Properties

Label 804.2.ba.b.41.16
Level 804
Weight 2
Character 804.41
Analytic conductor 6.420
Analytic rank 0
Dimension 440
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.ba (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(440\)
Relative dimension: \(22\) over \(\Q(\zeta_{66})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label 41.16
Character \(\chi\) = 804.41
Dual form 804.2.ba.b.353.16

$q$-expansion

\(f(q)\) \(=\) \(q+(0.995897 - 1.41711i) q^{3} +(-0.152781 + 1.06262i) q^{5} +(0.324444 + 3.39773i) q^{7} +(-1.01638 - 2.82258i) q^{9} +O(q^{10})\) \(q+(0.995897 - 1.41711i) q^{3} +(-0.152781 + 1.06262i) q^{5} +(0.324444 + 3.39773i) q^{7} +(-1.01638 - 2.82258i) q^{9} +(1.16153 - 0.465006i) q^{11} +(-1.83241 - 1.92178i) q^{13} +(1.35369 + 1.27477i) q^{15} +(3.09077 - 1.06973i) q^{17} +(6.96190 + 0.664781i) q^{19} +(5.13805 + 2.92402i) q^{21} +(6.97890 - 0.332446i) q^{23} +(3.69165 + 1.08397i) q^{25} +(-5.01211 - 1.37069i) q^{27} +(0.870238 - 0.502432i) q^{29} +(-4.01310 + 4.20882i) q^{31} +(0.497800 - 2.10911i) q^{33} +(-3.66006 - 0.174350i) q^{35} +(-3.99087 + 6.91239i) q^{37} +(-4.54826 + 0.682828i) q^{39} +(3.54601 + 0.683437i) q^{41} +(1.94811 + 1.68805i) q^{43} +(3.15461 - 0.648783i) q^{45} +(5.36003 - 10.3970i) q^{47} +(-4.56579 + 0.879983i) q^{49} +(1.56218 - 5.44529i) q^{51} +(4.61898 + 5.33059i) q^{53} +(0.316664 + 1.30531i) q^{55} +(7.87540 - 9.20369i) q^{57} +(-3.82125 - 13.0140i) q^{59} +(-3.61460 + 9.02884i) q^{61} +(9.26061 - 4.36914i) q^{63} +(2.32208 - 1.65354i) q^{65} +(-7.45395 - 3.38209i) q^{67} +(6.47915 - 10.2209i) q^{69} +(-10.5155 - 3.63946i) q^{71} +(-5.63753 - 2.25693i) q^{73} +(5.21260 - 4.15194i) q^{75} +(1.95681 + 3.79569i) q^{77} +(-9.16491 + 2.22338i) q^{79} +(-6.93395 + 5.73762i) q^{81} +(-8.90868 + 11.3283i) q^{83} +(0.664499 + 3.44775i) q^{85} +(0.154668 - 1.73359i) q^{87} +(7.82886 - 12.1820i) q^{89} +(5.93517 - 6.84955i) q^{91} +(1.96770 + 9.87853i) q^{93} +(-1.77006 + 7.29627i) q^{95} +(4.98536 + 2.87830i) q^{97} +(-2.49307 - 2.80589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440q - 12q^{7} + 4q^{9} + O(q^{10}) \) \( 440q - 12q^{7} + 4q^{9} - 2q^{15} - 10q^{19} + 22q^{21} - 68q^{25} + 50q^{31} + 11q^{33} - 22q^{37} - 45q^{39} + 22q^{43} + 22q^{45} - 18q^{49} - 6q^{51} + 126q^{55} - 183q^{57} - 56q^{61} - 141q^{63} - 12q^{67} + 33q^{69} + 356q^{73} + 165q^{75} + 228q^{79} + 24q^{81} - 6q^{85} + 75q^{87} - 4q^{91} - 75q^{93} + 12q^{97} + 88q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{53}{66}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.995897 1.41711i 0.574982 0.818166i
\(4\) 0 0
\(5\) −0.152781 + 1.06262i −0.0683259 + 0.475217i 0.926716 + 0.375762i \(0.122619\pi\)
−0.995042 + 0.0994551i \(0.968290\pi\)
\(6\) 0 0
\(7\) 0.324444 + 3.39773i 0.122628 + 1.28422i 0.822010 + 0.569472i \(0.192852\pi\)
−0.699382 + 0.714748i \(0.746541\pi\)
\(8\) 0 0
\(9\) −1.01638 2.82258i −0.338792 0.940861i
\(10\) 0 0
\(11\) 1.16153 0.465006i 0.350214 0.140204i −0.189884 0.981806i \(-0.560811\pi\)
0.540098 + 0.841602i \(0.318387\pi\)
\(12\) 0 0
\(13\) −1.83241 1.92178i −0.508220 0.533006i 0.418770 0.908092i \(-0.362461\pi\)
−0.926990 + 0.375087i \(0.877613\pi\)
\(14\) 0 0
\(15\) 1.35369 + 1.27477i 0.349521 + 0.329143i
\(16\) 0 0
\(17\) 3.09077 1.06973i 0.749623 0.259447i 0.0745693 0.997216i \(-0.476242\pi\)
0.675053 + 0.737769i \(0.264121\pi\)
\(18\) 0 0
\(19\) 6.96190 + 0.664781i 1.59717 + 0.152511i 0.855336 0.518074i \(-0.173351\pi\)
0.741833 + 0.670585i \(0.233957\pi\)
\(20\) 0 0
\(21\) 5.13805 + 2.92402i 1.12121 + 0.638073i
\(22\) 0 0
\(23\) 6.97890 0.332446i 1.45520 0.0693197i 0.695001 0.719009i \(-0.255404\pi\)
0.760200 + 0.649689i \(0.225101\pi\)
\(24\) 0 0
\(25\) 3.69165 + 1.08397i 0.738330 + 0.216793i
\(26\) 0 0
\(27\) −5.01211 1.37069i −0.964580 0.263789i
\(28\) 0 0
\(29\) 0.870238 0.502432i 0.161599 0.0932993i −0.417019 0.908898i \(-0.636925\pi\)
0.578619 + 0.815598i \(0.303592\pi\)
\(30\) 0 0
\(31\) −4.01310 + 4.20882i −0.720774 + 0.755926i −0.977586 0.210536i \(-0.932479\pi\)
0.256813 + 0.966461i \(0.417328\pi\)
\(32\) 0 0
\(33\) 0.497800 2.10911i 0.0866559 0.367148i
\(34\) 0 0
\(35\) −3.66006 0.174350i −0.618662 0.0294705i
\(36\) 0 0
\(37\) −3.99087 + 6.91239i −0.656095 + 1.13639i 0.325523 + 0.945534i \(0.394460\pi\)
−0.981618 + 0.190856i \(0.938874\pi\)
\(38\) 0 0
\(39\) −4.54826 + 0.682828i −0.728304 + 0.109340i
\(40\) 0 0
