0437356 0.00492781i
\(277\) −5.83761e11 2.81124e11i −0.357961 0.172385i 0.246256 0.969205i \(-0.420800\pi\)
−0.604217 + 0.796820i \(0.706514\pi\)
\(278\) −2.31451e12 + 2.31451e12i −1.39391 + 1.39391i
\(279\) −7.44487e11 2.12762e12i −0.440389 1.25856i
\(280\) −2.38539e11 3.79633e11i −0.138602 0.220584i
\(281\) −8.55403e11 + 4.11941e11i −0.488247 + 0.235127i −0.661776 0.749701i \(-0.730197\pi\)
0.173529 + 0.984829i \(0.444483\pi\)
\(282\) −1.04430e12 + 2.98445e12i −0.585573 + 1.67347i
\(283\) −6.07531e11 + 1.38665e11i −0.334685 + 0.0763897i −0.386561 0.922264i \(-0.626337\pi\)
0.0518759 + 0.998654i \(0.483480\pi\)
\(284\) −1.74297e11 + 2.18562e11i −0.0943407 + 0.118300i
\(285\) 2.59091e12 + 3.24890e12i 1.37793 + 1.72787i
\(286\) −1.76674e11 + 7.74061e11i −0.0923302 + 0.404525i
\(287\) 2.89435e11 4.60634e11i 0.148642 0.236563i
\(288\) 1.03868e11 9.21853e11i 0.0524226 0.465264i
\(289\) 4.22965e12i 2.09805i
\(290\) 3.58269e12 + 1.45081e12i 1.74670 + 0.707330i
\(291\) 4.06444e12 1.94776
\(292\) 1.02575e11 + 1.15574e10i 0.0483199 + 0.00544434i
\(293\) −1.83698e12 1.15425e12i −0.850681 0.534518i 0.0346928 0.999398i \(-0.488955\pi\)
−0.885374 + 0.464880i \(0.846098\pi\)
\(294\) −3.48404e12 7.95210e11i −1.58616 0.362030i
\(295\) −4.71371e11 + 3.75906e11i −0.210986 + 0.168255i
\(296\) −2.12628e12 1.69565e12i −0.935754 0.746239i
\(297\) 2.62496e11 + 1.15007e12i 0.113590 + 0.497671i
\(298\) 3.62443e12 + 1.26824e12i 1.54226 + 0.539661i
\(299\) 7.95997e10 + 1.65291e11i 0.0333085 + 0.0691659i
\(300\) −1.09991e12 + 6.91121e11i −0.452639 + 0.284412i
\(301\) 1.21307e11 4.24470e10i 0.0490967 0.0171797i
\(302\) 5.49691e11 + 5.49691e11i 0.218818 + 0.218818i
\(303\) −5.27353e11 + 1.09506e12i −0.206485 + 0.428770i
\(304\) 2.71889e11 + 2.41308e12i 0.104718 + 0.929401i
\(305\) −5.41682e12 + 6.10329e11i −2.05232 + 0.231241i
\(306\) −6.41368e12 3.08867e12i −2.39056 1.15123i
\(307\) 1.40103e12 1.40103e12i 0.513754 0.513754i −0.401921 0.915674i \(-0.631657\pi\)
0.915674 + 0.401921i \(0.131657\pi\)
\(308\) −2.16679e10 6.19234e10i −0.00781743 0.0223409i
\(309\) −2.02714e11 3.22617e11i −0.0719599 0.114523i
\(310\) −4.65003e12 + 2.23934e12i −1.62423 + 0.782188i
\(311\) 4.69520e11 1.34181e12i 0.161381 0.461200i −0.834591 0.550871i \(-0.814296\pi\)
0.995971 + 0.0896706i \(0.0285814\pi\)
\(312\) 1.83396e12 4.18589e11i 0.620321 0.141584i
\(313\) −2.52597e11 + 3.16746e11i −0.0840825 + 0.105436i −0.822093 0.569353i \(-0.807194\pi\)
0.738011 + 0.674789i \(0.235765\pi\)
\(314\) −1.13968e12 1.42911e12i −0.373365 0.468185i
\(315\) −2.79056e11 + 1.22263e12i −0.0899785 + 0.394222i
\(316\) 3.81813e11 6.07653e11i 0.121176 0.192850i
\(317\) −1.52300e11 + 1.35170e12i −0.0475776 + 0.422263i 0.947235 + 0.320540i \(0.103864\pi\)
−0.994813 + 0.101723i \(0.967564\pi\)
\(318\) 8.11593e11i 0.249576i
\(319\) −2.26958e12 1.58344e12i −0.687057 0.479346i
\(320\) 4.54634e12 1.35492
\(321\) 3.01292e12 + 3.39475e11i 0.884022 + 0.0996053i
\(322\) −8.84744e10 5.55922e10i −0.0255587 0.0160596i
\(323\) 4.94567e12 + 1.12882e12i 1.40673 + 0.321078i
\(324\) 2.13672e11 1.70397e11i 0.0598442 0.0477241i
\(325\) −2.64331e12 2.10797e12i −0.729006 0.581363i
\(326\) 5.35378e11 + 2.34564e12i 0.145403 + 0.637051i
\(327\) −5.84699e12 2.04595e12i −1.56384 0.547213i
\(328\) 2.48210e12 + 5.15414e12i 0.653808 + 1.35765i
\(329\) 5.75758e11 3.61773e11i 0.149369 0.0938548i
\(330\) 9.02278e12 3.15721e12i 2.30553 0.806740i
\(331\) −5.29932e12 5.29932e12i −1.33377 1.33377i −0.901970 0.431799i \(-0.857879\pi\)
−0.431799 0.901970i \(-0.642121\pi\)
\(332\) 1.98751e11 4.12711e11i 0.0492741 0.102319i
\(333\) 8.51699e11 + 7.55903e12i 0.208001 + 1.84606i
\(334\) 8.12179e12 9.15107e11i 1.95398 0.220160i
\(335\) −1.24327e13 5.98729e12i −2.94675 1.41908i
\(336\) −8.89973e11 + 8.89973e11i −0.207817 + 0.207817i
\(337\) −3.33188e11 9.52197e11i −0.0766549 0.219067i 0.899179 0.437581i \(-0.144165\pi\)
−0.975834 + 0.218514i \(0.929879\pi\)
\(338\) 2.00603e12 + 3.19257e12i 0.454730 + 0.723698i
\(339\) −4.04552e12 + 1.94822e12i −0.903600 + 0.435151i
\(340\) −7.80989e11 + 2.23194e12i −0.171890 + 0.491233i
\(341\) 3.60249e12 8.22244e11i 0.781323 0.178332i
\(342\) 3.60497e12 4.52049e12i 0.770498 0.966174i
\(343\) 9.72008e11 + 1.21886e12i 0.204738 + 0.256734i
\(344\) −3.00725e11 + 1.31756e12i −0.0624277 + 0.273513i
\(345\) 1.17516e12 1.87025e12i 0.240436 0.382652i
\(346\) 4.55312e11 4.04100e12i 0.0918181 0.814908i
\(347\) 6.96004e12i 1.38345i 0.722160 + 0.691726i \(0.243149\pi\)
−0.722160 + 0.691726i \(0.756851\pi\)
\(348\) 2.13977e11 1.32283e12i 0.0419247 0.259183i
\(349\) −4.11335e12 −0.794454 −0.397227 0.917720i \(-0.630027\pi\)
−0.397227 + 0.917720i \(0.630027\pi\)
\(350\) 1.91352e12 + 2.15602e11i 0.364328 + 0.0410499i
\(351\) −1.25880e12 7.90958e11i −0.236277 0.148463i
\(352\) 1.48261e12 + 3.38396e11i 0.274356 + 0.0626199i
\(353\) −5.50012e12 + 4.38620e12i −1.00346 + 0.800230i −0.979899 0.199492i \(-0.936071\pi\)
−0.0235575 + 0.999722i \(0.507499\pi\)
\(354\) 1.12641e12 + 8.98281e11i 0.202619 + 0.161583i
\(355\) 1.94926e12 + 8.54028e12i 0.345723 + 1.51471i
\(356\) 1.12720e11 + 3.94424e10i 0.0197129 + 0.00689784i
\(357\) 1.14079e12 + 2.36888e12i 0.196728 + 0.408509i
\(358\) 1.05488e12 6.62822e11i 0.179385 0.112715i
\(359\) 2.12971e12 7.45216e11i 0.357147 0.124971i −0.145741 0.989323i \(-0.546557\pi\)
0.502888 + 0.864352i \(0.332271\pi\)
\(360\) −9.32477e12 9.32477e12i −1.54215 1.54215i
\(361\) 8.72445e11 1.81165e12i 0.142299 0.295487i
\(362\) −6.00418e11 5.32885e12i −0.0965852 0.857217i
\(363\) 2.88947e12 3.25565e11i 0.458443 0.0516541i
\(364\) 7.44921e10 + 3.58735e10i 0.0116574 + 0.00561393i
\(365\) 2.28719e12 2.28719e12i 0.353052 0.353052i
\(366\) 4.30227e12 + 1.22952e13i 0.655077 + 1.87210i
