Properties

Label 1148.2.ba.a.113.4
Level $1148$
Weight $2$
Character 1148.113
Analytic conductor $9.167$
Analytic rank $0$
Dimension $80$
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.ba (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 113.4
Character \(\chi\) \(=\) 1148.113
Dual form 1148.2.ba.a.701.17

$q$-expansion

\(f(q)\) \(=\) \(q-2.09016i q^{3} +(-0.164331 - 0.505760i) q^{5} +(0.587785 + 0.809017i) q^{7} -1.36876 q^{9} +O(q^{10})\) \(q-2.09016i q^{3} +(-0.164331 - 0.505760i) q^{5} +(0.587785 + 0.809017i) q^{7} -1.36876 q^{9} +(4.19378 + 1.36264i) q^{11} +(0.411006 - 0.565701i) q^{13} +(-1.05712 + 0.343479i) q^{15} +(4.23116 + 1.37479i) q^{17} +(0.594887 + 0.818792i) q^{19} +(1.69097 - 1.22856i) q^{21} +(1.12468 + 0.817130i) q^{23} +(3.81630 - 2.77270i) q^{25} -3.40954i q^{27} +(-1.04111 + 0.338276i) q^{29} +(0.770024 - 2.36989i) q^{31} +(2.84814 - 8.76566i) q^{33} +(0.312577 - 0.430225i) q^{35} +(2.00349 + 6.16611i) q^{37} +(-1.18240 - 0.859067i) q^{39} +(-6.15241 + 1.77421i) q^{41} +(-6.05702 - 4.40069i) q^{43} +(0.224931 + 0.692266i) q^{45} +(4.37284 - 6.01869i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(2.87352 - 8.84379i) q^{51} +(-4.69734 + 1.52626i) q^{53} -2.34497i q^{55} +(1.71140 - 1.24341i) q^{57} +(1.18992 + 0.864530i) q^{59} +(3.97038 - 2.88465i) q^{61} +(-0.804539 - 1.10735i) q^{63} +(-0.353650 - 0.114908i) q^{65} +(7.41978 - 2.41083i) q^{67} +(1.70793 - 2.35077i) q^{69} +(-8.51336 - 2.76616i) q^{71} -11.9718 q^{73} +(-5.79539 - 7.97667i) q^{75} +(1.36264 + 4.19378i) q^{77} +7.66283i q^{79} -11.2328 q^{81} +12.3013 q^{83} -2.36587i q^{85} +(0.707050 + 2.17608i) q^{87} +(-6.03248 - 8.30300i) q^{89} +0.699244 q^{91} +(-4.95345 - 1.60947i) q^{93} +(0.316354 - 0.435423i) q^{95} +(-4.10362 + 1.33335i) q^{97} +(-5.74029 - 1.86513i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{5} - 60q^{9} + O(q^{10}) \) \( 80q - 4q^{5} - 60q^{9} + 10q^{11} + 20q^{15} - 10q^{17} - 30q^{19} - 4q^{21} - 20q^{25} + 2q^{31} + 10q^{33} + 10q^{37} + 36q^{39} - 14q^{41} + 30q^{43} + 44q^{45} - 60q^{47} + 20q^{49} - 32q^{51} + 16q^{57} - 60q^{59} + 44q^{61} - 10q^{65} - 10q^{67} - 40q^{71} - 88q^{73} - 70q^{75} - 8q^{77} - 40q^{81} + 28q^{83} - 24q^{87} + 24q^{91} - 100q^{93} + 120q^{97} - 100q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\)

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
\(3\) 2.09016i 1.20675i −0.797456 0.603377i \(-0.793821\pi\)
0.797456 0.603377i \(-0.206179\pi\)
\(4\) 0 0
\(5\) −0.164331 0.505760i −0.0734913 0.226183i 0.907563 0.419916i \(-0.137940\pi\)
−0.981054 + 0.193733i \(0.937940\pi\)
\(6\) 0 0
\(7\) 0.587785 + 0.809017i 0.222162 + 0.305780i
\(8\) 0 0
\(9\) −1.36876 −0.456255
\(10\) 0 0
\(11\) 4.19378 + 1.36264i 1.26447 + 0.410852i 0.863086 0.505057i \(-0.168529\pi\)
0.401386 + 0.915909i \(0.368529\pi\)
\(12\) 0 0
\(13\) 0.411006 0.565701i 0.113992 0.156897i −0.748208 0.663464i \(-0.769086\pi\)
0.862201 + 0.506567i \(0.169086\pi\)
\(14\) 0 0
\(15\) −1.05712 + 0.343479i −0.272947 + 0.0886859i
\(16\) 0 0
\(17\) 4.23116 + 1.37479i 1.02621 + 0.333435i 0.773289 0.634053i \(-0.218610\pi\)
0.252917 + 0.967488i \(0.418610\pi\)
\(18\) 0 0
\(19\) 0.594887 + 0.818792i 0.136476 + 0.187844i 0.871785 0.489889i \(-0.162963\pi\)
−0.735308 + 0.677733i \(0.762963\pi\)
\(20\) 0 0
\(21\) 1.69097 1.22856i 0.369001 0.268095i
\(22\) 0 0
\(23\) 1.12468 + 0.817130i 0.234513 + 0.170383i 0.698835 0.715283i \(-0.253702\pi\)
−0.464322 + 0.885666i \(0.653702\pi\)
\(24\) 0 0
\(25\) 3.81630 2.77270i 0.763259 0.554540i
\(26\) 0 0
\(27\) 3.40954i 0.656167i
\(28\) 0 0
\(29\) −1.04111 + 0.338276i −0.193329 + 0.0628162i −0.404081 0.914723i \(-0.632409\pi\)
0.210752 + 0.977539i \(0.432409\pi\)
\(30\) 0 0
\(31\) 0.770024 2.36989i 0.138300 0.425645i −0.857788 0.514003i \(-0.828162\pi\)
0.996089 + 0.0883582i \(0.0281620\pi\)
\(32\) 0 0
\(33\) 2.84814 8.76566i 0.495797 1.52591i
\(34\) 0 0
\(35\) 0.312577 0.430225i 0.0528352 0.0727214i
\(36\) 0 0
\(37\) 2.00349 + 6.16611i 0.329372 + 1.01370i 0.969428 + 0.245374i \(0.0789109\pi\)
−0.640057 + 0.768328i \(0.721089\pi\)
\(38\) 0 0
\(39\) −1.18240 0.859067i −0.189336 0.137561i
\(40\) 0 0
\(41\) −6.15241 + 1.77421i −0.960845 + 0.277086i
\(42\) 0 0
\(43\) −6.05702 4.40069i −0.923688 0.671098i 0.0207516 0.999785i \(-0.493394\pi\)
−0.944439 + 0.328686i \(0.893394\pi\)
