Properties

Label 1400.2.bh.g.249.3
Level $1400$
Weight $2$
Character 1400.249
Analytic conductor $11.179$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.bh (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1790562830\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 280)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 249.3
Root \(0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1400.249
Dual form 1400.2.bh.g.849.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.358719 + 0.207107i) q^{3} +(-2.09077 + 1.62132i) q^{7} +(-1.41421 - 2.44949i) q^{9} +O(q^{10})\) \(q+(0.358719 + 0.207107i) q^{3} +(-2.09077 + 1.62132i) q^{7} +(-1.41421 - 2.44949i) q^{9} +(-0.414214 + 0.717439i) q^{11} -2.00000i q^{13} +(6.63103 + 3.82843i) q^{17} +(-2.82843 - 4.89898i) q^{19} +(-1.08579 + 0.148586i) q^{21} +(4.83743 - 2.79289i) q^{23} -2.41421i q^{27} +7.82843 q^{29} +(-0.414214 + 0.717439i) q^{31} +(-0.297173 + 0.171573i) q^{33} +(4.89898 - 2.82843i) q^{37} +(0.414214 - 0.717439i) q^{39} +5.82843 q^{41} +6.89949i q^{43} +(10.0951 - 5.82843i) q^{47} +(1.74264 - 6.77962i) q^{49} +(1.58579 + 2.74666i) q^{51} +(-4.89898 - 2.82843i) q^{53} -2.34315i q^{57} +(-2.00000 + 3.46410i) q^{59} +(-3.32843 - 5.76500i) q^{61} +(6.92820 + 2.82843i) q^{63} +(11.1713 + 6.44975i) q^{67} +2.31371 q^{69} -12.0000 q^{71} +(3.16693 + 1.82843i) q^{73} +(-0.297173 - 2.17157i) q^{77} +(-2.00000 - 3.46410i) q^{79} +(-3.74264 + 6.48244i) q^{81} +4.75736i q^{83} +(2.80821 + 1.62132i) q^{87} +(-2.67157 - 4.62730i) q^{89} +(3.24264 + 4.18154i) q^{91} +(-0.297173 + 0.171573i) q^{93} +6.00000i q^{97} +2.34315 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q + 8q^{11} - 20q^{21} + 40q^{29} + 8q^{31} - 8q^{39} + 24q^{41} - 20q^{49} + 24q^{51} - 16q^{59} - 4q^{61} - 72q^{69} - 96q^{71} - 16q^{79} + 4q^{81} - 44q^{89} - 8q^{91} + 64q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(351\) \(701\) \(801\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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
\(3\) 0.358719 + 0.207107i 0.207107 + 0.119573i 0.599966 0.800025i \(-0.295181\pi\)
−0.392859 + 0.919599i \(0.628514\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.09077 + 1.62132i −0.790237 + 0.612801i
\(8\) 0 0
\(9\) −1.41421 2.44949i −0.471405 0.816497i
\(10\) 0 0
\(11\) −0.414214 + 0.717439i −0.124890 + 0.216316i −0.921690 0.387927i \(-0.873191\pi\)
0.796800 + 0.604243i \(0.206524\pi\)
\(12\) 0 0
\(13\) 2.00000i 0.554700i −0.960769 0.277350i \(-0.910544\pi\)
0.960769 0.277350i \(-0.0894562\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 6.63103 + 3.82843i 1.60826 + 0.928530i 0.989759 + 0.142747i \(0.0455934\pi\)
0.618502 + 0.785783i \(0.287740\pi\)
\(18\) 0 0
\(19\) −2.82843 4.89898i −0.648886 1.12390i −0.983389 0.181509i \(-0.941902\pi\)
0.334504 0.942394i \(-0.391431\pi\)
\(20\) 0 0
\(21\) −1.08579 + 0.148586i −0.236938 + 0.0324242i
\(22\) 0 0
\(23\) 4.83743 2.79289i 1.00867 0.582358i 0.0978712 0.995199i \(-0.468797\pi\)
0.910803 + 0.412841i \(0.135463\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 2.41421i 0.464616i
\(28\) 0 0
\(29\) 7.82843 1.45370 0.726851 0.686795i \(-0.240983\pi\)
0.726851 + 0.686795i \(0.240983\pi\)
\(30\) 0 0
\(31\) −0.414214 + 0.717439i −0.0743950 + 0.128856i −0.900823 0.434187i \(-0.857036\pi\)
0.826428 + 0.563042i \(0.190369\pi\)
\(32\) 0 0
\(33\) −0.297173 + 0.171573i −0.0517312 + 0.0298670i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.89898 2.82843i 0.805387 0.464991i −0.0399642 0.999201i \(-0.512724\pi\)
0.845351 + 0.534211i \(0.179391\pi\)
\(38\) 0 0
\(39\) 0.414214 0.717439i 0.0663273 0.114882i
\(40\) 0 0
\(41\) 5.82843 0.910247 0.455124 0.890428i \(-0.349595\pi\)
0.455124 + 0.890428i \(0.349595\pi\)
\(42\) 0 0
\(43\) 6.89949i 1.05216i 0.850434 + 0.526082i \(0.176339\pi\)
−0.850434 + 0.526082i \(0.823661\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.0951 5.82843i 1.47253 0.850163i 0.473004 0.881060i \(-0.343170\pi\)
