Properties

Label 1152.2.p.e.959.2
Level $1152$
Weight $2$
Character 1152.959
Analytic conductor $9.199$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: 16.0.9349208943630483456.9
Defining polynomial: \(x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + 9297 x^{8} - 11276 x^{7} + 11224 x^{6} - 9024 x^{5} + 5736 x^{4} - 2780 x^{3} + 972 x^{2} - 220 x + 25\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 959.2
Root \(0.500000 - 2.74530i\) of defining polynomial
Character \(\chi\) \(=\) 1152.959
Dual form 1152.2.p.e.191.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.65068 - 0.524648i) q^{3} +(1.57313 - 2.72474i) q^{5} +(-2.21650 + 1.27970i) q^{7} +(2.44949 + 1.73205i) q^{9} +O(q^{10})\) \(q+(-1.65068 - 0.524648i) q^{3} +(1.57313 - 2.72474i) q^{5} +(-2.21650 + 1.27970i) q^{7} +(2.44949 + 1.73205i) q^{9} +(-2.02166 + 1.16721i) q^{11} +(2.59808 + 1.50000i) q^{13} +(-4.02627 + 3.67234i) q^{15} +4.24264i q^{17} +8.08665 q^{19} +(4.33013 - 0.949490i) q^{21} +(0.642559 - 1.11295i) q^{23} +(-2.44949 - 4.24264i) q^{25} +(-3.13461 - 4.14418i) q^{27} +(1.18386 + 2.05051i) q^{29} +(7.64580 + 4.41431i) q^{31} +(3.94949 - 0.866025i) q^{33} +8.05254i q^{35} -7.34847i q^{37} +(-3.50162 - 3.83909i) q^{39} +(-8.17423 - 4.71940i) q^{41} +(-1.11295 - 1.92768i) q^{43} +(8.57277 - 3.94949i) q^{45} +(-4.78674 - 8.29088i) q^{47} +(-0.224745 + 0.389270i) q^{49} +(2.22589 - 7.00324i) q^{51} +8.34242 q^{53} +7.34468i q^{55} +(-13.3485 - 4.24264i) q^{57} +(1.11295 + 0.642559i) q^{59} +(7.79423 - 4.50000i) q^{61} +(-7.64580 - 0.704487i) q^{63} +(8.17423 - 4.71940i) q^{65} +(-0.204229 + 0.353736i) q^{67} +(-1.64456 + 1.50000i) q^{69} +14.5841 q^{71} -1.55051 q^{73} +(1.81743 + 8.28836i) q^{75} +(2.98735 - 5.17423i) q^{77} +(8.93092 - 5.15627i) q^{79} +(3.00000 + 8.48528i) q^{81} +(-2.93038 + 1.69185i) q^{83} +(11.5601 + 6.67423i) q^{85} +(-0.878383 - 4.00585i) q^{87} +6.14966i q^{89} -7.67819 q^{91} +(-10.3048 - 11.2980i) q^{93} +(12.7214 - 22.0341i) q^{95} +(6.62372 + 11.4726i) q^{97} +(-6.97370 - 0.642559i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q + 24q^{33} - 72q^{41} + 16q^{49} - 96q^{57} + 72q^{65} - 64q^{73} + 48q^{81} + 8q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.65068 0.524648i −0.953021 0.302905i
\(4\) 0 0
\(5\) 1.57313 2.72474i 0.703526 1.21854i −0.263695 0.964606i \(-0.584941\pi\)
0.967221 0.253937i \(-0.0817255\pi\)
\(6\) 0 0
\(7\) −2.21650 + 1.27970i −0.837759 + 0.483680i −0.856502 0.516144i \(-0.827367\pi\)
0.0187428 + 0.999824i \(0.494034\pi\)
\(8\) 0 0
\(9\) 2.44949 + 1.73205i 0.816497 + 0.577350i
\(10\) 0 0
\(11\) −2.02166 + 1.16721i −0.609554 + 0.351926i −0.772791 0.634661i \(-0.781140\pi\)
0.163237 + 0.986587i \(0.447807\pi\)
\(12\) 0 0
\(13\) 2.59808 + 1.50000i 0.720577 + 0.416025i 0.814965 0.579510i \(-0.196756\pi\)
−0.0943882 + 0.995535i \(0.530089\pi\)
\(14\) 0 0
\(15\) −4.02627 + 3.67234i −1.03958 + 0.948195i
\(16\) 0 0
\(17\) 4.24264i 1.02899i 0.857493 + 0.514496i \(0.172021\pi\)
−0.857493 + 0.514496i \(0.827979\pi\)
\(18\) 0 0
\(19\) 8.08665 1.85520 0.927602 0.373570i \(-0.121866\pi\)
0.927602 + 0.373570i \(0.121866\pi\)
\(20\) 0 0
\(21\) 4.33013 0.949490i 0.944911 0.207196i
\(22\) 0 0
\(23\) 0.642559 1.11295i 0.133983 0.232065i −0.791226 0.611524i \(-0.790557\pi\)
0.925208 + 0.379459i \(0.123890\pi\)
\(24\) 0 0
\(25\) −2.44949 4.24264i −0.489898 0.848528i
\(26\) 0 0
\(27\) −3.13461 4.14418i −0.603256 0.797548i
\(28\) 0 0
\(29\) 1.18386 + 2.05051i 0.219838 + 0.380770i 0.954758 0.297383i \(-0.0961139\pi\)
−0.734920 + 0.678153i \(0.762781\pi\)
\(30\) 0 0
\(31\) 7.64580 + 4.41431i 1.37323 + 0.792833i 0.991333 0.131374i \(-0.0419387\pi\)
0.381894 + 0.924206i \(0.375272\pi\)
\(32\) 0 0
\(33\) 3.94949 0.866025i 0.687518 0.150756i
\(34\) 0 0
\(35\) 8.05254i 1.36113i
\(36\) 0 0
\(37\) 7.34847i 1.20808i −0.796954 0.604040i \(-0.793557\pi\)
0.796954 0.604040i \(-0.206443\pi\)
\(38\) 0 0
\(39\) −3.50162 3.83909i −0.560708 0.614747i
\(40\) 0 0
\(41\) −8.17423 4.71940i −1.27660 0.737046i −0.300379 0.953820i \(-0.597113\pi\)
−0.976222 + 0.216774i \(0.930447\pi\)
\(42\) 0 0
\(43\) −1.11295 1.92768i −0.169723 0.293968i 0.768600 0.639730i \(-0.220954\pi\)
−0.938322 + 0.345762i \(0.887621\pi\)
\(44\) 0 0
\(45\) 8.57277 3.94949i 1.27795 0.588755i
