Properties

Label 12.20.b.a.11.19
Level 12
Weight 20
Character 12.11
Analytic conductor 27.458
Analytic rank 0
Dimension 36
CM No

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Newspace parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 20 \)
Character orbit: \([\chi]\) = 12.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(27.4580035868\)
Analytic rank: \(0\)
Dimension: \(36\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 11.19
Character \(\chi\) = 12.11
Dual form 12.20.b.a.11.20

$q$-expansion

\(f(q)\) \(=\) \(q+(74.5111 - 720.233i) q^{2} +(-32706.8 - 9618.97i) q^{3} +(-513184. - 107331. i) q^{4} -7.07022e6i q^{5} +(-9.36493e6 + 2.28398e7i) q^{6} +1.56654e8i q^{7} +(-1.15541e8 + 3.61615e8i) q^{8} +(9.77212e8 + 6.29212e8i) q^{9} +O(q^{10})\) \(q+(74.5111 - 720.233i) q^{2} +(-32706.8 - 9618.97i) q^{3} +(-513184. - 107331. i) q^{4} -7.07022e6i q^{5} +(-9.36493e6 + 2.28398e7i) q^{6} +1.56654e8i q^{7} +(-1.15541e8 + 3.61615e8i) q^{8} +(9.77212e8 + 6.29212e8i) q^{9} +(-5.09221e9 - 5.26810e8i) q^{10} -9.54672e9 q^{11} +(1.57522e10 + 8.44676e9i) q^{12} -2.20437e10 q^{13} +(1.12827e11 + 1.16725e10i) q^{14} +(-6.80083e10 + 2.31244e11i) q^{15} +(2.51838e11 + 1.10161e11i) q^{16} -1.32854e11i q^{17} +(5.25993e11 - 6.56937e11i) q^{18} +1.26419e11i q^{19} +(-7.58852e11 + 3.62833e12i) q^{20} +(1.50685e12 - 5.12365e12i) q^{21} +(-7.11337e11 + 6.87586e12i) q^{22} +1.44365e13 q^{23} +(7.25735e12 - 1.07159e13i) q^{24} -3.09145e13 q^{25} +(-1.64250e12 + 1.58766e13i) q^{26} +(-2.59091e13 - 2.99793e13i) q^{27} +(1.68138e13 - 8.03923e13i) q^{28} -5.22664e13i q^{29} +(1.61483e14 + 6.62121e13i) q^{30} -8.91820e12i q^{31} +(9.81063e13 - 1.73174e14i) q^{32} +(3.12243e14 + 9.18296e13i) q^{33} +(-9.56858e13 - 9.89909e12i) q^{34} +1.10758e15 q^{35} +(-4.33956e14 - 4.27787e14i) q^{36} -5.03102e14 q^{37} +(9.10509e13 + 9.41960e12i) q^{38} +(7.20978e14 + 2.12037e14i) q^{39} +(2.55670e15 + 8.16901e14i) q^{40} +1.92871e15i q^{41} +(-3.57795e15 - 1.46705e15i) q^{42} +1.96994e14i q^{43} +(4.89922e15 + 1.02466e15i) q^{44} +(4.44867e15 - 6.90910e15i) q^{45} +(1.07568e15 - 1.03976e16i) q^{46} -6.24266e15 q^{47} +(-7.17719e15 - 6.02544e15i) q^{48} -1.31415e16 q^{49} +(-2.30348e15 + 2.22657e16i) q^{50} +(-1.27792e15 + 4.34523e15i) q^{51} +(1.13125e16 + 2.36596e15i) q^{52} +9.61536e15i q^{53} +(-2.35226e16 + 1.64268e16i) q^{54} +6.74974e16i q^{55} +(-5.66484e16 - 1.81000e16i) q^{56} +(1.21602e15 - 4.13475e15i) q^{57} +(-3.76440e16 - 3.89443e15i) q^{58} +2.49085e16 q^{59} +(5.97204e16 - 1.11372e17i) q^{60} +1.42524e17 q^{61} +(-6.42318e15 - 6.64505e14i) q^{62} +(-9.85685e16 + 1.53084e17i) q^{63} +(-1.17416e17 - 8.35628e16i) q^{64} +1.55853e17i q^{65} +(8.94043e16 - 2.18045e17i) q^{66} +1.59598e17i q^{67} +(-1.42593e16 + 6.81785e16i) q^{68} +(-4.72171e17 - 1.38864e17i) q^{69} +(8.25268e16 - 7.97714e17i) q^{70} +6.13599e17 q^{71} +(-3.40441e17 + 2.80675e17i) q^{72} +4.40811e17 q^{73} +(-3.74867e16 + 3.62351e17i) q^{74} +(1.01112e18 + 2.97366e17i) q^{75} +(1.35686e16 - 6.48761e16i) q^{76} -1.49553e18i q^{77} +(2.06437e17 - 5.03473e17i) q^{78} +1.92328e18i q^{79} +(7.78862e17 - 1.78055e18i) q^{80} +(5.59035e17 + 1.22975e18i) q^{81} +(1.38912e18 + 1.43710e17i) q^{82} -1.68268e18 q^{83} +(-1.32322e18 + 2.46765e18i) q^{84} -9.39306e17 q^{85} +(1.41882e17 + 1.46782e16i) q^{86} +(-5.02749e17 + 1.70947e18i) q^{87} +(1.10304e18 - 3.45224e18i) q^{88} +2.75763e18i q^{89} +(-4.64469e18 - 3.71889e18i) q^{90} -3.45322e18i q^{91} +(-7.40856e18 - 1.54948e18i) q^{92} +(-8.57839e16 + 2.91686e17i) q^{93} +(-4.65148e17 + 4.49617e18i) q^{94} +8.93808e17 q^{95} +(-4.87450e18 + 4.72029e18i) q^{96} +7.95134e18 q^{97} +(-9.79191e17 + 9.46497e18i) q^{98} +(-9.32917e18 - 6.00691e18i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 47880q^{4} + 21771144q^{6} - 809473644q^{9} + O(q^{10}) \) \( 36q - 47880q^{4} + 21771144q^{6} - 809473644q^{9} - 4162950000q^{10} - 2268767880q^{12} - 25913431656q^{13} + 791689296672q^{16} + 2852271258192q^{18} - 1650825908424q^{21} + 7247870602416q^{22} + 23719435803936q^{24} - 118879690462380q^{25} - 7629081673968q^{28} + 37456727138640q^{30} + 529254701828640q^{33} - 248241675948480q^{34} - 1177548745309416q^{36} + 1847838600168120q^{37} - 40433256181440q^{40} - 2709671988768336q^{42} - 4365410114088000q^{45} + 17206125364795104q^{46} + 1561106052682272q^{48} - 49399737041580084q^{49} + 16558671470242896q^{52} + 40087412948587896q^{54} + 44803667812766472q^{57} - 34645536255764880q^{58} + 50260381053157440q^{60} + 174742350239997144q^{61} - 139766490424918656q^{64} - 87772097712685968q^{66} - 957190369821780672q^{69} + 244663962371376480q^{70} + 54134736422921280q^{72} - 1445122541399481432q^{73} + 2744130151937256048q^{76} + 1125465917961999024q^{78} + 1033298241353042436q^{81} + 1064985418859680800q^{82} + 1920709484261873424q^{84} - 1802899595088057600q^{85} - 9209792381828477760q^{88} - 5194944179528261040q^{90} + 6719944190337314136q^{93} - 3835186345170303552q^{94} - 11947184361208227456q^{96} + 12765226159947004488q^{97} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 74.5111 720.233i 0.102905 0.994691i
\(3\) −32706.8 9618.97i −0.959371 0.282148i
\(4\) −513184. 107331.i −0.978821 0.204717i
\(5\) 7.07022e6i 1.61889i −0.587194 0.809446i \(-0.699768\pi\)
0.587194 0.809446i \(-0.300232\pi\)
\(6\) −9.36493e6 + 2.28398e7i −0.379374 + 0.925243i
\(7\) 1.56654e8i 1.46727i 0.679544 + 0.733635i \(0.262178\pi\)
−0.679544 + 0.733635i \(0.737822\pi\)
\(8\) −1.15541e8 + 3.61615e8i −0.304356 + 0.952558i
\(9\) 9.77212e8 + 6.29212e8i 0.840785 + 0.541369i
\(10\) −5.09221e9 5.26810e8i −1.61030 0.166592i
\(11\) −9.54672e9 −1.22074 −0.610371 0.792116i \(-0.708979\pi\)
−0.610371 + 0.792116i \(0.708979\pi\)
\(12\) 1.57522e10 + 8.44676e9i 0.881292 + 0.472572i
\(13\) −2.20437e10 −0.576530 −0.288265 0.957551i \(-0.593078\pi\)
−0.288265 + 0.957551i \(0.593078\pi\)
\(14\) 1.12827e11 + 1.16725e10i 1.45948 + 0.150989i
\(15\) −6.80083e10 + 2.31244e11i −0.456767 + 1.55312i
\(16\) 2.51838e11 + 1.10161e11i 0.916182 + 0.400763i
\(17\) 1.32854e11i 0.271712i −0.990729 0.135856i \(-0.956621\pi\)
0.990729 0.135856i \(-0.0433785\pi\)
\(18\) 5.25993e11 6.56937e11i 0.625016 0.780612i
