Properties

Label 252.2.w.a.5.2
Level $252$
Weight $2$
Character 252.5
Analytic conductor $2.012$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.w (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} - 156 x^{7} + 558 x^{6} - 837 x^{5} + 1782 x^{4} - 4131 x^{3} + 3645 x^{2} - 4374 x + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 5.2
Root \(-1.61108 + 0.635951i\) of defining polynomial
Character \(\chi\) \(=\) 252.5
Dual form 252.2.w.a.101.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.43204 - 0.974295i) q^{3} +(1.09150 + 1.89054i) q^{5} +(-1.25859 + 2.32722i) q^{7} +(1.10150 + 2.79047i) q^{9} +O(q^{10})\) \(q+(-1.43204 - 0.974295i) q^{3} +(1.09150 + 1.89054i) q^{5} +(-1.25859 + 2.32722i) q^{7} +(1.10150 + 2.79047i) q^{9} +(-1.26889 - 0.732592i) q^{11} +(2.92752 + 1.69021i) q^{13} +(0.278862 - 3.77077i) q^{15} +(1.32136 + 2.28866i) q^{17} +(6.87816 + 3.97111i) q^{19} +(4.06975 - 2.10644i) q^{21} +(-3.47245 + 2.00482i) q^{23} +(0.117249 - 0.203081i) q^{25} +(1.14134 - 5.06925i) q^{27} +(-6.71261 + 3.87553i) q^{29} -0.706968i q^{31} +(1.10334 + 2.28537i) q^{33} +(-5.77345 + 0.160752i) q^{35} +(1.41738 - 2.45498i) q^{37} +(-2.54558 - 5.27272i) q^{39} +(3.74173 - 6.48086i) q^{41} +(-1.27112 - 2.20164i) q^{43} +(-4.07319 + 5.12822i) q^{45} -12.5508 q^{47} +(-3.83190 - 5.85803i) q^{49} +(0.337586 - 4.56485i) q^{51} +(-2.41675 + 1.39531i) q^{53} -3.19850i q^{55} +(-5.98079 - 12.3881i) q^{57} +13.4330 q^{59} +7.79493i q^{61} +(-7.88036 - 0.948624i) q^{63} +7.37945i q^{65} +5.84058 q^{67} +(6.92598 + 0.512200i) q^{69} -11.6854i q^{71} +(-3.95924 + 2.28587i) q^{73} +(-0.365767 + 0.176586i) q^{75} +(3.30191 - 2.03094i) q^{77} +9.38377 q^{79} +(-6.57340 + 6.14739i) q^{81} +(1.70847 + 2.95917i) q^{83} +(-2.88452 + 4.99614i) q^{85} +(13.3887 + 0.990137i) q^{87} +(4.61937 - 8.00099i) q^{89} +(-7.61803 + 4.68571i) q^{91} +(-0.688796 + 1.01241i) q^{93} +17.3379i q^{95} +(6.38394 - 3.68577i) q^{97} +(0.646596 - 4.34773i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - q^{7} + 6q^{9} + O(q^{10}) \) \( 16q - q^{7} + 6q^{9} - 6q^{11} - 3q^{13} - 3q^{15} + 9q^{17} + 6q^{21} + 21q^{23} - 8q^{25} + 9q^{27} + 6q^{29} - 15q^{35} + q^{37} - 3q^{39} - 6q^{41} - 2q^{43} - 30q^{45} - 36q^{47} - 5q^{49} - 33q^{51} + 15q^{57} - 30q^{59} - 15q^{63} + 14q^{67} + 21q^{69} - 57q^{75} + 3q^{77} + 2q^{79} + 18q^{81} + 6q^{85} + 48q^{87} + 21q^{89} + 9q^{91} + 21q^{93} - 3q^{97} - 9q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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
\(3\) −1.43204 0.974295i −0.826791 0.562509i
\(4\) 0 0
\(5\) 1.09150 + 1.89054i 0.488134 + 0.845473i 0.999907 0.0136476i \(-0.00434429\pi\)
−0.511773 + 0.859121i \(0.671011\pi\)
\(6\) 0 0
\(7\) −1.25859 + 2.32722i −0.475703 + 0.879606i
\(8\) 0 0
\(9\) 1.10150 + 2.79047i 0.367166 + 0.930155i
\(10\) 0 0
\(11\) −1.26889 0.732592i −0.382584 0.220885i 0.296358 0.955077i \(-0.404228\pi\)
−0.678942 + 0.734192i \(0.737561\pi\)
\(12\) 0 0
\(13\) 2.92752 + 1.69021i 0.811948 + 0.468779i 0.847632 0.530585i \(-0.178028\pi\)
−0.0356837 + 0.999363i \(0.511361\pi\)
\(14\) 0 0
\(15\) 0.278862 3.77077i 0.0720017 0.973610i
\(16\) 0 0
\(17\) 1.32136 + 2.28866i 0.320476 + 0.555081i 0.980586 0.196088i \(-0.0628238\pi\)
−0.660110 + 0.751169i \(0.729491\pi\)
\(18\) 0 0
\(19\) 6.87816 + 3.97111i 1.57796 + 0.911034i 0.995144 + 0.0984279i \(0.0313814\pi\)
0.582813 + 0.812606i \(0.301952\pi\)
\(20\) 0 0
\(21\) 4.06975 2.10644i 0.888093 0.459663i
\(22\) 0 0
\(23\) −3.47245 + 2.00482i −0.724056 + 0.418034i −0.816244 0.577708i \(-0.803947\pi\)
0.0921879 + 0.995742i \(0.470614\pi\)
\(24\) 0 0
\(25\) 0.117249 0.203081i 0.0234498 0.0406163i
\(26\) 0 0
\(27\) 1.14134 5.06925i 0.219651 0.975578i
\(28\) 0 0
\(29\) −6.71261 + 3.87553i −1.24650 + 0.719667i −0.970410 0.241464i \(-0.922372\pi\)
−0.276091 + 0.961132i \(0.589039\pi\)
\(30\) 0 0
\(31\) 0.706968i 0.126975i −0.997983 0.0634876i \(-0.979778\pi\)
0.997983 0.0634876i \(-0.0202223\pi\)
\(32\) 0 0
\(33\) 1.10334 + 2.28537i 0.192067 + 0.397833i
\(34\) 0 0
\(35\) −5.77345 + 0.160752i −0.975890 + 0.0271721i
\(36\) 0 0
\(37\) 1.41738 2.45498i 0.233016 0.403596i −0.725678 0.688034i \(-0.758474\pi\)
0.958694 + 0.284438i \(0.0918071\pi\)
\(38\) 0 0
\(39\) −2.54558 5.27272i −0.407619 0.844310i
\(40\) 0 0
\(41\) 3.74173 6.48086i 0.584360 1.01214i −0.410595 0.911818i \(-0.634679\pi\)