\(44\) 0 0
\(45\) 0.224931 + 0.692266i 0.0335307 + 0.103197i
\(46\) 0 0
\(47\) 4.37284 6.01869i 0.637844 0.877917i −0.360654 0.932699i \(-0.617447\pi\)
0.998498 + 0.0547828i \(0.0174466\pi\)
\(48\) 0 0
\(49\) −0.309017 + 0.951057i −0.0441453 + 0.135865i
\(50\) 0 0
\(51\) 2.87352 8.84379i 0.402373 1.23838i
\(52\) 0 0
\(53\) −4.69734 + 1.52626i −0.645229 + 0.209648i −0.613309 0.789843i \(-0.710162\pi\)
−0.0319198 + 0.999490i \(0.510162\pi\)
\(54\) 0 0
\(55\) 2.34497i 0.316196i
\(56\) 0 0
\(57\) 1.71140 1.24341i 0.226681 0.164693i
\(58\) 0 0
\(59\) 1.18992 + 0.864530i 0.154915 + 0.112552i 0.662542 0.749024i \(-0.269477\pi\)
−0.507628 + 0.861577i \(0.669477\pi\)
\(60\) 0 0
\(61\) 3.97038 2.88465i 0.508356 0.369342i −0.303844 0.952722i \(-0.598270\pi\)
0.812199 + 0.583380i \(0.198270\pi\)
\(62\) 0 0
\(63\) −0.804539 1.10735i −0.101362 0.139513i
\(64\) 0 0
\(65\) −0.353650 0.114908i −0.0438649 0.0142526i
\(66\) 0 0
\(67\) 7.41978 2.41083i 0.906470 0.294530i 0.181565 0.983379i \(-0.441884\pi\)
0.724905 + 0.688849i \(0.241884\pi\)
\(68\) 0 0
\(69\) 1.70793 2.35077i 0.205611 0.282999i
\(70\) 0 0
\(71\) −8.51336 2.76616i −1.01035 0.328283i −0.243356 0.969937i \(-0.578248\pi\)
−0.766994 + 0.641654i \(0.778248\pi\)
\(72\) 0 0
\(73\) −11.9718 −1.40119 −0.700597 0.713558i \(-0.747083\pi\)
−0.700597 + 0.713558i \(0.747083\pi\)
\(74\) 0 0
\(75\) −5.79539 7.97667i −0.669194 0.921066i
\(76\) 0 0
\(77\) 1.36264 + 4.19378i 0.155287 + 0.477925i
\(78\) 0 0
\(79\) 7.66283i 0.862135i 0.902320 + 0.431068i \(0.141863\pi\)
−0.902320 + 0.431068i \(0.858137\pi\)
\(80\) 0 0
\(81\) −11.2328 −1.24809
\(82\) 0 0
\(83\) 12.3013 1.35025 0.675123 0.737705i \(-0.264091\pi\)
0.675123 + 0.737705i \(0.264091\pi\)
\(84\) 0 0
\(85\) 2.36587i 0.256615i
\(86\) 0 0
\(87\) 0.707050 + 2.17608i 0.0758037 + 0.233300i
\(88\) 0 0
\(89\) −6.03248 8.30300i −0.639442 0.880116i 0.359144 0.933282i \(-0.383069\pi\)
−0.998586 + 0.0531661i \(0.983069\pi\)
\(90\) 0 0
\(91\) 0.699244 0.0733007
\(92\) 0 0
\(93\) −4.95345 1.60947i −0.513648 0.166894i
\(94\) 0 0
\(95\) 0.316354 0.435423i 0.0324572 0.0446735i
\(96\) 0 0
\(97\) −4.10362 + 1.33335i −0.416660 + 0.135381i −0.509842 0.860268i \(-0.670296\pi\)
0.0931822 + 0.995649i \(0.470296\pi\)
\(98\) 0 0
\(99\) −5.74029 1.86513i −0.576921 0.187453i
\(100\) 0 0
\(101\) −5.84818 8.04933i −0.581915 0.800938i 0.411988 0.911189i \(-0.364834\pi\)
−0.993904 + 0.110251i \(0.964834\pi\)
\(102\) 0 0
\(103\) 3.24756 2.35949i 0.319991 0.232487i −0.416181 0.909282i \(-0.636632\pi\)
0.736172 + 0.676795i \(0.236632\pi\)
\(104\) 0 0
\(105\) −0.899239 0.653336i −0.0877568 0.0637590i
\(106\) 0 0
\(107\) 5.50446 3.99923i 0.532136 0.386620i −0.289020 0.957323i \(-0.593329\pi\)
0.821156 + 0.570703i \(0.193329\pi\)
\(108\) 0 0
\(109\) 13.9941i 1.34039i 0.742183 + 0.670197i \(0.233790\pi\)
−0.742183 + 0.670197i \(0.766210\pi\)
\(110\) 0 0
\(111\) 12.8882 4.18761i 1.22329 0.397471i
\(112\) 0 0
\(113\) −1.03197 + 3.17609i −0.0970798 + 0.298781i −0.987790 0.155790i \(-0.950208\pi\)
0.890710 + 0.454571i \(0.150208\pi\)
\(114\) 0 0
\(115\) 0.228451 0.703101i 0.0213032 0.0655645i
\(116\) 0 0
\(117\) −0.562570 + 0.774311i −0.0520096 + 0.0715850i
\(118\) 0 0
\(119\) 1.37479 + 4.23116i 0.126026 + 0.387869i
\(120\) 0 0
\(121\) 6.83180 + 4.96359i 0.621072 + 0.451235i
\(122\) 0 0
\(123\) 3.70839 + 12.8595i 0.334374 + 1.15950i
\(124\) 0 0
\(125\) −4.18059 3.03737i −0.373923 0.271671i
\(126\) 0 0
\(127\) 0.157532 + 0.484833i 0.0139787 + 0.0430220i 0.957803 0.287427i \(-0.0927999\pi\)
−0.943824 + 0.330449i \(0.892800\pi\)
\(128\) 0 0
\(129\) −9.19813 + 12.6601i −0.809850 + 1.11466i
\(130\) 0 0
\(131\) 5.27596 16.2377i 0.460963 1.41870i −0.403027 0.915188i \(-0.632042\pi\)
0.863989 0.503510i \(-0.167958\pi\)
\(132\) 0 0
\(133\) −0.312751 + 0.962547i −0.0271189 + 0.0834634i
\(134\) 0 0
\(135\) −1.72441 + 0.560295i −0.148414 + 0.0482225i
\(136\) 0 0
\(137\) 3.21400i 0.274590i 0.990530 + 0.137295i \(0.0438409\pi\)
−0.990530 + 0.137295i \(0.956159\pi\)
\(138\) 0 0
\(139\) 9.22169 6.69995i 0.782174 0.568282i −0.123457 0.992350i \(-0.539398\pi\)
0.905631 + 0.424067i \(0.139398\pi\)
\(140\) 0 0
\(141\) −12.5800 9.13992i −1.05943 0.769720i
\(142\) 0 0
\(143\) 2.49451 1.81237i 0.208602 0.151558i
\(144\) 0 0
\(145\) 0.342173 + 0.470961i 0.0284159 + 0.0391112i