\(46\) 0 0
\(47\) −4.78674 8.29088i −0.698218 1.20935i −0.969084 0.246732i \(-0.920643\pi\)
0.270866 0.962617i \(-0.412690\pi\)
\(48\) 0 0
\(49\) −0.224745 + 0.389270i −0.0321064 + 0.0556099i
\(50\) 0 0
\(51\) 2.22589 7.00324i 0.311687 0.980650i
\(52\) 0 0
\(53\) 8.34242 1.14592 0.572960 0.819584i \(-0.305795\pi\)
0.572960 + 0.819584i \(0.305795\pi\)
\(54\) 0 0
\(55\) 7.34468i 0.990357i
\(56\) 0 0
\(57\) −13.3485 4.24264i −1.76805 0.561951i
\(58\) 0 0
\(59\) 1.11295 + 0.642559i 0.144893 + 0.0836541i 0.570694 0.821163i \(-0.306674\pi\)
−0.425801 + 0.904817i \(0.640008\pi\)
\(60\) 0 0
\(61\) 7.79423 4.50000i 0.997949 0.576166i 0.0903080 0.995914i \(-0.471215\pi\)
0.907641 + 0.419748i \(0.137882\pi\)
\(62\) 0 0
\(63\) −7.64580 0.704487i −0.963281 0.0887570i
\(64\) 0 0
\(65\) 8.17423 4.71940i 1.01389 0.585369i
\(66\) 0 0
\(67\) −0.204229 + 0.353736i −0.0249506 + 0.0432157i −0.878231 0.478237i \(-0.841276\pi\)
0.853281 + 0.521452i \(0.174610\pi\)
\(68\) 0 0
\(69\) −1.64456 + 1.50000i −0.197982 + 0.180579i
\(70\) 0 0
\(71\) 14.5841 1.73082 0.865409 0.501066i \(-0.167059\pi\)
0.865409 + 0.501066i \(0.167059\pi\)
\(72\) 0 0
\(73\) −1.55051 −0.181473 −0.0907367 0.995875i \(-0.528922\pi\)
−0.0907367 + 0.995875i \(0.528922\pi\)
\(74\) 0 0
\(75\) 1.81743 + 8.28836i 0.209859 + 0.957058i
\(76\) 0 0
\(77\) 2.98735 5.17423i 0.340440 0.589659i
\(78\) 0 0
\(79\) 8.93092 5.15627i 1.00481 0.580126i 0.0951401 0.995464i \(-0.469670\pi\)
0.909667 + 0.415338i \(0.136337\pi\)
\(80\) 0 0
\(81\) 3.00000 + 8.48528i 0.333333 + 0.942809i
\(82\) 0 0
\(83\) −2.93038 + 1.69185i −0.321651 + 0.185705i −0.652128 0.758109i \(-0.726124\pi\)
0.330477 + 0.943814i \(0.392790\pi\)
\(84\) 0 0
\(85\) 11.5601 + 6.67423i 1.25387 + 0.723922i
\(86\) 0 0
\(87\) −0.878383 4.00585i −0.0941726 0.429472i
\(88\) 0 0
\(89\) 6.14966i 0.651863i 0.945393 + 0.325932i \(0.105678\pi\)
−0.945393 + 0.325932i \(0.894322\pi\)
\(90\) 0 0
\(91\) −7.67819 −0.804893
\(92\) 0 0
\(93\) −10.3048 11.2980i −1.06856 1.17154i
\(94\) 0 0
\(95\) 12.7214 22.0341i 1.30518 2.26065i
\(96\) 0 0
\(97\) 6.62372 + 11.4726i 0.672537 + 1.16487i 0.977182 + 0.212403i \(0.0681289\pi\)
−0.304645 + 0.952466i \(0.598538\pi\)
\(98\) 0 0
\(99\) −6.97370 0.642559i −0.700883 0.0645797i
\(100\) 0 0
\(101\) −1.57313 2.72474i −0.156533 0.271122i 0.777083 0.629398i \(-0.216698\pi\)
−0.933616 + 0.358275i \(0.883365\pi\)
\(102\) 0 0
\(103\) 7.35698 + 4.24755i 0.724905 + 0.418524i 0.816555 0.577267i \(-0.195881\pi\)
−0.0916506 + 0.995791i \(0.529214\pi\)
\(104\) 0 0
\(105\) 4.22474 13.2922i 0.412293 1.29718i
\(106\) 0 0
\(107\) 18.2037i 1.75981i −0.475145 0.879907i \(-0.657604\pi\)
0.475145 0.879907i \(-0.342396\pi\)
\(108\) 0 0
\(109\) 1.34847i 0.129160i −0.997913 0.0645800i \(-0.979429\pi\)
0.997913 0.0645800i \(-0.0205708\pi\)
\(110\) 0 0
\(111\) −3.85536 + 12.1300i −0.365934 + 1.15133i
\(112\) 0 0
\(113\) 4.50000 + 2.59808i 0.423324 + 0.244406i 0.696499 0.717558i \(-0.254740\pi\)
−0.273174 + 0.961965i \(0.588074\pi\)
\(114\) 0 0
\(115\) −2.02166 3.50162i −0.188521 0.326528i
\(116\) 0 0
\(117\) 3.76588 + 8.17423i 0.348156 + 0.755708i
\(118\) 0 0
\(119\) −5.42930 9.40382i −0.497703 0.862047i
\(120\) 0 0
\(121\) −2.77526 + 4.80688i −0.252296 + 0.436989i
\(122\) 0 0
\(123\) 11.0170 + 12.0788i 0.993372 + 1.08911i
\(124\) 0 0
\(125\) 0.317837 0.0284282
\(126\) 0 0
\(127\) 21.2921i 1.88937i 0.327983 + 0.944684i \(0.393631\pi\)
−0.327983 + 0.944684i \(0.606369\pi\)
\(128\) 0 0
\(129\) 0.825765 + 3.76588i 0.0727046 + 0.331568i
\(130\) 0 0
\(131\) −1.52140 0.878383i −0.132926 0.0767447i 0.432063 0.901844i \(-0.357786\pi\)
−0.564988 + 0.825099i \(0.691119\pi\)
\(132\) 0 0
\(133\) −17.9241 + 10.3485i −1.55421 + 0.897326i
\(134\) 0 0
\(135\) −16.2230 + 2.02166i −1.39625 + 0.173997i
\(136\) 0 0
\(137\) 15.5227 8.96204i 1.32619 0.765679i 0.341485 0.939887i \(-0.389070\pi\)
0.984709 + 0.174209i \(0.0557367\pi\)
\(138\) 0 0
\(139\) −8.79114 + 15.2267i −0.745654 + 1.29151i 0.204234 + 0.978922i \(0.434530\pi\)
−0.949888 + 0.312589i \(0.898804\pi\)
\(140\) 0 0
\(141\) 3.55159 + 16.1969i 0.299098 + 1.36403i
\(142\) 0 0
\(143\) −7.00324 −0.585641
\(144\) 0 0
\(145\) 7.44949 0.618646
\(146\) 0 0
\(147\) 0.575211 0.524648i 0.0474426 0.0432722i
\(148\) 0 0