\(41\) 3.54601 + 0.683437i 0.553793 + 0.106735i 0.458467 0.888711i \(-0.348399\pi\)
0.0953258 + 0.995446i \(0.469611\pi\)
\(42\) 0 0
\(43\) 1.94811 + 1.68805i 0.297084 + 0.257424i 0.790629 0.612296i \(-0.209754\pi\)
−0.493545 + 0.869720i \(0.664299\pi\)
\(44\) 0 0
\(45\) 3.15461 0.648783i 0.470262 0.0967148i
\(46\) 0 0
\(47\) 5.36003 10.3970i 0.781841 1.51656i −0.0728031 0.997346i \(-0.523194\pi\)
0.854644 0.519214i \(-0.173775\pi\)
\(48\) 0 0
\(49\) −4.56579 + 0.879983i −0.652255 + 0.125712i
\(50\) 0 0
\(51\) 1.56218 5.44529i 0.218748 0.762493i
\(52\) 0 0
\(53\) 4.61898 + 5.33059i 0.634466 + 0.732213i 0.978386 0.206786i \(-0.0663004\pi\)
−0.343920 + 0.938999i \(0.611755\pi\)
\(54\) 0 0
\(55\) 0.316664 + 1.30531i 0.0426989 + 0.176007i
\(56\) 0 0
\(57\) 7.87540 9.20369i 1.04312 1.21906i
\(58\) 0 0
\(59\) −3.82125 13.0140i −0.497484 1.69428i −0.699280 0.714848i \(-0.746496\pi\)
0.201796 0.979428i \(-0.435322\pi\)
\(60\) 0 0
\(61\) −3.61460 + 9.02884i −0.462803 + 1.15603i 0.495075 + 0.868850i \(0.335140\pi\)
−0.957878 + 0.287175i \(0.907284\pi\)
\(62\) 0 0
\(63\) 9.26061 4.36914i 1.16673 0.550460i
\(64\) 0 0
\(65\) 2.32208 1.65354i 0.288018 0.205097i
\(66\) 0 0
\(67\) −7.45395 3.38209i −0.910646 0.413188i
\(68\) 0 0
\(69\) 6.47915 10.2209i 0.779998 1.23045i
\(70\) 0 0
\(71\) −10.5155 3.63946i −1.24796 0.431925i −0.378353 0.925661i \(-0.623509\pi\)
−0.869611 + 0.493737i \(0.835631\pi\)
\(72\) 0 0
\(73\) −5.63753 2.25693i −0.659823 0.264153i 0.0174913 0.999847i \(-0.494432\pi\)
−0.677314 + 0.735694i \(0.736856\pi\)
\(74\) 0 0
\(75\) 5.21260 4.15194i 0.601899 0.479425i
\(76\) 0 0
\(77\) 1.95681 + 3.79569i 0.223000 + 0.432559i
\(78\) 0 0
\(79\) −9.16491 + 2.22338i −1.03113 + 0.250150i −0.715413 0.698702i \(-0.753761\pi\)
−0.315720 + 0.948852i \(0.602246\pi\)
\(80\) 0 0
\(81\) −6.93395 + 5.73762i −0.770439 + 0.637513i
\(82\) 0 0
\(83\) −8.90868 + 11.3283i −0.977855 + 1.24344i −0.00794744 + 0.999968i \(0.502530\pi\)
−0.969907 + 0.243475i \(0.921713\pi\)
\(84\) 0 0
\(85\) 0.664499 + 3.44775i 0.0720750 + 0.373961i
\(86\) 0 0
\(87\) 0.154668 1.73359i 0.0165822 0.185860i
\(88\) 0 0
\(89\) 7.82886 12.1820i 0.829858 1.29128i −0.124380 0.992235i \(-0.539694\pi\)
0.954238 0.299050i \(-0.0966696\pi\)
\(90\) 0 0
\(91\) 5.93517 6.84955i 0.622174 0.718028i
\(92\) 0 0
\(93\) 1.96770 + 9.87853i 0.204041 + 1.02436i
\(94\) 0 0
\(95\) −1.77006 + 7.29627i −0.181604 + 0.748582i
\(96\) 0 0
\(97\) 4.98536 + 2.87830i 0.506186 + 0.292247i 0.731265 0.682094i \(-0.238930\pi\)
−0.225078 + 0.974341i \(0.572264\pi\)
\(98\) 0 0
\(99\) −2.49307 2.80589i −0.250563 0.282002i
\(100\) 0 0
\(101\) −6.06907 + 8.52281i −0.603895 + 0.848052i −0.997459 0.0712456i \(-0.977303\pi\)
0.393564 + 0.919297i \(0.371242\pi\)
\(102\) 0 0
\(103\) −9.39509 8.95820i −0.925726 0.882678i 0.0676357 0.997710i \(-0.478454\pi\)
−0.993362 + 0.115032i \(0.963303\pi\)
\(104\) 0 0
\(105\) −3.89211 + 5.01305i −0.379831 + 0.489224i
\(106\) 0 0
\(107\) −0.0851448 + 0.0122420i −0.00823125 + 0.00118348i −0.146429 0.989221i \(-0.546778\pi\)
0.138198 + 0.990405i \(0.455869\pi\)
\(108\) 0 0
\(109\) 3.46042 11.7851i 0.331448 1.12881i −0.610211 0.792239i \(-0.708915\pi\)
0.941659 0.336569i \(-0.109267\pi\)
\(110\) 0 0
\(111\) 5.82109 + 12.5395i 0.552514 + 1.19020i
\(112\) 0 0
\(113\) 9.11844 7.17082i 0.857790 0.674574i −0.0891377 0.996019i \(-0.528411\pi\)
0.946928 + 0.321446i \(0.104169\pi\)
\(114\) 0 0
\(115\) −0.712983 + 7.46669i −0.0664860 + 0.696273i
\(116\) 0 0
\(117\) −3.56196 + 7.12539i −0.329303 + 0.658742i
\(118\) 0 0
\(119\) 4.63742 + 10.1545i 0.425112 + 0.930865i
\(120\) 0 0
\(121\) −6.82816 + 6.51064i −0.620742 + 0.591876i
\(122\) 0 0
\(123\) 4.49996 4.34443i 0.405748 0.391724i
\(124\) 0 0
\(125\) −3.94569 + 8.63986i −0.352913 + 0.772773i
\(126\) 0 0
\(127\) 9.48549 0.905754i 0.841701 0.0803727i 0.334707 0.942322i \(-0.391363\pi\)
0.506994 + 0.861950i \(0.330757\pi\)
\(128\) 0 0
\(129\) 4.33225 1.07956i 0.381434 0.0950496i
\(130\) 0 0
\(131\) −2.19930 3.42218i −0.192154 0.298997i 0.731786 0.681534i \(-0.238687\pi\)
−0.923940 + 0.382537i \(0.875051\pi\)
\(132\) 0 0
\(133\) 23.8703i 2.06982i
\(134\) 0 0
\(135\) 2.22228 5.11654i 0.191263 0.440362i
\(136\) 0 0
\(137\) −13.1710 + 8.46452i −1.12528 + 0.723173i −0.964569 0.263829i \(-0.915014\pi\)
−0.160709 + 0.987002i \(0.551378\pi\)
\(138\) 0 0
\(139\) 9.29511 + 1.33643i 0.788401 + 0.113355i 0.524742 0.851261i \(-0.324162\pi\)
0.263658 + 0.964616i \(0.415071\pi\)
