Properties

Label 819.2.bm.f.550.6
Level $819$
Weight $2$
Character 819.550
Analytic conductor $6.540$
Analytic rank $0$
Dimension $12$
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.bm (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.2346760387617129.1
Defining polynomial: \(x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 550.6
Root \(1.32725 + 0.488273i\) of defining polynomial
Character \(\chi\) \(=\) 819.550
Dual form 819.2.bm.f.478.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.58860i q^{2} -4.70085 q^{4} +(1.39608 - 0.806027i) q^{5} +(1.06153 - 2.42346i) q^{7} -6.99143i q^{8} +O(q^{10})\) \(q+2.58860i q^{2} -4.70085 q^{4} +(1.39608 - 0.806027i) q^{5} +(1.06153 - 2.42346i) q^{7} -6.99143i q^{8} +(2.08648 + 3.61389i) q^{10} +(-2.34256 + 1.35248i) q^{11} +(2.36840 + 2.71858i) q^{13} +(6.27337 + 2.74787i) q^{14} +8.69632 q^{16} +3.12661 q^{17} +(3.18828 + 1.84075i) q^{19} +(-6.56276 + 3.78901i) q^{20} +(-3.50103 - 6.06396i) q^{22} +1.98604 q^{23} +(-1.20064 + 2.07957i) q^{25} +(-7.03732 + 6.13084i) q^{26} +(-4.99008 + 11.3923i) q^{28} +(-2.68636 + 4.65290i) q^{29} +(9.07425 + 5.23902i) q^{31} +8.52843i q^{32} +8.09354i q^{34} +(-0.471400 - 4.23896i) q^{35} +5.95346i q^{37} +(-4.76497 + 8.25317i) q^{38} +(-5.63528 - 9.76059i) q^{40} +(6.66970 + 3.85075i) q^{41} +(-1.67800 - 2.90638i) q^{43} +(11.0120 - 6.35780i) q^{44} +5.14106i q^{46} +(-0.913730 + 0.527542i) q^{47} +(-4.74633 - 5.14513i) q^{49} +(-5.38318 - 3.10798i) q^{50} +(-11.1335 - 12.7796i) q^{52} +(3.63284 - 6.29226i) q^{53} +(-2.18027 + 3.77633i) q^{55} +(-16.9435 - 7.42158i) q^{56} +(-12.0445 - 6.95390i) q^{58} -11.4241i q^{59} +(1.46254 - 2.53319i) q^{61} +(-13.5617 + 23.4896i) q^{62} -4.68406 q^{64} +(5.49772 + 1.88636i) q^{65} +(11.7622 - 6.79091i) q^{67} -14.6977 q^{68} +(10.9730 - 1.22027i) q^{70} +(-1.17009 + 0.675554i) q^{71} +(-7.88374 - 4.55168i) q^{73} -15.4111 q^{74} +(-14.9876 - 8.65311i) q^{76} +(0.790989 + 7.11280i) q^{77} +(3.10289 + 5.37436i) q^{79} +(12.1407 - 7.00946i) q^{80} +(-9.96806 + 17.2652i) q^{82} -2.69672i q^{83} +(4.36499 - 2.52013i) q^{85} +(7.52346 - 4.34367i) q^{86} +(9.45576 + 16.3779i) q^{88} -1.75988i q^{89} +(9.10249 - 2.85388i) q^{91} -9.33607 q^{92} +(-1.36560 - 2.36528i) q^{94} +5.93478 q^{95} +(-13.4078 + 7.74102i) q^{97} +(13.3187 - 12.2863i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 8q^{4} + 3q^{5} - 3q^{7} + O(q^{10}) \) \( 12q - 8q^{4} + 3q^{5} - 3q^{7} + 12q^{10} - 12q^{11} - 2q^{13} - 4q^{14} + 16q^{16} + 34q^{17} + 9q^{19} + 3q^{20} - 15q^{22} + 6q^{23} - 5q^{25} + 6q^{26} - 9q^{28} + q^{29} + 18q^{31} + 6q^{35} - 19q^{38} - q^{40} + 6q^{41} + 11q^{43} + 33q^{44} + 15q^{47} - 3q^{49} - 18q^{50} - 7q^{52} + 8q^{53} - 15q^{55} - 27q^{56} - 24q^{58} + 5q^{61} - 41q^{62} + 2q^{64} - 21q^{65} + 15q^{67} - 22q^{68} + 3q^{70} - 30q^{71} + 42q^{73} - 66q^{74} - 45q^{76} + 19q^{77} - 35q^{79} + 63q^{80} + 5q^{82} - 21q^{85} + 57q^{86} - 14q^{88} - 7q^{91} + 66q^{92} + q^{94} + 4q^{95} - 3q^{97} + 18q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.58860i 1.83042i 0.402981 + 0.915209i \(0.367974\pi\)
−0.402981 + 0.915209i \(0.632026\pi\)
\(3\) 0 0
\(4\) −4.70085 −2.35043
\(5\) 1.39608 0.806027i 0.624346 0.360466i −0.154213 0.988038i \(-0.549284\pi\)
0.778559 + 0.627571i \(0.215951\pi\)
\(6\) 0 0
\(7\) 1.06153 2.42346i 0.401219 0.915982i
\(8\) 6.99143i 2.47184i
\(9\) 0 0
\(10\) 2.08648 + 3.61389i 0.659803 + 1.14281i
\(11\) −2.34256 + 1.35248i −0.706309 + 0.407788i −0.809693 0.586854i \(-0.800366\pi\)
0.103384 + 0.994642i \(0.467033\pi\)
\(12\) 0 0
\(13\) 2.36840 + 2.71858i 0.656876 + 0.753998i
\(14\) 6.27337 + 2.74787i 1.67663 + 0.734398i
\(15\) 0 0
\(16\) 8.69632 2.17408
\(17\) 3.12661 0.758314 0.379157 0.925332i \(-0.376214\pi\)
0.379157 + 0.925332i \(0.376214\pi\)
\(18\) 0 0
\(19\) 3.18828 + 1.84075i 0.731441 + 0.422297i 0.818949 0.573866i \(-0.194557\pi\)
−0.0875083 + 0.996164i \(0.527890\pi\)
\(20\) −6.56276 + 3.78901i −1.46748 + 0.847249i
\(21\) 0 0
\(22\) −3.50103 6.06396i −0.746421 1.29284i
\(23\) 1.98604 0.414117 0.207059 0.978329i \(-0.433611\pi\)
0.207059 + 0.978329i \(0.433611\pi\)
\(24\) 0 0
\(25\) −1.20064 + 2.07957i −0.240128 + 0.415914i
\(26\) −7.03732 + 6.13084i −1.38013 + 1.20236i
\(27\) 0 0
\(28\) −4.99008 + 11.3923i −0.943036 + 2.15295i
\(29\) −2.68636 + 4.65290i −0.498844 + 0.864023i −0.999999 0.00133469i \(-0.999575\pi\)
0.501155 + 0.865357i \(0.332908\pi\)
\(30\) 0 0
\(31\) 9.07425 + 5.23902i 1.62978 + 0.940956i 0.984156 + 0.177303i \(0.0567372\pi\)
0.645627 + 0.763653i \(0.276596\pi\)
\(32\) 8.52843i 1.50763i
\(33\) 0 0
\(34\) 8.09354i 1.38803i
\(35\) −0.471400 4.23896i −0.0796811 0.716515i
\(36\) 0 0
\(37\) 5.95346i 0.978743i 0.872075 + 0.489371i \(0.162774\pi\)
