Properties

Label 2520.2.bi.r.361.1
Level $2520$
Weight $2$
Character 2520.361
Analytic conductor $20.122$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2520.bi (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(20.1223013094\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \(x^{10} + 29 x^{8} + 247 x^{6} + 855 x^{4} + 1212 x^{2} + 588\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(1.05780i\) of defining polynomial
Character \(\chi\) \(=\) 2520.361
Dual form 2520.2.bi.r.1801.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{5} +(-2.62478 - 0.332488i) q^{7} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{5} +(-2.62478 - 0.332488i) q^{7} +(-1.41608 + 2.45273i) q^{11} -1.08882 q^{13} +(-2.23314 + 3.86791i) q^{17} +(2.06886 + 3.58337i) q^{19} +(-3.69363 - 6.39756i) q^{23} +(-0.500000 + 0.866025i) q^{25} +9.17054 q^{29} +(5.37788 - 9.31476i) q^{31} +(1.02445 + 2.43937i) q^{35} +(0.0244456 + 0.0423411i) q^{37} +9.66694 q^{41} +6.20962 q^{43} +(-0.371671 - 0.643754i) q^{47} +(6.77890 + 1.74541i) q^{49} +(-3.46049 + 5.99375i) q^{53} +2.83217 q^{55} +(-1.75311 + 3.03647i) q^{59} +(-3.68070 - 6.37515i) q^{61} +(0.544411 + 0.942948i) q^{65} +(6.87433 - 11.9067i) q^{67} -7.50621 q^{71} +(4.97691 - 8.62026i) q^{73} +(4.53240 - 5.96703i) q^{77} +(-8.73001 - 15.1208i) q^{79} -12.5319 q^{83} +4.46628 q^{85} +(-1.33572 - 2.31353i) q^{89} +(2.85792 + 0.362020i) q^{91} +(2.06886 - 3.58337i) q^{95} +13.9725 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 5q^{5} - q^{7} + O(q^{10}) \) \( 10q - 5q^{5} - q^{7} - 2q^{11} + 6q^{13} + 2q^{17} + q^{19} + 8q^{23} - 5q^{25} + 7q^{31} - q^{35} - 11q^{37} + 20q^{41} + 6q^{43} - 23q^{49} - 14q^{53} + 4q^{55} + 4q^{59} - 6q^{61} - 3q^{65} - 7q^{67} - 32q^{71} + 3q^{73} + 8q^{77} - 19q^{79} + 28q^{83} - 4q^{85} - 18q^{89} - 21q^{91} + q^{95} + 48q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(1081\) \(1261\) \(2017\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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 0
\(4\) 0 0
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) −2.62478 0.332488i −0.992072 0.125668i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.41608 + 2.45273i −0.426965 + 0.739525i −0.996602 0.0823715i \(-0.973751\pi\)
0.569637 + 0.821897i \(0.307084\pi\)
\(12\) 0 0
\(13\) −1.08882 −0.301985 −0.150993 0.988535i \(-0.548247\pi\)
−0.150993 + 0.988535i \(0.548247\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.23314 + 3.86791i −0.541616 + 0.938106i 0.457196 + 0.889366i \(0.348854\pi\)
−0.998811 + 0.0487401i \(0.984479\pi\)
\(18\) 0 0
\(19\) 2.06886 + 3.58337i 0.474628 + 0.822080i 0.999578 0.0290530i \(-0.00924915\pi\)
−0.524950 + 0.851133i \(0.675916\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.69363 6.39756i −0.770176 1.33398i −0.937466 0.348076i \(-0.886835\pi\)
0.167290 0.985908i \(-0.446498\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 9.17054 1.70293 0.851463 0.524414i \(-0.175716\pi\)
0.851463 + 0.524414i \(0.175716\pi\)
\(30\) 0 0
\(31\) 5.37788 9.31476i 0.965896 1.67298i 0.258708 0.965956i \(-0.416703\pi\)
0.707188 0.707026i \(-0.249963\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.02445 + 2.43937i 0.173163 + 0.412328i
\(36\) 0 0
\(37\) 0.0244456 + 0.0423411i 0.00401884 + 0.00696083i 0.868028 0.496516i \(-0.165387\pi\)
−0.864009 + 0.503476i \(0.832054\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 9.66694 1.50972 0.754861 0.655884i \(-0.227704\pi\)
0.754861 + 0.655884i \(0.227704\pi\)
\(42\) 0 0
\(43\) 6.20962 0.946958 0.473479 0.880805i \(-0.342998\pi\)
0.473479 + 0.880805i \(0.342998\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −0.371671 0.643754i −0.0542138 0.0939011i 0.837645 0.546215i \(-0.183932\pi\)
−0.891859 + 0.452314i \(0.850599\pi\)
\(48\) 0 0
