Properties

Label 3024.2.q.l.2305.4
Level $3024$
Weight $2$
Character 3024.2305
Analytic conductor $24.147$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2305.4
Character \(\chi\) \(=\) 3024.2305
Dual form 3024.2.q.l.2881.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.891774 - 1.54460i) q^{5} +(2.54386 - 0.727153i) q^{7} +O(q^{10})\) \(q+(-0.891774 - 1.54460i) q^{5} +(2.54386 - 0.727153i) q^{7} +(2.80706 - 4.86196i) q^{11} +(3.14009 - 5.43879i) q^{13} +(-0.646279 - 1.11939i) q^{17} +(-0.559062 + 0.968324i) q^{19} +(-3.80857 - 6.59664i) q^{23} +(0.909478 - 1.57526i) q^{25} +(1.57496 + 2.72791i) q^{29} -1.00311 q^{31} +(-3.39171 - 3.28079i) q^{35} +(-5.96542 + 10.3324i) q^{37} +(-4.14160 + 7.17347i) q^{41} +(-2.34804 - 4.06693i) q^{43} -1.94400 q^{47} +(5.94250 - 3.69956i) q^{49} +(4.45992 + 7.72481i) q^{53} -10.0130 q^{55} +8.38679 q^{59} +4.82576 q^{61} -11.2010 q^{65} +2.55628 q^{67} -8.86178 q^{71} +(5.67598 + 9.83109i) q^{73} +(3.60538 - 14.4093i) q^{77} -13.4577 q^{79} +(-1.60203 - 2.77479i) q^{83} +(-1.15267 + 1.99648i) q^{85} +(0.404646 - 0.700867i) q^{89} +(4.03312 - 16.1189i) q^{91} +1.99423 q^{95} +(1.10781 + 1.91879i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - q^{5} - 5q^{7} + O(q^{10}) \) \( 22q - q^{5} - 5q^{7} + 3q^{11} + 7q^{13} + q^{17} - 13q^{19} - 22q^{25} + 7q^{29} + 12q^{31} + 2q^{35} + 6q^{37} - 4q^{41} - 2q^{43} - 34q^{47} - 25q^{49} - q^{53} - 2q^{55} + 42q^{59} - 62q^{61} - 6q^{65} - 52q^{67} - 32q^{71} + 17q^{73} + q^{77} - 32q^{79} - 36q^{83} + 28q^{85} + 2q^{89} - 15q^{91} + 48q^{95} + 19q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) −0.891774 1.54460i −0.398814 0.690765i 0.594766 0.803899i \(-0.297245\pi\)
−0.993580 + 0.113133i \(0.963911\pi\)
\(6\) 0 0
\(7\) 2.54386 0.727153i 0.961491 0.274838i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.80706 4.86196i 0.846359 1.46594i −0.0380759 0.999275i \(-0.512123\pi\)
0.884435 0.466663i \(-0.154544\pi\)
\(12\) 0 0
\(13\) 3.14009 5.43879i 0.870903 1.50845i 0.00983976 0.999952i \(-0.496868\pi\)
0.861064 0.508497i \(-0.169799\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.646279 1.11939i −0.156746 0.271491i 0.776948 0.629565i \(-0.216767\pi\)
−0.933693 + 0.358074i \(0.883434\pi\)
\(18\) 0 0
\(19\) −0.559062 + 0.968324i −0.128258 + 0.222149i −0.923002 0.384796i \(-0.874272\pi\)
0.794744 + 0.606945i \(0.207605\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.80857 6.59664i −0.794142 1.37549i −0.923382 0.383882i \(-0.874587\pi\)
0.129240 0.991613i \(-0.458746\pi\)
\(24\) 0 0
\(25\) 0.909478 1.57526i 0.181896 0.315052i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.57496 + 2.72791i 0.292462 + 0.506560i 0.974391 0.224859i \(-0.0721921\pi\)
−0.681929 + 0.731418i \(0.738859\pi\)
\(30\) 0 0
\(31\) −1.00311 −0.180163 −0.0900816 0.995934i \(-0.528713\pi\)
−0.0900816 + 0.995934i \(0.528713\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3.39171 3.28079i −0.573304 0.554555i
\(36\) 0 0
\(37\) −5.96542 + 10.3324i −0.980708 + 1.69864i −0.321067 + 0.947057i \(0.604041\pi\)
−0.659642 + 0.751580i \(0.729292\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −4.14160 + 7.17347i −0.646810 + 1.12031i 0.337071 + 0.941479i \(0.390564\pi\)
−0.983880 + 0.178828i \(0.942769\pi\)
\(42\) 0 0
\(43\) −2.34804 4.06693i −0.358073 0.620200i 0.629566 0.776947i \(-0.283233\pi\)
−0.987639 + 0.156747i \(0.949899\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.94400 −0.283562 −0.141781 0.989898i \(-0.545283\pi\)
−0.141781 + 0.989898i \(0.545283\pi\)
\(48\) 0 0
\(49\) 5.94250 3.69956i 0.848928 0.528508i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.45992 + 7.72481i 0.612617 + 1.06108i 0.990798 + 0.135352i \(0.0432166\pi\)
−0.378180 + 0.925732i \(0.623450\pi\)
