Properties

Label 3.17.b.a.2.1
Level 3
Weight 17
Character 3.2
Analytic conductor 4.870
Analytic rank 0
Dimension 4
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 17 \)
Character orbit: \([\chi]\) = 3.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(4.8697363157\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} + \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{6}\cdot 3^{8} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2.1
Root \(-52.1196i\)
Character \(\chi\) = 3.2
Dual form 3.17.b.a.2.4

$q$-expansion

\(f(q)\) \(=\) \(q-312.717i q^{2} +(-5369.70 - 3770.02i) q^{3} -32256.2 q^{4} +276758. i q^{5} +(-1.17895e6 + 1.67920e6i) q^{6} -7.10881e6 q^{7} -1.04072e7i q^{8} +(1.46206e7 + 4.04878e7i) q^{9} +O(q^{10})\) \(q-312.717i q^{2} +(-5369.70 - 3770.02i) q^{3} -32256.2 q^{4} +276758. i q^{5} +(-1.17895e6 + 1.67920e6i) q^{6} -7.10881e6 q^{7} -1.04072e7i q^{8} +(1.46206e7 + 4.04878e7i) q^{9} +8.65472e7 q^{10} -3.43468e8i q^{11} +(1.73206e8 + 1.21607e8i) q^{12} -7.14909e8 q^{13} +2.22305e9i q^{14} +(1.04338e9 - 1.48611e9i) q^{15} -5.36845e9 q^{16} -6.74629e8i q^{17} +(1.26612e10 - 4.57212e9i) q^{18} +4.70347e9 q^{19} -8.92717e9i q^{20} +(3.81722e10 + 2.68004e10i) q^{21} -1.07408e11 q^{22} -4.47377e10i q^{23} +(-3.92353e10 + 5.58834e10i) q^{24} +7.59927e10 q^{25} +2.23564e11i q^{26} +(7.41314e10 - 2.72527e11i) q^{27} +2.29303e11 q^{28} -3.75138e11i q^{29} +(-4.64732e11 - 3.26285e11i) q^{30} +6.58929e11 q^{31} +9.96762e11i q^{32} +(-1.29488e12 + 1.84432e12i) q^{33} -2.10968e11 q^{34} -1.96742e12i q^{35} +(-4.71605e11 - 1.30598e12i) q^{36} +3.89028e11 q^{37} -1.47086e12i q^{38} +(3.83885e12 + 2.69522e12i) q^{39} +2.88027e12 q^{40} +4.14027e12i q^{41} +(8.38094e12 - 1.19371e13i) q^{42} -1.68426e13 q^{43} +1.10790e13i q^{44} +(-1.12053e13 + 4.04638e12i) q^{45} -1.39903e13 q^{46} -9.08356e12i q^{47} +(2.88269e13 + 2.02392e13i) q^{48} +1.73022e13 q^{49} -2.37642e13i q^{50} +(-2.54336e12 + 3.62255e12i) q^{51} +2.30602e13 q^{52} -4.32802e13i q^{53} +(-8.52240e13 - 2.31822e13i) q^{54} +9.50576e13 q^{55} +7.39826e13i q^{56} +(-2.52562e13 - 1.77322e13i) q^{57} -1.17312e14 q^{58} +2.07085e14i q^{59} +(-3.36556e13 + 4.79362e13i) q^{60} +1.10641e14 q^{61} -2.06059e14i q^{62} +(-1.03935e14 - 2.87820e14i) q^{63} -4.01216e13 q^{64} -1.97857e14i q^{65} +(5.76750e14 + 4.04932e14i) q^{66} +1.61981e14 q^{67} +2.17610e13i q^{68} +(-1.68662e14 + 2.40228e14i) q^{69} -6.15247e14 q^{70} -8.06506e13i q^{71} +(4.21363e14 - 1.52159e14i) q^{72} -8.85416e14 q^{73} -1.21656e14i q^{74} +(-4.08058e14 - 2.86494e14i) q^{75} -1.51716e14 q^{76} +2.44165e15i q^{77} +(8.42843e14 - 1.20047e15i) q^{78} +2.35142e15 q^{79} -1.48576e15i q^{80} +(-1.42550e15 + 1.18391e15i) q^{81} +1.29474e15 q^{82} -3.93339e15i q^{83} +(-1.23129e15 - 8.64477e14i) q^{84} +1.86709e14 q^{85} +5.26696e15i q^{86} +(-1.41428e15 + 2.01438e15i) q^{87} -3.57453e15 q^{88} -3.56666e15i q^{89} +(1.26537e15 + 3.50410e15i) q^{90} +5.08215e15 q^{91} +1.44307e15i q^{92} +(-3.53825e15 - 2.48418e15i) q^{93} -2.84059e15 q^{94} +1.30172e15i q^{95} +(3.75781e15 - 5.35231e15i) q^{96} -1.51341e15 q^{97} -5.41071e15i q^{98} +(1.39062e16 - 5.02171e15i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2052q^{3} - 12464q^{4} - 403056q^{6} - 3141544q^{7} + 18618660q^{9} + O(q^{10}) \) \( 4q - 2052q^{3} - 12464q^{4} - 403056q^{6} - 3141544q^{7} + 18618660q^{9} - 18646560q^{10} + 572494608q^{12} - 1580730424q^{13} + 6829958880q^{15} - 14561268608q^{16} + 42304978080q^{18} - 56117116360q^{19} + 124455437064q^{21} - 173545812000q^{22} + 100515572352q^{24} - 8074048700q^{25} - 317983667652q^{27} + 746852001056q^{28} - 1762329117600q^{30} + 2471781156248q^{31} - 3610697951520q^{33} + 2721261612672q^{34} - 1219654126512q^{36} + 370563213896q^{37} + 7022170227384q^{39} - 11795287092480q^{40} + 27587883687840q^{42} - 28065022062664q^{43} + 18795326443200q^{45} - 43994579504832q^{46} + 41041959355008q^{48} + 29478262537164q^{49} - 82841575222656q^{51} + 42193089120416q^{52} - 107063660756304q^{54} + 290253653236800q^{55} - 335129108488344q^{57} + 8796421982880q^{58} + 56126440892160q^{60} + 362269793083208q^{61} - 266698363786344q^{63} - 653949742779392q^{64} + 1332768950045280q^{66} - 26774405363464q^{67} + 58823173290816q^{69} - 2292362286177600q^{70} + 2397649754476800q^{72} + 317628887539976q^{73} - 1511365865026500q^{75} - 2008642200508384q^{76} + 1538179445855520q^{78} + 4794017165184920q^{79} - 6444192852054396q^{81} + 1589112481320000q^{82} - 1210523902199136q^{84} + 7999994092573440q^{85} - 8850169595242080q^{87} - 3370289894104320q^{88} + 3549134645307360q^{90} + 9328538231657008q^{91} - 2064207396761784q^{93} - 12859596129667968q^{94} + 15507630559798272q^{96} - 13833795002601784q^{97} + 18943177097338560q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 312.717i 1.22155i −0.791803 0.610776i \(-0.790857\pi\)
0.791803 0.610776i \(-0.209143\pi\)
\(3\) −5369.70 3770.02i −0.818427 0.574611i
\(4\) −32256.2 −0.492190
\(5\) 276758.i 0.708501i 0.935150 + 0.354251i \(0.115264\pi\)
−0.935150 + 0.354251i \(0.884736\pi\)
\(6\) −1.17895e6 + 1.67920e6i −0.701917 + 0.999751i
\(7\) −7.10881e6 −1.23314 −0.616570 0.787300i \(-0.711478\pi\)
−0.616570 + 0.787300i \(0.711478\pi\)
\(8\) 1.04072e7i 0.620316i
\(9\) 1.46206e7 + 4.04878e7i 0.339645 + 0.940554i
\(10\) 8.65472e7 0.865472
\(11\) 3.43468e8i 1.60230i −0.598462 0.801151i \(-0.704221\pi\)
0.598462 0.801151i \(-0.295779\pi\)
\(12\) 1.73206e8 + 1.21607e8i 0.402822 + 0.282818i
