Properties

Label 35.10.k.a.12.16
Level $35$
Weight $10$
Character 35.12
Analytic conductor $18.026$
Analytic rank $0$
Dimension $136$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [35,10,Mod(3,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([9, 2]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.3");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 35.k (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(18.0262542657\)
Analytic rank: \(0\)
Dimension: \(136\)
Relative dimension: \(34\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 12.16
Character \(\chi\) \(=\) 35.12
Dual form 35.10.k.a.3.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-6.05635 + 1.62279i) q^{2} +(21.6603 - 80.8372i) q^{3} +(-409.359 + 236.344i) q^{4} +(1391.85 - 125.989i) q^{5} +524.728i q^{6} +(-6352.13 - 63.6305i) q^{7} +(4365.66 - 4365.66i) q^{8} +(10980.5 + 6339.59i) q^{9} +(-8225.08 + 3021.72i) q^{10} +(15736.1 + 27255.8i) q^{11} +(10238.5 + 38210.7i) q^{12} +(-51912.6 - 51912.6i) q^{13} +(38574.0 - 9922.83i) q^{14} +(19963.3 - 115242. i) q^{15} +(101653. - 176067. i) q^{16} +(-14537.4 - 3895.29i) q^{17} +(-76789.5 - 20575.7i) q^{18} +(391609. - 678286. i) q^{19} +(-539991. + 380530. i) q^{20} +(-142733. + 512110. i) q^{21} +(-139534. - 139534. i) q^{22} +(-158327. - 590883. i) q^{23} +(-258347. - 447470. i) q^{24} +(1.92138e6 - 350716. i) q^{25} +(398644. + 230157. i) q^{26} +(1.91509e6 - 1.91509e6i) q^{27} +(2.61534e6 - 1.47524e6i) q^{28} -7.28756e6i q^{29} +(66110.1 + 730344. i) q^{30} +(8.04245e6 - 4.64331e6i) q^{31} +(-1.14807e6 + 4.28465e6i) q^{32} +(2.54413e6 - 681698. i) q^{33} +94365.0 q^{34} +(-8.84924e6 + 711735. i) q^{35} -5.99328e6 q^{36} +(-3.86561e6 + 1.03579e6i) q^{37} +(-1.27100e6 + 4.74344e6i) q^{38} +(-5.32091e6 + 3.07203e6i) q^{39} +(5.52633e6 - 6.62638e6i) q^{40} -4.95585e6i q^{41} +(33388.7 - 3.33314e6i) q^{42} +(-9.30301e6 + 9.30301e6i) q^{43} +(-1.28835e7 - 7.43827e6i) q^{44} +(1.60819e7 + 7.44035e6i) q^{45} +(1.91776e6 + 3.32166e6i) q^{46} +(1.15867e7 + 4.32423e7i) q^{47} +(-1.20310e7 - 1.20310e7i) q^{48} +(4.03455e7 + 808378. i) q^{49} +(-1.10674e7 + 5.24206e6i) q^{50} +(-629769. + 1.09079e6i) q^{51} +(3.35201e7 + 8.98169e6i) q^{52} +(-7.99801e7 - 2.14306e7i) q^{53} +(-8.49068e6 + 1.47063e7i) q^{54} +(2.53363e7 + 3.59534e7i) q^{55} +(-2.80091e7 + 2.74535e7i) q^{56} +(-4.63484e7 - 4.63484e7i) q^{57} +(1.18262e7 + 4.41360e7i) q^{58} +(5.95342e7 + 1.03116e8i) q^{59} +(1.90647e7 + 5.18937e7i) q^{60} +(-8.24305e7 - 4.75913e7i) q^{61} +(-4.11728e7 + 4.11728e7i) q^{62} +(-6.93461e7 - 4.09686e7i) q^{63} +7.62797e7i q^{64} +(-7.87951e7 - 6.57142e7i) q^{65} +(-1.43019e7 + 8.25720e6i) q^{66} +(3.52475e7 - 1.31546e8i) q^{67} +(6.87166e6 - 1.84126e6i) q^{68} -5.11947e7 q^{69} +(5.24391e7 - 1.86710e7i) q^{70} +2.95103e8 q^{71} +(7.56136e7 - 2.02606e7i) q^{72} +(4.67359e7 - 1.74421e8i) q^{73} +(2.17306e7 - 1.25462e7i) q^{74} +(1.32666e7 - 1.62915e8i) q^{75} +3.70217e8i q^{76} +(-9.82237e7 - 1.74134e8i) q^{77} +(2.72400e7 - 2.72400e7i) q^{78} +(-3.03492e7 - 1.75221e7i) q^{79} +(1.19303e8 - 2.57867e8i) q^{80} +(1.14526e7 + 1.98366e7i) q^{81} +(8.04232e6 + 3.00144e7i) q^{82} +(2.43875e8 + 2.43875e8i) q^{83} +(-6.26051e7 - 2.43371e8i) q^{84} +(-2.07247e7 - 3.59011e6i) q^{85} +(4.12454e7 - 7.14391e7i) q^{86} +(-5.89106e8 - 1.57851e8i) q^{87} +(1.87688e8 + 5.02909e7i) q^{88} +(-3.20271e7 + 5.54726e7i) q^{89} +(-1.09472e8 - 1.89637e7i) q^{90} +(3.26452e8 + 3.33059e8i) q^{91} +(2.04464e8 + 2.04464e8i) q^{92} +(-2.01151e8 - 7.50705e8i) q^{93} +(-1.40347e8 - 2.43087e8i) q^{94} +(4.59605e8 - 9.93412e8i) q^{95} +(3.21492e8 + 1.85613e8i) q^{96} +(9.43605e8 - 9.43605e8i) q^{97} +(-2.45658e8 + 6.05766e7i) q^{98} +3.99042e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 136 q - 2 q^{2} - 6 q^{3} - 1710 q^{5} + 5940 q^{7} - 3484 q^{8} + 153786 q^{10} - 87752 q^{11} + 3066 q^{12} - 318872 q^{15} + 3132804 q^{16} - 1578678 q^{17} - 239036 q^{18} - 5745396 q^{21} + 2132088 q^{22}+ \cdots + 5117393178 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(22\) \(31\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.05635 + 1.62279i −0.267655 + 0.0717180i −0.390151 0.920751i \(-0.627577\pi\)
0.122495 + 0.992469i \(0.460910\pi\)
\(3\) 21.6603 80.8372i 0.154390 0.576190i −0.844767 0.535134i \(-0.820261\pi\)
0.999157 0.0410560i \(-0.0130722\pi\)
\(4\) −409.359 + 236.344i −0.799530 + 0.461609i
\(5\) 1391.85 125.989i 0.995928 0.0901505i
\(6\) 524.728i 0.165293i
\(7\) −6352.13 63.6305i −0.999950 0.0100167i
\(8\) 4365.66 4365.66i 0.376830 0.376830i
\(9\) 10980.5 + 6339.59i 0.557867 + 0.322084i
\(10\) −8225.08 + 3021.72i −0.260100 + 0.0955552i
\(11\) 15736.1 + 27255.8i 0.324064 + 0.561295i 0.981322 0.192370i \(-0.0616173\pi\)
−0.657258 + 0.753665i \(0.728284\pi\)
\(12\) 10238.5 + 38210.7i 0.142535 + 0.531948i
\(13\) −51912.6 51912.6i −0.504113 0.504113i 0.408601 0.912713i \(-0.366017\pi\)
−0.912713 + 0.408601i \(0.866017\pi\)
\(14\) 38574.0 9922.83i 0.268360 0.0690334i
\(15\) 19963.3 115242.i 0.101817 0.587762i
\(16\) 101653. 176067.i 0.387774 0.671644i
\(17\) −14537.4 3895.29i −0.0422151 0.0113115i 0.237650 0.971351i \(-0.423623\pi\)
−0.279865 + 0.960039i \(0.590290\pi\)
\(18\) −76789.5 20575.7i −0.172415 0.0461985i
\(19\) 391609. 678286.i 0.689384 1.19405i −0.282654 0.959222i \(-0.591215\pi\)
0.972038 0.234826i \(-0.0754519\pi\)
\(20\) −539991. + 380530.i −0.754660 + 0.531807i
\(21\) −142733. + 512110.i −0.160153 + 0.574615i
\(22\) −139534. 139534.i −0.126992 0.126992i
\(23\) −158327. 590883.i −0.117972 0.440277i 0.881520 0.472146i \(-0.156521\pi\)
−0.999492 + 0.0318693i \(0.989854\pi\)
\(24\) −258347. 447470.i −0.158947 0.275304i
\(25\) 1.92138e6 350716.i 0.983746 0.179567i
\(26\) 398644. + 230157.i 0.171082 + 0.0987745i
\(27\) 1.91509e6 1.91509e6i 0.693511 0.693511i
\(28\) 2.61534e6 1.47524e6i 0.804113 0.453577i
\(29\) 7.28756e6i 1.91334i −0.291179 0.956668i \(-0.594048\pi\)
0.291179 0.956668i \(-0.405952\pi\)
\(30\) 66110.1 + 730344.i 0.0149012 + 0.164620i
\(31\) 8.04245e6 4.64331e6i 1.56409 0.903026i 0.567251 0.823545i \(-0.308007\pi\)
0.996836 0.0794811i \(-0.0253263\pi\)
\(32\) −1.14807e6 + 4.28465e6i −0.193550 + 0.722339i
\(33\) 2.54413e6 681698.i 0.373445 0.100064i
\(34\) 94365.0 0.0121103
\(35\) −8.84924e6 + 711735.i −0.996781 + 0.0801700i
\(36\) −5.99328e6 −0.594708
\(37\) −3.86561e6 + 1.03579e6i −0.339087 + 0.0908580i −0.424344 0.905501i \(-0.639495\pi\)
0.0852576 + 0.996359i \(0.472829\pi\)
\(38\) −1.27100e6 + 4.74344e6i −0.0988825 + 0.369034i
\(39\) −5.32091e6 + 3.07203e6i −0.368295 + 0.212635i
\(40\) 5.52633e6 6.62638e6i 0.341324 0.409267i
\(41\) 4.95585e6i 0.273899i −0.990578 0.136950i \(-0.956270\pi\)
0.990578 0.136950i \(-0.0437299\pi\)
\(42\) 33388.7 3.33314e6i 0.00165569 0.165285i
\(43\) −9.30301e6 + 9.30301e6i −0.414969 + 0.414969i −0.883465 0.468497i \(-0.844796\pi\)
0.468497 + 0.883465i \(0.344796\pi\)
\(44\) −1.28835e7 7.43827e6i −0.518198 0.299182i
\(45\) 1.60819e7 + 7.44035e6i 0.584631 + 0.270481i
\(46\) 1.91776e6 + 3.32166e6i 0.0631516 + 0.109382i
\(47\) 1.15867e7 + 4.32423e7i 0.346354 + 1.29261i 0.891022 + 0.453960i \(0.149989\pi\)
−0.544668 + 0.838652i \(0.683344\pi\)
\(48\) −1.20310e7 1.20310e7i −0.327126 0.327126i
\(49\) 4.03455e7 + 808378.i 0.999799 + 0.0200324i
\(50\) −1.10674e7 + 5.24206e6i −0.250427 + 0.118614i
\(51\) −629769. + 1.09079e6i −0.0130351 + 0.0225775i
\(52\) 3.35201e7 + 8.98169e6i 0.635756 + 0.170350i
\(53\) −7.99801e7 2.14306e7i −1.39232 0.373072i −0.516742 0.856141i \(-0.672855\pi\)
−0.875582 + 0.483069i \(0.839522\pi\)
\(54\) −8.49068e6 + 1.47063e7i −0.135885 + 0.235359i
\(55\) 2.53363e7 + 3.59534e7i 0.373346 + 0.529795i
\(56\) −2.80091e7 + 2.74535e7i −0.380586 + 0.373036i
\(57\) −4.63484e7 4.63484e7i −0.581565 0.581565i
\(58\) 1.18262e7 + 4.41360e7i 0.137221 + 0.512115i
\(59\) 5.95342e7 + 1.03116e8i 0.639636 + 1.10788i 0.985513 + 0.169601i \(0.0542480\pi\)
−0.345877 + 0.938280i \(0.612419\pi\)
\(60\) 1.90647e7 + 5.18937e7i 0.189910 + 0.516933i
\(61\) −8.24305e7 4.75913e7i −0.762261 0.440091i 0.0678462 0.997696i \(-0.478387\pi\)
−0.830107 + 0.557604i \(0.811721\pi\)
\(62\) −4.11728e7 + 4.11728e7i −0.353873 + 0.353873i
\(63\) −6.93461e7 4.09686e7i −0.554612 0.327656i
\(64\) 7.62797e7i 0.568328i
\(65\) −7.87951e7 6.57142e7i −0.547506 0.456614i
\(66\) −1.43019e7 + 8.25720e6i −0.0927781 + 0.0535655i
\(67\) 3.52475e7 1.31546e8i 0.213694 0.797516i −0.772928 0.634493i \(-0.781209\pi\)
