Properties

Label 1400.2.x.c.993.10
Level $1400$
Weight $2$
Character 1400.993
Analytic conductor $11.179$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.x (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1790562830\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 993.10
Character \(\chi\) \(=\) 1400.993
Dual form 1400.2.x.c.657.10

$q$-expansion

\(f(q)\) \(=\) \(q+(0.409160 - 0.409160i) q^{3} +(-0.738062 - 2.54072i) q^{7} +2.66518i q^{9} +O(q^{10})\) \(q+(0.409160 - 0.409160i) q^{3} +(-0.738062 - 2.54072i) q^{7} +2.66518i q^{9} -3.54935 q^{11} +(2.95189 - 2.95189i) q^{13} +(5.59675 + 5.59675i) q^{17} +3.59597 q^{19} +(-1.34155 - 0.737576i) q^{21} +(0.0472877 + 0.0472877i) q^{23} +(2.31796 + 2.31796i) q^{27} -5.34827i q^{29} -10.3924i q^{31} +(-1.45225 + 1.45225i) q^{33} +(7.80067 - 7.80067i) q^{37} -2.41560i q^{39} -5.63913i q^{41} +(-6.93871 - 6.93871i) q^{43} +(3.44333 + 3.44333i) q^{47} +(-5.91053 + 3.75042i) q^{49} +4.57993 q^{51} +(0.646830 + 0.646830i) q^{53} +(1.47133 - 1.47133i) q^{57} +9.22732 q^{59} -3.51832i q^{61} +(6.77147 - 1.96707i) q^{63} +(-1.70777 + 1.70777i) q^{67} +0.0386965 q^{69} -8.54487 q^{71} +(2.43511 - 2.43511i) q^{73} +(2.61964 + 9.01790i) q^{77} +5.72713i q^{79} -6.09869 q^{81} +(2.04580 - 2.04580i) q^{83} +(-2.18830 - 2.18830i) q^{87} -8.18639 q^{89} +(-9.67862 - 5.32126i) q^{91} +(-4.25215 - 4.25215i) q^{93} +(6.23068 + 6.23068i) q^{97} -9.45963i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q - 16q^{11} - 40q^{21} + 32q^{51} + 128q^{71} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).

\(n\) \(351\) \(701\) \(801\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) 0.409160 0.409160i 0.236229 0.236229i −0.579058 0.815287i \(-0.696579\pi\)
0.815287 + 0.579058i \(0.196579\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −0.738062 2.54072i −0.278961 0.960302i
\(8\) 0 0
\(9\) 2.66518i 0.888392i
\(10\) 0 0
\(11\) −3.54935 −1.07017 −0.535084 0.844799i \(-0.679720\pi\)
−0.535084 + 0.844799i \(0.679720\pi\)
\(12\) 0 0
\(13\) 2.95189 2.95189i 0.818708 0.818708i −0.167213 0.985921i \(-0.553477\pi\)
0.985921 + 0.167213i \(0.0534766\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.59675 + 5.59675i 1.35741 + 1.35741i 0.877097 + 0.480314i \(0.159477\pi\)
0.480314 + 0.877097i \(0.340523\pi\)
\(18\) 0 0
\(19\) 3.59597 0.824972 0.412486 0.910964i \(-0.364661\pi\)
0.412486 + 0.910964i \(0.364661\pi\)
\(20\) 0 0
\(21\) −1.34155 0.737576i −0.292750 0.160952i
\(22\) 0 0
\(23\) 0.0472877 + 0.0472877i 0.00986016 + 0.00986016i 0.712020 0.702160i \(-0.247781\pi\)
−0.702160 + 0.712020i \(0.747781\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 2.31796 + 2.31796i 0.446092 + 0.446092i
\(28\) 0 0
\(29\) 5.34827i 0.993149i −0.867994 0.496574i \(-0.834591\pi\)
0.867994 0.496574i \(-0.165409\pi\)
\(30\) 0 0
\(31\) 10.3924i 1.86653i −0.359192 0.933264i \(-0.616948\pi\)
0.359192 0.933264i \(-0.383052\pi\)
\(32\) 0 0
\(33\) −1.45225 + 1.45225i −0.252804 + 0.252804i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 7.80067 7.80067i 1.28242 1.28242i 0.343137 0.939285i \(-0.388510\pi\)
0.939285 0.343137i \(-0.111490\pi\)
\(38\) 0 0
\(39\) 2.41560i 0.386805i
\(40\) 0 0
\(41\) 5.63913i 0.880685i −0.897830 0.440342i \(-0.854857\pi\)
0.897830 0.440342i \(-0.145143\pi\)
\(42\) 0 0
\(43\) −6.93871 6.93871i −1.05814 1.05814i −0.998202 0.0599420i \(-0.980908\pi\)
−0.0599420 0.998202i \(-0.519092\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.44333 + 3.44333i 0.502261 + 0.502261i 0.912140 0.409879i \(-0.134429\pi\)
−0.409879 + 0.912140i \(0.634429\pi\)
\(48\) 0 0
\(49\) −5.91053 + 3.75042i −0.844361 + 0.535774i
\(50\) 0 0
\(51\) 4.57993 0.641319
\(52\) 0 0
\(53\) 0.646830 + 0.646830i 0.0888490 + 0.0888490i 0.750134 0.661285i \(-0.229989\pi\)
