Properties

Label 260.2.bg.b.127.1
Level $260$
Weight $2$
Character 260.127
Analytic conductor $2.076$
Analytic rank $0$
Dimension $4$
CM discriminant -4
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.bg (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{12}]$

Embedding invariants

Embedding label 127.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 260.127
Dual form 260.2.bg.b.43.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.36603 + 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(-0.133975 - 2.23205i) q^{5} +(2.00000 + 2.00000i) q^{8} +(2.59808 + 1.50000i) q^{9} +O(q^{10})\) \(q+(1.36603 + 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(-0.133975 - 2.23205i) q^{5} +(2.00000 + 2.00000i) q^{8} +(2.59808 + 1.50000i) q^{9} +(0.633975 - 3.09808i) q^{10} +(-3.23205 - 1.59808i) q^{13} +(2.00000 + 3.46410i) q^{16} +(-0.133975 + 0.0358984i) q^{17} +(3.00000 + 3.00000i) q^{18} +(2.00000 - 4.00000i) q^{20} +(-4.96410 + 0.598076i) q^{25} +(-3.83013 - 3.36603i) q^{26} +(-9.23205 + 5.33013i) q^{29} +(1.46410 + 5.46410i) q^{32} -0.196152 q^{34} +(3.00000 + 5.19615i) q^{36} +(-10.6962 - 2.86603i) q^{37} +(4.19615 - 4.73205i) q^{40} +(10.3301 - 5.96410i) q^{41} +(3.00000 - 6.00000i) q^{45} +(-6.06218 + 3.50000i) q^{49} +(-7.00000 - 1.00000i) q^{50} +(-4.00000 - 6.00000i) q^{52} +(5.29423 - 5.29423i) q^{53} +(-14.5622 + 3.90192i) q^{58} +(1.33013 - 2.30385i) q^{61} +8.00000i q^{64} +(-3.13397 + 7.42820i) q^{65} +(-0.267949 - 0.0717968i) q^{68} +(2.19615 + 8.19615i) q^{72} +(1.16987 + 1.16987i) q^{73} +(-13.5622 - 7.83013i) q^{74} +(7.46410 - 4.92820i) q^{80} +(4.50000 + 7.79423i) q^{81} +(16.2942 - 4.36603i) q^{82} +(0.0980762 + 0.294229i) q^{85} +(5.00000 + 8.66025i) q^{89} +(6.29423 - 7.09808i) q^{90} +(-4.75833 - 17.7583i) q^{97} +(-9.56218 + 2.56218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 4 q^{5} + 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 4 q^{5} + 8 q^{8} + 6 q^{10} - 6 q^{13} + 8 q^{16} - 4 q^{17} + 12 q^{18} + 8 q^{20} - 6 q^{25} + 2 q^{26} - 30 q^{29} - 8 q^{32} + 20 q^{34} + 12 q^{36} - 22 q^{37} - 4 q^{40} + 24 q^{41} + 12 q^{45} - 28 q^{50} - 16 q^{52} - 10 q^{53} - 34 q^{58} - 12 q^{61} - 16 q^{65} - 8 q^{68} - 12 q^{72} + 22 q^{73} - 30 q^{74} + 16 q^{80} + 18 q^{81} + 34 q^{82} - 10 q^{85} + 20 q^{89} - 6 q^{90} + 26 q^{97} - 14 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36603 + 0.366025i 0.965926 + 0.258819i
\(3\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(4\) 1.73205 + 1.00000i 0.866025 + 0.500000i
\(5\) −0.133975 2.23205i −0.0599153 0.998203i
\(6\) 0 0
\(7\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(8\) 2.00000 + 2.00000i 0.707107 + 0.707107i
\(9\) 2.59808 + 1.50000i 0.866025 + 0.500000i
\(10\) 0.633975 3.09808i 0.200480 0.979698i
\(11\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) 0 0
\(13\) −3.23205 1.59808i −0.896410 0.443227i
\(14\) 0 0
\(15\) 0 0
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) −0.133975 + 0.0358984i −0.0324936 + 0.00870664i −0.275029 0.961436i \(-0.588688\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 3.00000 + 3.00000i 0.707107 + 0.707107i
\(19\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(20\) 2.00000 4.00000i 0.447214 0.894427i
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(24\) 0 0
\(25\) −4.96410 + 0.598076i −0.992820 + 0.119615i
