Properties

Label 17.10.d.a.8.11
Level $17$
Weight $10$
Character 17.8
Analytic conductor $8.756$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [17,10,Mod(2,17)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(17, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([7]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("17.2");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 17.d (of order \(8\), 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: \(8.75560921479\)
Analytic rank: \(0\)
Dimension: \(52\)
Relative dimension: \(13\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 8.11
Character \(\chi\) \(=\) 17.8
Dual form 17.10.d.a.15.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(17.9968 - 17.9968i) q^{2} +(-30.9190 + 74.6450i) q^{3} -135.770i q^{4} +(723.808 + 299.811i) q^{5} +(786.929 + 1899.81i) q^{6} +(5306.77 - 2198.13i) q^{7} +(6770.93 + 6770.93i) q^{8} +(9302.09 + 9302.09i) q^{9} +O(q^{10})\) \(q+(17.9968 - 17.9968i) q^{2} +(-30.9190 + 74.6450i) q^{3} -135.770i q^{4} +(723.808 + 299.811i) q^{5} +(786.929 + 1899.81i) q^{6} +(5306.77 - 2198.13i) q^{7} +(6770.93 + 6770.93i) q^{8} +(9302.09 + 9302.09i) q^{9} +(18421.9 - 7630.59i) q^{10} +(992.353 + 2395.75i) q^{11} +(10134.6 + 4197.88i) q^{12} -108940. i q^{13} +(55945.5 - 135064. i) q^{14} +(-44758.8 + 44758.8i) q^{15} +313225. q^{16} +(-49428.2 + 340800. i) q^{17} +334816. q^{18} +(-67635.2 + 67635.2i) q^{19} +(40705.5 - 98271.7i) q^{20} +464088. i q^{21} +(60975.1 + 25256.7i) q^{22} +(35562.3 + 85855.1i) q^{23} +(-714767. + 296066. i) q^{24} +(-947057. - 947057. i) q^{25} +(-1.96058e6 - 1.96058e6i) q^{26} +(-2.45120e6 + 1.01532e6i) q^{27} +(-298442. - 720502. i) q^{28} +(-2.69221e6 - 1.11515e6i) q^{29} +1.61103e6i q^{30} +(-834349. + 2.01430e6i) q^{31} +(2.17033e6 - 2.17033e6i) q^{32} -209513. q^{33} +(5.24377e6 + 7.02286e6i) q^{34} +4.50010e6 q^{35} +(1.26295e6 - 1.26295e6i) q^{36} +(4.20614e6 - 1.01545e7i) q^{37} +2.43444e6i q^{38} +(8.13185e6 + 3.36832e6i) q^{39} +(2.87085e6 + 6.93086e6i) q^{40} +(1.02771e7 - 4.25693e6i) q^{41} +(8.35210e6 + 8.35210e6i) q^{42} +(-8.53406e6 - 8.53406e6i) q^{43} +(325272. - 134732. i) q^{44} +(3.94406e6 + 9.52180e6i) q^{45} +(2.18513e6 + 905109. i) q^{46} -5.88161e7i q^{47} +(-9.68459e6 + 2.33807e7i) q^{48} +(-5.20434e6 + 5.20434e6i) q^{49} -3.40880e7 q^{50} +(-2.39108e7 - 1.42268e7i) q^{51} -1.47909e7 q^{52} +(1.31051e7 - 1.31051e7i) q^{53} +(-2.58413e7 + 6.23864e7i) q^{54} +2.03158e6i q^{55} +(5.08152e7 + 2.10483e7i) q^{56} +(-2.95742e6 - 7.13984e6i) q^{57} +(-6.85202e7 + 2.83820e7i) q^{58} +(-6.73109e7 - 6.73109e7i) q^{59} +(6.07692e6 + 6.07692e6i) q^{60} +(4.19344e7 - 1.73698e7i) q^{61} +(2.12353e7 + 5.12666e7i) q^{62} +(6.98113e7 + 2.89168e7i) q^{63} +8.22531e7i q^{64} +(3.26615e7 - 7.88519e7i) q^{65} +(-3.77057e6 + 3.77057e6i) q^{66} -2.09338e8 q^{67} +(4.62706e7 + 6.71088e6i) q^{68} -7.50820e6 q^{69} +(8.09875e7 - 8.09875e7i) q^{70} +(7.85924e7 - 1.89739e8i) q^{71} +1.25968e8i q^{72} +(1.07592e8 + 4.45659e7i) q^{73} +(-1.07052e8 - 2.58446e8i) q^{74} +(9.99751e7 - 4.14110e7i) q^{75} +(9.18286e6 + 9.18286e6i) q^{76} +(1.05324e7 + 1.05324e7i) q^{77} +(2.06966e8 - 8.57283e7i) q^{78} +(1.49467e8 + 3.60845e8i) q^{79} +(2.26715e8 + 9.39083e7i) q^{80} +4.45700e7i q^{81} +(1.08345e8 - 2.61567e8i) q^{82} +(-1.98863e8 + 1.98863e8i) q^{83} +6.30093e7 q^{84} +(-1.37952e8 + 2.31855e8i) q^{85} -3.07172e8 q^{86} +(1.66480e8 - 1.66480e8i) q^{87} +(-9.50232e6 + 2.29406e7i) q^{88} +9.72872e8i q^{89} +(2.42342e8 + 1.00382e8i) q^{90} +(-2.39465e8 - 5.78121e8i) q^{91} +(1.16566e7 - 4.82831e6i) q^{92} +(-1.24560e8 - 1.24560e8i) q^{93} +(-1.05850e9 - 1.05850e9i) q^{94} +(-6.92327e7 + 2.86771e7i) q^{95} +(9.48999e7 + 2.29109e8i) q^{96} +(-1.18185e9 - 4.89538e8i) q^{97} +1.87323e8i q^{98} +(-1.30545e7 + 3.15165e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52 q - 4 q^{2} - 4 q^{3} - 1140 q^{5} + 12308 q^{6} - 4 q^{7} + 2044 q^{8} - 83224 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 52 q - 4 q^{2} - 4 q^{3} - 1140 q^{5} + 12308 q^{6} - 4 q^{7} + 2044 q^{8} - 83224 q^{9} - 117636 q^{10} - 115768 q^{11} - 145528 q^{12} + 463660 q^{14} + 288244 q^{15} - 3407880 q^{16} - 271932 q^{17} + 2193336 q^{18} - 406700 q^{19} + 493564 q^{20} + 800964 q^{22} - 4172180 q^{23} + 15078440 q^{24} + 11946576 q^{25} - 14209012 q^{26} - 7973656 q^{27} + 13540804 q^{28} + 7833752 q^{29} + 5936252 q^{31} - 26730116 q^{32} - 1635208 q^{33} - 53493988 q^{34} + 46992776 q^{35} - 12761764 q^{36} + 74606796 q^{37} + 74096776 q^{39} - 69317672 q^{40} - 71362288 q^{41} - 308117664 q^{42} - 3765712 q^{43} + 163659820 q^{44} + 14167408 q^{45} + 72135428 q^{46} + 164621412 q^{48} - 284548508 q^{49} + 226223888 q^{50} - 406733132 q^{51} + 103553016 q^{52} - 244724728 q^{53} + 971226260 q^{54} + 470691652 q^{56} - 440646580 q^{57} - 308561768 q^{58} - 481734984 q^{59} + 379626176 q^{60} + 507966228 q^{61} + 358867236 q^{62} + 1070586456 q^{63} + 366263684 q^{65} - 2244715148 q^{66} - 311910088 q^{67} - 1839196668 q^{68} + 533688136 q^{69} + 34867672 q^{70} + 186006812 q^{71} + 487115192 q^{73} - 214149412 q^{74} + 533015920 q^{75} + 1104236912 q^{76} - 237869092 q^{77} - 2081523384 q^{78} - 136338052 q^{79} - 922534152 q^{80} + 1951892384 q^{82} + 1843663888 q^{83} - 2630025952 q^{84} - 395061976 q^{85} + 1538547296 q^{86} - 369395636 q^{87} - 3388839640 q^{88} + 874363684 q^{90} + 2087197720 q^{91} + 1061427500 q^{92} + 576415420 q^{93} + 6899365112 q^{94} + 5031766876 q^{95} + 490811364 q^{96} - 3419996368 q^{97} - 5630536112 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 17.9968 17.9968i 0.795354 0.795354i −0.187005 0.982359i \(-0.559878\pi\)
0.982359 + 0.187005i \(0.0598780\pi\)
\(3\) −30.9190 + 74.6450i −0.220384 + 0.532053i −0.994942 0.100449i \(-0.967972\pi\)
0.774559 + 0.632502i \(0.217972\pi\)
\(4\) 135.770i 0.265177i
\(5\) 723.808 + 299.811i 0.517915 + 0.214527i 0.626301 0.779582i \(-0.284568\pi\)
−0.108386 + 0.994109i \(0.534568\pi\)
\(6\) 786.929 + 1899.81i 0.247888 + 0.598454i
\(7\) 5306.77 2198.13i 0.835389 0.346029i 0.0763552 0.997081i \(-0.475672\pi\)
0.759034 + 0.651051i \(0.225672\pi\)
\(8\) 6770.93 + 6770.93i 0.584445 + 0.584445i
\(9\) 9302.09 + 9302.09i 0.472595 + 0.472595i
\(10\) 18421.9 7630.59i 0.582551 0.241300i
\(11\) 992.353 + 2395.75i 0.0204362 + 0.0493372i 0.933768 0.357878i \(-0.116500\pi\)
−0.913332 + 0.407216i \(0.866500\pi\)
\(12\) 10134.6 + 4197.88i 0.141088 + 0.0584406i
\(13\) 108940.i 1.05790i −0.848654 0.528949i \(-0.822586\pi\)
0.848654 0.528949i \(-0.177414\pi\)
\(14\) 55945.5 135064.i 0.389214 0.939646i
\(15\) −44758.8 + 44758.8i −0.228280 + 0.228280i
\(16\) 313225. 1.19486
\(17\) −49428.2 + 340800.i −0.143534 + 0.989645i
\(18\) 334816. 0.751761
\(19\) −67635.2 + 67635.2i −0.119064 + 0.119064i −0.764128 0.645064i \(-0.776831\pi\)
0.645064 + 0.764128i \(0.276831\pi\)
\(20\) 40705.5 98271.7i 0.0568876 0.137339i
\(21\) 464088.i 0.520731i
\(22\) 60975.1 + 25256.7i 0.0554946 + 0.0229866i
\(23\) 35562.3 + 85855.1i 0.0264981 + 0.0639721i 0.936575 0.350468i \(-0.113977\pi\)
−0.910077 + 0.414440i \(0.863977\pi\)
\(24\) −714767. + 296066.i −0.439758 + 0.182154i
\(25\) −947057. 947057.i −0.484893 0.484893i
\(26\) −1.96058e6 1.96058e6i −0.841403 0.841403i
\(27\) −2.45120e6 + 1.01532e6i −0.887651 + 0.367677i
\(28\) −298442. 720502.i −0.0917589 0.221526i
\(29\) −2.69221e6 1.11515e6i −0.706834 0.292780i 0.000160047 1.00000i \(-0.499949\pi\)
−0.706994 + 0.707220i \(0.749949\pi\)
\(30\) 1.61103e6i 0.363127i
\(31\) −834349. + 2.01430e6i −0.162263 + 0.391738i −0.984010 0.178115i \(-0.943000\pi\)
0.821746 + 0.569853i \(0.193000\pi\)
\(32\) 2.17033e6 2.17033e6i 0.365890 0.365890i
\(33\) −209513. −0.0307538
\(34\) 5.24377e6 + 7.02286e6i 0.672958 + 0.901279i
\(35\) 4.50010e6 0.506893
\(36\) 1.26295e6 1.26295e6i 0.125321 0.125321i
\(37\) 4.20614e6 1.01545e7i 0.368957 0.890741i −0.624965 0.780653i \(-0.714887\pi\)
0.993922 0.110088i \(-0.0351134\pi\)
\(38\) 2.43444e6i 0.189397i
\(39\) 8.13185e6 + 3.36832e6i 0.562858 + 0.233143i
\(40\) 2.87085e6 + 6.93086e6i 0.177313 + 0.428072i
\(41\) 1.02771e7 4.25693e6i 0.567996 0.235271i −0.0801567 0.996782i \(-0.525542\pi\)
0.648152 + 0.761511i \(0.275542\pi\)
\(42\) 8.35210e6 + 8.35210e6i 0.414165 + 0.414165i
