Properties

Label 1148.2.k.b.337.10
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 337.10
Character \(\chi\) \(=\) 1148.337
Dual form 1148.2.k.b.729.10

$q$-expansion

\(f(q)\) \(=\) \(q+(0.147004 + 0.147004i) q^{3} +2.61619i q^{5} +(0.707107 + 0.707107i) q^{7} -2.95678i q^{9} +O(q^{10})\) \(q+(0.147004 + 0.147004i) q^{3} +2.61619i q^{5} +(0.707107 + 0.707107i) q^{7} -2.95678i q^{9} +(-3.93415 - 3.93415i) q^{11} +(-4.00823 - 4.00823i) q^{13} +(-0.384591 + 0.384591i) q^{15} +(-3.80906 + 3.80906i) q^{17} +(2.63624 - 2.63624i) q^{19} +0.207895i q^{21} -6.55069 q^{23} -1.84446 q^{25} +(0.875671 - 0.875671i) q^{27} +(-5.02497 - 5.02497i) q^{29} +5.50289 q^{31} -1.15667i q^{33} +(-1.84993 + 1.84993i) q^{35} +3.96807 q^{37} -1.17845i q^{39} +(-0.0213092 - 6.40309i) q^{41} +5.74887i q^{43} +7.73551 q^{45} +(3.50887 - 3.50887i) q^{47} +1.00000i q^{49} -1.11990 q^{51} +(-5.19323 - 5.19323i) q^{53} +(10.2925 - 10.2925i) q^{55} +0.775077 q^{57} +6.18269 q^{59} -1.26120i q^{61} +(2.09076 - 2.09076i) q^{63} +(10.4863 - 10.4863i) q^{65} +(-6.45447 + 6.45447i) q^{67} +(-0.962978 - 0.962978i) q^{69} +(7.03066 + 7.03066i) q^{71} +8.69496i q^{73} +(-0.271144 - 0.271144i) q^{75} -5.56373i q^{77} +(-8.32949 - 8.32949i) q^{79} -8.61288 q^{81} -17.0514 q^{83} +(-9.96524 - 9.96524i) q^{85} -1.47738i q^{87} +(-6.59324 - 6.59324i) q^{89} -5.66849i q^{91} +(0.808947 + 0.808947i) q^{93} +(6.89692 + 6.89692i) q^{95} +(-6.38165 + 6.38165i) q^{97} +(-11.6324 + 11.6324i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + O(q^{10}) \) \( 36q - 12q^{11} - 16q^{17} - 4q^{19} - 36q^{23} - 64q^{25} + 12q^{27} + 16q^{29} - 28q^{31} + 12q^{35} + 48q^{37} + 4q^{41} + 36q^{45} + 12q^{47} - 12q^{51} - 12q^{53} + 12q^{55} + 76q^{57} + 20q^{59} - 4q^{65} - 44q^{67} + 72q^{69} - 20q^{71} + 72q^{75} - 8q^{79} - 100q^{81} - 40q^{83} - 8q^{85} - 16q^{89} + 20q^{93} + 76q^{95} - 16q^{97} + 56q^{99} + O(q^{100}) \)

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
\(3\) 0.147004 + 0.147004i 0.0848728 + 0.0848728i 0.748269 0.663396i \(-0.230885\pi\)
−0.663396 + 0.748269i \(0.730885\pi\)
\(4\) 0 0
\(5\) 2.61619i 1.17000i 0.811034 + 0.584998i \(0.198905\pi\)
−0.811034 + 0.584998i \(0.801095\pi\)
\(6\) 0 0
\(7\) 0.707107 + 0.707107i 0.267261 + 0.267261i
\(8\) 0 0
\(9\) 2.95678i 0.985593i
\(10\) 0 0
\(11\) −3.93415 3.93415i −1.18619 1.18619i −0.978112 0.208078i \(-0.933279\pi\)
−0.208078 0.978112i \(-0.566721\pi\)
\(12\) 0 0
\(13\) −4.00823 4.00823i −1.11168 1.11168i −0.992923 0.118760i \(-0.962108\pi\)
−0.118760 0.992923i \(-0.537892\pi\)
\(14\) 0 0
\(15\) −0.384591 + 0.384591i −0.0993010 + 0.0993010i
\(16\) 0 0
\(17\) −3.80906 + 3.80906i −0.923834 + 0.923834i −0.997298 0.0734642i \(-0.976595\pi\)
0.0734642 + 0.997298i \(0.476595\pi\)
\(18\) 0 0
\(19\) 2.63624 2.63624i 0.604796 0.604796i −0.336785 0.941581i \(-0.609340\pi\)
0.941581 + 0.336785i \(0.109340\pi\)
\(20\) 0 0
\(21\) 0.207895i 0.0453664i
\(22\) 0 0
\(23\) −6.55069 −1.36591 −0.682957 0.730459i \(-0.739306\pi\)
−0.682957 + 0.730459i \(0.739306\pi\)
\(24\) 0 0
\(25\) −1.84446 −0.368893
\(26\) 0 0
\(27\) 0.875671 0.875671i 0.168523 0.168523i
\(28\) 0 0
\(29\) −5.02497 5.02497i −0.933113 0.933113i 0.0647858 0.997899i \(-0.479364\pi\)
−0.997899 + 0.0647858i \(0.979364\pi\)
\(30\) 0 0
\(31\) 5.50289 0.988348 0.494174 0.869363i \(-0.335471\pi\)
0.494174 + 0.869363i \(0.335471\pi\)
\(32\) 0 0
\(33\) 1.15667i 0.201351i
\(34\) 0 0
\(35\) −1.84993 + 1.84993i −0.312695 + 0.312695i
\(36\) 0 0
\(37\) 3.96807 0.652347 0.326173 0.945310i \(-0.394241\pi\)
0.326173 + 0.945310i \(0.394241\pi\)
\(38\) 0 0
\(39\) 1.17845i 0.188703i
\(40\) 0 0
\(41\) −0.0213092 6.40309i −0.00332794 0.999994i
\(42\) 0 0
\(43\) 5.74887i 0.876695i 0.898806 + 0.438347i \(0.144436\pi\)
−0.898806 + 0.438347i \(0.855564\pi\)
\(44\) 0 0
\(45\) 7.73551 1.15314
\(46\) 0 0
\(47\) 3.50887 3.50887i 0.511822 0.511822i −0.403263 0.915084i \(-0.632124\pi\)