\(146\) 0 0
\(147\) 1.98786 + 0.645895i 0.163956 + 0.0532725i
\(148\) 0 0
\(149\) 11.9970 3.89807i 0.982835 0.319343i 0.226849 0.973930i \(-0.427158\pi\)
0.755986 + 0.654587i \(0.227158\pi\)
\(150\) 0 0
\(151\) −9.73931 + 13.4050i −0.792574 + 1.09088i 0.201209 + 0.979548i \(0.435513\pi\)
−0.993783 + 0.111336i \(0.964487\pi\)
\(152\) 0 0
\(153\) −5.79145 1.88176i −0.468211 0.152131i
\(154\) 0 0
\(155\) −1.32514 −0.106437
\(156\) 0 0
\(157\) 5.36817 + 7.38865i 0.428426 + 0.589678i 0.967591 0.252522i \(-0.0812600\pi\)
−0.539165 + 0.842200i \(0.681260\pi\)
\(158\) 0 0
\(159\) 3.19012 + 9.81819i 0.252993 + 0.778633i
\(160\) 0 0
\(161\) 1.39019i 0.109562i
\(162\) 0 0
\(163\) 4.18387 0.327706 0.163853 0.986485i \(-0.447608\pi\)
0.163853 + 0.986485i \(0.447608\pi\)
\(164\) 0 0
\(165\) −4.90136 −0.381571
\(166\) 0 0
\(167\) 6.71271i 0.519445i −0.965683 0.259722i \(-0.916369\pi\)
0.965683 0.259722i \(-0.0836311\pi\)
\(168\) 0 0
\(169\) 3.86613 + 11.8987i 0.297395 + 0.915286i
\(170\) 0 0
\(171\) −0.814260 1.12073i −0.0622680 0.0857045i
\(172\) 0 0
\(173\) 2.19087 0.166569 0.0832843 0.996526i \(-0.473459\pi\)
0.0832843 + 0.996526i \(0.473459\pi\)
\(174\) 0 0
\(175\) 4.48633 + 1.45770i 0.339134 + 0.110191i
\(176\) 0 0
\(177\) 1.80701 2.48713i 0.135823 0.186944i
\(178\) 0 0
\(179\) 13.6309 4.42894i 1.01882 0.331035i 0.248459 0.968642i \(-0.420076\pi\)
0.770361 + 0.637608i \(0.220076\pi\)
\(180\) 0 0
\(181\) 9.10874 + 2.95961i 0.677047 + 0.219986i 0.627302 0.778776i \(-0.284159\pi\)
0.0497450 + 0.998762i \(0.484159\pi\)
\(182\) 0 0
\(183\) −6.02938 8.29873i −0.445705 0.613460i
\(184\) 0 0
\(185\) 2.78934 2.02657i 0.205076 0.148997i
\(186\) 0 0
\(187\) 15.8712 + 11.5311i 1.16062 + 0.843237i
\(188\) 0 0
\(189\) 2.75838 2.00408i 0.200642 0.145775i
\(190\) 0 0
\(191\) 7.99148i 0.578243i 0.957292 + 0.289122i \(0.0933632\pi\)
−0.957292 + 0.289122i \(0.906637\pi\)
\(192\) 0 0
\(193\) −16.2471 + 5.27900i −1.16949 + 0.379991i −0.828453 0.560059i \(-0.810779\pi\)
−0.341038 + 0.940049i \(0.610779\pi\)
\(194\) 0 0
\(195\) −0.240176 + 0.739185i −0.0171993 + 0.0529341i
\(196\) 0 0
\(197\) −5.29217 + 16.2876i −0.377052 + 1.16045i 0.565032 + 0.825069i \(0.308864\pi\)
−0.942084 + 0.335377i \(0.891136\pi\)
\(198\) 0 0
\(199\) −10.3393 + 14.2308i −0.732935 + 1.00880i 0.266059 + 0.963957i \(0.414278\pi\)
−0.998994 + 0.0448414i \(0.985722\pi\)
\(200\) 0 0
\(201\) −5.03902 15.5085i −0.355425 1.09389i
\(202\) 0 0
\(203\) −0.885618 0.643439i −0.0621582 0.0451606i
\(204\) 0 0
\(205\) 1.90836 + 2.82009i 0.133286 + 0.196963i
\(206\) 0 0
\(207\) −1.53943 1.11846i −0.106998 0.0777382i
\(208\) 0 0
\(209\) 1.37910 + 4.24445i 0.0953947 + 0.293595i
\(210\) 0 0
\(211\) −7.28537 + 10.0274i −0.501545 + 0.690318i −0.982465 0.186447i \(-0.940303\pi\)
0.480920 + 0.876765i \(0.340303\pi\)
\(212\) 0 0
\(213\) −5.78171 + 17.7943i −0.396156 + 1.21924i
\(214\) 0 0
\(215\) −1.23033 + 3.78657i −0.0839080 + 0.258242i
\(216\) 0 0
\(217\) 2.36989 0.770024i 0.160879 0.0522726i
\(218\) 0 0
\(219\) 25.0230i 1.69090i
\(220\) 0 0
\(221\) 2.51675 1.82852i 0.169295 0.123000i
\(222\) 0 0
\(223\) 3.09436 + 2.24818i 0.207213 + 0.150549i 0.686552 0.727081i \(-0.259123\pi\)
−0.479339 + 0.877630i \(0.659123\pi\)
\(224\) 0 0
\(225\) −5.22361 + 3.79517i −0.348241 + 0.253012i
\(226\) 0 0
\(227\) 9.86346 + 13.5759i 0.654661 + 0.901063i 0.999290 0.0376759i \(-0.0119954\pi\)
−0.344629 + 0.938739i \(0.611995\pi\)
\(228\) 0 0
\(229\) −21.7245 7.05873i −1.43560 0.466454i −0.515076 0.857145i \(-0.672236\pi\)
−0.920522 + 0.390690i \(0.872236\pi\)
\(230\) 0 0
\(231\) 8.76566 2.84814i 0.576738 0.187394i
\(232\) 0 0
\(233\) 11.9022 16.3820i 0.779741 1.07322i −0.215569 0.976489i \(-0.569161\pi\)
0.995310 0.0967330i \(-0.0308393\pi\)
\(234\) 0 0
\(235\) −3.76261 1.22255i −0.245446 0.0797501i
\(236\) 0 0
\(237\) 16.0165 1.04039
\(238\) 0 0
\(239\) −13.6842 18.8347i −0.885157 1.21831i −0.974966 0.222356i \(-0.928625\pi\)
0.0898083 0.995959i \(-0.471375\pi\)
\(240\) 0 0
\(241\) 3.44438 + 10.6007i 0.221872 + 0.682852i 0.998594 + 0.0530085i \(0.0168811\pi\)
−0.776722 + 0.629844i \(0.783119\pi\)
\(242\) 0 0
\(243\) 13.2497i 0.849966i
\(244\) 0 0
\(245\) 0.531788 0.0339747
\(246\) 0 0
\(247\) 0.707693 0.0450294
\(248\) 0 0
\(249\) 25.7117i 1.62941i
\(250\) 0 0
\(251\) 2.94175 + 9.05378i 0.185682 + 0.571469i 0.999959 0.00900608i \(-0.00286676\pi\)
