Properties

Label 912.3.be.f.673.2
Level $912$
Weight $3$
Character 912.673
Analytic conductor $24.850$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 912.be (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.8502001097\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{6})\)
Coefficient field: 6.0.92607408.1
Defining polynomial: \(x^{6} - 3 x^{5} + 20 x^{4} - 35 x^{3} + 94 x^{2} - 77 x + 43\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 57)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 673.2
Root \(0.500000 + 2.69511i\) of defining polynomial
Character \(\chi\) \(=\) 912.673
Dual form 912.3.be.f.145.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 + 0.866025i) q^{3} +(2.32722 - 4.03087i) q^{5} +10.6817 q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(1.50000 + 0.866025i) q^{3} +(2.32722 - 4.03087i) q^{5} +10.6817 q^{7} +(1.50000 + 2.59808i) q^{9} +6.37280 q^{11} +(15.3770 - 8.87792i) q^{13} +(6.98167 - 4.03087i) q^{15} +(-5.84976 + 10.1321i) q^{17} +(3.88643 + 18.5983i) q^{19} +(16.0225 + 9.25062i) q^{21} +(-13.9817 - 24.2170i) q^{23} +(1.66807 + 2.88918i) q^{25} +5.19615i q^{27} +(-33.2498 + 19.1968i) q^{29} -42.9440i q^{31} +(9.55920 + 5.51901i) q^{33} +(24.8587 - 43.0565i) q^{35} -33.9790i q^{37} +30.7540 q^{39} +(16.3728 + 9.45284i) q^{41} +(-26.5089 + 45.9148i) q^{43} +13.9633 q^{45} +(12.0272 + 20.8318i) q^{47} +65.0986 q^{49} +(-17.5493 + 10.1321i) q^{51} +(-13.3224 + 7.69168i) q^{53} +(14.8309 - 25.6879i) q^{55} +(-10.2769 + 31.2632i) q^{57} +(-25.6539 - 14.8113i) q^{59} +(-21.3403 - 36.9626i) q^{61} +(16.0225 + 27.7519i) q^{63} -82.6436i q^{65} +(15.1585 - 8.75178i) q^{67} -48.4339i q^{69} +(74.6028 + 43.0719i) q^{71} +(46.2352 - 80.0817i) q^{73} +5.77836i q^{75} +68.0723 q^{77} +(26.3908 + 15.2367i) q^{79} +(-4.50000 + 7.79423i) q^{81} -77.1154 q^{83} +(27.2274 + 47.1592i) q^{85} -66.4996 q^{87} +(-76.8129 + 44.3479i) q^{89} +(164.253 - 94.8312i) q^{91} +(37.1906 - 64.4160i) q^{93} +(84.0118 + 27.6166i) q^{95} +(-1.82351 - 1.05281i) q^{97} +(9.55920 + 16.5570i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 9 q^{3} + 4 q^{5} + 22 q^{7} + 9 q^{9} + O(q^{10}) \) \( 6 q + 9 q^{3} + 4 q^{5} + 22 q^{7} + 9 q^{9} + 36 q^{11} - 3 q^{13} + 12 q^{15} + 38 q^{17} + 10 q^{19} + 33 q^{21} - 54 q^{23} - 21 q^{25} - 102 q^{29} + 54 q^{33} + 24 q^{35} - 6 q^{39} + 96 q^{41} - 107 q^{43} + 24 q^{45} + 50 q^{47} - 48 q^{49} + 114 q^{51} - 90 q^{53} - 148 q^{55} - 3 q^{57} + 27 q^{61} + 33 q^{63} + 39 q^{67} - 84 q^{71} - 77 q^{73} + 260 q^{77} - 9 q^{79} - 27 q^{81} + 348 q^{83} + 68 q^{85} - 204 q^{87} - 72 q^{89} + 393 q^{91} + 129 q^{93} - 104 q^{95} - 228 q^{97} + 54 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\) \(1\)

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
\(3\) 1.50000 + 0.866025i 0.500000 + 0.288675i
\(4\) 0 0
\(5\) 2.32722 4.03087i 0.465445 0.806174i −0.533777 0.845625i \(-0.679228\pi\)
0.999221 + 0.0394517i \(0.0125611\pi\)
\(6\) 0 0
\(7\) 10.6817 1.52596 0.762978 0.646424i \(-0.223736\pi\)
0.762978 + 0.646424i \(0.223736\pi\)
\(8\) 0 0
\(9\) 1.50000 + 2.59808i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 6.37280 0.579346 0.289673 0.957126i \(-0.406453\pi\)
0.289673 + 0.957126i \(0.406453\pi\)
\(12\) 0 0
\(13\) 15.3770 8.87792i 1.18285 0.682917i 0.226176 0.974087i \(-0.427378\pi\)
0.956671 + 0.291170i \(0.0940444\pi\)
\(14\) 0 0
\(15\) 6.98167 4.03087i 0.465445 0.268725i
\(16\) 0 0
\(17\) −5.84976 + 10.1321i −0.344104 + 0.596005i −0.985191 0.171463i \(-0.945151\pi\)
0.641087 + 0.767468i \(0.278484\pi\)
\(18\) 0 0
\(19\) 3.88643 + 18.5983i 0.204549 + 0.978856i
\(20\) 0 0
\(21\) 16.0225 + 9.25062i 0.762978 + 0.440506i
\(22\) 0 0
\(23\) −13.9817 24.2170i −0.607899 1.05291i −0.991586 0.129448i \(-0.958679\pi\)
0.383688 0.923463i \(-0.374654\pi\)
\(24\) 0 0
\(25\) 1.66807 + 2.88918i 0.0667228 + 0.115567i
\(26\) 0 0
\(27\) 5.19615i 0.192450i
\(28\) 0 0
\(29\) −33.2498 + 19.1968i −1.14655 + 0.661958i −0.948043 0.318142i \(-0.896941\pi\)
−0.198502 + 0.980100i \(0.563608\pi\)
\(30\) 0 0
\(31\) 42.9440i 1.38529i −0.721278 0.692645i \(-0.756445\pi\)
0.721278 0.692645i \(-0.243555\pi\)
\(32\) 0 0
\(33\) 9.55920 + 5.51901i 0.289673 + 0.167243i
\(34\) 0 0