0.994955 0.100323i \(-0.0319876\pi\)
\(42\) 0 0
\(43\) −1.27112 2.20164i −0.193844 0.335748i 0.752677 0.658390i \(-0.228762\pi\)
−0.946521 + 0.322642i \(0.895429\pi\)
\(44\) 0 0
\(45\) −4.07319 + 5.12822i −0.607195 + 0.764470i
\(46\) 0 0
\(47\) −12.5508 −1.83072 −0.915358 0.402640i \(-0.868093\pi\)
−0.915358 + 0.402640i \(0.868093\pi\)
\(48\) 0 0
\(49\) −3.83190 5.85803i −0.547414 0.836862i
\(50\) 0 0
\(51\) 0.337586 4.56485i 0.0472715 0.639206i
\(52\) 0 0
\(53\) −2.41675 + 1.39531i −0.331966 + 0.191661i −0.656714 0.754140i \(-0.728054\pi\)
0.324748 + 0.945801i \(0.394721\pi\)
\(54\) 0 0
\(55\) 3.19850i 0.431286i
\(56\) 0 0
\(57\) −5.98079 12.3881i −0.792176 1.64085i
\(58\) 0 0
\(59\) 13.4330 1.74883 0.874414 0.485180i \(-0.161246\pi\)
0.874414 + 0.485180i \(0.161246\pi\)
\(60\) 0 0
\(61\) 7.79493i 0.998039i 0.866591 + 0.499020i \(0.166306\pi\)
−0.866591 + 0.499020i \(0.833694\pi\)
\(62\) 0 0
\(63\) −7.88036 0.948624i −0.992832 0.119515i
\(64\) 0 0
\(65\) 7.37945i 0.915308i
\(66\) 0 0
\(67\) 5.84058 0.713541 0.356770 0.934192i \(-0.383878\pi\)
0.356770 + 0.934192i \(0.383878\pi\)
\(68\) 0 0
\(69\) 6.92598 + 0.512200i 0.833791 + 0.0616616i
\(70\) 0 0
\(71\) 11.6854i 1.38680i −0.720554 0.693398i \(-0.756113\pi\)
0.720554 0.693398i \(-0.243887\pi\)
\(72\) 0 0
\(73\) −3.95924 + 2.28587i −0.463394 + 0.267541i −0.713470 0.700685i \(-0.752878\pi\)
0.250076 + 0.968226i \(0.419544\pi\)
\(74\) 0 0
\(75\) −0.365767 + 0.176586i −0.0422351 + 0.0203904i
\(76\) 0 0
\(77\) 3.30191 2.03094i 0.376288 0.231448i
\(78\) 0 0
\(79\) 9.38377 1.05576 0.527879 0.849320i \(-0.322988\pi\)
0.527879 + 0.849320i \(0.322988\pi\)
\(80\) 0 0
\(81\) −6.57340 + 6.14739i −0.730378 + 0.683043i
\(82\) 0 0
\(83\) 1.70847 + 2.95917i 0.187529 + 0.324811i 0.944426 0.328724i \(-0.106619\pi\)
−0.756896 + 0.653535i \(0.773285\pi\)
\(84\) 0 0
\(85\) −2.88452 + 4.99614i −0.312871 + 0.541908i
\(86\) 0 0
\(87\) 13.3887 + 0.990137i 1.43541 + 0.106154i
\(88\) 0 0
\(89\) 4.61937 8.00099i 0.489653 0.848103i −0.510276 0.860010i \(-0.670457\pi\)
0.999929 + 0.0119070i \(0.00379021\pi\)
\(90\) 0 0
\(91\) −7.61803 + 4.68571i −0.798586 + 0.491196i
\(92\) 0 0
\(93\) −0.688796 + 1.01241i −0.0714248 + 0.104982i
\(94\) 0 0
\(95\) 17.3379i 1.77883i
\(96\) 0 0
\(97\) 6.38394 3.68577i 0.648191 0.374233i −0.139572 0.990212i \(-0.544573\pi\)
0.787763 + 0.615979i \(0.211239\pi\)
\(98\) 0 0
\(99\) 0.646596 4.34773i 0.0649853 0.436964i
\(100\) 0 0
\(101\) 3.96357 6.86510i 0.394390 0.683103i −0.598633 0.801023i \(-0.704289\pi\)
0.993023 + 0.117920i \(0.0376226\pi\)
\(102\) 0 0
\(103\) −3.26825 + 1.88693i −0.322031 + 0.185924i −0.652297 0.757963i \(-0.726195\pi\)
0.330267 + 0.943888i \(0.392861\pi\)
\(104\) 0 0
\(105\) 8.42445 + 5.39483i 0.822142 + 0.526482i
\(106\) 0 0
\(107\) −6.88241 3.97356i −0.665347 0.384138i 0.128964 0.991649i \(-0.458835\pi\)
−0.794311 + 0.607511i \(0.792168\pi\)
\(108\) 0 0
\(109\) 0.505142 + 0.874932i 0.0483838 + 0.0838033i 0.889203 0.457513i \(-0.151260\pi\)
−0.840819 + 0.541316i \(0.817926\pi\)
\(110\) 0 0
\(111\) −4.42163 + 2.13469i −0.419682 + 0.202616i
\(112\) 0 0
\(113\) −10.5557 6.09431i −0.992992 0.573304i −0.0868250 0.996224i \(-0.527672\pi\)
−0.906167 + 0.422919i \(0.861005\pi\)
\(114\) 0 0
\(115\) −7.58037 4.37653i −0.706873 0.408113i
\(116\) 0 0
\(117\) −1.49180 + 10.0309i −0.137917 + 0.927358i
\(118\) 0 0
\(119\) −6.98925 + 0.194605i −0.640703 + 0.0178394i
\(120\) 0 0
\(121\) −4.42662 7.66713i −0.402420 0.697012i
\(122\) 0 0
\(123\) −11.6726 + 5.63533i −1.05248 + 0.508121i
\(124\) 0 0
\(125\) 11.4269 1.02206
\(126\) 0 0
\(127\) 6.79350 0.602826 0.301413 0.953494i \(-0.402542\pi\)
0.301413 + 0.953494i \(0.402542\pi\)
\(128\) 0 0
\(129\) −0.324751 + 4.39130i −0.0285927 + 0.386632i
\(130\) 0 0
\(131\) 6.86790 + 11.8956i 0.600051 + 1.03932i 0.992813 + 0.119679i \(0.0381865\pi\)
−0.392761 + 0.919640i \(0.628480\pi\)
\(132\) 0 0
\(133\) −17.8984 + 11.0090i −1.55199 + 0.954600i
\(134\) 0 0
\(135\) 10.8294 3.37535i 0.932045 0.290504i
\(136\) 0 0
\(137\) 17.4028 + 10.0475i 1.48682 + 0.858416i 0.999887 0.0150235i \(-0.00478229\pi\)
0.486933 + 0.873439i \(0.338116\pi\)
\(138\) 0 0
\(139\) 8.51403 + 4.91558i 0.722151 + 0.416934i 0.815544 0.578695i \(-0.196438\pi\)
−0.0933930 + 0.995629i \(0.529771\pi\)
\(140\) 0 0
