Properties

Label 1008.4.bt.d.17.6
Level $1008$
Weight $4$
Character 1008.17
Analytic conductor $59.474$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.bt (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(59.4739252858\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.6
Character \(\chi\) \(=\) 1008.17
Dual form 1008.4.bt.d.593.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-5.74088 - 9.94350i) q^{5} +(-17.2542 - 6.73007i) q^{7} +O(q^{10})\) \(q+(-5.74088 - 9.94350i) q^{5} +(-17.2542 - 6.73007i) q^{7} +(49.6208 + 28.6486i) q^{11} +9.20923i q^{13} +(-14.5492 + 25.1999i) q^{17} +(32.6061 - 18.8252i) q^{19} +(-7.27174 + 4.19834i) q^{23} +(-3.41550 + 5.91583i) q^{25} +62.3892i q^{29} +(48.8957 + 28.2300i) q^{31} +(32.1337 + 210.203i) q^{35} +(146.068 + 252.997i) q^{37} -54.2417 q^{41} +438.235 q^{43} +(-128.386 - 222.371i) q^{47} +(252.412 + 232.243i) q^{49} +(-515.128 - 297.409i) q^{53} -657.873i q^{55} +(238.156 - 412.499i) q^{59} +(-548.703 + 316.794i) q^{61} +(91.5720 - 52.8691i) q^{65} +(308.827 - 534.904i) q^{67} -396.155i q^{71} +(39.8998 + 23.0361i) q^{73} +(-663.359 - 828.259i) q^{77} +(-344.924 - 597.425i) q^{79} +1288.72 q^{83} +334.100 q^{85} +(-595.784 - 1031.93i) q^{89} +(61.9787 - 158.897i) q^{91} +(-374.376 - 216.146i) q^{95} -946.768i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 24q^{7} + O(q^{10}) \) \( 48q + 24q^{7} - 540q^{19} - 924q^{25} - 648q^{31} - 132q^{37} + 792q^{43} + 672q^{49} + 12q^{67} + 2412q^{73} - 1680q^{79} + 480q^{85} - 1404q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)

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
\(5\) −5.74088 9.94350i −0.513480 0.889374i −0.999878 0.0156363i \(-0.995023\pi\)
0.486397 0.873738i \(-0.338311\pi\)
\(6\) 0 0
\(7\) −17.2542 6.73007i −0.931637 0.363390i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 49.6208 + 28.6486i 1.36011 + 0.785261i 0.989639 0.143581i \(-0.0458619\pi\)
0.370474 + 0.928843i \(0.379195\pi\)
\(12\) 0 0
\(13\) 9.20923i 0.196475i 0.995163 + 0.0982377i \(0.0313205\pi\)
−0.995163 + 0.0982377i \(0.968679\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −14.5492 + 25.1999i −0.207570 + 0.359522i −0.950949 0.309349i \(-0.899889\pi\)
0.743378 + 0.668871i \(0.233222\pi\)
\(18\) 0 0
\(19\) 32.6061 18.8252i 0.393703 0.227305i −0.290060 0.957008i \(-0.593675\pi\)
0.683763 + 0.729704i \(0.260342\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −7.27174 + 4.19834i −0.0659245 + 0.0380615i −0.532600 0.846367i \(-0.678785\pi\)
0.466675 + 0.884429i \(0.345452\pi\)
\(24\) 0 0
\(25\) −3.41550 + 5.91583i −0.0273240 + 0.0473266i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 62.3892i 0.399496i 0.979847 + 0.199748i \(0.0640124\pi\)
−0.979847 + 0.199748i \(0.935988\pi\)
\(30\) 0 0
\(31\) 48.8957 + 28.2300i 0.283288 + 0.163556i 0.634911 0.772585i \(-0.281037\pi\)
−0.351623 + 0.936142i \(0.614370\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 32.1337 + 210.203i 0.155188 + 1.01517i
\(36\) 0 0
\(37\) 146.068 + 252.997i 0.649012 + 1.12412i 0.983359 + 0.181672i \(0.0581509\pi\)
−0.334347 + 0.942450i \(0.608516\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −54.2417 −0.206613 −0.103306 0.994650i \(-0.532942\pi\)
−0.103306 + 0.994650i \(0.532942\pi\)
\(42\) 0 0
\(43\) 438.235 1.55419 0.777096 0.629382i \(-0.216692\pi\)
0.777096 + 0.629382i \(0.216692\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −128.386 222.371i −0.398446 0.690129i 0.595088 0.803661i \(-0.297117\pi\)
−0.993534 + 0.113531i \(0.963784\pi\)
\(48\) 0 0
\(49\) 252.412 + 232.243i 0.735896 + 0.677095i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −515.128 297.409i −1.33506 0.770799i −0.348992 0.937126i \(-0.613476\pi\)
−0.986071 + 0.166327i \(0.946809\pi\)
\(54\) 0 0
