Properties

Label 14.9.d.a.5.1
Level $14$
Weight $9$
Character 14.5
Analytic conductor $5.703$
Analytic rank $0$
Dimension $12$
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] = [14,9,Mod(3,14)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(14, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("14.3");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 14.d (of order \(6\), degree \(2\), 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: \(5.70330054086\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2 x^{11} + 1771 x^{10} + 26038 x^{9} + 2442597 x^{8} + 26522276 x^{7} + 1175865280 x^{6} + 6901058684 x^{5} + 370996492174 x^{4} + \cdots + 36\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{24}\cdot 3^{4}\cdot 7^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 5.1
Root \(3.92504 + 6.79836i\) of defining polynomial
Character \(\chi\) \(=\) 14.5
Dual form 14.9.d.a.3.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.65685 + 9.79796i) q^{2} +(-90.8670 + 52.4621i) q^{3} +(-64.0000 - 110.851i) q^{4} +(32.9005 + 18.9951i) q^{5} -1187.08i q^{6} +(1399.84 - 1950.71i) q^{7} +1448.15 q^{8} +(2224.04 - 3852.15i) q^{9} +O(q^{10})\) \(q+(-5.65685 + 9.79796i) q^{2} +(-90.8670 + 52.4621i) q^{3} +(-64.0000 - 110.851i) q^{4} +(32.9005 + 18.9951i) q^{5} -1187.08i q^{6} +(1399.84 - 1950.71i) q^{7} +1448.15 q^{8} +(2224.04 - 3852.15i) q^{9} +(-372.227 + 214.905i) q^{10} +(-7796.05 - 13503.2i) q^{11} +(11631.0 + 6715.15i) q^{12} -24124.1i q^{13} +(11194.3 + 24750.4i) q^{14} -3986.09 q^{15} +(-8192.00 + 14189.0i) q^{16} +(-116609. + 67324.1i) q^{17} +(25162.1 + 43582.1i) q^{18} +(16814.6 + 9707.91i) q^{19} -4862.75i q^{20} +(-24860.8 + 250693. i) q^{21} +176404. q^{22} +(193329. - 334855. i) q^{23} +(-131589. + 75973.2i) q^{24} +(-194591. - 337041. i) q^{25} +(236367. + 136467. i) q^{26} -221697. i q^{27} +(-305828. - 30328.4i) q^{28} -653074. q^{29} +(22548.7 - 39055.6i) q^{30} +(511920. - 295557. i) q^{31} +(-92681.9 - 160530. i) q^{32} +(1.41681e6 + 817994. i) q^{33} -1.52337e6i q^{34} +(83109.2 - 37589.2i) q^{35} -569354. q^{36} +(285739. - 494914. i) q^{37} +(-190235. + 109833. i) q^{38} +(1.26560e6 + 2.19209e6i) q^{39} +(47645.0 + 27507.9i) q^{40} +4.86784e6i q^{41} +(-2.31565e6 - 1.66172e6i) q^{42} -5.56831e6 q^{43} +(-997894. + 1.72840e6i) q^{44} +(146344. - 84491.7i) q^{45} +(2.18726e6 + 3.78845e6i) q^{46} +(1.97312e6 + 1.13918e6i) q^{47} -1.71908e6i q^{48} +(-1.84571e6 - 5.46134e6i) q^{49} +4.40309e6 q^{50} +(7.06393e6 - 1.22351e7i) q^{51} +(-2.67419e6 + 1.54395e6i) q^{52} +(-196895. - 341032. i) q^{53} +(2.17217e6 + 1.25411e6i) q^{54} -592347. i q^{55} +(2.02718e6 - 2.82493e6i) q^{56} -2.03719e6 q^{57} +(3.69434e6 - 6.39879e6i) q^{58} +(-1.17552e7 + 6.78688e6i) q^{59} +(255110. + 441863. i) q^{60} +(6.72748e6 + 3.88411e6i) q^{61} +6.68769e6i q^{62} +(-4.40112e6 - 9.73083e6i) q^{63} +2.09715e6 q^{64} +(458241. - 793697. i) q^{65} +(-1.60293e7 + 9.25454e6i) q^{66} +(-1.77485e7 - 3.07414e7i) q^{67} +(1.49259e7 + 8.61749e6i) q^{68} +4.05697e7i q^{69} +(-101840. + 1.02694e6i) q^{70} +3.53731e7 q^{71} +(3.22075e6 - 5.57851e6i) q^{72} +(-3.46798e7 + 2.00224e7i) q^{73} +(3.23276e6 + 5.59931e6i) q^{74} +(3.53638e7 + 2.04173e7i) q^{75} -2.48523e6i q^{76} +(-3.72539e7 - 3.69441e6i) q^{77} -2.86373e7 q^{78} +(1.81094e7 - 3.13663e7i) q^{79} +(-539042. + 311216. i) q^{80} +(2.62226e7 + 4.54188e7i) q^{81} +(-4.76949e7 - 2.75367e7i) q^{82} -2.35833e7i q^{83} +(2.93807e7 - 1.32885e7i) q^{84} -5.11532e6 q^{85} +(3.14991e7 - 5.45581e7i) q^{86} +(5.93429e7 - 3.42616e7i) q^{87} +(-1.12899e7 - 1.95547e7i) q^{88} +(3.04692e7 + 1.75914e7i) q^{89} +1.91183e6i q^{90} +(-4.70591e7 - 3.37699e7i) q^{91} -4.94921e7 q^{92} +(-3.10111e7 + 5.37128e7i) q^{93} +(-2.23233e7 + 1.28884e7i) q^{94} +(368806. + 638790. i) q^{95} +(1.68434e7 + 9.72457e6i) q^{96} -4.41048e7i q^{97} +(6.39510e7 + 1.28098e7i) q^{98} -6.93549e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 162 q^{3} - 768 q^{4} + 1674 q^{5} - 1308 q^{7} + 23604 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 162 q^{3} - 768 q^{4} + 1674 q^{5} - 1308 q^{7} + 23604 q^{9} + 17664 q^{10} + 10302 q^{11} - 20736 q^{12} + 56832 q^{14} - 255468 q^{15} - 98304 q^{16} + 173178 q^{17} + 16896 q^{18} + 405978 q^{19} - 656910 q^{21} - 941568 q^{22} + 158934 q^{23} + 98304 q^{24} + 838668 q^{25} + 1958400 q^{26} - 255744 q^{28} - 4355256 q^{29} + 916992 q^{30} + 4520250 q^{31} + 4954482 q^{33} - 5270790 q^{35} - 6042624 q^{36} + 134214 q^{37} + 1278720 q^{38} + 1335384 q^{39} - 2260992 q^{40} + 6660096 q^{42} - 12961896 q^{43} + 1318656 q^{44} - 8415396 q^{45} + 2345472 q^{46} + 18385002 q^{47} - 3659172 q^{49} + 2970624 q^{50} - 2673894 q^{51} - 3369984 q^{52} - 16540506 q^{53} - 19646208 q^{54} + 4325376 q^{56} + 100263780 q^{57} + 9176064 q^{58} + 31163922 q^{59} + 16349952 q^{60} - 85390158 q^{61} + 4361988 q^{63} + 25165824 q^{64} - 46506264 q^{65} - 111873024 q^{66} - 37750362 q^{67} - 22166784 q^{68} + 92031744 q^{70} + 45506424 q^{71} + 2162688 q^{72} + 9414786 q^{73} + 58837248 q^{74} + 9837540 q^{75} - 100614066 q^{77} - 25463808 q^{78} + 59730294 q^{79} - 27426816 q^{80} - 89677422 q^{81} - 93259776 q^{82} + 122616576 q^{84} - 64652220 q^{85} - 15144960 q^{86} + 334229724 q^{87} + 60260352 q^{88} + 323014482 q^{89} - 266861424 q^{91} - 40687104 q^{92} - 11119662 q^{93} - 443440128 q^{94} - 175918350 q^{95} - 12582912 q^{96} + 472166400 q^{98} - 346906296 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.65685 + 9.79796i −0.353553 + 0.612372i
\(3\) −90.8670 + 52.4621i −1.12181 + 0.647680i −0.941864 0.335996i \(-0.890927\pi\)
−0.179951 + 0.983676i \(0.557594\pi\)
\(4\) −64.0000 110.851i −0.250000 0.433013i
\(5\) 32.9005 + 18.9951i 0.0526408 + 0.0303922i 0.526089 0.850429i \(-0.323658\pi\)
−0.473449 + 0.880821i \(0.656991\pi\)
\(6\) 1187.08i 0.915958i
\(7\) 1399.84 1950.71i 0.583022 0.812456i
\(8\) 1448.15 0.353553
\(9\) 2224.04 3852.15i 0.338979 0.587128i
\(10\) −372.227 + 214.905i −0.0372227 + 0.0214905i
\(11\) −7796.05 13503.2i −0.532481 0.922283i −0.999281 0.0379205i \(-0.987927\pi\)
0.466800 0.884363i \(-0.345407\pi\)
\(12\) 11631.0 + 6715.15i 0.560907 + 0.323840i
\(13\) 24124.1i 0.844653i −0.906444 0.422327i \(-0.861213\pi\)
0.906444 0.422327i \(-0.138787\pi\)
\(14\) 11194.3 + 24750.4i 0.291396 + 0.644273i
\(15\) −3986.09 −0.0787376
\(16\) −8192.00 + 14189.0i −0.125000 + 0.216506i
\(17\) −116609. + 67324.1i −1.39616 + 0.806074i −0.993988 0.109489i \(-0.965078\pi\)
−0.402174 + 0.915563i \(0.631745\pi\)
\(18\) 25162.1 + 43582.1i 0.239694 + 0.415162i
\(19\) 16814.6 + 9707.91i 0.129024 + 0.0744923i 0.563123 0.826373i \(-0.309600\pi\)
−0.434099 + 0.900865i \(0.642933\pi\)
\(20\) 4862.75i 0.0303922i
\(21\) −24860.8 + 250693.i −0.127832 + 1.28904i
\(22\) 176404. 0.753041
\(23\) 193329. 334855.i 0.690852 1.19659i −0.280707 0.959793i \(-0.590569\pi\)
0.971559 0.236797i \(-0.0760977\pi\)
\(24\) −131589. + 75973.2i −0.396621 + 0.228989i
\(25\) −194591. 337041.i −0.498153 0.862826i
\(26\) 236367. + 136467.i 0.517243 + 0.298630i
\(27\) 221697.i 0.417161i
\(28\) −305828. 30328.4i −0.497559 0.0493421i
\(29\) −653074. −0.923359 −0.461679 0.887047i \(-0.652753\pi\)
−0.461679 + 0.887047i \(0.652753\pi\)
\(30\) 22548.7 39055.6i 0.0278380 0.0482168i
\(31\) 511920. 295557.i 0.554313 0.320033i −0.196547 0.980494i \(-0.562973\pi\)
0.750860 + 0.660462i \(0.229639\pi\)
\(32\) −92681.9 160530.i −0.0883883 0.153093i
\(33\) 1.41681e6 + 817994.i 1.19469 + 0.689754i
\(34\) 1.52337e6i 1.13996i
\(35\) 83109.2 37589.2i 0.0553831 0.0250490i
\(36\) −569354. −0.338979
\(37\) 285739. 494914.i 0.152462 0.264072i −0.779670 0.626191i \(-0.784613\pi\)
0.932132 + 0.362119i \(0.117946\pi\)
\(38\) −190235. + 109833.i −0.0912341 + 0.0526740i
\(39\) 1.26560e6 + 2.19209e6i 0.547065 + 0.947545i
\(40\) 47645.0 + 27507.9i 0.0186113 + 0.0107453i
\(41\) 4.86784e6i 1.72267i 0.508041 + 0.861333i \(0.330370\pi\)
−0.508041 + 0.861333i \(0.669630\pi\)
\(42\) −2.31565e6 1.66172e6i −0.744175 0.534024i
\(43\) −5.56831e6 −1.62873 −0.814366 0.580351i \(-0.802915\pi\)