\(141\) 17.9732 + 12.2281i 1.51362 + 1.02980i
\(142\) 0 0
\(143\) −2.47646 4.28936i −0.207092 0.358694i
\(144\) 0 0
\(145\) −14.6536 8.46029i −1.21692 0.702589i
\(146\) 0 0
\(147\) −0.220003 + 12.1224i −0.0181456 + 0.999835i
\(148\) 0 0
\(149\) 17.3512 10.0177i 1.42146 0.820682i 0.425038 0.905175i \(-0.360261\pi\)
0.996424 + 0.0844939i \(0.0269274\pi\)
\(150\) 0 0
\(151\) 11.1168 19.2549i 0.904675 1.56694i 0.0833218 0.996523i \(-0.473447\pi\)
0.821353 0.570420i \(-0.193220\pi\)
\(152\) 0 0
\(153\) −4.93094 + 6.20815i −0.398643 + 0.501899i
\(154\) 0 0
\(155\) 1.33655 0.771657i 0.107354 0.0619810i
\(156\) 0 0
\(157\) 8.02869i 0.640759i −0.947289 0.320380i \(-0.896189\pi\)
0.947289 0.320380i \(-0.103811\pi\)
\(158\) 0 0
\(159\) 4.82034 + 0.356480i 0.382278 + 0.0282707i
\(160\) 0 0
\(161\) −0.295263 10.6044i −0.0232700 0.835744i
\(162\) 0 0
\(163\) −6.22604 + 10.7838i −0.487661 + 0.844654i −0.999899 0.0141893i \(-0.995483\pi\)
0.512238 + 0.858844i \(0.328817\pi\)
\(164\) 0 0
\(165\) −3.11628 + 4.58039i −0.242602 + 0.356583i
\(166\) 0 0
\(167\) −9.85984 + 17.0777i −0.762978 + 1.32152i 0.178332 + 0.983970i \(0.442930\pi\)
−0.941309 + 0.337546i \(0.890403\pi\)
\(168\) 0 0
\(169\) −0.786412 1.36211i −0.0604933 0.104777i
\(170\) 0 0
\(171\) −3.50495 + 23.5674i −0.268030 + 1.80225i
\(172\) 0 0
\(173\) 1.82747 0.138940 0.0694699 0.997584i \(-0.477869\pi\)
0.0694699 + 0.997584i \(0.477869\pi\)
\(174\) 0 0
\(175\) 0.325046 + 0.528460i 0.0245712 + 0.0399479i
\(176\) 0 0
\(177\) −19.2367 13.0877i −1.44592 0.983732i
\(178\) 0 0
\(179\) 12.1182 6.99645i 0.905757 0.522939i 0.0266934 0.999644i \(-0.491502\pi\)
0.879064 + 0.476705i \(0.158169\pi\)
\(180\) 0 0
\(181\) 16.3594i 1.21599i −0.793942 0.607994i \(-0.791975\pi\)
0.793942 0.607994i \(-0.208025\pi\)
\(182\) 0 0
\(183\) 7.59456 11.1627i 0.561406 0.825170i
\(184\) 0 0
\(185\) 6.18830 0.454973
\(186\) 0 0
\(187\) 3.87206i 0.283153i
\(188\) 0 0
\(189\) 10.3608 + 9.03627i 0.753636 + 0.657292i
\(190\) 0 0
\(191\) 13.6631i 0.988624i 0.869285 + 0.494312i \(0.164580\pi\)
−0.869285 + 0.494312i \(0.835420\pi\)
\(192\) 0 0
\(193\) −4.37769 −0.315113 −0.157557 0.987510i \(-0.550362\pi\)
−0.157557 + 0.987510i \(0.550362\pi\)
\(194\) 0 0
\(195\) 7.18976 10.5677i 0.514869 0.756768i
\(196\) 0 0
\(197\) 1.00603i 0.0716767i 0.999358 + 0.0358384i \(0.0114101\pi\)
−0.999358 + 0.0358384i \(0.988590\pi\)
\(198\) 0 0
\(199\) −5.67639 + 3.27726i −0.402388 + 0.232319i −0.687514 0.726171i \(-0.741298\pi\)
0.285126 + 0.958490i \(0.407965\pi\)
\(200\) 0 0
\(201\) −8.36397 5.69045i −0.589949 0.401373i
\(202\) 0 0
\(203\) −0.570774 20.4994i −0.0400605 1.43878i
\(204\) 0 0
\(205\) 16.3364 1.14098
\(206\) 0 0
\(207\) −9.41928 7.48144i −0.654685 0.519996i
\(208\) 0 0
\(209\) −5.81840 10.0778i −0.402467 0.697094i
\(210\) 0 0
\(211\) −9.11202 + 15.7825i −0.627297 + 1.08651i 0.360794 + 0.932645i \(0.382506\pi\)
−0.988092 + 0.153866i \(0.950828\pi\)
\(212\) 0 0
\(213\) −11.3850 + 16.7339i −0.780086 + 1.14659i
\(214\) 0 0
\(215\) 2.77486 4.80620i 0.189244 0.327780i
\(216\) 0 0
\(217\) 1.64527 + 0.889784i 0.111688 + 0.0604024i
\(218\) 0 0
\(219\) 7.89692 + 0.584004i 0.533625 + 0.0394633i
\(220\) 0 0
\(221\) 8.93345i 0.600929i
\(222\) 0 0
\(223\) −8.71705 + 5.03279i −0.583737 + 0.337021i −0.762617 0.646850i \(-0.776086\pi\)
0.178880 + 0.983871i \(0.442753\pi\)
\(224\) 0 0
\(225\) 0.695841 + 0.103486i 0.0463894 + 0.00689904i
\(226\) 0 0
\(227\) 9.94372 17.2230i 0.659988 1.14313i −0.320630 0.947204i \(-0.603895\pi\)
0.980618 0.195928i \(-0.0627720\pi\)
\(228\) 0 0
\(229\) −15.3854 + 8.88275i −1.01669 + 0.586988i −0.913145 0.407636i \(-0.866353\pi\)
−0.103549 + 0.994624i \(0.533020\pi\)
\(230\) 0 0
\(231\) −6.70722 0.308634i −0.441303 0.0203066i
\(232\) 0 0
\(233\) −13.9077 8.02962i −0.911124 0.526038i −0.0303317 0.999540i \(-0.509656\pi\)
−0.880793 + 0.473502i \(0.842990\pi\)
\(234\) 0 0
\(235\) −13.6992 23.7277i −0.893636 1.54782i
\(236\) 0 0
\(237\) −13.4380 9.14256i −0.872890 0.593873i
\(238\) 0 0
\(239\) −7.11117 4.10564i −0.459983 0.265572i 0.252054 0.967713i \(-0.418894\pi\)
−0.712037 + 0.702142i \(0.752227\pi\)
\(240\) 0 0
\(241\) −24.6614 14.2382i −1.58858 0.917166i −0.993542 0.113468i \(-0.963804\pi\)
−0.595037 0.803698i \(-0.702863\pi\)
\(242\) 0 0
\(243\) 15.4028 2.39890i 0.988088 0.153890i
\(244\) 0 0
\(245\) 6.89230 13.6384i 0.440333 0.871325i