\(367\) 7.30330e11 + 1.16231e12i 0.109695 + 0.174579i 0.897061 0.441908i \(-0.145698\pi\)
−0.787365 + 0.616487i \(0.788555\pi\)
\(368\) 1.16293e12 5.60039e11i 0.172312 0.0829811i
\(369\) 5.28477e12 1.51030e13i 0.772492 2.20766i
\(370\) 1.69804e13 3.87567e12i 2.44872 0.558905i
\(371\) −1.08823e11 + 1.36460e11i −0.0154828 + 0.0194149i
\(372\) 1.11559e12 + 1.39890e12i 0.156599 + 0.196369i
\(373\) 1.48077e12 6.48769e12i 0.205090 0.898557i −0.762691 0.646763i \(-0.776122\pi\)
0.967781 0.251794i \(-0.0810206\pi\)
\(374\) 6.20853e12 9.88083e12i 0.848459 1.35032i
\(375\) −2.31917e12 + 2.05832e13i −0.312735 + 2.77560i
\(376\) 7.15040e12i 0.951462i
\(377\) 3.43361e12 6.11452e11i 0.450863 0.0802889i
\(378\) 8.46746e11 0.109722
\(379\) 1.08683e13 + 1.22456e12i 1.38984 + 0.156597i 0.774952 0.632020i \(-0.217774\pi\)
0.614884 + 0.788617i \(0.289203\pi\)
\(380\) −1.62623e12 1.02183e12i −0.205240 0.128961i
\(381\) 5.39119e12 + 1.23050e12i 0.671521 + 0.153270i
\(382\) −8.33741e12 + 6.64886e12i −1.02498 + 0.817392i
\(383\) −2.47810e12 1.97622e12i −0.300694 0.239795i 0.461506 0.887137i \(-0.347309\pi\)
−0.762200 + 0.647342i \(0.775881\pi\)
\(384\) −3.38311e12 1.48224e13i −0.405191 1.77526i
\(385\) −1.94041e12 6.78978e11i −0.229398 0.0802698i
\(386\) −5.32139e12 1.10500e13i −0.620996 1.28951i
\(387\) 3.20066e12 2.01111e12i 0.368709 0.231676i
\(388\) −1.77311e12 + 6.20437e11i −0.201640 + 0.0705568i
\(389\) 5.56299e12 + 5.56299e12i 0.624540 + 0.624540i 0.946689 0.322149i \(-0.104405\pi\)
−0.322149 + 0.946689i \(0.604405\pi\)
\(390\) −5.22708e12 + 1.08541e13i −0.579344 + 1.20302i
\(391\) −3.01903e11 2.67946e12i −0.0330357 0.293200i
\(392\) −8.03075e12 + 9.04848e11i −0.867612 + 0.0977564i
\(393\) 7.85859e12 + 3.78450e12i 0.838266 + 0.403688i
\(394\) −7.88520e12 + 7.88520e12i −0.830485 + 0.830485i
\(395\) −7.42732e12 2.12261e13i −0.772408 2.20742i
\(396\) −1.02661e12 1.63384e12i −0.105422 0.167777i
\(397\) 2.46281e12 1.18602e12i 0.249734 0.120266i −0.304830 0.952407i \(-0.598600\pi\)
0.554564 + 0.832141i \(0.312885\pi\)
\(398\) 6.00812e12 1.71702e13i 0.601621 1.71933i
\(399\) −2.08200e12 + 4.75203e11i −0.205881 + 0.0469910i
\(400\) −1.48310e13 + 1.85975e13i −1.44834 + 1.81616i
\(401\) −4.05688e12 5.08717e12i −0.391265 0.490631i 0.546716 0.837318i \(-0.315878\pi\)
−0.937981 + 0.346688i \(0.887306\pi\)
\(402\) −7.33772e12 + 3.21486e13i −0.698925 + 3.06219i
\(403\) −2.47760e12 + 3.94308e12i −0.233081 + 0.370946i
\(404\) 6.28961e10 5.58218e11i 0.00584409 0.0518677i
\(405\) 8.56391e12i 0.785953i
\(406\) −1.47060e12 + 1.33534e12i −0.133311 + 0.121049i
\(407\) −1.24698e13 −1.11657
\(408\) −2.74743e13 3.09561e12i −2.43011 0.273807i
\(409\) 1.29541e13 + 8.13961e12i 1.13186 + 0.711192i 0.961667 0.274220i \(-0.0884195\pi\)
0.170188 + 0.985412i \(0.445562\pi\)
\(410\) −3.57180e13 8.15241e12i −3.08296 0.703666i
\(411\) −2.43289e13 + 1.94016e13i −2.07450 + 1.65435i
\(412\) 1.37681e11 + 1.09797e11i 0.0115981 + 0.00924919i
\(413\) −6.89455e10 3.02070e11i −0.00573794 0.0251395i
\(414\) −2.90085e12 1.01505e12i −0.238519 0.0834615i
\(415\) −6.22798e12 1.29325e13i −0.505949 1.05061i
\(416\) −1.62278e12 + 1.01966e12i −0.130255 + 0.0818445i
\(417\) 3.35629e13 1.17442e13i 2.66182 0.931412i
\(418\) 6.70211e12 + 6.70211e12i 0.525206 + 0.525206i
\(419\) −3.11323e12 + 6.46469e12i −0.241069 + 0.500585i −0.986039 0.166513i \(-0.946749\pi\)
0.744970 + 0.667097i \(0.232464\pi\)
\(420\) −1.11455e11 9.89191e11i −0.00852812 0.0756892i
\(421\) −3.51666e12 + 3.96232e11i −0.265901 + 0.0299598i −0.243908 0.969798i \(-0.578430\pi\)
−0.0219924 + 0.999758i \(0.507001\pi\)
\(422\) 1.64094e13 + 7.90233e12i 1.22611 + 0.590464i
\(423\) 1.41421e13 1.41421e13i 1.04427 1.04427i
\(424\) −6.06184e11 1.73237e12i −0.0442359 0.126419i
\(425\) 2.64375e13 + 4.20751e13i 1.90667 + 3.03445i
\(426\) 1.88600e13 9.08251e12i 1.34429 0.647378i
\(427\) 9.25231e11 2.64416e12i 0.0651794 0.186272i
\(428\) −1.36620e12 + 3.11827e11i −0.0951255 + 0.0217118i
\(429\) 5.37773e12 6.74346e12i 0.370094 0.464084i
\(430\) −5.39631e12 6.76675e12i −0.367075 0.460297i
\(431\) 3.94098e11 1.72665e12i 0.0264983 0.116096i −0.959949 0.280174i \(-0.909608\pi\)
0.986447 + 0.164078i \(0.0524648\pi\)
\(432\) −5.56494e12 + 8.85655e12i −0.369863 + 0.588634i
\(433\) −6.09408e11 + 5.40864e12i −0.0400376 + 0.355344i 0.957681 + 0.287832i \(0.0929346\pi\)
−0.997718 + 0.0675117i \(0.978494\pi\)
\(434\) 2.65235e12i 0.172259i
\(435\) −2.82276e13 3.10869e13i −1.81229 1.99586i
\(436\) 2.86305e12 0.181718
\(437\) 2.17632e12 + 2.45212e11i 0.136557 + 0.0153863i
\(438\) −6.54474e12 4.11233e12i −0.405996 0.255104i
\(439\) −1.38058e13 3.15108e12i −0.846717 0.193258i −0.222913 0.974838i \(-0.571557\pi\)
−0.623804 + 0.781581i \(0.714414\pi\)
\(440\) 1.69013e13 1.34783e13i 1.02484 0.817284i
\(441\) 1.76729e13 + 1.40937e13i 1.05953 + 0.844949i
\(442\) 3.27255e12 + 1.43380e13i 0.193988 + 0.849917i
\(443\) −6.95321e12 2.43303e12i −0.407537 0.142603i 0.118723 0.992927i \(-0.462120\pi\)
−0.526259 + 0.850324i \(0.676406\pi\)
\(444\) −2.61986e12 5.44019e12i −0.151832 0.315282i
\(445\) 3.16856e12 1.99094e12i 0.181578 0.114093i
\(446\) −2.51217e13 + 8.79046e12i −1.42356 + 0.498124i
\(447\) −2.94967e13 2.94967e13i −1.65286 1.65286i
\(448\) −1.01373e12 + 2.10502e12i −0.0561734 + 0.116645i
\(449\) 3.62273e12 + 3.21526e13i 0.198520 + 1.76191i 0.559019 + 0.829155i \(0.311178\pi\)
−0.360499 + 0.932760i \(0.617393\pi\)
\(450\) 5.62813e13 6.34138e12i 3.05001 0.343654i
\(451\) 2.36324e13 + 1.13808e13i 1.26656 + 0.609943i
\(452\) 1.46746e12 1.46746e12i 0.0777809 0.0777809i
\(453\) −2.78921e12 7.97111e12i −0.146214 0.417857i
\(454\) −2.34656e12 3.73453e12i −0.121661 0.193623i
\(455\) 2.33425e12 1.12412e12i 0.119699 0.0576441i
\(456\) 7.41689e12 2.11962e13i 0.376182 1.07507i
