Properties

Label 224.3.o.d.79.3
Level 224
Weight 3
Character 224.79
Analytic conductor 6.104
Analytic rank 0
Dimension 12
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 79.3
Root \(-2.29733 + 1.90372i\) of \(x^{12} - 3 x^{11} - 4 x^{10} + 3 x^{9} + 86 x^{8} - 163 x^{7} + 155 x^{6} - 166 x^{5} + 164 x^{4} - 116 x^{3} + 60 x^{2} - 20 x + 4\)
Character \(\chi\) \(=\) 224.79
Dual form 224.3.o.d.207.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.824388 + 1.42788i) q^{3} +(-3.95004 - 2.28056i) q^{5} +(-6.75545 + 1.83408i) q^{7} +(3.14077 - 5.43997i) q^{9} +O(q^{10})\) \(q+(0.824388 + 1.42788i) q^{3} +(-3.95004 - 2.28056i) q^{5} +(-6.75545 + 1.83408i) q^{7} +(3.14077 - 5.43997i) q^{9} +(-6.18983 - 10.7211i) q^{11} -18.3741i q^{13} -7.52026i q^{15} +(6.51422 + 11.2830i) q^{17} +(-1.51262 + 2.61993i) q^{19} +(-8.18796 - 8.13400i) q^{21} +(-26.2611 - 15.1619i) q^{23} +(-2.09812 - 3.63405i) q^{25} +25.1958 q^{27} +22.7701i q^{29} +(19.5382 - 11.2804i) q^{31} +(10.2056 - 17.6767i) q^{33} +(30.8670 + 8.16151i) q^{35} +(-11.9335 - 6.88983i) q^{37} +(26.2361 - 15.1474i) q^{39} -60.5026 q^{41} -39.0188 q^{43} +(-24.8123 + 14.3254i) q^{45} +(-17.6115 - 10.1680i) q^{47} +(42.2723 - 24.7801i) q^{49} +(-10.7405 + 18.6031i) q^{51} +(-4.12744 + 2.38298i) q^{53} +56.4650i q^{55} -4.98794 q^{57} +(5.86884 + 10.1651i) q^{59} +(94.3137 + 54.4520i) q^{61} +(-11.2400 + 42.5099i) q^{63} +(-41.9033 + 72.5786i) q^{65} +(-39.5997 - 68.5887i) q^{67} -49.9970i q^{69} +12.9952i q^{71} +(49.2909 + 85.3744i) q^{73} +(3.45933 - 5.99173i) q^{75} +(61.4784 + 61.0732i) q^{77} +(113.644 + 65.6123i) q^{79} +(-7.49577 - 12.9831i) q^{81} -28.3732 q^{83} -59.4242i q^{85} +(-32.5130 + 18.7714i) q^{87} +(78.7090 - 136.328i) q^{89} +(33.6996 + 124.126i) q^{91} +(32.2141 + 18.5988i) q^{93} +(11.9498 - 6.89923i) q^{95} -39.6175 q^{97} -77.7633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 6q^{3} - 40q^{9} + O(q^{10}) \) \( 12q + 6q^{3} - 40q^{9} - 30q^{11} + 30q^{17} - 78q^{19} - 92q^{25} - 156q^{27} - 78q^{33} + 222q^{35} - 232q^{41} + 200q^{43} + 372q^{49} - 10q^{51} + 332q^{57} + 110q^{59} - 32q^{65} - 434q^{67} + 102q^{73} + 60q^{75} - 82q^{81} + 536q^{83} + 214q^{89} + 8q^{91} - 152q^{97} - 504q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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
\(3\) 0.824388 + 1.42788i 0.274796 + 0.475961i 0.970084 0.242771i \(-0.0780563\pi\)
−0.695288 + 0.718732i \(0.744723\pi\)
\(4\) 0 0
\(5\) −3.95004 2.28056i −0.790008 0.456111i 0.0499573 0.998751i \(-0.484091\pi\)
−0.839965 + 0.542640i \(0.817425\pi\)
\(6\) 0 0
\(7\) −6.75545 + 1.83408i −0.965065 + 0.262011i
\(8\) 0 0
\(9\) 3.14077 5.43997i 0.348974 0.604441i
\(10\) 0 0
\(11\) −6.18983 10.7211i −0.562712 0.974645i −0.997259 0.0739960i \(-0.976425\pi\)
0.434547 0.900649i \(-0.356909\pi\)
\(12\) 0 0
\(13\) 18.3741i 1.41340i −0.707516 0.706698i \(-0.750184\pi\)
0.707516 0.706698i \(-0.249816\pi\)
\(14\) 0 0
\(15\) 7.52026i 0.501350i
\(16\) 0 0
\(17\) 6.51422 + 11.2830i 0.383189 + 0.663703i 0.991516 0.129983i \(-0.0414924\pi\)
−0.608327 + 0.793687i \(0.708159\pi\)
\(18\) 0 0
\(19\) −1.51262 + 2.61993i −0.0796115 + 0.137891i −0.903082 0.429467i \(-0.858701\pi\)
0.823471 + 0.567359i \(0.192035\pi\)
\(20\) 0 0
\(21\) −8.18796 8.13400i −0.389903 0.387333i
\(22\) 0 0
\(23\) −26.2611 15.1619i −1.14179 0.659211i −0.194915 0.980820i \(-0.562443\pi\)
−0.946873 + 0.321609i \(0.895776\pi\)
\(24\) 0 0
\(25\) −2.09812 3.63405i −0.0839248 0.145362i
\(26\) 0 0
\(27\) 25.1958 0.933179
\(28\) 0 0
\(29\) 22.7701i 0.785176i 0.919714 + 0.392588i \(0.128420\pi\)
−0.919714 + 0.392588i \(0.871580\pi\)
\(30\) 0 0
\(31\) 19.5382 11.2804i 0.630264 0.363883i −0.150590 0.988596i \(-0.548117\pi\)
0.780855 + 0.624713i \(0.214784\pi\)
\(32\) 0 0
\(33\) 10.2056 17.6767i 0.309262 0.535657i
\(34\) 0 0
\(35\) 30.8670 + 8.16151i 0.881915 + 0.233186i
\(36\) 0 0
\(37\) −11.9335 6.88983i −0.322528 0.186212i 0.329991 0.943984i \(-0.392954\pi\)
−0.652519 + 0.757772i \(0.726288\pi\)
\(38\) 0 0
\(39\) 26.2361 15.1474i 0.672721 0.388395i
\(40\) 0 0
\(41\) −60.5026 −1.47567 −0.737837 0.674979i \(-0.764153\pi\)
−0.737837 + 0.674979i \(0.764153\pi\)
\(42\) 0 0