\(19\) 1.26419e11i 0.0898777i 0.998990 + 0.0449389i \(0.0143093\pi\)
−0.998990 + 0.0449389i \(0.985691\pi\)
\(20\) −7.58852e11 + 3.62833e12i −0.331415 + 1.58461i
\(21\) 1.50685e12 5.12365e12i 0.413987 1.40766i
\(22\) −7.11337e11 + 6.87586e12i −0.125620 + 1.21426i
\(23\) 1.44365e13 1.67127 0.835634 0.549287i \(-0.185101\pi\)
0.835634 + 0.549287i \(0.185101\pi\)
\(24\) 7.25735e12 1.07159e13i 0.560753 0.827983i
\(25\) −3.09145e13 −1.62081
\(26\) −1.64250e12 + 1.58766e13i −0.0593277 + 0.573469i
\(27\) −2.59091e13 2.99793e13i −0.653879 0.756599i
\(28\) 1.68138e13 8.03923e13i 0.300375 1.43619i
\(29\) 5.22664e13i 0.669024i −0.942391 0.334512i \(-0.891428\pi\)
0.942391 0.334512i \(-0.108572\pi\)
\(30\) 1.61483e14 + 6.62121e13i 1.49787 + 0.614166i
\(31\) 8.91820e12i 0.0605816i −0.999541 0.0302908i \(-0.990357\pi\)
0.999541 0.0302908i \(-0.00964334\pi\)
\(32\) 9.81063e13 1.73174e14i 0.492915 0.870077i
\(33\) 3.12243e14 + 9.18296e13i 1.17114 + 0.344430i
\(34\) −9.56858e13 9.89909e12i −0.270270 0.0279606i
\(35\) 1.10758e15 2.37535
\(36\) −4.33956e14 4.27787e14i −0.712151 0.702027i
\(37\) −5.03102e14 −0.636415 −0.318207 0.948021i \(-0.603081\pi\)
−0.318207 + 0.948021i \(0.603081\pi\)
\(38\) 9.10509e13 + 9.41960e12i 0.0894006 + 0.00924886i
\(39\) 7.20978e14 + 2.12037e14i 0.553106 + 0.162667i
\(40\) 2.55670e15 + 8.16901e14i 1.54209 + 0.492719i
\(41\) 1.92871e15i 0.920068i 0.887901 + 0.460034i \(0.152163\pi\)
−0.887901 + 0.460034i \(0.847837\pi\)
\(42\) −3.57795e15 1.46705e15i −1.35758 0.556644i
\(43\) 1.96994e14i 0.0597727i 0.999553 + 0.0298863i \(0.00951453\pi\)
−0.999553 + 0.0298863i \(0.990485\pi\)
\(44\) 4.89922e15 + 1.02466e15i 1.19489 + 0.249907i
\(45\) 4.44867e15 6.90910e15i 0.876418 1.36114i
\(46\) 1.07568e15 1.03976e16i 0.171982 1.66240i
\(47\) −6.24266e15 −0.813655 −0.406827 0.913505i \(-0.633365\pi\)
−0.406827 + 0.913505i \(0.633365\pi\)
\(48\) −7.17719e15 6.02544e15i −0.765884 0.642979i
\(49\) −1.31415e16 −1.15288
\(50\) −2.30348e15 + 2.22657e16i −0.166789 + 1.61221i
\(51\) −1.27792e15 + 4.34523e15i −0.0766631 + 0.260673i
\(52\) 1.13125e16 + 2.36596e15i 0.564320 + 0.118026i
\(53\) 9.61536e15i 0.400262i 0.979769 + 0.200131i \(0.0641369\pi\)
−0.979769 + 0.200131i \(0.935863\pi\)
\(54\) −2.35226e16 + 1.64268e16i −0.819870 + 0.572550i
\(55\) 6.74974e16i 1.97625i
\(56\) −5.66484e16 1.81000e16i −1.39766 0.446572i
\(57\) 1.21602e15 4.13475e15i 0.0253588 0.0862261i
\(58\) −3.76440e16 3.89443e15i −0.665472 0.0688459i
\(59\) 2.49085e16 0.374329 0.187165 0.982329i \(-0.440070\pi\)
0.187165 + 0.982329i \(0.440070\pi\)
\(60\) 5.97204e16 1.11372e17i 0.765043 1.42672i
\(61\) 1.42524e17 1.56047 0.780235 0.625487i \(-0.215099\pi\)
0.780235 + 0.625487i \(0.215099\pi\)
\(62\) −6.42318e15 6.64505e14i −0.0602600 0.00623415i
\(63\) −9.85685e16 + 1.53084e17i −0.794334 + 1.23366i
\(64\) −1.17416e17 8.35628e16i −0.814735 0.579834i
\(65\) 1.55853e17i 0.933339i
\(66\) 8.94043e16 2.18045e17i 0.463118 1.12948i
\(67\) 1.59598e17i 0.716664i 0.933594 + 0.358332i \(0.116654\pi\)
−0.933594 + 0.358332i \(0.883346\pi\)
\(68\) −1.42593e16 + 6.81785e16i −0.0556242 + 0.265958i
\(69\) −4.72171e17 1.38864e17i −1.60337 0.471545i
\(70\) 8.25268e16 7.97714e17i 0.244435 2.36274i
\(71\) 6.13599e17 1.58829 0.794146 0.607727i \(-0.207918\pi\)
0.794146 + 0.607727i \(0.207918\pi\)
\(72\) −3.40441e17 + 2.80675e17i −0.771584 + 0.636128i
\(73\) 4.40811e17 0.876365 0.438182 0.898886i \(-0.355622\pi\)
0.438182 + 0.898886i \(0.355622\pi\)
\(74\) −3.74867e16 + 3.62351e17i −0.0654902 + 0.633036i
\(75\) 1.01112e18 + 2.97366e17i 1.55496 + 0.457309i
\(76\) 1.35686e16 6.48761e16i 0.0183995 0.0879742i
\(77\) 1.49553e18i 1.79116i
\(78\) 2.06437e17 5.03473e17i 0.218720 0.533430i
\(79\) 1.92328e18i 1.80545i 0.430223 + 0.902723i \(0.358435\pi\)
−0.430223 + 0.902723i \(0.641565\pi\)
\(80\) 7.78862e17 1.78055e18i 0.648792 1.48320i
\(81\) 5.59035e17 + 1.22975e18i 0.413839 + 0.910350i
\(82\) 1.38912e18 + 1.43710e17i 0.915184 + 0.0946795i
\(83\) −1.68268e18 −0.988006 −0.494003 0.869460i \(-0.664467\pi\)
−0.494003 + 0.869460i \(0.664467\pi\)
\(84\) −1.32322e18 + 2.46765e18i −0.693390 + 1.29309i
\(85\) −9.39306e17 −0.439873
\(86\) 1.41882e17 + 1.46782e16i 0.0594553 + 0.00615090i
\(87\) −5.02749e17 + 1.70947e18i −0.188764 + 0.641842i
\(88\) 1.10304e18 3.45224e18i 0.371540 1.16283i
\(89\) 2.75763e18i 0.834317i 0.908834 + 0.417159i \(0.136974\pi\)
−0.908834 + 0.417159i \(0.863026\pi\)
\(90\) −4.64469e18 3.71889e18i −1.26373 1.01183i
\(91\) 3.45322e18i 0.845924i
\(92\) −7.40856e18 1.54948e18i −1.63587 0.342137i
\(93\) −8.57839e16 + 2.91686e17i −0.0170930 + 0.0581203i
\(94\) −4.65148e17 + 4.49617e18i −0.0837291 + 0.809335i
\(95\) 8.93808e17 0.145502
\(96\) −4.87450e18 + 4.72029e18i −0.718379 + 0.695652i
\(97\) 7.95134e18 1.06196 0.530981 0.847384i \(-0.321824\pi\)
0.530981 + 0.847384i \(0.321824\pi\)
\(98\) −9.79191e17 + 9.46497e18i −0.118637 + 1.14676i
\(99\) −9.32917e18 6.00691e18i −1.02638 0.660871i
\(100\) 1.58648e19 + 3.31808e18i 1.58648 + 0.331808i
\(101\) 1.14619e18i 0.104281i −0.998640 0.0521403i \(-0.983396\pi\)
0.998640 0.0521403i \(-0.0166043\pi\)
\(102\) 3.03436e18 + 1.24417e18i 0.251400 + 0.103081i
\(103\) 4.87634e18i 0.368248i −0.982903 0.184124i \(-0.941055\pi\)
0.982903 0.184124i \(-0.0589448\pi\)
\(104\) 2.54695e18 7.97132e18i 0.175470 0.549178i
\(105\) −3.62253e19 1.06538e19i −2.27884 0.670200i
\(106\) 6.92530e18 + 7.16451e17i 0.398138 + 0.0411890i
\(107\) −4.48993e18 −0.236099 −0.118049 0.993008i \(-0.537664\pi\)
−0.118049 + 0.993008i \(0.537664\pi\)
\(108\) 1.00785e19 + 1.81658e19i 0.485141 + 0.874436i
\(109\) 2.83035e19 1.24821 0.624106 0.781340i \(-0.285463\pi\)
0.624106 + 0.781340i \(0.285463\pi\)
\(110\) 4.86139e19 + 5.02931e18i 1.96576 + 0.203366i
\(111\) 1.64549e19 + 4.83933e18i 0.610558 + 0.179563i
\(112\) −1.72571e19 + 3.94514e19i −0.588027 + 1.34429i
\(113\) 7.79869e18i 0.244217i 0.992517 + 0.122109i \(0.0389656\pi\)
−0.992517 + 0.122109i \(0.961034\pi\)
\(114\) −2.88738e18 1.18390e18i −0.0831587 0.0340973i
\(115\) 1.02069e20i 2.70560i
\(116\) −5.60980e18 + 2.68223e19i −0.136961 + 0.654855i
\(117\) −2.15413e19 1.38701e19i −0.484738 0.312115i
