Properties

Label 1148.2.k.b.337.16
Level $1148$
Weight $2$
Character 1148.337
Analytic conductor $9.167$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 337.16
Character \(\chi\) \(=\) 1148.337
Dual form 1148.2.k.b.729.16

$q$-expansion

\(f(q)\) \(=\) \(q+(1.71130 + 1.71130i) q^{3} -2.46933i q^{5} +(-0.707107 - 0.707107i) q^{7} +2.85712i q^{9} +O(q^{10})\) \(q+(1.71130 + 1.71130i) q^{3} -2.46933i q^{5} +(-0.707107 - 0.707107i) q^{7} +2.85712i q^{9} +(-3.89109 - 3.89109i) q^{11} +(-2.36139 - 2.36139i) q^{13} +(4.22578 - 4.22578i) q^{15} +(1.41870 - 1.41870i) q^{17} +(2.77167 - 2.77167i) q^{19} -2.42015i q^{21} -6.33212 q^{23} -1.09761 q^{25} +(0.244504 - 0.244504i) q^{27} +(-1.38204 - 1.38204i) q^{29} +6.75810 q^{31} -13.3177i q^{33} +(-1.74608 + 1.74608i) q^{35} +0.731303 q^{37} -8.08211i q^{39} +(4.55889 + 4.49628i) q^{41} -7.12884i q^{43} +7.05519 q^{45} +(-5.61063 + 5.61063i) q^{47} +1.00000i q^{49} +4.85565 q^{51} +(4.60712 + 4.60712i) q^{53} +(-9.60841 + 9.60841i) q^{55} +9.48634 q^{57} -10.1934 q^{59} -9.57500i q^{61} +(2.02029 - 2.02029i) q^{63} +(-5.83106 + 5.83106i) q^{65} +(-3.13423 + 3.13423i) q^{67} +(-10.8362 - 10.8362i) q^{69} +(-2.44329 - 2.44329i) q^{71} +13.6735i q^{73} +(-1.87834 - 1.87834i) q^{75} +5.50284i q^{77} +(-1.22940 - 1.22940i) q^{79} +9.40821 q^{81} +6.98865 q^{83} +(-3.50324 - 3.50324i) q^{85} -4.73018i q^{87} +(11.5345 + 11.5345i) q^{89} +3.33951i q^{91} +(11.5652 + 11.5652i) q^{93} +(-6.84417 - 6.84417i) q^{95} +(11.0829 - 11.0829i) q^{97} +(11.1173 - 11.1173i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + O(q^{10}) \) \( 36q - 12q^{11} - 16q^{17} - 4q^{19} - 36q^{23} - 64q^{25} + 12q^{27} + 16q^{29} - 28q^{31} + 12q^{35} + 48q^{37} + 4q^{41} + 36q^{45} + 12q^{47} - 12q^{51} - 12q^{53} + 12q^{55} + 76q^{57} + 20q^{59} - 4q^{65} - 44q^{67} + 72q^{69} - 20q^{71} + 72q^{75} - 8q^{79} - 100q^{81} - 40q^{83} - 8q^{85} - 16q^{89} + 20q^{93} + 76q^{95} - 16q^{97} + 56q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.71130 + 1.71130i 0.988022 + 0.988022i 0.999929 0.0119072i \(-0.00379027\pi\)
−0.0119072 + 0.999929i \(0.503790\pi\)
\(4\) 0 0
\(5\) 2.46933i 1.10432i −0.833738 0.552160i \(-0.813804\pi\)
0.833738 0.552160i \(-0.186196\pi\)
\(6\) 0 0
\(7\) −0.707107 0.707107i −0.267261 0.267261i
\(8\) 0 0
\(9\) 2.85712i 0.952375i
\(10\) 0 0
\(11\) −3.89109 3.89109i −1.17321 1.17321i −0.981440 0.191768i \(-0.938578\pi\)
−0.191768 0.981440i \(-0.561422\pi\)
\(12\) 0 0
\(13\) −2.36139 2.36139i −0.654932 0.654932i 0.299245 0.954176i \(-0.403265\pi\)
−0.954176 + 0.299245i \(0.903265\pi\)
\(14\) 0 0
\(15\) 4.22578 4.22578i 1.09109 1.09109i
\(16\) 0 0
\(17\) 1.41870 1.41870i 0.344085 0.344085i −0.513816 0.857901i \(-0.671769\pi\)
0.857901 + 0.513816i \(0.171769\pi\)
\(18\) 0 0
\(19\) 2.77167 2.77167i 0.635864 0.635864i −0.313668 0.949533i \(-0.601558\pi\)
0.949533 + 0.313668i \(0.101558\pi\)
\(20\) 0 0
\(21\) 2.42015i 0.528120i
\(22\) 0 0
\(23\) −6.33212 −1.32034 −0.660169 0.751117i \(-0.729516\pi\)
−0.660169 + 0.751117i \(0.729516\pi\)
\(24\) 0 0
\(25\) −1.09761 −0.219522
\(26\) 0 0
\(27\) 0.244504 0.244504i 0.0470549 0.0470549i
\(28\) 0 0
\(29\) −1.38204 1.38204i −0.256638 0.256638i 0.567047 0.823685i \(-0.308086\pi\)
−0.823685 + 0.567047i \(0.808086\pi\)
\(30\) 0 0
\(31\) 6.75810 1.21379 0.606895 0.794782i \(-0.292415\pi\)
0.606895 + 0.794782i \(0.292415\pi\)
\(32\) 0 0
\(33\) 13.3177i 2.31831i
\(34\) 0 0
\(35\) −1.74608 + 1.74608i −0.295142 + 0.295142i
\(36\) 0 0
\(37\) 0.731303 0.120225 0.0601127 0.998192i \(-0.480854\pi\)
0.0601127 + 0.998192i \(0.480854\pi\)
\(38\) 0 0
\(39\) 8.08211i 1.29417i
\(40\) 0 0
\(41\) 4.55889 + 4.49628i 0.711980 + 0.702200i
\(42\) 0 0
\(43\) 7.12884i 1.08714i −0.839365 0.543569i \(-0.817073\pi\)
0.839365 0.543569i \(-0.182927\pi\)
\(44\) 0 0
\(45\) 7.05519 1.05173
\(46\) 0 0
\(47\) −5.61063 + 5.61063i −0.818395 + 0.818395i −0.985875 0.167480i \(-0.946437\pi\)
