Properties

Label 3024.2.q.l.2305.2
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 2305.2
Character \(\chi\) \(=\) 3024.2305
Dual form 3024.2.q.l.2881.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.89970 - 3.29038i) q^{5} +(0.841809 - 2.50826i) q^{7} +O(q^{10})\) \(q+(-1.89970 - 3.29038i) q^{5} +(0.841809 - 2.50826i) q^{7} +(-2.25706 + 3.90934i) q^{11} +(0.588451 - 1.01923i) q^{13} +(2.95973 + 5.12641i) q^{17} +(-2.55676 + 4.42844i) q^{19} +(2.09082 + 3.62140i) q^{23} +(-4.71772 + 8.17134i) q^{25} +(-2.11164 - 3.65747i) q^{29} +6.24283 q^{31} +(-9.85230 + 1.99507i) q^{35} +(-3.87179 + 6.70614i) q^{37} +(-0.754693 + 1.30717i) q^{41} +(5.01709 + 8.68986i) q^{43} -2.23665 q^{47} +(-5.58272 - 4.22295i) q^{49} +(-6.49368 - 11.2474i) q^{53} +17.1510 q^{55} +12.3922 q^{59} +1.45834 q^{61} -4.47152 q^{65} -1.62638 q^{67} +8.48517 q^{71} +(3.72984 + 6.46027i) q^{73} +(7.90563 + 8.95221i) q^{77} +1.84185 q^{79} +(-0.307606 - 0.532789i) q^{83} +(11.2452 - 19.4773i) q^{85} +(1.25572 - 2.17496i) q^{89} +(-2.06112 - 2.33398i) q^{91} +19.4283 q^{95} +(2.36751 + 4.10064i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - q^{5} - 5q^{7} + O(q^{10}) \) \( 22q - q^{5} - 5q^{7} + 3q^{11} + 7q^{13} + q^{17} - 13q^{19} - 22q^{25} + 7q^{29} + 12q^{31} + 2q^{35} + 6q^{37} - 4q^{41} - 2q^{43} - 34q^{47} - 25q^{49} - q^{53} - 2q^{55} + 42q^{59} - 62q^{61} - 6q^{65} - 52q^{67} - 32q^{71} + 17q^{73} + q^{77} - 32q^{79} - 36q^{83} + 28q^{85} + 2q^{89} - 15q^{91} + 48q^{95} + 19q^{97} + O(q^{100}) \)

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
\(5\) −1.89970 3.29038i −0.849572 1.47150i −0.881591 0.472014i \(-0.843527\pi\)
0.0320189 0.999487i \(-0.489806\pi\)
\(6\) 0 0
\(7\) 0.841809 2.50826i 0.318174 0.948032i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.25706 + 3.90934i −0.680529 + 1.17871i 0.294290 + 0.955716i \(0.404917\pi\)
−0.974820 + 0.222995i \(0.928417\pi\)
\(12\) 0 0
\(13\) 0.588451 1.01923i 0.163207 0.282683i −0.772810 0.634637i \(-0.781150\pi\)
0.936017 + 0.351955i \(0.114483\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.95973 + 5.12641i 0.717841 + 1.24334i 0.961853 + 0.273565i \(0.0882029\pi\)
−0.244012 + 0.969772i \(0.578464\pi\)
\(18\) 0 0
\(19\) −2.55676 + 4.42844i −0.586562 + 1.01595i 0.408117 + 0.912930i \(0.366185\pi\)
−0.994679 + 0.103025i \(0.967148\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.09082 + 3.62140i 0.435966 + 0.755115i 0.997374 0.0724243i \(-0.0230736\pi\)
−0.561408 + 0.827539i \(0.689740\pi\)
\(24\) 0 0
\(25\) −4.71772 + 8.17134i −0.943545 + 1.63427i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2.11164 3.65747i −0.392122 0.679175i 0.600607 0.799544i \(-0.294925\pi\)
−0.992729 + 0.120369i \(0.961592\pi\)
\(30\) 0 0
\(31\) 6.24283 1.12124 0.560622 0.828072i \(-0.310562\pi\)
0.560622 + 0.828072i \(0.310562\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −9.85230 + 1.99507i −1.66534 + 0.337229i
\(36\) 0 0
\(37\) −3.87179 + 6.70614i −0.636519 + 1.10248i 0.349672 + 0.936872i \(0.386293\pi\)
−0.986191 + 0.165611i \(0.947040\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −0.754693 + 1.30717i −0.117863 + 0.204145i −0.918921 0.394442i \(-0.870938\pi\)
0.801057 + 0.598587i \(0.204271\pi\)
\(42\) 0 0
\(43\) 5.01709 + 8.68986i 0.765099 + 1.32519i 0.940194 + 0.340639i \(0.110643\pi\)
−0.175095 + 0.984552i \(0.556023\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.23665 −0.326248 −0.163124 0.986606i \(-0.552157\pi\)
−0.163124 + 0.986606i \(0.552157\pi\)
\(48\) 0 0
\(49\) −5.58272 4.22295i −0.797531 0.603278i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −6.49368 11.2474i −0.891975 1.54495i −0.837504 0.546431i \(-0.815986\pi\)
−0.0544716 0.998515i \(-0.517347\pi\)
\(54\) 0 0
