Properties

Label 24.8.f.c.11.5
Level $24$
Weight $8$
Character 24.11
Analytic conductor $7.497$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [24,8,Mod(11,24)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(24, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("24.11");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 24.f (of order \(2\), degree \(1\), 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: \(7.49724061162\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 274 x^{18} + 45864 x^{16} - 5031360 x^{14} + 776389632 x^{12} - 102828146688 x^{10} + 12720367730688 x^{8} + \cdots + 11\!\cdots\!24 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{52}\cdot 3^{20} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 11.5
Root \(10.0085 - 5.27546i\) of defining polynomial
Character \(\chi\) \(=\) 24.11
Dual form 24.8.f.c.11.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-10.0085 - 5.27546i) q^{2} +(-43.1368 + 18.0615i) q^{3} +(72.3391 + 105.599i) q^{4} -277.669 q^{5} +(527.016 + 46.7976i) q^{6} +1066.27i q^{7} +(-166.924 - 1438.50i) q^{8} +(1534.56 - 1558.23i) q^{9} +O(q^{10})\) \(q+(-10.0085 - 5.27546i) q^{2} +(-43.1368 + 18.0615i) q^{3} +(72.3391 + 105.599i) q^{4} -277.669 q^{5} +(527.016 + 46.7976i) q^{6} +1066.27i q^{7} +(-166.924 - 1438.50i) q^{8} +(1534.56 - 1558.23i) q^{9} +(2779.04 + 1464.83i) q^{10} -5371.77i q^{11} +(-5027.75 - 3248.62i) q^{12} -7990.16i q^{13} +(5625.09 - 10671.8i) q^{14} +(11977.7 - 5015.12i) q^{15} +(-5918.10 + 15277.8i) q^{16} +16288.8i q^{17} +(-23579.0 + 7500.03i) q^{18} +45925.3 q^{19} +(-20086.3 - 29321.4i) q^{20} +(-19258.6 - 45995.7i) q^{21} +(-28338.5 + 53763.2i) q^{22} +51938.6 q^{23} +(33182.1 + 59037.4i) q^{24} -1025.17 q^{25} +(-42151.8 + 79969.3i) q^{26} +(-38051.9 + 94933.7i) q^{27} +(-112597. + 77133.4i) q^{28} -25340.1 q^{29} +(-146336. - 12994.2i) q^{30} -168492. i q^{31} +(139829. - 121687. i) q^{32} +(97022.4 + 231721. i) q^{33} +(85931.0 - 163026. i) q^{34} -296071. i q^{35} +(275556. + 49326.2i) q^{36} -240460. i q^{37} +(-459643. - 242277. i) q^{38} +(144315. + 344670. i) q^{39} +(46349.5 + 399427. i) q^{40} -247909. i q^{41} +(-49899.1 + 561944. i) q^{42} +288474. q^{43} +(567251. - 388589. i) q^{44} +(-426099. + 432672. i) q^{45} +(-519826. - 274000. i) q^{46} +895911. q^{47} +(-20653.0 - 765925. i) q^{48} -313399. q^{49} +(10260.4 + 5408.23i) q^{50} +(-294202. - 702648. i) q^{51} +(843749. - 578001. i) q^{52} -2.05527e6 q^{53} +(881660. - 749400. i) q^{54} +1.49157e6i q^{55} +(1.53384e6 - 177987. i) q^{56} +(-1.98107e6 + 829482. i) q^{57} +(253616. + 133681. i) q^{58} -574079. i q^{59} +(1.39605e6 + 902041. i) q^{60} -1.45277e6i q^{61} +(-888874. + 1.68635e6i) q^{62} +(1.66150e6 + 1.63626e6i) q^{63} +(-2.04142e6 + 480240. i) q^{64} +2.21862e6i q^{65} +(251386. - 2.83101e6i) q^{66} -209469. q^{67} +(-1.72008e6 + 1.17832e6i) q^{68} +(-2.24046e6 + 938092. i) q^{69} +(-1.56191e6 + 2.96322e6i) q^{70} -622084. q^{71} +(-2.49768e6 - 1.94736e6i) q^{72} +4.04297e6 q^{73} +(-1.26853e6 + 2.40663e6i) q^{74} +(44222.5 - 18516.1i) q^{75} +(3.32220e6 + 4.84965e6i) q^{76} +5.72778e6 q^{77} +(373921. - 4.21094e6i) q^{78} -7.77147e6i q^{79} +(1.64327e6 - 4.24217e6i) q^{80} +(-73212.3 - 4.78241e6i) q^{81} +(-1.30783e6 + 2.48119e6i) q^{82} +3.75733e6i q^{83} +(3.46393e6 - 5.36096e6i) q^{84} -4.52290e6i q^{85} +(-2.88719e6 - 1.52183e6i) q^{86} +(1.09309e6 - 457682. i) q^{87} +(-7.72730e6 + 896675. i) q^{88} -3.64625e6i q^{89} +(6.54715e6 - 2.08252e6i) q^{90} +8.51971e6 q^{91} +(3.75719e6 + 5.48464e6i) q^{92} +(3.04323e6 + 7.26821e6i) q^{93} +(-8.96670e6 - 4.72634e6i) q^{94} -1.27520e7 q^{95} +(-3.83390e6 + 7.77470e6i) q^{96} +220958. q^{97} +(3.13665e6 + 1.65332e6i) q^{98} +(-8.37046e6 - 8.24330e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 120 q^{3} + 548 q^{4} - 1416 q^{6} + 5076 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 120 q^{3} + 548 q^{4} - 1416 q^{6} + 5076 q^{9} - 3384 q^{10} - 26700 q^{12} - 33304 q^{16} - 11880 q^{18} + 133744 q^{19} - 166880 q^{22} - 74424 q^{24} + 711596 q^{25} + 85320 q^{27} - 669360 q^{28} - 41904 q^{30} + 263640 q^{33} + 24112 q^{34} - 409428 q^{36} - 437088 q^{40} + 1724040 q^{42} - 2292080 q^{43} + 1466400 q^{46} + 1846200 q^{48} + 2495228 q^{49} - 7417536 q^{51} - 2511360 q^{52} + 5680584 q^{54} - 5067120 q^{57} + 1427880 q^{58} + 2211120 q^{60} - 4070608 q^{64} + 1062024 q^{66} + 3654640 q^{67} + 11712816 q^{70} + 7004880 q^{72} + 19892680 q^{73} - 8612088 q^{75} - 11799464 q^{76} - 1226160 q^{78} - 6817932 q^{81} - 52710080 q^{82} - 6585408 q^{84} - 13470800 q^{88} + 10393704 q^{90} + 67826976 q^{91} - 24601920 q^{94} + 35857680 q^{96} + 5561800 q^{97} + 10152864 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/24\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(13\) \(17\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.0085 5.27546i −0.884633 0.466289i
\(3\) −43.1368 + 18.0615i −0.922408 + 0.386216i
\(4\) 72.3391 + 105.599i 0.565149 + 0.824989i
\(5\) −277.669 −0.993417 −0.496709 0.867917i \(-0.665458\pi\)
−0.496709 + 0.867917i \(0.665458\pi\)
\(6\) 527.016 + 46.7976i 0.996081 + 0.0884493i
\(7\) 1066.27i 1.17497i 0.809236 + 0.587484i \(0.199881\pi\)
−0.809236 + 0.587484i \(0.800119\pi\)
\(8\) −166.924 1438.50i −0.115267 0.993335i
\(9\) 1534.56 1558.23i 0.701674 0.712498i
\(10\) 2779.04 + 1464.83i 0.878809 + 0.463219i
\(11\) 5371.77i 1.21687i −0.793605 0.608433i \(-0.791798\pi\)
0.793605 0.608433i \(-0.208202\pi\)
\(12\) −5027.75 3248.62i −0.839922 0.542706i
\(13\) 7990.16i 1.00868i −0.863505 0.504341i \(-0.831736\pi\)
0.863505 0.504341i \(-0.168264\pi\)
\(14\) 5625.09 10671.8i 0.547874 1.03941i
\(15\) 11977.7 5015.12i 0.916336 0.383674i
\(16\) −5918.10 + 15277.8i −0.361212 + 0.932484i
\(17\) 16288.8i 0.804116i 0.915614 + 0.402058i \(0.131705\pi\)
−0.915614 + 0.402058i \(0.868295\pi\)
\(18\) −23579.0 + 7500.03i −0.952954 + 0.303116i
\(19\) 45925.3 1.53608 0.768042 0.640400i \(-0.221231\pi\)
0.768042 + 0.640400i \(0.221231\pi\)
\(20\) −20086.3 29321.4i −0.561429 0.819558i
\(21\) −19258.6 45995.7i −0.453792 1.08380i
\(22\) −28338.5 + 53763.2i −0.567411 + 1.07648i
\(23\) 51938.6 0.890109 0.445054 0.895504i \(-0.353184\pi\)
0.445054 + 0.895504i \(0.353184\pi\)
\(24\) 33182.1 + 59037.4i 0.489965 + 0.871742i
\(25\) −1025.17 −0.0131222
\(26\) −42151.8 + 79969.3i −0.470337 + 0.892312i
\(27\) −38051.9 + 94933.7i −0.372052 + 0.928212i
\(28\) −112597. + 77133.4i −0.969335 + 0.664032i
\(29\) −25340.1 −0.192937 −0.0964686 0.995336i \(-0.530755\pi\)
−0.0964686 + 0.995336i \(0.530755\pi\)
\(30\) −146336. 12994.2i −0.989524 0.0878671i
\(31\) 168492.i 1.01581i −0.861412 0.507907i \(-0.830419\pi\)
0.861412 0.507907i \(-0.169581\pi\)
\(32\) 139829. 121687.i 0.754347 0.656476i
\(33\) 97022.4 + 231721.i 0.469973 + 1.12245i
\(34\) 85931.0 163026.i 0.374950 0.711347i
\(35\) 296071.i 1.16723i
\(36\) 275556. + 49326.2i 0.984353 + 0.176205i
\(37\) 240460.i 0.780434i −0.920723 0.390217i \(-0.872400\pi\)
0.920723 0.390217i \(-0.127600\pi\)
\(38\) −459643. 242277.i −1.35887 0.716258i
\(39\) 144315. + 344670.i 0.389569 + 0.930416i
\(40\) 46349.5 + 399427.i 0.114508 + 0.986796i
\(41\) 247909.i 0.561757i −0.959743 0.280879i \(-0.909374\pi\)
0.959743 0.280879i \(-0.0906258\pi\)
\(42\) −49899.1 + 561944.i −0.103925 + 1.17036i
\(43\) 288474. 0.553309 0.276654 0.960969i \(-0.410774\pi\)
0.276654 + 0.960969i \(0.410774\pi\)
\(44\) 567251. 388589.i 1.00390 0.687711i
\(45\) −426099. + 432672.i −0.697055 + 0.707808i
\(46\) −519826. 274000.i −0.787419 0.415048i
\(47\) 895911. 1.25870 0.629350 0.777122i \(-0.283321\pi\)
0.629350 + 0.777122i \(0.283321\pi\)
\(48\) −20653.0 765925.i −0.0269550 0.999637i