0.915084 + 0.403263i \(0.132124\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) −1.11990 −0.156817
\(52\) 0 0
\(53\) −5.19323 5.19323i −0.713345 0.713345i 0.253889 0.967233i \(-0.418290\pi\)
−0.967233 + 0.253889i \(0.918290\pi\)
\(54\) 0 0
\(55\) 10.2925 10.2925i 1.38784 1.38784i
\(56\) 0 0
\(57\) 0.775077 0.102662
\(58\) 0 0
\(59\) 6.18269 0.804917 0.402459 0.915438i \(-0.368156\pi\)
0.402459 + 0.915438i \(0.368156\pi\)
\(60\) 0 0
\(61\) 1.26120i 0.161480i −0.996735 0.0807398i \(-0.974272\pi\)
0.996735 0.0807398i \(-0.0257283\pi\)
\(62\) 0 0
\(63\) 2.09076 2.09076i 0.263411 0.263411i
\(64\) 0 0
\(65\) 10.4863 10.4863i 1.30067 1.30067i
\(66\) 0 0
\(67\) −6.45447 + 6.45447i −0.788539 + 0.788539i −0.981255 0.192716i \(-0.938270\pi\)
0.192716 + 0.981255i \(0.438270\pi\)
\(68\) 0 0
\(69\) −0.962978 0.962978i −0.115929 0.115929i
\(70\) 0 0
\(71\) 7.03066 + 7.03066i 0.834386 + 0.834386i 0.988113 0.153728i \(-0.0491279\pi\)
−0.153728 + 0.988113i \(0.549128\pi\)
\(72\) 0 0
\(73\) 8.69496i 1.01767i 0.860865 + 0.508834i \(0.169923\pi\)
−0.860865 + 0.508834i \(0.830077\pi\)
\(74\) 0 0
\(75\) −0.271144 0.271144i −0.0313090 0.0313090i
\(76\) 0 0
\(77\) 5.56373i 0.634045i
\(78\) 0 0
\(79\) −8.32949 8.32949i −0.937140 0.937140i 0.0609974 0.998138i \(-0.480572\pi\)
−0.998138 + 0.0609974i \(0.980572\pi\)
\(80\) 0 0
\(81\) −8.61288 −0.956987
\(82\) 0 0
\(83\) −17.0514 −1.87164 −0.935820 0.352479i \(-0.885339\pi\)
−0.935820 + 0.352479i \(0.885339\pi\)
\(84\) 0 0
\(85\) −9.96524 9.96524i −1.08088 1.08088i
\(86\) 0 0
\(87\) 1.47738i 0.158392i
\(88\) 0 0
\(89\) −6.59324 6.59324i −0.698882 0.698882i 0.265287 0.964169i \(-0.414533\pi\)
−0.964169 + 0.265287i \(0.914533\pi\)
\(90\) 0 0
\(91\) 5.66849i 0.594220i
\(92\) 0 0
\(93\) 0.808947 + 0.808947i 0.0838839 + 0.0838839i
\(94\) 0 0
\(95\) 6.89692 + 6.89692i 0.707610 + 0.707610i
\(96\) 0 0
\(97\) −6.38165 + 6.38165i −0.647958 + 0.647958i −0.952499 0.304541i \(-0.901497\pi\)
0.304541 + 0.952499i \(0.401497\pi\)
\(98\) 0 0
\(99\) −11.6324 + 11.6324i −1.16910 + 1.16910i
\(100\) 0 0
\(101\) 4.56995 4.56995i 0.454727 0.454727i −0.442193 0.896920i \(-0.645799\pi\)
0.896920 + 0.442193i \(0.145799\pi\)
\(102\) 0 0
\(103\) 1.23098i 0.121292i 0.998159 + 0.0606459i \(0.0193161\pi\)
−0.998159 + 0.0606459i \(0.980684\pi\)
\(104\) 0 0
\(105\) −0.543894 −0.0530786
\(106\) 0 0
\(107\) 8.18167 0.790952 0.395476 0.918476i \(-0.370580\pi\)
0.395476 + 0.918476i \(0.370580\pi\)
\(108\) 0 0
\(109\) 4.30375 4.30375i 0.412225 0.412225i −0.470288 0.882513i \(-0.655850\pi\)
0.882513 + 0.470288i \(0.155850\pi\)
\(110\) 0 0
\(111\) 0.583322 + 0.583322i 0.0553665 + 0.0553665i
\(112\) 0 0
\(113\) −19.3440 −1.81973 −0.909863 0.414908i \(-0.863814\pi\)
−0.909863 + 0.414908i \(0.863814\pi\)
\(114\) 0 0
\(115\) 17.1379i 1.59811i
\(116\) 0 0
\(117\) −11.8515 + 11.8515i −1.09567 + 1.09567i
\(118\) 0 0
\(119\) −5.38683 −0.493810
\(120\) 0 0
\(121\) 19.9550i 1.81410i
\(122\) 0 0
\(123\) 0.938148 0.944413i 0.0845899 0.0851548i
\(124\) 0 0
\(125\) 8.25549i 0.738393i
\(126\) 0 0
\(127\) 5.00156 0.443817 0.221909 0.975067i \(-0.428771\pi\)
0.221909 + 0.975067i \(0.428771\pi\)
\(128\) 0 0
\(129\) −0.845108 + 0.845108i −0.0744076 + 0.0744076i
\(130\) 0 0
\(131\) 1.29068i 0.112767i −0.998409 0.0563836i \(-0.982043\pi\)
0.998409 0.0563836i \(-0.0179570\pi\)
\(132\) 0 0
\(133\) 3.72821 0.323277
\(134\) 0 0
\(135\) 2.29092 + 2.29092i 0.197171 + 0.197171i
\(136\) 0 0
\(137\) 3.22286 3.22286i 0.275347 0.275347i −0.555901 0.831248i \(-0.687627\pi\)
0.831248 + 0.555901i \(0.187627\pi\)
\(138\) 0 0
\(139\) 17.4218 1.47770 0.738850 0.673870i \(-0.235369\pi\)
0.738850 + 0.673870i \(0.235369\pi\)
\(140\) 0 0
\(141\) 1.03164 0.0868795
\(142\) 0 0
\(143\) 31.5379i 2.63734i
\(144\) 0 0
\(145\) 13.1463 13.1463i 1.09174 1.09174i
\(146\) 0 0
\(147\) −0.147004 + 0.147004i −0.0121247 + 0.0121247i
\(148\) 0 0
\(149\) 11.6075 11.6075i 0.950922 0.950922i −0.0479289 0.998851i \(-0.515262\pi\)
0.998851 + 0.0479289i \(0.0152621\pi\)
\(150\) 0 0
