Properties

Label 20.6.e.b.3.2
Level $20$
Weight $6$
Character 20.3
Analytic conductor $3.208$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [20,6,Mod(3,20)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(20, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("20.3");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 20.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: \(3.20767639626\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 3.2
Character \(\chi\) \(=\) 20.3
Dual form 20.6.e.b.7.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.11607 + 2.41367i) q^{2} +(-16.4802 + 16.4802i) q^{3} +(20.3484 - 24.6970i) q^{4} +(21.8249 - 51.4653i) q^{5} +(44.5361 - 124.092i) q^{6} +(-78.4623 - 78.4623i) q^{7} +(-44.4934 + 175.466i) q^{8} -300.193i q^{9} +O(q^{10})\) \(q+(-5.11607 + 2.41367i) q^{2} +(-16.4802 + 16.4802i) q^{3} +(20.3484 - 24.6970i) q^{4} +(21.8249 - 51.4653i) q^{5} +(44.5361 - 124.092i) q^{6} +(-78.4623 - 78.4623i) q^{7} +(-44.4934 + 175.466i) q^{8} -300.193i q^{9} +(12.5624 + 315.978i) q^{10} -208.153i q^{11} +(71.6663 + 742.357i) q^{12} +(-401.203 - 401.203i) q^{13} +(590.801 + 212.037i) q^{14} +(488.478 + 1207.84i) q^{15} +(-195.886 - 1005.09i) q^{16} +(-515.793 + 515.793i) q^{17} +(724.567 + 1535.81i) q^{18} -2467.80 q^{19} +(-826.937 - 1586.25i) q^{20} +2586.15 q^{21} +(502.414 + 1064.93i) q^{22} +(2925.63 - 2925.63i) q^{23} +(-2158.45 - 3624.97i) q^{24} +(-2172.35 - 2246.45i) q^{25} +(3020.96 + 1084.21i) q^{26} +(942.550 + 942.550i) q^{27} +(-3534.37 + 341.204i) q^{28} +6391.35i q^{29} +(-5414.41 - 5000.35i) q^{30} -556.567i q^{31} +(3428.12 + 4669.31i) q^{32} +(3430.41 + 3430.41i) q^{33} +(1393.88 - 3883.79i) q^{34} +(-5750.52 + 2325.65i) q^{35} +(-7413.87 - 6108.44i) q^{36} +(-1963.77 + 1963.77i) q^{37} +(12625.5 - 5956.46i) q^{38} +13223.8 q^{39} +(8059.34 + 6119.39i) q^{40} +6139.41 q^{41} +(-13230.9 + 6242.11i) q^{42} +(-7375.44 + 7375.44i) q^{43} +(-5140.77 - 4235.59i) q^{44} +(-15449.5 - 6551.68i) q^{45} +(-7906.22 + 22029.2i) q^{46} +(-825.227 - 825.227i) q^{47} +(19792.3 + 13335.8i) q^{48} -4494.33i q^{49} +(16536.1 + 6249.67i) q^{50} -17000.7i q^{51} +(-18072.4 + 1744.69i) q^{52} +(-14452.0 - 14452.0i) q^{53} +(-7097.16 - 2547.15i) q^{54} +(-10712.7 - 4542.93i) q^{55} +(17258.5 - 10276.4i) q^{56} +(40669.8 - 40669.8i) q^{57} +(-15426.6 - 32698.6i) q^{58} -771.460 q^{59} +(39769.7 + 12513.5i) q^{60} +10971.4 q^{61} +(1343.37 + 2847.44i) q^{62} +(-23553.8 + 23553.8i) q^{63} +(-28808.7 - 15614.2i) q^{64} +(-29404.3 + 11891.8i) q^{65} +(-25830.1 - 9270.33i) q^{66} +(3350.38 + 3350.38i) q^{67} +(2242.99 + 23234.1i) q^{68} +96429.7i q^{69} +(23806.7 - 25778.1i) q^{70} +10288.1i q^{71} +(52673.7 + 13356.6i) q^{72} +(-23632.3 - 23632.3i) q^{73} +(5306.88 - 14786.6i) q^{74} +(72822.6 + 1221.23i) q^{75} +(-50215.8 + 60947.4i) q^{76} +(-16332.2 + 16332.2i) q^{77} +(-67654.0 + 31917.9i) q^{78} +33412.2 q^{79} +(-56002.4 - 11854.7i) q^{80} +41880.1 q^{81} +(-31409.6 + 14818.5i) q^{82} +(43857.5 - 43857.5i) q^{83} +(52623.9 - 63870.1i) q^{84} +(15288.3 + 37802.5i) q^{85} +(19931.4 - 55535.2i) q^{86} +(-105331. - 105331. i) q^{87} +(36523.8 + 9261.44i) q^{88} +10661.0i q^{89} +(94854.4 - 3771.13i) q^{90} +62958.7i q^{91} +(-12722.5 - 131786. i) q^{92} +(9172.32 + 9172.32i) q^{93} +(6213.75 + 2230.09i) q^{94} +(-53859.6 + 127006. i) q^{95} +(-133447. - 20455.0i) q^{96} +(68421.1 - 68421.1i) q^{97} +(10847.8 + 22993.3i) q^{98} -62486.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 10 q^{2} - 80 q^{5} - 184 q^{6} + 500 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 10 q^{2} - 80 q^{5} - 184 q^{6} + 500 q^{8} + 590 q^{10} - 1280 q^{12} - 1320 q^{13} + 4024 q^{16} + 2440 q^{17} - 5190 q^{18} + 1260 q^{20} + 1632 q^{21} - 2440 q^{22} - 7320 q^{25} - 4668 q^{26} + 5920 q^{28} + 8600 q^{30} + 25800 q^{32} + 10400 q^{33} - 43460 q^{36} + 14120 q^{37} - 22160 q^{38} - 11220 q^{40} - 19552 q^{41} - 39400 q^{42} + 7960 q^{45} + 29416 q^{46} + 108160 q^{48} + 141010 q^{50} - 7540 q^{52} - 106520 q^{53} - 85984 q^{56} + 40320 q^{57} - 115160 q^{58} - 263840 q^{60} + 206048 q^{61} - 109400 q^{62} - 181800 q^{65} + 186000 q^{66} + 268100 q^{68} + 364240 q^{70} + 247620 q^{72} + 107960 q^{73} - 297600 q^{76} - 53280 q^{77} - 586200 q^{78} - 390000 q^{80} - 66744 q^{81} - 498360 q^{82} - 31880 q^{85} + 545416 q^{86} + 690080 q^{88} + 791790 q^{90} + 576800 q^{92} + 182240 q^{93} - 841984 q^{96} + 60760 q^{97} - 902450 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(17\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.11607 + 2.41367i −0.904402 + 0.426681i
\(3\) −16.4802 + 16.4802i −1.05720 + 1.05720i −0.0589430 + 0.998261i \(0.518773\pi\)
−0.998261 + 0.0589430i \(0.981227\pi\)
\(4\) 20.3484 24.6970i 0.635887 0.771782i
\(5\) 21.8249 51.4653i 0.390416 0.920639i
\(6\) 44.5361 124.092i 0.505049 1.40723i
\(7\) −78.4623 78.4623i −0.605224 0.605224i 0.336470 0.941694i \(-0.390767\pi\)
−0.941694 + 0.336470i \(0.890767\pi\)
\(8\) −44.4934 + 175.466i −0.245793 + 0.969322i
\(9\) 300.193i 1.23536i
\(10\) 12.5624 + 315.978i 0.0397257 + 0.999211i
\(11\) 208.153i 0.518683i −0.965786 0.259341i \(-0.916495\pi\)
0.965786 0.259341i \(-0.0835054\pi\)
\(12\) 71.6663 + 742.357i 0.143669 + 1.48819i
\(13\) −401.203 401.203i −0.658425 0.658425i 0.296582 0.955007i \(-0.404153\pi\)
−0.955007 + 0.296582i \(0.904153\pi\)
\(14\) 590.801 + 212.037i 0.805603 + 0.289129i
\(15\) 488.478 + 1207.84i 0.560554 + 1.38605i
\(16\) −195.886 1005.09i −0.191295 0.981533i
\(17\) −515.793 + 515.793i −0.432865 + 0.432865i −0.889602 0.456737i \(-0.849018\pi\)
0.456737 + 0.889602i \(0.349018\pi\)
\(18\) 724.567 + 1535.81i 0.527105 + 1.11726i
\(19\) −2467.80 −1.56829 −0.784145 0.620578i \(-0.786898\pi\)
−0.784145 + 0.620578i \(0.786898\pi\)
\(20\) −826.937 1586.25i −0.462272 0.886738i
\(21\) 2586.15 1.27969
\(22\) 502.414 + 1064.93i 0.221312 + 0.469098i
\(23\) 2925.63 2925.63i 1.15319 1.15319i 0.167276 0.985910i \(-0.446503\pi\)
0.985910 0.167276i \(-0.0534970\pi\)
\(24\) −2158.45 3624.97i −0.764918 1.28463i
\(25\) −2172.35 2246.45i −0.695151 0.718864i
\(26\) 3020.96 + 1084.21i 0.876418 + 0.314544i
\(27\) 942.550 + 942.550i 0.248826 + 0.248826i
\(28\) −3534.37 + 341.204i −0.851955 + 0.0822467i
\(29\) 6391.35i 1.41123i 0.708596 + 0.705614i \(0.249329\pi\)
−0.708596 + 0.705614i \(0.750671\pi\)
\(30\) −5414.41 5000.35i −1.09837 1.01437i
\(31\) 556.567i 0.104019i −0.998647 0.0520095i \(-0.983437\pi\)
0.998647 0.0520095i \(-0.0165626\pi\)
\(32\) 3428.12 + 4669.31i 0.591808 + 0.806079i
\(33\) 3430.41 + 3430.41i 0.548353 + 0.548353i
\(34\) 1393.88 3883.79i 0.206789 0.576180i
\(35\) −5750.52 + 2325.65i −0.793481 + 0.320903i
\(36\) −7413.87 6108.44i −0.953430 0.785551i
\(37\) −1963.77 + 1963.77i −0.235823 + 0.235823i −0.815118 0.579295i \(-0.803328\pi\)
0.579295 + 0.815118i \(0.303328\pi\)
\(38\) 12625.5 5956.46i 1.41836 0.669159i
\(39\) 13223.8 1.39218
\(40\) 8059.34 + 6119.39i 0.796434 + 0.604726i
\(41\) 6139.41 0.570383 0.285192 0.958471i \(-0.407943\pi\)
0.285192 + 0.958471i \(0.407943\pi\)
\(42\) −13230.9 + 6242.11i −1.15736 + 0.546019i
\(43\) −7375.44 + 7375.44i −0.608298 + 0.608298i −0.942501 0.334203i \(-0.891533\pi\)
0.334203 + 0.942501i \(0.391533\pi\)
\(44\) −5140.77 4235.59i −0.400310 0.329824i
\(45\) −15449.5 6551.68i −1.13732 0.482305i
\(46\) −7906.22 + 22029.2i −0.550902 + 1.53499i
\(47\) −825.227 825.227i −0.0544915 0.0544915i 0.679336 0.733827i \(-0.262268\pi\)
−0.733827 + 0.679336i \(0.762268\pi\)
\(48\) 19792.3 + 13335.8i 1.23992 + 0.835443i
\(49\) 4494.33i 0.267408i
\(50\) 16536.1 + 6249.67i 0.935421 + 0.353535i
\(51\) 17000.7i 0.915254i
\(52\) −18072.4 + 1744.69i −0.926844 + 0.0894765i
\(53\) −14452.0 14452.0i −0.706703 0.706703i 0.259137 0.965840i \(-0.416562\pi\)
−0.965840 + 0.259137i \(0.916562\pi\)
\(54\) −7097.16 2547.15i −0.331208 0.118869i
