Properties

Label 35.10.k.a.3.15
Level $35$
Weight $10$
Character 35.3
Analytic conductor $18.026$
Analytic rank $0$
Dimension $136$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [35,10,Mod(3,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([9, 2]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.3");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 35.k (of order \(12\), 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: \(18.0262542657\)
Analytic rank: \(0\)
Dimension: \(136\)
Relative dimension: \(34\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 3.15
Character \(\chi\) \(=\) 35.3
Dual form 35.10.k.a.12.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-6.27232 - 1.68066i) q^{2} +(15.1291 + 56.4624i) q^{3} +(-406.888 - 234.917i) q^{4} +(-873.884 - 1090.62i) q^{5} -379.577i q^{6} +(259.777 - 6347.14i) q^{7} +(4508.24 + 4508.24i) q^{8} +(14086.9 - 8133.05i) q^{9} +(3648.32 + 8309.42i) q^{10} +(-44961.3 + 77875.2i) q^{11} +(7108.13 - 26527.9i) q^{12} +(60467.0 - 60467.0i) q^{13} +(-12296.8 + 39374.7i) q^{14} +(48358.0 - 65841.7i) q^{15} +(99577.0 + 172472. i) q^{16} +(-452819. + 121333. i) q^{17} +(-102026. + 27337.8i) q^{18} +(-291502. - 504896. i) q^{19} +(99368.0 + 649050. i) q^{20} +(362305. - 81358.5i) q^{21} +(412894. - 412894. i) q^{22} +(-405811. + 1.51451e6i) q^{23} +(-186341. + 322752. i) q^{24} +(-425777. + 1.90615e6i) q^{25} +(-480893. + 277644. i) q^{26} +(1.48590e6 + 1.48590e6i) q^{27} +(-1.59675e6 + 2.52154e6i) q^{28} +3.27059e6i q^{29} +(-413974. + 331706. i) q^{30} +(6.78743e6 + 3.91873e6i) q^{31} +(-1.17958e6 - 4.40225e6i) q^{32} +(-5.07724e6 - 1.36044e6i) q^{33} +3.04415e6 q^{34} +(-7.14932e6 + 5.26334e6i) q^{35} -7.64236e6 q^{36} +(-1.62853e6 - 436363. i) q^{37} +(979833. + 3.65679e6i) q^{38} +(4.32892e6 + 2.49930e6i) q^{39} +(977095. - 8.85646e6i) q^{40} -7.67652e6i q^{41} +(-2.40923e6 - 98605.4i) q^{42} +(9.94440e6 + 9.94440e6i) q^{43} +(3.65884e7 - 2.11243e7i) q^{44} +(-2.11804e7 - 8.25606e6i) q^{45} +(5.09075e6 - 8.81743e6i) q^{46} +(-1.83835e6 + 6.86081e6i) q^{47} +(-8.23170e6 + 8.23170e6i) q^{48} +(-4.02186e7 - 3.29768e6i) q^{49} +(5.87421e6 - 1.12404e7i) q^{50} +(-1.37015e7 - 2.37316e7i) q^{51} +(-3.88080e7 + 1.03986e7i) q^{52} +(5.93925e7 - 1.59142e7i) q^{53} +(-6.82273e6 - 1.18173e7i) q^{54} +(1.24223e8 - 1.90183e7i) q^{55} +(2.97856e7 - 2.74433e7i) q^{56} +(2.40975e7 - 2.40975e7i) q^{57} +(5.49676e6 - 2.05142e7i) q^{58} +(-3.15723e7 + 5.46849e7i) q^{59} +(-3.51436e7 + 1.54301e7i) q^{60} +(-2.44912e7 + 1.41400e7i) q^{61} +(-3.59869e7 - 3.59869e7i) q^{62} +(-4.79622e7 - 9.15240e7i) q^{63} -7.23721e7i q^{64} +(-1.18788e8 - 1.31053e7i) q^{65} +(2.95597e7 + 1.70663e7i) q^{66} +(-1.16951e7 - 4.36465e7i) q^{67} +(2.12750e8 + 5.70061e7i) q^{68} -9.16521e7 q^{69} +(5.36888e7 - 2.09978e7i) q^{70} -2.78044e8 q^{71} +(1.00173e8 + 2.68412e7i) q^{72} +(5.00668e7 + 1.86852e8i) q^{73} +(9.48128e6 + 5.47402e6i) q^{74} +(-1.14067e8 + 4.79786e6i) q^{75} +2.73915e8i q^{76} +(4.82605e8 + 3.05606e8i) q^{77} +(-2.29519e7 - 2.29519e7i) q^{78} +(-1.28788e8 + 7.43557e7i) q^{79} +(1.01083e8 - 2.59322e8i) q^{80} +(9.86658e7 - 1.70894e8i) q^{81} +(-1.29016e7 + 4.81496e7i) q^{82} +(-4.43112e8 + 4.43112e8i) q^{83} +(-1.66530e8 - 5.20076e7i) q^{84} +(5.28039e8 + 3.87823e8i) q^{85} +(-4.56613e7 - 7.90876e7i) q^{86} +(-1.84665e8 + 4.94809e7i) q^{87} +(-5.53777e8 + 1.48384e8i) q^{88} +(-1.22183e8 - 2.11627e8i) q^{89} +(1.18974e8 + 8.73817e7i) q^{90} +(-3.68084e8 - 3.99500e8i) q^{91} +(5.20902e8 - 5.20902e8i) q^{92} +(-1.18573e8 + 4.42521e8i) q^{93} +(2.30614e7 - 3.99436e7i) q^{94} +(-2.95911e8 + 7.59139e8i) q^{95} +(2.30715e8 - 1.33204e8i) q^{96} +(-2.41447e8 - 2.41447e8i) q^{97} +(2.46722e8 + 8.82781e7i) q^{98} +1.46269e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 136 q - 2 q^{2} - 6 q^{3} - 1710 q^{5} + 5940 q^{7} - 3484 q^{8} + 153786 q^{10} - 87752 q^{11} + 3066 q^{12} - 318872 q^{15} + 3132804 q^{16} - 1578678 q^{17} - 239036 q^{18} - 5745396 q^{21} + 2132088 q^{22}+ \cdots + 5117393178 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.27232 1.68066i −0.277200 0.0742755i 0.117541 0.993068i \(-0.462499\pi\)
−0.394741 + 0.918793i \(0.629166\pi\)
\(3\) 15.1291 + 56.4624i 0.107837 + 0.402452i 0.998652 0.0519147i \(-0.0165324\pi\)
−0.890815 + 0.454366i \(0.849866\pi\)
\(4\) −406.888 234.917i −0.794702 0.458822i
\(5\) −873.884 1090.62i −0.625301 0.780384i
\(6\) 379.577i 0.119569i
\(7\) 259.777 6347.14i 0.0408940 0.999163i
\(8\) 4508.24 + 4508.24i 0.389137 + 0.389137i
\(9\) 14086.9 8133.05i 0.715687 0.413202i
\(10\) 3648.32 + 8309.42i 0.115370 + 0.262767i
\(11\) −44961.3 + 77875.2i −0.925916 + 1.60373i −0.135835 + 0.990731i \(0.543372\pi\)
−0.790081 + 0.613002i \(0.789962\pi\)
\(12\) 7108.13 26527.9i 0.0989555 0.369307i
\(13\) 60467.0 60467.0i 0.587183 0.587183i −0.349685 0.936867i \(-0.613711\pi\)
0.936867 + 0.349685i \(0.113711\pi\)
\(14\) −12296.8 + 39374.7i −0.0855492 + 0.273931i
\(15\) 48358.0 65841.7i 0.246636 0.335807i
\(16\) 99577.0 + 172472.i 0.379856 + 0.657930i
\(17\) −452819. + 121333.i −1.31494 + 0.352336i −0.847079 0.531468i \(-0.821641\pi\)
−0.467858 + 0.883804i \(0.654974\pi\)
\(18\) −102026. + 27337.8i −0.229079 + 0.0613816i
\(19\) −291502. 504896.i −0.513157 0.888814i −0.999884 0.0152598i \(-0.995142\pi\)
0.486726 0.873554i \(-0.338191\pi\)
\(20\) 99368.0 + 649050.i 0.138871 + 0.907074i
\(21\) 362305. 81358.5i 0.406525 0.0912885i
\(22\) 412894. 412894.i 0.375782 0.375782i
\(23\) −405811. + 1.51451e6i −0.302376 + 1.12848i 0.632804 + 0.774312i \(0.281904\pi\)
−0.935180 + 0.354172i \(0.884763\pi\)
\(24\) −186341. + 322752.i −0.114646 + 0.198572i
\(25\) −425777. + 1.90615e6i −0.217998 + 0.975949i
\(26\) −480893. + 277644.i −0.206380 + 0.119154i
\(27\) 1.48590e6 + 1.48590e6i 0.538086 + 0.538086i
\(28\) −1.59675e6 + 2.52154e6i −0.490936 + 0.775275i
\(29\) 3.27059e6i 0.858687i 0.903141 + 0.429344i \(0.141255\pi\)
−0.903141 + 0.429344i \(0.858745\pi\)
\(30\) −413974. + 331706.i −0.0933099 + 0.0747667i
\(31\) 6.78743e6 + 3.91873e6i 1.32001 + 0.762109i 0.983730 0.179652i \(-0.0574971\pi\)
0.336282 + 0.941761i \(0.390830\pi\)
\(32\) −1.17958e6 4.40225e6i −0.198862 0.742163i
\(33\) −5.07724e6 1.36044e6i −0.745273 0.199695i
\(34\) 3.04415e6 0.390670
\(35\) −7.14932e6 + 5.26334e6i −0.805302 + 0.592865i
\(36\) −7.64236e6 −0.758344
\(37\) −1.62853e6 436363.i −0.142853 0.0382772i 0.186684 0.982420i \(-0.440226\pi\)
−0.329537 + 0.944143i \(0.606893\pi\)
\(38\) 979833. + 3.65679e6i 0.0762300 + 0.284494i
\(39\) 4.32892e6 + 2.49930e6i 0.299632 + 0.172993i
\(40\) 977095. 8.85646e6i 0.0603485 0.547004i
\(41\) 7.67652e6i 0.424265i −0.977241 0.212132i \(-0.931959\pi\)
0.977241 0.212132i \(-0.0680408\pi\)
\(42\) −2.40923e6 98605.4i −0.119469 0.00488966i
\(43\) 9.94440e6 + 9.94440e6i 0.443578 + 0.443578i 0.893213 0.449634i \(-0.148446\pi\)
−0.449634 + 0.893213i \(0.648446\pi\)
\(44\) 3.65884e7 2.11243e7i 1.47166 0.849661i
\(45\) −2.11804e7 8.25606e6i −0.769976 0.300135i
\(46\) 5.09075e6 8.81743e6i 0.167638 0.290357i
\(47\) −1.83835e6 + 6.86081e6i −0.0549525 + 0.205086i −0.987944 0.154814i \(-0.950522\pi\)
0.932991 + 0.359899i \(0.117189\pi\)
\(48\) −8.23170e6 + 8.23170e6i −0.223823 + 0.223823i
\(49\) −4.02186e7 3.29768e6i −0.996655 0.0817196i
\(50\) 5.87421e6 1.12404e7i 0.132918 0.254341i
\(51\) −1.37015e7 2.37316e7i −0.283597 0.491204i
\(52\) −3.88080e7 + 1.03986e7i −0.736047 + 0.197223i
\(53\) 5.93925e7 1.59142e7i 1.03393 0.277040i 0.298333 0.954462i \(-0.403569\pi\)
0.735595 + 0.677422i \(0.236903\pi\)
\(54\) −6.82273e6 1.18173e7i −0.109191 0.189124i
\(55\) 1.24223e8 1.90183e7i 1.83050 0.280246i
\(56\) 2.97856e7 2.74433e7i 0.404725 0.372898i
\(57\) 2.40975e7 2.40975e7i 0.302368 0.302368i
\(58\) 5.49676e6 2.05142e7i 0.0637794 0.238028i
\(59\) −3.15723e7 + 5.46849e7i −0.339213 + 0.587534i −0.984285 0.176588i \(-0.943494\pi\)
0.645072 + 0.764122i \(0.276827\pi\)
\(60\) −3.51436e7 + 1.54301e7i −0.350078 + 0.153705i
\(61\) −2.44912e7 + 1.41400e7i −0.226477 + 0.130757i −0.608946 0.793212i \(-0.708407\pi\)
0.382468 + 0.923969i \(0.375074\pi\)
\(62\) −3.59869e7 3.59869e7i −0.309301 0.309301i
\(63\) −4.79622e7 9.15240e7i −0.383589 0.731986i
\(64\) 7.23721e7i 0.539214i
\(65\) −1.18788e8 1.31053e7i −0.825393 0.0910621i
\(66\) 2.95597e7 + 1.70663e7i 0.191757 + 0.110711i
\(67\) −1.16951e7 4.36465e7i −0.0709032 0.264614i 0.921370 0.388687i \(-0.127071\pi\)