\(13\) −7.14909e8 −0.876403 −0.438201 0.898877i \(-0.644384\pi\)
−0.438201 + 0.898877i \(0.644384\pi\)
\(14\) 2.22305e9i 1.50635i
\(15\) 1.04338e9 1.48611e9i 0.407112 0.579857i
\(16\) −5.36845e9 −1.24994
\(17\) 6.74629e8i 0.0967105i −0.998830 0.0483552i \(-0.984602\pi\)
0.998830 0.0483552i \(-0.0153980\pi\)
\(18\) 1.26612e10 4.57212e9i 1.14894 0.414894i
\(19\) 4.70347e9 0.276942 0.138471 0.990366i \(-0.455781\pi\)
0.138471 + 0.990366i \(0.455781\pi\)
\(20\) 8.92717e9i 0.348718i
\(21\) 3.81722e10 + 2.68004e10i 1.00924 + 0.708576i
\(22\) −1.07408e11 −1.95730
\(23\) 4.47377e10i 0.571283i −0.958337 0.285641i \(-0.907793\pi\)
0.958337 0.285641i \(-0.0922066\pi\)
\(24\) −3.92353e10 + 5.58834e10i −0.356440 + 0.507683i
\(25\) 7.59927e10 0.498026
\(26\) 2.23564e11i 1.07057i
\(27\) 7.41314e10 2.72527e11i 0.262477 0.964938i
\(28\) 2.29303e11 0.606940
\(29\) 3.75138e11i 0.749906i −0.927044 0.374953i \(-0.877659\pi\)
0.927044 0.374953i \(-0.122341\pi\)
\(30\) −4.64732e11 3.26285e11i −0.708325 0.497309i
\(31\) 6.58929e11 0.772583 0.386291 0.922377i \(-0.373756\pi\)
0.386291 + 0.922377i \(0.373756\pi\)
\(32\) 9.96762e11i 0.906550i
\(33\) −1.29488e12 + 1.84432e12i −0.920700 + 1.31137i
\(34\) −2.10968e11 −0.118137
\(35\) 1.96742e12i 0.873682i
\(36\) −4.71605e11 1.30598e12i −0.167170 0.462932i
\(37\) 3.89028e11 0.110756 0.0553779 0.998465i \(-0.482364\pi\)
0.0553779 + 0.998465i \(0.482364\pi\)
\(38\) 1.47086e12i 0.338299i
\(39\) 3.83885e12 + 2.69522e12i 0.717272 + 0.503590i
\(40\) 2.88027e12 0.439495
\(41\) 4.14027e12i 0.518511i 0.965809 + 0.259256i \(0.0834772\pi\)
−0.965809 + 0.259256i \(0.916523\pi\)
\(42\) 8.38094e12 1.19371e13i 0.865562 1.23283i
\(43\) −1.68426e13 −1.44099 −0.720494 0.693461i \(-0.756085\pi\)
−0.720494 + 0.693461i \(0.756085\pi\)
\(44\) 1.10790e13i 0.788638i
\(45\) −1.12053e13 + 4.04638e12i −0.666384 + 0.240639i
\(46\) −1.39903e13 −0.697852
\(47\) 9.08356e12i 0.381481i −0.981640 0.190741i \(-0.938911\pi\)
0.981640 0.190741i \(-0.0610889\pi\)
\(48\) 2.88269e13 + 2.02392e13i 1.02298 + 0.718228i
\(49\) 1.73022e13 0.520635
\(50\) 2.37642e13i 0.608365i
\(51\) −2.54336e12 + 3.62255e12i −0.0555709 + 0.0791504i
\(52\) 2.30602e13 0.431357
\(53\) 4.32802e13i 0.695155i −0.937651 0.347578i \(-0.887004\pi\)
0.937651 0.347578i \(-0.112996\pi\)
\(54\) −8.52240e13 2.31822e13i −1.17872 0.320630i
\(55\) 9.50576e13 1.13523
\(56\) 7.39826e13i 0.764937i
\(57\) −2.52562e13 1.77322e13i −0.226657 0.159134i
\(58\) −1.17312e14 −0.916049
\(59\) 2.07085e14i 1.41037i 0.709024 + 0.705185i \(0.249136\pi\)
−0.709024 + 0.705185i \(0.750864\pi\)
\(60\) −3.36556e13 + 4.79362e13i −0.200377 + 0.285400i
\(61\) 1.10641e14 0.577136 0.288568 0.957459i \(-0.406821\pi\)
0.288568 + 0.957459i \(0.406821\pi\)
\(62\) 2.06059e14i 0.943751i
\(63\) −1.03935e14 2.87820e14i −0.418830 1.15983i
\(64\) −4.01216e13 −0.142541
\(65\) 1.97857e14i 0.620933i
\(66\) 5.76750e14 + 4.04932e14i 1.60190 + 1.12468i
\(67\) 1.61981e14 0.398901 0.199451 0.979908i \(-0.436084\pi\)
0.199451 + 0.979908i \(0.436084\pi\)
\(68\) 2.17610e13i 0.0476000i
\(69\) −1.68662e14 + 2.40228e14i −0.328265 + 0.467553i
\(70\) −6.15247e14 −1.06725
\(71\) 8.06506e13i 0.124894i −0.998048 0.0624469i \(-0.980110\pi\)
0.998048 0.0624469i \(-0.0198904\pi\)
\(72\) 4.21363e14 1.52159e14i 0.583440 0.210687i
\(73\) −8.85416e14 −1.09790 −0.548952 0.835854i \(-0.684973\pi\)
−0.548952 + 0.835854i \(0.684973\pi\)
\(74\) 1.21656e14i 0.135294i
\(75\) −4.08058e14 2.86494e14i −0.407598 0.286171i
\(76\) −1.51716e14 −0.136308
\(77\) 2.44165e15i 1.97586i
\(78\) 8.42843e14 1.20047e15i 0.615162 0.876185i
\(79\) 2.35142e15 1.54993 0.774967 0.632002i \(-0.217766\pi\)
0.774967 + 0.632002i \(0.217766\pi\)
\(80\) 1.48576e15i 0.885584i
\(81\) −1.42550e15 + 1.18391e15i −0.769282 + 0.638909i
\(82\) 1.29474e15 0.633389
\(83\) 3.93339e15i 1.74640i −0.487365 0.873198i \(-0.662042\pi\)
0.487365 0.873198i \(-0.337958\pi\)
\(84\) −1.23129e15 8.64477e14i −0.496736 0.348754i
\(85\) 1.86709e14 0.0685195
\(86\) 5.26696e15i 1.76024i
\(87\) −1.41428e15 + 2.01438e15i −0.430904 + 0.613743i
\(88\) −3.57453e15 −0.993934
\(89\) 3.56666e15i 0.906028i −0.891503 0.453014i \(-0.850349\pi\)
0.891503 0.453014i \(-0.149651\pi\)
\(90\) 1.26537e15 + 3.50410e15i 0.293953 + 0.814023i
\(91\) 5.08215e15 1.08073
\(92\) 1.44307e15i 0.281180i
\(93\) −3.53825e15 2.48418e15i −0.632303 0.443934i
\(94\) −2.84059e15 −0.465999
\(95\) 1.30172e15i 0.196214i
\(96\) 3.75781e15 5.35231e15i 0.520913 0.741945i
\(97\) −1.51341e15 −0.193100 −0.0965502 0.995328i \(-0.530781\pi\)
−0.0965502 + 0.995328i \(0.530781\pi\)
\(98\) 5.41071e15i 0.635983i
\(99\) 1.39062e16 5.02171e15i 1.50705 0.544214i
\(100\) −2.45124e15 −0.245124
\(101\) 1.00976e16i 0.932499i 0.884653 + 0.466249i \(0.154395\pi\)
−0.884653 + 0.466249i \(0.845605\pi\)
\(102\) 1.13284e15 + 7.95354e14i 0.0966864 + 0.0678827i
\(103\) −2.41924e15 −0.190977 −0.0954884 0.995431i \(-0.530441\pi\)
−0.0954884 + 0.995431i \(0.530441\pi\)
\(104\) 7.44018e15i 0.543647i
\(105\) −7.41722e15 + 1.05645e16i −0.502027 + 0.715045i
\(106\) −1.35345e16 −0.849169
\(107\) 1.15781e16i 0.673857i −0.941530 0.336929i \(-0.890612\pi\)
0.941530 0.336929i \(-0.109388\pi\)
\(108\) −2.39120e15 + 8.79068e15i −0.129189 + 0.474933i
\(109\) −1.26180e16 −0.633253 −0.316627 0.948550i \(-0.602550\pi\)
−0.316627 + 0.948550i \(0.602550\pi\)
\(110\) 2.97262e16i 1.38675i
\(111\) −2.08896e15 1.46664e15i −0.0906456 0.0636415i
\(112\) 3.81633e16 1.54135
\(113\) 2.03120e16i 0.764057i 0.924151 + 0.382029i \(0.124774\pi\)