\(26\) −3.83013 3.36603i −0.751150 0.660132i
\(27\) 0 0
\(28\) 0 0
\(29\) −9.23205 + 5.33013i −1.71435 + 0.989780i −0.785872 + 0.618389i \(0.787786\pi\)
−0.928477 + 0.371391i \(0.878881\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 1.46410 + 5.46410i 0.258819 + 0.965926i
\(33\) 0 0
\(34\) −0.196152 −0.0336399
\(35\) 0 0
\(36\) 3.00000 + 5.19615i 0.500000 + 0.866025i
\(37\) −10.6962 2.86603i −1.75844 0.471172i −0.772043 0.635571i \(-0.780765\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 4.19615 4.73205i 0.663470 0.748203i
\(41\) 10.3301 5.96410i 1.61329 0.931436i 0.624695 0.780869i \(-0.285223\pi\)
0.988600 0.150567i \(-0.0481100\pi\)
\(42\) 0 0
\(43\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(44\) 0 0
\(45\) 3.00000 6.00000i 0.447214 0.894427i
\(46\) 0 0
\(47\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(48\) 0 0
\(49\) −6.06218 + 3.50000i −0.866025 + 0.500000i
\(50\) −7.00000 1.00000i −0.989949 0.141421i
\(51\) 0 0
\(52\) −4.00000 6.00000i −0.554700 0.832050i
\(53\) 5.29423 5.29423i 0.727218 0.727218i −0.242846 0.970065i \(-0.578081\pi\)
0.970065 + 0.242846i \(0.0780811\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −14.5622 + 3.90192i −1.91211 + 0.512348i
\(59\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) 0 0
\(61\) 1.33013 2.30385i 0.170305 0.294977i −0.768221 0.640184i \(-0.778858\pi\)
0.938527 + 0.345207i \(0.112191\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) −3.13397 + 7.42820i −0.388722 + 0.921355i
\(66\) 0 0
\(67\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(68\) −0.267949 0.0717968i −0.0324936 0.00870664i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(72\) 2.19615 + 8.19615i 0.258819 + 0.965926i
\(73\) 1.16987 + 1.16987i 0.136923 + 0.136923i 0.772246 0.635323i \(-0.219133\pi\)
−0.635323 + 0.772246i \(0.719133\pi\)
\(74\) −13.5622 7.83013i −1.57657 0.910234i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 7.46410 4.92820i 0.834512 0.550990i
\(81\) 4.50000 + 7.79423i 0.500000 + 0.866025i
\(82\) 16.2942 4.36603i 1.79940 0.482147i
\(83\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(84\) 0 0
\(85\) 0.0980762 + 0.294229i 0.0106379 + 0.0319136i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 5.00000 + 8.66025i 0.529999 + 0.917985i 0.999388 + 0.0349934i \(0.0111410\pi\)
−0.469389 + 0.882992i \(0.655526\pi\)
\(90\) 6.29423 7.09808i 0.663470 0.748203i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −4.75833 17.7583i −0.483135 1.80309i −0.588315 0.808632i \(-0.700208\pi\)
0.105180 0.994453i \(-0.466458\pi\)
\(98\) −9.56218 + 2.56218i −0.965926 + 0.258819i
\(99\) 0 0
\(100\) −9.19615 3.92820i −0.919615 0.392820i
\(101\) 9.16025 + 15.8660i 0.911479 + 1.57873i 0.811976 + 0.583691i \(0.198392\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 0 0
\(103\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(104\) −3.26795 9.66025i −0.320449 0.947266i
\(105\) 0 0
\(106\) 9.16987 5.29423i 0.890657 0.514221i
\(107\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(108\) 0 0
\(109\) 20.0000 1.91565 0.957826 0.287348i \(-0.0927736\pi\)
0.957826 + 0.287348i \(0.0927736\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2.42820 + 9.06218i 0.228426 + 0.852498i 0.981003 + 0.193993i \(0.0621440\pi\)
−0.752577 + 0.658505i \(0.771189\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −21.3205 −1.97956
