Properties

Label 405.2.r.a.197.3
Level $405$
Weight $2$
Character 405.197
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.r (of order \(36\), degree \(12\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(16\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 197.3
Character \(\chi\) \(=\) 405.197
Dual form 405.2.r.a.368.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.98905 + 0.174019i) q^{2} +(1.95641 - 0.344968i) q^{4} +(-0.840902 - 2.07193i) q^{5} +(1.15499 - 0.808730i) q^{7} +(0.0258608 - 0.00692938i) q^{8} +O(q^{10})\) \(q+(-1.98905 + 0.174019i) q^{2} +(1.95641 - 0.344968i) q^{4} +(-0.840902 - 2.07193i) q^{5} +(1.15499 - 0.808730i) q^{7} +(0.0258608 - 0.00692938i) q^{8} +(2.03315 + 3.97483i) q^{10} +(1.21986 + 3.35154i) q^{11} +(0.265789 - 3.03799i) q^{13} +(-2.15659 + 1.80959i) q^{14} +(-3.78380 + 1.37719i) q^{16} +(-3.91899 - 1.05009i) q^{17} +(-1.42357 - 0.821896i) q^{19} +(-2.35990 - 3.76346i) q^{20} +(-3.00959 - 6.45408i) q^{22} +(3.67339 - 5.24614i) q^{23} +(-3.58577 + 3.48458i) q^{25} +6.08895i q^{26} +(1.98064 - 1.98064i) q^{28} +(2.12205 + 1.78061i) q^{29} +(-1.13538 - 6.43905i) q^{31} +(7.23797 - 3.37512i) q^{32} +(7.97779 + 1.40670i) q^{34} +(-2.64686 - 1.71298i) q^{35} +(0.751675 - 2.80529i) q^{37} +(2.97456 + 1.38706i) q^{38} +(-0.0361036 - 0.0477548i) q^{40} +(-5.92728 - 7.06386i) q^{41} +(2.41117 - 5.17078i) q^{43} +(3.54272 + 6.13617i) q^{44} +(-6.39361 + 11.0741i) q^{46} +(-4.56850 - 6.52449i) q^{47} +(-1.71419 + 4.70971i) q^{49} +(6.52587 - 7.55498i) q^{50} +(-0.528015 - 6.03524i) q^{52} +(-8.37726 - 8.37726i) q^{53} +(5.91836 - 5.34577i) q^{55} +(0.0242649 - 0.0289177i) q^{56} +(-4.53071 - 3.17244i) q^{58} +(13.4607 + 4.89929i) q^{59} +(1.11559 - 6.32681i) q^{61} +(3.37884 + 12.6100i) q^{62} +(-6.83499 + 3.94619i) q^{64} +(-6.51799 + 2.00395i) q^{65} +(-11.6234 - 1.01692i) q^{67} +(-8.02940 - 0.702481i) q^{68} +(5.56282 + 2.94660i) q^{70} +(-0.966172 + 0.557819i) q^{71} +(2.19579 + 8.19480i) q^{73} +(-1.00694 + 5.71065i) q^{74} +(-3.06861 - 1.11688i) q^{76} +(4.11941 + 2.88444i) q^{77} +(-3.51532 + 4.18939i) q^{79} +(6.03525 + 6.68168i) q^{80} +(13.0189 + 13.0189i) q^{82} +(-0.529499 - 6.05220i) q^{83} +(1.11978 + 9.00288i) q^{85} +(-3.89612 + 10.7045i) q^{86} +(0.0547706 + 0.0782205i) q^{88} +(0.0742532 - 0.128610i) q^{89} +(-2.14993 - 3.72378i) q^{91} +(5.37690 - 11.5308i) q^{92} +(10.2223 + 12.1825i) q^{94} +(-0.505829 + 3.64066i) q^{95} +(11.6922 + 5.45218i) q^{97} +(2.59003 - 9.66613i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{13}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.98905 + 0.174019i −1.40647 + 0.123050i −0.764966 0.644071i \(-0.777244\pi\)
−0.641503 + 0.767121i \(0.721689\pi\)
\(3\) 0 0
\(4\) 1.95641 0.344968i 0.978205 0.172484i
\(5\) −0.840902 2.07193i −0.376063 0.926594i
\(6\) 0 0
\(7\) 1.15499 0.808730i 0.436543 0.305671i −0.334567 0.942372i \(-0.608590\pi\)
0.771111 + 0.636701i \(0.219701\pi\)
\(8\) 0.0258608 0.00692938i 0.00914317 0.00244991i
\(9\) 0 0
\(10\) 2.03315 + 3.97483i 0.642938 + 1.25695i
\(11\) 1.21986 + 3.35154i 0.367801 + 1.01053i 0.976196 + 0.216891i \(0.0695917\pi\)
−0.608394 + 0.793635i \(0.708186\pi\)
\(12\) 0 0
\(13\) 0.265789 3.03799i 0.0737167 0.842586i −0.865869 0.500271i \(-0.833234\pi\)
0.939585 0.342315i \(-0.111211\pi\)
\(14\) −2.15659 + 1.80959i −0.576372 + 0.483633i
\(15\) 0 0
\(16\) −3.78380 + 1.37719i −0.945951 + 0.344298i
\(17\) −3.91899 1.05009i −0.950495 0.254684i −0.249922 0.968266i \(-0.580405\pi\)
−0.700572 + 0.713582i \(0.747072\pi\)
\(18\) 0 0
\(19\) −1.42357 0.821896i −0.326588 0.188556i 0.327737 0.944769i \(-0.393714\pi\)
−0.654325 + 0.756213i \(0.727047\pi\)
\(20\) −2.35990 3.76346i −0.527689 0.841534i
\(21\) 0 0
\(22\) −3.00959 6.45408i −0.641646 1.37602i
\(23\) 3.67339 5.24614i 0.765954 1.09390i −0.226824 0.973936i \(-0.572834\pi\)
0.992779 0.119960i \(-0.0382767\pi\)
\(24\) 0 0
\(25\) −3.58577 + 3.48458i −0.717153 + 0.696916i
\(26\) 6.08895i 1.19414i
\(27\) 0 0
\(28\) 1.98064 1.98064i 0.374306 0.374306i
\(29\) 2.12205 + 1.78061i 0.394054 + 0.330651i 0.818190 0.574948i \(-0.194978\pi\)
−0.424136 + 0.905599i \(0.639422\pi\)
\(30\) 0 0
\(31\) −1.13538 6.43905i −0.203920 1.15649i −0.899130 0.437681i \(-0.855800\pi\)
0.695211 0.718806i \(-0.255311\pi\)
\(32\) 7.23797 3.37512i 1.27951 0.596643i
\(33\) 0 0
\(34\) 7.97779 + 1.40670i 1.36818 + 0.241247i
\(35\) −2.64686 1.71298i −0.447401 0.289547i
\(36\) 0 0
\(37\) 0.751675 2.80529i 0.123575 0.461186i −0.876210 0.481929i \(-0.839936\pi\)
0.999785 + 0.0207425i \(0.00660301\pi\)
\(38\) 2.97456 + 1.38706i 0.482538 + 0.225011i
\(39\) 0 0
\(40\) −0.0361036 0.0477548i −0.00570848 0.00755069i
\(41\) −5.92728 7.06386i −0.925686 1.10319i −0.994414 0.105554i \(-0.966339\pi\)
0.0687280 0.997635i \(-0.478106\pi\)
\(42\) 0 0
\(43\) 2.41117 5.17078i 0.367701 0.788536i −0.632205 0.774801i \(-0.717850\pi\)
0.999906 0.0137353i \(-0.00437223\pi\)
\(44\) 3.54272 + 6.13617i 0.534085 + 0.925062i
\(45\) 0 0
\(46\) −6.39361 + 11.0741i −0.942687 + 1.63278i
