Properties

Label 784.2.i.a.177.1
Level $784$
Weight $2$
Character 784.177
Analytic conductor $6.260$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26027151847\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 177.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 784.177
Dual form 784.2.i.a.753.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\) \(q+(-1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-3.00000 + 5.19615i) q^{9} +(-0.500000 - 0.866025i) q^{11} -2.00000 q^{13} +3.00000 q^{15} +(1.50000 + 2.59808i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(-1.50000 + 2.59808i) q^{23} +(2.00000 + 3.46410i) q^{25} +9.00000 q^{27} -6.00000 q^{29} +(0.500000 + 0.866025i) q^{31} +(-1.50000 + 2.59808i) q^{33} +(2.50000 - 4.33013i) q^{37} +(3.00000 + 5.19615i) q^{39} +10.0000 q^{41} +4.00000 q^{43} +(-3.00000 - 5.19615i) q^{45} +(-0.500000 + 0.866025i) q^{47} +(4.50000 - 7.79423i) q^{51} +(4.50000 + 7.79423i) q^{53} +1.00000 q^{55} +15.0000 q^{57} +(-1.50000 - 2.59808i) q^{59} +(1.50000 - 2.59808i) q^{61} +(1.00000 - 1.73205i) q^{65} +(5.50000 + 9.52628i) q^{67} +9.00000 q^{69} -16.0000 q^{71} +(3.50000 + 6.06218i) q^{73} +(6.00000 - 10.3923i) q^{75} +(-5.50000 + 9.52628i) q^{79} +(-4.50000 - 7.79423i) q^{81} -4.00000 q^{83} -3.00000 q^{85} +(9.00000 + 15.5885i) q^{87} +(-4.50000 + 7.79423i) q^{89} +(1.50000 - 2.59808i) q^{93} +(-2.50000 - 4.33013i) q^{95} -6.00000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 3q^{3} - q^{5} - 6q^{9} + O(q^{10}) \) \( 2q - 3q^{3} - q^{5} - 6q^{9} - q^{11} - 4q^{13} + 6q^{15} + 3q^{17} - 5q^{19} - 3q^{23} + 4q^{25} + 18q^{27} - 12q^{29} + q^{31} - 3q^{33} + 5q^{37} + 6q^{39} + 20q^{41} + 8q^{43} - 6q^{45} - q^{47} + 9q^{51} + 9q^{53} + 2q^{55} + 30q^{57} - 3q^{59} + 3q^{61} + 2q^{65} + 11q^{67} + 18q^{69} - 32q^{71} + 7q^{73} + 12q^{75} - 11q^{79} - 9q^{81} - 8q^{83} - 6q^{85} + 18q^{87} - 9q^{89} + 3q^{93} - 5q^{95} - 12q^{97} + 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(687\) \(689\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.50000 2.59808i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(4\) 0 0
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i −0.955901 0.293691i \(-0.905116\pi\)
0.732294 + 0.680989i \(0.238450\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −3.00000 + 5.19615i −1.00000 + 1.73205i
\(10\) 0 0
\(11\) −0.500000 0.866025i −0.150756 0.261116i 0.780750 0.624844i \(-0.214837\pi\)
−0.931505 + 0.363727i \(0.881504\pi\)
\(12\) 0 0
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 3.00000 0.774597
\(16\) 0 0
\(17\) 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i \(-0.0481447\pi\)
−0.624780 + 0.780801i \(0.714811\pi\)
\(18\) 0 0
\(19\) −2.50000 + 4.33013i −0.573539 + 0.993399i 0.422659 + 0.906289i \(0.361097\pi\)
−0.996199 + 0.0871106i \(0.972237\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.50000 + 2.59808i −0.312772 + 0.541736i −0.978961 0.204046i \(-0.934591\pi\)
0.666190 + 0.745782i \(0.267924\pi\)
\(24\) 0 0
\(25\) 2.00000 + 3.46410i 0.400000 + 0.692820i
\(26\) 0 0
\(27\) 9.00000 1.73205
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) 0.500000 + 0.866025i 0.0898027 + 0.155543i 0.907428 0.420208i \(-0.138043\pi\)
−0.817625 + 0.575751i \(0.804710\pi\)
\(32\) 0 0
\(33\) −1.50000 + 2.59808i −0.261116 + 0.452267i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.50000 4.33013i 0.410997 0.711868i −0.584002 0.811752i \(-0.698514\pi\)
0.994999 + 0.0998840i \(0.0318472\pi\)
\(38\) 0 0
\(39\) 3.00000 + 5.19615i 0.480384 + 0.832050i
\(40\) 0 0
\(41\) 10.0000 1.56174 0.780869 0.624695i \(-0.214777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) −3.00000 5.19615i −0.447214 0.774597i
\(46\) 0 0
