Properties

Label 405.2.r.a.152.10
Level $405$
Weight $2$
Character 405.152
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 152.10
Character \(\chi\) \(=\) 405.152
Dual form 405.2.r.a.8.10

$q$-expansion

\(f(q)\) \(=\) \(q+(0.807333 + 0.565301i) q^{2} +(-0.351818 - 0.966613i) q^{4} +(2.04189 - 0.911409i) q^{5} +(-0.275357 - 0.590505i) q^{7} +(0.772562 - 2.88324i) q^{8} +O(q^{10})\) \(q+(0.807333 + 0.565301i) q^{2} +(-0.351818 - 0.966613i) q^{4} +(2.04189 - 0.911409i) q^{5} +(-0.275357 - 0.590505i) q^{7} +(0.772562 - 2.88324i) q^{8} +(2.16371 + 0.418474i) q^{10} +(-0.890417 - 1.06116i) q^{11} +(-2.93770 - 4.19546i) q^{13} +(0.111508 - 0.632393i) q^{14} +(0.677632 - 0.568601i) q^{16} +(1.18168 + 4.41009i) q^{17} +(0.00652973 - 0.00376994i) q^{19} +(-1.59936 - 1.65307i) q^{20} +(-0.118990 - 1.36006i) q^{22} +(6.70560 + 3.12687i) q^{23} +(3.33867 - 3.72200i) q^{25} -5.04782i q^{26} +(-0.473914 + 0.473914i) q^{28} +(0.586508 + 3.32625i) q^{29} +(3.73277 - 1.35862i) q^{31} +(-5.07868 + 0.444327i) q^{32} +(-1.53902 + 4.22842i) q^{34} +(-1.10044 - 0.954786i) q^{35} +(1.60572 - 0.430252i) q^{37} +(0.00740282 + 0.000647662i) q^{38} +(-1.05032 - 6.59139i) q^{40} +(1.90299 + 0.335548i) q^{41} +(-0.929732 + 10.6269i) q^{43} +(-0.712464 + 1.23402i) q^{44} +(3.64603 + 6.31511i) q^{46} +(-6.61847 + 3.08624i) q^{47} +(4.22664 - 5.03711i) q^{49} +(4.79947 - 1.11755i) q^{50} +(-3.02186 + 4.31566i) q^{52} +(1.18766 + 1.18766i) q^{53} +(-2.78529 - 1.35524i) q^{55} +(-1.91530 + 0.337719i) q^{56} +(-1.40682 + 3.01694i) q^{58} +(7.77643 + 6.52520i) q^{59} +(-9.02437 - 3.28460i) q^{61} +(3.78162 + 1.01328i) q^{62} +(-5.88351 - 3.39685i) q^{64} +(-9.82225 - 5.88925i) q^{65} +(-12.3176 + 8.62489i) q^{67} +(3.84712 - 2.69378i) q^{68} +(-0.348682 - 1.39291i) q^{70} +(-5.41550 - 3.12664i) q^{71} +(12.1662 + 3.25991i) q^{73} +(1.53958 + 0.560360i) q^{74} +(-0.00594135 - 0.00498539i) q^{76} +(-0.381436 + 0.817993i) q^{77} +(-0.782046 + 0.137896i) q^{79} +(0.865425 - 1.77862i) q^{80} +(1.34666 + 1.34666i) q^{82} +(-5.32053 + 7.59850i) q^{83} +(6.43227 + 7.92795i) q^{85} +(-6.75799 + 8.05386i) q^{86} +(-3.74748 + 1.74748i) q^{88} +(-5.89645 - 10.2130i) q^{89} +(-1.66853 + 2.88997i) q^{91} +(0.663323 - 7.58182i) q^{92} +(-7.08796 - 1.24980i) q^{94} +(0.00989706 - 0.0136491i) q^{95} +(-2.18091 - 0.190805i) q^{97} +(6.25979 - 1.67731i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{17}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.807333 + 0.565301i 0.570871 + 0.399728i 0.823064 0.567949i \(-0.192263\pi\)
−0.252193 + 0.967677i \(0.581152\pi\)
\(3\) 0 0
\(4\) −0.351818 0.966613i −0.175909 0.483307i
\(5\) 2.04189 0.911409i 0.913163 0.407595i
\(6\) 0 0
\(7\) −0.275357 0.590505i −0.104075 0.223190i 0.847374 0.530997i \(-0.178183\pi\)
−0.951449 + 0.307807i \(0.900405\pi\)
\(8\) 0.772562 2.88324i 0.273142 1.01938i
\(9\) 0 0
\(10\) 2.16371 + 0.418474i 0.684225 + 0.132333i
\(11\) −0.890417 1.06116i −0.268471 0.319951i 0.614919 0.788591i \(-0.289189\pi\)
−0.883390 + 0.468639i \(0.844744\pi\)
\(12\) 0 0
\(13\) −2.93770 4.19546i −0.814770 1.16361i −0.984023 0.178040i \(-0.943024\pi\)
0.169253 0.985573i \(-0.445864\pi\)
\(14\) 0.111508 0.632393i 0.0298018 0.169014i
\(15\) 0 0
\(16\) 0.677632 0.568601i 0.169408 0.142150i
\(17\) 1.18168 + 4.41009i 0.286600 + 1.06961i 0.947662 + 0.319274i \(0.103439\pi\)
−0.661063 + 0.750331i \(0.729894\pi\)
\(18\) 0 0
\(19\) 0.00652973 0.00376994i 0.00149802 0.000864884i −0.499251 0.866458i \(-0.666391\pi\)
0.500749 + 0.865593i \(0.333058\pi\)
\(20\) −1.59936 1.65307i −0.357627 0.369638i
\(21\) 0 0
\(22\) −0.118990 1.36006i −0.0253687 0.289966i
\(23\) 6.70560 + 3.12687i 1.39822 + 0.651998i 0.968051 0.250752i \(-0.0806780\pi\)
0.430164 + 0.902751i \(0.358456\pi\)
\(24\) 0 0
\(25\) 3.33867 3.72200i 0.667733 0.744401i
\(26\) 5.04782i 0.989959i
\(27\) 0 0
\(28\) −0.473914 + 0.473914i −0.0895613 + 0.0895613i
\(29\) 0.586508 + 3.32625i 0.108912 + 0.617669i 0.989586 + 0.143946i \(0.0459791\pi\)
−0.880674 + 0.473723i \(0.842910\pi\)
\(30\) 0 0
\(31\) 3.73277 1.35862i 0.670426 0.244015i 0.0156946 0.999877i \(-0.495004\pi\)
0.654731 + 0.755862i \(0.272782\pi\)
\(32\) −5.07868 + 0.444327i −0.897792 + 0.0785466i
\(33\) 0 0
\(34\) −1.53902 + 4.22842i −0.263940 + 0.725168i
\(35\) −1.10044 0.954786i −0.186008 0.161388i
\(36\) 0 0
\(37\) 1.60572 0.430252i 0.263979 0.0707331i −0.124402 0.992232i \(-0.539701\pi\)
0.388381 + 0.921499i \(0.373034\pi\)
\(38\) 0.00740282 0.000647662i 0.00120090 0.000105065i
\(39\) 0 0
\(40\) −1.05032 6.59139i −0.166070 1.04219i
\(41\) 1.90299 + 0.335548i 0.297197 + 0.0524038i 0.320258 0.947330i \(-0.396230\pi\)
−0.0230615 + 0.999734i \(0.507341\pi\)
\(42\) 0 0
\(43\) −0.929732 + 10.6269i −0.141783 + 1.62058i 0.508617 + 0.860993i \(0.330157\pi\)
−0.650400 + 0.759592i \(0.725399\pi\)
\(44\) −0.712464 + 1.23402i −0.107408 + 0.186036i
\(45\) 0 0
\(46\) 3.64603 + 6.31511i 0.537578 + 0.931113i
\(47\) −6.61847 + 3.08624i −0.965403 + 0.450175i −0.840391 0.541980i \(-0.817675\pi\)
−0.125012 + 0.992155i \(0.539897\pi\)