−0.992273 + 0.124072i \(0.960404\pi\)
\(68\) 2.12750e8 + 5.70061e7i 1.20664 + 0.323319i
\(69\) −9.16521e7 −0.486768
\(70\) 5.36888e7 2.09978e7i 0.267265 0.104528i
\(71\) −2.78044e8 −1.29853 −0.649263 0.760564i \(-0.724923\pi\)
−0.649263 + 0.760564i \(0.724923\pi\)
\(72\) 1.00173e8 + 2.68412e7i 0.439292 + 0.117708i
\(73\) 5.00668e7 + 1.86852e8i 0.206347 + 0.770096i 0.989035 + 0.147682i \(0.0471813\pi\)
−0.782688 + 0.622414i \(0.786152\pi\)
\(74\) 9.48128e6 + 5.47402e6i 0.0367557 + 0.0212209i
\(75\) −1.14067e8 + 4.79786e6i −0.416281 + 0.0175094i
\(76\) 2.73915e8i 0.941791i
\(77\) 4.82605e8 + 3.05606e8i 1.56453 + 0.990725i
\(78\) −2.29519e7 2.29519e7i −0.0702090 0.0702090i
\(79\) −1.28788e8 + 7.43557e7i −0.372009 + 0.214779i −0.674336 0.738425i \(-0.735570\pi\)
0.302327 + 0.953204i \(0.402237\pi\)
\(80\) 1.01083e8 2.59322e8i 0.275914 0.707838i
\(81\) 9.86658e7 1.70894e8i 0.254674 0.441108i
\(82\) −1.29016e7 + 4.81496e7i −0.0315125 + 0.117606i
\(83\) −4.43112e8 + 4.43112e8i −1.02485 + 1.02485i −0.0251706 + 0.999683i \(0.508013\pi\)
−0.999683 + 0.0251706i \(0.991987\pi\)
\(84\) −1.66530e8 5.20076e7i −0.364951 0.113975i
\(85\) 5.28039e8 + 3.87823e8i 1.09719 + 0.805839i
\(86\) −4.56613e7 7.90876e7i −0.0900129 0.155907i
\(87\) −1.84665e8 + 4.94809e7i −0.345580 + 0.0925979i
\(88\) −5.53777e8 + 1.48384e8i −0.984380 + 0.263764i
\(89\) −1.22183e8 2.11627e8i −0.206422 0.357533i 0.744163 0.667998i \(-0.232849\pi\)
−0.950585 + 0.310465i \(0.899515\pi\)
\(90\) 1.18974e8 + 8.73817e7i 0.191145 + 0.140388i
\(91\) −3.68084e8 3.99500e8i −0.562679 0.610704i
\(92\) 5.20902e8 5.20902e8i 0.758072 0.758072i
\(93\) −1.18573e8 + 4.42521e8i −0.164367 + 0.613424i
\(94\) 2.30614e7 3.99436e7i 0.0304657 0.0527681i
\(95\) −2.95911e8 + 7.59139e8i −0.372739 + 0.956236i
\(96\) 2.30715e8 1.33204e8i 0.277240 0.160065i
\(97\) −2.41447e8 2.41447e8i −0.276916 0.276916i 0.554960 0.831877i \(-0.312733\pi\)
−0.831877 + 0.554960i \(0.812733\pi\)
\(98\) 2.46722e8 + 8.82781e7i 0.270203 + 0.0966798i
\(99\) 1.46269e9i 1.53036i
\(100\) 6.21030e8 6.75567e8i 0.621030 0.675567i
\(101\) −8.23980e8 4.75725e8i −0.787898 0.454893i 0.0513237 0.998682i \(-0.483656\pi\)
−0.839222 + 0.543789i \(0.816989\pi\)
\(102\) 4.60551e7 + 1.71880e8i 0.0421286 + 0.157226i
\(103\) 1.62415e9 + 4.35190e8i 1.42187 + 0.380988i 0.886146 0.463407i \(-0.153373\pi\)
0.535721 + 0.844395i \(0.320040\pi\)
\(104\) 5.45199e8 0.456989
\(105\) −4.05344e8 3.24039e8i −0.325440 0.260163i
\(106\) −3.99275e8 −0.307182
\(107\) −7.25044e8 1.94275e8i −0.534734 0.143281i −0.0186604 0.999826i \(-0.505940\pi\)
−0.516073 + 0.856544i \(0.672607\pi\)
\(108\) −2.55531e8 9.53655e8i −0.180733 0.674504i
\(109\) −1.54734e8 8.93357e7i −0.104995 0.0606186i 0.446583 0.894742i \(-0.352641\pi\)
−0.551578 + 0.834123i \(0.685974\pi\)
\(110\) −8.11131e8 8.94886e7i −0.528231 0.0582774i
\(111\) 9.85525e7i 0.0616189i
\(112\) 1.12057e9 5.87225e8i 0.672914 0.352633i
\(113\) −6.04469e8 6.04469e8i −0.348756 0.348756i 0.510890 0.859646i \(-0.329316\pi\)
−0.859646 + 0.510890i \(0.829316\pi\)
\(114\) −1.91647e8 + 1.10648e8i −0.106275 + 0.0613578i
\(115\) 2.00638e9 8.80918e8i 1.06973 0.469672i
\(116\) 7.68316e8 1.33076e9i 0.393984 0.682401i
\(117\) 3.60009e8 1.34357e9i 0.177614 0.662864i
\(118\) 2.89939e8 2.89939e8i 0.137669 0.137669i
\(119\) 6.52482e8 + 2.90562e9i 0.298268 + 1.32824i
\(120\) 5.14839e8 7.88207e7i 0.226650 0.0346996i
\(121\) −2.86406e9 4.96070e9i −1.21464 2.10382i
\(122\) 1.77381e8 4.75291e7i 0.0724916 0.0194241i
\(123\) 4.33435e8 1.16139e8i 0.170746 0.0457513i
\(124\) −1.84115e9 3.18896e9i −0.699345 1.21130i
\(125\) 2.45097e9 1.20139e9i 0.897929 0.440140i
\(126\) 1.47013e8 + 6.54676e8i 0.0519623 + 0.231398i
\(127\) −1.67878e9 + 1.67878e9i −0.572635 + 0.572635i −0.932864 0.360229i \(-0.882699\pi\)
0.360229 + 0.932864i \(0.382699\pi\)
\(128\) −7.25577e8 + 2.70789e9i −0.238912 + 0.891633i
\(129\) −4.11035e8 + 7.11934e8i −0.130685 + 0.226353i
\(130\) 7.23048e8 + 2.81843e8i 0.222035 + 0.0865489i
\(131\) 1.07942e9 6.23201e8i 0.320234 0.184887i −0.331263 0.943539i \(-0.607475\pi\)
0.651497 + 0.758651i \(0.274141\pi\)
\(132\) 1.74628e9 + 1.74628e9i 0.500646 + 0.500646i
\(133\) −3.28037e9 + 1.71904e9i −0.909056 + 0.476381i
\(134\) 2.93420e8i 0.0786174i
\(135\) 3.22046e8 2.91905e9i 0.0834480 0.756379i
\(136\) −2.58842e9 1.49442e9i −0.648797 0.374583i
\(137\) 1.55076e9 + 5.78750e9i 0.376098 + 1.40362i 0.851734 + 0.523975i \(0.175551\pi\)
−0.475636 + 0.879642i \(0.657782\pi\)
\(138\) 5.74872e8 + 1.54036e8i 0.134932 + 0.0361549i
\(139\) −5.13206e9 −1.16607 −0.583036 0.812446i \(-0.698135\pi\)
−0.583036 + 0.812446i \(0.698135\pi\)
\(140\) 4.14542e9 4.62094e8i 0.911995 0.101661i
\(141\) −4.15191e8 −0.0884629
\(142\) 1.74398e9 + 4.67298e8i 0.359952 + 0.0964487i
\(143\) 1.99021e9 + 7.42755e9i 0.398003 + 1.48537i
\(144\) 2.80546e9 + 1.61973e9i 0.543716 + 0.313915i
\(145\) 3.56697e9 2.85812e9i 0.670105 0.536938i
\(146\) 1.25614e9i 0.228797i
\(147\) −4.22275e8 2.32073e9i −0.0745877 0.409918i
\(148\) 5.60120e8 + 5.60120e8i 0.0959628 + 0.0959628i
\(149\) −5.87833e9 + 3.39385e9i −0.977047 + 0.564099i −0.901377 0.433034i \(-0.857443\pi\)
−0.0756699 + 0.997133i \(0.524110\pi\)
\(150\) 7.23531e8 + 1.61615e8i 0.116693 + 0.0260658i
\(151\) −5.45111e9 + 9.44160e9i −0.853274 + 1.47791i 0.0249632 + 0.999688i \(0.492053\pi\)
−0.878237 + 0.478225i \(0.841280\pi\)
\(152\) 9.62033e8 3.59036e9i 0.146182 0.545559i
\(153\) −5.39200e9 + 5.39200e9i −0.795497 + 0.795497i
\(154\) −2.51343e9 2.72795e9i −0.360101 0.390835i
\(155\) −1.65759e9 1.08270e10i −0.230667 1.50666i
\(156\) −1.17426e9 2.03387e9i −0.158746 0.274956i
\(157\) −8.07380e8 + 2.16337e8i −0.106055 + 0.0284172i −0.311456 0.950261i \(-0.600817\pi\)
0.205401 + 0.978678i \(0.434150\pi\)
\(158\) 9.32766e8 2.49934e8i 0.119074 0.0319057i
\(159\) 1.79711e9 + 3.11268e9i 0.222991 + 0.386231i
\(160\) −3.77036e9 + 5.13352e9i −0.454823 + 0.619264i
\(161\) 9.50735e9 + 2.96917e9i 1.11518 + 0.348272i
\(162\) −9.06079e8 + 9.06079e8i −0.103359 + 0.103359i
\(163\) 8.17087e8 3.04941e9i 0.0906617 0.338354i −0.905664 0.423996i \(-0.860627\pi\)
0.996326 + 0.0856413i \(0.0272939\pi\)
\(164\) −1.80334e9 + 3.12348e9i −0.194662 + 0.337164i
\(165\) 2.95320e9 + 6.72621e9i 0.310181 + 0.706469i
\(166\) 3.52406e9 2.03462e9i 0.360211 0.207968i
\(167\) 1.08077e10 + 1.08077e10i 1.07525 + 1.07525i 0.996928 + 0.0783248i \(0.0249571\pi\)
0.0783248 + 0.996928i \(0.475043\pi\)
\(168\) 2.00014e9 + 1.26657e9i 0.193717 + 0.122670i
\(169\) 3.29199e9i 0.310433i
\(170\) −2.66023e9 3.32001e9i −0.244286 0.304873i
\(171\) −8.21270e9 4.74160e9i −0.734520 0.424075i
\(172\) −1.71015e9 6.38236e9i −0.148989 0.556036i
\(173\) 2.85723e8 + 7.65592e7i 0.0242514 + 0.00649815i 0.270924 0.962601i \(-0.412671\pi\)
−0.246673 + 0.969099i \(0.579337\pi\)
\(174\) 1.24144e9 0.102673
\(175\) 1.19880e10 + 3.19764e9i 0.966218 + 0.257726i
\(176\) −1.79084e10 −1.40686
\(177\) −3.56530e9 9.55319e8i −0.273034 0.0731592i
\(178\) 4.10697e8 + 1.53274e9i 0.0306642 + 0.114440i
\(179\) −4.63733e9 2.67737e9i −0.337621 0.194926i 0.321598 0.946876i \(-0.395780\pi\)
−0.659220 + 0.751950i \(0.729113\pi\)
\(180\) 6.67854e9 + 8.33491e9i 0.474193 + 0.591799i
\(181\) 2.38648e10i 1.65274i −0.563128 0.826370i \(-0.690402\pi\)
0.563128 0.826370i \(-0.309598\pi\)
\(182\) 1.63732e9 + 3.12442e9i 0.110614 + 0.211080i
\(183\) −1.16890e9 1.16890e9i −0.0770459 0.0770459i
\(184\) −8.65725e9 + 4.99827e9i −0.556801 + 0.321469i
\(185\) 9.47240e8 + 2.15744e9i 0.0594549 + 0.135415i
\(186\) 1.48746e9 2.57635e9i 0.0911248 0.157833i
\(187\) 1.09105e10 4.07187e10i 0.652467 2.43504i
\(188\) 2.35972e9 2.35972e9i 0.137769 0.137769i
\(189\) 9.81719e9 9.04519e9i 0.559640 0.515631i
\(190\) 3.13190e9 4.26424e9i 0.174348 0.237383i
\(191\) −1.39276e10 2.41233e10i −0.757227 1.31156i −0.944259 0.329202i \(-0.893220\pi\)
0.187032 0.982354i \(-0.440113\pi\)
\(192\) 4.08630e9 1.09492e9i 0.217008 0.0581470i
\(193\) −1.37773e10 + 3.69162e9i −0.714755 + 0.191518i −0.597830 0.801623i \(-0.703970\pi\)
−0.116925 + 0.993141i \(0.537304\pi\)
\(194\) 1.10864e9 + 1.92022e9i 0.0561931 + 0.0973293i
\(195\) −1.05719e9 6.90530e9i −0.0523595 0.342001i
\(196\) 1.55898e10 + 1.07898e10i 0.754550 + 0.522230i
\(197\) −2.40693e10 + 2.40693e10i −1.13858 + 1.13858i −0.149878 + 0.988704i \(0.547888\pi\)
−0.988704 + 0.149878i \(0.952112\pi\)
\(198\) 2.45829e9 9.17446e9i 0.113668 0.424216i