\(35\) 24.8587 43.0565i 0.710248 1.23019i
\(36\) 0 0
\(37\) 33.9790i 0.918351i −0.888346 0.459176i \(-0.848145\pi\)
0.888346 0.459176i \(-0.151855\pi\)
\(38\) 0 0
\(39\) 30.7540 0.788565
\(40\) 0 0
\(41\) 16.3728 + 9.45284i 0.399337 + 0.230557i 0.686198 0.727415i \(-0.259278\pi\)
−0.286861 + 0.957972i \(0.592612\pi\)
\(42\) 0 0
\(43\) −26.5089 + 45.9148i −0.616486 + 1.06779i 0.373635 + 0.927576i \(0.378111\pi\)
−0.990122 + 0.140210i \(0.955222\pi\)
\(44\) 0 0
\(45\) 13.9633 0.310296
\(46\) 0 0
\(47\) 12.0272 + 20.8318i 0.255899 + 0.443230i 0.965139 0.261737i \(-0.0842952\pi\)
−0.709240 + 0.704967i \(0.750962\pi\)
\(48\) 0 0
\(49\) 65.0986 1.32854
\(50\) 0 0
\(51\) −17.5493 + 10.1321i −0.344104 + 0.198668i
\(52\) 0 0
\(53\) −13.3224 + 7.69168i −0.251366 + 0.145126i −0.620389 0.784294i \(-0.713025\pi\)
0.369024 + 0.929420i \(0.379692\pi\)
\(54\) 0 0
\(55\) 14.8309 25.6879i 0.269653 0.467053i
\(56\) 0 0
\(57\) −10.2769 + 31.2632i −0.180297 + 0.548476i
\(58\) 0 0
\(59\) −25.6539 14.8113i −0.434813 0.251039i 0.266582 0.963812i \(-0.414106\pi\)
−0.701395 + 0.712773i \(0.747439\pi\)
\(60\) 0 0
\(61\) −21.3403 36.9626i −0.349842 0.605944i 0.636379 0.771376i \(-0.280431\pi\)
−0.986221 + 0.165433i \(0.947098\pi\)
\(62\) 0 0
\(63\) 16.0225 + 27.7519i 0.254326 + 0.440506i
\(64\) 0 0
\(65\) 82.6436i 1.27144i
\(66\) 0 0
\(67\) 15.1585 8.75178i 0.226247 0.130624i −0.382593 0.923917i \(-0.624969\pi\)
0.608839 + 0.793294i \(0.291635\pi\)
\(68\) 0 0
\(69\) 48.4339i 0.701941i
\(70\) 0 0
\(71\) 74.6028 + 43.0719i 1.05074 + 0.606647i 0.922857 0.385142i \(-0.125847\pi\)
0.127886 + 0.991789i \(0.459181\pi\)
\(72\) 0 0
\(73\) 46.2352 80.0817i 0.633359 1.09701i −0.353502 0.935434i \(-0.615009\pi\)
0.986860 0.161576i \(-0.0516576\pi\)
\(74\) 0 0
\(75\) 5.77836i 0.0770448i
\(76\) 0 0
\(77\) 68.0723 0.884056
\(78\) 0 0
\(79\) 26.3908 + 15.2367i 0.334060 + 0.192870i 0.657642 0.753330i \(-0.271554\pi\)
−0.323582 + 0.946200i \(0.604887\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −77.1154 −0.929101 −0.464551 0.885547i \(-0.653784\pi\)
−0.464551 + 0.885547i \(0.653784\pi\)
\(84\) 0 0
\(85\) 27.2274 + 47.1592i 0.320322 + 0.554815i
\(86\) 0 0
\(87\) −66.4996 −0.764364
\(88\) 0 0
\(89\) −76.8129 + 44.3479i −0.863066 + 0.498291i −0.865038 0.501707i \(-0.832706\pi\)
0.00197195 + 0.999998i \(0.499372\pi\)
\(90\) 0 0
\(91\) 164.253 94.8312i 1.80497 1.04210i
\(92\) 0 0
\(93\) 37.1906 64.4160i 0.399899 0.692645i
\(94\) 0 0
\(95\) 84.0118 + 27.6166i 0.884334 + 0.290702i
\(96\) 0 0
\(97\) −1.82351 1.05281i −0.0187991 0.0108537i 0.490571 0.871401i \(-0.336788\pi\)
−0.509370 + 0.860548i \(0.670122\pi\)
\(98\) 0 0
\(99\) 9.55920 + 16.5570i 0.0965576 + 0.167243i
\(100\) 0 0
\(101\) −13.7690 23.8486i −0.136327 0.236125i 0.789777 0.613395i \(-0.210196\pi\)
−0.926104 + 0.377269i \(0.876863\pi\)
\(102\) 0 0
\(103\) 102.351i 0.993696i 0.867837 + 0.496848i \(0.165509\pi\)
−0.867837 + 0.496848i \(0.834491\pi\)
\(104\) 0 0
\(105\) 74.5760 43.0565i 0.710248 0.410062i
\(106\) 0 0
\(107\) 0.549592i 0.00513638i 0.999997 + 0.00256819i \(0.000817481\pi\)
−0.999997 + 0.00256819i \(0.999183\pi\)
\(108\) 0 0
\(109\) 80.7219 + 46.6048i 0.740568 + 0.427567i 0.822276 0.569089i \(-0.192704\pi\)
−0.0817076 + 0.996656i \(0.526037\pi\)
\(110\) 0 0
\(111\) 29.4267 50.9685i 0.265105 0.459176i
\(112\) 0 0
\(113\) 55.4186i 0.490430i 0.969469 + 0.245215i \(0.0788586\pi\)
−0.969469 + 0.245215i \(0.921141\pi\)
\(114\) 0 0
\(115\) −130.154 −1.13177
\(116\) 0 0
\(117\) 46.1310 + 26.6338i 0.394282 + 0.227639i
\(118\) 0 0
\(119\) −62.4854 + 108.228i −0.525087 + 0.909478i
\(120\) 0 0
\(121\) −80.3874 −0.664359
\(122\) 0 0
\(123\) 16.3728 + 28.3585i 0.133112 + 0.230557i
\(124\) 0 0
\(125\) 131.889 1.05511
\(126\) 0 0
\(127\) 82.7181 47.7573i 0.651324 0.376042i −0.137640 0.990482i \(-0.543952\pi\)
0.788963 + 0.614441i \(0.210618\pi\)
\(128\) 0 0
\(129\) −79.5267 + 45.9148i −0.616486 + 0.355929i
\(130\) 0 0
\(131\) 84.0762 145.624i 0.641803 1.11164i −0.343227 0.939252i \(-0.611520\pi\)
0.985030 0.172383i \(-0.0551466\pi\)
\(132\) 0 0
\(133\) 41.5136 + 198.661i 0.312133 + 1.49369i
\(134\) 0 0
\(135\) 20.9450 + 12.0926i 0.155148 + 0.0895748i
\(136\) 0 0
