Properties

Label 819.2.et.c.136.5
Level $819$
Weight $2$
Character 819.136
Analytic conductor $6.540$
Analytic rank $0$
Dimension $36$
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.et (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 136.5
Character \(\chi\) \(=\) 819.136
Dual form 819.2.et.c.271.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.374685 + 0.374685i) q^{2} +1.71922i q^{4} +(0.545981 - 2.03763i) q^{5} +(-2.03549 + 1.69021i) q^{7} +(-1.39354 - 1.39354i) q^{8} +O(q^{10})\) \(q+(-0.374685 + 0.374685i) q^{2} +1.71922i q^{4} +(0.545981 - 2.03763i) q^{5} +(-2.03549 + 1.69021i) q^{7} +(-1.39354 - 1.39354i) q^{8} +(0.558898 + 0.968040i) q^{10} +(0.745933 - 2.78386i) q^{11} +(2.80107 - 2.27024i) q^{13} +(0.129371 - 1.39596i) q^{14} -2.39417 q^{16} +3.29760 q^{17} +(6.53354 - 1.75066i) q^{19} +(3.50314 + 0.938663i) q^{20} +(0.763581 + 1.32256i) q^{22} +7.84515i q^{23} +(0.476290 + 0.274986i) q^{25} +(-0.198893 + 1.90015i) q^{26} +(-2.90584 - 3.49945i) q^{28} +(-0.677462 + 1.17340i) q^{29} +(6.38499 - 1.71085i) q^{31} +(3.68413 - 3.68413i) q^{32} +(-1.23556 + 1.23556i) q^{34} +(2.33268 + 5.07039i) q^{35} +(2.87856 + 2.87856i) q^{37} +(-1.79207 + 3.10396i) q^{38} +(-3.60036 + 2.07867i) q^{40} +(-6.61712 + 1.77305i) q^{41} +(-4.36301 + 2.51899i) q^{43} +(4.78608 + 1.28243i) q^{44} +(-2.93946 - 2.93946i) q^{46} +(3.53471 + 0.947124i) q^{47} +(1.28640 - 6.88078i) q^{49} +(-0.281492 + 0.0754255i) q^{50} +(3.90305 + 4.81566i) q^{52} +(3.87961 - 6.71968i) q^{53} +(-5.26521 - 3.03987i) q^{55} +(5.19189 + 0.481159i) q^{56} +(-0.185820 - 0.693490i) q^{58} +(2.01369 - 2.01369i) q^{59} +(-3.14962 - 1.81843i) q^{61} +(-1.75133 + 3.03339i) q^{62} -2.02756i q^{64} +(-3.09658 - 6.94705i) q^{65} +(1.82619 + 0.489326i) q^{67} +5.66931i q^{68} +(-2.77382 - 1.02578i) q^{70} +(9.87427 + 2.64580i) q^{71} +(1.82296 + 6.80337i) q^{73} -2.15710 q^{74} +(3.00977 + 11.2326i) q^{76} +(3.18696 + 6.92729i) q^{77} +(-1.13108 - 1.95909i) q^{79} +(-1.30717 + 4.87843i) q^{80} +(1.81500 - 3.14367i) q^{82} +(3.97225 + 3.97225i) q^{83} +(1.80043 - 6.71929i) q^{85} +(0.690929 - 2.57858i) q^{86} +(-4.91890 + 2.83993i) q^{88} +(-8.73455 + 8.73455i) q^{89} +(-1.86436 + 9.35543i) q^{91} -13.4876 q^{92} +(-1.67928 + 0.969531i) q^{94} -14.2688i q^{95} +(3.94107 - 14.7083i) q^{97} +(2.09613 + 3.06012i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 6q^{7} + O(q^{10}) \) \( 36q + 6q^{7} + 8q^{11} - 42q^{14} - 24q^{16} + 8q^{17} - 18q^{19} - 14q^{20} + 4q^{22} + 24q^{25} + 50q^{26} + 34q^{28} - 8q^{29} + 6q^{31} + 50q^{32} - 24q^{34} - 14q^{35} - 14q^{37} + 8q^{38} - 30q^{40} - 34q^{41} + 30q^{43} - 28q^{44} - 32q^{46} + 10q^{47} + 6q^{49} + 20q^{50} + 4q^{52} + 8q^{53} - 30q^{55} + 92q^{56} + 72q^{58} + 70q^{59} - 60q^{61} + 48q^{62} + 44q^{65} - 46q^{67} + 80q^{70} - 42q^{71} - 56q^{73} - 40q^{74} + 12q^{76} - 24q^{77} - 170q^{80} + 24q^{82} + 60q^{83} + 2q^{85} - 12q^{86} + 84q^{88} - 64q^{89} - 86q^{91} + 100q^{92} - 66q^{94} + 36q^{97} + 22q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.374685 + 0.374685i −0.264942 + 0.264942i −0.827058 0.562116i \(-0.809987\pi\)
0.562116 + 0.827058i \(0.309987\pi\)
\(3\) 0 0
\(4\) 1.71922i 0.859611i
\(5\) 0.545981 2.03763i 0.244170 0.911255i −0.729629 0.683844i \(-0.760307\pi\)
0.973799 0.227412i \(-0.0730263\pi\)
\(6\) 0 0
\(7\) −2.03549 + 1.69021i −0.769341 + 0.638838i
\(8\) −1.39354 1.39354i −0.492690 0.492690i
\(9\) 0 0
\(10\) 0.558898 + 0.968040i 0.176739 + 0.306121i
\(11\) 0.745933 2.78386i 0.224907 0.839366i −0.757534 0.652795i \(-0.773596\pi\)
0.982442 0.186570i \(-0.0597372\pi\)
\(12\) 0 0
\(13\) 2.80107 2.27024i 0.776877 0.629652i
\(14\) 0.129371 1.39596i 0.0345758 0.373086i
\(15\) 0 0
\(16\) −2.39417 −0.598543
\(17\) 3.29760 0.799786 0.399893 0.916562i \(-0.369047\pi\)
0.399893 + 0.916562i \(0.369047\pi\)
\(18\) 0 0
\(19\) 6.53354 1.75066i 1.49890 0.401628i 0.586166 0.810191i \(-0.300637\pi\)
0.912730 + 0.408563i \(0.133970\pi\)
\(20\) 3.50314 + 0.938663i 0.783325 + 0.209891i
\(21\) 0 0
\(22\) 0.763581 + 1.32256i 0.162796 + 0.281971i
\(23\) 7.84515i 1.63583i 0.575341 + 0.817914i \(0.304870\pi\)
−0.575341 + 0.817914i \(0.695130\pi\)
\(24\) 0 0
\(25\) 0.476290 + 0.274986i 0.0952579 + 0.0549972i
\(26\) −0.198893 + 1.90015i −0.0390061 + 0.372649i
\(27\) 0 0
\(28\) −2.90584 3.49945i −0.549152 0.661334i
\(29\) −0.677462 + 1.17340i −0.125802 + 0.217895i −0.922046 0.387080i \(-0.873484\pi\)
0.796244 + 0.604975i \(0.206817\pi\)
\(30\) 0 0
\(31\) 6.38499 1.71085i 1.14678 0.307278i 0.365105 0.930966i \(-0.381033\pi\)
0.781673 + 0.623688i \(0.214366\pi\)
\(32\) 3.68413 3.68413i 0.651269 0.651269i
\(33\) 0 0
\(34\) −1.23556 + 1.23556i −0.211897 + 0.211897i
\(35\) 2.33268 + 5.07039i 0.394294 + 0.857052i
\(36\) 0 0
\(37\) 2.87856 + 2.87856i 0.473232 + 0.473232i 0.902959 0.429727i \(-0.141390\pi\)
−0.429727 + 0.902959i \(0.641390\pi\)
\(38\) −1.79207 + 3.10396i −0.290713 + 0.503529i
\(39\) 0 0
\(40\) −3.60036 + 2.07867i −0.569266 + 0.328666i