\(199\) 4.43889e9 7.68839e9i 0.200649 0.347533i −0.748089 0.663598i \(-0.769028\pi\)
0.948738 + 0.316065i \(0.102362\pi\)
\(200\) −1.05129e10 + 6.67388e9i −0.464609 + 0.294947i
\(201\) 2.28745e9 1.32066e9i 0.0988485 0.0570702i
\(202\) 4.36873e9 + 4.36873e9i 0.184618 + 0.184618i
\(203\) 2.07589e10 + 8.49624e8i 0.857969 + 0.0351152i
\(204\) 1.28748e10i 0.520481i
\(205\) −8.37216e9 + 6.70839e9i −0.331089 + 0.265293i
\(206\) −9.45579e9 5.45930e9i −0.365843 0.211220i
\(207\) 6.60096e9 + 2.46351e10i 0.249885 + 0.932584i
\(208\) 1.64500e10 + 4.40777e9i 0.609370 + 0.163280i
\(209\) 5.24252e10 1.90056
\(210\) 1.99784e9 + 2.71372e9i 0.0708884 + 0.0962893i
\(211\) 2.30423e10 0.800302 0.400151 0.916449i \(-0.368958\pi\)
0.400151 + 0.916449i \(0.368958\pi\)
\(212\) −2.79046e10 7.47701e9i −0.948777 0.254224i
\(213\) −4.20654e9 1.56990e10i −0.140029 0.522594i
\(214\) 4.22120e9 + 2.43711e9i 0.137586 + 0.0794353i
\(215\) 2.15530e9 1.95358e10i 0.0687915 0.623531i
\(216\) 1.33976e10i 0.418778i
\(217\) 2.66359e10 4.20628e10i 0.815452 1.28774i
\(218\) 8.20398e8 + 8.20398e8i 0.0246020 + 0.0246020i
\(219\) −9.79265e9 + 5.65379e9i −0.287675 + 0.166089i
\(220\) −5.50126e10 2.14438e10i −1.58329 0.617163i
\(221\) −2.00440e10 + 3.47172e10i −0.565222 + 0.978993i
\(222\) −1.65633e8 + 6.18153e8i −0.00457678 + 0.0170808i
\(223\) −3.11011e10 + 3.11011e10i −0.842179 + 0.842179i −0.989142 0.146963i \(-0.953050\pi\)
0.146963 + 0.989142i \(0.453050\pi\)
\(224\) −2.82481e10 + 6.34334e9i −0.749674 + 0.168346i
\(225\) 9.50496e9 + 3.03146e10i 0.247246 + 0.788551i
\(226\) 2.77552e9 + 4.80733e9i 0.0707711 + 0.122579i
\(227\) 2.56966e10 6.88539e9i 0.642332 0.172112i 0.0770725 0.997025i \(-0.475443\pi\)
0.565259 + 0.824913i \(0.308776\pi\)
\(228\) −1.54659e10 + 4.14407e9i −0.379025 + 0.101559i
\(229\) −3.09771e10 5.36539e10i −0.744356 1.28926i −0.950495 0.310740i \(-0.899423\pi\)
0.206139 0.978523i \(-0.433910\pi\)
\(230\) −1.40652e10 + 2.15335e9i −0.331414 + 0.0507387i
\(231\) −9.95387e9 + 3.18725e10i −0.230005 + 0.736483i
\(232\) −1.47446e10 + 1.47446e10i −0.334147 + 0.334147i
\(233\) 6.68212e9 2.49380e10i 0.148529 0.554319i −0.851044 0.525095i \(-0.824030\pi\)
0.999573 0.0292240i \(-0.00930361\pi\)
\(234\) −4.51618e9 + 7.82225e9i −0.0984691 + 0.170553i
\(235\) 9.08904e9 3.99062e9i 0.194407 0.0853561i
\(236\) 2.56928e10 1.48337e10i 0.539147 0.311277i
\(237\) −6.14674e9 6.14674e9i −0.126554 0.126554i
\(238\) 7.90799e8 1.93216e10i 0.0159761 0.390344i
\(239\) 1.20764e10i 0.239412i −0.992809 0.119706i \(-0.961805\pi\)
0.992809 0.119706i \(-0.0381952\pi\)
\(240\) 1.61712e10 + 1.78410e9i 0.314624 + 0.0347111i
\(241\) 5.71490e10 + 3.29950e10i 1.09127 + 0.630044i 0.933914 0.357498i \(-0.116370\pi\)
0.157355 + 0.987542i \(0.449703\pi\)
\(242\) 9.62704e9 + 3.59286e10i 0.180436 + 0.673397i
\(243\) 5.10938e10 + 1.36906e10i 0.940027 + 0.251879i
\(244\) 1.32869e10 0.239976
\(245\) 3.15499e10 + 4.67450e10i 0.559437 + 0.828873i
\(246\) −2.91383e9 −0.0507290
\(247\) −4.81558e10 1.29033e10i −0.823213 0.220579i
\(248\) 1.29328e10 + 4.82660e10i 0.217101 + 0.810230i
\(249\) −3.17230e10 1.83153e10i −0.522971 0.301937i
\(250\) −1.73924e10 + 3.41628e9i −0.281598 + 0.0553126i
\(251\) 7.86729e10i 1.25110i 0.780183 + 0.625552i \(0.215126\pi\)
−0.780183 + 0.625552i \(0.784874\pi\)
\(252\) −1.98531e9 + 4.85071e10i −0.0310117 + 0.757710i
\(253\) −9.96967e10 9.96967e10i −1.52981 1.52981i
\(254\) 1.33513e10 7.70840e9i 0.201267 0.116202i
\(255\) −1.39087e10 + 3.56818e10i −0.205994 + 0.528464i
\(256\) −9.42516e9 + 1.63249e10i −0.137154 + 0.237558i
\(257\) −1.23835e10 + 4.62160e10i −0.177070 + 0.660835i 0.819119 + 0.573623i \(0.194463\pi\)
−0.996190 + 0.0872124i \(0.972204\pi\)
\(258\) 3.77467e9 3.77467e9i 0.0530383 0.0530383i
\(259\) −3.19271e9 + 1.02231e10i −0.0440870 + 0.141168i
\(260\) 4.52546e10 + 3.32376e10i 0.614161 + 0.451076i
\(261\) 2.65999e10 + 4.60723e10i 0.354811 + 0.614551i
\(262\) −7.81783e9 + 2.09478e9i −0.102502 + 0.0274652i
\(263\) 1.14245e11 3.06118e10i 1.47243 0.394538i 0.568670 0.822566i \(-0.307458\pi\)
0.903765 + 0.428028i \(0.140792\pi\)
\(264\) −1.67562e10 2.90227e10i −0.212304 0.367722i
\(265\) −6.92585e10 5.08675e10i −0.862714 0.633627i
\(266\) 2.34647e10 5.26919e9i 0.287374 0.0645321i
\(267\) 1.01005e10 1.01005e10i 0.121630 0.121630i
\(268\) −5.49473e9 + 2.05066e10i −0.0650638 + 0.242821i
\(269\) 6.61492e9 1.14574e10i 0.0770263 0.133414i −0.824939 0.565221i \(-0.808791\pi\)
0.901966 + 0.431808i \(0.142124\pi\)
\(270\) −6.92592e9 + 1.77680e10i −0.0793123 + 0.203470i
\(271\) 3.16240e10 1.82581e10i 0.356168 0.205634i −0.311230 0.950335i \(-0.600741\pi\)
0.667399 + 0.744701i \(0.267408\pi\)
\(272\) −6.60169e10 6.60169e10i −0.731299 0.731299i
\(273\) 1.69880e10 2.68270e10i 0.185101 0.292307i
\(274\) 3.89074e10i 0.417018i
\(275\) −1.29298e11 1.18860e11i −1.36332 1.25326i
\(276\) 3.72921e10 + 2.15306e10i 0.386835 + 0.223340i
\(277\) −3.00342e9 1.12089e10i −0.0306519 0.114394i 0.948905 0.315562i \(-0.102193\pi\)
−0.979557 + 0.201168i \(0.935526\pi\)
\(278\) 3.21900e10 + 8.62527e9i 0.323235 + 0.0866106i
\(279\) 1.27485e11 1.25962
\(280\) −5.59593e10 8.50246e9i −0.544078 0.0826672i
\(281\) −6.83073e9 −0.0653565 −0.0326782 0.999466i \(-0.510404\pi\)
−0.0326782 + 0.999466i \(0.510404\pi\)
\(282\) 2.60421e9 + 6.97795e8i 0.0245219 + 0.00657063i
\(283\) −3.08835e10 1.15259e11i −0.286212 1.06816i −0.947949 0.318421i \(-0.896847\pi\)
0.661738 0.749735i \(-0.269819\pi\)
\(284\) 1.13133e11 + 6.53172e10i 1.03194 + 0.595792i
\(285\) −4.73397e10 5.22278e9i −0.425034 0.0468921i
\(286\) 4.99329e10i 0.441305i
\(287\) −4.87239e10 1.99418e9i −0.423910 0.0173499i
\(288\) −5.24203e10 5.24203e10i −0.448986 0.448986i
\(289\) 8.76236e10 5.05895e10i 0.738891 0.426599i
\(290\) −2.71767e10 + 1.19321e10i −0.225635 + 0.0990667i
\(291\) 9.97980e9 1.72855e10i 0.0815837 0.141307i
\(292\) 2.35231e10 8.77893e10i 0.189353 0.706674i
\(293\) −1.00166e11 + 1.00166e11i −0.793991 + 0.793991i −0.982140 0.188149i \(-0.939751\pi\)
0.188149 + 0.982140i \(0.439751\pi\)
\(294\) −1.25172e9 + 1.52661e10i −0.00977115 + 0.119169i
\(295\) 8.72310e10 1.33549e10i 0.670613 0.102669i
\(296\) −5.37457e9 9.30904e9i −0.0406941 0.0704842i
\(297\) −1.82522e11 + 4.89067e10i −1.36117 + 0.364724i
\(298\) 4.25747e10 1.14079e10i 0.312736 0.0837974i
\(299\) 6.70394e10 + 1.16116e11i 0.485076 + 0.840177i
\(300\) 4.75397e10 + 2.48442e10i 0.338853 + 0.177084i
\(301\) 6.57018e10 6.05351e10i 0.461347 0.425068i
\(302\) 5.00592e10 5.00592e10i 0.346300 0.346300i
\(303\) 1.43945e10 5.37211e10i 0.0981083 0.366145i
\(304\) 5.80538e10 1.00552e11i 0.389852 0.675243i
\(305\) 3.68238e10 + 1.43538e10i 0.243657 + 0.0949770i
\(306\) 4.28825e10 2.47582e10i 0.279598 0.161426i
\(307\) −8.10579e9 8.10579e9i −0.0520802 0.0520802i 0.680587 0.732667i \(-0.261725\pi\)
−0.732667 + 0.680587i \(0.761725\pi\)
\(308\) −1.24574e11 2.37719e11i −0.788768 1.50517i
\(309\) 9.82875e10i 0.613317i
\(310\) −7.79963e9 + 7.06964e10i −0.0479674 + 0.434780i
\(311\) −5.74237e9 3.31536e9i −0.0348073 0.0200960i 0.482495 0.875899i \(-0.339731\pi\)
−0.517303 + 0.855803i \(0.673064\pi\)
\(312\) 8.24835e9 + 3.07833e10i 0.0492801 + 0.183916i
\(313\) −4.91256e10 1.31632e10i −0.289307 0.0775195i 0.111247 0.993793i \(-0.464516\pi\)
−0.400554 + 0.916273i \(0.631182\pi\)
\(314\) 5.42773e9 0.0315090
\(315\) −5.79045e10 + 1.32290e11i −0.331371 + 0.757058i
\(316\) 6.98696e10 0.394182
\(317\) 1.50628e11 + 4.03608e10i 0.837800 + 0.224488i 0.652114 0.758121i \(-0.273883\pi\)
0.185686 + 0.982609i \(0.440549\pi\)
\(318\) −6.04066e9 2.25440e10i −0.0331255 0.123626i
\(319\) −2.54698e11 1.47050e11i −1.37711 0.795072i
\(320\) −7.89305e10 + 6.32449e10i −0.420794 + 0.337171i
\(321\) 4.38769e10i 0.230655i
\(322\) −5.46430e10 3.46022e10i −0.283258 0.179371i
\(323\) 1.93258e11 + 1.93258e11i 0.987930 + 0.987930i
\(324\) −8.02918e10 + 4.63565e10i −0.404780 + 0.233700i
\(325\) 8.95137e10 + 1.41005e11i 0.445056 + 0.701065i
\(326\) −1.02501e10 + 1.77536e10i −0.0502629 + 0.0870578i
\(327\) 2.70313e9 1.00882e10i 0.0130738 0.0487921i
\(328\) 3.46076e10 3.46076e10i 0.165097 0.165097i
\(329\) 4.30689e10 + 1.34505e10i 0.202667 + 0.0632933i
\(330\) −7.21891e9 4.71523e10i −0.0335088 0.218872i
\(331\) 8.82408e10 + 1.52838e11i 0.404058 + 0.699848i 0.994211 0.107443i \(-0.0342662\pi\)
−0.590154 + 0.807291i \(0.700933\pi\)
\(332\) 2.84391e11 7.62024e10i 1.28468 0.344229i
\(333\) −2.64898e10 + 7.09793e9i −0.118054 + 0.0316324i
