Properties

Label 405.2.r.a.368.3
Level $405$
Weight $2$
Character 405.368
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 368.3
Character \(\chi\) \(=\) 405.368
Dual form 405.2.r.a.197.3

$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{18}\right)\)

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 −0.641503 0.767121i \(-0.721689\pi\)
−0.764966 + 0.644071i \(0.777244\pi\)
\(3\) 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 0.771111 0.636701i \(-0.219701\pi\)
−0.334567 + 0.942372i \(0.608590\pi\)
\(8\) 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 −0.608394 0.793635i \(-0.708186\pi\)
0.976196 0.216891i \(-0.0695917\pi\)
\(12\) 0 0
\(13\) 0.265789 + 3.03799i 0.0737167 + 0.842586i 0.939585 + 0.342315i \(0.111211\pi\)
−0.865869 + 0.500271i \(0.833234\pi\)
\(14\) −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 −0.700572 0.713582i \(-0.747072\pi\)
−0.249922 + 0.968266i \(0.580405\pi\)
\(18\) 0 0
\(19\) −1.42357 + 0.821896i −0.326588 + 0.188556i −0.654325 0.756213i \(-0.727047\pi\)
0.327737 + 0.944769i \(0.393714\pi\)
\(20\) −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 0.992779 + 0.119960i \(0.0382767\pi\)
−0.226824 + 0.973936i \(0.572834\pi\)
\(24\) 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 −0.424136 0.905599i \(-0.639422\pi\)
0.818190 + 0.574948i \(0.194978\pi\)
\(30\) 0 0
\(31\) −1.13538 + 6.43905i −0.203920 + 1.15649i 0.695211 + 0.718806i \(0.255311\pi\)
−0.899130 + 0.437681i \(0.855800\pi\)
\(32\) 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 0.999785 0.0207425i \(-0.00660301\pi\)
−0.876210 + 0.481929i \(0.839936\pi\)
\(38\) 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 0.0687280 + 0.997635i \(0.478106\pi\)
−0.994414 + 0.105554i \(0.966339\pi\)
\(42\) 0 0
\(43\) 2.41117 + 5.17078i 0.367701 + 0.788536i 0.999906 + 0.0137353i \(0.00437223\pi\)
−0.632205 + 0.774801i \(0.717850\pi\)
\(44\) 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 0.333576 + 0.942723i \(0.391745\pi\)
−0.999960 + 0.00897134i \(0.997144\pi\)
\(48\) 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 −0.164293 + 0.986412i \(0.552534\pi\)
−0.986412 + 0.164293i \(0.947466\pi\)
\(54\) 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 0.752643 0.658429i \(-0.228779\pi\)
0.999788 + 0.0205964i \(0.00655651\pi\)
\(60\) 0 0
\(61\) 1.11559 + 6.32681i 0.142836 + 0.810066i 0.969079 + 0.246751i \(0.0793630\pi\)
−0.826242 + 0.563315i \(0.809526\pi\)
\(62\) 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 −0.771147 0.636658i \(-0.780317\pi\)
−0.648877 + 0.760893i \(0.724761\pi\)
\(68\) −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 0.441571 0.897226i \(-0.354421\pi\)
−0.556235 + 0.831025i \(0.687755\pi\)
\(72\) 0 0
\(73\) 2.19579 8.19480i 0.256998 0.959129i −0.709970 0.704232i \(-0.751292\pi\)
0.966968 0.254898i \(-0.0820417\pi\)
\(74\) −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 0.531139 0.847284i \(-0.321764\pi\)
−0.926644 + 0.375941i \(0.877320\pi\)
\(80\) 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 0.910129 + 0.414326i \(0.135983\pi\)
−0.968249 + 0.249989i \(0.919573\pi\)
\(84\) 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 0.869934 0.493168i \(-0.164161\pi\)
−0.862063 + 0.506801i \(0.830828\pi\)
\(90\) 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 0.274222 0.961667i \(-0.411580\pi\)
0.912946 + 0.408081i \(0.133802\pi\)
\(98\) 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 0.0912166 0.995831i \(-0.470924\pi\)
0.426310 + 0.904577i \(0.359813\pi\)
\(102\) 0 0
\(103\) −2.92471 1.36382i −0.288181 0.134381i 0.273153 0.961971i \(-0.411934\pi\)
−0.561333 + 0.827590i \(0.689711\pi\)