−0.872075 + 0.489371i \(0.837226\pi\)
\(38\) −4.76497 + 8.25317i −0.772981 + 1.33884i
\(39\) 0 0
\(40\) −5.63528 9.76059i −0.891016 1.54329i
\(41\) 6.66970 + 3.85075i 1.04163 + 0.601386i 0.920295 0.391225i \(-0.127949\pi\)
0.121337 + 0.992611i \(0.461282\pi\)
\(42\) 0 0
\(43\) −1.67800 2.90638i −0.255892 0.443219i 0.709245 0.704962i \(-0.249036\pi\)
−0.965138 + 0.261743i \(0.915703\pi\)
\(44\) 11.0120 6.35780i 1.66013 0.958475i
\(45\) 0 0
\(46\) 5.14106i 0.758008i
\(47\) −0.913730 + 0.527542i −0.133281 + 0.0769500i −0.565158 0.824983i \(-0.691185\pi\)
0.431877 + 0.901933i \(0.357852\pi\)
\(48\) 0 0
\(49\) −4.74633 5.14513i −0.678046 0.735019i
\(50\) −5.38318 3.10798i −0.761297 0.439535i
\(51\) 0 0
\(52\) −11.1335 12.7796i −1.54394 1.77222i
\(53\) 3.63284 6.29226i 0.499009 0.864308i −0.500991 0.865453i \(-0.667031\pi\)
0.999999 + 0.00114437i \(0.000364265\pi\)
\(54\) 0 0
\(55\) −2.18027 + 3.77633i −0.293987 + 0.509201i
\(56\) −16.9435 7.42158i −2.26416 0.991751i
\(57\) 0 0
\(58\) −12.0445 6.95390i −1.58152 0.913092i
\(59\) 11.4241i 1.48729i −0.668577 0.743643i \(-0.733096\pi\)
0.668577 0.743643i \(-0.266904\pi\)
\(60\) 0 0
\(61\) 1.46254 2.53319i 0.187259 0.324341i −0.757077 0.653326i \(-0.773373\pi\)
0.944335 + 0.328985i \(0.106706\pi\)
\(62\) −13.5617 + 23.4896i −1.72234 + 2.98318i
\(63\) 0 0
\(64\) −4.68406 −0.585507
\(65\) 5.49772 + 1.88636i 0.681909 + 0.233974i
\(66\) 0 0
\(67\) 11.7622 6.79091i 1.43698 0.829642i 0.439343 0.898320i \(-0.355211\pi\)
0.997639 + 0.0686778i \(0.0218780\pi\)
\(68\) −14.6977 −1.78236
\(69\) 0 0
\(70\) 10.9730 1.22027i 1.31152 0.145850i
\(71\) −1.17009 + 0.675554i −0.138865 + 0.0801736i −0.567823 0.823151i \(-0.692214\pi\)
0.428958 + 0.903324i \(0.358881\pi\)
\(72\) 0 0
\(73\) −7.88374 4.55168i −0.922721 0.532733i −0.0382192 0.999269i \(-0.512169\pi\)
−0.884502 + 0.466536i \(0.845502\pi\)
\(74\) −15.4111 −1.79151
\(75\) 0 0
\(76\) −14.9876 8.65311i −1.71920 0.992579i
\(77\) 0.790989 + 7.11280i 0.0901416 + 0.810578i
\(78\) 0 0
\(79\) 3.10289 + 5.37436i 0.349102 + 0.604663i 0.986090 0.166211i \(-0.0531532\pi\)
−0.636988 + 0.770874i \(0.719820\pi\)
\(80\) 12.1407 7.00946i 1.35738 0.783682i
\(81\) 0 0
\(82\) −9.96806 + 17.2652i −1.10079 + 1.90662i
\(83\) 2.69672i 0.296003i −0.988987 0.148002i \(-0.952716\pi\)
0.988987 0.148002i \(-0.0472841\pi\)
\(84\) 0 0
\(85\) 4.36499 2.52013i 0.473450 0.273346i
\(86\) 7.52346 4.34367i 0.811275 0.468390i
\(87\) 0 0
\(88\) 9.45576 + 16.3779i 1.00799 + 1.74589i
\(89\) 1.75988i 0.186546i −0.995641 0.0932732i \(-0.970267\pi\)
0.995641 0.0932732i \(-0.0297330\pi\)
\(90\) 0 0
\(91\) 9.10249 2.85388i 0.954200 0.299168i
\(92\) −9.33607 −0.973353
\(93\) 0 0
\(94\) −1.36560 2.36528i −0.140851 0.243960i
\(95\) 5.93478 0.608896
\(96\) 0 0
\(97\) −13.4078 + 7.74102i −1.36136 + 0.785981i −0.989805 0.142430i \(-0.954509\pi\)
−0.371555 + 0.928411i \(0.621175\pi\)
\(98\) 13.3187 12.2863i 1.34539 1.24111i
\(99\) 0 0
\(100\) 5.64404 9.77576i 0.564404 0.977576i
\(101\) 0.639651 + 1.10791i 0.0636477 + 0.110241i 0.896093 0.443866i \(-0.146393\pi\)
−0.832446 + 0.554107i \(0.813060\pi\)
\(102\) 0 0
\(103\) −5.73367 9.93101i −0.564956 0.978532i −0.997054 0.0767054i \(-0.975560\pi\)
0.432098 0.901827i \(-0.357773\pi\)
\(104\) 19.0068 16.5585i 1.86377 1.62370i
\(105\) 0 0
\(106\) 16.2881 + 9.40397i 1.58204 + 0.913394i
\(107\) 5.13525 0.496444 0.248222 0.968703i \(-0.420154\pi\)
0.248222 + 0.968703i \(0.420154\pi\)
\(108\) 0 0
\(109\) 1.49635 + 0.863916i 0.143324 + 0.0827481i 0.569947 0.821681i \(-0.306964\pi\)
−0.426623 + 0.904429i \(0.640297\pi\)
\(110\) −9.77542 5.64384i −0.932050 0.538119i
\(111\) 0 0
\(112\) 9.23136 21.0752i 0.872282 1.99142i
\(113\) −4.29556 7.44014i −0.404093 0.699909i 0.590123 0.807314i \(-0.299079\pi\)
−0.994215 + 0.107404i \(0.965746\pi\)
\(114\) 0 0
\(115\) 2.77267 1.60080i 0.258552 0.149275i
\(116\) 12.6282 21.8726i 1.17250 2.03082i
\(117\) 0 0
\(118\) 29.5723 2.72235
\(119\) 3.31897 7.57721i 0.304250 0.694602i
\(120\) 0 0
\(121\) −1.84160 + 3.18975i −0.167419 + 0.289977i
\(122\) 6.55741 + 3.78592i 0.593680 + 0.342761i
\(123\) 0 0
\(124\) −42.6567 24.6279i −3.83069 2.21165i
\(125\) 11.9313i 1.06716i
\(126\) 0 0
\(127\) −1.56206 + 2.70556i −0.138610 + 0.240080i −0.926971 0.375133i \(-0.877597\pi\)
0.788361 + 0.615214i \(0.210930\pi\)
\(128\) 4.93170i 0.435904i
\(129\) 0 0
\(130\) −4.88303 + 14.2314i −0.428270 + 1.24818i
\(131\) 5.10460 + 8.84142i 0.445991 + 0.772479i 0.998121 0.0612793i \(-0.0195180\pi\)
−0.552130 + 0.833758i \(0.686185\pi\)
\(132\) 0 0
\(133\) 7.84543 5.77266i 0.680285 0.500553i
\(134\) 17.5790 + 30.4476i 1.51859 + 2.63028i
\(135\) 0 0
\(136\) 21.8595i 1.87443i
\(137\) 9.99261i 0.853726i 0.904316 + 0.426863i \(0.140381\pi\)
−0.904316 + 0.426863i \(0.859619\pi\)
\(138\) 0 0