\(41\) −6.61712 + 1.77305i −1.03342 + 0.276904i −0.735384 0.677651i \(-0.762998\pi\)
−0.298036 + 0.954555i \(0.596332\pi\)
\(42\) 0 0
\(43\) −4.36301 + 2.51899i −0.665353 + 0.384142i −0.794314 0.607508i \(-0.792169\pi\)
0.128961 + 0.991650i \(0.458836\pi\)
\(44\) 4.78608 + 1.28243i 0.721528 + 0.193333i
\(45\) 0 0
\(46\) −2.93946 2.93946i −0.433400 0.433400i
\(47\) 3.53471 + 0.947124i 0.515591 + 0.138152i 0.507226 0.861813i \(-0.330671\pi\)
0.00836456 + 0.999965i \(0.497337\pi\)
\(48\) 0 0
\(49\) 1.28640 6.88078i 0.183772 0.982969i
\(50\) −0.281492 + 0.0754255i −0.0398089 + 0.0106668i
\(51\) 0 0
\(52\) 3.90305 + 4.81566i 0.541256 + 0.667812i
\(53\) 3.87961 6.71968i 0.532905 0.923019i −0.466356 0.884597i \(-0.654433\pi\)
0.999262 0.0384223i \(-0.0122332\pi\)
\(54\) 0 0
\(55\) −5.26521 3.03987i −0.709961 0.409896i
\(56\) 5.19189 + 0.481159i 0.693795 + 0.0642976i
\(57\) 0 0
\(58\) −0.185820 0.693490i −0.0243994 0.0910597i
\(59\) 2.01369 2.01369i 0.262160 0.262160i −0.563771 0.825931i \(-0.690650\pi\)
0.825931 + 0.563771i \(0.190650\pi\)
\(60\) 0 0
\(61\) −3.14962 1.81843i −0.403267 0.232827i 0.284625 0.958639i \(-0.408131\pi\)
−0.687893 + 0.725812i \(0.741464\pi\)
\(62\) −1.75133 + 3.03339i −0.222419 + 0.385241i
\(63\) 0 0
\(64\) 2.02756i 0.253445i
\(65\) −3.09658 6.94705i −0.384084 0.861676i
\(66\) 0 0
\(67\) 1.82619 + 0.489326i 0.223104 + 0.0597807i 0.368640 0.929572i \(-0.379824\pi\)
−0.145535 + 0.989353i \(0.546490\pi\)
\(68\) 5.66931i 0.687505i
\(69\) 0 0
\(70\) −2.77382 1.02578i −0.331534 0.122604i
\(71\) 9.87427 + 2.64580i 1.17186 + 0.313999i 0.791693 0.610919i \(-0.209200\pi\)
0.380167 + 0.924918i \(0.375866\pi\)
\(72\) 0 0
\(73\) 1.82296 + 6.80337i 0.213361 + 0.796274i 0.986737 + 0.162326i \(0.0518997\pi\)
−0.773376 + 0.633947i \(0.781434\pi\)
\(74\) −2.15710 −0.250758
\(75\) 0 0
\(76\) 3.00977 + 11.2326i 0.345244 + 1.28847i
\(77\) 3.18696 + 6.92729i 0.363188 + 0.789438i
\(78\) 0 0
\(79\) −1.13108 1.95909i −0.127256 0.220414i 0.795356 0.606142i \(-0.207284\pi\)
−0.922613 + 0.385728i \(0.873950\pi\)
\(80\) −1.30717 + 4.87843i −0.146146 + 0.545425i
\(81\) 0 0
\(82\) 1.81500 3.14367i 0.200433 0.347160i
\(83\) 3.97225 + 3.97225i 0.436011 + 0.436011i 0.890667 0.454656i \(-0.150238\pi\)
−0.454656 + 0.890667i \(0.650238\pi\)
\(84\) 0 0
\(85\) 1.80043 6.71929i 0.195284 0.728810i
\(86\) 0.690929 2.57858i 0.0745048 0.278056i
\(87\) 0 0
\(88\) −4.91890 + 2.83993i −0.524356 + 0.302737i
\(89\) −8.73455 + 8.73455i −0.925861 + 0.925861i −0.997435 0.0715743i \(-0.977198\pi\)
0.0715743 + 0.997435i \(0.477198\pi\)
\(90\) 0 0
\(91\) −1.86436 + 9.35543i −0.195438 + 0.980716i
\(92\) −13.4876 −1.40618
\(93\) 0 0
\(94\) −1.67928 + 0.969531i −0.173204 + 0.0999995i
\(95\) 14.2688i 1.46394i
\(96\) 0 0
\(97\) 3.94107 14.7083i 0.400155 1.49340i −0.412664 0.910883i \(-0.635402\pi\)
0.812819 0.582516i \(-0.197932\pi\)
\(98\) 2.09613 + 3.06012i 0.211741 + 0.309119i
\(99\) 0 0
\(100\) −0.472762 + 0.818848i −0.0472762 + 0.0818848i
\(101\) −4.18736 7.25272i −0.416658 0.721673i 0.578943 0.815368i \(-0.303465\pi\)
−0.995601 + 0.0936951i \(0.970132\pi\)
\(102\) 0 0
\(103\) 3.94643 + 6.83541i 0.388853 + 0.673513i 0.992296 0.123893i \(-0.0395380\pi\)
−0.603442 + 0.797407i \(0.706205\pi\)
\(104\) −7.06706 0.739728i −0.692982 0.0725363i
\(105\) 0 0
\(106\) 1.06413 + 3.97140i 0.103358 + 0.385736i
\(107\) 20.0157 1.93499 0.967497 0.252883i \(-0.0813786\pi\)
0.967497 + 0.252883i \(0.0813786\pi\)
\(108\) 0 0
\(109\) −1.81100 6.75874i −0.173462 0.647370i −0.996808 0.0798304i \(-0.974562\pi\)
0.823346 0.567539i \(-0.192105\pi\)
\(110\) 3.11179 0.833802i 0.296698 0.0794999i
\(111\) 0 0
\(112\) 4.87330 4.04664i 0.460483 0.382372i
\(113\) −2.05899 3.56627i −0.193693 0.335486i 0.752778 0.658274i \(-0.228713\pi\)
−0.946471 + 0.322788i \(0.895380\pi\)
\(114\) 0 0
\(115\) 15.9855 + 4.28331i 1.49066 + 0.399420i
\(116\) −2.01733 1.16471i −0.187305 0.108140i
\(117\) 0 0
\(118\) 1.50900i 0.138914i
\(119\) −6.71223 + 5.57363i −0.615309 + 0.510934i
\(120\) 0 0
\(121\) 2.33281 + 1.34685i 0.212074 + 0.122441i
\(122\) 1.86145 0.498775i 0.168528 0.0451570i
\(123\) 0 0
\(124\) 2.94134 + 10.9772i 0.264140 + 0.985783i
\(125\) 8.27861 8.27861i 0.740461 0.740461i
\(126\) 0 0
\(127\) −15.0417 8.68434i −1.33474 0.770611i −0.348716 0.937229i \(-0.613382\pi\)
−0.986022 + 0.166618i \(0.946715\pi\)
\(128\) 8.12796 + 8.12796i 0.718417 + 0.718417i
\(129\) 0 0
\(130\) 3.76320 + 1.44271i 0.330054 + 0.126534i
\(131\) −6.59348 + 3.80675i −0.576075 + 0.332597i −0.759572 0.650423i \(-0.774592\pi\)
0.183497 + 0.983020i \(0.441258\pi\)
\(132\) 0 0
\(133\) −10.3400 + 14.6065i −0.896588 + 1.26654i
\(134\) −0.867588 + 0.500902i −0.0749482 + 0.0432714i
\(135\) 0 0
\(136\) −4.59533 4.59533i −0.394046 0.394046i
\(137\) −11.1157 11.1157i −0.949677 0.949677i 0.0491165 0.998793i \(-0.484359\pi\)
−0.998793 + 0.0491165i \(0.984359\pi\)
\(138\) 0 0
\(139\) 16.0562 9.27005i 1.36187 0.786275i 0.371996 0.928234i \(-0.378674\pi\)