\(47\) −0.500000 + 0.866025i −0.0729325 + 0.126323i −0.900185 0.435507i \(-0.856569\pi\)
0.827253 + 0.561830i \(0.189902\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 4.50000 7.79423i 0.630126 1.09141i
\(52\) 0 0
\(53\) 4.50000 + 7.79423i 0.618123 + 1.07062i 0.989828 + 0.142269i \(0.0454398\pi\)
−0.371706 + 0.928351i \(0.621227\pi\)
\(54\) 0 0
\(55\) 1.00000 0.134840
\(56\) 0 0
\(57\) 15.0000 1.98680
\(58\) 0 0
\(59\) −1.50000 2.59808i −0.195283 0.338241i 0.751710 0.659494i \(-0.229229\pi\)
−0.946993 + 0.321253i \(0.895896\pi\)
\(60\) 0 0
\(61\) 1.50000 2.59808i 0.192055 0.332650i −0.753876 0.657017i \(-0.771818\pi\)
0.945931 + 0.324367i \(0.105151\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.00000 1.73205i 0.124035 0.214834i
\(66\) 0 0
\(67\) 5.50000 + 9.52628i 0.671932 + 1.16382i 0.977356 + 0.211604i \(0.0678686\pi\)
−0.305424 + 0.952217i \(0.598798\pi\)
\(68\) 0 0
\(69\) 9.00000 1.08347
\(70\) 0 0
\(71\) −16.0000 −1.89885 −0.949425 0.313993i \(-0.898333\pi\)
−0.949425 + 0.313993i \(0.898333\pi\)
\(72\) 0 0
\(73\) 3.50000 + 6.06218i 0.409644 + 0.709524i 0.994850 0.101361i \(-0.0323196\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 0 0
\(75\) 6.00000 10.3923i 0.692820 1.20000i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −5.50000 + 9.52628i −0.618798 + 1.07179i 0.370907 + 0.928670i \(0.379047\pi\)
−0.989705 + 0.143120i \(0.954286\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 0 0
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) −3.00000 −0.325396
\(86\) 0 0
\(87\) 9.00000 + 15.5885i 0.964901 + 1.67126i
\(88\) 0 0
\(89\) −4.50000 + 7.79423i −0.476999 + 0.826187i −0.999653 0.0263586i \(-0.991609\pi\)
0.522654 + 0.852545i \(0.324942\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 1.50000 2.59808i 0.155543 0.269408i
\(94\) 0 0
\(95\) −2.50000 4.33013i −0.256495 0.444262i
\(96\) 0 0
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) 0 0
\(101\) −6.50000 11.2583i −0.646774 1.12025i −0.983889 0.178782i \(-0.942784\pi\)
0.337115 0.941464i \(-0.390549\pi\)
\(102\) 0 0
\(103\) −2.50000 + 4.33013i −0.246332 + 0.426660i −0.962505 0.271263i \(-0.912559\pi\)
0.716173 + 0.697923i \(0.245892\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.50000 + 2.59808i −0.145010 + 0.251166i −0.929377 0.369132i \(-0.879655\pi\)
0.784366 + 0.620298i \(0.212988\pi\)
\(108\) 0 0
\(109\) −5.50000 9.52628i −0.526804 0.912452i −0.999512 0.0312328i \(-0.990057\pi\)
0.472708 0.881219i \(-0.343277\pi\)
\(110\) 0 0
\(111\) −15.0000 −1.42374
\(112\) 0 0
\(113\) −10.0000 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) 0 0
\(115\) −1.50000 2.59808i −0.139876 0.242272i
\(116\) 0 0
\(117\) 6.00000 10.3923i 0.554700 0.960769i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) 0 0
\(123\) −15.0000 25.9808i −1.35250 2.34261i
\(124\) 0 0
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0 0
\(129\) −6.00000 10.3923i −0.528271 0.914991i
\(130\) 0 0
\(131\) −8.50000 + 14.7224i −0.742648 + 1.28630i 0.208637 + 0.977993i \(0.433097\pi\)
−0.951285 + 0.308312i \(0.900236\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −4.50000 + 7.79423i −0.387298 + 0.670820i
\(136\) 0 0
\(137\) −1.50000 2.59808i −0.128154 0.221969i 0.794808 0.606861i \(-0.207572\pi\)
−0.922961 + 0.384893i \(0.874238\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) 3.00000 0.252646
\(142\) 0 0
\(143\) 1.00000 + 1.73205i 0.0836242 + 0.144841i
\(144\) 0 0
\(145\) 3.00000 5.19615i 0.249136 0.431517i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −7.50000 + 12.9904i −0.614424 + 1.06421i 0.376061 + 0.926595i \(0.377278\pi\)
−0.990485 + 0.137619i \(0.956055\pi\)
\(150\) 0 0
\(151\) 7.50000 + 12.9904i 0.610341 + 1.05714i 0.991183 + 0.132502i \(0.0423010\pi\)
