Properties

Label 819.2.do.e.667.3
Level $819$
Weight $2$
Character 819.667
Analytic conductor $6.540$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.do (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.2346760387617129.1
Defining polynomial: \(x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 667.3
Root \(-1.18541 + 0.771231i\) of defining polynomial
Character \(\chi\) \(=\) 819.667
Dual form 819.2.do.e.361.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.433001 + 0.249993i) q^{2} +(-0.875007 + 1.51556i) q^{4} +(-0.902810 - 0.521238i) q^{5} +(1.52469 - 2.16225i) q^{7} -1.87496i q^{8} +O(q^{10})\) \(q+(-0.433001 + 0.249993i) q^{2} +(-0.875007 + 1.51556i) q^{4} +(-0.902810 - 0.521238i) q^{5} +(1.52469 - 2.16225i) q^{7} -1.87496i q^{8} +0.521224 q^{10} +3.96730i q^{11} +(-3.57504 + 0.468096i) q^{13} +(-0.119647 + 1.31742i) q^{14} +(-1.28129 - 2.21925i) q^{16} +(0.0710177 - 0.123006i) q^{17} +5.50977i q^{19} +(1.57993 - 0.912173i) q^{20} +(-0.991800 - 1.71785i) q^{22} +(-2.19549 - 3.80270i) q^{23} +(-1.95662 - 3.38897i) q^{25} +(1.43097 - 1.09642i) q^{26} +(1.94289 + 4.20274i) q^{28} +(-4.19880 + 7.27253i) q^{29} +(-2.46516 + 1.42326i) q^{31} +(4.35712 + 2.51558i) q^{32} +0.0710158i q^{34} +(-2.50355 + 1.15737i) q^{35} +(-0.730221 + 0.421593i) q^{37} +(-1.37740 - 2.38574i) q^{38} +(-0.977298 + 1.69273i) q^{40} +(-10.4766 - 6.04869i) q^{41} +(2.41161 + 4.17704i) q^{43} +(-6.01267 - 3.47142i) q^{44} +(1.90130 + 1.09772i) q^{46} +(-3.94602 - 2.27824i) q^{47} +(-2.35062 - 6.59353i) q^{49} +(1.69444 + 0.978285i) q^{50} +(2.41875 - 5.82776i) q^{52} +(-0.139800 - 0.242141i) q^{53} +(2.06791 - 3.58172i) q^{55} +(-4.05412 - 2.85873i) q^{56} -4.19868i q^{58} +(-9.33705 - 5.39075i) q^{59} -5.86354 q^{61} +(0.711612 - 1.23255i) q^{62} +2.60963 q^{64} +(3.47157 + 1.44084i) q^{65} -5.14447i q^{67} +(0.124282 + 0.215263i) q^{68} +(0.794706 - 1.12701i) q^{70} +(3.20326 - 1.84940i) q^{71} +(-5.72686 + 3.30640i) q^{73} +(0.210791 - 0.365101i) q^{74} +(-8.35036 - 4.82108i) q^{76} +(8.57829 + 6.04892i) q^{77} +(-5.96135 + 10.3254i) q^{79} +2.67142i q^{80} +6.04853 q^{82} +2.87321i q^{83} +(-0.128231 + 0.0740342i) q^{85} +(-2.08846 - 1.20578i) q^{86} +7.43852 q^{88} +(-1.51351 + 0.873824i) q^{89} +(-4.43870 + 8.44381i) q^{91} +7.68427 q^{92} +2.27818 q^{94} +(2.87190 - 4.97427i) q^{95} +(2.34079 - 1.35145i) q^{97} +(2.66616 + 2.26737i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 4q^{4} - 3q^{5} + 3q^{7} + O(q^{10}) \) \( 12q + 4q^{4} - 3q^{5} + 3q^{7} - 24q^{10} - 2q^{13} - 4q^{14} - 8q^{16} - 17q^{17} + 3q^{20} - 15q^{22} - 3q^{23} - 5q^{25} + 9q^{26} + 27q^{28} + q^{29} - 18q^{31} - 18q^{32} - 18q^{35} + 15q^{37} - 19q^{38} - q^{40} + 6q^{41} + 11q^{43} - 33q^{44} - 30q^{46} - 15q^{47} + 9q^{49} - 18q^{50} + 47q^{52} + 8q^{53} - 15q^{55} - 27q^{59} - 10q^{61} - 41q^{62} + 2q^{64} + 3q^{65} + 11q^{68} - 3q^{70} - 30q^{71} - 42q^{73} + 33q^{74} - 45q^{76} + 19q^{77} - 35q^{79} - 10q^{82} - 21q^{85} - 57q^{86} + 28q^{88} - 48q^{89} - 16q^{91} + 66q^{92} - 2q^{94} - 2q^{95} - 3q^{97} + 36q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.433001 + 0.249993i −0.306178 + 0.176772i −0.645215 0.764001i \(-0.723232\pi\)
0.339037 + 0.940773i \(0.389899\pi\)
\(3\) 0 0
\(4\) −0.875007 + 1.51556i −0.437503 + 0.757778i
\(5\) −0.902810 0.521238i −0.403749 0.233105i 0.284351 0.958720i \(-0.408222\pi\)
−0.688100 + 0.725616i \(0.741555\pi\)
\(6\) 0 0
\(7\) 1.52469 2.16225i 0.576280 0.817252i
\(8\) 1.87496i 0.662897i
\(9\) 0 0
\(10\) 0.521224 0.164825
\(11\) 3.96730i 1.19619i 0.801426 + 0.598094i \(0.204075\pi\)
−0.801426 + 0.598094i \(0.795925\pi\)
\(12\) 0 0
\(13\) −3.57504 + 0.468096i −0.991537 + 0.129827i
\(14\) −0.119647 + 1.31742i −0.0319770 + 0.352095i
\(15\) 0 0
\(16\) −1.28129 2.21925i −0.320322 0.554813i
\(17\) 0.0710177 0.123006i 0.0172243 0.0298334i −0.857285 0.514843i \(-0.827850\pi\)
0.874509 + 0.485009i \(0.161184\pi\)
\(18\) 0 0
\(19\) 5.50977i 1.26403i 0.774957 + 0.632014i \(0.217771\pi\)
−0.774957 + 0.632014i \(0.782229\pi\)
\(20\) 1.57993 0.912173i 0.353283 0.203968i
\(21\) 0 0
\(22\) −0.991800 1.71785i −0.211452 0.366246i
\(23\) −2.19549 3.80270i −0.457791 0.792917i 0.541053 0.840989i \(-0.318026\pi\)
−0.998844 + 0.0480711i \(0.984693\pi\)
\(24\) 0 0
\(25\) −1.95662 3.38897i −0.391325 0.677794i
\(26\) 1.43097 1.09642i 0.280637 0.215026i
\(27\) 0 0
\(28\) 1.94289 + 4.20274i 0.367171 + 0.794243i
\(29\) −4.19880 + 7.27253i −0.779697 + 1.35047i 0.152419 + 0.988316i \(0.451294\pi\)
−0.932116 + 0.362159i \(0.882040\pi\)
\(30\) 0 0
\(31\) −2.46516 + 1.42326i −0.442756 + 0.255625i −0.704766 0.709440i \(-0.748948\pi\)
0.262010 + 0.965065i \(0.415615\pi\)
\(32\) 4.35712 + 2.51558i 0.770237 + 0.444696i
\(33\) 0 0
\(34\) 0.0710158i 0.0121791i
\(35\) −2.50355 + 1.15737i −0.423178 + 0.195631i
\(36\) 0 0