\(48\) 0 0
\(49\) 4.22664 5.03711i 0.603806 0.719587i
\(50\) 4.79947 1.11755i 0.678747 0.158045i
\(51\) 0 0
\(52\) −3.02186 + 4.31566i −0.419056 + 0.598474i
\(53\) 1.18766 + 1.18766i 0.163138 + 0.163138i 0.783955 0.620817i \(-0.213199\pi\)
−0.620817 + 0.783955i \(0.713199\pi\)
\(54\) 0 0
\(55\) −2.78529 1.35524i −0.375568 0.182740i
\(56\) −1.91530 + 0.337719i −0.255942 + 0.0451295i
\(57\) 0 0
\(58\) −1.40682 + 3.01694i −0.184725 + 0.396144i
\(59\) 7.77643 + 6.52520i 1.01240 + 0.849508i 0.988654 0.150210i \(-0.0479948\pi\)
0.0237505 + 0.999718i \(0.492439\pi\)
\(60\) 0 0
\(61\) −9.02437 3.28460i −1.15545 0.420550i −0.307981 0.951392i \(-0.599653\pi\)
−0.847471 + 0.530842i \(0.821876\pi\)
\(62\) 3.78162 + 1.01328i 0.480266 + 0.128687i
\(63\) 0 0
\(64\) −5.88351 3.39685i −0.735439 0.424606i
\(65\) −9.82225 5.88925i −1.21830 0.730472i
\(66\) 0 0
\(67\) −12.3176 + 8.62489i −1.50484 + 1.05370i −0.525658 + 0.850696i \(0.676181\pi\)
−0.979178 + 0.203002i \(0.934930\pi\)
\(68\) 3.84712 2.69378i 0.466532 0.326669i
\(69\) 0 0
\(70\) −0.348682 1.39291i −0.0416754 0.166485i
\(71\) −5.41550 3.12664i −0.642702 0.371064i 0.142953 0.989730i \(-0.454340\pi\)
−0.785654 + 0.618666i \(0.787674\pi\)
\(72\) 0 0
\(73\) 12.1662 + 3.25991i 1.42394 + 0.381544i 0.886880 0.461999i \(-0.152868\pi\)
0.537061 + 0.843543i \(0.319534\pi\)
\(74\) 1.53958 + 0.560360i 0.178972 + 0.0651405i
\(75\) 0 0
\(76\) −0.00594135 0.00498539i −0.000681520 0.000571863i
\(77\) −0.381436 + 0.817993i −0.0434687 + 0.0932189i
\(78\) 0 0
\(79\) −0.782046 + 0.137896i −0.0879871 + 0.0155145i −0.217468 0.976067i \(-0.569780\pi\)
0.129481 + 0.991582i \(0.458669\pi\)
\(80\) 0.865425 1.77862i 0.0967575 0.198856i
\(81\) 0 0
\(82\) 1.34666 + 1.34666i 0.148714 + 0.148714i
\(83\) −5.32053 + 7.59850i −0.584004 + 0.834044i −0.997057 0.0766627i \(-0.975574\pi\)
0.413053 + 0.910707i \(0.364462\pi\)
\(84\) 0 0
\(85\) 6.43227 + 7.92795i 0.697678 + 0.859907i
\(86\) −6.75799 + 8.05386i −0.728733 + 0.868470i
\(87\) 0 0
\(88\) −3.74748 + 1.74748i −0.399482 + 0.186282i
\(89\) −5.89645 10.2130i −0.625023 1.08257i −0.988537 0.150982i \(-0.951756\pi\)
0.363514 0.931589i \(-0.381577\pi\)
\(90\) 0 0
\(91\) −1.66853 + 2.88997i −0.174909 + 0.302951i
\(92\) 0.663323 7.58182i 0.0691562 0.790459i
\(93\) 0 0
\(94\) −7.08796 1.24980i −0.731068 0.128907i
\(95\) 0.00989706 0.0136491i 0.00101542 0.00140037i
\(96\) 0 0
\(97\) −2.18091 0.190805i −0.221438 0.0193733i −0.0241031 0.999709i \(-0.507673\pi\)
−0.197335 + 0.980336i \(0.563229\pi\)
\(98\) 6.25979 1.67731i 0.632334 0.169433i
\(99\) 0 0
\(100\) −4.77234 1.91773i −0.477234 0.191773i
\(101\) −2.19882 + 6.04120i −0.218790 + 0.601122i −0.999724 0.0234923i \(-0.992521\pi\)
0.780934 + 0.624614i \(0.214744\pi\)
\(102\) 0 0
\(103\) 9.32840 0.816129i 0.919154 0.0804156i 0.382250 0.924059i \(-0.375149\pi\)
0.536904 + 0.843643i \(0.319594\pi\)
\(104\) −14.3661 + 5.22883i −1.40871 + 0.512729i
\(105\) 0 0
\(106\) 0.287452 + 1.63022i 0.0279198 + 0.158341i
\(107\) −2.45371 + 2.45371i −0.237210 + 0.237210i −0.815694 0.578484i \(-0.803644\pi\)
0.578484 + 0.815694i \(0.303644\pi\)
\(108\) 0 0
\(109\) 11.1343i 1.06647i −0.845967 0.533235i \(-0.820976\pi\)
0.845967 0.533235i \(-0.179024\pi\)
\(110\) −1.48254 2.66865i −0.141354 0.254446i
\(111\) 0 0
\(112\) −0.522352 0.243577i −0.0493576 0.0230158i
\(113\) −0.776537 8.87586i −0.0730505 0.834971i −0.941019 0.338353i \(-0.890130\pi\)
0.867969 0.496619i \(-0.165425\pi\)
\(114\) 0 0
\(115\) 16.5420 + 0.273199i 1.54255 + 0.0254760i
\(116\) 3.00885 1.73716i 0.279365 0.161291i
\(117\) 0 0
\(118\) 2.58947 + 9.66403i 0.238380 + 0.889646i
\(119\) 2.27880 1.91214i 0.208897 0.175285i
\(120\) 0 0
\(121\) 1.57692 8.94314i 0.143356 0.813013i
\(122\) −5.42888 7.75325i −0.491508 0.701946i
\(123\) 0 0
\(124\) −2.62652 3.13016i −0.235868 0.281097i
\(125\) 3.42494 10.6428i 0.306336 0.951924i
\(126\) 0 0
\(127\) 0.737710 2.75317i 0.0654611 0.244304i −0.925440 0.378893i \(-0.876305\pi\)
0.990902 + 0.134589i \(0.0429714\pi\)
\(128\) 1.47937 + 3.17252i 0.130759 + 0.280413i
\(129\) 0 0
\(130\) −4.60063 10.3071i −0.403502 0.903994i
\(131\) −2.22104 6.10227i −0.194053 0.533158i 0.804060 0.594548i \(-0.202669\pi\)
−0.998114 + 0.0613901i \(0.980447\pi\)
\(132\) 0 0
\(133\) −0.00402417 0.00281776i −0.000348940 0.000244330i
\(134\) −14.8201 −1.28026
\(135\) 0 0
\(136\) 13.6283 1.16862
\(137\) 15.1709 + 10.6228i 1.29614 + 0.907567i 0.998884 0.0472310i \(-0.0150397\pi\)
0.297256 + 0.954798i \(0.403929\pi\)
\(138\) 0 0
\(139\) 6.75787 + 18.5671i 0.573195 + 1.57484i 0.799424 + 0.600767i \(0.205138\pi\)
−0.226229 + 0.974074i \(0.572640\pi\)
\(140\) −0.535753 + 1.39961i −0.0452794 + 0.118289i
\(141\) 0 0
\(142\) −2.60462 5.58563i −0.218575 0.468735i
\(143\) −1.83628 + 6.85307i −0.153557 + 0.573083i
\(144\) 0 0
\(145\) 4.22916 + 6.25730i 0.351213 + 0.519641i
\(146\) 7.97931 + 9.50937i 0.660373 + 0.787001i
\(147\) 0 0
\(148\) −0.980811 1.40074i −0.0806222 0.115140i
\(149\) −2.60422 + 14.7692i −0.213346 + 1.20994i 0.670408 + 0.741992i \(0.266119\pi\)
−0.883754 + 0.467952i \(0.844992\pi\)
