Properties

Label 804.2.ba.b.41.3
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 41.3
Character \(\chi\) = 804.41
Dual form 804.2.ba.b.353.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.68954 - 0.381398i) q^{3} +(0.606307 - 4.21696i) q^{5} +(-0.295017 - 3.08956i) q^{7} +(2.70907 + 1.28877i) q^{9} +O(q^{10})\) \(q+(-1.68954 - 0.381398i) q^{3} +(0.606307 - 4.21696i) q^{5} +(-0.295017 - 3.08956i) q^{7} +(2.70907 + 1.28877i) q^{9} +(5.34850 - 2.14122i) q^{11} +(1.06287 + 1.11471i) q^{13} +(-2.63272 + 6.89346i) q^{15} +(3.13592 - 1.08535i) q^{17} +(0.373168 + 0.0356332i) q^{19} +(-0.679910 + 5.33244i) q^{21} +(-3.36039 + 0.160075i) q^{23} +(-12.6176 - 3.70487i) q^{25} +(-4.08554 - 3.21067i) q^{27} +(5.55526 - 3.20733i) q^{29} +(-5.06664 + 5.31374i) q^{31} +(-9.85315 + 1.57776i) q^{33} +(-13.2074 - 0.629146i) q^{35} +(2.92489 - 5.06605i) q^{37} +(-1.37061 - 2.28871i) q^{39} +(10.4018 + 2.00479i) q^{41} +(0.118743 + 0.102891i) q^{43} +(7.07723 - 10.6426i) q^{45} +(-2.91118 + 5.64690i) q^{47} +(-2.58483 + 0.498185i) q^{49} +(-5.71220 + 0.637708i) q^{51} +(-1.39615 - 1.61125i) q^{53} +(-5.78658 - 23.8526i) q^{55} +(-0.616890 - 0.202529i) q^{57} +(-0.864195 - 2.94318i) q^{59} +(-5.18649 + 12.9552i) q^{61} +(3.18252 - 8.75004i) q^{63} +(5.34509 - 3.80622i) q^{65} +(1.49951 + 8.04683i) q^{67} +(5.73856 + 1.01119i) q^{69} +(-4.54395 - 1.57268i) q^{71} +(2.76888 + 1.10849i) q^{73} +(19.9049 + 11.0719i) q^{75} +(-8.19331 - 15.8928i) q^{77} +(0.363719 - 0.0882373i) q^{79} +(5.67813 + 6.98276i) q^{81} +(-6.94036 + 8.82538i) q^{83} +(-2.67555 - 13.8821i) q^{85} +(-10.6091 + 3.30014i) q^{87} +(1.23838 - 1.92696i) q^{89} +(3.13038 - 3.61265i) q^{91} +(10.5869 - 7.04535i) q^{93} +(0.376518 - 1.55203i) q^{95} +(-0.393962 - 0.227454i) q^{97} +(17.2490 + 1.09230i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440q - 12q^{7} + 4q^{9} + O(q^{10}) \) \( 440q - 12q^{7} + 4q^{9} - 2q^{15} - 10q^{19} + 22q^{21} - 68q^{25} + 50q^{31} + 11q^{33} - 22q^{37} - 45q^{39} + 22q^{43} + 22q^{45} - 18q^{49} - 6q^{51} + 126q^{55} - 183q^{57} - 56q^{61} - 141q^{63} - 12q^{67} + 33q^{69} + 356q^{73} + 165q^{75} + 228q^{79} + 24q^{81} - 6q^{85} + 75q^{87} - 4q^{91} - 75q^{93} + 12q^{97} + 88q^{99} + O(q^{100}) \)

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
\(3\) −1.68954 0.381398i −0.975455 0.220200i
\(4\) 0 0
\(5\) 0.606307 4.21696i 0.271149 1.88588i −0.165442 0.986220i \(-0.552905\pi\)
0.436590 0.899660i \(-0.356186\pi\)
\(6\) 0 0
\(7\) −0.295017 3.08956i −0.111506 1.16774i −0.862015 0.506883i \(-0.830798\pi\)
0.750509 0.660860i \(-0.229808\pi\)
\(8\) 0 0
\(9\) 2.70907 + 1.28877i 0.903024 + 0.429591i
\(10\) 0 0
\(11\) 5.34850 2.14122i 1.61263 0.645601i 0.622108 0.782931i \(-0.286276\pi\)
0.990525 + 0.137330i \(0.0438522\pi\)
\(12\) 0 0
\(13\) 1.06287 + 1.11471i 0.294787 + 0.309164i 0.854426 0.519573i \(-0.173909\pi\)
−0.559639 + 0.828736i \(0.689060\pi\)
\(14\) 0 0
\(15\) −2.63272 + 6.89346i −0.679765 + 1.77988i
\(16\) 0 0
\(17\) 3.13592 1.08535i 0.760572 0.263236i 0.0808697 0.996725i \(-0.474230\pi\)
0.679702 + 0.733488i \(0.262109\pi\)
\(18\) 0 0
\(19\) 0.373168 + 0.0356332i 0.0856105 + 0.00817481i 0.137773 0.990464i \(-0.456005\pi\)
−0.0521629 + 0.998639i \(0.516611\pi\)
\(20\) 0 0
\(21\) −0.679910 + 5.33244i −0.148369 + 1.16363i
\(22\) 0 0
\(23\) −3.36039 + 0.160075i −0.700690 + 0.0333780i −0.394904 0.918722i \(-0.629222\pi\)
−0.305786 + 0.952100i \(0.598919\pi\)
\(24\) 0 0
\(25\) −12.6176 3.70487i −2.52353 0.740975i
\(26\) 0 0
\(27\) −4.08554 3.21067i −0.786262 0.617893i
\(28\) 0 0
\(29\) 5.55526 3.20733i 1.03159 0.595586i 0.114147 0.993464i \(-0.463586\pi\)
0.917438 + 0.397878i \(0.130253\pi\)
\(30\) 0 0
\(31\) −5.06664 + 5.31374i −0.909996 + 0.954376i −0.999133 0.0416434i \(-0.986741\pi\)
0.0891369 + 0.996019i \(0.471589\pi\)
\(32\) 0 0
\(33\) −9.85315 + 1.57776i −1.71521 + 0.274652i
\(34\) 0 0
\(35\) −13.2074 0.629146i −2.23246 0.106345i
\(36\) 0 0
\(37\) 2.92489 5.06605i 0.480848 0.832854i −0.518910 0.854829i \(-0.673662\pi\)
0.999759 + 0.0219750i \(0.00699543\pi\)
\(38\) 0 0
\(39\) −1.37061 2.28871i −0.219473 0.366487i
\(40\) 0 0
\(41\) 10.4018 + 2.00479i 1.62449 + 0.313095i 0.918590 0.395213i \(-0.129329\pi\)
0.705903 + 0.708308i \(0.250541\pi\)
\(42\) 0 0
\(43\) 0.118743 + 0.102891i 0.0181081 + 0.0156908i 0.663868 0.747850i \(-0.268914\pi\)
−0.645760 + 0.763541i \(0.723459\pi\)