−0.814366 + 0.580351i \(0.802915\pi\)
\(44\) −997894. + 1.72840e6i −0.266240 + 0.461142i
\(45\) 146344. 84491.7i 0.0356882 0.0206046i
\(46\) 2.18726e6 + 3.78845e6i 0.488506 + 0.846117i
\(47\) 1.97312e6 + 1.13918e6i 0.404354 + 0.233454i 0.688361 0.725368i \(-0.258331\pi\)
−0.284007 + 0.958822i \(0.591664\pi\)
\(48\) 1.71908e6i 0.323840i
\(49\) −1.84571e6 5.46134e6i −0.320170 0.947360i
\(50\) 4.40309e6 0.704494
\(51\) 7.06393e6 1.22351e7i 1.04416 1.80853i
\(52\) −2.67419e6 + 1.54395e6i −0.365746 + 0.211163i
\(53\) −196895. 341032.i −0.0249535 0.0432207i 0.853279 0.521455i \(-0.174610\pi\)
−0.878232 + 0.478234i \(0.841277\pi\)
\(54\) 2.17217e6 + 1.25411e6i 0.255458 + 0.147489i
\(55\) 592347.i 0.0647330i
\(56\) 2.02718e6 2.82493e6i 0.206130 0.287247i
\(57\) −2.03719e6 −0.192989
\(58\) 3.69434e6 6.39879e6i 0.326457 0.565439i
\(59\) −1.17552e7 + 6.78688e6i −0.970114 + 0.560096i −0.899271 0.437392i \(-0.855902\pi\)
−0.0708432 + 0.997487i \(0.522569\pi\)
\(60\) 255110. + 441863.i 0.0196844 + 0.0340944i
\(61\) 6.72748e6 + 3.88411e6i 0.485884 + 0.280525i 0.722865 0.690989i \(-0.242825\pi\)
−0.236981 + 0.971514i \(0.576158\pi\)
\(62\) 6.68769e6i 0.452595i
\(63\) −4.40112e6 9.73083e6i −0.279384 0.617714i
\(64\) 2.09715e6 0.125000
\(65\) 458241. 793697.i 0.0256709 0.0444632i
\(66\) −1.60293e7 + 9.25454e6i −0.844773 + 0.487730i
\(67\) −1.77485e7 3.07414e7i −0.880772 1.52554i −0.850484 0.526000i \(-0.823691\pi\)
−0.0302875 0.999541i \(-0.509642\pi\)
\(68\) 1.49259e7 + 8.61749e6i 0.698081 + 0.403037i
\(69\) 4.05697e7i 1.78980i
\(70\) −101840. + 1.02694e6i −0.00424155 + 0.0427712i
\(71\) 3.53731e7 1.39200 0.696000 0.718041i \(-0.254961\pi\)
0.696000 + 0.718041i \(0.254961\pi\)
\(72\) 3.22075e6 5.57851e6i 0.119847 0.207581i
\(73\) −3.46798e7 + 2.00224e7i −1.22119 + 0.705057i −0.965173 0.261614i \(-0.915745\pi\)
−0.256022 + 0.966671i \(0.582412\pi\)
\(74\) 3.23276e6 + 5.59931e6i 0.107807 + 0.186727i
\(75\) 3.53638e7 + 2.04173e7i 1.11767 + 0.645287i
\(76\) 2.48523e6i 0.0744923i
\(77\) −3.72539e7 3.69441e6i −1.05976 0.105095i
\(78\) −2.86373e7 −0.773667
\(79\) 1.81094e7 3.13663e7i 0.464938 0.805296i −0.534261 0.845320i \(-0.679410\pi\)
0.999199 + 0.0400239i \(0.0127434\pi\)
\(80\) −539042. + 311216.i −0.0131602 + 0.00759805i
\(81\) 2.62226e7 + 4.54188e7i 0.609166 + 1.05511i
\(82\) −4.76949e7 2.75367e7i −1.05491 0.609054i
\(83\) 2.35833e7i 0.496926i −0.968641 0.248463i \(-0.920075\pi\)
0.968641 0.248463i \(-0.0799255\pi\)
\(84\) 2.93807e7 1.32885e7i 0.590127 0.266907i
\(85\) −5.11532e6 −0.0979934
\(86\) 3.14991e7 5.45581e7i 0.575844 0.997391i
\(87\) 5.93429e7 3.42616e7i 1.03584 0.598041i
\(88\) −1.12899e7 1.95547e7i −0.188260 0.326076i
\(89\) 3.04692e7 + 1.75914e7i 0.485625 + 0.280376i 0.722758 0.691102i \(-0.242874\pi\)
−0.237133 + 0.971477i \(0.576208\pi\)
\(90\) 1.91183e6i 0.0291393i
\(91\) −4.70591e7 3.37699e7i −0.686244 0.492452i
\(92\) −4.94921e7 −0.690852
\(93\) −3.10111e7 + 5.37128e7i −0.414558 + 0.718035i
\(94\) −2.23233e7 + 1.28884e7i −0.285921 + 0.165077i
\(95\) 368806. + 638790.i 0.00452797 + 0.00784267i
\(96\) 1.68434e7 + 9.72457e6i 0.198311 + 0.114495i
\(97\) 4.41048e7i 0.498194i −0.968478 0.249097i \(-0.919866\pi\)
0.968478 0.249097i \(-0.0801339\pi\)
\(98\) 6.39510e7 + 1.28098e7i 0.693334 + 0.138879i
\(99\) −6.93549e7 −0.721998
\(100\) −2.49076e7 + 4.31413e7i −0.249076 + 0.431413i
\(101\) 1.03813e8 5.99362e7i 0.997618 0.575975i 0.0900757 0.995935i \(-0.471289\pi\)
0.907543 + 0.419960i \(0.137956\pi\)
\(102\) 7.99192e7 + 1.38424e8i 0.738330 + 1.27883i
\(103\) −1.79069e7 1.03386e7i −0.159100 0.0918567i 0.418336 0.908292i \(-0.362614\pi\)
−0.577436 + 0.816436i \(0.695947\pi\)
\(104\) 3.49355e7i 0.298630i
\(105\) −5.57988e6 + 7.77570e6i −0.0459058 + 0.0639709i
\(106\) 4.45523e6 0.0352896
\(107\) −6.79901e7 + 1.17762e8i −0.518693 + 0.898403i 0.481071 + 0.876682i \(0.340248\pi\)
−0.999764 + 0.0217212i \(0.993085\pi\)
\(108\) −2.45753e7 + 1.41886e7i −0.180636 + 0.104290i
\(109\) −2.87066e7 4.97212e7i −0.203365 0.352238i 0.746246 0.665670i \(-0.231854\pi\)
−0.949610 + 0.313433i \(0.898521\pi\)
\(110\) 5.80379e6 + 3.35082e6i 0.0396407 + 0.0228866i
\(111\) 5.99618e7i 0.394987i
\(112\) 1.62110e7 + 3.58424e7i 0.103024 + 0.227785i
\(113\) −6.28582e7 −0.385521 −0.192761 0.981246i \(-0.561744\pi\)
−0.192761 + 0.981246i \(0.561744\pi\)
\(114\) 1.15241e7 1.99603e7i 0.0682318 0.118181i
\(115\) 1.27212e7 7.34460e6i 0.0727340 0.0419930i
\(116\) 4.17967e7 + 7.23941e7i 0.230840 + 0.399826i
\(117\) −9.29298e7 5.36530e7i −0.495920 0.286320i
\(118\) 1.53570e8i 0.792095i
\(119\) −3.19037e7 + 3.21712e8i −0.159094 + 1.60428i
\(120\) −5.77248e6 −0.0278380
\(121\) −1.43773e7 + 2.49022e7i −0.0670710 + 0.116170i
\(122\) −7.61127e7 + 4.39437e7i −0.343572 + 0.198361i
\(123\) −2.55377e8 4.42326e8i −1.11574 1.93251i
\(124\) −6.55257e7 3.78313e7i −0.277157 0.160016i
\(125\) 2.96250e7i 0.121344i
\(126\) 1.20239e8 + 1.19239e7i 0.477048 + 0.0473081i
\(127\) 5.05315e8 1.94244 0.971220 0.238185i \(-0.0765526\pi\)
0.971220 + 0.238185i \(0.0765526\pi\)
\(128\) −1.18633e7 + 2.05478e7i −0.0441942 + 0.0765466i
\(129\) 5.05976e8 2.92125e8i 1.82714 1.05490i
\(130\) 5.18440e6 + 8.97965e6i 0.0181520 + 0.0314403i
\(131\) −1.50007e8 8.66067e7i −0.509363 0.294081i 0.223209 0.974771i \(-0.428347\pi\)
−0.732572 + 0.680690i \(0.761680\pi\)
\(132\) 2.09406e8i 0.689754i
\(133\) 4.24750e7 1.92109e7i 0.135746 0.0613960i
\(134\) 4.01604e8 1.24560
\(135\) 4.21115e6 7.29393e6i 0.0126784 0.0219597i
\(136\) −1.68868e8 + 9.74958e7i −0.493618 + 0.284990i
\(137\) −8.66504e7 1.50083e8i −0.245973 0.426039i 0.716431 0.697658i \(-0.245774\pi\)
−0.962405 + 0.271619i \(0.912441\pi\)
\(138\) −3.97500e8 2.29497e8i −1.09603 0.632791i
\(139\) 4.82237e8i 1.29182i 0.763414 + 0.645910i \(0.223522\pi\)
−0.763414 + 0.645910i \(0.776478\pi\)
\(140\) −9.48580e6 6.80706e6i −0.0246923 0.0177193i
\(141\) −2.39055e8 −0.604814
\(142\) −2.00100e8 + 3.46584e8i −0.492147 + 0.852423i
\(143\) −3.25752e8 + 1.88073e8i −0.779010 + 0.449762i
\(144\) 3.64387e7 + 6.31136e7i 0.0847447 + 0.146782i
\(145\) −2.14865e7 1.24052e7i −0.0486063 0.0280629i
\(146\) 4.53055e8i 0.997101i
\(147\) 4.54228e8 + 3.99426e8i 0.972757 + 0.855395i
\(148\) −7.31491e7 −0.152462
\(149\) −3.15004e8 + 5.45603e8i −0.639103 + 1.10696i 0.346527 + 0.938040i \(0.387361\pi\)
−0.985630 + 0.168919i \(0.945972\pi\)
\(150\) −4.00095e8 + 2.30995e8i −0.790312 + 0.456287i
\(151\) 6.62706e7 + 1.14784e8i 0.127471 + 0.220787i 0.922696 0.385528i \(-0.125981\pi\)
−0.795225 + 0.606315i \(0.792647\pi\)
\(152\) 2.43501e7 + 1.40586e7i 0.0456170 + 0.0263370i
\(153\) 5.98926e8i 1.09297i
\(154\) 2.46937e8 3.44113e8i 0.439040 0.611813i
\(155\) 2.24566e7 0.0389060
\(156\) 1.61997e8 2.80587e8i 0.273533 0.473772i
\(157\) 7.84287e8 4.52809e8i 1.29085 0.745274i 0.312047 0.950067i \(-0.398985\pi\)
0.978805 + 0.204793i \(0.0656520\pi\)
\(158\) 2.04884e8 + 3.54870e8i 0.328761 + 0.569430i
\(159\) 3.57825e7 + 2.06591e7i 0.0559864 + 0.0323238i
\(160\) 7.04201e6i 0.0107453i
\(161\) −3.82576e8 8.45870e8i −0.569395 1.25893i
\(162\) −5.93349e8 −0.861490
\(163\) −1.61604e8 + 2.79906e8i −0.228929 + 0.396517i −0.957491 0.288463i \(-0.906856\pi\)
0.728562 + 0.684980i \(0.240189\pi\)
\(164\) 5.39606e8 3.11542e8i 0.745936 0.430666i
\(165\) 3.10758e7 + 5.38248e7i 0.0419263 + 0.0726184i
\(166\) 2.31068e8 + 1.33407e8i 0.304304 + 0.175690i
\(167\) 6.81174e8i 0.875775i −0.899030 0.437887i \(-0.855727\pi\)
0.899030 0.437887i \(-0.144273\pi\)
\(168\) −3.60023e7 + 3.63043e8i −0.0451953 + 0.455743i
\(169\) 2.33756e8 0.286560
\(170\) 2.89366e7 5.01197e7i 0.0346459 0.0600085i
\(171\) 7.47927e7 4.31816e7i 0.0874731 0.0505026i
\(172\) 3.56372e8 + 6.17254e8i 0.407183 + 0.705262i
\(173\) −9.29478e8 5.36635e8i −1.03766 0.599093i −0.118490 0.992955i \(-0.537805\pi\)
−0.919169 + 0.393862i \(0.871139\pi\)
\(174\) 7.75252e8i 0.845757i
\(175\) −9.29864e8 9.22131e7i −0.991442 0.0983196i
\(176\) 2.55461e8 0.266240
\(177\) 7.12108e8 1.23341e9i 0.725526 1.25665i
\(178\) −3.44720e8 + 1.99024e8i −0.343389 + 0.198256i