\(150\) 0 0
\(151\) 0.694966 0.583146i 0.0565555 0.0474557i −0.614072 0.789250i \(-0.710469\pi\)
0.670627 + 0.741794i \(0.266025\pi\)
\(152\) −0.00582502 0.0217393i −0.000472472 0.00176329i
\(153\) 0 0
\(154\) −0.770358 + 0.444766i −0.0620772 + 0.0358403i
\(155\) 6.38367 6.17624i 0.512749 0.496087i
\(156\) 0 0
\(157\) 0.403811 + 4.61558i 0.0322276 + 0.368363i 0.995134 + 0.0985286i \(0.0314136\pi\)
−0.962907 + 0.269835i \(0.913031\pi\)
\(158\) −0.709324 0.330763i −0.0564308 0.0263141i
\(159\) 0 0
\(160\) −9.96516 + 5.53602i −0.787815 + 0.437661i
\(161\) 4.82070i 0.379924i
\(162\) 0 0
\(163\) −7.94001 + 7.94001i −0.621909 + 0.621909i −0.946019 0.324110i \(-0.894935\pi\)
0.324110 + 0.946019i \(0.394935\pi\)
\(164\) −0.345161 1.95751i −0.0269526 0.152856i
\(165\) 0 0
\(166\) −8.59088 + 3.12682i −0.666782 + 0.242689i
\(167\) −0.896457 + 0.0784299i −0.0693700 + 0.00606908i −0.121788 0.992556i \(-0.538863\pi\)
0.0524179 + 0.998625i \(0.483307\pi\)
\(168\) 0 0
\(169\) −4.52560 + 12.4340i −0.348123 + 0.956461i
\(170\) 0.711306 + 10.0367i 0.0545547 + 0.769777i
\(171\) 0 0
\(172\) 10.5992 2.84004i 0.808180 0.216551i
\(173\) 13.3057 + 1.16409i 1.01161 + 0.0885045i 0.580891 0.813981i \(-0.302704\pi\)
0.430720 + 0.902486i \(0.358260\pi\)
\(174\) 0 0
\(175\) −3.11718 0.946619i −0.235637 0.0715577i
\(176\) −1.20675 0.212783i −0.0909622 0.0160391i
\(177\) 0 0
\(178\) 1.01299 11.5785i 0.0759268 0.867847i
\(179\) 3.72605 6.45370i 0.278498 0.482372i −0.692514 0.721405i \(-0.743497\pi\)
0.971012 + 0.239032i \(0.0768302\pi\)
\(180\) 0 0
\(181\) −13.1147 22.7153i −0.974806 1.68841i −0.680574 0.732679i \(-0.738270\pi\)
−0.294232 0.955734i \(-0.595064\pi\)
\(182\) −2.98076 + 1.38995i −0.220949 + 0.103030i
\(183\) 0 0
\(184\) 14.1960 16.9182i 1.04655 1.24722i
\(185\) 2.88658 2.34200i 0.212226 0.172187i
\(186\) 0 0
\(187\) 3.62762 5.18077i 0.265278 0.378856i
\(188\) 5.31170 + 5.31170i 0.387396 + 0.387396i
\(189\) 0 0
\(190\) 0.0157061 0.00542454i 0.00113944 0.000393537i
\(191\) 1.57094 0.276999i 0.113669 0.0200430i −0.116524 0.993188i \(-0.537175\pi\)
0.230193 + 0.973145i \(0.426064\pi\)
\(192\) 0 0
\(193\) −3.55560 + 7.62500i −0.255937 + 0.548860i −0.991729 0.128348i \(-0.959032\pi\)
0.735792 + 0.677208i \(0.236810\pi\)
\(194\) −1.65286 1.38691i −0.118668 0.0995745i
\(195\) 0 0
\(196\) −6.35595 2.31338i −0.453996 0.165241i
\(197\) 10.9609 + 2.93696i 0.780931 + 0.209250i 0.627195 0.778862i \(-0.284203\pi\)
0.153736 + 0.988112i \(0.450869\pi\)
\(198\) 0 0
\(199\) −21.0022 12.1256i −1.48881 0.859563i −0.488889 0.872346i \(-0.662598\pi\)
−0.999918 + 0.0127826i \(0.995931\pi\)
\(200\) −8.15210 12.5017i −0.576441 0.884001i
\(201\) 0 0
\(202\) −5.19027 + 3.63427i −0.365186 + 0.255706i
\(203\) 1.80267 1.26224i 0.126522 0.0885920i
\(204\) 0 0
\(205\) 4.19153 1.04925i 0.292749 0.0732826i
\(206\) 7.99248 + 4.61446i 0.556863 + 0.321505i
\(207\) 0 0
\(208\) −4.37622 1.17261i −0.303436 0.0813055i
\(209\) −0.00981468 0.00357225i −0.000678896 0.000247098i
\(210\) 0 0
\(211\) 6.98736 + 5.86309i 0.481029 + 0.403632i 0.850799 0.525492i \(-0.176119\pi\)
−0.369769 + 0.929124i \(0.620563\pi\)
\(212\) 0.730167 1.56585i 0.0501481 0.107543i
\(213\) 0 0
\(214\) −3.36805 + 0.593878i −0.230235 + 0.0405967i
\(215\) 7.78703 + 22.5463i 0.531071 + 1.53765i
\(216\) 0 0
\(217\) −1.83011 1.83011i −0.124236 0.124236i
\(218\) 6.29421 8.98907i 0.426298 0.608817i
\(219\) 0 0
\(220\) −0.330076 + 3.16909i −0.0222537 + 0.213660i
\(221\) 15.0310 17.9132i 1.01109 1.20497i
\(222\) 0 0
\(223\) 14.8136 6.90768i 0.991990 0.462572i 0.142282 0.989826i \(-0.454556\pi\)
0.849708 + 0.527254i \(0.176778\pi\)
\(224\) 1.66083 + 2.87663i 0.110969 + 0.192203i
\(225\) 0 0
\(226\) 4.39061 7.60476i 0.292059 0.505861i
\(227\) −1.10129 + 12.5878i −0.0730949 + 0.835479i 0.867830 + 0.496862i \(0.165515\pi\)
−0.940924 + 0.338617i \(0.890041\pi\)
\(228\) 0 0
\(229\) 8.89322 + 1.56812i 0.587681 + 0.103624i 0.459579 0.888137i \(-0.348000\pi\)
0.128102 + 0.991761i \(0.459112\pi\)
\(230\) 13.2005 + 9.57177i 0.870413 + 0.631144i
\(231\) 0 0
\(232\) 10.0435 + 0.878692i 0.659388 + 0.0576889i
\(233\) −20.6198 + 5.52507i −1.35085 + 0.361959i −0.860449 0.509537i \(-0.829817\pi\)
−0.490402 + 0.871496i \(0.663150\pi\)
\(234\) 0 0
\(235\) −10.7014 + 12.3339i −0.698081 + 0.804576i
\(236\) 3.57145 9.81248i 0.232482 0.638738i
\(237\) 0 0
\(238\) 2.92068 0.255527i 0.189320 0.0165633i
\(239\) 5.43398 1.97781i 0.351495 0.127934i −0.160238 0.987078i \(-0.551226\pi\)
0.511733 + 0.859145i \(0.329004\pi\)
\(240\) 0 0
\(241\) −4.00297 22.7020i −0.257854 1.46236i −0.788639 0.614857i \(-0.789214\pi\)
0.530784 0.847507i \(-0.321897\pi\)
\(242\) 6.32866 6.32866i 0.406822 0.406822i
\(243\) 0 0
\(244\) 9.87866i 0.632416i
\(245\) 4.03948 14.1374i 0.258073 0.903208i
\(246\) 0 0
\(247\) −0.0349990 0.0163203i −0.00222693 0.00103844i
\(248\) −1.03342 11.8121i −0.0656225 0.750069i
\(249\) 0 0
\(250\) 8.78146 6.65619i 0.555389 0.420974i
\(251\) 2.17404 1.25518i 0.137224 0.0792266i −0.429816 0.902916i \(-0.641422\pi\)
0.567041 + 0.823690i \(0.308088\pi\)