\(246\) 0 0
\(247\) 13.4240 + 23.2510i 0.854147 + 1.47943i
\(248\) 0 0
\(249\) 0.436489 5.90221i 0.0276613 0.374038i
\(250\) 0 0
\(251\) 0.656343 0.0414280 0.0207140 0.999785i \(-0.493406\pi\)
0.0207140 + 0.999785i \(0.493406\pi\)
\(252\) 0 0
\(253\) 5.87486 0.369349
\(254\) 0 0
\(255\) 8.99848 4.34432i 0.563507 0.272052i
\(256\) 0 0
\(257\) −3.82042 6.61716i −0.238311 0.412767i 0.721918 0.691978i \(-0.243261\pi\)
−0.960230 + 0.279211i \(0.909927\pi\)
\(258\) 0 0
\(259\) 3.92937 + 6.38837i 0.244159 + 0.396954i
\(260\) 0 0
\(261\) −18.2085 14.4624i −1.12708 0.895201i
\(262\) 0 0
\(263\) −5.73888 3.31334i −0.353874 0.204310i 0.312516 0.949913i \(-0.398828\pi\)
−0.666390 + 0.745603i \(0.732162\pi\)
\(264\) 0 0
\(265\) −5.27577 3.04597i −0.324088 0.187112i
\(266\) 0 0
\(267\) −14.4105 + 6.95714i −0.881907 + 0.425770i
\(268\) 0 0
\(269\) 4.38347 + 7.59239i 0.267265 + 0.462916i 0.968154 0.250354i \(-0.0805469\pi\)
−0.700890 + 0.713270i \(0.747214\pi\)
\(270\) 0 0
\(271\) 14.2608 + 8.23346i 0.866280 + 0.500147i 0.866110 0.499853i \(-0.166613\pi\)
0.000169619 1.00000i \(0.499946\pi\)
\(272\) 0 0
\(273\) 15.4746 + 0.712068i 0.936566 + 0.0430963i
\(274\) 0 0
\(275\) −0.297551 + 0.171791i −0.0179430 + 0.0103594i
\(276\) 0 0
\(277\) 8.88732 15.3933i 0.533987 0.924893i −0.465225 0.885193i \(-0.654026\pi\)
0.999212 0.0397001i \(-0.0126402\pi\)
\(278\) 0 0
\(279\) 1.97277 0.778725i 0.118107 0.0466210i
\(280\) 0 0
\(281\) −14.0252 + 8.09748i −0.836676 + 0.483055i −0.856133 0.516755i \(-0.827140\pi\)
0.0194568 + 0.999811i \(0.493806\pi\)
\(282\) 0 0
\(283\) 28.3729i 1.68660i −0.537447 0.843298i \(-0.680611\pi\)
0.537447 0.843298i \(-0.319389\pi\)
\(284\) 0 0
\(285\) 16.8922 24.8286i 1.00061 1.47072i
\(286\) 0 0
\(287\) 10.3731 + 16.8646i 0.612304 + 0.995484i
\(288\) 0 0
\(289\) 5.00804 8.67417i 0.294590 0.510246i
\(290\) 0 0
\(291\) −12.7331 0.941657i −0.746429 0.0552009i
\(292\) 0 0
\(293\) −4.38260 + 7.59088i −0.256034 + 0.443464i −0.965176 0.261602i \(-0.915749\pi\)
0.709142 + 0.705066i \(0.249083\pi\)
\(294\) 0 0
\(295\) 14.6621 + 25.3956i 0.853663 + 1.47859i
\(296\) 0 0
\(297\) −5.16193 + 5.59617i −0.299525 + 0.324723i
\(298\) 0 0
\(299\) −13.5542 −0.783861
\(300\) 0 0
\(301\) 6.72353 0.187206i 0.387538 0.0107904i
\(302\) 0 0
\(303\) −12.3646 + 5.96944i −0.710330 + 0.342936i
\(304\) 0 0
\(305\) −14.7366 + 8.50818i −0.843816 + 0.487177i
\(306\) 0 0
\(307\) 12.8497i 0.733372i 0.930345 + 0.366686i \(0.119508\pi\)
−0.930345 + 0.366686i \(0.880492\pi\)
\(308\) 0 0
\(309\) 6.51871 + 0.482080i 0.370836 + 0.0274246i
\(310\) 0 0
\(311\) −6.59343 −0.373879 −0.186939 0.982371i \(-0.559857\pi\)
−0.186939 + 0.982371i \(0.559857\pi\)
\(312\) 0 0
\(313\) 3.41458i 0.193004i −0.995333 0.0965018i \(-0.969235\pi\)
0.995333 0.0965018i \(-0.0307654\pi\)
\(314\) 0 0
\(315\) −6.80802 15.9335i −0.383588 0.897753i
\(316\) 0 0
\(317\) 32.1010i 1.80297i 0.432810 + 0.901485i \(0.357522\pi\)
−0.432810 + 0.901485i \(0.642478\pi\)
\(318\) 0 0
\(319\) 11.3567 0.635854
\(320\) 0 0
\(321\) 5.98449 + 12.3958i 0.334022 + 0.691866i
\(322\) 0 0
\(323\) 20.9890i 1.16786i
\(324\) 0 0
\(325\) 0.686498 0.396350i 0.0380801 0.0219855i
\(326\) 0 0
\(327\) 0.129056 1.74510i 0.00713681 0.0965042i
\(328\) 0 0
\(329\) 15.7963 29.2084i 0.870877 1.61031i
\(330\) 0 0
\(331\) −28.8833 −1.58757 −0.793784 0.608199i \(-0.791892\pi\)
−0.793784 + 0.608199i \(0.791892\pi\)
\(332\) 0 0
\(333\) 8.41178 + 1.25100i 0.460963 + 0.0685544i
\(334\) 0 0
\(335\) 6.37501 + 11.0418i 0.348304 + 0.603280i
\(336\) 0 0
\(337\) 4.82568 8.35833i 0.262872 0.455307i −0.704132 0.710069i \(-0.748664\pi\)
0.967004 + 0.254762i \(0.0819971\pi\)
\(338\) 0 0
\(339\) 9.17851 + 19.0116i 0.498508 + 1.03257i
\(340\) 0 0
\(341\) −0.517919 + 0.897063i −0.0280469 + 0.0485787i
\(342\) 0 0
\(343\) 18.4557 1.54481i 0.996515 0.0834117i
\(344\) 0 0
\(345\) 6.59139 + 13.6529i 0.354869 + 0.735047i
\(346\) 0 0
\(347\) 12.3273i 0.661766i 0.943672 + 0.330883i \(0.107347\pi\)
−0.943672 + 0.330883i \(0.892653\pi\)
\(348\) 0 0
\(349\) −10.2211 + 5.90115i −0.547123 + 0.315881i −0.747961 0.663743i \(-0.768967\pi\)
0.200838 + 0.979624i \(0.435634\pi\)
\(350\) 0 0
\(351\) 11.9094 12.9112i 0.635676 0.689151i
\(352\) 0 0
\(353\) 6.59855 11.4290i 0.351205 0.608305i −0.635256 0.772302i \(-0.719105\pi\)
0.986461 + 0.163997i \(0.0524386\pi\)
\(354\) 0 0
