Properties

Label 24.8.f.c.11.4
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 11.4
Root \(10.4702 + 4.28654i\) of defining polynomial
Character \(\chi\) \(=\) 24.11
Dual form 24.8.f.c.11.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-10.4702 + 4.28654i) q^{2} +(-24.1914 + 40.0222i) q^{3} +(91.2511 - 89.7621i) q^{4} +477.520 q^{5} +(81.7320 - 522.739i) q^{6} +632.635i q^{7} +(-570.650 + 1330.98i) q^{8} +(-1016.56 - 1936.38i) q^{9} +O(q^{10})\) \(q+(-10.4702 + 4.28654i) q^{2} +(-24.1914 + 40.0222i) q^{3} +(91.2511 - 89.7621i) q^{4} +477.520 q^{5} +(81.7320 - 522.739i) q^{6} +632.635i q^{7} +(-570.650 + 1330.98i) q^{8} +(-1016.56 - 1936.38i) q^{9} +(-4999.74 + 2046.91i) q^{10} +4849.09i q^{11} +(1384.99 + 5823.54i) q^{12} -3229.57i q^{13} +(-2711.82 - 6623.83i) q^{14} +(-11551.9 + 19111.4i) q^{15} +(269.517 - 16381.8i) q^{16} +32288.3i q^{17} +(18944.0 + 15916.9i) q^{18} -21527.2 q^{19} +(43574.2 - 42863.2i) q^{20} +(-25319.5 - 15304.3i) q^{21} +(-20785.8 - 50771.1i) q^{22} -5755.11 q^{23} +(-39464.0 - 55036.9i) q^{24} +149900. q^{25} +(13843.7 + 33814.3i) q^{26} +(102090. + 6159.01i) q^{27} +(56786.7 + 57728.6i) q^{28} -131879. q^{29} +(39028.7 - 249618. i) q^{30} +147516. i q^{31} +(67399.3 + 172676. i) q^{32} +(-194071. - 117306. i) q^{33} +(-138405. - 338066. i) q^{34} +302096. i q^{35} +(-266576. - 85449.0i) q^{36} +19019.9i q^{37} +(225395. - 92277.3i) q^{38} +(129254. + 78127.7i) q^{39} +(-272496. + 635570. i) q^{40} +42800.6i q^{41} +(330703. + 51706.5i) q^{42} -325765. q^{43} +(435265. + 442485. i) q^{44} +(-485425. - 924662. i) q^{45} +(60257.3 - 24669.6i) q^{46} +976107. q^{47} +(649115. + 407084. i) q^{48} +423316. q^{49} +(-1.56949e6 + 642554. i) q^{50} +(-1.29225e6 - 781099. i) q^{51} +(-289893. - 294702. i) q^{52} +554605. q^{53} +(-1.09531e6 + 373128. i) q^{54} +2.31554e6i q^{55} +(-842026. - 361013. i) q^{56} +(520772. - 861566. i) q^{57} +(1.38081e6 - 565307. i) q^{58} -535369. i q^{59} +(661361. + 2.78086e6i) q^{60} -3.23726e6i q^{61} +(-632336. - 1.54453e6i) q^{62} +(1.22502e6 - 643109. i) q^{63} +(-1.44587e6 - 1.51905e6i) q^{64} -1.54218e6i q^{65} +(2.53481e6 + 396326. i) q^{66} +3.19490e6 q^{67} +(2.89827e6 + 2.94635e6i) q^{68} +(139224. - 230332. i) q^{69} +(-1.29495e6 - 3.16301e6i) q^{70} -2.17151e6 q^{71} +(3.15739e6 - 248019. i) q^{72} +569345. q^{73} +(-81529.8 - 199143. i) q^{74} +(-3.62629e6 + 5.99934e6i) q^{75} +(-1.96438e6 + 1.93233e6i) q^{76} -3.06771e6 q^{77} +(-1.68822e6 - 263959. i) q^{78} +1.27485e6i q^{79} +(128700. - 7.82263e6i) q^{80} +(-2.71620e6 + 3.93688e6i) q^{81} +(-183467. - 448132. i) q^{82} -3.57654e6i q^{83} +(-3.68418e6 + 876194. i) q^{84} +1.54183e7i q^{85} +(3.41083e6 - 1.39640e6i) q^{86} +(3.19035e6 - 5.27811e6i) q^{87} +(-6.45405e6 - 2.76713e6i) q^{88} +6.34057e6i q^{89} +(9.04612e6 + 7.60062e6i) q^{90} +2.04314e6 q^{91} +(-525160. + 516591. i) q^{92} +(-5.90394e6 - 3.56863e6i) q^{93} +(-1.02201e7 + 4.18413e6i) q^{94} -1.02797e7 q^{95} +(-8.54137e6 - 1.47980e6i) q^{96} +7.13949e6 q^{97} +(-4.43221e6 + 1.81456e6i) q^{98} +(9.38970e6 - 4.92937e6i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.4702 + 4.28654i −0.925446 + 0.378881i
\(3\) −24.1914 + 40.0222i −0.517292 + 0.855809i
\(4\) 91.2511 89.7621i 0.712899 0.701267i
\(5\) 477.520 1.70843 0.854214 0.519922i \(-0.174039\pi\)
0.854214 + 0.519922i \(0.174039\pi\)
\(6\) 81.7320 522.739i 0.154477 0.987996i
\(7\) 632.635i 0.697124i 0.937286 + 0.348562i \(0.113330\pi\)
−0.937286 + 0.348562i \(0.886670\pi\)
\(8\) −570.650 + 1330.98i −0.394053 + 0.919088i
\(9\) −1016.56 1936.38i −0.464817 0.885407i
\(10\) −4999.74 + 2046.91i −1.58106 + 0.647290i
\(11\) 4849.09i 1.09846i 0.835670 + 0.549232i \(0.185080\pi\)
−0.835670 + 0.549232i \(0.814920\pi\)
\(12\) 1384.99 + 5823.54i 0.231373 + 0.972865i
\(13\) 3229.57i 0.407702i −0.979002 0.203851i \(-0.934654\pi\)
0.979002 0.203851i \(-0.0653458\pi\)
\(14\) −2711.82 6623.83i −0.264127 0.645151i
\(15\) −11551.9 + 19111.4i −0.883756 + 1.46209i
\(16\) 269.517 16381.8i 0.0164500 0.999865i
\(17\) 32288.3i 1.59395i 0.604013 + 0.796974i \(0.293568\pi\)
−0.604013 + 0.796974i \(0.706432\pi\)
\(18\) 18944.0 + 15916.9i 0.765626 + 0.643285i
\(19\) −21527.2 −0.720029 −0.360014 0.932947i \(-0.617228\pi\)
−0.360014 + 0.932947i \(0.617228\pi\)
\(20\) 43574.2 42863.2i 1.21794 1.19806i
\(21\) −25319.5 15304.3i −0.596605 0.360617i
\(22\) −20785.8 50771.1i −0.416187 1.01657i
\(23\) −5755.11 −0.0986294 −0.0493147 0.998783i \(-0.515704\pi\)
−0.0493147 + 0.998783i \(0.515704\pi\)
\(24\) −39464.0 55036.9i −0.582723 0.812671i
\(25\) 149900. 1.91872
\(26\) 13843.7 + 33814.3i 0.154470 + 0.377306i
\(27\) 102090. + 6159.01i 0.998185 + 0.0602195i
\(28\) 56786.7 + 57728.6i 0.488870 + 0.496979i
\(29\) −131879. −1.00412 −0.502058 0.864834i \(-0.667424\pi\)
−0.502058 + 0.864834i \(0.667424\pi\)
\(30\) 39028.7 249618.i 0.263912 1.68792i
\(31\) 147516.i 0.889354i 0.895691 + 0.444677i \(0.146682\pi\)
−0.895691 + 0.444677i \(0.853318\pi\)
\(32\) 67399.3 + 172676.i 0.363606 + 0.931553i
\(33\) −194071. 117306.i −0.940075 0.568227i
\(34\) −138405. 338066.i −0.603916 1.47511i
\(35\) 302096.i 1.19099i
\(36\) −266576. 85449.0i −0.952274 0.305245i
\(37\) 19019.9i 0.0617309i 0.999524 + 0.0308655i \(0.00982634\pi\)
−0.999524 + 0.0308655i \(0.990174\pi\)
\(38\) 225395. 92277.3i 0.666347 0.272805i
\(39\) 129254. + 78127.7i 0.348915 + 0.210901i
\(40\) −272496. + 635570.i −0.673211 + 1.57019i
\(41\) 42800.6i 0.0969855i 0.998824 + 0.0484927i \(0.0154418\pi\)
−0.998824 + 0.0484927i \(0.984558\pi\)
\(42\) 330703. + 51706.5i 0.688756 + 0.107689i
\(43\) −325765. −0.624834 −0.312417 0.949945i \(-0.601139\pi\)
−0.312417 + 0.949945i \(0.601139\pi\)
\(44\) 435265. + 442485.i 0.770316 + 0.783094i
\(45\) −485425. 924662.i −0.794106 1.51265i
\(46\) 60257.3 24669.6i 0.0912762 0.0373688i
\(47\) 976107. 1.37137 0.685686 0.727898i \(-0.259502\pi\)
0.685686 + 0.727898i \(0.259502\pi\)
\(48\) 649115. + 407084.i 0.847183 + 0.531300i
\(49\) 423316. 0.514018
\(50\) −1.56949e6 + 642554.i −1.77567 + 0.726967i
\(51\) −1.29225e6 781099.i −1.36412 0.824538i
\(52\) −289893. 294702.i −0.285908 0.290650i
\(53\) 554605. 0.511703 0.255852 0.966716i \(-0.417644\pi\)
0.255852 + 0.966716i \(0.417644\pi\)
\(54\) −1.09531e6 + 373128.i −0.946582 + 0.322463i
\(55\) 2.31554e6i 1.87665i
\(56\) −842026. 361013.i −0.640718 0.274704i
\(57\) 520772. 861566.i 0.372465 0.616207i
\(58\) 1.38081e6 565307.i 0.929256 0.380440i
\(59\) 535369.i 0.339368i −0.985498 0.169684i \(-0.945725\pi\)
0.985498 0.169684i \(-0.0542748\pi\)
\(60\) 661361. + 2.78086e6i 0.395284 + 1.66207i
\(61\) 3.23726e6i 1.82609i −0.407856 0.913046i \(-0.633724\pi\)
0.407856 0.913046i \(-0.366276\pi\)
\(62\) −632336. 1.54453e6i −0.336959 0.823049i
\(63\) 1.22502e6 643109.i 0.617238 0.324035i
\(64\) −1.44587e6 1.51905e6i −0.689445 0.724338i
\(65\) 1.54218e6i 0.696529i
\(66\) 2.53481e6 + 396326.i 1.08528 + 0.169687i
\(67\) 3.19490e6 1.29776 0.648882 0.760889i \(-0.275237\pi\)
0.648882 + 0.760889i \(0.275237\pi\)
\(68\) 2.89827e6 + 2.94635e6i 1.11778 + 1.13632i
\(69\) 139224. 230332.i 0.0510203 0.0844079i
\(70\) −1.29495e6 3.16301e6i −0.451241 1.10219i
\(71\) −2.17151e6 −0.720042 −0.360021 0.932944i \(-0.617230\pi\)
−0.360021 + 0.932944i \(0.617230\pi\)
\(72\) 3.15739e6 248019.i 0.996929 0.0783107i
\(73\) 569345. 0.171295 0.0856477 0.996325i \(-0.472704\pi\)
0.0856477 + 0.996325i \(0.472704\pi\)
\(74\) −81529.8 199143.i −0.0233886 0.0571286i
