Properties

Label 336.4.q.j.193.1
Level $336$
Weight $4$
Character 336.193
Analytic conductor $19.825$
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: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 336.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.8246417619\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{1345})\)
Defining polynomial: \(x^{4} - x^{3} + 337 x^{2} + 336 x + 112896\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 193.1
Root \(9.41856 + 16.3134i\) of defining polynomial
Character \(\chi\) \(=\) 336.193
Dual form 336.4.q.j.289.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 2.59808i) q^{3} +(-10.4186 - 18.0455i) q^{5} +(18.3371 + 2.59808i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(1.50000 - 2.59808i) q^{3} +(-10.4186 - 18.0455i) q^{5} +(18.3371 + 2.59808i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(7.58144 - 13.1314i) q^{11} +2.16288 q^{13} -62.5114 q^{15} +(59.6742 - 103.359i) q^{17} +(-16.7557 - 29.0217i) q^{19} +(34.2557 - 43.7441i) q^{21} +(0.325758 + 0.564230i) q^{23} +(-154.593 + 267.763i) q^{25} -27.0000 q^{27} -163.208 q^{29} +(-111.663 + 193.406i) q^{31} +(-22.7443 - 39.3943i) q^{33} +(-144.163 - 357.970i) q^{35} +(-84.2670 - 145.955i) q^{37} +(3.24432 - 5.61932i) q^{39} -323.023 q^{41} -221.557 q^{43} +(-93.7670 + 162.409i) q^{45} +(254.023 + 439.980i) q^{47} +(329.500 + 95.2825i) q^{49} +(-179.023 - 310.076i) q^{51} +(88.2557 - 152.863i) q^{53} -315.951 q^{55} -100.534 q^{57} +(227.464 - 393.979i) q^{59} +(-19.3258 - 33.4732i) q^{61} +(-62.2670 - 154.615i) q^{63} +(-22.5341 - 39.0302i) q^{65} +(70.8958 - 122.795i) q^{67} +1.95455 q^{69} -602.742 q^{71} +(551.150 - 954.619i) q^{73} +(463.778 + 803.288i) q^{75} +(173.138 - 221.096i) q^{77} +(-58.1515 - 100.721i) q^{79} +(-40.5000 + 70.1481i) q^{81} +568.928 q^{83} -2486.88 q^{85} +(-244.812 + 424.028i) q^{87} +(191.580 + 331.825i) q^{89} +(39.6610 + 5.61932i) q^{91} +(334.989 + 580.217i) q^{93} +(-349.140 + 604.728i) q^{95} +334.701 q^{97} -136.466 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 6q^{3} - 5q^{5} - 18q^{9} + O(q^{10}) \) \( 4q + 6q^{3} - 5q^{5} - 18q^{9} + 67q^{11} + 82q^{13} - 30q^{15} + 92q^{17} + 43q^{19} + 27q^{21} + 148q^{23} - 435q^{25} - 108q^{27} + 154q^{29} - 520q^{31} - 201q^{33} - 650q^{35} - 7q^{37} + 123q^{39} - 852q^{41} + 214q^{43} - 45q^{45} + 576q^{47} + 1318q^{49} - 276q^{51} + 243q^{53} + 1010q^{55} + 258q^{57} - 7q^{59} - 224q^{61} + 81q^{63} + 570q^{65} + 687q^{67} + 888q^{69} - 944q^{71} + 921q^{73} + 1305q^{75} - 371q^{77} - 526q^{79} - 162q^{81} + 442q^{83} - 5840q^{85} + 231q^{87} - 774q^{89} - 1345q^{91} + 1560q^{93} - 1910q^{95} + 3906q^{97} - 1206q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 1.50000 2.59808i 0.288675 0.500000i
\(4\) 0 0
\(5\) −10.4186 18.0455i −0.931864 1.61404i −0.780132 0.625615i \(-0.784848\pi\)
−0.151732 0.988422i \(-0.548485\pi\)
\(6\) 0 0
\(7\) 18.3371 + 2.59808i 0.990111 + 0.140283i
\(8\) 0 0
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) 0 0
\(11\) 7.58144 13.1314i 0.207808 0.359934i −0.743216 0.669052i \(-0.766700\pi\)
0.951024 + 0.309118i \(0.100034\pi\)
\(12\) 0 0
\(13\) 2.16288 0.0461442 0.0230721 0.999734i \(-0.492655\pi\)
0.0230721 + 0.999734i \(0.492655\pi\)
\(14\) 0 0
\(15\) −62.5114 −1.07602
\(16\) 0 0
\(17\) 59.6742 103.359i 0.851361 1.47460i −0.0286202 0.999590i \(-0.509111\pi\)
0.879981 0.475009i \(-0.157555\pi\)
\(18\) 0 0
\(19\) −16.7557 29.0217i −0.202317 0.350423i 0.746958 0.664871i \(-0.231514\pi\)
−0.949274 + 0.314449i \(0.898180\pi\)
\(20\) 0 0
\(21\) 34.2557 43.7441i 0.355962 0.454560i
\(22\) 0 0
\(23\) 0.325758 + 0.564230i 0.00295327 + 0.00511522i 0.867498 0.497440i \(-0.165727\pi\)
−0.864545 + 0.502555i \(0.832393\pi\)
\(24\) 0 0
\(25\) −154.593 + 267.763i −1.23674 + 2.14210i
\(26\) 0 0
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) −163.208 −1.04507 −0.522535 0.852618i \(-0.675014\pi\)
−0.522535 + 0.852618i \(0.675014\pi\)
\(30\) 0 0
\(31\) −111.663 + 193.406i −0.646943 + 1.12054i 0.336906 + 0.941538i \(0.390620\pi\)
−0.983849 + 0.179000i \(0.942714\pi\)
\(32\) 0 0
\(33\) −22.7443 39.3943i −0.119978 0.207808i
\(34\) 0 0
\(35\) −144.163 357.970i −0.696228 1.72880i
\(36\) 0 0