\(252\) 0 0
\(253\) −2.65268 9.89993i −0.166772 0.622403i
\(254\) 2.15195 1.80570i 0.135025 0.113300i
\(255\) 0 0
\(256\) −2.95851 + 16.7785i −0.184907 + 1.04866i
\(257\) −7.24292 10.3440i −0.451801 0.645238i 0.527045 0.849837i \(-0.323300\pi\)
−0.978846 + 0.204599i \(0.934411\pi\)
\(258\) 0 0
\(259\) −0.696213 0.829715i −0.0432606 0.0515560i
\(260\) −2.23698 + 11.5663i −0.138732 + 0.717309i
\(261\) 0 0
\(262\) 1.65649 6.18212i 0.102339 0.381933i
\(263\) −7.09675 15.2190i −0.437604 0.938445i −0.994188 0.107654i \(-0.965666\pi\)
0.556584 0.830791i \(-0.312112\pi\)
\(264\) 0 0
\(265\) 3.50752 + 1.34263i 0.215465 + 0.0824772i
\(266\) −0.00165597 0.00454974i −0.000101534 0.000278962i
\(267\) 0 0
\(268\) 12.6705 + 8.87198i 0.773974 + 0.541942i
\(269\) 3.27377 0.199605 0.0998027 0.995007i \(-0.468179\pi\)
0.0998027 + 0.995007i \(0.468179\pi\)
\(270\) 0 0
\(271\) 8.46872 0.514438 0.257219 0.966353i \(-0.417194\pi\)
0.257219 + 0.966353i \(0.417194\pi\)
\(272\) 3.30833 + 2.31652i 0.200597 + 0.140459i
\(273\) 0 0
\(274\) 6.24292 + 17.1523i 0.377148 + 1.03621i
\(275\) −6.92244 0.228717i −0.417439 0.0137922i
\(276\) 0 0
\(277\) −1.04261 2.23589i −0.0626445 0.134342i 0.872493 0.488627i \(-0.162502\pi\)
−0.935137 + 0.354285i \(0.884724\pi\)
\(278\) −5.04014 + 18.8101i −0.302288 + 1.12815i
\(279\) 0 0
\(280\) −3.60304 + 2.43521i −0.215323 + 0.145531i
\(281\) 12.4917 + 14.8870i 0.745190 + 0.888082i 0.996816 0.0797423i \(-0.0254097\pi\)
−0.251626 + 0.967825i \(0.580965\pi\)
\(282\) 0 0
\(283\) −10.8099 15.4382i −0.642583 0.917703i 0.357285 0.933996i \(-0.383703\pi\)
−0.999867 + 0.0162923i \(0.994814\pi\)
\(284\) −1.11698 + 6.33470i −0.0662805 + 0.375896i
\(285\) 0 0
\(286\) −5.35653 + 4.49466i −0.316738 + 0.265775i
\(287\) −0.325858 1.21612i −0.0192348 0.0717853i
\(288\) 0 0
\(289\) −3.33013 + 1.92265i −0.195890 + 0.113097i
\(290\) −0.122916 + 7.44248i −0.00721789 + 0.437037i
\(291\) 0 0
\(292\) −1.12920 12.9069i −0.0660817 0.755317i
\(293\) −3.65580 1.70473i −0.213574 0.0995913i 0.312887 0.949790i \(-0.398704\pi\)
−0.526461 + 0.850199i \(0.676482\pi\)
\(294\) 0 0
\(295\) 21.8258 + 6.23626i 1.27075 + 0.363089i
\(296\) 4.96208i 0.288415i
\(297\) 0 0
\(298\) −10.4515 + 10.4515i −0.605441 + 0.605441i
\(299\) −6.58033 37.3189i −0.380551 2.15821i
\(300\) 0 0
\(301\) 6.53123 2.37717i 0.376454 0.137018i
\(302\) 0.890722 0.0779280i 0.0512553 0.00448426i
\(303\) 0 0
\(304\) 0.00228116 0.00626744i 0.000130834 0.000359462i
\(305\) −21.4204 + 1.51808i −1.22653 + 0.0869251i
\(306\) 0 0
\(307\) 8.60536 2.30580i 0.491134 0.131599i −0.00474824 0.999989i \(-0.501511\pi\)
0.495882 + 0.868390i \(0.334845\pi\)
\(308\) 0.924879 + 0.0809164i 0.0526999 + 0.00461064i
\(309\) 0 0
\(310\) 8.64518 1.37759i 0.491013 0.0782417i
\(311\) −26.8272 4.73035i −1.52123 0.268234i −0.650313 0.759666i \(-0.725362\pi\)
−0.870916 + 0.491433i \(0.836473\pi\)
\(312\) 0 0
\(313\) 1.36924 15.6505i 0.0773941 0.884618i −0.853921 0.520403i \(-0.825782\pi\)
0.931315 0.364215i \(-0.118663\pi\)
\(314\) −2.28318 + 3.95459i −0.128847 + 0.223170i
\(315\) 0 0
\(316\) 0.408430 + 0.707422i 0.0229760 + 0.0397956i
\(317\) −12.8207 + 5.97838i −0.720081 + 0.335779i −0.747880 0.663834i \(-0.768928\pi\)
0.0277988 + 0.999614i \(0.491150\pi\)
\(318\) 0 0
\(319\) 3.00744 3.58413i 0.168384 0.200673i
\(320\) −15.1094 1.57372i −0.844643 0.0879735i
\(321\) 0 0
\(322\) 2.72514 3.89191i 0.151866 0.216888i
\(323\) 0.0243419 + 0.0243419i 0.00135442 + 0.00135442i
\(324\) 0 0
\(325\) −25.4235 3.07315i −1.41024 0.170467i
\(326\) −10.8987 + 1.92174i −0.603624 + 0.106435i
\(327\) 0 0
\(328\) 2.43764 5.22754i 0.134596 0.288643i
\(329\) 3.64488 + 3.05842i 0.200949 + 0.168616i
\(330\) 0 0
\(331\) 15.8479 + 5.76816i 0.871078 + 0.317047i 0.738604 0.674140i \(-0.235485\pi\)
0.132475 + 0.991186i \(0.457708\pi\)
\(332\) 9.21668 + 2.46960i 0.505831 + 0.135537i
\(333\) 0 0
\(334\) −0.768076 0.443449i −0.0420273 0.0242645i
\(335\) −17.2905 + 28.8375i −0.944680 + 1.57556i
\(336\) 0 0
\(337\) −16.0410 + 11.2321i −0.873811 + 0.611849i −0.922086 0.386985i \(-0.873516\pi\)
0.0482752 + 0.998834i \(0.484628\pi\)
\(338\) −10.6826 + 7.48005i −0.581058 + 0.406861i
\(339\) 0 0
\(340\) 5.40027 9.00672i 0.292871 0.488458i
\(341\) −4.76543 2.75132i −0.258063 0.148993i
\(342\) 0 0
\(343\) −8.54371 2.28928i −0.461317 0.123610i
\(344\) 29.9216 + 10.8906i 1.61326 + 0.587180i
\(345\) 0 0
\(346\) 10.0840 + 8.46151i 0.542121 + 0.454894i
\(347\) −4.69183 + 10.0617i −0.251871 + 0.540138i −0.991069 0.133349i \(-0.957427\pi\)
0.739199 + 0.673488i \(0.235205\pi\)
\(348\) 0 0
\(349\) −5.91569 + 1.04309i −0.316659 + 0.0558356i −0.329719 0.944079i \(-0.606954\pi\)
0.0130596 + 0.999915i \(0.495843\pi\)
\(350\) −1.98148 2.52638i −0.105915 0.135041i
\(351\) 0 0
\(352\) 4.99364 + 4.99364i 0.266162 + 0.266162i
\(353\) −6.60297 + 9.43001i −0.351440 + 0.501909i −0.955484 0.295042i \(-0.904666\pi\)
0.604044 + 0.796951i \(0.293555\pi\)
\(354\) 0 0
\(355\) −13.9075 1.44853i −0.738135 0.0768802i
\(356\) −7.79749 + 9.29269i −0.413266 + 0.492512i
\(357\) 0 0