\(104\) −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 0.111256 0.993792i \(-0.464513\pi\)
−0.993792 + 0.111256i \(0.964513\pi\)
\(108\) 0 0
\(109\) 7.32304i 0.701420i 0.936484 + 0.350710i \(0.114060\pi\)
−0.936484 + 0.350710i \(0.885940\pi\)
\(110\) −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 −0.330273 0.943885i \(-0.607141\pi\)
0.935354 0.353714i \(-0.115081\pi\)
\(114\) 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 0.532253 0.846585i \(-0.321345\pi\)
0.0376522 + 0.999291i \(0.488012\pi\)
\(128\) −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 −0.359717 0.933062i \(-0.617127\pi\)
−0.657149 + 0.753761i \(0.728238\pi\)
\(132\) 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 0.590203 0.807255i \(-0.299048\pi\)
0.441059 + 0.897478i \(0.354603\pi\)
\(138\) 0 0
\(139\) 12.8272 + 2.26177i 1.08799 + 0.191841i 0.688744 0.725005i \(-0.258162\pi\)
0.399242 + 0.916846i \(0.369273\pi\)
\(140\) −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 0.523074 0.852288i \(-0.324785\pi\)
−0.748509 + 0.663125i \(0.769230\pi\)
\(150\) 0 0
\(151\) 0.415850 + 0.151357i 0.0338414 + 0.0123173i 0.358885 0.933382i \(-0.383157\pi\)
−0.325044 + 0.945699i \(0.605379\pi\)
\(152\) −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 −0.926635 0.375961i \(-0.877312\pi\)
0.883633 + 0.468180i \(0.155090\pi\)
\(158\) 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 0.601005 0.799245i \(-0.294767\pi\)
−0.799245 + 0.601005i \(0.794767\pi\)
\(164\) −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 0.796789 0.604258i \(-0.206530\pi\)
0.0492772 + 0.998785i \(0.484308\pi\)
\(168\) 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 −0.211980 0.977274i \(-0.567991\pi\)
0.612377 + 0.790566i \(0.290214\pi\)
\(174\) 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 0.226651 + 0.973976i \(0.427222\pi\)
−0.956813 + 0.290703i \(0.906111\pi\)
\(180\) 0 0
\(181\) 5.30360 + 9.18610i 0.394213 + 0.682797i 0.993000 0.118111i \(-0.0376838\pi\)
−0.598787 + 0.800908i \(0.704350\pi\)
\(182\) 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 0.865698 0.500566i \(-0.166875\pi\)
−0.643288 + 0.765624i \(0.722430\pi\)
\(192\) 0 0
\(193\) −4.45676 + 3.12066i −0.320804 + 0.224630i −0.722875 0.690979i \(-0.757180\pi\)
0.402070 + 0.915609i \(0.368291\pi\)
\(194\) −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 −0.851466 0.524410i \(-0.824286\pi\)
0.999596 0.0284197i \(-0.00904750\pi\)
\(198\) 0 0
\(199\) 10.5312 + 6.08020i 0.746539 + 0.431014i 0.824442 0.565947i \(-0.191489\pi\)
−0.0779033 + 0.996961i \(0.524823\pi\)
\(200\) −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 −0.243736 0.969842i \(-0.578373\pi\)
0.436690 + 0.899612i \(0.356151\pi\)
\(212\) −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 −0.633002 0.774151i \(-0.718177\pi\)
0.943963 + 0.330052i \(0.107066\pi\)
\(224\) 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 0.984264 0.176704i \(-0.0565435\pi\)
−0.768036 + 0.640407i \(0.778766\pi\)
\(228\) 0 0
\(229\) 2.93595 3.49893i 0.194013 0.231216i −0.660264 0.751033i \(-0.729556\pi\)
0.854277 + 0.519818i \(0.174000\pi\)
\(230\) 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 −0.898960 0.438032i \(-0.855676\pi\)
0.559506 0.828826i \(-0.310991\pi\)
\(234\) 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 −0.813875 0.581040i \(-0.802646\pi\)
0.963520 0.267638i \(-0.0862431\pi\)
\(240\) 0 0
\(241\) 19.5457 16.4008i 1.25905 1.05647i 0.263267 0.964723i \(-0.415200\pi\)
0.995783 0.0917454i \(-0.0292446\pi\)
\(242\) 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 −0.936917 0.349553i \(-0.886333\pi\)
−0.165736 + 0.986170i \(0.553000\pi\)
