Properties

Label 1300.2.bb.e.549.2
Level $1300$
Weight $2$
Character 1300.549
Analytic conductor $10.381$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1300.bb (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.3805522628\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 260)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 549.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1300.549
Dual form 1300.2.bb.e.1049.2

$q$-expansion

\(f(q)\) \(=\) \(q+(2.59808 - 1.50000i) q^{3} +(-2.59808 - 1.50000i) q^{7} +(3.00000 - 5.19615i) q^{9} +O(q^{10})\) \(q+(2.59808 - 1.50000i) q^{3} +(-2.59808 - 1.50000i) q^{7} +(3.00000 - 5.19615i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(-3.46410 - 1.00000i) q^{13} +(6.06218 + 3.50000i) q^{17} +(0.500000 - 0.866025i) q^{19} -9.00000 q^{21} +(6.06218 - 3.50000i) q^{23} -9.00000i q^{27} +(-2.50000 - 4.33013i) q^{29} -4.00000 q^{31} +(-7.79423 - 4.50000i) q^{33} +(-2.59808 + 1.50000i) q^{37} +(-10.5000 + 2.59808i) q^{39} +(-3.50000 - 6.06218i) q^{41} +(-7.79423 - 4.50000i) q^{43} +8.00000i q^{47} +(1.00000 + 1.73205i) q^{49} +21.0000 q^{51} +6.00000i q^{53} -3.00000i q^{57} +(2.50000 - 4.33013i) q^{59} +(2.50000 - 4.33013i) q^{61} +(-15.5885 + 9.00000i) q^{63} +(11.2583 - 6.50000i) q^{67} +(10.5000 - 18.1865i) q^{69} +(1.50000 - 2.59808i) q^{71} +14.0000i q^{73} +9.00000i q^{77} +8.00000 q^{79} +(-4.50000 - 7.79423i) q^{81} -12.0000i q^{83} +(-12.9904 - 7.50000i) q^{87} +(3.50000 + 6.06218i) q^{89} +(7.50000 + 7.79423i) q^{91} +(-10.3923 + 6.00000i) q^{93} +(9.52628 + 5.50000i) q^{97} -18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 12 q^{9} + O(q^{10}) \) \( 4 q + 12 q^{9} - 6 q^{11} + 2 q^{19} - 36 q^{21} - 10 q^{29} - 16 q^{31} - 42 q^{39} - 14 q^{41} + 4 q^{49} + 84 q^{51} + 10 q^{59} + 10 q^{61} + 42 q^{69} + 6 q^{71} + 32 q^{79} - 18 q^{81} + 14 q^{89} + 30 q^{91} - 72 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(651\) \(677\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\)

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
\(3\) 2.59808 1.50000i 1.50000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
1.00000 \(0\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.59808 1.50000i −0.981981 0.566947i −0.0791130 0.996866i \(-0.525209\pi\)
−0.902867 + 0.429919i \(0.858542\pi\)
\(8\) 0 0
\(9\) 3.00000 5.19615i 1.00000 1.73205i
\(10\) 0 0
\(11\) −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) 0 0
\(13\) −3.46410 1.00000i −0.960769 0.277350i
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 6.06218 + 3.50000i 1.47029 + 0.848875i 0.999444 0.0333386i \(-0.0106140\pi\)
0.470850 + 0.882213i \(0.343947\pi\)
\(18\) 0 0
\(19\) 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i \(-0.796740\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) 0 0
\(21\) −9.00000 −1.96396
\(22\) 0 0
\(23\) 6.06218 3.50000i 1.26405 0.729800i 0.290196 0.956967i \(-0.406280\pi\)
0.973856 + 0.227167i \(0.0729463\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 9.00000i 1.73205i
\(28\) 0 0
\(29\) −2.50000 4.33013i −0.464238 0.804084i 0.534928 0.844897i \(-0.320339\pi\)
−0.999167 + 0.0408130i \(0.987005\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) −7.79423 4.50000i −1.35680 0.783349i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.59808 + 1.50000i −0.427121 + 0.246598i −0.698119 0.715981i \(-0.745980\pi\)
0.270998 + 0.962580i \(0.412646\pi\)
\(38\) 0 0
\(39\) −10.5000 + 2.59808i −1.68135 + 0.416025i
\(40\) 0 0
\(41\) −3.50000 6.06218i −0.546608 0.946753i −0.998504 0.0546823i \(-0.982585\pi\)
0.451896 0.892071i \(-0.350748\pi\)
\(42\) 0 0
\(43\) −7.79423 4.50000i −1.18861 0.686244i −0.230618 0.973044i \(-0.574075\pi\)
−0.957990 + 0.286801i \(0.907408\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 8.00000i 1.16692i 0.812142 + 0.583460i \(0.198301\pi\)