−0.924151 + 0.382029i \(0.875226\pi\)
\(114\) −5.54516e15 + 7.89805e15i −0.194390 + 0.276873i
\(115\) 1.23815e16 0.404755
\(116\) 1.21005e16i 0.369096i
\(117\) −1.04524e16 2.89450e16i −0.297666 0.824304i
\(118\) 6.47591e16 1.72284
\(119\) 4.79581e15i 0.119258i
\(120\) −1.54662e16 1.08587e16i −0.359694 0.252538i
\(121\) −7.20203e16 −1.56737
\(122\) 3.45995e16i 0.705003i
\(123\) 1.56089e16 2.22320e16i 0.297942 0.424364i
\(124\) −2.12545e16 −0.380258
\(125\) 6.32616e16i 1.06135i
\(126\) −9.00062e16 + 3.25023e16i −1.41680 + 0.511623i
\(127\) 5.69808e16 0.841974 0.420987 0.907067i \(-0.361684\pi\)
0.420987 + 0.907067i \(0.361684\pi\)
\(128\) 7.78705e16i 1.08067i
\(129\) 9.04395e16 + 6.34968e16i 1.17934 + 0.828007i
\(130\) −6.18733e16 −0.758502
\(131\) 1.29909e17i 1.49786i −0.662651 0.748928i \(-0.730569\pi\)
0.662651 0.748928i \(-0.269431\pi\)
\(132\) 4.17679e16 5.94907e16i 0.453160 0.645442i
\(133\) −3.34360e16 −0.341509
\(134\) 5.06542e16i 0.487279i
\(135\) 7.54241e16 + 2.05165e16i 0.683660 + 0.185966i
\(136\) −7.02098e15 −0.0599911
\(137\) 1.41617e17i 1.14117i −0.821238 0.570586i \(-0.806716\pi\)
0.821238 0.570586i \(-0.193284\pi\)
\(138\) 7.51235e16 + 5.27436e16i 0.571141 + 0.400993i
\(139\) −3.68618e16 −0.264520 −0.132260 0.991215i \(-0.542223\pi\)
−0.132260 + 0.991215i \(0.542223\pi\)
\(140\) 6.34615e16i 0.430018i
\(141\) −3.42452e16 + 4.87760e16i −0.219203 + 0.312214i
\(142\) −2.52208e16 −0.152564
\(143\) 2.45548e17i 1.40426i
\(144\) −7.84900e16 2.17356e17i −0.424536 1.17563i
\(145\) 1.03822e17 0.531309
\(146\) 2.76885e17i 1.34115i
\(147\) −9.29077e16 6.52297e16i −0.426102 0.299162i
\(148\) −1.25486e16 −0.0545130
\(149\) 3.06216e17i 1.26049i −0.776398 0.630243i \(-0.782955\pi\)
0.776398 0.630243i \(-0.217045\pi\)
\(150\) −8.95917e16 + 1.27607e17i −0.349573 + 0.497902i
\(151\) −4.71608e17 −1.74488 −0.872440 0.488721i \(-0.837463\pi\)
−0.872440 + 0.488721i \(0.837463\pi\)
\(152\) 4.89498e16i 0.171792i
\(153\) 2.73142e16 9.86349e15i 0.0909614 0.0328472i
\(154\) 7.63545e17 2.41362
\(155\) 1.82364e17i 0.547376i
\(156\) −1.23827e17 8.69376e16i −0.353034 0.247862i
\(157\) 5.59035e17 1.51440 0.757202 0.653181i \(-0.226566\pi\)
0.757202 + 0.653181i \(0.226566\pi\)
\(158\) 7.35330e17i 1.89333i
\(159\) −1.63167e17 + 2.32401e17i −0.399444 + 0.568934i
\(160\) −2.75862e17 −0.642292
\(161\) 3.18032e17i 0.704472i
\(162\) 3.70230e17 + 4.45777e17i 0.780461 + 0.939719i
\(163\) 2.34231e17 0.470050 0.235025 0.971989i \(-0.424483\pi\)
0.235025 + 0.971989i \(0.424483\pi\)
\(164\) 1.33549e17i 0.255206i
\(165\) −5.10430e17 3.58369e17i −0.929105 0.652317i
\(166\) −1.23004e18 −2.13331
\(167\) 4.08862e17i 0.675842i 0.941175 + 0.337921i \(0.109724\pi\)
−0.941175 + 0.337921i \(0.890276\pi\)
\(168\) 2.78916e17 3.97264e17i 0.439541 0.626045i
\(169\) −1.54322e17 −0.231918
\(170\) 5.83872e16i 0.0837002i
\(171\) 6.87675e16 + 1.90433e17i 0.0940621 + 0.260479i
\(172\) 5.43277e17 0.709241
\(173\) 2.03093e16i 0.0253119i 0.999920 + 0.0126560i \(0.00402863\pi\)
−0.999920 + 0.0126560i \(0.995971\pi\)
\(174\) 6.29931e17 + 4.42269e17i 0.749719 + 0.526372i
\(175\) −5.40218e17 −0.614136
\(176\) 1.84389e18i 2.00278i
\(177\) 7.80715e17 1.11198e18i 0.810413 1.15428i
\(178\) −1.11536e18 −1.10676
\(179\) 1.38776e18i 1.31671i −0.752709 0.658354i \(-0.771253\pi\)
0.752709 0.658354i \(-0.228747\pi\)
\(180\) 3.61441e17 1.30521e17i 0.327988 0.118440i
\(181\) 2.00744e18 1.74267 0.871334 0.490691i \(-0.163256\pi\)
0.871334 + 0.490691i \(0.163256\pi\)
\(182\) 1.58928e18i 1.32017i
\(183\) −5.94110e17 4.17120e17i −0.472344 0.331629i
\(184\) −4.65593e17 −0.354376
\(185\) 1.07667e17i 0.0784707i
\(186\) −7.76845e17 + 1.10647e18i −0.542289 + 0.772391i
\(187\) −2.31713e17 −0.154959
\(188\) 2.93001e17i 0.187761i
\(189\) −5.26986e17 + 1.93734e18i −0.323671 + 1.18990i
\(190\) 4.07072e17 0.239686
\(191\) 7.92402e17i 0.447382i 0.974660 + 0.223691i \(0.0718107\pi\)
−0.974660 + 0.223691i \(0.928189\pi\)
\(192\) 2.15441e17 + 1.51259e17i 0.116659 + 0.0819053i
\(193\) −2.85892e17 −0.148506 −0.0742528 0.997239i \(-0.523657\pi\)
−0.0742528 + 0.997239i \(0.523657\pi\)
\(194\) 4.73270e17i 0.235882i
\(195\) −7.45925e17 + 1.06243e18i −0.356795 + 0.508188i
\(196\) −5.58104e17 −0.256251
\(197\) 1.08139e18i 0.476707i −0.971178 0.238353i \(-0.923392\pi\)
0.971178 0.238353i \(-0.0766077\pi\)
\(198\) −1.57038e18 4.34872e18i −0.664786 1.84094i
\(199\) 1.96655e18 0.799613 0.399806 0.916600i \(-0.369077\pi\)
0.399806 + 0.916600i \(0.369077\pi\)
\(200\) 7.90869e17i 0.308933i
\(201\) −8.69788e17 6.10671e17i −0.326471 0.229213i
\(202\) 3.15770e18 1.13910
\(203\) 2.66678e18i 0.924739i
\(204\) 8.20393e16 1.16850e17i 0.0273514 0.0389571i
\(205\) −1.14586e18 −0.367366
\(206\) 7.56538e17i 0.233288i
\(207\) 1.81133e18 6.54093e17i 0.537322 0.194033i
\(208\) 3.83795e18 1.09545
\(209\) 1.61549e18i 0.443745i
\(210\) 3.30369e18 + 2.31949e18i 0.873464 + 0.613252i
\(211\) −5.56143e18 −1.41556 −0.707778 0.706435i \(-0.750302\pi\)
−0.707778 + 0.706435i \(0.750302\pi\)
\(212\) 1.39605e18i 0.342149i
\(213\) −3.04054e17 + 4.33069e17i −0.0717653 + 0.102216i
\(214\) −3.62068e18 −0.823152
\(215\) 4.66132e18i 1.02094i
\(216\) −2.83624e18 7.71498e17i −0.598567 0.162819i
\(217\) −4.68420e18 −0.952703
\(218\) 3.94586e18i 0.773552i
\(219\) 4.75442e18 + 3.33804e18i 0.898554 + 0.630867i
\(220\) −3.06619e18 −0.558751
\(221\) 4.82298e17i 0.0847573i
\(222\) −4.58645e17 + 6.53255e17i −0.0777414 + 0.110728i