0.167480 + 0.985875i \(0.446437\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 4.85565 0.679927
\(52\) 0 0
\(53\) 4.60712 + 4.60712i 0.632836 + 0.632836i 0.948778 0.315942i \(-0.102321\pi\)
−0.315942 + 0.948778i \(0.602321\pi\)
\(54\) 0 0
\(55\) −9.60841 + 9.60841i −1.29560 + 1.29560i
\(56\) 0 0
\(57\) 9.48634 1.25650
\(58\) 0 0
\(59\) −10.1934 −1.32707 −0.663533 0.748147i \(-0.730944\pi\)
−0.663533 + 0.748147i \(0.730944\pi\)
\(60\) 0 0
\(61\) 9.57500i 1.22595i −0.790101 0.612976i \(-0.789972\pi\)
0.790101 0.612976i \(-0.210028\pi\)
\(62\) 0 0
\(63\) 2.02029 2.02029i 0.254533 0.254533i
\(64\) 0 0
\(65\) −5.83106 + 5.83106i −0.723254 + 0.723254i
\(66\) 0 0
\(67\) −3.13423 + 3.13423i −0.382908 + 0.382908i −0.872149 0.489241i \(-0.837274\pi\)
0.489241 + 0.872149i \(0.337274\pi\)
\(68\) 0 0
\(69\) −10.8362 10.8362i −1.30452 1.30452i
\(70\) 0 0
\(71\) −2.44329 2.44329i −0.289966 0.289966i 0.547101 0.837067i \(-0.315731\pi\)
−0.837067 + 0.547101i \(0.815731\pi\)
\(72\) 0 0
\(73\) 13.6735i 1.60036i 0.599759 + 0.800181i \(0.295263\pi\)
−0.599759 + 0.800181i \(0.704737\pi\)
\(74\) 0 0
\(75\) −1.87834 1.87834i −0.216893 0.216893i
\(76\) 0 0
\(77\) 5.50284i 0.627106i
\(78\) 0 0
\(79\) −1.22940 1.22940i −0.138318 0.138318i 0.634558 0.772876i \(-0.281182\pi\)
−0.772876 + 0.634558i \(0.781182\pi\)
\(80\) 0 0
\(81\) 9.40821 1.04536
\(82\) 0 0
\(83\) 6.98865 0.767104 0.383552 0.923519i \(-0.374701\pi\)
0.383552 + 0.923519i \(0.374701\pi\)
\(84\) 0 0
\(85\) −3.50324 3.50324i −0.379980 0.379980i
\(86\) 0 0
\(87\) 4.73018i 0.507129i
\(88\) 0 0
\(89\) 11.5345 + 11.5345i 1.22266 + 1.22266i 0.966683 + 0.255975i \(0.0823965\pi\)
0.255975 + 0.966683i \(0.417603\pi\)
\(90\) 0 0
\(91\) 3.33951i 0.350076i
\(92\) 0 0
\(93\) 11.5652 + 11.5652i 1.19925 + 1.19925i
\(94\) 0 0
\(95\) −6.84417 6.84417i −0.702197 0.702197i
\(96\) 0 0
\(97\) 11.0829 11.0829i 1.12530 1.12530i 0.134365 0.990932i \(-0.457100\pi\)
0.990932 0.134365i \(-0.0428996\pi\)
\(98\) 0 0
\(99\) 11.1173 11.1173i 1.11733 1.11733i
\(100\) 0 0
\(101\) −2.96559 + 2.96559i −0.295087 + 0.295087i −0.839086 0.543999i \(-0.816910\pi\)
0.543999 + 0.839086i \(0.316910\pi\)
\(102\) 0 0
\(103\) 11.0539i 1.08918i −0.838704 0.544588i \(-0.816686\pi\)
0.838704 0.544588i \(-0.183314\pi\)
\(104\) 0 0
\(105\) −5.97616 −0.583213
\(106\) 0 0
\(107\) −4.31574 −0.417218 −0.208609 0.977999i \(-0.566894\pi\)
−0.208609 + 0.977999i \(0.566894\pi\)
\(108\) 0 0
\(109\) 8.24007 8.24007i 0.789256 0.789256i −0.192116 0.981372i \(-0.561535\pi\)
0.981372 + 0.192116i \(0.0615350\pi\)
\(110\) 0 0
\(111\) 1.25148 + 1.25148i 0.118785 + 0.118785i
\(112\) 0 0
\(113\) 14.0370 1.32049 0.660246 0.751049i \(-0.270452\pi\)
0.660246 + 0.751049i \(0.270452\pi\)
\(114\) 0 0
\(115\) 15.6361i 1.45808i
\(116\) 0 0
\(117\) 6.74678 6.74678i 0.623740 0.623740i
\(118\) 0 0
\(119\) −2.00634 −0.183921
\(120\) 0 0
\(121\) 19.2812i 1.75284i
\(122\) 0 0
\(123\) 0.107159 + 15.4961i 0.00966217 + 1.39724i
\(124\) 0 0
\(125\) 9.63630i 0.861897i
\(126\) 0 0
\(127\) −3.91790 −0.347657 −0.173829 0.984776i \(-0.555614\pi\)
−0.173829 + 0.984776i \(0.555614\pi\)
\(128\) 0 0
\(129\) 12.1996 12.1996i 1.07412 1.07412i
\(130\) 0 0
\(131\) 2.98844i 0.261102i 0.991442 + 0.130551i \(0.0416746\pi\)
−0.991442 + 0.130551i \(0.958325\pi\)
\(132\) 0 0
\(133\) −3.91973 −0.339884
\(134\) 0 0
\(135\) −0.603763 0.603763i −0.0519637 0.0519637i
\(136\) 0 0
\(137\) −6.46592 + 6.46592i −0.552421 + 0.552421i −0.927139 0.374718i \(-0.877740\pi\)
0.374718 + 0.927139i \(0.377740\pi\)
\(138\) 0 0
\(139\) 9.71747 0.824225 0.412113 0.911133i \(-0.364791\pi\)
0.412113 + 0.911133i \(0.364791\pi\)
\(140\) 0 0
\(141\) −19.2030 −1.61718
\(142\) 0 0
\(143\) 18.3768i 1.53674i
\(144\) 0 0
\(145\) −3.41272 + 3.41272i −0.283411 + 0.283411i
\(146\) 0 0
\(147\) −1.71130 + 1.71130i −0.141146 + 0.141146i
\(148\) 0 0
\(149\) −3.19072 + 3.19072i −0.261394 + 0.261394i −0.825620 0.564226i \(-0.809175\pi\)
0.564226 + 0.825620i \(0.309175\pi\)
\(150\) 0 0