\(37\) −0.730221 + 0.421593i −0.120048 + 0.0693095i −0.558821 0.829288i \(-0.688746\pi\)
0.438774 + 0.898598i \(0.355413\pi\)
\(38\) −1.37740 2.38574i −0.223445 0.387017i
\(39\) 0 0
\(40\) −0.977298 + 1.69273i −0.154524 + 0.267644i
\(41\) −10.4766 6.04869i −1.63618 0.944647i −0.982133 0.188190i \(-0.939738\pi\)
−0.654044 0.756457i \(-0.726929\pi\)
\(42\) 0 0
\(43\) 2.41161 + 4.17704i 0.367768 + 0.636993i 0.989216 0.146463i \(-0.0467888\pi\)
−0.621448 + 0.783455i \(0.713455\pi\)
\(44\) −6.01267 3.47142i −0.906444 0.523336i
\(45\) 0 0
\(46\) 1.90130 + 1.09772i 0.280331 + 0.161849i
\(47\) −3.94602 2.27824i −0.575587 0.332315i 0.183791 0.982965i \(-0.441163\pi\)
−0.759378 + 0.650650i \(0.774496\pi\)
\(48\) 0 0
\(49\) −2.35062 6.59353i −0.335803 0.941932i
\(50\) 1.69444 + 0.978285i 0.239630 + 0.138350i
\(51\) 0 0
\(52\) 2.41875 5.82776i 0.335421 0.808164i
\(53\) −0.139800 0.242141i −0.0192030 0.0332606i 0.856264 0.516538i \(-0.172780\pi\)
−0.875467 + 0.483278i \(0.839446\pi\)
\(54\) 0 0
\(55\) 2.06791 3.58172i 0.278837 0.482959i
\(56\) −4.05412 2.85873i −0.541754 0.382014i
\(57\) 0 0
\(58\) 4.19868i 0.551314i
\(59\) −9.33705 5.39075i −1.21558 0.701815i −0.251611 0.967829i \(-0.580960\pi\)
−0.963969 + 0.266013i \(0.914294\pi\)
\(60\) 0 0
\(61\) −5.86354 −0.750749 −0.375374 0.926873i \(-0.622486\pi\)
−0.375374 + 0.926873i \(0.622486\pi\)
\(62\) 0.711612 1.23255i 0.0903748 0.156534i
\(63\) 0 0
\(64\) 2.60963 0.326204
\(65\) 3.47157 + 1.44084i 0.430595 + 0.178714i
\(66\) 0 0
\(67\) 5.14447i 0.628497i −0.949341 0.314248i \(-0.898247\pi\)
0.949341 0.314248i \(-0.101753\pi\)
\(68\) 0.124282 + 0.215263i 0.0150714 + 0.0261044i
\(69\) 0 0
\(70\) 0.794706 1.12701i 0.0949856 0.134704i
\(71\) 3.20326 1.84940i 0.380157 0.219484i −0.297730 0.954650i \(-0.596229\pi\)
0.677887 + 0.735167i \(0.262896\pi\)
\(72\) 0 0
\(73\) −5.72686 + 3.30640i −0.670278 + 0.386985i −0.796182 0.605057i \(-0.793150\pi\)
0.125904 + 0.992042i \(0.459817\pi\)
\(74\) 0.210791 0.365101i 0.0245040 0.0424421i
\(75\) 0 0
\(76\) −8.35036 4.82108i −0.957852 0.553016i
\(77\) 8.57829 + 6.04892i 0.977587 + 0.689339i
\(78\) 0 0
\(79\) −5.96135 + 10.3254i −0.670705 + 1.16169i 0.307000 + 0.951710i \(0.400675\pi\)
−0.977705 + 0.209985i \(0.932658\pi\)
\(80\) 2.67142i 0.298674i
\(81\) 0 0
\(82\) 6.04853 0.667948
\(83\) 2.87321i 0.315376i 0.987489 + 0.157688i \(0.0504040\pi\)
−0.987489 + 0.157688i \(0.949596\pi\)
\(84\) 0 0
\(85\) −0.128231 + 0.0740342i −0.0139086 + 0.00803013i
\(86\) −2.08846 1.20578i −0.225205 0.130022i
\(87\) 0 0
\(88\) 7.43852 0.792949
\(89\) −1.51351 + 0.873824i −0.160432 + 0.0926252i −0.578066 0.815990i \(-0.696193\pi\)
0.417635 + 0.908615i \(0.362859\pi\)
\(90\) 0 0
\(91\) −4.43870 + 8.44381i −0.465302 + 0.885152i
\(92\) 7.68427 0.801141
\(93\) 0 0
\(94\) 2.27818 0.234976
\(95\) 2.87190 4.97427i 0.294650 0.510350i
\(96\) 0 0
\(97\) 2.34079 1.35145i 0.237671 0.137219i −0.376435 0.926443i \(-0.622850\pi\)
0.614106 + 0.789224i \(0.289517\pi\)
\(98\) 2.66616 + 2.26737i 0.269323 + 0.229039i
\(99\) 0 0
\(100\) 6.84823 0.684823
\(101\) 11.4722 1.14153 0.570765 0.821114i \(-0.306647\pi\)
0.570765 + 0.821114i \(0.306647\pi\)
\(102\) 0 0
\(103\) 2.08475 3.61090i 0.205417 0.355792i −0.744849 0.667233i \(-0.767478\pi\)
0.950265 + 0.311441i \(0.100812\pi\)
\(104\) 0.877660 + 6.70304i 0.0860617 + 0.657287i
\(105\) 0 0
\(106\) 0.121067 + 0.0698982i 0.0117591 + 0.00678911i
\(107\) 4.24371 + 7.35032i 0.410255 + 0.710583i 0.994917 0.100694i \(-0.0321063\pi\)
−0.584662 + 0.811277i \(0.698773\pi\)
\(108\) 0 0
\(109\) −5.56886 + 3.21518i −0.533400 + 0.307958i −0.742400 0.669957i \(-0.766312\pi\)
0.209000 + 0.977916i \(0.432979\pi\)
\(110\) 2.06785i 0.197162i
\(111\) 0 0
\(112\) −6.75214 0.613225i −0.638018 0.0579443i
\(113\) 5.48164 + 9.49448i 0.515670 + 0.893166i 0.999835 + 0.0181892i \(0.00579012\pi\)
−0.484165 + 0.874977i \(0.660877\pi\)
\(114\) 0 0
\(115\) 4.57749i 0.426853i
\(116\) −7.34795 12.7270i −0.682240 1.18167i
\(117\) 0 0
\(118\) 5.39060 0.496245
\(119\) −0.157690 0.341105i −0.0144554 0.0312690i
\(120\) 0 0
\(121\) −4.73951 −0.430864
\(122\) 2.53892 1.46584i 0.229863 0.132711i
\(123\) 0 0
\(124\) 4.98145i 0.447348i
\(125\) 9.29184i 0.831087i
\(126\) 0 0
\(127\) −1.00394 + 1.73887i −0.0890849 + 0.154300i −0.907125 0.420862i \(-0.861728\pi\)
0.818040 + 0.575162i \(0.195061\pi\)
\(128\) −9.84421 + 5.68356i −0.870113 + 0.502360i
\(129\) 0 0
\(130\) −1.86339 + 0.243983i −0.163430 + 0.0213987i
\(131\) −6.22511 + 10.7822i −0.543890 + 0.942046i 0.454785 + 0.890601i \(0.349716\pi\)
−0.998676 + 0.0514449i \(0.983617\pi\)
\(132\) 0 0
\(133\) 11.9135 + 8.40071i 1.03303 + 0.728434i
\(134\) 1.28608 + 2.22756i 0.111101 + 0.192432i
\(135\) 0 0
\(136\) −0.230631 0.133155i −0.0197765 0.0114180i
\(137\) −4.54246 2.62259i −0.388088 0.224063i 0.293243 0.956038i \(-0.405265\pi\)
