Properties

Label 336.6.q.e.289.1
Level $336$
Weight $6$
Character 336.289
Analytic conductor $53.889$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 336.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(53.8889634572\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-83})\)
Defining polynomial: \( x^{4} - x^{3} - 20x^{2} - 21x + 441 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.1
Root \(-3.69493 + 2.71062i\) of defining polynomial
Character \(\chi\) \(=\) 336.289
Dual form 336.6.q.e.193.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.50000 - 7.79423i) q^{3} +(-19.3645 + 33.5404i) q^{5} +(87.5000 + 95.6596i) q^{7} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\) \(q+(-4.50000 - 7.79423i) q^{3} +(-19.3645 + 33.5404i) q^{5} +(87.5000 + 95.6596i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(-288.195 - 499.168i) q^{11} +391.491 q^{13} +348.562 q^{15} +(664.850 + 1151.55i) q^{17} +(471.237 - 816.206i) q^{19} +(351.842 - 1112.46i) q^{21} +(-816.040 + 1413.42i) q^{23} +(812.530 + 1407.34i) q^{25} +729.000 q^{27} -1463.54 q^{29} +(-1956.21 - 3388.25i) q^{31} +(-2593.75 + 4492.51i) q^{33} +(-4902.85 + 1082.38i) q^{35} +(8150.17 - 14116.5i) q^{37} +(-1761.71 - 3051.37i) q^{39} -13103.8 q^{41} -14733.5 q^{43} +(-1568.53 - 2716.77i) q^{45} +(-3407.26 + 5901.55i) q^{47} +(-1494.50 + 16740.4i) q^{49} +(5983.65 - 10364.0i) q^{51} +(1005.67 + 1741.87i) q^{53} +22323.0 q^{55} -8482.26 q^{57} +(25726.6 + 44559.7i) q^{59} +(-20548.9 + 35591.8i) q^{61} +(-10254.1 + 2263.74i) q^{63} +(-7581.04 + 13130.8i) q^{65} +(25289.1 + 43802.0i) q^{67} +14688.7 q^{69} -39970.6 q^{71} +(27843.3 + 48226.0i) q^{73} +(7312.77 - 12666.1i) q^{75} +(22533.2 - 71245.8i) q^{77} +(-31575.7 + 54690.7i) q^{79} +(-3280.50 - 5681.99i) q^{81} -45572.4 q^{83} -51498.1 q^{85} +(6585.95 + 11407.2i) q^{87} +(-7843.34 + 13585.1i) q^{89} +(34255.5 + 37449.9i) q^{91} +(-17605.9 + 30494.3i) q^{93} +(18250.6 + 31610.9i) q^{95} +3128.49 q^{97} +46687.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 18 q^{3} + 33 q^{5} + 350 q^{7} - 162 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 18 q^{3} + 33 q^{5} + 350 q^{7} - 162 q^{9} - 1137 q^{11} + 1850 q^{13} - 594 q^{15} + 324 q^{17} + 2311 q^{19} - 1575 q^{21} + 1596 q^{23} - 395 q^{25} + 2916 q^{27} - 4434 q^{29} + 4294 q^{31} - 10233 q^{33} - 15414 q^{35} + 19109 q^{37} - 8325 q^{39} - 25716 q^{41} + 5542 q^{43} + 2673 q^{45} - 23160 q^{47} - 5978 q^{49} + 2916 q^{51} + 31653 q^{53} - 35778 q^{55} - 41598 q^{57} + 41097 q^{59} - 42052 q^{61} - 14175 q^{63} + 23106 q^{65} + 30763 q^{67} - 28728 q^{69} - 204192 q^{71} + 28577 q^{73} - 3555 q^{75} - 96873 q^{77} - 18464 q^{79} - 13122 q^{81} - 122358 q^{83} - 247272 q^{85} + 19953 q^{87} - 29322 q^{89} + 161875 q^{91} + 38646 q^{93} - 61662 q^{95} - 19582 q^{97} + 184194 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −4.50000 7.79423i −0.288675 0.500000i
\(4\) 0 0
\(5\) −19.3645 + 33.5404i −0.346403 + 0.599988i −0.985608 0.169049i \(-0.945930\pi\)
0.639204 + 0.769037i \(0.279264\pi\)
\(6\) 0 0
\(7\) 87.5000 + 95.6596i 0.674937 + 0.737876i
\(8\) 0 0
\(9\) −40.5000 + 70.1481i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −288.195 499.168i −0.718133 1.24384i −0.961739 0.273968i \(-0.911664\pi\)
0.243606 0.969874i \(-0.421670\pi\)
\(12\) 0 0
\(13\) 391.491 0.642486 0.321243 0.946997i \(-0.395899\pi\)
0.321243 + 0.946997i \(0.395899\pi\)
\(14\) 0 0
\(15\) 348.562 0.399992
\(16\) 0 0
\(17\) 664.850 + 1151.55i 0.557958 + 0.966412i 0.997667 + 0.0682711i \(0.0217483\pi\)
−0.439709 + 0.898140i \(0.644918\pi\)
\(18\) 0 0
\(19\) 471.237 816.206i 0.299471 0.518699i −0.676544 0.736402i \(-0.736523\pi\)
0.976015 + 0.217703i \(0.0698564\pi\)
\(20\) 0 0
\(21\) 351.842 1112.46i 0.174100 0.550475i
\(22\) 0 0
\(23\) −816.040 + 1413.42i −0.321656 + 0.557124i −0.980830 0.194866i \(-0.937573\pi\)
0.659174 + 0.751991i \(0.270906\pi\)
\(24\) 0 0
\(25\) 812.530 + 1407.34i 0.260009 + 0.450350i
\(26\) 0 0
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) −1463.54 −0.323155 −0.161577 0.986860i \(-0.551658\pi\)
−0.161577 + 0.986860i \(0.551658\pi\)
\(30\) 0 0
\(31\) −1956.21 3388.25i −0.365604 0.633245i 0.623269 0.782008i \(-0.285804\pi\)
−0.988873 + 0.148763i \(0.952471\pi\)
\(32\) 0 0
\(33\) −2593.75 + 4492.51i −0.414614 + 0.718133i
