Properties

Label 69.8.g.a.5.17
Level $69$
Weight $8$
Character 69.5
Analytic conductor $21.555$
Analytic rank $0$
Dimension $540$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [69,8,Mod(5,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 1]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.5");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 69.g (of order \(22\), degree \(10\), 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: \(21.5545667584\)
Analytic rank: \(0\)
Dimension: \(540\)
Relative dimension: \(54\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 5.17
Character \(\chi\) \(=\) 69.5
Dual form 69.8.g.a.14.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.84941 + 9.70420i) q^{2} +(-46.0191 + 8.32112i) q^{3} +(21.6281 + 13.8995i) q^{4} +(66.9720 - 465.800i) q^{5} +(50.3775 - 470.289i) q^{6} +(593.781 - 271.171i) q^{7} +(-1174.89 + 1018.05i) q^{8} +(2048.52 - 765.861i) q^{9} +O(q^{10})\) \(q+(-2.84941 + 9.70420i) q^{2} +(-46.0191 + 8.32112i) q^{3} +(21.6281 + 13.8995i) q^{4} +(66.9720 - 465.800i) q^{5} +(50.3775 - 470.289i) q^{6} +(593.781 - 271.171i) q^{7} +(-1174.89 + 1018.05i) q^{8} +(2048.52 - 765.861i) q^{9} +(4329.39 + 1977.17i) q^{10} +(-3274.13 + 961.372i) q^{11} +(-1110.97 - 459.674i) q^{12} +(-3952.02 + 8653.71i) q^{13} +(939.569 + 6534.85i) q^{14} +(793.990 + 21993.0i) q^{15} +(-5164.53 - 11308.8i) q^{16} +(7639.54 - 4909.64i) q^{17} +(1595.00 + 22061.5i) q^{18} +(-10375.1 + 16143.9i) q^{19} +(7922.89 - 9143.50i) q^{20} +(-25068.8 + 17420.0i) q^{21} -34512.2i q^{22} +(-9884.93 - 57507.5i) q^{23} +(45596.0 - 56625.9i) q^{24} +(-137524. - 40380.8i) q^{25} +(-72716.4 - 63009.1i) q^{26} +(-87898.2 + 52290.2i) q^{27} +(16611.5 + 2388.37i) q^{28} +(87904.4 + 136782. i) q^{29} +(-215687. - 54962.1i) q^{30} +(26485.5 + 30565.9i) q^{31} +(-72504.9 + 10424.6i) q^{32} +(142673. - 71486.0i) q^{33} +(25875.9 + 88125.2i) q^{34} +(-86544.7 - 294744. i) q^{35} +(54950.7 + 11909.3i) q^{36} +(-453853. + 65254.3i) q^{37} +(-127101. - 146682. i) q^{38} +(109860. - 431121. i) q^{39} +(395522. + 615444. i) q^{40} +(-717054. - 103097. i) q^{41} +(-97615.4 - 292910. i) q^{42} +(147874. + 128133. i) q^{43} +(-84175.9 - 24716.3i) q^{44} +(-219545. - 1.00549e6i) q^{45} +(586231. + 67937.1i) q^{46} -321826. i q^{47} +(331769. + 477444. i) q^{48} +(-260264. + 300360. i) q^{49} +(783727. - 1.21950e6i) q^{50} +(-310711. + 289507. i) q^{51} +(-205757. + 132232. i) q^{52} +(466403. + 1.02128e6i) q^{53} +(-256977. - 1.00198e6i) q^{54} +(228532. + 1.58948e6i) q^{55} +(-421562. + 923091. i) q^{56} +(343116. - 829260. i) q^{57} +(-1.57783e6 + 463294. i) q^{58} +(-2.19588e6 - 1.00282e6i) q^{59} +(-288520. + 486703. i) q^{60} +(-2.28567e6 + 1.98055e6i) q^{61} +(-372086. + 169926. i) q^{62} +(1.00869e6 - 1.01025e6i) q^{63} +(331903. - 2.30843e6i) q^{64} +(3.76623e6 + 2.42041e6i) q^{65} +(287180. + 1.58822e6i) q^{66} +(885932. - 3.01721e6i) q^{67} +233470. q^{68} +(933423. + 2.56419e6i) q^{69} +3.10686e6 q^{70} +(-966834. + 3.29273e6i) q^{71} +(-1.62710e6 + 2.98529e6i) q^{72} +(-161431. - 103746. i) q^{73} +(659974. - 4.59022e6i) q^{74} +(6.66477e6 + 713932. i) q^{75} +(-448786. + 204953. i) q^{76} +(-1.68342e6 + 1.45869e6i) q^{77} +(3.87065e6 + 2.29454e6i) q^{78} +(6.18076e6 + 2.82266e6i) q^{79} +(-5.61350e6 + 1.64827e6i) q^{80} +(3.60988e6 - 3.13776e6i) q^{81} +(3.04365e6 - 6.66467e6i) q^{82} +(-254768. - 1.77195e6i) q^{83} +(-784321. + 28315.5i) q^{84} +(-1.77528e6 - 3.88731e6i) q^{85} +(-1.66479e6 + 1.06989e6i) q^{86} +(-5.18346e6 - 5.56312e6i) q^{87} +(2.86802e6 - 4.46272e6i) q^{88} +(-3.74860e6 + 4.32611e6i) q^{89} +(1.03831e7 + 734549. i) q^{90} +6.21008e6i q^{91} +(585535. - 1.38117e6i) q^{92} +(-1.47318e6 - 1.18623e6i) q^{93} +(3.12306e6 + 917013. i) q^{94} +(6.82500e6 + 5.91390e6i) q^{95} +(3.24987e6 - 1.08305e6i) q^{96} +(-4.12842e6 - 593578. i) q^{97} +(-2.17316e6 - 3.38150e6i) q^{98} +(-5.97084e6 + 4.47692e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 540 q - 35 q^{3} + 3362 q^{4} - 1280 q^{6} - 22 q^{7} - 659 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 540 q - 35 q^{3} + 3362 q^{4} - 1280 q^{6} - 22 q^{7} - 659 q^{9} - 22 q^{10} + 4756 q^{12} + 4970 q^{13} + 3828 q^{15} - 174622 q^{16} + 250050 q^{18} - 22 q^{19} - 221738 q^{21} + 94934 q^{24} - 788392 q^{25} + 1020934 q^{27} - 22 q^{28} - 1480875 q^{30} + 738458 q^{31} + 1215192 q^{33} + 1815924 q^{34} - 394502 q^{36} - 905234 q^{37} - 1635803 q^{39} + 10260228 q^{40} - 11 q^{42} - 1694330 q^{43} - 6978726 q^{46} + 134426 q^{48} + 7785740 q^{49} - 11 q^{51} + 16219654 q^{52} - 10697559 q^{54} - 1371960 q^{55} + 7508908 q^{57} - 21860696 q^{58} - 21971851 q^{60} - 11102850 q^{61} - 9022926 q^{63} + 2572060 q^{64} + 16582830 q^{66} + 6031564 q^{67} + 12019470 q^{69} - 2949828 q^{70} + 12828949 q^{72} - 1809596 q^{73} - 16620656 q^{75} - 42651158 q^{76} - 47106384 q^{78} - 1156914 q^{79} + 48837101 q^{81} + 47208588 q^{82} + 124183367 q^{84} + 5833252 q^{85} - 17916287 q^{87} + 360426 q^{88} - 142298860 q^{90} - 51670516 q^{93} - 18401348 q^{94} + 36462337 q^{96} - 63860500 q^{97} + 135683977 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{1}{22}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.84941 + 9.70420i −0.251855 + 0.857738i 0.732384 + 0.680892i \(0.238408\pi\)
−0.984239 + 0.176846i \(0.943410\pi\)
\(3\) −46.0191 + 8.32112i −0.984043 + 0.177933i
\(4\) 21.6281 + 13.8995i 0.168970 + 0.108590i
\(5\) 66.9720 465.800i 0.239606 1.66650i −0.414465 0.910065i \(-0.636031\pi\)
0.654071 0.756433i \(-0.273060\pi\)
\(6\) 50.3775 470.289i 0.0952154 0.888864i
\(7\) 593.781 271.171i 0.654309 0.298813i −0.0604628 0.998170i \(-0.519258\pi\)
0.714772 + 0.699357i \(0.246530\pi\)
\(8\) −1174.89 + 1018.05i −0.811300 + 0.702995i
\(9\) 2048.52 765.861i 0.936679 0.350188i
\(10\) 4329.39 + 1977.17i 1.36907 + 0.625235i
\(11\) −3274.13 + 961.372i −0.741689 + 0.217780i −0.630683 0.776040i \(-0.717225\pi\)
−0.111006 + 0.993820i \(0.535407\pi\)
\(12\) −1110.97 459.674i −0.185595 0.0767920i
\(13\) −3952.02 + 8653.71i −0.498904 + 1.09245i 0.477920 + 0.878403i \(0.341391\pi\)
−0.976824 + 0.214044i \(0.931336\pi\)
\(14\) 939.569 + 6534.85i 0.0915125 + 0.636484i
\(15\) 793.990 + 21993.0i 0.0607429 + 1.68254i
\(16\) −5164.53 11308.8i −0.315218 0.690232i
\(17\) 7639.54 4909.64i 0.377134 0.242370i −0.338317 0.941032i \(-0.609858\pi\)
0.715451 + 0.698663i \(0.246221\pi\)
\(18\) 1595.00 + 22061.5i 0.0644626 + 0.891622i
\(19\) −10375.1 + 16143.9i −0.347019 + 0.539972i −0.970262 0.242056i \(-0.922178\pi\)
0.623244 + 0.782028i \(0.285815\pi\)
\(20\) 7922.89 9143.50i 0.221451 0.255569i
\(21\) −25068.8 + 17420.0i −0.590699 + 0.410468i
\(22\) 34512.2i 0.691024i
\(23\) −9884.93 57507.5i −0.169405 0.985547i
\(24\) 45596.0 56625.9i 0.673267 0.836134i
\(25\) −137524. 40380.8i −1.76031 0.516874i
\(26\) −72716.4 63009.1i −0.811382 0.703067i
\(27\) −87898.2 + 52290.2i −0.859422 + 0.511266i
\(28\) 16611.5 + 2388.37i 0.143007 + 0.0205612i
\(29\) 87904.4 + 136782.i 0.669295 + 1.04144i 0.995372 + 0.0961002i \(0.0306369\pi\)
−0.326077 + 0.945343i \(0.605727\pi\)
\(30\) −215687. 54962.1i −1.45848 0.371654i
\(31\) 26485.5 + 30565.9i 0.159677 + 0.184277i 0.829950 0.557837i \(-0.188369\pi\)
−0.670273 + 0.742114i \(0.733823\pi\)
\(32\) −72504.9 + 10424.6i −0.391149 + 0.0562388i
\(33\) 142673. 71486.0i 0.691103 0.346276i
\(34\) 25875.9 + 88125.2i 0.112907 + 0.384524i
\(35\) −86544.7 294744.i −0.341195 1.16200i
\(36\) 54950.7 + 11909.3i 0.196297 + 0.0425430i
\(37\) −453853. + 65254.3i −1.47302 + 0.211789i −0.831590 0.555390i \(-0.812569\pi\)
−0.641433 + 0.767179i \(0.721660\pi\)
\(38\) −127101. 146682.i −0.375756 0.433646i
\(39\) 109860. 431121.i 0.296560 1.16379i
\(40\) 395522. + 615444.i 0.977148 + 1.52047i
\(41\) −717054. 103097.i −1.62483 0.233616i −0.731118 0.682251i \(-0.761001\pi\)
−0.893715 + 0.448636i \(0.851910\pi\)
\(42\) −97615.4 292910.i −0.203304 0.610044i
\(43\) 147874. + 128133.i 0.283630 + 0.245767i 0.785043 0.619441i \(-0.212641\pi\)
−0.501413 + 0.865208i \(0.667186\pi\)
\(44\) −84175.9 24716.3i −0.148972 0.0437420i
\(45\) −219545. 1.00549e6i −0.359153 1.64488i
\(46\) 586231. + 67937.1i 0.888006 + 0.102909i
\(47\) 321826.i 0.452145i −0.974110 0.226073i \(-0.927411\pi\)
0.974110 0.226073i \(-0.0725887\pi\)
\(48\) 331769. + 477444.i 0.433003 + 0.623129i
\(49\) −260264. + 300360.i −0.316029 + 0.364717i
\(50\) 783727. 1.21950e6i 0.886686 1.37971i
\(51\) −310711. + 289507.i −0.327991 + 0.305607i
