Properties

Label 10.9.c.b.3.1
Level 10
Weight 9
Character 10.3
Analytic conductor 4.074
Analytic rank 0
Dimension 4
CM No
Inner twists 2

Related objects

Downloads

Learn more about

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 3.1
Root \(-11.7577i\)
Character \(\chi\) = 10.3
Dual form 10.9.c.b.7.1

$q$-expansion

\(f(q)\) \(=\) \(q+(8.00000 - 8.00000i) q^{2} +(-39.7883 - 39.7883i) q^{3} -128.000i q^{4} +(-401.365 - 479.094i) q^{5} -636.612 q^{6} +(144.447 - 144.447i) q^{7} +(-1024.00 - 1024.00i) q^{8} -3394.79i q^{9} +O(q^{10})\) \(q+(8.00000 - 8.00000i) q^{2} +(-39.7883 - 39.7883i) q^{3} -128.000i q^{4} +(-401.365 - 479.094i) q^{5} -636.612 q^{6} +(144.447 - 144.447i) q^{7} +(-1024.00 - 1024.00i) q^{8} -3394.79i q^{9} +(-7043.67 - 621.836i) q^{10} +13600.3 q^{11} +(-5092.90 + 5092.90i) q^{12} +(30883.7 + 30883.7i) q^{13} -2311.15i q^{14} +(-3092.72 + 35031.9i) q^{15} -16384.0 q^{16} +(4949.02 - 4949.02i) q^{17} +(-27158.3 - 27158.3i) q^{18} -176579. i q^{19} +(-61324.1 + 51374.7i) q^{20} -11494.6 q^{21} +(108802. - 108802. i) q^{22} +(-229482. - 229482. i) q^{23} +81486.3i q^{24} +(-68437.7 + 384583. i) q^{25} +494139. q^{26} +(-396123. + 396123. i) q^{27} +(-18489.2 - 18489.2i) q^{28} -144167. i q^{29} +(255514. + 304997. i) q^{30} +1.50971e6 q^{31} +(-131072. + 131072. i) q^{32} +(-541132. - 541132. i) q^{33} -79184.4i q^{34} +(-127179. - 11227.8i) q^{35} -434533. q^{36} +(-1.60715e6 + 1.60715e6i) q^{37} +(-1.41263e6 - 1.41263e6i) q^{38} -2.45761e6i q^{39} +(-79595.0 + 901590. i) q^{40} +3.62276e6 q^{41} +(-91956.5 + 91956.5i) q^{42} +(-575576. - 575576. i) q^{43} -1.74084e6i q^{44} +(-1.62642e6 + 1.36255e6i) q^{45} -3.67171e6 q^{46} +(3.11186e6 - 3.11186e6i) q^{47} +(651891. + 651891. i) q^{48} +5.72307e6i q^{49} +(2.52916e6 + 3.62417e6i) q^{50} -393826. q^{51} +(3.95311e6 - 3.95311e6i) q^{52} +(8.16813e6 + 8.16813e6i) q^{53} +6.33798e6i q^{54} +(-5.45868e6 - 6.51582e6i) q^{55} -295827. q^{56} +(-7.02575e6 + 7.02575e6i) q^{57} +(-1.15334e6 - 1.15334e6i) q^{58} -1.54905e7i q^{59} +(4.48409e6 + 395868. i) q^{60} -1.92688e7 q^{61} +(1.20777e7 - 1.20777e7i) q^{62} +(-490366. - 490366. i) q^{63} +2.09715e6i q^{64} +(2.40057e6 - 2.71918e7i) q^{65} -8.65811e6 q^{66} +(-1.00075e7 + 1.00075e7i) q^{67} +(-633475. - 633475. i) q^{68} +1.82614e7i q^{69} +(-1.10726e6 + 927613. i) q^{70} +1.84257e7 q^{71} +(-3.47626e6 + 3.47626e6i) q^{72} +(2.45702e7 + 2.45702e7i) q^{73} +2.57144e7i q^{74} +(1.80249e7 - 1.25789e7i) q^{75} -2.26020e7 q^{76} +(1.96452e6 - 1.96452e6i) q^{77} +(-1.96609e7 - 1.96609e7i) q^{78} +2.17799e7i q^{79} +(6.57596e6 + 7.84948e6i) q^{80} +9.24891e6 q^{81} +(2.89820e7 - 2.89820e7i) q^{82} +(4.00189e6 + 4.00189e6i) q^{83} +1.47130e6i q^{84} +(-4.35741e6 - 384685. i) q^{85} -9.20921e6 q^{86} +(-5.73617e6 + 5.73617e6i) q^{87} +(-1.39267e7 - 1.39267e7i) q^{88} -6.14525e7i q^{89} +(-2.11100e6 + 2.39118e7i) q^{90} +8.92209e6 q^{91} +(-2.93737e7 + 2.93737e7i) q^{92} +(-6.00686e7 - 6.00686e7i) q^{93} -4.97898e7i q^{94} +(-8.45978e7 + 7.08724e7i) q^{95} +1.04303e7 q^{96} +(1.55814e7 - 1.55814e7i) q^{97} +(4.57846e7 + 4.57846e7i) q^{98} -4.61701e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 32q^{2} + 86q^{3} - 870q^{5} + 1376q^{6} + 5726q^{7} - 4096q^{8} + O(q^{10}) \) \( 4q + 32q^{2} + 86q^{3} - 870q^{5} + 1376q^{6} + 5726q^{7} - 4096q^{8} - 4640q^{10} - 14732q^{11} + 11008q^{12} + 45576q^{13} - 115090q^{15} - 65536q^{16} + 3616q^{17} + 60032q^{18} + 37120q^{20} + 877268q^{21} - 117856q^{22} - 456794q^{23} - 913600q^{25} + 729216q^{26} - 889240q^{27} - 732928q^{28} + 421920q^{30} + 4672348q^{31} - 524288q^{32} - 4553788q^{33} + 2956030q^{35} + 960512q^{36} - 5554884q^{37} - 3932480q^{38} + 1187840q^{40} + 10738708q^{41} + 7018144q^{42} + 4913286q^{43} - 12173390q^{45} - 7308704q^{46} - 5448474q^{47} - 1409024q^{48} - 1827200q^{50} - 1827812q^{51} + 5833728q^{52} + 20290316q^{53} - 9506940q^{55} - 11726848q^{56} - 2593360q^{57} - 4236800q^{58} + 21482240q^{60} - 43572012q^{61} + 37378784q^{62} + 37877126q^{63} + 15450660q^{65} - 72860608q^{66} + 9518486q^{67} - 462848q^{68} + 52077760q^{70} + 20406908q^{71} + 7684096q^{72} - 11608364q^{73} - 21302450q^{75} - 62919680q^{76} - 110066908q^{77} - 60769056q^{78} + 14254080q^{80} + 96218224q^{81} + 85909664q^{82} + 64264686q^{83} - 12424120q^{85} + 78612576q^{86} + 8501600q^{87} + 15085568q^{88} - 79432480q^{90} - 70189812q^{91} - 58469632q^{92} + 16706132q^{93} - 82819000q^{95} - 22544384q^{96} + 34113396q^{97} - 52691072q^{98} + O(q^{100}) \)

Character Values

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

\(n\) \(7\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) −39.7883 39.7883i −0.491213 0.491213i 0.417475 0.908688i \(-0.362915\pi\)
−0.908688 + 0.417475i \(0.862915\pi\)
\(4\) 128.000i 0.500000i
\(5\) −401.365 479.094i −0.642184 0.766551i
\(6\) −636.612 −0.491213
\(7\) 144.447 144.447i 0.0601610 0.0601610i −0.676386 0.736547i \(-0.736455\pi\)
0.736547 + 0.676386i \(0.236455\pi\)
\(8\) −1024.00 1024.00i −0.250000 0.250000i
\(9\) 3394.79i 0.517420i
\(10\) −7043.67 621.836i −0.704367 0.0621836i
\(11\) 13600.3 0.928918 0.464459 0.885595i \(-0.346249\pi\)
0.464459 + 0.885595i \(0.346249\pi\)
\(12\) −5092.90 + 5092.90i −0.245607 + 0.245607i
\(13\) 30883.7 + 30883.7i 1.08132 + 1.08132i 0.996386 + 0.0849366i \(0.0270688\pi\)
0.0849366 + 0.996386i \(0.472931\pi\)
\(14\) 2311.15i 0.0601610i
\(15\) −3092.72 + 35031.9i −0.0610908 + 0.691989i
\(16\) −16384.0 −0.250000
\(17\) 4949.02 4949.02i 0.0592549 0.0592549i −0.676858 0.736113i \(-0.736659\pi\)
0.736113 + 0.676858i \(0.236659\pi\)
\(18\) −27158.3 27158.3i −0.258710 0.258710i
\(19\) 176579.i 1.35495i −0.735546 0.677475i \(-0.763074\pi\)
0.735546 0.677475i \(-0.236926\pi\)
\(20\) −61324.1 + 51374.7i −0.383275 + 0.321092i
\(21\) −11494.6 −0.0591038
\(22\) 108802. 108802.i 0.464459 0.464459i
\(23\) −229482. 229482.i −0.820043 0.820043i 0.166071 0.986114i \(-0.446892\pi\)
−0.986114 + 0.166071i \(0.946892\pi\)
\(24\) 81486.3i 0.245607i