−0.661285 + 0.750134i \(0.729989\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 1.47133 1.47133i 0.194882 0.194882i
\(58\) 0 0
\(59\) 9.22732 1.20130 0.600648 0.799514i \(-0.294910\pi\)
0.600648 + 0.799514i \(0.294910\pi\)
\(60\) 0 0
\(61\) 3.51832i 0.450474i −0.974304 0.225237i \(-0.927684\pi\)
0.974304 0.225237i \(-0.0723157\pi\)
\(62\) 0 0
\(63\) 6.77147 1.96707i 0.853125 0.247827i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −1.70777 + 1.70777i −0.208637 + 0.208637i −0.803688 0.595051i \(-0.797132\pi\)
0.595051 + 0.803688i \(0.297132\pi\)
\(68\) 0 0
\(69\) 0.0386965 0.00465851
\(70\) 0 0
\(71\) −8.54487 −1.01409 −0.507045 0.861920i \(-0.669262\pi\)
−0.507045 + 0.861920i \(0.669262\pi\)
\(72\) 0 0
\(73\) 2.43511 2.43511i 0.285009 0.285009i −0.550094 0.835103i \(-0.685408\pi\)
0.835103 + 0.550094i \(0.185408\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.61964 + 9.01790i 0.298535 + 1.02768i
\(78\) 0 0
\(79\) 5.72713i 0.644352i 0.946680 + 0.322176i \(0.104414\pi\)
−0.946680 + 0.322176i \(0.895586\pi\)
\(80\) 0 0
\(81\) −6.09869 −0.677632
\(82\) 0 0
\(83\) 2.04580 2.04580i 0.224556 0.224556i −0.585858 0.810414i \(-0.699242\pi\)
0.810414 + 0.585858i \(0.199242\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −2.18830 2.18830i −0.234610 0.234610i
\(88\) 0 0
\(89\) −8.18639 −0.867756 −0.433878 0.900972i \(-0.642855\pi\)
−0.433878 + 0.900972i \(0.642855\pi\)
\(90\) 0 0
\(91\) −9.67862 5.32126i −1.01460 0.557820i
\(92\) 0 0
\(93\) −4.25215 4.25215i −0.440927 0.440927i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 6.23068 + 6.23068i 0.632629 + 0.632629i 0.948727 0.316097i \(-0.102373\pi\)
−0.316097 + 0.948727i \(0.602373\pi\)
\(98\) 0 0
\(99\) 9.45963i 0.950729i
\(100\) 0 0
\(101\) 13.7868i 1.37184i 0.727677 + 0.685920i \(0.240600\pi\)
−0.727677 + 0.685920i \(0.759400\pi\)
\(102\) 0 0
\(103\) 10.3752 10.3752i 1.02230 1.02230i 0.0225506 0.999746i \(-0.492821\pi\)
0.999746 0.0225506i \(-0.00717870\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.54863 4.54863i 0.439733 0.439733i −0.452189 0.891922i \(-0.649357\pi\)
0.891922 + 0.452189i \(0.149357\pi\)
\(108\) 0 0
\(109\) 3.76387i 0.360513i 0.983620 + 0.180257i \(0.0576928\pi\)
−0.983620 + 0.180257i \(0.942307\pi\)
\(110\) 0 0
\(111\) 6.38345i 0.605890i
\(112\) 0 0
\(113\) 4.83006 + 4.83006i 0.454374 + 0.454374i 0.896803 0.442429i \(-0.145883\pi\)
−0.442429 + 0.896803i \(0.645883\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 7.86732 + 7.86732i 0.727334 + 0.727334i
\(118\) 0 0
\(119\) 10.0890 18.3505i 0.924860 1.68219i
\(120\) 0 0
\(121\) 1.59785 0.145259
\(122\) 0 0
\(123\) −2.30731 2.30731i −0.208043 0.208043i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −9.86172 + 9.86172i −0.875086 + 0.875086i −0.993021 0.117936i \(-0.962372\pi\)
0.117936 + 0.993021i \(0.462372\pi\)
\(128\) 0 0
\(129\) −5.67809 −0.499928
\(130\) 0 0
\(131\) 13.8255i 1.20794i −0.797006 0.603971i \(-0.793584\pi\)
0.797006 0.603971i \(-0.206416\pi\)
\(132\) 0 0
\(133\) −2.65405 9.13636i −0.230135 0.792223i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 13.2776 13.2776i 1.13438 1.13438i 0.144938 0.989441i \(-0.453702\pi\)
0.989441 0.144938i \(-0.0462984\pi\)
\(138\) 0 0
\(139\) 7.55843 0.641097 0.320549 0.947232i \(-0.396133\pi\)
0.320549 + 0.947232i \(0.396133\pi\)
\(140\) 0 0
\(141\) 2.81774 0.237297
\(142\) 0 0
\(143\) −10.4773 + 10.4773i −0.876155 + 0.876155i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −0.883831 + 3.95288i −0.0728971 + 0.326028i
\(148\) 0 0
\(149\) 17.1912i 1.40836i 0.710021 + 0.704180i \(0.248685\pi\)
−0.710021 + 0.704180i \(0.751315\pi\)
\(150\) 0 0
\(151\) 6.81237 0.554383 0.277192 0.960815i \(-0.410596\pi\)
0.277192 + 0.960815i \(0.410596\pi\)
\(152\) 0 0
\(153\) −14.9163 + 14.9163i −1.20591 + 1.20591i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 1.15071 + 1.15071i 0.0918367 + 0.0918367i 0.751533 0.659696i \(-0.229315\pi\)
