Properties

Label 2520.2.bi.r.1801.4
Level $2520$
Weight $2$
Character 2520.1801
Analytic conductor $20.122$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 1801.4
Root \(4.17259i\) of defining polynomial
Character \(\chi\) \(=\) 2520.1801
Dual form 2520.2.bi.r.361.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{5} +(0.835066 + 2.51051i) q^{7} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{5} +(0.835066 + 2.51051i) q^{7} +(3.11357 + 5.39287i) q^{11} -3.77007 q^{13} +(0.313192 + 0.542464i) q^{17} +(-0.206663 + 0.357951i) q^{19} +(2.04173 - 3.53638i) q^{23} +(-0.500000 - 0.866025i) q^{25} -4.12720 q^{29} +(4.32848 + 7.49714i) q^{31} +(-2.59170 - 0.532067i) q^{35} +(-3.59170 + 6.22101i) q^{37} +4.88688 q^{41} -10.6236 q^{43} +(5.49861 - 9.52387i) q^{47} +(-5.60533 + 4.19288i) q^{49} +(-0.271463 - 0.470188i) q^{53} -6.22715 q^{55} +(-4.16354 - 7.21147i) q^{59} +(0.963468 - 1.66878i) q^{61} +(1.88504 - 3.26498i) q^{65} +(-3.50520 - 6.07118i) q^{67} -12.3271 q^{71} +(-2.58548 - 4.47818i) q^{73} +(-10.9388 + 12.3201i) q^{77} +(-3.57807 + 6.19739i) q^{79} +10.0541 q^{83} -0.626384 q^{85} +(-1.60653 + 2.78259i) q^{89} +(-3.14826 - 9.46481i) q^{91} +(-0.206663 - 0.357951i) q^{95} +13.7007 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 5q^{5} - q^{7} + O(q^{10}) \) \( 10q - 5q^{5} - q^{7} - 2q^{11} + 6q^{13} + 2q^{17} + q^{19} + 8q^{23} - 5q^{25} + 7q^{31} - q^{35} - 11q^{37} + 20q^{41} + 6q^{43} - 23q^{49} - 14q^{53} + 4q^{55} + 4q^{59} - 6q^{61} - 3q^{65} - 7q^{67} - 32q^{71} + 3q^{73} + 8q^{77} - 19q^{79} + 28q^{83} - 4q^{85} - 18q^{89} - 21q^{91} + q^{95} + 48q^{97} + O(q^{100}) \)

Character values

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

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

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
\(7\) 0.835066 + 2.51051i 0.315625 + 0.948884i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.11357 + 5.39287i 0.938777 + 1.62601i 0.767755 + 0.640743i \(0.221374\pi\)
0.171022 + 0.985267i \(0.445293\pi\)
\(12\) 0 0
\(13\) −3.77007 −1.04563 −0.522815 0.852446i \(-0.675118\pi\)
−0.522815 + 0.852446i \(0.675118\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.313192 + 0.542464i 0.0759602 + 0.131567i 0.901503 0.432772i \(-0.142464\pi\)
−0.825543 + 0.564339i \(0.809131\pi\)
\(18\) 0 0
\(19\) −0.206663 + 0.357951i −0.0474117 + 0.0821196i −0.888757 0.458378i \(-0.848431\pi\)
0.841346 + 0.540497i \(0.181764\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.04173 3.53638i 0.425730 0.737386i −0.570758 0.821118i \(-0.693351\pi\)
0.996488 + 0.0837323i \(0.0266841\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4.12720 −0.766403 −0.383201 0.923665i \(-0.625178\pi\)
−0.383201 + 0.923665i \(0.625178\pi\)
\(30\) 0 0
\(31\) 4.32848 + 7.49714i 0.777418 + 1.34653i 0.933426 + 0.358771i \(0.116804\pi\)
−0.156008 + 0.987756i \(0.549863\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.59170 0.532067i −0.438077 0.0899358i
\(36\) 0 0
\(37\) −3.59170 + 6.22101i −0.590472 + 1.02273i 0.403697 + 0.914893i \(0.367725\pi\)
−0.994169 + 0.107834i \(0.965608\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 4.88688 0.763203 0.381601 0.924327i \(-0.375373\pi\)
0.381601 + 0.924327i \(0.375373\pi\)
\(42\) 0 0
\(43\) −10.6236 −1.62008 −0.810042 0.586372i \(-0.800556\pi\)
−0.810042 + 0.586372i \(0.800556\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5.49861 9.52387i 0.802055 1.38920i −0.116207 0.993225i \(-0.537074\pi\)
0.918262 0.395974i \(-0.129593\pi\)
\(48\) 0 0
\(49\) −5.60533 + 4.19288i −0.800762 + 0.598983i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.271463 0.470188i −0.0372884 0.0645853i 0.846779 0.531945i \(-0.178539\pi\)
−0.884067 + 0.467360i \(0.845205\pi\)
\(54\) 0 0