\(25\) −68437.7 + 384583.i −0.175200 + 0.984533i
\(26\) 494139. 1.08132
\(27\) −396123. + 396123.i −0.745376 + 0.745376i
\(28\) −18489.2 18489.2i −0.0300805 0.0300805i
\(29\) 144167.i 0.203833i −0.994793 0.101917i \(-0.967503\pi\)
0.994793 0.101917i \(-0.0324975\pi\)
\(30\) 255514. + 304997.i 0.315449 + 0.376540i
\(31\) 1.50971e6 1.63473 0.817365 0.576120i \(-0.195434\pi\)
0.817365 + 0.576120i \(0.195434\pi\)
\(32\) −131072. + 131072.i −0.125000 + 0.125000i
\(33\) −541132. 541132.i −0.456297 0.456297i
\(34\) 79184.4i 0.0592549i
\(35\) −127179. 11227.8i −0.0847509 0.00748206i
\(36\) −434533. −0.258710
\(37\) −1.60715e6 + 1.60715e6i −0.857532 + 0.857532i −0.991047 0.133515i \(-0.957374\pi\)
0.133515 + 0.991047i \(0.457374\pi\)
\(38\) −1.41263e6 1.41263e6i −0.677475 0.677475i
\(39\) 2.45761e6i 1.06232i
\(40\) −79595.0 + 901590.i −0.0310918 + 0.352184i
\(41\) 3.62276e6 1.28205 0.641023 0.767522i \(-0.278510\pi\)
0.641023 + 0.767522i \(0.278510\pi\)
\(42\) −91956.5 + 91956.5i −0.0295519 + 0.0295519i
\(43\) −575576. 575576.i −0.168356 0.168356i 0.617900 0.786256i \(-0.287983\pi\)
−0.786256 + 0.617900i \(0.787983\pi\)
\(44\) 1.74084e6i 0.464459i
\(45\) −1.62642e6 + 1.36255e6i −0.396628 + 0.332278i
\(46\) −3.67171e6 −0.820043
\(47\) 3.11186e6 3.11186e6i 0.637718 0.637718i −0.312274 0.949992i \(-0.601091\pi\)
0.949992 + 0.312274i \(0.101091\pi\)
\(48\) 651891. + 651891.i 0.122803 + 0.122803i
\(49\) 5.72307e6i 0.992761i
\(50\) 2.52916e6 + 3.62417e6i 0.404666 + 0.579867i
\(51\) −393826. −0.0582135
\(52\) 3.95311e6 3.95311e6i 0.540661 0.540661i
\(53\) 8.16813e6 + 8.16813e6i 1.03519 + 1.03519i 0.999358 + 0.0358294i \(0.0114073\pi\)
0.0358294 + 0.999358i \(0.488593\pi\)
\(54\) 6.33798e6i 0.745376i
\(55\) −5.45868e6 6.51582e6i −0.596536 0.712063i
\(56\) −295827. −0.0300805
\(57\) −7.02575e6 + 7.02575e6i −0.665569 + 0.665569i
\(58\) −1.15334e6 1.15334e6i −0.101917 0.101917i
\(59\) 1.54905e7i 1.27837i −0.769051 0.639187i \(-0.779271\pi\)
0.769051 0.639187i \(-0.220729\pi\)
\(60\) 4.48409e6 + 395868.i 0.345994 + 0.0305454i
\(61\) −1.92688e7 −1.39167 −0.695833 0.718204i \(-0.744965\pi\)
−0.695833 + 0.718204i \(0.744965\pi\)
\(62\) 1.20777e7 1.20777e7i 0.817365 0.817365i
\(63\) −490366. 490366.i −0.0311285 0.0311285i
\(64\) 2.09715e6i 0.125000i
\(65\) 2.40057e6 2.71918e7i 0.134481 1.52330i
\(66\) −8.65811e6 −0.456297
\(67\) −1.00075e7 + 1.00075e7i −0.496624 + 0.496624i −0.910385 0.413761i \(-0.864215\pi\)
0.413761 + 0.910385i \(0.364215\pi\)
\(68\) −633475. 633475.i −0.0296274 0.0296274i
\(69\) 1.82614e7i 0.805632i
\(70\) −1.10726e6 + 927613.i −0.0461165 + 0.0386344i
\(71\) 1.84257e7 0.725087 0.362543 0.931967i \(-0.381908\pi\)
0.362543 + 0.931967i \(0.381908\pi\)
\(72\) −3.47626e6 + 3.47626e6i −0.129355 + 0.129355i
\(73\) 2.45702e7 + 2.45702e7i 0.865203 + 0.865203i 0.991937 0.126734i \(-0.0404494\pi\)
−0.126734 + 0.991937i \(0.540449\pi\)
\(74\) 2.57144e7i 0.857532i
\(75\) 1.80249e7 1.25789e7i 0.569676 0.397555i
\(76\) −2.26020e7 −0.677475
\(77\) 1.96452e6 1.96452e6i 0.0558847 0.0558847i
\(78\) −1.96609e7 1.96609e7i −0.531160 0.531160i
\(79\) 2.17799e7i 0.559176i 0.960120 + 0.279588i \(0.0901978\pi\)
−0.960120 + 0.279588i \(0.909802\pi\)
\(80\) 6.57596e6 + 7.84948e6i 0.160546 + 0.191638i
\(81\) 9.24891e6 0.214857
\(82\) 2.89820e7 2.89820e7i 0.641023 0.641023i
\(83\) 4.00189e6 + 4.00189e6i 0.0843242 + 0.0843242i 0.748011 0.663687i \(-0.231009\pi\)
−0.663687 + 0.748011i \(0.731009\pi\)
\(84\) 1.47130e6i 0.0295519i
\(85\) −4.35741e6 384685.i −0.0834744 0.00736936i
\(86\) −9.20921e6 −0.168356
\(87\) −5.73617e6 + 5.73617e6i −0.100126 + 0.100126i
\(88\) −1.39267e7 1.39267e7i −0.232229 0.232229i
\(89\) 6.14525e7i 0.979444i −0.871879 0.489722i \(-0.837098\pi\)
0.871879 0.489722i \(-0.162902\pi\)
\(90\) −2.11100e6 + 2.39118e7i −0.0321750 + 0.364453i
\(91\) 8.92209e6 0.130107
\(92\) −2.93737e7 + 2.93737e7i −0.410022 + 0.410022i
\(93\) −6.00686e7 6.00686e7i −0.803001 0.803001i
\(94\) 4.97898e7i 0.637718i
\(95\) −8.45978e7 + 7.08724e7i −1.03864 + 0.870127i
\(96\) 1.04303e7 0.122803
\(97\) 1.55814e7 1.55814e7i 0.176003 0.176003i −0.613608 0.789611i \(-0.710282\pi\)
0.789611 + 0.613608i \(0.210282\pi\)
\(98\) 4.57846e7 + 4.57846e7i 0.496381 + 0.496381i
\(99\) 4.61701e7i 0.480640i
\(100\) 4.92266e7 + 8.76002e6i 0.492266 + 0.0876002i
\(101\) 3.55113e7 0.341257 0.170629 0.985335i \(-0.445420\pi\)
0.170629 + 0.985335i \(0.445420\pi\)
\(102\) −3.15061e6 + 3.15061e6i −0.0291068 + 0.0291068i
\(103\) 2.91511e7 + 2.91511e7i 0.259004 + 0.259004i 0.824649 0.565645i \(-0.191373\pi\)
−0.565645 + 0.824649i \(0.691373\pi\)
\(104\) 6.32497e7i 0.540661i
\(105\) 4.61351e6 + 5.50698e6i 0.0379555 + 0.0453061i
\(106\) 1.30690e8 1.03519
\(107\) −9.89754e7 + 9.89754e7i −0.755079 + 0.755079i −0.975422 0.220344i \(-0.929282\pi\)
0.220344 + 0.975422i \(0.429282\pi\)
\(108\) 5.07038e7 + 5.07038e7i 0.372688 + 0.372688i
\(109\) 3.08220e7i 0.218351i 0.994022 + 0.109176i \(0.0348211\pi\)
−0.994022 + 0.109176i \(0.965179\pi\)
\(110\) −9.57960e7 8.45715e6i −0.654299 0.0577635i
\(111\) 1.27892e8 0.842461
\(112\) −2.36661e6 + 2.36661e6i −0.0150403 + 0.0150403i
\(113\) −6.07746e7 6.07746e7i −0.372742 0.372742i 0.495733 0.868475i \(-0.334900\pi\)
−0.868475 + 0.495733i \(0.834900\pi\)
\(114\) 1.12412e8i 0.665569i
\(115\) −1.78375e7 + 2.02049e8i −0.101987 + 1.15522i
\(116\) −1.84534e7 −0.101917
\(117\) 1.04844e8 1.04844e8i 0.559498 0.559498i
\(118\) −1.23924e8 1.23924e8i −0.639187 0.639187i
\(119\) 1.42974e6i 0.00712967i
\(120\) 3.90396e7 3.27057e7i 0.188270 0.157724i
\(121\) −2.93911e7 −0.137111
\(122\) −1.54150e8 + 1.54150e8i −0.695833 + 0.695833i
\(123\) −1.44143e8 1.44143e8i −0.629758 0.629758i
\(124\) 1.93243e8i 0.817365i
\(125\) 2.11720e8 1.21570e8i 0.867205 0.497951i
\(126\) −7.84586e6 −0.0311285
\(127\) 1.95509e8 1.95509e8i 0.751539 0.751539i −0.223228 0.974766i \(-0.571659\pi\)
0.974766 + 0.223228i \(0.0716593\pi\)
\(128\) 1.67772e7 + 1.67772e7i 0.0625000 + 0.0625000i
\(129\) 4.58023e7i 0.165397i
