Properties

Label 43.7.h.a.18.3
Level $43$
Weight $7$
Character 43.18
Analytic conductor $9.892$
Analytic rank $0$
Dimension $252$
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] = [43,7,Mod(3,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.3");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 43.h (of order \(42\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.89232559565\)
Analytic rank: \(0\)
Dimension: \(252\)
Relative dimension: \(21\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 18.3
Character \(\chi\) \(=\) 43.18
Dual form 43.7.h.a.12.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-6.07636 + 12.6177i) q^{2} +(28.9804 - 42.5064i) q^{3} +(-82.3806 - 103.302i) q^{4} +(88.1711 + 95.0259i) q^{5} +(360.237 + 623.949i) q^{6} +(-445.910 - 257.446i) q^{7} +(930.184 - 212.309i) q^{8} +(-700.598 - 1785.09i) q^{9} +O(q^{10})\) \(q+(-6.07636 + 12.6177i) q^{2} +(28.9804 - 42.5064i) q^{3} +(-82.3806 - 103.302i) q^{4} +(88.1711 + 95.0259i) q^{5} +(360.237 + 623.949i) q^{6} +(-445.910 - 257.446i) q^{7} +(930.184 - 212.309i) q^{8} +(-700.598 - 1785.09i) q^{9} +(-1734.77 + 535.104i) q^{10} +(-442.766 + 555.211i) q^{11} +(-6778.41 + 507.972i) q^{12} +(-2677.75 - 825.978i) q^{13} +(5957.88 - 4062.02i) q^{14} +(6594.44 - 993.952i) q^{15} +(-1091.61 + 4782.65i) q^{16} +(-1322.65 - 1227.24i) q^{17} +(26780.8 + 2006.95i) q^{18} +(-1750.74 - 687.114i) q^{19} +(2552.77 - 16936.5i) q^{20} +(-23865.7 + 11493.1i) q^{21} +(-4315.07 - 8960.34i) q^{22} +(15963.4 + 2406.10i) q^{23} +(17932.6 - 45691.6i) q^{24} +(-88.1112 + 1175.76i) q^{25} +(26692.9 - 28768.1i) q^{26} +(-59617.9 - 13607.4i) q^{27} +(10139.6 + 67271.9i) q^{28} +(-8812.34 - 12925.3i) q^{29} +(-27528.8 + 89246.2i) q^{30} +(-1652.05 - 22045.1i) q^{31} +(-5972.19 - 4762.66i) q^{32} +(10768.5 + 34910.6i) q^{33} +(23521.9 - 9231.67i) q^{34} +(-14852.3 - 65072.3i) q^{35} +(-126688. + 219430. i) q^{36} +(25271.7 - 14590.6i) q^{37} +(19307.9 - 17915.1i) q^{38} +(-112712. + 89884.6i) q^{39} +(102190. + 69672.1i) q^{40} +(-19275.5 - 9282.60i) q^{41} -370967. i q^{42} +(2035.33 - 79480.9i) q^{43} +93829.6 q^{44} +(107858. - 223969. i) q^{45} +(-127359. + 186801. i) q^{46} +(90257.9 + 113180. i) q^{47} +(171658. + 185003. i) q^{48} +(73732.6 + 127709. i) q^{49} +(-14300.0 - 8256.11i) q^{50} +(-90496.8 + 20655.3i) q^{51} +(135270. + 344662. i) q^{52} +(-117667. + 36295.4i) q^{53} +(533954. - 669557. i) q^{54} +(-91798.5 + 6879.35i) q^{55} +(-469436. - 144802. i) q^{56} +(-79943.7 + 54504.7i) q^{57} +(216635. - 32652.4i) q^{58} +(-25463.8 + 111564. i) q^{59} +(-645931. - 599336. i) q^{60} +(123278. + 9238.42i) q^{61} +(288197. + 113109. i) q^{62} +(-147162. + 976358. i) q^{63} +(-186486. + 89807.2i) q^{64} +(-157611. - 327283. i) q^{65} +(-505924. - 76255.8i) q^{66} +(-19257.8 + 49068.0i) q^{67} +(-17815.7 + 237734. i) q^{68} +(564901. - 608818. i) q^{69} +(911310. + 208000. i) q^{70} +(64115.7 + 425380. i) q^{71} +(-1.03068e6 - 1.51172e6i) q^{72} +(30832.3 - 99955.7i) q^{73} +(30540.0 + 407528. i) q^{74} +(47423.9 + 37819.3i) q^{75} +(73246.5 + 237459. i) q^{76} +(340370. - 133586. i) q^{77} +(-449259. - 1.96833e6i) q^{78} +(288362. - 499458. i) q^{79} +(-550724. + 317961. i) q^{80} +(-1.28137e6 + 1.18893e6i) q^{81} +(234250. - 186808. i) q^{82} +(-209542. - 142863. i) q^{83} +(3.15334e6 + 1.51857e6i) q^{84} -233894. i q^{85} +(990498. + 508636. i) q^{86} -804794. q^{87} +(-293978. + 610451. i) q^{88} +(395478. - 580060. i) q^{89} +(2.17059e6 + 2.72183e6i) q^{90} +(981392. + 1.05769e6i) q^{91} +(-1.06652e6 - 1.84727e6i) q^{92} +(-984935. - 568653. i) q^{93} +(-1.97651e6 + 451125. i) q^{94} +(-89070.9 - 226949. i) q^{95} +(-375520. + 115832. i) q^{96} +(898154. - 1.12625e6i) q^{97} +(-2.05941e6 + 154332. i) q^{98} +(1.30130e6 + 401399. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 252 q - 14 q^{2} - 11 q^{3} + 1180 q^{4} - 11 q^{5} - 118 q^{6} + 126 q^{7} - 2254 q^{8} - 8178 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 252 q - 14 q^{2} - 11 q^{3} + 1180 q^{4} - 11 q^{5} - 118 q^{6} + 126 q^{7} - 2254 q^{8} - 8178 q^{9} + 967 q^{10} + 4090 q^{11} - 484 q^{12} + 1527 q^{13} + 7812 q^{14} - 8923 q^{15} - 13760 q^{16} - 3655 q^{17} + 5596 q^{18} + 38605 q^{19} + 26085 q^{20} + 24873 q^{21} - 25214 q^{22} + 27991 q^{23} - 20480 q^{24} - 24146 q^{25} - 34923 q^{26} - 14 q^{27} - 77634 q^{28} - 112735 q^{29} + 375072 q^{30} + 290647 q^{31} - 344064 q^{32} - 152174 q^{33} - 198311 q^{34} - 182471 q^{35} - 930891 q^{36} + 282762 q^{37} + 487342 q^{38} + 857290 q^{39} + 745459 q^{40} + 27674 q^{41} + 148802 q^{43} - 1255832 q^{44} - 191310 q^{45} - 1344785 q^{46} + 69166 q^{47} - 871241 q^{48} + 1786604 q^{49} + 837705 q^{50} - 182756 q^{51} + 2906416 q^{52} + 7779 q^{53} + 487154 q^{54} - 529592 q^{55} - 2464007 q^{56} - 767855 q^{57} - 1523780 q^{58} + 1531338 q^{59} - 1858647 q^{60} + 646957 q^{61} - 448559 q^{62} - 2007847 q^{63} + 3937366 q^{64} - 1473542 q^{65} + 1513319 q^{66} - 575523 q^{67} + 2717157 q^{68} + 967041 q^{69} + 4624473 q^{70} - 2149319 q^{71} - 9986371 q^{72} - 514565 q^{73} - 882972 q^{74} - 6655138 q^{75} + 1152658 q^{76} - 341803 q^{77} + 6322388 q^{78} - 2476742 q^{79} + 10750038 q^{80} + 4308941 q^{81} + 5079172 q^{82} + 2318609 q^{83} + 5578407 q^{84} + 585292 q^{86} - 1990710 q^{87} - 2864890 q^{88} - 4561993 q^{89} - 17681545 q^{90} - 4648506 q^{91} - 1991714 q^{92} - 8868294 q^{93} - 10200218 q^{94} + 10091737 q^{95} + 6250318 q^{96} - 1676750 q^{97} + 7512700 q^{98} + 18452884 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{29}{42}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.07636 + 12.6177i −0.759545 + 1.57721i 0.0559413 + 0.998434i \(0.482184\pi\)
−0.815486 + 0.578777i \(0.803530\pi\)
\(3\) 28.9804 42.5064i 1.07335 1.57431i 0.285562 0.958360i \(-0.407820\pi\)
0.787785 0.615951i \(-0.211228\pi\)
\(4\) −82.3806 103.302i −1.28720 1.61409i
\(5\) 88.1711 + 95.0259i 0.705369 + 0.760207i 0.979491 0.201488i \(-0.0645777\pi\)
−0.274122 + 0.961695i \(0.588387\pi\)
\(6\) 360.237 + 623.949i 1.66777 + 2.88865i
\(7\) −445.910 257.446i −1.30003 0.750572i −0.319620 0.947546i \(-0.603555\pi\)
−0.980409 + 0.196974i \(0.936889\pi\)
\(8\) 930.184 212.309i 1.81677 0.414665i
\(9\) −700.598 1785.09i −0.961040 2.44869i
\(10\) −1734.77 + 535.104i −1.73477 + 0.535104i
\(11\) −442.766 + 555.211i −0.332656 + 0.417138i −0.919826 0.392326i \(-0.871671\pi\)
0.587170 + 0.809464i \(0.300242\pi\)
\(12\) −6778.41 + 507.972i −3.92269 + 0.293965i
\(13\) −2677.75 825.978i −1.21882 0.375957i −0.382377 0.924006i \(-0.624894\pi\)
−0.836446 + 0.548049i \(0.815371\pi\)
\(14\) 5957.88 4062.02i 2.17124 1.48033i
\(15\) 6594.44 993.952i 1.95391 0.294504i
\(16\) −1091.61 + 4782.65i −0.266506 + 1.16764i
\(17\) −1322.65 1227.24i −0.269215 0.249795i 0.533999 0.845485i \(-0.320688\pi\)
−0.803215 + 0.595689i \(0.796879\pi\)
\(18\) 26780.8 + 2006.95i 4.59205 + 0.344127i
\(19\) −1750.74 687.114i −0.255247 0.100177i 0.234268 0.972172i \(-0.424731\pi\)
−0.489514 + 0.871995i \(0.662826\pi\)
\(20\) 2552.77 16936.5i 0.319096 2.11707i
\(21\) −23865.7 + 11493.1i −2.57702 + 1.24103i
\(22\) −4315.07 8960.34i −0.405247 0.841504i
\(23\) 15963.4 + 2406.10i 1.31203 + 0.197756i 0.767533 0.641009i \(-0.221484\pi\)
0.544493 + 0.838765i \(0.316722\pi\)
\(24\) 17932.6 45691.6i 1.29721 3.30523i
\(25\) −88.1112 + 1175.76i −0.00563912 + 0.0752488i
\(26\) 26692.9 28768.1i 1.51871 1.63679i
\(27\) −59617.9 13607.4i −3.02891 0.691328i
\(28\) 10139.6 + 67271.9i 0.461899 + 3.06450i
\(29\) −8812.34 12925.3i −0.361325 0.529966i 0.601933 0.798547i \(-0.294398\pi\)
−0.963257 + 0.268581i \(0.913445\pi\)
\(30\) −27528.8 + 89246.2i −1.01958 + 3.30541i
\(31\) −1652.05 22045.1i −0.0554548 0.739992i −0.953750 0.300600i \(-0.902813\pi\)
0.898295 0.439392i \(-0.144806\pi\)
\(32\) −5972.19 4762.66i −0.182257 0.145345i
\(33\) 10768.5 + 34910.6i 0.299649 + 0.971438i
\(34\) 23521.9 9231.67i 0.598461 0.234879i
\(35\) −14852.3 65072.3i −0.346410 1.51772i
\(36\) −126688. + 219430.i −2.71537 + 4.70315i
\(37\) 25271.7 14590.6i 0.498917 0.288050i −0.229349 0.973344i \(-0.573660\pi\)
0.728266 + 0.685294i \(0.240326\pi\)
\(38\) 19307.9 17915.1i 0.351871 0.326489i
\(39\) −112712. + 89884.6i −1.90009 + 1.51527i
\(40\) 102190. + 69672.1i 1.59672 + 1.08863i
\(41\) −19275.5 9282.60i −0.279676 0.134685i 0.288788 0.957393i \(-0.406748\pi\)
−0.568464 + 0.822708i \(0.692462\pi\)
\(42\) 370967.i 5.00711i
