Properties

Label 1512.2.s.m.865.4
Level $1512$
Weight $2$
Character 1512.865
Analytic conductor $12.073$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1512.s (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.9391935744.3
Defining polynomial: \(x^{8} - 4 x^{7} + 5 x^{6} + 12 x^{5} - 76 x^{4} + 84 x^{3} + 245 x^{2} - 1372 x + 2401\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 865.4
Root \(0.295509 - 2.62920i\) of defining polynomial
Character \(\chi\) \(=\) 1512.865
Dual form 1512.2.s.m.1297.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.366025 + 0.633975i) q^{5} +(2.12920 + 1.57052i) q^{7} +O(q^{10})\) \(q+(0.366025 + 0.633975i) q^{5} +(2.12920 + 1.57052i) q^{7} +(1.92471 - 3.33369i) q^{11} -4.87308 q^{13} +(3.09808 - 5.36603i) q^{17} +(-1.39715 - 2.41993i) q^{19} +(3.69971 + 6.40809i) q^{23} +(2.23205 - 3.86603i) q^{25} +9.78474 q^{29} +(3.15676 - 5.46766i) q^{31} +(-0.216328 + 1.92471i) q^{35} +(2.82185 + 4.88759i) q^{37} +1.50267 q^{41} -12.1629 q^{43} +(-2.95704 - 5.12175i) q^{47} +(2.06696 + 6.68788i) q^{49} +(-6.43176 + 11.1401i) q^{53} +2.81796 q^{55} +(3.19265 - 5.52984i) q^{59} +(6.29779 + 10.9081i) q^{61} +(-1.78367 - 3.08941i) q^{65} +(-0.834905 + 1.44610i) q^{67} +13.3135 q^{71} +(0.720214 - 1.24745i) q^{73} +(9.33369 - 4.07529i) q^{77} +(-3.55390 - 6.15554i) q^{79} +7.98089 q^{83} +4.53590 q^{85} +(3.62442 + 6.27768i) q^{89} +(-10.3758 - 7.65326i) q^{91} +(1.02278 - 1.77151i) q^{95} +12.1629 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{5} - 2q^{7} + O(q^{10}) \) \( 8q - 4q^{5} - 2q^{7} - 2q^{11} - 8q^{13} + 4q^{17} - 6q^{19} + 2q^{23} + 4q^{25} + 16q^{29} - 6q^{31} - 2q^{35} - 16q^{41} - 20q^{47} - 6q^{49} - 10q^{53} + 16q^{55} + 22q^{59} + 2q^{61} - 14q^{65} + 2q^{67} + 44q^{71} - 10q^{73} + 54q^{77} + 8q^{79} - 40q^{83} + 64q^{85} - 16q^{89} - 24q^{91} - 30q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(5\) 0.366025 + 0.633975i 0.163692 + 0.283522i 0.936190 0.351495i \(-0.114326\pi\)
−0.772498 + 0.635017i \(0.780993\pi\)
\(6\) 0 0
\(7\) 2.12920 + 1.57052i 0.804761 + 0.593599i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.92471 3.33369i 0.580321 1.00514i −0.415121 0.909766i \(-0.636261\pi\)
0.995441 0.0953782i \(-0.0304061\pi\)
\(12\) 0 0
\(13\) −4.87308 −1.35155 −0.675775 0.737108i \(-0.736191\pi\)
−0.675775 + 0.737108i \(0.736191\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.09808 5.36603i 0.751394 1.30145i −0.195753 0.980653i \(-0.562715\pi\)
0.947147 0.320799i \(-0.103951\pi\)
\(18\) 0 0
\(19\) −1.39715 2.41993i −0.320527 0.555169i 0.660070 0.751204i \(-0.270527\pi\)
−0.980597 + 0.196035i \(0.937193\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.69971 + 6.40809i 0.771443 + 1.33618i 0.936772 + 0.349941i \(0.113798\pi\)
−0.165328 + 0.986239i \(0.552868\pi\)
\(24\) 0 0
\(25\) 2.23205 3.86603i 0.446410 0.773205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 9.78474 1.81698 0.908490 0.417907i \(-0.137236\pi\)
0.908490 + 0.417907i \(0.137236\pi\)
\(30\) 0 0
\(31\) 3.15676 5.46766i 0.566970 0.982021i −0.429893 0.902880i \(-0.641449\pi\)
0.996863 0.0791414i \(-0.0252179\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.216328 + 1.92471i −0.0365660 + 0.325335i
\(36\) 0 0
\(37\) 2.82185 + 4.88759i 0.463909 + 0.803515i 0.999152 0.0411839i \(-0.0131130\pi\)
−0.535242 + 0.844699i \(0.679780\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.50267 0.234678 0.117339 0.993092i \(-0.462564\pi\)
0.117339 + 0.993092i \(0.462564\pi\)
\(42\) 0 0
\(43\) −12.1629 −1.85483 −0.927414 0.374036i \(-0.877974\pi\)
−0.927414 + 0.374036i \(0.877974\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.95704 5.12175i −0.431329 0.747084i 0.565659 0.824639i \(-0.308622\pi\)
−0.996988 + 0.0775554i \(0.975289\pi\)
\(48\) 0 0