\(49\) 6.77890 + 1.74541i 0.968415 + 0.249344i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −3.46049 + 5.99375i −0.475335 + 0.823305i −0.999601 0.0282498i \(-0.991007\pi\)
0.524265 + 0.851555i \(0.324340\pi\)
\(54\) 0 0
\(55\) 2.83217 0.381889
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.75311 + 3.03647i −0.228235 + 0.395314i −0.957285 0.289146i \(-0.906629\pi\)
0.729050 + 0.684460i \(0.239962\pi\)
\(60\) 0 0
\(61\) −3.68070 6.37515i −0.471265 0.816255i 0.528195 0.849123i \(-0.322869\pi\)
−0.999460 + 0.0328685i \(0.989536\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.544411 + 0.942948i 0.0675259 + 0.116958i
\(66\) 0 0
\(67\) 6.87433 11.9067i 0.839833 1.45463i −0.0502009 0.998739i \(-0.515986\pi\)
0.890034 0.455894i \(-0.150681\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −7.50621 −0.890823 −0.445412 0.895326i \(-0.646943\pi\)
−0.445412 + 0.895326i \(0.646943\pi\)
\(72\) 0 0
\(73\) 4.97691 8.62026i 0.582503 1.00892i −0.412679 0.910877i \(-0.635407\pi\)
0.995182 0.0980481i \(-0.0312599\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.53240 5.96703i 0.516515 0.680006i
\(78\) 0 0
\(79\) −8.73001 15.1208i −0.982203 1.70123i −0.653760 0.756702i \(-0.726809\pi\)
−0.328443 0.944524i \(-0.606524\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −12.5319 −1.37556 −0.687779 0.725920i \(-0.741414\pi\)
−0.687779 + 0.725920i \(0.741414\pi\)
\(84\) 0 0
\(85\) 4.46628 0.484436
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.33572 2.31353i −0.141586 0.245234i 0.786508 0.617580i \(-0.211887\pi\)
−0.928094 + 0.372346i \(0.878553\pi\)
\(90\) 0 0
\(91\) 2.85792 + 0.362020i 0.299591 + 0.0379500i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.06886 3.58337i 0.212260 0.367646i
\(96\) 0 0
\(97\) 13.9725 1.41869 0.709346 0.704861i \(-0.248991\pi\)
0.709346 + 0.704861i \(0.248991\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 4.95377 8.58018i 0.492918 0.853759i −0.507048 0.861918i \(-0.669263\pi\)
0.999967 + 0.00815809i \(0.00259683\pi\)
\(102\) 0 0
\(103\) 7.24252 + 12.5444i 0.713627 + 1.23604i 0.963487 + 0.267756i \(0.0862822\pi\)
−0.249859 + 0.968282i \(0.580384\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.23314 2.13586i −0.119212 0.206481i 0.800244 0.599675i \(-0.204704\pi\)
−0.919456 + 0.393194i \(0.871370\pi\)
\(108\) 0 0
\(109\) 5.64119 9.77083i 0.540328 0.935876i −0.458557 0.888665i \(-0.651633\pi\)
0.998885 0.0472106i \(-0.0150332\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −8.49911 −0.799529 −0.399764 0.916618i \(-0.630908\pi\)
−0.399764 + 0.916618i \(0.630908\pi\)
\(114\) 0 0
\(115\) −3.69363 + 6.39756i −0.344433 + 0.596576i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 7.14752 9.40991i 0.655212 0.862605i
\(120\) 0 0
\(121\) 1.48942 + 2.57975i 0.135402 + 0.234523i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 8.85094 0.785394 0.392697 0.919668i \(-0.371542\pi\)
0.392697 + 0.919668i \(0.371542\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −3.16919 5.48919i −0.276893 0.479593i 0.693718 0.720247i \(-0.255972\pi\)
−0.970611 + 0.240654i \(0.922638\pi\)
\(132\) 0 0
\(133\) −4.23886 10.0934i −0.367556 0.875209i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1.72693 + 2.99113i −0.147542 + 0.255549i −0.930318 0.366753i \(-0.880469\pi\)
0.782777 + 0.622303i \(0.213803\pi\)
\(138\) 0 0
\(139\) 15.7158 1.33300 0.666500 0.745505i \(-0.267792\pi\)
0.666500 + 0.745505i \(0.267792\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1.54186 2.67058i 0.128937 0.223326i
\(144\) 0 0
\(145\) −4.58527 7.94192i −0.380786 0.659541i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 11.4362 + 19.8080i 0.936887 + 1.62274i 0.771235 + 0.636551i \(0.219639\pi\)
0.165652 + 0.986184i \(0.447027\pi\)
\(150\) 0 0
