Properties

Label 162.7.d.d.107.2
Level $162$
Weight $7$
Character 162.107
Analytic conductor $37.269$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 162.d (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(37.2687615464\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 18)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.2
Root \(-1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 162.107
Dual form 162.7.d.d.53.2

$q$-expansion

\(f(q)\) \(=\) \(q+(4.89898 + 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(-150.644 + 86.9741i) q^{5} +(242.000 - 419.156i) q^{7} +181.019i q^{8} +O(q^{10})\) \(q+(4.89898 + 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(-150.644 + 86.9741i) q^{5} +(242.000 - 419.156i) q^{7} +181.019i q^{8} -984.000 q^{10} +(1161.06 + 670.337i) q^{11} +(-1684.00 - 2916.77i) q^{13} +(2371.11 - 1368.96i) q^{14} +(-512.000 + 886.810i) q^{16} -12.7279i q^{17} +5744.00 q^{19} +(-4820.60 - 2783.17i) q^{20} +(3792.00 + 6567.94i) q^{22} +(2924.69 - 1688.57i) q^{23} +(7316.50 - 12672.5i) q^{25} -19052.3i q^{26} +15488.0 q^{28} +(25422.0 + 14677.4i) q^{29} +(19898.0 + 34464.3i) q^{31} +(-5016.55 + 2896.31i) q^{32} +(36.0000 - 62.3538i) q^{34} +84191.0i q^{35} +52526.0 q^{37} +(28139.7 + 16246.5i) q^{38} +(-15744.0 - 27269.4i) q^{40} +(32079.7 - 18521.2i) q^{41} +(-1900.00 + 3290.90i) q^{43} +42901.6i q^{44} +19104.0 q^{46} +(66503.6 + 38395.9i) q^{47} +(-58303.5 - 100985. i) q^{49} +(71686.8 - 41388.4i) q^{50} +(53888.0 - 93336.8i) q^{52} -238738. i q^{53} -233208. q^{55} +(75875.4 + 43806.7i) q^{56} +(83028.0 + 143809. i) q^{58} +(216368. - 124920. i) q^{59} +(-6625.00 + 11474.8i) q^{61} +225120. i q^{62} -32768.0 q^{64} +(507368. + 292929. i) q^{65} +(-84484.0 - 146331. i) q^{67} +(352.727 - 203.647i) q^{68} +(-238128. + 412450. i) q^{70} +531467. i q^{71} +236144. q^{73} +(257324. + 148566. i) q^{74} +(91904.0 + 159182. i) q^{76} +(561952. - 324443. i) q^{77} +(17558.0 - 30411.3i) q^{79} -178123. i q^{80} +209544. q^{82} +(-9508.92 - 5489.98i) q^{83} +(1107.00 + 1917.38i) q^{85} +(-18616.1 + 10748.0i) q^{86} +(-121344. + 210174. i) q^{88} +129328. i q^{89} -1.63011e6 q^{91} +(93590.1 + 54034.3i) q^{92} +(217200. + 376201. i) q^{94} +(-865297. + 499579. i) q^{95} +(160712. - 278361. i) q^{97} -659629. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 64 q^{4} + 968 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 64 q^{4} + 968 q^{7} - 3936 q^{10} - 6736 q^{13} - 2048 q^{16} + 22976 q^{19} + 15168 q^{22} + 29266 q^{25} + 61952 q^{28} + 79592 q^{31} + 144 q^{34} + 210104 q^{37} - 62976 q^{40} - 7600 q^{43} + 76416 q^{46} - 233214 q^{49} + 215552 q^{52} - 932832 q^{55} + 332112 q^{58} - 26500 q^{61} - 131072 q^{64} - 337936 q^{67} - 952512 q^{70} + 944576 q^{73} + 367616 q^{76} + 70232 q^{79} + 838176 q^{82} + 4428 q^{85} - 485376 q^{88} - 6520448 q^{91} + 868800 q^{94} + 642848 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.89898 + 2.82843i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 16.0000 + 27.7128i 0.250000 + 0.433013i
\(5\) −150.644 + 86.9741i −1.20515 + 0.695793i −0.961696 0.274120i \(-0.911614\pi\)
−0.243453 + 0.969913i \(0.578280\pi\)
\(6\) 0 0
\(7\) 242.000 419.156i 0.705539 1.22203i −0.260957 0.965350i \(-0.584038\pi\)
0.966497 0.256680i \(-0.0826285\pi\)
\(8\) 181.019i 0.353553i
\(9\) 0 0
\(10\) −984.000 −0.984000
\(11\) 1161.06 + 670.337i 0.872320 + 0.503634i 0.868119 0.496357i \(-0.165329\pi\)
0.00420160 + 0.999991i \(0.498663\pi\)
\(12\) 0 0
\(13\) −1684.00 2916.77i −0.766500 1.32762i −0.939450 0.342686i \(-0.888663\pi\)
0.172950 0.984931i \(-0.444670\pi\)
\(14\) 2371.11 1368.96i 0.864106 0.498892i
\(15\) 0 0
\(16\) −512.000 + 886.810i −0.125000 + 0.216506i
\(17\) 12.7279i 0.00259066i −0.999999 0.00129533i \(-0.999588\pi\)
0.999999 0.00129533i \(-0.000412317\pi\)
\(18\) 0 0
\(19\) 5744.00 0.837440 0.418720 0.908115i \(-0.362479\pi\)
0.418720 + 0.908115i \(0.362479\pi\)
\(20\) −4820.60 2783.17i −0.602574 0.347897i
\(21\) 0 0
\(22\) 3792.00 + 6567.94i 0.356123 + 0.616824i
\(23\) 2924.69 1688.57i 0.240379 0.138783i −0.374972 0.927036i \(-0.622348\pi\)
0.615351 + 0.788253i \(0.289014\pi\)
\(24\) 0 0
\(25\) 7316.50 12672.5i 0.468256 0.811043i
\(26\) 19052.3i 1.08399i
\(27\) 0 0
\(28\) 15488.0 0.705539
\(29\) 25422.0 + 14677.4i 1.04236 + 0.601805i 0.920500 0.390743i \(-0.127782\pi\)
0.121857 + 0.992548i \(0.461115\pi\)
\(30\) 0 0
\(31\) 19898.0 + 34464.3i 0.667920 + 1.15687i 0.978485 + 0.206319i \(0.0661484\pi\)
−0.310565 + 0.950552i \(0.600518\pi\)
\(32\) −5016.55 + 2896.31i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 36.0000 62.3538i 0.000915937 0.00158645i
\(35\) 84191.0i 1.96364i
\(36\) 0 0
\(37\) 52526.0 1.03698 0.518489 0.855085i \(-0.326495\pi\)
0.518489 + 0.855085i \(0.326495\pi\)
\(38\) 28139.7 + 16246.5i 0.512825 + 0.296080i