\(54\) 0 0
\(55\) −10.0130 −1.35016
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 8.38679 1.09187 0.545933 0.837829i \(-0.316175\pi\)
0.545933 + 0.837829i \(0.316175\pi\)
\(60\) 0 0
\(61\) 4.82576 0.617875 0.308937 0.951082i \(-0.400027\pi\)
0.308937 + 0.951082i \(0.400027\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −11.2010 −1.38931
\(66\) 0 0
\(67\) 2.55628 0.312299 0.156150 0.987733i \(-0.450092\pi\)
0.156150 + 0.987733i \(0.450092\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −8.86178 −1.05170 −0.525850 0.850577i \(-0.676253\pi\)
−0.525850 + 0.850577i \(0.676253\pi\)
\(72\) 0 0
\(73\) 5.67598 + 9.83109i 0.664323 + 1.15064i 0.979468 + 0.201598i \(0.0646135\pi\)
−0.315145 + 0.949044i \(0.602053\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.60538 14.4093i 0.410871 1.64210i
\(78\) 0 0
\(79\) −13.4577 −1.51410 −0.757052 0.653354i \(-0.773361\pi\)
−0.757052 + 0.653354i \(0.773361\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1.60203 2.77479i −0.175845 0.304573i 0.764608 0.644495i \(-0.222933\pi\)
−0.940453 + 0.339922i \(0.889599\pi\)
\(84\) 0 0
\(85\) −1.15267 + 1.99648i −0.125025 + 0.216549i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.404646 0.700867i 0.0428924 0.0742917i −0.843782 0.536686i \(-0.819676\pi\)
0.886675 + 0.462394i \(0.153009\pi\)
\(90\) 0 0
\(91\) 4.03312 16.1189i 0.422786 1.68972i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.99423 0.204604
\(96\) 0 0
\(97\) 1.10781 + 1.91879i 0.112481 + 0.194823i 0.916770 0.399415i \(-0.130787\pi\)
−0.804289 + 0.594238i \(0.797454\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 4.70134 8.14296i 0.467801 0.810254i −0.531522 0.847044i \(-0.678380\pi\)
0.999323 + 0.0367899i \(0.0117132\pi\)
\(102\) 0 0
\(103\) −1.76349 3.05446i −0.173762 0.300964i 0.765970 0.642876i \(-0.222259\pi\)
−0.939732 + 0.341912i \(0.888926\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.39276 + 5.87644i −0.327991 + 0.568097i −0.982113 0.188292i \(-0.939705\pi\)
0.654122 + 0.756389i \(0.273038\pi\)
\(108\) 0 0
\(109\) 0.681848 + 1.18099i 0.0653092 + 0.113119i 0.896831 0.442373i \(-0.145863\pi\)
−0.831522 + 0.555492i \(0.812530\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2.76458 4.78840i 0.260070 0.450455i −0.706190 0.708022i \(-0.749588\pi\)
0.966260 + 0.257568i \(0.0829210\pi\)
\(114\) 0 0
\(115\) −6.79277 + 11.7654i −0.633429 + 1.09713i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.45801 2.37763i −0.225326 0.217957i
\(120\) 0 0
\(121\) −10.2591 17.7693i −0.932649 1.61539i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −12.1619 −1.08780
\(126\) 0 0
\(127\) 12.8209 1.13767 0.568837 0.822450i \(-0.307394\pi\)
0.568837 + 0.822450i \(0.307394\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2.90955 + 5.03948i 0.254208 + 0.440302i 0.964680 0.263424i \(-0.0848518\pi\)
−0.710472 + 0.703726i \(0.751518\pi\)
\(132\) 0 0
\(133\) −0.718059 + 2.86981i −0.0622636 + 0.248844i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −7.67046 + 13.2856i −0.655332 + 1.13507i 0.326479 + 0.945205i \(0.394138\pi\)
−0.981810 + 0.189864i \(0.939195\pi\)
\(138\) 0 0
\(139\) 6.05803 10.4928i 0.513835 0.889988i −0.486036 0.873939i \(-0.661558\pi\)
0.999871 0.0160496i \(-0.00510897\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −17.6288 30.5340i −1.47419 2.55338i
\(144\) 0 0
\(145\) 2.80901 4.86535i 0.233276 0.404046i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2.36849 + 4.10235i 0.194035 + 0.336078i 0.946584 0.322458i \(-0.104509\pi\)
−0.752549 + 0.658536i \(0.771176\pi\)
\(150\) 0 0
\(151\) 12.1845 21.1041i 0.991559 1.71743i 0.383493 0.923544i \(-0.374721\pi\)
0.608066 0.793887i \(-0.291946\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.894545 + 1.54940i 0.0718516 + 0.124451i