\(55\) −6.22715 −0.839668
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.16354 7.21147i −0.542047 0.938853i −0.998786 0.0492526i \(-0.984316\pi\)
0.456739 0.889601i \(-0.349017\pi\)
\(60\) 0 0
\(61\) 0.963468 1.66878i 0.123359 0.213665i −0.797731 0.603013i \(-0.793967\pi\)
0.921090 + 0.389349i \(0.127300\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.88504 3.26498i 0.233810 0.404971i
\(66\) 0 0
\(67\) −3.50520 6.07118i −0.428228 0.741713i 0.568488 0.822692i \(-0.307529\pi\)
−0.996716 + 0.0809791i \(0.974195\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −12.3271 −1.46296 −0.731478 0.681865i \(-0.761169\pi\)
−0.731478 + 0.681865i \(0.761169\pi\)
\(72\) 0 0
\(73\) −2.58548 4.47818i −0.302607 0.524131i 0.674119 0.738623i \(-0.264524\pi\)
−0.976726 + 0.214492i \(0.931190\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −10.9388 + 12.3201i −1.24659 + 1.40400i
\(78\) 0 0
\(79\) −3.57807 + 6.19739i −0.402564 + 0.697261i −0.994035 0.109065i \(-0.965214\pi\)
0.591471 + 0.806327i \(0.298548\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 10.0541 1.10359 0.551793 0.833981i \(-0.313944\pi\)
0.551793 + 0.833981i \(0.313944\pi\)
\(84\) 0 0
\(85\) −0.626384 −0.0679409
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.60653 + 2.78259i −0.170292 + 0.294954i −0.938522 0.345220i \(-0.887804\pi\)
0.768230 + 0.640174i \(0.221138\pi\)
\(90\) 0 0
\(91\) −3.14826 9.46481i −0.330027 0.992181i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.206663 0.357951i −0.0212032 0.0367250i
\(96\) 0 0
\(97\) 13.7007 1.39110 0.695548 0.718480i \(-0.255162\pi\)
0.695548 + 0.718480i \(0.255162\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 7.67681 + 13.2966i 0.763871 + 1.32306i 0.940841 + 0.338847i \(0.110037\pi\)
−0.176970 + 0.984216i \(0.556630\pi\)
\(102\) 0 0
\(103\) −5.72513 + 9.91621i −0.564114 + 0.977073i 0.433018 + 0.901385i \(0.357449\pi\)
−0.997132 + 0.0756880i \(0.975885\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.31319 2.27452i 0.126951 0.219886i −0.795543 0.605897i \(-0.792814\pi\)
0.922494 + 0.386012i \(0.126148\pi\)
\(108\) 0 0
\(109\) −2.19200 3.79666i −0.209956 0.363654i 0.741744 0.670683i \(-0.233999\pi\)
−0.951700 + 0.307028i \(0.900665\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 5.34026 0.502370 0.251185 0.967939i \(-0.419180\pi\)
0.251185 + 0.967939i \(0.419180\pi\)
\(114\) 0 0
\(115\) 2.04173 + 3.53638i 0.190392 + 0.329769i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.10033 + 1.23927i −0.100867 + 0.113603i
\(120\) 0 0
\(121\) −13.8887 + 24.0559i −1.26261 + 2.18690i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −21.0510 −1.86798 −0.933988 0.357305i \(-0.883696\pi\)
−0.933988 + 0.357305i \(0.883696\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1.04997 + 1.81860i −0.0917363 + 0.158892i −0.908242 0.418446i \(-0.862575\pi\)
0.816505 + 0.577338i \(0.195908\pi\)
\(132\) 0 0
\(133\) −1.07122 0.219917i −0.0928863 0.0190693i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.64028 + 9.76925i 0.481882 + 0.834643i 0.999784 0.0207966i \(-0.00662023\pi\)
−0.517902 + 0.855440i \(0.673287\pi\)
\(138\) 0 0
\(139\) 3.70348 0.314125 0.157063 0.987589i \(-0.449798\pi\)
0.157063 + 0.987589i \(0.449798\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −11.7384 20.3315i −0.981614 1.70020i
\(144\) 0 0
\(145\) 2.06360 3.57426i 0.171373 0.296826i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −7.26686 + 12.5866i −0.595324 + 1.03113i 0.398177 + 0.917309i \(0.369643\pi\)
−0.993501 + 0.113823i \(0.963690\pi\)
\(150\) 0 0
\(151\) 2.93381 + 5.08151i 0.238750 + 0.413527i 0.960356 0.278777i \(-0.0899290\pi\)
−0.721606 + 0.692304i \(0.756596\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −8.65696 −0.695343