\(43\) −8.53406e6 8.53406e6i −0.380669 0.380669i 0.490674 0.871343i \(-0.336751\pi\)
−0.871343 + 0.490674i \(0.836751\pi\)
\(44\) 325272. 134732.i 0.0130831 0.00541919i
\(45\) 3.94406e6 + 9.52180e6i 0.143379 + 0.346149i
\(46\) 2.18513e6 + 905109.i 0.0719559 + 0.0298051i
\(47\) 5.88161e7i 1.75815i −0.476684 0.879075i \(-0.658161\pi\)
0.476684 0.879075i \(-0.341839\pi\)
\(48\) −9.68459e6 + 2.33807e7i −0.263327 + 0.635728i
\(49\) −5.20434e6 + 5.20434e6i −0.128968 + 0.128968i
\(50\) −3.40880e7 −0.771323
\(51\) −2.39108e7 1.42268e7i −0.494911 0.294469i
\(52\) −1.47909e7 −0.280530
\(53\) 1.31051e7 1.31051e7i 0.228139 0.228139i −0.583776 0.811915i \(-0.698425\pi\)
0.811915 + 0.583776i \(0.198425\pi\)
\(54\) −2.58413e7 + 6.23864e7i −0.413563 + 0.998431i
\(55\) 2.03158e6i 0.0299366i
\(56\) 5.08152e7 + 2.10483e7i 0.690474 + 0.286004i
\(57\) −2.95742e6 7.13984e6i −0.0371087 0.0895883i
\(58\) −6.85202e7 + 2.83820e7i −0.795047 + 0.329319i
\(59\) −6.73109e7 6.73109e7i −0.723189 0.723189i 0.246065 0.969253i \(-0.420862\pi\)
−0.969253 + 0.246065i \(0.920862\pi\)
\(60\) 6.07692e6 + 6.07692e6i 0.0605345 + 0.0605345i
\(61\) 4.19344e7 1.73698e7i 0.387780 0.160624i −0.180271 0.983617i \(-0.557697\pi\)
0.568051 + 0.822993i \(0.307697\pi\)
\(62\) 2.12353e7 + 5.12666e7i 0.182514 + 0.440627i
\(63\) 6.98113e7 + 2.89168e7i 0.558333 + 0.231269i
\(64\) 8.22531e7i 0.612833i
\(65\) 3.26615e7 7.88519e7i 0.226948 0.547901i
\(66\) −3.77057e6 + 3.77057e6i −0.0244602 + 0.0244602i
\(67\) −2.09338e8 −1.26915 −0.634574 0.772862i \(-0.718824\pi\)
−0.634574 + 0.772862i \(0.718824\pi\)
\(68\) 4.62706e7 + 6.71088e6i 0.262431 + 0.0380618i
\(69\) −7.50820e6 −0.0398763
\(70\) 8.09875e7 8.09875e7i 0.403160 0.403160i
\(71\) 7.85924e7 1.89739e8i 0.367044 0.886123i −0.627188 0.778868i \(-0.715794\pi\)
0.994232 0.107254i \(-0.0342060\pi\)
\(72\) 1.25968e8i 0.552412i
\(73\) 1.07592e8 + 4.45659e7i 0.443431 + 0.183675i 0.593216 0.805044i \(-0.297858\pi\)
−0.149785 + 0.988719i \(0.547858\pi\)
\(74\) −1.07052e8 2.58446e8i −0.415003 1.00191i
\(75\) 9.99751e7 4.14110e7i 0.364851 0.151126i
\(76\) 9.18286e6 + 9.18286e6i 0.0315731 + 0.0315731i
\(77\) 1.05324e7 + 1.05324e7i 0.0341443 + 0.0341443i
\(78\) 2.06966e8 8.57283e7i 0.633103 0.262240i
\(79\) 1.49467e8 + 3.60845e8i 0.431741 + 1.04231i 0.978726 + 0.205172i \(0.0657754\pi\)
−0.546985 + 0.837142i \(0.684225\pi\)
\(80\) 2.26715e8 + 9.39083e7i 0.618835 + 0.256330i
\(81\) 4.45700e7i 0.115043i
\(82\) 1.08345e8 2.61567e8i 0.264633 0.638882i
\(83\) −1.98863e8 + 1.98863e8i −0.459941 + 0.459941i −0.898636 0.438695i \(-0.855441\pi\)
0.438695 + 0.898636i \(0.355441\pi\)
\(84\) 6.30093e7 0.138086
\(85\) −1.37952e8 + 2.31855e8i −0.286644 + 0.481760i
\(86\) −3.07172e8 −0.605534
\(87\) 1.66480e8 1.66480e8i 0.311549 0.311549i
\(88\) −9.50232e6 + 2.29406e7i −0.0168911 + 0.0407787i
\(89\) 9.72872e8i 1.64362i 0.569763 + 0.821809i \(0.307035\pi\)
−0.569763 + 0.821809i \(0.692965\pi\)
\(90\) 2.42342e8 + 1.00382e8i 0.389348 + 0.161273i
\(91\) −2.39465e8 5.78121e8i −0.366064 0.883756i
\(92\) 1.16566e7 4.82831e6i 0.0169639 0.00702668i
\(93\) −1.24560e8 1.24560e8i −0.172665 0.172665i
\(94\) −1.05850e9 1.05850e9i −1.39835 1.39835i
\(95\) −6.92327e7 + 2.86771e7i −0.0872077 + 0.0361226i
\(96\) 9.48999e7 + 2.29109e8i 0.114037 + 0.275309i
\(97\) −1.18185e9 4.89538e8i −1.35547 0.561454i −0.417659 0.908604i \(-0.637149\pi\)
−0.937810 + 0.347150i \(0.887149\pi\)
\(98\) 1.87323e8i 0.205151i
\(99\) −1.30545e7 + 3.15165e7i −0.0136585 + 0.0329746i
\(100\) −1.28582e8 + 1.28582e8i −0.128582 + 0.128582i
\(101\) 8.97078e7 0.0857796 0.0428898 0.999080i \(-0.486344\pi\)
0.0428898 + 0.999080i \(0.486344\pi\)
\(102\) −6.86354e8 + 1.74281e8i −0.627837 + 0.159423i
\(103\) −1.43613e9 −1.25726 −0.628630 0.777705i \(-0.716384\pi\)
−0.628630 + 0.777705i \(0.716384\pi\)
\(104\) 7.37628e8 7.37628e8i 0.618283 0.618283i
\(105\) −1.39139e8 + 3.35910e8i −0.111711 + 0.269694i
\(106\) 4.71701e8i 0.362903i
\(107\) 2.04503e9 + 8.47080e8i 1.50825 + 0.624737i 0.975196 0.221344i \(-0.0710444\pi\)
0.533054 + 0.846081i \(0.321044\pi\)
\(108\) 1.37851e8 + 3.32801e8i 0.0974994 + 0.235384i
\(109\) 1.77706e9 7.36084e8i 1.20582 0.499468i 0.312947 0.949771i \(-0.398684\pi\)
0.892876 + 0.450302i \(0.148684\pi\)
\(110\) 3.65620e7 + 3.65620e7i 0.0238102 + 0.0238102i
\(111\) 6.27934e8 + 6.27934e8i 0.392610 + 0.392610i
\(112\) 1.66221e9 6.88510e8i 0.998171 0.413456i
\(113\) 1.10047e9 + 2.65678e9i 0.634932 + 1.53286i 0.833352 + 0.552743i \(0.186419\pi\)
−0.198420 + 0.980117i \(0.563581\pi\)
\(114\) −1.81718e8 7.52702e7i −0.100769 0.0417399i
\(115\) 7.28046e7i 0.0388167i
\(116\) −1.51404e8 + 3.65522e8i −0.0776384 + 0.187436i
\(117\) 1.01337e9 1.01337e9i 0.499957 0.499957i
\(118\) −2.42276e9 −1.15038
\(119\) 4.86821e8 + 1.91720e9i 0.222540 + 0.876406i
\(120\) −6.06118e8 −0.266834
\(121\) 1.66257e9 1.66257e9i 0.705090 0.705090i
\(122\) 4.42084e8 1.06729e9i 0.180670 0.436175i
\(123\) 8.98757e8i 0.354054i
\(124\) 2.73482e8 + 1.13280e8i 0.103880 + 0.0430284i
\(125\) −9.87118e8 2.38311e9i −0.361638 0.873071i
\(126\) 1.77679e9 7.35970e8i 0.628013 0.260131i
\(127\) −3.36229e9 3.36229e9i −1.14688 1.14688i −0.987163 0.159718i \(-0.948941\pi\)
−0.159718 0.987163i \(-0.551059\pi\)
\(128\) 2.59150e9 + 2.59150e9i 0.853310 + 0.853310i
\(129\) 9.00889e8 3.73161e8i 0.286430 0.118643i
\(130\) −8.31279e8 2.00688e9i −0.255271 0.616279i
\(131\) −3.07772e9 1.27483e9i −0.913080 0.378210i −0.123845 0.992302i \(-0.539523\pi\)
−0.789235 + 0.614092i \(0.789523\pi\)
\(132\) 2.84457e7i 0.00815519i
\(133\) −2.10253e8 + 5.07595e8i −0.0582652 + 0.140665i
\(134\) −3.76742e9 + 3.76742e9i −1.00942 + 1.00942i
\(135\) −2.07860e9 −0.538604
\(136\) −2.64221e9 + 1.97286e9i −0.662281 + 0.494506i
\(137\) 3.02387e8 0.0733366 0.0366683 0.999327i \(-0.488326\pi\)
0.0366683 + 0.999327i \(0.488326\pi\)
\(138\) −1.35124e8 + 1.35124e8i −0.0317158 + 0.0317158i
\(139\) −1.67307e9 + 4.03915e9i −0.380143 + 0.917747i 0.611794 + 0.791017i \(0.290448\pi\)
−0.991937 + 0.126730i \(0.959552\pi\)
\(140\) 6.10981e8i 0.134416i
\(141\) 4.39033e9 + 1.81853e9i 0.935429 + 0.387467i
\(142\) −2.00028e9 4.82911e9i −0.412851 0.996711i
\(143\) 2.60994e8 1.08107e8i 0.0521937 0.0216193i
\(144\) 2.91365e9 + 2.91365e9i 0.564684 + 0.564684i
\(145\) −1.61431e9 1.61431e9i −0.303270 0.303270i
\(146\) 2.73835e9 1.13426e9i 0.498771 0.206598i
\(147\) −2.27565e8 5.49391e8i −0.0401955 0.0970405i
\(148\) −1.37868e9 5.71069e8i −0.236204 0.0978388i
\(149\) 4.14348e9i 0.688696i 0.938842 + 0.344348i \(0.111900\pi\)
−0.938842 + 0.344348i \(0.888100\pi\)
\(150\) 1.05397e9 2.54450e9i 0.169987 0.410385i
\(151\) −1.77550e9 + 1.77550e9i −0.277923 + 0.277923i −0.832279 0.554356i \(-0.812964\pi\)
0.554356 + 0.832279i \(0.312964\pi\)
\(152\) −9.15907e8 −0.139173
\(153\) −3.62994e9 + 2.71037e9i −0.535535 + 0.399868i
\(154\) 3.79098e8 0.0543136
\(155\) −1.20782e9 + 1.20782e9i −0.168077 + 0.168077i
\(156\) 4.57318e8 1.10406e9i 0.0618241 0.149257i
\(157\) 1.22353e10i 1.60719i −0.595177 0.803594i \(-0.702918\pi\)
0.595177 0.803594i \(-0.297082\pi\)
\(158\) 9.18398e9 + 3.80413e9i 1.17240 + 0.485622i
\(159\) 5.73035e8 + 1.38343e9i 0.0711040 + 0.171660i
\(160\) 2.22159e9 9.20213e8i 0.267994 0.111007i
\(161\) 3.77442e8 + 3.77442e8i 0.0442725 + 0.0442725i
\(162\) 8.02117e8 + 8.02117e8i 0.0914998 + 0.0914998i
\(163\) 1.75318e9 7.26191e8i 0.194528 0.0805762i −0.283293 0.959033i \(-0.591427\pi\)
0.477821 + 0.878457i \(0.341427\pi\)
\(164\) −5.77965e8 1.39533e9i −0.0623885 0.150619i
\(165\) −1.51647e8 6.28144e7i −0.0159279 0.00659754i
\(166\) 7.15779e9i 0.731632i
\(167\) 3.67442e9 8.87084e9i 0.365565 0.882553i −0.628900 0.777486i \(-0.716494\pi\)
0.994465 0.105067i \(-0.0335056\pi\)
\(168\) −3.14231e9 + 3.14231e9i −0.304338 + 0.304338i
\(169\) −1.26349e9 −0.119147
\(170\) 1.68995e9 + 6.65534e9i 0.155186 + 0.611154i
\(171\) −1.25830e9 −0.112538
\(172\) −1.15867e9 + 1.15867e9i −0.100945 + 0.100945i
\(173\) 7.11789e9 1.71841e10i 0.604149 1.45854i −0.265125 0.964214i \(-0.585413\pi\)
0.869274 0.494331i \(-0.164587\pi\)
\(174\) 5.99223e9i 0.495584i
\(175\) −7.10757e9 2.94405e9i −0.572862 0.237287i
\(176\) 3.10830e8 + 7.50409e8i 0.0244183 + 0.0589510i
\(177\) 7.10561e9 2.94324e9i 0.544154 0.225396i