\(47\) −4.56850 6.52449i −0.666384 0.951695i −0.999960 0.00897134i \(-0.997144\pi\)
0.333576 0.942723i \(-0.391745\pi\)
\(48\) 0 0
\(49\) −1.71419 + 4.70971i −0.244885 + 0.672815i
\(50\) 6.52587 7.55498i 0.922898 1.06844i
\(51\) 0 0
\(52\) −0.528015 6.03524i −0.0732225 0.836937i
\(53\) −8.37726 8.37726i −1.15070 1.15070i −0.986412 0.164293i \(-0.947466\pi\)
−0.164293 0.986412i \(-0.552534\pi\)
\(54\) 0 0
\(55\) 5.91836 5.34577i 0.798031 0.720824i
\(56\) 0.0242649 0.0289177i 0.00324253 0.00386429i
\(57\) 0 0
\(58\) −4.53071 3.17244i −0.594911 0.416561i
\(59\) 13.4607 + 4.89929i 1.75243 + 0.637833i 0.999788 0.0205964i \(-0.00655651\pi\)
0.752643 + 0.658429i \(0.228779\pi\)
\(60\) 0 0
\(61\) 1.11559 6.32681i 0.142836 0.810066i −0.826242 0.563315i \(-0.809526\pi\)
0.969079 0.246751i \(-0.0793630\pi\)
\(62\) 3.37884 + 12.6100i 0.429113 + 1.60147i
\(63\) 0 0
\(64\) −6.83499 + 3.94619i −0.854374 + 0.493273i
\(65\) −6.51799 + 2.00395i −0.808457 + 0.248560i
\(66\) 0 0
\(67\) −11.6234 1.01692i −1.42002 0.124236i −0.648877 0.760893i \(-0.724761\pi\)
−0.771147 + 0.636658i \(0.780317\pi\)
\(68\) −8.02940 0.702481i −0.973708 0.0851884i
\(69\) 0 0
\(70\) 5.56282 + 2.94660i 0.664884 + 0.352186i
\(71\) −0.966172 + 0.557819i −0.114663 + 0.0662010i −0.556235 0.831025i \(-0.687755\pi\)
0.441571 + 0.897226i \(0.354421\pi\)
\(72\) 0 0
\(73\) 2.19579 + 8.19480i 0.256998 + 0.959129i 0.966968 + 0.254898i \(0.0820417\pi\)
−0.709970 + 0.704232i \(0.751292\pi\)
\(74\) −1.00694 + 5.71065i −0.117055 + 0.663850i
\(75\) 0 0
\(76\) −3.06861 1.11688i −0.351993 0.128115i
\(77\) 4.11941 + 2.88444i 0.469450 + 0.328712i
\(78\) 0 0
\(79\) −3.51532 + 4.18939i −0.395504 + 0.471344i −0.926644 0.375941i \(-0.877320\pi\)
0.531139 + 0.847284i \(0.321764\pi\)
\(80\) 6.03525 + 6.68168i 0.674761 + 0.747035i
\(81\) 0 0
\(82\) 13.0189 + 13.0189i 1.43770 + 1.43770i
\(83\) −0.529499 6.05220i −0.0581201 0.664315i −0.968249 0.249989i \(-0.919573\pi\)
0.910129 0.414326i \(-0.135983\pi\)
\(84\) 0 0
\(85\) 1.11978 + 9.00288i 0.121457 + 0.976500i
\(86\) −3.89612 + 10.7045i −0.420130 + 1.15430i
\(87\) 0 0
\(88\) 0.0547706 + 0.0782205i 0.00583856 + 0.00833833i
\(89\) 0.0742532 0.128610i 0.00787082 0.0136327i −0.862063 0.506801i \(-0.830828\pi\)
0.869934 + 0.493168i \(0.164161\pi\)
\(90\) 0 0
\(91\) −2.14993 3.72378i −0.225374 0.390358i
\(92\) 5.37690 11.5308i 0.560581 1.20217i
\(93\) 0 0
\(94\) 10.2223 + 12.1825i 1.05435 + 1.25653i
\(95\) −0.505829 + 3.64066i −0.0518970 + 0.373524i
\(96\) 0 0
\(97\) 11.6922 + 5.45218i 1.18717 + 0.553585i 0.912946 0.408081i \(-0.133802\pi\)
0.274222 + 0.961667i \(0.411580\pi\)
\(98\) 2.59003 9.66613i 0.261633 0.976427i
\(99\) 0 0
\(100\) −5.81316 + 8.05424i −0.581316 + 0.805424i
\(101\) 5.20108 + 0.917090i 0.517526 + 0.0912539i 0.426310 0.904577i \(-0.359813\pi\)
0.0912166 + 0.995831i \(0.470924\pi\)
\(102\) 0 0
\(103\) −2.92471 + 1.36382i −0.288181 + 0.134381i −0.561333 0.827590i \(-0.689711\pi\)
0.273153 + 0.961971i \(0.411934\pi\)
\(104\) −0.0141778 0.0804065i −0.00139025 0.00788451i
\(105\) 0 0
\(106\) 18.1206 + 15.2050i 1.76002 + 1.47684i
\(107\) −9.12902 + 9.12902i −0.882536 + 0.882536i −0.993792 0.111256i \(-0.964513\pi\)
0.111256 + 0.993792i \(0.464513\pi\)
\(108\) 0 0
\(109\) 7.32304i 0.701420i −0.936484 0.350710i \(-0.885940\pi\)
0.936484 0.350710i \(-0.114060\pi\)
\(110\) −10.8416 + 11.6629i −1.03371 + 1.11201i
\(111\) 0 0
\(112\) −3.25646 + 4.65071i −0.307707 + 0.439451i
\(113\) 6.43209 + 13.7937i 0.605081 + 1.29760i 0.935354 + 0.353714i \(0.115081\pi\)
−0.330273 + 0.943885i \(0.607141\pi\)
\(114\) 0 0
\(115\) −13.9586 3.19950i −1.30164 0.298355i
\(116\) 4.76585 + 2.75156i 0.442498 + 0.255476i
\(117\) 0 0
\(118\) −27.6265 7.40249i −2.54322 0.681455i
\(119\) −5.37561 + 1.95656i −0.492782 + 0.179358i
\(120\) 0 0
\(121\) −1.31824 + 1.10614i −0.119840 + 0.100558i
\(122\) −1.11797 + 12.7785i −0.101216 + 1.15691i
\(123\) 0 0
\(124\) −4.44253 12.2057i −0.398951 1.09611i
\(125\) 10.2351 + 4.49926i 0.915453 + 0.402426i
\(126\) 0 0
\(127\) 6.42251 1.72091i 0.569905 0.152706i 0.0376522 0.999291i \(-0.488012\pi\)
0.532253 + 0.846585i \(0.321345\pi\)
\(128\) −0.175446 + 0.122848i −0.0155074 + 0.0108584i
\(129\) 0 0
\(130\) 12.6159 5.12021i 1.10648 0.449072i
\(131\) −11.6386 + 2.05219i −1.01687 + 0.179301i −0.657149 0.753761i \(-0.728238\pi\)
−0.359717 + 0.933062i \(0.617127\pi\)
\(132\) 0 0
\(133\) −2.30889 + 0.202002i −0.200206 + 0.0175158i
\(134\) 23.2964 2.01251
\(135\) 0 0
\(136\) −0.108625 −0.00931449
\(137\) 12.0706 1.05604i 1.03126 0.0902237i 0.441059 0.897478i \(-0.354603\pi\)
0.590203 + 0.807255i \(0.299048\pi\)
\(138\) 0 0
\(139\) 12.8272 2.26177i 1.08799 0.191841i 0.399242 0.916846i \(-0.369273\pi\)
0.688744 + 0.725005i \(0.258162\pi\)
\(140\) −5.76927 2.43822i −0.487592 0.206067i
\(141\) 0 0
\(142\) 1.82469 1.27766i 0.153125 0.107219i
\(143\) 10.5061 2.81511i 0.878568 0.235412i
\(144\) 0 0
\(145\) 1.90486 5.89404i 0.158190 0.489474i
\(146\) −5.79358 15.9177i −0.479480 1.31736i
\(147\) 0 0
\(148\) 0.502850 5.74760i 0.0413340 0.472450i
