Properties

Label 819.2.fm.e.370.5
Level $819$
Weight $2$
Character 819.370
Analytic conductor $6.540$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.fm (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 370.5
Character \(\chi\) \(=\) 819.370
Dual form 819.2.fm.e.622.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.189683 + 0.707908i) q^{2} +(1.26690 - 0.731443i) q^{4} +(1.23329 + 1.23329i) q^{5} +(-2.64473 - 0.0736014i) q^{7} +(1.79455 + 1.79455i) q^{8} +O(q^{10})\) \(q+(0.189683 + 0.707908i) q^{2} +(1.26690 - 0.731443i) q^{4} +(1.23329 + 1.23329i) q^{5} +(-2.64473 - 0.0736014i) q^{7} +(1.79455 + 1.79455i) q^{8} +(-0.639122 + 1.10699i) q^{10} +(3.18977 - 0.854696i) q^{11} +(2.53031 - 2.56856i) q^{13} +(-0.449558 - 1.88618i) q^{14} +(0.532906 - 0.923019i) q^{16} +(0.433708 + 0.751205i) q^{17} +(-1.01858 + 3.80140i) q^{19} +(2.46454 + 0.660371i) q^{20} +(1.21009 + 2.09594i) q^{22} +(3.77196 + 2.17774i) q^{23} -1.95798i q^{25} +(2.29826 + 1.30401i) q^{26} +(-3.40443 + 1.84122i) q^{28} +(-2.65427 + 4.59734i) q^{29} +(0.220754 + 0.220754i) q^{31} +(5.65731 + 1.51587i) q^{32} +(-0.449517 + 0.449517i) q^{34} +(-3.17095 - 3.35249i) q^{35} +(-3.57217 + 0.957160i) q^{37} -2.88425 q^{38} +4.42641i q^{40} +(-1.90334 + 0.509998i) q^{41} +(9.99342 - 5.76970i) q^{43} +(3.41595 - 3.41595i) q^{44} +(-0.826162 + 3.08328i) q^{46} +(-3.68984 + 3.68984i) q^{47} +(6.98917 + 0.389311i) q^{49} +(1.38607 - 0.371397i) q^{50} +(1.32689 - 5.10489i) q^{52} +3.55843 q^{53} +(4.98801 + 2.87983i) q^{55} +(-4.61402 - 4.87818i) q^{56} +(-3.75796 - 1.00694i) q^{58} +(-8.89645 - 2.38380i) q^{59} +(4.78192 - 2.76084i) q^{61} +(-0.114400 + 0.198147i) q^{62} +2.16076i q^{64} +(6.28840 - 0.0471733i) q^{65} +(1.01969 + 3.80552i) q^{67} +(1.09893 + 0.634466i) q^{68} +(1.77178 - 2.88065i) q^{70} +(-11.9487 - 3.20164i) q^{71} +(5.55302 - 5.55302i) q^{73} +(-1.35516 - 2.34721i) q^{74} +(1.49007 + 5.56101i) q^{76} +(-8.49898 + 2.02567i) q^{77} -15.7334 q^{79} +(1.79558 - 0.481124i) q^{80} +(-0.722063 - 1.25065i) q^{82} +(3.80823 + 3.80823i) q^{83} +(-0.391566 + 1.46134i) q^{85} +(5.98000 + 5.98000i) q^{86} +(7.25801 + 4.19041i) q^{88} +(3.26801 + 12.1964i) q^{89} +(-6.88104 + 6.60691i) q^{91} +6.37158 q^{92} +(-3.31197 - 1.91217i) q^{94} +(-5.94444 + 3.43202i) q^{95} +(0.756697 - 2.82403i) q^{97} +(1.05013 + 5.02153i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + O(q^{10}) \) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + 2q^{10} + 4q^{11} + 6q^{13} - 34q^{14} + 14q^{16} + 8q^{17} + 2q^{19} - 44q^{20} - 4q^{22} + 18q^{23} + 28q^{26} - 32q^{28} + 18q^{29} - 14q^{31} + 8q^{32} - 66q^{34} - 22q^{35} - 24q^{37} - 24q^{38} - 6q^{43} + 20q^{44} - 58q^{46} + 28q^{47} + 8q^{49} - 70q^{50} + 28q^{52} + 80q^{53} + 60q^{55} + 54q^{56} - 4q^{58} + 42q^{59} + 36q^{61} - 52q^{62} - 14q^{65} + 26q^{67} + 72q^{68} - 116q^{70} + 4q^{71} + 12q^{73} + 18q^{74} - 48q^{76} - 28q^{77} - 4q^{79} + 98q^{80} + 20q^{82} + 36q^{83} - 10q^{85} + 40q^{86} + 96q^{88} + 54q^{89} + 148q^{91} + 4q^{92} - 60q^{95} - 40q^{97} - 36q^{98} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.189683 + 0.707908i 0.134126 + 0.500566i 1.00000 0.000303559i \(9.66258e-5\pi\)
−0.865874 + 0.500263i \(0.833237\pi\)
\(3\) 0 0
\(4\) 1.26690 0.731443i 0.633449 0.365722i
\(5\) 1.23329 + 1.23329i 0.551545 + 0.551545i 0.926887 0.375342i \(-0.122475\pi\)
−0.375342 + 0.926887i \(0.622475\pi\)
\(6\) 0 0
\(7\) −2.64473 0.0736014i −0.999613 0.0278187i
\(8\) 1.79455 + 1.79455i 0.634470 + 0.634470i
\(9\) 0 0
\(10\) −0.639122 + 1.10699i −0.202108 + 0.350062i
\(11\) 3.18977 0.854696i 0.961752 0.257701i 0.256410 0.966568i \(-0.417460\pi\)
0.705342 + 0.708867i \(0.250794\pi\)
\(12\) 0 0
\(13\) 2.53031 2.56856i 0.701783 0.712391i
\(14\) −0.449558 1.88618i −0.120149 0.504104i
\(15\) 0 0
\(16\) 0.532906 0.923019i 0.133226 0.230755i
\(17\) 0.433708 + 0.751205i 0.105190 + 0.182194i 0.913816 0.406129i \(-0.133122\pi\)
−0.808626 + 0.588323i \(0.799788\pi\)
\(18\) 0 0
\(19\) −1.01858 + 3.80140i −0.233679 + 0.872100i 0.745061 + 0.666996i \(0.232420\pi\)
−0.978740 + 0.205105i \(0.934247\pi\)
\(20\) 2.46454 + 0.660371i 0.551087 + 0.147663i
\(21\) 0 0
\(22\) 1.21009 + 2.09594i 0.257993 + 0.446856i
\(23\) 3.77196 + 2.17774i 0.786508 + 0.454090i 0.838732 0.544545i \(-0.183298\pi\)
−0.0522240 + 0.998635i \(0.516631\pi\)
\(24\) 0 0
\(25\) 1.95798i 0.391596i
\(26\) 2.29826 + 1.30401i 0.450727 + 0.255738i
\(27\) 0 0
\(28\) −3.40443 + 1.84122i −0.643377 + 0.347958i
\(29\) −2.65427 + 4.59734i −0.492886 + 0.853704i −0.999966 0.00819474i \(-0.997392\pi\)
0.507080 + 0.861899i \(0.330725\pi\)
\(30\) 0 0
\(31\) 0.220754 + 0.220754i 0.0396485 + 0.0396485i 0.726653 0.687005i \(-0.241075\pi\)
−0.687005 + 0.726653i \(0.741075\pi\)
\(32\) 5.65731 + 1.51587i 1.00008 + 0.267971i
\(33\) 0 0
\(34\) −0.449517 + 0.449517i −0.0770915 + 0.0770915i
\(35\) −3.17095 3.35249i −0.535988 0.566675i
\(36\) 0 0
\(37\) −3.57217 + 0.957160i −0.587261 + 0.157356i −0.540201 0.841536i \(-0.681652\pi\)