\(355\) 22.0916 12.7546i 1.17250 0.676943i
\(356\) 0 0
\(357\) 10.1985 + 6.53091i 0.539763 + 0.345652i
\(358\) 0 0
\(359\) −5.22483 3.01656i −0.275756 0.159208i 0.355745 0.934583i \(-0.384227\pi\)
−0.631501 + 0.775375i \(0.717561\pi\)
\(360\) 0 0
\(361\) 22.0394 + 38.1733i 1.15997 + 2.00912i
\(362\) 0 0
\(363\) −1.13093 + 15.2925i −0.0593585 + 0.802648i
\(364\) 0 0
\(365\) −8.64304 4.99006i −0.452397 0.261192i
\(366\) 0 0
\(367\) 14.8755 + 8.58836i 0.776494 + 0.448309i 0.835186 0.549967i \(-0.185360\pi\)
−0.0586924 + 0.998276i \(0.518693\pi\)
\(368\) 0 0
\(369\) 22.2061 + 3.30250i 1.15601 + 0.171921i
\(370\) 0 0
\(371\) −0.205496 7.38043i −0.0106688 0.383173i
\(372\) 0 0
\(373\) −2.35902 4.08595i −0.122146 0.211562i 0.798468 0.602037i \(-0.205644\pi\)
−0.920614 + 0.390475i \(0.872311\pi\)
\(374\) 0 0
\(375\) −16.3639 11.1332i −0.845026 0.574916i
\(376\) 0 0
\(377\) −26.2017 −1.34946
\(378\) 0 0
\(379\) 9.34015 0.479771 0.239886 0.970801i \(-0.422890\pi\)
0.239886 + 0.970801i \(0.422890\pi\)
\(380\) 0 0
\(381\) −9.72859 6.61887i −0.498411 0.339095i
\(382\) 0 0
\(383\) 2.85036 + 4.93696i 0.145646 + 0.252267i 0.929614 0.368535i \(-0.120140\pi\)
−0.783968 + 0.620802i \(0.786807\pi\)
\(384\) 0 0
\(385\) 7.44361 + 4.02560i 0.379362 + 0.205164i
\(386\) 0 0
\(387\) 4.74347 5.97212i 0.241124 0.303580i
\(388\) 0 0
\(389\) 6.63671 + 3.83171i 0.336495 + 0.194275i 0.658721 0.752387i \(-0.271098\pi\)
−0.322226 + 0.946663i \(0.604431\pi\)
\(390\) 0 0
\(391\) −9.17668 5.29816i −0.464085 0.267939i
\(392\) 0 0
\(393\) 1.75464 23.7263i 0.0885100 1.19683i
\(394\) 0 0
\(395\) 10.2424 + 17.7404i 0.515351 + 0.892615i
\(396\) 0 0
\(397\) −1.12810 0.651310i −0.0566178 0.0326883i 0.471424 0.881907i \(-0.343740\pi\)
−0.528042 + 0.849218i \(0.677074\pi\)
\(398\) 0 0
\(399\) 36.3573 + 1.67299i 1.82014 + 0.0837542i
\(400\) 0 0
\(401\) −8.18778 + 4.72722i −0.408878 + 0.236066i −0.690308 0.723516i \(-0.742525\pi\)
0.281429 + 0.959582i \(0.409191\pi\)
\(402\) 0 0
\(403\) 1.19492 2.06966i 0.0595233 0.103097i
\(404\) 0 0
\(405\) −18.7967 5.71736i −0.934018 0.284098i
\(406\) 0 0
\(407\) −3.59700 + 2.07673i −0.178296 + 0.102940i
\(408\) 0 0
\(409\) 19.0736i 0.943126i 0.881832 + 0.471563i \(0.156310\pi\)
−0.881832 + 0.471563i \(0.843690\pi\)
\(410\) 0 0
\(411\) −15.1323 31.3439i −0.746422 1.54608i
\(412\) 0 0
\(413\) −16.9067 + 31.2615i −0.831922 + 1.53828i
\(414\) 0 0
\(415\) −3.72961 + 6.45987i −0.183079 + 0.317102i
\(416\) 0 0
\(417\) −7.40324 15.3345i −0.362538 0.750934i
\(418\) 0 0
\(419\) −4.20003 + 7.27466i −0.205185 + 0.355390i −0.950192 0.311666i \(-0.899113\pi\)
0.745007 + 0.667057i \(0.232446\pi\)
\(420\) 0 0
\(421\) 19.7178 + 34.1522i 0.960985 + 1.66448i 0.720035 + 0.693938i \(0.244126\pi\)
0.240951 + 0.970537i \(0.422541\pi\)
\(422\) 0 0
\(423\) −13.8247 35.0225i −0.672178 1.70285i
\(424\) 0 0
\(425\) 0.619711 0.0300604
\(426\) 0 0
\(427\) −18.1405 9.81063i −0.877881 0.474770i
\(428\) 0 0
\(429\) −0.632697 + 8.55535i −0.0305469 + 0.413056i
\(430\) 0 0
\(431\) 10.3340 5.96634i 0.497772 0.287389i −0.230021 0.973186i \(-0.573880\pi\)
0.727793 + 0.685797i \(0.240546\pi\)
\(432\) 0 0
\(433\) 12.2121i 0.586875i 0.955978 + 0.293437i \(0.0947992\pi\)
−0.955978 + 0.293437i \(0.905201\pi\)
\(434\) 0 0
\(435\) 12.7419 + 26.3925i 0.610925 + 1.26542i
\(436\) 0 0
\(437\) −31.8454 −1.52337
\(438\) 0 0
\(439\) 16.7015i 0.797120i 0.917142 + 0.398560i \(0.130490\pi\)
−0.917142 + 0.398560i \(0.869510\pi\)
\(440\) 0 0
\(441\) 12.1258 17.1454i 0.577419 0.816448i
\(442\) 0 0
\(443\) 30.2997i 1.43958i −0.694190 0.719791i \(-0.744237\pi\)
0.694190 0.719791i \(-0.255763\pi\)
\(444\) 0 0
\(445\) 20.1682 0.956065
\(446\) 0 0
\(447\) −34.6078 2.55936i −1.63689 0.121054i
\(448\) 0 0
\(449\) 30.1253i 1.42170i 0.703343 + 0.710851i \(0.251690\pi\)
−0.703343 + 0.710851i \(0.748310\pi\)
\(450\) 0 0
\(451\) −9.49566 + 5.48232i −0.447133 + 0.258152i
\(452\) 0 0
\(453\) −34.6798 + 16.7428i −1.62940 + 0.786646i
\(454\) 0 0
\(455\) −17.1736 9.28770i −0.805110 0.435414i
\(456\) 0 0
\(457\) 25.2318 1.18029 0.590146 0.807297i \(-0.299070\pi\)
0.590146 + 0.807297i \(0.299070\pi\)
\(458\) 0 0
\(459\) 13.1099 4.08615i 0.611918 0.190725i
\(460\) 0 0
\(461\) −12.3174 21.3344i −0.573680 0.993643i −0.996184 0.0872820i \(-0.972182\pi\)
0.422503 0.906361i \(-0.361151\pi\)
\(462\) 0 0