\(334\) −4.96254e10 8.59537e10i −0.218195 0.377925i
\(335\) −3.73816e10 + 5.08969e10i −0.162165 + 0.220795i
\(336\) 5.01093e10 + 5.43862e10i 0.214483 + 0.232789i
\(337\) −2.86251e11 + 2.86251e11i −1.20896 + 1.20896i −0.237595 + 0.971364i \(0.576359\pi\)
−0.971364 + 0.237595i \(0.923641\pi\)
\(338\) 5.53273e9 2.06484e10i 0.0230576 0.0860521i
\(339\) 2.49847e10 4.32748e10i 0.102749 0.177966i
\(340\) −1.23747e11 2.81846e11i −0.502202 1.14382i
\(341\) −6.10343e11 + 3.52382e11i −2.44444 + 1.41130i
\(342\) 4.35436e10 + 4.35436e10i 0.172110 + 0.172110i
\(343\) −3.13787e10 + 2.54416e11i −0.122408 + 0.992480i
\(344\) 8.96635e10i 0.345225i
\(345\) 8.00934e10 + 9.99576e10i 0.304376 + 0.379866i
\(346\) −1.66347e9 9.60407e8i −0.00623984 0.00360257i
\(347\) −1.17798e11 4.39629e11i −0.436170 1.62781i −0.738251 0.674527i \(-0.764348\pi\)
0.302080 0.953282i \(-0.402319\pi\)
\(348\) 8.67619e10 + 2.32478e10i 0.317119 + 0.0849718i
\(349\) −8.78400e10 −0.316941 −0.158470 0.987364i \(-0.550656\pi\)
−0.158470 + 0.987364i \(0.550656\pi\)
\(350\) −6.98184e10 4.02044e10i −0.248693 0.143208i
\(351\) 1.79695e11 0.631910
\(352\) 3.95861e11 + 1.06071e11i 1.37436 + 0.368259i
\(353\) −1.49320e10 5.57270e10i −0.0511838 0.191020i 0.935600 0.353061i \(-0.114859\pi\)
−0.986784 + 0.162040i \(0.948192\pi\)
\(354\) 2.07571e10 + 1.19841e10i 0.0702510 + 0.0405594i
\(355\) 2.42978e11 + 3.03240e11i 0.811970 + 1.01335i
\(356\) 1.14811e11i 0.378843i
\(357\) −1.54187e11 + 8.08001e10i −0.502390 + 0.263272i
\(358\) 2.45871e10 + 2.45871e10i 0.0791104 + 0.0791104i
\(359\) −1.66527e11 + 9.61446e10i −0.529128 + 0.305492i −0.740661 0.671879i \(-0.765488\pi\)
0.211534 + 0.977371i \(0.432154\pi\)
\(360\) −5.82659e10 1.32706e11i −0.182832 0.416419i
\(361\) −8.60305e9 + 1.49009e10i −0.0266606 + 0.0461775i
\(362\) −4.01087e10 + 1.49688e11i −0.122758 + 0.458139i
\(363\) 2.36762e11 2.36762e11i 0.715703 0.715703i
\(364\) 5.59197e10 + 2.49021e11i 0.166958 + 0.743497i
\(365\) 1.60032e11 2.17891e11i 0.471942 0.642571i
\(366\) 5.36721e9 + 9.29628e9i 0.0156345 + 0.0270797i
\(367\) 3.14651e9 8.43105e8i 0.00905382 0.00242596i −0.254289 0.967128i \(-0.581842\pi\)
0.263343 + 0.964702i \(0.415175\pi\)
\(368\) −3.01620e11 + 8.08188e10i −0.857324 + 0.229719i
\(369\) −6.24336e10 1.08138e11i −0.175307 0.303641i
\(370\) −2.31547e9 1.51241e10i −0.00642290 0.0419530i
\(371\) −8.55806e10 3.81106e11i −0.234527 1.04439i
\(372\) 1.52202e11 1.52202e11i 0.412075 0.412075i
\(373\) −1.65534e11 + 6.17782e11i −0.442790 + 1.65251i 0.278916 + 0.960315i \(0.410025\pi\)
−0.721706 + 0.692200i \(0.756642\pi\)
\(374\) −1.36869e11 + 2.37064e11i −0.361728 + 0.626531i
\(375\) 1.04914e11 + 1.20211e11i 0.273965 + 0.313910i
\(376\) −3.92179e10 + 2.26425e10i −0.101190 + 0.0584223i
\(377\) 1.97763e11 + 1.97763e11i 0.504206 + 0.504206i
\(378\) −7.67785e10 + 4.02349e10i −0.193431 + 0.101365i
\(379\) 6.26332e11i 1.55929i −0.626219 0.779647i \(-0.715399\pi\)
0.626219 0.779647i \(-0.284601\pi\)
\(380\) 2.98737e11 2.39370e11i 0.734958 0.588902i
\(381\) −1.20187e11 6.93897e10i −0.292209 0.168707i
\(382\) 4.68152e10 + 1.74717e11i 0.112487 + 0.419807i
\(383\) −6.64395e10 1.78024e10i −0.157773 0.0422751i 0.179068 0.983837i \(-0.442692\pi\)
−0.336841 + 0.941562i \(0.609358\pi\)
\(384\) −1.63871e11 −0.384603
\(385\) −8.84413e10 7.93402e11i −0.205155 1.84043i
\(386\) 9.26202e10 0.212355
\(387\) 2.20964e11 + 5.92071e10i 0.500751 + 0.134176i
\(388\) 4.15218e10 + 1.54962e11i 0.0930109 + 0.347121i
\(389\) 1.56904e10 + 9.05888e9i 0.0347426 + 0.0200586i 0.517271 0.855822i \(-0.326948\pi\)
−0.482528 + 0.875880i \(0.660281\pi\)
\(390\) −4.97448e9 + 4.50891e10i −0.0108882 + 0.0986916i
\(391\) 7.35035e11i 1.59042i
\(392\) −1.66449e11 1.96182e11i −0.356035 0.419635i
\(393\) 5.15180e10 + 5.15180e10i 0.108941 + 0.108941i
\(394\) 1.91422e11 1.10518e11i 0.400184 0.231046i
\(395\) 1.93640e11 + 7.54803e10i 0.400228 + 0.156008i
\(396\) 3.43610e11 5.95151e11i 0.702163 1.21618i
\(397\) −6.92405e10 + 2.58409e11i −0.139895 + 0.522096i 0.860034 + 0.510236i \(0.170442\pi\)
−0.999930 + 0.0118601i \(0.996225\pi\)
\(398\) −4.07638e10 + 4.07638e10i −0.0814330 + 0.0814330i
\(399\) −1.46690e11 1.59210e11i −0.289750 0.314480i
\(400\) −3.71156e11 + 1.16374e11i −0.724915 + 0.227293i
\(401\) −9.05200e10 1.56785e11i −0.174821 0.302800i 0.765278 0.643700i \(-0.222602\pi\)
−0.940099 + 0.340900i \(0.889268\pi\)
\(402\) −1.65672e10 + 4.43917e9i −0.0316397 + 0.00847784i
\(403\) 6.47369e11 1.73462e11i 1.22259 0.327591i
\(404\) 2.23511e11 + 3.87133e11i 0.417430 + 0.723010i
\(405\) −2.72603e11 + 4.17349e10i −0.503481 + 0.0770818i
\(406\) −1.28778e11 4.02178e10i −0.235221 0.0734600i
\(407\) 1.07203e11 1.07203e11i 0.193656 0.193656i
\(408\) 4.52184e10 1.68757e11i 0.0807875 0.301503i
\(409\) −1.96145e11 + 3.39733e11i −0.346595 + 0.600320i −0.985642 0.168847i \(-0.945996\pi\)
0.639047 + 0.769168i \(0.279329\pi\)
\(410\) 6.37874e10 2.80064e10i 0.111483 0.0489474i
\(411\) −3.03315e11 + 1.75119e11i −0.524331 + 0.302723i
\(412\) −5.58614e11 5.58614e11i −0.955156 0.955156i
\(413\) 3.38891e11 + 2.14600e11i 0.573171 + 0.362956i
\(414\) 1.65613e11i 0.277073i
\(415\) 8.70495e11 + 9.60379e10i 1.44062 + 0.158937i
\(416\) −3.37516e11 1.94865e11i −0.552553 0.319017i
\(417\) −7.76433e10 2.89769e11i −0.125745 0.469288i
\(418\) −3.28828e11 8.81092e10i −0.526836 0.141165i
\(419\) 1.16519e11 0.184687 0.0923433 0.995727i \(-0.470564\pi\)
0.0923433 + 0.995727i \(0.470564\pi\)
\(420\) 8.88072e10 + 2.27069e11i 0.139260 + 0.356071i
\(421\) −9.23539e11 −1.43280 −0.716401 0.697689i \(-0.754212\pi\)
−0.716401 + 0.697689i \(0.754212\pi\)
\(422\) −1.44528e11 3.87263e10i −0.221844 0.0594428i
\(423\) 2.99028e10 + 1.11599e11i 0.0454130 + 0.169484i
\(424\) 3.39501e11 + 1.96011e11i 0.510146 + 0.294533i
\(425\) −3.84781e10 9.14802e11i −0.0572088 1.36012i
\(426\) 1.05539e11i 0.155264i
\(427\) 8.33861e10 + 1.59122e11i 0.121386 + 0.231635i
\(428\) 2.49373e11 + 2.49373e11i 0.359214 + 0.359214i
\(429\) −3.89268e11 + 2.24744e11i −0.554869 + 0.320354i
\(430\) −4.63519e10 + 1.18913e11i −0.0653821 + 0.167733i
\(431\) 3.05580e11 5.29280e11i 0.426557 0.738819i −0.570007 0.821640i \(-0.693060\pi\)
0.996564 + 0.0828210i \(0.0263930\pi\)
\(432\) −1.08315e11 + 4.04238e11i −0.149628 + 0.558419i
\(433\) −3.66141e9 + 3.66141e9i −0.00500556 + 0.00500556i −0.709605 0.704600i \(-0.751127\pi\)
0.704600 + 0.709605i \(0.251127\pi\)
\(434\) −2.37762e11 + 2.19065e11i −0.321691 + 0.296394i
\(435\) 2.15341e11 + 1.58159e11i 0.288353 + 0.211784i
\(436\) 4.19729e10 + 7.26992e10i 0.0556263 + 0.0963475i
\(437\) 8.82963e11 2.36589e11i 1.15818 0.310333i
\(438\) 7.09248e10 1.90042e10i 0.0920798 0.0246727i
\(439\) 5.74101e11 + 9.94372e11i 0.737731 + 1.27779i 0.953515 + 0.301346i \(0.0974360\pi\)
−0.215784 + 0.976441i \(0.569231\pi\)
\(440\) 6.45767e11 + 4.74289e11i 0.821370 + 0.603262i
\(441\) −5.93375e11 + 2.80646e11i −0.747060 + 0.353334i
\(442\) 1.84070e11 1.84070e11i 0.229395 0.229395i
\(443\) −1.26836e11 + 4.73357e11i −0.156468 + 0.583945i 0.842508 + 0.538684i \(0.181078\pi\)
−0.998975 + 0.0452605i \(0.985588\pi\)
\(444\) −2.31516e10 + 4.00998e10i −0.0282721 + 0.0489687i
\(445\) −1.24031e11 + 3.18193e11i −0.149937 + 0.384654i
\(446\) 2.47347e11 1.42806e11i 0.296005 0.170899i
\(447\) −2.80559e11 2.80559e11i −0.332384 0.332384i
\(448\) −4.59356e11 1.88006e10i −0.538763 0.0220506i
\(449\) 1.17618e12i 1.36573i −0.730545 0.682865i \(-0.760734\pi\)
0.730545 0.682865i \(-0.239266\pi\)
\(450\) −8.66962e9 2.06117e11i −0.00996653 0.236951i
\(451\) 5.97811e11 + 3.45146e11i 0.680408 + 0.392834i
\(452\) 1.03951e11 + 3.87951e11i 0.117140 + 0.437174i
\(453\) −6.15565e11 1.64940e11i −0.686803 0.184028i
\(454\) −1.72749e11 −0.190838
\(455\) −1.14040e11 + 7.50557e11i −0.124740 + 0.820979i
\(456\) 2.17275e11 0.235325
\(457\) 6.07755e11 + 1.62847e11i 0.651787 + 0.174646i 0.569537 0.821966i \(-0.307123\pi\)
0.0822503 + 0.996612i \(0.473789\pi\)
\(458\) 1.04124e11 + 3.88596e11i 0.110575 + 0.412671i
\(459\) −8.53130e11 4.92555e11i −0.897136 0.517962i
\(460\) −1.02331e12 1.12898e11i −1.06561 0.117564i
\(461\) 6.73735e10i 0.0694761i 0.999396 + 0.0347380i \(0.0110597\pi\)
−0.999396 + 0.0347380i \(0.988940\pi\)
\(462\) 1.16001e11 1.83186e11i 0.118460 0.187069i
\(463\) 2.82268e11 + 2.82268e11i 0.285461 + 0.285461i 0.835282 0.549821i \(-0.185304\pi\)
−0.549821 + 0.835282i \(0.685304\pi\)