\(117\) −6.00000 9.00000i −0.554700 0.832050i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 5.50000 9.52628i 0.500000 0.866025i
\(122\) 2.66025 2.66025i 0.240848 0.240848i
\(123\) 0 0
\(124\) 0 0
\(125\) 2.00000 + 11.0000i 0.178885 + 0.983870i
\(126\) 0 0
\(127\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(128\) −2.92820 + 10.9282i −0.258819 + 0.965926i
\(129\) 0 0
\(130\) −7.00000 + 9.00000i −0.613941 + 0.789352i
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −0.339746 0.196152i −0.0291330 0.0168199i
\(137\) 3.47372 + 12.9641i 0.296780 + 1.10760i 0.939793 + 0.341743i \(0.111017\pi\)
−0.643013 + 0.765855i \(0.722316\pi\)
\(138\) 0 0
\(139\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 12.0000i 1.00000i
\(145\) 13.1340 + 19.8923i 1.09072 + 1.65197i
\(146\) 1.16987 + 2.02628i 0.0968194 + 0.167696i
\(147\) 0 0
\(148\) −15.6603 15.6603i −1.28726 1.28726i
\(149\) 11.0622 19.1603i 0.906249 1.56967i 0.0870170 0.996207i \(-0.472267\pi\)
0.819232 0.573462i \(-0.194400\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) −0.401924 0.107695i −0.0324936 0.00870664i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −17.2224 17.2224i −1.37450 1.37450i −0.853646 0.520854i \(-0.825614\pi\)
−0.520854 0.853646i \(-0.674386\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 12.0000 4.00000i 0.948683 0.316228i
\(161\) 0 0
\(162\) 3.29423 + 12.2942i 0.258819 + 0.965926i
\(163\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(164\) 23.8564 1.86287
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(168\) 0 0
\(169\) 7.89230 + 10.3301i 0.607100 + 0.794625i
\(170\) 0.0262794 + 0.437822i 0.00201554 + 0.0335794i
\(171\) 0 0
\(172\) 0 0
\(173\) −5.49038 20.4904i −0.417426 1.55785i −0.779926 0.625871i \(-0.784744\pi\)
0.362500 0.931984i \(-0.381923\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 3.66025 + 13.6603i 0.274348 + 1.02388i
\(179\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(180\) 11.1962 7.39230i 0.834512 0.550990i
\(181\) 8.32051 0.618458 0.309229 0.950988i \(-0.399929\pi\)
0.309229 + 0.950988i \(0.399929\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −4.96410 + 24.2583i −0.364968 + 1.78351i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(192\) 0 0
\(193\) 1.89230 7.06218i 0.136211 0.508347i −0.863779 0.503871i \(-0.831909\pi\)
0.999990 0.00447566i \(-0.00142465\pi\)
\(194\) 26.0000i 1.86669i
\(195\) 0 0
\(196\) −14.0000 −1.00000
\(197\) 17.7583 + 4.75833i 1.26523 + 0.339017i 0.828201 0.560431i \(-0.189365\pi\)
0.437028 + 0.899448i \(0.356031\pi\)
\(198\) 0 0
\(199\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) −11.1244 8.73205i −0.786611 0.617449i
\(201\) 0 0
\(202\) 6.70577 + 25.0263i 0.471816 + 1.76084i
\(203\) 0 0
\(204\) 0 0
\(205\) −14.6962 22.2583i −1.02642 1.55459i
\(206\) 0 0
\(207\) 0 0
\(208\) −0.928203 14.3923i −0.0643593 0.997927i
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(212\) 14.4641 3.87564i 0.993399 0.266180i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 27.3205 + 7.32051i 1.85038 + 0.495807i
\(219\) 0 0
\(220\) 0 0
\(221\) 0.490381 + 0.0980762i 0.0329866 + 0.00659732i
\(222\) 0 0
\(223\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(224\) 0 0
\(225\) −13.7942 5.89230i −0.919615 0.392820i
\(226\) 13.2679i 0.882571i
\(227\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(228\) 0 0
\(229\) −30.0000 −1.98246 −0.991228 0.132164i \(-0.957808\pi\)