−0.814278 + 0.580475i \(0.802867\pi\)
\(252\) 0 0
\(253\) 3.60322 + 4.95940i 0.226532 + 0.311795i
\(254\) 0 0
\(255\) −4.94505 −0.309671
\(256\) 0 0
\(257\) 15.7402 + 5.11431i 0.981848 + 0.319022i 0.755590 0.655045i \(-0.227351\pi\)
0.226259 + 0.974067i \(0.427351\pi\)
\(258\) 0 0
\(259\) −3.81087 + 5.24521i −0.236796 + 0.325921i
\(260\) 0 0
\(261\) 1.42503 0.463020i 0.0882070 0.0286602i
\(262\) 0 0
\(263\) 3.99739 + 1.29883i 0.246489 + 0.0800892i 0.429656 0.902993i \(-0.358635\pi\)
−0.183167 + 0.983082i \(0.558635\pi\)
\(264\) 0 0
\(265\) 1.54384 + 2.12492i 0.0948374 + 0.130533i
\(266\) 0 0
\(267\) −17.3546 + 12.6088i −1.06208 + 0.771649i
\(268\) 0 0
\(269\) −7.16162 5.20322i −0.436652 0.317246i 0.347651 0.937624i \(-0.386979\pi\)
−0.784303 + 0.620378i \(0.786979\pi\)
\(270\) 0 0
\(271\) −11.8355 + 8.59903i −0.718958 + 0.522354i −0.886051 0.463587i \(-0.846562\pi\)
0.167093 + 0.985941i \(0.446562\pi\)
\(272\) 0 0
\(273\) 1.46153i 0.0884559i
\(274\) 0 0
\(275\) 19.7829 6.42785i 1.19295 0.387614i
\(276\) 0 0
\(277\) −8.58916 + 26.4347i −0.516072 + 1.58831i 0.265250 + 0.964180i \(0.414545\pi\)
−0.781322 + 0.624128i \(0.785455\pi\)
\(278\) 0 0
\(279\) −1.05398 + 3.24382i −0.0631002 + 0.194202i
\(280\) 0 0
\(281\) −1.79500 + 2.47060i −0.107081 + 0.147384i −0.859194 0.511650i \(-0.829035\pi\)
0.752113 + 0.659034i \(0.229035\pi\)
\(282\) 0 0
\(283\) −3.91798 12.0583i −0.232900 0.716791i −0.997393 0.0721598i \(-0.977011\pi\)
0.764494 0.644631i \(-0.222989\pi\)
\(284\) 0 0
\(285\) −0.910104 0.661229i −0.0539099 0.0391678i
\(286\) 0 0
\(287\) −5.05167 3.93455i −0.298190 0.232249i
\(288\) 0 0
\(289\) 2.25936 + 1.64152i 0.132903 + 0.0965599i
\(290\) 0 0
\(291\) 2.78691 + 8.57722i 0.163371 + 0.502806i
\(292\) 0 0
\(293\) −11.4707 + 15.7881i −0.670126 + 0.922349i −0.999763 0.0217584i \(-0.993074\pi\)
0.329637 + 0.944108i \(0.393074\pi\)
\(294\) 0 0
\(295\) 0.241703 0.743886i 0.0140725 0.0433107i
\(296\) 0 0
\(297\) 4.64598 14.2989i 0.269587 0.829704i
\(298\) 0 0
\(299\) 0.924502 0.300389i 0.0534654 0.0173719i
\(300\) 0 0
\(301\) 7.48689i 0.431537i
\(302\) 0 0
\(303\) −16.8244 + 12.2236i −0.966535 + 0.702229i
\(304\) 0 0
\(305\) −2.11140 1.53402i −0.120899 0.0878379i
\(306\) 0 0
\(307\) 18.8431 13.6903i 1.07543 0.781347i 0.0985514 0.995132i \(-0.468579\pi\)
0.976881 + 0.213785i \(0.0685791\pi\)
\(308\) 0 0
\(309\) −4.93170 6.78791i −0.280555 0.386151i
\(310\) 0 0
\(311\) −24.8796 8.08388i −1.41079 0.458395i −0.498129 0.867103i \(-0.665979\pi\)
−0.912665 + 0.408709i \(0.865979\pi\)
\(312\) 0 0
\(313\) 1.22612 0.398391i 0.0693045 0.0225184i −0.274160 0.961684i \(-0.588400\pi\)
0.343464 + 0.939166i \(0.388400\pi\)
\(314\) 0 0
\(315\) −0.427844 + 0.588877i −0.0241063 + 0.0331795i
\(316\) 0 0
\(317\) −20.1245 6.53885i −1.13031 0.367258i −0.316613 0.948555i \(-0.602546\pi\)
−0.813692 + 0.581296i \(0.802546\pi\)
\(318\) 0 0
\(319\) −4.82712 −0.270267
\(320\) 0 0
\(321\) −8.35902 11.5052i −0.466555 0.642158i
\(322\) 0 0
\(323\) 1.39140 + 4.28228i 0.0774194 + 0.238272i
\(324\) 0 0
\(325\) 3.29848i 0.182967i
\(326\) 0 0
\(327\) 29.2500 1.61753
\(328\) 0 0
\(329\) 7.43951 0.410154
\(330\) 0 0
\(331\) 12.8541i 0.706524i −0.935524 0.353262i \(-0.885072\pi\)
0.935524 0.353262i \(-0.114928\pi\)
\(332\) 0 0
\(333\) −2.74231 8.43995i −0.150277 0.462506i
\(334\) 0 0
\(335\) −2.43861 3.35645i −0.133235 0.183383i
\(336\) 0 0
\(337\) −21.6746 −1.18069 −0.590345 0.807151i \(-0.701008\pi\)
−0.590345 + 0.807151i \(0.701008\pi\)
\(338\) 0 0
\(339\) 6.63852 + 2.15699i 0.360555 + 0.117151i
\(340\) 0 0
\(341\) 6.45862 8.88953i 0.349754 0.481395i
\(342\) 0 0
\(343\) −0.951057 + 0.309017i −0.0513522 + 0.0166853i
\(344\) 0 0
\(345\) −1.46959 0.477499i −0.0791202 0.0257077i
\(346\) 0 0
\(347\) 9.04223 + 12.4456i 0.485412 + 0.668113i 0.979534 0.201280i \(-0.0645102\pi\)
−0.494121 + 0.869393i \(0.664510\pi\)
\(348\) 0 0
\(349\) −20.8550 + 15.1521i −1.11634 + 0.811072i −0.983651 0.180085i \(-0.942363\pi\)
−0.132693 + 0.991157i \(0.542363\pi\)
\(350\) 0 0
\(351\) −1.92878 1.40134i −0.102951 0.0747981i
\(352\) 0 0
\(353\) −7.73167 + 5.61739i −0.411515 + 0.298984i −0.774215 0.632923i \(-0.781855\pi\)
0.362700 + 0.931906i \(0.381855\pi\)
\(354\) 0 0
\(355\) 4.76029i 0.252650i
\(356\) 0 0
\(357\) 8.84379 2.87352i 0.468063 0.152083i