\(156\) 0 0
\(157\) −6.30458 −0.503160 −0.251580 0.967836i \(-0.580950\pi\)
−0.251580 + 0.967836i \(0.580950\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −14.4853 14.0116i −1.14160 1.10426i
\(162\) 0 0
\(163\) −0.350678 + 0.607392i −0.0274672 + 0.0475746i −0.879432 0.476024i \(-0.842078\pi\)
0.851965 + 0.523599i \(0.175411\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3.53822 6.12839i 0.273796 0.474229i −0.696035 0.718008i \(-0.745054\pi\)
0.969831 + 0.243780i \(0.0783873\pi\)
\(168\) 0 0
\(169\) −13.2203 22.8982i −1.01695 1.76140i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −6.63534 −0.504476 −0.252238 0.967665i \(-0.581167\pi\)
−0.252238 + 0.967665i \(0.581167\pi\)
\(174\) 0 0
\(175\) 1.16813 4.66858i 0.0883025 0.352912i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 5.63527 + 9.76057i 0.421200 + 0.729539i 0.996057 0.0887145i \(-0.0282759\pi\)
−0.574858 + 0.818253i \(0.694943\pi\)
\(180\) 0 0
\(181\) 21.1800 1.57430 0.787149 0.616762i \(-0.211556\pi\)
0.787149 + 0.616762i \(0.211556\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 21.2792 1.56448
\(186\) 0 0
\(187\) −7.25657 −0.530653
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −9.44088 −0.683118 −0.341559 0.939860i \(-0.610955\pi\)
−0.341559 + 0.939860i \(0.610955\pi\)
\(192\) 0 0
\(193\) −6.28042 −0.452074 −0.226037 0.974119i \(-0.572577\pi\)
−0.226037 + 0.974119i \(0.572577\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −15.4780 −1.10276 −0.551382 0.834253i \(-0.685899\pi\)
−0.551382 + 0.834253i \(0.685899\pi\)
\(198\) 0 0
\(199\) −2.19477 3.80145i −0.155583 0.269478i 0.777688 0.628650i \(-0.216392\pi\)
−0.933271 + 0.359173i \(0.883059\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 5.99009 + 5.79419i 0.420422 + 0.406673i
\(204\) 0 0
\(205\) 14.7735 1.03183
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 3.13864 + 5.43628i 0.217104 + 0.376035i
\(210\) 0 0
\(211\) −7.93101 + 13.7369i −0.545993 + 0.945688i 0.452550 + 0.891739i \(0.350514\pi\)
−0.998544 + 0.0539495i \(0.982819\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −4.18784 + 7.25356i −0.285609 + 0.494689i
\(216\) 0 0
\(217\) −2.55177 + 0.729412i −0.173225 + 0.0495157i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −8.11749 −0.546041
\(222\) 0 0
\(223\) −6.99253 12.1114i −0.468254 0.811040i 0.531088 0.847317i \(-0.321784\pi\)
−0.999342 + 0.0362769i \(0.988450\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5.38364 + 9.32474i −0.357325 + 0.618905i −0.987513 0.157538i \(-0.949644\pi\)
0.630188 + 0.776443i \(0.282978\pi\)
\(228\) 0 0
\(229\) 0.805015 + 1.39433i 0.0531969 + 0.0921397i 0.891398 0.453222i \(-0.149726\pi\)
−0.838201 + 0.545362i \(0.816392\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.510606 0.884395i 0.0334509 0.0579387i −0.848815 0.528690i \(-0.822684\pi\)
0.882266 + 0.470751i \(0.156017\pi\)
\(234\) 0 0
\(235\) 1.73361 + 3.00270i 0.113088 + 0.195875i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −6.96428 + 12.0625i −0.450482 + 0.780258i −0.998416 0.0562640i \(-0.982081\pi\)
0.547934 + 0.836522i \(0.315414\pi\)
\(240\) 0 0
\(241\) 7.28788 12.6230i 0.469454 0.813118i −0.529936 0.848037i \(-0.677784\pi\)
0.999390 + 0.0349197i \(0.0111175\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −11.0137 5.87960i −0.703639 0.375634i
\(246\) 0 0
\(247\) 3.51101 + 6.08124i 0.223400 + 0.386940i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 18.0287 1.13796 0.568981 0.822350i \(-0.307338\pi\)
0.568981 + 0.822350i \(0.307338\pi\)
\(252\) 0 0
\(253\) −42.7635 −2.68852
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 13.4633 + 23.3191i 0.839818 + 1.45461i 0.890047 + 0.455869i \(0.150672\pi\)
−0.0502291 + 0.998738i \(0.515995\pi\)