\(139\) 0.832100 + 1.44124i 0.0705778 + 0.122244i 0.899155 0.437631i \(-0.144182\pi\)
−0.828577 + 0.559875i \(0.810849\pi\)
\(140\) 2.21598 + 19.9267i 0.187285 + 1.68412i
\(141\) 0 0
\(142\) −1.74874 3.02891i −0.146751 0.254180i
\(143\) −9.22495 3.16523i −0.771429 0.264690i
\(144\) 0 0
\(145\) 8.66110i 0.719265i
\(146\) 11.7825 20.4078i 0.975124 1.68897i
\(147\) 0 0
\(148\) 27.9863i 2.30046i
\(149\) −17.1456 9.89902i −1.40462 0.810959i −0.409760 0.912193i \(-0.634387\pi\)
−0.994863 + 0.101234i \(0.967721\pi\)
\(150\) 0 0
\(151\) −6.52544 3.76746i −0.531033 0.306592i 0.210404 0.977614i \(-0.432522\pi\)
−0.741437 + 0.671023i \(0.765855\pi\)
\(152\) 12.8695 22.2906i 1.04385 1.80801i
\(153\) 0 0
\(154\) −18.4122 + 2.04755i −1.48370 + 0.164997i
\(155\) 16.8912 1.35673
\(156\) 0 0
\(157\) −7.00223 + 12.1282i −0.558839 + 0.967938i 0.438755 + 0.898607i \(0.355420\pi\)
−0.997594 + 0.0693309i \(0.977914\pi\)
\(158\) −13.9121 + 8.03214i −1.10679 + 0.639003i
\(159\) 0 0
\(160\) 6.87414 + 11.9064i 0.543448 + 0.941280i
\(161\) 2.10823 4.81308i 0.166152 0.379324i
\(162\) 0 0
\(163\) 6.20936 + 3.58498i 0.486355 + 0.280797i 0.723061 0.690784i \(-0.242735\pi\)
−0.236706 + 0.971581i \(0.576068\pi\)
\(164\) −31.3533 18.1018i −2.44828 1.41351i
\(165\) 0 0
\(166\) 6.98072 0.541809
\(167\) −15.5716 8.99027i −1.20497 0.695688i −0.243312 0.969948i \(-0.578234\pi\)
−0.961656 + 0.274260i \(0.911567\pi\)
\(168\) 0 0
\(169\) −1.78135 + 12.8774i −0.137027 + 0.990567i
\(170\) 6.52361 + 11.2992i 0.500338 + 0.866611i
\(171\) 0 0
\(172\) 7.88803 + 13.6625i 0.601456 + 1.04175i
\(173\) 6.40579 11.0952i 0.487023 0.843549i −0.512865 0.858469i \(-0.671416\pi\)
0.999889 + 0.0149198i \(0.00474930\pi\)
\(174\) 0 0
\(175\) 3.76525 + 5.11723i 0.284626 + 0.386826i
\(176\) −20.3717 + 11.7616i −1.53557 + 0.886562i
\(177\) 0 0
\(178\) 4.55561 0.341458
\(179\) −0.920110 1.59368i −0.0687723 0.119117i 0.829589 0.558375i \(-0.188575\pi\)
−0.898361 + 0.439258i \(0.855242\pi\)
\(180\) 0 0
\(181\) −3.29928 −0.245234 −0.122617 0.992454i \(-0.539129\pi\)
−0.122617 + 0.992454i \(0.539129\pi\)
\(182\) 7.38757 + 23.5627i 0.547603 + 1.74658i
\(183\) 0 0
\(184\) 13.8852i 1.02363i
\(185\) 4.79865 + 8.31150i 0.352804 + 0.611074i
\(186\) 0 0
\(187\) −7.32427 + 4.22867i −0.535604 + 0.309231i
\(188\) 4.29531 2.47990i 0.313268 0.180865i
\(189\) 0 0
\(190\) 15.3628i 1.11453i
\(191\) 2.44807 4.24018i 0.177136 0.306809i −0.763762 0.645498i \(-0.776650\pi\)
0.940898 + 0.338689i \(0.109983\pi\)
\(192\) 0 0
\(193\) 2.61462 1.50955i 0.188204 0.108660i −0.402937 0.915228i \(-0.632011\pi\)
0.591142 + 0.806568i \(0.298677\pi\)
\(194\) −20.0384 34.7075i −1.43867 2.49186i
\(195\) 0 0
\(196\) 22.3118 + 24.1865i 1.59370 + 1.72761i
\(197\) −4.02694 2.32496i −0.286908 0.165646i 0.349639 0.936885i \(-0.386304\pi\)
−0.636546 + 0.771238i \(0.719638\pi\)
\(198\) 0 0
\(199\) −0.410721 −0.0291152 −0.0145576 0.999894i \(-0.504634\pi\)
−0.0145576 + 0.999894i \(0.504634\pi\)
\(200\) 14.5392 + 8.39420i 1.02808 + 0.593560i
\(201\) 0 0
\(202\) −2.86793 + 1.65580i −0.201787 + 0.116502i
\(203\) 8.42450 + 11.4495i 0.591284 + 0.803594i
\(204\) 0 0
\(205\) 12.4152 0.867118
\(206\) 25.7074 14.8422i 1.79112 1.03410i
\(207\) 0 0
\(208\) 20.5964 + 23.6416i 1.42810 + 1.63925i
\(209\) −9.95831 −0.688831
\(210\) 0 0
\(211\) 3.75800 6.50905i 0.258711 0.448101i −0.707186 0.707028i \(-0.750035\pi\)
0.965897 + 0.258927i \(0.0833688\pi\)
\(212\) −17.0774 + 29.5790i −1.17288 + 2.03149i
\(213\) 0 0
\(214\) 13.2931i 0.908699i
\(215\) −4.68524 2.70502i −0.319531 0.184481i
\(216\) 0 0
\(217\) 22.3291 16.4297i 1.51580 1.11532i
\(218\) −2.23633 + 3.87344i −0.151464 + 0.262343i
\(219\) 0 0
\(220\) 10.2491 17.7520i 0.690996 1.19684i
\(221\) 7.40506 + 8.49993i 0.498118 + 0.571767i
\(222\) 0 0
\(223\) −19.5544 11.2897i −1.30946 0.756016i −0.327452 0.944868i \(-0.606190\pi\)
−0.982006 + 0.188852i \(0.939523\pi\)
\(224\) 20.6683 + 9.05315i 1.38096 + 0.604889i
\(225\) 0 0
\(226\) 19.2595 11.1195i 1.28113 0.739658i
\(227\) 13.6717i 0.907424i 0.891148 + 0.453712i \(0.149901\pi\)
−0.891148 + 0.453712i \(0.850099\pi\)
\(228\) 0 0
\(229\) 6.86832 3.96543i 0.453872 0.262043i −0.255592 0.966785i \(-0.582270\pi\)
0.709464 + 0.704742i \(0.248937\pi\)
\(230\) 4.14383 + 7.17733i 0.273236 + 0.473259i
\(231\) 0 0
\(232\) 32.5305 + 18.7815i 2.13573 + 1.23306i
\(233\) 3.28585 + 5.69127i 0.215263 + 0.372847i 0.953354 0.301854i \(-0.0976056\pi\)
−0.738091 + 0.674702i \(0.764272\pi\)
\(234\) 0 0
\(235\) −0.850427 + 1.47298i −0.0554757 + 0.0960868i
\(236\) 53.7028i 3.49576i
\(237\) 0 0
\(238\) 19.6144 + 8.59150i 1.27141 + 0.556904i
\(239\) 9.39284i 0.607572i −0.952740 0.303786i \(-0.901749\pi\)
0.952740 0.303786i \(-0.0982508\pi\)
\(240\) 0 0
\(241\) 10.0858i 0.649686i −0.945768 0.324843i \(-0.894689\pi\)