−0.812142 + 0.583460i \(0.801699\pi\)
\(48\) 0 0
\(49\) 1.00000 + 1.73205i 0.142857 + 0.247436i
\(50\) 0 0
\(51\) 21.0000 2.94059
\(52\) 0 0
\(53\) 6.00000i 0.824163i 0.911147 + 0.412082i \(0.135198\pi\)
−0.911147 + 0.412082i \(0.864802\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 3.00000i 0.397360i
\(58\) 0 0
\(59\) 2.50000 4.33013i 0.325472 0.563735i −0.656136 0.754643i \(-0.727810\pi\)
0.981608 + 0.190909i \(0.0611434\pi\)
\(60\) 0 0
\(61\) 2.50000 4.33013i 0.320092 0.554416i −0.660415 0.750901i \(-0.729619\pi\)
0.980507 + 0.196485i \(0.0629528\pi\)
\(62\) 0 0
\(63\) −15.5885 + 9.00000i −1.96396 + 1.13389i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 11.2583 6.50000i 1.37542 0.794101i 0.383819 0.923408i \(-0.374609\pi\)
0.991605 + 0.129307i \(0.0412752\pi\)
\(68\) 0 0
\(69\) 10.5000 18.1865i 1.26405 2.18940i
\(70\) 0 0
\(71\) 1.50000 2.59808i 0.178017 0.308335i −0.763184 0.646181i \(-0.776365\pi\)
0.941201 + 0.337846i \(0.109698\pi\)
\(72\) 0 0
\(73\) 14.0000i 1.63858i 0.573382 + 0.819288i \(0.305631\pi\)
−0.573382 + 0.819288i \(0.694369\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 9.00000i 1.02565i
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 0 0
\(83\) 12.0000i 1.31717i −0.752506 0.658586i \(-0.771155\pi\)
0.752506 0.658586i \(-0.228845\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −12.9904 7.50000i −1.39272 0.804084i
\(88\) 0 0
\(89\) 3.50000 + 6.06218i 0.370999 + 0.642590i 0.989720 0.143022i \(-0.0456819\pi\)
−0.618720 + 0.785611i \(0.712349\pi\)
\(90\) 0 0
\(91\) 7.50000 + 7.79423i 0.786214 + 0.817057i
\(92\) 0 0
\(93\) −10.3923 + 6.00000i −1.07763 + 0.622171i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 9.52628 + 5.50000i 0.967247 + 0.558440i 0.898396 0.439187i \(-0.144733\pi\)
0.0688512 + 0.997627i \(0.478067\pi\)
\(98\) 0 0
\(99\) −18.0000 −1.80907
\(100\) 0 0
\(101\) 4.50000 + 7.79423i 0.447767 + 0.775555i 0.998240 0.0592978i \(-0.0188862\pi\)
−0.550474 + 0.834853i \(0.685553\pi\)
\(102\) 0 0
\(103\) 16.0000i 1.57653i 0.615338 + 0.788263i \(0.289020\pi\)
−0.615338 + 0.788263i \(0.710980\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.59808 + 1.50000i −0.251166 + 0.145010i −0.620298 0.784366i \(-0.712988\pi\)
0.369132 + 0.929377i \(0.379655\pi\)
\(108\) 0 0
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 0 0
\(111\) −4.50000 + 7.79423i −0.427121 + 0.739795i
\(112\) 0 0
\(113\) 11.2583 + 6.50000i 1.05909 + 0.611469i 0.925182 0.379525i \(-0.123912\pi\)
0.133913 + 0.990993i \(0.457246\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −15.5885 + 15.0000i −1.44115 + 1.38675i
\(118\) 0 0
\(119\) −10.5000 18.1865i −0.962533 1.66716i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 0 0
\(123\) −18.1865 10.5000i −1.63982 0.946753i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0.866025 0.500000i 0.0768473 0.0443678i −0.461084 0.887357i \(-0.652539\pi\)
0.537931 + 0.842989i \(0.319206\pi\)
\(128\) 0 0
\(129\) −27.0000 −2.37722
\(130\) 0 0
\(131\) 4.00000 0.349482 0.174741 0.984614i \(-0.444091\pi\)
0.174741 + 0.984614i \(0.444091\pi\)
\(132\) 0 0
\(133\) −2.59808 + 1.50000i −0.225282 + 0.130066i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.59808 + 1.50000i 0.221969 + 0.128154i 0.606861 0.794808i \(-0.292428\pi\)
−0.384893 + 0.922961i \(0.625762\pi\)
\(138\) 0 0
\(139\) 6.50000 11.2583i 0.551323 0.954919i −0.446857 0.894606i \(-0.647457\pi\)
0.998179 0.0603135i \(-0.0192101\pi\)
\(140\) 0 0
\(141\) 12.0000 + 20.7846i 1.01058 + 1.75038i
\(142\) 0 0
\(143\) 2.59808 + 10.5000i 0.217262 + 0.878054i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 5.19615 + 3.00000i 0.428571 + 0.247436i
\(148\) 0 0
\(149\) 1.50000 2.59808i 0.122885 0.212843i −0.798019 0.602632i \(-0.794119\pi\)
0.920904 + 0.389789i \(0.127452\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 0 0