\(52\) −205757. + 132232.i −0.202929 + 0.130414i
\(53\) 466403. + 1.02128e6i 0.430324 + 0.942278i 0.993274 + 0.115787i \(0.0369391\pi\)
−0.562950 + 0.826491i \(0.690334\pi\)
\(54\) −256977. 1.00198e6i −0.222083 0.865924i
\(55\) 228532. + 1.58948e6i 0.185216 + 1.28821i
\(56\) −421562. + 923091.i −0.320777 + 0.702403i
\(57\) 343116. 829260.i 0.245402 0.593101i
\(58\) −1.57783e6 + 463294.i −1.06185 + 0.311788i
\(59\) −2.19588e6 1.00282e6i −1.39196 0.635686i −0.428500 0.903542i \(-0.640958\pi\)
−0.963459 + 0.267855i \(0.913685\pi\)
\(60\) −288520. + 486703.i −0.172443 + 0.290894i
\(61\) −2.28567e6 + 1.98055e6i −1.28932 + 1.11720i −0.302885 + 0.953027i \(0.597950\pi\)
−0.986432 + 0.164172i \(0.947505\pi\)
\(62\) −372086. + 169926.i −0.198277 + 0.0905501i
\(63\) 1.00869e6 1.01025e6i 0.508237 0.509023i
\(64\) 331903. 2.30843e6i 0.158264 1.10075i
\(65\) 3.76623e6 + 2.42041e6i 1.70102 + 1.09318i
\(66\) 287180. + 1.58822e6i 0.122956 + 0.679997i
\(67\) 885932. 3.01721e6i 0.359864 1.22558i −0.558385 0.829582i \(-0.688579\pi\)
0.918249 0.396003i \(-0.129603\pi\)
\(68\) 233470. 0.0900432
\(69\) 933423. + 2.56419e6i 0.342063 + 0.939677i
\(70\) 3.10686e6 1.08263
\(71\) −966834. + 3.29273e6i −0.320588 + 1.09182i 0.628760 + 0.777599i \(0.283563\pi\)
−0.949349 + 0.314224i \(0.898256\pi\)
\(72\) −1.62710e6 + 2.98529e6i −0.513747 + 0.942588i
\(73\) −161431. 103746.i −0.0485689 0.0312133i 0.516131 0.856510i \(-0.327372\pi\)
−0.564700 + 0.825296i \(0.691008\pi\)
\(74\) 659974. 4.59022e6i 0.189328 1.31681i
\(75\) 6.66477e6 + 713932.i 1.82419 + 0.195408i
\(76\) −448786. + 204953.i −0.117271 + 0.0535559i
\(77\) −1.68342e6 + 1.45869e6i −0.420219 + 0.364122i
\(78\) 3.87065e6 + 2.29454e6i 0.923534 + 0.547476i
\(79\) 6.18076e6 + 2.82266e6i 1.41042 + 0.644115i 0.967598 0.252497i \(-0.0812517\pi\)
0.442818 + 0.896612i \(0.353979\pi\)
\(80\) −5.61350e6 + 1.64827e6i −1.22580 + 0.359927i
\(81\) 3.60988e6 3.13776e6i 0.754737 0.656028i
\(82\) 3.04365e6 6.66467e6i 0.609603 1.33484i
\(83\) −254768. 1.77195e6i −0.0489072 0.340157i −0.999553 0.0298802i \(-0.990487\pi\)
0.950646 0.310277i \(-0.100422\pi\)
\(84\) −784321. + 28315.5i −0.144383 + 0.00521250i
\(85\) −1.77528e6 3.88731e6i −0.313545 0.686567i
\(86\) −1.66479e6 + 1.06989e6i −0.282237 + 0.181383i
\(87\) −5.18346e6 5.56312e6i −0.843922 0.905735i
\(88\) 2.86802e6 4.46272e6i 0.448634 0.698088i
\(89\) −3.74860e6 + 4.32611e6i −0.563643 + 0.650479i −0.964007 0.265878i \(-0.914338\pi\)
0.400364 + 0.916356i \(0.368884\pi\)
\(90\) 1.03831e7 + 734549.i 1.50133 + 0.106212i
\(91\) 6.21008e6i 0.863877i
\(92\) 585535. 1.38117e6i 0.0783963 0.184923i
\(93\) −1.47318e6 1.18623e6i −0.189918 0.152925i
\(94\) 3.12306e6 + 917013.i 0.387822 + 0.113875i
\(95\) 6.82500e6 + 5.91390e6i 0.816714 + 0.707687i
\(96\) 3.24987e6 1.08305e6i 0.374901 0.124940i
\(97\) −4.12842e6 593578.i −0.459286 0.0660354i −0.0912113 0.995832i \(-0.529074\pi\)
−0.368075 + 0.929796i \(0.619983\pi\)
\(98\) −2.17316e6 3.38150e6i −0.233238 0.362926i
\(99\) −5.97084e6 + 4.47692e6i −0.618461 + 0.463720i
\(100\) −2.41312e6 2.78489e6i −0.241312 0.278489i
\(101\) −1.20353e6 + 173042.i −0.116234 + 0.0167119i −0.200186 0.979758i \(-0.564155\pi\)
0.0839525 + 0.996470i \(0.473246\pi\)
\(102\) −1.92409e6 3.84013e6i −0.179525 0.358299i
\(103\) 3.82794e6 + 1.30368e7i 0.345171 + 1.17555i 0.930972 + 0.365091i \(0.118962\pi\)
−0.585801 + 0.810455i \(0.699220\pi\)
\(104\) −4.16670e6 1.41905e7i −0.363224 1.23703i
\(105\) 6.43532e6 + 1.28437e7i 0.542509 + 1.08275i
\(106\) −1.12397e7 + 1.61602e6i −0.916607 + 0.131788i
\(107\) −5.69455e6 6.57186e6i −0.449383 0.518615i 0.485180 0.874414i \(-0.338754\pi\)
−0.934562 + 0.355799i \(0.884209\pi\)
\(108\) −2.62788e6 90805.5i −0.200735 0.00693632i
\(109\) −301272. 468788.i −0.0222826 0.0346724i 0.829934 0.557862i \(-0.188378\pi\)
−0.852216 + 0.523190i \(0.824742\pi\)
\(110\) −1.60758e7 2.31135e6i −1.15159 0.165574i
\(111\) 2.03429e7 6.77951e6i 1.41183 0.470509i
\(112\) −6.13321e6 5.31445e6i −0.412500 0.357434i
\(113\) −1.97115e7 5.78782e6i −1.28512 0.377346i −0.433336 0.901233i \(-0.642664\pi\)
−0.851788 + 0.523886i \(0.824482\pi\)
\(114\) 7.06963e6 + 5.69256e6i 0.446920 + 0.359866i
\(115\) −2.74490e7 + 753012.i −1.68300 + 0.0461700i
\(116\) 4.18016e6i 0.248651i
\(117\) −1.46824e6 + 2.07540e7i −0.0847511 + 1.19798i
\(118\) 1.59886e7 1.84518e7i 0.895824 1.03384i
\(119\) 3.20487e6 4.98687e6i 0.174339 0.271277i
\(120\) −2.33227e7 2.50310e7i −1.23210 1.32234i
\(121\) −6.59794e6 + 4.24024e6i −0.338579 + 0.217591i
\(122\) −1.27068e7 2.78240e7i −0.633544 1.38727i
\(123\) 3.38561e7 1.22227e6i 1.64047 0.0592242i
\(124\) 147979. + 1.02922e6i 0.00696988 + 0.0484766i
\(125\) −1.27470e7 + 2.79121e7i −0.583745 + 1.27822i
\(126\) 6.92951e6 + 1.26672e7i 0.308607 + 0.564135i
\(127\) 3.50941e7 1.03046e7i 1.52027 0.446392i 0.588216 0.808704i \(-0.299831\pi\)
0.932057 + 0.362312i \(0.118012\pi\)
\(128\) 1.29270e7 + 5.90357e6i 0.544833 + 0.248817i
\(129\) −7.87124e6 4.66611e6i −0.322834 0.191378i
\(130\) −3.42196e7 + 2.96515e7i −1.36607 + 1.18371i
\(131\) 3.66677e6 1.67456e6i 0.142506 0.0650804i −0.342885 0.939377i \(-0.611404\pi\)
0.485392 + 0.874297i \(0.338677\pi\)
\(132\) 4.07937e6 + 436983.i 0.154378 + 0.0165370i
\(133\) −1.78276e6 + 1.23994e7i −0.0657070 + 0.457002i
\(134\) 2.67552e7 + 1.71945e7i 0.960597 + 0.617338i
\(135\) 1.84701e7 + 4.44450e7i 0.646102 + 1.55473i
\(136\) −3.97737e6 + 1.35457e7i −0.135584 + 0.461758i
\(137\) −3.78644e7 −1.25808 −0.629041 0.777372i \(-0.716552\pi\)
−0.629041 + 0.777372i \(0.716552\pi\)
\(138\) −2.75431e7 + 1.75169e6i −0.892147 + 0.0567388i
\(139\) −2.72874e7 −0.861807 −0.430903 0.902398i \(-0.641805\pi\)
−0.430903 + 0.902398i \(0.641805\pi\)
\(140\) 2.22501e6 7.57769e6i 0.0685305 0.233394i
\(141\) 2.67795e6 + 1.48101e7i 0.0804518 + 0.444930i
\(142\) −2.91984e7 1.87647e7i −0.855757 0.549962i
\(143\) 4.61999e6 3.21327e7i 0.132119 0.918907i
\(144\) −1.92406e7 1.92109e7i −0.536969 0.536140i
\(145\) 6.96002e7 3.17854e7i 1.89593 0.865843i
\(146\) 1.46675e6 1.27095e6i 0.0390052 0.0337982i
\(147\) 9.47777e6 1.59880e7i 0.246091 0.415129i
\(148\) −1.07230e7 4.89703e6i −0.271894 0.124170i
\(149\) −1.94417e6 + 570859.i −0.0481484 + 0.0141377i −0.305718 0.952122i \(-0.598897\pi\)
0.257570 + 0.966260i \(0.417078\pi\)
\(150\) −2.59188e7 + 6.26419e7i −0.627040 + 1.51546i
\(151\) 2.08051e7 4.55569e7i 0.491757 1.07680i −0.487304 0.873232i \(-0.662020\pi\)
0.979061 0.203566i \(-0.0652531\pi\)
\(152\) −4.24571e6 2.95295e7i −0.0980613 0.682031i
\(153\) 1.18896e7 1.59083e7i 0.268379 0.359091i
\(154\) −9.35869e6 2.04927e7i −0.206487 0.452144i
\(155\) 1.60114e7 1.02899e7i 0.345357 0.221948i
\(156\) 8.36844e6 7.79733e6i 0.176485 0.164441i
\(157\) 1.05997e7 1.64935e7i 0.218598 0.340146i −0.714584 0.699550i \(-0.753384\pi\)
0.933182 + 0.359404i \(0.117020\pi\)
\(158\) −4.50032e7 + 5.19364e7i −0.907702 + 1.04754i
\(159\) −2.99616e7 4.31174e7i −0.591120 0.850673i
\(160\) 3.44710e7i 0.665325i
\(161\) −2.14638e7 3.14664e7i −0.405338 0.594232i
\(162\) 2.01634e7 + 4.39718e7i 0.372616 + 0.812590i
\(163\) 7.27838e7 + 2.13713e7i 1.31637 + 0.386521i 0.863182 0.504893i \(-0.168468\pi\)
0.453189 + 0.891414i \(0.350286\pi\)
\(164\) −1.40755e7 1.21965e7i −0.249179 0.215915i
\(165\) −2.37431e7 7.12447e7i −0.411475 1.23469i
\(166\) 1.79213e7 + 2.57670e6i 0.304083 + 0.0437205i
\(167\) 6.35696e6 + 9.89163e6i 0.105619 + 0.164346i 0.890040 0.455882i \(-0.150676\pi\)
−0.784421 + 0.620229i \(0.787040\pi\)
\(168\) 1.17187e7 4.59877e7i 0.190677 0.748272i
\(169\) −1.81767e7 2.09770e7i −0.289675 0.334303i
\(170\) 4.27817e7 6.15108e6i 0.667863 0.0960241i
\(171\) −8.88950e6 + 4.10169e7i −0.135954 + 0.627302i
\(172\) 1.41724e6 + 4.82666e6i 0.0212370 + 0.0723265i
\(173\) 2.93551e6 + 9.99742e6i 0.0431044 + 0.146800i 0.978234 0.207507i \(-0.0665349\pi\)
−0.935129 + 0.354307i \(0.884717\pi\)
\(174\) 6.87554e7 3.44497e7i 0.989429 0.495751i
\(175\) −9.26095e7 + 1.33152e7i −1.30624 + 0.187809i
\(176\) 2.77813e7 + 3.20613e7i 0.384112 + 0.443289i
\(177\) 1.09397e8 + 2.78769e7i 1.48286 + 0.377867i
\(178\) −3.13002e7 4.87040e7i −0.415984 0.647284i
\(179\) 9.83728e6 + 1.41439e6i 0.128200 + 0.0184324i 0.206116 0.978528i \(-0.433917\pi\)
−0.0779159 + 0.996960i \(0.524827\pi\)
\(180\) 9.22753e6 2.47985e7i 0.117932 0.316935i
\(181\) 1.09151e8 + 9.45802e7i 1.36821 + 1.18556i 0.962409 + 0.271605i \(0.0875543\pi\)
0.405805 + 0.913960i \(0.366991\pi\)
\(182\) −6.02638e7 1.76951e7i −0.740981 0.217572i
\(183\) 8.87042e7 1.10162e8i 1.06996 1.32878i