\(179\) −2.23487e8 3.87091e8i −0.217691 0.377052i 0.736411 0.676535i \(-0.236519\pi\)
−0.954102 + 0.299483i \(0.903186\pi\)
\(180\) −1.87320e7 1.08149e7i −0.0178441 0.0103023i
\(181\) 4.47562e8i 0.417003i −0.978022 0.208502i \(-0.933141\pi\)
0.978022 0.208502i \(-0.0668586\pi\)
\(182\) 5.97083e8 2.70052e8i 0.544188 0.246129i
\(183\) −8.15074e8 −0.726763
\(184\) 2.79970e8 4.84922e8i 0.244253 0.423059i
\(185\) 1.88019e7 1.08553e7i 0.0160515 0.00926732i
\(186\) −3.50850e8 6.07690e8i −0.293137 0.507727i
\(187\) 1.81818e9 + 1.04972e9i 1.48686 + 0.858438i
\(188\) 2.91630e8i 0.233454i
\(189\) −4.32465e8 3.10339e8i −0.338925 0.243214i
\(190\) −8.34512e6 −0.00640351
\(191\) −3.93238e7 + 6.81108e7i −0.0295476 + 0.0511779i −0.880421 0.474193i \(-0.842740\pi\)
0.850873 + 0.525371i \(0.176073\pi\)
\(192\) −1.90562e8 + 1.10021e8i −0.140227 + 0.0809600i
\(193\) 6.90455e8 + 1.19590e9i 0.497629 + 0.861919i 0.999996 0.00273540i \(-0.000870706\pi\)
−0.502367 + 0.864654i \(0.667537\pi\)
\(194\) 4.32137e8 + 2.49494e8i 0.305081 + 0.176138i
\(195\) 9.61611e7i 0.0665060i
\(196\) −4.87271e8 + 5.54126e8i −0.330177 + 0.375478i
\(197\) −7.84102e8 −0.520604 −0.260302 0.965527i \(-0.583822\pi\)
−0.260302 + 0.965527i \(0.583822\pi\)
\(198\) 3.92330e8 6.79536e8i 0.255265 0.442132i
\(199\) −1.96768e9 + 1.13604e9i −1.25471 + 0.724404i −0.972040 0.234814i \(-0.924552\pi\)
−0.282665 + 0.959219i \(0.591218\pi\)
\(200\) −2.81798e8 4.88088e8i −0.176124 0.305055i
\(201\) 3.22551e9 + 1.86225e9i 1.97613 + 1.14092i
\(202\) 1.35620e9i 0.814552i
\(203\) −9.14197e8 + 1.27396e9i −0.538339 + 0.750188i
\(204\) −1.80837e9 −1.04416
\(205\) −9.24652e7 + 1.60154e8i −0.0523556 + 0.0906825i
\(206\) 2.02593e8 1.16967e8i 0.112501 0.0649525i
\(207\) −8.59941e8 1.48946e9i −0.468368 0.811237i
\(208\) 3.42297e8 + 1.97625e8i 0.182873 + 0.105582i
\(209\) 3.02733e8i 0.158663i
\(210\) −4.46214e7 9.86574e7i −0.0229438 0.0507286i
\(211\) 2.97735e9 1.50210 0.751051 0.660244i \(-0.229547\pi\)
0.751051 + 0.660244i \(0.229547\pi\)
\(212\) −2.52026e7 + 4.36522e7i −0.0124768 + 0.0216104i
\(213\) −3.21425e9 + 1.85575e9i −1.56157 + 0.901571i
\(214\) −7.69220e8 1.33233e9i −0.366771 0.635267i
\(215\) −1.83200e8 1.05771e8i −0.0857378 0.0495007i
\(216\) 3.21051e8i 0.147489i
\(217\) 1.40059e8 1.41234e9i 0.0631644 0.636941i
\(218\) 6.49555e8 0.287601
\(219\) 2.10083e9 3.63875e9i 0.913303 1.58189i
\(220\) −6.56624e7 + 3.79102e7i −0.0280302 + 0.0161832i
\(221\) 1.62414e9 + 2.81309e9i 0.680853 + 1.17927i
\(222\) −5.87503e8 3.39195e8i −0.241879 0.139649i
\(223\) 1.46122e9i 0.590877i −0.955362 0.295439i \(-0.904534\pi\)
0.955362 0.295439i \(-0.0954658\pi\)
\(224\) −4.42886e8 4.39203e7i −0.175914 0.0174451i
\(225\) −1.73111e9 −0.675452
\(226\) 3.55580e8 6.15882e8i 0.136302 0.236083i
\(227\) 6.79977e8 3.92585e8i 0.256089 0.147853i −0.366460 0.930434i \(-0.619430\pi\)
0.622549 + 0.782581i \(0.286097\pi\)
\(228\) 1.30380e8 + 2.25825e8i 0.0482472 + 0.0835666i
\(229\) −1.84873e9 1.06736e9i −0.672250 0.388124i 0.124678 0.992197i \(-0.460210\pi\)
−0.796929 + 0.604073i \(0.793543\pi\)
\(230\) 1.66189e8i 0.0593871i
\(231\) 3.57896e9 1.61872e9i 1.25693 0.568490i
\(232\) −9.45752e8 −0.326457
\(233\) −4.40863e8 + 7.63598e8i −0.149582 + 0.259084i −0.931073 0.364833i \(-0.881126\pi\)
0.781491 + 0.623917i \(0.214460\pi\)
\(234\) 1.05138e9 6.07015e8i 0.350668 0.202458i
\(235\) 4.32777e7 + 7.49592e7i 0.0141903 + 0.0245784i
\(236\) 1.50467e9 + 8.68721e8i 0.485057 + 0.280048i
\(237\) 3.80022e9i 1.20452i
\(238\) −2.97165e9 2.13247e9i −0.926168 0.664623i
\(239\) 1.10042e9 0.337261 0.168631 0.985679i \(-0.446065\pi\)
0.168631 + 0.985679i \(0.446065\pi\)
\(240\) 3.26541e7 5.65585e7i 0.00984220 0.0170472i
\(241\) 1.27360e9 7.35312e8i 0.377541 0.217973i −0.299207 0.954188i \(-0.596722\pi\)
0.676748 + 0.736215i \(0.263389\pi\)
\(242\) −1.62660e8 2.81736e8i −0.0474264 0.0821449i
\(243\) −3.50586e9 2.02411e9i −1.00547 0.580508i
\(244\) 9.94332e8i 0.280525i
\(245\) 4.30139e7 2.14740e8i 0.0119384 0.0596005i
\(246\) 5.77852e9 1.57789
\(247\) 2.34195e8 4.05638e8i 0.0629202 0.108981i
\(248\) 7.41339e8 4.28012e8i 0.195979 0.113149i
\(249\) 1.23723e9 + 2.14294e9i 0.321849 + 0.557459i
\(250\) 2.90265e8 + 1.67584e8i 0.0743078 + 0.0429016i
\(251\) 9.90977e8i 0.249671i −0.992177 0.124836i \(-0.960160\pi\)
0.992177 0.124836i \(-0.0398403\pi\)
\(252\) −7.97003e8 + 1.11064e9i −0.197632 + 0.275405i
\(253\) −6.02880e9 −1.47146
\(254\) −2.85849e9 + 4.95106e9i −0.686756 + 1.18950i
\(255\) 4.64813e8 2.68360e8i 0.109930 0.0634684i
\(256\) −1.34218e8 2.32472e8i −0.0312500 0.0541266i
\(257\) −7.82513e8 4.51784e8i −0.179374 0.103562i 0.407625 0.913150i \(-0.366357\pi\)
−0.586998 + 0.809588i \(0.699691\pi\)
\(258\) 6.61004e9i 1.49185i
\(259\) −5.65444e8 1.25019e9i −0.125658 0.277829i
\(260\) −1.17310e8 −0.0256709
\(261\) −1.45246e9 + 2.51574e9i −0.312999 + 0.542130i
\(262\) 1.69714e9 9.79843e8i 0.360174 0.207946i
\(263\) 8.16204e8 + 1.41371e9i 0.170599 + 0.295486i 0.938629 0.344927i \(-0.112096\pi\)
−0.768031 + 0.640413i \(0.778763\pi\)
\(264\) 2.05176e9 + 1.18458e9i 0.422386 + 0.243865i
\(265\) 1.49602e7i 0.00303357i
\(266\) −5.20476e7 + 5.24841e8i −0.0103962 + 0.104834i
\(267\) −3.69153e9 −0.726375
\(268\) −2.27181e9 + 3.93490e9i −0.440386 + 0.762771i
\(269\) −1.01166e9 + 5.84080e8i −0.193207 + 0.111548i −0.593483 0.804846i \(-0.702248\pi\)
0.400276 + 0.916395i \(0.368914\pi\)
\(270\) 4.76437e7 + 8.25214e7i 0.00896501 + 0.0155279i
\(271\) −3.72419e9 2.15016e9i −0.690486 0.398652i 0.113308 0.993560i \(-0.463855\pi\)
−0.803794 + 0.594908i \(0.797189\pi\)
\(272\) 2.20608e9i 0.403037i
\(273\) 6.04776e9 + 5.99746e8i 1.08879 + 0.107973i
\(274\) 1.96067e9 0.347859
\(275\) −3.03408e9 + 5.25518e9i −0.530513 + 0.918876i
\(276\) 4.49720e9 2.59646e9i 0.775008 0.447451i
\(277\) −3.71563e9 6.43567e9i −0.631123 1.09314i −0.987323 0.158727i \(-0.949261\pi\)
0.356200 0.934410i \(-0.384072\pi\)
\(278\) −4.72494e9 2.72795e9i −0.791075 0.456727i
\(279\) 2.62932e9i 0.433937i
\(280\) 1.20355e8 5.44349e7i 0.0195809 0.00885616i
\(281\) 1.14202e10 1.83168 0.915838 0.401548i \(-0.131528\pi\)
0.915838 + 0.401548i \(0.131528\pi\)
\(282\) 1.35230e9 2.34225e9i 0.213834 0.370371i
\(283\) 1.79244e9 1.03486e9i 0.279446 0.161338i −0.353727 0.935349i \(-0.615086\pi\)
0.633173 + 0.774011i \(0.281752\pi\)
\(284\) −2.26388e9 3.92115e9i −0.348000 0.602754i
\(285\) −6.70246e7 3.86966e7i −0.0101591 0.00586535i
\(286\) 4.25561e9i 0.636059i
\(287\) 9.49573e9 + 6.81418e9i 1.39959 + 1.00435i
\(288\) −8.24513e8 −0.119847
\(289\) 5.57720e9 9.65999e9i 0.799511 1.38479i
\(290\) 2.43092e8 1.40349e8i 0.0343699 0.0198435i
\(291\) 2.31383e9 + 4.00767e9i 0.322671 + 0.558882i
\(292\) 4.43901e9 + 2.56286e9i 0.610597 + 0.352529i
\(293\) 7.61645e9i 1.03343i −0.856157 0.516716i \(-0.827154\pi\)
0.856157 0.516716i \(-0.172846\pi\)
\(294\) −6.48306e9 + 2.19101e9i −0.867742 + 0.293262i
\(295\) −5.15670e8 −0.0680901
\(296\) 4.13794e8 7.16712e8i 0.0539035 0.0933636i
\(297\) −2.99360e9 + 1.72836e9i −0.384741 + 0.222130i
\(298\) −3.56386e9 6.17279e9i −0.451914 0.782738i
\(299\) −8.07810e9 4.66389e9i −1.01070 0.583531i
\(300\) 5.22682e9i 0.645287i
\(301\) −7.79473e9 + 1.08621e10i −0.949588 + 1.32327i
\(302\) −1.49953e9 −0.180272
\(303\) −6.28876e9 + 1.08924e10i −0.746095 + 1.29227i
\(304\) −2.75490e8 + 1.59054e8i −0.0322561 + 0.0186231i
\(305\) 1.47558e8 + 2.55578e8i 0.0170516 + 0.0295342i
\(306\) −5.86825e9 3.38804e9i −0.669303 0.386422i
\(307\) 1.33086e9i 0.149823i −0.997190 0.0749113i \(-0.976133\pi\)
0.997190 0.0749113i \(-0.0238674\pi\)
\(308\) 1.97472e9 + 4.36608e9i 0.219433 + 0.485164i
\(309\) 2.16953e9 0.237975
\(310\) −1.27033e8 + 2.20028e8i −0.0137553 + 0.0238250i
\(311\) 5.28874e9 3.05346e9i 0.565342 0.326400i −0.189945 0.981795i \(-0.560831\pi\)
0.755287 + 0.655395i \(0.227498\pi\)
\(312\) 1.83279e9 + 3.17448e9i 0.193417 + 0.335008i
\(313\) 7.85096e9 + 4.53276e9i 0.817986 + 0.472264i 0.849721 0.527232i \(-0.176770\pi\)
−0.0317357 + 0.999496i \(0.510103\pi\)
\(314\) 1.02459e10i 1.05398i
\(315\) 4.00391e7 4.03749e8i 0.00406670 0.0410081i