\(153\) 36.3731 21.0000i 2.94059 1.69775i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 6.00000i 0.478852i 0.970915 + 0.239426i \(0.0769593\pi\)
−0.970915 + 0.239426i \(0.923041\pi\)
\(158\) 0 0
\(159\) 9.00000 + 15.5885i 0.713746 + 1.23625i
\(160\) 0 0
\(161\) −21.0000 −1.65503
\(162\) 0 0
\(163\) 9.52628 + 5.50000i 0.746156 + 0.430793i 0.824303 0.566149i \(-0.191567\pi\)
−0.0781474 + 0.996942i \(0.524900\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0.866025 0.500000i 0.0670151 0.0386912i −0.466118 0.884723i \(-0.654348\pi\)
0.533133 + 0.846031i \(0.321014\pi\)
\(168\) 0 0
\(169\) 11.0000 + 6.92820i 0.846154 + 0.532939i
\(170\) 0 0
\(171\) −3.00000 5.19615i −0.229416 0.397360i
\(172\) 0 0
\(173\) −12.9904 7.50000i −0.987640 0.570214i −0.0830722 0.996544i \(-0.526473\pi\)
−0.904568 + 0.426329i \(0.859807\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 15.0000i 1.12747i
\(178\) 0 0
\(179\) 9.50000 + 16.4545i 0.710063 + 1.22987i 0.964833 + 0.262864i \(0.0846670\pi\)
−0.254770 + 0.967002i \(0.582000\pi\)
\(180\) 0 0
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) 0 0
\(183\) 15.0000i 1.10883i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 21.0000i 1.53567i
\(188\) 0 0
\(189\) −13.5000 + 23.3827i −0.981981 + 1.70084i
\(190\) 0 0
\(191\) 1.50000 2.59808i 0.108536 0.187990i −0.806641 0.591041i \(-0.798717\pi\)
0.915177 + 0.403051i \(0.132050\pi\)
\(192\) 0 0
\(193\) 12.9904 7.50000i 0.935068 0.539862i 0.0466572 0.998911i \(-0.485143\pi\)
0.888411 + 0.459049i \(0.151810\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −19.9186 + 11.5000i −1.41914 + 0.819341i −0.996223 0.0868274i \(-0.972327\pi\)
−0.422917 + 0.906168i \(0.638994\pi\)
\(198\) 0 0
\(199\) 4.50000 7.79423i 0.318997 0.552518i −0.661282 0.750137i \(-0.729987\pi\)
0.980279 + 0.197619i \(0.0633208\pi\)
\(200\) 0 0
\(201\) 19.5000 33.7750i 1.37542 2.38230i
\(202\) 0 0
\(203\) 15.0000i 1.05279i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 42.0000i 2.91920i
\(208\) 0 0
\(209\) −3.00000 −0.207514
\(210\) 0 0
\(211\) 2.50000 + 4.33013i 0.172107 + 0.298098i 0.939156 0.343490i \(-0.111609\pi\)
−0.767049 + 0.641588i \(0.778276\pi\)
\(212\) 0 0
\(213\) 9.00000i 0.616670i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 10.3923 + 6.00000i 0.705476 + 0.407307i
\(218\) 0 0
\(219\) 21.0000 + 36.3731i 1.41905 + 2.45786i
\(220\) 0 0
\(221\) −17.5000 18.1865i −1.17718 1.22336i
\(222\) 0 0
\(223\) 19.9186 11.5000i 1.33385 0.770097i 0.347960 0.937509i \(-0.386874\pi\)
0.985887 + 0.167412i \(0.0535411\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0.866025 + 0.500000i 0.0574801 + 0.0331862i 0.528465 0.848955i \(-0.322768\pi\)
−0.470985 + 0.882141i \(0.656101\pi\)
\(228\) 0 0
\(229\) −26.0000 −1.71813 −0.859064 0.511868i \(-0.828954\pi\)
−0.859064 + 0.511868i \(0.828954\pi\)
\(230\) 0 0
\(231\) 13.5000 + 23.3827i 0.888235 + 1.53847i
\(232\) 0 0
\(233\) 18.0000i 1.17922i −0.807688 0.589610i \(-0.799282\pi\)
0.807688 0.589610i \(-0.200718\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 20.7846 12.0000i 1.35011 0.779484i
\(238\) 0 0
\(239\) 16.0000 1.03495 0.517477 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) 0 0
\(241\) 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i \(-0.823079\pi\)
0.881680 + 0.471848i \(0.156413\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −2.59808 + 2.50000i −0.165312 + 0.159071i
\(248\) 0 0
\(249\) −18.0000 31.1769i −1.14070 1.97576i
\(250\) 0 0
\(251\) −2.50000 + 4.33013i −0.157799 + 0.273315i −0.934075 0.357078i \(-0.883773\pi\)
0.776276 + 0.630393i \(0.217106\pi\)
\(252\) 0 0
\(253\) −18.1865 10.5000i −1.14338 0.660129i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −16.4545 + 9.50000i −1.02640 + 0.592594i −0.915952 0.401288i \(-0.868563\pi\)
−0.110450 + 0.993882i \(0.535229\pi\)
\(258\) 0 0
\(259\) 9.00000 0.559233
\(260\) 0 0