−0.0470599 + 0.998892i \(0.514985\pi\)
\(38\) −2.88425 −0.467887
\(39\) 0 0
\(40\) 4.42641i 0.699878i
\(41\) −1.90334 + 0.509998i −0.297251 + 0.0796483i −0.404363 0.914599i \(-0.632507\pi\)
0.107111 + 0.994247i \(0.465840\pi\)
\(42\) 0 0
\(43\) 9.99342 5.76970i 1.52398 0.879872i 0.524386 0.851481i \(-0.324295\pi\)
0.999597 0.0283909i \(-0.00903832\pi\)
\(44\) 3.41595 3.41595i 0.514974 0.514974i
\(45\) 0 0
\(46\) −0.826162 + 3.08328i −0.121811 + 0.454605i
\(47\) −3.68984 + 3.68984i −0.538219 + 0.538219i −0.923006 0.384786i \(-0.874275\pi\)
0.384786 + 0.923006i \(0.374275\pi\)
\(48\) 0 0
\(49\) 6.98917 + 0.389311i 0.998452 + 0.0556159i
\(50\) 1.38607 0.371397i 0.196020 0.0525234i
\(51\) 0 0
\(52\) 1.32689 5.10489i 0.184006 0.707920i
\(53\) 3.55843 0.488788 0.244394 0.969676i \(-0.421411\pi\)
0.244394 + 0.969676i \(0.421411\pi\)
\(54\) 0 0
\(55\) 4.98801 + 2.87983i 0.672583 + 0.388316i
\(56\) −4.61402 4.87818i −0.616575 0.651875i
\(57\) 0 0
\(58\) −3.75796 1.00694i −0.493445 0.132218i
\(59\) −8.89645 2.38380i −1.15822 0.310344i −0.371965 0.928247i \(-0.621316\pi\)
−0.786255 + 0.617903i \(0.787983\pi\)
\(60\) 0 0
\(61\) 4.78192 2.76084i 0.612262 0.353490i −0.161588 0.986858i \(-0.551662\pi\)
0.773850 + 0.633369i \(0.218328\pi\)
\(62\) −0.114400 + 0.198147i −0.0145288 + 0.0251646i
\(63\) 0 0
\(64\) 2.16076i 0.270095i
\(65\) 6.28840 0.0471733i 0.779980 0.00585112i
\(66\) 0 0
\(67\) 1.01969 + 3.80552i 0.124575 + 0.464919i 0.999824 0.0187529i \(-0.00596958\pi\)
−0.875250 + 0.483672i \(0.839303\pi\)
\(68\) 1.09893 + 0.634466i 0.133265 + 0.0769403i
\(69\) 0 0
\(70\) 1.77178 2.88065i 0.211768 0.344304i
\(71\) −11.9487 3.20164i −1.41805 0.379965i −0.533258 0.845952i \(-0.679033\pi\)
−0.884791 + 0.465987i \(0.845699\pi\)
\(72\) 0 0
\(73\) 5.55302 5.55302i 0.649932 0.649932i −0.303044 0.952977i \(-0.598003\pi\)
0.952977 + 0.303044i \(0.0980030\pi\)
\(74\) −1.35516 2.34721i −0.157534 0.272858i
\(75\) 0 0
\(76\) 1.49007 + 5.56101i 0.170923 + 0.637892i
\(77\) −8.49898 + 2.02567i −0.968549 + 0.230846i
\(78\) 0 0
\(79\) −15.7334 −1.77015 −0.885073 0.465453i \(-0.845891\pi\)
−0.885073 + 0.465453i \(0.845891\pi\)
\(80\) 1.79558 0.481124i 0.200752 0.0537913i
\(81\) 0 0
\(82\) −0.722063 1.25065i −0.0797385 0.138111i
\(83\) 3.80823 + 3.80823i 0.418007 + 0.418007i 0.884516 0.466509i \(-0.154488\pi\)
−0.466509 + 0.884516i \(0.654488\pi\)
\(84\) 0 0
\(85\) −0.391566 + 1.46134i −0.0424713 + 0.158505i
\(86\) 5.98000 + 5.98000i 0.644841 + 0.644841i
\(87\) 0 0
\(88\) 7.25801 + 4.19041i 0.773706 + 0.446700i
\(89\) 3.26801 + 12.1964i 0.346409 + 1.29282i 0.890958 + 0.454086i \(0.150034\pi\)
−0.544549 + 0.838729i \(0.683299\pi\)
\(90\) 0 0
\(91\) −6.88104 + 6.60691i −0.721329 + 0.692593i
\(92\) 6.37158 0.664283
\(93\) 0 0
\(94\) −3.31197 1.91217i −0.341604 0.197225i
\(95\) −5.94444 + 3.43202i −0.609887 + 0.352118i
\(96\) 0 0
\(97\) 0.756697 2.82403i 0.0768309 0.286737i −0.916811 0.399321i \(-0.869246\pi\)
0.993642 + 0.112584i \(0.0359127\pi\)
\(98\) 1.05013 + 5.02153i 0.106079 + 0.507251i
\(99\) 0 0
\(100\) −1.43215 2.48056i −0.143215 0.248056i
\(101\) 4.75389 8.23397i 0.473029 0.819311i −0.526494 0.850179i \(-0.676494\pi\)
0.999523 + 0.0308679i \(0.00982712\pi\)
\(102\) 0 0
\(103\) −8.04351 −0.792551 −0.396275 0.918132i \(-0.629697\pi\)
−0.396275 + 0.918132i \(0.629697\pi\)
\(104\) 9.15020 0.0686414i 0.897251 0.00673085i
\(105\) 0 0
\(106\) 0.674975 + 2.51904i 0.0655594 + 0.244671i
\(107\) −5.49111 + 9.51088i −0.530845 + 0.919451i 0.468507 + 0.883460i \(0.344792\pi\)
−0.999352 + 0.0359912i \(0.988541\pi\)
\(108\) 0 0
\(109\) −2.13897 + 2.13897i −0.204876 + 0.204876i −0.802086 0.597209i \(-0.796276\pi\)
0.597209 + 0.802086i \(0.296276\pi\)
\(110\) −1.09251 + 4.07731i −0.104167 + 0.388756i
\(111\) 0 0
\(112\) −1.47733 + 2.40191i −0.139594 + 0.226959i
\(113\) −7.04028 12.1941i −0.662294 1.14713i −0.980011 0.198941i \(-0.936250\pi\)
0.317718 0.948185i \(-0.397084\pi\)
\(114\) 0 0
\(115\) 1.96614 + 7.33772i 0.183343 + 0.684246i
\(116\) 7.76581i 0.721037i
\(117\) 0 0
\(118\) 6.75004i 0.621391i
\(119\) −1.09175 2.01865i −0.100081 0.185050i
\(120\) 0 0
\(121\) −0.0821489 + 0.0474287i −0.00746808 + 0.00431170i
\(122\) 2.86147 + 2.86147i 0.259066 + 0.259066i
\(123\) 0 0
\(124\) 0.441141 + 0.118203i 0.0396156 + 0.0106150i
\(125\) 8.58122 8.58122i 0.767528 0.767528i
\(126\) 0 0
\(127\) 4.95962 + 2.86344i 0.440095 + 0.254089i 0.703638 0.710559i \(-0.251558\pi\)
−0.263543 + 0.964648i \(0.584891\pi\)
\(128\) 9.78499 2.62188i 0.864879 0.231744i
\(129\) 0 0
\(130\) 1.22620 + 4.44266i 0.107545 + 0.389647i
\(131\) 21.7908i 1.90387i −0.306294 0.951937i \(-0.599089\pi\)
0.306294 0.951937i \(-0.400911\pi\)
\(132\) 0 0
\(133\) 2.97366 9.97869i 0.257849 0.865262i
\(134\) −2.50054 + 1.44369i −0.216014 + 0.124716i
\(135\) 0 0
\(136\) −0.569764 + 2.12639i −0.0488569 + 0.182336i
\(137\) −0.00993599 + 0.0370816i −0.000848889 + 0.00316810i −0.966349 0.257235i \(-0.917189\pi\)
0.965500 + 0.260403i \(0.0838553\pi\)
\(138\) 0 0
