Properties

Label 637.2.u.g.361.1
Level $637$
Weight $2$
Character 637.361
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.u (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.1
Root \(1.32725 + 0.488273i\) of defining polynomial
Character \(\chi\) \(=\) 637.361
Dual form 637.2.u.g.30.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.24179 - 1.29430i) q^{2} -0.518466 q^{3} +(2.35043 + 4.07106i) q^{4} +(-1.39608 + 0.806027i) q^{5} +(1.16229 + 0.671051i) q^{6} -6.99143i q^{8} -2.73119 q^{9} +O(q^{10})\) \(q+(-2.24179 - 1.29430i) q^{2} -0.518466 q^{3} +(2.35043 + 4.07106i) q^{4} +(-1.39608 + 0.806027i) q^{5} +(1.16229 + 0.671051i) q^{6} -6.99143i q^{8} -2.73119 q^{9} +4.17296 q^{10} -2.70496i q^{11} +(-1.21862 - 2.11070i) q^{12} +(-2.36840 + 2.71858i) q^{13} +(0.723819 - 0.417897i) q^{15} +(-4.34816 + 7.53123i) q^{16} +(-1.56330 - 2.70772i) q^{17} +(6.12277 + 3.53498i) q^{18} -3.68150i q^{19} +(-6.56276 - 3.78901i) q^{20} +(-3.50103 + 6.06396i) q^{22} +(0.993019 - 1.71996i) q^{23} +3.62482i q^{24} +(-1.20064 + 2.07957i) q^{25} +(8.82813 - 3.02907i) q^{26} +2.97143 q^{27} +(2.68636 + 4.65290i) q^{29} -2.16354 q^{30} +(9.07425 + 5.23902i) q^{31} +(7.38583 - 4.26421i) q^{32} +1.40243i q^{33} +8.09354i q^{34} +(-6.41947 - 11.1188i) q^{36} +(5.15585 + 2.97673i) q^{37} +(-4.76497 + 8.25317i) q^{38} +(1.22794 - 1.40949i) q^{39} +(5.63528 + 9.76059i) q^{40} +(6.66970 - 3.85075i) q^{41} +(-1.67800 + 2.90638i) q^{43} +(11.0120 - 6.35780i) q^{44} +(3.81296 - 2.20141i) q^{45} +(-4.45229 + 2.57053i) q^{46} +(0.913730 - 0.527542i) q^{47} +(2.25437 - 3.90469i) q^{48} +(5.38318 - 3.10798i) q^{50} +(0.810520 + 1.40386i) q^{51} +(-16.6343 - 3.25208i) q^{52} +(-3.63284 + 6.29226i) q^{53} +(-6.66133 - 3.84592i) q^{54} +(2.18027 + 3.77633i) q^{55} +1.90873i q^{57} -13.9078i q^{58} +(9.89352 - 5.71203i) q^{59} +(3.40257 + 1.96447i) q^{60} +2.92507 q^{61} +(-13.5617 - 23.4896i) q^{62} -4.68406 q^{64} +(1.11523 - 5.70435i) q^{65} +(1.81516 - 3.14395i) q^{66} -13.5818i q^{67} +(7.34886 - 12.7286i) q^{68} +(-0.514846 + 0.891740i) q^{69} +(1.17009 + 0.675554i) q^{71} +19.0949i q^{72} +(-7.88374 - 4.55168i) q^{73} +(-7.70557 - 13.3464i) q^{74} +(0.622492 - 1.07819i) q^{75} +(14.9876 - 8.65311i) q^{76} +(-4.57708 + 1.57047i) q^{78} +(3.10289 + 5.37436i) q^{79} -14.0189i q^{80} +6.65300 q^{81} -19.9361 q^{82} +2.69672i q^{83} +(4.36499 + 2.52013i) q^{85} +(7.52346 - 4.34367i) q^{86} +(-1.39278 - 2.41237i) q^{87} -18.9115 q^{88} +(-1.52410 - 0.879938i) q^{89} -11.3972 q^{90} +9.33607 q^{92} +(-4.70469 - 2.71625i) q^{93} -2.73119 q^{94} +(2.96739 + 5.13967i) q^{95} +(-3.82930 + 2.21085i) q^{96} +(13.4078 + 7.74102i) q^{97} +7.38776i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9} + O(q^{10}) \) \( 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9} + 24 q^{10} + q^{12} + 2 q^{13} - 12 q^{15} - 8 q^{16} - 17 q^{17} - 3 q^{18} + 3 q^{20} - 15 q^{22} + 3 q^{23} - 5 q^{25} + 9 q^{26} - 12 q^{27} - q^{29} - 22 q^{30} + 18 q^{31} + 18 q^{32} - 13 q^{36} + 15 q^{37} - 19 q^{38} - q^{39} + q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 9 q^{45} - 30 q^{46} - 15 q^{47} - 19 q^{48} + 18 q^{50} + 4 q^{51} - 47 q^{52} - 8 q^{53} - 6 q^{54} + 15 q^{55} - 27 q^{59} + 30 q^{60} + 10 q^{61} - 41 q^{62} + 2 q^{64} - 3 q^{65} + 34 q^{66} + 11 q^{68} - 7 q^{69} + 30 q^{71} + 42 q^{73} - 33 q^{74} - q^{75} + 45 q^{76} + 44 q^{78} - 35 q^{79} - 28 q^{81} + 10 q^{82} - 21 q^{85} + 57 q^{86} - 10 q^{87} + 28 q^{88} - 48 q^{89} - 66 q^{92} - 81 q^{93} + 2 q^{94} + 2 q^{95} + 21 q^{96} + 3 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

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 \(-0.965359\pi\)
−0.591104 0.806596i \(-0.701308\pi\)
\(3\) −0.518466 −0.299336 −0.149668 0.988736i \(-0.547821\pi\)
−0.149668 + 0.988736i \(0.547821\pi\)
\(4\) 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 \(0.450716\pi\)
\(6\) 1.16229 + 0.671051i 0.474504 + 0.273955i
\(7\) 0 0
\(8\) 6.99143i 2.47184i
\(9\) −2.73119 −0.910398
\(10\) 4.17296 1.31961
\(11\) 2.70496i 0.815575i −0.913077 0.407788i \(-0.866300\pi\)
0.913077 0.407788i \(-0.133700\pi\)
\(12\) −1.21862 2.11070i −0.351784 0.609308i
\(13\) −2.36840 + 2.71858i −0.656876 + 0.753998i
\(14\) 0 0
\(15\) 0.723819 0.417897i 0.186889 0.107901i