\(258\) 0 0
\(259\) −7.66198 + 30.6220i −0.476092 + 1.90276i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −0.769419 + 1.33267i −0.0474444 + 0.0821761i −0.888772 0.458349i \(-0.848441\pi\)
0.841328 + 0.540525i \(0.181774\pi\)
\(264\) 0 0
\(265\) 7.95448 13.7776i 0.488640 0.846349i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −3.26461 5.65446i −0.199047 0.344759i 0.749173 0.662374i \(-0.230451\pi\)
−0.948220 + 0.317616i \(0.897118\pi\)
\(270\) 0 0
\(271\) 5.64494 9.77733i 0.342906 0.593930i −0.642065 0.766650i \(-0.721922\pi\)
0.984971 + 0.172720i \(0.0552555\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −5.10591 8.84370i −0.307898 0.533295i
\(276\) 0 0
\(277\) −0.905938 + 1.56913i −0.0544325 + 0.0942799i −0.891958 0.452119i \(-0.850668\pi\)
0.837525 + 0.546399i \(0.184002\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 2.98798 + 5.17533i 0.178248 + 0.308734i 0.941280 0.337626i \(-0.109624\pi\)
−0.763033 + 0.646360i \(0.776290\pi\)
\(282\) 0 0
\(283\) 19.9952 1.18859 0.594295 0.804247i \(-0.297431\pi\)
0.594295 + 0.804247i \(0.297431\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −5.31947 + 21.2599i −0.313998 + 1.25493i
\(288\) 0 0
\(289\) 7.66465 13.2756i 0.450862 0.780915i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 4.95166 8.57652i 0.289279 0.501046i −0.684359 0.729145i \(-0.739918\pi\)
0.973638 + 0.228099i \(0.0732511\pi\)
\(294\) 0 0
\(295\) −7.47912 12.9542i −0.435451 0.754224i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −47.8370 −2.76649
\(300\) 0 0
\(301\) −8.93038 8.63833i −0.514738 0.497905i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −4.30348 7.45385i −0.246417 0.426806i
\(306\) 0 0
\(307\) 23.7122 1.35332 0.676662 0.736293i \(-0.263426\pi\)
0.676662 + 0.736293i \(0.263426\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 20.3449 1.15365 0.576826 0.816867i \(-0.304291\pi\)
0.576826 + 0.816867i \(0.304291\pi\)
\(312\) 0 0
\(313\) 9.71871 0.549334 0.274667 0.961539i \(-0.411432\pi\)
0.274667 + 0.961539i \(0.411432\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.32838 0.186941 0.0934703 0.995622i \(-0.470204\pi\)
0.0934703 + 0.995622i \(0.470204\pi\)
\(318\) 0 0
\(319\) 17.6840 0.990113
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.44524 0.0804153
\(324\) 0 0
\(325\) −5.71168 9.89292i −0.316827 0.548760i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −4.94528 + 1.41359i −0.272642 + 0.0779335i
\(330\) 0 0
\(331\) 1.43469 0.0788578 0.0394289 0.999222i \(-0.487446\pi\)
0.0394289 + 0.999222i \(0.487446\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2.27962 3.94843i −0.124549 0.215726i
\(336\) 0 0
\(337\) 0.00257316 0.00445685i 0.000140169 0.000242780i −0.865955 0.500121i \(-0.833289\pi\)
0.866095 + 0.499879i \(0.166622\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.81578 + 4.87707i −0.152483 + 0.264108i
\(342\) 0 0
\(343\) 12.4268 13.7323i 0.670982 0.741473i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 23.1072 1.24046 0.620229 0.784421i \(-0.287040\pi\)
0.620229 + 0.784421i \(0.287040\pi\)
\(348\) 0 0
\(349\) 6.09723 + 10.5607i 0.326377 + 0.565302i 0.981790 0.189969i \(-0.0608387\pi\)
−0.655413 + 0.755271i \(0.727505\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 12.3536 21.3970i 0.657515 1.13885i −0.323742 0.946145i \(-0.604941\pi\)
0.981257 0.192704i \(-0.0617257\pi\)
\(354\) 0 0
\(355\) 7.90271 + 13.6879i 0.419432 + 0.726478i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 8.20362 14.2091i 0.432970 0.749927i −0.564157 0.825667i \(-0.690799\pi\)
0.997128 + 0.0757407i \(0.0241321\pi\)
\(360\) 0 0
\(361\) 8.87490 + 15.3718i 0.467100 + 0.809041i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 10.1234 17.5342i 0.529882 0.917783i