\(137\) 59.3774 + 102.845i 0.433412 + 0.750691i 0.997165 0.0752526i \(-0.0239763\pi\)
−0.563753 + 0.825943i \(0.690643\pi\)
\(138\) 0 0
\(139\) 55.1822 + 95.5784i 0.396994 + 0.687614i 0.993354 0.115104i \(-0.0367200\pi\)
−0.596359 + 0.802718i \(0.703387\pi\)
\(140\) 0 0
\(141\) 41.6636i 0.295487i
\(142\) 0 0
\(143\) 97.9947 56.5772i 0.685277 0.395645i
\(144\) 0 0
\(145\) 178.701i 1.23242i
\(146\) 0 0
\(147\) 97.6479 + 56.3770i 0.664271 + 0.383517i
\(148\) 0 0
\(149\) 28.8719 50.0077i 0.193771 0.335622i −0.752726 0.658334i \(-0.771261\pi\)
0.946497 + 0.322712i \(0.104595\pi\)
\(150\) 0 0
\(151\) 205.459i 1.36066i −0.732908 0.680328i \(-0.761837\pi\)
0.732908 0.680328i \(-0.238163\pi\)
\(152\) 0 0
\(153\) −35.0986 −0.229402
\(154\) 0 0
\(155\) −173.102 99.9403i −1.11678 0.644776i
\(156\) 0 0
\(157\) −55.6080 + 96.3159i −0.354191 + 0.613477i −0.986979 0.160848i \(-0.948577\pi\)
0.632788 + 0.774325i \(0.281910\pi\)
\(158\) 0 0
\(159\) −26.6448 −0.167577
\(160\) 0 0
\(161\) −149.348 258.678i −0.927627 1.60670i
\(162\) 0 0
\(163\) −69.1905 −0.424481 −0.212241 0.977217i \(-0.568076\pi\)
−0.212241 + 0.977217i \(0.568076\pi\)
\(164\) 0 0
\(165\) 44.4928 25.6879i 0.269653 0.155684i
\(166\) 0 0
\(167\) −181.817 + 104.972i −1.08873 + 0.628577i −0.933237 0.359261i \(-0.883029\pi\)
−0.155490 + 0.987837i \(0.549696\pi\)
\(168\) 0 0
\(169\) 73.1350 126.674i 0.432751 0.749547i
\(170\) 0 0
\(171\) −42.4901 + 37.9946i −0.248480 + 0.222191i
\(172\) 0 0
\(173\) −264.781 152.871i −1.53053 0.883649i −0.999337 0.0363949i \(-0.988413\pi\)
−0.531188 0.847254i \(-0.678254\pi\)
\(174\) 0 0
\(175\) 17.8178 + 30.8613i 0.101816 + 0.176351i
\(176\) 0 0
\(177\) −25.6539 44.4339i −0.144938 0.251039i
\(178\) 0 0
\(179\) 303.001i 1.69274i −0.532593 0.846371i \(-0.678782\pi\)
0.532593 0.846371i \(-0.321218\pi\)
\(180\) 0 0
\(181\) −62.8763 + 36.3016i −0.347383 + 0.200561i −0.663532 0.748148i \(-0.730943\pi\)
0.316149 + 0.948709i \(0.397610\pi\)
\(182\) 0 0
\(183\) 73.9251i 0.403962i
\(184\) 0 0
\(185\) −136.965 79.0767i −0.740350 0.427442i
\(186\) 0 0
\(187\) −37.2794 + 64.5698i −0.199355 + 0.345293i
\(188\) 0 0
\(189\) 55.5037i 0.293670i
\(190\) 0 0
\(191\) 48.5734 0.254311 0.127156 0.991883i \(-0.459415\pi\)
0.127156 + 0.991883i \(0.459415\pi\)
\(192\) 0 0
\(193\) 9.48401 + 5.47559i 0.0491399 + 0.0283710i 0.524369 0.851491i \(-0.324301\pi\)
−0.475229 + 0.879862i \(0.657635\pi\)
\(194\) 0 0
\(195\) 71.5715 123.965i 0.367033 0.635720i
\(196\) 0 0
\(197\) 104.442 0.530163 0.265082 0.964226i \(-0.414601\pi\)
0.265082 + 0.964226i \(0.414601\pi\)
\(198\) 0 0
\(199\) 140.643 + 243.602i 0.706751 + 1.22413i 0.966056 + 0.258333i \(0.0831731\pi\)
−0.259305 + 0.965795i \(0.583494\pi\)
\(200\) 0 0
\(201\) 30.3171 0.150831
\(202\) 0 0
\(203\) −355.164 + 205.054i −1.74958 + 1.01012i
\(204\) 0 0
\(205\) 76.2063 43.9977i 0.371738 0.214623i
\(206\) 0 0
\(207\) 41.9450 72.6509i 0.202633 0.350970i
\(208\) 0 0
\(209\) 24.7674 + 118.523i 0.118504 + 0.567096i
\(210\) 0 0
\(211\) −89.2808 51.5463i −0.423132 0.244295i 0.273285 0.961933i \(-0.411890\pi\)
−0.696416 + 0.717638i \(0.745223\pi\)
\(212\) 0 0
\(213\) 74.6028 + 129.216i 0.350248 + 0.606647i
\(214\) 0 0
\(215\) 123.384 + 213.708i 0.573880 + 0.993990i
\(216\) 0 0
\(217\) 458.715i 2.11389i
\(218\) 0 0
\(219\) 138.706 80.0817i 0.633359 0.365670i
\(220\) 0 0
\(221\) 207.735i 0.939977i
\(222\) 0 0
\(223\) 68.9560 + 39.8118i 0.309220 + 0.178528i 0.646577 0.762848i \(-0.276200\pi\)
−0.337357 + 0.941377i \(0.609533\pi\)
\(224\) 0 0
\(225\) −5.00421 + 8.66754i −0.0222409 + 0.0385224i
\(226\) 0 0
\(227\) 131.031i 0.577228i −0.957446 0.288614i \(-0.906806\pi\)
0.957446 0.288614i \(-0.0931944\pi\)
\(228\) 0 0
\(229\) 30.3537 0.132549 0.0662745 0.997801i \(-0.478889\pi\)
0.0662745 + 0.997801i \(0.478889\pi\)
\(230\) 0 0
\(231\) 102.108 + 58.9524i 0.442028 + 0.255205i
\(232\) 0 0
\(233\) −47.0484 + 81.4902i −0.201924 + 0.349743i −0.949148 0.314829i \(-0.898053\pi\)
0.747224 + 0.664572i \(0.231386\pi\)
\(234\) 0 0
\(235\) 111.960 0.476427
\(236\) 0 0
\(237\) 26.3908 + 45.7101i 0.111353 + 0.192870i
\(238\) 0 0
\(239\) −375.297 −1.57028 −0.785141 0.619317i \(-0.787409\pi\)
−0.785141 + 0.619317i \(0.787409\pi\)
\(240\) 0 0
\(241\) 0.482424 0.278528i 0.00200176 0.00115572i −0.498999 0.866603i \(-0.666299\pi\)