0.986622 0.163023i \(-0.0521245\pi\)
\(68\) 6.87166e6 1.84126e6i 0.0389737 0.0104430i
\(69\) −5.11947e7 −0.271897
\(70\) 5.24391e7 1.86710e7i 0.261044 0.0929451i
\(71\) 2.95103e8 1.37820 0.689099 0.724668i \(-0.258007\pi\)
0.689099 + 0.724668i \(0.258007\pi\)
\(72\) 7.56136e7 2.02606e7i 0.331592 0.0888498i
\(73\) 4.67359e7 1.74421e8i 0.192619 0.718862i −0.800252 0.599664i \(-0.795301\pi\)
0.992870 0.119198i \(-0.0380324\pi\)
\(74\) 2.17306e7 1.25462e7i 0.0842422 0.0486372i
\(75\) 1.32666e7 1.62915e8i 0.0484156 0.594548i
\(76\) 3.70217e8i 1.27290i
\(77\) −9.82237e7 1.74134e8i −0.318425 0.564513i
\(78\) 2.72400e7 2.72400e7i 0.0833262 0.0833262i
\(79\) −3.03492e7 1.75221e7i −0.0876649 0.0506133i 0.455527 0.890222i \(-0.349451\pi\)
−0.543192 + 0.839609i \(0.682784\pi\)
\(80\) 1.19303e8 2.57867e8i 0.325646 0.703867i
\(81\) 1.14526e7 + 1.98366e7i 0.0295613 + 0.0512016i
\(82\) 8.04232e6 + 3.00144e7i 0.0196435 + 0.0733106i
\(83\) 2.43875e8 + 2.43875e8i 0.564048 + 0.564048i 0.930455 0.366407i \(-0.119412\pi\)
−0.366407 + 0.930455i \(0.619412\pi\)
\(84\) −6.26051e7 2.43371e8i −0.137200 0.533350i
\(85\) −2.07247e7 3.59011e6i −0.0430629 0.00745973i
\(86\) 4.12454e7 7.14391e7i 0.0813079 0.140829i
\(87\) −5.89106e8 1.57851e8i −1.10245 0.295399i
\(88\) 1.87688e8 + 5.02909e7i 0.333630 + 0.0893959i
\(89\) −3.20271e7 + 5.54726e7i −0.0541082 + 0.0937181i −0.891811 0.452409i \(-0.850565\pi\)
0.837703 + 0.546127i \(0.183898\pi\)
\(90\) −1.09472e8 1.89637e7i −0.175878 0.0304671i
\(91\) 3.26452e8 + 3.33059e8i 0.499038 + 0.509137i
\(92\) 2.04464e8 + 2.04464e8i 0.297558 + 0.297558i
\(93\) −2.01151e8 7.50705e8i −0.278836 1.04063i
\(94\) −1.40347e8 2.43087e8i −0.185407 0.321135i
\(95\) 4.59605e8 9.93412e8i 0.578933 1.25133i
\(96\) 3.21492e8 + 1.85613e8i 0.386322 + 0.223043i
\(97\) 9.43605e8 9.43605e8i 1.08222 1.08222i 0.0859232 0.996302i \(-0.472616\pi\)
0.996302 0.0859232i \(-0.0273840\pi\)
\(98\) −2.45658e8 + 6.05766e7i −0.269038 + 0.0663419i
\(99\) 3.99042e8i 0.417504i
\(100\) −7.03644e8 + 5.97674e8i −0.703644 + 0.597674i
\(101\) 3.03333e8 1.75129e8i 0.290050 0.167461i −0.347914 0.937526i \(-0.613110\pi\)
0.637965 + 0.770066i \(0.279777\pi\)
\(102\) 2.04397e6 7.62821e6i 0.00186971 0.00697785i
\(103\) −1.17644e9 + 3.15227e8i −1.02992 + 0.275967i −0.733931 0.679224i \(-0.762316\pi\)
−0.295990 + 0.955191i \(0.595650\pi\)
\(104\) −4.53266e8 −0.379930
\(105\) −1.34142e8 + 7.30764e8i −0.107700 + 0.586713i
\(106\) 5.19165e8 0.399419
\(107\) 1.24471e9 3.33520e8i 0.918000 0.245977i 0.231269 0.972890i \(-0.425712\pi\)
0.686730 + 0.726912i \(0.259045\pi\)
\(108\) −3.31341e8 + 1.23658e9i −0.234352 + 0.874613i
\(109\) −1.03842e9 + 5.99532e8i −0.704618 + 0.406811i −0.809065 0.587719i \(-0.800026\pi\)
0.104447 + 0.994530i \(0.466693\pi\)
\(110\) −2.11790e8 1.76631e8i −0.137924 0.115027i
\(111\) 3.34921e8i 0.209406i
\(112\) −6.56913e8 + 1.11193e9i −0.394482 + 0.667726i
\(113\) −1.50124e9 + 1.50124e9i −0.866160 + 0.866160i −0.992045 0.125885i \(-0.959823\pi\)
0.125885 + 0.992045i \(0.459823\pi\)
\(114\) 3.55916e8 + 2.05488e8i 0.197367 + 0.113950i
\(115\) −2.94812e8 8.02474e8i −0.157183 0.427849i
\(116\) 1.72237e9 + 2.98323e9i 0.883213 + 1.52977i
\(117\) −2.40921e8 8.99130e8i −0.118861 0.443595i
\(118\) −5.27896e8 5.27896e8i −0.250657 0.250657i
\(119\) 9.20958e7 + 2.56684e7i 0.0420997 + 0.0117338i
\(120\) −4.15957e8 5.90263e8i −0.183119 0.259854i
\(121\) 6.83722e8 1.18424e9i 0.289965 0.502234i
\(122\) 5.76458e8 + 1.54462e8i 0.235586 + 0.0631250i
\(123\) −4.00617e8 1.07345e8i −0.157818 0.0422872i
\(124\) −2.19483e9 + 3.80156e9i −0.833689 + 1.44399i
\(125\) 2.63009e9 7.30218e8i 0.963552 0.267521i
\(126\) 4.86468e8 + 1.35586e8i 0.171944 + 0.0479232i
\(127\) −2.36202e9 2.36202e9i −0.805687 0.805687i 0.178291 0.983978i \(-0.442943\pi\)
−0.983978 + 0.178291i \(0.942943\pi\)
\(128\) −7.11598e8 2.65572e9i −0.234309 0.874455i
\(129\) 5.50524e8 + 9.53535e8i 0.175034 + 0.303168i
\(130\) 5.83851e8 + 2.70120e8i 0.179290 + 0.0829491i
\(131\) −1.40365e9 8.10397e8i −0.416426 0.240424i 0.277121 0.960835i \(-0.410620\pi\)
−0.693547 + 0.720411i \(0.743953\pi\)
\(132\) −8.80348e8 + 8.80348e8i −0.252390 + 0.252390i
\(133\) −2.53071e9 + 4.28364e9i −0.701310 + 1.18708i
\(134\) 8.53885e8i 0.228785i
\(135\) 2.42425e9 2.90681e9i 0.628167 0.753207i
\(136\) −8.04711e7 + 4.64600e7i −0.0201704 + 0.0116454i
\(137\) −1.01864e9 + 3.80162e9i −0.247047 + 0.921991i 0.725297 + 0.688436i \(0.241702\pi\)
−0.972344 + 0.233555i \(0.924964\pi\)
\(138\) 3.10053e8 8.30785e7i 0.0727746 0.0194999i
\(139\) 7.93977e7 0.0180402 0.00902010 0.999959i \(-0.497129\pi\)
0.00902010 + 0.999959i \(0.497129\pi\)
\(140\) 3.45430e9 2.38282e9i 0.759949 0.524221i
\(141\) 3.74656e9 0.798263
\(142\) −1.78725e9 + 4.78892e8i −0.368882 + 0.0988416i
\(143\) 5.98015e8 2.23182e9i 0.119591 0.446321i
\(144\) 2.23239e9 1.28887e9i 0.432652 0.249792i
\(145\) −9.18154e8 1.01432e10i −0.172488 1.90555i
\(146\) 1.13220e9i 0.206222i
\(147\) 9.39242e8 3.24391e9i 0.165901 0.572982i
\(148\) 1.33762e9 1.33762e9i 0.229169 0.229169i
\(149\) −5.19264e9 2.99797e9i −0.863078 0.498298i 0.00196393 0.999998i \(-0.499375\pi\)
−0.865042 + 0.501700i \(0.832708\pi\)
\(150\) 1.84031e8 + 1.00820e9i 0.0296811 + 0.162606i
\(151\) 4.20657e9 + 7.28599e9i 0.658464 + 1.14049i 0.981013 + 0.193940i \(0.0621268\pi\)
−0.322550 + 0.946553i \(0.604540\pi\)
\(152\) −1.25154e9 4.67080e9i −0.190172 0.709733i
\(153\) −1.34934e8 1.34934e8i −0.0199071 0.0199071i
\(154\) 8.77459e8 + 8.95217e8i 0.125714 + 0.128258i
\(155\) 1.06089e10 7.47607e9i 1.47631 1.04035i
\(156\) 1.45211e9 2.51513e9i 0.196308 0.340016i
\(157\) −3.24593e9 8.69745e8i −0.426374 0.114247i 0.0392494 0.999229i \(-0.487503\pi\)
−0.465624 + 0.884983i \(0.654170\pi\)
\(158\) 2.12240e8 + 5.68696e7i 0.0270939 + 0.00725978i
\(159\) −3.46478e9 + 6.00118e9i −0.429921 + 0.744645i
\(160\) −1.05812e9 + 6.10825e9i −0.127643 + 0.736846i
\(161\) 9.68113e8 + 3.76344e9i 0.113556 + 0.441437i
\(162\) −1.01552e8 1.01552e8i −0.0115843 0.0115843i
\(163\) −1.44709e9 5.40060e9i −0.160565 0.599236i −0.998564 0.0535649i \(-0.982942\pi\)
0.838000 0.545671i \(-0.183725\pi\)
\(164\) 1.17128e9 + 2.02872e9i 0.126434 + 0.218991i
\(165\) 3.45517e9 1.26935e9i 0.362903 0.133323i
\(166\) −1.87275e9 1.08123e9i −0.191423 0.110518i
\(167\) 7.57451e8 7.57451e8i 0.0753581 0.0753581i −0.668423 0.743781i \(-0.733030\pi\)
0.743781 + 0.668423i \(0.233030\pi\)
\(168\) 1.61258e9 + 2.85882e9i 0.156181 + 0.276883i
\(169\) 5.21466e9i 0.491741i
\(170\) 1.31342e8 1.18890e7i 0.0120610 0.00109175i
\(171\) 8.60011e9 4.96527e9i 0.769168 0.444080i
\(172\) 1.60957e9 6.00698e9i 0.140227 0.523333i
\(173\) −1.73436e10 + 4.64720e9i −1.47208 + 0.394443i −0.903644 0.428284i \(-0.859118\pi\)
−0.568437 + 0.822727i \(0.692452\pi\)
\(174\) 3.82399e9 0.316261
\(175\) −1.22272e10 + 2.10554e9i −0.985495 + 0.169704i
\(176\) 6.39847e9 0.502654
\(177\) 9.62516e9 2.57905e9i 0.737103 0.197506i
\(178\) 1.03947e8 3.87935e8i 0.00776106 0.0289647i
\(179\) −1.43711e9 + 8.29718e8i −0.104629 + 0.0604076i −0.551401 0.834240i \(-0.685907\pi\)
0.446772 + 0.894648i \(0.352573\pi\)
\(180\) −8.34176e9 + 7.55089e8i −0.592286 + 0.0536132i
\(181\) 2.30426e10i 1.59580i 0.602793 + 0.797898i \(0.294055\pi\)
−0.602793 + 0.797898i \(0.705945\pi\)
\(182\) −2.51759e9 1.48736e9i −0.170084 0.100483i
\(183\) −5.63261e9 + 5.63261e9i −0.371261 + 0.371261i
\(184\) −3.27080e9 1.88840e9i −0.210365 0.121454i
\(185\) −5.24986e9 + 1.92869e9i −0.329515 + 0.121057i
\(186\) 2.43648e9 + 4.22010e9i 0.149264 + 0.258532i
\(187\) −1.22594e8 4.57526e8i −0.00733130 0.0273608i
\(188\) −1.49632e10 1.49632e10i −0.873601 0.873601i
\(189\) −1.22868e10 + 1.20431e10i −0.700423 + 0.686530i
\(190\) −1.17142e9 + 6.76229e9i −0.0652112 + 0.376446i
\(191\) 6.88318e9 1.19220e10i 0.374230 0.648185i −0.615981 0.787761i \(-0.711240\pi\)
0.990211 + 0.139575i \(0.0445737\pi\)
\(192\) 6.16624e9 + 1.65224e9i 0.327465 + 0.0877440i
\(193\) 2.60310e10 + 6.97499e9i 1.35046 + 0.361856i 0.860306 0.509778i \(-0.170272\pi\)
0.490158 + 0.871633i \(0.336939\pi\)
\(194\) −4.18352e9 + 7.24608e9i −0.212048 + 0.367278i
\(195\) −7.01888e9 + 4.94619e9i −0.347626 + 0.244971i
\(196\) −1.67069e10 + 9.20449e9i −0.808616 + 0.445499i
\(197\) 6.92580e9 + 6.92580e9i 0.327621 + 0.327621i 0.851681 0.524060i \(-0.175583\pi\)
−0.524060 + 0.851681i \(0.675583\pi\)
\(198\) −6.47563e8 2.41674e9i −0.0299426 0.111747i