\(16\) −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 \(0.957119\pi\)
\(18\) 6.12277 + 3.53498i 1.44315 + 0.833204i
\(19\) 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 \(-0.766944\pi\)
0.950787 + 0.309846i \(0.100278\pi\)
\(24\) 3.62482i 0.739913i
\(25\) −1.20064 + 2.07957i −0.240128 + 0.415914i
\(26\) 8.82813 3.02907i 1.73134 0.594050i
\(27\) 2.97143 0.571852
\(28\) 0 0
\(29\) 2.68636 + 4.65290i 0.498844 + 0.864023i 0.999999 0.00133469i \(-0.000424845\pi\)
−0.501155 + 0.865357i \(0.667092\pi\)
\(30\) −2.16354 −0.395006
\(31\) 9.07425 + 5.23902i 1.62978 + 0.940956i 0.984156 + 0.177303i \(0.0567372\pi\)
0.645627 + 0.763653i \(0.276596\pi\)
\(32\) 7.38583 4.26421i 1.30564 0.753813i
\(33\) 1.40243i 0.244131i
\(34\) 8.09354i 1.38803i
\(35\) 0 0
\(36\) −6.41947 11.1188i −1.06991 1.85314i
\(37\) 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
\(39\) 1.22794 1.40949i 0.196627 0.225699i
\(40\) 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
\(45\) 3.81296 2.20141i 0.568403 0.328168i
\(46\) −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 \(0.308815\pi\)
\(48\) 2.25437 3.90469i 0.325390 0.563593i
\(49\) 0 0
\(50\) 5.38318 3.10798i 0.761297 0.439535i
\(51\) 0.810520 + 1.40386i 0.113495 + 0.196580i
\(52\) −16.6343 3.25208i −2.30676 0.450982i
\(53\) −3.63284 + 6.29226i −0.499009 + 0.864308i −0.999999 0.00114437i \(-0.999636\pi\)
0.500991 + 0.865453i \(0.332969\pi\)
\(54\) −6.66133 3.84592i −0.906492 0.523363i
\(55\) 2.18027 + 3.77633i 0.293987 + 0.509201i
\(56\) 0 0
\(57\) 1.90873i 0.252818i
\(58\) 13.9078i 1.82618i
\(59\) 9.89352 5.71203i 1.28803 0.743643i 0.309725 0.950826i \(-0.399763\pi\)
0.978302 + 0.207183i \(0.0664297\pi\)
\(60\) 3.40257 + 1.96447i 0.439270 + 0.253613i
\(61\) 2.92507 0.374517 0.187259 0.982311i \(-0.440040\pi\)
0.187259 + 0.982311i \(0.440040\pi\)
\(62\) −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
\(66\) 1.81516 3.14395i 0.223431 0.386994i
\(67\) 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
\(69\) −0.514846 + 0.891740i −0.0619802 + 0.107353i
\(70\) 0 0
\(71\) 1.17009 + 0.675554i 0.138865 + 0.0801736i 0.567823 0.823151i \(-0.307786\pi\)
−0.428958 + 0.903324i \(0.641119\pi\)
\(72\) 19.0949i 2.25036i
\(73\) −7.88374 4.55168i −0.922721 0.532733i −0.0382192 0.999269i \(-0.512169\pi\)
−0.884502 + 0.466536i \(0.845502\pi\)
\(74\) −7.70557 13.3464i −0.895754 1.55149i
\(75\) 0.622492 1.07819i 0.0718791 0.124498i
\(76\) 14.9876 8.65311i 1.71920 0.992579i
\(77\) 0 0
\(78\) −4.57708 + 1.57047i −0.518252 + 0.177821i
\(79\) 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
\(81\) 6.65300 0.739222
\(82\) −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
\(87\) −1.39278 2.41237i −0.149322 0.258633i
\(88\) −18.9115 −2.01597
\(89\) −1.52410 0.879938i −0.161554 0.0932732i 0.417043 0.908887i \(-0.363066\pi\)
−0.578597 + 0.815613i \(0.696400\pi\)
\(90\) −11.3972 −1.20137
\(91\) 0 0
\(92\) 9.33607 0.973353
\(93\) −4.70469 2.71625i −0.487853 0.281662i
\(94\) −2.73119 −0.281701
\(95\) 2.96739 + 5.13967i 0.304448 + 0.527319i
\(96\) −3.82930 + 2.21085i −0.390827 + 0.225644i
\(97\) 13.4078 + 7.74102i 1.36136 + 0.785981i 0.989805 0.142430i \(-0.0454915\pi\)
0.371555 + 0.928411i \(0.378825\pi\)
\(98\) 0 0
\(99\) 7.38776i 0.742498i
\(100\) −11.2881 −1.12881
\(101\) −1.27930 −0.127295 −0.0636477 0.997972i \(-0.520273\pi\)
−0.0636477 + 0.997972i \(0.520273\pi\)
\(102\) 4.19622i 0.415488i
\(103\) 5.73367 + 9.93101i 0.564956 + 0.978532i 0.997054 + 0.0767054i \(0.0244401\pi\)
−0.432098 + 0.901827i \(0.642227\pi\)
\(104\) 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 \(-0.753487\pi\)
0.963033 + 0.269385i \(0.0868205\pi\)
\(108\) 6.98412 + 12.0969i 0.672048 + 1.16402i
\(109\) −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
\(111\) −2.67313 1.54333i −0.253722 0.146487i
\(112\) 0 0
\(113\) 4.29556 7.44014i 0.404093 0.699909i −0.590123 0.807314i \(-0.700921\pi\)
0.994215 + 0.107404i \(0.0342540\pi\)
\(114\) 2.47048 4.27899i 0.231381 0.400764i
\(115\) 3.20160i 0.298551i
\(116\) −12.6282 + 21.8726i −1.17250 + 2.03082i
\(117\) 6.46856 7.42497i 0.598019 0.686438i
\(118\) −29.5723 −2.72235
\(119\) 0 0
\(120\) −2.92170 5.06053i −0.266714 0.461961i
\(121\) 3.68321 0.334837