\(464\) −5.64087e11 + 3.25676e11i −0.564956 + 0.326178i
\(465\) 5.86242e11 2.57394e11i 0.581485 0.255306i
\(466\) −8.38247e10 + 1.45189e11i −0.0823447 + 0.142625i
\(467\) −5.28219e10 + 1.97134e11i −0.0513911 + 0.191794i −0.986849 0.161643i \(-0.948321\pi\)
0.935458 + 0.353438i \(0.114987\pi\)
\(468\) −4.62110e11 + 4.62110e11i −0.445286 + 0.445286i
\(469\) −2.80069e11 + 6.28917e10i −0.267292 + 0.0600227i
\(470\) −6.37163e10 + 9.75481e9i −0.0602296 + 0.00922101i
\(471\) −2.44298e10 4.23136e10i −0.0228731 0.0396174i
\(472\) −3.88868e11 + 1.04197e11i −0.360632 + 0.0966309i
\(473\) −1.22154e12 + 3.27309e11i −1.12210 + 0.300665i
\(474\) 2.82237e10 + 4.88849e10i 0.0256810 + 0.0444808i
\(475\) 1.08652e12 3.40674e11i 0.979305 0.307056i
\(476\) 4.17093e11 1.33554e12i 0.372393 1.19241i
\(477\) 7.07223e11 7.07223e11i 0.625495 0.625495i
\(478\) −2.02963e10 + 7.57468e10i −0.0177824 + 0.0663649i
\(479\) 2.79003e11 4.83248e11i 0.242159 0.419431i −0.719170 0.694834i \(-0.755478\pi\)
0.961329 + 0.275403i \(0.0888113\pi\)
\(480\) −3.46893e11 1.35218e11i −0.298270 0.116265i
\(481\) −1.24858e11 + 7.20867e10i −0.106356 + 0.0614048i
\(482\) −3.03003e11 3.03003e11i −0.255703 0.255703i
\(483\) −2.38091e10 + 5.81729e11i −0.0199059 + 0.486360i
\(484\) 2.69126e12i 2.22922i
\(485\) −5.23300e10 + 4.74323e11i −0.0429450 + 0.389257i
\(486\) −2.97468e11 1.71743e11i −0.241867 0.139642i
\(487\) 5.20830e11 + 1.94376e12i 0.419581 + 1.56590i 0.775479 + 0.631373i \(0.217508\pi\)
−0.355898 + 0.934525i \(0.615825\pi\)
\(488\) −1.74158e11 4.66656e10i −0.139013 0.0372484i
\(489\) 1.84539e11 0.145948
\(490\) −1.19329e11 3.46225e11i −0.0935109 0.271316i
\(491\) −8.65785e11 −0.672269 −0.336135 0.941814i \(-0.609120\pi\)
−0.336135 + 0.941814i \(0.609120\pi\)
\(492\) −2.03642e11 5.45657e10i −0.156684 0.0419834i
\(493\) −3.96829e11 1.48099e12i −0.302546 1.12912i
\(494\) 2.80362e11 + 1.61867e11i 0.211811 + 0.122289i
\(495\) 1.59524e12 1.27822e12i 1.19427 0.956936i
\(496\) 1.56086e12i 1.15797i
\(497\) −7.22294e10 + 1.76478e12i −0.0531019 + 1.29744i
\(498\) 1.68195e11 + 1.68195e11i 0.122541 + 0.122541i
\(499\) 5.39904e11 3.11714e11i 0.389820 0.225063i −0.292262 0.956338i \(-0.594408\pi\)
0.682082 + 0.731276i \(0.261075\pi\)
\(500\) −1.27950e12 8.69401e10i −0.915532 0.0622093i
\(501\) −4.46720e11 + 7.73741e11i −0.316786 + 0.548689i
\(502\) 1.32223e11 4.93461e11i 0.0929264 0.346806i
\(503\) 4.23651e11 4.23651e11i 0.295088 0.295088i −0.543998 0.839086i \(-0.683090\pi\)
0.839086 + 0.543998i \(0.183090\pi\)
\(504\) 1.96387e11 6.28837e11i 0.135574 0.434111i
\(505\) 2.01228e11 + 1.31438e12i 0.137682 + 0.899308i
\(506\) 4.57773e11 + 7.92886e11i 0.310437 + 0.537692i
\(507\) −1.85874e11 + 4.98047e10i −0.124934 + 0.0334761i
\(508\) 1.07745e12 2.88702e11i 0.717812 0.192337i
\(509\) −7.92976e11 1.37347e12i −0.523636 0.906965i −0.999621 0.0275114i \(-0.991242\pi\)
0.475985 0.879453i \(-0.342092\pi\)
\(510\) 1.47209e11 2.00432e11i 0.0963535 0.131190i
\(511\) 1.19898e12 2.69241e11i 0.777890 0.174682i
\(512\) 1.10150e12 1.10150e12i 0.708385 0.708385i
\(513\) 3.17082e11 1.18337e12i 0.202136 0.754381i
\(514\) 1.55347e11 2.69069e11i 0.0981678 0.170032i
\(515\) −9.44694e11 2.15164e12i −0.591778 1.34783i
\(516\) 3.34490e11 1.93118e11i 0.207711 0.119922i
\(517\) −4.51633e11 4.51633e11i −0.278021 0.278021i
\(518\) 3.72074e10 5.87569e10i 0.0227062 0.0358571i
\(519\) 1.72909e10i 0.0104608i
\(520\) −4.76441e11 5.94605e11i −0.285755 0.356627i
\(521\) −1.47798e11 8.53312e10i −0.0878817 0.0507385i 0.455415 0.890279i \(-0.349491\pi\)
−0.543297 + 0.839541i \(0.682824\pi\)
\(522\) −8.94109e10 3.33686e11i −0.0527076 0.196707i
\(523\) 1.46303e12 + 3.92018e11i 0.855058 + 0.229112i 0.659616 0.751603i \(-0.270719\pi\)
0.195442 + 0.980715i \(0.437386\pi\)
\(524\) −5.85601e11 −0.339321
\(525\) 8.20554e8 + 7.25248e11i 0.000471401 + 0.416648i
\(526\) −7.68029e11 −0.437463
\(527\) −3.54895e12 9.50938e11i −2.00425 0.537037i
\(528\) −2.70938e11 1.01115e12i −0.151711 0.566193i
\(529\) −5.69201e11 3.28628e11i −0.316020 0.182454i
\(530\) 3.48920e11 + 4.35457e11i 0.192081 + 0.239720i
\(531\) 1.02712e12i 0.560654i
\(532\) 1.73857e12 + 7.11568e10i 0.941003 + 0.0385136i
\(533\) −4.64176e11 4.64176e11i −0.249121 0.249121i
\(534\) −8.03288e10 + 4.63779e10i −0.0427500 + 0.0246817i
\(535\) 4.21725e11 + 9.60522e11i 0.222555 + 0.506892i
\(536\) 1.44045e11 2.49493e11i 0.0753801 0.130562i
\(537\) 8.10120e10 3.02341e11i 0.0420402 0.156896i
\(538\) −6.07469e10 + 6.07469e10i −0.0312611 + 0.0312611i
\(539\) 2.06509e12 2.98377e12i 1.05388 1.52270i
\(540\) −8.16770e11 + 1.11207e12i −0.413360 + 0.562809i
\(541\) −1.46186e12 2.53201e12i −0.733697 1.27080i −0.955293 0.295662i \(-0.904460\pi\)
0.221596 0.975139i \(-0.428873\pi\)
\(542\) −2.29042e11 + 6.13716e10i −0.114003 + 0.0305471i
\(543\) 1.34746e12 3.61052e11i 0.665148 0.178226i
\(544\) 1.06827e12 + 1.85030e12i 0.522982 + 0.905831i
\(545\) 3.77884e10 + 2.46825e11i 0.0183474 + 0.119841i
\(546\) −1.51641e11 + 1.39716e11i −0.0730214 + 0.0672791i
\(547\) −1.38972e12 + 1.38972e12i −0.663719 + 0.663719i −0.956255 0.292536i \(-0.905501\pi\)
0.292536 + 0.956255i \(0.405501\pi\)
\(548\) 7.28597e11 2.71916e12i 0.345124 1.28802i
\(549\) −2.30002e11 + 3.98376e11i −0.108058 + 0.187162i
\(550\) 6.11237e11 + 9.62838e11i 0.284825 + 0.448664i
\(551\) 1.65131e12 9.53383e11i 0.763213 0.440641i
\(552\) −4.13190e11 4.13190e11i −0.189419 0.189419i
\(553\) 4.38490e11 + 8.36750e11i 0.199387 + 0.380481i
\(554\) 7.53536e10i 0.0339868i
\(555\) −1.07483e11 + 8.61235e10i −0.0480864 + 0.0385304i
\(556\) 2.08817e12 + 1.20561e12i 0.926681 + 0.535019i
\(557\) 4.72757e11 + 1.76435e12i 0.208109 + 0.776672i 0.988480 + 0.151355i \(0.0483636\pi\)
−0.780371 + 0.625317i \(0.784970\pi\)
\(558\) −7.99626e11 2.14259e11i −0.349167 0.0935590i
\(559\) 1.20262e12 0.520923
\(560\) −1.61969e12 7.08954e11i −0.695963 0.304629i
\(561\) 2.46414e12 1.05035
\(562\) 4.28445e10 + 1.14802e10i 0.0181168 + 0.00485439i
\(563\) −3.52630e11 1.31603e12i −0.147921 0.552050i −0.999608 0.0279988i \(-0.991087\pi\)
0.851686 0.524052i \(-0.175580\pi\)
\(564\) 1.68936e11 + 9.75352e10i 0.0703017 + 0.0405887i
\(565\) −1.31010e11 + 1.18748e12i −0.0540861 + 0.490241i
\(566\) 7.74844e11i 0.317351i
\(567\) −1.05906e12 6.70640e11i −0.430324 0.272499i
\(568\) −1.25349e12 1.25349e12i −0.505304 0.505304i
\(569\) −7.70812e11 + 4.45028e11i −0.308278 + 0.177985i −0.646156 0.763205i \(-0.723624\pi\)
0.337877 + 0.941190i \(0.390291\pi\)
\(570\) 2.88152e11 + 1.12321e11i 0.114336 + 0.0445681i
\(571\) −9.51420e11 + 1.64791e12i −0.374550 + 0.648739i −0.990260 0.139234i \(-0.955536\pi\)
0.615710 + 0.787973i \(0.288869\pi\)
\(572\) 9.35066e11 3.48971e12i 0.365225 1.36304i
\(573\) 1.15135e12 1.15135e12i 0.446181 0.446181i
\(574\) 3.02260e11 + 9.43966e10i 0.116219 + 0.0362955i
\(575\) −2.71409e12 1.41838e12i −1.03543 0.541111i
\(576\) −5.88606e11 1.01950e12i −0.222804 0.385909i
\(577\) −3.42904e12 + 9.18808e11i −1.28790 + 0.345091i −0.836862 0.547415i \(-0.815612\pi\)
−0.451036 + 0.892506i \(0.648945\pi\)
\(578\) −6.34627e11 + 1.70048e11i −0.236507 + 0.0633717i
\(579\) −4.16876e11 7.22050e11i −0.154153 0.267002i
\(580\) −2.12277e12 + 3.24992e11i −0.778893 + 0.119247i
\(581\) 2.69738e12 + 2.92760e12i 0.982086 + 1.06591i
\(582\) −9.16477e10 + 9.16477e10i −0.0331107 + 0.0331107i
\(583\) −1.43104e12 + 5.34073e12i −0.513032 + 1.91466i
\(584\) −6.16661e11 + 1.06809e12i −0.219376 + 0.379970i
\(585\) −1.77993e12 + 7.81493e11i −0.628350 + 0.275882i
\(586\) 7.96618e11 4.59928e11i 0.279069 0.161120i
\(587\) 3.16164e11 + 3.16164e11i 0.109911 + 0.109911i 0.759923 0.650013i \(-0.225236\pi\)
−0.650013 + 0.759923i \(0.725236\pi\)
\(588\) −3.73360e11 + 1.04348e12i −0.128804 + 0.359985i
\(589\) 4.56927e12i 1.56433i
\(590\) −5.69586e11 6.28399e10i −0.193520 0.0213502i
\(591\) −1.72315e12 9.94863e11i −0.581005 0.335444i
\(592\) −8.69035e10 3.24328e11i −0.0290797 0.108527i
\(593\) 1.26302e12 + 3.38426e11i 0.419436 + 0.112388i 0.462363 0.886691i \(-0.347002\pi\)
−0.0429271 + 0.999078i \(0.513668\pi\)
\(594\) 1.22703e12 0.404406
\(595\) 2.59874e12 3.25079e12i 0.850033 1.06332i
\(596\) 3.18909e12 1.03528
\(597\) 5.01261e11 + 1.34313e11i 0.161503 + 0.0432745i
\(598\) −2.25341e11 8.40985e11i −0.0720586 0.268926i
\(599\) 2.94190e12 + 1.69851e12i 0.933701 + 0.539072i 0.887980 0.459882i \(-0.152108\pi\)
0.0457205 + 0.998954i \(0.485442\pi\)
\(600\) −5.35874e11 4.92614e11i −0.168804 0.155177i