\(118\) 1.85596e18 1.79399e19i 0.0385203 0.372342i
\(119\) 2.08121e19 0.398675
\(120\) −7.57637e19 5.13111e19i −1.34042 0.907798i
\(121\) 2.99807e19 0.490209
\(122\) 1.06196e19 1.02651e20i 0.160580 1.55219i
\(123\) 1.85522e19 6.30819e19i 0.259595 0.882687i
\(124\) −9.57197e17 + 4.57668e18i −0.0124021 + 0.0592986i
\(125\) 8.37188e19i 1.00503i
\(126\) 1.02912e20 + 8.23988e19i 1.14537 + 0.917066i
\(127\) 1.25184e20i 1.29245i 0.763148 + 0.646224i \(0.223653\pi\)
−0.763148 + 0.646224i \(0.776347\pi\)
\(128\) −6.89335e19 + 7.83403e19i −0.660596 + 0.750742i
\(129\) 1.89488e18 6.44305e18i 0.0168647 0.0573442i
\(130\) 1.12251e20 + 1.16128e19i 0.928385 + 0.0960452i
\(131\) −1.02355e20 −0.787106 −0.393553 0.919302i \(-0.628754\pi\)
−0.393553 + 0.919302i \(0.628754\pi\)
\(132\) −1.50382e20 8.06388e19i −1.07583 0.576888i
\(133\) −1.98040e19 −0.131875
\(134\) 1.14947e20 + 1.18918e19i 0.712859 + 0.0737483i
\(135\) −2.11960e20 + 1.83183e20i −1.22485 + 1.05856i
\(136\) 4.80420e19 + 1.53501e19i 0.258822 + 0.0826973i
\(137\) 1.67435e20i 0.841396i −0.907201 0.420698i \(-0.861785\pi\)
0.907201 0.420698i \(-0.138215\pi\)
\(138\) −1.35196e20 + 3.29726e20i −0.634036 + 1.54633i
\(139\) 1.80123e20i 0.788731i 0.918954 + 0.394365i \(0.129036\pi\)
−0.918954 + 0.394365i \(0.870964\pi\)
\(140\) −5.68391e20 1.18877e20i −2.32504 0.486275i
\(141\) 2.04178e20 + 6.00480e19i 0.780597 + 0.229571i
\(142\) 4.57200e19 4.41935e20i 0.163443 1.57986i
\(143\) 2.10445e20 0.703794
\(144\) 1.76785e20 + 2.66110e20i 0.553351 + 0.832948i
\(145\) −3.69535e20 −1.08308
\(146\) 3.28453e19 3.17487e20i 0.0901823 0.871713i
\(147\) 4.29818e20 + 1.26408e20i 1.10604 + 0.325282i
\(148\) 2.58184e20 + 5.39984e19i 0.622936 + 0.130285i
\(149\) 1.23657e20i 0.279865i −0.990161 0.139932i \(-0.955311\pi\)
0.990161 0.139932i \(-0.0446885\pi\)
\(150\) 2.89512e20 7.06083e20i 0.614894 1.49965i
\(151\) 1.57724e20i 0.314497i 0.987559 + 0.157249i \(0.0502624\pi\)
−0.987559 + 0.157249i \(0.949738\pi\)
\(152\) −4.57149e19 1.46066e19i −0.0856138 0.0273548i
\(153\) 8.35933e19 1.29826e20i 0.147097 0.228452i
\(154\) −1.07713e21 1.11434e20i −1.78165 0.184319i
\(155\) −6.30536e19 −0.0980751
\(156\) −3.47236e20 1.86197e20i −0.508091 0.272452i
\(157\) 4.51136e20 0.621242 0.310621 0.950534i \(-0.399463\pi\)
0.310621 + 0.950534i \(0.399463\pi\)
\(158\) 1.38521e21 + 1.43305e20i 1.79586 + 0.185789i
\(159\) 9.24899e19 3.14488e20i 0.112933 0.384000i
\(160\) −1.22438e21 6.93633e20i −1.40856 0.797976i
\(161\) 2.26153e21i 2.45220i
\(162\) 9.27360e20 3.11006e20i 0.948103 0.317963i
\(163\) 1.58771e21i 1.53105i 0.643408 + 0.765523i \(0.277520\pi\)
−0.643408 + 0.765523i \(0.722480\pi\)
\(164\) 2.07010e20 9.89783e20i 0.188354 0.900582i
\(165\) 6.49256e20 2.20763e21i 0.557594 1.89596i
\(166\) −1.25378e20 + 1.21192e21i −0.101671 + 0.982761i
\(167\) 1.26877e21 0.971802 0.485901 0.874014i \(-0.338492\pi\)
0.485901 + 0.874014i \(0.338492\pi\)
\(168\) 1.67869e21 + 1.13689e21i 1.21487 + 0.822775i
\(169\) −9.75998e20 −0.667613
\(170\) −6.99888e19 + 6.76520e20i −0.0452651 + 0.437538i
\(171\) −7.95442e19 + 1.23538e20i −0.0486570 + 0.0755678i
\(172\) 2.11435e19 1.01094e20i 0.0122365 0.0585068i
\(173\) 7.11034e20i 0.389451i −0.980858 0.194725i \(-0.937618\pi\)
0.980858 0.194725i \(-0.0623816\pi\)
\(174\) 1.19376e21 + 4.89471e20i 0.619010 + 0.253810i
\(175\) 4.84288e21i 2.37817i
\(176\) −2.40423e21 1.05168e21i −1.11842 0.489228i
\(177\) −8.14679e20 2.39594e20i −0.359121 0.105616i
\(178\) 1.98614e21 + 2.05474e20i 0.829888 + 0.0858553i
\(179\) −1.51538e21 −0.600368 −0.300184 0.953881i \(-0.597048\pi\)
−0.300184 + 0.953881i \(0.597048\pi\)
\(180\) −3.02455e21 + 3.06816e21i −1.13651 + 1.15290i
\(181\) −1.11774e21 −0.398469 −0.199234 0.979952i \(-0.563845\pi\)
−0.199234 + 0.979952i \(0.563845\pi\)
\(182\) −2.48713e21 2.57304e20i −0.841433 0.0870498i
\(183\) −4.66152e21 1.37094e21i −1.49707 0.440283i
\(184\) −1.66800e21 + 5.22044e21i −0.508660 + 1.59198i
\(185\) 3.55705e21i 1.03029i
\(186\) 2.03690e20 + 8.35183e19i 0.0560528 + 0.0229831i
\(187\) 1.26832e21i 0.331691i
\(188\) 3.20364e21 + 6.70030e20i 0.796423 + 0.166569i
\(189\) 4.69638e21 4.05877e21i 1.11013 0.959416i
\(190\) 6.65986e19 6.43750e20i 0.0149729 0.144730i
\(191\) −4.84369e21 −1.03600 −0.518000 0.855381i \(-0.673323\pi\)
−0.518000 + 0.855381i \(0.673323\pi\)
\(192\) 3.03651e21 + 3.86249e21i 0.618034 + 0.786151i
\(193\) −6.01816e21 −1.16592 −0.582961 0.812500i \(-0.698106\pi\)
−0.582961 + 0.812500i \(0.698106\pi\)
\(194\) 5.92463e20 5.72682e21i 0.109281 1.05632i
\(195\) 1.49915e21 5.09747e21i 0.263340 0.895419i
\(196\) 6.74403e21 + 1.41049e21i 1.12846 + 0.236014i
\(197\) 9.66538e21i 1.54095i 0.637467 + 0.770477i \(0.279982\pi\)
−0.637467 + 0.770477i \(0.720018\pi\)
\(198\) −5.02151e21 + 6.27160e21i −0.762983 + 0.952925i
\(199\) 3.26555e21i 0.472990i −0.971633 0.236495i \(-0.924001\pi\)
0.971633 0.236495i \(-0.0759987\pi\)
\(200\) 3.57190e21 1.11792e22i 0.493304 1.54392i
\(201\) 1.53516e21 5.21993e21i 0.202205 0.687547i
\(202\) −8.25524e20 8.54039e19i −0.103727 0.0107310i
\(203\) 8.18774e21 0.981638
\(204\) 1.12218e21 2.09274e21i 0.128404 0.239458i
\(205\) 1.36364e22 1.48949
\(206\) −3.51211e21 3.63342e20i −0.366293 0.0378946i
\(207\) 1.41075e22 + 9.08359e21i 1.40518 + 0.904773i
\(208\) −5.55143e21 2.42835e21i −0.528206 0.231052i
\(209\) 1.20688e21i 0.109717i
\(210\) −1.03724e22 + 2.52969e22i −0.901146 + 2.19778i
\(211\) 1.05355e21i 0.0874930i −0.999043 0.0437465i \(-0.986071\pi\)
0.999043 0.0437465i \(-0.0139294\pi\)
\(212\) 1.03202e21 4.93445e21i 0.0819406 0.391785i
\(213\) −2.00689e22 5.90219e21i −1.52376 0.448133i
\(214\) −3.34550e20 + 3.23380e21i −0.0242957 + 0.234845i
\(215\) 1.39279e21 0.0967655
\(216\) 1.38345e22 5.90529e21i 0.919717 0.392582i
\(217\) 1.39707e21 0.0888896
\(218\) 2.10892e21 2.03851e22i 0.128447 1.24159i
\(219\) −1.44175e22 4.24015e21i −0.840759 0.247265i
\(220\) 7.24455e21 3.46386e22i 0.404572 1.93439i
\(221\) 2.92859e21i 0.156650i
\(222\) 4.71152e21 1.14908e22i 0.241439 0.588838i
\(223\) 1.15715e22i 0.568192i 0.958796 + 0.284096i \(0.0916934\pi\)
−0.958796 + 0.284096i \(0.908307\pi\)
\(224\) 2.71284e22 + 1.53687e22i 1.27664 + 0.723239i
\(225\) −3.02101e22 1.94518e22i −1.36275 0.877457i
