Properties

Label 405.2.r.a.152.4
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 152.4
Character \(\chi\) \(=\) 405.152
Dual form 405.2.r.a.8.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.23715 - 0.866263i) q^{2} +(0.0960923 + 0.264011i) q^{4} +(2.23168 + 0.140023i) q^{5} +(0.677826 + 1.45360i) q^{7} +(-0.671958 + 2.50778i) q^{8} +O(q^{10})\) \(q+(-1.23715 - 0.866263i) q^{2} +(0.0960923 + 0.264011i) q^{4} +(2.23168 + 0.140023i) q^{5} +(0.677826 + 1.45360i) q^{7} +(-0.671958 + 2.50778i) q^{8} +(-2.63963 - 2.10645i) q^{10} +(1.78545 + 2.12782i) q^{11} +(0.176418 + 0.251952i) q^{13} +(0.420628 - 2.38550i) q^{14} +(3.43416 - 2.88160i) q^{16} +(1.88139 + 7.02145i) q^{17} +(-5.07203 + 2.92834i) q^{19} +(0.177479 + 0.602644i) q^{20} +(-0.365624 - 4.17910i) q^{22} +(-0.116642 - 0.0543910i) q^{23} +(4.96079 + 0.624975i) q^{25} -0.464527i q^{26} +(-0.318634 + 0.318634i) q^{28} +(-1.51659 - 8.60103i) q^{29} +(4.22026 - 1.53605i) q^{31} +(-1.57207 + 0.137538i) q^{32} +(3.75485 - 10.3164i) q^{34} +(1.30915 + 3.33889i) q^{35} +(2.08386 - 0.558369i) q^{37} +(8.81158 + 0.770913i) q^{38} +(-1.85074 + 5.50247i) q^{40} +(4.62442 + 0.815410i) q^{41} +(-0.429127 + 4.90494i) q^{43} +(-0.390200 + 0.675847i) q^{44} +(0.0971868 + 0.168333i) q^{46} +(7.69135 - 3.58654i) q^{47} +(2.84600 - 3.39173i) q^{49} +(-5.59585 - 5.07053i) q^{50} +(-0.0495656 + 0.0707870i) q^{52} +(-0.483003 - 0.483003i) q^{53} +(3.68661 + 4.99861i) q^{55} +(-4.10079 + 0.723079i) q^{56} +(-5.57450 + 11.9546i) q^{58} +(-7.43127 - 6.23558i) q^{59} +(2.50049 + 0.910105i) q^{61} +(-6.55173 - 1.75553i) q^{62} +(-5.70071 - 3.29131i) q^{64} +(0.358430 + 0.586978i) q^{65} +(-0.884390 + 0.619257i) q^{67} +(-1.67295 + 1.17142i) q^{68} +(1.27273 - 5.26478i) q^{70} +(-9.03942 - 5.21891i) q^{71} +(-6.65047 - 1.78199i) q^{73} +(-3.06175 - 1.11439i) q^{74} +(-1.26050 - 1.05768i) q^{76} +(-1.88278 + 4.03763i) q^{77} +(2.04188 - 0.360038i) q^{79} +(8.06743 - 5.94995i) q^{80} +(-5.01475 - 5.01475i) q^{82} +(-7.55956 + 10.7962i) q^{83} +(3.21549 + 15.9331i) q^{85} +(4.77986 - 5.69642i) q^{86} +(-6.53585 + 3.04772i) q^{88} +(5.58181 + 9.66798i) q^{89} +(-0.246656 + 0.427222i) q^{91} +(0.00315146 - 0.0360214i) q^{92} +(-12.6222 - 2.22564i) q^{94} +(-11.7292 + 5.82491i) q^{95} +(-11.8062 - 1.03291i) q^{97} +(-6.45906 + 1.73070i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23715 0.866263i −0.874798 0.612540i 0.0475633 0.998868i \(-0.484854\pi\)
−0.922361 + 0.386328i \(0.873743\pi\)
\(3\) 0 0
\(4\) 0.0960923 + 0.264011i 0.0480461 + 0.132006i
\(5\) 2.23168 + 0.140023i 0.998037 + 0.0626204i
\(6\) 0 0
\(7\) 0.677826 + 1.45360i 0.256194 + 0.549410i 0.991770 0.128032i \(-0.0408661\pi\)
−0.735576 + 0.677442i \(0.763088\pi\)
\(8\) −0.671958 + 2.50778i −0.237573 + 0.886634i
\(9\) 0 0
\(10\) −2.63963 2.10645i −0.834724 0.666118i
\(11\) 1.78545 + 2.12782i 0.538334 + 0.641561i 0.964813 0.262936i \(-0.0846908\pi\)
−0.426479 + 0.904497i \(0.640246\pi\)
\(12\) 0 0
\(13\) 0.176418 + 0.251952i 0.0489296 + 0.0698788i 0.842871 0.538115i \(-0.180863\pi\)
−0.793942 + 0.607994i \(0.791975\pi\)
\(14\) 0.420628 2.38550i 0.112418 0.637552i
\(15\) 0 0
\(16\) 3.43416 2.88160i 0.858539 0.720400i
\(17\) 1.88139 + 7.02145i 0.456304 + 1.70295i 0.684225 + 0.729271i \(0.260141\pi\)
−0.227921 + 0.973680i \(0.573193\pi\)
\(18\) 0 0
\(19\) −5.07203 + 2.92834i −1.16360 + 0.671807i −0.952165 0.305584i \(-0.901148\pi\)
−0.211439 + 0.977391i \(0.567815\pi\)
\(20\) 0.177479 + 0.602644i 0.0396856 + 0.134755i
\(21\) 0 0
\(22\) −0.365624 4.17910i −0.0779514 0.890988i
\(23\) −0.116642 0.0543910i −0.0243215 0.0113413i 0.410419 0.911897i \(-0.365382\pi\)
−0.434741 + 0.900556i \(0.643160\pi\)
\(24\) 0 0
\(25\) 4.96079 + 0.624975i 0.992157 + 0.124995i
\(26\) 0.464527i 0.0911012i
\(27\) 0 0
\(28\) −0.318634 + 0.318634i −0.0602161 + 0.0602161i
\(29\) −1.51659 8.60103i −0.281625 1.59717i −0.717099 0.696971i \(-0.754531\pi\)
0.435475 0.900201i \(-0.356581\pi\)
\(30\) 0 0
\(31\) 4.22026 1.53605i 0.757981 0.275883i 0.0660211 0.997818i \(-0.478970\pi\)
0.691960 + 0.721936i \(0.256747\pi\)
\(32\) −1.57207 + 0.137538i −0.277905 + 0.0243135i
\(33\) 0 0
\(34\) 3.75485 10.3164i 0.643952 1.76924i
\(35\) 1.30915 + 3.33889i 0.221287 + 0.564375i
\(36\) 0 0
\(37\) 2.08386 0.558369i 0.342585 0.0917953i −0.0834245 0.996514i \(-0.526586\pi\)
0.426009 + 0.904719i \(0.359919\pi\)
\(38\) 8.81158 + 0.770913i 1.42943 + 0.125059i
\(39\) 0 0
\(40\) −1.85074 + 5.50247i −0.292628 + 0.870017i
\(41\) 4.62442 + 0.815410i 0.722213 + 0.127346i 0.522660 0.852541i \(-0.324940\pi\)
0.199553 + 0.979887i \(0.436051\pi\)
\(42\) 0 0
\(43\) −0.429127 + 4.90494i −0.0654412 + 0.747997i 0.890604 + 0.454779i \(0.150282\pi\)
−0.956046 + 0.293218i \(0.905274\pi\)
\(44\) −0.390200 + 0.675847i −0.0588249 + 0.101888i
\(45\) 0 0
\(46\) 0.0971868 + 0.168333i 0.0143294 + 0.0248193i
\(47\) 7.69135 3.58654i 1.12190 0.523150i 0.229009 0.973424i \(-0.426452\pi\)
0.892890 + 0.450274i \(0.148674\pi\)
\(48\) 0 0
\(49\) 2.84600 3.39173i 0.406571 0.484533i
