Properties

Label 10.9.c.b.7.2
Level 10
Weight 9
Character 10.7
Analytic conductor 4.074
Analytic rank 0
Dimension 4
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 9 \)
Character orbit: \([\chi]\) = 10.c (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(4.07378610061\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{601})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 5^{2} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 7.2
Root \(-12.7577i\)
Character \(\chi\) = 10.7
Dual form 10.9.c.b.3.2

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(8.00000 + 8.00000i) q^{2}\) \(+(82.7883 - 82.7883i) q^{3}\) \(+128.000i q^{4}\) \(+(-33.6352 - 624.094i) q^{5}\) \(+1324.61 q^{6}\) \(+(2718.55 + 2718.55i) q^{7}\) \(+(-1024.00 + 1024.00i) q^{8}\) \(-7146.79i q^{9}\) \(+O(q^{10})\) \(q\)\(+(8.00000 + 8.00000i) q^{2}\) \(+(82.7883 - 82.7883i) q^{3}\) \(+128.000i q^{4}\) \(+(-33.6352 - 624.094i) q^{5}\) \(+1324.61 q^{6}\) \(+(2718.55 + 2718.55i) q^{7}\) \(+(-1024.00 + 1024.00i) q^{8}\) \(-7146.79i q^{9}\) \(+(4723.67 - 5261.84i) q^{10}\) \(-20966.3 q^{11}\) \(+(10596.9 + 10596.9i) q^{12}\) \(+(-8095.66 + 8095.66i) q^{13}\) \(+43496.9i q^{14}\) \(+(-54452.3 - 48883.1i) q^{15}\) \(-16384.0 q^{16}\) \(+(-3141.02 - 3141.02i) q^{17}\) \(+(57174.3 - 57174.3i) q^{18}\) \(+69201.5i q^{19}\) \(+(79884.1 - 4305.31i) q^{20}\) \(+450129. q^{21}\) \(+(-167730. - 167730. i) q^{22}\) \(+(1084.70 - 1084.70i) q^{23}\) \(+169550. i q^{24}\) \(+(-388362. + 41983.1i) q^{25}\) \(-129531. q^{26}\) \(+(-48496.5 - 48496.5i) q^{27}\) \(+(-347975. + 347975. i) q^{28}\) \(+120633. i q^{29}\) \(+(-44553.6 - 826683. i) q^{30}\) \(+826466. q^{31}\) \(+(-131072. - 131072. i) q^{32}\) \(+(-1.73576e6 + 1.73576e6i) q^{33}\) \(-50256.4i q^{34}\) \(+(1.60519e6 - 1.78807e6i) q^{35}\) \(+914789. q^{36}\) \(+(-1.17029e6 - 1.17029e6i) q^{37}\) \(+(-553612. + 553612. i) q^{38}\) \(+1.34045e6i q^{39}\) \(+(673515. + 604630. i) q^{40}\) \(+1.74660e6 q^{41}\) \(+(3.60103e6 + 3.60103e6i) q^{42}\) \(+(3.03222e6 - 3.03222e6i) q^{43}\) \(-2.68368e6i q^{44}\) \(+(-4.46027e6 + 240384. i) q^{45}\) \(+17355.3 q^{46}\) \(+(-5.83610e6 - 5.83610e6i) q^{47}\) \(+(-1.35640e6 + 1.35640e6i) q^{48}\) \(+9.01626e6i q^{49}\) \(+(-3.44276e6 - 2.77103e6i) q^{50}\) \(-520080. q^{51}\) \(+(-1.03625e6 - 1.03625e6i) q^{52}\) \(+(1.97703e6 - 1.97703e6i) q^{53}\) \(-775944. i q^{54}\) \(+(705206. + 1.30849e7i) q^{55}\) \(-5.56760e6 q^{56}\) \(+(5.72907e6 + 5.72907e6i) q^{57}\) \(+(-965061. + 965061. i) q^{58}\) \(-1.58356e7i q^{59}\) \(+(6.25703e6 - 6.96989e6i) q^{60}\) \(-2.51723e6 q^{61}\) \(+(6.61173e6 + 6.61173e6i) q^{62}\) \(+(1.94289e7 - 1.94289e7i) q^{63}\) \(-2.09715e6i q^{64}\) \(+(5.32476e6 + 4.78016e6i) q^{65}\) \(-2.77722e7 q^{66}\) \(+(1.47668e7 + 1.47668e7i) q^{67}\) \(+(402051. - 402051. i) q^{68}\) \(-179602. i q^{69}\) \(+(2.71461e7 - 1.46303e6i) q^{70}\) \(-8.22222e6 q^{71}\) \(+(7.31831e6 + 7.31831e6i) q^{72}\) \(+(-3.03744e7 + 3.03744e7i) q^{73}\) \(-1.87246e7i q^{74}\) \(+(-2.86761e7 + 3.56275e7i) q^{75}\) \(-8.85779e6 q^{76}\) \(+(-5.69980e7 - 5.69980e7i) q^{77}\) \(+(-1.07236e7 + 1.07236e7i) q^{78}\) \(-4.69738e7i q^{79}\) \(+(551080. + 1.02252e7i) q^{80}\) \(+3.88602e7 q^{81}\) \(+(1.39728e7 + 1.39728e7i) q^{82}\) \(+(2.81305e7 - 2.81305e7i) q^{83}\) \(+5.76165e7i q^{84}\) \(+(-1.85465e6 + 2.06594e6i) q^{85}\) \(+4.85155e7 q^{86}\) \(+(9.98697e6 + 9.98697e6i) q^{87}\) \(+(2.14695e7 - 2.14695e7i) q^{88}\) \(+7.91918e7i q^{89}\) \(+(-3.76052e7 - 3.37591e7i) q^{90}\) \(-4.40170e7 q^{91}\) \(+(138842. + 138842. i) q^{92}\) \(+(6.84217e7 - 6.84217e7i) q^{93}\) \(-9.33776e7i q^{94}\) \(+(4.31883e7 - 2.32761e6i) q^{95}\) \(-2.17024e7 q^{96}\) \(+(1.47530e6 + 1.47530e6i) q^{97}\) \(+(-7.21301e7 + 7.21301e7i) q^{98}\) \(+1.49842e8i q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(4q \) \(\mathstrut +\mathstrut 32q^{2} \) \(\mathstrut +\mathstrut 86q^{3} \) \(\mathstrut -\mathstrut 870q^{5} \) \(\mathstrut +\mathstrut 1376q^{6} \) \(\mathstrut +\mathstrut 5726q^{7} \) \(\mathstrut -\mathstrut 4096q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 32q^{2} \) \(\mathstrut +\mathstrut 86q^{3} \) \(\mathstrut -\mathstrut 870q^{5} \) \(\mathstrut +\mathstrut 1376q^{6} \) \(\mathstrut +\mathstrut 5726q^{7} \) \(\mathstrut -\mathstrut 4096q^{8} \) \(\mathstrut -\mathstrut 4640q^{10} \) \(\mathstrut -\mathstrut 14732q^{11} \) \(\mathstrut +\mathstrut 11008q^{12} \) \(\mathstrut +\mathstrut 45576q^{13} \) \(\mathstrut -\mathstrut 115090q^{15} \) \(\mathstrut -\mathstrut 65536q^{16} \) \(\mathstrut +\mathstrut 3616q^{17} \) \(\mathstrut +\mathstrut 60032q^{18} \) \(\mathstrut +\mathstrut 37120q^{20} \) \(\mathstrut +\mathstrut 877268q^{21} \) \(\mathstrut -\mathstrut 117856q^{22} \) \(\mathstrut -\mathstrut 456794q^{23} \) \(\mathstrut -\mathstrut 913600q^{25} \) \(\mathstrut +\mathstrut 729216q^{26} \) \(\mathstrut -\mathstrut 889240q^{27} \) \(\mathstrut -\mathstrut 732928q^{28} \) \(\mathstrut +\mathstrut 421920q^{30} \) \(\mathstrut +\mathstrut 4672348q^{31} \) \(\mathstrut -\mathstrut 524288q^{32} \) \(\mathstrut -\mathstrut 4553788q^{33} \) \(\mathstrut +\mathstrut 2956030q^{35} \) \(\mathstrut +\mathstrut 960512q^{36} \) \(\mathstrut -\mathstrut 5554884q^{37} \) \(\mathstrut -\mathstrut 3932480q^{38} \) \(\mathstrut +\mathstrut 1187840q^{40} \) \(\mathstrut +\mathstrut 10738708q^{41} \) \(\mathstrut +\mathstrut 7018144q^{42} \) \(\mathstrut +\mathstrut 4913286q^{43} \) \(\mathstrut -\mathstrut 12173390q^{45} \) \(\mathstrut -\mathstrut 7308704q^{46} \) \(\mathstrut -\mathstrut 5448474q^{47} \) \(\mathstrut -\mathstrut 1409024q^{48} \) \(\mathstrut -\mathstrut 1827200q^{50} \) \(\mathstrut -\mathstrut 1827812q^{51} \) \(\mathstrut +\mathstrut 5833728q^{52} \) \(\mathstrut +\mathstrut 20290316q^{53} \) \(\mathstrut -\mathstrut 9506940q^{55} \) \(\mathstrut -\mathstrut 11726848q^{56} \) \(\mathstrut -\mathstrut 2593360q^{57} \) \(\mathstrut -\mathstrut 4236800q^{58} \) \(\mathstrut +\mathstrut 21482240q^{60} \) \(\mathstrut -\mathstrut 43572012q^{61} \) \(\mathstrut +\mathstrut 37378784q^{62} \) \(\mathstrut +\mathstrut 37877126q^{63} \) \(\mathstrut +\mathstrut 15450660q^{65} \) \(\mathstrut -\mathstrut 72860608q^{66} \) \(\mathstrut +\mathstrut 9518486q^{67} \) \(\mathstrut -\mathstrut 462848q^{68} \) \(\mathstrut +\mathstrut 52077760q^{70} \) \(\mathstrut +\mathstrut 20406908q^{71} \) \(\mathstrut +\mathstrut 7684096q^{72} \) \(\mathstrut -\mathstrut 11608364q^{73} \) \(\mathstrut -\mathstrut 21302450q^{75} \) \(\mathstrut -\mathstrut 62919680q^{76} \) \(\mathstrut -\mathstrut 110066908q^{77} \) \(\mathstrut -\mathstrut 60769056q^{78} \) \(\mathstrut +\mathstrut 14254080q^{80} \) \(\mathstrut +\mathstrut 96218224q^{81} \) \(\mathstrut +\mathstrut 85909664q^{82} \) \(\mathstrut +\mathstrut 64264686q^{83} \) \(\mathstrut -\mathstrut 12424120q^{85} \) \(\mathstrut +\mathstrut 78612576q^{86} \) \(\mathstrut +\mathstrut 8501600q^{87} \) \(\mathstrut +\mathstrut 15085568q^{88} \) \(\mathstrut -\mathstrut 79432480q^{90} \) \(\mathstrut -\mathstrut 70189812q^{91} \) \(\mathstrut -\mathstrut 58469632q^{92} \) \(\mathstrut +\mathstrut 16706132q^{93} \) \(\mathstrut -\mathstrut 82819000q^{95} \) \(\mathstrut -\mathstrut 22544384q^{96} \) \(\mathstrut +\mathstrut 34113396q^{97} \) \(\mathstrut -\mathstrut 52691072q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).