\(366\) 0 0
\(367\) −2.90900 + 5.03854i −0.151849 + 0.263010i −0.931907 0.362697i \(-0.881856\pi\)
0.780058 + 0.625707i \(0.215189\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 16.9626 + 16.4078i 0.880652 + 0.851852i
\(372\) 0 0
\(373\) −4.42483 7.66403i −0.229109 0.396829i 0.728435 0.685115i \(-0.240248\pi\)
−0.957544 + 0.288286i \(0.906915\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 19.7820 1.01883
\(378\) 0 0
\(379\) −17.3300 −0.890181 −0.445091 0.895486i \(-0.646829\pi\)
−0.445091 + 0.895486i \(0.646829\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −3.54545 6.14090i −0.181164 0.313785i 0.761113 0.648619i \(-0.224653\pi\)
−0.942277 + 0.334834i \(0.891320\pi\)
\(384\) 0 0
\(385\) −25.4718 + 7.28101i −1.29816 + 0.371075i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.32120 5.75249i 0.168392 0.291663i −0.769463 0.638691i \(-0.779476\pi\)
0.937854 + 0.347029i \(0.112809\pi\)
\(390\) 0 0
\(391\) −4.92280 + 8.52654i −0.248957 + 0.431206i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 12.0012 + 20.7867i 0.603845 + 1.04589i
\(396\) 0 0
\(397\) 7.86340 13.6198i 0.394653 0.683559i −0.598404 0.801195i \(-0.704198\pi\)
0.993057 + 0.117636i \(0.0375315\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.98280 + 5.16635i 0.148954 + 0.257995i 0.930841 0.365424i \(-0.119076\pi\)
−0.781887 + 0.623420i \(0.785743\pi\)
\(402\) 0 0
\(403\) −3.14984 + 5.45569i −0.156905 + 0.271767i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 33.4905 + 58.0073i 1.66006 + 2.87531i
\(408\) 0 0
\(409\) −17.6189 −0.871197 −0.435598 0.900141i \(-0.643463\pi\)
−0.435598 + 0.900141i \(0.643463\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 21.3349 6.09848i 1.04982 0.300086i
\(414\) 0 0
\(415\) −2.85729 + 4.94897i −0.140259 + 0.242936i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 9.62164 16.6652i 0.470048 0.814147i −0.529365 0.848394i \(-0.677570\pi\)
0.999413 + 0.0342470i \(0.0109033\pi\)
\(420\) 0 0
\(421\) 7.77999 + 13.4753i 0.379174 + 0.656748i 0.990942 0.134289i \(-0.0428750\pi\)
−0.611769 + 0.791037i \(0.709542\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2.35111 −0.114045
\(426\) 0 0
\(427\) 12.2761 3.50906i 0.594081 0.169815i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −16.9779 29.4067i −0.817799 1.41647i −0.907301 0.420482i \(-0.861861\pi\)
0.0895020 0.995987i \(-0.471472\pi\)
\(432\) 0 0
\(433\) −34.8338 −1.67401 −0.837004 0.547197i \(-0.815695\pi\)
−0.837004 + 0.547197i \(0.815695\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 8.51692 0.407419
\(438\) 0 0
\(439\) −15.5588 −0.742579 −0.371290 0.928517i \(-0.621084\pi\)
−0.371290 + 0.928517i \(0.621084\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 18.3242 0.870611 0.435305 0.900283i \(-0.356640\pi\)
0.435305 + 0.900283i \(0.356640\pi\)
\(444\) 0 0
\(445\) −1.44341 −0.0684242
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 2.75072 0.129815 0.0649073 0.997891i \(-0.479325\pi\)
0.0649073 + 0.997891i \(0.479325\pi\)
\(450\) 0 0
\(451\) 23.2514 + 40.2727i 1.09487 + 1.89637i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −28.4938 + 8.14483i −1.33581 + 0.381836i
\(456\) 0 0
\(457\) 20.6813 0.967433 0.483716 0.875225i \(-0.339287\pi\)
0.483716 + 0.875225i \(0.339287\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −6.40670 11.0967i −0.298390 0.516826i 0.677378 0.735635i \(-0.263116\pi\)
−0.975768 + 0.218809i \(0.929783\pi\)
\(462\) 0 0
\(463\) −5.54704 + 9.60775i −0.257793 + 0.446510i −0.965650 0.259845i \(-0.916328\pi\)
0.707858 + 0.706355i \(0.249662\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 5.36754 9.29686i 0.248380 0.430207i −0.714696 0.699435i \(-0.753435\pi\)
0.963077 + 0.269228i \(0.0867684\pi\)
\(468\) 0 0