−0.681332 + 0.731975i \(0.738599\pi\)
\(138\) 0 0
\(139\) 10.3693 + 17.9601i 0.879510 + 1.52336i 0.851880 + 0.523737i \(0.175463\pi\)
0.0276301 + 0.999618i \(0.491204\pi\)
\(140\) 0.436567 4.80698i 0.0368966 0.406264i
\(141\) 0 0
\(142\) −0.924676 + 1.60159i −0.0775971 + 0.134402i
\(143\) −1.85708 14.1833i −0.155297 1.18606i
\(144\) 0 0
\(145\) 7.58143 4.37714i 0.629604 0.363502i
\(146\) 1.65316 2.86335i 0.136816 0.236973i
\(147\) 0 0
\(148\) 1.47559i 0.121293i
\(149\) 0.0113760i 0.000931956i 1.00000 0.000465978i \(0.000148325\pi\)
−1.00000 0.000465978i \(0.999852\pi\)
\(150\) 0 0
\(151\) 16.3726 9.45271i 1.33238 0.769251i 0.346717 0.937970i \(-0.387296\pi\)
0.985664 + 0.168719i \(0.0539631\pi\)
\(152\) 10.3306 0.837920
\(153\) 0 0
\(154\) −5.22660 0.474676i −0.421171 0.0382505i
\(155\) 2.96743 0.238350
\(156\) 0 0
\(157\) −9.89687 17.1419i −0.789856 1.36807i −0.926054 0.377390i \(-0.876822\pi\)
0.136198 0.990682i \(-0.456512\pi\)
\(158\) 5.96119i 0.474247i
\(159\) 0 0
\(160\) −2.62243 4.54219i −0.207321 0.359091i
\(161\) −11.5698 1.05076i −0.911830 0.0828117i
\(162\) 0 0
\(163\) 8.93255i 0.699651i −0.936815 0.349825i \(-0.886241\pi\)
0.936815 0.349825i \(-0.113759\pi\)
\(164\) 18.3343 10.5853i 1.43167 0.826572i
\(165\) 0 0
\(166\) −0.718284 1.24410i −0.0557496 0.0965612i
\(167\) −5.31279 3.06734i −0.411116 0.237358i 0.280153 0.959955i \(-0.409615\pi\)
−0.691269 + 0.722597i \(0.742948\pi\)
\(168\) 0 0
\(169\) 12.5618 3.34692i 0.966290 0.257456i
\(170\) 0.0370161 0.0641138i 0.00283900 0.00491730i
\(171\) 0 0
\(172\) −8.44072 −0.643599
\(173\) 24.2628 1.84466 0.922332 0.386399i \(-0.126281\pi\)
0.922332 + 0.386399i \(0.126281\pi\)
\(174\) 0 0
\(175\) −10.3110 0.936441i −0.779441 0.0707883i
\(176\) 8.80446 5.08325i 0.663661 0.383165i
\(177\) 0 0
\(178\) 0.436901 0.756734i 0.0327471 0.0567196i
\(179\) −4.13675 −0.309195 −0.154598 0.987978i \(-0.549408\pi\)
−0.154598 + 0.987978i \(0.549408\pi\)
\(180\) 0 0
\(181\) −7.86568 −0.584651 −0.292326 0.956319i \(-0.594429\pi\)
−0.292326 + 0.956319i \(0.594429\pi\)
\(182\) −0.188936 4.76582i −0.0140049 0.353266i
\(183\) 0 0
\(184\) −7.12989 + 4.11645i −0.525623 + 0.303468i
\(185\) 0.879001 0.0646254
\(186\) 0 0
\(187\) 0.488003 + 0.281749i 0.0356863 + 0.0206035i
\(188\) 6.90560 3.98695i 0.503642 0.290778i
\(189\) 0 0
\(190\) 2.87182i 0.208344i
\(191\) 6.47866 0.468780 0.234390 0.972143i \(-0.424691\pi\)
0.234390 + 0.972143i \(0.424691\pi\)
\(192\) 0 0
\(193\) 4.82928i 0.347619i 0.984779 + 0.173810i \(0.0556077\pi\)
−0.984779 + 0.173810i \(0.944392\pi\)
\(194\) −0.675708 + 1.17036i −0.0485130 + 0.0840270i
\(195\) 0 0
\(196\) 12.0497 + 2.20689i 0.860690 + 0.157635i
\(197\) 22.3748 + 12.9181i 1.59414 + 0.920377i 0.992586 + 0.121545i \(0.0387850\pi\)
0.601554 + 0.798832i \(0.294548\pi\)
\(198\) 0 0
\(199\) 8.55731 14.8217i 0.606612 1.05068i −0.385183 0.922840i \(-0.625862\pi\)
0.991795 0.127842i \(-0.0408050\pi\)
\(200\) −6.35417 + 3.66858i −0.449308 + 0.259408i
\(201\) 0 0
\(202\) −4.96749 + 2.86798i −0.349511 + 0.201790i
\(203\) 9.32312 + 20.1672i 0.654355 + 1.41546i
\(204\) 0 0
\(205\) 6.30561 + 10.9216i 0.440403 + 0.762800i
\(206\) 2.08470i 0.145248i
\(207\) 0 0
\(208\) 5.61947 + 7.33415i 0.389640 + 0.508532i
\(209\) −21.8589 −1.51201
\(210\) 0 0
\(211\) −9.14557 + 15.8406i −0.629607 + 1.09051i 0.358024 + 0.933713i \(0.383451\pi\)
−0.987631 + 0.156799i \(0.949883\pi\)
\(212\) 0.489304 0.0336055
\(213\) 0 0
\(214\) −3.67506 2.12180i −0.251222 0.145043i
\(215\) 5.02810i 0.342913i
\(216\) 0 0
\(217\) −0.681174 + 7.50032i −0.0462411 + 0.509155i
\(218\) 1.60755 2.78435i 0.108877 0.188580i
\(219\) 0 0
\(220\) 3.61887 + 6.26806i 0.243984 + 0.422593i
\(221\) −0.196312 + 0.472995i −0.0132054 + 0.0318171i
\(222\) 0 0
\(223\) −9.96682 5.75435i −0.667428 0.385340i 0.127674 0.991816i \(-0.459249\pi\)
−0.795101 + 0.606477i \(0.792582\pi\)
\(224\) 12.0826 5.58567i 0.807301 0.373208i
\(225\) 0 0
\(226\) −4.74711 2.74075i −0.315773 0.182312i
\(227\) −15.5057 8.95223i −1.02915 0.594181i −0.112410 0.993662i \(-0.535857\pi\)
−0.916741 + 0.399481i \(0.869190\pi\)
\(228\) 0 0
\(229\) 3.34589 + 1.93175i 0.221103 + 0.127654i 0.606461 0.795113i \(-0.292589\pi\)
−0.385358 + 0.922767i \(0.625922\pi\)
\(230\) −1.14434 1.98206i −0.0754556 0.130693i
\(231\) 0 0
\(232\) 13.6357 + 7.87256i 0.895226 + 0.516859i
\(233\) −12.5321 + 21.7062i −0.821004 + 1.42202i 0.0839312 + 0.996472i \(0.473252\pi\)
−0.904935 + 0.425549i \(0.860081\pi\)
\(234\) 0 0
\(235\) 2.37501 + 4.11363i 0.154928 + 0.268344i
\(236\) 16.3400 9.43388i 1.06364 0.614093i
\(237\) 0 0
\(238\) 0.153554 + 0.108277i 0.00995340 + 0.00701858i
\(239\) 7.80462i 0.504839i 0.967618 + 0.252419i \(0.0812263\pi\)
−0.967618 + 0.252419i \(0.918774\pi\)
\(240\) 0 0
\(241\) 18.8493 + 10.8826i 1.21419 + 0.701012i 0.963669 0.267100i \(-0.0860655\pi\)
