Properties

Label 8.10.b.a.5.2
Level 8
Weight 10
Character 8.5
Analytic conductor 4.120
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 8.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.12028668931\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{28}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.2
Root \(9.73909 - 3.55976i\)
Character \(\chi\) = 8.5
Dual form 8.10.b.a.5.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-21.4782 + 7.11952i) q^{2} -100.481i q^{3} +(410.625 - 305.829i) q^{4} +2583.09i q^{5} +(715.380 + 2158.16i) q^{6} +6967.65 q^{7} +(-6642.12 + 9492.10i) q^{8} +9586.48 q^{9} +O(q^{10})\) \(q+(-21.4782 + 7.11952i) q^{2} -100.481i q^{3} +(410.625 - 305.829i) q^{4} +2583.09i q^{5} +(715.380 + 2158.16i) q^{6} +6967.65 q^{7} +(-6642.12 + 9492.10i) q^{8} +9586.48 q^{9} +(-18390.4 - 55480.1i) q^{10} +25054.5i q^{11} +(-30730.1 - 41260.2i) q^{12} +29701.4i q^{13} +(-149652. + 49606.3i) q^{14} +259553. q^{15} +(75081.4 - 251162. i) q^{16} -138527. q^{17} +(-205900. + 68251.2i) q^{18} +489569. i q^{19} +(789984. + 1.06068e6i) q^{20} -700119. i q^{21} +(-178376. - 538124. i) q^{22} +847079. q^{23} +(953780. + 667409. i) q^{24} -4.71924e6 q^{25} +(-211460. - 637933. i) q^{26} -2.94104e6i q^{27} +(2.86109e6 - 2.13091e6i) q^{28} -1.13646e6i q^{29} +(-5.57472e6 + 1.84789e6i) q^{30} +4.35747e6 q^{31} +(175542. + 5.92904e6i) q^{32} +2.51751e6 q^{33} +(2.97532e6 - 986249. i) q^{34} +1.79981e7i q^{35} +(3.93645e6 - 2.93182e6i) q^{36} +535315. i q^{37} +(-3.48550e6 - 1.05151e7i) q^{38} +2.98444e6 q^{39} +(-2.45190e7 - 1.71572e7i) q^{40} +1.45816e7 q^{41} +(4.98451e6 + 1.50373e7i) q^{42} -3.96441e7i q^{43} +(7.66238e6 + 1.02880e7i) q^{44} +2.47628e7i q^{45} +(-1.81937e7 + 6.03080e6i) q^{46} -4.48997e7 q^{47} +(-2.52371e7 - 7.54428e6i) q^{48} +8.19448e6 q^{49} +(1.01361e8 - 3.35988e7i) q^{50} +1.39194e7i q^{51} +(9.08355e6 + 1.21961e7i) q^{52} -4.85666e7i q^{53} +(2.09388e7 + 6.31682e7i) q^{54} -6.47180e7 q^{55} +(-4.62799e7 + 6.61376e7i) q^{56} +4.91926e7 q^{57} +(8.09108e6 + 2.44092e7i) q^{58} -4.19685e6i q^{59} +(1.06579e8 - 7.93787e7i) q^{60} +6.38659e7i q^{61} +(-9.35906e7 + 3.10231e7i) q^{62} +6.67952e7 q^{63} +(-4.59823e7 - 1.26095e8i) q^{64} -7.67215e7 q^{65} +(-5.40715e7 + 1.79235e7i) q^{66} -5.79621e7i q^{67} +(-5.68828e7 + 4.23657e7i) q^{68} -8.51157e7i q^{69} +(-1.28138e8 - 3.86566e8i) q^{70} +2.74912e8 q^{71} +(-6.36745e7 + 9.09959e7i) q^{72} -9.16969e7 q^{73} +(-3.81119e6 - 1.14976e7i) q^{74} +4.74196e8i q^{75} +(1.49724e8 + 2.01029e8i) q^{76} +1.74571e8i q^{77} +(-6.41004e7 + 2.12478e7i) q^{78} +2.02396e8 q^{79} +(6.48774e8 + 1.93942e8i) q^{80} -1.06829e8 q^{81} +(-3.13186e8 + 1.03814e8i) q^{82} -6.11053e8i q^{83} +(-2.14117e8 - 2.87486e8i) q^{84} -3.57829e8i q^{85} +(2.82247e8 + 8.51483e8i) q^{86} -1.14193e8 q^{87} +(-2.37819e8 - 1.66415e8i) q^{88} -7.71588e8 q^{89} +(-1.76299e8 - 5.31859e8i) q^{90} +2.06949e8i q^{91} +(3.47831e8 - 2.59061e8i) q^{92} -4.37845e8i q^{93} +(9.64363e8 - 3.19664e8i) q^{94} -1.26460e9 q^{95} +(5.95759e8 - 1.76387e7i) q^{96} +1.08292e9 q^{97} +(-1.76003e8 + 5.83408e7i) q^{98} +2.40184e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 18q^{2} - 428q^{4} + 4684q^{6} + 4800q^{7} - 3384q^{8} - 39368q^{9} + O(q^{10}) \) \( 8q - 18q^{2} - 428q^{4} + 4684q^{6} + 4800q^{7} - 3384q^{8} - 39368q^{9} + 26392q^{10} + 54760q^{12} - 72336q^{14} - 163136q^{15} + 185616q^{16} - 102000q^{17} - 23614q^{18} + 1245264q^{20} - 2373124q^{22} + 3412032q^{23} - 3961456q^{24} - 2423384q^{25} + 4551240q^{26} + 7509920q^{28} - 15284368q^{30} + 803584q^{31} - 14113248q^{32} + 58272q^{33} + 27757244q^{34} + 57226188q^{36} - 63661140q^{38} - 17590208q^{39} - 93063648q^{40} - 2180784q^{41} + 127541344q^{42} + 114013320q^{44} - 131840944q^{46} + 7432320q^{47} - 217917408q^{48} + 24436680q^{49} + 231784902q^{50} + 219270896q^{52} - 362934280q^{54} + 7056832q^{55} - 358503360q^{56} + 134003744q^{57} + 375425192q^{58} + 516952992q^{60} - 344291904q^{62} - 223198400q^{63} - 316815296q^{64} - 146501760q^{65} + 239713176q^{66} + 79875048q^{68} - 56202048q^{70} + 560234688q^{71} + 112273016q^{72} - 523987120q^{73} - 65773608q^{74} - 87532760q^{76} + 318117968q^{78} - 248943744q^{79} + 890441280q^{80} + 231960296q^{81} - 1051981172q^{82} - 1275608768q^{84} + 1492810428q^{86} + 540527424q^{87} + 1544767952q^{88} + 744827856q^{89} - 3218579800q^{90} - 2959012128q^{92} + 3068552352q^{94} - 1465245504q^{95} + 4296343616q^{96} - 9932784q^{97} - 3062604162q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −21.4782 + 7.11952i −0.949211 + 0.314642i
\(3\) 100.481i 0.716210i −0.933681 0.358105i \(-0.883423\pi\)
0.933681 0.358105i \(-0.116577\pi\)
\(4\) 410.625 305.829i 0.802001 0.597322i
\(5\) 2583.09i 1.84831i 0.382017 + 0.924155i \(0.375230\pi\)
−0.382017 + 0.924155i \(0.624770\pi\)
\(6\) 715.380 + 2158.16i 0.225349 + 0.679834i
\(7\) 6967.65 1.09684 0.548422 0.836202i \(-0.315229\pi\)
0.548422 + 0.836202i \(0.315229\pi\)
\(8\) −6642.12 + 9492.10i −0.573326 + 0.819327i
\(9\) 9586.48 0.487044
\(10\) −18390.4 55480.1i −0.581555 1.75444i
\(11\) 25054.5i 0.515962i 0.966150 + 0.257981i \(0.0830572\pi\)
−0.966150 + 0.257981i \(0.916943\pi\)
\(12\) −30730.1 41260.2i −0.427808 0.574401i
\(13\) 29701.4i 0.288425i 0.989547 + 0.144212i \(0.0460648\pi\)
−0.989547 + 0.144212i \(0.953935\pi\)
\(14\) −149652. + 49606.3i −1.04114 + 0.345113i
\(15\) 259553. 1.32378
\(16\) 75081.4 251162.i 0.286413 0.958106i
\(17\) −138527. −0.402268 −0.201134 0.979564i \(-0.564463\pi\)
−0.201134 + 0.979564i \(0.564463\pi\)
\(18\) −205900. + 68251.2i −0.462307 + 0.153244i
\(19\) 489569.i 0.861832i 0.902392 + 0.430916i \(0.141809\pi\)
−0.902392 + 0.430916i \(0.858191\pi\)
\(20\) 789984. + 1.06068e6i 1.10404 + 1.48235i
\(21\) 700119.i 0.785570i