−0.991228 + 0.132164i \(0.957808\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −29.1244 7.80385i −1.91211 0.512348i
\(233\) −5.00000 + 5.00000i −0.327561 + 0.327561i −0.851658 0.524097i \(-0.824403\pi\)
0.524097 + 0.851658i \(0.324403\pi\)
\(234\) −4.90192 14.4904i −0.320449 0.947266i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −18.9904 10.9641i −1.22328 0.706260i −0.257663 0.966235i \(-0.582952\pi\)
−0.965615 + 0.259975i \(0.916286\pi\)
\(242\) 11.0000 11.0000i 0.707107 0.707107i
\(243\) 0 0
\(244\) 4.60770 2.66025i 0.294977 0.170305i
\(245\) 8.62436 + 13.0622i 0.550990 + 0.834512i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −1.29423 + 15.7583i −0.0818542 + 0.996644i
\(251\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) −8.13397 + 30.3564i −0.507383 + 1.89358i −0.0623783 + 0.998053i \(0.519869\pi\)
−0.445005 + 0.895528i \(0.646798\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −12.8564 + 9.73205i −0.797320 + 0.603556i
\(261\) −31.9808 −1.97956
\(262\) 0 0
\(263\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(264\) 0 0
\(265\) −12.5263 11.1077i −0.769483 0.682340i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −22.5167 13.0000i −1.37287 0.792624i −0.381577 0.924337i \(-0.624619\pi\)
−0.991288 + 0.131713i \(0.957952\pi\)
\(270\) 0 0
\(271\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(272\) −0.392305 0.392305i −0.0237870 0.0237870i
\(273\) 0 0
\(274\) 18.9808i 1.14667i
\(275\) 0 0
\(276\) 0 0
\(277\) −30.6244 + 8.20577i −1.84004 + 0.493037i −0.998861 0.0477206i \(-0.984804\pi\)
−0.841178 + 0.540758i \(0.818138\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 22.7128i 1.35493i −0.735554 0.677466i \(-0.763078\pi\)
0.735554 0.677466i \(-0.236922\pi\)
\(282\) 0 0
\(283\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −4.39230 + 16.3923i −0.258819 + 0.965926i
\(289\) −14.7058 + 8.49038i −0.865045 + 0.499434i
\(290\) 10.6603 + 31.9808i 0.625992 + 1.87798i
\(291\) 0 0
\(292\) 0.856406 + 3.19615i 0.0501174 + 0.187041i
\(293\) 30.7224 8.23205i 1.79482 0.480922i 0.801673 0.597763i \(-0.203944\pi\)
0.993151 + 0.116841i \(0.0372769\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −15.6603 27.1244i −0.910234 1.57657i
\(297\) 0 0
\(298\) 22.1244 22.1244i 1.28163 1.28163i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −5.32051 2.66025i −0.304651 0.152326i
\(306\) −0.509619 0.294229i −0.0291330 0.0168199i
\(307\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 25.0000 25.0000i 1.41308 1.41308i 0.678280 0.734803i \(-0.262726\pi\)
0.734803 0.678280i \(-0.237274\pi\)
\(314\) −17.2224 29.8301i −0.971918 1.68341i
\(315\) 0 0
\(316\) 0 0
\(317\) 20.1506 20.1506i 1.13177 1.13177i 0.141890 0.989882i \(-0.454682\pi\)
0.989882 0.141890i \(-0.0453179\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 17.8564 1.07180i 0.998203 0.0599153i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 18.0000i 1.00000i
\(325\) 17.0000 + 6.00000i 0.942990 + 0.332820i
\(326\) 0 0
\(327\) 0 0
\(328\) 32.5885 + 8.73205i 1.79940 + 0.482147i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(332\) 0 0
\(333\) −23.4904 23.4904i −1.28726 1.28726i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 18.5622 + 18.5622i 1.01115 + 1.01115i 0.999937 + 0.0112091i \(0.00356804\pi\)
0.0112091 + 0.999937i \(0.496432\pi\)
\(338\) 7.00000 + 17.0000i 0.380750 + 0.924678i