\(140\) 0 0
\(141\) −9.39563 17.9501i −0.791254 1.51167i
\(142\) 0 0
\(143\) −3.02204 1.38012i −0.252715 0.115411i
\(144\) 0 0
\(145\) 0.400937 + 1.00149i 0.0332960 + 0.0831695i
\(146\) 0 0
\(147\) −3.30003 + 7.34658i −0.272182 + 0.605935i
\(148\) 0 0
\(149\) −13.8950 + 6.34561i −1.13832 + 0.519853i −0.893209 0.449642i \(-0.851552\pi\)
−0.245111 + 0.969495i \(0.578824\pi\)
\(150\) 0 0
\(151\) −0.869270 2.51159i −0.0707402 0.204390i 0.904089 0.427345i \(-0.140551\pi\)
−0.974829 + 0.222955i \(0.928430\pi\)
\(152\) 0 0
\(153\) −6.16079 7.63672i −0.498070 0.617392i
\(154\) 0 0
\(155\) −3.85924 4.90742i −0.309981 0.394173i
\(156\) 0 0
\(157\) 0.361765 + 7.59438i 0.0288720 + 0.606098i 0.966222 + 0.257710i \(0.0829678\pi\)
−0.937350 + 0.348388i \(0.886729\pi\)
\(158\) 0 0
\(159\) 12.1540 1.23687i 0.963878 0.0980899i
\(160\) 0 0
\(161\) 3.39382 + 23.6045i 0.267470 + 1.86030i
\(162\) 0 0
\(163\) −3.22544 5.58663i −0.252636 0.437579i 0.711615 0.702570i \(-0.247964\pi\)
−0.964251 + 0.264991i \(0.914631\pi\)
\(164\) 0 0
\(165\) 2.16512 + 0.851204i 0.168554 + 0.0662661i
\(166\) 0 0
\(167\) −9.05990 6.45152i −0.701076 0.499234i 0.173062 0.984911i \(-0.444634\pi\)
−0.874138 + 0.485677i \(0.838573\pi\)
\(168\) 0 0
\(169\) 0.283066 5.94229i 0.0217743 0.457099i
\(170\) 0 0
\(171\) −5.19952 20.3262i −0.397617 1.55438i
\(172\) 0 0
\(173\) −6.05483 1.46889i −0.460341 0.111677i −0.00111938 0.999999i \(-0.500356\pi\)
−0.459221 + 0.888322i \(0.651871\pi\)
\(174\) 0 0
\(175\) −2.48529 + 12.8949i −0.187870 + 0.974763i
\(176\) 0 0
\(177\) −22.2477 7.54547i −1.67224 0.567152i
\(178\) 0 0
\(179\) −6.62139 4.25531i −0.494906 0.318057i 0.269270 0.963065i \(-0.413218\pi\)
−0.764176 + 0.645008i \(0.776854\pi\)
\(180\) 0 0
\(181\) 5.80714 + 2.99379i 0.431641 + 0.222526i 0.660334 0.750972i \(-0.270415\pi\)
−0.228693 + 0.973499i \(0.573445\pi\)
\(182\) 0 0
\(183\) 9.19505 + 14.1141i 0.679718 + 1.04334i
\(184\) 0 0
\(185\) −6.73550 5.29686i −0.495204 0.389433i
\(186\) 0 0
\(187\) 3.09259 2.67974i 0.226153 0.195962i
\(188\) 0 0
\(189\) 3.03108 17.4745i 0.220479 1.27108i
\(190\) 0 0
\(191\) 13.6843 7.05474i 0.990160 0.510463i 0.114517 0.993421i \(-0.463468\pi\)
0.875643 + 0.482958i \(0.160438\pi\)
\(192\) 0 0
\(193\) 10.8125 3.17484i 0.778301 0.228530i 0.131630 0.991299i \(-0.457979\pi\)
0.646671 + 0.762769i \(0.276161\pi\)
\(194\) 0 0
\(195\) −0.0306960 4.93739i −0.00219819 0.353574i
\(196\) 0 0
\(197\) −4.30693 + 12.4440i −0.306856 + 0.886602i 0.681144 + 0.732149i \(0.261483\pi\)
−0.988000 + 0.154453i \(0.950639\pi\)
\(198\) 0 0
\(199\) 0.573623 + 0.805541i 0.0406631 + 0.0571033i 0.834407 0.551149i \(-0.185810\pi\)
−0.793744 + 0.608252i \(0.791871\pi\)
\(200\) 0 0
\(201\) −12.2162 + 7.19483i −0.861661 + 0.507484i
\(202\) 0 0
\(203\) 1.98947 + 2.79382i 0.139633 + 0.196088i
\(204\) 0 0
\(205\) −1.26800 + 3.66364i −0.0885607 + 0.255879i
\(206\) 0 0
\(207\) −8.03155 19.3606i −0.558231 1.34566i
\(208\) 0 0
\(209\) 8.39556 2.46516i 0.580733 0.170519i
\(210\) 0 0
\(211\) −6.01206 + 3.09943i −0.413888 + 0.213374i −0.652578 0.757722i \(-0.726312\pi\)
0.238690 + 0.971096i \(0.423282\pi\)
\(212\) 0 0
\(213\) −15.6299 + 11.2771i −1.07094 + 0.772694i
\(214\) 0 0
\(215\) −2.09138 + 1.81219i −0.142631 + 0.123591i
\(216\) 0 0
\(217\) −15.6024 12.2699i −1.05916 0.832934i
\(218\) 0 0
\(219\) −8.81271 + 5.74131i −0.595507 + 0.387962i
\(220\) 0 0
\(221\) −7.71935 3.97960i −0.519260 0.267697i
\(222\) 0 0
\(223\) −3.72053 2.39104i −0.249145 0.160116i 0.410108 0.912037i \(-0.365491\pi\)
−0.659253 + 0.751921i \(0.729127\pi\)
\(224\) 0 0
\(225\) −0.692524 11.5217i −0.0461683 0.768114i
\(226\) 0 0
\(227\) 2.92214 15.1615i 0.193949 1.00630i −0.746247 0.665669i \(-0.768146\pi\)
0.940196 0.340634i \(-0.110642\pi\)
\(228\) 0 0
\(229\) −1.16775 0.283294i −0.0771672 0.0187206i 0.196989 0.980406i \(-0.436884\pi\)
−0.274157 + 0.961685i \(0.588399\pi\)
\(230\) 0 0
\(231\) 7.32767 + 1.00710i 0.482126 + 0.0662626i
\(232\) 0 0
\(233\) 0.0185739 0.389913i 0.00121681 0.0255441i −0.998177 0.0603501i \(-0.980778\pi\)
0.999394 + 0.0348060i \(0.0110813\pi\)
\(234\) 0 0
\(235\) 10.2291 + 7.28414i 0.667276 + 0.475165i
\(236\) 0 0
\(237\) −5.97654 + 15.2019i −0.388218 + 0.987470i
\(238\) 0 0
\(239\) 2.07881 + 3.60060i 0.134467 + 0.232903i 0.925394 0.379007i \(-0.123734\pi\)
−0.790927 + 0.611911i \(0.790401\pi\)
\(240\) 0 0
\(241\) 1.04541 + 7.27101i 0.0673410 + 0.468367i 0.995390 + 0.0959090i \(0.0305758\pi\)