\(601\) 5.86013e12i 1.83220i 0.400954 + 0.916098i \(0.368679\pi\)
−0.400954 + 0.916098i \(0.631321\pi\)
\(602\) −5.13842e11 + 2.69273e11i −0.159458 + 0.0835620i
\(603\) −5.19726e11 5.19726e11i −0.160084 0.160084i
\(604\) 4.43598e12 2.56111e12i 1.35620 0.783001i
\(605\) −2.90738e12 + 7.45868e12i −0.882271 + 2.26341i
\(606\) −1.80574e11 + 3.12764e11i −0.0543912 + 0.0942084i
\(607\) 9.99843e11 3.73146e12i 0.298939 1.11566i −0.639099 0.769124i \(-0.720693\pi\)
0.938038 0.346532i \(-0.112641\pi\)
\(608\) −1.87883e12 + 1.87883e12i −0.557598 + 0.557598i
\(609\) 2.66090e11 + 1.18495e12i 0.0783883 + 0.349078i
\(610\) −2.06847e11 1.51920e11i −0.0604873 0.0444254i
\(611\) 3.03693e11 + 5.26012e11i 0.0881555 + 0.152690i
\(612\) 3.46061e12 9.27267e11i 0.997174 0.267192i
\(613\) −7.47647e10 + 2.00332e10i −0.0213858 + 0.00573030i −0.269496 0.963001i \(-0.586857\pi\)
0.248110 + 0.968732i \(0.420190\pi\)
\(614\) 3.72190e10 + 6.44652e10i 0.0105684 + 0.0183049i
\(615\) −5.05435e11 3.71221e11i −0.142471 0.104639i
\(616\) 7.97955e11 + 3.55344e12i 0.223288 + 0.994343i
\(617\) −3.09216e12 + 3.09216e12i −0.858971 + 0.858971i −0.991217 0.132246i \(-0.957781\pi\)
0.132246 + 0.991217i \(0.457781\pi\)
\(618\) 1.65188e11 6.16491e11i 0.0455545 0.170012i
\(619\) 4.24866e9 7.35889e9i 0.00116317 0.00201467i −0.865443 0.501007i \(-0.832963\pi\)
0.866606 + 0.498992i \(0.166296\pi\)
\(620\) −1.86899e12 + 4.79478e12i −0.507979 + 1.30318i
\(621\) −2.85339e12 + 1.64741e12i −0.769926 + 0.444517i
\(622\) 3.04460e10 + 3.04460e10i 0.00815593 + 0.00815593i
\(623\) −1.37497e12 + 7.20536e11i −0.365676 + 0.191628i
\(624\) 9.95493e11i 0.262850i
\(625\) −3.45212e12 1.62319e12i −0.904954 0.425510i
\(626\) 2.86009e11 + 1.65127e11i 0.0744380 + 0.0429768i
\(627\) 7.93144e11 + 2.96005e12i 0.204950 + 0.764884i
\(628\) 3.79334e11 + 1.01642e11i 0.0973203 + 0.0260769i
\(629\) 7.90375e11 0.201328
\(630\) 5.85530e11 7.32446e11i 0.148087 0.185244i
\(631\) −2.06194e12 −0.517778 −0.258889 0.965907i \(-0.583356\pi\)
−0.258889 + 0.965907i \(0.583356\pi\)
\(632\) −9.15821e11 2.45393e11i −0.228341 0.0611837i
\(633\) 3.48608e11 + 1.30102e12i 0.0863018 + 0.322083i
\(634\) −8.76957e11 5.06311e11i −0.215564 0.124456i
\(635\) 3.29798e12 + 3.63851e11i 0.804944 + 0.0888060i
\(636\) 1.68868e12i 0.409252i
\(637\) −2.63130e12 + 2.23250e12i −0.633203 + 0.537234i
\(638\) 1.35041e12 + 1.35041e12i 0.322679 + 0.322679i
\(639\) −3.91677e12 + 2.26135e12i −0.929338 + 0.536554i
\(640\) 3.58735e12 1.57505e12i 0.845208 0.371096i
\(641\) 1.86433e12 3.22912e12i 0.436176 0.755479i −0.561215 0.827670i \(-0.689666\pi\)
0.997391 + 0.0721909i \(0.0229991\pi\)
\(642\) −7.37424e10 + 2.75210e11i −0.0171321 + 0.0639377i
\(643\) 5.07481e12 5.07481e12i 1.17077 1.17077i 0.188741 0.982027i \(-0.439559\pi\)
0.982027 0.188741i \(-0.0604405\pi\)
\(644\) −3.17092e12 3.44155e12i −0.726438 0.788439i
\(645\) 1.13565e12 1.73865e11i 0.258360 0.0395542i
\(646\) −8.87375e11 1.53698e12i −0.200475 0.347233i
\(647\) 5.42252e12 1.45296e12i 1.21655 0.325975i 0.407224 0.913328i \(-0.366497\pi\)
0.809331 + 0.587353i \(0.199830\pi\)
\(648\) 1.21524e12 3.25623e11i 0.270754 0.0725484i
\(649\) −2.83907e12 4.91741e12i −0.628166 1.08802i
\(650\) −3.24477e11 1.03487e12i −0.0712975 0.227392i
\(651\) 2.77794e12 + 8.67557e11i 0.606190 + 0.189314i
\(652\) −1.04882e12 + 1.04882e12i −0.227293 + 0.227293i
\(653\) 7.50260e11 2.80001e12i 0.161474 0.602629i −0.836990 0.547219i \(-0.815687\pi\)
0.998464 0.0554104i \(-0.0176467\pi\)
\(654\) −3.39098e10 + 5.87335e10i −0.00724812 + 0.0125541i
\(655\) −1.62296e12 6.32626e11i −0.344526 0.134295i
\(656\) 1.32399e12 7.64405e11i 0.279137 0.161160i
\(657\) 2.22496e12 + 2.22496e12i 0.465885 + 0.465885i
\(658\) −2.47536e11 1.56750e11i −0.0514781 0.0325981i
\(659\) 5.11092e12i 1.05564i 0.849357 + 0.527819i \(0.176990\pi\)
−0.849357 + 0.527819i \(0.823010\pi\)
\(660\) 3.78480e11 3.43057e12i 0.0776417 0.703750i
\(661\) −4.61705e12 2.66566e12i −0.940715 0.543122i −0.0505308 0.998723i \(-0.516091\pi\)
−0.890184 + 0.455600i \(0.849425\pi\)
\(662\) −2.96606e11 1.10695e12i −0.0600232 0.224010i
\(663\) −2.26346e12 6.06493e11i −0.454949 0.121903i
\(664\) −3.99531e12 −0.797617
\(665\) 4.74149e12 + 2.07539e12i 0.940193 + 0.411531i
\(666\) 1.78082e11 0.0350741
\(667\) −4.95332e12 1.32724e12i −0.969015 0.259647i
\(668\) −1.85862e12 6.93645e12i −0.361157 1.34786i
\(669\) −2.22657e12 1.28551e12i −0.429754 0.248118i
\(670\) 3.20010e11 2.56416e11i 0.0613518 0.0491595i
\(671\) 2.54301e12i 0.484279i
\(672\) −7.85527e11 1.49899e12i −0.148593 0.283554i
\(673\) −2.87257e12 2.87257e12i −0.539763 0.539763i 0.383696 0.923459i \(-0.374651\pi\)
−0.923459 + 0.383696i \(0.874651\pi\)
\(674\) 2.27655e12 1.31436e12i 0.424920 0.245327i
\(675\) −3.46500e12 + 2.19968e12i −0.642446 + 0.407843i
\(676\) 7.73343e11 1.33947e12i 0.142434 0.246702i
\(677\) 9.31586e11 3.47673e12i 0.170441 0.636094i −0.826842 0.562434i \(-0.809865\pi\)
0.997283 0.0736605i \(-0.0234681\pi\)
\(678\) −2.29443e11 + 2.29443e11i −0.0417004 + 0.0417004i
\(679\) −1.59522e12 + 1.46977e12i −0.288009 + 0.265361i
\(680\) 6.32130e11 + 4.12893e12i 0.113375 + 0.740538i
\(681\) 7.77531e11 + 1.34672e12i 0.138534 + 0.239948i
\(682\) 4.42051e12 1.18447e12i 0.782424 0.209650i
\(683\) 1.49400e12 4.00316e11i 0.262698 0.0703897i −0.125066 0.992148i \(-0.539914\pi\)
0.387764 + 0.921759i \(0.373248\pi\)
\(684\) 2.22776e12 + 3.85860e12i 0.389150 + 0.674027i
\(685\) 4.95678e12 6.74889e12i 0.860186 1.17118i
\(686\) 6.24406e11 1.54304e12i 0.107649 0.266023i
\(687\) 2.56077e12 2.56077e12i 0.438597 0.438597i
\(688\) −7.24901e11 + 2.70537e12i −0.123348 + 0.460340i
\(689\) 2.62900e12 4.55357e12i 0.444431 0.769778i
\(690\) −3.34376e11 7.61576e11i −0.0561584 0.127906i
\(691\) −3.23684e12 + 1.86879e12i −0.540095 + 0.311824i −0.745117 0.666933i \(-0.767607\pi\)
0.205023 + 0.978757i \(0.434273\pi\)
\(692\) −9.82720e10 9.82720e10i −0.0162912 0.0162912i
\(693\) 9.28389e12 + 3.79973e11i 1.52908 + 0.0625826i
\(694\) 2.95547e12i 0.483625i
\(695\) 4.48483e12 + 5.59713e12i 0.729146 + 0.909984i
\(696\) −1.05559e12 6.09444e11i −0.170511 0.0984446i
\(697\) 9.31412e11 + 3.47608e12i 0.149484 + 0.557881i
\(698\) 5.50960e11 + 1.47629e11i 0.0878559 + 0.0235409i
\(699\) 1.50915e12 0.239104
\(700\) −4.12659e12 4.11726e12i −0.649606 0.648137i
\(701\) −6.73685e12 −1.05372 −0.526860 0.849952i \(-0.676631\pi\)
−0.526860 + 0.849952i \(0.676631\pi\)
\(702\) −1.12711e12 3.02007e11i −0.175165 0.0469354i
\(703\) 2.54402e11 + 9.49439e11i 0.0392845 + 0.146612i
\(704\) 5.63600e12 + 3.25394e12i 0.864756 + 0.499267i
\(705\) 3.62828e11 + 4.52815e11i 0.0553159 + 0.0690351i
\(706\) 3.74633e11i 0.0567526i
\(707\) −3.23354e12 + 5.10633e12i −0.486733 + 0.768637i
\(708\) 1.22626e12 + 1.22626e12i 0.183414 + 0.183414i
\(709\) 2.63583e12 1.52180e12i 0.391750 0.226177i −0.291168 0.956672i \(-0.594044\pi\)
0.682918 + 0.730495i \(0.260711\pi\)
\(710\) −1.01439e12 2.31038e12i −0.149811 0.341210i
\(711\) −1.20948e12 + 2.09488e12i −0.177495 + 0.307430i
\(712\) 4.03236e11 1.50490e12i 0.0588030 0.219456i
\(713\) −8.68934e12 + 8.68934e12i −1.25917 + 1.25917i
\(714\) 1.10291e12 2.47667e11i 0.158817 0.0356637i
\(715\) 6.36142e12 8.66138e12i 0.910284 1.23940i
\(716\) 1.25792e12 + 2.17877e12i 0.178872 + 0.309816i
\(717\) 6.81860e11 1.82704e11i 0.0963516 0.0258173i
\(718\) 1.20610e12 3.23173e11i 0.169365 0.0453811i
\(719\) 1.18211e12 + 2.04747e12i 0.164959 + 0.285718i 0.936641 0.350291i \(-0.113917\pi\)
−0.771681 + 0.636009i \(0.780584\pi\)
\(720\) −6.85134e11 4.47514e12i −0.0950122 0.620598i
\(721\) 3.18413e12 1.01957e13i 0.438815 1.40510i
\(722\) 7.90045e10 7.90045e10i 0.0108202 0.0108202i
\(723\) −9.98366e11 + 3.72595e12i −0.135884 + 0.507125i
\(724\) −5.60624e12 + 9.71030e12i −0.758313 + 1.31344i
\(725\) −6.23423e12 1.39254e12i −0.838035 0.187192i
\(726\) −1.88297e12 + 1.08713e12i −0.251552 + 0.145234i
\(727\) −4.39801e12 4.39801e12i −0.583917 0.583917i 0.352060 0.935977i \(-0.385481\pi\)
−0.935977 + 0.352060i \(0.885481\pi\)
\(728\) 1.41630e11 3.46045e12i 0.0186881 0.456606i
\(729\) 7.92072e11i 0.103870i
\(730\) −1.36997e12 + 1.09772e12i −0.178550 + 0.143067i
\(731\) −5.70959e12 3.29644e12i −0.739566 0.426989i
\(732\) 2.01018e11 + 7.50208e11i 0.0258782 + 0.0965788i
\(733\) 7.58215e12 + 2.03163e12i 0.970118 + 0.259942i 0.708878 0.705331i \(-0.249202\pi\)
0.261240 + 0.965274i \(0.415868\pi\)
