Properties

Label 819.2.do.e.667.6
Level $819$
Weight $2$
Character 819.667
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.do (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 667.6
Root \(1.32725 - 0.488273i\) of defining polynomial
Character \(\chi\) \(=\) 819.667
Dual form 819.2.do.e.361.6

$q$-expansion

\(f(q)\) \(=\) \(q+(2.24179 - 1.29430i) q^{2} +(2.35043 - 4.07106i) q^{4} +(-1.39608 - 0.806027i) q^{5} +(2.62954 + 0.292422i) q^{7} -6.99143i q^{8} +O(q^{10})\) \(q+(2.24179 - 1.29430i) q^{2} +(2.35043 - 4.07106i) q^{4} +(-1.39608 - 0.806027i) q^{5} +(2.62954 + 0.292422i) q^{7} -6.99143i q^{8} -4.17296 q^{10} -2.70496i q^{11} +(2.36840 + 2.71858i) q^{13} +(6.27337 - 2.74787i) q^{14} +(-4.34816 - 7.53123i) q^{16} +(-1.56330 + 2.70772i) q^{17} -3.68150i q^{19} +(-6.56276 + 3.78901i) q^{20} +(-3.50103 - 6.06396i) q^{22} +(-0.993019 - 1.71996i) q^{23} +(-1.20064 - 2.07957i) q^{25} +(8.82813 + 3.02907i) q^{26} +(7.37101 - 10.0177i) q^{28} +(-2.68636 + 4.65290i) q^{29} +(-9.07425 + 5.23902i) q^{31} +(-7.38583 - 4.26421i) q^{32} +8.09354i q^{34} +(-3.43535 - 2.52773i) q^{35} +(5.15585 - 2.97673i) q^{37} +(-4.76497 - 8.25317i) q^{38} +(-5.63528 + 9.76059i) q^{40} +(6.66970 + 3.85075i) q^{41} +(-1.67800 - 2.90638i) q^{43} +(-11.0120 - 6.35780i) q^{44} +(-4.45229 - 2.57053i) q^{46} +(0.913730 + 0.527542i) q^{47} +(6.82898 + 1.53787i) q^{49} +(-5.38318 - 3.10798i) q^{50} +(16.6343 - 3.25208i) q^{52} +(3.63284 + 6.29226i) q^{53} +(-2.18027 + 3.77633i) q^{55} +(2.04445 - 18.3843i) q^{56} +13.9078i q^{58} +(9.89352 + 5.71203i) q^{59} -2.92507 q^{61} +(-13.5617 + 23.4896i) q^{62} -4.68406 q^{64} +(-1.11523 - 5.70435i) q^{65} +13.5818i q^{67} +(7.34886 + 12.7286i) q^{68} +(-10.9730 - 1.22027i) q^{70} +(-1.17009 + 0.675554i) q^{71} +(7.88374 - 4.55168i) q^{73} +(7.70557 - 13.3464i) q^{74} +(-14.9876 - 8.65311i) q^{76} +(0.790989 - 7.11280i) q^{77} +(3.10289 - 5.37436i) q^{79} +14.0189i q^{80} +19.9361 q^{82} -2.69672i q^{83} +(4.36499 - 2.52013i) q^{85} +(-7.52346 - 4.34367i) q^{86} -18.9115 q^{88} +(-1.52410 + 0.879938i) q^{89} +(5.43284 + 7.84119i) q^{91} -9.33607 q^{92} +2.73119 q^{94} +(-2.96739 + 5.13967i) q^{95} +(-13.4078 + 7.74102i) q^{97} +(17.2996 - 5.39116i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 4q^{4} - 3q^{5} + 3q^{7} + O(q^{10}) \) \( 12q + 4q^{4} - 3q^{5} + 3q^{7} - 24q^{10} - 2q^{13} - 4q^{14} - 8q^{16} - 17q^{17} + 3q^{20} - 15q^{22} - 3q^{23} - 5q^{25} + 9q^{26} + 27q^{28} + q^{29} - 18q^{31} - 18q^{32} - 18q^{35} + 15q^{37} - 19q^{38} - q^{40} + 6q^{41} + 11q^{43} - 33q^{44} - 30q^{46} - 15q^{47} + 9q^{49} - 18q^{50} + 47q^{52} + 8q^{53} - 15q^{55} - 27q^{59} - 10q^{61} - 41q^{62} + 2q^{64} + 3q^{65} + 11q^{68} - 3q^{70} - 30q^{71} - 42q^{73} + 33q^{74} - 45q^{76} + 19q^{77} - 35q^{79} - 10q^{82} - 21q^{85} - 57q^{86} + 28q^{88} - 48q^{89} - 16q^{91} + 66q^{92} - 2q^{94} - 2q^{95} - 3q^{97} + 36q^{98} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.24179 1.29430i 1.58519 0.915209i 0.591104 0.806596i \(-0.298692\pi\)
0.994084 0.108613i \(-0.0346409\pi\)
\(3\) 0 0
\(4\) 2.35043 4.07106i 1.17521 2.03553i
\(5\) −1.39608 0.806027i −0.624346 0.360466i 0.154213 0.988038i \(-0.450716\pi\)
−0.778559 + 0.627571i \(0.784049\pi\)
\(6\) 0 0
\(7\) 2.62954 + 0.292422i 0.993873 + 0.110525i
\(8\) 6.99143i 2.47184i
\(9\) 0 0
\(10\) −4.17296 −1.31961
\(11\) 2.70496i 0.815575i −0.913077 0.407788i \(-0.866300\pi\)
0.913077 0.407788i \(-0.133700\pi\)
\(12\) 0 0
\(13\) 2.36840 + 2.71858i 0.656876 + 0.753998i
\(14\) 6.27337 2.74787i 1.67663 0.734398i
\(15\) 0 0
\(16\) −4.34816 7.53123i −1.08704 1.88281i
\(17\) −1.56330 + 2.70772i −0.379157 + 0.656719i −0.990940 0.134307i \(-0.957119\pi\)
0.611783 + 0.791026i \(0.290453\pi\)
\(18\) 0 0
\(19\) 3.68150i 0.844595i −0.906457 0.422297i \(-0.861224\pi\)
0.906457 0.422297i \(-0.138776\pi\)
