Properties

Label 2268.2.l.j.109.1
Level $2268$
Weight $2$
Character 2268.109
Analytic conductor $18.110$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.l (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.1100711784\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 756)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.1
Root \(0.500000 + 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 2268.109
Dual form 2268.2.l.j.541.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.28799 q^{5} +(-2.64400 - 0.0963576i) q^{7} +O(q^{10})\) \(q-4.28799 q^{5} +(-2.64400 - 0.0963576i) q^{7} -3.81089 q^{11} +(-1.64400 + 2.84748i) q^{13} +(0.405446 - 0.702253i) q^{17} +(-3.54944 - 6.14781i) q^{19} -6.47710 q^{23} +13.3869 q^{25} +(-1.90545 - 3.30033i) q^{29} +(-1.64400 - 2.84748i) q^{31} +(11.3374 + 0.413181i) q^{35} +(2.88255 + 4.99272i) q^{37} +(-1.04944 + 1.81769i) q^{41} +(4.38255 + 7.59079i) q^{43} +(-1.66690 + 2.88715i) q^{47} +(6.98143 + 0.509538i) q^{49} +(-4.93199 + 8.54245i) q^{53} +16.3411 q^{55} +(-1.73855 - 3.01126i) q^{59} +(-2.97710 + 5.15649i) q^{61} +(7.04944 - 12.2100i) q^{65} +(1.76145 + 3.05092i) q^{67} +6.05308 q^{71} +(5.19344 - 8.99530i) q^{73} +(10.0760 + 0.367208i) q^{77} +(2.57234 - 4.45543i) q^{79} +(0.856004 + 1.48264i) q^{83} +(-1.73855 + 3.01126i) q^{85} +(-6.26509 - 10.8515i) q^{89} +(4.62110 - 7.37033i) q^{91} +(15.2200 + 26.3618i) q^{95} +(-0.522900 - 0.905690i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 2q^{5} - 4q^{7} + O(q^{10}) \) \( 6q - 2q^{5} - 4q^{7} - 10q^{11} + 2q^{13} - 4q^{17} - 3q^{19} - 28q^{23} + 20q^{25} - 5q^{29} + 2q^{31} + 26q^{35} + 12q^{41} + 9q^{43} - 9q^{47} - 12q^{49} + 6q^{53} + 16q^{55} - 5q^{59} - 7q^{61} + 24q^{65} + 16q^{67} - 22q^{71} + q^{73} + 13q^{77} + 8q^{79} + 17q^{83} - 5q^{85} - 3q^{89} + 5q^{91} + 32q^{95} - 14q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1135\) \(1541\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −4.28799 −1.91765 −0.958824 0.284000i \(-0.908338\pi\)
−0.958824 + 0.284000i \(0.908338\pi\)
\(6\) 0 0
\(7\) −2.64400 0.0963576i −0.999337 0.0364197i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3.81089 −1.14903 −0.574514 0.818495i \(-0.694809\pi\)
−0.574514 + 0.818495i \(0.694809\pi\)
\(12\) 0 0
\(13\) −1.64400 + 2.84748i −0.455962 + 0.789750i −0.998743 0.0501244i \(-0.984038\pi\)
0.542781 + 0.839875i \(0.317372\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.405446 0.702253i 0.0983351 0.170321i −0.812661 0.582737i \(-0.801982\pi\)
0.910996 + 0.412416i \(0.135315\pi\)
\(18\) 0 0
\(19\) −3.54944 6.14781i −0.814298 1.41041i −0.909831 0.414979i \(-0.863789\pi\)
0.0955331 0.995426i \(-0.469544\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.47710 −1.35057 −0.675284 0.737557i \(-0.735979\pi\)
−0.675284 + 0.737557i \(0.735979\pi\)
\(24\) 0 0
\(25\) 13.3869 2.67738
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1.90545 3.30033i −0.353832 0.612856i 0.633085 0.774082i \(-0.281788\pi\)
−0.986917 + 0.161227i \(0.948455\pi\)
\(30\) 0 0
\(31\) −1.64400 2.84748i −0.295270 0.511423i 0.679777 0.733419i \(-0.262076\pi\)
−0.975048 + 0.221995i \(0.928743\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 11.3374 + 0.413181i 1.91638 + 0.0698403i
\(36\) 0 0
\(37\) 2.88255 + 4.99272i 0.473888 + 0.820797i 0.999553 0.0298939i \(-0.00951695\pi\)
−0.525665 + 0.850691i \(0.676184\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1.04944 + 1.81769i −0.163895 + 0.283875i −0.936262 0.351301i \(-0.885739\pi\)
0.772367 + 0.635176i \(0.219073\pi\)
\(42\) 0 0
\(43\) 4.38255 + 7.59079i 0.668332 + 1.15758i 0.978370 + 0.206861i \(0.0663248\pi\)
−0.310038 + 0.950724i \(0.600342\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.66690 + 2.88715i −0.243142 + 0.421134i −0.961608 0.274428i \(-0.911511\pi\)