\(75\) −3.62629e6 + 5.99934e6i −0.992541 + 1.64206i
\(76\) −1.96438e6 + 1.93233e6i −0.513308 + 0.504932i
\(77\) −3.06771e6 −0.765766
\(78\) −1.68822e6 263959.i −0.402808 0.0629804i
\(79\) 1.27485e6i 0.290914i 0.989365 + 0.145457i \(0.0464652\pi\)
−0.989365 + 0.145457i \(0.953535\pi\)
\(80\) 128700. 7.82263e6i 0.0281036 1.70820i
\(81\) −2.71620e6 + 3.93688e6i −0.567890 + 0.823104i
\(82\) −183467. 448132.i −0.0367459 0.0897548i
\(83\) 3.57654e6i 0.686578i −0.939230 0.343289i \(-0.888459\pi\)
0.939230 0.343289i \(-0.111541\pi\)
\(84\) −3.68418e6 + 876194.i −0.678208 + 0.161296i
\(85\) 1.54183e7i 2.72315i
\(86\) 3.41083e6 1.39640e6i 0.578250 0.236737i
\(87\) 3.19035e6 5.27811e6i 0.519422 0.859332i
\(88\) −6.45405e6 2.76713e6i −1.00959 0.432853i
\(89\) 6.34057e6i 0.953374i 0.879073 + 0.476687i \(0.158163\pi\)
−0.879073 + 0.476687i \(0.841837\pi\)
\(90\) 9.04612e6 + 7.60062e6i 1.30802 + 1.09901i
\(91\) 2.04314e6 0.284219
\(92\) −525160. + 516591.i −0.0703128 + 0.0691655i
\(93\) −5.90394e6 3.56863e6i −0.761117 0.460056i
\(94\) −1.02201e7 + 4.18413e6i −1.26913 + 0.519586i
\(95\) −1.02797e7 −1.23012
\(96\) −8.54137e6 1.47980e6i −0.985322 0.170708i
\(97\) 7.13949e6 0.794266 0.397133 0.917761i \(-0.370005\pi\)
0.397133 + 0.917761i \(0.370005\pi\)
\(98\) −4.43221e6 + 1.81456e6i −0.475696 + 0.194751i
\(99\) 9.38970e6 4.92937e6i 0.972588 0.510585i
\(100\) 1.36786e7 1.34554e7i 1.36786 1.34554i
\(101\) 1.83155e7 1.76886 0.884429 0.466675i \(-0.154548\pi\)
0.884429 + 0.466675i \(0.154548\pi\)
\(102\) 1.68784e7 + 2.63899e6i 1.57482 + 0.246228i
\(103\) 7.88089e6i 0.710633i −0.934746 0.355316i \(-0.884373\pi\)
0.934746 0.355316i \(-0.115627\pi\)
\(104\) 4.29850e6 + 1.84295e6i 0.374714 + 0.160656i
\(105\) −1.20905e7 7.30811e6i −1.01926 0.616088i
\(106\) −5.80684e6 + 2.37734e6i −0.473554 + 0.193874i
\(107\) 5.65137e6i 0.445975i 0.974821 + 0.222988i \(0.0715809\pi\)
−0.974821 + 0.222988i \(0.928419\pi\)
\(108\) 9.86869e6 8.60182e6i 0.753835 0.657064i
\(109\) 525457.i 0.0388637i 0.999811 + 0.0194319i \(0.00618574\pi\)
−0.999811 + 0.0194319i \(0.993814\pi\)
\(110\) −9.92565e6 2.42442e7i −0.711025 1.73673i
\(111\) −761219. 460118.i −0.0528299 0.0319329i
\(112\) 1.03637e7 + 170506.i 0.697030 + 0.0114677i
\(113\) 2.69478e6i 0.175691i −0.996134 0.0878454i \(-0.972002\pi\)
0.996134 0.0878454i \(-0.0279982\pi\)
\(114\) −1.75946e6 + 1.12531e7i −0.111228 + 0.711386i
\(115\) −2.74818e6 −0.168501
\(116\) −1.20341e7 + 1.18378e7i −0.715834 + 0.704154i
\(117\) −6.25369e6 + 3.28303e6i −0.360982 + 0.189507i
\(118\) 2.29488e6 + 5.60544e6i 0.128580 + 0.314067i
\(119\) −2.04267e7 −1.11118
\(120\) −1.88449e7 2.62812e7i −0.995539 1.38839i
\(121\) −4.02651e6 −0.206624
\(122\) 1.38766e7 + 3.38948e7i 0.691871 + 1.68995i
\(123\) −1.71298e6 1.03541e6i −0.0830010 0.0501699i
\(124\) 1.32414e7 + 1.34610e7i 0.623674 + 0.634019i
\(125\) 3.42741e7 1.56957
\(126\) −1.00696e7 + 1.19846e7i −0.448450 + 0.533737i
\(127\) 2.13324e7i 0.924117i −0.886849 0.462059i \(-0.847111\pi\)
0.886849 0.462059i \(-0.152889\pi\)
\(128\) 2.16500e7 + 9.70698e6i 0.912481 + 0.409119i
\(129\) 7.88069e6 1.30378e7i 0.323222 0.534738i
\(130\) 6.61064e6 + 1.61470e7i 0.263901 + 0.644600i
\(131\) 4.33587e7i 1.68510i −0.538615 0.842552i \(-0.681052\pi\)
0.538615 0.842552i \(-0.318948\pi\)
\(132\) −2.82389e7 + 6.71595e6i −1.06866 + 0.254155i
\(133\) 1.36189e7i 0.501950i
\(134\) −3.34513e7 + 1.36951e7i −1.20101 + 0.491698i
\(135\) 4.87501e7 + 2.94105e6i 1.70533 + 0.102881i
\(136\) −4.29752e7 1.84253e7i −1.46498 0.628100i
\(137\) 3.25183e7i 1.08045i 0.841520 + 0.540227i \(0.181662\pi\)
−0.841520 + 0.540227i \(0.818338\pi\)
\(138\) −470377. + 3.00842e6i −0.0152359 + 0.0974455i
\(139\) −1.58632e7 −0.501000 −0.250500 0.968117i \(-0.580595\pi\)
−0.250500 + 0.968117i \(0.580595\pi\)
\(140\) 2.71168e7 + 2.75666e7i 0.835199 + 0.849053i
\(141\) −2.36134e7 + 3.90660e7i −0.709400 + 1.17363i
\(142\) 2.27362e7 9.30828e6i 0.666360 0.272810i
\(143\) 1.56605e7 0.447846
\(144\) −3.19954e7 + 1.61311e7i −0.892933 + 0.450189i
\(145\) −6.29751e7 −1.71546
\(146\) −5.96117e6 + 2.44052e6i −0.158525 + 0.0649005i
\(147\) −1.02406e7 + 1.69420e7i −0.265898 + 0.439901i
\(148\) 1.70727e6 + 1.73559e6i 0.0432898 + 0.0440079i
\(149\) −9.55034e6 −0.236519 −0.118260 0.992983i \(-0.537732\pi\)
−0.118260 + 0.992983i \(0.537732\pi\)
\(150\) 1.22516e7 7.83587e7i 0.296398 1.89569i
\(151\) 1.00995e7i 0.238715i 0.992851 + 0.119358i \(0.0380835\pi\)
−0.992851 + 0.119358i \(0.961917\pi\)
\(152\) 1.22845e7 2.86523e7i 0.283729 0.661770i
\(153\) 6.25226e7 3.28229e7i 1.41129 0.740895i
\(154\) 3.21196e7 1.31499e7i 0.708675 0.290134i
\(155\) 7.04420e7i 1.51940i
\(156\) 1.88075e7 4.47292e6i 0.396639 0.0943312i
\(157\) 1.83230e7i 0.377875i −0.981989 0.188938i \(-0.939496\pi\)
0.981989 0.188938i \(-0.0605044\pi\)
\(158\) −5.46470e6 1.33480e7i −0.110222 0.269225i
\(159\) −1.34167e7 + 2.21965e7i −0.264700 + 0.437920i
\(160\) 3.21845e7 + 8.24563e7i 0.621194 + 1.59149i
\(161\) 3.64089e6i 0.0687570i
\(162\) 1.15636e7 5.28632e7i 0.213693 0.976901i
\(163\) 4.97051e7 0.898968 0.449484 0.893288i \(-0.351608\pi\)
0.449484 + 0.893288i \(0.351608\pi\)
\(164\) 3.84188e6 + 3.90560e6i 0.0680127 + 0.0691409i
\(165\) −9.26729e7 5.60160e7i −1.60605 0.970775i
\(166\) 1.53310e7 + 3.74472e7i 0.260131 + 0.635391i
\(167\) −9.61596e7 −1.59766 −0.798832 0.601555i \(-0.794548\pi\)
−0.798832 + 0.601555i \(0.794548\pi\)
\(168\) 3.48183e7 2.49663e7i 0.566533 0.406230i
\(169\) 5.23184e7 0.833779
\(170\) −6.60913e7 1.61433e8i −1.03175 2.52012i
\(171\) 2.18836e7 + 4.16849e7i 0.334682 + 0.637518i
\(172\) −2.97264e7 + 2.92413e7i −0.445443 + 0.438175i
\(173\) 2.49679e7 0.366624 0.183312 0.983055i \(-0.441318\pi\)
0.183312 + 0.983055i \(0.441318\pi\)
\(174\) −1.07788e7 + 6.89385e7i −0.155113 + 0.992064i
\(175\) 9.48322e7i 1.33759i
\(176\) 7.94368e7 + 1.30691e6i 1.09832 + 0.0180697i
\(177\) 2.14267e7 + 1.29513e7i 0.290434 + 0.175553i
\(178\) −2.71791e7 6.63872e7i −0.361215 0.882296i
\(179\) 7.35170e7i 0.958081i −0.877793 0.479040i \(-0.840985\pi\)
0.877793 0.479040i \(-0.159015\pi\)
\(180\) −1.27295e8 4.08036e7i −1.62689 0.521488i
\(181\) 1.26712e8i 1.58833i −0.607699 0.794167i \(-0.707907\pi\)
0.607699 0.794167i \(-0.292093\pi\)
\(182\) −2.13921e7 + 8.75800e6i −0.263029 + 0.107685i
\(183\) 1.29562e8 + 7.83137e7i 1.56279 + 0.944624i
\(184\) 3.28415e6 7.65995e6i 0.0388652 0.0906491i
\(185\) 9.08239e6i 0.105463i
\(186\) 7.71126e7 + 1.20568e7i 0.878678 + 0.137384i
\(187\) −1.56569e8 −1.75090
\(188\) 8.90709e7 8.76175e7i 0.977649 0.961697i
\(189\) −3.89640e6 + 6.45859e7i −0.0419805 + 0.695859i
\(190\) 1.07630e8 4.40642e7i 1.13841 0.466067i
\(191\) 4.33405e7 0.450067 0.225034 0.974351i \(-0.427751\pi\)
0.225034 + 0.974351i \(0.427751\pi\)
\(192\) 9.57732e7 2.11191e7i 0.976540 0.215338i
\(193\) 7.11547e7 0.712448 0.356224 0.934401i \(-0.384064\pi\)
0.356224 + 0.934401i \(0.384064\pi\)
\(194\) −7.47520e7 + 3.06037e7i −0.735050 + 0.300932i
\(195\) 6.17216e7 + 3.73075e7i 0.596096 + 0.360309i
\(196\) 3.86280e7 3.79977e7i 0.366443 0.360464i
\(197\) −2.11807e7 −0.197383 −0.0986913 0.995118i \(-0.531466\pi\)
−0.0986913 + 0.995118i \(0.531466\pi\)
\(198\) −7.71823e7 + 9.18610e7i −0.706626 + 0.841013i
\(199\) 2.72858e7i 0.245443i −0.992441 0.122722i \(-0.960838\pi\)
0.992441 0.122722i \(-0.0391622\pi\)
\(200\) −8.55405e7 + 1.99514e8i −0.756078 + 1.76347i
\(201\) −7.72891e7 + 1.27867e8i −0.671323 + 1.11064i
\(202\) −1.91767e8 + 7.85100e7i −1.63698 + 0.670186i
\(203\) 8.34316e7i 0.699994i
