Properties

Label 1152.2.p.e.959.1
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 959.1
Root \(0.500000 - 1.00333i\) of defining polynomial
Character \(\chi\) \(=\) 1152.959
Dual form 1152.2.p.e.191.1

$q$-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 \(0.415059\pi\)
−0.967221 + 0.253937i \(0.918274\pi\)
\(6\) 0 0
\(7\) 2.21650 1.27970i 0.837759 0.483680i −0.0187428 0.999824i \(-0.505966\pi\)
0.856502 + 0.516144i \(0.172633\pi\)
\(8\) 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 0.0943882 0.995535i \(-0.469911\pi\)
−0.814965 + 0.579510i \(0.803244\pi\)
\(14\) 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 −0.925208 0.379459i \(-0.876110\pi\)
0.791226 + 0.611524i \(0.209443\pi\)
\(24\) 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 0.734920 0.678153i \(-0.237219\pi\)
−0.954758 + 0.297383i \(0.903886\pi\)
\(30\) 0 0
\(31\) −7.64580 4.41431i −1.37323 0.792833i −0.381894 0.924206i \(-0.624728\pi\)
−0.991333 + 0.131374i \(0.958061\pi\)
\(32\) 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 \(0.206443\pi\)
−0.796954 + 0.604040i \(0.793557\pi\)
\(38\) 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 \(0.0793566\pi\)
−0.270866 + 0.962617i \(0.587310\pi\)
\(48\) 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 \(-0.694205\pi\)
−0.572960 + 0.819584i \(0.694205\pi\)
\(54\) 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 −0.907641 0.419748i \(-0.862118\pi\)
−0.0903080 + 0.995914i \(0.528785\pi\)
\(62\) 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 \(-0.832941\pi\)
−0.865409 + 0.501066i \(0.832941\pi\)
\(72\) 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 −0.909667 0.415338i \(-0.863663\pi\)
−0.0951401 + 0.995464i \(0.530330\pi\)
\(80\) 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 0.933616 0.358275i \(-0.116635\pi\)
−0.777083 + 0.629398i \(0.783302\pi\)
\(102\) 0 0
\(103\) −7.35698 4.24755i −0.724905 0.418524i 0.0916506 0.995791i \(-0.470786\pi\)
−0.816555 + 0.577267i \(0.804119\pi\)
\(104\) 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 \(0.0205708\pi\)
−0.997913 + 0.0645800i \(0.979429\pi\)
\(110\) 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 \(-0.606369\pi\)
0.327983 0.944684i \(-0.393631\pi\)
\(128\) 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 −0.528840 0.848722i \(-0.677373\pi\)
0.999434 + 0.0336278i \(0.0107061\pi\)
\(150\) 0 0
\(151\) −4.49792 + 2.59687i −0.366035 + 0.211331i −0.671725 0.740801i \(-0.734446\pi\)
0.305690 + 0.952131i \(0.401113\pi\)
\(152\) 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 0.740546 0.672005i \(-0.234567\pi\)
−0.211700 + 0.977335i \(0.567900\pi\)
\(158\) 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 −0.999406 0.0344659i \(-0.989027\pi\)
0.529551 + 0.848278i \(0.322360\pi\)
\(168\) 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 0.945945 0.324327i \(-0.105138\pi\)
−0.753848 + 0.657049i \(0.771804\pi\)
\(174\) 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 \(0.255437\pi\)
−0.694927 + 0.719080i \(0.744563\pi\)
\(182\) 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 0.604048 0.796948i \(-0.293554\pi\)
−0.992201 + 0.124647i \(0.960220\pi\)
\(192\) 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 \(-0.297400\pi\)
0.594373 + 0.804190i \(0.297400\pi\)
\(198\) 0 0
\(199\) 16.5068i 1.17014i −0.810984 0.585068i \(-0.801068\pi\)
0.810984 0.585068i \(-0.198932\pi\)
\(200\) 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 0.182367 0.983230i \(-0.441624\pi\)
0.942686 + 0.333680i \(0.108291\pi\)
\(224\) 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 −0.435941 0.899975i \(-0.643584\pi\)
−0.997372 + 0.0724517i \(0.976918\pi\)
\(230\) 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 −0.886059 0.463573i \(-0.846567\pi\)
0.844495 + 0.535563i \(0.179901\pi\)
\(240\) 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 \(0.100794\pi\)
−0.205472 + 0.978663i \(0.565873\pi\)
\(264\) 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 \(-0.467716\pi\)
0.101250 + 0.994861i \(0.467716\pi\)
\(270\) 0 0
\(271\) 13.2054i 0.802173i 0.916040 + 0.401087i \(0.131367\pi\)
−0.916040 + 0.401087i \(0.868633\pi\)
\(272\) 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 0.322268 0.946649i \(-0.395555\pi\)
0.980956 + 0.194232i \(0.0622215\pi\)
\(278\) 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 −0.915961 0.401268i \(-0.868569\pi\)
0.805489 + 0.592611i \(0.201903\pi\)
\(294\) 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 \(0.376323\pi\)