\(37\) −84.2670 145.955i −0.374417 0.648509i 0.615823 0.787885i \(-0.288824\pi\)
−0.990240 + 0.139376i \(0.955490\pi\)
\(38\) 0 0
\(39\) 3.24432 5.61932i 0.0133207 0.0230721i
\(40\) 0 0
\(41\) −323.023 −1.23043 −0.615216 0.788359i \(-0.710931\pi\)
−0.615216 + 0.788359i \(0.710931\pi\)
\(42\) 0 0
\(43\) −221.557 −0.785746 −0.392873 0.919593i \(-0.628519\pi\)
−0.392873 + 0.919593i \(0.628519\pi\)
\(44\) 0 0
\(45\) −93.7670 + 162.409i −0.310621 + 0.538012i
\(46\) 0 0
\(47\) 254.023 + 439.980i 0.788362 + 1.36548i 0.926970 + 0.375136i \(0.122404\pi\)
−0.138608 + 0.990347i \(0.544263\pi\)
\(48\) 0 0
\(49\) 329.500 + 95.2825i 0.960641 + 0.277791i
\(50\) 0 0
\(51\) −179.023 310.076i −0.491533 0.851361i
\(52\) 0 0
\(53\) 88.2557 152.863i 0.228733 0.396177i −0.728700 0.684833i \(-0.759875\pi\)
0.957433 + 0.288656i \(0.0932084\pi\)
\(54\) 0 0
\(55\) −315.951 −0.774596
\(56\) 0 0
\(57\) −100.534 −0.233615
\(58\) 0 0
\(59\) 227.464 393.979i 0.501920 0.869351i −0.498077 0.867133i \(-0.665960\pi\)
0.999998 0.00221868i \(-0.000706227\pi\)
\(60\) 0 0
\(61\) −19.3258 33.4732i −0.0405641 0.0702591i 0.845031 0.534718i \(-0.179582\pi\)
−0.885595 + 0.464459i \(0.846249\pi\)
\(62\) 0 0
\(63\) −62.2670 154.615i −0.124522 0.309201i
\(64\) 0 0
\(65\) −22.5341 39.0302i −0.0430001 0.0744784i
\(66\) 0 0
\(67\) 70.8958 122.795i 0.129273 0.223908i −0.794122 0.607758i \(-0.792069\pi\)
0.923395 + 0.383851i \(0.125402\pi\)
\(68\) 0 0
\(69\) 1.95455 0.00341015
\(70\) 0 0
\(71\) −602.742 −1.00750 −0.503749 0.863850i \(-0.668046\pi\)
−0.503749 + 0.863850i \(0.668046\pi\)
\(72\) 0 0
\(73\) 551.150 954.619i 0.883660 1.53054i 0.0364183 0.999337i \(-0.488405\pi\)
0.847242 0.531207i \(-0.178262\pi\)
\(74\) 0 0
\(75\) 463.778 + 803.288i 0.714034 + 1.23674i
\(76\) 0 0
\(77\) 173.138 221.096i 0.256246 0.327223i
\(78\) 0 0
\(79\) −58.1515 100.721i −0.0828172 0.143444i 0.821642 0.570004i \(-0.193058\pi\)
−0.904459 + 0.426561i \(0.859725\pi\)
\(80\) 0 0
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 568.928 0.752385 0.376193 0.926542i \(-0.377233\pi\)
0.376193 + 0.926542i \(0.377233\pi\)
\(84\) 0 0
\(85\) −2486.88 −3.17341
\(86\) 0 0
\(87\) −244.812 + 424.028i −0.301686 + 0.522535i
\(88\) 0 0
\(89\) 191.580 + 331.825i 0.228173 + 0.395207i 0.957267 0.289207i \(-0.0933915\pi\)
−0.729094 + 0.684414i \(0.760058\pi\)
\(90\) 0 0
\(91\) 39.6610 + 5.61932i 0.0456879 + 0.00647325i
\(92\) 0 0
\(93\) 334.989 + 580.217i 0.373513 + 0.646943i
\(94\) 0 0
\(95\) −349.140 + 604.728i −0.377063 + 0.653093i
\(96\) 0 0
\(97\) 334.701 0.350348 0.175174 0.984538i \(-0.443951\pi\)
0.175174 + 0.984538i \(0.443951\pi\)
\(98\) 0 0
\(99\) −136.466 −0.138539
\(100\) 0 0
\(101\) 7.37121 12.7673i 0.00726201 0.0125782i −0.862372 0.506276i \(-0.831022\pi\)
0.869634 + 0.493698i \(0.164355\pi\)
\(102\) 0 0
\(103\) −420.710 728.691i −0.402464 0.697088i 0.591559 0.806262i \(-0.298513\pi\)
−0.994023 + 0.109174i \(0.965180\pi\)
\(104\) 0 0
\(105\) −1146.28 162.409i −1.06538 0.150948i
\(106\) 0 0
\(107\) −357.835 619.789i −0.323301 0.559974i 0.657866 0.753135i \(-0.271459\pi\)
−0.981167 + 0.193161i \(0.938126\pi\)
\(108\) 0 0
\(109\) −300.009 + 519.632i −0.263630 + 0.456621i −0.967204 0.254001i \(-0.918253\pi\)
0.703574 + 0.710622i \(0.251587\pi\)
\(110\) 0 0
\(111\) −505.602 −0.432339
\(112\) 0 0
\(113\) 622.644 0.518349 0.259174 0.965831i \(-0.416550\pi\)
0.259174 + 0.965831i \(0.416550\pi\)
\(114\) 0 0
\(115\) 6.78787 11.7569i 0.00550410 0.00953339i
\(116\) 0 0
\(117\) −9.73296 16.8580i −0.00769070 0.0133207i
\(118\) 0 0
\(119\) 1362.79 1740.26i 1.04980 1.34059i
\(120\) 0 0
\(121\) 550.544 + 953.569i 0.413632 + 0.716431i
\(122\) 0 0
\(123\) −484.534 + 839.238i −0.355195 + 0.615216i
\(124\) 0 0
\(125\) 3837.90 2.74618
\(126\) 0 0
\(127\) 180.076 0.125820 0.0629100 0.998019i \(-0.479962\pi\)
0.0629100 + 0.998019i \(0.479962\pi\)
\(128\) 0 0
\(129\) −332.335 + 575.621i −0.226825 + 0.392873i
\(130\) 0 0
\(131\) 108.930 + 188.672i 0.0726508 + 0.125835i 0.900062 0.435761i \(-0.143521\pi\)
−0.827411 + 0.561596i \(0.810187\pi\)
\(132\) 0 0
\(133\) −231.850 575.707i −0.151158 0.375339i
\(134\) 0 0
\(135\) 281.301 + 487.228i 0.179337 + 0.310621i
\(136\) 0 0
\(137\) 1300.93 2253.27i 0.811283 1.40518i −0.100683 0.994919i \(-0.532103\pi\)