\(55\) −10712.7 4542.93i −0.477519 0.202502i
\(56\) 17258.5 10276.4i 0.735417 0.437897i
\(57\) 40669.8 40669.8i 1.65800 1.65800i
\(58\) −15426.6 32698.6i −0.602144 1.27632i
\(59\) −771.460 −0.0288525 −0.0144262 0.999896i \(-0.504592\pi\)
−0.0144262 + 0.999896i \(0.504592\pi\)
\(60\) 39769.7 + 12513.5i 1.42618 + 0.448748i
\(61\) 10971.4 0.377519 0.188759 0.982023i \(-0.439553\pi\)
0.188759 + 0.982023i \(0.439553\pi\)
\(62\) 1343.37 + 2847.44i 0.0443829 + 0.0940751i
\(63\) −23553.8 + 23553.8i −0.747671 + 0.747671i
\(64\) −28808.7 15614.2i −0.879171 0.476506i
\(65\) −29404.3 + 11891.8i −0.863231 + 0.349112i
\(66\) −25830.1 9270.33i −0.729904 0.261960i
\(67\) 3350.38 + 3350.38i 0.0911817 + 0.0911817i 0.751226 0.660045i \(-0.229463\pi\)
−0.660045 + 0.751226i \(0.729463\pi\)
\(68\) 2242.99 + 23234.1i 0.0588241 + 0.609331i
\(69\) 96429.7i 2.43831i
\(70\) 23806.7 25778.1i 0.580703 0.628789i
\(71\) 10288.1i 0.242209i 0.992640 + 0.121105i \(0.0386436\pi\)
−0.992640 + 0.121105i \(0.961356\pi\)
\(72\) 52673.7 + 13356.6i 1.19746 + 0.303644i
\(73\) −23632.3 23632.3i −0.519037 0.519037i 0.398243 0.917280i \(-0.369620\pi\)
−0.917280 + 0.398243i \(0.869620\pi\)
\(74\) 5306.88 14786.6i 0.112658 0.313899i
\(75\) 72822.6 + 1221.23i 1.49490 + 0.0250694i
\(76\) −50215.8 + 60947.4i −0.997255 + 1.21038i
\(77\) −16332.2 + 16332.2i −0.313919 + 0.313919i
\(78\) −67654.0 + 31917.9i −1.25909 + 0.594016i
\(79\) 33412.2 0.602333 0.301167 0.953572i \(-0.402624\pi\)
0.301167 + 0.953572i \(0.402624\pi\)
\(80\) −56002.4 11854.7i −0.978321 0.207092i
\(81\) 41880.1 0.709243
\(82\) −31409.6 + 14818.5i −0.515856 + 0.243371i
\(83\) 43857.5 43857.5i 0.698794 0.698794i −0.265357 0.964150i \(-0.585490\pi\)
0.964150 + 0.265357i \(0.0854897\pi\)
\(84\) 52623.9 63870.1i 0.813739 0.987642i
\(85\) 15288.3 + 37802.5i 0.229515 + 0.567510i
\(86\) 19931.4 55535.2i 0.290597 0.809696i
\(87\) −105331. 105331.i −1.49196 1.49196i
\(88\) 36523.8 + 9261.44i 0.502771 + 0.127489i
\(89\) 10661.0i 0.142667i 0.997453 + 0.0713336i \(0.0227255\pi\)
−0.997453 + 0.0713336i \(0.977275\pi\)
\(90\) 94854.4 3771.13i 1.23439 0.0490756i
\(91\) 62958.7i 0.796989i
\(92\) −12722.5 131786.i −0.156712 1.62330i
\(93\) 9172.32 + 9172.32i 0.109969 + 0.109969i
\(94\) 6213.75 + 2230.09i 0.0725327 + 0.0260318i
\(95\) −53859.6 + 127006.i −0.612285 + 1.44383i
\(96\) −133447. 20455.0i −1.47785 0.226527i
\(97\) 68421.1 68421.1i 0.738348 0.738348i −0.233911 0.972258i \(-0.575152\pi\)
0.972258 + 0.233911i \(0.0751523\pi\)
\(98\) 10847.8 + 22993.3i 0.114098 + 0.241844i
\(99\) −62486.2 −0.640761
\(100\) −99684.4 + 7938.86i −0.996844 + 0.0793886i
\(101\) −121679. −1.18689 −0.593445 0.804874i \(-0.702233\pi\)
−0.593445 + 0.804874i \(0.702233\pi\)
\(102\) 41034.1 + 86976.9i 0.390521 + 0.827758i
\(103\) 36175.4 36175.4i 0.335985 0.335985i −0.518869 0.854854i \(-0.673647\pi\)
0.854854 + 0.518869i \(0.173647\pi\)
\(104\) 88248.5 52546.7i 0.800062 0.476389i
\(105\) 56442.4 133097.i 0.499612 1.17813i
\(106\) 108820. + 39055.0i 0.940680 + 0.337607i
\(107\) 79388.5 + 79388.5i 0.670345 + 0.670345i 0.957795 0.287451i \(-0.0928077\pi\)
−0.287451 + 0.957795i \(0.592808\pi\)
\(108\) 42457.6 4098.80i 0.350264 0.0338141i
\(109\) 81481.2i 0.656887i −0.944524 0.328444i \(-0.893476\pi\)
0.944524 0.328444i \(-0.106524\pi\)
\(110\) 65771.9 2614.90i 0.518273 0.0206050i
\(111\) 64726.4i 0.498625i
\(112\) −63492.0 + 94231.3i −0.478271 + 0.709823i
\(113\) −32022.7 32022.7i −0.235918 0.235918i 0.579239 0.815157i \(-0.303350\pi\)
−0.815157 + 0.579239i \(0.803350\pi\)
\(114\) −109906. + 306233.i −0.792064 + 2.20694i
\(115\) −86716.6 214420.i −0.611445 1.51189i
\(116\) 157847. + 130054.i 1.08916 + 0.897382i
\(117\) −120438. + 120438.i −0.813393 + 0.813393i
\(118\) 3946.84 1862.05i 0.0260943 0.0123108i
\(119\) 80940.6 0.523961
\(120\) −233668. + 31970.7i −1.48131 + 0.202675i
\(121\) 117723. 0.730968
\(122\) −56130.6 + 26481.4i −0.341429 + 0.161080i
\(123\) −101179. + 101179.i −0.603012 + 0.603012i
\(124\) −13745.5 11325.2i −0.0802800 0.0661444i
\(125\) −163025. + 62771.8i −0.933212 + 0.359327i
\(126\) 63651.9 177354.i 0.357178 0.995212i
\(127\) 186866. + 186866.i 1.02807 + 1.02807i 0.999595 + 0.0284710i \(0.00906382\pi\)
0.0284710 + 0.999595i \(0.490936\pi\)
\(128\) 185075. + 10348.5i 0.998440 + 0.0558280i
\(129\) 243097.i 1.28619i
\(130\) 121731. 131812.i 0.631749 0.684061i
\(131\) 4183.83i 0.0213008i −0.999943 0.0106504i \(-0.996610\pi\)
0.999943 0.0106504i \(-0.00339019\pi\)
\(132\) 154524. 14917.6i 0.771900 0.0745184i
\(133\) 193629. + 193629.i 0.949166 + 0.949166i
\(134\) −25227.5 9054.09i −0.121370 0.0435595i
\(135\) 69079.7 27937.5i 0.326224 0.131933i
\(136\) −67554.7 113453.i −0.313190 0.525981i
\(137\) −115488. + 115488.i −0.525698 + 0.525698i −0.919287 0.393589i \(-0.871233\pi\)
0.393589 + 0.919287i \(0.371233\pi\)
\(138\) −232750. 493341.i −1.04038 2.20521i
\(139\) −313543. −1.37645 −0.688224 0.725498i \(-0.741609\pi\)
−0.688224 + 0.725498i \(0.741609\pi\)
\(140\) −59577.1 + 189344.i −0.256897 + 0.816453i
\(141\) 27199.8 0.115217
\(142\) −24832.2 52634.8i −0.103346 0.219055i
\(143\) −83511.8 + 83511.8i −0.341514 + 0.341514i
\(144\) −301721. + 58803.6i −1.21255 + 0.236318i
\(145\) 328932. + 139491.i 1.29923 + 0.550966i
\(146\) 177945. + 63863.8i 0.690881 + 0.247955i
\(147\) 74067.3 + 74067.3i 0.282705 + 0.282705i
\(148\) 8539.69 + 88458.6i 0.0320470 + 0.331960i
\(149\) 164850.i 0.608307i −0.952623 0.304153i \(-0.901627\pi\)
0.952623 0.304153i \(-0.0983735\pi\)
\(150\) −375513. + 169522.i −1.36269 + 0.615173i
\(151\) 401404.i 1.43265i −0.697769 0.716323i \(-0.745824\pi\)
0.697769 0.716323i \(-0.254176\pi\)
\(152\) 109801. 433016.i 0.385475 1.52018i
\(153\) 154837. + 154837.i 0.534745 + 0.534745i
\(154\) 44136.2 122977.i 0.149966 0.417852i
\(155\) −28643.9 12147.0i −0.0957640 0.0406107i
\(156\) 269083. 326589.i 0.885269 1.07446i
\(157\) −254436. + 254436.i −0.823814 + 0.823814i −0.986653 0.162838i \(-0.947935\pi\)
0.162838 + 0.986653i \(0.447935\pi\)
\(158\) −170939. + 80646.0i −0.544752 + 0.257004i
\(159\) 476342. 1.49426
\(160\) 315125. 74522.0i 0.973159 0.230136i
\(161\) −459103. −1.39587
\(162\) −214262. + 101085.i −0.641441 + 0.302620i
\(163\) 351837. 351837.i 1.03722 1.03722i 0.0379433 0.999280i \(-0.487919\pi\)
0.999280 0.0379433i \(-0.0120806\pi\)
\(164\) 124927. 151625.i 0.362699 0.440211i
\(165\) 251415. 101678.i 0.718921 0.290749i
\(166\) −118521. + 330236.i −0.333829 + 0.930152i
\(167\) −234023. 234023.i −0.649334 0.649334i 0.303498 0.952832i \(-0.401845\pi\)
−0.952832 + 0.303498i \(0.901845\pi\)
\(168\) −115066. + 453781.i −0.314540 + 1.24043i
\(169\) 49364.7i 0.132953i
\(170\) −169459. 156500.i −0.449719 0.415328i
\(171\) 740817.i 1.93741i
\(172\) 32073.1 + 332230.i 0.0826646 + 0.856283i
\(173\) −13019.0 13019.0i −0.0330721 0.0330721i 0.690377 0.723449i \(-0.257445\pi\)
−0.723449 + 0.690377i \(0.757445\pi\)
\(174\) 793112. + 284646.i 1.98592 + 0.712740i
\(175\) −5814.28 + 346709.i −0.0143516 + 0.855796i
\(176\) −209213. + 40774.3i −0.509104 + 0.0992213i
\(177\) 12713.8 12713.8i 0.0305030 0.0305030i
\(178\) −25732.2 54542.6i −0.0608733 0.129029i
\(179\) −598989. −1.39729 −0.698645 0.715469i \(-0.746213\pi\)
−0.698645 + 0.715469i \(0.746213\pi\)
\(180\) −476180. + 248241.i −1.09544 + 0.571073i
\(181\) −18538.3 −0.0420604 −0.0210302 0.999779i \(-0.506695\pi\)
−0.0210302 + 0.999779i \(0.506695\pi\)
\(182\) −151962. 322101.i −0.340060 0.720799i
\(183\) −180811. + 180811.i −0.399114 + 0.399114i
\(184\) 383177. + 643519.i 0.834363 + 1.40125i
\(185\) 58206.7 + 143925.i 0.125038 + 0.309176i
\(186\) −69065.2 24787.3i −0.146378 0.0525348i
\(187\) 107364. + 107364.i 0.224520 + 0.224520i
\(188\) −37172.7 + 3588.61i −0.0767060 + 0.00740511i
\(189\) 147909.i 0.301190i
\(190\) −31001.4 779772.i −0.0623014 1.56705i