\(n\) \(7\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.00000 + 8.00000i 0.500000 + 0.500000i
\(3\) 82.7883 82.7883i 1.02208 1.02208i 0.0223265 0.999751i \(-0.492893\pi\)
0.999751 0.0223265i \(-0.00710733\pi\)
\(4\) 128.000i 0.500000i
\(5\) −33.6352 624.094i −0.0538164 0.998551i
\(6\) 1324.61 1.02208
\(7\) 2718.55 + 2718.55i 1.13226 + 1.13226i 0.989801 + 0.142458i \(0.0455006\pi\)
0.142458 + 0.989801i \(0.454499\pi\)
\(8\) −1024.00 + 1024.00i −0.250000 + 0.250000i
\(9\) 7146.79i 1.08928i
\(10\) 4723.67 5261.84i 0.472367 0.526184i
\(11\) −20966.3 −1.43203 −0.716013 0.698087i \(-0.754035\pi\)
−0.716013 + 0.698087i \(0.754035\pi\)
\(12\) 10596.9 + 10596.9i 0.511039 + 0.511039i
\(13\) −8095.66 + 8095.66i −0.283452 + 0.283452i −0.834484 0.551032i \(-0.814234\pi\)
0.551032 + 0.834484i \(0.314234\pi\)
\(14\) 43496.9i 1.13226i
\(15\) −54452.3 48883.1i −1.07560 0.965592i
\(16\) −16384.0 −0.250000
\(17\) −3141.02 3141.02i −0.0376076 0.0376076i 0.688053 0.725661i \(-0.258466\pi\)
−0.725661 + 0.688053i \(0.758466\pi\)
\(18\) 57174.3 57174.3i 0.544642 0.544642i
\(19\) 69201.5i 0.531008i 0.964110 + 0.265504i \(0.0855383\pi\)
−0.964110 + 0.265504i \(0.914462\pi\)
\(20\) 79884.1 4305.31i 0.499275 0.0269082i
\(21\) 450129. 2.31451
\(22\) −167730. 167730.i −0.716013 0.716013i
\(23\) 1084.70 1084.70i 0.00387615 0.00387615i −0.705166 0.709042i \(-0.749128\pi\)
0.709042 + 0.705166i \(0.249128\pi\)
\(24\) 169550.i 0.511039i
\(25\) −388362. + 41983.1i −0.994208 + 0.107477i
\(26\) −129531. −0.283452
\(27\) −48496.5 48496.5i −0.0912547 0.0912547i
\(28\) −347975. + 347975.i −0.566129 + 0.566129i
\(29\) 120633.i 0.170558i 0.996357 + 0.0852792i \(0.0271782\pi\)
−0.996357 + 0.0852792i \(0.972822\pi\)
\(30\) −44553.6 826683.i −0.0550045 1.02060i
\(31\) 826466. 0.894908 0.447454 0.894307i \(-0.352331\pi\)
0.447454 + 0.894307i \(0.352331\pi\)
\(32\) −131072. 131072.i −0.125000 0.125000i
\(33\) −1.73576e6 + 1.73576e6i −1.46364 + 1.46364i
\(34\) 50256.4i 0.0376076i
\(35\) 1.60519e6 1.78807e6i 1.06968 1.19155i
\(36\) 914789. 0.544642
\(37\) −1.17029e6 1.17029e6i −0.624434 0.624434i 0.322228 0.946662i \(-0.395568\pi\)
−0.946662 + 0.322228i \(0.895568\pi\)
\(38\) −553612. + 553612.i −0.265504 + 0.265504i
\(39\) 1.34045e6i 0.579419i
\(40\) 673515. + 604630.i 0.263092 + 0.236184i
\(41\) 1.74660e6 0.618099 0.309049 0.951046i \(-0.399989\pi\)
0.309049 + 0.951046i \(0.399989\pi\)
\(42\) 3.60103e6 + 3.60103e6i 1.15726 + 1.15726i
\(43\) 3.03222e6 3.03222e6i 0.886925 0.886925i −0.107302 0.994226i \(-0.534221\pi\)
0.994226 + 0.107302i \(0.0342211\pi\)
\(44\) 2.68368e6i 0.716013i
\(45\) −4.46027e6 + 240384.i −1.08771 + 0.0586213i
\(46\) 17355.3 0.00387615
\(47\) −5.83610e6 5.83610e6i −1.19600 1.19600i −0.975354 0.220646i \(-0.929183\pi\)
−0.220646 0.975354i \(-0.570817\pi\)
\(48\) −1.35640e6 + 1.35640e6i −0.255519 + 0.255519i
\(49\) 9.01626e6i 1.56402i
\(50\) −3.44276e6 2.77103e6i −0.550842 0.443365i
\(51\) −520080. −0.0768758
\(52\) −1.03625e6 1.03625e6i −0.141726 0.141726i
\(53\) 1.97703e6 1.97703e6i 0.250559 0.250559i −0.570641 0.821200i \(-0.693305\pi\)
0.821200 + 0.570641i \(0.193305\pi\)
\(54\) 775944.i 0.0912547i
\(55\) 705206. + 1.30849e7i 0.0770664 + 1.42995i
\(56\) −5.56760e6 −0.566129
\(57\) 5.72907e6 + 5.72907e6i 0.542731 + 0.542731i
\(58\) −965061. + 965061.i −0.0852792 + 0.0852792i
\(59\) 1.58356e7i 1.30685i −0.756990 0.653427i \(-0.773331\pi\)
0.756990 0.653427i \(-0.226669\pi\)
\(60\) 6.25703e6 6.96989e6i 0.482796 0.537800i
\(61\) −2.51723e6 −0.181804 −0.0909019 0.995860i \(-0.528975\pi\)
−0.0909019 + 0.995860i \(0.528975\pi\)
\(62\) 6.61173e6 + 6.61173e6i 0.447454 + 0.447454i
\(63\) 1.94289e7 1.94289e7i 1.23335 1.23335i
\(64\) 2.09715e6i 0.125000i
\(65\) 5.32476e6 + 4.78016e6i 0.298295 + 0.267787i
\(66\) −2.77722e7 −1.46364
\(67\) 1.47668e7 + 1.47668e7i 0.732802 + 0.732802i 0.971174 0.238372i \(-0.0766138\pi\)
−0.238372 + 0.971174i \(0.576614\pi\)
\(68\) 402051. 402051.i 0.0188038 0.0188038i
\(69\) 179602.i 0.00792344i
\(70\) 2.71461e7 1.46303e6i 1.13062 0.0609341i
\(71\) −8.22222e6 −0.323561 −0.161780 0.986827i \(-0.551724\pi\)
−0.161780 + 0.986827i \(0.551724\pi\)
\(72\) 7.31831e6 + 7.31831e6i 0.272321 + 0.272321i
\(73\) −3.03744e7 + 3.03744e7i −1.06959 + 1.06959i −0.0721980 + 0.997390i \(0.523001\pi\)
−0.997390 + 0.0721980i \(0.976999\pi\)
\(74\) 1.87246e7i 0.624434i
\(75\) −2.86761e7 + 3.56275e7i −0.906307 + 1.12601i
\(76\) −8.85779e6 −0.265504
\(77\) −5.69980e7 5.69980e7i −1.62142 1.62142i
\(78\) −1.07236e7 + 1.07236e7i −0.289710 + 0.289710i
\(79\) 4.69738e7i 1.20600i −0.797741 0.603000i \(-0.793972\pi\)
0.797741 0.603000i \(-0.206028\pi\)
\(80\) 551080. + 1.02252e7i 0.0134541 + 0.249638i
\(81\) 3.88602e7 0.902745
\(82\) 1.39728e7 + 1.39728e7i 0.309049 + 0.309049i
\(83\) 2.81305e7 2.81305e7i 0.592740 0.592740i −0.345630 0.938371i \(-0.612335\pi\)
0.938371 + 0.345630i \(0.112335\pi\)
\(84\) 5.76165e7i 1.15726i
\(85\) −1.85465e6 + 2.06594e6i −0.0355292 + 0.0395770i
\(86\) 4.85155e7 0.886925
\(87\) 9.98697e6 + 9.98697e6i 0.174324 + 0.174324i
\(88\) 2.14695e7 2.14695e7i 0.358006 0.358006i
\(89\) 7.91918e7i 1.26218i 0.775711 + 0.631088i \(0.217391\pi\)
−0.775711 + 0.631088i \(0.782609\pi\)
\(90\) −3.76052e7 3.37591e7i −0.573163 0.514542i
\(91\) −4.40170e7 −0.641881
\(92\) 138842. + 138842.i 0.00193807 + 0.00193807i
\(93\) 6.84217e7 6.84217e7i 0.914665 0.914665i
\(94\) 9.33776e7i 1.19600i
\(95\) 4.31883e7 2.32761e6i 0.530238 0.0285769i
\(96\) −2.17024e7 −0.255519
\(97\) 1.47530e6 + 1.47530e6i 0.0166645 + 0.0166645i 0.715390 0.698725i \(-0.246249\pi\)
−0.698725 + 0.715390i \(0.746249\pi\)
\(98\) −7.21301e7 + 7.21301e7i −0.782010 + 0.782010i
\(99\) 1.49842e8i 1.55988i
\(100\) −5.37384e6 4.97104e7i −0.0537384 0.497104i
\(101\) 1.61256e8 1.54964 0.774818 0.632185i \(-0.217842\pi\)
0.774818 + 0.632185i \(0.217842\pi\)
\(102\) −4.16064e6 4.16064e6i −0.0384379 0.0384379i
\(103\) −1.34152e8 + 1.34152e8i −1.19192 + 1.19192i −0.215397 + 0.976526i \(0.569105\pi\)
−0.976526 + 0.215397i \(0.930895\pi\)
\(104\) 1.65799e7i 0.141726i
\(105\) −1.51402e7 2.80923e8i −0.124559 2.31116i
\(106\) 3.16325e7 0.250559
\(107\) 2.02907e7 + 2.02907e7i 0.154796 + 0.154796i 0.780256 0.625460i \(-0.215089\pi\)