0.250519 + 0.968112i \(0.419399\pi\)
\(242\) 2.05221 1.18484i 0.131921 0.0761647i
\(243\) 0 0
\(244\) 5.13063 8.88652i 0.328455 0.568901i
\(245\) −1.31463 + 7.17793i −0.0839888 + 0.458581i
\(246\) 0 0
\(247\) −2.57910 19.6976i −0.164104 1.25333i
\(248\) 2.66855 + 4.62207i 0.169453 + 0.293502i
\(249\) 0 0
\(250\) −2.32290 4.02338i −0.146913 0.254461i
\(251\) −3.83990 6.65090i −0.242372 0.419801i 0.719017 0.694992i \(-0.244592\pi\)
−0.961390 + 0.275191i \(0.911259\pi\)
\(252\) 0 0
\(253\) 15.0865 8.71017i 0.948478 0.547604i
\(254\) 1.00391i 0.0629909i
\(255\) 0 0
\(256\) 0.232070 0.401958i 0.0145044 0.0251224i
\(257\) −6.81187 11.7985i −0.424913 0.735971i 0.571499 0.820603i \(-0.306362\pi\)
−0.996412 + 0.0846316i \(0.973029\pi\)
\(258\) 0 0
\(259\) −0.201775 + 2.22172i −0.0125377 + 0.138051i
\(260\) −5.22132 + 4.00061i −0.323813 + 0.248107i
\(261\) 0 0
\(262\) 6.22494i 0.384578i
\(263\) 11.7232 0.722880 0.361440 0.932395i \(-0.382285\pi\)
0.361440 + 0.932395i \(0.382285\pi\)
\(264\) 0 0
\(265\) 0.291476i 0.0179052i
\(266\) −7.25867 0.659227i −0.445057 0.0404198i
\(267\) 0 0
\(268\) 7.79673 + 4.50144i 0.476261 + 0.274970i
\(269\) 4.59938 7.96636i 0.280429 0.485717i −0.691061 0.722796i \(-0.742857\pi\)
0.971490 + 0.237079i \(0.0761899\pi\)
\(270\) 0 0
\(271\) 2.22022 1.28184i 0.134869 0.0778665i −0.431048 0.902329i \(-0.641856\pi\)
0.565916 + 0.824463i \(0.308523\pi\)
\(272\) −0.363976 −0.0220693
\(273\) 0 0
\(274\) 2.62252 0.158432
\(275\) 13.4451 7.76252i 0.810769 0.468097i
\(276\) 0 0
\(277\) −0.466941 + 0.808765i −0.0280558 + 0.0485940i −0.879712 0.475506i \(-0.842265\pi\)
0.851657 + 0.524100i \(0.175598\pi\)
\(278\) −8.97981 5.18450i −0.538573 0.310945i
\(279\) 0 0
\(280\) 2.17002 + 4.69405i 0.129683 + 0.280523i
\(281\) 6.45288i 0.384947i 0.981302 + 0.192473i \(0.0616509\pi\)
−0.981302 + 0.192473i \(0.938349\pi\)
\(282\) 0 0
\(283\) −22.1746 −1.31814 −0.659071 0.752081i \(-0.729050\pi\)
−0.659071 + 0.752081i \(0.729050\pi\)
\(284\) 6.47296i 0.384099i
\(285\) 0 0
\(286\) 4.34984 + 5.67711i 0.257211 + 0.335695i
\(287\) −29.0524 + 13.4307i −1.71491 + 0.792788i
\(288\) 0 0
\(289\) 8.48991 + 14.7050i 0.499407 + 0.864998i
\(290\) −2.18851 + 3.79061i −0.128514 + 0.222593i
\(291\) 0 0
\(292\) 11.5725i 0.677229i
\(293\) 20.9600 12.1013i 1.22450 0.706964i 0.258624 0.965978i \(-0.416731\pi\)
0.965874 + 0.259014i \(0.0833976\pi\)
\(294\) 0 0
\(295\) 5.61972 + 9.73364i 0.327193 + 0.566714i
\(296\) 0.790469 + 1.36913i 0.0459451 + 0.0795792i
\(297\) 0 0
\(298\) −0.00284392 0.00492581i −0.000164744 0.000285345i
\(299\) 9.62898 + 12.5671i 0.556858 + 0.726773i
\(300\) 0 0
\(301\) 12.7088 + 1.15420i 0.732521 + 0.0665270i
\(302\) −4.72623 + 8.18607i −0.271964 + 0.471055i
\(303\) 0 0
\(304\) 12.2276 7.05959i 0.701299 0.404895i
\(305\) 5.29366 + 3.05630i 0.303114 + 0.175003i
\(306\) 0 0
\(307\) 24.2924i 1.38644i −0.720726 0.693220i \(-0.756191\pi\)
0.720726 0.693220i \(-0.243809\pi\)
\(308\) −16.6735 + 7.70803i −0.950063 + 0.439206i
\(309\) 0 0
\(310\) −1.28490 + 0.741837i −0.0729774 + 0.0421335i
\(311\) −1.99355 3.45294i −0.113044 0.195798i 0.803952 0.594694i \(-0.202727\pi\)
−0.916996 + 0.398896i \(0.869393\pi\)
\(312\) 0 0
\(313\) −14.2377 + 24.6604i −0.804763 + 1.39389i 0.111688 + 0.993743i \(0.464374\pi\)
−0.916451 + 0.400147i \(0.868959\pi\)
\(314\) 8.57071 + 4.94830i 0.483673 + 0.279249i
\(315\) 0 0
\(316\) −10.4324 18.0695i −0.586871 1.01649i
\(317\) −14.5632 8.40806i −0.817950 0.472244i 0.0317591 0.999496i \(-0.489889\pi\)
−0.849709 + 0.527252i \(0.823222\pi\)
\(318\) 0 0
\(319\) −28.8523 16.6579i −1.61542 0.932664i
\(320\) −2.35600 1.36024i −0.131704 0.0760396i
\(321\) 0 0
\(322\) 5.27243 2.43740i 0.293821 0.135831i
\(323\) 0.677736 + 0.391291i 0.0377102 + 0.0217720i
\(324\) 0 0
\(325\) 8.58136 + 11.1998i 0.476008 + 0.621253i
\(326\) 2.23308 + 3.86780i 0.123679 + 0.214218i
\(327\) 0 0
\(328\) −11.3410 + 19.6432i −0.626204 + 1.08462i
\(329\) −10.9426 + 5.05866i −0.603285 + 0.278893i
\(330\) 0 0
\(331\) 6.20917i 0.341287i −0.985333 0.170644i \(-0.945415\pi\)
0.985333 0.170644i \(-0.0545846\pi\)
\(332\) −4.35451 2.51408i −0.238985 0.137978i
\(333\) 0 0
\(334\) 3.06726 0.167833
\(335\) −2.68149 + 4.64448i −0.146505 + 0.253755i
\(336\) 0 0
\(337\) 7.69650 0.419255 0.209628 0.977781i \(-0.432775\pi\)
0.209628 + 0.977781i \(0.432775\pi\)
\(338\) −4.60255 + 4.58958i −0.250346 + 0.249640i
\(339\) 0 0
\(340\) 0.259122i 0.0140528i
\(341\) −5.64651 9.78005i −0.305776 0.529619i
\(342\) 0 0
\(343\) −17.8408 4.97049i −0.963313 0.268381i
\(344\) 7.83177 4.52167i 0.422261 0.243792i
\(345\) 0 0
\(346\) −10.5058 + 6.06553i −0.564795 + 0.326085i
\(347\) 15.2047 26.3353i 0.816231 1.41375i −0.0922088 0.995740i \(-0.529393\pi\)
0.908440 0.418015i \(-0.137274\pi\)
\(348\) 0 0
\(349\) −13.9933 8.07906i −0.749046 0.432462i 0.0763028 0.997085i \(-0.475688\pi\)