\(50\) −5.59585 5.07053i −0.791373 0.717082i
\(51\) 0 0
\(52\) −0.0495656 + 0.0707870i −0.00687352 + 0.00981640i
\(53\) −0.483003 0.483003i −0.0663456 0.0663456i 0.673155 0.739501i \(-0.264938\pi\)
−0.739501 + 0.673155i \(0.764938\pi\)
\(54\) 0 0
\(55\) 3.68661 + 4.99861i 0.497103 + 0.674013i
\(56\) −4.10079 + 0.723079i −0.547991 + 0.0966255i
\(57\) 0 0
\(58\) −5.57450 + 11.9546i −0.731968 + 1.56971i
\(59\) −7.43127 6.23558i −0.967469 0.811803i 0.0146830 0.999892i \(-0.495326\pi\)
−0.982152 + 0.188089i \(0.939771\pi\)
\(60\) 0 0
\(61\) 2.50049 + 0.910105i 0.320155 + 0.116527i 0.497099 0.867694i \(-0.334399\pi\)
−0.176943 + 0.984221i \(0.556621\pi\)
\(62\) −6.55173 1.75553i −0.832070 0.222952i
\(63\) 0 0
\(64\) −5.70071 3.29131i −0.712589 0.411413i
\(65\) 0.358430 + 0.586978i 0.0444578 + 0.0728056i
\(66\) 0 0
\(67\) −0.884390 + 0.619257i −0.108045 + 0.0756543i −0.626350 0.779542i \(-0.715452\pi\)
0.518305 + 0.855196i \(0.326563\pi\)
\(68\) −1.67295 + 1.17142i −0.202876 + 0.142055i
\(69\) 0 0
\(70\) 1.27273 5.26478i 0.152121 0.629261i
\(71\) −9.03942 5.21891i −1.07278 0.619371i −0.143842 0.989601i \(-0.545946\pi\)
−0.928940 + 0.370230i \(0.879279\pi\)
\(72\) 0 0
\(73\) −6.65047 1.78199i −0.778378 0.208566i −0.152309 0.988333i \(-0.548671\pi\)
−0.626070 + 0.779767i \(0.715337\pi\)
\(74\) −3.06175 1.11439i −0.355921 0.129545i
\(75\) 0 0
\(76\) −1.26050 1.05768i −0.144589 0.121325i
\(77\) −1.88278 + 4.03763i −0.214562 + 0.460130i
\(78\) 0 0
\(79\) 2.04188 0.360038i 0.229729 0.0405074i −0.0575985 0.998340i \(-0.518344\pi\)
0.287327 + 0.957832i \(0.407233\pi\)
\(80\) 8.06743 5.94995i 0.901966 0.665224i
\(81\) 0 0
\(82\) −5.01475 5.01475i −0.553787 0.553787i
\(83\) −7.55956 + 10.7962i −0.829770 + 1.18503i 0.150742 + 0.988573i \(0.451834\pi\)
−0.980512 + 0.196461i \(0.937055\pi\)
\(84\) 0 0
\(85\) 3.21549 + 15.9331i 0.348769 + 1.72818i
\(86\) 4.77986 5.69642i 0.515426 0.614261i
\(87\) 0 0
\(88\) −6.53585 + 3.04772i −0.696724 + 0.324888i
\(89\) 5.58181 + 9.66798i 0.591671 + 1.02480i 0.994007 + 0.109312i \(0.0348648\pi\)
−0.402337 + 0.915492i \(0.631802\pi\)
\(90\) 0 0
\(91\) −0.246656 + 0.427222i −0.0258566 + 0.0447850i
\(92\) 0.00315146 0.0360214i 0.000328562 0.00375549i
\(93\) 0 0
\(94\) −12.6222 2.22564i −1.30189 0.229558i
\(95\) −11.7292 + 5.82491i −1.20339 + 0.597623i
\(96\) 0 0
\(97\) −11.8062 1.03291i −1.19874 0.104876i −0.529754 0.848151i \(-0.677716\pi\)
−0.668986 + 0.743275i \(0.733271\pi\)
\(98\) −6.45906 + 1.73070i −0.652464 + 0.174827i
\(99\) 0 0
\(100\) 0.311693 + 1.36976i 0.0311693 + 0.136976i
\(101\) 4.61138 12.6697i 0.458850 1.26068i −0.467493 0.883997i \(-0.654843\pi\)
0.926343 0.376682i \(-0.122935\pi\)
\(102\) 0 0
\(103\) 2.96335 0.259260i 0.291988 0.0255456i 0.0597791 0.998212i \(-0.480960\pi\)
0.232209 + 0.972666i \(0.425405\pi\)
\(104\) −0.750384 + 0.273118i −0.0735813 + 0.0267814i
\(105\) 0 0
\(106\) 0.179140 + 1.01596i 0.0173997 + 0.0986783i
\(107\) −7.80800 + 7.80800i −0.754828 + 0.754828i −0.975376 0.220548i \(-0.929215\pi\)
0.220548 + 0.975376i \(0.429215\pi\)
\(108\) 0 0
\(109\) 0.464359i 0.0444775i −0.999753 0.0222388i \(-0.992921\pi\)
0.999753 0.0222388i \(-0.00707940\pi\)
\(110\) −0.230783 9.37762i −0.0220043 0.894121i
\(111\) 0 0
\(112\) 6.51646 + 3.03868i 0.615748 + 0.287128i
\(113\) −0.0417367 0.477053i −0.00392626 0.0448774i 0.993979 0.109572i \(-0.0349481\pi\)
−0.997905 + 0.0646950i \(0.979393\pi\)
\(114\) 0 0
\(115\) −0.252691 0.137716i −0.0235636 0.0128421i
\(116\) 2.12504 1.22689i 0.197305 0.113914i
\(117\) 0 0
\(118\) 3.79196 + 14.1518i 0.349078 + 1.30278i
\(119\) −8.93114 + 7.49411i −0.818716 + 0.686984i
\(120\) 0 0
\(121\) 0.570356 3.23465i 0.0518506 0.294059i
\(122\) −2.30510 3.29202i −0.208694 0.298046i
\(123\) 0 0
\(124\) 0.811069 + 0.966595i 0.0728362 + 0.0868028i
\(125\) 10.9834 + 2.08937i 0.982383 + 0.186879i
\(126\) 0 0
\(127\) 3.48210 12.9954i 0.308987 1.15315i −0.620473 0.784228i \(-0.713059\pi\)
0.929459 0.368925i \(-0.120274\pi\)
\(128\) 5.53535 + 11.8706i 0.489260 + 1.04922i
\(129\) 0 0
\(130\) 0.0650447 1.03667i 0.00570479 0.0909224i
\(131\) 2.11500 + 5.81092i 0.184788 + 0.507702i 0.997149 0.0754528i \(-0.0240402\pi\)
−0.812361 + 0.583155i \(0.801818\pi\)
\(132\) 0 0
\(133\) −7.69460 5.38781i −0.667206 0.467183i
\(134\) 1.63056 0.140859
\(135\) 0 0
\(136\) −18.8725 −1.61830
\(137\) 6.04873 + 4.23537i 0.516778 + 0.361852i 0.802683 0.596406i \(-0.203405\pi\)
−0.285905 + 0.958258i \(0.592294\pi\)
\(138\) 0 0
\(139\) 3.50715 + 9.63582i 0.297473 + 0.817299i 0.994921 + 0.100664i \(0.0320966\pi\)
−0.697448 + 0.716635i \(0.745681\pi\)
\(140\) −0.755705 + 0.666472i −0.0638687 + 0.0563272i
\(141\) 0 0
\(142\) 6.66218 + 14.2871i 0.559078 + 1.19895i
\(143\) −0.221121 + 0.825233i −0.0184910 + 0.0690095i
\(144\) 0 0
\(145\) −2.18021 19.4071i −0.181056 1.61167i
\(146\) 6.68396 + 7.96564i 0.553169 + 0.659241i
\(147\) 0 0
\(148\) 0.347659 + 0.496508i 0.0285774 + 0.0408127i
\(149\) 0.210055 1.19128i 0.0172084 0.0975937i −0.974994 0.222232i \(-0.928666\pi\)
0.992202 + 0.124638i \(0.0397770\pi\)
\(150\) 0 0