0.911966 0.410265i \(-0.134564\pi\)
\(138\) 0 0
\(139\) 2651.55 1.61800 0.808998 0.587811i \(-0.200010\pi\)
0.808998 + 0.587811i \(0.200010\pi\)
\(140\) 0 0
\(141\) 1524.14 0.910322
\(142\) 0 0
\(143\) 16.3977 28.4017i 0.00958914 0.0166089i
\(144\) 0 0
\(145\) 1700.40 + 2945.17i 0.973863 + 1.68678i
\(146\) 0 0
\(147\) 741.801 713.142i 0.416209 0.400129i
\(148\) 0 0
\(149\) −290.511 503.180i −0.159729 0.276659i 0.775042 0.631910i \(-0.217729\pi\)
−0.934771 + 0.355251i \(0.884395\pi\)
\(150\) 0 0
\(151\) −307.695 + 532.943i −0.165827 + 0.287221i −0.936949 0.349467i \(-0.886363\pi\)
0.771122 + 0.636688i \(0.219696\pi\)
\(152\) 0 0
\(153\) −1074.14 −0.567574
\(154\) 0 0
\(155\) 4653.47 2.41145
\(156\) 0 0
\(157\) 153.466 265.811i 0.0780122 0.135121i −0.824380 0.566037i \(-0.808476\pi\)
0.902392 + 0.430916i \(0.141809\pi\)
\(158\) 0 0
\(159\) −264.767 458.590i −0.132059 0.228733i
\(160\) 0 0
\(161\) 4.50756 + 11.1927i 0.00220649 + 0.00547893i
\(162\) 0 0
\(163\) 1757.25 + 3043.65i 0.844408 + 1.46256i 0.886135 + 0.463428i \(0.153381\pi\)
−0.0417271 + 0.999129i \(0.513286\pi\)
\(164\) 0 0
\(165\) −473.926 + 820.864i −0.223607 + 0.387298i
\(166\) 0 0
\(167\) −1123.30 −0.520502 −0.260251 0.965541i \(-0.583805\pi\)
−0.260251 + 0.965541i \(0.583805\pi\)
\(168\) 0 0
\(169\) −2192.32 −0.997871
\(170\) 0 0
\(171\) −150.801 + 261.195i −0.0674389 + 0.116808i
\(172\) 0 0
\(173\) −765.299 1325.54i −0.336327 0.582536i 0.647412 0.762141i \(-0.275852\pi\)
−0.983739 + 0.179605i \(0.942518\pi\)
\(174\) 0 0
\(175\) −3530.45 + 4508.35i −1.52501 + 1.94742i
\(176\) 0 0
\(177\) −682.392 1181.94i −0.289784 0.501920i
\(178\) 0 0
\(179\) 1706.72 2956.12i 0.712659 1.23436i −0.251197 0.967936i \(-0.580824\pi\)
0.963856 0.266425i \(-0.0858426\pi\)
\(180\) 0 0
\(181\) 1286.71 0.528399 0.264200 0.964468i \(-0.414892\pi\)
0.264200 + 0.964468i \(0.414892\pi\)
\(182\) 0 0
\(183\) −115.955 −0.0468394
\(184\) 0 0
\(185\) −1755.88 + 3041.28i −0.697811 + 1.20864i
\(186\) 0 0
\(187\) −904.833 1567.22i −0.353839 0.612868i
\(188\) 0 0
\(189\) −495.102 70.1481i −0.190547 0.0269975i
\(190\) 0 0
\(191\) 527.648 + 913.913i 0.199891 + 0.346222i 0.948493 0.316798i \(-0.102608\pi\)
−0.748602 + 0.663020i \(0.769274\pi\)
\(192\) 0 0
\(193\) 2385.42 4131.67i 0.889670 1.54095i 0.0494044 0.998779i \(-0.484268\pi\)
0.840266 0.542175i \(-0.182399\pi\)
\(194\) 0 0
\(195\) −135.205 −0.0496523
\(196\) 0 0
\(197\) 1622.31 0.586725 0.293363 0.956001i \(-0.405226\pi\)
0.293363 + 0.956001i \(0.405226\pi\)
\(198\) 0 0
\(199\) −1775.07 + 3074.51i −0.632318 + 1.09521i 0.354759 + 0.934958i \(0.384563\pi\)
−0.987077 + 0.160249i \(0.948770\pi\)
\(200\) 0 0
\(201\) −212.688 368.386i −0.0746359 0.129273i
\(202\) 0 0
\(203\) −2992.77 424.028i −1.03474 0.146605i
\(204\) 0 0
\(205\) 3365.43 + 5829.10i 1.14659 + 1.98596i
\(206\) 0 0
\(207\) 2.93183 5.07807i 0.000984425 0.00170507i
\(208\) 0 0
\(209\) −508.129 −0.168172
\(210\) 0 0
\(211\) −4653.39 −1.51826 −0.759129 0.650941i \(-0.774375\pi\)
−0.759129 + 0.650941i \(0.774375\pi\)
\(212\) 0 0
\(213\) −904.114 + 1565.97i −0.290840 + 0.503749i
\(214\) 0 0
\(215\) 2308.30 + 3998.10i 0.732209 + 1.26822i
\(216\) 0 0
\(217\) −2550.06 + 3256.40i −0.797739 + 1.01870i
\(218\) 0 0
\(219\) −1653.45 2863.86i −0.510181 0.883660i
\(220\) 0 0
\(221\) 129.068 223.553i 0.0392854 0.0680442i
\(222\) 0 0
\(223\) 4649.53 1.39621 0.698107 0.715993i \(-0.254026\pi\)
0.698107 + 0.715993i \(0.254026\pi\)
\(224\) 0 0
\(225\) 2782.67 0.824495
\(226\) 0 0
\(227\) 2075.86 3595.49i 0.606958 1.05128i −0.384780 0.923008i \(-0.625723\pi\)
0.991739 0.128274i \(-0.0409438\pi\)
\(228\) 0 0
\(229\) −2131.82 3692.41i −0.615172 1.06551i −0.990354 0.138558i \(-0.955753\pi\)
0.375182 0.926951i \(-0.377580\pi\)
\(230\) 0 0
\(231\) −314.716 781.470i −0.0896398 0.222584i
\(232\) 0 0
\(233\) −1524.95 2641.29i −0.428768 0.742647i 0.567996 0.823031i \(-0.307719\pi\)
−0.996764 + 0.0803838i \(0.974385\pi\)
\(234\) 0 0
\(235\) 5293.10 9167.92i 1.46929 2.54489i
\(236\) 0 0
\(237\) −348.909 −0.0956290
\(238\) 0 0
\(239\) −3987.20 −1.07912 −0.539562 0.841946i \(-0.681410\pi\)
−0.539562 + 0.841946i \(0.681410\pi\)
\(240\) 0 0
\(241\) 312.324 540.961i 0.0834795 0.144591i −0.821263 0.570550i \(-0.806730\pi\)