\(156\) 0 0
\(157\) 4.46330 + 7.73066i 0.356210 + 0.616974i 0.987324 0.158716i \(-0.0507355\pi\)
−0.631114 + 0.775690i \(0.717402\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 10.5831 + 2.17267i 0.834065 + 0.171231i
\(162\) 0 0
\(163\) −4.78694 + 8.29123i −0.374942 + 0.649419i −0.990318 0.138815i \(-0.955671\pi\)
0.615376 + 0.788234i \(0.289004\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2.08346 −0.161223 −0.0806114 0.996746i \(-0.525687\pi\)
−0.0806114 + 0.996746i \(0.525687\pi\)
\(168\) 0 0
\(169\) 1.21344 0.0933419
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.39867 2.42256i 0.106339 0.184184i −0.807946 0.589257i \(-0.799421\pi\)
0.914284 + 0.405073i \(0.132754\pi\)
\(174\) 0 0
\(175\) 1.75663 1.97844i 0.132789 0.149556i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −6.23337 10.7965i −0.465904 0.806969i 0.533338 0.845902i \(-0.320937\pi\)
−0.999242 + 0.0389331i \(0.987604\pi\)
\(180\) 0 0
\(181\) −26.2316 −1.94978 −0.974891 0.222683i \(-0.928518\pi\)
−0.974891 + 0.222683i \(0.928518\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −3.59170 6.22101i −0.264067 0.457377i
\(186\) 0 0
\(187\) −1.95029 + 3.37801i −0.142619 + 0.247024i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3.29652 + 5.70973i −0.238527 + 0.413142i −0.960292 0.278997i \(-0.909998\pi\)
0.721764 + 0.692139i \(0.243331\pi\)
\(192\) 0 0
\(193\) 2.05500 + 3.55936i 0.147922 + 0.256208i 0.930459 0.366395i \(-0.119408\pi\)
−0.782537 + 0.622604i \(0.786075\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 10.5170 0.749302 0.374651 0.927166i \(-0.377762\pi\)
0.374651 + 0.927166i \(0.377762\pi\)
\(198\) 0 0
\(199\) 2.08028 + 3.60315i 0.147467 + 0.255420i 0.930291 0.366823i \(-0.119555\pi\)
−0.782824 + 0.622244i \(0.786221\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3.44649 10.3614i −0.241896 0.727227i
\(204\) 0 0
\(205\) −2.44344 + 4.23216i −0.170657 + 0.295587i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.57384 −0.178036
\(210\) 0 0
\(211\) 10.3230 0.710668 0.355334 0.934739i \(-0.384367\pi\)
0.355334 + 0.934739i \(0.384367\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 5.31180 9.20031i 0.362262 0.627456i
\(216\) 0 0
\(217\) −15.2071 + 17.1273i −1.03233 + 1.16268i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.18076 2.04513i −0.0794263 0.137570i
\(222\) 0 0
\(223\) 22.8804 1.53219 0.766093 0.642730i \(-0.222198\pi\)
0.766093 + 0.642730i \(0.222198\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 4.14388 + 7.17741i 0.275039 + 0.476382i 0.970145 0.242526i \(-0.0779759\pi\)
−0.695106 + 0.718907i \(0.744643\pi\)
\(228\) 0 0
\(229\) −11.8521 + 20.5285i −0.783211 + 1.35656i 0.146850 + 0.989159i \(0.453086\pi\)
−0.930062 + 0.367403i \(0.880247\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.59672 11.4259i 0.432166 0.748533i −0.564894 0.825164i \(-0.691083\pi\)
0.997060 + 0.0766306i \(0.0244162\pi\)
\(234\) 0 0
\(235\) 5.49861 + 9.52387i 0.358690 + 0.621269i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 22.9086 1.48183 0.740916 0.671597i \(-0.234391\pi\)
0.740916 + 0.671597i \(0.234391\pi\)
\(240\) 0 0
\(241\) −9.60173 16.6307i −0.618502 1.07128i −0.989759 0.142746i \(-0.954407\pi\)
0.371258 0.928530i \(-0.378927\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −0.828478 6.95080i −0.0529295 0.444070i
\(246\) 0 0
\(247\) 0.779134 1.34950i 0.0495751 0.0858667i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 11.2255 0.708548 0.354274 0.935142i \(-0.384728\pi\)
0.354274 + 0.935142i \(0.384728\pi\)
\(252\) 0 0
\(253\) 25.4283 1.59866
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −8.89747 + 15.4109i −0.555009 + 0.961304i 0.442894 + 0.896574i \(0.353952\pi\)
−0.997903 + 0.0647296i \(0.979382\pi\)