0.945768 0.324843i \(-0.105311\pi\)
\(242\) −8.25699 4.76718i −0.530780 0.306446i
\(243\) 0 0
\(244\) −6.87517 + 11.9081i −0.440137 + 0.762340i
\(245\) −10.7734 3.35735i −0.688285 0.214493i
\(246\) 0 0
\(247\) 2.54689 + 13.0272i 0.162054 + 0.828902i
\(248\) 36.6282 63.4420i 2.32590 4.02857i
\(249\) 0 0
\(250\) −30.8853 −1.95336
\(251\) 5.17427 + 8.96209i 0.326597 + 0.565682i 0.981834 0.189741i \(-0.0607648\pi\)
−0.655237 + 0.755423i \(0.727431\pi\)
\(252\) 0 0
\(253\) −4.65242 + 2.68607i −0.292495 + 0.168872i
\(254\) −7.00363 4.04355i −0.439447 0.253715i
\(255\) 0 0
\(256\) −22.1343 −1.38339
\(257\) 7.98658 0.498189 0.249095 0.968479i \(-0.419867\pi\)
0.249095 + 0.968479i \(0.419867\pi\)
\(258\) 0 0
\(259\) 14.4280 + 6.31975i 0.896511 + 0.392690i
\(260\) −25.8440 8.86749i −1.60278 0.549939i
\(261\) 0 0
\(262\) −22.8869 + 13.2138i −1.41396 + 0.816349i
\(263\) 2.52967 + 4.38152i 0.155986 + 0.270176i 0.933418 0.358792i \(-0.116811\pi\)
−0.777431 + 0.628968i \(0.783478\pi\)
\(264\) 0 0
\(265\) 11.7127i 0.719503i
\(266\) 14.9431 + 20.3087i 0.916220 + 1.24521i
\(267\) 0 0
\(268\) −55.2924 + 31.9231i −3.37752 + 1.95001i
\(269\) −13.8902 −0.846902 −0.423451 0.905919i \(-0.639181\pi\)
−0.423451 + 0.905919i \(0.639181\pi\)
\(270\) 0 0
\(271\) 8.32721i 0.505842i −0.967487 0.252921i \(-0.918609\pi\)
0.967487 0.252921i \(-0.0813913\pi\)
\(272\) 27.1900 1.64863
\(273\) 0 0
\(274\) −25.8669 −1.56267
\(275\) 6.49537i 0.391685i
\(276\) 0 0
\(277\) 23.2116 1.39465 0.697325 0.716755i \(-0.254374\pi\)
0.697325 + 0.716755i \(0.254374\pi\)
\(278\) −3.73080 + 2.15398i −0.223758 + 0.129187i
\(279\) 0 0
\(280\) −29.6364 + 3.29576i −1.77111 + 0.196959i
\(281\) 27.1595i 1.62020i −0.586292 0.810100i \(-0.699413\pi\)
0.586292 0.810100i \(-0.300587\pi\)
\(282\) 0 0
\(283\) −8.07563 13.9874i −0.480046 0.831464i 0.519692 0.854354i \(-0.326047\pi\)
−0.999738 + 0.0228894i \(0.992713\pi\)
\(284\) 5.50044 3.17568i 0.326391 0.188442i
\(285\) 0 0
\(286\) 8.19351 23.8797i 0.484493 1.41204i
\(287\) 16.4122 12.0761i 0.968782 0.712828i
\(288\) 0 0
\(289\) −7.22433 −0.424960
\(290\) −22.4201 −1.31656
\(291\) 0 0
\(292\) 37.0603 + 21.3968i 2.16879 + 1.25215i
\(293\) 12.6831 7.32260i 0.740956 0.427791i −0.0814609 0.996677i \(-0.525959\pi\)
0.822417 + 0.568885i \(0.192625\pi\)
\(294\) 0 0
\(295\) −9.20810 15.9489i −0.536116 0.928580i
\(296\) 41.6232 2.41930
\(297\) 0 0
\(298\) 25.6246 44.3831i 1.48439 2.57104i
\(299\) 4.70373 + 5.39920i 0.272024 + 0.312244i
\(300\) 0 0
\(301\) −8.82474 + 0.981368i −0.508649 + 0.0565651i
\(302\) 9.75246 16.8918i 0.561191 0.972011i
\(303\) 0 0
\(304\) 27.7263 + 16.0078i 1.59021 + 0.918108i
\(305\) 4.71537i 0.270001i
\(306\) 0 0
\(307\) 8.97844i 0.512427i −0.966620 0.256213i \(-0.917525\pi\)
0.966620 0.256213i \(-0.0824750\pi\)
\(308\) −3.71832 33.4362i −0.211871 1.90521i
\(309\) 0 0
\(310\) 43.7245i 2.48338i
\(311\) −6.09080 + 10.5496i −0.345378 + 0.598212i −0.985422 0.170126i \(-0.945583\pi\)
0.640045 + 0.768338i \(0.278916\pi\)
\(312\) 0 0
\(313\) −6.56198 11.3657i −0.370905 0.642427i 0.618800 0.785549i \(-0.287619\pi\)
−0.989705 + 0.143122i \(0.954286\pi\)
\(314\) −31.3951 18.1260i −1.77173 1.02291i
\(315\) 0 0
\(316\) −14.5862 25.2641i −0.820540 1.42122i
\(317\) −14.4761 + 8.35775i −0.813056 + 0.469418i −0.848016 0.529971i \(-0.822203\pi\)
0.0349599 + 0.999389i \(0.488870\pi\)
\(318\) 0 0
\(319\) 14.5330i 0.813689i
\(320\) −6.53932 + 3.77548i −0.365559 + 0.211056i
\(321\) 0 0
\(322\) 12.4592 + 5.45737i 0.694321 + 0.304127i
\(323\) 9.96849 + 5.75531i 0.554661 + 0.320234i
\(324\) 0 0
\(325\) −8.49708 + 1.66122i −0.471333 + 0.0921480i
\(326\) −9.28007 + 16.0736i −0.513976 + 0.890232i
\(327\) 0 0
\(328\) 26.9223 46.6307i 1.48653 2.57475i
\(329\) 0.308530 + 2.77439i 0.0170098 + 0.152957i
\(330\) 0 0
\(331\) −3.43522 1.98332i −0.188817 0.109013i 0.402612 0.915371i \(-0.368102\pi\)
−0.591428 + 0.806357i \(0.701436\pi\)
\(332\) 12.6769i 0.695733i
\(333\) 0 0
\(334\) 23.2722 40.3087i 1.27340 2.20559i
\(335\) 10.9473 18.9613i 0.598116 1.03597i
\(336\) 0 0
\(337\) −13.7032 −0.746461 −0.373230 0.927739i \(-0.621750\pi\)
−0.373230 + 0.927739i \(0.621750\pi\)
\(338\) −33.3344 4.61121i −1.81315 0.250817i
\(339\) 0 0
\(340\) −20.5192 + 11.8468i −1.11281 + 0.642481i
\(341\) −28.3426 −1.53484
\(342\) 0 0
\(343\) −17.5074 + 6.04084i −0.945309 + 0.326175i
\(344\) −20.3197 + 11.7316i −1.09557 + 0.632526i
\(345\) 0 0
\(346\) 28.7209 + 16.5820i 1.54405 + 0.891456i
\(347\) 26.3979 1.41711 0.708556 0.705655i \(-0.249347\pi\)
0.708556 + 0.705655i \(0.249347\pi\)
\(348\) 0 0
\(349\) −4.23507 2.44512i −0.226698 0.130884i 0.382350 0.924018i \(-0.375115\pi\)
−0.609048 + 0.793133i \(0.708448\pi\)
\(350\) −13.2465 + 9.74673i −0.708053 + 0.520984i
\(351\) 0 0