\(34\) 0 0
\(35\) −4902.85 + 1082.38i −0.676517 + 0.149351i
\(36\) 0 0
\(37\) 8150.17 14116.5i 0.978729 1.69521i 0.311691 0.950184i \(-0.399105\pi\)
0.667038 0.745024i \(-0.267562\pi\)
\(38\) 0 0
\(39\) −1761.71 3051.37i −0.185470 0.321243i
\(40\) 0 0
\(41\) −13103.8 −1.21741 −0.608707 0.793395i \(-0.708312\pi\)
−0.608707 + 0.793395i \(0.708312\pi\)
\(42\) 0 0
\(43\) −14733.5 −1.21516 −0.607582 0.794257i \(-0.707860\pi\)
−0.607582 + 0.794257i \(0.707860\pi\)
\(44\) 0 0
\(45\) −1568.53 2716.77i −0.115468 0.199996i
\(46\) 0 0
\(47\) −3407.26 + 5901.55i −0.224989 + 0.389692i −0.956316 0.292335i \(-0.905568\pi\)
0.731327 + 0.682027i \(0.238901\pi\)
\(48\) 0 0
\(49\) −1494.50 + 16740.4i −0.0889213 + 0.996039i
\(50\) 0 0
\(51\) 5983.65 10364.0i 0.322137 0.557958i
\(52\) 0 0
\(53\) 1005.67 + 1741.87i 0.0491775 + 0.0851779i 0.889566 0.456806i \(-0.151007\pi\)
−0.840389 + 0.541984i \(0.817673\pi\)
\(54\) 0 0
\(55\) 22323.0 0.995054
\(56\) 0 0
\(57\) −8482.26 −0.345800
\(58\) 0 0
\(59\) 25726.6 + 44559.7i 0.962170 + 1.66653i 0.717035 + 0.697037i \(0.245499\pi\)
0.245135 + 0.969489i \(0.421168\pi\)
\(60\) 0 0
\(61\) −20548.9 + 35591.8i −0.707073 + 1.22469i 0.258865 + 0.965913i \(0.416651\pi\)
−0.965938 + 0.258773i \(0.916682\pi\)
\(62\) 0 0
\(63\) −10254.1 + 2263.74i −0.325496 + 0.0718581i
\(64\) 0 0
\(65\) −7581.04 + 13130.8i −0.222559 + 0.385484i
\(66\) 0 0
\(67\) 25289.1 + 43802.0i 0.688250 + 1.19208i 0.972404 + 0.233305i \(0.0749542\pi\)
−0.284153 + 0.958779i \(0.591712\pi\)
\(68\) 0 0
\(69\) 14688.7 0.371416
\(70\) 0 0
\(71\) −39970.6 −0.941012 −0.470506 0.882397i \(-0.655929\pi\)
−0.470506 + 0.882397i \(0.655929\pi\)
\(72\) 0 0
\(73\) 27843.3 + 48226.0i 0.611524 + 1.05919i 0.990984 + 0.133983i \(0.0427767\pi\)
−0.379459 + 0.925208i \(0.623890\pi\)
\(74\) 0 0
\(75\) 7312.77 12666.1i 0.150117 0.260009i
\(76\) 0 0
\(77\) 22533.2 71245.8i 0.433107 1.36941i
\(78\) 0 0
\(79\) −31575.7 + 54690.7i −0.569226 + 0.985929i 0.427416 + 0.904055i \(0.359424\pi\)
−0.996643 + 0.0818739i \(0.973910\pi\)
\(80\) 0 0
\(81\) −3280.50 5681.99i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −45572.4 −0.726116 −0.363058 0.931766i \(-0.618267\pi\)
−0.363058 + 0.931766i \(0.618267\pi\)
\(84\) 0 0
\(85\) −51498.1 −0.773114
\(86\) 0 0
\(87\) 6585.95 + 11407.2i 0.0932868 + 0.161577i
\(88\) 0 0
\(89\) −7843.34 + 13585.1i −0.104961 + 0.181797i −0.913722 0.406340i \(-0.866805\pi\)
0.808762 + 0.588137i \(0.200138\pi\)
\(90\) 0 0
\(91\) 34255.5 + 37449.9i 0.433637 + 0.474075i
\(92\) 0 0
\(93\) −17605.9 + 30494.3i −0.211082 + 0.365604i
\(94\) 0 0
\(95\) 18250.6 + 31610.9i 0.207476 + 0.359358i
\(96\) 0 0
\(97\) 3128.49 0.0337603 0.0168801 0.999858i \(-0.494627\pi\)
0.0168801 + 0.999858i \(0.494627\pi\)
\(98\) 0 0
\(99\) 46687.6 0.478755
\(100\) 0 0
\(101\) 84505.5 + 146368.i 0.824292 + 1.42772i 0.902459 + 0.430776i \(0.141760\pi\)
−0.0781663 + 0.996940i \(0.524907\pi\)
\(102\) 0 0
\(103\) 56410.1 97705.1i 0.523918 0.907453i −0.475694 0.879611i \(-0.657803\pi\)
0.999612 0.0278422i \(-0.00886360\pi\)
\(104\) 0 0
\(105\) 30499.1 + 33343.2i 0.269969 + 0.295144i
\(106\) 0 0
\(107\) −11154.7 + 19320.6i −0.0941890 + 0.163140i −0.909270 0.416207i \(-0.863359\pi\)
0.815081 + 0.579347i \(0.196692\pi\)
\(108\) 0 0
\(109\) 41909.8 + 72589.8i 0.337869 + 0.585207i 0.984032 0.177993i \(-0.0569604\pi\)
−0.646162 + 0.763200i \(0.723627\pi\)
\(110\) 0 0
\(111\) −146703. −1.13014
\(112\) 0 0
\(113\) −40928.4 −0.301529 −0.150764 0.988570i \(-0.548174\pi\)
−0.150764 + 0.988570i \(0.548174\pi\)
\(114\) 0 0
\(115\) −31604.4 54740.5i −0.222845 0.385980i
\(116\) 0 0
\(117\) −15855.4 + 27462.3i −0.107081 + 0.185470i
\(118\) 0 0
\(119\) −51982.8 + 164360.i −0.336505 + 1.06397i
\(120\) 0 0
\(121\) −85587.1 + 148241.i −0.531429 + 0.920462i
\(122\) 0 0
\(123\) 58967.2 + 102134.i 0.351437 + 0.608707i
\(124\) 0 0
\(125\) −183965. −1.05308
\(126\) 0 0
\(127\) −83270.1 −0.458120 −0.229060 0.973412i \(-0.573565\pi\)
−0.229060 + 0.973412i \(0.573565\pi\)
\(128\) 0 0
\(129\) 66300.7 + 114836.i 0.350788 + 0.607582i
\(130\) 0 0
\(131\) −83437.4 + 144518.i −0.424798 + 0.735772i −0.996402 0.0847580i \(-0.972988\pi\)
0.571603 + 0.820530i \(0.306322\pi\)
\(132\) 0 0
\(133\) 119311. 26339.7i 0.584860 0.129117i
\(134\) 0 0
\(135\) −14116.7 + 24450.9i −0.0666653 + 0.115468i
