Properties

Label 1148.2.k.b.337.12
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 337.12
Character \(\chi\) \(=\) 1148.337
Dual form 1148.2.k.b.729.12

$q$-expansion

\(f(q)\) \(=\) \(q+(0.805830 + 0.805830i) q^{3} -0.251332i q^{5} +(0.707107 + 0.707107i) q^{7} -1.70128i q^{9} +O(q^{10})\) \(q+(0.805830 + 0.805830i) q^{3} -0.251332i q^{5} +(0.707107 + 0.707107i) q^{7} -1.70128i q^{9} +(-2.93936 - 2.93936i) q^{11} +(1.89283 + 1.89283i) q^{13} +(0.202531 - 0.202531i) q^{15} +(2.33562 - 2.33562i) q^{17} +(1.33917 - 1.33917i) q^{19} +1.13962i q^{21} +6.67279 q^{23} +4.93683 q^{25} +(3.78843 - 3.78843i) q^{27} +(-0.0155144 - 0.0155144i) q^{29} -3.61614 q^{31} -4.73725i q^{33} +(0.177719 - 0.177719i) q^{35} +9.22196 q^{37} +3.05060i q^{39} +(-6.16529 + 1.72894i) q^{41} -1.97318i q^{43} -0.427585 q^{45} +(-2.41064 + 2.41064i) q^{47} +1.00000i q^{49} +3.76423 q^{51} +(3.16272 + 3.16272i) q^{53} +(-0.738756 + 0.738756i) q^{55} +2.15829 q^{57} -4.91005 q^{59} +9.53072i q^{61} +(1.20298 - 1.20298i) q^{63} +(0.475729 - 0.475729i) q^{65} +(8.59321 - 8.59321i) q^{67} +(5.37714 + 5.37714i) q^{69} +(-9.30998 - 9.30998i) q^{71} +5.52711i q^{73} +(3.97825 + 3.97825i) q^{75} -4.15689i q^{77} +(4.22270 + 4.22270i) q^{79} +1.00184 q^{81} +6.78231 q^{83} +(-0.587017 - 0.587017i) q^{85} -0.0250039i q^{87} +(-1.72662 - 1.72662i) q^{89} +2.67687i q^{91} +(-2.91399 - 2.91399i) q^{93} +(-0.336577 - 0.336577i) q^{95} +(-2.76074 + 2.76074i) q^{97} +(-5.00066 + 5.00066i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + O(q^{10}) \) \( 36q - 12q^{11} - 16q^{17} - 4q^{19} - 36q^{23} - 64q^{25} + 12q^{27} + 16q^{29} - 28q^{31} + 12q^{35} + 48q^{37} + 4q^{41} + 36q^{45} + 12q^{47} - 12q^{51} - 12q^{53} + 12q^{55} + 76q^{57} + 20q^{59} - 4q^{65} - 44q^{67} + 72q^{69} - 20q^{71} + 72q^{75} - 8q^{79} - 100q^{81} - 40q^{83} - 8q^{85} - 16q^{89} + 20q^{93} + 76q^{95} - 16q^{97} + 56q^{99} + O(q^{100}) \)

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
\(3\) 0.805830 + 0.805830i 0.465246 + 0.465246i 0.900370 0.435124i \(-0.143296\pi\)
−0.435124 + 0.900370i \(0.643296\pi\)
\(4\) 0 0
\(5\) 0.251332i 0.112399i −0.998420 0.0561996i \(-0.982102\pi\)
0.998420 0.0561996i \(-0.0178983\pi\)
\(6\) 0 0
\(7\) 0.707107 + 0.707107i 0.267261 + 0.267261i
\(8\) 0 0
\(9\) 1.70128i 0.567092i
\(10\) 0 0
\(11\) −2.93936 2.93936i −0.886251 0.886251i 0.107910 0.994161i \(-0.465584\pi\)
−0.994161 + 0.107910i \(0.965584\pi\)
\(12\) 0 0
\(13\) 1.89283 + 1.89283i 0.524977 + 0.524977i 0.919070 0.394094i \(-0.128941\pi\)
−0.394094 + 0.919070i \(0.628941\pi\)
\(14\) 0 0
\(15\) 0.202531 0.202531i 0.0522933 0.0522933i
\(16\) 0 0
\(17\) 2.33562 2.33562i 0.566472 0.566472i −0.364667 0.931138i \(-0.618817\pi\)
0.931138 + 0.364667i \(0.118817\pi\)
\(18\) 0 0
\(19\) 1.33917 1.33917i 0.307227 0.307227i −0.536606 0.843833i \(-0.680294\pi\)
0.843833 + 0.536606i \(0.180294\pi\)
\(20\) 0 0
\(21\) 1.13962i 0.248685i
\(22\) 0 0
\(23\) 6.67279 1.39137 0.695687 0.718345i \(-0.255100\pi\)
0.695687 + 0.718345i \(0.255100\pi\)
\(24\) 0 0
\(25\) 4.93683 0.987366
\(26\) 0 0
\(27\) 3.78843 3.78843i 0.729084 0.729084i
\(28\) 0 0
\(29\) −0.0155144 0.0155144i −0.00288095 0.00288095i 0.705665 0.708546i \(-0.250648\pi\)
−0.708546 + 0.705665i \(0.750648\pi\)
\(30\) 0 0
\(31\) −3.61614 −0.649478 −0.324739 0.945804i \(-0.605276\pi\)
−0.324739 + 0.945804i \(0.605276\pi\)
\(32\) 0 0
\(33\) 4.73725i 0.824650i
\(34\) 0 0
\(35\) 0.177719 0.177719i 0.0300399 0.0300399i
\(36\) 0 0
\(37\) 9.22196 1.51608 0.758040 0.652208i \(-0.226157\pi\)
0.758040 + 0.652208i \(0.226157\pi\)
\(38\) 0 0
\(39\) 3.05060i 0.488487i
\(40\) 0 0
\(41\) −6.16529 + 1.72894i −0.962856 + 0.270015i
\(42\) 0 0
\(43\) 1.97318i 0.300908i −0.988617 0.150454i \(-0.951927\pi\)
0.988617 0.150454i \(-0.0480735\pi\)
\(44\) 0 0
\(45\) −0.427585 −0.0637407
\(46\) 0 0
\(47\) −2.41064 + 2.41064i −0.351628 + 0.351628i −0.860715 0.509087i \(-0.829983\pi\)
0.509087 + 0.860715i \(0.329983\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 3.76423 0.527098