\(55\) 657.873i 1.61287i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 238.156 412.499i 0.525513 0.910216i −0.474045 0.880501i \(-0.657207\pi\)
0.999558 0.0297153i \(-0.00946005\pi\)
\(60\) 0 0
\(61\) −548.703 + 316.794i −1.15171 + 0.664939i −0.949303 0.314363i \(-0.898209\pi\)
−0.202406 + 0.979302i \(0.564876\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 91.5720 52.8691i 0.174740 0.100886i
\(66\) 0 0
\(67\) 308.827 534.904i 0.563123 0.975357i −0.434099 0.900865i \(-0.642933\pi\)
0.997222 0.0744918i \(-0.0237335\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 396.155i 0.662183i −0.943599 0.331092i \(-0.892583\pi\)
0.943599 0.331092i \(-0.107417\pi\)
\(72\) 0 0
\(73\) 39.8998 + 23.0361i 0.0639714 + 0.0369339i 0.531645 0.846968i \(-0.321574\pi\)
−0.467673 + 0.883901i \(0.654908\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −663.359 828.259i −0.981776 1.22583i
\(78\) 0 0
\(79\) −344.924 597.425i −0.491227 0.850831i 0.508722 0.860931i \(-0.330118\pi\)
−0.999949 + 0.0101004i \(0.996785\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1288.72 1.70428 0.852138 0.523317i \(-0.175306\pi\)
0.852138 + 0.523317i \(0.175306\pi\)
\(84\) 0 0
\(85\) 334.100 0.426333
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −595.784 1031.93i −0.709584 1.22904i −0.965012 0.262207i \(-0.915550\pi\)
0.255428 0.966828i \(-0.417784\pi\)
\(90\) 0 0
\(91\) 61.9787 158.897i 0.0713971 0.183044i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −374.376 216.146i −0.404318 0.233433i
\(96\) 0 0
\(97\) 946.768i 0.991028i −0.868600 0.495514i \(-0.834980\pi\)
0.868600 0.495514i \(-0.165020\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 636.416 1102.31i 0.626988 1.08597i −0.361165 0.932502i \(-0.617621\pi\)
0.988153 0.153473i \(-0.0490458\pi\)
\(102\) 0 0
\(103\) −338.095 + 195.199i −0.323431 + 0.186733i −0.652921 0.757426i \(-0.726457\pi\)
0.329490 + 0.944159i \(0.393123\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −67.4130 + 38.9209i −0.0609071 + 0.0351648i −0.530144 0.847907i \(-0.677862\pi\)
0.469237 + 0.883072i \(0.344529\pi\)
\(108\) 0 0
\(109\) −341.576 + 591.626i −0.300156 + 0.519886i −0.976171 0.217002i \(-0.930372\pi\)
0.676015 + 0.736888i \(0.263705\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 286.715i 0.238689i 0.992853 + 0.119345i \(0.0380793\pi\)
−0.992853 + 0.119345i \(0.961921\pi\)
\(114\) 0 0
\(115\) 83.4924 + 48.2044i 0.0677018 + 0.0390877i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 420.631 336.886i 0.324027 0.259515i
\(120\) 0 0
\(121\) 975.984 + 1690.45i 0.733271 + 1.27006i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1356.79 −0.970839
\(126\) 0 0
\(127\) 2655.85 1.85566 0.927830 0.373002i \(-0.121672\pi\)
0.927830 + 0.373002i \(0.121672\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1198.22 2075.38i −0.799151 1.38417i −0.920169 0.391521i \(-0.871949\pi\)
0.121018 0.992650i \(-0.461384\pi\)
\(132\) 0 0
\(133\) −689.286 + 105.371i −0.449389 + 0.0686978i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1553.97 + 897.184i 0.969084 + 0.559501i 0.898957 0.438037i \(-0.144326\pi\)
0.0701271 + 0.997538i \(0.477660\pi\)
\(138\) 0 0
\(139\) 101.014i 0.0616396i 0.999525 + 0.0308198i \(0.00981180\pi\)
−0.999525 + 0.0308198i \(0.990188\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −263.831 + 456.969i −0.154285 + 0.267229i
\(144\) 0 0
\(145\) 620.367 358.169i 0.355301 0.205133i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −744.159 + 429.640i −0.409154 + 0.236225i −0.690426 0.723403i \(-0.742577\pi\)
0.281272 + 0.959628i \(0.409244\pi\)
\(150\) 0 0
\(151\) 807.459 1398.56i 0.435166 0.753730i −0.562143 0.827040i \(-0.690023\pi\)
0.997309 + 0.0733102i \(0.0233563\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 648.260i 0.335932i