0.989873 + 0.141959i \(0.0453402\pi\)
\(140\) −8.71712 + 4.01039i −0.736731 + 0.338940i
\(141\) 0 0
\(142\) −4.69109 + 2.70840i −0.393667 + 0.227284i
\(143\) −4.23063 9.49124i −0.353783 0.793698i
\(144\) 0 0
\(145\) 2.02107 + 2.02107i 0.167841 + 0.167841i
\(146\) −3.23215 1.86608i −0.267495 0.154438i
\(147\) 0 0
\(148\) −4.94888 + 4.94888i −0.406795 + 0.406795i
\(149\) −5.71487 21.3282i −0.468181 1.74727i −0.646124 0.763233i \(-0.723611\pi\)
0.177943 0.984041i \(-0.443056\pi\)
\(150\) 0 0
\(151\) −17.2088 + 4.61110i −1.40044 + 0.375246i −0.878501 0.477740i \(-0.841456\pi\)
−0.521935 + 0.852986i \(0.674789\pi\)
\(152\) −11.5443 6.66512i −0.936369 0.540613i
\(153\) 0 0
\(154\) −3.78966 1.40144i −0.305379 0.112932i
\(155\) 13.9443i 1.12004i
\(156\) 0 0
\(157\) 3.29871 + 1.90451i 0.263265 + 0.151996i 0.625823 0.779965i \(-0.284763\pi\)
−0.362558 + 0.931961i \(0.618096\pi\)
\(158\) 1.15784 + 0.310242i 0.0921127 + 0.0246815i
\(159\) 0 0
\(160\) −5.49543 9.51836i −0.434452 0.752493i
\(161\) −13.2599 15.9687i −1.04503 1.25851i
\(162\) 0 0
\(163\) 7.66571 2.05402i 0.600425 0.160883i 0.0542114 0.998529i \(-0.482736\pi\)
0.546213 + 0.837646i \(0.316069\pi\)
\(164\) −3.04827 11.3763i −0.238030 0.888339i
\(165\) 0 0
\(166\) −2.97668 −0.231035
\(167\) 2.98897 + 11.1550i 0.231294 + 0.863200i 0.979785 + 0.200055i \(0.0641120\pi\)
−0.748491 + 0.663145i \(0.769221\pi\)
\(168\) 0 0
\(169\) 2.69199 12.7182i 0.207076 0.978325i
\(170\) 1.84302 + 3.19221i 0.141354 + 0.244832i
\(171\) 0 0
\(172\) −4.33070 7.50099i −0.330213 0.571945i
\(173\) −9.52913 + 16.5049i −0.724486 + 1.25485i 0.234699 + 0.972068i \(0.424589\pi\)
−0.959185 + 0.282779i \(0.908744\pi\)
\(174\) 0 0
\(175\) −1.43426 + 0.245298i −0.108420 + 0.0185428i
\(176\) −1.78589 + 6.66504i −0.134617 + 0.502396i
\(177\) 0 0
\(178\) 6.54541i 0.490599i
\(179\) −9.39442 + 5.42387i −0.702172 + 0.405399i −0.808156 0.588969i \(-0.799534\pi\)
0.105984 + 0.994368i \(0.466201\pi\)
\(180\) 0 0
\(181\) −5.71631 −0.424890 −0.212445 0.977173i \(-0.568143\pi\)
−0.212445 + 0.977173i \(0.568143\pi\)
\(182\) −2.80679 4.20389i −0.208053 0.311613i
\(183\) 0 0
\(184\) 10.9325 10.9325i 0.805955 0.805955i
\(185\) 7.43707 4.29379i 0.546784 0.315686i
\(186\) 0 0
\(187\) 2.45979 9.18007i 0.179878 0.671313i
\(188\) −1.62832 + 6.07696i −0.118757 + 0.443208i
\(189\) 0 0
\(190\) 5.34629 + 5.34629i 0.387860 + 0.387860i
\(191\) −11.5025 + 19.9230i −0.832294 + 1.44157i 0.0639213 + 0.997955i \(0.479639\pi\)
−0.896215 + 0.443620i \(0.853694\pi\)
\(192\) 0 0
\(193\) −1.29072 + 4.81703i −0.0929080 + 0.346737i −0.996694 0.0812474i \(-0.974110\pi\)
0.903786 + 0.427985i \(0.140776\pi\)
\(194\) 4.03431 + 6.98763i 0.289647 + 0.501683i
\(195\) 0 0
\(196\) 11.8296 + 2.21161i 0.844971 + 0.157972i
\(197\) −1.17127 4.37125i −0.0834496 0.311438i 0.911566 0.411153i \(-0.134874\pi\)
−0.995016 + 0.0997145i \(0.968207\pi\)
\(198\) 0 0
\(199\) −21.8071 −1.54587 −0.772934 0.634487i \(-0.781211\pi\)
−0.772934 + 0.634487i \(0.781211\pi\)
\(200\) −0.280524 1.04693i −0.0198361 0.0740292i
\(201\) 0 0
\(202\) 4.28643 + 1.14855i 0.301592 + 0.0808114i
\(203\) −0.604322 3.53349i −0.0424151 0.248002i
\(204\) 0 0
\(205\) 14.4513i 1.00932i
\(206\) −4.03979 1.08246i −0.281466 0.0754185i
\(207\) 0 0
\(208\) −6.70624 + 5.43535i −0.464994 + 0.376874i
\(209\) 19.4943i 1.34845i
\(210\) 0 0
\(211\) 5.12257 8.87255i 0.352652 0.610811i −0.634061 0.773283i \(-0.718613\pi\)
0.986713 + 0.162472i \(0.0519466\pi\)
\(212\) 11.5526 + 6.66991i 0.793438 + 0.458091i
\(213\) 0 0
\(214\) −7.49959 + 7.49959i −0.512662 + 0.512662i
\(215\) 2.75064 + 10.2655i 0.187592 + 0.700103i
\(216\) 0 0
\(217\) −10.1049 + 14.2744i −0.685963 + 0.969007i
\(218\) 3.21095 + 1.85384i 0.217473 + 0.125558i
\(219\) 0 0
\(220\) 5.22621 9.05207i 0.352351 0.610290i
\(221\) 9.23682 7.48636i 0.621336 0.503587i
\(222\) 0 0
\(223\) −20.9821 + 5.62213i −1.40506 + 0.376486i −0.880161 0.474675i \(-0.842565\pi\)
−0.524904 + 0.851161i \(0.675899\pi\)
\(224\) −1.27205 + 13.7259i −0.0849927 + 0.917103i
\(225\) 0 0
\(226\) 2.10770 + 0.564756i 0.140202 + 0.0375670i
\(227\) 8.25938 + 8.25938i 0.548194 + 0.548194i 0.925918 0.377724i \(-0.123293\pi\)
−0.377724 + 0.925918i \(0.623293\pi\)
\(228\) 0 0
\(229\) −4.69053 1.25682i −0.309959 0.0830532i 0.100487 0.994938i \(-0.467960\pi\)
−0.410445 + 0.911885i \(0.634627\pi\)
\(230\) −7.59442 + 4.38464i −0.500761 + 0.289115i
\(231\) 0 0
\(232\) 2.57924 0.691106i 0.169336 0.0453733i
\(233\) −1.91696 + 1.10676i −0.125584 + 0.0725060i −0.561476 0.827493i \(-0.689766\pi\)
0.435892 + 0.899999i \(0.356433\pi\)
\(234\) 0 0
\(235\) 3.85977 6.68532i 0.251784 0.436102i
\(236\) 3.46198 + 3.46198i 0.225355 + 0.225355i
\(237\) 0 0
\(238\) 0.426614 4.60333i 0.0276533 0.298389i
\(239\) 5.82013 5.82013i 0.376473 0.376473i −0.493355 0.869828i \(-0.664230\pi\)
0.869828 + 0.493355i \(0.164230\pi\)
\(240\) 0 0
\(241\) −10.2858 + 10.2858i −0.662564 + 0.662564i −0.955984 0.293420i \(-0.905207\pi\)
0.293420 + 0.955984i \(0.405207\pi\)
