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Properties

Label 27.7.f.a.5.1
Level $27$
Weight $7$
Character 27.5
Analytic conductor $6.211$
Analytic rank $0$
Dimension $102$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [27,7,Mod(2,27)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(27, base_ring=CyclotomicField(18))
 
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("27.2");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 27.f (of order \(18\), degree \(6\), 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: \(6.21146025774\)
Analytic rank: \(0\)
Dimension: \(102\)
Relative dimension: \(17\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.1
Character \(\chi\) \(=\) 27.5
Dual form 27.7.f.a.11.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-9.07449 - 10.8146i) q^{2} +(-10.8701 - 24.7152i) q^{3} +(-23.4948 + 133.245i) q^{4} +(72.7572 + 199.899i) q^{5} +(-168.644 + 341.833i) q^{6} +(-62.5083 - 354.502i) q^{7} +(871.728 - 503.293i) q^{8} +(-492.683 + 537.312i) q^{9} +O(q^{10})\) \(q+(-9.07449 - 10.8146i) q^{2} +(-10.8701 - 24.7152i) q^{3} +(-23.4948 + 133.245i) q^{4} +(72.7572 + 199.899i) q^{5} +(-168.644 + 341.833i) q^{6} +(-62.5083 - 354.502i) q^{7} +(871.728 - 503.293i) q^{8} +(-492.683 + 537.312i) q^{9} +(1501.58 - 2600.82i) q^{10} +(-422.390 + 1160.51i) q^{11} +(3548.58 - 867.711i) q^{12} +(279.909 + 234.872i) q^{13} +(-3266.55 + 3892.92i) q^{14} +(4149.66 - 3971.13i) q^{15} +(-5216.33 - 1898.59i) q^{16} +(5152.94 + 2975.05i) q^{17} +(10281.6 + 452.309i) q^{18} +(378.683 + 655.898i) q^{19} +(-28345.0 + 4998.00i) q^{20} +(-8082.12 + 5398.37i) q^{21} +(16383.3 - 5963.04i) q^{22} +(-4532.94 - 799.279i) q^{23} +(-21914.7 - 16074.1i) q^{24} +(-22696.5 + 19044.6i) q^{25} -5158.44i q^{26} +(18635.3 + 6336.13i) q^{27} +48704.4 q^{28} +(25769.1 + 30710.4i) q^{29} +(-80602.1 - 8840.84i) q^{30} +(2055.59 - 11657.8i) q^{31} +(4769.70 + 13104.7i) q^{32} +(33273.5 - 2175.34i) q^{33} +(-14586.4 - 82723.8i) q^{34} +(66316.6 - 38287.9i) q^{35} +(-60019.0 - 78271.8i) q^{36} +(-34125.4 + 59106.9i) q^{37} +(3656.89 - 10047.2i) q^{38} +(2762.27 - 9471.09i) q^{39} +(164032. + 137639. i) q^{40} +(-71839.0 + 85614.3i) q^{41} +(131722. + 38417.1i) q^{42} +(56516.0 + 20570.1i) q^{43} +(-144708. - 83547.3i) q^{44} +(-143254. - 59393.4i) q^{45} +(32490.3 + 56274.8i) q^{46} +(-86257.8 + 15209.6i) q^{47} +(9777.90 + 149560. i) q^{48} +(-11210.5 + 4080.30i) q^{49} +(411918. + 72632.3i) q^{50} +(17516.1 - 159695. i) q^{51} +(-37872.0 + 31778.4i) q^{52} -24119.7i q^{53} +(-100583. - 259030. i) q^{54} -262716. q^{55} +(-232908. - 277570. i) q^{56} +(12094.4 - 16488.9i) q^{57} +(98278.1 - 557363. i) q^{58} +(50421.6 + 138532. i) q^{59} +(431639. + 646225. i) q^{60} +(-21701.4 - 123075. i) q^{61} +(-144728. + 83558.6i) q^{62} +(221275. + 141071. i) q^{63} +(-79196.9 + 137173. i) q^{64} +(-26585.2 + 73042.2i) q^{65} +(-325466. - 340099. i) q^{66} +(50021.0 + 41972.6i) q^{67} +(-517479. + 616708. i) q^{68} +(29519.0 + 120721. i) q^{69} +(-1.01586e6 - 369742. i) q^{70} +(-81373.5 - 46981.0i) q^{71} +(-159060. + 716354. i) q^{72} +(-115937. - 200808. i) q^{73} +(948886. - 167314. i) q^{74} +(717405. + 353932. i) q^{75} +(-96292.6 + 35047.6i) q^{76} +(437805. + 77196.8i) q^{77} +(-127492. + 56072.6i) q^{78} +(-286190. + 240142. i) q^{79} -1.18087e6i q^{80} +(-45968.3 - 529449. i) q^{81} +1.57778e6 q^{82} +(-172181. - 205198. i) q^{83} +(-529421. - 1.20374e6i) q^{84} +(-219796. + 1.24652e6i) q^{85} +(-290397. - 797859. i) q^{86} +(478902. - 970713. i) q^{87} +(215865. + 1.22423e6i) q^{88} +(574942. - 331943. i) q^{89} +(657648. + 2.08820e6i) q^{90} +(65765.9 - 113910. i) q^{91} +(213001. - 585215. i) q^{92} +(-310470. + 75917.2i) q^{93} +(947230. + 794821. i) q^{94} +(-103561. + 123420. i) q^{95} +(272037. - 260333. i) q^{96} +(182940. + 66584.8i) q^{97} +(145856. + 84210.2i) q^{98} +(-415450. - 798716. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9.07449 − 10.8146i −1.13431 − 1.35182i −0.927669 − 0.373403i \(-0.878191\pi\)
−0.206642 − 0.978417i \(-0.566254\pi\)
\(3\) −10.8701 − 24.7152i −0.402595 − 0.915378i
\(4\) −23.4948 + 133.245i −0.367106 + 2.08196i
\(5\) 72.7572 + 199.899i 0.582058 + 1.59919i 0.784658 + 0.619929i \(0.212839\pi\)
−0.202600 + 0.979262i \(0.564939\pi\)
\(6\) −168.644 + 341.833i −0.780757 + 1.58256i
\(7\) −62.5083 − 354.502i −0.182240 − 1.03353i −0.929451 − 0.368947i \(-0.879719\pi\)
0.747211 − 0.664587i \(-0.231393\pi\)
\(8\) 871.728 − 503.293i 1.70259 − 0.982993i
\(9\) −492.683 + 537.312i −0.675834 + 0.737054i
\(10\) 1501.58 − 2600.82i 1.50158 − 2.60082i
\(11\) −422.390 + 1160.51i −0.317348 + 0.871905i 0.673773 + 0.738938i \(0.264673\pi\)
−0.991120 + 0.132967i \(0.957550\pi\)
\(12\) 3548.58 − 867.711i 2.05358 − 0.502147i
\(13\) 279.909 + 234.872i 0.127405 + 0.106906i 0.704264 − 0.709938i \(-0.251277\pi\)
−0.576859 + 0.816844i \(0.695722\pi\)
\(14\) −3266.55 + 3892.92i −1.19043 + 1.41870i
\(15\) 4149.66 − 3971.13i 1.22953 − 1.17663i
\(16\) −5216.33 − 1898.59i −1.27352 − 0.463523i
\(17\) 5152.94 + 2975.05i 1.04884 + 0.605546i 0.922324 − 0.386418i \(-0.126288\pi\)
0.126514 + 0.991965i \(0.459621\pi\)
\(18\) 10281.6 + 452.309i 1.76297 + 0.0775565i
\(19\) 378.683 + 655.898i 0.0552097 + 0.0956260i 0.892309 − 0.451424i \(-0.149084\pi\)
−0.837100 + 0.547050i \(0.815751\pi\)
\(20\) −28345.0 + 4998.00i −3.54313 + 0.624749i
\(21\) −8082.12 + 5398.37i −0.872705 + 0.582914i
\(22\) 16383.3 − 5963.04i 1.53863 − 0.560015i
\(23\) −4532.94 − 799.279i −0.372560 − 0.0656924i −0.0157667 − 0.999876i \(-0.505019\pi\)
−0.356793 + 0.934183i \(0.616130\pi\)
\(24\) −21914.7 − 16074.1i −1.58527 − 1.16277i
\(25\) −22696.5 + 19044.6i −1.45258 + 1.21886i
\(26\) − 5158.44i − 0.293493i
\(27\) 18635.3 + 6336.13i 0.946771 + 0.321909i
\(28\) 48704.4 2.21868
\(29\) 25769.1 + 30710.4i 1.05659 + 1.25919i 0.964680 + 0.263423i \(0.0848516\pi\)
0.0919063 + 0.995768i \(0.470704\pi\)
\(30\) −80602.1 − 8840.84i −2.98526 − 0.327438i
\(31\) 2055.59 − 11657.8i 0.0690004 − 0.391321i −0.930675 − 0.365847i \(-0.880779\pi\)
0.999675 − 0.0254739i \(-0.00810948\pi\)
\(32\) 4769.70 + 13104.7i 0.145560 + 0.399922i
\(33\) 33273.5 − 2175.34i 0.925886 − 0.0605322i
\(34\) −14586.4 − 82723.8i −0.371118 − 2.10472i
\(35\) 66316.6 − 38287.9i 1.54674 − 0.893013i
\(36\) −60019.0 − 78271.8i −1.28642 − 1.67764i
\(37\) −34125.4 + 59106.9i −0.673709 + 1.16690i 0.303135 + 0.952948i \(0.401967\pi\)
−0.976844 + 0.213951i \(0.931367\pi\)
\(38\) 3656.89 − 10047.2i 0.0666441 − 0.183103i
\(39\) 2762.27 − 9471.09i 0.0465663 − 0.159664i