\(199\) 1.26833e9 + 2.19681e9i 0.0573316 + 0.0993012i 0.893267 0.449527i \(-0.148407\pi\)
−0.835935 + 0.548828i \(0.815074\pi\)
\(200\) 6.85698e9 9.91920e9i 0.303039 0.438371i
\(201\) −9.87030e9 5.69862e9i −0.426529 0.246256i
\(202\) −1.55289e9 + 1.55289e9i −0.0656236 + 0.0656236i
\(203\) −4.63711e8 + 4.62916e10i −0.0191653 + 1.91324i
\(204\) 5.95368e8i 0.0240685i
\(205\) −6.24383e8 6.89781e9i −0.0246921 0.272784i
\(206\) 6.61341e9 3.81825e9i 0.255872 0.147728i
\(207\) 2.00745e9 7.49191e9i 0.0759938 0.283613i
\(208\) −1.44172e10 + 3.86307e9i −0.534066 + 0.143102i
\(209\) 2.46496e10 0.893618
\(210\) −3.73468e8 4.64345e9i −0.0132515 0.164761i
\(211\) 1.25279e10 0.435119 0.217559 0.976047i \(-0.430190\pi\)
0.217559 + 0.976047i \(0.430190\pi\)
\(212\) 3.78056e10 1.01300e10i 1.28542 0.344427i
\(213\) 6.39201e9 2.38553e10i 0.212779 0.794103i
\(214\) −6.99719e9 + 4.03983e9i −0.228066 + 0.131674i
\(215\) −1.17763e10 + 1.41205e10i −0.375869 + 0.450689i
\(216\) 1.67213e10i 0.522671i
\(217\) −5.13822e10 + 2.89832e10i −1.57305 + 0.887314i
\(218\) 5.31611e9 5.31611e9i 0.159419 0.159419i
\(219\) −1.30874e10 7.55601e9i −0.384463 0.221970i
\(220\) −1.88690e10 8.72979e9i −0.543059 0.251248i
\(221\) 5.52461e8 + 9.56891e8i 0.0155789 + 0.0269834i
\(222\) −5.43507e8 2.02840e9i −0.0150182 0.0560486i
\(223\) −1.96985e7 1.96985e7i −0.000533411 0.000533411i 0.706840 0.707373i \(-0.250120\pi\)
−0.707373 + 0.706840i \(0.750120\pi\)
\(224\) 7.56532e9 2.71436e10i 0.200776 0.720364i
\(225\) 2.33211e10 + 8.32971e9i 0.606635 + 0.216675i
\(226\) 6.65585e9 1.15283e10i 0.169713 0.293952i
\(227\) 2.66545e10 + 7.14206e9i 0.666277 + 0.178528i 0.576077 0.817395i \(-0.304583\pi\)
0.0901997 + 0.995924i \(0.471249\pi\)
\(228\) 2.99273e10 + 8.01899e9i 0.733433 + 0.196523i
\(229\) 2.91621e9 5.05102e9i 0.0700743 0.121372i −0.828859 0.559457i \(-0.811010\pi\)
0.898934 + 0.438085i \(0.144343\pi\)
\(230\) 3.08773e9 + 4.38164e9i 0.0727553 + 0.103243i
\(231\) −1.62040e10 + 4.16835e9i −0.374429 + 0.0963186i
\(232\) −3.18151e10 3.18151e10i −0.721003 0.721003i
\(233\) −1.57210e10 5.86715e10i −0.349444 1.30414i −0.887334 0.461128i \(-0.847445\pi\)
0.537890 0.843015i \(-0.319222\pi\)
\(234\) 2.91821e9 + 5.05448e9i 0.0636274 + 0.110206i
\(235\) 2.15751e10 + 5.87270e10i 0.461473 + 1.25612i
\(236\) −4.87417e10 2.81411e10i −1.02281 0.590523i
\(237\) −2.07381e9 + 2.07381e9i −0.0426975 + 0.0426975i
\(238\) −5.99419e8 6.00449e6i −0.0121097 0.000121305i
\(239\) 3.32434e10i 0.659044i −0.944148 0.329522i \(-0.893112\pi\)
0.944148 0.329522i \(-0.106888\pi\)
\(240\) −1.82611e10 1.52296e10i −0.355285 0.296303i
\(241\) −4.49640e10 + 2.59600e10i −0.858595 + 0.495710i −0.863541 0.504278i \(-0.831759\pi\)
0.00494685 + 0.999988i \(0.498425\pi\)
\(242\) −2.21908e9 + 8.28172e9i −0.0415914 + 0.155221i
\(243\) 5.33437e10 1.42934e10i 0.981420 0.262971i
\(244\) 4.49916e10 0.812600
\(245\) 5.62568e10 3.95795e9i 0.997534 0.0701816i
\(246\) 2.60048e9 0.0452736
\(247\) −5.55410e10 + 1.48822e10i −0.949462 + 0.254408i
\(248\) 1.48395e10 5.53818e10i 0.249108 0.929682i
\(249\) 2.49966e10 1.44318e10i 0.412082 0.237916i
\(250\) −1.47437e10 + 8.69054e9i −0.238714 + 0.140707i
\(251\) 5.44822e10i 0.866408i 0.901296 + 0.433204i \(0.142617\pi\)
−0.901296 + 0.433204i \(0.857383\pi\)
\(252\) 3.80701e10 + 3.81356e8i 0.594678 + 0.00595700i
\(253\) 1.36135e10 1.36135e10i 0.208895 0.208895i
\(254\) 1.81383e10 + 1.04721e10i 0.273429 + 0.157864i
\(255\) −7.39118e8 + 1.59757e9i −0.0109467 + 0.0236607i
\(256\) −1.09082e10 1.88936e10i −0.158736 0.274939i
\(257\) 7.23834e9 + 2.70138e10i 0.103500 + 0.386267i 0.998171 0.0604593i \(-0.0192565\pi\)
−0.894671 + 0.446726i \(0.852590\pi\)
\(258\) −4.88155e9 4.88155e9i −0.0685914 0.0685914i
\(259\) 2.46208e10 6.33349e9i 0.339980 0.0874569i
\(260\) 4.77866e10 + 8.27801e9i 0.648524 + 0.112343i
\(261\) 4.62002e10 8.00210e10i 0.616256 1.06739i
\(262\) 9.81610e9 + 2.63021e9i 0.128701 + 0.0344854i
\(263\) 3.37220e10 + 9.03579e9i 0.434623 + 0.116457i 0.469496 0.882935i \(-0.344436\pi\)
−0.0348724 + 0.999392i \(0.511102\pi\)
\(264\) 8.13075e9 1.40829e10i 0.103018 0.178432i
\(265\) −1.14020e11 1.97516e10i −1.42029 0.246034i
\(266\) 8.37538e9 3.00500e10i 0.102574 0.368025i
\(267\) 3.79053e9 + 3.79053e9i 0.0456457 + 0.0456457i
\(268\) 1.66611e10 + 6.21799e10i 0.197286 + 0.736281i
\(269\) −9.38488e9 1.62551e10i −0.109281 0.189280i 0.806198 0.591645i \(-0.201521\pi\)
−0.915479 + 0.402366i \(0.868188\pi\)
\(270\) −9.96493e9 + 2.15387e10i −0.114114 + 0.246651i
\(271\) −1.35677e11 7.83330e10i −1.52807 0.882232i −0.999443 0.0333779i \(-0.989374\pi\)
−0.528627 0.848854i \(-0.677293\pi\)
\(272\) −2.16360e9 + 2.16360e9i −0.0239672 + 0.0239672i
\(273\) 3.39946e10 1.91754e10i 0.370406 0.208935i
\(274\) 2.46770e10i 0.264493i
\(275\) 3.97941e10 + 4.68497e10i 0.419587 + 0.493981i
\(276\) 2.09570e10 1.20995e10i 0.217390 0.125510i
\(277\) −2.70257e10 + 1.00861e11i −0.275815 + 1.02935i 0.679479 + 0.733695i \(0.262206\pi\)
−0.955293 + 0.295659i \(0.904461\pi\)
\(278\) −4.80860e8 + 1.28846e8i −0.00482856 + 0.00129381i
\(279\) 1.17747e11 1.16340
\(280\) −3.55256e10 + 4.17400e10i −0.345407 + 0.405827i
\(281\) −8.29793e10 −0.793947 −0.396973 0.917830i \(-0.629940\pi\)
−0.396973 + 0.917830i \(0.629940\pi\)
\(282\) −2.26904e10 + 6.07989e9i −0.213659 + 0.0572499i
\(283\) −4.88082e10 + 1.82155e11i −0.452328 + 1.68811i 0.243498 + 0.969901i \(0.421705\pi\)
−0.695826 + 0.718210i \(0.744962\pi\)
\(284\) −1.20803e11 + 6.97457e10i −1.10191 + 0.636188i
\(285\) −7.03495e10 5.86707e10i −0.631625 0.526768i
\(286\) 1.44871e10i 0.128037i
\(287\) −3.15343e8 + 3.14802e10i −0.00274356 + 0.273886i
\(288\) −3.97693e10 + 3.97693e10i −0.340629 + 0.340629i
\(289\) −1.02504e11 5.91807e10i −0.864371 0.499045i
\(290\) 2.20210e10 + 5.99408e10i 0.182829 + 0.497659i
\(291\) −5.58397e10 9.67172e10i −0.456483 0.790651i
\(292\) 2.20915e10 + 8.24465e10i 0.177829 + 0.663666i
\(293\) −2.40273e10 2.40273e10i −0.190459 0.190459i 0.605435 0.795894i \(-0.292999\pi\)
−0.795894 + 0.605435i \(0.792999\pi\)
\(294\) −4.24179e8 + 2.11704e10i −0.00331121 + 0.165260i
\(295\) 9.58543e10 + 1.36022e11i 0.736907 + 1.04571i
\(296\) −1.23541e10 + 2.13979e10i −0.0935400 + 0.162016i
\(297\) 8.23336e10 + 2.20612e10i 0.614007 + 0.164523i
\(298\) 3.63135e10 + 9.73018e9i 0.266744 + 0.0714739i
\(299\) −2.24551e10 + 3.88934e10i −0.162478 + 0.281420i
\(300\) 3.30732e10 + 6.98264e10i 0.235739 + 0.497708i
\(301\) 5.96859e10 5.85020e10i 0.419105 0.410791i
\(302\) −3.73001e10 3.73001e10i −0.258035 0.258035i
\(303\) −7.58670e9 2.83139e10i −0.0517084 0.192978i
\(304\) −7.96160e10 1.37899e11i −0.534650 0.926040i
\(305\) −1.20727e11 5.58546e10i −0.798831 0.369581i
\(306\) 1.03617e9 + 5.98235e8i 0.00675595 + 0.00390055i
\(307\) 8.86323e9 8.86323e9i 0.0569468 0.0569468i −0.678060 0.735007i \(-0.737179\pi\)
0.735007 + 0.678060i \(0.237179\pi\)
\(308\) 8.13641e10 + 4.80686e10i 0.515175 + 0.304357i
\(309\) 1.01928e11i 0.636037i
\(310\) −5.21191e10 + 6.24937e10i −0.320530 + 0.384334i
\(311\) 1.89438e9 1.09372e9i 0.0114827 0.00662956i −0.494248 0.869321i \(-0.664556\pi\)
0.505730 + 0.862692i \(0.331223\pi\)
\(312\) −9.81786e9 + 3.66408e10i −0.0586572 + 0.218912i
\(313\) 2.26100e11 6.05834e10i 1.33153 0.356783i 0.478246 0.878226i \(-0.341273\pi\)
0.853286 + 0.521443i \(0.174606\pi\)
\(314\) 2.10699e10 0.122315
\(315\) −1.01681e11 4.82854e10i −0.581893 0.276324i
\(316\) 1.65650e10 0.0934542
\(317\) 2.87425e11 7.70152e10i 1.59866 0.428361i 0.654025 0.756473i \(-0.273079\pi\)
0.944639 + 0.328112i \(0.106412\pi\)
\(318\) 1.12452e10 4.19678e10i 0.0616662 0.230141i
\(319\) 1.98628e11 1.14678e11i 1.07395 0.620044i
\(320\) 9.61042e9 + 1.06170e11i 0.0512351 + 0.566014i
\(321\) 1.07843e11i 0.566919i
\(322\) −1.19705e10 2.12216e10i −0.0620528 0.110009i
\(323\) −8.33511e9 + 8.33511e9i −0.0426089 + 0.0426089i
\(324\) −9.37649e9 5.41352e9i −0.0472702 0.0272915i
\(325\) −1.17950e11 8.15372e10i −0.586441 0.405397i
\(326\) 1.75281e10 + 3.03596e10i 0.0859520 + 0.148873i
\(327\) 2.59720e10 + 9.69290e10i 0.125615 + 0.468801i
\(328\) −2.16356e10 2.16356e10i −0.103213 0.103213i
\(329\) −7.08489e10 2.75418e11i −0.333389 1.29602i
\(330\) −1.88658e10 + 1.32947e10i −0.0875714 + 0.0617113i
\(331\) −1.79417e11 + 3.10760e11i −0.821558 + 1.42298i 0.0829639 + 0.996553i \(0.473561\pi\)
−0.904522 + 0.426427i \(0.859772\pi\)
\(332\) −1.57471e11 4.21942e10i −0.711343 0.190604i
\(333\) −4.90128e10 1.31329e10i −0.218429 0.0585279i