\(139\) −14.5766 + 8.41579i −1.23637 + 0.713818i −0.968350 0.249596i \(-0.919702\pi\)
−0.268018 + 0.963414i \(0.586369\pi\)
\(140\) −6.46942 1.92789i −0.546766 0.162937i
\(141\) 0 0
\(142\) 9.06588i 0.760792i
\(143\) 5.87578 10.3558i 0.491357 0.865994i
\(144\) 0 0
\(145\) −8.94335 + 2.39636i −0.742705 + 0.199007i
\(146\) 4.98435 + 2.87771i 0.412507 + 0.238161i
\(147\) 0 0
\(148\) −3.82546 + 3.82546i −0.314451 + 0.314451i
\(149\) −13.8533 3.71198i −1.13491 0.304097i −0.358005 0.933720i \(-0.616543\pi\)
−0.776901 + 0.629622i \(0.783210\pi\)
\(150\) 0 0
\(151\) −16.8022 16.8022i −1.36735 1.36735i −0.864204 0.503142i \(-0.832177\pi\)
−0.503142 0.864204i \(-0.667823\pi\)
\(152\) −8.64971 + 4.99391i −0.701584 + 0.405060i
\(153\) 0 0
\(154\) −3.04610 5.63226i −0.245462 0.453860i
\(155\) 0.544507i 0.0437359i
\(156\) 0 0
\(157\) 15.4058i 1.22952i −0.788715 0.614758i \(-0.789254\pi\)
0.788715 0.614758i \(-0.210746\pi\)
\(158\) −2.98436 11.1378i −0.237423 0.886075i
\(159\) 0 0
\(160\) 5.10760 + 8.84662i 0.403791 + 0.699387i
\(161\) −9.81552 6.03715i −0.773571 0.475794i
\(162\) 0 0
\(163\) −0.340861 + 1.27211i −0.0266983 + 0.0996393i −0.977989 0.208655i \(-0.933091\pi\)
0.951291 + 0.308294i \(0.0997581\pi\)
\(164\) −2.03830 + 2.03830i −0.159164 + 0.159164i
\(165\) 0 0
\(166\) −1.97352 + 3.41823i −0.153175 + 0.265306i
\(167\) 6.28848 + 23.4689i 0.486617 + 1.81608i 0.572665 + 0.819789i \(0.305909\pi\)
−0.0860480 + 0.996291i \(0.527424\pi\)
\(168\) 0 0
\(169\) −0.195031 12.9985i −0.0150024 0.999887i
\(170\) −1.10877 −0.0850388
\(171\) 0 0
\(172\) 8.44042 14.6192i 0.643576 1.11471i
\(173\) 0.316932 + 0.548943i 0.0240959 + 0.0417353i 0.877822 0.478987i \(-0.158996\pi\)
−0.853726 + 0.520722i \(0.825663\pi\)
\(174\) 0 0
\(175\) −0.144110 + 5.17833i −0.0108937 + 0.391445i
\(176\) 0.910945 3.39969i 0.0686651 0.256261i
\(177\) 0 0
\(178\) −8.01403 + 4.62691i −0.600677 + 0.346801i
\(179\) −12.6821 7.32204i −0.947908 0.547275i −0.0554778 0.998460i \(-0.517668\pi\)
−0.892431 + 0.451185i \(0.851002\pi\)
\(180\) 0 0
\(181\) 6.41112 0.476535 0.238267 0.971200i \(-0.423421\pi\)
0.238267 + 0.971200i \(0.423421\pi\)
\(182\) −5.98230 3.61792i −0.443438 0.268178i
\(183\) 0 0
\(184\) 2.86091 + 10.6770i 0.210909 + 0.787122i
\(185\) −5.58598 3.22507i −0.410690 0.237112i
\(186\) 0 0
\(187\) 2.02548 + 2.02548i 0.148118 + 0.148118i
\(188\) −1.97574 + 7.37357i −0.144096 + 0.537773i
\(189\) 0 0
\(190\) −3.55712 3.55712i −0.258060 0.258060i
\(191\) −2.37706 4.11718i −0.171998 0.297909i 0.767120 0.641503i \(-0.221689\pi\)
−0.939118 + 0.343594i \(0.888356\pi\)
\(192\) 0 0
\(193\) −9.10651 + 2.44008i −0.655501 + 0.175641i −0.571215 0.820801i \(-0.693528\pi\)
−0.0842861 + 0.996442i \(0.526861\pi\)
\(194\) 2.14269 0.153836
\(195\) 0 0
\(196\) 9.13931 4.61896i 0.652808 0.329926i
\(197\) −2.90812 10.8532i −0.207195 0.773262i −0.988769 0.149450i \(-0.952250\pi\)
0.781574 0.623812i \(-0.214417\pi\)
\(198\) 0 0
\(199\) −6.27981 10.8770i −0.445164 0.771047i 0.552899 0.833248i \(-0.313521\pi\)
−0.998064 + 0.0622009i \(0.980188\pi\)
\(200\) 3.51370 3.51370i 0.248456 0.248456i
\(201\) 0 0
\(202\) 6.73063 + 1.80347i 0.473565 + 0.126891i
\(203\) 7.35820 11.9633i 0.516445 0.839662i
\(204\) 0 0
\(205\) −2.97635 1.71839i −0.207877 0.120018i
\(206\) −1.52572 5.69406i −0.106302 0.396724i
\(207\) 0 0
\(208\) −1.02242 3.70433i −0.0708918 0.256849i
\(209\) 12.9962i 0.898963i
\(210\) 0 0
\(211\) −5.70417 + 9.87991i −0.392691 + 0.680161i −0.992804 0.119755i \(-0.961789\pi\)
0.600112 + 0.799916i \(0.295123\pi\)
\(212\) 4.50817 2.60279i 0.309622 0.178760i
\(213\) 0 0
\(214\) −7.77440 2.08314i −0.531447 0.142401i
\(215\) 19.4405 + 5.20908i 1.32583 + 0.355256i
\(216\) 0 0
\(217\) −0.567585 0.600081i −0.0385302 0.0407362i
\(218\) −1.91992 1.10847i −0.130034 0.0750749i
\(219\) 0 0
\(220\) 8.42572 0.568062
\(221\) 3.02693 + 0.786776i 0.203614 + 0.0529243i
\(222\) 0 0
\(223\) 7.03645 1.88541i 0.471196 0.126257i −0.0154044 0.999881i \(-0.504904\pi\)
0.486600 + 0.873625i \(0.338237\pi\)
\(224\) −14.8505 4.42545i −0.992238 0.295688i
\(225\) 0 0
\(226\) 7.29689 7.29689i 0.485382 0.485382i
\(227\) 6.07133 22.6585i 0.402968 1.50390i −0.404804 0.914404i \(-0.632660\pi\)
0.807772 0.589495i \(-0.200673\pi\)
\(228\) 0 0
\(229\) 16.2331 16.2331i 1.07271 1.07271i 0.0755720 0.997140i \(-0.475922\pi\)
0.997140 0.0755720i \(-0.0240783\pi\)
\(230\) −4.82148 + 2.78368i −0.317919 + 0.183551i
\(231\) 0 0
\(232\) −13.0134 + 3.48693i −0.854372 + 0.228928i
\(233\) 16.5274i 1.08274i −0.840783 0.541372i \(-0.817905\pi\)
0.840783 0.541372i \(-0.182095\pi\)
\(234\) 0 0
\(235\) −9.10131 −0.593704
\(236\) −13.0145 + 3.48723i −0.847172 + 0.226999i
\(237\) 0 0
\(238\) 1.22193 1.15576i 0.0792062 0.0749170i
\(239\) −18.8339 + 18.8339i −1.21826 + 1.21826i −0.250025 + 0.968239i \(0.580439\pi\)
−0.968239 + 0.250025i \(0.919561\pi\)
\(240\) 0 0
\(241\) 1.11909 + 0.299860i 0.0720871 + 0.0193157i 0.294682 0.955595i \(-0.404786\pi\)
−0.222595 + 0.974911i \(0.571453\pi\)
\(242\) −0.0491574 0.0491574i −0.00315996 0.00315996i