\(40\) 164032. + 137639.i 2.56300 + 2.15061i
\(41\) −71839.0 + 85614.3i −1.04234 + 1.24221i −0.0727797 + 0.997348i \(0.523187\pi\)
−0.969558 + 0.244862i \(0.921257\pi\)
\(42\) 131722. + 38417.1i 1.77791 + 0.518533i
\(43\) 56516.0 + 20570.1i 0.710830 + 0.258721i 0.672028 − 0.740526i \(-0.265423\pi\)
0.0388024 + 0.999247i \(0.487646\pi\)
\(44\) −144708. − 83547.3i −1.69877 − 0.980787i
\(45\) −143254. − 59393.4i −1.57206 − 0.651779i
\(46\) 32490.3 + 56274.8i 0.333795 + 0.578150i
\(47\) −86257.8 + 15209.6i −0.830816 + 0.146495i −0.572851 − 0.819659i \(-0.694163\pi\)
−0.257964 + 0.966154i \(0.583052\pi\)
\(48\) 9777.90 + 149560.i 0.0884142 + 1.35236i
\(49\) −11210.5 + 4080.30i −0.0952879 + 0.0346820i
\(50\) 411918. + 72632.3i 3.29535 + 0.581059i
\(51\) 17516.1 − 159695.i 0.132047 − 1.20387i
\(52\) −37872.0 + 31778.4i −0.269345 + 0.226007i
\(53\) − 24119.7i − 0.162011i −0.996714 − 0.0810055i \(-0.974187\pi\)
0.996714 − 0.0810055i \(-0.0258131\pi\)
\(54\) −100583. − 259030.i −0.638770 − 1.64501i
\(55\) −262716. −1.57906
\(56\) −232908. − 277570.i −1.32624 − 1.58055i
\(57\) 12094.4 − 16488.9i 0.0653067 − 0.0890363i
\(58\) 98278.1 − 557363.i 0.503701 − 2.85663i
\(59\) 50421.6 + 138532.i 0.245505 + 0.674520i 0.999837 + 0.0180273i \(0.00573859\pi\)
−0.754332 + 0.656493i \(0.772039\pi\)
\(60\) 431639. + 646225.i 1.99833 + 2.99178i
\(61\) −21701.4 − 123075.i −0.0956087 − 0.542224i −0.994559 − 0.104174i \(-0.966780\pi\)
0.898950 − 0.438050i \(-0.144331\pi\)
\(62\) −144728. + 83558.6i −0.607263 + 0.350603i
\(63\) 221275. + 141071.i 0.884934 + 0.564176i
\(64\) −79196.9 + 137173.i −0.302112 + 0.523274i
\(65\) −26585.2 + 73042.2i −0.0968054 + 0.265971i
\(66\) −325466. − 340099.i −1.13207 − 1.18297i
\(67\) 50021.0 + 41972.6i 0.166314 + 0.139554i 0.722146 − 0.691741i \(-0.243156\pi\)
−0.555832 + 0.831294i \(0.687600\pi\)
\(68\) −517479. + 616708.i −1.64576 + 1.96134i
\(69\) 29519.0 + 120721.i 0.0898577 + 0.367481i
\(70\) −1.01586e6 − 369742.i −2.96168 − 1.07796i
\(71\) −81373.5 − 46981.0i −0.227357 − 0.131265i 0.381995 − 0.924164i \(-0.375237\pi\)
−0.609352 + 0.792900i \(0.708570\pi\)
\(72\) −159060. + 716354.i −0.426151 + 1.91924i
\(73\) −115937. − 200808.i −0.298025 − 0.516195i 0.677659 − 0.735376i \(-0.262995\pi\)
−0.975684 + 0.219182i \(0.929661\pi\)
\(74\) 948886. − 167314.i 2.34163 − 0.412893i
\(75\) 717405. + 353932.i 1.70051 + 0.838950i
\(76\) −96292.6 + 35047.6i −0.219357 + 0.0798395i
\(77\) 437805. + 77196.8i 0.958977 + 0.169093i
\(78\) −127492. + 56072.6i −0.268657 + 0.118159i
\(79\) −286190. + 240142.i −0.580462 + 0.487065i −0.885099 − 0.465403i \(-0.845909\pi\)
0.304637 + 0.952469i \(0.401465\pi\)
\(80\) − 1.18087e6i − 2.30640i
\(81\) −45968.3 − 529449.i −0.0864975 − 0.996252i
\(82\) 1.57778e6 2.86158
\(83\) −172181. − 205198.i −0.301128 − 0.358871i 0.594169 − 0.804341i \(-0.297481\pi\)
−0.895297 + 0.445470i \(0.853037\pi\)
\(84\) −529421. − 1.20374e6i −0.893230 − 2.03093i
\(85\) −219796. + 1.24652e6i −0.357900 + 2.02975i
\(86\) −290397. − 797859.i −0.456559 − 1.25438i
\(87\) 478902. − 970713.i 0.727259 − 1.47412i
\(88\) 215865. + 1.22423e6i 0.316763 + 1.79645i
\(89\) 574942. − 331943.i 0.815557 − 0.470862i −0.0333251 − 0.999445i \(-0.510610\pi\)
0.848882 + 0.528583i \(0.177276\pi\)
\(90\) 657648. + 2.08820e6i 0.902123 + 2.86447i
\(91\) 65765.9 − 113910.i 0.0872723 − 0.151160i
\(92\) 213001. − 585215.i 0.273538 − 0.751540i
\(93\) −310470. + 75917.2i −0.385986 + 0.0943825i
\(94\) 947230. + 794821.i 1.14044 + 0.956942i
\(95\) −103561. + 123420.i −0.120789 + 0.143951i
\(96\) 272037. − 260333.i 0.307478 − 0.294249i
\(97\) 182940. + 66584.8i 0.200444 + 0.0729558i 0.440291 − 0.897855i \(-0.354875\pi\)
−0.239847 + 0.970811i \(0.577097\pi\)
\(98\) 145856. + 84210.2i 0.154970 + 0.0894719i
\(99\) −415450. − 798716.i −0.428167 − 0.823165i
\(100\) −2.00436e6 − 3.47166e6i −2.00436 − 3.47166i
\(101\) 21604.7 − 3809.50i 0.0209693 − 0.00369746i −0.163154 − 0.986601i \(-0.552167\pi\)
0.184123 + 0.982903i \(0.441056\pi\)
\(102\) −1.88598e6 + 1.25972e6i −1.77720 + 1.18706i
\(103\) −364371. + 132620.i −0.333451 + 0.121366i −0.503319 − 0.864100i \(-0.667888\pi\)
0.169868 + 0.985467i \(0.445666\pi\)
\(104\) 362214. + 63868.1i 0.322007 + 0.0567785i
\(105\) −1.66716e6 − 1.22284e6i −1.44016 − 1.05633i
\(106\) −260844. + 218874.i −0.219010 + 0.183771i
\(107\) 2.44039e6i 1.99208i 0.0888825 + 0.996042i \(0.471670\pi\)
−0.0888825 + 0.996042i \(0.528330\pi\)
\(108\) −1.28209e6 + 2.33420e6i −1.01777 + 1.85297i
\(109\) 496845. 0.383656 0.191828 − 0.981429i \(-0.438558\pi\)
0.191828 + 0.981429i \(0.438558\pi\)
\(110\) 2.38401e6 + 2.84115e6i 1.79114 + 2.13460i
\(111\) 1.83179e6 + 200919.i 1.33939 + 0.146911i
\(112\) −346990. + 1.96788e6i −0.246980 + 1.40070i
\(113\) −739071. − 2.03058e6i −0.512213 − 1.40729i −0.878925 − 0.476960i \(-0.841739\pi\)
0.366712 − 0.930335i \(-0.380484\pi\)
\(114\) −288070. + 18833.3i −0.194439 + 0.0127120i
\(115\) −170029. − 964283.i −0.111797 − 0.634032i
\(116\) −4.69746e6 + 2.71208e6i −3.00947 + 1.73752i
\(117\) −264106. + 34681.5i −0.164900 + 0.0216541i
\(118\) 1.04061e6 − 1.80240e6i 0.633350 − 1.09699i
\(119\) 732560. − 2.01269e6i 0.434713 − 1.19436i
\(120\) 1.61874e6 − 5.55024e6i 0.936772 − 3.21194i
\(121\) 188734. + 158366.i 0.106535 + 0.0893936i
\(122\) −1.13407e6 + 1.35153e6i −0.624539 + 0.744296i
\(123\) 2.89687e6 + 844880.i 1.55673 + 0.454025i
\(124\) 1.50506e6 + 547796.i 0.789384 + 0.287312i
\(125\) −2.57977e6 − 1.48943e6i −1.32084 − 0.762590i
\(126\) −482343. − 3.67314e6i −0.241126 − 1.83622i
\(127\) −383566. − 664356.i −0.187253 − 0.324332i 0.757080 − 0.653322i \(-0.226625\pi\)
−0.944333 + 0.328990i \(0.893292\pi\)
\(128\) 3.08110e6 − 543281.i 1.46918 − 0.259057i
\(129\) −105938. − 1.62040e6i −0.0493495 − 0.754838i
\(130\) 1.03117e6 − 375314.i 0.469352 − 0.170830i
\(131\) −4.20084e6 − 740722.i −1.86863 − 0.329489i −0.879423 − 0.476040i \(-0.842072\pi\)
−0.989203 + 0.146551i \(0.953183\pi\)
\(132\) −491900. + 4.48466e6i −0.213872 + 1.94988i
\(133\) 208847. − 175243.i 0.0887713 − 0.0744879i
\(134\) − 921835.i − 0.383123i
\(135\) 89267.2 + 4.18617e6i 0.0362820 + 1.70144i
\(136\) 5.98928e6 2.38099
\(137\) −1.50436e6 − 1.79283e6i −0.585048 − 0.697233i 0.389598 − 0.920985i \(-0.372614\pi\)
−0.974646 + 0.223752i \(0.928169\pi\)
\(138\) 1.03767e6 − 1.41471e6i 0.394841 − 0.538309i
\(139\) 243171. − 1.37909e6i 0.0905456 − 0.513509i −0.905476 − 0.424397i \(-0.860486\pi\)
0.996022 − 0.0891120i \(-0.0284029\pi\)
\(140\) 3.54360e6 + 9.73596e6i 1.29140 + 3.54809i
\(141\) 1.31354e6 + 1.96655e6i 0.468581 + 0.701532i
