Properties

Label 819.2.bm.f.478.1
Level $819$
Weight $2$
Character 819.478
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 478.1
Root \(1.32725 - 0.488273i\) of defining polynomial
Character \(\chi\) \(=\) 819.478
Dual form 819.2.bm.f.550.6

$q$-expansion

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

Character values

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

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

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 \(-0.632026\pi\)
0.402981 0.915209i \(-0.367974\pi\)
\(3\) 0 0
\(4\) −4.70085 −2.35043
\(5\) 1.39608 + 0.806027i 0.624346 + 0.360466i 0.778559 0.627571i \(-0.215951\pi\)
−0.154213 + 0.988038i \(0.549284\pi\)
\(6\) 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 0.103384 0.994642i \(-0.467033\pi\)
−0.809693 + 0.586854i \(0.800366\pi\)
\(12\) 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 −0.0875083 0.996164i \(-0.527890\pi\)
0.818949 + 0.573866i \(0.194557\pi\)
\(20\) −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 0.501155 0.865357i \(-0.332908\pi\)
−0.999999 + 0.00133469i \(0.999575\pi\)
\(30\) 0 0
\(31\) 9.07425 5.23902i 1.62978 0.940956i 0.645627 0.763653i \(-0.276596\pi\)
0.984156 0.177303i \(-0.0567372\pi\)
\(32\) 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 \(-0.837226\pi\)
0.872075 0.489371i \(-0.162774\pi\)
\(38\) −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 0.121337 0.992611i \(-0.461282\pi\)
0.920295 + 0.391225i \(0.127949\pi\)
\(42\) 0 0
\(43\) −1.67800 + 2.90638i −0.255892 + 0.443219i −0.965138 0.261743i \(-0.915703\pi\)
0.709245 + 0.704962i \(0.249036\pi\)
\(44\) 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 0.431877 0.901933i \(-0.357852\pi\)
−0.565158 + 0.824983i \(0.691185\pi\)
\(48\) 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 0.999999 0.00114437i \(-0.000364265\pi\)
−0.500991 + 0.865453i \(0.667031\pi\)
\(54\) 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 \(0.266904\pi\)
−0.668577 + 0.743643i \(0.733096\pi\)
\(60\) 0 0
\(61\) 1.46254 + 2.53319i 0.187259 + 0.324341i 0.944335 0.328985i \(-0.106706\pi\)
−0.757077 + 0.653326i \(0.773373\pi\)
\(62\) −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 0.997639 0.0686778i \(-0.0218780\pi\)
0.439343 + 0.898320i \(0.355211\pi\)
\(68\) −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 0.428958 0.903324i \(-0.358881\pi\)
−0.567823 + 0.823151i \(0.692214\pi\)
\(72\) 0 0
\(73\) −7.88374 + 4.55168i −0.922721 + 0.532733i −0.884502 0.466536i \(-0.845502\pi\)
−0.0382192 + 0.999269i \(0.512169\pi\)
\(74\) −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 −0.636988 0.770874i \(-0.719820\pi\)
0.986090 + 0.166211i \(0.0531532\pi\)
\(80\) 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 \(0.0472841\pi\)
−0.988987 + 0.148002i \(0.952716\pi\)
\(84\) 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 \(0.0297330\pi\)
−0.995641 + 0.0932732i \(0.970267\pi\)
\(90\) 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 −0.371555 0.928411i \(-0.621175\pi\)
−0.989805 + 0.142430i \(0.954509\pi\)
\(98\) 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 −0.832446 0.554107i \(-0.813060\pi\)
0.896093 + 0.443866i \(0.146393\pi\)
\(102\) 0 0
\(103\) −5.73367 + 9.93101i −0.564956 + 0.978532i 0.432098 + 0.901827i \(0.357773\pi\)
−0.997054 + 0.0767054i \(0.975560\pi\)
\(104\) 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 −0.426623 0.904429i \(-0.640297\pi\)
0.569947 + 0.821681i \(0.306964\pi\)
\(110\) −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 −0.994215 0.107404i \(-0.965746\pi\)
0.590123 + 0.807314i \(0.299079\pi\)
\(114\) 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 0.788361 0.615214i \(-0.210930\pi\)
−0.926971 + 0.375133i \(0.877597\pi\)
\(128\) 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 −0.552130 0.833758i \(-0.686185\pi\)
0.998121 + 0.0612793i \(0.0195180\pi\)