\(20\) −6.56276 + 3.78901i −1.46748 + 0.847249i
\(21\) 0 0
\(22\) −3.50103 6.06396i −0.746421 1.29284i
\(23\) −0.993019 1.71996i −0.207059 0.358636i 0.743728 0.668482i \(-0.233056\pi\)
−0.950787 + 0.309846i \(0.899722\pi\)
\(24\) 0 0
\(25\) −1.20064 2.07957i −0.240128 0.415914i
\(26\) 8.82813 + 3.02907i 1.73134 + 0.594050i
\(27\) 0 0
\(28\) 7.37101 10.0177i 1.39299 1.89317i
\(29\) −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 −0.645627 + 0.763653i \(0.723404\pi\)
−0.984156 + 0.177303i \(0.943263\pi\)
\(32\) −7.38583 4.26421i −1.30564 0.753813i
\(33\) 0 0
\(34\) 8.09354i 1.38803i
\(35\) −3.43535 2.52773i −0.580680 0.427264i
\(36\) 0 0
\(37\) 5.15585 2.97673i 0.847616 0.489371i −0.0122297 0.999925i \(-0.503893\pi\)
0.859846 + 0.510554i \(0.170560\pi\)
\(38\) −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
\(46\) −4.45229 2.57053i −0.656454 0.379004i
\(47\) 0.913730 + 0.527542i 0.133281 + 0.0769500i 0.565158 0.824983i \(-0.308815\pi\)
−0.431877 + 0.901933i \(0.642148\pi\)
\(48\) 0 0
\(49\) 6.82898 + 1.53787i 0.975568 + 0.219696i
\(50\) −5.38318 3.10798i −0.761297 0.439535i
\(51\) 0 0
\(52\) 16.6343 3.25208i 2.30676 0.450982i
\(53\) 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
\(56\) 2.04445 18.3843i 0.273201 2.45670i
\(57\) 0 0
\(58\) 13.9078i 1.82618i
\(59\) 9.89352 + 5.71203i 1.28803 + 0.743643i 0.978302 0.207183i \(-0.0664297\pi\)
0.309725 + 0.950826i \(0.399763\pi\)
\(60\) 0 0
\(61\) −2.92507 −0.374517 −0.187259 0.982311i \(-0.559960\pi\)
−0.187259 + 0.982311i \(0.559960\pi\)
\(62\) −13.5617 + 23.4896i −1.72234 + 2.98318i
\(63\) 0 0
\(64\) −4.68406 −0.585507
\(65\) −1.11523 5.70435i −0.138327 0.707537i
\(66\) 0 0
\(67\) 13.5818i 1.65928i 0.558296 + 0.829642i \(0.311455\pi\)
−0.558296 + 0.829642i \(0.688545\pi\)
\(68\) 7.34886 + 12.7286i 0.891180 + 1.54357i
\(69\) 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 \(-0.487831\pi\)
0.884502 + 0.466536i \(0.154498\pi\)
\(74\) 7.70557 13.3464i 0.895754 1.55149i
\(75\) 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 \(0.0531532\pi\)
\(80\) 14.0189i 1.56736i
\(81\) 0 0
\(82\) 19.9361 2.20158
\(83\) 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
\(88\) −18.9115 −2.01597
\(89\) −1.52410 + 0.879938i −0.161554 + 0.0932732i −0.578597 0.815613i \(-0.696400\pi\)
0.417043 + 0.908887i \(0.363066\pi\)
\(90\) 0 0
\(91\) 5.43284 + 7.84119i 0.569516 + 0.821980i
\(92\) −9.33607 −0.973353
\(93\) 0 0
\(94\) 2.73119 0.281701
\(95\) −2.96739 + 5.13967i −0.304448 + 0.527319i
\(96\) 0 0
\(97\) −13.4078 + 7.74102i −1.36136 + 0.785981i −0.989805 0.142430i \(-0.954509\pi\)
−0.371555 + 0.928411i \(0.621175\pi\)
\(98\) 17.2996 5.39116i 1.74753 0.544589i
\(99\) 0 0
\(100\) −11.2881 −1.12881
\(101\) −1.27930 −0.127295 −0.0636477 0.997972i \(-0.520273\pi\)
−0.0636477 + 0.997972i \(0.520273\pi\)
\(102\) 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
\(107\) −2.56763 4.44726i −0.248222 0.429933i 0.714811 0.699318i \(-0.246513\pi\)
−0.963033 + 0.269385i \(0.913180\pi\)
\(108\) 0 0
\(109\) −1.49635 + 0.863916i −0.143324 + 0.0827481i −0.569947 0.821681i \(-0.693036\pi\)
0.426623 + 0.904429i \(0.359703\pi\)
\(110\) 11.2877i 1.07624i
\(111\) 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
\(115\) 3.20160i 0.298551i
\(116\) 12.6282 + 21.8726i 1.17250 + 2.03082i
\(117\) 0 0
\(118\) 29.5723 2.72235
\(119\) −4.90257 + 6.66292i −0.449418 + 0.610789i
\(120\) 0 0
\(121\) 3.68321 0.334837
\(122\) −6.55741 + 3.78592i −0.593680 + 0.342761i
\(123\) 0 0
\(124\) 49.2557i 4.42330i
\(125\) 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 \(0.210930\pi\)
\(128\) 4.27097 2.46585i 0.377504 0.217952i
\(129\) 0 0
\(130\) −9.88325 11.3445i −0.866818 0.994981i
\(131\) 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
\(133\) 1.07655 9.68067i 0.0933490 0.839420i