\(49\) 2.06696 + 6.68788i 0.295279 + 0.955411i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −6.43176 + 11.1401i −0.883471 + 1.53022i −0.0360142 + 0.999351i \(0.511466\pi\)
−0.847456 + 0.530865i \(0.821867\pi\)
\(54\) 0 0
\(55\) 2.81796 0.379974
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 3.19265 5.52984i 0.415648 0.719924i −0.579848 0.814725i \(-0.696888\pi\)
0.995496 + 0.0948008i \(0.0302214\pi\)
\(60\) 0 0
\(61\) 6.29779 + 10.9081i 0.806349 + 1.39664i 0.915376 + 0.402599i \(0.131893\pi\)
−0.109027 + 0.994039i \(0.534774\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.78367 3.08941i −0.221237 0.383194i
\(66\) 0 0
\(67\) −0.834905 + 1.44610i −0.102000 + 0.176669i −0.912509 0.409058i \(-0.865857\pi\)
0.810509 + 0.585727i \(0.199191\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 13.3135 1.58002 0.790012 0.613092i \(-0.210074\pi\)
0.790012 + 0.613092i \(0.210074\pi\)
\(72\) 0 0
\(73\) 0.720214 1.24745i 0.0842947 0.146003i −0.820796 0.571222i \(-0.806470\pi\)
0.905090 + 0.425219i \(0.139803\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 9.33369 4.07529i 1.06367 0.464423i
\(78\) 0 0
\(79\) −3.55390 6.15554i −0.399845 0.692552i 0.593861 0.804567i \(-0.297603\pi\)
−0.993706 + 0.112015i \(0.964269\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 7.98089 0.876016 0.438008 0.898971i \(-0.355684\pi\)
0.438008 + 0.898971i \(0.355684\pi\)
\(84\) 0 0
\(85\) 4.53590 0.491987
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 3.62442 + 6.27768i 0.384188 + 0.665432i 0.991656 0.128911i \(-0.0411483\pi\)
−0.607469 + 0.794344i \(0.707815\pi\)
\(90\) 0 0
\(91\) −10.3758 7.65326i −1.08767 0.802279i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.02278 1.77151i 0.104935 0.181753i
\(96\) 0 0
\(97\) 12.1629 1.23496 0.617479 0.786587i \(-0.288154\pi\)
0.617479 + 0.786587i \(0.288154\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 5.77412 10.0011i 0.574546 0.995143i −0.421545 0.906808i \(-0.638512\pi\)
0.996091 0.0883353i \(-0.0281547\pi\)
\(102\) 0 0
\(103\) −4.02756 6.97594i −0.396847 0.687360i 0.596488 0.802622i \(-0.296562\pi\)
−0.993335 + 0.115263i \(0.963229\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.02367 1.77305i −0.0989622 0.171408i 0.812293 0.583249i \(-0.198219\pi\)
−0.911255 + 0.411842i \(0.864886\pi\)
\(108\) 0 0
\(109\) −4.29779 + 7.44399i −0.411654 + 0.713005i −0.995071 0.0991678i \(-0.968382\pi\)
0.583417 + 0.812173i \(0.301715\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.260828 0.0245366 0.0122683 0.999925i \(-0.496095\pi\)
0.0122683 + 0.999925i \(0.496095\pi\)
\(114\) 0 0
\(115\) −2.70838 + 4.69105i −0.252558 + 0.437442i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 15.0238 6.55974i 1.37723 0.601331i
\(120\) 0 0
\(121\) −1.90898 3.30645i −0.173544 0.300587i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 6.92820 0.619677
\(126\) 0 0
\(127\) −3.15059 −0.279570 −0.139785 0.990182i \(-0.544641\pi\)
−0.139785 + 0.990182i \(0.544641\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1.17337 2.03234i −0.102518 0.177566i 0.810204 0.586149i \(-0.199357\pi\)
−0.912721 + 0.408582i \(0.866023\pi\)
\(132\) 0 0
\(133\) 0.825738 7.34674i 0.0716006 0.637043i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.28117 10.8793i 0.536637 0.929483i −0.462445 0.886648i \(-0.653028\pi\)
0.999082 0.0428346i \(-0.0136389\pi\)
\(138\) 0 0
\(139\) 4.48777 0.380648 0.190324 0.981721i \(-0.439046\pi\)
0.190324 + 0.981721i \(0.439046\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −9.37925 + 16.2453i −0.784332 + 1.35850i
\(144\) 0 0
\(145\) 3.58146 + 6.20327i 0.297424 + 0.515154i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.63397 2.83013i −0.133860 0.231853i 0.791301 0.611427i \(-0.209404\pi\)
−0.925162 + 0.379574i \(0.876071\pi\)
\(150\) 0 0