\(151\) −12.3858 + 10.3930i −1.00795 + 0.845766i −0.988065 0.154036i \(-0.950773\pi\)
−0.0198800 + 0.999802i \(0.506328\pi\)
\(152\) −3.93544 14.6873i −0.319206 1.19129i
\(153\) 0 0
\(154\) 5.82693 3.36418i 0.469547 0.271093i
\(155\) 9.63335 2.83703i 0.773770 0.227876i
\(156\) 0 0
\(157\) −1.80822 20.6680i −0.144311 1.64949i −0.630907 0.775858i \(-0.717317\pi\)
0.486596 0.873627i \(-0.338238\pi\)
\(158\) −2.83800 1.32338i −0.225779 0.105282i
\(159\) 0 0
\(160\) −3.52761 + 0.0868145i −0.278882 + 0.00686329i
\(161\) 0.206419i 0.0162681i
\(162\) 0 0
\(163\) 9.24417 9.24417i 0.724060 0.724060i −0.245370 0.969430i \(-0.578909\pi\)
0.969430 + 0.245370i \(0.0789094\pi\)
\(164\) 0.229094 + 1.29925i 0.0178892 + 0.101455i
\(165\) 0 0
\(166\) 18.7046 6.80794i 1.45176 0.528398i
\(167\) −16.0301 + 1.40245i −1.24044 + 0.108525i −0.688425 0.725307i \(-0.741698\pi\)
−0.552018 + 0.833832i \(0.686142\pi\)
\(168\) 0 0
\(169\) 4.41391 12.1271i 0.339531 0.932854i
\(170\) 9.82416 22.4971i 0.753479 1.72545i
\(171\) 0 0
\(172\) −1.33620 + 0.358033i −0.101884 + 0.0272997i
\(173\) 2.64260 + 0.231197i 0.200913 + 0.0175776i 0.187168 0.982328i \(-0.440069\pi\)
0.0137449 + 0.999906i \(0.495625\pi\)
\(174\) 0 0
\(175\) 2.45409 + 7.63464i 0.185511 + 0.577124i
\(176\) 12.2630 + 2.16231i 0.924362 + 0.162990i
\(177\) 0 0
\(178\) 1.46947 16.7961i 0.110141 1.25892i
\(179\) 3.43088 5.94245i 0.256436 0.444160i −0.708849 0.705360i \(-0.750785\pi\)
0.965284 + 0.261201i \(0.0841185\pi\)
\(180\) 0 0
\(181\) 10.0120 + 17.3412i 0.744183 + 1.28896i 0.950575 + 0.310494i \(0.100494\pi\)
−0.206392 + 0.978469i \(0.566172\pi\)
\(182\) 0.675238 0.314868i 0.0500519 0.0233396i
\(183\) 0 0
\(184\) 0.214779 0.255964i 0.0158337 0.0188699i
\(185\) 4.72870 0.954312i 0.347661 0.0701624i
\(186\) 0 0
\(187\) −11.5812 + 16.5397i −0.846903 + 1.20950i
\(188\) 1.68597 + 1.68597i 0.122962 + 0.122962i
\(189\) 0 0
\(190\) 19.5567 + 2.95426i 1.41879 + 0.214325i
\(191\) −9.22577 + 1.62675i −0.667553 + 0.117708i −0.497147 0.867666i \(-0.665619\pi\)
−0.170406 + 0.985374i \(0.554508\pi\)
\(192\) 0 0
\(193\) 8.90711 19.1014i 0.641148 1.37495i −0.269998 0.962861i \(-0.587023\pi\)
0.911146 0.412085i \(-0.135199\pi\)
\(194\) 13.7113 + 11.5052i 0.984414 + 0.826022i
\(195\) 0 0
\(196\) 1.16893 + 0.425457i 0.0834953 + 0.0303898i
\(197\) −7.09801 1.90191i −0.505712 0.135505i −0.00306257 0.999995i \(-0.500975\pi\)
−0.502650 + 0.864490i \(0.667642\pi\)
\(198\) 0 0
\(199\) 22.3449 + 12.9008i 1.58399 + 0.914516i 0.994269 + 0.106906i \(0.0340945\pi\)
0.589718 + 0.807609i \(0.299239\pi\)
\(200\) −4.90074 + 12.0206i −0.346534 + 0.849985i
\(201\) 0 0
\(202\) −16.6802 + 11.6796i −1.17362 + 0.821776i
\(203\) 11.4745 8.03453i 0.805352 0.563914i
\(204\) 0 0
\(205\) 10.2061 + 2.46726i 0.712821 + 0.172321i
\(206\) −3.89070 2.24630i −0.271078 0.156507i
\(207\) 0 0
\(208\) 1.33187 + 0.356874i 0.0923487 + 0.0247448i
\(209\) −15.2868 5.56395i −1.05741 0.384867i
\(210\) 0 0
\(211\) −0.268205 0.225051i −0.0184640 0.0154932i 0.633509 0.773735i \(-0.281614\pi\)
−0.651973 + 0.758242i \(0.726058\pi\)
\(212\) 0.0811054 0.173931i 0.00557035 0.0119456i
\(213\) 0 0
\(214\) 16.4235 2.89590i 1.12268 0.197960i
\(215\) −1.64448 + 10.8862i −0.112153 + 0.742431i
\(216\) 0 0
\(217\) 5.09341 + 5.09341i 0.345763 + 0.345763i
\(218\) −0.402257 + 0.574483i −0.0272443 + 0.0389089i
\(219\) 0 0
\(220\) −0.965436 + 1.45364i −0.0650897 + 0.0980041i
\(221\) −1.43715 + 1.71273i −0.0966733 + 0.115211i
\(222\) 0 0
\(223\) −14.2401 + 6.64028i −0.953590 + 0.444666i −0.836203 0.548420i \(-0.815230\pi\)
−0.117387 + 0.993086i \(0.537452\pi\)
\(224\) −1.26551 2.19193i −0.0845557 0.146455i
\(225\) 0 0
\(226\) −0.361618 + 0.626342i −0.0240545 + 0.0416636i
\(227\) 2.05222 23.4570i 0.136211 1.55690i −0.553522 0.832834i \(-0.686717\pi\)
0.689733 0.724064i \(-0.257728\pi\)
\(228\) 0 0
\(229\) −22.8004 4.02032i −1.50669 0.265671i −0.641505 0.767119i \(-0.721690\pi\)
−0.865188 + 0.501448i \(0.832801\pi\)
\(230\) 0.193319 + 0.389273i 0.0127471 + 0.0256679i
\(231\) 0 0
\(232\) 22.5886 + 1.97625i 1.48301 + 0.129747i
\(233\) 20.8931 5.59828i 1.36875 0.366755i 0.501728 0.865026i \(-0.332698\pi\)
0.867022 + 0.498270i \(0.166031\pi\)
\(234\) 0 0
\(235\) 17.6668 6.92703i 1.15246 0.451870i
\(236\) 0.932175 2.56113i 0.0606794 0.166715i
\(237\) 0 0
\(238\) 17.5410 1.53464i 1.13702 0.0994761i
\(239\) 13.3597 4.86252i 0.864165 0.314530i 0.128363 0.991727i \(-0.459028\pi\)
0.735802 + 0.677197i \(0.236805\pi\)
\(240\) 0 0
\(241\) −1.44826 8.21348i −0.0932905 0.529077i −0.995258 0.0972724i \(-0.968988\pi\)
0.901967 0.431804i \(-0.142123\pi\)
\(242\) −3.50767 + 3.50767i −0.225482 + 0.225482i
\(243\) 0 0
\(244\) 0.747612i 0.0478610i
\(245\) 6.82628 7.17075i 0.436115 0.458122i
\(246\) 0 0
\(247\) −1.63260 0.761293i −0.103880 0.0484399i
\(248\) 1.01624 + 11.6156i 0.0645311 + 0.737594i
\(249\) 0 0
\(250\) −11.7782 12.0994i −0.744916 0.765231i
\(251\) −4.13040 + 2.38469i −0.260708 + 0.150520i −0.624658 0.780899i \(-0.714761\pi\)
0.363949 + 0.931419i \(0.381428\pi\)
\(252\) 0 0