\(252\) 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 0.983245 + 0.182291i \(0.0583512\pi\)
−0.936653 + 0.350260i \(0.886093\pi\)
\(258\) 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 0.958941 0.283607i \(-0.0915312\pi\)
0.0614734 + 0.998109i \(0.480420\pi\)
\(264\) 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 −0.994144 0.108064i \(-0.965535\pi\)
−0.441564 0.897230i \(-0.645576\pi\)
\(278\) −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 −0.155450 0.987844i \(-0.549683\pi\)
0.754055 0.656811i \(-0.228095\pi\)
\(282\) 0 0
\(283\) 1.18317 + 13.5237i 0.0703324 + 0.803902i 0.946670 + 0.322205i \(0.104424\pi\)
−0.876338 + 0.481697i \(0.840020\pi\)
\(284\) −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 0.656620 0.754222i \(-0.271986\pi\)
−0.933314 + 0.359062i \(0.883097\pi\)
\(294\) 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 −0.999244 0.0388737i \(-0.987623\pi\)
0.845934 0.533288i \(-0.179044\pi\)
\(308\) 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 −0.296397 0.955065i \(-0.595785\pi\)
0.992024 + 0.126049i \(0.0402297\pi\)
\(312\) 0 0
\(313\) 6.95728 + 14.9199i 0.393249 + 0.843325i 0.998868 + 0.0475700i \(0.0151477\pi\)
−0.605619 + 0.795755i \(0.707075\pi\)
\(314\) 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 −0.921275 0.388912i \(-0.872851\pi\)
0.680553 + 0.732699i \(0.261740\pi\)
\(318\) 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 0.998455 + 0.0555668i \(0.0176966\pi\)
−0.919236 + 0.393707i \(0.871192\pi\)
\(332\) −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 0.347157 0.937807i \(-0.387147\pi\)
0.504731 + 0.863277i \(0.331592\pi\)
\(338\) −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 −0.593575 0.804779i \(-0.702284\pi\)
0.553230 + 0.833028i \(0.313395\pi\)
\(348\) 0 0
\(349\) −23.1000 27.5295i −1.23652 1.47362i −0.827861 0.560934i \(-0.810442\pi\)
−0.408655 0.912689i \(-0.634002\pi\)
\(350\) 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 −0.976742 0.214417i \(-0.931215\pi\)
0.999136 0.0415497i \(-0.0132295\pi\)
\(354\) 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 0.811892 0.583807i \(-0.198438\pi\)
−0.911538 + 0.411216i \(0.865104\pi\)
\(360\) 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 −0.914600 0.404361i \(-0.867494\pi\)
−0.278135 + 0.960542i \(0.589716\pi\)
\(368\) −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 0.663695 0.748003i \(-0.268987\pi\)
−0.146389 + 0.989227i \(0.546765\pi\)
\(374\) 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 \(0.0505134\pi\)
−0.987435 + 0.158027i \(0.949487\pi\)
\(380\) 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 0.618778 + 0.785566i \(0.287628\pi\)
−0.999521 + 0.0309400i \(0.990150\pi\)
\(384\) 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 0.654192 0.756329i \(-0.273009\pi\)
0.0149811 + 0.999888i \(0.495231\pi\)
\(390\) 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 −0.565248 0.824921i \(-0.691220\pi\)
−0.901980 + 0.431778i \(0.857886\pi\)
\(398\) −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 0.559151 0.829066i \(-0.311127\pi\)
0.241873 + 0.970308i \(0.422238\pi\)
\(402\) 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 0.628466 0.777837i \(-0.283683\pi\)
0.324529 + 0.945876i \(0.394794\pi\)
\(410\) 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 0.646228 0.763145i \(-0.276346\pi\)
−0.639334 + 0.768929i \(0.720790\pi\)
\(420\) 0 0
\(421\) −17.1952 6.25854i −0.838043 0.305023i −0.112887 0.993608i \(-0.536010\pi\)
−0.725155 + 0.688585i \(0.758232\pi\)
\(422\) −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 \(-0.836241\pi\)
0.870556 0.492069i \(-0.163759\pi\)
\(432\) 0 0