0.904742 + 0.425959i \(0.140063\pi\)
\(242\) 0 0
\(243\) 121.500 + 210.444i 0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) −1713.50 6938.69i −0.446822 1.80937i
\(246\) 0 0
\(247\) −36.2405 62.7704i −0.00933574 0.0161700i
\(248\) 0 0
\(249\) 853.392 1478.12i 0.217195 0.376193i
\(250\) 0 0
\(251\) 1328.78 0.334152 0.167076 0.985944i \(-0.446568\pi\)
0.167076 + 0.985944i \(0.446568\pi\)
\(252\) 0 0
\(253\) 9.87887 0.00245486
\(254\) 0 0
\(255\) −3730.32 + 6461.10i −0.916085 + 1.58671i
\(256\) 0 0
\(257\) 1613.09 + 2793.96i 0.391525 + 0.678141i 0.992651 0.121013i \(-0.0386144\pi\)
−0.601126 + 0.799154i \(0.705281\pi\)
\(258\) 0 0
\(259\) −1166.01 2895.32i −0.279740 0.694620i
\(260\) 0 0
\(261\) 734.437 + 1272.08i 0.174178 + 0.301686i
\(262\) 0 0
\(263\) 1625.31 2815.11i 0.381067 0.660028i −0.610148 0.792288i \(-0.708890\pi\)
0.991215 + 0.132260i \(0.0422233\pi\)
\(264\) 0 0
\(265\) −3677.99 −0.852593
\(266\) 0 0
\(267\) 1149.48 0.263471
\(268\) 0 0
\(269\) −1413.02 + 2447.42i −0.320273 + 0.554729i −0.980544 0.196298i \(-0.937108\pi\)
0.660271 + 0.751027i \(0.270441\pi\)
\(270\) 0 0
\(271\) −1198.38 2075.66i −0.268622 0.465268i 0.699884 0.714257i \(-0.253235\pi\)
−0.968506 + 0.248989i \(0.919902\pi\)
\(272\) 0 0
\(273\) 74.0909 94.6133i 0.0164256 0.0209753i
\(274\) 0 0
\(275\) 2344.07 + 4060.05i 0.514010 + 0.890292i
\(276\) 0 0
\(277\) −910.233 + 1576.57i −0.197439 + 0.341974i −0.947697 0.319170i \(-0.896596\pi\)
0.750258 + 0.661145i \(0.229929\pi\)
\(278\) 0 0
\(279\) 2009.93 0.431296
\(280\) 0 0
\(281\) 3083.81 0.654679 0.327339 0.944907i \(-0.393848\pi\)
0.327339 + 0.944907i \(0.393848\pi\)
\(282\) 0 0
\(283\) 1277.38 2212.49i 0.268313 0.464732i −0.700113 0.714032i \(-0.746867\pi\)
0.968426 + 0.249300i \(0.0802005\pi\)
\(284\) 0 0
\(285\) 1047.42 + 1814.19i 0.217698 + 0.377063i
\(286\) 0 0
\(287\) −5923.31 839.238i −1.21826 0.172608i
\(288\) 0 0
\(289\) −4665.53 8080.94i −0.949630 1.64481i
\(290\) 0 0
\(291\) 502.051 869.578i 0.101137 0.175174i
\(292\) 0 0
\(293\) −1846.47 −0.368163 −0.184081 0.982911i \(-0.558931\pi\)
−0.184081 + 0.982911i \(0.558931\pi\)
\(294\) 0 0
\(295\) −9479.39 −1.87089
\(296\) 0 0
\(297\) −204.699 + 354.549i −0.0399927 + 0.0692694i
\(298\) 0 0
\(299\) 0.704576 + 1.22036i 0.000136277 + 0.000236038i
\(300\) 0 0
\(301\) −4062.71 575.621i −0.777977 0.110227i
\(302\) 0 0
\(303\) −22.1136 38.3019i −0.00419272 0.00726201i
\(304\) 0 0
\(305\) −402.693 + 697.485i −0.0756005 + 0.130944i
\(306\) 0 0
\(307\) −7041.50 −1.30905 −0.654527 0.756039i \(-0.727132\pi\)
−0.654527 + 0.756039i \(0.727132\pi\)
\(308\) 0 0
\(309\) −2524.26 −0.464726
\(310\) 0 0
\(311\) −1343.00 + 2326.14i −0.244869 + 0.424126i −0.962095 0.272715i \(-0.912078\pi\)
0.717226 + 0.696841i \(0.245412\pi\)
\(312\) 0 0
\(313\) −1109.59 1921.87i −0.200377 0.347063i 0.748273 0.663391i \(-0.230883\pi\)
−0.948650 + 0.316328i \(0.897550\pi\)
\(314\) 0 0
\(315\) −2141.37 + 2734.50i −0.383024 + 0.489117i
\(316\) 0 0
\(317\) −1110.63 1923.67i −0.196780 0.340833i 0.750703 0.660640i \(-0.229715\pi\)
−0.947483 + 0.319807i \(0.896382\pi\)
\(318\) 0 0
\(319\) −1237.35 + 2143.16i −0.217174 + 0.376157i
\(320\) 0 0
\(321\) −2147.01 −0.373316
\(322\) 0 0
\(323\) −3999.53 −0.688978
\(324\) 0 0
\(325\) −334.366 + 579.138i −0.0570685 + 0.0988455i
\(326\) 0 0
\(327\) 900.028 + 1558.89i 0.152207 + 0.263630i
\(328\) 0 0
\(329\) 3514.94 + 8727.94i 0.589012 + 1.46257i
\(330\) 0 0
\(331\) 2077.03 + 3597.52i 0.344906 + 0.597394i 0.985337 0.170622i \(-0.0545775\pi\)
−0.640431 + 0.768016i \(0.721244\pi\)
\(332\) 0 0
\(333\) −758.403 + 1313.59i −0.124806 + 0.216170i
\(334\) 0 0
\(335\) −2954.53 −0.481860
\(336\) 0 0
\(337\) −254.167 −0.0410841 −0.0205420 0.999789i \(-0.506539\pi\)
−0.0205420 + 0.999789i \(0.506539\pi\)
\(338\) 0 0
\(339\) 933.966 1617.68i 0.149634 0.259174i
\(340\) 0 0
\(341\) 1693.13 + 2932.59i 0.268880 + 0.465714i
\(342\) 0 0
\(343\) 5794.53 + 2603.27i 0.912173 + 0.409806i
\(344\) 0 0
\(345\) −20.3636 35.2708i −0.00317780 0.00550410i
\(346\) 0 0
\(347\) −3112.32 + 5390.69i −0.481493 + 0.833970i −0.999774 0.0212401i \(-0.993239\pi\)
0.518282 + 0.855210i \(0.326572\pi\)
\(348\) 0 0
\(349\) 9732.21 1.49270 0.746352 0.665552i \(-0.231804\pi\)
0.746352 + 0.665552i \(0.231804\pi\)