−0.825349 + 0.564623i \(0.809022\pi\)
\(350\) 4.69880 2.17221i 0.251161 0.116110i
\(351\) 0 0
\(352\) −9.98008 + 17.2860i −0.531940 + 0.921347i
\(353\) 11.8424i 0.630306i 0.949041 + 0.315153i \(0.102056\pi\)
−0.949041 + 0.315153i \(0.897944\pi\)
\(354\) 0 0
\(355\) −3.85591 −0.204651
\(356\) 3.05841i 0.162095i
\(357\) 0 0
\(358\) 1.79122 1.03416i 0.0946688 0.0546571i
\(359\) −27.1631 15.6826i −1.43362 0.827698i −0.436221 0.899840i \(-0.643683\pi\)
−0.997394 + 0.0721417i \(0.977017\pi\)
\(360\) 0 0
\(361\) −11.3575 −0.597765
\(362\) 3.40585 1.96637i 0.179007 0.103350i
\(363\) 0 0
\(364\) −8.91318 14.1155i −0.467178 0.739852i
\(365\) 6.89369 0.360832
\(366\) 0 0
\(367\) 24.0774 1.25683 0.628415 0.777878i \(-0.283704\pi\)
0.628415 + 0.777878i \(0.283704\pi\)
\(368\) −5.62610 + 9.74470i −0.293281 + 0.507977i
\(369\) 0 0
\(370\) −0.380608 + 0.219744i −0.0197869 + 0.0114240i
\(371\) −0.736720 0.0669084i −0.0382486 0.00347371i
\(372\) 0 0
\(373\) −18.3922 −0.952314 −0.476157 0.879360i \(-0.657971\pi\)
−0.476157 + 0.879360i \(0.657971\pi\)
\(374\) −0.281741 −0.0145685
\(375\) 0 0
\(376\) −4.27160 + 7.39862i −0.220291 + 0.381555i
\(377\) 11.6066 27.9650i 0.597771 1.44027i
\(378\) 0 0
\(379\) −7.04719 4.06870i −0.361990 0.208995i 0.307963 0.951398i \(-0.400353\pi\)
−0.669953 + 0.742403i \(0.733686\pi\)
\(380\) 5.02586 + 8.70504i 0.257821 + 0.446559i
\(381\) 0 0
\(382\) −2.80527 + 1.61962i −0.143530 + 0.0828671i
\(383\) 22.3711i 1.14311i −0.820564 0.571555i \(-0.806340\pi\)
0.820564 0.571555i \(-0.193660\pi\)
\(384\) 0 0
\(385\) −4.59164 9.93236i −0.234012 0.506200i
\(386\) −1.20729 2.09108i −0.0614493 0.106433i
\(387\) 0 0
\(388\) 4.73012i 0.240136i
\(389\) 10.6973 + 18.5283i 0.542374 + 0.939420i 0.998767 + 0.0496415i \(0.0158079\pi\)
−0.456393 + 0.889778i \(0.650859\pi\)
\(390\) 0 0
\(391\) −0.623674 −0.0315406
\(392\) −12.3626 + 4.40731i −0.624404 + 0.222603i
\(393\) 0 0
\(394\) −12.9178 −0.650788
\(395\) 10.7639 6.21456i 0.541592 0.312689i
\(396\) 0 0
\(397\) 1.19673i 0.0600622i −0.999549 0.0300311i \(-0.990439\pi\)
0.999549 0.0300311i \(-0.00956063\pi\)
\(398\) 8.55708i 0.428928i
\(399\) 0 0
\(400\) −5.01399 + 8.68449i −0.250699 + 0.434224i
\(401\) −31.4150 + 18.1375i −1.56879 + 0.905741i −0.572479 + 0.819919i \(0.694018\pi\)
−0.996310 + 0.0858220i \(0.972648\pi\)
\(402\) 0 0
\(403\) 8.14682 6.24214i 0.405822 0.310943i
\(404\) −10.0383 + 17.3868i −0.499423 + 0.865026i
\(405\) 0 0
\(406\) −9.07859 6.40171i −0.450563 0.317711i
\(407\) −1.67259 2.89701i −0.0829072 0.143599i
\(408\) 0 0
\(409\) −12.7066 7.33616i −0.628301 0.362750i 0.151793 0.988412i \(-0.451495\pi\)
−0.780094 + 0.625662i \(0.784829\pi\)
\(410\) −5.46067 3.15272i −0.269683 0.155702i
\(411\) 0 0
\(412\) 3.64834 + 6.31912i 0.179741 + 0.311321i
\(413\) −25.8923 + 11.9698i −1.27407 + 0.588993i
\(414\) 0 0
\(415\) 1.49763 2.59397i 0.0735156 0.127333i
\(416\) −16.7544 6.95375i −0.821451 0.340936i
\(417\) 0 0
\(418\) 9.46494 5.46458i 0.462945 0.267282i
\(419\) −2.96674 + 5.13855i −0.144935 + 0.251034i −0.929349 0.369203i \(-0.879631\pi\)
0.784414 + 0.620238i \(0.212964\pi\)
\(420\) 0 0
\(421\) 2.63174i 0.128263i 0.997941 + 0.0641317i \(0.0204278\pi\)
−0.997941 + 0.0641317i \(0.979572\pi\)
\(422\) 9.14532i 0.445187i
\(423\) 0 0
\(424\) −0.454004 + 0.262119i −0.0220484 + 0.0127296i
\(425\) −0.555819 −0.0269612
\(426\) 0 0
\(427\) −8.94010 + 12.6784i −0.432642 + 0.613551i
\(428\) −14.8531 −0.717952
\(429\) 0 0
\(430\) 1.25699 + 2.17717i 0.0606175 + 0.104993i
\(431\) 18.8377i 0.907378i −0.891160 0.453689i \(-0.850108\pi\)
0.891160 0.453689i \(-0.149892\pi\)
\(432\) 0 0
\(433\) 9.56773 + 16.5718i 0.459796 + 0.796389i 0.998950 0.0458176i \(-0.0145893\pi\)
−0.539154 + 0.842207i \(0.681256\pi\)
\(434\) −1.58008 3.41794i −0.0758463 0.164066i
\(435\) 0 0
\(436\) 11.2532i 0.538931i
\(437\) 20.9520 12.0966i 1.00227 0.578660i
\(438\) 0 0
\(439\) −0.632554 1.09561i −0.0301901 0.0522908i 0.850536 0.525918i \(-0.176278\pi\)
−0.880726 + 0.473627i \(0.842945\pi\)
\(440\) −6.71557 3.87724i −0.320152 0.184840i
\(441\) 0 0
\(442\) −0.0332422 0.253884i −0.00158117 0.0120760i
\(443\) −10.4696 + 18.1339i −0.497426 + 0.861568i −0.999996 0.00296930i \(-0.999055\pi\)
0.502569 + 0.864537i \(0.332388\pi\)
\(444\) 0 0
\(445\) 1.82188 0.0863654
\(446\) 5.75419 0.272469
\(447\) 0 0
\(448\) 3.97889 5.64267i 0.187985 0.266591i
\(449\) −15.4700 + 8.93162i −0.730075 + 0.421509i −0.818450 0.574578i \(-0.805166\pi\)
0.0883746 + 0.996087i \(0.471833\pi\)
\(450\) 0 0
\(451\) 23.9970 41.5640i 1.12997 1.95717i
\(452\) −19.1859 −0.902429
\(453\) 0 0
\(454\) 8.95199 0.420138
\(455\) 8.40853 5.30954i 0.394198 0.248915i
\(456\) 0 0
\(457\) −5.68629 + 3.28298i −0.265994 + 0.153571i −0.627066 0.778966i \(-0.715744\pi\)
0.361072 + 0.932538i \(0.382411\pi\)