\(149\) −2.75179 + 2.30902i −0.225435 + 0.189162i −0.748509 0.663125i \(-0.769230\pi\)
0.523074 + 0.852288i \(0.324785\pi\)
\(150\) 0 0
\(151\) 0.415850 0.151357i 0.0338414 0.0123173i −0.325044 0.945699i \(-0.605379\pi\)
0.358885 + 0.933382i \(0.383157\pi\)
\(152\) −0.0425098 0.0113905i −0.00344800 0.000923888i
\(153\) 0 0
\(154\) −8.69564 5.02043i −0.700715 0.404558i
\(155\) −12.3865 + 7.76703i −0.994907 + 0.623863i
\(156\) 0 0
\(157\) −0.538818 1.15550i −0.0430024 0.0922189i 0.883633 0.468180i \(-0.155090\pi\)
−0.926635 + 0.375961i \(0.877312\pi\)
\(158\) 6.26310 8.94463i 0.498265 0.711597i
\(159\) 0 0
\(160\) −13.0794 12.1584i −1.03402 0.961207i
\(161\) 9.02999i 0.711663i
\(162\) 0 0
\(163\) −2.53097 + 2.53097i −0.198241 + 0.198241i −0.799245 0.601005i \(-0.794767\pi\)
0.601005 + 0.799245i \(0.294767\pi\)
\(164\) −14.0330 11.7751i −1.09579 0.919479i
\(165\) 0 0
\(166\) 2.10640 + 11.9460i 0.163488 + 0.927187i
\(167\) 10.9336 5.09841i 0.846066 0.394527i 0.0492772 0.998785i \(-0.484308\pi\)
0.796789 + 0.604258i \(0.206530\pi\)
\(168\) 0 0
\(169\) 3.64378 + 0.642497i 0.280291 + 0.0494228i
\(170\) −3.79396 17.7123i −0.290984 1.35847i
\(171\) 0 0
\(172\) 2.93349 10.9479i 0.223677 0.834773i
\(173\) 5.26639 + 2.45576i 0.400397 + 0.186708i 0.612377 0.790566i \(-0.290214\pi\)
−0.211980 + 0.977274i \(0.567991\pi\)
\(174\) 0 0
\(175\) −1.32343 + 6.92455i −0.100042 + 0.523447i
\(176\) −9.23141 11.0016i −0.695844 0.829274i
\(177\) 0 0
\(178\) −0.125312 + 0.268733i −0.00939256 + 0.0201424i
\(179\) −9.76891 16.9203i −0.730163 1.26468i −0.956813 0.290703i \(-0.906111\pi\)
0.226651 0.973976i \(-0.427222\pi\)
\(180\) 0 0
\(181\) 5.30360 9.18610i 0.394213 0.682797i −0.598787 0.800908i \(-0.704350\pi\)
0.993000 + 0.118111i \(0.0376838\pi\)
\(182\) 4.92432 + 7.03265i 0.365015 + 0.521295i
\(183\) 0 0
\(184\) 0.0586442 0.161124i 0.00432331 0.0118782i
\(185\) −6.44444 + 0.801558i −0.473804 + 0.0589317i
\(186\) 0 0
\(187\) −1.26120 14.4156i −0.0922282 1.05417i
\(188\) −11.1886 11.1886i −0.816012 0.816012i
\(189\) 0 0
\(190\) 0.372574 7.32947i 0.0270293 0.531735i
\(191\) 3.07377 3.66318i 0.222410 0.265058i −0.643288 0.765624i \(-0.722430\pi\)
0.865698 + 0.500566i \(0.166875\pi\)
\(192\) 0 0
\(193\) −4.45676 3.12066i −0.320804 0.224630i 0.402070 0.915609i \(-0.368291\pi\)
−0.722875 + 0.690979i \(0.757180\pi\)
\(194\) −24.2052 8.80997i −1.73783 0.632519i
\(195\) 0 0
\(196\) −1.72897 + 9.80546i −0.123498 + 0.700390i
\(197\) 2.07911 + 7.75934i 0.148130 + 0.552830i 0.999596 + 0.0284197i \(0.00904750\pi\)
−0.851466 + 0.524410i \(0.824286\pi\)
\(198\) 0 0
\(199\) 10.5312 6.08020i 0.746539 0.431014i −0.0779033 0.996961i \(-0.524823\pi\)
0.824442 + 0.565947i \(0.191489\pi\)
\(200\) −0.0685848 + 0.114961i −0.00484968 + 0.00812898i
\(201\) 0 0
\(202\) −10.5048 0.919049i −0.739114 0.0646641i
\(203\) 3.89096 + 0.340415i 0.273092 + 0.0238925i
\(204\) 0 0
\(205\) −9.65154 + 18.2209i −0.674092 + 1.27260i
\(206\) 5.58006 3.22165i 0.388781 0.224463i
\(207\) 0 0
\(208\) 3.17819 + 11.8612i 0.220368 + 0.822425i
\(209\) 1.01806 5.77373i 0.0704210 0.399377i
\(210\) 0 0
\(211\) 2.80282 + 1.02014i 0.192954 + 0.0702295i 0.436690 0.899612i \(-0.356151\pi\)
−0.243736 + 0.969842i \(0.578373\pi\)
\(212\) −19.2792 13.4995i −1.32410 0.927147i
\(213\) 0 0
\(214\) 16.5694 19.7467i 1.13266 1.34985i
\(215\) −12.7410 0.647657i −0.868932 0.0441698i
\(216\) 0 0
\(217\) −6.51879 6.51879i −0.442524 0.442524i
\(218\) 1.27435 + 14.5659i 0.0863097 + 0.986525i
\(219\) 0 0
\(220\) 9.73461 12.5002i 0.656307 0.842761i
\(221\) −4.23179 + 11.6267i −0.284661 + 0.782099i
\(222\) 0 0
\(223\) 4.64364 + 6.63181i 0.310961 + 0.444099i 0.943963 0.330052i \(-0.107066\pi\)
−0.633002 + 0.774151i \(0.718177\pi\)
\(224\) 5.63019 9.75178i 0.376183 0.651568i
\(225\) 0 0
\(226\) −15.1941 26.3170i −1.01070 1.75058i
\(227\) 3.25781 6.98639i 0.216228 0.463703i −0.768036 0.640407i \(-0.778766\pi\)
0.984264 + 0.176704i \(0.0565435\pi\)
\(228\) 0 0
\(229\) 2.93595 + 3.49893i 0.194013 + 0.231216i 0.854277 0.519818i \(-0.174000\pi\)
−0.660264 + 0.751033i \(0.729556\pi\)
\(230\) 28.3211 + 3.93490i 1.86743 + 0.259459i
\(231\) 0 0
\(232\) 0.0672163 + 0.0313435i 0.00441297 + 0.00205780i
\(233\) −5.18153 + 19.3377i −0.339454 + 1.26686i 0.559506 + 0.828826i \(0.310991\pi\)
−0.898960 + 0.438032i \(0.855676\pi\)
\(234\) 0 0
\(235\) −9.67661 + 14.9521i −0.631232 + 0.975364i
\(236\) 28.0247 + 4.94151i 1.82425 + 0.321665i
\(237\) 0 0
\(238\) 10.3519 4.82716i 0.671012 0.312898i
\(239\) 2.31345 + 13.1202i 0.149645 + 0.848678i 0.963520 + 0.267638i \(0.0862431\pi\)
−0.813875 + 0.581040i \(0.802646\pi\)
\(240\) 0 0
\(241\) 19.5457 + 16.4008i 1.25905 + 1.05647i 0.995783 + 0.0917454i \(0.0292446\pi\)
0.263267 + 0.964723i \(0.415200\pi\)
\(242\) 2.42956 2.42956i 0.156178 0.156178i
\(243\) 0 0
\(244\) 12.7627i 0.817047i
\(245\) 11.1996 0.408720i 0.715519 0.0261122i
\(246\) 0 0
\(247\) −2.87528 + 4.10632i −0.182950 + 0.261279i
\(248\) −0.0739804 0.158651i −0.00469776 0.0100744i
\(249\) 0 0
\(250\) −21.1410 7.16814i −1.33707 0.453353i