\(334\) −3.35820e9 + 5.81657e9i −0.0147655 + 0.0255745i
\(335\) 3.24860e10 1.87533e11i 0.140927 0.813533i
\(336\) 7.56568e10 + 7.71878e10i 0.323833 + 0.330386i
\(337\) −2.19428e11 2.19428e11i −0.926740 0.926740i 0.0707536 0.997494i \(-0.477460\pi\)
−0.997494 + 0.0707536i \(0.977460\pi\)
\(338\) 8.46232e9 + 3.15818e10i 0.0352667 + 0.131617i
\(339\) 8.88390e10 + 1.53874e11i 0.365347 + 0.632799i
\(340\) 9.33235e9 3.42851e9i 0.0378736 0.0139139i
\(341\) 2.53114e11 + 1.46136e11i 1.01373 + 0.585277i
\(342\) −4.40276e10 + 4.40276e10i −0.174023 + 0.174023i
\(343\) −2.56228e11 7.70213e9i −0.999549 0.0300460i
\(344\) 8.12276e10i 0.312745i
\(345\) −7.12555e10 + 6.44998e9i −0.270790 + 0.0245116i
\(346\) 9.74974e10 5.62902e10i 0.365722 0.211149i
\(347\) 1.17266e11 4.37644e11i 0.434201 1.62046i −0.308771 0.951136i \(-0.599918\pi\)
0.742972 0.669323i \(-0.233416\pi\)
\(348\) 2.78463e11 7.46140e10i 1.01780 0.272718i
\(349\) 9.68004e10 0.349271 0.174635 0.984633i \(-0.444125\pi\)
0.174635 + 0.984633i \(0.444125\pi\)
\(350\) 7.06351e10 3.25940e10i 0.251602 0.116100i
\(351\) −1.98835e11 −0.699216
\(352\) −1.34848e11 + 3.61323e10i −0.468168 + 0.125445i
\(353\) 9.02545e10 3.36834e11i 0.309373 1.15460i −0.619742 0.784806i \(-0.712763\pi\)
0.929115 0.369791i \(-0.120571\pi\)
\(354\) −5.41080e10 + 3.12393e10i −0.183125 + 0.105727i
\(355\) 4.10740e11 3.71798e10i 1.37259 0.124245i
\(356\) 3.02776e10i 0.0999072i
\(357\) 4.06979e9 6.88878e9i 0.0132606 0.0224458i
\(358\) 7.35720e9 7.35720e9i 0.0236722 0.0236722i
\(359\) 1.92984e11 + 1.11419e11i 0.613192 + 0.354027i 0.774214 0.632924i \(-0.218146\pi\)
−0.161022 + 0.986951i \(0.551479\pi\)
\(360\) 1.02690e11 3.77263e10i 0.322232 0.118381i
\(361\) −1.45371e11 2.51790e11i −0.450500 0.780289i
\(362\) −3.73933e10 1.39554e11i −0.114447 0.427123i
\(363\) −8.09212e10 8.09212e10i −0.244615 0.244615i
\(364\) −2.12353e11 5.91857e10i −0.634018 0.176710i
\(365\) 4.30744e10 2.48656e11i 0.127028 0.733300i
\(366\) 2.49725e10 4.32536e10i 0.0727439 0.125996i
\(367\) 8.89106e10 + 2.38235e10i 0.255833 + 0.0685502i 0.384456 0.923143i \(-0.374389\pi\)
−0.128623 + 0.991694i \(0.541056\pi\)
\(368\) −1.20129e11 3.21886e10i −0.341456 0.0914928i
\(369\) 3.14181e10 5.44177e10i 0.0882187 0.152799i
\(370\) 2.86651e10 2.02003e10i 0.0795145 0.0560337i
\(371\) 5.06680e11 + 1.41219e11i 1.38852 + 0.387000i
\(372\) 2.59767e11 + 2.59767e11i 0.703301 + 0.703301i
\(373\) 5.44454e10 + 2.03193e11i 0.145637 + 0.543525i 0.999726 + 0.0233982i \(0.00744855\pi\)
−0.854089 + 0.520127i \(0.825885\pi\)
\(374\) 1.48494e9 + 2.57199e9i 0.00392452 + 0.00679747i
\(375\) −2.06038e9 2.28426e11i −0.00538030 0.596492i
\(376\) 2.39365e11 + 1.38197e11i 0.617611 + 0.356578i
\(377\) −3.78316e11 + 3.78316e11i −0.964538 + 0.964538i
\(378\) 5.48697e10 9.28760e10i 0.138235 0.233986i
\(379\) 3.22937e11i 0.803973i 0.915646 + 0.401986i \(0.131680\pi\)
−0.915646 + 0.401986i \(0.868320\pi\)
\(380\) 4.66433e10 + 5.15287e11i 0.114753 + 1.26772i
\(381\) −2.42101e11 + 1.39777e11i −0.588618 + 0.339839i
\(382\) −2.23399e10 + 8.33738e10i −0.0536781 + 0.200329i
\(383\) −3.36410e11 + 9.01407e10i −0.798866 + 0.214056i −0.635086 0.772441i \(-0.719035\pi\)
−0.163780 + 0.986497i \(0.552369\pi\)
\(384\) −2.30094e11 −0.540027
\(385\) −1.58652e11 2.29993e11i −0.368020 0.533508i
\(386\) −1.68972e11 −0.387411
\(387\) −1.61129e11 + 4.31744e10i −0.365152 + 0.0978423i
\(388\) −1.63258e11 + 6.09288e11i −0.365706 + 1.36484i
\(389\) −3.54460e11 + 2.04648e11i −0.784864 + 0.453142i −0.838151 0.545438i \(-0.816363\pi\)
0.0532871 + 0.998579i \(0.483030\pi\)
\(390\) 3.44821e10 4.13460e10i 0.0754750 0.0904988i
\(391\) 9.20665e9i 0.0199208i
\(392\) 1.79664e11 1.72606e11i 0.384303 0.369205i
\(393\) −9.59137e10 + 9.59137e10i −0.202822 + 0.202822i
\(394\) −5.31842e10 3.07059e10i −0.111186 0.0641932i
\(395\) −4.44492e10 2.05645e10i −0.0918708 0.0425042i
\(396\) −9.43111e10 1.63352e11i −0.192723 0.333807i
\(397\) 1.51381e10 + 5.64962e10i 0.0305854 + 0.114146i 0.979531 0.201294i \(-0.0645145\pi\)
−0.948946 + 0.315440i \(0.897848\pi\)
\(398\) −1.12464e10 1.12464e10i −0.0224668 0.0224668i
\(399\) 2.91462e11 + 2.97360e11i 0.575710 + 0.587361i
\(400\) 1.33563e11 3.73943e11i 0.260866 0.730358i
\(401\) −2.55372e11 + 4.42317e11i −0.493200 + 0.854247i −0.999969 0.00783443i \(-0.997506\pi\)
0.506769 + 0.862082i \(0.330840\pi\)
\(402\) 6.90257e10 + 1.84954e10i 0.131824 + 0.0353220i
\(403\) −6.58551e11 1.76458e11i −1.24370 0.333249i
\(404\) −8.27814e10 + 1.43382e11i −0.154603 + 0.267780i
\(405\) 1.84396e10 + 2.61667e10i 0.0340568 + 0.0483282i
\(406\) −7.23132e10 2.81110e11i −0.132084 0.513464i
\(407\) −8.90610e10 8.90610e10i −0.160884 0.160884i
\(408\) 2.01267e9 + 7.51140e9i 0.00359586 + 0.0134199i
\(409\) 2.33222e11 + 4.03952e11i 0.412111 + 0.713797i 0.995120 0.0986685i \(-0.0314583\pi\)
−0.583010 + 0.812465i \(0.698125\pi\)
\(410\) 1.49752e10 + 4.07623e10i 0.0261725 + 0.0712412i
\(411\) 2.85249e11 + 1.64688e11i 0.493100 + 0.284692i
\(412\) 4.07086e11 4.07086e11i 0.696064 0.696064i
\(413\) −3.71608e11 6.58796e11i −0.628506 1.11423i
\(414\) 4.86313e10i 0.0813606i
\(415\) 3.70164e11 + 3.08712e11i 0.612601 + 0.510902i
\(416\) 2.82027e11 1.62828e11i 0.461711 0.266569i
\(417\) 1.71978e9 6.41829e9i 0.00278522 0.0103946i
\(418\) −1.49287e11 + 4.00012e10i −0.239182 + 0.0640885i
\(419\) −2.82987e9 −0.00448542 −0.00224271 0.999997i \(-0.500714\pi\)
−0.00224271 + 0.999997i \(0.500714\pi\)
\(420\) −1.17799e11 3.30849e11i −0.184723 0.518809i
\(421\) 6.93519e11 1.07594 0.537971 0.842963i \(-0.319191\pi\)
0.537971 + 0.842963i \(0.319191\pi\)
\(422\) −7.58734e10 + 2.03302e10i −0.116462 + 0.0312058i
\(423\) −1.46910e11 + 5.48276e11i −0.223111 + 0.832660i
\(424\) −4.42725e11 + 2.55607e11i −0.665254 + 0.384085i
\(425\) −2.92981e10 2.38582e9i −0.0435601 0.00354721i
\(426\) 1.54849e11i 0.227806i
\(427\) 5.20581e11 + 3.07551e11i 0.757814 + 0.447705i
\(428\) −4.30710e11 + 4.30710e11i −0.620423 + 0.620423i
\(429\) −1.67461e11 9.66837e10i −0.238702 0.137815i
\(430\) 4.84069e10 1.04629e11i 0.0682810 0.147586i
\(431\) 5.65826e11 + 9.80039e11i 0.789833 + 1.36803i 0.926069 + 0.377354i \(0.123166\pi\)
−0.136236 + 0.990676i \(0.543501\pi\)
\(432\) −1.42511e11 5.31860e11i −0.196867 0.734717i
\(433\) −5.88944e11 5.88944e11i −0.805154 0.805154i 0.178742 0.983896i \(-0.442797\pi\)
−0.983896 + 0.178742i \(0.942797\pi\)
\(434\) 2.64155e11 2.58915e11i 0.357400 0.350311i
\(435\) −8.39836e11 1.45484e11i −1.12459 0.194811i
\(436\) 2.83391e11 4.90848e11i 0.375575 0.650515i
\(437\) −4.62790e11 1.24004e11i −0.607040 0.162656i
\(438\) 9.15236e10 + 2.45237e10i 0.118823 + 0.0318385i
\(439\) 5.16062e11 8.93846e11i 0.663150 1.14861i −0.316634 0.948548i \(-0.602553\pi\)
0.979783 0.200061i \(-0.0641141\pi\)
\(440\) 2.67570e11 + 4.63508e10i 0.340331 + 0.0589550i
\(441\) 4.37889e11 + 2.64650e11i 0.551303 + 0.333195i
\(442\) −4.89873e9 4.89873e9i −0.00610497 0.00610497i
\(443\) 2.62266e11 + 9.78790e11i 0.323538 + 1.20746i 0.915774 + 0.401695i \(0.131579\pi\)
−0.592236 + 0.805765i \(0.701755\pi\)
\(444\) −7.91564e10 1.37103e11i −0.0966635 0.167426i
\(445\) −3.75881e10 + 8.12447e10i −0.0454391 + 0.0982143i
\(446\) 1.51268e8 + 8.73344e7i 0.000181025 + 0.000104515i
\(447\) −3.54822e11 + 3.54822e11i −0.420365 + 0.420365i
\(448\) 4.85372e9 4.84539e11i 0.00569277 0.568300i
\(449\) 5.75341e10i 0.0668062i 0.999442 + 0.0334031i \(0.0106345\pi\)
−0.999442 + 0.0334031i \(0.989365\pi\)
\(450\) −1.54758e11 1.26023e10i −0.177908 0.0144876i
\(451\) 1.35076e11 7.79859e10i 0.153738 0.0887609i
\(452\) 2.59738e11 9.69357e11i 0.292694 1.09235i
\(453\) 6.80095e11 1.82231e11i 0.758801 0.203320i
\(454\) −1.73019e11 −0.191136
\(455\) 4.96335e11 + 4.22439e11i 0.542905 + 0.462075i
\(456\) −4.04683e11 −0.438302
\(457\) −9.21358e10 + 2.46877e10i −0.0988111 + 0.0264764i −0.307886 0.951423i \(-0.599621\pi\)
0.209075 + 0.977900i \(0.432955\pi\)
\(458\) −9.46480e9 + 3.53231e10i −0.0100512 + 0.0375115i
\(459\) −3.53004e10 + 2.03807e10i −0.0371213 + 0.0214320i
\(460\) 3.10344e11 + 2.58823e11i 0.323171 + 0.269521i
\(461\) 5.60003e10i 0.0577479i 0.999583 + 0.0288740i \(0.00919214\pi\)
−0.999583 + 0.0288740i \(0.990808\pi\)
\(462\) 9.13728e10 5.15407e10i 0.0933100 0.0526334i
\(463\) 1.14526e12 1.14526e12i 1.15821 1.15821i 0.173352 0.984860i \(-0.444540\pi\)
0.984860 0.173352i \(-0.0554598\pi\)
\(464\) −1.28310e12 7.40799e11i −1.28508 0.741941i
\(465\) −3.74553e11 1.01953e12i −0.371514 1.01125i