\(339\) 0 0
\(340\) −0.124356 + 0.607695i −0.00674413 + 0.0329569i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 30.0000i 1.61281i
\(347\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(348\) 0 0
\(349\) −5.00000 8.66025i −0.267644 0.463573i 0.700609 0.713545i \(-0.252912\pi\)
−0.968253 + 0.249973i \(0.919578\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −9.57180 + 35.7224i −0.509455 + 1.90131i −0.0836583 + 0.996495i \(0.526660\pi\)
−0.425797 + 0.904819i \(0.640006\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 20.0000i 1.06000i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 18.0000 6.00000i 0.948683 0.316228i
\(361\) −9.50000 16.4545i −0.500000 0.866025i
\(362\) 11.3660 + 3.04552i 0.597385 + 0.160069i
\(363\) 0 0
\(364\) 0 0
\(365\) 2.45448 2.76795i 0.128473 0.144881i
\(366\) 0 0
\(367\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(368\) 0 0
\(369\) 35.7846 1.86287
\(370\) −15.6603 + 31.3205i −0.814138 + 1.62828i
\(371\) 0 0
\(372\) 0 0
\(373\) 8.06218 + 30.0885i 0.417444 + 1.55792i 0.779890 + 0.625917i \(0.215275\pi\)
−0.362446 + 0.932005i \(0.618058\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 38.3564 2.47372i 1.97546 0.127403i
\(378\) 0 0
\(379\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 5.16987 8.95448i 0.263140 0.455771i
\(387\) 0 0
\(388\) 9.51666 35.5167i 0.483135 1.80309i
\(389\) 34.3205i 1.74012i 0.492947 + 0.870059i \(0.335920\pi\)
−0.492947 + 0.870059i \(0.664080\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −19.1244 5.12436i −0.965926 0.258819i
\(393\) 0 0
\(394\) 22.5167 + 13.0000i 1.13437 + 0.654931i
\(395\) 0 0
\(396\) 0 0
\(397\) 4.75833 + 17.7583i 0.238814 + 0.891265i 0.976392 + 0.216004i \(0.0693024\pi\)
−0.737579 + 0.675261i \(0.764031\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −12.0000 16.0000i −0.600000 0.800000i
\(401\) −18.8205 + 10.8660i −0.939851 + 0.542623i −0.889914 0.456129i \(-0.849236\pi\)
−0.0499376 + 0.998752i \(0.515902\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 36.6410i 1.82296i
\(405\) 16.7942 11.0885i 0.834512 0.550990i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 12.5981 21.8205i 0.622935 1.07895i −0.366002 0.930614i \(-0.619274\pi\)
0.988936 0.148340i \(-0.0473931\pi\)
\(410\) −11.9282 35.7846i −0.589092 1.76728i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 4.00000 20.0000i 0.196116 0.980581i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(420\) 0 0
\(421\) 9.24871i 0.450755i 0.974272 + 0.225377i \(0.0723615\pi\)
−0.974272 + 0.225377i \(0.927639\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 21.1769 1.02844
\(425\) 0.643594 0.258330i 0.0312189 0.0125309i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(432\) 0 0
\(433\) 8.27757 + 30.8923i 0.397795 + 1.48459i 0.816968 + 0.576683i \(0.195653\pi\)
−0.419173 + 0.907906i \(0.637680\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 34.6410 + 20.0000i 1.65900 + 0.957826i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 0 0
\(441\) −21.0000 −1.00000
\(442\) 0.633975 + 0.313467i 0.0301551 + 0.0149101i
\(443\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(444\) 0 0
\(445\) 18.6603 12.3205i 0.884581 0.584048i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 20.0000 34.6410i 0.943858 1.63481i 0.185837 0.982581i \(-0.440500\pi\)
0.758021 0.652230i \(-0.226166\pi\)