\(149\) −5.74434 + 9.94949i −0.470595 + 0.815094i −0.999434 0.0336278i \(-0.989294\pi\)
0.528840 + 0.848722i \(0.322627\pi\)
\(150\) 0 0
\(151\) 4.49792 2.59687i 0.366035 0.211331i −0.305690 0.952131i \(-0.598887\pi\)
0.671725 + 0.740801i \(0.265554\pi\)
\(152\) 0 0
\(153\) −7.34847 + 10.3923i −0.594089 + 0.840168i
\(154\) 0 0
\(155\) 24.0557 13.8886i 1.93220 1.11556i
\(156\) 0 0
\(157\) −6.62642 3.82577i −0.528846 0.305329i 0.211700 0.977335i \(-0.432100\pi\)
−0.740546 + 0.672005i \(0.765433\pi\)
\(158\) 0 0
\(159\) −13.7707 4.37683i −1.09208 0.347105i
\(160\) 0 0
\(161\) 3.28913i 0.259220i
\(162\) 0 0
\(163\) 3.63487 0.284705 0.142352 0.989816i \(-0.454533\pi\)
0.142352 + 0.989816i \(0.454533\pi\)
\(164\) 0 0
\(165\) 3.85337 12.1237i 0.299985 0.943831i
\(166\) 0 0
\(167\) 6.07186 10.5168i 0.469855 0.813812i −0.529551 0.848278i \(-0.677640\pi\)
0.999406 + 0.0344659i \(0.0109730\pi\)
\(168\) 0 0
\(169\) −2.00000 3.46410i −0.153846 0.266469i
\(170\) 0 0
\(171\) 19.8082 + 14.0065i 1.51477 + 1.07110i
\(172\) 0 0
\(173\) −2.52664 4.37628i −0.192097 0.332722i 0.753848 0.657049i \(-0.228196\pi\)
−0.945945 + 0.324327i \(0.894862\pi\)
\(174\) 0 0
\(175\) 10.8586 + 6.26922i 0.820833 + 0.473908i
\(176\) 0 0
\(177\) −1.50000 1.64456i −0.112747 0.123613i
\(178\) 0 0
\(179\) 3.04189i 0.227361i −0.993517 0.113681i \(-0.963736\pi\)
0.993517 0.113681i \(-0.0362641\pi\)
\(180\) 0 0
\(181\) 19.3485i 1.43816i −0.694927 0.719080i \(-0.744563\pi\)
0.694927 0.719080i \(-0.255437\pi\)
\(182\) 0 0
\(183\) −15.2267 + 3.33884i −1.12559 + 0.246814i
\(184\) 0 0
\(185\) −20.0227 11.5601i −1.47210 0.849916i
\(186\) 0 0
\(187\) −4.95204 8.57719i −0.362129 0.627226i
\(188\) 0 0
\(189\) 12.2512 + 5.17423i 0.891141 + 0.376370i
\(190\) 0 0
\(191\) 5.36439 + 9.29139i 0.388153 + 0.672302i 0.992201 0.124647i \(-0.0397797\pi\)
−0.604048 + 0.796948i \(0.706446\pi\)
\(192\) 0 0
\(193\) 3.72474 6.45145i 0.268113 0.464385i −0.700262 0.713886i \(-0.746933\pi\)
0.968375 + 0.249501i \(0.0802666\pi\)
\(194\) 0 0
\(195\) −15.9691 + 3.50162i −1.14357 + 0.250756i
\(196\) 0 0
\(197\) −16.6848 −1.18875 −0.594373 0.804190i \(-0.702600\pi\)
−0.594373 + 0.804190i \(0.702600\pi\)
\(198\) 0 0
\(199\) 16.5068i 1.17014i 0.810984 + 0.585068i \(0.198932\pi\)
−0.810984 + 0.585068i \(0.801068\pi\)
\(200\) 0 0
\(201\) 0.522704 0.476756i 0.0368687 0.0336278i
\(202\) 0 0
\(203\) −5.24807 3.02997i −0.368342 0.212662i
\(204\) 0 0
\(205\) −25.7183 + 14.8485i −1.79624 + 1.03706i
\(206\) 0 0
\(207\) 3.50162 1.61320i 0.243380 0.112125i
\(208\) 0 0
\(209\) −16.3485 + 9.43879i −1.13085 + 0.652895i
\(210\) 0 0
\(211\) 3.83909 6.64951i 0.264294 0.457771i −0.703084 0.711107i \(-0.748194\pi\)
0.967378 + 0.253336i \(0.0815277\pi\)
\(212\) 0 0
\(213\) −24.0737 7.65153i −1.64951 0.524274i
\(214\) 0 0
\(215\) −7.00324 −0.477617
\(216\) 0 0
\(217\) −22.5959 −1.53391
\(218\) 0 0
\(219\) 2.55940 + 0.813472i 0.172948 + 0.0549693i
\(220\) 0 0
\(221\) −6.36396 + 11.0227i −0.428086 + 0.741467i
\(222\) 0 0
\(223\) −16.8006 + 9.69985i −1.12505 + 0.649550i −0.942686 0.333680i \(-0.891709\pi\)
−0.182367 + 0.983230i \(0.558376\pi\)
\(224\) 0 0
\(225\) 1.34847 14.6349i 0.0898979 0.975663i
\(226\) 0 0
\(227\) −20.4208 + 11.7900i −1.35538 + 0.782529i −0.988997 0.147936i \(-0.952737\pi\)
−0.366382 + 0.930464i \(0.619404\pi\)
\(228\) 0 0
\(229\) 21.6900 + 12.5227i 1.43331 + 0.827524i 0.997372 0.0724517i \(-0.0230823\pi\)
0.435941 + 0.899975i \(0.356416\pi\)
\(230\) 0 0
\(231\) −7.64580 + 6.97370i −0.503057 + 0.458836i
\(232\) 0 0
\(233\) 8.48528i 0.555889i 0.960597 + 0.277945i \(0.0896532\pi\)
−0.960597 + 0.277945i \(0.910347\pi\)
\(234\) 0 0
\(235\) −30.1207 −1.96486
\(236\) 0 0
\(237\) −17.4473 + 3.82577i −1.13333 + 0.248510i
\(238\) 0 0
\(239\) 0.642559 1.11295i 0.0415637 0.0719905i −0.844495 0.535563i \(-0.820099\pi\)
0.886059 + 0.463573i \(0.153433\pi\)
\(240\) 0 0
\(241\) −6.84847 11.8619i −0.441149 0.764092i 0.556626 0.830763i \(-0.312096\pi\)
−0.997775 + 0.0666710i \(0.978762\pi\)
\(242\) 0 0
\(243\) −0.500258 15.5804i −0.0320915 0.999485i
\(244\) 0 0
\(245\) 0.707107 + 1.22474i 0.0451754 + 0.0782461i
\(246\) 0 0
\(247\) 21.0097 + 12.1300i 1.33682 + 0.771812i
\(248\) 0 0
\(249\) 5.72474 1.25529i 0.362791 0.0795511i
\(250\) 0 0