−0.659696 + 0.751533i \(0.729315\pi\)
\(158\) 0 0
\(159\) 0.529315 0.0419774
\(160\) 0 0
\(161\) 0.0852436 0.155046i 0.00671814 0.0122193i
\(162\) 0 0
\(163\) 10.4137 + 10.4137i 0.815660 + 0.815660i 0.985476 0.169816i \(-0.0543172\pi\)
−0.169816 + 0.985476i \(0.554317\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −8.46637 8.46637i −0.655147 0.655147i 0.299080 0.954228i \(-0.403320\pi\)
−0.954228 + 0.299080i \(0.903320\pi\)
\(168\) 0 0
\(169\) 4.42736i 0.340566i
\(170\) 0 0
\(171\) 9.58389i 0.732899i
\(172\) 0 0
\(173\) 8.19971 8.19971i 0.623412 0.623412i −0.322990 0.946402i \(-0.604688\pi\)
0.946402 + 0.322990i \(0.104688\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 3.77545 3.77545i 0.283780 0.283780i
\(178\) 0 0
\(179\) 15.9103i 1.18919i 0.804025 + 0.594595i \(0.202688\pi\)
−0.804025 + 0.594595i \(0.797312\pi\)
\(180\) 0 0
\(181\) 15.5721i 1.15746i 0.815518 + 0.578732i \(0.196452\pi\)
−0.815518 + 0.578732i \(0.803548\pi\)
\(182\) 0 0
\(183\) −1.43955 1.43955i −0.106415 0.106415i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −19.8648 19.8648i −1.45266 1.45266i
\(188\) 0 0
\(189\) 4.17850 7.60010i 0.303941 0.552826i
\(190\) 0 0
\(191\) 6.52605 0.472209 0.236104 0.971728i \(-0.424129\pi\)
0.236104 + 0.971728i \(0.424129\pi\)
\(192\) 0 0
\(193\) 4.64028 + 4.64028i 0.334014 + 0.334014i 0.854109 0.520094i \(-0.174103\pi\)
−0.520094 + 0.854109i \(0.674103\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −7.95497 + 7.95497i −0.566768 + 0.566768i −0.931222 0.364453i \(-0.881256\pi\)
0.364453 + 0.931222i \(0.381256\pi\)
\(198\) 0 0
\(199\) −7.84512 −0.556126 −0.278063 0.960563i \(-0.589692\pi\)
−0.278063 + 0.960563i \(0.589692\pi\)
\(200\) 0 0
\(201\) 1.39750i 0.0985720i
\(202\) 0 0
\(203\) −13.5885 + 3.94736i −0.953723 + 0.277050i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.126030 + 0.126030i −0.00875969 + 0.00875969i
\(208\) 0 0
\(209\) −12.7633 −0.882859
\(210\) 0 0
\(211\) −13.9461 −0.960091 −0.480045 0.877244i \(-0.659380\pi\)
−0.480045 + 0.877244i \(0.659380\pi\)
\(212\) 0 0
\(213\) −3.49622 + 3.49622i −0.239557 + 0.239557i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −26.4041 + 7.67022i −1.79243 + 0.520689i
\(218\) 0 0
\(219\) 1.99270i 0.134654i
\(220\) 0 0
\(221\) 33.0420 2.22265
\(222\) 0 0
\(223\) 3.17116 3.17116i 0.212357 0.212357i −0.592911 0.805268i \(-0.702021\pi\)
0.805268 + 0.592911i \(0.202021\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2.25072 2.25072i −0.149386 0.149386i 0.628458 0.777844i \(-0.283686\pi\)
−0.777844 + 0.628458i \(0.783686\pi\)
\(228\) 0 0
\(229\) −12.1177 −0.800758 −0.400379 0.916350i \(-0.631122\pi\)
−0.400379 + 0.916350i \(0.631122\pi\)
\(230\) 0 0
\(231\) 4.76162 + 2.61791i 0.313291 + 0.172246i
\(232\) 0 0
\(233\) 4.60978 + 4.60978i 0.301996 + 0.301996i 0.841795 0.539798i \(-0.181499\pi\)
−0.539798 + 0.841795i \(0.681499\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 2.34331 + 2.34331i 0.152215 + 0.152215i
\(238\) 0 0
\(239\) 0.804297i 0.0520257i 0.999662 + 0.0260128i \(0.00828108\pi\)
−0.999662 + 0.0260128i \(0.991719\pi\)
\(240\) 0 0
\(241\) 17.1249i 1.10311i −0.834138 0.551555i \(-0.814035\pi\)
0.834138 0.551555i \(-0.185965\pi\)
\(242\) 0 0
\(243\) −9.44923 + 9.44923i −0.606169 + 0.606169i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 10.6149 10.6149i 0.675411 0.675411i
\(248\) 0 0
\(249\) 1.67412i 0.106093i
\(250\) 0 0
\(251\) 12.6371i 0.797645i 0.917028 + 0.398822i \(0.130581\pi\)
−0.917028 + 0.398822i \(0.869419\pi\)
\(252\) 0 0
\(253\) −0.167840 0.167840i −0.0105520 0.0105520i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6.59946 6.59946i −0.411663 0.411663i 0.470655 0.882318i \(-0.344018\pi\)
−0.882318 + 0.470655i \(0.844018\pi\)