\(258\) 0 0
\(259\) −18.6172 3.82205i −1.15682 0.237491i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −15.0238 26.0219i −0.926404 1.60458i −0.789287 0.614024i \(-0.789550\pi\)
−0.137117 0.990555i \(-0.543784\pi\)
\(264\) 0 0
\(265\) 0.542927 0.0333517
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 12.8404 + 22.2401i 0.782890 + 1.35601i 0.930251 + 0.366923i \(0.119589\pi\)
−0.147361 + 0.989083i \(0.547078\pi\)
\(270\) 0 0
\(271\) 9.67700 16.7611i 0.587836 1.01816i −0.406679 0.913571i \(-0.633313\pi\)
0.994515 0.104591i \(-0.0333533\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 3.11357 5.39287i 0.187755 0.325202i
\(276\) 0 0
\(277\) −15.6558 27.1166i −0.940663 1.62928i −0.764210 0.644968i \(-0.776871\pi\)
−0.176453 0.984309i \(-0.556462\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3.78621 0.225866 0.112933 0.993603i \(-0.463975\pi\)
0.112933 + 0.993603i \(0.463975\pi\)
\(282\) 0 0
\(283\) 9.26805 + 16.0527i 0.550929 + 0.954236i 0.998208 + 0.0598420i \(0.0190597\pi\)
−0.447279 + 0.894394i \(0.647607\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4.08087 + 12.2686i 0.240886 + 0.724191i
\(288\) 0 0
\(289\) 8.30382 14.3826i 0.488460 0.846038i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −29.1048 −1.70032 −0.850161 0.526523i \(-0.823495\pi\)
−0.850161 + 0.526523i \(0.823495\pi\)
\(294\) 0 0
\(295\) 8.32709 0.484822
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −7.69746 + 13.3324i −0.445156 + 0.771033i
\(300\) 0 0
\(301\) −8.87140 26.6707i −0.511339 1.53727i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0.963468 + 1.66878i 0.0551680 + 0.0955538i
\(306\) 0 0
\(307\) 14.0120 0.799709 0.399855 0.916579i \(-0.369061\pi\)
0.399855 + 0.916579i \(0.369061\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −3.88020 6.72071i −0.220026 0.381097i 0.734789 0.678295i \(-0.237281\pi\)
−0.954816 + 0.297199i \(0.903948\pi\)
\(312\) 0 0
\(313\) 6.09874 10.5633i 0.344721 0.597075i −0.640582 0.767890i \(-0.721307\pi\)
0.985303 + 0.170815i \(0.0546401\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.45284 + 4.24845i −0.137765 + 0.238617i −0.926650 0.375924i \(-0.877325\pi\)
0.788885 + 0.614541i \(0.210659\pi\)
\(318\) 0 0
\(319\) −12.8504 22.2575i −0.719482 1.24618i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −0.258901 −0.0144056
\(324\) 0 0
\(325\) 1.88504 + 3.26498i 0.104563 + 0.181108i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 28.5015 + 5.85126i 1.57134 + 0.322590i
\(330\) 0 0
\(331\) −5.65686 + 9.79798i −0.310929 + 0.538545i −0.978564 0.205944i \(-0.933974\pi\)
0.667634 + 0.744489i \(0.267307\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 7.01039 0.383019
\(336\) 0 0
\(337\) 16.8091 0.915647 0.457824 0.889043i \(-0.348629\pi\)
0.457824 + 0.889043i \(0.348629\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −26.9541 + 46.6858i −1.45964 + 2.52818i
\(342\) 0 0
\(343\) −15.2071 10.5709i −0.821106 0.570776i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3.93938 + 6.82321i 0.211477 + 0.366289i 0.952177 0.305547i \(-0.0988393\pi\)
−0.740700 + 0.671836i \(0.765506\pi\)
\(348\) 0 0
\(349\) 29.2472 1.56557 0.782783 0.622294i \(-0.213799\pi\)
0.782783 + 0.622294i \(0.213799\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 4.51380 + 7.81814i 0.240246 + 0.416117i 0.960784 0.277297i \(-0.0894387\pi\)
−0.720539 + 0.693415i \(0.756105\pi\)
\(354\) 0 0
\(355\) 6.16354 10.6756i 0.327127 0.566600i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 12.0302 20.8370i 0.634932 1.09973i −0.351597 0.936151i \(-0.614361\pi\)
0.986529 0.163584i \(-0.0523053\pi\)
\(360\) 0 0
\(361\) 9.41458 + 16.3065i 0.495504 + 0.858239i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 5.17095 0.270660
\(366\) 0 0