\(142\) 230344. + 1.30635e6i 0.0804475 + 0.456240i
\(143\) −390801. + 225629.i −0.133643 + 0.0771590i
\(144\) 3.59013e6 − 1.86740e6i 1.20233 − 0.625387i
\(145\) −4.26409e6 + 7.38562e6i −1.39869 + 2.42261i
\(146\) −1.11959e6 + 3.07604e6i −0.359749 + 0.988401i
\(147\) 222705. + 232717.i 0.0701096 + 0.0732616i
\(148\) −7.07396e6 − 5.93576e6i −2.18212 − 1.83101i
\(149\) 2.12061e6 − 2.52725e6i 0.641066 − 0.763992i −0.343473 − 0.939163i \(-0.611603\pi\)
0.984538 + 0.175171i \(0.0560477\pi\)
\(150\) −2.68246e6 − 1.09702e7i −0.794804 − 3.25042i
\(151\) 4.21986e6 + 1.53590e6i 1.22565 + 0.446101i 0.872107 − 0.489316i \(-0.162753\pi\)
0.353546 + 0.935417i \(0.384976\pi\)
\(152\) 660218. + 381177.i 0.187999 + 0.108541i
\(153\) −4.13729e6 + 1.30298e6i −1.15516 + 0.363801i
\(154\) −3.13800e6 − 5.43518e6i −0.859194 − 1.48817i
\(155\) 2.47995e6 − 437282.i 0.665959 − 0.117427i
\(156\) 1.19708e6 + 590581.i 0.315319 + 0.155563i
\(157\) 5.95997e6 − 2.16925e6i 1.54009 − 0.560545i 0.574020 − 0.818842i \(-0.305383\pi\)
0.966066 + 0.258296i \(0.0831611\pi\)
\(158\) 5.19406e6 + 915854.i 1.31685 + 0.232196i
\(159\) −596123. + 262183.i −0.148301 + 0.0652249i
\(160\) −2.27257e6 + 1.90692e6i −0.554828 + 0.465556i
\(161\) 1.65690e6i 0.397025i
\(162\) −5.30862e6 + 5.30161e6i −1.24864 + 1.24699i
\(163\) 1.87519e6 0.432996 0.216498 − 0.976283i \(-0.430537\pi\)
0.216498 + 0.976283i \(0.430537\pi\)
\(164\) −9.71988e6 − 1.15837e7i −2.20358 − 2.62613i
\(165\) 2.85574e6 + 6.49307e6i 0.635722 + 1.44543i
\(166\) −656665. + 3.72413e6i −0.143555 + 0.814143i
\(167\) −45015.1 − 123678.i −0.00966515 − 0.0265548i 0.934766 − 0.355263i \(-0.115609\pi\)
−0.944431 + 0.328709i \(0.893387\pi\)
\(168\) −4.32845e6 + 8.77358e6i −0.912862 + 1.85033i
\(169\) −814982. − 4.62199e6i −0.168845 − 0.957567i
\(170\) 1.54751e7 − 8.93457e6i 3.14983 − 1.81856i
\(171\) −538993. − 119679.i −0.107794 − 0.0239347i
\(172\) −4.06871e6 + 7.04721e6i −0.799597 + 1.38494i
\(173\) −989271. + 2.71800e6i −0.191063 + 0.524942i −0.997824 − 0.0659366i \(-0.978996\pi\)
0.806761 + 0.590878i \(0.201219\pi\)
\(174\) −1.48436e7 + 3.62961e6i −2.81768 + 0.688989i
\(175\) 8.17008e6 + 6.85551e6i 1.52445 + 1.27916i
\(176\) 4.40665e6 − 5.25164e6i 0.808296 − 0.963289i
\(177\) 2.87577e6 − 2.75204e6i 0.518602 − 0.496289i
\(178\) −8.80712e6 − 3.20553e6i −1.56162 − 0.568382i
\(179\) 639545. + 369241.i 0.111509 + 0.0643800i 0.554717 − 0.832039i \(-0.312826\pi\)
−0.443208 + 0.896419i \(0.646160\pi\)
\(180\) 1.12796e7 − 1.76926e7i 1.93409 − 3.03371i
\(181\) 2.30792e6 + 3.99743e6i 0.389211 + 0.674133i 0.992344 − 0.123508i \(-0.0394145\pi\)
−0.603133 + 0.797641i \(0.706081\pi\)
\(182\) −1.82868e6 + 322445.i −0.303335 + 0.0534862i
\(183\) −2.80592e6 + 1.87418e6i −0.457848 + 0.305815i
\(184\) −4.35376e6 + 1.58464e6i −0.698894 + 0.254377i
\(185\) −1.42983e7 − 2.52117e6i −2.25823 − 0.398187i
\(186\) 3.63837e6 + 2.66869e6i 0.565416 + 0.414724i
\(187\) −5.62911e6 + 4.72338e6i −0.860825 + 0.722318i
\(188\) − 1.18508e7i − 1.78351i
\(189\) 1.08131e6 − 7.00231e6i 0.160164 − 1.03718i
\(190\) 2.27450e6 0.331608
\(191\) 4.53799e6 + 5.40816e6i 0.651273 + 0.776157i 0.986105 − 0.166120i \(-0.0531240\pi\)
−0.334832 + 0.942278i \(0.608680\pi\)
\(192\) 4.25114e6 + 466286.i 0.600622 + 0.0658792i
\(193\) 78546.4 − 445459.i 0.0109258 − 0.0619635i −0.978857 − 0.204544i \(-0.934429\pi\)
0.989783 + 0.142580i \(0.0455400\pi\)
\(194\) −940004. − 2.58264e6i −0.128743 − 0.353719i
\(195\) 2.09424e6 − 136916.i 0.282437 − 0.0184650i
\(196\) −280292. − 1.58962e6i −0.0372257 − 0.211118i
\(197\) −4.54092e6 + 2.62170e6i −0.593944 + 0.342914i −0.766655 − 0.642059i \(-0.778080\pi\)
0.172712 + 0.984972i \(0.444747\pi\)
\(198\) −4.86777e6 + 1.17409e7i −0.627096 + 1.51253i
\(199\) −302738. + 524358.i −0.0384156 + 0.0665378i −0.884594 − 0.466362i \(-0.845564\pi\)
0.846178 + 0.532900i \(0.178898\pi\)
\(200\) −1.02002e7 + 2.80247e7i −1.27502 + 3.50309i
\(201\) 493629. − 1.69252e6i 0.0607873 − 0.208424i
\(202\) −237250. − 199076.i −0.0287841 − 0.0241527i
\(203\) 9.27612e6 − 1.10549e7i 1.10886 − 1.32149i
\(204\) 2.08671e7 + 6.08594e6i 2.45794 + 0.716865i
\(205\) −2.23410e7 − 8.13146e6i −2.59323 − 0.943859i
\(206\) 4.74071e6 + 2.73705e6i 0.542303 + 0.313099i
\(207\) 2.66276e6 − 2.04181e6i 0.300208 − 0.230200i
\(208\) −1.01417e6 − 1.75660e6i −0.112700 − 0.195201i
\(209\) −921126. + 162419.i −0.100897 + 0.0177909i
\(210\) 1.90420e6 + 2.91262e7i 0.205615 + 3.14504i
\(211\) 96817.7 − 35238.8i 0.0103064 − 0.00375123i −0.336862 − 0.941554i \(-0.609366\pi\)
0.347168 + 0.937803i \(0.387143\pi\)
\(212\) 3.21384e6 + 566687.i 0.337300 + 0.0594752i
\(213\) −276609. + 2.52185e6i −0.0286238 + 0.260964i
\(214\) 2.63917e7 − 2.21453e7i 2.69294 − 2.25964i
\(215\) 1.27941e7i 1.28734i
\(216\) 1.94338e7 − 3.85562e6i 1.92840 − 0.382589i
\(217\) −4.26122e6 −0.417018
\(218\) −4.50862e6 − 5.37316e6i −0.435185 − 0.518633i
\(219\) −3.70278e6 + 5.04821e6i −0.352530 + 0.480623i
\(220\) 6.17245e6 − 3.50057e7i 0.579681 − 3.28754i
\(221\) 743600. + 2.04302e6i 0.0688910 + 0.189276i
\(222\) −1.44497e7 − 2.16332e7i −1.32068 − 1.97725i
\(223\) −696069. − 3.94760e6i −0.0627679 − 0.355974i −0.999974 − 0.00719857i \(-0.997709\pi\)
0.937206 − 0.348776i \(-0.113403\pi\)
\(224\) 4.34748e6 − 2.51002e6i 0.386806 − 0.223323i
\(225\) 949261. − 2.15781e7i 0.0833370 − 1.89437i
\(226\) −1.52531e7 + 2.64192e7i −1.32140 + 2.28873i
\(227\) 7.72445e6 − 2.12228e7i 0.660374 − 1.81436i 0.0851497 − 0.996368i \(-0.472863\pi\)
0.575225 − 0.817995i \(-0.304915\pi\)
\(228\) 1.91292e6 + 1.99892e6i 0.161396 + 0.168652i
\(229\) 5.77596e6 + 4.84661e6i 0.480970 + 0.403582i 0.850777 − 0.525527i \(-0.176132\pi\)
−0.369807 + 0.929109i \(0.620576\pi\)
\(230\) −8.88536e6 + 1.05892e7i −0.730284 + 0.870318i
\(231\) −2.85104e6 − 1.16596e7i −0.231295 − 0.945903i
\(232\) 3.79200e7 + 1.38017e7i 3.03671 + 1.10527i
\(233\) 1.46323e7 + 8.44799e6i 1.15677 + 0.667860i 0.950527 − 0.310641i \(-0.100544\pi\)
0.206240 + 0.978501i \(0.433877\pi\)
\(234\) 2.77169e6 + 2.54147e6i 0.216320 + 0.198353i
\(235\) −9.31626e6 − 1.61362e7i −0.717857 − 1.24336i
\(236\) −1.96434e7 + 3.46367e6i −1.49445 + 0.263512i
\(237\) 9.04608e6 + 4.46289e6i 0.679540 + 0.335252i
\(238\) −2.84140e7 + 1.03418e7i −2.10766 + 0.767127i
\(239\) 1.57155e7 + 2.77107e6i 1.15116 + 0.202980i 0.716481 − 0.697606i \(-0.245751\pi\)
0.434677 + 0.900586i \(0.356863\pi\)
\(240\) −2.91856e7 + 1.28362e7i −2.11122 + 0.928544i
\(241\) −601371. + 504610.i −0.0429627 + 0.0360500i −0.664016 − 0.747718i \(-0.731149\pi\)
0.621053 + 0.783768i \(0.286705\pi\)