\(49\) −313399. −0.380550
\(50\) 10260.4 + 5408.23i 0.0116083 + 0.00611872i
\(51\) −294202. 702648.i −0.310563 0.741723i
\(52\) 843749. 578001.i 0.832150 0.570056i
\(53\) −2.05527e6 −1.89628 −0.948140 0.317854i \(-0.897038\pi\)
−0.948140 + 0.317854i \(0.897038\pi\)
\(54\) 881660. 749400.i 0.761944 0.647643i
\(55\) 1.49157e6i 1.20886i
\(56\) 1.53384e6 177987.i 1.16714 0.135434i
\(57\) −1.98107e6 + 829482.i −1.41690 + 0.593260i
\(58\) 253616. + 133681.i 0.170678 + 0.0899644i
\(59\) 574079.i 0.363906i −0.983307 0.181953i \(-0.941758\pi\)
0.983307 0.181953i \(-0.0582419\pi\)
\(60\) 1.39605e6 + 902041.i 0.834393 + 0.539134i
\(61\) 1.45277e6i 0.819489i −0.912200 0.409745i \(-0.865618\pi\)
0.912200 0.409745i \(-0.134382\pi\)
\(62\) −888874. + 1.68635e6i −0.473663 + 0.898622i
\(63\) 1.66150e6 + 1.63626e6i 0.837162 + 0.824445i
\(64\) −2.04142e6 + 480240.i −0.973427 + 0.228996i
\(65\) 2.21862e6i 1.00204i
\(66\) 251386. 2.83101e6i 0.107631 1.21210i
\(67\) −209469. −0.0850861 −0.0425431 0.999095i \(-0.513546\pi\)
−0.0425431 + 0.999095i \(0.513546\pi\)
\(68\) −1.72008e6 + 1.17832e6i −0.663387 + 0.454446i
\(69\) −2.24046e6 + 938092.i −0.821044 + 0.343774i
\(70\) −1.56191e6 + 2.96322e6i −0.544268 + 1.03257i
\(71\) −622084. −0.206274 −0.103137 0.994667i \(-0.532888\pi\)
−0.103137 + 0.994667i \(0.532888\pi\)
\(72\) −2.49768e6 1.94736e6i −0.788628 0.614870i
\(73\) 4.04297e6 1.21638 0.608192 0.793790i \(-0.291895\pi\)
0.608192 + 0.793790i \(0.291895\pi\)
\(74\) −1.26853e6 + 2.40663e6i −0.363908 + 0.690397i
\(75\) 44222.5 18516.1i 0.0121040 0.00506799i
\(76\) 3.32220e6 + 4.84965e6i 0.868116 + 1.26725i
\(77\) 5.72778e6 1.42978
\(78\) 373921. 4.21094e6i 0.0892172 1.00473i
\(79\) 7.77147e6i 1.77341i −0.462340 0.886703i \(-0.652990\pi\)
0.462340 0.886703i \(-0.347010\pi\)
\(80\) 1.64327e6 4.24217e6i 0.358835 0.926345i
\(81\) −73212.3 4.78241e6i −0.0153069 0.999883i
\(82\) −1.30783e6 + 2.48119e6i −0.261941 + 0.496949i
\(83\) 3.75733e6i 0.721283i 0.932705 + 0.360641i \(0.117442\pi\)
−0.932705 + 0.360641i \(0.882558\pi\)
\(84\) 3.46393e6 5.36096e6i 0.637663 0.986882i
\(85\) 4.52290e6i 0.798823i
\(86\) −2.88719e6 1.52183e6i −0.489475 0.258002i
\(87\) 1.09309e6 457682.i 0.177967 0.0745154i
\(88\) −7.72730e6 + 896675.i −1.20875 + 0.140264i
\(89\) 3.64625e6i 0.548253i −0.961694 0.274126i \(-0.911611\pi\)
0.961694 0.274126i \(-0.0883887\pi\)
\(90\) 6.54715e6 2.08252e6i 0.946681 0.301121i
\(91\) 8.51971e6 1.18517
\(92\) 3.75719e6 + 5.48464e6i 0.503044 + 0.734329i
\(93\) 3.04323e6 + 7.26821e6i 0.392324 + 0.936995i
\(94\) −8.96670e6 4.72634e6i −1.11349 0.586918i
\(95\) −1.27520e7 −1.52597
\(96\) −3.83390e6 + 7.77470e6i −0.442274 + 0.896880i
\(97\) 220958. 0.0245815 0.0122908 0.999924i \(-0.496088\pi\)
0.0122908 + 0.999924i \(0.496088\pi\)
\(98\) 3.13665e6 + 1.65332e6i 0.336647 + 0.177446i
\(99\) −8.37046e6 8.24330e6i −0.867015 0.853843i
\(100\) −74159.8 108256.i −0.00741598 0.0108256i
\(101\) 1.07470e7 1.03791 0.518957 0.854800i \(-0.326320\pi\)
0.518957 + 0.854800i \(0.326320\pi\)
\(102\) −762279. + 8.58448e6i −0.0711235 + 0.800965i
\(103\) 7.49934e6i 0.676227i −0.941105 0.338114i \(-0.890211\pi\)
0.941105 0.338114i \(-0.109789\pi\)
\(104\) −1.14939e7 + 1.33375e6i −1.00196 + 0.116267i
\(105\) 5.34750e6 + 1.27715e7i 0.450804 + 1.07667i
\(106\) 2.05701e7 + 1.08425e7i 1.67751 + 0.884214i
\(107\) 2.11831e7i 1.67165i 0.548995 + 0.835825i \(0.315010\pi\)
−0.548995 + 0.835825i \(0.684990\pi\)
\(108\) −1.27775e7 + 2.84919e6i −0.976029 + 0.217640i
\(109\) 3.25125e6i 0.240468i 0.992746 + 0.120234i \(0.0383645\pi\)
−0.992746 + 0.120234i \(0.961635\pi\)
\(110\) 7.86872e6 1.49283e7i 0.563676 1.06939i
\(111\) 4.34307e6 + 1.03727e7i 0.301416 + 0.719879i
\(112\) −1.62903e7 6.31032e6i −1.09564 0.424413i
\(113\) 1.41835e7i 0.924719i −0.886693 0.462359i \(-0.847003\pi\)
0.886693 0.462359i \(-0.152997\pi\)
\(114\) 2.42034e7 + 2.14920e6i 1.53006 + 0.135866i
\(115\) −1.44217e7 −0.884249
\(116\) −1.83308e6 2.67588e6i −0.109038 0.159171i
\(117\) −1.24505e7 1.22614e7i −0.718683 0.707765i
\(118\) −3.02853e6 + 5.74565e6i −0.169685 + 0.321923i
\(119\) −1.73684e7 −0.944811
\(120\) −9.21363e6 1.63928e7i −0.486739 0.866004i
\(121\) −9.36870e6 −0.480763
\(122\) −7.66404e6 + 1.45400e7i −0.382119 + 0.724947i
\(123\) 4.47762e6 + 1.06940e7i 0.216960 + 0.518169i
\(124\) 1.77925e7 1.21886e7i 0.838035 0.574086i
\(125\) 2.19775e7 1.00645
\(126\) −7.99709e6 2.51417e7i −0.356152 1.11969i
\(127\) 2.47641e7i 1.07278i 0.843970 + 0.536390i \(0.180212\pi\)
−0.843970 + 0.536390i \(0.819788\pi\)
\(128\) 2.29650e7 + 5.96297e6i 0.967904 + 0.251321i
\(129\) −1.24438e7 + 5.21029e6i −0.510377 + 0.213697i
\(130\) 1.17042e7 2.22050e7i 0.467241 0.886438i
\(131\) 3.82180e7i 1.48532i −0.669671 0.742658i \(-0.733565\pi\)
0.669671 0.742658i \(-0.266435\pi\)
\(132\) −1.74508e7 + 2.70079e7i −0.660401 + 1.02207i
\(133\) 4.89690e7i 1.80485i
\(134\) 2.09647e6 + 1.10505e6i 0.0752699 + 0.0396747i
\(135\) 1.05658e7 2.63601e7i 0.369603 0.922102i
\(136\) 2.34315e7 2.71899e6i 0.798756 0.0926877i
\(137\) 4.05577e7i 1.34757i −0.738927 0.673785i \(-0.764667\pi\)
0.738927 0.673785i \(-0.235333\pi\)
\(138\) 2.73725e7 + 2.43060e6i 0.886620 + 0.0787295i
\(139\) 137608. 0.00434603 0.00217301 0.999998i \(-0.499308\pi\)
0.00217301 + 0.999998i \(0.499308\pi\)
\(140\) 3.12647e7 2.14175e7i 0.962954 0.659661i
\(141\) −3.86467e7 + 1.61815e7i −1.16104 + 0.486130i
\(142\) 6.22611e6 + 3.28178e6i 0.182477 + 0.0961834i
\(143\) −4.29213e7 −1.22743
\(144\) 1.47247e7 + 3.26665e7i 0.410939 + 0.911663i
\(145\) 7.03616e6 0.191667
\(146\) −4.04640e7 2.13285e7i −1.07605 0.567187i
\(147\) 1.35190e7 5.66047e6i 0.351022 0.146974i
\(148\) 2.53922e7 1.73946e7i 0.643849 0.441062i
\(149\) 3.84188e7 0.951463 0.475731 0.879591i \(-0.342183\pi\)
0.475731 + 0.879591i \(0.342183\pi\)
\(150\) −540280. 47975.5i −0.0130707 0.00116065i
\(151\) 1.59332e7i 0.376604i 0.982111 + 0.188302i \(0.0602983\pi\)
−0.982111 + 0.188302i \(0.939702\pi\)
\(152\) −7.66603e6 6.60637e7i −0.177059 1.52584i
\(153\) 2.53818e7 + 2.49962e7i 0.572931 + 0.564228i
\(154\) −5.73263e7 3.02166e7i −1.26483 0.666690i
\(155\) 4.67850e7i 1.00913i
\(156\) −2.59570e7 + 4.01725e7i −0.547418 + 0.847214i
\(157\) 7.83329e7i 1.61546i −0.589555 0.807728i \(-0.700697\pi\)
0.589555 0.807728i \(-0.299303\pi\)
\(158\) −4.09980e7 + 7.77805e7i −0.826919 + 1.56881i
\(159\) 8.86575e7 3.71213e7i 1.74914 0.732374i
\(160\) −3.88260e7 + 3.37886e7i −0.749381 + 0.652155i
\(161\) 5.53808e7i 1.04585i
\(162\) −2.44966e7 + 4.82508e7i −0.452693 + 0.891666i
\(163\) −4.68043e7 −0.846505 −0.423252 0.906012i \(-0.639112\pi\)
−0.423252 + 0.906012i \(0.639112\pi\)
\(164\) 2.61788e7 1.79335e7i 0.463443 0.317477i
\(165\) −2.69401e7 6.43415e7i −0.466880 1.11506i
\(166\) 1.98216e7 3.76051e7i 0.336326 0.638070i
\(167\) 5.53695e7 0.919947 0.459973 0.887933i \(-0.347859\pi\)
0.459973 + 0.887933i \(0.347859\pi\)
\(168\) −6.29501e7 + 3.53813e7i −1.02427 + 0.575693i
\(169\) −1.09418e6 −0.0174376
\(170\) −2.38603e7 + 4.52673e7i −0.372482 + 0.706665i
\(171\) 7.04752e7 7.15624e7i 1.07783 1.09446i
\(172\) 2.08680e7 + 3.04625e7i 0.312702 + 0.456473i
\(173\) −6.23040e7 −0.914860 −0.457430 0.889246i \(-0.651230\pi\)
−0.457430 + 0.889246i \(0.651230\pi\)
\(174\) −1.33547e7 1.18586e6i −0.192181 0.0170652i
\(175\) 1.09311e6i 0.0154181i
\(176\) 8.20688e7 + 3.17907e7i 1.13471 + 0.439547i
\(177\) 1.03687e7 + 2.47639e7i 0.140546 + 0.335670i
\(178\) −1.92356e7 + 3.64934e7i −0.255644 + 0.485002i
\(179\) 3.51611e7i 0.458223i 0.973400 + 0.229111i \(0.0735820\pi\)
−0.973400 + 0.229111i \(0.926418\pi\)
\(180\) −7.65132e7 1.36963e7i −0.977874 0.175045i
\(181\) 2.24187e7i 0.281019i 0.990079 + 0.140510i \(0.0448741\pi\)
−0.990079 + 0.140510i \(0.955126\pi\)