\(39\) 0 0
\(40\) −15744.0 27269.4i −0.246000 0.426084i
\(41\) 32079.7 18521.2i 0.465457 0.268732i −0.248879 0.968535i \(-0.580062\pi\)
0.714336 + 0.699803i \(0.246729\pi\)
\(42\) 0 0
\(43\) −1900.00 + 3290.90i −0.0238973 + 0.0413913i −0.877727 0.479162i \(-0.840941\pi\)
0.853829 + 0.520553i \(0.174274\pi\)
\(44\) 42901.6i 0.503634i
\(45\) 0 0
\(46\) 19104.0 0.196269
\(47\) 66503.6 + 38395.9i 0.640548 + 0.369821i 0.784826 0.619717i \(-0.212752\pi\)
−0.144277 + 0.989537i \(0.546086\pi\)
\(48\) 0 0
\(49\) −58303.5 100985.i −0.495572 0.858355i
\(50\) 71686.8 41388.4i 0.573494 0.331107i
\(51\) 0 0
\(52\) 53888.0 93336.8i 0.383250 0.663808i
\(53\) 238738.i 1.60359i −0.597599 0.801795i \(-0.703879\pi\)
0.597599 0.801795i \(-0.296121\pi\)
\(54\) 0 0
\(55\) −233208. −1.40170
\(56\) 75875.4 + 43806.7i 0.432053 + 0.249446i
\(57\) 0 0
\(58\) 83028.0 + 143809.i 0.425540 + 0.737057i
\(59\) 216368. 124920.i 1.05351 0.608243i 0.129878 0.991530i \(-0.458541\pi\)
0.923629 + 0.383287i \(0.125208\pi\)
\(60\) 0 0
\(61\) −6625.00 + 11474.8i −0.0291875 + 0.0505542i −0.880250 0.474510i \(-0.842625\pi\)
0.851063 + 0.525064i \(0.175959\pi\)
\(62\) 225120.i 0.944581i
\(63\) 0 0
\(64\) −32768.0 −0.125000
\(65\) 507368. + 292929.i 1.84749 + 1.06665i
\(66\) 0 0
\(67\) −84484.0 146331.i −0.280899 0.486531i 0.690707 0.723134i \(-0.257299\pi\)
−0.971606 + 0.236603i \(0.923966\pi\)
\(68\) 352.727 203.647i 0.00112179 0.000647665i
\(69\) 0 0
\(70\) −238128. + 412450.i −0.694251 + 1.20248i
\(71\) 531467.i 1.48491i 0.669894 + 0.742457i \(0.266340\pi\)
−0.669894 + 0.742457i \(0.733660\pi\)
\(72\) 0 0
\(73\) 236144. 0.607027 0.303514 0.952827i \(-0.401840\pi\)
0.303514 + 0.952827i \(0.401840\pi\)
\(74\) 257324. + 148566.i 0.635016 + 0.366627i
\(75\) 0 0
\(76\) 91904.0 + 159182.i 0.209360 + 0.362622i
\(77\) 561952. 324443.i 1.23091 0.710668i
\(78\) 0 0
\(79\) 17558.0 30411.3i 0.0356118 0.0616814i −0.847670 0.530524i \(-0.821995\pi\)
0.883282 + 0.468842i \(0.155329\pi\)
\(80\) 178123.i 0.347897i
\(81\) 0 0
\(82\) 209544. 0.380044
\(83\) −9508.92 5489.98i −0.0166302 0.00960144i 0.491662 0.870786i \(-0.336390\pi\)
−0.508292 + 0.861185i \(0.669723\pi\)
\(84\) 0 0
\(85\) 1107.00 + 1917.38i 0.00180256 + 0.00312213i
\(86\) −18616.1 + 10748.0i −0.0292681 + 0.0168979i
\(87\) 0 0
\(88\) −121344. + 210174.i −0.178062 + 0.308412i
\(89\) 129328.i 0.183453i 0.995784 + 0.0917263i \(0.0292385\pi\)
−0.995784 + 0.0917263i \(0.970762\pi\)
\(90\) 0 0
\(91\) −1.63011e6 −2.16318
\(92\) 93590.1 + 54034.3i 0.120189 + 0.0693914i
\(93\) 0 0
\(94\) 217200. + 376201.i 0.261503 + 0.452936i
\(95\) −865297. + 499579.i −1.00924 + 0.582685i
\(96\) 0 0
\(97\) 160712. 278361.i 0.176089 0.304996i −0.764448 0.644685i \(-0.776989\pi\)
0.940538 + 0.339689i \(0.110322\pi\)
\(98\) 659629.i 0.700844i
\(99\) 0 0
\(100\) 468256. 0.468256
\(101\) 579181. + 334390.i 0.562147 + 0.324556i 0.754007 0.656867i \(-0.228119\pi\)
−0.191860 + 0.981422i \(0.561452\pi\)
\(102\) 0 0
\(103\) −996706. 1.72635e6i −0.912127 1.57985i −0.811054 0.584972i \(-0.801106\pi\)
−0.101073 0.994879i \(-0.532228\pi\)
\(104\) 527992. 304837.i 0.469383 0.270999i
\(105\) 0 0
\(106\) 675252. 1.16957e6i 0.566955 0.981994i
\(107\) 260668.i 0.212783i 0.994324 + 0.106391i \(0.0339296\pi\)
−0.994324 + 0.106391i \(0.966070\pi\)
\(108\) 0 0
\(109\) 194456. 0.150156 0.0750779 0.997178i \(-0.476079\pi\)
0.0750779 + 0.997178i \(0.476079\pi\)
\(110\) −1.14248e6 659612.i −0.858363 0.495576i
\(111\) 0 0
\(112\) 247808. + 429216.i 0.176385 + 0.305508i
\(113\) 711784. 410949.i 0.493302 0.284808i −0.232641 0.972563i \(-0.574737\pi\)
0.725943 + 0.687755i \(0.241404\pi\)
\(114\) 0 0
\(115\) −293724. + 508745.i −0.193128 + 0.334508i
\(116\) 939355.i 0.601805i
\(117\) 0 0
\(118\) 1.41331e6 0.860185
\(119\) −5334.99 3080.16i −0.00316587 0.00182781i
\(120\) 0 0
\(121\) 12923.5 + 22384.2i 0.00729498 + 0.0126353i
\(122\) −64911.5 + 37476.7i −0.0357472 + 0.0206387i
\(123\) 0 0
\(124\) −636736. + 1.10286e6i −0.333960 + 0.578436i
\(125\) 172557.i 0.0883490i
\(126\) 0 0
\(127\) 3.05721e6 1.49250 0.746250 0.665666i \(-0.231852\pi\)
0.746250 + 0.665666i \(0.231852\pi\)
\(128\) −160530. 92681.9i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) 1.65706e6 + 2.87011e6i 0.754236 + 1.30637i
\(131\) −2.66206e6 + 1.53694e6i −1.18414 + 0.683664i −0.956969 0.290191i \(-0.906281\pi\)
−0.227172 + 0.973855i \(0.572948\pi\)
\(132\) 0 0
\(133\) 1.39005e6 2.40763e6i 0.590847 1.02338i
\(134\) 955827.i 0.397251i
\(135\) 0 0
\(136\) 2304.00 0.000915937
\(137\) −3.88336e6 2.24206e6i −1.51024 0.871938i −0.999929 0.0119482i \(-0.996197\pi\)
−0.510312 0.859990i \(-0.670470\pi\)
\(138\) 0 0
\(139\) 546164. + 945984.i 0.203366 + 0.352241i 0.949611 0.313431i \(-0.101478\pi\)
−0.746245 + 0.665672i \(0.768145\pi\)
\(140\) −2.33317e6 + 1.34706e6i −0.850280 + 0.490909i