0.501001 + 0.865447i \(0.332965\pi\)
\(242\) 0 0
\(243\) −13.5000 + 7.79423i −0.0555556 + 0.0320750i
\(244\) 0 0
\(245\) 151.499 262.404i 0.618363 1.07104i
\(246\) 0 0
\(247\) 224.876 + 251.482i 0.910428 + 1.01815i
\(248\) 0 0
\(249\) −115.673 66.7839i −0.464551 0.268208i
\(250\) 0 0
\(251\) −117.309 203.185i −0.467367 0.809504i 0.531938 0.846783i \(-0.321464\pi\)
−0.999305 + 0.0372799i \(0.988131\pi\)
\(252\) 0 0
\(253\) −89.1024 154.330i −0.352183 0.610000i
\(254\) 0 0
\(255\) 94.3185i 0.369876i
\(256\) 0 0
\(257\) −11.0702 + 6.39141i −0.0430749 + 0.0248693i −0.521383 0.853323i \(-0.674584\pi\)
0.478308 + 0.878192i \(0.341250\pi\)
\(258\) 0 0
\(259\) 362.953i 1.40136i
\(260\) 0 0
\(261\) −99.7494 57.5904i −0.382182 0.220653i
\(262\) 0 0
\(263\) −106.457 + 184.389i −0.404780 + 0.701099i −0.994296 0.106657i \(-0.965985\pi\)
0.589516 + 0.807757i \(0.299319\pi\)
\(264\) 0 0
\(265\) 71.6010i 0.270193i
\(266\) 0 0
\(267\) −153.626 −0.575377
\(268\) 0 0
\(269\) −438.717 253.293i −1.63092 0.941610i −0.983811 0.179211i \(-0.942646\pi\)
−0.647106 0.762400i \(-0.724021\pi\)
\(270\) 0 0
\(271\) −110.063 + 190.635i −0.406136 + 0.703449i −0.994453 0.105182i \(-0.966457\pi\)
0.588317 + 0.808631i \(0.299791\pi\)
\(272\) 0 0
\(273\) 328.505 1.20332
\(274\) 0 0
\(275\) 10.6303 + 18.4122i 0.0386556 + 0.0669534i
\(276\) 0 0
\(277\) 262.083 0.946148 0.473074 0.881023i \(-0.343144\pi\)
0.473074 + 0.881023i \(0.343144\pi\)
\(278\) 0 0
\(279\) 111.572 64.4160i 0.399899 0.230882i
\(280\) 0 0
\(281\) −346.203 + 199.880i −1.23204 + 0.711317i −0.967454 0.253046i \(-0.918568\pi\)
−0.264583 + 0.964363i \(0.585234\pi\)
\(282\) 0 0
\(283\) −41.2358 + 71.4225i −0.145710 + 0.252376i −0.929637 0.368475i \(-0.879880\pi\)
0.783928 + 0.620852i \(0.213213\pi\)
\(284\) 0 0
\(285\) 102.101 + 114.181i 0.358249 + 0.400636i
\(286\) 0 0
\(287\) 174.889 + 100.972i 0.609370 + 0.351820i
\(288\) 0 0
\(289\) 76.0605 + 131.741i 0.263185 + 0.455850i
\(290\) 0 0
\(291\) −1.82351 3.15842i −0.00626637 0.0108537i
\(292\) 0 0
\(293\) 223.552i 0.762977i −0.924374 0.381489i \(-0.875412\pi\)
0.924374 0.381489i \(-0.124588\pi\)
\(294\) 0 0
\(295\) −119.405 + 68.9384i −0.404762 + 0.233690i
\(296\) 0 0
\(297\) 33.1141i 0.111495i
\(298\) 0 0
\(299\) −429.993 248.256i −1.43810 0.830289i
\(300\) 0 0
\(301\) −283.160 + 490.448i −0.940731 + 1.62939i
\(302\) 0 0
\(303\) 47.6973i 0.157417i
\(304\) 0 0
\(305\) −198.655 −0.651328
\(306\) 0 0
\(307\) −339.034 195.741i −1.10434 0.637594i −0.166986 0.985959i \(-0.553403\pi\)
−0.937359 + 0.348366i \(0.886737\pi\)
\(308\) 0 0
\(309\) −88.6383 + 153.526i −0.286855 + 0.496848i
\(310\) 0 0
\(311\) −375.828 −1.20845 −0.604224 0.796814i \(-0.706517\pi\)
−0.604224 + 0.796814i \(0.706517\pi\)
\(312\) 0 0
\(313\) 75.3935 + 130.585i 0.240874 + 0.417206i 0.960963 0.276675i \(-0.0892327\pi\)
−0.720090 + 0.693881i \(0.755899\pi\)
\(314\) 0 0
\(315\) 149.152 0.473499
\(316\) 0 0
\(317\) −438.163 + 252.973i −1.38222 + 0.798024i −0.992422 0.122878i \(-0.960788\pi\)
−0.389796 + 0.920901i \(0.627454\pi\)
\(318\) 0 0
\(319\) −211.895 + 122.337i −0.664246 + 0.383503i
\(320\) 0 0
\(321\) −0.475961 + 0.824389i −0.00148274 + 0.00256819i
\(322\) 0 0
\(323\) −211.174 69.4179i −0.653789 0.214916i
\(324\) 0 0
\(325\) 51.2998 + 29.6180i 0.157846 + 0.0911322i
\(326\) 0 0
\(327\) 80.7219 + 139.814i 0.246856 + 0.427567i
\(328\) 0 0
\(329\) 128.471 + 222.519i 0.390491 + 0.676349i
\(330\) 0 0
\(331\) 443.028i 1.33845i 0.743058 + 0.669227i \(0.233374\pi\)
−0.743058 + 0.669227i \(0.766626\pi\)
\(332\) 0 0
\(333\) 88.2800 50.9685i 0.265105 0.153059i
\(334\) 0 0
\(335\) 81.4694i 0.243192i
\(336\) 0 0
\(337\) 168.764 + 97.4357i 0.500782 + 0.289127i 0.729037 0.684475i \(-0.239968\pi\)
−0.228254 + 0.973602i \(0.573302\pi\)
\(338\) 0 0
\(339\) −47.9939 + 83.1279i −0.141575 + 0.245215i
\(340\) 0 0
\(341\) 273.674i 0.802562i
\(342\) 0 0
\(343\) 171.960 0.501341
\(344\) 0 0
\(345\) −195.231 112.717i −0.565886 0.326715i
\(346\) 0 0
\(347\) −262.446 + 454.570i −0.756329 + 1.31000i 0.188382 + 0.982096i \(0.439676\pi\)
−0.944711 + 0.327905i \(0.893658\pi\)
\(348\) 0 0
\(349\) −369.064 −1.05749 −0.528745 0.848781i \(-0.677337\pi\)
−0.528745 + 0.848781i \(0.677337\pi\)