\(43\) −39.0188 −0.907414 −0.453707 0.891151i \(-0.649899\pi\)
−0.453707 + 0.891151i \(0.649899\pi\)
\(44\) 0 0
\(45\) −24.8123 + 14.3254i −0.551385 + 0.318342i
\(46\) 0 0
\(47\) −17.6115 10.1680i −0.374713 0.216341i 0.300802 0.953686i \(-0.402746\pi\)
−0.675516 + 0.737346i \(0.736079\pi\)
\(48\) 0 0
\(49\) 42.2723 24.7801i 0.862700 0.505716i
\(50\) 0 0
\(51\) −10.7405 + 18.6031i −0.210598 + 0.364766i
\(52\) 0 0
\(53\) −4.12744 + 2.38298i −0.0778762 + 0.0449619i −0.538432 0.842669i \(-0.680983\pi\)
0.460556 + 0.887631i \(0.347650\pi\)
\(54\) 0 0
\(55\) 56.4650i 1.02664i
\(56\) 0 0
\(57\) −4.98794 −0.0875077
\(58\) 0 0
\(59\) 5.86884 + 10.1651i 0.0994718 + 0.172290i 0.911466 0.411375i \(-0.134951\pi\)
−0.811994 + 0.583665i \(0.801618\pi\)
\(60\) 0 0
\(61\) 94.3137 + 54.4520i 1.54613 + 0.892656i 0.998432 + 0.0559779i \(0.0178276\pi\)
0.547694 + 0.836679i \(0.315506\pi\)
\(62\) 0 0
\(63\) −11.2400 + 42.5099i −0.178412 + 0.674760i
\(64\) 0 0
\(65\) −41.9033 + 72.5786i −0.644666 + 1.11659i
\(66\) 0 0
\(67\) −39.5997 68.5887i −0.591041 1.02371i −0.994093 0.108535i \(-0.965384\pi\)
0.403052 0.915177i \(-0.367949\pi\)
\(68\) 0 0
\(69\) 49.9970i 0.724595i
\(70\) 0 0
\(71\) 12.9952i 0.183031i 0.995804 + 0.0915157i \(0.0291712\pi\)
−0.995804 + 0.0915157i \(0.970829\pi\)
\(72\) 0 0
\(73\) 49.2909 + 85.3744i 0.675218 + 1.16951i 0.976405 + 0.215947i \(0.0692839\pi\)
−0.301187 + 0.953565i \(0.597383\pi\)
\(74\) 0 0
\(75\) 3.45933 5.99173i 0.0461244 0.0798898i
\(76\) 0 0
\(77\) 61.4784 + 61.0732i 0.798421 + 0.793159i
\(78\) 0 0
\(79\) 113.644 + 65.6123i 1.43853 + 0.830535i 0.997748 0.0670794i \(-0.0213681\pi\)
0.440781 + 0.897615i \(0.354701\pi\)
\(80\) 0 0
\(81\) −7.49577 12.9831i −0.0925404 0.160285i
\(82\) 0 0
\(83\) −28.3732 −0.341846 −0.170923 0.985284i \(-0.554675\pi\)
−0.170923 + 0.985284i \(0.554675\pi\)
\(84\) 0 0
\(85\) 59.4242i 0.699108i
\(86\) 0 0
\(87\) −32.5130 + 18.7714i −0.373713 + 0.215763i
\(88\) 0 0
\(89\) 78.7090 136.328i 0.884371 1.53178i 0.0379380 0.999280i \(-0.487921\pi\)
0.846433 0.532495i \(-0.178746\pi\)
\(90\) 0 0
\(91\) 33.6996 + 124.126i 0.370325 + 1.36402i
\(92\) 0 0
\(93\) 32.2141 + 18.5988i 0.346388 + 0.199987i
\(94\) 0 0
\(95\) 11.9498 6.89923i 0.125788 0.0726235i
\(96\) 0 0
\(97\) −39.6175 −0.408428 −0.204214 0.978926i \(-0.565464\pi\)
−0.204214 + 0.978926i \(0.565464\pi\)
\(98\) 0 0
\(99\) −77.7633 −0.785488
\(100\) 0 0
\(101\) −37.7745 + 21.8091i −0.374005 + 0.215932i −0.675207 0.737628i \(-0.735946\pi\)
0.301202 + 0.953560i \(0.402612\pi\)
\(102\) 0 0
\(103\) 54.4748 + 31.4510i 0.528881 + 0.305350i 0.740561 0.671989i \(-0.234560\pi\)
−0.211679 + 0.977339i \(0.567893\pi\)
\(104\) 0 0
\(105\) 13.7927 + 50.8027i 0.131359 + 0.483836i
\(106\) 0 0
\(107\) 22.1133 38.3014i 0.206667 0.357957i −0.743996 0.668184i \(-0.767072\pi\)
0.950663 + 0.310227i \(0.100405\pi\)
\(108\) 0 0
\(109\) −7.63419 + 4.40760i −0.0700384 + 0.0404367i −0.534610 0.845099i \(-0.679542\pi\)
0.464572 + 0.885535i \(0.346208\pi\)
\(110\) 0 0
\(111\) 22.7196i 0.204681i
\(112\) 0 0
\(113\) −121.408 −1.07440 −0.537202 0.843454i \(-0.680519\pi\)
−0.537202 + 0.843454i \(0.680519\pi\)
\(114\) 0 0
\(115\) 69.1550 + 119.780i 0.601347 + 1.04156i
\(116\) 0 0
\(117\) −99.9548 57.7089i −0.854314 0.493239i
\(118\) 0 0
\(119\) −64.7003 64.2739i −0.543700 0.540117i
\(120\) 0 0
\(121\) −16.1279 + 27.9344i −0.133289 + 0.230863i
\(122\) 0 0
\(123\) −49.8776 86.3906i −0.405509 0.702363i
\(124\) 0 0
\(125\) 133.167i 1.06534i
\(126\) 0 0
\(127\) 222.845i 1.75468i −0.479868 0.877341i \(-0.659315\pi\)
0.479868 0.877341i \(-0.340685\pi\)
\(128\) 0 0
\(129\) −32.1666 55.7143i −0.249354 0.431893i
\(130\) 0 0
\(131\) 118.527 205.294i 0.904785 1.56713i 0.0835786 0.996501i \(-0.473365\pi\)
0.821206 0.570632i \(-0.193302\pi\)
\(132\) 0 0
\(133\) 5.41327 20.4731i 0.0407013 0.153933i
\(134\) 0 0
\(135\) −99.5246 57.4605i −0.737219 0.425634i
\(136\) 0 0
\(137\) 4.83138 + 8.36820i 0.0352656 + 0.0610818i 0.883119 0.469148i \(-0.155439\pi\)
−0.847854 + 0.530230i \(0.822106\pi\)
\(138\) 0 0
\(139\) 63.0621 0.453684 0.226842 0.973932i \(-0.427160\pi\)
0.226842 + 0.973932i \(0.427160\pi\)
\(140\) 0 0
\(141\) 33.5296i 0.237798i
\(142\) 0 0
\(143\) −196.991 + 113.733i −1.37756 + 0.795334i