\(457\) 2.21784e13 5.06207e12i 1.11262 0.253949i 0.373574 0.927600i \(-0.378132\pi\)
0.739050 + 0.673651i \(0.235275\pi\)
\(458\) 8.18333e12 1.02616e13i 0.406072 0.509198i
\(459\) 1.36236e13 + 1.70835e13i 0.668698 + 0.838521i
\(460\) −2.27166e11 + 9.95281e11i −0.0110295 + 0.0483233i
\(461\) −1.86752e12 + 2.97213e12i −0.0896932 + 0.142746i −0.888557 0.458766i \(-0.848292\pi\)
0.798864 + 0.601512i \(0.205435\pi\)
\(462\) −5.50032e11 + 4.88166e12i −0.0261323 + 0.231931i
\(463\) 2.95218e13i 1.38751i −0.720209 0.693757i \(-0.755954\pi\)
0.720209 0.693757i \(-0.244046\pi\)
\(464\) −4.30199e12 2.41578e13i −0.200023 1.12323i
\(465\) 5.60677e13 2.57898
\(466\) −1.42394e12 1.60439e11i −0.0647978 0.00730096i
\(467\) 2.07487e13 + 1.30373e13i 0.934127 + 0.586951i 0.910832 0.412778i \(-0.135441\pi\)
0.0232952 + 0.999729i \(0.492584\pi\)
\(468\) 2.37085e12 + 5.41131e11i 0.105603 + 0.0241031i
\(469\) 5.54441e12 4.42152e12i 0.244338 0.194853i
\(470\) −3.58024e13 2.85515e13i −1.56107 1.24491i
\(471\) 4.41865e12 + 1.93594e13i 0.190627 + 0.835193i
\(472\) 3.07529e12 + 1.07609e12i 0.131273 + 0.0459344i
\(473\) 2.68859e12 + 5.58291e12i 0.113558 + 0.235806i
\(474\) −4.55015e13 + 2.85905e13i −1.90167 + 1.19490i
\(475\) −3.80958e13 + 1.33303e13i −1.57546 + 0.551279i
\(476\) −8.59278e11 8.59278e11i −0.0351641 0.0351641i
\(477\) −2.22738e12 + 4.62521e12i −0.0901993 + 0.187301i
\(478\) −2.09320e12 1.85777e13i −0.0838825 0.744478i
\(479\) 1.14175e13 1.28644e12i 0.452785 0.0510166i 0.117372 0.993088i \(-0.462553\pi\)
0.335412 + 0.942071i \(0.391124\pi\)
\(480\) 2.07897e13 + 1.00118e13i 0.815908 + 0.392921i
\(481\) 1.11124e13 1.11124e13i 0.431601 0.431601i
\(482\) 1.31553e13 + 3.75956e13i 0.505666 + 1.44511i
\(483\) 6.03921e11 + 9.61135e11i 0.0229744 + 0.0365636i
\(484\) −1.21083e12 + 5.83105e11i −0.0455886 + 0.0219543i
\(485\) −1.94418e13 + 5.55614e13i −0.724481 + 2.07045i
\(486\) −3.73715e13 + 8.52980e12i −1.37835 + 0.314599i
\(487\) −1.74295e13 + 2.18560e13i −0.636269 + 0.797857i −0.990531 0.137290i \(-0.956161\pi\)
0.354261 + 0.935146i \(0.384732\pi\)
\(488\) 1.83667e13 + 2.30311e13i 0.663638 + 0.832176i
\(489\) 5.81604e12 2.54817e13i 0.208009 0.911348i
\(490\) 2.75361e13 4.38234e13i 0.974814 1.55141i
\(491\) −4.58155e11 + 4.06624e12i −0.0160548 + 0.142490i −0.999182 0.0404311i \(-0.987127\pi\)
0.983128 + 0.182922i \(0.0585554\pi\)
\(492\) 1.27012e13i 0.440573i
\(493\) −5.06023e13 8.18528e12i −1.73754 0.281060i
\(494\) −1.19451e13 −0.406027
\(495\) −6.00850e13 6.76996e12i −2.02181 0.227803i
\(496\) 2.77423e13 + 1.74316e13i 0.924132 + 0.580671i
\(497\) −4.38892e12 1.00174e12i −0.144736 0.0330350i
\(498\) −2.68176e13 + 2.13863e13i −0.875534 + 0.698215i
\(499\) 2.94001e12 + 2.34458e12i 0.0950267 + 0.0757813i 0.669851 0.742496i \(-0.266358\pi\)
−0.574824 + 0.818277i \(0.694930\pi\)
\(500\) −2.13029e12 9.33341e12i −0.0681693 0.298669i
\(501\) −8.38063e13 2.93251e13i −2.65514 0.929075i
\(502\) 2.77880e13 + 5.77025e13i 0.871644 + 1.80999i
\(503\) 5.22494e13 3.28304e13i 1.62271 1.01962i 0.659192 0.751975i \(-0.270899\pi\)
0.963519 0.267641i \(-0.0862443\pi\)
\(504\) 6.39671e12 2.23831e12i 0.196700 0.0688282i
\(505\) −1.24470e13 1.24470e13i −0.378974 0.378974i
\(506\) 2.18592e12 4.53911e12i 0.0658994 0.136841i
\(507\) −4.58613e12 4.07030e13i −0.136901 1.21503i
\(508\) −2.53973e12 + 2.86159e11i −0.0750705 + 0.00845842i
\(509\) 1.09046e13 + 5.25137e12i 0.319169 + 0.153703i 0.586608 0.809871i \(-0.300463\pi\)
−0.267439 + 0.963575i \(0.586177\pi\)
\(510\) 1.25204e14 1.25204e14i 3.62885 3.62885i
\(511\) 5.49014e11 + 1.56899e12i 0.0157572 + 0.0450315i
\(512\) −1.20042e13 1.91046e13i −0.341180 0.542985i
\(513\) −1.59900e13 + 7.70039e12i −0.450051 + 0.216733i
\(514\) 7.60680e12 2.17390e13i 0.212025 0.605932i
\(515\) 5.37986e12 1.22792e12i 0.148503 0.0338948i
\(516\) −1.87079e12 + 2.34590e12i −0.0511419 + 0.0641299i
\(517\) 2.04415e13 + 2.56328e13i 0.553426 + 0.693974i
\(518\) −1.99174e12 + 8.72637e12i −0.0534051 + 0.233983i
\(519\) −2.35035e13 + 3.74056e13i −0.624160 + 0.993346i
\(520\) −3.05036e12 + 2.70727e13i −0.0802295 + 0.712057i
\(521\) 3.85329e13i 1.00379i −0.864928 0.501896i \(-0.832636\pi\)
0.864928 0.501896i \(-0.167364\pi\)
\(522\) −3.34299e13 + 4.79158e13i −0.862547 + 1.23631i
\(523\) 2.39693e13 0.612557 0.306279 0.951942i \(-0.400916\pi\)
0.306279 + 0.951942i \(0.400916\pi\)
\(524\) −4.00600e12 4.51368e11i −0.101404 0.0114255i
\(525\) −1.77126e13 1.11295e13i −0.444104 0.279049i
\(526\) 1.85229e13 + 4.22774e12i 0.460024 + 0.104998i
\(527\) 5.35125e13 4.26748e13i 1.31644 1.04983i
\(528\) −4.74449e13 3.78360e13i −1.15617 0.922011i
\(529\) 8.95923e12 + 3.92529e13i 0.216268 + 0.947532i
\(530\) 1.10946e13 + 3.88216e12i 0.265296 + 0.0928311i
\(531\) −3.95403e12 8.21062e12i −0.0936628 0.194493i
\(532\) 8.35730e11 5.25124e11i 0.0196114 0.0123226i
\(533\) −3.12019e13 + 1.09180e13i −0.725345 + 0.253809i
\(534\) −6.32322e12 6.32322e12i −0.145624 0.145624i
\(535\) −1.90526e13 + 3.95631e13i −0.434696 + 0.902655i
\(536\) 8.34939e12 + 7.41029e13i 0.188726 + 1.67499i
\(537\) −1.34489e13 + 1.51533e12i −0.301172 + 0.0339340i
\(538\) 2.18235e13 + 1.05097e13i 0.484188 + 0.233172i
\(539\) −2.62019e13 + 2.62019e13i −0.575956 + 0.575956i
\(540\) −2.73232e12 7.80852e12i −0.0595063 0.170059i
\(541\) 3.33056e13 + 5.30055e13i 0.718672 + 1.14376i 0.983752 + 0.179534i \(0.0574588\pi\)
−0.265080 + 0.964226i \(0.585398\pi\)
\(542\) −2.46620e13 + 1.18766e13i −0.527268 + 0.253919i
\(543\) −1.92407e13 + 5.49868e13i −0.407588 + 1.16482i
\(544\) 2.74625e13 6.26813e12i 0.576428 0.131566i
\(545\) 5.59367e13 7.01424e13i 1.16336 1.45881i
\(546\) −3.86012e12 4.84043e12i −0.0795495 0.0997519i
\(547\) 1.83318e11 8.03168e11i 0.00374342 0.0164010i −0.973022 0.230714i \(-0.925894\pi\)