\(367\) −7.25183 12.5605i −0.378543 0.655655i 0.612308 0.790619i \(-0.290241\pi\)
−0.990850 + 0.134964i \(0.956908\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.953723 1.07415i 0.0495148 0.0557671i
\(372\) 0 0
\(373\) −10.5654 + 18.2999i −0.547057 + 0.947531i 0.451417 + 0.892313i \(0.350919\pi\)
−0.998474 + 0.0552177i \(0.982415\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 15.5599 0.801373
\(378\) 0 0
\(379\) 4.96626 0.255100 0.127550 0.991832i \(-0.459289\pi\)
0.127550 + 0.991832i \(0.459289\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 7.08125 12.2651i 0.361835 0.626716i −0.626428 0.779479i \(-0.715484\pi\)
0.988263 + 0.152763i \(0.0488171\pi\)
\(384\) 0 0
\(385\) −5.20007 15.6333i −0.265020 0.796748i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −12.0905 20.9413i −0.613012 1.06177i −0.990730 0.135847i \(-0.956625\pi\)
0.377718 0.925921i \(-0.376709\pi\)
\(390\) 0 0
\(391\) 2.55781 0.129354
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −3.57807 6.19739i −0.180032 0.311825i
\(396\) 0 0
\(397\) −4.29935 + 7.44670i −0.215778 + 0.373739i −0.953513 0.301352i \(-0.902562\pi\)
0.737735 + 0.675091i \(0.235896\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −19.0909 + 33.0665i −0.953356 + 1.65126i −0.215269 + 0.976555i \(0.569063\pi\)
−0.738087 + 0.674706i \(0.764270\pi\)
\(402\) 0 0
\(403\) −16.3187 28.2648i −0.812891 1.40797i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −44.7321 −2.21729
\(408\) 0 0
\(409\) 7.21167 + 12.4910i 0.356594 + 0.617639i 0.987389 0.158310i \(-0.0506046\pi\)
−0.630795 + 0.775949i \(0.717271\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 14.6276 16.4747i 0.719779 0.810666i
\(414\) 0 0
\(415\) −5.02707 + 8.70714i −0.246769 + 0.427417i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −10.8929 −0.532151 −0.266075 0.963952i \(-0.585727\pi\)
−0.266075 + 0.963952i \(0.585727\pi\)
\(420\) 0 0
\(421\) 3.95051 0.192536 0.0962679 0.995355i \(-0.469309\pi\)
0.0962679 + 0.995355i \(0.469309\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0.313192 0.542464i 0.0151920 0.0263134i
\(426\) 0 0
\(427\) 4.99404 + 1.02526i 0.241679 + 0.0496158i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 15.3002 + 26.5007i 0.736985 + 1.27650i 0.953847 + 0.300293i \(0.0970846\pi\)
−0.216862 + 0.976202i \(0.569582\pi\)
\(432\) 0 0
\(433\) 26.8636 1.29098 0.645491 0.763768i \(-0.276653\pi\)
0.645491 + 0.763768i \(0.276653\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.843900 + 1.46168i 0.0403692 + 0.0699215i
\(438\) 0 0
\(439\) 8.10312 14.0350i 0.386741 0.669855i −0.605268 0.796022i \(-0.706934\pi\)
0.992009 + 0.126167i \(0.0402675\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 12.8070 22.1824i 0.608479 1.05392i −0.383012 0.923743i \(-0.625113\pi\)
0.991491 0.130173i \(-0.0415533\pi\)
\(444\) 0 0
\(445\) −1.60653 2.78259i −0.0761568 0.131907i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 13.3527 0.630153 0.315077 0.949066i \(-0.397970\pi\)
0.315077 + 0.949066i \(0.397970\pi\)
\(450\) 0 0
\(451\) 15.2157 + 26.3543i 0.716478 + 1.24098i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 9.77089 + 2.00593i 0.458067 + 0.0940396i
\(456\) 0 0
\(457\) 2.94506 5.10099i 0.137764 0.238614i −0.788886 0.614540i \(-0.789342\pi\)
0.926650 + 0.375925i \(0.122675\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −7.14635 −0.332839 −0.166419 0.986055i \(-0.553221\pi\)
−0.166419 + 0.986055i \(0.553221\pi\)
\(462\) 0 0
\(463\) 1.97073 0.0915874 0.0457937 0.998951i \(-0.485418\pi\)
0.0457937 + 0.998951i \(0.485418\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 12.2709 21.2538i 0.567829 0.983509i −0.428951 0.903328i \(-0.641117\pi\)
0.996780 0.0801813i \(-0.0255499\pi\)
\(468\) 0 0
