Properties

Label 336.2.bc.f.17.7
Level 336
Weight 2
Character 336.17
Analytic conductor 2.683
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(2.68297350792\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 168)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.7
Root \(0.934861 + 1.45809i\)
Character \(\chi\) = 336.17
Dual form 336.2.bc.f.257.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.45809 - 0.934861i) q^{3} +(-1.90017 - 3.29119i) q^{5} +(-2.23495 + 1.41598i) q^{7} +(1.25207 - 2.72623i) q^{9} +O(q^{10})\) \(q+(1.45809 - 0.934861i) q^{3} +(-1.90017 - 3.29119i) q^{5} +(-2.23495 + 1.41598i) q^{7} +(1.25207 - 2.72623i) q^{9} +(0.309539 + 0.178712i) q^{11} -4.04570i q^{13} +(-5.84742 - 3.02246i) q^{15} +(-0.0519689 + 0.0900129i) q^{17} +(2.12615 - 1.22753i) q^{19} +(-1.93502 + 4.15400i) q^{21} +(-1.15188 + 0.665037i) q^{23} +(-4.72127 + 8.17749i) q^{25} +(-0.723015 - 5.14560i) q^{27} -4.97265i q^{29} +(6.83007 + 3.94335i) q^{31} +(0.618407 - 0.0287968i) q^{33} +(8.90704 + 4.66504i) q^{35} +(5.45622 + 9.45046i) q^{37} +(-3.78216 - 5.89900i) q^{39} +6.15464 q^{41} -0.502751 q^{43} +(-11.3517 + 1.05950i) q^{45} +(-5.72578 - 9.91734i) q^{47} +(2.99000 - 6.32929i) q^{49} +(0.00837401 + 0.179831i) q^{51} +(5.08143 + 2.93376i) q^{53} -1.35833i q^{55} +(1.95255 - 3.77751i) q^{57} +(-3.77364 + 6.53614i) q^{59} +(8.20485 - 4.73707i) q^{61} +(1.06198 + 7.86589i) q^{63} +(-13.3151 + 7.68750i) q^{65} +(1.34375 - 2.32744i) q^{67} +(-1.05783 + 2.04653i) q^{69} +5.78975i q^{71} +(-0.203925 - 0.117736i) q^{73} +(0.760762 + 16.3373i) q^{75} +(-0.944856 + 0.0388878i) q^{77} +(1.61247 + 2.79289i) q^{79} +(-5.86465 - 6.82685i) q^{81} +9.07747 q^{83} +0.394999 q^{85} +(-4.64874 - 7.25058i) q^{87} +(3.41213 + 5.90999i) q^{89} +(5.72862 + 9.04192i) q^{91} +(13.6454 - 0.635411i) q^{93} +(-8.08008 - 4.66504i) q^{95} +5.14243i q^{97} +(0.874774 - 0.620114i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{7} + 2q^{9} + O(q^{10}) \) \( 16q - 4q^{7} + 2q^{9} - 8q^{15} + 6q^{19} + 14q^{21} - 18q^{25} + 48q^{31} - 12q^{33} - 2q^{37} + 22q^{39} - 20q^{43} - 42q^{45} - 28q^{49} - 6q^{51} - 8q^{57} + 36q^{61} + 32q^{63} - 14q^{67} + 30q^{73} - 54q^{75} - 28q^{79} + 30q^{81} + 16q^{85} - 78q^{87} - 66q^{91} + 16q^{93} - 20q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.45809 0.934861i 0.841830 0.539743i
\(4\) 0 0
\(5\) −1.90017 3.29119i −0.849781 1.47186i −0.881404 0.472364i \(-0.843401\pi\)
0.0316229 0.999500i \(-0.489932\pi\)
\(6\) 0 0
\(7\) −2.23495 + 1.41598i −0.844732 + 0.535190i
\(8\) 0 0
\(9\) 1.25207 2.72623i 0.417356 0.908743i
\(10\) 0 0
\(11\) 0.309539 + 0.178712i 0.0933294 + 0.0538838i 0.545938 0.837825i \(-0.316173\pi\)
−0.452609 + 0.891709i \(0.649507\pi\)
\(12\) 0 0
\(13\) 4.04570i 1.12207i −0.827791 0.561037i \(-0.810403\pi\)
0.827791 0.561037i \(-0.189597\pi\)
\(14\) 0 0
\(15\) −5.84742 3.02246i −1.50980 0.780396i
\(16\) 0 0
\(17\) −0.0519689 + 0.0900129i −0.0126043 + 0.0218313i −0.872259 0.489045i \(-0.837346\pi\)
0.859654 + 0.510876i \(0.170679\pi\)
\(18\) 0 0
\(19\) 2.12615 1.22753i 0.487772 0.281615i −0.235878 0.971783i \(-0.575796\pi\)
0.723650 + 0.690167i \(0.242463\pi\)
\(20\) 0 0
\(21\) −1.93502 + 4.15400i −0.422256 + 0.906477i
\(22\) 0 0
\(23\) −1.15188 + 0.665037i −0.240183 + 0.138670i −0.615261 0.788323i \(-0.710949\pi\)
0.375078 + 0.926993i \(0.377616\pi\)
\(24\) 0 0
\(25\) −4.72127 + 8.17749i −0.944255 + 1.63550i
\(26\) 0 0
\(27\) −0.723015 5.14560i −0.139144 0.990272i
\(28\) 0 0
\(29\) 4.97265i 0.923398i −0.887037 0.461699i \(-0.847240\pi\)
0.887037 0.461699i \(-0.152760\pi\)
\(30\) 0 0
\(31\) 6.83007 + 3.94335i 1.22672 + 0.708246i 0.966342 0.257262i \(-0.0828202\pi\)
0.260376 + 0.965507i \(0.416154\pi\)
\(32\) 0 0
\(33\) 0.618407 0.0287968i 0.107651 0.00501288i
\(34\) 0 0
\(35\) 8.90704 + 4.66504i 1.50556 + 0.788535i
\(36\) 0 0
\(37\) 5.45622 + 9.45046i 0.896998 + 1.55365i 0.831312 + 0.555805i \(0.187590\pi\)
0.0656853 + 0.997840i \(0.479077\pi\)
\(38\) 0 0
\(39\) −3.78216 5.89900i −0.605631 0.944596i
\(40\) 0 0
\(41\) 6.15464 0.961193 0.480597 0.876942i \(-0.340420\pi\)
0.480597 + 0.876942i \(0.340420\pi\)
\(42\) 0 0
\(43\) −0.502751 −0.0766688 −0.0383344 0.999265i \(-0.512205\pi\)
−0.0383344 + 0.999265i \(0.512205\pi\)
\(44\) 0 0
\(45\) −11.3517 + 1.05950i −1.69221 + 0.157941i