\(130\) −1.98330e8 2.36739e8i −0.694408 0.828889i
\(131\) −3.40141e8 −1.15498 −0.577489 0.816399i \(-0.695967\pi\)
−0.577489 + 0.816399i \(0.695967\pi\)
\(132\) −6.92649e7 + 6.92649e7i −0.228148 + 0.228148i
\(133\) −2.55062e7 2.55062e7i −0.0815152 0.0815152i
\(134\) 1.60121e8i 0.496624i
\(135\) 3.48771e8 + 3.07905e7i 1.05004 + 0.0927004i
\(136\) −1.01356e7 −0.0296274
\(137\) −9.80014e7 + 9.80014e7i −0.278196 + 0.278196i −0.832388 0.554193i \(-0.813027\pi\)
0.554193 + 0.832388i \(0.313027\pi\)
\(138\) 1.46091e8 + 1.46091e8i 0.402816 + 0.402816i
\(139\) 3.51491e8i 0.941576i 0.882246 + 0.470788i \(0.156030\pi\)
−0.882246 + 0.470788i \(0.843970\pi\)
\(140\) −1.43715e6 + 1.62790e7i −0.00374103 + 0.0423755i
\(141\) −2.47631e8 −0.626511
\(142\) 1.47405e8 1.47405e8i 0.362543 0.362543i
\(143\) 4.20027e8 + 4.20027e8i 1.00446 + 1.00446i
\(144\) 5.56202e7i 0.129355i
\(145\) −6.90698e7 + 5.78637e7i −0.156249 + 0.130898i
\(146\) 3.93124e8 0.865203
\(147\) 2.27711e8 2.27711e8i 0.487657 0.487657i
\(148\) 2.05715e8 + 2.05715e8i 0.428766 + 0.428766i
\(149\) 1.71452e8i 0.347855i 0.984758 + 0.173927i \(0.0556458\pi\)
−0.984758 + 0.173927i \(0.944354\pi\)
\(150\) 4.35682e7 2.44830e8i 0.0860607 0.483615i
\(151\) −4.23728e8 −0.815042 −0.407521 0.913196i \(-0.633607\pi\)
−0.407521 + 0.913196i \(0.633607\pi\)
\(152\) −1.80816e8 + 1.80816e8i −0.338738 + 0.338738i
\(153\) −1.68009e7 1.68009e7i −0.0306596 0.0306596i
\(154\) 3.14323e7i 0.0558847i
\(155\) −6.05943e8 7.23292e8i −1.04980 1.25310i
\(156\) −3.14575e8 −0.531160
\(157\) 4.05135e6 4.05135e6i 0.00666808 0.00666808i −0.703765 0.710433i \(-0.748499\pi\)
0.710433 + 0.703765i \(0.248499\pi\)
\(158\) 1.74240e8 + 1.74240e8i 0.279588 + 0.279588i
\(159\) 6.49991e8i 1.01699i
\(160\) 1.15404e8 + 1.01882e7i 0.176092 + 0.0155459i
\(161\) −6.62957e7 −0.0986693
\(162\) 7.39913e7 7.39913e7i 0.107429 0.107429i
\(163\) −1.89503e8 1.89503e8i −0.268451 0.268451i 0.560025 0.828476i \(-0.310792\pi\)
−0.828476 + 0.560025i \(0.810792\pi\)
\(164\) 4.63713e8i 0.641023i
\(165\) −4.20619e7 + 4.76444e8i −0.0567483 + 0.642801i
\(166\) 6.40302e7 0.0843242
\(167\) 5.58235e8 5.58235e8i 0.717714 0.717714i −0.250423 0.968137i \(-0.580570\pi\)
0.968137 + 0.250423i \(0.0805696\pi\)
\(168\) 1.17704e7 + 1.17704e7i 0.0147759 + 0.0147759i
\(169\) 1.09187e9i 1.33852i
\(170\) −3.79368e7 + 3.17818e7i −0.0454219 + 0.0380525i
\(171\) −5.99447e8 −0.701078
\(172\) −7.36737e7 + 7.36737e7i −0.0841780 + 0.0841780i
\(173\) −1.00283e8 1.00283e8i −0.111955 0.111955i 0.648910 0.760865i \(-0.275225\pi\)
−0.760865 + 0.648910i \(0.775225\pi\)
\(174\) 9.17787e7i 0.100126i
\(175\) 4.56662e7 + 6.54373e7i 0.0486903 + 0.0697708i
\(176\) −2.22827e8 −0.232229
\(177\) −6.16341e8 + 6.16341e8i −0.627954 + 0.627954i
\(178\) −4.91620e8 4.91620e8i −0.489722 0.489722i
\(179\) 8.62971e8i 0.840590i −0.907388 0.420295i \(-0.861927\pi\)
0.907388 0.420295i \(-0.138073\pi\)
\(180\) 1.74406e8 + 2.08182e8i 0.166139 + 0.198314i
\(181\) 1.76106e9 1.64081 0.820407 0.571780i \(-0.193747\pi\)
0.820407 + 0.571780i \(0.193747\pi\)
\(182\) 7.13767e7 7.13767e7i 0.0650535 0.0650535i
\(183\) 7.66671e8 + 7.66671e8i 0.683604 + 0.683604i
\(184\) 4.69979e8i 0.410022i
\(185\) 1.41503e9 + 1.24923e8i 1.20803 + 0.106649i
\(186\) −9.61098e8 −0.803001
\(187\) 6.73082e7 6.73082e7i 0.0550429 0.0550429i
\(188\) −3.98318e8 3.98318e8i −0.318859 0.318859i
\(189\) 1.14437e8i 0.0896852i
\(190\) −1.09803e8 + 1.24376e9i −0.0842557 + 0.954383i
\(191\) 2.10501e9 1.58169 0.790843 0.612019i \(-0.209642\pi\)
0.790843 + 0.612019i \(0.209642\pi\)
\(192\) 8.34420e7 8.34420e7i 0.0614016 0.0614016i
\(193\) −1.38679e9 1.38679e9i −0.999496 0.999496i 0.000504122 1.00000i \(-0.499840\pi\)
−1.00000 0.000504122i \(0.999840\pi\)
\(194\) 2.49302e8i 0.176003i
\(195\) −1.17743e9 + 9.86400e8i −0.814322 + 0.682204i
\(196\) 7.32553e8 0.496381
\(197\) −1.65638e9 + 1.65638e9i −1.09976 + 1.09976i −0.105317 + 0.994439i \(0.533586\pi\)
−0.994439 + 0.105317i \(0.966414\pi\)
\(198\) −3.69361e8 3.69361e8i −0.240320 0.240320i
\(199\) 2.74335e8i 0.174932i −0.996168 0.0874659i \(-0.972123\pi\)
0.996168 0.0874659i \(-0.0278769\pi\)
\(200\) 4.63893e8 3.23733e8i 0.289933 0.202333i
\(201\) 7.96364e8 0.487896
\(202\) 2.84091e8 2.84091e8i 0.170629 0.170629i
\(203\) −2.08245e7 2.08245e7i −0.0122628 0.0122628i
\(204\) 5.04097e7i 0.0291068i
\(205\) −1.45405e9 1.73564e9i −0.823309 0.982753i
\(206\) 4.66417e8 0.259004
\(207\) −7.79042e8 + 7.79042e8i −0.424306 + 0.424306i
\(208\) −5.05998e8 5.05998e8i −0.270331 0.270331i
\(209\) 2.40152e9i 1.25864i
\(210\) 8.09639e7 + 7.14773e6i 0.0416308 + 0.00367529i
\(211\) −1.58670e9 −0.800506 −0.400253 0.916405i \(-0.631078\pi\)
−0.400253 + 0.916405i \(0.631078\pi\)
\(212\) 1.04552e9 1.04552e9i 0.517594 0.517594i
\(213\) −7.33125e8 7.33125e8i −0.356172 0.356172i
\(214\) 1.58361e9i 0.755079i
\(215\) −4.47392e7 + 5.06771e8i −0.0209380 + 0.237169i
\(216\) 8.11261e8 0.372688
\(217\) 2.18072e8 2.18072e8i 0.0983471 0.0983471i
\(218\) 2.46576e8 + 2.46576e8i 0.109176 + 0.109176i
\(219\) 1.95521e9i 0.849998i
\(220\) −8.34025e8 + 6.98711e8i −0.356031 + 0.298268i
\(221\) 3.05688e8 0.128147
\(222\) 1.02313e9 1.02313e9i 0.421231 0.421231i
\(223\) 2.50984e9 + 2.50984e9i 1.01491 + 1.01491i 0.999887 + 0.0150215i \(0.00478167\pi\)
0.0150215 + 0.999887i \(0.495218\pi\)
\(224\) 3.78658e7i 0.0150403i
\(225\) 1.30558e9 + 2.32331e8i 0.509417 + 0.0906521i
\(226\) −9.72394e8 −0.372742
\(227\) −1.53379e9 + 1.53379e9i −0.577645 + 0.577645i −0.934254 0.356609i \(-0.883933\pi\)
0.356609 + 0.934254i \(0.383933\pi\)
\(228\) 8.99296e8 + 8.99296e8i 0.332785 + 0.332785i
\(229\) 1.85362e9i 0.674031i 0.941499 + 0.337015i \(0.109417\pi\)
−0.941499 + 0.337015i \(0.890583\pi\)
\(230\) 1.47369e9 + 1.75909e9i 0.526618 + 0.628605i
\(231\) −1.56329e8 −0.0549026
\(232\) −1.47627e8 + 1.47627e8i −0.0509583 + 0.0509583i
\(233\) 7.16513e8 + 7.16513e8i 0.243109 + 0.243109i 0.818135 0.575026i \(-0.195008\pi\)
−0.575026 + 0.818135i \(0.695008\pi\)
\(234\) 1.67750e9i 0.559498i