\(52\) 0 0
\(53\) 3.16272 + 3.16272i 0.434434 + 0.434434i 0.890133 0.455700i \(-0.150611\pi\)
−0.455700 + 0.890133i \(0.650611\pi\)
\(54\) 0 0
\(55\) −0.738756 + 0.738756i −0.0996139 + 0.0996139i
\(56\) 0 0
\(57\) 2.15829 0.285873
\(58\) 0 0
\(59\) −4.91005 −0.639234 −0.319617 0.947547i \(-0.603554\pi\)
−0.319617 + 0.947547i \(0.603554\pi\)
\(60\) 0 0
\(61\) 9.53072i 1.22028i 0.792292 + 0.610142i \(0.208888\pi\)
−0.792292 + 0.610142i \(0.791112\pi\)
\(62\) 0 0
\(63\) 1.20298 1.20298i 0.151562 0.151562i
\(64\) 0 0
\(65\) 0.475729 0.475729i 0.0590070 0.0590070i
\(66\) 0 0
\(67\) 8.59321 8.59321i 1.04983 1.04983i 0.0511362 0.998692i \(-0.483716\pi\)
0.998692 0.0511362i \(-0.0162843\pi\)
\(68\) 0 0
\(69\) 5.37714 + 5.37714i 0.647332 + 0.647332i
\(70\) 0 0
\(71\) −9.30998 9.30998i −1.10489 1.10489i −0.993811 0.111080i \(-0.964569\pi\)
−0.111080 0.993811i \(-0.535431\pi\)
\(72\) 0 0
\(73\) 5.52711i 0.646899i 0.946245 + 0.323449i \(0.104843\pi\)
−0.946245 + 0.323449i \(0.895157\pi\)
\(74\) 0 0
\(75\) 3.97825 + 3.97825i 0.459369 + 0.459369i
\(76\) 0 0
\(77\) 4.15689i 0.473721i
\(78\) 0 0
\(79\) 4.22270 + 4.22270i 0.475091 + 0.475091i 0.903557 0.428467i \(-0.140946\pi\)
−0.428467 + 0.903557i \(0.640946\pi\)
\(80\) 0 0
\(81\) 1.00184 0.111315
\(82\) 0 0
\(83\) 6.78231 0.744455 0.372227 0.928142i \(-0.378594\pi\)
0.372227 + 0.928142i \(0.378594\pi\)
\(84\) 0 0
\(85\) −0.587017 0.587017i −0.0636709 0.0636709i
\(86\) 0 0
\(87\) 0.0250039i 0.00268070i
\(88\) 0 0
\(89\) −1.72662 1.72662i −0.183022 0.183022i 0.609649 0.792671i \(-0.291310\pi\)
−0.792671 + 0.609649i \(0.791310\pi\)
\(90\) 0 0
\(91\) 2.67687i 0.280612i
\(92\) 0 0
\(93\) −2.91399 2.91399i −0.302167 0.302167i
\(94\) 0 0
\(95\) −0.336577 0.336577i −0.0345321 0.0345321i
\(96\) 0 0
\(97\) −2.76074 + 2.76074i −0.280311 + 0.280311i −0.833233 0.552922i \(-0.813513\pi\)
0.552922 + 0.833233i \(0.313513\pi\)
\(98\) 0 0
\(99\) −5.00066 + 5.00066i −0.502586 + 0.502586i
\(100\) 0 0
\(101\) 11.9870 11.9870i 1.19275 1.19275i 0.216454 0.976293i \(-0.430551\pi\)
0.976293 0.216454i \(-0.0694491\pi\)
\(102\) 0 0
\(103\) 2.76891i 0.272829i −0.990652 0.136414i \(-0.956442\pi\)
0.990652 0.136414i \(-0.0435579\pi\)
\(104\) 0 0
\(105\) 0.286422 0.0279520
\(106\) 0 0
\(107\) −3.25137 −0.314322 −0.157161 0.987573i \(-0.550234\pi\)
−0.157161 + 0.987573i \(0.550234\pi\)
\(108\) 0 0
\(109\) −3.32806 + 3.32806i −0.318770 + 0.318770i −0.848295 0.529524i \(-0.822370\pi\)
0.529524 + 0.848295i \(0.322370\pi\)
\(110\) 0 0
\(111\) 7.43133 + 7.43133i 0.705351 + 0.705351i
\(112\) 0 0
\(113\) −6.47898 −0.609491 −0.304745 0.952434i \(-0.598571\pi\)
−0.304745 + 0.952434i \(0.598571\pi\)
\(114\) 0 0
\(115\) 1.67709i 0.156389i
\(116\) 0 0
\(117\) 3.22023 3.22023i 0.297710 0.297710i
\(118\) 0 0
\(119\) 3.30307 0.302792
\(120\) 0 0
\(121\) 6.27970i 0.570881i
\(122\) 0 0
\(123\) −6.36141 3.57494i −0.573589 0.322342i
\(124\) 0 0
\(125\) 2.49745i 0.223378i
\(126\) 0 0
\(127\) −14.7703 −1.31065 −0.655327 0.755345i \(-0.727469\pi\)
−0.655327 + 0.755345i \(0.727469\pi\)
\(128\) 0 0
\(129\) 1.59005 1.59005i 0.139996 0.139996i
\(130\) 0 0
\(131\) 9.39527i 0.820869i 0.911890 + 0.410434i \(0.134623\pi\)
−0.911890 + 0.410434i \(0.865377\pi\)
\(132\) 0 0
\(133\) 1.89388 0.164220
\(134\) 0 0
\(135\) −0.952155 0.952155i −0.0819484 0.0819484i
\(136\) 0 0
\(137\) 8.34033 8.34033i 0.712562 0.712562i −0.254508 0.967071i \(-0.581914\pi\)
0.967071 + 0.254508i \(0.0819137\pi\)
\(138\) 0 0
\(139\) 3.27568 0.277839 0.138920 0.990304i \(-0.455637\pi\)
0.138920 + 0.990304i \(0.455637\pi\)
\(140\) 0 0
\(141\) −3.88514 −0.327188
\(142\) 0 0
\(143\) 11.1274i 0.930522i
\(144\) 0 0
\(145\) −0.00389927 + 0.00389927i −0.000323817 + 0.000323817i
\(146\) 0 0
\(147\) −0.805830 + 0.805830i −0.0664638 + 0.0664638i
\(148\) 0 0
\(149\) −0.0335973 + 0.0335973i −0.00275239 + 0.00275239i −0.708482 0.705729i \(-0.750620\pi\)
0.705729 + 0.708482i \(0.250620\pi\)
\(150\) 0 0