\(358\) 0 0
\(359\) −7.94406 + 24.4493i −0.419272 + 1.29039i 0.489102 + 0.872226i \(0.337324\pi\)
−0.908374 + 0.418159i \(0.862676\pi\)
\(360\) 0 0
\(361\) 5.55479 17.0959i 0.292358 0.899784i
\(362\) 0 0
\(363\) 10.3747 14.2795i 0.544530 0.749481i
\(364\) 0 0
\(365\) 1.96734 + 6.05486i 0.102975 + 0.316926i
\(366\) 0 0
\(367\) 1.10730 + 0.804498i 0.0578004 + 0.0419944i 0.616310 0.787503i \(-0.288627\pi\)
−0.558510 + 0.829498i \(0.688627\pi\)
\(368\) 0 0
\(369\) 8.42120 2.42848i 0.438390 0.126422i
\(370\) 0 0
\(371\) −3.99580 2.90312i −0.207451 0.150722i
\(372\) 0 0
\(373\) 2.47578 + 7.61967i 0.128191 + 0.394532i 0.994469 0.105031i \(-0.0334941\pi\)
−0.866278 + 0.499563i \(0.833494\pi\)
\(374\) 0 0
\(375\) −6.34859 + 8.73809i −0.327840 + 0.451233i
\(376\) 0 0
\(377\) −0.236538 + 0.727988i −0.0121823 + 0.0374933i
\(378\) 0 0
\(379\) −9.16044 + 28.1929i −0.470540 + 1.44817i 0.381339 + 0.924435i \(0.375463\pi\)
−0.851879 + 0.523739i \(0.824537\pi\)
\(380\) 0 0
\(381\) 1.01338 0.329267i 0.0519170 0.0168688i
\(382\) 0 0
\(383\) 3.25043i 0.166089i 0.996546 + 0.0830446i \(0.0264644\pi\)
−0.996546 + 0.0830446i \(0.973536\pi\)
\(384\) 0 0
\(385\) 1.89712 1.37834i 0.0966863 0.0702467i
\(386\) 0 0
\(387\) 8.29064 + 6.02350i 0.421437 + 0.306192i
\(388\) 0 0
\(389\) −10.2799 + 7.46881i −0.521213 + 0.378683i −0.817061 0.576552i \(-0.804398\pi\)
0.295848 + 0.955235i \(0.404398\pi\)
\(390\) 0 0
\(391\) 3.63533 + 5.00361i 0.183847 + 0.253043i
\(392\) 0 0
\(393\) −33.9395 11.0276i −1.71202 0.556269i
\(394\) 0 0
\(395\) 3.87555 1.25924i 0.195000 0.0633594i
\(396\) 0 0
\(397\) 4.62509 6.36589i 0.232127 0.319495i −0.677025 0.735960i \(-0.736731\pi\)
0.909152 + 0.416465i \(0.136731\pi\)
\(398\) 0 0
\(399\) 2.01188 + 0.653698i 0.100720 + 0.0327259i
\(400\) 0 0
\(401\) −25.2325 −1.26005 −0.630026 0.776574i \(-0.716956\pi\)
−0.630026 + 0.776574i \(0.716956\pi\)
\(402\) 0 0
\(403\) −1.02416 1.40964i −0.0510172 0.0702192i
\(404\) 0 0
\(405\) 1.84590 + 5.68109i 0.0917234 + 0.282296i
\(406\) 0 0
\(407\) 28.5893i 1.41712i
\(408\) 0 0
\(409\) −17.5735 −0.868953 −0.434477 0.900683i \(-0.643067\pi\)
−0.434477 + 0.900683i \(0.643067\pi\)
\(410\) 0 0
\(411\) 6.71776 0.331363
\(412\) 0 0
\(413\) 1.47083i 0.0723746i
\(414\) 0 0
\(415\) −2.02150 6.22152i −0.0992313 0.305403i
\(416\) 0 0
\(417\) −14.0040 19.2748i −0.685777 0.943891i
\(418\) 0 0
\(419\) −6.93588 −0.338840 −0.169420 0.985544i \(-0.554189\pi\)
−0.169420 + 0.985544i \(0.554189\pi\)
\(420\) 0 0
\(421\) 11.7676 + 3.82354i 0.573520 + 0.186348i 0.581396 0.813621i \(-0.302507\pi\)
−0.00787556 + 0.999969i \(0.502507\pi\)
\(422\) 0 0
\(423\) −5.98538 + 8.23817i −0.291019 + 0.400554i
\(424\) 0 0
\(425\) 19.9592 6.48514i 0.968164 0.314576i
\(426\) 0 0
\(427\) 4.66747 + 1.51655i 0.225875 + 0.0733911i
\(428\) 0 0
\(429\) −3.78814 5.21393i −0.182893 0.251731i
\(430\) 0 0
\(431\) 25.4754 18.5090i 1.22711 0.891546i 0.230438 0.973087i \(-0.425984\pi\)
0.996670 + 0.0815412i \(0.0259842\pi\)
\(432\) 0 0
\(433\) 16.0501 + 11.6611i 0.771319 + 0.560396i 0.902361 0.430981i \(-0.141832\pi\)
−0.131042 + 0.991377i \(0.541832\pi\)
\(434\) 0 0
\(435\) 0.984383 0.715196i 0.0471975 0.0342910i
\(436\) 0 0
\(437\) 1.40698i 0.0673051i
\(438\) 0 0
\(439\) −17.2285 + 5.59789i −0.822273 + 0.267173i −0.689787 0.724012i \(-0.742296\pi\)
−0.132486 + 0.991185i \(0.542296\pi\)
\(440\) 0 0
\(441\) 0.422971 1.30177i 0.0201415 0.0619891i
\(442\) 0 0
\(443\) 4.01693 12.3628i 0.190850 0.587376i −0.809150 0.587602i \(-0.800072\pi\)
1.00000 0.000226160i \(7.19891e-5\pi\)
\(444\) 0 0
\(445\) −3.20800 + 4.41543i −0.152074 + 0.209312i
\(446\) 0 0
\(447\) −8.14759 25.0757i −0.385368 1.18604i
\(448\) 0 0
\(449\) −13.4620 9.78070i −0.635310 0.461580i 0.222926 0.974835i \(-0.428439\pi\)
−0.858236 + 0.513256i \(0.828439\pi\)
\(450\) 0 0
\(451\) −28.2195 0.942866i −1.32880 0.0443978i
\(452\) 0 0
\(453\) 28.0186 + 20.3567i 1.31643 + 0.956441i
\(454\) 0 0
\(455\) −0.114908 0.353650i −0.00538696 0.0165794i
\(456\) 0 0
\(457\) 14.3086 19.6941i 0.669330 0.921253i −0.330415 0.943836i \(-0.607189\pi\)
0.999745 + 0.0225822i \(0.00718876\pi\)
\(458\) 0 0
\(459\) 4.68739 14.4263i 0.218789 0.673362i
\(460\) 0 0
\(461\) −2.75637 + 8.48323i −0.128377 + 0.395103i −0.994501 0.104725i \(-0.966604\pi\)
0.866124 + 0.499829i \(0.166604\pi\)
\(462\) 0 0