−0.625460 + 0.780256i \(0.715089\pi\)
\(108\) 6.20755e6 6.20755e6i 0.0456274 0.0456274i
\(109\) 5.27998e7i 0.374047i −0.982355 0.187023i \(-0.940116\pi\)
0.982355 0.187023i \(-0.0598840\pi\)
\(110\) −9.90379e7 + 1.10321e8i −0.676442 + 0.753508i
\(111\) −1.93772e8 −1.27644
\(112\) −4.45408e7 4.45408e7i −0.283065 0.283065i
\(113\) −1.25553e8 + 1.25553e8i −0.770041 + 0.770041i −0.978113 0.208073i \(-0.933281\pi\)
0.208073 + 0.978113i \(0.433281\pi\)
\(114\) 9.16651e7i 0.542731i
\(115\) −713442. 640474.i −0.00407913 0.00366193i
\(116\) −1.54410e7 −0.0852792
\(117\) 5.78580e7 + 5.78580e7i 0.308759 + 0.308759i
\(118\) 1.26685e8 1.26685e8i 0.653427 0.653427i
\(119\) 1.70781e7i 0.0851631i
\(120\) 1.05815e8 5.70287e6i 0.510298 0.0275022i
\(121\) 2.25226e8 1.05070
\(122\) −2.01378e7 2.01378e7i −0.0909019 0.0909019i
\(123\) 1.44598e8 1.44598e8i 0.631745 0.631745i
\(124\) 1.05788e8i 0.447454i
\(125\) 3.92641e7 + 2.40963e8i 0.160826 + 0.986983i
\(126\) 3.10863e8 1.23335
\(127\) −9.69572e7 9.69572e7i −0.372705 0.372705i 0.495757 0.868462i \(-0.334891\pi\)
−0.868462 + 0.495757i \(0.834891\pi\)
\(128\) 1.67772e7 1.67772e7i 0.0625000 0.0625000i
\(129\) 5.02064e8i 1.81301i
\(130\) 4.35679e6 + 8.08393e7i 0.0152543 + 0.283041i
\(131\) 6.19413e7 0.210327 0.105164 0.994455i \(-0.466463\pi\)
0.105164 + 0.994455i \(0.466463\pi\)
\(132\) −2.22178e8 2.22178e8i −0.731820 0.731820i
\(133\) −1.88128e8 + 1.88128e8i −0.601238 + 0.601238i
\(134\) 2.36268e8i 0.732802i
\(135\) −2.86352e7 + 3.18976e7i −0.0862115 + 0.0960335i
\(136\) 6.43282e6 0.0188038
\(137\) 8.79898e6 + 8.79898e6i 0.0249776 + 0.0249776i 0.719485 0.694508i \(-0.244378\pi\)
−0.694508 + 0.719485i \(0.744378\pi\)
\(138\) 1.43681e6 1.43681e6i 0.00396172 0.00396172i
\(139\) 2.71570e7i 0.0727482i 0.999338 + 0.0363741i \(0.0115808\pi\)
−0.999338 + 0.0363741i \(0.988419\pi\)
\(140\) 2.28873e8 + 2.05465e8i 0.595776 + 0.534842i
\(141\) −9.66321e8 −2.44481
\(142\) −6.57777e7 6.57777e7i −0.161780 0.161780i
\(143\) 1.69736e8 1.69736e8i 0.405910 0.405910i
\(144\) 1.17093e8i 0.272321i
\(145\) 7.52862e7 4.05751e6i 0.170311 0.00917883i
\(146\) −4.85991e8 −1.06959
\(147\) 7.46441e8 + 7.46441e8i 1.59855 + 1.59855i
\(148\) 1.49797e8 1.49797e8i 0.312217 0.312217i
\(149\) 553367.i 0.00112271i 1.00000 0.000561355i \(0.000178685\pi\)
−1.00000 0.000561355i \(0.999821\pi\)
\(150\) −5.14429e8 + 5.56113e7i −1.01616 + 0.109850i
\(151\) −1.27298e8 −0.244858 −0.122429 0.992477i \(-0.539068\pi\)
−0.122429 + 0.992477i \(0.539068\pi\)
\(152\) −7.08623e7 7.08623e7i −0.132752 0.132752i
\(153\) −2.24482e7 + 2.24482e7i −0.0409653 + 0.0409653i
\(154\) 9.11968e8i 1.62142i
\(155\) −2.77984e7 5.15793e8i −0.0481607 0.893611i
\(156\) −1.71578e8 −0.289710
\(157\) 5.28456e8 + 5.28456e8i 0.869782 + 0.869782i 0.992448 0.122666i \(-0.0391443\pi\)
−0.122666 + 0.992448i \(0.539144\pi\)
\(158\) 3.75791e8 3.75791e8i 0.603000 0.603000i
\(159\) 3.27350e8i 0.512182i
\(160\) −7.73926e7 + 8.62099e7i −0.118092 + 0.131546i
\(161\) 5.89765e6 0.00877760
\(162\) 3.10882e8 + 3.10882e8i 0.451372 + 0.451372i
\(163\) 2.09644e8 2.09644e8i 0.296983 0.296983i −0.542848 0.839831i \(-0.682654\pi\)
0.839831 + 0.542848i \(0.182654\pi\)
\(164\) 2.23565e8i 0.309049i
\(165\) 1.14166e9 + 1.02490e9i 1.54029 + 1.38275i
\(166\) 4.50087e8 0.592740
\(167\) −7.26269e8 7.26269e8i −0.933753 0.933753i 0.0641853 0.997938i \(-0.479555\pi\)
−0.997938 + 0.0641853i \(0.979555\pi\)
\(168\) −4.60932e8 + 4.60932e8i −0.578628 + 0.578628i
\(169\) 6.84651e8i 0.839310i
\(170\) −3.13647e7 + 1.69039e6i −0.0375531 + 0.00202391i
\(171\) 4.94569e8 0.578418
\(172\) 3.88124e8 + 3.88124e8i 0.443462 + 0.443462i
\(173\) 6.00999e8 6.00999e8i 0.670949 0.670949i −0.286986 0.957935i \(-0.592653\pi\)
0.957935 + 0.286986i \(0.0926533\pi\)
\(174\) 1.59791e8i 0.174324i
\(175\) −1.16992e9 9.41650e8i −1.24739 1.00401i
\(176\) 3.43512e8 0.358006
\(177\) −1.31100e9 1.31100e9i −1.33571 1.33571i
\(178\) −6.33534e8 + 6.33534e8i −0.631088 + 0.631088i
\(179\) 9.25251e8i 0.901255i 0.892712 + 0.450627i \(0.148800\pi\)
−0.892712 + 0.450627i \(0.851200\pi\)
\(180\) −3.07692e7 5.70915e8i −0.0293107 0.543853i
\(181\) −8.31703e8 −0.774914 −0.387457 0.921888i \(-0.626647\pi\)
−0.387457 + 0.921888i \(0.626647\pi\)
\(182\) −3.52136e8 3.52136e8i −0.320941 0.320941i
\(183\) −2.08397e8 + 2.08397e8i −0.185818 + 0.185818i
\(184\) 2.22147e6i 0.00193807i
\(185\) −6.91008e8 + 7.69734e8i −0.589924 + 0.657134i
\(186\) 1.09475e9 0.914665
\(187\) 6.58556e7 + 6.58556e7i 0.0538551 + 0.0538551i
\(188\) 7.47021e8 7.47021e8i 0.598000 0.598000i
\(189\) 2.63681e8i 0.206648i
\(190\) 3.64127e8 + 3.26885e8i 0.279408 + 0.250831i
\(191\) 1.17089e9 0.879799 0.439900 0.898047i \(-0.355014\pi\)
0.439900 + 0.898047i \(0.355014\pi\)
\(192\) −1.73620e8 1.73620e8i −0.127760 0.127760i
\(193\) −1.41003e9 + 1.41003e9i −1.01624 + 1.01624i −0.0163773 + 0.999866i \(0.505213\pi\)
−0.999866 + 0.0163773i \(0.994787\pi\)
\(194\) 2.36047e7i 0.0166645i
\(195\) 8.36568e8 4.50864e7i 0.578579 0.0311822i
\(196\) −1.15408e9 −0.782010
\(197\) −7.98017e8 7.98017e8i −0.529843 0.529843i 0.390683 0.920525i \(-0.372239\pi\)
−0.920525 + 0.390683i \(0.872239\pi\)
\(198\) −1.19873e9 + 1.19873e9i −0.779941 + 0.779941i
\(199\) 3.89588e8i 0.248424i −0.992256 0.124212i \(-0.960360\pi\)
0.992256 0.124212i \(-0.0396402\pi\)
\(200\) 3.54692e8 4.40674e8i 0.221683 0.275421i
\(201\) 2.44503e9 1.49796
\(202\) 1.29005e9 + 1.29005e9i 0.774818 + 0.774818i
\(203\) −3.27946e8 + 3.27946e8i −0.193116 + 0.193116i
\(204\) 6.65702e7i 0.0384379i
\(205\) −5.87473e7 1.09004e9i −0.0332638 0.617203i
\(206\) −2.14643e9 −1.19192
\(207\) −7.75216e6 7.75216e6i −0.00422222 0.00422222i
\(208\) 1.32639e8 1.32639e8i 0.0708629 0.0708629i
\(209\) 1.45090e9i 0.760417i
\(210\) 2.12626e9 2.36850e9i 1.09330 1.21786i
\(211\) 3.73042e9 1.88204 0.941019 0.338354i \(-0.109870\pi\)
0.941019 + 0.338354i \(0.109870\pi\)
\(212\) 2.53060e8 + 2.53060e8i 0.125280 + 0.125280i
\(213\) −6.80703e8 + 6.80703e8i −0.330704 + 0.330704i
\(214\) 3.24651e8i 0.154796i
\(215\) −1.99438e9 1.79040e9i −0.933370 0.837908i
\(216\) 9.93209e7 0.0456274
\(217\) 2.24679e9 + 2.24679e9i 1.01327 + 1.01327i
