Properties

Label 1512.2.s.m.1297.4
Level $1512$
Weight $2$
Character 1512.1297
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 1297.4
Root \(0.295509 + 2.62920i\) of defining polynomial
Character \(\chi\) \(=\) 1512.1297
Dual form 1512.2.s.m.865.4

$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

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

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 −0.772498 0.635017i \(-0.780993\pi\)
0.936190 + 0.351495i \(0.114326\pi\)
\(6\) 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 0.995441 + 0.0953782i \(0.0304061\pi\)
−0.415121 + 0.909766i \(0.636261\pi\)
\(12\) 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 0.947147 + 0.320799i \(0.103951\pi\)
−0.195753 + 0.980653i \(0.562715\pi\)
\(18\) 0 0
\(19\) −1.39715 + 2.41993i −0.320527 + 0.555169i −0.980597 0.196035i \(-0.937193\pi\)
0.660070 + 0.751204i \(0.270527\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.69971 6.40809i 0.771443 1.33618i −0.165328 0.986239i \(-0.552868\pi\)
0.936772 0.349941i \(-0.113798\pi\)
\(24\) 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 0.996863 + 0.0791414i \(0.0252179\pi\)
−0.429893 + 0.902880i \(0.641449\pi\)
\(32\) 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 −0.535242 0.844699i \(-0.679780\pi\)
0.999152 + 0.0411839i \(0.0131130\pi\)
\(38\) 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 −0.996988 0.0775554i \(-0.975289\pi\)
0.565659 + 0.824639i \(0.308622\pi\)
\(48\) 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 −0.847456 0.530865i \(-0.821867\pi\)
−0.0360142 0.999351i \(-0.511466\pi\)
\(54\) 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 0.995496 0.0948008i \(-0.0302214\pi\)
−0.579848 + 0.814725i \(0.696888\pi\)
\(60\) 0 0
\(61\) 6.29779 10.9081i 0.806349 1.39664i −0.109027 0.994039i \(-0.534774\pi\)
0.915376 0.402599i \(-0.131893\pi\)
\(62\) 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 0.810509 0.585727i \(-0.199191\pi\)
−0.912509 + 0.409058i \(0.865857\pi\)
\(68\) 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 0.905090 0.425219i \(-0.139803\pi\)
−0.820796 + 0.571222i \(0.806470\pi\)
\(74\) 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 −0.993706 0.112015i \(-0.964269\pi\)
0.593861 + 0.804567i \(0.297603\pi\)
\(80\) 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 −0.607469 0.794344i \(-0.707815\pi\)
0.991656 + 0.128911i \(0.0411483\pi\)
\(90\) 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 0.996091 + 0.0883353i \(0.0281547\pi\)
−0.421545 + 0.906808i \(0.638512\pi\)
\(102\) 0 0
\(103\) −4.02756 + 6.97594i −0.396847 + 0.687360i −0.993335 0.115263i \(-0.963229\pi\)
0.596488 + 0.802622i \(0.296562\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.02367 + 1.77305i −0.0989622 + 0.171408i −0.911255 0.411842i \(-0.864886\pi\)
0.812293 + 0.583249i \(0.198219\pi\)
\(108\) 0 0
\(109\) −4.29779 7.44399i −0.411654 0.713005i 0.583417 0.812173i \(-0.301715\pi\)
−0.995071 + 0.0991678i \(0.968382\pi\)
\(110\) 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 −0.912721 0.408582i \(-0.866023\pi\)
0.810204 + 0.586149i \(0.199357\pi\)
\(132\) 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 0.999082 + 0.0428346i \(0.0136389\pi\)
−0.462445 + 0.886648i \(0.653028\pi\)
\(138\) 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 −0.925162 0.379574i \(-0.876071\pi\)
0.791301 + 0.611427i \(0.209404\pi\)
\(150\) 0 0
\(151\) −0.307345 0.532338i −0.0250114 0.0433210i 0.853249 0.521504i \(-0.174629\pi\)
−0.878260 + 0.478183i \(0.841296\pi\)
\(152\) 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 0.792482 0.609896i \(-0.208789\pi\)
−0.924426 + 0.381361i \(0.875455\pi\)
\(158\) 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 −0.856408 0.516299i \(-0.827309\pi\)
0.875332 + 0.483522i \(0.160643\pi\)
\(164\) 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 −0.158830 + 0.987306i \(0.550772\pi\)
−0.775617 + 0.631204i \(0.782561\pi\)
\(174\) 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 −0.909948 0.414722i \(-0.863879\pi\)
0.0958144 0.995399i \(-0.469454\pi\)
\(180\) 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 0.442179 + 0.896927i \(0.354206\pi\)
−0.997851 + 0.0655251i \(0.979128\pi\)
\(192\) 0 0
\(193\) −9.47861 16.4174i −0.682285 1.18175i −0.974282 0.225333i \(-0.927653\pi\)