\(469\) 6.50283 1.85881i 0.300273 0.0858317i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −26.3643 −1.21223
\(474\) 0 0
\(475\) 1.01691 + 1.76134i 0.0466590 + 0.0808157i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 3.89754 6.75074i 0.178083 0.308449i −0.763141 0.646232i \(-0.776344\pi\)
0.941224 + 0.337783i \(0.109677\pi\)
\(480\) 0 0
\(481\) 37.4639 + 64.8893i 1.70820 + 2.95870i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.97583 3.42225i 0.0897180 0.155396i
\(486\) 0 0
\(487\) −13.9984 24.2459i −0.634326 1.09868i −0.986657 0.162810i \(-0.947944\pi\)
0.352331 0.935875i \(-0.385389\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −12.1227 + 20.9971i −0.547089 + 0.947586i 0.451383 + 0.892330i \(0.350931\pi\)
−0.998472 + 0.0552556i \(0.982403\pi\)
\(492\) 0 0
\(493\) 2.03572 3.52598i 0.0916844 0.158802i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −22.5432 + 6.44387i −1.01120 + 0.289047i
\(498\) 0 0
\(499\) −16.8874 29.2499i −0.755984 1.30940i −0.944883 0.327407i \(-0.893825\pi\)
0.188899 0.981996i \(-0.439508\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −1.09819 −0.0489661 −0.0244830 0.999700i \(-0.507794\pi\)
−0.0244830 + 0.999700i \(0.507794\pi\)
\(504\) 0 0
\(505\) −16.7701 −0.746261
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 8.10672 + 14.0413i 0.359324 + 0.622368i 0.987848 0.155423i \(-0.0496739\pi\)
−0.628524 + 0.777790i \(0.716341\pi\)
\(510\) 0 0
\(511\) 21.5876 + 20.8817i 0.954981 + 0.923750i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −3.14527 + 5.44777i −0.138597 + 0.240057i
\(516\) 0 0
\(517\) −5.45692 + 9.45167i −0.239995 + 0.415684i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −19.1738 33.2099i −0.840017 1.45495i −0.889879 0.456197i \(-0.849211\pi\)
0.0498617 0.998756i \(-0.484122\pi\)
\(522\) 0 0
\(523\) −20.6021 + 35.6838i −0.900865 + 1.56034i −0.0744911 + 0.997222i \(0.523733\pi\)
−0.826374 + 0.563122i \(0.809600\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0.648287 + 1.12287i 0.0282398 + 0.0489128i
\(528\) 0 0
\(529\) −17.5105 + 30.3290i −0.761324 + 1.31865i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 26.0100 + 45.0506i 1.12662 + 1.95136i
\(534\) 0 0
\(535\) 12.1023 0.523229
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.30619 39.2771i −0.0562616 1.69178i
\(540\) 0 0
\(541\) −9.09371 + 15.7508i −0.390969 + 0.677178i −0.992578 0.121613i \(-0.961193\pi\)
0.601609 + 0.798791i \(0.294527\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.21611 2.10636i 0.0520924 0.0902266i
\(546\) 0 0
\(547\) −0.338699 0.586644i −0.0144817 0.0250831i 0.858694 0.512489i \(-0.171277\pi\)
−0.873175 + 0.487406i \(0.837943\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3.52200 −0.150042
\(552\) 0 0
\(553\) −34.2345 + 9.78577i −1.45580 + 0.416133i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −14.8659 25.7484i −0.629887 1.09100i −0.987574 0.157155i \(-0.949768\pi\)
0.357687 0.933842i \(-0.383565\pi\)
\(558\) 0 0
\(559\) −29.4922 −1.24739
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 21.3478 0.899705 0.449852 0.893103i \(-0.351477\pi\)
0.449852 + 0.893103i \(0.351477\pi\)
\(564\) 0 0
\(565\) −9.86153 −0.414878
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 15.1242 0.634041 0.317021 0.948419i \(-0.397318\pi\)
0.317021 + 0.948419i \(0.397318\pi\)
\(570\) 0 0
\(571\) −19.8863 −0.832215 −0.416107 0.909315i \(-0.636606\pi\)
−0.416107 + 0.909315i \(0.636606\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −13.8553 −0.577804
\(576\) 0 0
\(577\) 19.8090 + 34.3102i 0.824661 + 1.42835i 0.902178 + 0.431363i \(0.141967\pi\)
−0.0775179 + 0.996991i \(0.524700\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −6.09304 5.89378i −0.252782 0.244515i
\(582\) 0 0
