Properties

Label 16.12.e.a.13.7
Level $16$
Weight $12$
Character 16.13
Analytic conductor $12.293$
Analytic rank $0$
Dimension $42$
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] = [16,12,Mod(5,16)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(16, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 12, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("16.5");
 
S:= CuspForms(chi, 12);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 16.e (of order \(4\), degree \(2\), 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: \(12.2934908890\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(21\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 13.7
Character \(\chi\) \(=\) 16.13
Dual form 16.12.e.a.5.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-30.9382 + 33.0277i) q^{2} +(585.540 + 585.540i) q^{3} +(-133.660 - 2043.63i) q^{4} +(-6859.07 + 6859.07i) q^{5} +(-37454.6 + 1223.52i) q^{6} -19914.8i q^{7} +(71631.8 + 58811.8i) q^{8} +508568. i q^{9} +O(q^{10})\) \(q+(-30.9382 + 33.0277i) q^{2} +(585.540 + 585.540i) q^{3} +(-133.660 - 2043.63i) q^{4} +(-6859.07 + 6859.07i) q^{5} +(-37454.6 + 1223.52i) q^{6} -19914.8i q^{7} +(71631.8 + 58811.8i) q^{8} +508568. i q^{9} +(-14332.4 - 438747. i) q^{10} +(-96496.9 + 96496.9i) q^{11} +(1.11837e6 - 1.27489e6i) q^{12} +(-674561. - 674561. i) q^{13} +(657740. + 616127. i) q^{14} -8.03253e6 q^{15} +(-4.15857e6 + 546304. i) q^{16} +3.70861e6 q^{17} +(-1.67968e7 - 1.57342e7i) q^{18} +(-2.61985e6 - 2.61985e6i) q^{19} +(1.49342e7 + 1.31007e7i) q^{20} +(1.16609e7 - 1.16609e7i) q^{21} +(-201635. - 6.17251e6i) q^{22} -2.97611e7i q^{23} +(7.50660e6 + 7.63799e7i) q^{24} -4.52657e7i q^{25} +(4.31489e7 - 1.40953e6i) q^{26} +(-1.94060e8 + 1.94060e8i) q^{27} +(-4.06985e7 + 2.66181e6i) q^{28} +(4.14366e7 + 4.14366e7i) q^{29} +(2.48512e8 - 2.65296e8i) q^{30} +6.07925e7 q^{31} +(1.10615e8 - 1.54250e8i) q^{32} -1.13006e8 q^{33} +(-1.14738e8 + 1.22487e8i) q^{34} +(1.36597e8 + 1.36597e8i) q^{35} +(1.03933e9 - 6.79752e7i) q^{36} +(-4.37984e8 + 4.37984e8i) q^{37} +(1.67581e8 - 5.47432e6i) q^{38} -7.89965e8i q^{39} +(-8.94722e8 + 8.79330e7i) q^{40} +1.20680e9i q^{41} +(2.43661e7 + 7.45900e8i) q^{42} +(-1.45559e8 + 1.45559e8i) q^{43} +(2.10102e8 + 1.84306e8i) q^{44} +(-3.48830e9 - 3.48830e9i) q^{45} +(9.82941e8 + 9.20754e8i) q^{46} +1.52664e9 q^{47} +(-2.75490e9 - 2.11513e9i) q^{48} +1.58073e9 q^{49} +(1.49502e9 + 1.40044e9i) q^{50} +(2.17154e9 + 2.17154e9i) q^{51} +(-1.28839e9 + 1.46872e9i) q^{52} +(-2.52787e9 + 2.52787e9i) q^{53} +(-4.05499e8 - 1.24132e10i) q^{54} -1.32376e9i q^{55} +(1.17122e9 - 1.42653e9i) q^{56} -3.06806e9i q^{57} +(-2.65053e9 + 8.65839e7i) q^{58} +(-4.54873e9 + 4.54873e9i) q^{59} +(1.07363e9 + 1.64155e10i) q^{60} +(9.96512e7 + 9.96512e7i) q^{61} +(-1.88081e9 + 2.00784e9i) q^{62} +1.01280e10 q^{63} +(1.67228e9 + 8.42558e9i) q^{64} +9.25373e9 q^{65} +(3.49619e9 - 3.73232e9i) q^{66} +(7.32144e9 + 7.32144e9i) q^{67} +(-4.95693e8 - 7.57904e9i) q^{68} +(1.74263e10 - 1.74263e10i) q^{69} +(-8.73755e9 + 2.85426e8i) q^{70} +1.31476e9i q^{71} +(-2.99098e10 + 3.64296e10i) q^{72} -2.59505e9i q^{73} +(-9.15190e8 - 2.80160e10i) q^{74} +(2.65049e10 - 2.65049e10i) q^{75} +(-5.00385e9 + 5.70419e9i) q^{76} +(1.92171e9 + 1.92171e9i) q^{77} +(2.60907e10 + 2.44401e10i) q^{78} -4.08802e9 q^{79} +(2.47768e10 - 3.22711e10i) q^{80} -1.37169e11 q^{81} +(-3.98579e10 - 3.73363e10i) q^{82} +(3.03277e10 + 3.03277e10i) q^{83} +(-2.53892e10 - 2.22720e10i) q^{84} +(-2.54376e10 + 2.54376e10i) q^{85} +(-3.04154e8 - 9.31083e9i) q^{86} +4.85256e10i q^{87} +(-1.25874e10 + 1.23709e9i) q^{88} -5.68675e10i q^{89} +(2.23132e11 - 7.28899e9i) q^{90} +(-1.34337e10 + 1.34337e10i) q^{91} +(-6.08208e10 + 3.97787e9i) q^{92} +(3.55964e10 + 3.55964e10i) q^{93} +(-4.72314e10 + 5.04214e10i) q^{94} +3.59395e10 q^{95} +(1.55089e11 - 2.55497e10i) q^{96} -5.73135e10 q^{97} +(-4.89048e10 + 5.22078e10i) q^{98} +(-4.90752e10 - 4.90752e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42 q - 2 q^{2} - 2 q^{3} + 3080 q^{4} - 2 q^{5} + 30352 q^{6} + 74836 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 42 q - 2 q^{2} - 2 q^{3} + 3080 q^{4} - 2 q^{5} + 30352 q^{6} + 74836 q^{8} - 988948 q^{10} - 540846 q^{11} + 2300260 q^{12} - 2 q^{13} - 1829956 q^{14} - 6075004 q^{15} - 3721448 q^{16} - 4 q^{17} - 32219106 q^{18} - 11291290 q^{19} + 68655164 q^{20} + 354292 q^{21} - 85011388 q^{22} - 66180944 q^{24} + 305685384 q^{26} - 66463304 q^{27} - 322075880 q^{28} + 77673206 q^{29} + 290643636 q^{30} + 343549808 q^{31} + 404698568 q^{32} - 4 q^{33} - 882461836 q^{34} - 434731684 q^{35} + 1854387628 q^{36} - 522762058 q^{37} - 1276252832 q^{38} - 483241016 q^{40} + 2372079160 q^{42} + 3824193658 q^{43} - 2657283740 q^{44} + 97301954 q^{45} - 1032658964 q^{46} - 4586900144 q^{47} - 1058870552 q^{48} - 8474257474 q^{49} + 6515930886 q^{50} + 7074245796 q^{51} - 13915491564 q^{52} - 2100608058 q^{53} + 4385621536 q^{54} + 12910845976 q^{56} - 21491153128 q^{58} + 955824746 q^{59} + 25615752768 q^{60} + 2150827022 q^{61} - 15814519760 q^{62} + 27758037828 q^{63} + 9674332160 q^{64} - 1884965292 q^{65} + 10932459412 q^{66} - 3186519018 q^{67} + 13817664656 q^{68} - 16193060732 q^{69} - 27206453120 q^{70} - 20773133628 q^{72} + 14141420908 q^{74} + 28890034486 q^{75} - 11786004940 q^{76} - 22711870540 q^{77} + 37031200508 q^{78} + 48011833792 q^{79} - 8952586328 q^{80} - 90656394430 q^{81} - 81555388352 q^{82} + 55713221118 q^{83} + 61178517160 q^{84} - 84575506252 q^{85} + 10047297860 q^{86} - 162855622152 q^{88} + 160133627736 q^{90} - 147369662716 q^{91} - 169766721928 q^{92} - 69689773328 q^{93} + 160320530128 q^{94} + 375702304500 q^{95} + 230764310192 q^{96} - 4 q^{97} - 108887063494 q^{98} - 286271331106 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −30.9382 + 33.0277i −0.683643 + 0.729816i
\(3\) 585.540 + 585.540i 1.39120 + 1.39120i 0.822644 + 0.568557i \(0.192498\pi\)
0.568557 + 0.822644i \(0.307502\pi\)
\(4\) −133.660 2043.63i −0.0652637 0.997868i
\(5\) −6859.07 + 6859.07i −0.981591 + 0.981591i −0.999834 0.0182428i \(-0.994193\pi\)
0.0182428 + 0.999834i \(0.494193\pi\)
\(6\) −37454.6 + 1223.52i −1.96641 + 0.0642359i
\(7\) 19914.8i 0.447854i −0.974606 0.223927i \(-0.928112\pi\)
0.974606 0.223927i \(-0.0718877\pi\)
\(8\) 71631.8 + 58811.8i 0.772877 + 0.634555i
\(9\) 508568.i 2.87088i
\(10\) −14332.4 438747.i −0.0453230 1.38744i
\(11\) −96496.9 + 96496.9i −0.180656 + 0.180656i −0.791642 0.610985i \(-0.790773\pi\)
0.610985 + 0.791642i \(0.290773\pi\)
\(12\) 1.11837e6 1.27489e6i 1.29744 1.47903i
\(13\) −674561. 674561.i −0.503887 0.503887i 0.408757 0.912643i \(-0.365962\pi\)
−0.912643 + 0.408757i \(0.865962\pi\)
\(14\) 657740. + 616127.i 0.326851 + 0.306172i
\(15\) −8.03253e6 −2.73118
\(16\) −4.15857e6 + 546304.i −0.991481 + 0.130249i
\(17\) 3.70861e6 0.633494 0.316747 0.948510i \(-0.397409\pi\)
0.316747 + 0.948510i \(0.397409\pi\)
\(18\) −1.67968e7 1.57342e7i −2.09521 1.96266i
\(19\) −2.61985e6 2.61985e6i −0.242735 0.242735i 0.575246 0.817981i \(-0.304906\pi\)
−0.817981 + 0.575246i \(0.804906\pi\)
\(20\) 1.49342e7 + 1.31007e7i 1.04356 + 0.915436i
\(21\) 1.16609e7 1.16609e7i 0.623055 0.623055i
\(22\) −201635. 6.17251e6i −0.00834145 0.255351i
\(23\) 2.97611e7i 0.964153i −0.876129 0.482077i \(-0.839883\pi\)
0.876129 0.482077i \(-0.160117\pi\)
\(24\) 7.50660e6 + 7.63799e7i 0.192434 + 1.95802i
\(25\) 4.52657e7i 0.927041i
\(26\) 4.31489e7 1.40953e6i 0.712223 0.0232660i
\(27\) −1.94060e8 + 1.94060e8i −2.60277 + 2.60277i
\(28\) −4.06985e7 + 2.66181e6i −0.446899 + 0.0292286i
\(29\) 4.14366e7 + 4.14366e7i 0.375142 + 0.375142i 0.869346 0.494204i \(-0.164541\pi\)
−0.494204 + 0.869346i \(0.664541\pi\)
\(30\) 2.48512e8 2.65296e8i 1.86715 1.99326i
\(31\) 6.07925e7 0.381382 0.190691 0.981650i \(-0.438927\pi\)
0.190691 + 0.981650i \(0.438927\pi\)
\(32\) 1.10615e8 1.54250e8i 0.582762 0.812643i
\(33\) −1.13006e8 −0.502659
\(34\) −1.14738e8 + 1.22487e8i −0.433084 + 0.462334i
\(35\) 1.36597e8 + 1.36597e8i 0.439609 + 0.439609i
\(36\) 1.03933e9 6.79752e7i 2.86476 0.187364i
\(37\) −4.37984e8 + 4.37984e8i −1.03836 + 1.03836i −0.0391281 + 0.999234i \(0.512458\pi\)
−0.999234 + 0.0391281i \(0.987542\pi\)
\(38\) 1.67581e8 5.47432e6i 0.343096 0.0112078i