\(204\) −1.88032e8 + 4.47191e7i −1.55070 + 0.368797i
\(205\) 2.04382e7i 0.165693i
\(206\) 3.37818e7 + 8.25147e7i 0.269245 + 0.657652i
\(207\) 5.85039e6 + 1.11441e7i 0.0458447 + 0.0873272i
\(208\) −5.29061e7 870422.i −0.407647 0.00670669i
\(209\) 1.04387e8i 0.790926i
\(210\) 1.57917e8 + 2.46909e7i 1.17669 + 0.183979i
\(211\) −1.10815e8 −0.812102 −0.406051 0.913850i \(-0.633095\pi\)
−0.406051 + 0.913850i \(0.633095\pi\)
\(212\) 5.06083e7 4.97825e7i 0.364793 0.358841i
\(213\) 5.25318e7 8.69087e7i 0.372472 0.616218i
\(214\) −2.42249e7 5.91711e7i −0.168971 0.412726i
\(215\) −1.55559e8 −1.06748
\(216\) −6.64553e7 + 1.32366e8i −0.448685 + 0.893690i
\(217\) −9.33241e7 −0.619990
\(218\) −2.25240e6 5.50165e6i −0.0147247 0.0359663i
\(219\) −1.37732e7 + 2.27865e7i −0.0886098 + 0.146596i
\(220\) 2.07848e8 + 2.11295e8i 1.31603 + 1.33786i
\(221\) 1.04277e8 0.649856
\(222\) 9.94245e6 + 1.55454e6i 0.0609899 + 0.00953598i
\(223\) 2.73113e8i 1.64921i −0.565710 0.824604i \(-0.691398\pi\)
0.565710 0.824604i \(-0.308602\pi\)
\(224\) −1.09241e8 + 4.26392e7i −0.649408 + 0.253478i
\(225\) −1.52382e8 2.90264e8i −0.891855 1.69885i
\(226\) 1.15513e7 + 2.82150e7i 0.0665659 + 0.162592i
\(227\) 1.32485e8i 0.751753i 0.926670 + 0.375876i \(0.122658\pi\)
−0.926670 + 0.375876i \(0.877342\pi\)
\(228\) −2.98150e7 1.25364e8i −0.166595 0.700491i
\(229\) 3.24000e8i 1.78287i 0.453145 + 0.891437i \(0.350302\pi\)
−0.453145 + 0.891437i \(0.649698\pi\)
\(230\) 2.87741e7 1.17802e7i 0.155939 0.0638418i
\(231\) 7.42120e7 1.22776e8i 0.396125 0.655349i
\(232\) 7.52570e7 1.75529e8i 0.395675 0.922872i
\(233\) 5.56285e7i 0.288106i 0.989570 + 0.144053i \(0.0460135\pi\)
−0.989570 + 0.144053i \(0.953986\pi\)
\(234\) 5.14046e7 6.11808e7i 0.262269 0.312147i
\(235\) 4.66111e8 2.34289
\(236\) −4.80559e7 4.88530e7i −0.237988 0.241935i
\(237\) −5.10223e7 3.08404e7i −0.248966 0.150487i
\(238\) 2.13872e8 8.75601e7i 1.02834 0.421005i
\(239\) 3.45579e8 1.63740 0.818699 0.574222i \(-0.194696\pi\)
0.818699 + 0.574222i \(0.194696\pi\)
\(240\) 3.09965e8 + 1.94391e8i 1.44735 + 0.907688i
\(241\) −2.73635e7 −0.125925 −0.0629625 0.998016i \(-0.520055\pi\)
−0.0629625 + 0.998016i \(0.520055\pi\)
\(242\) 4.21585e7 1.72598e7i 0.191219 0.0782857i
\(243\) −9.18542e7 2.03947e8i −0.410655 0.911791i
\(244\) −2.90583e8 2.95403e8i −1.28058 1.30182i
\(245\) 2.02142e8 0.878162
\(246\) 2.23736e7 + 3.49818e6i 0.0958213 + 0.0149820i
\(247\) 6.95236e7i 0.293557i
\(248\) −1.96342e8 8.41802e7i −0.817394 0.350452i
\(249\) 1.43141e8 + 8.65215e7i 0.587580 + 0.355162i
\(250\) −3.58857e8 + 1.46917e8i −1.45255 + 0.594680i
\(251\) 2.95932e8i 1.18123i −0.806955 0.590614i \(-0.798886\pi\)
0.806955 0.590614i \(-0.201114\pi\)
\(252\) 5.40580e7 1.68645e8i 0.212793 0.663853i
\(253\) 2.79071e7i 0.108341i
\(254\) 9.14424e7 + 2.23355e8i 0.350130 + 0.855220i
\(255\) −6.17075e8 3.72990e8i −2.33049 1.40866i
\(256\) −2.68290e8 8.83032e6i −0.999459 0.0328955i
\(257\) 2.71775e8i 0.998720i 0.866395 + 0.499360i \(0.166432\pi\)
−0.866395 + 0.499360i \(0.833568\pi\)
\(258\) −2.66254e7 + 1.70290e8i −0.0965222 + 0.617333i
\(259\) −1.20327e7 −0.0430341
\(260\) −1.38430e8 1.40726e8i −0.488453 0.496555i
\(261\) 1.34063e8 + 2.55369e8i 0.466731 + 0.889052i
\(262\) 1.85859e8 + 4.53975e8i 0.638453 + 1.55947i
\(263\) −3.32668e8 −1.12763 −0.563814 0.825901i \(-0.690667\pi\)
−0.563814 + 0.825901i \(0.690667\pi\)
\(264\) 2.66879e8 1.91365e8i 0.892690 0.640100i
\(265\) 2.64835e8 0.874208
\(266\) 5.83779e7 + 1.42592e8i 0.190179 + 0.464527i
\(267\) −2.53764e8 1.53387e8i −0.815906 0.493173i
\(268\) 2.91538e8 2.86781e8i 0.925175 0.910079i
\(269\) −3.63197e8 −1.13765 −0.568825 0.822458i \(-0.692602\pi\)
−0.568825 + 0.822458i \(0.692602\pi\)
\(270\) −5.23032e8 + 1.78176e8i −1.61717 + 0.550905i
\(271\) 5.75287e8i 1.75587i 0.478782 + 0.877934i \(0.341078\pi\)
−0.478782 + 0.877934i \(0.658922\pi\)
\(272\) 5.28940e8 + 8.70224e6i 1.59373 + 0.0262204i
\(273\) −4.94263e7 + 8.17709e7i −0.147024 + 0.243237i
\(274\) −1.39391e8 3.40474e8i −0.409363 0.999901i
\(275\) 7.26880e8i 2.10765i
\(276\) −7.97078e6 3.35151e7i −0.0228202 0.0959531i
\(277\) 3.54054e8i 1.00090i 0.865765 + 0.500450i \(0.166832\pi\)
−0.865765 + 0.500450i \(0.833168\pi\)
\(278\) 1.66091e8 6.79981e7i 0.463648 0.189819i
\(279\) 2.85649e8 1.49959e8i 0.787440 0.413387i
\(280\) −4.02084e8 1.72391e8i −1.09462 0.469311i
\(281\) 3.30323e8i 0.888110i 0.896000 + 0.444055i \(0.146461\pi\)
−0.896000 + 0.444055i \(0.853539\pi\)
\(282\) 7.97792e7 5.10249e8i 0.211845 1.35491i
\(283\) 2.36463e8 0.620169 0.310085 0.950709i \(-0.399643\pi\)
0.310085 + 0.950709i \(0.399643\pi\)
\(284\) −1.98153e8 + 1.94919e8i −0.513317 + 0.504941i
\(285\) 2.48679e8 4.11415e8i 0.636330 1.05274i
\(286\) −1.63969e8 + 6.71293e7i −0.414457 + 0.169680i
\(287\) −2.70772e7 −0.0676109
\(288\) 2.65852e8 3.06046e8i 0.655793 0.754941i
\(289\) −6.32198e8 −1.54067
\(290\) 6.59363e8 2.69945e8i 1.58757 0.649955i
\(291\) −1.72714e8 + 2.85738e8i −0.410868 + 0.679740i
\(292\) 5.19534e7 5.11056e7i 0.122116 0.120124i
\(293\) −1.62422e8 −0.377232 −0.188616 0.982051i \(-0.560400\pi\)
−0.188616 + 0.982051i \(0.560400\pi\)
\(294\) 3.45984e7 2.21284e8i 0.0794037 0.507848i
\(295\) 2.55649e8i 0.579786i
\(296\) −2.53152e7 1.08537e7i −0.0567361 0.0243252i
\(297\) −2.98656e7 + 4.95045e8i −0.0661490 + 1.09647i
\(298\) 9.99942e7 4.09380e7i 0.218886 0.0896126i
\(299\) 1.85865e7i 0.0402114i
\(300\) 2.07610e8 + 8.72950e8i 0.443941 + 1.86666i
\(301\) 2.06090e8i 0.435587i
\(302\) −4.32919e7 1.05744e8i −0.0904445 0.220918i
\(303\) −4.43076e8 + 7.33025e8i −0.915016 + 1.51380i
\(304\) −5.80194e6 + 3.52654e8i −0.0118445 + 0.719931i
\(305\) 1.54585e9i 3.11975i
\(306\) −5.13929e8 + 6.11669e8i −1.02536 + 1.22037i
\(307\) 1.99590e8 0.393690 0.196845 0.980435i \(-0.436930\pi\)
0.196845 + 0.980435i \(0.436930\pi\)
\(308\) −2.79931e8 + 2.75364e8i −0.545914 + 0.537006i
\(309\) 3.15411e8 + 1.90650e8i 0.608166 + 0.367605i
\(310\) −3.01953e8 7.37544e8i −0.575670 1.40612i
\(311\) 5.88253e8 1.10893 0.554464 0.832208i \(-0.312923\pi\)
0.554464 + 0.832208i \(0.312923\pi\)
\(312\) −1.77745e8 + 1.27452e8i −0.331328 + 0.237577i
\(313\) 9.59109e8 1.76792 0.883961 0.467561i \(-0.154867\pi\)
0.883961 + 0.467561i \(0.154867\pi\)
\(314\) 7.85425e7 + 1.91846e8i 0.143170 + 0.349703i
\(315\) 5.84974e8 3.07097e8i 1.05451 0.553591i
\(316\) 1.14433e8 + 1.16331e8i 0.204008 + 0.207392i
\(317\) −5.95992e8 −1.05083 −0.525416 0.850846i \(-0.676090\pi\)
−0.525416 + 0.850846i \(0.676090\pi\)
\(318\) 4.53290e7 2.89914e8i 0.0790462 0.505561i
\(319\) 6.39496e8i 1.10299i
\(320\) −6.90432e8 7.25375e8i −1.17787 1.23748i
\(321\) −2.26180e8 1.36714e8i −0.381669 0.230700i
\(322\) 1.56068e7 + 3.81209e7i 0.0260507 + 0.0636308i
\(323\) 6.95077e8i 1.14769i
\(324\) 1.05527e8 + 6.03057e8i 0.172368 + 0.985033i
\(325\) 4.84113e8i 0.782267i
\(326\) −5.20423e8 + 2.13063e8i −0.831946 + 0.340601i
\(327\) −2.10300e7 1.27115e7i −0.0332599 0.0201039i
\(328\) −5.69669e7 2.44242e7i −0.0891382 0.0382174i
\(329\) 6.17520e8i 0.956016i
\(330\) 1.21042e9 + 1.89254e8i 1.85412 + 0.289898i
\(331\) −1.23121e9 −1.86609 −0.933047 0.359755i \(-0.882860\pi\)
−0.933047 + 0.359755i \(0.882860\pi\)
\(332\) −3.21038e8 3.26363e8i −0.481474 0.489461i
\(333\) 3.68299e7 1.93348e7i 0.0546570 0.0286936i
\(334\) 1.00681e9 4.12193e8i 1.47855 0.605324i
\(335\) 1.52563e9 2.21714
\(336\) −2.57536e8 + 4.10653e8i −0.370382 + 0.590592i
\(337\) 1.59873e8 0.227546 0.113773 0.993507i \(-0.463706\pi\)