\(458\) −1.93170 −0.0902624
\(459\) 0 0
\(460\) −6.93744 4.00533i −0.323460 0.186749i
\(461\) 4.42854 2.55682i 0.206258 0.119083i −0.393313 0.919404i \(-0.628671\pi\)
0.599571 + 0.800322i \(0.295338\pi\)
\(462\) 0 0
\(463\) 33.3239i 1.54869i 0.632761 + 0.774347i \(0.281921\pi\)
−0.632761 + 0.774347i \(0.718079\pi\)
\(464\) 21.5194 0.999015
\(465\) 0 0
\(466\) 12.5317i 0.580522i
\(467\) 6.47472 11.2145i 0.299614 0.518947i −0.676433 0.736504i \(-0.736475\pi\)
0.976048 + 0.217557i \(0.0698087\pi\)
\(468\) 0 0
\(469\) −11.1236 7.84374i −0.513641 0.362190i
\(470\) −2.05676 1.18747i −0.0948713 0.0547740i
\(471\) 0 0
\(472\) −10.1074 + 17.5066i −0.465231 + 0.805805i
\(473\) −16.5716 + 9.56761i −0.761962 + 0.439919i
\(474\) 0 0
\(475\) 18.6724 10.7805i 0.856750 0.494645i
\(476\) 0.654942 + 0.0594814i 0.0300192 + 0.00272633i
\(477\) 0 0
\(478\) −1.95110 3.37941i −0.0892414 0.154571i
\(479\) 27.0119i 1.23421i −0.786882 0.617104i \(-0.788306\pi\)
0.786882 0.617104i \(-0.211694\pi\)
\(480\) 0 0
\(481\) 2.41322 1.84903i 0.110033 0.0843083i
\(482\) −10.8823 −0.495677
\(483\) 0 0
\(484\) 4.14710 7.18299i 0.188505 0.326499i
\(485\) −2.81771 −0.127946
\(486\) 0 0
\(487\) 27.7854 + 16.0419i 1.25908 + 0.726928i 0.972895 0.231247i \(-0.0742805\pi\)
0.286182 + 0.958175i \(0.407614\pi\)
\(488\) 10.9939i 0.497669i
\(489\) 0 0
\(490\) −1.22520 3.43670i −0.0553488 0.155254i
\(491\) 14.3020 24.7718i 0.645440 1.11793i −0.338760 0.940873i \(-0.610008\pi\)
0.984200 0.177061i \(-0.0566591\pi\)
\(492\) 0 0
\(493\) 0.596378 + 1.03296i 0.0268595 + 0.0465220i
\(494\) 6.04103 + 7.88433i 0.271799 + 0.354733i
\(495\) 0 0
\(496\) 6.31716 + 3.64721i 0.283649 + 0.163765i
\(497\) 0.885125 9.74601i 0.0397033 0.437168i
\(498\) 0 0
\(499\) −1.55726 0.899082i −0.0697123 0.0402484i 0.464739 0.885448i \(-0.346148\pi\)
−0.534451 + 0.845199i \(0.679482\pi\)
\(500\) −14.0823 8.13042i −0.629780 0.363603i
\(501\) 0 0
\(502\) 3.32536 + 1.91990i 0.148418 + 0.0856893i
\(503\) 14.5386 + 25.1816i 0.648245 + 1.12279i 0.983542 + 0.180681i \(0.0578300\pi\)
−0.335297 + 0.942112i \(0.608837\pi\)
\(504\) 0 0
\(505\) −10.3572 5.97976i −0.460891 0.266096i
\(506\) −4.35497 + 7.54303i −0.193602 + 0.335329i
\(507\) 0 0
\(508\) −1.75690 3.04304i −0.0779499 0.135013i
\(509\) −20.0843 + 11.5957i −0.890220 + 0.513969i −0.874014 0.485900i \(-0.838492\pi\)
−0.0162054 + 0.999869i \(0.505159\pi\)
\(510\) 0 0
\(511\) −1.58245 + 17.4241i −0.0700033 + 0.770798i
\(512\) 22.5022i 0.994464i
\(513\) 0 0
\(514\) 5.89910 + 3.40585i 0.260198 + 0.150225i
\(515\) −3.76427 + 2.17330i −0.165874 + 0.0957671i
\(516\) 0 0
\(517\) 9.03847 15.6551i 0.397511 0.688510i
\(518\) −0.468046 1.01245i −0.0205648 0.0444844i
\(519\) 0 0
\(520\) 2.70151 6.50904i 0.118469 0.285440i
\(521\) 16.6255 + 28.7962i 0.728376 + 1.26158i 0.957569 + 0.288203i \(0.0930579\pi\)
−0.229193 + 0.973381i \(0.573609\pi\)
\(522\) 0 0
\(523\) −19.3560 33.5256i −0.846380 1.46597i −0.884417 0.466697i \(-0.845444\pi\)
0.0380367 0.999276i \(-0.487890\pi\)
\(524\) −10.8940 18.8690i −0.475908 0.824296i
\(525\) 0 0
\(526\) −5.07614 + 2.93071i −0.221330 + 0.127785i
\(527\) 0.404307i 0.0176119i
\(528\) 0 0
\(529\) 1.85966 3.22102i 0.0808546 0.140044i
\(530\) −0.0728671 0.126210i −0.00316514 0.00548219i
\(531\) 0 0
\(532\) −23.1561 + 10.7049i −1.00394 + 0.464115i
\(533\) 40.2857 + 16.7202i 1.74497 + 0.724233i
\(534\) 0 0
\(535\) 8.84793i 0.382529i
\(536\) −9.64566 −0.416629
\(537\) 0 0
\(538\) 4.59926i 0.198288i
\(539\) 26.1585 9.32562i 1.12673 0.401683i
\(540\) 0 0
\(541\) 19.6306 + 11.3337i 0.843986 + 0.487275i 0.858617 0.512618i \(-0.171324\pi\)
−0.0146313 + 0.999893i \(0.504657\pi\)
\(542\) −0.640905 + 1.11008i −0.0275292 + 0.0476820i
\(543\) 0 0
\(544\) 0.618865 0.357302i 0.0265336 0.0153192i
\(545\) 6.70349 0.287146
\(546\) 0 0
\(547\) −9.21134 −0.393848 −0.196924 0.980419i \(-0.563095\pi\)
−0.196924 + 0.980419i \(0.563095\pi\)
\(548\) 7.94936 4.58957i 0.339580 0.196057i
\(549\) 0 0
\(550\) −3.88116 + 6.72236i −0.165493 + 0.286642i
\(551\) −40.0699 23.1344i −1.70704 0.985558i
\(552\) 0 0
\(553\) 13.2367 + 28.6329i 0.562884 + 1.21760i
\(554\) 0.466928i 0.0198379i
\(555\) 0 0
\(556\) −36.2927 −1.53915
\(557\) 11.3281i 0.479986i −0.970775 0.239993i \(-0.922855\pi\)
0.970775 0.239993i \(-0.0771451\pi\)
\(558\) 0 0
\(559\) −10.5769 13.8042i −0.447354 0.583855i
\(560\) 5.77627 + 4.07310i 0.244092 + 0.172120i
\(561\) 0 0
\(562\) −1.61318 2.79411i −0.0680478 0.117862i
\(563\) −16.3193 + 28.2659i −0.687777 + 1.19127i 0.284778 + 0.958594i \(0.408080\pi\)
−0.972555 + 0.232672i \(0.925253\pi\)
\(564\) 0 0
\(565\) 11.4290i 0.480820i
\(566\) 9.60161 5.54349i 0.403586 0.233010i
\(567\) 0 0
\(568\) −3.46755 6.00597i −0.145495 0.252005i
\(569\) −17.5045 30.3188i −0.733829 1.27103i −0.955235 0.295847i \(-0.904398\pi\)
0.221407 0.975182i \(-0.428935\pi\)