\(44\) 0 0
\(45\) 7.07723 10.6426i 1.05501 1.58651i
\(46\) 0 0
\(47\) −2.91118 + 5.64690i −0.424639 + 0.823685i 0.575344 + 0.817911i \(0.304868\pi\)
−0.999983 + 0.00577368i \(0.998162\pi\)
\(48\) 0 0
\(49\) −2.58483 + 0.498185i −0.369261 + 0.0711692i
\(50\) 0 0
\(51\) −5.71220 + 0.637708i −0.799868 + 0.0892970i
\(52\) 0 0
\(53\) −1.39615 1.61125i −0.191776 0.221322i 0.651716 0.758463i \(-0.274050\pi\)
−0.843492 + 0.537142i \(0.819504\pi\)
\(54\) 0 0
\(55\) −5.78658 23.8526i −0.780263 3.21629i
\(56\) 0 0
\(57\) −0.616890 0.202529i −0.0817091 0.0268256i
\(58\) 0 0
\(59\) −0.864195 2.94318i −0.112509 0.383169i 0.883917 0.467644i \(-0.154897\pi\)
−0.996426 + 0.0844747i \(0.973079\pi\)
\(60\) 0 0
\(61\) −5.18649 + 12.9552i −0.664062 + 1.65875i 0.0851109 + 0.996371i \(0.472876\pi\)
−0.749173 + 0.662375i \(0.769549\pi\)
\(62\) 0 0
\(63\) 3.18252 8.75004i 0.400959 1.10240i
\(64\) 0 0
\(65\) 5.34509 3.80622i 0.662977 0.472104i
\(66\) 0 0
\(67\) 1.49951 + 8.04683i 0.183194 + 0.983077i
\(68\) 0 0
\(69\) 5.73856 + 1.01119i 0.690841 + 0.121734i
\(70\) 0 0
\(71\) −4.54395 1.57268i −0.539268 0.186642i 0.0438379 0.999039i \(-0.486041\pi\)
−0.583106 + 0.812396i \(0.698163\pi\)
\(72\) 0 0
\(73\) 2.76888 + 1.10849i 0.324073 + 0.129739i 0.527994 0.849248i \(-0.322944\pi\)
−0.203921 + 0.978987i \(0.565369\pi\)
\(74\) 0 0
\(75\) 19.9049 + 11.0719i 2.29842 + 1.27847i
\(76\) 0 0
\(77\) −8.19331 15.8928i −0.933714 1.81115i
\(78\) 0 0
\(79\) 0.363719 0.0882373i 0.0409216 0.00992748i −0.215246 0.976560i \(-0.569055\pi\)
0.256167 + 0.966632i \(0.417540\pi\)
\(80\) 0 0
\(81\) 5.67813 + 6.98276i 0.630903 + 0.775862i
\(82\) 0 0
\(83\) −6.94036 + 8.82538i −0.761803 + 0.968712i −0.999997 0.00250596i \(-0.999202\pi\)
0.238194 + 0.971218i \(0.423445\pi\)
\(84\) 0 0
\(85\) −2.67555 13.8821i −0.290204 1.50572i
\(86\) 0 0
\(87\) −10.6091 + 3.30014i −1.13741 + 0.353812i
\(88\) 0 0
\(89\) 1.23838 1.92696i 0.131268 0.204258i −0.769397 0.638771i \(-0.779443\pi\)
0.900665 + 0.434513i \(0.143080\pi\)
\(90\) 0 0
\(91\) 3.13038 3.61265i 0.328153 0.378709i
\(92\) 0 0
\(93\) 10.5869 7.04535i 1.09781 0.730569i
\(94\) 0 0
\(95\) 0.376518 1.55203i 0.0386299 0.159235i
\(96\) 0 0
\(97\) −0.393962 0.227454i −0.0400008 0.0230945i 0.479866 0.877342i \(-0.340685\pi\)
−0.519867 + 0.854247i \(0.674019\pi\)
\(98\) 0 0
\(99\) 17.2490 + 1.09230i 1.73359 + 0.109780i
\(100\) 0 0
\(101\) −7.12702 + 10.0085i −0.709165 + 0.995882i 0.290079 + 0.957003i \(0.406318\pi\)
−0.999244 + 0.0388797i \(0.987621\pi\)
\(102\) 0 0
\(103\) −13.1880 12.5747i −1.29945 1.23902i −0.953723 0.300686i \(-0.902784\pi\)
−0.345726 0.938336i \(-0.612367\pi\)
\(104\) 0 0
\(105\) 22.0744 + 6.10024i 2.15424 + 0.595323i
\(106\) 0 0
\(107\) 1.02067 0.146751i 0.0986721 0.0141869i −0.0928019 0.995685i \(-0.529582\pi\)
0.191474 + 0.981498i \(0.438673\pi\)
\(108\) 0 0
\(109\) −3.29791 + 11.2316i −0.315882 + 1.07580i 0.636598 + 0.771196i \(0.280341\pi\)
−0.952480 + 0.304601i \(0.901477\pi\)
\(110\) 0 0
\(111\) −6.87389 + 7.44373i −0.652441 + 0.706528i
\(112\) 0 0
\(113\) 7.84294 6.16776i 0.737802 0.580214i −0.176955 0.984219i \(-0.556625\pi\)
0.914757 + 0.404005i \(0.132382\pi\)
\(114\) 0 0
\(115\) −1.36240 + 14.2677i −0.127044 + 1.33047i
\(116\) 0 0
\(117\) 1.44279 + 4.38961i 0.133386 + 0.405820i
\(118\) 0 0
\(119\) −4.27841 9.36840i −0.392201 0.858800i
\(120\) 0 0
\(121\) 16.0606 15.3137i 1.46005 1.39216i
\(122\) 0 0
\(123\) −16.8097 7.35440i −1.51568 0.663124i
\(124\) 0 0
\(125\) −14.4244 + 31.5851i −1.29016 + 2.82506i
\(126\) 0 0
\(127\) 6.65841 0.635801i 0.590839 0.0564183i 0.204645 0.978836i \(-0.434396\pi\)
0.386193 + 0.922418i \(0.373790\pi\)
\(128\) 0 0
\(129\) −0.161378 0.219127i −0.0142085 0.0192930i
\(130\) 0 0
\(131\) 2.72329 + 4.23752i 0.237935 + 0.370234i 0.939601 0.342272i \(-0.111197\pi\)
−0.701666 + 0.712506i \(0.747560\pi\)
\(132\) 0 0
\(133\) 1.16343i 0.100883i
\(134\) 0 0
\(135\) −16.0163 + 15.2819i −1.37847 + 1.31526i
\(136\) 0 0
\(137\) −14.7333 + 9.46850i −1.25875 + 0.808948i −0.988112 0.153734i \(-0.950870\pi\)
−0.270636 + 0.962682i \(0.587234\pi\)
\(138\) 0 0
\(139\) 8.55641 + 1.23023i 0.725746 + 0.104346i 0.495279 0.868734i \(-0.335066\pi\)
0.230466 + 0.973080i \(0.425975\pi\)
\(140\) 0 0
\(141\) 7.07226 8.43033i 0.595592 0.709962i
\(142\) 0 0
\(143\) 8.07158 + 3.68617i 0.674980 + 0.308253i
\(144\) 0 0
\(145\) −10.1570 25.3709i −0.843491 2.10694i
\(146\) 0 0