\(261\) −30.0000 −1.85695
\(262\) 0 0
\(263\) 6.06218 3.50000i 0.373810 0.215819i −0.301312 0.953526i \(-0.597424\pi\)
0.675122 + 0.737706i \(0.264091\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 18.1865 + 10.5000i 1.11300 + 0.642590i
\(268\) 0 0
\(269\) 1.50000 2.59808i 0.0914566 0.158408i −0.816668 0.577108i \(-0.804181\pi\)
0.908124 + 0.418701i \(0.137514\pi\)
\(270\) 0 0
\(271\) −11.5000 19.9186i −0.698575 1.20997i −0.968960 0.247216i \(-0.920484\pi\)
0.270385 0.962752i \(-0.412849\pi\)
\(272\) 0 0
\(273\) 31.1769 + 9.00000i 1.88691 + 0.544705i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 19.9186 + 11.5000i 1.19679 + 0.690968i 0.959839 0.280553i \(-0.0905179\pi\)
0.236953 + 0.971521i \(0.423851\pi\)
\(278\) 0 0
\(279\) −12.0000 + 20.7846i −0.718421 + 1.24434i
\(280\) 0 0
\(281\) −10.0000 −0.596550 −0.298275 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) 0 0
\(283\) −0.866025 + 0.500000i −0.0514799 + 0.0297219i −0.525519 0.850782i \(-0.676129\pi\)
0.474039 + 0.880504i \(0.342796\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 21.0000i 1.23959i
\(288\) 0 0
\(289\) 16.0000 + 27.7128i 0.941176 + 1.63017i
\(290\) 0 0
\(291\) 33.0000 1.93449
\(292\) 0 0
\(293\) 7.79423 + 4.50000i 0.455344 + 0.262893i 0.710084 0.704117i \(-0.248657\pi\)
−0.254741 + 0.967009i \(0.581990\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −23.3827 + 13.5000i −1.35680 + 0.783349i
\(298\) 0 0
\(299\) −24.5000 + 6.06218i −1.41687 + 0.350585i
\(300\) 0 0
\(301\) 13.5000 + 23.3827i 0.778127 + 1.34776i
\(302\) 0 0
\(303\) 23.3827 + 13.5000i 1.34330 + 0.775555i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 28.0000i 1.59804i 0.601302 + 0.799022i \(0.294649\pi\)
−0.601302 + 0.799022i \(0.705351\pi\)
\(308\) 0 0
\(309\) 24.0000 + 41.5692i 1.36531 + 2.36479i
\(310\) 0 0
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 0 0
\(313\) 6.00000i 0.339140i 0.985518 + 0.169570i \(0.0542379\pi\)
−0.985518 + 0.169570i \(0.945762\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.00000i 0.112331i −0.998421 0.0561656i \(-0.982113\pi\)
0.998421 0.0561656i \(-0.0178875\pi\)
\(318\) 0 0
\(319\) −7.50000 + 12.9904i −0.419919 + 0.727322i
\(320\) 0 0
\(321\) −4.50000 + 7.79423i −0.251166 + 0.435031i
\(322\) 0 0
\(323\) 6.06218 3.50000i 0.337309 0.194745i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 36.3731 21.0000i 2.01144 1.16130i
\(328\) 0 0
\(329\) 12.0000 20.7846i 0.661581 1.14589i
\(330\) 0 0
\(331\) −6.50000 + 11.2583i −0.357272 + 0.618814i −0.987504 0.157593i \(-0.949627\pi\)
0.630232 + 0.776407i \(0.282960\pi\)
\(332\) 0 0
\(333\) 18.0000i 0.986394i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 18.0000i 0.980522i −0.871576 0.490261i \(-0.836901\pi\)
0.871576 0.490261i \(-0.163099\pi\)
\(338\) 0 0
\(339\) 39.0000 2.11819
\(340\) 0 0
\(341\) 6.00000 + 10.3923i 0.324918 + 0.562775i
\(342\) 0 0
\(343\) 15.0000i 0.809924i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 11.2583 + 6.50000i 0.604379 + 0.348938i 0.770762 0.637123i \(-0.219876\pi\)
−0.166383 + 0.986061i \(0.553209\pi\)
\(348\) 0 0
\(349\) −12.5000 21.6506i −0.669110 1.15893i −0.978153 0.207884i \(-0.933342\pi\)
0.309044 0.951048i \(-0.399991\pi\)
\(350\) 0 0
\(351\) −9.00000 + 31.1769i −0.480384 + 1.66410i
\(352\) 0 0
\(353\) −18.1865 + 10.5000i −0.967972 + 0.558859i −0.898617 0.438733i \(-0.855427\pi\)
−0.0693543 + 0.997592i \(0.522094\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −54.5596 31.5000i −2.88760 1.66716i
\(358\) 0 0
\(359\) 8.00000 0.422224 0.211112 0.977462i \(-0.432292\pi\)
0.211112 + 0.977462i \(0.432292\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) 0 0
\(363\) 6.00000i 0.314918i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 7.79423 4.50000i 0.406855 0.234898i −0.282582 0.959243i \(-0.591191\pi\)
0.689438 + 0.724345i \(0.257858\pi\)
\(368\) 0 0