\(258\) 0 0
\(259\) −25.5767 14.0620i −1.58926 0.873767i
\(260\) 0 0
\(261\) 14.2541 0.882306
\(262\) 0 0
\(263\) −7.56907 7.56907i −0.466729 0.466729i 0.434124 0.900853i \(-0.357058\pi\)
−0.900853 + 0.434124i \(0.857058\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −3.34955 + 3.34955i −0.204989 + 0.204989i
\(268\) 0 0
\(269\) 22.1148 1.34836 0.674181 0.738566i \(-0.264497\pi\)
0.674181 + 0.738566i \(0.264497\pi\)
\(270\) 0 0
\(271\) 29.7020i 1.80427i 0.431456 + 0.902134i \(0.358000\pi\)
−0.431456 + 0.902134i \(0.642000\pi\)
\(272\) 0 0
\(273\) −6.13735 + 1.78286i −0.371450 + 0.107904i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 3.38005 3.38005i 0.203087 0.203087i −0.598234 0.801321i \(-0.704131\pi\)
0.801321 + 0.598234i \(0.204131\pi\)
\(278\) 0 0
\(279\) 27.6975 1.65821
\(280\) 0 0
\(281\) −26.0224 −1.55237 −0.776184 0.630507i \(-0.782847\pi\)
−0.776184 + 0.630507i \(0.782847\pi\)
\(282\) 0 0
\(283\) 13.9610 13.9610i 0.829895 0.829895i −0.157607 0.987502i \(-0.550378\pi\)
0.987502 + 0.157607i \(0.0503778\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −14.3275 + 4.16203i −0.845724 + 0.245677i
\(288\) 0 0
\(289\) 45.6472i 2.68513i
\(290\) 0 0
\(291\) 5.09869 0.298891
\(292\) 0 0
\(293\) 6.51568 6.51568i 0.380650 0.380650i −0.490686 0.871336i \(-0.663254\pi\)
0.871336 + 0.490686i \(0.163254\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −8.22726 8.22726i −0.477394 0.477394i
\(298\) 0 0
\(299\) 0.279177 0.0161452
\(300\) 0 0
\(301\) −12.5081 + 22.7505i −0.720957 + 1.31132i
\(302\) 0 0
\(303\) 5.64102 + 5.64102i 0.324068 + 0.324068i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −6.13557 6.13557i −0.350176 0.350176i 0.509999 0.860175i \(-0.329646\pi\)
−0.860175 + 0.509999i \(0.829646\pi\)
\(308\) 0 0
\(309\) 8.49022i 0.482992i
\(310\) 0 0
\(311\) 1.36872i 0.0776131i −0.999247 0.0388065i \(-0.987644\pi\)
0.999247 0.0388065i \(-0.0123556\pi\)
\(312\) 0 0
\(313\) −13.9335 + 13.9335i −0.787565 + 0.787565i −0.981095 0.193529i \(-0.938007\pi\)
0.193529 + 0.981095i \(0.438007\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 8.42849 8.42849i 0.473391 0.473391i −0.429619 0.903010i \(-0.641352\pi\)
0.903010 + 0.429619i \(0.141352\pi\)
\(318\) 0 0
\(319\) 18.9829i 1.06284i
\(320\) 0 0
\(321\) 3.72224i 0.207755i
\(322\) 0 0
\(323\) 20.1257 + 20.1257i 1.11983 + 1.11983i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 1.54002 + 1.54002i 0.0851635 + 0.0851635i
\(328\) 0 0
\(329\) 6.20714 11.2899i 0.342211 0.622433i
\(330\) 0 0
\(331\) 25.5762 1.40580 0.702899 0.711290i \(-0.251889\pi\)
0.702899 + 0.711290i \(0.251889\pi\)
\(332\) 0 0
\(333\) 20.7902 + 20.7902i 1.13929 + 1.13929i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −19.0296 + 19.0296i −1.03661 + 1.03661i −0.0373062 + 0.999304i \(0.511878\pi\)
−0.999304 + 0.0373062i \(0.988122\pi\)
\(338\) 0 0
\(339\) 3.95254 0.214672
\(340\) 0 0
\(341\) 36.8862i 1.99750i
\(342\) 0 0
\(343\) 13.8911 + 12.2490i 0.750049 + 0.661382i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −10.1175 + 10.1175i −0.543135 + 0.543135i −0.924447 0.381311i \(-0.875473\pi\)
0.381311 + 0.924447i \(0.375473\pi\)
\(348\) 0 0
\(349\) −17.7082 −0.947898 −0.473949 0.880552i \(-0.657172\pi\)
−0.473949 + 0.880552i \(0.657172\pi\)
\(350\) 0 0
\(351\) 13.6848 0.730439
\(352\) 0 0
\(353\) −18.8566 + 18.8566i −1.00363 + 1.00363i −0.00364095 + 0.999993i \(0.501159\pi\)
−0.999993 + 0.00364095i \(0.998841\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −3.38027 11.6363i −0.178903 0.615860i
\(358\) 0 0
\(359\) 15.0844i 0.796123i 0.917359 + 0.398061i \(0.130317\pi\)
−0.917359 + 0.398061i \(0.869683\pi\)
\(360\) 0 0
\(361\) −6.06900 −0.319421
\(362\) 0 0
\(363\) 0.653777 0.653777i 0.0343144 0.0343144i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 5.09830 + 5.09830i 0.266129 + 0.266129i 0.827538 0.561409i \(-0.189741\pi\)
