Properties

Label 1148.2.k.b.337.11
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 337.11
Character \(\chi\) \(=\) 1148.337
Dual form 1148.2.k.b.729.11

$q$-expansion

\(f(q)\) \(=\) \(q+(0.178034 + 0.178034i) q^{3} -0.542323i q^{5} +(-0.707107 - 0.707107i) q^{7} -2.93661i q^{9} +O(q^{10})\) \(q+(0.178034 + 0.178034i) q^{3} -0.542323i q^{5} +(-0.707107 - 0.707107i) q^{7} -2.93661i q^{9} +(0.525032 + 0.525032i) q^{11} +(-2.31231 - 2.31231i) q^{13} +(0.0965521 - 0.0965521i) q^{15} +(0.596624 - 0.596624i) q^{17} +(-3.07297 + 3.07297i) q^{19} -0.251779i q^{21} -3.35862 q^{23} +4.70589 q^{25} +(1.05692 - 1.05692i) q^{27} +(-6.56855 - 6.56855i) q^{29} -8.61993 q^{31} +0.186947i q^{33} +(-0.383480 + 0.383480i) q^{35} -1.51447 q^{37} -0.823341i q^{39} +(-1.28597 + 6.27266i) q^{41} -7.10884i q^{43} -1.59259 q^{45} +(4.92171 - 4.92171i) q^{47} +1.00000i q^{49} +0.212439 q^{51} +(-3.28325 - 3.28325i) q^{53} +(0.284737 - 0.284737i) q^{55} -1.09419 q^{57} +9.28001 q^{59} -6.51233i q^{61} +(-2.07650 + 2.07650i) q^{63} +(-1.25402 + 1.25402i) q^{65} +(1.81360 - 1.81360i) q^{67} +(-0.597950 - 0.597950i) q^{69} +(-6.46972 - 6.46972i) q^{71} -12.1427i q^{73} +(0.837809 + 0.837809i) q^{75} -0.742507i q^{77} +(10.2071 + 10.2071i) q^{79} -8.43349 q^{81} -7.06535 q^{83} +(-0.323563 - 0.323563i) q^{85} -2.33885i q^{87} +(-2.76083 - 2.76083i) q^{89} +3.27010i q^{91} +(-1.53464 - 1.53464i) q^{93} +(1.66654 + 1.66654i) q^{95} +(-7.05222 + 7.05222i) q^{97} +(1.54181 - 1.54181i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + O(q^{10}) \) \( 36q - 12q^{11} - 16q^{17} - 4q^{19} - 36q^{23} - 64q^{25} + 12q^{27} + 16q^{29} - 28q^{31} + 12q^{35} + 48q^{37} + 4q^{41} + 36q^{45} + 12q^{47} - 12q^{51} - 12q^{53} + 12q^{55} + 76q^{57} + 20q^{59} - 4q^{65} - 44q^{67} + 72q^{69} - 20q^{71} + 72q^{75} - 8q^{79} - 100q^{81} - 40q^{83} - 8q^{85} - 16q^{89} + 20q^{93} + 76q^{95} - 16q^{97} + 56q^{99} + O(q^{100}) \)

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
\(3\) 0.178034 + 0.178034i 0.102788 + 0.102788i 0.756631 0.653842i \(-0.226844\pi\)
−0.653842 + 0.756631i \(0.726844\pi\)
\(4\) 0 0
\(5\) 0.542323i 0.242534i −0.992620 0.121267i \(-0.961304\pi\)
0.992620 0.121267i \(-0.0386957\pi\)
\(6\) 0 0
\(7\) −0.707107 0.707107i −0.267261 0.267261i
\(8\) 0 0
\(9\) 2.93661i 0.978869i
\(10\) 0 0
\(11\) 0.525032 + 0.525032i 0.158303 + 0.158303i 0.781814 0.623511i \(-0.214294\pi\)
−0.623511 + 0.781814i \(0.714294\pi\)
\(12\) 0 0
\(13\) −2.31231 2.31231i −0.641319 0.641319i 0.309560 0.950880i \(-0.399818\pi\)
−0.950880 + 0.309560i \(0.899818\pi\)
\(14\) 0 0
\(15\) 0.0965521 0.0965521i 0.0249296 0.0249296i
\(16\) 0 0
\(17\) 0.596624 0.596624i 0.144703 0.144703i −0.631044 0.775747i \(-0.717373\pi\)
0.775747 + 0.631044i \(0.217373\pi\)
\(18\) 0 0
\(19\) −3.07297 + 3.07297i −0.704988 + 0.704988i −0.965477 0.260489i \(-0.916116\pi\)
0.260489 + 0.965477i \(0.416116\pi\)
\(20\) 0 0
\(21\) 0.251779i 0.0549426i
\(22\) 0 0
\(23\) −3.35862 −0.700321 −0.350161 0.936690i \(-0.613873\pi\)
−0.350161 + 0.936690i \(0.613873\pi\)
\(24\) 0 0
\(25\) 4.70589 0.941177
\(26\) 0 0
\(27\) 1.05692 1.05692i 0.203404 0.203404i
\(28\) 0 0
\(29\) −6.56855 6.56855i −1.21975 1.21975i −0.967720 0.252029i \(-0.918902\pi\)
−0.252029 0.967720i \(-0.581098\pi\)
\(30\) 0 0
\(31\) −8.61993 −1.54818 −0.774092 0.633073i \(-0.781793\pi\)
−0.774092 + 0.633073i \(0.781793\pi\)
\(32\) 0 0
\(33\) 0.186947i 0.0325434i
\(34\) 0 0
\(35\) −0.383480 + 0.383480i −0.0648200 + 0.0648200i
\(36\) 0 0
\(37\) −1.51447 −0.248977 −0.124488 0.992221i \(-0.539729\pi\)
−0.124488 + 0.992221i \(0.539729\pi\)
\(38\) 0 0
\(39\) 0.823341i 0.131840i
\(40\) 0 0
\(41\) −1.28597 + 6.27266i −0.200834 + 0.979625i
\(42\) 0 0
\(43\) 7.10884i 1.08409i −0.840350 0.542044i \(-0.817651\pi\)
0.840350 0.542044i \(-0.182349\pi\)
\(44\) 0 0
\(45\) −1.59259 −0.237409
\(46\) 0 0
\(47\) 4.92171 4.92171i 0.717905 0.717905i −0.250271 0.968176i \(-0.580520\pi\)
0.968176 + 0.250271i \(0.0805196\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 0.212439 0.0297475