\(156\) 0 0
\(157\) 1622.84 + 936.947i 0.824948 + 0.476284i 0.852120 0.523347i \(-0.175317\pi\)
−0.0271720 + 0.999631i \(0.508650\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 153.723 23.4996i 0.0752488 0.0115033i
\(162\) 0 0
\(163\) 664.037 + 1150.15i 0.319088 + 0.552677i 0.980298 0.197524i \(-0.0632900\pi\)
−0.661210 + 0.750201i \(0.729957\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −595.681 −0.276019 −0.138010 0.990431i \(-0.544070\pi\)
−0.138010 + 0.990431i \(0.544070\pi\)
\(168\) 0 0
\(169\) 2112.19 0.961397
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1119.44 1938.93i −0.491962 0.852103i 0.507995 0.861360i \(-0.330387\pi\)
−0.999957 + 0.00925667i \(0.997053\pi\)
\(174\) 0 0
\(175\) 98.7456 79.0861i 0.0426541 0.0341620i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1660.97 958.960i −0.693556 0.400425i 0.111387 0.993777i \(-0.464471\pi\)
−0.804943 + 0.593352i \(0.797804\pi\)
\(180\) 0 0
\(181\) 4162.64i 1.70943i −0.519099 0.854714i \(-0.673732\pi\)
0.519099 0.854714i \(-0.326268\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1677.12 2904.86i 0.666510 1.15443i
\(186\) 0 0
\(187\) −1443.88 + 833.626i −0.564637 + 0.325994i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −267.384 + 154.374i −0.101294 + 0.0584823i −0.549791 0.835302i \(-0.685293\pi\)
0.448497 + 0.893784i \(0.351959\pi\)
\(192\) 0 0
\(193\) 2385.32 4131.49i 0.889632 1.54089i 0.0493214 0.998783i \(-0.484294\pi\)
0.840311 0.542105i \(-0.182373\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1115.98i 0.403607i −0.979426 0.201804i \(-0.935320\pi\)
0.979426 0.201804i \(-0.0646802\pi\)
\(198\) 0 0
\(199\) 2713.57 + 1566.68i 0.966634 + 0.558086i 0.898208 0.439570i \(-0.144869\pi\)
0.0684255 + 0.997656i \(0.478202\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 419.884 1076.47i 0.145173 0.372185i
\(204\) 0 0
\(205\) 311.395 + 539.352i 0.106092 + 0.183756i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2157.26 0.713974
\(210\) 0 0
\(211\) 513.831 0.167647 0.0838237 0.996481i \(-0.473287\pi\)
0.0838237 + 0.996481i \(0.473287\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2515.86 4357.59i −0.798047 1.38226i
\(216\) 0 0
\(217\) −653.665 816.156i −0.204487 0.255319i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −232.072 133.987i −0.0706372 0.0407824i
\(222\) 0 0
\(223\) 4529.37i 1.36013i 0.733151 + 0.680066i \(0.238049\pi\)
−0.733151 + 0.680066i \(0.761951\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −146.074 + 253.008i −0.0427105 + 0.0739767i −0.886590 0.462555i \(-0.846933\pi\)
0.843880 + 0.536532i \(0.180266\pi\)
\(228\) 0 0
\(229\) 5530.36 3192.96i 1.59588 0.921382i 0.603611 0.797279i \(-0.293728\pi\)
0.992269 0.124103i \(-0.0396052\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1468.47 + 847.822i −0.412887 + 0.238381i −0.692030 0.721869i \(-0.743283\pi\)
0.279142 + 0.960250i \(0.409950\pi\)
\(234\) 0 0
\(235\) −1474.10 + 2553.21i −0.409189 + 0.708736i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 962.214i 0.260420i −0.991486 0.130210i \(-0.958435\pi\)
0.991486 0.130210i \(-0.0415652\pi\)
\(240\) 0 0
\(241\) −4233.33 2444.11i −1.13150 0.653274i −0.187191 0.982324i \(-0.559938\pi\)
−0.944313 + 0.329049i \(0.893272\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 860.243 3843.15i 0.224322 1.00216i
\(246\) 0 0
\(247\) 173.365 + 300.277i 0.0446598 + 0.0773530i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −7473.53 −1.87938 −0.939691 0.342025i \(-0.888887\pi\)
−0.939691 + 0.342025i \(0.888887\pi\)
\(252\) 0 0
\(253\) −481.106 −0.119553
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2720.11 + 4711.37i 0.660217 + 1.14353i 0.980558 + 0.196227i \(0.0628691\pi\)
−0.320341 + 0.947302i \(0.603798\pi\)