\(43\) 2035.33 79480.9i 0.0255994 0.999672i
\(44\) 93829.6 1.10149
\(45\) 107858. 223969.i 1.18362 2.45782i
\(46\) −127359. + 186801.i −1.30845 + 1.91914i
\(47\) 90257.9 + 113180.i 0.869344 + 1.09012i 0.995179 + 0.0980722i \(0.0312676\pi\)
−0.125835 + 0.992051i \(0.540161\pi\)
\(48\) 171658. + 185003.i 1.55217 + 1.67285i
\(49\) 73732.6 + 127709.i 0.626716 + 1.08550i
\(50\) −14300.0 8256.11i −0.114400 0.0660489i
\(51\) −90496.8 + 20655.3i −0.682217 + 0.155712i
\(52\) 135270. + 344662.i 0.962035 + 2.45122i
\(53\) −117667. + 36295.4i −0.790362 + 0.243794i −0.663549 0.748132i \(-0.730951\pi\)
−0.126812 + 0.991927i \(0.540475\pi\)
\(54\) 533954. 669557.i 3.39096 4.25213i
\(55\) −91798.5 + 6879.35i −0.551757 + 0.0413484i
\(56\) −469436. 144802.i −2.67308 0.824537i
\(57\) −79943.7 + 54504.7i −0.431678 + 0.294313i
\(58\) 216635. 32652.4i 1.11031 0.167352i
\(59\) −25463.8 + 111564.i −0.123985 + 0.543212i 0.874338 + 0.485317i \(0.161296\pi\)
−0.998323 + 0.0578949i \(0.981561\pi\)
\(60\) −645931. 599336.i −2.99042 2.77470i
\(61\) 123278. + 9238.42i 0.543121 + 0.0407013i 0.343466 0.939165i \(-0.388399\pi\)
0.199655 + 0.979866i \(0.436018\pi\)
\(62\) 288197. + 113109.i 1.20924 + 0.474593i
\(63\) −147162. + 976358.i −0.588538 + 3.90470i
\(64\) −186486. + 89807.2i −0.711389 + 0.342587i
\(65\) −157611. 327283.i −0.573915 1.19175i
\(66\) −505924. 76255.8i −1.75976 0.265241i
\(67\) −19257.8 + 49068.0i −0.0640297 + 0.163145i −0.959308 0.282363i \(-0.908882\pi\)
0.895278 + 0.445508i \(0.146977\pi\)
\(68\) −17815.7 + 237734.i −0.0566599 + 0.756074i
\(69\) 564901. 608818.i 1.71959 1.85328i
\(70\) 911310. + 208000.i 2.65688 + 0.606415i
\(71\) 64115.7 + 425380.i 0.179139 + 1.18851i 0.879917 + 0.475128i \(0.157598\pi\)
−0.700778 + 0.713380i \(0.747164\pi\)
\(72\) −1.03068e6 1.51172e6i −2.76137 4.05019i
\(73\) 30832.3 99955.7i 0.0792569 0.256944i −0.907269 0.420551i \(-0.861837\pi\)
0.986526 + 0.163607i \(0.0523129\pi\)
\(74\) 30540.0 + 407528.i 0.0753657 + 1.00568i
\(75\) 47423.9 + 37819.3i 0.112412 + 0.0896458i
\(76\) 73246.5 + 237459.i 0.166858 + 0.540939i
\(77\) 340370. 133586.i 0.745555 0.292609i
\(78\) −449259. 1.96833e6i −0.946701 4.14777i
\(79\) 288362. 499458.i 0.584867 1.01302i −0.410025 0.912074i \(-0.634480\pi\)
0.994892 0.100945i \(-0.0321866\pi\)
\(80\) −550724. + 317961.i −1.07563 + 0.621017i
\(81\) −1.28137e6 + 1.18893e6i −2.41112 + 2.23719i
\(82\) 234250. 186808.i 0.424852 0.338808i
\(83\) −209542. 142863.i −0.366468 0.249854i 0.366059 0.930592i \(-0.380707\pi\)
−0.732527 + 0.680738i \(0.761659\pi\)
\(84\) 3.15334e6 + 1.51857e6i 5.32025 + 2.56210i
\(85\) 233894.i 0.380857i
\(86\) 990498. + 508636.i 1.55725 + 0.799671i
\(87\) −804794. −1.22216
\(88\) −293978. + 610451.i −0.431386 + 0.895783i
\(89\) 395478. 580060.i 0.560987 0.822816i −0.436036 0.899929i \(-0.643618\pi\)
0.997022 + 0.0771130i \(0.0245702\pi\)
\(90\) 2.17059e6 + 2.72183e6i 2.97748 + 3.73365i
\(91\) 981392. + 1.05769e6i 1.30232 + 1.40357i
\(92\) −1.06652e6 1.84727e6i −1.36964 2.37228i
\(93\) −984935. 568653.i −1.22450 0.706966i
\(94\) −1.97651e6 + 451125.i −2.37966 + 0.543142i
\(95\) −89070.9 226949.i −0.103888 0.264702i
\(96\) −375520. + 115832.i −0.424443 + 0.130923i
\(97\) 898154. 1.12625e6i 0.984092 1.23401i 0.0118755 0.999929i \(-0.496220\pi\)
0.972217 0.234083i \(-0.0752088\pi\)
\(98\) −2.05941e6 + 154332.i −2.18809 + 0.163975i
\(99\) 1.30130e6 + 401399.i 1.34114 + 0.413686i
\(100\) 128717. 87757.9i 0.128717 0.0877579i
\(101\) −872557. + 131517.i −0.846895 + 0.127649i −0.558133 0.829752i \(-0.688482\pi\)
−0.288763 + 0.957401i \(0.593244\pi\)
\(102\) 289269. 1.26737e6i 0.272584 1.19427i
\(103\) −100349. 93110.1i −0.0918334 0.0852089i 0.632920 0.774217i \(-0.281856\pi\)
−0.724754 + 0.689008i \(0.758047\pi\)
\(104\) −2.66617e6 199802.i −2.37021 0.177623i
\(105\) −3.19641e6 1.25450e6i −2.76118 1.08368i
\(106\) 257021. 1.70522e6i 0.215800 1.43174i
\(107\) −937814. + 451627.i −0.765536 + 0.368663i −0.775549 0.631287i \(-0.782527\pi\)
0.0100134 + 0.999950i \(0.496813\pi\)
\(108\) 3.50569e6 + 7.27963e6i 2.78293 + 5.77881i
\(109\) 1.18650e6 + 178836.i 0.916195 + 0.138094i 0.590181 0.807271i \(-0.299056\pi\)
0.326014 + 0.945365i \(0.394294\pi\)
\(110\) 470999. 1.20009e6i 0.353869 0.901642i
\(111\) 112188. 1.49705e6i 0.0820311 1.09463i
\(112\) 1.71803e6 1.85160e6i 1.22286 1.31793i
\(113\) 179900. + 41061.0i 0.124680 + 0.0284573i 0.284405 0.958704i \(-0.408204\pi\)
−0.159726 + 0.987161i \(0.551061\pi\)
\(114\) −201957. 1.33989e6i −0.136315 0.904391i
\(115\) 1.17887e6 + 1.72909e6i 0.775127 + 1.13690i
\(116\) −609246. + 1.97513e6i −0.390318 + 1.26538i
\(117\) 401581. + 5.35872e6i 0.250735 + 3.34583i
\(118\) −1.25296e6 999200.i −0.762588 0.608144i
\(119\) 273835. + 887753.i 0.162498 + 0.526807i
\(120\) 5.92302e6 2.32461e6i 3.42767 1.34526i
\(121\) 281992. + 1.23549e6i 0.159177 + 0.697401i
\(122\) −865649. + 1.49935e6i −0.476719 + 0.825702i
\(123\) −953182. + 550320.i −0.512224 + 0.295733i
\(124\) −2.14121e6 + 1.98675e6i −1.12304 + 1.04202i
\(125\) 1.46408e6 1.16757e6i 0.749611 0.597795i
\(126\) −1.14252e7 7.78954e6i −5.71151 3.89404i
\(127\) 2.31137e6 + 1.11310e6i 1.12839 + 0.543403i 0.902474 0.430744i \(-0.141749\pi\)
0.225914 + 0.974147i \(0.427463\pi\)
\(128\) 3.38761e6i 1.61534i
\(129\) −3.31946e6 2.38990e6i −1.54632 1.11330i
\(130\) 5.08726e6 2.31555
\(131\) 935115. 1.94179e6i 0.415960 0.863749i −0.582735 0.812662i \(-0.698017\pi\)
0.998694 0.0510865i \(-0.0162684\pi\)
\(132\) 2.71922e6 3.98836e6i 1.18228 1.73409i
\(133\) 603776. + 757111.i 0.256638 + 0.321814i
\(134\) −502107. 541143.i −0.208681 0.224904i
\(135\) −3.96352e6 6.86503e6i −1.61094 2.79024i
\(136\) −1.49087e6 860753.i −0.592683 0.342186i
\(137\) 511659. 116783.i 0.198984 0.0454169i −0.121867 0.992546i \(-0.538888\pi\)
0.320851 + 0.947130i \(0.396031\pi\)
\(138\) 4.24934e6 + 1.08271e7i 1.61690 + 4.11980i
\(139\) −4.83476e6 + 1.49133e6i −1.80024 + 0.555301i −0.999069 0.0431323i \(-0.986266\pi\)
−0.801173 + 0.598433i \(0.795790\pi\)
\(140\) −5.49855e6 + 6.89496e6i −2.00384 + 2.51274i
\(141\) 7.42658e6 556545.i 2.64930 0.198538i
\(142\) −5.75690e6 1.77577e6i −2.01059 0.620185i
\(143\) 1.64421e6 1.12100e6i 0.562275 0.383353i
\(144\) 9.30226e6 1.40209e6i 3.11531 0.469557i
\(145\) 451247. 1.97704e6i 0.148017 0.648503i
\(146\) 1.07386e6 + 996399.i 0.345056 + 0.320166i
\(147\) 7.56523e6 + 566935.i 2.38161 + 0.178477i
\(148\) −3.58913e6 1.40863e6i −1.10714 0.434522i
\(149\) 725753. 4.81506e6i 0.219397 1.45560i −0.559699 0.828696i \(-0.689083\pi\)
0.779095 0.626905i \(-0.215679\pi\)
\(150\) −765357. + 368576.i −0.226772 + 0.109208i
\(151\) −1.77751e6 3.69103e6i −0.516274 1.07205i −0.982305 0.187286i \(-0.940031\pi\)
0.466031 0.884768i \(-0.345683\pi\)
\(152\) −1.77439e6 267446.i −0.505263 0.0761562i
\(153\) −1.26410e6 + 3.22087e6i −0.352945 + 0.899288i
\(154\) −382672. + 5.10640e6i −0.104777 + 1.39815i
\(155\) 1.94919e6 2.10073e6i 0.523431 0.564125i
\(156\) 1.85705e7 + 4.23859e6i 4.89159 + 1.11647i
\(157\) −719088. 4.77084e6i −0.185816 1.23281i −0.866104 0.499864i \(-0.833383\pi\)
0.680288 0.732945i \(-0.261855\pi\)
\(158\) 4.54981e6 + 6.67335e6i 1.15351 + 1.69189i
\(159\) −1.86724e6 + 6.05344e6i −0.464524 + 1.50595i
\(160\) −73998.5 987441.i −0.0180660 0.241074i
\(161\) −6.49881e6 5.18263e6i −1.55724 1.24186i
\(162\) −7.21556e6 2.33923e7i −1.69717 5.50209i
\(163\) −2.36530e6 + 928313.i −0.546165 + 0.214354i −0.622349 0.782740i \(-0.713822\pi\)
0.0761840 + 0.997094i \(0.475726\pi\)
\(164\) 629017. + 2.75590e6i 0.142604 + 0.624788i
\(165\) −2.36794e6 + 4.10139e6i −0.527131 + 0.913018i
\(166\) 3.07585e6 1.77584e6i 0.672421 0.388223i
\(167\) −5.40254e6 + 5.01283e6i −1.15998 + 1.07630i −0.164020 + 0.986457i \(0.552446\pi\)
−0.995956 + 0.0898428i \(0.971364\pi\)
\(168\) −1.97594e7 + 1.57576e7i −4.16722 + 3.32325i
\(169\) 2.50004e6 + 1.70450e6i 0.517948 + 0.353131i
\(170\) 2.95120e6 + 1.42122e6i 0.600692 + 0.289278i
\(171\) 3.60662e6i 0.721294i
\(172\) −8.37821e6 + 6.33743e6i −1.64652 + 1.24545i
\(173\) 4.87240e6 0.941032 0.470516 0.882391i \(-0.344068\pi\)
0.470516 + 0.882391i \(0.344068\pi\)
\(174\) 4.89022e6 1.01546e7i 0.928283 1.92760i
\(175\) 341985. 501600.i 0.0638106 0.0935930i
\(176\) −2.17205e6 2.72367e6i −0.398412 0.499592i
\(177\) 4.00425e6 + 4.31555e6i 0.722106 + 0.778246i
\(178\) 4.91595e6 + 8.51467e6i 0.871660 + 1.50976i
\(179\) −2.02372e6 1.16839e6i −0.352850 0.203718i 0.313090 0.949724i \(-0.398636\pi\)