\(55\) 17.1510 2.31263
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 12.3922 1.61332 0.806662 0.591013i \(-0.201272\pi\)
0.806662 + 0.591013i \(0.201272\pi\)
\(60\) 0 0
\(61\) 1.45834 0.186722 0.0933608 0.995632i \(-0.470239\pi\)
0.0933608 + 0.995632i \(0.470239\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −4.47152 −0.554624
\(66\) 0 0
\(67\) −1.62638 −0.198694 −0.0993472 0.995053i \(-0.531675\pi\)
−0.0993472 + 0.995053i \(0.531675\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.48517 1.00700 0.503502 0.863994i \(-0.332045\pi\)
0.503502 + 0.863994i \(0.332045\pi\)
\(72\) 0 0
\(73\) 3.72984 + 6.46027i 0.436544 + 0.756117i 0.997420 0.0717827i \(-0.0228688\pi\)
−0.560876 + 0.827900i \(0.689535\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 7.90563 + 8.95221i 0.900930 + 1.02020i
\(78\) 0 0
\(79\) 1.84185 0.207224 0.103612 0.994618i \(-0.466960\pi\)
0.103612 + 0.994618i \(0.466960\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −0.307606 0.532789i −0.0337641 0.0584812i 0.848650 0.528956i \(-0.177416\pi\)
−0.882414 + 0.470474i \(0.844083\pi\)
\(84\) 0 0
\(85\) 11.2452 19.4773i 1.21972 2.11261i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1.25572 2.17496i 0.133106 0.230546i −0.791767 0.610824i \(-0.790838\pi\)
0.924872 + 0.380278i \(0.124172\pi\)
\(90\) 0 0
\(91\) −2.06112 2.33398i −0.216064 0.244668i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 19.4283 1.99330
\(96\) 0 0
\(97\) 2.36751 + 4.10064i 0.240384 + 0.416357i 0.960824 0.277160i \(-0.0893934\pi\)
−0.720440 + 0.693517i \(0.756060\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −5.71081 + 9.89141i −0.568247 + 0.984232i 0.428493 + 0.903545i \(0.359045\pi\)
−0.996739 + 0.0806872i \(0.974289\pi\)
\(102\) 0 0
\(103\) −3.18752 5.52095i −0.314076 0.543996i 0.665165 0.746697i \(-0.268361\pi\)
−0.979241 + 0.202701i \(0.935028\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.11999 1.93988i 0.108274 0.187536i −0.806797 0.590828i \(-0.798801\pi\)
0.915071 + 0.403293i \(0.132134\pi\)
\(108\) 0 0
\(109\) −2.73089 4.73005i −0.261572 0.453056i 0.705088 0.709120i \(-0.250908\pi\)
−0.966660 + 0.256064i \(0.917574\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 4.45456 7.71553i 0.419050 0.725816i −0.576794 0.816890i \(-0.695696\pi\)
0.995844 + 0.0910734i \(0.0290298\pi\)
\(114\) 0 0
\(115\) 7.94386 13.7592i 0.740768 1.28305i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 15.3499 3.10832i 1.40712 0.284939i
\(120\) 0 0
\(121\) −4.68864 8.12096i −0.426240 0.738269i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 16.8520 1.50729
\(126\) 0 0
\(127\) −0.434918 −0.0385927 −0.0192964 0.999814i \(-0.506143\pi\)
−0.0192964 + 0.999814i \(0.506143\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2.67633 + 4.63553i 0.233832 + 0.405009i 0.958933 0.283634i \(-0.0915402\pi\)
−0.725101 + 0.688643i \(0.758207\pi\)
\(132\) 0 0
\(133\) 8.95537 + 10.1409i 0.776529 + 0.879329i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.95121 5.11165i 0.252139 0.436718i −0.711976 0.702204i \(-0.752199\pi\)
0.964115 + 0.265487i \(0.0855326\pi\)
\(138\) 0 0
\(139\) −4.33649 + 7.51102i −0.367816 + 0.637077i −0.989224 0.146411i \(-0.953228\pi\)
0.621407 + 0.783488i \(0.286561\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2.65634 + 4.60091i 0.222134 + 0.384747i
\(144\) 0 0
\(145\) −8.02297 + 13.8962i −0.666271 + 1.15402i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.38860 9.33333i −0.441451 0.764616i 0.556346 0.830951i \(-0.312203\pi\)
−0.997797 + 0.0663346i \(0.978870\pi\)
\(150\) 0 0
\(151\) −8.41310 + 14.5719i −0.684648 + 1.18585i 0.288899 + 0.957360i \(0.406711\pi\)
−0.973547 + 0.228486i \(0.926622\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −11.8595 20.5413i −0.952578 1.64991i