\(223\) 8.62389e17 0.141015 0.0705074 0.997511i \(-0.477538\pi\)
0.0705074 + 0.997511i \(0.477538\pi\)
\(224\) 7.08579e18i 1.11790i
\(225\) 1.11106e18 + 3.07677e18i 0.169152 + 0.468420i
\(226\) 6.35193e18 0.933336
\(227\) 2.61451e18i 0.370837i 0.982660 + 0.185418i \(0.0593641\pi\)
−0.982660 + 0.185418i \(0.940636\pi\)
\(228\) 8.14669e17 + 5.71972e17i 0.111558 + 0.0783242i
\(229\) 5.58270e18 0.738176 0.369088 0.929394i \(-0.379670\pi\)
0.369088 + 0.929394i \(0.379670\pi\)
\(230\) 3.87192e18i 0.494429i
\(231\) 9.20505e18 1.31109e19i 1.13535 1.61710i
\(232\) −3.90412e18 −0.465179
\(233\) 1.35764e19i 1.56293i 0.623952 + 0.781463i \(0.285526\pi\)
−0.623952 + 0.781463i \(0.714474\pi\)
\(234\) −9.05162e18 + 3.26865e18i −1.00693 + 0.363615i
\(235\) 2.51395e18 0.270280
\(236\) 6.67978e18i 0.694170i
\(237\) −1.26264e19 8.86490e18i −1.26851 0.890609i
\(238\) 1.49973e18 0.145679
\(239\) 8.32183e18i 0.781692i −0.920456 0.390846i \(-0.872182\pi\)
0.920456 0.390846i \(-0.127818\pi\)
\(240\) −5.60136e18 + 7.97810e18i −0.508866 + 0.724785i
\(241\) 3.38184e18 0.297178 0.148589 0.988899i \(-0.452527\pi\)
0.148589 + 0.988899i \(0.452527\pi\)
\(242\) 2.25220e19i 1.91463i
\(243\) 1.21179e19 9.83099e17i 0.996725 0.0808625i
\(244\) −3.56887e18 −0.284061
\(245\) 4.78853e18i 0.368870i
\(246\) −6.95234e18 4.88118e18i −0.518382 0.363952i
\(247\) −3.36255e18 −0.242713
\(248\) 6.85759e18i 0.479246i
\(249\) −1.48290e19 + 2.11211e19i −1.00350 + 1.42930i
\(250\) 1.97830e19 1.29650
\(251\) 1.37972e19i 0.875789i −0.899026 0.437895i \(-0.855724\pi\)
0.899026 0.437895i \(-0.144276\pi\)
\(252\) 3.35255e18 + 9.28397e18i 0.206144 + 0.570859i
\(253\) −1.53660e19 −0.915368
\(254\) 1.78189e19i 1.02852i
\(255\) −1.00257e18 7.03897e17i −0.0560782 0.0393720i
\(256\) 2.17221e19 1.17756
\(257\) 1.93378e19i 1.01611i −0.861324 0.508057i \(-0.830364\pi\)
0.861324 0.508057i \(-0.169636\pi\)
\(258\) 1.98566e19 2.82820e19i 1.01145 1.44063i
\(259\) −2.76552e18 −0.136578
\(260\) 6.38211e18i 0.305617i
\(261\) 1.51885e19 5.48474e18i 0.705327 0.254702i
\(262\) −4.06249e19 −1.82971
\(263\) 4.15307e19i 1.81436i 0.420741 + 0.907181i \(0.361770\pi\)
−0.420741 + 0.907181i \(0.638230\pi\)
\(264\) 1.91941e19 + 1.34760e19i 0.813462 + 0.571125i
\(265\) 1.19781e19 0.492519
\(266\) 1.04560e19i 0.417171i
\(267\) −1.34464e19 + 1.91519e19i −0.520613 + 0.741518i
\(268\) −5.22488e18 −0.196335
\(269\) 4.45503e18i 0.162492i 0.996694 + 0.0812460i \(0.0258899\pi\)
−0.996694 + 0.0812460i \(0.974110\pi\)
\(270\) 6.41586e18 2.35864e19i 0.227167 0.835127i
\(271\) −1.72748e19 −0.593827 −0.296913 0.954904i \(-0.595957\pi\)
−0.296913 + 0.954904i \(0.595957\pi\)
\(272\) 3.62171e18i 0.120882i
\(273\) −2.72896e19 1.91598e19i −0.884497 0.620998i
\(274\) −4.42862e19 −1.39400
\(275\) 2.61010e19i 0.797988i
\(276\) 5.44040e18 7.74884e18i 0.161569 0.230125i
\(277\) 5.05204e19 1.45757 0.728784 0.684744i \(-0.240086\pi\)
0.728784 + 0.684744i \(0.240086\pi\)
\(278\) 1.15273e19i 0.323125i
\(279\) 9.63395e18 + 2.66786e19i 0.262404 + 0.726656i
\(280\) −2.04753e19 −0.541959
\(281\) 2.72214e18i 0.0700260i 0.999387 + 0.0350130i \(0.0111473\pi\)
−0.999387 + 0.0350130i \(0.988853\pi\)
\(282\) 1.52531e19 + 1.07091e19i 0.381386 + 0.267768i
\(283\) −3.84294e18 −0.0934054 −0.0467027 0.998909i \(-0.514871\pi\)
−0.0467027 + 0.998909i \(0.514871\pi\)
\(284\) 2.60148e18i 0.0614715i
\(285\) 4.90752e18 6.98986e18i 0.112747 0.160587i
\(286\) 7.67872e19 1.71538
\(287\) 2.94324e19i 0.639397i
\(288\) −4.03567e19 + 1.45733e19i −0.852659 + 0.307905i
\(289\) 4.82061e19 0.990647
\(290\) 3.24671e19i 0.649022i
\(291\) 8.12657e18 + 5.70559e18i 0.158039 + 0.110958i
\(292\) 2.85601e19 0.540378
\(293\) 4.00496e19i 0.737322i −0.929564 0.368661i \(-0.879816\pi\)
0.929564 0.368661i \(-0.120184\pi\)
\(294\) −2.03985e19 + 2.90539e19i −0.365442 + 0.520505i
\(295\) −5.73125e19 −0.999249
\(296\) 4.04868e18i 0.0687036i
\(297\) −9.36042e19 2.54617e19i −1.54612 0.420568i
\(298\) −9.57592e19 −1.53975
\(299\) 3.19834e19i 0.500674i
\(300\) 1.31624e19 + 9.24121e18i 0.200616 + 0.140851i
\(301\) 1.19731e20 1.77694
\(302\) 1.47480e20i 2.13146i
\(303\) 3.80683e19 5.42212e19i 0.535824 0.763182i
\(304\) −2.52503e19 −0.346161
\(305\) 3.06209e19i 0.408902i
\(306\) −3.08448e18 8.54163e18i −0.0401246 0.111114i
\(307\) −8.00171e19 −1.01409 −0.507044 0.861920i \(-0.669262\pi\)
−0.507044 + 0.861920i \(0.669262\pi\)
\(308\) 7.87582e19i 0.972501i
\(309\) 1.29906e19 + 9.12058e18i 0.156301 + 0.109737i
\(310\) 5.70284e19 0.668649
\(311\) 1.25107e20i 1.42955i 0.699355 + 0.714775i \(0.253471\pi\)
−0.699355 + 0.714775i \(0.746529\pi\)
\(312\) 2.80496e19 3.99515e19i 0.312385 0.444935i
\(313\) 4.69482e19 0.509641 0.254820 0.966988i \(-0.417984\pi\)
0.254820 + 0.966988i \(0.417984\pi\)
\(314\) 1.74820e20i 1.84992i
\(315\) 7.96565e19 2.87649e19i 0.821744 0.296742i
\(316\) −7.58478e19 −0.762863
\(317\) 5.48514e19i 0.537915i −0.963152 0.268957i \(-0.913321\pi\)
0.963152 0.268957i \(-0.0866791\pi\)
\(318\) 7.26760e19 + 5.10252e19i 0.694983 + 0.487941i
\(319\) −1.28848e20 −1.20158
\(320\) 1.11040e19i 0.100990i
\(321\) −4.36498e19 + 6.21710e19i −0.387206 + 0.551503i
\(322\) 9.94541e19 0.860549
\(323\) 3.17309e18i 0.0267832i
\(324\) 4.59811e19 3.81885e19i 0.378633 0.314465i
\(325\) −5.43278e19 −0.436471
\(326\) 7.32482e19i 0.574191i
\(327\) 6.77547e19 + 4.75700e19i 0.518271 + 0.363874i
\(328\) 4.30886e19 0.321641
\(329\) 6.45733e19i 0.470420i
\(330\) −1.12068e20 + 1.59620e20i −0.796840 + 1.13495i
\(331\) −1.44398e20 −1.00216 −0.501081 0.865401i \(-0.667064\pi\)