\(22\) −178376. 538124.i −0.162343 0.489757i
\(23\) 847079. 0.631173 0.315587 0.948897i \(-0.397799\pi\)
0.315587 + 0.948897i \(0.397799\pi\)
\(24\) 953780. + 667409.i 0.586810 + 0.410622i
\(25\) −4.71924e6 −2.41625
\(26\) −211460. 637933.i −0.0907503 0.273776i
\(27\) 2.94104e6i 1.06504i
\(28\) 2.86109e6 2.13091e6i 0.879671 0.655169i
\(29\) 1.13646e6i 0.298376i −0.988809 0.149188i \(-0.952334\pi\)
0.988809 0.149188i \(-0.0476660\pi\)
\(30\) −5.57472e6 + 1.84789e6i −1.25654 + 0.416515i
\(31\) 4.35747e6 0.847436 0.423718 0.905794i \(-0.360725\pi\)
0.423718 + 0.905794i \(0.360725\pi\)
\(32\) 175542. + 5.92904e6i 0.0295941 + 0.999562i
\(33\) 2.51751e6 0.369537
\(34\) 2.97532e6 986249.i 0.381837 0.126570i
\(35\) 1.79981e7i 2.02731i
\(36\) 3.93645e6 2.93182e6i 0.390610 0.290922i
\(37\) 535315.i 0.0469571i 0.999724 + 0.0234786i \(0.00747415\pi\)
−0.999724 + 0.0234786i \(0.992526\pi\)
\(38\) −3.48550e6 1.05151e7i −0.271168 0.818060i
\(39\) 2.98444e6 0.206572
\(40\) −2.45190e7 1.71572e7i −1.51437 1.05968i
\(41\) 1.45816e7 0.805894 0.402947 0.915223i \(-0.367986\pi\)
0.402947 + 0.915223i \(0.367986\pi\)
\(42\) 4.98451e6 + 1.50373e7i 0.247173 + 0.745672i
\(43\) 3.96441e7i 1.76836i −0.467148 0.884179i \(-0.654719\pi\)
0.467148 0.884179i \(-0.345281\pi\)
\(44\) 7.66238e6 + 1.02880e7i 0.308196 + 0.413802i
\(45\) 2.47628e7i 0.900208i
\(46\) −1.81937e7 + 6.03080e6i −0.599116 + 0.198593i
\(47\) −4.48997e7 −1.34216 −0.671078 0.741387i \(-0.734168\pi\)
−0.671078 + 0.741387i \(0.734168\pi\)
\(48\) −2.52371e7 7.54428e6i −0.686205 0.205131i
\(49\) 8.19448e6 0.203067
\(50\) 1.01361e8 3.35988e7i 2.29353 0.760253i
\(51\) 1.39194e7i 0.288108i
\(52\) 9.08355e6 + 1.21961e7i 0.172282 + 0.231317i
\(53\) 4.85666e7i 0.845466i −0.906254 0.422733i \(-0.861071\pi\)
0.906254 0.422733i \(-0.138929\pi\)
\(54\) 2.09388e7 + 6.31682e7i 0.335104 + 1.01094i
\(55\) −6.47180e7 −0.953658
\(56\) −4.62799e7 + 6.61376e7i −0.628849 + 0.898674i
\(57\) 4.91926e7 0.617252
\(58\) 8.09108e6 + 2.44092e7i 0.0938816 + 0.283222i
\(59\) 4.19685e6i 0.0450910i −0.999746 0.0225455i \(-0.992823\pi\)
0.999746 0.0225455i \(-0.00717706\pi\)
\(60\) 1.06579e8 7.93787e7i 1.06167 0.790722i
\(61\) 6.38659e7i 0.590588i 0.955406 + 0.295294i \(0.0954176\pi\)
−0.955406 + 0.295294i \(0.904582\pi\)
\(62\) −9.35906e7 + 3.10231e7i −0.804395 + 0.266638i
\(63\) 6.67952e7 0.534211
\(64\) −4.59823e7 1.26095e8i −0.342595 0.939483i
\(65\) −7.67215e7 −0.533098
\(66\) −5.40715e7 + 1.79235e7i −0.350768 + 0.116272i
\(67\) 5.79621e7i 0.351404i −0.984443 0.175702i \(-0.943780\pi\)
0.984443 0.175702i \(-0.0562196\pi\)
\(68\) −5.68828e7 + 4.23657e7i −0.322619 + 0.240284i
\(69\) 8.51157e7i 0.452052i
\(70\) −1.28138e8 3.86566e8i −0.637875 1.92434i
\(71\) 2.74912e8 1.28390 0.641950 0.766746i \(-0.278125\pi\)
0.641950 + 0.766746i \(0.278125\pi\)
\(72\) −6.36745e7 + 9.09959e7i −0.279235 + 0.399048i
\(73\) −9.16969e7 −0.377921 −0.188961 0.981985i \(-0.560512\pi\)
−0.188961 + 0.981985i \(0.560512\pi\)
\(74\) −3.81119e6 1.14976e7i −0.0147747 0.0445722i
\(75\) 4.74196e8i 1.73054i
\(76\) 1.49724e8 + 2.01029e8i 0.514791 + 0.691191i
\(77\) 1.74571e8i 0.565930i
\(78\) −6.41004e7 + 2.12478e7i −0.196081 + 0.0649962i
\(79\) 2.02396e8 0.584627 0.292314 0.956322i \(-0.405575\pi\)
0.292314 + 0.956322i \(0.405575\pi\)
\(80\) 6.48774e8 + 1.93942e8i 1.77088 + 0.529379i
\(81\) −1.06829e8 −0.275744
\(82\) −3.13186e8 + 1.03814e8i −0.764963 + 0.253568i
\(83\) 6.11053e8i 1.41328i −0.707574 0.706639i \(-0.750210\pi\)
0.707574 0.706639i \(-0.249790\pi\)
\(84\) −2.14117e8 2.87486e8i −0.469238 0.630028i
\(85\) 3.57829e8i 0.743516i
\(86\) 2.82247e8 + 8.51483e8i 0.556399 + 1.67854i
\(87\) −1.14193e8 −0.213700
\(88\) −2.37819e8 1.66415e8i −0.422742 0.295814i
\(89\) −7.71588e8 −1.30356 −0.651779 0.758409i \(-0.725977\pi\)
−0.651779 + 0.758409i \(0.725977\pi\)
\(90\) −1.76299e8 5.31859e8i −0.283243 0.854487i
\(91\) 2.06949e8i 0.316357i
\(92\) 3.47831e8 2.59061e8i 0.506202 0.377014i
\(93\) 4.37845e8i 0.606942i
\(94\) 9.64363e8 3.19664e8i 1.27399 0.422298i
\(95\) −1.26460e9 −1.59293
\(96\) 5.95759e8 1.76387e7i 0.715896 0.0211956i
\(97\) 1.08292e9 1.24200 0.621001 0.783810i \(-0.286726\pi\)
0.621001 + 0.783810i \(0.286726\pi\)
\(98\) −1.76003e8 + 5.83408e7i −0.192753 + 0.0638933i
\(99\) 2.40184e8i 0.251296i
\(100\) −1.93784e9 + 1.44328e9i −1.93784 + 1.44328i
\(101\) 6.22244e8i 0.594996i 0.954722 + 0.297498i \(0.0961522\pi\)
−0.954722 + 0.297498i \(0.903848\pi\)
\(102\) −9.90997e7 2.98964e8i −0.0906508 0.273475i
\(103\) 6.34170e8 0.555186 0.277593 0.960699i \(-0.410463\pi\)
0.277593 + 0.960699i \(0.410463\pi\)
\(104\) −2.81929e8 1.97280e8i −0.236314 0.165361i
\(105\) 1.80847e9 1.45198
\(106\) 3.45771e8 + 1.04312e9i 0.266019 + 0.802526i
\(107\) 1.54145e9i 1.13685i −0.822735 0.568425i \(-0.807553\pi\)
0.822735 0.568425i \(-0.192447\pi\)
\(108\) −8.99455e8 1.20766e9i −0.636169 0.854160i
\(109\) 2.19786e9i 1.49135i 0.666309 + 0.745676i \(0.267873\pi\)
−0.666309 + 0.745676i \(0.732127\pi\)
\(110\) 1.39002e9 4.60761e8i 0.905222 0.300060i
\(111\) 5.37892e7 0.0336311
\(112\) 5.23140e8 1.75001e9i 0.314150 1.05089i
\(113\) −5.43476e8 −0.313565 −0.156782 0.987633i \(-0.550112\pi\)
−0.156782 + 0.987633i \(0.550112\pi\)
\(114\) −1.05657e9 + 3.50228e8i −0.585902 + 0.194213i
\(115\) 2.18808e9i 1.16660i
\(116\) −3.47563e8 4.66660e8i −0.178227 0.239298i
\(117\) 2.84732e8i 0.140475i
\(118\) 2.98796e7 + 9.01407e7i 0.0141875 + 0.0428008i
\(119\) −9.65210e8 −0.441225
\(120\) −1.72398e9 + 2.46370e9i −0.758956 + 1.08461i
\(121\) 1.73022e9 0.733783
\(122\) −4.54695e8 1.37172e9i −0.185823 0.560592i
\(123\) 1.46518e9i 0.577189i
\(124\) 1.78929e9 1.33264e9i 0.679645 0.506192i
\(125\) 7.14513e9i 2.61767i
\(126\) −1.43464e9 + 4.75550e8i −0.507079 + 0.168085i
\(127\) −2.41305e9 −0.823093 −0.411547 0.911389i \(-0.635011\pi\)
