Properties

Label 1400.2.x.c.993.7
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 993.7
Character \(\chi\) \(=\) 1400.993
Dual form 1400.2.x.c.657.7

$q$-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 −0.815287 0.579058i \(-0.803421\pi\)
0.579058 + 0.815287i \(0.303421\pi\)
\(4\) 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 −0.985921 0.167213i \(-0.946523\pi\)
0.167213 + 0.985921i \(0.446523\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −5.59675 5.59675i −1.35741 1.35741i −0.877097 0.480314i \(-0.840523\pi\)
−0.480314 0.877097i \(-0.659477\pi\)
\(18\) 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 0.702160 0.712020i \(-0.252219\pi\)
−0.712020 + 0.702160i \(0.752219\pi\)
\(24\) 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 \(0.611490\pi\)
−0.939285 + 0.343137i \(0.888510\pi\)
\(38\) 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 \(0.0190916\pi\)
0.0599420 + 0.998202i \(0.480908\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.44333 3.44333i −0.502261 0.502261i 0.409879 0.912140i \(-0.365571\pi\)
−0.912140 + 0.409879i \(0.865571\pi\)
\(48\) 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 0.661285 0.750134i \(-0.270011\pi\)
−0.750134 + 0.661285i \(0.770011\pi\)
\(54\) 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 −0.595051 0.803688i \(-0.702868\pi\)
0.803688 + 0.595051i \(0.202868\pi\)
\(68\) 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 −0.835103 0.550094i \(-0.814592\pi\)
0.550094 + 0.835103i \(0.314592\pi\)
\(74\) 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 −0.810414 0.585858i \(-0.800758\pi\)
0.585858 + 0.810414i \(0.300758\pi\)
\(84\) 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 0.316097 0.948727i \(-0.397627\pi\)
−0.948727 + 0.316097i \(0.897627\pi\)
\(98\) 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 \(0.507179\pi\)
−0.999746 + 0.0225506i \(0.992821\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.54863 + 4.54863i −0.439733 + 0.439733i −0.891922 0.452189i \(-0.850643\pi\)
0.452189 + 0.891922i \(0.350643\pi\)
\(108\) 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 0.442429 0.896803i \(-0.354117\pi\)
−0.896803 + 0.442429i \(0.854117\pi\)
\(114\) 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 −0.117936 0.993021i \(-0.537628\pi\)
0.993021 + 0.117936i \(0.0376276\pi\)
\(128\) 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 \(0.546298\pi\)
−0.989441 + 0.144938i \(0.953702\pi\)
\(138\) 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 0.659696 0.751533i \(-0.270685\pi\)
−0.751533 + 0.659696i \(0.770685\pi\)
\(158\) 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 0.169816 0.985476i \(-0.445683\pi\)
−0.985476 + 0.169816i \(0.945683\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 8.46637 + 8.46637i 0.655147 + 0.655147i 0.954228 0.299080i \(-0.0966799\pi\)
−0.299080 + 0.954228i \(0.596680\pi\)
\(168\) 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 −0.946402 0.322990i \(-0.895312\pi\)
0.322990 + 0.946402i \(0.395312\pi\)
\(174\) 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 0.520094 0.854109i \(-0.325897\pi\)
−0.854109 + 0.520094i \(0.825897\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 7.95497 7.95497i 0.566768 0.566768i −0.364453 0.931222i \(-0.618744\pi\)
0.931222 + 0.364453i \(0.118744\pi\)
\(198\) 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 −0.805268 0.592911i \(-0.797979\pi\)
0.592911 + 0.805268i \(0.297979\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2.25072 + 2.25072i 0.149386 + 0.149386i 0.777844 0.628458i \(-0.216314\pi\)
−0.628458 + 0.777844i \(0.716314\pi\)
\(228\) 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 0.539798 0.841795i \(-0.318501\pi\)
−0.841795 + 0.539798i \(0.818501\pi\)
\(234\) 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 0.882318 0.470655i \(-0.155982\pi\)
−0.470655 + 0.882318i \(0.655982\pi\)
\(258\) 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 0.900853 0.434124i \(-0.142942\pi\)
−0.434124 + 0.900853i \(0.642942\pi\)
\(264\) 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 −0.801321 0.598234i \(-0.795869\pi\)
0.598234 + 0.801321i \(0.295869\pi\)
\(278\) 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 −0.987502 0.157607i \(-0.949622\pi\)
0.157607 + 0.987502i \(0.449622\pi\)
\(284\) 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 −0.871336 0.490686i \(-0.836746\pi\)
0.490686 + 0.871336i \(0.336746\pi\)
\(294\) 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 0.860175 0.509999i \(-0.170354\pi\)
−0.509999 + 0.860175i \(0.670354\pi\)
\(308\) 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 −0.193529 0.981095i \(-0.561993\pi\)
0.981095 + 0.193529i \(0.0619934\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8.42849 + 8.42849i −0.473391 + 0.473391i −0.903010 0.429619i \(-0.858648\pi\)
0.429619 + 0.903010i \(0.358648\pi\)
\(318\) 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 \(-0.488122\pi\)
0.999304 0.0373062i \(-0.0118777\pi\)