\(122\) −6.55741 3.78592i −0.593680 0.342761i
\(123\) −3.45801 + 1.99648i −0.311798 + 0.180017i
\(124\) 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
\(129\) 0.869985 1.50686i 0.0765979 0.132671i
\(130\) −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 \(0.686185\pi\)
\(132\) −5.70937 + 3.29630i −0.496936 + 0.286906i
\(133\) 0 0
\(134\) −17.5790 + 30.4476i −1.51859 + 2.63028i
\(135\) −4.14835 + 2.39505i −0.357033 + 0.206133i
\(136\) −18.9308 + 10.9297i −1.62331 + 0.937216i
\(137\) 8.65385 4.99630i 0.739348 0.426863i −0.0824839 0.996592i \(-0.526285\pi\)
0.821832 + 0.569729i \(0.192952\pi\)
\(138\) 2.30836 1.33273i 0.196501 0.113450i
\(139\) −0.832100 + 1.44124i −0.0705778 + 0.122244i −0.899155 0.437631i \(-0.855818\pi\)
0.828577 + 0.559875i \(0.189151\pi\)
\(140\) 0 0
\(141\) −0.473738 + 0.273513i −0.0398959 + 0.0230339i
\(142\) −1.74874 3.02891i −0.146751 0.254180i
\(143\) 7.35364 + 6.40642i 0.614942 + 0.535732i
\(144\) 11.8757 20.5692i 0.989638 1.71410i
\(145\) −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 \(0.698946\pi\)
\(150\) −2.79100 + 1.61138i −0.227884 + 0.131569i
\(151\) 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
\(153\) 4.26968 + 7.39531i 0.345183 + 0.597875i
\(154\) 0 0
\(155\) −16.8912 −1.35673
\(156\) 8.62429 + 1.68609i 0.690496 + 0.134995i
\(157\) 7.00223 12.1282i 0.558839 0.967938i −0.438755 0.898607i \(-0.644580\pi\)
0.997594 0.0693309i \(-0.0220864\pi\)
\(158\) 16.0643i 1.27801i
\(159\) 1.88350 3.26232i 0.149371 0.258719i
\(160\) −6.87414 + 11.9064i −0.543448 + 0.941280i
\(161\) 0 0
\(162\) −14.9146 8.61097i −1.17181 0.676542i
\(163\) 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
\(165\) −1.13039 1.95790i −0.0880011 0.152422i
\(166\) 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
\(171\) 10.0549i 0.768917i
\(172\) −15.7761 −1.20291
\(173\) −12.8116 −0.974047 −0.487023 0.873389i \(-0.661917\pi\)
−0.487023 + 0.873389i \(0.661917\pi\)
\(174\) 7.21072i 0.546643i
\(175\) 0 0
\(176\) 20.3717 + 11.7616i 1.53557 + 0.886562i
\(177\) −5.12945 + 2.96149i −0.385553 + 0.222599i
\(178\) 2.27781 + 3.94528i 0.170729 + 0.295711i
\(179\) −1.84022 −0.137545 −0.0687723 0.997632i \(-0.521908\pi\)
−0.0687723 + 0.997632i \(0.521908\pi\)
\(180\) 17.9242 + 10.3485i 1.33599 + 0.771334i
\(181\) 3.29928 0.245234 0.122617 0.992454i \(-0.460871\pi\)
0.122617 + 0.992454i \(0.460871\pi\)
\(182\) 0 0
\(183\) −1.51655 −0.112107
\(184\) −12.0250 6.94262i −0.886493 0.511817i
\(185\) −9.59730 −0.705607
\(186\) 7.03129 + 12.1786i 0.515560 + 0.892975i
\(187\) −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 \(-0.443317\pi\)
0.177136 + 0.984186i \(0.443317\pi\)
\(192\) 2.42852 0.175264
\(193\) 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
\(195\) −0.578207 + 2.95751i −0.0414063 + 0.211792i
\(196\) 0 0
\(197\) 4.02694 2.32496i 0.286908 0.165646i −0.349639 0.936885i \(-0.613696\pi\)
0.636546 + 0.771238i \(0.280362\pi\)
\(198\) 9.56198 16.5618i 0.679540 1.17700i
\(199\) −0.205360 0.355694i −0.0145576 0.0252145i 0.858655 0.512554i \(-0.171301\pi\)
−0.873212 + 0.487340i \(0.837967\pi\)
\(200\) 14.5392 + 8.39420i 1.02808 + 0.593560i
\(201\) 7.04171i 0.496684i
\(202\) 2.86793 + 1.65580i 0.201787 + 0.116502i
\(203\) 0 0
\(204\) −3.81013 + 6.59934i −0.266763 + 0.462047i
\(205\) −6.20762 + 10.7519i −0.433559 + 0.750946i
\(206\) 29.6844i 2.06821i
\(207\) −2.71213 + 4.69754i −0.188506 + 0.326502i
\(208\) −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
\(213\) −0.606654 0.350252i −0.0415672 0.0239989i
\(214\) −11.5122 + 6.64656i −0.786956 + 0.454349i
\(215\) 5.41005i 0.368962i
\(216\) 20.7745i 1.41353i
\(217\) 0 0
\(218\) 2.23633 + 3.87344i 0.151464 + 0.262343i
\(219\) 4.08745 + 2.35989i 0.276204 + 0.159467i
\(220\) −10.2491 + 17.7520i −0.690996 + 1.19684i
\(221\) 11.0637 + 2.16300i 0.744224 + 0.145499i
\(222\) 3.99507 + 6.91967i 0.268132 + 0.464418i
\(223\) 19.5544 11.2897i 1.30946 0.756016i 0.327452 0.944868i \(-0.393810\pi\)
0.982006 + 0.188852i \(0.0604766\pi\)
\(224\) 0 0
\(225\) 3.27918 5.67971i 0.218612 0.378648i
\(226\) −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 \(0.483234\pi\)
\(228\) −7.77057 + 4.48634i −0.514618 + 0.297115i
\(229\) 6.86832 3.96543i 0.453872 0.262043i −0.255592 0.966785i \(-0.582270\pi\)