\(132\) 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 \(-0.859619\pi\)
0.904316 0.426863i \(-0.140381\pi\)
\(138\) 0 0
\(139\) 0.832100 1.44124i 0.0705778 0.122244i −0.828577 0.559875i \(-0.810849\pi\)
0.899155 + 0.437631i \(0.144182\pi\)
\(140\) 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 −0.994863 0.101234i \(-0.967721\pi\)
−0.409760 + 0.912193i \(0.634387\pi\)
\(150\) 0 0
\(151\) −6.52544 + 3.76746i −0.531033 + 0.306592i −0.741437 0.671023i \(-0.765855\pi\)
0.210404 + 0.977614i \(0.432522\pi\)
\(152\) 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 −0.997594 0.0693309i \(-0.977914\pi\)
0.438755 0.898607i \(-0.355420\pi\)
\(158\) −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 −0.236706 0.971581i \(-0.576068\pi\)
0.723061 + 0.690784i \(0.242735\pi\)
\(164\) −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 −0.961656 0.274260i \(-0.911567\pi\)
−0.243312 + 0.969948i \(0.578234\pi\)
\(168\) 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 0.999889 0.0149198i \(-0.00474930\pi\)
−0.512865 + 0.858469i \(0.671416\pi\)
\(174\) 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 −0.898361 0.439258i \(-0.855242\pi\)
0.829589 + 0.558375i \(0.188575\pi\)
\(180\) 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 0.940898 0.338689i \(-0.109983\pi\)
−0.763762 + 0.645498i \(0.776650\pi\)
\(192\) 0 0
\(193\) 2.61462 + 1.50955i 0.188204 + 0.108660i 0.591142 0.806568i \(-0.298677\pi\)
−0.402937 + 0.915228i \(0.632011\pi\)
\(194\) −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 −0.636546 0.771238i \(-0.719638\pi\)
0.349639 + 0.936885i \(0.386304\pi\)
\(198\) 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 0.965897 0.258927i \(-0.0833688\pi\)
−0.707186 + 0.707028i \(0.750035\pi\)
\(212\) −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 −0.982006 0.188852i \(-0.939523\pi\)
−0.327452 + 0.944868i \(0.606190\pi\)
\(224\) 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 \(-0.850099\pi\)
0.891148 0.453712i \(-0.149901\pi\)
\(228\) 0 0
\(229\) 6.86832 + 3.96543i 0.453872 + 0.262043i 0.709464 0.704742i \(-0.248937\pi\)
−0.255592 + 0.966785i \(0.582270\pi\)
\(230\) 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 −0.738091 0.674702i \(-0.764272\pi\)
0.953354 + 0.301854i \(0.0976056\pi\)
\(234\) 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 \(0.0982508\pi\)
−0.952740 + 0.303786i \(0.901749\pi\)
\(240\) 0 0
\(241\) 10.0858i 0.649686i 0.945768 + 0.324843i \(0.105311\pi\)
−0.945768 + 0.324843i \(0.894689\pi\)
\(242\) −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 −0.655237 0.755423i \(-0.727431\pi\)
0.981834 + 0.189741i \(0.0607648\pi\)
\(252\) 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 −0.777431 0.628968i \(-0.783478\pi\)
0.933418 + 0.358792i \(0.116811\pi\)
\(264\) 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 \(0.0813913\pi\)
−0.967487 + 0.252921i \(0.918609\pi\)
\(272\) 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 \(0.300587\pi\)
−0.586292 + 0.810100i \(0.699413\pi\)
\(282\) 0 0
\(283\) −8.07563 + 13.9874i −0.480046 + 0.831464i −0.999738 0.0228894i \(-0.992713\pi\)
0.519692 + 0.854354i \(0.326047\pi\)
\(284\) 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 0.822417 0.568885i \(-0.192625\pi\)
−0.0814609 + 0.996677i \(0.525959\pi\)
\(294\) 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 \(0.0824750\pi\)
−0.966620 + 0.256213i \(0.917525\pi\)
\(308\) −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 0.640045 0.768338i \(-0.278916\pi\)
−0.985422 + 0.170126i \(0.945583\pi\)
\(312\) 0 0
\(313\) −6.56198 + 11.3657i −0.370905 + 0.642427i −0.989705 0.143122i \(-0.954286\pi\)
0.618800 + 0.785549i \(0.287619\pi\)
\(314\) −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 0.0349599 0.999389i \(-0.488870\pi\)
−0.848016 + 0.529971i \(0.822203\pi\)
\(318\) 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 −0.591428 0.806357i \(-0.701436\pi\)
0.402612 + 0.915371i \(0.368102\pi\)