\(583\) 50.0770 2.07398
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.13275 + 1.96199i 0.0467537 + 0.0809798i 0.888455 0.458963i \(-0.151779\pi\)
−0.841701 + 0.539943i \(0.818446\pi\)
\(588\) 0 0
\(589\) 0.560799 0.971332i 0.0231073 0.0400230i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −5.97295 + 10.3454i −0.245280 + 0.424837i −0.962210 0.272308i \(-0.912213\pi\)
0.716931 + 0.697145i \(0.245546\pi\)
\(594\) 0 0
\(595\) −1.48049 + 5.91695i −0.0606941 + 0.242571i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −2.95272 −0.120645 −0.0603224 0.998179i \(-0.519213\pi\)
−0.0603224 + 0.998179i \(0.519213\pi\)
\(600\) 0 0
\(601\) 15.9751 + 27.6697i 0.651638 + 1.12867i 0.982725 + 0.185071i \(0.0592514\pi\)
−0.331087 + 0.943600i \(0.607415\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −18.2977 + 31.6925i −0.743906 + 1.28848i
\(606\) 0 0
\(607\) 5.20069 + 9.00786i 0.211089 + 0.365618i 0.952056 0.305925i \(-0.0989655\pi\)
−0.740966 + 0.671542i \(0.765632\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −6.10433 + 10.5730i −0.246955 + 0.427739i
\(612\) 0 0
\(613\) 6.22441 + 10.7810i 0.251402 + 0.435441i 0.963912 0.266221i \(-0.0857751\pi\)
−0.712510 + 0.701662i \(0.752442\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 4.70100 8.14237i 0.189255 0.327799i −0.755747 0.654864i \(-0.772726\pi\)
0.945002 + 0.327064i \(0.106059\pi\)
\(618\) 0 0
\(619\) −11.0598 + 19.1561i −0.444531 + 0.769951i −0.998019 0.0629064i \(-0.979963\pi\)
0.553488 + 0.832857i \(0.313296\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0.519727 2.07715i 0.0208224 0.0832193i
\(624\) 0 0
\(625\) 6.29831 + 10.9090i 0.251932 + 0.436360i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 15.4213 0.614887
\(630\) 0 0
\(631\) −18.3705 −0.731316 −0.365658 0.930749i \(-0.619156\pi\)
−0.365658 + 0.930749i \(0.619156\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −11.4334 19.8032i −0.453720 0.785866i
\(636\) 0 0
\(637\) −1.46116 43.9369i −0.0578932 1.74084i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −16.8617 + 29.2052i −0.665995 + 1.15354i 0.313019 + 0.949747i \(0.398660\pi\)
−0.979014 + 0.203791i \(0.934674\pi\)
\(642\) 0 0
\(643\) −10.0635 + 17.4306i −0.396867 + 0.687394i −0.993338 0.115241i \(-0.963236\pi\)
0.596470 + 0.802635i \(0.296569\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −11.1891 19.3800i −0.439887 0.761907i 0.557793 0.829980i \(-0.311648\pi\)
−0.997680 + 0.0680731i \(0.978315\pi\)
\(648\) 0 0
\(649\) 23.5422 40.7763i 0.924112 1.60061i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −20.3377 35.2259i −0.795875 1.37850i −0.922282 0.386518i \(-0.873678\pi\)
0.126406 0.991979i \(-0.459656\pi\)
\(654\) 0 0
\(655\) 5.18932 8.98816i 0.202763 0.351197i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 7.69321 + 13.3250i 0.299685 + 0.519070i 0.976064 0.217484i \(-0.0697851\pi\)
−0.676379 + 0.736554i \(0.736452\pi\)
\(660\) 0 0
\(661\) 49.1473 1.91161 0.955804 0.294006i \(-0.0949885\pi\)
0.955804 + 0.294006i \(0.0949885\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 5.07305 1.45011i 0.196724 0.0562328i
\(666\) 0 0
\(667\) 11.9967 20.7789i 0.464513 0.804561i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 13.5462 23.4627i 0.522944 0.905766i
\(672\) 0 0
\(673\) −6.99961 12.1237i −0.269815 0.467334i 0.698999 0.715123i \(-0.253629\pi\)
−0.968814 + 0.247789i \(0.920296\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 46.7740 1.79767 0.898836 0.438285i \(-0.144414\pi\)
0.898836 + 0.438285i \(0.144414\pi\)
\(678\) 0 0
\(679\) 4.21337 + 4.07558i 0.161694 + 0.156406i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 21.6222 + 37.4508i 0.827352 + 1.43302i 0.900109 + 0.435665i \(0.143487\pi\)
−0.0727571 + 0.997350i \(0.523180\pi\)