0.291997 0.956419i \(-0.405680\pi\)
\(194\) 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 0.999706 0.0242614i \(-0.00772340\pi\)
−0.520864 + 0.853640i \(0.674390\pi\)
\(200\) 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 0.999999 + 0.00121627i \(0.000387152\pi\)
−0.498946 + 0.866633i \(0.666280\pi\)
\(228\) 0 0
\(229\) 5.28367 9.15159i 0.349155 0.604754i −0.636945 0.770910i \(-0.719802\pi\)
0.986100 + 0.166155i \(0.0531354\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.740716 1.28296i 0.0485259 0.0840493i −0.840742 0.541436i \(-0.817881\pi\)
0.889268 + 0.457386i \(0.151214\pi\)
\(234\) 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 −0.811256 0.584691i \(-0.801216\pi\)
−0.100729 0.994914i \(-0.532118\pi\)
\(242\) 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 −0.963226 0.268694i \(-0.913408\pi\)
0.714309 + 0.699831i \(0.246741\pi\)
\(258\) 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 −0.990317 0.138822i \(-0.955668\pi\)
0.374935 0.927051i \(-0.377665\pi\)
\(264\) 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 0.648078 0.761574i \(-0.275573\pi\)
−0.983581 + 0.180465i \(0.942240\pi\)
\(270\) 0 0
\(271\) 10.9652 18.9922i 0.666086 1.15370i −0.312903 0.949785i \(-0.601302\pi\)
0.978990 0.203910i \(-0.0653651\pi\)
\(272\) 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 0.999995 0.00329530i \(-0.00104893\pi\)
−0.502851 + 0.864373i \(0.667716\pi\)
\(278\) 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 0.924709 0.380674i \(-0.124308\pi\)
−0.792028 + 0.610485i \(0.790975\pi\)
\(284\) 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 0.951475 0.307725i \(-0.0995677\pi\)
−0.742235 + 0.670139i \(0.766234\pi\)
\(312\) 0 0
\(313\) −0.657974 + 1.13964i −0.0371909 + 0.0644165i −0.884022 0.467446i \(-0.845174\pi\)
0.846831 + 0.531862i \(0.178508\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.59452 6.22588i 0.201888 0.349680i −0.747249 0.664545i \(-0.768626\pi\)
0.949137 + 0.314864i \(0.101959\pi\)
\(318\) 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 −0.924653 0.380811i \(-0.875645\pi\)
0.792118 + 0.610368i \(0.208978\pi\)
\(332\) 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 −0.897914 0.440171i \(-0.854918\pi\)
0.0677573 0.997702i \(-0.478416\pi\)
\(348\) 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 0.670892 0.741555i \(-0.265912\pi\)
−0.977652 + 0.210231i \(0.932578\pi\)
\(354\) 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 −0.837747 0.546059i \(-0.816128\pi\)
0.891774 + 0.452481i \(0.149461\pi\)
\(360\) 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 0.981295 + 0.192508i \(0.0616623\pi\)
−0.323931 + 0.946081i \(0.605004\pi\)
\(368\) 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 −0.716944 0.697130i \(-0.754460\pi\)
0.962205 + 0.272327i \(0.0877932\pi\)
\(374\) 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 −0.383229 0.923654i \(-0.625188\pi\)
0.991522 0.129941i \(-0.0414788\pi\)
\(384\) 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 0.860740 0.509044i \(-0.170001\pi\)
−0.871215 + 0.490901i \(0.836668\pi\)
\(390\) 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 −0.965795 0.259307i \(-0.916506\pi\)
0.707464 + 0.706749i \(0.249839\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −0.225884 + 0.391242i −0.0112801 + 0.0195377i −0.871610 0.490199i \(-0.836924\pi\)
0.860330 + 0.509737i \(0.170257\pi\)
\(402\) 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 0.811155 0.584832i \(-0.198839\pi\)
−0.912056 + 0.410065i \(0.865506\pi\)
\(410\) 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 −0.997466 0.0711444i \(-0.977335\pi\)
0.437120 0.899403i \(-0.355998\pi\)
\(432\) 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 −0.855148 0.518385i \(-0.826534\pi\)
0.876508 + 0.481387i \(0.159867\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 8.02990 13.9082i 0.381512 0.660799i −0.609766 0.792581i \(-0.708737\pi\)
0.991279 + 0.131783i \(0.0420701\pi\)
\(444\) 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 −0.789297 0.614011i \(-0.789555\pi\)
0.926398 + 0.376546i \(0.122888\pi\)
\(458\) 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 −0.853334 0.521364i \(-0.825423\pi\)
0.878182 + 0.478327i \(0.158757\pi\)
\(468\) 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 0.957802 0.287427i \(-0.0928000\pi\)