\(52\) 0 0
\(53\) −3.28325 3.28325i −0.450989 0.450989i 0.444694 0.895683i \(-0.353313\pi\)
−0.895683 + 0.444694i \(0.853313\pi\)
\(54\) 0 0
\(55\) 0.284737 0.284737i 0.0383939 0.0383939i
\(56\) 0 0
\(57\) −1.09419 −0.144929
\(58\) 0 0
\(59\) 9.28001 1.20815 0.604077 0.796926i \(-0.293542\pi\)
0.604077 + 0.796926i \(0.293542\pi\)
\(60\) 0 0
\(61\) 6.51233i 0.833819i −0.908948 0.416909i \(-0.863113\pi\)
0.908948 0.416909i \(-0.136887\pi\)
\(62\) 0 0
\(63\) −2.07650 + 2.07650i −0.261614 + 0.261614i
\(64\) 0 0
\(65\) −1.25402 + 1.25402i −0.155542 + 0.155542i
\(66\) 0 0
\(67\) 1.81360 1.81360i 0.221566 0.221566i −0.587592 0.809158i \(-0.699924\pi\)
0.809158 + 0.587592i \(0.199924\pi\)
\(68\) 0 0
\(69\) −0.597950 0.597950i −0.0719848 0.0719848i
\(70\) 0 0
\(71\) −6.46972 6.46972i −0.767815 0.767815i 0.209907 0.977721i \(-0.432684\pi\)
−0.977721 + 0.209907i \(0.932684\pi\)
\(72\) 0 0
\(73\) 12.1427i 1.42120i −0.703596 0.710600i \(-0.748424\pi\)
0.703596 0.710600i \(-0.251576\pi\)
\(74\) 0 0
\(75\) 0.837809 + 0.837809i 0.0967419 + 0.0967419i
\(76\) 0 0
\(77\) 0.742507i 0.0846165i
\(78\) 0 0
\(79\) 10.2071 + 10.2071i 1.14839 + 1.14839i 0.986870 + 0.161516i \(0.0516382\pi\)
0.161516 + 0.986870i \(0.448362\pi\)
\(80\) 0 0
\(81\) −8.43349 −0.937054
\(82\) 0 0
\(83\) −7.06535 −0.775523 −0.387761 0.921760i \(-0.626752\pi\)
−0.387761 + 0.921760i \(0.626752\pi\)
\(84\) 0 0
\(85\) −0.323563 0.323563i −0.0350953 0.0350953i
\(86\) 0 0
\(87\) 2.33885i 0.250751i
\(88\) 0 0
\(89\) −2.76083 2.76083i −0.292647 0.292647i 0.545478 0.838125i \(-0.316348\pi\)
−0.838125 + 0.545478i \(0.816348\pi\)
\(90\) 0 0
\(91\) 3.27010i 0.342800i
\(92\) 0 0
\(93\) −1.53464 1.53464i −0.159135 0.159135i
\(94\) 0 0
\(95\) 1.66654 + 1.66654i 0.170984 + 0.170984i
\(96\) 0 0
\(97\) −7.05222 + 7.05222i −0.716045 + 0.716045i −0.967793 0.251748i \(-0.918995\pi\)
0.251748 + 0.967793i \(0.418995\pi\)
\(98\) 0 0
\(99\) 1.54181 1.54181i 0.154958 0.154958i
\(100\) 0 0
\(101\) 4.12741 4.12741i 0.410692 0.410692i −0.471287 0.881980i \(-0.656210\pi\)
0.881980 + 0.471287i \(0.156210\pi\)
\(102\) 0 0
\(103\) 15.9721i 1.57377i 0.617097 + 0.786887i \(0.288309\pi\)
−0.617097 + 0.786887i \(0.711691\pi\)
\(104\) 0 0
\(105\) −0.136545 −0.0133255
\(106\) 0 0
\(107\) 4.63533 0.448114 0.224057 0.974576i \(-0.428070\pi\)
0.224057 + 0.974576i \(0.428070\pi\)
\(108\) 0 0
\(109\) 10.0759 10.0759i 0.965099 0.965099i −0.0343125 0.999411i \(-0.510924\pi\)
0.999411 + 0.0343125i \(0.0109242\pi\)
\(110\) 0 0
\(111\) −0.269627 0.269627i −0.0255919 0.0255919i
\(112\) 0 0
\(113\) 2.73727 0.257501 0.128750 0.991677i \(-0.458903\pi\)
0.128750 + 0.991677i \(0.458903\pi\)
\(114\) 0 0
\(115\) 1.82146i 0.169852i
\(116\) 0 0
\(117\) −6.79035 + 6.79035i −0.627768 + 0.627768i
\(118\) 0 0
\(119\) −0.843754 −0.0773468
\(120\) 0 0
\(121\) 10.4487i 0.949880i
\(122\) 0 0
\(123\) −1.34570 + 0.887804i −0.121337 + 0.0800505i
\(124\) 0 0
\(125\) 5.26372i 0.470802i
\(126\) 0 0
\(127\) 12.9542 1.14950 0.574749 0.818330i \(-0.305100\pi\)
0.574749 + 0.818330i \(0.305100\pi\)
\(128\) 0 0
\(129\) 1.26562 1.26562i 0.111432 0.111432i
\(130\) 0 0
\(131\) 0.793872i 0.0693609i −0.999398 0.0346805i \(-0.988959\pi\)
0.999398 0.0346805i \(-0.0110413\pi\)
\(132\) 0 0
\(133\) 4.34583 0.376832
\(134\) 0 0
\(135\) −0.573192 0.573192i −0.0493325 0.0493325i
\(136\) 0 0
\(137\) −7.86929 + 7.86929i −0.672318 + 0.672318i −0.958250 0.285932i \(-0.907697\pi\)
0.285932 + 0.958250i \(0.407697\pi\)
\(138\) 0 0
\(139\) −0.697026 −0.0591210 −0.0295605 0.999563i \(-0.509411\pi\)
−0.0295605 + 0.999563i \(0.509411\pi\)
\(140\) 0 0
\(141\) 1.75247 0.147584
\(142\) 0 0
\(143\) 2.42807i 0.203046i
\(144\) 0 0
\(145\) −3.56227 + 3.56227i −0.295831 + 0.295831i
\(146\) 0 0
\(147\) −0.178034 + 0.178034i −0.0146840 + 0.0146840i
\(148\) 0 0
\(149\) −11.4542 + 11.4542i −0.938368 + 0.938368i −0.998208 0.0598400i \(-0.980941\pi\)
0.0598400 + 0.998208i \(0.480941\pi\)
\(150\) 0 0