\(184\) 7.01589e7 + 5.75015e7i 0.830273 + 0.680483i
\(185\) 2.15775e8i 2.50554i
\(186\) 1.57091e7 1.09160e7i 0.179001 0.124385i
\(187\) −2.02929e7 + 2.34192e7i −0.226933 + 0.261895i
\(188\) 4.47323e6 6.96048e6i 0.0490985 0.0763988i
\(189\) −3.80127e7 + 5.48843e7i −0.409555 + 0.591333i
\(190\) −7.68368e7 + 4.93800e7i −0.812703 + 0.522293i
\(191\) 2.59446e7 + 5.68108e7i 0.269420 + 0.589948i 0.995187 0.0979926i \(-0.0312421\pi\)
−0.725767 + 0.687941i \(0.758515\pi\)
\(192\) 3.93489e6 + 1.08994e8i 0.0401216 + 1.11134i
\(193\) −5.75292e6 4.00125e7i −0.0576021 0.400631i −0.998141 0.0609455i \(-0.980588\pi\)
0.940539 0.339686i \(-0.110321\pi\)
\(194\) 1.75238e7 3.83717e7i 0.172314 0.377316i
\(195\) −1.93459e8 8.00457e7i −1.86839 0.773067i
\(196\) −9.80387e6 + 2.87868e6i −0.0930040 + 0.0273084i
\(197\) 1.40763e8 + 6.42845e7i 1.31177 + 0.599066i 0.943722 0.330740i \(-0.107298\pi\)
0.368050 + 0.929806i \(0.380026\pi\)
\(198\) −2.64315e7 7.06988e7i −0.241988 0.647268i
\(199\) 4.14963e7 3.59567e7i 0.373270 0.323440i −0.447943 0.894062i \(-0.647843\pi\)
0.821213 + 0.570622i \(0.193298\pi\)
\(200\) 2.02685e8 9.25632e7i 1.79150 0.818151i
\(201\) −1.56633e7 + 1.46221e8i −0.136049 + 1.27006i
\(202\) 1.75012e6 1.21724e7i 0.0149396 0.103907i
\(203\) 8.92872e7 + 5.73814e7i 0.749123 + 0.481432i
\(204\) −1.07441e7 + 1.94274e6i −0.0886063 + 0.0160217i
\(205\) −9.60451e7 + 3.27100e8i −0.778640 + 2.65180i
\(206\) −1.37419e8 −1.09524
\(207\) −6.42922e7 1.10235e8i −0.503805 0.863818i
\(208\) 1.18273e8 0.911305
\(209\) 1.84490e7 6.28316e7i 0.139785 0.476065i
\(210\) −1.42975e8 + 2.58526e7i −1.06535 + 0.192635i
\(211\) 2.94065e7 + 1.88984e7i 0.215504 + 0.138496i 0.643940 0.765076i \(-0.277299\pi\)
−0.428436 + 0.903572i \(0.640935\pi\)
\(212\) −4.10791e6 + 2.85711e7i −0.0296105 + 0.205945i
\(213\) 1.70936e7 1.59574e8i 0.121201 1.13144i
\(214\) 8.00008e7 3.65351e7i 0.558015 0.254837i
\(215\) 6.95880e7 6.02984e7i 0.477529 0.413781i
\(216\) 5.00366e7 1.50919e8i 0.337831 1.01896i
\(217\) 2.40152e7 + 1.09674e7i 0.159543 + 0.0728607i
\(218\) 5.40766e6 1.58783e6i 0.0353518 0.0103802i
\(219\) 8.29222e6 + 3.43100e6i 0.0533478 + 0.0220732i
\(220\) −1.71503e7 + 3.75539e7i −0.108591 + 0.237780i
\(221\) 1.22950e7 + 8.55133e7i 0.0766221 + 0.532918i
\(222\) 7.82435e6 + 2.16730e8i 0.0479969 + 1.32948i
\(223\) −7.55418e7 1.65413e8i −0.456163 0.998858i −0.988345 0.152228i \(-0.951355\pi\)
0.532182 0.846630i \(-0.321372\pi\)
\(224\) −4.02252e7 + 2.58512e7i −0.239128 + 0.153678i
\(225\) −3.12647e8 + 2.26038e7i −1.82985 + 0.132295i
\(226\) 1.12332e8 1.74792e8i 0.647329 1.00726i
\(227\) 1.69684e7 1.95826e7i 0.0962833 0.111117i −0.705563 0.708647i \(-0.749306\pi\)
0.801846 + 0.597530i \(0.203851\pi\)
\(228\) 1.89473e7 1.31662e7i 0.105870 0.0735678i
\(229\) 6.98362e6i 0.0384288i 0.999815 + 0.0192144i \(0.00611650\pi\)
−0.999815 + 0.0192144i \(0.993883\pi\)
\(230\) 7.09062e7 2.68517e8i 0.384270 1.45520i
\(231\) 6.53316e7 8.11358e7i 0.348724 0.433082i
\(232\) −2.42528e8 7.12127e7i −1.27513 0.374412i
\(233\) −1.13179e8 9.80697e7i −0.586163 0.507913i 0.310532 0.950563i \(-0.399493\pi\)
−0.896694 + 0.442650i \(0.854038\pi\)
\(234\) −1.97217e8 7.33846e7i −1.00621 0.374412i
\(235\) −1.49907e8 2.15533e7i −0.753500 0.108337i
\(236\) −3.35539e7 5.22109e7i −0.166169 0.258565i
\(237\) −3.07921e8 7.84654e7i −1.50252 0.382877i
\(238\) 3.92616e7 + 4.53103e7i 0.188777 + 0.217860i
\(239\) 8.44144e7 1.21370e7i 0.399967 0.0575065i 0.0606034 0.998162i \(-0.480697\pi\)
0.339363 + 0.940655i \(0.389788\pi\)
\(240\) 2.44613e8 1.22563e8i 1.14219 0.572294i
\(241\) −1.31328e7 4.47263e7i −0.0604363 0.205827i 0.923740 0.383021i \(-0.125116\pi\)
−0.984176 + 0.177194i \(0.943298\pi\)
\(242\) −2.23479e7 7.61099e7i −0.101364 0.345213i
\(243\) −1.40014e8 + 1.74435e8i −0.625964 + 0.779852i
\(244\) −7.69634e7 + 1.10657e7i −0.339172 + 0.0487656i
\(245\) 1.22478e8 + 1.41347e8i 0.532078 + 0.614051i
\(246\) −8.46087e7 + 3.32029e8i −0.362362 + 1.42201i
\(247\) −9.87022e7 1.53584e8i −0.416761 0.648494i
\(248\) −6.22350e7 8.94804e6i −0.259092 0.0372518i
\(249\) 2.64689e7 + 7.94238e7i 0.108652 + 0.326026i
\(250\) −2.34543e8 2.03232e8i −0.949362 0.822627i
\(251\) −2.89974e8 8.51440e7i −1.15745 0.339857i −0.354006 0.935243i \(-0.615181\pi\)
−0.803440 + 0.595386i \(0.796999\pi\)
\(252\) 3.58581e7 7.82948e6i 0.141152 0.0308199i
\(253\) 8.76507e7 + 1.78784e8i 0.340278 + 0.694076i
\(254\) 3.69922e8i 1.41642i
\(255\) 1.14043e8 + 1.64118e8i 0.430705 + 0.619821i
\(256\) 1.01364e8 1.16980e8i 0.377610 0.435786i
\(257\) 2.49165e8 3.87708e8i 0.915633 1.42475i 0.0103481 0.999946i \(-0.496706\pi\)
0.905285 0.424806i \(-0.139658\pi\)
\(258\) 6.77093e7 6.30884e7i 0.245459 0.228708i
\(259\) −2.51794e8 + 1.61818e8i −0.900528 + 0.578734i
\(260\) 4.78138e7 + 1.04698e8i 0.168712 + 0.369428i
\(261\) 2.84830e8 + 2.12878e8i 0.991616 + 0.741120i
\(262\) 5.80211e6 + 4.03546e7i 0.0199311 + 0.138624i
\(263\) −3.45085e7 + 7.55632e7i −0.116972 + 0.256133i −0.959058 0.283211i \(-0.908600\pi\)
0.842086 + 0.539344i \(0.181328\pi\)
\(264\) −9.48487e7 + 2.29236e8i −0.317262 + 0.766776i
\(265\) 5.06948e8 1.48853e8i 1.67341 0.491358i
\(266\) −1.15246e8 5.26311e7i −0.375440 0.171458i
\(267\) 1.36509e8 2.30277e8i 0.438907 0.740389i
\(268\) 6.10988e7 5.29424e7i 0.193892 0.168009i
\(269\) −3.54844e7 + 1.62052e7i −0.111149 + 0.0507600i −0.470213 0.882553i \(-0.655823\pi\)
0.359065 + 0.933313i \(0.383096\pi\)
\(270\) −4.83932e8 + 5.25955e7i −1.49627 + 0.162620i
\(271\) 5.09264e7 3.54201e8i 0.155436 1.08108i −0.751477 0.659760i \(-0.770658\pi\)
0.906912 0.421319i \(-0.138433\pi\)
\(272\) −9.49765e7 6.10377e7i −0.286171 0.183911i
\(273\) −5.16748e7 2.85782e8i −0.153713 0.850092i
\(274\) 1.07891e8 3.67444e8i 0.316854 1.07910i
\(275\) 4.89094e8 1.41817
\(276\) −1.54529e7 + 6.84327e7i −0.0442413 + 0.195921i
\(277\) −3.14460e7 −0.0888969 −0.0444485 0.999012i \(-0.514153\pi\)
−0.0444485 + 0.999012i \(0.514153\pi\)
\(278\) 7.77529e7 2.64802e8i 0.217050 0.739204i
\(279\) 7.76653e7 + 4.23306e7i 0.214098 + 0.116692i
\(280\) 4.01743e8 + 2.58185e8i 1.09369 + 0.702874i
\(281\) 8.05446e7 5.60200e8i 0.216553 1.50616i −0.534076 0.845436i \(-0.679341\pi\)
0.750630 0.660723i \(-0.229750\pi\)
\(282\) −1.51351e8 1.62128e7i −0.401896 0.0430512i
\(283\) −4.86772e8 + 2.22301e8i −1.27665 + 0.583028i −0.934281 0.356537i \(-0.883957\pi\)
−0.342372 + 0.939565i \(0.611230\pi\)
\(284\) −6.66782e7 + 5.77770e7i −0.172731 + 0.149672i
\(285\) −3.63291e8 2.15361e8i −0.929602 0.551073i
\(286\) 2.98658e8 + 1.36393e8i 0.754907 + 0.344755i
\(287\) −4.53730e8 + 1.33227e8i −1.13295 + 0.332664i
\(288\) −1.40544e8 + 7.68838e7i −0.346687 + 0.189654i
\(289\) −1.36203e8 + 2.98242e8i −0.331928 + 0.726820i
\(290\) 1.10132e8 + 7.65984e8i 0.265167 + 1.84428i
\(291\) 1.94926e8 7.03719e6i 0.463707 0.0167407i
\(292\) −2.04944e6 4.48765e6i −0.00481720 0.0105482i
\(293\) −3.62305e8 + 2.32839e8i −0.841468 + 0.540779i −0.888903 0.458096i \(-0.848532\pi\)
0.0474350 + 0.998874i \(0.484895\pi\)
\(294\) 1.28145e8 + 1.37531e8i 0.294093 + 0.315634i
\(295\) −6.14179e8 + 9.55681e8i −1.39289 + 2.16738i
\(296\) 4.66795e8 5.38710e8i 1.04618 1.20735i
\(297\) 2.37520e8 2.55708e8i 0.526081 0.566365i
\(298\) 2.04932e7i 0.0448594i
\(299\) 5.36718e8 + 1.41729e8i 1.16117 + 0.306627i
\(300\) 1.34223e8 + 1.08078e8i 0.287013 + 0.231107i
\(301\) 1.22551e8 + 3.59841e7i 0.259020 + 0.0760551i
\(302\) 3.82810e8 + 3.31707e8i 0.799760 + 0.692996i
\(303\) 5.39455e7 1.79779e7i 0.111405 0.0371271i
\(304\) 2.36150e8 + 3.39532e7i 0.482092 + 0.0693144i
\(305\) 7.69463e8 + 1.19731e9i 1.55288 + 2.41633i
\(306\) 1.20499e8 + 1.60709e8i 0.240413 + 0.320638i
\(307\) −3.77314e8 4.35443e8i −0.744249 0.858909i 0.249749 0.968311i \(-0.419652\pi\)
−0.993998 + 0.109402i \(0.965106\pi\)
\(308\) −5.66844e7 + 8.14998e6i −0.110544 + 0.0158939i
\(309\) −2.84639e8 5.68088e8i −0.548832 1.09537i
\(310\) 5.42322e7 + 1.84698e8i 0.103393 + 0.352125i
\(311\) −1.54478e7 5.26105e7i −0.0291210 0.0991770i 0.943650 0.330945i \(-0.107367\pi\)
−0.972771 + 0.231768i \(0.925549\pi\)
\(312\) 3.09828e8 + 6.18361e8i 0.577537 + 1.15266i
\(313\) −3.89672e8 + 5.60264e7i −0.718280 + 0.103273i −0.491757 0.870733i \(-0.663645\pi\)
−0.226523 + 0.974006i \(0.572736\pi\)
\(314\) 1.29853e8 + 1.49859e8i 0.236701 + 0.273167i
\(315\) −4.03022e8 5.37508e8i −0.726510 0.968942i
\(316\) 9.44444e7 + 1.46958e8i 0.168373 + 0.261993i
\(317\) −4.22649e8 6.07677e7i −0.745199 0.107143i −0.240753 0.970587i \(-0.577394\pi\)
−0.504446 + 0.863443i \(0.668303\pi\)