\(352\) −11.5345 19.9784i −0.614792 1.06485i
\(353\) 11.7413 6.77886i 0.624928 0.360802i −0.153857 0.988093i \(-0.549170\pi\)
0.778785 + 0.627291i \(0.215836\pi\)
\(354\) 0 0
\(355\) −1.08903 + 1.88626i −0.0577997 + 0.100112i
\(356\) 8.27291i 0.438464i
\(357\) 0 0
\(358\) 4.12540 2.38180i 0.218034 0.125882i
\(359\) −7.43541 + 4.29284i −0.392426 + 0.226567i −0.683211 0.730221i \(-0.739417\pi\)
0.290785 + 0.956789i \(0.406084\pi\)
\(360\) 0 0
\(361\) −2.72326 4.71683i −0.143330 0.248254i
\(362\) 8.54053i 0.448880i
\(363\) 0 0
\(364\) −42.7895 + 13.4157i −2.24278 + 0.703173i
\(365\) −14.6751 −0.768130
\(366\) 0 0
\(367\) 0.831612 + 1.44039i 0.0434098 + 0.0751880i 0.886914 0.461935i \(-0.152845\pi\)
−0.843504 + 0.537123i \(0.819511\pi\)
\(368\) 17.2712 0.900324
\(369\) 0 0
\(370\) −21.5152 + 12.4218i −1.11852 + 0.645778i
\(371\) −11.3927 15.4834i −0.591479 0.803860i
\(372\) 0 0
\(373\) −6.98174 + 12.0927i −0.361501 + 0.626138i −0.988208 0.153117i \(-0.951069\pi\)
0.626707 + 0.779255i \(0.284402\pi\)
\(374\) −10.9463 18.9596i −0.566022 0.980378i
\(375\) 0 0
\(376\) 3.68828 + 6.38828i 0.190208 + 0.329450i
\(377\) −19.0117 + 3.71687i −0.979150 + 0.191429i
\(378\) 0 0
\(379\) −27.3454 15.7879i −1.40464 0.810969i −0.409775 0.912187i \(-0.634393\pi\)
−0.994864 + 0.101218i \(0.967726\pi\)
\(380\) −27.8985 −1.43116
\(381\) 0 0
\(382\) 10.9761 + 6.33707i 0.561588 + 0.324233i
\(383\) 27.6333 + 15.9541i 1.41200 + 0.815217i 0.995576 0.0939554i \(-0.0299511\pi\)
0.416420 + 0.909172i \(0.363284\pi\)
\(384\) 0 0
\(385\) 6.83739 + 9.29247i 0.348466 + 0.473588i
\(386\) 3.90762 + 6.76820i 0.198893 + 0.344492i
\(387\) 0 0
\(388\) 63.0283 36.3894i 3.19978 1.84739i
\(389\) 12.7075 22.0100i 0.644296 1.11595i −0.340168 0.940365i \(-0.610484\pi\)
0.984464 0.175589i \(-0.0561829\pi\)
\(390\) 0 0
\(391\) 6.20956 0.314031
\(392\) −35.9718 + 33.1836i −1.81685 + 1.67603i
\(393\) 0 0
\(394\) 6.01838 10.4241i 0.303202 0.525161i
\(395\) 8.66376 + 5.00203i 0.435921 + 0.251679i
\(396\) 0 0
\(397\) −3.60178 2.07949i −0.180768 0.104366i 0.406885 0.913479i \(-0.366615\pi\)
−0.587653 + 0.809113i \(0.699948\pi\)
\(398\) 1.06319i 0.0532930i
\(399\) 0 0
\(400\) −10.4412 + 18.0846i −0.522058 + 0.904231i
\(401\) 19.6013i 0.978844i 0.872047 + 0.489422i \(0.162792\pi\)
−0.872047 + 0.489422i \(0.837208\pi\)
\(402\) 0 0
\(403\) 7.24877 + 37.0772i 0.361087 + 1.84695i
\(404\) −3.00691 5.20811i −0.149599 0.259113i
\(405\) 0 0
\(406\) −29.6381 + 21.8077i −1.47091 + 1.08230i
\(407\) −8.05193 13.9463i −0.399119 0.691295i
\(408\) 0 0
\(409\) 17.6337i 0.871930i 0.899964 + 0.435965i \(0.143593\pi\)
−0.899964 + 0.435965i \(0.856407\pi\)
\(410\) 32.1381i 1.58719i
\(411\) 0 0
\(412\) 26.9532 + 46.6842i 1.32789 + 2.29997i
\(413\) −27.6858 12.1269i −1.36233 0.596727i
\(414\) 0 0
\(415\) −2.17363 3.76483i −0.106699 0.184808i
\(416\) −23.1852 + 20.1987i −1.13675 + 0.990324i
\(417\) 0 0
\(418\) 25.7781i 1.26085i
\(419\) 14.9455 25.8864i 0.730137 1.26463i −0.226688 0.973968i \(-0.572790\pi\)
0.956824 0.290666i \(-0.0938770\pi\)
\(420\) 0 0
\(421\) 12.8528i 0.626407i 0.949686 + 0.313203i \(0.101402\pi\)
−0.949686 + 0.313203i \(0.898598\pi\)
\(422\) 16.8493 + 9.72796i 0.820212 + 0.473550i
\(423\) 0 0
\(424\) −43.9919 25.3987i −2.13644 1.23347i
\(425\) −3.75393 + 6.50200i −0.182093 + 0.315394i
\(426\) 0 0
\(427\) −4.58656 6.23344i −0.221959 0.301657i
\(428\) −24.1401 −1.16685
\(429\) 0 0
\(430\) 7.00223 12.1282i 0.337677 0.584874i
\(431\) −7.76876 + 4.48530i −0.374208 + 0.216049i −0.675295 0.737547i \(-0.735984\pi\)
0.301087 + 0.953597i \(0.402650\pi\)
\(432\) 0 0
\(433\) −1.72531 2.98833i −0.0829132 0.143610i 0.821587 0.570083i \(-0.193089\pi\)
−0.904500 + 0.426473i \(0.859756\pi\)
\(434\) 42.5300 + 57.8012i 2.04151 + 2.77454i
\(435\) 0 0
\(436\) −7.03410 4.06114i −0.336872 0.194493i
\(437\) 6.33204 + 3.65580i 0.302902 + 0.174881i
\(438\) 0 0
\(439\) 38.5144 1.83819 0.919096 0.394034i \(-0.128921\pi\)
0.919096 + 0.394034i \(0.128921\pi\)
\(440\) 26.4020 + 15.2432i 1.25867 + 0.726691i
\(441\) 0 0
\(442\) −22.0029 + 19.1687i −1.04657 + 0.911764i
\(443\) −7.51997 13.0250i −0.357284 0.618835i 0.630222 0.776415i \(-0.282964\pi\)
−0.987506 + 0.157580i \(0.949631\pi\)
\(444\) 0 0
\(445\) −1.41851 2.45693i −0.0672437 0.116469i
\(446\) 29.2246 50.6185i 1.38382 2.39685i
\(447\) 0 0
\(448\) −4.97225 + 11.3516i −0.234917 + 0.536314i
\(449\) −33.7087 + 19.4617i −1.59081 + 0.918456i −0.597646 + 0.801760i \(0.703897\pi\)
−0.993168 + 0.116696i \(0.962770\pi\)
\(450\) 0 0
\(451\) −20.8322 −0.980952
\(452\) 20.1928 + 34.9750i 0.949790 + 1.64509i
\(453\) 0 0
\(454\) −35.3906 −1.66097
\(455\) 10.4075 11.3211i 0.487911 0.530741i
\(456\) 0 0
\(457\) 13.9396i 0.652069i −0.945358 0.326034i \(-0.894287\pi\)
0.945358 0.326034i \(-0.105713\pi\)