\(218\) 4.22398e8 4.22398e8i 0.187023 0.187023i
\(219\) 5.02929e9i 2.18640i
\(220\) −1.67487e9 + 9.02664e7i −0.714975 + 0.0385332i
\(221\) 5.08574e7 0.0213199
\(222\) −1.55018e9 1.55018e9i −0.638220 0.638220i
\(223\) 2.58624e9 2.58624e9i 1.04580 1.04580i 0.0469003 0.998900i \(-0.485066\pi\)
0.998900 0.0469003i \(-0.0149343\pi\)
\(224\) 7.12652e8i 0.283065i
\(225\) 3.00045e8 + 2.77554e9i 0.117073 + 1.08297i
\(226\) −2.00885e9 −0.770041
\(227\) 2.28574e8 + 2.28574e8i 0.0860844 + 0.0860844i 0.748838 0.662753i \(-0.230612\pi\)
−0.662753 + 0.748838i \(0.730612\pi\)
\(228\) −7.33321e8 + 7.33321e8i −0.271366 + 0.271366i
\(229\) 4.29778e9i 1.56280i −0.624033 0.781398i \(-0.714507\pi\)
0.624033 0.781398i \(-0.285493\pi\)
\(230\) −583749. 1.08313e7i −0.000208600 0.00387053i
\(231\) −9.43752e9 −3.31444
\(232\) −1.23528e8 1.23528e8i −0.0426396 0.0426396i
\(233\) 2.83013e8 2.83013e8i 0.0960247 0.0960247i −0.657463 0.753487i \(-0.728370\pi\)
0.753487 + 0.657463i \(0.228370\pi\)
\(234\) 9.25728e8i 0.308759i
\(235\) −3.44598e9 + 3.83858e9i −1.12990 + 1.25863i
\(236\) 2.02696e9 0.653427
\(237\) −3.88888e9 3.88888e9i −1.23263 1.23263i
\(238\) 1.36625e8 1.36625e8i 0.0425815 0.0425815i
\(239\) 5.19198e9i 1.59126i 0.605782 + 0.795630i \(0.292860\pi\)
−0.605782 + 0.795630i \(0.707140\pi\)
\(240\) 8.92146e8 + 8.00900e8i 0.268900 + 0.241398i
\(241\) 4.53061e9 1.34304 0.671519 0.740987i \(-0.265642\pi\)
0.671519 + 0.740987i \(0.265642\pi\)
\(242\) 1.80181e9 + 1.80181e9i 0.525349 + 0.525349i
\(243\) 3.53535e9 3.53535e9i 1.01393 1.01393i
\(244\) 3.22205e8i 0.0909019i
\(245\) 5.62700e9 3.03264e8i 1.56175 0.0841699i
\(246\) 2.31357e9 0.631745
\(247\) −5.60232e8 5.60232e8i −0.150515 0.150515i
\(248\) −8.46301e8 + 8.46301e8i −0.223727 + 0.223727i
\(249\) 4.65774e9i 1.21165i
\(250\) −1.61359e9 + 2.24181e9i −0.413079 + 0.573904i
\(251\) −3.40464e9 −0.857780 −0.428890 0.903357i \(-0.641095\pi\)
−0.428890 + 0.903357i \(0.641095\pi\)
\(252\) 2.48690e9 + 2.48690e9i 0.616675 + 0.616675i
\(253\) −2.27422e7 + 2.27422e7i −0.00555074 + 0.00555074i
\(254\) 1.55132e9i 0.372705i
\(255\) 1.74930e7 + 3.24579e8i 0.00413717 + 0.0767643i
\(256\) 2.68435e8 0.0625000
\(257\) 3.01159e7 + 3.01159e7i 0.00690341 + 0.00690341i 0.710550 0.703647i \(-0.248446\pi\)
−0.703647 + 0.710550i \(0.748446\pi\)
\(258\) 4.01651e9 4.01651e9i 0.906505 0.906505i
\(259\) 6.36299e9i 1.41404i
\(260\) −6.11860e8 + 6.81569e8i −0.133893 + 0.149148i
\(261\) 8.62136e8 0.185786
\(262\) 4.95531e8 + 4.95531e8i 0.105164 + 0.105164i
\(263\) −2.01502e9 + 2.01502e9i −0.421169 + 0.421169i −0.885606 0.464437i \(-0.846257\pi\)
0.464437 + 0.885606i \(0.346257\pi\)
\(264\) 3.55484e9i 0.731820i
\(265\) −1.30035e9 1.16736e9i −0.263680 0.236712i
\(266\) −3.01005e9 −0.601238
\(267\) 6.55615e9 + 6.55615e9i 1.29004 + 1.29004i
\(268\) −1.89015e9 + 1.89015e9i −0.366401 + 0.366401i
\(269\) 9.53840e9i 1.82166i 0.412785 + 0.910828i \(0.364556\pi\)
−0.412785 + 0.910828i \(0.635444\pi\)
\(270\) −4.84262e8 + 2.60991e7i −0.0911225 + 0.00491100i
\(271\) −3.84233e9 −0.712390 −0.356195 0.934412i \(-0.615926\pi\)
−0.356195 + 0.934412i \(0.615926\pi\)
\(272\) 5.14625e7 + 5.14625e7i 0.00940190 + 0.00940190i
\(273\) −3.64409e9 + 3.64409e9i −0.656052 + 0.656052i
\(274\) 1.40784e8i 0.0249776i
\(275\) 8.14252e9 8.80230e8i 1.42373 0.153910i
\(276\) 2.29890e7 0.00396172
\(277\) −2.80174e9 2.80174e9i −0.475892 0.475892i 0.427923 0.903815i \(-0.359245\pi\)
−0.903815 + 0.427923i \(0.859245\pi\)
\(278\) −2.17256e8 + 2.17256e8i −0.0363741 + 0.0363741i
\(279\) 5.90658e9i 0.974809i
\(280\) 1.87267e8 + 3.47471e9i 0.0304670 + 0.565309i
\(281\) −8.28718e9 −1.32917 −0.664586 0.747212i \(-0.731392\pi\)
−0.664586 + 0.747212i \(0.731392\pi\)
\(282\) −7.73057e9 7.73057e9i −1.22240 1.22240i
\(283\) −7.40766e7 + 7.40766e7i −0.0115488 + 0.0115488i −0.712858 0.701309i \(-0.752599\pi\)
0.701309 + 0.712858i \(0.252599\pi\)
\(284\) 1.05244e9i 0.161780i
\(285\) 3.38278e9 3.76818e9i 0.512737 0.571152i
\(286\) 2.71578e9 0.405910
\(287\) 4.74822e9 + 4.74822e9i 0.699848 + 0.699848i
\(288\) −9.36744e8 + 9.36744e8i −0.136160 + 0.136160i
\(289\) 6.95603e9i 0.997171i
\(290\) 6.34749e8 + 5.69829e8i 0.0897450 + 0.0805662i
\(291\) 2.44274e8 0.0340648
\(292\) −3.88793e9 3.88793e9i −0.534794 0.534794i
\(293\) −6.33070e9 + 6.33070e9i −0.858977 + 0.858977i −0.991218 0.132241i \(-0.957783\pi\)
0.132241 + 0.991218i \(0.457783\pi\)
\(294\) 1.19431e10i 1.59855i
\(295\) −9.88292e9 + 5.32635e8i −1.30496 + 0.0703302i
\(296\) 2.39675e9 0.312217
\(297\) 1.01679e9 + 1.01679e9i 0.130679 + 0.130679i
\(298\) −4.42693e6 + 4.42693e6i −0.000561355 + 0.000561355i
\(299\) 1.75628e7i 0.00219740i
\(300\) −4.56033e9 3.67054e9i −0.563003 0.453154i
\(301\) 1.64865e10 2.00846
\(302\) −1.01838e9 1.01838e9i −0.122429 0.122429i
\(303\) 1.33501e10 1.33501e10i 1.58385 1.58385i
\(304\) 1.13380e9i 0.132752i
\(305\) 8.46676e7 + 1.57099e9i 0.00978403 + 0.181540i
\(306\) −3.59172e8 −0.0409653
\(307\) 4.80692e9 + 4.80692e9i 0.541144 + 0.541144i 0.923864 0.382720i \(-0.125013\pi\)
−0.382720 + 0.923864i \(0.625013\pi\)
\(308\) 7.29574e9 7.29574e9i 0.810712 0.810712i
\(309\) 2.22124e10i 2.43648i
\(310\) 3.90396e9 4.34873e9i 0.422725 0.470886i
\(311\) 1.06468e10 1.13809 0.569047 0.822305i \(-0.307312\pi\)
0.569047 + 0.822305i \(0.307312\pi\)
\(312\) −1.37262e9 1.37262e9i −0.144855 0.144855i
\(313\) −1.05889e10 + 1.05889e10i −1.10325 + 1.10325i −0.109236 + 0.994016i \(0.534840\pi\)
−0.994016 + 0.109236i \(0.965160\pi\)
\(314\) 8.45530e9i 0.869782i
\(315\) −1.27790e10 1.14720e10i −1.29794 1.16519i
\(316\) 6.01265e9 0.603000
\(317\) −9.51101e9 9.51101e9i −0.941867 0.941867i 0.0565338 0.998401i \(-0.481995\pi\)
−0.998401 + 0.0565338i \(0.981995\pi\)
\(318\) 2.61880e9 2.61880e9i 0.256091 0.256091i
\(319\) 2.52922e9i 0.244244i
\(320\) −1.30882e9 + 7.05382e7i −0.124819 + 0.00672705i
\(321\) 3.35966e9 0.316428
\(322\) 4.71812e7 + 4.71812e7i 0.00438880 + 0.00438880i
\(323\) 2.17364e8 2.17364e8i 0.0199699 0.0199699i
\(324\) 4.97411e9i 0.451372i
\(325\) 2.80417e9 3.48393e9i 0.251345 0.312274i
\(326\) 3.35430e9 0.296983
\(327\) −4.37120e9 4.37120e9i −0.382305 0.382305i
\(328\) −1.78852e9 + 1.78852e9i −0.154525 + 0.154525i