\(226\) 5.61688e21 + 5.81089e20i 0.242921 + 0.0251312i
\(227\) 7.86342e21 0.326111 0.163056 0.986617i \(-0.447865\pi\)
0.163056 + 0.986617i \(0.447865\pi\)
\(228\) −1.06783e21 + 1.99137e21i −0.0424737 + 0.0792085i
\(229\) 4.83174e22 1.84360 0.921800 0.387665i \(-0.126718\pi\)
0.921800 + 0.387665i \(0.126718\pi\)
\(230\) −7.35134e22 7.60527e21i −2.69124 0.278420i
\(231\) −1.43855e22 + 4.89141e22i −0.505371 + 1.71838i
\(232\) 1.89003e22 + 6.03892e21i 0.637285 + 0.203621i
\(233\) 5.28275e22i 1.70993i 0.518683 + 0.854967i \(0.326423\pi\)
−0.518683 + 0.854967i \(0.673577\pi\)
\(234\) −1.15948e22 + 1.44813e22i −0.360340 + 0.450046i
\(235\) 4.41370e22i 1.31722i
\(236\) −1.27827e22 2.67345e21i −0.366401 0.0766317i
\(237\) 1.84999e22 6.29043e22i 0.509403 1.73209i
\(238\) 1.55073e21 1.49896e22i 0.0410257 0.396559i
\(239\) 2.89704e22 0.736502 0.368251 0.929726i \(-0.379957\pi\)
0.368251 + 0.929726i \(0.379957\pi\)
\(240\) −4.26012e22 + 5.07443e22i −1.04091 + 1.23988i
\(241\) −6.95255e21 −0.163299 −0.0816493 0.996661i \(-0.526019\pi\)
−0.0816493 + 0.996661i \(0.526019\pi\)
\(242\) 2.23390e21 2.15931e22i 0.0504449 0.487607i
\(243\) −6.45536e21 4.55985e22i −0.140172 0.990127i
\(244\) −7.31412e22 1.52972e22i −1.52742 0.319455i
\(245\) 9.29136e22i 1.86639i
\(246\) −4.40514e22 1.80622e22i −0.851287 0.349050i
\(247\) 2.78673e21i 0.0518172i
\(248\) 3.22495e21 + 1.03042e21i 0.0577076 + 0.0184384i
\(249\) 5.50351e22 + 1.61857e22i 0.947864 + 0.278764i
\(250\) 6.02970e22 + 6.23798e21i 0.999691 + 0.103422i
\(251\) −7.20931e22 −1.15078 −0.575391 0.817878i \(-0.695150\pi\)
−0.575391 + 0.817878i \(0.695150\pi\)
\(252\) 6.70145e22 6.79809e22i 1.03006 1.04492i
\(253\) −1.37821e23 −2.04019
\(254\) 9.01616e22 + 9.32759e21i 1.28559 + 0.132999i
\(255\) 3.07217e22 + 9.03516e21i 0.422002 + 0.124109i
\(256\) 5.12870e22 + 5.54854e22i 0.678778 + 0.734344i
\(257\) 8.57468e22i 1.09359i −0.837268 0.546793i \(-0.815848\pi\)
0.837268 0.546793i \(-0.184152\pi\)
\(258\) −4.49931e21 1.84483e21i −0.0553043 0.0226762i
\(259\) 7.88129e22i 0.933791i
\(260\) 1.67279e22 7.99815e22i 0.191071 0.913572i
\(261\) 3.28867e22 5.10754e22i 0.362189 0.562506i
\(262\) −7.62661e21 + 7.37197e22i −0.0809971 + 0.782927i
\(263\) −4.64463e22 −0.475742 −0.237871 0.971297i \(-0.576450\pi\)
−0.237871 + 0.971297i \(0.576450\pi\)
\(264\) −6.92839e22 + 1.02302e23i −0.684534 + 1.01075i
\(265\) 6.79827e22 0.647982
\(266\) −1.47562e21 + 1.42635e22i −0.0135706 + 0.131175i
\(267\) 2.65256e22 9.01934e22i 0.235401 0.800420i
\(268\) 1.71297e22 8.19029e22i 0.146713 0.701486i
\(269\) 7.11907e22i 0.588540i −0.955722 0.294270i \(-0.904923\pi\)
0.955722 0.294270i \(-0.0950766\pi\)
\(270\) 1.16141e23 + 1.66310e23i 0.926896 + 1.32728i
\(271\) 1.94909e23i 1.50184i −0.660395 0.750918i \(-0.729611\pi\)
0.660395 0.750918i \(-0.270389\pi\)
\(272\) 1.46353e22 3.34577e22i 0.108892 0.248938i
\(273\) −3.32165e22 + 1.12944e23i −0.238676 + 0.811555i
\(274\) −1.20592e23 1.24758e22i −0.836929 0.0865838i
\(275\) 2.95132e23 1.97859
\(276\) 2.27406e23 + 1.21941e23i 1.47287 + 0.789795i
\(277\) −1.58079e23 −0.989272 −0.494636 0.869100i \(-0.664699\pi\)
−0.494636 + 0.869100i \(0.664699\pi\)
\(278\) 1.29731e23 + 1.34212e22i 0.784543 + 0.0811643i
\(279\) 5.61144e21 8.71497e21i 0.0327970 0.0509361i
\(280\) −1.27971e23 + 4.00517e23i −0.722952 + 2.26266i
\(281\) 6.36293e22i 0.347494i −0.984790 0.173747i \(-0.944412\pi\)
0.984790 0.173747i \(-0.0555875\pi\)
\(282\) 5.84621e22 1.42581e23i 0.308680 0.752829i
\(283\) 1.94382e23i 0.992396i 0.868210 + 0.496198i \(0.165271\pi\)
−0.868210 + 0.496198i \(0.834729\pi\)
\(284\) −3.14889e23 6.58581e22i −1.55465 0.325151i
\(285\) −2.92336e22 8.59751e21i −0.139591 0.0410532i
\(286\) 1.56805e22 1.51569e23i 0.0724238 0.700057i
\(287\) −3.02140e23 −1.34999
\(288\) 2.04834e23 1.07498e23i 0.885469 0.464699i
\(289\) 2.21422e23 0.926172
\(290\) −2.75345e22 + 2.66152e23i −0.111454 + 1.07733i
\(291\) −2.60063e23 7.64837e22i −1.01881 0.299630i
\(292\) −2.26217e23 4.73126e22i −0.857805 0.179407i
\(293\) 3.73976e23i 1.37278i 0.727234 + 0.686390i \(0.240806\pi\)
−0.727234 + 0.686390i \(0.759194\pi\)
\(294\) 1.23070e23 3.00151e23i 0.437372 1.06669i
\(295\) 1.76109e23i 0.605999i
\(296\) 5.81290e22 1.81929e23i 0.193697 0.606222i
\(297\) 2.47347e23 + 2.86204e23i 0.798217 + 0.923612i
\(298\) −8.90617e22 9.21380e21i −0.278379 0.0287995i
\(299\) −3.18232e23 −0.963536
\(300\) −4.86972e23 2.61127e23i −1.42841 0.765950i
\(301\) −3.08599e22 −0.0877026
\(302\) 1.13598e23 + 1.17522e22i 0.312827 + 0.0323633i
\(303\) −1.10252e22 + 3.74882e22i −0.0294226 + 0.100044i
\(304\) −1.39264e22 + 3.18370e22i −0.0360197 + 0.0823443i
\(305\) 1.00768e24i 2.52623i
\(306\) −8.72767e22 6.98802e22i −0.212102 0.169825i
\(307\) 4.50247e23i 1.06081i 0.847746 + 0.530403i \(0.177959\pi\)
−0.847746 + 0.530403i \(0.822041\pi\)
\(308\) −1.60516e23 + 7.67483e23i −0.366680 + 1.75322i
\(309\) −4.69054e22 + 1.59490e23i −0.103900 + 0.353287i
\(310\) −4.69820e21 + 4.54133e22i −0.0100924 + 0.0975545i
\(311\) 4.05652e23 0.845142 0.422571 0.906330i \(-0.361128\pi\)
0.422571 + 0.906330i \(0.361128\pi\)
\(312\) −1.59979e23 + 2.36217e23i −0.323291 + 0.477357i
\(313\) −7.97913e23 −1.56417 −0.782086 0.623171i \(-0.785844\pi\)
−0.782086 + 0.623171i \(0.785844\pi\)
\(314\) 3.36147e22 3.24923e23i 0.0639289 0.617944i
\(315\) 1.08234e24 + 6.96901e23i 1.99716 + 1.28594i
\(316\) 2.06427e23 9.86995e23i 0.369606 1.76721i
\(317\) 4.17201e23i 0.724907i 0.932002 + 0.362454i \(0.118061\pi\)
−0.932002 + 0.362454i \(0.881939\pi\)
\(318\) −2.19613e23 9.00472e22i −0.370340 0.151849i
\(319\) 4.98973e23i 0.816705i
\(320\) −5.90808e23 + 8.30155e23i −0.938688 + 1.31897i
\(321\) 1.46851e23 + 4.31885e22i 0.226506 + 0.0666148i
\(322\) 1.62883e24 + 1.68509e23i 2.43918 + 0.252343i
\(323\) 1.67952e22 0.0244209
\(324\) −1.54898e23 6.91089e23i −0.218710 0.975790i
\(325\) 6.81469e23 0.934446
\(326\) 1.14352e24 + 1.18302e23i 1.52292 + 0.157552i
\(327\) −9.25718e23 2.72251e23i −1.19750 0.352180i
\(328\) −6.97450e23 2.22845e23i −0.876419 0.280028i
\(329\) 9.77937e23i 1.19385i
\(330\) −1.54163e24 6.32108e23i −1.82851 0.749737i
\(331\) 3.07288e23i 0.354144i 0.984198 + 0.177072i \(0.0566625\pi\)