\(151\) 14.8972 + 14.8972i 1.21232 + 1.21232i 0.970263 + 0.242054i \(0.0778212\pi\)
0.242054 + 0.970263i \(0.422179\pi\)
\(152\) 0 0
\(153\) 4.05340 + 4.05340i 0.327698 + 0.327698i
\(154\) 0 0
\(155\) 16.6880i 1.34041i
\(156\) 0 0
\(157\) −7.35695 7.35695i −0.587149 0.587149i 0.349710 0.936858i \(-0.386280\pi\)
−0.936858 + 0.349710i \(0.886280\pi\)
\(158\) 0 0
\(159\) 15.7684i 1.25051i
\(160\) 0 0
\(161\) 4.47749 + 4.47749i 0.352875 + 0.352875i
\(162\) 0 0
\(163\) 0.828390 0.0648845 0.0324422 0.999474i \(-0.489671\pi\)
0.0324422 + 0.999474i \(0.489671\pi\)
\(164\) 0 0
\(165\) −32.8858 −2.56016
\(166\) 0 0
\(167\) −11.3713 11.3713i −0.879941 0.879941i 0.113587 0.993528i \(-0.463766\pi\)
−0.993528 + 0.113587i \(0.963766\pi\)
\(168\) 0 0
\(169\) 1.84768i 0.142129i
\(170\) 0 0
\(171\) 7.91900 + 7.91900i 0.605581 + 0.605581i
\(172\) 0 0
\(173\) 8.39269i 0.638085i −0.947740 0.319042i \(-0.896639\pi\)
0.947740 0.319042i \(-0.103361\pi\)
\(174\) 0 0
\(175\) 0.776127 + 0.776127i 0.0586697 + 0.0586697i
\(176\) 0 0
\(177\) −17.4440 17.4440i −1.31117 1.31117i
\(178\) 0 0
\(179\) −11.4721 + 11.4721i −0.857467 + 0.857467i −0.991039 0.133572i \(-0.957355\pi\)
0.133572 + 0.991039i \(0.457355\pi\)
\(180\) 0 0
\(181\) 4.07525 4.07525i 0.302911 0.302911i −0.539241 0.842152i \(-0.681289\pi\)
0.842152 + 0.539241i \(0.181289\pi\)
\(182\) 0 0
\(183\) 16.3857 16.3857i 1.21127 1.21127i
\(184\) 0 0
\(185\) 1.80583i 0.132767i
\(186\) 0 0
\(187\) −11.0406 −0.807366
\(188\) 0 0
\(189\) −0.345782 −0.0251519
\(190\) 0 0
\(191\) 9.19834 9.19834i 0.665568 0.665568i −0.291119 0.956687i \(-0.594027\pi\)
0.956687 + 0.291119i \(0.0940274\pi\)
\(192\) 0 0
\(193\) 10.0353 + 10.0353i 0.722359 + 0.722359i 0.969085 0.246727i \(-0.0793550\pi\)
−0.246727 + 0.969085i \(0.579355\pi\)
\(194\) 0 0
\(195\) −19.9574 −1.42918
\(196\) 0 0
\(197\) 6.58657i 0.469274i −0.972083 0.234637i \(-0.924610\pi\)
0.972083 0.234637i \(-0.0753901\pi\)
\(198\) 0 0
\(199\) 0.494452 0.494452i 0.0350508 0.0350508i −0.689364 0.724415i \(-0.742110\pi\)
0.724415 + 0.689364i \(0.242110\pi\)
\(200\) 0 0
\(201\) −10.7273 −0.756642
\(202\) 0 0
\(203\) 1.95450i 0.137179i
\(204\) 0 0
\(205\) 11.1028 11.2574i 0.775454 0.786253i
\(206\) 0 0
\(207\) 18.0917i 1.25746i
\(208\) 0 0
\(209\) −21.5696 −1.49200
\(210\) 0 0
\(211\) 17.2804 17.2804i 1.18963 1.18963i 0.212462 0.977169i \(-0.431852\pi\)
0.977169 0.212462i \(-0.0681482\pi\)
\(212\) 0 0
\(213\) 8.36244i 0.572985i
\(214\) 0 0
\(215\) −17.6035 −1.20055
\(216\) 0 0
\(217\) −4.77869 4.77869i −0.324399 0.324399i
\(218\) 0 0
\(219\) −23.3995 + 23.3995i −1.58119 + 1.58119i
\(220\) 0 0
\(221\) −6.70020 −0.450704
\(222\) 0 0
\(223\) −19.6275 −1.31436 −0.657178 0.753736i \(-0.728250\pi\)
−0.657178 + 0.753736i \(0.728250\pi\)
\(224\) 0 0
\(225\) 3.13601i 0.209067i
\(226\) 0 0
\(227\) 5.16148 5.16148i 0.342579 0.342579i −0.514757 0.857336i \(-0.672118\pi\)
0.857336 + 0.514757i \(0.172118\pi\)
\(228\) 0 0
\(229\) −15.8018 + 15.8018i −1.04421 + 1.04421i −0.0452363 + 0.998976i \(0.514404\pi\)
−0.998976 + 0.0452363i \(0.985596\pi\)
\(230\) 0 0
\(231\) −9.41703 + 9.41703i −0.619595 + 0.619595i
\(232\) 0 0
\(233\) −9.81829 9.81829i −0.643218 0.643218i 0.308128 0.951345i \(-0.400298\pi\)
−0.951345 + 0.308128i \(0.900298\pi\)
\(234\) 0 0
\(235\) 13.8545 + 13.8545i 0.903770 + 0.903770i
\(236\) 0 0
\(237\) 4.20774i 0.273322i
\(238\) 0 0
\(239\) 14.0642 + 14.0642i 0.909736 + 0.909736i 0.996251 0.0865143i \(-0.0275728\pi\)
−0.0865143 + 0.996251i \(0.527573\pi\)
\(240\) 0 0
\(241\) 21.6985i 1.39773i −0.715256 0.698863i \(-0.753690\pi\)
0.715256 0.698863i \(-0.246310\pi\)
\(242\) 0 0
\(243\) 15.3668 + 15.3668i 0.985781 + 0.985781i
\(244\) 0 0
\(245\) 2.46933 0.157760
\(246\) 0 0
\(247\) −13.0900 −0.832895
\(248\) 0 0
\(249\) 11.9597 + 11.9597i 0.757916 + 0.757916i
\(250\) 0 0
\(251\) 28.9086i 1.82470i 0.409416 + 0.912348i \(0.365733\pi\)
−0.409416 + 0.912348i \(0.634267\pi\)
\(252\) 0 0
\(253\) 24.6389 + 24.6389i 1.54903 + 1.54903i