\(316\) −4.63600e9 −0.464938
\(317\) 1.26312e9 2.18778e9i 0.125085 0.216654i −0.796681 0.604400i \(-0.793413\pi\)
0.921766 + 0.387746i \(0.126746\pi\)
\(318\) −4.04833e8 + 2.33731e8i −0.0395884 + 0.0228564i
\(319\) 5.09140e9 + 8.81856e9i 0.491670 + 0.851598i
\(320\) 6.89974e7 + 3.98356e7i 0.00658010 + 0.00379902i
\(321\) 1.42676e10i 1.34379i
\(322\) 1.04520e10 + 1.03650e9i 0.972243 + 0.0964157i
\(323\) −2.61431e9 −0.240185
\(324\) 3.35649e9 5.81361e9i 0.304583 0.527553i
\(325\) −8.13083e9 + 4.69434e9i −0.728789 + 0.420766i
\(326\) −1.82834e9 3.16677e9i −0.161877 0.280380i
\(327\) 5.21696e9 + 3.01201e9i 0.456275 + 0.263430i
\(328\) 7.04939e9i 0.609054i
\(329\) 4.98425e9 2.25431e9i 0.425419 0.192411i
\(330\) −7.03164e8 −0.0592927
\(331\) −8.14718e9 + 1.41113e10i −0.678727 + 1.17559i 0.296637 + 0.954990i \(0.404135\pi\)
−0.975364 + 0.220600i \(0.929198\pi\)
\(332\) −2.61424e9 + 1.50933e9i −0.215175 + 0.124232i
\(333\) −1.27099e9 2.20142e9i −0.103363 0.179030i
\(334\) 6.67412e9 + 3.85330e9i 0.536300 + 0.309633i
\(335\) 1.34854e9i 0.107074i
\(336\) −3.35342e9 2.40643e9i −0.263106 0.188806i
\(337\) 1.18418e9 0.0918117 0.0459059 0.998946i \(-0.485383\pi\)
0.0459059 + 0.998946i \(0.485383\pi\)
\(338\) −1.32232e9 + 2.29033e9i −0.101314 + 0.175482i
\(339\) 5.71174e9 3.29767e9i 0.432483 0.249694i
\(340\) 3.27380e8 + 5.67039e8i 0.0244984 + 0.0424324i
\(341\) −7.98190e9 4.60835e9i −0.590322 0.340823i
\(342\) 9.77087e8i 0.0714215i
\(343\) −1.32372e10 4.04454e9i −0.956355 0.292209i
\(344\) −8.06378e9 −0.575844
\(345\) −7.70626e8 + 1.33476e9i −0.0543960 + 0.0942167i
\(346\) 1.05158e10 6.07133e9i 0.733736 0.423623i
\(347\) −1.03474e9 1.79223e9i −0.0713698 0.123616i 0.828132 0.560533i \(-0.189404\pi\)
−0.899502 + 0.436917i \(0.856070\pi\)
\(348\) −7.59589e9 4.38549e9i −0.517919 0.299020i
\(349\) 1.96039e10i 1.32142i 0.750641 + 0.660711i \(0.229745\pi\)
−0.750641 + 0.660711i \(0.770255\pi\)
\(350\) 6.16361e9 8.58914e9i 0.410736 0.572371i
\(351\) −5.34824e9 −0.352357
\(352\) −1.44510e9 + 2.50300e9i −0.0941301 + 0.163038i
\(353\) 6.15795e9 3.55529e9i 0.396586 0.228969i −0.288424 0.957503i \(-0.593131\pi\)
0.685010 + 0.728534i \(0.259798\pi\)
\(354\) 8.05658e9 + 1.39544e10i 0.513024 + 0.888584i
\(355\) 1.16379e9 + 6.71916e8i 0.0732760 + 0.0423059i
\(356\) 4.50340e9i 0.280376i
\(357\) −1.39787e10 3.09068e10i −0.860586 1.90275i
\(358\) 5.05694e9 0.307862
\(359\) 7.73192e9 1.33921e10i 0.465489 0.806251i −0.533734 0.845652i \(-0.679212\pi\)
0.999223 + 0.0394013i \(0.0125451\pi\)
\(360\) 2.11929e8 1.22357e8i 0.0126177 0.00728483i
\(361\) −8.30329e9 1.43817e10i −0.488902 0.846803i
\(362\) 4.38520e9 + 2.53180e9i 0.255361 + 0.147433i
\(363\) 3.01705e9i 0.173762i
\(364\) −7.31648e8 + 7.37784e9i −0.0416770 + 0.420265i
\(365\) −1.52131e9 −0.0857129
\(366\) 4.61075e9 7.98606e9i 0.256949 0.445049i
\(367\) 2.07751e10 1.19945e10i 1.14520 0.661179i 0.197483 0.980306i \(-0.436723\pi\)
0.947712 + 0.319127i \(0.103390\pi\)
\(368\) 3.16750e9 + 5.48627e9i 0.172713 + 0.299148i
\(369\) 1.87516e10 + 1.08263e10i 1.01143 + 0.583947i
\(370\) 2.45627e8i 0.0131060i
\(371\) −9.40876e8 9.33051e7i −0.0496634 0.00492504i
\(372\) 7.93884e9 0.414558
\(373\) 1.85295e10 3.20940e10i 0.957256 1.65802i 0.228138 0.973629i \(-0.426736\pi\)
0.729118 0.684387i \(-0.239930\pi\)
\(374\) −2.05703e10 + 1.18763e10i −1.05137 + 0.607007i
\(375\) 1.55419e9 + 2.69194e9i 0.0785922 + 0.136126i
\(376\) 2.85738e9 + 1.64971e9i 0.142961 + 0.0825384i
\(377\) 1.57549e10i 0.779918i
\(378\) 5.48708e9 2.48173e9i 0.268766 0.121559i
\(379\) 4.14946e9 0.201111 0.100555 0.994931i \(-0.467938\pi\)
0.100555 + 0.994931i \(0.467938\pi\)
\(380\) 4.72071e7 8.17652e7i 0.00226398 0.00392134i
\(381\) −4.59165e10 + 2.65099e10i −2.17906 + 1.25808i
\(382\) −4.44898e8 7.70586e8i −0.0208933 0.0361883i
\(383\) −1.82471e10 1.05350e10i −0.848007 0.489597i 0.0119707 0.999928i \(-0.496190\pi\)
−0.859978 + 0.510331i \(0.829523\pi\)
\(384\) 2.48949e9i 0.114495i
\(385\) −1.15550e9 8.29190e8i −0.0525927 0.0377408i
\(386\) −1.56232e10 −0.703754
\(387\) −1.23841e10 + 2.14500e10i −0.552106 + 0.956275i
\(388\) −4.88907e9 + 2.82271e9i −0.215725 + 0.124549i
\(389\) 8.84656e9 + 1.53227e10i 0.386346 + 0.669170i 0.991955 0.126592i \(-0.0404039\pi\)
−0.605609 + 0.795762i \(0.707071\pi\)
\(390\) −9.42182e8 5.43969e8i −0.0407264 0.0235134i
\(391\) 5.20627e10i 2.22751i
\(392\) −2.67288e9 7.90887e9i −0.113197 0.334942i
\(393\) 1.81743e10 0.761881
\(394\) 4.43555e9 7.68260e9i 0.184061 0.318804i
\(395\) 1.19161e9 6.87979e8i 0.0489494 0.0282609i
\(396\) 4.43871e9 + 7.68807e9i 0.180500 + 0.312634i
\(397\) 3.14727e10 + 1.81708e10i 1.26699 + 0.731494i 0.974416 0.224750i \(-0.0721566\pi\)
0.292569 + 0.956244i \(0.405490\pi\)
\(398\) 2.57056e10i 1.02446i
\(399\) −2.85173e9 + 3.97396e9i −0.112517 + 0.156795i
\(400\) 6.37635e9 0.249076
\(401\) 6.68116e9 1.15721e10i 0.258389 0.447543i −0.707421 0.706792i \(-0.750142\pi\)
0.965811 + 0.259249i \(0.0834750\pi\)
\(402\) −3.64925e10 + 2.10690e10i −1.39733 + 0.806750i
\(403\) −7.13006e9 1.23496e10i −0.270317 0.468203i
\(404\) −1.32880e10 7.67184e9i −0.498809 0.287988i
\(405\) 1.99240e9i 0.0740555i
\(406\) −7.31069e9 1.61638e10i −0.269063 0.594895i
\(407\) −8.91053e9 −0.324733
\(408\) 1.02297e10 1.77183e10i 0.369165 0.639413i
\(409\) −8.72089e8 + 5.03501e8i −0.0311650 + 0.0179931i −0.515502 0.856889i \(-0.672394\pi\)
0.484337 + 0.874882i \(0.339061\pi\)
\(410\) −1.04612e9 1.81194e9i −0.0370210 0.0641222i
\(411\) 1.57473e10 + 9.09172e9i 0.551873 + 0.318624i
\(412\) 2.64667e9i 0.0918567i
\(413\) −3.21618e9 + 3.24315e10i −0.110545 + 1.11472i
\(414\) 1.94582e10 0.662373
\(415\) 4.47967e8 7.75902e8i 0.0151027 0.0261586i
\(416\) −3.87264e9 + 2.23587e9i −0.129311 + 0.0746575i
\(417\) −2.52992e10 4.38195e10i −0.836685 1.44918i
\(418\) 2.96617e9 + 1.71252e9i 0.0971608 + 0.0560958i
\(419\) 1.91618e10i 0.621698i −0.950459 0.310849i \(-0.899387\pi\)
0.950459 0.310849i \(-0.100613\pi\)
\(420\) 1.21906e9 + 1.20892e8i 0.0391766 + 0.00388508i
\(421\) −1.60486e10 −0.510868 −0.255434 0.966827i \(-0.582218\pi\)
−0.255434 + 0.966827i \(0.582218\pi\)
\(422\) −1.68424e10 + 2.91719e10i −0.531073 + 0.919846i
\(423\) 8.77659e9 5.06716e9i 0.274135 0.158272i
\(424\) −2.85135e8 4.93868e8i −0.00882240 0.0152808i
\(425\) 4.53820e10 + 2.62013e10i 1.39100 + 0.803096i
\(426\) 4.19907e10i 1.27501i
\(427\) 1.69941e10 7.68621e9i 0.511196 0.231207i
\(428\) 1.74055e10 0.518693
\(429\) 1.97334e10 3.41793e10i 0.582603 1.00910i
\(430\) 2.07267e9 1.19666e9i 0.0606258 0.0350023i
\(431\) −1.19542e10 2.07053e10i −0.346428 0.600030i 0.639184 0.769054i \(-0.279272\pi\)
−0.985612 + 0.169023i \(0.945939\pi\)
\(432\) 3.14564e9 + 1.81614e9i 0.0903180 + 0.0521451i
\(433\) 2.55466e10i 0.726745i 0.931644 + 0.363372i \(0.118375\pi\)
−0.931644 + 0.363372i \(0.881625\pi\)
\(434\) 1.30457e10 + 9.36168e9i 0.367713 + 0.263873i
\(435\) 2.60321e9 0.0727031
\(436\) −3.67444e9 + 6.36432e9i −0.101682 + 0.176119i
\(437\) 6.50149e9 3.75364e9i 0.178274 0.102926i
\(438\) 2.37682e10 + 4.11677e10i 0.645803 + 1.11856i
\(439\) −4.07100e10 2.35039e10i −1.09608 0.632823i −0.160892 0.986972i \(-0.551437\pi\)
−0.935189 + 0.354149i \(0.884770\pi\)
\(440\) 8.57810e8i 0.0228866i
\(441\) −2.51428e10 5.03628e9i −0.664753 0.133154i
\(442\) −3.67500e10 −0.962872
\(443\) 1.48925e10 2.57945e10i 0.386681 0.669750i −0.605320 0.795982i \(-0.706955\pi\)
0.992001 + 0.126232i \(0.0402883\pi\)
\(444\) 6.64684e9 3.83755e9i 0.171034 0.0987467i
\(445\) 6.68301e8 + 1.15753e9i 0.0170425 + 0.0295184i
\(446\) 1.43170e10 + 8.26593e9i 0.361837 + 0.208907i
\(447\) 6.61030e10i 1.65574i
\(448\) 2.93567e9 4.09093e9i 0.0728778 0.101557i
\(449\) −6.09266e10 −1.49907 −0.749535 0.661965i \(-0.769723\pi\)
−0.749535 + 0.661965i \(0.769723\pi\)
\(450\) 9.79264e9 1.69614e10i 0.238809 0.413628i
\(451\) 6.57312e10 3.79499e10i 1.58879 0.917286i
\(452\) 4.02292e9 + 6.96791e9i 0.0963803 + 0.166936i
\(453\) −1.20436e10 6.95338e9i −0.285999 0.165121i
\(454\) 8.88319e9i 0.209096i
\(455\) −9.06807e8 2.00494e9i −0.0211577 0.0467795i