\(191\) 230250.i 0.456685i 0.973581 + 0.228343i \(0.0733306\pi\)
−0.973581 + 0.228343i \(0.926669\pi\)
\(192\) 732096. 217448.i 1.43323 0.425699i
\(193\) −621500. 621500.i −1.20101 1.20101i −0.973858 0.227156i \(-0.927057\pi\)
−0.227156 0.973858i \(-0.572943\pi\)
\(194\) −184901. + 515193.i −0.352725 + 0.982802i
\(195\) 288608. 680567.i 0.543529 1.28169i
\(196\) −110997. 91452.3i −0.206381 0.170041i
\(197\) 722564. 722564.i 1.32651 1.32651i 0.418119 0.908392i \(-0.362689\pi\)
0.908392 0.418119i \(-0.137311\pi\)
\(198\) 319684. 150821.i 0.579506 0.273400i
\(199\) −362735. −0.649318 −0.324659 0.945831i \(-0.605250\pi\)
−0.324659 + 0.945831i \(0.605250\pi\)
\(200\) 490831. 281221.i 0.867674 0.497133i
\(201\) −110430. −0.192795
\(202\) 622516. 293692.i 1.07343 0.506423i
\(203\) 501480. 501480.i 0.854109 0.854109i
\(204\) −419867. 345937.i −0.706377 0.581998i
\(205\) 133992. 315966.i 0.222687 0.525117i
\(206\) −97760.5 + 272392.i −0.160508 + 0.447225i
\(207\) −878252. 878252.i −1.42460 1.42460i
\(208\) −324655. + 481835.i −0.520312 + 0.772219i
\(209\) 513681.i 0.813445i
\(210\) 32488.1 + 817166.i 0.0508366 + 1.27868i
\(211\) 205008.i 0.317004i 0.987359 + 0.158502i \(0.0506665\pi\)
−0.987359 + 0.158502i \(0.949334\pi\)
\(212\) −650994. + 62846.2i −0.994804 + 0.0960372i
\(213\) −169550. 169550.i −0.256065 0.256065i
\(214\) −597775. 214540.i −0.892285 0.320238i
\(215\) 218611. + 540547.i 0.322534 + 0.797512i
\(216\) −207323. + 123448.i −0.302352 + 0.180033i
\(217\) −43669.5 + 43669.5i −0.0629548 + 0.0629548i
\(218\) 196669. + 416864.i 0.280281 + 0.594091i
\(219\) 778928. 1.09746
\(220\) −330182. + 172130.i −0.459936 + 0.239772i
\(221\) 413875. 0.570019
\(222\) 156228. + 331145.i 0.212754 + 0.450958i
\(223\) −627532. + 627532.i −0.845032 + 0.845032i −0.989508 0.144476i \(-0.953850\pi\)
0.144476 + 0.989508i \(0.453850\pi\)
\(224\) 97386.3 635343.i 0.129681 0.846035i
\(225\) −674368. + 652123.i −0.888057 + 0.858763i
\(226\) 241122. + 86538.1i 0.314027 + 0.112703i
\(227\) 469202. + 469202.i 0.604359 + 0.604359i 0.941466 0.337107i \(-0.109448\pi\)
−0.337107 + 0.941466i \(0.609448\pi\)
\(228\) −176858. 1.83199e6i −0.225314 2.33392i
\(229\) 245254.i 0.309049i 0.987989 + 0.154524i \(0.0493845\pi\)
−0.987989 + 0.154524i \(0.950615\pi\)
\(230\) 961187. + 887681.i 1.19809 + 1.10646i
\(231\) 538315.i 0.663753i
\(232\) −1.12146e6 284373.i −1.36794 0.346871i
\(233\) 1.14921e6 + 1.14921e6i 1.38679 + 1.38679i 0.831981 + 0.554805i \(0.187207\pi\)
0.554805 + 0.831981i \(0.312793\pi\)
\(234\) 325473. 906870.i 0.388575 1.08269i
\(235\) −60481.0 + 24460.0i −0.0714413 + 0.0288926i
\(236\) −15698.0 + 19052.8i −0.0183469 + 0.0222678i
\(237\) −550639. + 550639.i −0.636789 + 0.636789i
\(238\) −414098. + 195364.i −0.473871 + 0.223564i
\(239\) 822705. 0.931643 0.465821 0.884879i \(-0.345759\pi\)
0.465821 + 0.884879i \(0.345759\pi\)
\(240\) 1.11830e6 727563.i 1.25322 0.815347i
\(241\) −337052. −0.373813 −0.186907 0.982378i \(-0.559846\pi\)
−0.186907 + 0.982378i \(0.559846\pi\)
\(242\) −602280. + 284145.i −0.661090 + 0.311890i
\(243\) −919231. + 919231.i −0.998640 + 0.998640i
\(244\) 223251. 270961.i 0.240059 0.291362i
\(245\) −231302. 98088.3i −0.246186 0.104400i
\(246\) 273425. 761848.i 0.288072 0.802658i
\(247\) 990091. + 990091.i 1.03260 + 1.03260i
\(248\) 97658.6 + 24763.5i 0.100828 + 0.0255672i
\(249\) 1.44556e6i 1.47754i
\(250\) 682539. 714635.i 0.690681 0.723160i
\(251\) 1.86915e6i 1.87266i −0.351116 0.936332i \(-0.614198\pi\)
0.351116 0.936332i \(-0.385802\pi\)
\(252\) 102427. + 1.06099e6i 0.101604 + 1.05247i
\(253\) −608979. 608979.i −0.598137 0.598137i
\(254\) −1.40705e6 504987.i −1.36844 0.491129i
\(255\) −874946. 371039.i −0.842618 0.357330i
\(256\) −971833. + 393766.i −0.926813 + 0.375524i
\(257\) 863359. 863359.i 0.815377 0.815377i −0.170057 0.985434i \(-0.554395\pi\)
0.985434 + 0.170057i \(0.0543953\pi\)
\(258\) 586756. + 1.24370e6i 0.548793 + 1.16323i
\(259\) 308163. 0.285451
\(260\) −304637. + 968177.i −0.279479 + 0.888222i
\(261\) 1.91864e6 1.74338
\(262\) 10098.4 + 21404.8i 0.00908864 + 0.0192645i
\(263\) 582443. 582443.i 0.519235 0.519235i −0.398105 0.917340i \(-0.630332\pi\)
0.917340 + 0.398105i \(0.130332\pi\)
\(264\) −754550. + 449289.i −0.666313 + 0.396750i
\(265\) −1.05919e6 + 428361.i −0.926526 + 0.374710i
\(266\) −1.45798e6 523265.i −1.26342 0.453437i
\(267\) −175696. 175696.i −0.150828 0.150828i
\(268\) 150919. 14569.6i 0.128354 0.0123911i
\(269\) 1.43348e6i 1.20784i −0.797044 0.603921i \(-0.793604\pi\)
0.797044 0.603921i \(-0.206396\pi\)
\(270\) −285985. + 309666.i −0.238744 + 0.258514i
\(271\) 339680.i 0.280961i −0.990083 0.140481i \(-0.955135\pi\)
0.990083 0.140481i \(-0.0448648\pi\)
\(272\) 619454. + 417381.i 0.507676 + 0.342066i
\(273\) −1.03757e6 1.03757e6i −0.842580 0.842580i
\(274\) 312096. 869597.i 0.251137 0.699748i
\(275\) −467606. + 452181.i −0.372862 + 0.360563i
\(276\) 2.38153e6 + 1.96219e6i 1.88184 + 1.55049i
\(277\) 72217.7 72217.7i 0.0565515 0.0565515i −0.678265 0.734817i \(-0.737268\pi\)
0.734817 + 0.678265i \(0.237268\pi\)
\(278\) 1.60411e6 756789.i 1.24486 0.587304i
\(279\) −167077. −0.128501
\(280\) −152213. 1.11250e6i −0.116026 0.848015i
\(281\) 16374.4 0.0123709 0.00618544 0.999981i \(-0.498031\pi\)
0.00618544 + 0.999981i \(0.498031\pi\)
\(282\) −139156. + 65651.3i −0.104203 + 0.0491610i
\(283\) −513091. + 513091.i −0.380828 + 0.380828i −0.871400 0.490573i \(-0.836788\pi\)
0.490573 + 0.871400i \(0.336788\pi\)
\(284\) 254086. + 209347.i 0.186933 + 0.154018i
\(285\) −1.20547e6 2.98070e6i −0.879111 2.17373i
\(286\) 225683. 628823.i 0.163148 0.454583i
\(287\) −481712. 481712.i −0.345210 0.345210i
\(288\) 1.40169e6 1.02910e6i 0.995799 0.731098i
\(289\) 887773.i 0.625255i
\(290\) −2.01953e6 + 80290.4i −1.41011 + 0.0560620i
\(291\) 2.25519e6i 1.56117i
\(292\) −1.06452e6 + 102768.i −0.730632 + 0.0705343i
\(293\) 1.39773e6 + 1.39773e6i 0.951161 + 0.951161i 0.998862 0.0477009i \(-0.0151894\pi\)
−0.0477009 + 0.998862i \(0.515189\pi\)
\(294\) −557708. 200160.i −0.376304 0.135054i
\(295\) −16837.0 + 39703.4i −0.0112645 + 0.0265627i
\(296\) −257200. 431949.i −0.170624 0.286552i
\(297\) 196195. 196195.i 0.129062 0.129062i
\(298\) 397893. + 843383.i 0.259553 + 0.550154i
\(299\) −2.34754e6 −1.51857
\(300\) 1.51198e6 1.77365e6i 0.969938 1.13780i
\(301\) 1.15739e6 0.736314
\(302\) 968856. + 2.05361e6i 0.611282 + 1.29569i
\(303\) 2.00529e6 2.00529e6i 1.25479 1.25479i
\(304\) 483408. + 2.48036e6i 0.300006 + 1.53933i
\(305\) 239450. 564647.i 0.147389 0.347558i
\(306\) −1.16588e6 418433.i −0.711790 0.255459i
\(307\) −1.13123e6 1.13123e6i −0.685024 0.685024i 0.276104 0.961128i \(-0.410957\pi\)
−0.961128 + 0.276104i \(0.910957\pi\)
\(308\) 71022.7 + 735690.i 0.0426600 + 0.441894i
\(309\) 1.19236e6i 0.710411i
\(310\) 175863. 6991.79i 0.103937 0.00413223i
\(311\) 2.02590e6i 1.18773i 0.804566 + 0.593864i \(0.202398\pi\)
−0.804566 + 0.593864i \(0.797602\pi\)
\(312\) −588372. + 2.32033e6i −0.342189 + 1.34947i
\(313\) −1.34475e6 1.34475e6i −0.775855 0.775855i 0.203268 0.979123i \(-0.434844\pi\)
−0.979123 + 0.203268i \(0.934844\pi\)
\(314\) 687588. 1.91584e6i 0.393554 1.09657i
\(315\) 698144. + 1.72626e6i 0.396432 + 0.980237i
\(316\) 679884. 825181.i 0.383016 0.464870i
\(317\) −187111. + 187111.i −0.104581 + 0.104581i −0.757461 0.652880i \(-0.773560\pi\)
0.652880 + 0.757461i \(0.273560\pi\)
\(318\) −2.43700e6 + 1.14973e6i −1.35141 + 0.637571i
\(319\) 1.33038e6 0.731980
\(320\) −1.43233e6 + 1.14187e6i −0.781932 + 0.623363i
\(321\) −2.61667e6 −1.41738
\(322\) 2.34880e6 1.10812e6i 1.26243 0.595591i
\(323\) 1.27287e6 1.27287e6i 0.678858 0.678858i
\(324\) 852192. 1.03431e6i 0.450998 0.547381i
\(325\) −29730.3 + 1.77284e6i −0.0156132 + 0.931022i
\(326\) −950804. + 2.64924e6i −0.495504 + 1.38063i
\(327\) 1.34282e6 + 1.34282e6i 0.694464 + 0.694464i
\(328\) −273163. + 1.07726e6i −0.140196 + 0.552885i