\(235\) −2.73987e9 2.41884e8i −0.898376 0.0793113i
\(236\) −1.98279e9 −0.639187
\(237\) 8.66586e8 8.66586e8i 0.274674 0.274674i
\(238\) −1.14379e7 1.14379e7i −0.00356483 0.00356483i
\(239\) 3.15340e9i 0.966467i 0.875492 + 0.483233i \(0.160538\pi\)
−0.875492 + 0.483233i \(0.839462\pi\)
\(240\) 5.06712e7 5.73963e8i 0.0152727 0.172997i
\(241\) 1.08337e9 0.321152 0.160576 0.987023i \(-0.448665\pi\)
0.160576 + 0.987023i \(0.448665\pi\)
\(242\) −2.35128e8 + 2.35128e8i −0.0685557 + 0.0685557i
\(243\) 2.23097e9 + 2.23097e9i 0.639835 + 0.639835i
\(244\) 2.46640e9i 0.695833i
\(245\) 2.74189e9 2.29704e9i 0.761002 0.637535i
\(246\) −2.30629e9 −0.629758
\(247\) 5.45339e9 5.45339e9i 1.46514 1.46514i
\(248\) −1.54594e9 1.54594e9i −0.408683 0.408683i
\(249\) 3.18456e8i 0.0828423i
\(250\) 7.21200e8 2.66632e9i 0.184627 0.682578i
\(251\) −6.99442e9 −1.76221 −0.881103 0.472925i \(-0.843198\pi\)
−0.881103 + 0.472925i \(0.843198\pi\)
\(252\) −6.27669e7 + 6.27669e7i −0.0155643 + 0.0155643i
\(253\) −3.12102e9 3.12102e9i −0.761753 0.761753i
\(254\) 3.12814e9i 0.751539i
\(255\) 1.58068e8 + 1.88680e8i 0.0373838 + 0.0446236i
\(256\) 2.68435e8 0.0625000
\(257\) −2.42952e8 + 2.42952e8i −0.0556914 + 0.0556914i −0.734404 0.678713i \(-0.762538\pi\)
0.678713 + 0.734404i \(0.262538\pi\)
\(258\) 3.66418e8 + 3.66418e8i 0.0826987 + 0.0826987i
\(259\) 4.64296e8i 0.103180i
\(260\) −3.48055e9 3.07273e8i −0.761648 0.0672406i
\(261\) −4.89418e8 −0.105467
\(262\) −2.72113e9 + 2.72113e9i −0.577489 + 0.577489i
\(263\) 1.31782e9 + 1.31782e9i 0.275445 + 0.275445i 0.831287 0.555843i \(-0.187604\pi\)
−0.555843 + 0.831287i \(0.687604\pi\)
\(264\) 1.10824e9i 0.228148i
\(265\) 6.34905e8 7.19170e9i 0.128743 1.45830i
\(266\) −4.08099e8 −0.0815152
\(267\) −2.44509e9 + 2.44509e9i −0.481115 + 0.481115i
\(268\) 1.28096e9 + 1.28096e9i 0.248312 + 0.248312i
\(269\) 8.21589e9i 1.56908i 0.620077 + 0.784541i \(0.287101\pi\)
−0.620077 + 0.784541i \(0.712899\pi\)
\(270\) 3.03649e9 2.54384e9i 0.571369 0.478668i
\(271\) 7.16847e9 1.32908 0.664538 0.747255i \(-0.268629\pi\)
0.664538 + 0.747255i \(0.268629\pi\)
\(272\) −8.10848e7 + 8.10848e7i −0.0148137 + 0.0148137i
\(273\) −3.54994e8 3.54994e8i −0.0639103 0.0639103i
\(274\) 1.56802e9i 0.278196i
\(275\) −9.30772e8 + 5.23044e9i −0.162747 + 0.914550i
\(276\) 2.33745e9 0.402816
\(277\) 1.02569e9 1.02569e9i 0.174219 0.174219i −0.614611 0.788830i \(-0.710687\pi\)
0.788830 + 0.614611i \(0.210687\pi\)
\(278\) 2.81193e9 + 2.81193e9i 0.470788 + 0.470788i
\(279\) 5.12514e9i 0.845841i
\(280\) 1.18734e8 + 1.41729e8i 0.0193172 + 0.0230583i
\(281\) −6.99805e9 −1.12241 −0.561205 0.827677i \(-0.689662\pi\)
−0.561205 + 0.827677i \(0.689662\pi\)
\(282\) −1.98105e9 + 1.98105e9i −0.313256 + 0.313256i
\(283\) −5.65931e8 5.65931e8i −0.0882302 0.0882302i 0.661614 0.749844i \(-0.269872\pi\)
−0.749844 + 0.661614i \(0.769872\pi\)
\(284\) 2.35849e9i 0.362543i
\(285\) 6.18589e9 + 5.46108e8i 0.937610 + 0.0827750i
\(286\) 6.72043e9 1.00446
\(287\) 5.23295e8 5.23295e8i 0.0771292 0.0771292i
\(288\) 4.44962e8 + 4.44962e8i 0.0646774 + 0.0646774i
\(289\) 6.92677e9i 0.992978i
\(290\) −8.96485e7 + 1.01547e9i −0.0126751 + 0.143573i
\(291\) −1.23991e9 −0.172910
\(292\) 3.14499e9 3.14499e9i 0.432602 0.432602i
\(293\) −4.98809e9 4.98809e9i −0.676805 0.676805i 0.282471 0.959276i \(-0.408846\pi\)
−0.959276 + 0.282471i \(0.908846\pi\)
\(294\) 3.64338e9i 0.487657i
\(295\) −7.42142e9 + 6.21735e9i −0.979939 + 0.820951i
\(296\) 3.29145e9 0.428766
\(297\) −5.38739e9 + 5.38739e9i −0.692393 + 0.692393i
\(298\) 1.37162e9 + 1.37162e9i 0.173927 + 0.173927i
\(299\) 1.41745e10i 1.77346i
\(300\) −1.61010e9 2.30719e9i −0.198777 0.284838i
\(301\) −1.66280e8 −0.0202569
\(302\) −3.38983e9 + 3.38983e9i −0.407521 + 0.407521i
\(303\) −1.41293e9 1.41293e9i −0.167630 0.167630i
\(304\) 2.89306e9i 0.338738i
\(305\) 7.73381e9 + 9.23156e9i 0.893705 + 1.06678i
\(306\) −2.68814e8 −0.0306596
\(307\) 1.00289e10 1.00289e10i 1.12901 1.12901i 0.138672 0.990338i \(-0.455717\pi\)
0.990338 0.138672i \(-0.0442833\pi\)
\(308\) −2.51458e8 2.51458e8i −0.0279423 0.0279423i
\(309\) 2.31974e9i 0.254452i
\(310\) −1.06339e10 9.38791e8i −1.15145 0.101653i
\(311\) −6.55125e9 −0.700298 −0.350149 0.936694i \(-0.613869\pi\)
−0.350149 + 0.936694i \(0.613869\pi\)
\(312\) −2.51660e9 + 2.51660e9i −0.265580 + 0.265580i
\(313\) −2.50993e9 2.50993e9i −0.261508 0.261508i 0.564159 0.825666i \(-0.309201\pi\)
−0.825666 + 0.564159i \(0.809201\pi\)
\(314\) 6.48215e7i 0.00666808i
\(315\) −3.81159e7 + 4.31747e8i −0.00387137 + 0.0438518i
\(316\) 2.78783e9 0.279588
\(317\) 4.00611e9 4.00611e9i 0.396721 0.396721i −0.480354 0.877075i \(-0.659492\pi\)
0.877075 + 0.480354i \(0.159492\pi\)
\(318\) −5.19993e9 5.19993e9i −0.508497 0.508497i
\(319\) 1.96072e9i 0.189344i
\(320\) 1.00473e9 8.41723e8i 0.0958189 0.0802730i
\(321\) 7.87612e9 0.741809
\(322\) −5.30366e8 + 5.30366e8i −0.0493347 + 0.0493347i
\(323\) −8.73891e8 8.73891e8i −0.0802874 0.0802874i
\(324\) 1.18386e9i 0.107429i
\(325\) −1.39909e10 + 9.76373e9i −1.25405 + 0.875150i
\(326\) −3.03204e9 −0.268451
\(327\) 1.22636e9 1.22636e9i 0.107257 0.107257i
\(328\) −3.70970e9 3.70970e9i −0.320511 0.320511i
\(329\) 8.98996e8i 0.0767316i
\(330\) 3.47506e9 + 4.14805e9i 0.293026 + 0.349775i
\(331\) 1.60673e10 1.33854 0.669271 0.743018i \(-0.266606\pi\)
0.669271 + 0.743018i \(0.266606\pi\)
\(332\) 5.12241e8 5.12241e8i 0.0421621 0.0421621i
\(333\) 5.45594e9 + 5.45594e9i 0.443704 + 0.443704i
\(334\) 8.93176e9i 0.717714i
\(335\) 8.81122e9 + 7.77881e8i 0.699611 + 0.0617638i
\(336\) 1.88327e8 0.0147759
\(337\) −1.41455e10 + 1.41455e10i −1.09673 + 1.09673i −0.101938 + 0.994791i \(0.532504\pi\)
−0.994791 + 0.101938i \(0.967496\pi\)
\(338\) 8.73497e9 + 8.73497e9i 0.669259 + 0.669259i
\(339\) 4.83623e9i 0.366192i
\(340\) −4.92397e7 + 5.57749e8i −0.00368468 + 0.0417372i
\(341\) 2.05325e10 1.51853
\(342\) −4.79558e9 + 4.79558e9i −0.350539 + 0.350539i
\(343\) 1.65939e9 + 1.65939e9i 0.119887 + 0.119887i
\(344\) 1.17878e9i 0.0841780i