0.709464 + 0.704742i \(0.248937\pi\)
\(230\) 4.14383 7.17733i 0.273236 0.473259i
\(231\) 0 0
\(232\) 32.5305 18.7815i 2.13573 1.23306i
\(233\) −3.28585 5.69127i −0.215263 0.372847i 0.738091 0.674702i \(-0.235728\pi\)
−0.953354 + 0.301854i \(0.902394\pi\)
\(234\) −24.1113 + 8.27298i −1.57621 + 0.540822i
\(235\) −0.850427 + 1.47298i −0.0554757 + 0.0960868i
\(236\) 46.5080 + 26.8514i 3.02741 + 1.74788i
\(237\) −1.60874 2.78642i −0.104499 0.180998i
\(238\) 0 0
\(239\) 9.39284i 0.607572i −0.952740 0.303786i \(-0.901749\pi\)
0.952740 0.303786i \(-0.0982508\pi\)
\(240\) 7.26833i 0.469169i
\(241\) −8.73460 + 5.04292i −0.562645 + 0.324843i −0.754206 0.656637i \(-0.771978\pi\)
0.191562 + 0.981481i \(0.438645\pi\)
\(242\) −8.25699 4.76718i −0.530780 0.306446i
\(243\) −12.3636 −0.793128
\(244\) 6.87517 + 11.9081i 0.440137 + 0.762340i
\(245\) 0 0
\(246\) 10.3362 0.659012
\(247\) 10.0085 + 8.71928i 0.636823 + 0.554794i
\(248\) 36.6282 63.4420i 2.32590 4.02857i
\(249\) 1.39816i 0.0886045i
\(250\) −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
\(255\) −2.26310 1.30660i −0.141721 0.0818225i
\(256\) 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 \(0.246800\pi\)
\(258\) −3.90065 + 2.25204i −0.242844 + 0.140206i
\(259\) 0 0
\(260\) 25.8440 8.86749i 1.60278 0.549939i
\(261\) −7.33696 12.7080i −0.454146 0.786604i
\(262\) 26.4275i 1.63270i
\(263\) 5.05934 0.311972 0.155986 0.987759i \(-0.450144\pi\)
0.155986 + 0.987759i \(0.450144\pi\)
\(264\) 9.80498 0.603455
\(265\) 11.7127i 0.719503i
\(266\) 0 0
\(267\) 0.790192 + 0.456218i 0.0483590 + 0.0279201i
\(268\) 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 \(0.694152\pi\)
\(270\) 12.3997 0.754619
\(271\) 7.21158 + 4.16361i 0.438072 + 0.252921i 0.702780 0.711408i \(-0.251942\pi\)
−0.264707 + 0.964329i \(0.585275\pi\)
\(272\) 27.1900 1.64863
\(273\) 0 0
\(274\) −25.8669 −1.56267
\(275\) 5.62515 + 3.24768i 0.339210 + 0.195843i
\(276\) −4.84043 −0.291360
\(277\) −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
\(279\) −24.7835 14.3088i −1.48375 0.856644i
\(280\) 0 0
\(281\) 27.1595i 1.62020i −0.586292 0.810100i \(-0.699413\pi\)
0.586292 0.810100i \(-0.300587\pi\)
\(282\) 1.41603 0.0843234
\(283\) −16.1513 −0.960092 −0.480046 0.877243i \(-0.659380\pi\)
−0.480046 + 0.877243i \(0.659380\pi\)
\(284\) 6.35136i 0.376884i
\(285\) −1.53849 2.66474i −0.0911323 0.157846i
\(286\) −8.19351 23.8797i −0.484493 1.41204i
\(287\) 0 0
\(288\) −20.1721 + 11.6464i −1.18865 + 0.686270i
\(289\) 3.61216 6.25645i 0.212480 0.368027i
\(290\) 11.2101 + 19.4164i 0.658278 + 1.14017i
\(291\) −6.95151 4.01345i −0.407504 0.235273i
\(292\) 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
\(297\) 8.03758i 0.466388i
\(298\) 25.6246 44.3831i 1.48439 2.57104i
\(299\) 2.32398 + 6.77315i 0.134399 + 0.391702i
\(300\) 5.85248 0.337893
\(301\) 0 0
\(302\) −9.75246 16.8918i −0.561191 0.972011i
\(303\) 0.663274 0.0381041
\(304\) 27.7263 + 16.0078i 1.59021 + 0.918108i
\(305\) −4.08363 + 2.35769i −0.233828 + 0.135001i
\(306\) 22.1050i 1.26366i
\(307\) 8.97844i 0.512427i −0.966620 0.256213i \(-0.917525\pi\)
0.966620 0.256213i \(-0.0824750\pi\)
\(308\) 0 0
\(309\) −2.97271 5.14889i −0.169112 0.292910i
\(310\) 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 \(0.278916\pi\)
\(312\) −9.85436 8.58502i −0.557893 0.486031i
\(313\) 6.56198 + 11.3657i 0.370905 + 0.642427i 0.989705 0.143122i \(-0.0457141\pi\)
−0.618800 + 0.785549i \(0.712381\pi\)
\(314\) −31.3951 + 18.1260i −1.77173 + 1.02291i
\(315\) 0 0
\(316\) −14.5862 + 25.2641i −0.820540 + 1.42122i
\(317\) −14.4761 + 8.35775i −0.813056 + 0.469418i −0.848016 0.529971i \(-0.822203\pi\)
0.0349599 + 0.999389i \(0.488870\pi\)
\(318\) −8.44485 + 4.87563i −0.473564 + 0.273412i
\(319\) 12.5859 7.26648i 0.704675 0.406845i
\(320\) 6.53932 3.77548i 0.365559 0.211056i
\(321\) −1.33123 + 2.30575i −0.0743018 + 0.128695i
\(322\) 0 0
\(323\) −9.96849 + 5.75531i −0.554661 + 0.320234i
\(324\) 15.6374 + 27.0847i 0.868743 + 1.50471i
\(325\) −2.80988 8.18930i −0.155864 0.454261i
\(326\) 9.28007 16.0736i 0.513976 0.890232i
\(327\) 0.775804 + 0.447911i 0.0429021 + 0.0247695i
\(328\) −26.9223 46.6307i −1.48653 2.57475i
\(329\) 0 0
\(330\) 5.85228i 0.322157i
\(331\) 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