\(144\) 0 0
\(145\) 51.9285 89.9428i 0.358128 0.620295i
\(146\) 0 0
\(147\) 70.2318 + 39.9315i 0.477767 + 0.271643i
\(148\) 0 0
\(149\) −233.751 134.956i −1.56880 0.905746i −0.996309 0.0858343i \(-0.972644\pi\)
−0.572489 0.819912i \(1.30598\pi\)
\(150\) 0 0
\(151\) 93.6846 54.0888i 0.620428 0.358204i −0.156608 0.987661i \(-0.550056\pi\)
0.777036 + 0.629457i \(0.216723\pi\)
\(152\) 0 0
\(153\) 81.8386 0.534893
\(154\) 0 0
\(155\) −102.902 −0.663885
\(156\) 0 0
\(157\) 102.565 59.2159i 0.653280 0.377171i −0.136432 0.990649i \(-0.543563\pi\)
0.789712 + 0.613478i \(0.210230\pi\)
\(158\) 0 0
\(159\) −6.80523 3.92900i −0.0428002 0.0247107i
\(160\) 0 0
\(161\) 205.214 + 54.2603i 1.27462 + 0.337021i
\(162\) 0 0
\(163\) −41.0142 + 71.0387i −0.251621 + 0.435820i −0.963972 0.266003i \(-0.914297\pi\)
0.712351 + 0.701823i \(0.247630\pi\)
\(164\) 0 0
\(165\) −80.6254 + 46.5491i −0.488639 + 0.282116i
\(166\) 0 0
\(167\) 131.596i 0.788002i −0.919110 0.394001i \(-0.871091\pi\)
0.919110 0.394001i \(-0.128909\pi\)
\(168\) 0 0
\(169\) −168.609 −0.997687
\(170\) 0 0
\(171\) 9.50157 + 16.4572i 0.0555648 + 0.0962410i
\(172\) 0 0
\(173\) 95.3611 + 55.0568i 0.551220 + 0.318247i 0.749614 0.661875i \(-0.230239\pi\)
−0.198394 + 0.980122i \(0.563572\pi\)
\(174\) 0 0
\(175\) 20.8389 + 20.7015i 0.119079 + 0.118295i
\(176\) 0 0
\(177\) −9.67640 + 16.7600i −0.0546689 + 0.0946893i
\(178\) 0 0
\(179\) 76.9263 + 133.240i 0.429756 + 0.744359i 0.996851 0.0792929i \(-0.0252662\pi\)
−0.567095 + 0.823652i \(0.691933\pi\)
\(180\) 0 0
\(181\) 227.511i 1.25697i −0.777823 0.628484i \(-0.783676\pi\)
0.777823 0.628484i \(-0.216324\pi\)
\(182\) 0 0
\(183\) 179.558i 0.981194i
\(184\) 0 0
\(185\) 31.4253 + 54.4303i 0.169867 + 0.294218i
\(186\) 0 0
\(187\) 80.6438 139.679i 0.431250 0.746947i
\(188\) 0 0
\(189\) −170.209 + 46.2111i −0.900578 + 0.244503i
\(190\) 0 0
\(191\) −105.262 60.7728i −0.551107 0.318182i 0.198461 0.980109i \(-0.436406\pi\)
−0.749569 + 0.661927i \(0.769739\pi\)
\(192\) 0 0
\(193\) −42.7276 74.0064i −0.221386 0.383453i 0.733843 0.679319i \(-0.237725\pi\)
−0.955229 + 0.295867i \(0.904392\pi\)
\(194\) 0 0
\(195\) −138.178 −0.708606
\(196\) 0 0
\(197\) 214.100i 1.08680i −0.839474 0.543400i \(-0.817137\pi\)
0.839474 0.543400i \(-0.182863\pi\)
\(198\) 0 0
\(199\) 214.968 124.112i 1.08024 0.623677i 0.149279 0.988795i \(-0.452305\pi\)
0.930961 + 0.365118i \(0.118971\pi\)
\(200\) 0 0
\(201\) 65.2911 113.087i 0.324831 0.562624i
\(202\) 0 0
\(203\) −41.7621 153.822i −0.205725 0.757746i
\(204\) 0 0
\(205\) 238.988 + 137.980i 1.16579 + 0.673071i
\(206\) 0 0
\(207\) −164.960 + 95.2398i −0.796909 + 0.460096i
\(208\) 0 0
\(209\) 37.4514 0.179193
\(210\) 0 0
\(211\) −191.753 −0.908783 −0.454392 0.890802i \(-0.650143\pi\)
−0.454392 + 0.890802i \(0.650143\pi\)
\(212\) 0 0
\(213\) −18.5557 + 10.7131i −0.0871157 + 0.0502963i
\(214\) 0 0
\(215\) 154.126 + 88.9846i 0.716864 + 0.413882i
\(216\) 0 0
\(217\) −111.300 + 112.039i −0.512905 + 0.516307i
\(218\) 0 0
\(219\) −81.2697 + 140.763i −0.371095 + 0.642755i
\(220\) 0 0
\(221\) 207.315 119.693i 0.938075 0.541598i
\(222\) 0 0
\(223\) 41.2269i 0.184874i 0.995719 + 0.0924370i \(0.0294657\pi\)
−0.995719 + 0.0924370i \(0.970534\pi\)
\(224\) 0 0
\(225\) −26.3588 −0.117150
\(226\) 0 0
\(227\) 35.2219 + 61.0060i 0.155162 + 0.268749i 0.933118 0.359570i \(-0.117077\pi\)
−0.777956 + 0.628319i \(0.783743\pi\)
\(228\) 0 0
\(229\) 81.8558 + 47.2595i 0.357449 + 0.206373i 0.667961 0.744196i \(-0.267167\pi\)
−0.310512 + 0.950569i \(0.600501\pi\)
\(230\) 0 0
\(231\) −36.5233 + 138.132i −0.158110 + 0.597974i
\(232\) 0 0
\(233\) 68.1434 118.028i 0.292461 0.506557i −0.681930 0.731417i \(-0.738859\pi\)
0.974391 + 0.224860i \(0.0721925\pi\)
\(234\) 0 0
\(235\) 46.3775 + 80.3281i 0.197351 + 0.341822i
\(236\) 0 0
\(237\) 216.360i 0.912911i
\(238\) 0 0
\(239\) 173.230i 0.724813i 0.932020 + 0.362406i \(0.118045\pi\)
−0.932020 + 0.362406i \(0.881955\pi\)
\(240\) 0 0
\(241\) 164.461 + 284.856i 0.682413 + 1.18197i 0.974242 + 0.225503i \(0.0724027\pi\)
−0.291830 + 0.956470i \(0.594264\pi\)
\(242\) 0 0
\(243\) 125.740 217.788i 0.517449 0.896248i
\(244\) 0 0
\(245\) −223.490 + 1.47783i −0.912203 + 0.00603196i
\(246\) 0 0