\(182\) −8.52693e7 4.49454e7i −1.04844 0.552631i
\(183\) 2.62393e7 + 6.26679e7i 0.316500 + 0.755904i
\(184\) −8.66979e6 7.47138e7i −0.102600 0.884176i
\(185\) 6.67681e7i 0.775297i
\(186\) 7.88504e6 8.87981e7i 0.0898480 1.01183i
\(187\) 8.74998e7 0.978502
\(188\) 6.48094e7 + 9.46069e7i 0.711353 + 1.03841i
\(189\) −1.01225e8 4.05738e7i −1.09062 0.437149i
\(190\) 1.27628e8 + 6.72727e7i 1.34992 + 0.711544i
\(191\) 8.13272e6 0.0844538 0.0422269 0.999108i \(-0.486555\pi\)
0.0422269 + 0.999108i \(0.486555\pi\)
\(192\) 7.93866e7 5.75873e7i 0.809455 0.587182i
\(193\) −1.30873e8 −1.31039 −0.655195 0.755460i \(-0.727414\pi\)
−0.655195 + 0.755460i \(0.727414\pi\)
\(194\) −2.21145e6 1.16566e6i −0.0217456 0.0114621i
\(195\) −4.00716e7 9.57040e7i −0.387005 0.924291i
\(196\) −2.26710e7 3.30945e7i −0.215067 0.313949i
\(197\) 1.21828e7 0.113531 0.0567655 0.998388i \(-0.481921\pi\)
0.0567655 + 0.998388i \(0.481921\pi\)
\(198\) 4.02884e7 + 1.26661e8i 0.368852 + 1.15962i
\(199\) 7.30246e7i 0.656876i 0.944526 + 0.328438i \(0.106522\pi\)
−0.944526 + 0.328438i \(0.893478\pi\)
\(200\) 171125. + 1.47471e6i 0.00151255 + 0.0130347i
\(201\) 9.03583e6 3.78334e6i 0.0784841 0.0328616i
\(202\) −1.07561e8 5.66952e7i −0.918173 0.483968i
\(203\) 2.70195e7i 0.226695i
\(204\) 5.29163e7 8.18962e7i 0.436399 0.675395i
\(205\) 6.88365e7i 0.558059i
\(206\) −3.95624e7 + 7.50569e7i −0.315317 + 0.598213i
\(207\) 7.97030e7 8.09325e7i 0.624566 0.634201i
\(208\) 1.22072e8 + 4.72866e7i 0.940579 + 0.364348i
\(209\) 2.46700e8i 1.86921i
\(210\) 1.38554e7 1.56034e8i 0.103241 1.16266i
\(211\) 3.19442e7 0.234101 0.117051 0.993126i \(-0.462656\pi\)
0.117051 + 0.993126i \(0.462656\pi\)
\(212\) −1.48676e8 2.17033e8i −1.07168 1.56441i
\(213\) 2.68347e7 1.12358e7i 0.190269 0.0796664i
\(214\) 1.11750e8 2.12010e8i 0.779472 1.47880i
\(215\) −8.01002e7 −0.549666
\(216\) 1.42914e8 + 3.88911e7i 0.964910 + 0.262580i
\(217\) 1.79659e8 1.19355
\(218\) 1.71518e7 3.25400e7i 0.112128 0.212726i
\(219\) −1.74401e8 + 7.30224e7i −1.12200 + 0.469788i
\(220\) −1.57508e8 + 1.07899e8i −0.997292 + 0.683184i
\(221\) 1.30150e8 0.811097
\(222\) 1.12529e7 1.26726e8i 0.0690288 0.777375i
\(223\) 9.50382e6i 0.0573893i 0.999588 + 0.0286947i \(0.00913505\pi\)
−0.999588 + 0.0286947i \(0.990865\pi\)
\(224\) 1.29752e8 + 1.49096e8i 0.771338 + 0.886333i
\(225\) −1.57318e6 + 1.59745e6i −0.00920748 + 0.00934951i
\(226\) −7.48246e7 + 1.41955e8i −0.431186 + 0.818036i
\(227\) 7.02395e7i 0.398557i 0.979943 + 0.199279i \(0.0638599\pi\)
−0.979943 + 0.199279i \(0.936140\pi\)
\(228\) −2.30901e8 1.49194e8i −1.29019 0.833642i
\(229\) 1.17776e8i 0.648088i 0.946042 + 0.324044i \(0.105043\pi\)
−0.946042 + 0.324044i \(0.894957\pi\)
\(230\) 1.44339e8 + 7.60812e7i 0.782236 + 0.412316i
\(231\) −2.47078e8 + 1.03453e8i −1.31884 + 0.552204i
\(232\) 4.22987e6 + 3.64518e7i 0.0222392 + 0.191651i
\(233\) 2.28569e8i 1.18378i 0.806017 + 0.591892i \(0.201619\pi\)
−0.806017 + 0.591892i \(0.798381\pi\)
\(234\) 5.99264e7 + 1.88400e8i 0.305747 + 0.961226i
\(235\) −2.48766e8 −1.25041
\(236\) 6.06219e7 4.15283e7i 0.300218 0.205661i
\(237\) 1.40365e8 + 3.35236e8i 0.684918 + 1.63580i
\(238\) 1.73831e8 + 9.16261e7i 0.835810 + 0.440555i
\(239\) −3.68790e8 −1.74737 −0.873687 0.486488i \(-0.838278\pi\)
−0.873687 + 0.486488i \(0.838278\pi\)
\(240\) 5.73470e6 + 2.12673e8i 0.0267776 + 0.993056i
\(241\) −2.08742e8 −0.960615 −0.480307 0.877100i \(-0.659475\pi\)
−0.480307 + 0.877100i \(0.659475\pi\)
\(242\) 9.37664e7 + 4.94242e7i 0.425298 + 0.224174i
\(243\) 8.95358e7 + 2.04975e8i 0.400290 + 0.916388i
\(244\) 1.53411e8 1.05092e8i 0.676069 0.463134i
\(245\) 8.70211e7 0.378045
\(246\) 1.16015e7 1.30652e8i 0.0496870 0.559555i
\(247\) 3.66951e8i 1.54942i
\(248\) −2.42376e8 + 2.81254e7i −1.00904 + 0.117089i
\(249\) −6.78631e7 1.62079e8i −0.278571 0.665317i
\(250\) −2.19961e8 1.15941e8i −0.890341 0.469298i
\(251\) 9.64416e7i 0.384952i −0.981302 0.192476i \(-0.938348\pi\)
0.981302 0.192476i \(-0.0616517\pi\)
\(252\) −5.25953e7 + 2.93818e8i −0.207036 + 1.15658i
\(253\) 2.79002e8i 1.08314i
\(254\) 1.30642e8 2.47851e8i 0.500225 0.949015i
\(255\) 8.16905e7 + 1.95103e8i 0.308518 + 0.736841i
\(256\) −1.98388e8 1.80831e8i −0.739051 0.673649i
\(257\) 2.25242e8i 0.827722i −0.910340 0.413861i \(-0.864180\pi\)
0.910340 0.413861i \(-0.135820\pi\)
\(258\) 1.52031e8 + 1.34999e7i 0.551140 + 0.0489398i
\(259\) 2.56396e8 0.916985
\(260\) −2.34283e8 + 1.60493e8i −0.826673 + 0.566303i
\(261\) −3.88860e7 + 3.94858e7i −0.135379 + 0.137467i
\(262\) −2.01618e8 + 3.82504e8i −0.692586 + 1.31396i
\(263\) 3.53597e8 1.19857 0.599284 0.800536i \(-0.295452\pi\)
0.599284 + 0.800536i \(0.295452\pi\)
\(264\) 3.17135e8 1.78247e8i 1.06079 0.596221i
\(265\) 5.70683e8 1.88380
\(266\) 2.58334e8 4.90105e8i 0.841581 1.59663i
\(267\) 6.58568e7 + 1.57287e8i 0.211744 + 0.505713i
\(268\) −1.51528e7 2.21197e7i −0.0480864 0.0701951i
\(269\) 8.91983e7 0.279398 0.139699 0.990194i \(-0.455386\pi\)
0.139699 + 0.990194i \(0.455386\pi\)
\(270\) −2.44809e8 + 2.08085e8i −0.756928 + 0.643380i
\(271\) 1.70785e8i 0.521264i −0.965438 0.260632i \(-0.916069\pi\)
0.965438 0.260632i \(-0.0839309\pi\)
\(272\) −2.48858e8 9.63990e7i −0.749825 0.290457i
\(273\) −3.67513e8 + 1.53879e8i −1.09321 + 0.457731i
\(274\) −2.13960e8 + 4.05921e8i −0.628357 + 1.19210i
\(275\) 5.50697e6i 0.0159679i
\(276\) −2.61134e8 1.68729e8i −0.747622 0.483068i
\(277\) 3.99072e8i 1.12816i −0.825719 0.564082i \(-0.809230\pi\)
0.825719 0.564082i \(-0.190770\pi\)
\(278\) −1.37725e6 725946.i −0.00384464 0.00202651i
\(279\) −2.62550e8 2.58562e8i −0.723765 0.712770i
\(280\) −4.25899e8 + 4.94213e7i −1.15945 + 0.134543i
\(281\) 1.75976e8i 0.473131i −0.971616 0.236565i \(-0.923978\pi\)
0.971616 0.236565i \(-0.0760217\pi\)
\(282\) 4.72159e8 + 4.19265e7i 1.25377 + 0.111331i
\(283\) 1.29971e8 0.340873 0.170436 0.985369i \(-0.445482\pi\)
0.170436 + 0.985369i \(0.445482\pi\)
\(284\) −4.50010e7 6.56912e7i −0.116576 0.170174i
\(285\) 5.50081e8 2.30321e8i 1.40757 0.589355i
\(286\) 4.29577e8 + 2.26429e8i 1.08582 + 0.572337i
\(287\) 2.64339e8 0.660047
\(288\) 2.49590e7 4.04622e8i 0.0615678 0.998103i
\(289\) 1.45013e8 0.353397
\(290\) −7.04212e7 3.71189e7i −0.169555 0.0893722i
\(291\) −9.53142e6 + 3.99085e6i −0.0226742 + 0.00949379i
\(292\) 2.92465e8 + 4.26932e8i 0.687439 + 1.00350i
\(293\) −5.26105e8 −1.22190 −0.610950 0.791669i \(-0.709212\pi\)
−0.610950 + 0.791669i \(0.709212\pi\)
\(294\) −1.65166e8 1.46663e7i −0.379058 0.0336594i
\(295\) 1.59404e8i 0.361511i
\(296\) −3.45902e8 + 4.01384e7i −0.775232 + 0.0899579i
\(297\) 5.09962e8 + 2.04406e8i 1.12951 + 0.452737i
\(298\) −3.84514e8 2.02677e8i −0.841695 0.443657i
\(299\) 4.14998e8i 0.897836i
\(300\) 5.15429e6 + 3.33039e6i 0.0110216 + 0.00712148i
\(301\) 3.07593e8i 0.650120i
\(302\) 8.40551e7 1.59467e8i 0.175606 0.333156i
\(303\) −4.63590e8 + 1.94107e8i −0.957381 + 0.400859i
\(304\) −2.71791e8 + 7.01639e8i −0.554852 + 1.43237i
\(305\) 4.03389e8i 0.814095i
\(306\) −1.22167e8 3.84075e8i −0.243741 0.766285i
\(307\) 3.90214e7 0.0769695 0.0384848 0.999259i \(-0.487747\pi\)
0.0384848 + 0.999259i \(0.487747\pi\)
\(308\) 4.14343e8 + 6.04845e8i 0.808038 + 1.17955i
\(309\) 1.35450e8 + 3.23497e8i 0.261170 + 0.623758i
\(310\) 2.46812e8 4.68247e8i 0.470545 0.892706i
\(311\) 5.52970e8 1.04241 0.521207 0.853430i \(-0.325482\pi\)
0.521207 + 0.853430i \(0.325482\pi\)
\(312\) 4.71719e8 2.65131e8i 0.879310 0.494218i
\(313\) −3.46680e8 −0.639034 −0.319517 0.947581i \(-0.603521\pi\)
−0.319517 + 0.947581i \(0.603521\pi\)
\(314\) −4.13242e8 + 7.83993e8i −0.753270 + 1.42909i
\(315\) −4.61348e8 4.54339e8i −0.831652 0.819018i
\(316\) 8.20655e8 5.62181e8i 1.46304 1.00224i
\(317\) −3.95280e8 −0.696943 −0.348471 0.937319i \(-0.613299\pi\)