\(318\) 5.03793e8 1.67895e8i 0.878531 0.292780i
\(319\) −4.19309e8 3.63333e8i −0.723214 0.626669i
\(320\) −1.05304e9 3.09201e8i −1.79647 0.527492i
\(321\) 3.16743e8 + 2.55046e8i 0.534491 + 0.430379i
\(322\) 3.66515e8 1.18629e8i 0.611782 0.198013i
\(323\) 1.74270e8i 0.287749i
\(324\) 1.21688e8 1.76881e7i 0.198766 0.0288918i
\(325\) 8.92942e8 1.03051e9i 1.44288 1.66518i
\(326\) −4.14782e8 + 6.45413e8i −0.663068 + 1.03175i
\(327\) 1.77651e7 + 1.90663e7i 0.0280964 + 0.0301543i
\(328\) 9.47415e8 6.08867e8i 1.48246 0.952717i
\(329\) −8.72697e7 1.91094e8i −0.135107 0.295843i
\(330\) 7.59027e8 2.74023e7i 1.16267 0.0419748i
\(331\) −1.54429e7 1.07408e8i −0.0234063 0.162794i 0.974766 0.223230i \(-0.0716601\pi\)
−0.998172 + 0.0604357i \(0.980751\pi\)
\(332\) 1.91192e7 4.18652e7i 0.0286738 0.0627870i
\(333\) −8.79751e8 + 4.81263e8i −1.30558 + 0.714213i
\(334\) −1.14104e8 + 3.35039e7i −0.167567 + 0.0492021i
\(335\) −1.34608e9 6.14736e8i −1.95621 0.893371i
\(336\) 3.26467e8 + 1.93531e8i 0.469517 + 0.278332i
\(337\) 1.42636e8 1.23595e8i 0.203013 0.175912i −0.547421 0.836858i \(-0.684390\pi\)
0.750433 + 0.660946i \(0.229845\pi\)
\(338\) 2.55358e8 1.16618e8i 0.359700 0.164270i
\(339\) 9.55267e8 + 1.02329e8i 1.33176 + 0.142659i
\(340\) 1.56360e7 1.08751e8i 0.0215749 0.150057i
\(341\) −1.16102e8 7.46144e7i −0.158563 0.101902i
\(342\) −3.72707e8 2.03140e8i −0.503820 0.274602i
\(343\) −2.24546e8 + 7.64733e8i −0.300452 + 1.02325i
\(344\) −3.04181e8 −0.402881
\(345\) 1.25691e9 2.63060e8i 1.64793 0.344895i
\(346\) −1.05381e8 −0.136772
\(347\) 3.86405e8 1.31597e9i 0.496466 1.69081i −0.205549 0.978647i \(-0.565898\pi\)
0.702016 0.712162i \(-0.252284\pi\)
\(348\) −3.47836e7 1.92367e8i −0.0442433 0.244683i
\(349\) −5.07494e8 3.26146e8i −0.639060 0.410699i 0.180594 0.983558i \(-0.442198\pi\)
−0.819654 + 0.572859i \(0.805834\pi\)
\(350\) 1.34669e8 9.36642e8i 0.167891 1.16771i
\(351\) −1.05129e8 9.67297e8i −0.129762 1.19395i
\(352\) 2.27369e8 1.03836e8i 0.277864 0.126896i
\(353\) 1.10869e9 9.60687e8i 1.34153 1.16244i 0.369058 0.929406i \(-0.379680\pi\)
0.972469 0.233034i \(-0.0748652\pi\)
\(354\) −5.82240e8 + 9.82178e8i −0.697575 + 1.17674i
\(355\) 1.46901e9 + 6.70873e8i 1.74271 + 0.795868i
\(356\) −1.41206e8 + 4.14618e7i −0.165874 + 0.0487050i
\(357\) −1.05989e8 + 2.56159e8i −0.123288 + 0.297969i
\(358\) −4.17559e7 + 9.14327e7i −0.0480981 + 0.105320i
\(359\) 2.10526e8 + 1.46424e9i 0.240145 + 1.67025i 0.651405 + 0.758730i \(0.274180\pi\)
−0.411260 + 0.911518i \(0.634911\pi\)
\(360\) 1.28158e9 + 9.57833e8i 1.44772 + 1.08201i
\(361\) 2.18344e8 + 4.78107e8i 0.244268 + 0.534871i
\(362\) −1.22884e9 + 7.89729e8i −1.36149 + 0.874980i
\(363\) 2.68348e8 2.50034e8i 0.294459 0.274363i
\(364\) −8.63172e7 + 1.34312e8i −0.0938086 + 0.145969i
\(365\) −5.91362e7 + 6.82468e7i −0.0636544 + 0.0734611i
\(366\) 8.16282e8 + 1.17470e9i 0.870275 + 1.25240i
\(367\) 1.51278e9i 1.59751i −0.601656 0.798756i \(-0.705492\pi\)
0.601656 0.798756i \(-0.294508\pi\)
\(368\) −5.99287e8 + 4.08786e8i −0.626856 + 0.427591i
\(369\) −1.54786e9 + 3.37968e8i −1.60376 + 0.350174i
\(370\) −2.09393e9 6.14832e8i −2.14909 0.631031i
\(371\) 5.53882e8 + 4.79942e8i 0.563130 + 0.487955i
\(372\) −1.53741e7 4.61324e7i −0.0154843 0.0464628i
\(373\) 8.82939e7 + 1.26947e7i 0.0880947 + 0.0126661i 0.186221 0.982508i \(-0.440376\pi\)
−0.0981265 + 0.995174i \(0.531285\pi\)
\(374\) −1.69442e8 2.63657e8i −0.167483 0.260609i
\(375\) 3.54347e8 1.39056e9i 0.346991 1.36169i
\(376\) 3.27633e8 + 3.78109e8i 0.317856 + 0.366825i
\(377\) −1.53107e9 + 2.20135e8i −1.47164 + 0.211589i
\(378\) −4.24295e8 5.25271e8i −0.404061 0.500221i
\(379\) 4.71929e8 + 1.60724e9i 0.445286 + 1.51651i 0.810588 + 0.585617i \(0.199148\pi\)
−0.365302 + 0.930889i \(0.619034\pi\)
\(380\) 6.54114e7 + 2.22771e8i 0.0611520 + 0.208265i
\(381\) −1.52926e9 + 7.66229e8i −1.41658 + 0.709776i
\(382\) −6.25230e8 + 8.98945e7i −0.573876 + 0.0825109i
\(383\) −6.63735e8 7.65990e8i −0.603669 0.696671i 0.368852 0.929488i \(-0.379751\pi\)
−0.972520 + 0.232817i \(0.925206\pi\)
\(384\) −6.44014e8 1.64110e8i −0.580411 0.147902i
\(385\) 5.66718e8 + 8.81831e8i 0.506121 + 0.787540i
\(386\) 4.04681e8 + 5.81844e7i 0.358144 + 0.0514933i
\(387\) 4.01055e8 + 1.49233e8i 0.351735 + 0.130881i
\(388\) −8.10395e7 7.02211e7i −0.0704346 0.0610319i
\(389\) −8.54208e6 2.50818e6i −0.00735767 0.00216041i 0.278052 0.960566i \(-0.410311\pi\)
−0.285409 + 0.958406i \(0.592130\pi\)
\(390\) 1.32802e9 1.64928e9i 1.13365 1.40789i
\(391\) −3.57857e8 3.90800e8i −0.302755 0.330625i
\(392\) 6.17850e8i 0.518062i
\(393\) −1.54807e8 + 1.07573e8i −0.128652 + 0.0893985i
\(394\) −1.02492e9 + 1.18282e9i −0.844217 + 0.974279i
\(395\) 1.72873e9 2.68996e9i 1.41136 2.19612i
\(396\) −1.91365e8 + 1.38353e7i −0.154857 + 0.0111958i
\(397\) −4.19315e8 + 2.69478e8i −0.336337 + 0.216150i −0.697897 0.716198i \(-0.745881\pi\)
0.361560 + 0.932349i \(0.382244\pi\)
\(398\) 2.30691e8 + 5.05143e8i 0.183417 + 0.401628i
\(399\) −2.11356e7 5.85442e8i −0.0166575 0.461401i
\(400\) 2.53593e8 + 1.76378e9i 0.198120 + 1.37795i
\(401\) −8.05639e8 + 1.76410e9i −0.623929 + 1.36621i 0.288697 + 0.957420i \(0.406778\pi\)
−0.912627 + 0.408794i \(0.865949\pi\)
\(402\) −1.37433e9 5.68643e8i −1.05511 0.436565i
\(403\) −3.69180e8 + 1.08401e8i −0.280977 + 0.0825022i
\(404\) −2.84353e7 1.29860e7i −0.0214547 0.00979803i
\(405\) −1.21981e9 1.89163e9i −0.912430 1.41496i
\(406\) −8.11257e8 + 7.02958e8i −0.601613 + 0.521301i
\(407\) 1.42324e9 6.49973e8i 1.04640 0.477876i
\(408\) 7.03198e7 6.56456e8i 0.0512586 0.478514i
\(409\) 1.84539e8 1.28350e9i 0.133370 0.927605i −0.807748 0.589527i \(-0.799314\pi\)
0.941118 0.338078i \(-0.109777\pi\)
\(410\) −2.90057e9 1.86408e9i −2.07845 1.33574i
\(411\) 1.74249e9 3.15074e8i 1.23801 0.223855i
\(412\) −9.84139e7 + 3.35167e8i −0.0693292 + 0.236114i
\(413\) −1.57581e9 −1.10072
\(414\) 1.25293e9 3.09801e8i 0.867815 0.214576i
\(415\) −8.42439e8 −0.578589
\(416\) 1.96329e8 6.68635e8i 0.133708 0.455368i
\(417\) 1.25574e9 2.27061e8i 0.848054 0.153344i
\(418\) 5.57161e8 + 3.58066e8i 0.373133 + 0.239798i
\(419\) −1.88425e8 + 1.31052e9i −0.125138 + 0.870352i 0.826458 + 0.562999i \(0.190352\pi\)
−0.951595 + 0.307353i \(0.900557\pi\)
\(420\) −3.93382e7 + 3.67233e8i −0.0259085 + 0.241863i
\(421\) 5.12008e8 2.33826e8i 0.334418 0.152724i −0.241127 0.970493i \(-0.577517\pi\)
0.575545 + 0.817770i \(0.304790\pi\)
\(422\) −2.67185e8 + 2.31517e8i −0.173069 + 0.149965i
\(423\) −2.46474e8 6.59266e8i −0.158336 0.423515i
\(424\) −1.58768e9 7.25069e8i −1.01154 0.461954i
\(425\) −1.24888e9 + 3.66704e8i −0.789149 + 0.231715i
\(426\) 1.49983e9 + 6.20571e8i 0.939958 + 0.388918i
\(427\) −8.20123e8 + 1.79582e9i −0.509778 + 1.11626i
\(428\) −3.18165e7 2.21289e8i −0.0196155 0.136429i
\(429\) 5.47725e7 + 1.51716e9i 0.0334936 + 0.927752i
\(430\) 3.86863e8 + 8.47111e8i 0.234648 + 0.513808i
\(431\) 1.60940e8 1.03430e8i 0.0968262 0.0622264i −0.491332 0.870973i \(-0.663490\pi\)
0.588158 + 0.808746i \(0.299853\pi\)
\(432\) 1.04529e9 + 7.23964e8i 0.623798 + 0.432040i
\(433\) 1.50313e9 2.33891e9i 0.889791 1.38454i −0.0330883 0.999452i \(-0.510534\pi\)
0.922879 0.385089i \(-0.125829\pi\)
\(434\) −1.74859e8 + 2.01798e8i −0.102677 + 0.118496i
\(435\) −2.93845e9 + 2.04189e9i −1.71161 + 1.18938i
\(436\) 1.43265e7i 0.00827825i
\(437\) 1.03095e9 + 4.37062e8i 0.590954 + 0.250529i
\(438\) −5.69230e7 + 7.06930e7i −0.0323689 + 0.0401992i
\(439\) −1.28338e9 3.76836e8i −0.723987 0.212582i −0.101081 0.994878i \(-0.532230\pi\)
−0.622906 + 0.782296i \(0.714048\pi\)
\(440\) −1.88666e9 1.63480e9i −1.05587 0.914914i
\(441\) −3.03120e8 + 8.14619e8i −0.168298 + 0.452293i
\(442\) −8.64872e8 1.24350e8i −0.476402 0.0684963i
\(443\) −4.76540e7 7.41511e7i −0.0260427 0.0405233i 0.827988 0.560746i \(-0.189485\pi\)
−0.854031 + 0.520222i \(0.825849\pi\)
\(444\) 5.34211e8 + 1.36129e8i 0.289649 + 0.0738094i
\(445\) 1.76405e9 + 2.03583e9i 0.948969 + 1.09517i
\(446\) 1.82045e9 2.61742e8i 0.971645 0.139701i
\(447\) 8.47187e7 4.24481e7i 0.0448645 0.0224793i
\(448\) −4.28902e8 1.46071e9i −0.225364 0.767521i
\(449\) 7.82704e8 + 2.66564e9i 0.408071 + 1.38976i 0.865676 + 0.500605i \(0.166889\pi\)
−0.457605 + 0.889156i \(0.651293\pi\)
\(450\) 6.71509e8 3.09840e9i 0.347382 1.60285i
\(451\) 2.44685e9 3.51803e8i 1.25600 0.180585i
\(452\) −3.45874e8 3.99160e8i −0.176171 0.203312i
\(453\) −5.78349e8 + 2.26961e9i −0.292312 + 1.14712i
\(454\) 1.41683e8 + 2.20464e8i 0.0710597 + 0.110571i
\(455\) 2.89266e9 + 4.15901e8i 1.43965 + 0.206990i