\(463\) −9.07556 + 2.94883i −0.421777 + 0.137044i −0.512213 0.858859i \(-0.671174\pi\)
0.0904356 + 0.995902i \(0.471174\pi\)
\(464\) 0 0
\(465\) 2.76974i 0.128444i
\(466\) 0 0
\(467\) 30.4857 22.1491i 1.41071 1.02494i 0.417490 0.908682i \(-0.362910\pi\)
0.993219 0.116258i \(-0.0370900\pi\)
\(468\) 0 0
\(469\) 6.31164 + 4.58567i 0.291444 + 0.211747i
\(470\) 0 0
\(471\) 15.4434 11.2203i 0.711597 0.517005i
\(472\) 0 0
\(473\) −19.4053 26.7090i −0.892255 1.22808i
\(474\) 0 0
\(475\) 4.54053 + 1.47531i 0.208334 + 0.0676918i
\(476\) 0 0
\(477\) 6.42955 2.08909i 0.294389 0.0956527i
\(478\) 0 0
\(479\) 19.6091 26.9896i 0.895962 1.23319i −0.0757763 0.997125i \(-0.524144\pi\)
0.971738 0.236061i \(-0.0758565\pi\)
\(480\) 0 0
\(481\) 4.31162 + 1.40093i 0.196593 + 0.0638769i
\(482\) 0 0
\(483\) 2.90571 0.132214
\(484\) 0 0
\(485\) 1.34871 + 1.85634i 0.0612417 + 0.0842920i
\(486\) 0 0
\(487\) 1.82102 + 5.60453i 0.0825184 + 0.253965i 0.983800 0.179267i \(-0.0573727\pi\)
−0.901282 + 0.433233i \(0.857373\pi\)
\(488\) 0 0
\(489\) 8.74495i 0.395460i
\(490\) 0 0
\(491\) −6.77176 −0.305605 −0.152803 0.988257i \(-0.548830\pi\)
−0.152803 + 0.988257i \(0.548830\pi\)
\(492\) 0 0
\(493\) −4.87014 −0.219340
\(494\) 0 0
\(495\) 3.20971i 0.144266i
\(496\) 0 0
\(497\) −2.76616 8.51336i −0.124079 0.381877i
\(498\) 0 0
\(499\) −5.37442 7.39726i −0.240592 0.331147i 0.671597 0.740917i \(-0.265609\pi\)
−0.912189 + 0.409770i \(0.865609\pi\)
\(500\) 0 0
\(501\) −14.0306 −0.626842
\(502\) 0 0
\(503\) 6.73154 + 2.18721i 0.300145 + 0.0975229i 0.455218 0.890380i \(-0.349561\pi\)
−0.155073 + 0.987903i \(0.549561\pi\)
\(504\) 0 0
\(505\) −3.10999 + 4.28053i −0.138393 + 0.190481i
\(506\) 0 0
\(507\) 24.8702 8.08082i 1.10453 0.358882i
\(508\) 0 0
\(509\) 28.7873 + 9.35357i 1.27598 + 0.414590i 0.867161 0.498028i \(-0.165942\pi\)
0.408815 + 0.912617i \(0.365942\pi\)
\(510\) 0 0
\(511\) −7.03685 9.68539i −0.311292 0.428456i
\(512\) 0 0
\(513\) 2.79170 2.02829i 0.123257 0.0895513i
\(514\) 0 0
\(515\) −1.72701 1.25475i −0.0761012 0.0552907i
\(516\) 0 0
\(517\) 26.5400 19.2825i 1.16723 0.848042i
\(518\) 0 0
\(519\) 4.57926i 0.201007i
\(520\) 0 0
\(521\) 0.387709 0.125974i 0.0169858 0.00551903i −0.300512 0.953778i \(-0.597157\pi\)
0.317498 + 0.948259i \(0.397157\pi\)
\(522\) 0 0
\(523\) −6.29917 + 19.3868i −0.275443 + 0.847727i 0.713659 + 0.700494i \(0.247037\pi\)
−0.989102 + 0.147233i \(0.952963\pi\)
\(524\) 0 0
\(525\) 3.04682 9.37713i 0.132974 0.409252i
\(526\) 0 0
\(527\) 6.51618 8.96876i 0.283849 0.390685i
\(528\) 0 0
\(529\) −6.51018 20.0363i −0.283051 0.871142i
\(530\) 0 0
\(531\) −1.62872 1.18334i −0.0706806 0.0513525i
\(532\) 0 0
\(533\) −1.52500 + 4.20964i −0.0660551 + 0.182340i
\(534\) 0 0
\(535\) −2.92721 2.12674i −0.126554 0.0919470i
\(536\) 0 0
\(537\) −9.25720 28.4907i −0.399478 1.22947i
\(538\) 0 0
\(539\) −2.59190 + 3.56744i −0.111641 + 0.153661i
\(540\) 0 0
\(541\) 0.447995 1.37879i 0.0192608 0.0592786i −0.940964 0.338506i \(-0.890078\pi\)
0.960225 + 0.279228i \(0.0900784\pi\)
\(542\) 0 0
\(543\) 6.18605 19.0387i 0.265469 0.817029i
\(544\) 0 0
\(545\) 7.07767 2.29968i 0.303174 0.0985073i
\(546\) 0 0
\(547\) 0.0935609i 0.00400037i 0.999998 + 0.00200019i \(0.000636680\pi\)
−0.999998 + 0.00200019i \(0.999363\pi\)
\(548\) 0 0
\(549\) −5.43452 + 3.94841i −0.231940 + 0.168514i
\(550\) 0 0
\(551\) −0.896318 0.651213i −0.0381844 0.0277426i
\(552\) 0 0
\(553\) −6.19936 + 4.50410i −0.263624 + 0.191534i
\(554\) 0 0
\(555\) −4.23586 5.83016i −0.179802 0.247476i
\(556\) 0 0
\(557\) 1.07533 + 0.349397i 0.0455634 + 0.0148044i 0.331710 0.943381i \(-0.392374\pi\)
−0.286147 + 0.958186i \(0.592374\pi\)
\(558\) 0 0
\(559\) −4.97894 + 1.61776i −0.210587 + 0.0684238i
\(560\) 0 0
\(561\) 24.1018 33.1733i 1.01758 1.40058i
\(562\) 0 0
\(563\) −22.0557 7.16634i −0.929537 0.302025i −0.195164 0.980771i \(-0.562524\pi\)
−0.734373 + 0.678746i \(0.762524\pi\)
\(564\) 0 0
\(565\) 1.77592 0.0747137
\(566\) 0 0
\(567\) −6.60246 9.08751i −0.277277 0.381639i
\(568\) 0 0
\(569\) −4.32450 13.3094i −0.181293 0.557961i 0.818572 0.574404i \(-0.194766\pi\)
−0.999865 + 0.0164425i \(0.994766\pi\)
\(570\) 0 0
\(571\) 14.7350i 0.616642i 0.951282 + 0.308321i \(0.0997671\pi\)
−0.951282 + 0.308321i \(0.900233\pi\)
\(572\) 0 0
\(573\) 16.7035 0.697797
\(574\) 0 0
\(575\) 6.55778 0.273479
\(576\) 0 0