\(46\) 0 0
\(47\) −5.72578 9.91734i −0.835190 1.44659i −0.893875 0.448316i \(-0.852024\pi\)
0.0586849 0.998277i \(-0.481309\pi\)
\(48\) 0 0
\(49\) 2.99000 6.32929i 0.427143 0.904184i
\(50\) 0 0
\(51\) 0.00837401 + 0.179831i 0.00117260 + 0.0251814i
\(52\) 0 0
\(53\) 5.08143 + 2.93376i 0.697988 + 0.402983i 0.806597 0.591101i \(-0.201307\pi\)
−0.108610 + 0.994084i \(0.534640\pi\)
\(54\) 0 0
\(55\) 1.35833i 0.183158i
\(56\) 0 0
\(57\) 1.95255 3.77751i 0.258622 0.500344i
\(58\) 0 0
\(59\) −3.77364 + 6.53614i −0.491286 + 0.850933i −0.999950 0.0100329i \(-0.996806\pi\)
0.508664 + 0.860965i \(0.330140\pi\)
\(60\) 0 0
\(61\) 8.20485 4.73707i 1.05052 0.606520i 0.127727 0.991809i \(-0.459232\pi\)
0.922796 + 0.385289i \(0.125898\pi\)
\(62\) 0 0
\(63\) 1.06198 + 7.86589i 0.133797 + 0.991009i
\(64\) 0 0
\(65\) −13.3151 + 7.68750i −1.65154 + 0.953517i
\(66\) 0 0
\(67\) 1.34375 2.32744i 0.164165 0.284342i −0.772193 0.635388i \(-0.780840\pi\)
0.936358 + 0.351045i \(0.114174\pi\)
\(68\) 0 0
\(69\) −1.05783 + 2.04653i −0.127348 + 0.246374i
\(70\) 0 0
\(71\) 5.78975i 0.687117i 0.939131 + 0.343558i \(0.111632\pi\)
−0.939131 + 0.343558i \(0.888368\pi\)
\(72\) 0 0
\(73\) −0.203925 0.117736i −0.0238676 0.0137800i 0.488019 0.872833i \(-0.337720\pi\)
−0.511886 + 0.859053i \(0.671053\pi\)
\(74\) 0 0
\(75\) 0.760762 + 16.3373i 0.0878453 + 1.88647i
\(76\) 0 0
\(77\) −0.944856 + 0.0388878i −0.107676 + 0.00443168i
\(78\) 0 0
\(79\) 1.61247 + 2.79289i 0.181418 + 0.314224i 0.942364 0.334591i \(-0.108598\pi\)
−0.760946 + 0.648815i \(0.775265\pi\)
\(80\) 0 0
\(81\) −5.86465 6.82685i −0.651628 0.758539i
\(82\) 0 0
\(83\) 9.07747 0.996382 0.498191 0.867067i \(-0.333998\pi\)
0.498191 + 0.867067i \(0.333998\pi\)
\(84\) 0 0
\(85\) 0.394999 0.0428436
\(86\) 0 0
\(87\) −4.64874 7.25058i −0.498397 0.777344i
\(88\) 0 0
\(89\) 3.41213 + 5.90999i 0.361685 + 0.626457i 0.988238 0.152921i \(-0.0488681\pi\)
−0.626553 + 0.779379i \(0.715535\pi\)
\(90\) 0 0
\(91\) 5.72862 + 9.04192i 0.600523 + 0.947851i
\(92\) 0 0
\(93\) 13.6454 0.635411i 1.41496 0.0658890i
\(94\) 0 0
\(95\) −8.08008 4.66504i −0.828999 0.478623i
\(96\) 0 0
\(97\) 5.14243i 0.522134i 0.965321 + 0.261067i \(0.0840744\pi\)
−0.965321 + 0.261067i \(0.915926\pi\)
\(98\) 0 0
\(99\) 0.874774 0.620114i 0.0879181 0.0623238i
\(100\) 0 0
\(101\) −6.43891 + 11.1525i −0.640695 + 1.10972i 0.344583 + 0.938756i \(0.388020\pi\)
−0.985278 + 0.170960i \(0.945313\pi\)
\(102\) 0 0
\(103\) −4.88120 + 2.81816i −0.480959 + 0.277682i −0.720816 0.693126i \(-0.756233\pi\)
0.239857 + 0.970808i \(0.422899\pi\)
\(104\) 0 0
\(105\) 17.3484 1.52479i 1.69303 0.148804i
\(106\) 0 0
\(107\) −7.62737 + 4.40366i −0.737365 + 0.425718i −0.821111 0.570769i \(-0.806645\pi\)
0.0837453 + 0.996487i \(0.473312\pi\)
\(108\) 0 0
\(109\) 2.23862 3.87741i 0.214421 0.371389i −0.738672 0.674065i \(-0.764547\pi\)
0.953093 + 0.302676i \(0.0978801\pi\)
\(110\) 0 0
\(111\) 16.7905 + 8.67883i 1.59369 + 0.823758i
\(112\) 0 0
\(113\) 4.00000i 0.376288i −0.982141 0.188144i \(-0.939753\pi\)
0.982141 0.188144i \(-0.0602472\pi\)
\(114\) 0 0
\(115\) 4.37753 + 2.52737i 0.408206 + 0.235678i
\(116\) 0 0
\(117\) −11.0295 5.06549i −1.01968 0.468304i
\(118\) 0 0
\(119\) −0.0113084 0.274761i −0.00103664 0.0251873i
\(120\) 0 0
\(121\) −5.43612 9.41564i −0.494193 0.855968i
\(122\) 0 0
\(123\) 8.97404 5.75374i 0.809162 0.518797i
\(124\) 0 0
\(125\) 16.8832 1.51008
\(126\) 0 0
\(127\) −12.9198 −1.14645 −0.573223 0.819399i \(-0.694307\pi\)
−0.573223 + 0.819399i \(0.694307\pi\)
\(128\) 0 0
\(129\) −0.733058 + 0.470003i −0.0645421 + 0.0413814i
\(130\) 0 0
\(131\) −2.66384 4.61391i −0.232741 0.403119i 0.725873 0.687829i \(-0.241436\pi\)
−0.958614 + 0.284710i \(0.908103\pi\)
\(132\) 0 0
\(133\) −3.01367 + 5.75406i −0.261319 + 0.498940i
\(134\) 0 0
\(135\) −15.5613 + 12.1571i −1.33930 + 1.04632i
\(136\) 0 0
\(137\) −4.37380 2.52521i −0.373679 0.215744i 0.301386 0.953502i \(-0.402551\pi\)
−0.675064 + 0.737759i \(0.735884\pi\)
\(138\) 0 0
\(139\) 21.2651i 1.80368i −0.432067 0.901841i \(-0.642216\pi\)
0.432067 0.901841i \(-0.357784\pi\)
\(140\) 0 0
\(141\) −17.6200 9.10759i −1.48388 0.766997i
\(142\) 0 0
\(143\) 0.723015 1.25230i 0.0604616 0.104723i
\(144\) 0 0
\(145\) −16.3659 + 9.44887i −1.35912 + 0.784686i
\(146\) 0 0
\(147\) −1.55731 12.0239i −0.128445 0.991717i