−0.561409 + 0.827538i \(0.689741\pi\)
\(368\) 0 0
\(369\) 15.0293 0.782393
\(370\) 0 0
\(371\) 1.16601 2.12082i 0.0605365 0.110107i
\(372\) 0 0
\(373\) −12.5295 12.5295i −0.648754 0.648754i 0.303938 0.952692i \(-0.401698\pi\)
−0.952692 + 0.303938i \(0.901698\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −15.7875 15.7875i −0.813099 0.813099i
\(378\) 0 0
\(379\) 28.0665i 1.44168i −0.693103 0.720838i \(-0.743757\pi\)
0.693103 0.720838i \(-0.256243\pi\)
\(380\) 0 0
\(381\) 8.07004i 0.413441i
\(382\) 0 0
\(383\) −19.4556 + 19.4556i −0.994136 + 0.994136i −0.999983 0.00584671i \(-0.998139\pi\)
0.00584671 + 0.999983i \(0.498139\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 18.4929 18.4929i 0.940046 0.940046i
\(388\) 0 0
\(389\) 35.4128i 1.79550i −0.440505 0.897750i \(-0.645201\pi\)
0.440505 0.897750i \(-0.354799\pi\)
\(390\) 0 0
\(391\) 0.529315i 0.0267686i
\(392\) 0 0
\(393\) −5.65685 5.65685i −0.285351 0.285351i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −13.0002 13.0002i −0.652460 0.652460i 0.301124 0.953585i \(-0.402638\pi\)
−0.953585 + 0.301124i \(0.902638\pi\)
\(398\) 0 0
\(399\) −4.82416 2.65230i −0.241510 0.132781i
\(400\) 0 0
\(401\) 26.6516 1.33092 0.665460 0.746434i \(-0.268236\pi\)
0.665460 + 0.746434i \(0.268236\pi\)
\(402\) 0 0
\(403\) −30.6772 30.6772i −1.52814 1.52814i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −27.6873 + 27.6873i −1.37241 + 1.37241i
\(408\) 0 0
\(409\) −24.9874 −1.23555 −0.617775 0.786355i \(-0.711966\pi\)
−0.617775 + 0.786355i \(0.711966\pi\)
\(410\) 0 0
\(411\) 10.8653i 0.535946i
\(412\) 0 0
\(413\) −6.81034 23.4441i −0.335115 1.15361i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 3.09261 3.09261i 0.151446 0.151446i
\(418\) 0 0
\(419\) −29.7544 −1.45360 −0.726799 0.686850i \(-0.758993\pi\)
−0.726799 + 0.686850i \(0.758993\pi\)
\(420\) 0 0
\(421\) 6.60400 0.321859 0.160930 0.986966i \(-0.448551\pi\)
0.160930 + 0.986966i \(0.448551\pi\)
\(422\) 0 0
\(423\) −9.17707 + 9.17707i −0.446204 + 0.446204i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −8.93906 + 2.59674i −0.432592 + 0.125665i
\(428\) 0 0
\(429\) 8.57378i 0.413946i
\(430\) 0 0
\(431\) −18.0134 −0.867677 −0.433839 0.900991i \(-0.642841\pi\)
−0.433839 + 0.900991i \(0.642841\pi\)
\(432\) 0 0
\(433\) −3.25124 + 3.25124i −0.156244 + 0.156244i −0.780900 0.624656i \(-0.785239\pi\)
0.624656 + 0.780900i \(0.285239\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.170045 + 0.170045i 0.00813436 + 0.00813436i
\(438\) 0 0
\(439\) −11.5574 −0.551607 −0.275803 0.961214i \(-0.588944\pi\)
−0.275803 + 0.961214i \(0.588944\pi\)
\(440\) 0 0
\(441\) −9.99553 15.7526i −0.475978 0.750124i
\(442\) 0 0
\(443\) 22.0498 + 22.0498i 1.04762 + 1.04762i 0.998808 + 0.0488073i \(0.0155420\pi\)
0.0488073 + 0.998808i \(0.484458\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 7.03397 + 7.03397i 0.332695 + 0.332695i
\(448\) 0 0
\(449\) 22.8564i 1.07866i −0.842094 0.539330i \(-0.818677\pi\)
0.842094 0.539330i \(-0.181323\pi\)
\(450\) 0 0
\(451\) 20.0152i 0.942480i
\(452\) 0 0
\(453\) 2.78735 2.78735i 0.130961 0.130961i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −6.19406 + 6.19406i −0.289746 + 0.289746i −0.836980 0.547234i \(-0.815681\pi\)
0.547234 + 0.836980i \(0.315681\pi\)
\(458\) 0 0
\(459\) 25.9461i 1.21106i
\(460\) 0 0
\(461\) 9.63815i 0.448893i −0.974486 0.224447i \(-0.927943\pi\)
0.974486 0.224447i \(-0.0720575\pi\)
\(462\) 0 0
\(463\) −25.9680 25.9680i −1.20684 1.20684i −0.972046 0.234791i \(-0.924560\pi\)
−0.234791 0.972046i \(-0.575440\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 20.6556 + 20.6556i 0.955825 + 0.955825i 0.999065 0.0432393i \(-0.0137678\pi\)
−0.0432393 + 0.999065i \(0.513768\pi\)
\(468\) 0 0