\(456\) 4.41103e8 + 1.32359e9i 0.217853 + 0.653699i
\(457\) −4.07502e8 3.53103e8i −0.199721 0.173059i 0.549258 0.835653i \(-0.314910\pi\)
−0.748979 + 0.662593i \(0.769456\pi\)
\(458\) −6.77704e7 1.98992e7i −0.0329618 0.00967846i
\(459\) −4.14776e8 + 8.31021e8i −0.200202 + 0.401114i
\(460\) −6.04137e8 3.65243e8i −0.289390 0.174956i
\(461\) 3.26784e9i 1.55349i 0.629818 + 0.776743i \(0.283129\pi\)
−0.629818 + 0.776743i \(0.716871\pi\)
\(462\) 6.01201e8 + 8.65180e8i 0.283643 + 0.408188i
\(463\) 6.52444e8 7.52961e8i 0.305499 0.352565i −0.582153 0.813079i \(-0.697790\pi\)
0.887652 + 0.460514i \(0.152335\pi\)
\(464\) 1.09285e9 1.70050e9i 0.507863 0.790251i
\(465\) −6.51207e8 + 6.06765e8i −0.300354 + 0.279856i
\(466\) 1.27418e9 8.18866e8i 0.583284 0.374854i
\(467\) 4.28385e8 + 9.38033e8i 0.194637 + 0.426196i 0.981637 0.190757i \(-0.0610943\pi\)
−0.787000 + 0.616953i \(0.788367\pi\)
\(468\) −3.20226e8 + 4.28461e8i −0.144409 + 0.193219i
\(469\) −2.92129e8 2.03180e9i −0.130758 0.909444i
\(470\) 6.36303e8 1.39331e9i 0.282697 0.619020i
\(471\) −3.50546e8 + 8.47220e8i −0.154587 + 0.373614i
\(472\) 3.60083e9 1.05730e9i 1.57618 0.462808i
\(473\) −6.07343e8 2.77364e8i −0.263888 0.120514i
\(474\) 1.63884e9 2.76454e9i 0.706824 1.19234i
\(475\) 2.07873e9 1.80123e9i 0.889959 0.771154i
\(476\) 1.38630e8 6.33103e7i 0.0589161 0.0269061i
\(477\) 1.73759e9 + 1.73491e9i 0.733050 + 0.731918i
\(478\) −1.22752e8 + 8.53757e8i −0.0514079 + 0.357550i
\(479\) −1.67258e9 1.07490e9i −0.695364 0.446883i 0.144625 0.989487i \(-0.453802\pi\)
−0.839989 + 0.542603i \(0.817439\pi\)
\(480\) −2.86837e8 1.58632e9i −0.118384 0.654708i
\(481\) 1.22894e9 4.18540e9i 0.503529 1.71486i
\(482\) 4.71453e8 0.191767
\(483\) 1.24958e9 + 1.26945e9i 0.504603 + 0.512626i
\(484\) −2.01638e8 −0.0808377
\(485\) −5.52978e8 + 1.88327e9i −0.220096 + 0.749577i
\(486\) −1.29380e9 1.85576e9i −0.511257 0.733322i
\(487\) −3.52333e9 2.26431e9i −1.38230 0.888349i −0.382926 0.923779i \(-0.625084\pi\)
−0.999372 + 0.0354297i \(0.988720\pi\)
\(488\) 6.69121e8 4.65384e9i 0.260636 1.81277i
\(489\) −3.52728e9 3.77844e8i −1.36414 0.146127i
\(490\) −1.72064e9 + 7.85792e8i −0.660701 + 0.301732i
\(491\) −2.32827e9 + 2.01746e9i −0.887662 + 0.769164i −0.973868 0.227114i \(-0.927071\pi\)
0.0862060 + 0.996277i \(0.472526\pi\)
\(492\) 7.49232e8 + 4.44148e8i 0.283621 + 0.168132i
\(493\) 1.34310e9 + 6.13373e8i 0.504828 + 0.230547i
\(494\) 1.77165e9 5.20203e8i 0.661201 0.194146i
\(495\) 1.68547e9 + 3.08105e9i 0.624602 + 1.14177i
\(496\) 2.08877e8 4.57377e8i 0.0768608 0.168302i
\(497\) 3.18805e8 + 2.21734e9i 0.116487 + 0.810186i
\(498\) −8.46165e8 + 3.05482e7i −0.307010 + 0.0110836i
\(499\) −1.59633e9 3.49548e9i −0.575137 1.25937i −0.944017 0.329897i \(-0.892986\pi\)
0.368880 0.929477i \(-0.379741\pi\)
\(500\) −6.63658e8 + 4.26507e8i −0.237438 + 0.152592i
\(501\) −3.74851e8 4.02307e8i −0.133176 0.142931i
\(502\) 1.65251e9 2.57135e9i 0.583016 0.907191i
\(503\) −1.24749e9 + 1.43968e9i −0.437068 + 0.504403i −0.930961 0.365120i \(-0.881028\pi\)
0.493893 + 0.869523i \(0.335573\pi\)
\(504\) −1.56617e8 + 2.21383e9i −0.0544918 + 0.770259i
\(505\) 5.72194e8i 0.197708i
\(506\) −1.98471e9 + 3.41151e8i −0.681036 + 0.117063i
\(507\) 1.01103e9 + 8.14092e8i 0.344536 + 0.277425i
\(508\) 9.02248e8 + 2.64924e8i 0.305354 + 0.0896599i
\(509\) 4.12707e9 + 3.57612e9i 1.38717 + 1.20199i 0.953677 + 0.300831i \(0.0972641\pi\)
0.433492 + 0.901158i \(0.357281\pi\)
\(510\) −1.91759e9 + 6.39059e8i −0.640119 + 0.213327i
\(511\) −1.23988e8 1.78267e7i −0.0411060 0.00591016i
\(512\) 1.82982e9 + 2.84726e9i 0.602509 + 0.937522i
\(513\) 6.77801e7 1.96153e9i 0.0221662 0.641483i
\(514\) 3.05243e9 + 3.52269e9i 0.991458 + 1.14420i
\(515\) 6.32890e9 9.09958e8i 2.04175 0.293559i
\(516\) −1.05383e8 2.10326e8i −0.0337674 0.0673936i
\(517\) 3.09394e8 + 1.05370e9i 0.0984681 + 0.335351i
\(518\) −8.52853e8 2.90455e9i −0.269600 0.918174i
\(519\) −2.18279e8 4.35646e8i −0.0685372 0.136788i
\(520\) −6.88898e9 + 9.90485e8i −2.14854 + 0.308913i
\(521\) 2.92234e8 + 3.37256e8i 0.0905313 + 0.104479i 0.799208 0.601055i \(-0.205253\pi\)
−0.708676 + 0.705534i \(0.750707\pi\)
\(522\) −2.87740e9 + 2.15747e9i −0.885430 + 0.663893i
\(523\) 1.67981e9 + 2.61383e9i 0.513457 + 0.798955i 0.997083 0.0763198i \(-0.0243170\pi\)
−0.483626 + 0.875275i \(0.660681\pi\)
\(524\) 1.02581e8 + 1.47489e7i 0.0311463 + 0.00447816i
\(525\) 4.15101e9 1.38337e9i 1.25198 0.417235i
\(526\) −6.34951e8 5.50188e8i −0.190235 0.164839i
\(527\) 3.52405e8 + 1.03475e8i 0.104883 + 0.0307964i
\(528\) −1.54526e9 1.24426e9i −0.456859 0.367869i
\(529\) −3.20940e9 + 1.13692e9i −0.942604 + 0.333913i
\(530\) 5.34367e9i 1.55910i
\(531\) −5.26632e9 3.72565e8i −1.52643 0.107987i
\(532\) −2.10903e8 + 2.43395e8i −0.0607284 + 0.0700843i
\(533\) 3.72598e9 5.79774e9i 1.06585 1.65849i
\(534\) 1.84568e9 + 1.98086e9i 0.524520 + 0.562938i
\(535\) −3.44255e9 + 2.21239e9i −0.971946 + 0.624632i
\(536\) 2.03078e9 + 4.44680e9i 0.569622 + 1.24730i
\(537\) −4.64472e8 + 1.67683e7i −0.129434 + 0.00467283i
\(538\) −5.61488e7 3.90523e8i −0.0155454 0.108121i
\(539\) 5.63380e8 1.23363e9i 0.154967 0.339331i
\(540\) −2.18292e8 + 1.21799e9i −0.0596567 + 0.332862i
\(541\) 3.31495e9 9.73357e8i 0.900091 0.264291i 0.201227 0.979545i \(-0.435507\pi\)
0.698864 + 0.715254i \(0.253689\pi\)
\(542\) 3.29213e9 + 1.50346e9i 0.888135 + 0.405598i
\(543\) −5.81006e9 3.44423e9i −1.55733 0.923195i
\(544\) −5.02723e8 + 4.35612e8i −0.133885 + 0.116012i
\(545\) −2.38539e8 + 1.08937e8i −0.0631206 + 0.0288262i
\(546\) 2.92053e9 + 3.12848e8i 0.767870 + 0.0822545i
\(547\) −5.57286e8 + 3.87601e9i −0.145587 + 1.01258i 0.777746 + 0.628579i \(0.216363\pi\)
−0.923333 + 0.384001i \(0.874546\pi\)
\(548\) −8.18935e8 5.26297e8i −0.212578 0.136615i
\(549\) −3.16542e9 + 5.80769e9i −0.816446 + 1.49796i
\(550\) −1.39363e9 + 4.74627e9i −0.357173 + 1.21642i
\(551\) −3.12021e9 −0.794608
\(552\) −3.70713e9 2.06237e9i −0.938104 0.521891i
\(553\) 4.43544e9 1.11532
\(554\) 8.96027e7 3.05159e8i 0.0223891 0.0762503i
\(555\) −1.79549e9 9.92979e9i −0.445819 2.46555i
\(556\) −5.90174e8 3.79282e8i −0.145619 0.0935837i
\(557\) 1.06452e9 7.40392e9i 0.261013 1.81538i −0.264261 0.964451i \(-0.585128\pi\)
0.525274 0.850933i \(-0.323963\pi\)
\(558\) −6.32085e8 + 6.33062e8i −0.154012 + 0.154251i
\(559\) −1.69323e9 + 7.73272e8i −0.409991 + 0.187237i
\(560\) −2.88623e9 + 2.50093e9i −0.694500 + 0.601788i
\(561\) 7.38987e8 1.24659e9i 0.176712 0.298095i
\(562\) 5.20679e9 + 2.37786e9i 1.23735 + 0.565079i
\(563\) 6.53070e9 1.91759e9i 1.54234 0.452872i 0.603541 0.797332i \(-0.293756\pi\)
0.938801 + 0.344460i \(0.111938\pi\)
\(564\) −1.47935e8 + 3.57537e8i −0.0347211 + 0.0839159i
\(565\) −4.01609e9 + 8.79400e9i −0.936771 + 2.05124i
\(566\) −7.70243e8 5.35716e9i −0.178554 1.24187i
\(567\) 1.29261e9 2.84204e9i 0.297802 0.654770i
\(568\) −2.21623e9 4.85287e9i −0.507453 1.11117i
\(569\) −1.05727e9 + 6.79467e8i −0.240599 + 0.154623i −0.655384 0.755296i \(-0.727493\pi\)
0.414785 + 0.909919i \(0.363857\pi\)
\(570\) 3.12507e9 2.91179e9i 0.706801 0.658565i
\(571\) 2.12766e9 3.31070e9i 0.478273 0.744207i −0.515348 0.856981i \(-0.672337\pi\)
0.993621 + 0.112774i \(0.0359737\pi\)
\(572\) 5.46552e8 6.30754e8i 0.122108 0.140921i
\(573\) −1.66668e9 2.39849e9i −0.370093 0.532595i
\(574\) 4.78271e9i 1.05556i
\(575\) −9.62781e8 + 8.30785e9i −0.211198 + 1.82243i
\(576\) −1.08803e9 4.98306e9i −0.237226 1.08647i
\(577\) 8.18649e9 + 2.40377e9i 1.77412 + 0.520928i 0.994445 0.105259i \(-0.0335670\pi\)
0.779673 + 0.626187i \(0.215385\pi\)
\(578\) −2.50611e9 2.17155e9i −0.539824 0.467760i
\(579\) 5.97693e8 + 1.79347e9i 0.127969 + 0.383989i
\(580\) 1.94712e9 + 2.79954e8i 0.414377 + 0.0595784i
\(581\) −6.31779e8 9.83067e8i −0.133644 0.207954i
\(582\) −4.87133e8 + 1.91165e9i −0.102428 + 0.401955i
\(583\) −2.50889e9 2.89542e9i −0.524376 0.605162i
\(584\) 2.95282e8 4.24551e7i 0.0613467 0.00882033i
\(585\) 9.56888e9 + 2.07384e9i 1.97613 + 0.428282i
\(586\) −1.22716e9 4.17933e9i −0.251919 0.857957i
\(587\) 1.55350e8 + 5.29073e8i 0.0317013 + 0.107965i 0.973824 0.227304i \(-0.0729911\pi\)
−0.942123 + 0.335269i \(0.891173\pi\)
\(588\) 4.27212e8 2.14053e8i 0.0866608 0.0434212i
\(589\) −7.68242e8 + 1.10457e8i −0.154915 + 0.0222735i
\(590\) −7.52407e9 8.68324e9i −1.50824 1.74060i
\(591\) −7.01273e9 1.78701e9i −1.39743 0.356098i
\(592\) 3.08189e9 + 4.79551e9i 0.610507 + 0.949967i
\(593\) −2.29135e9 3.29446e8i −0.451232 0.0648774i −0.0870475 0.996204i \(-0.527743\pi\)
−0.364185 + 0.931327i \(0.618652\pi\)