\(329\) 129498.i 0.0659591i
\(330\) −1.04084e6 + 1.12703e6i −0.526137 + 0.569704i
\(331\) 3.52504e6i 1.76845i −0.467057 0.884227i \(-0.654686\pi\)
0.467057 0.884227i \(-0.345314\pi\)
\(332\) −190720. 1.97558e6i −0.0949624 0.983670i
\(333\) 589509. + 589509.i 0.291326 + 0.291326i
\(334\) 1.76214e6 + 632425.i 0.864317 + 0.310201i
\(335\) 245550. 99306.6i 0.119544 0.0483466i
\(336\) −506590. 2.59931e6i −0.244798 1.25606i
\(337\) −856784. + 856784.i −0.410957 + 0.410957i −0.882072 0.471115i \(-0.843852\pi\)
0.471115 + 0.882072i \(0.343852\pi\)
\(338\) 119150. + 252553.i 0.0567287 + 0.120243i
\(339\) 1.05548e6 0.498827
\(340\) 1.24470e6 + 391646.i 0.583940 + 0.183737i
\(341\) −115851. −0.0539529
\(342\) −1.78809e6 3.79007e6i −0.826653 1.75219i
\(343\) −1.67135e6 + 1.67135e6i −0.767066 + 0.767066i
\(344\) −965981. 1.62230e6i −0.440121 0.739153i
\(345\) 4.96278e6 + 2.10457e6i 2.24480 + 0.951953i
\(346\) 98029.4 + 35182.5i 0.0440216 + 0.0157992i
\(347\) −1.06737e6 1.06737e6i −0.475871 0.475871i 0.427937 0.903808i \(-0.359240\pi\)
−0.903808 + 0.427937i \(0.859240\pi\)
\(348\) −4.74466e6 + 458044.i −2.10018 + 0.202749i
\(349\) 1.38944e6i 0.610625i −0.952252 0.305313i \(-0.901239\pi\)
0.952252 0.305313i \(-0.0987610\pi\)
\(350\) −807095. 1.78782e6i −0.352172 0.780107i
\(351\) 756309.i 0.327666i
\(352\) 971932. 713575.i 0.418099 0.306961i
\(353\) −180470. 180470.i −0.0770848 0.0770848i 0.667513 0.744598i \(-0.267359\pi\)
−0.744598 + 0.667513i \(0.767359\pi\)
\(354\) −34357.8 + 95731.6i −0.0145719 + 0.0406020i
\(355\) 529481. + 224538.i 0.222987 + 0.0945623i
\(356\) 263296. + 216935.i 0.110108 + 0.0907203i
\(357\) −1.33392e6 + 1.33392e6i −0.553934 + 0.553934i
\(358\) 3.06447e6 1.44576e6i 1.26371 0.596196i
\(359\) −2.91768e6 −1.19482 −0.597409 0.801937i \(-0.703803\pi\)
−0.597409 + 0.801937i \(0.703803\pi\)
\(360\) 1.83700e6 2.41936e6i 0.747055 0.983884i
\(361\) 3.61395e6 1.45953
\(362\) 94843.2 44745.3i 0.0380395 0.0179464i
\(363\) −1.94010e6 + 1.94010e6i −0.772783 + 0.772783i
\(364\) 1.55489e6 + 1.28111e6i 0.615102 + 0.506795i
\(365\) −1.73201e6 + 700468.i −0.680485 + 0.275205i
\(366\) 488624. 1.36146e6i 0.190666 0.531254i
\(367\) −565943. 565943.i −0.219335 0.219335i 0.588883 0.808218i \(-0.299568\pi\)
−0.808218 + 0.588883i \(0.799568\pi\)
\(368\) −3.51361e6 2.36743e6i −1.35249 0.911291i
\(369\) 1.84301e6i 0.704630i
\(370\) −645176. 595837.i −0.245005 0.226268i
\(371\) 2.26787e6i 0.855427i
\(372\) 413171. 39887.1i 0.154801 0.0149443i
\(373\) 1.12747e6 + 1.12747e6i 0.419597 + 0.419597i 0.885065 0.465468i \(-0.154114\pi\)
−0.465468 + 0.885065i \(0.654114\pi\)
\(374\) −808423. 290141.i −0.298854 0.107258i
\(375\) 1.65220e6 3.72118e6i 0.606713 1.36648i
\(376\) 181516. 108082.i 0.0662135 0.0394262i
\(377\) 2.56423e6 2.56423e6i 0.929188 0.929188i
\(378\) 357005. + 756715.i 0.128512 + 0.272397i
\(379\) 4.54355e6 1.62479 0.812395 0.583107i \(-0.198163\pi\)
0.812395 + 0.583107i \(0.198163\pi\)
\(380\) 2.04072e6 + 3.91454e6i 0.724976 + 1.39066i
\(381\) −6.15917e6 −2.17375
\(382\) −555748. 1.17798e6i −0.194859 0.413027i
\(383\) 43026.1 43026.1i 0.0149877 0.0149877i −0.699573 0.714561i \(-0.746627\pi\)
0.714561 + 0.699573i \(0.246627\pi\)
\(384\) −3.22061e6 + 2.87952e6i −1.11458 + 0.996534i
\(385\) 484092. + 1.19699e6i 0.166447 + 0.411565i
\(386\) 4.67974e6 + 1.67954e6i 1.59865 + 0.573750i
\(387\) 2.21405e6 + 2.21405e6i 0.751469 + 0.751469i
\(388\) −297538. 3.08206e6i −0.100338 1.03935i
\(389\) 610934.i 0.204701i −0.994748 0.102351i \(-0.967364\pi\)
0.994748 0.102351i \(-0.0326364\pi\)
\(390\) 166122. + 4.17844e6i 0.0553053 + 1.39108i
\(391\) 3.01803e6i 0.998348i
\(392\) 788602. + 199968.i 0.259205 + 0.0657272i
\(393\) 68950.3 + 68950.3i 0.0225193 + 0.0225193i
\(394\) −1.95266e6 + 5.44072e6i −0.633703 + 1.76570i
\(395\) 729218. 1.71957e6i 0.235160 0.554531i
\(396\) −1.27149e6 + 1.54322e6i −0.407452 + 0.494528i
\(397\) −2.37469e6 + 2.37469e6i −0.756189 + 0.756189i −0.975627 0.219437i \(-0.929578\pi\)
0.219437 + 0.975627i \(0.429578\pi\)
\(398\) 1.85578e6 875524.i 0.587245 0.277051i
\(399\) −6.38210e6 −2.00693
\(400\) −1.83235e6 + 2.62345e6i −0.572610 + 0.819828i
\(401\) −6.03208e6 −1.87329 −0.936647 0.350275i \(-0.886088\pi\)
−0.936647 + 0.350275i \(0.886088\pi\)
\(402\) 564967. 266541.i 0.174365 0.0822620i
\(403\) −223296. + 223296.i −0.0684887 + 0.0684887i
\(404\) −2.47596e6 + 3.00510e6i −0.754729 + 0.916021i
\(405\) 914029. 2.15537e6i 0.276900 0.652956i
\(406\) −1.35520e6 + 3.77602e6i −0.408027 + 1.13689i
\(407\) 408764. + 408764.i 0.122317 + 0.122317i
\(408\) 2.98305e6 + 756419.i 0.887176 + 0.224963i
\(409\) 2.83617e6i 0.838347i −0.907906 0.419174i \(-0.862320\pi\)
0.907906 0.419174i \(-0.137680\pi\)
\(410\) 77125.4 + 1.93992e6i 0.0226589 + 0.569933i
\(411\) 3.80654e6i 1.11154i
\(412\) −157314. 1.62954e6i −0.0456587 0.472956i
\(413\) 60530.5 + 60530.5i 0.0174622 + 0.0174622i
\(414\) 6.61302e6 + 2.37339e6i 1.89626 + 0.680563i
\(415\) −1.29995e6 3.21433e6i −0.370516 0.916157i
\(416\) 497968. 3.24872e6i 0.141081 0.920404i
\(417\) 5.16724e6 5.16724e6i 1.45519 1.45519i
\(418\) −1.23986e6 2.62803e6i −0.347081 0.735681i
\(419\) 6.16608e6 1.71583 0.857914 0.513793i \(-0.171760\pi\)
0.857914 + 0.513793i \(0.171760\pi\)
\(420\) −2.13858e6 4.10226e6i −0.591565 1.13475i
\(421\) 6.27395e6 1.72518 0.862592 0.505900i \(-0.168839\pi\)
0.862592 + 0.505900i \(0.168839\pi\)
\(422\) −494822. 1.04884e6i −0.135260 0.286699i
\(423\) −247727. + 247727.i −0.0673167 + 0.0673167i
\(424\) 3.17884e6 1.89281e6i 0.858726 0.511320i
\(425\) 2.27918e6 + 38221.7i 0.612078 + 0.0102645i
\(426\) 1.27667e6 + 458193.i 0.340843 + 0.122328i
\(427\) −860843. 860843.i −0.228483 0.228483i
\(428\) 3.57609e6 345231.i 0.943624 0.0910963i
\(429\) 2.75258e6i 0.722099i
\(430\) −2.42313e6 2.23782e6i −0.631983 0.583653i
\(431\) 4.63552e6i 1.20200i 0.799249 + 0.601001i \(0.205231\pi\)
−0.799249 + 0.601001i \(0.794769\pi\)
\(432\) 762715. 1.13198e6i 0.196631 0.291830i
\(433\) −2.87725e6 2.87725e6i −0.737492 0.737492i 0.234600 0.972092i \(-0.424622\pi\)
−0.972092 + 0.234600i \(0.924622\pi\)
\(434\) 118013. 328820.i 0.0300749 0.0837981i
\(435\) −7.71970e6 + 3.12204e6i −1.95604 + 0.791070i
\(436\) −2.01234e6 1.65801e6i −0.506974 0.417706i
\(437\) −7.21987e6 + 7.21987e6i −1.80853 + 1.80853i
\(438\) −3.98505e6 + 1.88007e6i −0.992541 + 0.468263i
\(439\) −3.46636e6 −0.858445 −0.429223 0.903199i \(-0.641212\pi\)
−0.429223 + 0.903199i \(0.641212\pi\)
\(440\) 1.27377e6 1.67758e6i 0.313661 0.413096i
\(441\) −1.34917e6 −0.330346
\(442\) −2.11742e6 + 998959.i −0.515526 + 0.243216i
\(443\) −815745. + 815745.i −0.197490 + 0.197490i −0.798923 0.601433i \(-0.794597\pi\)
0.601433 + 0.798923i \(0.294597\pi\)
\(444\) −1.59855e6 1.31708e6i −0.384830 0.317069i
\(445\) 548673. + 232676.i 0.131345 + 0.0556995i
\(446\) 1.69584e6 4.72515e6i 0.403690 1.12481i
\(447\) 2.71675e6 + 2.71675e6i 0.643104 + 0.643104i
\(448\) 1.03527e6 + 3.48552e6i 0.243702 + 0.820488i
\(449\) 1.73838e6i 0.406939i −0.979081 0.203469i \(-0.934778\pi\)
0.979081 0.203469i \(-0.0652217\pi\)
\(450\) 1.87611e6 4.96401e6i 0.436743 1.15558i
\(451\) 1.27794e6i 0.295848i
\(452\) −1.44247e6 + 139255.i −0.332095 + 0.0320600i
\(453\) 6.61521e6 + 6.61521e6i 1.51460 + 1.51460i
\(454\) −3.53297e6 1.26797e6i −0.804452 0.288715i
\(455\) 3.24019e6 + 1.37407e6i 0.733739 + 0.311157i
\(456\) 5.32664e6 + 8.94571e6i 1.19961 + 2.01467i
\(457\) 512272. 512272.i 0.114739 0.114739i −0.647406 0.762145i \(-0.724146\pi\)
0.762145 + 0.647406i \(0.224146\pi\)
\(458\) −591962. 1.25474e6i −0.131865 0.279505i
\(459\) −972321. −0.215416
\(460\) −7.06007e6 2.22145e6i −1.55566 0.489489i
\(461\) −996982. −0.218492 −0.109246 0.994015i \(-0.534844\pi\)
−0.109246 + 0.994015i \(0.534844\pi\)
\(462\) 1.29932e6 + 2.75406e6i 0.283211 + 0.600300i
\(463\) 3.62219e6 3.62219e6i 0.785270 0.785270i −0.195445 0.980715i \(-0.562615\pi\)