\(358\) 6.65644 3.10395i 0.351804 0.164049i
\(359\) −7.64807 13.2468i −0.403649 0.699141i 0.590514 0.807028i \(-0.298925\pi\)
−0.994163 + 0.107886i \(0.965592\pi\)
\(360\) 0 0
\(361\) −9.49997 + 16.4544i −0.499999 + 0.866023i
\(362\) 2.25305 25.7525i 0.118418 1.35352i
\(363\) 0 0
\(364\) 3.38050 + 0.596074i 0.177187 + 0.0312428i
\(365\) 27.8131 4.43195i 1.45581 0.231979i
\(366\) 0 0
\(367\) −12.8423 1.12355i −0.670361 0.0586490i −0.253106 0.967439i \(-0.581452\pi\)
−0.417255 + 0.908790i \(0.637008\pi\)
\(368\) 6.32188 1.69394i 0.329551 0.0883028i
\(369\) 0 0
\(370\) 3.65437 0.258988i 0.189982 0.0134641i
\(371\) 0.374288 1.02835i 0.0194321 0.0533892i
\(372\) 0 0
\(373\) −16.1018 + 1.40873i −0.833720 + 0.0729411i −0.496018 0.868312i \(-0.665205\pi\)
−0.337702 + 0.941253i \(0.609650\pi\)
\(374\) 5.85739 2.13192i 0.302878 0.110239i
\(375\) 0 0
\(376\) 3.78520 + 21.4670i 0.195207 + 1.10707i
\(377\) 12.2322 12.2322i 0.629989 0.629989i
\(378\) 0 0
\(379\) 9.64380i 0.495369i 0.968841 + 0.247684i \(0.0796696\pi\)
−0.968841 + 0.247684i \(0.920330\pi\)
\(380\) −0.0166753 0.00476463i −0.000855427 0.000244420i
\(381\) 0 0
\(382\) 1.42486 + 0.664424i 0.0729023 + 0.0339949i
\(383\) 1.26741 + 14.4866i 0.0647619 + 0.740232i 0.957269 + 0.289199i \(0.0933888\pi\)
−0.892507 + 0.451033i \(0.851056\pi\)
\(384\) 0 0
\(385\) −0.0333266 + 2.01790i −0.00169848 + 0.102842i
\(386\) −7.18097 + 4.14594i −0.365502 + 0.211023i
\(387\) 0 0
\(388\) 0.582850 + 2.17522i 0.0295897 + 0.110430i
\(389\) 12.6045 10.5764i 0.639073 0.536246i −0.264660 0.964342i \(-0.585260\pi\)
0.903733 + 0.428096i \(0.140815\pi\)
\(390\) 0 0
\(391\) −5.86593 + 33.2673i −0.296653 + 1.68240i
\(392\) −11.2579 16.0779i −0.568608 0.812056i
\(393\) 0 0
\(394\) 7.18883 + 8.56731i 0.362168 + 0.431615i
\(395\) −1.47118 + 0.994333i −0.0740229 + 0.0500303i
\(396\) 0 0
\(397\) −5.64123 + 21.0533i −0.283125 + 1.05664i 0.667073 + 0.744992i \(0.267547\pi\)
−0.950199 + 0.311645i \(0.899120\pi\)
\(398\) −10.1012 21.6620i −0.506325 1.08582i
\(399\) 0 0
\(400\) 0.146054 4.42052i 0.00730270 0.221026i
\(401\) −9.14946 25.1379i −0.456902 1.25533i −0.927779 0.373130i \(-0.878285\pi\)
0.470877 0.882199i \(-0.343938\pi\)
\(402\) 0 0
\(403\) −16.6658 11.6695i −0.830182 0.581300i
\(404\) 6.61309 0.329013
\(405\) 0 0
\(406\) 2.16890 0.107641
\(407\) −1.88633 1.32082i −0.0935019 0.0654707i
\(408\) 0 0
\(409\) −6.85481 18.8334i −0.338949 0.931253i −0.985694 0.168547i \(-0.946092\pi\)
0.646745 0.762706i \(-0.276130\pi\)
\(410\) 3.97710 + 1.52238i 0.196415 + 0.0751850i
\(411\) 0 0
\(412\) −4.07078 8.72982i −0.200553 0.430088i
\(413\) 1.71187 6.38878i 0.0842355 0.314371i
\(414\) 0 0
\(415\) −3.93862 + 20.3645i −0.193339 + 0.999655i
\(416\) 16.7838 + 20.0021i 0.822892 + 0.980684i
\(417\) 0 0
\(418\) −0.00590432 0.00843224i −0.000288790 0.000412435i
\(419\) −0.389697 + 2.21008i −0.0190379 + 0.107969i −0.992846 0.119402i \(-0.961902\pi\)
0.973808 + 0.227372i \(0.0730133\pi\)
\(420\) 0 0
\(421\) −17.9696 + 15.0783i −0.875786 + 0.734872i −0.965308 0.261113i \(-0.915911\pi\)
0.0895219 + 0.995985i \(0.471466\pi\)
\(422\) 2.32672 + 8.68342i 0.113263 + 0.422702i
\(423\) 0 0
\(424\) 4.34185 2.50677i 0.210859 0.121739i
\(425\) 20.3596 + 10.3256i 0.987587 + 0.500866i
\(426\) 0 0
\(427\) 0.545349 + 6.23337i 0.0263913 + 0.301654i
\(428\) 3.23505 + 1.50853i 0.156372 + 0.0729176i
\(429\) 0 0
\(430\) −6.45874 + 22.6044i −0.311468 + 1.09008i
\(431\) 15.7591i 0.759089i 0.925173 + 0.379545i \(0.123919\pi\)
−0.925173 + 0.379545i \(0.876081\pi\)
\(432\) 0 0
\(433\) 14.0286 14.0286i 0.674170 0.674170i −0.284505 0.958675i \(-0.591829\pi\)
0.958675 + 0.284505i \(0.0918291\pi\)
\(434\) −0.442947 2.51208i −0.0212621 0.120584i
\(435\) 0 0
\(436\) −10.7625 + 3.91724i −0.515432 + 0.187602i
\(437\) 0.0555739 0.00486209i 0.00265846 0.000232585i
\(438\) 0 0
\(439\) 1.43394 3.93972i 0.0684382 0.188033i −0.900759 0.434320i \(-0.856989\pi\)
0.969197 + 0.246288i \(0.0792108\pi\)
\(440\) −6.05928 + 6.98365i −0.288865 + 0.332932i
\(441\) 0 0
\(442\) 22.2614 5.96491i 1.05886 0.283722i
\(443\) −21.2489 1.85904i −1.00957 0.0883257i −0.429646 0.902998i \(-0.641361\pi\)
−0.579922 + 0.814672i \(0.696917\pi\)
\(444\) 0 0
\(445\) −21.3481 15.4797i −1.01200 0.733808i
\(446\) 15.8644 + 2.79732i 0.751201 + 0.132457i
\(447\) 0 0
\(448\) −0.385789 + 4.40959i −0.0182268 + 0.208333i
\(449\) −9.32000 + 16.1427i −0.439838 + 0.761822i −0.997677 0.0681276i \(-0.978297\pi\)
0.557839 + 0.829949i \(0.311631\pi\)
\(450\) 0 0
\(451\) −1.33838 2.31815i −0.0630221 0.109157i
\(452\) −8.30633 + 3.87330i −0.390697 + 0.182185i
\(453\) 0 0
\(454\) −8.00497 + 9.53996i −0.375692 + 0.447732i
\(455\) −0.773008 + 7.42173i −0.0362392 + 0.347936i
\(456\) 0 0
\(457\) 8.19900 11.7094i 0.383533 0.547742i −0.580247 0.814441i \(-0.697044\pi\)
0.963780 + 0.266699i \(0.0859328\pi\)
\(458\) 6.29334 + 6.29334i 0.294068 + 0.294068i
\(459\) 0 0
\(460\) −5.55570 16.0858i −0.259036 0.750006i
\(461\) −24.9949 + 4.40727i −1.16413 + 0.205267i −0.722135 0.691752i \(-0.756839\pi\)
−0.441992 + 0.897019i \(0.645728\pi\)