\(39\) 7.89965e8i 1.40201i
\(40\) −8.94722e8 + 8.79330e7i −1.38152 + 0.135776i
\(41\) 1.20680e9i 1.62677i 0.581729 + 0.813383i \(0.302376\pi\)
−0.581729 + 0.813383i \(0.697624\pi\)
\(42\) 2.43661e7 + 7.45900e8i 0.0287683 + 0.880663i
\(43\) −1.45559e8 + 1.45559e8i −0.150995 + 0.150995i −0.778562 0.627567i \(-0.784051\pi\)
0.627567 + 0.778562i \(0.284051\pi\)
\(44\) 2.10102e8 + 1.84306e8i 0.192062 + 0.168481i
\(45\) −3.48830e9 3.48830e9i −2.81803 2.81803i
\(46\) 9.82941e8 + 9.20754e8i 0.703655 + 0.659137i
\(47\) 1.52664e9 0.970953 0.485476 0.874250i \(-0.338646\pi\)
0.485476 + 0.874250i \(0.338646\pi\)
\(48\) −2.75490e9 2.11513e9i −1.56055 1.19815i
\(49\) 1.58073e9 0.799427
\(50\) 1.49502e9 + 1.40044e9i 0.676570 + 0.633765i
\(51\) 2.17154e9 + 2.17154e9i 0.881317 + 0.881317i
\(52\) −1.28839e9 + 1.46872e9i −0.469927 + 0.535698i
\(53\) −2.52787e9 + 2.52787e9i −0.830306 + 0.830306i −0.987558 0.157252i \(-0.949736\pi\)
0.157252 + 0.987558i \(0.449736\pi\)
\(54\) −4.05499e8 1.24132e10i −0.120178 3.67891i
\(55\) 1.32376e9i 0.354661i
\(56\) 1.17122e9 1.42653e9i 0.284188 0.346136i
\(57\) 3.06806e9i 0.675386i
\(58\) −2.65053e9 + 8.65839e7i −0.530247 + 0.0173214i
\(59\) −4.54873e9 + 4.54873e9i −0.828332 + 0.828332i −0.987286 0.158954i \(-0.949188\pi\)
0.158954 + 0.987286i \(0.449188\pi\)
\(60\) 1.07363e9 + 1.64155e10i 0.178247 + 2.72536i
\(61\) 9.96512e7 + 9.96512e7i 0.0151067 + 0.0151067i 0.714620 0.699513i \(-0.246600\pi\)
−0.699513 + 0.714620i \(0.746600\pi\)
\(62\) −1.88081e9 + 2.00784e9i −0.260729 + 0.278339i
\(63\) 1.01280e10 1.28573
\(64\) 1.67228e9 + 8.42558e9i 0.194679 + 0.980867i
\(65\) 9.25373e9 0.989221
\(66\) 3.49619e9 3.73232e9i 0.343639 0.366849i
\(67\) 7.32144e9 + 7.32144e9i 0.662498 + 0.662498i 0.955968 0.293470i \(-0.0948101\pi\)
−0.293470 + 0.955968i \(0.594810\pi\)
\(68\) −4.95693e8 7.57904e9i −0.0413441 0.632143i
\(69\) 1.74263e10 1.74263e10i 1.34133 1.34133i
\(70\) −8.73755e9 + 2.85426e8i −0.621370 + 0.0202981i
\(71\) 1.31476e9i 0.0864822i 0.999065 + 0.0432411i \(0.0137684\pi\)
−0.999065 + 0.0432411i \(0.986232\pi\)
\(72\) −2.99098e10 + 3.64296e10i −1.82173 + 2.21884i
\(73\) 2.59505e9i 0.146511i −0.997313 0.0732556i \(-0.976661\pi\)
0.997313 0.0732556i \(-0.0233389\pi\)
\(74\) −9.15190e8 2.80160e10i −0.0479443 1.46768i
\(75\) 2.65049e10 2.65049e10i 1.28970 1.28970i
\(76\) −5.00385e9 + 5.70419e9i −0.226375 + 0.258059i
\(77\) 1.92171e9 + 1.92171e9i 0.0809077 + 0.0809077i
\(78\) 2.60907e10 + 2.44401e10i 1.02321 + 0.958478i
\(79\) −4.08802e9 −0.149473 −0.0747367 0.997203i \(-0.523812\pi\)
−0.0747367 + 0.997203i \(0.523812\pi\)
\(80\) 2.47768e10 3.22711e10i 0.845378 1.10108i
\(81\) −1.37169e11 −4.37107
\(82\) −3.98579e10 3.73363e10i −1.18724 1.11213i
\(83\) 3.03277e10 + 3.03277e10i 0.845103 + 0.845103i 0.989517 0.144415i \(-0.0461299\pi\)
−0.144415 + 0.989517i \(0.546130\pi\)
\(84\) −2.53892e10 2.22720e10i −0.662389 0.581064i
\(85\) −2.54376e10 + 2.54376e10i −0.621832 + 0.621832i
\(86\) −3.04154e8 9.31083e9i −0.00697191 0.213426i
\(87\) 4.85256e10i 1.04379i
\(88\) −1.25874e10 + 1.23709e9i −0.254262 + 0.0249888i
\(89\) 5.68675e10i 1.07949i −0.841828 0.539746i \(-0.818520\pi\)
0.841828 0.539746i \(-0.181480\pi\)
\(90\) 2.23132e11 7.28899e9i 3.98317 0.130117i
\(91\) −1.34337e10 + 1.34337e10i −0.225668 + 0.225668i
\(92\) −6.08208e10 + 3.97787e9i −0.962098 + 0.0629242i
\(93\) 3.55964e10 + 3.55964e10i 0.530579 + 0.530579i
\(94\) −4.72314e10 + 5.04214e10i −0.663785 + 0.708617i
\(95\) 3.59395e10 0.476532
\(96\) 1.55089e11 2.55497e10i 1.94129 0.319811i
\(97\) −5.73135e10 −0.677661 −0.338830 0.940847i \(-0.610031\pi\)
−0.338830 + 0.940847i \(0.610031\pi\)
\(98\) −4.89048e10 + 5.22078e10i −0.546523 + 0.583435i
\(99\) −4.90752e10 4.90752e10i −0.518643 0.518643i
\(100\) −9.25064e10 + 6.05021e9i −0.925064 + 0.0605021i
\(101\) 3.62044e10 3.62044e10i 0.342763 0.342763i −0.514642 0.857405i \(-0.672075\pi\)
0.857405 + 0.514642i \(0.172075\pi\)
\(102\) −1.38905e11 + 4.53755e9i −1.24571 + 0.0406930i
\(103\) 9.12485e10i 0.775570i −0.921750 0.387785i \(-0.873240\pi\)
0.921750 0.387785i \(-0.126760\pi\)
\(104\) −8.64784e9 8.79921e10i −0.0696987 0.709186i
\(105\) 1.59966e11i 1.22317i
\(106\) −5.28212e9 1.61698e11i −0.0383377 1.17360i
\(107\) 7.80580e10 7.80580e10i 0.538030 0.538030i −0.384920 0.922950i \(-0.625771\pi\)
0.922950 + 0.384920i \(0.125771\pi\)
\(108\) 4.22526e11 + 3.70650e11i 2.76709 + 2.42735i
\(109\) 3.50084e9 + 3.50084e9i 0.0217935 + 0.0217935i 0.717920 0.696126i \(-0.245095\pi\)
−0.696126 + 0.717920i \(0.745095\pi\)
\(110\) 4.37207e10 + 4.09547e10i 0.258838 + 0.242462i
\(111\) −5.12915e11 −2.88914
\(112\) 1.08795e10 + 8.28171e10i 0.0583326 + 0.444039i
\(113\) 3.13967e11 1.60307 0.801534 0.597949i \(-0.204018\pi\)
0.801534 + 0.597949i \(0.204018\pi\)
\(114\) 1.01331e11 + 9.49201e10i 0.492907 + 0.461723i
\(115\) 2.04134e11 + 2.04134e11i 0.946404 + 0.946404i
\(116\) 7.91428e10 9.02197e10i 0.349859 0.398825i
\(117\) 3.43060e11 3.43060e11i 1.44660 1.44660i
\(118\) −9.50482e9 2.90964e11i −0.0382466 1.17081i
\(119\) 7.38562e10i 0.283713i
\(120\) −5.75384e11 4.72407e11i −2.11087 1.73308i
\(121\) 2.66688e11i 0.934727i
\(122\) −6.37427e9 + 2.08226e8i −0.0213526 + 0.000697519i
\(123\) −7.06631e11 + 7.06631e11i −2.26316 + 2.26316i
\(124\) −8.12552e9 1.24238e11i −0.0248904 0.380569i
\(125\) −2.44352e10 2.44352e10i −0.0716160 0.0716160i
\(126\) −3.13342e11 + 3.34505e11i −0.878984 + 0.938350i
\(127\) 6.20048e11 1.66535 0.832673 0.553765i \(-0.186809\pi\)
0.832673 + 0.553765i \(0.186809\pi\)
\(128\) −3.30015e11 2.05440e11i −0.848944 0.528483i
\(129\) −1.70462e11 −0.420130
\(130\) −2.86293e11 + 3.05629e11i −0.676274 + 0.721949i
\(131\) 1.33237e9 + 1.33237e9i 0.00301739 + 0.00301739i 0.708614 0.705596i \(-0.249321\pi\)
−0.705596 + 0.708614i \(0.749321\pi\)
\(132\) 1.51043e10 + 2.30942e11i 0.0328054 + 0.501587i
\(133\) −5.21738e10 + 5.21738e10i −0.108710 + 0.108710i
\(134\) −4.68322e11 + 1.52985e10i −0.936415 + 0.0305895i
\(135\) 2.66215e12i 5.10971i
\(136\) 2.65654e11 + 2.18110e11i 0.489613 + 0.401987i
\(137\) 2.80780e11i 0.497054i −0.968625 0.248527i \(-0.920054\pi\)
0.968625 0.248527i \(-0.0799464\pi\)
\(138\) 3.64132e10 + 1.11469e12i 0.0619333 + 1.89592i
\(139\) 1.98123e11 1.98123e11i 0.323857 0.323857i −0.526388 0.850245i \(-0.676454\pi\)
0.850245 + 0.526388i \(0.176454\pi\)
\(140\) 2.60897e11 2.97412e11i 0.409982 0.467363i
\(141\) 8.93909e11 + 8.93909e11i 1.35079 + 1.35079i
\(142\) −4.34236e10 4.06764e10i −0.0631161 0.0591230i
\(143\) 1.30186e11 0.182061
\(144\) −2.77833e11 2.11492e12i −0.373929 2.84642i
\(145\) −5.68434e11 −0.736471
\(146\) 8.57087e10 + 8.02862e10i 0.106926 + 0.100161i
\(147\) 9.25580e11 + 9.25580e11i 1.11216 + 1.11216i
\(148\) 9.53620e11 + 8.36538e11i 1.10392 + 0.968381i
\(149\) 6.80120e11 6.80120e11i 0.758685 0.758685i −0.217398 0.976083i \(-0.569757\pi\)
0.976083 + 0.217398i \(0.0697571\pi\)
\(150\) 5.53833e10 + 1.69541e12i 0.0595493 + 1.82294i
\(151\) 1.24483e12i 1.29044i 0.763996 + 0.645221i \(0.223235\pi\)
−0.763996 + 0.645221i \(0.776765\pi\)
\(152\) −3.35864e10 3.41743e11i −0.0335756 0.341633i
\(153\) 1.88608e12i 1.81868i
\(154\) −1.22924e11 + 4.01552e9i −0.114360 + 0.00373575i
\(155\) −4.16980e11 + 4.16980e11i −0.374361 + 0.374361i
\(156\) −1.61440e12 + 1.05587e11i −1.39903 + 0.0915006i
\(157\) −5.32516e11 5.32516e11i −0.445538 0.445538i 0.448330 0.893868i \(-0.352019\pi\)
−0.893868 + 0.448330i \(0.852019\pi\)
\(158\) 1.26476e11 1.35018e11i 0.102187 0.109088i
\(159\) −2.96035e12 −2.31025
\(160\) 2.99291e11 + 1.81673e12i 0.225650 + 1.36972i
\(161\) −5.92686e11 −0.431800
\(162\) 4.24375e12 4.53037e12i 2.98825 3.19008i
\(163\) −2.47550e9 2.47550e9i −0.00168512 0.00168512i 0.706264 0.707949i \(-0.250379\pi\)
−0.707949 + 0.706264i \(0.750379\pi\)
\(164\) 2.46626e12 1.61301e11i 1.62330 0.106169i
\(165\) 7.75114e11 7.75114e11i 0.493405 0.493405i
\(166\) −1.93994e12 + 6.33712e10i −1.19452 + 0.0390209i
\(167\) 1.98829e12i 1.18451i 0.805751 + 0.592254i \(0.201762\pi\)
−0.805751 + 0.592254i \(0.798238\pi\)
\(168\) 1.52109e12 1.49492e11i 0.876908 0.0861823i
\(169\) 8.82095e11i 0.492197i
\(170\) −5.31533e10 1.62714e12i −0.0287118 0.878934i
\(171\) 1.33237e12 1.33237e12i 0.696862 0.696862i
\(172\) 3.16925e11 + 2.78014e11i 0.160528 + 0.140819i