0.999523 + 0.0308969i \(0.00983637\pi\)
\(48\) 0 0
\(49\) 1.74264 6.77962i 0.248949 0.968517i
\(50\) 0 0
\(51\) 1.58579 + 2.74666i 0.222055 + 0.384610i
\(52\) 0 0
\(53\) −4.89898 2.82843i −0.672927 0.388514i 0.124258 0.992250i \(-0.460345\pi\)
−0.797185 + 0.603736i \(0.793678\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 2.34315i 0.310357i
\(58\) 0 0
\(59\) −2.00000 + 3.46410i −0.260378 + 0.450988i −0.966342 0.257260i \(-0.917180\pi\)
0.705965 + 0.708247i \(0.250514\pi\)
\(60\) 0 0
\(61\) −3.32843 5.76500i −0.426161 0.738133i 0.570367 0.821390i \(-0.306801\pi\)
−0.996528 + 0.0832569i \(0.973468\pi\)
\(62\) 0 0
\(63\) 6.92820 + 2.82843i 0.872872 + 0.356348i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 11.1713 + 6.44975i 1.36479 + 0.787962i 0.990257 0.139251i \(-0.0444696\pi\)
0.374533 + 0.927213i \(0.377803\pi\)
\(68\) 0 0
\(69\) 2.31371 0.278538
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) 3.16693 + 1.82843i 0.370661 + 0.214001i 0.673747 0.738962i \(-0.264684\pi\)
−0.303086 + 0.952963i \(0.598017\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.297173 2.17157i −0.0338660 0.247474i
\(78\) 0 0
\(79\) −2.00000 3.46410i −0.225018 0.389742i 0.731307 0.682048i \(-0.238911\pi\)
−0.956325 + 0.292306i \(0.905577\pi\)
\(80\) 0 0
\(81\) −3.74264 + 6.48244i −0.415849 + 0.720272i
\(82\) 0 0
\(83\) 4.75736i 0.522188i 0.965313 + 0.261094i \(0.0840833\pi\)
−0.965313 + 0.261094i \(0.915917\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 2.80821 + 1.62132i 0.301072 + 0.173824i
\(88\) 0 0
\(89\) −2.67157 4.62730i −0.283186 0.490493i 0.688982 0.724779i \(-0.258058\pi\)
−0.972168 + 0.234286i \(0.924725\pi\)
\(90\) 0 0
\(91\) 3.24264 + 4.18154i 0.339921 + 0.438345i
\(92\) 0 0
\(93\) −0.297173 + 0.171573i −0.0308154 + 0.0177913i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 6.00000i 0.609208i 0.952479 + 0.304604i \(0.0985241\pi\)
−0.952479 + 0.304604i \(0.901476\pi\)
\(98\) 0 0
\(99\) 2.34315 0.235495
\(100\) 0 0
\(101\) 5.74264 9.94655i 0.571414 0.989718i −0.425007 0.905190i \(-0.639728\pi\)
0.996421 0.0845282i \(-0.0269383\pi\)
\(102\) 0 0
\(103\) −6.56948 + 3.79289i −0.647310 + 0.373725i −0.787425 0.616410i \(-0.788586\pi\)
0.140115 + 0.990135i \(0.455253\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.83743 + 2.79289i −0.467652 + 0.269999i −0.715256 0.698862i \(-0.753690\pi\)
0.247604 + 0.968861i \(0.420357\pi\)
\(108\) 0 0
\(109\) 9.15685 15.8601i 0.877068 1.51913i 0.0225237 0.999746i \(-0.492830\pi\)
0.854544 0.519379i \(-0.173837\pi\)
\(110\) 0 0
\(111\) 2.34315 0.222402
\(112\) 0 0
\(113\) 11.3137i 1.06430i −0.846649 0.532152i \(-0.821383\pi\)
0.846649 0.532152i \(-0.178617\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −4.89898 + 2.82843i −0.452911 + 0.261488i
\(118\) 0 0
\(119\) −20.0711 + 2.74666i −1.83991 + 0.251786i
\(120\) 0 0
\(121\) 5.15685 + 8.93193i 0.468805 + 0.811994i
\(122\) 0 0
\(123\) 2.09077 + 1.20711i 0.188518 + 0.108841i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 4.34315i 0.385392i −0.981259 0.192696i \(-0.938277\pi\)
0.981259 0.192696i \(-0.0617231\pi\)
\(128\) 0 0
\(129\) −1.42893 + 2.47498i −0.125810 + 0.217910i
\(130\) 0 0
\(131\) −6.82843 11.8272i −0.596602 1.03335i −0.993319 0.115404i \(-0.963184\pi\)
0.396716 0.917941i \(-0.370150\pi\)
\(132\) 0 0
\(133\) 13.8564 + 5.65685i 1.20150 + 0.490511i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.46410 + 2.00000i 0.295958 + 0.170872i 0.640626 0.767853i \(-0.278675\pi\)
−0.344668 + 0.938725i \(0.612008\pi\)
\(138\) 0 0
\(139\) −2.48528 −0.210799 −0.105399 0.994430i \(-0.533612\pi\)
−0.105399 + 0.994430i \(0.533612\pi\)
\(140\) 0 0
\(141\) 4.82843 0.406627
\(142\) 0 0
\(143\) 1.43488 + 0.828427i 0.119991 + 0.0692766i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 2.02922 2.07107i 0.167368 0.170819i
\(148\) 0 0
\(149\) 2.32843 + 4.03295i 0.190752 + 0.330392i 0.945500 0.325623i \(-0.105574\pi\)
−0.754748 + 0.656015i \(0.772241\pi\)