−0.348471 + 0.937319i \(0.613299\pi\)
\(318\) −1.08316e9 9.61815e7i −1.88885 0.167725i
\(319\) 1.36121e8i 0.234779i
\(320\) 5.66840e8 1.33348e8i 0.967019 0.227489i
\(321\) −3.82599e8 9.13769e8i −0.645619 1.54194i
\(322\) 2.92159e8 5.54278e8i 0.487668 0.925192i
\(323\) 7.48070e8i 1.23519i
\(324\) 4.99719e8 3.53686e8i 0.816241 0.577711i
\(325\) 8.19126e6i 0.0132361i
\(326\) 4.68440e8 + 2.46914e8i 0.748846 + 0.394716i
\(327\) −5.87226e7 1.40248e8i −0.0928727 0.221810i
\(328\) −3.56617e8 + 4.13819e7i −0.558013 + 0.0647518i
\(329\) 9.55287e8i 1.47893i
\(330\) −6.98020e7 + 7.86082e8i −0.106922 + 1.20412i
\(331\) −2.91427e8 −0.441704 −0.220852 0.975307i \(-0.570884\pi\)
−0.220852 + 0.975307i \(0.570884\pi\)
\(332\) −3.96768e8 + 2.71802e8i −0.595050 + 0.407632i
\(333\) −3.74692e8 3.69000e8i −0.556058 0.547610i
\(334\) −5.54164e8 2.92099e8i −0.813815 0.428961i
\(335\) 5.81631e7 0.0845260
\(336\) 8.16687e8 2.20218e7i 1.17454 0.0316713i
\(337\) −1.36132e9 −1.93757 −0.968783 0.247909i \(-0.920257\pi\)
−0.968783 + 0.247909i \(0.920257\pi\)
\(338\) 1.09511e7 + 5.77230e6i 0.0154258 + 0.00813094i
\(339\) 2.56176e8 + 6.11831e8i 0.357141 + 0.852968i
\(340\) 4.77611e8 3.27182e8i 0.659020 0.451454i
\(341\) −9.05101e8 −1.23611
\(342\) −1.08287e9 + 3.44441e8i −1.46382 + 0.465612i
\(343\) 5.43954e8i 0.727834i
\(344\) −4.81532e7 4.14971e8i −0.0637780 0.549621i
\(345\) 6.22106e8 2.60479e8i 0.815639 0.341511i
\(346\) 6.23568e8 + 3.28682e8i 0.809315 + 0.426589i
\(347\) 7.93766e8i 1.01986i −0.860217 0.509929i \(-0.829672\pi\)
0.860217 0.509929i \(-0.170328\pi\)
\(348\) 1.27404e8 + 8.23205e7i 0.162052 + 0.104708i
\(349\) 1.15068e9i 1.44899i 0.689278 + 0.724497i \(0.257928\pi\)
−0.689278 + 0.724497i \(0.742072\pi\)
\(350\) −5.76666e6 + 1.09404e7i −0.00718930 + 0.0136394i
\(351\) 7.58536e8 + 3.04041e8i 0.936270 + 0.375282i
\(352\) −6.53674e8 7.51127e8i −0.798843 0.917939i
\(353\) 4.69723e8i 0.568370i 0.958770 + 0.284185i \(0.0917229\pi\)
−0.958770 + 0.284185i \(0.908277\pi\)
\(354\) 2.68655e7 3.02549e8i 0.0321872 0.362480i
\(355\) 1.72733e8 0.204916
\(356\) 3.85038e8 2.63766e8i 0.452302 0.309845i
\(357\) 7.49216e8 3.13700e8i 0.871501 0.364901i
\(358\) 1.85491e8 3.51909e8i 0.213664 0.405359i
\(359\) 6.25489e8 0.713492 0.356746 0.934201i \(-0.383886\pi\)
0.356746 + 0.934201i \(0.383886\pi\)
\(360\) 6.93526e8 + 5.40722e8i 0.783437 + 0.610822i
\(361\) 1.21526e9 1.35955
\(362\) 1.18269e8 2.24377e8i 0.131036 0.248599i
\(363\) 4.04135e8 1.69213e8i 0.443459 0.185678i
\(364\) 6.16308e8 + 8.99669e8i 0.669797 + 0.977750i
\(365\) −1.12261e9 −1.20838
\(366\) 6.79863e7 7.65635e8i 0.0724833 0.816278i
\(367\) 3.01496e8i 0.318383i 0.987248 + 0.159192i \(0.0508888\pi\)
−0.987248 + 0.159192i \(0.949111\pi\)
\(368\) −3.07378e8 + 7.93508e8i −0.321518 + 0.830012i
\(369\) −3.86300e8 3.80431e8i −0.400251 0.394170i
\(370\) 3.52232e8 6.68247e8i 0.361512 0.685853i
\(371\) 2.19148e9i 2.22807i
\(372\) −5.47368e8 + 8.47137e8i −0.551289 + 0.853205i
\(373\) 8.91771e8i 0.889759i −0.895590 0.444879i \(-0.853247\pi\)
0.895590 0.444879i \(-0.146753\pi\)
\(374\) −8.75740e8 4.61601e8i −0.865614 0.456264i
\(375\) −9.48039e8 + 3.96948e8i −0.928361 + 0.388708i
\(376\) −1.49549e8 1.28877e9i −0.145086 1.25031i
\(377\) 2.02472e8i 0.194612i
\(378\) 7.99067e8 + 9.40092e8i 0.760960 + 0.895260i
\(379\) −1.31916e8 −0.124469 −0.0622345 0.998062i \(-0.519823\pi\)
−0.0622345 + 0.998062i \(0.519823\pi\)
\(380\) −9.22470e8 1.34659e9i −0.862402 1.25891i
\(381\) −4.47279e8 1.06825e9i −0.414325 0.989540i
\(382\) −8.13961e7 4.29038e7i −0.0747106 0.0393799i
\(383\) 1.57395e9 1.43152 0.715758 0.698348i \(-0.246081\pi\)
0.715758 + 0.698348i \(0.246081\pi\)
\(384\) −1.09834e9 + 1.57561e8i −0.989867 + 0.142000i
\(385\) −1.59042e9 −1.42037
\(386\) 1.30984e9 + 6.90417e8i 1.15921 + 0.611020i
\(387\) 4.42682e8 4.49510e8i 0.388242 0.394231i
\(388\) 1.59839e7 + 2.33329e7i 0.0138922 + 0.0202795i
\(389\) 1.00271e9 0.863674 0.431837 0.901952i \(-0.357866\pi\)
0.431837 + 0.901952i \(0.357866\pi\)
\(390\) −1.03826e8 + 1.16925e9i −0.0886299 + 0.998114i
\(391\) 8.46020e8i 0.715751i
\(392\) 5.23138e7 + 4.50825e8i 0.0438647 + 0.378013i
\(393\) 6.90277e8 + 1.64860e9i 0.573653 + 1.37007i
\(394\) −1.21931e8 6.42697e7i −0.100433 0.0529383i
\(395\) 2.15789e9i 1.76173i
\(396\) 2.64969e8 1.48022e9i 0.214418 1.19783i
\(397\) 1.01948e9i 0.817737i −0.912593 0.408869i \(-0.865923\pi\)
0.912593 0.408869i \(-0.134077\pi\)
\(398\) 3.85238e8 7.30865e8i 0.306294 0.581094i
\(399\) −8.84456e8 2.11237e9i −0.697062 1.66481i
\(400\) 6.06705e6 1.56623e7i 0.00473989 0.0122362i
\(401\) 2.14611e9i 1.66206i −0.556230 0.831028i \(-0.687753\pi\)
0.556230 0.831028i \(-0.312247\pi\)
\(402\) −1.10394e8 9.80267e6i −0.0847526 0.00752581i
\(403\) −1.34628e9 −1.02463
\(404\) 7.77427e8 + 1.13486e9i 0.586577 + 0.856267i
\(405\) 2.03288e7 + 1.32792e9i 0.0152061 + 0.993301i
\(406\) −1.42540e8 + 2.70424e8i −0.105705 + 0.200542i
\(407\) −1.29169e9 −0.949683
\(408\) −9.61651e8 + 5.40498e8i −0.700982 + 0.393989i
\(409\) 2.47509e9 1.78879 0.894396 0.447276i \(-0.147606\pi\)
0.894396 + 0.447276i \(0.147606\pi\)
\(410\) 3.63144e8 6.88948e8i 0.260217 0.493677i
\(411\) 7.32535e8 + 1.74953e9i 0.520453 + 1.24301i
\(412\) 7.91919e8 5.42495e8i 0.557880 0.382169i
\(413\) 6.12126e8 0.427578
\(414\) −1.22466e9 + 3.89541e8i −0.848232 + 0.269806i
\(415\) 1.04329e9i 0.716535i
\(416\) −9.72298e8 1.11725e9i −0.662175 0.760895i
\(417\) −5.93597e6 + 2.48542e6i −0.00400881 + 0.00167851i
\(418\) −1.30146e9 + 2.46909e9i −0.871591 + 1.65356i
\(419\) 9.09422e8i 0.603972i 0.953312 + 0.301986i \(0.0976495\pi\)
−0.953312 + 0.301986i \(0.902350\pi\)
\(420\) −9.61823e8 + 1.48857e9i −0.633465 + 0.980386i
\(421\) 1.82775e9i 1.19380i 0.802317 + 0.596899i \(0.203601\pi\)
−0.802317 + 0.596899i \(0.796399\pi\)
\(422\) −3.19713e8 1.68520e8i −0.207093 0.109159i
\(423\) 1.37483e9 1.39604e9i 0.883197 0.896821i
\(424\) 3.43073e8 + 2.95650e9i 0.218578 + 1.88364i
\(425\) 1.66988e7i 0.0105517i
\(426\) −3.27848e8 2.91121e7i −0.205466 0.0182448i
\(427\) 1.54906e9 0.962874
\(428\) −2.23690e9 + 1.53236e9i −1.37909 + 0.944732i
\(429\) 1.85149e9 7.75225e8i 1.13219 0.474053i
\(430\) 8.01681e8 + 4.22565e8i 0.486253 + 0.256303i
\(431\) −1.85756e9 −1.11756 −0.558781 0.829315i \(-0.688731\pi\)
−0.558781 + 0.829315i \(0.688731\pi\)
\(432\) −1.22518e9 1.14318e9i −0.731153 0.682214i
\(433\) −1.54099e9 −0.912206 −0.456103 0.889927i \(-0.650755\pi\)
−0.456103 + 0.889927i \(0.650755\pi\)
\(434\) −1.79811e9 9.47784e8i −1.05585 0.556538i
\(435\) −3.03517e8 + 1.27084e8i −0.176795 + 0.0740249i
\(436\) −3.43327e8 + 2.35192e8i −0.198383 + 0.135900i
\(437\) 2.38530e9 1.36728
\(438\) 2.13071e9 + 1.89202e8i 1.21162 + 0.107588i
\(439\) 1.21301e9i 0.684287i −0.939648 0.342144i \(-0.888847\pi\)
0.939648 0.342144i \(-0.111153\pi\)
\(440\) 2.14563e9 2.48979e8i 1.20080 0.139341i
\(441\) −4.80930e8 + 4.88349e8i −0.267022 + 0.271141i
\(442\) −1.30261e9 6.86603e8i −0.717523 0.378205i
\(443\) 2.37819e7i 0.0129967i 0.999979 + 0.00649835i \(0.00206850\pi\)
−0.999979 + 0.00649835i \(0.997931\pi\)
\(444\) −7.81163e8 + 1.20897e9i −0.423547 + 0.655504i
\(445\) 1.01245e9i 0.544644i
\(446\) 5.01370e7 9.51187e7i 0.0267600 0.0507685i
\(447\) −1.65726e9 + 6.93903e8i −0.877637 + 0.367470i
\(448\) −5.12068e8 2.17672e9i −0.269064 1.14375i
\(449\) 1.55906e8i 0.0812831i −0.999174 0.0406416i \(-0.987060\pi\)
0.999174 0.0406416i \(-0.0129402\pi\)
\(450\) 2.41725e7 7.68879e6i 0.0125048 0.00397754i
\(451\) −1.33171e9 −0.683583
\(452\) 1.49776e9 1.02602e9i 0.762882 0.522604i
\(453\) −2.87779e8 6.87308e8i −0.145450 0.347382i
\(454\) 3.70545e8 7.02990e8i 0.185843 0.352577i
\(455\) −2.36566e9 −1.17737
\(456\) 1.52390e9 + 2.71131e9i 0.752627 + 1.33907i