\(148\) 0 0
\(149\) −10.5482 + 6.09001i −0.864143 + 0.498913i −0.865398 0.501086i \(-0.832934\pi\)
0.00125437 + 0.999999i \(0.499601\pi\)
\(150\) 0 0
\(151\) −4.10880 + 7.11665i −0.334369 + 0.579145i −0.983363 0.181649i \(-0.941857\pi\)
0.648994 + 0.760793i \(0.275190\pi\)
\(152\) 0 0
\(153\) 0.180327 + 0.254381i 0.0145786 + 0.0205655i
\(154\) 0 0
\(155\) 29.9721i 2.40741i
\(156\) 0 0
\(157\) 11.2104 + 6.47230i 0.894683 + 0.516546i 0.875472 0.483270i \(-0.160551\pi\)
0.0192119 + 0.999815i \(0.493884\pi\)
\(158\) 0 0
\(159\) 10.1519 0.472732i 0.805094 0.0374901i
\(160\) 0 0
\(161\) 1.63271 3.11736i 0.128676 0.245683i
\(162\) 0 0
\(163\) −1.09237 1.89205i −0.0855613 0.148197i 0.820069 0.572265i \(-0.193935\pi\)
−0.905630 + 0.424068i \(0.860602\pi\)
\(164\) 0 0
\(165\) −1.26985 1.98058i −0.0988579 0.154188i
\(166\) 0 0
\(167\) −0.464592 −0.0359512 −0.0179756 0.999838i \(-0.505722\pi\)
−0.0179756 + 0.999838i \(0.505722\pi\)
\(168\) 0 0
\(169\) −3.36765 −0.259050
\(170\) 0 0
\(171\) −0.684452 7.33333i −0.0523414 0.560793i
\(172\) 0 0
\(173\) 4.62587 + 8.01224i 0.351698 + 0.609159i 0.986547 0.163477i \(-0.0522710\pi\)
−0.634849 + 0.772636i \(0.718938\pi\)
\(174\) 0 0
\(175\) −1.02735 24.9615i −0.0776603 1.88691i
\(176\) 0 0
\(177\) 0.608065 + 13.0581i 0.0457050 + 0.981509i
\(178\) 0 0
\(179\) −1.77096 1.02246i −0.132367 0.0764224i 0.432354 0.901704i \(-0.357683\pi\)
−0.564722 + 0.825282i \(0.691016\pi\)
\(180\) 0 0
\(181\) 17.6193i 1.30963i −0.755790 0.654815i \(-0.772747\pi\)
0.755790 0.654815i \(-0.227253\pi\)
\(182\) 0 0
\(183\) 7.53492 14.5775i 0.556998 1.07760i
\(184\) 0 0
\(185\) 20.7355 35.9149i 1.52450 2.64052i
\(186\) 0 0
\(187\) −0.0321728 + 0.0185750i −0.00235271 + 0.00135834i
\(188\) 0 0
\(189\) 8.90198 + 10.4764i 0.647524 + 0.762045i
\(190\) 0 0
\(191\) 19.4811 11.2474i 1.40960 0.813834i 0.414252 0.910162i \(-0.364043\pi\)
0.995350 + 0.0963279i \(0.0307097\pi\)
\(192\) 0 0
\(193\) −4.81985 + 8.34823i −0.346940 + 0.600918i −0.985704 0.168484i \(-0.946113\pi\)
0.638764 + 0.769403i \(0.279446\pi\)
\(194\) 0 0
\(195\) −12.2280 + 23.6569i −0.875662 + 1.69411i
\(196\) 0 0
\(197\) 15.3750i 1.09542i −0.836667 0.547712i \(-0.815499\pi\)
0.836667 0.547712i \(-0.184501\pi\)
\(198\) 0 0
\(199\) 3.96967 + 2.29189i 0.281403 + 0.162468i 0.634058 0.773285i \(-0.281388\pi\)
−0.352656 + 0.935753i \(0.614721\pi\)
\(200\) 0 0
\(201\) −0.216525 4.64985i −0.0152725 0.327975i
\(202\) 0 0
\(203\) 7.04117 + 11.1136i 0.494194 + 0.780023i
\(204\) 0 0
\(205\) −11.6948 20.2561i −0.816804 1.41475i
\(206\) 0 0
\(207\) 0.370814 + 3.97296i 0.0257734 + 0.276140i
\(208\) 0 0
\(209\) 0.877501 0.0606980
\(210\) 0 0
\(211\) 0.870400 0.0599208 0.0299604 0.999551i \(-0.490462\pi\)
0.0299604 + 0.999551i \(0.490462\pi\)
\(212\) 0 0
\(213\) 5.41261 + 8.44199i 0.370866 + 0.578436i
\(214\) 0 0
\(215\) 0.955311 + 1.65465i 0.0651517 + 0.112846i
\(216\) 0 0
\(217\) −20.8486 + 0.858072i −1.41529 + 0.0582497i
\(218\) 0 0
\(219\) −0.407409 + 0.0189714i −0.0275301 + 0.00128197i
\(220\) 0 0
\(221\) 0.364165 + 0.210251i 0.0244964 + 0.0141430i
\(222\) 0 0
\(223\) 1.21373i 0.0812777i 0.999174 + 0.0406388i \(0.0129393\pi\)
−0.999174 + 0.0406388i \(0.987061\pi\)
\(224\) 0 0
\(225\) 16.3823 + 23.1100i 1.09216 + 1.54067i
\(226\) 0 0
\(227\) −6.67205 + 11.5563i −0.442840 + 0.767021i −0.997899 0.0647898i \(-0.979362\pi\)
0.555059 + 0.831811i \(0.312696\pi\)
\(228\) 0 0
\(229\) 9.60627 5.54618i 0.634800 0.366502i −0.147808 0.989016i \(-0.547222\pi\)
0.782609 + 0.622514i \(0.213889\pi\)
\(230\) 0 0
\(231\) −1.34133 + 0.940012i −0.0882533 + 0.0618482i
\(232\) 0 0
\(233\) −7.08411 + 4.09001i −0.464095 + 0.267946i −0.713765 0.700386i \(-0.753011\pi\)
0.249669 + 0.968331i \(0.419678\pi\)
\(234\) 0 0
\(235\) −21.7599 + 37.6892i −1.41946 + 2.45857i
\(236\) 0 0
\(237\) 4.96210 + 2.56485i 0.322323 + 0.166605i
\(238\) 0 0
\(239\) 22.5944i 1.46151i 0.682638 + 0.730757i \(0.260833\pi\)
−0.682638 + 0.730757i \(0.739167\pi\)
\(240\) 0 0
\(241\) 4.24127 + 2.44870i 0.273205 + 0.157735i 0.630343 0.776317i \(-0.282914\pi\)
−0.357138 + 0.934051i \(0.616248\pi\)
\(242\) 0 0
\(243\) −14.9334 4.47154i −0.957976 0.286850i
\(244\) 0 0
\(245\) −26.5124 + 2.18606i −1.69381 + 0.139662i
\(246\) 0 0
\(247\) −4.96622 8.60175i −0.315993 0.547316i
\(248\) 0 0