\(151\) −0.307345 + 0.532338i −0.0250114 + 0.0433210i −0.878260 0.478183i \(-0.841296\pi\)
0.853249 + 0.521504i \(0.174629\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4.62181 0.371233
\(156\) 0 0
\(157\) −1.65326 + 2.86353i −0.131944 + 0.228534i −0.924426 0.381361i \(-0.875455\pi\)
0.792482 + 0.609896i \(0.208789\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −2.18660 + 19.4545i −0.172328 + 1.53323i
\(162\) 0 0
\(163\) 0.241607 + 0.418475i 0.0189241 + 0.0327775i 0.875332 0.483522i \(-0.160643\pi\)
−0.856408 + 0.516299i \(0.827309\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −20.7515 −1.60580 −0.802900 0.596114i \(-0.796711\pi\)
−0.802900 + 0.596114i \(0.796711\pi\)
\(168\) 0 0
\(169\) 10.7469 0.826688
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −12.2907 21.2882i −0.934447 1.61851i −0.775617 0.631204i \(-0.782561\pi\)
−0.158830 0.987306i \(-0.550772\pi\)
\(174\) 0 0
\(175\) 10.8241 4.72606i 0.818227 0.357256i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −10.8924 + 18.8661i −0.814134 + 1.41012i 0.0958144 + 0.995399i \(0.469454\pi\)
−0.909948 + 0.414722i \(0.863879\pi\)
\(180\) 0 0
\(181\) −6.54046 −0.486148 −0.243074 0.970008i \(-0.578156\pi\)
−0.243074 + 0.970008i \(0.578156\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2.06574 + 3.57796i −0.151876 + 0.263057i
\(186\) 0 0
\(187\) −11.9258 20.6560i −0.872099 1.51052i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −7.67954 13.3013i −0.555672 0.962452i −0.997851 0.0655251i \(-0.979128\pi\)
0.442179 0.896927i \(-0.354206\pi\)
\(192\) 0 0
\(193\) −9.47861 + 16.4174i −0.682285 + 1.18175i 0.291997 + 0.956419i \(0.405680\pi\)
−0.974282 + 0.225333i \(0.927653\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −8.26295 −0.588711 −0.294356 0.955696i \(-0.595105\pi\)
−0.294356 + 0.955696i \(0.595105\pi\)
\(198\) 0 0
\(199\) 6.75490 11.6998i 0.478842 0.829378i −0.520864 0.853640i \(-0.674390\pi\)
0.999706 + 0.0242614i \(0.00772340\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 20.8336 + 15.3671i 1.46223 + 1.07856i
\(204\) 0 0
\(205\) 0.550015 + 0.952654i 0.0384147 + 0.0665363i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −10.7564 −0.744034
\(210\) 0 0
\(211\) −6.87552 −0.473330 −0.236665 0.971591i \(-0.576054\pi\)
−0.236665 + 0.971591i \(0.576054\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −4.45194 7.71098i −0.303620 0.525885i
\(216\) 0 0
\(217\) 15.3084 6.68399i 1.03920 0.453739i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −15.0972 + 26.1491i −1.01555 + 1.75898i
\(222\) 0 0
\(223\) −13.9809 −0.936229 −0.468115 0.883668i \(-0.655067\pi\)
−0.468115 + 0.883668i \(0.655067\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 7.54912 13.0755i 0.501053 0.867849i −0.498946 0.866633i \(-0.666280\pi\)
0.999999 0.00121627i \(-0.000387152\pi\)
\(228\) 0 0
\(229\) 5.28367 + 9.15159i 0.349155 + 0.604754i 0.986100 0.166155i \(-0.0531354\pi\)
−0.636945 + 0.770910i \(0.719802\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.740716 + 1.28296i 0.0485259 + 0.0840493i 0.889268 0.457386i \(-0.151214\pi\)
−0.840742 + 0.541436i \(0.817881\pi\)
\(234\) 0 0
\(235\) 2.16471 3.74938i 0.141210 0.244583i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −6.88964 −0.445653 −0.222827 0.974858i \(-0.571528\pi\)
−0.222827 + 0.974858i \(0.571528\pi\)
\(240\) 0 0
\(241\) −14.1578 + 24.5221i −0.911985 + 1.57960i −0.100729 + 0.994914i \(0.532118\pi\)
−0.811256 + 0.584691i \(0.801216\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −3.48339 + 3.75833i −0.222545 + 0.240111i
\(246\) 0 0
\(247\) 6.80841 + 11.7925i 0.433209 + 0.750339i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −5.93532 −0.374634 −0.187317 0.982299i \(-0.559979\pi\)
−0.187317 + 0.982299i \(0.559979\pi\)
\(252\) 0 0
\(253\) 28.4834 1.79074