−0.411547 + 0.911389i \(0.635011\pi\)
\(128\) 1.88535e9 + 2.38093e9i 0.620795 + 0.783973i
\(129\) −3.98349e9 −1.26652
\(130\) 1.64784e9 5.46221e8i 0.506022 0.167735i
\(131\) 1.57746e9i 0.467990i 0.972238 + 0.233995i \(0.0751799\pi\)
−0.972238 + 0.233995i \(0.924820\pi\)
\(132\) 1.03375e9 7.69926e8i 0.296369 0.220733i
\(133\) 3.41114e9i 0.945295i
\(134\) 4.12662e8 + 1.24492e9i 0.110566 + 0.333557i
\(135\) 7.59698e9 1.96852
\(136\) 9.20115e8 1.31492e9i 0.230631 0.329589i
\(137\) −6.39076e9 −1.54992 −0.774961 0.632009i \(-0.782231\pi\)
−0.774961 + 0.632009i \(0.782231\pi\)
\(138\) 6.05983e8 + 1.82813e9i 0.142234 + 0.429093i
\(139\) 2.45897e9i 0.558710i −0.960188 0.279355i \(-0.909879\pi\)
0.960188 0.279355i \(-0.0901206\pi\)
\(140\) 5.50433e9 + 7.39045e9i 1.21096 + 1.62590i
\(141\) 4.51158e9i 0.961265i
\(142\) −5.90462e9 + 1.95724e9i −1.21869 + 0.403969i
\(143\) −7.44153e8 −0.148816
\(144\) 7.19766e8 2.40776e9i 0.139496 0.466640i
\(145\) 2.93559e9 0.551492
\(146\) 1.96948e9 6.52838e8i 0.358727 0.118910i
\(147\) 8.23393e8i 0.145438i
\(148\) 1.63715e8 + 2.19814e8i 0.0280485 + 0.0376597i
\(149\) 3.84540e9i 0.639150i −0.947561 0.319575i \(-0.896460\pi\)
0.947561 0.319575i \(-0.103540\pi\)
\(150\) −3.37605e9 1.01849e10i −0.544501 1.64265i
\(151\) 4.07627e9 0.638067 0.319034 0.947743i \(-0.396642\pi\)
0.319034 + 0.947743i \(0.396642\pi\)
\(152\) −4.64704e9 3.25177e9i −0.706123 0.494111i
\(153\) −1.32799e9 −0.195922
\(154\) −1.24286e9 3.74946e9i −0.178065 0.537187i
\(155\) 1.12557e10i 1.56632i
\(156\) 1.22549e9 9.12728e8i 0.165671 0.123390i
\(157\) 7.59409e9i 0.997533i −0.866736 0.498767i \(-0.833786\pi\)
0.866736 0.498767i \(-0.166214\pi\)
\(158\) −4.34709e9 + 1.44096e9i −0.554935 + 0.183948i
\(159\) −4.88004e9 −0.605531
\(160\) −1.53153e10 + 4.53441e8i −1.84750 + 0.0546991i
\(161\) 5.90214e9 0.692298
\(162\) 2.29449e9 7.60572e8i 0.261740 0.0867606i
\(163\) 7.71277e9i 0.855788i −0.903829 0.427894i \(-0.859256\pi\)
0.903829 0.427894i \(-0.140744\pi\)
\(164\) 5.98757e9 4.45948e9i 0.646328 0.481378i
\(165\) 6.50295e9i 0.683019i
\(166\) 4.35041e9 + 1.31243e10i 0.444676 + 1.34150i
\(167\) 1.01170e10 1.00653 0.503265 0.864132i \(-0.332132\pi\)
0.503265 + 0.864132i \(0.332132\pi\)
\(168\) 6.64560e9 + 4.65027e9i 0.643639 + 0.450388i
\(169\) 9.72232e9 0.916811
\(170\) 2.54757e9 + 7.68552e9i 0.233941 + 0.705753i
\(171\) 4.69324e9i 0.419750i
\(172\) −1.21243e10 1.62788e10i −1.05628 1.41823i
\(173\) 1.89724e10i 1.61033i 0.593053 + 0.805164i \(0.297922\pi\)
−0.593053 + 0.805164i \(0.702078\pi\)
\(174\) 2.45267e9 8.13003e8i 0.202846 0.0672389i
\(175\) −3.28820e10 −2.65025
\(176\) 6.29272e9 + 1.88112e9i 0.494347 + 0.147778i
\(177\) −4.21706e8 −0.0322946
\(178\) 1.65723e10 5.49334e9i 1.23735 0.410153i
\(179\) 1.72674e10i 1.25716i −0.777746 0.628578i \(-0.783637\pi\)
0.777746 0.628578i \(-0.216363\pi\)
\(180\) 7.57317e9 + 1.01682e10i 0.537714 + 0.721968i
\(181\) 1.03363e10i 0.715830i −0.933754 0.357915i \(-0.883488\pi\)
0.933754 0.357915i \(-0.116512\pi\)
\(182\) −1.47338e9 4.44489e9i −0.0995390 0.300289i
\(183\) 6.41733e9 0.422985
\(184\) −5.62640e9 + 8.04056e9i −0.361868 + 0.517137i
\(185\) −1.38277e9 −0.0867913
\(186\) 3.11725e9 + 9.40411e9i 0.190969 + 0.576115i
\(187\) 3.47073e9i 0.207555i
\(188\) −1.84369e10 + 1.37316e10i −1.07641 + 0.801699i
\(189\) 2.04921e10i 1.16818i
\(190\) 2.71613e10 9.00336e9i 1.51203 0.501203i
\(191\) −9.14299e9 −0.497094 −0.248547 0.968620i \(-0.579953\pi\)
−0.248547 + 0.968620i \(0.579953\pi\)
\(192\) −1.26702e10 + 4.62037e9i −0.672867 + 0.245370i
\(193\) 8.45502e8 0.0438639 0.0219319 0.999759i \(-0.493018\pi\)
0.0219319 + 0.999759i \(0.493018\pi\)
\(194\) −2.32591e10 + 7.70985e9i −1.17892 + 0.390785i
\(195\) 7.70909e9i 0.381810i
\(196\) 3.36486e9 2.50611e9i 0.162860 0.121296i
\(197\) 2.12407e9i 0.100478i 0.998737 + 0.0502390i \(0.0159983\pi\)
−0.998737 + 0.0502390i \(0.984002\pi\)
\(198\) −1.71000e9 5.15872e9i −0.0790682 0.238533i
\(199\) −2.92879e9 −0.132388 −0.0661941 0.997807i \(-0.521086\pi\)
−0.0661941 + 0.997807i \(0.521086\pi\)
\(200\) 3.13458e10 4.47955e10i 1.38530 1.97970i
\(201\) −5.82411e9 −0.251679
\(202\) −4.43008e9 1.33647e10i −0.187211 0.564777i
\(203\) 7.91848e9i 0.327272i
\(204\) 4.25696e9 + 5.71566e9i 0.172093 + 0.231063i
\(205\) 3.76656e10i 1.48954i
\(206\) −1.36208e10 + 4.51499e9i −0.526988 + 0.174684i
\(207\) 8.12051e9 0.307409
\(208\) 7.45986e9 + 2.23002e9i 0.276341 + 0.0826084i
\(209\) −1.22659e10 −0.444673
\(210\) −3.88427e10 + 1.28755e10i −1.37823 + 0.456852i
\(211\) 3.16571e10i 1.09951i 0.835325 + 0.549757i \(0.185280\pi\)
−0.835325 + 0.549757i \(0.814720\pi\)
\(212\) −1.48531e10 1.99427e10i −0.505016 0.678065i
\(213\) 2.76236e10i 0.919542i
\(214\) 1.09744e10 + 3.31076e10i 0.357700 + 1.07911i
\(215\) 1.02404e11 3.26847
\(216\) 2.79166e10 + 1.95347e10i 0.872612 + 0.610612i
\(217\) 3.03613e10 0.929505
\(218\) −1.56477e10 4.72059e10i −0.469241 1.41561i
\(219\) 9.21383e9i 0.270671i
\(220\) −2.65748e10 + 1.97926e10i −0.764835 + 0.569641i
\(221\) 4.11446e9i 0.116024i
\(222\) −1.15529e9 + 3.82953e8i −0.0319230 + 0.0105818i
\(223\) −4.92453e10 −1.33350 −0.666750 0.745282i \(-0.732315\pi\)
−0.666750 + 0.745282i \(0.732315\pi\)
\(224\) 1.22311e9 + 4.13115e10i 0.0324601 + 1.09636i
\(225\) −4.52409e10 −1.17682
\(226\) 1.16729e10 3.86929e9i 0.297639 0.0986605i
\(227\) 5.67209e10i 1.41784i 0.705290 + 0.708919i \(0.250817\pi\)
−0.705290 + 0.708919i \(0.749183\pi\)
\(228\) 2.01997e10 1.50445e10i 0.495037 0.368698i
\(229\) 3.33645e9i 0.0801723i −0.999196 0.0400862i \(-0.987237\pi\)
0.999196 0.0400862i \(-0.0127632\pi\)
\(230\) −1.55781e10 4.69960e10i −0.367062 1.10735i
\(231\) 1.75411e10 0.405324
\(232\) 1.07874e10 + 7.54852e9i 0.244468 + 0.171067i
\(233\) −4.60006e10 −1.02250 −0.511249 0.859433i \(-0.670817\pi\)