\(450\) −16.6865 13.0981i −0.786611 0.617449i
\(451\) 0 0
\(452\) −4.85641 + 18.1244i −0.228426 + 0.852498i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −17.9641 4.81347i −0.840325 0.225164i −0.187112 0.982339i \(-0.559913\pi\)
−0.653213 + 0.757174i \(0.726579\pi\)
\(458\) −40.9808 10.9808i −1.91491 0.513097i
\(459\) 0 0
\(460\) 0 0
\(461\) 19.8397 + 11.4545i 0.924029 + 0.533488i 0.884918 0.465746i \(-0.154214\pi\)
0.0391109 + 0.999235i \(0.487547\pi\)
\(462\) 0 0
\(463\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(464\) −36.9282 21.3205i −1.71435 0.989780i
\(465\) 0 0
\(466\) −8.66025 + 5.00000i −0.401179 + 0.231621i
\(467\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(468\) −1.39230 21.5885i −0.0643593 0.997927i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 21.6962 5.81347i 0.993399 0.266180i
\(478\) 0 0
\(479\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(480\) 0 0
\(481\) 29.9904 + 26.3564i 1.36744 + 1.20175i
\(482\) −21.9282 21.9282i −0.998802 0.998802i
\(483\) 0 0
\(484\) 19.0526 11.0000i 0.866025 0.500000i
\(485\) −39.0000 + 13.0000i −1.77090 + 0.590300i
\(486\) 0 0
\(487\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(488\) 7.26795 1.94744i 0.329005 0.0881565i
\(489\) 0 0
\(490\) 7.00000 + 21.0000i 0.316228 + 0.948683i
\(491\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(492\) 0 0
\(493\) 1.04552 1.04552i 0.0470877 0.0470877i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) −7.53590 + 21.0526i −0.337016 + 0.941499i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(504\) 0 0
\(505\) 34.1865 22.5718i 1.52128 1.00443i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16.5526 28.6699i −0.733679 1.27077i −0.955300 0.295637i \(-0.904468\pi\)
0.221621 0.975133i \(-0.428865\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −16.0000 + 16.0000i −0.707107 + 0.707107i
\(513\) 0 0
\(514\) −22.2224 + 38.4904i −0.980189 + 1.69774i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) −21.1244 + 8.58846i −0.926364 + 0.376629i
\(521\) −23.6410 −1.03573 −0.517866 0.855462i \(-0.673273\pi\)
−0.517866 + 0.855462i \(0.673273\pi\)
\(522\) −43.6865 11.7058i −1.91211 0.512348i
\(523\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 19.9186 + 11.5000i 0.866025 + 0.500000i
\(530\) −13.0455 19.7583i −0.566661 0.858247i
\(531\) 0 0
\(532\) 0 0
\(533\) −42.9186 + 2.76795i −1.85901 + 0.119893i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −26.0000 26.0000i −1.12094 1.12094i
\(539\) 0 0
\(540\) 0 0
\(541\) 46.3731i 1.99373i 0.0790969 + 0.996867i \(0.474796\pi\)
−0.0790969 + 0.996867i \(0.525204\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −0.392305 0.679492i −0.0168199 0.0291330i
\(545\) −2.67949 44.6410i −0.114777 1.91221i
\(546\) 0 0
\(547\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(548\) −6.94744 + 25.9282i −0.296780 + 1.10760i
\(549\) 6.91154 3.99038i 0.294977 0.170305i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −44.8372 −1.90495
\(555\) 0 0
\(556\) 0 0
\(557\) 28.4545 + 7.62436i 1.20566 + 0.323054i 0.805056 0.593199i \(-0.202135\pi\)
0.400599 + 0.916253i \(0.368802\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 8.31347 31.0263i 0.350682 1.30876i
\(563\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(564\) 0 0
\(565\) 19.9019 6.63397i 0.837280 0.279093i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −22.5167 + 13.0000i −0.943948 + 0.544988i −0.891196 0.453619i \(-0.850133\pi\)