\(254\) 0 0
\(255\) 11.9902i 0.750856i
\(256\) 0 0
\(257\) −17.7345 17.7345i −1.10625 1.10625i −0.993639 0.112611i \(-0.964079\pi\)
−0.112611 0.993639i \(-0.535921\pi\)
\(258\) 0 0
\(259\) −0.517109 0.517109i −0.0321316 0.0321316i
\(260\) 0 0
\(261\) 3.94866 3.94866i 0.244416 0.244416i
\(262\) 0 0
\(263\) −5.62764 + 5.62764i −0.347015 + 0.347015i −0.858997 0.511981i \(-0.828912\pi\)
0.511981 + 0.858997i \(0.328912\pi\)
\(264\) 0 0
\(265\) 11.3765 11.3765i 0.698853 0.698853i
\(266\) 0 0
\(267\) 39.4782i 2.41603i
\(268\) 0 0
\(269\) −9.20242 −0.561082 −0.280541 0.959842i \(-0.590514\pi\)
−0.280541 + 0.959842i \(0.590514\pi\)
\(270\) 0 0
\(271\) 4.97809 0.302398 0.151199 0.988503i \(-0.451687\pi\)
0.151199 + 0.988503i \(0.451687\pi\)
\(272\) 0 0
\(273\) −5.71492 + 5.71492i −0.345882 + 0.345882i
\(274\) 0 0
\(275\) 4.27090 + 4.27090i 0.257545 + 0.257545i
\(276\) 0 0
\(277\) 12.8880 0.774366 0.387183 0.922003i \(-0.373448\pi\)
0.387183 + 0.922003i \(0.373448\pi\)
\(278\) 0 0
\(279\) 19.3087i 1.15598i
\(280\) 0 0
\(281\) 7.70012 7.70012i 0.459351 0.459351i −0.439091 0.898442i \(-0.644700\pi\)
0.898442 + 0.439091i \(0.144700\pi\)
\(282\) 0 0
\(283\) −12.4347 −0.739166 −0.369583 0.929198i \(-0.620499\pi\)
−0.369583 + 0.929198i \(0.620499\pi\)
\(284\) 0 0
\(285\) 23.4249i 1.38757i
\(286\) 0 0
\(287\) −0.0442777 6.40297i −0.00261363 0.377955i
\(288\) 0 0
\(289\) 12.9746i 0.763211i
\(290\) 0 0
\(291\) 37.9324 2.22364
\(292\) 0 0
\(293\) −0.813768 + 0.813768i −0.0475409 + 0.0475409i −0.730478 0.682937i \(-0.760702\pi\)
0.682937 + 0.730478i \(0.260702\pi\)
\(294\) 0 0
\(295\) 25.1709i 1.46551i
\(296\) 0 0
\(297\) −1.90278 −0.110410
\(298\) 0 0
\(299\) 14.9526 + 14.9526i 0.864732 + 0.864732i
\(300\) 0 0
\(301\) −5.04085 + 5.04085i −0.290550 + 0.290550i
\(302\) 0 0
\(303\) −10.1501 −0.583105
\(304\) 0 0
\(305\) −23.6439 −1.35384
\(306\) 0 0
\(307\) 29.9471i 1.70917i 0.519310 + 0.854586i \(0.326189\pi\)
−0.519310 + 0.854586i \(0.673811\pi\)
\(308\) 0 0
\(309\) 18.9166 18.9166i 1.07613 1.07613i
\(310\) 0 0
\(311\) 0.623845 0.623845i 0.0353750 0.0353750i −0.689198 0.724573i \(-0.742037\pi\)
0.724573 + 0.689198i \(0.242037\pi\)
\(312\) 0 0
\(313\) −16.9142 + 16.9142i −0.956046 + 0.956046i −0.999074 0.0430274i \(-0.986300\pi\)
0.0430274 + 0.999074i \(0.486300\pi\)
\(314\) 0 0
\(315\) −4.98877 4.98877i −0.281086 0.281086i
\(316\) 0 0
\(317\) 13.1934 + 13.1934i 0.741016 + 0.741016i 0.972774 0.231757i \(-0.0744475\pi\)
−0.231757 + 0.972774i \(0.574448\pi\)
\(318\) 0 0
\(319\) 10.7553i 0.602181i
\(320\) 0 0
\(321\) −7.38555 7.38555i −0.412221 0.412221i
\(322\) 0 0
\(323\) 7.86432i 0.437582i
\(324\) 0 0
\(325\) 2.59188 + 2.59188i 0.143772 + 0.143772i
\(326\) 0 0
\(327\) 28.2025 1.55960
\(328\) 0 0
\(329\) 7.93464 0.437451
\(330\) 0 0
\(331\) −1.16080 1.16080i −0.0638035 0.0638035i 0.674485 0.738289i \(-0.264366\pi\)
−0.738289 + 0.674485i \(0.764366\pi\)
\(332\) 0 0
\(333\) 2.08942i 0.114500i
\(334\) 0 0
\(335\) 7.73947 + 7.73947i 0.422852 + 0.422852i
\(336\) 0 0
\(337\) 12.2758i 0.668703i −0.942448 0.334352i \(-0.891483\pi\)
0.942448 0.334352i \(-0.108517\pi\)
\(338\) 0 0
\(339\) 24.0216 + 24.0216i 1.30468 + 1.30468i
\(340\) 0 0
\(341\) −26.2964 26.2964i −1.42403 1.42403i
\(342\) 0 0
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) 0 0
\(345\) −26.7582 + 26.7582i −1.44061 + 1.44061i
\(346\) 0 0
\(347\) 4.90649 4.90649i 0.263394 0.263394i −0.563037 0.826432i \(-0.690367\pi\)
0.826432 + 0.563037i \(0.190367\pi\)
\(348\) 0 0
\(349\) 14.8998i 0.797567i 0.917045 + 0.398784i \(0.130568\pi\)
−0.917045 + 0.398784i \(0.869432\pi\)
\(350\) 0 0
\(351\) −1.15474 −0.0616355
\(352\) 0 0
\(353\) 32.5527 1.73260 0.866302 0.499521i \(-0.166491\pi\)
0.866302 + 0.499521i \(0.166491\pi\)
\(354\) 0 0
\(355\) −6.03331 + 6.03331i −0.320215 + 0.320215i
\(356\) 0 0
\(357\) −3.43346 3.43346i −0.181718 0.181718i
\(358\) 0 0
\(359\) −22.4786 −1.18638 −0.593188 0.805064i \(-0.702131\pi\)