−0.380841 + 0.924640i \(0.624366\pi\)
\(152\) 0 0
\(153\) −18.0000 −1.45521
\(154\) 0 0
\(155\) −1.00000 −0.0803219
\(156\) 0 0
\(157\) 7.50000 + 12.9904i 0.598565 + 1.03675i 0.993033 + 0.117836i \(0.0375956\pi\)
−0.394468 + 0.918910i \(0.629071\pi\)
\(158\) 0 0
\(159\) 13.5000 23.3827i 1.07062 1.85437i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 4.50000 7.79423i 0.352467 0.610491i −0.634214 0.773158i \(-0.718676\pi\)
0.986681 + 0.162667i \(0.0520095\pi\)
\(164\) 0 0
\(165\) −1.50000 2.59808i −0.116775 0.202260i
\(166\) 0 0
\(167\) −20.0000 −1.54765 −0.773823 0.633402i \(-0.781658\pi\)
−0.773823 + 0.633402i \(0.781658\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) −15.0000 25.9808i −1.14708 1.98680i
\(172\) 0 0
\(173\) −10.5000 + 18.1865i −0.798300 + 1.38270i 0.122422 + 0.992478i \(0.460934\pi\)
−0.920722 + 0.390218i \(0.872399\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −4.50000 + 7.79423i −0.338241 + 0.585850i
\(178\) 0 0
\(179\) −0.500000 0.866025i −0.0373718 0.0647298i 0.846735 0.532016i \(-0.178565\pi\)
−0.884106 + 0.467286i \(0.845232\pi\)
\(180\) 0 0
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 0 0
\(183\) −9.00000 −0.665299
\(184\) 0 0
\(185\) 2.50000 + 4.33013i 0.183804 + 0.318357i
\(186\) 0 0
\(187\) 1.50000 2.59808i 0.109691 0.189990i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 8.50000 14.7224i 0.615038 1.06528i −0.375339 0.926887i \(-0.622474\pi\)
0.990378 0.138390i \(-0.0441928\pi\)
\(192\) 0 0
\(193\) 2.50000 + 4.33013i 0.179954 + 0.311689i 0.941865 0.335993i \(-0.109072\pi\)
−0.761911 + 0.647682i \(0.775738\pi\)
\(194\) 0 0
\(195\) −6.00000 −0.429669
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) 4.50000 + 7.79423i 0.318997 + 0.552518i 0.980279 0.197619i \(-0.0633208\pi\)
−0.661282 + 0.750137i \(0.729987\pi\)
\(200\) 0 0
\(201\) 16.5000 28.5788i 1.16382 2.01580i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −5.00000 + 8.66025i −0.349215 + 0.604858i
\(206\) 0 0
\(207\) −9.00000 15.5885i −0.625543 1.08347i
\(208\) 0 0
\(209\) 5.00000 0.345857
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) 0 0
\(213\) 24.0000 + 41.5692i 1.64445 + 2.84828i
\(214\) 0 0
\(215\) −2.00000 + 3.46410i −0.136399 + 0.236250i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 10.5000 18.1865i 0.709524 1.22893i
\(220\) 0 0
\(221\) −3.00000 5.19615i −0.201802 0.349531i
\(222\) 0 0
\(223\) 24.0000 1.60716 0.803579 0.595198i \(-0.202926\pi\)
0.803579 + 0.595198i \(0.202926\pi\)
\(224\) 0 0
\(225\) −24.0000 −1.60000
\(226\) 0 0
\(227\) −3.50000 6.06218i −0.232303 0.402361i 0.726182 0.687502i \(-0.241293\pi\)
−0.958485 + 0.285141i \(0.907959\pi\)
\(228\) 0 0
\(229\) 3.50000 6.06218i 0.231287 0.400600i −0.726900 0.686743i \(-0.759040\pi\)
0.958187 + 0.286143i \(0.0923732\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.50000 11.2583i 0.425829 0.737558i −0.570668 0.821181i \(-0.693316\pi\)
0.996497 + 0.0836229i \(0.0266491\pi\)
\(234\) 0 0
\(235\) −0.500000 0.866025i −0.0326164 0.0564933i
\(236\) 0 0
\(237\) 33.0000 2.14358
\(238\) 0 0
\(239\) 4.00000 0.258738 0.129369 0.991596i \(-0.458705\pi\)
0.129369 + 0.991596i \(0.458705\pi\)
\(240\) 0 0
\(241\) −8.50000 14.7224i −0.547533 0.948355i −0.998443 0.0557856i \(-0.982234\pi\)
0.450910 0.892570i \(-0.351100\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 5.00000 8.66025i 0.318142 0.551039i
\(248\) 0 0
\(249\) 6.00000 + 10.3923i 0.380235 + 0.658586i
\(250\) 0 0
\(251\) 24.0000 1.51487 0.757433 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 0 0
\(253\) 3.00000 0.188608
\(254\) 0 0
\(255\) 4.50000 + 7.79423i 0.281801 + 0.488094i
\(256\) 0 0
\(257\) −6.50000 + 11.2583i −0.405459 + 0.702275i −0.994375 0.105919i \(-0.966222\pi\)