\(469\) 12.3147 13.8697i 0.568640 0.640442i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −33.0774 57.2917i −1.52090 2.63427i
\(474\) 0 0
\(475\) 0.413326 0.0189647
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 14.7071 + 25.4734i 0.671983 + 1.16391i 0.977341 + 0.211671i \(0.0678904\pi\)
−0.305358 + 0.952237i \(0.598776\pi\)
\(480\) 0 0
\(481\) 13.5410 23.4536i 0.617415 1.06939i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6.85035 + 11.8652i −0.311058 + 0.538769i
\(486\) 0 0
\(487\) −13.3624 23.1444i −0.605509 1.04877i −0.991971 0.126467i \(-0.959636\pi\)
0.386462 0.922305i \(-0.373697\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 28.9946 1.30851 0.654254 0.756275i \(-0.272983\pi\)
0.654254 + 0.756275i \(0.272983\pi\)
\(492\) 0 0
\(493\) −1.29261 2.23886i −0.0582161 0.100833i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −10.2939 30.9473i −0.461746 1.38818i
\(498\) 0 0
\(499\) −16.0424 + 27.7862i −0.718154 + 1.24388i 0.243576 + 0.969882i \(0.421680\pi\)
−0.961730 + 0.273998i \(0.911654\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −26.4528 −1.17947 −0.589737 0.807596i \(-0.700768\pi\)
−0.589737 + 0.807596i \(0.700768\pi\)
\(504\) 0 0
\(505\) −15.3536 −0.683227
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.38606 + 2.40073i −0.0614361 + 0.106411i −0.895108 0.445850i \(-0.852901\pi\)
0.833671 + 0.552261i \(0.186235\pi\)
\(510\) 0 0
\(511\) 9.08347 10.2304i 0.401829 0.452568i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −5.72513 9.91621i −0.252279 0.436960i
\(516\) 0 0
\(517\) 68.4813 3.01180
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.216885 + 0.375656i 0.00950190 + 0.0164578i 0.870737 0.491749i \(-0.163642\pi\)
−0.861235 + 0.508206i \(0.830309\pi\)
\(522\) 0 0
\(523\) 11.3483 19.6559i 0.496228 0.859492i −0.503763 0.863842i \(-0.668051\pi\)
0.999991 + 0.00435014i \(0.00138470\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.71129 + 4.69609i −0.118106 + 0.204565i
\(528\) 0 0
\(529\) 3.16269 + 5.47794i 0.137508 + 0.238171i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −18.4239 −0.798028
\(534\) 0 0
\(535\) 1.31319 + 2.27452i 0.0567742 + 0.0983359i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −40.0643 17.1740i −1.72569 0.739735i
\(540\) 0 0
\(541\) 7.52227 13.0290i 0.323408 0.560158i −0.657781 0.753209i \(-0.728505\pi\)
0.981189 + 0.193051i \(0.0618382\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4.38401 0.187790
\(546\) 0 0
\(547\) 14.5681 0.622889 0.311444 0.950264i \(-0.399187\pi\)
0.311444 + 0.950264i \(0.399187\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0.852941 1.47734i 0.0363365 0.0629366i
\(552\) 0 0
\(553\) −18.5465 3.80755i −0.788679 0.161913i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 8.66883 + 15.0149i 0.367310 + 0.636200i 0.989144 0.146949i \(-0.0469454\pi\)
−0.621834 + 0.783149i \(0.713612\pi\)
\(558\) 0 0
\(559\) 40.0517 1.69401
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −12.6108 21.8426i −0.531482 0.920554i −0.999325 0.0367425i \(-0.988302\pi\)
0.467842 0.883812i \(-0.345031\pi\)
\(564\) 0 0
\(565\) −2.67013 + 4.62480i −0.112333 + 0.194567i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 5.95671 10.3173i 0.249718 0.432525i −0.713729 0.700422i \(-0.752995\pi\)
0.963448 + 0.267897i \(0.0863287\pi\)
\(570\) 0 0
\(571\) 18.9693 + 32.8559i 0.793842 + 1.37498i 0.923572 + 0.383426i \(0.125256\pi\)
−0.129729 + 0.991549i \(0.541411\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −4.08346 −0.170292
\(576\) 0 0
\(577\) 8.94540 + 15.4939i 0.372402 + 0.645019i 0.989934 0.141526i \(-0.0452010\pi\)
−0.617533 + 0.786545i \(0.711868\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 8.39587 + 25.2410i 0.348319 + 1.04717i
\(582\) 0 0