\(458\) 10.2649 + 17.7793i 0.479648 + 0.830774i
\(459\) 0 0
\(460\) −13.0339 + 7.52512i −0.607709 + 0.350861i
\(461\) −32.4443 + 18.7317i −1.51108 + 0.872424i −0.511167 + 0.859481i \(0.670787\pi\)
−0.999916 + 0.0129430i \(0.995880\pi\)
\(462\) 0 0
\(463\) 6.75275i 0.313827i −0.987612 0.156913i \(-0.949846\pi\)
0.987612 0.156913i \(-0.0501544\pi\)
\(464\) −23.3614 + 40.4631i −1.08453 + 1.87845i
\(465\) 0 0
\(466\) −14.7324 + 8.50576i −0.682466 + 0.394022i
\(467\) −2.52516 4.37371i −0.116851 0.202391i 0.801667 0.597770i \(-0.203947\pi\)
−0.918518 + 0.395379i \(0.870613\pi\)
\(468\) 0 0
\(469\) −3.97162 35.7140i −0.183393 1.64912i
\(470\) −3.81296 2.20141i −0.175879 0.101544i
\(471\) 0 0
\(472\) −79.8705 −3.67634
\(473\) 7.86163 + 4.53892i 0.361478 + 0.208700i
\(474\) 0 0
\(475\) −7.65595 + 4.42017i −0.351279 + 0.202811i
\(476\) −15.6020 + 35.6194i −0.715117 + 1.63261i
\(477\) 0 0
\(478\) 24.3143 1.11211
\(479\) −8.18670 + 4.72659i −0.374060 + 0.215964i −0.675231 0.737607i \(-0.735956\pi\)
0.301171 + 0.953570i \(0.402623\pi\)
\(480\) 0 0
\(481\) −16.1850 + 14.1002i −0.737971 + 0.642913i
\(482\) 26.1082 1.18920
\(483\) 0 0
\(484\) 8.65711 14.9946i 0.393505 0.681571i
\(485\) −12.4789 + 21.6142i −0.566639 + 0.981448i
\(486\) 0 0
\(487\) 39.9996i 1.81255i −0.422684 0.906277i \(-0.638912\pi\)
0.422684 0.906277i \(-0.361088\pi\)
\(488\) −17.7106 10.2252i −0.801721 0.462874i
\(489\) 0 0
\(490\) 8.69084 27.8879i 0.392612 1.25985i
\(491\) 3.38049 5.85517i 0.152559 0.264240i −0.779608 0.626267i \(-0.784582\pi\)
0.932168 + 0.362027i \(0.117915\pi\)
\(492\) 0 0
\(493\) −8.39918 + 14.5478i −0.378280 + 0.655200i
\(494\) −33.7223 + 6.59287i −1.51724 + 0.296627i
\(495\) 0 0
\(496\) 78.9125 + 45.5602i 3.54328 + 2.04571i
\(497\) 0.395094 + 3.55280i 0.0177224 + 0.159365i
\(498\) 0 0
\(499\) −9.83591 + 5.67877i −0.440316 + 0.254217i −0.703732 0.710466i \(-0.748484\pi\)
0.263416 + 0.964682i \(0.415151\pi\)
\(500\) 56.0871i 2.50829i
\(501\) 0 0
\(502\) −23.1993 + 13.3941i −1.03543 + 0.597808i
\(503\) −6.96423 12.0624i −0.310520 0.537836i 0.667955 0.744202i \(-0.267170\pi\)
−0.978475 + 0.206365i \(0.933836\pi\)
\(504\) 0 0
\(505\) 1.78601 + 1.03115i 0.0794763 + 0.0458857i
\(506\) −6.95317 12.0432i −0.309106 0.535388i
\(507\) 0 0
\(508\) 7.34301 12.7185i 0.325793 0.564290i
\(509\) 19.8149i 0.878281i −0.898418 0.439141i \(-0.855283\pi\)
0.898418 0.439141i \(-0.144717\pi\)
\(510\) 0 0
\(511\) −19.3996 + 14.2742i −0.858188 + 0.631453i
\(512\) 47.4335i 2.09628i
\(513\) 0 0
\(514\) 20.6741i 0.911894i
\(515\) −16.0093 9.24299i −0.705455 0.407295i
\(516\) 0 0
\(517\) 1.42698 2.47160i 0.0627585 0.108701i
\(518\) −16.3593 + 37.3483i −0.718787 + 1.64099i
\(519\) 0 0
\(520\) 13.1883 38.4370i 0.578347 1.68557i
\(521\) −15.5476 + 26.9292i −0.681151 + 1.17979i 0.293479 + 0.955966i \(0.405187\pi\)
−0.974630 + 0.223823i \(0.928146\pi\)
\(522\) 0 0
\(523\) 22.7202 0.993485 0.496742 0.867898i \(-0.334529\pi\)
0.496742 + 0.867898i \(0.334529\pi\)
\(524\) −23.9960 41.5622i −1.04827 1.81565i
\(525\) 0 0
\(526\) −11.3420 + 6.54831i −0.494535 + 0.285520i
\(527\) 28.3716 + 16.3804i 1.23589 + 0.713540i
\(528\) 0 0
\(529\) −19.0557 −0.828507
\(530\) 30.3194 1.31699
\(531\) 0 0
\(532\) −36.8802 + 27.1364i −1.59896 + 1.17651i
\(533\) 5.32794 + 27.2522i 0.230779 + 1.18043i
\(534\) 0 0
\(535\) 7.16922 4.13915i 0.309952 0.178951i
\(536\) −47.4782 82.2346i −2.05074 3.55199i
\(537\) 0 0
\(538\) 35.9563i 1.55018i
\(539\) 18.0772 + 5.63349i 0.778642 + 0.242651i
\(540\) 0 0
\(541\) 1.81754 1.04936i 0.0781423 0.0451155i −0.460420 0.887701i \(-0.652301\pi\)
0.538562 + 0.842586i \(0.318968\pi\)
\(542\) 21.5558 0.925902
\(543\) 0 0
\(544\) 26.6650i 1.14325i
\(545\) 2.78536 0.119312
\(546\) 0 0
\(547\) 25.3770 1.08504 0.542521 0.840042i \(-0.317470\pi\)
0.542521 + 0.840042i \(0.317470\pi\)
\(548\) 46.9738i 2.00662i
\(549\) 0 0
\(550\) 16.8139 0.716948
\(551\) −17.1297 + 9.88983i −0.729749 + 0.421321i
\(552\) 0 0
\(553\) 16.3184 1.81471i 0.693927 0.0771692i
\(554\) 60.0855i 2.55279i
\(555\) 0 0
\(556\) −3.91158 6.77506i −0.165888 0.287327i
\(557\) 38.3219 22.1252i 1.62375 0.937473i 0.637846 0.770164i \(-0.279826\pi\)
0.985904 0.167309i \(-0.0535078\pi\)
\(558\) 0 0
\(559\) 3.92705 11.4452i 0.166097 0.484082i
\(560\) −4.09944 36.8634i −0.173233 1.55776i
\(561\) 0 0
\(562\) 70.3051 2.96564
\(563\) −38.8907 −1.63905 −0.819523 0.573046i \(-0.805762\pi\)
−0.819523 + 0.573046i \(0.805762\pi\)
\(564\) 0 0
\(565\) −11.9939 6.92468i −0.504587 0.291324i
\(566\) 36.2078 20.9046i 1.52193 0.878685i
\(567\) 0 0
\(568\) 4.72309 + 8.18063i 0.198177 + 0.343252i
\(569\) 46.1579 1.93504 0.967520 0.252796i \(-0.0813500\pi\)
0.967520 + 0.252796i \(0.0813500\pi\)
\(570\) 0 0
\(571\) 10.5684 18.3050i 0.442274 0.766041i −0.555584 0.831461i \(-0.687505\pi\)