\(462\) 0 0
\(463\) −5.43841 + 11.6627i −0.252744 + 0.542012i −0.991213 0.132276i \(-0.957772\pi\)
0.738469 + 0.674288i \(0.235549\pi\)
\(464\) 2.28875 + 1.92049i 0.106252 + 0.0891563i
\(465\) 0 0
\(466\) −19.7704 7.19584i −0.915846 0.333341i
\(467\) −26.2781 7.04119i −1.21600 0.325828i −0.406890 0.913477i \(-0.633387\pi\)
−0.809115 + 0.587650i \(0.800053\pi\)
\(468\) 0 0
\(469\) 8.48478 + 4.89869i 0.391791 + 0.226200i
\(470\) −15.6120 + 3.90808i −0.720126 + 0.180266i
\(471\) 0 0
\(472\) 24.8215 17.3802i 1.14250 0.799988i
\(473\) 12.1047 8.47577i 0.556572 0.389716i
\(474\) 0 0
\(475\) 0.00776886 0.0368902i 0.000356460 0.00169264i
\(476\) −2.65002 1.52999i −0.121464 0.0701270i
\(477\) 0 0
\(478\) 5.50508 + 1.47508i 0.251797 + 0.0674687i
\(479\) 17.2415 + 6.27539i 0.787784 + 0.286730i 0.704415 0.709789i \(-0.251210\pi\)
0.0833693 + 0.996519i \(0.473432\pi\)
\(480\) 0 0
\(481\) −6.52224 5.47281i −0.297388 0.249538i
\(482\) 9.60172 20.5910i 0.437346 0.937892i
\(483\) 0 0
\(484\) −9.19935 + 1.62209i −0.418152 + 0.0737315i
\(485\) −4.62709 + 1.59810i −0.210105 + 0.0725659i
\(486\) 0 0
\(487\) 4.34114 + 4.34114i 0.196716 + 0.196716i 0.798591 0.601875i \(-0.205579\pi\)
−0.601875 + 0.798591i \(0.705579\pi\)
\(488\) −16.4422 + 23.4819i −0.744302 + 1.06297i
\(489\) 0 0
\(490\) 11.2531 9.13011i 0.508364 0.412456i
\(491\) −17.5435 + 20.9075i −0.791728 + 0.943544i −0.999399 0.0346544i \(-0.988967\pi\)
0.207672 + 0.978199i \(0.433411\pi\)
\(492\) 0 0
\(493\) −13.9760 + 6.51712i −0.629448 + 0.293516i
\(494\) −0.0190300 0.0329609i −0.000856199 0.00148298i
\(495\) 0 0
\(496\) 1.75694 3.04310i 0.0788887 0.136639i
\(497\) −0.355101 + 4.05882i −0.0159284 + 0.182063i
\(498\) 0 0
\(499\) 43.3225 + 7.63893i 1.93938 + 0.341965i 1.00000 0.000905893i \(-0.000288355\pi\)
0.939382 + 0.342871i \(0.111399\pi\)
\(500\) −11.4925 + 0.433752i −0.513958 + 0.0193980i
\(501\) 0 0
\(502\) 2.46473 + 0.215636i 0.110006 + 0.00962432i
\(503\) 4.03331 1.08072i 0.179836 0.0481870i −0.167777 0.985825i \(-0.553659\pi\)
0.347613 + 0.937638i \(0.386992\pi\)
\(504\) 0 0
\(505\) 1.01625 + 14.3395i 0.0452226 + 0.638100i
\(506\) 3.45484 9.49210i 0.153586 0.421975i
\(507\) 0 0
\(508\) −2.92079 + 0.255536i −0.129589 + 0.0113376i
\(509\) 1.50937 0.549366i 0.0669017 0.0243502i −0.308353 0.951272i \(-0.599778\pi\)
0.375254 + 0.926922i \(0.377555\pi\)
\(510\) 0 0
\(511\) −1.42504 8.08181i −0.0630401 0.357518i
\(512\) −6.92298 + 6.92298i −0.305956 + 0.305956i
\(513\) 0 0
\(514\) 12.4454i 0.548945i
\(515\) 18.3038 10.1684i 0.806561 0.448075i
\(516\) 0 0
\(517\) 9.16819 + 4.27520i 0.403216 + 0.188023i
\(518\) −0.0930377 1.06343i −0.00408784 0.0467242i
\(519\) 0 0
\(520\) −24.5684 + 23.7701i −1.07740 + 1.04239i
\(521\) 28.3338 16.3586i 1.24133 0.716681i 0.271964 0.962308i \(-0.412327\pi\)
0.969365 + 0.245626i \(0.0789936\pi\)
\(522\) 0 0
\(523\) −10.7572 40.1466i −0.470381 1.75549i −0.638402 0.769703i \(-0.720404\pi\)
0.168021 0.985783i \(-0.446262\pi\)
\(524\) −5.11713 + 4.29378i −0.223543 + 0.187575i
\(525\) 0 0
\(526\) 2.87389 16.2986i 0.125307 0.710654i
\(527\) 10.4026 + 14.8564i 0.453144 + 0.647156i
\(528\) 0 0
\(529\) 20.4037 + 24.3162i 0.887116 + 1.05722i
\(530\) 2.07275 + 3.06676i 0.0900344 + 0.133211i
\(531\) 0 0
\(532\) −0.00130790 + 0.00488116i −5.67048e−5 + 0.000211625i
\(533\) −4.18262 8.96966i −0.181169 0.388519i
\(534\) 0 0
\(535\) −2.77389 + 7.24656i −0.119926 + 0.313296i
\(536\) 15.3515 + 42.1779i 0.663084 + 1.82181i
\(537\) 0 0
\(538\) 2.64303 + 1.85067i 0.113949 + 0.0797879i
\(539\) −9.10864 −0.392337
\(540\) 0 0
\(541\) 14.5826 0.626954 0.313477 0.949596i \(-0.398506\pi\)
0.313477 + 0.949596i \(0.398506\pi\)
\(542\) 6.83708 + 4.78737i 0.293678 + 0.205635i
\(543\) 0 0
\(544\) −7.96090 21.8724i −0.341321 0.937771i
\(545\) −10.1479 22.7350i −0.434687 0.973861i
\(546\) 0 0
\(547\) 5.97161 + 12.8062i 0.255327 + 0.547551i 0.991632 0.129099i \(-0.0412085\pi\)
−0.736304 + 0.676651i \(0.763431\pi\)
\(548\) 4.93072 18.4017i 0.210630 0.786082i
\(549\) 0 0
\(550\) −5.45942 4.09791i −0.232790 0.174735i
\(551\) 0.0163695 + 0.0195084i 0.000697364 + 0.000831086i
\(552\) 0 0
\(553\) 0.296770 + 0.423831i 0.0126199 + 0.0180231i
\(554\) 0.422214 2.39450i 0.0179382 0.101732i
\(555\) 0 0
\(556\) 15.5697 13.0645i 0.660301 0.554058i
\(557\) −6.98848 26.0814i −0.296111 1.10510i −0.940331 0.340262i \(-0.889484\pi\)
0.644220 0.764841i \(-0.277182\pi\)
\(558\) 0 0
\(559\) 47.3160 27.3179i 2.00125 1.15542i
\(560\) −1.28859 0.0212816i −0.0544527 0.000899314i
\(561\) 0 0
\(562\) 1.66931 + 19.0803i 0.0704155 + 0.804853i
\(563\) −4.52364 2.10941i −0.190649 0.0889009i 0.324950 0.945731i \(-0.394653\pi\)
−0.515598 + 0.856830i \(0.672430\pi\)
\(564\) 0 0
\(565\) −9.67515 17.4158i −0.407037 0.732690i
\(566\) 18.5746i 0.780748i
\(567\) 0 0
\(568\) −13.1987 + 13.1987i −0.553804 + 0.553804i
\(569\) 2.39518 + 13.5837i 0.100411 + 0.569459i 0.992954 + 0.118497i \(0.0378077\pi\)
−0.892543 + 0.450962i \(0.851081\pi\)
\(570\) 0 0
\(571\) 4.72552 1.71995i 0.197757 0.0719776i −0.241243 0.970465i \(-0.577555\pi\)