\(258\) 0 0
\(259\) −817.593 5348.31i −0.196150 1.28312i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 4868.13 + 2810.62i 1.14138 + 0.658974i 0.946771 0.321908i \(-0.104324\pi\)
0.194605 + 0.980882i \(0.437658\pi\)
\(264\) 0 0
\(265\) 6829.57i 1.58316i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2259.81 + 3914.11i −0.512206 + 0.887166i 0.487694 + 0.873014i \(0.337838\pi\)
−0.999900 + 0.0141516i \(0.995495\pi\)
\(270\) 0 0
\(271\) −4739.86 + 2736.56i −1.06246 + 0.613410i −0.926111 0.377252i \(-0.876869\pi\)
−0.136346 + 0.990661i \(0.543536\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −338.960 + 195.699i −0.0743275 + 0.0429130i
\(276\) 0 0
\(277\) 2082.99 3607.85i 0.451823 0.782580i −0.546677 0.837344i \(-0.684107\pi\)
0.998499 + 0.0547639i \(0.0174406\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5979.00i 1.26931i −0.772794 0.634657i \(-0.781142\pi\)
0.772794 0.634657i \(-0.218858\pi\)
\(282\) 0 0
\(283\) 6220.79 + 3591.57i 1.30667 + 0.754406i 0.981539 0.191263i \(-0.0612584\pi\)
0.325130 + 0.945669i \(0.394592\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 935.895 + 365.050i 0.192488 + 0.0750810i
\(288\) 0 0
\(289\) 2033.14 + 3521.51i 0.413829 + 0.716773i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 3741.42 0.745994 0.372997 0.927832i \(-0.378330\pi\)
0.372997 + 0.927832i \(0.378330\pi\)
\(294\) 0 0
\(295\) −5468.91 −1.07936
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −38.6635 66.9671i −0.00747815 0.0129525i
\(300\) 0 0
\(301\) −7561.38 2949.35i −1.44794 0.564777i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 6300.08 + 3637.35i 1.18276 + 0.682866i
\(306\) 0 0
\(307\) 4568.44i 0.849299i −0.905358 0.424649i \(-0.860397\pi\)
0.905358 0.424649i \(-0.139603\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1633.29 2828.95i 0.297799 0.515803i −0.677833 0.735216i \(-0.737081\pi\)
0.975632 + 0.219413i \(0.0704141\pi\)
\(312\) 0 0
\(313\) −3415.84 + 1972.13i −0.616852 + 0.356139i −0.775642 0.631173i \(-0.782574\pi\)
0.158791 + 0.987312i \(0.449241\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −5604.14 + 3235.55i −0.992934 + 0.573271i −0.906150 0.422956i \(-0.860992\pi\)
−0.0867840 + 0.996227i \(0.527659\pi\)
\(318\) 0 0
\(319\) −1787.36 + 3095.80i −0.313709 + 0.543360i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1095.56i 0.188727i
\(324\) 0 0
\(325\) −54.4802 31.4542i −0.00929851 0.00536850i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 718.619 + 4700.86i 0.120422 + 0.787742i
\(330\) 0 0
\(331\) −902.540 1563.24i −0.149873 0.259588i 0.781307 0.624147i \(-0.214553\pi\)
−0.931180 + 0.364559i \(0.881220\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −7091.76 −1.15661
\(336\) 0 0
\(337\) −6868.31 −1.11021 −0.555105 0.831780i \(-0.687322\pi\)
−0.555105 + 0.831780i \(0.687322\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1617.50 + 2801.59i 0.256869 + 0.444910i
\(342\) 0 0
\(343\) −2792.15 5705.92i −0.439539 0.898223i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4458.72 + 2574.24i 0.689788 + 0.398249i 0.803533 0.595261i \(-0.202951\pi\)
−0.113745 + 0.993510i \(0.536285\pi\)
\(348\) 0 0
\(349\) 9931.72i 1.52330i −0.647987 0.761652i \(-0.724389\pi\)
0.647987 0.761652i \(-0.275611\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 4125.94 7146.35i 0.622102 1.07751i −0.366992 0.930224i \(-0.619612\pi\)
0.989094 0.147288i \(-0.0470543\pi\)
\(354\) 0 0
\(355\) −3939.17 + 2274.28i −0.588928 + 0.340018i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 7280.23 4203.24i 1.07029 0.617935i 0.142033 0.989862i \(-0.454636\pi\)
0.928262 + 0.371927i \(0.121303\pi\)
\(360\) 0 0
\(361\) −2720.73 + 4712.44i −0.396665 + 0.687044i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 528.991i 0.0758593i