−0.665940 + 0.746005i \(0.731969\pi\)
\(180\) −3.20218e7 + 7.30876e6i −5.49070 + 1.25322i
\(181\) −2.72759e6 6.94978e6i −0.459984 1.17202i −0.953261 0.302148i \(-0.902296\pi\)
0.493277 0.869872i \(-0.335799\pi\)
\(182\) −1.93089e7 + 5.95600e6i −3.20290 + 0.987963i
\(183\) 3.96534e6 4.97238e6i 0.647034 0.811355i
\(184\) 1.53598e7 1.15106e6i 2.46565 0.184775i
\(185\) 3.61471e6 + 1.11499e6i 0.570898 + 0.176099i
\(186\) 1.31599e7 8.97227e6i 2.04510 1.39432i
\(187\) 1.26701e6 190970.i 0.193755 0.0292039i
\(188\) 4.25620e6 1.86476e7i 0.640544 2.80641i
\(189\) 2.30811e7 + 2.14161e7i 3.41877 + 3.17216i
\(190\) 3.40480e6 + 255154.i 0.496398 + 0.0371999i
\(191\) 339663. + 133308.i 0.0487471 + 0.0191318i 0.389589 0.920989i \(-0.372617\pi\)
−0.340842 + 0.940121i \(0.610712\pi\)
\(192\) −1.58707e6 + 1.05295e7i −0.224229 + 1.48766i
\(193\) 3.98902e6 1.92101e6i 0.554874 0.267213i −0.135364 0.990796i \(-0.543220\pi\)
0.690238 + 0.723583i \(0.257506\pi\)
\(194\) 8.75316e6 + 1.81761e7i 1.19884 + 2.48941i
\(195\) −1.84793e7 2.78530e6i −2.49219 0.375637i
\(196\) 7.11841e6 1.81374e7i 0.945398 2.40884i
\(197\) −271846. + 3.62753e6i −0.0355569 + 0.474474i 0.950795 + 0.309822i \(0.100269\pi\)
−0.986352 + 0.164653i \(0.947350\pi\)
\(198\) −1.29719e7 + 1.39804e7i −1.67112 + 1.80104i
\(199\) −1.28570e7 2.93452e6i −1.63147 0.372372i −0.693873 0.720097i \(-0.744097\pi\)
−0.937597 + 0.347725i \(0.886954\pi\)
\(200\) 167665. + 1.11238e6i 0.0209581 + 0.139048i
\(201\) 1.52761e6 + 2.24059e6i 0.188115 + 0.275914i
\(202\) 3.64253e6 1.18088e7i 0.441926 1.43269i
\(203\) 601933. + 8.03224e6i 0.0719548 + 0.960171i
\(204\) 9.58890e6 + 7.64690e6i 1.12948 + 0.900730i
\(205\) −817457. 2.65013e6i −0.0948863 0.307614i
\(206\) 1.78459e6 700400.i 0.204144 0.0801206i
\(207\) −6.88883e6 3.01819e7i −0.776666 3.40280i
\(208\) 6.87342e6 1.19051e7i 0.763806 1.32295i
\(209\) 1.15666e6 667797.i 0.126697 0.0731486i
\(210\) 3.52514e7 3.27086e7i 3.80644 3.53186i
\(211\) −674733. + 538081.i −0.0718264 + 0.0572797i −0.658745 0.752366i \(-0.728912\pi\)
0.586918 + 0.809646i \(0.300341\pi\)
\(212\) 1.34428e7 + 9.16516e6i 1.41086 + 0.961906i
\(213\) 1.99395e7 + 9.60234e6i 2.06336 + 0.993661i
\(214\) 1.45773e7i 1.48743i
\(215\) 7.73220e6 6.81451e6i 0.778015 0.685677i
\(216\) −5.83446e7 −5.78948
\(217\) −4.93876e6 + 1.02554e7i −0.483325 + 1.00363i
\(218\) −9.46609e6 + 1.38842e7i −0.913695 + 1.34014i
\(219\) −3.35523e6 4.20732e6i −0.319440 0.400565i
\(220\) 8.27306e6 + 8.91624e6i 0.776959 + 0.837363i
\(221\) 2.52807e6 + 4.37874e6i 0.234214 + 0.405670i
\(222\) 1.82076e7 + 1.05122e7i 1.66415 + 0.960800i
\(223\) 1.59538e7 3.64136e6i 1.43863 0.328359i 0.569115 0.822258i \(-0.307286\pi\)
0.869519 + 0.493899i \(0.164429\pi\)
\(224\) 1.43693e6 + 3.66123e6i 0.127847 + 0.325749i
\(225\) 2.16058e6 666450.i 0.189680 0.0585086i
\(226\) −1.61123e6 + 2.02042e6i −0.139583 + 0.175032i
\(227\) −2.67328e6 + 200335.i −0.228542 + 0.0171269i −0.188509 0.982071i \(-0.560365\pi\)
−0.0400334 + 0.999198i \(0.512746\pi\)
\(228\) 1.22162e7 + 3.76821e6i 1.03070 + 0.317930i
\(229\) 1.36697e6 931986.i 0.113829 0.0776073i −0.505067 0.863080i \(-0.668532\pi\)
0.618897 + 0.785473i \(0.287580\pi\)
\(230\) −2.89803e7 + 4.36808e6i −2.38188 + 0.359011i
\(231\) 4.18582e6 1.83393e7i 0.339582 1.48781i
\(232\) −1.09413e7 1.01520e7i −0.876200 0.812995i
\(233\) −1.31724e6 98713.5i −0.104135 0.00780385i 0.0225606 0.999745i \(-0.492818\pi\)
−0.126696 + 0.991942i \(0.540437\pi\)
\(234\) −7.00549e7 2.74945e7i −5.46752 2.14584i
\(235\) −2.79687e6 + 1.85560e7i −0.215511 + 1.42982i
\(236\) 1.36225e7 6.56027e6i 1.03639 0.499098i
\(237\) −1.28733e7 2.67317e7i −0.967042 2.00808i
\(238\) −1.28653e7 1.93913e6i −0.954310 0.143839i
\(239\) 5.13551e6 1.30851e7i 0.376175 0.958479i −0.609945 0.792444i \(-0.708808\pi\)
0.986120 0.166035i \(-0.0530964\pi\)
\(240\) −2.44482e6 + 3.26239e7i −0.176854 + 2.35995i
\(241\) −1.49237e7 + 1.60839e7i −1.06617 + 1.14906i −0.0778000 + 0.996969i \(0.524790\pi\)
−0.988367 + 0.152086i \(0.951401\pi\)
\(242\) −1.73025e7 3.94918e6i −1.22085 0.278651i
\(243\) 6.75866e6 + 4.48408e7i 0.471023 + 3.12503i
\(244\) −9.20137e6 1.34959e7i −0.633407 0.929038i
\(245\) −5.63453e6 + 1.82667e7i −0.383142 + 1.24212i
\(246\) −1.15189e6 1.53709e7i −0.0773758 1.03251i
\(247\) 4.12050e6 + 3.28599e6i 0.273438 + 0.218060i
\(248\) −6.21708e6 2.01553e7i −0.407597 1.32140i
\(249\) −1.21452e7 + 4.76664e6i −0.786695 + 0.308755i
\(250\) 5.83571e6 + 2.55679e7i 0.373485 + 1.63635i
\(251\) 1.12888e7 1.95527e7i 0.713881 1.23648i −0.249508 0.968373i \(-0.580269\pi\)
0.963389 0.268106i \(-0.0863977\pi\)
\(252\) 1.12983e8 6.52307e7i 7.06011 4.07615i
\(253\) −8.40395e6 + 7.79773e6i −0.518946 + 0.481511i
\(254\) −2.80894e7 + 2.24006e7i −1.71412 + 1.36697i
\(255\) −9.94199e6 6.77833e6i −0.599588 0.408792i
\(256\) 3.08086e7 + 1.48366e7i 1.83634 + 0.884333i
\(257\) 1.16683e7i 0.687397i 0.939080 + 0.343699i \(0.111680\pi\)
−0.939080 + 0.343699i \(0.888320\pi\)
\(258\) 5.03253e7 2.73621e7i 2.93040 1.59327i
\(259\) −1.50252e7 −0.864809
\(260\) −2.08249e7 + 4.32433e7i −1.18485 + 2.46036i
\(261\) −1.68990e7 + 2.47863e7i −0.950474 + 1.39409i
\(262\) 1.88188e7 + 2.35980e7i 1.04637 + 1.31211i
\(263\) −1.78064e6 1.91908e6i −0.0978835 0.105493i 0.682210 0.731156i \(-0.261019\pi\)
−0.780093 + 0.625663i \(0.784829\pi\)
\(264\) 1.74285e7 + 3.01870e7i 0.947214 + 1.64062i
\(265\) −1.38238e7 7.98117e6i −0.742831 0.428873i
\(266\) −1.32218e7 + 3.01778e6i −0.702496 + 0.160340i
\(267\) −1.31952e7 3.36207e7i −0.693235 1.76633i
\(268\) 6.65528e6 2.05288e6i 0.345750 0.106650i
\(269\) 1.94031e6 2.43307e6i 0.0996813 0.124996i −0.729489 0.683993i \(-0.760242\pi\)
0.829170 + 0.558996i \(0.188813\pi\)
\(270\) 1.10705e8 8.29616e6i 5.62437 0.421489i
\(271\) −7.13930e6 2.20218e6i −0.358714 0.110649i 0.110160 0.993914i \(-0.464864\pi\)
−0.468873 + 0.883265i \(0.655340\pi\)
\(272\) 7.31330e6 4.98613e6i 0.363418 0.247774i
\(273\) 7.33997e7 1.10632e7i 3.60750 0.543743i
\(274\) −1.63549e6 + 7.16557e6i −0.0795055 + 0.348337i
\(275\) −613783. 569507.i −0.0295132 0.0273843i
\(276\) −1.09429e8 8.20056e6i −5.20481 0.390047i
\(277\) 7.83026e6 + 3.07315e6i 0.368415 + 0.144592i 0.542324 0.840170i \(-0.317545\pi\)
−0.173909 + 0.984762i \(0.555640\pi\)
\(278\) 1.05607e7 7.00654e7i 0.491537 3.26114i
\(279\) −3.81952e7 + 1.83938e7i −1.75872 + 0.846954i
\(280\) −2.76308e7 5.73759e7i −1.25869 2.61370i
\(281\) −1.02017e6 153766.i −0.0459784 0.00693013i 0.126013 0.992029i \(-0.459782\pi\)
−0.171991 + 0.985098i \(0.555020\pi\)
\(282\) −3.81042e7 + 9.70880e7i −1.69913 + 4.32930i
\(283\) −2.54149e6 + 3.39139e7i −0.112132 + 1.49630i 0.603243 + 0.797558i \(0.293875\pi\)
−0.715375 + 0.698741i \(0.753744\pi\)
\(284\) 3.86607e7 4.16663e7i 1.68778 1.81899i
\(285\) −1.22281e7 2.79098e6i −0.528231 0.120565i
\(286\) 4.15366e6 + 2.75577e7i 0.177555 + 1.17800i
\(287\) 6.20537e6 + 9.10161e6i 0.262496 + 0.385011i
\(288\) −4.31770e6 + 1.39976e7i −0.180748 + 0.585972i
\(289\) −1.56052e6 2.08236e7i −0.0646509 0.862706i
\(290\) 2.22038e7 + 1.77069e7i 0.910400 + 0.726020i
\(291\) −2.18440e7 7.08164e7i −0.886447 2.87379i
\(292\) −1.28656e7 + 5.04938e6i −0.516751 + 0.202810i
\(293\) −3.94428e6 1.72810e7i −0.156807 0.687015i −0.990811 0.135257i \(-0.956814\pi\)
0.834004 0.551759i \(-0.186043\pi\)
\(294\) −5.31224e7 + 9.20107e7i −2.09043 + 3.62073i
\(295\) −1.28467e7 + 7.41703e6i −0.500409 + 0.288911i
\(296\) 2.04096e7 1.89373e7i 0.786972 0.730203i
\(297\) 3.39518e7 2.70756e7i 1.29596 1.03350i
\(298\) 5.63449e7 + 3.84153e7i 2.12915 + 1.45163i
\(299\) −4.07588e7 1.96284e7i −1.52478 0.734296i
\(300\) 8.01456e6i 0.296835i
\(301\) −2.13696e7 + 3.49173e7i −0.783606 + 1.28039i
\(302\) 5.73731e7 2.08299
\(303\) −1.96967e7 + 4.09007e7i −0.708053 + 1.47029i
\(304\) 5.19734e6 7.62310e6i 0.184995 0.271338i
\(305\) 9.99168e6 + 1.25292e7i 0.352159 + 0.441594i
\(306\) −3.29588e7 3.55211e7i −1.15029 1.23972i
\(307\) −3.09798e6 5.36585e6i −0.107069 0.185449i 0.807513 0.589850i \(-0.200813\pi\)
−0.914582 + 0.404402i \(0.867480\pi\)
\(308\) −4.18395e7 2.41561e7i −1.43197 0.826750i
\(309\) −6.86592e6 + 1.56710e6i −0.232714 + 0.0531156i
\(310\) 1.46624e7 + 3.73591e7i 0.492174 + 1.25404i
\(311\) 2.87549e7 8.86970e6i 0.955939 0.294868i 0.222737 0.974879i \(-0.428501\pi\)
0.733202 + 0.680010i \(0.238025\pi\)
\(312\) −8.57594e7 + 1.07539e8i −2.82370 + 3.54080i
\(313\) 3.80122e7 2.84862e6i 1.23962 0.0928969i 0.561270 0.827633i \(-0.310313\pi\)
0.678353 + 0.734736i \(0.262694\pi\)