\(577\) 15.1732i 0.631669i 0.948814 + 0.315834i \(0.102284\pi\)
−0.948814 + 0.315834i \(0.897716\pi\)
\(578\) 0 0
\(579\) 11.0339 + 33.9590i 0.458555 + 1.41129i
\(580\) 0 0
\(581\) 7.23054 + 9.95198i 0.299973 + 0.412878i
\(582\) 0 0
\(583\) −21.7793 −0.902008
\(584\) 0 0
\(585\) 0.484063 + 0.157282i 0.0200136 + 0.00650280i
\(586\) 0 0
\(587\) 6.22978 8.57456i 0.257131 0.353910i −0.660862 0.750507i \(-0.729809\pi\)
0.917993 + 0.396597i \(0.129809\pi\)
\(588\) 0 0
\(589\) 2.39852 0.779327i 0.0988294 0.0321116i
\(590\) 0 0
\(591\) 34.0437 + 11.0615i 1.40037 + 0.455009i
\(592\) 0 0
\(593\) 20.9159 + 28.7883i 0.858915 + 1.18219i 0.981827 + 0.189777i \(0.0607765\pi\)
−0.122913 + 0.992418i \(0.539223\pi\)
\(594\) 0 0
\(595\) 1.91403 1.39062i 0.0784676 0.0570100i
\(596\) 0 0
\(597\) 29.7447 + 21.6108i 1.21737 + 0.884472i
\(598\) 0 0
\(599\) 13.7616 9.99837i 0.562282 0.408522i −0.270011 0.962857i \(-0.587027\pi\)
0.832294 + 0.554335i \(0.187027\pi\)
\(600\) 0 0
\(601\) 32.9144i 1.34261i 0.741182 + 0.671304i \(0.234265\pi\)
−0.741182 + 0.671304i \(0.765735\pi\)
\(602\) 0 0
\(603\) −10.1559 + 3.29986i −0.413581 + 0.134381i
\(604\) 0 0
\(605\) 1.38771 4.27093i 0.0564183 0.173638i
\(606\) 0 0
\(607\) −6.99221 + 21.5198i −0.283805 + 0.873462i 0.702949 + 0.711240i \(0.251866\pi\)
−0.986754 + 0.162222i \(0.948134\pi\)
\(608\) 0 0
\(609\) −1.34489 + 1.85108i −0.0544977 + 0.0750096i
\(610\) 0 0
\(611\) −1.60752 4.94743i −0.0650332 0.200152i
\(612\) 0 0
\(613\) 33.3841 + 24.2549i 1.34837 + 0.979648i 0.999091 + 0.0426293i \(0.0135734\pi\)
0.349279 + 0.937019i \(0.386427\pi\)
\(614\) 0 0
\(615\) 5.89443 3.98878i 0.237686 0.160843i
\(616\) 0 0
\(617\) −14.2542 10.3563i −0.573853 0.416928i 0.262650 0.964891i \(-0.415404\pi\)
−0.836503 + 0.547963i \(0.815404\pi\)
\(618\) 0 0
\(619\) −6.76569 20.8227i −0.271936 0.836933i −0.990014 0.140970i \(-0.954978\pi\)
0.718078 0.695963i \(-0.245022\pi\)
\(620\) 0 0
\(621\) 2.78604 3.83466i 0.111800 0.153879i
\(622\) 0 0
\(623\) 3.17146 9.76076i 0.127062 0.391057i
\(624\) 0 0
\(625\) 6.43930 19.8181i 0.257572 0.792725i
\(626\) 0 0
\(627\) 8.87157 2.88255i 0.354296 0.115118i
\(628\) 0 0
\(629\) 28.8441i 1.15009i
\(630\) 0 0
\(631\) −20.4817 + 14.8809i −0.815365 + 0.592397i −0.915381 0.402588i \(-0.868111\pi\)
0.100016 + 0.994986i \(0.468111\pi\)
\(632\) 0 0
\(633\) 20.9590 + 15.2276i 0.833044 + 0.605242i
\(634\) 0 0
\(635\) 0.219322 0.159347i 0.00870353 0.00632348i
\(636\) 0 0
\(637\) 0.411006 + 0.565701i 0.0162846 + 0.0224139i
\(638\) 0 0
\(639\) 11.6528 + 3.78622i 0.460977 + 0.149781i
\(640\) 0 0
\(641\) 0.770926 0.250489i 0.0304497 0.00989372i −0.293753 0.955882i \(-0.594904\pi\)
0.324202 + 0.945988i \(0.394904\pi\)
\(642\) 0 0
\(643\) 21.1758 29.1460i 0.835093 1.14941i −0.151861 0.988402i \(-0.548527\pi\)
0.986954 0.161005i \(-0.0514734\pi\)
\(644\) 0 0
\(645\) 7.91454 + 2.57159i 0.311635 + 0.101256i
\(646\) 0 0
\(647\) −19.6981 −0.774411 −0.387206 0.921993i \(-0.626560\pi\)
−0.387206 + 0.921993i \(0.626560\pi\)
\(648\) 0 0
\(649\) 3.81223 + 5.24709i 0.149643 + 0.205966i
\(650\) 0 0
\(651\) −1.60947 4.95345i −0.0630802 0.194141i
\(652\) 0 0
\(653\) 40.1395i 1.57078i −0.619001 0.785390i \(-0.712462\pi\)
0.619001 0.785390i \(-0.287538\pi\)
\(654\) 0 0
\(655\) −9.07941 −0.354762
\(656\) 0 0
\(657\) 16.3866 0.639301
\(658\) 0 0
\(659\) 15.0449i 0.586067i 0.956102 + 0.293033i \(0.0946647\pi\)
−0.956102 + 0.293033i \(0.905335\pi\)
\(660\) 0 0
\(661\) −11.2617 34.6601i −0.438031 1.34812i −0.889948 0.456061i \(-0.849260\pi\)
0.451917 0.892060i \(-0.350740\pi\)
\(662\) 0 0
\(663\) −3.82190 5.26040i −0.148430 0.204297i
\(664\) 0 0
\(665\) 0.538213 0.0208710
\(666\) 0 0
\(667\) −1.44733 0.470266i −0.0560409 0.0182088i
\(668\) 0 0
\(669\) 4.69905 6.46769i 0.181676 0.250055i
\(670\) 0 0
\(671\) 20.5817 6.68739i 0.794546 0.258164i
\(672\) 0 0
\(673\) 12.5685 + 4.08377i 0.484482 + 0.157418i 0.541066 0.840980i \(-0.318021\pi\)
−0.0565843 + 0.998398i \(0.518021\pi\)
\(674\) 0 0
\(675\) −9.45364 13.0118i −0.363871 0.500825i
\(676\) 0 0
\(677\) −31.8299 + 23.1257i −1.22332 + 0.888795i −0.996371 0.0851119i \(-0.972875\pi\)
−0.226949 + 0.973907i \(0.572875\pi\)
\(678\) 0 0
\(679\) −3.49075 2.53618i −0.133963 0.0973296i
\(680\) 0 0
\(681\) 28.3757 20.6162i 1.08736 0.790014i
\(682\) 0 0
\(683\) 2.45943i 0.0941076i 0.998892 + 0.0470538i \(0.0149832\pi\)