0.976765 + 0.214313i \(0.0687511\pi\)
\(548\) 7.65177e12 1.21777e13i 0.154831 0.246413i
\(549\) 9.22529e12 8.18767e13i 0.184977 1.64172i
\(550\) 9.28447e13i 1.84478i
\(551\) 1.56273e13 3.85905e13i 0.307698 0.759839i
\(552\) −1.19364e13 −0.232905
\(553\) 1.14841e13 + 1.29395e12i 0.222061 + 0.0250202i
\(554\) −1.89869e13 1.19302e13i −0.363835 0.228613i
\(555\) −1.84465e14 4.21030e13i −3.50308 0.799555i
\(556\) −1.28490e13 + 1.02467e13i −0.241822 + 0.192847i
\(557\) −6.13060e13 4.88899e13i −1.14348 0.911891i −0.146470 0.989215i \(-0.546791\pi\)
−0.997006 + 0.0773238i \(0.975362\pi\)
\(558\) −1.73593e13 7.60562e13i −0.320894 1.40593i
\(559\) −7.37111e12 2.57926e12i −0.135044 0.0472538i
\(560\) −7.90894e12 1.64231e13i −0.143608 0.298205i
\(561\) −1.07340e14 + 6.74459e13i −1.93173 + 1.21378i
\(562\) −3.10146e13 + 1.08525e13i −0.553203 + 0.193574i
\(563\) 2.18825e13 + 2.18825e13i 0.386861 + 0.386861i 0.873566 0.486705i \(-0.161801\pi\)
−0.486705 + 0.873566i \(0.661801\pi\)
\(564\) −6.88813e12 + 1.43034e13i −0.120700 + 0.250635i
\(565\) −7.28113e12 6.46218e13i −0.126461 1.12237i
\(566\) −2.14310e13 + 2.41470e12i −0.368944 + 0.0415700i
\(567\) 3.96522e12 + 1.90955e12i 0.0676630 + 0.0325848i
\(568\) 3.34736e13 3.34736e13i 0.566188 0.566188i
\(569\) 2.60451e13 + 7.44325e13i 0.436681 + 1.24796i 0.926552 + 0.376167i \(0.122758\pi\)
−0.489871 + 0.871795i \(0.662956\pi\)
\(570\) 7.65151e13 + 1.21773e14i 1.27167 + 2.02384i
\(571\) 3.98500e13 1.91907e13i 0.656519 0.316163i −0.0758014 0.997123i \(-0.524152\pi\)
0.732321 + 0.680960i \(0.238437\pi\)
\(572\) −1.31664e12 + 3.76273e12i −0.0215024 + 0.0614502i
\(573\) 1.12942e14 2.57784e13i 1.82845 0.417333i
\(574\) 1.17390e13 1.47202e13i 0.188395 0.236240i
\(575\) 1.33759e13 + 1.67728e13i 0.212805 + 0.266850i
\(576\) −1.52915e13 + 6.69963e13i −0.241177 + 1.05667i
\(577\) 8.87079e12 1.41178e13i 0.138702 0.220743i −0.770149 0.637864i \(-0.779818\pi\)
0.908851 + 0.417121i \(0.136961\pi\)
\(578\) 1.63897e13 1.45463e14i 0.254057 2.25482i
\(579\) 1.33235e14i 2.04751i
\(580\) 1.70596e13 + 9.25266e12i 0.259914 + 0.140970i
\(581\) 7.37665e12 0.111424
\(582\) 1.39781e14 + 1.57495e13i 2.09331 + 0.235859i
\(583\) −7.12554e12 4.47727e12i −0.105797 0.0664769i
\(584\) −1.70415e13 3.88961e12i −0.250867 0.0572587i
\(585\) 5.95775e13 4.75115e13i 0.869567 0.693457i
\(586\) −5.87033e13 4.68143e13i −0.849521 0.677471i
\(587\) −1.01177e13 4.43284e13i −0.145174 0.636050i −0.994186 0.107676i \(-0.965659\pi\)
0.849012 0.528374i \(-0.177198\pi\)
\(588\) −1.69360e13 5.92617e12i −0.240949 0.0843116i
\(589\) 2.41207e13 + 5.00872e13i 0.340262 + 0.706562i
\(590\) −1.76676e13 + 1.11013e13i −0.247126 + 0.155279i
\(591\) 1.14344e14 4.00107e13i 1.58590 0.554930i
\(592\) −7.81835e13 7.81835e13i −1.07524 1.07524i
\(593\) 5.71373e12 1.18647e13i 0.0779195 0.161801i −0.858370 0.513032i \(-0.828522\pi\)
0.936289 + 0.351230i \(0.114237\pi\)
\(594\) 4.57108e12 + 4.05694e13i 0.0618139 + 0.548614i
\(595\) −3.78397e13 + 4.26351e12i −0.507414 + 0.0571719i
\(596\) 1.73705e13 + 8.36521e12i 0.230984 + 0.111236i
\(597\) −1.39736e14 + 1.39736e14i −1.84263 + 1.84263i
\(598\) 2.09703e12 + 5.99298e12i 0.0274220 + 0.0783676i
\(599\) 1.83329e13 + 2.91767e13i 0.237738 + 0.378357i 0.944189 0.329404i \(-0.106848\pi\)
−0.706451 + 0.707762i \(0.749705\pi\)
\(600\) 1.98190e14 9.54432e13i 2.54874 1.22741i
\(601\) 1.89501e13 5.41563e13i 0.241679 0.690680i −0.757600 0.652719i \(-0.773628\pi\)
0.999279 0.0379605i \(-0.0120861\pi\)
\(602\) 4.33636e12 9.89745e11i 0.0548457 0.0125182i
\(603\) 1.30048e14 1.63075e14i 1.63123 2.04550i
\(604\) 2.43358e12 + 3.05161e12i 0.0302734 + 0.0379616i
\(605\) −9.37092e12 + 4.10567e13i −0.115613 + 0.506532i
\(606\) −2.23796e13 + 3.56169e13i −0.273835 + 0.435806i
\(607\) 7.10420e12 6.30515e13i 0.0862127 0.765159i −0.874007 0.485913i \(-0.838487\pi\)
0.960220 0.279246i \(-0.0900844\pi\)
\(608\) 2.28793e13i 0.275375i
\(609\) 2.06878e13 6.13816e12i 0.246960 0.0732743i
\(610\) −1.88656e14 −2.23368
\(611\) −4.10589e13 4.62623e12i −0.482171 0.0543277i
\(612\) −3.02637e13 1.90159e13i −0.352505 0.221493i
\(613\) 3.32212e13 + 7.58251e12i 0.383807 + 0.0876014i 0.410071 0.912054i \(-0.365504\pi\)
−0.0262642 + 0.999655i \(0.508361\pi\)
\(614\) 5.36119e13 4.27541e13i 0.614355 0.489932i
\(615\) 3.11168e14 + 2.48148e14i 3.53687 + 2.82056i
\(616\) 2.47208e12 + 1.08309e13i 0.0278714 + 0.122113i
\(617\) −4.63609e13 1.62224e13i −0.518473 0.181422i 0.0583416 0.998297i \(-0.481419\pi\)
−0.576815 + 0.816875i \(0.695704\pi\)
\(618\) −5.72143e12 1.18807e13i −0.0634691 0.131795i
\(619\) 5.40533e13 3.39640e13i 0.594798 0.373736i −0.200736 0.979645i \(-0.564333\pi\)
0.795534 + 0.605909i \(0.207191\pi\)
\(620\) −2.44595e13 + 8.55873e12i −0.266986 + 0.0934224i
\(621\) 6.67050e12 + 6.67050e12i 0.0722271 + 0.0722271i
\(622\) 2.13468e13 4.43271e13i 0.229288 0.476121i
\(623\) 2.15321e11 + 1.91102e12i 0.00229427 + 0.0203623i
\(624\) 7.59978e13 8.56289e12i 0.803300 0.0905102i
\(625\) −9.53348e13 4.59108e13i −0.999658 0.481410i
\(626\) −9.91447e12 + 9.91447e12i −0.103133 + 0.103133i
\(627\) −3.40075e13 9.71877e13i −0.350943 1.00294i
\(628\) −4.88284e12 7.77099e12i −0.0499889 0.0795570i
\(629\) −2.08104e14 + 1.00218e14i −2.11363 + 1.01787i
\(630\) −1.43347e13 + 4.09662e13i −0.144439 + 0.412784i
\(631\) −7.84239e13 + 1.78997e13i −0.783974 + 0.178937i −0.595729 0.803185i \(-0.703137\pi\)
−0.188244 + 0.982122i \(0.560280\pi\)
\(632\) −7.57702e13 + 9.50128e13i −0.751472 + 0.942316i
\(633\) −1.23361e14 1.54690e14i −1.21383 1.52210i
\(634\) −1.04755e13 + 4.58963e13i −0.102266 + 0.448055i
\(635\) −4.26092e13 + 6.78121e13i −0.412700 + 0.656808i
\(636\) 4.56248e11 4.04931e12i 0.00438445 0.0389131i