0.588916 + 0.808194i \(0.299555\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 18.0000 31.1769i 1.11417 1.92980i
\(262\) 0 0
\(263\) 1.50000 + 2.59808i 0.0924940 + 0.160204i 0.908560 0.417755i \(-0.137183\pi\)
−0.816066 + 0.577959i \(0.803849\pi\)
\(264\) 0 0
\(265\) −9.00000 −0.552866
\(266\) 0 0
\(267\) 27.0000 1.65237
\(268\) 0 0
\(269\) −8.50000 14.7224i −0.518254 0.897643i −0.999775 0.0212079i \(-0.993249\pi\)
0.481521 0.876435i \(-0.340085\pi\)
\(270\) 0 0
\(271\) 1.50000 2.59808i 0.0911185 0.157822i −0.816864 0.576831i \(-0.804289\pi\)
0.907982 + 0.419009i \(0.137622\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.00000 3.46410i 0.120605 0.208893i
\(276\) 0 0
\(277\) −3.50000 6.06218i −0.210295 0.364241i 0.741512 0.670940i \(-0.234109\pi\)
−0.951807 + 0.306699i \(0.900776\pi\)
\(278\) 0 0
\(279\) −6.00000 −0.359211
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 0 0
\(283\) 8.50000 + 14.7224i 0.505273 + 0.875158i 0.999981 + 0.00609896i \(0.00194137\pi\)
−0.494709 + 0.869059i \(0.664725\pi\)
\(284\) 0 0
\(285\) −7.50000 + 12.9904i −0.444262 + 0.769484i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) 9.00000 + 15.5885i 0.527589 + 0.913812i
\(292\) 0 0
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 0 0
\(295\) 3.00000 0.174667
\(296\) 0 0
\(297\) −4.50000 7.79423i −0.261116 0.452267i
\(298\) 0 0
\(299\) 3.00000 5.19615i 0.173494 0.300501i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −19.5000 + 33.7750i −1.12025 + 1.94032i
\(304\) 0 0
\(305\) 1.50000 + 2.59808i 0.0858898 + 0.148765i
\(306\) 0 0
\(307\) 4.00000 0.228292 0.114146 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 0 0
\(309\) 15.0000 0.853320
\(310\) 0 0
\(311\) −5.50000 9.52628i −0.311876 0.540186i 0.666892 0.745154i \(-0.267624\pi\)
−0.978769 + 0.204968i \(0.934291\pi\)
\(312\) 0 0
\(313\) 15.5000 26.8468i 0.876112 1.51747i 0.0205381 0.999789i \(-0.493462\pi\)
0.855574 0.517681i \(-0.173205\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −13.5000 + 23.3827i −0.758236 + 1.31330i 0.185514 + 0.982642i \(0.440605\pi\)
−0.943750 + 0.330661i \(0.892728\pi\)
\(318\) 0 0
\(319\) 3.00000 + 5.19615i 0.167968 + 0.290929i
\(320\) 0 0
\(321\) 9.00000 0.502331
\(322\) 0 0
\(323\) −15.0000 −0.834622
\(324\) 0 0
\(325\) −4.00000 6.92820i −0.221880 0.384308i
\(326\) 0 0
\(327\) −16.5000 + 28.5788i −0.912452 + 1.58041i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −3.50000 + 6.06218i −0.192377 + 0.333207i −0.946038 0.324057i \(-0.894953\pi\)
0.753660 + 0.657264i \(0.228286\pi\)
\(332\) 0 0
\(333\) 15.0000 + 25.9808i 0.821995 + 1.42374i
\(334\) 0 0
\(335\) −11.0000 −0.600994
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 0 0
\(339\) 15.0000 + 25.9808i 0.814688 + 1.41108i
\(340\) 0 0
\(341\) 0.500000 0.866025i 0.0270765 0.0468979i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −4.50000 + 7.79423i −0.242272 + 0.419627i
\(346\) 0 0
\(347\) 1.50000 + 2.59808i 0.0805242 + 0.139472i 0.903475 0.428640i \(-0.141007\pi\)
−0.822951 + 0.568112i \(0.807674\pi\)
\(348\) 0 0
\(349\) 6.00000 0.321173 0.160586 0.987022i \(-0.448662\pi\)
0.160586 + 0.987022i \(0.448662\pi\)
\(350\) 0 0
\(351\) −18.0000 −0.960769
\(352\) 0 0
\(353\) −2.50000 4.33013i −0.133062 0.230469i 0.791794 0.610789i \(-0.209147\pi\)
−0.924855 + 0.380319i \(0.875814\pi\)
\(354\) 0 0
\(355\) 8.00000 13.8564i 0.424596 0.735422i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −7.50000 + 12.9904i −0.395835 + 0.685606i −0.993207 0.116358i \(-0.962878\pi\)
0.597372 + 0.801964i \(0.296211\pi\)
\(360\) 0 0
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) 0 0
\(363\) −30.0000 −1.57459
\(364\) 0 0
\(365\) −7.00000 −0.366397
\(366\) 0 0
\(367\) −9.50000 16.4545i −0.495896 0.858917i 0.504093 0.863649i \(-0.331827\pi\)