\(350\) 0 0
\(351\) 46.1310 + 79.9013i 0.131427 + 0.227639i
\(352\) 0 0
\(353\) 323.725 0.917067 0.458533 0.888677i \(-0.348375\pi\)
0.458533 + 0.888677i \(0.348375\pi\)
\(354\) 0 0
\(355\) 347.235 200.476i 0.978126 0.564721i
\(356\) 0 0
\(357\) −187.456 + 108.228i −0.525087 + 0.303159i
\(358\) 0 0
\(359\) 6.25614 10.8359i 0.0174266 0.0301837i −0.857181 0.515016i \(-0.827786\pi\)
0.874607 + 0.484832i \(0.161119\pi\)
\(360\) 0 0
\(361\) −330.791 + 144.562i −0.916320 + 0.400448i
\(362\) 0 0
\(363\) −120.581 69.6175i −0.332179 0.191784i
\(364\) 0 0
\(365\) −215.199 372.736i −0.589587 1.02119i
\(366\) 0 0
\(367\) 44.3159 + 76.7574i 0.120752 + 0.209148i 0.920064 0.391767i \(-0.128136\pi\)
−0.799313 + 0.600916i \(0.794803\pi\)
\(368\) 0 0
\(369\) 56.7171i 0.153705i
\(370\) 0 0
\(371\) −142.306 + 82.1602i −0.383573 + 0.221456i
\(372\) 0 0
\(373\) 406.489i 1.08978i −0.838507 0.544892i \(-0.816571\pi\)
0.838507 0.544892i \(-0.183429\pi\)
\(374\) 0 0
\(375\) 197.834 + 114.219i 0.527556 + 0.304585i
\(376\) 0 0
\(377\) −340.855 + 590.378i −0.904125 + 1.56599i
\(378\) 0 0
\(379\) 433.800i 1.14459i −0.820047 0.572296i \(-0.806053\pi\)
0.820047 0.572296i \(-0.193947\pi\)
\(380\) 0 0
\(381\) 165.436 0.434216
\(382\) 0 0
\(383\) 355.819 + 205.432i 0.929031 + 0.536377i 0.886505 0.462719i \(-0.153126\pi\)
0.0425263 + 0.999095i \(0.486459\pi\)
\(384\) 0 0
\(385\) 158.419 274.391i 0.411479 0.712703i
\(386\) 0 0
\(387\) −159.053 −0.410991
\(388\) 0 0
\(389\) −94.6013 163.854i −0.243191 0.421219i 0.718430 0.695599i \(-0.244861\pi\)
−0.961621 + 0.274380i \(0.911528\pi\)
\(390\) 0 0
\(391\) 327.158 0.836721
\(392\) 0 0
\(393\) 252.228 145.624i 0.641803 0.370545i
\(394\) 0 0
\(395\) 122.834 70.9185i 0.310973 0.179540i
\(396\) 0 0
\(397\) −220.839 + 382.504i −0.556269 + 0.963487i 0.441534 + 0.897244i \(0.354434\pi\)
−0.997804 + 0.0662425i \(0.978899\pi\)
\(398\) 0 0
\(399\) −109.775 + 333.943i −0.275125 + 0.836951i
\(400\) 0 0
\(401\) 320.526 + 185.056i 0.799316 + 0.461485i 0.843232 0.537550i \(-0.180650\pi\)
−0.0439159 + 0.999035i \(0.513983\pi\)
\(402\) 0 0
\(403\) −381.254 660.351i −0.946039 1.63859i
\(404\) 0 0
\(405\) 20.9450 + 36.2778i 0.0517161 + 0.0895748i
\(406\) 0 0
\(407\) 216.541i 0.532043i
\(408\) 0 0
\(409\) 418.387 241.556i 1.02295 0.590602i 0.107995 0.994151i \(-0.465557\pi\)
0.914958 + 0.403550i \(0.132224\pi\)
\(410\) 0 0
\(411\) 205.689i 0.500461i
\(412\) 0 0
\(413\) −274.028 158.210i −0.663505 0.383075i
\(414\) 0 0
\(415\) −179.465 + 310.842i −0.432445 + 0.749017i
\(416\) 0 0
\(417\) 191.157i 0.458409i
\(418\) 0 0
\(419\) 295.264 0.704687 0.352344 0.935871i \(-0.385385\pi\)
0.352344 + 0.935871i \(0.385385\pi\)
\(420\) 0 0
\(421\) −449.581 259.566i −1.06789 0.616545i −0.140284 0.990111i \(-0.544802\pi\)
−0.927604 + 0.373566i \(0.878135\pi\)
\(422\) 0 0
\(423\) −36.0817 + 62.4954i −0.0852996 + 0.147743i
\(424\) 0 0
\(425\) −39.0312 −0.0918382
\(426\) 0 0
\(427\) −227.951 394.823i −0.533843 0.924644i
\(428\) 0 0
\(429\) 195.989 0.456852
\(430\) 0 0
\(431\) 195.895 113.100i 0.454514 0.262414i −0.255221 0.966883i \(-0.582148\pi\)
0.709735 + 0.704469i \(0.248815\pi\)
\(432\) 0 0
\(433\) −251.769 + 145.359i −0.581452 + 0.335702i −0.761710 0.647918i \(-0.775640\pi\)
0.180258 + 0.983619i \(0.442307\pi\)
\(434\) 0 0
\(435\) −154.759 + 268.051i −0.355769 + 0.616210i
\(436\) 0 0
\(437\) 396.055 354.152i 0.906304 0.810417i
\(438\) 0 0
\(439\) −251.921 145.447i −0.573852 0.331314i 0.184834 0.982770i \(-0.440825\pi\)
−0.758686 + 0.651456i \(0.774158\pi\)
\(440\) 0 0
\(441\) 97.6479 + 169.131i 0.221424 + 0.383517i
\(442\) 0 0
\(443\) 217.722 + 377.106i 0.491473 + 0.851256i 0.999952 0.00981853i \(-0.00312539\pi\)
−0.508479 + 0.861074i \(0.669792\pi\)
\(444\) 0 0
\(445\) 412.830i 0.927708i
\(446\) 0 0
\(447\) 86.6158 50.0077i 0.193771 0.111874i
\(448\) 0 0
\(449\) 263.736i 0.587385i 0.955900 + 0.293692i \(0.0948842\pi\)
−0.955900 + 0.293692i \(0.905116\pi\)
\(450\) 0 0
\(451\) 104.341 + 60.2411i 0.231354 + 0.133572i
\(452\) 0 0
\(453\) 177.933 308.189i 0.392788 0.680328i
\(454\) 0 0
\(455\) 882.774i 1.94016i
\(456\) 0 0
\(457\) 641.042 1.40272 0.701359 0.712809i \(-0.252577\pi\)
0.701359 + 0.712809i \(0.252577\pi\)
\(458\) 0 0