\(243\) 0 0
\(244\) 4.03880 6.99541i 0.258558 0.447835i
\(245\) 8.13955 + 9.09982i 0.520017 + 0.581366i
\(246\) 0 0
\(247\) 7.18680 + 12.2350i 0.457285 + 0.778495i
\(248\) 0.792308i 0.0503116i
\(249\) 0 0
\(250\) 7.70243 + 4.44700i 0.487144 + 0.281253i
\(251\) −6.82617 11.8233i −0.430864 0.746278i 0.566084 0.824348i \(-0.308458\pi\)
−0.996948 + 0.0780693i \(0.975124\pi\)
\(252\) 0 0
\(253\) 13.8930 + 3.72262i 0.873445 + 0.234039i
\(254\) −1.08629 + 4.05410i −0.0681600 + 0.254377i
\(255\) 0 0
\(256\) 5.87286 + 10.1721i 0.367054 + 0.635756i
\(257\) 0.128138 0.221941i 0.00799302 0.0138443i −0.862001 0.506906i \(-0.830789\pi\)
0.869994 + 0.493062i \(0.164122\pi\)
\(258\) 0 0
\(259\) 9.51786 2.26851i 0.591411 0.140958i
\(260\) 7.93225 4.65937i 0.491938 0.288962i
\(261\) 0 0
\(262\) 15.4259 4.13336i 0.953015 0.255360i
\(263\) −6.21656 + 10.7674i −0.383329 + 0.663946i −0.991536 0.129833i \(-0.958556\pi\)
0.608206 + 0.793779i \(0.291889\pi\)
\(264\) 0 0
\(265\) 4.38858 + 4.38858i 0.269589 + 0.269589i
\(266\) 7.62805 + 0.212285i 0.467706 + 0.0130160i
\(267\) 0 0
\(268\) 4.07536 + 4.07536i 0.248942 + 0.248942i
\(269\) −23.9300 + 13.8160i −1.45904 + 0.842375i −0.998964 0.0455067i \(-0.985510\pi\)
−0.460072 + 0.887882i \(0.652176\pi\)
\(270\) 0 0
\(271\) 7.85980 + 29.3332i 0.477449 + 1.78186i 0.611891 + 0.790942i \(0.290409\pi\)
−0.134442 + 0.990921i \(0.542924\pi\)
\(272\) 0.924502 0.0560562
\(273\) 0 0
\(274\) −0.0281351 −0.00169970
\(275\) −1.67348 6.24551i −0.100915 0.376619i
\(276\) 0 0
\(277\) 9.29180 5.36462i 0.558290 0.322329i −0.194169 0.980968i \(-0.562201\pi\)
0.752459 + 0.658639i \(0.228868\pi\)
\(278\) −8.72253 8.72253i −0.523143 0.523143i
\(279\) 0 0
\(280\) 0.325790 11.7067i 0.0194697 0.699607i
\(281\) 17.6179 + 17.6179i 1.05099 + 1.05099i 0.998628 + 0.0523655i \(0.0166761\pi\)
0.0523655 + 0.998628i \(0.483324\pi\)
\(282\) 0 0
\(283\) −4.91523 + 8.51342i −0.292180 + 0.506070i −0.974325 0.225147i \(-0.927714\pi\)
0.682145 + 0.731217i \(0.261047\pi\)
\(284\) −17.4796 + 4.68364i −1.03722 + 0.277923i
\(285\) 0 0
\(286\) 8.44547 + 2.19519i 0.499391 + 0.129804i
\(287\) 5.07134 1.20872i 0.299352 0.0713483i
\(288\) 0 0
\(289\) 8.12379 14.0708i 0.477870 0.827696i
\(290\) −3.39281 5.87652i −0.199233 0.345081i
\(291\) 0 0
\(292\) 2.97339 11.0968i 0.174004 0.649393i
\(293\) 24.9107 + 6.67480i 1.45530 + 0.389946i 0.897863 0.440275i \(-0.145119\pi\)
0.557435 + 0.830221i \(0.311786\pi\)
\(294\) 0 0
\(295\) −8.03201 13.9118i −0.467641 0.809979i
\(296\) −8.12812 4.69277i −0.472437 0.272762i
\(297\) 0 0
\(298\) 10.5110i 0.608883i
\(299\) 15.1379 4.17815i 0.875447 0.241628i
\(300\) 0 0
\(301\) −26.8545 + 14.5238i −1.54787 + 0.837136i
\(302\) 8.70733 15.0815i 0.501050 0.867845i
\(303\) 0 0
\(304\) 2.96596 + 2.96596i 0.170109 + 0.170109i
\(305\) 9.30243 + 2.49258i 0.532656 + 0.142725i
\(306\) 0 0
\(307\) −3.13433 + 3.13433i −0.178886 + 0.178886i −0.790870 0.611984i \(-0.790372\pi\)
0.611984 + 0.790870i \(0.290372\pi\)
\(308\) −9.28567 + 8.78284i −0.529100 + 0.500448i
\(309\) 0 0
\(310\) −0.385461 + 0.103284i −0.0218927 + 0.00586614i
\(311\) −22.3642 −1.26816 −0.634078 0.773269i \(-0.718620\pi\)
−0.634078 + 0.773269i \(0.718620\pi\)
\(312\) 0 0
\(313\) 5.32563i 0.301022i 0.988608 + 0.150511i \(0.0480919\pi\)
−0.988608 + 0.150511i \(0.951908\pi\)
\(314\) 10.9059 2.92222i 0.615455 0.164911i
\(315\) 0 0
\(316\) −19.9326 + 11.5081i −1.12130 + 0.647380i
\(317\) −9.55320 + 9.55320i −0.536561 + 0.536561i −0.922517 0.385956i \(-0.873872\pi\)
0.385956 + 0.922517i \(0.373872\pi\)
\(318\) 0 0
\(319\) −4.53720 + 16.9331i −0.254034 + 0.948069i
\(320\) −2.66485 + 2.66485i −0.148970 + 0.148970i
\(321\) 0 0
\(322\) 2.41191 8.09363i 0.134410 0.451040i
\(323\) −3.29740 + 0.883534i −0.183472 + 0.0491612i
\(324\) 0 0
\(325\) −5.02920 4.95431i −0.278970 0.274816i
\(326\) −0.965192 −0.0534571
\(327\) 0 0
\(328\) −4.33086 2.50042i −0.239132 0.138063i
\(329\) 10.0302 9.48706i 0.552983 0.523038i
\(330\) 0 0
\(331\) 9.25799 + 2.48067i 0.508865 + 0.136350i 0.504111 0.863639i \(-0.331820\pi\)
0.00475394 + 0.999989i \(0.498487\pi\)
\(332\) 7.61014 + 2.03913i 0.417661 + 0.111912i
\(333\) 0 0
\(334\) −15.4210 + 8.90333i −0.843801 + 0.487169i
\(335\) −3.43575 + 5.95089i −0.187715 + 0.325132i
\(336\) 0 0
\(337\) 27.7219i 1.51011i 0.655663 + 0.755053i \(0.272389\pi\)
−0.655663 + 0.755053i \(0.727611\pi\)
\(338\) 9.16477 2.60367i 0.498498 0.141621i
\(339\) 0 0
\(340\) 0.572817 + 2.13778i 0.0310653 + 0.115937i
\(341\) 0.892831 + 0.515476i 0.0483495 + 0.0279146i
\(342\) 0 0
\(343\) −18.4558 1.54403i −0.996519 0.0833700i
\(344\) 28.2878 + 7.57968i 1.52517 + 0.408669i
\(345\) 0 0
\(346\) −0.328484 + 0.328484i −0.0176594 + 0.0176594i
\(347\) 11.5943 + 20.0819i 0.622413 + 1.07805i 0.989035 + 0.147681i \(0.0471808\pi\)
−0.366622 + 0.930370i \(0.619486\pi\)
\(348\) 0 0
\(349\) 4.20372 + 15.6885i 0.225020 + 0.839787i 0.982396 + 0.186808i \(0.0598142\pi\)
−0.757376 + 0.652979i \(0.773519\pi\)
\(350\) −3.69312 + 0.880226i −0.197405 + 0.0470501i