\(594\) 1.80465e9 + 3.03356e9i 0.353297 + 0.593881i
\(595\) −2.10825e9 1.82681e9i −0.410311 0.355536i
\(596\) −4.99834e7 1.46764e7i −0.00967082 0.00283961i
\(597\) −1.61042e9 + 1.99999e9i −0.309763 + 0.384696i
\(598\) −2.90470e9 + 4.80458e9i −0.555453 + 0.918758i
\(599\) 1.00342e8i 0.0190761i 0.999955 + 0.00953804i \(0.00303610\pi\)
−0.999955 + 0.00953804i \(0.996964\pi\)
\(600\) −8.55716e9 + 5.94625e9i −1.61734 + 1.12386i
\(601\) −1.24975e9 + 1.44229e9i −0.234834 + 0.271013i −0.860919 0.508742i \(-0.830111\pi\)
0.626085 + 0.779755i \(0.284656\pi\)
\(602\) −6.98395e8 + 1.08672e9i −0.130471 + 0.203016i
\(603\) −4.95914e8 6.85930e9i −0.0921077 1.27400i
\(604\) 1.08319e9 6.96127e8i 0.200022 0.128546i
\(605\) 1.53323e9 + 3.35730e9i 0.281490 + 0.616377i
\(606\) 2.07487e7 + 5.74724e8i 0.00378735 + 0.104907i
\(607\) −5.42331e8 3.77199e9i −0.0984246 0.684558i −0.977970 0.208744i \(-0.933063\pi\)
0.879546 0.475814i \(-0.157847\pi\)
\(608\) 5.83948e8 1.27867e9i 0.105369 0.230725i
\(609\) −4.58640e9 1.89767e9i −0.822832 0.340456i
\(610\) −1.38114e10 + 4.05540e9i −2.46368 + 0.723402i
\(611\) 2.78498e9 + 1.27186e9i 0.493945 + 0.225577i
\(612\) 4.78268e8 1.78806e8i 0.0843416 0.0315320i
\(613\) −5.15406e9 + 4.46602e9i −0.903729 + 0.783085i −0.976780 0.214243i \(-0.931272\pi\)
0.0730518 + 0.997328i \(0.476726\pi\)
\(614\) 5.30075e9 2.42077e9i 0.924161 0.422050i
\(615\) 1.69808e9 1.58520e10i 0.294370 2.74803i
\(616\) 4.92815e8 3.42760e9i 0.0849476 0.590824i
\(617\) −5.23010e9 3.36118e9i −0.896420 0.576094i 0.00930642 0.999957i \(-0.497038\pi\)
−0.905727 + 0.423862i \(0.860674\pi\)
\(618\) 6.32389e9 1.14348e9i 1.07777 0.194880i
\(619\) −1.86830e9 + 6.36285e9i −0.316614 + 1.07829i 0.635387 + 0.772194i \(0.280840\pi\)
−0.952001 + 0.306094i \(0.900978\pi\)
\(620\) 4.89321e8 0.0824562
\(621\) 3.87595e9 + 4.53792e9i 0.649467 + 0.760390i
\(622\) 5.54560e8 0.0924021
\(623\) −1.05273e9 + 3.58528e9i −0.174425 + 0.594038i
\(624\) −5.44282e9 + 9.84163e8i −0.896763 + 0.162152i
\(625\) 2.72767e9 + 1.75297e9i 0.446901 + 0.287206i
\(626\) 5.66644e8 3.94110e9i 0.0923209 0.642106i
\(627\) −3.26178e8 + 3.04497e9i −0.0528468 + 0.493340i
\(628\) 4.58505e8 2.09392e8i 0.0738729 0.0337366i
\(629\) −3.14686e9 + 2.72677e9i −0.504196 + 0.436889i
\(630\) 6.36446e9 2.37942e9i 1.01407 0.379123i
\(631\) 3.11565e9 + 1.42287e9i 0.493681 + 0.225457i 0.646668 0.762772i \(-0.276162\pi\)
−0.152987 + 0.988228i \(0.548889\pi\)
\(632\) −1.01353e10 + 2.97599e9i −1.59708 + 0.468945i
\(633\) −1.51052e9 6.24993e8i −0.236708 0.0979405i
\(634\) 1.79400e9 3.92832e9i 0.279583 0.612201i
\(635\) −2.44955e9 1.70370e10i −0.379645 2.64049i
\(636\) −4.87015e7 1.34900e9i −0.00750658 0.207928i
\(637\) −1.57066e9 3.43927e9i −0.240766 0.527204i
\(638\) 4.72064e9 3.03377e9i 0.719662 0.462499i
\(639\) 5.41200e8 + 7.48568e9i 0.0820550 + 1.13495i
\(640\) 3.61563e9 5.62603e9i 0.545198 0.848345i
\(641\) −1.17064e9 + 1.35099e9i −0.175558 + 0.202605i −0.836708 0.547649i \(-0.815523\pi\)
0.661150 + 0.750253i \(0.270069\pi\)
\(642\) −3.37755e9 + 2.34701e9i −0.503767 + 0.350060i
\(643\) 2.95078e9i 0.437721i −0.975756 0.218861i \(-0.929766\pi\)
0.975756 0.218861i \(-0.0702340\pi\)
\(644\) −2.68541e7 9.78895e8i −0.00396196 0.144423i
\(645\) −2.70063e9 + 3.35393e9i −0.396284 + 0.492147i
\(646\) −1.69115e9 4.96566e8i −0.246813 0.0724708i
\(647\) 7.16695e9 + 6.21020e9i 1.04033 + 0.901448i 0.995232 0.0975347i \(-0.0310957\pi\)
0.0450944 + 0.998983i \(0.485641\pi\)
\(648\) −1.04682e9 + 7.36154e9i −0.151133 + 1.06281i
\(649\) 8.15369e9 + 1.17232e9i 1.17084 + 0.168341i
\(650\) 7.45592e9 + 1.16016e10i 1.06489 + 1.65700i
\(651\) −1.19642e9 3.04875e8i −0.169961 0.0433101i
\(652\) 1.27713e9 + 1.47388e9i 0.180454 + 0.208255i
\(653\) −5.61834e9 + 8.07796e8i −0.789609 + 0.113529i −0.525309 0.850912i \(-0.676050\pi\)
−0.264300 + 0.964440i \(0.585141\pi\)
\(654\) −2.35643e8 + 1.18068e8i −0.0329407 + 0.0165049i
\(655\) −5.34439e8 1.82013e9i −0.0743110 0.253080i
\(656\) 2.53735e9 + 8.64144e9i 0.350928 + 1.19515i
\(657\) −4.10150e8 8.88909e7i −0.0564240 0.0122286i
\(658\) 2.10308e9 3.02377e8i 0.287783 0.0413770i
\(659\) 1.86611e9 + 2.15360e9i 0.254003 + 0.293135i 0.868402 0.495860i \(-0.165147\pi\)
−0.614400 + 0.788995i \(0.710602\pi\)
\(660\) 4.76750e8 1.87091e9i 0.0645487 0.253308i
\(661\) −1.62196e9 2.52382e9i −0.218441 0.339901i 0.714687 0.699444i \(-0.246569\pi\)
−0.933129 + 0.359543i \(0.882933\pi\)
\(662\) 1.08631e9 + 1.56188e8i 0.145530 + 0.0209240i
\(663\) −1.27737e9 3.83294e9i −0.170223 0.510781i
\(664\) 2.10325e9 + 1.82248e9i 0.278807 + 0.241587i
\(665\) 5.65623e9 + 1.66082e9i 0.745850 + 0.219001i
\(666\) −2.16350e9 9.90860e9i −0.283790 1.29973i
\(667\) 6.99706e9 6.40724e9i 0.913009 0.836047i
\(668\) 3.02296e8i 0.0392387i
\(669\) 4.85279e9 + 6.98358e9i 0.626614 + 0.901752i
\(670\) 9.80107e9 1.13110e10i 1.25896 1.45292i
\(671\) 5.57955e9 8.68195e9i 0.712969 1.10940i
\(672\) 1.63602e9 1.52437e9i 0.207967 0.193775i
\(673\) −1.97921e9 + 1.27196e9i −0.250287 + 0.160850i −0.659769 0.751468i \(-0.729346\pi\)
0.409482 + 0.912318i \(0.365710\pi\)
\(674\) 7.92958e8 + 1.73634e9i 0.0997564 + 0.218436i
\(675\) 1.41997e10 3.64178e9i 1.77711 0.455775i
\(676\) −1.01556e8 7.06340e8i −0.0126443 0.0879428i
\(677\) −1.58348e9 + 3.46734e9i −0.196134 + 0.429473i −0.981989 0.188937i \(-0.939496\pi\)
0.785855 + 0.618410i \(0.212223\pi\)
\(678\) −3.71496e9 + 8.97852e9i −0.457773 + 1.10637i
\(679\) −2.61234e9 + 7.67052e8i −0.320247 + 0.0940331i
\(680\) 6.04321e9 + 2.75984e9i 0.737032 + 0.336591i
\(681\) −6.17922e8 + 1.04237e9i −0.0749754 + 0.126476i
\(682\) 1.05490e9 9.14073e8i 0.127340 0.110341i
\(683\) −8.84159e9 + 4.03782e9i −1.06184 + 0.484925i −0.868234 0.496155i \(-0.834745\pi\)
−0.193603 + 0.981080i \(0.562018\pi\)
\(684\) −7.62379e8 + 7.63558e8i −0.0910908 + 0.0912317i
\(685\) −2.53585e9 + 1.76372e10i −0.301444 + 2.09659i
\(686\) −6.78130e9 4.35807e9i −0.802007 0.515419i
\(687\) −5.81115e7 3.21380e8i −0.00683776 0.0378155i
\(688\) 6.85330e8 2.33402e9i 0.0802306 0.273240i
\(689\) −1.06811e10 −1.24408
\(690\) −1.02868e9 + 1.29469e10i −0.119209 + 1.50036i
\(691\) −1.49267e10 −1.72104 −0.860519 0.509419i \(-0.829861\pi\)
−0.860519 + 0.509419i \(0.829861\pi\)
\(692\) −7.54701e7 + 2.57027e8i −0.00865772 + 0.0294855i
\(693\) −2.33136e9 + 4.27743e9i −0.266099 + 0.488221i
\(694\) 1.16695e10 + 7.49950e9i 1.32523 + 0.851676i
\(695\) −1.82749e9 + 1.27105e10i −0.206494 + 1.43620i
\(696\) 1.17535e10 + 1.25904e9i 1.32140 + 0.141549i
\(697\) −5.98413e9 + 2.73286e9i −0.669401 + 0.305705i
\(698\) 4.61105e9 3.99550e9i 0.513222 0.444710i
\(699\) 6.02443e9 + 3.57131e9i 0.667184 + 0.395510i
\(700\) −2.18804e9 9.99246e8i −0.241109 0.110111i
\(701\) 1.53919e10 4.51946e9i 1.68763 0.495534i 0.709709 0.704495i \(-0.248826\pi\)
0.977924 + 0.208961i \(0.0670083\pi\)
\(702\) 9.68640e9 + 1.73603e9i 1.05677 + 0.189399i
\(703\) 3.65530e9 8.00398e9i 0.396807 0.868885i
\(704\) 1.13257e9 + 7.87720e9i 0.122338 + 0.850879i
\(705\) 7.07791e9 2.55526e8i 0.760752 0.0274646i
\(706\) 6.16358e9 + 1.34964e10i 0.659199 + 1.44344i
\(707\) −6.67710e8 + 4.29111e8i −0.0710591 + 0.0456669i
\(708\) 1.97857e9 + 2.12349e9i 0.209525 + 0.224872i
\(709\) 3.79697e9 5.90821e9i 0.400107 0.622578i −0.581488 0.813555i \(-0.697529\pi\)
0.981595 + 0.190977i \(0.0611656\pi\)
\(710\) −1.06961e10 + 1.23439e10i −1.12155 + 1.29434i
\(711\) 1.48232e10 + 1.04866e9i 1.54667 + 0.109419i
\(712\) 8.89894e9i 0.923971i
\(713\) 1.49596e9 1.82526e9i 0.154564 0.188587i
\(714\) −2.18382e9 1.75844e9i −0.224529 0.180794i
\(715\) −1.46580e10 4.30399e9i −1.49970 0.440352i
\(716\) 1.93102e8 + 1.67324e8i 0.0196604 + 0.0170358i
\(717\) −3.78368e9 + 1.26095e9i −0.383352 + 0.127756i
\(718\) −1.48091e10 2.12923e9i −1.49312 0.214678i
\(719\) −5.92412e9 9.21811e9i −0.594392 0.924891i −0.999941 0.0108185i \(-0.996556\pi\)
0.405550 0.914073i \(-0.367080\pi\)
\(720\) −1.02370e10 + 7.67568e9i −1.02214 + 0.766396i
\(721\) 5.80815e9 + 6.70296e9i 0.577117 + 0.666029i
\(722\) −5.26179e9 + 7.56532e8i −0.520300 + 0.0748078i
\(723\) 9.76533e8 + 1.94898e9i 0.0960955 + 0.191789i
\(724\) 1.04612e9 + 3.56274e9i 0.102446 + 0.348899i
\(725\) −6.56564e9 2.23605e10i −0.639873 2.17921i
\(726\) 1.66175e9 + 3.31655e9i 0.161171 + 0.321668i
\(727\) 1.42062e10 2.04255e9i 1.37122 0.197152i 0.582966 0.812497i \(-0.301892\pi\)
0.788258 + 0.615344i \(0.210983\pi\)
\(728\) −6.32214e9 7.29614e9i −0.607302 0.700863i
\(729\) 4.99182e9 9.19243e9i 0.477213 0.878788i
\(730\) −4.93777e8 7.68333e8i −0.0469787 0.0731003i