−0.999989 + 0.00473247i \(0.998494\pi\)
\(368\) 0 0
\(369\) −30.0000 + 51.9615i −1.56174 + 2.70501i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −9.50000 + 16.4545i −0.491891 + 0.851981i −0.999956 0.00933789i \(-0.997028\pi\)
0.508065 + 0.861319i \(0.330361\pi\)
\(374\) 0 0
\(375\) 13.5000 + 23.3827i 0.697137 + 1.20748i
\(376\) 0 0
\(377\) 12.0000 0.618031
\(378\) 0 0
\(379\) 16.0000 0.821865 0.410932 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) 0 0
\(381\) −12.0000 20.7846i −0.614779 1.06483i
\(382\) 0 0
\(383\) −4.50000 + 7.79423i −0.229939 + 0.398266i −0.957790 0.287469i \(-0.907186\pi\)
0.727851 + 0.685736i \(0.240519\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −12.0000 + 20.7846i −0.609994 + 1.05654i
\(388\) 0 0
\(389\) −9.50000 16.4545i −0.481669 0.834275i 0.518110 0.855314i \(-0.326636\pi\)
−0.999779 + 0.0210389i \(0.993303\pi\)
\(390\) 0 0
\(391\) −9.00000 −0.455150
\(392\) 0 0
\(393\) 51.0000 2.57261
\(394\) 0 0
\(395\) −5.50000 9.52628i −0.276735 0.479319i
\(396\) 0 0
\(397\) −8.50000 + 14.7224i −0.426603 + 0.738898i −0.996569 0.0827707i \(-0.973623\pi\)
0.569966 + 0.821668i \(0.306956\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1.50000 + 2.59808i −0.0749064 + 0.129742i −0.901046 0.433724i \(-0.857199\pi\)
0.826139 + 0.563466i \(0.190532\pi\)
\(402\) 0 0
\(403\) −1.00000 1.73205i −0.0498135 0.0862796i
\(404\) 0 0
\(405\) 9.00000 0.447214
\(406\) 0 0
\(407\) −5.00000 −0.247841
\(408\) 0 0
\(409\) 9.50000 + 16.4545i 0.469745 + 0.813622i 0.999402 0.0345902i \(-0.0110126\pi\)
−0.529657 + 0.848212i \(0.677679\pi\)
\(410\) 0 0
\(411\) −4.50000 + 7.79423i −0.221969 + 0.384461i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 2.00000 3.46410i 0.0981761 0.170046i
\(416\) 0 0
\(417\) −6.00000 10.3923i −0.293821 0.508913i
\(418\) 0 0
\(419\) 20.0000 0.977064 0.488532 0.872546i \(-0.337533\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 0 0
\(423\) −3.00000 5.19615i −0.145865 0.252646i
\(424\) 0 0
\(425\) −6.00000 + 10.3923i −0.291043 + 0.504101i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 3.00000 5.19615i 0.144841 0.250873i
\(430\) 0 0
\(431\) −20.5000 35.5070i −0.987450 1.71031i −0.630497 0.776192i \(-0.717149\pi\)
−0.356953 0.934122i \(-0.616185\pi\)
\(432\) 0 0
\(433\) 26.0000 1.24948 0.624740 0.780833i \(-0.285205\pi\)
0.624740 + 0.780833i \(0.285205\pi\)
\(434\) 0 0
\(435\) −18.0000 −0.863034
\(436\) 0 0
\(437\) −7.50000 12.9904i −0.358774 0.621414i
\(438\) 0 0
\(439\) 7.50000 12.9904i 0.357955 0.619997i −0.629664 0.776868i \(-0.716807\pi\)
0.987619 + 0.156871i \(0.0501406\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −13.5000 + 23.3827i −0.641404 + 1.11094i 0.343715 + 0.939074i \(0.388315\pi\)
−0.985119 + 0.171871i \(0.945019\pi\)
\(444\) 0 0
\(445\) −4.50000 7.79423i −0.213320 0.369482i
\(446\) 0 0
\(447\) 45.0000 2.12843
\(448\) 0 0
\(449\) −2.00000 −0.0943858 −0.0471929 0.998886i \(-0.515028\pi\)
−0.0471929 + 0.998886i \(0.515028\pi\)
\(450\) 0 0
\(451\) −5.00000 8.66025i −0.235441 0.407795i
\(452\) 0 0
\(453\) 22.5000 38.9711i 1.05714 1.83102i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 8.50000 14.7224i 0.397613 0.688686i −0.595818 0.803120i \(-0.703172\pi\)
0.993431 + 0.114433i \(0.0365053\pi\)
\(458\) 0 0
\(459\) 13.5000 + 23.3827i 0.630126 + 1.09141i
\(460\) 0 0
\(461\) 6.00000 0.279448 0.139724 0.990190i \(-0.455378\pi\)
0.139724 + 0.990190i \(0.455378\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 0 0
\(465\) 1.50000 + 2.59808i 0.0695608 + 0.120483i
\(466\) 0 0
\(467\) −12.5000 + 21.6506i −0.578431 + 1.00187i 0.417229 + 0.908802i \(0.363001\pi\)
−0.995660 + 0.0930703i \(0.970332\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 22.5000 38.9711i 1.03675 1.79570i
