Properties

Label 819.2.do.e.361.6
Level $819$
Weight $2$
Character 819.361
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 361.6
Root \(1.32725 + 0.488273i\) of defining polynomial
Character \(\chi\) \(=\) 819.361
Dual form 819.2.do.e.667.6

$q$-expansion

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

Character values

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

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.24179 + 1.29430i 1.58519 + 0.915209i 0.994084 + 0.108613i \(0.0346409\pi\)
0.591104 + 0.806596i \(0.298692\pi\)
\(3\) 0 0
\(4\) 2.35043 + 4.07106i 1.17521 + 2.03553i
\(5\) −1.39608 + 0.806027i −0.624346 + 0.360466i −0.778559 0.627571i \(-0.784049\pi\)
0.154213 + 0.988038i \(0.450716\pi\)
\(6\) 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 \(0.133700\pi\)
−0.913077 + 0.407788i \(0.866300\pi\)
\(12\) 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 0.611783 0.791026i \(-0.290453\pi\)
−0.990940 + 0.134307i \(0.957119\pi\)
\(18\) 0 0
\(19\) 3.68150i 0.844595i 0.906457 + 0.422297i \(0.138776\pi\)
−0.906457 + 0.422297i \(0.861224\pi\)
\(20\) −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 −0.950787 0.309846i \(-0.899722\pi\)
0.743728 + 0.668482i \(0.233056\pi\)
\(24\) 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 0.501155 0.865357i \(-0.332908\pi\)
−0.999999 + 0.00133469i \(0.999575\pi\)
\(30\) 0 0
\(31\) −9.07425 5.23902i −1.62978 0.940956i −0.984156 0.177303i \(-0.943263\pi\)
−0.645627 0.763653i \(-0.723404\pi\)
\(32\) −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 0.859846 0.510554i \(-0.170560\pi\)
−0.0122297 + 0.999925i \(0.503893\pi\)
\(38\) −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
\(46\) −4.45229 + 2.57053i −0.656454 + 0.379004i
\(47\) 0.913730 0.527542i 0.133281 0.0769500i −0.431877 0.901933i \(-0.642148\pi\)
0.565158 + 0.824983i \(0.308815\pi\)
\(48\) 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 −0.500991 0.865453i \(-0.667031\pi\)
0.999999 + 0.00114437i \(0.000364265\pi\)
\(54\) 0 0
\(55\) −2.18027 3.77633i −0.293987 0.509201i
\(56\) 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 0.309725 0.950826i \(-0.399763\pi\)
0.978302 + 0.207183i \(0.0664297\pi\)
\(60\) 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 \(-0.688545\pi\)
0.558296 0.829642i \(-0.311455\pi\)
\(68\) 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 0.428958 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 \(-0.154498\pi\)
0.0382192 + 0.999269i \(0.487831\pi\)
\(74\) 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 0.986090 0.166211i \(-0.0531532\pi\)
−0.636988 + 0.770874i \(0.719820\pi\)
\(80\) 14.0189i 1.56736i
\(81\) 0 0
\(82\) 19.9361 2.20158
\(83\) 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
\(88\) −18.9115 −2.01597
\(89\) −1.52410 0.879938i −0.161554 0.0932732i 0.417043 0.908887i \(-0.363066\pi\)
−0.578597 + 0.815613i \(0.696400\pi\)
\(90\) 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 −0.371555 0.928411i \(-0.621175\pi\)
−0.989805 + 0.142430i \(0.954509\pi\)
\(98\) 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 −0.997054 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
\(107\) −2.56763 + 4.44726i −0.248222 + 0.429933i −0.963033 0.269385i \(-0.913180\pi\)
0.714811 + 0.699318i \(0.246513\pi\)
\(108\) 0 0
\(109\) −1.49635 0.863916i −0.143324 0.0827481i 0.426623 0.904429i \(-0.359703\pi\)
−0.569947 + 0.821681i \(0.693036\pi\)
\(110\) 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 −0.994215 0.107404i \(-0.965746\pi\)
0.590123 + 0.807314i \(0.299079\pi\)
\(114\) 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 0.788361 0.615214i \(-0.210930\pi\)
−0.926971 + 0.375133i \(0.877597\pi\)
\(128\) 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 0.998121 0.0612793i \(-0.0195180\pi\)