\(333\) −14.0816 8.13002i −0.771668 0.445523i
\(334\) 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
\(339\) −2.22710 + 3.85746i −0.120960 + 0.209508i
\(340\) 23.6935i 1.28496i
\(341\) 14.1713 24.5455i 0.767420 1.32921i
\(342\) 13.0141 22.5410i 0.703720 1.21888i
\(343\) 0 0
\(344\) 20.3197 + 11.7316i 1.09557 + 0.632526i
\(345\) 1.65992i 0.0893671i
\(346\) 28.7209 + 16.5820i 1.54405 + 0.891456i
\(347\) 13.1989 + 22.8612i 0.708556 + 1.22725i 0.965393 + 0.260800i \(0.0839863\pi\)
−0.256837 + 0.966455i \(0.582680\pi\)
\(348\) 6.54727 11.3402i 0.350971 0.607899i
\(349\) 4.23507 2.44512i 0.226698 0.130884i −0.382350 0.924018i \(-0.624885\pi\)
0.609048 + 0.793133i \(0.291552\pi\)
\(350\) 0 0
\(351\) −7.03753 + 8.07806i −0.375636 + 0.431175i
\(352\) −11.5345 19.9784i −0.614792 1.06485i
\(353\) 13.5577i 0.721605i −0.932642 0.360802i \(-0.882503\pi\)
0.932642 0.360802i \(-0.117497\pi\)
\(354\) 15.3322 0.814899
\(355\) −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 \(-0.739417\pi\)
0.290785 + 0.956789i \(0.406084\pi\)
\(360\) −15.3910 26.6581i −0.811179 1.40500i
\(361\) 5.44653 0.286659
\(362\) −7.39632 4.27026i −0.388742 0.224440i
\(363\) −1.90962 −0.100229
\(364\) 0 0
\(365\) 14.6751 0.768130
\(366\) 3.39979 + 1.96287i 0.177710 + 0.102601i
\(367\) 1.66322 0.0868196 0.0434098 0.999057i \(-0.486178\pi\)
0.0434098 + 0.999057i \(0.486178\pi\)
\(368\) 8.63560 + 14.9573i 0.450162 + 0.779703i
\(369\) −18.2162 + 10.5171i −0.948299 + 0.547501i
\(370\) 21.5152 + 12.4218i 1.11852 + 0.645778i
\(371\) 0 0
\(372\) 25.5374i 1.32405i
\(373\) 13.9635 0.723002 0.361501 0.932372i \(-0.382264\pi\)
0.361501 + 0.932372i \(0.382264\pi\)
\(374\) 21.8927 1.13204
\(375\) 6.18595i 0.319441i
\(376\) −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
\(381\) 0.809874 + 1.40274i 0.0414911 + 0.0718647i
\(382\) −10.9761 6.33707i −0.561588 0.324233i
\(383\) 31.9082i 1.63043i 0.579156 + 0.815217i \(0.303382\pi\)
−0.579156 + 0.815217i \(0.696618\pi\)
\(384\) 2.21435 + 1.27846i 0.113001 + 0.0652410i
\(385\) 0 0
\(386\) −3.90762 + 6.76820i −0.198893 + 0.344492i
\(387\) 4.58294 7.93788i 0.232964 0.403505i
\(388\) 72.7788i 3.69478i
\(389\) −12.7075 + 22.0100i −0.644296 + 1.11595i 0.340168 + 0.940365i \(0.389516\pi\)
−0.984464 + 0.175589i \(0.943817\pi\)
\(390\) 5.12413 5.88175i 0.259470 0.297834i
\(391\) −6.20956 −0.314031
\(392\) 0 0
\(393\) −2.64656 4.58398i −0.133501 0.231231i
\(394\) −12.0368 −0.606403
\(395\) −8.66376 5.00203i −0.435921 0.251679i
\(396\) −30.0760 + 17.3644i −1.51138 + 0.872593i
\(397\) 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 \(-0.496126\pi\)
−0.859875 + 0.510504i \(0.829459\pi\)
\(402\) 9.11409 15.7861i 0.454569 0.787337i
\(403\) −35.7342 + 12.2610i −1.78005 + 0.610762i
\(404\) −3.00691 5.20811i −0.149599 0.259113i
\(405\) −9.28811 + 5.36249i −0.461530 + 0.266464i
\(406\) 0 0
\(407\) 8.05193 13.9463i 0.399119 0.691295i
\(408\) 9.81500 5.66669i 0.485915 0.280543i
\(409\) 15.2712 8.81685i 0.755114 0.435965i −0.0724249 0.997374i \(-0.523074\pi\)
0.827539 + 0.561409i \(0.189740\pi\)
\(410\) 27.8324 16.0690i 1.37454 0.793594i
\(411\) −4.48673 + 2.59041i −0.221314 + 0.127776i
\(412\) −26.9532 + 46.6842i −1.32789 + 2.29997i
\(413\) 0 0
\(414\) 12.1601 7.02061i 0.597634 0.345044i
\(415\) −2.17363 3.76483i −0.106699 0.184808i
\(416\) −5.90001 + 30.1783i −0.289272 + 1.47962i
\(417\) 0.431416 0.747234i 0.0211265 0.0365922i
\(418\) 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
\(423\) −2.49557 + 1.44082i −0.121339 + 0.0700551i
\(424\) 43.9919 + 25.3987i 2.13644 + 1.23347i
\(425\) 7.50787 0.364185
\(426\) 0.906662 + 1.57038i 0.0439279 + 0.0760854i
\(427\) 0 0
\(428\) 24.1401 1.16685
\(429\) −3.81261 3.32151i −0.184075 0.160364i
\(430\) −7.00223 + 12.1282i −0.337677 + 0.584874i
\(431\) 8.97060i 0.432098i −0.976382 0.216049i \(-0.930683\pi\)
0.976382 0.216049i \(-0.0693172\pi\)
\(432\) −12.9202 + 22.3785i −0.621625 + 1.07669i
\(433\) 1.72531 2.98833i 0.0829132 0.143610i −0.821587 0.570083i \(-0.806911\pi\)
0.904500 + 0.426473i \(0.140244\pi\)
\(434\) 0 0
\(435\) 3.88887 + 2.24524i 0.186457 + 0.107651i
\(436\) 8.12228i 0.388987i
\(437\) −6.33204 3.65580i −0.302902 0.174881i
\(438\) −6.10881 10.5808i −0.291890 0.505569i