\(314\) 6.45664e7 + 1.99161e7i 2.08554 + 0.643303i
\(315\) −1.05755e8 + 7.21023e7i −3.38351 + 2.30684i
\(316\) −7.53504e7 + 1.13572e7i −2.38795 + 0.359925i
\(317\) 1.12125e7 4.91252e7i 0.351986 1.54215i −0.420603 0.907245i \(-0.638182\pi\)
0.772589 0.634906i \(-0.218961\pi\)
\(318\) −6.50344e7 6.03431e7i −2.02237 1.87649i
\(319\) 1.10781e7 + 830188.i 0.341266 + 0.0255743i
\(320\) −2.49767e7 9.80264e6i −0.762229 0.299153i
\(321\) −7.98114e6 + 5.29514e7i −0.241296 + 1.60089i
\(322\) 1.04882e8 5.05084e7i 3.14147 1.51285i
\(323\) 1.47236e6 + 3.05740e6i 0.0436926 + 0.0907286i
\(324\) 2.28379e8 + 3.44226e7i 6.71461 + 1.01207i
\(325\) 1.20709e6 3.07563e6i 0.0351634 0.0895949i
\(326\) 2.65926e6 3.54854e7i 0.0767554 1.02423i
\(327\) 4.19868e7 4.52511e7i 1.20080 1.29415i
\(328\) −1.99006e7 4.54217e6i −0.563954 0.128719i
\(329\) −1.11092e7 7.37046e7i −0.311957 2.06970i
\(330\) −3.73616e7 5.47994e7i −1.03964 1.52487i
\(331\) 7.51853e6 2.43745e7i 0.207324 0.672127i −0.790866 0.611989i \(-0.790370\pi\)
0.998190 0.0601383i \(-0.0191542\pi\)
\(332\) 2.50412e6 + 3.34152e7i 0.0684292 + 0.913125i
\(333\) −4.37509e7 3.48902e7i −1.18482 0.944866i
\(334\) −3.04225e7 9.86273e7i −0.816499 2.64702i
\(335\) −6.36070e6 + 2.49639e6i −0.169188 + 0.0664016i
\(336\) −2.89156e7 1.26687e8i −0.762280 3.33976i
\(337\) −1.68090e7 + 2.91141e7i −0.439191 + 0.760701i −0.997627 0.0688466i \(-0.978068\pi\)
0.558437 + 0.829547i \(0.311401\pi\)
\(338\) −3.66979e7 + 2.11875e7i −0.950366 + 0.548694i
\(339\) 6.95892e6 6.45693e6i 0.178625 0.165740i
\(340\) −2.41617e7 + 1.92683e7i −0.614739 + 0.490238i
\(341\) 1.29712e7 + 8.84358e6i 0.327126 + 0.223031i
\(342\) −4.55072e7 2.19151e7i −1.13763 0.547855i
\(343\) 1.53521e7i 0.380439i
\(344\) −1.49812e7 7.43640e7i −0.368021 1.82679i
\(345\) 1.07661e8 2.62182
\(346\) −2.96064e7 + 6.14784e7i −0.714756 + 1.48421i
\(347\) −2.67873e7 + 3.92897e7i −0.641121 + 0.940352i 0.358855 + 0.933393i \(0.383167\pi\)
−0.999976 + 0.00695854i \(0.997785\pi\)
\(348\) 6.62994e7 + 8.31368e7i 1.57316 + 1.97268i
\(349\) 1.48501e7 + 1.60046e7i 0.349343 + 0.376502i 0.883139 0.469111i \(-0.155426\pi\)
−0.533796 + 0.845613i \(0.679235\pi\)
\(350\) 4.25101e6 + 7.36296e6i 0.0991489 + 0.171731i
\(351\) 1.48403e8 + 8.56804e7i 3.43179 + 1.98135i
\(352\) 5.28856e6 1.20708e6i 0.121258 0.0276763i
\(353\) −1.26793e7 3.23064e7i −0.288252 0.734454i −0.999503 0.0315164i \(-0.989966\pi\)
0.711251 0.702938i \(-0.248129\pi\)
\(354\) −7.87836e7 + 2.43015e7i −1.77593 + 0.547802i
\(355\) −3.47689e7 + 4.35989e7i −0.777153 + 0.974519i
\(356\) −9.25010e7 + 6.93200e6i −2.05020 + 0.153641i
\(357\) 4.56710e7 + 1.40876e7i 1.00377 + 0.309623i
\(358\) 2.70393e7 1.84351e7i 0.589312 0.401786i
\(359\) −1.20896e7 + 1.82222e6i −0.261294 + 0.0393837i −0.278383 0.960470i \(-0.589798\pi\)
0.0170887 + 0.999854i \(0.494560\pi\)
\(360\) 5.27770e7 2.31231e8i 1.13119 4.95609i
\(361\) −3.18941e7 2.95934e7i −0.677936 0.629033i
\(362\) 1.04264e8 + 7.81350e6i 2.19790 + 0.164710i
\(363\) 6.06884e7 + 2.38184e7i 1.26878 + 0.497959i
\(364\) 2.84137e7 1.88513e8i 0.589148 3.90874i
\(365\) 1.22169e7 5.88335e6i 0.251236 0.120989i
\(366\) 3.86451e7 + 8.02473e7i 0.788226 + 1.63677i
\(367\) 7.52903e7 + 1.13482e7i 1.52314 + 0.229577i 0.856636 0.515922i \(-0.172550\pi\)
0.666507 + 0.745499i \(0.267789\pi\)
\(368\) −2.89334e7 + 7.37210e7i −0.580571 + 1.47927i
\(369\) −3.06593e6 + 4.09120e7i −0.0610216 + 0.814276i
\(370\) −3.60329e7 + 3.88343e7i −0.711368 + 0.766672i
\(371\) 6.18128e7 + 1.41084e7i 1.21048 + 0.276284i
\(372\) 2.23966e7 + 1.48592e8i 0.435064 + 2.88646i
\(373\) 3.33869e6 + 4.89696e6i 0.0643353 + 0.0943626i 0.857058 0.515220i \(-0.172290\pi\)
−0.792723 + 0.609582i \(0.791337\pi\)
\(374\) −5.28917e6 + 1.71471e7i −0.101105 + 0.327775i
\(375\) −7.19941e6 9.60695e7i −0.136522 1.82176i
\(376\) 1.07986e8 + 8.61156e7i 2.03143 + 1.62001i
\(377\) 1.29213e7 + 4.18897e7i 0.241146 + 0.781777i
\(378\) −4.10470e8 + 1.61098e8i −7.59987 + 2.98273i
\(379\) 9.42369e6 + 4.12879e7i 0.173103 + 0.758412i 0.984709 + 0.174207i \(0.0557362\pi\)
−0.811607 + 0.584204i \(0.801407\pi\)
\(380\) −1.61065e7 + 2.78974e7i −0.293529 + 0.508408i
\(381\) 1.14298e8 6.59901e7i 2.06664 1.19317i
\(382\) −3.74596e6 + 3.47574e6i −0.0672005 + 0.0623530i
\(383\) −5.07624e7 + 4.04816e7i −0.903536 + 0.720546i −0.960632 0.277823i \(-0.910387\pi\)
0.0570963 + 0.998369i \(0.481816\pi\)
\(384\) −1.43995e8 9.81741e7i −2.54304 1.73382i
\(385\) 4.27049e7 + 2.05656e7i 0.748334 + 0.360379i
\(386\) 6.20050e7i 1.07811i
\(387\) −1.43307e8 + 5.20509e7i −2.47249 + 0.898040i
\(388\) −1.90334e8 −3.25853
\(389\) −3.13355e6 + 6.50688e6i −0.0532338 + 0.110541i −0.925889 0.377796i \(-0.876682\pi\)
0.872655 + 0.488337i \(0.162396\pi\)
\(390\) 1.47431e8 2.16241e8i 2.48539 3.64539i
\(391\) −1.81612e7 2.27735e7i −0.303819 0.380977i
\(392\) 9.56985e7 + 1.03138e8i 1.58872 + 1.71223i
\(393\) −5.54384e7 9.60220e7i −0.913340 1.58195i
\(394\) −4.41192e7 2.54723e7i −0.721339 0.416465i
\(395\) 7.28866e7 1.66359e7i 1.18265 0.269932i
\(396\) −6.57368e7 1.67495e8i −1.05858 2.69722i
\(397\) 1.59376e7 4.91611e6i 0.254714 0.0785688i −0.164769 0.986332i \(-0.552688\pi\)
0.419482 + 0.907763i \(0.362212\pi\)
\(398\) 1.15150e8 1.44394e8i 1.82648 2.29034i
\(399\) 4.96797e7 3.72298e6i 0.782097 0.0586100i
\(400\) −5.52708e6 1.70488e6i −0.0863606 0.0266387i
\(401\) −6.04243e7 + 4.11966e7i −0.937084 + 0.638893i −0.932528 0.361097i \(-0.882402\pi\)
−0.00455532 + 0.999990i \(0.501450\pi\)
\(402\) −3.75533e7 + 5.66025e6i −0.578056 + 0.0871279i
\(403\) −1.37850e7 + 6.03960e7i −0.210616 + 0.922769i
\(404\) 8.54677e7 + 7.93024e7i 1.29616 + 1.20266i
\(405\) −2.25959e8 1.69333e7i −3.40145 0.254904i
\(406\) −1.05006e8 4.12117e7i −1.56904 0.615805i
\(407\) −3.08857e6 + 2.04913e7i −0.0458114 + 0.303939i
\(408\) −7.97934e7 + 3.84265e7i −1.17486 + 0.565783i
\(409\) 1.61231e7 + 3.34800e7i 0.235656 + 0.489345i 0.984938 0.172906i \(-0.0553156\pi\)
−0.749282 + 0.662251i \(0.769601\pi\)
\(410\) 3.84057e7 + 5.78872e6i 0.557242 + 0.0839907i
\(411\) 9.86405e6 2.51332e7i 0.142079 0.362011i
\(412\) −1.35166e6 + 1.80367e7i −0.0193276 + 0.257908i
\(413\) 4.00764e7 4.31921e7i 0.568904 0.613132i
\(414\) 4.22685e8 + 9.64752e7i 5.95684 + 1.35961i
\(415\) −4.89984e6 3.25083e7i −0.0685547 0.454831i
\(416\) 1.20582e7 + 1.76861e7i 0.167495 + 0.245670i
\(417\) −7.67223e7 + 2.48728e8i −1.05807 + 3.43017i
\(418\) 1.39778e6 + 1.86521e7i 0.0191386 + 0.255388i
\(419\) −2.31539e7 1.84647e7i −0.314762 0.251015i 0.453346 0.891335i \(-0.350230\pi\)
−0.768108 + 0.640320i \(0.778802\pi\)
\(420\) 1.33730e8 + 4.33542e8i 1.80502 + 5.85172i
\(421\) 1.07340e8 4.21280e7i 1.43852 0.564579i 0.487342 0.873211i \(-0.337966\pi\)
0.951182 + 0.308632i \(0.0998712\pi\)
\(422\) −2.68942e6 1.17831e7i −0.0357867 0.156792i
\(423\) 1.38802e8 2.40413e8i 1.83390 3.17641i
\(424\) −1.01746e8 + 5.87430e7i −1.33481 + 0.770653i
\(425\) 1.55949e6 1.44699e6i 0.0203149 0.0188495i
\(426\) −2.42319e8 + 1.93243e8i −3.13443 + 2.49962i
\(427\) −5.25925e7 3.58570e7i −0.675524 0.460564i
\(428\) 1.23912e8 + 5.96727e7i 1.58045 + 0.761105i
\(429\) 1.02376e8i 1.29667i
\(430\) 3.89998e7 + 1.38970e8i 0.490520 + 1.74790i
\(431\) 9.43935e7 1.17899 0.589495 0.807772i \(-0.299327\pi\)
0.589495 + 0.807772i \(0.299327\pi\)
\(432\) 1.30159e8 2.70278e8i 1.61444 3.35243i
\(433\) −7.74209e7 + 1.13556e8i −0.953662 + 1.39877i −0.0369060 + 0.999319i \(0.511750\pi\)
−0.916756 + 0.399447i \(0.869202\pi\)
\(434\) −9.93903e7 1.24632e8i −1.21584 1.52461i
\(435\) −7.09596e7 7.64763e7i −0.862072 0.929092i
\(436\) −7.92703e7 1.37300e8i −0.956426 1.65658i
\(437\) −2.62945e7 1.51811e7i −0.315080 0.181911i
\(438\) 7.34742e7 1.67700e7i 0.874405 0.199577i
\(439\) −5.28316e7 1.34613e8i −0.624454 1.59108i −0.795591 0.605834i \(-0.792839\pi\)
0.171137 0.985247i \(-0.445256\pi\)
\(440\) −8.39290e7 + 2.58887e7i −0.985267 + 0.303915i
\(441\) 1.76315e8 2.21092e8i 2.05576 2.57785i
\(442\) −7.06111e7 + 5.29157e6i −0.817723 + 0.0612798i
\(443\) 1.58811e8 + 4.89867e7i 1.82671 + 0.563465i 1.00000 0.000834650i \(0.000265677\pi\)
0.826709 + 0.562630i \(0.190211\pi\)
\(444\) −1.63890e8 + 1.11738e8i −1.87242 + 1.27660i
\(445\) 8.99905e7 1.35639e7i 1.02121 0.153923i
\(446\) −5.09957e7 + 2.23427e8i −0.574816 + 2.51843i
\(447\) −1.83638e8 1.70391e8i −2.05608 1.90776i
\(448\) 1.06277e8 + 7.96433e6i 1.18196 + 0.0885759i
\(449\) 330025. + 129525.i 0.00364592 + 0.00143092i 0.367163 0.930157i \(-0.380329\pi\)