\(242\) − 3.47816e6i − 0.245417i
\(243\) −1.25858e7 + 6.89127e6i −0.877124 + 0.480265i
\(244\) 1.69090e7 1.16399
\(245\) −1.63129e6 − 1.94410e6i −0.110926 − 0.132197i
\(246\) −1.71506e7 − 3.89952e7i −1.15206 − 2.61943i
\(247\) −48055.1 + 272534.i −0.00318896 + 0.0180855i
\(248\) −4.07539e6 − 1.11970e7i −0.267186 − 0.734087i
\(249\) −3.19988e6 + 6.48601e6i −0.207270 + 0.420126i
\(250\) 7.30258e6 + 4.14150e7i 0.467365 + 2.65056i
\(251\) −1.93818e7 + 1.11901e7i −1.22567 + 0.707641i −0.966121 − 0.258088i \(-0.916907\pi\)
−0.259550 + 0.965730i \(0.583574\pi\)
\(252\) −2.39958e7 + 2.61695e7i −1.49946 + 1.63529i
\(253\) 2.84223e6 − 4.92290e6i 0.175509 − 0.303990i
\(254\) −3.70405e6 + 1.01768e7i −0.226035 + 0.621026i
\(255\) 3.31973e7 − 8.11751e6i 2.00208 − 0.489556i
\(256\) −2.60692e7 − 2.18747e7i −1.55385 − 1.30383i
\(257\) −1.67964e7 + 2.00171e7i −0.989500 + 1.17924i −0.00569768 + 0.999984i \(0.501814\pi\)
−0.983802 + 0.179256i \(0.942631\pi\)
\(258\) −1.65626e7 + 1.58500e7i −0.964428 + 0.922933i
\(259\) 2.30866e7 + 8.40285e6i 1.32881 + 0.483646i
\(260\) −9.10793e6 − 5.25846e6i −0.518203 − 0.299184i
\(261\) −2.91971e7 − 1.28444e6i −1.64217 − 0.0722422i
\(262\) 3.01099e7 + 5.21519e7i 1.67419 + 2.89979i
\(263\) 2.18721e7 − 3.85663e6i 1.20233 − 0.212003i 0.463623 − 0.886033i \(-0.346549\pi\)
0.738704 + 0.674030i \(0.235438\pi\)
\(264\) 2.79107e7 − 1.86426e7i 1.51690 − 1.01320i
\(265\) 4.82150e6 − 1.75488e6i 0.259086 − 0.0942997i
\(266\) −3.79035e6 − 668341.i −0.201388 − 0.0355102i
\(267\) −1.44537e7 − 1.06016e7i −0.759356 − 0.556976i
\(268\) −6.76789e6 + 5.67893e6i −0.351600 + 0.295028i
\(269\) − 5.22990e6i − 0.268681i −0.990935 − 0.134340i \(-0.957108\pi\)
0.990935 − 0.134340i \(-0.0428915\pi\)
\(270\) 4.44615e7 − 3.89528e7i 2.25888 − 1.97901i
\(271\) −2.47107e7 −1.24159 −0.620794 − 0.783974i \(-0.713189\pi\)
−0.620794 + 0.783974i \(0.713189\pi\)
\(272\) −2.12310e7 − 2.53021e7i −1.05503 − 1.25733i
\(273\) −3.53019e6 − 387208.i −0.173504 − 0.0190308i
\(274\) −5.73734e6 + 3.25381e7i −0.278907 + 1.58176i
\(275\) −1.25146e7 − 3.43837e7i −0.601755 − 1.65331i
\(276\) −1.67790e7 + 1.09697e6i −0.798068 + 0.0521758i
\(277\) −6.84263e6 − 3.88065e7i −0.321946 − 1.82585i −0.530318 − 0.847799i \(-0.677927\pi\)
0.208371 − 0.978050i \(-0.433184\pi\)
\(278\) −1.71209e7 + 9.88476e6i −0.796879 + 0.460078i
\(279\) 5.25115e6 + 6.84811e6i 0.241792 + 0.315325i
\(280\) 3.85401e7 − 6.67533e7i 1.75565 − 3.04088i
\(281\) −1.10129e7 + 3.02576e7i −0.496342 + 1.36369i 0.398444 + 0.917193i \(0.369550\pi\)
−0.894786 + 0.446496i \(0.852672\pi\)
\(282\) 9.34769e6 − 3.20508e7i 0.416828 − 1.42919i
\(283\) 1.07772e7 + 9.04312e6i 0.475495 + 0.398987i 0.848794 − 0.528724i \(-0.177329\pi\)
−0.373300 + 0.927711i \(0.621774\pi\)
\(284\) 8.17186e6 − 9.73885e6i 0.356752 − 0.425160i
\(285\) 4.17606e6 + 1.21796e6i 0.180398 + 0.0526137i
\(286\) 5.98640e6 + 2.17887e6i 0.255898 + 0.0931394i
\(287\) 3.48410e7 + 2.01155e7i 1.47382 + 0.850911i
\(288\) −9.39124e6 − 3.89362e6i −0.393139 − 0.162995i
\(289\) 5.63305e6 + 9.75674e6i 0.233373 + 0.404214i
\(290\) 1.18567e8 − 2.09065e7i 4.86148 − 0.857210i
\(291\) −342917. − 5.24518e6i −0.0139159 − 0.212854i
\(292\) 2.94807e7 − 1.07301e7i 1.18410 − 0.430978i
\(293\) 2.88807e7 + 5.09245e6i 1.14817 + 0.202453i 0.715176 − 0.698945i \(-0.246347\pi\)
0.432992 + 0.901398i \(0.357458\pi\)
\(294\) 495803. − 4.52024e6i 0.0195104 − 0.177877i
\(295\) −2.40239e7 + 2.01585e7i −0.935788 + 0.785220i
\(296\) 6.87002e7i 2.64901i
\(297\) −1.52245e7 + 1.89500e7i −0.581129 + 0.723337i
\(298\) −4.65745e7 −1.75995
\(299\) −1.08108e6 − 1.28839e6i −0.0404432 − 0.0481984i
\(300\) −6.40151e7 + 8.72754e7i −2.37093 + 3.23242i
\(301\) 3.75944e6 − 2.13208e7i 0.137855 − 0.781816i
\(302\) −2.16830e7 − 5.95735e7i −0.787224 − 2.16288i
\(303\) −328998. − 492556.i −0.0118267 − 0.0177063i
\(304\) −730055. − 4.14035e6i −0.0259857 − 0.147372i
\(305\) 2.30235e7 − 1.32926e7i 0.811470 − 0.468502i
\(306\) 5.16350e7 + 3.29191e7i 1.80210 + 1.14890i
\(307\) 1.53270e7 − 2.65471e7i 0.529713 − 0.917490i −0.469686 − 0.882833i \(-0.655633\pi\)
0.999399 − 0.0346566i \(-0.0110337\pi\)
\(308\) −2.05722e7 + 5.65218e7i −0.704092 + 1.93448i
\(309\) 7.23848e6 + 7.56392e6i 0.245342 + 0.256372i
\(310\) −2.72333e7 − 2.28514e7i −0.914144 − 0.767058i
\(311\) 2.40225e6 − 2.86288e6i 0.0798613 − 0.0951750i −0.724634 − 0.689134i \(-0.757991\pi\)
0.804496 + 0.593959i \(0.202436\pi\)
\(312\) −2.35878e6 − 9.64645e6i −0.0776648 − 0.317617i
\(313\) 4.59174e7 + 1.67126e7i 1.49742 + 0.545017i 0.955392 − 0.295341i \(-0.0954334\pi\)
0.542031 + 0.840359i \(0.317656\pi\)
\(314\) −7.75431e7 − 4.47695e7i −2.50469 − 1.44608i
\(315\) −1.21005e7 + 5.44966e7i −0.387143 + 1.74356i
\(316\) −2.52739e7 − 4.37757e7i −0.800960 − 1.38730i
\(317\) −5.20189e7 + 9.17234e6i −1.63299 + 0.287940i −0.913584 − 0.406650i \(-0.866697\pi\)
−0.719406 + 0.694590i \(0.755586\pi\)
\(318\) 8.24491e6 + 4.06763e6i 0.256392 + 0.126491i
\(319\) −4.65242e7 + 1.69334e7i −1.43320 + 0.521642i
\(320\) −3.31829e7 − 5.85104e6i −1.01266 − 0.178559i
\(321\) 6.03147e7 − 2.65272e7i 1.82351 − 0.802004i
\(322\) 1.79186e7 − 1.50355e7i 0.536706 − 0.450350i
\(323\) 4.50640e6i 0.133728i
\(324\) 7.16267e7 + 6.31422e6i 2.10591 + 0.185646i
\(325\) −1.08260e7 −0.315368
\(326\) −1.70164e7 − 2.02794e7i −0.491152 − 0.585332i
\(327\) −5.40075e6 − 1.22796e7i −0.154458 − 0.351190i
\(328\) −1.95350e7 + 1.10788e8i −0.553594 + 3.13959i
\(329\) 1.07837e7 + 2.96278e7i 0.302816 + 0.831979i
\(330\) 4.43053e7 − 8.98049e7i 1.23286 − 2.49895i
\(331\) −335052. − 1.90018e6i −0.00923907 − 0.0523974i 0.979840 − 0.199785i \(-0.0640245\pi\)
−0.989079 + 0.147388i \(0.952913\pi\)
\(332\) 3.13870e7 − 1.81213e7i 0.857701 − 0.495194i
\(333\) −1.49459e7 − 4.74570e7i −0.404752 − 1.28519i
\(334\) −929033. + 1.60913e6i −0.0249340 + 0.0431869i
\(335\) −4.75089e6 + 1.30529e7i −0.126369 + 0.347196i
\(336\) 5.24083e7 − 1.28151e7i 1.38160 − 0.337833i
\(337\) 3.76621e7 + 3.16023e7i 0.984045 + 0.825711i 0.984695 − 0.174288i \(-0.0557625\pi\)
−0.000650048 1.00000i \(0.500207\pi\)
\(338\) −4.25893e7 + 5.07559e7i −1.10294 + 1.31443i
\(339\) −4.21525e7 + 4.03389e7i −1.08199 + 1.03544i
\(340\) −1.60929e8 − 5.85735e7i −4.09448 − 1.49027i
\(341\) 1.26607e7 + 7.30967e6i 0.319297 + 0.184346i
\(342\) 3.59682e6 + 6.91500e6i 0.0899166 + 0.172868i
\(343\) −1.90279e7 − 3.29573e7i −0.471529 − 0.816711i
\(344\) 5.96194e7 − 1.05125e7i 1.46458 − 0.258244i
\(345\) −2.19842e7 + 1.46841e7i −0.535370 + 0.357595i
\(346\) 3.83711e7 − 1.39659e7i 0.926352 − 0.337164i