\(459\) −52.6479 30.3963i −0.114701 0.0662228i
\(460\) 0 0
\(461\) −323.490 + 560.302i −0.701714 + 1.21540i 0.266150 + 0.963932i \(0.414248\pi\)
−0.967864 + 0.251473i \(0.919085\pi\)
\(462\) 0 0
\(463\) 407.362 0.879831 0.439916 0.898039i \(-0.355008\pi\)
0.439916 + 0.898039i \(0.355008\pi\)
\(464\) 0 0
\(465\) −173.102 299.821i −0.372262 0.644776i
\(466\) 0 0
\(467\) −146.962 −0.314694 −0.157347 0.987543i \(-0.550294\pi\)
−0.157347 + 0.987543i \(0.550294\pi\)
\(468\) 0 0
\(469\) 161.919 93.4838i 0.345242 0.199326i
\(470\) 0 0
\(471\) −166.824 + 96.3159i −0.354191 + 0.204492i
\(472\) 0 0
\(473\) −168.936 + 292.606i −0.357159 + 0.618617i
\(474\) 0 0
\(475\) −47.2509 + 42.2518i −0.0994757 + 0.0889512i
\(476\) 0 0
\(477\) −39.9672 23.0751i −0.0837886 0.0483754i
\(478\) 0 0
\(479\) 309.698 + 536.413i 0.646552 + 1.11986i 0.983941 + 0.178495i \(0.0571230\pi\)
−0.337389 + 0.941365i \(0.609544\pi\)
\(480\) 0 0
\(481\) −301.663 522.495i −0.627158 1.08627i
\(482\) 0 0
\(483\) 517.356i 1.07113i
\(484\) 0 0
\(485\) −8.48745 + 4.90023i −0.0174999 + 0.0101036i
\(486\) 0 0
\(487\) 343.861i 0.706080i −0.935608 0.353040i \(-0.885148\pi\)
0.935608 0.353040i \(-0.114852\pi\)
\(488\) 0 0
\(489\) −103.786 59.9207i −0.212241 0.122537i
\(490\) 0 0
\(491\) 250.993 434.733i 0.511187 0.885402i −0.488729 0.872436i \(-0.662539\pi\)
0.999916 0.0129665i \(-0.00412747\pi\)
\(492\) 0 0
\(493\) 449.187i 0.911129i
\(494\) 0 0
\(495\) 88.9856 0.179769
\(496\) 0 0
\(497\) 796.884 + 460.081i 1.60339 + 0.925717i
\(498\) 0 0
\(499\) −453.717 + 785.861i −0.909253 + 1.57487i −0.0941479 + 0.995558i \(0.530013\pi\)
−0.815105 + 0.579314i \(0.803321\pi\)
\(500\) 0 0
\(501\) −363.635 −0.725818
\(502\) 0 0
\(503\) −183.800 318.352i −0.365408 0.632906i 0.623433 0.781877i \(-0.285737\pi\)
−0.988842 + 0.148971i \(0.952404\pi\)
\(504\) 0 0
\(505\) −128.174 −0.253810
\(506\) 0 0
\(507\) 219.405 126.674i 0.432751 0.249849i
\(508\) 0 0
\(509\) 406.585 234.742i 0.798791 0.461182i −0.0442573 0.999020i \(-0.514092\pi\)
0.843048 + 0.537838i \(0.180759\pi\)
\(510\) 0 0
\(511\) 493.870 855.408i 0.966478 1.67399i
\(512\) 0 0
\(513\) −96.6395 + 20.1945i −0.188381 + 0.0393654i
\(514\) 0 0
\(515\) 412.562 + 238.193i 0.801092 + 0.462511i
\(516\) 0 0
\(517\) 76.6473 + 132.757i 0.148254 + 0.256783i
\(518\) 0 0
\(519\) −264.781 458.614i −0.510175 0.883649i
\(520\) 0 0
\(521\) 691.695i 1.32763i −0.747897 0.663815i \(-0.768936\pi\)
0.747897 0.663815i \(-0.231064\pi\)
\(522\) 0 0
\(523\) 70.7545 40.8501i 0.135286 0.0781073i −0.430830 0.902433i \(-0.641779\pi\)
0.566115 + 0.824326i \(0.308446\pi\)
\(524\) 0 0
\(525\) 61.7227i 0.117567i
\(526\) 0 0
\(527\) 435.113 + 251.212i 0.825640 + 0.476684i
\(528\) 0 0
\(529\) −126.474 + 219.060i −0.239081 + 0.414101i
\(530\) 0 0
\(531\) 88.8679i 0.167359i
\(532\) 0 0
\(533\) 335.686 0.629806
\(534\) 0 0
\(535\) 2.21533 + 1.27902i 0.00414081 + 0.00239070i
\(536\) 0 0
\(537\) 262.406 454.501i 0.488653 0.846371i
\(538\) 0 0
\(539\) 414.860 0.769685
\(540\) 0 0
\(541\) 373.182 + 646.370i 0.689800 + 1.19477i 0.971902 + 0.235384i \(0.0756349\pi\)
−0.282102 + 0.959384i \(0.591032\pi\)
\(542\) 0 0
\(543\) −125.753 −0.231588
\(544\) 0 0
\(545\) 375.716 216.920i 0.689387 0.398018i
\(546\) 0 0
\(547\) −404.687 + 233.646i −0.739830 + 0.427141i −0.822008 0.569476i \(-0.807146\pi\)
0.0821772 + 0.996618i \(0.473813\pi\)
\(548\) 0 0
\(549\) 64.0210 110.888i 0.116614 0.201981i
\(550\) 0 0
\(551\) −486.250 543.782i −0.882487 0.986900i
\(552\) 0 0
\(553\) 281.898 + 162.754i 0.509761 + 0.294311i
\(554\) 0 0
\(555\) −136.965 237.230i −0.246783 0.427442i
\(556\) 0 0
\(557\) 386.099 + 668.743i 0.693175 + 1.20061i 0.970792 + 0.239923i \(0.0771222\pi\)
−0.277617 + 0.960692i \(0.589544\pi\)
\(558\) 0 0
\(559\) 941.376i 1.68404i
\(560\) 0 0
\(561\) −111.838 + 64.5698i −0.199355 + 0.115098i
\(562\) 0 0
\(563\) 195.273i 0.346844i 0.984848 + 0.173422i \(0.0554825\pi\)
−0.984848 + 0.173422i \(0.944518\pi\)
\(564\) 0 0
\(565\) 223.385 + 128.971i 0.395372 + 0.228268i
\(566\) 0 0
\(567\) −48.0676 + 83.2556i −0.0847753 + 0.146835i
\(568\) 0 0
\(569\) 579.517i 1.01848i −0.860624 0.509242i \(-0.829926\pi\)
0.860624 0.509242i \(-0.170074\pi\)
\(570\) 0 0
\(571\) 145.886 0.255492 0.127746 0.991807i \(-0.459226\pi\)