0.980715 + 0.195445i \(0.0626150\pi\)
\(464\) 6.42388e6 1.25198e6i 1.38517 0.269961i
\(465\) 672241. 271871.i 0.144176 0.0583083i
\(466\) −8.65325e6 3.10562e6i −1.84593 0.662497i
\(467\) −4.58788e6 4.58788e6i −0.973464 0.973464i 0.0261933 0.999657i \(-0.491661\pi\)
−0.999657 + 0.0261933i \(0.991661\pi\)
\(468\) 523742. + 5.42520e6i 0.110536 + 1.14499i
\(469\) 525758.i 0.110371i
\(470\) 250387. 271120.i 0.0522838 0.0566132i
\(471\) 8.38630e6i 1.74188i
\(472\) 34324.8 135365.i 0.00709175 0.0279674i
\(473\) 1.53522e6 + 1.53522e6i 0.315514 + 0.315514i
\(474\) 1.48805e6 4.14617e6i 0.304208 0.847620i
\(475\) 5.36092e6 + 5.54379e6i 1.09020 + 1.12739i
\(476\) 1.64701e6 1.99899e6i 0.333180 0.404384i
\(477\) −4.33838e6 + 4.33838e6i −0.873034 + 0.873034i
\(478\) −4.20902e6 + 1.98574e6i −0.842580 + 0.397514i
\(479\) 4.86880e6 0.969580 0.484790 0.874631i \(-0.338896\pi\)
0.484790 + 0.874631i \(0.338896\pi\)
\(480\) −3.96519e6 + 6.42146e6i −0.785527 + 1.27213i
\(481\) 1.57574e6 0.310543
\(482\) 1.72438e6 813533.i 0.338077 0.159499i
\(483\) 7.56610e6 7.56610e6i 1.47572 1.47572i
\(484\) 2.39548e6 2.90741e6i 0.464813 0.564148i
\(485\) −2.02803e6 5.01460e6i −0.391489 0.968014i
\(486\) 2.48413e6 6.92157e6i 0.477072 1.32927i
\(487\) 2.54970e6 + 2.54970e6i 0.487154 + 0.487154i 0.907407 0.420253i \(-0.138059\pi\)
−0.420253 + 0.907407i \(0.638059\pi\)
\(488\) −488156. + 1.92511e6i −0.0927916 + 0.365937i
\(489\) 1.15967e7i 2.19311i
\(490\) 1.42011e6 56459.4i 0.267197 0.0106230i
\(491\) 5.98759e6i 1.12085i 0.828204 + 0.560426i \(0.189363\pi\)
−0.828204 + 0.560426i \(0.810637\pi\)
\(492\) 439988. + 4.55763e6i 0.0819461 + 0.848841i
\(493\) −3.29661e6 3.29661e6i −0.610872 0.610872i
\(494\) −7.45513e6 2.67562e6i −1.37448 0.493296i
\(495\) −1.36375e6 + 3.21587e6i −0.250163 + 0.589909i
\(496\) −559399. + 109024.i −0.102098 + 0.0198983i
\(497\) 807231. 807231.i 0.146591 0.146591i
\(498\) −3.48911e6 7.39559e6i −0.630436 1.33629i
\(499\) −1.08538e7 −1.95133 −0.975667 0.219256i \(-0.929637\pi\)
−0.975667 + 0.219256i \(0.929637\pi\)
\(500\) −1.76703e6 + 5.30355e6i −0.316095 + 0.948727i
\(501\) 7.71350e6 1.37296
\(502\) 4.51151e6 + 9.56271e6i 0.799029 + 1.69364i
\(503\) −1.50406e6 + 1.50406e6i −0.265060 + 0.265060i −0.827106 0.562046i \(-0.810014\pi\)
0.562046 + 0.827106i \(0.310014\pi\)
\(504\) −3.08491e6 5.18089e6i −0.540961 0.908506i
\(505\) −2.65562e6 + 6.26222e6i −0.463381 + 1.09270i
\(506\) 4.58545e6 + 1.64571e6i 0.796171 + 0.285743i
\(507\) 813539. + 813539.i 0.140559 + 0.140559i
\(508\) 8.41745e6 812611.i 1.44718 0.139709i
\(509\) 6.87244e6i 1.17575i 0.808950 + 0.587877i \(0.200036\pi\)
−0.808950 + 0.587877i \(0.799964\pi\)
\(510\) 5.37185e6 213569.i 0.914532 0.0363591i
\(511\) 3.70848e6i 0.628267i
\(512\) 4.02155e6 4.36022e6i 0.677983 0.735078i
\(513\) −2.32603e6 2.32603e6i −0.390231 0.390231i
\(514\) −2.33314e6 + 6.50087e6i −0.389523 + 1.08533i
\(515\) −1.07225e6 2.65130e6i −0.178147 0.440495i
\(516\) −6.00378e6 4.94664e6i −0.992659 0.817873i
\(517\) −171774. + 171774.i −0.0282638 + 0.0282638i
\(518\) −1.57659e6 + 743804.i −0.258162 + 0.121796i
\(519\) 429110. 0.0699278
\(520\) −778314. 5.68856e6i −0.126225 0.922558i
\(521\) 126327. 0.0203893 0.0101947 0.999948i \(-0.496755\pi\)
0.0101947 + 0.999948i \(0.496755\pi\)
\(522\) −9.81589e6 + 4.63096e6i −1.57672 + 0.743866i
\(523\) −6.53633e6 + 6.53633e6i −1.04491 + 1.04491i −0.0459698 + 0.998943i \(0.514638\pi\)
−0.998943 + 0.0459698i \(0.985362\pi\)
\(524\) −103328. 85134.2i −0.0164396 0.0135449i
\(525\) −5.61801e6 5.80965e6i −0.889578 0.919923i
\(526\) −1.57400e6 + 4.38565e6i −0.248050 + 0.691145i
\(527\) 287073. + 287073.i 0.0450262 + 0.0450262i
\(528\) 2.77590e6 4.11983e6i 0.433330 0.643124i
\(529\) 1.06822e7i 1.65968i
\(530\) 4.38495e6 4.74805e6i 0.678071 0.734219i
\(531\) 231587.i 0.0356433i
\(532\) 8.72212e6 842023.i 1.33611 0.128987i
\(533\) −2.46315e6 2.46315e6i −0.375554 0.375554i
\(534\) 1.32294e6 + 474801.i 0.200765 + 0.0720540i
\(535\) 5.81840e6 2.35310e6i 0.878859 0.355432i
\(536\) −736949. + 438809.i −0.110796 + 0.0659726i
\(537\) 9.87145e6 9.87145e6i 1.47722 1.47722i
\(538\) 3.45994e6 + 7.33377e6i 0.515363 + 1.09238i
\(539\) −935509. −0.138700
\(540\) 715687. 2.27455e6i 0.105618 0.335668i
\(541\) 7.75559e6 1.13926 0.569628 0.821903i \(-0.307087\pi\)
0.569628 + 0.821903i \(0.307087\pi\)
\(542\) 819875. + 1.73783e6i 0.119881 + 0.254102i
\(543\) 305514. 305514.i 0.0444664 0.0444664i
\(544\) −4.17659e6 640194.i −0.605097 0.0927501i
\(545\) −4.19345e6 1.77832e6i −0.604756 0.256459i
\(546\) 7.81264e6 + 2.80393e6i 1.12154 + 0.402519i
\(547\) −3.20243e6 3.20243e6i −0.457626 0.457626i 0.440249 0.897876i \(-0.354890\pi\)
−0.897876 + 0.440249i \(0.854890\pi\)
\(548\) 502216. + 5.20222e6i 0.0714396 + 0.740009i
\(549\) 3.29354e6i 0.466372i
\(550\) 1.30089e6 3.44204e6i 0.183372 0.485187i
\(551\) 1.57726e7i 2.21322i
\(552\) −1.69201e7 4.29048e6i −2.36350 0.599320i
\(553\) −2.62160e6 2.62160e6i −0.364547 0.364547i
\(554\) −195161. + 543780.i −0.0270159 + 0.0752747i
\(555\) −3.33116e6 1.41265e6i −0.459054 0.194671i
\(556\) −6.38009e6 + 7.74357e6i −0.875265 + 1.06232i
\(557\) 5.24556e6 5.24556e6i 0.716397 0.716397i −0.251468 0.967866i \(-0.580913\pi\)
0.967866 + 0.251468i \(0.0809135\pi\)
\(558\) 854780. 403270.i 0.116217 0.0548290i
\(559\) 5.91810e6 0.801038
\(560\) 3.46393e6 + 5.32422e6i 0.466766 + 0.717441i
\(561\) −3.53876e6 −0.474726
\(562\) −83772.8 + 39522.5i −0.0111882 + 0.00527841i
\(563\) −6.77321e6 + 6.77321e6i −0.900583 + 0.900583i −0.995486 0.0949039i \(-0.969746\pi\)
0.0949039 + 0.995486i \(0.469746\pi\)
\(564\) 553472. 671754.i 0.0732652 0.0889226i
\(565\) −2.34695e6 + 949163.i −0.309301 + 0.125089i
\(566\) 1.38658e6 3.86345e6i 0.181930 0.506913i
\(567\) −3.28601e6 3.28601e6i −0.429251 0.429251i
\(568\) −1.80522e6 457754.i −0.234779 0.0595334i
\(569\) 1.13795e7i 1.47348i 0.676178 + 0.736738i \(0.263635\pi\)
−0.676178 + 0.736738i \(0.736365\pi\)
\(570\) 1.33617e7 + 1.23399e7i 1.72256 + 1.59083i
\(571\) 5.61501e6i 0.720710i −0.932815 0.360355i \(-0.882656\pi\)
0.932815 0.360355i \(-0.117344\pi\)
\(572\) 363162. + 3.76182e6i 0.0464099 + 0.480738i
\(573\) −3.79457e6 3.79457e6i −0.482809 0.482809i
\(574\) 3.62717e6 + 1.30178e6i 0.459503 + 0.164914i
\(575\) −1.29277e7 216797.i −1.63062 0.0273454i
\(576\) −4.68726e6 + 8.64816e6i −0.588658 + 1.08609i
\(577\) −1.77450e6 + 1.77450e6i −0.221889 + 0.221889i −0.809294 0.587404i \(-0.800150\pi\)
0.587404 + 0.809294i \(0.300150\pi\)
\(578\) −2.14279e6 4.54191e6i −0.266784 0.565482i
\(579\) 2.04849e7 2.53943
\(580\) 1.01382e7 5.28524e6i 1.25139 0.652371i
\(581\) −6.88233e6 −0.845853
\(582\) −5.44327e6 1.15377e7i −0.666120 1.41192i
\(583\) −3.00822e6 + 3.00822e6i −0.366555 + 0.366555i
\(584\) 5.19814e6 3.09518e6i 0.630690 0.375538i
\(585\) 3.56984e6 + 8.82695e6i 0.431279 + 1.06640i
\(586\) −1.05245e7 3.77723e6i −1.26607 0.454390i
\(587\) 8.74762e6 + 8.74762e6i 1.04784 + 1.04784i 0.998797 + 0.0490427i \(0.0156170\pi\)
0.0490427 + 0.998797i \(0.484383\pi\)
\(588\) 3.33639e6 322092.i 0.397955 0.0384181i
\(589\) 1.37350e6i 0.163132i
\(590\) −9691.35 243764.i −0.00114618 0.0288297i
\(591\) 2.38160e7i 2.80479i
\(592\) 2.35843e6 + 1.58909e6i 0.276579 + 0.186356i
\(593\) 1.41270e6 + 1.41270e6i 0.164973 + 0.164973i 0.784766 0.619793i \(-0.212783\pi\)
−0.619793 + 0.784766i \(0.712783\pi\)
\(594\) −530198. + 1.47730e6i −0.0616555 + 0.171792i
\(595\) 1.76652e6 4.16563e6i 0.204563 0.482379i
\(596\) −4.07130e6 3.35443e6i −0.469480 0.386814i
\(597\) 5.97795e6 5.97795e6i 0.686462 0.686462i
\(598\) 1.20102e7 5.66619e6i 1.37340 0.647945i
\(599\) 2.42413e6 0.276051 0.138026 0.990429i \(-0.455924\pi\)
0.138026 + 0.990429i \(0.455924\pi\)
\(600\) −3.45441e6 + 1.27236e7i −0.391738 + 1.44288i
\(601\) −1.10729e7 −1.25048 −0.625240 0.780433i \(-0.714999\pi\)