\(151\) 2.69241 + 2.69241i 0.219105 + 0.219105i 0.808121 0.589016i \(-0.200485\pi\)
−0.589016 + 0.808121i \(0.700485\pi\)
\(152\) 0 0
\(153\) 11.2626 + 11.2626i 0.910524 + 0.910524i
\(154\) 0 0
\(155\) 14.3966i 1.15636i
\(156\) 0 0
\(157\) −10.4484 10.4484i −0.833872 0.833872i 0.154172 0.988044i \(-0.450729\pi\)
−0.988044 + 0.154172i \(0.950729\pi\)
\(158\) 0 0
\(159\) 1.52685i 0.121087i
\(160\) 0 0
\(161\) −4.63204 4.63204i −0.365056 0.365056i
\(162\) 0 0
\(163\) −4.99749 −0.391434 −0.195717 0.980660i \(-0.562703\pi\)
−0.195717 + 0.980660i \(0.562703\pi\)
\(164\) 0 0
\(165\) 3.02608 0.235580
\(166\) 0 0
\(167\) 4.83692 + 4.83692i 0.374292 + 0.374292i 0.869038 0.494746i \(-0.164739\pi\)
−0.494746 + 0.869038i \(0.664739\pi\)
\(168\) 0 0
\(169\) 19.1318i 1.47168i
\(170\) 0 0
\(171\) −7.79479 7.79479i −0.596083 0.596083i
\(172\) 0 0
\(173\) 16.9725i 1.29039i −0.764016 0.645197i \(-0.776775\pi\)
0.764016 0.645197i \(-0.223225\pi\)
\(174\) 0 0
\(175\) −1.30423 1.30423i −0.0985907 0.0985907i
\(176\) 0 0
\(177\) 0.908880 + 0.908880i 0.0683156 + 0.0683156i
\(178\) 0 0
\(179\) −2.54257 + 2.54257i −0.190041 + 0.190041i −0.795714 0.605673i \(-0.792904\pi\)
0.605673 + 0.795714i \(0.292904\pi\)
\(180\) 0 0
\(181\) 8.26228 8.26228i 0.614131 0.614131i −0.329889 0.944020i \(-0.607011\pi\)
0.944020 + 0.329889i \(0.107011\pi\)
\(182\) 0 0
\(183\) 0.185401 0.185401i 0.0137052 0.0137052i
\(184\) 0 0
\(185\) 10.3812i 0.763244i
\(186\) 0 0
\(187\) 29.9708 2.19169
\(188\) 0 0
\(189\) 1.23839 0.0900793
\(190\) 0 0
\(191\) 1.40300 1.40300i 0.101518 0.101518i −0.654524 0.756041i \(-0.727131\pi\)
0.756041 + 0.654524i \(0.227131\pi\)
\(192\) 0 0
\(193\) −7.76154 7.76154i −0.558688 0.558688i 0.370246 0.928934i \(-0.379273\pi\)
−0.928934 + 0.370246i \(0.879273\pi\)
\(194\) 0 0
\(195\) 3.08306 0.220782
\(196\) 0 0
\(197\) 18.3831i 1.30974i −0.755742 0.654870i \(-0.772723\pi\)
0.755742 0.654870i \(-0.227277\pi\)
\(198\) 0 0
\(199\) −7.84594 + 7.84594i −0.556184 + 0.556184i −0.928219 0.372035i \(-0.878660\pi\)
0.372035 + 0.928219i \(0.378660\pi\)
\(200\) 0 0
\(201\) −1.89767 −0.133851
\(202\) 0 0
\(203\) 7.10638i 0.498770i
\(204\) 0 0
\(205\) 16.7517 0.0557490i 1.16999 0.00389368i
\(206\) 0 0
\(207\) 19.3690i 1.34624i
\(208\) 0 0
\(209\) −20.7428 −1.43481
\(210\) 0 0
\(211\) −7.80238 + 7.80238i −0.537138 + 0.537138i −0.922687 0.385549i \(-0.874012\pi\)
0.385549 + 0.922687i \(0.374012\pi\)
\(212\) 0 0
\(213\) 2.06707i 0.141633i
\(214\) 0 0
\(215\) −15.0402 −1.02573
\(216\) 0 0
\(217\) 3.89113 + 3.89113i 0.264147 + 0.264147i
\(218\) 0 0
\(219\) −1.27819 + 1.27819i −0.0863724 + 0.0863724i
\(220\) 0 0
\(221\) 30.5352 2.05402
\(222\) 0 0
\(223\) −8.29621 −0.555555 −0.277777 0.960645i \(-0.589598\pi\)
−0.277777 + 0.960645i \(0.589598\pi\)
\(224\) 0 0
\(225\) 5.45367i 0.363578i
\(226\) 0 0
\(227\) −11.6971 + 11.6971i −0.776361 + 0.776361i −0.979210 0.202849i \(-0.934980\pi\)
0.202849 + 0.979210i \(0.434980\pi\)
\(228\) 0 0
\(229\) 11.7017 11.7017i 0.773269 0.773269i −0.205408 0.978676i \(-0.565852\pi\)
0.978676 + 0.205408i \(0.0658521\pi\)
\(230\) 0 0
\(231\) 0.817890 0.817890i 0.0538132 0.0538132i
\(232\) 0 0
\(233\) 0.269706 + 0.269706i 0.0176690 + 0.0176690i 0.715886 0.698217i \(-0.246023\pi\)
−0.698217 + 0.715886i \(0.746023\pi\)
\(234\) 0 0
\(235\) 9.17989 + 9.17989i 0.598830 + 0.598830i
\(236\) 0 0
\(237\) 2.44894i 0.159076i
\(238\) 0 0
\(239\) 19.7538 + 19.7538i 1.27777 + 1.27777i 0.941914 + 0.335854i \(0.109025\pi\)
0.335854 + 0.941914i \(0.390975\pi\)
\(240\) 0 0
\(241\) 4.20799i 0.271061i 0.990773 + 0.135530i \(0.0432738\pi\)
−0.990773 + 0.135530i \(0.956726\pi\)
\(242\) 0 0
\(243\) −3.89314 3.89314i −0.249745 0.249745i
\(244\) 0 0
\(245\) −2.61619 −0.167142
\(246\) 0 0
\(247\) −21.1334 −1.34468
\(248\) 0 0
\(249\) −2.50663 2.50663i −0.158851 0.158851i
\(250\) 0 0
\(251\) 1.41815i 0.0895131i 0.998998 + 0.0447565i \(0.0142512\pi\)
−0.998998 + 0.0447565i \(0.985749\pi\)
\(252\) 0 0
\(253\) 25.7714 + 25.7714i 1.62023 + 1.62023i