0.718466 + 0.695562i \(0.244845\pi\)
\(48\) 0 0
\(49\) 6.98143 + 0.509538i 0.997347 + 0.0727912i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.93199 + 8.54245i −0.677461 + 1.17340i 0.298282 + 0.954478i \(0.403586\pi\)
−0.975743 + 0.218919i \(0.929747\pi\)
\(54\) 0 0
\(55\) 16.3411 2.20343
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.73855 3.01126i −0.226340 0.392032i 0.730381 0.683040i \(-0.239343\pi\)
−0.956721 + 0.291008i \(0.906009\pi\)
\(60\) 0 0
\(61\) −2.97710 + 5.15649i −0.381179 + 0.660221i −0.991231 0.132140i \(-0.957815\pi\)
0.610052 + 0.792361i \(0.291148\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 7.04944 12.2100i 0.874376 1.51446i
\(66\) 0 0
\(67\) 1.76145 + 3.05092i 0.215195 + 0.372729i 0.953333 0.301921i \(-0.0976278\pi\)
−0.738138 + 0.674650i \(0.764295\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 6.05308 0.718369 0.359184 0.933267i \(-0.383055\pi\)
0.359184 + 0.933267i \(0.383055\pi\)
\(72\) 0 0
\(73\) 5.19344 8.99530i 0.607846 1.05282i −0.383749 0.923438i \(-0.625367\pi\)
0.991595 0.129383i \(-0.0412995\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 10.0760 + 0.367208i 1.14826 + 0.0418473i
\(78\) 0 0
\(79\) 2.57234 4.45543i 0.289411 0.501275i −0.684258 0.729240i \(-0.739874\pi\)
0.973669 + 0.227965i \(0.0732072\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0.856004 + 1.48264i 0.0939586 + 0.162741i 0.909174 0.416417i \(-0.136715\pi\)
−0.815215 + 0.579159i \(0.803381\pi\)
\(84\) 0 0
\(85\) −1.73855 + 3.01126i −0.188572 + 0.326617i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −6.26509 10.8515i −0.664098 1.15025i −0.979529 0.201304i \(-0.935482\pi\)
0.315430 0.948949i \(-0.397851\pi\)
\(90\) 0 0
\(91\) 4.62110 7.37033i 0.484422 0.772620i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 15.2200 + 26.3618i 1.56154 + 2.70466i
\(96\) 0 0
\(97\) −0.522900 0.905690i −0.0530925 0.0919589i 0.838258 0.545274i \(-0.183574\pi\)
−0.891350 + 0.453315i \(0.850241\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 17.9098 1.78209 0.891045 0.453916i \(-0.149973\pi\)
0.891045 + 0.453916i \(0.149973\pi\)
\(102\) 0 0
\(103\) −7.00000 −0.689730 −0.344865 0.938652i \(-0.612075\pi\)
−0.344865 + 0.938652i \(0.612075\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.45056 + 5.97654i 0.333578 + 0.577774i 0.983211 0.182474i \(-0.0584106\pi\)
−0.649633 + 0.760248i \(0.725077\pi\)
\(108\) 0 0
\(109\) 2.81089 4.86861i 0.269235 0.466328i −0.699430 0.714701i \(-0.746563\pi\)
0.968664 + 0.248373i \(0.0798959\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 10.0760 17.4521i 0.947869 1.64176i 0.197966 0.980209i \(-0.436566\pi\)
0.749903 0.661548i \(-0.230100\pi\)
\(114\) 0 0
\(115\) 27.7738 2.58992
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.13967 + 1.81769i −0.104473 + 0.166627i
\(120\) 0 0
\(121\) 3.52290 0.320264
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −35.9629 −3.21662
\(126\) 0 0
\(127\) −2.14468 −0.190310 −0.0951550 0.995462i \(-0.530335\pi\)
−0.0951550 + 0.995462i \(0.530335\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −3.38688 −0.295913 −0.147956 0.988994i \(-0.547270\pi\)
−0.147956 + 0.988994i \(0.547270\pi\)
\(132\) 0 0
\(133\) 8.79232 + 16.5968i 0.762391 + 1.43913i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −12.9542 −1.10675 −0.553376 0.832932i \(-0.686661\pi\)
−0.553376 + 0.832932i \(0.686661\pi\)
\(138\) 0 0
\(139\) 8.64400 14.9718i 0.733174 1.26989i −0.222346 0.974968i \(-0.571371\pi\)
0.955520 0.294927i \(-0.0952953\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 6.26509 10.8515i 0.523913 0.907444i
\(144\) 0 0
\(145\) 8.17054 + 14.1518i 0.678526 + 1.17524i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.56870 −0.128513 −0.0642565 0.997933i \(-0.520468\pi\)