\(251\) 7.71071i 0.486696i 0.969939 + 0.243348i \(0.0782457\pi\)
−0.969939 + 0.243348i \(0.921754\pi\)
\(252\) 0 0
\(253\) 3.00000i 0.188608i
\(254\) 0 0
\(255\) −15.5804 17.0820i −0.975684 1.06972i
\(256\) 0 0
\(257\) 11.8485 + 6.84072i 0.739087 + 0.426712i 0.821737 0.569866i \(-0.193005\pi\)
−0.0826501 + 0.996579i \(0.526338\pi\)
\(258\) 0 0
\(259\) 9.40382 + 16.2879i 0.584325 + 1.01208i
\(260\) 0 0
\(261\) −0.651729 + 7.07321i −0.0403410 + 0.437821i
\(262\) 0 0
\(263\) −12.0788 20.9211i −0.744811 1.29005i −0.950283 0.311388i \(-0.899206\pi\)
0.205472 0.978663i \(-0.434127\pi\)
\(264\) 0 0
\(265\) 13.1237 22.7310i 0.806184 1.39635i
\(266\) 0 0
\(267\) 3.22641 10.1511i 0.197453 0.621239i
\(268\) 0 0
\(269\) −3.32124 −0.202499 −0.101250 0.994861i \(-0.532284\pi\)
−0.101250 + 0.994861i \(0.532284\pi\)
\(270\) 0 0
\(271\) 13.2054i 0.802173i −0.916040 0.401087i \(-0.868633\pi\)
0.916040 0.401087i \(-0.131367\pi\)
\(272\) 0 0
\(273\) 12.6742 + 4.02834i 0.767080 + 0.243806i
\(274\) 0 0
\(275\) 9.90408 + 5.71812i 0.597239 + 0.344816i
\(276\) 0 0
\(277\) −21.6900 + 12.5227i −1.30322 + 0.752416i −0.980956 0.194232i \(-0.937778\pi\)
−0.322268 + 0.946649i \(0.604445\pi\)
\(278\) 0 0
\(279\) 11.0825 + 24.0557i 0.663493 + 1.44018i
\(280\) 0 0
\(281\) −13.8712 + 8.00853i −0.827485 + 0.477749i −0.852991 0.521926i \(-0.825214\pi\)
0.0255059 + 0.999675i \(0.491880\pi\)
\(282\) 0 0
\(283\) 7.38216 12.7863i 0.438824 0.760065i −0.558775 0.829319i \(-0.688729\pi\)
0.997599 + 0.0692539i \(0.0220618\pi\)
\(284\) 0 0
\(285\) −32.5590 + 29.6969i −1.92863 + 1.75909i
\(286\) 0 0
\(287\) 24.1576 1.42598
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) −4.91456 22.4128i −0.288097 1.31386i
\(292\) 0 0
\(293\) 1.89097 3.27526i 0.110472 0.191342i −0.805489 0.592611i \(-0.798097\pi\)
0.915961 + 0.401268i \(0.131431\pi\)
\(294\) 0 0
\(295\) 3.50162 2.02166i 0.203872 0.117706i
\(296\) 0 0
\(297\) 11.1742 + 4.71940i 0.648395 + 0.273847i
\(298\) 0 0
\(299\) 3.33884 1.92768i 0.193090 0.111481i
\(300\) 0 0
\(301\) 4.93369 + 2.84847i 0.284373 + 0.164183i
\(302\) 0 0
\(303\) 1.16721 + 5.32302i 0.0670543 + 0.305800i
\(304\) 0 0
\(305\) 28.3164i 1.62139i
\(306\) 0 0
\(307\) 23.4430 1.33796 0.668982 0.743279i \(-0.266730\pi\)
0.668982 + 0.743279i \(0.266730\pi\)
\(308\) 0 0
\(309\) −9.91555 10.8712i −0.564076 0.618439i
\(310\) 0 0
\(311\) 10.7937 18.6952i 0.612054 1.06011i −0.378840 0.925462i \(-0.623677\pi\)
0.990894 0.134646i \(-0.0429898\pi\)
\(312\) 0 0
\(313\) 8.94949 + 15.5010i 0.505855 + 0.876167i 0.999977 + 0.00677410i \(0.00215628\pi\)
−0.494122 + 0.869393i \(0.664510\pi\)
\(314\) 0 0
\(315\) −13.9474 + 19.7246i −0.785847 + 1.11136i
\(316\) 0 0
\(317\) 3.69445 + 6.39898i 0.207501 + 0.359402i 0.950927 0.309416i \(-0.100134\pi\)
−0.743426 + 0.668819i \(0.766800\pi\)
\(318\) 0 0
\(319\) −4.78674 2.76363i −0.268006 0.154733i
\(320\) 0 0
\(321\) −9.55051 + 30.0484i −0.533058 + 1.67714i
\(322\) 0 0
\(323\) 34.3087i 1.90899i
\(324\) 0 0
\(325\) 14.6969i 0.815239i
\(326\) 0 0
\(327\) −0.707471 + 2.22589i −0.0391232 + 0.123092i
\(328\) 0 0
\(329\) 21.2196 + 12.2512i 1.16988 + 0.675429i
\(330\) 0 0
\(331\) 9.69985 + 16.8006i 0.533152 + 0.923446i 0.999250 + 0.0387135i \(0.0123260\pi\)
−0.466098 + 0.884733i \(0.654341\pi\)
\(332\) 0 0
\(333\) 12.7279 18.0000i 0.697486 0.986394i
\(334\) 0 0
\(335\) 0.642559 + 1.11295i 0.0351068 + 0.0608067i
\(336\) 0 0
\(337\) −13.8485 + 23.9863i −0.754374 + 1.30661i 0.191311 + 0.981530i \(0.438726\pi\)
−0.945685 + 0.325085i \(0.894607\pi\)
\(338\) 0 0
\(339\) −6.06499 6.64951i −0.329405 0.361152i
\(340\) 0 0
\(341\) −20.6096 −1.11607
\(342\) 0 0
\(343\) 19.0662i 1.02948i
\(344\) 0 0
\(345\) 1.50000 + 6.84072i 0.0807573 + 0.368292i
\(346\) 0 0
\(347\) −6.47344 3.73745i −0.347513 0.200637i 0.316077 0.948734i \(-0.397634\pi\)
−0.663589 + 0.748097i \(0.730968\pi\)
\(348\) 0 0
\(349\) 1.43027 0.825765i 0.0765605 0.0442022i −0.461231 0.887280i \(-0.652592\pi\)
0.537792 + 0.843078i \(0.319259\pi\)
\(350\) 0 0
\(351\) −1.92768 15.4688i −0.102892 0.825664i
\(352\) 0 0
\(353\) −9.82577 + 5.67291i −0.522973 + 0.301938i −0.738150 0.674637i \(-0.764300\pi\)
0.215177 + 0.976575i \(0.430967\pi\)
\(354\) 0 0
\(355\) 22.9428 39.7380i 1.21768 2.10908i
\(356\) 0 0