\(249\) 13.2358 8.48618i 0.838785 0.537790i
\(250\) 0 0
\(251\) −9.17857 −0.579346 −0.289673 0.957126i \(-0.593547\pi\)
−0.289673 + 0.957126i \(0.593547\pi\)
\(252\) 0 0
\(253\) −0.475401 −0.0298882
\(254\) 0 0
\(255\) 0.575945 0.369269i 0.0360671 0.0231245i
\(256\) 0 0
\(257\) 6.31055 + 10.9302i 0.393641 + 0.681806i 0.992927 0.118729i \(-0.0378819\pi\)
−0.599286 + 0.800535i \(0.704549\pi\)
\(258\) 0 0
\(259\) −25.5760 13.3954i −1.58922 0.832349i
\(260\) 0 0
\(261\) −13.5566 6.22610i −0.839132 0.385386i
\(262\) 0 0
\(263\) 25.2489 + 14.5775i 1.55692 + 0.898886i 0.997549 + 0.0699665i \(0.0222892\pi\)
0.559367 + 0.828920i \(0.311044\pi\)
\(264\) 0 0
\(265\) 22.2986i 1.36979i
\(266\) 0 0
\(267\) 10.5002 + 5.42744i 0.642603 + 0.332154i
\(268\) 0 0
\(269\) 2.23640 3.87356i 0.136356 0.236175i −0.789759 0.613418i \(-0.789794\pi\)
0.926115 + 0.377242i \(0.123128\pi\)
\(270\) 0 0
\(271\) 14.4985 8.37071i 0.880721 0.508485i 0.00982495 0.999952i \(-0.496873\pi\)
0.870896 + 0.491467i \(0.163539\pi\)
\(272\) 0 0
\(273\) 16.8058 + 7.82849i 1.01713 + 0.473802i
\(274\) 0 0
\(275\) −2.92283 + 1.68750i −0.176254 + 0.101760i
\(276\) 0 0
\(277\) −0.510924 + 0.884946i −0.0306984 + 0.0531713i −0.880966 0.473179i \(-0.843106\pi\)
0.850268 + 0.526350i \(0.176440\pi\)
\(278\) 0 0
\(279\) 19.3022 13.6830i 1.15559 0.819181i
\(280\) 0 0
\(281\) 13.9453i 0.831907i 0.909386 + 0.415953i \(0.136552\pi\)
−0.909386 + 0.415953i \(0.863448\pi\)
\(282\) 0 0
\(283\) −14.0386 8.10519i −0.834508 0.481803i 0.0208856 0.999782i \(-0.493351\pi\)
−0.855394 + 0.517978i \(0.826685\pi\)
\(284\) 0 0
\(285\) −16.1427 + 0.751701i −0.956209 + 0.0445269i
\(286\) 0 0
\(287\) −13.7553 + 8.71485i −0.811950 + 0.514421i
\(288\) 0 0
\(289\) 8.49460 + 14.7131i 0.499682 + 0.865475i
\(290\) 0 0
\(291\) 4.80746 + 7.49814i 0.281818 + 0.439549i
\(292\) 0 0
\(293\) −19.2067 −1.12207 −0.561034 0.827793i \(-0.689596\pi\)
−0.561034 + 0.827793i \(0.689596\pi\)
\(294\) 0 0
\(295\) 28.6822 1.66994
\(296\) 0 0
\(297\) 0.695781 1.72198i 0.0403733 0.0999192i
\(298\) 0 0
\(299\) 2.69054 + 4.66015i 0.155598 + 0.269503i
\(300\) 0 0
\(301\) 1.12362 0.711886i 0.0647646 0.0410324i
\(302\) 0 0
\(303\) 1.03753 + 22.2809i 0.0596047 + 1.28000i
\(304\) 0 0
\(305\) −31.1812 18.0025i −1.78543 1.03082i
\(306\) 0 0
\(307\) 0.480498i 0.0274235i 0.999906 + 0.0137117i \(0.00436472\pi\)
−0.999906 + 0.0137117i \(0.995635\pi\)
\(308\) 0 0
\(309\) −4.48265 + 8.67239i −0.255009 + 0.493355i
\(310\) 0 0
\(311\) −4.66653 + 8.08266i −0.264615 + 0.458326i −0.967463 0.253014i \(-0.918578\pi\)
0.702848 + 0.711340i \(0.251911\pi\)
\(312\) 0 0
\(313\) 15.5147 8.95742i 0.876943 0.506303i 0.00729351 0.999973i \(-0.497678\pi\)
0.869649 + 0.493670i \(0.164345\pi\)
\(314\) 0 0
\(315\) 23.8702 18.4417i 1.34493 1.03907i
\(316\) 0 0
\(317\) 19.3275 11.1587i 1.08554 0.626736i 0.153153 0.988202i \(-0.451057\pi\)
0.932385 + 0.361467i \(0.117724\pi\)
\(318\) 0 0
\(319\) 0.888674 1.53923i 0.0497562 0.0861802i
\(320\) 0 0
\(321\) −7.00459 + 13.5515i −0.390958 + 0.756370i
\(322\) 0 0
\(323\) 0.255174i 0.0141983i
\(324\) 0 0
\(325\) 33.0836 + 19.1008i 1.83515 + 1.05952i
\(326\) 0 0
\(327\) −0.360721 7.74643i −0.0199479 0.428378i
\(328\) 0 0
\(329\) 26.8396 + 14.0572i 1.47971 + 0.774996i
\(330\) 0 0
\(331\) 7.05860 + 12.2259i 0.387976 + 0.671994i 0.992177 0.124838i \(-0.0398411\pi\)
−0.604201 + 0.796832i \(0.706508\pi\)
\(332\) 0 0
\(333\) 32.5957 3.04230i 1.78623 0.166717i
\(334\) 0 0
\(335\) −10.2134 −0.558018
\(336\) 0 0
\(337\) −18.4042 −1.00254 −0.501270 0.865291i \(-0.667134\pi\)
−0.501270 + 0.865291i \(0.667134\pi\)
\(338\) 0 0
\(339\) −3.73945 5.83237i −0.203099 0.316771i
\(340\) 0 0
\(341\) 1.40945 + 2.44124i 0.0763259 + 0.132200i
\(342\) 0 0
\(343\) 2.27965 + 18.3794i 0.123089 + 0.992396i
\(344\) 0 0
\(345\) 8.74557 0.407247i 0.470846 0.0219254i
\(346\) 0 0
\(347\) −27.6474 15.9623i −1.48419 0.856899i −0.484354 0.874872i \(-0.660945\pi\)
−0.999838 + 0.0179729i \(0.994279\pi\)
\(348\) 0 0
\(349\) 14.7367i 0.788840i 0.918930 + 0.394420i \(0.129055\pi\)
−0.918930 + 0.394420i \(0.870945\pi\)
\(350\) 0 0
\(351\) −20.8175 + 2.92510i −1.11116 + 0.156130i
\(352\) 0 0
\(353\) −13.5686 + 23.5016i −0.722185 + 1.25086i 0.237937 + 0.971281i \(0.423529\pi\)
−0.960122 + 0.279581i \(0.909804\pi\)
\(354\) 0 0