−0.0642565 + 0.997933i \(0.520468\pi\)
\(150\) 0 0
\(151\) −1.38688 −0.112862 −0.0564312 0.998406i \(-0.517972\pi\)
−0.0564312 + 0.998406i \(0.517972\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 7.04944 + 12.2100i 0.566225 + 0.980730i
\(156\) 0 0
\(157\) 8.43199 + 14.6046i 0.672946 + 1.16558i 0.977065 + 0.212942i \(0.0683047\pi\)
−0.304119 + 0.952634i \(0.598362\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 17.1254 + 0.624118i 1.34967 + 0.0491874i
\(162\) 0 0
\(163\) −8.64833 14.9793i −0.677389 1.17327i −0.975764 0.218824i \(-0.929778\pi\)
0.298375 0.954449i \(-0.403555\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.97779 12.0859i 0.539957 0.935234i −0.458948 0.888463i \(-0.651774\pi\)
0.998906 0.0467708i \(-0.0148930\pi\)
\(168\) 0 0
\(169\) 1.09455 + 1.89582i 0.0841964 + 0.145833i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −4.57165 + 7.91834i −0.347576 + 0.602020i −0.985818 0.167816i \(-0.946329\pi\)
0.638242 + 0.769836i \(0.279662\pi\)
\(174\) 0 0
\(175\) −35.3948 1.28993i −2.67560 0.0975093i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −8.53087 + 14.7759i −0.637627 + 1.10440i 0.348325 + 0.937374i \(0.386751\pi\)
−0.985952 + 0.167029i \(0.946583\pi\)
\(180\) 0 0
\(181\) −16.4400 −1.22197 −0.610986 0.791641i \(-0.709227\pi\)
−0.610986 + 0.791641i \(0.709227\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −12.3603 21.4087i −0.908750 1.57400i
\(186\) 0 0
\(187\) −1.54511 + 2.67621i −0.112990 + 0.195704i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.48143 + 2.56591i −0.107193 + 0.185663i −0.914632 0.404288i \(-0.867519\pi\)
0.807439 + 0.589951i \(0.200853\pi\)
\(192\) 0 0
\(193\) 8.71565 + 15.0959i 0.627366 + 1.08663i 0.988078 + 0.153953i \(0.0492004\pi\)
−0.360712 + 0.932677i \(0.617466\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 10.2880 0.732989 0.366495 0.930420i \(-0.380558\pi\)
0.366495 + 0.930420i \(0.380558\pi\)
\(198\) 0 0
\(199\) 3.50000 6.06218i 0.248108 0.429736i −0.714893 0.699234i \(-0.753524\pi\)
0.963001 + 0.269498i \(0.0868577\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 4.71998 + 8.90966i 0.331278 + 0.625336i
\(204\) 0 0
\(205\) 4.50000 7.79423i 0.314294 0.544373i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 13.5265 + 23.4287i 0.935650 + 1.62059i
\(210\) 0 0
\(211\) −8.21634 + 14.2311i −0.565636 + 0.979710i 0.431354 + 0.902183i \(0.358036\pi\)
−0.996990 + 0.0775277i \(0.975297\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −18.7923 32.5493i −1.28163 2.21984i
\(216\) 0 0
\(217\) 4.07234 + 7.68715i 0.276449 + 0.521838i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.33310 + 2.30900i 0.0896743 + 0.155320i
\(222\) 0 0
\(223\) −2.06801 3.58190i −0.138484 0.239862i 0.788439 0.615113i \(-0.210890\pi\)
−0.926923 + 0.375251i \(0.877556\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −21.2967 −1.41351 −0.706754 0.707459i \(-0.749841\pi\)
−0.706754 + 0.707459i \(0.749841\pi\)
\(228\) 0 0
\(229\) −5.85532 −0.386930 −0.193465 0.981107i \(-0.561973\pi\)
−0.193465 + 0.981107i \(0.561973\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4.02290 + 6.96787i 0.263549 + 0.456480i 0.967182 0.254083i \(-0.0817736\pi\)
−0.703633 + 0.710563i \(0.748440\pi\)
\(234\) 0 0
\(235\) 7.14764 12.3801i 0.466260 0.807587i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 7.04944 12.2100i 0.455991 0.789799i −0.542754 0.839892i \(-0.682618\pi\)
0.998745 + 0.0500930i \(0.0159518\pi\)
\(240\) 0 0
\(241\) −26.7280 −1.72170 −0.860849 0.508860i \(-0.830067\pi\)
−0.860849 + 0.508860i \(0.830067\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −29.9363 2.18490i −1.91256 0.139588i
\(246\) 0 0
\(247\) 23.3411 1.48516
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2.43268 0.153549 0.0767746 0.997048i \(-0.475538\pi\)