\(254\) 0 0
\(255\) 2.92986i 0.183475i
\(256\) 0 0
\(257\) −7.53877 7.53877i −0.470255 0.470255i 0.431742 0.901997i \(-0.357899\pi\)
−0.901997 + 0.431742i \(0.857899\pi\)
\(258\) 0 0
\(259\) 2.80585 + 2.80585i 0.174347 + 0.174347i
\(260\) 0 0
\(261\) −14.8577 + 14.8577i −0.919670 + 0.919670i
\(262\) 0 0
\(263\) −0.862520 + 0.862520i −0.0531853 + 0.0531853i −0.733199 0.680014i \(-0.761974\pi\)
0.680014 + 0.733199i \(0.261974\pi\)
\(264\) 0 0
\(265\) 13.5865 13.5865i 0.834611 0.834611i
\(266\) 0 0
\(267\) 1.93847i 0.118632i
\(268\) 0 0
\(269\) −28.7744 −1.75440 −0.877202 0.480121i \(-0.840593\pi\)
−0.877202 + 0.480121i \(0.840593\pi\)
\(270\) 0 0
\(271\) 21.4026 1.30012 0.650058 0.759884i \(-0.274744\pi\)
0.650058 + 0.759884i \(0.274744\pi\)
\(272\) 0 0
\(273\) 0.833292 0.833292i 0.0504331 0.0504331i
\(274\) 0 0
\(275\) 7.25639 + 7.25639i 0.437577 + 0.437577i
\(276\) 0 0
\(277\) −6.24067 −0.374966 −0.187483 0.982268i \(-0.560033\pi\)
−0.187483 + 0.982268i \(0.560033\pi\)
\(278\) 0 0
\(279\) 16.2708i 0.974109i
\(280\) 0 0
\(281\) −6.15101 + 6.15101i −0.366938 + 0.366938i −0.866359 0.499421i \(-0.833546\pi\)
0.499421 + 0.866359i \(0.333546\pi\)
\(282\) 0 0
\(283\) 14.6949 0.873521 0.436761 0.899578i \(-0.356126\pi\)
0.436761 + 0.899578i \(0.356126\pi\)
\(284\) 0 0
\(285\) 2.02775i 0.120114i
\(286\) 0 0
\(287\) 4.51260 4.54274i 0.266370 0.268149i
\(288\) 0 0
\(289\) 12.0179i 0.706937i
\(290\) 0 0
\(291\) −1.87626 −0.109988
\(292\) 0 0
\(293\) 16.0401 16.0401i 0.937076 0.937076i −0.0610587 0.998134i \(-0.519448\pi\)
0.998134 + 0.0610587i \(0.0194477\pi\)
\(294\) 0 0
\(295\) 16.1751i 0.941751i
\(296\) 0 0
\(297\) −6.89004 −0.399801
\(298\) 0 0
\(299\) 26.2567 + 26.2567i 1.51846 + 1.51846i
\(300\) 0 0
\(301\) −4.06507 + 4.06507i −0.234307 + 0.234307i
\(302\) 0 0
\(303\) 1.34360 0.0771880
\(304\) 0 0
\(305\) 3.29953 0.188931
\(306\) 0 0
\(307\) 12.1604i 0.694030i −0.937860 0.347015i \(-0.887195\pi\)
0.937860 0.347015i \(-0.112805\pi\)
\(308\) 0 0
\(309\) −0.180959 + 0.180959i −0.0102944 + 0.0102944i
\(310\) 0 0
\(311\) −13.8654 + 13.8654i −0.786233 + 0.786233i −0.980874 0.194642i \(-0.937646\pi\)
0.194642 + 0.980874i \(0.437646\pi\)
\(312\) 0 0
\(313\) −0.416709 + 0.416709i −0.0235538 + 0.0235538i −0.718786 0.695232i \(-0.755302\pi\)
0.695232 + 0.718786i \(0.255302\pi\)
\(314\) 0 0
\(315\) 5.46983 + 5.46983i 0.308190 + 0.308190i
\(316\) 0 0
\(317\) −3.09378 3.09378i −0.173764 0.173764i 0.614867 0.788631i \(-0.289210\pi\)
−0.788631 + 0.614867i \(0.789210\pi\)
\(318\) 0 0
\(319\) 39.5379i 2.21370i
\(320\) 0 0
\(321\) 1.20274 + 1.20274i 0.0671304 + 0.0671304i
\(322\) 0 0
\(323\) 20.0832i 1.11746i
\(324\) 0 0
\(325\) 7.39304 + 7.39304i 0.410092 + 0.410092i
\(326\) 0 0
\(327\) 1.26534 0.0699733
\(328\) 0 0
\(329\) 4.96229 0.273580
\(330\) 0 0
\(331\) −7.21883 7.21883i −0.396783 0.396783i 0.480314 0.877097i \(-0.340523\pi\)
−0.877097 + 0.480314i \(0.840523\pi\)
\(332\) 0 0
\(333\) 11.7327i 0.642949i
\(334\) 0 0
\(335\) −16.8861 16.8861i −0.922588 0.922588i
\(336\) 0 0
\(337\) 23.2574i 1.26691i 0.773779 + 0.633456i \(0.218364\pi\)
−0.773779 + 0.633456i \(0.781636\pi\)
\(338\) 0 0
\(339\) −2.84364 2.84364i −0.154445 0.154445i
\(340\) 0 0
\(341\) −21.6492 21.6492i −1.17237 1.17237i
\(342\) 0 0
\(343\) −0.707107 + 0.707107i −0.0381802 + 0.0381802i
\(344\) 0 0
\(345\) 2.51934 2.51934i 0.135637 0.135637i
\(346\) 0 0
\(347\) −13.3285 + 13.3285i −0.715512 + 0.715512i −0.967683 0.252171i \(-0.918856\pi\)
0.252171 + 0.967683i \(0.418856\pi\)
\(348\) 0 0
\(349\) 20.2304i 1.08291i −0.840730 0.541454i \(-0.817874\pi\)
0.840730 0.541454i \(-0.182126\pi\)
\(350\) 0 0
\(351\) −7.01978 −0.374688
\(352\) 0 0
\(353\) 16.4554 0.875830 0.437915 0.899016i \(-0.355717\pi\)
0.437915 + 0.899016i \(0.355717\pi\)
\(354\) 0 0
\(355\) −18.3936 + 18.3936i −0.976229 + 0.976229i
\(356\) 0 0
\(357\) −0.791886 0.791886i −0.0419110 0.0419110i
\(358\) 0 0
\(359\) 8.63094 0.455524 0.227762 0.973717i \(-0.426859\pi\)