\(156\) 0 0
\(157\) 8.96136 0.715194 0.357597 0.933876i \(-0.383596\pi\)
0.357597 + 0.933876i \(0.383596\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 10.8435 2.19578i 0.854586 0.173052i
\(162\) 0 0
\(163\) 3.71319 6.43144i 0.290840 0.503749i −0.683169 0.730261i \(-0.739399\pi\)
0.974009 + 0.226511i \(0.0727320\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −5.13764 + 8.89866i −0.397563 + 0.688599i −0.993425 0.114488i \(-0.963477\pi\)
0.595862 + 0.803087i \(0.296811\pi\)
\(168\) 0 0
\(169\) 5.80745 + 10.0588i 0.446727 + 0.773754i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 10.2099 0.776246 0.388123 0.921608i \(-0.373124\pi\)
0.388123 + 0.921608i \(0.373124\pi\)
\(174\) 0 0
\(175\) 16.5244 + 18.7120i 1.24913 + 1.41449i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 9.62985 + 16.6794i 0.719769 + 1.24668i 0.961091 + 0.276231i \(0.0890854\pi\)
−0.241323 + 0.970445i \(0.577581\pi\)
\(180\) 0 0
\(181\) −1.39163 −0.103439 −0.0517195 0.998662i \(-0.516470\pi\)
−0.0517195 + 0.998662i \(0.516470\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 29.4210 2.16307
\(186\) 0 0
\(187\) −26.7212 −1.95405
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2.71483 −0.196438 −0.0982190 0.995165i \(-0.531315\pi\)
−0.0982190 + 0.995165i \(0.531315\pi\)
\(192\) 0 0
\(193\) 1.84169 0.132568 0.0662839 0.997801i \(-0.478886\pi\)
0.0662839 + 0.997801i \(0.478886\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −21.9198 −1.56172 −0.780860 0.624706i \(-0.785219\pi\)
−0.780860 + 0.624706i \(0.785219\pi\)
\(198\) 0 0
\(199\) 0.726101 + 1.25764i 0.0514719 + 0.0891520i 0.890613 0.454761i \(-0.150275\pi\)
−0.839141 + 0.543913i \(0.816942\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −10.9515 + 2.21765i −0.768643 + 0.155649i
\(204\) 0 0
\(205\) 5.73476 0.400533
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −11.5415 19.9905i −0.798344 1.38277i
\(210\) 0 0
\(211\) −0.771347 + 1.33601i −0.0531017 + 0.0919749i −0.891354 0.453307i \(-0.850244\pi\)
0.838253 + 0.545282i \(0.183577\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 19.0619 33.0162i 1.30001 2.25169i
\(216\) 0 0
\(217\) 5.25527 15.6586i 0.356751 1.06298i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 6.96663 0.468626
\(222\) 0 0
\(223\) 0.346045 + 0.599368i 0.0231729 + 0.0401366i 0.877379 0.479797i \(-0.159290\pi\)
−0.854206 + 0.519934i \(0.825957\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −9.20797 + 15.9487i −0.611155 + 1.05855i 0.379892 + 0.925031i \(0.375961\pi\)
−0.991046 + 0.133520i \(0.957372\pi\)
\(228\) 0 0
\(229\) 2.69696 + 4.67127i 0.178220 + 0.308686i 0.941271 0.337652i \(-0.109633\pi\)
−0.763051 + 0.646338i \(0.776299\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 8.27352 14.3302i 0.542016 0.938800i −0.456772 0.889584i \(-0.650994\pi\)
0.998788 0.0492161i \(-0.0156723\pi\)
\(234\) 0 0
\(235\) 4.24896 + 7.35941i 0.277171 + 0.480075i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1.56724 + 2.71454i −0.101376 + 0.175589i −0.912252 0.409630i \(-0.865658\pi\)
0.810876 + 0.585219i \(0.198991\pi\)
\(240\) 0 0
\(241\) 8.23730 14.2674i 0.530611 0.919046i −0.468751 0.883330i \(-0.655296\pi\)
0.999362 0.0357151i \(-0.0113709\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −3.28960 + 26.3916i −0.210165 + 1.68610i
\(246\) 0 0
\(247\) 3.00906 + 5.21184i 0.191462 + 0.331621i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 12.8939 0.813858 0.406929 0.913460i \(-0.366600\pi\)
0.406929 + 0.913460i \(0.366600\pi\)
\(252\) 0 0
\(253\) −18.8764 −1.18675
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 10.3045 + 17.8478i 0.642774 + 1.11332i 0.984811 + 0.173631i \(0.0555501\pi\)
−0.342036 + 0.939687i \(0.611117\pi\)