−0.363517 + 0.931587i \(0.618424\pi\)
\(450\) −4.71939e6 + 3.13111e7i −0.0517902 + 0.343606i
\(451\) 1.36883e7 6.59196e6i 0.149218 0.0718596i
\(452\) −1.05786e7 2.19666e7i −0.114554 0.237875i
\(453\) −2.08405e8 3.14120e7i −2.24189 0.337910i
\(454\) 1.37160e7 3.49479e7i 0.146575 0.373468i
\(455\) −1.39774e7 + 1.86515e8i −0.148386 + 1.98007i
\(456\) −6.27906e7 + 6.76721e7i −0.662216 + 0.713700i
\(457\) −1.04998e8 2.39652e7i −1.10010 0.251091i −0.366329 0.930485i \(-0.619386\pi\)
−0.733774 + 0.679394i \(0.762243\pi\)
\(458\) 3.45329e6 + 2.29111e7i 0.0359449 + 0.238479i
\(459\) 6.21543e7 + 9.11637e7i 0.642737 + 0.942722i
\(460\) 8.15020e7 2.64223e8i 0.837326 2.71454i
\(461\) −4.16118e6 5.55271e7i −0.0424731 0.566764i −0.977328 0.211733i \(-0.932089\pi\)
0.934854 0.355031i \(-0.115530\pi\)
\(462\) 2.05965e8 + 1.64251e8i 2.08866 + 1.66565i
\(463\) 2.94114e7 + 9.53494e7i 0.296328 + 0.960672i 0.974237 + 0.225526i \(0.0724101\pi\)
−0.677909 + 0.735146i \(0.737114\pi\)
\(464\) 7.14370e7 2.80370e7i 0.715104 0.280658i
\(465\) −3.28061e7 1.43733e8i −0.326284 1.42954i
\(466\) 9.24956e6 1.60207e7i 0.0914036 0.158316i
\(467\) −1.42711e8 + 8.23943e7i −1.40122 + 0.808996i −0.994518 0.104564i \(-0.966655\pi\)
−0.406704 + 0.913560i \(0.633322\pi\)
\(468\) 5.20484e8 4.82939e8i 5.07773 4.71145i
\(469\) 2.12196e7 1.69221e7i 0.205692 0.164034i
\(470\) −2.17139e8 1.48043e8i −2.09144 1.42592i
\(471\) −2.23631e8 1.07695e8i −2.14027 1.03070i
\(472\) 1.09182e8i 1.03830i
\(473\) 4.32275e7 + 3.63215e7i 0.408485 + 0.343226i
\(474\) 4.15515e8 3.90168
\(475\) 962142. 1.99791e6i 0.00897756 0.0186421i
\(476\) 6.91479e7 1.01421e8i 0.641148 0.940391i
\(477\) 1.47228e8 + 1.84618e8i 1.35655 + 1.70105i
\(478\) 1.33898e8 + 1.44308e8i 1.22600 + 1.32131i
\(479\) 8.71669e7 + 1.50977e8i 0.793131 + 1.37374i 0.924019 + 0.382346i \(0.124884\pi\)
−0.130888 + 0.991397i \(0.541783\pi\)
\(480\) −4.41171e7 2.54710e7i −0.398917 0.230315i
\(481\) −7.97228e7 + 1.81962e7i −0.716387 + 0.163511i
\(482\) −1.12260e8 2.86034e8i −1.00250 2.55433i
\(483\) −4.08633e8 + 1.26046e8i −3.62653 + 1.11864i
\(484\) 1.04398e8 1.30911e8i 0.920777 1.15462i
\(485\) 1.86214e8 1.39548e7i 1.63225 0.122320i
\(486\) −6.06855e8 1.87190e8i −5.28659 1.63070i
\(487\) 3.43884e7 2.34456e7i 0.297732 0.202990i −0.405236 0.914212i \(-0.632810\pi\)
0.702967 + 0.711222i \(0.251858\pi\)
\(488\) 1.16633e8 1.75796e7i 1.00360 0.151269i
\(489\) −2.90881e7 + 1.27443e8i −0.248765 + 1.08991i
\(490\) −1.96246e8 1.82090e8i −1.66806 1.54774i
\(491\) −1.28335e8 9.61742e6i −1.08418 0.0812482i −0.479367 0.877614i \(-0.659134\pi\)
−0.604815 + 0.796366i \(0.706753\pi\)
\(492\) 1.35373e8 + 5.31299e7i 1.13667 + 0.446112i
\(493\) −4.20685e6 + 2.79107e7i −0.0351089 + 0.232932i
\(494\) −6.64993e7 + 3.20244e7i −0.551615 + 0.265644i
\(495\) 7.65941e7 + 1.59049e8i 0.631510 + 1.31134i
\(496\) 1.07237e8 + 1.61634e7i 0.878823 + 0.132461i
\(497\) 8.09226e7 2.06187e8i 0.659175 1.67955i
\(498\) 1.36546e7 1.82208e8i 0.110558 1.47530i
\(499\) −2.81791e7 + 3.03698e7i −0.226791 + 0.244422i −0.836188 0.548443i \(-0.815221\pi\)
0.609398 + 0.792865i \(0.291411\pi\)
\(500\) −2.41224e8 5.50578e7i −1.92979 0.440463i
\(501\) 5.65095e7 + 3.74916e8i 0.449375 + 2.98141i
\(502\) 1.78116e8 + 2.61248e8i 1.40796 + 2.06510i
\(503\) 5.70992e7 1.85111e8i 0.448669 1.45455i −0.395496 0.918468i \(-0.629427\pi\)
0.844166 0.536082i \(-0.180096\pi\)
\(504\) 7.04010e7 + 9.39436e8i 0.549905 + 7.33797i
\(505\) −8.94318e7 7.13195e7i −0.694413 0.553776i
\(506\) −4.73239e7 1.53420e8i −0.365282 1.18422i
\(507\) 1.44904e8 5.68706e7i 1.11188 0.436379i
\(508\) −7.54269e7 3.30467e8i −0.575354 2.52079i
\(509\) −4.22743e7 + 7.32212e7i −0.320570 + 0.555244i −0.980606 0.195991i \(-0.937208\pi\)
0.660036 + 0.751234i \(0.270541\pi\)
\(510\) 1.45938e8 8.42573e7i 1.10016 0.635180i
\(511\) −3.94816e7 + 3.66336e7i −0.295891 + 0.274547i
\(512\) −2.04902e8 + 1.63404e8i −1.52664 + 1.21745i
\(513\) 9.50255e7 + 6.47873e7i 0.703863 + 0.479886i
\(514\) −1.47227e8 7.09007e7i −1.08417 0.522109i
\(515\) 1.77454e7i 0.129916i
\(516\) 2.65778e7 + 5.39788e8i 0.193450 + 3.92893i
\(517\) −1.02802e8 −0.743925
\(518\) 9.12983e7 1.89583e8i 0.656861 1.36399i
\(519\) 1.41204e8 2.07108e8i 1.01005 1.48148i
\(520\) −2.16093e8 2.70972e8i −1.53684 1.92714i
\(521\) 3.49673e7 + 3.76857e7i 0.247257 + 0.266480i 0.844470 0.535603i \(-0.179916\pi\)
−0.597213 + 0.802083i \(0.703725\pi\)
\(522\) −2.10062e8 3.63837e8i −1.47685 2.55797i
\(523\) 1.28424e8 + 7.41457e7i 0.897722 + 0.518300i 0.876460 0.481474i \(-0.159898\pi\)
0.0212613 + 0.999774i \(0.493232\pi\)
\(524\) −2.77626e8 + 6.33662e7i −1.92959 + 0.440417i
\(525\) −1.14104e7 2.90731e7i −0.0788535 0.200916i
\(526\) 3.50341e7 1.08066e7i 0.240732 0.0742560i
\(527\) −2.48696e7 + 3.11856e7i −0.169917 + 0.213070i
\(528\) −1.78720e8 + 1.33932e7i −1.21415 + 0.0909878i
\(529\) 1.07583e8 + 3.31849e7i 0.726734 + 0.224168i
\(530\) 1.84702e8 1.25928e8i 1.24064 0.845852i
\(531\) 2.16993e8 3.27064e7i 1.44931 0.218449i
\(532\) 2.84717e7 1.24742e8i 0.189094 0.828475i
\(533\) 4.39479e7 + 4.07777e7i 0.290239 + 0.269303i
\(534\) 5.04394e8 + 3.77991e7i 3.31243 + 0.248232i
\(535\) −1.25604e8 4.92961e7i −0.820245 0.321922i
\(536\) −7.49572e6 + 4.97308e7i −0.0486765 + 0.322947i
\(537\) −1.08312e8 + 5.21604e7i −0.699447 + 0.336836i
\(538\) 1.89097e7 + 3.92664e7i 0.121433 + 0.252159i
\(539\) −1.03551e8 1.56079e7i −0.661286 0.0996729i
\(540\) −3.82653e8 + 9.74984e8i −2.43010 + 6.19179i
\(541\) 1.86484e7 2.48846e8i 0.117774 1.57159i −0.555068 0.831805i \(-0.687308\pi\)
0.672843 0.739785i \(-0.265073\pi\)
\(542\) 7.11674e7 7.67002e7i 0.446975 0.481725i
\(543\) −3.74456e8 8.54672e7i −2.33885 0.533827i
\(544\) 2.05419e6 + 1.36287e7i 0.0127598 + 0.0846559i
\(545\) 8.76209e7 + 1.28516e8i 0.541275 + 0.793905i
\(546\) −3.06410e8 + 9.93358e8i −1.88246 + 6.10278i
\(547\) −8.48025e6 1.13161e8i −0.0518139 0.691409i −0.961270 0.275609i \(-0.911121\pi\)
0.909456 0.415800i \(-0.136498\pi\)
\(548\) −5.42147e7 4.32348e7i −0.329439 0.262719i
\(549\) −6.98770e7 2.26536e8i −0.422296 1.36905i
\(550\) 1.09154e7 4.28399e6i 0.0656074 0.0257490i
\(551\) 6.54692e6 + 2.86839e7i 0.0391365 + 0.171468i
\(552\) 3.96205e8 6.86246e8i 2.35560 4.08003i
\(553\) −2.57167e8 + 1.48475e8i −1.52069 + 0.877969i
\(554\) −8.63555e7 + 8.01262e7i −0.507880 + 0.471244i
\(555\) 1.52150e8 1.21336e8i 0.890006 0.709756i
\(556\) 5.52348e8 + 3.76584e8i 3.21357 + 2.19098i
\(557\) 1.55764e8 + 7.50121e7i 0.901368 + 0.434076i 0.826383 0.563109i \(-0.190395\pi\)
0.0749849 + 0.997185i \(0.476109\pi\)
\(558\) 5.93702e8i 3.41717i
\(559\) −7.10996e7 + 2.11149e8i −0.407035 + 1.20880i
\(560\) 3.27431e8 1.86447
\(561\) 2.86008e7 5.93902e7i 0.161991 0.336377i
\(562\) 8.13910e6 1.19379e7i 0.0458529 0.0672539i
\(563\) 1.12748e8 + 1.41382e8i 0.631808 + 0.792262i 0.989952 0.141404i \(-0.0451618\pi\)
−0.358144 + 0.933666i \(0.616590\pi\)
\(564\) −6.69298e8 7.21331e8i −3.73063 4.02066i
\(565\) 1.19601e7 + 2.07155e7i 0.0663117 + 0.114855i
\(566\) −4.12472e8 2.38141e8i −2.27481 1.31336i
\(567\) 8.77461e8 2.00275e8i 4.81369 1.09869i
\(568\) 1.49951e8 + 3.82070e8i 0.818286 + 2.08496i
\(569\) 9.90139e7 3.05417e7i 0.537476 0.165789i −0.0141206 0.999900i \(-0.504495\pi\)
0.551597 + 0.834111i \(0.314019\pi\)
\(570\) 1.09518e8 1.37331e8i 0.591372 0.741557i
\(571\) 9.59388e7 7.18962e6i 0.515331 0.0386187i 0.185473 0.982649i \(-0.440618\pi\)
0.329858 + 0.944031i \(0.392999\pi\)
\(572\) −2.51253e8 7.75012e7i −1.34253 0.414114i
\(573\) 1.55100e7 1.05745e7i 0.0824420 0.0562080i
\(574\) −1.52547e8 + 2.29928e7i −0.806620 + 0.121578i
\(575\) −4.23556e6 + 1.85572e7i −0.0222796 + 0.0976133i
\(576\) 2.90966e8 + 2.69977e8i 1.52256 + 1.41273i
\(577\) 2.85702e7 + 2.14104e6i 0.148726 + 0.0111455i 0.148885 0.988855i \(-0.452432\pi\)
−0.000159142 1.00000i \(0.500051\pi\)
\(578\) 2.72228e8 + 1.06842e8i 1.40978 + 0.553296i
\(579\) 3.39480e7 2.25231e8i 0.174896 1.16036i
\(580\) −2.41406e8 + 1.16255e8i −1.23727 + 0.595838i
\(581\) 5.66572e7 + 1.17650e8i 0.288886 + 0.599878i
\(582\) 1.02627e9 + 1.54686e8i 5.20587 + 0.784659i
\(583\) 3.19472e7 8.14001e7i 0.161223 0.410790i
\(584\) 7.45823e6 9.95232e7i 0.0374453 0.499673i
\(585\) −4.73810e8 + 5.10645e8i −2.36666 + 2.55066i
\(586\) 2.42013e8 + 5.52380e7i 1.20267 + 0.274502i
\(587\) 4.43258e7 + 2.94083e8i 0.219151 + 1.45397i 0.779859 + 0.625956i \(0.215291\pi\)
−0.560708 + 0.828014i \(0.689471\pi\)
\(588\) −5.64662e8 8.28207e8i −2.77752 4.07387i