\(147\) 4.55717 + 0.144147i 0.375869 + 0.0118891i
\(148\) 0 0
\(149\) 9.94457 4.54153i 0.814691 0.372057i 0.0359117 0.999355i \(-0.488567\pi\)
0.778779 + 0.627298i \(0.215839\pi\)
\(150\) 0 0
\(151\) 3.03650 + 8.77339i 0.247107 + 0.713968i 0.998533 + 0.0541507i \(0.0172452\pi\)
−0.751426 + 0.659817i \(0.770634\pi\)
\(152\) 0 0
\(153\) 9.89420 + 1.10119i 0.799898 + 0.0890262i
\(154\) 0 0
\(155\) 19.3359 + 24.5876i 1.55309 + 1.97492i
\(156\) 0 0
\(157\) −0.126031 2.64571i −0.0100584 0.211151i −0.998301 0.0582601i \(-0.981445\pi\)
0.988243 0.152891i \(-0.0488583\pi\)
\(158\) 0 0
\(159\) 1.74433 + 3.25475i 0.138334 + 0.258119i
\(160\) 0 0
\(161\) 1.48593 + 10.3349i 0.117108 + 0.814504i
\(162\) 0 0
\(163\) 7.59768 + 13.1596i 0.595096 + 1.03074i 0.993533 + 0.113541i \(0.0362194\pi\)
−0.398437 + 0.917196i \(0.630447\pi\)
\(164\) 0 0
\(165\) 0.679296 + 42.5069i 0.0528831 + 3.30916i
\(166\) 0 0
\(167\) 9.89558 + 7.04661i 0.765743 + 0.545283i 0.894860 0.446346i \(-0.147275\pi\)
−0.129117 + 0.991629i \(0.541214\pi\)
\(168\) 0 0
\(169\) 0.505688 10.6157i 0.0388991 0.816592i
\(170\) 0 0
\(171\) 0.965014 + 0.577461i 0.0737965 + 0.0441596i
\(172\) 0 0
\(173\) 6.27092 + 1.52131i 0.476769 + 0.115663i 0.466941 0.884289i \(-0.345356\pi\)
0.00982875 + 0.999952i \(0.496871\pi\)
\(174\) 0 0
\(175\) −7.72400 + 40.0759i −0.583880 + 3.02946i
\(176\) 0 0
\(177\) 0.337566 + 5.30221i 0.0253730 + 0.398538i
\(178\) 0 0
\(179\) 19.2913 + 12.3978i 1.44190 + 0.926653i 0.999556 + 0.0298077i \(0.00948948\pi\)
0.442344 + 0.896845i \(0.354147\pi\)
\(180\) 0 0
\(181\) −11.7407 6.05273i −0.872677 0.449896i −0.0371268 0.999311i \(-0.511821\pi\)
−0.835550 + 0.549414i \(0.814851\pi\)
\(182\) 0 0
\(183\) 13.7039 19.9102i 1.01302 1.47180i
\(184\) 0 0
\(185\) −19.5899 15.4057i −1.44028 1.13265i
\(186\) 0 0
\(187\) 14.4485 12.5197i 1.05658 0.915530i
\(188\) 0 0
\(189\) −8.71423 + 13.5697i −0.633867 + 0.987051i
\(190\) 0 0
\(191\) −2.68091 + 1.38211i −0.193984 + 0.100006i −0.552482 0.833525i \(-0.686319\pi\)
0.358498 + 0.933530i \(0.383289\pi\)
\(192\) 0 0
\(193\) 6.64319 1.95062i 0.478187 0.140408i −0.0337517 0.999430i \(-0.510746\pi\)
0.511939 + 0.859022i \(0.328927\pi\)
\(194\) 0 0
\(195\) −10.4824 + 4.39214i −0.750661 + 0.314528i
\(196\) 0 0
\(197\) −3.87942 + 11.2088i −0.276397 + 0.798596i 0.718299 + 0.695735i \(0.244921\pi\)
−0.994696 + 0.102862i \(0.967200\pi\)
\(198\) 0 0
\(199\) −11.6192 16.3169i −0.823663 1.15667i −0.985470 0.169850i \(-0.945672\pi\)
0.161807 0.986822i \(-0.448268\pi\)
\(200\) 0 0
\(201\) 0.535570 14.1673i 0.0377762 0.999286i
\(202\) 0 0
\(203\) −11.5481 16.2171i −0.810519 1.13822i
\(204\) 0 0
\(205\) 14.7608 42.6485i 1.03094 2.97870i
\(206\) 0 0
\(207\) −9.30984 3.89713i −0.647079 0.270869i
\(208\) 0 0
\(209\) 2.07219 0.608449i 0.143336 0.0420873i
\(210\) 0 0
\(211\) 22.8993 11.8054i 1.57645 0.812718i 0.576463 0.817123i \(-0.304433\pi\)
0.999990 + 0.00440540i \(0.00140229\pi\)
\(212\) 0 0
\(213\) 7.07736 + 4.39015i 0.484933 + 0.300808i
\(214\) 0 0
\(215\) 0.505882 0.438350i 0.0345009 0.0298952i
\(216\) 0 0
\(217\) 17.9118 + 14.0860i 1.21594 + 0.956222i
\(218\) 0 0
\(219\) −4.25534 2.92888i −0.287550 0.197916i
\(220\) 0 0
\(221\) 4.54292 + 2.34204i 0.305590 + 0.157543i
\(222\) 0 0
\(223\) −11.7753 7.56750i −0.788530 0.506757i 0.0833246 0.996522i \(-0.473446\pi\)
−0.871854 + 0.489765i \(0.837083\pi\)
\(224\) 0 0
\(225\) −29.4073 26.2980i −1.96049 1.75320i
\(226\) 0 0
\(227\) 4.97463 25.8108i 0.330178 1.71312i −0.314999 0.949092i \(-0.602004\pi\)
0.645177 0.764033i \(-0.276784\pi\)
\(228\) 0 0
\(229\) 6.42665 + 1.55909i 0.424685 + 0.103027i 0.442405 0.896816i \(-0.354126\pi\)
−0.0177199 + 0.999843i \(0.505641\pi\)
\(230\) 0 0
\(231\) 7.78141 + 29.9764i 0.511979 + 1.97230i
\(232\) 0 0
\(233\) 0.980955 20.5928i 0.0642645 1.34908i −0.704572 0.709632i \(-0.748861\pi\)
0.768837 0.639445i \(-0.220836\pi\)
\(234\) 0 0
\(235\) 22.0477 + 15.7001i 1.43823 + 1.02416i
\(236\) 0 0
\(237\) −0.648171 + 0.0103583i −0.0421032 + 0.000672845i
\(238\) 0 0
\(239\) −3.37469 5.84513i −0.218290 0.378090i 0.735995 0.676987i \(-0.236715\pi\)
−0.954285 + 0.298897i \(0.903381\pi\)
\(240\) 0 0
\(241\) 3.90362 + 27.1503i 0.251454 + 1.74890i 0.589496 + 0.807771i \(0.299326\pi\)
−0.338042 + 0.941131i \(0.609765\pi\)
\(242\) 0 0
\(243\) −6.93019 13.9633i −0.444572 0.895743i
\(244\) 0 0
\(245\) 0.533624 + 11.2022i 0.0340920 + 0.715679i