\(242\) −1.37871 + 0.369425i −0.0886271 + 0.0237476i
\(243\) 0 0
\(244\) 3.12629 5.41490i 0.200140 0.346653i
\(245\) −13.3181 6.37799i −0.850864 0.407475i
\(246\) 0 0
\(247\) 14.3265 19.7364i 0.911572 1.25580i
\(248\) −11.2819 6.51358i −0.716399 0.413613i
\(249\) 0 0
\(250\) 6.20374i 0.392359i
\(251\) −10.7479 18.6160i −0.678403 1.17503i −0.975462 0.220169i \(-0.929339\pi\)
0.297058 0.954859i \(-0.403994\pi\)
\(252\) 0 0
\(253\) 21.8398 + 5.85196i 1.37306 + 0.367910i
\(254\) 8.88980 2.38201i 0.557796 0.149461i
\(255\) 0 0
\(256\) −2.03573 −0.127233
\(257\) 7.54278 0.470506 0.235253 0.971934i \(-0.424408\pi\)
0.235253 + 0.971934i \(0.424408\pi\)
\(258\) 0 0
\(259\) −10.7246 0.993906i −0.666395 0.0617583i
\(260\) 11.9435 5.32371i 0.740706 0.330163i
\(261\) 0 0
\(262\) 1.04415 3.89681i 0.0645076 0.240746i
\(263\) 11.9190 + 20.6443i 0.734955 + 1.27298i 0.954743 + 0.297432i \(0.0961303\pi\)
−0.219787 + 0.975548i \(0.570536\pi\)
\(264\) 0 0
\(265\) −11.5740 11.5740i −0.710987 0.710987i
\(266\) −1.59860 9.34705i −0.0980163 0.573104i
\(267\) 0 0
\(268\) −0.841260 + 3.13962i −0.0513881 + 0.191783i
\(269\) 27.6300i 1.68463i 0.538985 + 0.842316i \(0.318808\pi\)
−0.538985 + 0.842316i \(0.681192\pi\)
\(270\) 0 0
\(271\) −14.6246 + 14.6246i −0.888382 + 0.888382i −0.994368 0.105986i \(-0.966200\pi\)
0.105986 + 0.994368i \(0.466200\pi\)
\(272\) −7.89502 −0.478706
\(273\) 0 0
\(274\) 8.32976 0.503219
\(275\) 1.12080 1.12080i 0.0675870 0.0675870i
\(276\) 0 0
\(277\) 8.98397i 0.539795i −0.962889 0.269897i \(-0.913010\pi\)
0.962889 0.269897i \(-0.0869898\pi\)
\(278\) −2.54267 + 9.48936i −0.152499 + 0.569134i
\(279\) 0 0
\(280\) 3.81510 10.3164i 0.227996 0.616525i
\(281\) −13.3221 13.3221i −0.794731 0.794731i 0.187528 0.982259i \(-0.439952\pi\)
−0.982259 + 0.187528i \(0.939952\pi\)
\(282\) 0 0
\(283\) −9.69865 16.7985i −0.576525 0.998570i −0.995874 0.0907452i \(-0.971075\pi\)
0.419349 0.907825i \(-0.362258\pi\)
\(284\) −4.54873 + 16.9761i −0.269917 + 1.00734i
\(285\) 0 0
\(286\) 5.14138 + 1.97107i 0.304016 + 0.116552i
\(287\) 10.4722 14.7933i 0.618156 0.873222i
\(288\) 0 0
\(289\) −6.12581 −0.360342
\(290\) −1.51453 −0.0889362
\(291\) 0 0
\(292\) −11.6965 + 3.13407i −0.684486 + 0.183407i
\(293\) 25.2467 + 6.76482i 1.47493 + 0.395205i 0.904617 0.426225i \(-0.140157\pi\)
0.570309 + 0.821431i \(0.306824\pi\)
\(294\) 0 0
\(295\) −3.00371 5.20258i −0.174883 0.302906i
\(296\) 8.02275i 0.466313i
\(297\) 0 0
\(298\) 10.1326 + 5.85008i 0.586967 + 0.338886i
\(299\) 17.8104 + 21.9748i 1.03000 + 1.27084i
\(300\) 0 0
\(301\) 4.62324 12.5018i 0.266479 0.720589i
\(302\) 4.72019 8.17560i 0.271616 0.470453i
\(303\) 0 0
\(304\) −15.6424 + 4.19137i −0.897153 + 0.240391i
\(305\) −5.42493 + 5.42493i −0.310630 + 0.310630i
\(306\) 0 0
\(307\) 1.58354 1.58354i 0.0903771 0.0903771i −0.660473 0.750850i \(-0.729644\pi\)
0.750850 + 0.660473i \(0.229644\pi\)
\(308\) −11.9096 + 5.47910i −0.678610 + 0.312201i
\(309\) 0 0
\(310\) 5.22473 + 5.22473i 0.296745 + 0.296745i
\(311\) 7.59574 13.1562i 0.430715 0.746020i −0.566220 0.824254i \(-0.691595\pi\)
0.996935 + 0.0782342i \(0.0249282\pi\)
\(312\) 0 0
\(313\) −2.66705 + 1.53982i −0.150750 + 0.0870358i −0.573478 0.819221i \(-0.694406\pi\)
0.422727 + 0.906257i \(0.361073\pi\)
\(314\) −1.94957 + 0.522385i −0.110020 + 0.0294799i
\(315\) 0 0
\(316\) 3.36810 1.94458i 0.189471 0.109391i
\(317\) 7.94761 + 2.12956i 0.446382 + 0.119608i 0.475006 0.879982i \(-0.342446\pi\)
−0.0286238 + 0.999590i \(0.509112\pi\)
\(318\) 0 0
\(319\) 2.76124 + 2.76124i 0.154600 + 0.154600i
\(320\) −4.13142 1.10701i −0.230953 0.0618838i
\(321\) 0 0
\(322\) 10.9515 + 1.01494i 0.610305 + 0.0565601i
\(323\) 21.5450 5.77297i 1.19880 0.321217i
\(324\) 0 0
\(325\) 1.95841 0.311038i 0.108633 0.0172533i
\(326\) −2.10261 + 3.64184i −0.116453 + 0.201703i
\(327\) 0 0
\(328\) 11.6920 + 6.75038i 0.645583 + 0.372728i
\(329\) −8.79569 + 4.04654i −0.484922 + 0.223093i
\(330\) 0 0
\(331\) 5.70505 + 21.2915i 0.313578 + 1.17029i 0.925306 + 0.379221i \(0.123808\pi\)
−0.611728 + 0.791068i \(0.709525\pi\)
\(332\) −6.82918 + 6.82918i −0.374800 + 0.374800i
\(333\) 0 0
\(334\) −5.29953 3.05969i −0.289978 0.167419i
\(335\) 1.99413 3.45393i 0.108951 0.188709i
\(336\) 0 0
\(337\) 6.60942i 0.360038i −0.983663 0.180019i \(-0.942384\pi\)
0.983663 0.180019i \(-0.0576159\pi\)
\(338\) 3.75668 + 5.77398i 0.204336 + 0.314063i
\(339\) 0 0
\(340\) 11.5520 + 3.09534i 0.626493 + 0.167868i
\(341\) 19.0511i 1.03168i
\(342\) 0 0
\(343\) 9.01149 + 16.1800i 0.486574 + 0.873639i
\(344\) 9.59032 + 2.56972i 0.517075 + 0.138550i
\(345\) 0 0
\(346\) −2.61373 9.75457i −0.140515 0.524409i
\(347\) −15.4106 −0.827285 −0.413642 0.910439i \(-0.635744\pi\)
−0.413642 + 0.910439i \(0.635744\pi\)
\(348\) 0 0
\(349\) 0.658426 + 2.45728i 0.0352447 + 0.131535i 0.981307 0.192451i \(-0.0616436\pi\)
−0.946062 + 0.323986i \(0.894977\pi\)
\(350\) 0.445488 0.629307i 0.0238123 0.0336379i
\(351\) 0 0
\(352\) −7.50800 13.0042i −0.400178 0.693128i