\(247\) 48.1390 + 27.7931i 0.194895 + 0.112523i
\(248\) 0 0
\(249\) −23.3905 40.5136i −0.0939379 0.162705i
\(250\) 0 0
\(251\) −160.255 −0.638466 −0.319233 0.947676i \(-0.603425\pi\)
−0.319233 + 0.947676i \(0.603425\pi\)
\(252\) 0 0
\(253\) 375.397i 1.48378i
\(254\) 0 0
\(255\) 84.8507 48.9886i 0.332748 0.192112i
\(256\) 0 0
\(257\) −72.7208 + 125.956i −0.282960 + 0.490102i −0.972113 0.234515i \(-0.924650\pi\)
0.689152 + 0.724617i \(0.257983\pi\)
\(258\) 0 0
\(259\) 93.2530 + 24.6569i 0.360050 + 0.0952004i
\(260\) 0 0
\(261\) 123.869 + 71.5156i 0.474593 + 0.274006i
\(262\) 0 0
\(263\) −175.617 + 101.392i −0.667745 + 0.385523i −0.795222 0.606319i \(-0.792645\pi\)
0.127477 + 0.991842i \(0.459312\pi\)
\(264\) 0 0
\(265\) 21.7381 0.0820305
\(266\) 0 0
\(267\) 259.547 0.972087
\(268\) 0 0
\(269\) −191.662 + 110.656i −0.712497 + 0.411360i −0.811985 0.583679i \(-0.801613\pi\)
0.0994882 + 0.995039i \(0.468279\pi\)
\(270\) 0 0
\(271\) 101.651 + 58.6880i 0.375095 + 0.216561i 0.675682 0.737193i \(-0.263849\pi\)
−0.300587 + 0.953754i \(0.597183\pi\)
\(272\) 0 0
\(273\) −149.455 + 150.447i −0.547455 + 0.551087i
\(274\) 0 0
\(275\) −25.9740 + 44.9883i −0.0944509 + 0.163594i
\(276\) 0 0
\(277\) 221.277 127.755i 0.798835 0.461208i −0.0442283 0.999021i \(-0.514083\pi\)
0.843064 + 0.537814i \(0.180750\pi\)
\(278\) 0 0
\(279\) 141.716i 0.507944i
\(280\) 0 0
\(281\) −278.004 −0.989336 −0.494668 0.869082i \(-0.664710\pi\)
−0.494668 + 0.869082i \(0.664710\pi\)
\(282\) 0 0
\(283\) 28.3448 + 49.0947i 0.100158 + 0.173479i 0.911750 0.410746i \(-0.134732\pi\)
−0.811591 + 0.584225i \(0.801398\pi\)
\(284\) 0 0
\(285\) 19.7026 + 11.3753i 0.0691318 + 0.0399133i
\(286\) 0 0
\(287\) 408.723 110.967i 1.42412 0.386643i
\(288\) 0 0
\(289\) 59.6300 103.282i 0.206332 0.357378i
\(290\) 0 0
\(291\) −32.6602 56.5691i −0.112234 0.194396i
\(292\) 0 0
\(293\) 287.871i 0.982493i 0.871020 + 0.491247i \(0.163459\pi\)
−0.871020 + 0.491247i \(0.836541\pi\)
\(294\) 0 0
\(295\) 53.5369i 0.181481i
\(296\) 0 0
\(297\) −155.958 270.127i −0.525111 0.909518i
\(298\) 0 0
\(299\) −278.586 + 482.525i −0.931726 + 1.61380i
\(300\) 0 0
\(301\) 263.590 71.5635i 0.875713 0.237753i
\(302\) 0 0
\(303\) −62.2817 35.9584i −0.205550 0.118675i
\(304\) 0 0
\(305\) −248.362 430.176i −0.814302 1.41041i
\(306\) 0 0
\(307\) −53.6483 −0.174750 −0.0873750 0.996175i \(-0.527848\pi\)
−0.0873750 + 0.996175i \(0.527848\pi\)
\(308\) 0 0
\(309\) 103.711i 0.335636i
\(310\) 0 0
\(311\) 91.0263 52.5541i 0.292689 0.168984i −0.346465 0.938063i \(-0.612618\pi\)
0.639154 + 0.769079i \(0.279285\pi\)
\(312\) 0 0
\(313\) −105.245 + 182.290i −0.336246 + 0.582395i −0.983723 0.179690i \(-0.942491\pi\)
0.647477 + 0.762085i \(0.275824\pi\)
\(314\) 0 0
\(315\) 141.345 142.282i 0.448713 0.451690i
\(316\) 0 0
\(317\) −54.4626 31.4440i −0.171806 0.0991925i 0.411631 0.911351i \(-0.364959\pi\)
−0.583437 + 0.812158i \(0.698293\pi\)
\(318\) 0 0
\(319\) 244.120 140.943i 0.765268 0.441828i
\(320\) 0 0
\(321\) 72.9199 0.227165
\(322\) 0 0
\(323\) −39.4141 −0.122025
\(324\) 0 0
\(325\) −66.7725 + 38.5511i −0.205454 + 0.118619i
\(326\) 0 0
\(327\) −12.5871 7.26715i −0.0384926 0.0222237i
\(328\) 0 0
\(329\) 137.623 + 36.3887i 0.418306 + 0.110604i
\(330\) 0 0
\(331\) 98.2893 170.242i 0.296947 0.514327i −0.678489 0.734610i \(-0.737365\pi\)
0.975436 + 0.220284i \(0.0706983\pi\)
\(332\) 0 0
\(333\) −74.9610 + 43.2787i −0.225108 + 0.129966i
\(334\) 0 0
\(335\) 361.238i 1.07832i
\(336\) 0 0
\(337\) 591.516 1.75524 0.877620 0.479358i \(-0.159130\pi\)
0.877620 + 0.479358i \(0.159130\pi\)
\(338\) 0 0
\(339\) −100.087 173.356i −0.295242 0.511374i
\(340\) 0 0
\(341\) −241.876 139.647i −0.709314 0.409523i
\(342\) 0 0
\(343\) −240.120 + 244.931i −0.700059 + 0.714085i
\(344\) 0 0
\(345\) −114.021 + 197.490i −0.330496 + 0.572436i
\(346\) 0 0
\(347\) 123.770 + 214.376i 0.356685 + 0.617797i 0.987405 0.158214i \(-0.0505734\pi\)
−0.630719 + 0.776011i \(0.717240\pi\)
\(348\) 0 0
\(349\) 288.749i 0.827362i −0.910422 0.413681i \(-0.864243\pi\)
0.910422 0.413681i \(-0.135757\pi\)
\(350\) 0 0
\(351\) 462.952i 1.31895i
\(352\) 0 0
\(353\) 0.634830 + 1.09956i 0.00179839 + 0.00311490i 0.866923 0.498442i \(-0.166094\pi\)