0.227762 + 0.973717i \(0.426859\pi\)
\(360\) 0 0
\(361\) 5.10043i 0.268444i
\(362\) 0 0
\(363\) −2.93347 + 2.93347i −0.153967 + 0.153967i
\(364\) 0 0
\(365\) −22.7477 −1.19067
\(366\) 0 0
\(367\) 3.72546i 0.194467i −0.995262 0.0972337i \(-0.969001\pi\)
0.995262 0.0972337i \(-0.0309994\pi\)
\(368\) 0 0
\(369\) −18.9325 + 0.0630066i −0.985588 + 0.00327999i
\(370\) 0 0
\(371\) 7.34433i 0.381299i
\(372\) 0 0
\(373\) −23.7762 −1.23108 −0.615542 0.788104i \(-0.711063\pi\)
−0.615542 + 0.788104i \(0.711063\pi\)
\(374\) 0 0
\(375\) −1.21359 + 1.21359i −0.0626695 + 0.0626695i
\(376\) 0 0
\(377\) 40.2825i 2.07465i
\(378\) 0 0
\(379\) 33.9921 1.74606 0.873029 0.487669i \(-0.162153\pi\)
0.873029 + 0.487669i \(0.162153\pi\)
\(380\) 0 0
\(381\) 0.735250 + 0.735250i 0.0376680 + 0.0376680i
\(382\) 0 0
\(383\) 1.34885 1.34885i 0.0689230 0.0689230i −0.671805 0.740728i \(-0.734481\pi\)
0.740728 + 0.671805i \(0.234481\pi\)
\(384\) 0 0
\(385\) 14.5558 0.741831
\(386\) 0 0
\(387\) 16.9981 0.864065
\(388\) 0 0
\(389\) 29.4146i 1.49138i 0.666294 + 0.745689i \(0.267880\pi\)
−0.666294 + 0.745689i \(0.732120\pi\)
\(390\) 0 0
\(391\) 24.9520 24.9520i 1.26188 1.26188i
\(392\) 0 0
\(393\) 0.189735 0.189735i 0.00957088 0.00957088i
\(394\) 0 0
\(395\) 21.7915 21.7915i 1.09645 1.09645i
\(396\) 0 0
\(397\) 14.1375 + 14.1375i 0.709541 + 0.709541i 0.966439 0.256898i \(-0.0827003\pi\)
−0.256898 + 0.966439i \(0.582700\pi\)
\(398\) 0 0
\(399\) 0.548062 + 0.548062i 0.0274374 + 0.0274374i
\(400\) 0 0
\(401\) 1.00724i 0.0502991i −0.999684 0.0251495i \(-0.991994\pi\)
0.999684 0.0251495i \(-0.00800619\pi\)
\(402\) 0 0
\(403\) −22.0568 22.0568i −1.09873 1.09873i
\(404\) 0 0
\(405\) 22.5330i 1.11967i
\(406\) 0 0
\(407\) −15.6110 15.6110i −0.773807 0.773807i
\(408\) 0 0
\(409\) −5.37330 −0.265692 −0.132846 0.991137i \(-0.542412\pi\)
−0.132846 + 0.991137i \(0.542412\pi\)
\(410\) 0 0
\(411\) 0.947546 0.0467390
\(412\) 0 0
\(413\) 4.37182 + 4.37182i 0.215123 + 0.215123i
\(414\) 0 0
\(415\) 44.6099i 2.18981i
\(416\) 0 0
\(417\) 2.56108 + 2.56108i 0.125417 + 0.125417i
\(418\) 0 0
\(419\) 23.7358i 1.15957i 0.814770 + 0.579784i \(0.196863\pi\)
−0.814770 + 0.579784i \(0.803137\pi\)
\(420\) 0 0
\(421\) −10.3142 10.3142i −0.502682 0.502682i 0.409589 0.912270i \(-0.365672\pi\)
−0.912270 + 0.409589i \(0.865672\pi\)
\(422\) 0 0
\(423\) −10.3750 10.3750i −0.504448 0.504448i
\(424\) 0 0
\(425\) 7.02568 7.02568i 0.340796 0.340796i
\(426\) 0 0
\(427\) 0.891801 0.891801i 0.0431573 0.0431573i
\(428\) 0 0
\(429\) −4.63621 + 4.63621i −0.223838 + 0.223838i
\(430\) 0 0
\(431\) 17.0622i 0.821858i −0.911667 0.410929i \(-0.865204\pi\)
0.911667 0.410929i \(-0.134796\pi\)
\(432\) 0 0
\(433\) 5.09967 0.245074 0.122537 0.992464i \(-0.460897\pi\)
0.122537 + 0.992464i \(0.460897\pi\)
\(434\) 0 0
\(435\) 3.86512 0.185318
\(436\) 0 0
\(437\) −17.2692 + 17.2692i −0.826099 + 0.826099i
\(438\) 0 0
\(439\) −6.54986 6.54986i −0.312608 0.312608i 0.533311 0.845919i \(-0.320947\pi\)
−0.845919 + 0.533311i \(0.820947\pi\)
\(440\) 0 0
\(441\) 2.95678 0.140799
\(442\) 0 0
\(443\) 34.2324i 1.62643i −0.581962 0.813216i \(-0.697715\pi\)
0.581962 0.813216i \(-0.302285\pi\)
\(444\) 0 0
\(445\) 17.2492 17.2492i 0.817690 0.817690i
\(446\) 0 0
\(447\) 3.41269 0.161415
\(448\) 0 0
\(449\) 38.5413i 1.81887i 0.415841 + 0.909437i \(0.363487\pi\)
−0.415841 + 0.909437i \(0.636513\pi\)
\(450\) 0 0
\(451\) −25.1069 + 25.2745i −1.18224 + 1.19013i
\(452\) 0 0
\(453\) 0.791589i 0.0371921i
\(454\) 0 0
\(455\) 14.8299 0.695235
\(456\) 0 0
\(457\) 14.4341 14.4341i 0.675200 0.675200i −0.283710 0.958910i \(-0.591565\pi\)
0.958910 + 0.283710i \(0.0915653\pi\)
\(458\) 0 0
\(459\) 6.67097i 0.311374i
\(460\) 0 0
\(461\) −5.54610 −0.258308 −0.129154 0.991625i \(-0.541226\pi\)
−0.129154 + 0.991625i \(0.541226\pi\)
\(462\) 0 0
\(463\) −26.0335 26.0335i −1.20988 1.20988i −0.971065 0.238816i \(-0.923241\pi\)
−0.238816 0.971065i \(-0.576759\pi\)
\(464\) 0 0
\(465\) −2.11636 + 2.11636i −0.0981439 + 0.0981439i