\(637\) 4.66994e13i 0.445261i
\(638\) −7.19179e13 6.32510e13i −0.680352 0.598362i
\(639\) −1.32408e14 −1.24283
\(640\) 2.18806e14 + 2.46535e13i 2.03779 + 0.229604i
\(641\) 1.22770e14 + 7.71414e13i 1.13449 + 0.712849i 0.962240 0.272204i \(-0.0877524\pi\)
0.172253 + 0.985053i \(0.444895\pi\)
\(642\) 1.02303e14 + 2.33499e13i 0.938018 + 0.214096i
\(643\) 5.43153e13 4.33150e13i 0.494160 0.394080i −0.344456 0.938802i \(-0.611937\pi\)
0.838616 + 0.544723i \(0.183365\pi\)
\(644\) −4.10177e11 3.27105e11i −0.00370290 0.00295296i
\(645\) 2.09221e13 + 9.16656e13i 0.187416 + 0.821122i
\(646\) 1.65713e14 + 5.79855e13i 1.47297 + 0.515415i
\(647\) −3.69319e13 7.66899e13i −0.325747 0.676421i 0.672206 0.740364i \(-0.265347\pi\)
−0.997954 + 0.0639429i \(0.979632\pi\)
\(648\) −3.91860e13 + 2.46222e13i −0.342970 + 0.215502i
\(649\) 1.41006e13 4.93402e12i 0.122466 0.0428526i
\(650\) −8.27382e13 8.27382e13i −0.713082 0.713082i
\(651\) −1.25018e13 + 2.59602e13i −0.106922 + 0.222026i
\(652\) 1.35255e12 + 1.20042e13i 0.0114793 + 0.101881i
\(653\) 2.83936e13 3.19919e12i 0.239141 0.0269447i 0.00841947 0.999965i \(-0.497320\pi\)
0.230721 + 0.973020i \(0.425891\pi\)
\(654\) −1.93157e14 9.30194e13i −1.61444 0.777472i
\(655\) −8.93251e13 + 8.93251e13i −0.740913 + 0.740913i
\(656\) 7.68157e13 + 2.19527e14i 0.632311 + 1.80704i
\(657\) 2.60119e13 + 4.13976e13i 0.212493 + 0.338181i
\(658\) 2.12029e13 1.02108e13i 0.171896 0.0827806i
\(659\) 2.43832e13 6.96833e13i 0.196184 0.560663i −0.803201 0.595708i \(-0.796872\pi\)
0.999386 + 0.0350450i \(0.0111575\pi\)
\(660\) 4.67926e13 1.06801e13i 0.373643 0.0852817i
\(661\) −1.40582e14 + 1.76285e14i −1.11410 + 1.39704i −0.205862 + 0.978581i \(0.566000\pi\)
−0.908237 + 0.418455i \(0.862572\pi\)
\(662\) −1.61715e14 2.02785e14i −1.27192 1.59494i
\(663\) 3.55511e13 1.55759e14i 0.277514 1.21587i
\(664\) −4.12695e13 + 6.56800e13i −0.319734 + 0.508854i
\(665\) 3.46292e12 3.07342e13i 0.0266277 0.236328i
\(666\) 2.63264e14i 2.00919i
\(667\) −2.21047e13 1.06557e12i −0.167438 0.00807148i
\(668\) 4.10368e13 0.308526
\(669\) 2.87315e14 + 3.23726e13i 2.14401 + 0.241572i
\(670\) −4.04376e14 2.54086e14i −2.99510 1.88195i
\(671\) 1.31682e14 + 3.00555e13i 0.968085 + 0.220959i
\(672\) −9.27120e12 + 7.39354e12i −0.0676534 + 0.0539518i
\(673\) −7.09276e13 5.65629e13i −0.513736 0.409691i 0.332011 0.943276i \(-0.392273\pi\)
−0.845746 + 0.533585i \(0.820844\pi\)
\(674\) −7.76901e12 3.40382e13i −0.0558555 0.244719i
\(675\) −1.64092e14 5.74184e13i −1.17103 0.409762i
\(676\) 8.21400e12 + 1.70565e13i 0.0581863 + 0.120825i
\(677\) −1.07542e14 + 6.75733e13i −0.756198 + 0.475151i −0.854141 0.520041i \(-0.825917\pi\)
0.0979428 + 0.995192i \(0.468774\pi\)
\(678\) −1.46680e14 + 5.13254e13i −1.02381 + 0.358248i
\(679\) −2.13907e13 2.13907e13i −0.148209 0.148209i
\(680\) 1.73737e14 3.60769e14i 1.19495 2.48133i
\(681\) 5.36464e12 + 4.76125e13i 0.0366273 + 0.325076i
\(682\) 1.27080e14 1.43185e13i 0.861301 0.0970453i
\(683\) −2.99983e13 1.44464e13i −0.201833 0.0971978i 0.330237 0.943898i \(-0.392871\pi\)
−0.532070 + 0.846700i \(0.678586\pi\)
\(684\) 2.05277e13 2.05277e13i 0.137107 0.137107i
\(685\) −1.48848e14 4.25383e14i −0.986939 2.82051i
\(686\) 2.87055e13 + 4.56845e13i 0.188949 + 0.300710i
\(687\) −1.28463e14 + 6.18644e13i −0.839448 + 0.404257i
\(688\) −1.81469e13 + 5.18609e13i −0.117723 + 0.336432i
\(689\) 1.03398e13 2.35999e12i 0.0665910 0.0151990i
\(690\) 4.76621e13 5.97664e13i 0.304739 0.382130i
\(691\) −1.29540e14 1.62438e14i −0.822268 1.03109i −0.998904 0.0468152i \(-0.985093\pi\)
0.176636 0.984276i \(-0.443479\pi\)
\(692\) 4.54341e12 1.99060e13i 0.0286320 0.125445i
\(693\) 1.65321e13 2.63107e13i 0.103434 0.164614i
\(694\) −2.69698e13 + 2.39364e14i −0.167525 + 1.48683i
\(695\) 5.14985e14i 3.17593i
\(696\) −6.10873e13 + 2.18540e14i −0.374028 + 1.33809i
\(697\) 4.85860e14 2.95357
\(698\) −1.41463e14 1.59391e13i −0.853819 0.0962023i
\(699\) 1.31807e13 + 8.28198e12i 0.0789864 + 0.0496305i
\(700\) 9.42600e12 + 2.15142e12i 0.0560838 + 0.0128008i
\(701\) 3.39958e13 2.71108e13i 0.200833 0.160159i −0.517909 0.855436i \(-0.673290\pi\)
0.718742 + 0.695277i \(0.244718\pi\)
\(702\) −4.02268e13 3.20798e13i −0.235955 0.188168i
\(703\) −4.17463e13 1.82902e14i −0.243131 1.06523i
\(704\) −1.06329e14 3.72060e13i −0.614875 0.215154i
\(705\) 2.15844e14 + 4.48204e14i 1.23935 + 2.57354i
\(706\) −2.06152e14 + 1.29534e14i −1.17534 + 0.738516i
\(707\) 8.53856e12 2.98777e12i 0.0483379 0.0169142i
\(708\) 5.11505e12 + 5.11505e12i 0.0287530 + 0.0287530i
\(709\) 2.73395e13 5.67711e13i 0.152602 0.316881i −0.810627 0.585562i \(-0.800874\pi\)
0.963229 + 0.268682i \(0.0865880\pi\)
\(710\) 3.39442e13 + 3.01263e14i 0.188137 + 1.66976i
\(711\) 3.37776e14 3.80582e13i 1.85900 0.209459i
\(712\) −1.82200e13 8.77427e12i −0.0995744 0.0479525i
\(713\) 2.08947e13 2.08947e13i 0.113394 0.113394i
\(714\) 3.00539e13 + 8.58891e13i 0.161961 + 0.462857i
\(715\) 6.64601e13 + 1.05771e14i 0.355656 + 0.566024i
\(716\) 5.63574e12 2.71403e12i 0.0299493 0.0144228i
\(717\) −6.70777e13 + 1.91697e14i −0.353983 + 1.01163i
\(718\) 7.61308e13 1.73763e13i 0.398968 0.0910618i
\(719\) 8.36735e13 1.04923e14i 0.435455 0.546044i −0.514884 0.857260i \(-0.672165\pi\)
0.950339 + 0.311216i \(0.100736\pi\)
\(720\) −3.34276e14 4.19169e14i −1.72760 2.16634i
\(721\) −6.31036e11 + 2.76475e12i −0.00323876 + 0.0141899i
\(722\) 3.70245e13 5.89241e13i 0.188713 0.300336i
\(723\) 4.84468e13 4.29977e14i 0.245230 2.17648i
\(724\) 2.69250e13i 0.135351i
\(725\) 3.75541e14 1.59055e14i 1.87485 0.794069i
\(726\) 1.00634e14 0.498955
\(727\) 1.32253e14 + 1.49013e13i 0.651226 + 0.0733756i 0.431396 0.902163i \(-0.358021\pi\)
0.219830 + 0.975538i \(0.429450\pi\)
\(728\) −1.18549e13 7.44893e12i −0.0579750 0.0364281i