\(258\) 0 0
\(259\) 13.5614 + 15.3567i 0.842666 + 0.954222i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −4.56616 + 7.90883i −0.281562 + 0.487679i −0.971770 0.235932i \(-0.924186\pi\)
0.690208 + 0.723611i \(0.257519\pi\)
\(264\) 0 0
\(265\) −24.6721 + 42.7333i −1.51559 + 2.62509i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 12.4387 + 21.5445i 0.758401 + 1.31359i 0.943666 + 0.330900i \(0.107352\pi\)
−0.185265 + 0.982689i \(0.559314\pi\)
\(270\) 0 0
\(271\) −5.70814 + 9.88679i −0.346745 + 0.600580i −0.985669 0.168690i \(-0.946046\pi\)
0.638924 + 0.769270i \(0.279380\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −21.2964 36.8864i −1.28422 2.22433i
\(276\) 0 0
\(277\) −15.4938 + 26.8360i −0.930932 + 1.61242i −0.149200 + 0.988807i \(0.547670\pi\)
−0.781732 + 0.623615i \(0.785663\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 7.40910 + 12.8329i 0.441990 + 0.765549i 0.997837 0.0657354i \(-0.0209393\pi\)
−0.555847 + 0.831285i \(0.687606\pi\)
\(282\) 0 0
\(283\) −25.7431 −1.53027 −0.765134 0.643872i \(-0.777327\pi\)
−0.765134 + 0.643872i \(0.777327\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.64340 + 2.99335i 0.156035 + 0.176692i
\(288\) 0 0
\(289\) −9.02006 + 15.6232i −0.530592 + 0.919012i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −8.41185 + 14.5697i −0.491425 + 0.851174i −0.999951 0.00987288i \(-0.996857\pi\)
0.508526 + 0.861047i \(0.330191\pi\)
\(294\) 0 0
\(295\) −23.5414 40.7749i −1.37063 2.37401i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 4.92137 0.284610
\(300\) 0 0
\(301\) 26.0198 5.26896i 1.49976 0.303698i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2.77041 4.79849i −0.158633 0.274761i
\(306\) 0 0
\(307\) 28.2972 1.61501 0.807504 0.589862i \(-0.200818\pi\)
0.807504 + 0.589862i \(0.200818\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 19.8695 1.12670 0.563349 0.826219i \(-0.309513\pi\)
0.563349 + 0.826219i \(0.309513\pi\)
\(312\) 0 0
\(313\) −18.2859 −1.03358 −0.516789 0.856113i \(-0.672873\pi\)
−0.516789 + 0.856113i \(0.672873\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −13.9480 −0.783399 −0.391700 0.920093i \(-0.628113\pi\)
−0.391700 + 0.920093i \(0.628113\pi\)
\(318\) 0 0
\(319\) 19.0644 1.06740
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −30.2694 −1.68423
\(324\) 0 0
\(325\) 5.55230 + 9.61686i 0.307986 + 0.533447i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1.88283 + 5.61009i −0.103804 + 0.309294i
\(330\) 0 0
\(331\) −20.8399 −1.14547 −0.572733 0.819742i \(-0.694117\pi\)
−0.572733 + 0.819742i \(0.694117\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 3.08964 + 5.35142i 0.168805 + 0.292379i
\(336\) 0 0
\(337\) 15.4376 26.7387i 0.840939 1.45655i −0.0481619 0.998840i \(-0.515336\pi\)
0.889101 0.457710i \(-0.151330\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −14.0904 + 24.4054i −0.763040 + 1.32162i
\(342\) 0 0
\(343\) −15.2918 + 10.4480i −0.825681 + 0.564138i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −10.2685 −0.551244 −0.275622 0.961266i \(-0.588884\pi\)
−0.275622 + 0.961266i \(0.588884\pi\)
\(348\) 0 0
\(349\) 4.61262 + 7.98930i 0.246908 + 0.427657i 0.962666 0.270691i \(-0.0872521\pi\)
−0.715758 + 0.698348i \(0.753919\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 4.08660 7.07820i 0.217508 0.376735i −0.736538 0.676397i \(-0.763541\pi\)
0.954045 + 0.299662i \(0.0968739\pi\)
\(354\) 0 0
\(355\) −16.1193 27.9194i −0.855522 1.48181i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6.35957 11.0151i 0.335645 0.581355i −0.647963 0.761672i \(-0.724379\pi\)
0.983609 + 0.180317i \(0.0577123\pi\)
\(360\) 0 0
\(361\) −3.57407 6.19047i −0.188109 0.325814i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 14.1711 24.5452i 0.741752 1.28475i