−0.865125 + 0.501557i \(0.832761\pi\)
\(354\) 0 0
\(355\) 29.6364 51.3317i 0.0834827 0.144596i
\(356\) 0 0
\(357\) 38.4374 145.371i 0.107668 0.407202i
\(358\) 0 0
\(359\) −15.0707 8.70105i −0.0419796 0.0242369i 0.478863 0.877889i \(-0.341049\pi\)
−0.520843 + 0.853653i \(0.674382\pi\)
\(360\) 0 0
\(361\) 175.924 + 304.709i 0.487324 + 0.844070i
\(362\) 0 0
\(363\) −53.1828 −0.146509
\(364\) 0 0
\(365\) 449.643i 1.23190i
\(366\) 0 0
\(367\) −459.021 + 265.016i −1.25074 + 0.722115i −0.971256 0.238036i \(-0.923496\pi\)
−0.279483 + 0.960151i \(0.590163\pi\)
\(368\) 0 0
\(369\) −190.025 + 329.132i −0.514972 + 0.891958i
\(370\) 0 0
\(371\) 23.5122 23.6682i 0.0633751 0.0637956i
\(372\) 0 0
\(373\) 102.722 + 59.3066i 0.275394 + 0.158999i 0.631337 0.775509i \(-0.282507\pi\)
−0.355942 + 0.934508i \(0.615840\pi\)
\(374\) 0 0
\(375\) −190.147 + 109.782i −0.507059 + 0.292751i
\(376\) 0 0
\(377\) 418.381 1.10976
\(378\) 0 0
\(379\) 345.947 0.912790 0.456395 0.889777i \(-0.349140\pi\)
0.456395 + 0.889777i \(0.349140\pi\)
\(380\) 0 0
\(381\) 318.196 183.710i 0.835160 0.482180i
\(382\) 0 0
\(383\) −350.630 202.436i −0.915483 0.528555i −0.0332920 0.999446i \(-0.510599\pi\)
−0.882191 + 0.470891i \(0.843932\pi\)
\(384\) 0 0
\(385\) −103.561 381.447i −0.268990 0.990771i
\(386\) 0 0
\(387\) −122.549 + 212.261i −0.316664 + 0.548478i
\(388\) 0 0
\(389\) −116.391 + 67.1985i −0.299206 + 0.172747i −0.642086 0.766632i \(-0.721931\pi\)
0.342880 + 0.939379i \(0.388598\pi\)
\(390\) 0 0
\(391\) 395.070i 1.01041i
\(392\) 0 0
\(393\) 390.848 0.994525
\(394\) 0 0
\(395\) −299.265 518.342i −0.757633 1.31226i
\(396\) 0 0
\(397\) −530.424 306.240i −1.33608 0.771386i −0.349857 0.936803i \(-0.613770\pi\)
−0.986224 + 0.165417i \(0.947103\pi\)
\(398\) 0 0
\(399\) 33.6958 9.14828i 0.0844506 0.0229280i
\(400\) 0 0
\(401\) 63.1234 109.333i 0.157415 0.272651i −0.776521 0.630092i \(-0.783017\pi\)
0.933936 + 0.357441i \(0.116351\pi\)
\(402\) 0 0
\(403\) −207.267 358.998i −0.514311 0.890813i
\(404\) 0 0
\(405\) 68.3781i 0.168835i
\(406\) 0 0
\(407\) 170.588i 0.419134i
\(408\) 0 0
\(409\) −171.259 296.630i −0.418727 0.725257i 0.577084 0.816685i \(-0.304190\pi\)
−0.995812 + 0.0914275i \(0.970857\pi\)
\(410\) 0 0
\(411\) −7.96587 + 13.7973i −0.0193817 + 0.0335700i
\(412\) 0 0
\(413\) −58.2903 57.9061i −0.141139 0.140209i
\(414\) 0 0
\(415\) 112.075 + 64.7068i 0.270061 + 0.155920i
\(416\) 0 0
\(417\) 51.9876 + 90.0452i 0.124671 + 0.215936i
\(418\) 0 0
\(419\) 376.392 0.898311 0.449155 0.893454i \(-0.351725\pi\)
0.449155 + 0.893454i \(0.351725\pi\)
\(420\) 0 0
\(421\) 111.135i 0.263978i −0.991251 0.131989i \(-0.957864\pi\)
0.991251 0.131989i \(-0.0421363\pi\)
\(422\) 0 0
\(423\) −110.627 + 63.8708i −0.261531 + 0.150995i
\(424\) 0 0
\(425\) 27.3352 47.3460i 0.0643181 0.111402i
\(426\) 0 0
\(427\) −737.001 194.870i −1.72600 0.456369i
\(428\) 0 0
\(429\) −324.794 187.520i −0.757096 0.437109i
\(430\) 0 0
\(431\) −35.7481 + 20.6392i −0.0829422 + 0.0478867i −0.540898 0.841089i \(-0.681915\pi\)
0.457955 + 0.888975i \(0.348582\pi\)
\(432\) 0 0
\(433\) −675.176 −1.55930 −0.779649 0.626217i \(-0.784603\pi\)
−0.779649 + 0.626217i \(0.784603\pi\)
\(434\) 0 0
\(435\) 171.237 0.393648
\(436\) 0 0
\(437\) 79.4461 45.8682i 0.181799 0.104962i
\(438\) 0 0
\(439\) −459.215 265.128i −1.04605 0.603936i −0.124508 0.992219i \(-0.539735\pi\)
−0.921541 + 0.388282i \(0.873069\pi\)
\(440\) 0 0
\(441\) −2.03526 307.789i −0.00461510 0.697933i
\(442\) 0 0
\(443\) 166.016 287.549i 0.374755 0.649094i −0.615535 0.788109i \(-0.711060\pi\)
0.990290 + 0.139015i \(0.0443935\pi\)
\(444\) 0 0
\(445\) −621.808 + 359.001i −1.39732 + 0.806743i
\(446\) 0 0
\(447\) 445.025i 0.995582i
\(448\) 0 0
\(449\) −19.4200 −0.0432517 −0.0216259 0.999766i \(-0.506884\pi\)
−0.0216259 + 0.999766i \(0.506884\pi\)
\(450\) 0 0
\(451\) 374.501 + 648.654i 0.830379 + 1.43826i
\(452\) 0 0
\(453\) 154.465 + 89.1804i 0.340982 + 0.196866i
\(454\) 0 0
\(455\) 149.961 567.155i 0.329584 1.24650i
\(456\) 0 0
\(457\) 88.9796 154.117i 0.194704 0.337237i −0.752100 0.659049i \(-0.770959\pi\)
0.946803 + 0.321813i \(0.104292\pi\)
\(458\) 0 0
\(459\) 164.131 + 284.283i 0.357584 + 0.619354i
\(460\) 0 0
\(461\) 299.341i 0.649329i −0.945829 0.324664i \(-0.894749\pi\)