0.113773 + 0.993507i \(0.463706\pi\)
\(338\) −5.47785e8 + 2.24265e8i −0.771617 + 0.315903i
\(339\) 1.07851e8 + 6.51905e7i 0.150358 + 0.0908835i
\(340\) 1.38398e9 + 1.40694e9i 1.90965 + 1.94133i
\(341\) −7.15321e8 −0.976923
\(342\) −4.07810e8 3.42645e8i −0.551273 0.463184i
\(343\) 7.88807e8i 1.05546i
\(344\) 1.85897e8 4.33587e8i 0.246217 0.574277i
\(345\) 6.64823e7 1.09988e8i 0.0871644 0.144205i
\(346\) −2.61419e8 + 1.07026e8i −0.339290 + 0.138907i
\(347\) 2.81294e8i 0.361416i 0.983537 + 0.180708i \(0.0578390\pi\)
−0.983537 + 0.180708i \(0.942161\pi\)
\(348\) −1.82652e8 7.68005e8i −0.232325 0.976870i
\(349\) 3.00712e8i 0.378671i −0.981912 0.189336i \(-0.939367\pi\)
0.981912 0.189336i \(-0.0606334\pi\)
\(350\) −4.06502e8 9.92914e8i −0.506786 1.23787i
\(351\) 1.98909e7 3.29707e8i 0.0245516 0.406962i
\(352\) −8.37323e8 + 3.26826e8i −1.02328 + 0.399408i
\(353\) 6.30246e8i 0.762603i −0.924451 0.381302i \(-0.875476\pi\)
0.924451 0.381302i \(-0.124524\pi\)
\(354\) −2.79858e8 4.37568e7i −0.335295 0.0524245i
\(355\) −1.03694e9 −1.23014
\(356\) 5.69143e8 + 5.78584e8i 0.668570 + 0.679659i
\(357\) 4.94151e8 8.17523e8i 0.574805 0.950958i
\(358\) 3.15134e8 + 7.69739e8i 0.362998 + 0.886652i
\(359\) −1.05605e7 −0.0120463 −0.00602316 0.999982i \(-0.501917\pi\)
−0.00602316 + 0.999982i \(0.501917\pi\)
\(360\) 1.50772e9 1.18434e8i 1.70318 0.133788i
\(361\) −4.30452e8 −0.481559
\(362\) 5.43156e8 + 1.32670e9i 0.601789 + 1.46992i
\(363\) 9.74068e7 1.61150e8i 0.106885 0.176830i
\(364\) 1.86439e8 1.83396e8i 0.202619 0.199313i
\(365\) 2.71874e8 0.292646
\(366\) −1.69224e9 2.64587e8i −1.80417 0.282089i
\(367\) 5.74355e8i 0.606526i 0.952907 + 0.303263i \(0.0980761\pi\)
−0.952907 + 0.303263i \(0.901924\pi\)
\(368\) −1.55110e6 + 9.42790e7i −0.00162245 + 0.0986161i
\(369\) 8.28785e7 4.35092e7i 0.0858716 0.0450805i
\(370\) −3.89321e7 9.50947e7i −0.0399578 0.0976001i
\(371\) 3.50863e8i 0.356721i
\(372\) −8.59068e8 + 2.04309e8i −0.865221 + 0.205772i
\(373\) 1.54165e9i 1.53817i −0.639148 0.769084i \(-0.720713\pi\)
0.639148 0.769084i \(-0.279287\pi\)
\(374\) 1.63931e9 6.71140e8i 1.62036 0.663380i
\(375\) −8.29137e8 + 1.37173e9i −0.811927 + 1.34325i
\(376\) −5.57015e8 + 1.29918e9i −0.540393 + 1.26041i
\(377\) 4.25914e8i 0.409380i
\(378\) −2.36054e8 6.92931e8i −0.224797 0.659885i
\(379\) 8.07688e8 0.762090 0.381045 0.924556i \(-0.375564\pi\)
0.381045 + 0.924556i \(0.375564\pi\)
\(380\) −9.38030e8 + 9.22725e8i −0.876949 + 0.862640i
\(381\) 8.53771e8 + 5.16060e8i 0.790868 + 0.478039i
\(382\) −4.53785e8 + 1.85781e8i −0.416513 + 0.170522i
\(383\) −7.50741e8 −0.682801 −0.341401 0.939918i \(-0.610901\pi\)
−0.341401 + 0.939918i \(0.610901\pi\)
\(384\) −9.12239e8 + 6.31658e8i −0.822147 + 0.569276i
\(385\) −1.46489e9 −1.30826
\(386\) −7.45006e8 + 3.05008e8i −0.659332 + 0.269933i
\(387\) 3.31158e8 + 6.30806e8i 0.290433 + 0.553232i
\(388\) 6.51486e8 6.40856e8i 0.566232 0.556992i
\(389\) −5.35813e8 −0.461519 −0.230760 0.973011i \(-0.574121\pi\)
−0.230760 + 0.973011i \(0.574121\pi\)
\(390\) −8.06159e8 1.26046e8i −0.688168 0.107597i
\(391\) 1.85823e8i 0.157210i
\(392\) −2.41565e8 + 5.63425e8i −0.202550 + 0.472427i
\(393\) 1.73531e9 + 1.04891e9i 1.44213 + 0.871692i
\(394\) 2.21767e8 9.07921e7i 0.182667 0.0747844i
\(395\) 6.08766e8i 0.497005i
\(396\) 4.14350e8 1.29265e9i 0.335300 1.04604i
\(397\) 1.67867e9i 1.34648i 0.739426 + 0.673238i \(0.235097\pi\)
−0.739426 + 0.673238i \(0.764903\pi\)
\(398\) 1.16962e8 + 2.85688e8i 0.0929936 + 0.227144i
\(399\) 5.45057e8 + 3.29459e8i 0.429573 + 0.259655i
\(400\) 4.04006e7 2.45563e9i 0.0315630 1.91846i
\(401\) 1.55050e9i 1.20079i −0.799705 0.600393i \(-0.795011\pi\)
0.799705 0.600393i \(-0.204989\pi\)
\(402\) 2.61126e8 1.67010e9i 0.200474 1.28219i
\(403\) 4.76415e8 0.362591
\(404\) 1.67130e9 1.64403e9i 1.26102 1.24044i
\(405\) −1.29704e9 + 1.87994e9i −0.970199 + 1.40621i
\(406\) 3.57633e8 + 8.73547e8i 0.265214 + 0.647807i
\(407\) −9.22293e7 −0.0678092
\(408\) 1.77705e9 1.27423e9i 1.29536 0.928830i
\(409\) 6.81961e8 0.492865 0.246432 0.969160i \(-0.420742\pi\)
0.246432 + 0.969160i \(0.420742\pi\)
\(410\) −8.76091e7 2.13992e8i −0.0627777 0.153340i
\(411\) −1.30145e9 7.86663e8i −0.924662 0.558910i
\(412\) −7.07406e8 7.19140e8i −0.498343 0.506609i
\(413\) 3.38693e8 0.236582
\(414\) −1.09025e8 9.16034e7i −0.0755133 0.0634469i
\(415\) 1.70787e9i 1.17297i
\(416\) 5.57670e8 2.17671e8i 0.379796 0.148243i
\(417\) 3.83751e8 6.34878e8i 0.259163 0.428760i
\(418\) 4.47461e8 + 1.09296e9i 0.299666 + 0.731959i
\(419\) 1.11095e8i 0.0737811i −0.999319 0.0368906i \(-0.988255\pi\)
0.999319 0.0368906i \(-0.0117453\pi\)
\(420\) −1.75927e9 + 4.18400e8i −1.15867 + 0.275562i
\(421\) 1.07896e9i 0.704722i −0.935864 0.352361i \(-0.885379\pi\)
0.935864 0.352361i \(-0.114621\pi\)
\(422\) 1.16026e9 4.75014e8i 0.751557 0.307690i
\(423\) −9.92267e8 1.89012e9i −0.637437 1.21422i
\(424\) −3.16485e8 + 7.38169e8i −0.201638 + 0.470300i
\(425\) 4.84003e9i 3.05835i
\(426\) −1.77482e8 + 1.13513e9i −0.111230 + 0.711399i
\(427\) 2.04800e9 1.27301
\(428\) 5.07279e8 + 5.15694e8i 0.312748 + 0.317935i
\(429\) −3.78848e8 + 6.26767e8i −0.231667 + 0.383271i
\(430\) 1.62874e9 6.66811e8i 0.987897 0.404448i
\(431\) −1.33369e9 −0.802388 −0.401194 0.915993i \(-0.631405\pi\)
−0.401194 + 0.915993i \(0.631405\pi\)
\(432\) 1.28411e8 1.67076e9i 0.0766315 0.997059i
\(433\) −5.75068e8 −0.340417 −0.170209 0.985408i \(-0.554444\pi\)
−0.170209 + 0.985408i \(0.554444\pi\)
\(434\) 9.77124e8 4.00038e8i 0.573767 0.234902i
\(435\) 1.52345e9 2.52040e9i 0.887395 1.46811i
\(436\) 4.71662e7 + 4.79485e7i 0.0272538 + 0.0277059i
\(437\) 1.23891e8 0.0710160
\(438\) 4.65337e7 2.97619e8i 0.0264611 0.169239i
\(439\) 2.40435e9i 1.35635i −0.734899 0.678176i \(-0.762771\pi\)
0.734899 0.678176i \(-0.237229\pi\)
\(440\) −3.08194e9 1.32136e9i −1.72480 0.739498i
\(441\) −4.30324e8 8.19702e8i −0.238924 0.455115i
\(442\) −1.09181e9 + 4.46990e8i −0.601406 + 0.246218i
\(443\) 1.19487e9i 0.652990i 0.945199 + 0.326495i \(0.105868\pi\)
−0.945199 + 0.326495i \(0.894132\pi\)
\(444\) −1.10763e8 + 2.63424e7i −0.0600559 + 0.0142829i
\(445\) 3.02775e9i 1.62877i
\(446\) 1.17071e9 + 2.85955e9i 0.624853 + 1.52625i
\(447\) 2.31036e8 3.82226e8i 0.122350 0.202415i
\(448\) 9.61003e8 9.14708e8i 0.504954 0.480629i
\(449\) 1.27909e9i 0.666867i −0.942774 0.333433i \(-0.891793\pi\)
0.942774 0.333433i \(-0.108207\pi\)
\(450\) 2.83970e9 + 2.38594e9i 1.46902 + 1.23429i
\(451\) −2.07544e8 −0.106535
\(452\) −2.41889e8 2.45902e8i −0.123206 0.125250i
\(453\) −4.04204e8 2.44320e8i −0.204294 0.123485i
\(454\) −5.67901e8 1.38714e9i −0.284824 0.695706i
\(455\) 9.75639e8 0.485567
\(456\) 8.49550e8 + 1.18479e9i 0.419577 + 0.585147i
\(457\) −1.30300e9 −0.638612 −0.319306 0.947652i \(-0.603450\pi\)
−0.319306 + 0.947652i \(0.603450\pi\)
\(458\) −1.38884e9 3.39235e9i −0.675496 1.64995i
\(459\) −1.98864e8 + 3.29632e9i −0.0959869 + 1.59106i
\(460\) −2.50775e8 + 2.46683e8i −0.120124 + 0.118164i
\(461\) 3.73192e9 1.77410 0.887052 0.461669i \(-0.152749\pi\)
0.887052 + 0.461669i \(0.152749\pi\)
\(462\) −2.50730e8 + 1.60361e9i −0.118293 + 0.756574i
\(463\) 1.78625e9i 0.836391i 0.908357 + 0.418196i \(0.137337\pi\)
−0.908357 + 0.418196i \(0.862663\pi\)
\(464\) −3.55437e7 + 2.16042e9i −0.0165177 + 1.00398i
\(465\) −2.81925e9 1.70409e9i −1.30031 0.785972i
\(466\) −2.38454e8 5.82443e8i −0.109158 0.266626i
\(467\) 1.96394e9i 0.892319i −0.894953 0.446159i \(-0.852791\pi\)
0.894953 0.446159i \(-0.147209\pi\)
\(468\) −2.75963e8 + 8.60925e8i −0.124449 + 0.388244i