\(353\) 1.30540 4.87182i 0.0694794 0.259301i −0.922445 0.386127i \(-0.873813\pi\)
0.991925 + 0.126827i \(0.0404792\pi\)
\(354\) 0 0
\(355\) 10.7823 18.6756i 0.572267 0.991195i
\(356\) −15.0166 15.0166i −0.795880 0.795880i
\(357\) 0 0
\(358\) 1.48771 5.55219i 0.0786277 0.293443i
\(359\) 2.50899 9.36366i 0.132419 0.494195i −0.867576 0.497305i \(-0.834323\pi\)
0.999995 + 0.00310948i \(0.000989781\pi\)
\(360\) 0 0
\(361\) 23.1678 13.3760i 1.21936 0.703998i
\(362\) 2.14181 2.14181i 0.112571 0.112571i
\(363\) 0 0
\(364\) −16.0841 3.20525i −0.843034 0.168001i
\(365\) 14.8580 0.777705
\(366\) 0 0
\(367\) −6.48275 + 3.74282i −0.338397 + 0.195373i −0.659563 0.751649i \(-0.729259\pi\)
0.321166 + 0.947023i \(0.395925\pi\)
\(368\) 18.7826i 0.979113i
\(369\) 0 0
\(370\) −1.17774 + 4.39538i −0.0612277 + 0.228505i
\(371\) 3.46076 + 20.2352i 0.179674 + 1.05056i
\(372\) 0 0
\(373\) −9.46898 + 16.4008i −0.490285 + 0.849199i −0.999937 0.0111813i \(-0.996441\pi\)
0.509652 + 0.860381i \(0.329774\pi\)
\(374\) 2.51799 + 4.36128i 0.130202 + 0.225517i
\(375\) 0 0
\(376\) −3.60590 6.24561i −0.185960 0.322092i
\(377\) 0.766281 + 4.82478i 0.0394655 + 0.248489i
\(378\) 0 0
\(379\) 6.61698 + 24.6949i 0.339891 + 1.26849i 0.898468 + 0.439039i \(0.144681\pi\)
−0.558577 + 0.829453i \(0.688652\pi\)
\(380\) 24.5312 1.25842
\(381\) 0 0
\(382\) −3.15501 11.7747i −0.161424 0.602444i
\(383\) −8.70527 + 2.33257i −0.444819 + 0.119189i −0.474274 0.880377i \(-0.657289\pi\)
0.0294554 + 0.999566i \(0.490623\pi\)
\(384\) 0 0
\(385\) 15.8553 2.71168i 0.808060 0.138200i
\(386\) −1.32126 2.28848i −0.0672501 0.116481i
\(387\) 0 0
\(388\) 25.2868 + 6.77558i 1.28374 + 0.343978i
\(389\) −24.4866 14.1373i −1.24152 0.716792i −0.272116 0.962264i \(-0.587724\pi\)
−0.969404 + 0.245472i \(0.921057\pi\)
\(390\) 0 0
\(391\) 25.8702i 1.30831i
\(392\) −11.3813 + 7.79597i −0.574841 + 0.393756i
\(393\) 0 0
\(394\) 2.07670 + 1.19898i 0.104623 + 0.0604038i
\(395\) −4.60944 + 1.23510i −0.231926 + 0.0621444i
\(396\) 0 0
\(397\) 4.40344 + 16.4338i 0.221002 + 0.824791i 0.983967 + 0.178351i \(0.0570763\pi\)
−0.762965 + 0.646440i \(0.776257\pi\)
\(398\) 8.17081 8.17081i 0.409566 0.409566i
\(399\) 0 0
\(400\) −1.14032 0.658363i −0.0570159 0.0329182i
\(401\) −4.03016 4.03016i −0.201256 0.201256i 0.599282 0.800538i \(-0.295453\pi\)
−0.800538 + 0.599282i \(0.795453\pi\)
\(402\) 0 0
\(403\) 14.0008 19.2877i 0.697427 0.960789i
\(404\) 12.4690 7.19901i 0.620358 0.358164i
\(405\) 0 0
\(406\) 1.55038 + 1.09751i 0.0769438 + 0.0544687i
\(407\) 10.1607 5.86629i 0.503648 0.290781i
\(408\) 0 0
\(409\) −8.37498 8.37498i −0.414116 0.414116i 0.469054 0.883170i \(-0.344595\pi\)
−0.883170 + 0.469054i \(0.844595\pi\)
\(410\) −5.41468 5.41468i −0.267412 0.267412i
\(411\) 0 0
\(412\) −11.7516 + 6.78479i −0.578960 + 0.334262i
\(413\) −0.695284 + 7.50238i −0.0342127 + 0.369168i
\(414\) 0 0
\(415\) 10.2627 5.92519i 0.503778 0.290856i
\(416\) 1.95564 18.6834i 0.0958831 0.916029i
\(417\) 0 0
\(418\) 7.30424 + 7.30424i 0.357262 + 0.357262i
\(419\) 9.24123 + 5.33542i 0.451463 + 0.260653i 0.708448 0.705763i \(-0.249396\pi\)
−0.256985 + 0.966415i \(0.582729\pi\)
\(420\) 0 0
\(421\) −7.86566 + 7.86566i −0.383349 + 0.383349i −0.872307 0.488958i \(-0.837377\pi\)
0.488958 + 0.872307i \(0.337377\pi\)
\(422\) 1.40506 + 5.24376i 0.0683973 + 0.255262i
\(423\) 0 0
\(424\) −14.7705 + 3.95774i −0.717319 + 0.192205i
\(425\) 1.57061 + 0.906795i 0.0761860 + 0.0439860i
\(426\) 0 0
\(427\) 9.48453 1.62211i 0.458989 0.0784995i
\(428\) 34.4115i 1.66334i
\(429\) 0 0
\(430\) −4.87696 2.81571i −0.235188 0.135786i
\(431\) −6.29747 1.68740i −0.303338 0.0812793i 0.103939 0.994584i \(-0.466855\pi\)
−0.407278 + 0.913304i \(0.633522\pi\)
\(432\) 0 0
\(433\) 11.6587 + 20.1934i 0.560281 + 0.970435i 0.997472 + 0.0710664i \(0.0226402\pi\)
−0.437191 + 0.899369i \(0.644026\pi\)
\(434\) −1.56225 9.13453i −0.0749905 0.438472i
\(435\) 0 0
\(436\) 11.6198 3.11351i 0.556486 0.149110i
\(437\) 13.7342 + 51.2566i 0.656994 + 2.45194i
\(438\) 0 0
\(439\) 5.87248 0.280278 0.140139 0.990132i \(-0.455245\pi\)
0.140139 + 0.990132i \(0.455245\pi\)
\(440\) 3.10109 + 11.5734i 0.147839 + 0.551742i
\(441\) 0 0
\(442\) −0.655871 + 6.26593i −0.0311966 + 0.298040i
\(443\) 11.2685 + 19.5176i 0.535381 + 0.927308i 0.999145 + 0.0413488i \(0.0131655\pi\)
−0.463763 + 0.885959i \(0.653501\pi\)
\(444\) 0 0
\(445\) 13.0289 + 22.5667i 0.617628 + 1.06976i
\(446\) 5.75515 9.96820i 0.272514 0.472008i
\(447\) 0 0
\(448\) 3.42700 + 4.12707i 0.161910 + 0.194986i
\(449\) 1.20603 4.50095i 0.0569159 0.212413i −0.931611 0.363456i \(-0.881597\pi\)
0.988527 + 0.151043i \(0.0482632\pi\)
\(450\) 0 0
\(451\) 19.7437i 0.929695i
\(452\) 6.13121 3.53986i 0.288388 0.166501i
\(453\) 0 0
\(454\) −6.18933 −0.290480
\(455\) 18.0450 + 8.90676i 0.845963 + 0.417556i
\(456\) 0 0
\(457\) −19.2757 + 19.2757i −0.901678 + 0.901678i −0.995581 0.0939032i \(-0.970066\pi\)
0.0939032 + 0.995581i \(0.470066\pi\)
\(458\) 2.22838 1.28656i 0.104125 0.0601169i
\(459\) 0 0