\(433\) −1.40075 1.40075i −0.0673156 0.0673156i 0.672647 0.739963i \(-0.265157\pi\)
−0.739963 + 0.672647i \(0.765157\pi\)
\(434\) 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 0.169055 0.985607i \(-0.445929\pi\)
0.495957 + 0.868347i \(0.334817\pi\)
\(440\) 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 −0.736207 0.676757i \(-0.763385\pi\)
0.0452014 + 0.998978i \(0.485607\pi\)
\(444\) 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 −0.790561 0.612383i \(-0.790211\pi\)
0.925620 + 0.378455i \(0.123544\pi\)
\(450\) 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 −0.843145 0.537686i \(-0.819299\pi\)
0.923704 0.383107i \(-0.125146\pi\)
\(458\) −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 0.965633 0.259909i \(-0.0836924\pi\)
−0.423640 + 0.905830i \(0.639248\pi\)
\(462\) 0 0
\(463\) 10.7175 7.50444i 0.498082 0.348761i −0.297385 0.954758i \(-0.596114\pi\)
0.795467 + 0.605997i \(0.207226\pi\)
\(464\) −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 −0.899805 0.436292i \(-0.856292\pi\)
0.997400 + 0.0720628i \(0.0229582\pi\)
\(468\) 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 0.902540 + 0.430606i \(0.141700\pi\)
−0.700835 + 0.713324i \(0.747189\pi\)
\(480\) 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 −0.998616 0.0525891i \(-0.983253\pi\)
0.0525891 + 0.998616i \(0.483253\pi\)
\(488\) −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 0.997113 0.0759306i \(-0.0241927\pi\)
−0.812640 + 0.582766i \(0.801971\pi\)
\(492\) 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 −0.686649 0.726989i \(-0.740919\pi\)
0.835180 + 0.549977i \(0.185364\pi\)
\(500\) 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 0.999378 0.0352755i \(-0.0112309\pi\)
−0.883124 + 0.469139i \(0.844564\pi\)
\(504\) 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 −0.569097 0.822270i \(-0.692707\pi\)
0.816009 0.578039i \(-0.196182\pi\)
\(510\) 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 −0.372728 0.927941i \(-0.621578\pi\)
0.617256 + 0.786762i \(0.288244\pi\)
\(522\) 0 0
\(523\) −6.76374 + 1.81234i −0.295758 + 0.0792481i −0.403647 0.914915i \(-0.632258\pi\)
0.107889 + 0.994163i \(0.465591\pi\)
\(524\) −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 0.919451 0.393204i \(-0.128633\pi\)
−0.0550200 + 0.998485i \(0.517522\pi\)
\(548\) 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 −0.0738415 0.997270i \(-0.523526\pi\)
0.434686 + 0.900582i \(0.356859\pi\)
\(558\) 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 0.995374 0.0960749i \(-0.0306288\pi\)
−0.430719 + 0.902486i \(0.641740\pi\)
\(564\) 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 −0.680300 0.732934i \(-0.738150\pi\)
0.603667 + 0.797237i \(0.293706\pi\)
\(570\) 0 0
\(571\) 6.32573 35.8750i 0.264724 1.50132i −0.505097 0.863063i \(-0.668543\pi\)
0.769821 0.638260i \(-0.220346\pi\)
\(572\) 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 −0.958524 0.285012i \(-0.908002\pi\)
0.687600 0.726090i \(-0.258664\pi\)
\(578\) 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 0.276734 + 0.960947i \(0.410748\pi\)
−0.997643 + 0.0686181i \(0.978141\pi\)
\(588\) 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 0.103470 0.994633i \(-0.467005\pi\)
0.994633 0.103470i \(-0.0329946\pi\)
\(594\) 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 −0.319595 0.947554i \(-0.603547\pi\)
0.364252 + 0.931301i \(0.381325\pi\)
\(600\) 0 0
\(601\) 2.53128 + 14.3556i 0.103253 + 0.585578i 0.991904 + 0.126993i \(0.0405325\pi\)
−0.888650 + 0.458585i \(0.848356\pi\)
\(602\) 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 −0.735560 0.677459i \(-0.763081\pi\)
−0.606746 + 0.794896i \(0.707525\pi\)