\(173\) 2.52033e11 + 2.52033e11i 0.123653 + 0.123653i 0.766225 0.642572i \(-0.222133\pi\)
−0.642572 + 0.766225i \(0.722133\pi\)
\(174\) −1.60269e12 1.50129e12i −0.761778 0.713583i
\(175\) −9.01456e11 −0.415179
\(176\) 3.48573e11 4.54006e11i 0.155587 0.202648i
\(177\) −5.32693e12 −2.30475
\(178\) 1.87820e12 + 1.75938e12i 0.787830 + 0.737987i
\(179\) −1.45805e12 1.45805e12i −0.593037 0.593037i 0.345414 0.938451i \(-0.387739\pi\)
−0.938451 + 0.345414i \(0.887739\pi\)
\(180\) −6.66257e12 + 7.59506e12i −2.62811 + 2.99594i
\(181\) 1.35746e12 1.35746e12i 0.519392 0.519392i −0.397996 0.917387i \(-0.630294\pi\)
0.917387 + 0.397996i \(0.130294\pi\)
\(182\) −2.80705e10 8.59301e11i −0.0104197 0.318972i
\(183\) 1.16700e11i 0.0420328i
\(184\) 1.75030e12 2.13184e12i 0.611809 0.745172i
\(185\) 6.00833e12i 2.03849i
\(186\) −2.27696e12 + 7.43806e10i −0.749953 + 0.0244984i
\(187\) −3.57869e11 + 3.57869e11i −0.114445 + 0.114445i
\(188\) −2.04051e11 3.11989e12i −0.0633679 0.968883i
\(189\) 3.86467e12 + 3.86467e12i 1.16566 + 1.16566i
\(190\) −1.11190e12 + 1.18700e12i −0.325778 + 0.347781i
\(191\) 2.60506e12 0.741539 0.370770 0.928725i \(-0.379094\pi\)
0.370770 + 0.928725i \(0.379094\pi\)
\(192\) −3.95433e12 + 5.91271e12i −1.09375 + 1.63542i
\(193\) −2.54172e12 −0.683222 −0.341611 0.939841i \(-0.610973\pi\)
−0.341611 + 0.939841i \(0.610973\pi\)
\(194\) 1.77317e12 1.89293e12i 0.463278 0.494568i
\(195\) 5.41843e12 + 5.41843e12i 1.37620 + 1.37620i
\(196\) −2.11280e11 3.23043e12i −0.0521735 0.797723i
\(197\) −2.85642e12 + 2.85642e12i −0.685896 + 0.685896i −0.961322 0.275426i \(-0.911181\pi\)
0.275426 + 0.961322i \(0.411181\pi\)
\(198\) 3.13914e12 1.02545e11i 0.733081 0.0239473i
\(199\) 3.66476e12i 0.832442i −0.909263 0.416221i \(-0.863354\pi\)
0.909263 0.416221i \(-0.136646\pi\)
\(200\) 2.66215e12 3.24246e12i 0.588259 0.716489i
\(201\) 8.57399e12i 1.84334i
\(202\) 7.56510e10 + 2.31585e12i 0.0158264 + 0.484482i
\(203\) 8.25201e11 8.25201e11i 0.168009 0.168009i
\(204\) 4.14759e12 4.72808e12i 0.821920 0.936956i
\(205\) −8.27755e12 8.27755e12i −1.59682 1.59682i
\(206\) 3.01373e12 + 2.82306e12i 0.566024 + 0.530213i
\(207\) 1.51355e13 2.76797
\(208\) 3.17373e12 + 2.43670e12i 0.565225 + 0.433963i
\(209\) 5.05615e11 0.0877032
\(210\) −5.28331e12 4.94906e12i −0.892689 0.836212i
\(211\) 1.86773e12 + 1.86773e12i 0.307441 + 0.307441i 0.843916 0.536475i \(-0.180245\pi\)
−0.536475 + 0.843916i \(0.680245\pi\)
\(212\) 5.50393e12 + 4.82817e12i 0.882725 + 0.774347i
\(213\) −7.69847e11 + 7.69847e11i −0.120314 + 0.120314i
\(214\) 1.63106e11 + 4.99305e12i 0.0248425 + 0.760484i
\(215\) 1.99680e12i 0.296431i
\(216\) −2.53139e13 + 2.48784e12i −3.66322 + 0.360021i
\(217\) 1.21067e12i 0.170804i
\(218\) −2.23934e11 + 7.31518e9i −0.0308042 + 0.00100627i
\(219\) 1.51951e12 1.51951e12i 0.203826 0.203826i
\(220\) −2.70528e12 + 1.76934e11i −0.353905 + 0.0231465i
\(221\) −2.50168e12 2.50168e12i −0.319209 0.319209i
\(222\) 1.58686e13 1.69404e13i 1.97514 2.10854i
\(223\) −1.26372e13 −1.53453 −0.767263 0.641332i \(-0.778382\pi\)
−0.767263 + 0.641332i \(0.778382\pi\)
\(224\) −3.07185e12 2.20288e12i −0.363945 0.260992i
\(225\) 2.30207e13 2.66142
\(226\) −9.71355e12 + 1.03696e13i −1.09593 + 1.16995i
\(227\) 6.38980e12 + 6.38980e12i 0.703632 + 0.703632i 0.965188 0.261557i \(-0.0842358\pi\)
−0.261557 + 0.965188i \(0.584236\pi\)
\(228\) −6.26999e12 + 4.10077e11i −0.673946 + 0.0440781i
\(229\) 1.21476e12 1.21476e12i 0.127466 0.127466i −0.640496 0.767962i \(-0.721271\pi\)
0.767962 + 0.640496i \(0.221271\pi\)
\(230\) −1.30576e13 + 4.26548e11i −1.33770 + 0.0436983i
\(231\) 2.25048e12i 0.225118i
\(232\) 5.31216e11 + 5.40514e12i 0.0518904 + 0.527987i
\(233\) 1.65378e13i 1.57769i −0.614595 0.788843i \(-0.710681\pi\)
0.614595 0.788843i \(-0.289319\pi\)
\(234\) 7.16841e11 + 2.19441e13i 0.0667938 + 2.04471i
\(235\) −1.04713e13 + 1.04713e13i −0.953078 + 0.953078i
\(236\) 9.90393e12 + 8.68796e12i 0.880626 + 0.772506i
\(237\) −2.39370e12 2.39370e12i −0.207948 0.207948i
\(238\) 2.43930e12 + 2.28498e12i 0.207058 + 0.193958i
\(239\) 9.34650e12 0.775283 0.387642 0.921810i \(-0.373290\pi\)
0.387642 + 0.921810i \(0.373290\pi\)
\(240\) 3.34039e13 4.38820e12i 2.70791 0.355734i
\(241\) 1.11589e13 0.884150 0.442075 0.896978i \(-0.354243\pi\)
0.442075 + 0.896978i \(0.354243\pi\)
\(242\) −8.80811e12 8.25085e12i −0.682179 0.639020i
\(243\) −4.59407e13 4.59407e13i −3.47827 3.47827i
\(244\) 1.90331e11 2.16970e11i 0.0140885 0.0160604i
\(245\) −1.08423e13 + 1.08423e13i −0.784710 + 0.784710i
\(246\) −1.47654e12 4.52003e13i −0.104497 3.19888i
\(247\) 3.53450e12i 0.244622i
\(248\) 4.35467e12 + 3.57531e12i 0.294762 + 0.242008i
\(249\) 3.55161e13i 2.35142i
\(250\) 1.56302e12 5.10585e10i 0.101226 0.00330673i
\(251\) −8.13313e12 + 8.13313e12i −0.515291 + 0.515291i −0.916143 0.400852i \(-0.868714\pi\)
0.400852 + 0.916143i \(0.368714\pi\)
\(252\) −1.35371e12 2.06980e13i −0.0839118 1.28299i
\(253\) 2.87185e12 + 2.87185e12i 0.174180 + 0.174180i
\(254\) −1.91831e13 + 2.04788e13i −1.13850 + 1.21540i
\(255\) −2.97895e13 −1.73019
\(256\) 1.69953e13 4.54369e12i 0.966070 0.258279i
\(257\) 1.40965e13 0.784294 0.392147 0.919903i \(-0.371732\pi\)
0.392147 + 0.919903i \(0.371732\pi\)
\(258\) 5.27377e12 5.62996e12i 0.287219 0.306617i
\(259\) 8.72236e12 + 8.72236e12i 0.465035 + 0.465035i
\(260\) −1.23685e12 1.89112e13i −0.0645602 0.987112i
\(261\) −2.10733e13 + 2.10733e13i −1.07699 + 1.07699i
\(262\) −8.52261e10 + 2.78405e9i −0.00426496 + 0.000139322i
\(263\) 3.74224e13i 1.83390i 0.399003 + 0.916950i \(0.369356\pi\)
−0.399003 + 0.916950i \(0.630644\pi\)
\(264\) −8.09479e12 6.64606e12i −0.388494 0.318965i
\(265\) 3.46778e13i 1.63004i
\(266\) −1.09020e11 3.33734e12i −0.00501945 0.153657i
\(267\) 3.32982e13 3.32982e13i 1.50179 1.50179i
\(268\) 1.39837e13 1.59409e13i 0.617849 0.704323i
\(269\) 6.31416e12 + 6.31416e12i 0.273324 + 0.273324i 0.830437 0.557113i \(-0.188091\pi\)
−0.557113 + 0.830437i \(0.688091\pi\)
\(270\) 8.79246e13 + 8.23619e13i 3.72915 + 3.49322i
\(271\) −3.31124e12 −0.137613 −0.0688064 0.997630i \(-0.521919\pi\)
−0.0688064 + 0.997630i \(0.521919\pi\)
\(272\) −1.54225e13 + 2.02603e12i −0.628097 + 0.0825120i
\(273\) −1.57320e13 −0.627898
\(274\) 9.27353e12 + 8.68682e12i 0.362758 + 0.339807i
\(275\) 4.36799e12 + 4.36799e12i 0.167476 + 0.167476i
\(276\) −3.79422e13 3.32838e13i −1.42601 1.25093i
\(277\) 3.06698e13 3.06698e13i 1.12998 1.12998i 0.139803 0.990179i \(-0.455353\pi\)
0.990179 0.139803i \(-0.0446469\pi\)
\(278\) 4.13988e11 + 1.26731e13i 0.0149535 + 0.457759i
\(279\) 3.09171e13i 1.09490i
\(280\) 1.75117e12 + 1.78182e13i 0.0608077 + 0.618720i
\(281\) 1.12496e13i 0.383046i 0.981488 + 0.191523i \(0.0613427\pi\)
−0.981488 + 0.191523i \(0.938657\pi\)
\(282\) −5.71796e13 + 1.86787e12i −1.90929 + 0.0623700i
\(283\) 3.47187e13 3.47187e13i 1.13694 1.13694i 0.147946 0.988995i \(-0.452734\pi\)
0.988995 0.147946i \(-0.0472662\pi\)
\(284\) 2.68689e12 1.75731e11i 0.0862978 0.00564414i
\(285\) 2.10440e13 + 2.10440e13i 0.662952 + 0.662952i
\(286\) −4.02772e12 + 4.29975e12i −0.124465 + 0.132871i
\(287\) 2.40332e13 0.728553
\(288\) 7.84465e13 + 5.62555e13i 2.33300 + 1.67304i
\(289\) −2.05181e13 −0.598686
\(290\) 1.75863e13 1.87741e13i 0.503483 0.537489i
\(291\) −3.35594e13 3.35594e13i −0.942763 0.942763i
\(292\) −5.30334e12 + 3.46855e11i −0.146199 + 0.00956185i
\(293\) −4.28304e13 + 4.28304e13i −1.15873 + 1.15873i −0.173975 + 0.984750i \(0.555661\pi\)
−0.984750 + 0.173975i \(0.944339\pi\)
\(294\) −5.92055e13 + 1.93405e12i −1.57200 + 0.0513519i
\(295\) 6.24002e13i 1.62617i
\(296\) −5.71322e13 + 5.61494e12i −1.46143 + 0.143628i
\(297\) 3.74524e13i 0.940414i
\(298\) 1.42115e12 + 4.35045e13i 0.0350307 + 1.07237i
\(299\) −2.00757e13 + 2.00757e13i −0.485824 + 0.485824i
\(300\) −5.77089e13 5.06236e13i −1.37112 1.20278i
\(301\) 2.89878e12 + 2.89878e12i 0.0676238 + 0.0676238i
\(302\) −4.11140e13 3.85129e13i −0.941785 0.882202i
\(303\) 4.23983e13 0.953705
\(304\) 1.23261e13 + 9.46361e12i 0.272283 + 0.209051i
\(305\) −1.36703e12 −0.0296571
\(306\) −6.22929e13 5.83519e13i −1.32731 1.24333i
\(307\) 5.00993e11 + 5.00993e11i 0.0104851 + 0.0104851i 0.712330 0.701845i \(-0.247640\pi\)
−0.701845 + 0.712330i \(0.747640\pi\)
\(308\) 3.67042e12 4.18414e12i 0.0754549 0.0860155i