\(151\) −8.40102 + 14.5510i −0.683666 + 1.18414i 0.290189 + 0.956969i \(0.406282\pi\)
−0.973854 + 0.227174i \(0.927051\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −10.7558 −0.863924
\(156\) 0 0
\(157\) 2.03147 3.51862i 0.162129 0.280816i −0.773503 0.633793i \(-0.781497\pi\)
0.935632 + 0.352977i \(0.114831\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 7.56785 + 18.0203i 0.596430 + 1.42020i
\(162\) 0 0
\(163\) −5.32857 9.22935i −0.417365 0.722898i 0.578308 0.815818i \(-0.303713\pi\)
−0.995674 + 0.0929203i \(0.970380\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 9.38727 0.726409 0.363204 0.931710i \(-0.381683\pi\)
0.363204 + 0.931710i \(0.381683\pi\)
\(168\) 0 0
\(169\) −11.8145 −0.908805
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −8.71005 15.0862i −0.662213 1.14699i −0.980033 0.198835i \(-0.936284\pi\)
0.317820 0.948151i \(-0.397049\pi\)
\(174\) 0 0
\(175\) 1.60033 2.10688i 0.120974 0.159265i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1.12030 + 1.94041i −0.0837349 + 0.145033i −0.904851 0.425727i \(-0.860018\pi\)
0.821117 + 0.570761i \(0.193352\pi\)
\(180\) 0 0
\(181\) 22.6432 1.68305 0.841527 0.540215i \(-0.181657\pi\)
0.841527 + 0.540215i \(0.181657\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.0244456 0.0423411i 0.00179728 0.00311298i
\(186\) 0 0
\(187\) −6.32462 10.9546i −0.462502 0.801077i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 8.71583 + 15.0963i 0.630655 + 1.09233i 0.987418 + 0.158132i \(0.0505472\pi\)
−0.356762 + 0.934195i \(0.616119\pi\)
\(192\) 0 0
\(193\) −3.99297 + 6.91603i −0.287420 + 0.497827i −0.973193 0.229989i \(-0.926131\pi\)
0.685773 + 0.727816i \(0.259464\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 22.4457 1.59919 0.799596 0.600539i \(-0.205047\pi\)
0.799596 + 0.600539i \(0.205047\pi\)
\(198\) 0 0
\(199\) 4.89742 8.48258i 0.347169 0.601314i −0.638576 0.769558i \(-0.720476\pi\)
0.985745 + 0.168244i \(0.0538097\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −24.0706 3.04909i −1.68943 0.214004i
\(204\) 0 0
\(205\) −4.83347 8.37182i −0.337584 0.584713i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −11.7187 −0.810599
\(210\) 0 0
\(211\) −2.31451 −0.159337 −0.0796687 0.996821i \(-0.525386\pi\)
−0.0796687 + 0.996821i \(0.525386\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −3.10481 5.37769i −0.211746 0.366755i
\(216\) 0 0
\(217\) −17.2128 + 22.6611i −1.16848 + 1.53834i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2.43149 4.21147i 0.163560 0.283294i
\(222\) 0 0
\(223\) 3.67854 0.246333 0.123167 0.992386i \(-0.460695\pi\)
0.123167 + 0.992386i \(0.460695\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0.312151 0.540662i 0.0207182 0.0358850i −0.855480 0.517835i \(-0.826738\pi\)
0.876199 + 0.481950i \(0.160071\pi\)
\(228\) 0 0
\(229\) 8.17012 + 14.1511i 0.539896 + 0.935128i 0.998909 + 0.0466983i \(0.0148699\pi\)
−0.459013 + 0.888430i \(0.651797\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5.18661 8.98346i −0.339786 0.588526i 0.644606 0.764515i \(-0.277021\pi\)
−0.984392 + 0.175988i \(0.943688\pi\)
\(234\) 0 0
\(235\) −0.371671 + 0.643754i −0.0242452 + 0.0419939i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −13.3287 −0.862159 −0.431080 0.902314i \(-0.641867\pi\)
−0.431080 + 0.902314i \(0.641867\pi\)
\(240\) 0 0
\(241\) 6.31798 10.9431i 0.406977 0.704905i −0.587572 0.809172i \(-0.699916\pi\)
0.994549 + 0.104267i \(0.0332495\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.87788 6.74341i −0.119973 0.430821i
\(246\) 0 0
\(247\) −2.25262 3.90165i −0.143331 0.248256i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 18.5764 1.17253 0.586265 0.810120i \(-0.300598\pi\)
0.586265 + 0.810120i \(0.300598\pi\)
\(252\) 0 0
\(253\) 20.9220 1.31535