−0.511249 + 0.859433i \(0.670817\pi\)
\(234\) −2.02716e9 6.11553e9i −0.0441994 0.133341i
\(235\) 1.15980e11i 2.48072i
\(236\) −1.28352e9 1.72333e9i −0.0269338 0.0361630i
\(237\) 2.03370e10i 0.418716i
\(238\) 2.07310e10 6.87183e9i 0.418816 0.138828i
\(239\) −4.05955e10 −0.804798 −0.402399 0.915464i \(-0.631824\pi\)
−0.402399 + 0.915464i \(0.631824\pi\)
\(240\) 1.94876e10 6.51898e10i 0.379147 1.26832i
\(241\) 3.45208e10 0.659181 0.329590 0.944124i \(-0.393089\pi\)
0.329590 + 0.944124i \(0.393089\pi\)
\(242\) −3.71620e10 + 1.23184e10i −0.696515 + 0.230879i
\(243\) 4.71541e10i 0.867544i
\(244\) 1.95320e10 + 2.62249e10i 0.352771 + 0.473652i
\(245\) 2.11671e10i 0.375331i
\(246\) 1.04314e10 + 3.14694e10i 0.181608 + 0.547874i
\(247\) −1.45409e10 −0.248573
\(248\) −2.89428e10 + 4.13616e10i −0.485857 + 0.694327i
\(249\) −6.13995e10 −1.01220
\(250\) 5.08700e10 + 1.53465e11i 0.823629 + 2.48472i
\(251\) 7.83857e10i 1.24654i 0.782008 + 0.623268i \(0.214196\pi\)
−0.782008 + 0.623268i \(0.785804\pi\)
\(252\) 2.74278e10 2.04279e10i 0.428438 0.319096i
\(253\) 2.12231e10i 0.325661i
\(254\) 5.18279e10 1.71797e10i 0.781289 0.258979i
\(255\) −3.59552e10 −0.532513
\(256\) −5.74451e10 3.77151e10i −0.835936 0.548828i
\(257\) 1.06489e11 1.52267 0.761337 0.648356i \(-0.224543\pi\)
0.761337 + 0.648356i \(0.224543\pi\)
\(258\) 8.55582e10 2.83606e10i 1.20219 0.398498i
\(259\) 3.72988e9i 0.0515046i
\(260\) −3.15038e10 + 2.34637e10i −0.427545 + 0.318431i
\(261\) 1.08947e10i 0.145322i
\(262\) −1.12307e10 3.38809e10i −0.147249 0.444221i
\(263\) −6.39865e8 −0.00824684 −0.00412342 0.999991i \(-0.501313\pi\)
−0.00412342 + 0.999991i \(0.501313\pi\)
\(264\) −1.67216e10 + 2.38964e10i −0.211865 + 0.302772i
\(265\) 1.25452e11 1.56268
\(266\) −2.42857e10 7.32652e10i −0.297429 0.897284i
\(267\) 7.75302e10i 0.933620i
\(268\) −1.77265e10 2.38007e10i −0.209902 0.281827i
\(269\) 9.60820e10i 1.11881i −0.828894 0.559406i \(-0.811029\pi\)
0.828894 0.559406i \(-0.188971\pi\)
\(270\) −1.63169e11 + 5.40869e10i −1.86854 + 0.619377i
\(271\) −9.78435e10 −1.10197 −0.550986 0.834515i \(-0.685748\pi\)
−0.550986 + 0.834515i \(0.685748\pi\)
\(272\) −1.04008e10 + 3.47928e10i −0.115215 + 0.385416i
\(273\) 2.07945e10 0.226578
\(274\) 1.37262e11 4.54992e10i 1.47120 0.487670i
\(275\) 1.18238e11i 1.24669i
\(276\) −2.60308e10 3.49506e10i −0.270021 0.362547i
\(277\) 1.61396e11i 1.64716i 0.567202 + 0.823579i \(0.308026\pi\)
−0.567202 + 0.823579i \(0.691974\pi\)
\(278\) 1.75067e10 + 5.28142e10i 0.175793 + 0.530333i
\(279\) 4.17728e10 0.412738
\(280\) −1.70840e11 1.19545e11i −1.66103 1.16231i
\(281\) −2.71451e10 −0.259724 −0.129862 0.991532i \(-0.541453\pi\)
−0.129862 + 0.991532i \(0.541453\pi\)
\(282\) −3.21203e10 9.69006e10i −0.302454 0.912443i
\(283\) 2.80153e10i 0.259631i 0.991538 + 0.129815i \(0.0414385\pi\)
−0.991538 + 0.129815i \(0.958562\pi\)
\(284\) 1.12886e11 8.40761e10i 1.02969 0.766902i
\(285\) 1.27069e11i 1.14087i
\(286\) 1.59831e10 5.29801e9i 0.141258 0.0468237i
\(287\) 1.01599e11 0.883940
\(288\) 1.68283e9 + 5.68387e10i 0.0144136 + 0.486831i
\(289\) −9.93980e10 −0.838180
\(290\) −6.30511e10 + 2.09000e10i −0.523482 + 0.173522i
\(291\) 1.08813e11i 0.889534i
\(292\) −3.76530e10 + 2.80435e10i −0.303094 + 0.225741i
\(293\) 2.49001e10i 0.197377i −0.995118 0.0986884i \(-0.968535\pi\)
0.995118 0.0986884i \(-0.0314647\pi\)
\(294\) 5.86217e9 + 1.76850e10i 0.0457610 + 0.138052i
\(295\) 1.08409e10 0.0833421
\(296\) −5.08126e9 3.55562e9i −0.0384733 0.0269217i
\(297\) 7.36861e10 0.549518
\(298\) 2.73774e10 + 8.25921e10i 0.201103 + 0.606688i
\(299\) 2.51594e10i 0.182046i
\(300\) 1.45023e11 + 1.94717e11i 1.03369 + 1.38790i
\(301\) 2.76226e11i 1.93961i
\(302\) −8.75508e10 + 2.90211e10i −0.605660 + 0.200762i
\(303\) 6.25239e10 0.426142
\(304\) 1.22961e11 + 3.67575e10i 0.825727 + 0.246840i
\(305\) −1.64971e11 −1.09159
\(306\) 2.85228e10 9.45466e9i 0.185971 0.0616452i
\(307\) 1.71738e11i 1.10343i 0.834034 + 0.551713i \(0.186026\pi\)
−0.834034 + 0.551713i \(0.813974\pi\)
\(308\) 5.33887e10 + 7.16830e10i 0.338042 + 0.453877i
\(309\) 6.37223e10i 0.397629i
\(310\) −8.01356e10 2.41753e11i −0.492831 1.48677i
\(311\) −1.24783e11 −0.756371 −0.378185 0.925730i \(-0.623452\pi\)
−0.378185 + 0.925730i \(0.623452\pi\)
\(312\) −1.98230e10 + 2.83286e10i −0.118433 + 0.169250i
\(313\) −2.95278e10 −0.173893 −0.0869463 0.996213i \(-0.527711\pi\)
−0.0869463 + 0.996213i \(0.527711\pi\)
\(314\) 5.40663e10 + 1.63107e11i 0.313865 + 0.946869i
\(315\) 1.72538e11i 0.987388i
\(316\) 8.31087e10 6.18984e10i 0.468872 0.349211i
\(317\) 1.20582e11i 0.670678i 0.942098 + 0.335339i \(0.108851\pi\)
−0.942098 + 0.335339i \(0.891149\pi\)
\(318\) 1.04814e11 3.47436e10i 0.574777 0.190525i
\(319\) 2.84735e10 0.153951
\(320\) 3.25716e11 1.18777e11i 1.73646 0.633221i
\(321\) −1.54887e11 −0.814223
\(322\) −1.26767e11 + 4.20205e10i −0.657137 + 0.217826i
\(323\) 6.78187e10i 0.346687i
\(324\) −4.38666e10 + 3.26714e10i −0.221147 + 0.164708i
\(325\) 1.40168e11i 0.696906i
\(326\) 5.49112e10 + 1.65656e11i 0.269266 + 0.812323i
\(327\) 2.20844e11 1.06812
\(328\) −9.68527e10 + 1.38410e11i −0.462040 + 0.660291i
\(329\) −3.12845e11 −1.47214
\(330\) −4.62979e10 1.39672e11i −0.214906 0.648329i
\(331\) 4.18670e11i 1.91711i −0.284913 0.958553i \(-0.591965\pi\)
0.284913 0.958553i \(-0.408035\pi\)
\(332\) −1.86878e11 2.50914e11i −0.844182 1.13345i
\(333\) 5.13179e9i 0.0228702i
\(334\) −2.17294e11 + 7.20281e10i −0.955409 + 0.316696i
\(335\) 1.49721e11 0.649504
\(336\) −1.75843e11 5.25659e10i −0.752660 0.224997i
\(337\) 2.95362e11 1.24744 0.623721 0.781647i \(-0.285620\pi\)
0.623721 + 0.781647i \(0.285620\pi\)
\(338\) −2.08818e11 + 6.92183e10i −0.870247 + 0.288467i
\(339\) 5.46092e10i 0.224578i
\(340\) −1.09434e11 1.46933e11i −0.444119 0.596301i