\(457\) 2.81382e9 1.37908 0.689539 0.724248i \(-0.257813\pi\)
0.689539 + 0.724248i \(0.257813\pi\)
\(458\) 6.21324e8 1.17876e9i 0.302196 0.573319i
\(459\) −1.54636e9 6.19821e8i −0.746390 0.299173i
\(460\) −1.04325e9 1.52291e9i −0.499733 0.729495i
\(461\) 1.13935e9 0.541631 0.270816 0.962631i \(-0.412707\pi\)
0.270816 + 0.962631i \(0.412707\pi\)
\(462\) 3.01863e9 + 2.68047e8i 1.42417 + 0.126463i
\(463\) 2.52611e8i 0.118282i 0.998250 + 0.0591409i \(0.0188361\pi\)
−0.998250 + 0.0591409i \(0.981164\pi\)
\(464\) 1.49966e8 3.87142e8i 0.0696913 0.179911i
\(465\) −8.45009e8 2.01815e9i −0.389741 0.930827i
\(466\) 1.20581e9 2.28763e9i 0.551985 1.04721i
\(467\) 2.64646e8i 0.120242i −0.998191 0.0601210i \(-0.980851\pi\)
0.998191 0.0601210i \(-0.0191487\pi\)
\(468\) 3.94124e8 2.20174e9i 0.177735 0.992899i
\(469\) 2.23352e8i 0.0999735i
\(470\) 2.48977e9 + 1.31236e9i 1.10616 + 0.583054i
\(471\) 1.41481e9 + 3.37903e9i 0.623916 + 1.49011i
\(472\) −8.25813e8 + 9.58273e7i −0.361480 + 0.0419462i
\(473\) 1.54962e9i 0.673303i
\(474\) 3.63686e8 4.09569e9i 0.156857 1.76646i
\(475\) −4.70812e7 −0.0201567
\(476\) −1.25641e9 1.83408e9i −0.533959 0.779458i
\(477\) −3.15393e9 + 3.20258e9i −1.33057 + 1.35110i
\(478\) 3.69102e9 + 1.94553e9i 1.54578 + 0.814781i
\(479\) −7.70644e8 −0.320390 −0.160195 0.987085i \(-0.551212\pi\)
−0.160195 + 0.987085i \(0.551212\pi\)
\(480\) 1.06455e9 2.15879e9i 0.439363 0.890976i
\(481\) −1.92131e9 −0.787209
\(482\) 2.08918e9 + 1.10121e9i 0.849791 + 0.447924i
\(483\) −1.00026e9 2.38895e9i −0.403924 0.964700i
\(484\) −6.77724e8 9.89321e8i −0.271703 0.396624i
\(485\) −6.13531e7 −0.0244197
\(486\) 1.85221e8 2.52383e9i 0.0731921 0.997318i
\(487\) 1.64602e9i 0.645779i −0.946437 0.322889i \(-0.895346\pi\)
0.946437 0.322889i \(-0.104654\pi\)
\(488\) −2.08982e9 + 2.42502e8i −0.814027 + 0.0944597i
\(489\) 2.01899e9 8.45359e8i 0.780823 0.326934i
\(490\) −8.70948e8 4.59076e8i −0.334431 0.176278i
\(491\) 4.81674e7i 0.0183640i 0.999958 + 0.00918202i \(0.00292277\pi\)
−0.999958 + 0.00918202i \(0.997077\pi\)
\(492\) −8.05362e8 + 1.24642e9i −0.304869 + 0.471832i
\(493\) 4.12761e8i 0.155144i
\(494\) −1.93583e9 + 3.67262e9i −0.722476 + 1.37067i
\(495\) 2.32421e9 + 2.28891e9i 0.861307 + 0.848223i
\(496\) 2.57419e9 + 9.97155e8i 0.947230 + 0.366924i
\(497\) 6.63313e8i 0.242366i
\(498\) −1.75834e8 + 1.98017e9i −0.0637970 + 0.718456i
\(499\) 5.32745e8 0.191941 0.0959705 0.995384i \(-0.469405\pi\)
0.0959705 + 0.995384i \(0.469405\pi\)
\(500\) 1.58983e9 + 2.32079e9i 0.568796 + 0.830312i
\(501\) −2.38846e9 + 1.00006e9i −0.848566 + 0.355298i
\(502\) −5.08774e8 + 9.65234e8i −0.179499 + 0.340541i
\(503\) −9.39101e8 −0.329021 −0.164511 0.986375i \(-0.552605\pi\)
−0.164511 + 0.986375i \(0.552605\pi\)
\(504\) 2.07642e9 2.66321e9i 0.722453 0.926613i
\(505\) −2.98410e9 −1.03108
\(506\) −1.47186e9 + 2.79239e9i −0.505057 + 0.958183i
\(507\) 4.71994e7 1.97626e7i 0.0160845 0.00673467i
\(508\) −2.61506e9 + 1.79142e9i −0.885031 + 0.606281i
\(509\) 7.06297e8 0.237397 0.118699 0.992930i \(-0.462128\pi\)
0.118699 + 0.992930i \(0.462128\pi\)
\(510\) 2.11661e8 2.38364e9i 0.0706553 0.795692i
\(511\) 4.31092e9i 1.42921i
\(512\) 1.03159e9 + 2.85643e9i 0.339674 + 0.940543i
\(513\) −1.74755e9 + 4.35986e9i −0.571502 + 1.42581i
\(514\) −1.18826e9 + 2.25433e9i −0.385957 + 0.732230i
\(515\) 2.08233e9i 0.671776i
\(516\) −1.45038e9 9.37144e8i −0.464736 0.300284i
\(517\) 4.81262e9i 1.53167i
\(518\) −2.56613e9 1.35261e9i −0.811195 0.427580i
\(519\) 2.68759e9 1.12531e9i 0.843874 0.353334i
\(520\) 3.19149e9 3.70340e8i 0.995362 0.115502i
\(521\) 5.07307e9i 1.57159i 0.618488 + 0.785794i \(0.287745\pi\)
−0.618488 + 0.785794i \(0.712255\pi\)
\(522\) 5.97495e8 1.90052e8i 0.183860 0.0584824i
\(523\) 6.29698e9 1.92476 0.962379 0.271711i \(-0.0875893\pi\)
0.962379 + 0.271711i \(0.0875893\pi\)
\(524\) 4.03577e9 2.76466e9i 1.22537 0.839426i
\(525\) 1.97433e7 + 4.71533e7i 0.00595473 + 0.0142218i
\(526\) −3.53896e9 1.86538e9i −1.06029 0.558879i
\(527\) 2.74454e9 0.816832
\(528\) −4.11437e9 + 1.10943e8i −1.21642 + 0.0328006i
\(529\) −7.07205e8 −0.207707
\(530\) −5.71166e9 3.01061e9i −1.66647 0.878393i
\(531\) −8.94548e8 8.80959e8i −0.259282 0.255343i
\(532\) −5.17106e9 + 3.54238e9i −1.48898 + 1.02001i
\(533\) −1.98083e9 −0.566634
\(534\) 1.70636e8 1.92163e9i 0.0484926 0.546104i
\(535\) 5.88187e9i 1.66065i
\(536\) 3.49654e7 + 3.01322e8i 0.00980758 + 0.0845190i
\(537\) −6.35063e8 1.51673e9i −0.176973 0.422668i
\(538\) −8.92739e8 4.70562e8i −0.247165 0.130280i
\(539\) 1.68351e9i 0.463078i
\(540\) 3.54791e9 7.91131e8i 0.969604 0.216207i
\(541\) 5.85101e8i 0.158870i −0.996840 0.0794348i \(-0.974688\pi\)
0.996840 0.0794348i \(-0.0253115\pi\)
\(542\) −9.00970e8 + 1.70930e9i −0.243060 + 0.461127i
\(543\) −4.04917e8 9.67071e8i −0.108534 0.259214i
\(544\) 1.98214e9 + 2.27765e9i 0.527883 + 0.606583i
\(545\) 9.02770e8i 0.238885i
\(546\) 4.49002e9 + 3.98702e8i 1.18052 + 0.104827i
\(547\) −3.55096e9 −0.927662 −0.463831 0.885924i \(-0.653526\pi\)
−0.463831 + 0.885924i \(0.653526\pi\)
\(548\) 4.28283e9 2.93391e9i 1.11173 0.761578i
\(549\) −2.26376e9 2.22937e9i −0.583885 0.575014i
\(550\) 2.90518e7 5.51163e7i 0.00744566 0.0141257i
\(551\) −1.16375e9 −0.296368
\(552\) 1.72343e9 + 3.06632e9i 0.436122 + 0.775945i
\(553\) 8.28652e9 2.08370
\(554\) −2.10529e9 + 3.99410e9i −0.526050 + 0.998010i
\(555\) −1.20593e9 2.88016e9i −0.299432 0.715140i
\(556\) 9.95446e6 + 1.45312e7i 0.00245616 + 0.00358542i
\(557\) 3.19209e9 0.782677 0.391338 0.920247i \(-0.372012\pi\)
0.391338 + 0.920247i \(0.372012\pi\)
\(558\) 1.26370e9 + 3.97288e9i 0.307909 + 0.968023i
\(559\) 2.30496e9i 0.558112i
\(560\) 4.52332e9 + 1.75218e9i 1.08843 + 0.421619i
\(561\) −3.77446e9 + 1.58038e9i −0.902578 + 0.377913i
\(562\) −9.28353e8 + 1.76125e9i −0.220616 + 0.418547i
\(563\) 8.00588e8i 0.189073i −0.995521 0.0945365i \(-0.969863\pi\)
0.995521 0.0945365i \(-0.0301369\pi\)
\(564\) −4.50441e9 2.91048e9i −1.05721 0.683105i
\(565\) 3.93832e9i 0.918631i
\(566\) −1.30081e9 6.85654e8i −0.301547 0.158945i
\(567\) 5.09936e9 7.80645e7i 1.17483 0.0179851i
\(568\) 1.03841e8 + 8.94869e8i 0.0237765 + 0.204899i
\(569\) 1.33361e9i 0.303485i −0.988420 0.151743i \(-0.951512\pi\)
0.988420 0.151743i \(-0.0484884\pi\)
\(570\) −6.72052e9 5.96764e8i −1.51999 0.134971i
\(571\) −2.47645e9 −0.556677 −0.278339 0.960483i \(-0.589784\pi\)
−0.278339 + 0.960483i \(0.589784\pi\)
\(572\) −3.10489e9 4.53243e9i −0.693681 1.01262i
\(573\) −3.50819e8 + 1.46890e8i −0.0779009 + 0.0326174i
\(574\) −2.64563e9 1.39451e9i −0.583899 0.307772i
\(575\) −5.32458e7 −0.0116801
\(576\) −2.38437e9 + 3.91797e9i −0.519869 + 0.854246i
\(577\) 4.31495e9 0.935105 0.467552 0.883965i \(-0.345136\pi\)
0.467552 + 0.883965i \(0.345136\pi\)
\(578\) −1.45135e9 7.65007e8i −0.312627 0.164785i
\(579\) 5.64545e9 2.36377e9i 1.20871 0.506094i
\(580\) 5.08989e8 + 7.43008e8i 0.108321 + 0.158123i
\(581\) −4.00634e9 −0.847484
\(582\) 1.16449e8 + 1.03403e7i 0.0244852 + 0.00217422i
\(583\) 1.10404e10i 2.30752i
\(584\) −6.74869e8 5.81583e9i −0.140208 1.20828i
\(585\) 3.45712e9 + 3.40460e9i 0.713952 + 0.703106i
\(586\) 5.26551e9 + 2.77544e9i 1.08093 + 0.569759i
\(587\) 2.02446e9i 0.413120i 0.978434 + 0.206560i \(0.0662268\pi\)
−0.978434 + 0.206560i \(0.933773\pi\)
\(588\) 1.57569e9 + 1.01812e9i 0.319632 + 0.206527i
\(589\) 7.73806e9i 1.56037i
\(590\) 8.40927e8 1.59539e9i 0.168568 0.319804i
\(591\) −5.25526e8 + 2.20040e8i −0.104722 + 0.0438475i
\(592\) 3.67370e9 + 1.42306e9i 0.727742 + 0.281902i
\(593\) 8.39544e9i 1.65330i −0.562716 0.826650i \(-0.690244\pi\)
0.562716 0.826650i \(-0.309756\pi\)
\(594\) −4.02560e9 4.73607e9i −0.788095 0.927184i
\(595\) 4.82265e9 0.938591