\(369\) −42.0000 −2.18643
\(370\) 0 0
\(371\) 9.00000 15.5885i 0.467257 0.809312i
\(372\) 0 0
\(373\) −23.3827 13.5000i −1.21071 0.699004i −0.247796 0.968812i \(-0.579706\pi\)
−0.962914 + 0.269809i \(0.913039\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.33013 + 17.5000i 0.223013 + 0.901296i
\(378\) 0 0
\(379\) −4.50000 7.79423i −0.231149 0.400363i 0.726997 0.686640i \(-0.240915\pi\)
−0.958147 + 0.286278i \(0.907582\pi\)
\(380\) 0 0
\(381\) 1.50000 2.59808i 0.0768473 0.133103i
\(382\) 0 0
\(383\) −11.2583 6.50000i −0.575274 0.332134i 0.183979 0.982930i \(-0.441102\pi\)
−0.759253 + 0.650796i \(0.774435\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −46.7654 + 27.0000i −2.37722 + 1.37249i
\(388\) 0 0
\(389\) −18.0000 −0.912636 −0.456318 0.889817i \(-0.650832\pi\)
−0.456318 + 0.889817i \(0.650832\pi\)
\(390\) 0 0
\(391\) 49.0000 2.47804
\(392\) 0 0
\(393\) 10.3923 6.00000i 0.524222 0.302660i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −28.5788 16.5000i −1.43433 0.828111i −0.436884 0.899518i \(-0.643918\pi\)
−0.997447 + 0.0714068i \(0.977251\pi\)
\(398\) 0 0
\(399\) −4.50000 + 7.79423i −0.225282 + 0.390199i
\(400\) 0 0
\(401\) −7.50000 12.9904i −0.374532 0.648709i 0.615725 0.787961i \(-0.288863\pi\)
−0.990257 + 0.139253i \(0.955530\pi\)
\(402\) 0 0
\(403\) 13.8564 + 4.00000i 0.690237 + 0.199254i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 7.79423 + 4.50000i 0.386346 + 0.223057i
\(408\) 0 0
\(409\) −0.500000 + 0.866025i −0.0247234 + 0.0428222i −0.878122 0.478436i \(-0.841204\pi\)
0.853399 + 0.521258i \(0.174537\pi\)
\(410\) 0 0
\(411\) 9.00000 0.443937
\(412\) 0 0
\(413\) −12.9904 + 7.50000i −0.639215 + 0.369051i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 39.0000i 1.90984i
\(418\) 0 0
\(419\) −16.5000 28.5788i −0.806078 1.39617i −0.915561 0.402179i \(-0.868253\pi\)
0.109483 0.993989i \(-0.465080\pi\)
\(420\) 0 0
\(421\) 34.0000 1.65706 0.828529 0.559946i \(-0.189178\pi\)
0.828529 + 0.559946i \(0.189178\pi\)
\(422\) 0 0
\(423\) 41.5692 + 24.0000i 2.02116 + 1.16692i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −12.9904 + 7.50000i −0.628649 + 0.362950i
\(428\) 0 0
\(429\) 22.5000 + 23.3827i 1.08631 + 1.12893i
\(430\) 0 0
\(431\) 4.50000 + 7.79423i 0.216757 + 0.375435i 0.953815 0.300395i \(-0.0971186\pi\)
−0.737057 + 0.675830i \(0.763785\pi\)
\(432\) 0 0
\(433\) 0.866025 + 0.500000i 0.0416185 + 0.0240285i 0.520665 0.853761i \(-0.325684\pi\)
−0.479046 + 0.877790i \(0.659017\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.00000i 0.334855i
\(438\) 0 0
\(439\) 1.50000 + 2.59808i 0.0715911 + 0.123999i 0.899599 0.436717i \(-0.143859\pi\)
−0.828008 + 0.560717i \(0.810526\pi\)
\(440\) 0 0
\(441\) 12.0000 0.571429
\(442\) 0 0
\(443\) 24.0000i 1.14027i −0.821549 0.570137i \(-0.806890\pi\)
0.821549 0.570137i \(-0.193110\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 9.00000i 0.425685i
\(448\) 0 0
\(449\) −10.5000 + 18.1865i −0.495526 + 0.858276i −0.999987 0.00515887i \(-0.998358\pi\)
0.504461 + 0.863434i \(0.331691\pi\)
\(450\) 0 0
\(451\) −10.5000 + 18.1865i −0.494426 + 0.856370i
\(452\) 0 0
\(453\) −20.7846 + 12.0000i −0.976546 + 0.563809i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −19.9186 + 11.5000i −0.931752 + 0.537947i −0.887365 0.461067i \(-0.847467\pi\)
−0.0443868 + 0.999014i \(0.514133\pi\)
\(458\) 0 0
\(459\) 31.5000 54.5596i 1.47029 2.54662i
\(460\) 0 0
\(461\) −5.50000 + 9.52628i −0.256161 + 0.443683i −0.965210 0.261476i \(-0.915791\pi\)
0.709050 + 0.705159i \(0.249124\pi\)
\(462\) 0 0
\(463\) 28.0000i 1.30127i 0.759390 + 0.650635i \(0.225497\pi\)
−0.759390 + 0.650635i \(0.774503\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 20.0000i 0.925490i 0.886492 + 0.462745i \(0.153135\pi\)
−0.886492 + 0.462745i \(0.846865\pi\)
\(468\) 0 0
\(469\) −39.0000 −1.80085
\(470\) 0 0