−0.0527519 + 0.998608i \(0.516799\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −12.0000 + 20.7846i −0.500000 + 0.866025i
\(577\) −33.1506 + 33.1506i −1.38008 + 1.38008i −0.535620 + 0.844459i \(0.679922\pi\)
−0.844459 + 0.535620i \(0.820078\pi\)
\(578\) −23.1962 + 6.21539i −0.964833 + 0.258526i
\(579\) 0 0
\(580\) 2.85641 + 47.5885i 0.118606 + 1.97600i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 4.67949i 0.193639i
\(585\) −19.2846 + 14.5981i −0.797320 + 0.603556i
\(586\) 44.9808 1.85814
\(587\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −11.4641 42.7846i −0.471172 1.75844i
\(593\) −2.50962 2.50962i −0.103058 0.103058i 0.653698 0.756756i \(-0.273217\pi\)
−0.756756 + 0.653698i \(0.773217\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 38.3205 22.1244i 1.56967 0.906249i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) −7.66987 13.2846i −0.312861 0.541891i 0.666120 0.745845i \(-0.267954\pi\)
−0.978980 + 0.203954i \(0.934621\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −22.0000 11.0000i −0.894427 0.447214i
\(606\) 0 0
\(607\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −6.29423 5.58142i −0.254846 0.225985i
\(611\) 0 0
\(612\) −0.588457 0.588457i −0.0237870 0.0237870i
\(613\) −11.2776 + 42.0885i −0.455497 + 1.69994i 0.231127 + 0.972924i \(0.425759\pi\)
−0.686624 + 0.727013i \(0.740908\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −10.5455 39.3564i −0.424547 1.58443i −0.764911 0.644136i \(-0.777217\pi\)
0.340365 0.940294i \(-0.389449\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 24.2846 5.93782i 0.971384 0.237513i
\(626\) 43.3013 25.0000i 1.73067 0.999201i
\(627\) 0 0
\(628\) −12.6077 47.0526i −0.503102 1.87760i
\(629\) 1.53590 0.0612403
\(630\) 0 0
\(631\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 34.9019 20.1506i 1.38613 0.800284i
\(635\) 0 0
\(636\) 0 0
\(637\) 25.1865 1.62436i 0.997927 0.0643593i
\(638\) 0 0
\(639\) 0 0
\(640\) 24.7846 + 5.07180i 0.979698 + 0.200480i
\(641\) 19.6506 34.0359i 0.776153 1.34434i −0.157991 0.987441i \(-0.550502\pi\)
0.934144 0.356897i \(-0.116165\pi\)
\(642\) 0 0
\(643\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(648\) −6.58846 + 24.5885i −0.258819 + 0.965926i
\(649\) 0 0
\(650\) 21.0263 + 14.4186i 0.824719 + 0.565543i
\(651\) 0 0
\(652\) 0 0
\(653\) −47.8109 12.8109i −1.87098 0.501329i −0.999949 0.0101092i \(-0.996782\pi\)
−0.871036 0.491220i \(-0.836551\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 41.3205 + 23.8564i 1.61329 + 0.931436i
\(657\) 1.28461 + 4.79423i 0.0501174 + 0.187041i
\(658\) 0 0
\(659\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(660\) 0 0
\(661\) −12.6506 + 7.30385i −0.492053 + 0.284087i −0.725426 0.688301i \(-0.758357\pi\)
0.233373 + 0.972387i \(0.425024\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −23.4904 40.6865i −0.910234 1.57657i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 10.8923 + 2.91858i 0.419867 + 0.112503i 0.462566 0.886585i \(-0.346929\pi\)
−0.0426985 + 0.999088i \(0.513595\pi\)
\(674\) 18.5622 + 32.1506i 0.714988 + 1.23840i
\(675\) 0 0
\(676\) 3.33975 + 25.7846i 0.128452 + 0.991716i
\(677\) 25.0000 + 25.0000i 0.960828 + 0.960828i 0.999261 0.0384331i \(-0.0122367\pi\)
−0.0384331 + 0.999261i \(0.512237\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −0.392305 + 0.784610i −0.0150442 + 0.0300884i