\(151\) −1.45616 1.45616i −0.118501 0.118501i 0.645370 0.763870i \(-0.276703\pi\)
−0.763870 + 0.645370i \(0.776703\pi\)
\(152\) 0 0
\(153\) −3.97354 3.97354i −0.321241 0.321241i
\(154\) 0 0
\(155\) 0.908852i 0.0730008i
\(156\) 0 0
\(157\) 6.76143 + 6.76143i 0.539621 + 0.539621i 0.923418 0.383797i \(-0.125384\pi\)
−0.383797 + 0.923418i \(0.625384\pi\)
\(158\) 0 0
\(159\) 5.09724i 0.404237i
\(160\) 0 0
\(161\) 4.71838 + 4.71838i 0.371860 + 0.371860i
\(162\) 0 0
\(163\) −16.6072 −1.30078 −0.650388 0.759602i \(-0.725394\pi\)
−0.650388 + 0.759602i \(0.725394\pi\)
\(164\) 0 0
\(165\) −1.19062 −0.0926900
\(166\) 0 0
\(167\) −5.56993 5.56993i −0.431014 0.431014i 0.457959 0.888973i \(-0.348581\pi\)
−0.888973 + 0.457959i \(0.848581\pi\)
\(168\) 0 0
\(169\) 5.83438i 0.448799i
\(170\) 0 0
\(171\) −2.27830 2.27830i −0.174226 0.174226i
\(172\) 0 0
\(173\) 20.6379i 1.56907i 0.620082 + 0.784537i \(0.287099\pi\)
−0.620082 + 0.784537i \(0.712901\pi\)
\(174\) 0 0
\(175\) 3.49087 + 3.49087i 0.263885 + 0.263885i
\(176\) 0 0
\(177\) −3.95667 3.95667i −0.297401 0.297401i
\(178\) 0 0
\(179\) −13.8890 + 13.8890i −1.03811 + 1.03811i −0.0388691 + 0.999244i \(0.512376\pi\)
−0.999244 + 0.0388691i \(0.987624\pi\)
\(180\) 0 0
\(181\) 0.658651 0.658651i 0.0489572 0.0489572i −0.682204 0.731162i \(-0.738979\pi\)
0.731162 + 0.682204i \(0.238979\pi\)
\(182\) 0 0
\(183\) −7.68015 + 7.68015i −0.567733 + 0.567733i
\(184\) 0 0
\(185\) 2.31778i 0.170406i
\(186\) 0 0
\(187\) −13.7305 −1.00407
\(188\) 0 0
\(189\) 5.35765 0.389712
\(190\) 0 0
\(191\) 0.280520 0.280520i 0.0202977 0.0202977i −0.696885 0.717183i \(-0.745431\pi\)
0.717183 + 0.696885i \(0.245431\pi\)
\(192\) 0 0
\(193\) 0.497202 + 0.497202i 0.0357894 + 0.0357894i 0.724775 0.688986i \(-0.241944\pi\)
−0.688986 + 0.724775i \(0.741944\pi\)
\(194\) 0 0
\(195\) 0.766714 0.0549056
\(196\) 0 0
\(197\) 20.6787i 1.47329i −0.676277 0.736647i \(-0.736408\pi\)
0.676277 0.736647i \(-0.263592\pi\)
\(198\) 0 0
\(199\) −18.3611 + 18.3611i −1.30159 + 1.30159i −0.374262 + 0.927323i \(0.622104\pi\)
−0.927323 + 0.374262i \(0.877896\pi\)
\(200\) 0 0
\(201\) 13.8493 0.976857
\(202\) 0 0
\(203\) 0.0219407i 0.00153993i
\(204\) 0 0
\(205\) 0.434539 + 1.54954i 0.0303495 + 0.108224i
\(206\) 0 0
\(207\) 11.3523i 0.789037i
\(208\) 0 0
\(209\) −7.87263 −0.544561
\(210\) 0 0
\(211\) −9.29562 + 9.29562i −0.639937 + 0.639937i −0.950540 0.310603i \(-0.899469\pi\)
0.310603 + 0.950540i \(0.399469\pi\)
\(212\) 0 0
\(213\) 15.0045i 1.02809i
\(214\) 0 0
\(215\) −0.495925 −0.0338218
\(216\) 0 0
\(217\) −2.55700 2.55700i −0.173580 0.173580i
\(218\) 0 0
\(219\) −4.45391 + 4.45391i −0.300967 + 0.300967i
\(220\) 0 0
\(221\) 8.84188 0.594769
\(222\) 0 0
\(223\) 16.8455 1.12805 0.564027 0.825756i \(-0.309251\pi\)
0.564027 + 0.825756i \(0.309251\pi\)
\(224\) 0 0
\(225\) 8.39891i 0.559927i
\(226\) 0 0
\(227\) 3.51778 3.51778i 0.233483 0.233483i −0.580662 0.814145i \(-0.697206\pi\)
0.814145 + 0.580662i \(0.197206\pi\)
\(228\) 0 0
\(229\) 18.4731 18.4731i 1.22074 1.22074i 0.253365 0.967371i \(-0.418463\pi\)
0.967371 0.253365i \(-0.0815374\pi\)
\(230\) 0 0
\(231\) 3.34974 3.34974i 0.220397 0.220397i
\(232\) 0 0
\(233\) 18.7275 + 18.7275i 1.22688 + 1.22688i 0.965138 + 0.261740i \(0.0842962\pi\)
0.261740 + 0.965138i \(0.415704\pi\)
\(234\) 0 0
\(235\) 0.605872 + 0.605872i 0.0395228 + 0.0395228i
\(236\) 0 0
\(237\) 6.80555i 0.442068i
\(238\) 0 0
\(239\) −18.4946 18.4946i −1.19631 1.19631i −0.975262 0.221051i \(-0.929051\pi\)
−0.221051 0.975262i \(-0.570949\pi\)
\(240\) 0 0
\(241\) 4.82354i 0.310711i −0.987859 0.155356i \(-0.950348\pi\)
0.987859 0.155356i \(-0.0496524\pi\)
\(242\) 0 0
\(243\) −10.5580 10.5580i −0.677295 0.677295i
\(244\) 0 0
\(245\) 0.251332 0.0160570
\(246\) 0 0
\(247\) 5.06966 0.322575
\(248\) 0 0
\(249\) 5.46539 + 5.46539i 0.346355 + 0.346355i
\(250\) 0 0
\(251\) 3.48952i 0.220256i 0.993917 + 0.110128i \(0.0351261\pi\)
−0.993917 + 0.110128i \(0.964874\pi\)
\(252\) 0 0
\(253\) −19.6138 19.6138i −1.23311 1.23311i
\(254\) 0 0