−0.998892 + 0.0470538i \(0.985017\pi\)
\(684\) 0 0
\(685\) 1.62551 0.528161i 0.0621076 0.0201800i
\(686\) 0 0
\(687\) −14.7539 + 45.4077i −0.562895 + 1.73241i
\(688\) 0 0
\(689\) −1.06723 + 3.28459i −0.0406581 + 0.125133i
\(690\) 0 0
\(691\) 2.64271 3.63737i 0.100533 0.138372i −0.755787 0.654818i \(-0.772745\pi\)
0.856320 + 0.516446i \(0.172745\pi\)
\(692\) 0 0
\(693\) −1.86513 5.74029i −0.0708506 0.218056i
\(694\) 0 0
\(695\) −4.90398 3.56295i −0.186019 0.135150i
\(696\) 0 0
\(697\) −28.4710 0.951269i −1.07842 0.0360319i
\(698\) 0 0
\(699\) −34.2410 24.8776i −1.29511 0.940956i
\(700\) 0 0
\(701\) −6.52158 20.0714i −0.246317 0.758085i −0.995417 0.0956285i \(-0.969514\pi\)
0.749100 0.662457i \(-0.230486\pi\)
\(702\) 0 0
\(703\) −3.85691 + 5.30858i −0.145466 + 0.200217i
\(704\) 0 0
\(705\) −2.55532 + 7.86445i −0.0962388 + 0.296192i
\(706\) 0 0
\(707\) 3.07457 9.46255i 0.115631 0.355876i
\(708\) 0 0
\(709\) 36.0307 11.7071i 1.35316 0.439669i 0.459407 0.888226i \(-0.348062\pi\)
0.893754 + 0.448557i \(0.148062\pi\)
\(710\) 0 0
\(711\) 10.4886i 0.393353i
\(712\) 0 0
\(713\) 2.80254 2.03617i 0.104956 0.0762550i
\(714\) 0 0
\(715\) −1.32655 0.963796i −0.0496102 0.0360439i
\(716\) 0 0
\(717\) −39.3675 + 28.6022i −1.47021 + 1.06817i
\(718\) 0 0
\(719\) −15.0307 20.6880i −0.560551 0.771532i 0.430846 0.902426i \(-0.358215\pi\)
−0.991396 + 0.130894i \(0.958215\pi\)
\(720\) 0 0
\(721\) 3.81773 + 1.24046i 0.142180 + 0.0461970i
\(722\) 0 0
\(723\) 22.1572 7.19930i 0.824034 0.267745i
\(724\) 0 0
\(725\) −3.03523 + 4.17764i −0.112726 + 0.155154i
\(726\) 0 0
\(727\) 16.5801 + 5.38722i 0.614924 + 0.199801i 0.599885 0.800086i \(-0.295213\pi\)
0.0150385 + 0.999887i \(0.495213\pi\)
\(728\) 0 0
\(729\) −6.00444 −0.222387
\(730\) 0 0
\(731\) −19.5782 26.9471i −0.724126 0.996674i
\(732\) 0 0
\(733\) 6.33860 + 19.5082i 0.234122 + 0.720552i 0.997237 + 0.0742897i \(0.0236690\pi\)
−0.763115 + 0.646263i \(0.776331\pi\)
\(734\) 0 0
\(735\) 1.11152i 0.0409991i
\(736\) 0 0
\(737\) 34.4020 1.26721
\(738\) 0 0
\(739\) −49.3409 −1.81504 −0.907518 0.420014i \(-0.862025\pi\)
−0.907518 + 0.420014i \(0.862025\pi\)
\(740\) 0 0
\(741\) 1.47919i 0.0543394i
\(742\) 0 0
\(743\) −3.63097 11.1750i −0.133207 0.409970i 0.862099 0.506739i \(-0.169149\pi\)
−0.995307 + 0.0967688i \(0.969149\pi\)
\(744\) 0 0
\(745\) −3.94298 5.42705i −0.144460 0.198832i
\(746\) 0 0
\(747\) −16.8376 −0.616056
\(748\) 0 0
\(749\) 6.47088 + 2.10252i 0.236441 + 0.0768243i
\(750\) 0 0
\(751\) 9.60141 13.2152i 0.350361 0.482230i −0.597071 0.802188i \(-0.703669\pi\)
0.947432 + 0.319958i \(0.103669\pi\)
\(752\) 0 0
\(753\) 18.9238 6.14872i 0.689623 0.224072i
\(754\) 0 0
\(755\) 8.38020 + 2.72289i 0.304987 + 0.0990961i
\(756\) 0 0
\(757\) 26.4147 + 36.3567i 0.960058 + 1.32141i 0.946912 + 0.321493i \(0.104185\pi\)
0.0131457 + 0.999914i \(0.495815\pi\)
\(758\) 0 0
\(759\) 10.3659 7.53130i 0.376260 0.273369i
\(760\) 0 0
\(761\) −21.5650 15.6679i −0.781732 0.567961i 0.123767 0.992311i \(-0.460503\pi\)
−0.905498 + 0.424350i \(0.860503\pi\)
\(762\) 0 0
\(763\) −11.3215 + 8.22554i −0.409865 + 0.297785i
\(764\) 0 0
\(765\) 3.23832i 0.117082i
\(766\) 0 0
\(767\) 0.978130 0.317814i 0.0353182 0.0114756i
\(768\) 0 0
\(769\) −11.1258 + 34.2418i −0.401208 + 1.23479i 0.522812 + 0.852448i \(0.324883\pi\)
−0.924020 + 0.382344i \(0.875117\pi\)
\(770\) 0 0
\(771\) 10.6897 32.8996i 0.384981 1.18485i
\(772\) 0 0
\(773\) 20.4452 28.1405i 0.735364 1.01214i −0.263508 0.964657i \(-0.584879\pi\)
0.998872 0.0474849i \(-0.0151206\pi\)
\(774\) 0 0
\(775\) −3.63236 11.1792i −0.130478 0.401570i
\(776\) 0 0
\(777\) 10.9633 + 7.96531i 0.393307 + 0.285754i
\(778\) 0 0
\(779\) −5.11270 3.98209i −0.183182 0.142673i
\(780\) 0 0
\(781\) −31.9339 23.2013i −1.14268 0.830208i
\(782\) 0 0
\(783\) 1.15337 + 3.54970i 0.0412179 + 0.126856i
\(784\) 0 0
\(785\) 2.85473 3.92919i 0.101890 0.140239i
\(786\) 0 0
\(787\) −0.116039 + 0.357133i −0.00413636 + 0.0127304i −0.953103 0.302645i \(-0.902130\pi\)
0.948967 + 0.315375i \(0.102130\pi\)
\(788\) 0 0
\(789\) 2.71476 8.35517i 0.0966480 0.297452i
\(790\) 0 0
\(791\) −3.17609 + 1.03197i −0.112929 + 0.0366927i
\(792\) 0 0
\(793\) 3.43166i 0.121862i
\(794\) 0 0
\(795\) 4.44141 3.22687i 0.157521 0.114445i
\(796\) 0 0
\(797\) 1.10487 + 0.802735i 0.0391365 + 0.0284343i