\(136\) 0 0
\(137\) −19111.9 33102.9i −0.0869969 0.150683i 0.819244 0.573446i \(-0.194394\pi\)
−0.906240 + 0.422763i \(0.861060\pi\)
\(138\) 0 0
\(139\) −106263. −0.466492 −0.233246 0.972418i \(-0.574935\pi\)
−0.233246 + 0.972418i \(0.574935\pi\)
\(140\) 0 0
\(141\) 61330.7 0.259795
\(142\) 0 0
\(143\) −112826. 195420.i −0.461390 0.799151i
\(144\) 0 0
\(145\) 28340.8 49087.8i 0.111942 0.193889i
\(146\) 0 0
\(147\) 137204. 63683.4i 0.523689 0.243071i
\(148\) 0 0
\(149\) −96277.8 + 166758.i −0.355271 + 0.615348i −0.987164 0.159708i \(-0.948945\pi\)
0.631893 + 0.775056i \(0.282278\pi\)
\(150\) 0 0
\(151\) 70849.3 + 122715.i 0.252868 + 0.437980i 0.964314 0.264761i \(-0.0852929\pi\)
−0.711447 + 0.702740i \(0.751960\pi\)
\(152\) 0 0
\(153\) −107706. −0.371972
\(154\) 0 0
\(155\) 151524. 0.506586
\(156\) 0 0
\(157\) −282885. 489972.i −0.915928 1.58643i −0.805536 0.592546i \(-0.798123\pi\)
−0.110392 0.993888i \(-0.535211\pi\)
\(158\) 0 0
\(159\) 9051.04 15676.9i 0.0283926 0.0491775i
\(160\) 0 0
\(161\) −206611. + 45612.4i −0.628186 + 0.138682i
\(162\) 0 0
\(163\) −215101. + 372565.i −0.634121 + 1.09833i 0.352579 + 0.935782i \(0.385305\pi\)
−0.986701 + 0.162549i \(0.948029\pi\)
\(164\) 0 0
\(165\) −100454. 173991.i −0.287247 0.497527i
\(166\) 0 0
\(167\) 240265. 0.666653 0.333327 0.942811i \(-0.391829\pi\)
0.333327 + 0.942811i \(0.391829\pi\)
\(168\) 0 0
\(169\) −218028. −0.587212
\(170\) 0 0
\(171\) 38170.2 + 66112.7i 0.0998238 + 0.172900i
\(172\) 0 0
\(173\) 89650.1 155279.i 0.227738 0.394454i −0.729399 0.684088i \(-0.760200\pi\)
0.957137 + 0.289634i \(0.0935337\pi\)
\(174\) 0 0
\(175\) −63529.4 + 200869.i −0.156812 + 0.495812i
\(176\) 0 0
\(177\) 231539. 401037.i 0.555509 0.962170i
\(178\) 0 0
\(179\) −287780. 498449.i −0.671317 1.16275i −0.977531 0.210792i \(-0.932396\pi\)
0.306214 0.951963i \(-0.400938\pi\)
\(180\) 0 0
\(181\) 581006. 1.31821 0.659105 0.752051i \(-0.270935\pi\)
0.659105 + 0.752051i \(0.270935\pi\)
\(182\) 0 0
\(183\) 369880. 0.816458
\(184\) 0 0
\(185\) 315648. + 546719.i 0.678070 + 1.17445i
\(186\) 0 0
\(187\) 383213. 663744.i 0.801376 1.38802i
\(188\) 0 0
\(189\) 63787.5 + 69735.8i 0.129892 + 0.142004i
\(190\) 0 0
\(191\) −330280. + 572062.i −0.655087 + 1.13464i 0.326785 + 0.945099i \(0.394035\pi\)
−0.981872 + 0.189545i \(0.939299\pi\)
\(192\) 0 0
\(193\) 278655. + 482645.i 0.538485 + 0.932684i 0.998986 + 0.0450243i \(0.0143365\pi\)
−0.460501 + 0.887659i \(0.652330\pi\)
\(194\) 0 0
\(195\) 136459. 0.256989
\(196\) 0 0
\(197\) −761400. −1.39781 −0.698904 0.715216i \(-0.746328\pi\)
−0.698904 + 0.715216i \(0.746328\pi\)
\(198\) 0 0
\(199\) −67929.9 117658.i −0.121598 0.210615i 0.798800 0.601597i \(-0.205469\pi\)
−0.920398 + 0.390982i \(0.872135\pi\)
\(200\) 0 0
\(201\) 227602. 394218.i 0.397361 0.688250i
\(202\) 0 0
\(203\) −128060. 140002.i −0.218109 0.238448i
\(204\) 0 0
\(205\) 253750. 439507.i 0.421716 0.730434i
\(206\) 0 0
\(207\) −66099.2 114487.i −0.107219 0.185708i
\(208\) 0 0
\(209\) −543232. −0.860240
\(210\) 0 0
\(211\) 991157. 1.53263 0.766313 0.642467i \(-0.222089\pi\)
0.766313 + 0.642467i \(0.222089\pi\)
\(212\) 0 0
\(213\) 179868. + 311540.i 0.271647 + 0.470506i
\(214\) 0 0
\(215\) 285307. 494167.i 0.420937 0.729084i
\(216\) 0 0
\(217\) 152951. 483602.i 0.220496 0.697170i
\(218\) 0 0
\(219\) 250590. 434034.i 0.353064 0.611524i
\(220\) 0 0
\(221\) 260283. + 450823.i 0.358480 + 0.620906i
\(222\) 0 0
\(223\) −543344. −0.731666 −0.365833 0.930681i \(-0.619216\pi\)
−0.365833 + 0.930681i \(0.619216\pi\)
\(224\) 0 0
\(225\) −131630. −0.173340
\(226\) 0 0
\(227\) 8.16704 + 14.1457i 1.05196e−5 + 1.82205e-5i 0.866031 0.499991i \(-0.166663\pi\)
−0.866020 + 0.500009i \(0.833330\pi\)
\(228\) 0 0
\(229\) 38689.5 67012.2i 0.0487534 0.0844433i −0.840619 0.541627i \(-0.817808\pi\)
0.889372 + 0.457184i \(0.151142\pi\)
\(230\) 0 0
\(231\) −656705. + 144978.i −0.809731 + 0.178760i
\(232\) 0 0
\(233\) 51828.6 89769.9i 0.0625432 0.108328i −0.833058 0.553185i \(-0.813412\pi\)
0.895602 + 0.444857i \(0.146746\pi\)
\(234\) 0 0
\(235\) −131960. 228561.i −0.155874 0.269981i
\(236\) 0 0
\(237\) 568362. 0.657286
\(238\) 0 0
\(239\) −689109. −0.780356 −0.390178 0.920739i \(-0.627587\pi\)
−0.390178 + 0.920739i \(0.627587\pi\)
\(240\) 0 0
\(241\) −110148. 190782.i −0.122161 0.211590i 0.798458 0.602050i \(-0.205649\pi\)