\(246\) 0 0
\(247\) 0.356908 + 0.453845i 0.0227095 + 0.0288775i
\(248\) 0 0
\(249\) 15.0920 12.2638i 0.956415 0.777185i
\(250\) 0 0
\(251\) 3.62965 + 10.4872i 0.229101 + 0.661945i 0.999697 + 0.0246205i \(0.00783774\pi\)
−0.770595 + 0.637325i \(0.780041\pi\)
\(252\) 0 0
\(253\) −17.6303 + 8.05149i −1.10841 + 0.506193i
\(254\) 0 0
\(255\) −0.774159 + 24.4747i −0.0484797 + 1.53267i
\(256\) 0 0
\(257\) −7.02930 17.5583i −0.438475 1.09526i −0.968884 0.247516i \(-0.920386\pi\)
0.530408 0.847742i \(-0.322039\pi\)
\(258\) 0 0
\(259\) −16.5147 7.54203i −1.02618 0.468639i
\(260\) 0 0
\(261\) 19.1831 1.52941i 1.18740 0.0946684i
\(262\) 0 0
\(263\) 13.9779 + 2.00973i 0.861917 + 0.123925i 0.559076 0.829116i \(-0.311156\pi\)
0.302841 + 0.953041i \(0.402065\pi\)
\(264\) 0 0
\(265\) −7.64106 + 4.91061i −0.469386 + 0.301656i
\(266\) 0 0
\(267\) −2.82724 + 2.78336i −0.173024 + 0.170339i
\(268\) 0 0
\(269\) 16.1978i 0.987597i −0.869576 0.493799i \(-0.835608\pi\)
0.869576 0.493799i \(-0.164392\pi\)
\(270\) 0 0
\(271\) 2.88664 + 4.49170i 0.175351 + 0.272851i 0.917793 0.397059i \(-0.129969\pi\)
−0.742442 + 0.669910i \(0.766333\pi\)
\(272\) 0 0
\(273\) −6.66676 + 4.90979i −0.403490 + 0.297154i
\(274\) 0 0
\(275\) −75.4184 + 7.20158i −4.54790 + 0.434272i
\(276\) 0 0
\(277\) −10.0366 + 21.9772i −0.603043 + 1.32048i 0.324189 + 0.945992i \(0.394909\pi\)
−0.927232 + 0.374487i \(0.877819\pi\)
\(278\) 0 0
\(279\) −20.5741 + 7.86555i −1.23174 + 0.470898i
\(280\) 0 0
\(281\) 13.0301 12.4242i 0.777312 0.741166i −0.193476 0.981105i \(-0.561976\pi\)
0.970788 + 0.239939i \(0.0771275\pi\)
\(282\) 0 0
\(283\) 1.76612 + 3.86727i 0.104985 + 0.229885i 0.954833 0.297142i \(-0.0960336\pi\)
−0.849848 + 0.527028i \(0.823306\pi\)
\(284\) 0 0
\(285\) −1.22808 + 2.47860i −0.0727452 + 0.146820i
\(286\) 0 0
\(287\) 3.12519 32.7285i 0.184474 1.93190i
\(288\) 0 0
\(289\) −4.70691 + 3.70155i −0.276877 + 0.217738i
\(290\) 0 0
\(291\) 0.578863 + 0.534549i 0.0339335 + 0.0313358i
\(292\) 0 0
\(293\) 2.18836 7.45288i 0.127845 0.435402i −0.870547 0.492086i \(-0.836235\pi\)
0.998392 + 0.0566841i \(0.0180528\pi\)
\(294\) 0 0
\(295\) −12.9352 + 1.85980i −0.753117 + 0.108282i
\(296\) 0 0
\(297\) −28.7262 8.42422i −1.66687 0.488823i
\(298\) 0 0
\(299\) −3.75010 3.57571i −0.216874 0.206789i
\(300\) 0 0
\(301\) 0.282857 0.397217i 0.0163036 0.0228952i
\(302\) 0 0
\(303\) 15.8586 14.1915i 0.911052 0.815280i
\(304\) 0 0
\(305\) 51.4870 + 29.7260i 2.94814 + 1.70211i
\(306\) 0 0
\(307\) 1.30583 5.38272i 0.0745279 0.307208i −0.922332 0.386399i \(-0.873719\pi\)
0.996859 + 0.0791913i \(0.0252338\pi\)
\(308\) 0 0
\(309\) 17.4856 + 26.2753i 0.994720 + 1.49475i
\(310\) 0 0
\(311\) 7.91488 9.13426i 0.448812 0.517956i −0.485586 0.874189i \(-0.661394\pi\)
0.934397 + 0.356233i \(0.115939\pi\)
\(312\) 0 0
\(313\) −15.9193 + 24.7709i −0.899813 + 1.40014i 0.0165828 + 0.999862i \(0.494721\pi\)
−0.916396 + 0.400274i \(0.868915\pi\)
\(314\) 0 0
\(315\) −34.9689 18.7257i −1.97028 1.05508i
\(316\) 0 0
\(317\) 2.77787 + 14.4130i 0.156021 + 0.809514i 0.972637 + 0.232332i \(0.0746355\pi\)
−0.816616 + 0.577182i \(0.804152\pi\)
\(318\) 0 0
\(319\) 22.8447 29.0494i 1.27906 1.62646i
\(320\) 0 0
\(321\) −1.78043 0.141342i −0.0993742 0.00788896i
\(322\) 0 0
\(323\) 1.20890 0.293275i 0.0672649 0.0163183i
\(324\) 0 0
\(325\) −9.28107 18.0028i −0.514821 0.998613i
\(326\) 0 0
\(327\) 9.85567 17.7185i 0.545020 0.979833i
\(328\) 0 0
\(329\) 18.3053 + 7.32832i 1.00920 + 0.404024i
\(330\) 0 0
\(331\) 4.93615 + 1.70842i 0.271315 + 0.0939031i 0.459338 0.888262i \(-0.348087\pi\)
−0.188023 + 0.982165i \(0.560208\pi\)
\(332\) 0 0
\(333\) 14.4527 9.95478i 0.792004 0.545518i
\(334\) 0 0
\(335\) 34.8423 1.44452i 1.90364 0.0789226i
\(336\) 0 0
\(337\) 15.9342 11.3467i 0.867990 0.618093i −0.0568779 0.998381i \(-0.518115\pi\)
0.924868 + 0.380288i \(0.124175\pi\)
\(338\) 0 0
\(339\) −15.6033 + 7.42937i −0.847455 + 0.403508i
\(340\) 0 0
\(341\) −15.7211 + 39.2693i −0.851343 + 2.12655i
\(342\) 0 0
\(343\) −3.81898 13.0062i −0.206206 0.702271i
\(344\) 0 0
\(345\) 7.74349 23.5862i 0.416896 1.26984i
\(346\) 0 0
\(347\) −1.90110 7.83645i −0.102056 0.420683i 0.897747 0.440512i \(-0.145203\pi\)
−0.999803 + 0.0198291i \(0.993688\pi\)
\(348\) 0 0
\(349\) 3.25401 + 3.75533i 0.174183 + 0.201018i 0.836128 0.548535i \(-0.184814\pi\)
−0.661945 + 0.749553i \(0.730269\pi\)
\(350\) 0 0