\(355\) 19.0551 11.0015i 1.01134 0.583899i
\(356\) 0 0
\(357\) −0.273352 0.390055i −0.0144673 0.0206439i
\(358\) 0 0
\(359\) 16.9479 9.78486i 0.894475 0.516425i 0.0190713 0.999818i \(-0.493929\pi\)
0.875404 + 0.483393i \(0.160596\pi\)
\(360\) 0 0
\(361\) −6.48633 + 11.2346i −0.341386 + 0.591297i
\(362\) 0 0
\(363\) −16.7287 8.64686i −0.878029 0.453842i
\(364\) 0 0
\(365\) 0.894875i 0.0468399i
\(366\) 0 0
\(367\) 1.16258 + 0.671213i 0.0606860 + 0.0350371i 0.530036 0.847975i \(-0.322178\pi\)
−0.469350 + 0.883012i \(0.655512\pi\)
\(368\) 0 0
\(369\) 7.70603 16.7790i 0.401160 0.873478i
\(370\) 0 0
\(371\) −15.5109 + 0.638387i −0.805285 + 0.0331434i
\(372\) 0 0
\(373\) −6.52378 11.2995i −0.337788 0.585066i 0.646228 0.763144i \(-0.276345\pi\)
−0.984016 + 0.178078i \(0.943012\pi\)
\(374\) 0 0
\(375\) 24.6172 15.7834i 1.27123 0.815053i
\(376\) 0 0
\(377\) −20.1178 −1.03612
\(378\) 0 0
\(379\) 20.0822 1.03156 0.515778 0.856722i \(-0.327503\pi\)
0.515778 + 0.856722i \(0.327503\pi\)
\(380\) 0 0
\(381\) −18.8383 + 12.0782i −0.965113 + 0.618786i
\(382\) 0 0
\(383\) 11.2613 + 19.5052i 0.575428 + 0.996670i 0.995995 + 0.0894085i \(0.0284977\pi\)
−0.420567 + 0.907261i \(0.638169\pi\)
\(384\) 0 0
\(385\) 1.92337 + 3.03581i 0.0980242 + 0.154719i
\(386\) 0 0
\(387\) −0.629479 + 1.37061i −0.0319982 + 0.0696723i
\(388\) 0 0
\(389\) 32.1899 + 18.5848i 1.63209 + 0.942289i 0.983447 + 0.181197i \(0.0579973\pi\)
0.648645 + 0.761091i \(0.275336\pi\)
\(390\) 0 0
\(391\) 0.138245i 0.00699136i
\(392\) 0 0
\(393\) −8.19750 4.23719i −0.413509 0.213738i
\(394\) 0 0
\(395\) 6.12795 10.6139i 0.308330 0.534044i
\(396\) 0 0
\(397\) −24.0288 + 13.8730i −1.20597 + 0.696268i −0.961877 0.273483i \(-0.911824\pi\)
−0.244095 + 0.969751i \(0.578491\pi\)
\(398\) 0 0
\(399\) 0.985032 + 11.2073i 0.0493133 + 0.561068i
\(400\) 0 0
\(401\) 19.7233 11.3872i 0.984933 0.568651i 0.0811773 0.996700i \(-0.474132\pi\)
0.903756 + 0.428048i \(0.140799\pi\)
\(402\) 0 0
\(403\) 15.9536 27.6324i 0.794704 1.37647i
\(404\) 0 0
\(405\) −11.3246 + 32.2738i −0.562725 + 1.60370i
\(406\) 0 0
\(407\) 3.90038i 0.193334i
\(408\) 0 0
\(409\) −22.6849 13.0972i −1.12170 0.647613i −0.179865 0.983691i \(-0.557566\pi\)
−0.941834 + 0.336078i \(0.890899\pi\)
\(410\) 0 0
\(411\) −8.73813 + 0.406900i −0.431020 + 0.0200709i
\(412\) 0 0
\(413\) −0.821144 19.9513i −0.0404059 0.981741i
\(414\) 0 0
\(415\) −17.2487 29.8757i −0.846707 1.46654i
\(416\) 0 0
\(417\) −19.8799 31.0065i −0.973524 1.51839i
\(418\) 0 0
\(419\) 8.93992 0.436744 0.218372 0.975866i \(-0.429925\pi\)
0.218372 + 0.975866i \(0.429925\pi\)
\(420\) 0 0
\(421\) −5.00735 −0.244043 −0.122022 0.992527i \(-0.538938\pi\)
−0.122022 + 0.992527i \(0.538938\pi\)
\(422\) 0 0
\(423\) −34.2060 + 3.19260i −1.66315 + 0.155229i
\(424\) 0 0
\(425\) −0.490719 0.849951i −0.0238034 0.0412287i
\(426\) 0 0
\(427\) −11.6298 + 22.2050i −0.562807 + 1.07458i
\(428\) 0 0
\(429\) −0.116503 2.50189i −0.00562482 0.120792i
\(430\) 0 0
\(431\) −5.62468 3.24741i −0.270931 0.156422i 0.358379 0.933576i \(-0.383329\pi\)
−0.629311 + 0.777154i \(0.716663\pi\)
\(432\) 0 0
\(433\) 1.05254i 0.0505818i 0.999680 + 0.0252909i \(0.00805120\pi\)
−0.999680 + 0.0252909i \(0.991949\pi\)
\(434\) 0 0
\(435\) −15.0296 + 29.0772i −0.720616 + 1.39414i
\(436\) 0 0
\(437\) −1.63271 + 2.82794i −0.0781032 + 0.135279i
\(438\) 0 0
\(439\) −25.8990 + 14.9528i −1.23609 + 0.713658i −0.968293 0.249817i \(-0.919630\pi\)
−0.267799 + 0.963475i \(0.586296\pi\)
\(440\) 0 0
\(441\) −13.5114 16.0761i −0.643400 0.765530i
\(442\) 0 0
\(443\) 26.7104 15.4212i 1.26905 0.732685i 0.294240 0.955732i \(-0.404934\pi\)
0.974808 + 0.223047i \(0.0716002\pi\)
\(444\) 0 0
\(445\) 12.9672 22.4599i 0.614707 1.06470i
\(446\) 0 0
\(447\) −9.68695 + 18.7409i −0.458177 + 0.886415i
\(448\) 0 0
\(449\) 36.6953i 1.73176i 0.500253 + 0.865879i \(0.333240\pi\)
−0.500253 + 0.865879i \(0.666760\pi\)
\(450\) 0 0
\(451\) 1.90510 + 1.09991i 0.0897076 + 0.0517927i
\(452\) 0 0
\(453\) 0.662071 + 14.2179i 0.0311068 + 0.668015i
\(454\) 0 0
\(455\) 18.8733 36.0351i 0.884795 1.68935i
\(456\) 0 0
\(457\) 11.8750 + 20.5681i 0.555489 + 0.962135i 0.997865 + 0.0653057i \(0.0208022\pi\)
−0.442376 + 0.896830i \(0.645864\pi\)
\(458\) 0 0
\(459\) 0.500745 + 0.202331i 0.0233728 + 0.00944400i
\(460\) 0 0
\(461\) 10.5938 0.493404 0.246702 0.969091i \(-0.420653\pi\)