−0.920620 + 0.390460i \(0.872316\pi\)
\(242\) 0 0
\(243\) −29524.5 + 51137.9i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) −532539. 374297.i −0.566809 0.398383i
\(246\) 0 0
\(247\) 184485. 319537.i 0.192406 0.333257i
\(248\) 0 0
\(249\) 205076. + 355201.i 0.209612 + 0.363058i
\(250\) 0 0
\(251\) −1.43641e6 −1.43912 −0.719558 0.694433i \(-0.755655\pi\)
−0.719558 + 0.694433i \(0.755655\pi\)
\(252\) 0 0
\(253\) 940714. 0.923966
\(254\) 0 0
\(255\) 231741. + 401388.i 0.223179 + 0.386557i
\(256\) 0 0
\(257\) 454598. 787388.i 0.429334 0.743628i −0.567480 0.823387i \(-0.692082\pi\)
0.996814 + 0.0797589i \(0.0254151\pi\)
\(258\) 0 0
\(259\) 2.06352e6 455553.i 1.91143 0.421977i
\(260\) 0 0
\(261\) 59273.5 102665.i 0.0538592 0.0932868i
\(262\) 0 0
\(263\) 374528. + 648702.i 0.333884 + 0.578304i 0.983270 0.182155i \(-0.0583073\pi\)
−0.649386 + 0.760459i \(0.724974\pi\)
\(264\) 0 0
\(265\) −77897.4 −0.0681410
\(266\) 0 0
\(267\) 141180. 0.121198
\(268\) 0 0
\(269\) −334972. 580189.i −0.282246 0.488865i 0.689691 0.724104i \(-0.257746\pi\)
−0.971938 + 0.235238i \(0.924413\pi\)
\(270\) 0 0
\(271\) 270330. 468225.i 0.223599 0.387285i −0.732299 0.680983i \(-0.761553\pi\)
0.955898 + 0.293698i \(0.0948860\pi\)
\(272\) 0 0
\(273\) 137743. 435519.i 0.111857 0.353672i
\(274\) 0 0
\(275\) 468334. 811178.i 0.373443 0.646821i
\(276\) 0 0
\(277\) 200955. + 348064.i 0.157362 + 0.272558i 0.933916 0.357491i \(-0.116368\pi\)
−0.776555 + 0.630050i \(0.783035\pi\)
\(278\) 0 0
\(279\) 316906. 0.243736
\(280\) 0 0
\(281\) −429139. −0.324214 −0.162107 0.986773i \(-0.551829\pi\)
−0.162107 + 0.986773i \(0.551829\pi\)
\(282\) 0 0
\(283\) −170463. 295251.i −0.126522 0.219142i 0.795805 0.605553i \(-0.207048\pi\)
−0.922327 + 0.386411i \(0.873715\pi\)
\(284\) 0 0
\(285\) 164255. 284498.i 0.119786 0.207476i
\(286\) 0 0
\(287\) −1.14658e6 1.25351e6i −0.821678 0.898301i
\(288\) 0 0
\(289\) −174123. + 301590.i −0.122634 + 0.212409i
\(290\) 0 0
\(291\) −14078.2 24384.2i −0.00974575 0.0168801i
\(292\) 0 0
\(293\) −388847. −0.264612 −0.132306 0.991209i \(-0.542238\pi\)
−0.132306 + 0.991209i \(0.542238\pi\)
\(294\) 0 0
\(295\) −1.99273e6 −1.33319
\(296\) 0 0
\(297\) −210094. 363894.i −0.138205 0.239378i
\(298\) 0 0
\(299\) −319472. + 553342.i −0.206659 + 0.357945i
\(300\) 0 0
\(301\) −1.28918e6 1.40940e6i −0.820158 0.896640i
\(302\) 0 0
\(303\) 760549. 1.31731e6i 0.475905 0.824292i
\(304\) 0 0
\(305\) −795840. 1.37844e6i −0.489865 0.848471i
\(306\) 0 0
\(307\) 2.35747e6 1.42758 0.713789 0.700361i \(-0.246978\pi\)
0.713789 + 0.700361i \(0.246978\pi\)
\(308\) 0 0
\(309\) −1.01538e6 −0.604969
\(310\) 0 0
\(311\) −718314. 1.24416e6i −0.421127 0.729414i 0.574923 0.818208i \(-0.305032\pi\)
−0.996050 + 0.0887939i \(0.971699\pi\)
\(312\) 0 0
\(313\) 411400. 712566.i 0.237358 0.411116i −0.722598 0.691269i \(-0.757052\pi\)
0.959955 + 0.280153i \(0.0903853\pi\)
\(314\) 0 0
\(315\) 122639. 387762.i 0.0696388 0.220186i
\(316\) 0 0
\(317\) 883467. 1.53021e6i 0.493790 0.855269i −0.506184 0.862425i \(-0.668944\pi\)
0.999974 + 0.00715584i \(0.00227779\pi\)
\(318\) 0 0
\(319\) 421786. + 730555.i 0.232068 + 0.401954i
\(320\) 0 0
\(321\) 200785. 0.108760
\(322\) 0 0
\(323\) 1.25321e6 0.668370
\(324\) 0 0
\(325\) 318098. + 550962.i 0.167052 + 0.289343i
\(326\) 0 0
\(327\) 377188. 653309.i 0.195069 0.337869i
\(328\) 0 0
\(329\) −862675. + 190448.i −0.439397 + 0.0970036i
\(330\) 0 0
\(331\) −1526.14 + 2643.35i −0.000765638 + 0.00132612i −0.866408 0.499337i \(-0.833577\pi\)
0.865642 + 0.500663i \(0.166910\pi\)
\(332\) 0 0
\(333\) 660164. + 1.14344e6i 0.326243 + 0.565069i
\(334\) 0 0
\(335\) −1.95885e6 −0.953649
\(336\) 0 0
\(337\) 2.02939e6 0.973398 0.486699 0.873570i \(-0.338201\pi\)
0.486699 + 0.873570i \(0.338201\pi\)
\(338\) 0 0
\(339\) 184178. + 319006.i 0.0870439 + 0.150764i
\(340\) 0 0
\(341\) −1.12754e6 + 1.95295e6i −0.525104 + 0.909507i
\(342\) 0 0
\(343\) −1.73215e6 + 1.32182e6i −0.794969 + 0.606650i
\(344\) 0 0
\(345\) −284440. + 492665.i −0.128660 + 0.222845i
\(346\) 0 0
\(347\) 1.89109e6 + 3.27547e6i 0.843119 + 1.46033i 0.887245 + 0.461299i \(0.152617\pi\)
−0.0441252 + 0.999026i \(0.514050\pi\)
\(348\) 0 0
\(349\) 291147. 0.127953 0.0639763 0.997951i \(-0.479622\pi\)
0.0639763 + 0.997951i \(0.479622\pi\)
\(350\) 0 0
\(351\) 285397. 0.123646