−0.928049 + 0.372458i \(0.878515\pi\)
\(242\) 0 0
\(243\) 1.22531 + 15.5402i 0.0786036 + 0.996906i
\(244\) 0 0
\(245\) −0.237519 4.98613i −0.0151745 0.318552i
\(246\) 0 0
\(247\) −11.4795 14.5974i −0.730423 0.928809i
\(248\) 0 0
\(249\) 7.18128 + 23.9064i 0.455095 + 1.51500i
\(250\) 0 0
\(251\) 7.51263 + 21.7063i 0.474193 + 1.37009i 0.888049 + 0.459749i \(0.152061\pi\)
−0.413856 + 0.910343i \(0.635818\pi\)
\(252\) 0 0
\(253\) 7.95159 3.63137i 0.499912 0.228302i
\(254\) 0 0
\(255\) 5.54759 + 2.49194i 0.347404 + 0.156051i
\(256\) 0 0
\(257\) 0.867445 + 2.16677i 0.0541098 + 0.135160i 0.952960 0.303097i \(-0.0980205\pi\)
−0.898850 + 0.438256i \(0.855596\pi\)
\(258\) 0 0
\(259\) −24.7812 11.3172i −1.53983 0.703218i
\(260\) 0 0
\(261\) −2.30265 1.94566i −0.142530 0.120433i
\(262\) 0 0
\(263\) 15.9922 + 2.29933i 0.986119 + 0.141783i 0.616461 0.787385i \(-0.288566\pi\)
0.369658 + 0.929168i \(0.379475\pi\)
\(264\) 0 0
\(265\) −6.37008 + 4.09380i −0.391311 + 0.251480i
\(266\) 0 0
\(267\) −9.46637 23.2263i −0.579332 1.42143i
\(268\) 0 0
\(269\) 22.0639i 1.34526i −0.739978 0.672631i \(-0.765164\pi\)
0.739978 0.672631i \(-0.234836\pi\)
\(270\) 0 0
\(271\) −10.4091 16.1968i −0.632305 0.983886i −0.998574 0.0533769i \(-0.983002\pi\)
0.366269 0.930509i \(-0.380635\pi\)
\(272\) 0 0
\(273\) −3.79572 15.2322i −0.229727 0.921895i
\(274\) 0 0
\(275\) 4.79200 0.457581i 0.288969 0.0275932i
\(276\) 0 0
\(277\) −2.65963 + 5.82378i −0.159802 + 0.349917i −0.972549 0.232700i \(-0.925244\pi\)
0.812747 + 0.582617i \(0.197971\pi\)
\(278\) 0 0
\(279\) 15.9586 + 7.04956i 0.955414 + 0.422046i
\(280\) 0 0
\(281\) −12.9657 + 12.3628i −0.773468 + 0.737501i −0.970028 0.242991i \(-0.921871\pi\)
0.196560 + 0.980492i \(0.437023\pi\)
\(282\) 0 0
\(283\) −5.54205 12.1354i −0.329441 0.721375i 0.670345 0.742049i \(-0.266146\pi\)
−0.999786 + 0.0206743i \(0.993419\pi\)
\(284\) 0 0
\(285\) 8.57679 + 9.77469i 0.508045 + 0.579003i
\(286\) 0 0
\(287\) −1.17165 + 12.2701i −0.0691605 + 0.724281i
\(288\) 0 0
\(289\) −4.95434 + 3.89614i −0.291432 + 0.229184i
\(290\) 0 0
\(291\) 9.04375 4.19829i 0.530154 0.246108i
\(292\) 0 0
\(293\) 0.725462 2.47070i 0.0423819 0.144340i −0.935584 0.353104i \(-0.885126\pi\)
0.977966 + 0.208765i \(0.0669443\pi\)
\(294\) 0 0
\(295\) 14.4127 2.07223i 0.839140 0.120650i
\(296\) 0 0
\(297\) −6.45908 + 0.738565i −0.374794 + 0.0428559i
\(298\) 0 0
\(299\) −13.4271 12.8027i −0.776509 0.740400i
\(300\) 0 0
\(301\) −5.10347 + 7.16682i −0.294159 + 0.413088i
\(302\) 0 0
\(303\) 6.03356 + 17.0884i 0.346619 + 0.981700i
\(304\) 0 0
\(305\) −9.04197 5.22038i −0.517742 0.298918i
\(306\) 0 0
\(307\) −5.08377 + 20.9556i −0.290146 + 1.19600i 0.620966 + 0.783838i \(0.286741\pi\)
−0.911111 + 0.412160i \(0.864774\pi\)
\(308\) 0 0
\(309\) −22.0513 + 4.39239i −1.25445 + 0.249874i
\(310\) 0 0
\(311\) 7.70833 8.89589i 0.437099 0.504440i −0.493871 0.869535i \(-0.664418\pi\)
0.930970 + 0.365096i \(0.118964\pi\)
\(312\) 0 0
\(313\) 4.49750 6.99824i 0.254214 0.395564i −0.690567 0.723269i \(-0.742639\pi\)
0.944780 + 0.327705i \(0.106275\pi\)
\(314\) 0 0
\(315\) 3.22788 + 10.5080i 0.181870 + 0.592060i
\(316\) 0 0
\(317\) −1.16133 6.02556i −0.0652268 0.338429i 0.934625 0.355634i \(-0.115735\pi\)
−0.999852 + 0.0172055i \(0.994523\pi\)
\(318\) 0 0
\(319\) 0.777172 0.988255i 0.0435133 0.0553316i
\(320\) 0 0
\(321\) −0.0674473 + 0.132851i −0.00376454 + 0.00741501i
\(322\) 0 0
\(323\) 22.2288 5.39264i 1.23684 0.300055i
\(324\) 0 0
\(325\) −4.68148 9.08081i −0.259682 0.503713i
\(326\) 0 0
\(327\) −13.2545 16.6405i −0.732976 0.920223i
\(328\) 0 0
\(329\) 37.0652 + 14.8387i 2.04347 + 0.818083i
\(330\) 0 0
\(331\) 4.35721 + 1.50804i 0.239494 + 0.0828896i 0.444178 0.895938i \(-0.353496\pi\)
−0.204685 + 0.978828i \(0.565617\pi\)
\(332\) 0 0
\(333\) 23.5670 + 4.23897i 1.29147 + 0.232294i
\(334\) 0 0
\(335\) 4.73270 7.40399i 0.258575 0.404523i
\(336\) 0 0
\(337\) 26.3193 18.7419i 1.43370 1.02094i 0.441374 0.897323i \(-0.354491\pi\)
0.992330 0.123613i \(-0.0394482\pi\)
\(338\) 0 0
\(339\) −1.08078 20.0632i −0.0587000 1.08968i
\(340\) 0 0
\(341\) −2.70420 + 6.75477i −0.146441 + 0.365791i
\(342\) 0 0
\(343\) 2.25995 + 7.69668i 0.122026 + 0.415581i
\(344\) 0 0
\(345\) 9.87104 + 8.44643i 0.531439 + 0.454741i
\(346\) 0 0
\(347\) −1.90552 7.85464i −0.102293 0.421659i 0.897520 0.440974i \(-0.145367\pi\)
−0.999813 + 0.0193145i \(0.993852\pi\)
\(348\) 0 0