\(141\) 0 0
\(142\) −1.50322e6 + 2.60365e6i −0.524996 + 0.909321i
\(143\) 4.51539e6i 1.54414i
\(144\) 0 0
\(145\) −5.10622e6 −1.67493
\(146\) 1.15686e6 + 667916.i 0.371727 + 0.214617i
\(147\) 0 0
\(148\) 840416. + 1.45564e6i 0.259244 + 0.449024i
\(149\) 1.92333e6 1.11044e6i 0.581428 0.335687i −0.180273 0.983617i \(-0.557698\pi\)
0.761701 + 0.647929i \(0.224365\pi\)
\(150\) 0 0
\(151\) 2.03935e6 3.53226e6i 0.592327 1.02594i −0.401591 0.915819i \(-0.631543\pi\)
0.993918 0.110122i \(-0.0351241\pi\)
\(152\) 1.03978e6i 0.296080i
\(153\) 0 0
\(154\) 3.67066e6 1.00504
\(155\) −5.99501e6 3.46122e6i −1.60989 0.929468i
\(156\) 0 0
\(157\) −3.07784e6 5.33097e6i −0.795329 1.37755i −0.922630 0.385686i \(-0.873965\pi\)
0.127301 0.991864i \(-0.459369\pi\)
\(158\) 172033. 99323.0i 0.0436154 0.0251813i
\(159\) 0 0
\(160\) 503808. 872621.i 0.123000 0.213042i
\(161\) 1.63454e6i 0.391667i
\(162\) 0 0
\(163\) 800696. 0.184886 0.0924432 0.995718i \(-0.470532\pi\)
0.0924432 + 0.995718i \(0.470532\pi\)
\(164\) 1.02655e6 + 592680.i 0.232728 + 0.134366i
\(165\) 0 0
\(166\) −31056.0 53790.6i −0.00678924 0.0117593i
\(167\) −4.16097e6 + 2.40234e6i −0.893398 + 0.515804i −0.875052 0.484028i \(-0.839173\pi\)
−0.0183455 + 0.999832i \(0.505840\pi\)
\(168\) 0 0
\(169\) −3.25831e6 + 5.64355e6i −0.675044 + 1.16921i
\(170\) 12524.3i 0.00254921i
\(171\) 0 0
\(172\) −121600. −0.0238973
\(173\) −3.09164e6 1.78496e6i −0.597106 0.344739i 0.170796 0.985306i \(-0.445366\pi\)
−0.767902 + 0.640567i \(0.778699\pi\)
\(174\) 0 0
\(175\) −3.54119e6 6.13351e6i −0.660746 1.14445i
\(176\) −1.18892e6 + 686425.i −0.218080 + 0.125909i
\(177\) 0 0
\(178\) −365796. + 633577.i −0.0648603 + 0.112341i
\(179\) 7.43698e6i 1.29669i 0.761345 + 0.648347i \(0.224539\pi\)
−0.761345 + 0.648347i \(0.775461\pi\)
\(180\) 0 0
\(181\) −1.03812e7 −1.75070 −0.875350 0.483491i \(-0.839369\pi\)
−0.875350 + 0.483491i \(0.839369\pi\)
\(182\) −7.98589e6 4.61065e6i −1.32467 0.764801i
\(183\) 0 0
\(184\) 305664. + 529426.i 0.0490671 + 0.0849868i
\(185\) −7.91271e6 + 4.56840e6i −1.24971 + 0.721521i
\(186\) 0 0
\(187\) 8532.00 14777.9i 0.00130475 0.00225989i
\(188\) 2.45734e6i 0.369821i
\(189\) 0 0
\(190\) −5.65210e6 −0.824041
\(191\) 1.12532e7 + 6.49703e6i 1.61501 + 0.932426i 0.988185 + 0.153266i \(0.0489793\pi\)
0.626825 + 0.779160i \(0.284354\pi\)
\(192\) 0 0
\(193\) 1.96598e6 + 3.40517e6i 0.273468 + 0.473660i 0.969747 0.244110i \(-0.0784959\pi\)
−0.696279 + 0.717771i \(0.745163\pi\)
\(194\) 1.57465e6 909124.i 0.215665 0.124514i
\(195\) 0 0
\(196\) 1.86571e6 3.23151e6i 0.247786 0.429178i
\(197\) 5.37967e6i 0.703651i −0.936066 0.351825i \(-0.885561\pi\)
0.936066 0.351825i \(-0.114439\pi\)
\(198\) 0 0
\(199\) −565900. −0.0718093 −0.0359046 0.999355i \(-0.511431\pi\)
−0.0359046 + 0.999355i \(0.511431\pi\)
\(200\) 2.29398e6 + 1.32443e6i 0.286747 + 0.165553i
\(201\) 0 0
\(202\) 1.89160e6 + 3.27634e6i 0.229496 + 0.397498i
\(203\) 1.23043e7 7.10387e6i 1.47085 0.849194i
\(204\) 0 0
\(205\) −3.22174e6 + 5.58022e6i −0.373963 + 0.647723i
\(206\) 1.12764e7i 1.28994i
\(207\) 0 0
\(208\) 3.44883e6 0.383250
\(209\) 6.66912e6 + 3.85042e6i 0.730516 + 0.421763i
\(210\) 0 0
\(211\) 6.75825e6 + 1.17056e7i 0.719427 + 1.24608i 0.961227 + 0.275759i \(0.0889291\pi\)
−0.241799 + 0.970326i \(0.577738\pi\)
\(212\) 6.61609e6 3.81980e6i 0.694375 0.400897i
\(213\) 0 0
\(214\) −737280. + 1.27701e6i −0.0752300 + 0.130302i
\(215\) 661003.i 0.0665102i
\(216\) 0 0
\(217\) 1.92613e7 1.88497
\(218\) 952636. + 550005.i 0.0919512 + 0.0530881i
\(219\) 0 0
\(220\) −3.73133e6 6.46285e6i −0.350425 0.606954i
\(221\) −37124.5 + 21433.8i −0.00343941 + 0.00198574i
\(222\) 0 0
\(223\) 2.67742e6 4.63742e6i 0.241436 0.418179i −0.719688 0.694298i \(-0.755715\pi\)
0.961123 + 0.276119i \(0.0890484\pi\)
\(224\) 2.80363e6i 0.249446i
\(225\) 0 0
\(226\) 4.64935e6 0.402779
\(227\) −1.17834e7 6.80317e6i −1.00738 0.581612i −0.0969580 0.995288i \(-0.530911\pi\)
−0.910424 + 0.413676i \(0.864245\pi\)
\(228\) 0 0
\(229\) −2.17320e6 3.76410e6i −0.180965 0.313440i 0.761245 0.648465i \(-0.224589\pi\)
−0.942209 + 0.335025i \(0.891255\pi\)
\(230\) −2.87790e6 + 1.66155e6i −0.236533 + 0.136562i
\(231\) 0 0
\(232\) −2.65690e6 + 4.60188e6i −0.212770 + 0.368529i
\(233\) 2.02333e7i 1.59956i 0.600297 + 0.799778i \(0.295049\pi\)
−0.600297 + 0.799778i \(0.704951\pi\)
\(234\) 0 0
\(235\) −1.33578e7 −1.02927
\(236\) 6.92379e6 + 3.99745e6i 0.526754 + 0.304121i
\(237\) 0 0
\(238\) −17424.0 30179.3i −0.00129246 0.00223861i
\(239\) 1.76623e7 1.01973e7i 1.29376 0.746953i 0.314442 0.949277i \(-0.398183\pi\)
0.979319 + 0.202324i \(0.0648494\pi\)
\(240\) 0 0
\(241\) 1.56046e6 2.70280e6i 0.111481 0.193092i −0.804886 0.593429i \(-0.797774\pi\)
0.916368 + 0.400337i \(0.131107\pi\)
\(242\) 146213.i 0.0103167i
\(243\) 0 0
\(244\) −424000. −0.0291875