\(352\) 0 0
\(353\) −192538. 333486.i −0.0822394 0.142443i 0.821972 0.569528i \(-0.192874\pi\)
−0.904212 + 0.427085i \(0.859541\pi\)
\(354\) 0 0
\(355\) 774013. 1.34063e6i 0.325970 0.564596i
\(356\) 0 0
\(357\) 1.51498e6 334456.i 0.629126 0.138889i
\(358\) 0 0
\(359\) −1.61507e6 + 2.79738e6i −0.661385 + 1.14555i 0.318866 + 0.947800i \(0.396698\pi\)
−0.980252 + 0.197753i \(0.936635\pi\)
\(360\) 0 0
\(361\) 793921. + 1.37511e6i 0.320634 + 0.555354i
\(362\) 0 0
\(363\) 1.54057e6 0.613641
\(364\) 0 0
\(365\) −2.15669e6 −0.847336
\(366\) 0 0
\(367\) −239779. 415310.i −0.0929280 0.160956i 0.815814 0.578314i \(-0.196289\pi\)
−0.908742 + 0.417358i \(0.862956\pi\)
\(368\) 0 0
\(369\) 530705. 919208.i 0.202902 0.351437i
\(370\) 0 0
\(371\) −78630.6 + 248616.i −0.0296590 + 0.0937766i
\(372\) 0 0
\(373\) −436333. + 755751.i −0.162385 + 0.281259i −0.935724 0.352734i \(-0.885252\pi\)
0.773339 + 0.633993i \(0.218585\pi\)
\(374\) 0 0
\(375\) 827844. + 1.43387e6i 0.303998 + 0.526540i
\(376\) 0 0
\(377\) −572965. −0.207622
\(378\) 0 0
\(379\) 2.43493e6 0.870742 0.435371 0.900251i \(-0.356617\pi\)
0.435371 + 0.900251i \(0.356617\pi\)
\(380\) 0 0
\(381\) 374715. + 649026.i 0.132248 + 0.229060i
\(382\) 0 0
\(383\) −1.80584e6 + 3.12781e6i −0.629047 + 1.08954i 0.358696 + 0.933454i \(0.383222\pi\)
−0.987743 + 0.156087i \(0.950112\pi\)
\(384\) 0 0
\(385\) 1.95327e6 + 2.13541e6i 0.671598 + 0.734226i
\(386\) 0 0
\(387\) 596707. 1.03353e6i 0.202527 0.350788i
\(388\) 0 0
\(389\) 87616.2 + 151756.i 0.0293569 + 0.0508477i 0.880331 0.474361i \(-0.157321\pi\)
−0.850974 + 0.525208i \(0.823987\pi\)
\(390\) 0 0
\(391\) −2.17018e6 −0.717882
\(392\) 0 0
\(393\) 1.50187e6 0.490515
\(394\) 0 0
\(395\) −1.22290e6 2.11812e6i −0.394364 0.683058i
\(396\) 0 0
\(397\) −942577. + 1.63259e6i −0.300152 + 0.519878i −0.976170 0.217007i \(-0.930371\pi\)
0.676019 + 0.736885i \(0.263704\pi\)
\(398\) 0 0
\(399\) −742198. 811409.i −0.233393 0.255157i
\(400\) 0 0
\(401\) −669915. + 1.16033e6i −0.208046 + 0.360346i −0.951099 0.308887i \(-0.900044\pi\)
0.743053 + 0.669232i \(0.233377\pi\)
\(402\) 0 0
\(403\) −765839. 1.32647e6i −0.234895 0.406851i
\(404\) 0 0
\(405\) 254101. 0.0769785
\(406\) 0 0
\(407\) −9.39535e6 −2.81143
\(408\) 0 0
\(409\) −3.29314e6 5.70388e6i −0.973423 1.68602i −0.685043 0.728503i \(-0.740217\pi\)
−0.288381 0.957516i \(-0.593117\pi\)
\(410\) 0 0
\(411\) −172008. + 297926.i −0.0502277 + 0.0869969i
\(412\) 0 0
\(413\) −2.01149e6 + 6.35996e6i −0.580286 + 1.83476i
\(414\) 0 0
\(415\) 882487. 1.52851e6i 0.251529 0.435661i
\(416\) 0 0
\(417\) 478182. + 828236.i 0.134665 + 0.233246i
\(418\) 0 0
\(419\) 6.96869e6 1.93917 0.969585 0.244754i \(-0.0787071\pi\)
0.969585 + 0.244754i \(0.0787071\pi\)
\(420\) 0 0
\(421\) 3.84041e6 1.05602 0.528010 0.849238i \(-0.322938\pi\)
0.528010 + 0.849238i \(0.322938\pi\)
\(422\) 0 0
\(423\) −275988. 478025.i −0.0749962 0.129897i
\(424\) 0 0
\(425\) −1.08042e6 + 1.87134e6i −0.290149 + 0.502552i
\(426\) 0 0
\(427\) −5.20272e6 + 1.14858e6i −1.38090 + 0.304854i
\(428\) 0 0
\(429\) −1.01543e6 + 1.75878e6i −0.266384 + 0.461390i
\(430\) 0 0
\(431\) 1.51818e6 + 2.62957e6i 0.393668 + 0.681854i 0.992930 0.118699i \(-0.0378725\pi\)
−0.599262 + 0.800553i \(0.704539\pi\)
\(432\) 0 0
\(433\) −941529. −0.241332 −0.120666 0.992693i \(-0.538503\pi\)
−0.120666 + 0.992693i \(0.538503\pi\)
\(434\) 0 0
\(435\) −510135. −0.129259
\(436\) 0 0
\(437\) 769096. + 1.33211e6i 0.192653 + 0.333686i
\(438\) 0 0
\(439\) 670546. 1.16142e6i 0.166061 0.287626i −0.770971 0.636871i \(-0.780229\pi\)
0.937031 + 0.349245i \(0.113562\pi\)
\(440\) 0 0
\(441\) −1.11378e6 782823.i −0.272711 0.191676i
\(442\) 0 0
\(443\) −386171. + 668867.i −0.0934910 + 0.161931i −0.908978 0.416844i \(-0.863136\pi\)
0.815487 + 0.578776i \(0.196469\pi\)
\(444\) 0 0
\(445\) −303765. 526137.i −0.0727174 0.125950i
\(446\) 0 0
\(447\) 1.73300e6 0.410232
\(448\) 0 0
\(449\) 2.25684e6 0.528304 0.264152 0.964481i \(-0.414908\pi\)
0.264152 + 0.964481i \(0.414908\pi\)
\(450\) 0 0
\(451\) 3.77646e6 + 6.54101e6i 0.874265 + 1.51427i
\(452\) 0 0
\(453\) 637644. 1.10443e6i 0.145993 0.252868i
\(454\) 0 0
\(455\) −1.91942e6 + 423742.i −0.434653 + 0.0959561i
\(456\) 0 0
\(457\) −2.14235e6 + 3.71066e6i −0.479844 + 0.831114i −0.999733 0.0231196i \(-0.992640\pi\)