\(251\) −17.4693 10.0859i −1.10265 0.636617i −0.165736 0.986170i \(-0.553000\pi\)
−0.936917 + 0.349553i \(0.886333\pi\)
\(252\) 0 0
\(253\) 22.0636 + 5.91193i 1.38713 + 0.371680i
\(254\) −12.4752 + 4.54060i −0.782764 + 0.284903i
\(255\) 0 0
\(256\) 12.4194 10.4211i 0.776213 0.651320i
\(257\) 0.746929 8.53743i 0.0465921 0.532550i −0.936653 0.350260i \(-0.886093\pi\)
0.983245 0.182291i \(-0.0583512\pi\)
\(258\) 0 0
\(259\) −1.40055 3.84797i −0.0870257 0.239101i
\(260\) −12.0606 + 6.16905i −0.747964 + 0.382588i
\(261\) 0 0
\(262\) 22.7925 6.10724i 1.40813 0.377307i
\(263\) 16.5483 11.5873i 1.02041 0.714501i 0.0614734 0.998109i \(-0.480420\pi\)
0.958941 + 0.283607i \(0.0915312\pi\)
\(264\) 0 0
\(265\) −10.3126 + 24.4015i −0.633499 + 1.49897i
\(266\) 4.55734 0.803581i 0.279428 0.0492707i
\(267\) 0 0
\(268\) −23.0909 + 2.02019i −1.41050 + 0.123403i
\(269\) 11.8522 0.722639 0.361320 0.932442i \(-0.382326\pi\)
0.361320 + 0.932442i \(0.382326\pi\)
\(270\) 0 0
\(271\) 24.7671 1.50450 0.752249 0.658879i \(-0.228969\pi\)
0.752249 + 0.658879i \(0.228969\pi\)
\(272\) 16.2749 1.42387i 0.986808 0.0863345i
\(273\) 0 0
\(274\) −23.8252 + 4.20103i −1.43934 + 0.253794i
\(275\) −16.0528 7.76713i −0.968021 0.468375i
\(276\) 0 0
\(277\) −23.8949 + 16.7314i −1.43571 + 1.00529i −0.441564 + 0.897230i \(0.645576\pi\)
−0.994144 + 0.108064i \(0.965535\pi\)
\(278\) −25.1202 + 6.73095i −1.50661 + 0.403695i
\(279\) 0 0
\(280\) −0.0803198 0.0259580i −0.00480003 0.00155129i
\(281\) 10.0345 + 27.5694i 0.598605 + 1.64465i 0.754055 + 0.656811i \(0.228095\pi\)
−0.155450 + 0.987844i \(0.549683\pi\)
\(282\) 0 0
\(283\) 1.18317 13.5237i 0.0703324 0.803902i −0.876338 0.481697i \(-0.840020\pi\)
0.946670 0.322205i \(-0.104424\pi\)
\(284\) −1.69780 + 1.42462i −0.100746 + 0.0845357i
\(285\) 0 0
\(286\) −20.4073 + 7.42766i −1.20671 + 0.439207i
\(287\) −12.5587 3.36509i −0.741315 0.198635i
\(288\) 0 0
\(289\) −0.466643 0.269416i −0.0274496 0.0158480i
\(290\) −2.76317 + 12.0550i −0.162259 + 0.707895i
\(291\) 0 0
\(292\) 7.12281 + 15.2749i 0.416831 + 0.893897i
\(293\) −4.73624 + 6.76405i −0.276694 + 0.395160i −0.933314 0.359062i \(-0.883097\pi\)
0.656620 + 0.754222i \(0.271986\pi\)
\(294\) 0 0
\(295\) −1.16815 32.0094i −0.0680124 1.86366i
\(296\) 0.0777556i 0.00451945i
\(297\) 0 0
\(298\) 5.07162 5.07162i 0.293791 0.293791i
\(299\) −14.9614 12.5541i −0.865238 0.726021i
\(300\) 0 0
\(301\) −1.39689 7.92216i −0.0805155 0.456626i
\(302\) −0.800806 + 0.373422i −0.0460812 + 0.0214880i
\(303\) 0 0
\(304\) 6.51840 + 1.14937i 0.373856 + 0.0659209i
\(305\) −14.0468 + 3.00882i −0.804317 + 0.172284i
\(306\) 0 0
\(307\) −2.68621 + 10.0251i −0.153310 + 0.572161i 0.845934 + 0.533288i \(0.179044\pi\)
−0.999244 + 0.0388737i \(0.987623\pi\)
\(308\) 9.05429 + 4.22208i 0.515916 + 0.240575i
\(309\) 0 0
\(310\) 23.2857 17.6045i 1.32254 0.999867i
\(311\) 12.2675 + 14.6199i 0.695627 + 0.829016i 0.992024 0.126049i \(-0.0402297\pi\)
−0.296397 + 0.955065i \(0.595785\pi\)
\(312\) 0 0
\(313\) 6.95728 14.9199i 0.393249 0.843325i −0.605619 0.795755i \(-0.707075\pi\)
0.998868 0.0475700i \(-0.0151477\pi\)
\(314\) 1.27281 + 2.20458i 0.0718291 + 0.124412i
\(315\) 0 0
\(316\) −5.43220 + 9.40884i −0.305585 + 0.529289i
\(317\) −4.28594 6.12095i −0.240722 0.343787i 0.680553 0.732699i \(-0.261740\pi\)
−0.921275 + 0.388912i \(0.872851\pi\)
\(318\) 0 0
\(319\) −3.37917 + 9.28420i −0.189197 + 0.519816i
\(320\) 13.9238 + 10.8433i 0.778363 + 0.606156i
\(321\) 0 0
\(322\) 1.57139 + 17.9611i 0.0875702 + 1.00093i
\(323\) 4.71587 + 4.71587i 0.262398 + 0.262398i
\(324\) 0 0
\(325\) 9.63304 + 11.8197i 0.534345 + 0.655638i
\(326\) 4.59378 5.47465i 0.254426 0.303213i
\(327\) 0 0
\(328\) −0.202232 0.141605i −0.0111664 0.00781881i
\(329\) −10.5531 3.84101i −0.581811 0.211762i
\(330\) 0 0
\(331\) 1.44127 8.17383i 0.0792192 0.449274i −0.919236 0.393707i \(-0.871192\pi\)
0.998455 0.0555668i \(-0.0176966\pi\)
\(332\) −3.12373 11.6579i −0.171437 0.639812i
\(333\) 0 0
\(334\) −20.8602 + 12.0436i −1.14142 + 0.658998i
\(335\) 7.66717 + 24.9380i 0.418902 + 1.36251i
\(336\) 0 0
\(337\) 15.6386 + 1.36820i 0.851888 + 0.0745305i 0.504731 0.863277i \(-0.331592\pi\)
0.347157 + 0.937807i \(0.387147\pi\)
\(338\) −7.35946 0.643869i −0.400302 0.0350219i
\(339\) 0 0
\(340\) 5.29645 + 17.2270i 0.287240 + 0.934268i
\(341\) 20.1957 11.6600i 1.09366 0.631424i
\(342\) 0 0
\(343\) 4.38351 + 16.3595i 0.236687 + 0.883330i
\(344\) 0.0265246 0.150428i 0.00143011 0.00811056i
\(345\) 0 0
\(346\) −10.9025 3.96817i −0.586120 0.213330i
\(347\) −0.751529 0.526226i −0.0403442 0.0282493i 0.553230 0.833028i \(-0.313395\pi\)
−0.593575 + 0.804779i \(0.702284\pi\)
\(348\) 0 0
\(349\) −23.1000 + 27.5295i −1.23652 + 1.47362i −0.408655 + 0.912689i \(0.634002\pi\)
−0.827861 + 0.560934i \(0.810442\pi\)
\(350\) 1.42736 14.0036i 0.0762953 0.748522i
\(351\) 0 0
\(352\) 20.1412 + 20.1412i 1.07353 + 1.07353i
\(353\) 0.420748 + 4.80917i 0.0223942 + 0.255966i 0.999136 + 0.0415497i \(0.0132295\pi\)
−0.976742 + 0.214417i \(0.931215\pi\)
\(354\) 0 0
\(355\) 1.96822 + 1.53277i 0.104462 + 0.0813508i