\(439\) 19.2572 33.3544i 0.919096 1.59192i 0.118304 0.992977i \(-0.462254\pi\)
0.800792 0.598943i \(-0.204412\pi\)
\(440\) 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 \(-0.0503693\pi\)
−0.630222 + 0.776415i \(0.717036\pi\)
\(444\) 14.5100i 0.688612i
\(445\) 2.83701 0.134487
\(446\) −58.4492 −2.76765
\(447\) 10.2646i 0.485499i
\(448\) 0 0
\(449\) 33.7087 + 19.4617i 1.59081 + 0.918456i 0.993168 + 0.116696i \(0.0372304\pi\)
0.597646 + 0.801760i \(0.296103\pi\)
\(450\) −14.7025 + 8.48850i −0.693083 + 0.400152i
\(451\) −10.4161 18.0412i −0.490476 0.849529i
\(452\) 40.3856 1.89958
\(453\) −3.38322 1.95330i −0.158957 0.0917741i
\(454\) 35.3906 1.66097
\(455\) 0 0
\(456\) 13.3448 0.624927
\(457\) −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
\(459\) −4.64524 8.04580i −0.216821 0.375546i
\(460\) −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
\(465\) 8.75749 0.406119
\(466\) 17.0115i 0.788044i
\(467\) −2.52516 4.37371i −0.116851 0.202391i 0.801667 0.597770i \(-0.203947\pi\)
−0.918518 + 0.395379i \(0.870613\pi\)
\(468\) 45.4314 + 8.88205i 2.10006 + 0.410573i
\(469\) 0 0
\(470\) 3.81296 2.20141i 0.175879 0.101544i
\(471\) −3.63042 + 6.28807i −0.167281 + 0.289739i
\(472\) −39.9353 69.1699i −1.83817 3.18380i
\(473\) 7.86163 + 4.53892i 0.361478 + 0.208700i
\(474\) 8.32878i 0.382554i
\(475\) 7.65595 + 4.42017i 0.351279 + 0.202811i
\(476\) 0 0
\(477\) 9.92198 17.1854i 0.454296 0.786864i
\(478\) −12.1572 + 21.0568i −0.556055 + 0.963116i
\(479\) 9.45319i 0.431927i 0.976401 + 0.215964i \(0.0692892\pi\)
−0.976401 + 0.215964i \(0.930711\pi\)
\(480\) 3.56401 6.17304i 0.162674 0.281759i
\(481\) −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
\(486\) 27.7167 + 16.0023i 1.25726 + 0.725877i
\(487\) 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
\(489\) 3.71737i 0.168105i
\(490\) 0 0
\(491\) −3.38049 5.85517i −0.152559 0.264240i 0.779608 0.626267i \(-0.215418\pi\)
−0.932168 + 0.362027i \(0.882085\pi\)
\(492\) −16.2556 9.38518i −0.732859 0.423116i
\(493\) 8.39918 14.5478i 0.378280 0.655200i
\(494\) −11.1515 32.5008i −0.501732 1.46228i
\(495\) −5.95473 10.3139i −0.267645 0.463575i
\(496\) −78.9125 + 45.5602i −3.54328 + 2.04571i
\(497\) 0 0
\(498\) −1.80963 + 3.13438i −0.0810916 + 0.140455i
\(499\) 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
\(501\) 8.07335 4.66115i 0.360691 0.208245i
\(502\) −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
\(507\) 0.923570 + 6.67648i 0.0410172 + 0.296513i
\(508\) 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 \(0.811384\pi\)
\(510\) 3.38227 + 5.85826i 0.149769 + 0.259408i
\(511\) 0 0
\(512\) 47.4335i 2.09628i
\(513\) 10.9393i 0.482983i
\(514\) 17.9043 10.3370i 0.789724 0.455947i
\(515\) −16.0093 9.24299i −0.705455 0.407295i
\(516\) 8.17934 0.360076
\(517\) −1.42698 2.47160i −0.0627585 0.108701i
\(518\) 0 0
\(519\) 6.64237 0.291568
\(520\) −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 \(0.928146\pi\)
\(522\) 37.9849i 1.66255i
\(523\) 11.3601 19.6763i 0.496742 0.860383i −0.503251 0.864140i \(-0.667863\pi\)
0.999993 + 0.00375758i \(0.00119608\pi\)
\(524\) −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
\(528\) −10.5620 6.09798i −0.459652 0.265380i
\(529\) 9.52783 + 16.5027i 0.414253 + 0.717508i
\(530\) −15.1597 + 26.2574i −0.658495 + 1.14055i
\(531\) −27.0211 + 15.6007i −1.17262 + 0.677011i
\(532\) 0 0
\(533\) −5.32794 + 27.2522i −0.230779 + 1.18043i
\(534\) −1.18097 2.04549i −0.0511054 0.0885171i
\(535\) 8.27830i 0.357902i
\(536\) −94.9564 −4.10149
\(537\) 0.954091 0.0411721
\(538\) 35.9563i 1.55018i
\(539\) 0 0
\(540\) −19.5008 11.2588i −0.839180 0.484501i
\(541\) −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
\(543\) −1.71057 −0.0734074
\(544\) −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
\(549\) −7.98894 −0.340959
\(550\) −8.40696 14.5613i −0.358474 0.620895i
\(551\) 17.1297 9.88983i 0.729749 0.421321i
\(552\) 6.23454 + 3.59951i 0.265360 + 0.153205i
\(553\) 0 0
\(554\) 60.0855i 2.55279i
\(555\) 4.97587 0.211214
\(556\) −7.82316 −0.331776
\(557\) 44.2503i 1.87495i 0.348058 + 0.937473i \(0.386841\pi\)
−0.348058 + 0.937473i \(0.613159\pi\)
\(558\) 37.0397 + 64.1547i 1.56802 + 2.71588i
\(559\) −3.92705 11.4452i −0.166097 0.484082i
\(560\) 0 0
\(561\) 3.79738 2.19242i 0.160326 0.0925641i