\(456\) −2.95017e9 −0.0682318
\(457\) −3.43113e10 + 5.94289e10i −0.786633 + 1.36249i 0.141385 + 0.989955i \(0.454844\pi\)
−0.928019 + 0.372534i \(0.878489\pi\)
\(458\) 2.09160e10 1.20758e10i 0.475353 0.274445i
\(459\) 1.49255e10 + 2.58518e10i 0.336263 + 0.582424i
\(460\) −1.62832e9 9.40109e8i −0.0363670 0.0209965i
\(461\) 5.86982e10i 1.29963i 0.760091 + 0.649817i \(0.225155\pi\)
−0.760091 + 0.649817i \(0.774845\pi\)
\(462\) −4.38556e9 + 4.42234e10i −0.0962625 + 0.970698i
\(463\) 4.40726e10 0.959058 0.479529 0.877526i \(-0.340808\pi\)
0.479529 + 0.877526i \(0.340808\pi\)
\(464\) 5.34998e9 9.26644e9i 0.115420 0.199913i
\(465\) −2.04056e9 + 1.17812e9i −0.0436453 + 0.0251986i
\(466\) −4.98780e9 8.63912e9i −0.105771 0.183200i
\(467\) −3.60907e10 2.08370e10i −0.758800 0.438094i 0.0700645 0.997542i \(-0.477679\pi\)
−0.828865 + 0.559449i \(0.811013\pi\)
\(468\) 1.37352e10i 0.286320i
\(469\) −8.48125e10 8.41071e9i −1.75295 0.173837i
\(470\) −9.79263e8 −0.0200682
\(471\) −4.75106e10 + 8.22907e10i −0.965398 + 1.67212i
\(472\) −1.70234e10 + 9.82846e9i −0.342987 + 0.198024i
\(473\) 4.34108e10 + 7.51898e10i 0.867268 + 1.50215i
\(474\) −3.72344e10 2.14973e10i −0.737617 0.425863i
\(475\) 7.55629e9i 0.148434i
\(476\) 3.77041e10 1.70530e10i 0.734447 0.332180i
\(477\) −1.75161e9 −0.0338348
\(478\) −6.22491e9 + 1.07819e10i −0.119240 + 0.206530i
\(479\) 2.94123e9 1.69812e9i 0.0558710 0.0322572i −0.471804 0.881703i \(-0.656397\pi\)
0.527675 + 0.849446i \(0.323064\pi\)
\(480\) 3.69439e8 + 6.39886e8i 0.00695949 + 0.0120542i
\(481\) −1.19394e10 6.89320e9i −0.223050 0.128778i
\(482\) 1.66382e10i 0.308261i
\(483\) 7.91396e10 + 5.67910e10i 1.45414 + 1.04350i
\(484\) 3.68058e9 0.0670710
\(485\) 8.37776e8 1.45107e9i 0.0151412 0.0262254i
\(486\) 3.96642e10 2.29002e10i 0.710974 0.410481i
\(487\) −5.44393e10 9.42917e10i −0.967825 1.67632i −0.701826 0.712349i \(-0.747631\pi\)
−0.265999 0.963973i \(-0.585702\pi\)
\(488\) 9.74243e9 + 5.62479e9i 0.171786 + 0.0991807i
\(489\) 3.39122e10i 0.593091i
\(490\) 1.86069e9 + 1.63620e9i 0.0322768 + 0.0283827i
\(491\) 1.75034e9 0.0301159 0.0150580 0.999887i \(-0.495207\pi\)
0.0150580 + 0.999887i \(0.495207\pi\)
\(492\) −3.26883e10 + 5.66177e10i −0.557868 + 0.966256i
\(493\) 7.61542e10 4.39676e10i 1.28916 0.744296i
\(494\) 2.64962e9 + 4.58927e9i 0.0444913 + 0.0770612i
\(495\) −2.28181e9 1.31740e9i −0.0380066 0.0219431i
\(496\) 9.68481e9i 0.160016i
\(497\) 4.95165e10 6.90025e10i 0.811568 1.13094i
\(498\) −2.79953e10 −0.455163
\(499\) −1.78791e10 + 3.09675e10i −0.288365 + 0.499463i −0.973420 0.229029i \(-0.926445\pi\)
0.685055 + 0.728492i \(0.259778\pi\)
\(500\) −3.28397e9 + 1.89600e9i −0.0525436 + 0.0303360i
\(501\) 3.57358e10 + 6.18963e10i 0.567222 + 0.982457i
\(502\) 9.70955e9 + 5.60581e9i 0.152892 + 0.0882721i
\(503\) 1.08232e11i 1.69077i −0.534155 0.845387i \(-0.679370\pi\)
0.534155 0.845387i \(-0.320630\pi\)
\(504\) −6.37350e9 1.40917e10i −0.0987771 0.218395i
\(505\) 4.55398e9 0.0700206
\(506\) 3.41040e10 5.90699e10i 0.520240 0.901082i
\(507\) −2.12407e10 + 1.22633e10i −0.321468 + 0.185599i
\(508\) −3.23402e10 5.60148e10i −0.485610 0.841101i
\(509\) −2.51632e10 1.45280e10i −0.374882 0.216438i 0.300707 0.953717i \(-0.402777\pi\)
−0.675589 + 0.737278i \(0.736111\pi\)
\(510\) 6.07230e9i 0.0897578i
\(511\) −9.48824e9 + 9.56782e10i −0.139156 + 1.40323i
\(512\) 3.03700e9 0.0441942
\(513\) 2.15221e9 3.72774e9i 0.0310753 0.0538240i
\(514\) 8.85313e9 5.11135e9i 0.126836 0.0732291i
\(515\) −3.92764e8 6.80287e8i −0.00558345 0.00967082i
\(516\) −6.47649e10 3.73920e10i −0.913568 0.527449i
\(517\) 3.55244e10i 0.497239i
\(518\) 1.54480e10 + 1.53195e9i 0.214562 + 0.0212777i
\(519\) 1.12612e11 1.55208
\(520\) 6.63604e8 1.14940e9i 0.00907602 0.0157201i
\(521\) −1.24290e11 + 7.17587e10i −1.68688 + 0.973920i −0.729995 + 0.683453i \(0.760477\pi\)
−0.956885 + 0.290467i \(0.906189\pi\)
\(522\) −1.64327e10 2.84623e10i −0.221324 0.383344i
\(523\) −6.16752e10 3.56082e10i −0.824335 0.475930i 0.0275739 0.999620i \(-0.491222\pi\)
−0.851909 + 0.523690i \(0.824555\pi\)
\(524\) 2.21713e10i 0.294081i
\(525\) 8.93316e10 4.04035e10i 1.17589 0.531841i
\(526\) −1.84686e10 −0.241263
\(527\) −3.97962e10 + 6.89291e10i −0.515941 + 0.893635i
\(528\) −2.32130e10 + 1.34020e10i −0.298672 + 0.172438i
\(529\) −3.55965e10 6.16549e10i −0.454553 0.787309i
\(530\) 1.46579e8 + 8.46276e7i 0.00185767 + 0.00107253i
\(531\) 6.03772e10i 0.759442i
\(532\) −4.84795e9 3.47891e9i −0.0605217 0.0434307i
\(533\) 1.17433e11 1.45506
\(534\) 2.08824e10 3.61694e10i 0.256812 0.444812i
\(535\) −4.47382e9 + 2.58296e9i −0.0546088 + 0.0315284i
\(536\) −2.57026e10 4.45183e10i −0.311400 0.539360i
\(537\) 4.06152e10 + 2.34492e10i 0.488418 + 0.281988i
\(538\) 1.32162e10i 0.157753i
\(539\) −5.93561e10 + 6.74998e10i −0.703250 + 0.799738i
\(540\) −1.07805e9 −0.0126784
\(541\) 4.48466e10 7.76767e10i 0.523529 0.906779i −0.476096 0.879393i \(-0.657948\pi\)
0.999625 0.0273857i \(-0.00871823\pi\)
\(542\) 4.21344e10 2.43263e10i 0.488247 0.281890i
\(543\) 2.34801e10 + 4.06687e10i 0.270085 + 0.467800i
\(544\) 2.16151e10 + 1.24795e10i 0.246809 + 0.142495i
\(545\) 2.18114e9i 0.0247228i
\(546\) −4.00876e10 + 5.58630e10i −0.451065 + 0.628570i
\(547\) 8.66476e10 0.967848 0.483924 0.875110i \(-0.339211\pi\)
0.483924 + 0.875110i \(0.339211\pi\)
\(548\) −1.10913e10 + 1.92106e10i −0.122987 + 0.213019i
\(549\) 2.99243e10 1.72768e10i 0.329409 0.190184i
\(550\) −3.43267e10 5.94556e10i −0.375129 0.649743i
\(551\) −1.09812e10 6.33999e9i −0.119136 0.0687831i
\(552\) 5.87512e10i 0.632791i
\(553\) −3.58364e10 7.92338e10i −0.383198 0.847247i
\(554\) 8.40752e10 0.892542
\(555\) −1.13898e9 + 1.97277e9i −0.0120045 + 0.0207924i
\(556\) 5.34566e10 3.08632e10i 0.559374 0.322955i
\(557\) 3.55004e10 + 6.14884e10i 0.368818 + 0.638811i 0.989381 0.145345i \(-0.0464293\pi\)
−0.620563 + 0.784156i \(0.713096\pi\)
\(558\) 2.57620e10 + 1.48737e10i 0.265731 + 0.153420i
\(559\) 1.34331e11i 1.37571i
\(560\) −1.47480e8 + 1.48716e9i −0.00149961 + 0.0151219i
\(561\) −2.20283e11 −2.22397
\(562\) −6.46024e10 + 1.11895e11i −0.647595 + 1.12167i
\(563\) −1.38669e11 + 8.00603e10i −1.38021 + 0.796863i −0.992184 0.124786i \(-0.960175\pi\)
−0.388024 + 0.921649i \(0.626842\pi\)
\(564\) 1.52995e10 + 2.64996e10i 0.151203 + 0.261892i
\(565\) −2.06807e9 1.19400e9i −0.0202941 0.0117168i
\(566\) 2.34163e10i 0.228167i
\(567\) 1.25306e11 + 1.24264e10i 1.21238 + 0.120230i
\(568\) 5.12257e10 0.492147
\(569\) 4.05505e10 7.02356e10i 0.386854 0.670052i −0.605170 0.796096i \(-0.706895\pi\)
0.992025 + 0.126045i \(0.0402282\pi\)
\(570\) 7.58296e8 4.37803e8i 0.00718356 0.00414743i
\(571\) −2.86381e10 4.96026e10i −0.269401 0.466616i 0.699306 0.714822i \(-0.253492\pi\)
−0.968707 + 0.248206i \(0.920159\pi\)
\(572\) 4.16963e10 + 2.40733e10i 0.389505 + 0.224881i
\(573\) 8.25203e9i 0.0765495i
\(574\) −1.20481e11 + 5.44919e10i −1.10987 + 0.501978i
\(575\) −1.50480e11 −1.37660
\(576\) 4.66415e9 8.07854e9i 0.0423723 0.0733910i
\(577\) −8.57413e9 + 4.95028e9i −0.0773547 + 0.0446608i −0.538178 0.842831i \(-0.680887\pi\)
0.460824 + 0.887492i \(0.347554\pi\)
\(578\) 6.30988e10 + 1.09290e11i 0.565340 + 0.979197i
\(579\) −1.25479e11 7.24454e10i −1.11650 0.644609i
\(580\) 3.17573e9i 0.0280629i
\(581\) −4.60041e10 3.30127e10i −0.403731 0.289719i
\(582\) −5.23560e10 −0.456325
\(583\) −3.07001e9 + 5.31741e9i −0.0265745 + 0.0460284i
\(584\) −5.02217e10 + 2.89955e10i −0.431758 + 0.249275i
\(585\) −2.03829e9 3.53042e9i −0.0174037 0.0301442i
\(586\) 7.46256e10 + 4.30851e10i 0.632845 + 0.365373i
\(587\) 1.86462e11i 1.57050i −0.619181 0.785249i \(-0.712535\pi\)
0.619181 0.785249i \(-0.287465\pi\)
\(588\) 1.52063e10 7.59150e10i 0.127208 0.635065i
\(589\) 1.14770e10 0.0953600
\(590\) 2.91707e9 5.05252e9i 0.0240735 0.0416965i
\(591\) 7.12490e10 4.11356e10i 0.584021 0.337185i
\(592\) 4.68154e9 + 8.10867e9i 0.0381155 + 0.0660181i
\(593\) 1.37576e11 + 7.94296e10i 1.11256 + 0.642338i 0.939492 0.342571i \(-0.111298\pi\)
0.173071 + 0.984909i \(0.444631\pi\)
\(594\) 3.91083e10i 0.314140i
\(595\) −7.16061e9 + 9.97849e9i −0.0571324 + 0.0796153i