\(463\) −6.33215 + 10.9676i −0.294280 + 0.509708i −0.974817 0.223006i \(-0.928413\pi\)
0.680537 + 0.732713i \(0.261746\pi\)
\(464\) 0 0
\(465\) −2.66582 0.197146i −0.123624 0.00914244i
\(466\) 0 0
\(467\) 10.4723 18.1385i 0.484599 0.839350i −0.515245 0.857043i \(-0.672299\pi\)
0.999843 + 0.0176932i \(0.00563223\pi\)
\(468\) 0 0
\(469\) −7.35090 + 13.5923i −0.339433 + 0.627635i
\(470\) 0 0
\(471\) −7.82231 + 11.4974i −0.360433 + 0.529774i
\(472\) 0 0
\(473\) 3.72485i 0.171269i
\(474\) 0 0
\(475\) 1.61291 0.931217i 0.0740056 0.0427271i
\(476\) 0 0
\(477\) −6.55562 5.20692i −0.300161 0.238409i
\(478\) 0 0
\(479\) 15.8852 27.5141i 0.725816 1.25715i −0.232822 0.972519i \(-0.574796\pi\)
0.958637 0.284630i \(-0.0918707\pi\)
\(480\) 0 0
\(481\) 8.29884 4.79134i 0.378394 0.218466i
\(482\) 0 0
\(483\) −9.90898 + 15.4736i −0.450874 + 0.704075i
\(484\) 0 0
\(485\) 13.9362 + 8.04605i 0.632809 + 0.365352i
\(486\) 0 0
\(487\) −17.7821 30.7995i −0.805784 1.39566i −0.915761 0.401724i \(-0.868411\pi\)
0.109977 0.993934i \(-0.464922\pi\)
\(488\) 0 0
\(489\) 19.4226 9.37691i 0.878320 0.424038i
\(490\) 0 0
\(491\) 2.75734 + 1.59195i 0.124437 + 0.0718437i 0.560926 0.827866i \(-0.310445\pi\)
−0.436490 + 0.899709i \(0.643778\pi\)
\(492\) 0 0
\(493\) −17.7395 10.2419i −0.798947 0.461272i
\(494\) 0 0
\(495\) 8.92531 3.52315i 0.401163 0.158354i
\(496\) 0 0
\(497\) 27.1944 + 14.7071i 1.21983 + 0.659703i
\(498\) 0 0
\(499\) −16.0214 27.7498i −0.717215 1.24225i −0.962099 0.272700i \(-0.912083\pi\)
0.244884 0.969552i \(-0.421250\pi\)
\(500\) 0 0
\(501\) 30.7585 14.8497i 1.37419 0.663435i
\(502\) 0 0
\(503\) 11.6608 0.519930 0.259965 0.965618i \(-0.416289\pi\)
0.259965 + 0.965618i \(0.416289\pi\)
\(504\) 0 0
\(505\) 17.3050 0.770061
\(506\) 0 0
\(507\) −0.200916 + 2.71679i −0.00892299 + 0.120657i
\(508\) 0 0
\(509\) −13.4427 23.2834i −0.595836 1.03202i −0.993428 0.114457i \(-0.963487\pi\)
0.397592 0.917562i \(-0.369846\pi\)
\(510\) 0 0
\(511\) −0.336655 12.0910i −0.0148927 0.534875i
\(512\) 0 0
\(513\) 27.9809 30.3347i 1.23539 1.33931i
\(514\) 0 0
\(515\) −7.13461 4.11917i −0.314388 0.181512i
\(516\) 0 0
\(517\) 15.9255 + 9.19459i 0.700402 + 0.404378i
\(518\) 0 0
\(519\) −2.61701 1.78049i −0.114874 0.0781549i
\(520\) 0 0
\(521\) 17.0385 + 29.5116i 0.746471 + 1.29293i 0.949504 + 0.313754i \(0.101587\pi\)
−0.203033 + 0.979172i \(0.565080\pi\)
\(522\) 0 0
\(523\) 4.71003 + 2.71933i 0.205955 + 0.118908i 0.599430 0.800427i \(-0.295394\pi\)
−0.393475 + 0.919335i \(0.628727\pi\)
\(524\) 0 0
\(525\) 0.0493959 1.07347i 0.00215581 0.0468500i
\(526\) 0 0
\(527\) 1.61801 0.934157i 0.0704815 0.0406925i
\(528\) 0 0
\(529\) −3.46140 + 5.99532i −0.150496 + 0.260666i
\(530\) 0 0
\(531\) 14.7964 + 37.4843i 0.642111 + 1.62668i
\(532\) 0 0
\(533\) 21.9080 12.6486i 0.948940 0.547871i
\(534\) 0 0
\(535\) 17.3486i 0.750045i
\(536\) 0 0
\(537\) −24.1704 1.78748i −1.04303 0.0771356i
\(538\) 0 0
\(539\) 0.570698 + 10.2404i 0.0245817 + 0.441085i
\(540\) 0 0
\(541\) 11.8329 20.4952i 0.508737 0.881158i −0.491212 0.871040i \(-0.663446\pi\)
0.999949 0.0101183i \(-0.00322080\pi\)
\(542\) 0 0
\(543\) −15.9389 + 23.4274i −0.684004 + 1.00537i
\(544\) 0 0
\(545\) −1.10273 + 1.90998i −0.0472356 + 0.0818145i
\(546\) 0 0
\(547\) −12.0824 20.9273i −0.516606 0.894788i −0.999814 0.0192822i \(-0.993862\pi\)
0.483208 0.875505i \(-0.339471\pi\)
\(548\) 0 0
\(549\) −21.7515 + 8.58611i −0.928331 + 0.366446i
\(550\) 0 0
\(551\) −61.5605 −2.62257
\(552\) 0 0
\(553\) −11.8103 + 21.8381i −0.502226 + 0.928650i
\(554\) 0 0
\(555\) −8.86192 6.02923i −0.376167 0.255927i
\(556\) 0 0
\(557\) −7.36315 + 4.25111i −0.311987 + 0.180126i −0.647815 0.761798i \(-0.724317\pi\)
0.335829 + 0.941923i \(0.390984\pi\)
\(558\) 0 0
\(559\) 8.59381i 0.363480i
\(560\) 0 0
\(561\) −3.77253 + 5.54496i −0.159276 + 0.234108i
\(562\) 0 0
\(563\) 0.947553 0.0399346 0.0199673 0.999801i \(-0.493644\pi\)
0.0199673 + 0.999801i \(0.493644\pi\)
\(564\) 0 0
\(565\) 26.6078i 1.11940i
\(566\) 0 0
\(567\) −6.03311 23.0348i −0.253367 0.967370i
\(568\) 0 0
\(569\) 18.2280i 0.764158i 0.924130 + 0.382079i \(0.124792\pi\)
−0.924130 + 0.382079i \(0.875208\pi\)
\(570\) 0 0
\(571\) −12.2424 −0.512330 −0.256165 0.966633i \(-0.582459\pi\)
−0.256165 + 0.966633i \(0.582459\pi\)
\(572\) 0 0
\(573\) 13.3118 19.5661i 0.556110 0.817385i
\(574\) 0 0
\(575\) 0.940253i 0.0392112i