\(351\) −0.763449 7.96669i −0.0407499 0.425231i
\(352\) 0 0
\(353\) −26.5842 + 5.12369i −1.41493 + 0.272706i −0.838707 0.544583i \(-0.816688\pi\)
−0.576228 + 0.817289i \(0.695476\pi\)
\(354\) 0 0
\(355\) −9.38694 + 18.2081i −0.498207 + 0.966387i
\(356\) 0 0
\(357\) 3.65543 + 17.4600i 0.193466 + 0.924083i
\(358\) 0 0
\(359\) −15.4265 13.3671i −0.814177 0.705489i 0.144649 0.989483i \(-0.453795\pi\)
−0.958826 + 0.283995i \(0.908340\pi\)
\(360\) 0 0
\(361\) −18.5187 3.56918i −0.974666 0.187852i
\(362\) 0 0
\(363\) −32.9756 + 19.7476i −1.73077 + 1.03648i
\(364\) 0 0
\(365\) 6.35325 11.0041i 0.332544 0.575984i
\(366\) 0 0
\(367\) −17.2173 0.820159i −0.898734 0.0428120i −0.406872 0.913485i \(-0.633381\pi\)
−0.491862 + 0.870673i \(0.663684\pi\)
\(368\) 0 0
\(369\) 25.5956 + 18.8367i 1.33245 + 0.980600i
\(370\) 0 0
\(371\) −4.56615 + 4.78884i −0.237063 + 0.248624i
\(372\) 0 0
\(373\) −6.10626 + 3.52545i −0.316170 + 0.182541i −0.649684 0.760204i \(-0.725099\pi\)
0.333514 + 0.942745i \(0.391765\pi\)
\(374\) 0 0
\(375\) 36.4172 47.8628i 1.88057 2.47162i
\(376\) 0 0
\(377\) 9.47974 + 2.78350i 0.488232 + 0.143358i
\(378\) 0 0
\(379\) −0.768266 + 0.0365970i −0.0394632 + 0.00187986i −0.0673042 0.997732i \(-0.521440\pi\)
0.0278410 + 0.999612i \(0.491137\pi\)
\(380\) 0 0
\(381\) −11.4921 1.46530i −0.588760 0.0750695i
\(382\) 0 0
\(383\) 7.47379 + 0.713661i 0.381893 + 0.0364663i 0.284237 0.958754i \(-0.408260\pi\)
0.0976555 + 0.995220i \(0.468866\pi\)
\(384\) 0 0
\(385\) −71.9869 + 24.9149i −3.66879 + 1.26978i
\(386\) 0 0
\(387\) 0.189079 + 0.431772i 0.00961144 + 0.0219482i
\(388\) 0 0
\(389\) −11.1481 11.6917i −0.565229 0.592795i 0.377643 0.925951i \(-0.376735\pi\)
−0.942872 + 0.333156i \(0.891886\pi\)
\(390\) 0 0
\(391\) −10.3642 + 4.14919i −0.524139 + 0.209834i
\(392\) 0 0
\(393\) −2.98491 8.19810i −0.150569 0.413539i
\(394\) 0 0
\(395\) −0.151568 1.58729i −0.00762619 0.0798651i
\(396\) 0 0
\(397\) 3.11736 21.6817i 0.156456 1.08818i −0.748643 0.662974i \(-0.769294\pi\)
0.905099 0.425202i \(-0.139797\pi\)
\(398\) 0 0
\(399\) −0.443732 + 1.96567i −0.0222144 + 0.0984064i
\(400\) 0 0
\(401\) 27.5475 1.37566 0.687829 0.725873i \(-0.258564\pi\)
0.687829 + 0.725873i \(0.258564\pi\)
\(402\) 0 0
\(403\) −11.3084 −0.563313
\(404\) 0 0
\(405\) 32.8887 19.7107i 1.63425 0.979433i
\(406\) 0 0
\(407\) 4.79624 33.3586i 0.237741 1.65352i
\(408\) 0 0
\(409\) 2.08694 + 21.8554i 0.103193 + 1.08068i 0.887656 + 0.460507i \(0.152332\pi\)
−0.784464 + 0.620175i \(0.787062\pi\)
\(410\) 0 0
\(411\) 28.5037 10.3781i 1.40598 0.511915i
\(412\) 0 0
\(413\) −8.83816 + 3.53827i −0.434897 + 0.174107i
\(414\) 0 0
\(415\) 33.0083 + 34.6181i 1.62031 + 1.69933i
\(416\) 0 0
\(417\) −13.9872 5.34192i −0.684955 0.261595i
\(418\) 0 0
\(419\) −20.6175 + 7.13577i −1.00723 + 0.348605i −0.780367 0.625322i \(-0.784968\pi\)
−0.226862 + 0.973927i \(0.572847\pi\)
\(420\) 0 0
\(421\) 9.37835 + 0.895524i 0.457073 + 0.0436452i 0.321054 0.947061i \(-0.395963\pi\)
0.136019 + 0.990706i \(0.456569\pi\)
\(422\) 0 0
\(423\) −15.1642 + 11.5460i −0.737307 + 0.561386i
\(424\) 0 0
\(425\) −43.5890 + 2.07640i −2.11438 + 0.100720i
\(426\) 0 0
\(427\) 41.5560 + 12.2019i 2.01104 + 0.590493i
\(428\) 0 0
\(429\) −12.2313 9.30641i −0.590535 0.449318i
\(430\) 0 0
\(431\) −23.2702 + 13.4351i −1.12089 + 0.647144i −0.941627 0.336657i \(-0.890704\pi\)
−0.179260 + 0.983802i \(0.557370\pi\)
\(432\) 0 0
\(433\) −23.0976 + 24.2241i −1.11000 + 1.16414i −0.124899 + 0.992169i \(0.539861\pi\)
−0.985103 + 0.171967i \(0.944988\pi\)
\(434\) 0 0
\(435\) 7.48417 + 46.7389i 0.358838 + 2.24096i
\(436\) 0 0
\(437\) −1.25969 0.0600066i −0.0602593 0.00287050i
\(438\) 0 0
\(439\) −7.23239 + 12.5269i −0.345183 + 0.597875i −0.985387 0.170330i \(-0.945517\pi\)
0.640204 + 0.768205i \(0.278850\pi\)
\(440\) 0 0
\(441\) −7.64453 1.98164i −0.364025 0.0943637i
\(442\) 0 0
\(443\) 36.6488 + 7.06347i 1.74124 + 0.335596i 0.958139 0.286304i \(-0.0924268\pi\)
0.783097 + 0.621900i \(0.213639\pi\)
\(444\) 0 0
\(445\) −7.37508 6.39054i −0.349612 0.302941i
\(446\) 0 0
\(447\) −18.5339 + 3.88025i −0.876621 + 0.183529i
\(448\) 0 0
\(449\) 2.78293 5.39814i 0.131335 0.254754i −0.813994 0.580874i \(-0.802711\pi\)
0.945328 + 0.326120i \(0.105741\pi\)
\(450\) 0 0
\(451\) 59.9269 11.5500i 2.82185 0.543866i
\(452\) 0 0
\(453\) −1.78412 15.9811i −0.0838254 0.750857i
\(454\) 0 0
\(455\) −13.3364 15.3911i −0.625221 0.721544i
\(456\) 0 0