\(151\) −13.4949 13.4949i −1.09820 1.09820i −0.994621 0.103581i \(-0.966970\pi\)
−0.103581 0.994621i \(-0.533030\pi\)
\(152\) 0 0
\(153\) −1.75205 1.75205i −0.141645 0.141645i
\(154\) 0 0
\(155\) 4.67478i 0.375488i
\(156\) 0 0
\(157\) −1.08910 1.08910i −0.0869198 0.0869198i 0.662310 0.749230i \(-0.269576\pi\)
−0.749230 + 0.662310i \(0.769576\pi\)
\(158\) 0 0
\(159\) 1.16906i 0.0927127i
\(160\) 0 0
\(161\) 2.37491 + 2.37491i 0.187169 + 0.187169i
\(162\) 0 0
\(163\) 7.02927 0.550575 0.275287 0.961362i \(-0.411227\pi\)
0.275287 + 0.961362i \(0.411227\pi\)
\(164\) 0 0
\(165\) 0.101386 0.00789287
\(166\) 0 0
\(167\) 14.8750 + 14.8750i 1.15106 + 1.15106i 0.986341 + 0.164718i \(0.0526714\pi\)
0.164718 + 0.986341i \(0.447329\pi\)
\(168\) 0 0
\(169\) 2.30644i 0.177419i
\(170\) 0 0
\(171\) 9.02410 + 9.02410i 0.690091 + 0.690091i
\(172\) 0 0
\(173\) 17.5019i 1.33065i 0.746555 + 0.665324i \(0.231707\pi\)
−0.746555 + 0.665324i \(0.768293\pi\)
\(174\) 0 0
\(175\) −3.32756 3.32756i −0.251540 0.251540i
\(176\) 0 0
\(177\) 1.65216 + 1.65216i 0.124184 + 0.124184i
\(178\) 0 0
\(179\) 2.55909 2.55909i 0.191275 0.191275i −0.604972 0.796247i \(-0.706816\pi\)
0.796247 + 0.604972i \(0.206816\pi\)
\(180\) 0 0
\(181\) 9.22014 9.22014i 0.685328 0.685328i −0.275868 0.961196i \(-0.588965\pi\)
0.961196 + 0.275868i \(0.0889652\pi\)
\(182\) 0 0
\(183\) 1.15942 1.15942i 0.0857067 0.0857067i
\(184\) 0 0
\(185\) 0.821330i 0.0603854i
\(186\) 0 0
\(187\) 0.626493 0.0458137
\(188\) 0 0
\(189\) −1.49471 −0.108724
\(190\) 0 0
\(191\) −14.9361 + 14.9361i −1.08074 + 1.08074i −0.0842972 + 0.996441i \(0.526865\pi\)
−0.996441 + 0.0842972i \(0.973135\pi\)
\(192\) 0 0
\(193\) 11.1364 + 11.1364i 0.801613 + 0.801613i 0.983348 0.181734i \(-0.0581711\pi\)
−0.181734 + 0.983348i \(0.558171\pi\)
\(194\) 0 0
\(195\) −0.446517 −0.0319757
\(196\) 0 0
\(197\) 23.9212i 1.70431i −0.523286 0.852157i \(-0.675294\pi\)
0.523286 0.852157i \(-0.324706\pi\)
\(198\) 0 0
\(199\) 3.11493 3.11493i 0.220812 0.220812i −0.588029 0.808840i \(-0.700096\pi\)
0.808840 + 0.588029i \(0.200096\pi\)
\(200\) 0 0
\(201\) 0.645765 0.0455488
\(202\) 0 0
\(203\) 9.28933i 0.651983i
\(204\) 0 0
\(205\) 3.40181 + 0.697408i 0.237593 + 0.0487091i
\(206\) 0 0
\(207\) 9.86296i 0.685523i
\(208\) 0 0
\(209\) −3.22681 −0.223203
\(210\) 0 0
\(211\) 9.25001 9.25001i 0.636797 0.636797i −0.312967 0.949764i \(-0.601323\pi\)
0.949764 + 0.312967i \(0.101323\pi\)
\(212\) 0 0
\(213\) 2.30367i 0.157845i
\(214\) 0 0
\(215\) −3.85529 −0.262928
\(216\) 0 0
\(217\) 6.09521 + 6.09521i 0.413770 + 0.413770i
\(218\) 0 0
\(219\) 2.16182 2.16182i 0.146083 0.146083i
\(220\) 0 0
\(221\) −2.75916 −0.185601
\(222\) 0 0
\(223\) 14.7508 0.987788 0.493894 0.869522i \(-0.335573\pi\)
0.493894 + 0.869522i \(0.335573\pi\)
\(224\) 0 0
\(225\) 13.8193i 0.921289i
\(226\) 0 0
\(227\) −16.8150 + 16.8150i −1.11605 + 1.11605i −0.123738 + 0.992315i \(0.539488\pi\)
−0.992315 + 0.123738i \(0.960512\pi\)
\(228\) 0 0
\(229\) −3.08954 + 3.08954i −0.204162 + 0.204162i −0.801781 0.597618i \(-0.796114\pi\)
0.597618 + 0.801781i \(0.296114\pi\)
\(230\) 0 0
\(231\) 0.132192 0.132192i 0.00869758 0.00869758i
\(232\) 0 0
\(233\) 12.5638 + 12.5638i 0.823084 + 0.823084i 0.986549 0.163465i \(-0.0522671\pi\)
−0.163465 + 0.986549i \(0.552267\pi\)
\(234\) 0 0
\(235\) −2.66916 2.66916i −0.174116 0.174116i
\(236\) 0 0
\(237\) 3.63442i 0.236081i
\(238\) 0 0
\(239\) 0.469822 + 0.469822i 0.0303903 + 0.0303903i 0.722139 0.691748i \(-0.243159\pi\)
−0.691748 + 0.722139i \(0.743159\pi\)
\(240\) 0 0
\(241\) 19.9067i 1.28230i −0.767414 0.641152i \(-0.778457\pi\)
0.767414 0.641152i \(-0.221543\pi\)
\(242\) 0 0
\(243\) −4.67221 4.67221i −0.299722 0.299722i
\(244\) 0 0
\(245\) 0.542323 0.0346477
\(246\) 0 0
\(247\) 14.2113 0.904244
\(248\) 0 0
\(249\) −1.25787 1.25787i −0.0797146 0.0797146i
\(250\) 0 0
\(251\) 30.1954i 1.90591i 0.303106 + 0.952957i \(0.401976\pi\)
−0.303106 + 0.952957i \(0.598024\pi\)
\(252\) 0 0
\(253\) −1.76338 1.76338i −0.110863 0.110863i
\(254\) 0 0