\(253\) −0.0925243 0.345305i −0.00581695 0.0217092i
\(254\) −15.5653 + 13.0608i −0.976654 + 0.819510i
\(255\) 0 0
\(256\) 1.14887 6.51557i 0.0718045 0.407223i
\(257\) 2.70759 + 3.86684i 0.168895 + 0.241207i 0.894673 0.446722i \(-0.147409\pi\)
−0.725778 + 0.687929i \(0.758520\pi\)
\(258\) 0 0
\(259\) 2.22414 + 2.65063i 0.138202 + 0.164702i
\(260\) −0.120526 + 0.151034i −0.00747473 + 0.00936671i
\(261\) 0 0
\(262\) 2.41720 9.02113i 0.149335 0.557327i
\(263\) −1.40761 3.01862i −0.0867967 0.186136i 0.858118 0.513452i \(-0.171634\pi\)
−0.944915 + 0.327316i \(0.893856\pi\)
\(264\) 0 0
\(265\) −1.01028 1.14554i −0.0620608 0.0703700i
\(266\) 4.85212 + 13.3311i 0.297502 + 0.817381i
\(267\) 0 0
\(268\) −0.248474 0.173983i −0.0151780 0.0106277i
\(269\) 8.37429 0.510589 0.255295 0.966863i \(-0.417828\pi\)
0.255295 + 0.966863i \(0.417828\pi\)
\(270\) 0 0
\(271\) −13.7893 −0.837641 −0.418821 0.908069i \(-0.637556\pi\)
−0.418821 + 0.908069i \(0.637556\pi\)
\(272\) 26.6940 + 18.6913i 1.61856 + 1.13333i
\(273\) 0 0
\(274\) −3.81425 10.4796i −0.230428 0.633094i
\(275\) 7.52741 + 11.6715i 0.453920 + 0.703819i
\(276\) 0 0
\(277\) 0.0519757 + 0.111462i 0.00312292 + 0.00669711i 0.907863 0.419267i \(-0.137713\pi\)
−0.904740 + 0.425964i \(0.859935\pi\)
\(278\) 4.00827 14.9591i 0.240400 0.897186i
\(279\) 0 0
\(280\) −9.25289 + 1.03947i −0.552966 + 0.0621205i
\(281\) −15.4444 18.4059i −0.921334 1.09800i −0.994915 0.100714i \(-0.967887\pi\)
0.0735813 0.997289i \(-0.476557\pi\)
\(282\) 0 0
\(283\) −9.14396 13.0589i −0.543552 0.776273i 0.449584 0.893238i \(-0.351572\pi\)
−0.993136 + 0.116965i \(0.962683\pi\)
\(284\) 0.509233 2.88801i 0.0302174 0.171372i
\(285\) 0 0
\(286\) 0.988429 0.829390i 0.0584470 0.0490429i
\(287\) 1.94927 + 7.27478i 0.115062 + 0.429417i
\(288\) 0 0
\(289\) −31.0386 + 17.9202i −1.82580 + 1.05413i
\(290\) −14.1144 + 25.8982i −0.828827 + 1.52079i
\(291\) 0 0
\(292\) −0.168594 1.92703i −0.00986619 0.112771i
\(293\) 4.77657 + 2.22735i 0.279050 + 0.130123i 0.557105 0.830442i \(-0.311912\pi\)
−0.278055 + 0.960565i \(0.589690\pi\)
\(294\) 0 0
\(295\) −15.7111 14.9564i −0.914735 0.870793i
\(296\) 5.60107i 0.325555i
\(297\) 0 0
\(298\) −1.29183 + 1.29183i −0.0748340 + 0.0748340i
\(299\) −0.00687388 0.0389837i −0.000397526 0.00225448i
\(300\) 0 0
\(301\) −7.42071 + 2.70092i −0.427723 + 0.155678i
\(302\) 24.3262 2.12827i 1.39981 0.122468i
\(303\) 0 0
\(304\) −8.97985 + 24.6719i −0.515030 + 1.41503i
\(305\) 5.45286 + 2.38119i 0.312230 + 0.136347i
\(306\) 0 0
\(307\) −21.3785 + 5.72834i −1.22013 + 0.326934i −0.810730 0.585420i \(-0.800930\pi\)
−0.409403 + 0.912353i \(0.634263\pi\)
\(308\) −1.24690 0.109090i −0.0710487 0.00621596i
\(309\) 0 0
\(310\) −14.3755 4.83517i −0.816476 0.274619i
\(311\) −14.1711 2.49874i −0.803567 0.141691i −0.243244 0.969965i \(-0.578212\pi\)
−0.560322 + 0.828275i \(0.689323\pi\)
\(312\) 0 0
\(313\) −1.85245 + 21.1736i −0.104707 + 1.19680i 0.744088 + 0.668081i \(0.232884\pi\)
−0.848795 + 0.528722i \(0.822671\pi\)
\(314\) −15.6669 + 27.1358i −0.884133 + 1.53136i
\(315\) 0 0
\(316\) 0.291263 + 0.504482i 0.0163848 + 0.0283793i
\(317\) −20.8348 + 9.71542i −1.17020 + 0.545672i −0.907848 0.419300i \(-0.862275\pi\)
−0.262350 + 0.964973i \(0.584498\pi\)
\(318\) 0 0
\(319\) 15.5936 18.5838i 0.873076 1.04049i
\(320\) −12.2613 8.14338i −0.685428 0.455229i
\(321\) 0 0
\(322\) −0.178813 + 0.255371i −0.00996485 + 0.0142313i
\(323\) −30.1036 30.1036i −1.67501 1.67501i
\(324\) 0 0
\(325\) 0.717710 + 1.36013i 0.0398114 + 0.0754467i
\(326\) −19.4443 + 3.42856i −1.07692 + 0.189890i
\(327\) 0 0
\(328\) −5.15228 + 11.0491i −0.284487 + 0.610085i
\(329\) 10.4268 + 8.74912i 0.574848 + 0.482355i
\(330\) 0 0
\(331\) 13.1133 + 4.77285i 0.720772 + 0.262340i 0.676253 0.736669i \(-0.263602\pi\)
0.0445184 + 0.999009i \(0.485825\pi\)
\(332\) −3.57673 0.958382i −0.196298 0.0525980i
\(333\) 0 0
\(334\) 21.0465 + 12.1512i 1.15161 + 0.664884i
\(335\) −2.06039 + 1.25815i −0.112571 + 0.0687399i
\(336\) 0 0
\(337\) 11.8702 8.31162i 0.646612 0.452763i −0.203705 0.979032i \(-0.565299\pi\)
0.850318 + 0.526269i \(0.176410\pi\)
\(338\) −15.9659 + 11.1795i −0.868432 + 0.608083i
\(339\) 0 0
\(340\) −3.89752 + 2.37997i −0.211373 + 0.129072i
\(341\) 10.8035 + 6.23741i 0.585043 + 0.337775i
\(342\) 0 0
\(343\) 17.7039 + 4.74374i 0.955920 + 0.256138i
\(344\) −12.0122 4.37207i −0.647652 0.235726i
\(345\) 0 0
\(346\) −3.06901 2.57521i −0.164991 0.138444i
\(347\) 3.83685 8.22815i 0.205973 0.441710i −0.776000 0.630733i \(-0.782754\pi\)
0.981973 + 0.189023i \(0.0605320\pi\)
\(348\) 0 0
\(349\) 8.20842 1.44737i 0.439387 0.0774757i 0.0504212 0.998728i \(-0.483944\pi\)
0.388966 + 0.921252i \(0.372833\pi\)
\(350\) 3.57753 11.5711i 0.191227 0.618501i
\(351\) 0 0
\(352\) −3.09950 3.09950i −0.165204 0.165204i
\(353\) 1.51501 2.16366i 0.0806358 0.115160i −0.776808 0.629738i \(-0.783162\pi\)
0.857444 + 0.514578i \(0.172051\pi\)
\(354\) 0 0
\(355\) −19.4423 12.9127i −1.03189 0.685333i
\(356\) −2.01609 + 2.40268i −0.106852 + 0.127342i
\(357\) 0 0