0.246702 + 0.969091i \(0.420653\pi\)
\(462\) 0 0
\(463\) 0.367649 0.0170861 0.00854305 0.999964i \(-0.497281\pi\)
0.00854305 + 0.999964i \(0.497281\pi\)
\(464\) 0 0
\(465\) −28.0197 43.7021i −1.29938 2.02663i
\(466\) 0 0
\(467\) −15.7847 27.3399i −0.730428 1.26514i −0.956700 0.291075i \(-0.905987\pi\)
0.226272 0.974064i \(-0.427346\pi\)
\(468\) 0 0
\(469\) 0.292400 + 7.10444i 0.0135018 + 0.328053i
\(470\) 0 0
\(471\) 22.3964 1.04291i 1.03197 0.0480549i
\(472\) 0 0
\(473\) −0.155621 0.0898478i −0.00715546 0.00413120i
\(474\) 0 0
\(475\) 23.1821i 1.06367i
\(476\) 0 0
\(477\) 14.3604 10.1799i 0.657518 0.466104i
\(478\) 0 0
\(479\) 6.01497 10.4182i 0.274831 0.476022i −0.695261 0.718757i \(-0.744711\pi\)
0.970093 + 0.242735i \(0.0780447\pi\)
\(480\) 0 0
\(481\) 38.2337 22.0742i 1.74331 1.00650i
\(482\) 0 0
\(483\) −0.533658 6.07176i −0.0242823 0.276275i
\(484\) 0 0
\(485\) 16.9247 9.77148i 0.768511 0.443700i
\(486\) 0 0
\(487\) −9.47737 + 16.4153i −0.429461 + 0.743848i −0.996825 0.0796188i \(-0.974630\pi\)
0.567365 + 0.823467i \(0.307963\pi\)
\(488\) 0 0
\(489\) −3.36159 1.73756i −0.152016 0.0785753i
\(490\) 0 0
\(491\) 15.8373i 0.714727i 0.933965 + 0.357364i \(0.116324\pi\)
−0.933965 + 0.357364i \(0.883676\pi\)
\(492\) 0 0
\(493\) 0.447602 + 0.258423i 0.0201590 + 0.0116388i
\(494\) 0 0
\(495\) −3.70313 1.70073i −0.166443 0.0764419i
\(496\) 0 0
\(497\) −8.19817 12.9398i −0.367738 0.580429i
\(498\) 0 0
\(499\) 10.0988 + 17.4916i 0.452084 + 0.783033i 0.998515 0.0544710i \(-0.0173473\pi\)
−0.546431 + 0.837504i \(0.684014\pi\)
\(500\) 0 0
\(501\) −0.677418 + 0.434329i −0.0302648 + 0.0194044i
\(502\) 0 0
\(503\) −36.8663 −1.64379 −0.821893 0.569641i \(-0.807082\pi\)
−0.821893 + 0.569641i \(0.807082\pi\)
\(504\) 0 0
\(505\) 48.9400 2.17780
\(506\) 0 0
\(507\) −4.91034 + 3.14829i −0.218076 + 0.139820i
\(508\) 0 0
\(509\) −5.13197 8.88884i −0.227471 0.393991i 0.729587 0.683888i \(-0.239712\pi\)
−0.957058 + 0.289897i \(0.906379\pi\)
\(510\) 0 0
\(511\) 0.622475 0.0256194i 0.0275367 0.00113334i
\(512\) 0 0
\(513\) −7.85364 10.0528i −0.346747 0.443842i
\(514\) 0 0
\(515\) 18.5502 + 10.7100i 0.817419 + 0.471937i
\(516\) 0 0
\(517\) 4.09307i 0.180013i
\(518\) 0 0
\(519\) 14.2353 + 7.35804i 0.624859 + 0.322982i
\(520\) 0 0
\(521\) 7.98887 13.8371i 0.349999 0.606216i −0.636250 0.771483i \(-0.719515\pi\)
0.986249 + 0.165267i \(0.0528486\pi\)
\(522\) 0 0
\(523\) −0.676700 + 0.390693i −0.0295900 + 0.0170838i −0.514722 0.857357i \(-0.672105\pi\)
0.485132 + 0.874441i \(0.338772\pi\)
\(524\) 0 0
\(525\) −24.8335 35.4358i −1.08382 1.54654i
\(526\) 0 0
\(527\) −0.709904 + 0.409863i −0.0309239 + 0.0178539i
\(528\) 0 0
\(529\) −10.6155 + 18.3865i −0.461541 + 0.799413i
\(530\) 0 0
\(531\) 13.0942 + 18.4715i 0.568238 + 0.801595i
\(532\) 0 0
\(533\) 24.8998i 1.07853i
\(534\) 0 0
\(535\) 28.9865 + 16.7354i 1.25320 + 0.723534i
\(536\) 0 0
\(537\) −3.53808 + 0.164754i −0.152679 + 0.00710967i
\(538\) 0 0
\(539\) 2.05664 1.42481i 0.0885859 0.0613709i
\(540\) 0 0
\(541\) 3.63362 + 6.29362i 0.156222 + 0.270584i 0.933503 0.358569i \(-0.116735\pi\)
−0.777282 + 0.629153i \(0.783402\pi\)
\(542\) 0 0
\(543\) −16.4716 25.6905i −0.706863 1.10249i
\(544\) 0 0
\(545\) −17.0150 −0.728845
\(546\) 0 0
\(547\) −41.2546 −1.76392 −0.881960 0.471325i \(-0.843776\pi\)
−0.881960 + 0.471325i \(0.843776\pi\)
\(548\) 0 0
\(549\) −2.64131 28.2994i −0.112729 1.20779i
\(550\) 0 0
\(551\) −6.10409 10.5726i −0.260043 0.450408i
\(552\) 0 0
\(553\) −7.55847 3.95873i −0.321419 0.168342i
\(554\) 0 0
\(555\) −3.34121 71.7521i −0.141826 3.04571i
\(556\) 0 0
\(557\) −5.48798 3.16849i −0.232533 0.134253i 0.379207 0.925312i \(-0.376197\pi\)
−0.611740 + 0.791059i \(0.709530\pi\)
\(558\) 0 0
\(559\) 2.03398i 0.0860281i
\(560\) 0 0
\(561\) −0.0295459 + 0.0571611i −0.00124743 + 0.00241335i
\(562\) 0 0
\(563\) 7.73130 13.3910i 0.325836 0.564364i −0.655846 0.754895i \(-0.727688\pi\)
0.981681 + 0.190531i \(0.0610211\pi\)
\(564\) 0 0
\(565\) −13.1647 + 7.60067i −0.553845 + 0.319763i
\(566\) 0 0
\(567\) 22.7739 + 6.95343i 0.956413 + 0.292017i
\(568\) 0 0
\(569\) 10.2364 5.90999i 0.429132 0.247760i −0.269845 0.962904i \(-0.586972\pi\)
0.698977 + 0.715144i \(0.253639\pi\)
\(570\) 0 0
\(571\) 18.0386 31.2438i 0.754892 1.30751i −0.190536 0.981680i \(-0.561023\pi\)