\(466\) 1.90423e11 + 3.29823e11i 0.187061 + 0.323999i
\(467\) 2.25493e11 + 8.41550e11i 0.219385 + 0.818755i 0.984577 + 0.174953i \(0.0559774\pi\)
−0.765192 + 0.643802i \(0.777356\pi\)
\(468\) 3.11127e11 + 3.11127e11i 0.299800 + 0.299800i
\(469\) −2.32267e11 + 8.33352e11i −0.221672 + 0.795336i
\(470\) −2.25968e11 3.20659e11i −0.213603 0.303112i
\(471\) −1.40616e11 + 2.43553e11i −0.131656 + 0.228034i
\(472\) 7.10077e11 + 1.90265e11i 0.658517 + 0.176449i
\(473\) −3.99954e11 1.07167e11i −0.367397 0.0984436i
\(474\) 9.19436e9 1.59251e10i 0.00836602 0.0144904i
\(475\) 5.14542e11 1.44059e12i 0.463767 1.29843i
\(476\) −4.37668e10 + 1.12586e10i −0.0390763 + 0.0100521i
\(477\) −7.42359e11 7.42359e11i −0.656571 0.656571i
\(478\) 5.39471e10 + 2.01333e11i 0.0472653 + 0.176397i
\(479\) −3.88617e11 6.73104e11i −0.337296 0.584214i 0.646627 0.762806i \(-0.276179\pi\)
−0.983923 + 0.178592i \(0.942846\pi\)
\(480\) 4.70854e11 + 2.17842e11i 0.404857 + 0.187308i
\(481\) 2.54444e11 + 1.46904e11i 0.216741 + 0.125135i
\(482\) 2.30190e11 2.30190e11i 0.194256 0.194256i
\(483\) 3.25196e11 + 3.25754e9i 0.271883 + 0.00272351i
\(484\) 6.46373e11i 0.535401i
\(485\) 1.19447e12 1.43224e12i 0.980255 1.17538i
\(486\) −2.99873e11 + 1.73132e11i −0.243822 + 0.140771i
\(487\) 1.29318e11 4.82621e11i 0.104178 0.388799i −0.894072 0.447923i \(-0.852164\pi\)
0.998251 + 0.0591235i \(0.0188306\pi\)
\(488\) −5.67631e11 + 1.52096e11i −0.453082 + 0.121403i
\(489\) −4.67914e11 −0.370063
\(490\) −3.34288e11 + 1.15264e11i −0.261962 + 0.0903256i
\(491\) −3.22411e11 −0.250347 −0.125174 0.992135i \(-0.539949\pi\)
−0.125174 + 0.992135i \(0.539949\pi\)
\(492\) 1.89367e11 5.07406e10i 0.145700 0.0390403i
\(493\) −2.83872e10 + 1.05943e11i −0.0216427 + 0.0807717i
\(494\) 3.12225e11 1.80263e11i 0.235883 0.136187i
\(495\) 5.02750e10 + 5.55408e11i 0.0376382 + 0.415804i
\(496\) 1.88802e12i 1.40068i
\(497\) −1.87453e12 1.87776e10i −1.37813 0.0138050i
\(498\) −1.27968e11 + 1.27968e11i −0.0932331 + 0.0932331i
\(499\) 1.59337e12 + 9.19933e11i 1.15044 + 0.664208i 0.948995 0.315292i \(-0.102102\pi\)
0.201447 + 0.979499i \(0.435436\pi\)
\(500\) −9.04068e11 + 9.20526e11i −0.646898 + 0.658675i
\(501\) −4.48236e10 7.76368e10i −0.0317861 0.0550551i
\(502\) −8.84133e10 3.29963e11i −0.0621371 0.231899i
\(503\) 1.81776e12 + 1.81776e12i 1.26613 + 1.26613i 0.948069 + 0.318065i \(0.103033\pi\)
0.318065 + 0.948069i \(0.396967\pi\)
\(504\) −4.81597e11 + 1.23887e11i −0.332465 + 0.0855239i
\(505\) 4.00130e11 2.81971e11i 0.273773 0.192927i
\(506\) −6.03563e10 + 1.04540e11i −0.0409303 + 0.0708934i
\(507\) −4.21539e11 1.12951e11i −0.283336 0.0759197i
\(508\) 1.52516e12 + 4.08666e11i 1.01608 + 0.272258i
\(509\) −1.99720e10 + 3.45925e10i −0.0131884 + 0.0228430i −0.872544 0.488535i \(-0.837531\pi\)
0.859356 + 0.511378i \(0.170865\pi\)
\(510\) 1.88383e9 1.08749e10i 0.00123304 0.00711799i
\(511\) −3.07971e11 + 1.10497e12i −0.199810 + 0.716897i
\(512\) 1.09211e12 + 1.09211e12i 0.702350 + 0.702350i
\(513\) −5.49014e11 2.04895e12i −0.349990 1.30618i
\(514\) −8.76758e10 1.51859e11i −0.0554046 0.0959635i
\(515\) −1.59772e12 + 5.86969e11i −1.00085 + 0.367691i
\(516\) −4.50724e11 2.60226e11i −0.279890 0.161594i
\(517\) −9.96271e11 + 9.96271e11i −0.613296 + 0.613296i
\(518\) −1.38834e11 + 7.83123e10i −0.0847251 + 0.0477910i
\(519\) 1.50267e12i 0.909096i
\(520\) −6.30879e11 + 5.71066e10i −0.378383 + 0.0342508i
\(521\) 3.98317e11 2.29968e11i 0.236842 0.136741i −0.376882 0.926261i \(-0.623004\pi\)
0.613725 + 0.789520i \(0.289671\pi\)
\(522\) −1.49947e11 + 5.59609e11i −0.0883933 + 0.329888i
\(523\) −2.99113e12 + 8.01470e11i −1.74814 + 0.468414i −0.984228 0.176903i \(-0.943392\pi\)
−0.763915 + 0.645317i \(0.776725\pi\)
\(524\) 7.66129e11 0.443926
\(525\) −9.46378e10 + 1.03402e12i −0.0543686 + 0.594033i
\(526\) −2.18896e11 −0.124681
\(527\) −1.35004e11 + 3.61741e10i −0.0762426 + 0.0204292i
\(528\) 1.38593e11 5.17234e11i 0.0776046 0.289624i
\(529\) 1.23577e12 7.13471e11i 0.686099 0.396119i
\(530\) 7.22600e11 6.54091e10i 0.397793 0.0360078i
\(531\) 1.50969e12i 0.824067i
\(532\) 2.35571e10 2.35166e12i 0.0127503 1.27284i
\(533\) −2.57271e11 + 2.57271e11i −0.138076 + 0.138076i
\(534\) −2.91080e10 1.68055e10i −0.0154909 0.00894369i
\(535\) 1.69044e12 6.21031e11i 0.892087 0.327734i
\(536\) −4.20405e11 7.28162e11i −0.220002 0.381054i
\(537\) 3.59438e10 + 1.34144e11i 0.0186526 + 0.0696125i
\(538\) 8.32167e10 + 8.32167e10i 0.0428243 + 0.0428243i
\(539\) 6.12849e11 + 1.11237e12i 0.312755 + 0.567675i
\(540\) −3.05382e11 + 1.76288e12i −0.154551 + 0.892179i
\(541\) 3.47779e11 6.02371e11i 0.174548 0.302327i −0.765457 0.643488i \(-0.777487\pi\)
0.940005 + 0.341161i \(0.110820\pi\)
\(542\) 9.48823e11 + 2.54236e11i 0.472268 + 0.126544i
\(543\) 1.86270e12 + 4.99108e11i 0.919481 + 0.246374i
\(544\) 3.33800e10 5.78158e10i 0.0163415 0.0283042i
\(545\) −1.36979e12 + 9.65289e11i −0.665074 + 0.468676i
\(546\) −1.74765e11 + 1.71299e11i −0.0841567 + 0.0824874i
\(547\) 2.15129e12 + 2.15129e12i 1.02744 + 1.02744i 0.999613 + 0.0278237i \(0.00885771\pi\)
0.0278237 + 0.999613i \(0.491142\pi\)
\(548\) −4.81499e11 1.79698e12i −0.228078 0.851197i
\(549\) −6.03418e11 1.04515e12i −0.283493 0.491025i
\(550\) −3.17034e11 2.19161e11i −0.147732 0.102125i
\(551\) −4.94305e12 2.85387e12i −2.28462 1.31902i
\(552\) −2.23499e11 + 2.23499e11i −0.102459 + 0.102459i
\(553\) 1.91667e11 + 1.13234e11i 0.0871535 + 0.0514889i
\(554\) 6.54707e11i 0.295293i
\(555\) 4.21964e10 + 4.66160e11i 0.0188780 + 0.208553i
\(556\) −3.25022e10 + 1.87651e10i −0.0144237 + 0.00832751i
\(557\) −1.27804e11 + 4.76973e11i −0.0562597 + 0.209964i −0.988334 0.152304i \(-0.951331\pi\)
0.932074 + 0.362268i \(0.117997\pi\)
\(558\) −7.13115e11 + 1.91079e11i −0.311391 + 0.0834369i
\(559\) 9.65887e11 0.418382
\(560\) −7.74234e11 + 1.63041e12i −0.332680 + 0.700569i
\(561\) −3.96405e10 −0.0168969
\(562\) 5.02552e11 1.34658e11i 0.212504 0.0569403i
\(563\) −5.34457e11 + 1.99462e12i −0.224195 + 0.836706i 0.758531 + 0.651637i \(0.225917\pi\)
−0.982726 + 0.185069i \(0.940749\pi\)
\(564\) −1.53369e12 + 8.85475e11i −0.638235 + 0.368485i
\(565\) −1.90037e12 + 2.27865e12i −0.784549 + 0.940718i
\(566\) 1.18240e12i 0.484272i
\(567\) −7.14865e10 1.26733e11i −0.0290469 0.0514952i
\(568\) 1.28832e12 1.28832e12i 0.519346 0.519346i
\(569\) 1.05636e10 + 6.09889e9i 0.00422480 + 0.00243919i 0.502111 0.864803i \(-0.332557\pi\)
−0.497886 + 0.867242i \(0.665890\pi\)
\(570\) 5.21272e11 + 2.41168e11i 0.206836 + 0.0956934i
\(571\) 1.66349e11 + 2.88125e11i 0.0654873 + 0.113427i 0.896910 0.442213i \(-0.145806\pi\)
−0.831423 + 0.555640i \(0.812473\pi\)
\(572\) 2.82674e11 + 1.05495e12i 0.110409 + 0.412051i
\(573\) −8.14651e11 8.14651e11i −0.315701 0.315701i
\(574\) −4.91761e10 1.91167e11i −0.0189082 0.0735037i
\(575\) −5.11438e11 1.07978e12i −0.195114 0.411937i
\(576\) −4.83582e11 + 8.37589e11i −0.183050 + 0.317051i
\(577\) 1.37266e12 + 3.67804e11i 0.515553 + 0.138142i 0.507209 0.861823i \(-0.330677\pi\)
0.00834410 + 0.999965i \(0.497344\pi\)
\(578\) 7.16838e11 + 1.92076e11i 0.267144 + 0.0715810i
\(579\) 1.12768e12 1.95319e12i 0.416995 0.722257i
\(580\) 2.77314e12 + 3.93522e12i 1.01753 + 1.44392i
\(581\) −1.53361e12 1.56464e12i −0.558370 0.569670i
\(582\) 4.95136e11 + 4.95136e11i 0.178884 + 0.178884i
\(583\) −6.74469e11 2.51715e12i −0.241799 0.902405i
\(584\) −5.57430e11 9.65497e11i −0.198304 0.343473i
\(585\) −4.48607e11 1.22110e12i −0.158367 0.431073i
\(586\) 1.84509e11 + 1.06526e11i 0.0646367 + 0.0373180i
\(587\) −2.56314e12 + 2.56314e12i −0.891047 + 0.891047i −0.994622 0.103575i \(-0.966972\pi\)
0.103575 + 0.994622i \(0.466972\pi\)
\(588\) 3.82190e11 + 1.54991e12i 0.131850 + 0.534697i
\(589\) 7.27345e12i 2.49013i
\(590\) −8.01263e11 6.68244e11i −0.272233 0.227039i
\(591\) 7.09877e11 4.09848e11i 0.239353 0.138191i
\(592\) −2.10581e11 + 7.85899e11i −0.0704647 + 0.262978i
\(593\) 2.52518e12 6.76620e11i 0.838584 0.224698i 0.186129 0.982525i \(-0.440406\pi\)
0.652455 + 0.757827i \(0.273739\pi\)
\(594\) −5.34442e11 −0.176141
\(595\) 1.31418e11 + 2.41236e10i 0.0429860 + 0.00789070i
\(596\) 2.83421e12 0.920075
\(597\) 2.05057e11 5.49448e10i 0.0660678 0.0177028i
\(598\) 7.28800e10 2.71992e11i 0.0233052 0.0869763i
\(599\) 3.70542e12 2.13932e12i 1.17603 0.678979i 0.220934 0.975289i \(-0.429090\pi\)
0.955092 + 0.296310i \(0.0957562\pi\)
\(600\) −6.53317e11 7.69152e11i −0.205799 0.242288i