\(347\) −1.27845e7 − 2.25425e6i −0.305981 − 0.0539527i 0.0185494 − 0.999828i \(-0.494095\pi\)
−0.324531 + 0.945875i \(0.605206\pi\)
\(348\) 1.18091e8 + 8.66182e7i 2.80208 + 2.05528i
\(349\) −1.32220e6 + 1.10946e6i −0.0311044 + 0.0260997i −0.658207 − 0.752837i \(-0.728685\pi\)
0.627103 + 0.778936i \(0.284241\pi\)
\(350\) − 1.50566e8i − 3.51174i
\(351\) 3.72801e6 + 6.15044e6i 0.0862097 + 0.142228i
\(352\) −1.72227e7 −0.394887
\(353\) −1.37819e7 − 1.64247e7i −0.313318 − 0.373398i 0.586286 − 0.810104i \(-0.300590\pi\)
−0.899604 + 0.436706i \(0.856145\pi\)
\(354\) −5.58582e7 − 6.12680e6i −1.25915 − 0.138110i
\(355\) 3.47094e6 − 1.96847e7i 0.0775822 − 0.439991i
\(356\) 3.07218e7 + 8.44074e7i 0.680920 + 1.87081i
\(357\) −5.77071e7 + 3.77275e6i −1.26831 + 0.0829188i
\(358\) −1.81036e6 − 1.02671e7i −0.0394563 − 0.223768i
\(359\) −1.50160e7 + 8.66951e6i −0.324543 + 0.187375i −0.653416 − 0.756999i \(-0.726665\pi\)
0.328873 + 0.944374i \(0.393331\pi\)
\(360\) −1.54771e8 + 2.03240e7i −3.31728 + 0.435614i
\(361\) 2.32361e7 − 4.02462e7i 0.493904 − 0.855466i
\(362\) 2.22873e7 − 6.12338e7i 0.469820 − 1.29082i
\(363\) 1.86251e6 − 6.38604e6i 0.0389384 − 0.133509i
\(364\) 1.36328e7 + 1.14393e7i 0.282671 + 0.237189i
\(365\) 3.17061e7 − 3.77859e7i 0.652026 − 0.777054i
\(366\) 4.57307e7 + 1.33375e7i 0.932749 + 0.272039i
\(367\) −5.26329e7 − 1.91568e7i −1.06478 − 0.387547i −0.250556 − 0.968102i \(-0.580613\pi\)
−0.814221 + 0.580555i \(0.802836\pi\)
\(368\) 2.21278e7 + 1.27755e7i 0.444012 + 0.256350i
\(369\) −1.06078e7 − 8.07807e7i −0.211129 − 1.60779i
\(370\) 1.02484e8 + 1.77508e8i 2.02326 + 3.50439i
\(371\) −8.55048e6 + 1.50768e6i −0.167444 + 0.0295248i
\(372\) −2.82120e6 − 4.31524e7i −0.0548031 − 0.838255i
\(373\) 5.45760e7 − 1.98640e7i 1.05166 − 0.382773i 0.242371 − 0.970184i \(-0.422075\pi\)
0.809289 + 0.587411i \(0.199853\pi\)
\(374\) 1.02163e8 + 1.80140e7i 1.95289 + 0.344347i
\(375\) −8.76930e6 + 7.99499e7i −0.166292 + 1.51609i
\(376\) −6.75385e7 + 5.66715e7i −1.27054 + 1.06611i
\(377\) 1.46486e7i 0.273383i
\(378\) −8.55392e7 + 5.18485e7i −1.58376 + 0.959977i
\(379\) 3.71623e7 0.682629 0.341315 − 0.939949i \(-0.389128\pi\)
0.341315 + 0.939949i \(0.389128\pi\)
\(380\) −1.40120e7 − 1.66988e7i −0.255357 − 0.304323i
\(381\) −1.22503e7 + 1.67015e7i −0.221499 + 0.301982i
\(382\) 1.73070e7 − 9.81527e7i 0.310478 − 1.76081i
\(383\) 3.30860e6 + 9.09030e6i 0.0588908 + 0.161801i 0.965649 − 0.259850i \(-0.0836730\pi\)
−0.906758 + 0.421651i \(0.861451\pi\)
\(384\) −4.69191e7 − 7.02445e7i −0.828621 − 1.24056i
\(385\) 1.64219e7 + 9.31333e7i 0.287767 + 1.63201i
\(386\) −5.53021e6 + 3.19287e6i −0.0961567 + 0.0555161i
\(387\) −3.88970e7 + 2.02322e7i −0.671095 + 0.349068i
\(388\) −1.31703e7 + 2.28116e7i −0.225475 + 0.390535i
\(389\) 2.23311e7 − 6.13542e7i 0.379369 − 1.04231i −0.592250 − 0.805754i \(-0.701760\pi\)
0.971619 − 0.236553i \(-0.0760177\pi\)
\(390\) −2.04848e7 − 2.14058e7i −0.345333 − 0.360859i
\(391\) −2.09801e7 − 1.76044e7i −0.350975 − 0.294503i
\(392\) −7.71895e6 + 9.19908e6i −0.128144 + 0.152717i
\(393\) 2.73564e7 + 1.11876e8i 0.450693 + 1.84315i
\(394\) 6.95591e7 + 2.53174e7i 1.13727 + 0.413934i
\(395\) −6.88266e7 − 3.97370e7i −1.11677 − 0.644769i
\(396\) 1.16186e8 − 3.65912e7i 1.87098 − 0.589238i
\(397\) 3.08641e7 + 5.34581e7i 0.493267 + 0.854363i 0.999970 − 0.00775772i \(-0.00246938\pi\)
−0.506703 + 0.862120i \(0.669136\pi\)
\(398\) 8.41789e6 − 1.48430e6i 0.133522 − 0.0235436i
\(399\) −6.60135e6 − 3.25678e6i −0.103924 − 0.0512707i
\(400\) 1.54550e8 − 5.62517e7i 2.41485 − 0.878933i
\(401\) 5.46545e7 + 9.63706e6i 0.847604 + 0.149455i 0.580548 − 0.814226i \(-0.302838\pi\)
0.267055 + 0.963681i \(0.413949\pi\)
\(402\) −2.27833e7 + 1.00204e7i −0.350703 + 0.154244i
\(403\) 3.31348e6 − 2.78034e6i 0.0506254 − 0.0424798i
\(404\) 2.96824e6i 0.0450147i
\(405\) 1.02492e8 − 4.77103e7i 1.54285 − 0.718202i
\(406\) −2.03729e8 −3.04422
\(407\) −5.41797e7 − 6.45689e7i −0.803625 − 0.957723i
\(408\) −6.51040e7 − 1.48026e8i −0.958577 − 2.17951i
\(409\) −1.42492e6 + 8.08111e6i −0.0208267 + 0.118114i −0.993449 − 0.114279i \(-0.963544\pi\)
0.972622 + 0.232393i \(0.0746554\pi\)
\(410\) 1.14795e8 + 3.15397e8i 1.66560 + 4.57621i
\(411\) −2.79576e7 + 5.66689e7i −0.402694 + 0.816243i
\(412\) −9.11024e6 − 5.16667e7i −0.130268 − 0.738787i
\(413\) 4.59582e7 − 2.65340e7i 0.652399 − 0.376662i
\(414\) −4.62445e7 − 1.02682e7i −0.651718 − 0.144708i
\(415\) 2.84914e7 − 4.93485e7i 0.398629 − 0.690446i
\(416\) −1.74283e6 + 4.78838e6i −0.0242089 + 0.0665133i
\(417\) −3.67278e7 + 8.98080e6i −0.506508 + 0.123853i
\(418\) 1.01152e7 + 8.48770e6i 0.138499 + 0.116215i
\(419\) 5.22084e7 − 6.22196e7i 0.709738 − 0.845833i −0.283853 − 0.958868i \(-0.591613\pi\)
0.993591 + 0.113035i \(0.0360571\pi\)
\(420\) 2.02107e8 − 1.93411e8i 2.72793 − 2.61056i
\(421\) −4.62055e7 − 1.68174e7i −0.619223 − 0.225379i 0.0133107 − 0.999911i \(-0.495763\pi\)
−0.632534 + 0.774533i \(0.717985\pi\)
\(422\) −1.25966e6 − 727267.i −0.0167617 − 0.00967735i
\(423\) 3.43254e7 − 5.38409e7i 0.453518 − 0.711363i
\(424\) −1.21393e7 − 2.10258e7i −0.159256 − 0.275839i
\(425\) −1.73612e8 + 3.06125e7i −2.26159 + 0.398779i
\(426\) 2.97828e7 − 1.98931e7i 0.385245 − 0.257320i
\(427\) −4.22737e7 + 1.53864e7i −0.542983 + 0.197630i
\(428\) −3.25171e8 − 5.73364e7i −4.14744 − 0.731306i
\(429\) 9.82450e6 + 7.20612e6i 0.124434 + 0.0912703i
\(430\) 1.38363e8 − 1.16100e8i 1.74026 − 1.46025i
\(431\) 5.65783e7i 0.706672i 0.935496 + 0.353336i \(0.114953\pi\)
−0.935496 + 0.353336i \(0.885047\pi\)
\(432\) −8.51781e7 − 6.84321e7i −1.05652 − 0.848806i
\(433\) 1.17880e8 1.45203 0.726017 − 0.687676i \(-0.241369\pi\)
0.726017 + 0.687676i \(0.241369\pi\)
\(434\) 3.86684e7 + 4.60832e7i 0.473028 + 0.563733i
\(435\) 2.28888e8 + 2.51056e7i 2.78071 + 0.305002i
\(436\) −1.16733e7 + 6.62024e7i −0.140842 + 0.798756i
\(437\) −1.19230e6 − 3.27582e6i −0.0142870 − 0.0392533i
\(438\) 8.81950e7 − 5.76597e6i 1.04959 − 0.0686199i
\(439\) −2.38262e6 − 1.35125e7i −0.0281619 − 0.159714i 0.967484 − 0.252933i \(-0.0813953\pi\)
−0.995646 + 0.0932194i \(0.970284\pi\)
\(440\) −2.29017e8 + 1.32223e8i −2.68849 + 1.55220i
\(441\) 3.33084e6 − 8.03385e6i 0.0388363 − 0.0936716i
\(442\) 1.53466e7 − 2.65811e7i 0.177724 − 0.307827i
\(443\) −3.88609e7 + 1.06769e8i −0.446994 + 1.22811i 0.487813 + 0.872948i \(0.337795\pi\)
−0.934807 + 0.355157i \(0.884427\pi\)
\(444\) −6.98090e7 + 2.39357e8i −0.797558 + 2.73462i
\(445\) 1.08186e8 + 9.07790e7i 1.22770 + 1.03016i
\(446\) −3.63751e7 + 4.33501e7i −0.410015 + 0.488637i
\(447\) −8.55127e7 − 2.49400e7i −0.957432 − 0.279238i