\(255\) 0.115211i 0.00721477i
\(256\) 0 0
\(257\) 14.5388 + 14.5388i 0.906906 + 0.906906i 0.996021 0.0891155i \(-0.0284040\pi\)
−0.0891155 + 0.996021i \(0.528404\pi\)
\(258\) 0 0
\(259\) 1.07089 + 1.07089i 0.0665419 + 0.0665419i
\(260\) 0 0
\(261\) −19.2892 + 19.2892i −1.19397 + 1.19397i
\(262\) 0 0
\(263\) 0.607933 0.607933i 0.0374867 0.0374867i −0.688115 0.725602i \(-0.741562\pi\)
0.725602 + 0.688115i \(0.241562\pi\)
\(264\) 0 0
\(265\) −1.78058 + 1.78058i −0.109380 + 0.109380i
\(266\) 0 0
\(267\) 0.983044i 0.0601613i
\(268\) 0 0
\(269\) 5.24006 0.319492 0.159746 0.987158i \(-0.448932\pi\)
0.159746 + 0.987158i \(0.448932\pi\)
\(270\) 0 0
\(271\) 3.57926 0.217425 0.108712 0.994073i \(-0.465327\pi\)
0.108712 + 0.994073i \(0.465327\pi\)
\(272\) 0 0
\(273\) −0.582190 + 0.582190i −0.0352358 + 0.0352358i
\(274\) 0 0
\(275\) 2.47074 + 2.47074i 0.148991 + 0.148991i
\(276\) 0 0
\(277\) 7.44984 0.447618 0.223809 0.974633i \(-0.428151\pi\)
0.223809 + 0.974633i \(0.428151\pi\)
\(278\) 0 0
\(279\) 25.3133i 1.51547i
\(280\) 0 0
\(281\) 18.6123 18.6123i 1.11031 1.11031i 0.117207 0.993108i \(-0.462606\pi\)
0.993108 0.117207i \(-0.0373941\pi\)
\(282\) 0 0
\(283\) 21.0100 1.24891 0.624457 0.781059i \(-0.285320\pi\)
0.624457 + 0.781059i \(0.285320\pi\)
\(284\) 0 0
\(285\) 0.593403i 0.0351502i
\(286\) 0 0
\(287\) 5.34476 3.52613i 0.315491 0.208141i
\(288\) 0 0
\(289\) 16.2881i 0.958122i
\(290\) 0 0
\(291\) −2.51108 −0.147202
\(292\) 0 0
\(293\) −3.02331 + 3.02331i −0.176624 + 0.176624i −0.789882 0.613259i \(-0.789858\pi\)
0.613259 + 0.789882i \(0.289858\pi\)
\(294\) 0 0
\(295\) 5.03276i 0.293019i
\(296\) 0 0
\(297\) 1.10983 0.0643990
\(298\) 0 0
\(299\) 7.76618 + 7.76618i 0.449130 + 0.449130i
\(300\) 0 0
\(301\) −5.02671 + 5.02671i −0.289735 + 0.289735i
\(302\) 0 0
\(303\) 1.46964 0.0844287
\(304\) 0 0
\(305\) −3.53179 −0.202230
\(306\) 0 0
\(307\) 27.1611i 1.55017i 0.631858 + 0.775084i \(0.282292\pi\)
−0.631858 + 0.775084i \(0.717708\pi\)
\(308\) 0 0
\(309\) −2.84358 + 2.84358i −0.161765 + 0.161765i
\(310\) 0 0
\(311\) 4.52300 4.52300i 0.256476 0.256476i −0.567143 0.823619i \(-0.691951\pi\)
0.823619 + 0.567143i \(0.191951\pi\)
\(312\) 0 0
\(313\) −12.7717 + 12.7717i −0.721899 + 0.721899i −0.968992 0.247093i \(-0.920525\pi\)
0.247093 + 0.968992i \(0.420525\pi\)
\(314\) 0 0
\(315\) 1.12613 + 1.12613i 0.0634503 + 0.0634503i
\(316\) 0 0
\(317\) −23.3262 23.3262i −1.31013 1.31013i −0.921315 0.388816i \(-0.872884\pi\)
−0.388816 0.921315i \(-0.627116\pi\)
\(318\) 0 0
\(319\) 6.89739i 0.386180i
\(320\) 0 0
\(321\) 0.825248 + 0.825248i 0.0460609 + 0.0460609i
\(322\) 0 0
\(323\) 3.66682i 0.204027i
\(324\) 0 0
\(325\) −10.8815 10.8815i −0.603595 0.603595i
\(326\) 0 0
\(327\) 3.58772 0.198401
\(328\) 0 0
\(329\) −6.96035 −0.383736
\(330\) 0 0
\(331\) −5.71859 5.71859i −0.314322 0.314322i 0.532259 0.846581i \(-0.321343\pi\)
−0.846581 + 0.532259i \(0.821343\pi\)
\(332\) 0 0
\(333\) 4.44740i 0.243716i
\(334\) 0 0
\(335\) −0.983555 0.983555i −0.0537373 0.0537373i
\(336\) 0 0
\(337\) 13.5107i 0.735973i −0.929831 0.367987i \(-0.880047\pi\)
0.929831 0.367987i \(-0.119953\pi\)
\(338\) 0 0
\(339\) 0.487328 + 0.487328i 0.0264681 + 0.0264681i
\(340\) 0 0
\(341\) −4.52573 4.52573i −0.245082 0.245082i
\(342\) 0 0
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) 0 0
\(345\) −0.324282 + 0.324282i −0.0174588 + 0.0174588i
\(346\) 0 0
\(347\) 23.7234 23.7234i 1.27354 1.27354i 0.329323 0.944217i \(-0.393180\pi\)
0.944217 0.329323i \(-0.106820\pi\)
\(348\) 0 0
\(349\) 32.5406i 1.74186i −0.491406 0.870930i \(-0.663517\pi\)
0.491406 0.870930i \(-0.336483\pi\)
\(350\) 0 0
\(351\) −4.88785 −0.260894
\(352\) 0 0
\(353\) −24.1907 −1.28754 −0.643772 0.765218i \(-0.722631\pi\)
−0.643772 + 0.765218i \(0.722631\pi\)
\(354\) 0 0
\(355\) −3.50868 + 3.50868i −0.186221 + 0.186221i
\(356\) 0 0
\(357\) −0.150217 0.150217i −0.00795034 0.00795034i
\(358\) 0 0
\(359\) 14.4843 0.764451 0.382225 0.924069i \(-0.375158\pi\)
0.382225 + 0.924069i \(0.375158\pi\)