−0.625240 + 0.780433i \(0.714999\pi\)
\(602\) −5.92128e6 + 2.79355e6i −0.665924 + 0.314171i
\(603\) 1.00576e6 1.00576e6i 0.112642 0.112642i
\(604\) −9.91348e6 8.16792e6i −1.10569 0.911001i
\(605\) 2.56930e6 6.05865e6i 0.285382 0.672958i
\(606\) −5.41909e6 + 1.50993e7i −0.599439 + 1.67022i
\(607\) −5.92774e6 5.92774e6i −0.653007 0.653007i 0.300709 0.953716i \(-0.402777\pi\)
−0.953716 + 0.300709i \(0.902777\pi\)
\(608\) −8.45992e6 1.15229e7i −0.928127 1.26416i
\(609\) 1.65290e7i 1.80594i
\(610\) 137827. + 3.46673e6i 0.0149972 + 0.377221i
\(611\) 662168.i 0.0717571i
\(612\) 6.97471e6 673330.i 0.752744 0.0726691i
\(613\) 1.15257e7 + 1.15257e7i 1.23884 + 1.23884i 0.960477 + 0.278361i \(0.0897912\pi\)
0.278361 + 0.960477i \(0.410209\pi\)
\(614\) 8.51788e6 + 3.05704e6i 0.911823 + 0.327251i
\(615\) 2.99897e6 + 7.41539e6i 0.319730 + 0.790581i
\(616\) −2.13907e6 3.59242e6i −0.227129 0.381448i
\(617\) −34923.5 + 34923.5i −0.00369322 + 0.00369322i −0.708951 0.705258i \(-0.750831\pi\)
0.705258 + 0.708951i \(0.250831\pi\)
\(618\) −2.87795e6 6.10017e6i −0.303118 0.642497i
\(619\) −6.68625e6 −0.701384 −0.350692 0.936491i \(-0.614054\pi\)
−0.350692 + 0.936491i \(0.614054\pi\)
\(620\) −882852. + 460246.i −0.0922377 + 0.0480851i
\(621\) 5.51510e6 0.573884
\(622\) −4.88985e6 1.03646e7i −0.506780 1.07418i
\(623\) 836489. 836489.i 0.0863456 0.0863456i
\(624\) −2.59036e6 1.32911e7i −0.266317 1.36647i
\(625\) −327445. + 9.76013e6i −0.0335304 + 0.999438i
\(626\) 1.01256e7 + 3.63405e6i 1.03273 + 0.370643i
\(627\) −8.46556e6 8.46556e6i −0.859977 0.859977i
\(628\) 1.10645e6 + 1.14612e7i 0.111952 + 1.15966i
\(629\) 2.02579e6i 0.204159i
\(630\) −7.73839e6 7.14661e6i −0.776782 0.717379i
\(631\) 6.84731e6i 0.684615i −0.939588 0.342308i \(-0.888791\pi\)
0.939588 0.342308i \(-0.111209\pi\)
\(632\) −1.48662e6 + 5.86270e6i −0.148050 + 0.583855i
\(633\) −3.37857e6 3.37857e6i −0.335138 0.335138i
\(634\) 505650. 1.40890e6i 0.0499605 0.139206i
\(635\) 1.36954e7 5.53877e6i 1.34785 0.545104i
\(636\) 9.69279e6 1.17642e7i 0.950180 1.15324i
\(637\) −1.80314e6 + 1.80314e6i −0.176068 + 0.176068i
\(638\) −6.80632e6 + 3.21110e6i −0.662004 + 0.312322i
\(639\) 3.08842e6 0.299216
\(640\) 4.57183e6 9.29906e6i 0.441204 0.897407i
\(641\) 2.99452e6 0.287860 0.143930 0.989588i \(-0.454026\pi\)
0.143930 + 0.989588i \(0.454026\pi\)
\(642\) 1.33871e7 6.31579e6i 1.28188 0.604770i
\(643\) 9.65074e6 9.65074e6i 0.920520 0.920520i −0.0765462 0.997066i \(-0.524389\pi\)
0.997066 + 0.0765462i \(0.0243893\pi\)
\(644\) −9.34201e6 + 1.13385e7i −0.887617 + 1.07731i
\(645\) −1.25111e7 5.30557e6i −1.18412 0.502150i
\(646\) −3.43982e6 + 9.58441e6i −0.324305 + 0.903617i
\(647\) −6.64651e6 6.64651e6i −0.624213 0.624213i 0.322393 0.946606i \(-0.395513\pi\)
−0.946606 + 0.322393i \(0.895513\pi\)
\(648\) −1.86339e6 + 7.34853e6i −0.174327 + 0.687485i
\(649\) 160582.i 0.0149653i
\(650\) −4.12694e6 9.14172e6i −0.383129 0.848681i
\(651\) 1.43936e6i 0.133112i
\(652\) −1.53001e6 1.58486e7i −0.140953 1.46007i
\(653\) 195330. + 195330.i 0.0179261 + 0.0179261i 0.716013 0.698087i \(-0.245965\pi\)
−0.698087 + 0.716013i \(0.745965\pi\)
\(654\) −1.01111e7 3.62885e6i −0.924390 0.331761i
\(655\) −215322. 91311.7i −0.0196103 0.00831617i
\(656\) −1.20262e6 6.17065e6i −0.109111 0.559850i
\(657\) −7.09424e6 + 7.09424e6i −0.641198 + 0.641198i
\(658\) −312567. 662523.i −0.0281435 0.0596536i
\(659\) −8.86513e6 −0.795191 −0.397596 0.917561i \(-0.630155\pi\)
−0.397596 + 0.917561i \(0.630155\pi\)
\(660\) 2.60474e6 8.27819e6i 0.232758 0.739734i
\(661\) 2.15678e7 1.92001 0.960004 0.279986i \(-0.0903299\pi\)
0.960004 + 0.279986i \(0.0903299\pi\)
\(662\) 8.50828e6 + 1.80344e7i 0.754565 + 1.59939i
\(663\) −6.82074e6 + 6.82074e6i −0.602626 + 0.602626i
\(664\) 5.74414e6 + 9.64688e6i 0.505597 + 0.849115i
\(665\) 1.41911e7 5.73925e6i 1.24441 0.503270i
\(666\) −4.43885e6 1.59309e6i −0.387779 0.139173i
\(667\) 1.86987e7 + 1.86987e7i 1.62741 + 1.62741i
\(668\) −1.05417e7 + 1.01768e6i −0.914047 + 0.0882411i
\(669\) 2.06837e7i 1.78674i
\(670\) −1.01656e6 + 1.10074e6i −0.0874875 + 0.0947320i
\(671\) 2.28374e6i 0.195812i
\(672\) 8.86563e6 + 1.20755e7i 0.757332 + 1.03153i
\(673\) −1.42793e7 1.42793e7i −1.21526 1.21526i −0.969274 0.245984i \(-0.920889\pi\)
−0.245984 0.969274i \(-0.579111\pi\)
\(674\) 2.31537e6 6.45136e6i 0.196323 0.547018i
\(675\) 69845.6 4.16494e6i 0.00590038 0.351843i
\(676\) −1.21916e6 1.00449e6i −0.102611 0.0845434i
\(677\) 1.44888e6 1.44888e6i 0.121496 0.121496i −0.643745 0.765240i \(-0.722620\pi\)
0.765240 + 0.643745i \(0.222620\pi\)
\(678\) −5.39990e6 + 2.54758e6i −0.451141 + 0.212840i
\(679\) −1.07370e7 −0.893731
\(680\) −7.31329e6 + 1.00061e6i −0.606513 + 0.0829838i
\(681\) −1.54651e7 −1.27786
\(682\) 592703. 279627.i 0.0487951 0.0230207i
\(683\) 5.58544e6 5.58544e6i 0.458148 0.458148i −0.439899 0.898047i \(-0.644986\pi\)
0.898047 + 0.439899i \(0.144986\pi\)
\(684\) 1.82960e7 + 1.50744e7i 1.49525 + 1.23197i
\(685\) 3.42311e6 + 8.46415e6i 0.278737 + 0.689219i
\(686\) 4.51666e6 1.25848e7i 0.366444 1.02103i
\(687\) −4.04183e6 4.04183e6i −0.326728 0.326728i
\(688\) 8.85772e6 + 5.96823e6i 0.713429 + 0.480700i
\(689\) 1.15963e7i 0.930622i
\(690\) −3.04697e7 + 1.21138e6i −2.43638 + 0.0968633i
\(691\) 1.36653e7i 1.08874i 0.838845 + 0.544371i \(0.183232\pi\)
−0.838845 + 0.544371i \(0.816768\pi\)
\(692\) −586445. + 56614.7i −0.0465545 + 0.00449432i
\(693\) 4.90281e6 + 4.90281e6i 0.387804 + 0.387804i
\(694\) 8.03699e6 + 2.88445e6i 0.633424 + 0.227334i
\(695\) −6.84304e6 + 1.61366e7i −0.537387 + 1.26721i
\(696\) 2.31685e7 1.37954e7i 1.81290 1.07947i
\(697\) −3.16666e6 + 3.16666e6i −0.246899 + 0.246899i
\(698\) 3.35364e6 + 7.10845e6i 0.260542 + 0.552251i
\(699\) −3.78784e7 −2.93223
\(700\) 8.44437e6 + 7.19857e6i 0.651362 + 0.555266i
\(701\) 3.99831e6 0.307314 0.153657 0.988124i \(-0.450895\pi\)
0.153657 + 0.988124i \(0.450895\pi\)
\(702\) 1.82548e6 + 3.86933e6i 0.139809 + 0.296342i
\(703\) 4.84618e6 4.84618e6i 0.369838 0.369838i
\(704\) −3.25014e6 + 5.99662e6i −0.247155 + 0.456011i
\(705\) 593633. 1.39984e6i 0.0449827 0.106073i
\(706\) 1.35889e6 + 487703.i 0.102606 + 0.0368251i
\(707\) 9.54719e6 + 9.54719e6i 0.718335 + 0.718335i
\(708\) −55287.6 572698.i −0.00414519 0.0429381i
\(709\) 1.77886e7i 1.32901i −0.747285 0.664504i \(-0.768643\pi\)
0.747285 0.664504i \(-0.231357\pi\)
\(710\) −3.25082e6 + 129243.i −0.242018 + 0.00962192i
\(711\) 1.00301e7i 0.744100i
\(712\) −1.87065e6 474345.i −0.138291 0.0350667i
\(713\) −1.62831e6 1.62831e6i −0.119953 0.119953i
\(714\) 3.60478e6 1.00440e7i 0.264626 0.737332i
\(715\) 2.47532e6 + 6.12060e6i 0.181078 + 0.447743i
\(716\) −1.21885e7 + 1.47932e7i −0.888518 + 1.07840i
\(717\) −1.35583e7 + 1.35583e7i −0.984937 + 0.984937i
\(718\) 1.49271e7 7.04232e6i 1.08060 0.509806i
\(719\) 2.25149e7 1.62423 0.812116 0.583496i \(-0.198316\pi\)
0.812116 + 0.583496i \(0.198316\pi\)
\(720\) −3.55869e6 + 1.68115e7i −0.255834 + 1.20858i
\(721\) −5.67681e6 −0.406693
\(722\) −1.84892e7 + 8.72288e6i −1.32000 + 0.622754i
\(723\) 5.55468e6 5.55468e6i 0.395197 0.395197i
\(724\) −377224. + 457841.i −0.0267457 + 0.0324614i
\(725\) 1.43578e7 1.38842e7i 1.01448 0.981017i
\(726\) 5.24293e6 1.46085e7i 0.369175 1.02864i
\(727\) 2.44435e6 + 2.44435e6i 0.171525 + 0.171525i 0.787649 0.616124i \(-0.211298\pi\)
−0.616124 + 0.787649i \(0.711298\pi\)
\(728\) −1.10471e7 2.80124e6i −0.772539 0.195895i
\(729\) 2.01213e7i 1.40229i
\(730\) 7.17040e6 7.76415e6i 0.498008 0.539246i
\(731\) 7.60839e6i 0.526623i
\(732\) 786281. + 8.14471e6i 0.0542375 + 0.561821i
\(733\) 4.63529e6 + 4.63529e6i 0.318652 + 0.318652i 0.848249 0.529597i \(-0.177657\pi\)
−0.529597 + 0.848249i \(0.677657\pi\)
\(734\) 4.26141e6 + 1.52941e6i 0.291953 + 0.104781i
\(735\) 5.42841e6 2.19538e6i 0.370642 0.149897i
\(736\) 2.36900e7 + 3.63124e6i 1.61202 + 0.247093i
\(737\) 697394. 697394.i 0.0472944 0.0472944i