\(178\) 1.75086e10 + 1.75086e10i 1.30726 + 1.30726i
\(179\) 6.11560e8 + 6.11560e8i 0.0445247 + 0.0445247i 0.729019 0.684494i \(-0.239977\pi\)
−0.684494 + 0.729019i \(0.739977\pi\)
\(180\) 1.29278e9 5.35486e8i 0.0917905 0.0380209i
\(181\) 5.21259e9 + 1.25843e10i 0.360994 + 0.871516i 0.995155 + 0.0983156i \(0.0313455\pi\)
−0.634161 + 0.773201i \(0.718655\pi\)
\(182\) −1.47139e10 6.09471e9i −0.994049 0.411749i
\(183\) 3.66725e9i 0.241719i
\(184\) −3.40529e8 + 8.22109e8i −0.0219015 + 0.0528749i
\(185\) 6.08887e9 6.08887e9i 0.382177 0.382177i
\(186\) −4.48337e9 −0.274660
\(187\) −8.65523e8 + 2.19776e8i −0.0517596 + 0.0131430i
\(188\) −7.98548e9 −0.466220
\(189\) −1.07761e10 + 1.07761e10i −0.614307 + 0.614307i
\(190\) −7.29871e8 + 1.76206e9i −0.0406307 + 0.0980913i
\(191\) 1.73416e10i 0.942844i −0.881908 0.471422i \(-0.843741\pi\)
0.881908 0.471422i \(-0.156259\pi\)
\(192\) −6.13978e9 2.54318e9i −0.326060 0.135058i
\(193\) 8.71191e9 + 2.10324e10i 0.451966 + 1.09114i 0.971574 + 0.236737i \(0.0760780\pi\)
−0.519608 + 0.854405i \(0.673922\pi\)
\(194\) −3.00797e10 + 1.24594e10i −1.52463 + 0.631523i
\(195\) 4.87604e9 + 4.87604e9i 0.241497 + 0.241497i
\(196\) 7.06595e8 + 7.06595e8i 0.0341994 + 0.0341994i
\(197\) 1.61643e10 6.69549e9i 0.764645 0.316726i 0.0339440 0.999424i \(-0.489193\pi\)
0.730701 + 0.682697i \(0.239193\pi\)
\(198\) 3.32256e8 + 8.02136e8i 0.0153631 + 0.0370898i
\(199\) −2.58758e10 1.07181e10i −1.16965 0.484483i −0.288570 0.957459i \(-0.593180\pi\)
−0.881075 + 0.472976i \(0.843180\pi\)
\(200\) 1.28249e10i 0.566787i
\(201\) 6.47253e9 1.56261e10i 0.279699 0.675254i
\(202\) 1.61445e9 1.61445e9i 0.0682252 0.0682252i
\(203\) −1.67381e10 −0.691792
\(204\) −1.93157e9 + 3.24637e9i −0.0780863 + 0.131239i
\(205\) 8.71495e9 0.344645
\(206\) −2.58457e10 + 2.58457e10i −0.999966 + 0.999966i
\(207\) −4.67828e8 + 1.12944e9i −0.0177100 + 0.0427558i
\(208\) 3.41228e10i 1.26404i
\(209\) −2.29155e8 9.49192e7i −0.00830752 0.00344109i
\(210\) 3.54126e9 + 8.54936e9i 0.125653 + 0.303352i
\(211\) −3.18357e10 + 1.31868e10i −1.10572 + 0.458003i −0.859460 0.511202i \(-0.829200\pi\)
−0.246256 + 0.969205i \(0.579200\pi\)
\(212\) −1.77929e9 1.77929e9i −0.0604972 0.0604972i
\(213\) 1.17331e10 + 1.17331e10i 0.390574 + 0.390574i
\(214\) 5.20488e10 2.15593e10i 1.69648 0.702705i
\(215\) −3.61842e9 8.73563e9i −0.115490 0.278818i
\(216\) −2.34716e10 9.72226e9i −0.733670 0.303896i
\(217\) 1.25234e10i 0.383402i
\(218\) 1.87343e10 4.52286e10i 0.561802 1.35631i
\(219\) −6.65325e9 + 6.65325e9i −0.195450 + 0.195450i
\(220\) 2.75829e8 0.00793848
\(221\) 3.71269e10 + 5.38472e9i 1.04694 + 0.151844i
\(222\) 2.26016e10 0.624527
\(223\) −3.91078e10 + 3.91078e10i −1.05899 + 1.05899i −0.0608404 + 0.998148i \(0.519378\pi\)
−0.998148 + 0.0608404i \(0.980622\pi\)
\(224\) 6.74676e9 1.62881e10i 0.179052 0.432270i
\(225\) 1.76192e10i 0.458316i
\(226\) 6.76186e10 + 2.80085e10i 1.72416 + 0.714171i
\(227\) 1.91727e10 + 4.62870e10i 0.479255 + 1.15702i 0.959959 + 0.280141i \(0.0903814\pi\)
−0.480703 + 0.876883i \(0.659619\pi\)
\(228\) −9.69379e8 + 4.01530e8i −0.0237567 + 0.00984036i
\(229\) 5.11775e10 + 5.11775e10i 1.22976 + 1.22976i 0.964056 + 0.265701i \(0.0856033\pi\)
0.265701 + 0.964056i \(0.414397\pi\)
\(230\) 1.31025e9 + 1.31025e9i 0.0308730 + 0.0308730i
\(231\) −1.11184e9 + 4.60539e8i −0.0256914 + 0.0106417i
\(232\) −1.06781e10 2.57793e10i −0.241991 0.584219i
\(233\) 4.12045e10 + 1.70675e10i 0.915890 + 0.379374i 0.790309 0.612709i \(-0.209920\pi\)
0.125582 + 0.992083i \(0.459920\pi\)
\(234\) 3.64749e10i 0.795286i
\(235\) 1.76337e10 4.25716e10i 0.377171 0.910572i
\(236\) −9.13883e9 + 9.13883e9i −0.191773 + 0.191773i
\(237\) −3.15566e10 −0.649715
\(238\) 4.32646e10 + 2.57422e10i 0.874051 + 0.520055i
\(239\) −6.46746e10 −1.28216 −0.641081 0.767473i \(-0.721514\pi\)
−0.641081 + 0.767473i \(0.721514\pi\)
\(240\) −1.40196e10 + 1.40196e10i −0.272762 + 0.272762i
\(241\) −2.67036e9 + 6.44682e9i −0.0509909 + 0.123103i −0.947322 0.320282i \(-0.896222\pi\)
0.896331 + 0.443385i \(0.146222\pi\)
\(242\) 5.98418e10i 1.12159i
\(243\) −5.15740e10 2.13626e10i −0.948860 0.393031i
\(244\) −2.35830e9 5.69344e9i −0.0425937 0.102830i
\(245\) −5.32726e9 + 2.20662e9i −0.0944619 + 0.0391274i
\(246\) 1.61748e10 + 1.61748e10i 0.281598 + 0.281598i
\(247\) 7.36820e9 + 7.36820e9i 0.125958 + 0.125958i
\(248\) −1.92880e10 + 7.98935e9i −0.323783 + 0.134115i
\(249\) −8.69548e9 2.09927e10i −0.143350 0.346077i
\(250\) −6.06534e10 2.51235e10i −0.982031 0.406770i
\(251\) 4.27892e10i 0.680460i 0.940342 + 0.340230i \(0.110505\pi\)
−0.940342 + 0.340230i \(0.889495\pi\)
\(252\) 3.92604e9 9.47830e9i 0.0613271 0.148057i
\(253\) −1.70397e8 + 1.70397e8i −0.00261469 + 0.00261469i
\(254\) −1.21021e11 −1.82435
\(255\) −1.30415e10 1.74661e10i −0.193150 0.258682i
\(256\) 5.11640e10 0.744534
\(257\) −2.02385e10 + 2.02385e10i −0.289387 + 0.289387i −0.836838 0.547451i \(-0.815598\pi\)
0.547451 + 0.836838i \(0.315598\pi\)
\(258\) 9.49744e9 2.29288e10i 0.133450 0.322176i
\(259\) 6.31333e10i 0.871786i
\(260\) −1.07057e10 4.43447e9i −0.145290 0.0601813i
\(261\) −1.46699e10 3.54163e10i −0.195680 0.472413i
\(262\) −7.83322e10 + 3.24462e10i −1.02703 + 0.425411i
\(263\) 8.12031e10 + 8.12031e10i 1.04658 + 1.04658i 0.998861 + 0.0477174i \(0.0151947\pi\)
0.0477174 + 0.998861i \(0.484805\pi\)
\(264\) −1.41860e9 1.41860e9i −0.0179739 0.0179739i
\(265\) 1.34147e10 5.55653e9i 0.167099 0.0692146i
\(266\) 5.35122e9 + 1.29190e10i 0.0655368 + 0.158220i
\(267\) −7.26201e10 3.00802e10i −0.874492 0.362226i
\(268\) 2.84219e10i 0.336548i
\(269\) 3.18504e10 7.68937e10i 0.370877 0.895376i −0.622726 0.782440i \(-0.713975\pi\)
0.993602 0.112935i \(-0.0360253\pi\)
\(270\) −3.74083e10 + 3.74083e10i −0.428381 + 0.428381i
\(271\) 2.33646e10 0.263146 0.131573 0.991307i \(-0.457997\pi\)
0.131573 + 0.991307i \(0.457997\pi\)
\(272\) −1.54821e10 + 1.06747e11i −0.171503 + 1.18249i
\(273\) 5.05578e10 0.550879
\(274\) 5.44200e9 5.44200e9i 0.0583285 0.0583285i
\(275\) 1.32910e9 3.20873e9i 0.0140139 0.0338326i
\(276\) 1.01939e9i 0.0105743i
\(277\) 1.17836e11 + 4.88092e10i 1.20259 + 0.498130i 0.891836 0.452359i \(-0.149417\pi\)
0.310757 + 0.950489i \(0.399417\pi\)
\(278\) 4.25819e10 + 1.02802e11i 0.427585 + 1.03228i
\(279\) −2.64984e10 + 1.09760e10i −0.261818 + 0.108449i
\(280\) 3.04699e10 + 3.04699e10i 0.296251 + 0.296251i
\(281\) −3.28616e10 3.28616e10i −0.314420 0.314420i 0.532199 0.846619i \(-0.321366\pi\)
−0.846619 + 0.532199i \(0.821366\pi\)
\(282\) 1.11740e11 4.62841e10i 1.05217 0.435824i
\(283\) 1.60474e10 + 3.87419e10i 0.148719 + 0.359039i 0.980630 0.195870i \(-0.0627531\pi\)
−0.831911 + 0.554909i \(0.812753\pi\)
\(284\) −2.57609e10 1.06705e10i −0.234979 0.0973315i
\(285\) 6.05454e9i 0.0543600i
\(286\) 2.75147e9 6.64264e9i 0.0243175 0.0587075i
\(287\) 4.51811e10 4.51811e10i 0.393086 0.393086i
\(288\) 4.03772e10 0.345836
\(289\) −1.13702e11 3.36903e10i −0.958796 0.284095i
\(290\) −5.81047e10 −0.482415
\(291\) 7.30832e10 7.30832e10i 0.597446 0.597446i
\(292\) 6.05073e9 1.46078e10i 0.0487063 0.117587i
\(293\) 1.45256e11i 1.15141i −0.817658 0.575705i \(-0.804728\pi\)
0.817658 0.575705i \(-0.195272\pi\)
\(294\) −1.39827e10 5.79183e9i −0.109151 0.0452119i
\(295\) −2.85396e10 6.89007e10i −0.219406 0.529694i
\(296\) 9.72351e10 4.02761e10i 0.736224 0.304954i
\(297\) −4.86492e9 4.86492e9i −0.0362803 0.0362803i
\(298\) 7.45695e10 + 7.45695e10i 0.547757 + 0.547757i
\(299\) 9.35308e9 3.87417e9i 0.0676759 0.0280323i
\(300\) −5.62239e9 1.35737e10i −0.0400752 0.0967500i
\(301\) −6.40473e10 2.65293e10i −0.449730 0.186284i
\(302\) 6.39067e10i 0.442095i
\(303\) −2.77367e9 + 6.69624e9i −0.0189044 + 0.0456393i
\(304\) −2.11850e10 + 2.11850e10i −0.142265 + 0.142265i
\(305\) 3.55601e10 0.235295
\(306\) −1.65493e10 + 1.14105e11i −0.107903 + 0.743977i
\(307\) −1.59150e11 −1.02255 −0.511275 0.859417i \(-0.670827\pi\)
−0.511275 + 0.859417i \(0.670827\pi\)
\(308\) 1.42998e9 1.42998e9i 0.00905426 0.00905426i
\(309\) 4.44035e10 1.07200e11i 0.277079 0.668929i
\(310\) 4.34737e10i 0.267362i
\(311\) 5.95397e10 + 2.46622e10i 0.360899 + 0.149489i 0.555762 0.831341i \(-0.312426\pi\)
−0.194864 + 0.980830i \(0.562426\pi\)
\(312\) 3.22535e10 + 7.78669e10i 0.192700 + 0.465219i
\(313\) 1.35521e11 5.61348e10i 0.798102 0.330584i 0.0539057 0.998546i \(-0.482833\pi\)