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3.99044 6.91165i −0.248917 0.431137i 0.714309 0.699831i \(-0.246741\pi\)
−0.963226 + 0.268694i \(0.913408\pi\)
\(258\) 0 0
\(259\) −1.66776 + 14.8384i −0.103630 + 0.922013i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −9.97982 + 17.2856i −0.615382 + 1.06587i 0.374935 + 0.927051i \(0.377665\pi\)
−0.990317 + 0.138822i \(0.955668\pi\)
\(264\) 0 0
\(265\) −9.41676 −0.578467
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −5.50267 + 9.53090i −0.335504 + 0.581109i −0.983581 0.180465i \(-0.942240\pi\)
0.648078 + 0.761574i \(0.275573\pi\)
\(270\) 0 0
\(271\) 10.9652 + 18.9922i 0.666086 + 1.15370i 0.978990 + 0.203910i \(0.0653651\pi\)
−0.312903 + 0.949785i \(0.601302\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −8.59208 14.8819i −0.518122 0.897414i
\(276\) 0 0
\(277\) 8.27412 14.3312i 0.497143 0.861078i −0.502851 0.864373i \(-0.667716\pi\)
0.999995 + 0.00329530i \(0.00104893\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 24.8250 1.48093 0.740466 0.672093i \(-0.234605\pi\)
0.740466 + 0.672093i \(0.234605\pi\)
\(282\) 0 0
\(283\) 2.23205 3.86603i 0.132682 0.229811i −0.792028 0.610485i \(-0.790975\pi\)
0.924709 + 0.380674i \(0.124308\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3.19948 + 2.35997i 0.188859 + 0.139304i
\(288\) 0 0
\(289\) −10.6962 18.5263i −0.629185 1.08978i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −9.20327 −0.537661 −0.268830 0.963188i \(-0.586637\pi\)
−0.268830 + 0.963188i \(0.586637\pi\)
\(294\) 0 0
\(295\) 4.67437 0.272152
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −18.0290 31.2272i −1.04264 1.80591i
\(300\) 0 0
\(301\) −25.8973 19.1021i −1.49269 1.10103i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −4.61030 + 7.98528i −0.263985 + 0.457236i
\(306\) 0 0
\(307\) −33.8900 −1.93420 −0.967102 0.254390i \(-0.918125\pi\)
−0.967102 + 0.254390i \(0.918125\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 3.68999 6.39124i 0.209240 0.362414i −0.742235 0.670139i \(-0.766234\pi\)
0.951475 + 0.307725i \(0.0995677\pi\)
\(312\) 0 0
\(313\) −0.657974 1.13964i −0.0371909 0.0644165i 0.846831 0.531862i \(-0.178508\pi\)
−0.884022 + 0.467446i \(0.845174\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.59452 + 6.22588i 0.201888 + 0.349680i 0.949137 0.314864i \(-0.101959\pi\)
−0.747249 + 0.664545i \(0.768626\pi\)
\(318\) 0 0
\(319\) 18.8327 32.6193i 1.05443 1.82633i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −17.3139 −0.963369
\(324\) 0 0
\(325\) −10.8770 + 18.8395i −0.603346 + 1.04503i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.74767 15.5493i 0.0963519 0.857260i
\(330\) 0 0
\(331\) −2.41126 4.17643i −0.132535 0.229557i 0.792118 0.610368i \(-0.208978\pi\)
−0.924653 + 0.380811i \(0.875645\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.22239 −0.0667861
\(336\) 0 0
\(337\) −12.7561 −0.694867 −0.347434 0.937705i \(-0.612947\pi\)
−0.347434 + 0.937705i \(0.612947\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −12.1517 21.0473i −0.658049 1.13977i
\(342\) 0 0
\(343\) −6.10247 + 17.4860i −0.329502 + 0.944155i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −15.4641 + 26.7846i −0.830156 + 1.43787i 0.0677573 + 0.997702i \(0.478416\pi\)
−0.897914 + 0.440171i \(0.854918\pi\)
\(348\) 0 0
\(349\) 17.2368 0.922667 0.461334 0.887227i \(-0.347371\pi\)
0.461334 + 0.887227i \(0.347371\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −5.76350 + 9.98267i −0.306760 + 0.531324i −0.977652 0.210231i \(-0.932578\pi\)
0.670892 + 0.741555i \(0.265912\pi\)
\(354\) 0 0
\(355\) 4.87308 + 8.44043i 0.258636 + 0.447971i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.02367 + 1.77305i 0.0540274 + 0.0935782i 0.891774 0.452481i \(-0.149461\pi\)
−0.837747 + 0.546059i \(0.816128\pi\)