\(596\) 8.06410e10 0.639103
\(597\) 1.19198e11 2.06457e11i 0.938364 1.62529i
\(598\) 9.13932e10 5.27659e10i 0.714676 0.412618i
\(599\) 5.16598e10 + 8.94774e10i 0.401278 + 0.695034i 0.993880 0.110461i \(-0.0352328\pi\)
−0.592602 + 0.805495i \(0.701899\pi\)
\(600\) 5.12122e10 + 2.95674e10i 0.395156 + 0.228143i
\(601\) 1.71095e9i 0.0131142i −0.999979 0.00655708i \(-0.997913\pi\)
0.999979 0.00655708i \(-0.00208720\pi\)
\(602\) −6.23332e10 1.37818e11i −0.474606 1.04935i
\(603\) −1.57894e11 −1.19425
\(604\) 8.48263e9 1.46923e10i 0.0637357 0.110393i
\(605\) −9.46039e8 + 5.46196e8i −0.00706135 + 0.00407687i
\(606\) −7.11492e10 1.23234e11i −0.527569 0.913776i
\(607\) 2.14248e11 + 1.23696e11i 1.57820 + 0.911174i 0.995111 + 0.0987661i \(0.0314896\pi\)
0.583089 + 0.812408i \(0.301844\pi\)
\(608\) 3.59899e9i 0.0263370i
\(609\) 1.62360e10 1.63721e11i 0.118034 1.19024i
\(610\) −3.33886e9 −0.0241145
\(611\) 2.74818e10 4.75998e10i 0.197188 0.341539i
\(612\) 6.63917e10 3.83313e10i 0.473269 0.273242i
\(613\) 7.81112e10 + 1.35293e11i 0.553186 + 0.958147i 0.998042 + 0.0625445i \(0.0199215\pi\)
−0.444856 + 0.895602i \(0.646745\pi\)
\(614\) 1.30397e10 + 7.52846e9i 0.0917472 + 0.0529703i
\(615\) 1.94037e10i 0.135639i
\(616\) −5.39494e10 5.35007e9i −0.374683 0.0371567i
\(617\) −1.94981e11 −1.34540 −0.672700 0.739916i \(-0.734865\pi\)
−0.672700 + 0.739916i \(0.734865\pi\)
\(618\) −1.22727e10 + 2.12569e10i −0.0841369 + 0.145729i
\(619\) 1.04394e11 6.02720e10i 0.711072 0.410538i −0.100386 0.994949i \(-0.532008\pi\)
0.811458 + 0.584411i \(0.198674\pi\)
\(620\) −1.43722e9 2.48934e9i −0.00972650 0.0168468i
\(621\) −7.42362e10 4.28603e10i −0.499171 0.288197i
\(622\) 6.90919e10i 0.461600i
\(623\) 7.69676e10 3.48114e10i 0.510923 0.231084i
\(624\) −4.14713e10 −0.273533
\(625\) −7.54493e10 + 1.30682e11i −0.494465 + 0.856438i
\(626\) −8.88235e10 + 5.12823e10i −0.578403 + 0.333941i
\(627\) 1.58820e10 + 2.75085e10i 0.102763 + 0.177990i
\(628\) −1.00389e11 5.79595e10i −0.645426 0.372637i
\(629\) 7.69484e10i 0.491583i
\(630\) 3.72942e9 + 2.67625e9i 0.0236744 + 0.0169889i
\(631\) 9.17945e10 0.579028 0.289514 0.957174i \(-0.406506\pi\)
0.289514 + 0.957174i \(0.406506\pi\)
\(632\) 2.62252e10 4.54233e10i 0.164380 0.284715i
\(633\) −2.70542e11 + 1.56198e11i −1.68508 + 0.972882i
\(634\) 1.42905e10 + 2.47519e10i 0.0884486 + 0.153197i
\(635\) 1.66251e10 + 9.59852e9i 0.102252 + 0.0590350i
\(636\) 5.28872e9i 0.0323238i
\(637\) −1.31750e11 + 4.45263e10i −0.800191 + 0.270432i
\(638\) −1.15205e11 −0.695327
\(639\) 7.86711e10 1.36262e11i 0.471859 0.817283i
\(640\) −7.80616e8 + 4.50689e8i −0.00465283 + 0.00268631i
\(641\) 3.30840e10 + 5.73032e10i 0.195968 + 0.339427i 0.947218 0.320592i \(-0.103882\pi\)
−0.751249 + 0.660019i \(0.770548\pi\)
\(642\) 1.39793e11 + 8.07098e10i 0.822899 + 0.475101i
\(643\) 6.09339e10i 0.356464i 0.983989 + 0.178232i \(0.0570377\pi\)
−0.983989 + 0.178232i \(0.942962\pi\)
\(644\) −6.92809e10 + 9.65447e10i −0.402782 + 0.561287i
\(645\) 2.21958e10 0.128243
\(646\) 1.47888e10 2.56149e10i 0.0849184 0.147083i
\(647\) −1.73942e11 + 1.00425e11i −0.992627 + 0.573094i −0.906059 0.423152i \(-0.860924\pi\)
−0.0865686 + 0.996246i \(0.527590\pi\)
\(648\) 3.79744e10 + 6.57735e10i 0.215373 + 0.373036i
\(649\) 1.83289e11 + 1.05822e11i 1.03313 + 0.596480i
\(650\) 1.06221e11i 0.595053i
\(651\) 6.13674e10 + 1.35683e11i 0.341675 + 0.755441i
\(652\) 4.13705e10 0.228929
\(653\) 1.46187e11 2.53203e11i 0.804000 1.39257i −0.112964 0.993599i \(-0.536034\pi\)
0.916964 0.398970i \(-0.130632\pi\)
\(654\) −5.90231e10 + 3.40770e10i −0.322635 + 0.186273i
\(655\) −3.29021e9 5.69881e9i −0.0178755 0.0309613i
\(656\) −6.90696e10 3.98774e10i −0.372968 0.215333i
\(657\) 1.78122e11i 0.955997i
\(658\) −6.10756e9 + 6.15878e10i −0.0325810 + 0.328542i
\(659\) 1.36692e11 0.724771 0.362386 0.932028i \(-0.381962\pi\)
0.362386 + 0.932028i \(0.381962\pi\)
\(660\) 3.97770e9 6.88957e9i 0.0209631 0.0363092i
\(661\) 1.34976e11 7.79281e10i 0.707048 0.408215i −0.102919 0.994690i \(-0.532818\pi\)
0.809967 + 0.586475i \(0.199485\pi\)
\(662\) −9.21748e10 1.59651e11i −0.479933 0.831268i
\(663\) −2.95161e11 1.70411e11i −1.52758 0.881950i
\(664\) 3.41522e10i 0.175690i
\(665\) 1.76236e9 + 1.74770e8i 0.00901173 + 0.000893678i
\(666\) 2.87592e10 0.146177
\(667\) −1.26258e11 + 2.18685e11i −0.637904 + 1.10488i
\(668\) −7.55090e10 + 4.35952e10i −0.379222 + 0.218944i
\(669\) 7.66588e10 + 1.32777e11i 0.382699 + 0.662855i
\(670\) 1.32130e10 + 7.62851e9i 0.0655694 + 0.0378565i
\(671\) 1.21123e11i 0.597497i
\(672\) 4.25479e10 1.92438e10i 0.208642 0.0943657i
\(673\) 5.07973e10 0.247617 0.123808 0.992306i \(-0.460489\pi\)
0.123808 + 0.992306i \(0.460489\pi\)
\(674\) −6.69874e9 + 1.16026e10i −0.0324604 + 0.0562230i
\(675\) −7.47209e10 + 4.31401e10i −0.359937 + 0.207810i
\(676\) −1.49604e10 2.59122e10i −0.0716401 0.124084i
\(677\) 1.62600e11 + 9.38771e10i 0.774044 + 0.446895i 0.834315 0.551288i \(-0.185863\pi\)
−0.0602713 + 0.998182i \(0.519197\pi\)
\(678\) 7.46178e10i 0.353121i
\(679\) −8.60355e10 6.17395e10i −0.404761 0.290459i
\(680\) −7.40777e9 −0.0346459
\(681\) −4.11917e10 + 7.13460e10i −0.191523 + 0.331727i
\(682\) 9.03049e10 5.21376e10i 0.417421 0.240998i
\(683\) −1.04863e11 1.81628e11i −0.481879 0.834639i 0.517904 0.855439i \(-0.326712\pi\)
−0.999784 + 0.0207991i \(0.993379\pi\)
\(684\) −9.57346e9 5.52724e9i −0.0437365 0.0252513i
\(685\) 6.58374e9i 0.0299027i
\(686\) 1.14509e11 1.06818e11i 0.517063 0.482334i
\(687\) 2.23984e11 1.00552
\(688\) 4.56156e10 7.90086e10i 0.203592 0.352631i
\(689\) −8.22712e9 + 4.74993e9i −0.0365066 + 0.0210771i
\(690\) −8.71864e9 1.51011e10i −0.0384638 0.0666213i
\(691\) 2.11477e11 + 1.22096e11i 0.927577 + 0.535537i 0.886044 0.463600i \(-0.153443\pi\)
0.0415327 + 0.999137i \(0.486776\pi\)
\(692\) 1.37378e11i 0.599093i
\(693\) −9.70855e10 + 1.35291e11i −0.420941 + 0.586592i
\(694\) 2.34135e10 0.100932
\(695\) −9.16016e9 + 1.58659e10i −0.0392612 + 0.0680024i
\(696\) 8.59376e10 4.96161e10i 0.366224 0.211439i
\(697\) −3.27723e11 5.67633e11i −1.38860 2.40512i
\(698\) −1.92078e11 1.10897e11i −0.809202 0.467193i
\(699\) 9.25144e10i 0.387526i
\(700\) 4.92894e10 + 1.08978e11i 0.205287 + 0.453887i
\(701\) 2.65250e11 1.09846 0.549228 0.835672i \(-0.314922\pi\)
0.549228 + 0.835672i \(0.314922\pi\)
\(702\) 3.02542e10 5.24018e10i 0.124577 0.215773i
\(703\) 9.60916e9 5.54785e9i 0.0393427 0.0227145i
\(704\) −1.63495e10 2.83182e10i −0.0665601 0.115285i
\(705\) −7.86503e9 4.54088e9i −0.0318379 0.0183816i
\(706\) 8.04471e10i 0.323811i
\(707\) 2.84027e10 2.86409e11i 0.113679 1.14633i
\(708\) −1.82300e11 −0.725526
\(709\) −4.18040e10 + 7.24067e10i −0.165437 + 0.286546i −0.936810 0.349837i \(-0.886237\pi\)
0.771373 + 0.636383i \(0.219570\pi\)
\(710\) −1.31668e10 + 7.60186e9i −0.0518140 + 0.0299148i
\(711\) −8.05518e10 1.39520e11i −0.315208 0.545956i
\(712\) 4.41241e10 + 2.54751e10i 0.171694 + 0.0991278i
\(713\) 2.28559e11i 0.884381i
\(714\) 3.81899e11 + 3.78723e10i 1.46945 + 0.145723i
\(715\) −1.42899e10 −0.0546769
\(716\) −2.86064e10 + 4.95477e10i −0.108846 + 0.188526i
\(717\) −9.99918e10 + 5.77303e10i −0.378345 + 0.218437i
\(718\) 8.74767e10 + 1.51514e11i 0.329151 + 0.570106i
\(719\) −4.20241e11 2.42626e11i −1.57247 0.907868i −0.995865 0.0908469i \(-0.971043\pi\)
−0.576608 0.817021i \(-0.695624\pi\)
\(720\) 2.76863e9i 0.0103023i
\(721\) −4.52342e10 + 2.04588e10i −0.167389 + 0.0757076i
\(722\) 1.87882e11 0.691412
\(723\) −7.71520e10 + 1.33631e11i −0.282354 + 0.489052i
\(724\) −4.96129e10 + 2.86440e10i −0.180568 + 0.104251i
\(725\) 1.27082e11 + 2.20113e11i 0.459973 + 0.796697i
\(726\) 2.95609e10 + 1.70670e10i 0.106407 + 0.0614342i
\(727\) 8.33994e10i 0.298556i 0.988795 + 0.149278i \(0.0476949\pi\)
−0.988795 + 0.149278i \(0.952305\pi\)
\(728\) −6.81489e10 4.89040e10i −0.242624 0.174108i
\(729\) 8.06626e10 0.285603
\(730\) 8.60583e9 1.49057e10i 0.0303041 0.0524882i
\(731\) 6.49314e11 3.74882e11i 2.27397 1.31288i
\(732\) 5.21647e10 + 9.03520e10i 0.181691 + 0.314698i
\(733\) −4.29858e11 2.48179e11i −1.48905 0.859703i −0.489127 0.872212i \(-0.662685\pi\)