0.519889 + 0.854234i \(0.325973\pi\)
\(458\) 0 0
\(459\) 484676. + 839483.i 0.107379 + 0.185986i
\(460\) 0 0
\(461\) −3.10462e6 −0.680387 −0.340193 0.940355i \(-0.610493\pi\)
−0.340193 + 0.940355i \(0.610493\pi\)
\(462\) 0 0
\(463\) 3.53386e6 0.766121 0.383060 0.923723i \(-0.374870\pi\)
0.383060 + 0.923723i \(0.374870\pi\)
\(464\) 0 0
\(465\) −681859. 1.18102e6i −0.146239 0.253293i
\(466\) 0 0
\(467\) 1.36230e6 2.35957e6i 0.289054 0.500657i −0.684530 0.728985i \(-0.739993\pi\)
0.973584 + 0.228328i \(0.0733258\pi\)
\(468\) 0 0
\(469\) −1.97728e6 + 6.25182e6i −0.415085 + 1.31242i
\(470\) 0 0
\(471\) −2.54597e6 + 4.40975e6i −0.528812 + 0.915928i
\(472\) 0 0
\(473\) 4.24612e6 + 7.35449e6i 0.872649 + 1.51147i
\(474\) 0 0
\(475\) 1.53158e6 0.311461
\(476\) 0 0
\(477\) −162919. −0.0327850
\(478\) 0 0
\(479\) 489342. + 847566.i 0.0974482 + 0.168785i 0.910628 0.413228i \(-0.135599\pi\)
−0.813180 + 0.582013i \(0.802265\pi\)
\(480\) 0 0
\(481\) 3.19072e6 5.52649e6i 0.628819 1.08915i
\(482\) 0 0
\(483\) 1.28526e6 + 1.40512e6i 0.250682 + 0.274059i
\(484\) 0 0
\(485\) −60581.8 + 104931.i −0.0116947 + 0.0202558i
\(486\) 0 0
\(487\) 1.96372e6 + 3.40126e6i 0.375195 + 0.649857i 0.990356 0.138544i \(-0.0442423\pi\)
−0.615161 + 0.788401i \(0.710909\pi\)
\(488\) 0 0
\(489\) 3.87181e6 0.732220
\(490\) 0 0
\(491\) −2.63241e6 −0.492777 −0.246388 0.969171i \(-0.579244\pi\)
−0.246388 + 0.969171i \(0.579244\pi\)
\(492\) 0 0
\(493\) −973037. 1.68535e6i −0.180307 0.312301i
\(494\) 0 0
\(495\) −904083. + 1.56592e6i −0.165842 + 0.287247i
\(496\) 0 0
\(497\) −3.49743e6 3.82357e6i −0.635123 0.694350i
\(498\) 0 0
\(499\) 1.06272e6 1.84069e6i 0.191059 0.330924i −0.754542 0.656251i \(-0.772141\pi\)
0.945601 + 0.325327i \(0.105474\pi\)
\(500\) 0 0
\(501\) −1.08119e6 1.87268e6i −0.192446 0.333327i
\(502\) 0 0
\(503\) −2.60929e6 −0.459835 −0.229917 0.973210i \(-0.573846\pi\)
−0.229917 + 0.973210i \(0.573846\pi\)
\(504\) 0 0
\(505\) −6.54564e6 −1.14215
\(506\) 0 0
\(507\) 981124. + 1.69936e6i 0.169513 + 0.293606i
\(508\) 0 0
\(509\) 5.00911e6 8.67603e6i 0.856970 1.48432i −0.0178348 0.999841i \(-0.505677\pi\)
0.874805 0.484475i \(-0.160989\pi\)
\(510\) 0 0
\(511\) −2.17699e6 + 6.88326e6i −0.368811 + 1.16612i
\(512\) 0 0
\(513\) 343532. 595014.i 0.0576333 0.0998238i
\(514\) 0 0
\(515\) 2.18471e6 + 3.78403e6i 0.362974 + 0.628689i
\(516\) 0 0
\(517\) 3.92782e6 0.646287
\(518\) 0 0
\(519\) −1.61370e6 −0.262969
\(520\) 0 0
\(521\) 2.08970e6 + 3.61947e6i 0.337280 + 0.584186i 0.983920 0.178609i \(-0.0571598\pi\)
−0.646640 + 0.762795i \(0.723826\pi\)
\(522\) 0 0
\(523\) 1.80263e6 3.12224e6i 0.288172 0.499128i −0.685202 0.728353i \(-0.740286\pi\)
0.973373 + 0.229225i \(0.0736193\pi\)
\(524\) 0 0
\(525\) 1.85150e6 408746.i 0.293174 0.0647225i
\(526\) 0 0
\(527\) 2.60117e6 4.50536e6i 0.407983 0.706648i
\(528\) 0 0
\(529\) 1.88633e6 + 3.26722e6i 0.293075 + 0.507621i
\(530\) 0 0
\(531\) −4.16770e6 −0.641446
\(532\) 0 0
\(533\) −5.13003e6 −0.782172
\(534\) 0 0
\(535\) −432013. 748268.i −0.0652547 0.113025i
\(536\) 0 0
\(537\) −2.59002e6 + 4.48604e6i −0.387585 + 0.671317i
\(538\) 0 0
\(539\) 8.78699e6 4.07850e6i 1.30277 0.604684i
\(540\) 0 0
\(541\) 3.34083e6 5.78648e6i 0.490751 0.850005i −0.509193 0.860653i \(-0.670056\pi\)
0.999943 + 0.0106475i \(0.00338926\pi\)
\(542\) 0 0
\(543\) −2.61453e6 4.52850e6i −0.380534 0.659105i
\(544\) 0 0
\(545\) −3.24625e6 −0.468156
\(546\) 0 0
\(547\) −8.69076e6 −1.24191 −0.620954 0.783847i \(-0.713255\pi\)
−0.620954 + 0.783847i \(0.713255\pi\)
\(548\) 0 0
\(549\) −1.66446e6 2.88293e6i −0.235691 0.408229i
\(550\) 0 0
\(551\) −689676. + 1.19455e6i −0.0967756 + 0.167620i
\(552\) 0 0
\(553\) −7.99456e6 + 1.76492e6i −1.11168 + 0.245421i
\(554\) 0 0
\(555\) 2.84084e6 4.92047e6i 0.391484 0.678070i
\(556\) 0 0
\(557\) −3.12371e6 5.41042e6i −0.426612 0.738913i 0.569958 0.821674i \(-0.306960\pi\)
−0.996569 + 0.0827611i \(0.973626\pi\)
\(558\) 0 0
\(559\) −5.76803e6 −0.780725
\(560\) 0 0
\(561\) −6.89783e6 −0.925349
\(562\) 0 0
\(563\) −5.95223e6 1.03096e7i −0.791423 1.37078i −0.925086 0.379758i \(-0.876007\pi\)
0.133663 0.991027i \(-0.457326\pi\)
\(564\) 0 0
\(565\) 792560. 1.37275e6i 0.104451 0.180914i
\(566\) 0 0
\(567\) 256493. 810986.i 0.0335057 0.105939i
\(568\) 0 0
\(569\) −10707.2 + 18545.4i −0.00138642 + 0.00240135i −0.866718 0.498799i \(-0.833775\pi\)