\(309\) 5.34297e13 5.34297e13i 1.07897 1.07897i
\(310\) −8.71301e11 2.66725e13i −0.0172854 0.529145i
\(311\) 6.71357e13i 1.30849i 0.756282 + 0.654246i \(0.227014\pi\)
−0.756282 + 0.654246i \(0.772986\pi\)
\(312\) 4.64593e13 5.65866e13i 0.889656 1.08359i
\(313\) 1.16967e13i 0.220075i −0.993927 0.110037i \(-0.964903\pi\)
0.993927 0.110037i \(-0.0350971\pi\)
\(314\) 3.40629e13 1.11272e12i 0.629750 0.0205718i
\(315\) −6.94688e13 + 6.94688e13i −1.26207 + 1.26207i
\(316\) 5.46405e11 + 8.35442e12i 0.00975519 + 0.149155i
\(317\) 5.42552e13 + 5.42552e13i 0.951952 + 0.951952i 0.998897 0.0469451i \(-0.0149486\pi\)
−0.0469451 + 0.998897i \(0.514949\pi\)
\(318\) 9.15876e13 9.77734e13i 1.57938 1.68605i
\(319\) −7.99701e12 −0.135543
\(320\) −6.92620e13 4.63214e13i −1.15391 0.771715i
\(321\) 9.14122e13 1.49702
\(322\) 1.83366e13 1.95751e13i 0.295197 0.315134i
\(323\) −9.71601e12 9.71601e12i −0.153771 0.153771i
\(324\) 1.83340e13 + 2.80323e14i 0.285272 + 4.36175i
\(325\) −3.05345e13 + 3.05345e13i −0.467123 + 0.467123i
\(326\) 1.58348e11 5.17270e9i 0.00238186 7.78073e-5i
\(327\) 4.09976e12i 0.0606381i
\(328\) −7.09742e13 + 8.64454e13i −1.03227 + 1.25729i
\(329\) 3.04027e13i 0.434845i
\(330\) 1.61964e12 + 4.95808e13i 0.0227820 + 0.697408i
\(331\) 9.47342e13 9.47342e13i 1.31055 1.31055i 0.389537 0.921011i \(-0.372635\pi\)
0.921011 0.389537i \(-0.127365\pi\)
\(332\) 5.79250e13 6.60322e13i 0.788146 0.898455i
\(333\) −2.22745e14 2.22745e14i −2.98101 2.98101i
\(334\) −6.56685e13 6.15139e13i −0.864474 0.809781i
\(335\) −1.00437e14 −1.30060
\(336\) −4.21223e13 + 5.48631e13i −0.536595 + 0.698899i
\(337\) −2.48393e13 −0.311298 −0.155649 0.987812i \(-0.549747\pi\)
−0.155649 + 0.987812i \(0.549747\pi\)
\(338\) 2.91336e13 + 2.72904e13i 0.359213 + 0.336487i
\(339\) 1.83840e14 + 1.83840e14i 2.23019 + 2.23019i
\(340\) 5.53852e13 + 4.85852e13i 0.661089 + 0.579923i
\(341\) −5.86628e12 + 5.86628e12i −0.0688992 + 0.0688992i
\(342\) 2.78406e12 + 8.52264e13i 0.0321762 + 0.984987i
\(343\) 7.08579e13i 0.805880i
\(344\) −1.89873e13 + 1.86606e12i −0.212516 + 0.0208860i
\(345\) 2.39057e14i 2.63328i
\(346\) −1.61215e13 + 5.26637e11i −0.174778 + 0.00570943i
\(347\) −4.05821e13 + 4.05821e13i −0.433035 + 0.433035i −0.889659 0.456625i \(-0.849058\pi\)
0.456625 + 0.889659i \(0.349058\pi\)
\(348\) 9.91686e13 6.48593e12i 1.04157 0.0681219i
\(349\) −5.40864e13 5.40864e13i −0.559175 0.559175i 0.369897 0.929073i \(-0.379393\pi\)
−0.929073 + 0.369897i \(0.879393\pi\)
\(350\) 2.78894e13 2.97730e13i 0.283834 0.303004i
\(351\) 2.61811e14 2.62300
\(352\) 4.21058e12 + 2.55587e13i 0.0415296 + 0.252089i
\(353\) 1.19115e14 1.15666 0.578328 0.815805i \(-0.303706\pi\)
0.578328 + 0.815805i \(0.303706\pi\)
\(354\) 1.64806e14 1.75936e14i 1.57563 1.68205i
\(355\) −9.01806e12 9.01806e12i −0.0848901 0.0848901i
\(356\) −1.16216e14 + 7.60091e12i −1.07719 + 0.0704516i
\(357\) 4.32458e13 4.32458e13i 0.394701 0.394701i
\(358\) 9.32657e13 3.04668e12i 0.838234 0.0273823i
\(359\) 1.67025e14i 1.47830i −0.673541 0.739150i \(-0.735228\pi\)
0.673541 0.739150i \(-0.264772\pi\)
\(360\) −4.47199e13 4.55027e14i −0.389796 3.96619i
\(361\) 1.02763e14i 0.882160i
\(362\) 2.83648e12 + 8.68312e13i 0.0239819 + 0.734139i
\(363\) −1.56157e14 + 1.56157e14i −1.30039 + 1.30039i
\(364\) 2.92492e13 + 2.56581e13i 0.239914 + 0.210459i
\(365\) 1.77997e13 + 1.77997e13i 0.143814 + 0.143814i
\(366\) −3.85432e12 3.61047e12i −0.0306762 0.0287354i
\(367\) −1.32967e14 −1.04251 −0.521255 0.853401i \(-0.674536\pi\)
−0.521255 + 0.853401i \(0.674536\pi\)
\(368\) 1.62586e13 + 1.23764e14i 0.125580 + 0.955940i
\(369\) −6.13741e14 −4.67025
\(370\) 1.98441e14 + 1.85887e14i 1.48773 + 1.39360i
\(371\) 5.03421e13 + 5.03421e13i 0.371856 + 0.371856i
\(372\) 6.79883e13 7.75039e13i 0.494821 0.564076i
\(373\) −1.58936e14 + 1.58936e14i −1.13979 + 1.13979i −0.151297 + 0.988488i \(0.548345\pi\)
−0.988488 + 0.151297i \(0.951655\pi\)
\(374\) −7.47787e11 2.28914e13i −0.00528426 0.161763i
\(375\) 2.86156e13i 0.199265i
\(376\) 1.09356e14 + 8.97844e13i 0.750427 + 0.616123i
\(377\) 5.59030e13i 0.378058i
\(378\) −2.47207e14 + 8.07542e12i −1.64761 + 0.0538220i
\(379\) 2.82445e12 2.82445e12i 0.0185532 0.0185532i −0.697769 0.716323i \(-0.745824\pi\)
0.716323 + 0.697769i \(0.245824\pi\)
\(380\) −4.80368e12 7.34472e13i −0.0311003 0.475516i
\(381\) 3.63063e14 + 3.63063e14i 2.31683 + 2.31683i
\(382\) −8.05958e13 + 8.60392e13i −0.506948 + 0.541188i
\(383\) −5.92249e13 −0.367207 −0.183604 0.983000i \(-0.558776\pi\)
−0.183604 + 0.983000i \(0.558776\pi\)
\(384\) −7.29434e13 3.13531e14i −0.445825 1.91628i
\(385\) −2.63624e13 −0.158836
\(386\) 7.86360e13 8.39471e13i 0.467080 0.498627i
\(387\) −7.40268e13 7.40268e13i −0.433489 0.433489i
\(388\) 7.66052e12 + 1.17128e14i 0.0442266 + 0.676216i
\(389\) 2.33475e13 2.33475e13i 0.132898 0.132898i −0.637529 0.770427i \(-0.720043\pi\)
0.770427 + 0.637529i \(0.220043\pi\)
\(390\) −3.46595e14 + 1.13221e13i −1.94521 + 0.0635435i
\(391\) 1.10372e14i 0.610785i
\(392\) 1.13230e14 + 9.29655e13i 0.617859 + 0.507281i
\(393\) 1.56031e12i 0.00839560i
\(394\) −5.96864e12 1.82714e14i −0.0316699 0.969486i
\(395\) 2.80400e13 2.80400e13i 0.146722 0.146722i
\(396\) −9.37323e13 + 1.06851e14i −0.483689 + 0.551386i
\(397\) 2.18990e13 + 2.18990e13i 0.111449 + 0.111449i 0.760632 0.649183i \(-0.224889\pi\)
−0.649183 + 0.760632i \(0.724889\pi\)
\(398\) 1.21039e14 + 1.13381e14i 0.607530 + 0.569094i
\(399\) −6.10997e13 −0.302474
\(400\) 2.47288e13 + 1.88241e14i 0.120746 + 0.919144i
\(401\) 7.84224e13 0.377699 0.188850 0.982006i \(-0.439524\pi\)
0.188850 + 0.982006i \(0.439524\pi\)
\(402\) −2.83179e14 2.65264e14i −1.34530 1.26018i
\(403\) −4.10082e13 4.10082e13i −0.192173 0.192173i
\(404\) −7.88277e13 6.91495e13i −0.364403 0.319663i
\(405\) 9.40851e14 9.40851e14i 4.29060 4.29060i
\(406\) 1.72430e12 + 5.27847e13i 0.00775746 + 0.237473i
\(407\) 8.45282e13i 0.375174i
\(408\) 2.78391e13 + 2.83264e14i 0.121906 + 1.24039i
\(409\) 5.44125e13i 0.235083i 0.993068 + 0.117541i \(0.0375013\pi\)
−0.993068 + 0.117541i \(0.962499\pi\)
\(410\) 5.29481e14 1.72964e13i 2.25704 0.0737299i
\(411\) 1.64408e14 1.64408e14i 0.691502 0.691502i
\(412\) −1.86478e14 + 1.21963e13i −0.773916 + 0.0506165i
\(413\) 9.05871e13 + 9.05871e13i 0.370972 + 0.370972i
\(414\) −4.68266e14 + 4.99892e14i −1.89230 + 2.02011i
\(415\) −4.16039e14 −1.65909
\(416\) −1.78668e14 + 2.94341e13i −0.703126 + 0.115834i
\(417\) 2.32018e14 0.901100
\(418\) −1.56428e13 + 1.66993e13i −0.0599577 + 0.0640072i
\(419\) 2.47223e14 + 2.47223e14i 0.935214 + 0.935214i 0.998025 0.0628113i \(-0.0200066\pi\)
−0.0628113 + 0.998025i \(0.520007\pi\)
\(420\) 3.26912e14 2.13811e13i 1.22056 0.0798285i
\(421\) −3.01416e14 + 3.01416e14i −1.11074 + 1.11074i −0.117695 + 0.993050i \(0.537551\pi\)
−0.993050 + 0.117695i \(0.962449\pi\)
\(422\) −1.19471e14 + 3.90272e12i −0.434555 + 0.0141955i
\(423\) 7.76399e14i 2.78749i
\(424\) −3.29745e14 + 3.24072e13i −1.16860 + 0.114850i
\(425\) 1.67873e14i 0.587274i
\(426\) −1.60863e12 4.92439e13i −0.00555526 0.170059i
\(427\) 1.98453e12 1.98453e12i 0.00676557 0.00676557i
\(428\) −1.69955e14 1.49089e14i −0.571997 0.501769i
\(429\) 7.62292e13 + 7.62292e13i 0.253283 + 0.253283i
\(430\) 6.59499e13 + 6.17775e13i 0.216340 + 0.202653i
\(431\) −4.56713e14 −1.47917 −0.739586 0.673062i \(-0.764979\pi\)
−0.739586 + 0.673062i \(0.764979\pi\)
\(432\) 7.00998e14 9.13030e14i 2.24159 2.91961i
\(433\) 1.87325e14 0.591443 0.295721 0.955274i \(-0.404440\pi\)
0.295721 + 0.955274i \(0.404440\pi\)
\(434\) 3.99856e13 + 3.74559e13i 0.124655 + 0.116769i
\(435\) −3.32841e14 3.32841e14i −1.02458 1.02458i
\(436\) 6.68650e12 7.62235e12i 0.0203247 0.0231693i
\(437\) −7.79697e13 + 7.79697e13i −0.234033 + 0.234033i
\(438\) 3.17509e12 + 9.71967e13i 0.00941128 + 0.288100i
\(439\) 6.17945e14i 1.80882i −0.426667 0.904409i \(-0.640312\pi\)
0.426667 0.904409i \(-0.359688\pi\)
\(440\) 7.78526e13 9.48231e13i 0.225052 0.274110i
\(441\) 8.03907e14i 2.29506i
\(442\) 1.60022e14 5.22740e12i 0.451189 0.0147388i
\(443\) 3.84254e14 3.84254e14i 1.07004 1.07004i 0.0726803 0.997355i \(-0.476845\pi\)
0.997355 0.0726803i \(-0.0231553\pi\)
\(444\) 6.85562e13 + 1.04821e15i 0.188556 + 2.88298i
\(445\) 3.90058e14 + 3.90058e14i 1.05962 + 1.05962i