\(562\) −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 \(0.527572\pi\)
\(564\) −2.22697 1.28574i −0.0937725 0.0541396i
\(565\) 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 \(-0.414683\pi\)
0.702687 0.711499i \(-0.251983\pi\)
\(570\) 7.96508i 0.333620i
\(571\) 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
\(573\) −2.53848 −0.106047
\(574\) 0 0
\(575\) 2.38452 + 4.13011i 0.0994413 + 0.172237i
\(576\) 12.7931 0.533045
\(577\) 21.9368 + 12.6652i 0.913239 + 0.527259i 0.881472 0.472237i \(-0.156553\pi\)
0.0317671 + 0.999495i \(0.489887\pi\)
\(578\) −16.1955 + 9.35045i −0.673642 + 0.388927i
\(579\) 1.56530i 0.0650517i
\(580\) 40.7146i 1.69058i
\(581\) 0 0
\(582\) 10.3892 + 17.9947i 0.430647 + 0.745903i
\(583\) 17.0203 + 9.82667i 0.704908 + 0.406979i
\(584\) −31.8227 + 55.1186i −1.31683 + 2.28082i
\(585\) −3.04590 + 15.5797i −0.125933 + 0.644140i
\(586\) −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
\(591\) −2.08783 + 1.20541i −0.0858819 + 0.0495839i
\(592\) −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 \(0.159052\pi\)
\(594\) −10.4030 + 18.0186i −0.426842 + 0.739312i
\(595\) 0 0
\(596\) −80.5990 + 46.5338i −3.30146 + 1.90610i
\(597\) 0.106472 + 0.184415i 0.00435762 + 0.00754762i
\(598\) 3.55661 18.1919i 0.145441 0.743924i
\(599\) −5.46078 + 9.45835i −0.223122 + 0.386458i −0.955754 0.294166i \(-0.904958\pi\)
0.732633 + 0.680624i \(0.238291\pi\)
\(600\) −7.53807 4.35211i −0.307740 0.177674i
\(601\) 12.1282 + 21.0067i 0.494720 + 0.856880i 0.999981 0.00608649i \(-0.00193740\pi\)
−0.505262 + 0.862966i \(0.668604\pi\)
\(602\) 0 0
\(603\) 37.0946i 1.51061i
\(604\) 35.4206i 1.44124i
\(605\) −5.14205 + 2.96876i −0.209054 + 0.120697i
\(606\) −1.48692 0.858476i −0.0604022 0.0348732i
\(607\) 9.85447 0.399981 0.199990 0.979798i \(-0.435909\pi\)
0.199990 + 0.979798i \(0.435909\pi\)
\(608\) −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
\(612\) −20.0712 + 34.7643i −0.811328 + 1.40526i
\(613\) 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
\(615\) 3.21844 5.57450i 0.129780 0.224785i
\(616\) 0 0
\(617\) 16.2352 + 9.37341i 0.653605 + 0.377359i 0.789836 0.613318i \(-0.210166\pi\)
−0.136231 + 0.990677i \(0.543499\pi\)
\(618\) 15.3903i 0.619090i
\(619\) 13.7650 + 7.94725i 0.553264 + 0.319427i 0.750437 0.660942i \(-0.229843\pi\)
−0.197174 + 0.980369i \(0.563176\pi\)
\(620\) −39.7014 68.7649i −1.59445 2.76167i
\(621\) 2.95068 5.11073i 0.118407 0.205087i
\(622\) 27.3086 15.7667i 1.09498 0.632185i
\(623\) 0 0
\(624\) 5.27594 + 15.3765i 0.211207 + 0.615555i
\(625\) 3.61371 + 6.25913i 0.144549 + 0.250365i
\(626\) 33.9727i 1.35782i
\(627\) 5.16304 0.206192
\(628\) 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
\(633\) −1.94839 3.37472i −0.0774417 0.134133i
\(634\) 43.2698 1.71846
\(635\) 4.36151 + 2.51812i 0.173081 + 0.0999286i
\(636\) 17.7081 0.702173
\(637\) 0 0
\(638\) −37.6200 −1.48939
\(639\) −3.19575 1.84507i −0.126422 0.0729898i
\(640\) 7.95016 0.314258
\(641\) −14.8893 25.7890i −0.588092 1.01860i −0.994482 0.104905i \(-0.966546\pi\)
0.406390 0.913699i \(-0.366787\pi\)
\(642\) 5.96867 3.44601i 0.235565 0.136003i
\(643\) −10.0220 5.78623i −0.395231 0.228187i 0.289193 0.957271i \(-0.406613\pi\)
−0.684424 + 0.729084i \(0.739946\pi\)
\(644\) 0 0
\(645\) 2.80493i 0.110444i
\(646\) 29.7964 1.17232
\(647\) 25.5065 1.00276 0.501382 0.865226i \(-0.332825\pi\)
0.501382 + 0.865226i \(0.332825\pi\)
\(648\) 46.5140i 1.82724i
\(649\) −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 \(-0.492774\pi\)
0.854452 0.519530i \(-0.173893\pi\)
\(654\) −1.15946 2.00825i −0.0453386 0.0785287i
\(655\) −14.2529 8.22889i −0.556905 0.321529i
\(656\) 66.9747i 2.61492i
\(657\) 21.5320 + 12.4315i 0.840043 + 0.484999i
\(658\) 0 0
\(659\) −20.5867 + 35.6572i −0.801944 + 1.38901i 0.116390 + 0.993204i \(0.462868\pi\)
−0.918335 + 0.395805i \(0.870466\pi\)
\(660\) 5.31382 9.20380i 0.206840 0.358258i
\(661\) 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
\(663\) −5.73614 1.12144i −0.222773 0.0435533i
\(664\) 18.8539 0.731673
\(665\) 0 0
\(666\) 21.0454 + 36.4517i 0.815492 + 1.41247i
\(667\) 10.6704 0.413160
\(668\) −73.1999 42.2620i −2.83219 1.63516i
\(669\) −10.1383 + 5.85334i −0.391968 + 0.226303i