0.865331 + 0.501200i \(0.167108\pi\)
\(570\) 0 0
\(571\) 3.55823e6 + 6.16304e6i 0.456714 + 0.791051i 0.998785 0.0492811i \(-0.0156930\pi\)
−0.542071 + 0.840333i \(0.682360\pi\)
\(572\) 0 0
\(573\) 5.94504e6 0.756429
\(574\) 0 0
\(575\) −2.65223e6 −0.334534
\(576\) 0 0
\(577\) 5.33259e6 + 9.23632e6i 0.666805 + 1.15494i 0.978793 + 0.204854i \(0.0656719\pi\)
−0.311988 + 0.950086i \(0.600995\pi\)
\(578\) 0 0
\(579\) 2.50790e6 4.34380e6i 0.310895 0.538485i
\(580\) 0 0
\(581\) −3.98758e6 4.35943e6i −0.490083 0.535784i
\(582\) 0 0
\(583\) 579659. 1.00400e6i 0.0706319 0.122338i
\(584\) 0 0
\(585\) −614065. 1.06359e6i −0.0741864 0.128495i
\(586\) 0 0
\(587\) 1.30101e7 1.55843 0.779213 0.626759i \(-0.215619\pi\)
0.779213 + 0.626759i \(0.215619\pi\)
\(588\) 0 0
\(589\) −3.68735e6 −0.437952
\(590\) 0 0
\(591\) 3.42630e6 + 5.93453e6i 0.403512 + 0.698904i
\(592\) 0 0
\(593\) −2.13043e6 + 3.69002e6i −0.248789 + 0.430915i −0.963190 0.268821i \(-0.913366\pi\)
0.714401 + 0.699736i \(0.246699\pi\)
\(594\) 0 0
\(595\) −4.50608e6 4.92628e6i −0.521803 0.570462i
\(596\) 0 0
\(597\) −611369. + 1.05892e6i −0.0702049 + 0.121598i
\(598\) 0 0
\(599\) −6.89790e6 1.19475e7i −0.785507 1.36054i −0.928696 0.370842i \(-0.879069\pi\)
0.143189 0.989695i \(-0.454264\pi\)
\(600\) 0 0
\(601\) 4.99695e6 0.564311 0.282155 0.959369i \(-0.408951\pi\)
0.282155 + 0.959369i \(0.408951\pi\)
\(602\) 0 0
\(603\) −4.09683e6 −0.458833
\(604\) 0 0
\(605\) −3.31471e6 5.74125e6i −0.368177 0.637702i
\(606\) 0 0
\(607\) −1.52473e6 + 2.64091e6i −0.167966 + 0.290926i −0.937705 0.347434i \(-0.887053\pi\)
0.769739 + 0.638359i \(0.220387\pi\)
\(608\) 0 0
\(609\) −514937. + 1.62814e6i −0.0562614 + 0.177889i
\(610\) 0 0
\(611\) −1.33391e6 + 2.31040e6i −0.144552 + 0.250372i
\(612\) 0 0
\(613\) 3.51813e6 + 6.09357e6i 0.378147 + 0.654969i 0.990793 0.135388i \(-0.0432282\pi\)
−0.612646 + 0.790357i \(0.709895\pi\)
\(614\) 0 0
\(615\) −4.56749e6 −0.486956
\(616\) 0 0
\(617\) 1.00066e7 1.05822 0.529108 0.848554i \(-0.322527\pi\)
0.529108 + 0.848554i \(0.322527\pi\)
\(618\) 0 0
\(619\) −3.27533e6 5.67304e6i −0.343581 0.595099i 0.641514 0.767111i \(-0.278307\pi\)
−0.985095 + 0.172012i \(0.944973\pi\)
\(620\) 0 0
\(621\) −594893. + 1.03038e6i −0.0619027 + 0.107219i
\(622\) 0 0
\(623\) −1.98583e6 + 438403.i −0.204985 + 0.0452536i
\(624\) 0 0
\(625\) 1.02325e6 1.77232e6i 0.104781 0.181485i
\(626\) 0 0
\(627\) 2.44455e6 + 4.23408e6i 0.248330 + 0.430120i
\(628\) 0 0
\(629\) 2.16746e7 2.18436
\(630\) 0 0
\(631\) −2.22672e6 −0.222635 −0.111317 0.993785i \(-0.535507\pi\)
−0.111317 + 0.993785i \(0.535507\pi\)
\(632\) 0 0
\(633\) −4.46021e6 7.72531e6i −0.442431 0.766313i
\(634\) 0 0
\(635\) 1.61249e6 2.79291e6i 0.158694 0.274867i
\(636\) 0 0
\(637\) −585084. + 6.55373e6i −0.0571307 + 0.639941i
\(638\) 0 0
\(639\) 1.61881e6 2.80386e6i 0.156835 0.271647i
\(640\) 0 0
\(641\) 7.96698e6 + 1.37992e7i 0.765859 + 1.32651i 0.939791 + 0.341749i \(0.111019\pi\)
−0.173932 + 0.984758i \(0.555647\pi\)
\(642\) 0 0
\(643\) 1.49933e7 1.43011 0.715056 0.699067i \(-0.246401\pi\)
0.715056 + 0.699067i \(0.246401\pi\)
\(644\) 0 0
\(645\) −5.13553e6 −0.486056
\(646\) 0 0
\(647\) 6.49027e6 + 1.12415e7i 0.609540 + 1.05575i 0.991316 + 0.131500i \(0.0419792\pi\)
−0.381776 + 0.924255i \(0.624687\pi\)
\(648\) 0 0
\(649\) 1.48285e7 2.56838e7i 1.38193 2.39357i
\(650\) 0 0
\(651\) −4.45758e6 + 984079.i −0.412237 + 0.0910075i
\(652\) 0 0
\(653\) 8.27460e6 1.43320e7i 0.759389 1.31530i −0.183774 0.982969i \(-0.558831\pi\)
0.943163 0.332332i \(-0.107835\pi\)
\(654\) 0 0
\(655\) −3.23145e6 5.59704e6i −0.294303 0.509748i
\(656\) 0 0
\(657\) −4.51062e6 −0.407683
\(658\) 0 0
\(659\) −5.86879e6 −0.526423 −0.263212 0.964738i \(-0.584782\pi\)
−0.263212 + 0.964738i \(0.584782\pi\)
\(660\) 0 0
\(661\) −3.63843e6 6.30195e6i −0.323900 0.561011i 0.657389 0.753551i \(-0.271661\pi\)
−0.981289 + 0.192540i \(0.938327\pi\)
\(662\) 0 0
\(663\) 2.34255e6 4.05741e6i 0.206969 0.358480i
\(664\) 0 0
\(665\) −1.42696e6 + 4.51179e6i −0.125129 + 0.395635i
\(666\) 0 0
\(667\) 1.19431e6 2.06861e6i 0.103945 0.180038i
\(668\) 0 0
\(669\) 2.44505e6 + 4.23495e6i 0.211214 + 0.365833i
\(670\) 0 0
\(671\) 2.36884e7 2.03109
\(672\) 0 0
\(673\) −1.82417e7 −1.55248 −0.776241 0.630437i \(-0.782876\pi\)
−0.776241 + 0.630437i \(0.782876\pi\)