−0.984198 + 0.177072i \(0.943337\pi\)
\(332\) 8.63525e23 + 1.80603e23i 0.967081 + 0.202262i
\(333\) −4.91638e23 3.16558e23i −0.535088 0.344535i
\(334\) 9.45378e22 9.13813e23i 0.100003 0.966643i
\(335\) 1.12839e24 1.16020
\(336\) 9.43908e23 1.12433e24i 0.943424 1.12376i
\(337\) 1.65432e24 1.60745 0.803723 0.595003i \(-0.202849\pi\)
0.803723 + 0.595003i \(0.202849\pi\)
\(338\) −7.27227e22 + 7.02946e23i −0.0687007 + 0.664069i
\(339\) 7.50154e22 2.55070e23i 0.0689054 0.234295i
\(340\) 4.82037e23 + 1.00816e23i 0.430557 + 0.0900496i
\(341\) 8.51395e22i 0.0739545i
\(342\) 8.30492e22 + 6.64953e22i 0.0701596 + 0.0561750i
\(343\) 2.72992e23i 0.224314i
\(344\) −7.12360e22 2.27609e22i −0.0569370 0.0181922i
\(345\) −9.81798e23 + 3.33835e24i −0.763380 + 2.59568i
\(346\) −5.12111e23 5.29800e22i −0.387383 0.0400764i
\(347\) −2.76687e23 −0.203638 −0.101819 0.994803i \(-0.532466\pi\)
−0.101819 + 0.994803i \(0.532466\pi\)
\(348\) 4.41482e23 8.23312e23i 0.316162 0.589606i
\(349\) −1.31829e24 −0.918689 −0.459345 0.888258i \(-0.651916\pi\)
−0.459345 + 0.888258i \(0.651916\pi\)
\(350\) −3.48800e24 3.60848e23i −2.36554 0.244725i
\(351\) 5.71132e23 + 6.60854e23i 0.376980 + 0.436202i
\(352\) −9.36593e23 + 1.65324e24i −0.601722 + 1.06214i
\(353\) 1.45203e24i 0.908063i −0.890986 0.454032i \(-0.849985\pi\)
0.890986 0.454032i \(-0.150015\pi\)
\(354\) −2.33267e23 + 5.68906e23i −0.142011 + 0.346346i
\(355\) 4.33828e24i 2.57127i
\(356\) 2.95979e23 1.41517e24i 0.170799 0.816647i
\(357\) −6.80697e23 2.00191e23i −0.382477 0.112485i
\(358\) −1.12913e23 + 1.09143e24i −0.0617809 + 0.597181i
\(359\) −2.45344e24 −1.30731 −0.653654 0.756794i \(-0.726765\pi\)
−0.653654 + 0.756794i \(0.726765\pi\)
\(360\) 1.98443e24 + 2.40699e24i 1.02982 + 1.24911i
\(361\) 1.96244e24 0.991922
\(362\) −8.32840e22 + 8.05033e23i −0.0410044 + 0.396353i
\(363\) −9.80575e23 2.88384e23i −0.470292 0.138311i
\(364\) −3.70637e23 + 1.77214e24i −0.173175 + 0.828009i
\(365\) 3.11663e24i 1.41874i
\(366\) −1.33473e24 + 3.25523e24i −0.592002 + 1.44381i
\(367\) 4.44673e24i 1.92182i 0.276858 + 0.960911i \(0.410707\pi\)
−0.276858 + 0.960911i \(0.589293\pi\)
\(368\) 3.63565e24 + 1.59033e24i 1.53119 + 0.669783i
\(369\) −1.21357e24 + 1.88476e24i −0.498096 + 0.773580i
\(370\) 2.56190e24 + 2.65039e23i 1.02482 + 0.106022i
\(371\) −1.50628e24 −0.587293
\(372\) 7.53298e22 1.40481e23i 0.0286292 0.0533901i
\(373\) 2.95955e24 1.09646 0.548229 0.836328i \(-0.315302\pi\)
0.548229 + 0.836328i \(0.315302\pi\)
\(374\) 9.13486e23 + 9.45039e22i 0.329930 + 0.0341326i
\(375\) 8.05289e23 2.73818e24i 0.283566 0.964194i
\(376\) 7.21285e23 2.25744e24i 0.247641 0.775054i
\(377\) 1.15214e24i 0.385712i
\(378\) −2.57333e24 3.68491e24i −0.840084 1.20297i
\(379\) 3.84264e24i 1.22337i −0.791102 0.611684i \(-0.790493\pi\)
0.791102 0.611684i \(-0.209507\pi\)
\(380\) −4.58688e23 9.59331e22i −0.142421 0.0297868i
\(381\) 1.20414e24 4.09437e24i 0.364662 1.23994i
\(382\) −3.60909e23 + 3.48859e24i −0.106609 + 1.03050i
\(383\) −4.60507e24 −1.32693 −0.663465 0.748207i \(-0.730915\pi\)
−0.663465 + 0.748207i \(0.730915\pi\)
\(384\) 3.00815e24 1.89919e24i 0.845576 0.533854i
\(385\) −1.05737e25 −2.89969
\(386\) −4.48420e23 + 4.33448e24i −0.119979 + 1.15973i
\(387\) −1.23951e23 + 1.92505e23i −0.0323591 + 0.0502560i
\(388\) −4.08050e24 8.53423e23i −1.03947 0.217402i
\(389\) 6.56690e24i 1.63245i 0.577736 + 0.816223i \(0.303936\pi\)
−0.577736 + 0.816223i \(0.696064\pi\)
\(390\) −3.55967e24 1.45956e24i −0.863566 0.354085i
\(391\) 1.91794e24i 0.454104i
\(392\) 1.51839e24 4.75218e24i 0.350885 1.09818i
\(393\) 3.34772e24 + 9.84553e23i 0.755126 + 0.222080i
\(394\) 6.96133e24 + 7.20178e23i 1.53277 + 0.158572i
\(395\) 1.35980e25 2.92282
\(396\) 4.14286e24 + 4.08396e24i 0.869352 + 0.856993i
\(397\) 3.23839e24 0.663466 0.331733 0.943373i \(-0.392367\pi\)
0.331733 + 0.943373i \(0.392367\pi\)
\(398\) −2.35196e24 2.43320e23i −0.470479 0.0486730i
\(399\) 6.47725e23 + 1.90494e23i 0.126517 + 0.0372082i
\(400\) −7.78546e24 3.40557e24i −1.48496 0.649561i
\(401\) 1.62463e24i 0.302610i −0.988487 0.151305i \(-0.951652\pi\)
0.988487 0.151305i \(-0.0483476\pi\)
\(402\) −3.64518e24 1.49462e24i −0.663089 0.271884i
\(403\) 1.96590e23i 0.0349271i
\(404\) −1.23021e23 + 5.88206e23i −0.0213480 + 0.102072i
\(405\) 8.69459e24 3.95250e24i 1.47376 0.669961i
\(406\) 6.10078e23 5.89708e24i 0.101015 0.976427i
\(407\) 4.80298e24 0.776897
\(408\) −1.42365e24 9.64167e23i −0.224973 0.152363i
\(409\) −1.66095e24 −0.256440 −0.128220 0.991746i \(-0.540926\pi\)
−0.128220 + 0.991746i \(0.540926\pi\)
\(410\) 1.01606e24 9.82139e24i 0.153276 1.48158i
\(411\) −1.61055e24 + 5.47626e24i −0.237398 + 0.807211i
\(412\) −5.23382e23 + 2.50246e24i −0.0753868 + 0.360449i
\(413\) 3.90202e24i 0.549242i
\(414\) 7.59347e24 9.48385e24i 1.04457 1.30461i
\(415\) 1.18969e25i 1.59948i
\(416\) −2.16262e24 + 3.81739e24i −0.284180 + 0.501625i
\(417\) 1.73260e24 5.89125e24i 0.222539 0.756685i
\(418\) −8.69238e23 8.99262e22i −0.109135 0.0112905i
\(419\) −6.70697e24 −0.823177 −0.411589 0.911370i \(-0.635026\pi\)
−0.411589 + 0.911370i \(0.635026\pi\)
\(420\) 1.74468e25 + 9.35544e24i 2.09338 + 1.12252i
\(421\) −1.21764e25 −1.42836 −0.714181 0.699961i \(-0.753201\pi\)
−0.714181 + 0.699961i \(0.753201\pi\)
\(422\) −7.58805e23 7.85015e22i −0.0870285 0.00900346i
\(423\) −6.10041e24 3.92796e24i −0.684109 0.440488i
\(424\) −3.47706e24 1.11097e24i −0.381273 0.121822i
\(425\) 4.10712e24i 0.440395i
\(426\) −5.74631e24 + 1.40145e25i −0.602557 + 1.46956i
\(427\) 2.23270e25i 2.28963i
\(428\) 2.30416e24 + 4.81908e23i 0.231098 + 0.0483335i
\(429\) −6.88297e24 2.02426e24i −0.675199 0.198574i
\(430\) 1.03778e23 1.00313e24i 0.00995765 0.0962518i
\(431\) −1.13156e25 −1.06204 −0.531022 0.847358i \(-0.678192\pi\)
−0.531022 + 0.847358i \(0.678192\pi\)
\(432\) −3.22236e24 1.04041e25i −0.295854 0.955233i
\(433\) 1.07201e25 0.962859 0.481429 0.876485i \(-0.340118\pi\)
0.481429 + 0.876485i \(0.340118\pi\)
\(434\) 1.04097e23 1.00622e24i 0.00914717 0.0884177i
\(435\) 1.20863e25 + 3.55455e24i 1.03907 + 0.305588i
\(436\) −1.45249e25 3.03784e24i −1.22178 0.255530i
\(437\) 1.82504e24i 0.150210i
\(438\) −4.12816e24 + 1.00680e25i −0.332470 + 0.810851i