\(360\) 0 0
\(361\) 0.113719i 0.00598523i
\(362\) 0 0
\(363\) 1.86022 1.86022i 0.0976365 0.0976365i
\(364\) 0 0
\(365\) −6.58528 −0.344689
\(366\) 0 0
\(367\) 1.24383i 0.0649276i 0.999473 + 0.0324638i \(0.0103354\pi\)
−0.999473 + 0.0324638i \(0.989665\pi\)
\(368\) 0 0
\(369\) 18.4203 + 3.77637i 0.958925 + 0.196590i
\(370\) 0 0
\(371\) 4.64322i 0.241064i
\(372\) 0 0
\(373\) 29.8916 1.54773 0.773865 0.633350i \(-0.218321\pi\)
0.773865 + 0.633350i \(0.218321\pi\)
\(374\) 0 0
\(375\) 0.937124 0.937124i 0.0483929 0.0483929i
\(376\) 0 0
\(377\) 30.3770i 1.56450i
\(378\) 0 0
\(379\) 19.9846 1.02654 0.513270 0.858227i \(-0.328434\pi\)
0.513270 + 0.858227i \(0.328434\pi\)
\(380\) 0 0
\(381\) 2.30629 + 2.30629i 0.118155 + 0.118155i
\(382\) 0 0
\(383\) −13.8655 + 13.8655i −0.708493 + 0.708493i −0.966218 0.257725i \(-0.917027\pi\)
0.257725 + 0.966218i \(0.417027\pi\)
\(384\) 0 0
\(385\) −0.402678 −0.0205224
\(386\) 0 0
\(387\) −20.8759 −1.06118
\(388\) 0 0
\(389\) 2.77902i 0.140902i 0.997515 + 0.0704510i \(0.0224439\pi\)
−0.997515 + 0.0704510i \(0.977556\pi\)
\(390\) 0 0
\(391\) −2.00384 + 2.00384i −0.101338 + 0.101338i
\(392\) 0 0
\(393\) 0.141337 0.141337i 0.00712949 0.00712949i
\(394\) 0 0
\(395\) 5.53553 5.53553i 0.278523 0.278523i
\(396\) 0 0
\(397\) −0.847681 0.847681i −0.0425439 0.0425439i 0.685515 0.728059i \(-0.259577\pi\)
−0.728059 + 0.685515i \(0.759577\pi\)
\(398\) 0 0
\(399\) 0.773708 + 0.773708i 0.0387338 + 0.0387338i
\(400\) 0 0
\(401\) 10.4156i 0.520132i −0.965591 0.260066i \(-0.916256\pi\)
0.965591 0.260066i \(-0.0837443\pi\)
\(402\) 0 0
\(403\) 19.9319 + 19.9319i 0.992881 + 0.992881i
\(404\) 0 0
\(405\) 4.57367i 0.227268i
\(406\) 0 0
\(407\) −0.795143 0.795143i −0.0394138 0.0394138i
\(408\) 0 0
\(409\) 33.0820 1.63580 0.817901 0.575359i \(-0.195138\pi\)
0.817901 + 0.575359i \(0.195138\pi\)
\(410\) 0 0
\(411\) −2.80201 −0.138213
\(412\) 0 0
\(413\) −6.56196 6.56196i −0.322893 0.322893i
\(414\) 0 0
\(415\) 3.83170i 0.188091i
\(416\) 0 0
\(417\) −0.124095 0.124095i −0.00607694 0.00607694i
\(418\) 0 0
\(419\) 22.3241i 1.09060i −0.838240 0.545301i \(-0.816415\pi\)
0.838240 0.545301i \(-0.183585\pi\)
\(420\) 0 0
\(421\) −20.0024 20.0024i −0.974855 0.974855i 0.0248364 0.999692i \(-0.492094\pi\)
−0.999692 + 0.0248364i \(0.992094\pi\)
\(422\) 0 0
\(423\) −14.4531 14.4531i −0.702735 0.702735i
\(424\) 0 0
\(425\) 2.80765 2.80765i 0.136191 0.136191i
\(426\) 0 0
\(427\) −4.60492 + 4.60492i −0.222847 + 0.222847i
\(428\) 0 0
\(429\) 0.432280 0.432280i 0.0208707 0.0208707i
\(430\) 0 0
\(431\) 3.47963i 0.167608i 0.996482 + 0.0838039i \(0.0267069\pi\)
−0.996482 + 0.0838039i \(0.973293\pi\)
\(432\) 0 0
\(433\) 14.1883 0.681848 0.340924 0.940091i \(-0.389260\pi\)
0.340924 + 0.940091i \(0.389260\pi\)
\(434\) 0 0
\(435\) −1.26841 −0.0608158
\(436\) 0 0
\(437\) 10.3209 10.3209i 0.493718 0.493718i
\(438\) 0 0
\(439\) 19.7765 + 19.7765i 0.943881 + 0.943881i 0.998507 0.0546263i \(-0.0173968\pi\)
−0.0546263 + 0.998507i \(0.517397\pi\)
\(440\) 0 0
\(441\) 2.93661 0.139838
\(442\) 0 0
\(443\) 11.7065i 0.556193i −0.960553 0.278096i \(-0.910296\pi\)
0.960553 0.278096i \(-0.0897035\pi\)
\(444\) 0 0
\(445\) −1.49726 + 1.49726i −0.0709768 + 0.0709768i
\(446\) 0 0
\(447\) −4.07850 −0.192906
\(448\) 0 0
\(449\) 5.26429i 0.248437i −0.992255 0.124219i \(-0.960358\pi\)
0.992255 0.124219i \(-0.0396424\pi\)
\(450\) 0 0
\(451\) −3.96852 + 2.61817i −0.186870 + 0.123285i
\(452\) 0 0
\(453\) 4.80512i 0.225764i
\(454\) 0 0
\(455\) 1.77345 0.0831406
\(456\) 0 0
\(457\) −12.6685 + 12.6685i −0.592608 + 0.592608i −0.938335 0.345727i \(-0.887632\pi\)
0.345727 + 0.938335i \(0.387632\pi\)
\(458\) 0 0
\(459\) 1.26117i 0.0588663i
\(460\) 0 0
\(461\) −33.5860 −1.56425 −0.782127 0.623119i \(-0.785865\pi\)
−0.782127 + 0.623119i \(0.785865\pi\)
\(462\) 0 0
\(463\) −11.9326 11.9326i −0.554555 0.554555i 0.373197 0.927752i \(-0.378262\pi\)
−0.927752 + 0.373197i \(0.878262\pi\)
\(464\) 0 0
\(465\) −0.832272 + 0.832272i −0.0385957 + 0.0385957i