\(457\) −2.94610 12.1440i −0.137813 0.568073i −0.998283 0.0585720i \(-0.981345\pi\)
0.860470 0.509501i \(-0.170170\pi\)
\(458\) 0 0
\(459\) −16.2966 5.63414i −0.760661 0.262979i
\(460\) 0 0
\(461\) 3.50252 + 11.9285i 0.163129 + 0.555566i 0.999967 + 0.00811540i \(0.00258324\pi\)
−0.836838 + 0.547450i \(0.815599\pi\)
\(462\) 0 0
\(463\) 7.60634 18.9997i 0.353497 0.882992i −0.639921 0.768441i \(-0.721033\pi\)
0.993417 0.114551i \(-0.0365429\pi\)
\(464\) 0 0
\(465\) −23.2910 48.9163i −1.08009 2.26844i
\(466\) 0 0
\(467\) 7.51464 5.35115i 0.347736 0.247622i −0.392821 0.919615i \(-0.628501\pi\)
0.740557 + 0.671993i \(0.234562\pi\)
\(468\) 0 0
\(469\) 24.4188 7.00677i 1.12755 0.323543i
\(470\) 0 0
\(471\) −0.796137 + 4.51810i −0.0366841 + 0.208183i
\(472\) 0 0
\(473\) 0.855409 + 0.296060i 0.0393317 + 0.0136128i
\(474\) 0 0
\(475\) −4.57648 1.83215i −0.209983 0.0840646i
\(476\) 0 0
\(477\) −1.70575 6.16431i −0.0781008 0.282244i
\(478\) 0 0
\(479\) −8.80975 17.0885i −0.402528 0.780795i 0.597246 0.802058i \(-0.296262\pi\)
−0.999774 + 0.0212630i \(0.993231\pi\)
\(480\) 0 0
\(481\) 8.75593 2.12417i 0.399236 0.0968536i
\(482\) 0 0
\(483\) 1.43117 18.0279i 0.0651206 0.820299i
\(484\) 0 0
\(485\) −1.19803 + 1.52341i −0.0543995 + 0.0691747i
\(486\) 0 0
\(487\) 0.0504807 + 0.261919i 0.00228750 + 0.0118687i 0.983055 0.183313i \(-0.0586823\pi\)
−0.980767 + 0.195182i \(0.937470\pi\)
\(488\) 0 0
\(489\) −7.81752 25.1313i −0.353521 1.13648i
\(490\) 0 0
\(491\) 4.10090 6.38112i 0.185071 0.287976i −0.736304 0.676651i \(-0.763431\pi\)
0.921375 + 0.388675i \(0.127067\pi\)
\(492\) 0 0
\(493\) 13.9398 16.0873i 0.627815 0.724537i
\(494\) 0 0
\(495\) 15.0644 72.0760i 0.677093 3.23958i
\(496\) 0 0
\(497\) −3.51833 + 14.5028i −0.157819 + 0.650538i
\(498\) 0 0
\(499\) −28.5894 16.5061i −1.27984 0.738915i −0.303019 0.952984i \(-0.597995\pi\)
−0.976818 + 0.214070i \(0.931328\pi\)
\(500\) 0 0
\(501\) −14.0314 15.6797i −0.626876 0.700516i
\(502\) 0 0
\(503\) 12.8092 17.9880i 0.571133 0.802045i −0.423457 0.905916i \(-0.639184\pi\)
0.994591 + 0.103871i \(0.0331230\pi\)
\(504\) 0 0
\(505\) 37.8842 + 36.1225i 1.68583 + 1.60743i
\(506\) 0 0
\(507\) −4.90319 + 17.7428i −0.217758 + 0.787983i
\(508\) 0 0
\(509\) 11.2173 1.61280i 0.497197 0.0714861i 0.110845 0.993838i \(-0.464644\pi\)
0.386352 + 0.922352i \(0.373735\pi\)
\(510\) 0 0
\(511\) 2.60788 8.88163i 0.115366 0.392900i
\(512\) 0 0
\(513\) −1.41018 1.34370i −0.0622612 0.0593257i
\(514\) 0 0
\(515\) −61.0229 + 47.9889i −2.68899 + 2.11465i
\(516\) 0 0
\(517\) −3.47921 + 36.4359i −0.153015 + 1.60245i
\(518\) 0 0
\(519\) −10.0147 4.96203i −0.439598 0.217809i
\(520\) 0 0
\(521\) −11.8525 25.9534i −0.519269 1.13704i −0.969715 0.244238i \(-0.921462\pi\)
0.450446 0.892804i \(-0.351265\pi\)
\(522\) 0 0
\(523\) −9.57913 + 9.13368i −0.418866 + 0.399388i −0.869987 0.493075i \(-0.835873\pi\)
0.451121 + 0.892463i \(0.351024\pi\)
\(524\) 0 0
\(525\) 28.3349 64.7638i 1.23664 2.82653i
\(526\) 0 0
\(527\) −10.1213 + 22.1625i −0.440890 + 0.965416i
\(528\) 0 0
\(529\) −11.6292 + 1.11046i −0.505619 + 0.0482808i
\(530\) 0 0
\(531\) 1.45192 9.08702i 0.0630081 0.394343i
\(532\) 0 0
\(533\) 8.82104 + 13.7258i 0.382082 + 0.594531i
\(534\) 0 0
\(535\) 4.39311i 0.189931i
\(536\) 0 0
\(537\) −27.8649 28.3042i −1.20246 1.22141i
\(538\) 0 0
\(539\) −12.7582 + 8.19921i −0.549536 + 0.353165i
\(540\) 0 0
\(541\) 29.6342 + 4.26075i 1.27407 + 0.183184i 0.745960 0.665991i \(-0.231991\pi\)
0.528112 + 0.849175i \(0.322900\pi\)
\(542\) 0 0
\(543\) 17.5278 + 14.7042i 0.752189 + 0.631017i
\(544\) 0 0
\(545\) 45.3638 + 20.7170i 1.94317 + 0.887417i
\(546\) 0 0
\(547\) 12.9717 + 32.4018i 0.554631 + 1.38540i 0.895404 + 0.445255i \(0.146887\pi\)
−0.340773 + 0.940146i \(0.610689\pi\)
\(548\) 0 0
\(549\) −30.7469 + 28.4124i −1.31225 + 1.21261i
\(550\) 0 0
\(551\) 2.18733 0.998920i 0.0931834 0.0425554i
\(552\) 0 0
\(553\) −0.379918 1.09770i −0.0161557 0.0466789i
\(554\) 0 0
\(555\) 27.2222 + 33.5001i 1.15552 + 1.42200i
\(556\) 0 0
\(557\) −13.7885 17.5335i −0.584238 0.742919i 0.400627 0.916241i \(-0.368792\pi\)
−0.984865 + 0.173322i \(0.944550\pi\)
\(558\) 0 0
\(559\) 0.0115147 + 0.241723i 0.000487020 + 0.0102238i
\(560\) 0 0
\(561\) −29.1862 + 15.6418i −1.23224 + 0.660399i
\(562\) 0 0
\(563\) −1.75169 12.1833i −0.0738250 0.513464i −0.992860 0.119288i \(-0.961939\pi\)
0.919035 0.394176i \(-0.128970\pi\)
\(564\) 0 0