\(360\) 0 0
\(361\) 5.59597 9.69250i 0.294525 0.510132i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.05447 0.0551933
\(366\) 0 0
\(367\) 12.5933 21.8122i 0.657365 1.13859i −0.323931 0.946081i \(-0.605004\pi\)
0.981295 0.192508i \(-0.0616623\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −31.1903 + 13.6184i −1.61932 + 0.707030i
\(372\) 0 0
\(373\) 4.73677 + 8.20432i 0.245260 + 0.424804i 0.962205 0.272327i \(-0.0877932\pi\)
−0.716944 + 0.697130i \(0.754460\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −47.6818 −2.45574
\(378\) 0 0
\(379\) −21.6176 −1.11042 −0.555211 0.831710i \(-0.687362\pi\)
−0.555211 + 0.831710i \(0.687362\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 11.9045 + 20.6193i 0.608293 + 1.05359i 0.991522 + 0.129941i \(0.0414788\pi\)
−0.383229 + 0.923654i \(0.625188\pi\)
\(384\) 0 0
\(385\) 6.00000 + 4.42566i 0.305788 + 0.225552i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −0.206600 + 0.357841i −0.0104750 + 0.0181433i −0.871215 0.490901i \(-0.836668\pi\)
0.860740 + 0.509044i \(0.170001\pi\)
\(390\) 0 0
\(391\) 45.8480 2.31863
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.60164 4.50617i 0.130903 0.226730i
\(396\) 0 0
\(397\) −5.14720 8.91521i −0.258331 0.447442i 0.707464 0.706749i \(-0.249839\pi\)
−0.965795 + 0.259307i \(0.916506\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −0.225884 0.391242i −0.0112801 0.0195377i 0.860330 0.509737i \(-0.170257\pi\)
−0.871610 + 0.490199i \(0.836924\pi\)
\(402\) 0 0
\(403\) −15.3831 + 26.6444i −0.766289 + 1.32725i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 21.7249 1.07686
\(408\) 0 0
\(409\) −2.04061 + 3.53445i −0.100902 + 0.174767i −0.912056 0.410065i \(-0.865506\pi\)
0.811155 + 0.584832i \(0.198839\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 15.4825 6.76000i 0.761844 0.332638i
\(414\) 0 0
\(415\) 2.92121 + 5.05968i 0.143396 + 0.248370i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −9.14347 −0.446688 −0.223344 0.974740i \(-0.571697\pi\)
−0.223344 + 0.974740i \(0.571697\pi\)
\(420\) 0 0
\(421\) 8.30574 0.404797 0.202398 0.979303i \(-0.435126\pi\)
0.202398 + 0.979303i \(0.435126\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −13.8301 23.9545i −0.670860 1.16196i
\(426\) 0 0
\(427\) −3.72211 + 33.1163i −0.180125 + 1.60261i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −11.6331 + 20.1491i −0.560346 + 0.970548i 0.437120 + 0.899403i \(0.355998\pi\)
−0.997466 + 0.0711444i \(0.977335\pi\)
\(432\) 0 0
\(433\) 11.7989 0.567017 0.283508 0.958970i \(-0.408502\pi\)
0.283508 + 0.958970i \(0.408502\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 10.3381 17.9061i 0.494537 0.856564i
\(438\) 0 0
\(439\) 0.447550 + 0.775179i 0.0213604 + 0.0369973i 0.876508 0.481387i \(-0.159867\pi\)
−0.855148 + 0.518385i \(0.826534\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 8.02990 + 13.9082i 0.381512 + 0.660799i 0.991279 0.131783i \(-0.0420701\pi\)
−0.609766 + 0.792581i \(0.708737\pi\)
\(444\) 0 0
\(445\) −2.65326 + 4.59558i −0.125777 + 0.217851i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 27.6411 1.30447 0.652233 0.758018i \(-0.273832\pi\)
0.652233 + 0.758018i \(0.273832\pi\)
\(450\) 0 0
\(451\) 2.89220 5.00943i 0.136188 0.235885i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.05418 9.37925i 0.0494208 0.439706i
\(456\) 0 0
\(457\) 2.93087 + 5.07642i 0.137100 + 0.237465i 0.926398 0.376546i \(-0.122888\pi\)
−0.789297 + 0.614011i \(0.789555\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −26.4573 −1.23224 −0.616120 0.787652i \(-0.711296\pi\)
−0.616120 + 0.787652i \(0.711296\pi\)
\(462\) 0 0
\(463\) 0.727834 0.0338253 0.0169126 0.999857i \(-0.494616\pi\)
0.0169126 + 0.999857i \(0.494616\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0.536961 + 0.930044i 0.0248476 + 0.0430373i 0.878182 0.478327i \(-0.158757\pi\)