\(738\) 4.44841e6 + 9.42895e6i 0.300652 + 0.637269i
\(739\) 4.68504e6 0.315575 0.157787 0.987473i \(-0.449564\pi\)
0.157787 + 0.987473i \(0.449564\pi\)
\(740\) 4.73892e6 + 1.49110e6i 0.318127 + 0.100099i
\(741\) −3.26337e7 −2.18334
\(742\) −5.47389e6 1.16026e7i −0.364994 0.773650i
\(743\) 1.69427e6 1.69427e6i 0.112593 0.112593i −0.648566 0.761159i \(-0.724631\pi\)
0.761159 + 0.648566i \(0.224631\pi\)
\(744\) −2.01754e6 + 1.20132e6i −0.133626 + 0.0795660i
\(745\) −8.48403e6 3.59783e6i −0.560030 0.237493i
\(746\) −8.48955e6 3.04687e6i −0.558519 0.200451i
\(747\) −1.31657e7 1.31657e7i −0.863263 0.863263i
\(748\) 4.83625e6 466886.i 0.316049 0.0305110i
\(749\) 1.24580e7i 0.811417i
\(750\) 528942. + 2.30257e7i 0.0343364 + 1.49472i
\(751\) 1.18303e7i 0.765412i −0.923870 0.382706i \(-0.874992\pi\)
0.923870 0.382706i \(-0.125008\pi\)
\(752\) −667777. + 991077.i −0.0430612 + 0.0639091i
\(753\) 3.08039e7 + 3.08039e7i 1.97979 + 1.97979i
\(754\) −6.92958e6 + 1.93080e7i −0.443893 + 1.23683i
\(755\) −2.06583e7 8.76060e6i −1.31895 0.559328i
\(756\) −3.65292e6 3.00972e6i −0.232453 0.191523i
\(757\) −1.23025e7 + 1.23025e7i −0.780285 + 0.780285i −0.979879 0.199594i \(-0.936038\pi\)
0.199594 + 0.979879i \(0.436038\pi\)
\(758\) −2.32451e7 + 1.09666e7i −1.46946 + 0.693267i
\(759\) 2.00722e7 1.26471
\(760\) −1.98889e7 1.51015e7i −1.24904 0.948385i
\(761\) 2.23354e7 1.39808 0.699039 0.715083i \(-0.253611\pi\)
0.699039 + 0.715083i \(0.253611\pi\)
\(762\) 3.15108e7 1.48662e7i 1.96595 0.927497i
\(763\) −6.39320e6 + 6.39320e6i −0.397564 + 0.397564i
\(764\) 5.68650e6 + 4.68522e6i 0.352461 + 0.290400i
\(765\) 1.13481e7 4.58943e6i 0.701080 0.283534i
\(766\) −116274. + 323976.i −0.00715996 + 0.0199499i
\(767\) 309512. + 309512.i 0.0189972 + 0.0189972i
\(768\) 9.52666e6 2.25053e7i 0.582824 1.37684i
\(769\) 1.43454e7i 0.874777i −0.899273 0.437389i \(-0.855903\pi\)
0.899273 0.437389i \(-0.144097\pi\)
\(770\) −5.36579e6 4.95545e6i −0.326142 0.301201i
\(771\) 2.84566e7i 1.72404i
\(772\) −2.79957e7 + 2.70268e6i −1.69063 + 0.163211i
\(773\) −5.20960e6 5.20960e6i −0.313585 0.313585i 0.532711 0.846297i \(-0.321173\pi\)
−0.846297 + 0.532711i \(0.821173\pi\)
\(774\) −1.66713e7 5.98327e6i −1.00027 0.358993i
\(775\) −1.25030e6 + 1.20906e6i −0.0747756 + 0.0723090i
\(776\) 8.96130e6 + 1.50499e7i 0.534216 + 0.897178i
\(777\) −5.07859e6 + 5.07859e6i −0.301780 + 0.301780i
\(778\) 1.47459e6 + 3.12558e6i 0.0873421 + 0.185132i
\(779\) −1.51508e7 −0.894526
\(780\) −1.09353e7 2.09762e7i −0.643565 1.23450i
\(781\) 2.14151e6 0.125630
\(782\) −7.28454e6 1.54405e7i −0.425976 0.902908i
\(783\) −6.02417e6 + 6.02417e6i −0.351150 + 0.351150i
\(784\) −4.51720e6 + 880375.i −0.262470 + 0.0511538i
\(785\) 7.54157e6 + 1.86477e7i 0.436805 + 1.08007i
\(786\) −519178. 186331.i −0.0299750 0.0107580i
\(787\) 4.82403e6 + 4.82403e6i 0.277634 + 0.277634i 0.832164 0.554530i \(-0.187102\pi\)
−0.554530 + 0.832164i \(0.687102\pi\)
\(788\) −3.14217e6 3.25482e7i −0.180266 1.86729i
\(789\) 1.91975e7i 1.09788i
\(790\) 419736. + 1.05575e7i 0.0239281 + 0.601858i
\(791\) 5.02514e6i 0.285567i
\(792\) 2.78022e6 1.09642e7i 0.157495 0.621104i
\(793\) −4.40177e6 4.40177e6i −0.248568 0.248568i
\(794\) 6.41736e6 1.78808e7i 0.361248 1.00655i
\(795\) 1.03961e7 2.45151e7i 0.583382 1.37567i
\(796\) −7.38108e6 + 8.95849e6i −0.412893 + 0.501132i
\(797\) 3.09154e6 3.09154e6i 0.172397 0.172397i −0.615635 0.788031i \(-0.711100\pi\)
0.788031 + 0.615635i \(0.211100\pi\)
\(798\) 3.26513e7 1.54043e7i 1.81507 0.856316i
\(799\) 851292. 0.0471750
\(800\) 3.04229e6 1.78445e7i 0.168065 0.985776i
\(801\) 3.20037e6 0.176246
\(802\) 3.08605e7 1.45594e7i 1.69421 0.799298i
\(803\) −4.91913e6 + 4.91913e6i −0.269215 + 0.269215i
\(804\) −2.24707e6 + 2.72729e6i −0.122596 + 0.148796i
\(805\) −1.00199e7 + 2.36279e7i −0.544970 + 1.28509i
\(806\) 603437. 1.68136e6i 0.0327186 0.0911642i
\(807\) 2.36240e7 + 2.36240e7i 1.27694 + 1.27694i
\(808\) 5.41389e6 2.13505e7i 0.291730 1.15048i
\(809\) 8.65788e6i 0.465093i 0.972585 + 0.232547i \(0.0747059\pi\)
−0.972585 + 0.232547i \(0.925294\pi\)
\(810\) 526113. + 1.32332e7i 0.0281751 + 0.708683i
\(811\) 1.67690e7i 0.895272i −0.894216 0.447636i \(-0.852266\pi\)
0.894216 0.447636i \(-0.147734\pi\)
\(812\) −2.18075e6 2.25894e7i −0.116069 1.20230i
\(813\) 5.59798e6 + 5.59798e6i 0.297033 + 0.297033i
\(814\) −3.07789e6 1.10465e6i −0.162814 0.0584335i
\(815\) −1.04286e7 2.57862e7i −0.549959 1.35986i
\(816\) −1.70872e7 + 3.33020e6i −0.898352 + 0.175083i
\(817\) 1.82011e7 1.82011e7i 0.953988 0.953988i
\(818\) 6.84558e6 + 1.45100e7i 0.357706 + 0.758203i
\(819\) 1.88998e7 0.984570
\(820\) −5.07690e6 9.73861e6i −0.263672 0.505781i
\(821\) −1.54461e7 −0.799764 −0.399882 0.916567i \(-0.630949\pi\)
−0.399882 + 0.916567i \(0.630949\pi\)
\(822\) 9.18772e6 + 1.94745e7i 0.474273 + 1.00528i
\(823\) −3.86609e6 + 3.86609e6i −0.198963 + 0.198963i −0.799555 0.600592i \(-0.794931\pi\)
0.600592 + 0.799555i \(0.294931\pi\)
\(824\) 4.73799e6 + 7.95712e6i 0.243095 + 0.408261i
\(825\) 254203. 1.51583e7i 0.0130031 0.775380i
\(826\) −455779. 163578.i −0.0232437 0.00834208i
\(827\) 5.10258e6 + 5.10258e6i 0.259434 + 0.259434i 0.824824 0.565390i \(-0.191274\pi\)
−0.565390 + 0.824824i \(0.691274\pi\)
\(828\) −3.95612e7 + 3.81920e6i −2.00537 + 0.193596i
\(829\) 3.45153e7i 1.74432i 0.489222 + 0.872159i \(0.337281\pi\)
−0.489222 + 0.872159i \(0.662719\pi\)
\(830\) 1.44090e7 + 1.33071e7i 0.726002 + 0.670482i
\(831\) 2.38032e6i 0.119573i
\(832\) 5.29369e6 + 1.78226e7i 0.265125 + 0.892612i
\(833\) 2.31814e6 + 2.31814e6i 0.115752 + 0.115752i
\(834\) −1.39640e7 + 3.89080e7i −0.695174 + 1.93697i
\(835\) −1.71516e7 + 6.93654e6i −0.851312 + 0.344292i
\(836\) 1.26864e7 + 1.04526e7i 0.627802 + 0.517259i
\(837\) 524592. 524592.i 0.0258826 0.0258826i
\(838\) −3.15461e7 + 1.48829e7i −1.55180 + 0.732111i
\(839\) −2.12861e6 −0.104398 −0.0521988 0.998637i \(-0.516623\pi\)
−0.0521988 + 0.998637i \(0.516623\pi\)
\(840\) 2.08426e7 + 1.58257e7i 1.01919 + 0.773862i
\(841\) −2.03382e7 −0.991567
\(842\) −3.20980e7 + 1.51432e7i −1.56026 + 0.736103i
\(843\) −269854. + 269854.i −0.0130785 + 0.0130785i
\(844\) 5.06309e6 + 4.17159e6i 0.244658 + 0.201579i
\(845\) −2.54057e6 1.07738e6i −0.122402 0.0519071i
\(846\) 669459. 1.86532e6i 0.0321587 0.0896041i
\(847\) −9.23683e6 9.23683e6i −0.442400 0.442400i
\(848\) −1.16946e7 + 1.73564e7i −0.558463 + 0.828841i
\(849\) 1.69117e7i 0.805226i
\(850\) −1.17527e7 + 5.30565e6i −0.557944 + 0.251879i
\(851\) 1.14905e7i 0.543894i
\(852\) −7.63746e6 + 737312.i −0.360454 + 0.0347978i
\(853\) −1.38712e7 1.38712e7i −0.652742 0.652742i 0.300910 0.953652i \(-0.402709\pi\)
−0.953652 + 0.300910i \(0.902709\pi\)
\(854\) 6.48193e6 + 2.32634e6i 0.304130 + 0.109151i
\(855\) 3.81263e7 + 1.61683e7i 1.78365 + 0.756394i
\(856\) −1.74623e7 + 1.03977e7i −0.814547 + 0.485014i
\(857\) −6.68264e6 + 6.68264e6i −0.310811 + 0.310811i −0.845224 0.534413i \(-0.820533\pi\)
0.534413 + 0.845224i \(0.320533\pi\)
\(858\) 6.64382e6 + 1.40824e7i 0.308106 + 0.653068i
\(859\) 1.52768e7 0.706397 0.353199 0.935548i \(-0.385094\pi\)
0.353199 + 0.935548i \(0.385094\pi\)
\(860\) 1.77983e7 + 5.60023e6i 0.820601 + 0.258202i
\(861\) 1.58774e7 0.729914
\(862\) −1.11886e7 2.37156e7i −0.512871 1.08709i
\(863\) 1.24879e7 1.24879e7i 0.570773 0.570773i −0.361572 0.932344i \(-0.617760\pi\)
0.932344 + 0.361572i \(0.117760\pi\)
\(864\) −1.16988e6 + 7.63223e6i −0.0533159 + 0.347830i
\(865\) −954162. + 385887.i −0.0433593 + 0.0175356i
\(866\) 2.16649e7 + 7.77547e6i 0.981663 + 0.352316i
\(867\) −1.46307e7 1.46307e7i −0.661023 0.661023i
\(868\) 189903. + 1.96711e6i 0.00855523 + 0.0886196i
\(869\) 6.95485e6i 0.312420i
\(870\) 3.19590e7 3.46054e7i 1.43151 1.55005i
\(871\) 2.68837e6i 0.120073i
\(872\) 1.42972e7 + 3.62537e6i 0.636736 + 0.161459i
\(873\) −2.05395e7 2.05395e7i −0.912127 0.912127i