\(460\) −7.36396 + 27.4827i −0.343346 + 1.28139i
\(461\) 5.21155 19.4498i 0.242726 0.905866i −0.731787 0.681534i \(-0.761313\pi\)
0.974513 0.224332i \(-0.0720200\pi\)
\(462\) 0 0
\(463\) 6.95272 + 6.95272i 0.323120 + 0.323120i 0.849963 0.526843i \(-0.176624\pi\)
−0.526843 + 0.849963i \(0.676624\pi\)
\(464\) 1.62196 2.80932i 0.0752976 0.130419i
\(465\) 0 0
\(466\) 0.303570 1.13294i 0.0140626 0.0524824i
\(467\) −7.90161 13.6860i −0.365643 0.633312i 0.623236 0.782034i \(-0.285817\pi\)
−0.988879 + 0.148722i \(0.952484\pi\)
\(468\) 0 0
\(469\) −4.54424 + 2.09062i −0.209834 + 0.0965359i
\(470\) 1.05869 + 3.95109i 0.0488338 + 0.182250i
\(471\) 0 0
\(472\) −5.61229 −0.258327
\(473\) 3.75799 + 14.0250i 0.172793 + 0.644871i
\(474\) 0 0
\(475\) 3.59326 + 0.962812i 0.164870 + 0.0441768i
\(476\) −9.58231 11.5398i −0.439205 0.528926i
\(477\) 0 0
\(478\) 4.36143i 0.199487i
\(479\) 31.8547 + 8.53543i 1.45548 + 0.389994i 0.897925 0.440148i \(-0.145074\pi\)
0.557552 + 0.830142i \(0.311741\pi\)
\(480\) 0 0
\(481\) 14.5981 + 1.52802i 0.665615 + 0.0696716i
\(482\) 7.70784i 0.351082i
\(483\) 0 0
\(484\) −2.31553 + 4.01062i −0.105252 + 0.182301i
\(485\) −27.8183 16.0609i −1.26316 0.729287i
\(486\) 0 0
\(487\) 19.1464 19.1464i 0.867606 0.867606i −0.124601 0.992207i \(-0.539765\pi\)
0.992207 + 0.124601i \(0.0397651\pi\)
\(488\) 1.85506 + 6.92316i 0.0839745 + 0.313397i
\(489\) 0 0
\(490\) 7.37984 2.60037i 0.333387 0.117473i
\(491\) 10.9028 + 6.29476i 0.492038 + 0.284078i 0.725420 0.688307i \(-0.241646\pi\)
−0.233381 + 0.972385i \(0.574979\pi\)
\(492\) 0 0
\(493\) −2.23400 + 3.86941i −0.100614 + 0.174269i
\(494\) 2.02703 + 12.7629i 0.0912002 + 0.574228i
\(495\) 0 0
\(496\) −15.2868 + 4.09607i −0.686396 + 0.183919i
\(497\) −24.5709 + 11.3041i −1.10216 + 0.507057i
\(498\) 0 0
\(499\) 24.0438 + 6.44253i 1.07635 + 0.288407i 0.753100 0.657906i \(-0.228558\pi\)
0.323251 + 0.946313i \(0.395224\pi\)
\(500\) 14.2328 + 14.2328i 0.636509 + 0.636509i
\(501\) 0 0
\(502\) 11.0022 + 2.94803i 0.491052 + 0.131577i
\(503\) −22.2573 + 12.8503i −0.992404 + 0.572965i −0.905992 0.423295i \(-0.860873\pi\)
−0.0864120 + 0.996259i \(0.527540\pi\)
\(504\) 0 0
\(505\) −17.0646 + 4.57244i −0.759364 + 0.203471i
\(506\) −10.3757 + 5.99041i −0.461256 + 0.266306i
\(507\) 0 0
\(508\) 14.9303 25.8601i 0.662426 1.14735i
\(509\) −6.37261 6.37261i −0.282461 0.282461i 0.551629 0.834090i \(-0.314007\pi\)
−0.834090 + 0.551629i \(0.814007\pi\)
\(510\) 0 0
\(511\) −15.2097 10.7670i −0.672837 0.476303i
\(512\) −15.4932 + 15.4932i −0.684708 + 0.684708i
\(513\) 0 0
\(514\) −2.82617 + 2.82617i −0.124657 + 0.124657i
\(515\) 16.0827 4.30935i 0.708689 0.189893i
\(516\) 0 0
\(517\) 5.27332 9.13366i 0.231920 0.401698i
\(518\) 4.39076 3.64595i 0.192919 0.160194i
\(519\) 0 0
\(520\) −5.36577 + 13.9962i −0.235305 + 0.613773i
\(521\) 10.2174 + 5.89904i 0.447634 + 0.258442i 0.706831 0.707383i \(-0.250124\pi\)
−0.259196 + 0.965825i \(0.583458\pi\)
\(522\) 0 0
\(523\) 28.6286i 1.25184i −0.779888 0.625920i \(-0.784724\pi\)
0.779888 0.625920i \(-0.215276\pi\)
\(524\) −6.54464 11.3357i −0.285904 0.495200i
\(525\) 0 0
\(526\) −12.2010 3.26924i −0.531987 0.142545i
\(527\) 21.0552 5.64172i 0.917178 0.245757i
\(528\) 0 0
\(529\) −38.5465 −1.67593
\(530\) 8.67323 0.376741
\(531\) 0 0
\(532\) −25.1118 17.7767i −1.08873 0.770717i
\(533\) −14.5098 + 19.9889i −0.628487 + 0.865815i
\(534\) 0 0
\(535\) 10.9282 40.7846i 0.472468 1.76327i
\(536\) −1.86297 3.22675i −0.0804679 0.139375i
\(537\) 0 0
\(538\) −10.3525 10.3525i −0.446330 0.446330i
\(539\) −18.1956 8.71378i −0.783739 0.375329i
\(540\) 0 0
\(541\) 5.54336 20.6881i 0.238328 0.889451i −0.738293 0.674480i \(-0.764368\pi\)
0.976621 0.214971i \(-0.0689655\pi\)
\(542\) 10.9592i 0.470740i
\(543\) 0 0
\(544\) 12.1488 12.1488i 0.520876 0.520876i
\(545\) −14.7606 −0.632273
\(546\) 0 0
\(547\) −26.1223 −1.11691 −0.558455 0.829535i \(-0.688606\pi\)
−0.558455 + 0.829535i \(0.688606\pi\)
\(548\) 19.1103 19.1103i 0.816353 0.816353i
\(549\) 0 0
\(550\) 0.839896i 0.0358133i
\(551\) −2.37201 + 8.85245i −0.101051 + 0.377127i
\(552\) 0 0
\(553\) 5.61355 + 2.07593i 0.238713 + 0.0882777i
\(554\) 3.36616 + 3.36616i 0.143014 + 0.143014i
\(555\) 0 0
\(556\) 15.9373 + 27.6042i 0.675891 + 1.17068i
\(557\) −8.92401 + 33.3049i −0.378123 + 1.41117i 0.470606 + 0.882344i \(0.344035\pi\)
−0.848728 + 0.528829i \(0.822631\pi\)
\(558\) 0 0
\(559\) −6.50239 + 16.9610i −0.275022 + 0.717372i
\(560\) −5.58483 12.1394i −0.236002 0.512982i
\(561\) 0 0
\(562\) 9.98320 0.421116
\(563\) −16.0219 −0.675243 −0.337622 0.941282i \(-0.609622\pi\)
−0.337622 + 0.941282i \(0.609622\pi\)
\(564\) 0 0
\(565\) −8.39090 + 2.24834i −0.353008 + 0.0945882i
\(566\) 9.92810 + 2.66023i 0.417309 + 0.111818i
\(567\) 0 0
\(568\) −10.0731 17.4472i −0.422660 0.732068i
\(569\) 26.4737i 1.10983i 0.831906 + 0.554917i \(0.187250\pi\)
−0.831906 + 0.554917i \(0.812750\pi\)
\(570\) 0 0
\(571\) −13.5784 7.83948i −0.568237 0.328072i 0.188208 0.982129i \(-0.439732\pi\)