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 13.3247 + 23.0790i 0.831170 + 1.43963i 0.897111 + 0.441805i \(0.145662\pi\)
−0.0659410 + 0.997824i \(0.521005\pi\)
\(258\) 0 0
\(259\) −0.0500864 0.119264i −0.00311222 0.00741069i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2.65798 + 4.60376i −0.163898 + 0.283880i −0.936263 0.351299i \(-0.885740\pi\)
0.772365 + 0.635179i \(0.219074\pi\)
\(264\) 0 0
\(265\) 6.92099 0.425153
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 7.70687 13.3487i 0.469896 0.813884i −0.529511 0.848303i \(-0.677625\pi\)
0.999408 + 0.0344187i \(0.0109580\pi\)
\(270\) 0 0
\(271\) 0.710817 + 1.23117i 0.0431791 + 0.0747883i 0.886807 0.462140i \(-0.152918\pi\)
−0.843628 + 0.536928i \(0.819585\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.41608 2.45273i −0.0853930 0.147905i
\(276\) 0 0
\(277\) −5.64114 + 9.77074i −0.338943 + 0.587067i −0.984234 0.176870i \(-0.943403\pi\)
0.645291 + 0.763937i \(0.276736\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 21.2388 1.26700 0.633500 0.773742i \(-0.281617\pi\)
0.633500 + 0.773742i \(0.281617\pi\)
\(282\) 0 0
\(283\) 2.67846 4.63923i 0.159218 0.275774i −0.775369 0.631509i \(-0.782436\pi\)
0.934587 + 0.355735i \(0.115769\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −25.3736 3.21414i −1.49775 0.189725i
\(288\) 0 0
\(289\) −1.47382 2.55274i −0.0866955 0.150161i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 18.9585 1.10757 0.553785 0.832660i \(-0.313183\pi\)
0.553785 + 0.832660i \(0.313183\pi\)
\(294\) 0 0
\(295\) 3.50621 0.204139
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 4.02171 + 6.96581i 0.232582 + 0.402843i
\(300\) 0 0
\(301\) −16.2989 2.06462i −0.939451 0.119003i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −3.68070 + 6.37515i −0.210756 + 0.365040i
\(306\) 0 0
\(307\) −23.1572 −1.32165 −0.660825 0.750540i \(-0.729794\pi\)
−0.660825 + 0.750540i \(0.729794\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −4.46362 + 7.73122i −0.253109 + 0.438397i −0.964380 0.264520i \(-0.914786\pi\)
0.711271 + 0.702917i \(0.248120\pi\)
\(312\) 0 0
\(313\) −1.77625 3.07655i −0.100399 0.173897i 0.811450 0.584422i \(-0.198679\pi\)
−0.911849 + 0.410525i \(0.865345\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5.49876 + 9.52413i 0.308841 + 0.534928i 0.978109 0.208093i \(-0.0667256\pi\)
−0.669268 + 0.743021i \(0.733392\pi\)
\(318\) 0 0
\(319\) −12.9862 + 22.4928i −0.727090 + 1.25936i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −18.4802 −1.02826
\(324\) 0 0
\(325\) 0.544411 0.942948i 0.0301985 0.0523053i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0.761514 + 1.81329i 0.0419836 + 0.0999697i
\(330\) 0 0
\(331\) 0.950215 + 1.64582i 0.0522285 + 0.0904625i 0.890958 0.454086i \(-0.150034\pi\)
−0.838729 + 0.544549i \(0.816701\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −13.7487 −0.751170
\(336\) 0 0
\(337\) 21.3951 1.16546 0.582732 0.812664i \(-0.301984\pi\)
0.582732 + 0.812664i \(0.301984\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 15.2311 + 26.3810i 0.824808 + 1.42861i
\(342\) 0 0
\(343\) −17.2128 6.83522i −0.929403 0.369067i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.54353 4.40553i 0.136544 0.236501i −0.789642 0.613568i \(-0.789734\pi\)
0.926186 + 0.377066i \(0.123067\pi\)
\(348\) 0 0
\(349\) −4.41924 −0.236557 −0.118278 0.992980i \(-0.537738\pi\)
−0.118278 + 0.992980i \(0.537738\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −6.46663 + 11.2005i −0.344184 + 0.596144i −0.985205 0.171379i \(-0.945178\pi\)
0.641021 + 0.767523i \(0.278511\pi\)
\(354\) 0 0
\(355\) 3.75311 + 6.50057i 0.199194 + 0.345014i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −13.5507 23.4704i −0.715176 1.23872i −0.962892 0.269889i \(-0.913013\pi\)
0.247715 0.968833i \(-0.420320\pi\)
\(360\) 0 0