\(356\) 0.100903 0.277229i 0.00534786 0.0146931i
\(357\) 0 0
\(358\) 22.3753 + 31.9552i 1.18257 + 1.68889i
\(359\) −1.88801 + 3.27013i −0.0996454 + 0.172591i −0.911538 0.411216i \(-0.865104\pi\)
0.811892 + 0.583807i \(0.198438\pi\)
\(360\) 0 0
\(361\) −8.14897 14.1144i −0.428893 0.742865i
\(362\) −8.95055 + 19.1945i −0.470430 + 1.00884i
\(363\) 0 0
\(364\) −5.49072 6.54359i −0.287792 0.342977i
\(365\) 15.1326 11.4406i 0.792076 0.598826i
\(366\) 0 0
\(367\) −22.8495 10.6549i −1.19273 0.556181i −0.278135 0.960542i \(-0.589716\pi\)
−0.914600 + 0.404361i \(0.867494\pi\)
\(368\) −6.67443 + 24.9093i −0.347929 + 1.29849i
\(369\) 0 0
\(370\) 12.6788 2.71579i 0.659140 0.141187i
\(371\) −16.4505 2.90067i −0.854070 0.150596i
\(372\) 0 0
\(373\) 9.99084 4.65880i 0.517306 0.241224i −0.146389 0.989227i \(-0.546765\pi\)
0.663695 + 0.748003i \(0.268987\pi\)
\(374\) 5.01718 + 28.4538i 0.259432 + 1.47131i
\(375\) 0 0
\(376\) −0.163356 0.137072i −0.00842442 0.00706893i
\(377\) 5.97348 5.97348i 0.307650 0.307650i
\(378\) 0 0
\(379\) 6.15292i 0.316054i −0.987435 0.158027i \(-0.949487\pi\)
0.987435 0.158027i \(-0.0505134\pi\)
\(380\) 0.266301 + 7.29712i 0.0136610 + 0.374334i
\(381\) 0 0
\(382\) −5.47641 + 7.82113i −0.280198 + 0.400164i
\(383\) −7.45128 15.9793i −0.380743 0.816506i −0.999521 0.0309400i \(-0.990150\pi\)
0.618778 0.785566i \(-0.287628\pi\)
\(384\) 0 0
\(385\) 2.51233 10.9606i 0.128040 0.558606i
\(386\) 9.40775 + 5.43157i 0.478842 + 0.276460i
\(387\) 0 0
\(388\) 24.7556 + 6.63326i 1.25678 + 0.336753i
\(389\) 13.1982 4.80373i 0.669173 0.243559i 0.0149811 0.999888i \(-0.495231\pi\)
0.654192 + 0.756329i \(0.273009\pi\)
\(390\) 0 0
\(391\) −19.9049 + 16.7022i −1.00663 + 0.844666i
\(392\) −0.0116951 + 0.133675i −0.000590689 + 0.00675161i
\(393\) 0 0
\(394\) −5.48572 15.0719i −0.276366 0.759311i
\(395\) 11.6362 + 3.76061i 0.585479 + 0.189217i
\(396\) 0 0
\(397\) −29.2343 + 7.83331i −1.46723 + 0.393143i −0.901980 0.431778i \(-0.857886\pi\)
−0.565248 + 0.824921i \(0.691220\pi\)
\(398\) −19.8890 + 13.9264i −0.996947 + 0.698070i
\(399\) 0 0
\(400\) 8.76890 18.1232i 0.438445 0.906162i
\(401\) 16.0405 2.82837i 0.801024 0.141242i 0.241873 0.970308i \(-0.422238\pi\)
0.559151 + 0.829066i \(0.311127\pi\)
\(402\) 0 0
\(403\) −19.8635 + 1.73783i −0.989472 + 0.0865676i
\(404\) 10.4918 0.521987
\(405\) 0 0
\(406\) −7.79855 −0.387035
\(407\) 10.3190 0.902792i 0.511492 0.0447497i
\(408\) 0 0
\(409\) 19.2731 3.39837i 0.952995 0.168039i 0.324529 0.945876i \(-0.394794\pi\)
0.628466 + 0.777837i \(0.283683\pi\)
\(410\) 16.0266 37.9218i 0.791496 1.87282i
\(411\) 0 0
\(412\) −5.25147 + 3.67712i −0.258721 + 0.181159i
\(413\) 19.5091 5.22744i 0.959979 0.257226i
\(414\) 0 0
\(415\) −12.0945 + 6.18639i −0.593694 + 0.303678i
\(416\) −8.32980 22.8859i −0.408402 1.12208i
\(417\) 0 0
\(418\) −1.02024 + 11.6614i −0.0499015 + 0.570377i
\(419\) 0.141106 0.118402i 0.00689349 0.00578432i −0.639334 0.768929i \(-0.720790\pi\)
0.646228 + 0.763145i \(0.276346\pi\)
\(420\) 0 0
\(421\) −17.1952 + 6.25854i −0.838043 + 0.305023i −0.725155 0.688585i \(-0.758232\pi\)
−0.112887 + 0.993608i \(0.536010\pi\)
\(422\) −5.75246 1.54137i −0.280025 0.0750325i
\(423\) 0 0
\(424\) −0.274692 0.158593i −0.0133402 0.00770197i
\(425\) 17.7117 9.89064i 0.859144 0.479767i
\(426\) 0 0
\(427\) −3.82819 8.20959i −0.185259 0.397290i
\(428\) −14.7109 + 21.0093i −0.711078 + 1.01552i
\(429\) 0 0
\(430\) 25.4552 0.928965i 1.22756 0.0447987i
\(431\) 20.4312i 0.984138i 0.870556 + 0.492069i \(0.163759\pi\)
−0.870556 + 0.492069i \(0.836241\pi\)
\(432\) 0 0
\(433\) −1.40075 + 1.40075i −0.0673156 + 0.0673156i −0.739963 0.672647i \(-0.765157\pi\)
0.672647 + 0.739963i \(0.265157\pi\)
\(434\) 14.1006 + 11.8318i 0.676849 + 0.567944i
\(435\) 0 0
\(436\) −2.52621 14.3269i −0.120984 0.686132i
\(437\) −9.54109 + 4.44908i −0.456412 + 0.212829i
\(438\) 0 0
\(439\) 13.9335 + 2.45686i 0.665012 + 0.117259i 0.495957 0.868347i \(-0.334817\pi\)
0.169055 + 0.985607i \(0.445929\pi\)
\(440\) 0.116010 0.179257i 0.00553058 0.00854572i
\(441\) 0 0
\(442\) 6.39395 23.8625i 0.304129 1.13503i
\(443\) −14.5440 6.78197i −0.691005 0.322221i 0.0452014 0.998978i \(-0.485607\pi\)
−0.736207 + 0.676757i \(0.763385\pi\)
\(444\) 0 0
\(445\) −0.328911 0.0456985i −0.0155919 0.00216632i
\(446\) −10.3905 12.3829i −0.492004 0.586347i
\(447\) 0 0
\(448\) −4.70292 + 10.0854i −0.222192 + 0.476493i
\(449\) 2.86184 + 4.95685i 0.135059 + 0.233928i 0.925620 0.378455i \(-0.123544\pi\)
−0.790561 + 0.612383i \(0.790211\pi\)
\(450\) 0 0
\(451\) 16.4443 28.4824i 0.774333 1.34118i
\(452\) 17.3422 + 24.7672i 0.815708 + 1.16495i
\(453\) 0 0
\(454\) −5.26417 + 14.4632i −0.247060 + 0.678791i
\(455\) −5.90753 + 7.58583i −0.276949 + 0.355629i
\(456\) 0 0
\(457\) 1.72215 + 19.6843i 0.0805589 + 0.920793i 0.923704 + 0.383107i \(0.125146\pi\)
−0.843145 + 0.537686i \(0.819299\pi\)
\(458\) −6.44862 6.44862i −0.301324 0.301324i
\(459\) 0 0
\(460\) −28.4124 1.44427i −1.32474 0.0673394i
\(461\) 11.6371 13.8685i 0.541993 0.645922i −0.423640 0.905830i \(-0.639248\pi\)