\(446\) 3.90972e14 4.17378e14i 1.04907 1.11992i
\(447\) 7.96476e14 2.11097
\(448\) 1.67794e14 3.33031e13i 0.439285 0.0871878i
\(449\) 3.39135e12 0.00877037 0.00438518 0.999990i \(-0.498604\pi\)
0.00438518 + 0.999990i \(0.498604\pi\)
\(450\) −7.12217e14 + 7.60320e14i −1.81946 + 1.94235i
\(451\) −1.16453e14 1.16453e14i −0.293886 0.293886i
\(452\) −4.19648e13 6.41633e14i −0.104622 1.59965i
\(453\) −7.28901e14 + 7.28901e14i −1.79526 + 1.79526i
\(454\) −4.08729e14 + 1.33518e13i −0.994555 + 0.0324888i
\(455\) 1.84286e14i 0.443026i
\(456\) 1.80438e14 2.19770e14i 0.428570 0.521990i
\(457\) 6.33305e14i 1.48619i −0.669187 0.743094i \(-0.733357\pi\)
0.669187 0.743094i \(-0.266643\pi\)
\(458\) 2.53830e12 + 7.77030e13i 0.00588549 + 0.180168i
\(459\) −7.19694e14 + 7.19694e14i −1.64884 + 1.64884i
\(460\) 3.89890e14 4.44459e14i 0.882620 1.00615i
\(461\) −4.96950e14 4.96950e14i −1.11162 1.11162i −0.992931 0.118692i \(-0.962130\pi\)
−0.118692 0.992931i \(-0.537870\pi\)
\(462\) −7.43283e13 6.96258e13i −0.164295 0.153900i
\(463\) 6.46594e14 1.41233 0.706165 0.708047i \(-0.250424\pi\)
0.706165 + 0.708047i \(0.250424\pi\)
\(464\) −1.94954e14 1.49680e14i −0.420808 0.323084i
\(465\) −4.88317e14 −1.04162
\(466\) 5.46206e14 + 5.11650e14i 1.15142 + 1.07857i
\(467\) 2.80275e14 + 2.80275e14i 0.583904 + 0.583904i 0.935974 0.352070i \(-0.114522\pi\)
−0.352070 + 0.935974i \(0.614522\pi\)
\(468\) −7.46942e14 6.55236e14i −1.53792 1.34910i
\(469\) 1.45805e14 1.45805e14i 0.296702 0.296702i
\(470\) −2.18804e13 6.69808e14i −0.0440065 1.34714i
\(471\) 6.23619e14i 1.23967i
\(472\) −5.93353e14 + 5.83146e13i −1.16582 + 0.114577i
\(473\) 2.80920e13i 0.0545566i
\(474\) 1.53115e14 5.00176e12i 0.293926 0.00960157i
\(475\) −1.18589e14 + 1.18589e14i −0.225025 + 0.225025i
\(476\) −1.50935e14 + 9.87162e12i −0.283108 + 0.0185161i
\(477\) −1.28560e15 1.28560e15i −2.38371 2.38371i
\(478\) −2.89163e14 + 3.08693e14i −0.530017 + 0.565814i
\(479\) −7.99937e14 −1.44947 −0.724737 0.689025i \(-0.758039\pi\)
−0.724737 + 0.689025i \(0.758039\pi\)
\(480\) −8.88522e14 + 1.23902e15i −1.59163 + 2.21947i
\(481\) 5.90894e14 1.04643
\(482\) −3.45234e14 + 3.68551e14i −0.604443 + 0.645267i
\(483\) −3.47042e14 3.47042e14i −0.600720 0.600720i
\(484\) 5.45013e14 3.56456e13i 0.932734 0.0610037i
\(485\) 3.93118e14 3.93118e14i 0.665186 0.665186i
\(486\) 2.93864e15 9.59955e13i 4.91639 0.160602i
\(487\) 5.92515e14i 0.980145i 0.871682 + 0.490072i \(0.163030\pi\)
−0.871682 + 0.490072i \(0.836970\pi\)
\(488\) 1.27752e12 + 1.29988e13i 0.00208958 + 0.0212616i
\(489\) 2.89902e12i 0.00468869i
\(490\) −2.26556e13 6.93539e14i −0.0362324 1.10916i
\(491\) −3.01153e14 + 3.01153e14i −0.476254 + 0.476254i −0.903932 0.427677i \(-0.859332\pi\)
0.427677 + 0.903932i \(0.359332\pi\)
\(492\) 1.53854e15 + 1.34965e15i 2.40603 + 2.11063i
\(493\) 1.53672e14 + 1.53672e14i 0.237650 + 0.237650i
\(494\) −1.16736e14 1.09351e14i −0.178529 0.167234i
\(495\) 6.73221e14 1.01819
\(496\) −2.52810e14 + 3.32112e13i −0.378133 + 0.0496747i
\(497\) 2.61832e13 0.0387314
\(498\) −1.17302e15 1.09880e15i −1.71610 1.60753i
\(499\) 4.74558e14 + 4.74558e14i 0.686651 + 0.686651i 0.961490 0.274839i \(-0.0886245\pi\)
−0.274839 + 0.961490i \(0.588625\pi\)
\(500\) −4.66705e13 + 5.32025e13i −0.0667894 + 0.0761373i
\(501\) −1.16422e15 + 1.16422e15i −1.64789 + 1.64789i
\(502\) −1.69946e13 5.20243e14i −0.0237925 0.728343i
\(503\) 8.88794e14i 1.23077i 0.788226 + 0.615385i \(0.211000\pi\)
−0.788226 + 0.615385i \(0.789000\pi\)
\(504\) 7.25488e14 + 5.95647e14i 0.993715 + 0.815870i
\(505\) 4.96658e14i 0.672907i
\(506\) −1.83701e14 + 6.00089e12i −0.246197 + 0.00804244i
\(507\) 5.16502e14 5.16502e14i 0.684744 0.684744i
\(508\) −8.28756e13 1.26715e15i −0.108687 1.66180i
\(509\) 6.54049e14 + 6.54049e14i 0.848521 + 0.848521i 0.989949 0.141428i \(-0.0451694\pi\)
−0.141428 + 0.989949i \(0.545169\pi\)
\(510\) 9.21633e14 9.83880e14i 1.18283 1.26272i
\(511\) −5.16799e13 −0.0656156
\(512\) −3.75735e14 + 7.01889e14i −0.471951 + 0.881625i
\(513\) 1.01682e15 1.26357
\(514\) −4.36120e14 + 4.65575e14i −0.536177 + 0.572391i
\(515\) 6.25880e14 + 6.25880e14i 0.761292 + 0.761292i
\(516\) 2.27839e13 + 3.48361e14i 0.0274192 + 0.419234i
\(517\) −1.47316e14 + 1.47316e14i −0.175409 + 0.175409i
\(518\) −5.57933e14 + 1.82258e13i −0.657308 + 0.0214720i
\(519\) 2.95151e14i 0.344052i
\(520\) 6.62861e14 + 5.44228e14i 0.764546 + 0.627715i
\(521\) 6.02759e14i 0.687918i −0.938985 0.343959i \(-0.888232\pi\)
0.938985 0.343959i \(-0.111768\pi\)
\(522\) −4.40338e13 1.34797e15i −0.0497277 1.52228i
\(523\) −1.41456e14 + 1.41456e14i −0.158075 + 0.158075i −0.781713 0.623638i \(-0.785654\pi\)
0.623638 + 0.781713i \(0.285654\pi\)
\(524\) 2.54479e12 2.90096e12i 0.00281403 0.00320789i
\(525\) −5.27839e14 5.27839e14i −0.577597 0.577597i
\(526\) −1.23598e15 1.15778e15i −1.33841 1.25373i
\(527\) 2.25456e14 0.241603
\(528\) 4.69942e14 6.17354e13i 0.498377 0.0654708i
\(529\) 6.70861e13 0.0704087
\(530\) 1.14533e15 + 1.07287e15i 1.18963 + 1.11437i
\(531\) −2.31334e15 2.31334e15i −2.37804 2.37804i
\(532\) 1.13598e14 + 9.96506e13i 0.115573 + 0.101383i
\(533\) 8.14062e14 8.14062e14i 0.819705 0.819705i
\(534\) 6.95783e13 + 2.12995e15i 0.0693421 + 2.12272i
\(535\) 1.07081e15i 1.05625i
\(536\) 9.38605e13 + 9.55034e14i 0.0916382 + 0.932422i
\(537\) 1.70750e15i 1.65007i
\(538\) −4.03891e14 + 1.31938e13i −0.386333 + 0.0126202i
\(539\) −1.52535e14 + 1.52535e14i −0.144422 + 0.144422i
\(540\) −5.44045e15 + 3.55823e14i −5.09882 + 0.333478i
\(541\) 3.03750e14 + 3.03750e14i 0.281794 + 0.281794i 0.833824 0.552030i \(-0.186147\pi\)
−0.552030 + 0.833824i \(0.686147\pi\)
\(542\) 1.02444e14 1.09363e14i 0.0940781 0.100432i
\(543\) 1.58970e15 1.44516
\(544\) 4.10230e14 5.72053e14i 0.369176 0.514804i
\(545\) −4.80250e13 −0.0427845
\(546\) 4.86719e14 5.19592e14i 0.429258 0.458250i
\(547\) 3.85320e14 + 3.85320e14i 0.336427 + 0.336427i 0.855021 0.518594i \(-0.173544\pi\)
−0.518594 + 0.855021i \(0.673544\pi\)
\(548\) −5.73812e14 + 3.75291e13i −0.495994 + 0.0324395i
\(549\) −5.06794e13 + 5.06794e13i −0.0433694 + 0.0433694i
\(550\) −2.79403e14 + 9.12715e12i −0.236720 + 0.00773286i
\(551\) 2.17116e14i 0.182120i
\(552\) 2.27315e15 2.23405e14i 1.88783 0.185536i
\(553\) 8.14121e13i 0.0669423i
\(554\) 6.40860e13 + 1.96182e15i 0.0521747 + 1.59718i
\(555\) 3.51812e15 3.51812e15i 2.83595 2.83595i
\(556\) −4.31372e14 3.78410e14i −0.344303 0.302030i
\(557\) −7.16583e14 7.16583e14i −0.566321 0.566321i 0.364775 0.931096i \(-0.381146\pi\)
−0.931096 + 0.364775i \(0.881146\pi\)
\(558\) −1.02112e15 9.56518e14i −0.799078 0.748523i
\(559\) 1.96377e14 0.152169
\(560\) −6.42672e14 4.93425e14i −0.493123 0.378606i
\(561\) −4.19094e14 −0.318431
\(562\) −3.71547e14 3.48041e14i −0.279553 0.261867i
\(563\) 8.55321e14 + 8.55321e14i 0.637284 + 0.637284i 0.949885 0.312600i \(-0.101200\pi\)
−0.312600 + 0.949885i \(0.601200\pi\)
\(564\) 1.70734e15 1.94630e15i 1.25975 1.43607i
\(565\) −2.15352e15 + 2.15352e15i −1.57356 + 1.57356i
\(566\) 7.25465e13 + 2.22081e15i 0.0524960 + 1.60702i
\(567\) 2.73169e15i 1.95760i
\(568\) −7.73236e13 + 9.41788e13i −0.0548777 + 0.0668401i
\(569\) 1.81588e15i 1.27635i −0.769891 0.638175i \(-0.779689\pi\)
0.769891 0.638175i \(-0.220311\pi\)
\(570\) −1.34610e15 + 4.39726e13i −0.937056 + 0.0306105i
\(571\) 1.13410e15 1.13410e15i 0.781901 0.781901i −0.198251 0.980151i \(-0.563526\pi\)
0.980151 + 0.198251i \(0.0635260\pi\)
\(572\) −1.74007e13 2.66053e14i −0.0118820 0.181673i
\(573\) 1.52537e15 + 1.52537e15i 1.03163 + 1.03163i
\(574\) −7.43543e14 + 7.93762e14i −0.498071 + 0.531710i
\(575\) −1.34716e15 −0.893809
\(576\) −4.28498e15 + 8.50468e14i −2.81595 + 0.558900i
\(577\) −2.48933e15 −1.62038 −0.810188 0.586170i \(-0.800635\pi\)
−0.810188 + 0.586170i \(0.800635\pi\)
\(578\) 6.34792e14 6.77666e14i 0.409288 0.436931i
\(579\) −1.48828e15 1.48828e15i −0.950499 0.950499i
\(580\) 7.59768e13 + 1.16167e15i 0.0480648 + 0.734901i
\(581\) 6.03969e14 6.03969e14i 0.378483 0.378483i
\(582\) 2.14665e15 7.01240e13i 1.33256 0.0435302i
\(583\) 4.87864e14i 0.300000i
\(584\) 1.52620e14 1.85888e14i 0.0929694 0.113235i
\(585\) 4.70615e15i 2.83993i
\(586\) −8.94964e13 2.73969e15i −0.0535018 1.63781i
\(587\) −1.17168e15 + 1.17168e15i −0.693903 + 0.693903i −0.963088 0.269185i \(-0.913246\pi\)