−0.999922 + 0.0125096i \(0.996018\pi\)
\(734\) 2.71405e11i 0.935048i
\(735\) 7.35719e9 + 2.17694e10i 0.0252094 + 0.0745929i
\(736\) −7.16723e10 −0.244253
\(737\) −2.76737e11 + 4.79322e11i −0.937988 + 1.62464i
\(738\) −2.12151e11 + 1.22485e11i −0.715186 + 0.412913i
\(739\) 1.27525e11 + 2.20881e11i 0.427582 + 0.740593i 0.996658 0.0816918i \(-0.0260323\pi\)
−0.569076 + 0.822285i \(0.692699\pi\)
\(740\) −2.40664e9 1.38948e9i −0.00802573 0.00463366i
\(741\) 4.91455e10i 0.163009i
\(742\) 6.23660e9 8.69085e9i 0.0205746 0.0286712i
\(743\) −3.20873e11 −1.05288 −0.526439 0.850213i \(-0.676473\pi\)
−0.526439 + 0.850213i \(0.676473\pi\)
\(744\) −4.49088e10 + 7.77844e10i −0.146568 + 0.253864i
\(745\) −2.07276e10 + 1.19671e10i −0.0672858 + 0.0388475i
\(746\) 2.09637e11 + 3.63102e11i 0.676882 + 1.17239i
\(747\) −9.08463e10 5.24501e10i −0.291759 0.168447i
\(748\) 2.68729e11i 0.858438i
\(749\) 1.34545e11 + 2.97477e11i 0.427503 + 0.945204i
\(750\) −3.51673e10 −0.111146
\(751\) −9.00753e10 + 1.56015e11i −0.283169 + 0.490463i −0.972164 0.234303i \(-0.924719\pi\)
0.688994 + 0.724767i \(0.258052\pi\)
\(752\) −3.23276e10 + 1.86643e10i −0.101089 + 0.0583635i
\(753\) 5.19887e10 + 9.00471e10i 0.161707 + 0.280085i
\(754\) −1.54365e11 8.91229e10i −0.477600 0.275743i
\(755\) 5.03527e9i 0.0154965i
\(756\) −6.72371e9 + 6.78010e10i −0.0205836 + 0.207562i
\(757\) −5.54116e10 −0.168740 −0.0843698 0.996435i \(-0.526888\pi\)
−0.0843698 + 0.996435i \(0.526888\pi\)
\(758\) −2.34729e10 + 4.06562e10i −0.0711033 + 0.123155i
\(759\) 5.47819e11 3.16283e11i 1.65071 0.953036i
\(760\) 5.34088e8 + 9.25067e8i 0.00160088 + 0.00277280i
\(761\) 3.90637e11 + 2.25535e11i 1.16476 + 0.672472i 0.952439 0.304728i \(-0.0985657\pi\)
0.212317 + 0.977201i \(0.431899\pi\)
\(762\) 5.99850e11i 1.77919i
\(763\) −1.37176e11 1.36035e10i −0.404744 0.0401378i
\(764\) 1.00669e10 0.0295476
\(765\) −1.13767e10 + 1.97050e10i −0.0332177 + 0.0575347i
\(766\) 2.06443e11 1.19190e11i 0.599632 0.346198i
\(767\) 1.63728e11 + 2.83585e11i 0.473087 + 0.819410i
\(768\) 2.43919e10 + 1.40827e10i 0.0701134 + 0.0404800i
\(769\) 2.81725e11i 0.805600i 0.915288 + 0.402800i \(0.131963\pi\)
−0.915288 + 0.402800i \(0.868037\pi\)
\(770\) 1.46608e10 6.63090e9i 0.0417057 0.0188629i
\(771\) 9.48062e10 0.268299
\(772\) 8.83782e10 1.53076e11i 0.248815 0.430960i
\(773\) −2.50780e11 + 1.44788e11i −0.702383 + 0.405521i −0.808234 0.588861i \(-0.799577\pi\)
0.105851 + 0.994382i \(0.466243\pi\)
\(774\) −1.40111e11 2.42679e11i −0.390398 0.676188i
\(775\) −1.99230e11 1.15025e11i −0.552265 0.318850i
\(776\) 6.38706e10i 0.176138i
\(777\) 1.16968e11 + 8.39367e10i 0.320909 + 0.230286i
\(778\) −2.00175e11 −0.546375
\(779\) −4.72566e10 + 8.18508e10i −0.128325 + 0.222266i
\(780\) 1.06596e10 6.15431e9i 0.0287979 0.0166265i
\(781\) −2.75770e11 4.77648e11i −0.741213 1.28382i
\(782\) −5.10109e11 2.94511e11i −1.36407 0.787544i
\(783\) 1.44784e11i 0.385189i
\(784\) 9.26109e10 + 1.85506e10i 0.245131 + 0.0491013i
\(785\) 3.44046e10 0.0906020
\(786\) −1.02809e11 + 1.78071e11i −0.269365 + 0.466555i
\(787\) 4.10914e11 2.37241e11i 1.07115 0.618431i 0.142658 0.989772i \(-0.454435\pi\)
0.928497 + 0.371341i \(0.121102\pi\)
\(788\) 5.01825e10 + 8.69187e10i 0.130151 + 0.225428i
\(789\) −1.48332e11 8.56395e10i −0.382760 0.220987i
\(790\) 1.55672e10i 0.0399670i
\(791\) −8.79912e10 + 1.22618e11i −0.224767 + 0.313219i
\(792\) −1.00437e11 −0.255265
\(793\) 9.37009e10 1.62295e11i 0.236947 0.410404i
\(794\) −3.56073e11 + 2.05579e11i −0.895894 + 0.517245i
\(795\) 7.84842e8 + 1.35939e9i 0.00196478 + 0.00340310i
\(796\) 2.51863e11 + 1.45413e11i 0.627353 + 0.362202i
\(797\) 8.62187e10i 0.213682i 0.994276 + 0.106841i \(0.0340736\pi\)
−0.994276 + 0.106841i \(0.965926\pi\)
\(798\) −2.28049e10 5.04213e10i −0.0562362 0.124338i
\(799\) −3.06777e11 −0.752725
\(800\) −3.60701e10 + 6.24753e10i −0.0880618 + 0.152527i
\(801\) 1.35529e11 7.82479e10i 0.329233 0.190083i
\(802\) 7.55887e10 + 1.30923e11i 0.182709 + 0.316461i
\(803\) 5.40730e11 + 3.12191e11i 1.30052 + 0.750858i
\(804\) 4.76736e11i 1.14092i
\(805\) 3.48047e9 3.50966e10i 0.00828810 0.0835760i
\(806\) 1.61335e11 0.382286
\(807\) 6.12841e10 1.06147e11i 0.144495 0.250273i
\(808\) 1.50337e11 8.67969e10i 0.352711 0.203638i
\(809\) −2.07528e11 3.59449e11i −0.484488 0.839158i 0.515353 0.856978i \(-0.327661\pi\)
−0.999841 + 0.0178202i \(0.994327\pi\)
\(810\) −1.95215e10 1.12707e10i −0.0453495 0.0261826i
\(811\) 1.55490e11i 0.359435i −0.983718 0.179717i \(-0.942482\pi\)
0.983718 0.179717i \(-0.0575183\pi\)
\(812\) 1.99728e11 + 1.98067e10i 0.459426 + 0.0455605i
\(813\) 4.51208e11 1.03280
\(814\) 5.04056e10 8.73050e10i 0.114810 0.198857i
\(815\) −1.06337e10 + 6.13936e9i −0.0241020 + 0.0139153i
\(816\) 1.15735e11 + 2.00460e11i 0.261039 + 0.452133i
\(817\) −9.36290e10 5.40567e10i −0.210146 0.121328i
\(818\) 1.13929e10i 0.0254461i
\(819\) −2.34748e11 + 1.06173e11i −0.521754 + 0.235982i
\(820\) 2.36711e10 0.0523556
\(821\) 2.57357e11 4.45756e11i 0.566453 0.981125i −0.430460 0.902610i \(-0.641649\pi\)
0.996913 0.0785156i \(-0.0250180\pi\)
\(822\) −1.78161e11 + 1.02861e11i −0.390233 + 0.225301i
\(823\) −2.04046e11 3.53418e11i −0.444763 0.770352i 0.553273 0.833000i \(-0.313379\pi\)
−0.998036 + 0.0626483i \(0.980045\pi\)
\(824\) −2.59320e10 1.49718e10i −0.0562505 0.0324762i
\(825\) 6.36696e11i 1.37441i
\(826\) −2.99569e11 2.14972e11i −0.643542 0.461809i
\(827\) −4.64921e11 −0.993933 −0.496966 0.867770i \(-0.665553\pi\)
−0.496966 + 0.867770i \(0.665553\pi\)
\(828\) −1.10072e11 + 1.90651e11i −0.234184 + 0.405619i
\(829\) 8.50589e10 4.91088e10i 0.180095 0.103978i −0.407242 0.913320i \(-0.633510\pi\)
0.587337 + 0.809342i \(0.300176\pi\)
\(830\) 5.06817e9 + 8.77833e9i 0.0106792 + 0.0184969i
\(831\) 6.75257e11 + 3.89860e11i 1.41601 + 0.817531i
\(832\) 5.05920e10i 0.105582i
\(833\) 5.82907e11 + 5.12580e11i 1.21065 + 1.06459i
\(834\) 5.72455e11 1.18325
\(835\) 1.29390e10 2.24110e10i 0.0266167 0.0461015i
\(836\) −3.35584e10 + 1.93749e10i −0.0687030 + 0.0396657i
\(837\) −6.55240e10 1.13491e11i −0.133505 0.231238i
\(838\) 1.87746e11 + 1.08395e11i 0.380711 + 0.219804i
\(839\) 2.57355e11i 0.519379i 0.965692 + 0.259690i \(0.0836202\pi\)
−0.965692 + 0.259690i \(0.916380\pi\)
\(840\) −8.08053e9 + 1.12604e10i −0.0162302 + 0.0226171i
\(841\) −7.37408e10 −0.147409
\(842\) 9.07845e10 1.57243e11i 0.180619 0.312841i
\(843\) −1.03772e12 + 5.99128e11i −2.05480 + 1.18634i
\(844\) −1.90550e11 3.30043e11i −0.375526 0.650429i
\(845\) 7.69070e9 + 4.44023e9i 0.0150848 + 0.00870920i
\(846\) 1.14657e11i 0.223830i
\(847\) 2.84510e10 + 6.29048e10i 0.0552795 + 0.122222i
\(848\) 6.45186e9 0.0124768
\(849\) −1.08582e11 + 1.88070e11i −0.208991 + 0.361983i
\(850\) −5.13439e11 + 2.96434e11i −0.983588 + 0.567875i
\(851\) −1.10483e11 1.91362e11i −0.210658 0.364870i
\(852\) 4.11423e11 + 2.37535e11i 0.780783 + 0.450786i
\(853\) 7.12644e11i 1.34610i 0.739598 + 0.673049i \(0.235016\pi\)
−0.739598 + 0.673049i \(0.764984\pi\)
\(854\) −2.08241e10 + 2.09988e11i −0.0391503 + 0.394786i
\(855\) 3.28095e9 0.00613954
\(856\) −9.84602e10 + 1.70538e11i −0.183386 + 0.317633i
\(857\) 7.02742e11 4.05728e11i 1.30278 0.752163i 0.321903 0.946773i \(-0.395677\pi\)
0.980881 + 0.194610i \(0.0623442\pi\)
\(858\) 2.23258e11 + 3.86694e11i 0.411963 + 0.713540i
\(859\) −1.69870e11 9.80744e10i −0.311992 0.180129i 0.335826 0.941924i \(-0.390985\pi\)
−0.647818 + 0.761796i \(0.724318\pi\)
\(860\) 2.70773e10i 0.0495007i
\(861\) −1.22033e12 1.21019e11i −2.22058 0.220211i
\(862\) 2.70493e11 0.489923
\(863\) −3.83209e10 + 6.63738e10i −0.0690864 + 0.119661i −0.898499 0.438975i \(-0.855342\pi\)
0.829413 + 0.558636i \(0.188675\pi\)
\(864\) −3.55889e10 + 2.05473e10i −0.0638645 + 0.0368722i
\(865\) −2.03869e10 3.53111e10i −0.0364155 0.0630735i
\(866\) −2.50305e11 1.44513e11i −0.445038 0.256943i
\(867\) 1.17037e12i 2.07131i
\(868\) −1.65523e11 + 7.48639e10i −0.291595 + 0.131884i
\(869\) −5.64726e11 −0.990281
\(870\) −1.47260e10 + 2.55062e10i −0.0257044 + 0.0445213i
\(871\) −7.41609e11 + 4.28168e11i −1.28855 + 0.743947i