0.997858 + 0.0654194i \(0.0208385\pi\)
\(572\) 43.3651 + 14.8793i 1.81319 + 0.622134i
\(573\) 0 0
\(574\) 31.2601 + 42.4846i 1.30477 + 1.77327i
\(575\) −2.38452 + 4.13011i −0.0994413 + 0.172237i
\(576\) 0 0
\(577\) 21.9368 + 12.6652i 0.913239 + 0.527259i 0.881472 0.472237i \(-0.156553\pi\)
0.0317671 + 0.999495i \(0.489887\pi\)
\(578\) 18.7009i 0.777855i
\(579\) 0 0
\(580\) 40.7146i 1.69058i
\(581\) −6.53539 2.86263i −0.271133 0.118762i
\(582\) 0 0
\(583\) 19.6533i 0.813958i
\(584\) −31.8227 + 55.1186i −1.31683 + 2.28082i
\(585\) 0 0
\(586\) 18.9553 + 32.8315i 0.783036 + 1.35626i
\(587\) −3.08554 1.78144i −0.127354 0.0735278i 0.434970 0.900445i \(-0.356759\pi\)
−0.562324 + 0.826917i \(0.690092\pi\)
\(588\) 0 0
\(589\) 19.2875 + 33.4069i 0.794727 + 1.37651i
\(590\) 41.2853 23.8361i 1.69969 0.981316i
\(591\) 0 0
\(592\) 51.7732i 2.12786i
\(593\) −21.9568 + 12.6768i −0.901659 + 0.520573i −0.877738 0.479141i \(-0.840948\pi\)
−0.0239212 + 0.999714i \(0.507615\pi\)
\(594\) 0 0
\(595\) −1.47388 13.2536i −0.0604233 0.543343i
\(596\) 80.5990 + 46.5338i 3.30146 + 1.90610i
\(597\) 0 0
\(598\) −13.9764 + 12.1761i −0.571537 + 0.497917i
\(599\) 5.46078 9.45835i 0.223122 0.386458i −0.732633 0.680624i \(-0.761709\pi\)
0.955754 + 0.294166i \(0.0950420\pi\)
\(600\) 0 0
\(601\) −12.1282 + 21.0067i −0.494720 + 0.856880i −0.999981 0.00608649i \(-0.998063\pi\)
0.505262 + 0.862966i \(0.331396\pi\)
\(602\) −2.54037 22.8437i −0.103538 0.931040i
\(603\) 0 0
\(604\) 30.6751 + 17.7103i 1.24815 + 0.720621i
\(605\) 5.93753i 0.241395i
\(606\) 0 0
\(607\) 4.92724 8.53422i 0.199990 0.346393i −0.748535 0.663096i \(-0.769242\pi\)
0.948525 + 0.316702i \(0.102576\pi\)
\(608\) −15.6987 + 27.1910i −0.636667 + 1.10274i
\(609\) 0 0
\(610\) 12.2062 0.494215
\(611\) −3.59825 1.23462i −0.145569 0.0499472i
\(612\) 0 0
\(613\) −3.18428 + 1.83844i −0.128612 + 0.0742540i −0.562926 0.826508i \(-0.690324\pi\)
0.434314 + 0.900762i \(0.356991\pi\)
\(614\) 23.2416 0.937955
\(615\) 0 0
\(616\) 49.7286 5.53015i 2.00362 0.222816i
\(617\) −16.2352 + 9.37341i −0.653605 + 0.377359i −0.789836 0.613318i \(-0.789834\pi\)
0.136231 + 0.990677i \(0.456501\pi\)
\(618\) 0 0
\(619\) 13.7650 + 7.94725i 0.553264 + 0.319427i 0.750437 0.660942i \(-0.229843\pi\)
−0.197174 + 0.980369i \(0.563176\pi\)
\(620\) −79.4029 −3.18890
\(621\) 0 0
\(622\) −27.3086 15.7667i −1.09498 0.632185i
\(623\) −4.26499 1.86815i −0.170873 0.0748460i
\(624\) 0 0
\(625\) 3.61371 + 6.25913i 0.144549 + 0.250365i
\(626\) 29.4212 16.9864i 1.17591 0.678911i
\(627\) 0 0
\(628\) 32.9165 57.0130i 1.31351 2.27507i
\(629\) 18.6141i 0.742194i
\(630\) 0 0
\(631\) −17.0998 + 9.87255i −0.680731 + 0.393020i −0.800130 0.599826i \(-0.795236\pi\)
0.119400 + 0.992846i \(0.461903\pi\)
\(632\) 37.5745 21.6936i 1.49463 0.862927i
\(633\) 0 0
\(634\) −21.6349 37.4727i −0.859231 1.48823i
\(635\) 5.03624i 0.199857i
\(636\) 0 0
\(637\) 2.74625 25.0890i 0.108811 0.994063i
\(638\) 37.6200 1.48939
\(639\) 0 0
\(640\) 3.97508 + 6.88504i 0.157129 + 0.272155i
\(641\) −29.7786 −1.17618 −0.588092 0.808794i \(-0.700121\pi\)
−0.588092 + 0.808794i \(0.700121\pi\)
\(642\) 0 0
\(643\) 10.0220 5.78623i 0.395231 0.228187i −0.289193 0.957271i \(-0.593387\pi\)
0.684424 + 0.729084i \(0.260054\pi\)
\(644\) −9.91048 + 22.6256i −0.390528 + 0.891574i
\(645\) 0 0
\(646\) −14.8982 + 25.8044i −0.586162 + 1.01526i
\(647\) −12.7533 22.0893i −0.501382 0.868420i −0.999999 0.00159698i \(-0.999492\pi\)
0.498616 0.866823i \(-0.333842\pi\)
\(648\) 0 0
\(649\) 15.4508 + 26.7616i 0.606497 + 1.05048i
\(650\) −4.30024 21.9956i −0.168669 0.862737i
\(651\) 0 0
\(652\) −29.1893 16.8524i −1.14314 0.659993i
\(653\) 44.8293 1.75430 0.877152 0.480212i \(-0.159440\pi\)
0.877152 + 0.480212i \(0.159440\pi\)
\(654\) 0 0
\(655\) 14.2529 + 8.22889i 0.556905 + 0.321529i
\(656\) 58.0018 + 33.4874i 2.26459 + 1.30746i
\(657\) 0 0
\(658\) −7.18179 + 0.798661i −0.279975 + 0.0311350i
\(659\) 20.5867 + 35.6572i 0.801944 + 1.38901i 0.918335 + 0.395805i \(0.129534\pi\)
−0.116390 + 0.993204i \(0.537132\pi\)
\(660\) 0 0
\(661\) −18.9606 + 10.9469i −0.737481 + 0.425785i −0.821153 0.570709i \(-0.806669\pi\)
0.0836719 + 0.996493i \(0.473335\pi\)
\(662\) 5.13404 8.89241i 0.199540 0.345613i
\(663\) 0 0
\(664\) −18.8539 −0.731673
\(665\) 6.29993 14.3827i 0.244301 0.557738i
\(666\) 0 0
\(667\) −5.33520 + 9.24084i −0.206580 + 0.357807i
\(668\) 73.1999 + 42.2620i 2.83219 + 1.63516i
\(669\) 0 0
\(670\) 49.0832 + 28.3382i 1.89625 + 1.09480i
\(671\) 7.91219i 0.305447i
\(672\) 0 0
\(673\) 17.8344 30.8901i 0.687466 1.19073i −0.285189 0.958471i \(-0.592056\pi\)
0.972655 0.232254i \(-0.0746102\pi\)
\(674\) 35.4721i 1.36633i
\(675\) 0 0
\(676\) 8.37388 60.5347i 0.322072 2.32826i