\(608\) −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 −0.876297 0.481772i \(-0.839994\pi\)
0.999781 + 0.0209221i \(0.00666018\pi\)
\(614\) 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 −0.545935 + 0.837827i \(0.683826\pi\)
−0.974021 + 0.226458i \(0.927285\pi\)
\(618\) 0 0
\(619\) 8.15117 + 9.71419i 0.327623 + 0.390446i 0.904563 0.426341i \(-0.140198\pi\)
−0.576939 + 0.816787i \(0.695753\pi\)
\(620\) −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 −0.312847 0.949804i \(-0.601283\pi\)
0.978977 0.203969i \(-0.0653841\pi\)
\(632\) −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 −0.133427 0.991059i \(-0.542598\pi\)
0.213582 + 0.976925i \(0.431487\pi\)
\(642\) 0 0
\(643\) −29.5810 13.7938i −1.16656 0.543976i −0.259816 0.965658i \(-0.583662\pi\)
−0.906744 + 0.421682i \(0.861440\pi\)
\(644\) −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 0.886602 0.462533i \(-0.153059\pi\)
−0.462533 + 0.886602i \(0.653059\pi\)
\(648\) 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 −0.696347 0.717705i \(-0.745193\pi\)
0.997397 + 0.0721010i \(0.0229704\pi\)
\(654\) 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 0.379604 0.925149i \(-0.376060\pi\)
−0.303881 + 0.952710i \(0.598283\pi\)
\(660\) 0 0
\(661\) 10.2051 + 8.56308i 0.396932 + 0.333065i 0.819306 0.573356i \(-0.194359\pi\)
−0.422374 + 0.906421i \(0.638803\pi\)
\(662\) −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 0.797132 0.603805i \(-0.206349\pi\)
0.680172 + 0.733052i \(0.261905\pi\)
\(674\) −31.3440 −1.20732
\(675\) 0 0
\(676\) 7.35037 0.282707
\(677\) −12.9913 1.13659i −0.499297 0.0436829i −0.165274 0.986248i \(-0.552851\pi\)
−0.334023 + 0.942565i \(0.608406\pi\)
\(678\) 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 −0.193033 0.981192i \(-0.561833\pi\)
−0.657768 + 0.753221i \(0.728499\pi\)
\(684\) 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 −0.0730269 0.997330i \(-0.523266\pi\)
−0.697013 + 0.717058i \(0.745488\pi\)
\(692\) 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 \(0.0643430\pi\)
−0.979639 + 0.200766i \(0.935657\pi\)
\(702\) 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 −0.301250 0.953545i \(-0.597404\pi\)
0.0430488 + 0.999073i \(0.486293\pi\)
\(710\) −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 −0.913820 0.406118i \(-0.866882\pi\)
0.808619 + 0.588333i \(0.200215\pi\)
\(720\) 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 0.951108 + 0.308858i \(0.0999469\pi\)
−0.990291 + 0.139008i \(0.955609\pi\)
\(728\) −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 −0.594703 0.803945i \(-0.702730\pi\)
0.552061 + 0.833804i \(0.313842\pi\)
\(734\) 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 0.634215 0.773157i \(-0.281324\pi\)
−0.352466 + 0.935824i \(0.614657\pi\)
\(740\) −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 −0.452480 0.891775i \(-0.649461\pi\)
−0.290751 + 0.956799i \(0.593905\pi\)
\(744\) 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 −0.500906 0.865501i \(-0.667000\pi\)
0.172617 + 0.984989i \(0.444778\pi\)
\(752\) 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 −0.975909 0.218179i \(-0.929988\pi\)
0.218179 + 0.975909i \(0.429988\pi\)
\(758\) 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 0.988923 + 0.148428i \(0.0474214\pi\)
−0.662151 + 0.749370i \(0.730356\pi\)
\(762\) 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 −0.0332544 + 0.999447i \(0.510587\pi\)
−0.978489 + 0.206301i \(0.933857\pi\)
\(770\) −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 0.998917 0.0465178i \(-0.0148124\pi\)
−0.888347 + 0.459173i \(0.848146\pi\)
\(774\) 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
\(787\) 31.0074