\(472\) 0 0
\(473\) −2.00000 3.46410i −0.0919601 0.159280i
\(474\) 0 0
\(475\) −20.0000 −0.917663
\(476\) 0 0
\(477\) −54.0000 −2.47249
\(478\) 0 0
\(479\) 10.5000 + 18.1865i 0.479757 + 0.830964i 0.999730 0.0232187i \(-0.00739140\pi\)
−0.519973 + 0.854183i \(0.674058\pi\)
\(480\) 0 0
\(481\) −5.00000 + 8.66025i −0.227980 + 0.394874i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3.00000 5.19615i 0.136223 0.235945i
\(486\) 0 0
\(487\) −6.50000 11.2583i −0.294543 0.510164i 0.680335 0.732901i \(-0.261834\pi\)
−0.974879 + 0.222737i \(0.928501\pi\)
\(488\) 0 0
\(489\) −27.0000 −1.22098
\(490\) 0 0
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) −9.00000 15.5885i −0.405340 0.702069i
\(494\) 0 0
\(495\) −3.00000 + 5.19615i −0.134840 + 0.233550i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −3.50000 + 6.06218i −0.156682 + 0.271380i −0.933670 0.358134i \(-0.883413\pi\)
0.776989 + 0.629515i \(0.216746\pi\)
\(500\) 0 0
\(501\) 30.0000 + 51.9615i 1.34030 + 2.32147i
\(502\) 0 0
\(503\) 16.0000 0.713405 0.356702 0.934218i \(-0.383901\pi\)
0.356702 + 0.934218i \(0.383901\pi\)
\(504\) 0 0
\(505\) 13.0000 0.578492
\(506\) 0 0
\(507\) 13.5000 + 23.3827i 0.599556 + 1.03846i
\(508\) 0 0
\(509\) 3.50000 6.06218i 0.155135 0.268701i −0.777973 0.628297i \(-0.783752\pi\)
0.933108 + 0.359596i \(0.117085\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −22.5000 + 38.9711i −0.993399 + 1.72062i
\(514\) 0 0
\(515\) −2.50000 4.33013i −0.110163 0.190808i
\(516\) 0 0
\(517\) 1.00000 0.0439799
\(518\) 0 0
\(519\) 63.0000 2.76539
\(520\) 0 0
\(521\) 7.50000 + 12.9904i 0.328581 + 0.569119i 0.982231 0.187678i \(-0.0600963\pi\)
−0.653650 + 0.756797i \(0.726763\pi\)
\(522\) 0 0
\(523\) −6.50000 + 11.2583i −0.284225 + 0.492292i −0.972421 0.233233i \(-0.925070\pi\)
0.688196 + 0.725525i \(0.258403\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.50000 + 2.59808i −0.0653410 + 0.113174i
\(528\) 0 0
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) 0 0
\(531\) 18.0000 0.781133
\(532\) 0 0
\(533\) −20.0000 −0.866296
\(534\) 0 0
\(535\) −1.50000 2.59808i −0.0648507 0.112325i
\(536\) 0 0
\(537\) −1.50000 + 2.59808i −0.0647298 + 0.112115i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 12.5000 21.6506i 0.537417 0.930834i −0.461625 0.887075i \(-0.652733\pi\)
0.999042 0.0437584i \(-0.0139332\pi\)
\(542\) 0 0
\(543\) 33.0000 + 57.1577i 1.41617 + 2.45287i
\(544\) 0 0
\(545\) 11.0000 0.471188
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 0 0
\(549\) 9.00000 + 15.5885i 0.384111 + 0.665299i
\(550\) 0 0
\(551\) 15.0000 25.9808i 0.639021 1.10682i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 7.50000 12.9904i 0.318357 0.551411i
\(556\) 0 0
\(557\) −5.50000 9.52628i −0.233042 0.403641i 0.725660 0.688054i \(-0.241535\pi\)
−0.958702 + 0.284413i \(0.908201\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) −9.00000 −0.379980
\(562\) 0 0
\(563\) −5.50000 9.52628i −0.231797 0.401485i 0.726540 0.687124i \(-0.241127\pi\)
−0.958337 + 0.285640i \(0.907794\pi\)
\(564\) 0 0
\(565\) 5.00000 8.66025i 0.210352 0.364340i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0.500000 0.866025i 0.0209611 0.0363057i −0.855355 0.518043i \(-0.826661\pi\)
0.876316 + 0.481737i \(0.159994\pi\)
\(570\) 0 0
\(571\) −8.50000 14.7224i −0.355714 0.616115i 0.631526 0.775355i \(-0.282429\pi\)
−0.987240 + 0.159240i \(0.949096\pi\)
\(572\) 0 0
\(573\) −51.0000 −2.13056
\(574\) 0 0
\(575\) −12.0000 −0.500435
\(576\) 0 0
\(577\) 15.5000 + 26.8468i 0.645273 + 1.11765i 0.984238 + 0.176847i \(0.0565899\pi\)
−0.338965 + 0.940799i \(0.610077\pi\)
\(578\) 0 0
\(579\) 7.50000 12.9904i 0.311689 0.539862i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 4.50000 7.79423i 0.186371 0.322804i