\(245\) 1.75661e7 + 1.01418e7i 1.19448 + 0.689631i
\(246\) 0 0
\(247\) −9.67290e6 1.67539e7i −0.641897 1.11180i
\(248\) −6.23871e6 + 3.60192e6i −0.409016 + 0.236145i
\(249\) 0 0
\(250\) 488064. 845352.i 0.0312361 0.0541025i
\(251\) 5.09519e6i 0.322210i −0.986937 0.161105i \(-0.948494\pi\)
0.986937 0.161105i \(-0.0515058\pi\)
\(252\) 0 0
\(253\) 4.52765e6 0.279583
\(254\) 1.49772e7 + 8.64710e6i 0.913966 + 0.527678i
\(255\) 0 0
\(256\) −524288. 908093.i −0.0312500 0.0541266i
\(257\) −1.25031e7 + 7.21869e6i −0.736580 + 0.425264i −0.820824 0.571181i \(-0.806486\pi\)
0.0842448 + 0.996445i \(0.473152\pi\)
\(258\) 0 0
\(259\) 1.27113e7 2.20166e7i 0.731628 1.26722i
\(260\) 1.87474e7i 1.06665i
\(261\) 0 0
\(262\) −1.73885e7 −0.966847
\(263\) 2.70691e7 + 1.56283e7i 1.48801 + 0.859104i 0.999906 0.0136808i \(-0.00435487\pi\)
0.488105 + 0.872785i \(0.337688\pi\)
\(264\) 0 0
\(265\) 2.07640e7 + 3.59643e7i 1.11577 + 1.93256i
\(266\) 1.36196e7 7.86330e6i 0.723637 0.417792i
\(267\) 0 0
\(268\) 2.70349e6 4.68258e6i 0.140449 0.243266i
\(269\) 251338.i 0.0129122i −0.999979 0.00645612i \(-0.997945\pi\)
0.999979 0.00645612i \(-0.00205506\pi\)
\(270\) 0 0
\(271\) 2.96399e7 1.48925 0.744627 0.667481i \(-0.232627\pi\)
0.744627 + 0.667481i \(0.232627\pi\)
\(272\) 11287.2 + 6516.70i 0.000560895 + 0.000323833i
\(273\) 0 0
\(274\) −1.26830e7 2.19676e7i −0.616553 1.06790i
\(275\) 1.69898e7 9.80904e6i 0.816938 0.471660i
\(276\) 0 0
\(277\) −6.61064e6 + 1.14500e7i −0.311031 + 0.538722i −0.978586 0.205839i \(-0.934008\pi\)
0.667555 + 0.744561i \(0.267341\pi\)
\(278\) 6.17914e6i 0.287603i
\(279\) 0 0
\(280\) −1.52402e7 −0.694251
\(281\) −5.30320e6 3.06180e6i −0.239011 0.137993i 0.375711 0.926737i \(-0.377399\pi\)
−0.614722 + 0.788744i \(0.710732\pi\)
\(282\) 0 0
\(283\) 3.37162e6 + 5.83982e6i 0.148758 + 0.257656i 0.930769 0.365609i \(-0.119139\pi\)
−0.782011 + 0.623265i \(0.785806\pi\)
\(284\) −1.47284e7 + 8.50347e6i −0.642987 + 0.371229i
\(285\) 0 0
\(286\) 1.27715e7 2.21208e7i 0.545937 0.945590i
\(287\) 1.79286e7i 0.758403i
\(288\) 0 0
\(289\) 2.41374e7 0.999993
\(290\) −2.50153e7 1.44426e7i −1.02568 0.592176i
\(291\) 0 0
\(292\) 3.77830e6 + 6.54421e6i 0.151757 + 0.262851i
\(293\) 8.68096e6 5.01195e6i 0.345116 0.199253i −0.317416 0.948286i \(-0.602815\pi\)
0.662532 + 0.749034i \(0.269482\pi\)
\(294\) 0 0
\(295\) −2.17297e7 + 3.76369e7i −0.846422 + 1.46605i
\(296\) 9.50822e6i 0.366627i
\(297\) 0 0
\(298\) 1.25632e7 0.474734
\(299\) −9.85036e6 5.68711e6i −0.368501 0.212754i
\(300\) 0 0
\(301\) 919600. + 1.59279e6i 0.0337209 + 0.0584064i
\(302\) 1.99815e7 1.15363e7i 0.725450 0.418839i
\(303\) 0 0
\(304\) −2.94093e6 + 5.09384e6i −0.104680 + 0.181311i
\(305\) 2.30481e6i 0.0812337i
\(306\) 0 0
\(307\) −5.23060e6 −0.180774 −0.0903871 0.995907i \(-0.528810\pi\)
−0.0903871 + 0.995907i \(0.528810\pi\)
\(308\) 1.79825e7 + 1.03822e7i 0.615456 + 0.355334i
\(309\) 0 0
\(310\) −1.95796e7 3.39129e7i −0.657233 1.13836i
\(311\) −2.70392e7 + 1.56111e7i −0.898901 + 0.518981i −0.876844 0.480776i \(-0.840355\pi\)
−0.0220578 + 0.999757i \(0.507022\pi\)
\(312\) 0 0
\(313\) −1.12389e7 + 1.94664e7i −0.366515 + 0.634822i −0.989018 0.147795i \(-0.952782\pi\)
0.622503 + 0.782617i \(0.286116\pi\)
\(314\) 3.48218e7i 1.12477i
\(315\) 0 0
\(316\) 1.12371e6 0.0356118
\(317\) −2.39206e7 1.38106e7i −0.750921 0.433544i 0.0751058 0.997176i \(-0.476071\pi\)
−0.826026 + 0.563631i \(0.809404\pi\)
\(318\) 0 0
\(319\) 1.96776e7 + 3.40827e7i 0.606179 + 1.04993i
\(320\) 4.93629e6 2.84997e6i 0.150644 0.0869741i
\(321\) 0 0
\(322\) 4.62317e6 8.00756e6i 0.138475 0.239846i
\(323\) 73109.2i 0.00216952i
\(324\) 0 0
\(325\) −4.92839e7 −1.43567
\(326\) 3.92259e6 + 2.26471e6i 0.113219 + 0.0653672i
\(327\) 0 0
\(328\) 3.35270e6 + 5.80705e6i 0.0950110 + 0.164564i
\(329\) 3.21878e7 1.85836e7i 0.903864 0.521846i
\(330\) 0 0
\(331\) 2.88069e6 4.98950e6i 0.0794352 0.137586i −0.823571 0.567213i \(-0.808022\pi\)
0.903006 + 0.429627i \(0.141355\pi\)
\(332\) 351359.i 0.00960144i
\(333\) 0 0
\(334\) −2.71793e7 −0.729456
\(335\) 2.54540e7 + 1.46958e7i 0.677050 + 0.390895i
\(336\) 0 0
\(337\) 2.00526e7 + 3.47321e7i 0.523939 + 0.907489i 0.999612 + 0.0278665i \(0.00887132\pi\)
−0.475673 + 0.879622i \(0.657795\pi\)
\(338\) −3.19248e7 + 1.84318e7i −0.826756 + 0.477328i
\(339\) 0 0
\(340\) −35424.0 + 61356.2i −0.000901282 + 0.00156107i
\(341\) 5.33535e7i 1.34555i
\(342\) 0 0
\(343\) 504328. 0.0124977
\(344\) −595716. 343937.i −0.0146340 0.00844896i
\(345\) 0 0
\(346\) −1.00973e7 1.74890e7i −0.243767 0.422217i
\(347\) −5.87275e7 + 3.39064e7i −1.40557 + 0.811508i −0.994957 0.100301i \(-0.968020\pi\)
−0.410616 + 0.911808i \(0.634686\pi\)
\(348\) 0 0
\(349\) 2.10319e7 3.64284e7i 0.494769 0.856965i −0.505213 0.862995i \(-0.668586\pi\)
0.999982 + 0.00602956i \(0.00191928\pi\)