\(466\) 0 0
\(467\) 35.6276 1.64865 0.824324 0.566118i \(-0.191555\pi\)
0.824324 + 0.566118i \(0.191555\pi\)
\(468\) 0 0
\(469\) −9.12800 −0.421492
\(470\) 0 0
\(471\) 3.07191i 0.141546i
\(472\) 0 0
\(473\) 22.6169 22.6169i 1.03993 1.03993i
\(474\) 0 0
\(475\) −4.86246 + 4.86246i −0.223105 + 0.223105i
\(476\) 0 0
\(477\) −15.3552 + 15.3552i −0.703068 + 0.703068i
\(478\) 0 0
\(479\) 8.89051 + 8.89051i 0.406218 + 0.406218i 0.880417 0.474200i \(-0.157263\pi\)
−0.474200 + 0.880417i \(0.657263\pi\)
\(480\) 0 0
\(481\) −15.9049 15.9049i −0.725203 0.725203i
\(482\) 0 0
\(483\) 1.36186i 0.0619666i
\(484\) 0 0
\(485\) −16.6956 16.6956i −0.758109 0.758109i
\(486\) 0 0
\(487\) 5.72829i 0.259573i −0.991542 0.129787i \(-0.958571\pi\)
0.991542 0.129787i \(-0.0414293\pi\)
\(488\) 0 0
\(489\) −0.734651 0.734651i −0.0332221 0.0332221i
\(490\) 0 0
\(491\) −3.18019 −0.143520 −0.0717600 0.997422i \(-0.522862\pi\)
−0.0717600 + 0.997422i \(0.522862\pi\)
\(492\) 0 0
\(493\) 38.2809 1.72408
\(494\) 0 0
\(495\) −30.4326 30.4326i −1.36784 1.36784i
\(496\) 0 0
\(497\) 9.94285i 0.445998i
\(498\) 0 0
\(499\) 24.4414 + 24.4414i 1.09415 + 1.09415i 0.995081 + 0.0990657i \(0.0315854\pi\)
0.0990657 + 0.995081i \(0.468415\pi\)
\(500\) 0 0
\(501\) 1.42209i 0.0635345i
\(502\) 0 0
\(503\) 18.0344 + 18.0344i 0.804114 + 0.804114i 0.983736 0.179622i \(-0.0574874\pi\)
−0.179622 + 0.983736i \(0.557487\pi\)
\(504\) 0 0
\(505\) 11.9559 + 11.9559i 0.532029 + 0.532029i
\(506\) 0 0
\(507\) −2.81246 + 2.81246i −0.124906 + 0.124906i
\(508\) 0 0
\(509\) 4.87660 4.87660i 0.216151 0.216151i −0.590723 0.806874i \(-0.701157\pi\)
0.806874 + 0.590723i \(0.201157\pi\)
\(510\) 0 0
\(511\) −6.14827 + 6.14827i −0.271983 + 0.271983i
\(512\) 0 0
\(513\) 4.61697i 0.203844i
\(514\) 0 0
\(515\) −3.22048 −0.141911
\(516\) 0 0
\(517\) −27.6088 −1.21424
\(518\) 0 0
\(519\) 2.49502 2.49502i 0.109519 0.109519i
\(520\) 0 0
\(521\) −9.83224 9.83224i −0.430758 0.430758i 0.458128 0.888886i \(-0.348520\pi\)
−0.888886 + 0.458128i \(0.848520\pi\)
\(522\) 0 0
\(523\) −7.21345 −0.315422 −0.157711 0.987485i \(-0.550411\pi\)
−0.157711 + 0.987485i \(0.550411\pi\)
\(524\) 0 0
\(525\) 0.383455i 0.0167354i
\(526\) 0 0
\(527\) −20.9609 + 20.9609i −0.913069 + 0.913069i
\(528\) 0 0
\(529\) 19.9116 0.865720
\(530\) 0 0
\(531\) 18.2808i 0.793321i
\(532\) 0 0
\(533\) −25.5796 + 25.7505i −1.10798 + 1.11538i
\(534\) 0 0
\(535\) 21.4048i 0.925412i
\(536\) 0 0
\(537\) −0.747536 −0.0322586
\(538\) 0 0
\(539\) 3.93415 3.93415i 0.169456 0.169456i
\(540\) 0 0
\(541\) 38.2955i 1.64645i −0.567714 0.823226i \(-0.692172\pi\)
0.567714 0.823226i \(-0.307828\pi\)
\(542\) 0 0
\(543\) 2.42918 0.104246
\(544\) 0 0
\(545\) 11.2594 + 11.2594i 0.482301 + 0.482301i
\(546\) 0 0
\(547\) 22.5254 22.5254i 0.963115 0.963115i −0.0362285 0.999344i \(-0.511534\pi\)
0.999344 + 0.0362285i \(0.0115344\pi\)
\(548\) 0 0
\(549\) −3.72908 −0.159153
\(550\) 0 0
\(551\) −26.4941 −1.12869
\(552\) 0 0
\(553\) 11.7797i 0.500923i
\(554\) 0 0
\(555\) −1.52608 + 1.52608i −0.0647787 + 0.0647787i
\(556\) 0 0
\(557\) −26.5838 + 26.5838i −1.12639 + 1.12639i −0.135634 + 0.990759i \(0.543307\pi\)
−0.990759 + 0.135634i \(0.956693\pi\)
\(558\) 0 0
\(559\) 23.0428 23.0428i 0.974607 0.974607i
\(560\) 0 0
\(561\) 4.40584 + 4.40584i 0.186015 + 0.186015i
\(562\) 0 0
\(563\) −1.96161 1.96161i −0.0826722 0.0826722i 0.664561 0.747234i \(-0.268618\pi\)
−0.747234 + 0.664561i \(0.768618\pi\)
\(564\) 0 0
\(565\) 50.6075i 2.12907i
\(566\) 0 0
\(567\) −6.09023 6.09023i −0.255766 0.255766i
\(568\) 0 0
\(569\) 32.9570i 1.38163i −0.723031 0.690816i \(-0.757252\pi\)
0.723031 0.690816i \(-0.242748\pi\)
\(570\) 0 0
\(571\) −28.9481 28.9481i −1.21144 1.21144i −0.970553 0.240886i \(-0.922562\pi\)
−0.240886 0.970553i \(-0.577438\pi\)
\(572\) 0 0
\(573\) 0.412494 0.0172322
\(574\) 0 0
\(575\) 12.0825 0.503876
\(576\) 0 0
\(577\) 16.5820 + 16.5820i 0.690317 + 0.690317i 0.962302 0.271985i \(-0.0876801\pi\)
−0.271985 + 0.962302i \(0.587680\pi\)