\(583\) 1.69044 2.92793i 0.0700110 0.121263i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −3.76676 −0.155471 −0.0777355 0.996974i \(-0.524769\pi\)
−0.0777355 + 0.996974i \(0.524769\pi\)
\(588\) 0 0
\(589\) −3.57814 −0.147435
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 18.0905 31.3337i 0.742889 1.28672i −0.208285 0.978068i \(-0.566788\pi\)
0.951175 0.308654i \(-0.0998784\pi\)
\(594\) 0 0
\(595\) −0.523072 1.57254i −0.0214439 0.0644680i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 20.7404 + 35.9234i 0.847430 + 1.46779i 0.883494 + 0.468443i \(0.155185\pi\)
−0.0360636 + 0.999349i \(0.511482\pi\)
\(600\) 0 0
\(601\) 0.243447 0.00993042 0.00496521 0.999988i \(-0.498420\pi\)
0.00496521 + 0.999988i \(0.498420\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −13.8887 24.0559i −0.564655 0.978011i
\(606\) 0 0
\(607\) −0.985363 + 1.70670i −0.0399947 + 0.0692728i −0.885330 0.464964i \(-0.846067\pi\)
0.845335 + 0.534236i \(0.179401\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −20.7302 + 35.9057i −0.838652 + 1.45259i
\(612\) 0 0
\(613\) −15.1837 26.2989i −0.613262 1.06220i −0.990687 0.136161i \(-0.956524\pi\)
0.377424 0.926040i \(-0.376810\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 46.1284 1.85706 0.928529 0.371259i \(-0.121074\pi\)
0.928529 + 0.371259i \(0.121074\pi\)
\(618\) 0 0
\(619\) −21.4648 37.1781i −0.862742 1.49431i −0.869272 0.494335i \(-0.835412\pi\)
0.00652956 0.999979i \(-0.497922\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −8.32728 1.70956i −0.333625 0.0684922i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −4.49957 −0.179409
\(630\) 0 0
\(631\) 44.3019 1.76363 0.881816 0.471594i \(-0.156321\pi\)
0.881816 + 0.471594i \(0.156321\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 10.5255 18.2307i 0.417692 0.723464i
\(636\) 0 0
\(637\) 21.1325 15.8075i 0.837300 0.626315i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 18.1774 + 31.4841i 0.717963 + 1.24355i 0.961805 + 0.273734i \(0.0882588\pi\)
−0.243842 + 0.969815i \(0.578408\pi\)
\(642\) 0 0
\(643\) −3.17731 −0.125301 −0.0626504 0.998036i \(-0.519955\pi\)
−0.0626504 + 0.998036i \(0.519955\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 17.5687 + 30.4299i 0.690697 + 1.19632i 0.971610 + 0.236589i \(0.0760294\pi\)
−0.280913 + 0.959733i \(0.590637\pi\)
\(648\) 0 0
\(649\) 25.9270 44.9069i 1.01772 1.76275i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.58835 + 2.75110i −0.0621569 + 0.107659i −0.895429 0.445204i \(-0.853131\pi\)
0.833272 + 0.552863i \(0.186465\pi\)
\(654\) 0 0
\(655\) −1.04997 1.81860i −0.0410257 0.0710587i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 2.70542 0.105388 0.0526941 0.998611i \(-0.483219\pi\)
0.0526941 + 0.998611i \(0.483219\pi\)
\(660\) 0 0
\(661\) 13.8490 + 23.9871i 0.538662 + 0.932990i 0.998976 + 0.0452341i \(0.0144034\pi\)
−0.460314 + 0.887756i \(0.652263\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0.726062 0.817742i 0.0281555 0.0317107i
\(666\) 0 0
\(667\) −8.42663 + 14.5954i −0.326280 + 0.565134i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 11.9993 0.463228
\(672\) 0 0
\(673\) −27.0997 −1.04462 −0.522309 0.852757i \(-0.674929\pi\)
−0.522309 + 0.852757i \(0.674929\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −23.5828 + 40.8466i −0.906360 + 1.56986i −0.0872789 + 0.996184i \(0.527817\pi\)
−0.819081 + 0.573678i \(0.805516\pi\)
\(678\) 0 0
\(679\) 11.4410 + 34.3958i 0.439065 + 1.31999i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 12.8742 + 22.2988i 0.492619 + 0.853242i 0.999964 0.00850171i \(-0.00270621\pi\)
−0.507345 + 0.861743i \(0.669373\pi\)
\(684\) 0 0
\(685\) −11.2806 −0.431008
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.02344 + 1.77264i 0.0389898 + 0.0675324i