0.965633 + 0.259909i \(0.0836924\pi\)
\(462\) 0 0
\(463\) 10.7175 + 7.50444i 0.498082 + 0.348761i 0.795467 0.605997i \(-0.207226\pi\)
−0.297385 + 0.954758i \(0.596114\pi\)
\(464\) −10.4816 3.81501i −0.486598 0.177107i
\(465\) 0 0
\(466\) 6.94118 39.3654i 0.321544 1.82357i
\(467\) 2.10904 + 7.87106i 0.0975949 + 0.364229i 0.997400 0.0720628i \(-0.0229582\pi\)
−0.899805 + 0.436292i \(0.856292\pi\)
\(468\) 0 0
\(469\) −14.2473 + 8.22566i −0.657877 + 0.379826i
\(470\) 16.6453 31.4242i 0.767790 1.44949i
\(471\) 0 0
\(472\) 0.382053 + 0.0334253i 0.0175854 + 0.00153852i
\(473\) 20.2713 + 1.77351i 0.932077 + 0.0815462i
\(474\) 0 0
\(475\) 7.96853 2.01340i 0.365621 0.0923810i
\(476\) −9.84196 + 5.68226i −0.451105 + 0.260446i
\(477\) 0 0
\(478\) −6.88474 25.6942i −0.314901 1.17523i
\(479\) 4.41454 25.0361i 0.201706 1.14393i −0.700835 0.713324i \(-0.747189\pi\)
0.902540 0.430606i \(-0.141700\pi\)
\(480\) 0 0
\(481\) −8.32264 3.02919i −0.379480 0.138119i
\(482\) −41.7314 29.2206i −1.90081 1.33096i
\(483\) 0 0
\(484\) −2.19744 + 2.61881i −0.0998838 + 0.119037i
\(485\) 1.46449 28.8102i 0.0664991 1.30821i
\(486\) 0 0
\(487\) −20.8770 20.8770i −0.946027 0.946027i 0.0525891 0.998616i \(-0.483253\pi\)
−0.998616 + 0.0525891i \(0.983253\pi\)
\(488\) −0.0149909 0.171347i −0.000678606 0.00775651i
\(489\) 0 0
\(490\) −22.2055 + 2.76191i −1.00314 + 0.124771i
\(491\) 4.08765 11.2307i 0.184473 0.506835i −0.812640 0.582766i \(-0.801971\pi\)
0.997113 + 0.0759306i \(0.0241927\pi\)
\(492\) 0 0
\(493\) −6.44648 9.20652i −0.290335 0.414641i
\(494\) 5.00448 8.66802i 0.225162 0.389993i
\(495\) 0 0
\(496\) 13.1638 + 22.8004i 0.591074 + 1.02377i
\(497\) −0.664789 + 1.42564i −0.0298199 + 0.0639489i
\(498\) 0 0
\(499\) 3.31792 + 3.95415i 0.148531 + 0.177012i 0.835180 0.549977i \(-0.185364\pi\)
−0.686649 + 0.726989i \(0.740919\pi\)
\(500\) 21.5761 + 5.27162i 0.964912 + 0.235754i
\(501\) 0 0
\(502\) 36.5024 + 17.0214i 1.62918 + 0.759700i
\(503\) 2.60729 9.73055i 0.116253 0.433864i −0.883124 0.469139i \(-0.844564\pi\)
0.999378 + 0.0352755i \(0.0112309\pi\)
\(504\) 0 0
\(505\) −2.47345 11.5474i −0.110067 0.513854i
\(506\) −44.9144 7.91962i −1.99669 0.352070i
\(507\) 0 0
\(508\) 11.9714 5.58236i 0.531145 0.247677i
\(509\) 5.57060 + 31.5924i 0.246912 + 1.40031i 0.816009 + 0.578039i \(0.196182\pi\)
−0.569097 + 0.822270i \(0.692707\pi\)
\(510\) 0 0
\(511\) 9.16349 + 7.68908i 0.405369 + 0.340145i
\(512\) −22.5864 + 22.5864i −0.998188 + 0.998188i
\(513\) 0 0
\(514\) 17.1113i 0.754749i
\(515\) 5.28513 + 4.91296i 0.232891 + 0.216491i
\(516\) 0 0
\(517\) 16.2941 23.2704i 0.716615 1.02343i
\(518\) 3.45537 + 7.41007i 0.151820 + 0.325580i
\(519\) 0 0
\(520\) −0.154674 + 0.0969895i −0.00678292 + 0.00425327i
\(521\) 5.58144 + 3.22245i 0.244528 + 0.141178i 0.617256 0.786762i \(-0.288244\pi\)
−0.372728 + 0.927941i \(0.621578\pi\)
\(522\) 0 0
\(523\) −6.76374 1.81234i −0.295758 0.0792481i 0.107889 0.994163i \(-0.465591\pi\)
−0.403647 + 0.914915i \(0.632258\pi\)
\(524\) −22.0619 + 8.02986i −0.963777 + 0.350786i
\(525\) 0 0
\(526\) −30.8990 + 25.9273i −1.34726 + 1.13049i
\(527\) −2.31205 + 26.4268i −0.100714 + 1.15117i
\(528\) 0 0
\(529\) −6.16176 16.9293i −0.267902 0.736056i
\(530\) 16.2659 50.3304i 0.706547 2.18621i
\(531\) 0 0
\(532\) −4.44745 + 1.19169i −0.192821 + 0.0516663i
\(533\) −23.0353 + 16.1295i −0.997770 + 0.698646i
\(534\) 0 0
\(535\) 26.5913 + 11.2381i 1.14964 + 0.485863i
\(536\) −0.307637 + 0.0542447i −0.0132879 + 0.00234301i
\(537\) 0 0
\(538\) −23.5745 + 2.06250i −1.01637 + 0.0889208i
\(539\) −17.8758 −0.769966
\(540\) 0 0
\(541\) −34.0530 −1.46405 −0.732026 0.681276i \(-0.761425\pi\)
−0.732026 + 0.681276i \(0.761425\pi\)
\(542\) −49.2630 + 4.30996i −2.11603 + 0.185128i
\(543\) 0 0
\(544\) −31.9097 + 5.62655i −1.36812 + 0.241236i
\(545\) −15.1728 + 6.15796i −0.649931 + 0.263778i
\(546\) 0 0
\(547\) 20.2173 14.1563i 0.864431 0.605281i −0.0550200 0.998485i \(-0.517522\pi\)
0.919451 + 0.393204i \(0.128633\pi\)
\(548\) 23.2508 6.23002i 0.993224 0.266133i
\(549\) 0 0
\(550\) 33.2814 + 12.6557i 1.41913 + 0.539640i
\(551\) −1.55740 4.27891i −0.0663474 0.182288i
\(552\) 0 0
\(553\) −0.672056 + 7.68163i −0.0285787 + 0.326656i
\(554\) 44.6166 37.4378i 1.89558 1.59058i
\(555\) 0 0
\(556\) 24.3149 8.84992i 1.03118 0.375320i
\(557\) 8.51625 + 2.28192i 0.360845 + 0.0966881i 0.434686 0.900582i \(-0.356859\pi\)
−0.0738415 + 0.997270i \(0.523526\pi\)
\(558\) 0 0
\(559\) −15.0679 8.69945i −0.637304 0.367948i
\(560\) 12.3743 + 2.83636i 0.522910 + 0.119858i
\(561\) 0 0
\(562\) −24.7566 53.0907i −1.04429 2.23950i
\(563\) 13.3979 19.1342i 0.564655 0.806411i −0.430719 0.902486i \(-0.641740\pi\)
0.995374 + 0.0960749i \(0.0306288\pi\)
\(564\) 0 0
\(565\) 23.1707 24.9260i 0.974800 1.04864i
\(566\) 27.1052i 1.13932i
\(567\) 0 0
\(568\) −0.0211206 + 0.0211206i −0.000886202 + 0.000886202i
\(569\) −1.82798 1.53386i −0.0766330 0.0643027i 0.603667 0.797237i \(-0.293706\pi\)
−0.680300 + 0.732934i \(0.738150\pi\)
\(570\) 0 0
\(571\) 6.32573 + 35.8750i 0.264724 + 1.50132i 0.769821 + 0.638260i \(0.220346\pi\)