\(448\) 5.35786e7 + 1.95010e7i 0.595878 + 0.216882i
\(449\) −1.00263e8 − 5.78870e7i −1.10765 − 0.639502i −0.169431 − 0.985542i \(-0.554193\pi\)
−0.938220 + 0.346040i \(0.887526\pi\)
\(450\) −2.41971e8 + 1.85544e8i −2.65538 + 2.03615i
\(451\) −6.90119e7 − 1.19532e8i −0.752306 − 1.30303i
\(452\) 2.87930e8 − 5.07699e7i 3.11797 − 0.549782i
\(453\) −7.91004e6 − 1.20990e8i −0.0850911 − 1.30153i
\(454\) −2.99610e8 + 1.09049e8i −3.20176 + 1.16535i
\(455\) 2.75554e7 + 4.85876e6i 0.292531 + 0.0515812i
\(456\) 2.24425e6 − 2.04608e7i 0.0236688 − 0.215789i
\(457\) −1.11493e8 + 9.35540e7i −1.16815 + 0.980198i −0.999985 − 0.00555976i \(-0.998230\pi\)
−0.168170 + 0.985758i \(0.553786\pi\)
\(458\) − 1.06445e8i − 1.10797i
\(459\) 7.71762e7 + 8.80906e7i 0.798078 + 0.910943i
\(460\) 1.32481e8 1.36107
\(461\) 6.59993e7 + 7.86549e7i 0.673654 + 0.802829i 0.989276 − 0.146056i \(-0.0466579\pi\)
−0.315623 + 0.948885i \(0.602213\pi\)
\(462\) −1.00221e8 + 1.36637e8i −1.01633 + 1.38562i
\(463\) 1.66181e7 − 9.42459e7i 0.167432 − 0.949553i −0.779090 − 0.626912i \(-0.784318\pi\)
0.946522 − 0.322641i \(-0.104571\pi\)
\(464\) −7.61136e7 − 2.09120e8i −0.761919 − 2.09335i
\(465\) −3.77647e7 − 5.65391e7i −0.375602 − 0.562329i
\(466\) −4.14198e7 − 2.34903e8i −0.409308 − 2.32130i
\(467\) 1.28537e8 − 7.42109e7i 1.26205 − 0.728647i 0.288582 − 0.957455i \(-0.406816\pi\)
0.973471 + 0.228809i \(0.0734830\pi\)
\(468\) 1.58396e6 − 3.60058e7i 0.0154528 − 0.351265i
\(469\) 1.17526e7 − 2.03562e7i 0.113924 − 0.197323i
\(470\) −8.99659e7 + 2.47179e8i −0.866531 + 2.38078i
\(471\) −1.18399e8 − 1.23722e8i −1.13314 − 1.18409i
\(472\) 1.13676e8 + 9.53857e7i 1.08104 + 0.907104i
\(473\) −4.77435e7 + 5.68985e7i −0.451161 + 0.537672i
\(474\) −3.38244e7 − 1.38328e8i −0.317610 − 1.29890i
\(475\) −2.10861e7 − 7.67472e6i −0.196751 − 0.0716113i
\(476\) 2.50971e8 + 1.44898e8i 2.32703 + 1.34351i
\(477\) 1.29598e7 + 1.18834e7i 0.119411 + 0.109492i
\(478\) −1.12642e8 − 1.95102e8i −1.03138 − 1.78640i
\(479\) 1.16827e8 − 2.05998e7i 1.06301 − 0.187438i 0.385320 − 0.922783i \(-0.374091\pi\)
0.677693 + 0.735345i \(0.262980\pi\)
\(480\) 7.18329e7 + 3.54388e7i 0.649531 + 0.320446i
\(481\) −2.34346e7 + 8.52948e6i −0.210582 + 0.0766457i
\(482\) 1.09143e7 + 1.92448e6i 0.0974661 + 0.0171859i
\(483\) 4.09506e7 − 1.80106e7i 0.363428 − 0.159841i
\(484\) −2.55358e7 + 2.14271e7i −0.225224 + 0.188985i
\(485\) 4.14140e7i 0.363013i
\(486\) 1.88735e8 + 7.35747e7i 1.64416 + 0.640944i
\(487\) −8.09911e7 −0.701213 −0.350607 − 0.936523i \(-0.614025\pi\)
−0.350607 + 0.936523i \(0.614025\pi\)
\(488\) −8.08602e7 − 9.63654e7i −0.695785 − 0.829205i
\(489\) −2.03835e7 − 4.63458e7i −0.174322 − 0.396355i
\(490\) −6.22142e6 + 3.52834e7i −0.0528812 + 0.299904i
\(491\) −5.70243e7 − 1.56673e8i −0.481743 − 1.32358i −0.907998 − 0.418975i \(-0.862390\pi\)
0.426255 − 0.904603i \(-0.359833\pi\)
\(492\) −1.80638e8 + 3.66145e8i −1.51675 + 3.07438i
\(493\) 4.14215e7 + 2.34913e8i 0.345689 + 1.96050i
\(494\) 3.38341e6 − 1.95341e6i 0.0280656 − 0.0162037i
\(495\) 1.29436e8 − 1.41160e8i 1.06718 − 1.16385i
\(496\) −3.28561e7 + 5.69084e7i −0.269259 + 0.466371i
\(497\) −1.15684e7 + 3.17838e7i −0.0942328 + 0.258903i
\(498\) 9.91806e7 − 2.42520e7i 0.803043 − 0.196363i
\(499\) −5.38683e7 − 4.52008e7i −0.433542 − 0.363785i 0.399744 − 0.916627i \(-0.369099\pi\)
−0.833286 + 0.552842i \(0.813543\pi\)
\(500\) 2.59072e8 − 3.08749e8i 2.07257 − 2.47000i
\(501\) −2.56741e6 + 2.45695e6i −0.0204165 + 0.0195381i
\(502\) 2.96896e8 + 1.08061e8i 2.34690 + 0.854200i
\(503\) 8.08095e7 + 4.66554e7i 0.634977 + 0.366604i 0.782677 − 0.622428i \(-0.213854\pi\)
−0.147700 + 0.989032i \(0.547187\pi\)
\(504\) 2.63892e8 + 1.16091e7i 2.06127 + 0.0906791i
\(505\) 2.33341e6 + 4.04159e6i 0.0181183 + 0.0313818i
\(506\) −7.90308e7 + 1.39353e7i −0.610021 + 0.107563i
\(507\) −1.05375e8 + 7.03839e7i −0.808560 + 0.540069i
\(508\) 9.75343e7 − 3.54996e7i 0.743988 − 0.270790i
\(509\) −1.57260e7 − 2.77292e6i −0.119252 − 0.0210273i 0.113704 − 0.993515i \(-0.463729\pi\)
−0.232955 + 0.972487i \(0.574840\pi\)
\(510\) −3.89035e8 − 2.85351e8i −2.93277 − 2.15114i
\(511\) −6.39400e7 + 5.36520e7i −0.479192 + 0.402090i
\(512\) 2.80196e8i 2.08762i
\(513\) 2.90101e6 + 1.46222e7i 0.0214881 + 0.108308i
\(514\) 3.68895e8 2.71652
\(515\) −5.30213e7 − 6.31883e7i −0.388176 − 0.462610i
\(516\) 2.18400e8 + 2.39552e7i 1.58966 + 0.174362i
\(517\) 1.87836e7 − 1.06527e8i 0.135927 − 0.770883i
\(518\) −1.18626e8 − 3.25923e8i −0.853478 − 2.34491i
\(519\) 7.79294e7 − 5.09483e6i 0.557441 − 0.0364442i
\(520\) 1.35865e7 + 7.70531e7i 0.0966270 + 0.547999i
\(521\) −5.88645e7 + 3.39854e7i −0.416237 + 0.240314i −0.693466 − 0.720489i \(-0.743917\pi\)
0.277229 + 0.960804i \(0.410584\pi\)
\(522\) 2.51058e8 + 3.27409e8i 1.76507 + 2.30186i
\(523\) −5.11261e7 + 8.85530e7i −0.357386 + 0.619011i −0.987523 − 0.157473i \(-0.949665\pi\)
0.630137 + 0.776484i \(0.282999\pi\)
\(524\) 1.97396e8 − 5.42340e8i 1.37197 − 3.76945i
\(525\) 8.06259e7 − 2.76445e8i 0.557182 − 1.91043i
\(526\) −2.40186e8 − 2.01540e8i −1.65040 − 1.38485i
\(527\) 4.52750e7 − 5.39566e7i 0.309333 − 0.368649i
\(528\) −1.77696e8 − 5.18255e7i −1.20719 − 0.352080i
\(529\) −1.19200e8 − 4.33851e7i −0.805207 − 0.293071i
\(530\) −6.27309e7 − 3.62177e7i −0.421361 − 0.243273i
\(531\) −9.92770e7 − 4.11603e7i −0.663079 − 0.274913i
\(532\) 1.84435e7 + 3.19452e7i 0.122492 + 0.212163i
\(533\) −4.02168e7 + 7.09130e6i −0.265599 + 0.0468322i
\(534\) 1.65088e7 + 2.52514e8i 0.108415 + 1.65830i
\(535\) −4.87831e8 + 1.77556e8i −3.18572 + 1.15951i
\(536\) 6.47292e7 + 1.14135e7i 0.420345 + 0.0741182i
\(537\) 2.17397e6 − 1.98202e7i 0.0140388 − 0.127992i
\(538\) −5.65590e7 + 4.74587e7i −0.363208 + 0.304767i
\(539\) − 1.47334e7i − 0.0940882i
\(540\) −5.59886e8 − 8.64587e7i −3.55564 − 0.549070i
\(541\) −1.70062e8 −1.07403 −0.537015 − 0.843573i \(-0.680448\pi\)
−0.537015 + 0.843573i \(0.680448\pi\)
\(542\) 2.24237e8 + 2.67235e8i 1.40835 + 1.67840i
\(543\) 7.37101e7 − 1.00493e8i 0.460392 − 0.627678i
\(544\) −1.44090e7 + 8.17175e7i −0.0895030 + 0.507596i
\(545\) 3.61491e7 + 9.93188e7i 0.223310 + 0.613539i
\(546\) 2.78471e7 + 4.16911e7i 0.171081 + 0.256133i
\(547\) 4.79491e7 + 2.71933e8i 0.292967 + 1.66150i 0.675354 + 0.737494i \(0.263991\pi\)
−0.382387 + 0.924002i \(0.624898\pi\)
\(548\) 2.74232e8 − 1.58328e8i 1.66639 − 0.962089i
\(549\) 7.68214e7 + 4.89763e7i 0.464264 + 0.295984i
\(550\) −2.58280e8 + 4.47355e8i −1.55240 + 2.68883i
\(551\) −1.03846e7 + 2.85314e7i −0.0620775 + 0.170557i
\(552\) 8.64905e7 + 9.03790e7i 0.514222 + 0.537341i
\(553\) 1.03020e8 + 8.64442e7i 0.609182 + 0.511164i