\(674\) 0 0
\(675\) 592334. + 1.02595e6i 0.0500388 + 0.0866698i
\(676\) 0 0
\(677\) 3.88203e6 6.72387e6i 0.325527 0.563829i −0.656092 0.754681i \(-0.727792\pi\)
0.981619 + 0.190852i \(0.0611250\pi\)
\(678\) 0 0
\(679\) 273743. + 299270.i 0.0227860 + 0.0249109i
\(680\) 0 0
\(681\) 73.5034 127.312i 6.07351e−6 1.05196e-5i
\(682\) 0 0
\(683\) 4.28162e6 + 7.41598e6i 0.351201 + 0.608299i 0.986460 0.164001i \(-0.0524399\pi\)
−0.635259 + 0.772299i \(0.719107\pi\)
\(684\) 0 0
\(685\) 1.48038e6 0.120544
\(686\) 0 0
\(687\) −696411. −0.0562955
\(688\) 0 0
\(689\) 393712. + 681928.i 0.0315959 + 0.0547256i
\(690\) 0 0
\(691\) 8.22547e6 1.42469e7i 0.655338 1.13508i −0.326471 0.945207i \(-0.605860\pi\)
0.981809 0.189872i \(-0.0608071\pi\)
\(692\) 0 0
\(693\) 4.08516e6 + 4.46611e6i 0.323129 + 0.353262i
\(694\) 0 0
\(695\) 2.05773e6 3.56409e6i 0.161594 0.279890i
\(696\) 0 0
\(697\) −8.71208e6 1.50898e7i −0.679266 1.17652i
\(698\) 0 0
\(699\) −932916. −0.0722187
\(700\) 0 0
\(701\) −1.66928e7 −1.28302 −0.641512 0.767113i \(-0.721693\pi\)
−0.641512 + 0.767113i \(0.721693\pi\)
\(702\) 0 0
\(703\) −7.68132e6 1.33044e7i −0.586202 1.01533i
\(704\) 0 0
\(705\) −1.18764e6 + 2.05705e6i −0.0899937 + 0.155874i
\(706\) 0 0
\(707\) −6.60725e6 + 2.08909e7i −0.497132 + 1.57184i
\(708\) 0 0
\(709\) −2.80890e6 + 4.86515e6i −0.209855 + 0.363480i −0.951669 0.307126i \(-0.900633\pi\)
0.741813 + 0.670606i \(0.233966\pi\)
\(710\) 0 0
\(711\) −2.55763e6 4.42994e6i −0.189742 0.328643i
\(712\) 0 0
\(713\) 6.38537e6 0.470395
\(714\) 0 0
\(715\) 8.73927e6 0.639308
\(716\) 0 0
\(717\) 3.10099e6 + 5.37107e6i 0.225269 + 0.390178i
\(718\) 0 0
\(719\) 5.18592e6 8.98227e6i 0.374113 0.647983i −0.616081 0.787683i \(-0.711280\pi\)
0.990194 + 0.139700i \(0.0446138\pi\)
\(720\) 0 0
\(721\) 1.42823e7 3.15303e6i 1.02320 0.225887i
\(722\) 0 0
\(723\) −991332. + 1.71704e6i −0.0705299 + 0.122161i
\(724\) 0 0
\(725\) −1.18917e6 2.05971e6i −0.0840233 0.145533i
\(726\) 0 0
\(727\) −1.15369e7 −0.809565 −0.404783 0.914413i \(-0.632653\pi\)
−0.404783 + 0.914413i \(0.632653\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 0 0
\(731\) −9.79557e6 1.69664e7i −0.678010 1.17435i
\(732\) 0 0
\(733\) −7.47349e6 + 1.29445e7i −0.513764 + 0.889865i 0.486109 + 0.873898i \(0.338416\pi\)
−0.999873 + 0.0159667i \(0.994917\pi\)
\(734\) 0 0
\(735\) −520925. + 5.83507e6i −0.0355678 + 0.398408i
\(736\) 0 0
\(737\) 1.45764e7 2.52470e7i 0.988510 1.71215i
\(738\) 0 0
\(739\) 4.50682e6 + 7.80604e6i 0.303570 + 0.525799i 0.976942 0.213505i \(-0.0684880\pi\)
−0.673372 + 0.739304i \(0.735155\pi\)
\(740\) 0 0
\(741\) −3.32073e6 −0.222171
\(742\) 0 0
\(743\) 2.10239e7 1.39714 0.698571 0.715541i \(-0.253820\pi\)
0.698571 + 0.715541i \(0.253820\pi\)
\(744\) 0 0
\(745\) −3.72875e6 6.45838e6i −0.246134 0.426317i
\(746\) 0 0
\(747\) 1.84568e6 3.19681e6i 0.121019 0.209612i
\(748\) 0 0
\(749\) −2.82424e6 + 623493.i −0.183949 + 0.0406094i
\(750\) 0 0
\(751\) 2.02110e6 3.50064e6i 0.130764 0.226489i −0.793207 0.608952i \(-0.791590\pi\)
0.923971 + 0.382462i \(0.124924\pi\)
\(752\) 0 0
\(753\) 6.46387e6 + 1.11957e7i 0.415437 + 0.719558i
\(754\) 0 0
\(755\) −5.48786e6 −0.350377
\(756\) 0 0
\(757\) −1.82059e7 −1.15471 −0.577353 0.816495i \(-0.695914\pi\)
−0.577353 + 0.816495i \(0.695914\pi\)
\(758\) 0 0
\(759\) −4.23321e6 7.33214e6i −0.266726 0.461983i
\(760\) 0 0
\(761\) 9.45999e6 1.63852e7i 0.592146 1.02563i −0.401797 0.915729i \(-0.631614\pi\)
0.993943 0.109898i \(-0.0350526\pi\)
\(762\) 0 0
\(763\) −3.27681e6 + 1.03607e7i −0.203770 + 0.644283i
\(764\) 0 0
\(765\) 2.08567e6 3.61249e6i 0.128852 0.223179i
\(766\) 0 0
\(767\) 1.00717e7 + 1.74447e7i 0.618180 + 1.07072i
\(768\) 0 0
\(769\) −1.12831e7 −0.688037 −0.344019 0.938963i \(-0.611788\pi\)
−0.344019 + 0.938963i \(0.611788\pi\)
\(770\) 0 0
\(771\) −8.18277e6 −0.495752
\(772\) 0 0
\(773\) 1.84282e6 + 3.19186e6i 0.110926 + 0.192130i 0.916144 0.400849i \(-0.131285\pi\)
−0.805218 + 0.592979i \(0.797952\pi\)
\(774\) 0 0
\(775\) 3.17896e6 5.50611e6i 0.190121 0.329299i
\(776\) 0 0
\(777\) −1.28365e7 1.40335e7i −0.762772 0.833902i
\(778\) 0 0
\(779\) −6.17501e6 + 1.06954e7i −0.364581 + 0.631472i
\(780\) 0 0
\(781\) 1.15193e7 + 1.99521e7i 0.675771 + 1.17047i
\(782\) 0 0
\(783\) −1.06692e6 −0.0621912
\(784\) 0 0
\(785\) 2.19118e7 1.26912
\(786\) 0 0
\(787\)