\(366\) 0 0
\(367\) −10.9431 + 18.9540i −0.571224 + 0.989388i 0.425217 + 0.905091i \(0.360198\pi\)
−0.996441 + 0.0842970i \(0.973136\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −33.6778 + 6.81968i −1.74846 + 0.354060i
\(372\) 0 0
\(373\) 6.73126 + 11.6589i 0.348531 + 0.603674i 0.985989 0.166811i \(-0.0533471\pi\)
−0.637457 + 0.770486i \(0.720014\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4.97038 −0.255988
\(378\) 0 0
\(379\) 11.2180 0.576231 0.288115 0.957596i \(-0.406971\pi\)
0.288115 + 0.957596i \(0.406971\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 4.00330 + 6.93392i 0.204559 + 0.354307i 0.949992 0.312274i \(-0.101091\pi\)
−0.745433 + 0.666581i \(0.767757\pi\)
\(384\) 0 0
\(385\) 14.4378 43.0190i 0.735819 2.19245i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 14.3931 24.9296i 0.729759 1.26398i −0.227226 0.973842i \(-0.572966\pi\)
0.956985 0.290137i \(-0.0937009\pi\)
\(390\) 0 0
\(391\) −12.3765 + 21.4368i −0.625908 + 1.08410i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −3.49897 6.06039i −0.176052 0.304931i
\(396\) 0 0
\(397\) 10.8138 18.7301i 0.542731 0.940037i −0.456015 0.889972i \(-0.650724\pi\)
0.998746 0.0500651i \(-0.0159429\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 13.4966 + 23.3768i 0.673987 + 1.16738i 0.976764 + 0.214318i \(0.0687530\pi\)
−0.302777 + 0.953062i \(0.597914\pi\)
\(402\) 0 0
\(403\) 3.67360 6.36285i 0.182995 0.316956i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −17.4777 30.2723i −0.866339 1.50054i
\(408\) 0 0
\(409\) −20.9473 −1.03578 −0.517889 0.855448i \(-0.673282\pi\)
−0.517889 + 0.855448i \(0.673282\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 10.4318 31.0828i 0.513317 1.52948i
\(414\) 0 0
\(415\) −1.16872 + 2.02428i −0.0573701 + 0.0993680i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 6.91450 11.9763i 0.337795 0.585079i −0.646222 0.763149i \(-0.723652\pi\)
0.984018 + 0.178070i \(0.0569855\pi\)
\(420\) 0 0
\(421\) −6.86872 11.8970i −0.334761 0.579823i 0.648678 0.761063i \(-0.275322\pi\)
−0.983439 + 0.181240i \(0.941989\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −55.8529 −2.70926
\(426\) 0 0
\(427\) 1.22764 3.65790i 0.0594099 0.177018i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −9.20392 15.9417i −0.443337 0.767882i 0.554598 0.832119i \(-0.312872\pi\)
−0.997935 + 0.0642362i \(0.979539\pi\)
\(432\) 0 0
\(433\) 24.3558 1.17047 0.585233 0.810865i \(-0.301003\pi\)
0.585233 + 0.810865i \(0.301003\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −21.3829 −1.02288
\(438\) 0 0
\(439\) 5.83655 0.278564 0.139282 0.990253i \(-0.455521\pi\)
0.139282 + 0.990253i \(0.455521\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 14.8400 0.705071 0.352536 0.935798i \(-0.385320\pi\)
0.352536 + 0.935798i \(0.385320\pi\)
\(444\) 0 0
\(445\) −9.54194 −0.452331
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 4.26289 0.201178 0.100589 0.994928i \(-0.467927\pi\)
0.100589 + 0.994928i \(0.467927\pi\)
\(450\) 0 0
\(451\) −3.40677 5.90070i −0.160419 0.277853i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −3.76416 + 11.2157i −0.176467 + 0.525801i
\(456\) 0 0
\(457\) 39.7459 1.85924 0.929618 0.368525i \(-0.120137\pi\)
0.929618 + 0.368525i \(0.120137\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2.68671 + 4.65353i 0.125133 + 0.216736i 0.921785 0.387702i \(-0.126731\pi\)
−0.796652 + 0.604438i \(0.793398\pi\)
\(462\) 0 0
\(463\) −19.8205 + 34.3301i −0.921136 + 1.59545i −0.123474 + 0.992348i \(0.539404\pi\)
−0.797661 + 0.603106i \(0.793930\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 9.43069 16.3344i 0.436400 0.755867i −0.561009 0.827810i \(-0.689587\pi\)
0.997409 + 0.0719427i \(0.0229199\pi\)