\(345\) 8.74891e9 7.32946e9i 0.617558 0.517364i
\(346\) −1.60453e9 −0.111955
\(347\) 6.70725e8 6.70725e8i 0.0462622 0.0462622i −0.683597 0.729859i \(-0.739585\pi\)
0.729859 + 0.683597i \(0.239585\pi\)
\(348\) 7.34229e8 + 7.34229e8i 0.0500628 + 0.0500628i
\(349\) 1.51291e10i 1.01979i 0.860236 + 0.509896i \(0.170316\pi\)
−0.860236 + 0.509896i \(0.829684\pi\)
\(350\) 8.88828e8 + 1.58169e8i 0.0592305 + 0.0105402i
\(351\) −2.44675e10 −1.61198
\(352\) −1.78262e9 + 1.78262e9i −0.116115 + 0.116115i
\(353\) −3.57220e9 3.57220e9i −0.230058 0.230058i 0.582659 0.812717i \(-0.302012\pi\)
−0.812717 + 0.582659i \(0.802012\pi\)
\(354\) 9.86145e9i 0.627954i
\(355\) −7.39541e9 8.82763e9i −0.465639 0.555816i
\(356\) −7.86592e9 −0.489722
\(357\) −5.68869e7 + 5.68869e7i −0.00350219 + 0.00350219i
\(358\) −6.90377e9 6.90377e9i −0.420295 0.420295i
\(359\) 1.30385e10i 0.784963i −0.919760 0.392482i \(-0.871617\pi\)
0.919760 0.392482i \(-0.128383\pi\)
\(360\) 3.06071e9 + 2.70208e8i 0.182227 + 0.0160875i
\(361\) −1.41964e10 −0.835891
\(362\) 1.40885e10 1.40885e10i 0.820407 0.820407i
\(363\) 1.16942e9 + 1.16942e9i 0.0673509 + 0.0673509i
\(364\) 1.14203e9i 0.0650535i
\(365\) 1.90983e9 2.16331e10i 0.107603 1.21884i
\(366\) 1.22667e10 0.683604
\(367\) −2.24627e9 + 2.24627e9i −0.123822 + 0.123822i −0.766302 0.642480i \(-0.777906\pi\)
0.642480 + 0.766302i \(0.277906\pi\)
\(368\) 3.75983e9 + 3.75983e9i 0.205011 + 0.205011i
\(369\) 1.22985e10i 0.663356i
\(370\) 1.23196e10 1.03209e10i 0.657342 0.550693i
\(371\) 2.35972e9 0.124556
\(372\) −7.68879e9 + 7.68879e9i −0.401500 + 0.401500i
\(373\) −1.21704e10 1.21704e10i −0.628736 0.628736i 0.319014 0.947750i \(-0.396648\pi\)
−0.947750 + 0.319014i \(0.896648\pi\)
\(374\) 1.07693e9i 0.0550429i
\(375\) −1.32610e10 3.58691e9i −0.670582 0.181383i
\(376\) −6.37309e9 −0.318859
\(377\) 4.45242e9 4.45242e9i 0.220410 0.220410i
\(378\) 9.15500e8 + 9.15500e8i 0.0448426 + 0.0448426i
\(379\) 3.40471e10i 1.65015i 0.565024 + 0.825075i \(0.308867\pi\)
−0.565024 + 0.825075i \(0.691133\pi\)
\(380\) 9.07167e9 + 1.08285e10i 0.435064 + 0.519319i
\(381\) −1.55579e10 −0.738331
\(382\) 1.68401e10 1.68401e10i 0.790843 0.790843i
\(383\) 7.51136e9 + 7.51136e9i 0.349079 + 0.349079i 0.859766 0.510687i \(-0.170609\pi\)
−0.510687 + 0.859766i \(0.670609\pi\)
\(384\) 1.33507e9i 0.0614016i
\(385\) −1.72968e9 1.52701e8i −0.0787267 0.00695022i
\(386\) −2.21886e10 −0.999496
\(387\) −1.95396e9 + 1.95396e9i −0.0871107 + 0.0871107i
\(388\) −1.99442e9 1.99442e9i −0.0880014 0.0880014i
\(389\) 9.40651e9i 0.410800i 0.978678 + 0.205400i \(0.0658495\pi\)
−0.978678 + 0.205400i \(0.934150\pi\)
\(390\) −1.52823e9 + 1.73106e10i −0.0660589 + 0.748263i
\(391\) −2.27142e9 −0.0971831
\(392\) 5.86043e9 5.86043e9i 0.248190 0.248190i
\(393\) 1.35336e10 + 1.35336e10i 0.567340 + 0.567340i
\(394\) 2.65021e10i 1.09976i
\(395\) 1.04346e10 8.74170e9i 0.428637 0.359093i
\(396\) −5.90977e9 −0.240320
\(397\) 9.53889e9 9.53889e9i 0.384004 0.384004i −0.488538 0.872542i \(-0.662470\pi\)
0.872542 + 0.488538i \(0.162470\pi\)
\(398\) −2.19468e9 2.19468e9i −0.0874659 0.0874659i
\(399\) 2.02969e9i 0.0800827i
\(400\) 1.12128e9 6.30101e9i 0.0438001 0.246133i
\(401\) 1.29102e10 0.499293 0.249646 0.968337i \(-0.419686\pi\)
0.249646 + 0.968337i \(0.419686\pi\)
\(402\) 6.37092e9 6.37092e9i 0.243948 0.243948i
\(403\) 4.66253e10 + 4.66253e10i 1.76767 + 1.76767i
\(404\) 4.54545e9i 0.170629i
\(405\) −3.71219e9 4.43110e9i −0.137978 0.164699i
\(406\) −3.33192e8 −0.0122628
\(407\) −2.18577e10 + 2.18577e10i −0.796577 + 0.796577i
\(408\) 4.03278e8 + 4.03278e8i 0.0145534 + 0.0145534i
\(409\) 3.89504e10i 1.39194i −0.718073 0.695968i \(-0.754976\pi\)
0.718073 0.695968i \(-0.245024\pi\)
\(410\) −2.55175e10 2.25276e9i −0.903031 0.0797222i
\(411\) 7.79861e9 0.273307
\(412\) 3.73134e9 3.73134e9i 0.129502 0.129502i
\(413\) −2.23755e9 2.23755e9i −0.0769083 0.0769083i
\(414\) 1.24647e10i 0.424306i
\(415\) 3.11065e8 3.52350e9i 0.0104872 0.118790i
\(416\) −8.09597e9 −0.270331
\(417\) 1.39852e10 1.39852e10i 0.462514 0.462514i
\(418\) −1.92121e10 1.92121e10i −0.629319 0.629319i
\(419\) 6.53853e9i 0.212141i −0.994359 0.106070i \(-0.966173\pi\)
0.994359 0.106070i \(-0.0338269\pi\)
\(420\) 7.04893e8 5.90530e8i 0.0226530 0.0189777i
\(421\) 1.36111e10 0.433277 0.216638 0.976252i \(-0.430491\pi\)
0.216638 + 0.976252i \(0.430491\pi\)
\(422\) −1.26936e10 + 1.26936e10i −0.400253 + 0.400253i
\(423\) −1.05641e10 1.05641e10i −0.329968 0.329968i
\(424\) 1.67283e10i 0.517594i
\(425\) 1.56461e9 + 2.24201e9i 0.0479569 + 0.0687198i
\(426\) −1.17300e10 −0.356172
\(427\) −2.78331e9 + 2.78331e9i −0.0837241 + 0.0837241i
\(428\) 1.26689e10 + 1.26689e10i 0.377539 + 0.377539i
\(429\) 3.34243e10i 0.986808i
\(430\) 3.69625e9 + 4.41208e9i 0.108115 + 0.129053i
\(431\) −2.81277e10 −0.815126 −0.407563 0.913177i \(-0.633621\pi\)
−0.407563 + 0.913177i \(0.633621\pi\)
\(432\) 6.49009e9 6.49009e9i 0.186344 0.186344i
\(433\) −2.09524e9 2.09524e9i −0.0596051 0.0596051i 0.676676 0.736281i \(-0.263420\pi\)
−0.736281 + 0.676676i \(0.763420\pi\)
\(434\) 3.48916e9i 0.0983471i
\(435\) 5.05046e9 + 4.45869e8i 0.141050 + 0.0124523i
\(436\) 3.94522e9 0.109176
\(437\) −4.05215e10 + 4.05215e10i −1.11112 + 1.11112i
\(438\) −1.56417e10 1.56417e10i −0.424999 0.424999i
\(439\) 1.07942e10i 0.290623i 0.989386 + 0.145312i \(0.0464185\pi\)
−0.989386 + 0.145312i \(0.953581\pi\)
\(440\) −1.08252e9 + 1.22619e10i −0.0288817 + 0.327150i
\(441\) 1.94286e10 0.513674
\(442\) 2.44550e9 2.44550e9i 0.0640736 0.0640736i
\(443\) −3.89099e10 3.89099e10i −1.01029 1.01029i −0.999947 0.0103426i \(-0.996708\pi\)
−0.0103426 0.999947i \(-0.503292\pi\)
\(444\) 1.63701e10i 0.421231i
\(445\) −2.94415e10 + 2.46649e10i −0.750793 + 0.628983i
\(446\) 4.01575e10 1.01491
\(447\) 6.82178e9 6.82178e9i 0.170871 0.170871i
\(448\) 3.02927e8 + 3.02927e8i 0.00752013 + 0.00752013i
\(449\) 4.43789e9i 0.109192i 0.998509 + 0.0545961i \(0.0173871\pi\)
−0.998509 + 0.0545961i \(0.982613\pi\)
\(450\) 1.23033e10 8.58598e9i 0.300034 0.209382i
\(451\) 4.92705e10 1.19092