−0.505097 + 0.863063i \(0.668543\pi\)
\(572\) 19.5832 9.13180i 0.818815 0.381820i
\(573\) 0 0
\(574\) 25.5654 + 4.50787i 1.06708 + 0.188155i
\(575\) 5.10868 + 31.6116i 0.213047 + 1.31830i
\(576\) 0 0
\(577\) −6.50782 + 24.2875i −0.270924 + 1.01110i 0.687600 + 0.726090i \(0.258664\pi\)
−0.958524 + 0.285012i \(0.908002\pi\)
\(578\) 0.975058 + 0.454677i 0.0405571 + 0.0189121i
\(579\) 0 0
\(580\) 1.69343 12.1883i 0.0703157 0.506091i
\(581\) −5.50616 6.56198i −0.228434 0.272237i
\(582\) 0 0
\(583\) 17.8576 38.2957i 0.739586 1.58605i
\(584\) 0.113570 + 0.196709i 0.00469955 + 0.00813986i
\(585\) 0 0
\(586\) 8.24353 14.2782i 0.340537 0.589828i
\(587\) −17.4662 24.9444i −0.720909 1.02956i −0.997643 0.0686181i \(-0.978141\pi\)
0.276734 0.960947i \(-0.410748\pi\)
\(588\) 0 0
\(589\) −3.67594 + 10.0996i −0.151465 + 0.416145i
\(590\) 7.89375 + 63.4649i 0.324980 + 2.61281i
\(591\) 0 0
\(592\) 1.01923 + 11.6499i 0.0418901 + 0.478806i
\(593\) 26.7405 + 26.7405i 1.09810 + 1.09810i 0.994633 + 0.103470i \(0.0329946\pi\)
0.103470 + 0.994633i \(0.467005\pi\)
\(594\) 0 0
\(595\) 8.57423 + 9.49260i 0.351509 + 0.389159i
\(596\) −4.58708 + 5.46667i −0.187894 + 0.223924i
\(597\) 0 0
\(598\) 31.9435 + 22.3671i 1.30627 + 0.914658i
\(599\) 1.09294 + 0.397799i 0.0446564 + 0.0162536i 0.364252 0.931301i \(-0.381325\pi\)
−0.319595 + 0.947554i \(0.603547\pi\)
\(600\) 0 0
\(601\) 2.53128 14.3556i 0.103253 0.585578i −0.888650 0.458585i \(-0.848356\pi\)
0.991904 0.126993i \(-0.0405325\pi\)
\(602\) 4.15709 + 15.5145i 0.169430 + 0.632323i
\(603\) 0 0
\(604\) 0.761360 0.439571i 0.0309793 0.0178859i
\(605\) 3.40035 + 1.80115i 0.138244 + 0.0732272i
\(606\) 0 0
\(607\) −33.0709 2.89333i −1.34231 0.117437i −0.606746 0.794896i \(-0.707525\pi\)
−0.735560 + 0.677459i \(0.763081\pi\)
\(608\) −13.0777 1.14415i −0.530372 0.0464015i
\(609\) 0 0
\(610\) 27.4162 8.42909i 1.11005 0.341284i
\(611\) −21.0356 + 12.1449i −0.851008 + 0.491330i
\(612\) 0 0
\(613\) 3.05733 + 11.4101i 0.123484 + 0.460849i 0.999781 0.0209221i \(-0.00666018\pi\)
−0.876297 + 0.481772i \(0.839994\pi\)
\(614\) 3.59845 20.4078i 0.145221 0.823592i
\(615\) 0 0
\(616\) 0.126518 + 0.0460490i 0.00509757 + 0.00185537i
\(617\) −37.7549 26.4363i −1.51996 1.06428i −0.974021 0.226458i \(-0.927285\pi\)
−0.545935 0.837827i \(-0.683826\pi\)
\(618\) 0 0
\(619\) 8.15117 9.71419i 0.327623 0.390446i −0.576939 0.816787i \(-0.695753\pi\)
0.904563 + 0.426341i \(0.140198\pi\)
\(620\) −21.5537 + 19.4684i −0.865617 + 0.781871i
\(621\) 0 0
\(622\) −26.9448 26.9448i −1.08039 1.08039i
\(623\) −0.0182496 0.208594i −0.000731154 0.00835713i
\(624\) 0 0
\(625\) 0.715439 24.9898i 0.0286176 0.999590i
\(626\) −11.2420 + 30.8872i −0.449321 + 1.23450i
\(627\) 0 0
\(628\) −1.45276 2.07476i −0.0579714 0.0827918i
\(629\) −5.89161 + 10.2046i −0.234914 + 0.406883i
\(630\) 0 0
\(631\) 16.7330 + 28.9824i 0.666131 + 1.15377i 0.978977 + 0.203969i \(0.0653841\pi\)
−0.312847 + 0.949804i \(0.601283\pi\)
\(632\) −0.0618790 + 0.132700i −0.00246142 + 0.00527852i
\(633\) 0 0
\(634\) 9.59010 + 11.4290i 0.380871 + 0.453905i
\(635\) −8.96630 11.8599i −0.355817 0.470644i
\(636\) 0 0
\(637\) 13.8524 + 6.45949i 0.548853 + 0.255934i
\(638\) 5.10571 19.0548i 0.202137 0.754385i
\(639\) 0 0
\(640\) 0.402066 + 0.260207i 0.0158930 + 0.0102856i
\(641\) 2.02936 + 0.357831i 0.0801548 + 0.0141335i 0.213582 0.976925i \(-0.431487\pi\)
−0.133427 + 0.991059i \(0.542598\pi\)
\(642\) 0 0
\(643\) −29.5810 + 13.7938i −1.16656 + 0.543976i −0.906744 0.421682i \(-0.861440\pi\)
−0.259816 + 0.965658i \(0.583662\pi\)
\(644\) −3.11506 17.6664i −0.122750 0.696153i
\(645\) 0 0
\(646\) −10.2007 8.55944i −0.401343 0.336767i
\(647\) 10.7867 10.7867i 0.424069 0.424069i −0.462533 0.886602i \(-0.653059\pi\)
0.886602 + 0.462533i \(0.153059\pi\)
\(648\) 0 0
\(649\) 51.0904i 2.00547i
\(650\) −21.2174 21.8336i −0.832216 0.856383i
\(651\) 0 0
\(652\) −4.07851 + 5.82472i −0.159727 + 0.228114i
\(653\) 7.69299 + 16.4977i 0.301050 + 0.645604i 0.997397 0.0721010i \(-0.0229704\pi\)
−0.696347 + 0.717705i \(0.745193\pi\)
\(654\) 0 0
\(655\) 14.0389 + 22.3886i 0.548545 + 0.874794i
\(656\) 32.1559 + 18.5652i 1.25548 + 0.724851i
\(657\) 0 0
\(658\) 21.6590 + 5.80351i 0.844356 + 0.226245i
\(659\) 1.94388 0.707516i 0.0757229 0.0275609i −0.303881 0.952710i \(-0.598283\pi\)
0.379604 + 0.925149i \(0.376060\pi\)
\(660\) 0 0
\(661\) 10.2051 8.56308i 0.396932 0.333065i −0.422374 0.906421i \(-0.638803\pi\)
0.819306 + 0.573356i \(0.194359\pi\)
\(662\) −1.44434 + 16.5089i −0.0561360 + 0.641638i
\(663\) 0 0
\(664\) −0.0556313 0.152846i −0.00215891 0.00593156i
\(665\) 2.36008 + 4.61399i 0.0915201 + 0.178923i
\(666\) 0 0
\(667\) 17.1364 4.59169i 0.663525 0.177791i
\(668\) 19.6318 13.7463i 0.759576 0.531861i
\(669\) 0 0
\(670\) −19.5900 48.2685i −0.756829 1.86478i
\(671\) 22.5654 3.97889i 0.871128 0.153603i
\(672\) 0 0
\(673\) 38.3246 3.35297i 1.47730 0.129247i 0.680172 0.733052i \(-0.261905\pi\)
0.797132 + 0.603805i \(0.206349\pi\)
\(674\) −31.3440 −1.20732
\(675\) 0 0
\(676\) 7.35037 0.282707