\(150\) 0 0
\(151\) 5.58579 9.67487i 0.454565 0.787329i −0.544098 0.839022i \(-0.683128\pi\)
0.998663 + 0.0516921i \(0.0164614\pi\)
\(152\) 0 0
\(153\) 21.6569i 1.75085i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −1.13770 0.656854i −0.0907987 0.0524227i 0.453913 0.891046i \(-0.350028\pi\)
−0.544712 + 0.838623i \(0.683361\pi\)
\(158\) 0 0
\(159\) −1.17157 2.02922i −0.0929118 0.160928i
\(160\) 0 0
\(161\) −5.58579 + 13.6823i −0.440222 + 1.07832i
\(162\) 0 0
\(163\) 13.5592 7.82843i 1.06204 0.613170i 0.136045 0.990703i \(-0.456561\pi\)
0.925996 + 0.377533i \(0.123227\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.07107i 0.160264i 0.996784 + 0.0801320i \(0.0255342\pi\)
−0.996784 + 0.0801320i \(0.974466\pi\)
\(168\) 0 0
\(169\) 9.00000 0.692308
\(170\) 0 0
\(171\) −8.00000 + 13.8564i −0.611775 + 1.05963i
\(172\) 0 0
\(173\) −8.95743 + 5.17157i −0.681021 + 0.393187i −0.800239 0.599681i \(-0.795294\pi\)
0.119219 + 0.992868i \(0.461961\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −1.43488 + 0.828427i −0.107852 + 0.0622684i
\(178\) 0 0
\(179\) −3.24264 + 5.61642i −0.242366 + 0.419791i −0.961388 0.275197i \(-0.911257\pi\)
0.719022 + 0.694988i \(0.244590\pi\)
\(180\) 0 0
\(181\) −4.17157 −0.310071 −0.155035 0.987909i \(-0.549549\pi\)
−0.155035 + 0.987909i \(0.549549\pi\)
\(182\) 0 0
\(183\) 2.75736i 0.203830i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −5.49333 + 3.17157i −0.401712 + 0.231928i
\(188\) 0 0
\(189\) 3.91421 + 5.04757i 0.284717 + 0.367156i
\(190\) 0 0
\(191\) 2.75736 + 4.77589i 0.199516 + 0.345571i 0.948371 0.317162i \(-0.102730\pi\)
−0.748856 + 0.662733i \(0.769397\pi\)
\(192\) 0 0
\(193\) −4.60181 2.65685i −0.331245 0.191245i 0.325149 0.945663i \(-0.394586\pi\)
−0.656394 + 0.754418i \(0.727919\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0.343146i 0.0244481i 0.999925 + 0.0122241i \(0.00389114\pi\)
−0.999925 + 0.0122241i \(0.996109\pi\)
\(198\) 0 0
\(199\) −11.6569 + 20.1903i −0.826332 + 1.43125i 0.0745642 + 0.997216i \(0.476243\pi\)
−0.900897 + 0.434034i \(0.857090\pi\)
\(200\) 0 0
\(201\) 2.67157 + 4.62730i 0.188438 + 0.326385i
\(202\) 0 0
\(203\) −16.3674 + 12.6924i −1.14877 + 0.890831i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −13.6823 7.89949i −0.950987 0.549053i
\(208\) 0 0
\(209\) 4.68629 0.324158
\(210\) 0 0
\(211\) 26.6274 1.83311 0.916553 0.399912i \(-0.130959\pi\)
0.916553 + 0.399912i \(0.130959\pi\)
\(212\) 0 0
\(213\) −4.30463 2.48528i −0.294949 0.170289i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −0.297173 2.17157i −0.0201734 0.147416i
\(218\) 0 0
\(219\) 0.757359 + 1.31178i 0.0511776 + 0.0886422i
\(220\) 0 0
\(221\) 7.65685 13.2621i 0.515056 0.892103i
\(222\) 0 0
\(223\) 14.9706i 1.00250i 0.865302 + 0.501252i \(0.167127\pi\)
−0.865302 + 0.501252i \(0.832873\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −12.1244 7.00000i −0.804722 0.464606i 0.0403978 0.999184i \(-0.487137\pi\)
−0.845120 + 0.534577i \(0.820471\pi\)
\(228\) 0 0
\(229\) −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i \(-0.319740\pi\)
−0.999088 + 0.0426906i \(0.986407\pi\)
\(230\) 0 0
\(231\) 0.343146 0.840532i 0.0225773 0.0553029i
\(232\) 0 0
\(233\) −10.0951 + 5.82843i −0.661354 + 0.381833i −0.792793 0.609491i \(-0.791374\pi\)
0.131439 + 0.991324i \(0.458040\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 1.65685i 0.107624i
\(238\) 0 0
\(239\) 30.4853 1.97193 0.985964 0.166955i \(-0.0533936\pi\)
0.985964 + 0.166955i \(0.0533936\pi\)
\(240\) 0 0
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) 0 0
\(243\) −8.95743 + 5.17157i −0.574619 + 0.331757i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −9.79796 + 5.65685i −0.623429 + 0.359937i
\(248\) 0 0
\(249\) −0.985281 + 1.70656i −0.0624397 + 0.108149i
\(250\) 0 0
\(251\) −27.4558 −1.73300 −0.866499 0.499179i \(-0.833635\pi\)
−0.866499 + 0.499179i \(0.833635\pi\)
\(252\) 0 0