\(584\) 0 0
\(585\) 6.00000 + 10.3923i 0.248069 + 0.429669i
\(586\) 0 0
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 0 0
\(589\) −5.00000 −0.206021
\(590\) 0 0
\(591\) −27.0000 46.7654i −1.11063 1.92367i
\(592\) 0 0
\(593\) 21.5000 37.2391i 0.882899 1.52923i 0.0347964 0.999394i \(-0.488922\pi\)
0.848103 0.529832i \(-0.177745\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 13.5000 23.3827i 0.552518 0.956990i
\(598\) 0 0
\(599\) −10.5000 18.1865i −0.429018 0.743082i 0.567768 0.823189i \(-0.307807\pi\)
−0.996786 + 0.0801071i \(0.974474\pi\)
\(600\) 0 0
\(601\) 34.0000 1.38689 0.693444 0.720510i \(-0.256092\pi\)
0.693444 + 0.720510i \(0.256092\pi\)
\(602\) 0 0
\(603\) −66.0000 −2.68773
\(604\) 0 0
\(605\) 5.00000 + 8.66025i 0.203279 + 0.352089i
\(606\) 0 0
\(607\) 3.50000 6.06218i 0.142061 0.246056i −0.786212 0.617957i \(-0.787961\pi\)
0.928272 + 0.371901i \(0.121294\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.00000 1.73205i 0.0404557 0.0700713i
\(612\) 0 0
\(613\) 10.5000 + 18.1865i 0.424091 + 0.734547i 0.996335 0.0855362i \(-0.0272603\pi\)
−0.572244 + 0.820083i \(0.693927\pi\)
\(614\) 0 0
\(615\) 30.0000 1.20972
\(616\) 0 0
\(617\) 22.0000 0.885687 0.442843 0.896599i \(-0.353970\pi\)
0.442843 + 0.896599i \(0.353970\pi\)
\(618\) 0 0
\(619\) 2.50000 + 4.33013i 0.100483 + 0.174042i 0.911884 0.410448i \(-0.134628\pi\)
−0.811400 + 0.584491i \(0.801294\pi\)
\(620\) 0 0
\(621\) −13.5000 + 23.3827i −0.541736 + 0.938315i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −5.50000 + 9.52628i −0.220000 + 0.381051i
\(626\) 0 0
\(627\) −7.50000 12.9904i −0.299521 0.518786i
\(628\) 0 0
\(629\) 15.0000 0.598089
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) 18.0000 + 31.1769i 0.715436 + 1.23917i
\(634\) 0 0
\(635\) −4.00000 + 6.92820i −0.158735 + 0.274937i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 48.0000 83.1384i 1.89885 3.28891i
\(640\) 0 0
\(641\) −7.50000 12.9904i −0.296232 0.513089i 0.679039 0.734103i \(-0.262397\pi\)
−0.975271 + 0.221013i \(0.929064\pi\)
\(642\) 0 0
\(643\) −44.0000 −1.73519 −0.867595 0.497271i \(-0.834335\pi\)
−0.867595 + 0.497271i \(0.834335\pi\)
\(644\) 0 0
\(645\) 12.0000 0.472500
\(646\) 0 0
\(647\) −21.5000 37.2391i −0.845252 1.46402i −0.885402 0.464826i \(-0.846117\pi\)
0.0401498 0.999194i \(-0.487216\pi\)
\(648\) 0 0
\(649\) −1.50000 + 2.59808i −0.0588802 + 0.101983i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.50000 4.33013i 0.0978326 0.169451i −0.812955 0.582327i \(-0.802142\pi\)
0.910787 + 0.412876i \(0.135476\pi\)
\(654\) 0 0
\(655\) −8.50000 14.7224i −0.332122 0.575253i
\(656\) 0 0
\(657\) −42.0000 −1.63858
\(658\) 0 0
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0 0
\(661\) −0.500000 0.866025i −0.0194477 0.0336845i 0.856138 0.516748i \(-0.172857\pi\)
−0.875585 + 0.483063i \(0.839524\pi\)
\(662\) 0 0
\(663\) −9.00000 + 15.5885i −0.349531 + 0.605406i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 9.00000 15.5885i 0.348481 0.603587i
\(668\) 0 0
\(669\) −36.0000 62.3538i −1.39184 2.41074i
\(670\) 0 0
\(671\) −3.00000 −0.115814
\(672\) 0 0
\(673\) −2.00000 −0.0770943 −0.0385472 0.999257i \(-0.512273\pi\)
−0.0385472 + 0.999257i \(0.512273\pi\)
\(674\) 0 0
\(675\) 18.0000 + 31.1769i 0.692820 + 1.20000i
\(676\) 0 0
\(677\) −4.50000 + 7.79423i −0.172949 + 0.299557i −0.939450 0.342687i \(-0.888663\pi\)
0.766501 + 0.642244i \(0.221996\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −10.5000 + 18.1865i −0.402361 + 0.696909i
\(682\) 0 0
\(683\) 19.5000 + 33.7750i 0.746147 + 1.29236i 0.949657 + 0.313291i \(0.101432\pi\)
−0.203510 + 0.979073i \(0.565235\pi\)
\(684\) 0 0
\(685\) 3.00000 0.114624
\(686\) 0 0
\(687\) −21.0000 −0.801200