\(596\) 2.77918e9 + 4.05697e9i 0.537719 + 0.784946i
\(597\) −1.31894e9 3.15005e9i −0.253696 0.605908i
\(598\) −2.18930e9 + 4.15350e9i −0.418651 + 0.794255i
\(599\) 1.37052e9 0.260550 0.130275 0.991478i \(-0.458414\pi\)
0.130275 + 0.991478i \(0.458414\pi\)
\(600\) −3.40173e7 6.05233e7i −0.00642939 0.0114391i
\(601\) −7.26524e9 −1.36518 −0.682589 0.730803i \(-0.739146\pi\)
−0.682589 + 0.730803i \(0.739146\pi\)
\(602\) 1.62269e9 3.07854e9i 0.303144 0.575117i
\(603\) −3.21444e8 + 3.26402e8i −0.0597027 + 0.0606237i
\(604\) −1.68253e9 + 1.15260e9i −0.310694 + 0.212837i
\(605\) 2.60139e9 0.477598
\(606\) 5.66383e9 + 5.02933e8i 1.03385 + 0.0918028i
\(607\) 9.56273e9i 1.73549i −0.497012 0.867744i \(-0.665570\pi\)
0.497012 0.867744i \(-0.334430\pi\)
\(608\) 6.42168e9 5.58851e9i 1.15874 1.00840i
\(609\) 4.88015e8 + 1.16554e9i 0.0875533 + 0.209105i
\(610\) 2.12806e9 4.03731e9i 0.379603 0.720175i
\(611\) 7.15847e9i 1.26963i
\(612\) −8.03467e8 + 4.48849e9i −0.141690 + 0.791535i
\(613\) 3.60560e9i 0.632216i 0.948723 + 0.316108i \(0.102376\pi\)
−0.948723 + 0.316108i \(0.897624\pi\)
\(614\) −3.90545e8 2.05856e8i −0.0680898 0.0358900i
\(615\) −1.24329e9 2.96938e9i −0.215531 0.514758i
\(616\) −9.56103e8 8.23942e9i −0.164806 1.42025i
\(617\) 7.59055e9i 1.30099i 0.759509 + 0.650496i \(0.225439\pi\)
−0.759509 + 0.650496i \(0.774561\pi\)
\(618\) 3.50951e8 3.95227e9i 0.0598118 0.673577i
\(619\) −4.61817e9 −0.782623 −0.391311 0.920258i \(-0.627978\pi\)
−0.391311 + 0.920258i \(0.627978\pi\)
\(620\) −4.94043e9 + 3.38439e9i −0.832518 + 0.570307i
\(621\) −1.97636e9 + 4.93072e9i −0.331166 + 0.826209i
\(622\) −5.53438e9 2.91717e9i −0.922153 0.486066i
\(623\) 3.88790e9 0.644180
\(624\) −6.11987e9 + 1.65021e8i −1.00831 + 0.0271890i
\(625\) −6.02237e9 −0.986706
\(626\) 3.46974e9 + 1.82890e9i 0.565310 + 0.297974i
\(627\) 4.45579e9 + 1.06418e10i 0.721918 + 1.72417i
\(628\) 8.27184e9 5.66653e9i 1.33273 0.912974i
\(629\) 3.91681e9 0.627560
\(630\) 2.22054e9 + 6.98106e9i 0.353807 + 1.11232i
\(631\) 4.70050e9i 0.744803i 0.928072 + 0.372401i \(0.121465\pi\)
−0.928072 + 0.372401i \(0.878535\pi\)
\(632\) −1.11793e10 + 1.29724e9i −1.76159 + 0.204414i
\(633\) −1.37797e9 + 5.76961e8i −0.215937 + 0.0904136i
\(634\) 3.95615e9 + 2.08528e9i 0.616538 + 0.324977i
\(635\) 6.87623e9i 1.06572i
\(636\) 1.03334e10 + 6.67678e9i 1.59273 + 1.02912i
\(637\) 2.50411e9i 0.383853i
\(638\) 7.18102e8 1.36237e9i 0.109475 0.207693i
\(639\) −9.54626e8 + 9.69352e8i −0.144737 + 0.146970i
\(640\) −6.37667e9 1.65573e9i −0.961532 0.249666i
\(641\) 1.82869e9i 0.274244i 0.990554 + 0.137122i \(0.0437853\pi\)
−0.990554 + 0.137122i \(0.956215\pi\)
\(642\) −9.91317e8 + 1.11638e10i −0.147856 + 1.66510i
\(643\) −2.97581e9 −0.441435 −0.220718 0.975338i \(-0.570840\pi\)
−0.220718 + 0.975338i \(0.570840\pi\)
\(644\) −5.84814e9 + 4.00620e9i −0.862814 + 0.591061i
\(645\) 3.45527e9 1.44673e9i 0.507017 0.212290i
\(646\) 3.94641e9 7.48704e9i 0.575955 1.09269i
\(647\) −7.48887e9 −1.08705 −0.543527 0.839392i \(-0.682911\pi\)
−0.543527 + 0.839392i \(0.682911\pi\)
\(648\) −6.86728e9 + 9.03614e8i −0.991454 + 0.130458i
\(649\) −3.08382e9 −0.442825
\(650\) 4.32127e7 8.19821e7i 0.00617183 0.0117091i
\(651\) −7.74991e9 + 3.24492e9i −1.10094 + 0.460968i
\(652\) −3.38578e9 4.94247e9i −0.478402 0.698357i
\(653\) −8.06258e9 −1.13313 −0.566563 0.824019i \(-0.691727\pi\)
−0.566563 + 0.824019i \(0.691727\pi\)
\(654\) −1.52151e8 + 1.71346e9i −0.0212692 + 0.239526i
\(655\) 1.06119e10i 1.47554i
\(656\) 3.78750e9 + 1.46715e9i 0.523829 + 0.202914i
\(657\) 6.20419e9 6.29990e9i 0.853506 0.866672i
\(658\) 5.03957e9 9.56097e9i 0.689610 1.30831i
\(659\) 1.09269e10i 1.48729i 0.668573 + 0.743647i \(0.266906\pi\)
−0.668573 + 0.743647i \(0.733094\pi\)
\(660\) 4.84555e9 7.49924e9i 0.656054 1.01534i
\(661\) 6.97813e9i 0.939797i 0.882721 + 0.469898i \(0.155709\pi\)
−0.882721 + 0.469898i \(0.844291\pi\)
\(662\) 2.91674e9 + 1.53741e9i 0.390746 + 0.205962i
\(663\) −5.61427e9 + 2.35072e9i −0.748162 + 0.313259i
\(664\) 5.40492e9 6.27187e8i 0.716475 0.0831397i
\(665\) 1.35972e10i 1.79297i
\(666\) 1.80345e9 + 5.66980e9i 0.236562 + 0.743717i
\(667\) −1.31613e9 −0.171735
\(668\) 4.00538e9 + 5.84693e9i 0.519907 + 0.758945i
\(669\) −1.71654e8 4.09964e8i −0.0221647 0.0529364i
\(670\) −5.82124e8 3.06837e8i −0.0747745 0.0394135i
\(671\) −7.80396e9 −0.997209
\(672\) −8.28997e9 4.08799e9i −1.05381 0.519658i
\(673\) −6.64233e8 −0.0839978 −0.0419989 0.999118i \(-0.513373\pi\)
−0.0419989 + 0.999118i \(0.513373\pi\)
\(674\) 1.36248e10 + 7.18160e9i 1.71403 + 0.903466i
\(675\) 3.90096e7 9.73230e7i 0.00488212 0.0121801i
\(676\) −7.91521e7 1.15544e8i −0.00985482 0.0143858i
\(677\) 7.98141e9 0.988597 0.494298 0.869292i \(-0.335425\pi\)
0.494298 + 0.869292i \(0.335425\pi\)
\(678\) 6.63755e8 7.47495e9i 0.0817907 0.921094i
\(679\) 2.35602e8i 0.0288825i
\(680\) −6.50620e9 + 7.54979e8i −0.793498 + 0.0920775i
\(681\) −1.26863e9 3.02990e9i −0.153929 0.367633i
\(682\) 9.05868e9 + 4.77482e9i 1.09350 + 0.576384i
\(683\) 4.75611e9i 0.571188i −0.958351 0.285594i \(-0.907809\pi\)
0.958351 0.285594i \(-0.0921909\pi\)
\(684\) 1.26550e10 + 2.26532e9i 1.51205 + 0.270666i
\(685\) 1.12616e10i 1.33870i
\(686\) 2.86960e9 5.44415e9i 0.339381 0.643866i
\(687\) −2.12722e9 5.08049e9i −0.250302 0.597801i
\(688\) −1.70722e9 + 4.40726e9i −0.199862 + 0.515951i
\(689\) 1.64219e10i 1.91274i
\(690\) −7.60048e9 6.74902e8i −0.880784 0.0782112i
\(691\) −7.05427e9 −0.813353 −0.406676 0.913572i \(-0.633312\pi\)
−0.406676 + 0.913572i \(0.633312\pi\)
\(692\) −4.50702e9 6.57921e9i −0.517032 0.754749i
\(693\) 8.78963e9 8.92522e9i 1.00324 1.01871i
\(694\) −4.18748e9 + 7.94439e9i −0.475548 + 0.902199i
\(695\) −3.82095e7 −0.00431742
\(696\) −8.40839e8 1.49602e9i −0.0945324 0.168191i
\(697\) 4.03815e9 0.451718
\(698\) 6.07038e9 1.15166e10i 0.675650 1.28183i
\(699\) −4.12832e9 9.85974e9i −0.457196 1.09193i
\(700\) 1.15431e8 7.90747e7i 0.0127198 0.00871354i
\(701\) 3.79183e9 0.415754 0.207877 0.978155i \(-0.433345\pi\)
0.207877 + 0.978155i \(0.433345\pi\)
\(702\) −5.98783e9 7.04461e9i −0.653265 0.768558i
\(703\) 1.10432e10i 1.19881i
\(704\) 2.57974e9 + 1.09661e10i 0.278658 + 1.18453i
\(705\) 1.07310e10 4.49310e9i 1.15339 0.482930i
\(706\) 2.47801e9 4.70122e9i 0.265024 0.502798i
\(707\) 1.14592e10i 1.21952i
\(708\) −1.86496e9 + 2.88632e9i −0.197494 + 0.305653i
\(709\) 7.97581e9i 0.840452i 0.907419 + 0.420226i \(0.138049\pi\)
−0.907419 + 0.420226i \(0.861951\pi\)
\(710\) −1.72880e9 9.11246e8i −0.181276 0.0955502i
\(711\) −1.21098e10 1.19258e10i −1.26355 1.24435i
\(712\) −5.24513e9 + 6.08645e8i −0.544599 + 0.0631952i
\(713\) 8.75126e9i 0.904184i
\(714\) −9.15341e9 8.12799e8i −0.941108 0.0835679i
\(715\) 1.19179e10 1.21935
\(716\) −3.71296e9 + 2.54352e9i −0.378028 + 0.258964i
\(717\) 1.59084e10 6.66091e9i 1.61179 0.674864i
\(718\) −6.26019e9 3.29974e9i −0.631178 0.332693i
\(719\) 6.39397e9 0.641533 0.320767 0.947158i \(-0.396059\pi\)
0.320767 + 0.947158i \(0.396059\pi\)
\(720\) −4.08859e9 9.07047e9i −0.408234 0.905661i
\(721\) 7.99635e9 0.794545
\(722\) −1.21629e10 6.41108e9i −1.20270 0.633944i
\(723\) 9.00443e9 3.77019e9i 0.886079 0.371005i
\(724\) −2.36738e9 + 1.62175e9i −0.231838 + 0.158818i
\(725\) 2.59779e7 0.00253175
\(726\) −4.93746e9 4.38433e8i −0.478878 0.0425231i
\(727\) 1.26715e10i 1.22309i −0.791210 0.611545i \(-0.790549\pi\)
0.791210 0.611545i \(-0.209451\pi\)
\(728\) −1.42214e9 1.22556e10i −0.136610 1.17727i
\(729\) −7.56446e9 7.22482e9i −0.723155 0.690686i
\(730\) 1.12356e10 + 5.92226e9i 1.06897 + 0.563453i
\(731\) 4.69891e9i 0.444925i
\(732\) −4.71951e9 + 7.30418e9i −0.444742 + 0.688308i
\(733\) 1.13503e10i 1.06449i −0.846590 0.532246i \(-0.821348\pi\)
0.846590 0.532246i \(-0.178652\pi\)
