Properties

Label 162.7.d.d.53.1
Level $162$
Weight $7$
Character 162.53
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 53.1
Root \(1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 162.53
Dual form 162.7.d.d.107.1

$q$-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 \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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 \(-0.0883864\pi\)
0.243453 + 0.969913i \(0.421720\pi\)
\(6\) 0 0
\(7\) 242.000 + 419.156i 0.705539 + 1.22203i 0.966497 + 0.256680i \(0.0826285\pi\)
−0.260957 + 0.965350i \(0.584038\pi\)
\(8\) 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 \(-0.834671\pi\)
−0.00420160 + 0.999991i \(0.501337\pi\)
\(12\) 0 0
\(13\) −1684.00 + 2916.77i −0.766500 + 1.32762i 0.172950 + 0.984931i \(0.444670\pi\)
−0.939450 + 0.342686i \(0.888663\pi\)
\(14\) −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 \(-0.377652\pi\)
−0.615351 + 0.788253i \(0.710986\pi\)
\(24\) 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 \(-0.872218\pi\)
−0.121857 + 0.992548i \(0.538885\pi\)
\(30\) 0 0
\(31\) 19898.0 34464.3i 0.667920 1.15687i −0.310565 0.950552i \(-0.600518\pi\)
0.978485 0.206319i \(-0.0661484\pi\)
\(32\) 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 \(-0.419938\pi\)
−0.714336 + 0.699803i \(0.753271\pi\)
\(42\) 0 0
\(43\) −1900.00 3290.90i −0.0238973 0.0413913i 0.853829 0.520553i \(-0.174274\pi\)
−0.877727 + 0.479162i \(0.840941\pi\)
\(44\) 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 \(-0.787248\pi\)
0.144277 + 0.989537i \(0.453914\pi\)
\(48\) 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 \(-0.541459\pi\)
−0.923629 + 0.383287i \(0.874792\pi\)
\(60\) 0 0
\(61\) −6625.00 11474.8i −0.0291875 0.0505542i 0.851063 0.525064i \(-0.175959\pi\)
−0.880250 + 0.474510i \(0.842625\pi\)
\(62\) 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 −0.971606 0.236603i \(-0.923966\pi\)
0.690707 + 0.723134i \(0.257299\pi\)
\(68\) −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 0.883282 0.468842i \(-0.155329\pi\)
−0.847670 + 0.530524i \(0.821995\pi\)
\(80\) 178123.i 0.347897i
\(81\) 0 0
\(82\) 209544. 0.380044
\(83\) 9508.92 5489.98i 0.0166302 0.00960144i −0.491662 0.870786i \(-0.663610\pi\)
0.508292 + 0.861185i \(0.330277\pi\)
\(84\) 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 0.940538 0.339689i \(-0.110322\pi\)
−0.764448 + 0.644685i \(0.776989\pi\)
\(98\) 659629.i 0.700844i
\(99\) 0 0
\(100\) 468256. 0.468256
\(101\) −579181. + 334390.i −0.562147 + 0.324556i −0.754007 0.656867i \(-0.771881\pi\)
0.191860 + 0.981422i \(0.438548\pi\)
\(102\) 0 0
\(103\) −996706. + 1.72635e6i −0.912127 + 1.57985i −0.101073 + 0.994879i \(0.532228\pi\)
−0.811054 + 0.584972i \(0.801106\pi\)
\(104\) −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 \(-0.425263\pi\)
−0.725943 + 0.687755i \(0.758596\pi\)
\(114\) 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 \(-0.0937187\pi\)
0.227172 + 0.973855i \(0.427052\pi\)
\(132\) 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 0.510312 0.859990i \(-0.329530\pi\)
0.999929 0.0119482i \(-0.00380331\pi\)
\(138\) 0 0
\(139\) 546164. 945984.i 0.203366 0.352241i −0.746245 0.665672i \(-0.768145\pi\)
0.949611 + 0.313431i \(0.101478\pi\)
\(140\) 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 \(-0.442302\pi\)
−0.761701 + 0.647929i \(0.775635\pi\)
\(150\) 0 0
\(151\) 2.03935e6 + 3.53226e6i 0.592327 + 1.02594i 0.993918 + 0.110122i \(0.0351241\pi\)
−0.401591 + 0.915819i \(0.631543\pi\)
\(152\) 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 0.127301 + 0.991864i \(0.459369\pi\)
−0.922630 + 0.385686i \(0.873965\pi\)
\(158\) −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 \(-0.160827\pi\)
0.0183455 + 0.999832i \(0.494160\pi\)
\(168\) 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 \(-0.554634\pi\)
0.767902 + 0.640567i \(0.221301\pi\)
\(174\) 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 −0.626825 + 0.779160i \(0.715646\pi\)
−0.988185 + 0.153266i \(0.951021\pi\)
\(192\) 0 0
\(193\) 1.96598e6 3.40517e6i 0.273468 0.473660i −0.696279 0.717771i \(-0.745163\pi\)