\(466\) 0 0
\(467\) −17.5318 −0.811277 −0.405638 0.914034i \(-0.632951\pi\)
−0.405638 + 0.914034i \(0.632951\pi\)
\(468\) 0 0
\(469\) −2.56481 −0.118432
\(470\) 0 0
\(471\) 0.387795i 0.0178687i
\(472\) 0 0
\(473\) 3.73237 3.73237i 0.171614 0.171614i
\(474\) 0 0
\(475\) −14.4610 + 14.4610i −0.663518 + 0.663518i
\(476\) 0 0
\(477\) −9.64162 + 9.64162i −0.441459 + 0.441459i
\(478\) 0 0
\(479\) −16.6065 16.6065i −0.758772 0.758772i 0.217327 0.976099i \(-0.430266\pi\)
−0.976099 + 0.217327i \(0.930266\pi\)
\(480\) 0 0
\(481\) 3.50192 + 3.50192i 0.159674 + 0.159674i
\(482\) 0 0
\(483\) 0.845630i 0.0384775i
\(484\) 0 0
\(485\) 3.82458 + 3.82458i 0.173665 + 0.173665i
\(486\) 0 0
\(487\) 42.1727i 1.91103i −0.294947 0.955514i \(-0.595302\pi\)
0.294947 0.955514i \(-0.404698\pi\)
\(488\) 0 0
\(489\) 1.25145 + 1.25145i 0.0565926 + 0.0565926i
\(490\) 0 0
\(491\) −1.47451 −0.0665436 −0.0332718 0.999446i \(-0.510593\pi\)
−0.0332718 + 0.999446i \(0.510593\pi\)
\(492\) 0 0
\(493\) −7.83791 −0.353002
\(494\) 0 0
\(495\) −0.836159 0.836159i −0.0375826 0.0375826i
\(496\) 0 0
\(497\) 9.14957i 0.410414i
\(498\) 0 0
\(499\) 0.702287 + 0.702287i 0.0314387 + 0.0314387i 0.722651 0.691213i \(-0.242923\pi\)
−0.691213 + 0.722651i \(0.742923\pi\)
\(500\) 0 0
\(501\) 5.29651i 0.236630i
\(502\) 0 0
\(503\) 0.729439 + 0.729439i 0.0325241 + 0.0325241i 0.723182 0.690658i \(-0.242679\pi\)
−0.690658 + 0.723182i \(0.742679\pi\)
\(504\) 0 0
\(505\) −2.23839 2.23839i −0.0996069 0.0996069i
\(506\) 0 0
\(507\) 0.410626 0.410626i 0.0182366 0.0182366i
\(508\) 0 0
\(509\) −14.6468 + 14.6468i −0.649209 + 0.649209i −0.952802 0.303593i \(-0.901814\pi\)
0.303593 + 0.952802i \(0.401814\pi\)
\(510\) 0 0
\(511\) −8.58621 + 8.58621i −0.379832 + 0.379832i
\(512\) 0 0
\(513\) 6.49577i 0.286795i
\(514\) 0 0
\(515\) 8.66201 0.381694
\(516\) 0 0
\(517\) 5.16811 0.227293
\(518\) 0 0
\(519\) −3.11595 + 3.11595i −0.136775 + 0.136775i
\(520\) 0 0
\(521\) 3.48443 + 3.48443i 0.152656 + 0.152656i 0.779303 0.626647i \(-0.215573\pi\)
−0.626647 + 0.779303i \(0.715573\pi\)
\(522\) 0 0
\(523\) −20.6067 −0.901066 −0.450533 0.892760i \(-0.648766\pi\)
−0.450533 + 0.892760i \(0.648766\pi\)
\(524\) 0 0
\(525\) 1.18484i 0.0517107i
\(526\) 0 0
\(527\) −5.14286 + 5.14286i −0.224026 + 0.224026i
\(528\) 0 0
\(529\) −11.7196 −0.509550
\(530\) 0 0
\(531\) 27.2517i 1.18263i
\(532\) 0 0
\(533\) 17.4779 11.5308i 0.757051 0.499454i
\(534\) 0 0
\(535\) 2.51385i 0.108683i
\(536\) 0 0
\(537\) 0.911212 0.0393217
\(538\) 0 0
\(539\) −0.525032 + 0.525032i −0.0226147 + 0.0226147i
\(540\) 0 0
\(541\) 29.0500i 1.24896i −0.781041 0.624479i \(-0.785311\pi\)
0.781041 0.624479i \(-0.214689\pi\)
\(542\) 0 0
\(543\) 3.28300 0.140887
\(544\) 0 0
\(545\) −5.46440 5.46440i −0.234069 0.234069i
\(546\) 0 0
\(547\) 28.2391 28.2391i 1.20742 1.20742i 0.235558 0.971860i \(-0.424308\pi\)
0.971860 0.235558i \(-0.0756918\pi\)
\(548\) 0 0
\(549\) −19.1242 −0.816200
\(550\) 0 0
\(551\) 40.3699 1.71981
\(552\) 0 0
\(553\) 14.4350i 0.613838i
\(554\) 0 0
\(555\) −0.146225 + 0.146225i −0.00620691 + 0.00620691i
\(556\) 0 0
\(557\) −28.4820 + 28.4820i −1.20682 + 1.20682i −0.234769 + 0.972051i \(0.575433\pi\)
−0.972051 + 0.234769i \(0.924567\pi\)
\(558\) 0 0
\(559\) −16.4379 + 16.4379i −0.695247 + 0.695247i
\(560\) 0 0
\(561\) 0.111537 + 0.111537i 0.00470911 + 0.00470911i
\(562\) 0 0
\(563\) −30.2705 30.2705i −1.27575 1.27575i −0.943023 0.332726i \(-0.892032\pi\)
−0.332726 0.943023i \(-0.607968\pi\)
\(564\) 0 0
\(565\) 1.48448i 0.0624527i
\(566\) 0 0
\(567\) 5.96338 + 5.96338i 0.250438 + 0.250438i
\(568\) 0 0
\(569\) 19.7654i 0.828609i 0.910138 + 0.414304i \(0.135975\pi\)
−0.910138 + 0.414304i \(0.864025\pi\)
\(570\) 0 0
\(571\) −15.0922 15.0922i −0.631587 0.631587i 0.316879 0.948466i \(-0.397365\pi\)
−0.948466 + 0.316879i \(0.897365\pi\)
\(572\) 0 0
\(573\) −5.31828 −0.222174
\(574\) 0 0
\(575\) −15.8053 −0.659127
\(576\) 0 0
\(577\) 2.39982 + 2.39982i 0.0999058 + 0.0999058i 0.755293 0.655387i \(-0.227495\pi\)