0.127746 + 0.991807i \(0.459226\pi\)
\(572\) 0 0
\(573\) 72.8602 + 42.0658i 0.127156 + 0.0734133i
\(574\) 0 0
\(575\) 46.6448 80.7911i 0.0811214 0.140506i
\(576\) 0 0
\(577\) −1037.54 −1.79817 −0.899084 0.437777i \(-0.855766\pi\)
−0.899084 + 0.437777i \(0.855766\pi\)
\(578\) 0 0
\(579\) 9.48401 + 16.4268i 0.0163800 + 0.0283710i
\(580\) 0 0
\(581\) −823.723 −1.41777
\(582\) 0 0
\(583\) −84.9009 + 49.0176i −0.145628 + 0.0840782i
\(584\) 0 0
\(585\) 214.714 123.965i 0.367033 0.211907i
\(586\) 0 0
\(587\) −441.521 + 764.737i −0.752165 + 1.30279i 0.194606 + 0.980882i \(0.437657\pi\)
−0.946771 + 0.321907i \(0.895676\pi\)
\(588\) 0 0
\(589\) 798.684 166.899i 1.35600 0.283360i
\(590\) 0 0
\(591\) 156.663 + 90.4495i 0.265082 + 0.153045i
\(592\) 0 0
\(593\) 119.583 + 207.125i 0.201658 + 0.349283i 0.949063 0.315087i \(-0.102034\pi\)
−0.747404 + 0.664369i \(0.768700\pi\)
\(594\) 0 0
\(595\) 290.835 + 503.741i 0.488798 + 0.846623i
\(596\) 0 0
\(597\) 487.203i 0.816086i
\(598\) 0 0
\(599\) 793.604 458.187i 1.32488 0.764920i 0.340378 0.940289i \(-0.389445\pi\)
0.984503 + 0.175368i \(0.0561116\pi\)
\(600\) 0 0
\(601\) 789.891i 1.31429i −0.753762 0.657147i \(-0.771763\pi\)
0.753762 0.657147i \(-0.228237\pi\)
\(602\) 0 0
\(603\) 45.4756 + 26.2553i 0.0754155 + 0.0435412i
\(604\) 0 0
\(605\) −187.079 + 324.031i −0.309222 + 0.535588i
\(606\) 0 0
\(607\) 653.712i 1.07696i 0.842640 + 0.538478i \(0.181000\pi\)
−0.842640 + 0.538478i \(0.819000\pi\)
\(608\) 0 0
\(609\) −710.329 −1.16639
\(610\) 0 0
\(611\) 369.886 + 213.554i 0.605379 + 0.349515i
\(612\) 0 0
\(613\) 528.343 915.118i 0.861898 1.49285i −0.00819687 0.999966i \(-0.502609\pi\)
0.870095 0.492885i \(-0.164057\pi\)
\(614\) 0 0
\(615\) 152.413 0.247825
\(616\) 0 0
\(617\) −501.032 867.813i −0.812045 1.40650i −0.911430 0.411455i \(-0.865021\pi\)
0.0993850 0.995049i \(-0.468312\pi\)
\(618\) 0 0
\(619\) −252.948 −0.408640 −0.204320 0.978904i \(-0.565498\pi\)
−0.204320 + 0.978904i \(0.565498\pi\)
\(620\) 0 0
\(621\) 125.835 72.6509i 0.202633 0.116990i
\(622\) 0 0
\(623\) −820.491 + 473.711i −1.31700 + 0.760371i
\(624\) 0 0
\(625\) 265.233 459.398i 0.424373 0.735036i
\(626\) 0 0
\(627\) −65.4929 + 199.234i −0.104454 + 0.317757i
\(628\) 0 0
\(629\) 344.278 + 198.769i 0.547342 + 0.316008i
\(630\) 0 0
\(631\) 605.640 + 1049.00i 0.959809 + 1.66244i 0.722957 + 0.690893i \(0.242783\pi\)
0.236853 + 0.971546i \(0.423884\pi\)
\(632\) 0 0
\(633\) −89.2808 154.639i −0.141044 0.244295i
\(634\) 0 0
\(635\) 444.568i 0.700107i
\(636\) 0 0
\(637\) 1001.02 577.940i 1.57146 0.907284i
\(638\) 0 0
\(639\) 258.432i 0.404431i
\(640\) 0 0
\(641\) 89.1040 + 51.4442i 0.139008 + 0.0802562i 0.567891 0.823104i \(-0.307759\pi\)
−0.428883 + 0.903360i \(0.641093\pi\)
\(642\) 0 0
\(643\) 384.990 666.822i 0.598740 1.03705i −0.394267 0.918996i \(-0.629002\pi\)
0.993007 0.118052i \(-0.0376650\pi\)
\(644\) 0 0
\(645\) 427.416i 0.662660i
\(646\) 0 0
\(647\) 790.984 1.22254 0.611270 0.791422i \(-0.290659\pi\)
0.611270 + 0.791422i \(0.290659\pi\)
\(648\) 0 0
\(649\) −163.488 94.3896i −0.251907 0.145438i
\(650\) 0 0
\(651\) 397.259 688.072i 0.610228 1.05695i
\(652\) 0 0
\(653\) 320.503 0.490816 0.245408 0.969420i \(-0.421078\pi\)
0.245408 + 0.969420i \(0.421078\pi\)
\(654\) 0 0
\(655\) −391.328 677.800i −0.597447 1.03481i
\(656\) 0 0
\(657\) 277.411 0.422239
\(658\) 0 0
\(659\) 616.112 355.713i 0.934920 0.539776i 0.0465558 0.998916i \(-0.485175\pi\)
0.888364 + 0.459139i \(0.151842\pi\)
\(660\) 0 0
\(661\) −410.779 + 237.163i −0.621451 + 0.358795i −0.777434 0.628965i \(-0.783479\pi\)
0.155983 + 0.987760i \(0.450146\pi\)
\(662\) 0 0
\(663\) −179.904 + 311.602i −0.271348 + 0.469989i
\(664\) 0 0
\(665\) 897.388 + 294.993i 1.34946 + 0.443598i
\(666\) 0 0
\(667\) 929.776 + 536.806i 1.39397 + 0.804807i
\(668\) 0 0
\(669\) 68.9560 + 119.435i 0.103073 + 0.178528i
\(670\) 0 0
\(671\) −135.998 235.555i −0.202679 0.351051i
\(672\) 0 0
\(673\) 648.662i 0.963836i 0.876216 + 0.481918i \(0.160060\pi\)
−0.876216 + 0.481918i \(0.839940\pi\)
\(674\) 0 0
\(675\) −15.0126 + 8.66754i −0.0222409 + 0.0128408i
\(676\) 0 0
\(677\) 860.699i 1.27134i −0.771960 0.635671i \(-0.780723\pi\)
0.771960 0.635671i \(-0.219277\pi\)
\(678\) 0 0