−0.593188 + 0.805064i \(0.702131\pi\)
\(360\) 0 0
\(361\) 3.63571i 0.191353i
\(362\) 0 0
\(363\) −32.9960 + 32.9960i −1.73184 + 1.73184i
\(364\) 0 0
\(365\) 33.7644 1.76731
\(366\) 0 0
\(367\) 20.8441i 1.08805i −0.839068 0.544026i \(-0.816899\pi\)
0.839068 0.544026i \(-0.183101\pi\)
\(368\) 0 0
\(369\) −12.8464 + 13.0253i −0.668758 + 0.678071i
\(370\) 0 0
\(371\) 6.51545i 0.338265i
\(372\) 0 0
\(373\) 31.3888 1.62525 0.812626 0.582786i \(-0.198037\pi\)
0.812626 + 0.582786i \(0.198037\pi\)
\(374\) 0 0
\(375\) 16.4906 16.4906i 0.851573 0.851573i
\(376\) 0 0
\(377\) 6.52707i 0.336161i
\(378\) 0 0
\(379\) 7.34594 0.377335 0.188668 0.982041i \(-0.439583\pi\)
0.188668 + 0.982041i \(0.439583\pi\)
\(380\) 0 0
\(381\) −6.70471 6.70471i −0.343493 0.343493i
\(382\) 0 0
\(383\) −0.758270 + 0.758270i −0.0387458 + 0.0387458i −0.726214 0.687468i \(-0.758722\pi\)
0.687468 + 0.726214i \(0.258722\pi\)
\(384\) 0 0
\(385\) 13.5883 0.692526
\(386\) 0 0
\(387\) 20.3680 1.03536
\(388\) 0 0
\(389\) 38.8495i 1.96975i −0.173274 0.984874i \(-0.555435\pi\)
0.173274 0.984874i \(-0.444565\pi\)
\(390\) 0 0
\(391\) −8.98337 + 8.98337i −0.454308 + 0.454308i
\(392\) 0 0
\(393\) −5.11414 + 5.11414i −0.257974 + 0.257974i
\(394\) 0 0
\(395\) −3.03579 + 3.03579i −0.152747 + 0.152747i
\(396\) 0 0
\(397\) −0.931306 0.931306i −0.0467409 0.0467409i 0.683350 0.730091i \(-0.260522\pi\)
−0.730091 + 0.683350i \(0.760522\pi\)
\(398\) 0 0
\(399\) −6.70785 6.70785i −0.335813 0.335813i
\(400\) 0 0
\(401\) 5.00028i 0.249702i −0.992175 0.124851i \(-0.960155\pi\)
0.992175 0.124851i \(-0.0398453\pi\)
\(402\) 0 0
\(403\) −15.9585 15.9585i −0.794949 0.794949i
\(404\) 0 0
\(405\) 23.2320i 1.15441i
\(406\) 0 0
\(407\) −2.84557 2.84557i −0.141050 0.141050i
\(408\) 0 0
\(409\) 20.2256 1.00009 0.500046 0.865999i \(-0.333316\pi\)
0.500046 + 0.865999i \(0.333316\pi\)
\(410\) 0 0
\(411\) −22.1303 −1.09161
\(412\) 0 0
\(413\) 7.20782 + 7.20782i 0.354673 + 0.354673i
\(414\) 0 0
\(415\) 17.2573i 0.847128i
\(416\) 0 0
\(417\) 16.6295 + 16.6295i 0.814352 + 0.814352i
\(418\) 0 0
\(419\) 22.6402i 1.10605i 0.833165 + 0.553024i \(0.186526\pi\)
−0.833165 + 0.553024i \(0.813474\pi\)
\(420\) 0 0
\(421\) 1.01713 + 1.01713i 0.0495717 + 0.0495717i 0.731458 0.681886i \(-0.238840\pi\)
−0.681886 + 0.731458i \(0.738840\pi\)
\(422\) 0 0
\(423\) −16.0303 16.0303i −0.779419 0.779419i
\(424\) 0 0
\(425\) −1.55718 + 1.55718i −0.0755342 + 0.0755342i
\(426\) 0 0
\(427\) −6.77055 + 6.77055i −0.327650 + 0.327650i
\(428\) 0 0
\(429\) −31.4483 + 31.4483i −1.51834 + 1.51834i
\(430\) 0 0
\(431\) 11.1361i 0.536408i −0.963362 0.268204i \(-0.913570\pi\)
0.963362 0.268204i \(-0.0864300\pi\)
\(432\) 0 0
\(433\) 10.4182 0.500668 0.250334 0.968160i \(-0.419460\pi\)
0.250334 + 0.968160i \(0.419460\pi\)
\(434\) 0 0
\(435\) −11.6804 −0.560032
\(436\) 0 0
\(437\) −17.5505 + 17.5505i −0.839556 + 0.839556i
\(438\) 0 0
\(439\) 13.3721 + 13.3721i 0.638217 + 0.638217i 0.950115 0.311899i \(-0.100965\pi\)
−0.311899 + 0.950115i \(0.600965\pi\)
\(440\) 0 0
\(441\) −2.85712 −0.136054
\(442\) 0 0
\(443\) 39.9456i 1.89787i −0.315467 0.948937i \(-0.602161\pi\)
0.315467 0.948937i \(-0.397839\pi\)
\(444\) 0 0
\(445\) 28.4826 28.4826i 1.35021 1.35021i
\(446\) 0 0
\(447\) −10.9206 −0.516526
\(448\) 0 0
\(449\) 11.3177i 0.534117i 0.963680 + 0.267059i \(0.0860517\pi\)
−0.963680 + 0.267059i \(0.913948\pi\)
\(450\) 0 0
\(451\) −0.243653 35.2345i −0.0114732 1.65913i
\(452\) 0 0
\(453\) 50.9873i 2.39559i
\(454\) 0 0
\(455\) 8.24636 0.386596
\(456\) 0 0
\(457\) 0.162747 0.162747i 0.00761300 0.00761300i −0.703290 0.710903i \(-0.748286\pi\)
0.710903 + 0.703290i \(0.248286\pi\)
\(458\) 0 0
\(459\) 0.693756i 0.0323818i
\(460\) 0 0
\(461\) 5.70236 0.265585 0.132793 0.991144i \(-0.457606\pi\)
0.132793 + 0.991144i \(0.457606\pi\)
\(462\) 0 0
\(463\) 5.84943 + 5.84943i 0.271846 + 0.271846i 0.829843 0.557997i \(-0.188430\pi\)
−0.557997 + 0.829843i \(0.688430\pi\)
\(464\) 0 0