\(357\) 4.02834 + 18.3712i 0.213203 + 0.972306i
\(358\) 0 0
\(359\) −2.57024 −0.135652 −0.0678260 0.997697i \(-0.521606\pi\)
−0.0678260 + 0.997697i \(0.521606\pi\)
\(360\) 0 0
\(361\) 46.3939 2.44178
\(362\) 0 0
\(363\) 7.10298 6.47860i 0.372810 0.340038i
\(364\) 0 0
\(365\) −2.43916 + 4.22474i −0.127671 + 0.221133i
\(366\) 0 0
\(367\) 2.50533 1.44645i 0.130777 0.0755041i −0.433184 0.901305i \(-0.642610\pi\)
0.563961 + 0.825801i \(0.309277\pi\)
\(368\) 0 0
\(369\) −11.8485 25.7183i −0.616807 1.33884i
\(370\) 0 0
\(371\) −18.4910 + 10.6758i −0.960004 + 0.554259i
\(372\) 0 0
\(373\) −0.262459 0.151531i −0.0135896 0.00784597i 0.493190 0.869922i \(-0.335831\pi\)
−0.506779 + 0.862076i \(0.669164\pi\)
\(374\) 0 0
\(375\) −0.524648 0.166753i −0.0270927 0.00861106i
\(376\) 0 0
\(377\) 7.10318i 0.365832i
\(378\) 0 0
\(379\) 6.26922 0.322028 0.161014 0.986952i \(-0.448524\pi\)
0.161014 + 0.986952i \(0.448524\pi\)
\(380\) 0 0
\(381\) 11.1708 35.1464i 0.572300 1.80061i
\(382\) 0 0
\(383\) −4.78674 + 8.29088i −0.244591 + 0.423644i −0.962017 0.272991i \(-0.911987\pi\)
0.717426 + 0.696635i \(0.245320\pi\)
\(384\) 0 0
\(385\) −9.39898 16.2795i −0.479016 0.829681i
\(386\) 0 0
\(387\) 0.612688 6.64951i 0.0311447 0.338013i
\(388\) 0 0
\(389\) 11.0119 + 19.0732i 0.558327 + 0.967050i 0.997636 + 0.0687146i \(0.0218898\pi\)
−0.439310 + 0.898336i \(0.644777\pi\)
\(390\) 0 0
\(391\) 4.72183 + 2.72615i 0.238793 + 0.137867i
\(392\) 0 0
\(393\) 2.05051 + 2.24813i 0.103435 + 0.113403i
\(394\) 0 0
\(395\) 32.4460i 1.63253i
\(396\) 0 0
\(397\) 28.0454i 1.40756i −0.710419 0.703779i \(-0.751494\pi\)
0.710419 0.703779i \(-0.248506\pi\)
\(398\) 0 0
\(399\) 35.0162 7.67819i 1.75300 0.384390i
\(400\) 0 0
\(401\) 11.4773 + 6.62642i 0.573149 + 0.330908i 0.758406 0.651782i \(-0.225978\pi\)
−0.185257 + 0.982690i \(0.559312\pi\)
\(402\) 0 0
\(403\) 13.2429 + 22.9374i 0.659677 + 1.14259i
\(404\) 0 0
\(405\) 27.8396 + 5.17423i 1.38336 + 0.257110i
\(406\) 0 0
\(407\) 8.57719 + 14.8561i 0.425155 + 0.736391i
\(408\) 0 0
\(409\) −13.2980 + 23.0327i −0.657542 + 1.13890i 0.323708 + 0.946157i \(0.395070\pi\)
−0.981250 + 0.192739i \(0.938263\pi\)
\(410\) 0 0
\(411\) −30.3249 + 6.64951i −1.49582 + 0.327996i
\(412\) 0 0
\(413\) −3.28913 −0.161847
\(414\) 0 0
\(415\) 10.6460i 0.522594i
\(416\) 0 0
\(417\) 22.5000 20.5222i 1.10183 1.00497i
\(418\) 0 0
\(419\) 13.7432 + 7.93463i 0.671398 + 0.387632i 0.796606 0.604499i \(-0.206627\pi\)
−0.125208 + 0.992131i \(0.539960\pi\)
\(420\) 0 0
\(421\) −15.3260 + 8.84847i −0.746943 + 0.431248i −0.824588 0.565733i \(-0.808593\pi\)
0.0776450 + 0.996981i \(0.475260\pi\)
\(422\) 0 0
\(423\) 2.63515 28.5993i 0.128125 1.39055i
\(424\) 0 0
\(425\) 18.0000 10.3923i 0.873128 0.504101i
\(426\) 0 0
\(427\) −11.5173 + 19.9485i −0.557360 + 0.965377i
\(428\) 0 0
\(429\) 11.5601 + 3.67423i 0.558128 + 0.177394i
\(430\) 0 0
\(431\) −2.57024 −0.123804 −0.0619020 0.998082i \(-0.519717\pi\)
−0.0619020 + 0.998082i \(0.519717\pi\)
\(432\) 0 0
\(433\) −22.4495 −1.07885 −0.539427 0.842032i \(-0.681359\pi\)
−0.539427 + 0.842032i \(0.681359\pi\)
\(434\) 0 0
\(435\) −12.2967 3.90836i −0.589583 0.187391i
\(436\) 0 0
\(437\) 5.19615 9.00000i 0.248566 0.430528i
\(438\) 0 0
\(439\) 13.9416 8.04917i 0.665395 0.384166i −0.128935 0.991653i \(-0.541156\pi\)
0.794330 + 0.607487i \(0.207822\pi\)
\(440\) 0 0
\(441\) −1.22474 + 0.564242i −0.0583212 + 0.0268687i
\(442\) 0 0
\(443\) −10.0165 + 5.78304i −0.475899 + 0.274760i −0.718706 0.695314i \(-0.755265\pi\)
0.242807 + 0.970075i \(0.421932\pi\)
\(444\) 0 0
\(445\) 16.7563 + 9.67423i 0.794323 + 0.458603i
\(446\) 0 0
\(447\) 14.7020 13.4097i 0.695383 0.634256i
\(448\) 0 0
\(449\) 31.6055i 1.49156i −0.666194 0.745778i \(-0.732078\pi\)
0.666194 0.745778i \(-0.267922\pi\)
\(450\) 0 0
\(451\) 22.0341 1.03754
\(452\) 0 0
\(453\) −8.78706 + 1.92679i −0.412852 + 0.0905283i
\(454\) 0 0
\(455\) −12.0788 + 20.9211i −0.566263 + 0.980797i
\(456\) 0 0
\(457\) −0.926786 1.60524i −0.0433532 0.0750900i 0.843535 0.537075i \(-0.180471\pi\)
−0.886888 + 0.461985i \(0.847137\pi\)
\(458\) 0 0
\(459\) 17.5823 13.2990i 0.820670 0.620745i
\(460\) 0 0
\(461\) −12.1797 21.0959i −0.567267 0.982535i −0.996835 0.0795004i \(-0.974668\pi\)
0.429568 0.903034i \(-0.358666\pi\)
\(462\) 0 0