\(439\) 1.99268e25i 1.57045i −0.619212 0.785224i \(-0.712548\pi\)
0.619212 0.785224i \(-0.287452\pi\)
\(440\) −2.44081e25 7.79873e24i −1.88249 0.601483i
\(441\) −1.28421e25 8.26882e24i −0.969323 0.624133i
\(442\) 2.10926e24 + 2.18212e23i 0.155819 + 0.0161201i
\(443\) 1.19783e25 0.866082 0.433041 0.901374i \(-0.357441\pi\)
0.433041 + 0.901374i \(0.357441\pi\)
\(444\) −7.92498e24 4.24958e24i −0.560867 0.300752i
\(445\) 1.94971e25 1.35067
\(446\) 8.33421e24 + 8.62208e23i 0.565175 + 0.0584697i
\(447\) −1.18945e24 + 4.04442e24i −0.0789633 + 0.268494i
\(448\) 1.30904e25 1.83936e25i 0.850772 1.19544i
\(449\) 8.98737e24i 0.571864i 0.958250 + 0.285932i \(0.0923031\pi\)
−0.958250 + 0.285932i \(0.907697\pi\)
\(450\) −1.62608e25 + 2.03089e25i −1.01303 + 1.26522i
\(451\) 1.84128e25i 1.12316i
\(452\) 8.37040e23 4.00217e24i 0.0499955 0.239045i
\(453\) 1.51714e24 5.15865e24i 0.0887347 0.301719i
\(454\) 5.85912e23 5.66350e24i 0.0335585 0.324380i
\(455\) −2.44150e25 −1.36946
\(456\) 1.35469e24 + 9.17464e23i 0.0744172 + 0.0503992i
\(457\) 4.70541e24 0.253159 0.126579 0.991956i \(-0.459600\pi\)
0.126579 + 0.991956i \(0.459600\pi\)
\(458\) 3.60019e24 3.47998e25i 0.189716 1.83381i
\(459\) −3.98287e24 + 3.44213e24i −0.205578 + 0.177667i
\(460\) −1.09551e25 + 5.23801e25i −0.553883 + 2.64830i
\(461\) 2.20436e25i 1.09175i 0.837867 + 0.545875i \(0.183802\pi\)
−0.837867 + 0.545875i \(0.816198\pi\)
\(462\) 3.41577e25 + 1.40055e25i 1.65725 + 0.679518i
\(463\) 1.60558e24i 0.0763155i 0.999272 + 0.0381577i \(0.0121489\pi\)
−0.999272 + 0.0381577i \(0.987851\pi\)
\(464\) 5.75772e24 1.31627e25i 0.268120 0.612948i
\(465\) 2.06228e24 + 6.06511e23i 0.0940904 + 0.0276717i
\(466\) 3.80482e25 + 3.93624e24i 1.70086 + 0.175961i
\(467\) 2.53433e25 1.11007 0.555037 0.831825i \(-0.312704\pi\)
0.555037 + 0.831825i \(0.312704\pi\)
\(468\) 9.56597e24 + 9.42998e24i 0.410576 + 0.404739i
\(469\) −2.50016e25 −1.05154
\(470\) 3.17889e25 + 3.28870e24i 1.31023 + 0.135548i
\(471\) −1.47552e25 4.33947e24i −0.596002 0.175282i
\(472\) −2.87796e24 + 9.00730e24i −0.113929 + 0.356571i
\(473\) 1.88065e24i 0.0729670i
\(474\) −4.39273e25 1.80113e25i −1.67048 0.684939i
\(475\) 3.90817e24i 0.145675i
\(476\) −1.06804e25 2.23378e24i −0.390232 0.0816157i
\(477\) −6.05010e24 + 9.39625e24i −0.216690 + 0.336535i
\(478\) 2.15861e24 2.08654e25i 0.0757897 0.732592i
\(479\) 1.93936e25 0.667530 0.333765 0.942656i \(-0.391681\pi\)
0.333765 + 0.942656i \(0.391681\pi\)
\(480\) 3.33735e25 + 3.44638e25i 1.12619 + 1.16298i
\(481\) 1.10902e25 0.366912
\(482\) −5.18042e23 + 5.00746e24i −0.0168042 + 0.162432i
\(483\) 2.17536e25 7.39674e25i 0.691883 2.35257i
\(484\) −1.53856e25 3.21786e24i −0.479827 0.100354i
\(485\) 5.62177e25i 1.71920i
\(486\) −3.33226e25 + 1.25177e24i −0.999295 + 0.0375388i
\(487\) 2.01956e25i 0.593925i −0.954889 0.296962i \(-0.904026\pi\)
0.954889 0.296962i \(-0.0959736\pi\)
\(488\) −1.64674e25 + 5.15389e25i −0.474938 + 1.48644i
\(489\) 1.52721e25 5.19289e25i 0.431982 1.46884i
\(490\) 6.69195e25 + 6.92309e24i 1.85648 + 0.192060i
\(491\) 2.36318e25 0.643017 0.321508 0.946907i \(-0.395810\pi\)
0.321508 + 0.946907i \(0.395810\pi\)
\(492\) −1.62913e25 + 3.03814e25i −0.434799 + 0.810849i
\(493\) −6.94380e24 −0.181782
\(494\) −2.00710e24 2.07642e23i −0.0515421 0.00533224i
\(495\) −4.24702e25 + 6.59593e25i −1.06988 + 1.66160i
\(496\) 9.82437e23 2.24594e24i 0.0242789 0.0555038i
\(497\) 9.61227e25i 2.33045i
\(498\) 1.57582e25 3.84321e25i 0.374824 0.914146i
\(499\) 6.80557e25i 1.58821i −0.607777 0.794107i \(-0.707939\pi\)
0.607777 0.794107i \(-0.292061\pi\)
\(500\) 8.98560e24 4.29631e25i 0.205746 0.983742i
\(501\) −4.14976e25 1.22043e25i −0.932318 0.274192i
\(502\) −5.37174e24 + 5.19238e25i −0.118421 + 1.14467i
\(503\) −8.02098e25 −1.73513 −0.867564 0.497325i \(-0.834316\pi\)
−0.867564 + 0.497325i \(0.834316\pi\)
\(504\) −4.39688e25 5.33314e25i −0.933371 1.13212i
\(505\) −8.10381e24 −0.168819
\(506\) −1.02692e25 + 9.92631e25i −0.209945 + 2.02935i
\(507\) 3.19218e25 + 9.38810e24i 0.640489 + 0.188366i
\(508\) 1.34361e25 6.42424e25i 0.264586 1.26508i
\(509\) 1.15430e25i 0.223101i 0.993759 + 0.111550i \(0.0355816\pi\)
−0.993759 + 0.111550i \(0.964418\pi\)
\(510\) 8.79654e24 2.14536e25i 0.166876 0.406990i
\(511\) 6.90547e25i 1.28586i
\(512\) 4.37839e25 3.28043e25i 0.800295 0.599607i
\(513\) 3.78995e24 3.27540e24i 0.0680014 0.0587691i
\(514\) −6.17577e25 6.38909e24i −1.08778 0.112535i
\(515\) −3.44768e25 −0.596154
\(516\) −1.66396e24 + 3.10309e24i −0.0282469 + 0.0526772i
\(517\) 5.95970e25 0.993262
\(518\) −5.67637e25 5.87244e24i −0.928834 0.0960917i
\(519\) −6.83942e24 + 2.32557e25i −0.109883 + 0.373628i
\(520\) −5.63590e25 1.80075e25i −0.889060 0.284067i
\(521\) 6.64890e25i 1.02989i −0.857223 0.514946i \(-0.827812\pi\)
0.857223 0.514946i \(-0.172188\pi\)
\(522\) −3.43358e25 2.74918e25i −0.522248 0.418151i
\(523\) 1.08349e26i 1.61830i 0.587599 + 0.809152i \(0.300073\pi\)
−0.587599 + 0.809152i \(0.699927\pi\)
\(524\) 5.25271e25 + 1.09859e25i 0.770436 + 0.161134i
\(525\) −4.65835e25 + 1.58395e26i −0.670995 + 2.28154i
\(526\) −3.46077e24 + 3.34522e25i −0.0489562 + 0.473216i
\(527\) −1.18482e24 −0.0164608
\(528\) 6.85186e25 + 5.75232e25i 0.934946 + 0.784911i
\(529\) 1.33796e26 1.79314
\(530\) 5.06547e24 4.89634e25i 0.0666805 0.644542i
\(531\) 2.43409e25 + 1.56728e25i 0.314731 + 0.202650i
\(532\) 1.01631e25 + 2.12558e24i 0.129082 + 0.0269970i
\(533\) 4.25158e25i 0.530447i
\(534\) −6.29838e25 2.58250e25i −0.771946 0.316518i
\(535\) 3.17448e25i 0.382218i
\(536\) −5.77129e25 1.84401e25i −0.682664 0.218121i
\(537\) 4.95633e25 + 1.45764e25i 0.575976 + 0.169393i
\(538\) −5.12739e25 5.30450e24i −0.585416 0.0605637i
\(539\) 1.25459e26 1.40737
\(540\) 1.28436e26 7.12569e25i 1.41562 0.785391i
\(541\) −1.45055e26 −1.57093 −0.785467 0.618904i \(-0.787577\pi\)
−0.785467 + 0.618904i \(0.787577\pi\)
\(542\) −1.40380e26 1.45229e25i −1.49386 0.154546i
\(543\) 3.65577e25 + 1.07515e25i 0.382279 + 0.112427i
\(544\) −2.30068e25 1.30338e25i −0.236411 0.133931i
\(545\) 2.00112e26i 2.02072i
\(546\) 7.88710e25 + 3.23392e25i 0.782686 + 0.320922i
\(547\) 4.44080e24i 0.0433093i −0.999766 0.0216547i \(-0.993107\pi\)
0.999766 0.0216547i \(-0.00689343\pi\)