\(329\) 3.17315e10i 2.70836i
\(330\) 9.34125e8 + 1.73325e10i 0.0787679 + 1.46152i
\(331\) −1.31018e10 −1.09149 −0.545744 0.837952i \(-0.683753\pi\)
−0.545744 + 0.837952i \(0.683753\pi\)
\(332\) 3.60070e9 + 3.60070e9i 0.296370 + 0.296370i
\(333\) −8.36381e9 + 8.36381e9i −0.680186 + 0.680186i
\(334\) 1.16203e10i 0.933753i
\(335\) 8.71918e9 9.71254e9i 0.692303 0.771176i
\(336\) −7.37491e9 −0.578628
\(337\) 1.33341e10 + 1.33341e10i 1.03382 + 1.03382i 0.999408 + 0.0344141i \(0.0109565\pi\)
0.0344141 + 0.999408i \(0.489043\pi\)
\(338\) −5.47721e9 + 5.47721e9i −0.419655 + 0.419655i
\(339\) 2.07886e10i 1.57408i
\(340\) −2.64441e8 2.37395e8i −0.0197885 0.0177646i
\(341\) −1.73279e10 −1.28153
\(342\) 3.95655e9 + 3.95655e9i 0.289209 + 0.289209i
\(343\) −8.83927e9 + 8.83927e9i −0.638616 + 0.638616i
\(344\) 6.20998e9i 0.443462i
\(345\) −1.12088e8 + 6.04094e6i −0.00791196 + 0.000426411i
\(346\) 9.61599e9 0.670949
\(347\) −1.09024e10 1.09024e10i −0.751973 0.751973i 0.222874 0.974847i \(-0.428456\pi\)
−0.974847 + 0.222874i \(0.928456\pi\)
\(348\) −1.27833e9 + 1.27833e9i −0.0871619 + 0.0871619i
\(349\) 9.67778e9i 0.652340i 0.945311 + 0.326170i \(0.105758\pi\)
−0.945311 + 0.326170i \(0.894242\pi\)
\(350\) −1.82613e9 1.68925e10i −0.121692 1.12570i
\(351\) 7.85223e8 0.0517326
\(352\) 2.74809e9 + 2.74809e9i 0.179003 + 0.179003i
\(353\) 6.27335e9 6.27335e9i 0.404018 0.404018i −0.475628 0.879646i \(-0.657779\pi\)
0.879646 + 0.475628i \(0.157779\pi\)
\(354\) 2.09761e10i 1.33571i
\(355\) 2.76556e8 + 5.13144e9i 0.0174129 + 0.323092i
\(356\) −1.01365e10 −0.631088
\(357\) −1.41386e9 1.41386e9i −0.0870432 0.0870432i
\(358\) −7.40201e9 + 7.40201e9i −0.450627 + 0.450627i
\(359\) 7.91205e9i 0.476334i 0.971224 + 0.238167i \(0.0765465\pi\)
−0.971224 + 0.238167i \(0.923454\pi\)
\(360\) 4.32116e9 4.81347e9i 0.257271 0.286582i
\(361\) 1.21947e10 0.718031
\(362\) −6.65362e9 6.65362e9i −0.387457 0.387457i
\(363\) 1.86461e10 1.86461e10i 1.07389 1.07389i
\(364\) 5.63417e9i 0.320941i
\(365\) 1.99782e10 + 1.79349e10i 1.12560 + 1.01048i
\(366\) −3.33435e9 −0.185818
\(367\) 6.65934e9 + 6.65934e9i 0.367085 + 0.367085i 0.866413 0.499328i \(-0.166420\pi\)
−0.499328 + 0.866413i \(0.666420\pi\)
\(368\) −1.77718e7 + 1.77718e7i −0.000969036 + 0.000969036i
\(369\) 1.24826e10i 0.673285i
\(370\) −1.16859e10 + 6.29808e8i −0.623529 + 0.0336048i
\(371\) 1.07493e10 0.567396
\(372\) 8.75798e9 + 8.75798e9i 0.457333 + 0.457333i
\(373\) 1.63417e10 1.63417e10i 0.844230 0.844230i −0.145176 0.989406i \(-0.546375\pi\)
0.989406 + 0.145176i \(0.0463748\pi\)
\(374\) 1.05369e9i 0.0538551i
\(375\) 2.31995e10 + 1.66983e10i 1.17315 + 0.844396i
\(376\) 1.19523e10 0.598000
\(377\) −9.76602e8 9.76602e8i −0.0483450 0.0483450i
\(378\) 2.10945e9 2.10945e9i 0.103324 0.103324i
\(379\) 9.14573e9i 0.443263i −0.975130 0.221632i \(-0.928862\pi\)
0.975130 0.221632i \(-0.0711382\pi\)
\(380\) 2.97934e8 + 5.52810e9i 0.0142885 + 0.265119i
\(381\) −1.60538e10 −0.761867
\(382\) 9.36714e9 + 9.36714e9i 0.439900 + 0.439900i
\(383\) −6.52966e9 + 6.52966e9i −0.303456 + 0.303456i −0.842364 0.538909i \(-0.818837\pi\)
0.538909 + 0.842364i \(0.318837\pi\)
\(384\) 2.77791e9i 0.127760i
\(385\) −3.36550e10 + 3.74892e10i −1.53181 + 1.70633i
\(386\) −2.25604e10 −1.01624
\(387\) −2.16706e10 2.16706e10i −0.966112 0.966112i
\(388\) −1.88838e8 + 1.88838e8i −0.00833225 + 0.00833225i
\(389\) 2.04596e10i 0.893507i −0.894657 0.446754i \(-0.852580\pi\)
0.894657 0.446754i \(-0.147420\pi\)
\(390\) 7.05324e9 + 6.33186e9i 0.304881 + 0.273699i
\(391\) −6.81417e6 −0.000291545
\(392\) −9.23265e9 9.23265e9i −0.391005 0.391005i
\(393\) 5.12801e9 5.12801e9i 0.214971 0.214971i
\(394\) 1.27683e10i 0.529843i
\(395\) −2.93161e10 + 1.57998e9i −1.20425 + 0.0649026i
\(396\) −1.91797e10 −0.779941
\(397\) −7.68996e9 7.68996e9i −0.309572 0.309572i 0.535171 0.844744i \(-0.320247\pi\)
−0.844744 + 0.535171i \(0.820247\pi\)
\(398\) 3.11670e9 3.11670e9i 0.124212 0.124212i
\(399\) 3.11496e10i 1.22902i
\(400\) 6.36293e9 6.87851e8i 0.248552 0.0268692i
\(401\) −5.85624e9 −0.226486 −0.113243 0.993567i \(-0.536124\pi\)
−0.113243 + 0.993567i \(0.536124\pi\)
\(402\) 1.95602e10 + 1.95602e10i 0.748980 + 0.748980i
\(403\) −6.69079e9 + 6.69079e9i −0.253663 + 0.253663i
\(404\) 2.06407e10i 0.774818i
\(405\) −1.30707e9 2.42524e10i −0.0485825 0.901437i
\(406\) −5.24714e9 −0.193116
\(407\) 2.45366e10 + 2.45366e10i 0.894205 + 0.894205i
\(408\) 5.32562e8 5.32562e8i 0.0192189 0.0192189i
\(409\) 1.32972e10i 0.475191i 0.971364 + 0.237596i \(0.0763593\pi\)
−0.971364 + 0.237596i \(0.923641\pi\)
\(410\) 8.25036e9 9.19032e9i 0.291970 0.325233i
\(411\) 1.45690e9 0.0510580
\(412\) −1.71715e10 1.71715e10i −0.595962 0.595962i
\(413\) 4.30500e10 4.30500e10i 1.47970 1.47970i
\(414\) 1.24034e8i 0.00422222i
\(415\) −1.85022e10 1.66099e10i −0.623780 0.559982i
\(416\) 2.12223e9 0.0708629
\(417\) 2.24828e9 + 2.24828e9i 0.0743542 + 0.0743542i
\(418\) 1.16072e10 1.16072e10i 0.380209 0.380209i
\(419\) 6.98994e9i 0.226786i −0.993550 0.113393i \(-0.963828\pi\)
0.993550 0.113393i \(-0.0361720\pi\)
\(420\) 3.59581e10 1.93794e9i 1.15558 0.0622793i
\(421\) −2.54099e10 −0.808864 −0.404432 0.914568i \(-0.632531\pi\)
−0.404432 + 0.914568i \(0.632531\pi\)
\(422\) 2.98434e10 + 2.98434e10i 0.941019 + 0.941019i
\(423\) −4.17094e10 + 4.17094e10i −1.30278 + 1.30278i
\(424\) 4.04896e9i 0.125280i
\(425\) 1.35173e9 + 1.08799e9i 0.0414317 + 0.0333478i
\(426\) −1.08912e10 −0.330704
\(427\) −6.84322e9 6.84322e9i −0.205849 0.205849i
\(428\) −2.59720e9 + 2.59720e9i −0.0773982 + 0.0773982i
\(429\) 2.81043e10i 0.829743i
\(430\) −1.63183e9 3.02782e10i −0.0477311 0.885639i
\(431\) 3.72373e10 1.07912 0.539559 0.841948i \(-0.318591\pi\)
0.539559 + 0.841948i \(0.318591\pi\)
\(432\) 7.94567e8 + 7.94567e8i 0.0228137 + 0.0228137i
\(433\) 1.34378e10 1.34378e10i 0.382277 0.382277i −0.489645 0.871922i \(-0.662874\pi\)
0.871922 + 0.489645i \(0.162874\pi\)
\(434\) 3.59487e10i 1.01327i
\(435\) 5.89689e9 6.56872e9i 0.164690 0.183453i
\(436\) 6.75837e9 0.187023
\(437\) 7.50632e7 + 7.50632e7i 0.00205826 + 0.00205826i
\(438\) −4.02343e10 + 4.02343e10i −1.09320 + 1.09320i
\(439\) 4.19540e10i 1.12957i −0.825237 0.564787i \(-0.808958\pi\)