\(358\) −9.39224 + 4.37967i −0.496395 + 0.231473i
\(359\) 7.06131 + 12.2306i 0.372682 + 0.645504i 0.989977 0.141228i \(-0.0451049\pi\)
−0.617295 + 0.786732i \(0.711772\pi\)
\(360\) 0 0
\(361\) 7.65033 13.2508i 0.402649 0.697408i
\(362\) 2.63575 30.1267i 0.138532 1.58342i
\(363\) 0 0
\(364\) −0.136493 0.0240674i −0.00715418 0.00126148i
\(365\) −14.5922 4.90804i −0.763790 0.256899i
\(366\) 0 0
\(367\) −13.7173 1.20011i −0.716037 0.0626451i −0.276686 0.960961i \(-0.589236\pi\)
−0.439351 + 0.898315i \(0.644792\pi\)
\(368\) −0.557300 + 0.149328i −0.0290513 + 0.00778426i
\(369\) 0 0
\(370\) −6.67680 2.91567i −0.347110 0.151578i
\(371\) 0.374703 1.02949i 0.0194536 0.0534483i
\(372\) 0 0
\(373\) −20.2366 + 1.77048i −1.04781 + 0.0916718i −0.598036 0.801469i \(-0.704052\pi\)
−0.449777 + 0.893141i \(0.648497\pi\)
\(374\) 28.6555 10.4297i 1.48174 0.539309i
\(375\) 0 0
\(376\) 3.82598 + 21.6982i 0.197310 + 1.11900i
\(377\) 1.89949 1.89949i 0.0978286 0.0978286i
\(378\) 0 0
\(379\) 20.8542i 1.07121i 0.844469 + 0.535605i \(0.179916\pi\)
−0.844469 + 0.535605i \(0.820084\pi\)
\(380\) −2.66493 2.53691i −0.136708 0.130141i
\(381\) 0 0
\(382\) 12.8229 + 5.97940i 0.656075 + 0.305933i
\(383\) −1.27835 14.6116i −0.0653206 0.746618i −0.956264 0.292504i \(-0.905512\pi\)
0.890944 0.454114i \(-0.150044\pi\)
\(384\) 0 0
\(385\) −4.76712 + 8.74706i −0.242955 + 0.445791i
\(386\) −27.5662 + 15.9154i −1.40308 + 0.810071i
\(387\) 0 0
\(388\) −0.861786 3.21623i −0.0437506 0.163279i
\(389\) 4.79561 4.02400i 0.243147 0.204025i −0.513067 0.858348i \(-0.671491\pi\)
0.756215 + 0.654323i \(0.227047\pi\)
\(390\) 0 0
\(391\) 0.162455 0.921326i 0.00821568 0.0465934i
\(392\) 6.59332 + 9.41624i 0.333013 + 0.475592i
\(393\) 0 0
\(394\) 7.13377 + 8.50169i 0.359394 + 0.428309i
\(395\) 4.60723 0.517578i 0.231815 0.0260422i
\(396\) 0 0
\(397\) 0.120732 0.450577i 0.00605935 0.0226138i −0.962830 0.270108i \(-0.912941\pi\)
0.968889 + 0.247494i \(0.0796072\pi\)
\(398\) −16.4685 35.3168i −0.825492 1.77027i
\(399\) 0 0
\(400\) 18.8371 12.1487i 0.941853 0.607437i
\(401\) −3.19304 8.77280i −0.159453 0.438093i 0.834079 0.551644i \(-0.185999\pi\)
−0.993532 + 0.113552i \(0.963777\pi\)
\(402\) 0 0
\(403\) 1.13154 + 0.792314i 0.0563661 + 0.0394680i
\(404\) 3.78805 0.188463
\(405\) 0 0
\(406\) −21.1557 −1.04994
\(407\) 4.90874 + 3.43714i 0.243317 + 0.170373i
\(408\) 0 0
\(409\) −0.240362 0.660389i −0.0118851 0.0326541i 0.933608 0.358296i \(-0.116642\pi\)
−0.945493 + 0.325641i \(0.894420\pi\)
\(410\) −10.4891 11.8935i −0.518021 0.587378i
\(411\) 0 0
\(412\) 0.353203 + 0.757446i 0.0174010 + 0.0373167i
\(413\) 4.02694 15.0288i 0.198153 0.739517i
\(414\) 0 0
\(415\) −18.3822 + 23.0351i −0.902349 + 1.13075i
\(416\) −0.311994 0.371820i −0.0152968 0.0182300i
\(417\) 0 0
\(418\) 14.0923 + 20.1259i 0.689276 + 0.984389i
\(419\) 3.72329 21.1158i 0.181894 1.03157i −0.747986 0.663714i \(-0.768979\pi\)
0.929881 0.367861i \(-0.119910\pi\)
\(420\) 0 0
\(421\) 13.6486 11.4526i 0.665194 0.558164i −0.246445 0.969157i \(-0.579262\pi\)
0.911638 + 0.410993i \(0.134818\pi\)
\(422\) 0.136857 + 0.510759i 0.00666211 + 0.0248633i
\(423\) 0 0
\(424\) 1.53582 0.886708i 0.0745862 0.0430623i
\(425\) 4.94495 + 36.0077i 0.239865 + 1.74663i
\(426\) 0 0
\(427\) 0.371968 + 4.25162i 0.0180008 + 0.205750i
\(428\) −2.81169 1.31111i −0.135908 0.0633750i
\(429\) 0 0
\(430\) 11.4648 12.0433i 0.552880 0.580779i
\(431\) 13.6942i 0.659624i −0.944047 0.329812i \(-0.893015\pi\)
0.944047 0.329812i \(-0.106985\pi\)
\(432\) 0 0
\(433\) 22.8337 22.8337i 1.09732 1.09732i 0.102594 0.994723i \(-0.467286\pi\)
0.994723 0.102594i \(-0.0327142\pi\)
\(434\) −1.88909 10.7136i −0.0906791 0.514267i
\(435\) 0 0
\(436\) 0.122596 0.0446213i 0.00587129 0.00213697i
\(437\) 0.750887 0.0656941i 0.0359198 0.00314257i
\(438\) 0 0
\(439\) 3.85214 10.5837i 0.183852 0.505130i −0.813189 0.582000i \(-0.802270\pi\)
0.997041 + 0.0768697i \(0.0244925\pi\)
\(440\) −15.0127 + 5.88635i −0.715701 + 0.280621i
\(441\) 0 0
\(442\) 3.26165 0.873956i 0.155141 0.0415699i
\(443\) −6.73147 0.588927i −0.319822 0.0279808i −0.0738853 0.997267i \(-0.523540\pi\)
−0.245936 + 0.969286i \(0.579095\pi\)
\(444\) 0 0
\(445\) 11.1031 + 22.3574i 0.526336 + 1.05984i
\(446\) 23.3694 + 4.12066i 1.10657 + 0.195119i
\(447\) 0 0
\(448\) 0.920162 10.5175i 0.0434736 0.496905i
\(449\) 5.70190 9.87598i 0.269089 0.466076i −0.699538 0.714596i \(-0.746611\pi\)
0.968627 + 0.248519i \(0.0799440\pi\)
\(450\) 0 0
\(451\) 6.52164 + 11.2958i 0.307092 + 0.531899i
\(452\) 0.121937 0.0568601i 0.00573542 0.00267447i
\(453\) 0 0
\(454\) −22.8589 + 27.2421i −1.07282 + 1.27854i
\(455\) −0.610279 + 0.918884i −0.0286103 + 0.0430779i
\(456\) 0 0
\(457\) −4.25450 + 6.07605i −0.199017 + 0.284226i −0.906239 0.422766i \(-0.861059\pi\)
0.707222 + 0.706992i \(0.249948\pi\)
\(458\) 24.7249 + 24.7249i 1.15532 + 1.15532i
\(459\) 0 0
\(460\) 0.0120769 0.0799468i 0.000563088 0.00372754i
\(461\) 41.0458 7.23749i 1.91170 0.337083i 0.914046 0.405611i \(-0.132941\pi\)
0.997649 + 0.0685275i \(0.0218301\pi\)
\(462\) 0 0