\(366\) 0 0
\(367\) 4673.36 + 2698.17i 0.664707 + 0.383769i 0.794068 0.607829i \(-0.207959\pi\)
−0.129361 + 0.991598i \(0.541293\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 6886.52 + 8598.40i 0.963694 + 1.20325i
\(372\) 0 0
\(373\) 3007.56 + 5209.25i 0.417495 + 0.723123i 0.995687 0.0927779i \(-0.0295747\pi\)
−0.578191 + 0.815901i \(0.696241\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −574.556 −0.0784911
\(378\) 0 0
\(379\) −1456.39 −0.197388 −0.0986939 0.995118i \(-0.531466\pi\)
−0.0986939 + 0.995118i \(0.531466\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 806.803 + 1397.42i 0.107639 + 0.186436i 0.914813 0.403877i \(-0.132338\pi\)
−0.807174 + 0.590313i \(0.799004\pi\)
\(384\) 0 0
\(385\) −4427.53 + 11351.0i −0.586098 + 1.50261i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −7423.22 4285.80i −0.967537 0.558608i −0.0690527 0.997613i \(-0.521998\pi\)
−0.898485 + 0.439005i \(0.855331\pi\)
\(390\) 0 0
\(391\) 244.329i 0.0316017i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −3960.33 + 6859.50i −0.504471 + 0.873770i
\(396\) 0 0
\(397\) 11677.0 6741.72i 1.47620 0.852286i 0.476562 0.879141i \(-0.341883\pi\)
0.999639 + 0.0268551i \(0.00854927\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −10042.0 + 5797.73i −1.25055 + 0.722007i −0.971219 0.238187i \(-0.923447\pi\)
−0.279333 + 0.960194i \(0.590113\pi\)
\(402\) 0 0
\(403\) −259.976 + 450.292i −0.0321348 + 0.0556591i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 16738.6i 2.03858i
\(408\) 0 0
\(409\) −2081.47 1201.74i −0.251643 0.145286i 0.368873 0.929480i \(-0.379744\pi\)
−0.620517 + 0.784193i \(0.713077\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −6885.33 + 5514.51i −0.820351 + 0.657025i
\(414\) 0 0
\(415\) −7398.37 12814.3i −0.875112 1.51574i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 6175.24 0.720001 0.360001 0.932952i \(-0.382777\pi\)
0.360001 + 0.932952i \(0.382777\pi\)
\(420\) 0 0
\(421\) 3082.19 0.356809 0.178405 0.983957i \(-0.442906\pi\)
0.178405 + 0.983957i \(0.442906\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −99.3855 172.141i −0.0113433 0.0196472i
\(426\) 0 0
\(427\) 11599.5 1773.20i 1.31461 0.200963i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1931.19 + 1114.97i 0.215829 + 0.124609i 0.604017 0.796971i \(-0.293566\pi\)
−0.388189 + 0.921580i \(0.626899\pi\)
\(432\) 0 0
\(433\) 9238.69i 1.02536i 0.858578 + 0.512682i \(0.171348\pi\)
−0.858578 + 0.512682i \(0.828652\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −158.069 + 273.783i −0.0173031 + 0.0299699i
\(438\) 0 0
\(439\) 2806.74 1620.47i 0.305145 0.176175i −0.339607 0.940567i \(-0.610294\pi\)
0.644752 + 0.764392i \(0.276961\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6001.79 3465.14i 0.643688 0.371633i −0.142346 0.989817i \(-0.545465\pi\)
0.786034 + 0.618184i \(0.212131\pi\)
\(444\) 0 0
\(445\) −6840.65 + 11848.4i −0.728715 + 1.26217i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 6773.64i 0.711955i 0.934495 + 0.355978i \(0.115852\pi\)
−0.934495 + 0.355978i \(0.884148\pi\)
\(450\) 0 0
\(451\) −2691.52 1553.95i −0.281017 0.162245i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1935.81 + 295.926i −0.199455 + 0.0304906i
\(456\) 0 0
\(457\) 6687.33 + 11582.8i 0.684508 + 1.18560i 0.973591 + 0.228299i \(0.0733164\pi\)
−0.289083 + 0.957304i \(0.593350\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −13126.6 −1.32618 −0.663090 0.748540i \(-0.730755\pi\)
−0.663090 + 0.748540i \(0.730755\pi\)
\(462\) 0 0
\(463\) 12805.7 1.28538 0.642690 0.766126i \(-0.277818\pi\)
0.642690 + 0.766126i \(0.277818\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −665.256 1152.26i −0.0659194 0.114176i 0.831182 0.556000i \(-0.187665\pi\)
−0.897101 + 0.441825i \(0.854331\pi\)