0.744196 + 0.667962i \(0.232833\pi\)
\(314\) −2.20197e11 2.20197e11i −1.27828 1.27828i
\(315\) 4.18604e10 + 4.18604e10i 0.239555 + 0.239555i
\(316\) 4.89920e10 2.02932e10i 0.276397 0.114487i
\(317\) 1.03220e11 + 2.49194e11i 0.574110 + 1.38603i 0.898027 + 0.439940i \(0.145000\pi\)
−0.323917 + 0.946086i \(0.605000\pi\)
\(318\) 3.52101e10 + 1.45845e10i 0.193084 + 0.0799779i
\(319\) 7.55648e9i 0.0408565i
\(320\) −2.46604e10 + 5.95354e10i −0.131469 + 0.317395i
\(321\) −1.26461e11 + 1.26461e11i −0.664787 + 0.664787i
\(322\) 1.35855e10 0.0704246
\(323\) −1.97070e10 2.63932e10i −0.100742 0.134921i
\(324\) 6.05128e9 0.0305067
\(325\) −1.03173e11 + 1.03173e11i −0.512967 + 0.512967i
\(326\) 1.84825e10 4.46208e10i 0.0906321 0.218805i
\(327\) 1.55408e11i 0.751637i
\(328\) 9.84092e10 + 4.07624e10i 0.469465 + 0.194459i
\(329\) −1.29286e11 3.12123e11i −0.608372 1.46874i
\(330\) −3.85963e9 + 1.59871e9i −0.0179157 + 0.00742091i
\(331\) −4.83018e10 4.83018e10i −0.221175 0.221175i 0.587818 0.808993i \(-0.299987\pi\)
−0.808993 + 0.587818i \(0.799987\pi\)
\(332\) 2.69997e10 + 2.69997e10i 0.121966 + 0.121966i
\(333\) 1.33584e11 5.53324e10i 0.595327 0.246593i
\(334\) −9.35190e10 2.25775e11i −0.411188 0.992696i
\(335\) −1.51521e11 6.27619e10i −0.657310 0.272267i
\(336\) 1.45364e11i 0.622199i
\(337\) −1.27264e11 + 3.07241e11i −0.537489 + 1.29761i 0.388982 + 0.921246i \(0.372827\pi\)
−0.926470 + 0.376368i \(0.877173\pi\)
\(338\) −2.27388e10 + 2.27388e10i −0.0947638 + 0.0947638i
\(339\) −2.32341e11 −0.955492
\(340\) 3.14790e10 + 1.87298e10i 0.127751 + 0.0760113i
\(341\) −5.65373e9 −0.0226433
\(342\) −2.26453e10 + 2.26453e10i −0.0895079 + 0.0895079i
\(343\) −1.04881e11 + 2.53205e11i −0.409141 + 0.987755i
\(344\) 1.15567e11i 0.444960i
\(345\) −5.43450e9 2.25104e9i −0.0206525 0.00855456i
\(346\) −1.81160e11 4.37359e11i −0.679547 1.64057i
\(347\) 4.54077e11 1.88085e11i 1.68131 0.696420i 0.681919 0.731427i \(-0.261145\pi\)
0.999387 + 0.0350075i \(0.0111455\pi\)
\(348\) −2.26031e10 2.26031e10i −0.0826155 0.0826155i
\(349\) −2.61028e11 2.61028e11i −0.941832 0.941832i 0.0565669 0.998399i \(-0.481985\pi\)
−0.998399 + 0.0565669i \(0.981985\pi\)
\(350\) −1.80897e11 + 7.49300e10i −0.644355 + 0.266901i
\(351\) 1.10609e11 + 2.67035e11i 0.388965 + 0.939044i
\(352\) 7.35331e9 + 3.04584e9i 0.0255294 + 0.0105746i
\(353\) 6.87046e10i 0.235505i 0.993043 + 0.117752i \(0.0375689\pi\)
−0.993043 + 0.117752i \(0.962431\pi\)
\(354\) 7.49094e10 1.80847e11i 0.253525 0.612064i
\(355\) 1.13772e11 1.13772e11i 0.380195 0.380195i
\(356\) 1.32087e11 0.435849
\(357\) −1.58161e11 2.29390e10i −0.515339 0.0747425i
\(358\) 2.20123e10 0.0708258
\(359\) 2.01838e11 2.01838e11i 0.641325 0.641325i −0.309556 0.950881i \(-0.600180\pi\)
0.950881 + 0.309556i \(0.100180\pi\)
\(360\) −3.77665e10 + 9.11764e10i −0.118507 + 0.286102i
\(361\) 3.13539e11i 0.971647i
\(362\) 3.20287e11 + 1.32667e11i 0.980282 + 0.406046i
\(363\) 7.26974e10 + 1.75507e11i 0.219755 + 0.530536i
\(364\) −7.84917e10 + 3.25123e10i −0.234351 + 0.0970715i
\(365\) 6.45143e10 + 6.45143e10i 0.190256 + 0.190256i
\(366\) 6.59987e10 + 6.59987e10i 0.192252 + 0.192252i
\(367\) 1.48959e11 6.17008e10i 0.428617 0.177539i −0.157937 0.987449i \(-0.550484\pi\)
0.586554 + 0.809910i \(0.300484\pi\)
\(368\) 1.11390e10 + 2.68919e10i 0.0316615 + 0.0764376i
\(369\) 1.35197e11 + 5.60005e10i 0.379620 + 0.157244i
\(370\) 2.19161e11i 0.607932i
\(371\) 4.07390e10 9.83527e10i 0.111642 0.269528i
\(372\) −1.69116e10 + 1.69116e10i −0.0457868 + 0.0457868i
\(373\) 1.20896e10 0.0323388 0.0161694 0.999869i \(-0.494853\pi\)
0.0161694 + 0.999869i \(0.494853\pi\)
\(374\) −1.16214e10 + 1.95319e10i −0.0307139 + 0.0516206i
\(375\) 2.08408e11 0.544219
\(376\) 3.98240e11 3.98240e11i 1.02754 1.02754i
\(377\) −1.21485e11 + 2.93290e11i −0.309731 + 0.747757i
\(378\) 3.87873e11i 0.977183i
\(379\) −3.11000e11 1.28820e11i −0.774254 0.320707i −0.0396600 0.999213i \(-0.512627\pi\)
−0.734594 + 0.678507i \(0.762627\pi\)
\(380\) 3.89350e9 + 9.39975e9i 0.00957887 + 0.0231254i
\(381\) 3.54937e11 1.47020e11i 0.862956 0.357448i
\(382\) −3.12094e11 3.12094e11i −0.749895 0.749895i
\(383\) 1.95748e11 + 1.95748e11i 0.464840 + 0.464840i 0.900238 0.435398i \(-0.143392\pi\)
−0.435398 + 0.900238i \(0.643392\pi\)
\(384\) −2.73569e11 + 1.13316e11i −0.642062 + 0.265951i
\(385\) 4.46569e9 + 1.07811e10i 0.0103589 + 0.0250087i
\(386\) 5.35303e11 + 2.21730e11i 1.22732 + 0.508371i
\(387\) 1.58769e11i 0.359805i
\(388\) −6.64648e10 + 1.60460e11i −0.148884 + 0.359439i
\(389\) 1.11941e11 1.11941e11i 0.247866 0.247866i −0.572228 0.820094i \(-0.693921\pi\)
0.820094 + 0.572228i \(0.193921\pi\)
\(390\) 1.75506e11 0.384151
\(391\) −3.10172e10 + 7.87599e9i −0.0671131 + 0.0170416i
\(392\) −7.04764e10 −0.150750
\(393\) 1.90320e11 1.90320e11i 0.402456 0.402456i
\(394\) 1.70409e11 4.11404e11i 0.356254 0.860074i
\(395\) 3.05994e11i 0.632450i
\(396\) 4.27900e9 + 1.77242e9i 0.00874408 + 0.00362192i
\(397\) 1.04553e11 + 2.52413e11i 0.211241 + 0.509982i 0.993615 0.112828i \(-0.0359910\pi\)
−0.782373 + 0.622810i \(0.785991\pi\)
\(398\) −6.58573e11 + 2.72790e11i −1.31562 + 0.544947i
\(399\) −3.13886e10 3.13886e10i −0.0620004 0.0620004i
\(400\) −2.96642e11 2.96642e11i −0.579378 0.579378i
\(401\) −8.51169e11 + 3.52566e11i −1.64386 + 0.680911i −0.996680 0.0814226i \(-0.974054\pi\)
−0.647184 + 0.762333i \(0.724054\pi\)
\(402\) −1.64734e11 3.97704e11i −0.314606 0.759526i
\(403\) 2.19438e11 + 9.08943e10i 0.414419 + 0.171658i
\(404\) 1.21797e10i 0.0227467i
\(405\) −1.33626e10 + 3.22601e10i −0.0246798 + 0.0595824i
\(406\) −3.01233e11 + 3.01233e11i −0.550219 + 0.550219i
\(407\) 2.85017e10 0.0514868
\(408\) −6.55697e10 2.58227e11i −0.117147 0.461350i
\(409\) −8.51756e11 −1.50508 −0.752541 0.658545i \(-0.771172\pi\)
−0.752541 + 0.658545i \(0.771172\pi\)
\(410\) 1.56841e11 1.56841e11i 0.274115 0.274115i
\(411\) −9.34949e9 + 2.25717e10i −0.0161622 + 0.0390189i
\(412\) 1.94983e11i 0.333396i
\(413\) −5.05162e11 2.09245e11i −0.854388 0.353899i
\(414\) 1.19068e10 + 2.87456e10i 0.0199203 + 0.0480917i
\(415\) −2.03560e11 + 8.43172e10i −0.336880 + 0.139540i
\(416\) −2.36436e11 2.36436e11i −0.387074 0.387074i
\(417\) −2.49773e11 2.49773e11i −0.404513 0.404513i
\(418\) −5.83230e9 + 2.41582e9i −0.00934430 + 0.00387054i
\(419\) 6.92759e10 + 1.67247e11i 0.109804 + 0.265091i 0.969224 0.246179i \(-0.0791752\pi\)
−0.859420 + 0.511270i \(0.829175\pi\)
\(420\) 4.56067e10 + 1.88909e10i 0.0715165 + 0.0296231i
\(421\) 4.26322e11i 0.661406i −0.943735 0.330703i \(-0.892714\pi\)
0.943735 0.330703i \(-0.107286\pi\)
\(422\) −3.35621e11 + 8.10262e11i −0.515162 + 1.24371i
\(423\) 5.47113e11 5.47113e11i 0.830893 0.830893i
\(424\) 1.77468e11 0.266670
\(425\) 3.69568e11 2.75946e11i 0.549471 0.410274i
\(426\) 4.22315e11 0.621289
\(427\) 1.84355e11 1.84355e11i 0.268367 0.268367i
\(428\) 1.15008e11 2.77655e11i 0.165666 0.399952i
\(429\) 2.28245e10i 0.0325344i
\(430\) −2.22333e11 9.20935e10i −0.313615 0.129904i
\(431\) 1.27320e10 + 3.07378e10i 0.0177725 + 0.0429067i 0.932517 0.361127i \(-0.117608\pi\)
−0.914744 + 0.404034i \(0.867608\pi\)
\(432\) −7.67778e11 + 3.18024e11i −1.06062 + 0.439322i
\(433\) 6.04122e11 + 6.04122e11i 0.825904 + 0.825904i 0.986947 0.161044i \(-0.0514860\pi\)
−0.161044 + 0.986947i \(0.551486\pi\)
\(434\) 2.25382e11 + 2.25382e11i 0.304940 + 0.304940i
\(435\) 1.70413e11 7.05872e10i 0.228192 0.0945201i
\(436\) −9.99384e10 2.41273e11i −0.132447 0.319756i
\(437\) −8.21209e9 3.40156e9i −0.0107718 0.00446181i
\(438\) 2.39474e11i 0.310903i
\(439\) −1.22952e11 + 2.96834e11i −0.157996 + 0.381437i −0.982978 0.183722i \(-0.941185\pi\)
0.824982 + 0.565159i \(0.191185\pi\)
\(440\) −1.37557e10 + 1.37557e10i −0.0174963 + 0.0174963i
\(441\) −9.68224e10 −0.121900
\(442\) 7.65073e11 5.71257e11i 0.953460 0.711921i
\(443\) 1.17716e12 1.45218 0.726089 0.687601i \(-0.241336\pi\)
0.726089 + 0.687601i \(0.241336\pi\)
\(444\) 8.52549e10 8.52549e10i 0.104111 0.104111i
\(445\) −2.91678e11 + 7.04173e11i −0.352601 + 0.851254i
\(446\) 1.40763e12i 1.68454i
\(447\) −3.09290e11 1.28112e11i −0.366423 0.151777i
\(448\) 1.80803e11 + 4.36498e11i 0.212058 + 0.511954i
\(449\) −3.84889e10 + 1.59426e10i −0.0446918 + 0.0185119i −0.404917 0.914353i \(-0.632700\pi\)