\(576\) 0 0
\(577\) −10.2500 + 5.91784i −0.426713 + 0.246363i −0.697945 0.716151i \(-0.745902\pi\)
0.271232 + 0.962514i \(0.412569\pi\)
\(578\) 0 0
\(579\) 6.26905 + 4.26516i 0.260533 + 0.177254i
\(580\) 0 0
\(581\) −9.03690 + 0.251618i −0.374914 + 0.0104389i
\(582\) 0 0
\(583\) 4.08878 0.169340
\(584\) 0 0
\(585\) −20.5921 + 8.12845i −0.851378 + 0.336070i
\(586\) 0 0
\(587\) 3.57681 + 6.19521i 0.147631 + 0.255704i 0.930351 0.366669i \(-0.119502\pi\)
−0.782721 + 0.622373i \(0.786169\pi\)
\(588\) 0 0
\(589\) 2.80745 4.86264i 0.115679 0.200362i
\(590\) 0 0
\(591\) 0.980171 1.44068i 0.0403188 0.0592617i
\(592\) 0 0
\(593\) 13.4811 23.3500i 0.553603 0.958869i −0.444408 0.895825i \(-0.646586\pi\)
0.998011 0.0630442i \(-0.0200809\pi\)
\(594\) 0 0
\(595\) −7.99668 13.0010i −0.327832 0.532990i
\(596\) 0 0
\(597\) 11.3219 + 0.837289i 0.463373 + 0.0342680i
\(598\) 0 0
\(599\) 35.2441i 1.44004i −0.693955 0.720018i \(-0.744133\pi\)
0.693955 0.720018i \(-0.255867\pi\)
\(600\) 0 0
\(601\) 3.39266 1.95875i 0.138389 0.0798991i −0.429207 0.903206i \(-0.641207\pi\)
0.567596 + 0.823307i \(0.307874\pi\)
\(602\) 0 0
\(603\) 6.43340 + 16.2979i 0.261988 + 0.663704i
\(604\) 0 0
\(605\) 9.66332 16.7374i 0.392870 0.680470i
\(606\) 0 0
\(607\) −12.5377 + 7.23862i −0.508888 + 0.293807i −0.732376 0.680900i \(-0.761589\pi\)
0.223488 + 0.974707i \(0.428256\pi\)
\(608\) 0 0
\(609\) −19.1551 + 29.9122i −0.776204 + 1.21210i
\(610\) 0 0
\(611\) −36.7426 21.2134i −1.48645 0.858201i
\(612\) 0 0
\(613\) −6.51761 11.2888i −0.263244 0.455952i 0.703858 0.710341i \(-0.251459\pi\)
−0.967102 + 0.254389i \(0.918126\pi\)
\(614\) 0 0
\(615\) −23.3944 15.9165i −0.943355 0.641814i
\(616\) 0 0
\(617\) −3.14491 1.81571i −0.126609 0.0730979i 0.435358 0.900258i \(-0.356622\pi\)
−0.561967 + 0.827160i \(0.689955\pi\)
\(618\) 0 0
\(619\) −14.2737 8.24091i −0.573708 0.331230i 0.184921 0.982753i \(-0.440797\pi\)
−0.758629 + 0.651523i \(0.774130\pi\)
\(620\) 0 0
\(621\) 6.19969 + 19.8909i 0.248785 + 0.798195i
\(622\) 0 0
\(623\) 12.8062 + 20.8203i 0.513068 + 0.834147i
\(624\) 0 0
\(625\) 11.8863 + 20.5876i 0.475450 + 0.823504i
\(626\) 0 0
\(627\) −1.48651 + 20.1006i −0.0593655 + 0.802742i
\(628\) 0 0
\(629\) 7.49147 0.298704
\(630\) 0 0
\(631\) −34.8383 −1.38689 −0.693446 0.720508i \(-0.743909\pi\)
−0.693446 + 0.720508i \(0.743909\pi\)
\(632\) 0 0
\(633\) 28.4256 13.7234i 1.12982 0.545457i
\(634\) 0 0
\(635\) 7.41512 + 12.8434i 0.294260 + 0.509673i
\(636\) 0 0
\(637\) −1.31669 23.6262i −0.0521692 0.936105i
\(638\) 0 0
\(639\) 32.6076 12.8714i 1.28994 0.509185i
\(640\) 0 0
\(641\) 7.25538 + 4.18889i 0.286570 + 0.165451i 0.636394 0.771364i \(-0.280425\pi\)
−0.349824 + 0.936815i \(0.613759\pi\)
\(642\) 0 0
\(643\) −18.0021 10.3935i −0.709934 0.409881i 0.101103 0.994876i \(-0.467763\pi\)
−0.811037 + 0.584995i \(0.801096\pi\)
\(644\) 0 0
\(645\) −8.65637 + 4.17915i −0.340844 + 0.164554i
\(646\) 0 0
\(647\) 4.74770 + 8.22325i 0.186651 + 0.323289i 0.944132 0.329568i \(-0.106903\pi\)
−0.757480 + 0.652858i \(0.773570\pi\)
\(648\) 0 0
\(649\) −17.0450 9.84091i −0.669073 0.386290i
\(650\) 0 0
\(651\) −1.48919 2.87719i −0.0583659 0.112766i
\(652\) 0 0
\(653\) −6.64747 + 3.83792i −0.260136 + 0.150189i −0.624396 0.781108i \(-0.714655\pi\)
0.364261 + 0.931297i \(0.381322\pi\)
\(654\) 0 0
\(655\) −14.9927 + 25.9680i −0.585811 + 1.01465i
\(656\) 0 0
\(657\) −10.7397 8.53025i −0.418997 0.332797i
\(658\) 0 0
\(659\) 38.0493 21.9678i 1.48219 0.855743i 0.482395 0.875954i \(-0.339767\pi\)
0.999796 + 0.0202102i \(0.00643354\pi\)
\(660\) 0 0
\(661\) 25.5938i 0.995484i 0.867325 + 0.497742i \(0.165837\pi\)
−0.867325 + 0.497742i \(0.834163\pi\)
\(662\) 0 0
\(663\) 8.70382 12.7931i 0.338028 0.496843i
\(664\) 0 0
\(665\) −40.3490 21.8213i −1.56467 0.846193i
\(666\) 0 0
\(667\) 15.5395 26.9151i 0.601691 1.04216i
\(668\) 0 0
\(669\) 17.3866 + 1.28580i 0.672206 + 0.0497119i
\(670\) 0 0
\(671\) 5.71051 9.89089i 0.220452 0.381834i
\(672\) 0 0
\(673\) −7.64671 13.2445i −0.294759 0.510538i 0.680170 0.733055i \(-0.261906\pi\)
−0.974929 + 0.222517i \(0.928573\pi\)
\(674\) 0 0
\(675\) −0.895649 0.826150i −0.0344736 0.0317985i
\(676\) 0 0
\(677\) 45.2918 1.74070 0.870352 0.492430i \(-0.163891\pi\)
0.870352 + 0.492430i \(0.163891\pi\)
\(678\) 0 0
\(679\) 0.542827 + 19.4957i 0.0208318 + 0.748177i
\(680\) 0 0