−0.756445 + 0.654057i \(0.773065\pi\)
\(572\) 16.3176 7.27339i 0.682271 0.304116i
\(573\) 0 0
\(574\) 1.61905 + 9.46662i 0.0675777 + 0.395129i
\(575\) −2.15731 + 3.73657i −0.0899660 + 0.155826i
\(576\) 0 0
\(577\) 28.1675 7.54746i 1.17263 0.314205i 0.380630 0.924728i \(-0.375707\pi\)
0.791999 + 0.610523i \(0.209041\pi\)
\(578\) 2.29525 2.29525i 0.0954698 0.0954698i
\(579\) 0 0
\(580\) −3.47467 + 3.47467i −0.144278 + 0.144278i
\(581\) −14.7994 1.37153i −0.613981 0.0569008i
\(582\) 0 0
\(583\) −15.8127 15.8127i −0.654896 0.654896i
\(584\) 6.94038 12.0211i 0.287195 0.497436i
\(585\) 0 0
\(586\) −11.9942 + 6.92487i −0.495477 + 0.286064i
\(587\) −7.40030 + 1.98290i −0.305443 + 0.0818432i −0.408285 0.912854i \(-0.633873\pi\)
0.102842 + 0.994698i \(0.467206\pi\)
\(588\) 0 0
\(589\) 38.7215 22.3558i 1.59549 0.921157i
\(590\) 3.07478 + 0.823884i 0.126587 + 0.0339188i
\(591\) 0 0
\(592\) −6.89176 6.89176i −0.283249 0.283249i
\(593\) 17.5955 + 4.71470i 0.722561 + 0.193610i 0.601314 0.799013i \(-0.294644\pi\)
0.121247 + 0.992622i \(0.461311\pi\)
\(594\) 0 0
\(595\) 7.69225 + 16.7201i 0.315351 + 0.685458i
\(596\) 36.6679 9.82514i 1.50198 0.402453i
\(597\) 0 0
\(598\) −14.9069 1.56035i −0.609590 0.0638073i
\(599\) 7.09934 12.2964i 0.290071 0.502418i −0.683755 0.729712i \(-0.739654\pi\)
0.973826 + 0.227293i \(0.0729876\pi\)
\(600\) 0 0
\(601\) 11.4194 + 6.59300i 0.465807 + 0.268934i 0.714483 0.699653i \(-0.246662\pi\)
−0.248676 + 0.968587i \(0.579995\pi\)
\(602\) 2.95196 + 6.41648i 0.120313 + 0.261516i
\(603\) 0 0
\(604\) −7.92750 29.5858i −0.322565 1.20383i
\(605\) 4.01805 4.01805i 0.163357 0.163357i
\(606\) 0 0
\(607\) 9.77151 + 5.64158i 0.396613 + 0.228985i 0.685022 0.728523i \(-0.259793\pi\)
−0.288408 + 0.957508i \(0.593126\pi\)
\(608\) 17.6208 30.5201i 0.714617 1.23775i
\(609\) 0 0
\(610\) 4.06528i 0.164598i
\(611\) 12.0512 5.37170i 0.487539 0.217316i
\(612\) 0 0
\(613\) −9.62690 2.57952i −0.388827 0.104186i 0.0591091 0.998252i \(-0.481174\pi\)
−0.447936 + 0.894066i \(0.647841\pi\)
\(614\) 1.18665i 0.0478894i
\(615\) 0 0
\(616\) 5.21228 14.0946i 0.210009 0.567887i
\(617\) −37.7991 10.1282i −1.52173 0.407747i −0.601422 0.798932i \(-0.705399\pi\)
−0.920312 + 0.391184i \(0.872065\pi\)
\(618\) 0 0
\(619\) −5.02957 18.7706i −0.202156 0.754455i −0.990298 0.138962i \(-0.955624\pi\)
0.788142 0.615493i \(-0.211043\pi\)
\(620\) 23.9734 0.962795
\(621\) 0 0
\(622\) 2.08342 + 7.77544i 0.0835376 + 0.311767i
\(623\) 3.01586 32.5423i 0.120828 1.30378i
\(624\) 0 0
\(625\) −10.9738 19.0072i −0.438953 0.760290i
\(626\) 0.422355 1.57625i 0.0168807 0.0629996i
\(627\) 0 0
\(628\) −3.27427 + 5.67121i −0.130658 + 0.226306i
\(629\) 9.49234 + 9.49234i 0.378484 + 0.378484i
\(630\) 0 0
\(631\) −2.13268 + 7.95928i −0.0849008 + 0.316854i −0.995295 0.0968871i \(-0.969111\pi\)
0.910395 + 0.413741i \(0.135778\pi\)
\(632\) −1.15386 + 4.30626i −0.0458980 + 0.171294i
\(633\) 0 0
\(634\) −3.77576 + 2.17994i −0.149955 + 0.0865764i
\(635\) −25.9080 + 25.9080i −1.02813 + 1.02813i
\(636\) 0 0
\(637\) −12.0177 22.1940i −0.476160 0.879359i
\(638\) −2.06919 −0.0819200
\(639\) 0 0
\(640\) 20.9995 12.1241i 0.830078 0.479246i
\(641\) 39.9291i 1.57710i −0.614968 0.788552i \(-0.710831\pi\)
0.614968 0.788552i \(-0.289169\pi\)
\(642\) 0 0
\(643\) 3.71724 13.8729i 0.146594 0.547095i −0.853086 0.521771i \(-0.825272\pi\)
0.999679 0.0253239i \(-0.00806170\pi\)
\(644\) 27.4537 22.7968i 1.08183 0.898319i
\(645\) 0 0
\(646\) −5.90955 + 10.2356i −0.232508 + 0.402716i
\(647\) −4.52657 7.84025i −0.177958 0.308232i 0.763223 0.646135i \(-0.223616\pi\)
−0.941181 + 0.337903i \(0.890282\pi\)
\(648\) 0 0
\(649\) −4.10375 7.10790i −0.161086 0.279010i
\(650\) −0.617244 + 0.850327i −0.0242103 + 0.0333526i
\(651\) 0 0
\(652\) 3.53132 + 13.1791i 0.138297 + 0.516132i
\(653\) −33.8493 −1.32462 −0.662312 0.749228i \(-0.730425\pi\)
−0.662312 + 0.749228i \(0.730425\pi\)
\(654\) 0 0
\(655\) 4.15682 + 15.5135i 0.162420 + 0.606161i
\(656\) 15.8425 4.24499i 0.618546 0.165739i
\(657\) 0 0
\(658\) 1.77944 4.81179i 0.0693697 0.187583i
\(659\) −14.7702 25.5827i −0.575365 0.996561i −0.996002 0.0893323i \(-0.971527\pi\)
0.420637 0.907229i \(-0.361807\pi\)
\(660\) 0 0
\(661\) −20.8758 5.59365i −0.811973 0.217568i −0.171139 0.985247i \(-0.554745\pi\)
−0.640834 + 0.767679i \(0.721411\pi\)
\(662\) −10.1152 5.84002i −0.393139 0.226979i
\(663\) 0 0
\(664\) 11.0709i 0.429636i
\(665\) 24.1171 + 29.0438i 0.935223 + 1.12627i
\(666\) 0 0
\(667\) −9.20550 5.31480i −0.356438 0.205790i
\(668\) −19.1779 + 5.13871i −0.742016 + 0.198823i
\(669\) 0 0
\(670\) 0.546967 + 2.04131i 0.0211312 + 0.0788626i
\(671\) −7.41167 + 7.41167i −0.286124 + 0.286124i
\(672\) 0 0
\(673\) −40.0862 23.1438i −1.54521 0.892126i −0.998497 0.0548050i \(-0.982546\pi\)
−0.546711 0.837321i \(-0.684120\pi\)
\(674\) 2.47645 + 2.47645i 0.0953893 + 0.0953893i
\(675\) 0 0
\(676\) 21.8655 + 4.62813i 0.840979 + 0.178005i
\(677\) −3.29683 + 1.90343i −0.126707 + 0.0731546i −0.562014 0.827128i \(-0.689973\pi\)