\(361\) 0.939662 1.62754i 0.0494559 0.0856601i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −9.95382 −0.521007
\(366\) 0 0
\(367\) 8.55337 14.8149i 0.446482 0.773330i −0.551672 0.834061i \(-0.686010\pi\)
0.998154 + 0.0607312i \(0.0193432\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 11.0759 14.5817i 0.575031 0.757043i
\(372\) 0 0
\(373\) −14.0680 24.3666i −0.728415 1.26165i −0.957553 0.288258i \(-0.906924\pi\)
0.229137 0.973394i \(-0.426410\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −9.98509 −0.514258
\(378\) 0 0
\(379\) −1.47949 −0.0759960 −0.0379980 0.999278i \(-0.512098\pi\)
−0.0379980 + 0.999278i \(0.512098\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2.05468 3.55880i −0.104989 0.181846i 0.808745 0.588160i \(-0.200147\pi\)
−0.913734 + 0.406314i \(0.866814\pi\)
\(384\) 0 0
\(385\) −7.43380 0.941660i −0.378862 0.0479914i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −0.391713 + 0.678466i −0.0198606 + 0.0343996i −0.875785 0.482702i \(-0.839656\pi\)
0.855924 + 0.517101i \(0.172989\pi\)
\(390\) 0 0
\(391\) 32.9936 1.66856
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −8.73001 + 15.1208i −0.439255 + 0.760811i
\(396\) 0 0
\(397\) 12.0097 + 20.8015i 0.602751 + 1.04400i 0.992403 + 0.123033i \(0.0392622\pi\)
−0.389651 + 0.920963i \(0.627404\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −7.64257 13.2373i −0.381652 0.661040i 0.609647 0.792673i \(-0.291311\pi\)
−0.991299 + 0.131633i \(0.957978\pi\)
\(402\) 0 0
\(403\) −5.85556 + 10.1421i −0.291686 + 0.505215i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.138468 −0.00686361
\(408\) 0 0
\(409\) 0.799763 1.38523i 0.0395458 0.0684953i −0.845575 0.533857i \(-0.820742\pi\)
0.885121 + 0.465361i \(0.154076\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 5.61110 7.38716i 0.276104 0.363498i
\(414\) 0 0
\(415\) 6.26597 + 10.8530i 0.307584 + 0.532751i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0.416537 0.0203492 0.0101746 0.999948i \(-0.496761\pi\)
0.0101746 + 0.999948i \(0.496761\pi\)
\(420\) 0 0
\(421\) −35.1154 −1.71142 −0.855709 0.517457i \(-0.826879\pi\)
−0.855709 + 0.517457i \(0.826879\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2.23314 3.86791i −0.108323 0.187621i
\(426\) 0 0
\(427\) 7.54135 + 17.9571i 0.364951 + 0.869007i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 15.5292 26.8974i 0.748017 1.29560i −0.200756 0.979641i \(-0.564340\pi\)
0.948772 0.315961i \(-0.102327\pi\)
\(432\) 0 0
\(433\) −3.62276 −0.174099 −0.0870494 0.996204i \(-0.527744\pi\)
−0.0870494 + 0.996204i \(0.527744\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 15.2832 26.4713i 0.731095 1.26629i
\(438\) 0 0
\(439\) −1.94631 3.37111i −0.0928925 0.160894i 0.815835 0.578285i \(-0.196278\pi\)
−0.908727 + 0.417391i \(0.862945\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −11.2585 19.5003i −0.534908 0.926488i −0.999168 0.0407889i \(-0.987013\pi\)
0.464260 0.885699i \(-0.346320\pi\)
\(444\) 0 0
\(445\) −1.33572 + 2.31353i −0.0633191 + 0.109672i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 7.40582 0.349502 0.174751 0.984613i \(-0.444088\pi\)
0.174751 + 0.984613i \(0.444088\pi\)
\(450\) 0 0
\(451\) −13.6892 + 23.7104i −0.644599 + 1.11648i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.11544 2.65604i −0.0522926 0.124517i
\(456\) 0 0
\(457\) −12.6107 21.8424i −0.589905 1.02174i −0.994244 0.107136i \(-0.965832\pi\)
0.404340 0.914609i \(-0.367501\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 31.2593 1.45589 0.727946 0.685634i \(-0.240475\pi\)
0.727946 + 0.685634i \(0.240475\pi\)
\(462\) 0 0
\(463\) −17.2062 −0.799641 −0.399821 0.916593i \(-0.630928\pi\)
−0.399821 + 0.916593i \(0.630928\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.38456 + 2.39813i 0.0640698 + 0.110972i 0.896281 0.443487i \(-0.146259\pi\)