0.0767746 + 0.997048i \(0.475538\pi\)
\(252\) 0 0
\(253\) 24.6835 1.55184
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −12.5302 −0.781611 −0.390806 0.920473i \(-0.627804\pi\)
−0.390806 + 0.920473i \(0.627804\pi\)
\(258\) 0 0
\(259\) −7.14035 13.4785i −0.443680 0.837512i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −6.90112 −0.425541 −0.212771 0.977102i \(-0.568249\pi\)
−0.212771 + 0.977102i \(0.568249\pi\)
\(264\) 0 0
\(265\) 21.1483 36.6300i 1.29913 2.25016i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −10.9054 + 18.8888i −0.664917 + 1.15167i 0.314391 + 0.949294i \(0.398200\pi\)
−0.979308 + 0.202376i \(0.935134\pi\)
\(270\) 0 0
\(271\) −3.76145 6.51502i −0.228492 0.395759i 0.728870 0.684653i \(-0.240046\pi\)
−0.957361 + 0.288893i \(0.906713\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −51.0159 −3.07638
\(276\) 0 0
\(277\) 9.23491 0.554872 0.277436 0.960744i \(-0.410515\pi\)
0.277436 + 0.960744i \(0.410515\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6.83743 + 11.8428i 0.407887 + 0.706481i 0.994653 0.103276i \(-0.0329323\pi\)
−0.586766 + 0.809757i \(0.699599\pi\)
\(282\) 0 0
\(283\) −1.07165 1.85616i −0.0637032 0.110337i 0.832415 0.554153i \(-0.186958\pi\)
−0.896118 + 0.443816i \(0.853624\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.94987 4.70484i 0.174125 0.277718i
\(288\) 0 0
\(289\) 8.17123 + 14.1530i 0.480660 + 0.832528i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −4.64833 + 8.05114i −0.271558 + 0.470353i −0.969261 0.246035i \(-0.920872\pi\)
0.697703 + 0.716387i \(0.254206\pi\)
\(294\) 0 0
\(295\) 7.45489 + 12.9122i 0.434040 + 0.751780i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 10.6483 18.4434i 0.615809 1.06661i
\(300\) 0 0
\(301\) −10.8560 20.4923i −0.625730 1.18116i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 12.7658 22.1110i 0.730966 1.26607i
\(306\) 0 0
\(307\) −10.3869 −0.592810 −0.296405 0.955062i \(-0.595788\pi\)
−0.296405 + 0.955062i \(0.595788\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.28799 2.23087i −0.0730353 0.126501i 0.827195 0.561915i \(-0.189935\pi\)
−0.900230 + 0.435414i \(0.856602\pi\)
\(312\) 0 0
\(313\) 5.74219 9.94577i 0.324568 0.562168i −0.656857 0.754015i \(-0.728114\pi\)
0.981425 + 0.191847i \(0.0614478\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7.59820 13.1605i 0.426757 0.739165i −0.569826 0.821766i \(-0.692989\pi\)
0.996583 + 0.0826006i \(0.0263226\pi\)
\(318\) 0 0
\(319\) 7.26145 + 12.5772i 0.406563 + 0.704188i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −5.75643 −0.320296
\(324\) 0 0
\(325\) −22.0080 + 38.1189i −1.22078 + 2.11446i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 4.68547 7.47299i 0.258318 0.411999i
\(330\) 0 0
\(331\) −7.76578 + 13.4507i −0.426846 + 0.739319i −0.996591 0.0825028i \(-0.973709\pi\)
0.569745 + 0.821822i \(0.307042\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −7.55308 13.0823i −0.412669 0.714764i
\(336\) 0 0
\(337\) 1.50433 2.60558i 0.0819461 0.141935i −0.822140 0.569286i \(-0.807220\pi\)
0.904086 + 0.427351i \(0.140553\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 6.26509 + 10.8515i 0.339274 + 0.587639i
\(342\) 0 0
\(343\) −18.4098 2.01993i −0.994035 0.109066i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 11.4327 + 19.8020i 0.613738 + 1.06303i 0.990604 + 0.136758i \(0.0436683\pi\)
−0.376866 + 0.926268i \(0.622998\pi\)
\(348\) 0 0
\(349\) −4.52221 7.83270i −0.242068 0.419275i 0.719235 0.694767i \(-0.244493\pi\)
−0.961303 + 0.275492i \(0.911159\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 18.1964 0.968496 0.484248 0.874931i \(-0.339093\pi\)
0.484248 + 0.874931i \(0.339093\pi\)
\(354\) 0 0
\(355\) −25.9556 −1.37758
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 12.1934 + 21.1197i 0.643545 + 1.11465i 0.984636 + 0.174622i \(0.0558704\pi\)