\(469\) 2.02121e9i 0.904703i
\(470\) −4.88028e9 + 1.99800e9i −2.16822 + 0.887675i
\(471\) 7.33328e8 + 4.43259e8i 0.323389 + 0.195472i
\(472\) 7.12567e8 + 3.05508e8i 0.311909 + 0.133729i
\(473\) 1.57966e9i 0.686357i
\(474\) 6.66413e8 + 1.04196e8i 0.287422 + 0.0449394i
\(475\) −3.22693e9 −1.38154
\(476\) −1.86396e9 + 1.83355e9i −0.792159 + 0.779234i
\(477\) −5.63787e8 1.07393e9i −0.237849 0.453066i
\(478\) −3.61829e9 + 1.48134e9i −1.51532 + 0.620379i
\(479\) −2.97496e9 −1.23682 −0.618410 0.785856i \(-0.712223\pi\)
−0.618410 + 0.785856i \(0.712223\pi\)
\(480\) −4.07867e9 7.06635e8i −1.68335 0.291643i
\(481\) 6.14261e7 0.0251678
\(482\) 2.86502e8 1.17295e8i 0.116537 0.0477105i
\(483\) 1.45716e8 + 8.80781e7i 0.0588428 + 0.0355675i
\(484\) −3.67424e8 + 3.61428e8i −0.147302 + 0.144898i
\(485\) 3.40925e9 1.35695
\(486\) 1.83596e9 + 1.74163e9i 0.725499 + 0.688224i
\(487\) 1.25599e9i 0.492759i 0.969173 + 0.246379i \(0.0792409\pi\)
−0.969173 + 0.246379i \(0.920759\pi\)
\(488\) 4.30873e9 + 1.84734e9i 1.67834 + 0.719577i
\(489\) −1.20243e9 + 1.98931e9i −0.465029 + 0.769344i
\(490\) −2.11647e9 + 8.66489e8i −0.812691 + 0.332719i
\(491\) 2.96100e9i 1.12890i −0.825469 0.564448i \(-0.809089\pi\)
0.825469 0.564448i \(-0.190911\pi\)
\(492\) −2.49251e8 + 5.92785e7i −0.0943538 + 0.0224398i
\(493\) 4.25817e9i 1.60051i
\(494\) −2.98016e8 7.27927e8i −0.111223 0.271671i
\(495\) 4.48377e9 2.35387e9i 1.66159 0.872297i
\(496\) 2.41658e9 + 3.97581e7i 0.889234 + 0.0146299i
\(497\) 1.37377e9i 0.501959i
\(498\) −1.86960e9 2.92318e8i −0.678337 0.106060i
\(499\) 1.51883e9 0.547214 0.273607 0.961842i \(-0.411783\pi\)
0.273607 + 0.961842i \(0.411783\pi\)
\(500\) 3.12755e9 3.07652e9i 1.11895 1.10069i
\(501\) 2.32623e9 3.84852e9i 0.826459 1.36729i
\(502\) 1.26852e9 + 3.09847e9i 0.447544 + 1.09316i
\(503\) 5.67657e8 0.198883 0.0994417 0.995043i \(-0.468294\pi\)
0.0994417 + 0.995043i \(0.468294\pi\)
\(504\) 1.56906e8 + 1.99747e9i 0.0545923 + 0.694983i
\(505\) 8.74599e9 3.02196
\(506\) 1.19625e8 + 2.92193e8i 0.0410483 + 0.100264i
\(507\) −1.26565e9 + 2.09390e9i −0.431308 + 0.713555i
\(508\) −1.91484e9 1.94661e9i −0.648053 0.658802i
\(509\) −4.49543e9 −1.51098 −0.755490 0.655160i \(-0.772601\pi\)
−0.755490 + 0.655160i \(0.772601\pi\)
\(510\) 8.05976e9 + 1.26017e9i 2.69046 + 0.420662i
\(511\) 3.60188e8i 0.119414i
\(512\) 2.84691e9 1.05758e9i 0.937408 0.348233i
\(513\) −2.19772e9 1.32586e8i −0.718722 0.0433598i
\(514\) −1.16498e9 2.84555e9i −0.378396 0.924261i
\(515\) 3.76328e9i 1.21406i
\(516\) −4.51181e8 1.89710e9i −0.144570 0.607879i
\(517\) 4.73323e9i 1.50640i
\(518\) 1.25985e8 5.15786e7i 0.0398257 0.0163048i
\(519\) −6.04007e8 + 9.99270e8i −0.189652 + 0.313760i
\(520\) 2.05262e9 + 8.80046e8i 0.640171 + 0.274469i
\(521\) 2.67557e9i 0.828865i 0.910080 + 0.414432i \(0.136020\pi\)
−0.910080 + 0.414432i \(0.863980\pi\)
\(522\) −2.49832e9 2.09911e9i −0.768778 0.645934i
\(523\) −1.14640e9 −0.350414 −0.175207 0.984532i \(-0.556060\pi\)
−0.175207 + 0.984532i \(0.556060\pi\)
\(524\) −3.89197e9 3.95653e9i −1.18171 1.20131i
\(525\) −3.79539e9 2.29412e9i −1.14472 0.691924i
\(526\) 3.48311e9 1.42600e9i 1.04356 0.427237i
\(527\) −4.76306e9 −1.41758
\(528\) −1.97399e9 + 3.14762e9i −0.583615 + 0.930601i
\(529\) −3.37170e9 −0.990272
\(530\) −2.77288e9 + 1.13523e9i −0.809032 + 0.331220i
\(531\) −1.03668e9 + 5.44232e8i −0.300479 + 0.157744i
\(532\) −1.22246e9 1.24274e9i −0.352000 0.357839i
\(533\) 1.38228e8 0.0395412
\(534\) 3.31446e9 + 5.18228e8i 0.941930 + 0.147274i
\(535\) 2.69864e9i 0.761916i
\(536\) −1.82317e9 + 4.25235e9i −0.511388 + 1.19276i
\(537\) 2.94231e9 + 1.77848e9i 0.819934 + 0.495608i
\(538\) 3.80275e9 1.55686e9i 1.05283 0.431034i
\(539\) 2.05270e9i 0.564630i
\(540\) 4.71250e9 4.10754e9i 1.28787 1.12255i
\(541\) 3.82086e9i 1.03746i −0.854938 0.518730i \(-0.826405\pi\)
0.854938 0.518730i \(-0.173595\pi\)
\(542\) −2.46599e9 6.02338e9i −0.665264 1.62496i
\(543\) 5.07129e9 + 3.06533e9i 1.35931 + 0.821633i
\(544\) −5.57543e9 + 2.17621e9i −1.48485 + 0.579569i
\(545\) 2.50916e8i 0.0663959i
\(546\) 1.66990e8 1.06803e9i 0.0439052 0.280807i
\(547\) 2.86256e9 0.747823 0.373911 0.927464i \(-0.378016\pi\)
0.373911 + 0.927464i \(0.378016\pi\)
\(548\) 2.91891e9 + 2.96733e9i 0.757686 + 0.770254i
\(549\) −6.26857e9 + 3.29085e9i −1.61683 + 0.848799i
\(550\) −3.11580e9 7.61059e9i −0.798547 1.95051i
\(551\) 2.83900e9 0.722993
\(552\) 2.27120e8 + 3.16744e8i 0.0574736 + 0.0801533i
\(553\) −8.06515e8 −0.202803
\(554\) −1.51767e9 3.70703e9i −0.379222 0.926279i
\(555\) −3.63497e8 2.19716e8i −0.0902560 0.0545551i
\(556\) −1.44753e9 + 1.42391e9i −0.357162 + 0.351335i
\(557\) 1.15130e9 0.282289 0.141144 0.989989i \(-0.454922\pi\)
0.141144 + 0.989989i \(0.454922\pi\)
\(558\) −2.34800e9 + 2.79455e9i −0.572108 + 0.680913i
\(559\) 1.05208e9i 0.254746i
\(560\) 4.94887e9 + 8.14198e7i 1.19082 + 0.0195917i
\(561\) 3.78762e9 6.26624e9i 0.905725 1.49843i
\(562\) −1.41594e9 3.45856e9i −0.336488 0.821897i
\(563\) 7.38735e9i 1.74465i 0.488923 + 0.872327i \(0.337390\pi\)
−0.488923 + 0.872327i \(0.662610\pi\)
\(564\) 1.35190e9 + 5.68440e9i 0.317298 + 1.33416i
\(565\) 1.28681e9i 0.300155i
\(566\) −2.47582e9 + 1.01361e9i −0.573933 + 0.234970i
\(567\) −2.49061e9 1.71836e9i −0.573806 0.395890i
\(568\) 1.23917e9 2.89024e9i 0.283735 0.661782i
\(569\) 3.67854e9i 0.837109i −0.908192 0.418555i \(-0.862537\pi\)
0.908192 0.418555i \(-0.137463\pi\)
\(570\) −8.40178e8 + 5.37358e9i −0.190024 + 1.21535i
\(571\) 6.87971e9 1.54648 0.773239 0.634114i \(-0.218635\pi\)
0.773239 + 0.634114i \(0.218635\pi\)
\(572\) 1.42903e9 1.40572e9i 0.319269 0.314059i
\(573\) −1.04847e9 + 1.73458e9i −0.232816 + 0.385171i
\(574\) 2.83504e8 1.16068e8i 0.0625702 0.0256165i
\(575\) −8.62693e8 −0.189243
\(576\) −1.47165e9 + 4.34396e9i −0.320868 + 0.947124i
\(577\) 2.23949e9 0.485326 0.242663 0.970111i \(-0.421979\pi\)
0.242663 + 0.970111i \(0.421979\pi\)
\(578\) 6.61925e9 2.70994e9i 1.42581 0.583731i
\(579\) −1.72133e9 + 2.84777e9i −0.368544 + 0.609719i
\(580\) −5.74654e9 + 5.65278e9i −1.22295 + 1.20300i
\(581\) 2.26265e9 0.478630
\(582\) 5.83525e8 3.73209e9i 0.122696 0.784732i
\(583\) 2.68933e9i 0.562088i
\(584\) −3.24897e8 + 7.57788e8i −0.0674994 + 0.157435i
\(585\) −2.98626e9 + 1.56771e9i −0.616711 + 0.323759i
\(586\) 1.70060e9 6.96230e8i 0.349108 0.142926i
\(587\) 2.74509e9i 0.560174i 0.959975 + 0.280087i \(0.0903633\pi\)
−0.959975 + 0.280087i \(0.909637\pi\)
\(588\) 5.86289e8 + 2.46520e9i 0.118930 + 0.500070i
\(589\) 3.17562e9i 0.640360i
\(590\) 1.09585e9 + 2.67671e9i 0.219670 + 0.536561i
\(591\) 5.12390e8 8.47699e8i 0.102104 0.168922i
\(592\) 3.11580e8 + 5.12618e6i 0.0617226 + 0.00101547i
\(593\) 6.07047e9i 1.19545i 0.801702 + 0.597724i \(0.203928\pi\)
−0.801702 + 0.597724i \(0.796072\pi\)
\(594\) −1.80933e9 5.31125e9i −0.354214 1.03979i
\(595\) −9.75417e9 −1.89837
\(596\) −8.71479e8 + 8.57259e8i −0.168614 + 0.165863i
\(597\) 1.09204e9 + 6.60081e8i 0.210052 + 0.126966i
\(598\) −7.96720e7 1.94605e8i −0.0152353 0.0372135i
\(599\) 2.94693e9 0.560242 0.280121 0.959965i \(-0.409625\pi\)
0.280121 + 0.959965i \(0.409625\pi\)
\(600\) −5.91567e9 8.25005e9i −1.11808 1.55929i
\(601\) −9.07995e9 −1.70617 −0.853086 0.521771i \(-0.825272\pi\)
−0.853086 + 0.521771i \(0.825272\pi\)
\(602\) 8.83415e8 + 2.15781e9i 0.165035 + 0.403112i
\(603\) −3.24779e9 6.18656e9i −0.603223 1.14905i
\(604\) 9.06551e8 + 9.21588e8i 0.167403 + 0.170180i
\(605\) −1.92274e9 −0.353002
\(606\) 1.49696e9 9.57420e9i 0.273247 1.74762i