0.969747 + 0.244110i \(0.0784959\pi\)
\(194\) −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 −0.241799 0.970326i \(-0.577738\pi\)
0.961227 0.275759i \(-0.0889291\pi\)
\(212\) −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 0.961123 0.276119i \(-0.0890484\pi\)
−0.719688 + 0.694298i \(0.755715\pi\)
\(224\) 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 \(-0.469089\pi\)
0.910424 + 0.413676i \(0.135755\pi\)
\(228\) 0 0
\(229\) −2.17320e6 + 3.76410e6i −0.180965 + 0.313440i −0.942209 0.335025i \(-0.891255\pi\)
0.761245 + 0.648465i \(0.224589\pi\)
\(230\) 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 \(-0.601817\pi\)
−0.979319 + 0.202324i \(0.935151\pi\)
\(240\) 0 0
\(241\) 1.56046e6 + 2.70280e6i 0.111481 + 0.193092i 0.916368 0.400337i \(-0.131107\pi\)
−0.804886 + 0.593429i \(0.797774\pi\)
\(242\) 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 \(-0.193514\pi\)
−0.0842448 + 0.996445i \(0.526848\pi\)
\(258\) 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 \(-0.995645\pi\)
−0.488105 + 0.872785i \(0.662312\pi\)
\(264\) 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 0.667555 0.744561i \(-0.267341\pi\)
−0.978586 + 0.205839i \(0.934008\pi\)
\(278\) 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 \(-0.622601\pi\)
0.614722 + 0.788744i \(0.289268\pi\)
\(282\) 0 0
\(283\) 3.37162e6 5.83982e6i 0.148758 0.257656i −0.782011 0.623265i \(-0.785806\pi\)
0.930769 + 0.365609i \(0.119139\pi\)
\(284\) 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 \(-0.397185\pi\)
−0.662532 + 0.749034i \(0.730518\pi\)
\(294\) 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 \(-0.159645\pi\)
0.0220578 + 0.999757i \(0.492978\pi\)
\(312\) 0 0
\(313\) −1.12389e7 1.94664e7i −0.366515 0.634822i 0.622503 0.782617i \(-0.286116\pi\)
−0.989018 + 0.147795i \(0.952782\pi\)
\(314\) 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 \(-0.523929\pi\)
0.826026 + 0.563631i \(0.190596\pi\)
\(318\) 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 0.903006 0.429627i \(-0.141355\pi\)
−0.823571 + 0.567213i \(0.808022\pi\)
\(332\) 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 −0.475673 0.879622i \(-0.657795\pi\)
0.999612 0.0278665i \(-0.00887132\pi\)
\(338\) 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 \(-0.0319804\pi\)
0.410616 + 0.911808i \(0.365314\pi\)
\(348\) 0 0
\(349\) 2.10319e7 + 3.64284e7i 0.494769 + 0.856965i 0.999982 0.00602956i \(-0.00191928\pi\)
−0.505213 + 0.862995i \(0.668586\pi\)
\(350\) 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 \(-0.602562\pi\)
0.663127 + 0.748507i \(0.269229\pi\)
\(354\) 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 0.968582 0.248694i \(-0.0800013\pi\)
−0.699666 + 0.714470i \(0.746668\pi\)
\(368\) 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 −0.939223 0.343307i \(-0.888453\pi\)
0.766924 + 0.641737i \(0.221786\pi\)
\(374\) −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 \(-0.308701\pi\)
−0.431554 + 0.902087i \(0.642035\pi\)
\(384\) 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 \(-0.528710\pi\)
0.817468 + 0.575974i \(0.195377\pi\)
\(390\) 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 \(-0.453273\pi\)
−0.783575 + 0.621297i \(0.786606\pi\)
\(402\) 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 −0.0421850 0.999110i \(-0.513432\pi\)
0.886347 0.463022i \(-0.153235\pi\)
\(410\) 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 0.901577 + 0.432618i \(0.142410\pi\)
0.825447 + 0.564480i \(0.190923\pi\)
\(420\) 0 0
\(421\) −6.96194e7 1.20584e8i −0.933005 1.61601i −0.778153 0.628075i \(-0.783843\pi\)
−0.154852 0.987938i \(-0.549490\pi\)
\(422\) 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 0.906378 + 0.422468i \(0.138836\pi\)
−0.0873208 + 0.996180i \(0.527831\pi\)
\(440\) 4.22152e7i 0.495576i
\(441\) 0 0
\(442\) −242496. −0.00280826
\(443\) 9.65121e7 5.57213e7i 1.11012 0.640929i 0.171261 0.985226i \(-0.445216\pi\)
0.938861 + 0.344296i \(0.111883\pi\)
\(444\) 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 0.757352 0.653007i \(-0.226493\pi\)