0.435307 + 0.900282i \(0.356640\pi\)
\(678\) 0 0
\(679\) 16.8380 + 36.5997i 0.646184 + 1.40457i
\(680\) −11.8725 + 6.85462i −0.455291 + 0.262863i
\(681\) 0 0
\(682\) 7.13816 + 7.13816i 0.273334 + 0.273334i
\(683\) 7.72051 + 7.72051i 0.295417 + 0.295417i 0.839216 0.543799i \(-0.183015\pi\)
−0.543799 + 0.839216i \(0.683015\pi\)
\(684\) 0 0
\(685\) −28.7186 + 16.5807i −1.09728 + 0.633515i
\(686\) −9.43888 2.68594i −0.360378 0.102550i
\(687\) 0 0
\(688\) 10.4458 6.03088i 0.398242 0.229925i
\(689\) −4.38825 27.6300i −0.167179 1.05262i
\(690\) 0 0
\(691\) −16.3121 16.3121i −0.620541 0.620541i 0.325129 0.945670i \(-0.394592\pi\)
−0.945670 + 0.325129i \(0.894592\pi\)
\(692\) −28.3756 16.3827i −1.07868 0.622776i
\(693\) 0 0
\(694\) 5.77412 5.77412i 0.219183 0.219183i
\(695\) −10.1225 37.7778i −0.383970 1.43300i
\(696\) 0 0
\(697\) −21.8206 + 5.84682i −0.826515 + 0.221464i
\(698\) −1.16741 0.674003i −0.0441870 0.0255114i
\(699\) 0 0
\(700\) −0.421722 2.46582i −0.0159396 0.0931992i
\(701\) 12.3895i 0.467945i 0.972243 + 0.233973i \(0.0751726\pi\)
−0.972243 + 0.233973i \(0.924827\pi\)
\(702\) 0 0
\(703\) 23.8465 + 13.7678i 0.899389 + 0.519262i
\(704\) −5.64445 1.51243i −0.212733 0.0570017i
\(705\) 0 0
\(706\) 1.33628 + 2.31451i 0.0502917 + 0.0871077i
\(707\) 20.7819 + 7.68531i 0.781584 + 0.289036i
\(708\) 0 0
\(709\) 23.0444 6.17472i 0.865449 0.231896i 0.201330 0.979523i \(-0.435474\pi\)
0.664119 + 0.747627i \(0.268807\pi\)
\(710\) 2.95747 + 11.0374i 0.110992 + 0.414227i
\(711\) 0 0
\(712\) 24.3438 0.912324
\(713\) 13.4219 + 50.0912i 0.502654 + 1.87593i
\(714\) 0 0
\(715\) −21.6495 + 3.43842i −0.809645 + 0.128589i
\(716\) −9.32484 16.1511i −0.348486 0.603595i
\(717\) 0 0
\(718\) 2.56834 + 4.44850i 0.0958498 + 0.166017i
\(719\) −20.8277 + 36.0747i −0.776744 + 1.34536i 0.157065 + 0.987588i \(0.449797\pi\)
−0.933809 + 0.357771i \(0.883537\pi\)
\(720\) 0 0
\(721\) −19.5862 7.24311i −0.729427 0.269747i
\(722\) −3.66887 + 13.6924i −0.136541 + 0.509579i
\(723\) 0 0
\(724\) 9.82760i 0.365240i
\(725\) −0.645337 + 0.372585i −0.0239672 + 0.0138375i
\(726\) 0 0
\(727\) 31.5386 1.16970 0.584851 0.811141i \(-0.301153\pi\)
0.584851 + 0.811141i \(0.301153\pi\)
\(728\) 15.6352 10.4391i 0.579479 0.386898i
\(729\) 0 0
\(730\) −5.56708 + 5.56708i −0.206047 + 0.206047i
\(731\) −14.3875 + 8.30662i −0.532140 + 0.307231i
\(732\) 0 0
\(733\) −8.44436 + 31.5148i −0.311899 + 1.16402i 0.614942 + 0.788572i \(0.289179\pi\)
−0.926842 + 0.375452i \(0.877487\pi\)
\(734\) 1.02661 3.83137i 0.0378929 0.141418i
\(735\) 0 0
\(736\) 28.9026 + 28.9026i 1.06536 + 1.06536i
\(737\) 2.72443 4.71885i 0.100356 0.173821i
\(738\) 0 0
\(739\) 8.60509 32.1146i 0.316543 1.18136i −0.606001 0.795464i \(-0.707227\pi\)
0.922544 0.385892i \(-0.126106\pi\)
\(740\) 7.38199 + 12.7860i 0.271367 + 0.470022i
\(741\) 0 0
\(742\) −8.87850 6.28512i −0.325940 0.230734i
\(743\) −8.41303 31.3979i −0.308644 1.15188i −0.929763 0.368159i \(-0.879988\pi\)
0.621118 0.783717i \(-0.286679\pi\)
\(744\) 0 0
\(745\) −46.5792 −1.70653
\(746\) −2.59723 9.69301i −0.0950915 0.354886i
\(747\) 0 0
\(748\) 15.7826 + 4.22893i 0.577068 + 0.154625i
\(749\) −40.7417 + 33.8307i −1.48867 + 1.23615i
\(750\) 0 0
\(751\) 42.9234i 1.56630i 0.621835 + 0.783148i \(0.286387\pi\)
−0.621835 + 0.783148i \(0.713613\pi\)
\(752\) −8.46271 2.26758i −0.308603 0.0826900i
\(753\) 0 0
\(754\) −2.09489 1.52066i −0.0762912 0.0553791i
\(755\) 37.5828i 1.36778i
\(756\) 0 0
\(757\) 6.45620 11.1825i 0.234654 0.406433i −0.724518 0.689256i \(-0.757937\pi\)
0.959172 + 0.282823i \(0.0912708\pi\)
\(758\) −11.7321 6.77353i −0.426129 0.246026i
\(759\) 0 0
\(760\) −19.8840 + 19.8840i −0.721270 + 0.721270i
\(761\) −9.87024 36.8362i −0.357796 1.33531i −0.876929 0.480619i \(-0.840412\pi\)
0.519134 0.854693i \(-0.326255\pi\)
\(762\) 0 0
\(763\) 15.1099 + 10.6964i 0.547016 + 0.387234i
\(764\) −34.2520 19.7754i −1.23919 0.715449i
\(765\) 0 0
\(766\) 2.38776 4.13571i 0.0862731 0.149429i
\(767\) 1.06892 10.2120i 0.0385965 0.368735i
\(768\) 0 0
\(769\) 0.0137463 0.00368331i 0.000495704 0.000132824i −0.258571 0.965992i \(-0.583252\pi\)
0.259067 + 0.965859i \(0.416585\pi\)
\(770\) −4.92471 + 6.95676i −0.177474 + 0.250704i
\(771\) 0 0
\(772\) −8.28154 2.21903i −0.298059 0.0798647i
\(773\) −12.1599 12.1599i −0.437360 0.437360i 0.453763 0.891123i \(-0.350081\pi\)
−0.891123 + 0.453763i \(0.850081\pi\)
\(774\) 0 0
\(775\) 3.51157 + 0.940921i 0.126139 + 0.0337989i
\(776\) −25.9886 + 15.0045i −0.932935 + 0.538630i
\(777\) 0 0
\(778\) 14.4718 3.87771i 0.518840 0.139023i
\(779\) −40.1292 + 23.1686i −1.43778 + 0.830101i
\(780\) 0 0
\(781\) 14.7311 25.5150i 0.527120 0.912999i
\(782\) −9.69318 9.69318i −0.346627 0.346627i
\(783\) 0 0
\(784\) −3.07987 + 16.4738i −0.109995 + 0.588349i
\(785\) 5.68171 5.68171i 0.202789 0.202789i
\(786\) 0 0
\(787\) −23.9249 + 23.9249i −0.852829 + 0.852829i −0.990481 0.137652i \(-0.956045\pi\)
0.137652 + 0.990481i \(0.456045\pi\)
\(788\) 7.51514 2.01368i 0.267716 0.0717343i