\(677\) −12.9913 + 1.13659i −0.499297 + 0.0436829i −0.334023 0.942565i \(-0.608406\pi\)
−0.165274 + 0.986248i \(0.552851\pi\)
\(678\) 0 0
\(679\) 17.9137 3.15867i 0.687465 0.121219i
\(680\) 0.0913427 + 0.225062i 0.00350283 + 0.00863075i
\(681\) 0 0
\(682\) −38.1411 + 26.7067i −1.46050 + 1.02265i
\(683\) −22.2351 + 5.95787i −0.850801 + 0.227972i −0.657768 0.753221i \(-0.728499\pi\)
−0.193033 + 0.981192i \(0.561833\pi\)
\(684\) 0 0
\(685\) −12.3382 24.1214i −0.471420 0.921631i
\(686\) −11.5659 31.7770i −0.441587 1.21325i
\(687\) 0 0
\(688\) −2.00225 + 22.8859i −0.0763352 + 0.872515i
\(689\) −27.6766 + 23.2234i −1.05439 + 0.884741i
\(690\) 0 0
\(691\) −20.2420 + 7.36747i −0.770040 + 0.280272i −0.697013 0.717058i \(-0.745488\pi\)
−0.0730269 + 0.997330i \(0.523266\pi\)
\(692\) 11.1504 + 2.98774i 0.423874 + 0.113577i
\(693\) 0 0
\(694\) 1.58640 + 0.915908i 0.0602189 + 0.0347674i
\(695\) −15.4726 24.6750i −0.586910 0.935977i
\(696\) 0 0
\(697\) 15.8113 + 33.9074i 0.598894 + 1.28433i
\(698\) 41.1564 58.7774i 1.55779 2.22476i
\(699\) 0 0
\(700\) −0.200418 + 14.0038i −0.00757510 + 0.529294i
\(701\) 10.6311i 0.401531i −0.979639 0.200766i \(-0.935657\pi\)
0.979639 0.200766i \(-0.0643430\pi\)
\(702\) 0 0
\(703\) −3.37571 + 3.37571i −0.127317 + 0.127317i
\(704\) −21.5635 18.0939i −0.812705 0.681941i
\(705\) 0 0
\(706\) −1.67378 9.49245i −0.0629934 0.357253i
\(707\) 6.74885 3.14704i 0.253816 0.118357i
\(708\) 0 0
\(709\) −6.87515 1.21227i −0.258202 0.0455279i 0.0430488 0.999073i \(-0.486293\pi\)
−0.301250 + 0.953545i \(0.597404\pi\)
\(710\) −4.18161 2.70624i −0.156933 0.101563i
\(711\) 0 0
\(712\) 0.00102906 0.00384049i 3.85655e−5 0.000143929i
\(713\) −37.9508 17.6968i −1.42127 0.662749i
\(714\) 0 0
\(715\) −14.6674 19.4007i −0.548528 0.725546i
\(716\) −24.9489 29.7330i −0.932386 1.11117i
\(717\) 0 0
\(718\) 3.18628 6.83299i 0.118911 0.255005i
\(719\) −2.82089 4.88592i −0.105201 0.182214i 0.808619 0.588333i \(-0.200215\pi\)
−0.913820 + 0.406118i \(0.866882\pi\)
\(720\) 0 0
\(721\) −2.27504 + 3.94049i −0.0847271 + 0.146752i
\(722\) 18.6649 + 26.6562i 0.694635 + 0.992041i
\(723\) 0 0
\(724\) 7.20710 19.8013i 0.267850 0.735911i
\(725\) −13.8138 + 1.00959i −0.513033 + 0.0374952i
\(726\) 0 0
\(727\) −1.05650 12.0758i −0.0391832 0.447867i −0.990291 0.139008i \(-0.955609\pi\)
0.951108 0.308858i \(-0.0999469\pi\)
\(728\) −0.0814023 0.0814023i −0.00301697 0.00301697i
\(729\) 0 0
\(730\) −28.1086 + 25.3892i −1.04034 + 0.939695i
\(731\) −14.8791 + 17.7323i −0.550325 + 0.655852i
\(732\) 0 0
\(733\) −1.15449 0.808383i −0.0426421 0.0298583i 0.552061 0.833804i \(-0.313842\pi\)
−0.594703 + 0.803945i \(0.702730\pi\)
\(734\) 47.3029 + 17.2169i 1.74598 + 0.635486i
\(735\) 0 0
\(736\) 8.88151 50.3696i 0.327377 1.85665i
\(737\) −10.7707 40.1967i −0.396743 1.48066i
\(738\) 0 0
\(739\) 7.65920 4.42204i 0.281748 0.162667i −0.352466 0.935824i \(-0.614657\pi\)
0.634215 + 0.773157i \(0.281324\pi\)
\(740\) −12.3315 + 3.79130i −0.453313 + 0.139371i
\(741\) 0 0
\(742\) 33.2257 + 2.90687i 1.21975 + 0.106715i
\(743\) −20.2590 1.77243i −0.743230 0.0650242i −0.290751 0.956799i \(-0.593905\pi\)
−0.452480 + 0.891775i \(0.649461\pi\)
\(744\) 0 0
\(745\) 7.09811 + 3.75984i 0.260055 + 0.137750i
\(746\) −19.0615 + 11.0052i −0.697892 + 0.402928i
\(747\) 0 0
\(748\) −7.44034 27.7677i −0.272046 1.01529i
\(749\) −3.16098 + 17.9268i −0.115500 + 0.655031i
\(750\) 0 0
\(751\) −8.99657 3.27448i −0.328290 0.119488i 0.172617 0.984989i \(-0.444778\pi\)
−0.500906 + 0.865501i \(0.667000\pi\)
\(752\) 26.2718 + 18.3957i 0.958032 + 0.670822i
\(753\) 0 0
\(754\) −10.8420 + 12.9210i −0.394844 + 0.470556i
\(755\) −0.663290 0.734334i −0.0241396 0.0267252i
\(756\) 0 0
\(757\) −20.8479 20.8479i −0.757730 0.757730i 0.218179 0.975909i \(-0.429988\pi\)
−0.975909 + 0.218179i \(0.929988\pi\)
\(758\) 1.07073 + 12.2385i 0.0388905 + 0.444521i
\(759\) 0 0
\(760\) 0.0121464 + 0.0976554i 0.000440595 + 0.00354233i
\(761\) 9.01441 24.7669i 0.326772 0.897799i −0.662151 0.749370i \(-0.730356\pi\)
0.988923 0.148428i \(-0.0474214\pi\)
\(762\) 0 0
\(763\) −5.92236 8.45800i −0.214404 0.306200i
\(764\) 4.74988 8.22703i 0.171845 0.297644i
\(765\) 0 0
\(766\) 17.6017 + 30.4870i 0.635974 + 1.10154i
\(767\) 18.4617 39.5912i 0.666612 1.42955i
\(768\) 0 0
\(769\) −28.0565 33.4364i −1.01174 1.20575i −0.978489 0.206301i \(-0.933857\pi\)
−0.0332544 0.999447i \(-0.510587\pi\)
\(770\) −3.08978 + 22.2384i −0.111348 + 0.801417i
\(771\) 0 0
\(772\) −9.79577 4.56784i −0.352558 0.164400i
\(773\) 3.07418 11.4730i 0.110571 0.412655i −0.888347 0.459173i \(-0.848146\pi\)
0.998917 + 0.0465178i \(0.0148124\pi\)
\(774\) 0 0
\(775\) 26.5086 + 19.1326i 0.952216 + 0.687263i
\(776\) 0.340151 + 0.0599778i 0.0122107 + 0.00215308i
\(777\) 0 0
\(778\) −25.4158 + 11.8516i −0.911201 + 0.424900i
\(779\) 2.63212 + 14.9275i 0.0943053 + 0.534832i
\(780\) 0 0
\(781\) −3.04814 2.55770i −0.109071 0.0915216i
\(782\) 36.6853 36.6853i 1.31186 1.31186i
\(783\) 0 0
\(784\) 20.1814i 0.720763i
\(785\) −1.94102 + 2.08806i −0.0692779 + 0.0745259i
\(786\) 0 0