\(468\) 0 0
\(469\) −8928.49 + 7150.89i −0.879061 + 0.704046i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 21745.6 + 12554.8i 2.11388 + 1.22045i
\(474\) 0 0
\(475\) 257.190i 0.0248435i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −5608.11 + 9713.54i −0.534950 + 0.926561i 0.464215 + 0.885722i \(0.346336\pi\)
−0.999166 + 0.0408390i \(0.986997\pi\)
\(480\) 0 0
\(481\) −2329.91 + 1345.17i −0.220862 + 0.127515i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −9414.19 + 5435.28i −0.881394 + 0.508873i
\(486\) 0 0
\(487\) 1480.99 2565.15i 0.137803 0.238682i −0.788862 0.614571i \(-0.789329\pi\)
0.926665 + 0.375889i \(0.122663\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 4452.75i 0.409266i −0.978839 0.204633i \(-0.934400\pi\)
0.978839 0.204633i \(-0.0656001\pi\)
\(492\) 0 0
\(493\) −1572.20 907.711i −0.143628 0.0829234i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2666.15 + 6835.33i −0.240630 + 0.616914i
\(498\) 0 0
\(499\) −6419.64 11119.1i −0.575917 0.997518i −0.995941 0.0900049i \(-0.971312\pi\)
0.420024 0.907513i \(-0.362022\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 3169.30 0.280939 0.140469 0.990085i \(-0.455139\pi\)
0.140469 + 0.990085i \(0.455139\pi\)
\(504\) 0 0
\(505\) −14614.4 −1.28778
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 5393.25 + 9341.38i 0.469649 + 0.813456i 0.999398 0.0346984i \(-0.0110471\pi\)
−0.529749 + 0.848155i \(0.677714\pi\)
\(510\) 0 0
\(511\) −533.402 665.997i −0.0461768 0.0576556i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 3881.92 + 2241.23i 0.332151 + 0.191768i
\(516\) 0 0
\(517\) 14712.3i 1.25154i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 8319.38 14409.6i 0.699575 1.21170i −0.269039 0.963129i \(-0.586706\pi\)
0.968614 0.248570i \(-0.0799606\pi\)
\(522\) 0 0
\(523\) −17007.8 + 9819.46i −1.42199 + 0.820984i −0.996469 0.0839657i \(-0.973241\pi\)
−0.425518 + 0.904950i \(0.639908\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1422.78 + 821.445i −0.117604 + 0.0678988i
\(528\) 0 0
\(529\) −6048.25 + 10475.9i −0.497103 + 0.861007i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 499.524i 0.0405943i
\(534\) 0 0
\(535\) 774.021 + 446.881i 0.0625492 + 0.0361128i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 5871.46 + 18755.4i 0.469205 + 1.49880i
\(540\) 0 0
\(541\) −8795.99 15235.1i −0.699019 1.21074i −0.968807 0.247816i \(-0.920287\pi\)
0.269788 0.962920i \(-0.413046\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 7843.78 0.616497
\(546\) 0 0
\(547\) −9961.21 −0.778630 −0.389315 0.921105i \(-0.627288\pi\)
−0.389315 + 0.921105i \(0.627288\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1174.49 + 2034.27i 0.0908073 + 0.157283i
\(552\) 0 0
\(553\) 1930.66 + 12629.4i 0.148463 + 0.971172i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1255.36 724.783i −0.0954961 0.0551347i 0.451491 0.892275i \(-0.350892\pi\)
−0.546988 + 0.837141i \(0.684225\pi\)
\(558\) 0 0
\(559\) 4035.81i 0.305360i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 6356.42 11009.6i 0.475828 0.824159i −0.523788 0.851848i \(-0.675482\pi\)
0.999617 + 0.0276898i \(0.00881507\pi\)
\(564\) 0 0
\(565\) 2850.95 1646.00i 0.212284 0.122562i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 11895.7 6867.98i 0.876438 0.506012i 0.00695552 0.999976i \(-0.497786\pi\)
0.869482 + 0.493964i \(0.164453\pi\)
\(570\) 0 0
\(571\) −11893.2 + 20599.7i −0.871656 + 1.50975i −0.0113732 + 0.999935i \(0.503620\pi\)
−0.860283 + 0.509817i \(0.829713\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 57.3578i 0.00415998i
\(576\) 0 0
\(577\) −16470.3 9509.14i −1.18833 0.686085i −0.230406 0.973095i \(-0.574005\pi\)
−0.957928 + 0.287010i \(0.907339\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −22235.7 8673.14i −1.58777 0.619316i