\(565\) −21.2539 36.8129i −0.894159 1.54873i
\(566\) 0 0
\(567\) 19.8985 19.6029i 0.835658 0.823246i
\(568\) 0 0
\(569\) −26.8976 19.1537i −1.12761 0.802965i −0.145141 0.989411i \(-0.546364\pi\)
−0.982465 + 0.186446i \(0.940303\pi\)
\(570\) 0 0
\(571\) 0.0868183 1.82254i 0.00363323 0.0762710i −0.996322 0.0856827i \(-0.972693\pi\)
0.999956 + 0.00941174i \(0.00299589\pi\)
\(572\) 0 0
\(573\) 5.05663 1.31262i 0.211244 0.0548357i
\(574\) 0 0
\(575\) 42.9933 + 10.4301i 1.79294 + 0.434963i
\(576\) 0 0
\(577\) −0.209927 + 1.08920i −0.00873936 + 0.0453441i −0.986037 0.166529i \(-0.946744\pi\)
0.977297 + 0.211873i \(0.0679563\pi\)
\(578\) 0 0
\(579\) −11.9679 + 0.761937i −0.497368 + 0.0316650i
\(580\) 0 0
\(581\) 29.3141 + 18.8390i 1.21615 + 0.781573i
\(582\) 0 0
\(583\) −10.9174 5.62829i −0.452151 0.233100i
\(584\) 0 0
\(585\) 19.3856 3.42271i 0.801495 0.141512i
\(586\) 0 0
\(587\) 14.1258 + 11.1087i 0.583036 + 0.458505i 0.865595 0.500746i \(-0.166941\pi\)
−0.282559 + 0.959250i \(0.591183\pi\)
\(588\) 0 0
\(589\) −2.08005 + 1.80238i −0.0857070 + 0.0742656i
\(590\) 0 0
\(591\) 10.8294 17.4581i 0.445464 0.718132i
\(592\) 0 0
\(593\) 9.58828 4.94310i 0.393744 0.202989i −0.249973 0.968253i \(-0.580422\pi\)
0.643717 + 0.765264i \(0.277392\pi\)
\(594\) 0 0
\(595\) −42.1002 + 12.3617i −1.72594 + 0.506781i
\(596\) 0 0
\(597\) 13.4078 + 31.9995i 0.548746 + 1.30965i
\(598\) 0 0
\(599\) −1.04442 + 3.01765i −0.0426738 + 0.123298i −0.964325 0.264722i \(-0.914720\pi\)
0.921651 + 0.388020i \(0.126841\pi\)
\(600\) 0 0
\(601\) −3.69220 5.18497i −0.150608 0.211499i 0.732379 0.680898i \(-0.238410\pi\)
−0.882986 + 0.469399i \(0.844471\pi\)
\(602\) 0 0
\(603\) −6.30826 + 23.7320i −0.256892 + 0.966440i
\(604\) 0 0
\(605\) −54.8397 77.0115i −2.22955 3.13096i
\(606\) 0 0
\(607\) 4.49809 12.9964i 0.182572 0.527506i −0.816162 0.577824i \(-0.803902\pi\)
0.998733 + 0.0503174i \(0.0160233\pi\)
\(608\) 0 0
\(609\) 13.3258 + 31.8038i 0.539989 + 1.28875i
\(610\) 0 0
\(611\) −9.38884 + 2.75681i −0.379832 + 0.111529i
\(612\) 0 0
\(613\) −23.7393 + 12.2385i −0.958823 + 0.494308i −0.865270 0.501307i \(-0.832853\pi\)
−0.0935533 + 0.995614i \(0.529823\pi\)
\(614\) 0 0
\(615\) −41.2050 + 66.4265i −1.66155 + 2.67858i
\(616\) 0 0
\(617\) −4.81268 + 4.17021i −0.193751 + 0.167886i −0.746334 0.665572i \(-0.768188\pi\)
0.552583 + 0.833458i \(0.313642\pi\)
\(618\) 0 0
\(619\) −12.7834 10.0530i −0.513809 0.404064i 0.327308 0.944918i \(-0.393859\pi\)
−0.841116 + 0.540854i \(0.818101\pi\)
\(620\) 0 0
\(621\) 14.2430 + 10.1351i 0.571550 + 0.406708i
\(622\) 0 0
\(623\) −6.31881 3.25757i −0.253158 0.130512i
\(624\) 0 0
\(625\) 69.1337 + 44.4295i 2.76535 + 1.77718i
\(626\) 0 0
\(627\) −3.73310 + 0.237668i −0.149085 + 0.00949155i
\(628\) 0 0
\(629\) 3.67376 19.0613i 0.146482 0.760022i
\(630\) 0 0
\(631\) 34.7069 + 8.41980i 1.38166 + 0.335187i 0.856645 0.515906i \(-0.172545\pi\)
0.525014 + 0.851093i \(0.324060\pi\)
\(632\) 0 0
\(633\) −43.1918 + 11.2119i −1.71672 + 0.445634i
\(634\) 0 0
\(635\) 1.35589 28.4637i 0.0538070 1.12955i
\(636\) 0 0
\(637\) −3.30266 2.35182i −0.130856 0.0931823i
\(638\) 0 0
\(639\) −10.2831 10.1166i −0.406792 0.400207i
\(640\) 0 0
\(641\) −1.91537 3.31751i −0.0756524 0.131034i 0.825717 0.564084i \(-0.190771\pi\)
−0.901370 + 0.433050i \(0.857437\pi\)
\(642\) 0 0
\(643\) −4.05839 28.2267i −0.160047 1.11315i −0.898540 0.438892i \(-0.855371\pi\)
0.738492 0.674262i \(-0.235538\pi\)
\(644\) 0 0
\(645\) −1.02189 + 0.547665i −0.0402370 + 0.0215643i
\(646\) 0 0
\(647\) 1.47317 + 30.9257i 0.0579164 + 1.21581i 0.821539 + 0.570152i \(0.193116\pi\)
−0.763623 + 0.645663i \(0.776581\pi\)
\(648\) 0 0
\(649\) −10.9241 13.8912i −0.428809 0.545275i
\(650\) 0 0
\(651\) −24.8903 30.6304i −0.975529 1.20050i
\(652\) 0 0
\(653\) −4.31635 12.4713i −0.168912 0.488038i 0.828496 0.559995i \(-0.189197\pi\)
−0.997408 + 0.0719565i \(0.977076\pi\)
\(654\) 0 0
\(655\) 19.5206 8.91475i 0.762732 0.348328i
\(656\) 0 0
\(657\) 6.07249 + 6.57144i 0.236910 + 0.256376i
\(658\) 0 0
\(659\) 4.60925 + 11.5134i 0.179551 + 0.448497i 0.990653 0.136408i \(-0.0435560\pi\)
−0.811102 + 0.584905i \(0.801132\pi\)
\(660\) 0 0
\(661\) −38.1537 17.4242i −1.48401 0.677723i −0.501707 0.865038i \(-0.667294\pi\)
−0.982300 + 0.187314i \(0.940022\pi\)
\(662\) 0 0
\(663\) −6.78218 5.68962i −0.263398 0.220967i
\(664\) 0 0
\(665\) −4.90615 0.705398i −0.190252 0.0273542i