\(463\) 1.40671 3.01669i 0.0653752 0.140198i −0.870905 0.491451i \(-0.836467\pi\)
0.936280 + 0.351253i \(0.114244\pi\)
\(464\) −29.9930 25.1671i −1.39239 1.16835i
\(465\) 0 0
\(466\) −30.6975 11.1730i −1.42203 0.517577i
\(467\) 4.32129 + 1.15789i 0.199966 + 0.0535806i 0.357412 0.933947i \(-0.383659\pi\)
−0.157446 + 0.987528i \(0.550326\pi\)
\(468\) 0 0
\(469\) −1.49962 0.865804i −0.0692458 0.0399791i
\(470\) −27.8572 6.73433i −1.28496 0.310632i
\(471\) 0 0
\(472\) 20.6309 14.4459i 0.949616 0.664929i
\(473\) −11.2030 + 7.84443i −0.515115 + 0.360687i
\(474\) 0 0
\(475\) −26.9914 + 11.3570i −1.23845 + 0.521093i
\(476\) −2.83674 1.63780i −0.130022 0.0750682i
\(477\) 0 0
\(478\) −20.7402 5.55731i −0.948632 0.254185i
\(479\) 34.5314 + 12.5684i 1.57778 + 0.574264i 0.974719 0.223432i \(-0.0717262\pi\)
0.603059 + 0.797697i \(0.293948\pi\)
\(480\) 0 0
\(481\) 0.508314 + 0.426526i 0.0231771 + 0.0194479i
\(482\) −5.32332 + 11.4159i −0.242470 + 0.519980i
\(483\) 0 0
\(484\) 0.908792 0.160244i 0.0413087 0.00728384i
\(485\) −26.2031 3.95827i −1.18982 0.179736i
\(486\) 0 0
\(487\) 9.05628 + 9.05628i 0.410379 + 0.410379i 0.881871 0.471492i \(-0.156284\pi\)
−0.471492 + 0.881871i \(0.656284\pi\)
\(488\) −3.96257 + 5.65913i −0.179377 + 0.256177i
\(489\) 0 0
\(490\) −14.6569 + 2.95795i −0.662131 + 0.133627i
\(491\) −14.7648 + 17.5960i −0.666326 + 0.794096i −0.988279 0.152660i \(-0.951216\pi\)
0.321953 + 0.946756i \(0.395661\pi\)
\(492\) 0 0
\(493\) 57.5384 26.8306i 2.59140 1.20839i
\(494\) 1.36029 + 2.35609i 0.0612024 + 0.106006i
\(495\) 0 0
\(496\) 10.0668 17.4361i 0.452011 0.782906i
\(497\) 1.45907 16.6772i 0.0654482 0.748076i
\(498\) 0 0
\(499\) −9.11992 1.60809i −0.408264 0.0719879i −0.0342550 0.999413i \(-0.510906\pi\)
−0.374009 + 0.927425i \(0.622017\pi\)
\(500\) 0.503800 + 3.10051i 0.0225306 + 0.138659i
\(501\) 0 0
\(502\) 7.17569 + 0.627792i 0.320267 + 0.0280197i
\(503\) −8.31780 + 2.22875i −0.370873 + 0.0993750i −0.439441 0.898271i \(-0.644823\pi\)
0.0685686 + 0.997646i \(0.478157\pi\)
\(504\) 0 0
\(505\) 12.0652 27.6289i 0.536893 1.22947i
\(506\) −0.184659 + 0.507345i −0.00820908 + 0.0225543i
\(507\) 0 0
\(508\) 3.76553 0.329441i 0.167068 0.0146166i
\(509\) −20.6614 + 7.52013i −0.915799 + 0.333324i −0.756566 0.653917i \(-0.773124\pi\)
−0.159233 + 0.987241i \(0.550902\pi\)
\(510\) 0 0
\(511\) −1.91756 10.8750i −0.0848278 0.481082i
\(512\) 11.4575 11.4575i 0.506354 0.506354i
\(513\) 0 0
\(514\) 7.12936i 0.314463i
\(515\) 6.64955 0.163646i 0.293014 0.00721109i
\(516\) 0 0
\(517\) 21.3640 + 9.96221i 0.939589 + 0.438138i
\(518\) −0.455459 5.20593i −0.0200117 0.228735i
\(519\) 0 0
\(520\) −1.71286 + 0.504440i −0.0751139 + 0.0221211i
\(521\) 4.43677 2.56157i 0.194378 0.112224i −0.399652 0.916667i \(-0.630869\pi\)
0.594031 + 0.804442i \(0.297536\pi\)
\(522\) 0 0
\(523\) 2.02890 + 7.57196i 0.0887177 + 0.331099i 0.995992 0.0894400i \(-0.0285077\pi\)
−0.907275 + 0.420539i \(0.861841\pi\)
\(524\) −1.33091 + 1.11677i −0.0581412 + 0.0487863i
\(525\) 0 0
\(526\) −0.873497 + 4.95385i −0.0380863 + 0.215998i
\(527\) 18.7252 + 26.7424i 0.815685 + 1.16492i
\(528\) 0 0
\(529\) −14.7735 17.6063i −0.642325 0.765493i
\(530\) 0.257526 + 2.29237i 0.0111862 + 0.0995742i
\(531\) 0 0
\(532\) 0.683053 2.54919i 0.0296141 0.110521i
\(533\) 0.610389 + 1.30898i 0.0264389 + 0.0566984i
\(534\) 0 0
\(535\) −18.5183 + 16.3317i −0.800614 + 0.706079i
\(536\) −0.958687 2.63397i −0.0414090 0.113770i
\(537\) 0 0
\(538\) −10.3603 7.25433i −0.446663 0.312757i
\(539\) 12.2984 0.529729
\(540\) 0 0
\(541\) −12.2903 −0.528401 −0.264200 0.964468i \(-0.585108\pi\)
−0.264200 + 0.964468i \(0.585108\pi\)
\(542\) 17.0595 + 11.9452i 0.732767 + 0.513089i
\(543\) 0 0
\(544\) −3.92339 10.7794i −0.168214 0.462164i
\(545\) 0.0650212 1.03630i 0.00278520 0.0443903i
\(546\) 0 0
\(547\) −0.220177 0.472172i −0.00941410 0.0201886i 0.901545 0.432686i \(-0.142434\pi\)
−0.910959 + 0.412498i \(0.864656\pi\)
\(548\) −0.536948 + 2.00392i −0.0229373 + 0.0856032i
\(549\) 0 0
\(550\) 0.798052 20.9602i 0.0340290 0.893744i
\(551\) 32.8789 + 39.1836i 1.40069 + 1.66928i
\(552\) 0 0
\(553\) 1.90739 + 2.72403i 0.0811104 + 0.115838i
\(554\) 0.0322538 0.182920i 0.00137033 0.00777153i
\(555\) 0 0
\(556\) −2.20695 + 1.85185i −0.0935957 + 0.0785361i
\(557\) −6.03527 22.5239i −0.255723 0.954370i −0.967687 0.252155i \(-0.918861\pi\)
0.711964 0.702216i \(-0.247806\pi\)
\(558\) 0 0
\(559\) −1.31151 + 0.757203i −0.0554711 + 0.0320263i
\(560\) 14.1172 + 7.69381i 0.596559 + 0.325123i
\(561\) 0 0
\(562\) 3.16269 + 36.1498i 0.133410 + 1.52489i
\(563\) −31.1449 14.5231i −1.31260 0.612076i −0.364844 0.931069i \(-0.618878\pi\)
−0.947757 + 0.318993i \(0.896656\pi\)
\(564\) 0 0
\(565\) −0.0263444 1.07047i −0.00110832 0.0450351i
\(566\) 24.0770i 1.01203i
\(567\) 0 0
\(568\) 19.1620 19.1620i 0.804019 0.804019i
\(569\) −0.227444 1.28990i −0.00953495 0.0540754i 0.979669 0.200620i \(-0.0642958\pi\)
−0.989204 + 0.146545i \(0.953185\pi\)
\(570\) 0 0
\(571\) −17.9969 + 6.55033i −0.753146 + 0.274123i −0.689929 0.723877i \(-0.742358\pi\)
−0.0632171 + 0.998000i \(0.520136\pi\)