\(582\) 0 0
\(583\) −17040.7 29515.4i −1.21056 2.09675i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 2636.09 0.185354 0.0926772 0.995696i \(-0.470458\pi\)
0.0926772 + 0.995696i \(0.470458\pi\)
\(588\) 0 0
\(589\) 2125.73 0.148709
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 8294.23 + 14366.0i 0.574373 + 0.994843i 0.996109 + 0.0881246i \(0.0280874\pi\)
−0.421737 + 0.906718i \(0.638579\pi\)
\(594\) 0 0
\(595\) −5764.62 2248.52i −0.397187 0.154925i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 5022.26 + 2899.61i 0.342578 + 0.197787i 0.661411 0.750023i \(-0.269958\pi\)
−0.318834 + 0.947811i \(0.603291\pi\)
\(600\) 0 0
\(601\) 19240.0i 1.30585i −0.757422 0.652926i \(-0.773541\pi\)
0.757422 0.652926i \(-0.226459\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 11206.0 19409.4i 0.753041 1.30430i
\(606\) 0 0
\(607\) −10321.5 + 5959.14i −0.690178 + 0.398474i −0.803679 0.595064i \(-0.797127\pi\)
0.113501 + 0.993538i \(0.463793\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 2047.86 1182.33i 0.135593 0.0782849i
\(612\) 0 0
\(613\) −2031.64 + 3518.90i −0.133862 + 0.231855i −0.925162 0.379573i \(-0.876071\pi\)
0.791300 + 0.611428i \(0.209404\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 15705.9i 1.02479i 0.858750 + 0.512395i \(0.171242\pi\)
−0.858750 + 0.512395i \(0.828758\pi\)
\(618\) 0 0
\(619\) 20914.5 + 12075.0i 1.35803 + 0.784061i 0.989359 0.145497i \(-0.0464781\pi\)
0.368675 + 0.929558i \(0.379811\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 3334.81 + 21814.7i 0.214456 + 1.40287i
\(624\) 0 0
\(625\) 8216.11 + 14230.7i 0.525831 + 0.910766i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −8500.68 −0.538862
\(630\) 0 0
\(631\) 23965.9 1.51199 0.755996 0.654576i \(-0.227153\pi\)
0.755996 + 0.654576i \(0.227153\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −15247.0 26408.5i −0.952845 1.65038i
\(636\) 0 0
\(637\) −2138.78 + 2324.52i −0.133032 + 0.144585i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 8093.10 + 4672.55i 0.498687 + 0.287917i 0.728171 0.685395i \(-0.240371\pi\)
−0.229484 + 0.973312i \(0.573704\pi\)
\(642\) 0 0
\(643\) 9283.22i 0.569354i −0.958623 0.284677i \(-0.908114\pi\)
0.958623 0.284677i \(-0.0918864\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 11327.2 19619.2i 0.688280 1.19214i −0.284114 0.958791i \(-0.591699\pi\)
0.972394 0.233345i \(-0.0749673\pi\)
\(648\) 0 0
\(649\) 23635.0 13645.7i 1.42951 0.825331i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −11545.5 + 6665.79i −0.691899 + 0.399468i −0.804323 0.594192i \(-0.797472\pi\)
0.112424 + 0.993660i \(0.464138\pi\)
\(654\) 0 0
\(655\) −13757.7 + 23829.0i −0.820697 + 1.42149i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 5190.48i 0.306817i 0.988163 + 0.153409i \(0.0490250\pi\)
−0.988163 + 0.153409i \(0.950975\pi\)
\(660\) 0 0
\(661\) 2286.98 + 1320.39i 0.134574 + 0.0776963i 0.565776 0.824559i \(-0.308577\pi\)
−0.431202 + 0.902256i \(0.641910\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 5004.87 + 6249.00i 0.291850 + 0.364400i
\(666\) 0 0
\(667\) −261.931 453.678i −0.0152054 0.0263366i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −36302.8 −2.08860
\(672\) 0 0
\(673\) 6119.56 0.350507 0.175254 0.984523i \(-0.443925\pi\)
0.175254 + 0.984523i \(0.443925\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −10363.3 17949.7i −0.588320 1.01900i −0.994453 0.105186i \(-0.966456\pi\)
0.406133 0.913814i \(-0.366877\pi\)
\(678\) 0 0
\(679\) −6371.81 + 16335.7i −0.360129 + 0.923278i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −6056.22 3496.56i −0.339290 0.195889i 0.320668 0.947192i \(-0.396093\pi\)
−0.659958 + 0.751303i \(0.729426\pi\)
\(684\) 0 0
\(685\) 20602.5i 1.14917i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2738.91 4743.93i 0.151443 0.262307i