\(471\) 9.00000 + 15.5885i 0.414698 + 0.718278i
\(472\) 0 0
\(473\) 27.0000i 1.24146i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 31.1769 + 18.0000i 1.42749 + 0.824163i
\(478\) 0 0
\(479\) −0.500000 0.866025i −0.0228456 0.0395697i 0.854377 0.519654i \(-0.173939\pi\)
−0.877222 + 0.480085i \(0.840606\pi\)
\(480\) 0 0
\(481\) 10.5000 2.59808i 0.478759 0.118462i
\(482\) 0 0
\(483\) −54.5596 + 31.5000i −2.48255 + 1.43330i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 14.7224 + 8.50000i 0.667137 + 0.385172i 0.794991 0.606621i \(-0.207476\pi\)
−0.127854 + 0.991793i \(0.540809\pi\)
\(488\) 0 0
\(489\) 33.0000 1.49231
\(490\) 0 0
\(491\) −11.5000 19.9186i −0.518988 0.898913i −0.999757 0.0220657i \(-0.992976\pi\)
0.480769 0.876847i \(-0.340358\pi\)
\(492\) 0 0
\(493\) 35.0000i 1.57632i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −7.79423 + 4.50000i −0.349619 + 0.201853i
\(498\) 0 0
\(499\) 16.0000 0.716258 0.358129 0.933672i \(-0.383415\pi\)
0.358129 + 0.933672i \(0.383415\pi\)
\(500\) 0 0
\(501\) 1.50000 2.59808i 0.0670151 0.116073i
\(502\) 0 0
\(503\) 9.52628 + 5.50000i 0.424756 + 0.245233i 0.697110 0.716964i \(-0.254469\pi\)
−0.272354 + 0.962197i \(0.587802\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 38.9711 + 1.50000i 1.73077 + 0.0666173i
\(508\) 0 0
\(509\) 7.50000 + 12.9904i 0.332432 + 0.575789i 0.982988 0.183669i \(-0.0587976\pi\)
−0.650556 + 0.759458i \(0.725464\pi\)
\(510\) 0 0
\(511\) 21.0000 36.3731i 0.928985 1.60905i
\(512\) 0 0
\(513\) −7.79423 4.50000i −0.344124 0.198680i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 20.7846 12.0000i 0.914106 0.527759i
\(518\) 0 0
\(519\) −45.0000 −1.97528
\(520\) 0 0
\(521\) −34.0000 −1.48957 −0.744784 0.667306i \(-0.767447\pi\)
−0.744784 + 0.667306i \(0.767447\pi\)
\(522\) 0 0
\(523\) 19.9186 11.5000i 0.870979 0.502860i 0.00330547 0.999995i \(-0.498948\pi\)
0.867673 + 0.497135i \(0.165615\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −24.2487 14.0000i −1.05629 0.609850i
\(528\) 0 0
\(529\) 13.0000 22.5167i 0.565217 0.978985i
\(530\) 0 0
\(531\) −15.0000 25.9808i −0.650945 1.12747i
\(532\) 0 0
\(533\) 6.06218 + 24.5000i 0.262582 + 1.06121i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 49.3634 + 28.5000i 2.13019 + 1.22987i
\(538\) 0 0
\(539\) 3.00000 5.19615i 0.129219 0.223814i
\(540\) 0 0
\(541\) 10.0000 0.429934 0.214967 0.976621i \(-0.431036\pi\)
0.214967 + 0.976621i \(0.431036\pi\)
\(542\) 0 0
\(543\) −36.3731 + 21.0000i −1.56092 + 0.901196i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 16.0000i 0.684111i −0.939680 0.342055i \(-0.888877\pi\)
0.939680 0.342055i \(-0.111123\pi\)
\(548\) 0 0
\(549\) −15.0000 25.9808i −0.640184 1.10883i
\(550\) 0 0
\(551\) −5.00000 −0.213007
\(552\) 0 0
\(553\) −20.7846 12.0000i −0.883852 0.510292i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −16.4545 + 9.50000i −0.697199 + 0.402528i −0.806303 0.591502i \(-0.798535\pi\)
0.109104 + 0.994030i \(0.465202\pi\)
\(558\) 0 0
\(559\) 22.5000 + 23.3827i 0.951649 + 0.988982i
\(560\) 0 0
\(561\) −31.5000 54.5596i −1.32993 2.30351i
\(562\) 0 0
\(563\) −38.9711 22.5000i −1.64244 0.948262i −0.979963 0.199177i \(-0.936173\pi\)
−0.662474 0.749085i \(-0.730494\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 27.0000i 1.13389i
\(568\) 0 0
\(569\) 9.50000 + 16.4545i 0.398261 + 0.689808i 0.993511 0.113732i \(-0.0362806\pi\)
−0.595251 + 0.803540i \(0.702947\pi\)
\(570\) 0 0
\(571\) −40.0000 −1.67395 −0.836974 0.547243i \(-0.815677\pi\)
−0.836974 + 0.547243i \(0.815677\pi\)
\(572\) 0 0
\(573\) 9.00000i 0.375980i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 2.00000i 0.0832611i 0.999133 + 0.0416305i \(0.0132552\pi\)
−0.999133 + 0.0416305i \(0.986745\pi\)
\(578\) 0 0
\(579\) 22.5000 38.9711i 0.935068 1.61959i
\(580\) 0 0
\(581\) −18.0000 + 31.1769i −0.746766 + 1.29344i
\(582\) 0 0