0.360226 + 0.932865i \(0.382700\pi\)
\(450\) −3.17090e11 3.17090e11i −0.364524 0.364524i
\(451\) 2.03971e10 + 2.03971e10i 0.0232153 + 0.0232153i
\(452\) 3.60712e11 1.49412e11i 0.406479 0.168369i
\(453\) −7.76356e10 1.87429e11i −0.0866202 0.209120i
\(454\) 1.17807e12 + 4.87971e11i 1.30142 + 0.539067i
\(455\) 4.90243e11i 0.536241i
\(456\) 2.83189e10 6.83678e10i 0.0306715 0.0740474i
\(457\) 6.76392e11 6.76392e11i 0.725397 0.725397i −0.244302 0.969699i \(-0.578559\pi\)
0.969699 + 0.244302i \(0.0785590\pi\)
\(458\) 1.84206e12 1.95618
\(459\) −2.24863e11 8.85556e11i −0.236462 0.931234i
\(460\) 9.88471e9 0.0102933
\(461\) −1.02810e12 + 1.02810e12i −1.06018 + 1.06018i −0.0621115 + 0.998069i \(0.519783\pi\)
−0.998069 + 0.0621115i \(0.980217\pi\)
\(462\) −1.17213e10 + 2.82978e10i −0.0119698 + 0.0288977i
\(463\) 3.76717e11i 0.380978i −0.981689 0.190489i \(-0.938993\pi\)
0.981689 0.190489i \(-0.0610074\pi\)
\(464\) −8.43266e11 3.49292e11i −0.844566 0.349831i
\(465\) −5.28130e10 1.27502e11i −0.0523845 0.126467i
\(466\) 1.04871e12 4.34390e11i 1.03019 0.426720i
\(467\) −5.72661e11 5.72661e11i −0.557150 0.557150i 0.371345 0.928495i \(-0.378897\pi\)
−0.928495 + 0.371345i \(0.878897\pi\)
\(468\) −1.37586e11 1.37586e11i −0.132577 0.132577i
\(469\) −1.11091e12 + 4.60154e11i −1.06023 + 0.439162i
\(470\) −4.48802e11 1.08350e12i −0.424242 1.02421i
\(471\) 9.13305e11 + 3.78303e11i 0.855110 + 0.354198i
\(472\) 9.11516e11i 0.845328i
\(473\) 1.19767e10 2.89143e10i 0.0110018 0.0265606i
\(474\) −5.67919e11 + 5.67919e11i −0.516754 + 0.516754i
\(475\) 1.28109e11 0.115467
\(476\) 2.60298e11 6.60958e10i 0.232402 0.0590123i
\(477\) 2.43810e11 0.215635
\(478\) −1.16394e12 + 1.16394e12i −1.01977 + 1.01977i
\(479\) −1.02463e11 + 2.47369e11i −0.0889322 + 0.214701i −0.962088 0.272741i \(-0.912070\pi\)
0.873155 + 0.487442i \(0.162070\pi\)
\(480\) 1.94283e11i 0.167051i
\(481\) −1.10624e12 4.58218e11i −0.942313 0.390319i
\(482\) 6.79642e10 + 1.64080e11i 0.0573546 + 0.138466i
\(483\) −3.98443e10 + 1.65040e10i −0.0333122 + 0.0137984i
\(484\) −2.25727e11 2.25727e11i −0.186973 0.186973i
\(485\) −7.08663e11 7.08663e11i −0.581570 0.581570i
\(486\) −1.31263e12 + 5.43707e11i −1.06728 + 0.442081i
\(487\) 3.41055e11 + 8.23380e11i 0.274754 + 0.663315i 0.999674 0.0255175i \(-0.00812335\pi\)
−0.724920 + 0.688833i \(0.758123\pi\)
\(488\) 4.01544e11 + 1.66325e11i 0.320512 + 0.132760i
\(489\) 1.53319e11i 0.121257i
\(490\) −5.61615e10 + 1.35586e11i −0.0440105 + 0.106251i
\(491\) 1.07530e12 1.07530e12i 0.834959 0.834959i −0.153232 0.988190i \(-0.548968\pi\)
0.988190 + 0.153232i \(0.0489681\pi\)
\(492\) 1.22025e11 0.0938868
\(493\) 5.13113e11 8.62384e11i 0.391203 0.657491i
\(494\) 2.65208e11 0.200362
\(495\) −1.88980e10 + 1.88980e10i −0.0141479 + 0.0141479i
\(496\) −2.61339e11 + 6.30928e11i −0.193882 + 0.468072i
\(497\) 1.17966e12i 0.867265i
\(498\) −5.34293e11 2.21312e11i −0.389267 0.161240i
\(499\) 6.43615e11 + 1.55382e12i 0.464701 + 1.12189i 0.966445 + 0.256872i \(0.0826919\pi\)
−0.501744 + 0.865016i \(0.667308\pi\)
\(500\) −3.23556e11 + 1.34021e11i −0.231518 + 0.0958979i
\(501\) 5.48555e11 + 5.48555e11i 0.389000 + 0.389000i
\(502\) 7.70070e11 + 7.70070e11i 0.541207 + 0.541207i
\(503\) −1.56183e12 + 6.46931e11i −1.08787 + 0.450611i −0.853264 0.521479i \(-0.825381\pi\)
−0.234608 + 0.972090i \(0.575381\pi\)
\(504\) 2.76894e11 + 6.68481e11i 0.191151 + 0.461479i
\(505\) 6.49312e10 + 2.68954e10i 0.0444265 + 0.0184021i
\(506\) 6.13321e9i 0.00415921i
\(507\) 3.90658e10 9.43132e10i 0.0262580 0.0633923i
\(508\) −4.56499e11 + 4.56499e11i −0.304126 + 0.304126i
\(509\) −5.84673e11 −0.386085 −0.193043 0.981190i \(-0.561836\pi\)
−0.193043 + 0.981190i \(0.561836\pi\)
\(510\) −5.49040e11 7.96303e10i −0.359367 0.0521210i
\(511\) 6.68926e11 0.433994
\(512\) −4.06061e11 + 4.06061e11i −0.261142 + 0.261142i
\(513\) 9.71161e10 2.34459e11i 0.0619103 0.149465i
\(514\) 7.28456e11i 0.460330i
\(515\) −1.03948e12 4.30566e11i −0.651153 0.269716i
\(516\) −5.06642e10 1.22314e11i −0.0314613 0.0759544i
\(517\) 1.40909e11 5.83663e10i 0.0867422 0.0359298i
\(518\) −1.13620e12 1.13620e12i −0.693378 0.693378i
\(519\) 1.06263e12 + 1.06263e12i 0.642879 + 0.642879i
\(520\) 7.55050e11 3.12752e11i 0.452856 0.187579i
\(521\) −5.60234e11 1.35252e12i −0.333119 0.804221i −0.998341 0.0575754i \(-0.981663\pi\)
0.665222 0.746646i \(-0.268337\pi\)
\(522\) −9.01393e11 3.73369e11i −0.531370 0.220101i
\(523\) 1.26928e12i 0.741822i 0.928668 + 0.370911i \(0.120955\pi\)
−0.928668 + 0.370911i \(0.879045\pi\)
\(524\) −1.73085e11 + 4.17864e11i −0.100292 + 0.242127i
\(525\) 4.39517e11 4.39517e11i 0.252499 0.252499i
\(526\) 2.92279e12 1.66480
\(527\) −6.45232e11 3.83909e11i −0.364392 0.216811i
\(528\) −6.56248e10 −0.0367465
\(529\) 1.26750e12 1.26750e12i 0.703716 0.703716i
\(530\) 1.41421e11 3.41421e11i 0.0778526 0.187953i
\(531\) 1.25226e12i 0.683551i
\(532\) 6.89164e10 + 2.85461e10i 0.0373010 + 0.0154506i
\(533\) −4.63751e11 1.11959e12i −0.248893 0.600881i
\(534\) −1.84828e12 + 7.65581e11i −0.983629 + 0.407433i
\(535\) 1.22625e12 + 1.22625e12i 0.647121 + 0.647121i
\(536\) −1.41742e12 1.41742e12i −0.741747 0.741747i
\(537\) −6.45587e10 + 2.67411e10i −0.0335020 + 0.0138770i
\(538\) −8.10635e11 1.95705e12i −0.417162 1.00712i
\(539\) −1.76328e10 7.30376e9i −0.00899856 0.00372732i
\(540\) 2.82213e11i 0.142825i
\(541\) −1.02244e12 + 2.46839e12i −0.513158 + 1.23887i 0.428879 + 0.903362i \(0.358909\pi\)
−0.942037 + 0.335510i \(0.891091\pi\)
\(542\) 4.20488e11 4.20488e11i 0.209294 0.209294i
\(543\) −1.10052e12 −0.543250
\(544\) 6.32373e11 + 8.46924e11i 0.309584 + 0.414619i
\(545\) 1.50694e12 0.731663
\(546\) 9.09880e11 9.09880e11i 0.438144 0.438144i
\(547\) 5.19582e11 1.25438e12i 0.248148 0.599083i −0.749899 0.661553i \(-0.769898\pi\)
0.998047 + 0.0624701i \(0.0198978\pi\)
\(548\) 4.10552e10i 0.0194471i
\(549\) 5.51652e11 + 2.28502e11i 0.259173 + 0.107353i
\(550\) −3.38273e10 8.16664e10i −0.0157629 0.0380550i
\(551\) 2.57511e11 1.06665e11i 0.119018 0.0492990i
\(552\) −5.08375e10 5.08375e10i −0.0233055 0.0233055i
\(553\) 1.58637e12 + 1.58637e12i 0.721343 + 0.721343i
\(554\) 2.99908e12 1.24226e12i 1.35268 0.560297i
\(555\) 2.66242e11 + 6.42766e11i 0.119113 + 0.287564i
\(556\) 5.48397e11 + 2.27153e11i 0.243365 + 0.100805i
\(557\) 2.10630e11i 0.0927199i −0.998925 0.0463599i \(-0.985238\pi\)
0.998925 0.0463599i \(-0.0147621\pi\)
\(558\) −2.79353e11 + 6.74419e11i −0.121983 + 0.294494i
\(559\) −9.29703e11 + 9.29703e11i −0.402709 + 0.402709i
\(560\) 1.40954e12 0.605665
\(561\) 1.03559e10 7.14022e10i 0.00441422 0.0304354i
\(562\) −1.18281e12 −0.500151
\(563\) 1.29784e12 1.29784e12i 0.544418 0.544418i −0.380403 0.924821i \(-0.624215\pi\)
0.924821 + 0.380403i \(0.124215\pi\)
\(564\) 2.46903e11 5.96076e11i 0.102747 0.248054i
\(565\) 2.25293e12i 0.930101i
\(566\) 9.86032e11 + 4.08428e11i 0.403847 + 0.167279i
\(567\) 9.79708e10 + 2.36522e11i 0.0398082 + 0.0961055i
\(568\) 1.81685e12 7.52565e11i 0.732407 0.303373i
\(569\) 2.51282e12 + 2.51282e12i 1.00498 + 1.00498i 0.999988 + 0.00499102i \(0.00158870\pi\)
0.00499102 + 0.999988i \(0.498411\pi\)
\(570\) −1.08962e11 1.08962e11i −0.0432354 0.0432354i
\(571\) −2.66365e12 + 1.10332e12i −1.04861 + 0.434350i −0.839396 0.543520i \(-0.817091\pi\)
−0.209217 + 0.977869i \(0.567091\pi\)
\(572\) −1.46778e10 3.54353e10i −0.00573294 0.0138406i
\(573\) 1.29447e12 + 5.36185e11i 0.501643 + 0.207787i
\(574\) 1.62623e12i 0.625286i
\(575\) 4.76301e10 1.14989e11i 0.0181709 0.0438684i
\(576\) −7.65125e11 + 7.65125e11i −0.289622 + 0.289622i
\(577\) −1.69258e12 −0.635710 −0.317855 0.948139i \(-0.602963\pi\)
−0.317855 + 0.948139i \(0.602963\pi\)
\(578\) −2.65258e12 + 1.43995e12i −0.988539 + 0.536626i
\(579\) −1.83933e12 −0.680151
\(580\) −2.19175e11 + 2.19175e11i −0.0804202 + 0.0804202i
\(581\) −6.18191e11 + 1.49245e12i −0.225077 + 0.543383i
\(582\) 2.63053e12i 0.950363i
\(583\) 4.44016e10 + 1.83917e10i 0.0159180 + 0.00659347i
\(584\) 4.26743e11 + 1.03025e12i 0.151813 + 0.366509i
\(585\) 1.03731e12 4.29667e11i 0.366190 0.151681i
\(586\) −2.61414e12 2.61414e12i −0.915778 0.915778i
\(587\) −8.07074e11 8.07074e11i −0.280570 0.280570i 0.552766 0.833336i \(-0.313572\pi\)
−0.833336 + 0.552766i \(0.813572\pi\)
\(588\) −7.45910e10 + 3.08966e10i −0.0257329 + 0.0106589i