\(134\) 17.5790 + 30.4476i 1.51859 + 2.63028i
\(135\) 0 0
\(136\) 18.9308 + 10.9297i 1.62331 + 0.937216i
\(137\) −8.65385 4.99630i −0.739348 0.426863i 0.0824839 0.996592i \(-0.473715\pi\)
−0.821832 + 0.569729i \(0.807048\pi\)
\(138\) 0 0
\(139\) 0.832100 + 1.44124i 0.0705778 + 0.122244i 0.899155 0.437631i \(-0.144182\pi\)
−0.828577 + 0.559875i \(0.810849\pi\)
\(140\) −18.3651 + 8.04427i −1.55213 + 0.679865i
\(141\) 0 0
\(142\) −1.74874 + 3.02891i −0.146751 + 0.254180i
\(143\) 7.35364 6.40642i 0.614942 0.535732i
\(144\) 0 0
\(145\) 7.50073 4.33055i 0.622902 0.359633i
\(146\) 11.7825 20.4078i 0.975124 1.68897i
\(147\) 0 0
\(148\) 27.9863i 2.30046i
\(149\) 19.7980i 1.62192i 0.585103 + 0.810959i \(0.301054\pi\)
−0.585103 + 0.810959i \(0.698946\pi\)
\(150\) 0 0
\(151\) 6.52544 3.76746i 0.531033 0.306592i −0.210404 0.977614i \(-0.567478\pi\)
0.741437 + 0.671023i \(0.234145\pi\)
\(152\) −25.7390 −2.08771
\(153\) 0 0
\(154\) −7.43286 16.9692i −0.598957 1.36742i
\(155\) 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 \(-0.355420\pi\)
\(158\) 16.0643i 1.27801i
\(159\) 0 0
\(160\) 6.87414 + 11.9064i 0.543448 + 0.941280i
\(161\) −2.10823 4.81308i −0.166152 0.379324i
\(162\) 0 0
\(163\) 7.16995i 0.561594i −0.959767 0.280797i \(-0.909401\pi\)
0.959767 0.280797i \(-0.0905987\pi\)
\(164\) 31.3533 18.1018i 2.44828 1.41351i
\(165\) 0 0
\(166\) −3.49036 6.04548i −0.270904 0.469220i
\(167\) −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
\(172\) −15.7761 −1.20291
\(173\) −12.8116 −0.974047 −0.487023 0.873389i \(-0.661917\pi\)
−0.487023 + 0.873389i \(0.661917\pi\)
\(174\) 0 0
\(175\) −2.54902 5.81942i −0.192688 0.439906i
\(176\) −20.3717 + 11.7616i −1.53557 + 0.886562i
\(177\) 0 0
\(178\) −2.27781 + 3.94528i −0.170729 + 0.295711i
\(179\) 1.84022 0.137545 0.0687723 0.997632i \(-0.478092\pi\)
0.0687723 + 0.997632i \(0.478092\pi\)
\(180\) 0 0
\(181\) −3.29928 −0.245234 −0.122617 0.992454i \(-0.539129\pi\)
−0.122617 + 0.992454i \(0.539129\pi\)
\(182\) 22.3282 + 10.5466i 1.65507 + 0.781767i
\(183\) 0 0
\(184\) −12.0250 + 6.94262i −0.886493 + 0.511817i
\(185\) −9.59730 −0.705607
\(186\) 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
\(191\) −4.89614 −0.354272 −0.177136 0.984186i \(-0.556683\pi\)
−0.177136 + 0.984186i \(0.556683\pi\)
\(192\) 0 0
\(193\) 3.01910i 0.217320i 0.994079 + 0.108660i \(0.0346559\pi\)
−0.994079 + 0.108660i \(0.965344\pi\)
\(194\) −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
\(199\) 0.205360 0.355694i 0.0145576 0.0252145i −0.858655 0.512554i \(-0.828699\pi\)
0.873212 + 0.487340i \(0.162033\pi\)
\(200\) −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
\(205\) −6.20762 10.7519i −0.433559 0.750946i
\(206\) 29.6844i 2.06821i
\(207\) 0 0
\(208\) 10.1761 29.6578i 0.705583 2.05640i
\(209\) −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 \(0.0833688\pi\)
\(212\) 34.1549 2.34577
\(213\) 0 0
\(214\) −11.5122 6.64656i −0.786956 0.454349i
\(215\) 5.41005i 0.368962i
\(216\) 0 0
\(217\) −25.3931 + 11.1227i −1.72380 + 0.755059i
\(218\) −2.23633 + 3.87344i −0.151464 + 0.262343i
\(219\) 0 0
\(220\) 10.2491 + 17.7520i 0.690996 + 1.19684i
\(221\) −11.0637 + 2.16300i −0.744224 + 0.145499i
\(222\) 0 0
\(223\) −19.5544 11.2897i −1.30946 0.756016i −0.327452 0.944868i \(-0.606190\pi\)
−0.982006 + 0.188852i \(0.939523\pi\)
\(224\) −18.1744 13.3727i −1.21433 0.893502i
\(225\) 0 0
\(226\) −19.2595 11.1195i −1.28113 0.739658i
\(227\) −11.8401 6.83586i −0.785853 0.453712i 0.0526478 0.998613i \(-0.483234\pi\)
−0.838500 + 0.544901i \(0.816567\pi\)
\(228\) 0 0
\(229\) −6.86832 3.96543i −0.453872 0.262043i 0.255592 0.966785i \(-0.417730\pi\)
−0.709464 + 0.704742i \(0.751063\pi\)
\(230\) 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
\(236\) 46.5080 26.8514i 3.02741 1.74788i
\(237\) 0 0
\(238\) −2.36673 + 21.2823i −0.153412 + 1.37953i