\(583\) 15.5885 9.00000i 0.645608 0.372742i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 32.0429 18.5000i 1.32255 0.763577i 0.338418 0.940996i \(-0.390108\pi\)
0.984135 + 0.177419i \(0.0567748\pi\)
\(588\) 0 0
\(589\) −2.00000 + 3.46410i −0.0824086 + 0.142736i
\(590\) 0 0
\(591\) −34.5000 + 59.7558i −1.41914 + 2.45802i
\(592\) 0 0
\(593\) 26.0000i 1.06769i −0.845582 0.533846i \(-0.820746\pi\)
0.845582 0.533846i \(-0.179254\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 27.0000i 1.10504i
\(598\) 0 0
\(599\) −8.00000 −0.326871 −0.163436 0.986554i \(-0.552258\pi\)
−0.163436 + 0.986554i \(0.552258\pi\)
\(600\) 0 0
\(601\) 6.50000 + 11.2583i 0.265141 + 0.459237i 0.967600 0.252486i \(-0.0812483\pi\)
−0.702460 + 0.711723i \(0.747915\pi\)
\(602\) 0 0
\(603\) 78.0000i 3.17641i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 7.79423 + 4.50000i 0.316358 + 0.182649i 0.649768 0.760133i \(-0.274866\pi\)
−0.333410 + 0.942782i \(0.608199\pi\)
\(608\) 0 0
\(609\) 22.5000 + 38.9711i 0.911746 + 1.57919i
\(610\) 0 0
\(611\) 8.00000 27.7128i 0.323645 1.12114i
\(612\) 0 0
\(613\) 26.8468 15.5000i 1.08433 0.626039i 0.152270 0.988339i \(-0.451342\pi\)
0.932062 + 0.362300i \(0.118008\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −25.1147 14.5000i −1.01108 0.583748i −0.0995732 0.995030i \(-0.531748\pi\)
−0.911508 + 0.411282i \(0.865081\pi\)
\(618\) 0 0
\(619\) −12.0000 −0.482321 −0.241160 0.970485i \(-0.577528\pi\)
−0.241160 + 0.970485i \(0.577528\pi\)
\(620\) 0 0
\(621\) −31.5000 54.5596i −1.26405 2.18940i
\(622\) 0 0
\(623\) 21.0000i 0.841347i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −7.79423 + 4.50000i −0.311272 + 0.179713i
\(628\) 0 0
\(629\) −21.0000 −0.837325
\(630\) 0 0
\(631\) 7.50000 12.9904i 0.298570 0.517139i −0.677239 0.735763i \(-0.736824\pi\)
0.975809 + 0.218624i \(0.0701569\pi\)
\(632\) 0 0
\(633\) 12.9904 + 7.50000i 0.516321 + 0.298098i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −1.73205 7.00000i −0.0686264 0.277350i
\(638\) 0 0
\(639\) −9.00000 15.5885i −0.356034 0.616670i
\(640\) 0 0
\(641\) 10.5000 18.1865i 0.414725 0.718325i −0.580674 0.814136i \(-0.697211\pi\)
0.995400 + 0.0958109i \(0.0305444\pi\)
\(642\) 0 0
\(643\) 6.06218 + 3.50000i 0.239069 + 0.138027i 0.614749 0.788723i \(-0.289257\pi\)
−0.375680 + 0.926750i \(0.622591\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 14.7224 8.50000i 0.578799 0.334169i −0.181857 0.983325i \(-0.558211\pi\)
0.760656 + 0.649155i \(0.224878\pi\)
\(648\) 0 0
\(649\) −15.0000 −0.588802
\(650\) 0 0
\(651\) 36.0000 1.41095
\(652\) 0 0
\(653\) 9.52628 5.50000i 0.372792 0.215232i −0.301885 0.953344i \(-0.597616\pi\)
0.674678 + 0.738113i \(0.264283\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 72.7461 + 42.0000i 2.83810 + 1.63858i
\(658\) 0 0
\(659\) −7.50000 + 12.9904i −0.292159 + 0.506033i −0.974320 0.225168i \(-0.927707\pi\)
0.682161 + 0.731202i \(0.261040\pi\)
\(660\) 0 0
\(661\) 8.50000 + 14.7224i 0.330612 + 0.572636i 0.982632 0.185565i \(-0.0594116\pi\)
−0.652020 + 0.758202i \(0.726078\pi\)
\(662\) 0 0
\(663\) −72.7461 21.0000i −2.82523 0.815572i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −30.3109 17.5000i −1.17364 0.677603i
\(668\) 0 0
\(669\) 34.5000 59.7558i 1.33385 2.31029i
\(670\) 0 0
\(671\) −15.0000 −0.579069
\(672\) 0 0
\(673\) −11.2583 + 6.50000i −0.433977 + 0.250557i −0.701039 0.713123i \(-0.747280\pi\)
0.267063 + 0.963679i \(0.413947\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 22.0000i 0.845529i 0.906240 + 0.422764i \(0.138940\pi\)
−0.906240 + 0.422764i \(0.861060\pi\)
\(678\) 0 0
\(679\) −16.5000 28.5788i −0.633212 1.09676i
\(680\) 0 0
\(681\) 3.00000 0.114960
\(682\) 0 0
\(683\) 26.8468 + 15.5000i 1.02726 + 0.593091i 0.916200 0.400722i \(-0.131241\pi\)
0.111064 + 0.993813i \(0.464574\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −67.5500 + 39.0000i −2.57719 + 1.48794i