\(469\) 5.59939 + 3.07852i 0.258556 + 0.142153i
\(470\) 0 0
\(471\) 0.941650 0.0433889
\(472\) 0 0
\(473\) 24.6279 + 24.6279i 1.13239 + 1.13239i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −1.72392 + 1.72392i −0.0789327 + 0.0789327i
\(478\) 0 0
\(479\) −8.74688 −0.399655 −0.199828 0.979831i \(-0.564038\pi\)
−0.199828 + 0.979831i \(0.564038\pi\)
\(480\) 0 0
\(481\) 46.0535i 2.09986i
\(482\) 0 0
\(483\) −0.0285604 0.0983170i −0.00129954 0.00447358i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −6.18084 + 6.18084i −0.280081 + 0.280081i −0.833141 0.553061i \(-0.813460\pi\)
0.553061 + 0.833141i \(0.313460\pi\)
\(488\) 0 0
\(489\) 8.52170 0.385365
\(490\) 0 0
\(491\) −11.4596 −0.517166 −0.258583 0.965989i \(-0.583256\pi\)
−0.258583 + 0.965989i \(0.583256\pi\)
\(492\) 0 0
\(493\) 29.9329 29.9329i 1.34811 1.34811i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 6.30665 + 21.7101i 0.282892 + 0.973833i
\(498\) 0 0
\(499\) 37.1794i 1.66438i 0.554493 + 0.832189i \(0.312912\pi\)
−0.554493 + 0.832189i \(0.687088\pi\)
\(500\) 0 0
\(501\) −6.92820 −0.309529
\(502\) 0 0
\(503\) −6.72761 + 6.72761i −0.299969 + 0.299969i −0.841002 0.541032i \(-0.818034\pi\)
0.541032 + 0.841002i \(0.318034\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.81150 1.81150i −0.0804516 0.0804516i
\(508\) 0 0
\(509\) 42.5874 1.88765 0.943826 0.330442i \(-0.107198\pi\)
0.943826 + 0.330442i \(0.107198\pi\)
\(510\) 0 0
\(511\) −7.98421 4.38968i −0.353201 0.194188i
\(512\) 0 0
\(513\) 8.33533 + 8.33533i 0.368014 + 0.368014i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −12.2216 12.2216i −0.537503 0.537503i
\(518\) 0 0
\(519\) 6.70999i 0.294536i
\(520\) 0 0
\(521\) 18.0438i 0.790512i 0.918571 + 0.395256i \(0.129344\pi\)
−0.918571 + 0.395256i \(0.870656\pi\)
\(522\) 0 0
\(523\) 19.0355 19.0355i 0.832363 0.832363i −0.155477 0.987840i \(-0.549691\pi\)
0.987840 + 0.155477i \(0.0496914\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 58.1635 58.1635i 2.53364 2.53364i
\(528\) 0 0
\(529\) 22.9955i 0.999806i
\(530\) 0 0
\(531\) 24.5924i 1.06722i
\(532\) 0 0
\(533\) −16.6461 16.6461i −0.721024 0.721024i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 6.50985 + 6.50985i 0.280921 + 0.280921i
\(538\) 0 0
\(539\) 20.9785 13.3115i 0.903608 0.573368i
\(540\) 0 0
\(541\) −3.51876 −0.151283 −0.0756416 0.997135i \(-0.524100\pi\)
−0.0756416 + 0.997135i \(0.524100\pi\)
\(542\) 0 0
\(543\) 6.37147 + 6.37147i 0.273426 + 0.273426i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 10.4209 10.4209i 0.445564 0.445564i −0.448313 0.893877i \(-0.647975\pi\)
0.893877 + 0.448313i \(0.147975\pi\)
\(548\) 0 0
\(549\) 9.37693 0.400198
\(550\) 0 0
\(551\) 19.2322i 0.819320i
\(552\) 0 0
\(553\) 14.5510 4.22698i 0.618773 0.179749i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.59156 + 1.59156i −0.0674367 + 0.0674367i −0.740021 0.672584i \(-0.765184\pi\)
0.672584 + 0.740021i \(0.265184\pi\)
\(558\) 0 0
\(559\) −40.9647 −1.73262
\(560\) 0 0
\(561\) −16.2558 −0.686319
\(562\) 0 0
\(563\) −12.0816 + 12.0816i −0.509178 + 0.509178i −0.914274 0.405096i \(-0.867238\pi\)
0.405096 + 0.914274i \(0.367238\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 4.50121 + 15.4951i 0.189033 + 0.650732i
\(568\) 0 0
\(569\) 29.0881i 1.21944i 0.792619 + 0.609718i \(0.208717\pi\)
−0.792619 + 0.609718i \(0.791283\pi\)
\(570\) 0 0
\(571\) 5.95879 0.249368 0.124684 0.992197i \(-0.460208\pi\)
0.124684 + 0.992197i \(0.460208\pi\)
\(572\) 0 0
\(573\) 2.67020 2.67020i 0.111549 0.111549i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −14.6203 14.6203i −0.608650 0.608650i 0.333943 0.942593i \(-0.391621\pi\)
−0.942593 + 0.333943i \(0.891621\pi\)
\(578\) 0 0
\(579\) 3.79723 0.157808
\(580\) 0 0
\(581\) −6.70774 3.68788i −0.278284 0.152999i
\(582\) 0 0