\(731\) 1.75878e9 + 2.52874e8i 0.166533 + 0.0239438i
\(732\) 3.44971e9 1.14965e9i 0.325083 0.108337i
\(733\) −8.56155e9 7.41863e9i −0.802950 0.695760i 0.153342 0.988173i \(-0.450996\pi\)
−0.956292 + 0.292413i \(0.905542\pi\)
\(734\) 1.46803e10 + 4.31052e9i 1.37025 + 0.402341i
\(735\) −6.81247e9 5.48550e9i −0.632847 0.509578i
\(736\) 1.31620e9 + 4.06653e9i 0.121689 + 0.375969i
\(737\) 1.07305e10i 0.987374i
\(738\) 1.13077e9 1.59837e10i 0.103556 1.46380i
\(739\) 1.28226e10 1.47981e10i 1.16875 1.34880i 0.243288 0.969954i \(-0.421774\pi\)
0.925458 0.378850i \(-0.123680\pi\)
\(740\) −2.99918e9 + 4.66681e9i −0.272076 + 0.423359i
\(741\) 5.82018e9 + 6.24647e9i 0.525500 + 0.563989i
\(742\) −6.23569e9 + 4.00743e9i −0.560365 + 0.360124i
\(743\) −6.15118e9 1.34692e10i −0.550171 1.20471i −0.956702 0.291069i \(-0.905989\pi\)
0.406531 0.913637i \(-0.366738\pi\)
\(744\) 2.93846e9 1.06084e8i 0.261586 0.00944375i
\(745\) 1.35702e8 + 9.43826e8i 0.0120237 + 0.0836267i
\(746\) −3.74778e8 + 8.20649e8i −0.0330512 + 0.0723721i
\(747\) −1.87897e9 3.43476e9i −0.164929 0.301491i
\(748\) −7.64413e8 + 2.24452e8i −0.0667840 + 0.0196096i
\(749\) −5.16341e9 2.35805e9i −0.449004 0.205053i
\(750\) 1.24846e10 + 7.40092e9i 1.08059 + 0.640577i
\(751\) 2.36244e9 2.04707e9i 0.203527 0.176357i −0.547134 0.837045i \(-0.684281\pi\)
0.750660 + 0.660688i \(0.229736\pi\)
\(752\) −3.63945e9 + 1.66208e9i −0.312085 + 0.142524i
\(753\) 1.40528e10 + 1.50534e9i 1.19945 + 0.128485i
\(754\) 2.22642e9 1.54851e10i 0.189150 1.31557i
\(755\) −1.98270e10 1.27421e10i −1.67665 1.07752i
\(756\) −1.58501e9 + 6.58685e8i −0.133415 + 0.0554436i
\(757\) −6.43705e9 + 2.19226e10i −0.539326 + 1.83678i 0.00816878 + 0.999967i \(0.497400\pi\)
−0.547495 + 0.836809i \(0.684418\pi\)
\(758\) −1.69417e10 −1.41291
\(759\) −5.52129e9 7.49814e9i −0.458347 0.622454i
\(760\) −1.40392e10 −1.16010
\(761\) −4.45804e9 + 1.51827e10i −0.366689 + 1.24883i 0.545171 + 0.838325i \(0.316465\pi\)
−0.911860 + 0.410502i \(0.865353\pi\)
\(762\) −3.07817e9 1.70235e10i −0.252029 1.39382i
\(763\) −3.06011e8 1.96661e8i −0.0249403 0.0160281i
\(764\) −2.28511e8 + 1.58933e9i −0.0185387 + 0.128940i
\(765\) −6.61382e9 6.60361e9i −0.534118 0.533294i
\(766\) 9.32458e9 4.25839e9i 0.749598 0.342330i
\(767\) 1.73563e10 1.50393e10i 1.38891 1.20350i
\(768\) −3.69127e9 + 6.22679e9i −0.294044 + 0.496021i
\(769\) 1.76213e9 + 8.04736e8i 0.139732 + 0.0638133i 0.484054 0.875038i \(-0.339164\pi\)
−0.344322 + 0.938852i \(0.611891\pi\)
\(770\) −1.01723e10 + 2.98685e9i −0.802972 + 0.235774i
\(771\) −8.24019e9 + 1.99153e10i −0.647510 + 1.56494i
\(772\) 4.31730e8 9.45356e8i 0.0337716 0.0739495i
\(773\) 2.48226e9 + 1.72645e10i 0.193294 + 1.34439i 0.823214 + 0.567731i \(0.192179\pi\)
−0.629920 + 0.776660i \(0.716912\pi\)
\(774\) −2.59095e9 + 3.46669e9i −0.200847 + 0.268733i
\(775\) −2.40813e9 5.27307e9i −0.185833 0.406918i
\(776\) 5.45472e9 3.50554e9i 0.419041 0.269301i
\(777\) 1.02408e10 9.54196e9i 0.783181 0.729733i
\(778\) 4.86798e7 7.57472e7i 0.00370613 0.00576684i
\(779\) 9.10386e9 1.05064e10i 0.689993 0.796294i
\(780\) −3.07155e9 4.42023e9i −0.231754 0.333513i
\(781\) 1.17103e10i 0.879611i
\(782\) 4.81208e9 2.35917e9i 0.359840 0.176415i
\(783\) −1.48790e10 7.42634e9i −1.10766 0.552852i
\(784\) 4.74084e9 + 1.39204e9i 0.351357 + 0.103168i
\(785\) −6.97281e9 6.04197e9i −0.514475 0.445795i
\(786\) −6.02803e8 1.80880e9i −0.0442789 0.132865i
\(787\) 1.90777e10 + 2.74296e9i 1.39513 + 0.200589i 0.798532 0.601953i \(-0.205611\pi\)
0.596596 + 0.802542i \(0.296520\pi\)
\(788\) 2.15092e9 + 3.34690e9i 0.156597 + 0.243669i
\(789\) 9.59283e8 3.76450e9i 0.0695308 0.272859i
\(790\) 2.11781e10 + 2.44408e10i 1.52824 + 1.76368i
\(791\) −1.32738e10 + 1.90848e9i −0.953625 + 0.137111i
\(792\) 2.45736e9 1.13385e10i 0.175764 0.810991i
\(793\) −8.10605e9 2.76067e10i −0.577236 1.96588i
\(794\) −1.42026e9 4.83697e9i −0.100693 0.342927i
\(795\) −2.20907e10 + 1.10685e10i −1.55928 + 0.781274i
\(796\) 1.39727e9 2.00897e8i 0.0981937 0.0141181i
\(797\) 1.52085e9 + 1.75515e9i 0.106410 + 0.122804i 0.806456 0.591294i \(-0.201383\pi\)
−0.700046 + 0.714098i \(0.746837\pi\)
\(798\) 5.74147e9 + 1.46306e9i 0.399957 + 0.101918i
\(799\) −1.58005e9 2.45860e9i −0.109586 0.170520i
\(800\) 1.03922e10 + 1.49417e9i 0.717614 + 0.103177i
\(801\) −4.36587e9 + 1.17330e10i −0.300163 + 0.806671i
\(802\) −1.48236e10 1.28447e10i −1.01472 0.879256i
\(803\) 6.28286e8 + 1.84482e8i 0.0428207 + 0.0125733i
\(804\) −2.37117e9 + 2.94477e9i −0.160904 + 0.199828i
\(805\) −1.60945e10 + 7.89050e9i −1.08741 + 0.533113i
\(806\) 3.89147e9i 0.261783i
\(807\) 1.49812e9 1.04102e9i 0.100343 0.0697271i
\(808\) 1.23785e9 1.42855e9i 0.0825520 0.0952701i
\(809\) −4.90585e9 + 7.63365e9i −0.325758 + 0.506889i −0.965047 0.262078i \(-0.915592\pi\)
0.639289 + 0.768966i \(0.279229\pi\)
\(810\) 2.18325e10 6.44725e9i 1.44346 0.426263i
\(811\) −1.05168e10 + 6.75875e9i −0.692327 + 0.444932i −0.838913 0.544266i \(-0.816808\pi\)
0.146585 + 0.989198i \(0.453172\pi\)
\(812\) 1.13354e9 + 2.48210e9i 0.0743002 + 0.162695i
\(813\) 6.03761e8 + 1.67238e10i 0.0394047 + 1.09148i
\(814\) 2.25207e9 + 1.56635e10i 0.146351 + 1.01789i
\(815\) 1.48292e10 3.24715e10i 0.959548 2.10112i
\(816\) 4.87864e9 + 2.01859e9i 0.314328 + 0.130057i
\(817\) −3.60277e9 + 1.05787e9i −0.231132 + 0.0678664i
\(818\) 1.19295e10 + 5.44801e9i 0.762053 + 0.348018i
\(819\) 4.75606e9 + 1.27215e10i 0.302520 + 0.809176i
\(820\) −6.62381e9 + 5.73956e9i −0.419526 + 0.363522i
\(821\) −1.89374e10 + 8.64842e9i −1.19432 + 0.545426i −0.910523 0.413459i \(-0.864320\pi\)
−0.283794 + 0.958885i \(0.591593\pi\)
\(822\) −1.90751e9 + 1.78072e10i −0.119789 + 1.11826i
\(823\) −3.77531e9 + 2.62578e10i −0.236077 + 1.64195i 0.434906 + 0.900476i \(0.356782\pi\)
−0.670983 + 0.741473i \(0.734128\pi\)
\(824\) −1.77694e10 1.14197e10i −1.10644 0.711066i
\(825\) −2.25077e10 + 4.06981e9i −1.39554 + 0.252340i
\(826\) 4.49012e9 1.52920e10i 0.277222 0.944133i
\(827\) 7.48043e9 0.459894 0.229947 0.973203i \(-0.426145\pi\)
0.229947 + 0.973203i \(0.426145\pi\)
\(828\) 1.41692e8 3.27780e9i 0.00867440 0.200667i
\(829\) −1.98491e10 −1.21004 −0.605020 0.796211i \(-0.706835\pi\)
−0.605020 + 0.796211i \(0.706835\pi\)
\(830\) 2.40045e9 8.17520e9i 0.145720 0.496278i
\(831\) 1.44712e9 2.61666e8i 0.0874784 0.0158177i
\(832\) 1.86648e10 + 1.19952e10i 1.12355 + 0.722062i
\(833\) −5.13636e8 + 3.57241e9i −0.0307891 + 0.214143i
\(834\) −1.37467e9 + 1.28329e10i −0.0820573 + 0.766029i
\(835\) 5.03326e9 2.29861e9i 0.299190 0.136635i
\(836\) 1.27235e9 1.10249e9i 0.0753154 0.0652611i
\(837\) −3.92633e9 1.30175e9i −0.231445 0.0767344i
\(838\) −1.21807e10 5.56272e9i −0.715018 0.326538i
\(839\) 5.24088e9 1.53886e9i 0.306364 0.0899565i −0.124937 0.992165i \(-0.539873\pi\)
0.431301 + 0.902208i \(0.358055\pi\)
\(840\) −2.06363e10 8.53848e9i −1.20131 0.497054i
\(841\) −3.81625e9 + 8.35643e9i −0.221234 + 0.484434i
\(842\) 8.10176e8 + 5.63490e9i 0.0467721 + 0.325307i
\(843\) 9.54900e8 + 2.64501e10i 0.0548986 + 1.52066i
\(844\) 3.73328e8 + 8.17474e8i 0.0213743 + 0.0468032i
\(845\) −1.09884e10 + 7.06183e9i −0.626523 + 0.402642i
\(846\) 7.09995e9 5.13313e8i 0.403143 0.0291465i
\(847\) −2.76790e9 + 4.30694e9i −0.156516 + 0.243544i
\(848\) 9.14065e9 1.05489e10i 0.514744 0.594046i
\(849\) 2.05510e10 1.42806e10i 1.15254 0.800883i
\(850\) 1.31643e10i 0.735242i
\(851\) 8.23892e9 + 2.54549e10i 0.458265 + 1.41585i
\(852\) 2.58770e9 3.21369e9i 0.143343 0.178018i
\(853\) −1.78712e10 5.24747e9i −0.985901 0.289487i −0.251243 0.967924i \(-0.580839\pi\)
−0.734658 + 0.678438i \(0.762657\pi\)
\(854\) −1.50901e10 1.30757e10i −0.829067 0.718391i
\(855\) 1.85104e10 + 6.88772e9i 1.01282 + 0.376872i
\(856\) 1.33809e10 + 1.92388e9i 0.729168 + 0.104839i
\(857\) −5.05753e9 7.86967e9i −0.274477 0.427094i 0.676460 0.736479i \(-0.263513\pi\)
−0.950937 + 0.309385i \(0.899877\pi\)
\(858\) −1.48789e10 3.79150e9i −0.804204 0.204930i
\(859\) −2.15401e10 2.48586e10i −1.15950 1.33813i −0.931185 0.364547i \(-0.881224\pi\)
−0.228315 0.973587i \(-0.573322\pi\)
\(860\) 2.34318e9 3.36898e8i 0.125620 0.0180615i
\(861\) 1.97717e10 9.90654e9i 1.05568 0.528945i
\(862\) 5.45119e8 + 1.85651e9i 0.0289879 + 0.0987236i
\(863\) −2.78563e8 9.48698e8i −0.0147532 0.0502447i 0.951787 0.306758i \(-0.0992443\pi\)
−0.966541 + 0.256514i \(0.917426\pi\)
\(864\) 5.82794e9 4.70760e9i 0.307409 0.248314i
\(865\) 4.85340e9 6.97814e8i 0.254970 0.0366592i
\(866\) 1.84142e10 + 2.12512e10i 0.963476 + 1.11191i
\(867\) 3.78622e9 1.48582e10i 0.197305 0.774283i