0.269185 + 0.963088i \(0.413246\pi\)
\(588\) 1.76783e15 2.01526e15i 1.03721 1.18238i
\(589\) −1.59267e14 1.59267e14i −0.0925747 0.0925747i
\(590\) 2.06094e15 + 1.93055e15i 1.18680 + 1.11172i
\(591\) −3.34510e15 −1.90844
\(592\) 1.58212e15 2.06066e15i 0.894271 1.16476i
\(593\) 2.16626e15 1.21314 0.606569 0.795031i \(-0.292545\pi\)
0.606569 + 0.795031i \(0.292545\pi\)
\(594\) 1.23697e15 + 1.15871e15i 0.686330 + 0.642908i
\(595\) 5.06585e14 + 5.06585e14i 0.278490 + 0.278490i
\(596\) −1.48082e15 1.29901e15i −0.806582 0.707553i
\(597\) 2.14587e15 2.14587e15i 1.15809 1.15809i
\(598\) −4.19492e13 1.28416e15i −0.0224319 0.686692i
\(599\) 2.29916e15i 1.21821i 0.793089 + 0.609105i \(0.208471\pi\)
−0.793089 + 0.609105i \(0.791529\pi\)
\(600\) 3.45739e15 3.39791e14i 1.81517 0.178394i
\(601\) 7.60944e14i 0.395861i 0.980216 + 0.197931i \(0.0634221\pi\)
−0.980216 + 0.197931i \(0.936578\pi\)
\(602\) −1.85423e14 + 6.05715e12i −0.0955836 + 0.00312240i
\(603\) −3.72345e15 + 3.72345e15i −1.90195 + 1.90195i
\(604\) 2.54399e15 1.66385e14i 1.28769 0.0842189i
\(605\) −1.82924e15 1.82924e15i −0.917519 0.917519i
\(606\) −1.31173e15 + 1.40032e15i −0.651994 + 0.696030i
\(607\) 1.83671e15 0.904694 0.452347 0.891842i \(-0.350587\pi\)
0.452347 + 0.891842i \(0.350587\pi\)
\(608\) −6.93908e14 + 1.14316e14i −0.338713 + 0.0558002i
\(609\) 9.66377e14 0.467467
\(610\) 4.22934e13 4.51499e13i 0.0202749 0.0216442i
\(611\) −1.02981e15 1.02981e15i −0.489250 0.489250i
\(612\) 3.85446e15 2.52093e14i 1.81481 0.118694i
\(613\) 8.30874e14 8.30874e14i 0.387706 0.387706i −0.486162 0.873868i \(-0.661604\pi\)
0.873868 + 0.486162i \(0.161604\pi\)
\(614\) −3.20465e13 + 1.04685e12i −0.0148202 + 0.000484127i
\(615\) 9.69367e15i 4.44299i
\(616\) 2.46363e13 + 2.50675e14i 0.0111913 + 0.113872i
\(617\) 2.95927e15i 1.33234i −0.745799 0.666171i \(-0.767932\pi\)
0.745799 0.666171i \(-0.232068\pi\)
\(618\) 1.11644e14 + 3.41768e15i 0.0498194 + 1.52509i
\(619\) −1.00184e15 + 1.00184e15i −0.443100 + 0.443100i −0.893052 0.449953i \(-0.851441\pi\)
0.449953 + 0.893052i \(0.351441\pi\)
\(620\) 9.07888e14 + 7.96421e14i 0.397995 + 0.349131i
\(621\) 5.77545e15 + 5.77545e15i 2.50947 + 2.50947i
\(622\) −2.21734e15 2.07705e15i −0.954959 0.894542i
\(623\) −1.13250e15 −0.483454
\(624\) 4.31561e14 + 3.28513e15i 0.182611 + 1.39007i
\(625\) 2.54544e15 1.06764
\(626\) 3.86316e14 + 3.61875e14i 0.160614 + 0.150453i
\(627\) 2.96058e14 + 2.96058e14i 0.122013 + 0.122013i
\(628\) −1.01709e15 + 1.15944e15i −0.415510 + 0.473665i
\(629\) −1.62431e15 + 1.62431e15i −0.657796 + 0.657796i
\(630\) −1.45159e14 4.44363e15i −0.0582733 1.78388i
\(631\) 2.54047e15i 1.01100i −0.862825 0.505502i \(-0.831307\pi\)
0.862825 0.505502i \(-0.168693\pi\)
\(632\) −2.92832e14 2.40424e14i −0.115525 0.0948492i
\(633\) 2.18727e15i 0.855423i
\(634\) −3.47048e15 + 1.13369e14i −1.34555 + 0.0439545i
\(635\) −4.25295e15 + 4.25295e15i −1.63469 + 1.63469i
\(636\) 3.95680e14 + 6.04986e15i 0.150775 + 2.30532i
\(637\) −1.06630e15 1.06630e15i −0.402820 0.402820i
\(638\) 2.47413e14 2.64123e14i 0.0926634 0.0989218i
\(639\) −6.68646e14 −0.248280
\(640\) 3.67273e15 8.54466e14i 1.35207 0.314561i
\(641\) −2.18928e15 −0.799064 −0.399532 0.916719i \(-0.630827\pi\)
−0.399532 + 0.916719i \(0.630827\pi\)
\(642\) −2.82812e15 + 3.01914e15i −1.02342 + 1.09255i
\(643\) 1.65718e15 + 1.65718e15i 0.594577 + 0.594577i 0.938864 0.344287i \(-0.111879\pi\)
−0.344287 + 0.938864i \(0.611879\pi\)
\(644\) 7.92184e13 + 1.21123e15i 0.0281808 + 0.430879i
\(645\) 1.16921e15 1.16921e15i 0.412395 0.412395i
\(646\) 6.21493e14 2.03021e13i 0.217349 0.00710006i
\(647\) 1.95252e15i 0.677051i 0.940957 + 0.338526i \(0.109928\pi\)
−0.940957 + 0.338526i \(0.890072\pi\)
\(648\) −9.82565e15 8.06715e15i −3.37830 2.77369i
\(649\) 8.77877e14i 0.299287i
\(650\) −6.38033e13 1.95316e15i −0.0215685 0.660260i
\(651\) 7.08895e14 7.08895e14i 0.237622 0.237622i
\(652\) −4.72815e12 + 5.38990e12i −0.00157155 + 0.00179151i
\(653\) −1.59179e15 1.59179e15i −0.524642 0.524642i 0.394328 0.918970i \(-0.370978\pi\)
−0.918970 + 0.394328i \(0.870978\pi\)
\(654\) −1.35406e14 1.26839e14i −0.0442547 0.0414549i
\(655\) −1.82776e13 −0.00592369
\(656\) −6.59281e14 5.01858e15i −0.211885 1.61291i
\(657\) 1.31976e15 0.420616
\(658\) 1.00413e15 + 9.40603e14i 0.317357 + 0.297279i
\(659\) −1.25231e15 1.25231e15i −0.392502 0.392502i 0.483077 0.875578i \(-0.339519\pi\)
−0.875578 + 0.483077i \(0.839519\pi\)
\(660\) −1.68765e15 1.48045e15i −0.524555 0.460152i
\(661\) −1.31167e15 + 1.31167e15i −0.404311 + 0.404311i −0.879749 0.475438i \(-0.842290\pi\)
0.475438 + 0.879749i \(0.342290\pi\)
\(662\) 1.97952e14 + 6.05976e15i 0.0605119 + 1.85241i
\(663\) 2.92967e15i 0.888168i
\(664\) 3.88799e14 + 3.95605e15i 0.116896 + 1.18943i
\(665\) 7.15728e14i 0.213417i
\(666\) 1.42481e16 4.65436e14i 4.21354 0.137642i
\(667\) 1.23320e15 1.23320e15i 0.361694 0.361694i
\(668\) 4.06333e15 2.65754e14i 1.18198 0.0773054i
\(669\) −7.39959e15 7.39959e15i −2.13483 2.13483i
\(670\) 3.10732e15 3.31719e15i 0.889150 0.949202i
\(671\) −1.92320e13 −0.00545823
\(672\) −5.08816e14 3.08857e15i −0.143229 0.869414i
\(673\) −4.42717e15 −1.23607 −0.618035 0.786151i \(-0.712071\pi\)
−0.618035 + 0.786151i \(0.712071\pi\)
\(674\) 7.68484e14 8.20387e14i 0.212816 0.227190i
\(675\) 8.78426e15 + 8.78426e15i 2.41287 + 2.41287i
\(676\) −1.80268e15 + 1.17901e14i −0.491147 + 0.0321226i
\(677\) 4.02631e15 4.02631e15i 1.08810 1.08810i 0.0923785 0.995724i \(-0.470553\pi\)
0.995724 0.0923785i \(-0.0294470\pi\)
\(678\) −1.17595e16 + 3.84143e14i −3.15228 + 0.102975i
\(679\) 1.14139e15i 0.303493i
\(680\) −3.31818e15 + 3.26109e14i −0.875186 + 0.0860131i
\(681\) 7.48297e15i 1.95779i
\(682\) −1.22579e13 3.75242e14i −0.00318128 0.0973862i
\(683\) 1.78162e15 1.78162e15i 0.458671 0.458671i −0.439548 0.898219i \(-0.644861\pi\)
0.898219 + 0.439548i \(0.144861\pi\)
\(684\) −2.90097e15 2.54480e15i −0.740856 0.649897i
\(685\) 1.92589e15 + 1.92589e15i 0.487903 + 0.487903i
\(686\) 2.34027e15 + 2.19221e15i 0.588145 + 0.550935i
\(687\) 1.42258e15 0.354662
\(688\) 5.25799e14 6.84839e14i 0.130042 0.169376i
\(689\) 3.41041e15 0.836760
\(690\) −7.89550e15 7.39598e15i −1.92181 1.80022i
\(691\) −2.83219e15 2.83219e15i −0.683902 0.683902i 0.276975 0.960877i \(-0.410668\pi\)
−0.960877 + 0.276975i \(0.910668\pi\)
\(692\) 4.81377e14 5.48751e14i 0.115319 0.131459i
\(693\) −9.77322e14 + 9.77322e14i −0.232276 + 0.232276i
\(694\) −8.47985e13 2.59587e15i −0.0199945 0.612077i
\(695\) 2.71788e15i 0.635790i
\(696\) −2.85388e15 + 3.47597e15i −0.662345 + 0.806725i
\(697\) 4.47556e15i 1.03055i
\(698\) 3.45968e15 1.13016e14i 0.790372 0.0258188i
\(699\) 9.68356e15 9.68356e15i 2.19488 2.19488i
\(700\) 1.20489e14 + 1.84225e15i 0.0270961 + 0.414294i
\(701\) 2.66761e15 + 2.66761e15i 0.595214 + 0.595214i 0.939035 0.343821i \(-0.111721\pi\)
−0.343821 + 0.939035i \(0.611721\pi\)
\(702\) −8.09995e15 + 8.64702e15i −1.79320 + 1.91431i
\(703\) 2.29491e15 0.504093
\(704\) −9.74412e14 6.51673e14i −0.212370 0.142030i
\(705\) −1.22628e16 −2.65185
\(706\) −3.68519e15 + 3.93408e15i −0.790740 + 0.844146i
\(707\) −7.21004e14 7.21004e14i −0.153508 0.153508i
\(708\) 7.11998e14 + 1.08863e16i 0.150417 + 2.29984i
\(709\) 2.91989e15 2.91989e15i 0.612085 0.612085i −0.331404 0.943489i \(-0.607522\pi\)
0.943489 + 0.331404i \(0.107522\pi\)
\(710\) 5.76848e14 1.88437e13i 0.119989 0.00391963i
\(711\) 2.07904e15i 0.429120i
\(712\) 3.34448e15 4.07352e15i 0.684997 0.834314i
\(713\) 1.80925e15i 0.367711i
\(714\) 9.03643e13 + 2.76625e15i 0.0182245 + 0.557894i
\(715\) −8.92956e14 + 8.92956e14i −0.178709 + 0.178709i
\(716\) −2.78484e15 + 3.17461e15i −0.553069 + 0.630477i
\(717\) 5.47275e15 + 5.47275e15i 1.07857 + 1.07857i
\(718\) 5.51646e15 + 5.16745e15i 1.07889 + 1.01063i
\(719\) 7.46765e15 1.44935 0.724677 0.689088i \(-0.241989\pi\)
0.724677 + 0.689088i \(0.241989\pi\)
\(720\) 1.64120e16 + 1.26007e16i 3.16107 + 2.42698i
\(721\) −1.81719e15 −0.347342
\(722\) 3.39403e15 + 3.17930e15i 0.643815 + 0.603083i
\(723\) 6.53396e15 + 6.53396e15i 1.23003 + 1.23003i
\(724\) −2.95559e15 2.59271e15i −0.552182 0.484387i
\(725\) 1.87566e15 1.87566e15i 0.347772 0.347772i
\(726\) −3.26298e14 9.98871e15i −0.0600430 1.83805i
\(727\) 8.34141e13i 0.0152335i 0.999971 + 0.00761676i \(0.00242451\pi\)