\(239\) 9.39284i 0.607572i −0.952740 0.303786i \(-0.901749\pi\)
0.952740 0.303786i \(-0.0982508\pi\)
\(240\) 0 0
\(241\) 8.73460 + 5.04292i 0.562645 + 0.324843i 0.754206 0.656637i \(-0.228022\pi\)
−0.191562 + 0.981481i \(0.561355\pi\)
\(242\) 8.25699 4.76718i 0.530780 0.306446i
\(243\) 0 0
\(244\) −6.87517 + 11.9081i −0.440137 + 0.762340i
\(245\) −8.29423 7.65133i −0.529899 0.488826i
\(246\) 0 0
\(247\) 10.0085 8.71928i 0.636823 0.554794i
\(248\) 36.6282 + 63.4420i 2.32590 + 4.02857i
\(249\) 0 0
\(250\) 15.4426 + 26.7474i 0.976678 + 1.69166i
\(251\) 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
\(254\) 8.08709i 0.507429i
\(255\) 0 0
\(256\) 11.0672 19.1689i 0.691697 1.19805i
\(257\) −3.99329 6.91658i −0.249095 0.431445i 0.714180 0.699962i \(-0.246800\pi\)
−0.963275 + 0.268517i \(0.913466\pi\)
\(258\) 0 0
\(259\) 14.4280 6.31975i 0.896511 0.392690i
\(260\) −25.8440 8.86749i −1.60278 0.549939i
\(261\) 0 0
\(262\) 26.4275i 1.63270i
\(263\) −5.05934 −0.311972 −0.155986 0.987759i \(-0.549856\pi\)
−0.155986 + 0.987759i \(0.549856\pi\)
\(264\) 0 0
\(265\) 11.7127i 0.719503i
\(266\) −10.1163 23.0954i −0.620269 1.41607i
\(267\) 0 0
\(268\) 55.2924 + 31.9231i 3.37752 + 1.95001i
\(269\) 6.94512 12.0293i 0.423451 0.733439i −0.572823 0.819679i \(-0.694152\pi\)
0.996274 + 0.0862400i \(0.0274852\pi\)
\(270\) 0 0
\(271\) −7.21158 + 4.16361i −0.438072 + 0.252921i −0.702780 0.711408i \(-0.748058\pi\)
0.264707 + 0.964329i \(0.414725\pi\)
\(272\) 27.1900 1.64863
\(273\) 0 0
\(274\) −25.8669 −1.56267
\(275\) −5.62515 + 3.24768i −0.339210 + 0.195843i
\(276\) 0 0
\(277\) −11.6058 + 20.1018i −0.697325 + 1.20780i 0.272066 + 0.962279i \(0.412293\pi\)
−0.969391 + 0.245523i \(0.921040\pi\)
\(278\) 3.73080 + 2.15398i 0.223758 + 0.129187i
\(279\) 0 0
\(280\) −17.6724 + 24.0180i −1.05613 + 1.43535i
\(281\) 27.1595i 1.62020i −0.586292 0.810100i \(-0.699413\pi\)
0.586292 0.810100i \(-0.300587\pi\)
\(282\) 0 0
\(283\) 16.1513 0.960092 0.480046 0.877243i \(-0.340620\pi\)
0.480046 + 0.877243i \(0.340620\pi\)
\(284\) 6.35136i 0.376884i
\(285\) 0 0
\(286\) 8.19351 23.8797i 0.484493 1.41204i
\(287\) 16.4122 + 12.0761i 0.968782 + 0.712828i
\(288\) 0 0
\(289\) 3.61216 + 6.25645i 0.212480 + 0.368027i
\(290\) 11.2101 19.4164i 0.658278 1.14017i
\(291\) 0 0
\(292\) 42.7935i 2.50430i
\(293\) 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
\(296\) −20.8116 36.0468i −1.20965 2.09517i
\(297\) 0 0
\(298\) 25.6246 + 44.3831i 1.48439 + 2.57104i
\(299\) 2.32398 6.77315i 0.134399 0.391702i
\(300\) 0 0
\(301\) −3.56248 8.13313i −0.205338 0.468786i
\(302\) 9.75246 16.8918i 0.561191 0.972011i
\(303\) 0 0
\(304\) −27.7263 + 16.0078i −1.59021 + 0.918108i
\(305\) 4.08363 + 2.35769i 0.233828 + 0.135001i
\(306\) 0 0
\(307\) 8.97844i 0.512427i −0.966620 0.256213i \(-0.917525\pi\)
0.966620 0.256213i \(-0.0824750\pi\)
\(308\) −27.0975 19.9383i −1.54402 1.13609i
\(309\) 0 0
\(310\) 37.8665 21.8622i 2.15067 1.24169i
\(311\) −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 0.848016 0.529971i \(-0.177797\pi\)
−0.0349599 + 0.999389i \(0.511130\pi\)
\(318\) 0 0
\(319\) 12.5859 + 7.26648i 0.704675 + 0.406845i
\(320\) 6.53932 + 3.77548i 0.365559 + 0.211056i
\(321\) 0 0
\(322\) −10.9558 8.06126i −0.610543 0.449236i
\(323\) 9.96849 + 5.75531i 0.554661 + 0.320234i
\(324\) 0 0
\(325\) 2.80988 8.18930i 0.155864 0.454261i
\(326\) −9.28007 16.0736i −0.513976 0.890232i
\(327\) 0 0
\(328\) 26.9223 46.6307i 1.48653 2.57475i
\(329\) 2.24843 + 1.65439i 0.123960 + 0.0912094i
\(330\) 0 0
\(331\) 3.96665i 0.218027i 0.994040 + 0.109013i \(0.0347691\pi\)
−0.994040 + 0.109013i \(0.965231\pi\)
\(332\) −10.9785 6.33843i −0.602523 0.347867i
\(333\) 0 0
\(334\) −46.5445 −2.54680
\(335\) 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 \(0.621750\pi\)
\(338\) 12.6738 + 31.1740i 0.689362 + 1.69564i