\(465\) 28.5582 28.5582i 1.32436 1.32436i
\(466\) 0 0
\(467\) 21.2083 0.981402 0.490701 0.871328i \(-0.336741\pi\)
0.490701 + 0.871328i \(0.336741\pi\)
\(468\) 0 0
\(469\) 4.43248 0.204673
\(470\) 0 0
\(471\) 25.1800i 1.16023i
\(472\) 0 0
\(473\) −27.7390 + 27.7390i −1.27544 + 1.27544i
\(474\) 0 0
\(475\) −3.04221 + 3.04221i −0.139586 + 0.139586i
\(476\) 0 0
\(477\) −13.1631 + 13.1631i −0.602697 + 0.602697i
\(478\) 0 0
\(479\) −29.5963 29.5963i −1.35229 1.35229i −0.883094 0.469196i \(-0.844544\pi\)
−0.469196 0.883094i \(-0.655456\pi\)
\(480\) 0 0
\(481\) −1.72689 1.72689i −0.0787395 0.0787395i
\(482\) 0 0
\(483\) 15.3247i 0.697297i
\(484\) 0 0
\(485\) −27.3674 27.3674i −1.24269 1.24269i
\(486\) 0 0
\(487\) 12.1422i 0.550217i 0.961413 + 0.275109i \(0.0887138\pi\)
−0.961413 + 0.275109i \(0.911286\pi\)
\(488\) 0 0
\(489\) 1.41763 + 1.41763i 0.0641073 + 0.0641073i
\(490\) 0 0
\(491\) 24.9160 1.12444 0.562222 0.826986i \(-0.309947\pi\)
0.562222 + 0.826986i \(0.309947\pi\)
\(492\) 0 0
\(493\) −3.92139 −0.176611
\(494\) 0 0
\(495\) −27.4524 27.4524i −1.23389 1.23389i
\(496\) 0 0
\(497\) 3.45534i 0.154993i
\(498\) 0 0
\(499\) 17.5105 + 17.5105i 0.783877 + 0.783877i 0.980483 0.196606i \(-0.0629920\pi\)
−0.196606 + 0.980483i \(0.562992\pi\)
\(500\) 0 0
\(501\) 38.9197i 1.73880i
\(502\) 0 0
\(503\) 9.02603 + 9.02603i 0.402451 + 0.402451i 0.879096 0.476645i \(-0.158147\pi\)
−0.476645 + 0.879096i \(0.658147\pi\)
\(504\) 0 0
\(505\) 7.32303 + 7.32303i 0.325871 + 0.325871i
\(506\) 0 0
\(507\) 3.16194 3.16194i 0.140426 0.140426i
\(508\) 0 0
\(509\) −10.1880 + 10.1880i −0.451575 + 0.451575i −0.895877 0.444302i \(-0.853452\pi\)
0.444302 + 0.895877i \(0.353452\pi\)
\(510\) 0 0
\(511\) 9.66862 9.66862i 0.427715 0.427715i
\(512\) 0 0
\(513\) 1.35537i 0.0598411i
\(514\) 0 0
\(515\) −27.2958 −1.20280
\(516\) 0 0
\(517\) 43.6630 1.92030
\(518\) 0 0
\(519\) 14.3624 14.3624i 0.630442 0.630442i
\(520\) 0 0
\(521\) −1.30470 1.30470i −0.0571600 0.0571600i 0.677949 0.735109i \(-0.262869\pi\)
−0.735109 + 0.677949i \(0.762869\pi\)
\(522\) 0 0
\(523\) 7.85916 0.343657 0.171828 0.985127i \(-0.445033\pi\)
0.171828 + 0.985127i \(0.445033\pi\)
\(524\) 0 0
\(525\) 2.65638i 0.115934i
\(526\) 0 0
\(527\) 9.58769 9.58769i 0.417647 0.417647i
\(528\) 0 0
\(529\) 17.0958 0.743295
\(530\) 0 0
\(531\) 29.1238i 1.26386i
\(532\) 0 0
\(533\) −0.147866 21.3828i −0.00640478 0.926191i
\(534\) 0 0
\(535\) 10.6570i 0.460743i
\(536\) 0 0
\(537\) −39.2646 −1.69439
\(538\) 0 0
\(539\) 3.89109 3.89109i 0.167601 0.167601i
\(540\) 0 0
\(541\) 15.0287i 0.646134i 0.946376 + 0.323067i \(0.104714\pi\)
−0.946376 + 0.323067i \(0.895286\pi\)
\(542\) 0 0
\(543\) 13.9480 0.598565
\(544\) 0 0
\(545\) −20.3475 20.3475i −0.871591 0.871591i
\(546\) 0 0
\(547\) −27.9351 + 27.9351i −1.19442 + 1.19442i −0.218608 + 0.975813i \(0.570152\pi\)
−0.975813 + 0.218608i \(0.929848\pi\)
\(548\) 0 0
\(549\) 27.3570 1.16757
\(550\) 0 0
\(551\) −7.66111 −0.326374
\(552\) 0 0
\(553\) 1.73863i 0.0739340i
\(554\) 0 0
\(555\) 3.09033 3.09033i 0.131177 0.131177i
\(556\) 0 0
\(557\) 9.05263 9.05263i 0.383572 0.383572i −0.488815 0.872387i \(-0.662571\pi\)
0.872387 + 0.488815i \(0.162571\pi\)
\(558\) 0 0
\(559\) −16.8340 + 16.8340i −0.712001 + 0.712001i
\(560\) 0 0
\(561\) −18.8938 18.8938i −0.797696 0.797696i
\(562\) 0 0
\(563\) −23.5537 23.5537i −0.992671 0.992671i 0.00730207 0.999973i \(-0.497676\pi\)
−0.999973 + 0.00730207i \(0.997676\pi\)
\(564\) 0 0
\(565\) 34.6621i 1.45825i
\(566\) 0 0
\(567\) −6.65261 6.65261i −0.279383 0.279383i
\(568\) 0 0
\(569\) 10.9470i 0.458924i −0.973318 0.229462i \(-0.926303\pi\)
0.973318 0.229462i \(-0.0736967\pi\)
\(570\) 0 0
\(571\) −10.3870 10.3870i −0.434683 0.434683i 0.455535 0.890218i \(-0.349448\pi\)
−0.890218 + 0.455535i \(0.849448\pi\)
\(572\) 0 0
\(573\) 31.4823 1.31519
\(574\) 0 0
\(575\) 6.95020 0.289843
\(576\) 0 0
\(577\) −23.6991 23.6991i −0.986608 0.986608i 0.0133038 0.999912i \(-0.495765\pi\)
−0.999912 + 0.0133038i \(0.995765\pi\)