−0.341090 + 0.940030i \(0.610796\pi\)
\(360\) 0 0
\(361\) −15.6971 + 27.1881i −0.826162 + 1.43095i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −22.2694 + 38.5718i −1.16563 + 2.01894i
\(366\) 0 0
\(367\) −8.86535 −0.462768 −0.231384 0.972863i \(-0.574325\pi\)
−0.231384 + 0.972863i \(0.574325\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 13.8633 22.1110i 0.719746 1.14794i
\(372\) 0 0
\(373\) −3.15197 −0.163203 −0.0816014 0.996665i \(-0.526003\pi\)
−0.0816014 + 0.996665i \(0.526003\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 12.5302 0.645337
\(378\) 0 0
\(379\) −2.28799 −0.117526 −0.0587631 0.998272i \(-0.518716\pi\)
−0.0587631 + 0.998272i \(0.518716\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 28.2509 1.44355 0.721776 0.692127i \(-0.243326\pi\)
0.721776 + 0.692127i \(0.243326\pi\)
\(384\) 0 0
\(385\) −43.2057 1.57459i −2.20197 0.0802484i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −0.720669 −0.0365394 −0.0182697 0.999833i \(-0.505816\pi\)
−0.0182697 + 0.999833i \(0.505816\pi\)
\(390\) 0 0
\(391\) −2.62612 + 4.54856i −0.132808 + 0.230031i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −11.0302 + 19.1048i −0.554989 + 0.961269i
\(396\) 0 0
\(397\) −10.5753 18.3169i −0.530759 0.919301i −0.999356 0.0358892i \(-0.988574\pi\)
0.468597 0.883412i \(-0.344760\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 28.4944 1.42294 0.711472 0.702715i \(-0.248029\pi\)
0.711472 + 0.702715i \(0.248029\pi\)
\(402\) 0 0
\(403\) 10.8109 0.538529
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −10.9851 19.0267i −0.544510 0.943119i
\(408\) 0 0
\(409\) 5.38186 + 9.32165i 0.266116 + 0.460926i 0.967855 0.251508i \(-0.0809263\pi\)
−0.701740 + 0.712434i \(0.747593\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 4.30656 + 8.12927i 0.211912 + 0.400015i
\(414\) 0 0
\(415\) −3.67054 6.35756i −0.180180 0.312080i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 17.0302 29.4971i 0.831979 1.44103i −0.0644877 0.997919i \(-0.520541\pi\)
0.896467 0.443111i \(-0.146125\pi\)
\(420\) 0 0
\(421\) −10.2916 17.8256i −0.501584 0.868768i −0.999998 0.00182949i \(-0.999418\pi\)
0.498415 0.866939i \(-0.333916\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 5.42766 9.40098i 0.263280 0.456014i
\(426\) 0 0
\(427\) 8.36831 13.3469i 0.404971 0.645900i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 11.9814 20.7524i 0.577125 0.999610i −0.418682 0.908133i \(-0.637508\pi\)
0.995807 0.0914772i \(-0.0291589\pi\)
\(432\) 0 0
\(433\) 29.9642 1.43999 0.719995 0.693980i \(-0.244144\pi\)
0.719995 + 0.693980i \(0.244144\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 22.9901 + 39.8200i 1.09977 + 1.90485i
\(438\) 0 0
\(439\) −14.4098 + 24.9585i −0.687741 + 1.19120i 0.284826 + 0.958579i \(0.408064\pi\)
−0.972567 + 0.232623i \(0.925269\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 16.0043 27.7203i 0.760389 1.31703i −0.182262 0.983250i \(-0.558342\pi\)
0.942650 0.333782i \(-0.108325\pi\)
\(444\) 0 0
\(445\) 26.8647 + 46.5310i 1.27351 + 2.20578i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 32.0087 1.51058 0.755291 0.655390i \(-0.227496\pi\)
0.755291 + 0.655390i \(0.227496\pi\)
\(450\) 0 0
\(451\) 3.99931 6.92701i 0.188320 0.326180i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −19.8152 + 31.6039i −0.928952 + 1.48161i
\(456\) 0 0
\(457\) 10.4277 18.0612i 0.487785 0.844869i −0.512116 0.858916i \(-0.671138\pi\)
0.999901 + 0.0140474i \(0.00447158\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 12.6254 + 21.8679i 0.588025 + 1.01849i 0.994491 + 0.104823i \(0.0334276\pi\)
−0.406466 + 0.913666i \(0.633239\pi\)
\(462\) 0 0
\(463\) 10.5760 18.3181i 0.491508 0.851316i −0.508445 0.861095i \(-0.669779\pi\)