\(332\) 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 −0.609048 0.793133i \(-0.708448\pi\)
0.382350 + 0.924018i \(0.375115\pi\)
\(350\) −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 0.778785 0.627291i \(-0.215836\pi\)
−0.153857 + 0.988093i \(0.549170\pi\)
\(354\) 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 0.290785 0.956789i \(-0.406084\pi\)
−0.683211 + 0.730221i \(0.739417\pi\)
\(360\) 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 −0.843504 0.537123i \(-0.819511\pi\)
0.886914 + 0.461935i \(0.152845\pi\)
\(368\) 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 0.626707 0.779255i \(-0.284402\pi\)
−0.988208 + 0.153117i \(0.951069\pi\)
\(374\) −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 −0.994864 0.101218i \(-0.967726\pi\)
−0.409775 + 0.912187i \(0.634393\pi\)
\(380\) −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 0.416420 0.909172i \(-0.363284\pi\)
0.995576 + 0.0939554i \(0.0299511\pi\)
\(384\) 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 0.984464 + 0.175589i \(0.0561829\pi\)
−0.340168 + 0.940365i \(0.610484\pi\)
\(390\) 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 −0.587653 0.809113i \(-0.699948\pi\)
0.406885 + 0.913479i \(0.366615\pi\)
\(398\) 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 \(-0.837208\pi\)
0.872047 0.489422i \(-0.162792\pi\)
\(402\) 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 \(-0.856407\pi\)
0.899964 0.435965i \(-0.143593\pi\)
\(410\) 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 0.956824 + 0.290666i \(0.0938770\pi\)
−0.226688 + 0.973968i \(0.572790\pi\)
\(420\) 0 0
\(421\) 12.8528i 0.626407i −0.949686 0.313203i \(-0.898598\pi\)
0.949686 0.313203i \(-0.101402\pi\)
\(422\) 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 0.301087 0.953597i \(-0.402650\pi\)
−0.675295 + 0.737547i \(0.735984\pi\)
\(432\) 0 0
\(433\) −1.72531 + 2.98833i −0.0829132 + 0.143610i −0.904500 0.426473i \(-0.859756\pi\)
0.821587 + 0.570083i \(0.193089\pi\)
\(434\) 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 −0.987506 0.157580i \(-0.949631\pi\)
0.630222 + 0.776415i \(0.282964\pi\)
\(444\) 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 −0.993168 0.116696i \(-0.962770\pi\)
−0.597646 0.801760i \(-0.703897\pi\)
\(450\) 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 \(0.105713\pi\)
−0.945358 + 0.326034i \(0.894287\pi\)
\(458\) 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 −0.999916 0.0129430i \(-0.995880\pi\)
−0.511167 0.859481i \(-0.670787\pi\)
\(462\) 0 0
\(463\) 6.75275i 0.313827i 0.987612 + 0.156913i \(0.0501544\pi\)
−0.987612 + 0.156913i \(0.949846\pi\)
\(464\) −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 −0.918518 0.395379i \(-0.870613\pi\)
0.801667 + 0.597770i \(0.203947\pi\)
\(468\) 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 0.301171 0.953570i \(-0.402623\pi\)
−0.675231 + 0.737607i \(0.735956\pi\)
\(480\) 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 \(0.361088\pi\)
−0.422684 + 0.906277i \(0.638912\pi\)
\(488\) −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 0.932168 0.362027i \(-0.117915\pi\)
−0.779608 + 0.626267i \(0.784582\pi\)
\(492\) 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 0.263416 0.964682i \(-0.415151\pi\)
−0.703732 + 0.710466i \(0.748484\pi\)
\(500\) 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 −0.978475 0.206365i \(-0.933836\pi\)
0.667955 + 0.744202i \(0.267170\pi\)
\(504\) 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 \(0.144717\pi\)
−0.898418 + 0.439141i \(0.855283\pi\)
\(510\) 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 −0.974630 0.223823i \(-0.928146\pi\)
0.293479 0.955966i \(-0.405187\pi\)
\(522\) 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 0.538562 0.842586i \(-0.318968\pi\)
−0.460420 + 0.887701i \(0.652301\pi\)
\(542\) 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 0.985904 + 0.167309i \(0.0535078\pi\)
0.637846 + 0.770164i \(0.279826\pi\)