\(452\) −7.77915e9 + 7.77915e9i −0.186371 + 0.186371i
\(453\) 1.68594e10 + 1.68594e10i 0.400359 + 0.400359i
\(454\) 2.45406e10i 0.577645i
\(455\) −3.58101e9 4.27452e9i −0.0835526 0.0997337i
\(456\) 1.43887e10 0.332785
\(457\) 1.68505e10 1.68505e10i 0.386321 0.386321i −0.487052 0.873373i \(-0.661928\pi\)
0.873373 + 0.487052i \(0.161928\pi\)
\(458\) 1.48290e10 + 1.48290e10i 0.337015 + 0.337015i
\(459\) 3.92085e9i 0.0883343i
\(460\) 2.58623e10 + 2.28320e9i 0.577612 + 0.0509933i
\(461\) 3.57328e10 0.791158 0.395579 0.918432i \(-0.370544\pi\)
0.395579 + 0.918432i \(0.370544\pi\)
\(462\) −1.25063e9 + 1.25063e9i −0.0274513 + 0.0274513i
\(463\) −6.28237e10 6.28237e10i −1.36710 1.36710i −0.864550 0.502547i \(-0.832397\pi\)
−0.502547 0.864550i \(-0.667603\pi\)
\(464\) 2.36204e9i 0.0509583i
\(465\) −4.66911e9 + 5.28880e10i −0.0998670 + 1.13121i
\(466\) 1.14642e10 0.243109
\(467\) −2.40702e10 + 2.40702e10i −0.506071 + 0.506071i −0.913318 0.407247i \(-0.866489\pi\)
0.407247 + 0.913318i \(0.366489\pi\)
\(468\) −1.34200e10 1.34200e10i −0.279749 0.279749i
\(469\) 2.89111e9i 0.0597548i
\(470\) −2.38540e10 + 1.99839e10i −0.488844 + 0.409532i
\(471\) −3.22392e8 −0.00655089
\(472\) −1.58623e10 + 1.58623e10i −0.319594 + 0.319594i
\(473\) −7.82799e9 7.82799e9i −0.156389 0.156389i
\(474\) 1.38654e10i 0.274674i
\(475\) 6.79091e10 + 1.20846e10i 1.33399 + 0.237388i
\(476\) −1.83007e8 −0.00356483
\(477\) 2.77291e10 2.77291e10i 0.535626 0.535626i
\(478\) 2.52272e10 + 2.52272e10i 0.483233 + 0.483233i
\(479\) 6.79331e10i 1.29044i 0.763995 + 0.645222i \(0.223235\pi\)
−0.763995 + 0.645222i \(0.776765\pi\)
\(480\) −4.18634e9 4.99707e9i −0.0788622 0.0941349i
\(481\) −9.92695e10 −1.85454
\(482\) 8.66700e9 8.66700e9i 0.160576 0.160576i
\(483\) 2.63779e9 + 2.63779e9i 0.0484677 + 0.0484677i
\(484\) 3.76206e9i 0.0685557i
\(485\) −1.37188e10 1.21113e9i −0.247941 0.0218890i
\(486\) 3.56955e10 0.639835
\(487\) 9.43406e9 9.43406e9i 0.167719 0.167719i −0.618257 0.785976i \(-0.712161\pi\)
0.785976 + 0.618257i \(0.212161\pi\)
\(488\) 1.97312e10 + 1.97312e10i 0.347916 + 0.347916i
\(489\) 1.50800e10i 0.263733i
\(490\) 3.55881e9 4.03114e10i 0.0617335 0.699269i
\(491\) 5.75323e10 0.989887 0.494943 0.868925i \(-0.335189\pi\)
0.494943 + 0.868925i \(0.335189\pi\)
\(492\) −1.84503e10 + 1.84503e10i −0.314879 + 0.314879i
\(493\) −7.13488e8 7.13488e8i −0.0120781 0.0120781i
\(494\) 8.72543e10i 1.46514i
\(495\) −2.21198e10 + 1.85311e10i −0.368435 + 0.308659i
\(496\) −2.47351e10 −0.408683
\(497\) 2.66153e9 2.66153e9i 0.0436220 0.0436220i
\(498\) −2.54765e9 2.54765e9i −0.0414211 0.0414211i
\(499\) 1.11776e11i 1.80280i −0.432988 0.901400i \(-0.642541\pi\)
0.432988 0.901400i \(-0.357459\pi\)
\(500\) −1.55610e10 2.71002e10i −0.248975 0.433603i
\(501\) −4.44224e10 −0.705101
\(502\) −5.59553e10 + 5.59553e10i −0.881103 + 0.881103i
\(503\) −4.45397e10 4.45397e10i −0.695785 0.695785i 0.267714 0.963499i \(-0.413732\pi\)
−0.963499 + 0.267714i \(0.913732\pi\)
\(504\) 1.00427e9i 0.0155643i
\(505\) −1.42530e10 1.70133e10i −0.219150 0.261591i
\(506\) −4.99363e10 −0.761753
\(507\) 4.34436e10 4.34436e10i 0.657498 0.657498i
\(508\) −2.50251e10 2.50251e10i −0.375769 0.375769i
\(509\) 2.54580e10i 0.379275i 0.981854 + 0.189637i \(0.0607312\pi\)
−0.981854 + 0.189637i \(0.939269\pi\)
\(510\) 2.77398e9 + 2.44895e8i 0.0410037 + 0.00361993i
\(511\) 7.09818e9 0.104103
\(512\) 2.14748e9 2.14748e9i 0.0312500 0.0312500i
\(513\) 6.99469e10 + 6.99469e10i 1.00995 + 1.00995i
\(514\) 3.88723e9i 0.0556914i
\(515\) 2.26590e9 2.56663e10i 0.0322116 0.364867i
\(516\) 5.86269e9 0.0826987
\(517\) 4.23222e10 4.23222e10i 0.592388 0.592388i
\(518\) 3.71437e9 + 3.71437e9i 0.0515900 + 0.0515900i
\(519\) 7.98017e9i 0.109987i
\(520\) −3.03026e10 + 2.53862e10i −0.414445 + 0.347204i
\(521\) 7.42766e9 0.100809 0.0504047 0.998729i \(-0.483949\pi\)
0.0504047 + 0.998729i \(0.483949\pi\)
\(522\) −3.91534e9 + 3.91534e9i −0.0527336 + 0.0527336i
\(523\) 5.49185e10 + 5.49185e10i 0.734027 + 0.734027i 0.971415 0.237388i \(-0.0762913\pi\)
−0.237388 + 0.971415i \(0.576291\pi\)
\(524\) 4.35380e10i 0.577489i
\(525\) 7.86661e8 4.42061e9i 0.0103550 0.0581896i
\(526\) 2.10852e10 0.275445
\(527\) 7.47158e9 7.47158e9i 0.0968657 0.0968657i
\(528\) 8.86590e9 + 8.86590e9i 0.114074 + 0.114074i
\(529\) 2.70127e10i 0.344942i
\(530\) −5.24544e10 6.26128e10i −0.664780 0.793524i
\(531\) −5.25871e10 −0.661456
\(532\) −3.26479e9 + 3.26479e9i −0.0407576 + 0.0407576i
\(533\) 1.11884e11 + 1.11884e11i 1.38631 + 1.38631i
\(534\) 3.91214e10i 0.481115i
\(535\) 8.71438e10 + 7.69331e9i 1.06371 + 0.0939071i
\(536\) 2.04954e10 0.248312
\(537\) −3.43361e10 + 3.43361e10i −0.412909 + 0.412909i
\(538\) 6.57271e10 + 6.57271e10i 0.784541 + 0.784541i
\(539\) 7.78354e10i 0.922194i
\(540\) 3.94118e9 4.46426e10i 0.0463502 0.525019i
\(541\) −1.34348e11 −1.56835 −0.784174 0.620540i \(-0.786913\pi\)
−0.784174 + 0.620540i \(0.786913\pi\)
\(542\) 5.73478e10 5.73478e10i 0.664538 0.664538i
\(543\) −7.00694e10 7.00694e10i −0.805989 0.805989i
\(544\) 1.29736e9i 0.0148137i
\(545\) 1.47667e10 1.23709e10i 0.167377 0.140222i
\(546\) −5.67991e9 −0.0639103
\(547\) −2.62302e10 + 2.62302e10i −0.292990 + 0.292990i −0.838260 0.545271i \(-0.816427\pi\)
0.545271 + 0.838260i \(0.316427\pi\)
\(548\) 1.25442e10 + 1.25442e10i 0.139098 + 0.139098i
\(549\) 6.54135e10i 0.720075i
\(550\) 3.43974e10 + 4.92897e10i 0.375902 + 0.538648i
\(551\) −2.54569e10 −0.276184
\(552\) 1.86996e10 1.86996e10i 0.201408 0.201408i
\(553\) 3.14604e9 + 3.14604e9i 0.0336406 + 0.0336406i
\(554\) 1.64110e10i 0.174219i
\(555\) −5.13312e10 6.12721e10i −0.541015 0.645789i
\(556\) 4.49909e10 0.470788
\(557\) 1.10867e11 1.10867e11i 1.15181 1.15181i 0.165621 0.986189i \(-0.447037\pi\)
0.986189 0.165621i \(-0.0529629\pi\)
\(558\) −4.10011e10 4.10011e10i −0.422921 0.422921i
\(559\) 3.55518e10i 0.364094i
\(560\) 2.08371e9 + 1.83956e8i 0.0211877 + 0.00187052i
\(561\) −5.35615e9 −0.0540756
\(562\) −5.59844e10 + 5.59844e10i −0.561205 + 0.561205i