\(677\) 1.27766 + 2.21297i 0.0491044 + 0.0850514i 0.889533 0.456871i \(-0.151030\pi\)
−0.840428 + 0.541923i \(0.817697\pi\)
\(678\) 0 0
\(679\) 4.52729 + 40.7107i 0.173741 + 1.56233i
\(680\) −17.6193 30.5175i −0.675670 1.17029i
\(681\) 0 0
\(682\) 73.3678i 2.80940i
\(683\) 35.7399i 1.36755i −0.729693 0.683775i \(-0.760337\pi\)
0.729693 0.683775i \(-0.239663\pi\)
\(684\) 0 0
\(685\) 8.05431 + 13.9505i 0.307739 + 0.533020i
\(686\) −15.6373 45.3196i −0.597036 1.73031i
\(687\) 0 0
\(688\) −14.5924 25.2748i −0.556330 0.963592i
\(689\) 25.7100 5.02643i 0.979474 0.191492i
\(690\) 0 0
\(691\) 26.0292i 0.990197i 0.868837 + 0.495099i \(0.164868\pi\)
−0.868837 + 0.495099i \(0.835132\pi\)
\(692\) −30.1127 + 52.1567i −1.14471 + 1.98270i
\(693\) 0 0
\(694\) 68.3335i 2.59391i
\(695\) 2.32336 + 1.34139i 0.0881299 + 0.0508818i
\(696\) 0 0
\(697\) 20.8535 + 12.0398i 0.789884 + 0.456040i
\(698\) 6.32944 10.9629i 0.239573 0.414952i
\(699\) 0 0
\(700\) −17.6999 24.0553i −0.668993 0.909206i
\(701\) 1.12731 0.0425779 0.0212890 0.999773i \(-0.493223\pi\)
0.0212890 + 0.999773i \(0.493223\pi\)
\(702\) 0 0
\(703\) −10.9588 + 18.9813i −0.413321 + 0.715892i
\(704\) 10.9727 6.33509i 0.413549 0.238763i
\(705\) 0 0
\(706\) 17.5478 + 30.3936i 0.660419 + 1.14388i
\(707\) 3.36398 0.374096i 0.126515 0.0140693i
\(708\) 0 0
\(709\) −5.23972 3.02515i −0.196782 0.113612i 0.398372 0.917224i \(-0.369575\pi\)
−0.595153 + 0.803612i \(0.702909\pi\)
\(710\) −4.88276 2.81906i −0.183247 0.105798i
\(711\) 0 0
\(712\) −12.3040 −0.461114
\(713\) 18.0218 + 10.4049i 0.674922 + 0.389666i
\(714\) 0 0
\(715\) −15.4300 + 3.01664i −0.577050 + 0.112816i
\(716\) 4.32530 + 7.49164i 0.161644 + 0.279976i
\(717\) 0 0
\(718\) −11.1124 19.2473i −0.414713 0.718304i
\(719\) −23.5589 + 40.8052i −0.878597 + 1.52178i −0.0257170 + 0.999669i \(0.508187\pi\)
−0.852880 + 0.522106i \(0.825146\pi\)
\(720\) 0 0
\(721\) −30.1539 + 3.35331i −1.12299 + 0.124884i
\(722\) 12.2100 7.04944i 0.454409 0.262353i
\(723\) 0 0
\(724\) 15.5095 0.576404
\(725\) −6.45070 11.1729i −0.239573 0.414953i
\(726\) 0 0
\(727\) 17.9215 0.664671 0.332335 0.943161i \(-0.392163\pi\)
0.332335 + 0.943161i \(0.392163\pi\)
\(728\) −19.9527 63.6394i −0.739498 2.35863i
\(729\) 0 0
\(730\) 37.9880i 1.40600i
\(731\) −5.24644 9.08711i −0.194047 0.336099i
\(732\) 0 0
\(733\) −39.2037 + 22.6343i −1.44802 + 0.836016i −0.998364 0.0571848i \(-0.981788\pi\)
−0.449658 + 0.893201i \(0.648454\pi\)
\(734\) −3.72861 + 2.15271i −0.137625 + 0.0794581i
\(735\) 0 0
\(736\) 16.9378i 0.624335i
\(737\) −18.3691 + 31.8163i −0.676635 + 1.17197i
\(738\) 0 0
\(739\) 16.6808 9.63066i 0.613613 0.354270i −0.160765 0.986993i \(-0.551396\pi\)
0.774378 + 0.632723i \(0.218063\pi\)
\(740\) −22.5577 39.0712i −0.829239 1.43628i
\(741\) 0 0
\(742\) 40.0804 29.4911i 1.47140 1.08265i
\(743\) −30.2115 17.4426i −1.10835 0.639908i −0.169951 0.985453i \(-0.554361\pi\)
−0.938402 + 0.345545i \(0.887694\pi\)
\(744\) 0 0
\(745\) −31.9155 −1.16929
\(746\) −31.3032 18.0729i −1.14609 0.661697i
\(747\) 0 0
\(748\) 34.4303 19.8784i 1.25890 0.726825i
\(749\) 5.45120 12.4451i 0.199183 0.454733i
\(750\) 0 0
\(751\) 24.9668 0.911051 0.455526 0.890223i \(-0.349451\pi\)
0.455526 + 0.890223i \(0.349451\pi\)
\(752\) −7.94609 + 4.58767i −0.289764 + 0.167295i
\(753\) 0 0
\(754\) −9.62150 49.2136i −0.350394 1.79225i
\(755\) −12.1467 −0.442064
\(756\) 0 0
\(757\) 5.30243 9.18408i 0.192720 0.333801i −0.753431 0.657527i \(-0.771602\pi\)
0.946151 + 0.323726i \(0.104936\pi\)
\(758\) 40.8685 70.7863i 1.48441 2.57108i
\(759\) 0 0
\(760\) 41.4926i 1.50510i
\(761\) −28.2660 16.3194i −1.02464 0.591578i −0.109198 0.994020i \(-0.534828\pi\)
−0.915446 + 0.402442i \(0.868162\pi\)
\(762\) 0 0
\(763\) 3.68208 2.70927i 0.133300 0.0980820i
\(764\) −11.5080 + 19.9325i −0.416345 + 0.721131i
\(765\) 0 0
\(766\) −41.2988 + 71.5316i −1.49219 + 2.58454i
\(767\) 31.0572 27.0568i 1.12141 0.976963i
\(768\) 0 0
\(769\) −45.1851 26.0876i −1.62942 0.940744i −0.984267 0.176686i \(-0.943462\pi\)
−0.645148 0.764057i \(-0.723204\pi\)
\(770\) −24.0545 + 17.6993i −0.866864 + 0.637837i
\(771\) 0 0
\(772\) −12.2909 + 7.09618i −0.442360 + 0.255397i
\(773\) 35.7057i 1.28425i −0.766602 0.642123i \(-0.778054\pi\)
0.766602 0.642123i \(-0.221946\pi\)
\(774\) 0 0
\(775\) −21.7898 + 12.5804i −0.782714 + 0.451900i
\(776\) 54.1208 + 93.7400i 1.94282 + 3.36507i
\(777\) 0 0
\(778\) 56.9752 + 32.8947i 2.04266 + 1.17933i
\(779\) 14.1766 + 24.5545i 0.507928 + 0.879757i
\(780\) 0 0
\(781\) 1.82735 3.16506i 0.0653876 0.113255i
\(782\) 16.0741i 0.574808i
\(783\) 0 0
\(784\) −41.2755 44.7437i −1.47413 1.59799i
\(785\) 22.5760i 0.805770i
\(786\) 0 0
\(787\) 6.10621i 0.217663i −0.994060 0.108831i \(-0.965289\pi\)
0.994060 0.108831i \(-0.0347109\pi\)
\(788\) 18.9301 + 10.9293i 0.674356 + 0.389339i