\(339\) 0 0
\(340\) 23.6935i 1.28496i
\(341\) 14.1713 + 24.5455i 0.767420 + 1.32921i
\(342\) 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
\(347\) −13.1989 + 22.8612i −0.708556 + 1.22725i 0.256837 + 0.966455i \(0.417320\pi\)
−0.965393 + 0.260800i \(0.916014\pi\)
\(348\) 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
\(353\) 13.5577i 0.721605i 0.932642 + 0.360802i \(0.117497\pi\)
−0.932642 + 0.360802i \(0.882503\pi\)
\(354\) 0 0
\(355\) 2.17806 0.115599
\(356\) 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 \(-0.260583\pi\)
−0.290785 + 0.956789i \(0.593916\pi\)
\(360\) 0 0
\(361\) 5.44653 0.286659
\(362\) −7.39632 + 4.27026i −0.388742 + 0.224440i
\(363\) 0 0
\(364\) 44.6914 3.68725i 2.34247 0.193264i
\(365\) −14.6751 −0.768130
\(366\) 0 0
\(367\) −1.66322 −0.0868196 −0.0434098 0.999057i \(-0.513822\pi\)
−0.0434098 + 0.999057i \(0.513822\pi\)
\(368\) −8.63560 + 14.9573i −0.450162 + 0.779703i
\(369\) 0 0
\(370\) −21.5152 + 12.4218i −1.11852 + 0.645778i
\(371\) 7.71270 + 17.6081i 0.400424 + 0.914166i
\(372\) 0 0
\(373\) 13.9635 0.723002 0.361501 0.932372i \(-0.382264\pi\)
0.361501 + 0.932372i \(0.382264\pi\)
\(374\) 21.8927 1.13204
\(375\) 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 \(0.967726\pi\)
\(380\) 13.9493 + 24.1608i 0.715582 + 1.23943i
\(381\) 0 0
\(382\) −10.9761 + 6.33707i −0.561588 + 0.324233i
\(383\) 31.9082i 1.63043i −0.579156 0.815217i \(-0.696618\pi\)
0.579156 0.815217i \(-0.303382\pi\)
\(384\) 0 0
\(385\) −6.83739 + 9.29247i −0.348466 + 0.473588i
\(386\) 3.90762 + 6.76820i 0.198893 + 0.344492i
\(387\) 0 0
\(388\) 72.7788i 3.69478i
\(389\) 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
\(392\) 10.7519 47.7443i 0.543054 2.41145i
\(393\) 0 0
\(394\) −12.0368 −0.606403
\(395\) −8.66376 + 5.00203i −0.435921 + 0.251679i
\(396\) 0 0
\(397\) 4.15897i 0.208733i 0.994539 + 0.104366i \(0.0332815\pi\)
−0.994539 + 0.104366i \(0.966719\pi\)
\(398\) 1.06319i 0.0532930i
\(399\) 0 0
\(400\) −10.4412 + 18.0846i −0.522058 + 0.904231i
\(401\) 16.9753 9.80067i 0.847704 0.489422i −0.0121716 0.999926i \(-0.503874\pi\)
0.859875 + 0.510504i \(0.170541\pi\)
\(402\) 0 0
\(403\) −35.7342 12.2610i −1.78005 0.610762i
\(404\) −3.00691 + 5.20811i −0.149599 + 0.259113i
\(405\) 0 0
\(406\) −4.06695 + 36.5711i −0.201839 + 1.81500i
\(407\) −8.05193 13.9463i −0.399119 0.691295i
\(408\) 0 0
\(409\) −15.2712 8.81685i −0.755114 0.435965i 0.0724249 0.997374i \(-0.476926\pi\)
−0.827539 + 0.561409i \(0.810260\pi\)
\(410\) −27.8324 16.0690i −1.37454 0.793594i
\(411\) 0 0
\(412\) 26.9532 + 46.6842i 1.32789 + 2.29997i
\(413\) 24.3451 + 17.9131i 1.19794 + 0.881446i
\(414\) 0 0
\(415\) −2.17363 + 3.76483i −0.106699 + 0.184808i
\(416\) −5.90001 30.1783i −0.289272 1.47962i
\(417\) 0 0
\(418\) −22.3245 + 12.8890i −1.09193 + 0.630424i
\(419\) 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 \(0.898598\pi\)
\(422\) 19.4559i 0.947100i
\(423\) 0 0
\(424\) 43.9919 25.3987i 2.13644 1.23347i
\(425\) 7.50787 0.364185
\(426\) 0 0
\(427\) −7.69160 0.855355i −0.372223 0.0413936i
\(428\) −24.1401 −1.16685
\(429\) 0 0
\(430\) 7.00223 + 12.1282i 0.337677 + 0.584874i
\(431\) 8.97060i 0.432098i −0.976382 0.216049i \(-0.930683\pi\)
0.976382 0.216049i \(-0.0693172\pi\)
\(432\) 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
\(436\) 8.12228i 0.388987i
\(437\) −6.33204 + 3.65580i −0.302902 + 0.174881i
\(438\) 0 0
\(439\) −19.2572 33.3544i −0.919096 1.59192i −0.800792 0.598943i \(-0.795588\pi\)
−0.118304 0.992977i \(-0.537746\pi\)
\(440\) 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
\(445\) 2.83701 0.134487
\(446\) −58.4492 −2.76765
\(447\) 0 0
\(448\) −12.3169 1.36972i −0.581920 0.0647133i
\(449\) −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
\(451\) 10.4161 18.0412i 0.490476 0.849529i
\(452\) −40.3856 −1.89958
\(453\) 0 0