−0.853334 + 0.521364i \(0.825423\pi\)
\(468\) 0 0
\(469\) −4.04880 + 1.76779i −0.186956 + 0.0816292i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −23.4100 + 40.5474i −1.07640 + 1.86437i
\(474\) 0 0
\(475\) −12.4740 −0.572346
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 5.03340 8.71811i 0.229982 0.398340i −0.727821 0.685768i \(-0.759467\pi\)
0.957802 + 0.287427i \(0.0928000\pi\)
\(480\) 0 0
\(481\) −13.7511 23.8176i −0.626997 1.08599i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 4.45194 + 7.71098i 0.202152 + 0.350138i
\(486\) 0 0
\(487\) 0.964491 1.67055i 0.0437052 0.0756997i −0.843345 0.537372i \(-0.819417\pi\)
0.887051 + 0.461672i \(0.152750\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −6.89510 −0.311172 −0.155586 0.987822i \(-0.549726\pi\)
−0.155586 + 0.987822i \(0.549726\pi\)
\(492\) 0 0
\(493\) 30.3139 52.5051i 1.36527 2.36471i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 28.3471 + 20.9091i 1.27154 + 0.937901i
\(498\) 0 0
\(499\) −6.31796 10.9430i −0.282831 0.489878i 0.689250 0.724524i \(-0.257940\pi\)
−0.972081 + 0.234646i \(0.924607\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −25.9493 −1.15702 −0.578511 0.815674i \(-0.696366\pi\)
−0.578511 + 0.815674i \(0.696366\pi\)
\(504\) 0 0
\(505\) 8.45389 0.376193
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 11.1551 + 19.3213i 0.494443 + 0.856401i 0.999979 0.00640446i \(-0.00203862\pi\)
−0.505536 + 0.862805i \(0.668705\pi\)
\(510\) 0 0
\(511\) 3.49262 1.52495i 0.154504 0.0674600i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2.94838 5.10674i 0.129921 0.225030i
\(516\) 0 0
\(517\) −22.7657 −1.00124
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 5.36164 9.28663i 0.234898 0.406855i −0.724345 0.689437i \(-0.757858\pi\)
0.959243 + 0.282583i \(0.0911912\pi\)
\(522\) 0 0
\(523\) −13.9017 24.0785i −0.607879 1.05288i −0.991589 0.129424i \(-0.958687\pi\)
0.383710 0.923454i \(-0.374646\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −19.5597 33.8785i −0.852036 1.47577i
\(528\) 0 0
\(529\) −15.8758 + 27.4976i −0.690250 + 1.19555i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −7.32263 −0.317178
\(534\) 0 0
\(535\) 0.749381 1.29797i 0.0323985 0.0561159i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 26.2736 + 5.98161i 1.13168 + 0.257646i
\(540\) 0 0
\(541\) −9.51451 16.4796i −0.409061 0.708514i 0.585724 0.810510i \(-0.300810\pi\)
−0.994785 + 0.101997i \(0.967477\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −6.29240 −0.269537
\(546\) 0 0
\(547\) −27.9233 −1.19392 −0.596958 0.802273i \(-0.703624\pi\)
−0.596958 + 0.802273i \(0.703624\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −13.6707 23.6783i −0.582391 1.00873i
\(552\) 0 0
\(553\) 2.10042 18.6878i 0.0893189 0.794687i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −8.17687 + 14.1628i −0.346465 + 0.600095i −0.985619 0.168984i \(-0.945951\pi\)
0.639154 + 0.769079i \(0.279285\pi\)
\(558\) 0 0
\(559\) 59.2709 2.50689
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 10.8817 18.8477i 0.458611 0.794338i −0.540277 0.841487i \(-0.681680\pi\)
0.998888 + 0.0471498i \(0.0150138\pi\)
\(564\) 0 0
\(565\) 0.0954697 + 0.165358i 0.00401644 + 0.00695668i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −8.45105 14.6376i −0.354286 0.613642i 0.632709 0.774389i \(-0.281943\pi\)
−0.986996 + 0.160748i \(0.948610\pi\)
\(570\) 0 0
\(571\) 3.31123 5.73522i 0.138571 0.240012i −0.788385 0.615182i \(-0.789082\pi\)
0.926956 + 0.375170i \(0.122416\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 33.0318 1.37752
\(576\) 0 0
\(577\) −16.7631 + 29.0346i −0.697857 + 1.20872i 0.271351 + 0.962481i \(0.412530\pi\)
−0.969208 + 0.246244i \(0.920804\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 16.9929 + 12.5341i 0.704983 + 0.520003i