−0.655387 + 0.755293i \(0.727495\pi\)
\(578\) 0 0
\(579\) 3.96531i 0.164793i
\(580\) 0 0
\(581\) 4.99596 + 4.99596i 0.207267 + 0.207267i
\(582\) 0 0
\(583\) 3.44762i 0.142786i
\(584\) 0 0
\(585\) 3.68256 + 3.68256i 0.152255 + 0.152255i
\(586\) 0 0
\(587\) −18.8590 18.8590i −0.778392 0.778392i 0.201165 0.979557i \(-0.435527\pi\)
−0.979557 + 0.201165i \(0.935527\pi\)
\(588\) 0 0
\(589\) 26.4888 26.4888i 1.09145 1.09145i
\(590\) 0 0
\(591\) 4.25879 4.25879i 0.175183 0.175183i
\(592\) 0 0
\(593\) −8.60759 + 8.60759i −0.353471 + 0.353471i −0.861399 0.507928i \(-0.830412\pi\)
0.507928 + 0.861399i \(0.330412\pi\)
\(594\) 0 0
\(595\) 0.457587i 0.0187592i
\(596\) 0 0
\(597\) 1.10913 0.0453937
\(598\) 0 0
\(599\) 2.60470 0.106425 0.0532125 0.998583i \(-0.483054\pi\)
0.0532125 + 0.998583i \(0.483054\pi\)
\(600\) 0 0
\(601\) 18.1861 18.1861i 0.741827 0.741827i −0.231102 0.972930i \(-0.574233\pi\)
0.972930 + 0.231102i \(0.0742331\pi\)
\(602\) 0 0
\(603\) −5.32582 5.32582i −0.216884 0.216884i
\(604\) 0 0
\(605\) −5.66656 −0.230378
\(606\) 0 0
\(607\) 15.3043i 0.621182i −0.950544 0.310591i \(-0.899473\pi\)
0.950544 0.310591i \(-0.100527\pi\)
\(608\) 0 0
\(609\) −1.65382 + 1.65382i −0.0670161 + 0.0670161i
\(610\) 0 0
\(611\) −22.7610 −0.920813
\(612\) 0 0
\(613\) 23.9660i 0.967979i −0.875074 0.483990i \(-0.839187\pi\)
0.875074 0.483990i \(-0.160813\pi\)
\(614\) 0 0
\(615\) 0.481476 + 0.729801i 0.0194150 + 0.0294284i
\(616\) 0 0
\(617\) 15.5475i 0.625917i −0.949767 0.312959i \(-0.898680\pi\)
0.949767 0.312959i \(-0.101320\pi\)
\(618\) 0 0
\(619\) −7.03135 −0.282614 −0.141307 0.989966i \(-0.545130\pi\)
−0.141307 + 0.989966i \(0.545130\pi\)
\(620\) 0 0
\(621\) −3.54980 + 3.54980i −0.142448 + 0.142448i
\(622\) 0 0
\(623\) 3.90440i 0.156426i
\(624\) 0 0
\(625\) 20.6748 0.826992
\(626\) 0 0
\(627\) −0.574483 0.574483i −0.0229427 0.0229427i
\(628\) 0 0
\(629\) −0.903568 + 0.903568i −0.0360276 + 0.0360276i
\(630\) 0 0
\(631\) −12.1914 −0.485332 −0.242666 0.970110i \(-0.578022\pi\)
−0.242666 + 0.970110i \(0.578022\pi\)
\(632\) 0 0
\(633\) 3.29364 0.130910
\(634\) 0 0
\(635\) 7.02534i 0.278792i
\(636\) 0 0
\(637\) 2.31231 2.31231i 0.0916171 0.0916171i
\(638\) 0 0
\(639\) −18.9990 + 18.9990i −0.751590 + 0.751590i
\(640\) 0 0
\(641\) 6.18625 6.18625i 0.244342 0.244342i −0.574302 0.818644i \(-0.694726\pi\)
0.818644 + 0.574302i \(0.194726\pi\)
\(642\) 0 0
\(643\) 4.79421 + 4.79421i 0.189065 + 0.189065i 0.795292 0.606227i \(-0.207318\pi\)
−0.606227 + 0.795292i \(0.707318\pi\)
\(644\) 0 0
\(645\) −0.686374 0.686374i −0.0270259 0.0270259i
\(646\) 0 0
\(647\) 26.8812i 1.05681i 0.848993 + 0.528404i \(0.177209\pi\)
−0.848993 + 0.528404i \(0.822791\pi\)
\(648\) 0 0
\(649\) 4.87230 + 4.87230i 0.191254 + 0.191254i
\(650\) 0 0
\(651\) 2.17031i 0.0850613i
\(652\) 0 0
\(653\) 9.53665 + 9.53665i 0.373198 + 0.373198i 0.868641 0.495443i \(-0.164994\pi\)
−0.495443 + 0.868641i \(0.664994\pi\)
\(654\) 0 0
\(655\) −0.430535 −0.0168224
\(656\) 0 0
\(657\) −35.6585 −1.39117
\(658\) 0 0
\(659\) −33.3554 33.3554i −1.29934 1.29934i −0.928826 0.370516i \(-0.879181\pi\)
−0.370516 0.928826i \(-0.620819\pi\)
\(660\) 0 0
\(661\) 41.2348i 1.60385i −0.597425 0.801925i \(-0.703809\pi\)
0.597425 0.801925i \(-0.296191\pi\)
\(662\) 0 0
\(663\) −0.491226 0.491226i −0.0190776 0.0190776i
\(664\) 0 0
\(665\) 2.35684i 0.0913945i
\(666\) 0 0
\(667\) 22.0613 + 22.0613i 0.854216 + 0.854216i
\(668\) 0 0
\(669\) 2.62615 + 2.62615i 0.101533 + 0.101533i
\(670\) 0 0
\(671\) 3.41918 3.41918i 0.131996 0.131996i
\(672\) 0 0
\(673\) 10.5127 10.5127i 0.405235 0.405235i −0.474838 0.880073i \(-0.657493\pi\)
0.880073 + 0.474838i \(0.157493\pi\)
\(674\) 0 0
\(675\) 4.97375 4.97375i 0.191440 0.191440i
\(676\) 0 0
\(677\) 16.7826i 0.645007i 0.946568 + 0.322504i \(0.104524\pi\)
−0.946568 + 0.322504i \(0.895476\pi\)
\(678\) 0 0
\(679\) 9.97335 0.382742
\(680\) 0 0
\(681\) −5.98731 −0.229434
\(682\) 0 0
\(683\) 3.85566 3.85566i 0.147533 0.147533i −0.629482 0.777015i \(-0.716733\pi\)