\(589\) −1.22552e7 + 3.97303e7i −0.0599755 + 0.194436i
\(590\) −1.55248e7 2.07164e8i −0.0755909 1.00869i
\(591\) 1.46315e8 + 1.16682e8i 0.708805 + 0.565253i
\(592\) 4.21950e7 + 1.36793e8i 0.203374 + 0.659323i
\(593\) −5.98275e7 + 2.34806e7i −0.286904 + 0.112602i −0.504429 0.863453i \(-0.668297\pi\)
0.217525 + 0.976055i \(0.430202\pi\)
\(594\) 1.35329e8 + 5.92914e8i 0.645700 + 2.82899i
\(595\) −6.02151e7 + 1.04296e8i −0.285861 + 0.495125i
\(596\) −5.57193e8 + 3.21695e8i −2.63188 + 1.51952i
\(597\) −4.97335e8 + 4.61460e8i −2.33736 + 2.16876i
\(598\) 4.95330e8 3.95012e8i 2.31628 1.84717i
\(599\) −2.84231e8 1.93786e8i −1.32249 0.901656i −0.323480 0.946235i \(-0.604853\pi\)
−0.999006 + 0.0445790i \(0.985805\pi\)
\(600\) 5.21423e7 + 2.51104e7i 0.241400 + 0.116252i
\(601\) 3.06672e8i 1.41270i −0.707861 0.706352i \(-0.750340\pi\)
0.707861 0.706352i \(-0.249660\pi\)
\(602\) −3.10727e8 4.81806e8i −1.42426 2.20842i
\(603\) 1.01083e8 0.461026
\(604\) −2.34859e8 + 4.87689e8i −1.06585 + 2.21326i
\(605\) −9.25398e7 + 1.35731e8i −0.417890 + 0.612932i
\(606\) −3.96387e8 4.97054e8i −1.78116 2.23350i
\(607\) 2.32153e8 + 2.50201e8i 1.03802 + 1.11872i 0.992804 + 0.119747i \(0.0382084\pi\)
0.0452200 + 0.998977i \(0.485601\pi\)
\(608\) 7.18324e6 + 1.24417e7i 0.0319602 + 0.0553567i
\(609\) 3.58866e8 + 2.07191e8i 1.58884 + 0.917317i
\(610\) −2.18802e8 + 4.99402e7i −0.963967 + 0.220019i
\(611\) −1.48205e8 3.77619e8i −0.649737 1.65550i
\(612\) 4.36859e8 1.34753e8i 1.90584 0.587875i
\(613\) −7.37894e7 + 9.25290e7i −0.320341 + 0.401695i −0.915763 0.401718i \(-0.868413\pi\)
0.595423 + 0.803413i \(0.296985\pi\)
\(614\) 8.65290e7 6.48445e6i 0.373815 0.0280136i
\(615\) −1.36338e8 4.20546e7i −0.586125 0.180796i
\(616\) 2.88246e8 1.96523e8i 1.23316 0.840757i
\(617\) −1.98169e8 + 2.98691e7i −0.843683 + 0.127165i −0.556641 0.830753i \(-0.687910\pi\)
−0.287042 + 0.957918i \(0.592672\pi\)
\(618\) 2.19466e7 9.61543e7i 0.0929826 0.407383i
\(619\) −1.81907e8 1.68785e8i −0.766967 0.711642i 0.196194 0.980565i \(-0.437142\pi\)
−0.963162 + 0.268923i \(0.913332\pi\)
\(620\) −3.77585e8 2.82961e7i −1.58431 0.118727i
\(621\) −9.18966e8 3.60668e8i −3.83729 1.50603i
\(622\) −6.28098e7 + 4.16716e8i −0.261009 + 1.73168i
\(623\) −3.25682e8 + 1.56840e8i −1.34688 + 0.648624i
\(624\) −3.06849e8 6.37179e8i −1.26291 2.62245i
\(625\) 2.58256e8 + 3.89259e7i 1.05782 + 0.159440i
\(626\) −1.95033e8 + 4.96935e8i −0.795031 + 2.02571i
\(627\) 5.13474e6 6.85184e7i 0.0208313 0.277974i
\(628\) −4.33598e8 + 4.67308e8i −1.75069 + 1.88679i
\(629\) −5.13319e7 1.17162e7i −0.206270 0.0470797i
\(630\) −2.67161e8 1.77250e9i −1.06844 7.08866i
\(631\) 9.53949e6 + 1.39919e7i 0.0379697 + 0.0556913i 0.844754 0.535154i \(-0.179747\pi\)
−0.806785 + 0.590846i \(0.798794\pi\)
\(632\) 1.62191e8 5.25810e8i 0.642503 2.08294i
\(633\) 3.31790e6 + 4.42742e7i 0.0130813 + 0.174558i
\(634\) 5.51716e8 + 4.39979e8i 2.16495 + 1.72649i
\(635\) 9.80231e7 + 3.17783e8i 0.382831 + 1.24111i
\(636\) 7.79156e8 3.05796e8i 3.02868 1.18867i
\(637\) −9.19533e7 4.02874e8i −0.355753 1.55866i
\(638\) −7.77895e7 + 1.34735e8i −0.299543 + 0.518823i
\(639\) 7.14424e8 4.12473e8i 2.73813 1.58086i
\(640\) 3.21910e8 2.98689e8i 1.22799 1.13941i
\(641\) 2.20236e8 1.75633e8i 0.836210 0.666855i −0.108740 0.994070i \(-0.534682\pi\)
0.944950 + 0.327215i \(0.106110\pi\)
\(642\) −6.19628e8 4.22455e8i −2.34167 1.59652i
\(643\) 1.37488e8 + 6.62108e7i 0.517168 + 0.249055i 0.674214 0.738536i \(-0.264483\pi\)
−0.157045 + 0.987591i \(0.550197\pi\)
\(644\) 1.09829e9i 4.11205i
\(645\) −6.55784e7 5.26155e8i −0.244389 1.96081i
\(646\) −4.75239e7 −0.176285
\(647\) −2.10237e8 + 4.36561e8i −0.776240 + 1.61188i 0.0146291 + 0.999893i \(0.495343\pi\)
−0.790869 + 0.611986i \(0.790371\pi\)
\(648\) −9.39486e8 + 1.37797e9i −3.45275 + 5.06426i
\(649\) −5.06672e7 6.35347e7i −0.185350 0.232422i
\(650\) 3.14725e7 + 3.39193e7i 0.114602 + 0.123511i
\(651\) 2.92795e8 + 5.07136e8i 1.06126 + 1.83815i
\(652\) 2.90752e8 + 1.67865e8i 1.04901 + 0.605646i
\(653\) −4.85828e8 + 1.10887e8i −1.74479 + 0.398237i −0.971730 0.236096i \(-0.924132\pi\)
−0.773060 + 0.634333i \(0.781275\pi\)
\(654\) 3.15837e8 + 8.04739e8i 1.12909 + 2.87688i
\(655\) 2.66970e8 8.23493e7i 0.950033 0.293046i
\(656\) 6.54368e7 8.20551e7i 0.231798 0.290666i
\(657\) −2.00031e8 + 1.49903e7i −0.705346 + 0.0528584i
\(658\) 9.97485e8 + 3.07683e8i 3.50129 + 1.08001i
\(659\) 3.10300e8 2.11559e8i 1.08424 0.739223i 0.117013 0.993130i \(-0.462668\pi\)
0.967229 + 0.253907i \(0.0817157\pi\)
\(660\) 6.18753e8 9.32621e7i 2.15222 0.324394i
\(661\) 5.86863e7 2.57121e8i 0.203204 0.890295i −0.765767 0.643119i \(-0.777640\pi\)
0.968971 0.247176i \(-0.0795026\pi\)
\(662\) 2.61864e8 + 2.42975e8i 0.902615 + 0.837504i
\(663\) 2.59389e8 + 1.94385e7i 0.890043 + 0.0666995i
\(664\) −2.25244e8 8.84016e7i −0.769393 0.301964i
\(665\) −1.87095e7 + 1.24130e8i −0.0636207 + 0.422095i
\(666\) 7.06079e8 3.40030e8i 2.39018 1.15105i
\(667\) −1.09576e8 2.27536e8i −0.369263 0.766783i
\(668\) 9.62899e8 + 1.45134e8i 3.23036 + 0.486899i
\(669\) 3.07567e8 7.83668e8i 1.02721 2.61730i
\(670\) 7.15122e6 9.54264e7i 0.0237769 0.317281i
\(671\) −5.97126e7 + 6.43549e7i −0.197651 + 0.213017i
\(672\) 1.97269e8 + 4.50253e7i 0.650055 + 0.148371i
\(673\) −3.05744e7 2.02848e8i −0.100303 0.665466i −0.981320 0.192382i \(-0.938379\pi\)
0.881017 0.473084i \(-0.156859\pi\)
\(674\) −2.65215e8 3.88999e8i −0.866200 1.27048i
\(675\) 2.12521e7 6.88976e7i 0.0691019 0.224023i
\(676\) −2.98766e7 3.98676e8i −0.0967144 1.29056i
\(677\) −8.41803e7 6.71315e7i −0.271297 0.216352i 0.478385 0.878150i \(-0.341222\pi\)
−0.749682 + 0.661798i \(0.769794\pi\)
\(678\) 3.91867e7 + 1.27040e8i 0.125733 + 0.407617i
\(679\) −6.90445e8 + 2.70980e8i −2.20556 + 0.865620i
\(680\) −4.96577e7 2.17564e8i −0.157928 0.691929i
\(681\) −6.89571e7 + 1.19437e8i −0.218342 + 0.378180i
\(682\) −1.90403e8 + 1.09929e8i −0.600234 + 0.346545i
\(683\) 3.67057e8 3.40579e8i 1.15205 1.06895i 0.155342 0.987861i \(-0.450352\pi\)
0.996707 0.0810844i \(-0.0258383\pi\)
\(684\) 3.72571e8 2.97115e8i 1.16424 0.928447i
\(685\) 5.62110e7 + 3.83240e7i 0.174884 + 0.119234i
\(686\) 1.93708e8 + 9.32848e7i 0.600033 + 0.288960i
\(687\) 8.51143e7i 0.262502i
\(688\) 3.77908e8 + 9.64964e7i 1.16043 + 0.296310i
\(689\) 3.45062e8 1.05497
\(690\) −6.54189e8 + 1.35844e9i −1.99139 + 4.13516i
\(691\) −6.87563e7 + 1.00847e8i −0.208391 + 0.305653i −0.916177 0.400773i \(-0.868741\pi\)
0.707787 + 0.706426i \(0.249694\pi\)
\(692\) −4.01391e8 5.03328e8i −1.21129 1.51891i
\(693\) −4.76926e8 5.14004e8i −1.43302 1.54442i
\(694\) −3.32976e8 5.76732e8i −0.996173 1.72542i
\(695\) −5.68001e8 3.27936e8i −1.69198 0.976864i
\(696\) −7.48607e8 + 1.70865e8i −2.22037 + 0.506786i
\(697\) 1.41028e7 + 3.59335e7i 0.0416494 + 0.106121i
\(698\) −2.92175e8 + 9.01240e7i −0.859165 + 0.265017i
\(699\) −4.23701e7 + 5.31304e7i −0.124059 + 0.155565i
\(700\) −7.99892e7 + 5.99436e6i −0.233205 + 0.0174763i
\(701\) 3.13009e8 + 9.65504e7i 0.908662 + 0.280285i 0.713639 0.700513i \(-0.247046\pi\)
0.195023 + 0.980799i \(0.437522\pi\)
\(702\) −1.98284e9 + 1.35188e9i −5.73160 + 3.90774i
\(703\) −5.42694e7 + 8.17980e6i −0.156203 + 0.0235438i
\(704\) 3.27079e7 1.43303e8i 0.0937422 0.410711i
\(705\) 7.07696e8 + 6.56646e8i 2.01966 + 1.87397i
\(706\) 4.84677e8 + 3.63215e7i 1.37733 + 0.103217i
\(707\) 4.22940e8 + 1.65992e8i 1.19680 + 0.469709i
\(708\) 1.15933e8 7.69164e8i 0.326668 2.16730i
\(709\) −1.54836e8 + 7.45651e7i −0.434443 + 0.209217i −0.638306 0.769783i \(-0.720365\pi\)
0.203863 + 0.978999i \(0.434650\pi\)
\(710\) −3.38848e8 7.03626e8i −0.946739 1.96592i
\(711\) −1.09361e9 1.64835e8i −3.04265 0.458606i
\(712\) 2.44716e8 6.23526e8i 0.677989 1.72749i
\(713\) 2.66703e7 3.55891e8i 0.0735800 0.981856i
\(714\) −4.55267e8 + 4.90661e8i −1.25075 + 1.34799i
\(715\) 2.51496e8 + 5.74023e7i 0.688039 + 0.157040i
\(716\) 4.60176e7 + 3.05307e8i 0.125367 + 0.831759i
\(717\) −4.07370e8 5.97502e8i −1.10518 1.62100i
\(718\) 5.04687e7 1.63616e8i 0.136348 0.442029i
\(719\) 1.62953e7 + 2.17446e8i 0.0438406 + 0.585012i 0.975260 + 0.221063i \(0.0709526\pi\)
−0.931419 + 0.363949i \(0.881428\pi\)
\(720\) 9.53426e8 + 7.60332e8i 2.55440 + 2.03707i
\(721\) 2.07757e7 + 6.73531e7i 0.0554306 + 0.179702i
\(722\) 5.67201e8 2.22610e8i 1.50704 0.591470i
\(723\) 2.51175e8 + 1.10047e9i 0.664602 + 2.91181i
\(724\) −4.93225e8 + 8.54291e8i −1.29966 + 2.25108i
\(725\) 1.59736e7 9.22235e6i 0.0419168 0.0242007i