\(463\) −21.6523 12.5010i −1.00627 0.580969i −0.0961706 0.995365i \(-0.530659\pi\)
−0.910097 + 0.414396i \(0.863993\pi\)
\(464\) 0 0
\(465\) −46.9949 + 10.3048i −2.17934 + 0.477875i
\(466\) 0 0
\(467\) 25.9144i 1.19917i 0.800309 + 0.599587i \(0.204669\pi\)
−0.800309 + 0.599587i \(0.795331\pi\)
\(468\) 0 0
\(469\) 1.04541i 0.0482724i
\(470\) 0 0
\(471\) 8.93092 + 9.79165i 0.411515 + 0.451175i
\(472\) 0 0
\(473\) 4.50000 + 2.59808i 0.206910 + 0.119460i
\(474\) 0 0
\(475\) −19.8082 34.3087i −0.908861 1.57419i
\(476\) 0 0
\(477\) 20.4347 + 14.4495i 0.935639 + 0.661597i
\(478\) 0 0
\(479\) −1.22021 2.11346i −0.0557527 0.0965665i 0.836802 0.547506i \(-0.184423\pi\)
−0.892555 + 0.450939i \(0.851089\pi\)
\(480\) 0 0
\(481\) 11.0227 19.0919i 0.502592 0.870515i
\(482\) 0 0
\(483\) 1.72563 5.42930i 0.0785191 0.247042i
\(484\) 0 0
\(485\) 41.6800 1.89259
\(486\) 0 0
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) −6.00000 1.90702i −0.271329 0.0862386i
\(490\) 0 0
\(491\) −7.97422 4.60392i −0.359871 0.207772i 0.309153 0.951012i \(-0.399954\pi\)
−0.669024 + 0.743240i \(0.733288\pi\)
\(492\) 0 0
\(493\) −8.69958 + 5.02270i −0.391809 + 0.226211i
\(494\) 0 0
\(495\) −12.7214 + 17.9907i −0.571783 + 0.808623i
\(496\) 0 0
\(497\) −32.3258 + 18.6633i −1.45001 + 0.837163i
\(498\) 0 0
\(499\) −9.19959 + 15.9342i −0.411830 + 0.713311i −0.995090 0.0989747i \(-0.968444\pi\)
0.583260 + 0.812286i \(0.301777\pi\)
\(500\) 0 0
\(501\) −15.5403 + 14.1742i −0.694289 + 0.633258i
\(502\) 0 0
\(503\) −20.8799 −0.930989 −0.465494 0.885051i \(-0.654123\pi\)
−0.465494 + 0.885051i \(0.654123\pi\)
\(504\) 0 0
\(505\) −9.89898 −0.440499
\(506\) 0 0
\(507\) 1.48393 + 6.76742i 0.0659035 + 0.300552i
\(508\) 0 0
\(509\) 11.2262 19.4444i 0.497594 0.861857i −0.502403 0.864634i \(-0.667550\pi\)
0.999996 + 0.00277650i \(0.000883790\pi\)
\(510\) 0 0
\(511\) 3.43671 1.98419i 0.152031 0.0877752i
\(512\) 0 0
\(513\) −25.3485 33.5125i −1.11916 1.47961i
\(514\) 0 0
\(515\) 23.1470 13.3639i 1.01998 0.588885i
\(516\) 0 0
\(517\) 19.3543 + 11.1742i 0.851203 + 0.491442i
\(518\) 0 0
\(519\) 1.87468 + 8.54943i 0.0822892 + 0.375278i
\(520\) 0 0
\(521\) 18.8776i 0.827042i −0.910495 0.413521i \(-0.864299\pi\)
0.910495 0.413521i \(-0.135701\pi\)
\(522\) 0 0
\(523\) −22.4425 −0.981343 −0.490671 0.871345i \(-0.663248\pi\)
−0.490671 + 0.871345i \(0.663248\pi\)
\(524\) 0 0
\(525\) −14.6349 16.0454i −0.638721 0.700279i
\(526\) 0 0
\(527\) −18.7283 + 32.4384i −0.815818 + 1.41304i
\(528\) 0 0
\(529\) 10.6742 + 18.4883i 0.464097 + 0.803840i
\(530\) 0 0
\(531\) 1.61320 + 3.50162i 0.0700071 + 0.151957i
\(532\) 0 0
\(533\) −14.1582 24.5227i −0.613259 1.06220i
\(534\) 0 0
\(535\) −49.6003 28.6368i −2.14441 1.23808i
\(536\) 0 0
\(537\) −1.59592 + 5.02118i −0.0688689 + 0.216680i
\(538\) 0 0
\(539\) 1.04930i 0.0451963i
\(540\) 0 0
\(541\) 8.69694i 0.373911i −0.982368 0.186955i \(-0.940138\pi\)
0.982368 0.186955i \(-0.0598620\pi\)
\(542\) 0 0
\(543\) −10.1511 + 31.9381i −0.435627 + 1.37060i
\(544\) 0 0
\(545\) −3.67423 2.12132i −0.157387 0.0908674i
\(546\) 0 0
\(547\) −7.88242 13.6527i −0.337028 0.583749i 0.646844 0.762622i \(-0.276088\pi\)
−0.983872 + 0.178873i \(0.942755\pi\)
\(548\) 0 0
\(549\) 26.8861 + 2.47730i 1.14747 + 0.105728i
\(550\) 0 0
\(551\) 9.57348 + 16.5818i 0.407844 + 0.706407i
\(552\) 0 0
\(553\) −13.1969 + 22.8578i −0.561191 + 0.972011i
\(554\) 0 0
\(555\) 26.9861 + 29.5869i 1.14550 + 1.25589i
\(556\) 0 0
\(557\) 20.6417 0.874619 0.437309 0.899311i \(-0.355931\pi\)
0.437309 + 0.899311i \(0.355931\pi\)
\(558\) 0 0
\(559\) 6.67767i 0.282436i
\(560\) 0 0
\(561\) 3.67423 + 16.7563i 0.155126 + 0.707450i
\(562\) 0 0
\(563\) −36.5941 21.1276i −1.54226 0.890424i −0.998696 0.0510558i \(-0.983741\pi\)
−0.543564 0.839368i \(-0.682925\pi\)
\(564\) 0 0
\(565\) 14.1582 8.17423i 0.595640 0.343893i
\(566\) 0 0
\(567\) −17.5081 14.9686i −0.735271 0.628620i
\(568\) 0 0
\(569\) 13.5000 7.79423i 0.565949 0.326751i −0.189580 0.981865i \(-0.560713\pi\)
0.755530 + 0.655114i \(0.227379\pi\)
\(570\) 0 0
\(571\) −6.47344 + 11.2123i −0.270905 + 0.469222i −0.969094 0.246692i \(-0.920656\pi\)
0.698189 + 0.715914i \(0.253990\pi\)
\(572\) 0 0
\(573\) −3.98018 18.1515i −0.166274 0.758291i
\(574\) 0 0
\(575\) −6.29577 −0.262552
\(576\) 0 0