\(350\) 4.00639e7i 0.934436i
\(351\) 0 0
\(352\) −7.76602e6 −0.178062
\(353\) −1.52399e7 8.79878e6i −0.346465 0.200032i 0.316662 0.948538i \(-0.397438\pi\)
−0.663127 + 0.748507i \(0.730771\pi\)
\(354\) 0 0
\(355\) −4.62239e7 8.00621e7i −1.03319 1.78954i
\(356\) −3.58405e6 + 2.06925e6i −0.0794373 + 0.0458632i
\(357\) 0 0
\(358\) −2.10349e7 + 3.64336e7i −0.458450 + 0.794059i
\(359\) 1.39920e7i 0.302410i 0.988502 + 0.151205i \(0.0483154\pi\)
−0.988502 + 0.151205i \(0.951685\pi\)
\(360\) 0 0
\(361\) −1.40523e7 −0.298694
\(362\) −5.08572e7 2.93624e7i −1.07208 0.618966i
\(363\) 0 0
\(364\) −2.60818e7 4.51750e7i −0.540796 0.936686i
\(365\) −3.55736e7 + 2.05384e7i −0.731559 + 0.422365i
\(366\) 0 0
\(367\) 1.32927e7 2.30237e7i 0.268916 0.465776i −0.699666 0.714470i \(-0.746668\pi\)
0.968582 + 0.248694i \(0.0800013\pi\)
\(368\) 3.45819e6i 0.0693914i
\(369\) 0 0
\(370\) −5.16856e7 −1.02039
\(371\) −1.00068e8 5.77745e7i −1.95963 1.13140i
\(372\) 0 0
\(373\) −8.94146e6 1.54871e7i −0.172299 0.298430i 0.766924 0.641737i \(-0.221786\pi\)
−0.939223 + 0.343307i \(0.888453\pi\)
\(374\) 83596.2 48264.3i 0.00159798 0.000922595i
\(375\) 0 0
\(376\) −6.95040e6 + 1.20384e7i −0.130751 + 0.226468i
\(377\) 9.88671e7i 1.84513i
\(378\) 0 0
\(379\) 7.20978e7 1.32435 0.662177 0.749347i \(-0.269633\pi\)
0.662177 + 0.749347i \(0.269633\pi\)
\(380\) −2.76895e7 1.59865e7i −0.504620 0.291342i
\(381\) 0 0
\(382\) 3.67527e7 + 6.36576e7i 0.659325 + 1.14198i
\(383\) −7.52272e6 + 4.34324e6i −0.133899 + 0.0773068i −0.565453 0.824780i \(-0.691299\pi\)
0.431554 + 0.902087i \(0.357965\pi\)
\(384\) 0 0
\(385\) −5.64363e7 + 9.77506e7i −0.988955 + 1.71292i
\(386\) 2.22425e7i 0.386742i
\(387\) 0 0
\(388\) 1.02856e7 0.176089
\(389\) −4.28173e7 2.47206e7i −0.727395 0.419962i 0.0900736 0.995935i \(-0.471290\pi\)
−0.817468 + 0.575974i \(0.804623\pi\)
\(390\) 0 0
\(391\) −21492.0 37225.2i −0.000359539 0.000622741i
\(392\) 1.82802e7 1.05541e7i 0.303474 0.175211i
\(393\) 0 0
\(394\) 1.52160e7 2.63549e7i 0.248778 0.430896i
\(395\) 6.10837e6i 0.0991137i
\(396\) 0 0
\(397\) 1.56911e7 0.250774 0.125387 0.992108i \(-0.459983\pi\)
0.125387 + 0.992108i \(0.459983\pi\)
\(398\) −2.77233e6 1.60061e6i −0.0439740 0.0253884i
\(399\) 0 0
\(400\) 7.49210e6 + 1.29767e7i 0.117064 + 0.202761i
\(401\) 4.10941e7 2.37257e7i 0.637304 0.367947i −0.146272 0.989244i \(-0.546727\pi\)
0.783575 + 0.621297i \(0.213394\pi\)
\(402\) 0 0
\(403\) 6.70165e7 1.16076e8i 1.02392 1.77348i
\(404\) 2.14010e7i 0.324556i
\(405\) 0 0
\(406\) 8.03711e7 1.20094
\(407\) 6.09857e7 + 3.52101e7i 0.904576 + 0.522257i
\(408\) 0 0
\(409\) 5.77558e7 + 1.00036e8i 0.844162 + 1.46213i 0.886347 + 0.463022i \(0.153235\pi\)
−0.0421850 + 0.999110i \(0.513432\pi\)
\(410\) −3.15665e7 + 1.82249e7i −0.458009 + 0.264432i
\(411\) 0 0
\(412\) 3.18946e7 5.52431e7i 0.456064 0.789925i
\(413\) 1.20923e8i 1.71656i
\(414\) 0 0
\(415\) 1.90994e6 0.0267225
\(416\) 1.68958e7 + 9.75477e6i 0.234692 + 0.135499i
\(417\) 0 0
\(418\) 2.17812e7 + 3.77262e7i 0.298232 + 0.516553i
\(419\) −1.27040e8 + 7.33466e7i −1.72702 + 0.997098i −0.825447 + 0.564480i \(0.809077\pi\)
−0.901577 + 0.432618i \(0.857590\pi\)
\(420\) 0 0
\(421\) −6.96194e7 + 1.20584e8i −0.933005 + 1.61601i −0.154852 + 0.987938i \(0.549490\pi\)
−0.778153 + 0.628075i \(0.783843\pi\)
\(422\) 7.64609e7i 1.01742i
\(423\) 0 0
\(424\) 4.32161e7 0.566955
\(425\) −161295. 93123.8i −0.00210114 0.00121309i
\(426\) 0 0
\(427\) 3.20650e6 + 5.55382e6i 0.0411858 + 0.0713359i
\(428\) −7.22384e6 + 4.17069e6i −0.0921376 + 0.0531957i
\(429\) 0 0
\(430\) 1.86960e6 3.23824e6i 0.0235149 0.0407290i
\(431\) 1.00392e8i 1.25391i 0.779056 + 0.626954i \(0.215699\pi\)
−0.779056 + 0.626954i \(0.784301\pi\)
\(432\) 0 0
\(433\) −4.00631e7 −0.493493 −0.246747 0.969080i \(-0.579362\pi\)
−0.246747 + 0.969080i \(0.579362\pi\)
\(434\) 9.43605e7 + 5.44791e7i 1.15431 + 0.666439i
\(435\) 0 0
\(436\) 3.11130e6 + 5.38892e6i 0.0375389 + 0.0650193i
\(437\) 1.67994e7 9.69915e6i 0.201303 0.116222i
\(438\) 0 0
\(439\) 6.92959e7 1.20024e8i 0.819057 1.41865i −0.0873208 0.996180i \(-0.527831\pi\)
0.906378 0.422468i \(-0.138836\pi\)
\(440\) 4.22152e7i 0.495576i
\(441\) 0 0
\(442\) −242496. −0.00280826
\(443\) −9.65121e7 5.57213e7i −1.11012 0.640929i −0.171261 0.985226i \(-0.554784\pi\)
−0.938861 + 0.344296i \(0.888117\pi\)
\(444\) 0 0
\(445\) −1.12482e7 1.94825e7i −0.127645 0.221088i
\(446\) 2.62332e7 1.51458e7i 0.295697 0.170721i
\(447\) 0 0
\(448\) −7.92986e6 + 1.37349e7i −0.0881924 + 0.152754i
\(449\) 6.11166e7i 0.675181i 0.941293 + 0.337591i \(0.109612\pi\)
−0.941293 + 0.337591i \(0.890388\pi\)
\(450\) 0 0
\(451\) 4.96619e7 0.541370
\(452\) 2.27771e7 + 1.31504e7i 0.246651 + 0.142404i
\(453\) 0 0
\(454\) −3.84845e7 6.66572e7i −0.411262 0.712327i
\(455\) 2.45566e8 1.41778e8i 2.60696 1.50513i
\(456\) 0 0