\(607\) 6.49347e9i 1.17846i 0.807964 + 0.589232i \(0.200570\pi\)
−0.807964 + 0.589232i \(0.799430\pi\)
\(608\) −1.45092e9 3.71723e9i −0.261807 0.670745i
\(609\) 3.33912e9 + 2.01832e9i 0.599061 + 0.362102i
\(610\) 6.62637e9 + 1.61854e10i 1.18201 + 2.88715i
\(611\) 3.15241e9i 0.559111i
\(612\) 2.75901e9 8.60729e9i 0.486545 1.51788i
\(613\) 6.06636e8i 0.106369i 0.998585 + 0.0531847i \(0.0169372\pi\)
−0.998585 + 0.0531847i \(0.983063\pi\)
\(614\) −2.08975e9 + 8.55550e8i −0.364338 + 0.149161i
\(615\) −8.17980e8 4.94427e8i −0.141801 0.0857115i
\(616\) 1.75058e9 4.08306e9i 0.301752 0.703806i
\(617\) 6.41175e9i 1.09895i 0.835510 + 0.549476i \(0.185173\pi\)
−0.835510 + 0.549476i \(0.814827\pi\)
\(618\) −4.11965e9 6.44121e8i −0.702102 0.109776i
\(619\) 2.94457e9 0.499005 0.249503 0.968374i \(-0.419733\pi\)
0.249503 + 0.968374i \(0.419733\pi\)
\(620\) 6.32303e9 + 6.42791e9i 1.06550 + 1.08318i
\(621\) −5.87541e8 3.54458e7i −0.0984504 0.00593942i
\(622\) −6.15914e9 + 2.52157e9i −1.02625 + 0.420151i
\(623\) −4.01127e9 −0.664620
\(624\) 1.31471e9 2.09636e9i 0.216612 0.345398i
\(625\) 4.65561e9 0.762775
\(626\) −1.00421e10 + 4.11126e9i −1.63611 + 0.669831i
\(627\) 4.17781e9 + 2.52527e9i 0.676881 + 0.409140i
\(628\) −1.64471e9 1.67200e9i −0.264991 0.269387i
\(629\) −6.14122e8 −0.0983959
\(630\) −4.80842e9 + 5.72289e9i −0.766144 + 0.911850i
\(631\) 8.02707e9i 1.27190i −0.771729 0.635952i \(-0.780608\pi\)
0.771729 0.635952i \(-0.219392\pi\)
\(632\) −1.69680e9 7.27492e8i −0.267375 0.114635i
\(633\) 2.68077e9 4.43507e9i 0.420094 0.695004i
\(634\) 6.24017e9 2.55475e9i 0.972487 0.398140i
\(635\) 1.01867e10i 1.57879i
\(636\) 7.68123e8 + 3.22976e9i 0.118394 + 0.497818i
\(637\) 1.36713e9i 0.209566i
\(638\) 2.74123e9 + 6.69566e9i 0.417900 + 1.02075i
\(639\) 2.20746e9 + 4.20488e9i 0.334688 + 0.637530i
\(640\) 1.03383e10 + 4.63528e9i 1.55891 + 0.698949i
\(641\) 5.90994e9i 0.886299i −0.896448 0.443149i \(-0.853861\pi\)
0.896448 0.443149i \(-0.146139\pi\)
\(642\) 2.95419e9 + 4.61898e8i 0.440622 + 0.0688927i
\(643\) −4.88948e9 −0.725311 −0.362656 0.931923i \(-0.618130\pi\)
−0.362656 + 0.931923i \(0.618130\pi\)
\(644\) −3.26814e8 3.32235e8i −0.0482170 0.0490168i
\(645\) 3.76319e9 6.22582e9i 0.552201 0.913561i
\(646\) 2.97948e9 + 7.27761e9i 0.434837 + 1.06212i
\(647\) −4.04673e9 −0.587408 −0.293704 0.955896i \(-0.594888\pi\)
−0.293704 + 0.955896i \(0.594888\pi\)
\(648\) −3.68992e9 5.86179e9i −0.532727 0.846287i
\(649\) 2.59605e9 0.372784
\(650\) 2.07517e9 + 5.06877e9i 0.296386 + 0.723946i
\(651\) 2.25764e9 3.73504e9i 0.320716 0.530593i
\(652\) 4.53564e9 4.46163e9i 0.640873 0.630416i
\(653\) 7.55767e9 1.06216 0.531082 0.847320i \(-0.321786\pi\)
0.531082 + 0.847320i \(0.321786\pi\)
\(654\) 2.74677e8 + 4.29467e7i 0.0383972 + 0.00600354i
\(655\) 2.07046e10i 2.87888i
\(656\) 7.01151e8 + 1.15355e7i 0.0969724 + 0.00159541i
\(657\) −5.78771e8 1.10247e9i −0.0796210 0.151666i
\(658\) −2.64703e9 6.46557e9i −0.362216 0.884741i
\(659\) 1.79440e9i 0.244242i −0.992515 0.122121i \(-0.961030\pi\)
0.992515 0.122121i \(-0.0389697\pi\)
\(660\) −1.34846e10 + 3.20700e9i −1.82572 + 0.434205i
\(661\) 1.49795e9i 0.201741i 0.994900 + 0.100870i \(0.0321627\pi\)
−0.994900 + 0.100870i \(0.967837\pi\)
\(662\) 1.28910e10 5.27763e9i 1.72697 0.707027i
\(663\) −2.52261e9 + 4.17341e9i −0.336166 + 0.556152i
\(664\) 4.76031e9 + 2.04095e9i 0.631026 + 0.270548i
\(665\) 6.50328e9i 0.857544i
\(666\) −3.02738e8 + 3.60313e8i −0.0397106 + 0.0472628i
\(667\) 7.58982e8 0.0990355
\(668\) −8.77467e9 + 8.63150e9i −1.13897 + 1.12039i
\(669\) 1.09306e10 + 6.60698e9i 1.41141 + 0.853123i
\(670\) −1.59737e10 + 6.53968e9i −2.05184 + 0.840029i
\(671\) 1.56978e10 2.00590
\(672\) 9.36175e8 5.40357e9i 0.119005 0.686892i
\(673\) −1.02064e10 −1.29069 −0.645343 0.763893i \(-0.723286\pi\)
−0.645343 + 0.763893i \(0.723286\pi\)
\(674\) −1.67390e9 + 6.85301e8i −0.210582 + 0.0862128i
\(675\) 1.53034e10 + 9.23236e8i 1.91524 + 0.115545i
\(676\) 4.77411e9 4.69621e9i 0.594400 0.584702i
\(677\) −2.46012e8 −0.0304716 −0.0152358 0.999884i \(-0.504850\pi\)
−0.0152358 + 0.999884i \(0.504850\pi\)
\(678\) −1.40867e9 2.20250e8i −0.173582 0.0271401i
\(679\) 4.51669e9i 0.553702i
\(680\) −2.05215e10 8.79846e9i −2.50281 1.07306i
\(681\) −5.30233e9 3.20498e9i −0.643356 0.388876i
\(682\) 7.48957e9 3.06625e9i 0.904089 0.370137i
\(683\) 7.16878e9i 0.860940i 0.902605 + 0.430470i \(0.141652\pi\)
−0.902605 + 0.430470i \(0.858348\pi\)
\(684\) 5.73863e9 + 1.83948e9i 0.685665 + 0.219785i
\(685\) 1.55281e10i 1.84588i
\(686\) −3.38125e9 8.25898e9i −0.399893 0.976769i
\(687\) −1.29672e10 7.83800e9i −1.52580 0.922267i
\(688\) −8.77990e7 + 5.33661e9i −0.0102785 + 0.624749i
\(689\) 1.79113e9i 0.208622i
\(690\) −2.24614e8 + 1.43658e9i −0.0260295 + 0.166479i
\(691\) −1.06347e10 −1.22617 −0.613087 0.790016i \(-0.710072\pi\)
−0.613087 + 0.790016i \(0.710072\pi\)
\(692\) 2.27835e9 2.24117e9i 0.261366 0.257101i
\(693\) 3.11849e9 + 5.94026e9i 0.355941 + 0.678014i
\(694\) −1.20578e9 2.94521e9i −0.136934 0.334471i
\(695\) −7.57497e9 −0.855922
\(696\) 5.20450e9 + 7.25824e9i 0.585122 + 0.816017i
\(697\) −1.38196e9 −0.154590
\(698\) 1.28902e9 + 3.14852e9i 0.143471 + 0.350439i
\(699\) −2.22638e9 1.34573e9i −0.246563 0.149035i
\(700\) 8.51234e9 + 8.65354e9i 0.938006 + 0.953565i
\(701\) −4.61502e8 −0.0506012 −0.0253006 0.999680i \(-0.508054\pi\)
−0.0253006 + 0.999680i \(0.508054\pi\)
\(702\) 1.20504e9 + 3.53737e9i 0.131469 + 0.385923i
\(703\) 4.09446e8i 0.0444480i
\(704\) 7.36600e9 7.01116e9i 0.795660 0.757330i
\(705\) −1.12759e10 + 1.86548e10i −1.21196 + 2.00506i
\(706\) 2.70158e9 + 6.59881e9i 0.288935 + 0.705748i
\(707\) 1.15870e10i 1.23311i
\(708\) 3.11774e9 7.41482e8i 0.330160 0.0785207i
\(709\) 1.37159e10i 1.44532i −0.691206 0.722658i \(-0.742920\pi\)
0.691206 0.722658i \(-0.257080\pi\)
\(710\) 1.08570e10 4.44489e9i 1.13843 0.466076i
\(711\) 2.46860e9 1.29595e9i 0.257577 0.135222i
\(712\) −8.43918e9 3.61824e9i −0.876234 0.375680i
\(713\) 8.48974e8i 0.0877165i
\(714\) −1.66952e9 + 1.06778e10i −0.171651 + 1.09784i
\(715\) 7.47819e9 0.765112
\(716\) −6.59904e9 6.70850e9i −0.671870 0.683015i
\(717\) −8.36002e9 + 1.38308e10i −0.847014 + 1.40130i
\(718\) 1.10571e8 4.52681e7i 0.0111482 0.00456412i
\(719\) −6.27355e8 −0.0629452 −0.0314726 0.999505i \(-0.510020\pi\)
−0.0314726 + 0.999505i \(0.510020\pi\)
\(720\) −1.52784e10 + 7.70292e9i −1.52551 + 0.769116i
\(721\) 4.98573e9 0.495399
\(722\) 4.50692e9 1.84515e9i 0.445656 0.182453i
\(723\) 6.61960e8 1.09515e9i 0.0651400 0.107768i
\(724\) −1.13739e10 1.15626e10i −1.11385 1.13232i
\(725\) −1.97688e10 −1.92662
\(726\) −3.29095e8 + 2.10481e9i −0.0319185 + 0.204144i
\(727\) 1.42234e10i 1.37288i −0.727184 0.686442i \(-0.759172\pi\)
0.727184 0.686442i \(-0.240828\pi\)
\(728\) −1.16592e9 + 2.71938e9i −0.111997 + 0.261222i
\(729\) 1.03845e10 + 1.25755e9i 0.992747 + 0.120221i
\(730\) −2.84658e9 + 1.16540e9i −0.270828 + 0.110878i
\(731\) 1.05184e10i 0.995953i
\(732\) 1.88523e10 4.48357e9i 1.77654 0.422508i
\(733\) 7.60365e9i 0.713113i 0.934274 + 0.356556i \(0.116049\pi\)
−0.934274 + 0.356556i \(0.883951\pi\)
\(734\) −2.46200e9 6.01363e9i −0.229801 0.561307i
\(735\) −4.89008e9 + 8.09016e9i −0.454266 + 0.751539i
\(736\) −3.87891e8 9.93771e8i −0.0358622 0.0918785i
\(737\) 1.54924e10i 1.42555i
\(738\) −6.81252e8 + 8.10814e8i −0.0623894 + 0.0742547i
\(739\) 3.49238e9 0.318321 0.159161 0.987253i \(-0.449121\pi\)
0.159161 + 0.987253i \(0.449121\pi\)
\(740\) 8.15255e8 + 8.28778e8i 0.0739575 + 0.0751843i