\(548\) −1.79709e25 + 8.59249e25i −0.172248 + 0.823576i
\(549\) 1.39276e26 + 8.96780e25i 1.31202 + 0.844790i
\(550\) 2.19906e25 2.12564e26i 0.203607 1.96809i
\(551\) 6.60745e24 0.0601304
\(552\) 1.04770e26 1.54700e26i 0.937168 1.38378i
\(553\) −3.01289e26 −2.64907
\(554\) −1.17786e25 + 1.13854e26i −0.101801 + 0.984020i
\(555\) 3.42151e25 1.16340e26i 0.290693 0.988427i
\(556\) 1.93327e25 9.24363e25i 0.161467 0.772026i
\(557\) 6.95977e25i 0.571440i −0.958313 0.285720i \(-0.907767\pi\)
0.958313 0.285720i \(-0.0922328\pi\)
\(558\) −5.85870e24 4.69091e24i −0.0472908 0.0378645i
\(559\) 4.34247e24i 0.0344607i
\(560\) 2.78930e26 + 1.22012e26i 2.17625 + 0.951953i
\(561\) 1.21999e25 4.14827e25i 0.0935858 0.318214i
\(562\) −4.58280e25 4.74109e24i −0.345649 0.0357589i
\(563\) 2.00683e26 1.48827 0.744133 0.668032i \(-0.232863\pi\)
0.744133 + 0.668032i \(0.232863\pi\)
\(564\) −9.83358e25 5.27303e25i −0.717068 0.384511i
\(565\) 5.51385e25 0.395362
\(566\) 1.40000e26 + 1.44836e25i 0.987127 + 0.102122i
\(567\) −1.92645e26 + 8.75751e25i −1.33573 + 0.607213i
\(568\) −7.08959e25 + 2.21887e26i −0.483406 + 1.51294i
\(569\) 1.48358e26i 0.994822i 0.867515 + 0.497411i \(0.165716\pi\)
−0.867515 + 0.497411i \(0.834284\pi\)
\(570\) −8.37045e24 + 2.04144e25i −0.0551998 + 0.134625i
\(571\) 1.80490e25i 0.117061i −0.998286 0.0585303i \(-0.981359\pi\)
0.998286 0.0585303i \(-0.0186414\pi\)
\(572\) −1.07997e26 2.25872e25i −0.688888 0.144079i
\(573\) 1.58422e26 + 4.65914e25i 0.993908 + 0.292305i
\(574\) −2.25128e25 + 2.17611e26i −0.138920 + 1.34282i
\(575\) −4.46296e26 −2.70881
\(576\) −6.21613e25 1.55538e26i −0.371113 0.928588i
\(577\) 3.86284e25 0.226849 0.113424 0.993547i \(-0.463818\pi\)
0.113424 + 0.993547i \(0.463818\pi\)
\(578\) 1.64984e25 1.59476e26i 0.0953077 0.921255i
\(579\) 1.96835e26 + 5.78885e25i 1.11855 + 0.328962i
\(580\) 1.89640e26 + 3.96625e25i 1.06014 + 0.221725i
\(581\) 2.63598e26i 1.44967i
\(582\) −7.44637e25 + 1.81607e26i −0.402881 + 0.982573i
\(583\) 9.17952e25i 0.488617i
\(584\) −5.09318e25 + 1.59404e26i −0.266727 + 0.834789i
\(585\) −9.80649e25 + 1.52302e26i −0.505281 + 0.784738i
\(586\) 2.69350e26 + 2.78653e25i 1.36549 + 0.141266i
\(587\) 1.28094e26 0.638948 0.319474 0.947595i \(-0.396494\pi\)
0.319474 + 0.947595i \(0.396494\pi\)
\(588\) −2.07008e26 1.11003e26i −1.01602 0.544818i
\(589\) 1.12743e24 0.00544494
\(590\) −1.26839e26 1.31221e25i −0.602782 0.0623603i
\(591\) 9.29711e25 3.16124e26i 0.434777 1.47835i
\(592\) −1.26700e26 5.54222e25i −0.583071 0.255051i
\(593\) 2.75550e26i 1.24790i 0.781463 + 0.623952i \(0.214474\pi\)
−0.781463 + 0.623952i \(0.785526\pi\)
\(594\) 2.24564e26 1.56822e26i 1.00085 0.698935i
\(595\) 1.47146e26i 0.645412i
\(596\) −1.32722e25 + 6.34587e25i −0.0572931 + 0.273938i
\(597\) −3.14112e25 + 1.06806e26i −0.133453 + 0.453773i
\(598\) −2.37118e25 + 2.29201e26i −0.0991526 + 0.958420i
\(599\) −2.45383e26 −1.00992 −0.504962 0.863142i \(-0.668494\pi\)
−0.504962 + 0.863142i \(0.668494\pi\)
\(600\) −2.24358e26 + 3.31277e26i −0.908874 + 1.34201i
\(601\) 1.70604e26 0.680270 0.340135 0.940377i \(-0.389527\pi\)
0.340135 + 0.940377i \(0.389527\pi\)
\(602\) −2.29940e24 + 2.22263e25i −0.00902503 + 0.0872370i
\(603\) −1.00421e26 + 1.55961e26i −0.387980 + 0.602560i
\(604\) 1.69286e25 8.09414e25i 0.0643830 0.307836i
\(605\) 2.11970e26i 0.793596i
\(606\) 2.61788e25 + 1.07340e25i 0.0964849 + 0.0395614i
\(607\) 9.35857e25i 0.339560i −0.985482 0.169780i \(-0.945694\pi\)
0.985482 0.169780i \(-0.0543057\pi\)
\(608\) 2.18924e25 + 1.24025e25i 0.0782006 + 0.0443021i
\(609\) −2.67795e26 7.87576e25i −0.941755 0.276967i
\(610\) −7.25763e26 7.50832e25i −2.51282 0.259962i
\(611\) 1.37611e26 0.469096
\(612\) −5.68331e25 + 5.76527e25i −0.190749 + 0.193500i
\(613\) 1.98207e26 0.655004 0.327502 0.944850i \(-0.393793\pi\)
0.327502 + 0.944850i \(0.393793\pi\)
\(614\) 3.24283e26 + 3.35484e25i 1.05517 + 0.109162i
\(615\) −4.46003e26 1.31168e26i −1.42897 0.420257i
\(616\) 5.40806e26 + 1.72795e26i 1.70618 + 0.545149i
\(617\) 3.17344e26i 0.985873i 0.870065 + 0.492937i \(0.164077\pi\)
−0.870065 + 0.492937i \(0.835923\pi\)
\(618\) 1.11375e26 + 4.56666e25i 0.340719 + 0.139704i
\(619\) 3.39238e26i 1.02198i −0.859586 0.510992i \(-0.829278\pi\)
0.859586 0.510992i \(-0.170722\pi\)
\(620\) 3.23581e25 + 6.76760e24i 0.0959980 + 0.0200777i
\(621\) −3.74036e26 4.32795e26i −1.09281 1.26448i
\(622\) 3.02256e25 2.92164e26i 0.0869693 0.840656i
\(623\) −4.31994e26 −1.22417
\(624\) 1.58212e26 + 1.32823e26i 0.441555 + 0.370697i
\(625\) 2.26228e24 0.00621851
\(626\) −5.94534e25 + 5.74684e26i −0.160961 + 1.55587i
\(627\) −1.16090e25 + 3.94733e25i −0.0309565 + 0.105260i
\(628\) −2.31516e26 4.84208e25i −0.608085 0.127179i
\(629\) 6.68391e25i 0.172922i
\(630\) 5.82578e26 7.27609e26i 1.48463 1.85423i
\(631\) 3.28708e26i 0.825147i 0.910924 + 0.412573i \(0.135370\pi\)
−0.910924 + 0.412573i \(0.864630\pi\)
\(632\) −6.95486e26 2.22218e26i −1.71979 0.549498i
\(633\) −1.01341e25 + 3.44584e25i −0.0246860 + 0.0839382i
\(634\) 3.00482e26 + 3.10861e25i 0.721059 + 0.0745965i
\(635\) 8.85078e26 2.09233
\(636\) −8.12186e25 + 1.51463e26i −0.189153 + 0.352748i
\(637\) 2.89688e26 0.664669
\(638\) 3.59377e26 + 3.71790e25i 0.812370 + 0.0840430i
\(639\) 5.99616e26 + 3.86084e26i 1.33541 + 0.859852i
\(640\) 5.53883e26 + 4.87375e26i 1.21537 + 1.06943i
\(641\) 7.50904e26i 1.62343i −0.584054 0.811715i \(-0.698535\pi\)
0.584054 0.811715i \(-0.301465\pi\)
\(642\) 4.20479e25 1.02549e26i 0.0895697 0.218449i
\(643\) 2.12377e26i 0.445763i 0.974846 + 0.222882i \(0.0715463\pi\)
−0.974846 + 0.222882i \(0.928454\pi\)
\(644\) 2.42731e26 1.16058e27i 0.502008 2.40026i
\(645\) −4.55538e25 1.33972e25i −0.0928340 0.0273022i
\(646\) 1.25143e24 1.20965e25i 0.00251303 0.0242912i
\(647\) 7.48256e26 1.48067 0.740337 0.672236i \(-0.234666\pi\)
0.740337 + 0.672236i \(0.234666\pi\)
\(648\) −5.09287e26 + 6.00691e25i −0.993116 + 0.117136i
\(649\) −2.37795e26 −0.456959
\(650\) 5.07770e25 4.90817e26i 0.0961591 0.929485i
\(651\) −4.56937e25 1.34384e25i −0.0852781 0.0250800i
\(652\) 1.70410e26 8.14787e26i 0.313432 1.49862i
\(653\) 7.54361e26i 1.36743i 0.729751 + 0.683713i \(0.239636\pi\)
−0.729751 + 0.683713i \(0.760364\pi\)