\(578\) 0 0
\(579\) 34.3470i 1.42741i
\(580\) 0 0
\(581\) −4.94172 4.94172i −0.205017 0.205017i
\(582\) 0 0
\(583\) 35.8534i 1.48490i
\(584\) 0 0
\(585\) −16.6601 16.6601i −0.688809 0.688809i
\(586\) 0 0
\(587\) −31.4013 31.4013i −1.29607 1.29607i −0.930966 0.365106i \(-0.881033\pi\)
−0.365106 0.930966i \(-0.618967\pi\)
\(588\) 0 0
\(589\) 18.7312 18.7312i 0.771806 0.771806i
\(590\) 0 0
\(591\) 11.2716 11.2716i 0.463653 0.463653i
\(592\) 0 0
\(593\) −30.3528 + 30.3528i −1.24644 + 1.24644i −0.289162 + 0.957280i \(0.593377\pi\)
−0.957280 + 0.289162i \(0.906623\pi\)
\(594\) 0 0
\(595\) 4.95433i 0.203108i
\(596\) 0 0
\(597\) 1.69231 0.0692618
\(598\) 0 0
\(599\) 34.4104 1.40597 0.702985 0.711204i \(-0.251850\pi\)
0.702985 + 0.711204i \(0.251850\pi\)
\(600\) 0 0
\(601\) 21.0421 21.0421i 0.858324 0.858324i −0.132816 0.991141i \(-0.542402\pi\)
0.991141 + 0.132816i \(0.0424021\pi\)
\(602\) 0 0
\(603\) −8.95489 8.95489i −0.364671 0.364671i
\(604\) 0 0
\(605\) 47.6117 1.93569
\(606\) 0 0
\(607\) 20.5145i 0.832656i −0.909214 0.416328i \(-0.863317\pi\)
0.909214 0.416328i \(-0.136683\pi\)
\(608\) 0 0
\(609\) −3.34474 + 3.34474i −0.135536 + 0.135536i
\(610\) 0 0
\(611\) 26.4978 1.07199
\(612\) 0 0
\(613\) 24.1384i 0.974941i −0.873140 0.487470i \(-0.837920\pi\)
0.873140 0.487470i \(-0.162080\pi\)
\(614\) 0 0
\(615\) 38.2652 0.264611i 1.54300 0.0106701i
\(616\) 0 0
\(617\) 9.57610i 0.385519i 0.981246 + 0.192760i \(0.0617438\pi\)
−0.981246 + 0.192760i \(0.938256\pi\)
\(618\) 0 0
\(619\) −2.76769 −0.111243 −0.0556215 0.998452i \(-0.517714\pi\)
−0.0556215 + 0.998452i \(0.517714\pi\)
\(620\) 0 0
\(621\) −1.54823 + 1.54823i −0.0621284 + 0.0621284i
\(622\) 0 0
\(623\) 16.3123i 0.653538i
\(624\) 0 0
\(625\) −29.2833 −1.17133
\(626\) 0 0
\(627\) −36.9122 36.9122i −1.47413 1.47413i
\(628\) 0 0
\(629\) 1.03750 1.03750i 0.0413677 0.0413677i
\(630\) 0 0
\(631\) 8.64602 0.344193 0.172096 0.985080i \(-0.444946\pi\)
0.172096 + 0.985080i \(0.444946\pi\)
\(632\) 0 0
\(633\) 59.1440 2.35076
\(634\) 0 0
\(635\) 9.67460i 0.383925i
\(636\) 0 0
\(637\) 2.36139 2.36139i 0.0935617 0.0935617i
\(638\) 0 0
\(639\) 6.98079 6.98079i 0.276156 0.276156i
\(640\) 0 0
\(641\) 2.20348 2.20348i 0.0870323 0.0870323i −0.662250 0.749283i \(-0.730398\pi\)
0.749283 + 0.662250i \(0.230398\pi\)
\(642\) 0 0
\(643\) −10.6065 10.6065i −0.418278 0.418278i 0.466332 0.884610i \(-0.345575\pi\)
−0.884610 + 0.466332i \(0.845575\pi\)
\(644\) 0 0
\(645\) −30.1249 30.1249i −1.18617 1.18617i
\(646\) 0 0
\(647\) 40.9173i 1.60863i 0.594206 + 0.804313i \(0.297466\pi\)
−0.594206 + 0.804313i \(0.702534\pi\)
\(648\) 0 0
\(649\) 39.6634 + 39.6634i 1.55693 + 1.55693i
\(650\) 0 0
\(651\) 16.3556i 0.641027i
\(652\) 0 0
\(653\) −22.7064 22.7064i −0.888569 0.888569i 0.105816 0.994386i \(-0.466254\pi\)
−0.994386 + 0.105816i \(0.966254\pi\)
\(654\) 0 0
\(655\) 7.37947 0.288340
\(656\) 0 0
\(657\) −39.0669 −1.52414
\(658\) 0 0
\(659\) 4.10062 + 4.10062i 0.159737 + 0.159737i 0.782450 0.622713i \(-0.213970\pi\)
−0.622713 + 0.782450i \(0.713970\pi\)
\(660\) 0 0
\(661\) 5.07644i 0.197451i 0.995115 + 0.0987254i \(0.0314765\pi\)
−0.995115 + 0.0987254i \(0.968523\pi\)
\(662\) 0 0
\(663\) −11.4661 11.4661i −0.445305 0.445305i
\(664\) 0 0
\(665\) 9.67912i 0.375340i
\(666\) 0 0
\(667\) 8.75125 + 8.75125i 0.338850 + 0.338850i
\(668\) 0 0
\(669\) −33.5886 33.5886i −1.29861 1.29861i
\(670\) 0 0
\(671\) −37.2572 + 37.2572i −1.43830 + 1.43830i
\(672\) 0 0
\(673\) −1.53374 + 1.53374i −0.0591213 + 0.0591213i −0.736049 0.676928i \(-0.763311\pi\)
0.676928 + 0.736049i \(0.263311\pi\)
\(674\) 0 0
\(675\) −0.268371 + 0.268371i −0.0103296 + 0.0103296i
\(676\) 0 0
\(677\) 16.1845i 0.622019i 0.950407 + 0.311010i \(0.100667\pi\)
−0.950407 + 0.311010i \(0.899333\pi\)
\(678\) 0 0
\(679\) −15.6736 −0.601497
\(680\) 0 0
\(681\) 17.6657 0.676952
\(682\) 0 0
\(683\) 29.3842 29.3842i 1.12435 1.12435i 0.133275 0.991079i \(-0.457451\pi\)
0.991079 0.133275i \(-0.0425495\pi\)