\(457\) −1.78332e7 + 3.08881e7i −0.186845 + 0.323625i −0.944197 0.329382i \(-0.893160\pi\)
0.757352 + 0.653007i \(0.226493\pi\)
\(458\) 2.45870e7i 0.255923i
\(459\) 0 0
\(460\) −1.87983e7 −0.193128
\(461\) 1.31621e8 + 7.59914e7i 1.34345 + 0.775642i 0.987312 0.158791i \(-0.0507595\pi\)
0.356139 + 0.934433i \(0.384093\pi\)
\(462\) 0 0
\(463\) −5.74891e7 9.95740e7i −0.579218 1.00324i −0.995569 0.0940314i \(-0.970025\pi\)
0.416351 0.909204i \(-0.363309\pi\)
\(464\) −2.60322e7 + 1.50297e7i −0.260589 + 0.150451i
\(465\) 0 0
\(466\) −5.72284e7 + 9.91226e7i −0.565528 + 0.979523i
\(467\) 8.81705e7i 0.865711i −0.901463 0.432855i \(-0.857506\pi\)
0.901463 0.432855i \(-0.142494\pi\)
\(468\) 0 0
\(469\) −8.17805e7 −0.792741
\(470\) −6.54396e7 3.77816e7i −0.630300 0.363904i
\(471\) 0 0
\(472\) 2.26130e7 + 3.91669e7i 0.215046 + 0.372471i
\(473\) −4.41202e6 + 2.54728e6i −0.0416921 + 0.0240710i
\(474\) 0 0
\(475\) 4.20260e7 7.27911e7i 0.392136 0.679200i
\(476\) 197130.i 0.00182781i
\(477\) 0 0
\(478\) 1.15370e8 1.05635
\(479\) −7.74563e7 4.47194e7i −0.704774 0.406902i 0.104349 0.994541i \(-0.466724\pi\)
−0.809123 + 0.587639i \(0.800057\pi\)
\(480\) 0 0
\(481\) −8.84538e7 1.53206e8i −0.794843 1.37671i
\(482\) 1.52894e7 8.82732e6i 0.136536 0.0788293i
\(483\) 0 0
\(484\) −413552. + 716293.i −0.00364749 + 0.00631764i
\(485\) 5.59111e7i 0.490087i
\(486\) 0 0
\(487\) −7.51688e7 −0.650805 −0.325403 0.945576i \(-0.605500\pi\)
−0.325403 + 0.945576i \(0.605500\pi\)
\(488\) −2.07717e6 1.19925e6i −0.0178736 0.0103193i
\(489\) 0 0
\(490\) 5.73706e7 + 9.93689e7i 0.487642 + 0.844621i
\(491\) −3.90424e7 + 2.25411e7i −0.329831 + 0.190428i −0.655766 0.754964i \(-0.727654\pi\)
0.325935 + 0.945392i \(0.394321\pi\)
\(492\) 0 0
\(493\) 186813. 323570.i 0.00155907 0.00270039i
\(494\) 1.09436e8i 0.907780i
\(495\) 0 0
\(496\) −4.07511e7 −0.333960
\(497\) 2.22768e8 + 1.28615e8i 1.81461 + 1.04767i
\(498\) 0 0
\(499\) −4.57729e7 7.92810e7i −0.368389 0.638069i 0.620925 0.783870i \(-0.286757\pi\)
−0.989314 + 0.145801i \(0.953424\pi\)
\(500\) 4.78203e6 2.76091e6i 0.0382562 0.0220873i
\(501\) 0 0
\(502\) 1.44114e7 2.49612e7i 0.113919 0.197313i
\(503\) 1.61043e8i 1.26543i 0.774386 + 0.632713i \(0.218059\pi\)
−0.774386 + 0.632713i \(0.781941\pi\)
\(504\) 0 0
\(505\) −1.16333e8 −0.903295
\(506\) 2.21809e7 + 1.28061e7i 0.171209 + 0.0988476i
\(507\) 0 0
\(508\) 4.89154e7 + 8.47239e7i 0.373125 + 0.646272i
\(509\) −2.07841e7 + 1.19997e7i −0.157608 + 0.0909951i −0.576730 0.816935i \(-0.695671\pi\)
0.419122 + 0.907930i \(0.362338\pi\)
\(510\) 0 0
\(511\) 5.71468e7 9.89812e7i 0.428282 0.741806i
\(512\) 5.93164e6i 0.0441942i
\(513\) 0 0
\(514\) −8.16702e7 −0.601415
\(515\) 3.00295e8 + 1.73375e8i 2.19850 + 1.26930i
\(516\) 0 0
\(517\) 5.14764e7 + 8.91597e7i 0.372509 + 0.645204i
\(518\) 1.24545e8 7.19059e7i 0.896058 0.517339i
\(519\) 0 0
\(520\) −5.30258e7 + 9.18434e7i −0.377118 + 0.653187i
\(521\) 9.00897e7i 0.637033i 0.947917 + 0.318517i \(0.103185\pi\)
−0.947917 + 0.318517i \(0.896815\pi\)
\(522\) 0 0
\(523\) −3.77691e7 −0.264016 −0.132008 0.991249i \(-0.542143\pi\)
−0.132008 + 0.991249i \(0.542143\pi\)
\(524\) −8.51858e7 4.91820e7i −0.592070 0.341832i
\(525\) 0 0
\(526\) 8.84073e7 + 1.53126e8i 0.607478 + 1.05218i
\(527\) 438660. 253260.i 0.00299706 0.00173035i
\(528\) 0 0
\(529\) −6.83154e7 + 1.18326e8i −0.461479 + 0.799304i
\(530\) 2.34918e8i 1.57793i
\(531\) 0 0
\(532\) 8.89631e7 0.590847
\(533\) −1.08045e8 6.23796e7i −0.713545 0.411965i
\(534\) 0 0
\(535\) −2.26714e7 3.92679e7i −0.148053 0.256435i
\(536\) 2.64887e7 1.52932e7i 0.172015 0.0993128i
\(537\) 0 0
\(538\) 710892. 1.23130e6i 0.00456517 0.00790710i
\(539\) 1.56332e8i 0.998347i
\(540\) 0 0
\(541\) 2.54800e7 0.160919 0.0804595 0.996758i \(-0.474361\pi\)
0.0804595 + 0.996758i \(0.474361\pi\)
\(542\) 1.45205e8 + 8.38343e7i 0.911978 + 0.526531i
\(543\) 0 0
\(544\) 36864.0 + 63850.3i 0.000228984 + 0.000396612i
\(545\) −2.92936e7 + 1.69126e7i −0.180960 + 0.104477i
\(546\) 0 0
\(547\) −1.02608e8 + 1.77722e8i −0.626930 + 1.08587i 0.361234 + 0.932475i \(0.382355\pi\)
−0.988164 + 0.153399i \(0.950978\pi\)
\(548\) 1.43492e8i 0.871938i
\(549\) 0 0
\(550\) 1.10977e8 0.667027
\(551\) 1.46024e8 + 8.43071e7i 0.872911 + 0.503975i
\(552\) 0 0
\(553\) −8.49807e6 1.47191e7i −0.0502510 0.0870373i
\(554\) −6.47707e7 + 3.73954e7i −0.380934 + 0.219932i
\(555\) 0 0
\(556\) −1.74772e7 + 3.02715e7i −0.101683 + 0.176120i
\(557\) 2.41143e8i 1.39543i 0.716375 + 0.697715i \(0.245800\pi\)
−0.716375 + 0.697715i \(0.754200\pi\)
\(558\) 0 0
\(559\) 1.27984e7 0.0732690
\(560\) −7.46614e7 4.31058e7i −0.425140 0.245455i
\(561\) 0 0
\(562\) −1.73202e7 2.99994e7i −0.0975760 0.169007i
\(563\) 1.46252e8 8.44386e7i 0.819552 0.473168i −0.0307102 0.999528i \(-0.509777\pi\)
0.850262 + 0.526360i \(0.176444\pi\)
\(564\) 0 0
\(565\) −7.14838e7 + 1.23814e8i −0.396335 + 0.686472i