−0.501081 + 0.865401i \(0.667064\pi\)
\(332\) 1.26876e20i 0.859560i
\(333\) 5.68782e18 + 1.57509e19i 0.0376177 + 0.104172i
\(334\) 1.27858e20 0.825576
\(335\) 4.48295e19i 0.282622i
\(336\) −2.04925e20 1.43876e20i −1.26148 0.885676i
\(337\) −1.23577e20 −0.742846 −0.371423 0.928464i \(-0.621130\pi\)
−0.371423 + 0.928464i \(0.621130\pi\)
\(338\) 4.82592e19i 0.283300i
\(339\) 7.65768e19 1.09070e20i 0.439035 0.625325i
\(340\) −6.02253e18 −0.0337246
\(341\) 2.26321e20i 1.23791i
\(342\) 5.95516e19 2.15048e19i 0.318189 0.114902i
\(343\) 1.13248e20 0.591125
\(344\) 1.75283e20i 0.893868i
\(345\) −6.64851e19 4.66787e19i −0.331262 0.232576i
\(346\) 6.35106e18 0.0309198
\(347\) 2.90213e20i 1.38064i −0.723504 0.690320i \(-0.757470\pi\)
0.723504 0.690320i \(-0.242530\pi\)
\(348\) 4.56192e19 6.49761e19i 0.212087 0.302078i
\(349\) 4.26107e20 1.93604 0.968021 0.250869i \(-0.0807164\pi\)
0.968021 + 0.250869i \(0.0807164\pi\)
\(350\) 1.68935e20i 0.750199i
\(351\) −5.29972e19 + 1.94832e20i −0.230036 + 0.845675i
\(352\) 3.42356e20 1.45257
\(353\) 3.04382e20i 1.26247i 0.775591 + 0.631236i \(0.217452\pi\)
−0.775591 + 0.631236i \(0.782548\pi\)
\(354\) −3.47737e20 2.44143e20i −1.41002 0.989962i
\(355\) 2.23207e19 0.0884874
\(356\) 1.15047e20i 0.445938i
\(357\) 1.80803e19 2.57520e19i 0.0685267 0.0976036i
\(358\) −4.33976e20 −1.60843
\(359\) 6.70999e19i 0.243202i −0.992579 0.121601i \(-0.961197\pi\)
0.992579 0.121601i \(-0.0388028\pi\)
\(360\) 4.21114e19 + 1.16616e20i 0.149272 + 0.413368i
\(361\) −2.66319e20 −0.923303
\(362\) 6.27762e20i 2.12876i
\(363\) 3.86727e20 + 2.71518e20i 1.28278 + 0.900629i
\(364\) −1.63931e20 −0.531924
\(365\) 2.45046e20i 0.777866i
\(366\) −1.30441e20 + 1.85789e20i −0.405102 + 0.576993i
\(367\) −1.14079e20 −0.346639 −0.173320 0.984866i \(-0.555449\pi\)
−0.173320 + 0.984866i \(0.555449\pi\)
\(368\) 2.40172e20i 0.714069i
\(369\) −1.67630e20 + 6.05333e19i −0.487688 + 0.176110i
\(370\) 3.36692e19 0.0958561
\(371\) 3.07670e20i 0.857224i
\(372\) 1.14130e20 + 8.01301e19i 0.311213 + 0.218500i
\(373\) −8.72192e19 −0.232778 −0.116389 0.993204i \(-0.537132\pi\)
−0.116389 + 0.993204i \(0.537132\pi\)
\(374\) 7.24608e19i 0.189291i
\(375\) 2.38497e20 3.39696e20i 0.609865 0.868640i
\(376\) −9.45342e19 −0.236639
\(377\) 2.68189e20i 0.657220i
\(378\) 6.05841e20 + 1.64798e20i 1.45353 + 0.395382i
\(379\) 4.07877e20 0.958111 0.479056 0.877785i \(-0.340979\pi\)
0.479056 + 0.877785i \(0.340979\pi\)
\(380\) 4.19886e19i 0.0965746i
\(381\) −3.05970e20 2.14819e20i −0.689094 0.483807i
\(382\) 2.47798e20 0.546501
\(383\) 9.15624e20i 1.97755i −0.149422 0.988774i \(-0.547741\pi\)
0.149422 0.988774i \(-0.452259\pi\)
\(384\) 2.93574e20 4.18141e20i 0.620965 0.884450i
\(385\) −6.75746e20 −1.39990
\(386\) 8.94033e19i 0.181407i
\(387\) −2.46249e20 6.81917e20i −0.489425 1.35533i
\(388\) 4.88169e19 0.0950422
\(389\) 9.02288e20i 1.72087i 0.509559 + 0.860436i \(0.329809\pi\)
−0.509559 + 0.860436i \(0.670191\pi\)
\(390\) 3.32241e20 + 2.33264e20i 0.620778 + 0.435843i
\(391\) −3.01814e19 −0.0552490
\(392\) 1.80067e20i 0.322958i
\(393\) −4.89761e20 + 6.97574e20i −0.860684 + 1.22589i
\(394\) −3.38169e20 −0.582322
\(395\) 6.50775e20i 1.09813i
\(396\) −4.48562e20 + 1.61981e20i −0.741756 + 0.267857i
\(397\) 1.05321e21 1.70684 0.853419 0.521226i \(-0.174525\pi\)
0.853419 + 0.521226i \(0.174525\pi\)
\(398\) 6.14973e20i 0.976769i
\(399\) 1.79541e20 + 1.26055e20i 0.279500 + 0.196234i
\(400\) −4.07963e20 −0.622502
\(401\) 2.31809e20i 0.346717i 0.984859 + 0.173358i \(0.0554619\pi\)
−0.984859 + 0.173358i \(0.944538\pi\)
\(402\) −1.90967e20 + 2.71998e20i −0.279995 + 0.398802i
\(403\) −4.71074e20 −0.677094
\(404\) 3.25711e20i 0.458967i
\(405\) −3.27657e20 3.94518e20i −0.452668 0.545038i
\(406\) 8.33949e20 1.12962
\(407\) 1.33618e20i 0.177464i
\(408\) 3.77005e19 + 2.64692e19i 0.0490983 + 0.0344715i
\(409\) −2.32833e19 −0.0297343 −0.0148671 0.999889i \(-0.504733\pi\)
−0.0148671 + 0.999889i \(0.504733\pi\)
\(410\) 3.58329e20i 0.448757i
\(411\) −5.33900e20 + 7.60442e20i −0.655730 + 0.933966i
\(412\) 7.80354e19 0.0939970
\(413\) 1.47213e21i 1.73918i
\(414\) −2.04546e20 5.66434e20i −0.237022 0.656367i
\(415\) 1.08860e21 1.23732
\(416\) 7.12594e20i 0.794503i
\(417\) 1.97937e20 + 1.38970e20i 0.216490 + 0.151996i
\(418\) −5.05191e20 −0.542058
\(419\) 3.12205e20i 0.328645i 0.986407 + 0.164323i \(0.0525438\pi\)
−0.986407 + 0.164323i \(0.947456\pi\)
\(420\) 2.39251e20 3.40769e20i 0.247093 0.351938i
\(421\) 1.66124e21 1.68336 0.841679 0.539978i \(-0.181567\pi\)
0.841679 + 0.539978i \(0.181567\pi\)
\(422\) 1.73916e21i 1.72918i
\(423\) 3.67773e20 1.32807e20i 0.358803 0.129568i
\(424\) −4.50424e20 −0.431216
\(425\) 5.12669e19i 0.0481643i
\(426\) 1.35428e20 + 9.50831e19i 0.124863 + 0.0876651i
\(427\) −7.86528e20 −0.711690
\(428\) 3.73466e20i 0.331666i
\(429\) 9.25721e20 1.31852e21i 0.806904 1.14929i
\(430\) −1.45768e21 −1.24713
\(431\) 1.02197e20i 0.0858259i −0.999079 0.0429129i \(-0.986336\pi\)
0.999079 0.0429129i \(-0.0136638\pi\)
\(432\) −3.97970e20 + 1.46305e21i −0.328081 + 1.20611i
\(433\) −2.16790e21 −1.75443 −0.877216 0.480096i \(-0.840602\pi\)
−0.877216 + 0.480096i \(0.840602\pi\)
\(434\) 1.46483e21i 1.16378i
\(435\) −5.57495e20 3.91413e20i −0.434838 0.305296i
\(436\) 4.07007e20 0.311681
\(437\) 2.10422e20i 0.158212i
\(438\) 1.04386e21 1.48679e21i 0.770638 1.09763i
\(439\) −7.18216e20 −0.520641 −0.260321 0.965522i \(-0.583828\pi\)
−0.260321 + 0.965522i \(0.583828\pi\)
\(440\) 9.89281e20i 0.704203i