\(350\) 0 0
\(351\) −58.3977 −0.00888046
\(352\) 0 0
\(353\) −712.807 + 1234.62i −0.107476 + 0.186153i −0.914747 0.404027i \(-0.867610\pi\)
0.807271 + 0.590180i \(0.200943\pi\)
\(354\) 0 0
\(355\) 6279.71 + 10876.8i 0.938852 + 1.62614i
\(356\) 0 0
\(357\) −2477.16 6151.02i −0.367241 0.911896i
\(358\) 0 0
\(359\) −2883.25 4993.93i −0.423877 0.734177i 0.572438 0.819948i \(-0.305998\pi\)
−0.996315 + 0.0857714i \(0.972665\pi\)
\(360\) 0 0
\(361\) 2867.99 4967.51i 0.418136 0.724233i
\(362\) 0 0
\(363\) 3303.26 0.477621
\(364\) 0 0
\(365\) −22968.7 −3.29381
\(366\) 0 0
\(367\) 5772.67 9998.56i 0.821065 1.42213i −0.0838244 0.996481i \(-0.526713\pi\)
0.904890 0.425646i \(-0.139953\pi\)
\(368\) 0 0
\(369\) 1453.60 + 2517.71i 0.205072 + 0.355195i
\(370\) 0 0
\(371\) 2015.51 2573.78i 0.282048 0.360172i
\(372\) 0 0
\(373\) 3239.79 + 5611.47i 0.449731 + 0.778957i 0.998368 0.0571033i \(-0.0181864\pi\)
−0.548637 + 0.836061i \(0.684853\pi\)
\(374\) 0 0
\(375\) 5756.85 9971.15i 0.792753 1.37309i
\(376\) 0 0
\(377\) −353.000 −0.0482239
\(378\) 0 0
\(379\) −611.996 −0.0829449 −0.0414725 0.999140i \(-0.513205\pi\)
−0.0414725 + 0.999140i \(0.513205\pi\)
\(380\) 0 0
\(381\) 270.114 467.851i 0.0363211 0.0629100i
\(382\) 0 0
\(383\) 2180.41 + 3776.57i 0.290897 + 0.503848i 0.974022 0.226453i \(-0.0727130\pi\)
−0.683125 + 0.730301i \(0.739380\pi\)
\(384\) 0 0
\(385\) −5793.63 820.864i −0.766937 0.108663i
\(386\) 0 0
\(387\) 997.006 + 1726.86i 0.130958 + 0.226825i
\(388\) 0 0
\(389\) 6573.46 11385.6i 0.856781 1.48399i −0.0182021 0.999834i \(-0.505794\pi\)
0.874983 0.484154i \(-0.160872\pi\)
\(390\) 0 0
\(391\) 77.7575 0.0100572
\(392\) 0 0
\(393\) 653.580 0.0838899
\(394\) 0 0
\(395\) −1211.71 + 2098.74i −0.154349 + 0.267340i
\(396\) 0 0
\(397\) 4239.02 + 7342.20i 0.535895 + 0.928198i 0.999119 + 0.0419565i \(0.0133591\pi\)
−0.463224 + 0.886241i \(0.653308\pi\)
\(398\) 0 0
\(399\) −1843.51 261.195i −0.231305 0.0327722i
\(400\) 0 0
\(401\) −1401.50 2427.47i −0.174533 0.302299i 0.765467 0.643475i \(-0.222508\pi\)
−0.939999 + 0.341176i \(0.889175\pi\)
\(402\) 0 0
\(403\) −241.513 + 418.313i −0.0298527 + 0.0517064i
\(404\) 0 0
\(405\) 1687.81 0.207081
\(406\) 0 0
\(407\) −2555.46 −0.311227
\(408\) 0 0
\(409\) 3192.69 5529.91i 0.385987 0.668548i −0.605919 0.795526i \(-0.707194\pi\)
0.991906 + 0.126978i \(0.0405278\pi\)
\(410\) 0 0
\(411\) −3902.78 6759.82i −0.468395 0.811283i
\(412\) 0 0
\(413\) 5194.62 6633.48i 0.618912 0.790344i
\(414\) 0 0
\(415\) −5927.41 10266.6i −0.701121 1.21438i
\(416\) 0 0
\(417\) 3977.32 6888.93i 0.467075 0.808998i
\(418\) 0 0
\(419\) −4831.66 −0.563346 −0.281673 0.959510i \(-0.590889\pi\)
−0.281673 + 0.959510i \(0.590889\pi\)
\(420\) 0 0
\(421\) 7475.37 0.865385 0.432693 0.901542i \(-0.357564\pi\)
0.432693 + 0.901542i \(0.357564\pi\)
\(422\) 0 0
\(423\) 2286.20 3959.82i 0.262787 0.455161i
\(424\) 0 0
\(425\) 18450.4 + 31957.1i 2.10583 + 3.64740i
\(426\) 0 0
\(427\) −267.413 664.012i −0.0303068 0.0752548i
\(428\) 0 0
\(429\) −49.1932 85.2051i −0.00553630 0.00958914i
\(430\) 0 0
\(431\) 3495.97 6055.19i 0.390707 0.676725i −0.601836 0.798620i \(-0.705564\pi\)
0.992543 + 0.121895i \(0.0388972\pi\)
\(432\) 0 0
\(433\) −7699.26 −0.854510 −0.427255 0.904131i \(-0.640519\pi\)
−0.427255 + 0.904131i \(0.640519\pi\)
\(434\) 0 0
\(435\) 10202.4 1.12452
\(436\) 0 0
\(437\) 10.9166 18.9081i 0.00119499 0.00206979i
\(438\) 0 0
\(439\) 4706.16 + 8151.31i 0.511646 + 0.886198i 0.999909 + 0.0135008i \(0.00429758\pi\)
−0.488262 + 0.872697i \(0.662369\pi\)
\(440\) 0 0
\(441\) −740.097 2996.97i −0.0799154 0.323612i
\(442\) 0 0
\(443\) −3129.09 5419.74i −0.335593 0.581263i 0.648006 0.761635i \(-0.275603\pi\)
−0.983598 + 0.180372i \(0.942270\pi\)
\(444\) 0 0
\(445\) 3991.97 6914.29i 0.425252 0.736559i
\(446\) 0 0
\(447\) −1743.07 −0.184439
\(448\) 0 0
\(449\) −11633.8 −1.22279 −0.611396 0.791325i \(-0.709392\pi\)
−0.611396 + 0.791325i \(0.709392\pi\)
\(450\) 0 0
\(451\) −2448.98 + 4241.75i −0.255694 + 0.442874i
\(452\) 0 0
\(453\) 923.085 + 1598.83i 0.0957402 + 0.165827i
\(454\) 0 0
\(455\) −311.807 774.246i −0.0321269 0.0797741i
\(456\) 0 0
\(457\) 6552.31 + 11348.9i 0.670688 + 1.16167i 0.977709 + 0.209963i \(0.0673343\pi\)
−0.307022 + 0.951703i \(0.599332\pi\)