\(582\) 0 0
\(583\) 24.7585 + 42.8830i 1.02539 + 1.77603i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 11.7705 0.485820 0.242910 0.970049i \(-0.421898\pi\)
0.242910 + 0.970049i \(0.421898\pi\)
\(588\) 0 0
\(589\) −17.6418 −0.726917
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −16.6472 28.8338i −0.683619 1.18406i −0.973869 0.227111i \(-0.927072\pi\)
0.290250 0.956951i \(-0.406261\pi\)
\(594\) 0 0
\(595\) 9.65782 + 7.12370i 0.395932 + 0.292043i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −3.51312 + 6.08490i −0.143542 + 0.248622i −0.928828 0.370511i \(-0.879183\pi\)
0.785286 + 0.619133i \(0.212516\pi\)
\(600\) 0 0
\(601\) −43.0389 −1.75559 −0.877797 0.479033i \(-0.840987\pi\)
−0.877797 + 0.479033i \(0.840987\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.39747 2.42049i 0.0568153 0.0984070i
\(606\) 0 0
\(607\) −0.526497 0.911919i −0.0213698 0.0370137i 0.855143 0.518393i \(-0.173469\pi\)
−0.876513 + 0.481379i \(0.840136\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 14.4099 + 24.9587i 0.582963 + 1.00972i
\(612\) 0 0
\(613\) −4.12353 + 7.14216i −0.166548 + 0.288469i −0.937204 0.348782i \(-0.886595\pi\)
0.770656 + 0.637251i \(0.219929\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −16.8441 −0.678117 −0.339058 0.940765i \(-0.610108\pi\)
−0.339058 + 0.940765i \(0.610108\pi\)
\(618\) 0 0
\(619\) −13.0215 + 22.5539i −0.523378 + 0.906518i 0.476251 + 0.879309i \(0.341995\pi\)
−0.999630 + 0.0272087i \(0.991338\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2.14210 + 19.0586i −0.0858213 + 0.763567i
\(624\) 0 0
\(625\) −8.62436 14.9378i −0.344974 0.597513i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 34.9692 1.39431
\(630\) 0 0
\(631\) 17.1124 0.681232 0.340616 0.940202i \(-0.389364\pi\)
0.340616 + 0.940202i \(0.389364\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.15320 1.99739i −0.0457632 0.0792641i
\(636\) 0 0
\(637\) −10.0724 32.5906i −0.399085 1.29129i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −10.3399 + 17.9093i −0.408402 + 0.707373i −0.994711 0.102714i \(-0.967247\pi\)
0.586309 + 0.810088i \(0.300581\pi\)
\(642\) 0 0
\(643\) 11.3012 0.445675 0.222837 0.974856i \(-0.428468\pi\)
0.222837 + 0.974856i \(0.428468\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 7.31351 12.6674i 0.287524 0.498006i −0.685694 0.727890i \(-0.740501\pi\)
0.973218 + 0.229884i \(0.0738346\pi\)
\(648\) 0 0
\(649\) −12.2898 21.2866i −0.482418 0.835573i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −8.24261 14.2766i −0.322558 0.558687i 0.658457 0.752618i \(-0.271209\pi\)
−0.981015 + 0.193931i \(0.937876\pi\)
\(654\) 0 0
\(655\) 0.858967 1.48777i 0.0335626 0.0581322i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 44.5836 1.73673 0.868365 0.495926i \(-0.165171\pi\)
0.868365 + 0.495926i \(0.165171\pi\)
\(660\) 0 0
\(661\) −16.5364 + 28.6419i −0.643191 + 1.11404i 0.341525 + 0.939873i \(0.389057\pi\)
−0.984716 + 0.174167i \(0.944277\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 4.95989 2.16560i 0.192336 0.0839783i
\(666\) 0 0
\(667\) 36.2007 + 62.7015i 1.40170 + 2.42781i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 48.4856 1.87176
\(672\) 0 0
\(673\) 47.2968 1.82316 0.911580 0.411124i \(-0.134864\pi\)
0.911580 + 0.411124i \(0.134864\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 12.7585 + 22.0984i 0.490349 + 0.849309i 0.999938 0.0111083i \(-0.00353596\pi\)
−0.509589 + 0.860418i \(0.670203\pi\)
\(678\) 0 0
\(679\) 25.8973 + 19.1021i 0.993845 + 0.733070i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 21.4248 37.1089i 0.819798 1.41993i −0.0860333 0.996292i \(-0.527419\pi\)
0.905831 0.423639i \(-0.139248\pi\)
\(684\) 0 0
\(685\) 9.19628 0.351372