\(729\) 3.15441e14 + 7.19973e13i 1.53207 + 0.349686i
\(730\) 8.75219e13 6.97964e13i 0.422185 0.336681i
\(731\) 8.97380e13 + 7.15636e13i 0.429922 + 0.342851i
\(732\) 1.45536e13 + 6.37634e13i 0.0692491 + 0.303400i
\(733\) −3.59298e14 1.25724e14i −1.69799 0.594152i −0.704668 0.709538i \(-0.748904\pi\)
−0.993321 + 0.115386i \(0.963190\pi\)
\(734\) 2.06130e13 + 4.28033e13i 0.0967521 + 0.200908i
\(735\) −4.76072e14 + 2.99136e14i −2.21940 + 1.39454i
\(736\) 1.14787e13 4.01659e12i 0.0531503 0.0185981i
\(737\) 2.41775e14 + 2.41775e14i 1.11192 + 1.11192i
\(738\) 2.40273e14 4.98931e14i 1.09755 2.27908i
\(739\) −3.96921e12 3.52277e13i −0.0180087 0.159831i 0.981489 0.191517i \(-0.0613409\pi\)
−0.999498 + 0.0316862i \(0.989912\pi\)
\(740\) 8.68998e13 9.79125e12i 0.391616 0.0441245i
\(741\) 1.16914e14 + 5.63028e13i 0.523330 + 0.252022i
\(742\) −4.27132e12 + 4.27132e12i −0.0189908 + 0.0189908i
\(743\) −1.04629e14 2.99012e14i −0.462070 1.32052i −0.905551 0.424237i \(-0.860542\pi\)
0.443481 0.896284i \(-0.353743\pi\)
\(744\) −1.61201e14 2.56550e14i −0.707137 1.12540i
\(745\) 5.44316e14 2.62129e14i 2.37176 1.14218i
\(746\) 7.60650e13 2.17381e14i 0.329223 0.940866i
\(747\) 2.11525e14 4.82793e13i 0.909410 0.207567i
\(748\) 3.65311e13 4.58086e13i 0.156011 0.195631i
\(749\) −1.40700e13 1.76433e13i −0.0596879 0.0748463i
\(750\) −1.59518e14 + 6.98893e14i −0.672207 + 2.94513i
\(751\) −1.53657e14 + 2.44543e14i −0.643208 + 1.02366i 0.352912 + 0.935657i \(0.385192\pi\)
−0.996120 + 0.0880035i \(0.971951\pi\)
\(752\) −3.25487e13 + 2.88878e14i −0.135346 + 1.20123i
\(753\) 6.95747e14i 2.87393i
\(754\) 1.20455e14 7.72346e12i 0.494275 0.0316924i
\(755\) 1.22308e14 0.498562
\(756\) 4.22470e12 + 4.76010e11i 0.0171075 + 0.00192756i
\(757\) −2.58005e14 1.62116e14i −1.03789 0.652147i −0.0985449 0.995133i \(-0.531419\pi\)
−0.939341 + 0.342986i \(0.888562\pi\)
\(758\) 3.69027e14 + 8.42279e13i 1.47473 + 0.336597i
\(759\) −4.27898e13 + 3.41237e13i −0.169876 + 0.135471i
\(760\) 2.54277e14 + 2.02779e14i 1.00286 + 0.799752i
\(761\) 3.46931e13 + 1.52000e14i 0.135931 + 0.595555i 0.996305 + 0.0858900i \(0.0273734\pi\)
−0.860373 + 0.509665i \(0.829770\pi\)
\(762\) 1.80641e14 + 6.32090e13i 0.703140 + 0.246039i
\(763\) 2.00044e13 + 4.15396e13i 0.0773577 + 0.160635i
\(764\) −4.53359e13 + 2.84864e13i −0.174171 + 0.109439i
\(765\) −1.05715e15 + 3.69912e14i −4.03486 + 1.41186i
\(766\) −7.75669e13 7.75669e13i −0.294126 0.294126i
\(767\) −8.16878e12 + 1.69626e13i −0.0307737 + 0.0639023i
\(768\) −2.29224e13 2.03442e14i −0.0857936 0.761439i
\(769\) −5.04766e14 + 5.68735e13i −1.87697 + 0.211484i −0.975293 0.220916i \(-0.929095\pi\)
−0.901682 + 0.432400i \(0.857667\pi\)
\(770\) −6.41019e13 3.08698e13i −0.236819 0.114046i
\(771\) −1.76918e14 + 1.76918e14i −0.649383 + 0.649383i
\(772\) −2.03383e13 5.81236e13i −0.0741700 0.211966i
\(773\) −1.39485e14 2.21989e14i −0.505393 0.804329i 0.492425 0.870355i \(-0.336111\pi\)
−0.997818 + 0.0660263i \(0.978968\pi\)
\(774\) 1.17867e14 5.67619e13i 0.424315 0.204339i
\(775\) −1.79858e14 + 5.14004e14i −0.643310 + 1.83848i
\(776\) 3.10131e14 7.07853e13i 1.10214 0.251556i
\(777\) 6.06257e13 7.60223e13i 0.214068 0.268433i
\(778\) 1.69761e14 + 2.12874e14i 0.595581 + 0.746835i
\(779\) −8.78126e13 + 3.84732e14i −0.306104 + 1.34113i
\(780\) −3.21815e13 + 5.12165e13i −0.111464 + 0.177393i
\(781\) 2.43024e13 2.15690e14i 0.0836363 0.742292i
\(782\) 9.33196e13i 0.319109i
\(783\) 1.56265e14 8.79900e13i 0.530950 0.298968i
\(784\) −3.28563e14 −1.10927
\(785\) −2.85781e14 3.21998e13i −0.958704 0.108020i
\(786\) 2.55601e14 + 1.60605e14i 0.852021 + 0.535361i
\(787\) 6.20970e13 + 1.41732e13i 0.205682 + 0.0469456i 0.324121 0.946016i \(-0.394932\pi\)
−0.118438 + 0.992961i \(0.537789\pi\)
\(788\) −4.37747e13 + 3.49092e13i −0.144076 + 0.114897i
\(789\) −1.61368e14 1.28687e14i −0.527755 0.420870i
\(790\) −1.73184e14 7.58770e14i −0.562825 2.46590i
\(791\) 3.15444e13 + 1.10379e13i 0.101868 + 0.0356453i
\(792\) 1.41774e14 + 2.94397e14i 0.454957 + 0.944728i
\(793\) −1.44132e14 + 9.05639e13i −0.459614 + 0.288795i
\(794\) 8.92946e13 3.12455e13i 0.282958 0.0990114i
\(795\) −9.02908e13 9.02908e13i −0.284320 0.284320i
\(796\) 3.96290e13 8.22904e13i 0.124007 0.257504i
\(797\) 5.05238e12 + 4.48411e13i 0.0157110 + 0.139439i 0.999119 0.0419690i \(-0.0133631\pi\)
−0.983408 + 0.181408i \(0.941935\pi\)
\(798\) −7.34438e13 + 8.27513e12i −0.226956 + 0.0255717i
\(799\) 5.47148e14 + 2.63493e14i 1.68024 + 0.809161i
\(800\) −1.58474e14 + 1.58474e14i −0.483624 + 0.483624i
\(801\) 1.86817e13 + 5.33894e13i 0.0566572 + 0.161917i
\(802\) −1.19808e14 1.90674e14i −0.361090 0.574672i
\(803\) −7.22100e13 + 3.47745e13i −0.216282 + 0.104156i
\(804\) −5.46831e13 + 1.56275e14i −0.162770 + 0.465169i
\(805\) −1.60276e13 + 3.65820e12i −0.0474121 + 0.0108215i
\(806\) −1.00487e14 + 1.26007e14i −0.295416 + 0.370440i
\(807\) −1.64063e14 2.05729e14i −0.479340 0.601073i
\(808\) −2.11675e13 + 9.27409e13i −0.0614628 + 0.269286i
\(809\) −2.70327e14 + 4.30222e14i −0.780093 + 1.24151i 0.185805 + 0.982587i \(0.440511\pi\)
−0.965898 + 0.258924i \(0.916632\pi\)
\(810\) 3.31847e13 2.94523e14i 0.0951729 0.844683i
\(811\) 4.61751e12i 0.0131614i 0.999978 + 0.00658072i \(0.00209472\pi\)
−0.999978 + 0.00658072i \(0.997905\pi\)
\(812\) −8.08801e12 + 5.83575e12i −0.0229119 + 0.0165316i
\(813\) 2.97362e14 0.837206
\(814\) −4.28851e14 4.83199e13i −1.20001 0.135208i
\(815\) 3.20517e14 + 2.01394e14i 0.891381 + 0.560092i
\(816\) −1.09588e15 2.50126e14i −3.02908 0.691367i
\(817\) −7.28872e13 + 5.81256e13i −0.200235 + 0.159682i
\(818\) 4.13966e14 + 3.30127e14i 1.13031 + 0.901394i
\(819\) 8.71416e12 + 3.81792e13i 0.0236486 + 0.103611i
\(820\) −1.73626e14 6.07545e13i −0.468324 0.163874i