\(684\) 0 0
\(685\) 15.9665 + 15.9665i 0.610049 + 0.610049i
\(686\) 0 0
\(687\) −54.0834 −2.06341
\(688\) 0 0
\(689\) 21.7584i 0.828929i
\(690\) 0 0
\(691\) −5.78735 + 5.78735i −0.220161 + 0.220161i −0.808566 0.588405i \(-0.799756\pi\)
0.588405 + 0.808566i \(0.299756\pi\)
\(692\) 0 0
\(693\) −15.7223 −0.597240
\(694\) 0 0
\(695\) 23.9957i 0.910208i
\(696\) 0 0
\(697\) 12.8465 0.0888362i 0.486598 0.00336491i
\(698\) 0 0
\(699\) 33.6042i 1.27103i
\(700\) 0 0
\(701\) 46.6444 1.76173 0.880867 0.473364i \(-0.156960\pi\)
0.880867 + 0.473364i \(0.156960\pi\)
\(702\) 0 0
\(703\) 2.02693 2.02693i 0.0764471 0.0764471i
\(704\) 0 0
\(705\) 47.4186i 1.78589i
\(706\) 0 0
\(707\) 4.19398 0.157731
\(708\) 0 0
\(709\) 29.9441 + 29.9441i 1.12457 + 1.12457i 0.991045 + 0.133528i \(0.0426305\pi\)
0.133528 + 0.991045i \(0.457369\pi\)
\(710\) 0 0
\(711\) 3.51254 3.51254i 0.131730 0.131730i
\(712\) 0 0
\(713\) −42.7931 −1.60261
\(714\) 0 0
\(715\) 45.3784 1.69706
\(716\) 0 0
\(717\) 48.1362i 1.79768i
\(718\) 0 0
\(719\) −14.6174 + 14.6174i −0.545135 + 0.545135i −0.925030 0.379895i \(-0.875960\pi\)
0.379895 + 0.925030i \(0.375960\pi\)
\(720\) 0 0
\(721\) −7.81631 + 7.81631i −0.291094 + 0.291094i
\(722\) 0 0
\(723\) 37.1328 37.1328i 1.38098 1.38098i
\(724\) 0 0
\(725\) 1.51694 + 1.51694i 0.0563378 + 0.0563378i
\(726\) 0 0
\(727\) −21.8827 21.8827i −0.811585 0.811585i 0.173287 0.984871i \(-0.444561\pi\)
−0.984871 + 0.173287i \(0.944561\pi\)
\(728\) 0 0
\(729\) 24.3699i 0.902589i
\(730\) 0 0
\(731\) −10.1137 10.1137i −0.374067 0.374067i
\(732\) 0 0
\(733\) 47.8460i 1.76723i 0.468211 + 0.883617i \(0.344899\pi\)
−0.468211 + 0.883617i \(0.655101\pi\)
\(734\) 0 0
\(735\) 4.22578 + 4.22578i 0.155870 + 0.155870i
\(736\) 0 0
\(737\) 24.3912 0.898461
\(738\) 0 0
\(739\) 27.7356 1.02027 0.510135 0.860094i \(-0.329595\pi\)
0.510135 + 0.860094i \(0.329595\pi\)
\(740\) 0 0
\(741\) −22.4009 22.4009i −0.822919 0.822919i
\(742\) 0 0
\(743\) 7.35243i 0.269734i −0.990864 0.134867i \(-0.956939\pi\)
0.990864 0.134867i \(-0.0430608\pi\)
\(744\) 0 0
\(745\) 7.87896 + 7.87896i 0.288663 + 0.288663i
\(746\) 0 0
\(747\) 19.9674i 0.730571i
\(748\) 0 0
\(749\) 3.05169 + 3.05169i 0.111506 + 0.111506i
\(750\) 0 0
\(751\) 19.9471 + 19.9471i 0.727881 + 0.727881i 0.970197 0.242316i \(-0.0779072\pi\)
−0.242316 + 0.970197i \(0.577907\pi\)
\(752\) 0 0
\(753\) −49.4714 + 49.4714i −1.80284 + 1.80284i
\(754\) 0 0
\(755\) 36.7862 36.7862i 1.33879 1.33879i
\(756\) 0 0
\(757\) 33.3190 33.3190i 1.21100 1.21100i 0.240301 0.970699i \(-0.422754\pi\)
0.970699 0.240301i \(-0.0772460\pi\)
\(758\) 0 0
\(759\) 84.3292i 3.06096i
\(760\) 0 0
\(761\) 35.1208 1.27313 0.636565 0.771223i \(-0.280355\pi\)
0.636565 + 0.771223i \(0.280355\pi\)
\(762\) 0 0
\(763\) −11.6532 −0.421875
\(764\) 0 0
\(765\) 10.0092 10.0092i 0.361883 0.361883i
\(766\) 0 0
\(767\) 24.0706 + 24.0706i 0.869138 + 0.869138i
\(768\) 0 0
\(769\) 51.8614 1.87017 0.935085 0.354423i \(-0.115323\pi\)
0.935085 + 0.354423i \(0.115323\pi\)
\(770\) 0 0
\(771\) 60.6984i 2.18600i
\(772\) 0 0
\(773\) 7.18747 7.18747i 0.258515 0.258515i −0.565935 0.824450i \(-0.691485\pi\)
0.824450 + 0.565935i \(0.191485\pi\)
\(774\) 0 0
\(775\) −7.41775 −0.266454
\(776\) 0 0
\(777\) 1.76986i 0.0634935i
\(778\) 0 0
\(779\) 25.0979 0.173557i 0.899226 0.00621831i
\(780\) 0 0
\(781\) 19.0142i 0.680380i
\(782\) 0 0
\(783\) −0.675830 −0.0241522
\(784\) 0 0
\(785\) −18.1668 + 18.1668i −0.648400 + 0.648400i
\(786\) 0 0
\(787\) 24.0153i 0.856052i 0.903767 + 0.428026i \(0.140791\pi\)
−0.903767 + 0.428026i \(0.859209\pi\)
\(788\) 0 0
\(789\) −19.2612 −0.685718
\(790\) 0 0
\(791\) −9.92568 9.92568i −0.352916 0.352916i
\(792\) 0 0
\(793\) −22.6103 + 22.6103i −0.802915 + 0.802915i
\(794\) 0 0
\(795\) 38.9373 1.38097
\(796\) 0 0
\(797\) −19.2773 −0.682836 −0.341418 0.939911i \(-0.610907\pi\)
−0.341418 + 0.939911i \(0.610907\pi\)
\(798\) 0 0
\(799\) 15.9196i 0.563195i
\(800\) 0 0
\(801\) −32.9556 +