\(341\) 1.09174e11i 0.437245i
\(342\) −3.34137e10 1.00802e11i −0.132071 0.398431i
\(343\) −2.24073e11 −0.874111
\(344\) 3.76306e11 + 2.63321e11i 1.44886 + 1.01385i
\(345\) 2.19862e11 0.835533
\(346\) −1.35074e11 4.07492e11i −0.506676 1.52854i
\(347\) 1.55047e10i 0.0574093i 0.999588 + 0.0287046i \(0.00913822\pi\)
−0.999588 + 0.0287046i \(0.990862\pi\)
\(348\) −4.68907e10 + 3.49237e10i −0.171388 + 0.127648i
\(349\) 3.06969e11i 1.10759i 0.832652 + 0.553797i \(0.186822\pi\)
−0.832652 + 0.553797i \(0.813178\pi\)
\(350\) 7.06246e11 2.34104e11i 2.51565 0.833879i
\(351\) 8.73531e10 0.307182
\(352\) −1.48549e11 + 4.39810e9i −0.515736 + 0.0152694i
\(353\) 2.99671e11 1.02721 0.513604 0.858028i \(-0.328310\pi\)
0.513604 + 0.858028i \(0.328310\pi\)
\(354\) 9.05747e9 3.00234e9i 0.0306544 0.0101612i
\(355\) 7.10124e11i 2.37305i
\(356\) −3.16833e11 + 2.35974e11i −1.04546 + 0.778644i
\(357\) 9.69856e10i 0.316010i
\(358\) 1.22936e11 + 3.70873e11i 0.395554 + 1.19331i
\(359\) −4.04368e11 −1.28485 −0.642424 0.766349i \(-0.722071\pi\)
−0.642424 + 0.766349i \(0.722071\pi\)
\(360\) −2.35051e11 1.64477e11i −0.737565 0.516113i
\(361\) 8.30100e10 0.257246
\(362\) 7.35893e10 + 2.22004e11i 0.225230 + 0.679474i
\(363\) 1.73855e11i 0.525542i
\(364\) 6.32910e10 + 8.49784e10i 0.188967 + 0.253719i
\(365\) 2.36861e11i 0.698516i
\(366\) −1.37833e11 + 4.56884e10i −0.401502 + 0.133089i
\(367\) 5.07965e11 1.46163 0.730813 0.682578i \(-0.239141\pi\)
0.730813 + 0.682578i \(0.239141\pi\)
\(368\) 6.35998e10 2.12754e11i 0.180776 0.604731i
\(369\) 1.39786e11 0.392506
\(370\) 2.96993e10 9.84465e9i 0.0823833 0.0273082i
\(371\) 3.38395e11i 0.927345i
\(372\) −1.33906e11 1.79790e11i −0.362540 0.486768i
\(373\) 6.94617e10i 0.185804i −0.995675 0.0929022i \(-0.970386\pi\)
0.995675 0.0929022i \(-0.0296144\pi\)
\(374\) 2.47099e10 + 7.45449e10i 0.0653054 + 0.197013i
\(375\) −7.17953e11 −1.87480
\(376\) 2.98229e11 4.26192e11i 0.769493 1.09966i
\(377\) 3.37546e10 0.0860591
\(378\) 1.45894e11 + 4.40134e11i 0.367557 + 1.10885i
\(379\) 4.45070e11i 1.10803i −0.832507 0.554015i \(-0.813095\pi\)
0.832507 0.554015i \(-0.186905\pi\)
\(380\) −5.19277e11 + 3.86752e11i −1.27753 + 0.951494i
\(381\) 2.42466e11i 0.589507i
\(382\) 1.96375e11 6.50938e10i 0.471847 0.156406i
\(383\) −4.50375e11 −1.06950 −0.534749 0.845011i \(-0.679594\pi\)
−0.534749 + 0.845011i \(0.679594\pi\)
\(384\) 2.39239e11 1.89443e11i 0.561489 0.444619i
\(385\) −4.50932e11 −1.04601
\(386\) −1.81598e10 + 6.01957e9i −0.0416360 + 0.0138014i
\(387\) 3.80047e11i 0.861268i
\(388\) 4.44672e11 3.31187e11i 0.996087 0.741875i
\(389\) 5.76192e11i 1.27583i −0.770106 0.637916i \(-0.779797\pi\)
0.770106 0.637916i \(-0.220203\pi\)
\(390\) −5.48850e10 1.65577e11i −0.120133 0.362418i
\(391\) −1.17344e11 −0.253901
\(392\) −5.44287e10 + 7.77829e10i −0.116424 + 0.166378i
\(393\) 1.58505e11 0.335179
\(394\) −1.51224e10 4.56212e10i −0.0316145 0.0953748i
\(395\) 5.22807e11i 1.08057i
\(396\) 7.34552e10 + 9.86255e10i 0.150105 + 0.201540i
\(397\) 3.22788e11i 0.652169i 0.945341 + 0.326084i \(0.105729\pi\)
−0.945341 + 0.326084i \(0.894271\pi\)
\(398\) 6.29051e10 2.08516e10i 0.125664 0.0416548i
\(399\) 3.42756e11 0.677030
\(400\) −3.54327e11 + 1.18529e12i −0.692045 + 2.31503i
\(401\) 1.47838e11 0.285520 0.142760 0.989757i \(-0.454402\pi\)
0.142760 + 0.989757i \(0.454402\pi\)
\(402\) 1.25091e11 4.14649e10i 0.238897 0.0791887i
\(403\) 1.29423e11i 0.244421i
\(404\) 1.90300e11 + 2.55509e11i 0.355404 + 0.477188i
\(405\) 2.75949e11i 0.509661i
\(406\) 5.63758e10 + 1.70074e11i 0.102973 + 0.310650i
\(407\) −1.34120e10 −0.0242281
\(408\) −1.32125e11 9.24545e10i −0.236055 0.165180i
\(409\) −7.24078e11 −1.27947 −0.639735 0.768595i \(-0.720956\pi\)
−0.639735 + 0.768595i \(0.720956\pi\)
\(410\) −2.68161e11 8.08990e11i −0.468672 1.41389i
\(411\) 6.42153e11i 1.11007i
\(412\) 2.60406e11 1.93948e11i 0.445260 0.331625i
\(413\) 2.92422e10i 0.0494578i
\(414\) −1.74414e11 + 5.78141e10i −0.291796 + 0.0967236i
\(415\) 1.57841e12 2.61218
\(416\) −1.76101e11 + 5.21384e9i −0.288298 + 0.00853567i
\(417\) −2.47081e11 −0.400153
\(418\) 2.63449e11 8.73272e10i 0.422088 0.139912i
\(419\) 6.10316e11i 0.967368i −0.875243 0.483684i \(-0.839298\pi\)
0.875243 0.483684i \(-0.160702\pi\)
\(420\) 7.42603e11 5.53083e11i 1.16449 0.867298i
\(421\) 7.16040e11i 1.11088i 0.831556 + 0.555441i \(0.187450\pi\)
−0.831556 + 0.555441i \(0.812550\pi\)
\(422\) −2.25384e11 6.79938e11i −0.345953 1.04367i
\(423\) −4.30430e11 −0.653689
\(424\) 4.60999e11 + 3.22585e11i 0.692714 + 0.484728i
\(425\) 6.53744e11 0.971981
\(426\) 1.96667e11 + 5.93304e11i 0.289326 + 0.872839i
\(427\) 4.44995e11i 0.647783i
\(428\) −4.71421e11 6.32959e11i −0.679066 0.911756i
\(429\) 7.47735e10i 0.106584i
\(430\) −2.19946e12 + 7.29070e11i −3.10247 + 1.02840i
\(431\) 4.78823e11 0.668385 0.334193 0.942505i \(-0.391536\pi\)
0.334193 + 0.942505i \(0.391536\pi\)
\(432\) −7.38677e11 2.20817e11i −1.02042 0.305039i
\(433\) −3.13312e11 −0.428334 −0.214167 0.976797i \(-0.568704\pi\)
−0.214167 + 0.976797i \(0.568704\pi\)
\(434\) −6.52106e11 + 2.16158e11i −0.882296 + 0.292461i
\(435\) 2.94972e11i 0.394984i
\(436\) 6.72168e11 + 9.02494e11i 0.890817 + 1.19607i
\(437\) 4.14703e11i 0.543965i
\(438\) −6.55981e10 1.97896e11i −0.0851643 0.256924i
\(439\) 6.95985e11 0.894354 0.447177 0.894445i \(-0.352429\pi\)
0.447177 + 0.894445i \(0.352429\pi\)
\(440\) 4.29864e11 6.14310e11i 0.546757 0.781358i
\(441\) 7.85563e10 0.0989025
\(442\) 2.92930e10 + 8.83711e10i 0.0365059 + 0.110131i
\(443\) 3.55482e11i 0.438531i 0.975665 + 0.219266i \(0.0703661\pi\)
−0.975665 + 0.219266i \(0.929634\pi\)
\(444\) 2.20872e10 1.64503e10i 0.0269722 0.0200886i
\(445\) 1.99308e12i 2.40938i
\(446\) 1.05770e12 3.50603e11i 1.26577 0.419574i
\(447\) −3.86391e11 −0.457765
\(448\) −3.20388e11 8.78587e11i −0.375773 1.03047i