\(589\) −7.98060e10 1.92669e11i −0.0273223 0.0659618i
\(590\) −1.75362e12 7.26371e11i −0.595800 0.246788i
\(591\) 1.41360e12i 0.476633i
\(592\) 1.31747e12 3.18065e12i 0.440851 1.06431i
\(593\) −1.98187e12 + 1.98187e12i −0.658157 + 0.658157i −0.954944 0.296787i \(-0.904085\pi\)
0.296787 + 0.954944i \(0.404085\pi\)
\(594\) −1.75106e11 −0.0577115
\(595\) −2.22432e11 + 1.53364e12i −0.0727563 + 0.501644i
\(596\) 5.62562e11 0.182626
\(597\) 1.60010e12 1.60010e12i 0.515542 0.515542i
\(598\) 9.86028e10 2.38048e11i 0.0315307 0.0761219i
\(599\) 1.23194e12i 0.390993i 0.980704 + 0.195497i \(0.0626318\pi\)
−0.980704 + 0.195497i \(0.937368\pi\)
\(600\) 9.57316e11 + 3.96533e11i 0.301561 + 0.124910i
\(601\) −6.03708e11 1.45748e12i −0.188752 0.455688i 0.800968 0.598708i \(-0.204319\pi\)
−0.989720 + 0.143019i \(0.954319\pi\)
\(602\) −1.63009e12 + 6.75205e11i −0.505856 + 0.209533i
\(603\) −1.94728e12 1.94728e12i −0.599793 0.599793i
\(604\) 2.41060e11 + 2.41060e11i 0.0736987 + 0.0736987i
\(605\) 1.70183e12 7.04923e11i 0.516438 0.213916i
\(606\) 7.05937e10 + 1.70428e11i 0.0212637 + 0.0513351i
\(607\) −5.72522e12 2.37147e12i −1.71176 0.709035i −0.999978 0.00663652i \(-0.997888\pi\)
−0.711784 0.702398i \(-0.752112\pi\)
\(608\) 2.93581e11i 0.0871289i
\(609\) 5.17526e11 1.24942e12i 0.152460 0.368070i
\(610\) 6.39968e11 6.39968e11i 0.187143 0.187143i
\(611\) −6.40744e12 −1.85994
\(612\) 3.67988e11 + 4.92838e11i 0.106036 + 0.142011i
\(613\) −6.17001e12 −1.76487 −0.882436 0.470432i \(-0.844098\pi\)
−0.882436 + 0.470432i \(0.844098\pi\)
\(614\) −2.86420e12 + 2.86420e12i −0.813290 + 0.813290i
\(615\) −2.69457e11 + 6.50527e11i −0.0759542 + 0.183370i
\(616\) 1.42628e11i 0.0399109i
\(617\) 4.85303e12 + 2.01019e12i 1.34812 + 0.558411i 0.935770 0.352612i \(-0.114706\pi\)
0.412355 + 0.911023i \(0.364706\pi\)
\(618\) −1.13013e12 2.72837e12i −0.311659 0.752412i
\(619\) 3.56705e12 1.47752e12i 0.976566 0.404507i 0.163414 0.986558i \(-0.447749\pi\)
0.813153 + 0.582051i \(0.197749\pi\)
\(620\) 1.63986e11 + 1.63986e11i 0.0445701 + 0.0445701i
\(621\) −1.74341e11 1.74341e11i −0.0470422 0.0470422i
\(622\) 1.51537e12 6.27685e11i 0.405939 0.168145i
\(623\) 2.13850e12 + 5.16281e12i 0.568740 + 1.37306i
\(624\) 2.54710e12 + 1.05504e12i 0.672535 + 0.278573i
\(625\) 5.95035e11i 0.155985i
\(626\) 1.42870e12 3.44920e12i 0.371842 0.897705i
\(627\) 1.41705e10 1.41705e10i 0.00366168 0.00366168i
\(628\) −1.66119e12 −0.426189
\(629\) 3.25276e12 + 1.93537e12i 0.828560 + 0.492988i
\(630\) 1.50671e12 0.381063
\(631\) 9.86448e11 9.86448e11i 0.247709 0.247709i −0.572321 0.820030i \(-0.693957\pi\)
0.820030 + 0.572321i \(0.193957\pi\)
\(632\) −1.43123e12 + 3.45529e12i −0.356847 + 0.861504i
\(633\) 2.78410e12i 0.689236i
\(634\) 6.34232e12 + 2.62708e12i 1.55900 + 0.645760i
\(635\) −1.42560e12 3.44170e12i −0.347949 0.840024i
\(636\) 1.87829e11 7.78012e10i 0.0455203 0.0188551i
\(637\) 5.66962e11 + 5.66962e11i 0.136435 + 0.136435i
\(638\) −1.35992e11 1.35992e11i −0.0324954 0.0324954i
\(639\) 2.49604e12 1.03389e12i 0.592241 0.245314i
\(640\) 1.09879e12 + 2.65271e12i 0.258883 + 0.625000i
\(641\) −4.11529e11 1.70461e11i −0.0962808 0.0398808i 0.334023 0.942565i \(-0.391594\pi\)
−0.430304 + 0.902684i \(0.641594\pi\)
\(642\) 4.55177e12i 1.05748i
\(643\) 7.82410e11 1.88891e12i 0.180503 0.435774i −0.807567 0.589776i \(-0.799216\pi\)
0.988071 + 0.154002i \(0.0492162\pi\)
\(644\) 5.12455e10 5.12455e10i 0.0117400 0.0117400i
\(645\) 7.63949e11 0.173798
\(646\) −8.29656e11 1.20330e11i −0.187435 0.0271848i
\(647\) 5.07293e12 1.13812 0.569062 0.822295i \(-0.307307\pi\)
0.569062 + 0.822295i \(0.307307\pi\)
\(648\) −3.01780e11 + 3.01780e11i −0.0672362 + 0.0672362i
\(649\) 9.44641e10 2.28057e11i 0.0209009 0.0504593i
\(650\) 3.71356e12i 0.815981i
\(651\) −9.34810e11 3.87211e11i −0.203990 0.0844955i
\(652\) −9.85952e10 2.38030e11i −0.0213669 0.0515843i
\(653\) 5.84908e12 2.42277e12i 1.25886 0.521438i 0.349303 0.937010i \(-0.386419\pi\)
0.909560 + 0.415572i \(0.136419\pi\)
\(654\) 2.79684e12 + 2.79684e12i 0.597817 + 0.597817i
\(655\) −1.84547e12 1.84547e12i −0.391761 0.391761i
\(656\) 3.21906e12 1.33338e12i 0.678674 0.281116i
\(657\) 5.86271e11 + 1.41538e12i 0.122759 + 0.296367i
\(658\) −7.94395e12 3.29049e12i −1.65204 0.684297i
\(659\) 3.82450e12i 0.789934i −0.918695 0.394967i \(-0.870756\pi\)
0.918695 0.394967i \(-0.129244\pi\)
\(660\) −8.52834e9 + 2.05892e10i −0.00174951 + 0.00422370i
\(661\) 3.78748e12 3.78748e12i 0.771692 0.771692i −0.206710 0.978402i \(-0.566276\pi\)
0.978402 + 0.206710i \(0.0662758\pi\)
\(662\) −1.73855e12 −0.351826
\(663\) −1.54987e12 + 2.60484e12i −0.311518 + 0.523565i
\(664\) −2.69297e12 −0.537620
\(665\) −3.04365e11 + 3.04365e11i −0.0603529 + 0.0603529i
\(666\) 1.40828e12 3.39989e12i 0.277368 0.669625i
\(667\) 2.70797e11i 0.0529758i
\(668\) −1.20440e12 4.98878e11i −0.234032 0.0969394i
\(669\) −1.71003e12 4.12837e12i −0.330054 0.796821i
\(670\) −3.85641e12 + 1.59738e12i −0.739343 + 0.306246i
\(671\) 8.32274e10 + 8.32274e10i 0.0158495 + 0.0158495i
\(672\) 1.00722e12 + 1.00722e12i 0.190530 + 0.190530i
\(673\) 8.95634e12 3.70984e12i 1.68292 0.697087i 0.683459 0.729989i \(-0.260475\pi\)
0.999459 + 0.0329017i \(0.0104748\pi\)
\(674\) 3.23903e12 + 7.81970e12i 0.604568 + 1.45956i
\(675\) 3.28300e12 + 1.35986e12i 0.608700 + 0.252132i
\(676\) 1.71545e11i 0.0315949i
\(677\) −1.84625e12 + 4.45724e12i −0.337786 + 0.815488i 0.660142 + 0.751141i \(0.270496\pi\)
−0.997928 + 0.0643465i \(0.979504\pi\)
\(678\) −4.18139e12 + 4.18139e12i −0.759954 + 0.759954i
\(679\) −7.34787e12 −1.32662
\(680\) −2.50394e12 + 6.35808e11i −0.449090 + 0.114034i
\(681\) −4.04789e12 −0.721219
\(682\) −1.01749e11 + 1.01749e11i −0.0180095 + 0.0180095i
\(683\) 2.80822e12 6.77964e12i 0.493785 1.19210i −0.458994 0.888439i \(-0.651790\pi\)
0.952779 0.303663i \(-0.0982098\pi\)
\(684\) 1.70840e11i 0.0298425i
\(685\) 2.18870e11 + 9.06590e10i 0.0379821 + 0.0157327i
\(686\) 2.66936e12 + 6.44441e12i 0.460202 + 1.11103i
\(687\) −5.40249e12 + 2.23779e12i −0.925314 + 0.383278i
\(688\) −2.67308e12 2.67308e12i −0.454846 0.454846i
\(689\) −1.42768e12 1.42768e12i −0.241348 0.241348i
\(690\) −1.38315e11 + 5.72920e10i −0.0232300 + 0.00962218i
\(691\) −2.90650e12 7.01690e12i −0.484974 1.17083i −0.957219 0.289364i \(-0.906556\pi\)
0.472245 0.881467i \(-0.343444\pi\)
\(692\) −2.33309e12 9.66399e11i −0.386772 0.160206i
\(693\) 1.95946e11i 0.0322728i
\(694\) 4.78701e12 1.15569e13i 0.783334 1.89113i
\(695\) −2.42196e12 + 2.42196e12i −0.393764 + 0.393764i
\(696\) 2.25446e12 0.364167
\(697\) 9.42782e11 + 3.71286e12i 0.151309 + 0.595884i
\(698\) −9.39536e12 −1.49818
\(699\) −2.54800e12 + 2.54800e12i −0.403695 + 0.403695i
\(700\) −3.99715e11 + 9.64997e11i −0.0629230 + 0.151909i
\(701\) 5.36973e12i 0.839887i −0.907550 0.419944i \(-0.862050\pi\)
0.907550 0.419944i \(-0.137950\pi\)
\(702\) 6.79639e12 + 2.81516e12i 1.05624 + 0.437508i
\(703\) 4.02320e11 + 9.71286e11i 0.0621259 + 0.149985i
\(704\) −1.97058e11 + 8.16241e10i −0.0302355 + 0.0125240i
\(705\) 2.63254e12 + 2.63254e12i 0.401350 + 0.401350i
\(706\) 1.23646e12 + 1.23646e12i 0.187310 + 0.187310i
\(707\) 4.76058e11 1.97190e11i 0.0716594 0.0296823i
\(708\) −3.99605e11 9.64731e11i −0.0597697 0.144297i
\(709\) −6.48681e12 2.68693e12i −0.964103 0.399344i −0.155589 0.987822i \(-0.549728\pi\)
−0.808514 + 0.588477i \(0.799728\pi\)
\(710\) 4.09505e12i 0.604780i
\(711\) −1.96626e12 + 4.74697e12i −0.288554 + 0.696631i
\(712\) −6.58725e12 + 6.58725e12i −0.960604 + 0.960604i
\(713\) −2.02609e11 −0.0293600
\(714\) −3.25922e12 + 2.43357e12i −0.469323 + 0.350430i
\(715\) 2.21321e11 0.0316698
\(716\) 8.30318e10 8.30318e10i 0.0118069 0.0118069i
\(717\) 1.99967e12 4.82763e12i 0.282568 0.682179i
\(718\) 7.26489e12i 1.02016i
\(719\) 2.75925e12 + 1.14292e12i 0.385044 + 0.159491i 0.566805 0.823852i \(-0.308179\pi\)
−0.181760 + 0.983343i \(0.558179\pi\)
\(720\) 1.23538e12 + 2.98246e12i 0.171318 + 0.413598i
\(721\) −7.62118e12 + 3.15680e12i −1.05030 + 0.435049i
\(722\) 5.64270e12 + 5.64270e12i 0.772804 + 0.772804i
\(723\) −3.98658e11 3.98658e11i −0.0542598 0.0542598i
\(724\) 1.70858e12 7.07715e11i 0.231106 0.0957271i
\(725\) 1.49356e12 + 3.60578e12i 0.200772 + 0.484706i
\(726\) 4.46689e12 + 1.85025e12i 0.596747 + 0.247181i