\(349\) −4.97083 5.73664i −0.266082 0.307075i 0.606948 0.794742i \(-0.292394\pi\)
−0.873030 + 0.487666i \(0.837848\pi\)
\(350\) 0 0
\(351\) 6.55009 + 12.1438i 0.349618 + 0.648190i
\(352\) 0 0
\(353\) −6.62243 + 1.27637i −0.352476 + 0.0679343i −0.362416 0.932016i \(-0.618048\pi\)
0.00993986 + 0.999951i \(0.496836\pi\)
\(354\) 0 0
\(355\) 5.47394 10.6180i 0.290526 0.563543i
\(356\) 0 0
\(357\) 19.0085 + 3.54116i 1.00603 + 0.187418i
\(358\) 0 0
\(359\) −28.2755 24.5009i −1.49232 1.29311i −0.850141 0.526555i \(-0.823483\pi\)
−0.642183 0.766551i \(-0.721971\pi\)
\(360\) 0 0
\(361\) 29.3694 + 5.66049i 1.54576 + 0.297921i
\(362\) 0 0
\(363\) 2.42612 + 16.1601i 0.127338 + 0.848188i
\(364\) 0 0
\(365\) 3.25956 5.64573i 0.170613 0.295511i
\(366\) 0 0
\(367\) 26.1307 + 1.24476i 1.36401 + 0.0649760i 0.716771 0.697308i \(-0.245619\pi\)
0.647242 + 0.762284i \(0.275922\pi\)
\(368\) 0 0
\(369\) −1.67502 10.7035i −0.0871983 0.557204i
\(370\) 0 0
\(371\) −16.6133 + 17.4235i −0.862519 + 0.904584i
\(372\) 0 0
\(373\) 10.3411 5.97047i 0.535444 0.309139i −0.207786 0.978174i \(-0.566626\pi\)
0.743231 + 0.669035i \(0.233293\pi\)
\(374\) 0 0
\(375\) 8.31409 + 14.1959i 0.429338 + 0.733072i
\(376\) 0 0
\(377\) −2.56020 0.751742i −0.131857 0.0387167i
\(378\) 0 0
\(379\) −33.2501 + 1.58390i −1.70794 + 0.0813592i −0.878653 0.477462i \(-0.841557\pi\)
−0.829288 + 0.558821i \(0.811254\pi\)
\(380\) 0 0
\(381\) 8.16302 14.3440i 0.418204 0.734864i
\(382\) 0 0
\(383\) 18.4651 + 1.76320i 0.943522 + 0.0900955i 0.555465 0.831540i \(-0.312540\pi\)
0.388057 + 0.921635i \(0.373146\pi\)
\(384\) 0 0
\(385\) −4.33233 + 1.49943i −0.220796 + 0.0764183i
\(386\) 0 0
\(387\) 2.78464 7.21439i 0.141551 0.366728i
\(388\) 0 0
\(389\) 12.6712 + 13.2892i 0.642455 + 0.673787i 0.961769 0.273862i \(-0.0883011\pi\)
−0.319314 + 0.947649i \(0.603453\pi\)
\(390\) 0 0
\(391\) 21.2146 8.49303i 1.07287 0.429511i
\(392\) 0 0
\(393\) −7.03987 0.291497i −0.355115 0.0147041i
\(394\) 0 0
\(395\) −0.962379 10.0785i −0.0484226 0.507104i
\(396\) 0 0
\(397\) −1.34766 + 9.37317i −0.0676370 + 0.470426i 0.927650 + 0.373451i \(0.121826\pi\)
−0.995287 + 0.0969747i \(0.969083\pi\)
\(398\) 0 0
\(399\) 33.8268 + 23.7724i 1.69346 + 1.19011i
\(400\) 0 0
\(401\) −28.6827 −1.43235 −0.716174 0.697922i \(-0.754108\pi\)
−0.716174 + 0.697922i \(0.754108\pi\)
\(402\) 0 0
\(403\) 15.4421 0.769224
\(404\) 0 0
\(405\) −5.03752 8.24475i −0.250316 0.409685i
\(406\) 0 0
\(407\) −1.42121 + 9.88472i −0.0704467 + 0.489967i
\(408\) 0 0
\(409\) 1.22216 + 12.7991i 0.0604320 + 0.632872i 0.974055 + 0.226310i \(0.0726664\pi\)
−0.913623 + 0.406562i \(0.866728\pi\)
\(410\) 0 0
\(411\) −1.12189 + 27.0946i −0.0553389 + 1.33648i
\(412\) 0 0
\(413\) 42.9782 17.2059i 2.11482 0.846645i
\(414\) 0 0
\(415\) −10.6766 11.1973i −0.524093 0.549653i
\(416\) 0 0
\(417\) 11.1508 11.8412i 0.546059 0.579866i
\(418\) 0 0
\(419\) 1.30845 0.452859i 0.0639220 0.0221236i −0.294920 0.955522i \(-0.595293\pi\)
0.358842 + 0.933398i \(0.383172\pi\)
\(420\) 0 0
\(421\) 32.1300 + 3.06804i 1.56592 + 0.149527i 0.841663 0.540003i \(-0.181577\pi\)
0.724257 + 0.689530i \(0.242183\pi\)
\(422\) 0 0
\(423\) −34.7943 4.56185i −1.69175 0.221805i
\(424\) 0 0
\(425\) 12.5696 0.598764i 0.609715 0.0290443i
\(426\) 0 0
\(427\) −31.8503 9.35209i −1.54134 0.452579i
\(428\) 0 0
\(429\) −4.96541 + 2.90809i −0.239732 + 0.140404i
\(430\) 0 0
\(431\) 11.4511 6.61130i 0.551580 0.318455i −0.198179 0.980166i \(-0.563503\pi\)
0.749759 + 0.661711i \(0.230169\pi\)
\(432\) 0 0
\(433\) −11.3091 + 11.8607i −0.543482 + 0.569988i −0.937000 0.349329i \(-0.886409\pi\)
0.393518 + 0.919317i \(0.371258\pi\)
\(434\) 0 0
\(435\) 1.81851 + 0.429214i 0.0871911 + 0.0205792i
\(436\) 0 0
\(437\) 48.8074 + 2.32498i 2.33477 + 0.111219i
\(438\) 0 0
\(439\) −20.0048 + 34.6493i −0.954777 + 1.65372i −0.219899 + 0.975523i \(0.570573\pi\)
−0.734878 + 0.678200i \(0.762760\pi\)
\(440\) 0 0
\(441\) 7.12439 + 11.9929i 0.339257 + 0.571091i
\(442\) 0 0
\(443\) −13.9459 2.68786i −0.662591 0.127704i −0.153141 0.988204i \(-0.548939\pi\)
−0.509450 + 0.860500i \(0.670151\pi\)
\(444\) 0 0
\(445\) 11.7487 + 10.1803i 0.556940 + 0.482591i
\(446\) 0 0
\(447\) −4.84554 + 26.0102i −0.229186 + 1.23024i
\(448\) 0 0
\(449\) −9.31873 + 18.0758i −0.439778 + 0.853051i 0.559921 + 0.828546i \(0.310831\pi\)
−0.999700 + 0.0245051i \(0.992199\pi\)
\(450\) 0 0
\(451\) 4.43659 0.855082i 0.208911 0.0402643i
\(452\) 0 0