0.999952 + 0.00977849i \(0.00311264\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7.95853 + 13.7846i 0.368277 + 0.637874i 0.989296 0.145921i \(-0.0466145\pi\)
−0.621019 + 0.783795i \(0.713281\pi\)
\(468\) 0 0
\(469\) −4.36329 8.23635i −0.201478 0.380319i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −16.7014 28.9277i −0.767932 1.33010i
\(474\) 0 0
\(475\) −47.5159 82.3000i −2.18018 3.77618i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 1.95558 0.0893526 0.0446763 0.999002i \(-0.485774\pi\)
0.0446763 + 0.999002i \(0.485774\pi\)
\(480\) 0 0
\(481\) −18.9556 −0.864300
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.24219 + 3.88359i 0.101813 + 0.176345i
\(486\) 0 0
\(487\) −9.98143 + 17.2883i −0.452302 + 0.783410i −0.998529 0.0542276i \(-0.982730\pi\)
0.546227 + 0.837637i \(0.316064\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 11.0488 19.1370i 0.498623 0.863641i −0.501375 0.865230i \(-0.667172\pi\)
0.999999 + 0.00158899i \(0.000505790\pi\)
\(492\) 0 0
\(493\) −3.09022 −0.139177
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −16.0043 0.583261i −0.717892 0.0261628i
\(498\) 0 0
\(499\) −33.1148 −1.48242 −0.741212 0.671271i \(-0.765749\pi\)
−0.741212 + 0.671271i \(0.765749\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4.76509 0.212465 0.106232 0.994341i \(-0.466121\pi\)
0.106232 + 0.994341i \(0.466121\pi\)
\(504\) 0 0
\(505\) −76.7970 −3.41742
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 10.7651 0.477154 0.238577 0.971124i \(-0.423319\pi\)
0.238577 + 0.971124i \(0.423319\pi\)
\(510\) 0 0
\(511\) −14.5982 + 23.2831i −0.645786 + 1.02998i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 30.0159 1.32266
\(516\) 0 0
\(517\) 6.35236 11.0026i 0.279377 0.483894i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.617454 + 1.06946i −0.0270512 + 0.0468540i −0.879234 0.476390i \(-0.841945\pi\)
0.852183 + 0.523244i \(0.175278\pi\)
\(522\) 0 0
\(523\) 4.28435 + 7.42071i 0.187342 + 0.324485i 0.944363 0.328905i \(-0.106680\pi\)
−0.757022 + 0.653390i \(0.773346\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.66621 −0.116142
\(528\) 0 0
\(529\) 18.9528 0.824036
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −3.45056 5.97654i −0.149460 0.258873i
\(534\) 0 0
\(535\) −14.7960 25.6274i −0.639685 1.10797i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −26.6055 1.94180i −1.14598 0.0836390i
\(540\) 0 0
\(541\) 7.50433 + 12.9979i 0.322636 + 0.558823i 0.981031 0.193850i \(-0.0620976\pi\)
−0.658395 + 0.752673i \(0.728764\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −12.0531 + 20.8766i −0.516297 + 0.894253i
\(546\) 0 0
\(547\) −6.12543 10.6095i −0.261904 0.453632i 0.704844 0.709363i \(-0.251017\pi\)
−0.966748 + 0.255731i \(0.917684\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −13.5265 + 23.4287i −0.576250 + 0.998094i
\(552\) 0 0
\(553\) −7.23058 + 11.5323i −0.307475 + 0.490402i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 12.8905 22.3270i 0.546189 0.946027i −0.452342 0.891844i \(-0.649411\pi\)
0.998531 0.0541823i \(-0.0172552\pi\)
\(558\) 0 0
\(559\) −28.8196 −1.21894
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −12.3418 21.3766i −0.520143 0.900915i −0.999726 0.0234179i \(-0.992545\pi\)
0.479582 0.877497i \(-0.340788\pi\)
\(564\) 0 0
\(565\) −43.2057 + 74.8345i −1.81768 + 3.14831i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −6.11677 + 10.5945i −0.256428 + 0.444147i −0.965282 0.261208i \(-0.915879\pi\)
0.708854 + 0.705355i \(0.249212\pi\)
\(570\) 0 0
\(571\) −17.6563 30.5816i −0.738893 1.27980i −0.952994 0.302989i \(-0.902015\pi\)
0.214101 0.976812i \(-0.431318\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −86.7081 −3.61598
\(576\) 0 0
\(577\) −4.52221 + 7.83270i −0.188262 + 0.326080i −0.944671 0.328020i \(-0.893619\pi\)