\(578\) 0 0
\(579\) 2.28195i 0.0948348i
\(580\) 0 0
\(581\) −12.0572 12.0572i −0.500217 0.500217i
\(582\) 0 0
\(583\) 40.8619i 1.69233i
\(584\) 0 0
\(585\) −31.0057 31.0057i −1.28193 1.28193i
\(586\) 0 0
\(587\) 8.44304 + 8.44304i 0.348481 + 0.348481i 0.859544 0.511062i \(-0.170748\pi\)
−0.511062 + 0.859544i \(0.670748\pi\)
\(588\) 0 0
\(589\) 14.5070 14.5070i 0.597749 0.597749i
\(590\) 0 0
\(591\) 2.70239 2.70239i 0.111161 0.111161i
\(592\) 0 0
\(593\) 22.7237 22.7237i 0.933149 0.933149i −0.0647527 0.997901i \(-0.520626\pi\)
0.997901 + 0.0647527i \(0.0206259\pi\)
\(594\) 0 0
\(595\) 14.0930i 0.577756i
\(596\) 0 0
\(597\) −2.30677 −0.0944099
\(598\) 0 0
\(599\) 21.0230 0.858975 0.429487 0.903073i \(-0.358694\pi\)
0.429487 + 0.903073i \(0.358694\pi\)
\(600\) 0 0
\(601\) 15.6364 15.6364i 0.637823 0.637823i −0.312195 0.950018i \(-0.601064\pi\)
0.950018 + 0.312195i \(0.101064\pi\)
\(602\) 0 0
\(603\) 19.0844 + 19.0844i 0.777179 + 0.777179i
\(604\) 0 0
\(605\) −52.2062 −2.12249
\(606\) 0 0
\(607\) 20.3207i 0.824793i −0.911005 0.412396i \(-0.864692\pi\)
0.911005 0.412396i \(-0.135308\pi\)
\(608\) 0 0
\(609\) 1.04467 1.04467i 0.0423320 0.0423320i
\(610\) 0 0
\(611\) −28.1287 −1.13797
\(612\) 0 0
\(613\) 36.4246i 1.47118i 0.677428 + 0.735589i \(0.263094\pi\)
−0.677428 + 0.735589i \(0.736906\pi\)
\(614\) 0 0
\(615\) 2.47077 + 2.45437i 0.0996309 + 0.0989699i
\(616\) 0 0
\(617\) 1.60897i 0.0647748i −0.999475 0.0323874i \(-0.989689\pi\)
0.999475 0.0323874i \(-0.0103110\pi\)
\(618\) 0 0
\(619\) 17.0273 0.684383 0.342192 0.939630i \(-0.388831\pi\)
0.342192 + 0.939630i \(0.388831\pi\)
\(620\) 0 0
\(621\) −5.73625 + 5.73625i −0.230188 + 0.230188i
\(622\) 0 0
\(623\) 9.32425i 0.373568i
\(624\) 0 0
\(625\) −30.8203 −1.23281
\(626\) 0 0
\(627\) −3.04927 3.04927i −0.121776 0.121776i
\(628\) 0 0
\(629\) −15.1146 + 15.1146i −0.602660 + 0.602660i
\(630\) 0 0
\(631\) −21.9730 −0.874732 −0.437366 0.899284i \(-0.644089\pi\)
−0.437366 + 0.899284i \(0.644089\pi\)
\(632\) 0 0
\(633\) −2.29396 −0.0911769
\(634\) 0 0
\(635\) 13.0851i 0.519265i
\(636\) 0 0
\(637\) 4.00823 4.00823i 0.158812 0.158812i
\(638\) 0 0
\(639\) 20.7881 20.7881i 0.822365 0.822365i
\(640\) 0 0
\(641\) −12.7012 + 12.7012i −0.501667 + 0.501667i −0.911956 0.410289i \(-0.865428\pi\)
0.410289 + 0.911956i \(0.365428\pi\)
\(642\) 0 0
\(643\) −26.9035 26.9035i −1.06097 1.06097i −0.998016 0.0629561i \(-0.979947\pi\)
−0.0629561 0.998016i \(-0.520053\pi\)
\(644\) 0 0
\(645\) −2.21096 2.21096i −0.0870566 0.0870566i
\(646\) 0 0
\(647\) 36.0313i 1.41653i −0.705944 0.708267i \(-0.749477\pi\)
0.705944 0.708267i \(-0.250523\pi\)
\(648\) 0 0
\(649\) −24.3236 24.3236i −0.954785 0.954785i
\(650\) 0 0
\(651\) 1.14402i 0.0448378i
\(652\) 0 0
\(653\) 31.8866 + 31.8866i 1.24782 + 1.24782i 0.956681 + 0.291137i \(0.0940335\pi\)
0.291137 + 0.956681i \(0.405967\pi\)
\(654\) 0 0
\(655\) 3.37667 0.131937
\(656\) 0 0
\(657\) 25.7091 1.00301
\(658\) 0 0
\(659\) −11.6363 11.6363i −0.453284 0.453284i 0.443159 0.896443i \(-0.353858\pi\)
−0.896443 + 0.443159i \(0.853858\pi\)
\(660\) 0 0
\(661\) 48.9963i 1.90573i −0.303387 0.952867i \(-0.598118\pi\)
0.303387 0.952867i \(-0.401882\pi\)
\(662\) 0 0
\(663\) 4.48880 + 4.48880i 0.174331 + 0.174331i
\(664\) 0 0
\(665\) 9.75372i 0.378233i
\(666\) 0 0
\(667\) 32.9170 + 32.9170i 1.27455 + 1.27455i
\(668\) 0 0
\(669\) −1.21958 1.21958i −0.0471515 0.0471515i
\(670\) 0 0
\(671\) −4.96173 + 4.96173i −0.191546 + 0.191546i
\(672\) 0 0
\(673\) 3.20595 3.20595i 0.123580 0.123580i −0.642612 0.766192i \(-0.722149\pi\)
0.766192 + 0.642612i \(0.222149\pi\)
\(674\) 0 0
\(675\) −1.61514 + 1.61514i −0.0621669 + 0.0621669i
\(676\) 0 0
\(677\) 22.6084i 0.868910i −0.900694 0.434455i \(-0.856941\pi\)
0.900694 0.434455i \(-0.143059\pi\)
\(678\) 0 0
\(679\) −9.02502 −0.346348
\(680\) 0 0
\(681\) −3.43903 −0.131784
\(682\) 0 0
\(683\) 12.5968 12.5968i 0.482003 0.482003i −0.423768 0.905771i \(-0.639293\pi\)
0.905771 + 0.423768i \(0.139293\pi\)