\(572\) −0.239119 + 0.0209202i −0.00999807 + 0.000874718i
\(573\) 0 0
\(574\) 3.89033 10.6886i 0.162379 0.446133i
\(575\) −0.544643 0.342721i −0.0227132 0.0142924i
\(576\) 0 0
\(577\) −12.6473 + 3.38883i −0.526514 + 0.141079i −0.512278 0.858820i \(-0.671198\pi\)
−0.0142358 + 0.999899i \(0.504532\pi\)
\(578\) 53.9231 + 4.71766i 2.24290 + 0.196229i
\(579\) 0 0
\(580\) 4.91420 2.44047i 0.204051 0.101335i
\(581\) −20.8174 3.67067i −0.863652 0.152285i
\(582\) 0 0
\(583\) 0.165364 1.89012i 0.00684869 0.0782808i
\(584\) 8.93766 15.4805i 0.369843 0.640587i
\(585\) 0 0
\(586\) −3.97987 6.89333i −0.164407 0.284761i
\(587\) −26.3137 + 12.2703i −1.08608 + 0.506449i −0.881396 0.472379i \(-0.843395\pi\)
−0.204687 + 0.978827i \(0.565618\pi\)
\(588\) 0 0
\(589\) −16.9072 + 20.1492i −0.696650 + 0.830235i
\(590\) 6.48086 + 32.1132i 0.266813 + 1.32208i
\(591\) 0 0
\(592\) 5.54732 7.92239i 0.227993 0.325608i
\(593\) 18.8092 + 18.8092i 0.772402 + 0.772402i 0.978526 0.206124i \(-0.0660851\pi\)
−0.206124 + 0.978526i \(0.566085\pi\)
\(594\) 0 0
\(595\) −20.9808 + 15.4739i −0.860128 + 0.634368i
\(596\) 0.334697 0.0590161i 0.0137097 0.00241739i
\(597\) 0 0
\(598\) −0.0252661 + 0.0541833i −0.00103321 + 0.00221572i
\(599\) −3.51169 2.94665i −0.143484 0.120397i 0.568221 0.822876i \(-0.307632\pi\)
−0.711704 + 0.702479i \(0.752076\pi\)
\(600\) 0 0
\(601\) 25.1131 + 9.14041i 1.02438 + 0.372845i 0.798940 0.601411i \(-0.205395\pi\)
0.225443 + 0.974256i \(0.427617\pi\)
\(602\) 11.5202 + 3.08684i 0.469530 + 0.125810i
\(603\) 0 0
\(604\) −3.93404 2.27132i −0.160074 0.0924187i
\(605\) 1.72578 7.13884i 0.0701629 0.290235i
\(606\) 0 0
\(607\) 29.2803 20.5023i 1.18845 0.832163i 0.199428 0.979913i \(-0.436092\pi\)
0.989025 + 0.147749i \(0.0472028\pi\)
\(608\) 7.57081 5.30114i 0.307037 0.214990i
\(609\) 0 0
\(610\) −4.68328 7.66950i −0.189620 0.310529i
\(611\) 2.26053 + 1.30512i 0.0914512 + 0.0527994i
\(612\) 0 0
\(613\) −35.8682 9.61085i −1.44870 0.388179i −0.553130 0.833095i \(-0.686567\pi\)
−0.895572 + 0.444916i \(0.853233\pi\)
\(614\) 31.4107 + 11.4325i 1.26763 + 0.461380i
\(615\) 0 0
\(616\) −8.86034 7.43471i −0.356993 0.299553i
\(617\) −19.6545 + 42.1491i −0.791258 + 1.69686i −0.0769428 + 0.997036i \(0.524516\pi\)
−0.714316 + 0.699824i \(0.753262\pi\)
\(618\) 0 0
\(619\) −13.9352 + 2.45716i −0.560104 + 0.0987615i −0.446531 0.894768i \(-0.647341\pi\)
−0.113573 + 0.993530i \(0.536230\pi\)
\(620\) 1.67470 + 2.27070i 0.0672576 + 0.0911934i
\(621\) 0 0
\(622\) 15.3672 + 15.3672i 0.616168 + 0.616168i
\(623\) −10.2699 + 14.6669i −0.411455 + 0.587619i
\(624\) 0 0
\(625\) 24.2188 + 6.20074i 0.968752 + 0.248029i
\(626\) 20.6337 24.5903i 0.824687 0.982824i
\(627\) 0 0
\(628\) 5.28283 2.46342i 0.210808 0.0983013i
\(629\) 7.84112 + 13.5812i 0.312646 + 0.541519i
\(630\) 0 0
\(631\) 16.2979 28.2288i 0.648810 1.12377i −0.334597 0.942361i \(-0.608600\pi\)
0.983407 0.181411i \(-0.0580664\pi\)
\(632\) −0.469158 + 5.36250i −0.0186621 + 0.213309i
\(633\) 0 0
\(634\) 34.1919 + 6.02895i 1.35793 + 0.239440i
\(635\) 9.59059 28.5139i 0.380591 1.13154i
\(636\) 0 0
\(637\) 1.35664 + 0.118690i 0.0537520 + 0.00470269i
\(638\) −35.3901 + 9.48275i −1.40111 + 0.375426i
\(639\) 0 0
\(640\) 10.6910 + 27.2664i 0.422597 + 1.07780i
\(641\) 11.8689 32.6096i 0.468794 1.28800i −0.449916 0.893071i \(-0.648546\pi\)
0.918711 0.394931i \(-0.129232\pi\)
\(642\) 0 0
\(643\) 8.82626 0.772198i 0.348074 0.0304525i 0.0882215 0.996101i \(-0.471882\pi\)
0.259852 + 0.965648i \(0.416326\pi\)
\(644\) 0.0544969 0.0198352i 0.00214748 0.000781618i
\(645\) 0 0
\(646\) 11.1651 + 63.3204i 0.439285 + 2.49131i
\(647\) 14.1426 14.1426i 0.556003 0.556003i −0.372164 0.928167i \(-0.621384\pi\)
0.928167 + 0.372164i \(0.121384\pi\)
\(648\) 0 0
\(649\) 26.9457i 1.05771i
\(650\) 0.290318 2.30442i 0.0113872 0.0903867i
\(651\) 0 0
\(652\) 3.32886 + 1.55227i 0.130368 + 0.0607917i
\(653\) 0.173231 + 1.98004i 0.00677904 + 0.0774848i 0.998831 0.0483474i \(-0.0153955\pi\)
−0.992052 + 0.125832i \(0.959840\pi\)
\(654\) 0 0
\(655\) 3.90634 + 13.2643i 0.152633 + 0.518277i
\(656\) 18.2307 10.5255i 0.711788 0.410951i
\(657\) 0 0
\(658\) −5.32049 19.8563i −0.207414 0.774081i
\(659\) 9.93910 8.33989i 0.387172 0.324876i −0.428338 0.903619i \(-0.640901\pi\)
0.815510 + 0.578742i \(0.196456\pi\)
\(660\) 0 0
\(661\) 2.91716 16.5440i 0.113464 0.643489i −0.874035 0.485864i \(-0.838505\pi\)
0.987499 0.157625i \(-0.0503837\pi\)
\(662\) −12.0886 17.2643i −0.469836 0.670996i
\(663\) 0 0
\(664\) −21.9947 26.2123i −0.853561 1.01723i
\(665\) −16.4174 13.1013i −0.636641 0.508047i
\(666\) 0 0
\(667\) −0.290921 + 1.08573i −0.0112645 + 0.0420396i
\(668\) −1.91063 4.09735i −0.0739244 0.158531i
\(669\) 0 0
\(670\) 3.63890 + 0.228317i 0.140583 + 0.00882066i
\(671\) 2.52797 + 6.94554i 0.0975912 + 0.268130i
\(672\) 0 0
\(673\) 7.48390 + 5.24028i 0.288483 + 0.201998i 0.708856 0.705353i \(-0.249212\pi\)
−0.420373 + 0.907352i \(0.638101\pi\)
\(674\) −21.8853 −0.842991
\(675\) 0 0
\(676\) 3.62584 0.139455