−0.832211 + 0.554459i \(0.812925\pi\)
\(468\) 0 0
\(469\) −22.0024 + 28.9668i −1.01598 + 1.33756i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −8.79334 + 15.2305i −0.404318 + 0.700300i
\(474\) 0 0
\(475\) −4.13771 −0.189851
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −13.5969 + 23.5505i −0.621258 + 1.07605i 0.367994 + 0.929828i \(0.380045\pi\)
−0.989252 + 0.146222i \(0.953289\pi\)
\(480\) 0 0
\(481\) −0.0266169 0.0461019i −0.00121363 0.00210207i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6.98624 12.1005i −0.317229 0.549457i
\(486\) 0 0
\(487\) −1.07229 + 1.85725i −0.0485899 + 0.0841601i −0.889297 0.457329i \(-0.848806\pi\)
0.840708 + 0.541489i \(0.182139\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 22.9253 1.03460 0.517302 0.855803i \(-0.326937\pi\)
0.517302 + 0.855803i \(0.326937\pi\)
\(492\) 0 0
\(493\) −20.4791 + 35.4708i −0.922332 + 1.59753i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 19.7021 + 2.49572i 0.883761 + 0.111948i
\(498\) 0 0
\(499\) −8.34505 14.4541i −0.373576 0.647053i 0.616537 0.787326i \(-0.288535\pi\)
−0.990113 + 0.140274i \(0.955202\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −42.1562 −1.87965 −0.939825 0.341656i \(-0.889012\pi\)
−0.939825 + 0.341656i \(0.889012\pi\)
\(504\) 0 0
\(505\) −9.90753 −0.440879
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −14.3712 24.8917i −0.636992 1.10330i −0.986089 0.166217i \(-0.946845\pi\)
0.349097 0.937087i \(-0.386488\pi\)
\(510\) 0 0
\(511\) −15.9294 + 20.9715i −0.704675 + 0.927724i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 7.24252 12.5444i 0.319144 0.552773i
\(516\) 0 0
\(517\) 2.10527 0.0925897
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −20.6053 + 35.6895i −0.902737 + 1.56359i −0.0788096 + 0.996890i \(0.525112\pi\)
−0.823927 + 0.566696i \(0.808221\pi\)
\(522\) 0 0
\(523\) 7.57589 + 13.1218i 0.331270 + 0.573777i 0.982761 0.184879i \(-0.0591895\pi\)
−0.651491 + 0.758656i \(0.725856\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 24.0191 + 41.6023i 1.04629 + 1.81223i
\(528\) 0 0
\(529\) −15.7859 + 27.3419i −0.686342 + 1.18878i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −10.5256 −0.455914
\(534\) 0 0
\(535\) −1.23314 + 2.13586i −0.0533133 + 0.0923413i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −13.8805 + 14.1552i −0.597876 + 0.609706i
\(540\) 0 0
\(541\) −19.4197 33.6359i −0.834917 1.44612i −0.894098 0.447871i \(-0.852182\pi\)
0.0591814 0.998247i \(-0.481151\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −11.2824 −0.483284
\(546\) 0 0
\(547\) −25.2415 −1.07925 −0.539625 0.841906i \(-0.681434\pi\)
−0.539625 + 0.841906i \(0.681434\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 18.9725 + 32.8614i 0.808257 + 1.39994i
\(552\) 0 0
\(553\) 17.8868 + 42.5914i 0.760626 + 1.81117i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 4.58475 7.94103i 0.194262 0.336472i −0.752396 0.658711i \(-0.771102\pi\)
0.946658 + 0.322239i \(0.104435\pi\)
\(558\) 0 0
\(559\) −6.76118 −0.285967
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 7.69021 13.3198i 0.324104 0.561364i −0.657227 0.753693i \(-0.728271\pi\)
0.981331 + 0.192329i \(0.0616041\pi\)
\(564\) 0 0
\(565\) 4.24955 + 7.36044i 0.178780 + 0.309656i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 8.03413 + 13.9155i 0.336808 + 0.583369i 0.983831 0.179102i \(-0.0573192\pi\)
−0.647022 + 0.762471i \(0.723986\pi\)
\(570\) 0 0
\(571\) −19.6200 + 33.9829i −0.821073 + 1.42214i 0.0838115 + 0.996482i \(0.473291\pi\)
−0.904884 + 0.425658i \(0.860043\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 7.38727 0.308070
\(576\) 0 0
\(577\) −11.0351 + 19.1133i −0.459396 + 0.795696i −0.998929 0.0462677i \(-0.985267\pi\)