\(566\) 3.81456e7i 0.210375i
\(567\) 0 0
\(568\) −9.62058e7 −0.524996
\(569\) −2.11306e8 1.21998e8i −1.14703 0.662238i −0.198869 0.980026i \(-0.563727\pi\)
−0.948162 + 0.317788i \(0.897060\pi\)
\(570\) 0 0
\(571\) −1.20751e8 2.09147e8i −0.648608 1.12342i −0.983456 0.181149i \(-0.942018\pi\)
0.334848 0.942272i \(-0.391315\pi\)
\(572\) 1.25134e8 7.22463e7i 0.668633 0.386036i
\(573\) 0 0
\(574\) 5.07096e7 8.78317e7i 0.268136 0.464425i
\(575\) 4.94177e7i 0.259944i
\(576\) 0 0
\(577\) −4.93979e7 −0.257147 −0.128573 0.991700i \(-0.541040\pi\)
−0.128573 + 0.991700i \(0.541040\pi\)
\(578\) 1.18249e8 + 6.82709e7i 0.612368 + 0.353551i
\(579\) 0 0
\(580\) −8.16996e7 1.41508e8i −0.418732 0.725264i
\(581\) −4.60232e6 + 2.65715e6i −0.0234665 + 0.0135484i
\(582\) 0 0
\(583\) 1.60035e8 2.77188e8i 0.807623 1.39884i
\(584\) 4.27466e7i 0.214617i
\(585\) 0 0
\(586\) 5.67038e7 0.281786
\(587\) −1.49001e8 8.60260e7i −0.736675 0.425320i 0.0841840 0.996450i \(-0.473172\pi\)
−0.820859 + 0.571131i \(0.806505\pi\)
\(588\) 0 0
\(589\) 1.14294e8 + 1.97963e8i 0.559343 + 0.968810i
\(590\) −2.12906e8 + 1.22922e8i −1.03665 + 0.598511i
\(591\) 0 0
\(592\) −2.68933e7 + 4.65806e7i −0.129622 + 0.224512i
\(593\) 2.70643e8i 1.29788i −0.760841 0.648938i \(-0.775213\pi\)
0.760841 0.648938i \(-0.224787\pi\)
\(594\) 0 0
\(595\) 1.07158e6 0.00508712
\(596\) 6.15467e7 + 3.55340e7i 0.290714 + 0.167844i
\(597\) 0 0
\(598\) −3.21711e7 5.57220e7i −0.150440 0.260569i
\(599\) 1.50082e8 8.66497e7i 0.698308 0.403169i −0.108409 0.994106i \(-0.534575\pi\)
0.806717 + 0.590938i \(0.201242\pi\)
\(600\) 0 0
\(601\) 2.15545e8 3.73335e8i 0.992921 1.71979i 0.393598 0.919282i \(-0.371230\pi\)
0.599323 0.800507i \(-0.295437\pi\)
\(602\) 1.04041e7i 0.0476886i
\(603\) 0 0
\(604\) 1.30519e8 0.592327
\(605\) −3.89369e6 2.24802e6i −0.0175831 0.0101516i
\(606\) 0 0
\(607\) −8.34953e6 1.44618e7i −0.0373332 0.0646631i 0.846755 0.531983i \(-0.178553\pi\)
−0.884088 + 0.467320i \(0.845220\pi\)
\(608\) −2.88151e7 + 1.66364e7i −0.128206 + 0.0740199i
\(609\) 0 0
\(610\) 6.51900e6 1.12912e7i 0.0287205 0.0497453i
\(611\) 2.58635e8i 1.13387i
\(612\) 0 0
\(613\) −1.92321e8 −0.834920 −0.417460 0.908695i \(-0.637080\pi\)
−0.417460 + 0.908695i \(0.637080\pi\)
\(614\) −2.56246e7 1.47944e7i −0.110701 0.0639133i
\(615\) 0 0
\(616\) 5.87305e7 + 1.01724e8i 0.251259 + 0.435193i
\(617\) 1.61967e8 9.35117e7i 0.689558 0.398117i −0.113888 0.993494i \(-0.536331\pi\)
0.803447 + 0.595377i \(0.202997\pi\)
\(618\) 0 0
\(619\) −1.27437e8 + 2.20727e8i −0.537307 + 0.930643i 0.461741 + 0.887015i \(0.347225\pi\)
−0.999048 + 0.0436278i \(0.986108\pi\)
\(620\) 2.21518e8i 0.929468i
\(621\) 0 0
\(622\) −1.76619e8 −0.733950
\(623\) 5.42088e7 + 3.12975e7i 0.224185 + 0.129433i
\(624\) 0 0
\(625\) 1.29328e8 + 2.24003e8i 0.529729 + 0.917517i
\(626\) −1.10118e8 + 6.35769e7i −0.448887 + 0.259165i
\(627\) 0 0
\(628\) 9.84908e7 1.70591e8i 0.397665 0.688775i
\(629\) 668547.i 0.00268646i
\(630\) 0 0
\(631\) 9.23602e7 0.367618 0.183809 0.982962i \(-0.441157\pi\)
0.183809 + 0.982962i \(0.441157\pi\)
\(632\) 5.50504e6 + 3.17834e6i 0.0218077 + 0.0125907i
\(633\) 0 0
\(634\) −7.81243e7 1.35315e8i −0.306562 0.530981i
\(635\) −4.60549e8 + 2.65898e8i −1.79869 + 1.03847i
\(636\) 0 0
\(637\) −1.96366e8 + 3.40116e8i −0.759711 + 1.31586i
\(638\) 2.22627e8i 0.857267i
\(639\) 0 0
\(640\) 3.22437e7 0.123000
\(641\) −3.67771e8 2.12333e8i −1.39638 0.806200i −0.402368 0.915478i \(-0.631813\pi\)
−0.994011 + 0.109278i \(0.965146\pi\)
\(642\) 0 0
\(643\) −1.87973e8 3.25579e8i −0.707071 1.22468i −0.965939 0.258770i \(-0.916683\pi\)
0.258868 0.965913i \(-0.416650\pi\)
\(644\) 4.52976e7 2.61526e7i 0.169597 0.0979168i
\(645\) 0 0
\(646\) 206784. 358160.i 0.000767042 0.00132856i
\(647\) 2.63747e7i 0.0973813i −0.998814 0.0486906i \(-0.984495\pi\)
0.998814 0.0486906i \(-0.0155048\pi\)
\(648\) 0 0
\(649\) 3.34955e8 1.22533
\(650\) −2.41441e8 1.39396e8i −0.879166 0.507587i
\(651\) 0 0
\(652\) 1.28111e7 + 2.21895e7i 0.0462216 + 0.0800581i
\(653\) −2.24090e8 + 1.29378e8i −0.804790 + 0.464645i −0.845143 0.534540i \(-0.820485\pi\)
0.0403536 + 0.999185i \(0.487152\pi\)
\(654\) 0 0
\(655\) 2.67348e8 4.63060e8i 0.951377 1.64783i
\(656\) 3.79315e7i 0.134366i
\(657\) 0 0
\(658\) 2.10250e8 0.738002
\(659\) −1.20676e8 6.96725e7i −0.421663 0.243447i 0.274126 0.961694i \(-0.411612\pi\)
−0.695789 + 0.718247i \(0.744945\pi\)
\(660\) 0 0
\(661\) 2.36272e8 + 4.09236e8i 0.818104 + 1.41700i 0.907077 + 0.420964i \(0.138308\pi\)
−0.0889731 + 0.996034i \(0.528359\pi\)
\(662\) 2.82249e7 1.62957e7i 0.0972878 0.0561691i
\(663\) 0 0
\(664\) 993792. 1.72130e6i 0.00339462 0.00587966i
\(665\) 4.83593e8i 1.64443i
\(666\) 0 0
\(667\) 9.91354e7 0.334081
\(668\) −1.33151e8 7.68747e7i −0.446699 0.257902i
\(669\) 0 0
\(670\) 8.31323e7 + 1.43989e8i 0.276405 + 0.478747i