\(726\) −6.69298e8 + 6.21018e8i −1.74908 + 1.62291i
\(727\) −6.81841e7 + 5.43750e7i −0.177452 + 0.141513i −0.708188 0.706024i \(-0.750487\pi\)
0.530736 + 0.847537i \(0.321916\pi\)
\(728\) 1.13743e9 + 7.75488e8i 2.94803 + 2.00993i
\(729\) 9.53798e8 + 4.59325e8i 2.46192 + 1.18560i
\(730\) 1.89898e8i 0.488149i
\(731\) −1.00235e8 + 1.02628e8i −0.256605 + 0.262732i
\(732\) −8.40323e8 −2.14246
\(733\) 1.22271e8 2.53898e8i 0.310464 0.644686i −0.686100 0.727507i \(-0.740679\pi\)
0.996564 + 0.0828214i \(0.0263931\pi\)
\(734\) −6.00678e8 + 8.81033e8i −1.51899 + 2.22794i
\(735\) 6.13161e8 + 7.68879e8i 1.54423 + 1.93641i
\(736\) −8.38771e7 9.03981e7i −0.210383 0.226739i
\(737\) −1.87164e7 3.24177e7i −0.0467541 0.0809804i
\(738\) −4.97585e8 2.87281e8i −1.23794 0.714723i
\(739\) 1.82032e8 4.15476e7i 0.451039 0.102947i 0.00903368 0.999959i \(-0.497124\pi\)
0.442005 + 0.897013i \(0.354267\pi\)
\(740\) −1.82601e8 4.65261e8i −0.450618 1.14816i
\(741\) 2.59089e8 7.99185e7i 0.636788 0.196423i
\(742\) −5.53612e8 + 6.94207e8i −1.35517 + 1.69933i
\(743\) 5.97166e7 4.47514e6i 0.145589 0.0109104i −0.00173616 0.999998i \(-0.500553\pi\)
0.147325 + 0.989088i \(0.452934\pi\)
\(744\) −1.03690e9 3.19842e8i −2.51778 0.776634i
\(745\) 5.21545e8 3.55584e8i 1.26131 0.859949i
\(746\) −8.20754e7 + 1.23709e7i −0.197695 + 0.0297978i
\(747\) −1.08220e8 + 4.74142e8i −0.259624 + 1.13749i
\(748\) −1.24104e8 1.15152e8i −0.296539 0.275148i
\(749\) 5.34450e8 + 4.00515e7i 1.27193 + 0.0953177i
\(750\) 1.25592e9 + 4.92913e8i 2.97700 + 1.16839i
\(751\) −1.62777e7 + 1.07996e8i −0.0384303 + 0.254968i −0.999794 0.0203142i \(-0.993533\pi\)
0.961363 + 0.275283i \(0.0887714\pi\)
\(752\) −6.39826e8 + 3.08124e8i −1.50456 + 0.724556i
\(753\) −5.03964e8 1.04649e9i −1.18036 2.45104i
\(754\) −6.07065e8 9.15003e7i −1.41619 0.213456i
\(755\) 1.94019e8 4.94352e8i 0.450819 1.14867i
\(756\) 3.10894e8 4.14859e9i 0.719526 9.60140i
\(757\) 5.61185e8 6.04813e8i 1.29365 1.39423i 0.420118 0.907470i \(-0.361989\pi\)
0.873537 0.486758i \(-0.161821\pi\)
\(758\) −5.78219e8 1.31975e8i −1.32765 0.303028i
\(759\) 8.79036e7 + 5.83203e8i 0.201040 + 1.33381i
\(760\) −1.31035e8 1.92194e8i −0.298503 0.437823i
\(761\) −6.30995e7 + 2.04563e8i −0.143176 + 0.464167i −0.998549 0.0538462i \(-0.982852\pi\)
0.855373 + 0.518013i \(0.173328\pi\)
\(762\) 1.38126e8 + 1.84316e9i 0.312183 + 4.16579i
\(763\) −4.83031e8 3.85204e8i −1.08743 0.867197i
\(764\) −1.42107e7 4.60699e7i −0.0318665 0.103309i
\(765\) −4.17523e8 + 1.63866e8i −0.932601 + 0.366019i
\(766\) −2.02334e8 8.86484e8i −0.450177 1.97235i
\(767\) 1.60336e8 2.77710e8i 0.355340 0.615467i
\(768\) 1.52350e9 8.79592e8i 3.36324 1.94177i
\(769\) −2.20131e8 + 2.04252e8i −0.484063 + 0.449145i −0.884061 0.467371i \(-0.845201\pi\)
0.399998 + 0.916516i \(0.369011\pi\)
\(770\) −5.18981e8 + 4.13873e8i −1.13679 + 0.906557i
\(771\) 4.95977e8 + 3.38151e8i 1.08218 + 0.737816i
\(772\) −5.27062e8 2.53820e8i −1.14554 0.551662i
\(773\) 4.81812e8i 1.04313i 0.853211 + 0.521566i \(0.174652\pi\)
−0.853211 + 0.521566i \(0.825348\pi\)
\(774\) 2.14022e8 2.12448e9i 0.461568 4.58174i
\(775\) 2.60654e7 0.0559962
\(776\) 5.96337e8 1.23831e9i 1.27616 2.64998i
\(777\) −4.35435e8 + 6.38666e8i −0.928240 + 1.36148i
\(778\) −6.30612e7 7.90762e7i −0.133913 0.167922i
\(779\) 2.73682e7 + 2.94959e7i 0.0578940 + 0.0623949i
\(780\) 1.23461e9 + 2.13840e9i 2.60162 + 4.50614i
\(781\) −2.64564e8 1.52746e8i −0.555363 0.320639i
\(782\) 3.97703e8 9.07730e7i 0.831646 0.189818i
\(783\) 3.49494e8 + 8.90495e8i 0.728038 + 1.85501i
\(784\) −6.91272e8 + 2.13229e8i −1.43450 + 0.442485i
\(785\) 3.89950e8 4.88982e8i 0.806121 1.01084i
\(786\) 1.54844e9 1.16039e8i 3.18879 0.238967i
\(787\) 6.10716e7 + 1.88381e7i 0.125290 + 0.0386467i 0.356766 0.934194i \(-0.383879\pi\)
−0.231476 + 0.972841i \(0.574356\pi\)
\(788\) 3.97126e8 2.70756e8i 0.811614 0.553349i
\(789\) −1.33177e8 + 2.00732e7i −0.271142 + 0.0408681i
\(790\) −2.32979e8 + 1.02075e9i −0.472536 + 2.07032i
\(791\) −6.96482e7 6.46240e7i −0.140728 0.130576i
\(792\) 1.29567e9 + 9.70973e7i 2.60807 + 0.195448i
\(793\) −3.22478e8 1.26563e8i −0.646667 0.253798i
\(794\) −3.48129e7 + 2.30968e8i −0.0695470 + 0.461414i
\(795\) −7.39870e8 + 3.56302e8i −1.47250 + 0.709116i
\(796\) 7.56022e8 + 1.56990e9i 1.49898 + 3.11266i
\(797\) 4.67825e8 + 7.05133e7i 0.924077 + 0.139282i 0.593810 0.804605i \(-0.297623\pi\)
0.330267 + 0.943887i \(0.392861\pi\)
\(798\) −2.54896e8 + 6.49465e8i −0.501597 + 1.27805i
\(799\) 1.95193e7 2.60466e8i 0.0382669 0.510636i
\(800\) 6.12597e6 6.60223e6i 0.0119648 0.0128950i
\(801\) −1.31253e9 2.99577e8i −2.55395 0.582923i
\(802\) −1.52646e8 1.01274e9i −0.295912 1.96325i
\(803\) 4.18450e7 + 6.13754e7i 0.0808160 + 0.118535i
\(804\) 1.05612e8 3.42385e8i 0.203210 0.658790i
\(805\) −8.05236e7 1.07451e9i −0.154360 2.05980i
\(806\) −6.78295e8 5.40922e8i −1.29543 1.03307i
\(807\) −4.71901e7 1.52987e8i −0.0897905 0.291094i
\(808\) −7.83717e8 + 3.07586e8i −1.48568 + 0.583086i
\(809\) 1.60500e8 + 7.03197e8i 0.303131 + 1.32810i 0.865373 + 0.501129i \(0.167082\pi\)
−0.562242 + 0.826973i \(0.690061\pi\)
\(810\) 1.58667e9 2.74819e9i 2.98559 5.17120i
\(811\) 2.28837e8 1.32119e8i 0.429006 0.247687i −0.269917 0.962884i \(-0.586996\pi\)
0.698923 + 0.715197i \(0.253663\pi\)
\(812\) 7.80158e8 7.23881e8i 1.45718 1.35207i
\(813\) −3.00506e8 + 2.39646e8i −0.559219 + 0.445963i
\(814\) −2.39786e8 1.63483e8i −0.444580 0.303110i
\(815\) −2.96765e8 1.42915e8i −0.548201 0.264000i
\(816\) 4.55362e8i 0.838081i
\(817\) −5.81758e7 + 1.37752e8i −0.106678 + 0.252599i
\(818\) −5.20410e8 −0.950792
\(819\) 1.20051e9 2.49289e9i 2.18532 4.53787i
\(820\) −2.06421e8 + 3.02764e8i −0.374380 + 0.549114i
\(821\) 2.88127e8 + 3.61300e8i 0.520661 + 0.652888i 0.970749 0.240096i \(-0.0771788\pi\)
−0.450088 + 0.892984i \(0.648607\pi\)
\(822\) 2.57185e8 + 2.77180e8i 0.463053 + 0.499052i
\(823\) 3.17554e8 + 5.50019e8i 0.569662 + 0.986684i 0.996599 + 0.0824025i \(0.0262593\pi\)
−0.426937 + 0.904281i \(0.640407\pi\)
\(824\) −1.13111e8 6.53047e7i −0.202173 0.116725i
\(825\) −4.19954e7 + 9.58517e6i −0.0747893 + 0.0170702i
\(826\) 3.01466e8 + 7.68122e8i 0.534931 + 1.36298i
\(827\) 5.83256e7 1.79911e7i 0.103120 0.0318083i −0.242766 0.970085i \(-0.578055\pi\)
0.345886 + 0.938277i \(0.387578\pi\)
\(828\) −2.55035e9 + 3.19803e9i −4.49271 + 5.63368i
\(829\) −2.37074e8 + 1.77662e7i −0.416121 + 0.0311840i −0.281146 0.959665i \(-0.590714\pi\)
−0.134975 + 0.990849i \(0.543095\pi\)
\(830\) 4.39953e8 + 1.35707e8i 0.769434 + 0.237339i
\(831\) 3.57552e8 2.43775e8i 0.623070 0.424802i
\(832\) 5.73544e8 8.64478e7i 0.995856 0.150101i
\(833\) 5.92069e7 2.59402e8i 0.102432 0.448785i
\(834\) −2.67217e9 2.47942e9i −4.60645 4.27416i
\(835\) −9.52696e8 7.13947e7i −1.63642 0.122633i
\(836\) −1.64271e8 6.44716e7i −0.281152 0.110344i
\(837\) −2.01485e8 + 1.33676e9i −0.343610 + 2.27970i
\(838\) 3.73673e8 1.79951e8i 0.634979 0.305790i
\(839\) 2.50964e8 + 5.21132e8i 0.424938 + 0.882392i 0.998020 + 0.0628944i \(0.0200331\pi\)
−0.573083 + 0.819498i \(0.694253\pi\)
\(840\) −3.23959e9 4.88290e8i −5.46579 0.823835i
\(841\) 1.27906e8 3.25900e8i 0.215033 0.547895i
\(842\) −1.20681e8 + 1.61037e9i −0.202163 + 2.69768i
\(843\) −3.61010e7 + 3.89076e7i −0.0602610 + 0.0649459i
\(844\) 1.11170e8 + 2.53738e7i 0.184909 + 0.0422044i
\(845\) 5.84598e7 + 3.87855e8i 0.0968918 + 0.642835i
\(846\) 2.19004e9 + 3.21220e9i 3.61693 + 5.30507i
\(847\) 1.92329e8 6.23514e8i 0.316515 1.02611i
\(848\) −4.51421e7 6.02379e8i −0.0740276 0.987830i
\(849\) 1.36790e9 + 1.09087e9i 2.23528 + 1.78258i
\(850\) 8.78170e6 + 2.84696e7i 0.0142995 + 0.0463580i
\(851\) 4.38529e8 1.72110e8i 0.711557 0.279265i
\(852\) −6.50684e8 2.85083e9i −1.05209 4.60949i
\(853\) −4.27166e7 + 7.39873e7i −0.0688255 + 0.119209i −0.898385 0.439210i \(-0.855258\pi\)
0.829559 + 0.558419i \(0.188592\pi\)
\(854\) 7.72003e8 4.45716e8i 1.23950 0.715624i
\(855\) −3.42722e8 + 3.18000e8i −0.548333 + 0.508778i
\(856\) −7.76456e8 + 6.19203e8i −1.23793 + 0.987215i
\(857\) 9.61546e7 + 6.55571e7i 0.152766 + 0.104154i 0.637291 0.770623i \(-0.280055\pi\)
−0.484525 + 0.874778i \(0.661007\pi\)
\(858\) 1.29175e9 + 6.22076e8i 2.04512 + 0.984876i
\(859\) 5.87245e8i 0.926488i −0.886231 0.463244i \(-0.846685\pi\)
0.886231 0.463244i \(-0.153315\pi\)
\(860\) −1.34094e9 2.37368e8i −2.10820 0.373187i
\(861\) 5.66711e8 0.887875
\(862\) −5.73569e8 + 1.19103e9i −0.895496 + 1.85952i
\(863\) −5.58940e8 + 8.19815e8i −0.869627 + 1.27551i 0.0904866 + 0.995898i \(0.471158\pi\)