0.945829 0.324664i \(-0.105251\pi\)
\(462\) 0 0
\(463\) 505.213i 1.09117i 0.838055 + 0.545586i \(0.183693\pi\)
−0.838055 + 0.545586i \(0.816307\pi\)
\(464\) 0 0
\(465\) −84.8314 146.932i −0.182433 0.315983i
\(466\) 0 0
\(467\) −325.162 + 563.197i −0.696278 + 1.20599i 0.273470 + 0.961881i \(0.411829\pi\)
−0.969748 + 0.244108i \(0.921505\pi\)
\(468\) 0 0
\(469\) 393.311 + 390.719i 0.838617 + 0.833089i
\(470\) 0 0
\(471\) 169.107 + 97.6338i 0.359037 + 0.207290i
\(472\) 0 0
\(473\) 241.520 + 418.324i 0.510612 + 0.884407i
\(474\) 0 0
\(475\) 12.6946 0.0267255
\(476\) 0 0
\(477\) 29.9375i 0.0627621i
\(478\) 0 0
\(479\) 572.400 330.475i 1.19499 0.689928i 0.235556 0.971861i \(-0.424309\pi\)
0.959434 + 0.281933i \(0.0909755\pi\)
\(480\) 0 0
\(481\) −126.595 + 219.269i −0.263191 + 0.455860i
\(482\) 0 0
\(483\) 91.6985 + 337.753i 0.189852 + 0.699281i
\(484\) 0 0
\(485\) 156.491 + 90.3500i 0.322661 + 0.186289i
\(486\) 0 0
\(487\) 334.373 193.050i 0.686597 0.396407i −0.115739 0.993280i \(-0.536924\pi\)
0.802336 + 0.596873i \(0.203590\pi\)
\(488\) 0 0
\(489\) −135.246 −0.276578
\(490\) 0 0
\(491\) 898.359 1.82965 0.914826 0.403848i \(-0.132328\pi\)
0.914826 + 0.403848i \(0.132328\pi\)
\(492\) 0 0
\(493\) −256.914 + 148.329i −0.521124 + 0.300871i
\(494\) 0 0
\(495\) 307.168 + 177.344i 0.620542 + 0.358270i
\(496\) 0 0
\(497\) −23.8343 87.7887i −0.0479563 0.176637i
\(498\) 0 0
\(499\) 395.588 685.178i 0.792761 1.37310i −0.131490 0.991318i \(-0.541976\pi\)
0.924251 0.381785i \(-0.124691\pi\)
\(500\) 0 0
\(501\) 187.904 108.486i 0.375058 0.216540i
\(502\) 0 0
\(503\) 798.990i 1.58845i 0.607624 + 0.794225i \(0.292123\pi\)
−0.607624 + 0.794225i \(0.707877\pi\)
\(504\) 0 0
\(505\) 198.948 0.393956
\(506\) 0 0
\(507\) −138.999 240.754i −0.274160 0.474860i
\(508\) 0 0
\(509\) 477.272 + 275.553i 0.937666 + 0.541362i 0.889228 0.457465i \(-0.151242\pi\)
0.0484379 + 0.998826i \(0.484576\pi\)
\(510\) 0 0
\(511\) −489.566 486.339i −0.958055 0.951741i
\(512\) 0 0
\(513\) −38.1117 + 66.0114i −0.0742918 + 0.128677i
\(514\) 0 0
\(515\) −143.452 248.466i −0.278547 0.482458i
\(516\) 0 0
\(517\) 251.753i 0.486950i
\(518\) 0 0
\(519\) 181.553i 0.349812i
\(520\) 0 0
\(521\) −71.3914 123.654i −0.137028 0.237339i 0.789343 0.613953i \(-0.210422\pi\)
−0.926370 + 0.376614i \(0.877088\pi\)
\(522\) 0 0
\(523\) −416.255 + 720.976i −0.795900 + 1.37854i 0.126367 + 0.991984i \(0.459668\pi\)
−0.922266 + 0.386555i \(0.873665\pi\)
\(524\) 0 0
\(525\) −12.3800 + 46.8216i −0.0235810 + 0.0891839i
\(526\) 0 0
\(527\) 254.552 + 146.966i 0.483021 + 0.278872i
\(528\) 0 0
\(529\) 195.264 + 338.207i 0.369119 + 0.639333i
\(530\) 0 0
\(531\) 73.7306 0.138852
\(532\) 0 0
\(533\) 1111.68i 2.08571i
\(534\) 0 0
\(535\) −174.697 + 100.862i −0.326537 + 0.188526i
\(536\) 0 0
\(537\) −126.834 + 219.683i −0.236191 + 0.409094i
\(538\) 0 0
\(539\) −527.328 299.821i −0.978345 0.556255i
\(540\) 0 0
\(541\) −533.874 308.232i −0.986829 0.569746i −0.0825038 0.996591i \(-0.526292\pi\)
−0.904325 + 0.426845i \(0.859625\pi\)
\(542\) 0 0
\(543\) 324.859 187.557i 0.598267 0.345410i
\(544\) 0 0
\(545\) 40.2071 0.0737746
\(546\) 0 0
\(547\) −577.704 −1.05613 −0.528065 0.849204i \(-0.677082\pi\)
−0.528065 + 0.849204i \(0.677082\pi\)
\(548\) 0 0
\(549\) 592.435 342.043i 1.07912 0.623028i
\(550\) 0 0
\(551\) −59.6562 34.4425i −0.108269 0.0625091i
\(552\) 0 0
\(553\) −888.053 234.809i −1.60588 0.424610i
\(554\) 0 0
\(555\) −51.8133 + 89.7433i −0.0933573 + 0.161700i
\(556\) 0 0
\(557\) 445.752 257.355i 0.800273 0.462038i −0.0432939 0.999062i \(-0.513785\pi\)
0.843566 + 0.537025i \(0.180452\pi\)
\(558\) 0 0
\(559\) 716.937i 1.28253i
\(560\) 0 0
\(561\) 265.927 0.474023
\(562\) 0 0
\(563\) −304.360 527.166i −0.540603 0.936352i −0.998869 0.0475374i \(-0.984863\pi\)
0.458266 0.888815i \(-0.348471\pi\)
\(564\) 0 0
\(565\) 479.565 + 276.877i 0.848788 + 0.490048i
\(566\) 0 0
\(567\) 74.4493 + 73.9586i 0.131304 + 0.130438i
\(568\) 0 0
\(569\) −93.1872 + 161.405i −0.163774 + 0.283664i −0.936219 0.351417i \(-0.885700\pi\)
0.772445 + 0.635081i \(0.219033\pi\)
\(570\) 0 0
\(571\) 91.8878 + 159.154i 0.160924 + 0.278729i 0.935200 0.354119i \(-0.115219\pi\)
−0.774276 + 0.632848i \(0.781886\pi\)