\(351\) 0 0
\(352\) 19.3411 1.03088
\(353\) −12.1897 + 3.26621i −0.648790 + 0.173843i −0.568182 0.822903i \(-0.692353\pi\)
−0.0806085 + 0.996746i \(0.525686\pi\)
\(354\) 0 0
\(355\) −10.7877 18.6848i −0.572550 0.991686i
\(356\) 13.0612 + 13.0612i 0.692243 + 0.692243i
\(357\) 0 0
\(358\) 2.77774 10.3667i 0.146808 0.547895i
\(359\) 2.03793 + 2.03793i 0.107558 + 0.107558i 0.758838 0.651280i \(-0.225768\pi\)
−0.651280 + 0.758838i \(0.725768\pi\)
\(360\) 0 0
\(361\) 3.04137 + 1.75593i 0.160072 + 0.0924176i
\(362\) 1.21608 + 4.53848i 0.0639159 + 0.238537i
\(363\) 0 0
\(364\) −3.88498 + 13.4034i −0.203628 + 0.702527i
\(365\) 13.6970 0.716934
\(366\) 0 0
\(367\) −24.3990 14.0868i −1.27362 0.735325i −0.297953 0.954581i \(-0.596304\pi\)
−0.975667 + 0.219256i \(0.929637\pi\)
\(368\) 4.02019 2.32106i 0.209567 0.120994i
\(369\) 0 0
\(370\) 1.22348 4.56610i 0.0636059 0.237380i
\(371\) −9.41108 0.261906i −0.488599 0.0135975i
\(372\) 0 0
\(373\) 12.9669 + 22.4593i 0.671400 + 1.16290i 0.977507 + 0.210902i \(0.0676402\pi\)
−0.306107 + 0.951997i \(0.599026\pi\)
\(374\) −1.04965 + 1.81805i −0.0542763 + 0.0940094i
\(375\) 0 0
\(376\) −13.2432 −0.682968
\(377\) 5.09241 + 18.4504i 0.262272 + 0.950243i
\(378\) 0 0
\(379\) −8.41204 31.3942i −0.432097 1.61261i −0.747918 0.663791i \(-0.768946\pi\)
0.315821 0.948819i \(-0.397720\pi\)
\(380\) −5.02066 + 8.69604i −0.257555 + 0.446098i
\(381\) 0 0
\(382\) 2.46370 2.46370i 0.126054 0.126054i
\(383\) 1.42917 5.33373i 0.0730271 0.272541i −0.919752 0.392501i \(-0.871610\pi\)
0.992779 + 0.119960i \(0.0382767\pi\)
\(384\) 0 0
\(385\) −12.9800 7.98348i −0.661520 0.406876i
\(386\) −3.45471 5.98373i −0.175840 0.304564i
\(387\) 0 0
\(388\) −1.10696 4.13124i −0.0561975 0.209732i
\(389\) 24.3224i 1.23319i −0.787279 0.616597i \(-0.788511\pi\)
0.787279 0.616597i \(-0.211489\pi\)
\(390\) 0 0
\(391\) 3.77802i 0.191063i
\(392\) 11.8438 + 13.2411i 0.598202 + 0.668775i
\(393\) 0 0
\(394\) 7.13148 4.11736i 0.359279 0.207430i
\(395\) −19.4039 19.4039i −0.976315 0.976315i
\(396\) 0 0
\(397\) −10.3563 2.77495i −0.519765 0.139271i −0.0106073 0.999944i \(-0.503376\pi\)
−0.509158 + 0.860673i \(0.670043\pi\)
\(398\) 6.50871 6.50871i 0.326252 0.326252i
\(399\) 0 0
\(400\) −1.80726 1.04342i −0.0903628 0.0521710i
\(401\) −25.6010 + 6.85977i −1.27845 + 0.342561i −0.833264 0.552875i \(-0.813531\pi\)
−0.445190 + 0.895436i \(0.646864\pi\)
\(402\) 0 0
\(403\) 1.12560 0.00844380i 0.0560699 0.000420616i
\(404\) 13.9088i 0.691988i
\(405\) 0 0
\(406\) 9.86468 + 2.93968i 0.489576 + 0.145894i
\(407\) −10.5763 + 6.10624i −0.524249 + 0.302675i
\(408\) 0 0
\(409\) 0.225314 0.840884i 0.0111411 0.0415790i −0.960132 0.279549i \(-0.909815\pi\)
0.971273 + 0.237970i \(0.0764819\pi\)
\(410\) 0.651902 2.43293i 0.0321951 0.120154i
\(411\) 0 0
\(412\) −10.1903 + 5.88337i −0.502040 + 0.289853i
\(413\) 23.3532 + 6.95929i 1.14914 + 0.342444i
\(414\) 0 0
\(415\) 9.39332i 0.461100i
\(416\) 18.2084 10.6955i 0.892738 0.524391i
\(417\) 0 0
\(418\) −9.20009 + 2.46516i −0.449991 + 0.120575i
\(419\) 24.0763 + 13.9005i 1.17621 + 0.679083i 0.955134 0.296174i \(-0.0957110\pi\)
0.221072 + 0.975257i \(0.429044\pi\)
\(420\) 0 0
\(421\) 6.14872 6.14872i 0.299670 0.299670i −0.541214 0.840885i \(-0.682035\pi\)
0.840885 + 0.541214i \(0.182035\pi\)
\(422\) −8.07605 2.16397i −0.393136 0.105340i
\(423\) 0 0
\(424\) 6.38579 + 6.38579i 0.310122 + 0.310122i
\(425\) 1.47085 0.849193i 0.0713465 0.0411919i
\(426\) 0 0
\(427\) −12.8501 + 6.94972i −0.621859 + 0.336321i
\(428\) 16.0657i 0.776567i
\(429\) 0 0
\(430\) 14.7502i 0.711317i
\(431\) 7.07164 + 26.3917i 0.340629 + 1.27124i 0.897636 + 0.440737i \(0.145283\pi\)
−0.557007 + 0.830507i \(0.688051\pi\)
\(432\) 0 0
\(433\) 11.5716 + 20.0425i 0.556094 + 0.963182i 0.997818 + 0.0660314i \(0.0210338\pi\)
−0.441724 + 0.897151i \(0.645633\pi\)
\(434\) 0.317141 0.515624i 0.0152232 0.0247507i
\(435\) 0 0
\(436\) −1.14532 + 4.27440i −0.0548509 + 0.204706i
\(437\) −12.1205 + 12.1205i −0.579802 + 0.579802i
\(438\) 0 0
\(439\) 20.4076 35.3470i 0.974003 1.68702i 0.290814 0.956779i \(-0.406074\pi\)
0.683188 0.730242i \(-0.260593\pi\)
\(440\) 3.78324 + 14.1192i 0.180359 + 0.673109i
\(441\) 0 0
\(442\) 0.0171940 + 2.29203i 0.000817833 + 0.109021i
\(443\) 6.05837 0.287842 0.143921 0.989589i \(-0.454029\pi\)
0.143921 + 0.989589i \(0.454029\pi\)
\(444\) 0 0
\(445\) −11.0113 + 19.0721i −0.521986 + 0.904106i
\(446\) 2.66940 + 4.62353i 0.126400 + 0.218930i
\(447\) 0 0
\(448\) 0.159035 5.71463i 0.00751371 0.269991i
\(449\) 1.65796 6.18758i 0.0782438 0.292010i −0.915705 0.401850i \(-0.868367\pi\)
0.993949 + 0.109840i \(0.0350340\pi\)
\(450\) 0 0
\(451\) −5.63532 + 3.25355i −0.265357 + 0.153204i
\(452\) −17.8386 10.2991i −0.839058 0.484430i
\(453\) 0 0
\(454\) 17.1918 0.806850
\(455\) −16.6346 0.338075i −0.779841 0.0158492i
\(456\) 0 0
\(457\) −7.61312 28.4126i −0.356127 1.32908i −0.879061 0.476710i \(-0.841829\pi\)
0.522934 0.852373i \(-0.324837\pi\)
\(458\) 14.5707 + 8.41238i 0.680843 + 0.393085i
\(459\) 0 0