\(821\) −2.63239e14 5.46622e14i −0.705724 1.46545i −0.877131 0.480251i \(-0.840546\pi\)
0.171407 0.985200i \(-0.445169\pi\)
\(822\) −9.11878e14 + 5.72971e14i −2.42984 + 1.52677i
\(823\) −1.19376e14 + 4.17715e13i −0.316168 + 0.110632i −0.483698 0.875235i \(-0.660707\pi\)
0.167530 + 0.985867i \(0.446421\pi\)
\(824\) −2.10863e13 2.10863e13i −0.0555092 0.0555092i
\(825\) 4.37620e14 9.08728e14i 1.14506 2.37774i
\(826\) −1.20061e12 1.06557e13i −0.00312249 0.0277129i
\(827\) 1.87017e14 2.10717e13i 0.483451 0.0544719i 0.133124 0.991099i \(-0.457499\pi\)
0.350327 + 0.936627i \(0.386070\pi\)
\(828\) −1.39027e13 6.69518e12i −0.0357229 0.0172033i
\(829\) 2.64721e14 2.64721e14i 0.676109 0.676109i −0.283009 0.959117i \(-0.591333\pi\)
0.959117 + 0.283009i \(0.0913325\pi\)
\(830\) −1.64075e14 4.68898e14i −0.416534 1.19039i
\(831\) 1.29603e14 + 2.06262e14i 0.327047 + 0.520493i
\(832\) 1.27910e14 6.15984e13i 0.320840 0.154509i
\(833\) −2.26695e14 + 6.47856e14i −0.565218 + 1.61530i
\(834\) 1.19977e15 2.73841e14i 2.97351 0.678684i
\(835\) 8.01754e14 1.00537e15i 1.97519 2.47681i
\(836\) 2.96714e13 + 3.72068e13i 0.0726619 + 0.0911151i
\(837\) −5.32844e13 + 2.33454e14i −0.129710 + 0.568295i
\(838\) −1.32118e14 + 2.10265e14i −0.319699 + 0.508799i
\(839\) −2.42886e13 + 2.15567e14i −0.0584242 + 0.518529i 0.930082 + 0.367351i \(0.119735\pi\)
−0.988507 + 0.151178i \(0.951693\pi\)
\(840\) 1.68568e14i 0.403068i
\(841\) −1.32634e14 + 3.99253e14i −0.315265 + 0.949004i
\(842\) −1.22477e14 −0.289398
\(843\) 3.54711e14 + 3.99663e13i 0.833176 + 0.0938764i
\(844\) 7.74295e13 + 4.86522e13i 0.180798 + 0.113603i
\(845\) 5.78351e14 + 1.32005e14i 1.34248 + 0.306413i
\(846\) 5.41164e14 4.31564e14i 1.24875 0.995848i
\(847\) −1.69204e13 1.34935e13i −0.0388144 0.0309534i
\(848\) −1.66042e13 7.27476e13i −0.0378650 0.165897i
\(849\) 2.21140e14 + 7.73802e13i 0.501336 + 0.175425i
\(850\) 7.46179e14 + 1.54946e15i 1.68170 + 3.49208i
\(851\) −8.44351e13 + 5.30541e13i −0.189180 + 0.118870i
\(852\) 9.92049e13 3.47133e13i 0.220971 0.0773210i
\(853\) −2.60514e14 2.60514e14i −0.576880 0.576880i 0.357162 0.934042i \(-0.383744\pi\)
−0.934042 + 0.357162i \(0.883744\pi\)
\(854\) 4.20657e13 8.73504e13i 0.0926060 0.192298i
\(855\) −1.01853e14 9.03969e14i −0.222917 1.97844i
\(856\) 2.35808e14 2.65692e13i 0.513086 0.0578109i
\(857\) −3.50018e14 1.68560e14i −0.757157 0.364627i 0.0151434 0.999885i \(-0.495180\pi\)
−0.772300 + 0.635258i \(0.780894\pi\)
\(858\) 2.11077e14 2.11077e14i 0.453946 0.453946i
\(859\) −1.25432e14 3.58465e14i −0.268190 0.766444i −0.996682 0.0813896i \(-0.974064\pi\)
0.728492 0.685054i \(-0.240222\pi\)
\(860\) −2.31200e13 3.67952e13i −0.0491468 0.0782167i
\(861\) −1.84279e14 + 8.87442e13i −0.389458 + 0.187553i
\(862\) 2.02442e13 5.78545e13i 0.0425367 0.121563i
\(863\) 8.65038e14 1.97439e14i 1.80710 0.412458i 0.819970 0.572406i \(-0.193990\pi\)
0.987125 + 0.159948i \(0.0511328\pi\)
\(864\) −6.14445e13 + 7.70490e13i −0.127619 + 0.160029i
\(865\) −3.98913e14 5.00221e14i −0.823754 1.03295i
\(866\) −4.19165e13 + 1.83648e14i −0.0860588 + 0.377048i
\(867\) −8.46049e14 + 1.34648e15i −1.72703 + 2.74855i
\(868\) 1.49106e12 1.32335e13i 0.00302618 0.0268581i
\(869\) 5.57213e14i 1.12440i
\(870\) −8.50319e14 1.17849e15i −1.70603 2.36446i
\(871\) −4.30914e14 −0.859607
\(872\) −4.81776e14 5.42832e13i −0.955571 0.107667i
\(873\) −7.53378e14 4.73378e14i −1.48574 0.933549i
\(874\) 7.38959e13 + 1.68663e13i 0.144898 + 0.0330721i
\(875\) 1.20532e14 9.61214e13i 0.234998 0.187404i
\(876\) −3.03421e13 2.41970e13i −0.0588200 0.0469074i
\(877\) 6.33373e13 + 2.77499e14i 0.122085 + 0.534889i 0.998570 + 0.0534597i \(0.0170249\pi\)
−0.876485 + 0.481429i \(0.840118\pi\)
\(878\) −4.62586e14 1.61866e14i −0.886585 0.310229i
\(879\) 3.53907e14 + 7.34896e14i 0.674442 + 1.40049i
\(880\) 7.44169e14 4.67593e14i 1.41013 0.886042i
\(881\) −5.94130e14 + 2.07895e14i −1.11944 + 0.391710i −0.825663 0.564163i \(-0.809199\pi\)
−0.293779 + 0.955873i \(0.594913\pi\)
\(882\) 5.53179e14 + 5.53179e14i 1.03639 + 1.03639i
\(883\) −2.29485e14 + 4.76531e14i −0.427515 + 0.887743i 0.570285 + 0.821447i \(0.306833\pi\)
−0.997800 + 0.0662966i \(0.978882\pi\)
\(884\) 8.26757e12 + 7.33767e13i 0.0153150 + 0.135924i
\(885\) 2.25249e14 2.53795e13i 0.414904 0.0467484i
\(886\) −2.29701e14 1.10618e14i −0.420721 0.202609i
\(887\) 6.03401e14 6.03401e14i 1.09898 1.09898i 0.104445 0.994531i \(-0.466693\pi\)
0.994531 0.104445i \(-0.0333066\pi\)
\(888\) 3.37708e14 + 9.65113e14i 0.611612 + 1.74789i
\(889\) −2.18972e13 3.48492e13i −0.0394348 0.0627601i
\(890\) 1.16685e14 5.61927e13i 0.208962 0.100631i
\(891\) −7.00846e13 + 2.00290e14i −0.124806 + 0.356674i
\(892\) −1.30282e14 + 2.97361e13i −0.230707 + 0.0526574i
\(893\) −3.07539e14 + 3.85641e14i −0.541555 + 0.679088i
\(894\) −9.00127e14 1.12872e15i −1.57622 1.97651i
\(895\) 4.36164e13 1.91096e14i 0.0759513 0.332764i
\(896\) −6.02034e13 + 9.58132e13i −0.104251 + 0.165915i
\(897\) 7.72274e12 6.85412e13i 0.0132987 0.118029i
\(898\) 1.11980e15i 1.91761i
\(899\) −2.75620e14 4.89487e14i −0.469367 0.833570i
\(900\) 2.84371e14 0.481585
\(901\) −1.54899e14 1.74529e13i −0.260870 0.0293930i
\(902\) 7.68647e14 + 4.82973e14i 1.28734 + 0.808891i
\(903\) −4.71077e13 1.07520e13i −0.0784608 0.0179082i
\(904\) −2.74757e14 + 2.19112e14i −0.455100 + 0.362930i
\(905\) −6.59639e14 5.26045e14i −1.08658 0.866523i
\(906\) −6.50365e13 2.84944e14i −0.106541 0.466786i
\(907\) 8.63045e14 + 3.01993e14i 1.40604 + 0.491994i 0.923404 0.383829i \(-0.125395\pi\)
0.482633 + 0.875822i \(0.339680\pi\)
\(908\) −9.60836e12 1.99520e13i −0.0155675 0.0323263i
\(909\) 2.25289e14 1.41558e14i 0.363011 0.228095i
\(910\) 8.46336e13 2.96146e13i 0.135624 0.0474568i
\(911\) −1.58659e14 1.58659e14i −0.252856 0.252856i 0.569284 0.822141i \(-0.307220\pi\)