\(454\) −35.3906 −1.66097
\(455\) −1.26446 15.3259i −0.0592788 0.718491i
\(456\) 0 0
\(457\) −12.0721 + 6.96982i −0.564708 + 0.326034i −0.755033 0.655687i \(-0.772379\pi\)
0.190325 + 0.981721i \(0.439046\pi\)
\(458\) −20.5298 −0.959295
\(459\) 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 \(-0.0501544\pi\)
\(464\) 46.7228 2.16905
\(465\) 0 0
\(466\) 17.0115i 0.788044i
\(467\) −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
\(472\) 39.9353 69.1699i 1.83817 3.18380i
\(473\) −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
\(478\) −12.1572 21.0568i −0.556055 0.963116i
\(479\) 9.45319i 0.431927i −0.976401 0.215964i \(-0.930711\pi\)
0.976401 0.215964i \(-0.0692892\pi\)
\(480\) 0 0
\(481\) 20.3036 + 6.96649i 0.925764 + 0.317645i
\(482\) 26.1082 1.18920
\(483\) 0 0
\(484\) 8.65711 14.9946i 0.393505 0.681571i
\(485\) 24.9579 1.13328
\(486\) 0 0
\(487\) 34.6407 + 19.9998i 1.56972 + 0.906277i 0.996201 + 0.0870831i \(0.0277546\pi\)
0.573517 + 0.819194i \(0.305579\pi\)
\(488\) 20.4504i 0.925748i
\(489\) 0 0
\(490\) −28.4971 6.41748i −1.28737 0.289912i
\(491\) 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
\(494\) 11.1515 32.5008i 0.501732 1.46228i
\(495\) 0 0
\(496\) 78.9125 + 45.5602i 3.54328 + 2.04571i
\(497\) −3.27436 + 1.43424i −0.146875 + 0.0643343i
\(498\) 0 0
\(499\) 9.83591 + 5.67877i 0.440316 + 0.254217i 0.703732 0.710466i \(-0.251516\pi\)
−0.263416 + 0.964682i \(0.584849\pi\)
\(500\) 48.5729 + 28.0436i 2.17225 + 1.25415i
\(501\) 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
\(509\) −17.1602 + 9.90746i −0.760614 + 0.439141i −0.829516 0.558483i \(-0.811384\pi\)
0.0689022 + 0.997623i \(0.478050\pi\)
\(510\) 0 0
\(511\) 22.0616 9.66345i 0.975949 0.427486i
\(512\) 47.4335i 2.09628i
\(513\) 0 0
\(514\) −17.9043 10.3370i −0.789724 0.455947i
\(515\) 16.0093 9.24299i 0.705455 0.407295i
\(516\) 0 0
\(517\) 1.42698 2.47160i 0.0627585 0.108701i
\(518\) 24.1649 32.8417i 1.06174 1.44298i
\(519\) 0 0
\(520\) −39.8816 + 7.79704i −1.74892 + 0.341923i
\(521\) −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
\(523\) −11.3601 19.6763i −0.496742 0.860383i 0.503251 0.864140i \(-0.332137\pi\)
−0.999993 + 0.00375758i \(0.998804\pi\)
\(524\) −23.9960 41.5622i −1.04827 1.81565i
\(525\) 0 0
\(526\) −11.3420 + 6.54831i −0.494535 + 0.285520i
\(527\) 32.7607i 1.42708i
\(528\) 0 0
\(529\) 9.52783 16.5027i 0.414253 0.717508i
\(530\) −15.1597 26.2574i −0.658495 1.14055i
\(531\) 0 0
\(532\) −36.8802 27.1364i −1.59896 1.17651i
\(533\) 5.32794 + 27.2522i 0.230779 + 1.18043i
\(534\) 0 0
\(535\) 8.27830i 0.357902i
\(536\) 94.9564 4.10149
\(537\) 0 0
\(538\) 35.9563i 1.55018i
\(539\) 4.15988 18.4721i 0.179179 0.795649i
\(540\) 0 0
\(541\) −1.81754 1.04936i −0.0781423 0.0451155i 0.460420 0.887701i \(-0.347699\pi\)
−0.538562 + 0.842586i \(0.681032\pi\)
\(542\) −10.7779 + 18.6679i −0.462951 + 0.801855i
\(543\) 0 0
\(544\) 23.0926 13.3325i 0.990087 0.571627i
\(545\) 2.78536 0.119312
\(546\) 0 0
\(547\) 25.3770 1.08504 0.542521 0.840042i \(-0.317470\pi\)
0.542521 + 0.840042i \(0.317470\pi\)
\(548\) −40.6805 + 23.4869i −1.73778 + 1.00331i
\(549\) 0 0
\(550\) −8.40696 + 14.5613i −0.358474 + 0.620895i
\(551\) 17.1297 + 9.88983i 0.729749 + 0.421321i
\(552\) 0 0
\(553\) 9.73076 13.2248i 0.413794 0.562374i
\(554\) 60.0855i 2.55279i
\(555\) 0 0
\(556\) 7.82316 0.331776
\(557\) 44.2503i 1.87495i 0.348058 + 0.937473i \(0.386841\pi\)
−0.348058 + 0.937473i \(0.613159\pi\)
\(558\) 0 0
\(559\) 3.92705 11.4452i 0.166097 0.484082i
\(560\) −4.09944 + 36.8634i −0.173233 + 1.55776i
\(561\) 0 0
\(562\) −35.1526 60.8860i −1.48282 2.56832i
\(563\) 19.4453 33.6803i 0.819523 1.41946i −0.0865108 0.996251i \(-0.527572\pi\)
0.906034 0.423205i \(-0.139095\pi\)
\(564\) 0 0
\(565\) 13.8494i 0.582647i
\(566\) 36.2078 20.9046i 1.52193 0.878685i
\(567\) 0 0