0.825237 0.564787i \(-0.191042\pi\)
\(440\) −1.41211e10 1.26768e10i −0.376754 0.338221i
\(441\) 6.44373e10 1.70366
\(442\) 4.06859e8 + 4.06859e8i 0.0106599 + 0.0106599i
\(443\) −3.76709e10 + 3.76709e10i −0.978119 + 0.978119i −0.999766 0.0216469i \(-0.993109\pi\)
0.0216469 + 0.999766i \(0.493109\pi\)
\(444\) 2.48029e10i 0.638220i
\(445\) 4.94231e10 2.66363e9i 1.26035 0.0679258i
\(446\) 4.13798e10 1.04580
\(447\) 4.58122e7 + 4.58122e7i 0.00114750 + 0.00114750i
\(448\) 5.70122e9 5.70122e9i 0.141532 0.141532i
\(449\) 5.05667e10i 1.24417i 0.782950 + 0.622085i \(0.213714\pi\)
−0.782950 + 0.622085i \(0.786286\pi\)
\(450\) −1.98040e10 + 2.46047e10i −0.482951 + 0.600023i
\(451\) −3.66197e10 −0.885133
\(452\) −1.60708e10 1.60708e10i −0.385020 0.385020i
\(453\) −1.05388e10 + 1.05388e10i −0.250264 + 0.250264i
\(454\) 3.65719e9i 0.0860844i
\(455\) 1.48052e9 + 2.74708e10i 0.0345437 + 0.640951i
\(456\) −1.17331e10 −0.271366
\(457\) 1.52066e10 + 1.52066e10i 0.348631 + 0.348631i 0.859599 0.510968i \(-0.170713\pi\)
−0.510968 + 0.859599i \(0.670713\pi\)
\(458\) 3.43822e10 3.43822e10i 0.781398 0.781398i
\(459\) 3.04657e8i 0.00686374i
\(460\) 8.19806e7 9.13206e7i 0.00183096 0.00203956i
\(461\) −2.73791e10 −0.606199 −0.303100 0.952959i \(-0.598021\pi\)
−0.303100 + 0.952959i \(0.598021\pi\)
\(462\) −7.55002e10 7.55002e10i −1.65722 1.65722i
\(463\) 3.53408e10 3.53408e10i 0.769046 0.769046i −0.208893 0.977939i \(-0.566986\pi\)
0.977939 + 0.208893i \(0.0669859\pi\)
\(464\) 1.97645e9i 0.0426396i
\(465\) −4.50030e10 4.04002e10i −0.962563 0.864116i
\(466\) 4.52821e9 0.0960247
\(467\) −4.85998e10 4.85998e10i −1.02180 1.02180i −0.999757 0.0220454i \(-0.992982\pi\)
−0.0220454 0.999757i \(-0.507018\pi\)
\(468\) −7.40583e9 + 7.40583e9i −0.154380 + 0.154380i
\(469\) 8.02885e10i 1.65944i
\(470\) −5.82764e10 + 3.14078e9i −1.19427 + 0.0643644i
\(471\) 8.75000e10 1.77797
\(472\) 1.62157e10 + 1.62157e10i 0.326713 + 0.326713i
\(473\) −6.35744e10 + 6.35744e10i −1.27010 + 1.27010i
\(474\) 6.22221e10i 1.23263i
\(475\) −2.90529e9 2.68753e10i −0.0570710 0.527932i
\(476\) 2.18600e9 0.0425815
\(477\) −1.41294e10 1.41294e10i −0.272930 0.272930i
\(478\) −4.15358e10 + 4.15358e10i −0.795630 + 0.795630i
\(479\) 5.06476e10i 0.962093i 0.876695 + 0.481047i \(0.159743\pi\)
−0.876695 + 0.481047i \(0.840257\pi\)
\(480\) 7.29967e8 + 1.35444e10i 0.0137511 + 0.255149i
\(481\) 1.89485e10 0.353994
\(482\) 3.62449e10 + 3.62449e10i 0.671519 + 0.671519i
\(483\) 4.88257e8 4.88257e8i 0.00897139 0.00897139i
\(484\) 2.88290e10i 0.525349i
\(485\) 8.71102e8 9.70346e8i 0.0157435 0.0175372i
\(486\) 5.65657e10 1.01393
\(487\) 3.99713e9 + 3.99713e9i 0.0710612 + 0.0710612i 0.741744 0.670683i \(-0.233999\pi\)
−0.670683 + 0.741744i \(0.733999\pi\)
\(488\) 2.57764e9 2.57764e9i 0.0454510 0.0454510i
\(489\) 3.47121e10i 0.607079i
\(490\) 4.74421e10 + 4.25899e10i 0.822962 + 0.738792i
\(491\) 4.99004e10 0.858575 0.429288 0.903168i \(-0.358765\pi\)
0.429288 + 0.903168i \(0.358765\pi\)
\(492\) 1.85085e10 + 1.85085e10i 0.315872 + 0.315872i
\(493\) 3.78910e8 3.78910e8i 0.00641429 0.00641429i
\(494\) 8.96371e9i 0.150515i
\(495\) 9.35153e10 5.03996e9i 1.55762 0.0839472i
\(496\) −1.35408e10 −0.223727
\(497\) −2.23525e10 2.23525e10i −0.366354 0.366354i
\(498\) 3.72619e10 3.72619e10i 0.605826 0.605826i
\(499\) 7.43519e10i 1.19920i −0.800302 0.599598i \(-0.795327\pi\)
0.800302 0.599598i \(-0.204673\pi\)
\(500\) −3.08432e10 + 5.02580e9i −0.493491 + 0.0804128i
\(501\) −1.20253e11 −1.90873
\(502\) −2.72371e10 2.72371e10i −0.428890 0.428890i
\(503\) 5.52095e10 5.52095e10i 0.862465 0.862465i −0.129158 0.991624i \(-0.541228\pi\)
0.991624 + 0.129158i \(0.0412276\pi\)
\(504\) 3.97904e10i 0.616675i
\(505\) −5.42387e9 1.00639e11i −0.0833958 1.54739i
\(506\) −3.63876e8 −0.00555074
\(507\) 5.66811e10 + 5.66811e10i 0.857840 + 0.857840i
\(508\) 1.24105e10 1.24105e10i 0.186352 0.186352i
\(509\) 1.27030e10i 0.189249i 0.995513 + 0.0946245i \(0.0301650\pi\)
−0.995513 + 0.0946245i \(0.969835\pi\)
\(510\) −2.45669e9 + 2.73658e9i −0.0363136 + 0.0404508i
\(511\) −1.65149e11 −2.42210
\(512\) 2.14748e9 + 2.14748e9i 0.0312500 + 0.0312500i
\(513\) 3.35603e9 3.35603e9i 0.0484570 0.0484570i
\(514\) 4.81855e8i 0.00690341i
\(515\) 8.82358e10 + 7.92113e10i 1.25434 + 1.12605i
\(516\) 6.42642e10 0.906505
\(517\) 1.22361e11 + 1.22361e11i 1.71270 + 1.71270i
\(518\) 5.09039e10 5.09039e10i 0.707021 0.707021i
\(519\) 9.95114e10i 1.37152i
\(520\) −1.03474e10 + 5.57670e8i −0.141520 + 0.00762717i
\(521\) −3.13323e10 −0.425247 −0.212623 0.977134i \(-0.568201\pi\)
−0.212623 + 0.977134i \(0.568201\pi\)
\(522\) 6.89709e9 + 6.89709e9i 0.0928932 + 0.0928932i
\(523\) −1.15624e10 + 1.15624e10i −0.154539 + 0.154539i −0.780142 0.625603i \(-0.784853\pi\)
0.625603 + 0.780142i \(0.284853\pi\)
\(524\) 7.92849e9i 0.105164i
\(525\) −1.74813e11 + 1.88978e10i −2.30111 + 0.248756i
\(526\) −3.22403e10 −0.421169
\(527\) −2.59595e9 2.59595e9i −0.0336553 0.0336553i
\(528\) 2.84387e10 2.84387e10i 0.365910 0.365910i
\(529\) 7.83086e10i 0.999970i
\(530\) −1.06397e9 1.97417e10i −0.0134842 0.250196i
\(531\) −1.13174e11 −1.42353
\(532\) −2.40804e10 2.40804e10i −0.300619 0.300619i
\(533\) −1.41399e10 + 1.41399e10i −0.175201 + 0.175201i
\(534\) 1.04898e11i 1.29004i
\(535\) 1.19808e10 1.33458e10i 0.146242 0.162903i
\(536\) −3.02424e10 −0.366401
\(537\) 7.65999e10 + 7.65999e10i 0.921152 + 0.921152i
\(538\) −7.63072e10 + 7.63072e10i −0.910828 + 0.910828i
\(539\) 1.89038e11i 2.23972i
\(540\) −4.08289e9 3.66531e9i −0.0480168 0.0431058i
\(541\) 1.21976e11 1.42392 0.711961 0.702219i \(-0.247807\pi\)
0.711961 + 0.702219i \(0.247807\pi\)
\(542\) −3.07387e10 3.07387e10i −0.356195 0.356195i
\(543\) −6.88552e10 + 6.88552e10i −0.792022 + 0.792022i
\(544\) 8.23401e8i 0.00940190i
\(545\) −3.29520e10 + 1.77593e9i −0.373505 + 0.0201298i
\(546\) −5.83054e10 −0.656052
\(547\) −1.11157e11 1.11157e11i −1.24161 1.24161i −0.959331 0.282283i \(-0.908908\pi\)
−0.282283 0.959331i \(-0.591092\pi\)
\(548\) −1.12627e9 + 1.12627e9i −0.0124888 + 0.0124888i
\(549\) 1.79901e10i 0.198036i
\(550\) 7.21820e10 + 5.80983e10i 0.788820 + 0.634911i
\(551\) −8.34796e9 −0.0905678
\(552\) 1.83912e8 + 1.83912e8i 0.00198086 + 0.00198086i