−0.552130 + 0.833758i \(0.686185\pi\)
\(132\) 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 −0.821832 0.569729i \(-0.807048\pi\)
0.0824839 + 0.996592i \(0.473715\pi\)
\(138\) 0 0
\(139\) 0.832100 1.44124i 0.0705778 0.122244i −0.828577 0.559875i \(-0.810849\pi\)
0.899155 + 0.437631i \(0.144182\pi\)
\(140\) −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 \(-0.698946\pi\)
0.585103 0.810959i \(-0.301054\pi\)
\(150\) 0 0
\(151\) 6.52544 + 3.76746i 0.531033 + 0.306592i 0.741437 0.671023i \(-0.234145\pi\)
−0.210404 + 0.977614i \(0.567478\pi\)
\(152\) −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 0.438755 + 0.898607i \(0.355420\pi\)
−0.997594 + 0.0693309i \(0.977914\pi\)
\(158\) 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 \(0.0905987\pi\)
−0.959767 + 0.280797i \(0.909401\pi\)
\(164\) 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 −0.961656 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
\(172\) −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 \(-0.965344\pi\)
0.994079 0.108660i \(-0.0346559\pi\)
\(194\) −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
\(199\) 0.205360 + 0.355694i 0.0145576 + 0.0252145i 0.873212 0.487340i \(-0.162033\pi\)
−0.858655 + 0.512554i \(0.828699\pi\)
\(200\) −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 0.965897 0.258927i \(-0.0833688\pi\)
−0.707186 + 0.707028i \(0.750035\pi\)
\(212\) 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 −0.982006 0.188852i \(-0.939523\pi\)
−0.327452 + 0.944868i \(0.606190\pi\)
\(224\) −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 −0.838500 0.544901i \(-0.816567\pi\)
0.0526478 + 0.998613i \(0.483234\pi\)
\(228\) 0 0
\(229\) −6.86832 + 3.96543i −0.453872 + 0.262043i −0.709464 0.704742i \(-0.751063\pi\)
0.255592 + 0.966785i \(0.417730\pi\)
\(230\) 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
\(236\) 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 \(0.0982508\pi\)
−0.952740 + 0.303786i \(0.901749\pi\)
\(240\) 0 0
\(241\) 8.73460 5.04292i 0.562645 0.324843i −0.191562 0.981481i \(-0.561355\pi\)
0.754206 + 0.656637i \(0.228022\pi\)
\(242\) 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 −0.655237 0.755423i \(-0.727431\pi\)
0.981834 + 0.189741i \(0.0607648\pi\)
\(252\) 0 0
\(253\) −4.65242 2.68607i −0.292495 0.168872i
\(254\) 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 −0.963275 0.268517i \(-0.913466\pi\)
0.714180 + 0.699962i \(0.246800\pi\)
\(258\) 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 0.996274 0.0862400i \(-0.0274852\pi\)
−0.572823 + 0.819679i \(0.694152\pi\)
\(270\) 0 0
\(271\) −7.21158 4.16361i −0.438072 0.252921i 0.264707 0.964329i \(-0.414725\pi\)
−0.702780 + 0.711408i \(0.748058\pi\)
\(272\) 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 −0.969391 0.245523i \(-0.921040\pi\)
0.272066 0.962279i \(-0.412293\pi\)
\(278\) 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 \(0.300587\pi\)
−0.586292 + 0.810100i \(0.699413\pi\)
\(282\) 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 0.822417 0.568885i \(-0.192625\pi\)
−0.0814609 + 0.996677i \(0.525959\pi\)
\(294\) 0 0
\(295\) −9.20810 + 15.9489i −0.536116 + 0.928580i
\(296\) −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 \(0.0824750\pi\)
−0.966620 + 0.256213i \(0.917525\pi\)
\(308\) −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 −0.985422 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 −0.0349599 0.999389i \(-0.511130\pi\)
0.848016 + 0.529971i \(0.177797\pi\)
\(318\) 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 \(-0.965231\pi\)
0.994040 0.109013i \(-0.0347691\pi\)
\(332\) −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 −0.965393 0.260800i \(-0.916014\pi\)
0.256837 0.966455i \(-0.417320\pi\)
\(348\) 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