\(684\) 0 0
\(685\) 8.43161 + 8.43161i 0.322155 + 0.322155i
\(686\) 0 0
\(687\) 3.44039 0.131259
\(688\) 0 0
\(689\) 41.6313i 1.58603i
\(690\) 0 0
\(691\) 27.1819 27.1819i 1.03405 1.03405i 0.0346483 0.999400i \(-0.488969\pi\)
0.999400 0.0346483i \(-0.0110311\pi\)
\(692\) 0 0
\(693\) −16.4507 −0.624911
\(694\) 0 0
\(695\) 45.5788i 1.72890i
\(696\) 0 0
\(697\) 24.4709 + 24.3086i 0.926903 + 0.920754i
\(698\) 0 0
\(699\) 0.0792958i 0.00299924i
\(700\) 0 0
\(701\) −21.3332 −0.805745 −0.402872 0.915256i \(-0.631988\pi\)
−0.402872 + 0.915256i \(0.631988\pi\)
\(702\) 0 0
\(703\) 10.4608 10.4608i 0.394537 0.394537i
\(704\) 0 0
\(705\) 2.69896i 0.101649i
\(706\) 0 0
\(707\) 6.46289 0.243062
\(708\) 0 0
\(709\) −33.0165 33.0165i −1.23996 1.23996i −0.960016 0.279946i \(-0.909683\pi\)
−0.279946 0.960016i \(-0.590317\pi\)
\(710\) 0 0
\(711\) −24.6285 + 24.6285i −0.923639 + 0.923639i
\(712\) 0 0
\(713\) −36.0477 −1.35000
\(714\) 0 0
\(715\) −82.5093 −3.08567
\(716\) 0 0
\(717\) 5.80778i 0.216896i
\(718\) 0 0
\(719\) 2.95246 2.95246i 0.110108 0.110108i −0.649906 0.760014i \(-0.725192\pi\)
0.760014 + 0.649906i \(0.225192\pi\)
\(720\) 0 0
\(721\) −0.870433 + 0.870433i −0.0324166 + 0.0324166i
\(722\) 0 0
\(723\) −0.618592 + 0.618592i −0.0230057 + 0.0230057i
\(724\) 0 0
\(725\) 9.26837 + 9.26837i 0.344219 + 0.344219i
\(726\) 0 0
\(727\) 20.3491 + 20.3491i 0.754706 + 0.754706i 0.975354 0.220647i \(-0.0708170\pi\)
−0.220647 + 0.975354i \(0.570817\pi\)
\(728\) 0 0
\(729\) 24.6940i 0.914594i
\(730\) 0 0
\(731\) −21.8978 21.8978i −0.809920 0.809920i
\(732\) 0 0
\(733\) 42.0371i 1.55268i 0.630316 + 0.776338i \(0.282925\pi\)
−0.630316 + 0.776338i \(0.717075\pi\)
\(734\) 0 0
\(735\) −0.384591 0.384591i −0.0141859 0.0141859i
\(736\) 0 0
\(737\) 50.7857 1.87071
\(738\) 0 0
\(739\) −39.3349 −1.44696 −0.723478 0.690347i \(-0.757458\pi\)
−0.723478 + 0.690347i \(0.757458\pi\)
\(740\) 0 0
\(741\) −3.10669 3.10669i −0.114127 0.114127i
\(742\) 0 0
\(743\) 38.7296i 1.42085i −0.703773 0.710425i \(-0.748503\pi\)
0.703773 0.710425i \(-0.251497\pi\)
\(744\) 0 0
\(745\) 30.3674 + 30.3674i 1.11258 + 1.11258i
\(746\) 0 0
\(747\) 50.4174i 1.84468i
\(748\) 0 0
\(749\) 5.78532 + 5.78532i 0.211391 + 0.211391i
\(750\) 0 0
\(751\) 7.22182 + 7.22182i 0.263528 + 0.263528i 0.826486 0.562958i \(-0.190337\pi\)
−0.562958 + 0.826486i \(0.690337\pi\)
\(752\) 0 0
\(753\) −0.208474 + 0.208474i −0.00759723 + 0.00759723i
\(754\) 0 0
\(755\) −7.04385 + 7.04385i −0.256352 + 0.256352i
\(756\) 0 0
\(757\) 26.7177 26.7177i 0.971070 0.971070i −0.0285234 0.999593i \(-0.509081\pi\)
0.999593 + 0.0285234i \(0.00908050\pi\)
\(758\) 0 0
\(759\) 7.57700i 0.275028i
\(760\) 0 0
\(761\) 45.2274 1.63949 0.819746 0.572728i \(-0.194115\pi\)
0.819746 + 0.572728i \(0.194115\pi\)
\(762\) 0 0
\(763\) 6.08642 0.220343
\(764\) 0 0
\(765\) −29.4650 + 29.4650i −1.06531 + 1.06531i
\(766\) 0 0
\(767\) −24.7816 24.7816i −0.894813 0.894813i
\(768\) 0 0
\(769\) −16.2917 −0.587495 −0.293747 0.955883i \(-0.594902\pi\)
−0.293747 + 0.955883i \(0.594902\pi\)
\(770\) 0 0
\(771\) 2.21646i 0.0798238i
\(772\) 0 0
\(773\) −11.2627 + 11.2627i −0.405090 + 0.405090i −0.880022 0.474932i \(-0.842473\pi\)
0.474932 + 0.880022i \(0.342473\pi\)
\(774\) 0 0
\(775\) −10.1499 −0.364594
\(776\) 0 0
\(777\) 0.824943i 0.0295946i
\(778\) 0 0
\(779\) −16.9363 16.8239i −0.606805 0.602780i
\(780\) 0 0
\(781\) 55.3193i 1.97948i
\(782\) 0 0
\(783\) −8.80044 −0.314502
\(784\) 0 0
\(785\) 27.3350 27.3350i 0.975627 0.975627i
\(786\) 0 0
\(787\) 29.3868i 1.04753i −0.851864 0.523764i \(-0.824528\pi\)
0.851864 0.523764i \(-0.175472\pi\)
\(788\) 0 0
\(789\) −0.253588 −0.00902797
\(790\) 0 0
\(791\) −13.6782 13.6782i −0.486342 0.486342i
\(792\) 0 0
\(793\) −5.05517 + 5.05517i −0.179514 + 0.179514i
\(794\) 0 0
\(795\) 3.99454 0.141672
\(796\) 0 0
\(797\) −10.0350 −0.355457 −0.177728 0.984080i \(-0.556875\pi\)
−0.177728 + 0.984080i \(0.556875\pi\)
\(798\) 0 0
\(799\) 26.7310i 0.945676i
\(800\) 0 0