\(601\) 1.96323e12i 0.613812i −0.951740 0.306906i \(-0.900706\pi\)
0.951740 0.306906i \(-0.0992937\pi\)
\(602\) −2.66542e11 + 4.51166e11i −0.0827144 + 0.140008i
\(603\) 1.22098e12 1.22098e12i 0.376080 0.376080i
\(604\) −3.44400e12 1.98839e12i −1.05292 0.607905i
\(605\) 8.02439e11 1.73443e12i 0.243508 0.526330i
\(606\) 9.18954e10 + 1.59167e11i 0.0276800 + 0.0479432i
\(607\) −4.48162e10 1.67256e11i −0.0133994 0.0500073i 0.958902 0.283736i \(-0.0915739\pi\)
−0.972302 + 0.233729i \(0.924907\pi\)
\(608\) 2.45663e12 + 2.45663e12i 0.729076 + 0.729076i
\(609\) 3.73204e12 + 1.04017e12i 1.09943 + 0.306427i
\(610\) 8.21805e11 + 1.42360e11i 0.240317 + 0.0416298i
\(611\) 1.64332e12 2.84632e12i 0.477020 0.826224i
\(612\) 8.71270e10 + 2.33456e10i 0.0251056 + 0.00672704i
\(613\) 2.89776e12 + 7.76452e11i 0.828876 + 0.222097i 0.648223 0.761450i \(-0.275512\pi\)
0.180653 + 0.983547i \(0.442179\pi\)
\(614\) −3.92956e10 + 6.80620e10i −0.0111580 + 0.0193262i
\(615\) −5.71124e11 9.89350e10i −0.160988 0.0278877i
\(616\) −1.18902e12 3.31397e11i −0.332718 0.0927333i
\(617\) −1.83960e12 1.83960e12i −0.511024 0.511024i 0.403816 0.914840i \(-0.367683\pi\)
−0.914840 + 0.403816i \(0.867683\pi\)
\(618\) −1.65409e11 6.17314e11i −0.0456153 0.170239i
\(619\) 1.51261e12 + 2.61992e12i 0.414114 + 0.717266i 0.995335 0.0964797i \(-0.0307583\pi\)
−0.581221 + 0.813745i \(0.697425\pi\)
\(620\) −2.57593e12 + 5.56774e12i −0.700118 + 1.51327i
\(621\) −1.43481e12 8.28386e11i −0.387152 0.223522i
\(622\) −9.69814e9 + 9.69814e9i −0.00259795 + 0.00259795i
\(623\) 2.06970e11 3.50331e11i 0.0550442 0.0931714i
\(624\) 1.24912e12i 0.329817i
\(625\) 3.56869e12 1.34772e12i 0.935512 0.353296i
\(626\) −1.27103e12 + 7.33828e11i −0.330804 + 0.190990i
\(627\) 5.33917e11 1.99261e12i 0.137965 0.514894i
\(628\) 1.53431e12 4.11117e11i 0.393636 0.105474i
\(629\) 6.02308e10 0.0153423
\(630\) 6.94173e11 + 1.27425e11i 0.175564 + 0.0322273i
\(631\) −4.44649e12 −1.11657 −0.558284 0.829650i \(-0.688540\pi\)
−0.558284 + 0.829650i \(0.688540\pi\)
\(632\) −2.08990e11 + 5.59988e10i −0.0521074 + 0.0139621i
\(633\) 2.71358e11 1.01272e12i 0.0671778 0.250711i
\(634\) −1.61576e12 + 9.32862e11i −0.397170 + 0.229306i
\(635\) −3.58517e12 2.98999e12i −0.875039 0.729773i
\(636\) 3.27551e12i 0.793821i
\(637\) −2.05248e12 2.13641e12i −0.493913 0.514110i
\(638\) −1.01686e12 + 1.01686e12i −0.242979 + 0.242979i
\(639\) 3.24038e12 + 1.87083e12i 0.768850 + 0.443896i
\(640\) −1.32503e12 3.60671e12i −0.312188 0.849771i
\(641\) 3.63629e12 + 6.29823e12i 0.850740 + 1.47353i 0.880541 + 0.473970i \(0.157179\pi\)
−0.0298010 + 0.999556i \(0.509487\pi\)
\(642\) 1.75007e11 + 6.53137e11i 0.0406583 + 0.151739i
\(643\) −3.24579e12 3.24579e12i −0.748809 0.748809i 0.225446 0.974256i \(-0.427616\pi\)
−0.974256 + 0.225446i \(0.927616\pi\)
\(644\) −1.28577e12 1.31179e12i −0.294562 0.300523i
\(645\) 8.86383e11 + 1.25782e12i 0.201652 + 0.286154i
\(646\) 3.69542e10 6.40065e10i 0.00834866 0.0144603i
\(647\) 3.97352e12 + 1.06470e12i 0.891468 + 0.238868i 0.675349 0.737499i \(-0.263993\pi\)
0.216120 + 0.976367i \(0.430660\pi\)
\(648\) 1.36598e11 + 3.66014e10i 0.0304339 + 0.00815474i
\(649\) −1.87368e12 + 3.24530e12i −0.414566 + 0.718049i
\(650\) 8.46666e11 + 3.02408e11i 0.186038 + 0.0664483i
\(651\) 1.22997e12 + 4.78138e12i 0.268398 + 1.04337i
\(652\) 1.86877e12 + 1.86877e12i 0.404988 + 0.404988i
\(653\) −8.31481e11 3.10313e12i −0.178955 0.667868i −0.995844 0.0910737i \(-0.970970\pi\)
0.816890 0.576794i \(-0.195697\pi\)
\(654\) −3.14591e11 5.44888e11i −0.0672430 0.116468i
\(655\) −2.05577e12 9.51108e11i −0.436405 0.201904i
\(656\) −8.72563e11 5.03775e11i −0.183963 0.106211i
\(657\) 1.61894e12 1.61894e12i 0.338990 0.338990i
\(658\) 8.76032e11 + 1.55305e12i 0.182181 + 0.322976i
\(659\) 3.51029e12i 0.725035i −0.931977 0.362517i \(-0.881917\pi\)
0.931977 0.362517i \(-0.118083\pi\)
\(660\) −1.11440e12 + 1.33623e12i −0.228609 + 0.274115i
\(661\) −6.14805e12 + 3.54958e12i −1.25265 + 0.723220i −0.971636 0.236483i \(-0.924005\pi\)
−0.281017 + 0.959703i \(0.590672\pi\)
\(662\) 5.82314e11 2.17323e12i 0.117841 0.439789i
\(663\) 8.93189e10 2.39329e10i 0.0179528 0.00481044i
\(664\) 2.12935e12 0.425100
\(665\) −2.98268e12 + 6.28104e12i −0.591438 + 1.24547i
\(666\) 3.18151e11 0.0626612
\(667\) −4.30610e12 + 1.15382e12i −0.842398 + 0.225720i
\(668\) −1.31051e11 + 4.89088e11i −0.0254651 + 0.0950370i
\(669\) −2.01905e9 + 1.16570e9i −0.000389699 + 0.000224993i
\(670\) 1.07580e11 + 1.18848e12i 0.0206251 + 0.227854i
\(671\) 2.99561e12i 0.570471i
\(672\) −2.03035e12 1.19950e12i −0.384069 0.226902i
\(673\) −5.31516e12 + 5.31516e12i −0.998730 + 0.998730i −0.999999 0.00126883i \(-0.999596\pi\)
0.00126883 + 0.999999i \(0.499596\pi\)
\(674\) 1.68502e12 + 9.72847e11i 0.314511 + 0.181583i
\(675\) 3.00797e12 4.35128e12i 0.557707 0.806770i
\(676\) 1.23245e12 + 2.13467e12i 0.226992 + 0.393161i
\(677\) 5.45308e11 + 2.03512e12i 0.0997683 + 0.372340i 0.997699 0.0677961i \(-0.0215967\pi\)
−0.897931 + 0.440136i \(0.854930\pi\)
\(678\) −7.87745e11 7.87745e11i −0.143170 0.143170i
\(679\) −6.05395e12 + 5.93386e12i −1.09301 + 1.07133i
\(680\) −1.06150e11 + 7.48039e10i −0.0190384 + 0.0134163i
\(681\) 1.15469e12 1.99998e12i 0.205732 0.356339i
\(682\) −1.77010e12 4.74296e11i −0.313305 0.0839498i
\(683\) 2.51579e12 + 6.74105e11i 0.442366 + 0.118532i 0.473125 0.880995i \(-0.343126\pi\)
−0.0307592 + 0.999527i \(0.509793\pi\)
\(684\) −2.34702e12 + 4.06516e12i −0.409982 + 0.710109i
\(685\) −9.38835e11 + 5.41963e12i −0.162923 + 0.940508i
\(686\) 1.56431e12 3.69159e11i 0.269689 0.0636437i
\(687\) −3.45144e11 3.45144e11i −0.0591147 0.0591147i
\(688\) 6.92282e11 + 2.58363e12i 0.117797 + 0.439625i
\(689\) 3.03946e12 + 5.26449e12i 0.513818 + 0.889959i
\(690\) 4.21081e11 1.54696e11i 0.0707204 0.0259812i
\(691\) −2.94124e12 1.69812e12i −0.490771 0.283347i 0.234123 0.972207i \(-0.424778\pi\)
−0.724894 + 0.688860i \(0.758111\pi\)
\(692\) 6.00142e12 6.00142e12i 0.994894 0.994894i
\(693\) 2.53913e10 2.53477e12i 0.00418201 0.417483i
\(694\) 2.84082e12i 0.464864i
\(695\) 1.10510e11 1.00032e10i 0.0179668 0.00162633i
\(696\) −3.26096e12 + 1.88272e12i −0.526750 + 0.304119i
\(697\) −1.93045e10 + 7.20454e10i −0.00309821 + 0.0115627i
\(698\) −5.86257e11 + 1.57087e11i −0.0934842 + 0.0250490i
\(699\) −5.08336e12 −0.805385
\(700\) 4.50767e12 3.75173e12i 0.709596 0.590596i
\(701\) 8.69134e12 1.35943 0.679713 0.733478i \(-0.262104\pi\)
0.679713 + 0.733478i \(0.262104\pi\)
\(702\) 1.20421e12 3.22668e11i 0.187149 0.0501463i
\(703\) −8.11247e11 + 3.02762e12i −0.125272 + 0.467522i
\(704\) −2.07906e12 + 1.20035e12i −0.319000 + 0.184175i
\(705\) 5.21465e12 4.72025e11i 0.795013 0.0719638i
\(706\) 2.18645e12i 0.331221i
\(707\) −1.93795e12 + 1.09314e12i −0.291713 + 0.164547i
\(708\) −3.33060e12 + 3.33060e12i −0.498165 + 0.498165i
\(709\) 7.10831e12 + 4.10398e12i 1.05647 + 0.609955i 0.924454 0.381292i \(-0.124521\pi\)
0.132018 + 0.991247i \(0.457854\pi\)
\(710\) −2.42725e12 + 8.91720e11i −0.358469 + 0.131694i
\(711\) −2.22166e11 3.84803e11i −0.0326035 0.0564710i
\(712\) 1.02355e11 + 3.81994e11i 0.0149262 + 0.0557053i
\(713\) −4.01699e12 4.01699e12i −0.582100 0.582100i
\(714\) −1.34690e10 + 4.83253e10i −0.00193951 + 0.00695877i
\(715\) 5.51163e11 3.18171e12i 0.0788684 0.455285i
\(716\) 3.92197e11 6.79305e11i 0.0557693 0.0965953i
\(717\) −2.68730e12 7.20060e11i −0.379734 0.101750i
\(718\) −1.34959e12 3.61621e11i −0.189514 0.0507802i
\(719\) 3.76974e12 6.52938e12i 0.526055 0.911154i −0.473484 0.880802i \(-0.657004\pi\)
0.999539 0.0303520i \(-0.00966284\pi\)
\(720\) 2.94477e12 2.07517e12i 0.408371 0.287778i
\(721\) 7.49299e12 1.92751e12i 1.03263 0.265636i
\(722\) 1.28902e12 + 1.28902e12i 0.176539 + 0.176539i
\(723\) 1.12460e12 + 4.19706e12i 0.153065 + 0.571246i
\(724\) −5.44596e12 9.43269e12i −0.736633 1.27589i
\(725\) −2.55587e12 1.40022e13i −0.343572 1.88224i
\(726\) 6.21405e11 + 3.58768e11i 0.0830157 + 0.0479291i
\(727\) −6.95723e12 + 6.95723e12i −0.923701 + 0.923701i −0.997289 0.0735879i \(-0.976555\pi\)
0.0735879 + 0.997289i \(0.476555\pi\)
\(728\) 2.87920e12 + 2.88415e10i 0.379910 + 0.00380563i
\(729\) 4.17091e12i 0.546961i
\(730\) 1.42644e11 + 1.57585e12i 0.0185910 + 0.205382i
\(731\) 1.71480e11 9.90040e10i 0.0222119 0.0128240i
\(732\) 9.74529e11 3.63699e12i 0.125457 0.468212i
\(733\) −4.58336e12 + 1.22811e12i −0.586430 + 0.157133i −0.539821 0.841780i \(-0.681508\pi\)
−0.0466090 + 0.998913i \(0.514841\pi\)