\(255\) 0.946072i 0.0592453i
\(256\) 0 0
\(257\) −1.97950 1.97950i −0.123478 0.123478i 0.642668 0.766145i \(-0.277828\pi\)
−0.766145 + 0.642668i \(0.777828\pi\)
\(258\) 0 0
\(259\) 6.52091 + 6.52091i 0.405190 + 0.405190i
\(260\) 0 0
\(261\) −0.0263943 + 0.0263943i −0.00163376 + 0.00163376i
\(262\) 0 0
\(263\) −8.28189 + 8.28189i −0.510683 + 0.510683i −0.914736 0.404053i \(-0.867601\pi\)
0.404053 + 0.914736i \(0.367601\pi\)
\(264\) 0 0
\(265\) 0.794895 0.794895i 0.0488300 0.0488300i
\(266\) 0 0
\(267\) 2.78273i 0.170300i
\(268\) 0 0
\(269\) −10.6204 −0.647536 −0.323768 0.946136i \(-0.604950\pi\)
−0.323768 + 0.946136i \(0.604950\pi\)
\(270\) 0 0
\(271\) −12.9253 −0.785157 −0.392578 0.919719i \(-0.628417\pi\)
−0.392578 + 0.919719i \(0.628417\pi\)
\(272\) 0 0
\(273\) −2.15710 + 2.15710i −0.130554 + 0.130554i
\(274\) 0 0
\(275\) −14.5111 14.5111i −0.875054 0.875054i
\(276\) 0 0
\(277\) −26.9179 −1.61734 −0.808671 0.588261i \(-0.799813\pi\)
−0.808671 + 0.588261i \(0.799813\pi\)
\(278\) 0 0
\(279\) 6.15205i 0.368313i
\(280\) 0 0
\(281\) −8.65940 + 8.65940i −0.516576 + 0.516576i −0.916534 0.399957i \(-0.869025\pi\)
0.399957 + 0.916534i \(0.369025\pi\)
\(282\) 0 0
\(283\) −15.0160 −0.892610 −0.446305 0.894881i \(-0.647260\pi\)
−0.446305 + 0.894881i \(0.647260\pi\)
\(284\) 0 0
\(285\) 0.542449i 0.0321319i
\(286\) 0 0
\(287\) −5.58206 3.13697i −0.329499 0.185169i
\(288\) 0 0
\(289\) 6.08974i 0.358220i
\(290\) 0 0
\(291\) −4.44938 −0.260827
\(292\) 0 0
\(293\) 1.60587 1.60587i 0.0938161 0.0938161i −0.658641 0.752457i \(-0.728868\pi\)
0.752457 + 0.658641i \(0.228868\pi\)
\(294\) 0 0
\(295\) 1.23405i 0.0718494i
\(296\) 0 0
\(297\) −22.2711 −1.29230
\(298\) 0 0
\(299\) 12.6305 + 12.6305i 0.730439 + 0.730439i
\(300\) 0 0
\(301\) 1.39525 1.39525i 0.0804210 0.0804210i
\(302\) 0 0
\(303\) 19.3189 1.10984
\(304\) 0 0
\(305\) 2.39538 0.137159
\(306\) 0 0
\(307\) 32.4083i 1.84964i 0.380406 + 0.924820i \(0.375784\pi\)
−0.380406 + 0.924820i \(0.624216\pi\)
\(308\) 0 0
\(309\) 2.23127 2.23127i 0.126933 0.126933i
\(310\) 0 0
\(311\) 5.87863 5.87863i 0.333346 0.333346i −0.520509 0.853856i \(-0.674258\pi\)
0.853856 + 0.520509i \(0.174258\pi\)
\(312\) 0 0
\(313\) −14.7559 + 14.7559i −0.834051 + 0.834051i −0.988068 0.154017i \(-0.950779\pi\)
0.154017 + 0.988068i \(0.450779\pi\)
\(314\) 0 0
\(315\) −0.302348 0.302348i −0.0170354 0.0170354i
\(316\) 0 0
\(317\) 15.4241 + 15.4241i 0.866306 + 0.866306i 0.992061 0.125755i \(-0.0401353\pi\)
−0.125755 + 0.992061i \(0.540135\pi\)
\(318\) 0 0
\(319\) 0.0912049i 0.00510649i
\(320\) 0 0
\(321\) −2.62005 2.62005i −0.146237 0.146237i
\(322\) 0 0
\(323\) 6.25561i 0.348071i
\(324\) 0 0
\(325\) 9.34459 + 9.34459i 0.518344 + 0.518344i
\(326\) 0 0
\(327\) −5.36370 −0.296613
\(328\) 0 0
\(329\) −3.40916 −0.187953
\(330\) 0 0
\(331\) 2.74721 + 2.74721i 0.151001 + 0.151001i 0.778565 0.627564i \(-0.215948\pi\)
−0.627564 + 0.778565i \(0.715948\pi\)
\(332\) 0 0
\(333\) 15.6891i 0.859757i
\(334\) 0 0
\(335\) −2.15975 2.15975i −0.118000 0.118000i
\(336\) 0 0
\(337\) 1.03529i 0.0563957i 0.999602 + 0.0281978i \(0.00897684\pi\)
−0.999602 + 0.0281978i \(0.991023\pi\)
\(338\) 0 0
\(339\) −5.22096 5.22096i −0.283563 0.283563i
\(340\) 0 0
\(341\) 10.6291 + 10.6291i 0.575600 + 0.575600i
\(342\) 0 0
\(343\) −0.707107 + 0.707107i −0.0381802 + 0.0381802i
\(344\) 0 0
\(345\) 1.35145 1.35145i 0.0727596 0.0727596i
\(346\) 0 0
\(347\) −19.4454 + 19.4454i −1.04389 + 1.04389i −0.0448940 + 0.998992i \(0.514295\pi\)
−0.998992 + 0.0448940i \(0.985705\pi\)
\(348\) 0 0
\(349\) 10.7361i 0.574692i 0.957827 + 0.287346i \(0.0927729\pi\)
−0.957827 + 0.287346i \(0.907227\pi\)
\(350\) 0 0
\(351\) 14.3417 0.765504
\(352\) 0 0
\(353\) −28.7630 −1.53090 −0.765450 0.643495i \(-0.777484\pi\)
−0.765450 + 0.643495i \(0.777484\pi\)
\(354\) 0 0
\(355\) −2.33990 + 2.33990i −0.124189 + 0.124189i
\(356\) 0 0
\(357\) 2.66171 + 2.66171i 0.140873 + 0.140873i
\(358\) 0 0
\(359\) −16.6893 −0.880830 −0.440415 0.897794i \(-0.645169\pi\)
−0.440415 + 0.897794i \(0.645169\pi\)