\(734\) −2.11529e10 −0.00268991
\(735\) −2.16202e12 + 2.48859e12i −0.273254 + 0.314529i
\(736\) 7.14591e12 0.897651
\(737\) 3.92481e12 + 1.05165e12i 0.490021 + 0.131301i
\(738\) 2.09860e11 + 7.83207e11i 0.0260420 + 0.0971902i
\(739\) −1.17477e13 6.78251e12i −1.44894 0.836548i −0.450525 0.892764i \(-0.648763\pi\)
−0.998419 + 0.0562162i \(0.982096\pi\)
\(740\) 1.21398e11 1.10036e12i 0.0148822 0.134893i
\(741\) 2.91421e12i 0.355090i
\(742\) −1.03723e11 + 2.53425e12i −0.0125619 + 0.306925i
\(743\) −7.53425e12 7.53425e12i −0.906965 0.906965i 0.0890612 0.996026i \(-0.471613\pi\)
−0.996026 + 0.0890612i \(0.971613\pi\)
\(744\) −2.52955e12 + 1.46044e12i −0.302667 + 0.174745i
\(745\) 8.83838e12 + 3.44518e12i 1.05116 + 0.409741i
\(746\) 2.07657e12 3.59672e12i 0.245483 0.425189i
\(747\) −2.63820e12 + 9.84591e12i −0.310003 + 1.15695i
\(748\) −1.40049e13 + 1.40049e13i −1.63577 + 1.63577i
\(749\) −1.42144e12 + 4.55149e12i −0.165029 + 0.528427i
\(750\) −4.56022e11 9.30330e11i −0.0526272 0.107365i
\(751\) 1.29672e12 + 2.24599e12i 0.148754 + 0.257649i 0.930767 0.365613i \(-0.119141\pi\)
−0.782013 + 0.623262i \(0.785807\pi\)
\(752\) −1.36636e12 + 3.66115e11i −0.155806 + 0.0417481i
\(753\) −4.44206e12 + 1.19025e12i −0.503509 + 0.134915i
\(754\) −9.08058e11 1.57280e12i −0.102316 0.177216i
\(755\) 1.50608e13 2.30578e12i 1.68689 0.258259i
\(756\) −6.11936e12 + 1.37415e12i −0.681331 + 0.152998i
\(757\) 1.03813e13 1.03813e13i 1.14900 1.14900i 0.162248 0.986750i \(-0.448125\pi\)
0.986750 0.162248i \(-0.0518746\pi\)
\(758\) −1.05265e12 + 3.92855e12i −0.115817 + 0.432236i
\(759\) 4.12080e12 7.13743e12i 0.450706 0.780646i
\(760\) −4.75642e12 + 2.08834e12i −0.517153 + 0.227060i
\(761\) −5.08472e12 + 2.93567e12i −0.549587 + 0.317304i −0.748955 0.662621i \(-0.769444\pi\)
0.199369 + 0.979925i \(0.436111\pi\)
\(762\) 6.37228e11 + 6.37228e11i 0.0684695 + 0.0684695i
\(763\) −6.07222e11 + 9.58910e11i −0.0648616 + 0.102428i
\(764\) 1.30873e13i 1.38973i
\(765\) 1.05926e13 + 1.16864e12i 1.11822 + 0.123368i
\(766\) 3.86810e11 + 2.23325e11i 0.0405946 + 0.0234373i
\(767\) 1.39755e12 + 5.21571e12i 0.145810 + 0.544170i
\(768\) −1.06433e12 2.85188e11i −0.110396 0.0295805i
\(769\) 7.42780e12 0.765934 0.382967 0.923762i \(-0.374902\pi\)
0.382967 + 0.923762i \(0.374902\pi\)
\(770\) −7.78709e11 + 5.12511e12i −0.0798302 + 0.525406i
\(771\) −2.79682e12 −0.285049
\(772\) 6.47305e12 + 1.73445e12i 0.655890 + 0.175745i
\(773\) 4.82352e12 + 1.80016e13i 0.485911 + 1.81344i 0.575925 + 0.817503i \(0.304642\pi\)
−0.0900138 + 0.995941i \(0.528691\pi\)
\(774\) −1.28645e12 7.42731e11i −0.128842 0.0743870i
\(775\) −1.03596e13 + 1.12694e13i −1.03154 + 1.12213i
\(776\) 2.17700e12i 0.215517i
\(777\) −6.25526e11 2.56017e10i −0.0615674 0.00251984i
\(778\) −8.31905e10 8.31905e10i −0.00814077 0.00814077i
\(779\) −3.87585e12 + 2.23772e12i −0.377093 + 0.217715i
\(780\) −1.19202e12 + 3.05803e12i −0.115307 + 0.295813i
\(781\) 1.25012e13 2.16527e13i 1.20233 2.08249i
\(782\) −1.23535e12 + 4.61038e12i −0.118130 + 0.440865i
\(783\) −4.85976e12 + 4.85976e12i −0.462048 + 0.462048i
\(784\) −3.43609e12 7.26498e12i −0.324820 0.686772i
\(785\) 9.41498e11 + 6.91491e11i 0.0884924 + 0.0649940i
\(786\) −2.36553e11 4.09722e11i −0.0221068 0.0382902i
\(787\) 1.22263e13 3.27604e12i 1.13608 0.304412i 0.358708 0.933450i \(-0.383217\pi\)
0.777375 + 0.629038i \(0.216551\pi\)
\(788\) 1.54478e13 4.13921e12i 1.42724 0.382428i
\(789\) 3.45684e12 + 5.98742e12i 0.317565 + 0.550038i
\(790\) −1.08771e12 7.98879e11i −0.0993556 0.0729725i
\(791\) −3.99368e12 + 3.67962e12i −0.362726 + 0.334202i
\(792\) −6.59416e12 + 6.59416e12i −0.595520 + 0.595520i
\(793\) −6.25905e11 + 2.33591e12i −0.0562055 + 0.209762i
\(794\) 8.68597e11 1.50445e12i 0.0775579 0.134334i
\(795\) 1.82428e12 4.68008e12i 0.161972 0.415529i
\(796\) −3.61226e12 + 2.08554e12i −0.318912 + 0.184124i
\(797\) −1.26672e13 1.26672e13i −1.11204 1.11204i −0.992875 0.119162i \(-0.961979\pi\)
−0.119162 0.992875i \(-0.538021\pi\)
\(798\) 6.52509e11 + 1.24515e12i 0.0569605 + 0.108695i
\(799\) 3.32976e12i 0.289036i
\(800\) 8.89358e12 3.74078e11i 0.767665 0.0322892i
\(801\) −3.44235e12 1.98744e12i −0.295467 0.170588i
\(802\) 3.04267e11 + 1.13554e12i 0.0259699 + 0.0969210i
\(803\) −1.68022e13 4.50214e12i −1.42609 0.382119i
\(804\) −1.24098e12 −0.104740
\(805\) −5.07009e12 1.29636e13i −0.425534 1.08804i
\(806\) −4.35204e12 −0.363233
\(807\) 7.46988e11 + 2.00155e11i 0.0619987 + 0.0166125i
\(808\) −1.57002e12 5.85938e12i −0.129585 0.483616i
\(809\) −7.69845e12 4.44470e12i −0.631880 0.364816i 0.149600 0.988747i \(-0.452202\pi\)
−0.781480 + 0.623930i \(0.785535\pi\)
\(810\) 1.78000e12 + 1.96379e11i 0.145290 + 0.0160292i
\(811\) 1.87779e13i 1.52424i 0.647435 + 0.762121i \(0.275842\pi\)
−0.647435 + 0.762121i \(0.724158\pi\)
\(812\) −8.24694e12 5.22231e12i −0.665718 0.421561i
\(813\) 1.50934e12 + 1.50934e12i 0.121166 + 0.121166i
\(814\) −8.52581e11 + 4.92238e11i −0.0680653 + 0.0392975i
\(815\) −4.03979e12 + 1.77370e12i −0.320737 + 0.140822i
\(816\) 2.72870e12 4.72625e12i 0.215452 0.373174i
\(817\) 2.12208e12 7.91970e12i 0.166633 0.621884i
\(818\) 1.80126e12 1.80126e12i 0.140665 0.140665i
\(819\) −8.43431e12 2.63405e12i −0.655046 0.204572i
\(820\) 4.98244e12 7.62801e11i 0.384840 0.0589181i
\(821\) 4.66957e12 + 8.08794e12i 0.358701 + 0.621289i 0.987744 0.156082i \(-0.0498863\pi\)
−0.629043 + 0.777371i \(0.716553\pi\)
\(822\) 2.19680e12 5.88632e11i 0.167829 0.0449698i
\(823\) 1.30472e13 3.49600e12i 0.991332 0.265627i 0.273522 0.961866i \(-0.411811\pi\)
0.717810 + 0.696239i \(0.245145\pi\)
\(824\) 5.36013e12 + 9.28401e12i 0.405044 + 0.701557i
\(825\) 4.75499e12 9.09875e12i 0.357360 0.683815i
\(826\) −1.76496e12 1.91560e12i −0.131924 0.143184i
\(827\) 1.44832e13 1.44832e13i 1.07668 1.07668i 0.0798805 0.996804i \(-0.474546\pi\)
0.996804 0.0798805i \(-0.0254539\pi\)
\(828\) 3.10135e12 1.15744e13i 0.229305 0.855779i
\(829\) −1.25767e13 + 2.17835e13i −0.924851 + 1.60189i −0.133050 + 0.991109i \(0.542477\pi\)
−0.791801 + 0.610779i \(0.790856\pi\)
\(830\) −5.29862e12 2.06539e12i −0.387535 0.151060i
\(831\) 5.87443e11 3.39161e11i 0.0427328 0.0246718i
\(832\) −4.37612e12 4.37612e12i −0.316617 0.316617i
\(833\) 1.86119e13 3.38658e12i 1.33933 0.243702i
\(834\) 1.94801e12i 0.139426i
\(835\) 2.34242e12 2.12318e13i 0.166754 1.51147i
\(836\) −2.13312e13 1.23156e13i −1.51038 0.872019i
\(837\) 4.26260e12 + 1.59083e13i 0.300200 + 1.12036i
\(838\) −7.30847e11 1.95830e11i −0.0511951 0.0137177i
\(839\) 2.35415e13 1.64024 0.820118 0.572195i \(-0.193908\pi\)
0.820118 + 0.572195i \(0.193908\pi\)
\(840\) −3.66542e11 3.28823e12i −0.0254020 0.227880i
\(841\) 3.81040e12 0.262657
\(842\) 5.79273e12 + 1.55216e12i 0.397173 + 0.106422i
\(843\) −1.03342e11 3.85679e11i −0.00704782 0.0263028i
\(844\) −9.37561e12 5.41301e12i −0.636002 0.367196i
\(845\) 3.59031e12 2.87682e12i 0.242257 0.194114i
\(846\) 7.50240e11i 0.0503539i
\(847\) −3.22302e13 + 1.68899e13i −2.15173 + 1.12759i
\(848\) 8.65889e12 + 8.65889e12i 0.575017 + 0.575017i
\(849\) 6.04055e12 3.48751e12i 0.399017 0.230373i
\(850\) −1.29613e12 + 5.80260e12i −0.0851653 + 0.381274i
\(851\) 1.32175e12 2.28934e12i 0.0863905 0.149633i
\(852\) −1.97637e12 + 7.37593e12i −0.128496 + 0.479555i
\(853\) 1.53128e13 1.53128e13i 0.990342 0.990342i −0.00961185 0.999954i \(-0.503060\pi\)
0.999954 + 0.00961185i \(0.00305959\pi\)
\(854\) −2.55594e11 1.13821e12i −0.0164433 0.0732253i
\(855\) 2.00566e12 + 1.31005e13i 0.128354 + 0.838382i
\(856\) −2.39284e12 4.14451e12i −0.152328 0.263841i
\(857\) 1.56156e13 4.18419e12i 0.988884 0.264971i 0.272103 0.962268i \(-0.412281\pi\)
0.716782 + 0.697297i \(0.245614\pi\)
\(858\) 2.81933e12 7.55437e11i 0.177604 0.0475889i
\(859\) −1.13702e13 1.96938e13i −0.712525 1.23413i −0.963906 0.266241i \(-0.914218\pi\)
0.251381 0.967888i \(-0.419115\pi\)
\(860\) −5.46625e12 + 7.44256e12i −0.340759 + 0.463959i
\(861\) −6.24550e11 2.78124e12i −0.0387305 0.172474i
\(862\) −2.80624e12 + 2.80624e12i −0.173118 + 0.173118i
\(863\) −5.82787e12 + 2.17499e13i −0.357652 + 1.33478i 0.519461 + 0.854494i \(0.326133\pi\)
−0.877114 + 0.480283i \(0.840534\pi\)
\(864\) 4.78855e12 8.29401e12i 0.292343 0.506352i
\(865\) −1.66192e11 3.78519e11i −0.0100934 0.0229887i
\(866\) 2.91191e10 1.68119e10i 0.00175933 0.00101575i
\(867\) 4.18207e12 + 4.18207e12i 0.251365 + 0.251365i
\(868\) −2.07191e13 + 1.08576e13i −1.23889 + 0.649225i
\(869\) 1.33725e13i 0.795471i