0.756409 + 0.654099i \(0.226952\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −2.12041 4.00258i −0.0879693 0.166055i
\(582\) 0 0
\(583\) 18.7953 32.5544i 0.778421 1.34826i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −17.9098 31.0206i −0.739216 1.28036i −0.952849 0.303445i \(-0.901863\pi\)
0.213633 0.976914i \(-0.431470\pi\)
\(588\) 0 0
\(589\) −11.6705 + 20.2140i −0.480876 + 0.832902i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 22.0309 + 38.1586i 0.904700 + 1.56699i 0.821320 + 0.570468i \(0.193238\pi\)
0.0833794 + 0.996518i \(0.473429\pi\)
\(594\) 0 0
\(595\) 4.88688 7.79423i 0.200342 0.319532i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −15.0316 26.0354i −0.614173 1.06378i −0.990529 0.137304i \(-0.956156\pi\)
0.376356 0.926475i \(-0.377177\pi\)
\(600\) 0 0
\(601\) −14.5982 25.2848i −0.595473 1.03139i −0.993480 0.114007i \(-0.963631\pi\)
0.398007 0.917382i \(-0.369702\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −15.1062 −0.614153
\(606\) 0 0
\(607\) −16.1433 −0.655237 −0.327618 0.944810i \(-0.606246\pi\)
−0.327618 + 0.944810i \(0.606246\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −5.48074 9.49292i −0.221727 0.384043i
\(612\) 0 0
\(613\) −23.5581 + 40.8038i −0.951503 + 1.64805i −0.209327 + 0.977846i \(0.567127\pi\)
−0.742175 + 0.670206i \(0.766206\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −19.0073 + 32.9216i −0.765204 + 1.32537i 0.174934 + 0.984580i \(0.444029\pi\)
−0.940138 + 0.340793i \(0.889305\pi\)
\(618\) 0 0
\(619\) 12.1818 0.489629 0.244814 0.969570i \(-0.421273\pi\)
0.244814 + 0.969570i \(0.421273\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 15.5193 + 29.2949i 0.621766 + 1.17368i
\(624\) 0 0
\(625\) 87.2741 3.49096
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 4.67487 0.186399
\(630\) 0 0
\(631\) −10.8640 −0.432488 −0.216244 0.976339i \(-0.569381\pi\)
−0.216244 + 0.976339i \(0.569381\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 9.19639 0.364948
\(636\) 0 0
\(637\) −12.9283 + 19.0418i −0.512240 + 0.754465i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −30.4400 −1.20231 −0.601153 0.799134i \(-0.705292\pi\)
−0.601153 + 0.799134i \(0.705292\pi\)
\(642\) 0 0
\(643\) 18.9320 32.7912i 0.746605 1.29316i −0.202837 0.979213i \(-0.565016\pi\)
0.949441 0.313945i \(-0.101651\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 18.0982 31.3470i 0.711513 1.23238i −0.252775 0.967525i \(-0.581343\pi\)
0.964289 0.264853i \(-0.0853233\pi\)
\(648\) 0 0
\(649\) 6.62543 + 11.4756i 0.260071 + 0.450456i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 22.0975 0.864742 0.432371 0.901696i \(-0.357677\pi\)
0.432371 + 0.901696i \(0.357677\pi\)
\(654\) 0 0
\(655\) 14.5229 0.567457
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 22.0338 + 38.1637i 0.858316 + 1.48665i 0.873534 + 0.486763i \(0.161822\pi\)
−0.0152182 + 0.999884i \(0.504844\pi\)
\(660\) 0 0
\(661\) −2.95351 5.11563i −0.114878 0.198975i 0.802853 0.596177i \(-0.203314\pi\)
−0.917731 + 0.397202i \(0.869981\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −37.7014 71.1670i −1.46200 2.75974i
\(666\) 0 0
\(667\) 12.3418 + 21.3766i 0.477875 + 0.827704i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 11.3454 19.6508i 0.437985 0.758612i
\(672\) 0 0
\(673\) 1.09888 + 1.90332i 0.0423589 + 0.0733677i 0.886428 0.462867i \(-0.153179\pi\)
−0.844069 + 0.536235i \(0.819846\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −15.0316 + 26.0354i −0.577710 + 1.00062i 0.418032 + 0.908432i \(0.362720\pi\)
−0.995741 + 0.0921903i \(0.970613\pi\)
\(678\) 0 0
\(679\) 1.29528 + 2.44503i 0.0497081 + 0.0938315i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 4.14764 7.18392i 0.158705 0.274885i −0.775697 0.631106i \(-0.782601\pi\)
0.934402 + 0.356221i \(0.115935\pi\)
\(684\) 0 0
\(685\) 55.5475 2.12236