\(353\) 13.5577i 0.721605i −0.932642 0.360802i \(-0.882503\pi\)
0.932642 0.360802i \(-0.117497\pi\)
\(354\) 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 −0.290785 0.956789i \(-0.593916\pi\)
0.683211 + 0.730221i \(0.260583\pi\)
\(360\) 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 −0.994864 0.101218i \(-0.967726\pi\)
−0.409775 + 0.912187i \(0.634393\pi\)
\(380\) 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 \(0.303382\pi\)
−0.579156 + 0.815217i \(0.696618\pi\)
\(384\) 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 −0.340168 0.940365i \(-0.610484\pi\)
0.984464 0.175589i \(-0.0561829\pi\)
\(390\) 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 \(-0.966719\pi\)
0.994539 0.104366i \(-0.0332815\pi\)
\(398\) 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 0.859875 0.510504i \(-0.170541\pi\)
−0.0121716 + 0.999926i \(0.503874\pi\)
\(402\) 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 −0.827539 0.561409i \(-0.810260\pi\)
0.0724249 + 0.997374i \(0.476926\pi\)
\(410\) −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 0.956824 + 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 \(-0.101402\pi\)
\(422\) 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 \(0.0693172\pi\)
−0.976382 + 0.216049i \(0.930683\pi\)
\(432\) 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
\(436\) 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 −0.118304 + 0.992977i \(0.537746\pi\)
−0.800792 + 0.598943i \(0.795588\pi\)
\(440\) 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
\(445\) 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 −0.993168 0.116696i \(-0.962770\pi\)
−0.597646 0.801760i \(-0.703897\pi\)
\(450\) 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 0.190325 0.981721i \(-0.439046\pi\)
−0.755033 + 0.655687i \(0.772379\pi\)
\(458\) −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 −0.999916 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 \(0.949846\pi\)
\(464\) 46.7228 2.16905
\(465\) 0 0
\(466\) 17.0115i 0.788044i
\(467\) −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
\(472\) 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 \(0.0692892\pi\)
−0.976401 + 0.215964i \(0.930711\pi\)
\(480\) 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 0.573517 0.819194i \(-0.305579\pi\)
0.996201 0.0870831i \(-0.0277546\pi\)
\(488\) 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 0.932168 0.362027i \(-0.117915\pi\)
−0.779608 + 0.626267i \(0.784582\pi\)
\(492\) 0 0
\(493\) −8.39918 + 14.5478i −0.378280 + 0.655200i
\(494\) 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 −0.263416 0.964682i \(-0.584849\pi\)
0.703732 + 0.710466i \(0.251516\pi\)
\(500\) 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 −0.978475 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
\(509\) −17.1602 9.90746i −0.760614 0.439141i 0.0689022 0.997623i \(-0.478050\pi\)
−0.829516 + 0.558483i \(0.811384\pi\)
\(510\) 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 0.293479 + 0.955966i \(0.405187\pi\)
−0.974630 + 0.223823i \(0.928146\pi\)
\(522\) 0 0
\(523\) −11.3601 + 19.6763i −0.496742 + 0.860383i −0.999993 0.00375758i \(-0.998804\pi\)
0.503251 + 0.864140i \(0.332137\pi\)
\(524\) −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 −0.538562 0.842586i \(-0.681032\pi\)
0.460420 + 0.887701i \(0.347699\pi\)
\(542\) −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 \(-0.613159\pi\)
0.348058 0.937473i \(-0.386841\pi\)
\(558\) 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 0.906034 + 0.423205i \(0.139095\pi\)
−0.0865108 + 0.996251i \(0.527572\pi\)
\(564\) 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 −0.264832 + 0.964294i \(0.585317\pi\)
−0.702687 + 0.711499i \(0.748017\pi\)
\(570\) 0 0