\(554\) −3.57581e8 + 4.26149e8i −2.10303 + 2.50629i
\(555\) 9.31121e7 + 3.80790e8i 0.544662 + 2.22744i
\(556\) 1.78044e8 + 6.48029e7i 1.03587 + 0.377025i
\(557\) −3.42230e7 − 1.97586e7i −0.198040 − 0.114338i 0.397701 − 0.917515i \(-0.369808\pi\)
−0.595741 + 0.803177i \(0.703141\pi\)
\(558\) 2.64078e7 − 1.18932e8i 0.151995 − 0.684535i
\(559\) 1.09880e7 + 1.90318e7i 0.0629047 + 0.108954i
\(560\) −4.18622e8 + 7.38144e7i −2.38374 + 0.420317i
\(561\) 1.77928e8 + 8.77810e7i 1.00776 + 0.497178i
\(562\) 4.27158e8 − 1.55473e8i 2.40647 − 0.875882i
\(563\) 1.16379e8 + 2.05208e7i 0.652155 + 0.114993i 0.489931 − 0.871761i \(-0.337022\pi\)
0.162225 + 0.986754i \(0.448133\pi\)
\(564\) −2.92895e8 + 1.28819e8i −1.63258 + 0.718031i
\(565\) 3.52138e8 − 2.95479e8i 1.95240 − 1.63825i
\(566\) − 1.98612e8i − 1.09536i
\(567\) −1.84817e8 + 4.93908e7i −1.01390 + 0.270955i
\(568\) −9.45808e7 −0.516129
\(569\) −4.30119e7 − 5.12595e7i −0.233481 − 0.278252i 0.636564 − 0.771224i \(-0.280355\pi\)
−0.870045 + 0.492972i \(0.835911\pi\)
\(570\) −2.47240e7 − 5.62147e7i −0.133504 − 0.303546i
\(571\) −5.32239e6 + 3.01848e7i −0.0285889 + 0.162136i −0.995760 − 0.0919908i \(-0.970677\pi\)
0.967171 + 0.254127i \(0.0817881\pi\)
\(572\) −2.08823e7 − 5.73736e7i −0.111581 − 0.306566i
\(573\) 8.43356e7 − 1.70944e8i 0.448278 − 0.908639i
\(574\) −9.86245e7 − 5.59327e8i −0.521494 − 2.95754i
\(575\) 1.18104e8 − 6.81873e7i 0.621241 − 0.358674i
\(576\) −3.46858e7 − 1.10136e8i −0.181503 − 0.576319i
\(577\) 8.73474e7 − 1.51290e8i 0.454697 − 0.787559i −0.543973 − 0.839102i \(-0.683081\pi\)
0.998671 + 0.0515435i \(0.0164141\pi\)
\(578\) 5.43977e7 − 1.49456e8i 0.281706 − 0.773982i
\(579\) −1.18634e7 + 2.90088e6i −0.0611187 + 0.0149449i
\(580\) −8.83916e8 − 7.41694e8i −4.53030 − 3.80138i
\(581\) −6.19803e7 + 7.38652e7i −0.316028 + 0.376627i
\(582\) −5.36125e7 + 5.13059e7i −0.271955 + 0.260254i
\(583\) 2.79911e7 + 1.01879e7i 0.141258 + 0.0514138i
\(584\) −2.02131e8 − 1.16700e8i −1.01483 − 0.585913i
\(585\) −2.61484e7 − 5.02712e7i −0.130610 − 0.251103i
\(586\) −2.07005e8 − 3.58544e8i −1.02870 − 1.78176i
\(587\) −1.44819e8 + 2.55355e7i −0.715998 + 0.126250i −0.519767 − 0.854308i \(-0.673981\pi\)
−0.196231 + 0.980558i \(0.562870\pi\)
\(588\) −3.62409e7 + 2.42068e7i −0.178265 + 0.119071i
\(589\) 8.42477e6 − 3.06637e6i 0.0412299 − 0.0150065i
\(590\) 4.36010e8 + 7.68802e7i 2.12295 + 0.374333i
\(591\) 1.14156e8 + 8.37317e7i 0.553015 + 0.405628i
\(592\) 2.90229e8 − 2.43531e8i 1.39886 − 1.17379i
\(593\) 2.31218e8i 1.10881i 0.832247 + 0.554406i \(0.187054\pi\)
−0.832247 + 0.554406i \(0.812946\pi\)
\(594\) 3.43091e8 − 7.31617e6i 1.63700 − 0.0349080i
\(595\) 4.55634e8 2.16304
\(596\) 2.86921e8 + 3.41939e8i 1.35526 + 1.61514i
\(597\) 1.62504e7 + 1.78242e6i 0.0763732 + 0.00837699i
\(598\) −4.12303e6 + 2.33829e7i −0.0192803 + 0.109344i
\(599\) 9.95845e7 + 2.73606e8i 0.463352 + 1.27305i 0.922949 + 0.384922i \(0.125772\pi\)
−0.459597 + 0.888128i \(0.652006\pi\)
\(600\) 8.03513e8 − 5.25318e7i 3.71997 − 0.243203i
\(601\) 7.09700e6 + 4.02491e7i 0.0326928 + 0.185410i 0.996781 − 0.0801721i \(-0.0255470\pi\)
−0.964088 + 0.265582i \(0.914436\pi\)
\(602\) −2.64690e8 + 1.52819e8i −1.21325 + 0.700468i
\(603\) −4.71969e7 + 6.19773e6i −0.215259 + 0.0282670i
\(604\) −3.03797e8 + 5.26192e8i −1.37871 + 2.38799i
\(605\) −1.79255e7 + 4.92499e7i −0.0809478 + 0.222402i
\(606\) −2.34129e6 + 8.02766e6i −0.0105205 + 0.0360721i
\(607\) 2.70198e8 + 2.26723e8i 1.20814 + 1.01375i 0.999360 + 0.0357825i \(0.0113924\pi\)
0.208776 + 0.977964i \(0.433052\pi\)
\(608\) −6.78911e6 + 8.09095e6i −0.0302066 + 0.0359989i
\(609\) −3.74055e8 − 1.09094e8i −1.65609 − 0.483003i
\(610\) −3.52681e8 − 1.28365e8i −1.55379 − 0.565533i
\(611\) −2.77167e7 − 1.60022e7i −0.121511 − 0.0701547i
\(612\) −7.64116e7 − 5.81889e8i −0.333354 − 2.53855i
\(613\) −5.83784e7 − 1.01114e8i −0.253437 − 0.438966i 0.711033 − 0.703159i \(-0.248228\pi\)
−0.964470 + 0.264193i \(0.914894\pi\)
\(614\) −4.26179e8 + 7.51469e7i −1.84114 + 0.324643i
\(615\) 4.18778e7 + 6.40552e8i 0.180035 + 2.75378i
\(616\) 4.20499e8 − 1.53049e8i 1.79897 − 0.654770i
\(617\) −5.28622e6 − 932103.i −0.0225056 − 0.00396834i 0.162384 − 0.986728i \(-0.448082\pi\)
−0.184890 + 0.982759i \(0.559193\pi\)
\(618\) 1.61149e7 − 1.46920e8i 0.0682750 − 0.622464i
\(619\) −7.34474e7 + 6.16297e7i −0.309674 + 0.259847i −0.784357 − 0.620310i \(-0.787007\pi\)
0.474683 + 0.880157i \(0.342563\pi\)
\(620\) 3.40716e8i 1.42961i
\(621\) −7.94083e7 − 4.36161e7i −0.331582 − 0.182126i
\(622\) −5.27600e7 −0.219247
\(623\) −1.53613e8 − 1.83069e8i −0.635279 − 0.757096i
\(624\) −3.23906e7 + 4.41599e7i −0.133311 + 0.181750i
\(625\) 2.96501e7 − 1.68154e8i 0.121447 − 0.688758i
\(626\) −2.35938e8 − 6.48235e8i −0.961778 − 2.64246i
\(627\) 1.40269e7 + 2.10003e7i 0.0569063 + 0.0851967i
\(628\) 1.49015e8 + 8.45105e8i 0.601659 + 3.41218i
\(629\) −3.51692e8 + 2.03050e8i −1.41322 + 0.815925i
\(630\) 6.99162e8 − 3.63667e8i 2.79612 − 1.45439i
\(631\) −2.10371e8 + 3.64373e8i −0.837332 + 1.45030i 0.0547851 + 0.998498i \(0.482553\pi\)
−0.892117 + 0.451804i \(0.850781\pi\)
\(632\) −1.28618e8 + 3.53376e8i −0.509509 + 1.39987i
\(633\) −1.92335e6 − 2.00982e6i −0.00758311 − 0.00792404i
\(634\) 5.71240e8 + 4.79327e8i 2.24156 + 1.88089i
\(635\) 1.04897e8 − 1.25011e8i 0.409677 − 0.488234i
\(636\) −2.09289e7 − 8.55907e7i −0.0813534 − 0.332702i
\(637\) −4.09628e6 − 1.49092e6i −0.0158479 − 0.00576815i
\(638\) 6.05311e8 + 3.49476e8i 2.33086 + 1.34572i
\(639\) 6.53348e7 − 2.05763e7i 0.250405 − 0.0788613i
\(640\) 3.32774e8 + 5.76381e8i 1.26943 + 2.19872i
\(641\) −1.73785e8 + 3.06430e7i −0.659839 + 0.116347i −0.493534 − 0.869727i \(-0.664295\pi\)
−0.166306 + 0.986074i \(0.553184\pi\)
\(642\) −8.34205e8 − 4.11556e8i −3.15259 − 1.55533i
\(643\) 2.99262e8 − 1.08922e8i 1.12569 − 0.409717i 0.288964 − 0.957340i \(-0.406689\pi\)
0.836725 + 0.547623i \(0.184467\pi\)
\(644\) −2.20774e8 − 3.89284e7i −0.826591 − 0.145750i
\(645\) 3.16209e8 − 1.39073e8i 1.17841 − 0.518279i
\(646\) 4.87348e7 − 4.08933e7i 0.180776 − 0.151689i
\(647\) − 5.07579e8i − 1.87409i −0.349208 − 0.937045i \(-0.613549\pi\)
0.349208 − 0.937045i \(-0.386451\pi\)
\(648\) −3.06540e8 − 4.38400e8i −1.12658 − 1.61119i
\(649\) −1.82065e8 −0.666028
\(650\) 9.82405e7 + 1.17078e8i 0.357726 + 0.426321i
\(651\) 4.63198e7 + 1.05317e8i 0.167889 + 0.381729i
\(652\) −4.40573e7 + 2.49861e8i −0.158955 + 0.901480i
\(653\) −8.46209e7 − 2.32494e8i −0.303905 − 0.834973i −0.993812 − 0.111075i \(-0.964571\pi\)
0.689907 − 0.723898i \(-0.257652\pi\)
\(654\) −8.37898e7 + 1.69838e8i −0.299542 + 0.607158i