\(568\) 4.72309 + 8.18063i 0.198177 + 0.343252i
\(569\) −23.0789 39.9739i −0.967520 1.67579i −0.702687 0.711499i \(-0.748017\pi\)
−0.264832 0.964294i \(-0.585317\pi\)
\(570\) 0 0
\(571\) 10.5684 + 18.3050i 0.442274 + 0.766041i 0.997858 0.0654194i \(-0.0208385\pi\)
−0.555584 + 0.831461i \(0.687505\pi\)
\(572\) −8.79673 44.9949i −0.367810 1.88133i
\(573\) 0 0
\(574\) 52.4229 + 5.82976i 2.18809 + 0.243329i
\(575\) −2.38452 + 4.13011i −0.0994413 + 0.172237i
\(576\) 0 0
\(577\) −21.9368 + 12.6652i −0.913239 + 0.527259i −0.881472 0.472237i \(-0.843447\pi\)
−0.0317671 + 0.999495i \(0.510113\pi\)
\(578\) 16.1955 + 9.35045i 0.673642 + 0.388927i
\(579\) 0 0
\(580\) 40.7146i 1.69058i
\(581\) 0.788579 7.09113i 0.0327158 0.294190i
\(582\) 0 0
\(583\) 17.0203 9.82667i 0.704908 0.406979i
\(584\) −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
\(592\) −44.8369 25.8866i −1.84278 1.06393i
\(593\) 21.9568 + 12.6768i 0.901659 + 0.520573i 0.877738 0.479141i \(-0.159052\pi\)
0.0239212 + 0.999714i \(0.492385\pi\)
\(594\) 0 0
\(595\) 12.2149 5.35037i 0.500761 0.219344i
\(596\) 80.5990 + 46.5338i 3.30146 + 1.90610i
\(597\) 0 0
\(598\) −3.55661 18.1919i −0.145441 0.743924i
\(599\) 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 −0.999981 0.00608649i \(-0.998063\pi\)
0.505262 + 0.862966i \(0.331396\pi\)
\(602\) −18.5131 13.6219i −0.754536 0.555187i
\(603\) 0 0
\(604\) 35.4206i 1.44124i
\(605\) −5.14205 2.96876i −0.209054 0.120697i
\(606\) 0 0
\(607\) −9.85447 −0.399981 −0.199990 0.979798i \(-0.564091\pi\)
−0.199990 + 0.979798i \(0.564091\pi\)
\(608\) −15.6987 + 27.1910i −0.636667 + 1.10274i
\(609\) 0 0
\(610\) 12.2062 0.494215
\(611\) 0.729914 + 3.73348i 0.0295291 + 0.151040i
\(612\) 0 0
\(613\) 3.67688i 0.148508i −0.997239 0.0742540i \(-0.976342\pi\)
0.997239 0.0742540i \(-0.0236575\pi\)
\(614\) −11.6208 20.1278i −0.468977 0.812293i
\(615\) 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 \(-0.770157\pi\)
0.197174 + 0.980369i \(0.436824\pi\)
\(620\) 39.7014 68.7649i 1.59445 2.76167i
\(621\) 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
\(626\) 33.9727i 1.35782i
\(627\) 0 0
\(628\) −65.8330 −2.62702
\(629\) 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
\(634\) 43.2698 1.71846
\(635\) 4.36151 2.51812i 0.173081 0.0999286i
\(636\) 0 0
\(637\) 11.9929 + 22.2074i 0.475177 + 0.879890i
\(638\) 37.6200 1.48939
\(639\) 0 0
\(640\) −7.95016 −0.314258
\(641\) 14.8893 25.7890i 0.588092 1.01860i −0.406390 0.913699i \(-0.633213\pi\)
0.994482 0.104905i \(-0.0334539\pi\)
\(642\) 0 0
\(643\) 10.0220 5.78623i 0.395231 0.228187i −0.289193 0.957271i \(-0.593387\pi\)
0.684424 + 0.729084i \(0.260054\pi\)
\(644\) −24.5496 2.73007i −0.967389 0.107580i
\(645\) 0 0
\(646\) 29.7964 1.17232
\(647\) 25.5065 1.00276 0.501382 0.865226i \(-0.332825\pi\)
0.501382 + 0.865226i \(0.332825\pi\)
\(648\) 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
\(653\) −22.4146 38.8233i −0.877152 1.51927i −0.854452 0.519530i \(-0.826107\pi\)
−0.0227004 0.999742i \(-0.507226\pi\)
\(654\) 0 0
\(655\) −14.2529 + 8.22889i −0.556905 + 0.321529i
\(656\) 66.9747i 2.61492i
\(657\) 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
\(661\) 21.8938i 0.851569i −0.904825 0.425785i \(-0.859998\pi\)
0.904825 0.425785i \(-0.140002\pi\)
\(662\) 5.13404 + 8.89241i 0.199540 + 0.345613i
\(663\) 0 0
\(664\) −18.8539 −0.731673
\(665\) −9.30583 + 12.6473i −0.360865 + 0.490439i
\(666\) 0 0
\(667\) 10.6704 0.413160
\(668\) −73.1999 + 42.2620i −2.83219 + 1.63516i
\(669\) 0 0
\(670\) 56.6764i 2.18960i
\(671\) 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 \(-0.0746102\pi\)
\(674\) −30.7197 + 17.7361i −1.18328 + 0.683167i
\(675\) 0 0
\(676\) 48.2376 + 37.5193i 1.85529 + 1.44305i
\(677\) 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
\(679\) −37.5201 + 16.4346i −1.43989 + 0.630701i