0.439000 + 0.898487i \(0.355333\pi\)
\(572\) 7.27031 0.636069i 0.303987 0.0265954i
\(573\) 0 0
\(574\) 0.424397 1.16602i 0.0177140 0.0486688i
\(575\) 34.0260 14.5187i 1.41898 0.605471i
\(576\) 0 0
\(577\) −2.65137 + 0.710433i −0.110378 + 0.0295757i −0.313585 0.949560i \(-0.601530\pi\)
0.203207 + 0.979136i \(0.434863\pi\)
\(578\) −3.77540 0.330305i −0.157036 0.0137389i
\(579\) 0 0
\(580\) 4.56050 6.28940i 0.189364 0.261153i
\(581\) 5.95200 + 1.04950i 0.246930 + 0.0435405i
\(582\) 0 0
\(583\) 0.202782 2.31781i 0.00839837 0.0959938i
\(584\) 18.7982 32.5595i 0.777876 1.34732i
\(585\) 0 0
\(586\) −1.98777 3.44291i −0.0821138 0.142225i
\(587\) −18.7722 + 8.75362i −0.774811 + 0.361300i −0.769468 0.638685i \(-0.779479\pi\)
−0.00534328 + 0.999986i \(0.501701\pi\)
\(588\) 0 0
\(589\) 0.0192521 0.0229437i 0.000793268 0.000945380i
\(590\) 14.0953 + 17.3729i 0.580295 + 0.715229i
\(591\) 0 0
\(592\) 0.843448 1.20457i 0.0346655 0.0495075i
\(593\) −33.2020 33.2020i −1.36344 1.36344i −0.869487 0.493956i \(-0.835550\pi\)
−0.493956 0.869487i \(-0.664450\pi\)
\(594\) 0 0
\(595\) 2.91032 5.98130i 0.119312 0.245209i
\(596\) 15.1924 2.67882i 0.622303 0.109729i
\(597\) 0 0
\(598\) 15.7839 33.8487i 0.645452 1.38418i
\(599\) 9.01503 + 7.56451i 0.368344 + 0.309078i 0.808106 0.589037i \(-0.200493\pi\)
−0.439762 + 0.898114i \(0.644937\pi\)
\(600\) 0 0
\(601\) 13.4574 + 4.89809i 0.548938 + 0.199797i 0.601575 0.798817i \(-0.294540\pi\)
−0.0526366 + 0.998614i \(0.516763\pi\)
\(602\) 6.61670 + 1.77294i 0.269677 + 0.0722596i
\(603\) 0 0
\(604\) −0.808178 0.466602i −0.0328843 0.0189858i
\(605\) −4.93096 19.6982i −0.200472 0.800844i
\(606\) 0 0
\(607\) 16.7167 11.7051i 0.678509 0.475097i −0.182819 0.983147i \(-0.558522\pi\)
0.861328 + 0.508049i \(0.169633\pi\)
\(608\) −0.0314873 + 0.0220476i −0.00127698 + 0.000894150i
\(609\) 0 0
\(610\) −18.1516 10.8834i −0.734936 0.440655i
\(611\) 32.3913 + 18.7011i 1.31041 + 0.756566i
\(612\) 0 0
\(613\) 32.1941 + 8.62637i 1.30031 + 0.348416i 0.841566 0.540155i \(-0.181634\pi\)
0.458740 + 0.888571i \(0.348301\pi\)
\(614\) 8.25087 + 3.00307i 0.332978 + 0.121194i
\(615\) 0 0
\(616\) 2.06379 + 1.73172i 0.0831523 + 0.0697731i
\(617\) 0.373483 0.800937i 0.0150359 0.0322445i −0.898646 0.438674i \(-0.855448\pi\)
0.913682 + 0.406429i \(0.133226\pi\)
\(618\) 0 0
\(619\) −11.2863 + 1.99007i −0.453633 + 0.0799877i −0.395796 0.918338i \(-0.629531\pi\)
−0.0578365 + 0.998326i \(0.518420\pi\)
\(620\) −8.21593 3.99763i −0.329960 0.160549i
\(621\) 0 0
\(622\) −18.9844 18.9844i −0.761204 0.761204i
\(623\) −4.40717 + 6.29409i −0.176569 + 0.252167i
\(624\) 0 0
\(625\) −2.70661 24.8531i −0.108264 0.994122i
\(626\) 9.95267 11.8611i 0.397789 0.474066i
\(627\) 0 0
\(628\) 4.31941 2.01418i 0.172363 0.0803744i
\(629\) 3.79491 + 6.57297i 0.151313 + 0.262082i
\(630\) 0 0
\(631\) 0.493720 0.855149i 0.0196547 0.0340429i −0.856031 0.516925i \(-0.827077\pi\)
0.875685 + 0.482882i \(0.160410\pi\)
\(632\) −0.206592 + 2.36136i −0.00821780 + 0.0939299i
\(633\) 0 0
\(634\) −13.7301 2.42099i −0.545293 0.0961500i
\(635\) −1.00294 6.29404i −0.0398004 0.249771i
\(636\) 0 0
\(637\) −33.5496 2.93521i −1.32928 0.116297i
\(638\) 4.45412 1.19348i 0.176340 0.0472502i
\(639\) 0 0
\(640\) 5.91217 + 5.12963i 0.233699 + 0.202766i
\(641\) 9.55555 26.2536i 0.377421 1.03696i −0.595000 0.803726i \(-0.702848\pi\)
0.972421 0.233231i \(-0.0749298\pi\)
\(642\) 0 0
\(643\) −29.9171 + 2.61741i −1.17982 + 0.103221i −0.660140 0.751142i \(-0.729503\pi\)
−0.519677 + 0.854363i \(0.673948\pi\)
\(644\) −4.65975 + 1.69601i −0.183620 + 0.0668322i
\(645\) 0 0
\(646\) 0.00589152 + 0.0334124i 0.000231799 + 0.00131460i
\(647\) 22.0995 22.0995i 0.868820 0.868820i −0.123522 0.992342i \(-0.539419\pi\)
0.992342 + 0.123522i \(0.0394188\pi\)
\(648\) 0 0
\(649\) 14.0622i 0.551988i
\(650\) −18.7880 16.8530i −0.736926 0.661028i
\(651\) 0 0
\(652\) 10.4684 + 4.88147i 0.409972 + 0.191173i
\(653\) 0.292733 + 3.34596i 0.0114555 + 0.130937i 0.999769 0.0214986i \(-0.00684375\pi\)
−0.988313 + 0.152436i \(0.951288\pi\)
\(654\) 0 0
\(655\) −10.0968 10.4359i −0.394515 0.407765i
\(656\) 1.48032 0.854663i 0.0577968 0.0333690i
\(657\) 0 0
\(658\) 1.21371 + 4.52962i 0.0473152 + 0.176583i
\(659\) −19.8580 + 16.6629i −0.773560 + 0.649094i −0.941618 0.336683i \(-0.890695\pi\)
0.168058 + 0.985777i \(0.446250\pi\)
\(660\) 0 0
\(661\) 6.41723 36.3939i 0.249601 1.41556i −0.559958 0.828521i \(-0.689183\pi\)
0.809559 0.587038i \(-0.199706\pi\)
\(662\) 9.53378 + 13.6156i 0.370541 + 0.529187i
\(663\) 0 0
\(664\) 17.7979 + 21.2107i 0.690692 + 0.823134i
\(665\) −0.0107851 0.00208589i −0.000418227 8.08875e-5i
\(666\) 0 0
\(667\) −6.46788 + 24.1385i −0.250437 + 0.934645i
\(668\) 0.391202 + 0.838935i 0.0151360 + 0.0324594i
\(669\) 0 0
\(670\) −30.2610 + 13.5072i −1.16909 + 0.521827i
\(671\) 4.54997 + 12.5009i 0.175650 + 0.482593i
\(672\) 0 0
\(673\) −4.90829 3.43682i −0.189201 0.132480i 0.475138 0.879911i \(-0.342398\pi\)
−0.664339 + 0.747431i \(0.731287\pi\)
\(674\) −19.2999 −0.743406
\(675\) 0 0
\(676\) 13.6111 0.523502