\(684\) 0 0
\(685\) 27.3613 1.04542
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 56.0181 2.13412
\(690\) 0 0
\(691\) 11.7214 0.445905 0.222952 0.974829i \(-0.428431\pi\)
0.222952 + 0.974829i \(0.428431\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −21.6096 −0.819697
\(696\) 0 0
\(697\) 10.7065 0.405538
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −0.0120975 −0.000456915 −0.000228458 1.00000i \(-0.500073\pi\)
−0.000228458 1.00000i \(0.500073\pi\)
\(702\) 0 0
\(703\) −6.67008 11.5529i −0.251567 0.435726i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 6.03839 24.1332i 0.227097 0.907621i
\(708\) 0 0
\(709\) 1.07478 0.0403640 0.0201820 0.999796i \(-0.493575\pi\)
0.0201820 + 0.999796i \(0.493575\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 3.82041 + 6.61714i 0.143075 + 0.247814i
\(714\) 0 0
\(715\) −31.4418 + 54.4588i −1.17586 + 2.03664i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 12.7777 22.1317i 0.476529 0.825372i −0.523109 0.852266i \(-0.675228\pi\)
0.999638 + 0.0268932i \(0.00856140\pi\)
\(720\) 0 0
\(721\) −6.70714 6.48779i −0.249787 0.241618i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 5.72956 0.212790
\(726\) 0 0
\(727\) −6.20522 10.7478i −0.230139 0.398612i 0.727710 0.685885i \(-0.240585\pi\)
−0.957849 + 0.287273i \(0.907251\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −3.03498 + 5.25674i −0.112253 + 0.194427i
\(732\) 0 0
\(733\) −14.7095 25.4775i −0.543307 0.941035i −0.998711 0.0507502i \(-0.983839\pi\)
0.455405 0.890285i \(-0.349495\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 7.17562 12.4285i 0.264317 0.457811i
\(738\) 0 0
\(739\) −7.75910 13.4392i −0.285423 0.494368i 0.687288 0.726385i \(-0.258801\pi\)
−0.972712 + 0.232017i \(0.925468\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −13.6333 + 23.6136i −0.500159 + 0.866301i 0.499841 + 0.866117i \(0.333392\pi\)
−1.00000 0.000183414i \(0.999942\pi\)
\(744\) 0 0
\(745\) 4.22432 7.31674i 0.154767 0.268065i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −4.35766 + 17.4159i −0.159226 + 0.636364i
\(750\) 0 0
\(751\) −4.57176 7.91853i −0.166826 0.288951i 0.770476 0.637469i \(-0.220018\pi\)
−0.937302 + 0.348518i \(0.886685\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −43.4632 −1.58179
\(756\) 0 0
\(757\) −20.6307 −0.749834 −0.374917 0.927058i \(-0.622329\pi\)
−0.374917 + 0.927058i \(0.622329\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −0.239208 0.414321i −0.00867130 0.0150191i 0.861657 0.507491i \(-0.169427\pi\)
−0.870328 + 0.492472i \(0.836094\pi\)
\(762\) 0 0
\(763\) 2.59329 + 2.50848i 0.0938835 + 0.0908132i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 26.3352 45.6140i 0.950910 1.64702i
\(768\) 0 0
\(769\) −13.3518 + 23.1261i −0.481480 + 0.833948i −0.999774 0.0212548i \(-0.993234\pi\)
0.518294 + 0.855202i \(0.326567\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 13.5143 + 23.4074i 0.486074 + 0.841905i 0.999872 0.0160062i \(-0.00509514\pi\)
−0.513798 + 0.857911i \(0.671762\pi\)
\(774\) 0 0
\(775\) −0.912303 + 1.58016i −0.0327709 + 0.0567609i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −4.63083 8.02083i −0.165917 0.287376i
\(780\) 0 0
\(781\) −24.8755 + 43.0857i −0.890116 + 1.54173i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 5.62226 + 9.73804i 0.200667 + 0.347566i
\(786\) 0 0
\(787\) −49.1830 −1.75319 −0.876593 0.481233i \(-0.840189\pi\)
−0.876593 + 0.481233i \(0.840189\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 3.55083 14.1913i 0.126253 0.504585i
\(792\) 0 0
\(793\) 15.1533 26.2463i 0.538109 0.932032i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −22.1538 + 38.3715i −0.784728 + 1.35919i 0.144434 + 0.989514i \(0.453864\pi\)
−0.929162 + 0.369674i \(0.879469\pi\)