\(655\) −1.57572e8 − 8.93637e8i −0.560733 − 3.18007i
\(656\) 5.37282e8 − 3.10200e8i 1.90323 − 1.09883i
\(657\) 1.65017e8 + 3.66406e7i 0.581879 + 0.129201i
\(658\) 2.22556e8 − 3.85478e8i 0.781198 − 1.35308i
\(659\) 1.28484e8 − 3.53006e8i 0.448943 − 1.23346i −0.484518 − 0.874781i \(-0.661005\pi\)
0.933461 − 0.358680i \(-0.116773\pi\)
\(660\) −9.32268e8 + 2.27961e8i −3.24272 + 0.792920i
\(661\) 3.67605e8 + 3.08457e8i 1.27285 + 1.06805i 0.994188 + 0.107659i \(0.0343354\pi\)
0.278662 + 0.960389i \(0.410109\pi\)
\(662\) −1.75091e7 + 2.08666e7i −0.0603518 + 0.0719245i
\(663\) 4.24108e7 − 4.05860e7i 0.145524 − 0.139263i
\(664\) −2.53370e8 − 9.22191e7i −0.865467 − 0.315004i
\(665\) 5.02260e7 + 2.89980e7i 0.170790 + 0.0986059i
\(666\) −3.77600e8 + 5.92281e8i −1.27823 + 2.00496i
\(667\) −9.22635e7 − 1.59805e8i −0.310923 − 0.538534i
\(668\) 1.75371e7 − 3.09227e6i 0.0588341 − 0.0103740i
\(669\) −8.99994e7 + 6.01142e7i −0.300581 + 0.200770i
\(670\) 1.84274e8 − 6.70702e7i 0.612687 − 0.223000i
\(671\) 1.51995e8 + 2.68008e7i 0.503109 + 0.0887117i
\(672\) −1.09293e8 − 8.01648e7i −0.360151 − 0.264165i
\(673\) −1.82468e8 + 1.53109e8i −0.598608 + 0.502292i −0.890998 − 0.454007i \(-0.849994\pi\)
0.292390 + 0.956299i \(0.405550\pi\)
\(674\) − 6.94073e8i − 2.26686i
\(675\) −5.43625e8 + 2.11094e8i −1.76762 + 0.686380i
\(676\) 6.35008e8 2.05560
\(677\) 316395. + 377065.i 0.00101968 + 0.00121521i 0.766554 − 0.642180i \(-0.221970\pi\)
−0.765534 + 0.643395i \(0.777525\pi\)
\(678\) 8.18759e8 + 8.98056e7i 2.62704 + 0.288147i
\(679\) 1.21692e7 − 6.90147e7i 0.0388733 − 0.220461i
\(680\) 4.35764e8 + 1.19725e9i 1.38588 + 3.80766i
\(681\) −6.08490e8 + 3.97816e7i −1.92669 + 0.125962i
\(682\) −3.58388e7 − 2.03252e8i −0.112980 − 0.640739i
\(683\) 3.85330e8 − 2.22470e8i 1.20940 − 0.698249i 0.246773 − 0.969073i \(-0.420630\pi\)
0.962629 + 0.270825i \(0.0872963\pi\)
\(684\) 2.86102e7 − 6.90066e7i 0.0894030 − 0.215636i
\(685\) 2.48932e8 − 4.31162e8i 0.774477 − 1.34143i
\(686\) −1.83750e8 + 5.04848e8i −0.569186 + 1.56383i
\(687\) 5.69998e7 − 1.95437e8i 0.175794 − 0.602750i
\(688\) −2.55752e8 − 2.14601e8i −0.785332 − 0.658972i
\(689\) 5.66504e6 − 6.75133e6i 0.0173199 − 0.0206410i
\(690\) 3.58298e8 + 1.04499e8i 1.09068 + 0.318100i
\(691\) −1.28528e8 − 4.67803e7i −0.389550 − 0.141785i 0.139817 − 0.990177i \(-0.455348\pi\)
−0.529367 + 0.848393i \(0.677571\pi\)
\(692\) −3.38919e8 − 1.95675e8i −1.02277 − 0.590495i
\(693\) −2.57178e8 + 1.97204e8i −0.772740 + 0.592539i
\(694\) 9.16340e7 + 1.58715e8i 0.274144 + 0.474831i
\(695\) 2.93371e8 − 5.17292e7i 0.873902 − 0.154093i
\(696\) −7.10802e7 − 1.08723e9i −0.210824 − 3.22472i
\(697\) −6.24888e8 + 2.27441e8i −1.84546 + 0.671692i
\(698\) 2.39966e7 + 4.23125e6i 0.0705640 + 0.0124423i
\(699\) 4.97390e7 − 4.53472e8i 0.145635 − 1.32776i
\(700\) −1.10542e9 + 9.27557e8i −3.22280 + 2.70425i
\(701\) − 4.51860e7i − 0.131175i −0.997847 − 0.0655873i \(-0.979108\pi\)
0.997847 − 0.0655873i \(-0.0208921\pi\)
\(702\) 3.26845e7 − 9.61290e7i 0.0944780 − 0.277871i
\(703\) −5.16909e7 −0.148781
\(704\) −1.25738e8 − 1.49849e8i −0.360370 − 0.429473i
\(705\) −2.97542e8 + 4.05655e8i −0.849143 + 1.15768i
\(706\) −5.25615e7 + 2.98091e8i −0.149367 + 0.847100i
\(707\) −2.70095e6 − 7.42080e6i −0.00764290 − 0.0209987i
\(708\) 2.99131e8 + 4.47842e8i 0.842872 + 1.26190i
\(709\) 1.34161e7 + 7.60864e7i 0.0376432 + 0.213485i 0.997827 − 0.0658825i \(-0.0209862\pi\)
−0.960184 + 0.279368i \(0.909875\pi\)
\(710\) −2.44378e8 + 1.41092e8i −0.682790 + 0.394209i
\(711\) 1.19697e7 − 2.72088e8i 0.0333022 − 0.757007i
\(712\) 3.34129e8 − 5.78728e8i 0.925708 − 1.60337i
\(713\) −1.86357e7 + 5.12013e7i −0.0514136 + 0.141258i
\(714\) 5.64463e8 + 5.89841e8i 1.55075 + 1.62047i
\(715\) −7.35366e7 − 6.17045e7i −0.201180 − 0.168810i
\(716\) −6.42257e7 + 7.65412e7i −0.174972 + 0.208524i
\(717\) −1.02341e8 − 4.18534e8i −0.277647 − 1.13546i
\(718\) 2.30020e8 + 8.37204e7i 0.621430 + 0.226182i
\(719\) 2.99661e8 + 1.73009e8i 0.806200 + 0.465460i 0.845635 − 0.533762i \(-0.179222\pi\)
−0.0394344 + 0.999222i \(0.512556\pi\)
\(720\) 6.34499e8 + 5.81797e8i 1.69994 + 1.55874i
\(721\) 6.97904e7 + 1.20880e8i 0.186204 + 0.322515i
\(722\) −6.46101e8 + 1.13925e8i −1.71668 + 0.302696i
\(723\) 1.90085e7 + 9.37786e6i 0.0502959 + 0.0248135i
\(724\) −5.86864e8 + 2.13601e8i −1.54640 + 0.562843i
\(725\) −1.16974e9 − 2.06256e8i −3.06954 − 0.541244i
\(726\) −8.59635e7 + 3.78079e7i −0.224649 + 0.0988036i
\(727\) 3.69257e8 − 3.09844e8i 0.961006 − 0.806380i −0.0201105 − 0.999798i \(-0.506402\pi\)
0.981116 + 0.193418i \(0.0619574\pi\)
\(728\) − 1.32398e8i − 0.343152i
\(729\) 3.07127e8 + 2.36151e8i 0.792750 + 0.609547i
\(730\) −6.96355e8 −1.79004
\(731\) 2.30026e8 + 2.74134e8i 0.588878 + 0.701797i
\(732\) −1.83802e8 − 4.17909e8i −0.468616 − 1.06549i
\(733\) 9.87164e7 − 5.59849e8i 0.250656 − 1.42154i −0.556327 − 0.830963i \(-0.687790\pi\)
0.806983 − 0.590575i \(-0.201099\pi\)
\(734\) 2.70444e8 + 7.43039e8i 0.683895 + 1.87899i
\(735\) −3.03165e7 + 6.14503e7i −0.0763515 + 0.154761i
\(736\) −1.11465e7 − 6.32149e7i −0.0279579 − 0.158557i
\(737\) −6.98378e7 + 4.03209e7i −0.174457 + 0.100723i
\(738\) −7.77347e8 + 8.47762e8i −1.93395 + 2.10914i
\(739\) −3.75317e8 + 6.50068e8i −0.929962 + 1.61074i −0.146582 + 0.989199i \(0.546827\pi\)
−0.783380 + 0.621543i \(0.786506\pi\)
\(740\) 6.71870e8 − 1.84595e9i 1.65802 − 4.55537i
\(741\) 7.25810e6 − 1.77477e6i 0.0178389 − 0.00436203i
\(742\) 9.38962e7 + 7.87882e7i 0.229846 + 0.192863i
\(743\) −1.16910e8 + 1.39328e8i −0.285027 + 0.339681i −0.889493 − 0.456949i \(-0.848942\pi\)
0.604466 + 0.796631i \(0.293386\pi\)
\(744\) −2.32437e8 + 2.22437e8i −0.564400 + 0.540116i
\(745\) 6.59484e8 + 2.40032e8i 1.59491 + 0.580499i
\(746\) −7.10070e8 − 4.09959e8i −1.71035 − 0.987471i
\(747\) 1.95086e8 + 8.58221e6i 0.468020 + 0.0205891i
\(748\) −4.97115e8 − 8.61028e8i −1.18782 − 2.05737i
\(749\) 8.65123e8 − 1.52545e8i 2.05889 − 0.363037i
\(750\) 9.44200e8 − 6.30669e8i 2.23810 − 1.49492i
\(751\) 7.87682e8 − 2.86693e8i 1.85965 − 0.676857i 0.880387 − 0.474255i \(-0.157283\pi\)
0.979261 − 0.202602i \(-0.0649397\pi\)
\(752\) 4.78826e8 + 8.44299e7i 1.12596 + 0.198538i
\(753\) 4.87248e8 + 3.57389e8i 1.14121 + 0.837059i
\(754\) 1.58418e8 − 1.32928e8i 0.369564 − 0.310101i
\(755\) 9.55294e8i 2.21971i
\(756\) 9.07621e8 + 3.08597e8i 2.10058 + 0.714212i
\(757\) −1.61364e8 −0.371979 −0.185989 − 0.982552i \(-0.559549\pi\)
−0.185989 + 0.982552i \(0.559549\pi\)
\(758\) −3.37229e8 − 4.01894e8i −0.774314 − 0.922792i
\(759\) −1.52566e8 − 1.67342e7i −0.348925 − 0.0382718i