\(453\) −4.42489 1.26944i −0.207900 0.0596434i
\(454\) 0 0
\(455\) 6.37167 + 7.35330i 0.298709 + 0.344728i
\(456\) 0 0
\(457\) 2.03728 + 8.39776i 0.0952997 + 0.392831i 0.999405 0.0344780i \(-0.0109769\pi\)
−0.904106 + 0.427309i \(0.859462\pi\)
\(458\) 0 0
\(459\) −16.9575 + 1.12510i −0.791511 + 0.0525151i
\(460\) 0 0
\(461\) −5.51343 18.7770i −0.256786 0.874533i −0.982457 0.186491i \(-0.940289\pi\)
0.725671 0.688042i \(-0.241530\pi\)
\(462\) 0 0
\(463\) 4.70448 11.7512i 0.218636 0.546125i −0.777984 0.628284i \(-0.783757\pi\)
0.996619 + 0.0821593i \(0.0261816\pi\)
\(464\) 0 0
\(465\) −10.7977 + 0.581662i −0.500733 + 0.0269739i
\(466\) 0 0
\(467\) −14.8938 + 10.6058i −0.689203 + 0.490779i −0.870196 0.492705i \(-0.836008\pi\)
0.180993 + 0.983484i \(0.442069\pi\)
\(468\) 0 0
\(469\) 9.07304 26.4238i 0.418954 1.22014i
\(470\) 0 0
\(471\) 11.1223 + 7.05057i 0.512490 + 0.324873i
\(472\) 0 0
\(473\) 3.04773 + 1.05483i 0.140135 + 0.0485012i
\(474\) 0 0
\(475\) 24.9803 + 10.0006i 1.14617 + 0.458859i
\(476\) 0 0
\(477\) 10.3514 18.4554i 0.473958 0.845012i
\(478\) 0 0
\(479\) 15.6875 + 30.4295i 0.716780 + 1.39036i 0.912243 + 0.409648i \(0.134349\pi\)
−0.195463 + 0.980711i \(0.562621\pi\)
\(480\) 0 0
\(481\) 20.5970 4.99678i 0.939143 0.227834i
\(482\) 0 0
\(483\) 36.8300 + 18.6983i 1.67582 + 0.850801i
\(484\) 0 0
\(485\) −3.82020 + 4.85778i −0.173466 + 0.220580i
\(486\) 0 0
\(487\) −3.77448 19.5839i −0.171038 0.887430i −0.961476 0.274888i \(-0.911359\pi\)
0.790438 0.612542i \(-0.209853\pi\)
\(488\) 0 0
\(489\) −11.1291 0.992917i −0.503273 0.0449012i
\(490\) 0 0
\(491\) −15.4080 + 23.9753i −0.695352 + 1.08199i 0.296554 + 0.955016i \(0.404162\pi\)
−0.991906 + 0.126973i \(0.959474\pi\)
\(492\) 0 0
\(493\) 2.15224 2.48382i 0.0969321 0.111866i
\(494\) 0 0
\(495\) 3.36248 2.22049i 0.151132 0.0998037i
\(496\) 0 0
\(497\) 8.95420 36.9097i 0.401651 1.65563i
\(498\) 0 0
\(499\) −29.8604 17.2399i −1.33674 0.771765i −0.350414 0.936595i \(-0.613959\pi\)
−0.986322 + 0.164830i \(0.947292\pi\)
\(500\) 0 0
\(501\) −18.1652 + 6.41378i −0.811562 + 0.286546i
\(502\) 0 0
\(503\) 24.5267 34.4430i 1.09359 1.53574i 0.274929 0.961464i \(-0.411346\pi\)
0.818664 0.574272i \(-0.194715\pi\)
\(504\) 0 0
\(505\) −8.12926 7.75123i −0.361747 0.344925i
\(506\) 0 0
\(507\) −8.13895 6.31905i −0.361464 0.280639i
\(508\) 0 0
\(509\) −25.5162 + 3.66868i −1.13099 + 0.162611i −0.682296 0.731076i \(-0.739018\pi\)
−0.448690 + 0.893687i \(0.648109\pi\)
\(510\) 0 0
\(511\) 5.83936 19.8870i 0.258318 0.879751i
\(512\) 0 0
\(513\) −33.9826 12.8745i −1.50037 0.568425i
\(514\) 0 0
\(515\) 10.9545 8.61475i 0.482715 0.379611i
\(516\) 0 0
\(517\) 1.39116 14.5689i 0.0611831 0.640738i
\(518\) 0 0
\(519\) −8.11156 + 7.11748i −0.356058 + 0.312423i
\(520\) 0 0
\(521\) −5.35842 11.7333i −0.234756 0.514045i 0.755187 0.655510i \(-0.227546\pi\)
−0.989943 + 0.141465i \(0.954819\pi\)
\(522\) 0 0
\(523\) 8.37239 7.98306i 0.366099 0.349075i −0.484592 0.874740i \(-0.661032\pi\)
0.850691 + 0.525665i \(0.176184\pi\)
\(524\) 0 0
\(525\) 15.7984 + 16.3639i 0.689497 + 0.714180i
\(526\) 0 0
\(527\) −7.90129 + 17.3014i −0.344186 + 0.753661i
\(528\) 0 0
\(529\) 25.6986 2.45392i 1.11733 0.106692i
\(530\) 0 0
\(531\) −32.8492 + 24.0129i −1.42553 + 1.04207i
\(532\) 0 0
\(533\) −5.18433 8.06698i −0.224558 0.349420i
\(534\) 0 0
\(535\) 0.0923467i 0.00399250i
\(536\) 0 0
\(537\) −12.6245 + 5.14536i −0.544785 + 0.222039i
\(538\) 0 0
\(539\) −4.89409 + 3.14524i −0.210803 + 0.135475i
\(540\) 0 0
\(541\) 18.6189 + 2.67700i 0.800490 + 0.115093i 0.530406 0.847744i \(-0.322039\pi\)
0.270084 + 0.962837i \(0.412949\pi\)
\(542\) 0 0
\(543\) 10.0258 5.24782i 0.430249 0.225206i
\(544\) 0 0
\(545\) 11.9944 + 5.47765i 0.513783 + 0.234637i
\(546\) 0 0
\(547\) 11.5509 + 28.8527i 0.493879 + 1.23365i 0.940765 + 0.339059i \(0.110109\pi\)
−0.446886 + 0.894591i \(0.647467\pi\)
\(548\) 0 0
\(549\) 29.1585 + 1.02581i 1.24445 + 0.0437804i
\(550\) 0 0
\(551\) 6.39251 2.91936i 0.272330 0.124369i
\(552\) 0 0
\(553\) −10.5279 30.4185i −0.447694 1.29353i
\(554\) 0 0
\(555\) −14.2141 + 4.26979i −0.603354 + 0.181243i
\(556\) 0 0
\(557\) −21.7296 27.6314i −0.920712 1.17078i −0.984949 0.172846i \(-0.944704\pi\)
0.0642371 0.997935i \(-0.479539\pi\)
\(558\) 0 0
\(559\) −0.325688 6.83703i −0.0137751 0.289175i
\(560\) 0 0
\(561\) −0.717580 7.05128i −0.0302962 0.297705i
\(562\) 0 0
\(563\) −5.63565 39.1968i −0.237515 1.65195i −0.664204 0.747552i \(-0.731229\pi\)