\(460\) 7.85801 + 7.85801i 0.366382 + 0.366382i
\(461\) 3.01129 11.2383i 0.140250 0.523419i −0.859671 0.510848i \(-0.829332\pi\)
0.999921 0.0125715i \(-0.00400175\pi\)
\(462\) 0 0
\(463\) 8.42591 + 8.42591i 0.391585 + 0.391585i 0.875252 0.483667i \(-0.160695\pi\)
−0.483667 + 0.875252i \(0.660695\pi\)
\(464\) 2.82895 + 4.89989i 0.131331 + 0.227472i
\(465\) 0 0
\(466\) 11.6999 3.13497i 0.541985 0.145225i
\(467\) 21.2254 0.982195 0.491097 0.871105i \(-0.336596\pi\)
0.491097 + 0.871105i \(0.336596\pi\)
\(468\) 0 0
\(469\) −2.41670 10.1396i −0.111593 0.468204i
\(470\) −1.72637 6.44289i −0.0796314 0.297188i
\(471\) 0 0
\(472\) −11.6873 20.2430i −0.537952 0.931760i
\(473\) 26.9454 26.9454i 1.23895 1.23895i
\(474\) 0 0
\(475\) 7.44307 + 1.99436i 0.341511 + 0.0915077i
\(476\) −2.85967 1.75887i −0.131073 0.0806178i
\(477\) 0 0
\(478\) −16.9052 9.76019i −0.773224 0.446421i
\(479\) 5.66017 + 21.1241i 0.258620 + 0.965183i 0.966041 + 0.258390i \(0.0831920\pi\)
−0.707421 + 0.706793i \(0.750141\pi\)
\(480\) 0 0
\(481\) −6.58018 + 11.5973i −0.300030 + 0.528789i
\(482\) 0.849093i 0.0386751i
\(483\) 0 0
\(484\) −0.0693828 + 0.120174i −0.00315376 + 0.00546248i
\(485\) 4.41608 2.54963i 0.200524 0.115773i
\(486\) 0 0
\(487\) 28.6992 + 7.68994i 1.30049 + 0.348464i 0.841634 0.540048i \(-0.181594\pi\)
0.458852 + 0.888512i \(0.348261\pi\)
\(488\) 13.5359 + 3.62693i 0.612741 + 0.164183i
\(489\) 0 0
\(490\) −4.89789 + 7.48813i −0.221264 + 0.338279i
\(491\) 23.9204 + 13.8105i 1.07951 + 0.623258i 0.930765 0.365617i \(-0.119142\pi\)
0.148749 + 0.988875i \(0.452475\pi\)
\(492\) 0 0
\(493\) −4.60472 −0.207386
\(494\) −7.29805 + 7.40837i −0.328355 + 0.333318i
\(495\) 0 0
\(496\) 0.321401 0.0861191i 0.0144313 0.00386686i
\(497\) 31.3654 + 9.34692i 1.40693 + 0.419267i
\(498\) 0 0
\(499\) 5.32994 5.32994i 0.238601 0.238601i −0.577670 0.816271i \(-0.696038\pi\)
0.816271 + 0.577670i \(0.196038\pi\)
\(500\) 4.59485 17.1482i 0.205488 0.766891i
\(501\) 0 0
\(502\) 7.07498 7.07498i 0.315772 0.315772i
\(503\) −16.3880 + 9.46160i −0.730703 + 0.421872i −0.818679 0.574251i \(-0.805293\pi\)
0.0879761 + 0.996123i \(0.471960\pi\)
\(504\) 0 0
\(505\) 16.0178 4.29196i 0.712784 0.190990i
\(506\) 10.5411i 0.468608i
\(507\) 0 0
\(508\) 8.37777 0.371703
\(509\) −19.9100 + 5.33488i −0.882497 + 0.236464i −0.671484 0.741019i \(-0.734343\pi\)
−0.211013 + 0.977483i \(0.567676\pi\)
\(510\) 0 0
\(511\) −15.0949 + 14.2775i −0.667761 + 0.631600i
\(512\) 8.23930 8.23930i 0.364129 0.364129i
\(513\) 0 0
\(514\) 0.181420 + 0.0486112i 0.00800208 + 0.00214415i
\(515\) −9.91999 9.91999i −0.437127 0.437127i
\(516\) 0 0
\(517\) −8.61606 + 14.9235i −0.378934 + 0.656333i
\(518\) 3.41128 + 6.30747i 0.149883 + 0.277134i
\(519\) 0 0
\(520\) 11.3695 + 11.2002i 0.498587 + 0.491162i
\(521\) 8.90519i 0.390144i −0.980789 0.195072i \(-0.937506\pi\)
0.980789 0.195072i \(-0.0624940\pi\)
\(522\) 0 0
\(523\) 36.0214 + 20.7970i 1.57511 + 0.909387i 0.995528 + 0.0944702i \(0.0301157\pi\)
0.579577 + 0.814917i \(0.303218\pi\)
\(524\) −15.9388 27.6067i −0.696288 1.20601i
\(525\) 0 0
\(526\) −8.80150 2.35835i −0.383764 0.102829i
\(527\) −0.0700885 + 0.261574i −0.00305310 + 0.0113943i
\(528\) 0 0
\(529\) −2.01489 3.48989i −0.0876038 0.151734i
\(530\) −2.27427 + 3.93915i −0.0987881 + 0.171106i
\(531\) 0 0
\(532\) −3.53153 14.8170i −0.153111 0.642400i
\(533\) −3.50608 + 6.17930i −0.151865 + 0.267655i
\(534\) 0 0
\(535\) −18.5018 + 4.95755i −0.799904 + 0.214334i
\(536\) −4.99933 + 8.65909i −0.215938 + 0.374016i
\(537\) 0 0
\(538\) −14.3196 14.3196i −0.617360 0.617360i
\(539\) 22.6266 4.73180i 0.974596 0.203813i
\(540\) 0 0
\(541\) 22.8055 + 22.8055i 0.980484 + 0.980484i 0.999813 0.0193293i \(-0.00615308\pi\)
−0.0193293 + 0.999813i \(0.506153\pi\)
\(542\) −19.2743 + 11.1280i −0.827903 + 0.477990i
\(543\) 0 0
\(544\) 1.31489 + 4.90724i 0.0563755 + 0.210396i
\(545\) −5.27596 −0.225997
\(546\) 0 0
\(547\) 15.4775 0.661769 0.330884 0.943671i \(-0.392653\pi\)
0.330884 + 0.943671i \(0.392653\pi\)
\(548\) 0.0145352 + 0.0542462i 0.000620914 + 0.00231728i
\(549\) 0 0
\(550\) 4.10382 2.36934i 0.174987 0.101029i
\(551\) −14.7727 14.7727i −0.629339 0.629339i
\(552\) 0 0
\(553\) 41.6105 + 1.15800i 1.76946 + 0.0492432i
\(554\) 5.56016 + 5.56016i 0.236228 + 0.236228i
\(555\) 0 0
\(556\) −12.3113 + 21.3239i −0.522117 + 0.904333i
\(557\) 16.8975 4.52767i 0.715969 0.191843i 0.117597 0.993061i \(-0.462481\pi\)
0.598373 + 0.801218i \(0.295814\pi\)
\(558\) 0 0
\(559\) 10.4666 40.2679i 0.442692 1.70315i
\(560\) −4.78423 + 1.14029i −0.202171 + 0.0481859i
\(561\) 0 0
\(562\) −9.13001 + 15.8136i −0.385126 + 0.667058i
\(563\) −13.0176 22.5472i −0.548628 0.950251i −0.998369 0.0570920i \(-0.981817\pi\)
0.449741 0.893159i \(-0.351516\pi\)
\(564\) 0 0
\(565\) 6.35619 23.7216i 0.267407 0.997977i
\(566\) −6.95905 1.86467i −0.292511 0.0783780i
\(567\) 0 0
\(568\) −15.6971 27.1881i −0.658634 1.14079i
\(569\) 5.70128 + 3.29163i 0.239010 + 0.137992i 0.614722 0.788744i \(-0.289268\pi\)
−0.375712 + 0.926737i \(0.622602\pi\)