\(458\) 0 0
\(459\) −1611.20 + 2790.69i −0.163844 + 0.283787i
\(460\) 0 0
\(461\) −2594.63 −0.262134 −0.131067 0.991373i \(-0.541840\pi\)
−0.131067 + 0.991373i \(0.541840\pi\)
\(462\) 0 0
\(463\) 14136.2 1.41893 0.709465 0.704741i \(-0.248937\pi\)
0.709465 + 0.704741i \(0.248937\pi\)
\(464\) 0 0
\(465\) 6980.20 12090.1i 0.696127 1.20573i
\(466\) 0 0
\(467\) 7795.12 + 13501.5i 0.772409 + 1.33785i 0.936239 + 0.351363i \(0.114282\pi\)
−0.163830 + 0.986489i \(0.552385\pi\)
\(468\) 0 0
\(469\) 1619.06 2067.52i 0.159405 0.203559i
\(470\) 0 0
\(471\) −460.398 797.432i −0.0450404 0.0780122i
\(472\) 0 0
\(473\) −1679.72 + 2909.36i −0.163285 + 0.282817i
\(474\) 0 0
\(475\) 10361.2 1.00085
\(476\) 0 0
\(477\) −1588.60 −0.152489
\(478\) 0 0
\(479\) −4226.75 + 7320.95i −0.403184 + 0.698336i −0.994108 0.108391i \(-0.965430\pi\)
0.590924 + 0.806727i \(0.298763\pi\)
\(480\) 0 0
\(481\) −182.259 315.683i −0.0172772 0.0299249i
\(482\) 0 0
\(483\) 35.8408 + 5.07807i 0.00337643 + 0.000478386i
\(484\) 0 0
\(485\) −3487.10 6039.83i −0.326476 0.565474i
\(486\) 0 0
\(487\) −2005.53 + 3473.69i −0.186611 + 0.323219i −0.944118 0.329607i \(-0.893084\pi\)
0.757507 + 0.652827i \(0.226417\pi\)
\(488\) 0 0
\(489\) 10543.5 0.975038
\(490\) 0 0
\(491\) −13927.9 −1.28016 −0.640079 0.768309i \(-0.721098\pi\)
−0.640079 + 0.768309i \(0.721098\pi\)
\(492\) 0 0
\(493\) −9739.33 + 16869.0i −0.889731 + 1.54106i
\(494\) 0 0
\(495\) 1421.78 + 2462.59i 0.129099 + 0.223607i
\(496\) 0 0
\(497\) −11052.6 1565.97i −0.997535 0.141335i
\(498\) 0 0
\(499\) −1973.77 3418.68i −0.177071 0.306695i 0.763805 0.645447i \(-0.223329\pi\)
−0.940876 + 0.338751i \(0.889995\pi\)
\(500\) 0 0
\(501\) −1684.95 + 2918.43i −0.150256 + 0.260251i
\(502\) 0 0
\(503\) 13725.3 1.21666 0.608331 0.793684i \(-0.291839\pi\)
0.608331 + 0.793684i \(0.291839\pi\)
\(504\) 0 0
\(505\) −307.190 −0.0270688
\(506\) 0 0
\(507\) −3288.48 + 5695.82i −0.288060 + 0.498935i
\(508\) 0 0
\(509\) −3915.05 6781.07i −0.340926 0.590502i 0.643679 0.765296i \(-0.277407\pi\)
−0.984605 + 0.174794i \(0.944074\pi\)
\(510\) 0 0
\(511\) 12586.7 16073.0i 1.08963 1.39145i
\(512\) 0 0
\(513\) 452.403 + 783.586i 0.0389359 + 0.0674389i
\(514\) 0 0
\(515\) −8766.39 + 15183.8i −0.750084 + 1.29918i
\(516\) 0 0
\(517\) 7703.43 0.655312
\(518\) 0 0
\(519\) −4591.80 −0.388357
\(520\) 0 0
\(521\) 2953.69 5115.95i 0.248376 0.430199i −0.714700 0.699431i \(-0.753437\pi\)
0.963075 + 0.269232i \(0.0867700\pi\)
\(522\) 0 0
\(523\) 3954.03 + 6848.58i 0.330588 + 0.572595i 0.982627 0.185590i \(-0.0594196\pi\)
−0.652039 + 0.758185i \(0.726086\pi\)
\(524\) 0 0
\(525\) 6417.36 + 15934.9i 0.533479 + 1.32468i
\(526\) 0 0
\(527\) 13326.8 + 23082.7i 1.10156 + 1.90797i
\(528\) 0 0
\(529\) 6083.29 10536.6i 0.499983 0.865995i
\(530\) 0 0
\(531\) −4094.35 −0.334613
\(532\) 0 0
\(533\) −698.659 −0.0567773
\(534\) 0 0
\(535\) −7456.26 + 12914.6i −0.602546 + 1.04364i
\(536\) 0 0
\(537\) −5120.15 8868.36i −0.411454 0.712659i
\(538\) 0 0
\(539\) 3749.28 3604.43i 0.299616 0.288040i
\(540\) 0 0
\(541\) 1970.52 + 3413.04i 0.156598 + 0.271235i 0.933640 0.358214i \(-0.116614\pi\)
−0.777042 + 0.629449i \(0.783281\pi\)
\(542\) 0 0
\(543\) 1930.06 3342.97i 0.152536 0.264200i
\(544\) 0 0
\(545\) 12502.7 0.982670
\(546\) 0 0
\(547\) 1828.71 0.142943 0.0714717 0.997443i \(-0.477230\pi\)
0.0714717 + 0.997443i \(0.477230\pi\)
\(548\) 0 0
\(549\) −173.932 + 301.259i −0.0135214 + 0.0234197i
\(550\) 0 0
\(551\) 2734.67 + 4736.58i 0.211435 + 0.366216i
\(552\) 0 0
\(553\) −804.650 1998.02i −0.0618756 0.153643i
\(554\) 0 0
\(555\) 5267.65 + 9123.83i 0.402881 + 0.697811i
\(556\) 0 0
\(557\) −11266.0 + 19513.3i −0.857011 + 1.48439i 0.0177556 + 0.999842i \(0.494348\pi\)
−0.874767 + 0.484544i \(0.838985\pi\)
\(558\) 0 0
\(559\) −479.201 −0.0362577
\(560\) 0 0
\(561\) −5429.00 −0.408579
\(562\) 0 0
\(563\) 11677.9 20226.6i 0.874179 1.51412i 0.0165446 0.999863i \(-0.494733\pi\)
0.857635 0.514260i \(-0.171933\pi\)
\(564\) 0 0
\(565\) −6487.05 11235.9i −0.483031 0.836634i
\(566\) 0 0
\(567\) −924.903 + 1181.09i −0.0685049 + 0.0874800i
\(568\) 0 0
\(569\) 10443.8 + 18089.2i 0.769468 + 1.33276i 0.937852 + 0.347036i \(0.112812\pi\)
−0.168384 + 0.985721i \(0.553855\pi\)
\(570\) 0 0