\(570\) 0 0
\(571\) 13.1273 + 22.7371i 0.549360 + 0.951519i 0.998319 + 0.0579663i \(0.0184616\pi\)
−0.448959 + 0.893552i \(0.648205\pi\)
\(572\) 23.1205 + 9.59594i 0.966716 + 0.401226i
\(573\) 0 0
\(574\) 9.22215 13.0784i 0.384925 0.545882i
\(575\) −8.59149 + 14.8809i −0.358290 + 0.620576i
\(576\) 0 0
\(577\) −21.2806 + 12.2863i −0.885922 + 0.511487i −0.872606 0.488424i \(-0.837572\pi\)
−0.0133154 + 0.999911i \(0.504239\pi\)
\(578\) −7.35228 4.24484i −0.305815 0.176562i
\(579\) 0 0
\(580\) 15.3201i 0.636133i
\(581\) 6.21259 + 4.38077i 0.257742 + 0.181745i
\(582\) 0 0
\(583\) 0.960646 0.554629i 0.0397859 0.0229704i
\(584\) 6.19936 + 10.7376i 0.256531 + 0.444325i
\(585\) 0 0
\(586\) −6.05048 + 10.4797i −0.249943 + 0.432914i
\(587\) −17.7777 10.2640i −0.733765 0.423639i 0.0860331 0.996292i \(-0.472581\pi\)
−0.819798 + 0.572653i \(0.805914\pi\)
\(588\) 0 0
\(589\) −7.84184 13.5825i −0.323117 0.559656i
\(590\) −4.86669 2.80978i −0.200358 0.115677i
\(591\) 0 0
\(592\) 1.87124 + 1.08036i 0.0769077 + 0.0444027i
\(593\) 33.1545 + 19.1417i 1.36149 + 0.786057i 0.989822 0.142308i \(-0.0454524\pi\)
0.371669 + 0.928365i \(0.378786\pi\)
\(594\) 0 0
\(595\) −0.0354328 + 0.390146i −0.00145260 + 0.0159944i
\(596\) −0.0172409 0.00995405i −0.000706216 0.000407734i
\(597\) 0 0
\(598\) −7.31105 3.03438i −0.298971 0.124085i
\(599\) 7.03567 + 12.1861i 0.287470 + 0.497912i 0.973205 0.229939i \(-0.0738526\pi\)
−0.685735 + 0.727851i \(0.740519\pi\)
\(600\) 0 0
\(601\) 10.1171 17.5233i 0.412685 0.714791i −0.582498 0.812832i \(-0.697925\pi\)
0.995182 + 0.0980417i \(0.0312579\pi\)
\(602\) −5.79145 + 2.67734i −0.236042 + 0.109120i
\(603\) 0 0
\(604\) 33.0847i 1.34620i
\(605\) 4.27887 + 2.47041i 0.173961 + 0.100436i
\(606\) 0 0
\(607\) 6.55127 0.265908 0.132954 0.991122i \(-0.457554\pi\)
0.132954 + 0.991122i \(0.457554\pi\)
\(608\) −13.8603 + 24.0067i −0.562108 + 0.973600i
\(609\) 0 0
\(610\) −3.05621 −0.123742
\(611\) 15.1736 + 6.29767i 0.613859 + 0.254776i
\(612\) 0 0
\(613\) 33.3244i 1.34596i 0.739660 + 0.672980i \(0.234986\pi\)
−0.739660 + 0.672980i \(0.765014\pi\)
\(614\) 6.07294 + 10.5186i 0.245084 + 0.424498i
\(615\) 0 0
\(616\) 11.3415 16.0839i 0.456961 0.648040i
\(617\) −5.85466 + 3.38019i −0.235700 + 0.136081i −0.613199 0.789929i \(-0.710117\pi\)
0.377499 + 0.926010i \(0.376784\pi\)
\(618\) 0 0
\(619\) −15.2582 + 8.80931i −0.613278 + 0.354076i −0.774247 0.632883i \(-0.781871\pi\)
0.160970 + 0.986959i \(0.448538\pi\)
\(620\) −2.59652 + 4.49731i −0.104279 + 0.180616i
\(621\) 0 0
\(622\) 1.72642 + 0.996751i 0.0692233 + 0.0399661i
\(623\) −0.418213 + 4.60489i −0.0167554 + 0.184491i
\(624\) 0 0
\(625\) −4.93986 + 8.55609i −0.197594 + 0.342244i
\(626\) 14.2373i 0.569038i
\(627\) 0 0
\(628\) 34.6393 1.38226
\(629\) 0.119762i 0.00477524i
\(630\) 0 0
\(631\) 13.6416 7.87596i 0.543062 0.313537i −0.203257 0.979125i \(-0.565153\pi\)
0.746319 + 0.665588i \(0.231819\pi\)
\(632\) 19.3596 + 11.1773i 0.770084 + 0.444608i
\(633\) 0 0
\(634\) 8.40783 0.333918
\(635\) 1.81273 1.04658i 0.0719359 0.0415322i
\(636\) 0 0
\(637\) 11.4899 + 22.4718i 0.455248 + 0.890364i
\(638\) 16.6575 0.659475
\(639\) 0 0
\(640\) 11.8499 0.468410
\(641\) 10.4702 18.1350i 0.413550 0.716289i −0.581725 0.813385i \(-0.697622\pi\)
0.995275 + 0.0970962i \(0.0309554\pi\)
\(642\) 0 0
\(643\) −16.3952 + 9.46576i −0.646563 + 0.373293i −0.787138 0.616777i \(-0.788438\pi\)
0.140575 + 0.990070i \(0.455105\pi\)
\(644\) 11.7162 16.6153i 0.461681 0.654734i
\(645\) 0 0
\(646\) −0.391280 −0.0153947
\(647\) −37.6768 −1.48123 −0.740614 0.671930i \(-0.765465\pi\)
−0.740614 + 0.671930i \(0.765465\pi\)
\(648\) 0 0
\(649\) 21.3867 37.0429i 0.839503 1.45406i
\(650\) −6.51562 2.70424i −0.255563 0.106069i
\(651\) 0 0
\(652\) 13.5378 + 7.81604i 0.530180 + 0.306100i
\(653\) 14.5163 + 25.1430i 0.568066 + 0.983920i 0.996757 + 0.0804686i \(0.0256417\pi\)
−0.428691 + 0.903451i \(0.641025\pi\)
\(654\) 0 0
\(655\) 11.2402 6.48952i 0.439190 0.253567i
\(656\) 31.0004i 1.21036i
\(657\) 0 0
\(658\) 3.47352 4.92598i 0.135412 0.192035i
\(659\) −0.709152 1.22829i −0.0276247 0.0478473i 0.851883 0.523733i \(-0.175461\pi\)
−0.879507 + 0.475886i \(0.842128\pi\)
\(660\) 0 0
\(661\) 4.59298i 0.178646i −0.996003 0.0893231i \(-0.971530\pi\)
0.996003 0.0893231i \(-0.0284704\pi\)
\(662\) 1.55225 + 2.68858i 0.0603300 + 0.104495i
\(663\) 0 0
\(664\) 5.38715 0.209062
\(665\) −6.37684 13.7940i −0.247283 0.534908i
\(666\) 0 0
\(667\) 36.8736 1.42775
\(668\) 9.29746 5.36789i 0.359730 0.207690i
\(669\) 0 0
\(670\) 2.68142i 0.103592i
\(671\) 23.2624i 0.898036i
\(672\) 0 0
\(673\) −2.10111 + 3.63924i −0.0809920 + 0.140282i −0.903676 0.428216i \(-0.859142\pi\)
0.822684 + 0.568499i \(0.192475\pi\)
\(674\) −3.33259 + 1.92407i −0.128367 + 0.0741126i
\(675\) 0 0
\(676\) −5.91919 + 21.9666i −0.227661 + 0.844871i