\(583\) −2.29582 2.29582i −0.0950833 0.0950833i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 23.5748 + 23.5748i 0.973035 + 0.973035i 0.999646 0.0266107i \(-0.00847144\pi\)
−0.0266107 + 0.999646i \(0.508471\pi\)
\(588\) 0 0
\(589\) 37.3707i 1.53983i
\(590\) 0 0
\(591\) 6.50972i 0.267774i
\(592\) 0 0
\(593\) 6.48482 6.48482i 0.266300 0.266300i −0.561308 0.827607i \(-0.689701\pi\)
0.827607 + 0.561308i \(0.189701\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −3.20991 + 3.20991i −0.131373 + 0.131373i
\(598\) 0 0
\(599\) 26.8124i 1.09552i 0.836634 + 0.547762i \(0.184520\pi\)
−0.836634 + 0.547762i \(0.815480\pi\)
\(600\) 0 0
\(601\) 42.1513i 1.71939i −0.510811 0.859693i \(-0.670655\pi\)
0.510811 0.859693i \(-0.329345\pi\)
\(602\) 0 0
\(603\) −4.55150 4.55150i −0.185351 0.185351i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 21.1320 + 21.1320i 0.857720 + 0.857720i 0.991069 0.133349i \(-0.0425732\pi\)
−0.133349 + 0.991069i \(0.542573\pi\)
\(608\) 0 0
\(609\) −3.94476 + 7.17496i −0.159850 + 0.290744i
\(610\) 0 0
\(611\) 20.3287 0.822410
\(612\) 0 0
\(613\) −0.374096 0.374096i −0.0151096 0.0151096i 0.699512 0.714621i \(-0.253401\pi\)
−0.714621 + 0.699512i \(0.753401\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 10.3289 10.3289i 0.415826 0.415826i −0.467936 0.883762i \(-0.655002\pi\)
0.883762 + 0.467936i \(0.155002\pi\)
\(618\) 0 0
\(619\) −9.30472 −0.373988 −0.186994 0.982361i \(-0.559875\pi\)
−0.186994 + 0.982361i \(0.559875\pi\)
\(620\) 0 0
\(621\) 0.219222i 0.00879709i
\(622\) 0 0
\(623\) 6.04206 + 20.7993i 0.242070 + 0.833308i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −5.22225 + 5.22225i −0.208557 + 0.208557i
\(628\) 0 0
\(629\) 87.3168 3.48155
\(630\) 0 0
\(631\) 6.74964 0.268699 0.134349 0.990934i \(-0.457106\pi\)
0.134349 + 0.990934i \(0.457106\pi\)
\(632\) 0 0
\(633\) −5.70620 + 5.70620i −0.226801 + 0.226801i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −6.37642 + 28.5181i −0.252643 + 1.12993i
\(638\) 0 0
\(639\) 22.7736i 0.900909i
\(640\) 0 0
\(641\) −12.2287 −0.483006 −0.241503 0.970400i \(-0.577640\pi\)
−0.241503 + 0.970400i \(0.577640\pi\)
\(642\) 0 0
\(643\) 5.61879 5.61879i 0.221584 0.221584i −0.587581 0.809165i \(-0.699920\pi\)
0.809165 + 0.587581i \(0.199920\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −5.37047 5.37047i −0.211135 0.211135i 0.593615 0.804749i \(-0.297700\pi\)
−0.804749 + 0.593615i \(0.797700\pi\)
\(648\) 0 0
\(649\) −32.7510 −1.28559
\(650\) 0 0
\(651\) −7.66518 + 13.9419i −0.300422 + 0.546425i
\(652\) 0 0
\(653\) −20.1562 20.1562i −0.788774 0.788774i 0.192519 0.981293i \(-0.438334\pi\)
−0.981293 + 0.192519i \(0.938334\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 6.49001 + 6.49001i 0.253199 + 0.253199i
\(658\) 0 0
\(659\) 0.712783i 0.0277661i −0.999904 0.0138830i \(-0.995581\pi\)
0.999904 0.0138830i \(-0.00441925\pi\)
\(660\) 0 0
\(661\) 28.3507i 1.10271i −0.834269 0.551357i \(-0.814110\pi\)
0.834269 0.551357i \(-0.185890\pi\)
\(662\) 0 0
\(663\) 13.5195 13.5195i 0.525053 0.525053i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.252907 0.252907i 0.00979261 0.00979261i
\(668\) 0 0
\(669\) 2.59503i 0.100330i
\(670\) 0 0
\(671\) 12.4877i 0.482083i
\(672\) 0 0
\(673\) 5.58066 + 5.58066i 0.215119 + 0.215119i 0.806438 0.591319i \(-0.201393\pi\)
−0.591319 + 0.806438i \(0.701393\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 8.82232 + 8.82232i 0.339069 + 0.339069i 0.856017 0.516948i \(-0.172932\pi\)
−0.516948 + 0.856017i \(0.672932\pi\)
\(678\) 0 0
\(679\) 11.2318 20.4290i 0.431037 0.783995i
\(680\) 0 0
\(681\) −1.84181 −0.0705784
\(682\) 0 0
\(683\) −6.51153 6.51153i −0.249157 0.249157i 0.571468 0.820625i \(-0.306374\pi\)
−0.820625 + 0.571468i \(0.806374\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −4.95807 + 4.95807i −0.189162 + 0.189162i
\(688\) 0 0