\(677\) 0.0991212 + 0.0694054i 0.00380954 + 0.00266747i 0.575480 0.817816i \(-0.304815\pi\)
−0.571670 + 0.820484i \(0.693704\pi\)
\(678\) 0 0
\(679\) −6.50112 17.8617i −0.249490 0.685468i
\(680\) −42.1173 2.64259i −1.61512 0.101339i
\(681\) 0 0
\(682\) −7.96234 17.0753i −0.304894 0.653847i
\(683\) −3.58403 + 13.3758i −0.137139 + 0.511810i 0.862841 + 0.505476i \(0.168683\pi\)
−0.999980 + 0.00633429i \(0.997984\pi\)
\(684\) 0 0
\(685\) 12.9058 + 10.2989i 0.493104 + 0.393502i
\(686\) −17.7931 21.2049i −0.679342 0.809608i
\(687\) 0 0
\(688\) 12.6604 + 18.0809i 0.482673 + 0.689329i
\(689\) 0.0364828 0.206904i 0.00138988 0.00788241i
\(690\) 0 0
\(691\) 17.4891 14.6751i 0.665315 0.558266i −0.246359 0.969179i \(-0.579234\pi\)
0.911675 + 0.410913i \(0.134790\pi\)
\(692\) 0.192894 + 0.719892i 0.00733274 + 0.0273662i
\(693\) 0 0
\(694\) −11.8745 + 6.85575i −0.450750 + 0.260241i
\(695\) 6.47759 + 21.9951i 0.245709 + 0.834323i
\(696\) 0 0
\(697\) 2.97498 + 34.0042i 0.112686 + 1.28800i
\(698\) −11.4089 5.32004i −0.431832 0.201366i
\(699\) 0 0
\(700\) −1.77981 + 1.38154i −0.0672706 + 0.0522172i
\(701\) 15.6693i 0.591821i 0.955216 + 0.295910i \(0.0956230\pi\)
−0.955216 + 0.295910i \(0.904377\pi\)
\(702\) 0 0
\(703\) −8.93432 + 8.93432i −0.336964 + 0.336964i
\(704\) −3.17504 18.0065i −0.119664 0.678647i
\(705\) 0 0
\(706\) −3.74859 + 1.36438i −0.141080 + 0.0513490i
\(707\) 21.5424 1.88471i 0.810184 0.0708820i
\(708\) 0 0
\(709\) −2.91839 + 8.01821i −0.109602 + 0.301130i −0.982353 0.187036i \(-0.940112\pi\)
0.872751 + 0.488166i \(0.162334\pi\)
\(710\) 12.8673 + 32.8171i 0.482902 + 1.23160i
\(711\) 0 0
\(712\) −27.9959 + 7.50148i −1.04919 + 0.281130i
\(713\) −0.575807 0.0503766i −0.0215641 0.00188662i
\(714\) 0 0
\(715\) −0.609022 + 1.81069i −0.0227761 + 0.0677161i
\(716\) 1.89856 + 0.334767i 0.0709523 + 0.0125108i
\(717\) 0 0
\(718\) 1.85896 21.2480i 0.0693758 0.792968i
\(719\) −19.9277 + 34.5157i −0.743176 + 1.28722i 0.207866 + 0.978157i \(0.433348\pi\)
−0.951042 + 0.309062i \(0.899985\pi\)
\(720\) 0 0
\(721\) 2.38550 + 4.13180i 0.0888406 + 0.153876i
\(722\) −20.9433 + 9.76600i −0.779427 + 0.363453i
\(723\) 0 0
\(724\) −3.61621 + 4.30963i −0.134395 + 0.160166i
\(725\) −2.14807 43.6157i −0.0797773 1.61985i
\(726\) 0 0
\(727\) 26.2725 37.5210i 0.974393 1.39158i 0.0548911 0.998492i \(-0.482519\pi\)
0.919502 0.393085i \(-0.128592\pi\)
\(728\) −0.905635 0.905635i −0.0335651 0.0335651i
\(729\) 0 0
\(730\) 13.8011 + 18.7127i 0.510801 + 0.692587i
\(731\) −35.2471 + 6.21502i −1.30366 + 0.229871i
\(732\) 0 0
\(733\) −15.6365 + 33.5325i −0.577546 + 1.23855i 0.372961 + 0.927847i \(0.378343\pi\)
−0.950507 + 0.310704i \(0.899435\pi\)
\(734\) 15.9308 + 13.3675i 0.588015 + 0.493403i
\(735\) 0 0
\(736\) 0.190850 + 0.0694636i 0.00703481 + 0.00256046i
\(737\) −2.89670 0.776169i −0.106701 0.0285906i
\(738\) 0 0
\(739\) −9.45965 5.46153i −0.347979 0.200906i 0.315816 0.948820i \(-0.397722\pi\)
−0.663795 + 0.747915i \(0.731055\pi\)
\(740\) 0.706341 + 1.15673i 0.0259656 + 0.0425222i
\(741\) 0 0
\(742\) −1.35537 + 0.949040i −0.0497572 + 0.0348404i
\(743\) 6.78635 4.75185i 0.248967 0.174329i −0.442431 0.896802i \(-0.645884\pi\)
0.691398 + 0.722474i \(0.256995\pi\)
\(744\) 0 0
\(745\) 0.635584 2.62915i 0.0232860 0.0963246i
\(746\) 26.5695 + 15.3399i 0.972778 + 0.561633i
\(747\) 0 0
\(748\) −5.47954 1.46824i −0.200352 0.0536841i
\(749\) −16.6422 6.05726i −0.608093 0.221328i
\(750\) 0 0
\(751\) 1.01418 + 0.851000i 0.0370080 + 0.0310534i 0.661104 0.750294i \(-0.270088\pi\)
−0.624096 + 0.781348i \(0.714533\pi\)
\(752\) 16.0783 34.4801i 0.586317 1.25736i
\(753\) 0 0
\(754\) −3.99541 + 0.704499i −0.145504 + 0.0256563i
\(755\) −29.0965 + 21.4594i −1.05893 + 0.780989i
\(756\) 0 0
\(757\) −26.5719 26.5719i −0.965772 0.965772i 0.0336615 0.999433i \(-0.489283\pi\)
−0.999433 + 0.0336615i \(0.989283\pi\)
\(758\) 18.0652 25.7998i 0.656159 0.937092i
\(759\) 0 0
\(760\) −6.72608 33.3283i −0.243980 1.20894i
\(761\) −6.97127 + 8.30804i −0.252708 + 0.301166i −0.877453 0.479663i \(-0.840759\pi\)
0.624744 + 0.780829i \(0.285203\pi\)
\(762\) 0 0
\(763\) 0.674994 0.314755i 0.0244364 0.0113949i
\(764\) −1.31601 2.27939i −0.0476114 0.0824654i
\(765\) 0 0
\(766\) −11.0760 + 19.1841i −0.400191 + 0.693151i
\(767\) 0.260050 2.97239i 0.00938988 0.107327i
\(768\) 0 0
\(769\) 44.1842 + 7.79087i 1.59332 + 0.280946i 0.898745 0.438471i \(-0.144480\pi\)
0.694579 + 0.719417i \(0.255591\pi\)
\(770\) 13.4749 6.69186i 0.485602 0.241158i
\(771\) 0 0
\(772\) 5.89888 + 0.516085i 0.212305 + 0.0185743i
\(773\) 30.3757 8.13915i 1.09254 0.292745i 0.332816 0.942992i \(-0.392001\pi\)
0.759723 + 0.650247i \(0.225334\pi\)
\(774\) 0 0
\(775\) 21.8958 4.98246i 0.786521 0.178975i
\(776\) 10.5236 28.9133i 0.377775 1.03793i
\(777\) 0 0
\(778\) −9.41874 + 0.824033i −0.337678 + 0.0295430i
\(779\) −25.8430 + 9.40608i −0.925922 + 0.337008i
\(780\) 0 0
\(781\) −5.03455 28.5524i −0.180150 1.02168i
\(782\) −0.999091 + 0.999091i −0.0357274 + 0.0357274i
\(783\) 0 0
\(784\) 19.8488i 0.708885i
\(785\) −1.14135 46.3775i −0.0407366 1.65529i
\(786\) 0 0
\(787\)