\(677\) 4.04354 7.00361i 0.155406 0.269171i −0.777801 0.628511i \(-0.783665\pi\)
0.933207 + 0.359340i \(0.116998\pi\)
\(678\) 0 0
\(679\) 0.646806 7.12191i 0.0248222 0.273314i
\(680\) 0.138811 + 0.240427i 0.00532315 + 0.00921997i
\(681\) 0 0
\(682\) 4.88989 + 2.82318i 0.187244 + 0.108105i
\(683\) −21.3792 12.3433i −0.818051 0.472302i 0.0316929 0.999498i \(-0.489910\pi\)
−0.849744 + 0.527196i \(0.823243\pi\)
\(684\) 0 0
\(685\) 2.73398 + 4.73540i 0.104460 + 0.180930i
\(686\) 8.96768 2.30785i 0.342388 0.0881142i
\(687\) 0 0
\(688\) 6.17994 10.7040i 0.235608 0.408085i
\(689\) 0.613136 + 0.800222i 0.0233586 + 0.0304860i
\(690\) 0 0
\(691\) −9.74859 + 5.62835i −0.370854 + 0.214113i −0.673831 0.738885i \(-0.735353\pi\)
0.302978 + 0.952998i \(0.402019\pi\)
\(692\) −21.2301 + 36.7716i −0.807047 + 1.39785i
\(693\) 0 0
\(694\) 15.2043i 0.577147i
\(695\) 21.6194i 0.820071i
\(696\) 0 0
\(697\) −1.48805 + 0.859128i −0.0563640 + 0.0325418i
\(698\) 8.07884 0.305789
\(699\) 0 0
\(700\) 10.4415 14.8076i 0.394650 0.559673i
\(701\) −22.2305 −0.839635 −0.419818 0.907608i \(-0.637906\pi\)
−0.419818 + 0.907608i \(0.637906\pi\)
\(702\) 0 0
\(703\) −2.32288 4.02335i −0.0876091 0.151743i
\(704\) 10.3532i 0.390201i
\(705\) 0 0
\(706\) −2.96052 5.12776i −0.111420 0.192986i
\(707\) 17.4916 24.8058i 0.657841 0.932918i
\(708\) 0 0
\(709\) 23.7741i 0.892854i −0.894820 0.446427i \(-0.852696\pi\)
0.894820 0.446427i \(-0.147304\pi\)
\(710\) 1.66961 0.963952i 0.0626595 0.0361765i
\(711\) 0 0
\(712\) 1.63838 + 2.83776i 0.0614010 + 0.106350i
\(713\) 10.8245 + 6.24951i 0.405380 + 0.234046i
\(714\) 0 0
\(715\) −5.71626 + 13.7728i −0.213776 + 0.515072i
\(716\) 3.61969 6.26948i 0.135274 0.234301i
\(717\) 0 0
\(718\) 15.6822 0.585255
\(719\) 20.7808 0.774992 0.387496 0.921871i \(-0.373340\pi\)
0.387496 + 0.921871i \(0.373340\pi\)
\(720\) 0 0
\(721\) −4.62904 10.0133i −0.172394 0.372913i
\(722\) 4.91782 2.83931i 0.183022 0.105668i
\(723\) 0 0
\(724\) 6.88252 11.9209i 0.255787 0.443036i
\(725\) 32.8618 1.22046
\(726\) 0 0
\(727\) −26.7719 −0.992915 −0.496457 0.868061i \(-0.665366\pi\)
−0.496457 + 0.868061i \(0.665366\pi\)
\(728\) 15.8318 + 8.32236i 0.586765 + 0.308447i
\(729\) 0 0
\(730\) −2.98497 + 1.72338i −0.110479 + 0.0637850i
\(731\) 0.685069 0.0253382
\(732\) 0 0
\(733\) −4.55224 2.62824i −0.168141 0.0970761i 0.413568 0.910473i \(-0.364282\pi\)
−0.581709 + 0.813397i \(0.697616\pi\)
\(734\) −10.4255 + 6.01919i −0.384814 + 0.222172i
\(735\) 0 0
\(736\) 22.0917i 0.814312i
\(737\) 20.4097 0.751800
\(738\) 0 0
\(739\) 7.15001i 0.263017i 0.991315 + 0.131509i \(0.0419821\pi\)
−0.991315 + 0.131509i \(0.958018\pi\)
\(740\) −0.769132 + 1.33218i −0.0282738 + 0.0489717i
\(741\) 0 0
\(742\) 0.335727 0.155204i 0.0123249 0.00569771i
\(743\) 0.618032 + 0.356821i 0.0226734 + 0.0130905i 0.511294 0.859406i \(-0.329166\pi\)
−0.488620 + 0.872496i \(0.662500\pi\)
\(744\) 0 0
\(745\) 0.00592959 0.0102703i 0.000217243 0.000376276i
\(746\) 7.96386 4.59794i 0.291578 0.168342i
\(747\) 0 0
\(748\) −0.854012 + 0.493064i −0.0312258 + 0.0180282i
\(749\) 22.3636 + 2.03104i 0.817147 + 0.0742127i
\(750\) 0 0
\(751\) −12.8507 22.2580i −0.468927 0.812205i 0.530442 0.847721i \(-0.322026\pi\)
−0.999369 + 0.0355158i \(0.988693\pi\)
\(752\) 11.6763i 0.425791i
\(753\) 0 0
\(754\) 1.96539 + 15.0104i 0.0715752 + 0.546648i
\(755\) −19.7084 −0.717263
\(756\) 0 0
\(757\) −8.19425 + 14.1928i −0.297825 + 0.515848i −0.975638 0.219386i \(-0.929594\pi\)
0.677813 + 0.735234i \(0.262928\pi\)
\(758\) 4.06859 0.147778
\(759\) 0 0
\(760\) −9.32654 5.38468i −0.338309 0.195323i
\(761\) 8.31998i 0.301599i 0.988564 + 0.150800i \(0.0481848\pi\)
−0.988564 + 0.150800i \(0.951815\pi\)
\(762\) 0 0
\(763\) −1.53879 + 16.9434i −0.0557079 + 0.613392i
\(764\) −5.66888 + 9.81878i −0.205093 + 0.355231i
\(765\) 0 0
\(766\) 5.59263 + 9.68671i 0.202070 + 0.349995i
\(767\) 35.9037 + 14.9015i 1.29641 + 0.538061i
\(768\) 0 0
\(769\) 22.1346 + 12.7794i 0.798194 + 0.460838i 0.842839 0.538165i \(-0.180882\pi\)
−0.0446452 + 0.999003i \(0.514216\pi\)
\(770\) 4.47121 + 3.15284i 0.161131 + 0.113621i
\(771\) 0 0
\(772\) −7.31905 4.22565i −0.263418 0.152085i
\(773\) −7.27528 4.20038i −0.261674 0.151077i 0.363424 0.931624i \(-0.381608\pi\)
−0.625098 + 0.780546i \(0.714941\pi\)
\(774\) 0 0
\(775\) 9.64678 + 5.56957i 0.346523 + 0.200065i
\(776\) −2.53392 4.38887i −0.0909623 0.157551i
\(777\) 0 0
\(778\) −9.26388 5.34850i −0.332126 0.191753i
\(779\) 33.3269 57.7238i 1.19406 2.06817i
\(780\) 0 0
\(781\) 7.33714 + 12.7083i 0.262544 + 0.454739i
\(782\) 0.270052 0.155914i 0.00965703 0.00557549i
\(783\) 0 0
\(784\) −11.6209 + 13.6648i −0.415032 + 0.488029i
\(785\) 20.6345i 0.736476i
\(786\) 0 0
\(787\) −30.3667 17.5322i −1.08246 0.624956i −0.150898 0.988549i \(-0.548216\pi\)
−0.931558 + 0.363593i \(0.881550\pi\)
\(788\) −39.1562 + 22.6069i