\(572\) 0 0
\(573\) 200.401i 0.349741i
\(574\) 0 0
\(575\) 127.246i 0.221297i
\(576\) 0 0
\(577\) −67.2281 116.442i −0.116513 0.201807i 0.801870 0.597498i \(-0.203838\pi\)
−0.918384 + 0.395691i \(0.870505\pi\)
\(578\) 0 0
\(579\) 70.4482 122.020i 0.121672 0.210743i
\(580\) 0 0
\(581\) 191.674 52.0387i 0.329904 0.0895675i
\(582\) 0 0
\(583\) 51.0963 + 29.5005i 0.0876437 + 0.0506011i
\(584\) 0 0
\(585\) 263.217 + 455.905i 0.449944 + 0.779325i
\(586\) 0 0
\(587\) 921.405 1.56968 0.784842 0.619696i \(-0.212744\pi\)
0.784842 + 0.619696i \(0.212744\pi\)
\(588\) 0 0
\(589\) 68.2517i 0.115877i
\(590\) 0 0
\(591\) 305.709 176.501i 0.517274 0.298648i
\(592\) 0 0
\(593\) −48.1873 + 83.4628i −0.0812602 + 0.140747i −0.903791 0.427973i \(-0.859228\pi\)
0.822531 + 0.568720i \(0.192561\pi\)
\(594\) 0 0
\(595\) 108.989 + 401.437i 0.183174 + 0.674684i
\(596\) 0 0
\(597\) 354.434 + 204.632i 0.593692 + 0.342768i
\(598\) 0 0
\(599\) −144.711 + 83.5489i −0.241587 + 0.139481i −0.615906 0.787820i \(-0.711210\pi\)
0.374319 + 0.927300i \(0.377877\pi\)
\(600\) 0 0
\(601\) 88.4635 0.147194 0.0735969 0.997288i \(-0.476552\pi\)
0.0735969 + 0.997288i \(0.476552\pi\)
\(602\) 0 0
\(603\) −497.494 −0.825032
\(604\) 0 0
\(605\) 127.412 73.5614i 0.210598 0.121589i
\(606\) 0 0
\(607\) 48.1243 + 27.7846i 0.0792822 + 0.0457736i 0.539117 0.842231i \(-0.318758\pi\)
−0.459835 + 0.888004i \(0.652091\pi\)
\(608\) 0 0
\(609\) 185.212 186.441i 0.304125 0.306142i
\(610\) 0 0
\(611\) −186.829 + 323.597i −0.305775 + 0.529618i
\(612\) 0 0
\(613\) −752.678 + 434.559i −1.22786 + 0.708905i −0.966582 0.256359i \(-0.917477\pi\)
−0.261278 + 0.965264i \(0.584144\pi\)
\(614\) 0 0
\(615\) 454.995i 0.739829i
\(616\) 0 0
\(617\) −249.359 −0.404147 −0.202074 0.979370i \(-0.564768\pi\)
−0.202074 + 0.979370i \(0.564768\pi\)
\(618\) 0 0
\(619\) −248.837 430.998i −0.401998 0.696280i 0.591969 0.805961i \(-0.298351\pi\)
−0.993967 + 0.109680i \(0.965017\pi\)
\(620\) 0 0
\(621\) −661.671 382.016i −1.06549 0.615162i
\(622\) 0 0
\(623\) −281.679 + 1065.32i −0.452133 + 1.70998i
\(624\) 0 0
\(625\) 251.243 435.165i 0.401988 0.696264i
\(626\) 0 0
\(627\) 30.8745 + 53.4762i 0.0492416 + 0.0852890i
\(628\) 0 0
\(629\) 179.527i 0.285417i
\(630\) 0 0
\(631\) 172.763i 0.273792i −0.990585 0.136896i \(-0.956287\pi\)
0.990585 0.136896i \(-0.0437126\pi\)
\(632\) 0 0
\(633\) −158.079 273.801i −0.249730 0.432545i
\(634\) 0 0
\(635\) −508.210 + 880.245i −0.800330 + 1.38621i
\(636\) 0 0
\(637\) −455.312 776.717i −0.714776 1.21934i
\(638\) 0 0
\(639\) 70.6937 + 40.8150i 0.110632 + 0.0638732i
\(640\) 0 0
\(641\) 213.949 + 370.570i 0.333774 + 0.578113i 0.983248 0.182270i \(-0.0583446\pi\)
−0.649475 + 0.760383i \(0.725011\pi\)
\(642\) 0 0
\(643\) 15.9463 0.0247998 0.0123999 0.999923i \(-0.496053\pi\)
0.0123999 + 0.999923i \(0.496053\pi\)
\(644\) 0 0
\(645\) 293.431i 0.454932i
\(646\) 0 0
\(647\) 450.510 260.102i 0.696306 0.402012i −0.109664 0.993969i \(-0.534978\pi\)
0.805970 + 0.591956i \(0.201644\pi\)
\(648\) 0 0
\(649\) 72.6542 125.841i 0.111948 0.193899i
\(650\) 0 0
\(651\) −251.733 66.5603i −0.386686 0.102243i
\(652\) 0 0
\(653\) 367.687 + 212.284i 0.563074 + 0.325091i 0.754378 0.656440i \(-0.227939\pi\)
−0.191305 + 0.981531i \(0.561272\pi\)
\(654\) 0 0
\(655\) −936.371 + 540.614i −1.42957 + 0.825365i
\(656\) 0 0
\(657\) 619.246 0.942535
\(658\) 0 0
\(659\) −304.044 −0.461372 −0.230686 0.973028i \(-0.574097\pi\)
−0.230686 + 0.973028i \(0.574097\pi\)
\(660\) 0 0
\(661\) −155.112 + 89.5542i −0.234663 + 0.135483i −0.612722 0.790299i \(-0.709925\pi\)
0.378058 + 0.925782i \(0.376592\pi\)
\(662\) 0 0
\(663\) 341.815 + 197.347i 0.515559 + 0.297658i
\(664\) 0 0
\(665\) −68.0727 + 68.5243i −0.102365 + 0.103044i
\(666\) 0 0
\(667\) 345.237 597.968i 0.517597 0.896504i
\(668\) 0 0
\(669\) −58.8671 + 33.9870i −0.0879927 + 0.0508026i
\(670\) 0 0
\(671\) 1348.20i 2.00923i
\(672\) 0 0
\(673\) 544.352 0.808844 0.404422 0.914573i \(-0.367473\pi\)
0.404422 + 0.914573i \(0.367473\pi\)
\(674\) 0 0
\(675\) −52.8639 91.5629i −0.0783168 0.135649i
\(676\) 0 0
\(677\) 471.416 + 272.172i 0.696330 + 0.402027i 0.805979 0.591944i \(-0.201639\pi\)
−0.109649 + 0.993970i \(0.534973\pi\)
\(678\) 0 0