0.945428 0.325831i \(-0.105644\pi\)
\(572\) 0 0
\(573\) 17.8905 34.6119i 0.747385 1.44593i
\(574\) 0 0
\(575\) 12.5593i 0.523759i
\(576\) 0 0
\(577\) −20.4253 11.7926i −0.850316 0.490930i 0.0104412 0.999945i \(-0.496676\pi\)
−0.860758 + 0.509015i \(0.830010\pi\)
\(578\) 0 0
\(579\) 0.776646 + 16.6784i 0.0322763 + 0.693130i
\(580\) 0 0
\(581\) −20.2877 + 12.8535i −0.841676 + 0.533254i
\(582\) 0 0
\(583\) 1.04860 + 1.81623i 0.0434285 + 0.0752204i
\(584\) 0 0
\(585\) 4.28642 + 45.9254i 0.177222 + 1.89878i
\(586\) 0 0
\(587\) −0.287490 −0.0118660 −0.00593298 0.999982i \(-0.501889\pi\)
−0.00593298 + 0.999982i \(0.501889\pi\)
\(588\) 0 0
\(589\) 19.3623 0.797812
\(590\) 0 0
\(591\) −14.3735 22.4182i −0.591247 0.922160i
\(592\) 0 0
\(593\) −5.71589 9.90021i −0.234723 0.406553i 0.724469 0.689308i \(-0.242085\pi\)
−0.959192 + 0.282755i \(0.908752\pi\)
\(594\) 0 0
\(595\) −0.882803 + 0.559311i −0.0361914 + 0.0229295i
\(596\) 0 0
\(597\) 7.93076 0.369304i 0.324584 0.0151146i
\(598\) 0 0
\(599\) −18.7842 10.8451i −0.767502 0.443117i 0.0644810 0.997919i \(-0.479461\pi\)
−0.831983 + 0.554802i \(0.812794\pi\)
\(600\) 0 0
\(601\) 23.7036i 0.966889i 0.875375 + 0.483445i \(0.160615\pi\)
−0.875375 + 0.483445i \(0.839385\pi\)
\(602\) 0 0
\(603\) −4.66268 6.57749i −0.189879 0.267856i
\(604\) 0 0
\(605\) −20.6591 + 35.7826i −0.839912 + 1.45477i
\(606\) 0 0
\(607\) 18.5031 10.6828i 0.751017 0.433600i −0.0750445 0.997180i \(-0.523910\pi\)
0.826061 + 0.563580i \(0.190577\pi\)
\(608\) 0 0
\(609\) 20.6564 + 9.62217i 0.837039 + 0.389910i
\(610\) 0 0
\(611\) −40.1225 + 23.1647i −1.62318 + 0.937145i
\(612\) 0 0
\(613\) −19.8248 + 34.3376i −0.800716 + 1.38688i 0.118429 + 0.992962i \(0.462214\pi\)
−0.919145 + 0.393918i \(0.871119\pi\)
\(614\) 0 0
\(615\) −35.9888 18.6022i −1.45121 0.750112i
\(616\) 0 0
\(617\) 28.6296i 1.15258i 0.817244 + 0.576292i \(0.195501\pi\)
−0.817244 + 0.576292i \(0.804499\pi\)
\(618\) 0 0
\(619\) 32.9529 + 19.0254i 1.32449 + 0.764694i 0.984441 0.175714i \(-0.0562235\pi\)
0.340047 + 0.940408i \(0.389557\pi\)
\(620\) 0 0
\(621\) 4.25485 + 5.44628i 0.170741 + 0.218552i
\(622\) 0 0
\(623\) −15.9944 8.37701i −0.640801 0.335618i
\(624\) 0 0
\(625\) −8.47450 14.6783i −0.338980 0.587130i
\(626\) 0 0
\(627\) 1.27948 0.820342i 0.0510974 0.0327613i
\(628\) 0 0
\(629\) −1.13422 −0.0452242
\(630\) 0 0
\(631\) 3.65235 0.145398 0.0726989 0.997354i \(-0.476839\pi\)
0.0726989 + 0.997354i \(0.476839\pi\)
\(632\) 0 0
\(633\) 1.26912 0.813704i 0.0504432 0.0323418i
\(634\) 0 0
\(635\) 24.5498 + 42.5215i 0.974228 + 1.68741i
\(636\) 0 0
\(637\) −25.6064 12.0966i −1.01456 0.479286i
\(638\) 0 0
\(639\) 15.7842 + 7.24916i 0.624413 + 0.286772i
\(640\) 0 0
\(641\) 21.2563 + 12.2723i 0.839574 + 0.484728i 0.857119 0.515118i \(-0.172252\pi\)
−0.0175456 + 0.999846i \(0.505585\pi\)
\(642\) 0 0
\(643\) 27.3936i 1.08030i −0.841569 0.540149i \(-0.818368\pi\)
0.841569 0.540149i \(-0.181632\pi\)
\(644\) 0 0
\(645\) 2.93980 + 1.51955i 0.115754 + 0.0598321i
\(646\) 0 0
\(647\) 16.1181 27.9173i 0.633667 1.09754i −0.353129 0.935575i \(-0.614882\pi\)
0.986796 0.161969i \(-0.0517845\pi\)
\(648\) 0 0
\(649\) −2.33618 + 1.34879i −0.0917029 + 0.0529447i
\(650\) 0 0
\(651\) −29.5970 + 20.7417i −1.16000 + 0.812930i
\(652\) 0 0
\(653\) −13.5027 + 7.79579i −0.528401 + 0.305073i −0.740365 0.672205i \(-0.765347\pi\)
0.211964 + 0.977278i \(0.432014\pi\)
\(654\) 0 0
\(655\) −10.1235 + 17.5344i −0.395558 + 0.685126i
\(656\) 0 0
\(657\) −0.576304 + 0.408533i −0.0224838 + 0.0159384i
\(658\) 0 0
\(659\) 35.1100i 1.36769i 0.729626 + 0.683847i \(0.239694\pi\)
−0.729626 + 0.683847i \(0.760306\pi\)
\(660\) 0 0
\(661\) 6.96082 + 4.01883i 0.270745 + 0.156314i 0.629226 0.777222i \(-0.283372\pi\)
−0.358481 + 0.933537i \(0.616705\pi\)
\(662\) 0 0
\(663\) 0.727541 0.0338787i 0.0282553 0.00131574i
\(664\) 0 0
\(665\) 24.6642 1.01511i 0.956436 0.0393644i
\(666\) 0 0
\(667\) 3.30700 + 5.72789i 0.128047 + 0.221785i
\(668\) 0 0
\(669\) 1.13467 + 1.76974i 0.0438690 + 0.0684220i
\(670\) 0 0
\(671\) 3.38629 0.130726
\(672\) 0 0
\(673\) 28.1744 1.08604 0.543022 0.839719i \(-0.317280\pi\)
0.543022 + 0.839719i \(0.317280\pi\)
\(674\) 0 0
\(675\) 45.4917 + 18.3814i 1.75098 + 0.707499i
\(676\) 0 0
\(677\) −17.3844 30.1106i −0.668135 1.15724i −0.978425 0.206602i \(-0.933760\pi\)