\(360\) 0 0
\(361\) 15.4132i 0.811223i
\(362\) 0 0
\(363\) −5.06037 + 5.06037i −0.265600 + 0.265600i
\(364\) 0 0
\(365\) 1.38914 0.0727109
\(366\) 0 0
\(367\) 14.5495i 0.759478i 0.925094 + 0.379739i \(0.123986\pi\)
−0.925094 + 0.379739i \(0.876014\pi\)
\(368\) 0 0
\(369\) 2.94141 + 10.4888i 0.153123 + 0.546028i
\(370\) 0 0
\(371\) 4.47277i 0.232215i
\(372\) 0 0
\(373\) 36.4059 1.88502 0.942512 0.334172i \(-0.108457\pi\)
0.942512 + 0.334172i \(0.108457\pi\)
\(374\) 0 0
\(375\) 2.01252 2.01252i 0.103926 0.103926i
\(376\) 0 0
\(377\) 0.0587323i 0.00302487i
\(378\) 0 0
\(379\) −20.6143 −1.05889 −0.529443 0.848346i \(-0.677599\pi\)
−0.529443 + 0.848346i \(0.677599\pi\)
\(380\) 0 0
\(381\) −11.9024 11.9024i −0.609777 0.609777i
\(382\) 0 0
\(383\) 15.1886 15.1886i 0.776101 0.776101i −0.203065 0.979165i \(-0.565090\pi\)
0.979165 + 0.203065i \(0.0650902\pi\)
\(384\) 0 0
\(385\) −1.04476 −0.0532459
\(386\) 0 0
\(387\) −3.35693 −0.170642
\(388\) 0 0
\(389\) 15.8359i 0.802911i −0.915879 0.401456i \(-0.868504\pi\)
0.915879 0.401456i \(-0.131496\pi\)
\(390\) 0 0
\(391\) 15.5851 15.5851i 0.788174 0.788174i
\(392\) 0 0
\(393\) −7.57099 + 7.57099i −0.381906 + 0.381906i
\(394\) 0 0
\(395\) 1.06130 1.06130i 0.0533998 0.0533998i
\(396\) 0 0
\(397\) 21.2558 + 21.2558i 1.06680 + 1.06680i 0.997603 + 0.0691953i \(0.0220432\pi\)
0.0691953 + 0.997603i \(0.477957\pi\)
\(398\) 0 0
\(399\) 1.52614 + 1.52614i 0.0764027 + 0.0764027i
\(400\) 0 0
\(401\) 9.85414i 0.492092i −0.969258 0.246046i \(-0.920869\pi\)
0.969258 0.246046i \(-0.0791315\pi\)
\(402\) 0 0
\(403\) −6.84474 6.84474i −0.340961 0.340961i
\(404\) 0 0
\(405\) 0.251794i 0.0125117i
\(406\) 0 0
\(407\) −27.1067 27.1067i −1.34363 1.34363i
\(408\) 0 0
\(409\) −35.0043 −1.73085 −0.865426 0.501037i \(-0.832952\pi\)
−0.865426 + 0.501037i \(0.832952\pi\)
\(410\) 0 0
\(411\) 13.4418 0.663034
\(412\) 0 0
\(413\) −3.47193 3.47193i −0.170843 0.170843i
\(414\) 0 0
\(415\) 1.70461i 0.0836761i
\(416\) 0 0
\(417\) 2.63964 + 2.63964i 0.129264 + 0.129264i
\(418\) 0 0
\(419\) 10.1050i 0.493660i −0.969059 0.246830i \(-0.920611\pi\)
0.969059 0.246830i \(-0.0793889\pi\)
\(420\) 0 0
\(421\) 12.4472 + 12.4472i 0.606642 + 0.606642i 0.942067 0.335425i \(-0.108880\pi\)
−0.335425 + 0.942067i \(0.608880\pi\)
\(422\) 0 0
\(423\) 4.10117 + 4.10117i 0.199406 + 0.199406i
\(424\) 0 0
\(425\) 11.5306 11.5306i 0.559315 0.559315i
\(426\) 0 0
\(427\) −6.73924 + 6.73924i −0.326135 + 0.326135i
\(428\) 0 0
\(429\) 8.96682 8.96682i 0.432922 0.432922i
\(430\) 0 0
\(431\) 28.9838i 1.39610i −0.716048 0.698051i \(-0.754051\pi\)
0.716048 0.698051i \(-0.245949\pi\)
\(432\) 0 0
\(433\) 9.54664 0.458782 0.229391 0.973334i \(-0.426327\pi\)
0.229391 + 0.973334i \(0.426327\pi\)
\(434\) 0 0
\(435\) −0.00628430 −0.000301309
\(436\) 0 0
\(437\) 8.93603 8.93603i 0.427468 0.427468i
\(438\) 0 0
\(439\) 18.1559 + 18.1559i 0.866534 + 0.866534i 0.992087 0.125553i \(-0.0400704\pi\)
−0.125553 + 0.992087i \(0.540070\pi\)
\(440\) 0 0
\(441\) 1.70128 0.0810131
\(442\) 0 0
\(443\) 9.77375i 0.464365i 0.972672 + 0.232182i \(0.0745866\pi\)
−0.972672 + 0.232182i \(0.925413\pi\)
\(444\) 0 0
\(445\) −0.433956 + 0.433956i −0.0205715 + 0.0205715i
\(446\) 0 0
\(447\) −0.0541474 −0.00256108
\(448\) 0 0
\(449\) 5.24705i 0.247624i −0.992306 0.123812i \(-0.960488\pi\)
0.992306 0.123812i \(-0.0395119\pi\)
\(450\) 0 0
\(451\) 23.2040 + 13.0400i 1.09263 + 0.614031i
\(452\) 0 0
\(453\) 2.34684i 0.110264i
\(454\) 0 0
\(455\) 0.672783 0.0315406
\(456\) 0 0
\(457\) −5.36459 + 5.36459i −0.250945 + 0.250945i −0.821358 0.570413i \(-0.806783\pi\)
0.570413 + 0.821358i \(0.306783\pi\)
\(458\) 0 0
\(459\) 17.6967i 0.826010i
\(460\) 0 0
\(461\) 25.2557 1.17627 0.588137 0.808762i \(-0.299862\pi\)
0.588137 + 0.808762i \(0.299862\pi\)
\(462\) 0 0
\(463\) 2.71331 + 2.71331i 0.126098 + 0.126098i 0.767339 0.641241i \(-0.221580\pi\)
−0.641241 + 0.767339i \(0.721580\pi\)
\(464\) 0 0
\(465\) −0.732381 + 0.732381i −0.0339633 + 0.0339633i
\(466\) 0 0