\(441\) 2.52969e20 + 7.00528e20i 0.176831 + 0.489685i
\(442\) 1.50823e20 0.103536
\(443\) 2.80285e20i 0.188960i 0.995527 + 0.0944802i \(0.0301189\pi\)
−0.995527 + 0.0944802i \(0.969881\pi\)
\(444\) 6.73819e19 + 4.73083e19i 0.0446149 + 0.0313237i
\(445\) 9.87103e20 0.641922
\(446\) 2.69684e20i 0.172257i
\(447\) −1.15444e21 + 1.64429e21i −0.724289 + 1.03162i
\(448\) 2.85217e20 0.175772
\(449\) 1.90690e21i 1.15440i −0.816603 0.577200i \(-0.804145\pi\)
0.816603 0.577200i \(-0.195855\pi\)
\(450\) 9.62161e20 3.47448e20i 0.572200 0.206628i
\(451\) 1.42205e21 0.830812
\(452\) 6.55189e20i 0.376062i
\(453\) 2.53239e21 + 1.77797e21i 1.42806 + 1.00263i
\(454\) 8.17602e20 0.452997
\(455\) 1.40653e21i 0.765697i
\(456\) −1.84542e20 + 2.62846e20i −0.0987133 + 0.140599i
\(457\) −1.24426e21 −0.654005 −0.327002 0.945024i \(-0.606038\pi\)
−0.327002 + 0.945024i \(0.606038\pi\)
\(458\) 1.74581e21i 0.901721i
\(459\) −1.83855e20 5.00112e19i −0.0933196 0.0253843i
\(460\) −3.99381e20 −0.199216
\(461\) 1.67655e21i 0.821879i −0.911663 0.410940i \(-0.865201\pi\)
0.911663 0.410940i \(-0.134799\pi\)
\(462\) −4.10001e21 2.87858e21i −1.97537 1.38689i
\(463\) −2.07466e21 −0.982422 −0.491211 0.871041i \(-0.663446\pi\)
−0.491211 + 0.871041i \(0.663446\pi\)
\(464\) 2.01391e21i 0.937336i
\(465\) 6.87517e20 9.79240e20i 0.314528 0.447987i
\(466\) 4.24559e21 1.90920
\(467\) 1.45238e21i 0.642016i 0.947076 + 0.321008i \(0.104022\pi\)
−0.947076 + 0.321008i \(0.895978\pi\)
\(468\) 3.37155e20 + 9.33657e20i 0.146508 + 0.405715i
\(469\) −1.15149e21 −0.491901
\(470\) 7.86156e20i 0.330161i
\(471\) −3.00185e21 2.10757e21i −1.23943 0.870193i
\(472\) 2.15517e21 0.874875
\(473\) 5.78487e21i 2.30890i
\(474\) −2.77221e21 + 3.94850e21i −1.08793 + 1.54955i
\(475\) 3.57429e20 0.137924
\(476\) 1.54694e20i 0.0586974i
\(477\) 1.75232e21 6.32782e20i 0.653831 0.236106i
\(478\) −2.60238e21 −0.954878
\(479\) 5.43994e20i 0.196295i −0.995172 0.0981477i \(-0.968708\pi\)
0.995172 0.0981477i \(-0.0312918\pi\)
\(480\) 1.48130e21 + 1.04001e21i 0.525669 + 0.369068i
\(481\) −2.78119e20 −0.0970668
\(482\) 1.05756e21i 0.363019i
\(483\) 1.19899e21 1.70774e21i 0.404797 0.576559i
\(484\) 2.32310e21 0.771446
\(485\) 4.18849e20i 0.136812i
\(486\) −3.07432e20 3.78946e21i −0.0987778 1.21755i
\(487\) 8.43207e20 0.266503 0.133252 0.991082i \(-0.457458\pi\)
0.133252 + 0.991082i \(0.457458\pi\)
\(488\) 1.15146e21i 0.358007i
\(489\) −1.25775e21 8.83057e20i −0.384702 0.270096i
\(490\) 1.49746e21 0.450595
\(491\) 6.07036e21i 1.79706i −0.438911 0.898530i \(-0.644636\pi\)
0.438911 0.898530i \(-0.355364\pi\)
\(492\) −5.03484e20 + 7.17120e20i −0.146644 + 0.208868i
\(493\) −2.53079e20 −0.0725237
\(494\) 1.05153e21i 0.296487i
\(495\) 1.38980e21 + 3.84867e21i 0.385577 + 1.06775i
\(496\) −3.53743e21 −0.965682
\(497\) 5.73330e20i 0.154012i
\(498\) 6.60495e21 + 4.63728e21i 1.74596 + 1.22583i
\(499\) 1.14493e21 0.297834 0.148917 0.988850i \(-0.452421\pi\)
0.148917 + 0.988850i \(0.452421\pi\)
\(500\) 2.04058e21i 0.522388i
\(501\) 1.54142e21 2.19547e21i 0.388346 0.553127i
\(502\) −4.31461e21 −1.06982
\(503\) 4.27994e21i 1.04446i 0.852803 + 0.522232i \(0.174901\pi\)
−0.852803 + 0.522232i \(0.825099\pi\)
\(504\) −2.99539e21 + 1.08167e21i −0.719464 + 0.259807i
\(505\) −2.79460e21 −0.660677
\(506\) 4.80520e21i 1.11817i
\(507\) 8.28663e20 + 5.81797e20i 0.189808 + 0.133262i
\(508\) −1.83798e21 −0.414412
\(509\) 4.76935e21i 1.05856i −0.848446 0.529282i \(-0.822461\pi\)
0.848446 0.529282i \(-0.177539\pi\)
\(510\) −2.20121e20 + 3.13522e20i −0.0480950 + 0.0685025i
\(511\) 6.29425e21 1.35387
\(512\) 1.68955e21i 0.357775i
\(513\) 3.48674e20 1.28182e21i 0.0726911 0.267232i
\(514\) −6.04727e21 −1.24124
\(515\) 6.69544e20i 0.135307i
\(516\) −2.91723e21 2.04816e21i −0.580462 0.407537i
\(517\) −3.11991e21 −0.611248
\(518\) 8.64827e20i 0.166837i
\(519\) 7.65663e19 1.09055e20i 0.0145445 0.0207160i
\(520\) −2.05913e21 −0.385175
\(521\) 6.64803e21i 1.22459i 0.790629 + 0.612295i \(0.209754\pi\)
−0.790629 + 0.612295i \(0.790246\pi\)
\(522\) −1.71517e21 4.74970e21i −0.311132 0.861593i
\(523\) −5.95294e20 −0.106345 −0.0531727 0.998585i \(-0.516933\pi\)
−0.0531727 + 0.998585i \(0.516933\pi\)
\(524\) 4.19038e21i 0.737231i
\(525\) 2.90081e21 + 2.03663e21i 0.502625 + 0.352889i
\(526\) 1.29874e22 2.21634
\(527\) 4.44533e20i 0.0747169i
\(528\) 6.95150e21 9.90112e21i 1.15082 1.63913i
\(529\) 4.13115e21 0.673636
\(530\) 3.74578e21i 0.601637i
\(531\) −8.38441e21 + 3.02771e21i −1.32653 + 0.479025i
\(532\) 1.07852e21 0.168087
\(533\) 2.95992e21i 0.454425i
\(534\) 5.98913e21 + 4.20492e21i 0.905803 + 0.635957i
\(535\) 3.20434e21 0.477429
\(536\) 1.68576e21i 0.247445i
\(537\) −5.23187e21 + 7.45184e21i −0.756594 + 1.07763i
\(538\) 1.39316e21 0.198492
\(539\) 5.94275e21i 0.834214i
\(540\) −2.43290e21 6.61783e20i −0.336491 0.0915305i
\(541\) −6.55475e21 −0.893260 −0.446630 0.894719i \(-0.647376\pi\)
−0.446630 + 0.894719i \(0.647376\pi\)
\(542\) 5.40214e21i 0.725390i
\(543\) −1.07794e22 7.56810e21i −1.42625 1.00136i
\(544\) 6.72445e20 0.0876729
\(545\) 3.49213e21i 0.448661i
\(546\) −5.99161e21 + 8.53394e21i −0.758581 + 1.08046i
\(547\) 1.34210e22 1.67451 0.837253 0.546816i \(-0.184160\pi\)
0.837253 + 0.546816i \(0.184160\pi\)
\(548\) 4.56803e21i 0.561674i
\(549\) 1.61764e21 + 4.47962e21i 0.196022 + 0.542828i
\(550\) −8.16225e21 −0.974784
\(551\) 1.76445e21i 0.207681i
\(552\) 2.50010e21 + 1.75530e21i 0.290031 + 0.203628i
\(553\) −1.67158e22 −1.91129
\(554\) 1.57986e22i 1.78050i