\(654\) −2.65060e26 + 6.46447e26i −0.473539 + 1.15490i
\(655\) 7.23675e26i 1.27424i
\(656\) −2.12468e26 + 4.85722e26i −0.368729 + 0.842950i
\(657\) 4.30766e26 + 2.77364e26i 0.736835 + 0.474437i
\(658\) −7.04343e26 7.28672e25i −1.18751 0.122853i
\(659\) −2.34534e26 −0.389758 −0.194879 0.980827i \(-0.562431\pi\)
−0.194879 + 0.980827i \(0.562431\pi\)
\(660\) −5.70134e26 + 1.06323e27i −0.933920 + 1.74165i
\(661\) 4.60565e26 0.743665 0.371832 0.928300i \(-0.378730\pi\)
0.371832 + 0.928300i \(0.378730\pi\)
\(662\) 2.21319e26 + 2.28964e25i 0.352264 + 0.0364432i
\(663\) 2.81700e25 9.57847e25i 0.0441986 0.150286i
\(664\) 1.94419e26 6.08482e26i 0.300706 0.941134i
\(665\) 1.40018e26i 0.213491i
\(666\) −2.64628e26 + 3.30507e26i −0.397769 + 0.496793i
\(667\) 7.54542e26i 1.11812i
\(668\) −6.51115e26 1.36178e26i −0.951220 0.198945i
\(669\) 1.11306e26 3.78468e26i 0.160314 0.545107i
\(670\) 8.40776e25 8.12704e26i 0.119390 1.15404i
\(671\) −1.36064e27 −1.90493
\(672\) −7.39452e26 7.63610e26i −1.02071 1.05406i
\(673\) −1.70271e26 −0.231738 −0.115869 0.993264i \(-0.536965\pi\)
−0.115869 + 0.993264i \(0.536965\pi\)
\(674\) 1.23266e26 1.19150e27i 0.165414 1.59891i
\(675\) 8.00969e26 + 9.26796e26i 1.05981 + 1.22631i
\(676\) 5.00867e26 + 1.04755e26i 0.653474 + 0.136672i
\(677\) 8.34714e26i 1.07385i 0.843629 + 0.536927i \(0.180415\pi\)
−0.843629 + 0.536927i \(0.819585\pi\)
\(678\) −1.78121e26 7.30342e25i −0.225961 0.0926497i
\(679\) 1.24561e27i 1.55818i
\(680\) 1.08529e26 3.39667e26i 0.133878 0.419005i
\(681\) −2.57188e26 7.56380e25i −0.312862 0.0920116i
\(682\) 6.13203e25 + 6.34384e24i 0.0735619 + 0.00761028i
\(683\) −6.93137e26 −0.820016 −0.410008 0.912082i \(-0.634474\pi\)
−0.410008 + 0.912082i \(0.634474\pi\)
\(684\) 5.40802e25 5.48601e25i 0.0630965 0.0640065i
\(685\) −1.18380e27 −1.36213
\(686\) −1.96618e26 2.03409e25i −0.223123 0.0230830i
\(687\) −1.58031e27 4.64764e26i −1.76870 0.520168i
\(688\) −2.17010e25 + 4.96106e25i −0.0239547 + 0.0547626i
\(689\) 2.11958e26i 0.230763i
\(690\) 2.33124e27 + 9.55868e26i 2.50334 + 1.02644i
\(691\) 7.13134e24i 0.00755317i 0.999993 + 0.00377659i \(0.00120213\pi\)
−0.999993 + 0.00377659i \(0.998798\pi\)
\(692\) −7.63159e25 + 3.64892e26i −0.0797273 + 0.381203i
\(693\) 9.41006e26 1.46145e27i 0.969676 1.50598i
\(694\) −2.06162e25 + 1.99279e26i −0.0209553 + 0.202557i
\(695\) 1.27351e27 1.27687
\(696\) −5.60082e26 3.79316e26i −0.553941 0.375157i
\(697\) 2.56236e26 0.249994
\(698\) −9.82271e25 + 9.49475e26i −0.0945376 + 0.913812i
\(699\) 5.08147e26 1.72782e27i 0.482454 1.64046i
\(700\) −5.19790e26 + 2.48529e27i −0.486852 + 2.32780i
\(701\) 1.41335e27i 1.30596i 0.757376 + 0.652979i \(0.226481\pi\)
−0.757376 + 0.652979i \(0.773519\pi\)
\(702\) 5.18525e26 3.62107e26i 0.472680 0.330092i
\(703\) 6.36015e25i 0.0571995i
\(704\) 1.12093e27 + 7.97751e26i 0.994580 + 0.707827i
\(705\) 4.24553e26 1.44358e27i 0.371651 1.26370i
\(706\) −1.04580e27 1.08192e26i −0.903242 0.0934442i
\(707\) 1.79555e26 0.153008
\(708\) 3.92364e26 + 2.10396e26i 0.329893 + 0.176898i
\(709\) −7.45463e26 −0.618424 −0.309212 0.950993i \(-0.600065\pi\)
−0.309212 + 0.950993i \(0.600065\pi\)
\(710\) −3.12457e27 3.23250e26i −2.55762 0.264597i
\(711\) −1.21015e27 + 1.87945e27i −0.977412 + 1.51799i
\(712\) −9.97201e26 3.18620e26i −0.794736 0.253929i
\(713\) 1.28747e26i 0.101248i
\(714\) −1.94904e26 + 4.75344e26i −0.151247 + 0.368872i
\(715\) 1.48789e27i 1.13937i
\(716\) 7.77669e26 + 1.62647e26i 0.587653 + 0.122906i
\(717\) −9.47529e26 2.78665e26i −0.706579 0.207803i
\(718\) −1.82808e26 + 1.76705e27i −0.134528 + 1.30037i
\(719\) 1.36111e27 0.988478 0.494239 0.869326i \(-0.335447\pi\)
0.494239 + 0.869326i \(0.335447\pi\)
\(720\) 1.88146e27 1.24991e27i 1.34845 0.895816i
\(721\) 7.63898e26 0.540319
\(722\) 1.46223e26 1.41341e27i 0.102074 0.986656i
\(723\) 2.27396e26 + 6.68764e25i 0.156664 + 0.0460743i
\(724\) 5.73606e26 + 1.19968e26i 0.390030 + 0.0815734i
\(725\) 1.61579e27i 1.08436i
\(726\) −2.80767e26 + 6.84755e26i −0.185973 + 0.453563i
\(727\) 1.81528e27i 1.18677i −0.804917 0.593387i \(-0.797790\pi\)
0.804917 0.593387i \(-0.202210\pi\)
\(728\) 1.24874e27 + 3.98989e26i 0.805792 + 0.257462i
\(729\) −2.27476e26 + 1.55348e27i −0.144885 + 0.989448i
\(730\) −2.24470e27 2.32224e26i −1.41121 0.145995i
\(731\) 2.61714e25 0.0162410
\(732\) 2.24507e27 + 1.20387e27i 1.37523 + 0.737435i
\(733\) 3.36526e26 0.203484 0.101742 0.994811i \(-0.467558\pi\)
0.101742 + 0.994811i \(0.467558\pi\)
\(734\) 3.20268e27 + 3.31331e26i 1.91162 + 0.197765i
\(735\) 8.93733e26 3.03891e27i 0.526597 1.79056i
\(736\) 1.41631e27 2.50002e27i 0.823793 1.45413i
\(737\) 1.52363e27i 0.874861i
\(738\) 1.26704e27 + 1.01449e27i 0.718216 + 0.575057i
\(739\) 1.25717e27i 0.703513i 0.936091 + 0.351757i \(0.114416\pi\)
−0.936091 + 0.351757i \(0.885584\pi\)
\(740\) 3.81780e26 1.82542e27i 0.210917 1.00847i
\(741\) −2.68055e25 + 9.11451e25i −0.0146201 + 0.0497119i
\(742\) −1.12235e26 + 1.08488e27i −0.0604353 + 0.584175i
\(743\) −2.74092e27 −1.45715 −0.728573 0.684968i \(-0.759816\pi\)
−0.728573 + 0.684968i \(0.759816\pi\)
\(744\) −9.55665e25 6.47225e25i −0.0501606 0.0339713i
\(745\) −8.74280e26 −0.453071
\(746\) 2.20519e26 2.13157e27i 0.112831 1.09064i
\(747\) −1.64434e27 1.05876e27i −0.830701 0.534876i
\(748\) 1.36130e26 6.50881e26i 0.0679028 0.324666i
\(749\) 7.03365e26i 0.346420i
\(750\) −1.91212e27 7.84020e26i −0.929894 0.381281i
\(751\) 4.00986e27i 1.92553i −0.270347 0.962763i \(-0.587138\pi\)
0.270347 0.962763i \(-0.412862\pi\)
\(752\) −1.57214e27 6.87698e26i −0.745456 0.326083i
\(753\) 2.35794e27 + 6.93462e26i 1.10403 + 0.324691i
\(754\) 8.29812e26 + 8.58475e25i 0.383665 + 0.0396917i
\(755\) 1.11514e27 0.509137
\(756\) −2.84574e27 + 1.57883e27i −1.28303 + 0.711833i
\(757\) −1.39285e27 −0.620145 −0.310072 0.950713i \(-0.600353\pi\)
−0.310072 + 0.950713i \(0.600353\pi\)
\(758\) −2.76760e27 2.86319e26i −1.21687 0.125891i
\(759\) 4.50768e27 + 1.32569e27i 1.95729 + 0.575634i
\(760\) −1.03272e26 + 3.23214e26i −0.0442845 + 0.138599i
\(761\) 1.03070e27i 0.436492i 0.975894 + 0.218246i \(0.0700335\pi\)
−0.975894 + 0.218246i \(0.929966\pi\)
\(762\) −2.85918e27 1.17234e27i −1.19583 0.490321i
\(763\) 4.43385e27i