\(689\) 3.81875 0.145483
\(690\) 0 0
\(691\) 26.2458i 0.998436i 0.866476 + 0.499218i \(0.166379\pi\)
−0.866476 + 0.499218i \(0.833621\pi\)
\(692\) 0 0
\(693\) −24.0343 + 6.98179i −0.912987 + 0.265216i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 31.5608 31.5608i 1.19545 1.19545i
\(698\) 0 0
\(699\) 3.77227 0.142680
\(700\) 0 0
\(701\) −12.5261 −0.473103 −0.236551 0.971619i \(-0.576017\pi\)
−0.236551 + 0.971619i \(0.576017\pi\)
\(702\) 0 0
\(703\) 28.0510 28.0510i 1.05796 1.05796i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 35.0285 10.1755i 1.31738 0.382690i
\(708\) 0 0
\(709\) 32.8204i 1.23260i 0.787512 + 0.616299i \(0.211369\pi\)
−0.787512 + 0.616299i \(0.788631\pi\)
\(710\) 0 0
\(711\) −15.2638 −0.572437
\(712\) 0 0
\(713\) 0.491432 0.491432i 0.0184043 0.0184043i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0.329086 + 0.329086i 0.0122900 + 0.0122900i
\(718\) 0 0
\(719\) −19.4184 −0.724186 −0.362093 0.932142i \(-0.617938\pi\)
−0.362093 + 0.932142i \(0.617938\pi\)
\(720\) 0 0
\(721\) −34.0179 18.7029i −1.26689 0.696533i
\(722\) 0 0
\(723\) −7.00682 7.00682i −0.260586 0.260586i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 5.73374 + 5.73374i 0.212653 + 0.212653i 0.805393 0.592741i \(-0.201954\pi\)
−0.592741 + 0.805393i \(0.701954\pi\)
\(728\) 0 0
\(729\) 10.5636i 0.391243i
\(730\) 0 0
\(731\) 77.6685i 2.87267i
\(732\) 0 0
\(733\) 8.52329 8.52329i 0.314815 0.314815i −0.531957 0.846772i \(-0.678543\pi\)
0.846772 + 0.531957i \(0.178543\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6.06145 6.06145i 0.223276 0.223276i
\(738\) 0 0
\(739\) 42.1938i 1.55212i 0.630656 + 0.776062i \(0.282786\pi\)
−0.630656 + 0.776062i \(0.717214\pi\)
\(740\) 0 0
\(741\) 8.68641i 0.319103i
\(742\) 0 0
\(743\) 4.65010 + 4.65010i 0.170596 + 0.170596i 0.787241 0.616645i \(-0.211509\pi\)
−0.616645 + 0.787241i \(0.711509\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 5.45242 + 5.45242i 0.199494 + 0.199494i
\(748\) 0 0
\(749\) −14.9140 8.19963i −0.544945 0.299608i
\(750\) 0 0
\(751\) −12.7801 −0.466353 −0.233176 0.972434i \(-0.574912\pi\)
−0.233176 + 0.972434i \(0.574912\pi\)
\(752\) 0 0
\(753\) 5.17059 + 5.17059i 0.188427 + 0.188427i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −10.6724 + 10.6724i −0.387893 + 0.387893i −0.873935 0.486042i \(-0.838440\pi\)
0.486042 + 0.873935i \(0.338440\pi\)
\(758\) 0 0
\(759\) −0.137347 −0.00498539
\(760\) 0 0
\(761\) 28.1860i 1.02174i −0.859657 0.510871i \(-0.829323\pi\)
0.859657 0.510871i \(-0.170677\pi\)
\(762\) 0 0
\(763\) 9.56294 2.77797i 0.346201 0.100569i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 27.2381 27.2381i 0.983510 0.983510i
\(768\) 0 0
\(769\) −14.1998 −0.512058 −0.256029 0.966669i \(-0.582414\pi\)
−0.256029 + 0.966669i \(0.582414\pi\)
\(770\) 0 0
\(771\) −5.40047 −0.194493
\(772\) 0 0
\(773\) 34.8461 34.8461i 1.25333 1.25333i 0.299110 0.954219i \(-0.403310\pi\)
0.954219 0.299110i \(-0.0966899\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −16.2186 + 4.71138i −0.581838 + 0.169020i
\(778\) 0 0
\(779\) 20.2782i 0.726540i
\(780\) 0 0
\(781\) 30.3287 1.08525
\(782\) 0 0
\(783\) 12.3971 12.3971i 0.443036 0.443036i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 19.6599 + 19.6599i 0.700799 + 0.700799i 0.964582 0.263783i \(-0.0849704\pi\)
−0.263783 + 0.964582i \(0.584970\pi\)
\(788\) 0 0
\(789\) −6.19393 −0.220510
\(790\) 0 0
\(791\) 8.70696 15.8367i 0.309584 0.563089i
\(792\) 0 0
\(793\) −10.3857 10.3857i −0.368807 0.368807i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 15.8992 + 15.8992i 0.563178 + 0.563178i 0.930209 0.367031i \(-0.119626\pi\)
−0.367031 + 0.930209i \(0.619626\pi\)
\(798\) 0 0
\(799\) 38.5429i 1.36355i
\(800\) 0 0
\(801\) 21.8182i 0.770907i
\(802\) 0 0
\(803\) −8.64306 + 8.64306i −0.305007 + 0.305007i
\(804\) 0