\(680\) −17.6193 30.5175i −0.675670 1.17029i
\(681\) 0 0
\(682\) 63.5384 + 36.6839i 2.43301 + 1.40470i
\(683\) 30.9517 + 17.8700i 1.18433 + 0.683775i 0.957013 0.290045i \(-0.0936704\pi\)
0.227320 + 0.973820i \(0.427004\pi\)
\(684\) 0 0
\(685\) 8.05431 + 13.9505i 0.307739 + 0.533020i
\(686\) 47.0666 9.11748i 1.79701 0.348107i
\(687\) 0 0
\(688\) −14.5924 + 25.2748i −0.556330 + 0.963592i
\(689\) −8.50199 + 24.7788i −0.323900 + 0.943995i
\(690\) 0 0
\(691\) 22.5419 13.0146i 0.857536 0.495099i −0.00565028 0.999984i \(-0.501799\pi\)
0.863186 + 0.504885i \(0.168465\pi\)
\(692\) −30.1127 + 52.1567i −1.14471 + 1.98270i
\(693\) 0 0
\(694\) 68.3335i 2.59391i
\(695\) 2.68278i 0.101764i
\(696\) 0 0
\(697\) −20.8535 + 12.0398i −0.789884 + 0.456040i
\(698\) −12.6589 −0.479146
\(699\) 0 0
\(700\) −29.6825 3.30088i −1.12189 0.124762i
\(701\) 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
\(704\) 12.6702i 0.477525i
\(705\) 0 0
\(706\) 17.5478 + 30.3936i 0.660419 + 1.14388i
\(707\) −3.36398 0.374096i −0.126515 0.0140693i
\(708\) 0 0
\(709\) 6.05031i 0.227224i 0.993525 + 0.113612i \(0.0362421\pi\)
−0.993525 + 0.113612i \(0.963758\pi\)
\(710\) 4.88276 2.81906i 0.183247 0.105798i
\(711\) 0 0
\(712\) 6.15202 + 10.6556i 0.230557 + 0.399336i
\(713\) 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
\(718\) 22.2249 0.829425
\(719\) 47.1177 1.75719 0.878597 0.477563i \(-0.158480\pi\)
0.878597 + 0.477563i \(0.158480\pi\)
\(720\) 0 0
\(721\) −17.9810 + 24.4374i −0.669647 + 0.910095i
\(722\) 12.2100 7.04944i 0.454409 0.262353i
\(723\) 0 0
\(724\) −7.75473 + 13.4316i −0.288202 + 0.499181i
\(725\) 12.9014 0.479146
\(726\) 0 0
\(727\) 17.9215 0.664671 0.332335 0.943161i \(-0.392163\pi\)
0.332335 + 0.943161i \(0.392163\pi\)
\(728\) 54.8211 37.9833i 2.03181 1.40775i
\(729\) 0 0
\(730\) −32.8985 + 18.9940i −1.21763 + 0.702999i
\(731\) 10.4929 0.388093
\(732\) 0 0
\(733\) 39.2037 + 22.6343i 1.44802 + 0.836016i 0.998364 0.0571848i \(-0.0182124\pi\)
0.449658 + 0.893201i \(0.351546\pi\)
\(734\) −3.72861 + 2.15271i −0.137625 + 0.0794581i
\(735\) 0 0
\(736\) 16.9378i 0.624335i
\(737\) 36.7382 1.35327
\(738\) 0 0
\(739\) 19.2613i 0.708539i 0.935143 + 0.354270i \(0.115270\pi\)
−0.935143 + 0.354270i \(0.884730\pi\)
\(740\) −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
\(745\) 15.9577 27.6396i 0.584647 1.01264i
\(746\) 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
\(751\) −12.4834 21.6219i −0.455526 0.788993i 0.543193 0.839608i \(-0.317215\pi\)
−0.998718 + 0.0506146i \(0.983882\pi\)
\(752\) 9.17535i 0.334591i
\(753\) 0 0
\(754\) −37.8095 + 32.9393i −1.37694 + 1.19958i
\(755\) −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 \(0.104936\pi\)
\(758\) −81.7370 −2.96882
\(759\) 0 0
\(760\) 35.9337 + 20.7463i 1.30345 + 0.752548i
\(761\) 32.6388i 1.18316i 0.806248 + 0.591578i \(0.201495\pi\)
−0.806248 + 0.591578i \(0.798505\pi\)
\(762\) 0 0
\(763\) −4.18733 + 1.83414i −0.151592 + 0.0664002i
\(764\) −11.5080 + 19.9325i −0.416345 + 0.721131i
\(765\) 0 0
\(766\) −41.2988 71.5316i −1.49219 2.58454i
\(767\) 7.90323 + 40.4247i 0.285369 + 1.45965i
\(768\) 0 0
\(769\) −45.1851 26.0876i −1.62942 0.940744i −0.984267 0.176686i \(-0.943462\pi\)
−0.645148 0.764057i \(-0.723204\pi\)
\(770\) −3.30077 + 29.6814i −0.118951 + 1.06964i
\(771\) 0 0
\(772\) 12.2909 + 7.09618i 0.442360 + 0.255397i
\(773\) 30.9221 + 17.8529i 1.11219 + 0.642123i 0.939396 0.342835i \(-0.111387\pi\)
0.172794 + 0.984958i \(0.444721\pi\)
\(774\) 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
\(782\) 13.9206 8.03703i 0.497798 0.287404i
\(783\) 0 0
\(784\) −18.1114 58.1175i −0.646836 2.07563i
\(785\) 22.5760i 0.805770i
\(786\) 0 0
\(787\) 5.28813 + 3.05310i 0.188501 + 0.108831i 0.591281 0.806466i \(-0.298622\pi\)
−0.402779 + 0.915297i \(0.631956\pi\)
\(788\) −18.9301 + 10.9293i −0.674356 + 0.389339i