\(563\) −1.20925e11 1.20925e11i −1.20361 1.20361i −0.973062 0.230543i \(-0.925950\pi\)
−0.230543 0.973062i \(-0.574050\pi\)
\(564\) 3.16968e10i 0.313256i
\(565\) −4.72398e9 + 5.35096e10i −0.0463569 + 0.525095i
\(566\) −9.05489e9 −0.0882302
\(567\) 1.33597e9 1.33597e9i 0.0129260 0.0129260i
\(568\) −1.88679e10 1.88679e10i −0.181272 0.181272i
\(569\) 6.53746e10i 0.623677i −0.950135 0.311839i \(-0.899055\pi\)
0.950135 0.311839i \(-0.100945\pi\)
\(570\) 5.38560e10 4.51182e10i 0.510193 0.427418i
\(571\) −5.53735e10 −0.520904 −0.260452 0.965487i \(-0.583872\pi\)
−0.260452 + 0.965487i \(0.583872\pi\)
\(572\) 5.37634e10 5.37634e10i 0.502230 0.502230i
\(573\) −8.37546e10 8.37546e10i −0.776945 0.776945i
\(574\) 8.37272e9i 0.0771292i
\(575\) 1.03960e11 7.25496e10i 0.951031 0.663688i
\(576\) 7.11939e9 0.0646774
\(577\) −5.29155e10 + 5.29155e10i −0.477397 + 0.477397i −0.904298 0.426901i \(-0.859605\pi\)
0.426901 + 0.904298i \(0.359605\pi\)
\(578\) 5.54142e10 + 5.54142e10i 0.496489 + 0.496489i
\(579\) 1.10356e11i 0.981931i
\(580\) 7.40655e9 + 8.84093e9i 0.0654492 + 0.0781243i
\(581\) 1.15612e9 0.0101461
\(582\) −9.91931e9 + 9.91931e9i −0.0864549 + 0.0864549i
\(583\) 1.11089e11 + 1.11089e11i 0.961604 + 0.961604i
\(584\) 5.03199e10i 0.432602i
\(585\) −9.23105e10 8.14944e9i −0.788184 0.0695832i
\(586\) −7.98094e10 −0.676805
\(587\) −1.57769e11 + 1.57769e11i −1.32883 + 1.32883i −0.422445 + 0.906389i \(0.638828\pi\)
−0.906389 + 0.422445i \(0.861172\pi\)
\(588\) −2.91470e10 2.91470e10i −0.243829 0.243829i
\(589\) 2.66582e11i 2.21498i
\(590\) −9.63257e9 + 1.09110e11i −0.0794939 + 0.900445i
\(591\) 1.31809e11 1.08043
\(592\) 2.63316e10 2.63316e10i 0.214383 0.214383i
\(593\) −3.09235e10 3.09235e10i −0.250075 0.250075i 0.570927 0.821001i \(-0.306584\pi\)
−0.821001 + 0.570927i \(0.806584\pi\)
\(594\) 8.61983e10i 0.692393i
\(595\) −6.84980e8 + 5.73847e8i −0.00546525 + 0.00457856i
\(596\) 2.19459e10 0.173927
\(597\) −1.09153e10 + 1.09153e10i −0.0859288 + 0.0859288i
\(598\) −1.13396e11 1.13396e11i −0.886732 0.886732i
\(599\) 1.42432e11i 1.10637i 0.833059 + 0.553184i \(0.186587\pi\)
−0.833059 + 0.553184i \(0.813413\pi\)
\(600\) −3.13383e10 5.57673e9i −0.241808 0.0430304i
\(601\) 9.37468e10 0.718553 0.359276 0.933231i \(-0.383024\pi\)
0.359276 + 0.933231i \(0.383024\pi\)
\(602\) −1.33024e9 + 1.33024e9i −0.0101285 + 0.0101285i
\(603\) 3.39735e10 + 3.39735e10i 0.256963 + 0.256963i
\(604\) 5.42372e10i 0.407521i
\(605\) 1.17965e10 + 1.40811e10i 0.0880507 + 0.105103i
\(606\) −2.26070e10 −0.167630
\(607\) −1.60965e10 + 1.60965e10i −0.118571 + 0.118571i −0.763902 0.645332i \(-0.776719\pi\)
0.645332 + 0.763902i \(0.276719\pi\)
\(608\) 2.31445e10 + 2.31445e10i 0.169369 + 0.169369i
\(609\) 1.65714e9i 0.0120473i
\(610\) 1.35723e11 + 1.19820e10i 0.980244 + 0.0865388i
\(611\) 1.92211e11 1.37916
\(612\) −2.15052e9 + 2.15052e9i −0.0153298 + 0.0153298i
\(613\) 8.07997e10 + 8.07997e10i 0.572226 + 0.572226i 0.932750 0.360524i \(-0.117402\pi\)
−0.360524 + 0.932750i \(0.617402\pi\)
\(614\) 1.60462e11i 1.12901i
\(615\) −1.12042e10 + 1.26912e11i −0.0783212 + 0.887161i
\(616\) −4.02333e9 −0.0279423
\(617\) 1.53536e11 1.53536e11i 1.05942 1.05942i 0.0613041 0.998119i \(-0.480474\pi\)
0.998119 0.0613041i \(-0.0195260\pi\)
\(618\) −1.85579e10 1.85579e10i −0.127226 0.127226i
\(619\) 4.56835e10i 0.311169i −0.987823 0.155585i \(-0.950274\pi\)
0.987823 0.155585i \(-0.0497261\pi\)
\(620\) −9.25814e10 + 7.75608e10i −0.626552 + 0.524898i
\(621\) 1.81806e11 1.22248
\(622\) −5.24100e10 + 5.24100e10i −0.350149 + 0.350149i
\(623\) −8.87661e9 8.87661e9i −0.0589244 0.0589244i
\(624\) 4.02656e10i 0.265580i
\(625\) −1.43220e11 5.26399e10i −0.938610 0.344981i
\(626\) −4.01589e10 −0.261508
\(627\) −9.55522e10 + 9.55522e10i −0.618259 + 0.618259i
\(628\) −5.18572e8 5.18572e8i −0.00333404 0.00333404i
\(629\) 1.59077e10i 0.101626i
\(630\) 3.14905e9 + 3.75891e9i 0.0199902 + 0.0238616i
\(631\) 6.87475e10 0.433650 0.216825 0.976210i \(-0.430430\pi\)
0.216825 + 0.976210i \(0.430430\pi\)
\(632\) 2.23027e10 2.23027e10i 0.139794 0.139794i
\(633\) 6.31320e10 + 6.31320e10i 0.393219 + 0.393219i
\(634\) 6.40977e10i 0.396721i
\(635\) −1.72137e11 1.51968e10i −1.05872 0.0934668i
\(636\) −8.31988e10 −0.508497
\(637\) −1.76749e11 + 1.76749e11i −1.07350 + 1.07350i
\(638\) −1.56857e10 1.56857e10i −0.0946722 0.0946722i
\(639\) 6.25513e10i 0.375174i
\(640\) 1.30408e9 1.47717e10i 0.00777295 0.0880459i
\(641\) 9.51984e9 0.0563894 0.0281947 0.999602i \(-0.491024\pi\)
0.0281947 + 0.999602i \(0.491024\pi\)
\(642\) 6.30089e10 6.30089e10i 0.370904 0.370904i
\(643\) −9.40725e10 9.40725e10i −0.550325 0.550325i 0.376210 0.926534i \(-0.377227\pi\)
−0.926534 + 0.376210i \(0.877227\pi\)
\(644\) 8.48585e9i 0.0493347i
\(645\) 2.19436e10 1.83834e10i 0.126785 0.106215i
\(646\) −1.39823e10 −0.0802874
\(647\) 1.03789e11 1.03789e11i 0.592289 0.592289i −0.345960 0.938249i \(-0.612447\pi\)
0.938249 + 0.345960i \(0.112447\pi\)
\(648\) −9.47088e9 9.47088e9i −0.0537144 0.0537144i
\(649\) 2.10676e11i 1.18750i
\(650\) −3.38177e10 + 1.90037e11i −0.189448 + 1.06460i
\(651\) −1.73534e10 −0.0966187
\(652\) −2.42563e10 + 2.42563e10i −0.134225 + 0.134225i
\(653\) −1.14827e11 1.14827e11i −0.631527 0.631527i 0.316924 0.948451i \(-0.397350\pi\)
−0.948451 + 0.316924i \(0.897350\pi\)
\(654\) 1.96217e10i 0.107257i
\(655\) 1.36521e11 + 1.62959e11i 0.741708 + 0.885349i
\(656\) −5.93552e10 −0.320511
\(657\) 8.34108e10 8.34108e10i 0.447673 0.447673i
\(658\) −7.19197e9 7.19197e9i −0.0383658 0.0383658i
\(659\) 1.16978e10i 0.0620246i −0.999519 0.0310123i \(-0.990127\pi\)
0.999519 0.0310123i \(-0.00987310\pi\)
\(660\) 6.09849e10 + 5.38392e9i 0.321400 + 0.0283742i
\(661\) −1.06677e11 −0.558809 −0.279404 0.960174i \(-0.590137\pi\)
−0.279404 + 0.960174i \(0.590137\pi\)
\(662\) 1.28539e11 1.28539e11i 0.669271 0.669271i
\(663\) −1.21628e10 1.21628e10i −0.0629476 0.0629476i
\(664\) 8.19586e9i 0.0421621i
\(665\) −1.98258e9 + 2.24571e10i −0.0101378 + 0.114833i
\(666\) 8.72951e10 0.443704