\(688\) 0 0
\(689\) 6.00000 20.7846i 0.228582 0.791831i
\(690\) 0 0
\(691\) 12.5000 + 21.6506i 0.475522 + 0.823629i 0.999607 0.0280373i \(-0.00892572\pi\)
−0.524084 + 0.851666i \(0.675592\pi\)
\(692\) 0 0
\(693\) 46.7654 + 27.0000i 1.77647 + 1.02565i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 49.0000i 1.85601i
\(698\) 0 0
\(699\) −27.0000 46.7654i −1.02123 1.76883i
\(700\) 0 0
\(701\) 2.00000 0.0755390 0.0377695 0.999286i \(-0.487975\pi\)
0.0377695 + 0.999286i \(0.487975\pi\)
\(702\) 0 0
\(703\) 3.00000i 0.113147i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 27.0000i 1.01544i
\(708\) 0 0
\(709\) 17.5000 30.3109i 0.657226 1.13835i −0.324104 0.946021i \(-0.605063\pi\)
0.981331 0.192328i \(-0.0616038\pi\)
\(710\) 0 0
\(711\) 24.0000 41.5692i 0.900070 1.55897i
\(712\) 0 0
\(713\) −24.2487 + 14.0000i −0.908121 + 0.524304i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 41.5692 24.0000i 1.55243 0.896296i
\(718\) 0 0
\(719\) 0.500000 0.866025i 0.0186469 0.0322973i −0.856551 0.516062i \(-0.827398\pi\)
0.875198 + 0.483764i \(0.160731\pi\)
\(720\) 0 0
\(721\) 24.0000 41.5692i 0.893807 1.54812i
\(722\) 0 0
\(723\) 3.00000i 0.111571i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 28.0000i 1.03846i −0.854634 0.519231i \(-0.826218\pi\)
0.854634 0.519231i \(-0.173782\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) −31.5000 54.5596i −1.16507 2.01796i
\(732\) 0 0
\(733\) 14.0000i 0.517102i −0.965998 0.258551i \(-0.916755\pi\)
0.965998 0.258551i \(-0.0832450\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −33.7750 19.5000i −1.24412 0.718292i
\(738\) 0 0
\(739\) 19.5000 + 33.7750i 0.717319 + 1.24243i 0.962058 + 0.272844i \(0.0879643\pi\)
−0.244739 + 0.969589i \(0.578702\pi\)
\(740\) 0 0
\(741\) −3.00000 + 10.3923i −0.110208 + 0.381771i
\(742\) 0 0
\(743\) −0.866025 + 0.500000i −0.0317714 + 0.0183432i −0.515802 0.856708i \(-0.672506\pi\)
0.484030 + 0.875051i \(0.339172\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −62.3538 36.0000i −2.28141 1.31717i
\(748\) 0 0
\(749\) 9.00000 0.328853
\(750\) 0 0
\(751\) 6.50000 + 11.2583i 0.237188 + 0.410822i 0.959906 0.280321i \(-0.0904408\pi\)
−0.722718 + 0.691143i \(0.757107\pi\)
\(752\) 0 0
\(753\) 15.0000i 0.546630i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0.866025 0.500000i 0.0314762 0.0181728i −0.484179 0.874969i \(-0.660882\pi\)
0.515656 + 0.856796i \(0.327548\pi\)
\(758\) 0 0
\(759\) −63.0000 −2.28676
\(760\) 0 0
\(761\) −25.5000 + 44.1673i −0.924374 + 1.60106i −0.131810 + 0.991275i \(0.542079\pi\)
−0.792564 + 0.609788i \(0.791255\pi\)
\(762\) 0 0
\(763\) −36.3731 21.0000i −1.31679 0.760251i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −12.9904 + 12.5000i −0.469055 + 0.451349i
\(768\) 0 0
\(769\) −2.50000 4.33013i −0.0901523 0.156148i 0.817423 0.576038i \(-0.195402\pi\)
−0.907575 + 0.419890i \(0.862069\pi\)
\(770\) 0 0
\(771\) −28.5000 + 49.3634i −1.02640 + 1.77778i
\(772\) 0 0
\(773\) 21.6506 + 12.5000i 0.778719 + 0.449594i 0.835976 0.548766i \(-0.184902\pi\)
−0.0572570 + 0.998359i \(0.518235\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 23.3827 13.5000i 0.838849 0.484310i
\(778\) 0 0
\(779\) −7.00000 −0.250801
\(780\) 0 0
\(781\) −9.00000 −0.322045
\(782\) 0 0
\(783\) −38.9711 + 22.5000i −1.39272 + 0.804084i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 0.866025 + 0.500000i 0.0308705 + 0.0178231i 0.515356 0.856976i \(-0.327660\pi\)
−0.484485 + 0.874799i \(0.660993\pi\)
\(788\) 0 0
\(789\) 10.5000 18.1865i 0.373810 0.647458i
\(790\) 0 0
\(791\) −19.5000 33.7750i −0.693340 1.20090i
\(792\) 0 0
\(793\) −12.9904 + 12.5000i −0.461302 + 0.443888i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 6.06218 + 3.50000i 0.214733 + 0.123976i 0.603509 0.797356i \(-0.293769\pi\)
−0.388776 + 0.921332i \(0.627102\pi\)
\(798\) 0 0
\(799\) −28.0000 +