−0.727821 + 0.685768i \(0.759467\pi\)
\(480\) 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 0.887051 0.461672i \(-0.152750\pi\)
−0.843345 + 0.537372i \(0.819417\pi\)
\(488\) 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 −0.972081 0.234646i \(-0.924607\pi\)
0.689250 + 0.724524i \(0.257940\pi\)
\(500\) 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 −0.505536 0.862805i \(-0.668705\pi\)
0.999979 + 0.00640446i \(0.00203862\pi\)
\(510\) 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 0.959243 0.282583i \(-0.0911912\pi\)
−0.724345 + 0.689437i \(0.757858\pi\)
\(522\) 0 0
\(523\) −13.9017 + 24.0785i −0.607879 + 1.05288i 0.383710 + 0.923454i \(0.374646\pi\)
−0.991589 + 0.129424i \(0.958687\pi\)
\(524\) 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 −0.994785 0.101997i \(-0.967477\pi\)
0.585724 + 0.810510i \(0.300810\pi\)
\(542\) 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 0.639154 0.769079i \(-0.279285\pi\)
−0.985619 + 0.168984i \(0.945951\pi\)
\(558\) 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 0.998888 0.0471498i \(-0.0150138\pi\)
−0.540277 + 0.841487i \(0.681680\pi\)
\(564\) 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 −0.986996 0.160748i \(-0.948610\pi\)
0.632709 + 0.774389i \(0.281943\pi\)
\(570\) 0 0
\(571\) 3.31123 + 5.73522i 0.138571 + 0.240012i 0.926956 0.375170i \(-0.122416\pi\)
−0.788385 + 0.615182i \(0.789082\pi\)
\(572\) 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 −0.969208 0.246244i \(-0.920804\pi\)
0.271351 0.962481i \(-0.412530\pi\)
\(578\) 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 0.290250 + 0.956951i \(0.406261\pi\)
−0.973869 + 0.227111i \(0.927072\pi\)
\(594\) 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 0.785286 0.619133i \(-0.212516\pi\)
−0.928828 + 0.370511i \(0.879183\pi\)
\(600\) 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 −0.876513 0.481379i \(-0.840136\pi\)
0.855143 + 0.518393i \(0.173469\pi\)
\(608\) 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 0.770656 0.637251i \(-0.219929\pi\)
−0.937204 + 0.348782i \(0.886595\pi\)
\(614\) 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 −0.999630 0.0272087i \(-0.991338\pi\)
0.476251 0.879309i \(-0.341995\pi\)
\(620\) 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 0.586309 0.810088i \(-0.300581\pi\)
−0.994711 + 0.102714i \(0.967247\pi\)
\(642\) 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 0.973218 0.229884i \(-0.0738346\pi\)
−0.685694 + 0.727890i \(0.740501\pi\)
\(648\) 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 −0.981015 0.193931i \(-0.937876\pi\)
0.658457 + 0.752618i \(0.271209\pi\)
\(654\) 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 −0.984716 0.174167i \(-0.944277\pi\)
0.341525 0.939873i \(-0.389057\pi\)
\(662\) 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 −0.509589 0.860418i \(-0.670203\pi\)
0.999938 + 0.0111083i \(0.00353596\pi\)
\(678\) 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 0.905831 + 0.423639i \(0.139248\pi\)
−0.0860333 + 0.996292i \(0.527419\pi\)
\(684\) 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 −0.758257 0.651956i \(-0.773949\pi\)
0.943739 + 0.330691i \(0.107282\pi\)
\(692\) 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 −0.995000 0.0998727i \(-0.968156\pi\)
0.583992 + 0.811759i \(0.301490\pi\)
\(710\) 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 0.00515726 + 0.999987i \(0.498358\pi\)
−0.868593 + 0.495527i \(0.834975\pi\)
\(720\) 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 −0.573362 0.819302i \(-0.694361\pi\)
0.996217 + 0.0868950i \(0.0276944\pi\)
\(734\) 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 0.761498 0.648167i \(-0.224464\pi\)
−0.942078 + 0.335393i \(0.891131\pi\)
\(740\) 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 −0.296743 0.954957i \(-0.595901\pi\)
0.975389 0.220491i \(-0.0707660\pi\)
\(752\) 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 −0.822279 0.569084i \(-0.807298\pi\)
0.903981 + 0.427573i \(0.140631\pi\)
\(762\) 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 0.669658 0.742670i \(-0.266441\pi\)
−0.978000 + 0.208606i \(0.933107\pi\)
\(774\) 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 0.999884 0.0152288i \(-0.00484765\pi\)
−0.513131 + 0.858311i \(0.671514\pi\)
\(788\) 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