0.426689 0.904398i \(-0.359680\pi\)
\(564\) 0 0
\(565\) 6.22671 + 10.7850i 0.261960 + 0.453728i
\(566\) 0 0
\(567\) −21.7445 21.6982i −0.913185 0.911237i
\(568\) 0 0
\(569\) 1.61100 + 1.14719i 0.0675368 + 0.0480927i 0.613327 0.789829i \(-0.289831\pi\)
−0.545790 + 0.837922i \(0.683770\pi\)
\(570\) 0 0
\(571\) 2.04251 42.8776i 0.0854765 1.79437i −0.396344 0.918102i \(-0.629721\pi\)
0.481821 0.876270i \(-0.339976\pi\)
\(572\) 0 0
\(573\) 3.63083 26.4179i 0.151680 1.10362i
\(574\) 0 0
\(575\) 26.1240 + 6.33761i 1.08945 + 0.264297i
\(576\) 0 0
\(577\) −1.44529 + 7.49887i −0.0601682 + 0.312182i −0.999527 0.0307538i \(-0.990209\pi\)
0.939359 + 0.342936i \(0.111421\pi\)
\(578\) 0 0
\(579\) 6.26906 18.4843i 0.260533 0.768180i
\(580\) 0 0
\(581\) −41.3809 26.5939i −1.71677 1.10330i
\(582\) 0 0
\(583\) 7.84383 + 4.04378i 0.324858 + 0.167476i
\(584\) 0 0
\(585\) −7.02737 4.87363i −0.290546 0.201500i
\(586\) 0 0
\(587\) −26.2994 20.6821i −1.08549 0.853641i −0.0955945 0.995420i \(-0.530475\pi\)
−0.989898 + 0.141779i \(0.954718\pi\)
\(588\) 0 0
\(589\) −30.7367 + 26.6335i −1.26648 + 1.09741i
\(590\) 0 0
\(591\) 13.3453 + 18.4964i 0.548951 + 0.760839i
\(592\) 0 0
\(593\) 32.6745 16.8449i 1.34178 0.691736i 0.370312 0.928907i \(-0.379251\pi\)
0.971468 + 0.237172i \(0.0762204\pi\)
\(594\) 0 0
\(595\) −11.4989 + 3.37638i −0.471409 + 0.138418i
\(596\) 0 0
\(597\) 1.71281 0.0106486i 0.0701005 0.000435819i
\(598\) 0 0
\(599\) −3.14596 + 9.08965i −0.128540 + 0.371393i −0.990846 0.134995i \(-0.956898\pi\)
0.862306 + 0.506388i \(0.169019\pi\)
\(600\) 0 0
\(601\) −4.55869 6.40178i −0.185953 0.261134i 0.711067 0.703124i \(-0.248212\pi\)
−0.897020 + 0.441990i \(0.854273\pi\)
\(602\) 0 0
\(603\) −1.97021 + 24.4769i −0.0802331 + 0.996776i
\(604\) 0 0
\(605\) −5.87510 8.25043i −0.238857 0.335428i
\(606\) 0 0
\(607\) 2.62671 7.58939i 0.106615 0.308044i −0.879057 0.476716i \(-0.841827\pi\)
0.985672 + 0.168673i \(0.0539481\pi\)
\(608\) 0 0
\(609\) 5.94045 0.0369321i 0.240719 0.00149656i
\(610\) 0 0
\(611\) −29.8026 + 8.75082i −1.20568 + 0.354020i
\(612\) 0 0
\(613\) −15.3235 + 7.89982i −0.618911 + 0.319071i −0.739013 0.673691i \(-0.764708\pi\)
0.120102 + 0.992762i \(0.461678\pi\)
\(614\) 0 0
\(615\) 3.92896 + 5.44549i 0.158431 + 0.219583i
\(616\) 0 0
\(617\) −7.70303 + 6.67472i −0.310112 + 0.268714i −0.795986 0.605315i \(-0.793047\pi\)
0.485873 + 0.874029i \(0.338502\pi\)
\(618\) 0 0
\(619\) 29.4092 + 23.1276i 1.18205 + 0.929578i 0.998571 0.0534445i \(-0.0170200\pi\)
0.183484 + 0.983023i \(0.441262\pi\)
\(620\) 0 0
\(621\) −35.4347 7.89964i −1.42194 0.317002i
\(622\) 0 0
\(623\) 43.9310 + 22.6480i 1.76006 + 0.907373i
\(624\) 0 0
\(625\) 7.60557 + 4.88780i 0.304223 + 0.195512i
\(626\) 0 0
\(627\) 4.86773 14.3524i 0.194398 0.573182i
\(628\) 0 0
\(629\) −4.94051 + 25.6338i −0.196991 + 1.02209i
\(630\) 0 0
\(631\) −36.1058 8.75918i −1.43735 0.348698i −0.559978 0.828507i \(-0.689190\pi\)
−0.877373 + 0.479810i \(0.840706\pi\)
\(632\) 0 0
\(633\) −1.59517 + 11.6064i −0.0634024 + 0.461315i
\(634\) 0 0
\(635\) −0.486735 + 10.2178i −0.0193155 + 0.405482i
\(636\) 0 0
\(637\) 10.0575 + 7.16194i 0.398494 + 0.283766i
\(638\) 0 0
\(639\) 0.415067 + 33.3800i 0.0164198 + 1.32049i
\(640\) 0 0
\(641\) 4.70490 + 8.14913i 0.185833 + 0.321871i 0.943857 0.330355i \(-0.107168\pi\)
−0.758024 + 0.652226i \(0.773835\pi\)
\(642\) 0 0
\(643\) −4.78557 33.2844i −0.188724 1.31261i −0.835316 0.549771i \(-0.814715\pi\)
0.646591 0.762837i \(-0.276194\pi\)
\(644\) 0 0
\(645\) 0.485267 + 4.76847i 0.0191074 + 0.187758i
\(646\) 0 0
\(647\) 0.466056 + 9.78372i 0.0183226 + 0.384638i 0.989340 + 0.145627i \(0.0465200\pi\)
−0.971017 + 0.239011i \(0.923177\pi\)
\(648\) 0 0
\(649\) −10.4901 13.3392i −0.411771 0.523609i
\(650\) 0 0
\(651\) −32.9261 + 9.89075i −1.29048 + 0.387649i
\(652\) 0 0
\(653\) 7.31137 + 21.1248i 0.286116 + 0.826678i 0.992868 + 0.119217i \(0.0380383\pi\)
−0.706752 + 0.707461i \(0.749841\pi\)
\(654\) 0 0
\(655\) 3.97248 1.81417i 0.155218 0.0708856i
\(656\) 0 0
\(657\) −0.640505 + 18.2063i −0.0249885 + 0.710295i
\(658\) 0 0
\(659\) 16.3965 + 40.9565i 0.638718 + 1.59544i 0.794238 + 0.607607i \(0.207870\pi\)
−0.155520 + 0.987833i \(0.549705\pi\)
\(660\) 0 0
\(661\) −43.2103 19.7335i −1.68069 0.767544i −0.999368 0.0355573i \(-0.988679\pi\)
−0.681319 0.731987i \(-0.738593\pi\)
\(662\) 0 0
\(663\) −13.3272 + 6.97586i −0.517585 + 0.270920i
\(664\) 0 0