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 31.3425 54.2868i 1.19406 2.06816i
\(690\) 0 0
\(691\) 4.87575 + 8.44505i 0.185482 + 0.321265i 0.943739 0.330691i \(-0.107282\pi\)
−0.758257 + 0.651956i \(0.773949\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.64264 + 2.84514i 0.0623089 + 0.107922i
\(696\) 0 0
\(697\) 4.65538 8.06336i 0.176335 0.305422i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 22.2174 0.839139 0.419570 0.907723i \(-0.362181\pi\)
0.419570 + 0.907723i \(0.362181\pi\)
\(702\) 0 0
\(703\) 7.88507 13.6574i 0.297391 0.515097i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 28.0011 12.2259i 1.05309 0.459802i
\(708\) 0 0
\(709\) −10.9439 18.9554i −0.411008 0.711886i 0.583992 0.811759i \(-0.301490\pi\)
−0.995000 + 0.0998727i \(0.968156\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 46.7164 1.74954
\(714\) 0 0
\(715\) −13.7322 −0.513554
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −23.1523 40.1010i −0.863435 1.49551i −0.868593 0.495527i \(-0.834975\pi\)
0.00515726 0.999987i \(-0.498358\pi\)
\(720\) 0 0
\(721\) 2.38036 21.1785i 0.0886492 0.788728i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 21.8400 37.8280i 0.811118 1.40490i
\(726\) 0 0
\(727\) 25.3662 0.940780 0.470390 0.882459i \(-0.344113\pi\)
0.470390 + 0.882459i \(0.344113\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −37.6817 + 65.2666i −1.39371 + 2.41397i
\(732\) 0 0
\(733\) 11.4484 + 19.8292i 0.422856 + 0.732407i 0.996217 0.0868950i \(-0.0276944\pi\)
−0.573362 + 0.819302i \(0.694361\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3.21389 + 5.56663i 0.118385 + 0.205049i
\(738\) 0 0
\(739\) −4.90898 + 8.50261i −0.180580 + 0.312773i −0.942078 0.335393i \(-0.891131\pi\)
0.761498 + 0.648167i \(0.224464\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 12.4118 0.455343 0.227672 0.973738i \(-0.426889\pi\)
0.227672 + 0.973738i \(0.426889\pi\)
\(744\) 0 0
\(745\) 1.19615 2.07180i 0.0438236 0.0759048i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0.605009 5.38287i 0.0221065 0.196686i
\(750\) 0 0
\(751\) 18.5979 + 32.2124i 0.678646 + 1.17545i 0.975389 + 0.220491i \(0.0707660\pi\)
−0.296743 + 0.954957i \(0.595901\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −0.449985 −0.0163766
\(756\) 0 0
\(757\) −44.3035 −1.61024 −0.805119 0.593113i \(-0.797899\pi\)
−0.805119 + 0.593113i \(0.797899\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 2.25383 + 3.90375i 0.0817014 + 0.141511i 0.903981 0.427573i \(-0.140631\pi\)
−0.822279 + 0.569084i \(0.807298\pi\)
\(762\) 0 0
\(763\) −20.8417 + 9.09997i −0.754522 + 0.329441i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −15.5581 + 26.9474i −0.561769 + 0.973013i
\(768\) 0 0
\(769\) −38.9328 −1.40395 −0.701976 0.712201i \(-0.747698\pi\)
−0.701976 + 0.712201i \(0.747698\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −8.57280 + 14.8485i −0.308342 + 0.534064i −0.978000 0.208606i \(-0.933107\pi\)
0.669658 + 0.742670i \(0.266441\pi\)
\(774\) 0 0
\(775\) −14.0921 24.4082i −0.506202 0.876768i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.09945 3.63635i −0.0752205 0.130286i
\(780\) 0 0
\(781\) 25.6246 44.3831i 0.916920 1.58815i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −2.42054 −0.0863927
\(786\) 0 0
\(787\) 13.6551 23.6514i 0.486754 0.843082i −0.513131 0.858311i \(-0.671514\pi\)
0.999884 + 0.0152288i \(0.00484765\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0.555354 + 0.409635i 0.0197461 + 0.0145649i
\(792\) 0 0
\(793\) −30.6897 53.1560i −1.08982 1.88763i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −4.56201 −0.161595 −0.0807973 0.996731i \(-0.525747\pi\)
−0.0807973 + 0.996731i \(0.525747\pi\)
\(798\) 0 0
\(799\) −36.6446 −1.29639
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −2.77240 4.80194i −0.0978359 0.169457i
\(804\) 0 0