−0.999971 + 0.00761676i \(0.997575\pi\)
\(728\) −1.75234e15 + 1.72220e14i −0.317612 + 0.0312148i
\(729\) 2.95012e16i 5.30687i
\(730\) −1.13857e15 + 3.71933e13i −0.203275 + 0.00664032i
\(731\) −5.39823e14 + 5.39823e14i −0.0956546 + 0.0956546i
\(732\) 2.38491e14 1.55981e13i 0.0419432 0.00274321i
\(733\) 7.73562e15 + 7.73562e15i 1.35028 + 1.35028i 0.885346 + 0.464933i \(0.153921\pi\)
0.464933 + 0.885346i \(0.346079\pi\)
\(734\) 4.11375e15 4.39159e15i 0.712705 0.760841i
\(735\) −1.26972e16 −2.18338
\(736\) −4.59065e15 3.29204e15i −0.783512 0.561872i
\(737\) −1.41299e15 −0.239369
\(738\) 1.89880e16 2.02705e16i 3.19278 3.40842i
\(739\) −2.34299e15 2.34299e15i −0.391044 0.391044i 0.484015 0.875060i \(-0.339178\pi\)
−0.875060 + 0.484015i \(0.839178\pi\)
\(740\) −1.22788e16 + 8.03074e14i −2.03415 + 0.133040i
\(741\) −2.06959e15 + 2.06959e15i −0.340318 + 0.340318i
\(742\) −3.22018e15 + 1.05192e14i −0.525603 + 0.0171697i
\(743\) 7.38859e15i 1.19708i 0.801093 + 0.598540i \(0.204252\pi\)
−0.801093 + 0.598540i \(0.795748\pi\)
\(744\) 4.56345e14 + 4.64333e15i 0.0733909 + 0.746755i
\(745\) 9.32999e15i 1.48944i
\(746\) −3.32104e14 1.01665e16i −0.0526273 1.61104i
\(747\) −1.54237e16 + 1.54237e16i −2.42619 + 2.42619i
\(748\) 7.79187e14 + 6.83521e14i 0.121670 + 0.106732i
\(749\) −1.55451e15 1.55451e15i −0.240959 0.240959i
\(750\) 9.45106e14 + 8.85313e14i 0.145427 + 0.136226i
\(751\) 2.74146e14 0.0418758 0.0209379 0.999781i \(-0.493335\pi\)
0.0209379 + 0.999781i \(0.493335\pi\)
\(752\) −6.34864e15 + 8.34009e14i −0.962682 + 0.126466i
\(753\) −9.52455e15 −1.43375
\(754\) 1.84635e15 + 1.72954e15i 0.275913 + 0.258457i
\(755\) −8.53841e15 8.53841e15i −1.26669 1.26669i
\(756\) 7.38141e15 8.41451e15i 1.08710 1.23925i
\(757\) 1.20145e15 1.20145e15i 0.175662 0.175662i −0.613800 0.789462i \(-0.710360\pi\)
0.789462 + 0.613800i \(0.210360\pi\)
\(758\) 5.90184e12 + 1.80669e14i 0.000856656 + 0.0262242i
\(759\) 3.36317e15i 0.484640i
\(760\) 2.57441e15 + 2.11367e15i 0.368301 + 0.302386i
\(761\) 5.15297e15i 0.731883i 0.930638 + 0.365942i \(0.119253\pi\)
−0.930638 + 0.365942i \(0.880747\pi\)
\(762\) −2.32236e16 + 7.58639e14i −3.27475 + 0.106975i
\(763\) 6.97184e13 6.97184e13i 0.00976028 0.00976028i
\(764\) −3.48192e14 5.32379e15i −0.0483956 0.739959i
\(765\) −1.29368e16 1.29368e16i −1.78520 1.78520i
\(766\) 1.83231e15 1.95606e15i 0.251039 0.267994i
\(767\) 6.13680e15 0.834771
\(768\) 1.26119e16 + 7.29091e15i 1.70332 + 0.984680i
\(769\) −8.26093e14 −0.110773 −0.0553866 0.998465i \(-0.517639\pi\)
−0.0553866 + 0.998465i \(0.517639\pi\)
\(770\) 8.15603e14 8.70688e14i 0.108587 0.115921i
\(771\) 8.25407e15 + 8.25407e15i 1.09111 + 1.09111i
\(772\) 3.39726e14 + 5.19434e15i 0.0445896 + 0.681766i
\(773\) 5.16962e15 5.16962e15i 0.673707 0.673707i −0.284861 0.958569i \(-0.591948\pi\)
0.958569 + 0.284861i \(0.0919476\pi\)
\(774\) 4.73519e15 1.54683e14i 0.612720 0.0200155i
\(775\) 2.75181e15i 0.353557i
\(776\) −4.10547e15 3.37071e15i −0.523749 0.430013i
\(777\) 1.02146e16i 1.29391i
\(778\) 4.87859e13 + 1.49345e15i 0.00613630 + 0.187846i
\(779\) 3.16164e15 3.16164e15i 0.394873 0.394873i
\(780\) 1.03491e16 1.17975e16i 1.28345 1.46309i
\(781\) −1.26871e14 1.26871e14i −0.0156236 0.0156236i
\(782\) 3.64535e15 + 3.41472e15i 0.445761 + 0.417559i
\(783\) −1.60824e16 −1.95281
\(784\) −6.57358e15 + 8.63558e14i −0.792617 + 0.104125i
\(785\) 7.30513e15 0.874672
\(786\) −5.15335e13 4.82731e13i −0.00612725 0.00573960i
\(787\) −5.98784e15 5.98784e15i −0.706983 0.706983i 0.258917 0.965900i \(-0.416635\pi\)
−0.965900 + 0.258917i \(0.916635\pi\)
\(788\) 6.21927e15 + 5.45569e15i 0.729198 + 0.639670i
\(789\) −2.19123e16 + 2.19123e16i −2.55132 + 2.55132i
\(790\) 5.85911e13 + 1.79361e15i 0.00677458 + 0.207385i
\(791\) 6.25258e15i 0.717940i
\(792\) −6.29142e14 6.40154e15i −0.0717398 0.729955i
\(793\) 1.34442e14i 0.0152241i
\(794\) −1.40079e15 + 4.57592e13i −0.157529 + 0.00514595i
\(795\) 2.03052e16 2.03052e16i 2.26772 2.26772i
\(796\) −7.48944e15 + 4.89832e14i −0.830668 + 0.0543282i
\(797\) −1.83817e15 1.83817e15i −0.202472 0.202472i 0.598586 0.801058i \(-0.295729\pi\)
−0.801058 + 0.598586i \(0.795729\pi\)
\(798\) 1.89031e15 2.01798e15i 0.206784 0.220750i
\(799\) 5.66171e15 0.615092
\(800\) −6.98222e15 5.00708e15i −0.753353 0.540244i
\(801\) 2.89210e16 3.09909
\(802\) −2.42625e15 + 2.59011e15i −0.258212 + 0.275651i
\(803\) 2.50415e14 + 2.50415e14i 0.0264682 + 0.0264682i
\(804\) 1.75221e16 1.14600e15i 1.83941 0.120303i
\(805\) 4.06528e15 4.06528e15i 0.423851 0.423851i
\(806\) 2.62313e15 8.56888e13i 0.271629 0.00887322i
\(807\) 7.39439e15i 0.760498i
\(808\) 4.72264e15 4.64139e14i 0.482416 0.0474117i
\(809\) 7.03952e14i 0.0714211i −0.999362 0.0357105i \(-0.988631\pi\)
0.999362 0.0357105i \(-0.0113694\pi\)
\(810\) 1.96596e15 + 6.01824e16i 0.198110 + 6.06459i
\(811\) −7.23162e15 + 7.23162e15i −0.723804 + 0.723804i −0.969378 0.245574i \(-0.921023\pi\)
0.245574 + 0.969378i \(0.421023\pi\)
\(812\) −1.79671e15 1.57611e15i −0.178615 0.156686i
\(813\) −1.93886e15 1.93886e15i −0.191447 0.191447i
\(814\) 2.79177e15 + 2.61515e15i 0.273808 + 0.256485i
\(815\) 3.39593e13 0.00330821
\(816\) −1.02168e16 7.84419e15i −0.988600 0.759019i
\(817\) 7.62688e14 0.0733036
\(818\) −1.79712e15 1.68342e15i −0.171567 0.160713i
\(819\) −6.83196e15 6.83196e15i −0.647864 0.647864i
\(820\) −1.58099e16 + 1.80227e16i −1.48920 + 1.69763i
\(821\) 3.15400e15 3.15400e15i 0.295103 0.295103i −0.543989 0.839092i \(-0.683087\pi\)
0.839092 + 0.543989i \(0.183087\pi\)
\(822\) 3.43539e14 + 1.05165e16i 0.0319287 + 0.977409i
\(823\) 7.95562e15i 0.734471i −0.930128 0.367236i \(-0.880304\pi\)
0.930128 0.367236i \(-0.119696\pi\)
\(824\) 5.36649e15 6.53629e15i 0.492142 0.599420i
\(825\) 5.11527e15i 0.465985i
\(826\) −5.79448e15 + 1.89286e14i −0.524354 + 0.0171289i
\(827\) −7.06259e15 + 7.06259e15i −0.634869 + 0.634869i −0.949285 0.314417i \(-0.898191\pi\)
0.314417 + 0.949285i \(0.398191\pi\)
\(828\) −2.02302e15 3.09315e16i −0.180648 2.76207i
\(829\) −7.83457e15 7.83457e15i −0.694969 0.694969i 0.268352 0.963321i \(-0.413521\pi\)
−0.963321 + 0.268352i \(0.913521\pi\)
\(830\) 1.28715e16 1.37408e16i 1.13423 1.21083i
\(831\) 3.59168e16 3.14406
\(832\) 4.55551e15 6.81163e15i 0.396150 0.592342i
\(833\) 5.86231e15 0.506432
\(834\) −7.17821e15 + 7.66302e15i −0.616031 + 0.657638i
\(835\) −1.36378e16 1.36378e16i −1.16270 1.16270i
\(836\) −6.75805e13 1.03329e15i −0.00572383 0.0875162i
\(837\) −1.17974e16 + 1.17974e16i −0.992650 + 0.992650i
\(838\) −1.58138e16 + 5.16584e14i −1.32189 + 0.0431816i
\(839\) 5.19905e15i 0.431751i −0.976421 0.215876i \(-0.930739\pi\)
0.976421 0.215876i \(-0.0692606\pi\)
\(840\) −9.40789e15 + 1.14586e16i −0.776169 + 0.945360i
\(841\) 8.76652e15i 0.718538i
\(842\) −6.29824e14 1.92803e16i −0.0512864 1.56999i
\(843\) −6.58707e15 + 6.58707e15i −0.532894 + 0.532894i
\(844\) 3.56732e15 4.06660e15i 0.286721 0.326850i
\(845\) 6.05036e15 + 6.05036e15i 0.483136 + 0.483136i
\(846\) −2.56427e16 2.40204e16i −2.03435 1.90565i
\(847\) 5.31104e15 0.418621
\(848\) 9.13137e15 1.18933e16i 0.715087 0.931380i
\(849\) 4.06584e16 3.16343
\(850\) 5.54445e15 + 5.19368e15i 0.428603 + 0.401486i
\(851\) 1.30349e16 + 1.30349e16i 1.00114 + 1.00114i
\(852\) 1.67618e15 + 1.47039e15i 0.127910 + 0.112205i
\(853\) −6.77512e15 + 6.77512e15i −0.513686 + 0.513686i −0.915654 0.401968i \(-0.868326\pi\)
0.401968 + 0.915654i \(0.368326\pi\)
\(854\) 4.14678e12 + 1.26942e14i 0.000312387 + 0.00956286i
\(855\) 1.82777e16i 1.36807i
\(856\) 1.01822e16 1.00070e15i 0.757241 0.0744215i
\(857\) 1.61172e16i 1.19095i 0.803372 + 0.595477i \(0.203037\pi\)
−0.803372 + 0.595477i \(0.796963\pi\)
\(858\) −4.87607e15 + 1.59285e14i −0.358005 + 0.0116948i
\(859\) −2.67447e15 + 2.67447e15i −0.195108 + 0.195108i −0.797899 0.602791i \(-0.794055\pi\)
0.602791 + 0.797899i \(0.294055\pi\)
\(860\) −4.08074e15 + 2.66893e14i −0.295799 + 0.0193462i
\(861\) 1.40724e16 + 1.40724e16i 1.01356 + 1.01356i
\(862\) 1.41299e16 1.50842e16i 1.01123 1.07952i
\(863\) −1.60361e16 −1.14036 −0.570178 0.821521i \(-0.693126\pi\)
−0.570178 + 0.821521i \(0.693126\pi\)
\(864\) 8.46770e15 + 5.13998e16i 0.598329 + 3.63192i
\(865\) −3.45743e15 −0.242753
\(866\) −5.79550e15 + 6.18692e15i −0.404336 + 0.431645i
\(867\) −1.20142e16 1.20142e16i −0.832892 0.832892i