\(679\) −19.4782 11.2458i −0.0286866 0.0165622i
\(680\) 0 0
\(681\) 113.476 196.546i 0.166631 0.288614i
\(682\) 0 0
\(683\) 194.789i 0.285196i 0.989781 + 0.142598i \(0.0455456\pi\)
−0.989781 + 0.142598i \(0.954454\pi\)
\(684\) 0 0
\(685\) 552.738 0.806916
\(686\) 0 0
\(687\) 45.5306 + 26.2871i 0.0662745 + 0.0382636i
\(688\) 0 0
\(689\) −136.572 + 236.550i −0.198218 + 0.343324i
\(690\) 0 0
\(691\) −719.067 −1.04062 −0.520309 0.853978i \(-0.674183\pi\)
−0.520309 + 0.853978i \(0.674183\pi\)
\(692\) 0 0
\(693\) 102.108 + 176.857i 0.147343 + 0.255205i
\(694\) 0 0
\(695\) 513.685 0.739115
\(696\) 0 0
\(697\) −191.554 + 110.594i −0.274826 + 0.158671i
\(698\) 0 0
\(699\) −141.145 + 81.4902i −0.201924 + 0.116581i
\(700\) 0 0
\(701\) 242.353 419.767i 0.345724 0.598812i −0.639761 0.768574i \(-0.720967\pi\)
0.985485 + 0.169762i \(0.0542999\pi\)
\(702\) 0 0
\(703\) 631.951 132.057i 0.898934 0.187848i
\(704\) 0 0
\(705\) 167.941 + 96.9605i 0.238213 + 0.137533i
\(706\) 0 0
\(707\) −147.076 254.744i −0.208029 0.360317i
\(708\) 0 0
\(709\) 620.485 + 1074.71i 0.875156 + 1.51581i 0.856597 + 0.515987i \(0.172575\pi\)
0.0185591 + 0.999828i \(0.494092\pi\)
\(710\) 0 0
\(711\) 91.4203i 0.128580i
\(712\) 0 0
\(713\) −1039.97 + 600.429i −1.45859 + 0.842116i
\(714\) 0 0
\(715\) 526.671i 0.736603i
\(716\) 0 0
\(717\) −562.946 325.017i −0.785141 0.453301i
\(718\) 0 0
\(719\) −65.3191 + 113.136i −0.0908471 + 0.157352i −0.907868 0.419256i \(-0.862291\pi\)
0.817021 + 0.576608i \(0.195624\pi\)
\(720\) 0 0
\(721\) 1093.28i 1.51634i
\(722\) 0 0
\(723\) 0.964848 0.00133451
\(724\) 0 0
\(725\) −110.926 64.0432i −0.153001 0.0883354i
\(726\) 0 0
\(727\) 566.505 981.216i 0.779237 1.34968i −0.153145 0.988204i \(-0.548940\pi\)
0.932382 0.361475i \(-0.117727\pi\)
\(728\) 0 0
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) −310.142 537.181i −0.424271 0.734858i
\(732\) 0 0
\(733\) −837.144 −1.14208 −0.571040 0.820922i \(-0.693460\pi\)
−0.571040 + 0.820922i \(0.693460\pi\)
\(734\) 0 0
\(735\) 454.497 262.404i 0.618363 0.357012i
\(736\) 0 0
\(737\) 96.6023 55.7734i 0.131075 0.0756762i
\(738\) 0 0
\(739\) −144.463 + 250.216i −0.195484 + 0.338588i −0.947059 0.321060i \(-0.895961\pi\)
0.751575 + 0.659647i \(0.229294\pi\)
\(740\) 0 0
\(741\) 119.523 + 571.972i 0.161300 + 0.771892i
\(742\) 0 0
\(743\) 66.4928 + 38.3896i 0.0894923 + 0.0516684i 0.544078 0.839034i \(-0.316879\pi\)
−0.454586 + 0.890703i \(0.650213\pi\)
\(744\) 0 0
\(745\) −134.383 232.758i −0.180380 0.312427i
\(746\) 0 0
\(747\) −115.673 200.352i −0.154850 0.268208i
\(748\) 0 0
\(749\) 5.87058i 0.00783789i
\(750\) 0 0
\(751\) −923.318 + 533.078i −1.22945 + 0.709824i −0.966915 0.255098i \(-0.917892\pi\)
−0.262536 + 0.964922i \(0.584559\pi\)
\(752\) 0 0
\(753\) 406.371i 0.539669i
\(754\) 0 0
\(755\) −828.179 478.149i −1.09693 0.633310i
\(756\) 0 0
\(757\) 4.94030 8.55684i 0.00652615 0.0113036i −0.862744 0.505641i \(-0.831256\pi\)
0.869270 + 0.494338i \(0.164589\pi\)
\(758\) 0 0
\(759\) 308.660i 0.406666i
\(760\) 0 0
\(761\) 1147.50 1.50788 0.753940 0.656944i \(-0.228151\pi\)
0.753940 + 0.656944i \(0.228151\pi\)
\(762\) 0 0
\(763\) 862.247 + 497.819i 1.13007 + 0.652449i
\(764\) 0 0
\(765\) −81.6822 + 141.478i −0.106774 + 0.184938i
\(766\) 0 0
\(767\) −525.975 −0.685756
\(768\) 0 0
\(769\) 299.227 + 518.276i 0.389112 + 0.673961i 0.992330 0.123615i \(-0.0394486\pi\)
−0.603218 + 0.797576i \(0.706115\pi\)
\(770\) 0 0
\(771\) −22.1405 −0.0287166
\(772\) 0 0
\(773\) 858.414 495.605i 1.11050 0.641145i 0.171538 0.985177i \(-0.445126\pi\)
0.938958 + 0.344032i \(0.111793\pi\)
\(774\) 0 0
\(775\) 124.073 71.6336i 0.160094 0.0924305i
\(776\) 0 0
\(777\) 314.327 544.430i 0.404539 0.700682i
\(778\) 0 0
\(779\) −112.175 + 341.244i −0.143998 + 0.438053i
\(780\) 0 0
\(781\) 475.429 + 274.489i 0.608744 + 0.351458i
\(782\) 0 0
\(783\) −99.7494 172.771i −0.127394 0.220653i
\(784\) 0 0
\(785\) 258.824 + 448.297i 0.329713 + 0.571079i
\(786\) 0 0
\(787\) 1226.83i 1.55887i −0.626480 0.779437i \(-0.715505\pi\)
0.626480 0.779437i \(-0.284495\pi\)
\(788\) 0 0
\(789\) −319.371 + 184.389i −0.404780 + 0.233700i
\(790\) 0 0
\(791\) 591.965i 0.748375i
\(792\) 0 0
\(793\) −656.302 378.916i −0.827619 0.477826i
\(794\) 0 0
\(795\)