\(870\) −1.08488e12 1.35394e12i −0.0642012 0.0801240i
\(871\) −3.34634e12 1.93201e12i −0.197010 0.113744i
\(872\) −2.94831e11 1.10033e12i −0.0172683 0.0644462i
\(873\) −5.36493e12 1.43753e12i −0.312608 0.0837630i
\(874\) −5.93585e12 −0.344098
\(875\) −6.98871e12 1.58687e13i −0.403052 0.915177i
\(876\) 5.31268e12 0.304821
\(877\) 5.35580e11 + 1.43508e11i 0.0305722 + 0.00819179i 0.274073 0.961709i \(-0.411629\pi\)
−0.243501 + 0.969901i \(0.578296\pi\)
\(878\) −1.92974e12 7.20189e12i −0.109591 0.408998i
\(879\) −7.17103e12 4.14019e12i −0.405164 0.233922i
\(880\) 1.56499e13 + 1.95313e13i 0.879711 + 1.09789i
\(881\) 2.76382e13i 1.54568i −0.634603 0.772839i \(-0.718836\pi\)
0.634603 0.772839i \(-0.281164\pi\)
\(882\) 4.19351e12 7.63041e11i 0.233329 0.0424560i
\(883\) −4.14609e12 4.14609e12i −0.229518 0.229518i 0.582974 0.812491i \(-0.301889\pi\)
−0.812491 + 0.582974i \(0.801889\pi\)
\(884\) 1.63113e13 9.41734e12i 0.898367 0.518672i
\(885\) 2.07377e12 + 4.72322e12i 0.113636 + 0.258818i
\(886\) 1.59111e12 2.75588e12i 0.0867456 0.150248i
\(887\) 1.77130e12 6.61057e12i 0.0960804 0.358577i −0.901101 0.433610i \(-0.857240\pi\)
0.997181 + 0.0750330i \(0.0239062\pi\)
\(888\) 4.44298e11 4.44298e11i 0.0239782 0.0239782i
\(889\) 1.02194e13 + 1.10916e13i 0.548739 + 0.595573i
\(890\) 1.31274e12 1.78735e12i 0.0701330 0.0954895i
\(891\) 8.87228e12 + 1.53672e13i 0.471613 + 0.816858i
\(892\) 1.99608e13 5.34849e12i 1.05569 0.282872i
\(893\) 3.99988e12 1.07177e12i 0.210482 0.0563986i
\(894\) 1.28823e12 + 2.23128e12i 0.0674488 + 0.116825i
\(895\) 1.13251e12 + 7.39727e12i 0.0589979 + 0.385361i
\(896\) 1.69989e13 + 5.30878e12i 0.881117 + 0.275175i
\(897\) −5.54193e12 + 5.54193e12i −0.285821 + 0.285821i
\(898\) −1.97676e12 + 7.37737e12i −0.101440 + 0.378580i
\(899\) −1.28165e13 + 2.21989e13i −0.654413 + 1.13348i
\(900\) 3.25394e12 1.45675e13i 0.165317 0.740105i
\(901\) −2.49632e13 + 1.44125e13i −1.26194 + 0.728580i
\(902\) −3.16959e12 3.16959e12i −0.159431 0.159431i
\(903\) 4.41196e12 + 2.79384e12i 0.220819 + 0.139832i
\(904\) 5.45019e12i 0.271427i
\(905\) −2.60274e13 + 2.08551e13i −1.28977 + 1.03346i
\(906\) 3.58381e12 + 2.06912e12i 0.176713 + 0.102025i
\(907\) −6.33622e11 2.36471e12i −0.0310883 0.116023i 0.948638 0.316363i \(-0.102462\pi\)
−0.979726 + 0.200340i \(0.935795\pi\)
\(908\) −1.20731e13 3.23498e12i −0.589432 0.157938i
\(909\) −1.54764e13 −0.751851
\(910\) 1.97673e12 4.51607e12i 0.0955565 0.218310i
\(911\) −6.50713e12 −0.313009 −0.156505 0.987677i \(-0.550023\pi\)
−0.156505 + 0.987677i \(0.550023\pi\)
\(912\) 6.55572e12 + 1.75660e12i 0.313793 + 0.0840806i
\(913\) −1.45846e13 5.44303e13i −0.694664 2.59252i
\(914\) −3.53834e12 2.04286e12i −0.167703 0.0968236i
\(915\) −2.53343e11 + 2.29632e12i −0.0119485 + 0.108302i
\(916\) 2.91081e13i 1.36611i
\(917\) −3.67513e12 7.01309e12i −0.171637 0.327527i
\(918\) 4.52329e12 + 4.52329e12i 0.210214 + 0.210214i
\(919\) 1.31374e13 7.58490e12i 0.607562 0.350776i −0.164449 0.986386i \(-0.552584\pi\)
0.772011 + 0.635609i \(0.219251\pi\)
\(920\) 1.30166e13 + 5.07386e12i 0.599037 + 0.233503i
\(921\) 3.35040e11 5.80306e11i 0.0153436 0.0265759i
\(922\) 1.13232e11 4.22588e11i 0.00516037 0.0192588i
\(923\) −1.68125e13 + 1.68125e13i −0.762472 + 0.762472i
\(924\) 1.15375e13 1.06302e13i 0.520700 0.479753i
\(925\) 1.52516e12 2.91843e12i 0.0684982 0.131072i
\(926\) −1.29608e12 2.24487e12i −0.0579270 0.100333i
\(927\) 2.64186e13 7.07885e12i 1.17504 0.314850i
\(928\) 1.43979e13 3.85791e12i 0.637286 0.170760i
\(929\) 1.98471e13 + 3.43762e13i 0.874233 + 1.51422i 0.857578 + 0.514354i \(0.171968\pi\)
0.0166544 + 0.999861i \(0.494698\pi\)
\(930\) −4.10969e12 + 6.29184e11i −0.180151 + 0.0275806i
\(931\) 1.00588e13 + 2.12675e13i 0.438807 + 0.927777i
\(932\) −8.57722e12 + 8.57722e12i −0.372370 + 0.372370i
\(933\) 1.00317e11 3.74387e11i 0.00433416 0.0161753i
\(934\) 6.62632e11 1.14771e12i 0.0284912 0.0493483i
\(935\) −5.39431e13 + 2.36842e13i −2.30826 + 1.01346i
\(936\) 7.68015e12 4.43414e12i 0.327061 0.188829i
\(937\) −1.34462e13 1.34462e13i −0.569863 0.569863i 0.362227 0.932090i \(-0.382016\pi\)
−0.932090 + 0.362227i \(0.882016\pi\)
\(938\) 1.86238e12 + 7.62239e10i 0.0785517 + 0.00321498i
\(939\) 2.97290e12i 0.124791i
\(940\) −4.63568e12 5.11435e11i −0.193659 0.0213656i
\(941\) 2.17510e13 + 1.25579e13i 0.904326 + 0.522113i 0.878601 0.477556i \(-0.158477\pi\)
0.0257249 + 0.999669i \(0.491811\pi\)
\(942\) 8.21165e10 + 3.06463e11i 0.00339783 + 0.0126809i
\(943\) 1.16261e13 + 3.11521e12i 0.478776 + 0.128288i
\(944\) −1.25755e13 −0.515409
\(945\) −1.84439e13 2.80237e12i −0.752334 0.114310i
\(946\) 8.21196e12 0.333378
\(947\) −4.49201e13 1.20363e13i −1.81495 0.486315i −0.818811 0.574063i \(-0.805366\pi\)
−0.996143 + 0.0877476i \(0.972033\pi\)
\(948\) 1.05706e12 + 3.94501e12i 0.0425072 + 0.158639i
\(949\) 1.43258e13 + 8.27099e12i 0.573350 + 0.331024i
\(950\) −7.38758e12 + 3.10733e11i −0.294270 + 0.0123775i
\(951\) 9.11546e12i 0.361382i
\(952\) −1.01577e13 + 1.60408e13i −0.400802 + 0.632936i
\(953\) 4.90434e12 + 4.90434e12i 0.192603 + 0.192603i 0.796820 0.604217i \(-0.206514\pi\)
−0.604217 + 0.796820i \(0.706514\pi\)
\(954\) −5.62454e12 + 3.24733e12i −0.219846 + 0.126928i
\(955\) −1.41382e13 + 3.62707e13i −0.550022 + 1.41104i
\(956\) −2.83694e12 + 4.91372e12i −0.109847 + 0.190261i
\(957\) 4.44945e12 1.66056e13i 0.171476 0.639956i
\(958\) −2.56218e12 + 2.56218e12i −0.0982798 + 0.0982798i
\(959\) 3.71369e13 8.33940e12i 1.41782 0.318384i
\(960\) −4.76510e12 3.49977e12i −0.181072 0.132990i
\(961\) 1.74930e13 + 3.02988e13i 0.661622 + 1.14596i
\(962\) 9.04302e11 2.42307e11i 0.0340428 0.00912175i
\(963\) −1.17937e13 + 3.16010e12i −0.441906 + 0.118408i
\(964\) −1.55021e13 2.68505e13i −0.578156 1.00140i
\(965\) 1.60659e13 + 1.17998e13i 0.596394 + 0.438027i
\(966\) 1.12703e12 3.60877e12i 0.0416426 0.133341i
\(967\) −8.16941e12 + 8.16941e12i −0.300450 + 0.300450i −0.841190 0.540740i \(-0.818144\pi\)
0.540740 + 0.841190i \(0.318144\pi\)
\(968\) 9.45215e12 3.52759e13i 0.346012 1.29134i
\(969\) −7.98800e12 + 1.38356e13i −0.291059 + 0.504129i
\(970\) 1.12541e12 2.88716e12i 0.0408166 0.104712i
\(971\) 1.42976e13 8.25474e12i 0.516152 0.298000i −0.219207 0.975678i \(-0.570347\pi\)
0.735359 + 0.677678i \(0.237014\pi\)
\(972\) −1.75733e13 1.75733e13i −0.631474 0.631474i
\(973\) −1.33319e12 + 3.25739e13i −0.0476854 + 1.16510i
\(974\) 1.30673e13i 0.465231i
\(975\) −6.60720e12 + 7.18743e12i −0.234151 + 0.254714i
\(976\) −4.87751e12 2.81603e12i −0.172058 0.0993376i
\(977\) 1.15642e13 + 4.31580e13i 0.406058 + 1.51543i 0.802096 + 0.597195i \(0.203718\pi\)
−0.396038 + 0.918234i \(0.629615\pi\)
\(978\) −1.15749e12 3.10148e11i −0.0404568 0.0108404i
\(979\) 2.19740e13 0.764518
\(980\) −1.85609e12 2.64316e13i −0.0642808 0.915389i
\(981\) −2.90629e12 −0.100191
\(982\) 5.43048e12 + 1.45509e12i 0.186353 + 0.0499332i
\(983\) −9.34229e12 3.48659e13i −0.319126 1.19099i −0.920086 0.391716i \(-0.871882\pi\)
0.600960 0.799279i \(-0.294785\pi\)
\(984\) 2.47761e12 + 1.43045e12i 0.0842471 + 0.0486401i
\(985\) 4.72841e13 + 5.21665e12i 1.60049 + 0.176575i
\(986\) 9.95615e12i 0.335464i
\(987\) −1.07857e11 + 2.63527e12i −0.00361760 + 0.0883889i
\(988\) 1.65628e13 + 1.65628e13i 0.553003 + 0.553003i
\(989\) −1.90964e13 + 1.10253e13i −0.634699 + 0.366444i
\(990\) −1.21541e13 + 5.33636e12i −0.402128 + 0.176558i
\(991\) 1.04843e13 1.81594e13i 0.345311 0.598096i −0.640099 0.768292i \(-0.721107\pi\)
0.985410 + 0.170196i \(0.0544402\pi\)
\(992\) 9.24489e12 3.45024e13i 0.303109 1.13122i
\(993\) −7.29457e12 + 7.29457e12i −0.238083 + 0.238083i
\(994\) 3.41905e12 1.09479e13i 0.111088 0.355706i
\(995\) −1.22642e13 + 1.87762e12i −0.396675 + 0.0607301i
\(996\) 8.60514e12 + 1.49045e13i 0.277071 + 0.479901i
\(997\) −2.68293e13 + 7.18889e12i −0.859966 + 0.230427i −0.661744 0.749730i \(-0.730183\pi\)
−0.198222 + 0.980157i \(0.563517\pi\)
\(998\) −3.91033e12 + 1.04777e12i −0.124775 + 0.0334333i
\(999\) −1.77144e12 3.06822e12i −0.0562705 0.0974634i
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 35.10.k.a.3.15 136
5.2 odd 4 inner 35.10.k.a.17.20 yes 136
7.5 odd 6 inner 35.10.k.a.33.20 yes 136
35.12 even 12 inner 35.10.k.a.12.15 yes 136
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.10.k.a.3.15 136 1.1 even 1 trivial
35.10.k.a.12.15 yes 136 35.12 even 12 inner
35.10.k.a.17.20 yes 136 5.2 odd 4 inner
35.10.k.a.33.20 yes 136 7.5 odd 6 inner