\(741\) −2.78249e9 1.68187e9i −0.251229 0.151855i
\(742\) −1.50399e9 3.67361e9i −0.135155 0.330126i
\(743\) 7.32860e9 0.655481 0.327741 0.944768i \(-0.393713\pi\)
0.327741 + 0.944768i \(0.393713\pi\)
\(744\) 8.11885e9 5.82159e9i 0.722752 0.518247i
\(745\) −4.56048e9 −0.404076
\(746\) 6.60833e9 + 1.61414e10i 0.582782 + 1.42349i
\(747\) −6.92556e9 + 3.63575e9i −0.607901 + 0.319133i
\(748\) −1.42871e10 + 1.40540e10i −1.24821 + 1.22785i
\(749\) −3.57526e9 −0.310900
\(750\) 2.80129e9 1.79164e10i 0.242462 1.55073i
\(751\) 7.77694e9i 0.669991i 0.942220 + 0.334996i \(0.108735\pi\)
−0.942220 + 0.334996i \(0.891265\pi\)
\(752\) 2.63077e8 1.59904e10i 0.0225590 1.37119i
\(753\) 1.18438e10 + 7.15899e9i 1.01090 + 0.611040i
\(754\) −1.82570e9 4.45941e9i −0.155106 0.378859i
\(755\) 4.82270e9i 0.407827i
\(756\) 5.44182e9 + 6.24328e9i 0.458055 + 0.525517i
\(757\) 1.65306e9i 0.138501i 0.997599 + 0.0692504i \(0.0220607\pi\)
−0.997599 + 0.0692504i \(0.977939\pi\)
\(758\) −8.45667e9 + 3.46219e9i −0.705273 + 0.288741i
\(759\) 1.11690e9 + 6.75110e8i 0.0927191 + 0.0560439i
\(760\) 5.86609e9 1.36820e10i 0.484731 1.13059i
\(761\) 1.81550e10i 1.49331i −0.665211 0.746655i \(-0.731659\pi\)
0.665211 0.746655i \(-0.268341\pi\)
\(762\) −1.11513e10 1.74354e9i −0.913025 0.142755i
\(763\) −3.32423e8 −0.0270929
\(764\) 3.95487e9 3.89034e9i 0.320853 0.315617i
\(765\) 2.98558e10 1.56736e10i 2.41109 1.26576i
\(766\) 7.86042e9 3.21808e9i 0.631895 0.258700i
\(767\) −1.72901e9 −0.138361
\(768\) 6.84372e9 1.05239e10i 0.545165 0.838329i
\(769\) 1.35979e10 1.07827 0.539137 0.842218i \(-0.318750\pi\)
0.539137 + 0.842218i \(0.318750\pi\)
\(770\) 1.53377e10 6.27932e9i 1.21072 0.495673i
\(771\) −1.08770e10 6.57461e9i −0.854714 0.516630i
\(772\) 6.49295e9 6.38700e9i 0.507904 0.499616i
\(773\) 9.94999e7 0.00774808 0.00387404 0.999992i \(-0.498767\pi\)
0.00387404 + 0.999992i \(0.498767\pi\)
\(774\) −6.17127e9 5.18515e9i −0.478389 0.401946i
\(775\) 2.21128e10i 1.70642i
\(776\) −4.07415e9 + 9.50253e9i −0.312983 + 0.730000i
\(777\) 2.91087e8 4.81574e8i 0.0222612 0.0368290i
\(778\) 5.61008e9 2.29679e9i 0.427111 0.174861i
\(779\) 9.21378e8i 0.0698324i
\(780\) 8.98096e9 2.13591e9i 0.677629 0.161158i
\(781\) 1.05299e10i 0.790940i
\(782\) 7.96539e8 + 1.94561e9i 0.0595639 + 0.145490i
\(783\) −1.34636e10 8.12247e8i −1.00229 0.0604675i
\(784\) 1.14091e8 6.93467e9i 0.00845559 0.513948i
\(785\) 8.74961e9i 0.645573i
\(786\) −2.26653e10 3.54379e9i −1.66488 0.260309i
\(787\) 1.60892e10 1.17658 0.588291 0.808650i \(-0.299801\pi\)
0.588291 + 0.808650i \(0.299801\pi\)
\(788\) −1.93276e9 + 1.90123e9i −0.140714 + 0.138418i
\(789\) 8.04770e9 1.33141e10i 0.583314 0.965035i
\(790\) −2.60950e9 6.37391e9i −0.188305 0.459951i
\(791\) 1.70481e9 0.122478
\(792\) 1.20267e9 + 1.53105e10i 0.0860215 + 1.09509i
\(793\) −1.04549e10 −0.744501
\(794\) −7.19570e9 1.75761e10i −0.510154 1.24609i
\(795\) −6.40672e9 + 1.05993e10i −0.452221 + 0.748155i
\(796\) −2.44923e9 2.48986e9i −0.172121 0.174976i
\(797\) −2.62634e10 −1.83758 −0.918791 0.394745i \(-0.870833\pi\)
−0.918791 + 0.394745i \(0.870833\pi\)
\(798\) −7.11911e9 1.11310e9i −0.495924 0.0775395i
\(799\) 3.15169e10i 2.18590i
\(800\) 1.01032e10 + 2.58842e10i 0.697659 + 1.78739i
\(801\) 1.22778e10 6.44554e9i 0.844124 0.443145i
\(802\) 6.64627e9 + 1.62340e10i 0.454954 + 1.11126i
\(803\) 2.76081e9i 0.188162i
\(804\) 4.42491e9 + 1.86056e10i 0.300267 + 1.26255i
\(805\) 1.73860e9i 0.117466i
\(806\) −4.98817e9 + 2.04217e9i −0.335558 + 0.137379i
\(807\) 8.78622e9 1.45359e10i 0.588498 0.973611i
\(808\) −1.04517e10 + 2.43775e10i −0.697023 + 1.62574i
\(809\) 6.29708e9i 0.418138i −0.977901 0.209069i \(-0.932957\pi\)
0.977901 0.209069i \(-0.0670433\pi\)
\(810\) 5.52185e9 2.52432e10i 0.365079 1.66896i
\(811\) 2.22720e10 1.46617 0.733087 0.680134i \(-0.238079\pi\)
0.733087 + 0.680134i \(0.238079\pi\)
\(812\) −7.48900e9 7.61322e9i −0.490883 0.499025i
\(813\) −2.30242e10 1.39170e10i −1.50269 0.908297i
\(814\) 9.65662e8 3.95345e8i 0.0627537 0.0256916i
\(815\) 2.37352e10 1.53582
\(816\) −1.31441e10 + 2.09588e10i −0.846866 + 1.35037i
\(817\) 7.01280e9 0.449898
\(818\) −7.14028e9 + 2.92325e9i −0.456119 + 0.186737i
\(819\) −2.07696e9 3.95630e9i −0.132110 0.251649i
\(820\) 1.83457e9 + 1.86500e9i 0.116195 + 0.118122i
\(821\) 6.22873e9 0.392825 0.196412 0.980521i \(-0.437071\pi\)
0.196412 + 0.980521i \(0.437071\pi\)
\(822\) 1.69986e10 + 2.65779e9i 1.06748 + 0.166905i
\(823\) 5.68307e9i 0.355372i −0.984087 0.177686i \(-0.943139\pi\)
0.984087 0.177686i \(-0.0568612\pi\)
\(824\) 1.04893e10 + 4.49723e9i 0.653134 + 0.280027i
\(825\) −2.90913e10 1.75842e10i −1.80374 1.09027i
\(826\) −3.54620e9 + 1.45182e9i −0.218944 + 0.0896363i
\(827\) 5.74742e9i 0.353349i 0.984269 + 0.176674i \(0.0565340\pi\)
−0.984269 + 0.176674i \(0.943466\pi\)
\(828\) 1.53417e9 + 4.91769e8i 0.0939222 + 0.0301061i
\(829\) 1.72035e10i 1.04876i −0.851484 0.524381i \(-0.824297\pi\)
0.851484 0.524381i \(-0.175703\pi\)
\(830\) 7.32086e9 + 1.78818e10i 0.444415 + 1.08552i
\(831\) −1.41700e10 8.56506e9i −0.856579 0.517758i
\(832\) −4.90587e9 + 4.66954e9i −0.295314 + 0.281088i
\(833\) 1.36682e10i 0.819318i
\(834\) −1.29653e9 + 8.29228e9i −0.0773928 + 0.494986i
\(835\) −4.59181e10 −2.72949
\(836\) −9.37003e9 9.52546e9i −0.554650 0.563850i
\(837\) −9.08555e8 + 1.50600e10i −0.0535565 + 0.887740i
\(838\) 4.76213e8 + 1.16319e9i 0.0279542 + 0.0682804i
\(839\) 1.00089e10 0.585085 0.292543 0.956252i \(-0.405499\pi\)
0.292543 + 0.956252i \(0.405499\pi\)
\(840\) 1.66264e10 1.19219e10i 0.967880 0.694015i
\(841\) 1.42324e8 0.00825073
\(842\) 4.62501e9 + 1.12969e10i 0.267005 + 0.652182i
\(843\) −1.32203e10 7.99097e9i −0.760052 0.459413i
\(844\) −1.01120e10 + 9.94701e9i −0.578947 + 0.569500i
\(845\) 2.49831e10 1.42445
\(846\) 1.84913e10 + 1.55366e10i 1.04996 + 0.882183i
\(847\) 2.54731e9i 0.144042i
\(848\) 1.49475e8 9.08542e9i 0.00841751 0.511634i
\(849\) −5.72036e9 + 9.46376e9i −0.320809 + 0.530746i
\(850\) −2.07470e10 5.06762e10i −1.15875 2.83033i
\(851\) 1.09462e8i 0.00608849i
\(852\) −3.00752e9 1.26459e10i −0.166598 0.700504i
\(853\) 4.78706e9i 0.264087i 0.991244 + 0.132044i \(0.0421539\pi\)
−0.991244 + 0.132044i \(0.957846\pi\)
\(854\) −2.14430e10 + 8.77885e9i −1.17810 + 0.482320i
\(855\) 1.04498e10 + 1.99054e10i 0.571779 + 1.08915i
\(856\) −7.52187e9 3.22495e9i −0.409890 0.175738i
\(857\) 6.87322e9i 0.373016i 0.982453 + 0.186508i \(0.0597171\pi\)
−0.982453 + 0.186508i \(0.940283\pi\)
\(858\) 1.27996e9 8.18634e9i 0.0691817 0.442470i
\(859\) −1.29437e10 −0.696760 −0.348380 0.937353i \(-0.613268\pi\)
−0.348380 + 0.937353i \(0.613268\pi\)
\(860\) −1.41949e10 + 1.39633e10i −0.761007 + 0.748590i
\(861\) 6.55034e8 1.08369e9i 0.0349746 0.0578620i
\(862\) 1.39640e10 5.71692e9i 0.742566 0.304009i
\(863\) 3.10825e10 1.64618 0.823091 0.567909i \(-0.192248\pi\)
0.823091 + 0.567909i \(0.192248\pi\)
\(864\) 5.81730e9 + 1.80437e10i 0.306848 + 0.951758i
\(865\) 1.19227e10 0.626350
\(866\) 6.02109e9 2.46505e9i 0.315037 0.128977i
\(867\) 1.52937e10 2.53020e10i 0.796979 1.31852i
\(868\) −8.51592e9 + 8.37697e9i −0.441990 + 0.434778i
\(869\) −6.18186e9 −0.319558
\(870\) −5.14708e9 + 3.29195e10i −0.264999 + 1.69487i
\(871\) 1.03182e10i 0.529101i
\(872\) −6.99374e8 2.99852e8i −0.0357192 0.0153144i
\(873\) −7.25768e9 1.38248e10i −0.369189 0.703249i
\(874\) −1.29717e9 + 5.31066e8i −0.0657215 + 0.0269066i
\(875\) 2.16830e10i 1.09419i
\(876\) 7.88538e8 + 3.31560e9i 0.0396331 + 0.166647i