\(667\) −3.30838e10 + 3.30838e10i −0.167152 + 0.167152i
\(668\) −7.14541e10 7.14541e10i −0.358857 0.358857i
\(669\) 1.99724e11i 0.997073i
\(670\) 7.67128e10 6.42667e10i 0.380688 0.318924i
\(671\) −2.62061e11 −1.29274
\(672\) 1.50662e9 1.50662e9i 0.00738797 0.00738797i
\(673\) 5.13966e10 + 5.13966e10i 0.250539 + 0.250539i 0.821191 0.570653i \(-0.193310\pi\)
−0.570653 + 0.821191i \(0.693310\pi\)
\(674\) 2.26328e11i 1.09673i
\(675\) −1.25233e11 1.79452e11i −0.603257 0.864438i
\(676\) 1.39759e11 0.669259
\(677\) −2.46063e11 + 2.46063e11i −1.17136 + 1.17136i −0.189479 + 0.981885i \(0.560680\pi\)
−0.981885 + 0.189479i \(0.939320\pi\)
\(678\) 3.86899e10 + 3.86899e10i 0.183096 + 0.183096i
\(679\) 4.50136e9i 0.0211770i
\(680\) 4.06807e9 + 4.85591e9i 0.0190262 + 0.0227109i
\(681\) 1.22053e11 0.567494
\(682\) 1.64260e11 1.64260e11i 0.759265 0.759265i
\(683\) 1.11448e11 + 1.11448e11i 0.512142 + 0.512142i 0.915182 0.403040i \(-0.132047\pi\)
−0.403040 + 0.915182i \(0.632047\pi\)
\(684\) 7.67292e10i 0.350539i
\(685\) 8.62863e10 + 7.61760e9i 0.391904 + 0.0345984i
\(686\) 2.65502e10 0.119887
\(687\) 7.37525e10 7.37525e10i 0.331093 0.331093i
\(688\) 9.43023e9 + 9.43023e9i 0.0420890 + 0.0420890i
\(689\) 5.04523e11i 2.23874i
\(690\) 1.13556e10 1.28627e11i 0.0500971 0.567461i
\(691\) −2.73439e11 −1.19936 −0.599678 0.800241i \(-0.704705\pi\)
−0.599678 + 0.800241i \(0.704705\pi\)
\(692\) −1.28362e10 + 1.28362e10i −0.0559774 + 0.0559774i
\(693\) −6.66912e9 6.66912e9i −0.0289158 0.0289158i
\(694\) 1.07316e10i 0.0462622i
\(695\) 1.68397e11 1.41076e11i 0.721766 0.604664i
\(696\) 1.17477e10 0.0500628
\(697\) 1.79291e10 1.79291e10i 0.0759674 0.0759674i
\(698\) 1.21033e11 + 1.21033e11i 0.509896 + 0.509896i
\(699\) 5.70176e10i 0.238836i
\(700\) 8.37598e9 5.84527e9i 0.0348854 0.0243451i
\(701\) 7.12259e10 0.294962 0.147481 0.989065i \(-0.452883\pi\)
0.147481 + 0.989065i \(0.452883\pi\)
\(702\) −1.95740e11 + 1.95740e11i −0.805992 + 0.805992i
\(703\) 2.83789e11 + 2.83789e11i 1.16191 + 1.16191i
\(704\) 2.85219e10i 0.116115i
\(705\) 9.93904e10 + 1.18639e11i 0.402335 + 0.480253i
\(706\) −5.71552e10 −0.230058
\(707\) 5.12950e9 5.12950e9i 0.0205304 0.0205304i
\(708\) 7.88916e10 + 7.88916e10i 0.313977 + 0.313977i
\(709\) 3.40136e11i 1.34607i 0.739610 + 0.673036i \(0.235010\pi\)
−0.739610 + 0.673036i \(0.764990\pi\)
\(710\) −1.29784e11 1.14577e10i −0.510727 0.0450885i
\(711\) 7.39383e10 0.289328
\(712\) −6.29273e10 + 6.29273e10i −0.244861 + 0.244861i
\(713\) −3.46450e11 3.46450e11i −1.34055 1.34055i
\(714\) 9.10190e8i 0.00350219i
\(715\) 3.26485e10 3.69816e11i 0.124922 1.41502i
\(716\) −1.10460e11 −0.420295
\(717\) 1.25468e11 1.25468e11i 0.474741 0.474741i
\(718\) −1.04308e11 1.04308e11i −0.392482 0.392482i
\(719\) 3.73670e10i 0.139821i 0.997553 + 0.0699105i \(0.0222714\pi\)
−0.997553 + 0.0699105i \(0.977729\pi\)
\(720\) 2.66473e10 2.23240e10i 0.0991571 0.0830696i
\(721\) 8.42155e9 0.0311639
\(722\) −1.13571e11 + 1.13571e11i −0.417945 + 0.417945i
\(723\) −4.31056e10 4.31056e10i −0.157754 0.157754i
\(724\) 2.25415e11i 0.820407i
\(725\) 5.54443e10 + 9.86648e9i 0.200680 + 0.0357117i
\(726\) 1.87107e10 0.0673509
\(727\) 2.20574e11 2.20574e11i 0.789618 0.789618i −0.191814 0.981431i \(-0.561437\pi\)
0.981431 + 0.191814i \(0.0614369\pi\)
\(728\) −9.13622e9 9.13622e9i −0.0325268 0.0325268i
\(729\) 2.38215e11i 0.843448i
\(730\) −1.57786e11 1.88343e11i −0.555619 0.663222i
\(731\) −5.69708e9 −0.0199518
\(732\) 9.81339e10 9.81339e10i 0.341802 0.341802i
\(733\) 2.40945e11 + 2.40945e11i 0.834646 + 0.834646i 0.988148 0.153502i \(-0.0490552\pi\)
−0.153502 + 0.988148i \(0.549055\pi\)
\(734\) 3.59404e10i 0.123822i
\(735\) −2.00490e11 1.76999e10i −0.686980 0.0606486i
\(736\) 6.01573e10 0.205011
\(737\) −1.36105e11 + 1.36105e11i −0.461323 + 0.461323i
\(738\) −9.83879e10 9.83879e10i −0.331678 0.331678i
\(739\) 1.27384e11i 0.427106i −0.976931 0.213553i \(-0.931496\pi\)
0.976931 0.213553i \(-0.0685037\pi\)
\(740\) 1.59902e10 1.81124e11i 0.0533244 0.604017i
\(741\) −4.33962e11 −1.43939
\(742\) 1.88777e10 1.88777e10i 0.0622780 0.0622780i
\(743\) −2.08172e11 2.08172e11i −0.683072 0.683072i 0.277619 0.960691i \(-0.410455\pi\)
−0.960691 + 0.277619i \(0.910455\pi\)
\(744\) 1.23021e11i 0.401500i
\(745\) 8.21417e10 6.88148e10i 0.266648 0.223387i
\(746\) −1.94726e11 −0.628736
\(747\) 1.35856e10 1.35856e10i 0.0436310 0.0436310i
\(748\) −8.61544e9 8.61544e9i −0.0275214 0.0275214i
\(749\) 2.85933e10i 0.0908527i
\(750\) −1.34784e11 + 7.73929e10i −0.425983 + 0.244600i
\(751\) −8.78634e10 −0.276216 −0.138108 0.990417i \(-0.544102\pi\)
−0.138108 + 0.990417i \(0.544102\pi\)
\(752\) −5.09848e10 + 5.09848e10i −0.159430 + 0.159430i
\(753\) 2.78296e11 + 2.78296e11i 0.865618 + 0.865618i
\(754\) 7.12387e10i 0.220410i
\(755\) 1.70070e11 + 2.03006e11i 0.523406 + 0.624771i
\(756\) 1.46480e10 0.0448426
\(757\) 1.18459e11 1.18459e11i 0.360733 0.360733i −0.503350 0.864083i \(-0.667899\pi\)
0.864083 + 0.503350i \(0.167899\pi\)
\(758\) 2.72377e11 + 2.72377e11i 0.825075 + 0.825075i
\(759\) 2.48360e11i 0.748366i
\(760\) 1.59201e11 + 1.40548e10i 0.477191 + 0.0421279i
\(761\) −5.02471e10 −0.149821 −0.0749105 0.997190i \(-0.523867\pi\)
−0.0749105 + 0.997190i \(0.523867\pi\)
\(762\) −1.24463e11 + 1.24463e11i −0.369166 + 0.369166i
\(763\) 4.45214e9 + 4.45214e9i 0.0131362 + 0.0131362i
\(764\) 2.69441e11i 0.790843i
\(765\) −1.30593e9 + 1.47925e10i −0.00381305 + 0.0431913i
\(766\) 1.20182e11 0.349079
\(767\) 4.78404e11 4.78404e11i 1.38234 1.38234i
\(768\) −1.06806e10 1.06806e10i −0.0307008 0.0307008i
\(769\) 6.28311e11i 1.79668i 0.439306 + 0.898338i \(0.355224\pi\)
−0.439306 + 0.898338i \(0.644776\pi\)
\(770\) −1.50590e10 + 1.26158e10i −0.0428384 + 0.0358882i
\(771\) 1.93333e10 0.0547126
\(772\) −1.77509e11 + 1.77509e11i −0.499748 + 0.499748i
\(773\) −7.85266e10 7.85266e10i −0.219937 0.219937i 0.588535 0.808472i \(-0.299705\pi\)
−0.808472 + 0.588535i \(0.799705\pi\)
\(774\) 3.12633e10i 0.0871107i
\(775\) −1.03321e11 + 5.80608e11i −0.286405 + 1.60945i
\(776\) −3.19107e10