\(577\) 9.34847 0.389182 0.194591 0.980884i \(-0.437662\pi\)
0.194591 + 0.980884i \(0.437662\pi\)
\(578\) 0 0
\(579\) −9.53310 + 8.69510i −0.396182 + 0.361356i
\(580\) 0 0
\(581\) 4.33013 7.50000i 0.179644 0.311152i
\(582\) 0 0
\(583\) −16.8655 + 9.73733i −0.698500 + 0.403279i
\(584\) 0 0
\(585\) 28.1969 + 2.59808i 1.16580 + 0.107417i
\(586\) 0 0
\(587\) 16.2857 9.40257i 0.672184 0.388086i −0.124720 0.992192i \(-0.539803\pi\)
0.796904 + 0.604106i \(0.206470\pi\)
\(588\) 0 0
\(589\) 61.8289 + 35.6969i 2.54762 + 1.47087i
\(590\) 0 0
\(591\) 27.5413 + 8.75366i 1.13290 + 0.360077i
\(592\) 0 0
\(593\) 25.0273i 1.02775i −0.857866 0.513873i \(-0.828210\pi\)
0.857866 0.513873i \(-0.171790\pi\)
\(594\) 0 0
\(595\) −34.1640 −1.40059
\(596\) 0 0
\(597\) 8.66025 27.2474i 0.354441 1.11516i
\(598\) 0 0
\(599\) −15.6453 + 27.0985i −0.639251 + 1.10722i 0.346346 + 0.938107i \(0.387422\pi\)
−0.985597 + 0.169109i \(0.945911\pi\)
\(600\) 0 0
\(601\) −0.623724 1.08032i −0.0254422 0.0440673i 0.853024 0.521872i \(-0.174766\pi\)
−0.878466 + 0.477805i \(0.841433\pi\)
\(602\) 0 0
\(603\) −1.11295 + 0.512736i −0.0453227 + 0.0208802i
\(604\) 0 0
\(605\) 8.73169 + 15.1237i 0.354994 + 0.614867i
\(606\) 0 0
\(607\) −10.5049 6.06499i −0.426379 0.246170i 0.271424 0.962460i \(-0.412506\pi\)
−0.697803 + 0.716290i \(0.745839\pi\)
\(608\) 0 0
\(609\) 7.07321 + 7.75490i 0.286621 + 0.314245i
\(610\) 0 0
\(611\) 28.7204i 1.16190i
\(612\) 0 0
\(613\) 40.0454i 1.61742i −0.588208 0.808709i \(-0.700167\pi\)
0.588208 0.808709i \(-0.299833\pi\)
\(614\) 0 0
\(615\) 50.2429 11.0170i 2.02599 0.444249i
\(616\) 0 0
\(617\) 13.8712 + 8.00853i 0.558432 + 0.322411i 0.752516 0.658574i \(-0.228840\pi\)
−0.194084 + 0.980985i \(0.562173\pi\)
\(618\) 0 0
\(619\) −0.612688 1.06121i −0.0246260 0.0426535i 0.853450 0.521175i \(-0.174506\pi\)
−0.878076 + 0.478522i \(0.841173\pi\)
\(620\) 0 0
\(621\) −6.62642 + 0.825765i −0.265909 + 0.0331368i
\(622\) 0 0
\(623\) −7.86971 13.6307i −0.315293 0.546104i
\(624\) 0 0
\(625\) 12.7474 22.0792i 0.509898 0.883169i
\(626\) 0 0
\(627\) 31.9381 7.00324i 1.27549 0.279683i
\(628\) 0 0
\(629\) 31.1769 1.24310
\(630\) 0 0
\(631\) 2.96786i 0.118148i −0.998254 0.0590742i \(-0.981185\pi\)
0.998254 0.0590742i \(-0.0188149\pi\)
\(632\) 0 0
\(633\) −9.82577 + 8.96204i −0.390539 + 0.356209i
\(634\) 0 0
\(635\) 58.0155 + 33.4953i 2.30228 + 1.32922i
\(636\) 0 0
\(637\) −1.16781 + 0.674235i −0.0462703 + 0.0267141i
\(638\) 0 0
\(639\) 35.7237 + 25.2605i 1.41321 + 0.999288i
\(640\) 0 0
\(641\) −19.1969 + 11.0834i −0.758233 + 0.437766i −0.828661 0.559751i \(-0.810897\pi\)
0.0704277 + 0.997517i \(0.477564\pi\)
\(642\) 0 0
\(643\) −0.204229 + 0.353736i −0.00805402 + 0.0139500i −0.870024 0.493009i \(-0.835897\pi\)
0.861970 + 0.506959i \(0.169230\pi\)
\(644\) 0 0
\(645\) 11.5601 + 3.67423i 0.455179 + 0.144673i
\(646\) 0 0
\(647\) 19.1470 0.752745 0.376372 0.926468i \(-0.377171\pi\)
0.376372 + 0.926468i \(0.377171\pi\)
\(648\) 0 0
\(649\) −3.00000 −0.117760
\(650\) 0 0
\(651\) 37.2986 + 11.8549i 1.46185 + 0.464630i
\(652\) 0 0
\(653\) −15.2546 + 26.4217i −0.596957 + 1.03396i 0.396310 + 0.918117i \(0.370290\pi\)
−0.993267 + 0.115844i \(0.963043\pi\)
\(654\) 0 0
\(655\) −4.78674 + 2.76363i −0.187033 + 0.107984i
\(656\) 0 0
\(657\) −3.79796 2.68556i −0.148172 0.104774i
\(658\) 0 0
\(659\) 1.20474 0.695560i 0.0469302 0.0270952i −0.476351 0.879255i \(-0.658041\pi\)
0.523282 + 0.852160i \(0.324708\pi\)
\(660\) 0 0
\(661\) −8.96204 5.17423i −0.348583 0.201254i 0.315478 0.948933i \(-0.397835\pi\)
−0.664061 + 0.747678i \(0.731168\pi\)
\(662\) 0 0
\(663\) 16.2879 14.8561i 0.632570 0.576964i
\(664\) 0 0
\(665\) 65.1180i 2.52517i
\(666\) 0 0
\(667\) 3.04281 0.117818
\(668\) 0 0
\(669\) 32.8215 7.19694i 1.26895 0.278250i
\(670\) 0 0
\(671\) −10.5049 + 18.1950i −0.405536 + 0.702409i
\(672\) 0 0
\(673\) −9.62372 16.6688i −0.370967 0.642534i 0.618747 0.785590i \(-0.287640\pi\)
−0.989715 + 0.143056i \(0.954307\pi\)
\(674\) 0 0
\(675\) −9.90408 + 23.4501i −0.381208 + 0.902596i
\(676\) 0 0
\(677\) −5.18010 8.97219i −0.199087 0.344829i 0.749145 0.662406i \(-0.230464\pi\)
−0.948233 + 0.317576i \(0.897131\pi\)
\(678\) 0 0
\(679\) −29.3630 16.9527i −1.12685 0.650586i
\(680\) 0 0
\(681\) 39.8939 8.74774i 1.52874 0.335214i
\(682\) 0 0