\(571\) 11872.6 20564.0i 0.870147 1.50714i 0.00830301 0.999966i \(-0.497357\pi\)
0.861844 0.507173i \(-0.169310\pi\)
\(572\) 0 0
\(573\) 3165.89 0.230815
\(574\) 0 0
\(575\) −201.440 −0.0146098
\(576\) 0 0
\(577\) −1227.20 + 2125.57i −0.0885422 + 0.153360i −0.906895 0.421356i \(-0.861554\pi\)
0.818353 + 0.574716i \(0.194887\pi\)
\(578\) 0 0
\(579\) −7156.26 12395.0i −0.513651 0.889670i
\(580\) 0 0
\(581\) 10432.5 + 1478.12i 0.744945 + 0.105547i
\(582\) 0 0
\(583\) −1338.21 2317.85i −0.0950652 0.164658i
\(584\) 0 0
\(585\) −202.807 + 351.272i −0.0143334 + 0.0248261i
\(586\) 0 0
\(587\) −18567.5 −1.30556 −0.652780 0.757547i \(-0.726397\pi\)
−0.652780 + 0.757547i \(0.726397\pi\)
\(588\) 0 0
\(589\) 7483.95 0.523550
\(590\) 0 0
\(591\) 2433.47 4214.89i 0.169373 0.293363i
\(592\) 0 0
\(593\) −8556.47 14820.2i −0.592533 1.02630i −0.993890 0.110375i \(-0.964795\pi\)
0.401357 0.915922i \(-0.368539\pi\)
\(594\) 0 0
\(595\) −45602.2 6461.10i −3.14203 0.445175i
\(596\) 0 0
\(597\) 5325.20 + 9223.52i 0.365069 + 0.632318i
\(598\) 0 0
\(599\) 11632.4 20147.9i 0.793469 1.37433i −0.130338 0.991470i \(-0.541606\pi\)
0.923807 0.382859i \(-0.125060\pi\)
\(600\) 0 0
\(601\) 25322.3 1.71867 0.859334 0.511416i \(-0.170879\pi\)
0.859334 + 0.511416i \(0.170879\pi\)
\(602\) 0 0
\(603\) −1276.13 −0.0861821
\(604\) 0 0
\(605\) 11471.7 19869.6i 0.770897 1.33523i
\(606\) 0 0
\(607\) −10867.2 18822.5i −0.726665 1.25862i −0.958285 0.285814i \(-0.907736\pi\)
0.231620 0.972806i \(-0.425597\pi\)
\(608\) 0 0
\(609\) −5590.81 + 7139.41i −0.372005 + 0.475046i
\(610\) 0 0
\(611\) 549.420 + 951.624i 0.0363784 + 0.0630092i
\(612\) 0 0
\(613\) 6786.19 11754.0i 0.447131 0.774454i −0.551067 0.834461i \(-0.685779\pi\)
0.998198 + 0.0600072i \(0.0191124\pi\)
\(614\) 0 0
\(615\) 20192.6 1.32397
\(616\) 0 0
\(617\) −8497.12 −0.554427 −0.277213 0.960808i \(-0.589411\pi\)
−0.277213 + 0.960808i \(0.589411\pi\)
\(618\) 0 0
\(619\) −11491.5 + 19903.8i −0.746173 + 1.29241i 0.203472 + 0.979081i \(0.434777\pi\)
−0.949645 + 0.313329i \(0.898556\pi\)
\(620\) 0 0
\(621\) −8.79548 15.2342i −0.000568358 0.000984425i
\(622\) 0 0
\(623\) 2650.91 + 6582.46i 0.170476 + 0.423308i
\(624\) 0 0
\(625\) −20661.3 35786.4i −1.32232 2.29033i
\(626\) 0 0
\(627\) −762.193 + 1320.16i −0.0485471 + 0.0840861i
\(628\) 0 0
\(629\) −20114.3 −1.27505
\(630\) 0 0
\(631\) 15717.9 0.991635 0.495817 0.868427i \(-0.334869\pi\)
0.495817 + 0.868427i \(0.334869\pi\)
\(632\) 0 0
\(633\) −6980.08 + 12089.9i −0.438283 + 0.759129i
\(634\) 0 0
\(635\) −1876.13 3249.55i −0.117247 0.203078i
\(636\) 0 0
\(637\) 712.669 + 206.084i 0.0443280 + 0.0128185i
\(638\) 0 0
\(639\) 2712.34 + 4697.91i 0.167916 + 0.290840i
\(640\) 0 0
\(641\) −14553.7 + 25207.7i −0.896780 + 1.55327i −0.0651930 + 0.997873i \(0.520766\pi\)
−0.831587 + 0.555395i \(0.812567\pi\)
\(642\) 0 0
\(643\) 3112.26 0.190880 0.0954398 0.995435i \(-0.469574\pi\)
0.0954398 + 0.995435i \(0.469574\pi\)
\(644\) 0 0
\(645\) 13849.8 0.845482
\(646\) 0 0
\(647\) −3928.80 + 6804.87i −0.238728 + 0.413489i −0.960349 0.278799i \(-0.910064\pi\)
0.721622 + 0.692288i \(0.243397\pi\)
\(648\) 0 0
\(649\) −3449.01 5973.86i −0.208606 0.361317i
\(650\) 0 0
\(651\) 4635.28 + 11509.8i 0.279064 + 0.692944i
\(652\) 0 0
\(653\) 9761.01 + 16906.6i 0.584958 + 1.01318i 0.994881 + 0.101057i \(0.0322224\pi\)
−0.409923 + 0.912120i \(0.634444\pi\)
\(654\) 0 0
\(655\) 2269.79 3931.38i 0.135401 0.234522i
\(656\) 0 0
\(657\) −9920.69 −0.589107
\(658\) 0 0
\(659\) −664.061 −0.0392536 −0.0196268 0.999807i \(-0.506248\pi\)
−0.0196268 + 0.999807i \(0.506248\pi\)
\(660\) 0 0
\(661\) −7960.82 + 13788.5i −0.468442 + 0.811365i −0.999349 0.0360650i \(-0.988518\pi\)
0.530908 + 0.847430i \(0.321851\pi\)
\(662\) 0 0
\(663\) −387.205 670.658i −0.0226814 0.0392854i
\(664\) 0 0
\(665\) −7973.36 + 10181.9i −0.464953 + 0.593739i
\(666\) 0 0
\(667\) −53.1665 92.0870i −0.00308638 0.00534576i
\(668\) 0 0
\(669\) 6974.30 12079.8i 0.403052 0.698107i
\(670\) 0 0
\(671\) −586.068 −0.0337182
\(672\) 0 0
\(673\) 24631.0 1.41078 0.705391 0.708819i \(-0.250771\pi\)
0.705391 + 0.708819i \(0.250771\pi\)
\(674\) 0 0
\(675\) 4174.01 7229.59i 0.238011 0.412247i
\(676\) 0 0
\(677\) −8546.39 14802.8i −0.485177 0.840350i 0.514678 0.857383i \(-0.327911\pi\)
−0.999855 + 0.0170329i \(0.994578\pi\)