\(734\) −5.77134e11 −0.0733913
\(735\) 8.98588e11 4.63338e12i 0.113571 0.585605i
\(736\) 2.71350e12 0.340863
\(737\) 4.14004e12 1.10932e12i 0.516893 0.138501i
\(738\) −1.01970e11 + 3.80557e11i −0.0126537 + 0.0472244i
\(739\) −5.40813e12 + 3.12238e12i −0.667032 + 0.385111i −0.794951 0.606673i \(-0.792504\pi\)
0.127919 + 0.991785i \(0.459170\pi\)
\(740\) 1.69325e12 2.03030e12i 0.207576 0.248896i
\(741\) 4.81213e12i 0.586348i
\(742\) −3.29780e12 3.30347e10i −0.399399 0.00400085i
\(743\) 1.89917e12 1.89917e12i 0.228620 0.228620i −0.583496 0.812116i \(-0.698316\pi\)
0.812116 + 0.583496i \(0.198316\pi\)
\(744\) −4.15548e12 2.39917e12i −0.497214 0.287067i
\(745\) −7.60510e12 3.51852e12i −0.904485 0.418462i
\(746\) −6.59481e11 1.14225e12i −0.0779610 0.135032i
\(747\) 1.13180e12 + 4.22394e12i 0.132992 + 0.496335i
\(748\) 1.58318e11 + 1.58318e11i 0.0184916 + 0.0184916i
\(749\) −7.92781e12 + 2.03936e12i −0.920417 + 0.236770i
\(750\) 3.83166e11 + 1.38008e12i 0.0442193 + 0.159268i
\(751\) −6.43190e12 + 1.11404e13i −0.737836 + 1.27797i 0.215632 + 0.976475i \(0.430819\pi\)
−0.953468 + 0.301495i \(0.902515\pi\)
\(752\) 8.79137e12 + 2.35564e12i 1.00248 + 0.268614i
\(753\) 4.40419e12 + 1.18010e12i 0.499216 + 0.133764i
\(754\) 1.67729e12 2.90515e12i 0.188989 0.327338i
\(755\) 6.77288e12 + 9.61104e12i 0.758599 + 1.07649i
\(756\) 2.18341e12 7.83385e12i 0.243101 0.872222i
\(757\) −8.48245e12 8.48245e12i −0.938837 0.938837i 0.0593979 0.998234i \(-0.481082\pi\)
−0.998234 + 0.0593979i \(0.981082\pi\)
\(758\) −5.24060e11 1.95582e12i −0.0576593 0.215188i
\(759\) −8.05607e11 1.39535e12i −0.0881120 0.152614i
\(760\) −2.33042e12 6.34338e12i −0.253381 0.689699i
\(761\) 1.32422e13 + 7.64538e12i 1.43129 + 0.826357i 0.997220 0.0745202i \(-0.0237425\pi\)
0.434073 + 0.900878i \(0.357076\pi\)
\(762\) 1.23942e12 1.23942e12i 0.133174 0.133174i
\(763\) 6.63432e12 3.74223e12i 0.708657 0.399733i
\(764\) 6.50718e12i 0.690991i
\(765\) −2.04808e11 1.70807e11i −0.0216207 0.0180314i
\(766\) 1.89114e12 1.09185e12i 0.198469 0.114586i
\(767\) 2.26246e12 8.44361e12i 0.236049 0.880945i
\(768\) −1.76358e12 + 4.72551e11i −0.182924 + 0.0490144i
\(769\) 7.14188e12 0.736451 0.368226 0.929736i \(-0.379965\pi\)
0.368226 + 0.929736i \(0.379965\pi\)
\(770\) 1.33408e12 + 1.13546e12i 0.136765 + 0.116403i
\(771\) 2.34051e12 0.238542
\(772\) −1.23045e13 + 3.29699e12i −1.24677 + 0.334072i
\(773\) −1.88672e12 + 7.04134e12i −0.190064 + 0.709329i 0.803425 + 0.595405i \(0.203009\pi\)
−0.993490 + 0.113923i \(0.963658\pi\)
\(774\) 9.05789e11 5.22958e11i 0.0907179 0.0523760i
\(775\) 1.38241e13 1.17422e13i 1.37651 1.16921i
\(776\) 8.23893e12i 0.815629i
\(777\) 2.13112e10 2.12746e12i 0.00209755 0.209395i
\(778\) 1.81463e12 1.81463e12i 0.177575 0.177575i
\(779\) −3.36148e12 1.94075e12i −0.327049 0.188822i
\(780\) 1.70424e12 3.68363e12i 0.164856 0.356329i
\(781\) 4.64378e12 + 8.04327e12i 0.446624 + 0.773576i
\(782\) −1.49405e10 5.57587e10i −0.00142868 0.00533190i
\(783\) −1.39564e13 1.39564e13i −1.32692 1.32692i
\(784\) 4.24355e12 7.02135e12i 0.401150 0.663741i
\(785\) −4.62744e12 8.01604e11i −0.434938 0.0753436i
\(786\) 4.25238e11 7.36535e11i 0.0397403 0.0688322i
\(787\) 1.81498e13 + 4.86323e12i 1.68650 + 0.451896i 0.969482 0.245161i \(-0.0788408\pi\)
0.717016 + 0.697057i \(0.245507\pi\)
\(788\) −4.47201e12 1.19827e12i −0.413175 0.110710i
\(789\) 1.46086e12 2.53028e12i 0.134203 0.232446i
\(790\) 3.02572e11 + 5.24141e10i 0.0276380 + 0.00478769i
\(791\) 9.63162e12 9.44057e12i 0.874793 0.857441i
\(792\) 1.74208e12 + 1.74208e12i 0.157328 + 0.157328i
\(793\) 1.80859e12 + 6.74977e12i 0.162410 + 0.606121i
\(794\) −1.83363e11 3.17595e11i −0.0163727 0.0283584i
\(795\) −4.06638e12 + 8.78927e12i −0.361040 + 0.780370i
\(796\) −1.03841e12 5.99524e11i −0.0916766 0.0529295i
\(797\) −9.09936e12 + 9.09936e12i −0.798819 + 0.798819i −0.982909 0.184091i \(-0.941066\pi\)
0.184091 + 0.982909i \(0.441066\pi\)
\(798\) −2.24775e12 1.32793e12i −0.196216 0.115921i
\(799\) 6.73765e11i 0.0584855i
\(800\) −7.03178e11 + 8.63509e12i −0.0606960 + 0.745353i
\(801\) −7.03347e11 + 4.06077e11i −0.0603703 + 0.0348548i
\(802\) 8.28831e11 3.09324e12i 0.0707426 0.264015i
\(803\) 5.48942e12 1.47089e12i 0.465915 0.124842i
\(804\) 5.38733e12 0.454696
\(805\) 1.82162e12 + 5.11618e12i 0.152889 + 0.429402i
\(806\) 4.27477e12 0.356784
\(807\) −1.51729e12 + 4.06558e11i −0.125933 + 0.0337436i
\(808\) 5.59694e11 2.08881e12i 0.0461955 0.172404i
\(809\) −1.37655e13 + 7.94749e12i −1.12985 + 0.652321i −0.943898 0.330237i \(-0.892871\pi\)
−0.185956 + 0.982558i \(0.559538\pi\)
\(810\) −1.54140e11 1.28551e11i −0.0125815 0.0104928i
\(811\) 8.23210e12i 0.668216i 0.942535 + 0.334108i \(0.108435\pi\)
−0.942535 + 0.334108i \(0.891565\pi\)
\(812\) −1.07509e13 1.90595e13i −0.867845 1.53854i
\(813\) −9.27101e12 + 9.27101e12i −0.744251 + 0.744251i
\(814\) 6.83912e11 + 3.94857e11i 0.0545997 + 0.0315232i
\(815\) −2.69455e12 7.33451e12i −0.213932 0.582321i
\(816\) 1.28035e11 + 2.21764e11i 0.0101094 + 0.0175099i
\(817\) 2.66696e12 + 9.95324e12i 0.209420 + 0.781565i
\(818\) −2.06800e12 2.06800e12i −0.161496 0.161496i
\(819\) 1.47315e12 + 5.72672e12i 0.114412 + 0.444763i
\(820\) 1.88585e12 + 2.67611e12i 0.145662 + 0.206701i
\(821\) −2.01457e12 + 3.48933e12i −0.154752 + 0.268039i −0.932969 0.359957i \(-0.882791\pi\)
0.778216 + 0.627996i \(0.216125\pi\)
\(822\) −1.99482e12 5.34510e11i −0.152398 0.0408350i
\(823\) −2.03729e13 5.45890e12i −1.54794 0.414769i −0.619117 0.785299i \(-0.712509\pi\)
−0.928821 + 0.370530i \(0.879176\pi\)
\(824\) −3.75978e12 + 6.51214e12i −0.284113 + 0.492097i
\(825\) 4.64915e12 2.20207e12i 0.349407 0.165496i
\(826\) 3.31968e12 + 3.38686e12i 0.248134 + 0.253155i
\(827\) 1.74099e12 + 1.74099e12i 0.129426 + 0.129426i 0.768852 0.639426i \(-0.220828\pi\)
−0.639426 + 0.768852i \(0.720828\pi\)
\(828\) 9.48896e11 + 3.54133e12i 0.0701588 + 0.261836i
\(829\) 6.02736e12 + 1.04397e13i 0.443233 + 0.767702i 0.997927 0.0643522i \(-0.0204981\pi\)
−0.554694 + 0.832054i \(0.687165\pi\)
\(830\) −2.74282e12 1.26897e12i −0.200607 0.0928112i
\(831\) 7.56795e12 + 4.36936e12i 0.550521 + 0.317843i
\(832\) 3.95988e12 3.95988e12i 0.286502 0.286502i
\(833\) −5.83371e11 1.68909e11i −0.0419800 0.0121549i
\(834\) 4.16622e10i 0.00298192i
\(835\) 9.58829e11 1.14969e12i 0.0682577 0.0818449i
\(836\) −1.00905e13 + 5.82578e12i −0.714474 + 0.412502i
\(837\) 6.50968e12 2.42944e13i 0.458453 1.71097i
\(838\) 1.71387e10 4.59229e9i 0.00120055 0.000321685i
\(839\) 3.46989e12 0.241761 0.120881 0.992667i \(-0.461428\pi\)
0.120881 + 0.992667i \(0.461428\pi\)
\(840\) 2.60465e12 + 3.77589e12i 0.180507 + 0.261675i
\(841\) −3.86015e13 −2.66086
\(842\) −4.20019e12 + 1.12544e12i −0.287982 + 0.0771645i
\(843\) −1.79735e12 + 6.70782e12i −0.122577 + 0.457464i
\(844\) −5.12842e12 + 2.96089e12i −0.347890 + 0.200854i
\(845\) −6.56991e11 7.25804e12i −0.0443306 0.489738i
\(846\) 3.55896e12i 0.238867i
\(847\) −4.41845e12 + 7.47895e12i −0.294981 + 0.499304i
\(848\) −1.19034e13 + 1.19034e13i −0.790478 + 0.790478i
\(849\) 1.36677e13 + 7.89103e12i 0.902838 + 0.521254i
\(850\) 1.81311e11 3.30954e10i 0.0119135 0.00217461i
\(851\) 1.22406e12 + 2.12013e12i 0.0800054 + 0.138573i
\(852\) 3.02142e12 + 1.12761e13i 0.196442 + 0.733130i
\(853\) 1.17980e12 + 1.17980e12i 0.0763026 + 0.0763026i 0.744228 0.667926i \(-0.232818\pi\)
−0.667926 + 0.744228i \(0.732818\pi\)
\(854\) −3.65191e12 1.01784e12i −0.234941 0.0654816i
\(855\) 1.13445e13 7.99445e12i 0.726002 0.511612i
\(856\) 3.97797e12 6.89004e12i 0.253238 0.438621i
\(857\) 2.51740e13 + 6.74536e12i 1.59419 + 0.427161i 0.943281 0.331997i \(-0.107722\pi\)
0.650906 + 0.759158i \(0.274389\pi\)
\(858\) 1.17110e12 + 3.13795e11i 0.0737737 + 0.0197676i
\(859\) −5.00271e12 + 8.66496e12i −0.313499 + 0.542997i −0.979117 0.203296i \(-0.934835\pi\)
0.665618 + 0.746293i \(0.268168\pi\)
\(860\) 1.48346e12 8.56361e12i 0.0924770 0.533844i
\(861\) 2.53794e12 + 7.07361e11i 0.157387 + 0.0438659i
\(862\) −5.01724e12 5.01724e12i −0.309515 0.309515i
\(863\) −1.93480e11 7.22078e11i −0.0118738 0.0443135i 0.959735 0.280908i \(-0.0906355\pi\)
−0.971609 + 0.236594i \(0.923969\pi\)
\(864\) 6.00686e12 + 1.04042e13i 0.366721 + 0.635179i
\(865\) −2.35542e13 + 8.65332e12i −1.43053 + 0.525546i
\(866\) 4.52259e12 + 2.61112e12i 0.273248 + 0.157760i
\(867\) −7.00426e12 + 7.00426e12i −0.420995 + 0.420995i
\(868\) 1.41838e13 2.40084e13i 0.848111 1.43557i
\(869\) 1.10292e12i 0.0656079i