\(679\) 267.634 72.6616i 0.394159 0.107013i
\(680\) 0 0
\(681\) −58.0730 + 100.585i −0.0852760 + 0.147702i
\(682\) 0 0
\(683\) 443.494 + 768.154i 0.649332 + 1.12468i 0.983283 + 0.182086i \(0.0582848\pi\)
−0.333951 + 0.942591i \(0.608382\pi\)
\(684\) 0 0
\(685\) 44.0730i 0.0643401i
\(686\) 0 0
\(687\) 155.841i 0.226842i
\(688\) 0 0
\(689\) 43.7852 + 75.8382i 0.0635489 + 0.110070i
\(690\) 0 0
\(691\) 589.242 1020.60i 0.852738 1.47698i −0.0259906 0.999662i \(-0.508274\pi\)
0.878728 0.477323i \(-0.158393\pi\)
\(692\) 0 0
\(693\) 525.326 142.624i 0.758046 0.205807i
\(694\) 0 0
\(695\) −249.098 143.817i −0.358414 0.206930i
\(696\) 0 0
\(697\) −394.127 682.648i −0.565462 0.979409i
\(698\) 0 0
\(699\) 224.706 0.321468
\(700\) 0 0
\(701\) 901.601i 1.28616i −0.765797 0.643082i \(-0.777655\pi\)
0.765797 0.643082i \(-0.222345\pi\)
\(702\) 0 0
\(703\) 36.1018 20.8434i 0.0513539 0.0296492i
\(704\) 0 0
\(705\) −76.4661 + 132.443i −0.108463 + 0.187863i
\(706\) 0 0
\(707\) 215.184 216.612i 0.304363 0.306382i
\(708\) 0 0
\(709\) 288.215 + 166.401i 0.406510 + 0.234698i 0.689289 0.724487i \(-0.257923\pi\)
−0.282779 + 0.959185i \(0.591256\pi\)
\(710\) 0 0
\(711\) 713.858 412.146i 1.00402 0.579671i
\(712\) 0 0
\(713\) −684.126 −0.959504
\(714\) 0 0
\(715\) 1037.50 1.45104
\(716\) 0 0
\(717\) −247.352 + 142.809i −0.344982 + 0.199176i
\(718\) 0 0
\(719\) −1026.20 592.475i −1.42726 0.824027i −0.430353 0.902661i \(-0.641611\pi\)
−0.996904 + 0.0786341i \(0.974944\pi\)
\(720\) 0 0
\(721\) −425.685 112.555i −0.590410 0.156109i
\(722\) 0 0
\(723\) −271.160 + 469.663i −0.375049 + 0.649603i
\(724\) 0 0
\(725\) 82.7477 47.7744i 0.114135 0.0658957i
\(726\) 0 0
\(727\) 19.9398i 0.0274275i 0.999906 + 0.0137138i \(0.00436536\pi\)
−0.999906 + 0.0137138i \(0.995635\pi\)
\(728\) 0 0
\(729\) 279.711 0.383691
\(730\) 0 0
\(731\) −254.177 440.247i −0.347711 0.602254i
\(732\) 0 0
\(733\) −898.325 518.648i −1.22555 0.707569i −0.259450 0.965756i \(-0.583541\pi\)
−0.966095 + 0.258188i \(0.916875\pi\)
\(734\) 0 0
\(735\) −186.352 317.899i −0.253541 0.432515i
\(736\) 0 0
\(737\) −490.231 + 849.105i −0.665171 + 1.15211i
\(738\) 0 0
\(739\) −209.986 363.706i −0.284148 0.492160i 0.688254 0.725470i \(-0.258378\pi\)
−0.972402 + 0.233310i \(0.925044\pi\)
\(740\) 0 0
\(741\) 91.6491i 0.123683i
\(742\) 0 0
\(743\) 1241.67i 1.67116i −0.549370 0.835579i \(-0.685132\pi\)
0.549370 0.835579i \(-0.314868\pi\)
\(744\) 0 0
\(745\) 615.551 + 1066.17i 0.826243 + 1.43109i
\(746\) 0 0
\(747\) −89.1137 + 154.349i −0.119295 + 0.206626i
\(748\) 0 0
\(749\) −79.1379 + 299.301i −0.105658 + 0.399601i
\(750\) 0 0
\(751\) −561.008 323.898i −0.747015 0.431289i 0.0775992 0.996985i \(-0.475275\pi\)
−0.824614 + 0.565695i \(0.808608\pi\)
\(752\) 0 0
\(753\) −132.112 228.825i −0.175448 0.303885i
\(754\) 0 0
\(755\) −493.411 −0.653524
\(756\) 0 0
\(757\) 105.310i 0.139116i 0.997578 + 0.0695578i \(0.0221588\pi\)
−0.997578 + 0.0695578i \(0.977841\pi\)
\(758\) 0 0
\(759\) −536.023 + 309.473i −0.706223 + 0.407738i
\(760\) 0 0
\(761\) 210.942 365.362i 0.277190 0.480108i −0.693495 0.720461i \(-0.743930\pi\)
0.970685 + 0.240354i \(0.0772634\pi\)
\(762\) 0 0
\(763\) 43.4885 43.7770i 0.0569967 0.0573749i
\(764\) 0 0
\(765\) −323.266 186.638i −0.422570 0.243971i
\(766\) 0 0
\(767\) 186.775 107.835i 0.243514 0.140593i
\(768\) 0 0
\(769\) −189.767 −0.246772 −0.123386 0.992359i \(-0.539375\pi\)
−0.123386 + 0.992359i \(0.539375\pi\)
\(770\) 0 0
\(771\) −239.801 −0.311025
\(772\) 0 0
\(773\) −729.875 + 421.394i −0.944211 + 0.545141i −0.891278 0.453457i \(-0.850190\pi\)
−0.0529334 + 0.998598i \(0.516857\pi\)
\(774\) 0 0
\(775\) −81.9870 47.3352i −0.105790 0.0610777i
\(776\) 0 0
\(777\) 41.6695 + 153.481i 0.0536287 + 0.197530i
\(778\) 0 0
\(779\) 91.5174 158.513i 0.117481 0.203482i
\(780\) 0 0
\(781\) 139.323 80.4382i 0.178391 0.102994i
\(782\) 0 0
\(783\) 573.712i 0.732710i
\(784\) 0 0
\(785\) −540.181 −0.688128
\(786\) 0 0
\(787\) 747.098 + 1294.01i 0.949298 + 1.64423i 0.746907 + 0.664928i \(0.231538\pi\)
0.202391 + 0.979305i \(0.435129\pi\)
\(788\) 0 0
\(789\) −289.553 167.173i −0.366987 0.211880i
\(790\) 0 0
\(791\) 820.164 222.671i 1.03687 0.281506i
\(792\) 0 0
\(793\) 1000.51 1732.93i 1.26168 2.18529i </