\(553\) 1.27701e11 1.27701e11i 1.36550 1.36550i
\(554\) 4.48278e10i 0.475892i
\(555\) 6.51758e9 + 1.20932e11i 0.0686933 + 1.27459i
\(556\) −3.47609e9 −0.0363741
\(557\) −2.14972e10 2.14972e10i −0.223337 0.223337i 0.586565 0.809902i \(-0.300480\pi\)
−0.809902 + 0.586565i \(0.800480\pi\)
\(558\) 4.72526e10 4.72526e10i 0.487404 0.487404i
\(559\) 4.90957e10i 0.502801i
\(560\) −2.62995e10 + 2.92958e10i −0.267421 + 0.297888i
\(561\) 1.09041e10 0.110088
\(562\) −6.62974e10 6.62974e10i −0.664586 0.664586i
\(563\) −2.68020e10 + 2.68020e10i −0.266768 + 0.266768i −0.827796 0.561029i \(-0.810406\pi\)
0.561029 + 0.827796i \(0.310406\pi\)
\(564\) 1.23689e11i 1.22240i
\(565\) 8.25800e10 + 7.41340e10i 0.810366 + 0.727484i
\(566\) −1.18523e9 −0.0115488
\(567\) 1.05644e11 + 1.05644e11i 1.02214 + 1.02214i
\(568\) 8.41955e9 8.41955e9i 0.0808901 0.0808901i
\(569\) 9.52278e10i 0.908479i −0.890880 0.454240i \(-0.849911\pi\)
0.890880 0.454240i \(-0.150089\pi\)
\(570\) 5.72077e10 3.08318e9i 0.541945 0.0292078i
\(571\) 1.93929e11 1.82431 0.912154 0.409848i \(-0.134418\pi\)
0.912154 + 0.409848i \(0.134418\pi\)
\(572\) 2.17262e10 + 2.17262e10i 0.202955 + 0.202955i
\(573\) 9.69361e10 9.69361e10i 0.899223 0.899223i
\(574\) 7.59716e10i 0.699848i
\(575\) −3.75719e8 + 4.66798e8i −0.00343710 + 0.00427029i
\(576\) −1.49879e10 −0.136160
\(577\) −1.25849e11 1.25849e11i −1.13540 1.13540i −0.989265 0.146131i \(-0.953318\pi\)
−0.146131 0.989265i \(-0.546682\pi\)
\(578\) 5.56482e10 5.56482e10i 0.498586 0.498586i
\(579\) 2.33467e11i 2.07736i
\(580\) 5.19361e8 + 9.63663e9i 0.00458942 + 0.0851556i
\(581\) 1.52948e11 1.34227
\(582\) 1.95420e9 + 1.95420e9i 0.0170324 + 0.0170324i
\(583\) −4.14510e10 + 4.14510e10i −0.358807 + 0.358807i
\(584\) 6.22068e10i 0.534794i
\(585\) 3.41628e10 3.80549e10i 0.291696 0.324928i
\(586\) −1.01291e11 −0.858977
\(587\) 3.41535e10 + 3.41535e10i 0.287662 + 0.287662i 0.836155 0.548493i \(-0.184798\pi\)
−0.548493 + 0.836155i \(0.684798\pi\)
\(588\) −9.55444e10 + 9.55444e10i −0.799275 + 0.799275i
\(589\) 5.71927e10i 0.475203i
\(590\) −8.33244e10 7.48023e10i −0.687645 0.617315i
\(591\) −1.32133e11 −1.08308
\(592\) 1.91740e10 + 1.91740e10i 0.156108 + 0.156108i
\(593\) −1.67663e11 + 1.67663e11i −1.35588 + 1.35588i −0.476939 + 0.878937i \(0.658254\pi\)
−0.878937 + 0.476939i \(0.841746\pi\)
\(594\) 1.62687e10i 0.130679i
\(595\) −1.06583e10 + 5.74426e8i −0.0850397 + 0.00458317i
\(596\) −7.08309e7 −0.000561355
\(597\) −3.22533e10 3.22533e10i −0.253908 0.253908i
\(598\) −1.40502e8 + 1.40502e8i −0.00109870 + 0.00109870i
\(599\) 2.21439e11i 1.72007i −0.510231 0.860037i \(-0.670440\pi\)
0.510231 0.860037i \(-0.329560\pi\)
\(600\) −7.11825e9 6.58470e10i −0.0549248 0.508078i
\(601\) −2.25242e11 −1.72644 −0.863220 0.504828i \(-0.831556\pi\)
−0.863220 + 0.504828i \(0.831556\pi\)
\(602\) 1.31892e11 + 1.31892e11i 1.00423 + 1.00423i
\(603\) 1.05535e11 1.05535e11i 0.798229 0.798229i
\(604\) 1.62942e10i 0.122429i
\(605\) −7.57554e9 1.40562e11i −0.0565447 1.04917i
\(606\) 2.13601e11 1.58385
\(607\) −8.03075e10 8.03075e10i −0.591563 0.591563i 0.346490 0.938054i \(-0.387373\pi\)
−0.938054 + 0.346490i \(0.887373\pi\)
\(608\) 9.07038e9 9.07038e9i 0.0663760 0.0663760i
\(609\) 5.43002e10i 0.394759i
\(610\) −1.18906e10 + 1.32452e10i −0.0858782 + 0.0956622i
\(611\) 9.44942e10 0.678017
\(612\) −2.87338e9 2.87338e9i −0.0204827 0.0204827i
\(613\) −5.38969e10 + 5.38969e10i −0.381700 + 0.381700i −0.871714 0.490014i \(-0.836992\pi\)
0.490014 + 0.871714i \(0.336992\pi\)
\(614\) 7.69107e10i 0.541144i
\(615\) −9.51063e10 8.53791e10i −0.664827 0.596831i
\(616\) 1.16732e11 0.810712
\(617\) −1.37064e10 1.37064e10i −0.0945766 0.0945766i 0.658235 0.752812i \(-0.271303\pi\)
−0.752812 + 0.658235i \(0.771303\pi\)
\(618\) −1.77699e11 + 1.77699e11i −1.21824 + 1.21824i
\(619\) 1.67460e11i 1.14064i 0.821423 + 0.570320i \(0.193181\pi\)
−0.821423 + 0.570320i \(0.806819\pi\)
\(620\) 6.60215e10 3.55819e9i 0.446806 0.0240804i
\(621\) −1.05209e8 −0.000707433
\(622\) 8.51746e10 + 8.51746e10i 0.569047 + 0.569047i
\(623\) −2.15287e11 + 2.15287e11i −1.42911 + 1.42911i
\(624\) 2.19620e10i 0.144855i
\(625\) 1.49063e11 3.26093e10i 0.976897 0.213708i
\(626\) −1.69423e11 −1.10325
\(627\) −1.20117e11 1.20117e11i −0.777205 0.777205i
\(628\) −6.76424e10 + 6.76424e10i −0.434891 + 0.434891i
\(629\) 7.35182e9i 0.0469669i
\(630\) −1.04559e10 1.94008e11i −0.0663745 1.23156i
\(631\) 9.05920e10 0.571442 0.285721 0.958313i \(-0.407767\pi\)
0.285721 + 0.958313i \(0.407767\pi\)
\(632\) 4.81012e10 + 4.81012e10i 0.301500 + 0.301500i
\(633\) 3.08835e11 3.08835e11i 1.92359 1.92359i
\(634\) 1.52176e11i 0.941867i
\(635\) −5.72493e10 + 6.37716e10i −0.352107 + 0.392223i
\(636\) 4.19008e10 0.256091
\(637\) −7.29926e10 7.29926e10i −0.443324 0.443324i
\(638\) 2.02338e10 2.02338e10i 0.122122 0.122122i
\(639\) 5.87625e10i 0.352449i
\(640\) −1.10349e10 9.90626e9i −0.0657730 0.0590459i
\(641\) −2.71517e10 −0.160829 −0.0804147 0.996761i \(-0.525624\pi\)
−0.0804147 + 0.996761i \(0.525624\pi\)
\(642\) 2.68773e10 + 2.68773e10i 0.158214 + 0.158214i
\(643\) −2.63399e10 + 2.63399e10i −0.154089 + 0.154089i −0.779941 0.625853i \(-0.784751\pi\)
0.625853 + 0.779941i \(0.284751\pi\)
\(644\) 7.54900e8i 0.00438880i
\(645\) −3.13335e11 + 1.68870e10i −1.81038 + 0.0975697i
\(646\) 3.47782e9 0.0199699
\(647\) −2.14034e9 2.14034e9i −0.0122142 0.0122142i 0.700973 0.713188i \(-0.252749\pi\)
−0.713188 + 0.700973i \(0.752749\pi\)
\(648\) −3.97928e10 + 3.97928e10i −0.225686 + 0.225686i
\(649\) 3.32014e11i 1.87145i
\(650\) 5.03048e10 5.43810e9i 0.281810 0.0304645i
\(651\) 3.72016e11 2.07127
\(652\) 2.68344e10 + 2.68344e10i 0.148491 + 0.148491i
\(653\) 1.29525e11 1.29525e11i 0.712364 0.712364i −0.254665 0.967029i \(-0.581965\pi\)
0.967029 + 0.254665i \(0.0819653\pi\)
\(654\) 6.99392e10i 0.382305i
\(655\) −2.08341e9 3.86572e10i −0.0113190 0.210022i
\(656\) −2.86163e10 −0.154525
\(657\) 2.17080e11 + 2.17080e11i 1.16509 + 1.16509i
\(658\) 2.53852e11 2.53852e11i 1.35418 1.35418i
\(659\) 1.29660e11i 0.687485i 0.939064 + 0.343742i \(0.111695\pi\)
−0.939064 + 0.343742i \(0.888305\pi\)
\(660\) −1.31187e11 + 1.46133e11i −0.691376 + 0.770144i
\(661\) 4.35428e10 0.228092 0.114046 0.993475i \(-0.463619\pi\)