\(449\) −8.15188e11 −0.946562 −0.473281 0.880911i \(-0.656931\pi\)
−0.473281 + 0.880911i \(0.656931\pi\)
\(450\) 9.71693e11 3.22094e11i 1.11705 0.370277i
\(451\) 3.65334e11i 0.415811i
\(452\) −2.23165e11 + 1.66211e11i −0.251479 + 0.187299i
\(453\) 4.09589e11i 0.456990i
\(454\) −4.03826e11 1.21826e12i −0.446111 1.34583i
\(455\) −5.34568e11 −0.584725
\(456\) −3.26743e11 + 4.66941e11i −0.353887 + 0.505732i
\(457\) −5.94548e11 −0.637623 −0.318811 0.947818i \(-0.603284\pi\)
−0.318811 + 0.947818i \(0.603284\pi\)
\(458\) 2.37539e10 + 7.16608e10i 0.0252255 + 0.0761004i
\(459\) 4.07414e11i 0.428429i
\(460\) 6.69179e11 + 8.98481e11i 0.696838 + 0.935618i
\(461\) 1.42516e12i 1.46964i 0.678265 + 0.734818i \(0.262732\pi\)
−0.678265 + 0.734818i \(0.737268\pi\)
\(462\) −3.76751e11 + 1.24884e11i −0.384738 + 0.127532i
\(463\) −1.04996e12 −1.06183 −0.530917 0.847424i \(-0.678153\pi\)
−0.530917 + 0.847424i \(0.678153\pi\)
\(464\) −2.85436e11 8.53272e10i −0.285876 0.0854588i
\(465\) 1.13099e12 1.12182
\(466\) 9.88010e11 3.27503e11i 0.970565 0.321720i
\(467\) 1.15656e11i 0.112523i −0.998416 0.0562616i \(-0.982082\pi\)
0.998416 0.0562616i \(-0.0179181\pi\)
\(468\) 8.70793e10 + 1.16918e11i 0.0839090 + 0.112661i
\(469\) 4.03859e11i 0.385436i
\(470\) 8.25722e11 + 2.49104e12i 0.780537 + 2.35473i
\(471\) −7.63065e11 −0.714443
\(472\) 3.98369e10 + 2.78760e10i 0.0369443 + 0.0258518i
\(473\) 9.93261e11 0.912406
\(474\) 1.44790e11 + 4.36802e11i 0.131745 + 0.397449i
\(475\) 2.31039e12i 2.08240i
\(476\) −3.96339e11 + 2.95189e11i −0.353863 + 0.263554i
\(477\) 4.65583e11i 0.411779i
\(478\) 8.71917e11 2.89020e11i 0.763923 0.253223i
\(479\) 1.37302e12 1.19170 0.595849 0.803096i \(-0.296816\pi\)
0.595849 + 0.803096i \(0.296816\pi\)
\(480\) 4.55623e10 + 1.53890e12i 0.0391760 + 1.32320i
\(481\) −1.58996e10 −0.0135436
\(482\) −7.41444e11 + 2.45772e11i −0.625701 + 0.207406i
\(483\) 5.93056e11i 0.495831i
\(484\) 7.10472e11 5.29152e11i 0.588495 0.438305i
\(485\) 2.79727e12i 2.29561i
\(486\) 3.35715e11 + 1.01279e12i 0.272965 + 0.823482i
\(487\) −1.53458e12 −1.23626 −0.618131 0.786075i \(-0.712110\pi\)
−0.618131 + 0.786075i \(0.712110\pi\)
\(488\) −6.06221e11 4.24205e11i −0.483885 0.338599i
\(489\) −7.74990e11 −0.612923
\(490\) −1.50700e11 4.54631e11i −0.118095 0.356268i
\(491\) 5.12475e11i 0.397929i −0.980007 0.198965i \(-0.936242\pi\)
0.980007 0.198965i \(-0.0637579\pi\)
\(492\) −4.48095e11 6.01639e11i −0.344768 0.462907i
\(493\) 1.57431e11i 0.120027i
\(494\) 3.12312e11 1.03524e11i 0.235949 0.0782115i
\(495\) −6.20418e11 −0.464473
\(496\) 3.27165e11 1.09443e12i 0.242716 0.811934i
\(497\) 1.91549e12 1.40824
\(498\) 1.31875e12 4.37135e11i 0.960794 0.318481i
\(499\) 2.45745e12i 1.77432i 0.461463 + 0.887159i \(0.347325\pi\)
−0.461463 + 0.887159i \(0.652675\pi\)
\(500\) −2.18519e12 2.93397e12i −1.56359 2.09938i
\(501\) 1.01657e12i 0.720887i
\(502\) −5.58069e11 1.68358e12i −0.392212 1.18323i
\(503\) −2.11765e11 −0.147502 −0.0737512 0.997277i \(-0.523497\pi\)
−0.0737512 + 0.997277i \(0.523497\pi\)
\(504\) −4.43662e11 + 6.34027e11i −0.306277 + 0.437694i
\(505\) −1.60731e12 −1.09974
\(506\) −1.51098e11 4.55833e11i −0.102467 0.309121i
\(507\) 9.76913e11i 0.656629i
\(508\) −9.90857e11 + 7.37979e11i −0.660122 + 0.491652i
\(509\) 2.27707e12i 1.50365i −0.659363 0.751824i \(-0.729174\pi\)
0.659363 0.751824i \(-0.270826\pi\)
\(510\) 7.72252e11 2.55984e11i 0.505467 0.167551i
\(511\) −6.38911e11 −0.414521
\(512\) 1.50233e12 + 4.01071e11i 0.966163 + 0.257933i
\(513\) 1.43984e12 0.917881
\(514\) −2.28720e12 + 7.58153e11i −1.44534 + 0.479097i
\(515\) 1.63812e12i 1.02616i
\(516\) −1.63572e12 + 1.21827e12i −1.01575 + 0.756517i
\(517\) 1.12494e12i 0.692501i
\(518\) −2.65550e10 8.01111e10i −0.0162055 0.0488888i
\(519\) 1.90637e12 1.15333
\(520\) 5.09593e11 7.28249e11i 0.305639 0.436782i
\(521\) 3.15742e12 1.87742 0.938712 0.344703i \(-0.112020\pi\)
0.938712 + 0.344703i \(0.112020\pi\)
\(522\) 7.75650e10 + 2.33998e11i 0.0457245 + 0.137942i
\(523\) 6.70464e11i 0.391848i 0.980619 + 0.195924i \(0.0627706\pi\)
−0.980619 + 0.195924i \(0.937229\pi\)
\(524\) 4.82431e11 + 6.47742e11i 0.279541 + 0.375328i
\(525\) 3.30403e12i 1.89814i
\(526\) 1.37431e10 4.55553e9i 0.00782799 0.00259480i
\(527\) −6.03629e11 −0.340896
\(528\) 1.89018e11 6.32302e11i 0.105840 0.354056i
\(529\) −1.08361e12 −0.601621
\(530\) −2.69448e12 + 8.93159e11i −1.48332 + 0.491685i
\(531\) 4.02330e10i 0.0219613i
\(532\) 1.04323e12 + 1.40070e12i 0.564646 + 0.758128i
\(533\) 4.33094e11i 0.232440i
\(534\) −5.51978e11 1.66521e12i −0.293756 0.886202i
\(535\) 3.98172e12 2.10125
\(536\) 5.50182e11 + 3.84991e11i 0.287915 + 0.201469i
\(537\) −1.73506e12 −0.900387
\(538\) 6.84058e11 + 2.06367e12i 0.352025 + 1.06199i
\(539\) 2.05308e11i 0.104775i
\(540\) 3.11951e12 2.32338e12i 1.57875 1.17584i
\(541\) 6.87645e11i 0.345125i 0.984999 + 0.172562i \(0.0552047\pi\)
−0.984999 + 0.172562i \(0.944795\pi\)
\(542\) 2.10150e12 6.96599e11i 1.04600 0.346726i
\(543\) −1.03860e12 −0.512685
\(544\) −2.43173e10 8.21335e11i −0.0119048 0.402092i
\(545\) −5.67726e12 −2.75648
\(546\) −4.46629e11 + 1.48047e11i −0.215070 + 0.0712908i
\(547\) 2.73174e12i 1.30466i −0.757936 0.652328i \(-0.773792\pi\)
0.757936 0.652328i \(-0.226208\pi\)
\(548\) −2.62420e12 + 1.95448e12i −1.24304 + 0.925803i
\(549\) 6.12249e11i 0.287642i
\(550\) 8.41798e11 + 2.53954e12i 0.392262 + 1.18338i
\(551\) 5.56377e11 0.257150
\(552\) 8.07927e11 + 5.65348e11i 0.370379 + 0.259173i
\(553\) 1.41022e12 0.641245
\(554\) −1.14907e12 3.46650e12i −0.518264 1.56350i
\(555\) 1.38942e11i 0.0621608i
\(556\) −7.52024e11 1.00971e12i −0.333730 0.448086i
\(557\) 3.59464e12i 1.58236i −0.611580 0.791182i \(-0.709466\pi\)
0.611580 0.791182i \(-0.290534\pi\)
\(558\) −8.97204e11 + 2.97403e11i −0.391776 + 0.129865i