0.310290 0.950642i \(-0.399574\pi\)
\(678\) 0 0
\(679\) −7.28158 11.4931i −0.279441 0.441063i
\(680\) 0 0
\(681\) 1.07510 + 23.0877i 0.0411980 + 0.884721i
\(682\) 0 0
\(683\) 40.7393 + 23.5209i 1.55885 + 0.900001i 0.997368 + 0.0725098i \(0.0231009\pi\)
0.561479 + 0.827491i \(0.310232\pi\)
\(684\) 0 0
\(685\) 19.1933i 0.733339i
\(686\) 0 0
\(687\) 8.82192 17.0674i 0.336577 0.651161i
\(688\) 0 0
\(689\) 11.8691 20.5579i 0.452177 0.783194i
\(690\) 0 0
\(691\) 27.1758 15.6900i 1.03382 0.596874i 0.115740 0.993279i \(-0.463076\pi\)
0.918076 + 0.396406i \(0.129743\pi\)
\(692\) 0 0
\(693\) −1.07701 + 2.62459i −0.0409121 + 0.0996998i
\(694\) 0 0
\(695\) −69.9874 + 40.4073i −2.65478 + 1.53274i
\(696\) 0 0
\(697\) −0.319850 + 0.553997i −0.0121152 + 0.0209841i
\(698\) 0 0
\(699\) −6.50569 + 12.5863i −0.246068 + 0.476057i
\(700\) 0 0
\(701\) 29.9818i 1.13240i 0.824268 + 0.566199i \(0.191587\pi\)
−0.824268 + 0.566199i \(0.808413\pi\)
\(702\) 0 0
\(703\) 23.2015 + 13.3954i 0.875061 + 0.505217i
\(704\) 0 0
\(705\) 3.50628 + 75.2968i 0.132054 + 2.83584i
\(706\) 0 0
\(707\) −1.40111 34.0427i −0.0526940 1.28031i
\(708\) 0 0
\(709\) −11.5451 19.9968i −0.433587 0.750995i 0.563592 0.826053i \(-0.309419\pi\)
−0.997179 + 0.0750583i \(0.976086\pi\)
\(710\) 0 0
\(711\) 9.63298 0.899089i 0.361265 0.0337185i
\(712\) 0 0
\(713\) −10.4899 −0.392849
\(714\) 0 0
\(715\) −5.49540 −0.205516
\(716\) 0 0
\(717\) 21.1227 + 32.9448i 0.788841 + 1.23035i
\(718\) 0 0
\(719\) 22.5340 + 39.0300i 0.840376 + 1.45557i 0.889577 + 0.456785i \(0.150999\pi\)
−0.0492012 + 0.998789i \(0.515668\pi\)
\(720\) 0 0
\(721\) 6.91877 13.2101i 0.257669 0.491971i
\(722\) 0 0
\(723\) 8.47337 0.394571i 0.315128 0.0146743i
\(724\) 0 0
\(725\) 40.6638 + 23.4772i 1.51022 + 0.871923i
\(726\) 0 0
\(727\) 3.14662i 0.116702i −0.998296 0.0583508i \(-0.981416\pi\)
0.998296 0.0583508i \(-0.0185842\pi\)
\(728\) 0 0
\(729\) −25.9545 + 7.44070i −0.961278 + 0.275582i
\(730\) 0 0
\(731\) 0.0261274 0.0452541i 0.000966358 0.00167378i
\(732\) 0 0
\(733\) 14.9590 8.63657i 0.552522 0.318999i −0.197616 0.980279i \(-0.563320\pi\)
0.750139 + 0.661281i \(0.229987\pi\)
\(734\) 0 0
\(735\) −36.6138 + 27.9729i −1.35052 + 1.03180i
\(736\) 0 0
\(737\) 0.831885 0.480289i 0.0306429 0.0176917i
\(738\) 0 0
\(739\) 0.996550 1.72607i 0.0366587 0.0634947i −0.847114 0.531411i \(-0.821662\pi\)
0.883773 + 0.467917i \(0.154995\pi\)
\(740\) 0 0
\(741\) −15.2827 7.89942i −0.561423 0.290192i
\(742\) 0 0
\(743\) 5.54435i 0.203402i −0.994815 0.101701i \(-0.967571\pi\)
0.994815 0.101701i \(-0.0324286\pi\)
\(744\) 0 0
\(745\) 40.0867 + 23.1441i 1.46866 + 0.847934i
\(746\) 0 0
\(747\) 11.3656 24.7473i 0.415846 0.905456i
\(748\) 0 0
\(749\) 10.8113 20.6422i 0.395036 0.754248i
\(750\) 0 0
\(751\) −22.0897 38.2605i −0.806065 1.39615i −0.915569 0.402160i \(-0.868260\pi\)
0.109504 0.993986i \(-0.465074\pi\)
\(752\) 0 0
\(753\) −13.3832 + 8.58069i −0.487711 + 0.312698i
\(754\) 0 0
\(755\) 31.2296 1.13656
\(756\) 0 0
\(757\) 10.6250 0.386172 0.193086 0.981182i \(-0.438150\pi\)
0.193086 + 0.981182i \(0.438150\pi\)
\(758\) 0 0
\(759\) −0.693179 + 0.444434i −0.0251608 + 0.0161319i
\(760\) 0 0
\(761\) −13.9084 24.0900i −0.504178 0.873262i −0.999988 0.00483132i \(-0.998462\pi\)
0.495810 0.868431i \(-0.334871\pi\)
\(762\) 0 0
\(763\) 0.487125 + 11.8357i 0.0176351 + 0.428480i
\(764\) 0 0
\(765\) 0.494565 1.07686i 0.0178811 0.0389339i
\(766\) 0 0
\(767\) 26.4432 + 15.2670i 0.954809 + 0.551259i
\(768\) 0 0
\(769\) 10.2707i 0.370369i 0.982704 + 0.185185i \(0.0592883\pi\)
−0.982704 + 0.185185i \(0.940712\pi\)
\(770\) 0 0
\(771\) 19.4196 + 10.0377i 0.699379 + 0.361500i
\(772\) 0 0
\(773\) −20.2953 + 35.1525i −0.729972 + 1.26435i 0.226923 + 0.973913i \(0.427133\pi\)
−0.956895 + 0.290435i \(0.906200\pi\)
\(774\) 0 0
\(775\) −64.4933 + 37.2352i −2.31667 + 1.33753i
\(776\) 0 0
\(777\) −49.8151 + 4.37834i −1.78711 + 0.157072i
\(778\) 0 0
\(779\) 13.0857 7.55502i 0.468843 0.270687i
\(780\) 0 0
\(781\) −1.03470 + 1.79215i −0.0370244 + 0.0641282i
\(782\) 0 0
\(783\) −25.5873 + 3.59530i −0.914415 + 0.128486i
\(784\) 0 0
\(785\) 49.1938i 1.75580i
\(786\) 0 0
\(787\) −22.6225 13.0611i −0.806404 0.465578i 0.0393014 0.999227i \(-0.487487\pi\)
−0.845706 + 0.533650i \(0.820820\pi\)
\(788\) 0 0
\(789\) 50.4432 2.34894i 1.79583 0.0836246i