\(868\) 3.66961e8 + 5.71003e8i 0.0190459 + 0.0296360i
\(869\) −2.29503e10 3.29975e9i −1.18637 0.170574i
\(870\) −1.14420e10 3.43335e10i −0.589095 1.76767i
\(871\) 2.26088e10 + 1.95906e10i 1.15935 + 1.00458i
\(872\) 8.31208e8 + 2.44065e8i 0.0424524 + 0.0124651i
\(873\) −8.91175e9 + 1.94585e9i −0.453329 + 0.0989825i
\(874\) −7.17895e9 + 8.75920e9i −0.363723 + 0.443787i
\(875\) 2.00303e10i 1.01078i
\(876\) 1.31656e8 + 1.89464e8i 0.00661721 + 0.00952274i
\(877\) −2.27607e10 + 2.62672e10i −1.13943 + 1.31497i −0.197061 + 0.980391i \(0.563140\pi\)
−0.942368 + 0.334579i \(0.891406\pi\)
\(878\) 7.31378e9 1.13805e10i 0.364679 0.567452i
\(879\) 1.47355e10 1.37298e10i 0.731818 0.681874i
\(880\) 1.67947e10 1.07933e10i 0.830776 0.533908i
\(881\) −4.52267e9 9.90326e9i −0.222833 0.487936i 0.764888 0.644163i \(-0.222794\pi\)
−0.987721 + 0.156227i \(0.950067\pi\)
\(882\) −7.04151e9 5.26272e9i −0.345562 0.258268i
\(883\) 1.93954e9 + 1.34898e10i 0.0948062 + 0.659392i 0.980702 + 0.195508i \(0.0626355\pi\)
−0.885896 + 0.463884i \(0.846455\pi\)
\(884\) −9.22679e8 + 2.02038e9i −0.0449229 + 0.0983674i
\(885\) 2.03116e10 4.90902e10i 0.985016 2.38064i
\(886\) 8.55363e8 2.51157e8i 0.0413174 0.0121319i
\(887\) 2.00037e10 + 9.13540e9i 0.962451 + 0.439536i 0.833747 0.552147i \(-0.186191\pi\)
0.128704 + 0.991683i \(0.458918\pi\)
\(888\) −1.69988e10 + 2.86752e10i −0.814654 + 1.37424i
\(889\) 1.80439e10 1.56352e10i 0.861341 0.746356i
\(890\) −2.47826e10 + 1.13178e10i −1.17837 + 0.538144i
\(891\) −8.80268e9 + 1.37439e10i −0.416911 + 0.650935i
\(892\) 6.65344e8 4.62757e9i 0.0313884 0.218311i
\(893\) 5.19552e9 + 3.33896e9i 0.244146 + 0.156903i
\(894\) 1.70527e8 + 9.43080e8i 0.00798198 + 0.0441435i
\(895\) 1.31764e9 4.48748e9i 0.0614352 0.209229i
\(896\) 9.27669e9 0.430839
\(897\) −2.58787e10 2.05616e9i −1.19720 0.0951224i
\(898\) −2.80982e10 −1.29483
\(899\) −1.85267e9 + 6.30962e9i −0.0850432 + 0.289630i
\(900\) −7.07615e9 3.85678e9i −0.323555 0.176350i
\(901\) 8.57722e9 + 5.51224e9i 0.390670 + 0.251068i
\(902\) −3.55810e9 + 2.47471e10i −0.161434 + 1.12280i
\(903\) −5.93911e9 6.36199e8i −0.268419 0.0287532i
\(904\) 2.90510e10 1.32672e10i 1.30789 0.597295i
\(905\) 5.13656e10 4.45085e10i 2.30357 1.99606i
\(906\) −2.03768e10 1.20795e10i −0.910305 0.539633i
\(907\) 2.40636e10 + 1.09895e10i 1.07087 + 0.489049i 0.871257 0.490827i \(-0.163305\pi\)
0.199610 + 0.979875i \(0.436032\pi\)
\(908\) 6.39184e8 1.87681e8i 0.0283351 0.00831994i
\(909\) −2.33293e9 + 1.27622e9i −0.103021 + 0.0563573i
\(910\) −1.22784e10 + 2.68858e10i −0.540126 + 1.18271i
\(911\) 3.66464e9 + 2.54882e10i 0.160590 + 1.11693i 0.897526 + 0.440963i \(0.145363\pi\)
−0.736936 + 0.675963i \(0.763728\pi\)
\(912\) −1.11499e10 + 4.02534e8i −0.486732 + 0.0175720i
\(913\) 2.53765e9 + 5.55669e9i 0.110353 + 0.241640i
\(914\) 4.58772e9 2.94835e9i 0.198740 0.127722i
\(915\) −4.53730e10 4.86963e10i −1.95805 2.10146i
\(916\) −9.70690e7 + 1.51042e8i −0.00417298 + 0.00649329i
\(917\) 1.72317e9 1.98864e9i 0.0737963 0.0851655i
\(918\) −6.88253e9 6.39299e9i −0.293629 0.272744i
\(919\) 5.15379e9i 0.219040i 0.993985 + 0.109520i \(0.0349313\pi\)
−0.993985 + 0.109520i \(0.965069\pi\)
\(920\) 3.14829e10 2.88291e10i 1.33296 1.22060i
\(921\) 2.09870e10 + 1.68990e10i 0.885201 + 0.712776i
\(922\) −3.17117e10 9.31141e9i −1.33248 0.391253i
\(923\) −2.46734e10 2.13796e10i −1.03282 0.894941i
\(924\) 2.54075e9 8.46733e8i 0.105952 0.0353097i
\(925\) 6.50510e10 + 9.35291e9i 2.70245 + 0.388554i
\(926\) 5.44780e9 + 8.47694e9i 0.225467 + 0.350833i
\(927\) 1.78260e10 + 2.37744e10i 0.734977 + 0.980235i
\(928\) −7.79940e9 9.00099e9i −0.320364 0.369720i
\(929\) 4.26149e9 6.12710e8i 0.174384 0.0250726i −0.0545696 0.998510i \(-0.517379\pi\)
0.228954 + 0.973437i \(0.426470\pi\)
\(930\) −4.03261e9 8.04837e9i −0.164398 0.328109i
\(931\) −2.14874e9 7.31792e9i −0.0872689 0.297210i
\(932\) −1.08471e9 3.69419e9i −0.0438893 0.149473i
\(933\) 1.14867e9 + 2.29254e9i 0.0463032 + 0.0924128i
\(934\) −1.03235e10 + 1.48430e9i −0.414584 + 0.0596082i
\(935\) 9.54964e9 + 1.10209e10i 0.382073 + 0.440936i
\(936\) −1.94035e10 2.58783e10i −0.773417 1.03150i
\(937\) 1.21761e10 + 1.89464e10i 0.483526 + 0.752381i 0.994218 0.107383i \(-0.0342470\pi\)
−0.510692 + 0.859764i \(0.670611\pi\)
\(938\) 2.05494e10 + 2.95455e9i 0.812997 + 0.116891i
\(939\) 1.74662e10 5.82079e9i 0.688443 0.229431i
\(940\) −2.94261e9 2.54979e9i −0.115554 0.100128i
\(941\) 2.28742e10 + 6.71646e9i 0.894914 + 0.262771i 0.696678 0.717384i \(-0.254661\pi\)
0.198236 + 0.980154i \(0.436479\pi\)
\(942\) −7.22274e9 5.81585e9i −0.281529 0.226691i
\(943\) 1.15919e9 + 4.22551e10i 0.0450156 + 1.64092i
\(944\) 3.00118e10i 1.16115i
\(945\) 2.30194e10 + 2.13820e10i 0.887324 + 0.824210i
\(946\) 4.42217e9 5.10345e9i 0.169831 0.195995i
\(947\) −3.22540e9 + 5.01883e9i −0.123413 + 0.192034i −0.897462 0.441091i \(-0.854592\pi\)
0.774050 + 0.633125i \(0.218228\pi\)
\(948\) −5.56911e9 5.97701e9i −0.212303 0.227853i
\(949\) 1.53576e9 9.86976e8i 0.0583301 0.0374865i
\(950\) 1.15563e10 + 2.53048e10i 0.437308 + 0.957571i
\(951\) 1.99556e10 7.20435e8i 0.752372 0.0271621i
\(952\) 1.31150e9 + 9.12171e9i 0.0492652 + 0.342647i
\(953\) 5.32728e9 1.16651e10i 0.199380 0.436580i −0.783362 0.621566i \(-0.786497\pi\)
0.982741 + 0.184986i \(0.0592239\pi\)
\(954\) −2.17870e10 + 1.19185e10i −0.812416 + 0.444428i
\(955\) 2.82000e10 8.28028e9i 1.04770 0.307633i
\(956\) 1.99442e9 + 9.10822e8i 0.0738268 + 0.0337156i
\(957\) 2.23196e10 + 1.32312e10i 0.823179 + 0.487985i
\(958\) 1.51969e10 1.31682e10i 0.558439 0.483891i
\(959\) −2.24832e10 + 1.02677e10i −0.823175 + 0.375931i
\(960\) 5.10329e10 + 5.46667e9i 1.86166 + 0.199422i
\(961\) 3.68266e9 2.56135e10i 0.133854 0.930972i
\(962\) 3.71142e10 + 2.38518e10i 1.34409 + 0.863792i
\(963\) −1.66985e10 9.10134e9i −0.602540 0.328408i
\(964\) 3.37636e8 1.14988e9i 0.0121389 0.0413413i
\(965\) −1.90231e10 −0.681453
\(966\) −1.58796e10 + 8.50901e9i −0.566786 + 0.303710i
\(967\) −1.19139e10 −0.423704 −0.211852 0.977302i \(-0.567949\pi\)
−0.211852 + 0.977302i \(0.567949\pi\)
\(968\) 3.43508e9 1.16988e10i 0.121723 0.414551i
\(969\) −1.45012e9 8.01974e9i −0.0512001 0.283157i
\(970\) −1.67000e10 1.07324e10i −0.587509 0.377569i
\(971\) −2.28628e9 + 1.59014e10i −0.0801423 + 0.557402i 0.909704 + 0.415258i \(0.136309\pi\)
−0.989846 + 0.142144i \(0.954600\pi\)
\(972\) −5.45280e9 + 1.82657e9i −0.190453 + 0.0637978i
\(973\) −1.62027e10 + 7.39954e9i −0.563888 + 0.257519i
\(974\) 3.20127e10 2.77391e10i 1.11011 0.961915i
\(975\) −3.25174e10 + 5.48535e10i −1.12357 + 1.89534i
\(976\) 3.42019e10 + 1.56195e10i 1.17754 + 0.537765i
\(977\) −2.95364e10 + 8.67266e9i −1.01327 + 0.297523i −0.745891 0.666068i \(-0.767976\pi\)
−0.267381 + 0.963591i \(0.586158\pi\)
\(978\) 1.37173e10 3.31528e10i 0.468904 1.13327i
\(979\) 8.11441e9 1.77681e10i 0.276387 0.605203i
\(980\) 6.84304e8 + 4.75944e9i 0.0232251 + 0.161534i
\(981\) −9.76188e8 7.29589e8i −0.0330135 0.0246738i
\(982\) −1.29436e10 2.83425e10i −0.436179 0.955099i
\(983\) −2.22457e10 + 1.42964e10i −0.746979 + 0.480054i −0.857927 0.513772i \(-0.828248\pi\)
0.110948 + 0.993826i \(0.464611\pi\)
\(984\) −3.85328e10 + 3.59031e10i −1.28928 + 1.20129i
\(985\) 3.93710e10 6.12624e10i 1.31265 2.04252i
\(986\) −9.77933e9 + 1.12860e10i −0.324893 + 0.374946i
\(987\) 5.60619e9 + 8.06779e9i 0.185591 + 0.267082i
\(988\) 4.69364e9i 0.154832i
\(989\) 5.90691e9 9.77045e9i 0.194166 0.321164i
\(990\) −3.47017e10 + 7.57698e9i −1.13665 + 0.248184i
\(991\) −2.76716e10 8.12513e9i −0.903186 0.265199i −0.203016 0.979175i \(-0.565074\pi\)
−0.700170 + 0.713976i \(0.746892\pi\)
\(992\) −2.23897e9 1.94008e9i −0.0728211 0.0630998i
\(993\) 1.60443e9 + 4.81432e9i 0.0519993 + 0.156032i
\(994\) −2.24259e10 3.22436e9i −0.724266 0.104134i
\(995\) −1.39696e10 2.17371e10i −0.449575 0.699552i
\(996\) −5.31483e8 + 2.08569e9i −0.0170444 + 0.0668871i
\(997\) 1.44401e10 + 1.66648e10i 0.461463 + 0.532557i 0.938017 0.346588i \(-0.112660\pi\)
−0.476554 + 0.879145i \(0.658114\pi\)
\(998\) 3.84694e10 5.53107e9i 1.22506 0.176138i
\(999\) 3.64807e10 2.94678e10i 1.15767 0.935123i
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 69.8.g.a.5.17 540
3.2 odd 2 inner 69.8.g.a.5.38 yes 540
23.14 odd 22 inner 69.8.g.a.14.38 yes 540
69.14 even 22 inner 69.8.g.a.14.17 yes 540
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.8.g.a.5.17 540 1.1 even 1 trivial
69.8.g.a.5.38 yes 540 3.2 odd 2 inner
69.8.g.a.14.17 yes 540 69.14 even 22 inner
69.8.g.a.14.38 yes 540 23.14 odd 22 inner