\(559\) 1.17749e12 0.510038
\(560\) 4.52043e12 + 1.35132e12i 1.94238 + 0.580647i
\(561\) −3.48744e11 −0.148653
\(562\) 5.83027e11 1.93260e11i 0.246533 0.0817200i
\(563\) 4.60263e11i 0.193072i −0.995330 0.0965358i \(-0.969224\pi\)
0.995330 0.0965358i \(-0.0307762\pi\)
\(564\) 1.37977e12 + 1.85257e12i 0.574185 + 0.770936i
\(565\) 1.40385e12i 0.579565i
\(566\) −1.99455e11 6.01717e11i −0.0816906 0.246444i
\(567\) −7.44347e11 −0.302449
\(568\) −1.82600e12 + 2.60950e12i −0.736094 + 1.05194i
\(569\) −1.91911e12 −0.767527 −0.383764 0.923431i \(-0.625372\pi\)
−0.383764 + 0.923431i \(0.625372\pi\)
\(570\) −9.04671e11 2.72921e12i −0.358966 1.08293i
\(571\) 2.01838e12i 0.794586i 0.917692 + 0.397293i \(0.130050\pi\)
−0.917692 + 0.397293i \(0.869950\pi\)
\(572\) −3.05568e11 + 2.27583e11i −0.119351 + 0.0888912i
\(573\) 9.18701e11i 0.356023i
\(574\) −2.18217e12 + 7.23340e11i −0.839046 + 0.278124i
\(575\) −3.99757e12 −1.52507
\(576\) −4.40808e11 1.20881e12i −0.166859 0.457570i
\(577\) −6.91957e11 −0.259889 −0.129945 0.991521i \(-0.541480\pi\)
−0.129945 + 0.991521i \(0.541480\pi\)
\(578\) 2.13489e12 7.07667e11i 0.795610 0.263726i
\(579\) 8.49572e10i 0.0314157i
\(580\) 1.20543e12 8.97788e11i 0.442298 0.329419i
\(581\) 4.25760e12i 1.55015i
\(582\) 7.74697e11 + 2.33711e12i 0.279884 + 0.844355i
\(583\) 1.21681e12 0.436229
\(584\) 6.09061e11 8.70396e11i 0.216672 0.309641i
\(585\) −7.35490e11 −0.259642
\(586\) 1.77277e11 + 5.34808e11i 0.0621029 + 0.187352i
\(587\) 1.99542e12i 0.693686i 0.937923 + 0.346843i \(0.112746\pi\)
−0.937923 + 0.346843i \(0.887254\pi\)
\(588\) −2.51817e11 3.38106e11i −0.0868736 0.116642i
\(589\) 2.13328e12i 0.730347i
\(590\) −2.32842e11 + 7.71817e10i −0.0791092 + 0.0262229i
\(591\) 2.13430e11 0.0719633
\(592\) 1.34451e11 + 4.01922e10i 0.0449899 + 0.0134491i
\(593\) 5.19417e12 1.72492 0.862462 0.506121i \(-0.168921\pi\)
0.862462 + 0.506121i \(0.168921\pi\)
\(594\) −1.58264e12 + 5.24610e11i −0.521608 + 0.172901i
\(595\) 2.49323e12i 0.815521i
\(596\) −1.17603e12 1.57901e12i −0.381778 0.512599i
\(597\) 2.94289e11i 0.0948177i
\(598\) −1.79123e11 5.40379e11i −0.0572792 0.172800i
\(599\) 4.47443e12 1.42010 0.710048 0.704154i \(-0.248673\pi\)
0.710048 + 0.704154i \(0.248673\pi\)
\(600\) −4.50112e12 3.14967e12i −1.41788 0.992165i
\(601\) 3.10552e12 0.970955 0.485477 0.874249i \(-0.338646\pi\)
0.485477 + 0.874249i \(0.338646\pi\)
\(602\) 1.96660e12 + 5.93283e12i 0.610283 + 1.84110i
\(603\) 5.55652e11i 0.171149i
\(604\) 1.67382e12 1.24664e12i 0.511731 0.381132i
\(605\) 4.46932e12i 1.35626i
\(606\) −1.34290e12 + 4.45141e11i −0.404499 + 0.134082i
\(607\) −3.79043e12 −1.13329 −0.566643 0.823964i \(-0.691758\pi\)
−0.566643 + 0.823964i \(0.691758\pi\)
\(608\) −2.90268e12 + 8.59398e10i −0.861455 + 0.0255052i
\(609\) −7.95660e11 −0.234396
\(610\) 3.54329e12 1.17452e12i 1.03615 0.343459i
\(611\) 1.33358e12i 0.387111i
\(612\) −5.45306e11 + 4.06138e11i −0.157130 + 0.117029i
\(613\) 6.09780e12i 1.74422i 0.489310 + 0.872110i \(0.337249\pi\)
−0.489310 + 0.872110i \(0.662751\pi\)
\(614\) −1.22269e12 3.68862e12i −0.347184 1.04738i
\(615\) 3.78470e12 1.06682
\(616\) −1.65704e12 1.15952e12i −0.463682 0.324462i
\(617\) −2.07665e12 −0.576872 −0.288436 0.957499i \(-0.593135\pi\)
−0.288436 + 0.957499i \(0.593135\pi\)
\(618\) 4.53673e11 + 1.36864e12i 0.125111 + 0.377434i
\(619\) 6.03694e12i 1.65276i 0.563115 + 0.826379i \(0.309603\pi\)
−0.563115 + 0.826379i \(0.690397\pi\)
\(620\) 3.44233e12 + 4.62189e12i 0.935600 + 1.25619i
\(621\) 2.49129e12i 0.672221i
\(622\) 2.68012e12 8.88398e11i 0.717955 0.237986i
\(623\) −5.37615e12 −1.42980
\(624\) 2.24076e11 7.49578e11i 0.0591649 0.197918i
\(625\) 9.23927e12 2.42202
\(626\) 6.34202e11 2.10224e11i 0.165061 0.0547138i
\(627\) 1.23249e12i 0.318479i
\(628\) −2.32249e12 3.11832e12i −0.595849 0.800023i
\(629\) 7.41558e10i 0.0188893i
\(630\) −1.22839e12 3.70581e12i −0.310673 0.937239i
\(631\) −7.01879e12 −1.76250 −0.881252 0.472648i \(-0.843298\pi\)
−0.881252 + 0.472648i \(0.843298\pi\)
\(632\) −1.34434e12 + 1.92116e12i −0.335182 + 0.479001i
\(633\) 3.18095e12 0.787482
\(634\) −8.58483e11 2.58987e12i −0.211023 0.636615i
\(635\) 6.23312e12i 1.52133i
\(636\) −2.00387e12 + 1.49246e12i −0.485637 + 0.361697i
\(637\) 2.43388e11i 0.0585695i
\(638\) −6.11558e11 + 2.02718e11i −0.146132 + 0.0484394i
\(639\) 2.63544e12 0.625316
\(640\) −6.15015e12 + 4.87005e12i −1.44903 + 1.14742i
\(641\) −6.65994e12 −1.55815 −0.779075 0.626931i \(-0.784311\pi\)
−0.779075 + 0.626931i \(0.784311\pi\)
\(642\) 3.32670e12 1.10272e12i 0.772869 0.256188i
\(643\) 3.60863e12i 0.832516i −0.909247 0.416258i \(-0.863341\pi\)
0.909247 0.416258i \(-0.136659\pi\)
\(644\) 2.42357e12 1.80505e12i 0.555224 0.413525i
\(645\) 1.02897e13i 2.34091i
\(646\) 4.82837e11 + 1.45662e12i 0.109082 + 0.329079i
\(647\) 3.26245e12 0.731938 0.365969 0.930627i \(-0.380738\pi\)
0.365969 + 0.930627i \(0.380738\pi\)
\(648\) 7.09571e11 1.01403e12i 0.158091 0.225925i
\(649\) 1.05150e11 0.0232652
\(650\) 9.97931e11 + 3.01056e12i 0.219276 + 0.661511i
\(651\) 3.05075e12i 0.665720i
\(652\) −2.35879e12 3.16705e12i −0.511181 0.686343i
\(653\) 4.35965e11i 0.0938302i −0.998899 0.0469151i \(-0.985061\pi\)
0.998899 0.0469151i \(-0.0149390\pi\)
\(654\) −4.74332e12 + 1.57230e12i −1.01387 + 0.336075i
\(655\) −4.07471e12 −0.864990
\(656\) 1.09481e12 3.66234e12i 0.230818 0.772132i
\(657\) −8.79050e11 −0.184064
\(658\) 6.71934e12 2.22731e12i 1.39737 0.463195i
\(659\) 2.27883e12i 0.470683i 0.971913 + 0.235341i \(0.0756208\pi\)
−0.971913 + 0.235341i \(0.924379\pi\)
\(660\) 1.98879e12 + 2.67027e12i 0.407982 + 0.547782i
\(661\) 6.28607e12i 1.28077i 0.768052 + 0.640387i \(0.221226\pi\)
−0.768052 + 0.640387i \(0.778774\pi\)
\(662\) 2.98073e12 + 8.99228e12i 0.603201 + 1.81974i
\(663\) −4.13427e11 −0.0830975