−0.822141 + 0.569284i \(0.807220\pi\)
\(912\) 3.96129e14 8.22571e14i 0.627860 1.30376i
\(913\) 3.98221e13 + 3.53431e14i 0.0627726 + 0.557122i
\(914\) 7.82355e14 8.81502e13i 1.22652 0.138195i
\(915\) 1.84649e15 + 8.89222e14i 2.87900 + 1.38645i
\(916\) 4.65981e13 4.65981e13i 0.0722588 0.0722588i
\(917\) −2.14415e13 6.12762e13i −0.0330680 0.0945029i
\(918\) 4.02335e14 + 6.40313e14i 0.617127 + 0.982153i
\(919\) −3.98160e14 + 1.91744e14i −0.607407 + 0.292512i −0.712194 0.701983i \(-0.752298\pi\)
0.104787 + 0.994495i \(0.466584\pi\)
\(920\) 5.70965e13 1.63172e14i 0.0866304 0.247575i
\(921\) −7.26252e14 + 1.65762e14i −1.09595 + 0.250143i
\(922\) −7.57429e13 + 9.49786e13i −0.113681 + 0.142551i
\(923\) 1.70554e14 + 2.13868e14i 0.254598 + 0.319255i
\(924\) −5.48859e12 + 2.40471e13i −0.00814893 + 0.0357028i
\(925\) 9.77722e14 1.55604e15i 1.44380 2.29779i
\(926\) 1.14395e14 1.01529e15i 0.168017 1.49119i
\(927\) 8.34093e13i 0.121847i
\(928\) −1.47933e13 2.30716e14i −0.0214943 0.335226i
\(929\) −5.40920e14 −0.781726 −0.390863 0.920449i \(-0.627823\pi\)
−0.390863 + 0.920449i \(0.627823\pi\)
\(930\) 1.92823e15 + 2.17260e14i 2.77169 + 0.312295i
\(931\) −4.72038e14 2.96601e14i −0.674883 0.424057i
\(932\) −7.01430e12 1.60097e12i −0.00997481 0.00227669i
\(933\) −4.17868e14 + 3.33239e14i −0.591059 + 0.471354i
\(934\) 6.63052e14 + 5.28767e14i 0.932853 + 0.743926i
\(935\) −4.08547e14 1.78996e15i −0.571721 2.50487i
\(936\) −3.88692e14 1.36009e14i −0.541036 0.189317i
\(937\) −1.25449e14 2.60497e14i −0.173688 0.360666i 0.795893 0.605437i \(-0.207002\pi\)
−0.969581 + 0.244771i \(0.921287\pi\)
\(938\) 2.07812e14 1.30577e14i 0.286191 0.179826i
\(939\) 1.43770e14 5.03074e13i 0.196943 0.0689135i
\(940\) −1.62580e14 1.62580e14i −0.221527 0.221527i
\(941\) −1.46290e14 + 3.03775e14i −0.198275 + 0.411721i −0.976273 0.216545i \(-0.930521\pi\)
0.777998 + 0.628267i \(0.216235\pi\)
\(942\) 7.69459e13 + 6.82914e14i 0.103736 + 0.920685i
\(943\) 2.08440e14 2.34855e13i 0.279526 0.0314950i
\(944\) 1.19344e14 + 5.74730e13i 0.159199 + 0.0766662i
\(945\) 9.42017e13 9.42017e13i 0.124997 0.124997i
\(946\) 7.08302e13 + 2.02421e14i 0.0934894 + 0.267177i
\(947\) −3.35957e14 5.34672e14i −0.441097 0.702001i 0.549997 0.835166i \(-0.314629\pi\)
−0.991094 + 0.133165i \(0.957486\pi\)
\(948\) −2.43095e14 + 1.17068e14i −0.317493 + 0.152897i
\(949\) 3.33605e13 9.53388e13i 0.0433412 0.123862i
\(950\) −1.36181e15 + 3.10825e14i −1.75994 + 0.401696i
\(951\) 3.18861e14 3.99839e14i 0.409919 0.514023i
\(952\) 1.28302e14 + 1.60886e14i 0.164077 + 0.205747i
\(953\) 9.65544e13 4.23033e14i 0.122831 0.538157i −0.875644 0.482957i \(-0.839563\pi\)
0.998475 0.0552010i \(-0.0175799\pi\)
\(954\) −9.45248e13 + 1.50435e14i −0.119620 + 0.190374i
\(955\) −1.87853e14 + 1.66724e15i −0.236484 + 2.09885i
\(956\) 9.38670e13i 0.117550i
\(957\) 4.05773e14 + 9.58058e14i 0.505502 + 1.19353i
\(958\) 3.97644e14 0.492796
\(959\) 2.30148e14 + 2.59315e13i 0.283736 + 0.0319694i
\(960\) −1.44730e15 9.09396e14i −1.77501 1.11531i
\(961\) −6.78057e13 1.54762e13i −0.0827274 0.0188820i
\(962\) 4.25229e14 3.39109e14i 0.516116 0.411589i
\(963\) −5.18932e14 4.13834e14i −0.626583 0.499684i
\(964\) 4.45012e13 + 1.94972e14i 0.0534547 + 0.234200i
\(965\) −1.82134e15 6.37313e14i −2.17647 0.761581i
\(966\) 1.70452e13 + 3.53947e13i 0.0202636 + 0.0420778i
\(967\) −9.61492e14 + 6.04146e14i −1.13714 + 0.714512i −0.962811 0.270176i \(-0.912918\pi\)
−0.174328 + 0.984688i \(0.555775\pi\)
\(968\) 2.14806e14 7.51640e13i 0.252738 0.0884368i
\(969\) −1.34862e15 1.34862e15i −1.57860 1.57860i
\(970\) −8.83923e14 + 1.83548e15i −1.02933 + 2.13743i
\(971\) 7.84531e13 + 6.96291e14i 0.0908896 + 0.806668i 0.953622 + 0.301007i \(0.0973227\pi\)
−0.862732 + 0.505661i \(0.831249\pi\)
\(972\) −1.91254e14 + 2.15492e13i −0.220435 + 0.0248370i
\(973\) −2.38446e14 1.14829e14i −0.273417 0.131671i
\(974\) −6.84113e14 + 6.84113e14i −0.780428 + 0.780428i
\(975\) 4.19825e14 + 1.19979e15i 0.476481 + 1.36170i
\(976\) 6.37180e14 + 1.01407e15i 0.719470 + 1.14503i
\(977\) 7.01502e14 3.37825e14i 0.788054 0.379507i 0.00383620 0.999993i \(-0.498779\pi\)
0.784218 + 0.620486i \(0.213065\pi\)
\(978\) 2.98761e14 8.53809e14i 0.333910 0.954259i
\(979\) −9.03988e13 + 2.06329e13i −0.100519 + 0.0229429i
\(980\) 1.62023e14 2.03170e14i 0.179244 0.224765i
\(981\) 8.45499e14 + 1.06022e15i 0.930611 + 1.16695i
\(982\) −3.15130e13 + 1.38067e14i −0.0345090 + 0.151194i
\(983\) 4.41663e14 7.02902e14i 0.481197 0.765821i −0.514598 0.857432i \(-0.672059\pi\)
0.995795 + 0.0916106i \(0.0292015\pi\)
\(984\) 2.40813e14 2.13727e15i 0.261038 2.31678i
\(985\) 1.75448e15i 1.89220i
\(986\) −1.70855e15 4.77583e14i −1.83334 0.512465i
\(987\) −2.55653e14 −0.272939
\(988\) −5.95982e13 6.71510e12i −0.0633065 0.00713293i
\(989\) 4.19580e13 + 2.63639e13i 0.0443438 + 0.0278631i
\(990\) −2.04016e15 4.65653e14i −2.14530 0.489651i
\(991\) 1.08443e15 8.64808e14i 1.13458 0.904797i 0.138250 0.990397i \(-0.455852\pi\)
0.996330 + 0.0855999i \(0.0272807\pi\)
\(992\) 2.41349e14 + 1.92469e14i 0.251239 + 0.200356i
\(993\) 6.26988e14 + 2.74701e15i 0.649401 + 2.84521i
\(994\) −1.47058e14 5.14579e13i −0.151551 0.0530298i
\(995\) −1.24180e15 2.57862e15i −1.27331 2.64406i
\(996\) −1.45825e14 + 9.16277e13i −0.148776 + 0.0934824i
\(997\) −3.24340e14 + 1.13491e14i −0.329249 + 0.115209i −0.489841 0.871812i \(-0.662945\pi\)
0.160592 + 0.987021i \(0.448660\pi\)
\(998\) 9.20252e13 + 9.20252e13i 0.0929510 + 0.0929510i
\(999\) 3.50616e14 7.28062e14i 0.352374 0.731713i
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 29.11.f.a.2.18 288
29.15 odd 28 inner 29.11.f.a.15.18 yes 288
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.11.f.a.2.18 288 1.1 even 1 trivial
29.11.f.a.15.18 yes 288 29.15 odd 28 inner