0.777015 + 0.629482i \(0.216733\pi\)
\(684\) 0 0
\(685\) 4.26769 + 4.26769i 0.163060 + 0.163060i
\(686\) 0 0
\(687\) −1.10009 −0.0419710
\(688\) 0 0
\(689\) 15.1838i 0.578456i
\(690\) 0 0
\(691\) 14.4058 14.4058i 0.548021 0.548021i −0.377847 0.925868i \(-0.623335\pi\)
0.925868 + 0.377847i \(0.123335\pi\)
\(692\) 0 0
\(693\) −2.18045 −0.0828285
\(694\) 0 0
\(695\) 0.378013i 0.0143389i
\(696\) 0 0
\(697\) 2.97519 + 4.50966i 0.112693 + 0.170816i
\(698\) 0 0
\(699\) 4.47359i 0.169207i
\(700\) 0 0
\(701\) 12.8055 0.483656 0.241828 0.970319i \(-0.422253\pi\)
0.241828 + 0.970319i \(0.422253\pi\)
\(702\) 0 0
\(703\) 4.65391 4.65391i 0.175526 0.175526i
\(704\) 0 0
\(705\) 0.950403i 0.0357942i
\(706\) 0 0
\(707\) −5.83704 −0.219524
\(708\) 0 0
\(709\) 15.9790 + 15.9790i 0.600106 + 0.600106i 0.940341 0.340235i \(-0.110507\pi\)
−0.340235 + 0.940341i \(0.610507\pi\)
\(710\) 0 0
\(711\) 29.9742 29.9742i 1.12412 1.12412i
\(712\) 0 0
\(713\) 28.9511 1.08423
\(714\) 0 0
\(715\) −1.31680 −0.0492455
\(716\) 0 0
\(717\) 0.167289i 0.00624752i
\(718\) 0 0
\(719\) 9.84421 9.84421i 0.367127 0.367127i −0.499301 0.866428i \(-0.666410\pi\)
0.866428 + 0.499301i \(0.166410\pi\)
\(720\) 0 0
\(721\) 11.2940 11.2940i 0.420609 0.420609i
\(722\) 0 0
\(723\) 3.54408 3.54408i 0.131806 0.131806i
\(724\) 0 0
\(725\) −30.9108 30.9108i −1.14800 1.14800i
\(726\) 0 0
\(727\) 28.7199 + 28.7199i 1.06516 + 1.06516i 0.997723 + 0.0674405i \(0.0214833\pi\)
0.0674405 + 0.997723i \(0.478517\pi\)
\(728\) 0 0
\(729\) 23.6368i 0.875438i
\(730\) 0 0
\(731\) −4.24131 4.24131i −0.156871 0.156871i
\(732\) 0 0
\(733\) 31.5061i 1.16370i −0.813295 0.581851i \(-0.802329\pi\)
0.813295 0.581851i \(-0.197671\pi\)
\(734\) 0 0
\(735\) 0.0965521 + 0.0965521i 0.00356138 + 0.00356138i
\(736\) 0 0
\(737\) 1.90439 0.0701491
\(738\) 0 0
\(739\) −46.1899 −1.69912 −0.849562 0.527489i \(-0.823134\pi\)
−0.849562 + 0.527489i \(0.823134\pi\)
\(740\) 0 0
\(741\) 2.53010 + 2.53010i 0.0929456 + 0.0929456i
\(742\) 0 0
\(743\) 21.0119i 0.770851i 0.922739 + 0.385425i \(0.125945\pi\)
−0.922739 + 0.385425i \(0.874055\pi\)
\(744\) 0 0
\(745\) 6.21189 + 6.21189i 0.227586 + 0.227586i
\(746\) 0 0
\(747\) 20.7482i 0.759135i
\(748\) 0 0
\(749\) −3.27767 3.27767i −0.119764 0.119764i
\(750\) 0 0
\(751\) −36.4416 36.4416i −1.32977 1.32977i −0.905566 0.424205i \(-0.860553\pi\)
−0.424205 0.905566i \(-0.639447\pi\)
\(752\) 0 0
\(753\) −5.37581 + 5.37581i −0.195905 + 0.195905i
\(754\) 0 0
\(755\) −7.31861 + 7.31861i −0.266351 + 0.266351i
\(756\) 0 0
\(757\) −14.6038 + 14.6038i −0.530785 + 0.530785i −0.920806 0.390021i \(-0.872468\pi\)
0.390021 + 0.920806i \(0.372468\pi\)
\(758\) 0 0
\(759\) 0.627886i 0.0227908i
\(760\) 0 0
\(761\) −51.3546 −1.86160 −0.930801 0.365525i \(-0.880889\pi\)
−0.930801 + 0.365525i \(0.880889\pi\)
\(762\) 0 0
\(763\) −14.2495 −0.515867
\(764\) 0 0
\(765\) −0.950177 + 0.950177i −0.0343537 + 0.0343537i
\(766\) 0 0
\(767\) −21.4583 21.4583i −0.774813 0.774813i
\(768\) 0 0
\(769\) 24.6372 0.888442 0.444221 0.895917i \(-0.353481\pi\)
0.444221 + 0.895917i \(0.353481\pi\)
\(770\) 0 0
\(771\) 5.17681i 0.186438i
\(772\) 0 0
\(773\) 13.4553 13.4553i 0.483954 0.483954i −0.422438 0.906392i \(-0.638826\pi\)
0.906392 + 0.422438i \(0.138826\pi\)
\(774\) 0 0
\(775\) −40.5644 −1.45712
\(776\) 0 0
\(777\) 0.381311i 0.0136794i
\(778\) 0 0
\(779\) −15.3240 23.2274i −0.549038 0.832209i
\(780\) 0 0
\(781\) 6.79362i 0.243095i
\(782\) 0 0
\(783\) −13.8849 −0.496204
\(784\) 0 0
\(785\) −0.590645 + 0.590645i −0.0210810 + 0.0210810i
\(786\) 0 0
\(787\) 17.6923i 0.630663i 0.948982 + 0.315332i \(0.102116\pi\)
−0.948982 + 0.315332i \(0.897884\pi\)
\(788\) 0 0
\(789\) 0.216466 0.00770639
\(790\) 0 0
\(791\) −1.93554 1.93554i −0.0688200 0.0688200i
\(792\) 0 0
\(793\) −15.0585 + 15.0585i −0.534744 + 0.534744i
\(794\) 0 0
\(795\) −0.634009 −0.0224860
\(796\) 0 0
\(797\) 13.6888 0.484883 0.242442 0.970166i \(-0.422052\pi\)
0.242442 + 0.970166i \(0.422052\pi\)
\(798\) 0 0
\(799\) 5.87282i 0.207766i
\(800\) 0 0