\(868\) −2.47416e15 + 1.61818e14i −0.170439 + 0.0111473i
\(869\) 3.94481e14 3.94481e14i 0.0270033 0.0270033i
\(870\) 2.12904e16 6.95488e14i 1.44820 0.0473079i
\(871\) 9.87751e15i 0.667648i
\(872\) 4.48806e13 + 4.56661e14i 0.00301452 + 0.0306728i
\(873\) 2.91478e16i 1.94548i
\(874\) −1.62922e14 4.98740e15i −0.0108060 0.330797i
\(875\) −4.86621e14 + 4.86621e14i −0.0320735 + 0.0320735i
\(876\) −3.30842e15 2.90222e15i −0.216694 0.190089i
\(877\) −9.67974e15 9.67974e15i −0.630037 0.630037i 0.318041 0.948077i \(-0.396975\pi\)
−0.948077 + 0.318041i \(0.896975\pi\)
\(878\) 2.04093e16 + 1.91181e16i 1.32010 + 1.23659i
\(879\) −5.01579e16 −3.22404
\(880\) 7.23175e14 + 5.50495e15i 0.0461943 + 0.351640i
\(881\) −5.86163e15 −0.372093 −0.186046 0.982541i \(-0.559567\pi\)
−0.186046 + 0.982541i \(0.559567\pi\)
\(882\) −2.65512e16 2.48714e16i −1.67497 1.56900i
\(883\) −7.35372e15 7.35372e15i −0.461024 0.461024i 0.437967 0.898991i \(-0.355699\pi\)
−0.898991 + 0.437967i \(0.855699\pi\)
\(884\) −4.77815e15 + 5.44690e15i −0.297696 + 0.339361i
\(885\) 3.65378e16 3.65378e16i 2.26232 2.26232i
\(886\) 8.02919e14 + 2.45792e16i 0.0494068 + 1.51245i
\(887\) 2.65254e16i 1.62211i 0.584967 + 0.811057i \(0.301108\pi\)
−0.584967 + 0.811057i \(0.698892\pi\)
\(888\) −3.67410e16 3.01654e16i −2.23295 1.83332i
\(889\) 1.23481e16i 0.745832i
\(890\) −2.49504e16 + 8.15047e14i −1.49773 + 0.0489258i
\(891\) 1.32364e16 1.32364e16i 0.789662 0.789662i
\(892\) 1.68909e15 + 2.58258e16i 0.100149 + 1.53125i
\(893\) −3.99957e15 3.99957e15i −0.235684 0.235684i
\(894\) −2.46415e16 + 2.63058e16i −1.44315 + 1.54062i
\(895\) 2.00018e16 1.16424
\(896\) −4.09130e15 + 6.57218e15i −0.236683 + 0.380203i
\(897\) −2.35102e16 −1.35176
\(898\) −1.04922e14 + 1.12009e14i −0.00599580 + 0.00640076i
\(899\) 2.51903e15 + 2.51903e15i 0.143072 + 0.143072i
\(900\) −3.07694e15 4.70458e16i −0.173694 2.65575i
\(901\) −9.37491e15 + 9.37491e15i −0.525994 + 0.525994i
\(902\) 7.44900e15 2.43334e14i 0.415396 0.0135696i
\(903\) 3.39471e15i 0.188157i
\(904\) 2.24900e16 + 1.84649e16i 1.23898 + 1.01724i
\(905\) 1.86218e16i 1.01966i
\(906\) −1.52308e15 4.66248e16i −0.0828927 2.53753i
\(907\) 1.45137e16 1.45137e16i 0.785124 0.785124i −0.195567 0.980690i \(-0.562655\pi\)
0.980690 + 0.195567i \(0.0626547\pi\)
\(908\) 1.22044e16 1.39125e16i 0.656210 0.748053i
\(909\) 1.84124e16 + 1.84124e16i 0.984032 + 0.984032i
\(910\) 6.08654e15 + 5.70147e15i 0.323328 + 0.302872i
\(911\) −2.74199e16 −1.44782 −0.723910 0.689895i \(-0.757657\pi\)
−0.723910 + 0.689895i \(0.757657\pi\)
\(912\) 1.67609e15 + 1.27587e16i 0.0879683 + 0.669632i
\(913\) −5.85305e15 −0.305346
\(914\) 2.09166e16 + 1.95933e16i 1.08464 + 1.01602i
\(915\) −8.00451e14 8.00451e14i −0.0412590 0.0412590i
\(916\) −2.64488e15 2.32015e15i −0.135513 0.118875i
\(917\) 2.65338e13 2.65338e13i 0.00135135 0.00135135i
\(918\) −1.50384e15 4.60359e16i −0.0761318 2.33057i
\(919\) 1.55320e16i 0.781612i −0.920473 0.390806i \(-0.872196\pi\)
0.920473 0.390806i \(-0.127804\pi\)
\(920\) 2.61698e15 + 2.66279e16i 0.130909 + 1.33200i
\(921\) 5.86704e14i 0.0291737i
\(922\) 3.17878e16 1.03840e15i 1.57123 0.0513270i
\(923\) 8.86888e14 8.86888e14i 0.0435772 0.0435772i
\(924\) 4.59916e15 3.00799e14i 0.224638 0.0146920i
\(925\) 1.98256e16 + 1.98256e16i 0.962604 + 0.962604i
\(926\) −2.00044e16 + 2.13555e16i −0.965530 + 1.03074i
\(927\) 4.64060e16 2.22657
\(928\) 1.09751e16 1.80806e15i 0.523474 0.0862381i
\(929\) −1.93944e16 −0.919579 −0.459790 0.888028i \(-0.652075\pi\)
−0.459790 + 0.888028i \(0.652075\pi\)
\(930\) 1.51076e16 1.61280e16i 0.712099 0.760194i
\(931\) −4.14127e15 4.14127e15i −0.194049 0.194049i
\(932\) −3.37972e16 + 2.21044e15i −1.57432 + 0.102966i
\(933\) −3.93106e16 + 3.93106e16i −1.82038 + 1.82038i
\(934\) −1.79280e16 + 5.85649e14i −0.825325 + 0.0269606i
\(935\) 4.90931e15i 0.224676i
\(936\) 4.47500e16 4.39801e15i 2.03599 0.200096i
\(937\) 2.03964e16i 0.922543i −0.887259 0.461272i \(-0.847393\pi\)
0.887259 0.461272i \(-0.152607\pi\)
\(938\) 3.04667e14 + 9.32653e15i 0.0136996 + 0.419377i
\(939\) 6.84890e15 6.84890e15i 0.306168 0.306168i
\(940\) 2.27992e16 + 2.00000e16i 1.01325 + 0.888845i
\(941\) −2.84300e16 2.84300e16i −1.25613 1.25613i −0.952926 0.303204i \(-0.901944\pi\)
−0.303204 0.952926i \(-0.598056\pi\)
\(942\) 2.05967e16 + 1.92936e16i 0.904728 + 0.847489i
\(943\) 3.59158e16 1.56845
\(944\) 1.64313e16 2.14012e16i 0.713386 0.929165i
\(945\) −5.30161e16 −2.28840
\(946\) 9.27816e14 + 8.69116e14i 0.0398163 + 0.0372972i
\(947\) 1.73191e15 + 1.73191e15i 0.0738925 + 0.0738925i 0.743087 0.669195i \(-0.233361\pi\)
−0.669195 + 0.743087i \(0.733361\pi\)
\(948\) −4.57191e15 + 5.21179e15i −0.193933 + 0.221076i
\(949\) −1.75052e15 + 1.75052e15i −0.0738250 + 0.0738250i
\(950\) −2.47799e14 7.58567e15i −0.0103901 0.318064i
\(951\) 6.35372e16i 2.64871i
\(952\) 4.34362e15 5.29045e15i 0.180031 0.219275i
\(953\) 2.78400e16i 1.14725i 0.819118 + 0.573625i \(0.194463\pi\)
−0.819118 + 0.573625i \(0.805537\pi\)
\(954\) 8.22343e16 2.68632e15i 3.36928 0.110063i
\(955\) −1.78683e16 + 1.78683e16i −0.727888 + 0.727888i
\(956\) −1.24925e15 1.91008e16i −0.0505978 0.773630i
\(957\) −4.68257e15 4.68257e15i −0.188568 0.188568i
\(958\) 2.47486e16 2.64201e16i 0.990924 1.05785i
\(959\) −5.59168e15 −0.222607
\(960\) −1.34326e16 6.76787e16i −0.531704 2.67892i
\(961\) −2.17128e16 −0.854548
\(962\) −1.82812e16 + 1.95159e16i −0.715387 + 0.763704i
\(963\) 3.96978e16 + 3.96978e16i 1.54462 + 1.54462i
\(964\) −1.49149e15 2.28046e16i −0.0577029 0.882265i
\(965\) 1.74338e16 1.74338e16i 0.670645 0.670645i
\(966\) 2.21988e16 7.25161e14i 0.849094 0.0277371i
\(967\) 1.07368e16i 0.408348i 0.978935 + 0.204174i \(0.0654508\pi\)
−0.978935 + 0.204174i \(0.934549\pi\)
\(968\) −1.56844e16 + 1.91034e16i −0.593136 + 0.722429i
\(969\) 1.13782e16i 0.427852i
\(970\) 8.21439e14 + 2.51461e16i 0.0307136 + 0.940213i
\(971\) 2.12051e15 2.12051e15i 0.0788377 0.0788377i −0.666588 0.745426i \(-0.732246\pi\)
0.745426 + 0.666588i \(0.232246\pi\)
\(972\) −8.77455e16 + 1.00026e17i −3.24385 + 3.69786i
\(973\) −3.94558e15 3.94558e15i −0.145041 0.145041i
\(974\) −1.95694e16 1.83313e16i −0.715326 0.670069i
\(975\) −3.57583e16 −1.29973
\(976\) −4.68847e14 3.59967e14i −0.0169456 0.0130103i
\(977\) −2.75619e16 −0.990579 −0.495289 0.868728i \(-0.664938\pi\)
−0.495289 + 0.868728i \(0.664938\pi\)
\(978\) 9.57479e13 + 8.96902e13i 0.00342188 + 0.00320539i
\(979\) 5.48754e15 + 5.48754e15i 0.195017 + 0.195017i
\(980\) 2.36069e16 + 2.07086e16i 0.834250 + 0.731824i
\(981\) −1.78041e15 + 1.78041e15i −0.0625664 + 0.0625664i
\(982\) −6.29275e14 1.92635e16i −0.0219901 0.673166i
\(983\) 7.69115e15i 0.267268i 0.991031 + 0.133634i \(0.0426646\pi\)
−0.991031 + 0.133634i \(0.957335\pi\)
\(984\) −9.21755e16 + 9.05898e15i −3.18524 + 0.313045i
\(985\) 3.91848e16i 1.34654i
\(986\) −9.82978e15 + 3.21106e14i −0.335908 + 0.0109730i
\(987\) 1.78020e16 1.78020e16i 0.604957 0.604957i
\(988\) 7.22322e15 4.72421e14i 0.244100 0.0159649i
\(989\) 4.33201e15 + 4.33201e15i 0.145583 + 0.145583i
\(990\) −2.08282e16 + 2.22349e16i −0.696079 + 0.743092i
\(991\) 5.13881e14 0.0170788 0.00853939 0.999964i \(-0.497282\pi\)
0.00853939 + 0.999964i \(0.497282\pi\)
\(992\) 6.72459e15 9.37723e15i 0.222255 0.309928i
\(993\) 1.10941e17 3.64647
\(994\) −8.10061e14 + 8.64772e14i −0.0264784 + 0.0282668i
\(995\) 2.51369e16 + 2.51369e16i 0.817118 + 0.817118i
\(996\) 7.25820e16 4.74709e15i 2.34640 0.153462i
\(997\) 2.49674e16 2.49674e16i 0.802693 0.802693i −0.180822 0.983516i \(-0.557876\pi\)
0.983516 + 0.180822i \(0.0578759\pi\)
\(998\) −3.03555e16 + 9.91613e14i −0.970554 + 0.0317048i
\(999\) 1.69991e17i 5.40524i
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 16.12.e.a.13.7 yes 42
4.3 odd 2 64.12.e.a.17.1 42
8.3 odd 2 128.12.e.a.33.21 42
8.5 even 2 128.12.e.b.33.1 42
16.3 odd 4 128.12.e.a.97.21 42
16.5 even 4 inner 16.12.e.a.5.7 42
16.11 odd 4 64.12.e.a.49.1 42
16.13 even 4 128.12.e.b.97.1 42
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
16.12.e.a.5.7 42 16.5 even 4 inner
16.12.e.a.13.7 yes 42 1.1 even 1 trivial
64.12.e.a.17.1 42 4.3 odd 2
64.12.e.a.49.1 42 16.11 odd 4
128.12.e.a.33.21 42 8.3 odd 2
128.12.e.a.97.21 42 16.3 odd 4
128.12.e.b.33.1 42 8.5 even 2
128.12.e.b.97.1 42 16.13 even 4