\(688\) 0 0
\(689\) −9.00000 15.5885i −0.342873 0.593873i
\(690\) 0 0
\(691\) 23.5000 40.7032i 0.893982 1.54842i 0.0589228 0.998263i \(-0.481233\pi\)
0.835059 0.550160i \(-0.185433\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.00000 + 3.46410i −0.0758643 + 0.131401i
\(696\) 0 0
\(697\) 15.0000 + 25.9808i 0.568166 + 0.984092i
\(698\) 0 0
\(699\) −39.0000 −1.47512
\(700\) 0 0
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) 12.5000 + 21.6506i 0.471446 + 0.816569i
\(704\) 0 0
\(705\) −1.50000 + 2.59808i −0.0564933 + 0.0978492i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −13.5000 + 23.3827i −0.507003 + 0.878155i 0.492964 + 0.870050i \(0.335913\pi\)
−0.999967 + 0.00810550i \(0.997420\pi\)
\(710\) 0 0
\(711\) −33.0000 57.1577i −1.23760 2.14358i
\(712\) 0 0
\(713\) −3.00000 −0.112351
\(714\) 0 0
\(715\) −2.00000 −0.0747958
\(716\) 0 0
\(717\) −6.00000 10.3923i −0.224074 0.388108i
\(718\) 0 0
\(719\) −14.5000 + 25.1147i −0.540759 + 0.936622i 0.458102 + 0.888900i \(0.348529\pi\)
−0.998861 + 0.0477220i \(0.984804\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −25.5000 + 44.1673i −0.948355 + 1.64260i
\(724\) 0 0
\(725\) −12.0000 20.7846i −0.445669 0.771921i
\(726\) 0 0
\(727\) 16.0000 0.593407 0.296704 0.954970i \(-0.404113\pi\)
0.296704 + 0.954970i \(0.404113\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 6.00000 + 10.3923i 0.221918 + 0.384373i
\(732\) 0 0
\(733\) 5.50000 9.52628i 0.203147 0.351861i −0.746394 0.665505i \(-0.768216\pi\)
0.949541 + 0.313644i \(0.101550\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5.50000 9.52628i 0.202595 0.350905i
\(738\) 0 0
\(739\) −20.5000 35.5070i −0.754105 1.30615i −0.945818 0.324697i \(-0.894738\pi\)
0.191714 0.981451i \(-0.438596\pi\)
\(740\) 0 0
\(741\) −30.0000 −1.10208
\(742\) 0 0
\(743\) −32.0000 −1.17397 −0.586983 0.809599i \(-0.699684\pi\)
−0.586983 + 0.809599i \(0.699684\pi\)
\(744\) 0 0
\(745\) −7.50000 12.9904i −0.274779 0.475931i
\(746\) 0 0
\(747\) 12.0000 20.7846i 0.439057 0.760469i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −23.5000 + 40.7032i −0.857527 + 1.48528i 0.0167534 + 0.999860i \(0.494667\pi\)
−0.874281 + 0.485421i \(0.838666\pi\)
\(752\) 0 0
\(753\) −36.0000 62.3538i −1.31191 2.27230i
\(754\) 0 0
\(755\) −15.0000 −0.545906
\(756\) 0 0
\(757\) 34.0000 1.23575 0.617876 0.786276i \(-0.287994\pi\)
0.617876 + 0.786276i \(0.287994\pi\)
\(758\) 0 0
\(759\) −4.50000 7.79423i −0.163340 0.282913i
\(760\) 0 0
\(761\) 13.5000 23.3827i 0.489375 0.847622i −0.510551 0.859848i \(-0.670558\pi\)
0.999925 + 0.0122260i \(0.00389175\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 9.00000 15.5885i 0.325396 0.563602i
\(766\) 0 0
\(767\) 3.00000 + 5.19615i 0.108324 + 0.187622i
\(768\) 0 0
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 0 0
\(771\) 39.0000 1.40455
\(772\) 0 0
\(773\) 17.5000 + 30.3109i 0.629431 + 1.09021i 0.987666 + 0.156575i \(0.0500454\pi\)
−0.358235 + 0.933632i \(0.616621\pi\)
\(774\) 0 0
\(775\) −2.00000 + 3.46410i −0.0718421 + 0.124434i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −25.0000 + 43.3013i −0.895718 + 1.55143i
\(780\) 0 0
\(781\) 8.00000 + 13.8564i 0.286263 + 0.495821i
\(782\) 0 0
\(783\) −54.0000 −1.92980
\(784\) 0 0
\(785\) −15.0000 −0.535373
\(786\) 0 0
\(787\) 6.50000 + 11.2583i 0.231700 + 0.401316i 0.958308 0.285736i \(-0.0922379\pi\)
−0.726609 + 0.687052i \(0.758905\pi\)
\(788\) 0 0
\(789\) 4.50000 7.79423i 0.160204 0.277482i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −3.00000 + 5.19615i −0.106533 + 0.184521i
\(794\) 0 0
\(795\) 13.5000 + 23.3827i 0.478796 + 0.829298i
\(796\) 0 0
\(797\) −42.0000 −1.48772 −0.743858 0.668338i \(-0.767006\pi\)
−0.743858 + 0.668338i \(0.767006\pi\)
\(798\) 0 0