\(467\) −9.12402 −0.422209 −0.211105 0.977463i \(-0.567706\pi\)
−0.211105 + 0.977463i \(0.567706\pi\)
\(468\) 0 0
\(469\) 12.1526 0.561157
\(470\) 0 0
\(471\) 10.8971i 0.502113i
\(472\) 0 0
\(473\) −5.79990 + 5.79990i −0.266680 + 0.266680i
\(474\) 0 0
\(475\) 6.61127 6.61127i 0.303346 0.303346i
\(476\) 0 0
\(477\) 5.38066 5.38066i 0.246364 0.246364i
\(478\) 0 0
\(479\) −3.86377 3.86377i −0.176540 0.176540i 0.613306 0.789846i \(-0.289839\pi\)
−0.789846 + 0.613306i \(0.789839\pi\)
\(480\) 0 0
\(481\) 17.4556 + 17.4556i 0.795907 + 0.795907i
\(482\) 0 0
\(483\) 7.60442i 0.346013i
\(484\) 0 0
\(485\) 0.693863 + 0.693863i 0.0315067 + 0.0315067i
\(486\) 0 0
\(487\) 4.69099i 0.212569i −0.994336 0.106285i \(-0.966105\pi\)
0.994336 0.106285i \(-0.0338955\pi\)
\(488\) 0 0
\(489\) −13.3826 13.3826i −0.605182 0.605182i
\(490\) 0 0
\(491\) 10.5610 0.476609 0.238305 0.971190i \(-0.423408\pi\)
0.238305 + 0.971190i \(0.423408\pi\)
\(492\) 0 0
\(493\) −0.0724715 −0.00326395
\(494\) 0 0
\(495\) 1.25683 + 1.25683i 0.0564902 + 0.0564902i
\(496\) 0 0
\(497\) 13.1663i 0.590589i
\(498\) 0 0
\(499\) 0.375630 + 0.375630i 0.0168155 + 0.0168155i 0.715465 0.698649i \(-0.246215\pi\)
−0.698649 + 0.715465i \(0.746215\pi\)
\(500\) 0 0
\(501\) 8.97684i 0.401055i
\(502\) 0 0
\(503\) 16.0124 + 16.0124i 0.713959 + 0.713959i 0.967361 0.253402i \(-0.0815495\pi\)
−0.253402 + 0.967361i \(0.581550\pi\)
\(504\) 0 0
\(505\) −3.01271 3.01271i −0.134064 0.134064i
\(506\) 0 0
\(507\) 4.70152 4.70152i 0.208802 0.208802i
\(508\) 0 0
\(509\) 12.8161 12.8161i 0.568065 0.568065i −0.363521 0.931586i \(-0.618425\pi\)
0.931586 + 0.363521i \(0.118425\pi\)
\(510\) 0 0
\(511\) −3.90825 + 3.90825i −0.172891 + 0.172891i
\(512\) 0 0
\(513\) 10.1467i 0.447989i
\(514\) 0 0
\(515\) −0.695916 −0.0306657
\(516\) 0 0
\(517\) 14.1715 0.623262
\(518\) 0 0
\(519\) −16.6307 + 16.6307i −0.730006 + 0.730006i
\(520\) 0 0
\(521\) −25.9848 25.9848i −1.13841 1.13841i −0.988735 0.149678i \(-0.952176\pi\)
−0.149678 0.988735i \(-0.547824\pi\)
\(522\) 0 0
\(523\) 14.4566 0.632142 0.316071 0.948736i \(-0.397636\pi\)
0.316071 + 0.948736i \(0.397636\pi\)
\(524\) 0 0
\(525\) 5.62609i 0.245543i
\(526\) 0 0
\(527\) −8.44593 + 8.44593i −0.367911 + 0.367911i
\(528\) 0 0
\(529\) 21.5262 0.935921
\(530\) 0 0
\(531\) 8.35335i 0.362504i
\(532\) 0 0
\(533\) −14.9424 8.39725i −0.647229 0.363725i
\(534\) 0 0
\(535\) 0.817174i 0.0353295i
\(536\) 0 0
\(537\) −22.3844 −0.965957
\(538\) 0 0
\(539\) 2.93936 2.93936i 0.126607 0.126607i
\(540\) 0 0
\(541\) 15.2484i 0.655578i −0.944751 0.327789i \(-0.893696\pi\)
0.944751 0.327789i \(-0.106304\pi\)
\(542\) 0 0
\(543\) 1.06152 0.0455543
\(544\) 0 0
\(545\) 0.836449 + 0.836449i 0.0358295 + 0.0358295i
\(546\) 0 0
\(547\) 27.9756 27.9756i 1.19615 1.19615i 0.220839 0.975310i \(-0.429120\pi\)
0.975310 0.220839i \(-0.0708795\pi\)
\(548\) 0 0
\(549\) 16.2144 0.692013
\(550\) 0 0
\(551\) −0.0415529 −0.00177021
\(552\) 0 0
\(553\) 5.97180i 0.253947i
\(554\) 0 0
\(555\) 1.86773 1.86773i 0.0792809 0.0792809i
\(556\) 0 0
\(557\) 3.14092 3.14092i 0.133085 0.133085i −0.637426 0.770511i \(-0.720001\pi\)
0.770511 + 0.637426i \(0.220001\pi\)
\(558\) 0 0
\(559\) 3.73490 3.73490i 0.157970 0.157970i
\(560\) 0 0
\(561\) −11.0644 11.0644i −0.467141 0.467141i
\(562\) 0 0
\(563\) 26.3968 + 26.3968i 1.11249 + 1.11249i 0.992812 + 0.119681i \(0.0381871\pi\)
0.119681 + 0.992812i \(0.461813\pi\)
\(564\) 0 0
\(565\) 1.62838i 0.0685063i
\(566\) 0 0
\(567\) 0.708406 + 0.708406i 0.0297502 + 0.0297502i
\(568\) 0 0
\(569\) 4.73462i 0.198486i 0.995063 + 0.0992429i \(0.0316421\pi\)
−0.995063 + 0.0992429i \(0.968358\pi\)
\(570\) 0 0
\(571\) 0.339810 + 0.339810i 0.0142206 + 0.0142206i 0.714181 0.699961i \(-0.246799\pi\)
−0.699961 + 0.714181i \(0.746799\pi\)
\(572\) 0 0
\(573\) 0.452103 0.0188869
\(574\) 0 0
\(575\) 32.9425 1.37380
\(576\) 0 0
\(577\) 17.2352 + 17.2352i 0.717511 + 0.717511i 0.968095 0.250584i \(-0.0806225\pi\)
−0.250584 + 0.968095i \(0.580623\pi\)
\(578\) 0 0
\(579\) 0.801321i 0.0333018i