\(670\) 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
\(675\) −3.56762 + 6.17930i −0.137318 + 0.237841i
\(676\) 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 \(0.817697\pi\)
\(678\) 9.98541 5.76508i 0.383488 0.221407i
\(679\) 0 0
\(680\) 17.6193 30.5175i 0.675670 1.17029i
\(681\) 6.13867 3.54416i 0.235234 0.135813i
\(682\) −63.5384 + 36.6839i −2.43301 + 1.40470i
\(683\) −30.9517 + 17.8700i −1.18433 + 0.683775i −0.957013 0.290045i \(-0.906330\pi\)
−0.227320 + 0.973820i \(0.572996\pi\)
\(684\) −40.9341 + 23.6333i −1.56515 + 0.903642i
\(685\) −8.05431 + 13.9505i −0.307739 + 0.533020i
\(686\) 0 0
\(687\) −3.56099 + 2.05594i −0.135860 + 0.0784390i
\(688\) −14.5924 25.2748i −0.556330 0.963592i
\(689\) −8.50199 24.7788i −0.323900 0.943995i
\(690\) −2.14843 + 3.72120i −0.0817895 + 0.141664i
\(691\) −22.5419 13.0146i −0.857536 0.495099i 0.00565028 0.999984i \(-0.498201\pi\)
−0.863186 + 0.504885i \(0.831535\pi\)
\(692\) −30.1127 52.1567i −1.14471 1.98270i
\(693\) 0 0
\(694\) 68.3335i 2.59391i
\(695\) 2.68278i 0.101764i
\(696\) −16.8659 + 9.73755i −0.639301 + 0.369101i
\(697\) −20.8535 12.0398i −0.789884 0.456040i
\(698\) −12.6589 −0.479146
\(699\) 1.70360 + 2.95073i 0.0644362 + 0.111607i
\(700\) 0 0
\(701\) −1.12731 −0.0425779 −0.0212890 0.999773i \(-0.506777\pi\)
−0.0212890 + 0.999773i \(0.506777\pi\)
\(702\) 26.2321 9.00067i 0.990068 0.339709i
\(703\) 10.9588 18.9813i 0.413321 0.715892i
\(704\) 12.6702i 0.477525i
\(705\) 0.440917 0.763691i 0.0166059 0.0287623i
\(706\) −17.5478 + 30.3936i −0.660419 + 1.14388i
\(707\) 0 0
\(708\) −24.1128 13.9215i −0.906215 0.523203i
\(709\) 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
\(711\) −8.47459 14.6784i −0.317822 0.550484i
\(712\) −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
\(717\) 4.86986i 0.181868i
\(718\) 22.2249 0.829425
\(719\) 47.1177 1.75719 0.878597 0.477563i \(-0.158480\pi\)
0.878597 + 0.477563i \(0.158480\pi\)
\(720\) 38.2884i 1.42692i
\(721\) 0 0
\(722\) −12.2100 7.04944i −0.454409 0.262353i
\(723\) 4.52859 2.61458i 0.168420 0.0972374i
\(724\) 7.75473 + 13.4316i 0.288202 + 0.499181i
\(725\) −12.9014 −0.479146
\(726\) 4.28097 + 2.47162i 0.158882 + 0.0917303i
\(727\) −17.9215 −0.664671 −0.332335 0.943161i \(-0.607837\pi\)
−0.332335 + 0.943161i \(0.607837\pi\)
\(728\) 0 0
\(729\) −13.5489 −0.501810
\(730\) −32.8985 18.9940i −1.21763 0.702999i
\(731\) 10.4929 0.388093
\(732\) −3.56454 6.17396i −0.131749 0.228196i
\(733\) −39.2037 + 22.6343i −1.44802 + 0.836016i −0.998364 0.0571848i \(-0.981788\pi\)
−0.449658 + 0.893201i \(0.648454\pi\)
\(734\) −3.72861 2.15271i −0.137625 0.0794581i
\(735\) 0 0
\(736\) 16.9378i 0.624335i
\(737\) −36.7382 −1.35327
\(738\) 54.4494 2.00431
\(739\) 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
\(741\) −5.18905 4.52065i −0.190624 0.166070i
\(742\) 0 0
\(743\) 30.2115 17.4426i 1.10835 0.639908i 0.169951 0.985453i \(-0.445639\pi\)
0.938402 + 0.345545i \(0.112306\pi\)
\(744\) −18.9905 + 32.8925i −0.696225 + 1.20590i
\(745\) −15.9577 27.6396i −0.584647 1.01264i
\(746\) −31.3032 18.0729i −1.14609 0.661697i
\(747\) 7.36525i 0.269480i
\(748\) −34.4303 19.8784i −1.25890 0.726825i
\(749\) 0 0
\(750\) 8.00648 13.8676i 0.292355 0.506374i
\(751\) −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
\(753\) −2.68268 + 4.64654i −0.0977623 + 0.169329i
\(754\) 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
\(759\) 2.41212 + 1.39264i 0.0875543 + 0.0505495i
\(760\) 35.9337 20.7463i 1.30345 0.752548i
\(761\) 32.6388i 1.18316i −0.806248 0.591578i \(-0.798505\pi\)
0.806248 0.591578i \(-0.201495\pi\)
\(762\) 4.19288i 0.151892i
\(763\) 0 0
\(764\) 11.5080 + 19.9325i 0.416345 + 0.721131i
\(765\) −11.9216 6.88296i −0.431028 0.248854i
\(766\) 41.2988 71.5316i 1.49219 2.58454i
\(767\) −7.90323 + 40.4247i −0.285369 + 1.45965i
\(768\) −5.73794 9.93841i −0.207050 0.358621i
\(769\) 45.1851 26.0876i 1.62942 0.940744i 0.645148 0.764057i \(-0.276796\pi\)
0.984267 0.176686i \(-0.0565378\pi\)
\(770\) 0 0
\(771\) 2.07039 3.58601i 0.0745631 0.129147i
\(772\) 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 \(0.111387\pi\)
\(774\) −20.5480 + 11.8634i −0.738583 + 0.426421i
\(775\) −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
\(780\) −13.3992 + 4.59749i −0.479769 + 0.164617i
\(781\)