\(870\) 5.32243e12 4.81781e11i 0.314973 0.0285111i
\(871\) −8.65866e12 + 4.99908e12i −0.509764 + 0.294312i
\(872\) −1.91604e12 + 7.15074e12i −0.112222 + 0.418820i
\(873\) 1.63433e13 4.37918e12i 0.952305 0.255169i
\(874\) 3.00405e12 0.174143
\(875\) −1.67531e13 + 4.47109e12i −0.966183 + 0.257856i
\(876\) 7.14326e12 0.409853
\(877\) −1.05603e13 + 2.82963e12i −0.602808 + 0.161522i −0.547300 0.836936i \(-0.684344\pi\)
−0.0555076 + 0.998458i \(0.517678\pi\)
\(878\) −1.67492e12 + 6.25090e12i −0.0951196 + 0.354991i
\(879\) −2.46274e12 + 1.42186e12i −0.139145 + 0.0803356i
\(880\) 8.90572e12 8.06137e11i 0.500607 0.0453145i
\(881\) 1.64269e13i 0.918681i −0.888260 0.459341i \(-0.848086\pi\)
0.888260 0.459341i \(-0.151914\pi\)
\(882\) −3.08148e12 8.92211e11i −0.171455 0.0496431i
\(883\) 5.67686e12 5.67686e12i 0.314257 0.314257i −0.532299 0.846556i \(-0.678672\pi\)
0.846556 + 0.532299i \(0.178672\pi\)
\(884\) −4.52310e11 2.61141e11i −0.0249116 0.0143827i
\(885\) 1.30719e13 4.80233e12i 0.716297 0.263152i
\(886\) −3.17675e12 5.50229e12i −0.173193 0.299979i
\(887\) −1.81783e12 6.78424e12i −0.0986047 0.367998i 0.898937 0.438079i \(-0.144341\pi\)
−0.997541 + 0.0700810i \(0.977674\pi\)
\(888\) 1.46215e12 + 1.46215e12i 0.0789104 + 0.0789104i
\(889\) 1.48535e13 + 1.51541e13i 0.797576 + 0.813717i
\(890\) 9.58030e10 5.53044e11i 0.00511828 0.0295464i
\(891\) −3.60441e11 + 6.24302e11i −0.0191595 + 0.0331852i
\(892\) 1.27194e10 + 3.40815e9i 0.000672704 + 0.000180251i
\(893\) 3.38681e13 + 9.07493e12i 1.78221 + 0.477542i
\(894\) 1.57312e12 2.72473e12i 0.0823651 0.142661i
\(895\) −1.89571e12 + 1.33590e12i −0.0987572 + 0.0695940i
\(896\) 4.35118e12 + 1.69148e13i 0.225539 + 0.876758i
\(897\) 2.65765e12 + 2.65765e12i 0.137067 + 0.137067i
\(898\) −9.33660e10 3.48447e11i −0.00479121 0.0178810i
\(899\) −3.38384e13 5.86099e13i −1.72779 2.99263i
\(900\) −1.15154e13 + 2.10194e12i −0.585041 + 0.106790i
\(901\) 1.07923e12 + 6.23092e11i 0.0545571 + 0.0314986i
\(902\) −6.91510e11 + 6.91510e11i −0.0347831 + 0.0347831i
\(903\) −3.43632e12 6.09201e12i −0.171988 0.304906i
\(904\) 1.31079e13i 0.652790i
\(905\) 2.90311e12 + 3.20718e13i 0.143862 + 1.58930i
\(906\) −3.82317e12 + 2.20731e12i −0.188515 + 0.108839i
\(907\) 1.03662e13 3.86873e13i 0.508614 1.89817i 0.0747346 0.997203i \(-0.476189\pi\)
0.433880 0.900971i \(-0.357144\pi\)
\(908\) −1.25993e13 + 3.37596e12i −0.615118 + 0.164820i
\(909\) 4.44099e12 0.215746
\(910\) −3.69151e12 1.75299e12i −0.178450 0.0847409i
\(911\) −3.74604e12 −0.180194 −0.0900970 0.995933i \(-0.528718\pi\)
−0.0900970 + 0.995933i \(0.528718\pi\)
\(912\) −1.28719e13 + 3.44901e12i −0.616119 + 0.165089i
\(913\) −2.80936e12 + 1.04847e13i −0.133810 + 0.499385i
\(914\) 5.17944e11 2.99035e11i 0.0245485 0.0141731i
\(915\) −7.13011e12 + 8.54941e12i −0.336280 + 0.403219i
\(916\) 2.75691e12i 0.129388i
\(917\) 8.86460e12 + 5.23706e12i 0.413997 + 0.244583i
\(918\) 1.80718e11 1.80718e11i 0.00839865 0.00839865i
\(919\) −9.77955e12 5.64623e12i −0.452271 0.261119i 0.256518 0.966540i \(-0.417425\pi\)
−0.708789 + 0.705421i \(0.750758\pi\)
\(920\) −4.79038e12 2.21628e12i −0.220458 0.101995i
\(921\) −5.24499e11 9.08459e11i −0.0240202 0.0416042i
\(922\) −9.08770e10 3.39157e11i −0.00414157 0.0154565i
\(923\) −1.53196e13 1.53196e13i −0.694767 0.694767i
\(924\) 5.64810e12 5.53607e12i 0.254905 0.249849i
\(925\) −7.06404e12 + 3.34587e12i −0.317260 + 0.150270i
\(926\) −5.07755e12 + 8.79458e12i −0.226937 + 0.393066i
\(927\) −1.49163e13 3.99682e12i −0.663443 0.177769i
\(928\) 3.12247e13 + 8.36663e12i 1.38208 + 0.370326i
\(929\) 1.06673e13 1.84763e13i 0.469876 0.813849i −0.529531 0.848291i \(-0.677632\pi\)
0.999407 + 0.0344417i \(0.0109653\pi\)
\(930\) 3.92290e12 + 5.56679e12i 0.171963 + 0.244023i
\(931\) 1.63480e13 2.70492e13i 0.713165 1.18000i
\(932\) 2.03021e13 + 2.03021e13i 0.881394 + 0.881394i
\(933\) −4.73805e10 1.76827e11i −0.00204707 0.00763977i
\(934\) −2.73132e12 4.73079e12i −0.117439 0.203410i
\(935\) −2.28276e11 6.21363e11i −0.00976804 0.0265885i
\(936\) −4.97708e12 2.87352e12i −0.211950 0.122369i
\(937\) −2.03074e13 + 2.03074e13i −0.860650 + 0.860650i −0.991414 0.130764i \(-0.958257\pi\)
0.130764 + 0.991414i \(0.458257\pi\)
\(938\) 5.43331e10 5.42399e12i 0.00229167 0.228774i
\(939\) 1.95896e13i 0.822299i
\(940\) −2.27117e13 1.89413e13i −0.948799 0.791288i
\(941\) −1.28151e13 + 7.39878e12i −0.532804 + 0.307614i −0.742157 0.670226i \(-0.766197\pi\)
0.209354 + 0.977840i \(0.432864\pi\)
\(942\) 4.56380e11 1.70323e12i 0.0188842 0.0704766i
\(943\) −2.92833e12 + 7.84643e11i −0.120592 + 0.0323124i
\(944\) 2.42072e13 0.992135
\(945\) −1.55841e13 + 1.83102e13i −0.635680 + 0.746878i
\(946\) 2.59617e12 0.105396
\(947\) 4.39239e13 1.17694e13i 1.77470 0.475530i 0.785102 0.619366i \(-0.212610\pi\)
0.989602 + 0.143836i \(0.0459438\pi\)
\(948\) 3.58802e11 1.33907e12i 0.0144284 0.0538474i
\(949\) −1.14808e13 + 6.62846e12i −0.459489 + 0.265286i
\(950\) −7.78471e11 + 9.55970e12i −0.0310089 + 0.380792i
\(951\) 2.49028e13i 0.987269i
\(952\) 5.14119e11 2.90000e11i 0.0202861 0.0114428i
\(953\) 2.09083e13 2.09083e13i 0.821109 0.821109i −0.165158 0.986267i \(-0.552813\pi\)
0.986267 + 0.165158i \(0.0528134\pi\)
\(954\) 5.70068e12 + 3.29129e12i 0.222823 + 0.128647i
\(955\) 8.07832e12 1.74609e13i 0.314272 0.679283i
\(956\) 7.85686e12 + 1.36085e13i 0.304220 + 0.526925i
\(957\) −4.96792e12 1.85405e13i −0.191457 0.714526i
\(958\) 3.44591e12 + 3.44591e12i 0.132178 + 0.132178i
\(959\) 6.71244e12 2.40836e13i 0.256270 0.919470i
\(960\) 8.79066e12 + 1.52279e12i 0.334042 + 0.0578656i
\(961\) 2.99009e13 5.17899e13i 1.13091 1.95880i
\(962\) −1.77940e12 4.76788e11i −0.0669862 0.0179489i
\(963\) 1.57819e13 + 4.22876e12i 0.591347 + 0.158451i
\(964\) 1.22709e13 2.12539e13i 0.457648 0.792669i
\(965\) 3.71101e13 + 6.42853e12i 1.37759 + 0.238637i
\(966\) −1.97478e12 + 5.07996e11i −0.0729663 + 0.0187700i
\(967\) 1.12861e13 + 1.12861e13i 0.415072 + 0.415072i 0.883501 0.468429i \(-0.155180\pi\)
−0.468429 + 0.883501i \(0.655180\pi\)
\(968\) −2.18510e12 8.15490e12i −0.0799893 0.298524i
\(969\) 4.93246e11 + 8.54328e11i 0.0179724 + 0.0311292i
\(970\) −4.90992e12 + 1.06125e13i −0.178074 + 0.384899i
\(971\) −4.32293e13 2.49585e13i −1.56060 0.901014i −0.997196 0.0748338i \(-0.976157\pi\)
−0.563406 0.826180i \(-0.690509\pi\)
\(972\) −1.84586e13 + 1.84586e13i −0.663284 + 0.663284i
\(973\) −5.04345e11 5.05212e9i −0.0180393 0.000180703i
\(974\) 3.13277e12i 0.111536i
\(975\) −9.14607e12 + 7.76866e12i −0.324126 + 0.275312i
\(976\) −1.67585e13 + 9.67554e12i −0.591169 + 0.341312i
\(977\) 3.12817e12 1.16745e13i 0.109841 0.409933i −0.889008 0.457891i \(-0.848605\pi\)
0.998849 + 0.0479586i \(0.0152716\pi\)
\(978\) 2.83385e12 7.59327e11i 0.0990493 0.0265402i
\(979\) −2.01593e12 −0.0701380
\(980\) −2.20938e13 + 1.49162e13i −0.765162 + 0.516583i
\(981\) −1.52031e13 −0.524110
\(982\) 1.95263e12 5.23206e11i 0.0670068 0.0179544i
\(983\) −6.76220e12 + 2.52369e13i −0.230992 + 0.862074i 0.748923 + 0.662657i \(0.230571\pi\)
−0.979915 + 0.199417i \(0.936095\pi\)
\(984\) −2.21759e12 + 1.28033e12i −0.0754056 + 0.0435355i
\(985\) 1.05123e13 + 8.76711e12i 0.355822 + 0.296752i
\(986\) 6.87691e11i 0.0231711i
\(987\) −2.37986e13 2.38395e11i −0.798223 0.00799595i
\(988\) 1.92189e13 1.92189e13i 0.641686 0.641686i
\(989\) 6.96990e12 + 4.02408e12i 0.231656 + 0.133747i
\(990\) −1.20580e12 3.28216e12i −0.0398947 0.108593i
\(991\) 1.12128e13 + 1.94212e13i 0.369304 + 0.639653i 0.989457 0.144828i \(-0.0462629\pi\)
−0.620153 + 0.784481i \(0.712930\pi\)
\(992\) 1.06617e13 + 3.97900e13i 0.349561 + 1.30458i
\(993\) 2.12347e13 + 2.12347e13i 0.693067 + 0.693067i
\(994\) 1.13833e13 2.92826e12i 0.369853 0.0951416i
\(995\) 2.04210e12 + 2.89784e12i 0.0660502 + 0.0937284i
\(996\) −6.82172e12 + 1.18156e13i −0.219648 + 0.380441i
\(997\) 4.80151e13 + 1.28656e13i 1.53904 + 0.412385i 0.925956 0.377632i \(-0.123262\pi\)
0.613085 + 0.790017i \(0.289928\pi\)
\(998\) −1.11429e13 2.98572e12i −0.355557 0.0952713i
\(999\) −5.41938e12 + 9.38665e12i −0.172149 + 0.298171i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 35.10.k.a.12.16 yes 136
5.3 odd 4 inner 35.10.k.a.33.19 yes 136
7.3 odd 6 inner 35.10.k.a.17.19 yes 136
35.3 even 12 inner 35.10.k.a.3.16 136
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.10.k.a.3.16 136 35.3 even 12 inner
35.10.k.a.12.16 yes 136 1.1 even 1 trivial
35.10.k.a.17.19 yes 136 7.3 odd 6 inner
35.10.k.a.33.19 yes 136 5.3 odd 4 inner