\(683\) 31.7385i 1.21444i −0.794534 0.607220i \(-0.792285\pi\)
0.794534 0.607220i \(-0.207715\pi\)
\(684\) 0 0
\(685\) 56.3939i 2.15470i
\(686\) 0 0
\(687\) −29.2332 32.0506i −1.11532 1.22281i
\(688\) 0 0
\(689\) 21.6742 + 12.5136i 0.825723 + 0.476731i
\(690\) 0 0
\(691\) −3.74730 6.49051i −0.142554 0.246911i 0.785904 0.618349i \(-0.212198\pi\)
−0.928458 + 0.371438i \(0.878865\pi\)
\(692\) 0 0
\(693\) 16.2795 7.50000i 0.618407 0.284901i
\(694\) 0 0
\(695\) 27.6592 + 47.9072i 1.04917 + 1.81722i
\(696\) 0 0
\(697\) 20.0227 34.6803i 0.758414 1.31361i
\(698\) 0 0
\(699\) 4.45178 14.0065i 0.168382 0.529774i
\(700\) 0 0
\(701\) −1.76416 −0.0666314 −0.0333157 0.999445i \(-0.510607\pi\)
−0.0333157 + 0.999445i \(0.510607\pi\)
\(702\) 0 0
\(703\) 59.4245i 2.24124i
\(704\) 0 0
\(705\) 49.7196 + 15.8028i 1.87255 + 0.595166i
\(706\) 0 0
\(707\) 6.97370 + 4.02627i 0.262273 + 0.151423i
\(708\) 0 0
\(709\) 8.96204 5.17423i 0.336576 0.194322i −0.322181 0.946678i \(-0.604416\pi\)
0.658757 + 0.752356i \(0.271083\pi\)
\(710\) 0 0
\(711\) 30.8071 + 2.83858i 1.15536 + 0.106455i
\(712\) 0 0
\(713\) 9.82577 5.67291i 0.367978 0.212452i
\(714\) 0 0
\(715\) −11.0170 + 19.0820i −0.412013 + 0.713628i
\(716\) 0 0
\(717\) −1.64456 + 1.50000i −0.0614174 + 0.0560185i
\(718\) 0 0
\(719\) −28.0130 −1.04471 −0.522354 0.852729i \(-0.674946\pi\)
−0.522354 + 0.852729i \(0.674946\pi\)
\(720\) 0 0
\(721\) −21.7423 −0.809727
\(722\) 0 0
\(723\) 5.08132 + 23.1732i 0.188976 + 0.861822i
\(724\) 0 0
\(725\) 5.79972 10.0454i 0.215396 0.373077i
\(726\) 0 0
\(727\) −32.5109 + 18.7702i −1.20576 + 0.696147i −0.961831 0.273645i \(-0.911771\pi\)
−0.243931 + 0.969792i \(0.578437\pi\)
\(728\) 0 0
\(729\) −7.34847 + 25.9808i −0.272166 + 0.962250i
\(730\) 0 0
\(731\) 8.17845 4.72183i 0.302491 0.174643i
\(732\) 0 0
\(733\) −12.9904 7.50000i −0.479811 0.277019i 0.240527 0.970642i \(-0.422680\pi\)
−0.720338 + 0.693624i \(0.756013\pi\)
\(734\) 0 0
\(735\) −0.524648 2.39264i −0.0193519 0.0882540i
\(736\) 0 0
\(737\) 0.953512i 0.0351231i
\(738\) 0 0
\(739\) −1.00052 −0.0368046 −0.0184023 0.999831i \(-0.505858\pi\)
−0.0184023 + 0.999831i \(0.505858\pi\)
\(740\) 0 0
\(741\) −28.3164 31.0454i −1.04023 1.14048i
\(742\) 0 0
\(743\) −18.7932 + 32.5508i −0.689457 + 1.19417i 0.282557 + 0.959250i \(0.408817\pi\)
−0.972014 + 0.234923i \(0.924516\pi\)
\(744\) 0 0
\(745\) 18.0732 + 31.3037i 0.662151 + 1.14688i
\(746\) 0 0
\(747\) −10.1083 0.931383i −0.369844 0.0340775i
\(748\) 0 0
\(749\) 23.2952 + 40.3485i 0.851188 + 1.47430i
\(750\) 0 0
\(751\) 14.8080 + 8.54943i 0.540353 + 0.311973i 0.745222 0.666816i \(-0.232343\pi\)
−0.204869 + 0.978789i \(0.565677\pi\)
\(752\) 0 0
\(753\) 4.04541 12.7279i 0.147423 0.463831i
\(754\) 0 0
\(755\) 16.3409i 0.594706i
\(756\) 0 0
\(757\) 12.0000i 0.436147i 0.975932 + 0.218074i \(0.0699773\pi\)
−0.975932 + 0.218074i \(0.930023\pi\)
\(758\) 0 0
\(759\) 1.57394 4.95204i 0.0571305 0.179748i
\(760\) 0 0
\(761\) −42.5227 24.5505i −1.54145 0.889955i −0.998748 0.0500275i \(-0.984069\pi\)
−0.542699 0.839927i \(-0.682598\pi\)
\(762\) 0 0
\(763\) 1.72563 + 2.98889i 0.0624721 + 0.108205i
\(764\) 0 0
\(765\) 16.7563 + 36.3712i 0.605824 + 1.31500i
\(766\) 0 0
\(767\) 1.92768 + 3.33884i 0.0696044 + 0.120558i
\(768\) 0 0
\(769\) −13.2980 + 23.0327i −0.479537 + 0.830582i −0.999725 0.0234700i \(-0.992529\pi\)
0.520188 + 0.854052i \(0.325862\pi\)
\(770\) 0 0
\(771\) −15.9691 17.5081i −0.575112 0.630539i
\(772\) 0 0
\(773\) −42.9192 −1.54370 −0.771848 0.635807i \(-0.780668\pi\)
−0.771848 + 0.635807i \(0.780668\pi\)
\(774\) 0 0
\(775\) 43.2512i 1.55363i
\(776\) 0 0
\(777\) −6.97730 31.8198i −0.250309 1.14153i
\(778\) 0 0
\(779\) −66.1022 38.1641i −2.36836 1.36737i
\(780\) 0 0
\(781\) −29.4842 + 17.0227i −1.05503 + 0.609120i
\(782\) 0 0
\(783\) 4.78674 11.3337i 0.171064 0.405033i
\(784\) 0 0
\(785\) −20.8485 + 12.0369i −0.744114 + 0.429614i
\(786\) 0 0
\(787\) −19.1037 + 33.0885i −0.680972 + 1.17948i 0.293712 + 0.955894i \(0.405109\pi\)
−0.974684 + 0.223585i \(0.928224\pi\)
\(788\) 0 0
\(789\) 8.96204 + 40.8712i 0.319057 + 1.45505i
\(790\) 0 0
\(791\) −13.2990 −0.472859
\(792\) 0 0
\(793\) 27.0000 0.958798
\(794\) 0 0
\(795\) −33.5888 + 30.6362i −1.19127 + 1.08655i
\(796\) 0 0
\(797\) 17.0902 29.6010i 0.605364 1.04852i