\(872\) −4.15715e10 7.20040e10i −0.0719002 0.124535i
\(873\) −1.69898e11 9.80908e10i −0.292504 0.168877i
\(874\) 8.49351e10i 0.145560i
\(875\) −5.77898e10 4.14702e10i −0.0985868 0.0707464i
\(876\) −5.37813e11 −0.913303
\(877\) 3.20076e11 5.54389e11i 0.541072 0.937165i −0.457771 0.889070i \(-0.651352\pi\)
0.998843 0.0480942i \(-0.0153148\pi\)
\(878\) 4.60581e11 2.65916e11i 0.775046 0.447473i
\(879\) 3.99575e11 + 6.92084e11i 0.669333 + 1.15932i
\(880\) 8.40479e9 + 4.85251e9i 0.0140151 + 0.00809162i
\(881\) 8.09070e11i 1.34302i −0.740996 0.671510i \(-0.765646\pi\)
0.740996 0.671510i \(-0.234354\pi\)
\(882\) 1.91575e11 2.17859e11i 0.316566 0.359999i
\(883\) 3.24834e11 0.534341 0.267171 0.963649i \(-0.413911\pi\)
0.267171 + 0.963649i \(0.413911\pi\)
\(884\) 2.07890e11 3.60075e11i 0.340427 0.589636i
\(885\) 4.68574e10 2.70531e10i 0.0763845 0.0441006i
\(886\) 1.68489e11 + 2.91832e11i 0.273424 + 0.473585i
\(887\) −3.16246e11 1.82585e11i −0.510894 0.294965i 0.222307 0.974977i \(-0.428641\pi\)
−0.733201 + 0.680012i \(0.761975\pi\)
\(888\) 8.68339e10i 0.139649i
\(889\) 7.07359e11 9.85722e11i 1.13249 1.57815i
\(890\) −1.51219e10 −0.0241017
\(891\) 4.08865e11 7.08175e11i 0.648738 1.12365i
\(892\) −1.61978e11 + 9.35183e10i −0.255857 + 0.147719i
\(893\) 2.21181e10 + 3.83097e10i 0.0347811 + 0.0602425i
\(894\) 6.47675e11 + 3.73935e11i 1.01393 + 0.585391i
\(895\) 1.69807e10i 0.0264644i
\(896\) 2.34761e10 + 5.19054e10i 0.0364245 + 0.0805342i
\(897\) 9.78709e11 1.51176
\(898\) 3.44653e11 5.96957e11i 0.530001 0.917989i
\(899\) −3.34322e11 + 1.93021e11i −0.511830 + 0.295505i
\(900\) 1.10791e11 + 1.91896e11i 0.168863 + 0.292479i
\(901\) 4.59194e10 + 2.65116e10i 0.0696783 + 0.0402288i
\(902\) 8.58709e11i 1.29724i
\(903\) 1.38433e11 1.39594e12i 0.208204 2.09950i
\(904\) −9.10284e10 −0.136302
\(905\) 8.50150e9 1.47250e10i 0.0126736 0.0219514i
\(906\) 1.36258e11 7.86685e10i 0.202232 0.116758i
\(907\) 2.49774e11 + 4.32622e11i 0.369078 + 0.639263i 0.989422 0.145068i \(-0.0463400\pi\)
−0.620343 + 0.784330i \(0.713007\pi\)
\(908\) −8.70371e10 5.02509e10i −0.128045 0.0739265i
\(909\) 5.33202e11i 0.780973i
\(910\) 2.47740e10 + 2.45679e9i 0.0361269 + 0.00358264i
\(911\) 8.72045e10 0.126609 0.0633046 0.997994i \(-0.479836\pi\)
0.0633046 + 0.997994i \(0.479836\pi\)
\(912\) 1.66887e10 2.89056e10i 0.0241236 0.0417833i
\(913\) −3.18449e11 + 1.83856e11i −0.458307 + 0.264604i
\(914\) −3.88188e11 6.72361e11i −0.556234 0.963425i
\(915\) −2.68163e10 1.54824e10i −0.0382574 0.0220879i
\(916\) 2.73245e11i 0.388124i
\(917\) −3.78930e11 + 1.71385e11i −0.535897 + 0.242379i
\(918\) −3.37726e11 −0.475548
\(919\) −1.50979e11 + 2.61504e11i −0.211668 + 0.366620i −0.952237 0.305361i \(-0.901223\pi\)
0.740568 + 0.671981i \(0.234556\pi\)
\(920\) 1.84223e10 1.06361e10i 0.0257154 0.0148468i
\(921\) 6.98194e10 + 1.20931e11i 0.0970371 + 0.168073i
\(922\) −5.75123e11 3.32047e11i −0.795860 0.459490i
\(923\) 8.53345e11i 1.17576i
\(924\) −4.08490e11 2.93135e11i −0.560395 0.402142i
\(925\) −2.22409e11 −0.303798
\(926\) −2.49312e11 + 4.31822e11i −0.339078 + 0.587301i
\(927\) −7.96513e10 + 4.59867e10i −0.107863 + 0.0622749i
\(928\) 6.05281e10 + 1.04838e11i 0.0816141 + 0.141360i
\(929\) 4.35609e11 + 2.51499e11i 0.584835 + 0.337655i 0.763053 0.646336i \(-0.223700\pi\)
−0.178217 + 0.983991i \(0.557033\pi\)
\(930\) 2.66578e10i 0.0356362i
\(931\) 2.19833e10 1.09748e11i 0.0292613 0.146083i
\(932\) 1.12861e11 0.149582
\(933\) −3.20382e11 + 5.54917e11i −0.422806 + 0.732321i
\(934\) 4.08319e11 2.35743e11i 0.536553 0.309779i
\(935\) 3.98793e10 + 6.90729e10i 0.0521796 + 0.0903777i
\(936\) −1.34577e11 7.76979e10i −0.175334 0.101229i
\(937\) 1.22221e12i 1.58557i 0.609499 + 0.792787i \(0.291371\pi\)
−0.609499 + 0.792787i \(0.708629\pi\)
\(938\) 5.62180e11 7.83411e11i 0.726213 1.01199i
\(939\) −9.51191e11 −1.22350
\(940\) 5.53955e9 9.59478e9i 0.00709517 0.0122892i
\(941\) −3.75495e10 + 2.16792e10i −0.0478902 + 0.0276494i −0.523754 0.851870i \(-0.675469\pi\)
0.475864 + 0.879519i \(0.342136\pi\)
\(942\) −5.37521e11 9.31013e11i −0.682640 1.18237i
\(943\) 1.63002e12 + 9.41093e11i 2.06133 + 1.19011i
\(944\) 2.22393e11i 0.280048i
\(945\) −8.33339e9 1.84250e10i −0.0104495 0.0231037i
\(946\) −9.82275e11 −1.22650
\(947\) 2.10378e11 3.64385e11i 0.261578 0.453066i −0.705084 0.709124i \(-0.749091\pi\)
0.966661 + 0.256058i \(0.0824239\pi\)
\(948\) 4.21259e11 2.43214e11i 0.521574 0.301131i
\(949\) 4.83023e11 + 8.36620e11i 0.595529 + 1.03149i
\(950\) 7.40362e10 + 4.27448e10i 0.0908970 + 0.0524794i
\(951\) 2.65063e11i 0.324061i
\(952\) −4.62015e10 + 4.65889e11i −0.0562481 + 0.567198i
\(953\) −4.33447e11 −0.525490 −0.262745 0.964865i \(-0.584628\pi\)
−0.262745 + 0.964865i \(0.584628\pi\)
\(954\) 9.90860e9 1.71622e10i 0.0119624 0.0207195i
\(955\) −2.58755e9 + 1.49392e9i −0.00311082 + 0.00179603i
\(956\) −7.04269e10 1.21983e11i −0.0843154 0.146039i
\(957\) −9.25279e11 5.34210e11i −1.10313 0.636890i
\(958\) 3.84240e10i 0.0456185i
\(959\) −4.14064e11 4.10621e10i −0.489546 0.0485474i
\(960\) −8.35944e9 −0.00984220
\(961\) −2.51738e11 + 4.36022e11i −0.295158 + 0.511229i
\(962\) 1.35079e11 7.79877e10i 0.157720 0.0910596i
\(963\) 3.02425e11 + 5.23816e11i 0.351652 + 0.609079i
\(964\) −1.63021e11 9.41200e10i −0.188771 0.108987i
\(965\) 5.24610e10i 0.0604961i
\(966\) −1.00412e12 + 4.54148e11i −1.15312 + 0.521542i
\(967\) 1.45662e12 1.66587 0.832936 0.553369i \(-0.186658\pi\)
0.832936 + 0.553369i \(0.186658\pi\)
\(968\) −2.08205e10 + 3.60622e10i −0.0237132 + 0.0410725i
\(969\) 2.37554e11 1.37152e11i 0.269443 0.155563i
\(970\) 9.47835e9 + 1.64170e10i 0.0107065 + 0.0185441i
\(971\) −1.03111e11 5.95314e10i −0.115992 0.0669683i 0.440881 0.897565i \(-0.354666\pi\)
−0.556874 + 0.830597i \(0.687999\pi\)
\(972\) 5.18171e11i 0.580508i
\(973\) 9.40704e11 + 6.75054e11i 1.04955 + 0.753160i
\(974\) 1.23182e12 1.36871
\(975\) 4.92550e11 8.53121e11i 0.545044 0.944044i
\(976\) −1.10223e11 + 6.36373e10i −0.121471 + 0.0701314i
\(977\) 1.24713e11 + 2.16010e11i 0.136878 + 0.237080i 0.926313 0.376754i \(-0.122960\pi\)
−0.789435 + 0.613834i \(0.789626\pi\)
\(978\) 3.32271e11 + 1.91837e11i 0.363192 + 0.209689i
\(979\) 5.48573e11i 0.597178i
\(980\) −2.65571e10 + 8.97524e9i −0.0287923 + 0.00973065i
\(981\) −2.55378e11 −0.275745
\(982\) −9.90142e9 + 1.71498e10i −0.0106476 + 0.0184422i
\(983\) −4.93986e11 + 2.85203e11i −0.529055 + 0.305450i −0.740632 0.671911i \(-0.765474\pi\)
0.211576 + 0.977361i \(0.432140\pi\)
\(984\) −3.69825e11 6.40556e11i −0.394472 0.683246i
\(985\) −2.57973e10 1.48941e10i −0.0274050 0.0158223i
\(986\) 9.94874e11i 1.05259i
\(987\) −3.34638e11 + 4.66326e11i −0.352620 + 0.491385i
\(988\) −5.99540e10 −0.0629202
\(989\) −1.07651e12 + 1.86458e12i −1.12521 + 1.94893i
\(990\) 2.58157e10 1.49047e10i 0.0268747 0.0155161i
\(991\) −3.22979e11 5.59416e11i −0.334873 0.580017i 0.648588 0.761140i \(-0.275360\pi\)
−0.983460 + 0.181123i \(0.942027\pi\)
\(992\) −9.48914e10 5.47856e10i −0.0979897 0.0565744i
\(993\) 1.70967e12i 1.75839i
\(994\) 3.95976e11 + 8.75498e11i 0.405624 + 0.896829i
\(995\) −8.63168e10 −0.0880649
\(996\) 1.58365e11 2.74297e11i 0.160925 0.278730i
\(997\) −1.02509e12 + 5.91835e11i −1.03748 + 0.598991i −0.919119 0.393980i \(-0.871098\pi\)
−0.118363 + 0.992970i \(0.537765\pi\)
\(998\) −2.02279e11 3.50357e11i −0.203905 0.353174i
\(999\) −1.09721e11 6.33473e10i −0.110161 0.0636013i
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 14.9.d.a.5.1 yes 12
3.2 odd 2 126.9.n.b.19.5 12
4.3 odd 2 112.9.s.c.33.6 12
7.2 even 3 98.9.b.c.97.8 12
7.3 odd 6 inner 14.9.d.a.3.1 12
7.4 even 3 98.9.d.b.31.3 12
7.5 odd 6 98.9.b.c.97.11 12
7.6 odd 2 98.9.d.b.19.3 12
21.17 even 6 126.9.n.b.73.5 12
28.3 even 6 112.9.s.c.17.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.9.d.a.3.1 12 7.3 odd 6 inner
14.9.d.a.5.1 yes 12 1.1 even 1 trivial
98.9.b.c.97.8 12 7.2 even 3
98.9.b.c.97.11 12 7.5 odd 6
98.9.d.b.19.3 12 7.6 odd 2
98.9.d.b.31.3 12 7.4 even 3
112.9.s.c.17.6 12 28.3 even 6
112.9.s.c.33.6 12 4.3 odd 2
126.9.n.b.19.5 12 3.2 odd 2
126.9.n.b.73.5 12 21.17 even 6