\(877\) 1.59764e10i 0.799799i 0.916559 + 0.399900i \(0.130955\pi\)
−0.916559 + 0.399900i \(0.869045\pi\)
\(878\) 1.03064e10 + 2.51741e10i 0.513896 + 1.25523i
\(879\) 3.92922e9 6.50050e9i 0.195139 0.322839i
\(880\) 3.79326e10 + 6.24076e8i 1.87639 + 0.0308708i
\(881\) 2.70049e10i 1.33054i 0.746604 + 0.665269i \(0.231683\pi\)
−0.746604 + 0.665269i \(0.768317\pi\)
\(882\) 8.01928e9 + 6.73786e9i 0.393546 + 0.330660i
\(883\) 1.73646e10 0.848794 0.424397 0.905476i \(-0.360486\pi\)
0.424397 + 0.905476i \(0.360486\pi\)
\(884\) 9.51542e9 9.36016e9i 0.463282 0.455722i
\(885\) 1.02317e10 + 6.18451e9i 0.496186 + 0.299919i
\(886\) −5.12185e9 1.25105e10i −0.247405 0.604306i
\(887\) −2.27435e10 −1.09427 −0.547136 0.837043i \(-0.684282\pi\)
−0.547136 + 0.837043i \(0.684282\pi\)
\(888\) 1.04680e9 7.50603e8i 0.0501669 0.0359720i
\(889\) 1.34956e10 0.644224
\(890\) −1.29786e10 3.17012e10i −0.617109 1.50734i
\(891\) −1.90903e10 1.31711e10i −0.904151 0.623807i
\(892\) −2.45152e10 2.49219e10i −1.15653 1.17572i
\(893\) −2.10129e10 −0.987427
\(894\) −7.80568e8 + 4.99233e9i −0.0365367 + 0.233680i
\(895\) 3.51058e10i 1.63681i
\(896\) −6.14098e9 + 1.36966e10i −0.285206 + 0.636113i
\(897\) −7.43874e8 4.49634e8i −0.0344133 0.0208011i
\(898\) 5.48288e9 + 1.33924e10i 0.252663 + 0.617149i
\(899\) 1.94544e10i 0.893015i
\(900\) −3.99598e10 1.28088e10i −1.82715 0.585680i
\(901\) 1.79073e10i 0.815629i
\(902\) 2.17303e9 8.89648e8i 0.0985924 0.0403641i
\(903\) 8.24819e9 + 4.98560e9i 0.372779 + 0.225326i
\(904\) 3.58671e9 + 1.53778e9i 0.161475 + 0.0692315i
\(905\) 6.05074e10i 2.71355i
\(906\) 5.27939e9 + 8.25451e8i 0.235850 + 0.0368759i
\(907\) 1.70413e10 0.758362 0.379181 0.925322i \(-0.376206\pi\)
0.379181 + 0.925322i \(0.376206\pi\)
\(908\) 1.18921e10 + 1.20894e10i 0.527179 + 0.535924i
\(909\) −1.86187e10 3.54658e10i −0.822195 1.56616i
\(910\) −1.02152e10 + 4.18212e9i −0.449366 + 0.183972i
\(911\) −1.00724e10 −0.441385 −0.220692 0.975343i \(-0.570832\pi\)
−0.220692 + 0.975343i \(0.570832\pi\)
\(912\) −1.39736e10 8.76339e9i −0.609997 0.382552i
\(913\) 1.73430e10 0.754182
\(914\) 1.36427e10 5.58536e9i 0.591000 0.241958i
\(915\) 6.18685e10 + 3.73963e10i 2.66991 + 1.61382i
\(916\) 2.90829e10 + 2.95653e10i 1.25027 + 1.27101i
\(917\) 2.74302e10 1.17473
\(918\) −1.20477e10 3.53657e10i −0.513990 1.50880i
\(919\) 3.16312e10i 1.34435i 0.740393 + 0.672174i \(0.234639\pi\)
−0.740393 + 0.672174i \(0.765361\pi\)
\(920\) 1.56825e9 3.65778e9i 0.0663984 0.154867i
\(921\) −4.82835e9 + 7.98802e9i −0.203653 + 0.336923i
\(922\) −3.90740e10 + 1.59970e10i −1.64184 + 0.672174i
\(923\) 7.01304e9i 0.293562i
\(924\) −4.24874e9 1.78649e10i −0.177178 0.744987i
\(925\) 2.85109e9i 0.118445i
\(926\) −7.65685e9 1.87025e10i −0.316892 0.774034i
\(927\) −1.52604e10 + 8.01136e9i −0.629199 + 0.330314i
\(928\) −8.88859e9 2.27724e10i −0.365103 0.935388i
\(929\) 1.74385e10i 0.713597i 0.934181 + 0.356799i \(0.116132\pi\)
−0.934181 + 0.356799i \(0.883868\pi\)
\(930\) 3.68228e10 + 5.75737e9i 1.50116 + 0.234711i
\(931\) −9.11280e9 −0.370108
\(932\) 4.99334e9 + 5.07616e9i 0.202039 + 0.205390i
\(933\) −1.42307e10 + 2.35432e10i −0.573640 + 0.949029i
\(934\) 8.41854e9 + 2.05629e10i 0.338082 + 0.825793i
\(935\) −7.47648e10 −2.99128
\(936\) −8.00994e8 1.01970e10i −0.0319274 0.406450i
\(937\) −3.67462e10 −1.45923 −0.729615 0.683858i \(-0.760301\pi\)
−0.729615 + 0.683858i \(0.760301\pi\)
\(938\) −8.66400e9 2.11625e10i −0.342774 0.837253i
\(939\) −2.32022e10 + 3.83857e10i −0.914532 + 1.51300i
\(940\) 4.25331e10 4.18391e10i 1.67024 1.64299i
\(941\) −9.56897e8 −0.0374371 −0.0187185 0.999825i \(-0.505959\pi\)
−0.0187185 + 0.999825i \(0.505959\pi\)
\(942\) −9.57816e9 1.49758e9i −0.373340 0.0583729i
\(943\) 2.46323e8i 0.00956563i
\(944\) −8.77030e9 1.44291e8i −0.339323 0.00558261i
\(945\) −1.86061e9 + 3.08410e10i −0.0717206 + 1.18882i
\(946\) 6.77129e9 + 1.65394e10i 0.260047 + 0.635186i
\(947\) 4.40484e10i 1.68541i −0.538377 0.842704i \(-0.680962\pi\)
0.538377 0.842704i \(-0.319038\pi\)
\(948\) −7.42414e9 + 1.76565e9i −0.283020 + 0.0673095i
\(949\) 1.83874e9i 0.0698375i
\(950\) 3.37867e10 1.38324e10i 1.27854 0.523437i
\(951\) 1.44179e10 2.38529e10i 0.543587 0.899311i
\(952\) 1.16565e10 2.71876e10i 0.437864 1.02127i
\(953\) 1.16259e10i 0.435113i 0.976048 + 0.217557i \(0.0698087\pi\)
−0.976048 + 0.217557i \(0.930191\pi\)
\(954\) 1.05064e10 + 8.82757e9i 0.391774 + 0.329171i
\(955\) 2.06960e10 0.768907
\(956\) 3.15344e10 3.10199e10i 1.16730 1.14825i
\(957\) 2.55940e10 + 1.54703e10i 0.943945 + 0.570567i
\(958\) 3.11484e10 1.27523e10i 1.14461 0.468607i
\(959\) −2.05722e10 −0.753210
\(960\) 4.57336e10 1.00848e10i 1.66835 0.367889i
\(961\) 5.75150e9 0.209050
\(962\) −6.43145e8 + 2.63306e8i −0.0232914 + 0.00953560i
\(963\) 1.09432e10 5.74493e9i 0.394869 0.207297i
\(964\) −2.49695e9 + 2.45620e9i −0.0897717 + 0.0883070i
\(965\) 3.39778e10 1.21717
\(966\) −1.90323e9 2.97577e8i −0.0679316 0.0106213i
\(967\) 1.71012e10i 0.608183i −0.952643 0.304092i \(-0.901647\pi\)
0.952643 0.304092i \(-0.0983529\pi\)
\(968\) 2.29773e9 5.35921e9i 0.0814207 0.189905i
\(969\) 2.78185e10 + 1.68149e10i 0.982202 + 0.593691i
\(970\) −3.56956e10 + 1.46139e10i −1.25578 + 0.514120i
\(971\) 2.77609e10i 0.973121i 0.873647 + 0.486560i \(0.161749\pi\)
−0.873647 + 0.486560i \(0.838251\pi\)
\(972\) −2.66885e10 1.03654e10i −0.932164 0.362036i
\(973\) 1.00356e10i 0.349259i
\(974\) −5.38385e9 1.31505e10i −0.186697 0.456021i
\(975\) 1.93753e10 + 1.17114e10i 0.669471 + 0.404661i
\(976\) −5.30320e10 8.72494e8i −1.82585 0.0300392i
\(977\) 3.13262e10i 1.07467i 0.843368 + 0.537337i \(0.180570\pi\)
−0.843368 + 0.537337i \(0.819430\pi\)
\(978\) 4.06250e9 2.59828e10i 0.138870 0.888177i
\(979\) −3.07460e10 −1.04725
\(980\) 1.84456e10 1.81447e10i 0.626041 0.615826i
\(981\) 1.01749e9 5.34156e8i 0.0344102 0.0180645i
\(982\) 1.26925e10 + 3.10024e10i 0.427717 + 1.04473i
\(983\) 4.78593e9 0.160705 0.0803524 0.996767i \(-0.474395\pi\)
0.0803524 + 0.996767i \(0.474395\pi\)
\(984\) 2.35562e9 1.68909e9i 0.0788173 0.0565157i
\(985\) −1.01142e10 −0.337214
\(986\) 1.82528e10 + 4.45840e10i 0.606403 + 1.48119i
\(987\) −2.47145e10 1.49387e10i −0.818167 0.494540i
\(988\) 6.24058e9 + 6.34410e9i 0.205862 + 0.209277i
\(989\) 1.87481e9 0.0616270
\(990\) −3.68561e10 + 4.38654e10i −1.20722 + 1.43681i
\(991\) 1.38921e10i 0.453431i −0.973961 0.226715i \(-0.927201\pi\)
0.973961 0.226715i \(-0.0727987\pi\)
\(992\) −2.54726e10 + 9.94251e9i −0.828480 + 0.323374i
\(993\) 2.97846e10 4.92757e10i 0.965316 1.59702i
\(994\) 5.88874e9 + 1.43837e10i 0.190182 + 0.464535i
\(995\) 1.30295e10i 0.419321i
\(996\) 2.08281e10 4.95348e9i 0.667948 0.158856i
\(997\) 2.60033e10i 0.830989i 0.909596 + 0.415494i \(0.136391\pi\)
−0.909596 + 0.415494i \(0.863609\pi\)
\(998\) −1.59025e10 + 6.51053e9i −0.506417 + 0.207329i
\(999\) −1.17144e8 + 1.94175e9i −0.00371741 + 0.0616189i
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.11.4 yes 20
3.2 odd 2 inner 24.8.f.c.11.17 yes 20
4.3 odd 2 96.8.f.c.47.14 20
8.3 odd 2 inner 24.8.f.c.11.18 yes 20
8.5 even 2 96.8.f.c.47.13 20
12.11 even 2 96.8.f.c.47.15 20
24.5 odd 2 96.8.f.c.47.16 20
24.11 even 2 inner 24.8.f.c.11.3 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
24.8.f.c.11.3 20 24.11 even 2 inner
24.8.f.c.11.4 yes 20 1.1 even 1 trivial
24.8.f.c.11.17 yes 20 3.2 odd 2 inner
24.8.f.c.11.18 yes 20 8.3 odd 2 inner
96.8.f.c.47.13 20 8.5 even 2
96.8.f.c.47.14 20 4.3 odd 2
96.8.f.c.47.15 20 12.11 even 2
96.8.f.c.47.16 20 24.5 odd 2