\(555\) 4.05906e20 5.78138e20i 0.0450901 0.0642225i
\(556\) 1.18902e21 0.130194
\(557\) 1.06083e22i 1.14500i 0.819905 + 0.572500i \(0.194026\pi\)
−0.819905 + 0.572500i \(0.805974\pi\)
\(558\) 8.34285e21 3.01270e21i 0.887648 0.320540i
\(559\) 1.20409e22 1.26289
\(560\) 1.05620e22i 1.09205i
\(561\) 1.24423e21 + 8.73563e20i 0.126823 + 0.0890413i
\(562\) 8.51259e20 0.0855404
\(563\) 1.02060e22i 1.01109i 0.862801 + 0.505544i \(0.168708\pi\)
−0.862801 + 0.505544i \(0.831292\pi\)
\(564\) 1.10462e21 1.57333e21i 0.107890 0.153669i
\(565\) −5.62153e21 −0.541336
\(566\) 1.20175e21i 0.114100i
\(567\) 1.01336e22 8.41620e21i 0.948633 0.787864i
\(568\) −8.39345e20 −0.0774736
\(569\) 1.29597e22i 1.17950i −0.807587 0.589749i \(-0.799227\pi\)
0.807587 0.589749i \(-0.200773\pi\)
\(570\) −2.18585e21 1.53467e21i −0.196165 0.137726i
\(571\) −2.34308e21 −0.207347 −0.103673 0.994611i \(-0.533060\pi\)
−0.103673 + 0.994611i \(0.533060\pi\)
\(572\) 7.92045e21i 0.691164i
\(573\) 2.98737e21 4.25496e21i 0.257071 0.366150i
\(574\) −9.20403e21 −0.781057
\(575\) 3.39974e21i 0.284514i
\(576\) −5.86602e20 1.62443e21i −0.0484132 0.134067i
\(577\) 1.87414e22 1.52544 0.762720 0.646729i \(-0.223864\pi\)
0.762720 + 0.646729i \(0.223864\pi\)
\(578\) 1.50749e22i 1.21013i
\(579\) 1.53515e21 + 1.07782e21i 0.121541 + 0.0853329i
\(580\) −3.34892e21 −0.261505
\(581\) 2.79617e22i 2.15355i
\(582\) 1.78424e21 2.54132e21i 0.135541 0.193052i
\(583\) −1.48653e22 −1.11385
\(584\) 9.21468e21i 0.681047i
\(585\) 8.01078e21 2.89279e21i 0.584021 0.210897i
\(586\) −1.25242e22 −0.900677
\(587\) 3.32847e21i 0.236124i −0.993006 0.118062i \(-0.962332\pi\)
0.993006 0.118062i \(-0.0376681\pi\)
\(588\) 2.99685e21 + 2.10406e21i 0.209723 + 0.147245i
\(589\) 3.09925e21 0.213961
\(590\) 1.79226e22i 1.22063i
\(591\) −4.07685e21 + 5.80672e21i −0.273921 + 0.390150i
\(592\) −2.08847e21 −0.138438
\(593\) 1.79460e22i 1.17363i −0.809722 0.586814i \(-0.800382\pi\)
0.809722 0.586814i \(-0.199618\pi\)
\(594\) −7.96233e21 + 2.92717e22i −0.513746 + 1.88867i
\(595\) −1.32728e21 −0.0844942
\(596\) 9.87737e21i 0.620399i
\(597\) −1.05598e22 7.41392e21i −0.654424 0.459466i
\(598\) 1.00018e22 0.611600
\(599\) 5.13326e21i 0.309727i −0.987936 0.154863i \(-0.950506\pi\)
0.987936 0.154863i \(-0.0494938\pi\)
\(600\) −2.98159e21 + 4.24673e21i −0.177516 + 0.252839i
\(601\) −2.68398e21 −0.157682 −0.0788411 0.996887i \(-0.525122\pi\)
−0.0788411 + 0.996887i \(0.525122\pi\)
\(602\) 3.74418e22i 2.17063i
\(603\) 2.36826e21 + 6.55824e21i 0.135485 + 0.375188i
\(604\) 1.52123e22 0.858813
\(605\) 1.99322e22i 1.11049i
\(606\) −1.69559e22 1.19046e22i −0.932267 0.654537i
\(607\) −9.52751e21 −0.516975 −0.258488 0.966015i \(-0.583224\pi\)
−0.258488 + 0.966015i \(0.583224\pi\)
\(608\) 4.68824e21i 0.251062i
\(609\) 1.00538e22 1.43198e22i 0.531365 0.756831i
\(610\) 9.57569e21 0.499495
\(611\) 6.49391e21i 0.334331i
\(612\) −8.81052e20 + 3.18158e20i −0.0447703 + 0.0161671i
\(613\) 2.23921e22 1.12308 0.561541 0.827449i \(-0.310209\pi\)
0.561541 + 0.827449i \(0.310209\pi\)
\(614\) 2.50227e22i 1.23876i
\(615\) 6.15290e21 + 4.31990e21i 0.300662 + 0.211092i
\(616\) 2.54106e22 1.22566
\(617\) 1.75829e22i 0.837162i 0.908179 + 0.418581i \(0.137472\pi\)
−0.908179 + 0.418581i \(0.862528\pi\)
\(618\) 2.85216e21 4.06238e21i 0.134050 0.190929i
\(619\) −2.16013e22 −1.00220 −0.501101 0.865389i \(-0.667071\pi\)
−0.501101 + 0.865389i \(0.667071\pi\)
\(620\) 5.88237e21i 0.269413i
\(621\) −1.21922e22 3.31647e21i −0.551253 0.149949i
\(622\) 3.91232e22 1.74627
\(623\) 2.53547e22i 1.11726i
\(624\) −2.06086e22 1.44692e22i −0.896546 0.629457i
\(625\) −5.91261e21 −0.253945
\(626\) 1.46815e22i 0.622553i
\(627\) −6.09042e21 + 8.67469e21i −0.254981 + 0.363173i
\(628\) −1.80323e22 −0.745375
\(629\) 2.62449e20i 0.0107113i
\(630\) −8.99529e21 2.49100e22i −0.362486 1.00380i
\(631\) −2.28393e22 −0.908757 −0.454379 0.890809i \(-0.650139\pi\)
−0.454379 + 0.890809i \(0.650139\pi\)
\(632\) 2.44716e22i 0.961449i
\(633\) 2.98632e22 + 2.09667e22i 1.15853 + 0.813393i
\(634\) −1.71530e22 −0.657091
\(635\) 1.57699e22i 0.596540i
\(636\) 5.26315e21 7.49639e21i 0.196602 0.280024i
\(637\) −1.23695e22 −0.456286
\(638\) 4.02929e22i 1.46779i
\(639\) 3.26536e21 1.17916e21i 0.117469 0.0424196i
\(640\) −2.15513e22 −0.765657
\(641\) 2.43535e22i 0.854470i −0.904141 0.427235i \(-0.859488\pi\)
0.904141 0.427235i \(-0.140512\pi\)
\(642\) 1.94420e22 + 1.36500e22i 0.673690 + 0.472992i
\(643\) −3.79348e22 −1.29822 −0.649112 0.760693i \(-0.724859\pi\)
−0.649112 + 0.760693i \(0.724859\pi\)
\(644\) 1.02585e22i 0.346734i
\(645\) −1.75733e22 + 2.50299e22i −0.586644 + 0.835567i
\(646\) −9.92281e20 −0.0327171
\(647\) 1.51186e22i 0.492354i −0.969225 0.246177i \(-0.920826\pi\)
0.969225 0.246177i \(-0.0791744\pi\)
\(648\) 1.23212e22 + 1.48354e22i 0.396325 + 0.477198i
\(649\) 7.11271e22 2.25984
\(650\) 1.69893e22i 0.533173i
\(651\) 2.51527e22 + 1.76595e22i 0.779718 + 0.547433i
\(652\) −7.55541e21 −0.231354
\(653\) 3.13376e22i 0.947896i −0.880553 0.473948i \(-0.842828\pi\)
0.880553 0.473948i \(-0.157172\pi\)
\(654\) 1.48760e22 2.11881e22i 0.444491 0.633096i
\(655\) 3.59535e22 1.06123
\(656\) 2.22268e22i 0.648107i
\(657\) −1.29453e22 3.58485e22i −0.372898 1.03264i
\(658\) 2.01932e22 0.574642
\(659\) 2.15993e22i 0.607235i −0.952794 0.303617i \(-0.901806\pi\)
0.952794 0.303617i \(-0.0981945\pi\)
\(660\) 1.64645e22 + 1.15596e22i 0.457297 + 0.321064i
\(661\) −5.48959e22 −1.50636 −0.753179 0.657815i \(-0.771481\pi\)
−0.753179 + 0.657815i \(0.771481\pi\)