0.539534 + 0.841964i \(0.318601\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 32.8935 + 4.16671i 1.36465 + 0.172864i
\(582\) 0 0
\(583\) −9.80069 16.9753i −0.405903 0.703045i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 23.6421 0.975815 0.487908 0.872895i \(-0.337760\pi\)
0.487908 + 0.872895i \(0.337760\pi\)
\(588\) 0 0
\(589\) 44.5043 1.83377
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −15.2120 26.3479i −0.624681 1.08198i −0.988602 0.150550i \(-0.951896\pi\)
0.363921 0.931430i \(-0.381438\pi\)
\(594\) 0 0
\(595\) −11.7230 1.48498i −0.480596 0.0608783i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 11.3685 19.6908i 0.464504 0.804545i −0.534675 0.845058i \(-0.679566\pi\)
0.999179 + 0.0405131i \(0.0128992\pi\)
\(600\) 0 0
\(601\) −10.5185 −0.429058 −0.214529 0.976718i \(-0.568822\pi\)
−0.214529 + 0.976718i \(0.568822\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.48942 2.57975i 0.0605535 0.104882i
\(606\) 0 0
\(607\) 8.60311 + 14.9010i 0.349190 + 0.604814i 0.986106 0.166119i \(-0.0531236\pi\)
−0.636916 + 0.770933i \(0.719790\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0.404684 + 0.700934i 0.0163718 + 0.0283567i
\(612\) 0 0
\(613\) −14.4449 + 25.0193i −0.583425 + 1.01052i 0.411645 + 0.911344i \(0.364954\pi\)
−0.995070 + 0.0991770i \(0.968379\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −31.7125 −1.27670 −0.638349 0.769747i \(-0.720382\pi\)
−0.638349 + 0.769747i \(0.720382\pi\)
\(618\) 0 0
\(619\) 8.70701 15.0810i 0.349964 0.606156i −0.636278 0.771460i \(-0.719527\pi\)
0.986243 + 0.165303i \(0.0528604\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2.73674 + 6.51661i 0.109645 + 0.261082i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −0.218362 −0.00870666
\(630\) 0 0
\(631\) −7.02512 −0.279666 −0.139833 0.990175i \(-0.544657\pi\)
−0.139833 + 0.990175i \(0.544657\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −4.42547 7.66514i −0.175619 0.304182i
\(636\) 0 0
\(637\) −7.38102 1.90044i −0.292447 0.0752983i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −12.7864 + 22.1468i −0.505034 + 0.874744i 0.494949 + 0.868922i \(0.335187\pi\)
−0.999983 + 0.00582234i \(0.998147\pi\)
\(642\) 0 0
\(643\) 40.5232 1.59808 0.799039 0.601279i \(-0.205342\pi\)
0.799039 + 0.601279i \(0.205342\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 15.4893 26.8283i 0.608948 1.05473i −0.382466 0.923970i \(-0.624925\pi\)
0.991414 0.130760i \(-0.0417417\pi\)
\(648\) 0 0
\(649\) −4.96508 8.59978i −0.194897 0.337571i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −14.4724 25.0670i −0.566349 0.980946i −0.996923 0.0783902i \(-0.975022\pi\)
0.430573 0.902556i \(-0.358311\pi\)
\(654\) 0 0
\(655\) −3.16919 + 5.48919i −0.123830 + 0.214481i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −9.18836 −0.357928 −0.178964 0.983856i \(-0.557275\pi\)
−0.178964 + 0.983856i \(0.557275\pi\)
\(660\) 0 0
\(661\) 8.11457 14.0549i 0.315620 0.546670i −0.663949 0.747778i \(-0.731121\pi\)
0.979569 + 0.201108i \(0.0644541\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −6.62171 + 8.71766i −0.256779 + 0.338057i
\(666\) 0 0
\(667\) −33.8726 58.6691i −1.31155 2.27168i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 20.8487 0.804854
\(672\) 0 0
\(673\) −3.68822 −0.142171 −0.0710853 0.997470i \(-0.522646\pi\)
−0.0710853 + 0.997470i \(0.522646\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −12.9857 22.4919i −0.499082 0.864436i 0.500917 0.865495i \(-0.332996\pi\)
−0.999999 + 0.00105961i \(0.999663\pi\)
\(678\) 0 0
\(679\) −36.6747 4.64568i −1.40744 0.178285i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 16.0050 27.7214i 0.612413 1.06073i −0.378419 0.925634i \(-0.623532\pi\)
0.990832 0.135096i \(-0.0431344\pi\)
\(684\) 0 0
\(685\) 3.45386 0.131965
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 3.76786 6.52613i 0.143544 0.248626i