\(253\) 4.62742i 0.290923i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 13.2621 7.65685i 0.827265 0.477621i −0.0256506 0.999671i \(-0.508166\pi\)
0.852915 + 0.522050i \(0.174832\pi\)
\(258\) 0 0
\(259\) −5.65685 + 13.8564i −0.351500 + 0.860995i
\(260\) 0 0
\(261\) −11.0711 19.1757i −0.685282 1.18694i
\(262\) 0 0
\(263\) −13.6208 7.86396i −0.839893 0.484913i 0.0173347 0.999850i \(-0.494482\pi\)
−0.857228 + 0.514937i \(0.827815\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 2.21320i 0.135446i
\(268\) 0 0
\(269\) −3.32843 + 5.76500i −0.202938 + 0.351499i −0.949474 0.313847i \(-0.898382\pi\)
0.746536 + 0.665345i \(0.231716\pi\)
\(270\) 0 0
\(271\) 1.65685 + 2.86976i 0.100647 + 0.174325i 0.911951 0.410298i \(-0.134575\pi\)
−0.811305 + 0.584624i \(0.801242\pi\)
\(272\) 0 0
\(273\) 0.297173 + 2.17157i 0.0179857 + 0.131430i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −24.7921 14.3137i −1.48961 0.860027i −0.489682 0.871901i \(-0.662887\pi\)
−0.999930 + 0.0118739i \(0.996220\pi\)
\(278\) 0 0
\(279\) 2.34315 0.140280
\(280\) 0 0
\(281\) 2.68629 0.160251 0.0801254 0.996785i \(-0.474468\pi\)
0.0801254 + 0.996785i \(0.474468\pi\)
\(282\) 0 0
\(283\) 15.5885 + 9.00000i 0.926638 + 0.534994i 0.885747 0.464169i \(-0.153647\pi\)
0.0408910 + 0.999164i \(0.486980\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −12.1859 + 9.44975i −0.719311 + 0.557801i
\(288\) 0 0
\(289\) 20.8137 + 36.0504i 1.22434 + 2.12061i
\(290\) 0 0
\(291\) −1.24264 + 2.15232i −0.0728449 + 0.126171i
\(292\) 0 0
\(293\) 16.9706i 0.991431i −0.868485 0.495715i \(-0.834906\pi\)
0.868485 0.495715i \(-0.165094\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 1.73205 + 1.00000i 0.100504 + 0.0580259i
\(298\) 0 0
\(299\) −5.58579 9.67487i −0.323034 0.559512i
\(300\) 0 0
\(301\) −11.1863 14.4253i −0.644767 0.831458i
\(302\) 0 0
\(303\) 4.11999 2.37868i 0.236687 0.136652i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 4.75736i 0.271517i 0.990742 + 0.135758i \(0.0433471\pi\)
−0.990742 + 0.135758i \(0.956653\pi\)
\(308\) 0 0
\(309\) −3.14214 −0.178750
\(310\) 0 0
\(311\) −10.8284 + 18.7554i −0.614024 + 1.06352i 0.376531 + 0.926404i \(0.377117\pi\)
−0.990555 + 0.137116i \(0.956217\pi\)
\(312\) 0 0
\(313\) −18.1610 + 10.4853i −1.02652 + 0.592663i −0.915987 0.401209i \(-0.868590\pi\)
−0.110536 + 0.993872i \(0.535257\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −19.0526 + 11.0000i −1.07010 + 0.617822i −0.928208 0.372061i \(-0.878651\pi\)
−0.141890 + 0.989882i \(0.545318\pi\)
\(318\) 0 0
\(319\) −3.24264 + 5.61642i −0.181553 + 0.314459i
\(320\) 0 0
\(321\) −2.31371 −0.129139
\(322\) 0 0
\(323\) 43.3137i 2.41004i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 6.56948 3.79289i 0.363293 0.209747i
\(328\) 0 0
\(329\) −11.6569 + 28.5533i −0.642663 + 1.57420i
\(330\) 0 0
\(331\) −13.2426 22.9369i −0.727881 1.26073i −0.957777 0.287512i \(-0.907172\pi\)
0.229896 0.973215i \(-0.426162\pi\)
\(332\) 0 0
\(333\) −13.8564 8.00000i −0.759326 0.438397i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 24.9706i 1.36023i 0.733104 + 0.680117i \(0.238071\pi\)
−0.733104 + 0.680117i \(0.761929\pi\)
\(338\) 0 0
\(339\) 2.34315 4.05845i 0.127262 0.220425i
\(340\) 0 0
\(341\) −0.343146 0.594346i −0.0185824 0.0321856i
\(342\) 0 0
\(343\) 7.34847 + 17.0000i 0.396780 + 0.917914i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −9.85951 5.69239i −0.529286 0.305583i 0.211440 0.977391i \(-0.432185\pi\)
−0.740726 + 0.671808i \(0.765518\pi\)
\(348\) 0 0
\(349\) −9.82843 −0.526104 −0.263052 0.964782i \(-0.584729\pi\)
−0.263052 + 0.964782i \(0.584729\pi\)
\(350\) 0 0
\(351\) −4.82843 −0.257722
\(352\) 0 0
\(353\) 29.1477 + 16.8284i 1.55138 + 0.895687i 0.998030 + 0.0627345i \(0.0199821\pi\)
0.553345 + 0.832952i \(0.313351\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −7.76874 3.17157i −0.411165 0.167857i
\(358\) 0 0
\(359\) −3.24264 5.61642i −0.171140 0.296423i 0.767679 0.640835i \(-0.221412\pi\)
−0.938819 + 0.344412i \(0.888078\pi\)
\(360\) 0 0