\(734\) 1.59053e9 3.01752e9i 0.148459 0.281652i
\(735\) −3.75381e9 + 1.57174e9i −0.348712 + 0.146007i
\(736\) 7.26250e9 6.32025e9i 0.671451 0.584335i
\(737\) 1.12522e9i 0.103538i
\(738\) 1.85932e9 + 5.84544e9i 0.170278 + 0.535328i
\(739\) 4.31419e8 0.0393228 0.0196614 0.999807i \(-0.493741\pi\)
0.0196614 + 0.999807i \(0.493741\pi\)
\(740\) −7.05061e9 + 4.82994e9i −0.639611 + 0.438158i
\(741\) 6.62770e9 + 1.58291e10i 0.598410 + 1.42920i
\(742\) −1.15610e10 + 2.19333e10i −1.03892 + 1.97102i
\(743\) 2.01007e10 1.79784 0.898920 0.438114i \(-0.144353\pi\)
0.898920 + 0.438114i \(0.144353\pi\)
\(744\) 9.94735e9 5.59093e9i 0.885528 0.497713i
\(745\) −1.06677e10 −0.945200
\(746\) −4.70450e9 + 8.92527e9i −0.414885 + 0.787110i
\(747\) 5.85479e9 + 5.76585e9i 0.513912 + 0.506105i
\(748\) 6.32966e9 + 9.23985e9i 0.553000 + 0.807253i
\(749\) −2.25870e10 −1.96414
\(750\) 1.15825e10 + 1.02850e9i 1.00251 + 0.0890201i
\(751\) 1.14279e10i 0.984526i 0.870447 + 0.492263i \(0.163830\pi\)
−0.870447 + 0.492263i \(0.836170\pi\)
\(752\) −5.30209e9 + 1.36876e10i −0.454658 + 1.17372i
\(753\) 1.74188e9 + 4.16018e9i 0.148675 + 0.355083i
\(754\) 1.06813e9 2.02643e9i 0.0907454 0.172160i
\(755\) 4.42416e9i 0.374125i
\(756\) −3.03802e9 1.36243e10i −0.255720 1.14680i
\(757\) 2.20045e10i 1.84364i −0.387614 0.921822i \(-0.626701\pi\)
0.387614 0.921822i \(-0.373299\pi\)
\(758\) 1.32028e9 + 6.95919e8i 0.110109 + 0.0580385i
\(759\) 5.03921e9 + 1.20352e10i 0.418327 + 0.999100i
\(760\) 2.12862e9 + 1.83438e10i 0.175893 + 1.51580i
\(761\) 8.44405e9i 0.694551i 0.937763 + 0.347276i \(0.112893\pi\)
−0.937763 + 0.347276i \(0.887107\pi\)
\(762\) −1.15890e9 + 1.30511e10i −0.0948866 + 1.06857i
\(763\) −3.46672e9 −0.282542
\(764\) 5.88314e8 + 8.58804e8i 0.0477290 + 0.0696734i
\(765\) −7.04773e9 6.94066e9i −0.569160 0.560513i
\(766\) −1.57529e10 8.30332e9i −1.26637 0.667500i
\(767\) −4.58698e9 −0.367065
\(768\) 1.18239e10 + 4.21729e9i 0.941881 + 0.335946i
\(769\) 1.61336e10 1.27935 0.639676 0.768645i \(-0.279069\pi\)
0.639676 + 0.768645i \(0.279069\pi\)
\(770\) 1.59177e10 + 8.39021e9i 1.25650 + 0.662301i
\(771\) 4.06823e9 + 9.71623e9i 0.319680 + 0.763497i
\(772\) −9.46726e9 1.38200e10i −0.740566 1.08106i
\(773\) −8.78345e9 −0.683970 −0.341985 0.939705i \(-0.611099\pi\)
−0.341985 + 0.939705i \(0.611099\pi\)
\(774\) −6.80194e9 + 2.16356e9i −0.527278 + 0.167717i
\(775\) 1.72733e8i 0.0133297i
\(776\) −3.68832e7 3.17849e8i −0.00283343 0.0244177i
\(777\) −1.10601e10 + 4.63091e9i −0.845834 + 0.354154i
\(778\) −1.00356e10 5.28973e9i −0.764034 0.402721i
\(779\) 1.13853e10i 0.862906i
\(780\) 7.20745e9 1.11546e10i 0.543814 0.841637i
\(781\) 3.34169e9i 0.251008i
\(782\) 4.46314e9 8.46737e9i 0.333747 0.633176i
\(783\) 9.64240e8 2.40563e9i 0.0717826 0.179087i
\(784\) 1.85473e9 4.78805e9i 0.137459 0.354856i
\(785\) 2.17506e10i 1.60482i
\(786\) 1.78851e9 2.01415e10i 0.131375 1.47949i
\(787\) 8.83738e8 0.0646267 0.0323133 0.999478i \(-0.489713\pi\)
0.0323133 + 0.999478i \(0.489713\pi\)
\(788\) 8.81292e8 + 1.28648e9i 0.0641620 + 0.0936618i
\(789\) −1.52530e10 + 6.38650e9i −1.10557 + 0.462907i
\(790\) 1.13839e10 2.15972e10i 0.821476 1.55849i
\(791\) 1.51235e10 1.08651
\(792\) −1.04608e10 + 1.34169e10i −0.748214 + 0.959655i
\(793\) −1.16079e10 −0.826603
\(794\) −5.37825e9 + 1.02035e10i −0.381302 + 0.723397i
\(795\) −2.46174e10 + 1.03074e10i −1.73763 + 0.727553i
\(796\) −7.71129e9 + 5.28254e9i −0.541915 + 0.371233i
\(797\) 1.20034e9 0.0839850 0.0419925 0.999118i \(-0.486629\pi\)
0.0419925 + 0.999118i \(0.486629\pi\)
\(798\) −2.29163e9 + 2.58075e10i −0.159638 + 1.79777i
\(799\) 1.45933e10i 1.01214i
\(800\) −1.43348e8 + 1.24750e8i −0.00989866 + 0.00861438i
\(801\) −5.68170e9 5.59539e9i −0.390629 0.384695i
\(802\) −1.13217e10 + 2.14792e10i −0.774998 + 1.47031i
\(803\) 2.17179e10i 1.48018i
\(804\) 1.05316e9 + 6.80487e8i 0.0714657 + 0.0461768i
\(805\) 1.53775e10i 1.03896i
\(806\) 1.34742e10 + 7.10224e9i 0.906423 + 0.477774i
\(807\) −3.84773e9 + 1.61106e9i −0.257719 + 0.107908i
\(808\) −1.79393e9 1.54595e10i −0.119637 1.03100i
\(809\) 2.60136e9i 0.172735i 0.996263 + 0.0863676i \(0.0275260\pi\)
−0.996263 + 0.0863676i \(0.972474\pi\)
\(810\) 6.80195e9 1.33977e10i 0.449713 0.885797i
\(811\) 8.84876e9 0.582518 0.291259 0.956644i \(-0.405926\pi\)
0.291259 + 0.956644i \(0.405926\pi\)
\(812\) 2.85322e9 1.95457e9i 0.187021 0.128117i
\(813\) 3.08464e9 + 7.36712e9i 0.201321 + 0.480818i
\(814\) 1.29279e10 + 6.81427e9i 0.840121 + 0.442827i
\(815\) 1.29961e10 0.840933
\(816\) 1.24760e10 3.36414e8i 0.803824 0.0216750i
\(817\) 1.32483e10 0.849928
\(818\) −2.47719e10 1.30572e10i −1.58242 0.834094i
\(819\) 1.30740e10 1.32757e10i 0.831602 0.844430i
\(820\) −7.26903e9 + 4.97957e9i −0.460392 + 0.315387i
\(821\) −1.11459e10 −0.702936 −0.351468 0.936200i \(-0.614317\pi\)
−0.351468 + 0.936200i \(0.614317\pi\)
\(822\) 1.89800e9 2.13746e10i 0.119192 1.34229i
\(823\) 9.79662e9i 0.612600i −0.951935 0.306300i \(-0.900909\pi\)
0.951935 0.306300i \(-0.0990911\pi\)
\(824\) −1.07878e10 + 1.25182e9i −0.671720 + 0.0779464i
\(825\) −9.94643e7 2.37553e8i −0.00616706 0.0147289i
\(826\) −6.12644e9 3.22924e9i −0.378249 0.199375i
\(827\) 6.77886e9i 0.416761i −0.978048 0.208381i \(-0.933181\pi\)
0.978048 0.208381i \(-0.0668193\pi\)
\(828\) 1.43120e10 + 2.56194e9i 0.876181 + 0.156842i
\(829\) 1.21324e10i 0.739614i −0.929109 0.369807i \(-0.879424\pi\)
0.929109 0.369807i \(-0.120576\pi\)
\(830\) −5.50384e9 + 1.04418e10i −0.334112 + 0.633870i
\(831\) 7.20786e9 + 1.72147e10i 0.435715 + 1.04063i
\(832\) 3.83720e9 + 1.63113e10i 0.230984 + 0.981878i
\(833\) 5.10491e9i 0.306006i
\(834\) 7.25218e7 + 6.43974e6i 0.00432900 + 0.000384403i
\(835\) −1.53744e10 −0.913891
\(836\) 2.60512e10 1.78461e10i 1.54207 1.05638i
\(837\) 1.59956e10 + 6.41145e9i 0.942890 + 0.377935i
\(838\) 4.79762e9 9.10193e9i 0.281625 0.534293i
\(839\) 8.22569e9 0.480846 0.240423 0.970668i \(-0.422714\pi\)
0.240423 + 0.970668i \(0.422714\pi\)
\(840\) 1.74793e10 9.82426e9i 1.01753 0.571903i
\(841\) −1.66078e10 −0.962775
\(842\) 9.64224e9 1.82930e10i 0.556654 1.05607i
\(843\) 3.17840e9 + 7.59103e9i 0.182731 + 0.436420i
\(844\) 2.31081e9 + 3.37326e9i 0.132302 + 0.193131i
\(845\) 3.03820e8 0.0173228
\(846\) −2.11247e10 + 6.71935e9i −1.19948 + 0.381532i
\(847\) 9.98961e9i 0.564881i
\(848\) 1.21633e10 3.14000e10i 0.684960 1.76825i
\(849\) −5.60651e9 + 2.34747e9i −0.314424 + 0.131651i
\(850\) −8.80938e7 + 1.67130e8i −0.00492016 + 0.00933441i
\(851\) 1.24891e10i 0.694671i
\(852\) 3.12768e9 + 2.02092e9i 0.173254 + 0.111946i
\(853\) 2.56199e10i 1.41337i 0.707529 + 0.706684i \(0.249810\pi\)
−0.707529 + 0.706684i \(0.750190\pi\)
\(854\) −1.55037e10 8.17197e9i −0.851789 0.448977i
\(855\) −1.95688e10 + 1.98706e10i −1.07073 + 1.08725i
\(856\) 3.04719e10 3.53596e9i 1.66051 0.192685i
\(857\) 1.50932e10i 0.819119i −0.912283 0.409560i \(-0.865682\pi\)
0.912283 0.409560i \(-0.134318\pi\)
\(858\) −2.26202e10 2.00861e9i −1.22262 0.108565i
\(859\) 2.80901e10 1.51209 0.756045 0.654519i \(-0.227129\pi\)
0.756045 + 0.654519i \(0.227129\pi\)
\(860\) −5.79438e9 8.45847e9i −0.310644 0.453469i
\(861\) −1.14027e10 + 4.77437e9i −0.608832 + 0.254921i
\(862\) 1.85913e10 + 9.79947e9i 0.988632 + 0.521107i
\(863\) −2.00363e10 −1.06116 −0.530578 0.847636i \(-0.678025\pi\)
−0.530578 + 0.847636i \(0.678025\pi\)
\(864\) 6.23144e9 + 1.79049e10i 0.328693 + 0.944437i
\(865\) 1.72999e10 0.908837
\(866\) 1.54230e10 + 8.12944e9i 0.806967 + 0.425352i
\(867\) −6.25537e9 + 2.61915e9i −0.325976 + 0.136488i
\(868\) 1.29964e10 + 1.89717e10i 0.674533 + 0.984664i
\(869\) −4.17465e10 −2.15800
\(870\) 3.70817e9 + 3.29275e8i 0.190916 + 0.0169528i
\(871\) 1.67369e9i 0.0858248i
\(872\) 4.67693e9 5.42711e8i 0.238865 0.0277179i