\(570\) 0 0
\(571\) 9.46828i 0.396235i 0.980178 + 0.198118i \(0.0634828\pi\)
−0.980178 + 0.198118i \(0.936517\pi\)
\(572\) −0.130660 17.4175i −0.00546315 0.728262i
\(573\) 0 0
\(574\) 1.81761 + 3.36077i 0.0758656 + 0.140276i
\(575\) 4.26398 7.38543i 0.177820 0.307994i
\(576\) 0 0
\(577\) 14.5583 + 14.5583i 0.606069 + 0.606069i 0.941916 0.335847i \(-0.109023\pi\)
−0.335847 + 0.941916i \(0.609023\pi\)
\(578\) 11.5018 + 3.08190i 0.478412 + 0.128190i
\(579\) 0 0
\(580\) −9.57750 + 9.57750i −0.397684 + 0.397684i
\(581\) −9.79144 10.3520i −0.406217 0.429474i
\(582\) 0 0
\(583\) 11.3506 3.04138i 0.470093 0.125961i
\(584\) 19.9304 0.824725
\(585\) 0 0
\(586\) 18.9006i 0.780775i
\(587\) −28.3013 + 7.58332i −1.16812 + 0.312997i −0.790205 0.612843i \(-0.790026\pi\)
−0.377916 + 0.925840i \(0.623359\pi\)
\(588\) 0 0
\(589\) −1.06403 + 0.614317i −0.0438425 + 0.0253125i
\(590\) 8.32476 8.32476i 0.342725 0.342725i
\(591\) 0 0
\(592\) −1.02015 + 3.80726i −0.0419280 + 0.156477i
\(593\) −21.9121 + 21.9121i −0.899821 + 0.899821i −0.995420 0.0955990i \(-0.969523\pi\)
0.0955990 + 0.995420i \(0.469523\pi\)
\(594\) 0 0
\(595\) 1.14314 3.83604i 0.0468643 0.157262i
\(596\) −20.2658 + 5.43021i −0.830120 + 0.222430i
\(597\) 0 0
\(598\) 5.82915 + 9.92371i 0.238372 + 0.405811i
\(599\) −15.8653 −0.648240 −0.324120 0.946016i \(-0.605068\pi\)
−0.324120 + 0.946016i \(0.605068\pi\)
\(600\) 0 0
\(601\) −0.177063 0.102227i −0.00722256 0.00416995i 0.496384 0.868103i \(-0.334661\pi\)
−0.503607 + 0.863933i \(0.667994\pi\)
\(602\) −15.3753 16.2556i −0.626652 0.662530i
\(603\) 0 0
\(604\) −33.5766 8.99681i −1.36621 0.366075i
\(605\) −0.159807 0.0428201i −0.00649707 0.00174089i
\(606\) 0 0
\(607\) 24.0567 13.8891i 0.976430 0.563742i 0.0752394 0.997165i \(-0.476028\pi\)
0.901190 + 0.433423i \(0.142695\pi\)
\(608\) −11.5249 + 19.9616i −0.467394 + 0.809551i
\(609\) 0 0
\(610\) 7.05806i 0.285773i
\(611\) 0.141136 + 18.8141i 0.00570976 + 0.761135i
\(612\) 0 0
\(613\) 1.20950 + 4.51392i 0.0488513 + 0.182315i 0.986040 0.166506i \(-0.0532486\pi\)
−0.937189 + 0.348822i \(0.886582\pi\)
\(614\) −2.81335 1.62429i −0.113537 0.0655508i
\(615\) 0 0
\(616\) −18.8870 11.6167i −0.760980 0.468050i
\(617\) −0.205999 0.0551971i −0.00829319 0.00222215i 0.254670 0.967028i \(-0.418033\pi\)
−0.262963 + 0.964806i \(0.584700\pi\)
\(618\) 0 0
\(619\) −10.1547 + 10.1547i −0.408152 + 0.408152i −0.881094 0.472941i \(-0.843192\pi\)
0.472941 + 0.881094i \(0.343192\pi\)
\(620\) 0.398276 + 0.689835i 0.0159952 + 0.0277044i
\(621\) 0 0
\(622\) −4.24211 15.8318i −0.170093 0.634797i
\(623\) −7.74533 32.4967i −0.310310 1.30195i
\(624\) 0 0
\(625\) 11.3764 0.455056
\(626\) −3.77005 + 1.01018i −0.150682 + 0.0403750i
\(627\) 0 0
\(628\) −11.2685 19.5176i −0.449661 0.778836i
\(629\) −2.26830 2.26830i −0.0904431 0.0904431i
\(630\) 0 0
\(631\) −2.58932 + 9.66347i −0.103079 + 0.384697i −0.998120 0.0612871i \(-0.980479\pi\)
0.895041 + 0.445984i \(0.147146\pi\)
\(632\) −28.2344 28.2344i −1.12310 1.12310i
\(633\) 0 0
\(634\) −8.57487 4.95070i −0.340551 0.196617i
\(635\) 2.58520 + 9.64811i 0.102591 + 0.382873i
\(636\) 0 0
\(637\) 18.6847 16.9670i 0.740317 0.672258i
\(638\) −12.8477 −0.508644
\(639\) 0 0
\(640\) 15.3013 + 8.83420i 0.604837 + 0.349203i
\(641\) 19.6180 11.3265i 0.774866 0.447369i −0.0597418 0.998214i \(-0.519028\pi\)
0.834608 + 0.550845i \(0.185694\pi\)
\(642\) 0 0
\(643\) −4.29092 + 16.0139i −0.169217 + 0.631527i 0.828247 + 0.560363i \(0.189338\pi\)
−0.997465 + 0.0711645i \(0.977328\pi\)
\(644\) −16.8511 0.468957i −0.664026 0.0184795i
\(645\) 0 0
\(646\) −1.25092 2.16666i −0.0492169 0.0852461i
\(647\) −12.5163 + 21.6789i −0.492068 + 0.852287i −0.999958 0.00913503i \(-0.997092\pi\)
0.507890 + 0.861422i \(0.330426\pi\)
\(648\) 0 0
\(649\) −30.4151 −1.19390
\(650\) 2.55324 4.49996i 0.100146 0.176503i
\(651\) 0 0
\(652\) 0.498641 + 1.86095i 0.0195283 + 0.0728805i
\(653\) 9.18955 15.9168i 0.359615 0.622871i −0.628282 0.777986i \(-0.716241\pi\)
0.987896 + 0.155115i \(0.0495747\pi\)
\(654\) 0 0
\(655\) 26.8745 26.8745i 1.05007 1.05007i
\(656\) −0.543561 + 2.02860i −0.0212225 + 0.0792034i
\(657\) 0 0
\(658\) 8.61853 + 5.30093i 0.335985 + 0.206652i
\(659\) 2.47281 + 4.28303i 0.0963269 + 0.166843i 0.910162 0.414253i \(-0.135957\pi\)
−0.813835 + 0.581096i \(0.802624\pi\)
\(660\) 0 0
\(661\) −0.736202 2.74754i −0.0286349 0.106867i 0.950129 0.311856i \(-0.100951\pi\)
−0.978764 + 0.204989i \(0.934284\pi\)
\(662\) 7.02435i 0.273009i
\(663\) 0 0
\(664\) 13.6681i 0.530426i
\(665\) 15.9740 8.63925i 0.619446 0.335016i
\(666\) 0 0
\(667\) −20.0236 + 11.5606i −0.775318 + 0.447630i
\(668\) 25.1331 + 25.1331i 0.972427 + 0.972427i
\(669\) 0 0
\(670\) −4.86439 1.30341i −0.187928 0.0503551i
\(671\) 12.8935 12.8935i 0.497750 0.497750i
\(672\) 0 0
\(673\) −23.4111 13.5164i −0.902431 0.521019i −0.0244432 0.999701i \(-0.507781\pi\)
−0.877988 + 0.478682i \(0.841115\pi\)
\(674\) −19.6245 + 5.25838i −0.755909 + 0.202545i
\(675\) 0 0
\(676\) −9.75478 16.3252i −0.375184 0.627891i