\(874\) 1.95110e7 5.43637e7i 0.863974 2.40730i
\(875\) 1.77166e7 + 7.86613e6i 0.782275 + 0.347329i
\(876\) 1.58499e7 1.92372e7i 0.697858 0.846996i
\(877\) 8.82023e6 8.82023e6i 0.387241 0.387241i −0.486461 0.873702i \(-0.661713\pi\)
0.873702 + 0.486461i \(0.161713\pi\)
\(878\) 1.77342e7 8.36666e6i 0.776380 0.366282i
\(879\) −4.60697e7 −2.01114
\(880\) −2.46759e6 + 1.16571e7i −0.107415 + 0.507438i
\(881\) −8.35484e6 −0.362659 −0.181329 0.983422i \(-0.558040\pi\)
−0.181329 + 0.983422i \(0.558040\pi\)
\(882\) 6.90243e6 3.25644e6i 0.298765 0.140952i
\(883\) −4.76596e6 + 4.76596e6i −0.205707 + 0.205707i −0.802440 0.596733i \(-0.796465\pi\)
0.596733 + 0.802440i \(0.296465\pi\)
\(884\) 8.42170e6 1.02215e7i 0.362467 0.439930i
\(885\) −376841. 931796.i −0.0161734 0.0399911i
\(886\) 2.20447e6 6.14235e6i 0.0943452 0.262876i
\(887\) −2.28968e7 2.28968e7i −0.977161 0.977161i 0.0225840 0.999745i \(-0.492811\pi\)
−0.999745 + 0.0225840i \(0.992811\pi\)
\(888\) 1.13573e7 + 2.87990e6i 0.483328 + 0.122559i
\(889\) 2.93239e7i 1.24442i
\(890\) −3.36865e6 + 133928.i −0.142555 + 0.00566755i
\(891\) 8.71748e6i 0.367872i
\(892\) 2.72890e6 + 2.82674e7i 0.114835 + 1.18953i
\(893\) 2.03650e6 + 2.03650e6i 0.0854585 + 0.0854585i
\(894\) −2.04565e7 7.34176e6i −0.856025 0.307225i
\(895\) −1.30729e7 + 3.08271e7i −0.545524 + 1.28640i
\(896\) −1.37094e7 1.53334e7i −0.570492 0.638068i
\(897\) 3.86879e7 3.86879e7i 1.60544 1.60544i
\(898\) 4.19588e6 + 8.89368e6i 0.173633 + 0.368036i
\(899\) 3.55721e6 0.146795
\(900\) 2.38319e6 + 2.99245e7i 0.0980737 + 1.23146i
\(901\) 1.49084e7 0.611814
\(902\) 3.08452e6 + 6.53802e6i 0.126233 + 0.267565i
\(903\) −1.90740e7 + 1.90740e7i −0.778434 + 0.778434i
\(904\) 7.04369e6 4.19409e6i 0.286668 0.170694i
\(905\) −404596. + 954078.i −0.0164210 + 0.0387224i
\(906\) −4.98108e7 1.78769e7i −2.01606 0.723557i
\(907\) −1.83453e7 1.83453e7i −0.740467 0.740467i 0.232201 0.972668i \(-0.425407\pi\)
−0.972668 + 0.232201i \(0.925407\pi\)
\(908\) 2.11354e7 2.04039e6i 0.850738 0.0821292i
\(909\) 3.65271e7i 1.46624i
\(910\) −1.98936e7 + 790910.i −0.796360 + 0.0316609i
\(911\) 1.68004e6i 0.0670694i −0.999438 0.0335347i \(-0.989324\pi\)
0.999438 0.0335347i \(-0.0106764\pi\)
\(912\) −4.88435e7 3.29102e7i −1.94455 1.31022i
\(913\) −9.12909e6 9.12909e6i −0.362452 0.362452i
\(914\) −1.38436e6 + 3.85727e6i −0.0548131 + 0.152727i
\(915\) 5.35930e6 + 1.32517e7i 0.211619 + 0.523261i
\(916\) 6.05704e6 + 4.99052e6i 0.238518 + 0.196520i
\(917\) −328273. + 328273.i −0.0128917 + 0.0128917i
\(918\) 4.97446e6 2.34686e6i 0.194823 0.0919138i
\(919\) −2.09762e7 −0.819291 −0.409645 0.912245i \(-0.634348\pi\)
−0.409645 + 0.912245i \(0.634348\pi\)
\(920\) 4.14817e7 5.67557e6i 1.61580 0.221075i
\(921\) 3.72858e7 1.44842
\(922\) 5.10063e6 2.40639e6i 0.197604 0.0932262i
\(923\) 4.12763e6 4.12763e6i 0.159477 0.159477i
\(924\) −1.32948e7 1.09538e7i −0.512273 0.422072i
\(925\) 8.67748e6 + 145521.i 0.333457 + 0.00559204i
\(926\) −9.78862e6 + 2.72742e7i −0.375141 + 1.04526i
\(927\) −1.08596e7 1.08596e7i −0.415064 0.415064i
\(928\) −2.98432e7 + 2.19103e7i −1.13756 + 0.835177i
\(929\) 2.25118e6i 0.0855797i 0.999084 + 0.0427899i \(0.0136246\pi\)
−0.999084 + 0.0427899i \(0.986375\pi\)
\(930\) −2.78303e6 + 3.01348e6i −0.105514 + 0.114251i
\(931\) 1.10911e7i 0.419373i
\(932\) 5.17666e7 4.99749e6i 1.95213 0.188457i
\(933\) −3.33872e7 3.33872e7i −1.25567 1.25567i
\(934\) 3.45455e7 + 1.23983e7i 1.29576 + 0.465045i
\(935\) 7.86872e6 3.18231e6i 0.294358 0.119045i
\(936\) −1.57741e7 2.64916e7i −0.588513 0.988367i
\(937\) −1.78477e7 + 1.78477e7i −0.664099 + 0.664099i −0.956344 0.292244i \(-0.905598\pi\)
0.292244 + 0.956344i \(0.405598\pi\)
\(938\) 1.26901e6 + 2.68982e6i 0.0470930 + 0.0998195i
\(939\) 4.43234e7 1.64047
\(940\) −626602. + 1.99142e6i −0.0231298 + 0.0735096i
\(941\) −1.56180e7 −0.574979 −0.287489 0.957784i \(-0.592821\pi\)
−0.287489 + 0.957784i \(0.592821\pi\)
\(942\) 2.02418e7 + 4.29049e7i 0.743227 + 1.57536i
\(943\) 1.79616e7 1.79616e7i 0.657758 0.657758i
\(944\) 151118. + 775386.i 0.00551933 + 0.0283197i
\(945\) −7.61220e6 3.22811e6i −0.277288 0.117590i
\(946\) −1.15598e7 4.14879e6i −0.419975 0.150728i
\(947\) 1.89678e7 + 1.89678e7i 0.687292 + 0.687292i 0.961633 0.274341i \(-0.0884597\pi\)
−0.274341 + 0.961633i \(0.588460\pi\)
\(948\) 2.39452e6 + 2.48037e7i 0.0865363 + 0.896389i
\(949\) 1.89627e7i 0.683493i
\(950\) −4.08077e7 1.54229e7i −1.46701 0.554445i
\(951\) 6.16726e6i 0.221126i
\(952\) −3.60132e6 + 1.42023e7i −0.128786 + 0.507887i
\(953\) 3.98360e6 + 3.98360e6i 0.142083 + 0.142083i 0.774571 0.632487i \(-0.217966\pi\)
−0.632487 + 0.774571i \(0.717966\pi\)
\(954\) 1.17240e7 3.26668e7i 0.417067 1.16208i
\(955\) 1.18499e7 + 5.02519e6i 0.420442 + 0.178297i
\(956\) 1.67407e7 2.03184e7i 0.592420 0.719025i
\(957\) −2.19249e7 + 2.19249e7i −0.773852 + 0.773852i
\(958\) −2.49092e7 + 1.17517e7i −0.876890 + 0.413701i
\(959\) 1.81230e7 0.636330
\(960\) 4.78691e6 4.24233e7i 0.167640 1.48568i
\(961\) 2.83194e7 0.989180
\(962\) −8.06159e6 + 3.80331e6i −0.280856 + 0.132503i
\(963\) 2.38319e7 2.38319e7i 0.828118 0.828118i
\(964\) −6.85847e6 + 8.32418e6i −0.237703 + 0.288502i
\(965\) −4.55499e7 + 1.84215e7i −1.57459 + 0.636805i
\(966\) −2.04466e7 + 5.69708e7i −0.704984 + 1.96431i
\(967\) 1.23916e7 + 1.23916e7i 0.426149 + 0.426149i 0.887314 0.461166i \(-0.152569\pi\)
−0.461166 + 0.887314i \(0.652569\pi\)
\(968\) −5.23790e6 + 2.06564e7i −0.179667 + 0.708544i
\(969\) 4.19544e7i 1.43538i
\(970\) 2.24791e7 + 2.07600e7i 0.767096 + 0.708433i
\(971\) 5.72516e6i 0.194867i −0.995242 0.0974337i \(-0.968937\pi\)
0.995242 0.0974337i \(-0.0310634\pi\)
\(972\) 3.99740e6 + 4.14071e7i 0.135710 + 1.40576i
\(973\) 2.46013e7 + 2.46013e7i 0.833059 + 0.833059i
\(974\) −1.91985e7 6.89030e6i −0.648442 0.232724i
\(975\) −2.87267e7 2.97066e7i −0.967775 1.00079i
\(976\) −2.14915e6 1.10273e7i −0.0722174 0.370547i
\(977\) 4.31515e6 4.31515e6i 0.144630 0.144630i −0.631084 0.775714i \(-0.717390\pi\)
0.775714 + 0.631084i \(0.217390\pi\)
\(978\) −2.79905e7 5.93294e7i −0.935759 1.98346i
\(979\) 2.21913e6 0.0739990
\(980\) −7.12911e6 + 3.71653e6i −0.237121 + 0.123615i
\(981\) −2.44601e7 −0.811494
\(982\) −1.44521e7 3.06330e7i −0.478246 1.01370i
\(983\) −1.85871e7 + 1.85871e7i −0.613520 + 0.613520i −0.943862 0.330341i \(-0.892836\pi\)
0.330341 + 0.943862i \(0.392836\pi\)
\(984\) −1.32516e7 2.22552e7i −0.436296 0.732729i
\(985\) −2.14171e7 5.29569e7i −0.703347 1.73913i
\(986\) 2.48226e7 + 8.90876e6i 0.813121 + 0.291827i
\(987\) −2.13416e6 2.13416e6i −0.0697323 0.0697323i
\(988\) 4.45990e7 4.30554e6i 1.45356 0.140325i
\(989\) 4.31556e7i 1.40296i
\(990\) −784974. 1.97443e7i −0.0254546 0.640255i
\(991\) 2.05031e7i 0.663187i 0.943422 + 0.331593i \(0.107586\pi\)
−0.943422 + 0.331593i \(0.892414\pi\)
\(992\) 2.59878e6 1.90798e6i 0.0838476 0.0615594i
\(993\) 5.80933e7 + 5.80933e7i 1.86962 + 1.86962i
\(994\) −2.18146e6 + 6.07824e6i −0.0700296 + 0.195125i
\(995\) −7.91667e6 + 1.86683e7i −0.253504 + 0.597787i
\(996\) 3.57010e7 + 2.94148e7i 1.14034 + 0.939546i
\(997\) 3.87741e7 3.87741e7i 1.23539 1.23539i 0.273524 0.961865i \(-0.411811\pi\)
0.961865 0.273524i \(-0.0881893\pi\)
\(998\) 5.55290e7 2.61976e7i 1.76479 0.832597i
\(999\) −3.70190e6 −0.117357
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 20.6.e.b.3.2 24
4.3 odd 2 inner 20.6.e.b.3.5 yes 24
5.2 odd 4 inner 20.6.e.b.7.5 yes 24
5.3 odd 4 100.6.e.e.7.8 24
5.4 even 2 100.6.e.e.43.11 24
20.3 even 4 100.6.e.e.7.11 24
20.7 even 4 inner 20.6.e.b.7.2 yes 24
20.19 odd 2 100.6.e.e.43.8 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
20.6.e.b.3.2 24 1.1 even 1 trivial
20.6.e.b.3.5 yes 24 4.3 odd 2 inner
20.6.e.b.7.2 yes 24 20.7 even 4 inner
20.6.e.b.7.5 yes 24 5.2 odd 4 inner
100.6.e.e.7.8 24 5.3 odd 4
100.6.e.e.7.11 24 20.3 even 4
100.6.e.e.43.8 24 20.19 odd 2
100.6.e.e.43.11 24 5.4 even 2