\(690\) 0 0
\(691\) 23.3085 40.3715i 0.886696 1.53580i 0.0429396 0.999078i \(-0.486328\pi\)
0.843757 0.536726i \(-0.180339\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.85174 + 3.20731i −0.0702406 + 0.121660i
\(696\) 0 0
\(697\) 1.53053 + 2.65096i 0.0579731 + 0.100412i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −3.52122 −0.132995 −0.0664974 0.997787i \(-0.521182\pi\)
−0.0664974 + 0.997787i \(0.521182\pi\)
\(702\) 0 0
\(703\) −1.48454 2.57130i −0.0559906 0.0969785i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −26.9707 + 30.3763i −1.01434 + 1.14242i
\(708\) 0 0
\(709\) −13.5337 + 23.4410i −0.508267 + 0.880345i 0.491687 + 0.870772i \(0.336380\pi\)
−0.999954 + 0.00957261i \(0.996953\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 35.3503 1.32388
\(714\) 0 0
\(715\) 23.4768 0.877982
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −2.59672 + 4.49766i −0.0968415 + 0.167734i −0.910376 0.413783i \(-0.864207\pi\)
0.813534 + 0.581517i \(0.197541\pi\)
\(720\) 0 0
\(721\) −29.6756 6.09231i −1.10518 0.226889i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2.06360 + 3.57426i 0.0766403 + 0.132745i
\(726\) 0 0
\(727\) −11.9507 −0.443228 −0.221614 0.975134i \(-0.571133\pi\)
−0.221614 + 0.975134i \(0.571133\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −3.32723 5.76293i −0.123062 0.213150i
\(732\) 0 0
\(733\) 3.79754 6.57754i 0.140265 0.242947i −0.787331 0.616530i \(-0.788538\pi\)
0.927597 + 0.373584i \(0.121871\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 21.8274 37.8061i 0.804022 1.39261i
\(738\) 0 0
\(739\) −24.8275 43.0025i −0.913294 1.58187i −0.809380 0.587285i \(-0.800197\pi\)
−0.103913 0.994586i \(-0.533136\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −18.3163 −0.671960 −0.335980 0.941869i \(-0.609067\pi\)
−0.335980 + 0.941869i \(0.609067\pi\)
\(744\) 0 0
\(745\) −7.26686 12.5866i −0.266237 0.461136i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 6.80680 + 1.39741i 0.248715 + 0.0510604i
\(750\) 0 0
\(751\) −15.2827 + 26.4704i −0.557673 + 0.965918i 0.440017 + 0.897989i \(0.354972\pi\)
−0.997690 + 0.0679284i \(0.978361\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −5.86762 −0.213544
\(756\) 0 0
\(757\) 3.82022 0.138848 0.0694241 0.997587i \(-0.477884\pi\)
0.0694241 + 0.997587i \(0.477884\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 19.6217 33.9857i 0.711285 1.23198i −0.253090 0.967443i \(-0.581447\pi\)
0.964375 0.264539i \(-0.0852196\pi\)
\(762\) 0 0
\(763\) 7.70110 8.67352i 0.278798 0.314002i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 15.6969 + 27.1878i 0.566781 + 0.981693i
\(768\) 0 0
\(769\) 14.4415 0.520774 0.260387 0.965504i \(-0.416150\pi\)
0.260387 + 0.965504i \(0.416150\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −9.63807 16.6936i −0.346657 0.600428i 0.638996 0.769210i \(-0.279350\pi\)
−0.985653 + 0.168782i \(0.946017\pi\)
\(774\) 0 0
\(775\) 4.32848 7.49714i 0.155484 0.269305i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.00994 + 1.74926i −0.0361848 + 0.0626739i
\(780\) 0 0
\(781\) −38.3813 66.4783i −1.37339 2.37878i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −8.92659 −0.318604
\(786\) 0 0
\(787\) 1.97274 + 3.41688i 0.0703205 + 0.121799i 0.899042 0.437863i \(-0.144264\pi\)
−0.828721 + 0.559662i \(0.810931\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 4.45947 + 13.4068i 0.158560 + 0.476690i
\(792\) 0 0
\(793\) −3.63234 + 6.29141i −0.128988 + 0.223414i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −34.9932 −1.23952 −0.619761 0.784791i \(-0.712770\pi\)
−0.619761 + 0.784791i \(0.712770\pi\)
\(798\) 0 0
\(799\) 6.88848 0.243697
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 16.1001 27.8863i 0.568161 0.984084i
\(804\) 0 0