0.114046 + 0.993475i \(0.463619\pi\)
\(662\) −1.04814e11 1.04814e11i −0.545744 0.545744i
\(663\) 4.21039e9 4.21039e9i 0.0217906 0.0217906i
\(664\) 5.76112e10i 0.296370i
\(665\) 1.23737e11 + 1.11082e11i 0.632724 + 0.568011i
\(666\) −1.33821e11 −0.680186
\(667\) 1.30851e8 + 1.30851e8i 0.000661109 + 0.000661109i
\(668\) 9.29625e10 9.29625e10i 0.466876 0.466876i
\(669\) 4.28220e11i 2.13778i
\(670\) 1.47454e11 7.94694e9i 0.731740 0.0394367i
\(671\) 5.27769e10 0.260348
\(672\) −5.89993e10 5.89993e10i −0.289314 0.289314i
\(673\) 1.08117e11 1.08117e11i 0.527028 0.527028i −0.392657 0.919685i \(-0.628444\pi\)
0.919685 + 0.392657i \(0.128444\pi\)
\(674\) 2.13346e11i 1.03382i
\(675\) 2.08703e10 + 1.67982e10i 0.100534 + 0.0809184i
\(676\) −8.76353e10 −0.419655
\(677\) −7.02840e10 7.02840e10i −0.334581 0.334581i 0.519742 0.854323i \(-0.326028\pi\)
−0.854323 + 0.519742i \(0.826028\pi\)
\(678\) −1.66309e11 + 1.66309e11i −0.787041 + 0.787041i
\(679\) 8.02135e9i 0.0377371i
\(680\) −2.16369e8 4.01469e9i −0.00101195 0.0187766i
\(681\) 3.78466e10 0.175970
\(682\) −1.38623e11 1.38623e11i −0.640766 0.640766i
\(683\) −1.25091e11 + 1.25091e11i −0.574834 + 0.574834i −0.933475 0.358642i \(-0.883240\pi\)
0.358642 + 0.933475i \(0.383240\pi\)
\(684\) 6.33048e10i 0.289209i
\(685\) 5.19544e9 5.78735e9i 0.0235972 0.0262856i
\(686\) −1.41428e11 −0.638616
\(687\) −3.55806e11 3.55806e11i −1.59730 1.59730i
\(688\) −4.96799e10 + 4.96799e10i −0.221731 + 0.221731i
\(689\) 3.20108e10i 0.142043i
\(690\) −9.45034e8 8.48379e8i −0.00416918 0.00374277i
\(691\) −1.67070e11 −0.732800 −0.366400 0.930457i \(-0.619410\pi\)
−0.366400 + 0.930457i \(0.619410\pi\)
\(692\) 7.69279e10 + 7.69279e10i 0.335475 + 0.335475i
\(693\) −4.07353e11 + 4.07353e11i −1.76619 + 1.76619i
\(694\) 1.74438e11i 0.751973i
\(695\) 1.69485e10 9.13431e8i 0.0726427 0.00391504i
\(696\) −2.04533e10 −0.0871619
\(697\) −5.48611e9 5.48611e9i −0.0232452 0.0232452i
\(698\) −7.74223e10 + 7.74223e10i −0.326170 + 0.326170i
\(699\) 4.68603e10i 0.196289i
\(700\) 1.20531e11 1.49749e11i 0.502004 0.623696i
\(701\) 1.66014e11 0.687498 0.343749 0.939062i \(-0.388303\pi\)
0.343749 + 0.939062i \(0.388303\pi\)
\(702\) 6.28178e9 + 6.28178e9i 0.0258663 + 0.0258663i
\(703\) 8.09858e10 8.09858e10i 0.331579 0.331579i
\(704\) 4.39695e10i 0.179003i
\(705\) 3.25024e10 + 6.03075e11i 0.131571 + 2.44127i
\(706\) 1.00374e11 0.404018
\(707\) 4.38382e11 + 4.38382e11i 1.75459 + 1.75459i
\(708\) 1.67808e11 1.67808e11i 0.667853 0.667853i
\(709\) 3.71810e11i 1.47142i −0.677297 0.735710i \(-0.736849\pi\)
0.677297 0.735710i \(-0.263151\pi\)
\(710\) −3.88391e10 + 4.32640e10i −0.152839 + 0.170252i
\(711\) −3.35712e11 −1.31368
\(712\) −8.10924e10 8.10924e10i −0.315544 0.315544i
\(713\) 8.96472e8 8.96472e8i 0.00346879 0.00346879i
\(714\) 2.26218e10i 0.0870432i
\(715\) −1.11640e11 1.00222e11i −0.427167 0.383477i
\(716\) −1.18432e11 −0.450627
\(717\) 4.29835e11 + 4.29835e11i 1.62639 + 1.62639i
\(718\) −6.32964e10 + 6.32964e10i −0.238167 + 0.238167i
\(719\) 3.16803e11i 1.18543i −0.805414 0.592713i \(-0.798057\pi\)
0.805414 0.592713i \(-0.201943\pi\)
\(720\) 7.30771e10 3.93845e9i 0.271926 0.0146553i
\(721\) −7.29399e11 −2.69913
\(722\) 9.75577e10 + 9.75577e10i 0.359015 + 0.359015i
\(723\) 3.75081e11 3.75081e11i 1.37269 1.37269i
\(724\) 1.06458e11i 0.387457i
\(725\) −5.06454e9 4.68492e10i −0.0183311 0.169570i
\(726\) 2.98338e11 1.07389
\(727\) 1.86694e11 + 1.86694e11i 0.668333 + 0.668333i 0.957330 0.288997i \(-0.0933218\pi\)
−0.288997 + 0.957330i \(0.593322\pi\)
\(728\) 4.50734e10 4.50734e10i 0.160470 0.160470i
\(729\) 3.30410e11i 1.16988i
\(730\) 1.63464e10 + 3.03304e11i 0.0575614 + 1.06804i
\(731\) −1.90485e10 −0.0667102
\(732\) −2.66748e10 2.66748e10i −0.0929088 0.0929088i
\(733\) 8.03537e10 8.03537e10i 0.278349 0.278349i −0.554101 0.832450i \(-0.686938\pi\)
0.832450 + 0.554101i \(0.186938\pi\)
\(734\) 1.06549e11i 0.367085i
\(735\) 4.40743e11 4.90956e11i 1.51020 1.68226i
\(736\) −2.84349e8 −0.000969036
\(737\) −3.09604e11 3.09604e11i −1.04939 1.04939i
\(738\) 9.98606e10 9.98606e10i 0.336642 0.336642i
\(739\) 2.44359e11i 0.819315i 0.912239 + 0.409658i \(0.134352\pi\)
−0.912239 + 0.409658i \(0.865648\pi\)
\(740\) −9.85260e10 8.84490e10i −0.328567 0.294962i
\(741\) −9.27613e10 −0.307676
\(742\) 8.59947e10 + 8.59947e10i 0.283698 + 0.283698i
\(743\) 1.76095e10 1.76095e10i 0.0577818 0.0577818i −0.677625 0.735407i \(-0.736991\pi\)
0.735407 + 0.677625i \(0.236991\pi\)
\(744\) 1.40128e11i 0.457333i
\(745\) 3.45353e8 1.86126e7i 0.00112108 6.04202e-5i
\(746\) 2.61466e11 0.844230
\(747\) −2.01042e11 2.01042e11i −0.645662 0.645662i
\(748\) −8.42952e9 + 8.42952e9i −0.0269275 + 0.0269275i
\(749\) 1.10322e11i 0.350539i
\(750\) 5.20097e10 + 3.19182e11i 0.164376 + 1.00877i
\(751\) 9.35354e10 0.294047 0.147023 0.989133i \(-0.453031\pi\)
0.147023 + 0.989133i \(0.453031\pi\)
\(752\) 9.56187e10 + 9.56187e10i 0.299000 + 0.299000i
\(753\) −2.81864e11 + 2.81864e11i −0.876717 + 0.876717i
\(754\) 1.56256e10i 0.0483450i
\(755\) 4.28170e9 + 7.94460e10i 0.0131774 + 0.244503i
\(756\) 3.37511e10 0.103324
\(757\) 6.80194e10 + 6.80194e10i 0.207133 + 0.207133i 0.803048 0.595915i \(-0.203210\pi\)
−0.595915 + 0.803048i \(0.703210\pi\)
\(758\) 7.31659e10 7.31659e10i 0.221632 0.221632i
\(759\) 3.76558e9i 0.0113466i
\(760\) −4.18413e10 + 4.66082e10i −0.125415 + 0.139704i
\(761\) 1.73217e11 0.516478 0.258239 0.966081i \(-0.416858\pi\)
0.258239 + 0.966081i \(0.416858\pi\)
\(762\) −1.28431e11 1.28431e11i −0.380933 0.380933i
\(763\) 1.43539e11 1.43539e11i 0.423518 0.423518i
\(764\) 1.49874e11i 0.439900i
\(765\) 1.47649e10 + 1.32548e10i 0.0431106 + 0.0387014i
\(766\) −1.04475e11 −0.303456
\(767\) 1.28200e11 + 1.28200e11i 0.370430 + 0.370430i
\(768\) 2.22233e10 2.22233e10i 0.0638798 0.0638798i
\(769\) 6.23925e11i 1.78413i 0.451905 + 0.892066i \(0.350745\pi\)
−0.451905 + 0.892066i \(0.649255\pi\)
\(770\) −5.69154e11 + 3.06742e10i −1.61907 + 0.0872592i
\(771\) 4.98649e9 0.0141116
\(772\) −1.80483e11 1.80483e11i −0.508122 0.508122i
\(773\) −2.80444e11 + 2.80444e11i −0.785466 + 0.785466i −0.980747 0.195281i \(-0.937438\pi\)
0.195281 + 0.980747i \(0.437438\pi\)
\(774\)