\(690\) 0 0
\(691\) 13.8191 + 23.9354i 0.525705 + 0.910547i 0.999552 + 0.0299401i \(0.00953166\pi\)
−0.473847 + 0.880607i \(0.657135\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −7.85792 13.6103i −0.298068 0.516268i
\(696\) 0 0
\(697\) −21.5876 + 37.3909i −0.817690 + 1.41628i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 33.7157 1.27342 0.636712 0.771102i \(-0.280294\pi\)
0.636712 + 0.771102i \(0.280294\pi\)
\(702\) 0 0
\(703\) −0.101149 + 0.175195i −0.00381491 + 0.00660761i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −15.8553 + 20.8740i −0.596301 + 0.785047i
\(708\) 0 0
\(709\) 2.26863 + 3.92937i 0.0852000 + 0.147571i 0.905476 0.424397i \(-0.139514\pi\)
−0.820276 + 0.571967i \(0.806180\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −79.4557 −2.97564
\(714\) 0 0
\(715\) −3.08373 −0.115325
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 9.18661 + 15.9117i 0.342603 + 0.593405i 0.984915 0.173038i \(-0.0553582\pi\)
−0.642313 + 0.766443i \(0.722025\pi\)
\(720\) 0 0
\(721\) −14.8391 35.3344i −0.552639 1.31592i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −4.58527 + 7.94192i −0.170293 + 0.294956i
\(726\) 0 0
\(727\) 17.7650 0.658866 0.329433 0.944179i \(-0.393142\pi\)
0.329433 + 0.944179i \(0.393142\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −13.8670 + 24.0183i −0.512888 + 0.888348i
\(732\) 0 0
\(733\) 6.11096 + 10.5845i 0.225713 + 0.390947i 0.956533 0.291623i \(-0.0941954\pi\)
−0.730820 + 0.682570i \(0.760862\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 19.4692 + 33.7217i 0.717159 + 1.24216i
\(738\) 0 0
\(739\) 6.02182 10.4301i 0.221516 0.383677i −0.733752 0.679417i \(-0.762233\pi\)
0.955269 + 0.295740i \(0.0955661\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −46.7408 −1.71475 −0.857376 0.514690i \(-0.827907\pi\)
−0.857376 + 0.514690i \(0.827907\pi\)
\(744\) 0 0
\(745\) 11.4362 19.8080i 0.418988 0.725709i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 2.52657 + 6.01616i 0.0923188 + 0.219826i
\(750\) 0 0
\(751\) 10.4924 + 18.1734i 0.382874 + 0.663157i 0.991472 0.130322i \(-0.0416010\pi\)
−0.608598 + 0.793479i \(0.708268\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 16.8020 0.611489
\(756\) 0 0
\(757\) −37.3254 −1.35661 −0.678307 0.734778i \(-0.737286\pi\)
−0.678307 + 0.734778i \(0.737286\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −21.1880 36.6987i −0.768065 1.33033i −0.938611 0.344977i \(-0.887887\pi\)
0.170546 0.985350i \(-0.445447\pi\)
\(762\) 0 0
\(763\) −18.0555 + 23.7706i −0.653655 + 0.860554i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.90882 3.30617i 0.0689235 0.119379i
\(768\) 0 0
\(769\) −7.14491 −0.257652 −0.128826 0.991667i \(-0.541121\pi\)
−0.128826 + 0.991667i \(0.541121\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −4.60566 + 7.97724i −0.165654 + 0.286921i −0.936887 0.349631i \(-0.886307\pi\)
0.771233 + 0.636553i \(0.219640\pi\)
\(774\) 0 0
\(775\) 5.37788 + 9.31476i 0.193179 + 0.334596i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 19.9995 + 34.6402i 0.716557 + 1.24111i
\(780\) 0 0
\(781\) 10.6294 18.4107i 0.380350 0.658786i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −4.06295 −0.145013
\(786\) 0 0
\(787\) 19.5089 33.7904i 0.695418 1.20450i −0.274622 0.961552i \(-0.588553\pi\)
0.970040 0.242947i \(-0.0781140\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 22.3083 + 2.82585i 0.793190 + 0.100476i
\(792\) 0 0
\(793\) 4.00763 + 6.94141i 0.142315 + 0.246497i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −15.4359 −0.546769 −0.273384 0.961905i \(-0.588143\pi\)
−0.273384 + 0.961905i \(0.588143\pi\)
\(798\) 0 0
\(799\) 3.31998 0.117452
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 14.0954 + 24.4140i 0.497417 + 0.861551i
\(804\) 0