\(468\) 0 0
\(469\) −1.36910 + 4.07939i −0.0632193 + 0.188369i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −45.2955 −2.08269
\(474\) 0 0
\(475\) −24.1242 41.7843i −1.10689 1.91720i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −9.50287 + 16.4595i −0.434197 + 0.752052i −0.997230 0.0743830i \(-0.976301\pi\)
0.563032 + 0.826435i \(0.309635\pi\)
\(480\) 0 0
\(481\) 4.55672 + 7.89247i 0.207768 + 0.359866i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 8.99511 15.5800i 0.408447 0.707451i
\(486\) 0 0
\(487\) 5.21626 + 9.03482i 0.236371 + 0.409407i 0.959670 0.281128i \(-0.0907085\pi\)
−0.723299 + 0.690535i \(0.757375\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −14.3311 + 24.8221i −0.646752 + 1.12021i 0.337142 + 0.941454i \(0.390540\pi\)
−0.983894 + 0.178753i \(0.942794\pi\)
\(492\) 0 0
\(493\) 12.4998 21.6503i 0.562962 0.975079i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 7.14289 21.2830i 0.320402 0.954673i
\(498\) 0 0
\(499\) −16.5396 28.6475i −0.740416 1.28244i −0.952306 0.305145i \(-0.901295\pi\)
0.211890 0.977294i \(-0.432038\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −28.9523 −1.29092 −0.645460 0.763794i \(-0.723334\pi\)
−0.645460 + 0.763794i \(0.723334\pi\)
\(504\) 0 0
\(505\) 43.3953 1.93107
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 15.8820 + 27.5085i 0.703959 + 1.21929i 0.967066 + 0.254526i \(0.0819194\pi\)
−0.263107 + 0.964767i \(0.584747\pi\)
\(510\) 0 0
\(511\) 19.3438 3.91709i 0.855721 0.173282i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −12.1107 + 20.9763i −0.533660 + 0.924327i
\(516\) 0 0
\(517\) 5.04825 8.74382i 0.222022 0.384553i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2.87897 + 4.98652i 0.126130 + 0.218463i 0.922174 0.386775i \(-0.126411\pi\)
−0.796044 + 0.605239i \(0.793078\pi\)
\(522\) 0 0
\(523\) 22.3123 38.6461i 0.975650 1.68987i 0.297875 0.954605i \(-0.403722\pi\)
0.677774 0.735270i \(-0.262945\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 18.4771 + 32.0033i 0.804876 + 1.39409i
\(528\) 0 0
\(529\) 2.75696 4.77520i 0.119868 0.207617i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0.888199 + 1.53841i 0.0384722 + 0.0666357i
\(534\) 0 0
\(535\) −8.51060 −0.367945
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 29.1095 12.2933i 1.25383 0.529510i
\(540\) 0 0
\(541\) 15.6719 27.1445i 0.673786 1.16703i −0.303036 0.952979i \(-0.598000\pi\)
0.976822 0.214053i \(-0.0686665\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −10.3758 + 17.9713i −0.444449 + 0.769808i
\(546\) 0 0
\(547\) −1.37567 2.38273i −0.0588195 0.101878i 0.835116 0.550073i \(-0.185400\pi\)
−0.893936 + 0.448195i \(0.852067\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 21.5959 0.920014
\(552\) 0 0
\(553\) 1.55049 4.61984i 0.0659334 0.196455i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −3.42197 5.92703i −0.144994 0.251136i 0.784377 0.620284i \(-0.212983\pi\)
−0.929371 + 0.369148i \(0.879650\pi\)
\(558\) 0 0
\(559\) 11.8092 0.499478
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 15.1001 0.636395 0.318197 0.948025i \(-0.396923\pi\)
0.318197 + 0.948025i \(0.396923\pi\)
\(564\) 0 0
\(565\) −33.8494 −1.42405
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 27.5276 1.15402 0.577008 0.816738i \(-0.304220\pi\)
0.577008 + 0.816738i \(0.304220\pi\)
\(570\) 0 0
\(571\) 38.8755 1.62689 0.813444 0.581643i \(-0.197590\pi\)
0.813444 + 0.581643i \(0.197590\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −39.4556 −1.64541
\(576\) 0 0
\(577\) −9.84330 17.0491i −0.409782 0.709763i 0.585083 0.810973i \(-0.301062\pi\)
−0.994865 + 0.101210i \(0.967729\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.59532 + 0.323049i −0.0661849 + 0.0134023i
\(582\) 0 0
\(583\) 58.6265 2.42806