\(580\) 0 0
\(581\) 4.79581 + 4.79581i 0.198964 + 0.198964i
\(582\) 0 0
\(583\) 18.5928i 0.770034i
\(584\) 0 0
\(585\) −0.809347 0.809347i −0.0334624 0.0334624i
\(586\) 0 0
\(587\) 29.5688 + 29.5688i 1.22043 + 1.22043i 0.967478 + 0.252955i \(0.0814025\pi\)
0.252955 + 0.967478i \(0.418598\pi\)
\(588\) 0 0
\(589\) −4.84264 + 4.84264i −0.199537 + 0.199537i
\(590\) 0 0
\(591\) 16.6635 16.6635i 0.685445 0.685445i
\(592\) 0 0
\(593\) 20.7699 20.7699i 0.852918 0.852918i −0.137573 0.990492i \(-0.543930\pi\)
0.990492 + 0.137573i \(0.0439303\pi\)
\(594\) 0 0
\(595\) 0.830168i 0.0340336i
\(596\) 0 0
\(597\) −29.5919 −1.21112
\(598\) 0 0
\(599\) −6.18039 −0.252524 −0.126262 0.991997i \(-0.540298\pi\)
−0.126262 + 0.991997i \(0.540298\pi\)
\(600\) 0 0
\(601\) −15.2543 + 15.2543i −0.622236 + 0.622236i −0.946103 0.323867i \(-0.895017\pi\)
0.323867 + 0.946103i \(0.395017\pi\)
\(602\) 0 0
\(603\) −14.6194 14.6194i −0.595349 0.595349i
\(604\) 0 0
\(605\) 1.57829 0.0641666
\(606\) 0 0
\(607\) 24.5297i 0.995631i −0.867283 0.497815i \(-0.834136\pi\)
0.867283 0.497815i \(-0.165864\pi\)
\(608\) 0 0
\(609\) 0.0176805 0.0176805i 0.000716448 0.000716448i
\(610\) 0 0
\(611\) −9.12588 −0.369194
\(612\) 0 0
\(613\) 30.7130i 1.24049i 0.784409 + 0.620244i \(0.212966\pi\)
−0.784409 + 0.620244i \(0.787034\pi\)
\(614\) 0 0
\(615\) −0.898498 + 1.59883i −0.0362309 + 0.0644709i
\(616\) 0 0
\(617\) 0.0231327i 0.000931289i 1.00000 0.000465645i \(0.000148219\pi\)
−1.00000 0.000465645i \(0.999852\pi\)
\(618\) 0 0
\(619\) −19.6769 −0.790882 −0.395441 0.918491i \(-0.629408\pi\)
−0.395441 + 0.918491i \(0.629408\pi\)
\(620\) 0 0
\(621\) 25.2794 25.2794i 1.01443 1.01443i
\(622\) 0 0
\(623\) 2.44181i 0.0978293i
\(624\) 0 0
\(625\) 24.0565 0.962259
\(626\) 0 0
\(627\) −6.34400 6.34400i −0.253355 0.253355i
\(628\) 0 0
\(629\) 21.5390 21.5390i 0.858816 0.858816i
\(630\) 0 0
\(631\) 1.80666 0.0719221 0.0359610 0.999353i \(-0.488551\pi\)
0.0359610 + 0.999353i \(0.488551\pi\)
\(632\) 0 0
\(633\) −14.9814 −0.595456
\(634\) 0 0
\(635\) 3.71226i 0.147316i
\(636\) 0 0
\(637\) −1.89283 + 1.89283i −0.0749967 + 0.0749967i
\(638\) 0 0
\(639\) −15.8388 + 15.8388i −0.626575 + 0.626575i
\(640\) 0 0
\(641\) 24.2949 24.2949i 0.959592 0.959592i −0.0396225 0.999215i \(-0.512616\pi\)
0.999215 + 0.0396225i \(0.0126155\pi\)
\(642\) 0 0
\(643\) 12.3547 + 12.3547i 0.487223 + 0.487223i 0.907429 0.420206i \(-0.138042\pi\)
−0.420206 + 0.907429i \(0.638042\pi\)
\(644\) 0 0
\(645\) −0.399631 0.399631i −0.0157355 0.0157355i
\(646\) 0 0
\(647\) 13.8408i 0.544136i 0.962278 + 0.272068i \(0.0877076\pi\)
−0.962278 + 0.272068i \(0.912292\pi\)
\(648\) 0 0
\(649\) 14.4324 + 14.4324i 0.566522 + 0.566522i
\(650\) 0 0
\(651\) 4.12101i 0.161515i
\(652\) 0 0
\(653\) 7.41607 + 7.41607i 0.290213 + 0.290213i 0.837164 0.546951i \(-0.184212\pi\)
−0.546951 + 0.837164i \(0.684212\pi\)
\(654\) 0 0
\(655\) 2.36133 0.0922650
\(656\) 0 0
\(657\) 9.40313 0.366851
\(658\) 0 0
\(659\) −12.5341 12.5341i −0.488258 0.488258i 0.419498 0.907756i \(-0.362206\pi\)
−0.907756 + 0.419498i \(0.862206\pi\)
\(660\) 0 0
\(661\) 17.7094i 0.688815i −0.938820 0.344408i \(-0.888080\pi\)
0.938820 0.344408i \(-0.111920\pi\)
\(662\) 0 0
\(663\) 7.12505 + 7.12505i 0.276714 + 0.276714i
\(664\) 0 0
\(665\) 0.475992i 0.0184582i
\(666\) 0 0
\(667\) −0.103524 0.103524i −0.00400848 0.00400848i
\(668\) 0 0
\(669\) 13.5746 + 13.5746i 0.524823 + 0.524823i
\(670\) 0 0
\(671\) 28.0142 28.0142i 1.08148 1.08148i
\(672\) 0 0
\(673\) −11.3633 + 11.3633i −0.438024 + 0.438024i −0.891347 0.453322i \(-0.850239\pi\)
0.453322 + 0.891347i \(0.350239\pi\)
\(674\) 0 0
\(675\) 18.7028 18.7028i 0.719873 0.719873i
\(676\) 0 0
\(677\) 2.90980i 0.111833i −0.998435 0.0559164i \(-0.982192\pi\)
0.998435 0.0559164i \(-0.0178080\pi\)
\(678\) 0 0
\(679\) −3.90428 −0.149832
\(680\) 0 0
\(681\) 5.66947 0.217254
\(682\) 0 0
\(683\) −1.92137 + 1.92137i −0.0735191 + 0.0735191i −0.742910 0.669391i \(-0.766555\pi\)
0.669391 + 0.742910i \(0.266555\pi\)