−0.960113 + 0.279611i \(0.909795\pi\)
\(864\) 2.91242e8 + 3.65206e8i 0.451557 + 0.566235i
\(865\) 4.29605e8 + 4.63004e8i 0.663775 + 0.715379i
\(866\) −9.62372e8 1.66688e9i −1.48180 2.56655i
\(867\) −9.30362e8 5.37145e8i −1.42756 0.824203i
\(868\) 1.46627e9 3.34666e8i 2.24209 0.511743i
\(869\) 1.49627e8 + 3.81245e8i 0.228009 + 0.580958i
\(870\) 1.39613e9 4.30649e8i 2.12016 0.653982i
\(871\) 9.20966e7 1.15486e8i 0.139376 0.174772i
\(872\) 1.14163e9 8.55534e7i 1.72177 0.129029i
\(873\) −2.63971e9 8.14242e8i −3.96747 1.22380i
\(874\) 3.51326e8 2.39530e8i 0.526230 0.358777i
\(875\) −9.53436e8 + 1.43707e8i −1.42320 + 0.214514i
\(876\) −1.58219e8 + 6.93203e8i −0.235368 + 1.03121i
\(877\) −2.36693e8 2.19619e8i −0.350902 0.325590i 0.484953 0.874540i \(-0.338837\pi\)
−0.835855 + 0.548951i \(0.815027\pi\)
\(878\) 2.01952e9 + 1.51342e8i 2.98377 + 0.223603i
\(879\) −8.48860e8 3.33153e8i −1.24988 0.490543i
\(880\) 6.73065e7 4.46550e8i 0.0987664 0.655272i
\(881\) 4.89665e8 2.35810e8i 0.716096 0.344854i −0.0401030 0.999196i \(-0.512769\pi\)
0.756199 + 0.654342i \(0.227054\pi\)
\(882\) 1.71832e9 + 3.56812e9i 2.50436 + 5.20036i
\(883\) 5.17139e8 + 7.79462e7i 0.751147 + 0.113217i 0.513447 0.858121i \(-0.328368\pi\)
0.237700 + 0.971339i \(0.423606\pi\)
\(884\) 2.44069e8 6.21878e8i 0.353310 0.900219i
\(885\) −5.70301e7 + 7.61014e8i −0.0822763 + 1.09790i
\(886\) −1.58309e9 + 1.70617e9i −2.27617 + 2.45313i
\(887\) 9.53750e8 + 2.17687e8i 1.36667 + 0.311934i 0.842048 0.539402i \(-0.181350\pi\)
0.524622 + 0.851335i \(0.324207\pi\)
\(888\) −2.13480e8 1.41635e9i −0.304873 2.02270i
\(889\) −7.44100e8 1.09139e9i −1.05907 1.55338i
\(890\) −3.75669e8 + 1.21789e9i −0.532888 + 1.72758i
\(891\) −9.27639e7 1.23785e9i −0.131143 1.74998i
\(892\) −1.69044e9 1.34808e9i −2.38181 1.89943i
\(893\) −8.02505e7 2.60166e8i −0.112692 0.365339i
\(894\) 3.26579e9 1.28173e9i 4.57063 1.79384i
\(895\) −6.74058e7 2.95324e8i −0.0940217 0.411936i
\(896\) −8.72126e8 + 1.51057e9i −1.21243 + 2.09998i
\(897\) −2.01554e9 + 1.16367e9i −2.79263 + 1.61233i
\(898\) −3.63966e6 + 3.37711e6i −0.00502611 + 0.00466354i
\(899\) −2.70382e8 + 2.15622e8i −0.372133 + 0.296767i
\(900\) −2.46835e8 1.68289e8i −0.338594 0.230850i
\(901\) 2.00176e8 + 9.63995e7i 0.273676 + 0.131795i
\(902\) 2.12770e8i 0.289929i
\(903\) 8.64911e8 + 1.92026e9i 1.17465 + 2.60794i
\(904\) 1.76058e8 0.238314
\(905\) 4.19914e8 8.71961e8i 0.566519 1.17639i
\(906\) 1.66269e9 2.43872e9i 2.23577 3.27927i
\(907\) −1.14503e8 1.43582e8i −0.153460 0.192433i 0.699158 0.714967i \(-0.253558\pi\)
−0.852619 + 0.522534i \(0.824987\pi\)
\(908\) 2.40921e8 + 2.59651e8i 0.321823 + 0.346843i
\(909\) 8.46082e8 + 1.46546e9i 1.12647 + 1.95111i
\(910\) −2.26846e9 1.30970e9i −3.01028 1.73799i
\(911\) −1.07677e9 + 2.45767e8i −1.42419 + 0.325063i −0.864081 0.503353i \(-0.832100\pi\)
−0.560113 + 0.828416i \(0.689242\pi\)
\(912\) −1.73410e8 4.41841e8i −0.228607 0.582480i
\(913\) 1.72097e8 5.30849e7i 0.226131 0.0697523i
\(914\) 9.40392e8 1.17921e9i 1.23160 1.54438i
\(915\) 8.22132e8 6.16103e7i 1.07319 0.0804248i
\(916\) −2.08888e8 6.44334e7i −0.271786 0.0838348i
\(917\) −9.16882e8 + 6.25120e8i −1.18907 + 0.810691i
\(918\) −1.52795e9 + 2.30301e8i −1.97506 + 0.297692i
\(919\) −1.03587e8 + 4.53843e8i −0.133462 + 0.584735i 0.863326 + 0.504647i \(0.168377\pi\)
−0.996788 + 0.0800879i \(0.974480\pi\)
\(920\) 1.46367e9 + 1.35809e9i 1.87966 + 1.74407i
\(921\) −3.17863e8 2.38206e7i −0.406876 0.0304911i
\(922\) 7.25909e8 + 2.84898e8i 0.926167 + 0.363494i
\(923\) 1.79668e8 1.19202e9i 0.228490 1.51593i
\(924\) −2.23931e9 + 1.07840e9i −2.83857 + 1.36698i
\(925\) 1.49284e7 + 3.09991e7i 0.0188620 + 0.0391673i
\(926\) −1.38180e9 2.08273e8i −1.74026 0.262302i
\(927\) −9.59062e7 + 2.44365e8i −0.120395 + 0.306761i
\(928\) −8.93001e6 + 1.19163e8i −0.0111740 + 0.149106i
\(929\) 5.13405e8 5.53319e8i 0.640343 0.690126i −0.326587 0.945167i \(-0.605899\pi\)
0.966930 + 0.255041i \(0.0820891\pi\)
\(930\) 2.01292e9 + 4.59436e8i 2.50252 + 0.571184i
\(931\) −4.13360e7 2.74247e8i −0.0512247 0.339854i
\(932\) 9.83177e7 + 1.44206e8i 0.121446 + 0.178129i
\(933\) 4.56308e8 1.47931e9i 0.561840 1.82144i
\(934\) −1.72462e8 2.30134e9i −0.211666 2.82449i
\(935\) 1.29860e8 + 1.03560e8i 0.158870 + 0.126695i
\(936\) 1.51125e9 + 4.89934e9i 1.84293 + 5.97462i
\(937\) −2.08818e8 + 8.19549e7i −0.253833 + 0.0996222i −0.488846 0.872370i \(-0.662582\pi\)
0.235013 + 0.971992i \(0.424487\pi\)
\(938\) 8.45794e7 + 3.70567e8i 0.102484 + 0.449012i
\(939\) 9.80522e8 1.69831e9i 1.18430 2.05126i
\(940\) 2.14728e9 1.23973e9i 2.58527 1.49261i
\(941\) −1.70905e8 + 1.58577e8i −0.205110 + 0.190314i −0.776038 0.630686i \(-0.782774\pi\)
0.570929 + 0.821000i \(0.306583\pi\)
\(942\) 2.71772e9 2.16731e9i 3.25126 2.59279i
\(943\) −2.85369e8 1.94561e8i −0.340307 0.232018i
\(944\) −5.05777e8 2.43569e8i −0.601233 0.289539i
\(945\) 4.08158e9i 4.83652i
\(946\) −7.20959e8 + 3.24729e8i −0.851602 + 0.383572i
\(947\) −2.16468e8 −0.254885 −0.127442 0.991846i \(-0.540677\pi\)
−0.127442 + 0.991846i \(0.540677\pi\)
\(948\) −1.70093e9 + 3.53201e9i −1.99646 + 4.14569i
\(949\) −1.65122e8 + 2.42190e8i −0.193200 + 0.283373i
\(950\) 1.93627e7 + 2.42800e7i 0.0225836 + 0.0283190i
\(951\) −1.76319e9 1.90027e9i −2.05002 2.20940i
\(952\) 4.43195e8 + 7.67636e8i 0.513670 + 0.889702i
\(953\) 6.75509e8 + 3.90006e8i 0.780464 + 0.450601i 0.836595 0.547823i \(-0.184543\pi\)
−0.0561309 + 0.998423i \(0.517876\pi\)
\(954\) −3.22406e9 + 7.35870e8i −3.71328 + 0.847532i
\(955\) 1.72808e7 + 4.40307e7i 0.0198405 + 0.0505529i
\(956\) −1.77478e9 + 5.47447e8i −2.03128 + 0.626568i
\(957\) 3.56335e8 4.46830e8i 0.406558 0.509808i
\(958\) −2.43464e9 + 1.82451e8i −2.76910 + 0.207515i
\(959\) −2.58219e8 7.96501e7i −0.292774 0.0903089i
\(960\) −1.14051e9 + 7.77586e8i −1.28910 + 0.878891i
\(961\) 3.94333e8 5.94362e7i 0.444317 0.0669701i
\(962\) 2.54830e8 1.11648e9i 0.286237 1.25409i
\(963\) 1.46323e9 + 1.35768e9i 1.63845 + 1.52026i
\(964\) 2.89092e9 + 2.16645e8i 3.22705 + 0.241834i
\(965\) 5.34262e8 + 2.09682e8i 0.594528 + 0.233335i
\(966\) 8.92583e8 5.92190e9i 0.990187 6.56946i
\(967\) 8.48266e8 4.08504e8i 0.938108 0.451769i 0.0986066 0.995126i \(-0.468561\pi\)
0.839501 + 0.543358i \(0.182847\pi\)
\(968\) 5.24609e8 + 1.08936e9i 0.578375 + 1.20101i
\(969\) 1.72629e8 + 2.60196e7i 0.189732 + 0.0285975i
\(970\) −9.55426e8 + 2.43439e9i −1.04684 + 2.66731i
\(971\) −4.47704e7 + 5.97420e8i −0.0489028 + 0.652562i 0.917863 + 0.396898i \(0.129913\pi\)
−0.966766 + 0.255664i \(0.917706\pi\)
\(972\) 4.07536e9 4.39219e9i 4.43779 4.78280i
\(973\) 2.53981e9 + 5.79694e8i 2.75716 + 0.629304i
\(974\) 8.68732e7 + 5.76366e8i 0.0940175 + 0.623765i
\(975\) −9.57517e7 1.40442e8i −0.103308 0.151525i
\(976\) −1.78756e8 + 5.79511e8i −0.192269 + 0.623322i
\(977\) 2.81411e7 + 3.75517e8i 0.0301757 + 0.402667i 0.991756 + 0.128142i \(0.0409014\pi\)
−0.961580 + 0.274524i \(0.911480\pi\)
\(978\) −1.43129e9 1.14142e9i −1.53007 1.22019i
\(979\) 1.46951e8 + 4.76404e8i 0.156612 + 0.507724i
\(980\) 2.35116e9 9.22763e8i 2.49807 0.980420i
\(981\) −5.12020e8 2.24331e9i −0.542350 2.37619i
\(982\) 9.01162e8 1.56086e9i 0.951630 1.64827i
\(983\) −3.51216e8 + 2.02775e8i −0.369755 + 0.213478i −0.673351 0.739323i \(-0.735146\pi\)
0.303597 + 0.952801i \(0.401812\pi\)
\(984\) −7.69797e8 + 7.14267e8i −0.807962 + 0.749679i
\(985\) −3.68678e8 + 2.94011e8i −0.385779 + 0.307649i
\(986\) −3.26606e8 2.22676e8i −0.340716 0.232296i
\(987\) −3.45486e9 1.66377e9i −3.59318 1.73039i
\(988\) 6.96358e8i 0.722041i
\(989\) 2.23730e8 1.26389e9i 0.231278 1.30653i
\(990\) −2.47225e9 −2.54792
\(991\) −4.45592e8 + 9.25280e8i −0.457842 + 0.950719i 0.536440 + 0.843938i \(0.319769\pi\)
−0.994283 + 0.106781i \(0.965946\pi\)
\(992\) −9.51270e7 + 1.39526e8i −0.0974471 + 0.142929i
\(993\) −8.18182e8 1.02597e9i −0.835607 1.04782i
\(994\) 2.10989e9 + 2.27393e9i 2.14833 + 2.31535i
\(995\) −8.54757e8 1.48048e9i −0.867708 1.50291i
\(996\) 1.49293e9 + 8.61944e8i 1.51099 + 0.872371i
\(997\) 7.34351e8 1.67611e8i 0.741000 0.169128i 0.164674 0.986348i \(-0.447343\pi\)
0.576326 + 0.817220i \(0.304486\pi\)
\(998\) −2.11971e8 5.40092e8i −0.213248 0.543346i
\(999\) −1.70518e9 + 5.25980e8i −1.71031 + 0.527561i
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 43.7.h.a.18.3 yes 252
43.12 odd 42 inner 43.7.h.a.12.3 252
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.7.h.a.12.3 252 43.12 odd 42 inner
43.7.h.a.18.3 yes 252 1.1 even 1 trivial