\(662\) 4.51558e22i 1.22419i
\(663\) 1.81827e21 2.58980e21i 0.0487025 0.0693677i
\(664\) −4.09355e22 −1.08332
\(665\) 9.25370e21i 0.241959i
\(666\) 4.92557e21 1.77868e21i 0.127251 0.0459520i
\(667\) −1.67828e22 −0.428408
\(668\) 1.31883e22i 0.332643i
\(669\) −4.63077e21 3.25123e21i −0.115410 0.0810286i
\(670\) 1.40190e22 0.345238
\(671\) 3.80017e22i 0.924747i
\(672\) −2.67136e22 + 3.80486e22i −0.642359 + 0.914922i
\(673\) 2.63360e22 0.625791 0.312896 0.949787i \(-0.398701\pi\)
0.312896 + 0.949787i \(0.398701\pi\)
\(674\) 3.86447e22i 0.907426i
\(675\) 5.63344e21 2.07101e22i 0.130721 0.480564i
\(676\) 4.97784e21 0.114148
\(677\) 8.67255e22i 1.96534i 0.185365 + 0.982670i \(0.440653\pi\)
−0.185365 + 0.982670i \(0.559347\pi\)
\(678\) −3.41079e22 2.39469e22i −0.763867 0.536305i
\(679\) 1.07586e22 0.238120
\(680\) 1.94312e21i 0.0425037i
\(681\) 9.85675e21 1.40391e22i 0.213087 0.303503i
\(682\) −7.07745e22 −1.51217
\(683\) 5.07014e22i 1.07067i 0.844641 + 0.535333i \(0.179814\pi\)
−0.844641 + 0.535333i \(0.820186\pi\)
\(684\) −2.21818e21 6.14263e21i −0.0462965 0.128205i
\(685\) 3.91937e22 0.808522
\(686\) 3.54147e22i 0.722090i
\(687\) −2.99774e22 2.10469e22i −0.604143 0.424164i
\(688\) 9.04184e22 1.80115
\(689\) 3.09414e22i 0.609236i
\(690\) −1.45972e22 + 2.07911e22i −0.284104 + 0.404654i
\(691\) 6.54722e22 1.25960 0.629800 0.776758i \(-0.283137\pi\)
0.629800 + 0.776758i \(0.283137\pi\)
\(692\) 6.55099e20i 0.0124583i
\(693\) −9.88567e22 + 3.56984e22i −1.85841 + 0.671092i
\(694\) −9.07546e22 −1.68653
\(695\) 1.02018e22i 0.187413i
\(696\) 2.09640e22 + 1.47186e22i 0.380715 + 0.267297i
\(697\) 2.79315e21 0.0501455
\(698\) 1.33251e23i 2.36498i
\(699\) 5.11834e22 7.29014e22i 0.898074 1.27914i
\(700\) 1.74254e22 0.302272
\(701\) 1.53086e21i 0.0262537i −0.999914 0.0131269i \(-0.995821\pi\)
0.999914 0.0131269i \(-0.00417853\pi\)
\(702\) 6.09274e22 + 1.65731e22i 1.03304 + 0.281001i
\(703\) 1.82978e21 0.0306730
\(704\) 1.37805e22i 0.228393i
\(705\) −1.34992e22 9.47764e21i −0.221204 0.155306i
\(706\) 9.51857e22 1.54218
\(707\) 7.17821e22i 1.14990i
\(708\) −2.51829e22 + 3.58684e22i −0.398878 + 0.568128i
\(709\) 1.08542e22 0.169991 0.0849956 0.996381i \(-0.472912\pi\)
0.0849956 + 0.996381i \(0.472912\pi\)
\(710\) 6.98008e21i 0.108092i
\(711\) 3.43792e22 + 9.52037e22i 0.526428 + 1.45780i
\(712\) −3.71189e22 −0.562024
\(713\) 2.94790e22i 0.441363i
\(714\) −8.05311e21 5.65402e21i −0.119228 0.0837089i
\(715\) −6.79575e22 −0.994922
\(716\) 4.47638e22i 0.648071i
\(717\) −3.13735e22 + 4.46857e22i −0.449169 + 0.639758i
\(718\) −2.09833e22 −0.297083
\(719\) 1.17168e23i 1.64051i 0.571997 + 0.820256i \(0.306169\pi\)
−0.571997 + 0.820256i \(0.693831\pi\)
\(720\) 6.01552e22 2.17228e22i 0.832939 0.300784i
\(721\) 1.71979e22 0.235501
\(722\) 8.32825e22i 1.12786i
\(723\) −1.81595e22 1.27496e22i −0.243219 0.170762i
\(724\) −6.47524e22 −0.857724
\(725\) 2.85077e22i 0.373472i
\(726\) 8.49084e22 1.20936e23i 1.10017 1.56698i
\(727\) −6.75278e22 −0.865381 −0.432691 0.901542i \(-0.642436\pi\)
−0.432691 + 0.901542i \(0.642436\pi\)
\(728\) 5.28908e22i 0.670393i
\(729\) −6.87755e22 4.04056e22i −0.862211 0.506549i
\(730\) −7.66302e22 −0.950205
\(731\) 1.13625e22i 0.139359i
\(732\) 1.91637e22 + 1.34547e22i 0.232483 + 0.163225i
\(733\) −8.14391e22 −0.977240 −0.488620 0.872497i \(-0.662500\pi\)
−0.488620 + 0.872497i \(0.662500\pi\)
\(734\) 3.56745e22i 0.423438i
\(735\) 1.80529e22 2.57130e22i 0.211957 0.301894i
\(736\) 4.45929e22 0.517897
\(737\) 5.56352e22i 0.639160i
\(738\) 1.89298e22 + 5.24209e22i 0.215127 + 0.595736i
\(739\) 2.72207e22 0.306016 0.153008 0.988225i \(-0.451104\pi\)
0.153008 + 0.988225i \(0.451104\pi\)
\(740\) 3.47292e21i 0.0386225i
\(741\) 1.80559e22 + 1.26769e22i 0.198643 + 0.139465i
\(742\) 9.62139e22 1.04714
\(743\) 1.77551e22i 0.191167i 0.995421 + 0.0955833i \(0.0304716\pi\)
−0.995421 + 0.0955833i \(0.969528\pi\)
\(744\) −2.58533e22 + 3.68232e22i −0.275380 + 0.392227i
\(745\) 8.47479e22 0.893056
\(746\) 2.72750e22i 0.284350i
\(747\) 1.59254e23 5.75086e22i 1.64258 0.593155i
\(748\) 7.47419e21 0.0762695
\(749\) 8.23067e22i 0.830961i
\(750\) −1.06229e23 7.45823e22i −1.06109 0.744982i
\(751\) −2.88558e22 −0.285177 −0.142588 0.989782i \(-0.545543\pi\)
−0.142588 + 0.989782i \(0.545543\pi\)
\(752\) 4.87646e22i 0.476828i
\(753\) −5.20155e22 + 7.40865e22i −0.503238 + 0.716770i
\(754\) 8.38674e22 0.802828
\(755\) 1.30521e23i 1.23625i
\(756\) 1.69986e22 6.24913e22i 0.159308 0.585659i
\(757\) −5.88768e22 −0.545981 −0.272990 0.962017i \(-0.588013\pi\)
−0.272990 + 0.962017i \(0.588013\pi\)
\(758\) 1.27550e23i 1.17038i
\(759\) 8.25106e22 + 5.79300e22i 0.749162 + 0.525980i
\(760\) 1.35473e22 0.121715
\(761\) 4.74458e22i 0.421814i −0.977506 0.210907i \(-0.932358\pi\)
0.977506 0.210907i \(-0.0676417\pi\)
\(762\) −6.71776e22 + 9.56821e22i −0.590996 + 0.841765i
\(763\) 8.96987e22 0.780890
\(764\) 2.55599e22i 0.220197i
\(765\) 2.72980e21 + 7.55943e21i 0.0232723 + 0.0644463i
\(766\) −2.86331e23 −2.41568
\(767\) 1.48047e23i 1.23605i
\(768\) −1.16641e23 8.18926e22i −0.963743 0.676636i
\(769\) 1.15591e23 0.945176 0.472588 0.881283i \(-0.343320\pi\)
0.472588 + 0.881283i \(0.343320\pi\)
\(770\) 2.11318e23i 1.71005i
\(771\) −7.29039e22 + 1.03838e23i −0.583870 + 0.831615i
\(772\) 9.22178e21 0.0730931
\(773\) 6.88499e22i 0.540091i 0.962848 + 0.270046i \(0.0870388\pi\)
−0.962848 + 0.270046i \(0.912961\pi\)
\(774\) −2.13247e23 + 7.70062e22i −1.65560 + 0.597858i
\(775\) 5.00738e22 0.384766