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −16.2163 28.0875i −0.617793 1.07005i
\(690\) 0 0
\(691\) 0.598196 1.03611i 0.0227564 0.0394153i −0.854423 0.519578i \(-0.826089\pi\)
0.877179 + 0.480163i \(0.159422\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −37.0654 + 64.1991i −1.40597 + 2.43521i
\(696\) 0 0
\(697\) 0.850985 + 1.47395i 0.0322333 + 0.0558298i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −31.8813 −1.20414 −0.602070 0.798443i \(-0.705657\pi\)
−0.602070 + 0.798443i \(0.705657\pi\)
\(702\) 0 0
\(703\) 20.4629 35.4427i 0.771771 1.33675i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −47.3534 1.72574i −1.78091 0.0649032i
\(708\) 0 0
\(709\) 10.7163 18.5612i 0.402461 0.697082i −0.591562 0.806260i \(-0.701488\pi\)
0.994022 + 0.109178i \(0.0348217\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 10.6483 + 18.4434i 0.398783 + 0.690712i
\(714\) 0 0
\(715\) −26.8647 + 46.5310i −1.00468 + 1.74016i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 21.6304 + 37.4650i 0.806680 + 1.39721i 0.915151 + 0.403110i \(0.132071\pi\)
−0.108472 + 0.994100i \(0.534596\pi\)
\(720\) 0 0
\(721\) 18.5080 + 0.674503i 0.689273 + 0.0251198i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −25.5080 44.1811i −0.947342 1.64085i
\(726\) 0 0
\(727\) −6.09091 10.5498i −0.225899 0.391269i 0.730689 0.682710i \(-0.239199\pi\)
−0.956589 + 0.291441i \(0.905865\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 7.10755 0.262882
\(732\) 0 0
\(733\) 13.4486 0.496736 0.248368 0.968666i \(-0.420106\pi\)
0.248368 + 0.968666i \(0.420106\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −6.71270 11.6267i −0.247265 0.428276i
\(738\) 0 0
\(739\) 4.93632 8.54995i 0.181585 0.314515i −0.760835 0.648945i \(-0.775210\pi\)
0.942421 + 0.334430i \(0.108544\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 11.2844 19.5451i 0.413983 0.717039i −0.581338 0.813662i \(-0.697471\pi\)
0.995321 + 0.0966229i \(0.0308041\pi\)
\(744\) 0 0
\(745\) 6.72658 0.246443
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −8.54738 16.1344i −0.312314 0.589540i
\(750\) 0 0
\(751\) −0.575984 −0.0210180 −0.0105090 0.999945i \(-0.503345\pi\)
−0.0105090 + 0.999945i \(0.503345\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 5.94692 0.216430
\(756\) 0 0
\(757\) 22.8196 0.829391 0.414695 0.909960i \(-0.363888\pi\)
0.414695 + 0.909960i \(0.363888\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 19.7810 0.717062 0.358531 0.933518i \(-0.383278\pi\)
0.358531 + 0.933518i \(0.383278\pi\)
\(762\) 0 0
\(763\) −7.90112 + 12.6017i −0.286040 + 0.456213i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 11.4327 0.412810
\(768\) 0 0
\(769\) 14.3603 24.8728i 0.517847 0.896937i −0.481938 0.876205i \(-0.660067\pi\)
0.999785 0.0207319i \(-0.00659965\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −4.10253 + 7.10578i −0.147558 + 0.255577i −0.930324 0.366738i \(-0.880475\pi\)
0.782767 + 0.622315i \(0.213808\pi\)
\(774\) 0 0
\(775\) −22.0080 38.1189i −0.790550 1.36927i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 14.8997 0.533839
\(780\) 0 0
\(781\) −23.0677 −0.825425
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −36.1563 62.6245i −1.29047 2.23517i
\(786\) 0 0
\(787\) 26.3182 + 45.5844i 0.938142 + 1.62491i 0.768934 + 0.639329i \(0.220788\pi\)
0.169208 + 0.985580i \(0.445879\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −28.3225 + 45.1724i −1.00703 + 1.60615i
\(792\) 0 0
\(793\) −9.78868 16.9545i −0.347606 0.602072i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 8.76647 15.1840i 0.310524 0.537844i −0.667952 0.744205i \(-0.732829\pi\)
0.978476 + 0.206361i \(0.0661621\pi\)
\(798\) 0 0
\(799\) 1.35167 + 2.34117i 0.0478188 + 0.0828245i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −19.7916 + 34.2801i