\(677\) 28.2910 + 19.8096i 1.08731 + 0.761345i 0.972700 0.232066i \(-0.0745484\pi\)
0.114613 + 0.993410i \(0.463437\pi\)
\(678\) 0 0
\(679\) 0.487857 + 1.34038i 0.0187222 + 0.0514389i
\(680\) 27.8275 12.4209i 1.06714 0.476321i
\(681\) 0 0
\(682\) −2.29197 4.91514i −0.0877639 0.188210i
\(683\) 0.984841 3.67548i 0.0376839 0.140638i −0.944521 0.328451i \(-0.893473\pi\)
0.982205 + 0.187813i \(0.0601399\pi\)
\(684\) 0 0
\(685\) 40.6591 + 7.86371i 1.55351 + 0.300457i
\(686\) −5.60349 6.67798i −0.213942 0.254966i
\(687\) 0 0
\(688\) 5.41244 + 7.72977i 0.206347 + 0.294695i
\(689\) 1.49380 8.47177i 0.0569093 0.322749i
\(690\) 0 0
\(691\) 0.658559 0.552596i 0.0250528 0.0210218i −0.630175 0.776453i \(-0.717017\pi\)
0.655228 + 0.755431i \(0.272573\pi\)
\(692\) −3.55595 13.2710i −0.135177 0.504487i
\(693\) 0 0
\(694\) −9.47573 + 5.47082i −0.359694 + 0.207669i
\(695\) 30.7211 + 31.7529i 1.16532 + 1.20446i
\(696\) 0 0
\(697\) 0.768927 + 8.78887i 0.0291252 + 0.332902i
\(698\) −5.36559 2.50202i −0.203091 0.0947027i
\(699\) 0 0
\(700\) 0.181668 + 3.34615i 0.00686641 + 0.126473i
\(701\) 28.2369i 1.06649i 0.845960 + 0.533246i \(0.179028\pi\)
−0.845960 + 0.533246i \(0.820972\pi\)
\(702\) 0 0
\(703\) 0.00886291 0.00886291i 0.000334271 0.000334271i
\(704\) 1.63419 + 9.26794i 0.0615908 + 0.349299i
\(705\) 0 0
\(706\) −10.6616 + 3.88050i −0.401254 + 0.146045i
\(707\) 4.17282 0.365074i 0.156935 0.0137300i
\(708\) 0 0
\(709\) −2.66301 + 7.31657i −0.100012 + 0.274780i −0.979600 0.200955i \(-0.935596\pi\)
0.879589 + 0.475735i \(0.157818\pi\)
\(710\) −10.4092 9.03139i −0.390649 0.338942i
\(711\) 0 0
\(712\) −34.0018 + 9.11075i −1.27427 + 0.341440i
\(713\) 29.2787 + 2.56156i 1.09650 + 0.0959310i
\(714\) 0 0
\(715\) 2.49647 + 15.6668i 0.0933628 + 0.585907i
\(716\) −7.54913 1.33111i −0.282124 0.0497461i
\(717\) 0 0
\(718\) 1.31391 15.0181i 0.0490347 0.560469i
\(719\) 5.23184 9.06182i 0.195115 0.337949i −0.751823 0.659365i \(-0.770825\pi\)
0.946938 + 0.321416i \(0.104159\pi\)
\(720\) 0 0
\(721\) −3.05057 5.28374i −0.113609 0.196777i
\(722\) −16.9713 + 7.91387i −0.631608 + 0.294524i
\(723\) 0 0
\(724\) −17.3429 + 20.6685i −0.644544 + 0.768138i
\(725\) 14.3385 + 8.92226i 0.532517 + 0.331364i
\(726\) 0 0
\(727\) 10.3885 14.8363i 0.385289 0.550250i −0.578923 0.815382i \(-0.696527\pi\)
0.964212 + 0.265133i \(0.0854157\pi\)
\(728\) 7.04345 + 7.04345i 0.261048 + 0.261048i
\(729\) 0 0
\(730\) 24.9598 + 12.1447i 0.923805 + 0.449496i
\(731\) −47.9642 + 8.45739i −1.77402 + 0.312808i
\(732\) 0 0
\(733\) 12.7723 27.3902i 0.471755 1.01168i −0.516133 0.856509i \(-0.672629\pi\)
0.987887 0.155173i \(-0.0495934\pi\)
\(734\) −9.73284 8.16683i −0.359246 0.301443i
\(735\) 0 0
\(736\) −35.4450 12.9009i −1.30652 0.475534i
\(737\) 20.1202 + 5.39119i 0.741137 + 0.198587i
\(738\) 0 0
\(739\) −3.17194 1.83132i −0.116682 0.0673663i 0.440523 0.897741i \(-0.354793\pi\)
−0.557205 + 0.830375i \(0.688126\pi\)
\(740\) −3.27936 1.96625i −0.120552 0.0722808i
\(741\) 0 0
\(742\) 0.883502 0.618635i 0.0324344 0.0227108i
\(743\) −26.5204 + 18.5698i −0.972939 + 0.681259i −0.947947 0.318429i \(-0.896845\pi\)
−0.0249919 + 0.999688i \(0.507956\pi\)
\(744\) 0 0
\(745\) 8.14329 + 32.5308i 0.298347 + 1.19183i
\(746\) −13.7959 7.96506i −0.505103 0.291621i
\(747\) 0 0
\(748\) −6.28407 1.68381i −0.229768 0.0615662i
\(749\) 2.12458 + 0.773283i 0.0776303 + 0.0282551i
\(750\) 0 0
\(751\) −16.4509 13.8040i −0.600303 0.503714i 0.291240 0.956650i \(-0.405932\pi\)
−0.891543 + 0.452936i \(0.850377\pi\)
\(752\) −2.73005 + 5.85460i −0.0995546 + 0.213495i
\(753\) 0 0
\(754\) 16.7903 2.96058i 0.611467 0.107818i
\(755\) 0.887563 1.82412i 0.0323017 0.0663865i
\(756\) 0 0
\(757\) 20.3709 + 20.3709i 0.740395 + 0.740395i 0.972654 0.232259i \(-0.0746118\pi\)
−0.232259 + 0.972654i \(0.574612\pi\)
\(758\) −5.45165 + 7.78576i −0.198013 + 0.282792i
\(759\) 0 0
\(760\) −0.0317075 0.0390804i −0.00115015 0.00141759i
\(761\) −20.6946 + 24.6629i −0.750179 + 0.894028i −0.997185 0.0749859i \(-0.976109\pi\)
0.247006 + 0.969014i \(0.420553\pi\)
\(762\) 0 0
\(763\) −6.57484 + 3.06590i −0.238025 + 0.110993i
\(764\) −0.820438 1.42104i −0.0296824 0.0514114i
\(765\) 0 0
\(766\) −7.16607 + 12.4120i −0.258921 + 0.448464i
\(767\) 4.53146 51.7948i 0.163621 1.87020i
\(768\) 0 0
\(769\) −3.27352 0.577210i −0.118046 0.0208147i 0.114313 0.993445i \(-0.463533\pi\)
−0.232359 + 0.972630i \(0.574644\pi\)
\(770\) −1.16763 + 1.61028i −0.0420783 + 0.0580304i
\(771\) 0 0
\(772\) 8.62135 + 0.754271i 0.310289 + 0.0271468i
\(773\) 3.47814 0.931964i 0.125100 0.0335204i −0.195726 0.980659i \(-0.562706\pi\)
0.320826 + 0.947138i \(0.396040\pi\)
\(774\) 0 0
\(775\) 7.40570 18.4294i 0.266021 0.662002i
\(776\) −2.23502 + 6.14068i −0.0802327 + 0.220437i
\(777\) 0 0
\(778\) 16.1549 1.41337i 0.579181 0.0506718i
\(779\) 0.0136910 0.00498312i 0.000490531 0.000178539i
\(780\) 0 0
\(781\) 1.50420 + 8.53071i 0.0538243 + 0.305253i
\(782\) −23.5418 + 23.5418i −0.841853 + 0.841853i
\(783\) 0 0
\(784\) 5.81658i 0.207735i
\(785\) 5.03122 + 9.05649i 0.179572 + 0.323240i
\(786\) 0 0