\(361\) −6.50000 + 11.2583i −0.342105 + 0.592544i
\(362\) 0 0
\(363\) 4.27208i 0.224226i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −18.6938 10.7929i −0.975810 0.563384i −0.0748078 0.997198i \(-0.523834\pi\)
−0.901003 + 0.433814i \(0.857168\pi\)
\(368\) 0 0
\(369\) −8.24264 14.2767i −0.429095 0.743214i
\(370\) 0 0
\(371\) 14.8284 2.02922i 0.769854 0.105352i
\(372\) 0 0
\(373\) −10.3923 + 6.00000i −0.538093 + 0.310668i −0.744306 0.667839i \(-0.767219\pi\)
0.206213 + 0.978507i \(0.433886\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 15.6569i 0.806369i
\(378\) 0 0
\(379\) −4.68629 −0.240719 −0.120359 0.992730i \(-0.538405\pi\)
−0.120359 + 0.992730i \(0.538405\pi\)
\(380\) 0 0
\(381\) 0.899495 1.55797i 0.0460825 0.0798173i
\(382\) 0 0
\(383\) 0.778985 0.449747i 0.0398043 0.0229810i −0.479966 0.877287i \(-0.659351\pi\)
0.519770 + 0.854306i \(0.326018\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 16.9002 9.75736i 0.859088 0.495994i
\(388\) 0 0
\(389\) 2.65685 4.60181i 0.134708 0.233321i −0.790778 0.612103i \(-0.790324\pi\)
0.925486 + 0.378782i \(0.123657\pi\)
\(390\) 0 0
\(391\) 42.7696 2.16295
\(392\) 0 0
\(393\) 5.65685i 0.285351i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −21.3280 + 12.3137i −1.07042 + 0.618007i −0.928296 0.371842i \(-0.878726\pi\)
−0.142124 + 0.989849i \(0.545393\pi\)
\(398\) 0 0
\(399\) 3.79899 + 4.89898i 0.190187 + 0.245256i
\(400\) 0 0
\(401\) 16.1569 + 27.9845i 0.806835 + 1.39748i 0.915045 + 0.403351i \(0.132155\pi\)
−0.108211 + 0.994128i \(0.534512\pi\)
\(402\) 0 0
\(403\) 1.43488 + 0.828427i 0.0714764 + 0.0412669i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 4.68629i 0.232291i
\(408\) 0 0
\(409\) −12.5711 + 21.7737i −0.621599 + 1.07664i 0.367589 + 0.929988i \(0.380183\pi\)
−0.989188 + 0.146653i \(0.953150\pi\)
\(410\) 0 0
\(411\) 0.828427 + 1.43488i 0.0408633 + 0.0707773i
\(412\) 0 0
\(413\) −1.43488 10.4853i −0.0706057 0.515947i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −0.891519 0.514719i −0.0436579 0.0252059i
\(418\) 0 0
\(419\) 15.3137 0.748124 0.374062 0.927404i \(-0.377965\pi\)
0.374062 + 0.927404i \(0.377965\pi\)
\(420\) 0 0
\(421\) 27.3431 1.33262 0.666312 0.745673i \(-0.267872\pi\)
0.666312 + 0.745673i \(0.267872\pi\)
\(422\) 0 0
\(423\) −28.5533 16.4853i −1.38831 0.801542i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 16.3059 + 6.65685i 0.789098 + 0.322148i
\(428\) 0 0
\(429\) 0.343146 + 0.594346i 0.0165672 + 0.0286953i
\(430\) 0 0
\(431\) 0.414214 0.717439i 0.0199520 0.0345578i −0.855877 0.517179i \(-0.826982\pi\)
0.875829 + 0.482622i \(0.160315\pi\)
\(432\) 0 0
\(433\) 19.3137i 0.928158i 0.885794 + 0.464079i \(0.153615\pi\)
−0.885794 + 0.464079i \(0.846385\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −27.3647 15.7990i −1.30903 0.755768i
\(438\) 0 0
\(439\) −9.17157 15.8856i −0.437735 0.758180i 0.559779 0.828642i \(-0.310886\pi\)
−0.997514 + 0.0704621i \(0.977553\pi\)
\(440\) 0 0
\(441\) −19.0711 + 5.31925i −0.908146 + 0.253297i
\(442\) 0 0
\(443\) 13.4977 7.79289i 0.641294 0.370252i −0.143819 0.989604i \(-0.545938\pi\)
0.785113 + 0.619353i \(0.212605\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 1.92893i 0.0912354i
\(448\) 0 0
\(449\) 7.48528 0.353252 0.176626 0.984278i \(-0.443482\pi\)
0.176626 + 0.984278i \(0.443482\pi\)
\(450\) 0 0
\(451\) −2.41421 + 4.18154i −0.113681 + 0.196901i
\(452\) 0 0
\(453\) 4.00746 2.31371i 0.188287 0.108708i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 25.0892 14.4853i 1.17363 0.677593i 0.219094 0.975704i \(-0.429690\pi\)
0.954531 + 0.298111i \(0.0963565\pi\)
\(458\) 0 0
\(459\) 9.24264 16.0087i 0.431410 0.747223i
\(460\) 0 0
\(461\) 1.31371 0.0611855 0.0305928 0.999532i \(-0.490261\pi\)
0.0305928 + 0.999532i \(0.490261\pi\)
\(462\) 0 0
\(463\) 14.8995i 0.692438i −0.938154 0.346219i \(-0.887465\pi\)
0.938154 0.346219i \(-0.112535\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −32.7964 + 18.9350i −1.51764 + 0.876209i −0.517853 + 0.855470i \(0.673269\pi\)