\(727\) 1.37734e13i 1.82868i 0.404950 + 0.914339i \(0.367289\pi\)
−0.404950 + 0.914339i \(0.632711\pi\)
\(728\) 2.29301e12 5.53582e12i 0.302563 0.730451i
\(729\) 2.56890e12 2.56890e12i 0.336879 0.336879i
\(730\) 2.32210e12 0.302642
\(731\) 3.33023e12 2.48659e12i 0.431367 0.322089i
\(732\) 4.97903e11 0.0640981
\(733\) 2.46022e10 2.46022e10i 0.00314779 0.00314779i −0.705531 0.708679i \(-0.749291\pi\)
0.708679 + 0.705531i \(0.249291\pi\)
\(734\) 1.57037e12 3.79120e12i 0.199696 0.482108i
\(735\) 4.65880e11i 0.0588818i
\(736\) 2.63516e11 + 1.09152e11i 0.0331022 + 0.0137114i
\(737\) −2.07738e11 5.01523e11i −0.0259365 0.0626162i
\(738\) 3.44095e12 1.42529e12i 0.426997 0.176868i
\(739\) 2.53429e12 + 2.53429e12i 0.312577 + 0.312577i 0.845907 0.533330i \(-0.179060\pi\)
−0.533330 + 0.845907i \(0.679060\pi\)
\(740\) −8.26689e11 8.26689e11i −0.101344 0.101344i
\(741\) −7.77816e11 + 3.22182e11i −0.0947753 + 0.0392572i
\(742\) −1.03686e12 2.50321e12i −0.125575 0.303165i
\(743\) −6.58956e12 2.72949e12i −0.793244 0.328572i −0.0509969 0.998699i \(-0.516240\pi\)
−0.742247 + 0.670126i \(0.766240\pi\)
\(744\) 1.68677e12i 0.201827i
\(745\) −1.24226e12 + 2.99909e12i −0.147744 + 0.356686i
\(746\) 2.17575e11 2.17575e11i 0.0257208 0.0257208i
\(747\) −3.69968e12 −0.434732
\(748\) 2.98391e10 + 1.17512e11i 0.00348521 + 0.0137254i
\(749\) 1.27145e13 1.47615
\(750\) 3.75068e12 3.75068e12i 0.432847 0.432847i
\(751\) −2.67180e12 + 6.45029e12i −0.306495 + 0.739945i 0.693318 + 0.720632i \(0.256148\pi\)
−0.999813 + 0.0193136i \(0.993852\pi\)
\(752\) 1.84227e13i 2.10074i
\(753\) −3.19400e12 1.32300e12i −0.362041 0.149962i
\(754\) 3.09194e12 + 7.46461e12i 0.348386 + 0.841078i
\(755\) −1.81744e12 + 7.52807e11i −0.203563 + 0.0843184i
\(756\) 1.46308e12 + 1.46308e12i 0.162900 + 0.162900i
\(757\) 5.06422e12 + 5.06422e12i 0.560507 + 0.560507i 0.929451 0.368944i \(-0.120281\pi\)
−0.368944 + 0.929451i \(0.620281\pi\)
\(758\) −7.91536e12 + 3.27865e12i −0.870882 + 0.360731i
\(759\) −7.45079e9 1.79878e10i −0.000814919 0.00196739i
\(760\) −6.62941e11 2.74599e11i −0.0720798 0.0298564i
\(761\) 1.69932e12i 0.183672i −0.995774 0.0918360i \(-0.970726\pi\)
0.995774 0.0918360i \(-0.0292736\pi\)
\(762\) 3.74184e12 9.03361e12i 0.402058 0.970653i
\(763\) 7.81245e12 7.81245e12i 0.834501 0.834501i
\(764\) −2.35448e12 −0.250020
\(765\) −3.43998e12 + 8.73490e11i −0.363144 + 0.0922108i
\(766\) 7.04569e12 0.739425
\(767\) −7.33287e12 + 7.33287e12i −0.765059 + 0.765059i
\(768\) −1.58194e12 + 3.81913e12i −0.164083 + 0.396132i
\(769\) 5.97176e12i 0.615791i 0.951420 + 0.307896i \(0.0996248\pi\)
−0.951420 + 0.307896i \(0.900375\pi\)
\(770\) 2.74394e11 + 1.13658e11i 0.0281298 + 0.0116517i
\(771\) −8.84948e11 2.13645e12i −0.0901931 0.217745i
\(772\) 2.85558e12 1.18282e12i 0.289345 0.119851i
\(773\) 2.28680e12 + 2.28680e12i 0.230367 + 0.230367i 0.812846 0.582479i \(-0.197917\pi\)
−0.582479 + 0.812846i \(0.697917\pi\)
\(774\) −2.85734e12 2.85734e12i −0.286172 0.286172i
\(775\) 2.69783e12 1.11748e12i 0.268631 0.111271i
\(776\) −4.68760e12 1.13169e13i −0.464058 1.12034i
\(777\) 4.71259e12 + 1.95202e12i 0.463836 + 0.192127i
\(778\) 4.02917e12i 0.394283i
\(779\) −4.07178e11 + 9.83015e11i −0.0396156 + 0.0956404i
\(780\) 6.62021e11 6.62021e11i 0.0640393 0.0640393i
\(781\) 5.32559e11 0.0512198
\(782\) −4.16468e11 + 6.99953e11i −0.0398246 + 0.0669328i
\(783\) 7.73137e12 0.735070
\(784\) −1.63013e12 + 1.63013e12i −0.154099 + 0.154099i
\(785\) 3.66828e12 8.85602e12i 0.344786 0.832387i
\(786\) 6.85031e12i 0.640190i
\(787\) −1.24477e13 5.15599e12i −1.15665 0.479100i −0.279891 0.960032i \(-0.590298\pi\)
−0.876758 + 0.480932i \(0.840298\pi\)
\(788\) −9.09049e11 2.19464e12i −0.0839884 0.202766i
\(789\) −8.57212e12 + 3.55069e12i −0.787484 + 0.326187i
\(790\) 5.50692e12 + 5.50692e12i 0.503022 + 0.503022i
\(791\) 1.16799e13 + 1.16799e13i 1.06083 + 1.06083i
\(792\) −3.01787e11 + 1.25004e11i −0.0272545 + 0.0112892i
\(793\) −1.89227e12 4.56834e12i −0.169924 0.410232i
\(794\) 6.42425e12 + 2.66101e12i 0.573628 + 0.237604i
\(795\) 1.17314e12i 0.104159i
\(796\) −1.45520e12 + 3.51316e12i −0.128474 + 0.310163i
\(797\) −2.25602e12 + 2.25602e12i −0.198053 + 0.198053i −0.799165 0.601112i \(-0.794724\pi\)
0.601112 + 0.799165i \(0.294724\pi\)
\(798\) −1.12979e12 −0.0986246
\(799\) 2.00445e13 + 2.90717e12i 1.73994 + 0.252354i
\(800\) −4.11085e12 −0.354835
\(801\) −9.04975e12 + 9.04975e12i −0.776766 + 0.776766i
\(802\) −8.97326e12 + 2.16634e13i −0.765889 + 1.84902i
\(803\) 3.01988e11i 0.0256313i
\(804\) −2.12156e12 8.78777e11i −0.179062 0.0741697i
\(805\) 1.60034e11 + 3.86357e11i 0.0134317 + 0.0324270i
\(806\) 5.58499e12 2.31338e12i 0.466139 0.193081i
\(807\) 4.75495e12 + 4.75495e12i 0.394652 + 0.394652i
\(808\) 6.07406e11 + 6.07406e11i 0.0501335 + 0.0501335i
\(809\) 5.45999e11 2.26160e11i 0.0448150 0.0185630i −0.360163 0.932889i \(-0.617279\pi\)
0.404978 + 0.914326i \(0.367279\pi\)
\(810\) 3.40095e11 + 8.21062e11i 0.0277599 + 0.0670183i
\(811\) −1.11154e13 4.60413e12i −0.902256 0.373727i −0.117169 0.993112i \(-0.537382\pi\)
−0.785087 + 0.619385i \(0.787382\pi\)
\(812\) 2.27254e12i 0.183447i
\(813\) −7.22409e11 + 1.74405e12i −0.0579930 + 0.140008i
\(814\) 5.12939e11 5.12939e11i 0.0409502 0.0409502i
\(815\) 1.48669e12 0.118035
\(816\) −7.48944e12 4.45617e12i −0.591349 0.351849i
\(817\) 1.15441e12 0.0906482
\(818\) −1.53289e13 + 1.53289e13i −1.19707 + 1.19707i
\(819\) 3.15020e12 7.60526e12i 0.244659 0.590659i
\(820\) 1.18323e12i 0.0913919i
\(821\) −1.23476e13 5.11454e12i −0.948501 0.392882i −0.145834 0.989309i \(-0.546587\pi\)
−0.802667 + 0.596427i \(0.796587\pi\)
\(822\) 2.37957e11 + 5.74479e11i 0.0181792 + 0.0438885i
\(823\) 1.08146e13 4.47955e12i 0.821695 0.340357i 0.0680855 0.997679i \(-0.478311\pi\)
0.753610 + 0.657322i \(0.228311\pi\)
\(824\) −9.72391e12 9.72391e12i −0.734799 0.734799i
\(825\) 1.98421e11 + 1.98421e11i 0.0149123 + 0.0149123i
\(826\) −1.28570e13 + 5.32556e12i −0.961017 + 0.398066i
\(827\) −7.99800e12 1.93089e13i −0.594575 1.43543i −0.879042 0.476745i \(-0.841817\pi\)
0.284467 0.958686i \(-0.408183\pi\)
\(828\) 1.53344e11 + 6.35171e10i 0.0113378 + 0.00469628i
\(829\) 3.37506e12i 0.248191i −0.992270 0.124096i \(-0.960397\pi\)
0.992270 0.124096i \(-0.0396029\pi\)
\(830\) −2.14599e12 + 5.18087e12i −0.156955 + 0.378923i
\(831\) −7.28673e12 + 7.28673e12i −0.530064 + 0.530064i
\(832\) 8.96067e12 0.648314
\(833\) −1.51640e12 2.03088e12i −0.109122 0.146144i
\(834\) −8.99022e12 −0.643462
\(835\) 5.31915e12 5.31915e12i 0.378663 0.378663i
\(836\) −1.28872e10 + 3.11125e10i −0.000912495 + 0.00220296i
\(837\) 5.78458e12i 0.407387i
\(838\) 4.25666e12 + 1.76316e12i 0.298174 + 0.123508i
\(839\) 5.13434e12 + 1.23954e13i 0.357730 + 0.863637i 0.995618 + 0.0935084i \(0.0298082\pi\)
−0.637888 + 0.770129i \(0.720192\pi\)
\(840\) −3.21652e12 + 1.33233e12i −0.222910 + 0.0923324i
\(841\) −4.25369e12 4.25369e12i −0.293213 0.293213i
\(842\) −7.67243e12 7.67243e12i −0.526052 0.526052i
\(843\) 3.46900e12 1.43691e12i 0.236581 0.0979952i
\(844\) 1.79038e12 + 4.32235e12i 0.121452 + 0.293210i
\(845\) −9.14524e11 3.78808e11i −0.0617078 0.0255602i
\(846\) 1.96926e13i 1.32171i
\(847\) 5.16831e12 1.24774e13i 0.345043 0.833007i
\(848\) 4.10485e12 4.10485e12i 0.272594 0.272594i
\(849\) −3.38806e12 −0.223803
\(850\) 1.68491e12 1.16172e13i 0.110711 0.763337i
\(851\) 1.02140e12 0.0667593
\(852\) 1.59300e12 1.59300e12i 0.103571 0.103571i
\(853\) −2.74937e12 + 6.63757e12i −0.177813 + 0.429278i −0.987507 0.157574i \(-0.949633\pi\)
0.809694 + 0.586852i \(0.199633\pi\)
\(854\) 6.63559e12i 0.426893i
\(855\) −9.10766e11 3.77251e11i −0.0582853 0.0241426i
\(856\) 8.11125e12 + 1.95823e13i 0.516364 + 1.24661i
\(857\) −1.64212e13 + 6.80189e12i −1.03990 + 0.430741i −0.836276 0.548308i \(-0.815272\pi\)
−0.203624 + 0.979049i \(0.565272\pi\)
\(858\) 4.10767e11 + 4.10767e11i 0.0258764 + 0.0258764i
\(859\) 3.06601e12 + 3.06601e12i 0.192134 + 0.192134i 0.796618 0.604484i \(-0.206621\pi\)
−0.604484 + 0.796618i \(0.706621\pi\)
\(860\) −1.18604e12 + 4.91274e11i −0.0739360 + 0.0306253i
\(861\) 1.97559e12 + 4.76949e12i 0.122513 + 0.295773i
\(862\) 7.82319e11 + 3.24047e11i 0.0482615 + 0.0199906i
\(863\) 2.34250e13i 1.43758i 0.695228 + 0.718790i \(0.255304\pi\)
−0.695228 + 0.718790i \(0.744696\pi\)