\(671\) −1.53840e7 + 8.88197e6i −0.0509216 + 0.0293996i
\(672\) 0 0
\(673\) −2.74417e8 + 4.75304e8i −0.900254 + 1.55929i −0.0730906 + 0.997325i \(0.523286\pi\)
−0.827164 + 0.561961i \(0.810047\pi\)
\(674\) 2.26869e8i 0.740961i
\(675\) 0 0
\(676\) −2.08532e8 −0.675044
\(677\) −8.72609e7 5.03801e7i −0.281225 0.162365i 0.352753 0.935717i \(-0.385246\pi\)
−0.633978 + 0.773351i \(0.718579\pi\)
\(678\) 0 0
\(679\) −7.77846e7 1.34727e8i −0.248476 0.430373i
\(680\) −347083. + 200388.i −0.00110384 + 0.000637303i
\(681\) 0 0
\(682\) −1.50906e8 + 2.61378e8i −0.475724 + 0.823977i
\(683\) 313056.i 0.000982562i 1.00000 0.000491281i \(0.000156380\pi\)
−1.00000 0.000491281i \(0.999844\pi\)
\(684\) 0 0
\(685\) 7.80005e8 2.42675
\(686\) 2.47069e6 + 1.42645e6i 0.00765326 + 0.00441861i
\(687\) 0 0
\(688\) −1.94560e6 3.36988e6i −0.00597432 0.0103478i
\(689\) −6.96344e8 + 4.02034e8i −2.12895 + 1.22915i
\(690\) 0 0
\(691\) 1.86406e8 3.22865e8i 0.564971 0.978558i −0.432082 0.901834i \(-0.642221\pi\)
0.997052 0.0767236i \(-0.0244459\pi\)
\(692\) 1.14238e8i 0.344739i
\(693\) 0 0
\(694\) −3.83607e8 −1.14765
\(695\) −1.64552e8 9.50043e7i −0.490173 0.283002i
\(696\) 0 0
\(697\) −235737. 408308.i −0.000696193 0.00120584i
\(698\) 2.06070e8 1.18975e8i 0.605966 0.349855i
\(699\) 0 0
\(700\) 1.13318e8 1.96272e8i 0.330373 0.572223i
\(701\) 6.21170e8i 1.80325i −0.432517 0.901626i \(-0.642374\pi\)
0.432517 0.901626i \(-0.357626\pi\)
\(702\) 0 0
\(703\) 3.01709e8 0.868406
\(704\) −3.80456e7 2.19656e7i −0.109040 0.0629543i
\(705\) 0 0
\(706\) −4.97734e7 8.62101e7i −0.141444 0.244988i
\(707\) 2.80323e8 1.61845e8i 0.793234 0.457974i
\(708\) 0 0
\(709\) 1.23255e8 2.13484e8i 0.345833 0.599000i −0.639672 0.768648i \(-0.720930\pi\)
0.985505 + 0.169648i \(0.0542631\pi\)
\(710\) 5.22964e8i 1.46116i
\(711\) 0 0
\(712\) −2.34109e7 −0.0648603
\(713\) 1.16391e8 + 6.71984e7i 0.321108 + 0.185392i
\(714\) 0 0
\(715\) 3.92722e8 + 6.80215e8i 1.07440 + 1.86092i
\(716\) −2.06100e8 + 1.18992e8i −0.561485 + 0.324173i
\(717\) 0 0
\(718\) −3.95754e7 + 6.85466e7i −0.106918 + 0.185188i
\(719\) 9.60389e7i 0.258381i 0.991620 + 0.129191i \(0.0412379\pi\)
−0.991620 + 0.129191i \(0.958762\pi\)
\(720\) 0 0
\(721\) −9.64811e8 −2.57417
\(722\) −6.88421e7 3.97460e7i −0.182912 0.105604i
\(723\) 0 0
\(724\) −1.66099e8 2.87692e8i −0.437675 0.758075i
\(725\) 3.72001e8 2.14775e8i 0.976179 0.563597i
\(726\) 0 0
\(727\) −1.95685e8 + 3.38937e8i −0.509278 + 0.882096i 0.490664 + 0.871349i \(0.336754\pi\)
−0.999942 + 0.0107471i \(0.996579\pi\)
\(728\) 2.95082e8i 0.764801i
\(729\) 0 0
\(730\) −2.32366e8 −0.597315
\(731\) 41886.3 + 24183.1i 0.000107231 + 6.19097e-5i
\(732\) 0 0
\(733\) −1.74539e7 3.02311e7i −0.0443181 0.0767611i 0.843015 0.537889i \(-0.180778\pi\)
−0.887334 + 0.461128i \(0.847445\pi\)
\(734\) 1.30242e8 7.51951e7i 0.329353 0.190152i
\(735\) 0 0
\(736\) −9.78125e6 + 1.69416e7i −0.0245336 + 0.0424934i
\(737\) 2.26531e8i 0.565881i
\(738\) 0 0
\(739\) −3.02999e8 −0.750773 −0.375386 0.926868i \(-0.622490\pi\)
−0.375386 + 0.926868i \(0.622490\pi\)
\(740\) −2.53207e8 1.46189e8i −0.624856 0.360761i
\(741\) 0 0
\(742\) −3.26822e8 5.66072e8i −0.800018 1.38567i
\(743\) −2.12720e8 + 1.22814e8i −0.518612 + 0.299421i −0.736367 0.676583i \(-0.763460\pi\)
0.217754 + 0.976004i \(0.430127\pi\)
\(744\) 0 0
\(745\) −1.93159e8 + 3.34560e8i −0.467138 + 0.809107i
\(746\) 1.01161e8i 0.243667i
\(747\) 0 0
\(748\) 546048. 0.00130475
\(749\) 1.09261e8 + 6.30816e7i 0.260027 + 0.150127i
\(750\) 0 0
\(751\) 4.11635e7 + 7.12973e7i 0.0971835 + 0.168327i 0.910518 0.413470i \(-0.135683\pi\)
−0.813334 + 0.581797i \(0.802350\pi\)
\(752\) −6.80997e7 + 3.93174e7i −0.160137 + 0.0924552i
\(753\) 0 0
\(754\) 2.79638e8 4.84348e8i 0.652353 1.12991i
\(755\) 7.09484e8i 1.64855i
\(756\) 0 0
\(757\) −6.03579e8 −1.39138 −0.695691 0.718341i \(-0.744902\pi\)
−0.695691 + 0.718341i \(0.744902\pi\)
\(758\) 3.53205e8 + 2.03923e8i 0.810998 + 0.468230i
\(759\) 0 0
\(760\) −9.04335e7 1.56635e8i −0.206010 0.356820i
\(761\) 2.01769e8 1.16491e8i 0.457825 0.264325i −0.253304 0.967387i \(-0.581517\pi\)
0.711129 + 0.703061i \(0.248184\pi\)
\(762\) 0 0
\(763\) 4.70584e7 8.15075e7i 0.105941 0.183495i
\(764\) 4.15810e8i 0.932426i
\(765\) 0 0
\(766\) −4.91382e7 −0.109328
\(767\) −7.28729e8 4.20732e8i −1.61503 0.932436i
\(768\) 0 0
\(769\) −4.07898e8 7.06500e8i −0.896958 1.55358i −0.831362 0.555731i \(-0.812438\pi\)
−0.0655965 0.997846i \(-0.520895\pi\)
\(770\) −5.52961e8 + 3.19252e8i −1.21122 + 0.699297i
\(771\) 0 0
\(772\) −6.29113e7 + 1.08966e8i −0.136734 + 0.236830i
\(773\) 3.66587e8i 0.793667i 0.917891 + 0.396833i \(0.129891\pi\)
−0.917891 + 0.396833i \(0.870109\pi\)
\(774\) 0 0
\(775\) 5.82335e8 1.25103
\(776\) 5.03888e7 + 2.90920e7i 0.107832 + 0.0622570i
\(777\) 0 0
\(778\) −1.39841e8 2.42211e8i −0.296958 0.514346i