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 3.14068 + 5.43982i 0.129630 + 0.224525i 0.923533 0.383519i \(-0.125288\pi\)
−0.793903 + 0.608044i \(0.791954\pi\)
\(588\) 0 0
\(589\) −15.9614 + 27.6460i −0.657679 + 1.13913i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −7.79280 + 13.4975i −0.320012 + 0.554277i −0.980490 0.196568i \(-0.937020\pi\)
0.660478 + 0.750845i \(0.270354\pi\)
\(594\) 0 0
\(595\) −39.3877 44.6021i −1.61474 1.82851i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.05557 0.0431292 0.0215646 0.999767i \(-0.493135\pi\)
0.0215646 + 0.999767i \(0.493135\pi\)
\(600\) 0 0
\(601\) −12.1622 21.0656i −0.496107 0.859283i 0.503883 0.863772i \(-0.331904\pi\)
−0.999990 + 0.00448941i \(0.998571\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −17.8140 + 30.8548i −0.724243 + 1.25443i
\(606\) 0 0
\(607\) 2.16502 + 3.74993i 0.0878756 + 0.152205i 0.906613 0.421963i \(-0.138659\pi\)
−0.818737 + 0.574168i \(0.805326\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.31616 + 2.27965i −0.0532460 + 0.0922247i
\(612\) 0 0
\(613\) −24.3556 42.1852i −0.983714 1.70384i −0.647518 0.762050i \(-0.724193\pi\)
−0.336196 0.941792i \(-0.609140\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −14.6366 + 25.3514i −0.589249 + 1.02061i 0.405082 + 0.914280i \(0.367243\pi\)
−0.994331 + 0.106329i \(0.966090\pi\)
\(618\) 0 0
\(619\) −18.2381 + 31.5893i −0.733050 + 1.26968i 0.222523 + 0.974927i \(0.428571\pi\)
−0.955573 + 0.294753i \(0.904763\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −4.39830 4.98056i −0.176214 0.199542i
\(624\) 0 0
\(625\) −8.42523 14.5929i −0.337009 0.583717i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −45.8379 −1.82768
\(630\) 0 0
\(631\) −0.501625 −0.0199694 −0.00998468 0.999950i \(-0.503178\pi\)
−0.00998468 + 0.999950i \(0.503178\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.826214 + 1.43104i 0.0327873 + 0.0567893i
\(636\) 0 0
\(637\) −7.58929 + 3.20506i −0.300699 + 0.126989i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −17.5112 + 30.3303i −0.691651 + 1.19797i 0.279646 + 0.960103i \(0.409783\pi\)
−0.971297 + 0.237871i \(0.923551\pi\)
\(642\) 0 0
\(643\) −7.29049 + 12.6275i −0.287509 + 0.497980i −0.973215 0.229899i \(-0.926160\pi\)
0.685706 + 0.727879i \(0.259494\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −11.6503 20.1790i −0.458022 0.793318i 0.540834 0.841129i \(-0.318109\pi\)
−0.998856 + 0.0478116i \(0.984775\pi\)
\(648\) 0 0
\(649\) −27.9699 + 48.4453i −1.09791 + 1.90164i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4.26780 7.39204i −0.167012 0.289273i 0.770356 0.637614i \(-0.220078\pi\)
−0.937368 + 0.348341i \(0.886745\pi\)
\(654\) 0 0
\(655\) 10.1684 17.6123i 0.397314 0.688168i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.81616 3.14568i −0.0707476 0.122538i 0.828482 0.560016i \(-0.189205\pi\)
−0.899229 + 0.437478i \(0.855872\pi\)
\(660\) 0 0
\(661\) −31.0231 −1.20666 −0.603330 0.797492i \(-0.706160\pi\)
−0.603330 + 0.797492i \(0.706160\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 16.3549 48.7313i 0.634217 1.88972i
\(666\) 0 0
\(667\) 8.83011 15.2942i 0.341903 0.592194i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −3.29156 + 5.70116i −0.127069 + 0.220091i
\(672\) 0 0
\(673\) 0.291838 + 0.505478i 0.0112495 + 0.0194848i 0.871595 0.490226i \(-0.163086\pi\)
−0.860346 + 0.509711i \(0.829752\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 33.7332 1.29647 0.648237 0.761439i \(-0.275507\pi\)
0.648237 + 0.761439i \(0.275507\pi\)
\(678\) 0 0
\(679\) 12.2785 2.48636i 0.471204 0.0954178i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.60312 2.77668i −0.0613417 0.106247i 0.833724 0.552182i \(-0.186205\pi\)
−0.895065 + 0.445935i \(0.852871\pi\)