\(681\) −31.0202 + 14.9760i −1.18870 + 0.573882i
\(682\) 0 0
\(683\) 24.0891 13.9079i 0.921744 0.532169i 0.0375529 0.999295i \(-0.488044\pi\)
0.884191 + 0.467126i \(0.154710\pi\)
\(684\) 0 0
\(685\) 43.8674i 1.67609i
\(686\) 0 0
\(687\) 30.6869 + 2.26940i 1.17078 + 0.0865831i
\(688\) 0 0
\(689\) −9.43345 −0.359386
\(690\) 0 0
\(691\) 16.2946i 0.619875i 0.950757 + 0.309938i \(0.100308\pi\)
−0.950757 + 0.309938i \(0.899692\pi\)
\(692\) 0 0
\(693\) 9.30433 + 6.97679i 0.353442 + 0.265026i
\(694\) 0 0
\(695\) 21.4614i 0.814079i
\(696\) 0 0
\(697\) 19.7766 0.749093
\(698\) 0 0
\(699\) 12.0932 + 25.0490i 0.457408 + 0.947439i
\(700\) 0 0
\(701\) 0.393403i 0.0148586i −0.999972 0.00742932i \(-0.997635\pi\)
0.999972 0.00742932i \(-0.00236485\pi\)
\(702\) 0 0
\(703\) 19.4980 11.2572i 0.735379 0.424572i
\(704\) 0 0
\(705\) −3.49992 + 47.3261i −0.131815 + 1.78240i
\(706\) 0 0
\(707\) 10.9881 + 17.8644i 0.413250 + 0.671862i
\(708\) 0 0
\(709\) −32.6366 −1.22569 −0.612846 0.790202i \(-0.709975\pi\)
−0.612846 + 0.790202i \(0.709975\pi\)
\(710\) 0 0
\(711\) 10.3362 + 26.1851i 0.387638 + 0.982018i
\(712\) 0 0
\(713\) 1.41734 + 2.45491i 0.0530799 + 0.0919372i
\(714\) 0 0
\(715\) 5.40612 9.36368i 0.202178 0.350182i
\(716\) 0 0
\(717\) 6.18341 + 12.8078i 0.230924 + 0.478317i
\(718\) 0 0
\(719\) 0.106604 0.184643i 0.00397565 0.00688602i −0.864031 0.503439i \(-0.832068\pi\)
0.868006 + 0.496553i \(0.165401\pi\)
\(720\) 0 0
\(721\) −0.277900 9.98081i −0.0103495 0.371705i
\(722\) 0 0
\(723\) 21.4439 + 44.4172i 0.797508 + 1.65190i
\(724\) 0 0
\(725\) 1.81761i 0.0675042i
\(726\) 0 0
\(727\) 31.8208 18.3717i 1.18017 0.681370i 0.224114 0.974563i \(-0.428051\pi\)
0.956053 + 0.293193i \(0.0947180\pi\)
\(728\) 0 0
\(729\) −24.3947 11.5715i −0.903507 0.428574i
\(730\) 0 0
\(731\) 3.35920 5.81831i 0.124245 0.215198i
\(732\) 0 0
\(733\) 9.41829 5.43765i 0.347873 0.200844i −0.315875 0.948801i \(-0.602298\pi\)
0.663748 + 0.747956i \(0.268965\pi\)
\(734\) 0 0
\(735\) −23.1579 + 12.8156i −0.854192 + 0.472712i
\(736\) 0 0
\(737\) −7.41104 4.27877i −0.272989 0.157610i
\(738\) 0 0
\(739\) 6.91282 + 11.9734i 0.254292 + 0.440447i 0.964703 0.263340i \(-0.0848242\pi\)
−0.710411 + 0.703787i \(0.751491\pi\)
\(740\) 0 0
\(741\) 3.42961 46.3753i 0.125990 1.70364i
\(742\) 0 0
\(743\) −15.8751 9.16552i −0.582403 0.336250i 0.179685 0.983724i \(-0.442492\pi\)
−0.762088 + 0.647474i \(0.775825\pi\)
\(744\) 0 0
\(745\) 37.8776 + 21.8687i 1.38773 + 0.801206i
\(746\) 0 0
\(747\) −6.37557 + 8.02696i −0.233270 + 0.293691i
\(748\) 0 0
\(749\) 17.9095 11.0158i 0.654398 0.402508i
\(750\) 0 0
\(751\) 9.97084 + 17.2700i 0.363841 + 0.630191i 0.988589 0.150635i \(-0.0481318\pi\)
−0.624748 + 0.780826i \(0.714798\pi\)
\(752\) 0 0
\(753\) −0.939912 0.639471i −0.0342523 0.0233036i
\(754\) 0 0
\(755\) 48.5362 1.76641
\(756\) 0 0
\(757\) −46.9292 −1.70567 −0.852836 0.522178i \(-0.825119\pi\)
−0.852836 + 0.522178i \(0.825119\pi\)
\(758\) 0 0
\(759\) −8.41306 5.72385i −0.305375 0.207762i
\(760\) 0 0
\(761\) 26.7769 + 46.3789i 0.970661 + 1.68123i 0.693568 + 0.720391i \(0.256038\pi\)
0.277093 + 0.960843i \(0.410629\pi\)
\(762\) 0 0
\(763\) −2.67193 + 0.0743955i −0.0967302 + 0.00269330i
\(764\) 0 0
\(765\) −17.1189 2.54592i −0.618934 0.0920479i
\(766\) 0 0
\(767\) 39.3254 + 22.7045i 1.41996 + 0.819813i
\(768\) 0 0
\(769\) −34.7306 20.0517i −1.25242 0.723085i −0.280830 0.959758i \(-0.590610\pi\)
−0.971589 + 0.236673i \(0.923943\pi\)
\(770\) 0 0
\(771\) −0.976058 + 13.1983i −0.0351519 + 0.475325i
\(772\) 0 0
\(773\) −7.82375 13.5511i −0.281401 0.487400i 0.690329 0.723495i \(-0.257466\pi\)
−0.971730 + 0.236095i \(0.924132\pi\)
\(774\) 0 0
\(775\) −0.143572 0.0828913i −0.00515726 0.00297755i
\(776\) 0 0
\(777\) 0.597130 12.9768i 0.0214219 0.465540i
\(778\) 0 0
\(779\) 51.4724 29.7176i 1.84419 1.06474i
\(780\) 0 0
\(781\) −8.56060 + 14.8274i −0.306322 + 0.530566i
\(782\) 0 0
\(783\) 11.9847 + 38.4512i 0.428297 + 1.37413i
\(784\) 0 0
\(785\) 15.1785 8.76333i 0.541745 0.312777i
\(786\) 0 0
\(787\) 46.1788i 1.64610i 0.567972 + 0.823048i \(0.307728\pi\)
−0.567972 + 0.823048i \(0.692272\pi\)
\(788\) 0 0
\(789\) 4.99015 + 10.3362i 0.177654 + 0.367979i
\(790\) 0 0
\(791\) 27.4680 16.8951i 0.976651 0.600720i
\(792\) 0 0
\(793\) −13.1750 + 22.8198i −0.467859 + 0.810356i
\(794\) 0 0
\(795\) 4.58747 + 9.50212i 0.162701 + 0.337005i
\(796\) 0