\(665\) −25.3650 3.64694i −0.983614 0.141422i
\(666\) 0 0
\(667\) 5.90627 3.79573i 0.228692 0.146971i
\(668\) 0 0
\(669\) −7.09363 + 2.89116i −0.274255 + 0.111779i
\(670\) 0 0
\(671\) 12.1681i 0.469743i
\(672\) 0 0
\(673\) 23.9329 + 37.2404i 0.922547 + 1.43551i 0.900061 + 0.435763i \(0.143522\pi\)
0.0224854 + 0.999747i \(0.492842\pi\)
\(674\) 0 0
\(675\) −17.0172 10.4931i −0.654991 0.403878i
\(676\) 0 0
\(677\) 19.4425 1.85653i 0.747236 0.0713524i 0.285511 0.958375i \(-0.407837\pi\)
0.461725 + 0.887023i \(0.347231\pi\)
\(678\) 0 0
\(679\) −8.16220 + 17.8727i −0.313237 + 0.685892i
\(680\) 0 0
\(681\) −18.5753 19.2403i −0.711806 0.737288i
\(682\) 0 0
\(683\) −26.8772 + 25.6273i −1.02843 + 0.980603i −0.999820 0.0189880i \(-0.993956\pi\)
−0.0286069 + 0.999591i \(0.509107\pi\)
\(684\) 0 0
\(685\) −6.98226 15.2890i −0.266778 0.584163i
\(686\) 0 0
\(687\) −1.56442 + 1.37270i −0.0596863 + 0.0523717i
\(688\) 0 0
\(689\) 1.78033 18.6445i 0.0678253 0.710299i
\(690\) 0 0
\(691\) 8.55640 6.72883i 0.325501 0.255977i −0.442014 0.897008i \(-0.645736\pi\)
0.767514 + 0.641032i \(0.221493\pi\)
\(692\) 0 0
\(693\) 8.72478 9.38112i 0.331427 0.356359i
\(694\) 0 0
\(695\) −2.84024 + 9.67297i −0.107736 + 0.366917i
\(696\) 0 0
\(697\) 11.6910 1.68091i 0.442828 0.0636690i
\(698\) 0 0
\(699\) −0.534051 0.414635i −0.0201997 0.0156829i
\(700\) 0 0
\(701\) −16.5837 15.8125i −0.626358 0.597231i 0.308945 0.951080i \(-0.400024\pi\)
−0.935303 + 0.353849i \(0.884873\pi\)
\(702\) 0 0
\(703\) −32.3793 + 45.4703i −1.22121 + 1.71495i
\(704\) 0 0
\(705\) 20.5096 7.24152i 0.772435 0.272732i
\(706\) 0 0
\(707\) −30.9273 17.8559i −1.16314 0.671539i
\(708\) 0 0
\(709\) 5.35357 22.0677i 0.201058 0.828771i −0.778506 0.627637i \(-0.784022\pi\)
0.979564 0.201134i \(-0.0644626\pi\)
\(710\) 0 0
\(711\) 15.5907 + 23.6089i 0.584697 + 0.885404i
\(712\) 0 0
\(713\) −26.6078 + 30.7070i −0.996470 + 1.14999i
\(714\) 0 0
\(715\) 1.92825 3.00041i 0.0721124 0.112209i
\(716\) 0 0
\(717\) 7.17271 + 0.639938i 0.267870 + 0.0238989i
\(718\) 0 0
\(719\) 2.01198 + 10.4392i 0.0750343 + 0.389315i 0.999958 + 0.00916223i \(0.00291647\pi\)
−0.924924 + 0.380153i \(0.875871\pi\)
\(720\) 0 0
\(721\) 27.3894 34.8284i 1.02003 1.29708i
\(722\) 0 0
\(723\) 11.3449 + 5.75972i 0.421922 + 0.214206i
\(724\) 0 0
\(725\) 3.75723 0.911495i 0.139540 0.0338521i
\(726\) 0 0
\(727\) −5.86785 11.3820i −0.217627 0.422137i 0.754598 0.656188i \(-0.227832\pi\)
−0.972224 + 0.234051i \(0.924802\pi\)
\(728\) 0 0
\(729\) 23.2424 + 13.7401i 0.860831 + 0.508892i
\(730\) 0 0
\(731\) 7.82691 + 3.13342i 0.289489 + 0.115894i
\(732\) 0 0
\(733\) −16.0598 5.55836i −0.593183 0.205303i 0.0139503 0.999903i \(-0.495559\pi\)
−0.607133 + 0.794600i \(0.707681\pi\)
\(734\) 0 0
\(735\) −7.30242 4.62909i −0.269354 0.170746i
\(736\) 0 0
\(737\) −10.2307 0.462265i −0.376852 0.0170277i
\(738\) 0 0
\(739\) −36.7435 + 26.1649i −1.35163 + 0.962491i −0.351981 + 0.936007i \(0.614492\pi\)
−0.999649 + 0.0264840i \(0.991569\pi\)
\(740\) 0 0
\(741\) −32.1184 + 1.73018i −1.17990 + 0.0635599i
\(742\) 0 0
\(743\) 12.6837 31.6823i 0.465319 1.16231i −0.491305 0.870987i \(-0.663480\pi\)
0.956625 0.291324i \(-0.0940956\pi\)
\(744\) 0 0
\(745\) −4.62007 15.7345i −0.169266 0.576469i
\(746\) 0 0
\(747\) 41.0297 + 13.6317i 1.50120 + 0.498756i
\(748\) 0 0
\(749\) −0.0692195 0.285327i −0.00252923 0.0104256i
\(750\) 0 0
\(751\) −12.4611 14.3809i −0.454713 0.524767i 0.481383 0.876510i \(-0.340135\pi\)
−0.936097 + 0.351743i \(0.885589\pi\)
\(752\) 0 0
\(753\) 38.2420 + 10.9711i 1.39362 + 0.399808i
\(754\) 0 0
\(755\) 2.80167 0.539977i 0.101963 0.0196518i
\(756\) 0 0
\(757\) 9.08557 17.6236i 0.330221 0.640539i −0.664019 0.747716i \(-0.731151\pi\)
0.994240 + 0.107177i \(0.0341810\pi\)
\(758\) 0 0
\(759\) 2.77293 14.8847i 0.100651 0.540281i
\(760\) 0 0
\(761\) −11.7391 10.1720i −0.425542 0.368734i 0.415601 0.909547i \(-0.363571\pi\)
−0.841143 + 0.540813i \(0.818117\pi\)
\(762\) 0 0
\(763\) 41.1653 + 7.93396i 1.49028 + 0.287228i
\(764\) 0 0
\(765\) 9.05617 5.37981i 0.327427 0.194508i
\(766\) 0 0
\(767\) −18.0079 + 31.1906i −0.650227 + 1.12623i
\(768\) 0 0
\(769\) 33.5752 + 1.59938i 1.21075 + 0.0576752i 0.643223 0.765679i \(-0.277597\pi\)
0.567528 + 0.823354i \(0.307900\pi\)
\(770\) 0 0
\(771\) 3.93443 + 0.928622i 0.141695 + 0.0334435i
\(772\) 0 0
\(773\) −6.40397 + 6.71629i −0.230335 + 0.241568i −0.828751 0.559617i \(-0.810948\pi\)
0.598417 + 0.801185i \(0.295797\pi\)