−0.999785 + 0.0207390i \(0.993398\pi\)
\(468\) 0 0
\(469\) −33.8137 + 4.62730i −1.56137 + 0.213669i
\(470\) 0 0
\(471\) −0.272078 0.471253i −0.0125367 0.0217142i
\(472\) 0 0
\(473\) −4.94997 2.85786i −0.227600 0.131405i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 16.0000i 0.732590i
\(478\) 0 0
\(479\) −0.757359 + 1.31178i −0.0346046 + 0.0599370i −0.882809 0.469732i \(-0.844351\pi\)
0.848204 + 0.529669i \(0.177684\pi\)
\(480\) 0 0
\(481\) −5.65685 9.79796i −0.257930 0.446748i
\(482\) 0 0
\(483\) −4.83743 + 3.75126i −0.220111 + 0.170688i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 33.1552 + 19.1421i 1.50240 + 0.867413i 0.999996 + 0.00278182i \(0.000885482\pi\)
0.502407 + 0.864631i \(0.332448\pi\)
\(488\) 0 0
\(489\) 6.48528 0.293275
\(490\) 0 0
\(491\) 1.51472 0.0683583 0.0341791 0.999416i \(-0.489118\pi\)
0.0341791 + 0.999416i \(0.489118\pi\)
\(492\) 0 0
\(493\) 51.9105 + 29.9706i 2.33793 + 1.34981i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 25.0892 19.4558i 1.12541 0.872714i
\(498\) 0 0
\(499\) 22.0711 + 38.2282i 0.988037 + 1.71133i 0.627576 + 0.778555i \(0.284047\pi\)
0.360461 + 0.932774i \(0.382619\pi\)
\(500\) 0 0
\(501\) −0.428932 + 0.742932i −0.0191633 + 0.0331918i
\(502\) 0 0
\(503\) 3.92893i 0.175182i 0.996157 + 0.0875912i \(0.0279169\pi\)
−0.996157 + 0.0875912i \(0.972083\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 3.22848 + 1.86396i 0.143382 + 0.0827814i
\(508\) 0 0
\(509\) −16.7426 28.9991i −0.742105 1.28536i −0.951535 0.307539i \(-0.900494\pi\)
0.209431 0.977823i \(-0.432839\pi\)
\(510\) 0 0
\(511\) −9.58579 + 1.31178i −0.424050 + 0.0580299i
\(512\) 0 0
\(513\) −11.8272 + 6.82843i −0.522183 + 0.301482i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 9.65685i 0.424708i
\(518\) 0 0
\(519\) −4.28427 −0.188059
\(520\) 0 0
\(521\) −18.3137 + 31.7203i −0.802338 + 1.38969i 0.115735 + 0.993280i \(0.463078\pi\)
−0.918073 + 0.396410i \(0.870256\pi\)
\(522\) 0 0
\(523\) −24.1977 + 13.9706i −1.05809 + 0.610890i −0.924904 0.380201i \(-0.875855\pi\)
−0.133189 + 0.991091i \(0.542522\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5.49333 + 3.17157i −0.239293 + 0.138156i
\(528\) 0 0
\(529\) 4.10051 7.10228i 0.178283 0.308795i
\(530\) 0 0
\(531\) 11.3137 0.490973
\(532\) 0 0
\(533\) 11.6569i 0.504914i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −2.32640 + 1.34315i −0.100391 + 0.0579610i
\(538\) 0 0
\(539\) 4.14214 + 4.05845i 0.178414 + 0.174810i
\(540\) 0 0
\(541\) 11.7426 + 20.3389i 0.504856 + 0.874435i 0.999984 + 0.00561582i \(0.00178758\pi\)
−0.495129 + 0.868820i \(0.664879\pi\)
\(542\) 0 0
\(543\) −1.49642 0.863961i −0.0642177 0.0370761i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 2.27208i 0.0971470i −0.998820 0.0485735i \(-0.984532\pi\)
0.998820 0.0485735i \(-0.0154675\pi\)
\(548\) 0 0
\(549\) −9.41421 + 16.3059i −0.401789 + 0.695919i
\(550\) 0 0
\(551\) −22.1421 38.3513i −0.943287 1.63382i
\(552\) 0 0
\(553\) 9.79796 + 4.00000i 0.416652 + 0.170097i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 14.9941 + 8.65685i 0.635321 + 0.366803i 0.782810 0.622261i \(-0.213786\pi\)
−0.147489 + 0.989064i \(0.547119\pi\)
\(558\) 0 0
\(559\) 13.7990 0.583635
\(560\) 0 0
\(561\) −2.62742 −0.110930
\(562\) 0 0
\(563\) −3.52565 2.03553i −0.148588 0.0857875i 0.423863 0.905727i \(-0.360674\pi\)
−0.572451 + 0.819939i \(0.694007\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −2.68512 19.6213i −0.112764 0.824018i
\(568\) 0 0
\(569\) −18.3137 31.7203i −0.767751 1.32978i −0.938780 0.344517i \(-0.888043\pi\)
0.171029 0.985266i \(-0.445291\pi\)
\(570\) 0 0
\(571\) 10.4853 18.1610i 0.438795 0.760016i −0.558801 0.829301i \(-0.688739\pi\)
0.997597 + 0.0692856i \(0.0220720\pi\)
\(572\) 0 0
\(573\) 2.28427i 0.0954268i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 19.2987 + 11.1421i 0.803417 + 0.463853i 0.844665 0.535296i \(-0.179800\pi\)
−0.0412474 + 0.999149i \(0.513133\pi\)
\(578\) 0 0