\(666\) 0 0
\(667\) −18.1544 + 11.6671i −0.702942 + 0.451754i
\(668\) 0 0
\(669\) 17.0085 + 17.2766i 0.657587 + 0.667953i
\(670\) 0 0
\(671\) 80.3964i 3.10367i
\(672\) 0 0
\(673\) −3.70299 5.76197i −0.142740 0.222107i 0.762521 0.646963i \(-0.223961\pi\)
−0.905261 + 0.424856i \(0.860325\pi\)
\(674\) 0 0
\(675\) 39.6548 + 55.6474i 1.52631 + 2.14187i
\(676\) 0 0
\(677\) −14.1584 + 1.35197i −0.544153 + 0.0519603i −0.363513 0.931589i \(-0.618423\pi\)
−0.180640 + 0.983549i \(0.557817\pi\)
\(678\) 0 0
\(679\) −0.586507 + 1.28427i −0.0225081 + 0.0492858i
\(680\) 0 0
\(681\) −18.2490 + 41.7110i −0.699304 + 1.59837i
\(682\) 0 0
\(683\) 25.8052 24.6052i 0.987407 0.941490i −0.0108837 0.999941i \(-0.503464\pi\)
0.998290 + 0.0584504i \(0.0186160\pi\)
\(684\) 0 0
\(685\) 30.9953 + 67.8703i 1.18427 + 2.59319i
\(686\) 0 0
\(687\) −10.2634 5.08525i −0.391574 0.194014i
\(688\) 0 0
\(689\) 0.312137 3.26885i 0.0118915 0.124533i
\(690\) 0 0
\(691\) −19.2125 + 15.1089i −0.730879 + 0.574770i −0.912733 0.408556i \(-0.866033\pi\)
0.181854 + 0.983325i \(0.441790\pi\)
\(692\) 0 0
\(693\) −1.71403 53.6140i −0.0651108 2.03663i
\(694\) 0 0
\(695\) 10.3756 35.3361i 0.393570 1.34038i
\(696\) 0 0
\(697\) 34.7952 5.00279i 1.31796 0.189494i
\(698\) 0 0
\(699\) −9.51141 + 34.4181i −0.359755 + 1.30181i
\(700\) 0 0
\(701\) 18.2783 + 17.4283i 0.690361 + 0.658258i 0.951714 0.306986i \(-0.0993203\pi\)
−0.261353 + 0.965243i \(0.584169\pi\)
\(702\) 0 0
\(703\) 1.27199 1.78626i 0.0479741 0.0673702i
\(704\) 0 0
\(705\) −31.2624 34.9348i −1.17741 1.31572i
\(706\) 0 0
\(707\) 33.0244 + 19.0666i 1.24201 + 0.717075i
\(708\) 0 0
\(709\) −4.47237 + 18.4354i −0.167964 + 0.692355i 0.824081 + 0.566471i \(0.191692\pi\)
−0.992045 + 0.125884i \(0.959823\pi\)
\(710\) 0 0
\(711\) 1.09906 + 0.229710i 0.0412179 + 0.00861482i
\(712\) 0 0
\(713\) 16.1753 18.6673i 0.605770 0.699096i
\(714\) 0 0
\(715\) 20.4383 31.8026i 0.764348 1.18935i
\(716\) 0 0
\(717\) 3.47234 + 11.1627i 0.129677 + 0.416878i
\(718\) 0 0
\(719\) 1.18605 + 6.15381i 0.0442322 + 0.229498i 0.997317 0.0732054i \(-0.0233229\pi\)
−0.953085 + 0.302704i \(0.902111\pi\)
\(720\) 0 0
\(721\) −34.9596 + 44.4547i −1.30196 + 1.65558i
\(722\) 0 0
\(723\) 3.75976 47.3602i 0.139827 1.76135i
\(724\) 0 0
\(725\) −81.9770 + 19.8874i −3.04455 + 0.738600i
\(726\) 0 0
\(727\) 21.9554 + 42.5875i 0.814279 + 1.57948i 0.814985 + 0.579482i \(0.196745\pi\)
−0.000705458 1.00000i \(0.500225\pi\)
\(728\) 0 0
\(729\) 6.38326 + 26.2346i 0.236417 + 0.971652i
\(730\) 0 0
\(731\) 0.484041 + 0.193781i 0.0179029 + 0.00716724i
\(732\) 0 0
\(733\) 22.7614 + 7.87781i 0.840713 + 0.290973i 0.713285 0.700874i \(-0.247207\pi\)
0.127428 + 0.991848i \(0.459328\pi\)
\(734\) 0 0
\(735\) 3.37090 19.1300i 0.124338 0.705620i
\(736\) 0 0
\(737\) 25.2501 + 39.8277i 0.930101 + 1.46707i
\(738\) 0 0
\(739\) 14.7241 10.4850i 0.541635 0.385696i −0.276244 0.961088i \(-0.589090\pi\)
0.817878 + 0.575391i \(0.195150\pi\)
\(740\) 0 0
\(741\) −0.429913 0.902913i −0.0157933 0.0331693i
\(742\) 0 0
\(743\) −0.522599 + 1.30539i −0.0191723 + 0.0478901i −0.937645 0.347594i \(-0.886999\pi\)
0.918473 + 0.395484i \(0.129423\pi\)
\(744\) 0 0
\(745\) −13.1220 44.6894i −0.480752 1.63729i
\(746\) 0 0
\(747\) −30.1758 + 14.9640i −1.10408 + 0.547506i
\(748\) 0 0
\(749\) −0.754510 3.11013i −0.0275692 0.113642i
\(750\) 0 0
\(751\) 24.2455 + 27.9808i 0.884732 + 1.02104i 0.999617 + 0.0276568i \(0.00880456\pi\)
−0.114885 + 0.993379i \(0.536650\pi\)
\(752\) 0 0
\(753\) −2.13263 19.1028i −0.0777175 0.696146i
\(754\) 0 0
\(755\) 38.8380 7.48542i 1.41346 0.272422i
\(756\) 0 0
\(757\) 3.14182 6.09427i 0.114191 0.221500i −0.824813 0.565406i \(-0.808720\pi\)
0.939004 + 0.343905i \(0.111750\pi\)
\(758\) 0 0
\(759\) 32.8579 6.87912i 1.19267 0.249696i
\(760\) 0 0
\(761\) 36.1610 + 31.3337i 1.31084 + 1.13585i 0.981464 + 0.191645i \(0.0613821\pi\)
0.329371 + 0.944201i \(0.393163\pi\)
\(762\) 0 0
\(763\) 35.6738 + 6.87555i 1.29148 + 0.248912i
\(764\) 0 0
\(765\) 10.6426 41.0557i 0.384784 1.48437i
\(766\) 0 0
\(767\) 2.36225 4.09154i 0.0852959 0.147737i
\(768\) 0 0
\(769\) −20.6084 0.981699i −0.743158 0.0354010i −0.327412 0.944882i \(-0.606176\pi\)
−0.415746 + 0.909481i \(0.636479\pi\)
\(770\) 0 0
\(771\) 5.17954 + 32.3464i 0.186536 + 1.16493i
\(772\) 0 0
\(773\) 28.8887 30.2976i 1.03905 1.08973i 0.0431718 0.999068i \(-0.486254\pi\)
0.995882 0.0906604i \(-0.0288978\pi\)
\(774\)