\(677\) 1.97396i 0.0758653i −0.999280 0.0379327i \(-0.987923\pi\)
0.999280 0.0379327i \(-0.0120772\pi\)
\(678\) 0 0
\(679\) −2.20911 + 7.41310i −0.0847779 + 0.284489i
\(680\) −3.32514 + 1.91977i −0.127513 + 0.0736199i
\(681\) 0 0
\(682\) −0.195554 + 0.729819i −0.00748817 + 0.0279462i
\(683\) 0.854547 3.18921i 0.0326983 0.122032i −0.947648 0.319318i \(-0.896546\pi\)
0.980346 + 0.197286i \(0.0632128\pi\)
\(684\) 0 0
\(685\) −0.0579865 + 0.0334785i −0.00221555 + 0.00127915i
\(686\) −2.40772 13.3579i −0.0919272 0.510006i
\(687\) 0 0
\(688\) 12.2988i 0.468889i
\(689\) 9.00395 9.14006i 0.343023 0.348208i
\(690\) 0 0
\(691\) 43.3678 11.6204i 1.64979 0.442060i 0.690236 0.723585i \(-0.257507\pi\)
0.959554 + 0.281525i \(0.0908402\pi\)
\(692\) 0.803041 + 0.463636i 0.0305270 + 0.0176248i
\(693\) 0 0
\(694\) −12.0169 + 12.0169i −0.456154 + 0.456154i
\(695\) −28.3563 7.59804i −1.07562 0.288210i
\(696\) 0 0
\(697\) −1.20861 1.20861i −0.0457792 0.0457792i
\(698\) −10.3086 + 5.95170i −0.390188 + 0.225275i
\(699\) 0 0
\(700\) 3.60508 + 6.66582i 0.136259 + 0.251944i
\(701\) 23.5928i 0.891086i 0.895260 + 0.445543i \(0.146989\pi\)
−0.895260 + 0.445543i \(0.853011\pi\)
\(702\) 0 0
\(703\) 14.5542i 0.548921i
\(704\) 1.84680 + 6.89234i 0.0696038 + 0.259765i
\(705\) 0 0
\(706\) −4.62435 8.00961i −0.174040 0.301446i
\(707\) −13.1788 + 21.4267i −0.495638 + 0.805835i
\(708\) 0 0
\(709\) 9.42663 35.1807i 0.354025 1.32124i −0.527683 0.849441i \(-0.676939\pi\)
0.881708 0.471796i \(-0.156394\pi\)
\(710\) 11.1809 11.1809i 0.419611 0.419611i
\(711\) 0 0
\(712\) −16.0224 + 27.7517i −0.600467 + 1.04004i
\(713\) 0.351929 + 1.31342i 0.0131799 + 0.0491879i
\(714\) 0 0
\(715\) 20.0182 5.52515i 0.748640 0.206629i
\(716\) −21.4226 −0.800602
\(717\) 0 0
\(718\) −1.05610 + 1.82922i −0.0394134 + 0.0682660i
\(719\) 26.2044 + 45.3874i 0.977260 + 1.69266i 0.672266 + 0.740309i \(0.265321\pi\)
0.304994 + 0.952354i \(0.401346\pi\)
\(720\) 0 0
\(721\) 21.2729 + 0.592014i 0.792244 + 0.0220477i
\(722\) −0.666143 + 2.48608i −0.0247913 + 0.0925223i
\(723\) 0 0
\(724\) 8.12223 4.68937i 0.301860 0.174279i
\(725\) 9.00151 + 5.19702i 0.334308 + 0.193013i
\(726\) 0 0
\(727\) −27.7907 −1.03070 −0.515350 0.856980i \(-0.672338\pi\)
−0.515350 + 0.856980i \(0.672338\pi\)
\(728\) −24.2048 0.491930i −0.897091 0.0182321i
\(729\) 0 0
\(730\) 2.59809 + 9.69621i 0.0961597 + 0.358873i
\(731\) 8.66846 + 5.00474i 0.320615 + 0.185107i
\(732\) 0 0
\(733\) 5.10977 + 5.10977i 0.188734 + 0.188734i 0.795149 0.606415i \(-0.207393\pi\)
−0.606415 + 0.795149i \(0.707393\pi\)
\(734\) 5.34406 19.9443i 0.197253 0.736158i
\(735\) 0 0
\(736\) 18.0379 + 18.0379i 0.664887 + 0.664887i
\(737\) 6.50513 + 11.2672i 0.239620 + 0.415034i
\(738\) 0 0
\(739\) 0.0573095 0.0153560i 0.00210816 0.000564880i −0.257765 0.966208i \(-0.582986\pi\)
0.259873 + 0.965643i \(0.416319\pi\)
\(740\) −9.43582 −0.346868
\(741\) 0 0
\(742\) −1.59972 6.71186i −0.0587276 0.246400i
\(743\) −9.83505 36.7049i −0.360813 1.34657i −0.873009 0.487704i \(-0.837835\pi\)
0.512196 0.858868i \(-0.328832\pi\)
\(744\) 0 0
\(745\) −12.5072 21.6631i −0.458228 0.793675i
\(746\) −13.4395 + 13.4395i −0.492056 + 0.492056i
\(747\) 0 0
\(748\) 4.04760 + 1.08455i 0.147995 + 0.0396551i
\(749\) 15.2225 24.7495i 0.556218 0.904328i
\(750\) 0 0
\(751\) −9.18336 5.30202i −0.335106 0.193473i 0.323000 0.946399i \(-0.395309\pi\)
−0.658106 + 0.752926i \(0.728642\pi\)
\(752\) 1.43946 + 5.37214i 0.0524917 + 0.195902i
\(753\) 0 0
\(754\) −12.0952 + 7.10468i −0.440482 + 0.258737i
\(755\) 41.4441i 1.50831i
\(756\) 0 0
\(757\) −7.44655 + 12.8978i −0.270649 + 0.468778i −0.969028 0.246950i \(-0.920572\pi\)
0.698379 + 0.715728i \(0.253905\pi\)
\(758\) 20.6285 11.9099i 0.749263 0.432587i
\(759\) 0 0
\(760\) −16.8266 4.50866i −0.610364 0.163546i
\(761\) 44.9797 + 12.0523i 1.63051 + 0.436895i 0.954066 0.299595i \(-0.0968517\pi\)
0.676448 + 0.736490i \(0.263518\pi\)
\(762\) 0 0
\(763\) 5.81443 5.49957i 0.210497 0.199098i
\(764\) −6.02297 3.47737i −0.217904 0.125807i
\(765\) 0 0
\(766\) 4.04688 0.146220
\(767\) −28.6337 + 16.8193i −1.03390 + 0.607311i
\(768\) 0 0
\(769\) −6.79488 + 1.82068i −0.245030 + 0.0656555i −0.379244 0.925297i \(-0.623816\pi\)
0.134214 + 0.990952i \(0.457149\pi\)
\(770\) 3.18949 10.7030i 0.114941 0.385708i
\(771\) 0 0
\(772\) −9.75223 + 9.75223i −0.350990 + 0.350990i
\(773\) −2.05344 + 7.66353i −0.0738570 + 0.275638i −0.992972 0.118352i \(-0.962239\pi\)
0.919115 + 0.393990i \(0.128906\pi\)
\(774\) 0 0
\(775\) 0.432232 0.432232i 0.0155262 0.0155262i
\(776\) 6.42581 3.70994i 0.230673 0.133179i
\(777\) 0 0
\(778\) 17.2180 4.61355i 0.617295 0.165404i
\(779\) 7.75482i 0.277845i
\(780\) 0 0
\(781\) −40.8500 −1.46173
\(782\) −2.67449 + 0.716627i −0.0956395 + 0.0256265i
\(783\) 0 0
\(784\) 4.08391 6.24367i 0.145854 0.222988i
\(785\) 18.9999 18.9999i 0.678134 0.678134i
\(786\) 0 0
\(787\) 1.90514 + 0.510480i 0.0679109 + 0.0181967i 0.292615 0.956230i \(-0.405475\pi\)
−0.224704 + 0.974427i \(0.572141\pi\)
\(788\) −11.6228 11.6228i −0.414046