\(579\) −1.10051 1.90613i −0.0457354 0.0792161i
\(580\) 0 0
\(581\) −7.71320 9.94655i −0.319998 0.412652i
\(582\) 0 0
\(583\) 4.05845 2.34315i 0.168084 0.0970432i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 22.6863i 0.936363i −0.883632 0.468182i \(-0.844909\pi\)
0.883632 0.468182i \(-0.155091\pi\)
\(588\) 0 0
\(589\) 4.68629 0.193095
\(590\) 0 0
\(591\) −0.0710678 + 0.123093i −0.00292334 + 0.00506337i
\(592\) 0 0
\(593\) −25.9298 + 14.9706i −1.06481 + 0.614767i −0.926758 0.375658i \(-0.877417\pi\)
−0.138050 + 0.990425i \(0.544083\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −8.36308 + 4.82843i −0.342278 + 0.197614i
\(598\) 0 0
\(599\) 21.3137 36.9164i 0.870855 1.50836i 0.00974040 0.999953i \(-0.496899\pi\)
0.861114 0.508412i \(-0.169767\pi\)
\(600\) 0 0
\(601\) −34.0000 −1.38689 −0.693444 0.720510i \(-0.743908\pi\)
−0.693444 + 0.720510i \(0.743908\pi\)
\(602\) 0 0
\(603\) 36.4853i 1.48580i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 23.5928 13.6213i 0.957603 0.552872i 0.0621685 0.998066i \(-0.480198\pi\)
0.895434 + 0.445193i \(0.146865\pi\)
\(608\) 0 0
\(609\) −8.50000 + 1.16320i −0.344437 + 0.0471352i
\(610\) 0 0
\(611\) −11.6569 20.1903i −0.471586 0.816811i
\(612\) 0 0
\(613\) 33.7495 + 19.4853i 1.36313 + 0.787003i 0.990039 0.140792i \(-0.0449649\pi\)
0.373090 + 0.927795i \(0.378298\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 12.6863i 0.510731i −0.966845 0.255365i \(-0.917804\pi\)
0.966845 0.255365i \(-0.0821958\pi\)
\(618\) 0 0
\(619\) 19.7279 34.1698i 0.792932 1.37340i −0.131212 0.991354i \(-0.541887\pi\)
0.924144 0.382044i \(-0.124780\pi\)
\(620\) 0 0
\(621\) −6.74264 11.6786i −0.270573 0.468646i
\(622\) 0 0
\(623\) 13.0880 + 5.34315i 0.524359 + 0.214069i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 1.68106 + 0.970563i 0.0671352 + 0.0387605i
\(628\) 0 0
\(629\) 43.3137 1.72703
\(630\) 0 0
\(631\) −1.51472 −0.0603000 −0.0301500 0.999545i \(-0.509598\pi\)
−0.0301500 + 0.999545i \(0.509598\pi\)
\(632\) 0 0
\(633\) 9.55177 + 5.51472i 0.379649 + 0.219190i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −13.5592 3.48528i −0.537236 0.138092i
\(638\) 0 0
\(639\) 16.9706 + 29.3939i 0.671345 + 1.16280i
\(640\) 0 0
\(641\) −7.05635 + 12.2220i −0.278709 + 0.482738i −0.971064 0.238819i \(-0.923240\pi\)
0.692355 + 0.721557i \(0.256573\pi\)
\(642\) 0 0
\(643\) 26.0000i 1.02534i −0.858586 0.512670i \(-0.828656\pi\)
0.858586 0.512670i \(-0.171344\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 17.9764 + 10.3787i 0.706725 + 0.408028i 0.809847 0.586641i \(-0.199550\pi\)
−0.103122 + 0.994669i \(0.532883\pi\)
\(648\) 0 0
\(649\) −1.65685 2.86976i −0.0650372 0.112648i
\(650\) 0 0
\(651\) 0.343146 0.840532i 0.0134489 0.0329430i
\(652\) 0 0
\(653\) 13.5592 7.82843i 0.530614 0.306350i −0.210653 0.977561i \(-0.567559\pi\)
0.741266 + 0.671211i \(0.234226\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 10.3431i 0.403525i
\(658\) 0 0
\(659\) −12.6863 −0.494188 −0.247094 0.968992i \(-0.579476\pi\)
−0.247094 + 0.968992i \(0.579476\pi\)
\(660\) 0 0
\(661\) 25.1569 43.5729i 0.978488 1.69479i 0.310581 0.950547i \(-0.399476\pi\)
0.667907 0.744244i \(-0.267190\pi\)
\(662\) 0 0
\(663\) 5.49333 3.17157i 0.213343 0.123174i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 37.8695 21.8640i 1.46631 0.846576i
\(668\) 0 0
\(669\) −3.10051 + 5.37023i −0.119872 + 0.207625i
\(670\) 0 0
\(671\) 5.51472 0.212893
\(672\) 0 0
\(673\) 5.65685i 0.218056i 0.994039 + 0.109028i \(0.0347738\pi\)
−0.994039 + 0.109028i \(0.965226\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 19.8931 11.4853i 0.764554 0.441415i −0.0663747 0.997795i \(-0.521143\pi\)
0.830928 + 0.556380i \(0.187810\pi\)
\(678\) 0 0
\(679\) −9.72792 12.5446i −0.373323 0.481418i
\(680\) 0 0
\(681\) −2.89949 5.02207i −0.111109 0.192446i
\(682\) 0 0
\(683\) −1.67050 0.964466i −0.0639201 0.0369043i 0.467699 0.883888i \(-0.345083\pi\)