\(571\) 10.5684 18.3050i 0.442274 0.766041i −0.555584 0.831461i \(-0.687505\pi\)
0.997858 + 0.0654194i \(0.0208385\pi\)
\(572\) −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 −0.0317671 0.999495i \(-0.510113\pi\)
−0.881472 + 0.472237i \(0.843447\pi\)
\(578\) 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 −0.562324 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
\(592\) −44.8369 + 25.8866i −1.84278 + 1.06393i
\(593\) 21.9568 12.6768i 0.901659 0.520573i 0.0239212 0.999714i \(-0.492385\pi\)
0.877738 + 0.479141i \(0.159052\pi\)
\(594\) 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 −0.732633 0.680624i \(-0.761709\pi\)
0.955754 + 0.294166i \(0.0950420\pi\)
\(600\) 0 0
\(601\) −12.1282 21.0067i −0.494720 0.856880i 0.505262 0.862966i \(-0.331396\pi\)
−0.999981 + 0.00608649i \(0.998063\pi\)
\(602\) −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 \(0.0236575\pi\)
−0.997239 + 0.0742540i \(0.976342\pi\)
\(614\) −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 0.136231 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 \(-0.436824\pi\)
−0.750437 + 0.660942i \(0.770157\pi\)
\(620\) 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 0.119400 0.992846i \(-0.461903\pi\)
−0.800130 + 0.599826i \(0.795236\pi\)
\(632\) −37.5745 + 21.6936i −1.49463 + 0.862927i
\(633\) 0 0
\(634\) 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 0.994482 + 0.104905i \(0.0334539\pi\)
−0.406390 + 0.913699i \(0.633213\pi\)
\(642\) 0 0
\(643\) 10.0220 + 5.78623i 0.395231 + 0.228187i 0.684424 0.729084i \(-0.260054\pi\)
−0.289193 + 0.957271i \(0.593387\pi\)
\(644\) −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 −0.0227004 + 0.999742i \(0.507226\pi\)
−0.854452 + 0.519530i \(0.826107\pi\)
\(654\) 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 −0.116390 0.993204i \(-0.537132\pi\)
0.918335 0.395805i \(-0.129534\pi\)
\(660\) 0 0
\(661\) 21.8938i 0.851569i 0.904825 + 0.425785i \(0.140002\pi\)
−0.904825 + 0.425785i \(0.859998\pi\)
\(662\) 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 0.972655 + 0.232254i \(0.0746102\pi\)
−0.285189 + 0.958471i \(0.592056\pi\)
\(674\) −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 0.889533 0.456871i \(-0.151030\pi\)
−0.840428 + 0.541923i \(0.817697\pi\)
\(678\) 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 0.227320 0.973820i \(-0.427004\pi\)
0.957013 + 0.290045i \(0.0936704\pi\)
\(684\) 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 0.863186 0.504885i \(-0.168465\pi\)
−0.00565028 + 0.999984i \(0.501799\pi\)
\(692\) −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 \(-0.963758\pi\)
0.993525 0.113612i \(-0.0362421\pi\)
\(710\) 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 0.449658 0.893201i \(-0.351546\pi\)
0.998364 + 0.0571848i \(0.0182124\pi\)
\(734\) −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 \(-0.884730\pi\)
0.935143 0.354270i \(-0.115270\pi\)
\(740\) −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
\(745\) 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 −0.998718 0.0506146i \(-0.983882\pi\)
0.543193 + 0.839608i \(0.317215\pi\)
\(752\) 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 0.946151 0.323726i \(-0.104936\pi\)
−0.753431 + 0.657527i \(0.771602\pi\)
\(758\) −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 \(-0.798505\pi\)
0.806248 0.591578i \(-0.201495\pi\)
\(762\) 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 −0.645148 + 0.764057i \(0.723204\pi\)
−0.984267 + 0.176686i \(0.943462\pi\)
\(770\) −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 0.172794 0.984958i \(-0.444721\pi\)
0.939396 + 0.342835i \(0.111387\pi\)
\(774\) 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 −0.402779 0.915297i \(-0.631956\pi\)
0.591281 + 0.806466i \(0.298622\pi\)
\(788\) −18.9301 10.9293i