\(690\) 0 0
\(691\) 18475.9 10667.1i 1.01716 0.587256i 0.103878 0.994590i \(-0.466875\pi\)
0.913279 + 0.407334i \(0.133541\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1004.43 579.910i 0.0548207 0.0316507i
\(696\) 0 0
\(697\) 789.171 1366.88i 0.0428867 0.0742819i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 7995.09i 0.430771i −0.976529 0.215385i \(-0.930899\pi\)
0.976529 0.215385i \(-0.0691007\pi\)
\(702\) 0 0
\(703\) 9525.43 + 5499.51i 0.511036 + 0.295047i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −18399.4 + 14736.2i −0.978757 + 0.783894i
\(708\) 0 0
\(709\) −1680.51 2910.73i −0.0890167 0.154181i 0.818079 0.575106i \(-0.195039\pi\)
−0.907096 + 0.420924i \(0.861706\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −474.076 −0.0249008
\(714\) 0 0
\(715\) 6058.50 0.316888
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −11653.3 20184.1i −0.604444 1.04693i −0.992139 0.125139i \(-0.960062\pi\)
0.387696 0.921787i \(-0.373271\pi\)
\(720\) 0 0
\(721\) 7147.24 1092.60i 0.369178 0.0564360i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −369.084 213.091i −0.0189068 0.0109158i
\(726\) 0 0
\(727\) 27744.2i 1.41537i 0.706526 + 0.707687i \(0.250261\pi\)
−0.706526 + 0.707687i \(0.749739\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −6375.96 + 11043.5i −0.322604 + 0.558766i
\(732\) 0 0
\(733\) 30453.8 17582.5i 1.53457 0.885983i 0.535425 0.844583i \(-0.320151\pi\)
0.999143 0.0414005i \(-0.0131819\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 30648.5 17694.9i 1.53182 0.884397i
\(738\) 0 0
\(739\) −4158.66 + 7203.01i −0.207008 + 0.358548i −0.950771 0.309896i \(-0.899706\pi\)
0.743763 + 0.668444i \(0.233039\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 34257.4i 1.69150i −0.533582 0.845748i \(-0.679154\pi\)
0.533582 0.845748i \(-0.320846\pi\)
\(744\) 0 0
\(745\) 8544.26 + 4933.03i 0.420185 + 0.242594i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1425.10 217.854i 0.0695219 0.0106278i
\(750\) 0 0
\(751\) −3760.57 6513.49i −0.182723 0.316486i 0.760084 0.649825i \(-0.225158\pi\)
−0.942807 + 0.333339i \(0.891824\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −18542.1 −0.893797
\(756\) 0 0
\(757\) −13575.7 −0.651806 −0.325903 0.945403i \(-0.605668\pi\)
−0.325903 + 0.945403i \(0.605668\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 20338.8 + 35227.8i 0.968830 + 1.67806i 0.698953 + 0.715167i \(0.253650\pi\)
0.269876 + 0.962895i \(0.413017\pi\)
\(762\) 0 0
\(763\) 9875.29 7909.19i 0.468558 0.375271i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3798.79 + 2193.23i 0.178835 + 0.103250i
\(768\) 0 0
\(769\) 5230.17i 0.245260i −0.992452 0.122630i \(-0.960867\pi\)
0.992452 0.122630i \(-0.0391328\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −38.3831 + 66.4815i −0.00178596 + 0.00309337i −0.866917 0.498453i \(-0.833902\pi\)
0.865131 + 0.501546i \(0.167235\pi\)
\(774\) 0 0
\(775\) −334.007 + 192.839i −0.0154811 + 0.00893804i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1768.61 + 1021.11i −0.0813441 + 0.0469641i
\(780\) 0 0
\(781\) 11349.3 19657.6i 0.519987 0.900644i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 21515.6i 0.978249i
\(786\) 0 0
\(787\) 26841.7 + 15497.0i 1.21576 + 0.701919i 0.964008 0.265873i \(-0.0856603\pi\)
0.251751 + 0.967792i \(0.418994\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1929.61 4947.03i 0.0867372 0.222372i
\(792\) 0 0
\(793\) −2917.43 5053.13i −0.130644 0.226282i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −12755.8 −0.566920 −0.283460 0.958984i \(-0.591482\pi\)
−0.283460 + 0.958984i \(0.591482\pi\)
\(798\) 0 0
\(799\) 7471.62 0.330822
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1319.91 + 2286.14i