\(558\) 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 0.997858 0.0654194i \(-0.0208385\pi\)
−0.555584 + 0.831461i \(0.687505\pi\)
\(572\) 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 0.0317671 0.999495i \(-0.489887\pi\)
0.881472 + 0.472237i \(0.156553\pi\)
\(578\) 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 −0.562324 0.826917i \(-0.690092\pi\)
0.434970 + 0.900445i \(0.356759\pi\)
\(588\) 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 −0.0239212 0.999714i \(-0.507615\pi\)
−0.877738 + 0.479141i \(0.840948\pi\)
\(594\) 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 0.955754 0.294166i \(-0.0950420\pi\)
−0.732633 + 0.680624i \(0.761709\pi\)
\(600\) 0 0
\(601\) −12.1282 21.0067i −0.494720 0.856880i 0.505262 0.862966i \(-0.331396\pi\)
−0.999981 + 0.00608649i \(0.998063\pi\)
\(602\) −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 0.948525 0.316702i \(-0.102576\pi\)
−0.748535 + 0.663096i \(0.769242\pi\)
\(608\) −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 0.434314 0.900762i \(-0.356991\pi\)
−0.562926 + 0.826508i \(0.690324\pi\)
\(614\) 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 0.136231 0.990677i \(-0.456501\pi\)
−0.789836 + 0.613318i \(0.789834\pi\)
\(618\) 0 0
\(619\) 13.7650 7.94725i 0.553264 0.319427i −0.197174 0.980369i \(-0.563176\pi\)
0.750437 + 0.660942i \(0.229843\pi\)
\(620\) −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 0.119400 0.992846i \(-0.461903\pi\)
−0.800130 + 0.599826i \(0.795236\pi\)
\(632\) 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 0.684424 0.729084i \(-0.260054\pi\)
−0.289193 + 0.957271i \(0.593387\pi\)
\(644\) −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 0.498616 + 0.866823i \(0.333842\pi\)
−0.999999 + 0.00159698i \(0.999492\pi\)
\(648\) 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 −0.116390 0.993204i \(-0.537132\pi\)
0.918335 0.395805i \(-0.129534\pi\)
\(660\) 0 0
\(661\) −18.9606 10.9469i −0.737481 0.425785i 0.0836719 0.996493i \(-0.473335\pi\)
−0.821153 + 0.570709i \(0.806669\pi\)
\(662\) 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 0.972655 + 0.232254i \(0.0746102\pi\)
−0.285189 + 0.958471i \(0.592056\pi\)
\(674\) 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 −0.840428 0.541923i \(-0.817697\pi\)
0.889533 + 0.456871i \(0.151030\pi\)
\(678\) 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 \(0.239663\pi\)
−0.729693 + 0.683775i \(0.760337\pi\)
\(684\) 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 \(-0.835132\pi\)
0.868837 0.495099i \(-0.164868\pi\)
\(692\) −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 −0.595153 0.803612i \(-0.702909\pi\)
0.398372 + 0.917224i \(0.369575\pi\)
\(710\) −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 −0.852880 0.522106i \(-0.825146\pi\)
−0.0257170 0.999669i \(-0.508187\pi\)
\(720\) 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 −0.449658 0.893201i \(-0.648454\pi\)
−0.998364 + 0.0571848i \(0.981788\pi\)
\(734\) −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 0.774378 0.632723i \(-0.218063\pi\)
−0.160765 + 0.986993i \(0.551396\pi\)
\(740\) −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 −0.938402 0.345545i \(-0.887694\pi\)
−0.169951 + 0.985453i \(0.554361\pi\)
\(744\) 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 0.946151 0.323726i \(-0.104936\pi\)
−0.753431 + 0.657527i \(0.771602\pi\)
\(758\) 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 −0.915446 0.402442i \(-0.868162\pi\)
−0.109198 + 0.994020i \(0.534828\pi\)
\(762\) 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 −0.645148 + 0.764057i \(0.723204\pi\)
−0.984267 + 0.176686i \(0.943462\pi\)
\(770\) −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 \(0.221946\pi\)
−0.766602 + 0.642123i \(0.778054\pi\)
\(774\) 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 \(0.0347109\pi\)
−0.994060 + 0.108831i \(0.965289\pi\)
\(788\) 18.9301 10.9293i 0.674356