\(684\) 0 0
\(685\) −2.09619 2.09619i −0.0800914 0.0800914i
\(686\) 0 0
\(687\) 29.7723 1.13589
\(688\) 0 0
\(689\) 11.9730i 0.456135i
\(690\) 0 0
\(691\) 27.1912 27.1912i 1.03440 1.03440i 0.0350170 0.999387i \(-0.488851\pi\)
0.999387 0.0350170i \(-0.0111485\pi\)
\(692\) 0 0
\(693\) −7.07201 −0.268643
\(694\) 0 0
\(695\) 0.823283i 0.0312289i
\(696\) 0 0
\(697\) −10.3616 + 18.4379i −0.392475 + 0.698387i
\(698\) 0 0
\(699\) 30.1823i 1.14160i
\(700\) 0 0
\(701\) −15.7290 −0.594076 −0.297038 0.954866i \(-0.595999\pi\)
−0.297038 + 0.954866i \(0.595999\pi\)
\(702\) 0 0
\(703\) 12.3498 12.3498i 0.465781 0.465781i
\(704\) 0 0
\(705\) 0.976461i 0.0367756i
\(706\) 0 0
\(707\) 16.9521 0.637550
\(708\) 0 0
\(709\) 1.87844 + 1.87844i 0.0705463 + 0.0705463i 0.741500 0.670953i \(-0.234115\pi\)
−0.670953 + 0.741500i \(0.734115\pi\)
\(710\) 0 0
\(711\) 7.18397 7.18397i 0.269420 0.269420i
\(712\) 0 0
\(713\) −24.1298 −0.903666
\(714\) 0 0
\(715\) −2.79668 −0.104590
\(716\) 0 0
\(717\) 29.8069i 1.11316i
\(718\) 0 0
\(719\) −3.04723 + 3.04723i −0.113642 + 0.113642i −0.761641 0.647999i \(-0.775606\pi\)
0.647999 + 0.761641i \(0.275606\pi\)
\(720\) 0 0
\(721\) 1.95792 1.95792i 0.0729166 0.0729166i
\(722\) 0 0
\(723\) 3.88695 3.88695i 0.144557 0.144557i
\(724\) 0 0
\(725\) −0.0765920 0.0765920i −0.00284455 0.00284455i
\(726\) 0 0
\(727\) 8.14245 + 8.14245i 0.301987 + 0.301987i 0.841791 0.539804i \(-0.181502\pi\)
−0.539804 + 0.841791i \(0.681502\pi\)
\(728\) 0 0
\(729\) 20.0214i 0.741533i
\(730\) 0 0
\(731\) −4.60861 4.60861i −0.170456 0.170456i
\(732\) 0 0
\(733\) 48.1604i 1.77884i 0.457087 + 0.889422i \(0.348893\pi\)
−0.457087 + 0.889422i \(0.651107\pi\)
\(734\) 0 0
\(735\) 0.202531 + 0.202531i 0.00747047 + 0.00747047i
\(736\) 0 0
\(737\) −50.5171 −1.86082
\(738\) 0 0
\(739\) −39.0976 −1.43823 −0.719114 0.694892i \(-0.755452\pi\)
−0.719114 + 0.694892i \(0.755452\pi\)
\(740\) 0 0
\(741\) 4.08528 + 4.08528i 0.150077 + 0.150077i
\(742\) 0 0
\(743\) 41.5962i 1.52602i 0.646389 + 0.763008i \(0.276278\pi\)
−0.646389 + 0.763008i \(0.723722\pi\)
\(744\) 0 0
\(745\) 0.00844407 + 0.00844407i 0.000309367 + 0.000309367i
\(746\) 0 0
\(747\) 11.5386i 0.422174i
\(748\) 0 0
\(749\) −2.29907 2.29907i −0.0840061 0.0840061i
\(750\) 0 0
\(751\) 37.4849 + 37.4849i 1.36784 + 1.36784i 0.863507 + 0.504337i \(0.168263\pi\)
0.504337 + 0.863507i \(0.331737\pi\)
\(752\) 0 0
\(753\) −2.81196 + 2.81196i −0.102473 + 0.102473i
\(754\) 0 0
\(755\) −0.365981 + 0.365981i −0.0133194 + 0.0133194i
\(756\) 0 0
\(757\) −7.22630 + 7.22630i −0.262644 + 0.262644i −0.826128 0.563483i \(-0.809461\pi\)
0.563483 + 0.826128i \(0.309461\pi\)
\(758\) 0 0
\(759\) 31.6107i 1.14740i
\(760\) 0 0
\(761\) 41.1038 1.49001 0.745005 0.667059i \(-0.232447\pi\)
0.745005 + 0.667059i \(0.232447\pi\)
\(762\) 0 0
\(763\) −4.70659 −0.170390
\(764\) 0 0
\(765\) −0.998678 + 0.998678i −0.0361073 + 0.0361073i
\(766\) 0 0
\(767\) −9.29390 9.29390i −0.335583 0.335583i
\(768\) 0 0
\(769\) −34.5557 −1.24611 −0.623055 0.782178i \(-0.714109\pi\)
−0.623055 + 0.782178i \(0.714109\pi\)
\(770\) 0 0
\(771\) 3.19028i 0.114895i
\(772\) 0 0
\(773\) −15.8386 + 15.8386i −0.569673 + 0.569673i −0.932037 0.362364i \(-0.881970\pi\)
0.362364 + 0.932037i \(0.381970\pi\)
\(774\) 0 0
\(775\) −17.8523 −0.641273
\(776\) 0 0
\(777\) 10.5095i 0.377026i
\(778\) 0 0
\(779\) −5.94103 + 10.5717i −0.212860 + 0.378772i
\(780\) 0 0
\(781\) 54.7308i 1.95842i
\(782\) 0 0
\(783\) −0.117550 −0.00420091
\(784\) 0 0
\(785\) 1.69936 1.69936i 0.0606529 0.0606529i
\(786\) 0 0
\(787\) 13.9193i 0.496171i −0.968738 0.248085i \(-0.920199\pi\)
0.968738 0.248085i \(-0.0798014\pi\)
\(788\) 0 0
\(789\) −13.3476 −0.475187
\(790\) 0 0
\(791\) −4.58133 4.58133i −0.162893 0.162893i
\(792\) 0 0
\(793\) −18.0400 + 18.0400i −0.640621 + 0.640621i
\(794\) 0 0
\(795\) 1.28110 0.0454359
\(796\) 0 0
\(797\) −54.7723 −1.94014 −0.970068 0.242834i \(-0.921923\pi\)
−0.970068 + 0.242834i \(0.921923\pi\)
\(798\) 0 0
\(799\) 11.2607i 0.398375i
\(800\) 0 0