\(338\) 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 −0.381311 0.924447i \(-0.624527\pi\)
0.924447 + 0.381311i \(0.124527\pi\)
\(348\) 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 \(-0.498841\pi\)
0.999993 0.00364095i \(-0.00115895\pi\)
\(354\) 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 0.561409 0.827538i \(-0.310259\pi\)
−0.827538 + 0.561409i \(0.810259\pi\)
\(368\) 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 0.952692 0.303938i \(-0.0983016\pi\)
−0.303938 + 0.952692i \(0.598302\pi\)
\(374\) 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 −0.00584671 0.999983i \(-0.501861\pi\)
0.999983 + 0.00584671i \(0.00186108\pi\)
\(384\) 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 0.953585 0.301124i \(-0.0973620\pi\)
−0.301124 + 0.953585i \(0.597362\pi\)
\(398\) 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 −0.624656 0.780900i \(-0.714761\pi\)
0.780900 + 0.624656i \(0.214761\pi\)
\(434\) 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 \(-0.984458\pi\)
−0.0488073 0.998808i \(-0.515542\pi\)
\(444\) 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 −0.547234 0.836980i \(-0.684319\pi\)
0.836980 + 0.547234i \(0.184319\pi\)
\(458\) 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 \(0.0754404\pi\)
0.234791 + 0.972046i \(0.424560\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −20.6556 20.6556i −0.955825 0.955825i 0.0432393 0.999065i \(-0.486232\pi\)
−0.999065 + 0.0432393i \(0.986232\pi\)
\(468\) 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 −0.553061 0.833141i \(-0.686540\pi\)
0.833141 + 0.553061i \(0.186540\pi\)
\(488\) 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 −0.541032 0.841002i \(-0.681966\pi\)
0.841002 + 0.541032i \(0.181966\pi\)
\(504\) 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 −0.987840 0.155477i \(-0.950309\pi\)
0.155477 + 0.987840i \(0.450309\pi\)
\(524\) 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 −0.893877 0.448313i \(-0.852025\pi\)
0.448313 + 0.893877i \(0.352025\pi\)
\(548\) 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 −0.672584 0.740021i \(-0.734816\pi\)
0.740021 + 0.672584i \(0.234816\pi\)
\(558\) 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 −0.405096 0.914274i \(-0.632762\pi\)
0.914274 + 0.405096i \(0.132762\pi\)
\(564\) 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 0.942593 0.333943i \(-0.108379\pi\)
−0.333943 + 0.942593i \(0.608379\pi\)
\(578\) 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 0.0266107 0.999646i \(-0.491529\pi\)
−0.999646 + 0.0266107i \(0.991529\pi\)
\(588\) 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 −0.827607 0.561308i \(-0.810299\pi\)
0.561308 + 0.827607i \(0.310299\pi\)
\(594\) 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 0.133349 0.991069i \(-0.457427\pi\)
−0.991069 + 0.133349i \(0.957427\pi\)
\(608\) 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 0.714621 0.699512i \(-0.246599\pi\)
−0.699512 + 0.714621i \(0.746599\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −10.3289 + 10.3289i −0.415826 + 0.415826i −0.883762 0.467936i \(-0.844998\pi\)
0.467936 + 0.883762i \(0.344998\pi\)
\(618\) 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 −0.809165 0.587581i \(-0.800080\pi\)
0.587581 + 0.809165i \(0.300080\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5.37047 + 5.37047i 0.211135 + 0.211135i 0.804749 0.593615i \(-0.202300\pi\)
−0.593615 + 0.804749i \(0.702300\pi\)
\(648\) 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 0.981293 0.192519i \(-0.0616657\pi\)
−0.192519 + 0.981293i \(0.561666\pi\)
\(654\) 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 0.591319 0.806438i \(-0.298607\pi\)
−0.806438 + 0.591319i \(0.798607\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −8.82232 8.82232i −0.339069 0.339069i 0.516948 0.856017i \(-0.327068\pi\)
−0.856017 + 0.516948i \(0.827068\pi\)
\(678\) 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 0.820625 0.571468i \(-0.193626\pi\)
−0.571468 + 0.820625i \(0.693626\pi\)
\(684\) 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 0.592741 0.805393i \(-0.298046\pi\)
−0.805393 + 0.592741i \(0.798046\pi\)
\(728\) 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 −0.846772 0.531957i \(-0.821457\pi\)
0.531957 + 0.846772i \(0.321457\pi\)
\(734\) 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 0.616645 0.787241i \(-0.288491\pi\)
−0.787241 + 0.616645i \(0.788491\pi\)
\(744\) 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 −0.486042 0.873935i \(-0.661560\pi\)
0.873935 + 0.486042i \(0.161560\pi\)
\(758\) 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 \(0.596690\pi\)
−0.954219 + 0.299110i \(0.903310\pi\)
\(774\) 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 0.263783 0.964582i \(-0.415030\pi\)
−0.964582 + 0.263783i \(0.915030\pi\)
\(788\) 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 0.367031 0.930209i \(-0.380374\pi\)
−0.930209 + 0.367031i \(0.880374\pi\)
\(798\) 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
\(804\)