\(864\) −3.11634e12 + 7.52350e12i −0.190253 + 0.459313i
\(865\) 1.03040e13 1.03040e13i 0.625795 0.625795i
\(866\) 2.17446e13 1.31377
\(867\) 6.03034e12 7.44559e12i 0.362457 0.447521i
\(868\) 1.70031e12 0.101669
\(869\) −7.16171e11 + 7.16171e11i −0.0426018 + 0.0426018i
\(870\) 1.79654e12 4.33723e12i 0.106316 0.256670i
\(871\) 2.28054e13i 1.34263i
\(872\) 1.70163e13 + 7.04840e12i 0.996649 + 0.412825i
\(873\) −6.43995e12 1.55474e13i −0.375248 0.905928i
\(874\) −2.09009e11 + 8.65742e10i −0.0121161 + 0.00501865i
\(875\) −1.04768e13 1.04768e13i −0.604216 0.604216i
\(876\) 9.03314e11 + 9.03314e11i 0.0518287 + 0.0518287i
\(877\) 8.47113e12 3.50886e12i 0.483552 0.200294i −0.127571 0.991829i \(-0.540718\pi\)
0.611123 + 0.791536i \(0.290718\pi\)
\(878\) 3.12930e12 + 7.55481e12i 0.177714 + 0.429040i
\(879\) 1.08426e13 + 4.49116e12i 0.612611 + 0.253752i
\(880\) 6.36342e11i 0.0357700i
\(881\) −1.18548e13 + 2.86200e13i −0.662984 + 1.60058i 0.130120 + 0.991498i \(0.458464\pi\)
−0.793104 + 0.609087i \(0.791536\pi\)
\(882\) −1.74250e12 + 1.74250e12i −0.0969534 + 0.0969534i
\(883\) 3.55305e13 1.96688 0.983441 0.181231i \(-0.0580082\pi\)
0.983441 + 0.181231i \(0.0580082\pi\)
\(884\) 7.31086e11 5.04073e12i 0.0402655 0.277625i
\(885\) 6.02551e12 0.330179
\(886\) 2.11852e13 2.11852e13i 1.15500 1.15500i
\(887\) 1.27540e13 3.07909e13i 0.691817 1.67019i −0.0492715 0.998785i \(-0.515690\pi\)
0.741088 0.671408i \(-0.234310\pi\)
\(888\) 8.50340e12i 0.458917i
\(889\) −2.52337e13 1.04521e13i −1.35495 0.561237i
\(890\) 7.42359e12 + 1.79221e13i 0.396606 + 0.957491i
\(891\) −1.06779e11 + 4.42291e10i −0.00567590 + 0.00235103i
\(892\) 5.30967e12 + 5.30967e12i 0.280819 + 0.280819i
\(893\) 3.97804e12 + 3.97804e12i 0.209333 + 0.209333i
\(894\) −7.87185e12 + 3.26063e12i −0.412153 + 0.170719i
\(895\) 2.59300e11 + 6.26005e11i 0.0135082 + 0.0326118i
\(896\) 1.94490e13 + 8.05603e12i 1.00812 + 0.417575i
\(897\) 8.17946e11i 0.0421851i
\(898\) −4.05761e11 + 9.79595e11i −0.0208222 + 0.0502693i
\(899\) 4.49248e12 4.49248e12i 0.229386 0.229386i
\(900\) −2.39217e12 −0.121535
\(901\) 3.81847e12 + 5.11399e12i 0.193031 + 0.258523i
\(902\) 7.34166e11 0.0369287
\(903\) 3.96055e12 3.96055e12i 0.198226 0.198226i
\(904\) −1.05376e13 + 2.54401e13i −0.524790 + 1.26695i
\(905\) 1.06714e13i 0.528814i
\(906\) −4.77032e12 1.97593e12i −0.235218 0.0974304i
\(907\) −1.22044e13 2.94640e13i −0.598803 1.44564i −0.874803 0.484480i \(-0.839009\pi\)
0.276000 0.961158i \(-0.410991\pi\)
\(908\) 6.28440e12 2.60309e12i 0.306816 0.127087i
\(909\) 8.34470e11 + 8.34470e11i 0.0405390 + 0.0405390i
\(910\) −8.82281e12 8.82281e12i −0.426501 0.426501i
\(911\) −7.03465e12 + 2.91385e12i −0.338384 + 0.140163i −0.545404 0.838174i \(-0.683624\pi\)
0.207020 + 0.978337i \(0.433624\pi\)
\(912\) −9.26337e11 2.23637e12i −0.0443396 0.107045i
\(913\) −6.73768e11 2.79084e11i −0.0320916 0.0132928i
\(914\) 2.43458e13i 1.15389i
\(915\) −1.09948e12 + 2.65438e12i −0.0518552 + 0.125190i
\(916\) 6.94838e12 6.94838e12i 0.326102 0.326102i
\(917\) −1.91350e13 −0.893649
\(918\) −1.99840e13 1.18904e13i −0.928732 0.552590i
\(919\) −2.31210e13 −1.06927 −0.534635 0.845083i \(-0.679551\pi\)
−0.534635 + 0.845083i \(0.679551\pi\)
\(920\) −4.92955e11 + 4.92955e11i −0.0226862 + 0.0226862i
\(921\) 4.92076e12 1.18798e13i 0.225353 0.544051i
\(922\) 3.70049e13i 1.68644i
\(923\) −2.06702e13 8.56188e12i −0.937427 0.388295i
\(924\) 6.25275e10 + 1.50955e11i 0.00282194 + 0.00681276i
\(925\) −1.36004e13 + 5.63345e12i −0.610819 + 0.253010i
\(926\) −6.77970e12 6.77970e12i −0.303013 0.303013i
\(927\) −1.33590e13 1.33590e13i −0.594175 0.594175i
\(928\) −8.26321e12 + 3.42274e12i −0.365749 + 0.151498i
\(929\) 6.54737e12 + 1.58067e13i 0.288400 + 0.696260i 0.999980 0.00634543i \(-0.00201983\pi\)
−0.711579 + 0.702606i \(0.752020\pi\)
\(930\) −3.24510e12 1.34416e12i −0.142251 0.0589221i
\(931\) 7.03993e11i 0.0307110i
\(932\) 2.31726e12 5.59436e12i 0.100601 0.242873i
\(933\) −3.68181e12 + 3.68181e12i −0.159072 + 0.159072i
\(934\) −2.06122e13 −0.886263
\(935\) −6.92364e11 1.00417e11i −0.0296266 0.00429692i
\(936\) 1.37230e13 0.584395
\(937\) 1.41808e13 1.41808e13i 0.600998 0.600998i −0.339580 0.940577i \(-0.610285\pi\)
0.940577 + 0.339580i \(0.110285\pi\)
\(938\) −1.17115e13 + 2.82741e13i −0.493970 + 1.19255i
\(939\) 1.18516e13i 0.497488i
\(940\) −5.77996e12 2.39414e12i −0.241462 0.100017i
\(941\) −1.21408e13 2.93105e13i −0.504770 1.21862i −0.946858 0.321651i \(-0.895762\pi\)
0.442088 0.896972i \(-0.354238\pi\)
\(942\) 2.32448e13 9.62833e12i 0.961828 0.398402i
\(943\) 7.30958e11 + 7.30958e11i 0.0301016 + 0.0301016i
\(944\) −2.10835e13 2.10835e13i −0.864108 0.864108i
\(945\) −1.10307e13 + 4.56905e12i −0.449944 + 0.186373i
\(946\) −3.04823e11 7.35908e11i −0.0123748 0.0298754i
\(947\) 3.12283e13 + 1.29352e13i 1.26175 + 0.522634i 0.910446 0.413628i \(-0.135739\pi\)
0.351304 + 0.936262i \(0.385739\pi\)
\(948\) 4.28445e12i 0.172289i
\(949\) 4.85502e12 1.17211e13i 0.194309 0.469104i
\(950\) 2.30555e12 2.30555e12i 0.0918371 0.0918371i
\(951\) −2.17925e13 −0.863964
\(952\) −9.68498e12 + 1.62774e13i −0.382149 + 0.642273i
\(953\) 1.11972e13 0.439737 0.219868 0.975530i \(-0.429437\pi\)
0.219868 + 0.975530i \(0.429437\pi\)
\(954\) 4.38781e12 4.38781e12i 0.171506 0.171506i
\(955\) 5.19921e12 1.25520e13i 0.202266 0.488313i
\(956\) 8.78089e12i 0.339999i
\(957\) 5.64053e11 + 2.33638e11i 0.0217378 + 0.00900411i
\(958\) 2.60783e12 + 6.29586e12i 0.100031 + 0.241496i
\(959\) 1.60470e12 6.64687e11i 0.0612645 0.0253766i
\(960\) −3.68155e12 3.68155e12i −0.139897 0.139897i
\(961\) 1.53344e13 + 1.53344e13i 0.579977 + 0.579977i
\(962\) −2.81552e13 + 1.16623e13i −1.05991 + 0.439031i
\(963\) 1.11435e13 + 2.69027e13i 0.417544 + 1.00804i
\(964\) 8.75287e11 + 3.62556e11i 0.0326440 + 0.0135216i
\(965\) 1.78354e13i 0.662077i
\(966\) −4.20050e11 + 1.01409e12i −0.0155204 + 0.0374696i
\(967\) −5.69066e12 + 5.69066e12i −0.209288 + 0.209288i −0.803965 0.594677i \(-0.797280\pi\)
0.594677 + 0.803965i \(0.297280\pi\)
\(968\) 2.25142e13 0.824173
\(969\) 2.57944e12 6.54979e11i 0.0939871 0.0238655i
\(970\) −2.55074e13 −0.925109
\(971\) 2.33616e13 2.33616e13i 0.843367 0.843367i −0.145928 0.989295i \(-0.546617\pi\)
0.989295 + 0.145928i \(0.0466168\pi\)
\(972\) −2.90041e12 + 7.00222e12i −0.104223 + 0.251615i
\(973\) 2.51124e13i 0.898217i
\(974\) 2.09561e13 + 8.68031e12i 0.746098 + 0.309044i
\(975\) −4.51133e12 1.08913e13i −0.159876 0.385975i
\(976\) 1.31349e13 5.44065e12i 0.463342 0.191923i
\(977\) −3.08299e13 3.08299e13i −1.08255 1.08255i −0.996271 0.0862737i \(-0.972504\pi\)
−0.0862737 0.996271i \(-0.527496\pi\)
\(978\) 2.75926e12 + 2.75926e12i 0.0964422 + 0.0964422i
\(979\) −2.33076e12 + 9.65433e11i −0.0810916 + 0.0335892i
\(980\) 2.99594e11 + 7.23284e11i 0.0103757 + 0.0250491i
\(981\) 2.33775e13 + 9.68329e12i 0.805912 + 0.333820i
\(982\) 3.87041e13i 1.32818i
\(983\) −1.99635e13 + 4.81962e13i −0.681940 + 1.64635i 0.0784783 + 0.996916i \(0.474994\pi\)
−0.760418 + 0.649433i \(0.775006\pi\)
\(984\) −6.08542e12 + 6.08542e12i −0.206925 + 0.206925i
\(985\) 1.37073e13 0.463968
\(986\) −6.28576e12 2.47546e13i −0.211793 0.834083i
\(987\) 2.72958e13 0.915522
\(988\) 1.00038e12 1.00038e12i 0.0334010 0.0334010i
\(989\) 4.29201e11 1.03618e12i 0.0142652 0.0344392i
\(990\) 6.80206e11i 0.0225052i
\(991\) 5.20461e13 + 2.15582e13i 1.71418 + 0.710038i 0.999949 + 0.0101303i \(0.00322464\pi\)
0.714234 + 0.699907i \(0.246775\pi\)
\(992\) 2.56088e12 + 6.18250e12i 0.0839627 + 0.202704i
\(993\) 5.09892e12 2.11204e12i 0.166421 0.0689336i
\(994\) −2.12301e13 2.12301e13i −0.689783 0.689783i
\(995\) −1.55157e13 1.55157e13i −0.501842 0.501842i
\(996\) −2.85019e12 + 1.18059e12i −0.0917714 + 0.0380130i
\(997\) −9.58201e12 2.31330e13i −0.307134 0.741488i −0.999795 0.0202249i \(-0.993562\pi\)
0.692661 0.721263i \(-0.256438\pi\)
\(998\) 3.95469e13 + 1.63809e13i 1.26190 + 0.522696i
\(999\) 2.91614e13i 0.926325i
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 17.10.d.a.8.11 52
17.7 odd 16 289.10.a.i.1.14 52
17.10 odd 16 289.10.a.i.1.13 52
17.15 even 8 inner 17.10.d.a.15.11 yes 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.d.a.8.11 52 1.1 even 1 trivial
17.10.d.a.15.11 yes 52 17.15 even 8 inner
289.10.a.i.1.13 52 17.10 odd 16
289.10.a.i.1.14 52 17.7 odd 16