\(678\) 0 0
\(679\) 6137.45 + 869.578i 0.346883 + 0.0491478i
\(680\) 0 0
\(681\) −6227.57 10786.5i −0.350428 0.606958i
\(682\) 0 0
\(683\) −9581.79 + 16596.1i −0.536804 + 0.929771i 0.462270 + 0.886739i \(0.347035\pi\)
−0.999074 + 0.0430322i \(0.986298\pi\)
\(684\) 0 0
\(685\) −54215.2 −3.02402
\(686\) 0 0
\(687\) −12790.9 −0.710339
\(688\) 0 0
\(689\) 190.886 330.625i 0.0105547 0.0182813i
\(690\) 0 0
\(691\) 4047.94 + 7011.23i 0.222852 + 0.385991i 0.955673 0.294431i \(-0.0951300\pi\)
−0.732821 + 0.680422i \(0.761797\pi\)
\(692\) 0 0
\(693\) −2502.39 354.549i −0.137169 0.0194346i
\(694\) 0 0
\(695\) −27625.3 47848.5i −1.50775 2.61150i
\(696\) 0 0
\(697\) −19276.1 + 33387.2i −1.04754 + 1.81439i
\(698\) 0 0
\(699\) −9149.70 −0.495098
\(700\) 0 0
\(701\) 12354.7 0.665664 0.332832 0.942986i \(-0.391996\pi\)
0.332832 + 0.942986i \(0.391996\pi\)
\(702\) 0 0
\(703\) −2823.90 + 4891.14i −0.151501 + 0.262408i
\(704\) 0 0
\(705\) −15879.3 27503.8i −0.848297 1.46929i
\(706\) 0 0
\(707\) 168.337 214.965i 0.00895470 0.0114350i
\(708\) 0 0
\(709\) −1914.41 3315.85i −0.101406 0.175641i 0.810858 0.585243i \(-0.199001\pi\)
−0.912264 + 0.409602i \(0.865668\pi\)
\(710\) 0 0
\(711\) −523.364 + 906.492i −0.0276057 + 0.0478145i
\(712\) 0 0
\(713\) −145.500 −0.00764241
\(714\) 0 0
\(715\) −683.363 −0.0357431
\(716\) 0 0
\(717\) −5980.81 + 10359.1i −0.311516 + 0.539562i
\(718\) 0 0
\(719\) 611.500 + 1059.15i 0.0317178 + 0.0549368i 0.881449 0.472280i \(-0.156569\pi\)
−0.849731 + 0.527217i \(0.823236\pi\)
\(720\) 0 0
\(721\) −5821.42 14455.1i −0.300695 0.746654i
\(722\) 0 0
\(723\) −936.972 1622.88i −0.0481969 0.0834795i
\(724\) 0 0
\(725\) 25230.8 43701.1i 1.29248 2.23864i
\(726\) 0 0
\(727\) −6368.21 −0.324875 −0.162437 0.986719i \(-0.551936\pi\)
−0.162437 + 0.986719i \(0.551936\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −13221.2 + 22899.9i −0.668954 + 1.15866i
\(732\) 0 0
\(733\) 12577.0 + 21784.0i 0.633753 + 1.09769i 0.986778 + 0.162079i \(0.0518199\pi\)
−0.353024 + 0.935614i \(0.614847\pi\)
\(734\) 0 0
\(735\) −20597.5 5956.24i −1.03367 0.298910i
\(736\) 0 0
\(737\) −1074.98 1861.93i −0.0537281 0.0930597i
\(738\) 0 0
\(739\) −5369.55 + 9300.34i −0.267283 + 0.462948i −0.968159 0.250335i \(-0.919459\pi\)
0.700876 + 0.713283i \(0.252793\pi\)
\(740\) 0 0
\(741\) −217.443 −0.0107800
\(742\) 0 0
\(743\) −28166.3 −1.39074 −0.695370 0.718652i \(-0.744760\pi\)
−0.695370 + 0.718652i \(0.744760\pi\)
\(744\) 0 0
\(745\) −6053.42 + 10484.8i −0.297691 + 0.515617i
\(746\) 0 0
\(747\) −2560.18 4434.36i −0.125398 0.217195i
\(748\) 0 0
\(749\) −4951.41 12294.8i −0.241549 0.599791i
\(750\) 0 0
\(751\) 14328.5 + 24817.7i 0.696211 + 1.20587i 0.969771 + 0.244018i \(0.0784657\pi\)
−0.273559 + 0.961855i \(0.588201\pi\)
\(752\) 0 0
\(753\) 1993.18 3452.28i 0.0964613 0.167076i
\(754\) 0 0
\(755\) 12823.0 0.618113
\(756\) 0 0
\(757\) −23604.1 −1.13330 −0.566648 0.823960i \(-0.691760\pi\)
−0.566648 + 0.823960i \(0.691760\pi\)
\(758\) 0 0
\(759\) 14.8183 25.6661i 0.000708657 0.00122743i
\(760\) 0 0
\(761\) −2315.48 4010.54i −0.110297 0.191041i 0.805593 0.592470i \(-0.201847\pi\)
−0.915890 + 0.401429i \(0.868514\pi\)
\(762\) 0 0
\(763\) −6851.35 + 8749.10i −0.325079 + 0.415123i
\(764\) 0 0
\(765\) 11191.0 + 19383.3i 0.528902 + 0.916085i
\(766\) 0 0
\(767\) 491.977 852.129i 0.0231607 0.0401155i
\(768\) 0 0
\(769\) 33276.8 1.56046 0.780228 0.625495i \(-0.215103\pi\)
0.780228 + 0.625495i \(0.215103\pi\)
\(770\) 0 0
\(771\) 9678.55 0.452094
\(772\) 0 0
\(773\) 11469.4 19865.6i 0.533668 0.924340i −0.465558 0.885017i \(-0.654147\pi\)
0.999227 0.0393231i \(-0.0125202\pi\)
\(774\) 0 0
\(775\) −34524.6 59798.3i −1.60020 2.77164i
\(776\) 0 0
\(777\) −9271.29 1313.59i −0.428064 0.0606498i
\(778\) 0 0
\(779\) 5412.47 + 9374.67i 0.248937 + 0.431171i
\(780\) 0 0
\(781\) −4569.66 + 7914.88i −0.209366 + 0.362633i
\(782\) 0 0
\(783\) 4406.62 0.201124
\(784\) 0 0
\(785\) −6395.58 −0.290787
\(786\) 0 0
\(787\) −6757.23 + 11703.9i −0.306060 + 0.530112i −0.977497 0.210950i \(-0.932344\pi\)
0.671437 + 0.741062i \(0.265678\pi\)
\(788\) 0 0
\(789\) −4875.92 8445.34i −0.220009 0.381067i
\(790\) 0 0
\(791\) 11417.5 + 1617.68i 0.513223 + 0.0727155i
\(792\) 0 0
\(793\) −41.7993 72.3985i