\(664\) 5.80018e12 + 4.05869e12i 1.15794 + 0.810269i
\(665\) −8.81130e12 −1.74720
\(666\) −3.65359e10 1.10221e11i −0.00719591 0.0217086i
\(667\) 9.62674e11i 0.188327i
\(668\) 4.15428e12 3.09407e12i 0.807239 0.601223i
\(669\) 4.94824e12i 0.955065i
\(670\) −3.21574e12 + 1.06594e12i −0.616516 + 0.204361i
\(671\) −1.60012e12 −0.304721
\(672\) 4.15104e12 1.22900e11i 0.785226 0.0232483i
\(673\) −1.30391e12 −0.245007 −0.122504 0.992468i \(-0.539092\pi\)
−0.122504 + 0.992468i \(0.539092\pi\)
\(674\) −6.34385e12 + 2.10284e12i −1.18409 + 0.392497i
\(675\) 1.38795e13i 2.57339i
\(676\) 3.99223e12 2.97337e12i 0.735284 0.547632i
\(677\) 3.77662e12i 0.690962i 0.938426 + 0.345481i \(0.112284\pi\)
−0.938426 + 0.345481i \(0.887716\pi\)
\(678\) −3.88792e11 1.17291e12i −0.0706616 0.213172i
\(679\) 7.54538e12 1.36228
\(680\) 3.39655e12 + 2.37674e12i 0.609183 + 0.426277i
\(681\) 5.69939e12 1.01547
\(682\) −7.77267e11 2.34486e12i −0.137575 0.415037i
\(683\) 8.09351e12i 1.42313i −0.702622 0.711563i \(-0.747987\pi\)
0.702622 0.711563i \(-0.252013\pi\)
\(684\) 1.43533e12 + 1.92716e12i 0.250726 + 0.336640i
\(685\) 1.65079e13i 2.86474i
\(686\) 4.81269e12 1.59530e12i 0.829716 0.275032i
\(687\) −3.35251e11 −0.0574202
\(688\) −9.95708e12 2.97653e12i −1.69428 0.506480i
\(689\) 1.44250e12 0.243853
\(690\) −4.72223e12 + 1.56531e12i −0.793097 + 0.262893i
\(691\) 1.04215e12i 0.173891i −0.996213 0.0869455i \(-0.972289\pi\)
0.996213 0.0869455i \(-0.0277106\pi\)
\(692\) 5.80230e12 + 7.79052e12i 0.961884 + 1.29148i
\(693\) 1.67352e12i 0.275633i
\(694\) −1.10386e11 3.33014e11i −0.0180633 0.0544935i
\(695\) 6.35174e12 1.03267
\(696\) 7.58486e11 1.08394e12i 0.122520 0.175090i
\(697\) −2.01995e12 −0.324185
\(698\) −2.18548e12 6.59315e12i −0.348495 1.05134i
\(699\) 4.62221e12i 0.732322i
\(700\) −1.35022e13 + 1.00563e13i −2.12551 + 1.58305i
\(701\) 2.19669e12i 0.343587i −0.985133 0.171794i \(-0.945044\pi\)
0.985133 0.171794i \(-0.0549562\pi\)
\(702\) −1.87618e12 + 6.21912e11i −0.291581 + 0.0966523i
\(703\) −2.62073e11 −0.0404692
\(704\) 3.15925e12 1.15206e12i 0.484738 0.176766i
\(705\) −1.16538e13 −1.77672
\(706\) −6.43638e12 + 2.13351e12i −0.975036 + 0.323202i
\(707\) 4.33557e12i 0.652618i
\(708\) −1.73163e11 + 1.28970e11i −0.0259003 + 0.0192903i
\(709\) 7.02990e11i 0.104482i −0.998635 0.0522410i \(-0.983364\pi\)
0.998635 0.0522410i \(-0.0166364\pi\)
\(710\) −5.05574e12 1.52522e13i −0.746659 2.25252i
\(711\) 1.94026e12 0.284739
\(712\) 5.12498e12 7.32399e12i 0.747363 1.06804i
\(713\) 3.69112e12 0.534879
\(714\) −6.90492e11 2.08308e12i −0.0994298 0.299960i
\(715\) 1.92222e12i 0.275058i
\(716\) −5.28088e12 7.09044e12i −0.750927 1.00824i
\(717\) 4.07909e12i 0.576404i
\(718\) 8.68510e12 2.87891e12i 1.21959 0.404267i
\(719\) 1.18349e13 1.65152 0.825759 0.564022i \(-0.190747\pi\)
0.825759 + 0.564022i \(0.190747\pi\)
\(720\) 6.21946e12 + 1.85922e12i 0.862495 + 0.257831i
\(721\) 4.41867e12 0.608952
\(722\) −1.78290e12 + 5.90992e11i −0.244180 + 0.0809401i
\(723\) 3.46870e12i 0.472111i
\(724\) −3.16113e12 4.24433e12i −0.427581 0.574097i
\(725\) 5.36325e12i 0.720953i
\(726\) 1.23777e12 + 3.73409e12i 0.165357 + 0.498850i
\(727\) −4.66170e12 −0.618927 −0.309464 0.950911i \(-0.600150\pi\)
−0.309464 + 0.950911i \(0.600150\pi\)
\(728\) −1.96438e12 1.37458e12i −0.259200 0.181376i
\(729\) −6.84083e12 −0.897088
\(730\) 1.68634e12 + 5.08735e12i 0.219782 + 0.663039i
\(731\) 5.49179e12i 0.711354i
\(732\) 2.63512e12 1.96261e12i 0.339234 0.252658i
\(733\) 1.16839e13i 1.49493i 0.664300 + 0.747466i \(0.268730\pi\)
−0.664300 + 0.747466i \(0.731270\pi\)
\(734\) −1.09102e13 + 3.61647e12i −1.38739 + 0.459888i
\(735\) 2.12690e12 0.268815
\(736\) 1.48698e11 + 5.02237e12i 0.0186790 + 0.630897i
\(737\) 1.45221e12 0.181311
\(738\) −3.00236e12 + 9.95212e11i −0.372571 + 0.123499i
\(739\) 1.25228e13i 1.54455i −0.635290 0.772274i \(-0.719119\pi\)
0.635290 0.772274i \(-0.280881\pi\)
\(740\) −5.67799e11 + 4.22890e11i −0.0696068 + 0.0518424i
\(741\) 1.46109e12i 0.178031i
\(742\) 2.40921e12 + 7.26811e12i 0.291781 + 0.880246i
\(743\) −1.10289e13 −1.32765 −0.663823 0.747890i \(-0.731067\pi\)
−0.663823 + 0.747890i \(0.731067\pi\)
\(744\) 4.15607e12 + 2.90822e12i 0.497284 + 0.347975i
\(745\) 9.93301e12 1.18135
\(746\) 4.94534e11 + 1.49191e12i 0.0584617 + 0.176367i
\(747\) 5.85785e12i 0.688328i
\(748\) −1.06145e12 1.42517e12i −0.123977 0.166459i
\(749\) 1.07403e13i 1.24695i
\(750\) 1.54203e13 5.11149e12i 1.77958 0.589891i
\(751\) −6.45522e12 −0.740511 −0.370255 0.928930i \(-0.620730\pi\)
−0.370255 + 0.928930i \(0.620730\pi\)
\(752\) −3.37113e12 + 1.12771e13i −0.384410 + 1.28593i
\(753\) 7.87631e12 0.892781
\(754\) −7.24987e11 + 2.40317e11i −0.0816882 + 0.0270778i
\(755\) 1.05294e13i 1.17935i
\(756\) −6.26708e12 8.41457e12i −0.697778 0.936880i
\(757\) 6.48010e12i 0.717217i −0.933488 0.358608i \(-0.883251\pi\)
0.933488 0.358608i \(-0.116749\pi\)
\(758\) 3.16868e12 + 9.55929e12i 0.348632 + 1.05175i
\(759\) 2.13253e12 0.233242
\(760\) 8.39963e12 1.20037e13i 0.913270 1.30513i
\(761\) 2.62886e12 0.284142 0.142071 0.989856i \(-0.454624\pi\)
0.142071 + 0.989856i \(0.454624\pi\)
\(762\) −1.72625e12 5.20774e12i −0.185483 0.559566i
\(763\) 1.53139e13i 1.63578i
\(764\) −3.75434e12 + 2.79619e12i −0.398670 + 0.296925i
\(765\) 3.43032e12i 0.362125i
\(766\) 9.67325e12 3.20646e12i 1.01518 0.336509i
\(767\) 1.24652e11 0.0130053
\(768\) −3.78967e12 + 5.77216e12i −0.393076 + 0.598705i
\(769\) −1.43517e13 −1.47991 −0.739955 0.672656i \(-0.765153\pi\)
−0.739955 + 0.672656i \(0.765153\pi\)
\(770\) 9.68520e12 3.21042e12i 0.992888 0.329120i
\(771\) 1.07002e13i 1.09055i
\(772\) 3.47184e11 2.58579e11i 0.0351789 0.0262008i
\(773\) 6.56407e12i 0.661250i −0.943762 0.330625i \(-0.892740\pi\)
0.943762 0.330625i \(-0.107260\pi\)
\(774\) 2.70576e12 + 8.16273e12i