−0.990894 + 0.134646i \(0.957010\pi\)
\(312\) 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 0.743426 0.668819i \(-0.233200\pi\)
−0.950927 + 0.309416i \(0.899866\pi\)
\(318\) 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 −0.537792 0.843078i \(-0.680741\pi\)
0.461231 + 0.887280i \(0.347408\pi\)
\(350\) 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 \(-0.478394\pi\)
0.0678260 + 0.997697i \(0.478394\pi\)
\(360\) 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 −0.563961 0.825801i \(-0.690723\pi\)
0.433184 + 0.901305i \(0.357390\pi\)
\(368\) 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 0.506779 0.862076i \(-0.330836\pi\)
−0.493190 + 0.869922i \(0.664169\pi\)
\(374\) 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 −0.717426 0.696635i \(-0.754680\pi\)
0.962017 + 0.272991i \(0.0880130\pi\)
\(384\) 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 \(-0.978110\pi\)
0.439310 0.898336i \(-0.355223\pi\)
\(390\) 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 \(0.248506\pi\)
−0.710419 + 0.703779i \(0.751494\pi\)
\(398\) 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 −0.0776450 0.996981i \(-0.524740\pi\)
0.824588 + 0.565733i \(0.191407\pi\)
\(422\) 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 \(-0.480283\pi\)
0.0619020 + 0.998082i \(0.480283\pi\)
\(432\) 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 −0.794330 0.607487i \(-0.792178\pi\)
0.128935 + 0.991653i \(0.458844\pi\)
\(440\) 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 \(0.0253325\pi\)
−0.429568 + 0.903034i \(0.641334\pi\)
\(462\) 0 0
\(463\) 21.6523 + 12.5010i 1.00627 + 0.580969i 0.910097 0.414396i \(-0.136007\pi\)
0.0961706 + 0.995365i \(0.469341\pi\)
\(464\) 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 0.892555 0.450939i \(-0.148911\pi\)
−0.836802 + 0.547506i \(0.815577\pi\)
\(480\) 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 \(-0.345877\pi\)
0.465494 + 0.885051i \(0.345877\pi\)
\(504\) 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 −0.999996 0.00277650i \(-0.999116\pi\)
0.502403 + 0.864634i \(0.332450\pi\)
\(510\) 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 \(0.0598620\pi\)
−0.982368 + 0.186955i \(0.940138\pi\)
\(542\) 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 \(-0.644069\pi\)
−0.437309 + 0.899311i \(0.644069\pi\)
\(558\) 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 \(-0.612578\pi\)
0.985597 0.169109i \(-0.0540889\pi\)
\(600\) 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 0.697803 0.716290i \(-0.254161\pi\)
−0.271424 + 0.962460i \(0.587494\pi\)
\(608\) 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 \(0.299833\pi\)
−0.588208 + 0.808709i \(0.700167\pi\)
\(614\) 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 \(0.0188149\pi\)
−0.998254 + 0.0590742i \(0.981185\pi\)
\(632\) 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 \(-0.622829\pi\)
−0.376372 + 0.926468i \(0.622829\pi\)
\(648\) 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 \(-0.629710\pi\)
0.993267 0.115844i \(-0.0369572\pi\)
\(654\) 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 0.664061 0.747678i \(-0.268832\pi\)
−0.315478 + 0.948933i \(0.602165\pi\)
\(662\) 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 0.948233 0.317576i \(-0.102869\pi\)
−0.749145 + 0.662406i \(0.769536\pi\)
\(678\) 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 \(-0.489393\pi\)
0.0333157 + 0.999445i \(0.489393\pi\)
\(702\) 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 −0.658757 0.752356i \(-0.728917\pi\)
0.322181 + 0.946678i \(0.395584\pi\)
\(710\) 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 \(-0.325054\pi\)
0.522354 + 0.852729i \(0.325054\pi\)
\(720\) 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 0.243931 0.969792i \(-0.421563\pi\)
0.961831 + 0.273645i \(0.0882295\pi\)
\(728\) 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 0.720338 0.693624i \(-0.243987\pi\)
−0.240527 + 0.970642i \(0.577320\pi\)
\(734\) 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 \(-0.591183\pi\)
0.972014 0.234923i \(-0.0754839\pi\)
\(744\) 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 0.204869 0.978789i \(-0.434323\pi\)
−0.745222 + 0.666816i \(0.767657\pi\)
\(752\) 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 \(-0.930023\pi\)
0.975932 0.218074i \(-0.0699773\pi\)
\(758\) 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 \(-0.219332\pi\)
0.771848 + 0.635807i \(0.219332\pi\)
\(774\) 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 0.386629