\(684\) 0 0
\(685\) −22.4257 −0.856841
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −15.2848 −0.582306
\(690\) 0 0
\(691\) 32.3674 1.23131 0.615657 0.788014i \(-0.288891\pi\)
0.615657 + 0.788014i \(0.288891\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 32.9521 1.24995
\(696\) 0 0
\(697\) −8.93476 −0.338428
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −21.2591 −0.802943 −0.401472 0.915871i \(-0.631501\pi\)
−0.401472 + 0.915871i \(0.631501\pi\)
\(702\) 0 0
\(703\) −19.7985 34.2920i −0.746715 1.29335i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 20.0028 + 22.6509i 0.752283 + 0.851873i
\(708\) 0 0
\(709\) 31.6544 1.18880 0.594402 0.804168i \(-0.297389\pi\)
0.594402 + 0.804168i \(0.297389\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 13.0526 + 22.6078i 0.488824 + 0.846669i
\(714\) 0 0
\(715\) 10.0925 17.4807i 0.377438 0.653741i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −14.9776 + 25.9420i −0.558571 + 0.967473i 0.439045 + 0.898465i \(0.355317\pi\)
−0.997616 + 0.0690079i \(0.978017\pi\)
\(720\) 0 0
\(721\) −16.5313 + 3.34755i −0.615656 + 0.124669i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 39.8486 1.47994
\(726\) 0 0
\(727\) 13.6310 + 23.6095i 0.505544 + 0.875629i 0.999979 + 0.00641398i \(0.00204165\pi\)
−0.494435 + 0.869215i \(0.664625\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −29.6985 + 51.4393i −1.09844 + 1.90255i
\(732\) 0 0
\(733\) 11.2717 + 19.5232i 0.416330 + 0.721105i 0.995567 0.0940545i \(-0.0299828\pi\)
−0.579237 + 0.815159i \(0.696649\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3.67085 6.35809i 0.135217 0.234203i
\(738\) 0 0
\(739\) 8.82742 + 15.2895i 0.324722 + 0.562435i 0.981456 0.191687i \(-0.0613960\pi\)
−0.656734 + 0.754122i \(0.728063\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −3.31474 + 5.74130i −0.121606 + 0.210628i −0.920401 0.390975i \(-0.872138\pi\)
0.798795 + 0.601603i \(0.205471\pi\)
\(744\) 0 0
\(745\) −20.4735 + 35.4611i −0.750089 + 1.29919i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.92291 4.44224i −0.143340 0.162316i
\(750\) 0 0
\(751\) 3.93721 + 6.81944i 0.143671 + 0.248845i 0.928876 0.370390i \(-0.120776\pi\)
−0.785206 + 0.619235i \(0.787443\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 63.9295 2.32663
\(756\) 0 0
\(757\) −37.1503 −1.35025 −0.675125 0.737703i \(-0.735910\pi\)
−0.675125 + 0.737703i \(0.735910\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −16.2273 28.1065i −0.588238 1.01886i −0.994463 0.105085i \(-0.966488\pi\)
0.406225 0.913773i \(-0.366845\pi\)
\(762\) 0 0
\(763\) −14.1631 + 2.86799i −0.512737 + 0.103828i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 7.29218 12.6304i 0.263305 0.456058i
\(768\) 0 0
\(769\) 11.4992 19.9172i 0.414671 0.718232i −0.580723 0.814101i \(-0.697230\pi\)
0.995394 + 0.0958699i \(0.0305633\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −13.2117 22.8834i −0.475194 0.823059i 0.524403 0.851470i \(-0.324289\pi\)
−0.999596 + 0.0284109i \(0.990955\pi\)
\(774\) 0 0
\(775\) −29.4519 + 51.0123i −1.05794 + 1.83241i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3.85914 6.68423i −0.138268 0.239487i
\(780\) 0 0
\(781\) −19.1515 + 33.1714i −0.685296 + 1.18697i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −17.0239 29.4862i −0.607609 1.05241i
\(786\) 0 0
\(787\) 9.11300 0.324843 0.162422 0.986721i \(-0.448069\pi\)
0.162422 + 0.986721i \(0.448069\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −15.6027 17.6682i −0.554767 0.628209i
\(792\) 0 0
\(793\) 0.858162 1.48638i 0.0304742 0.0527829i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 27.5330 47.6886i 0.975270 1.68922i 0.296228 0.955117i \(-0.404271\pi\)
0.679042 0.734099i \(-0.262395\pi\)
\(798\)