\(873\) 3.39074e8 3.44304e8i 0.0172482 0.0175143i
\(874\) −2.38732e10 1.25835e10i −1.20954 0.637548i
\(875\) 2.34341e10i 1.18255i
\(876\) −2.03271e10 1.31341e10i −1.02167 0.660140i
\(877\) 3.48884e10i 1.74655i 0.487224 + 0.873277i \(0.338009\pi\)
−0.487224 + 0.873277i \(0.661991\pi\)
\(878\) −6.39918e9 + 1.21404e10i −0.319075 + 0.605343i
\(879\) 2.26945e10 9.50227e9i 1.12709 0.471918i
\(880\) −2.27879e10 8.82727e9i −1.12724 0.436654i
\(881\) 2.29713e10i 1.13180i −0.824474 0.565900i \(-0.808529\pi\)
0.824474 0.565900i \(-0.191471\pi\)
\(882\) 7.38964e9 2.35050e9i 0.362646 0.115351i
\(883\) −2.74703e10 −1.34277 −0.671383 0.741110i \(-0.734300\pi\)
−0.671383 + 0.741110i \(0.734300\pi\)
\(884\) 9.41497e9 + 1.37437e10i 0.458391 + 0.669146i
\(885\) −2.87907e9 6.87615e9i −0.139621 0.333460i
\(886\) 1.25460e8 2.38020e8i 0.00606022 0.0114973i
\(887\) 3.67506e9 0.176820 0.0884100 0.996084i \(-0.471821\pi\)
0.0884100 + 0.996084i \(0.471821\pi\)
\(888\) 1.41961e10 7.97896e9i 0.680337 0.382385i
\(889\) −2.64054e10 −1.26048
\(890\) 5.34112e9 1.01331e10i 0.253961 0.481810i
\(891\) −2.56900e10 + 3.93280e8i −1.21672 + 0.0186264i
\(892\) −1.00359e9 + 6.87498e8i −0.0473455 + 0.0324335i
\(893\) 4.11450e10 1.93347
\(894\) 2.02473e10 + 1.79791e9i 0.947734 + 0.0841562i
\(895\) 9.76312e9i 0.455206i
\(896\) −6.35817e9 + 2.44870e10i −0.295294 + 1.13726i
\(897\) 7.49550e9 + 1.79017e10i 0.346759 + 0.828171i
\(898\) −8.22475e8 + 1.56038e9i −0.0379014 + 0.0719057i
\(899\) 4.26962e9i 0.195988i
\(900\) −2.82491e8 5.05677e7i −0.0129168 0.00231219i
\(901\) 3.34779e10i 1.52483i
\(902\) 1.33284e10 + 7.02537e9i 0.604720 + 0.318747i
\(903\) −5.55560e9 1.32686e10i −0.251087 0.599676i
\(904\) −2.04030e10 + 2.36757e9i −0.918555 + 0.106589i
\(905\) 6.22497e9i 0.279169i
\(906\) −7.45638e8 + 8.39707e9i −0.0333104 + 0.375128i
\(907\) 4.10522e10 1.82689 0.913443 0.406967i \(-0.133414\pi\)
0.913443 + 0.406967i \(0.133414\pi\)
\(908\) −7.41719e9 + 5.08106e9i −0.328805 + 0.225244i
\(909\) 1.64919e10 1.67463e10i 0.728277 0.739512i
\(910\) 2.36766e10 + 1.24799e10i 1.04154 + 0.548993i
\(911\) −1.57769e10 −0.691364 −0.345682 0.938352i \(-0.612352\pi\)
−0.345682 + 0.938352i \(0.612352\pi\)
\(912\) −9.48497e8 3.51754e10i −0.0414051 1.53553i
\(913\) 2.01835e10 0.877704
\(914\) −2.81620e10 1.48442e10i −1.21998 0.643049i
\(915\) −7.28584e9 1.74009e10i −0.314417 0.750928i
\(916\) −1.24370e10 + 8.51983e9i −0.534665 + 0.366266i
\(917\) 4.07509e10 1.74520
\(918\) 1.22069e10 + 1.43612e10i 0.520780 + 0.612692i
\(919\) 1.27768e10i 0.543023i 0.962435 + 0.271512i \(0.0875236\pi\)
−0.962435 + 0.271512i \(0.912476\pi\)
\(920\) 2.40733e9 + 2.07457e10i 0.101924 + 0.878355i
\(921\) −1.68326e9 + 7.04787e8i −0.0709973 + 0.0297269i
\(922\) −1.14031e10 6.01059e9i −0.479144 0.252557i
\(923\) 4.97055e9i 0.208065i
\(924\) −2.87978e10 1.86074e10i −1.20090 0.775950i
\(925\) 2.46512e8i 0.0102410i
\(926\) 1.33264e9 2.52825e9i 0.0551535 0.104636i
\(927\) −1.16857e10 1.15082e10i −0.481810 0.474491i
\(928\) −3.54328e9 + 3.08356e9i −0.145542 + 0.126659i
\(929\) 3.88487e10i 1.58972i 0.606790 + 0.794862i \(0.292457\pi\)
−0.606790 + 0.794862i \(0.707543\pi\)
\(930\) −2.18943e9 + 2.46565e10i −0.0892566 + 1.00517i
\(931\) −1.43930e10 −0.584556
\(932\) −2.41366e10 + 1.65345e10i −0.976608 + 0.669015i
\(933\) −2.38533e10 + 9.98749e9i −0.961531 + 0.402597i
\(934\) −1.39613e9 + 2.64870e9i −0.0560675 + 0.106370i
\(935\) −2.42959e10 −0.972060
\(936\) −1.55598e10 + 1.99568e10i −0.620208 + 0.795475i
\(937\) 2.21198e9 0.0878400 0.0439200 0.999035i \(-0.486015\pi\)
0.0439200 + 0.999035i \(0.486015\pi\)
\(938\) −1.17828e9 + 2.23541e9i −0.0466165 + 0.0884398i
\(939\) 1.49547e10 6.26158e9i 0.589450 0.246805i
\(940\) −1.79955e10 2.62693e10i −0.706671 1.03158i
\(941\) −1.29579e10 −0.506958 −0.253479 0.967341i \(-0.581575\pi\)
−0.253479 + 0.967341i \(0.581575\pi\)
\(942\) 3.66579e9 4.12827e10i 0.142886 1.60913i
\(943\) 1.28760e10i 0.500025i
\(944\) 8.77066e9 + 3.39746e9i 0.339336 + 0.131447i
\(945\) 2.81071e10 + 1.12661e10i 1.08344 + 0.434271i
\(946\) −8.17493e9 + 1.55093e10i −0.313953 + 0.595625i
\(947\) 2.11532e10i 0.809379i 0.914454 + 0.404690i \(0.132620\pi\)
−0.914454 + 0.404690i \(0.867380\pi\)
\(948\) −2.52466e10 + 3.90730e10i −0.962439 + 1.48952i
\(949\) 3.23040e10i 1.22694i
\(950\) 4.71211e8 + 2.48375e8i 0.0178313 + 0.00939886i
\(951\) 1.70511e10 7.13936e9i 0.642866 0.269170i
\(952\) 2.89919e9 + 2.49844e10i 0.108905 + 0.938513i
\(953\) 1.40357e10i 0.525302i 0.964891 + 0.262651i \(0.0845968\pi\)
−0.964891 + 0.262651i \(0.915403\pi\)
\(954\) 4.84611e10 1.54145e10i 1.80707 0.574793i
\(955\) −2.25820e9 −0.0838978
\(956\) −2.66779e10 3.89436e10i −0.987528 1.44156i
\(957\) −2.45856e9 5.87183e9i −0.0906753 0.216562i
\(958\) 7.71297e9 + 4.06550e9i 0.283428 + 0.149394i
\(959\) 4.32457e10 1.58335
\(960\) −2.20432e10 + 1.59902e10i −0.804127 + 0.583316i
\(961\) −8.77029e8 −0.0318773
\(962\) 1.92294e10 + 1.01358e10i 0.696391 + 0.367067i
\(963\) 3.30082e10 + 3.25067e10i 1.19105 + 1.17295i
\(964\) −1.51002e10 2.20428e10i −0.542891 0.792496i
\(965\) 3.63394e10 1.30176
\(966\) −2.59169e9 + 2.91866e10i −0.0925046 + 1.04175i
\(967\) 2.83172e8i 0.0100706i 0.999987 + 0.00503532i \(0.00160280\pi\)
−0.999987 + 0.00503532i \(0.998397\pi\)
\(968\) 1.56386e9 + 1.34769e10i 0.0554158 + 0.477558i
\(969\) −1.35113e10 3.22693e10i −0.477050 1.13935i
\(970\) 6.14051e8 + 3.23666e8i 0.0216025 + 0.0113866i
\(971\) 4.40952e10i 1.54570i 0.634590 + 0.772849i \(0.281169\pi\)
−0.634590 + 0.772849i \(0.718831\pi\)
\(972\) −1.51682e10 + 2.42826e10i −0.529786 + 0.848131i
\(973\) 1.46728e8i 0.00510645i
\(974\) −8.68351e9 + 1.64742e10i −0.301119 + 0.571277i
\(975\) −1.47947e8 3.53345e8i −0.00511199 0.0122091i
\(976\) 2.21952e10 + 8.59766e9i 0.764160 + 0.296010i
\(977\) 3.64943e10i 1.25197i −0.779836 0.625984i \(-0.784697\pi\)
0.779836 0.625984i \(-0.215303\pi\)
\(978\) −2.46666e10 2.19033e9i −0.843187 0.0748728i
\(979\) −1.95868e10 −0.667150
\(980\) 6.29503e9 + 9.18930e9i 0.213652 + 0.311883i
\(981\) 5.06620e9 + 4.98924e9i 0.171333 + 0.168730i
\(982\) 2.54105e8 4.82082e8i 0.00856295 0.0162454i
\(983\) −4.42163e10 −1.48472 −0.742362 0.669999i \(-0.766294\pi\)
−0.742362 + 0.669999i \(0.766294\pi\)
\(984\) 1.46359e10 8.22614e9i 0.489707 0.275241i
\(985\) −3.38278e9 −0.112784
\(986\) −2.17750e9 + 4.13111e9i −0.0723419 + 0.137245i
\(987\) −1.72540e10 4.12080e10i −0.571188 1.36418i
\(988\) 3.87495e10 2.65449e10i 1.27825 0.875653i
\(989\) 1.49830e10 0.492505
\(990\) −1.11868e10 3.51698e10i −0.366424 1.15198i
\(991\) 1.76435e10i 0.575874i −0.957649 0.287937i \(-0.907031\pi\)
0.957649 0.287937i \(-0.0929695\pi\)
\(992\) −2.05033e10 2.35600e10i −0.666857 0.766276i
\(993\) 1.25712e10 5.26362e9i 0.407432 0.170593i
\(994\) −3.49928e9 + 6.63875e9i −0.113012 + 0.214404i
\(995\) 2.02766e10i 0.652552i
\(996\) 1.22061e10 1.88909e10i 0.391445 0.605821i
\(997\) 4.33270e10i 1.38460i 0.721608 + 0.692302i \(0.243403\pi\)
−0.721608 + 0.692302i \(0.756597\pi\)
\(998\) −5.33197e9 2.81048e9i −0.169797 0.0895000i
\(999\) 2.28277e10 + 9.14995e9i 0.724408 + 0.290362i
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 24.8.f.c.11.5 20
3.2 odd 2 inner 24.8.f.c.11.16 yes 20
4.3 odd 2 96.8.f.c.47.17 20
8.3 odd 2 inner 24.8.f.c.11.15 yes 20
8.5 even 2 96.8.f.c.47.18 20
12.11 even 2 96.8.f.c.47.20 20
24.5 odd 2 96.8.f.c.47.19 20
24.11 even 2 inner 24.8.f.c.11.6 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
24.8.f.c.11.5 20 1.1 even 1 trivial
24.8.f.c.11.6 yes 20 24.11 even 2 inner
24.8.f.c.11.15 yes 20 8.3 odd 2 inner
24.8.f.c.11.16 yes 20 3.2 odd 2 inner
96.8.f.c.47.17 20 4.3 odd 2
96.8.f.c.47.18 20 8.5 even 2
96.8.f.c.47.19 20 24.5 odd 2
96.8.f.c.47.20 20 12.11 even 2