−0.531619 + 0.846983i \(0.678416\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 5.79899i 0.221245i
\(688\) 0 0
\(689\) −5.65685 + 9.79796i −0.215509 + 0.373273i
\(690\) 0 0
\(691\) 21.3848 + 37.0395i 0.813515 + 1.40905i 0.910389 + 0.413753i \(0.135782\pi\)
−0.0968739 + 0.995297i \(0.530884\pi\)
\(692\) 0 0
\(693\) −4.89898 + 3.79899i −0.186097 + 0.144312i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 38.6485 + 22.3137i 1.46392 + 0.845192i
\(698\) 0 0
\(699\) −4.82843 −0.182628
\(700\) 0 0
\(701\) −11.0000 −0.415464 −0.207732 0.978186i \(-0.566608\pi\)
−0.207732 + 0.978186i \(0.566608\pi\)
\(702\) 0 0
\(703\) −27.7128 16.0000i −1.04521 0.603451i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 4.11999 + 30.1066i 0.154948 + 1.13228i
\(708\) 0 0
\(709\) −17.7132 30.6802i −0.665233 1.15222i −0.979222 0.202791i \(-0.934999\pi\)
0.313989 0.949427i \(-0.398335\pi\)
\(710\) 0 0
\(711\) −5.65685 + 9.79796i −0.212149 + 0.367452i
\(712\) 0 0
\(713\) 4.62742i 0.173298i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 10.9357 + 6.31371i 0.408400 + 0.235790i
\(718\) 0 0
\(719\) −12.8995 22.3426i −0.481070 0.833238i 0.518694 0.854960i \(-0.326418\pi\)
−0.999764 + 0.0217223i \(0.993085\pi\)
\(720\) 0 0
\(721\) 7.58579 18.5813i 0.282509 0.692004i
\(722\) 0 0
\(723\) 3.58719 2.07107i 0.133409 0.0770238i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 38.0711i 1.41198i 0.708223 + 0.705989i \(0.249497\pi\)
−0.708223 + 0.705989i \(0.750503\pi\)
\(728\) 0 0
\(729\) 18.1716 0.673021
\(730\) 0 0
\(731\) −26.4142 + 45.7508i −0.976965 + 1.69215i
\(732\) 0 0
\(733\) −6.63103 + 3.82843i −0.244923 + 0.141406i −0.617437 0.786620i \(-0.711829\pi\)
0.372514 + 0.928026i \(0.378496\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −9.25460 + 5.34315i −0.340898 + 0.196817i
\(738\) 0 0
\(739\) 8.41421 14.5738i 0.309522 0.536108i −0.668736 0.743500i \(-0.733164\pi\)
0.978258 + 0.207392i \(0.0664977\pi\)
\(740\) 0 0
\(741\) −4.68629 −0.172155
\(742\) 0 0
\(743\) 10.7574i 0.394649i 0.980338 + 0.197325i \(0.0632253\pi\)
−0.980338 + 0.197325i \(0.936775\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 11.6531 6.72792i 0.426365 0.246162i
\(748\) 0 0
\(749\) 5.58579 13.6823i 0.204100 0.499941i
\(750\) 0 0
\(751\) 6.00000 + 10.3923i 0.218943 + 0.379221i 0.954485 0.298259i \(-0.0964058\pi\)
−0.735542 + 0.677479i \(0.763072\pi\)
\(752\) 0 0
\(753\) −9.84895 5.68629i −0.358916 0.207220i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 6.00000i 0.218074i 0.994038 + 0.109037i \(0.0347767\pi\)
−0.994038 + 0.109037i \(0.965223\pi\)
\(758\) 0 0
\(759\) −0.958369 + 1.65994i −0.0347866 + 0.0602522i
\(760\) 0 0
\(761\) 21.9706 + 38.0541i 0.796432 + 1.37946i 0.921926 + 0.387367i \(0.126615\pi\)
−0.125493 + 0.992094i \(0.540051\pi\)
\(762\) 0 0
\(763\) 6.56948 + 48.0061i 0.237831 + 1.73794i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 6.92820 + 4.00000i 0.250163 + 0.144432i
\(768\) 0 0
\(769\) −43.2548 −1.55981 −0.779905 0.625898i \(-0.784732\pi\)
−0.779905 + 0.625898i \(0.784732\pi\)
\(770\) 0 0
\(771\) 6.34315 0.228443
\(772\) 0 0
\(773\) 21.0818 + 12.1716i 0.758259 + 0.437781i 0.828670 0.559737i \(-0.189098\pi\)
−0.0704113 + 0.997518i \(0.522431\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −4.89898 + 3.79899i −0.175750 + 0.136288i
\(778\) 0 0
\(779\) −16.4853 28.5533i −0.590647 1.02303i
\(780\) 0 0
\(781\) 4.97056 8.60927i 0.177861 0.308064i
\(782\) 0 0
\(783\) 18.8995i 0.675413i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 1.37333 + 0.792893i 0.0489540 + 0.0282636i 0.524277 0.851548i \(-0.324336\pi\)
−0.475323 + 0.879811i \(0.657669\pi\)
\(788\) 0 0
\(789\) −3.25736 5.64191i −0.115965 0.200857i
\(790\) 0 0
\(791\) 18.3431 + 23.6544i 0.652207 + 0.841052i
\(792\) 0 0
\(793\) −11.5300 + 6.65685i −0.409443 + 0.236392i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 35.3137i 1.25088i −0.780274 0.625438i \(-0.784920\pi\)
0.780274 0.625438i \(-0.215080\pi\)
\(798\) 0 0
\(799\) 89.2548 3.15761
\(800\) 0 0