−0.944197 + 0.329382i \(0.893160\pi\)
\(458\) 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 \(-0.949241\pi\)
−0.356139 + 0.934433i \(0.615907\pi\)
\(462\) 0 0
\(463\) −5.74891e7 + 9.95740e7i −0.579218 + 1.00324i 0.416351 + 0.909204i \(0.363309\pi\)
−0.995569 + 0.0940314i \(0.970025\pi\)
\(464\) 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 \(-0.533276\pi\)
0.809123 + 0.587639i \(0.199943\pi\)
\(480\) 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 \(-0.272346\pi\)
−0.325935 + 0.945392i \(0.605679\pi\)
\(492\) 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 −0.989314 0.145801i \(-0.953424\pi\)
0.620925 + 0.783870i \(0.286757\pi\)
\(500\) −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 \(-0.304329\pi\)
−0.419122 + 0.907930i \(0.637662\pi\)
\(510\) 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 −0.988164 0.153399i \(-0.950978\pi\)
0.361234 0.932475i \(-0.382355\pi\)
\(548\) 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 \(-0.490223\pi\)
−0.850262 + 0.526360i \(0.823556\pi\)
\(564\) 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 \(-0.436273\pi\)
0.948162 + 0.317788i \(0.102940\pi\)
\(570\) 0 0
\(571\) −1.20751e8 + 2.09147e8i −0.648608 + 1.12342i 0.334848 + 0.942272i \(0.391315\pi\)
−0.983456 + 0.181149i \(0.942018\pi\)
\(572\) −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 \(-0.526828\pi\)
0.820859 + 0.571131i \(0.193495\pi\)
\(588\) 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 \(-0.465425\pi\)
−0.806717 + 0.590938i \(0.798758\pi\)
\(600\) 0 0
\(601\) 2.15545e8 + 3.73335e8i 0.992921 + 1.71979i 0.599323 + 0.800507i \(0.295437\pi\)
0.393598 + 0.919282i \(0.371230\pi\)
\(602\) 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 −0.884088 0.467320i \(-0.845220\pi\)
0.846755 + 0.531983i \(0.178553\pi\)
\(608\) 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 \(-0.463669\pi\)
−0.803447 + 0.595377i \(0.797003\pi\)
\(618\) 0 0
\(619\) −1.27437e8 2.20727e8i −0.537307 0.930643i −0.999048 0.0436278i \(-0.986108\pi\)
0.461741 0.887015i \(-0.347225\pi\)
\(620\) 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 \(-0.368187\pi\)
0.994011 + 0.109278i \(0.0348537\pi\)
\(642\) 0 0
\(643\) −1.87973e8 + 3.25579e8i −0.707071 + 1.22468i 0.258868 + 0.965913i \(0.416650\pi\)
−0.965939 + 0.258770i \(0.916683\pi\)
\(644\) −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 \(-0.179515\pi\)
−0.0403536 + 0.999185i \(0.512848\pi\)
\(654\) 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 \(-0.588388\pi\)
0.695789 + 0.718247i \(0.255055\pi\)
\(660\) 0 0
\(661\) 2.36272e8 4.09236e8i 0.818104 1.41700i −0.0889731 0.996034i \(-0.528359\pi\)
0.907077 0.420964i \(-0.138308\pi\)
\(662\) −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 −0.827164 0.561961i \(-0.810047\pi\)
−0.0730906 0.997325i \(-0.523286\pi\)
\(674\) 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 \(-0.614754\pi\)
0.633978 + 0.773351i \(0.281421\pi\)
\(678\) 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 0.997052 + 0.0767236i \(0.0244459\pi\)
−0.432082 + 0.901834i \(0.642221\pi\)
\(692\) 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 0.985505 0.169648i \(-0.0542631\pi\)
−0.639672 + 0.768648i \(0.720930\pi\)
\(710\) 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 −0.999942 0.0107471i \(-0.996579\pi\)
0.490664 0.871349i \(-0.336754\pi\)
\(728\) 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 −0.887334 0.461128i \(-0.847445\pi\)
0.843015 + 0.537889i \(0.180778\pi\)
\(734\) −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 \(-0.236540\pi\)
−0.217754 + 0.976004i \(0.569873\pi\)
\(744\) 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 −0.813334 0.581797i \(-0.802350\pi\)
0.910518 + 0.413470i \(0.135683\pi\)
\(752\) 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 \(-0.418483\pi\)
−0.711129 + 0.703061i \(0.751816\pi\)
\(762\) 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 −0.0655965 + 0.997846i \(0.520895\pi\)
−0.831362 + 0.555731i \(0.812438\pi\)
\(770\) 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