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(684\) 0 0
\(685\) 28.4711 9.49038i 1.08783 0.362609i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −25.5718 + 8.65064i −0.974208 + 0.329563i
\(690\) 0 0
\(691\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(692\) 10.9808 40.9808i 0.417426 1.55785i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −1.16987 + 1.16987i −0.0443121 + 0.0443121i
\(698\) −3.66025 13.6603i −0.138543 0.517048i
\(699\) 0 0
\(700\) 0 0
\(701\) 52.0000 1.96401 0.982006 0.188847i \(-0.0604752\pi\)
0.982006 + 0.188847i \(0.0604752\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −26.1506 + 45.2942i −0.984192 + 1.70467i
\(707\) 0 0
\(708\) 0 0
\(709\) −11.5526 + 20.0096i −0.433865 + 0.751477i −0.997202 0.0747503i \(-0.976184\pi\)
0.563337 + 0.826227i \(0.309517\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −7.32051 + 27.3205i −0.274348 + 1.02388i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(720\) 26.7846 1.60770i 0.998203 0.0599153i
\(721\) 0 0
\(722\) −6.95448 25.9545i −0.258819 0.965926i
\(723\) 0 0
\(724\) 14.4115 + 8.32051i 0.535601 + 0.309229i
\(725\) 42.6410 31.9808i 1.58365 1.18774i
\(726\) 0 0
\(727\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(728\) 0 0
\(729\) 27.0000i 1.00000i
\(730\) 4.36603 2.88269i 0.161594 0.106693i
\(731\) 0 0
\(732\) 0 0
\(733\) −7.15064 7.15064i −0.264115 0.264115i 0.562609 0.826723i \(-0.309798\pi\)
−0.826723 + 0.562609i \(0.809798\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 48.8827 + 13.0981i 1.79940 + 0.482147i
\(739\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(740\) −32.8564 + 37.0526i −1.20783 + 1.36208i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(744\) 0 0
\(745\) −44.2487 22.1244i −1.62115 0.810574i
\(746\) 44.0526i 1.61288i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 53.3013 + 10.6603i 1.94112 + 0.388224i
\(755\) 0 0
\(756\) 0 0
\(757\) 12.8109 47.8109i 0.465620 1.73772i −0.189207 0.981937i \(-0.560592\pi\)
0.654827 0.755779i \(-0.272742\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −34.6410 20.0000i −1.25574 0.724999i −0.283493 0.958974i \(-0.591493\pi\)
−0.972243 + 0.233975i \(0.924827\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −0.186533 + 0.911543i −0.00674413 + 0.0329569i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −25.0000 43.3013i −0.901523 1.56148i −0.825518 0.564376i \(-0.809117\pi\)
−0.0760054 0.997107i \(-0.524217\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 10.3397 10.3397i 0.372136 0.372136i
\(773\) −53.2750 + 14.2750i −1.91617 + 0.513436i −0.925172 + 0.379549i \(0.876079\pi\)
−0.990997 + 0.133887i \(0.957254\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 26.0000 45.0333i 0.933346 1.61660i
\(777\) 0 0
\(778\) −12.5622 + 46.8827i −0.450376 + 1.68083i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −24.2487 14.0000i −0.866025 0.500000i
\(785\) −36.1340 + 40.7487i −1.28968 + 1.45438i
\(786\) 0 0
\(787\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(788\) 26.0000 + 26.0000i 0.926212 + 0.926212i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −7.98076 + 5.32051i −0.283405 + 0.188937i
\(794\) 26.0000i 0.922705i
\(795\) 0 0
\(796\) 0 0
\(797\) 20.4904 5.49038i 0.725807 0.194479i 0.123045 0.992401i \(-0.460734\pi\)
0.602761 + 0.797922i \(0.294067\pi\)
\(798\) 0 0