Properties

Label 637.2.u.g.30.1
Level $637$
Weight $2$
Character 637.30
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 30.1
Root \(1.32725 - 0.488273i\) of defining polynomial
Character \(\chi\) \(=\) 637.30
Dual form 637.2.u.g.361.1

$q$-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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 6q^{3} + 4q^{4} - 3q^{5} + 9q^{6} + 2q^{9} + O(q^{10}) \) \( 12q - 6q^{3} + 4q^{4} - 3q^{5} + 9q^{6} + 2q^{9} + 24q^{10} + q^{12} + 2q^{13} - 12q^{15} - 8q^{16} - 17q^{17} - 3q^{18} + 3q^{20} - 15q^{22} + 3q^{23} - 5q^{25} + 9q^{26} - 12q^{27} - q^{29} - 22q^{30} + 18q^{31} + 18q^{32} - 13q^{36} + 15q^{37} - 19q^{38} - q^{39} + q^{40} + 6q^{41} + 11q^{43} + 33q^{44} + 9q^{45} - 30q^{46} - 15q^{47} - 19q^{48} + 18q^{50} + 4q^{51} - 47q^{52} - 8q^{53} - 6q^{54} + 15q^{55} - 27q^{59} + 30q^{60} + 10q^{61} - 41q^{62} + 2q^{64} - 3q^{65} + 34q^{66} + 11q^{68} - 7q^{69} + 30q^{71} + 42q^{73} - 33q^{74} - q^{75} + 45q^{76} + 44q^{78} - 35q^{79} - 28q^{81} + 10q^{82} - 21q^{85} + 57q^{86} - 10q^{87} + 28q^{88} - 48q^{89} - 66q^{92} - 81q^{93} + 2q^{94} + 2q^{95} + 21q^{96} + 3q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

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 \(0.701308\pi\)
−0.994084 + 0.108613i \(0.965359\pi\)
\(3\) −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 0.154213 0.988038i \(-0.450716\pi\)
−0.778559 + 0.627571i \(0.784049\pi\)
\(6\) 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 \(0.133700\pi\)
−0.913077 + 0.407788i \(0.866300\pi\)
\(12\) −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 −0.990940 0.134307i \(-0.957119\pi\)
0.611783 + 0.791026i \(0.290453\pi\)
\(18\) 6.12277 3.53498i 1.44315 0.833204i
\(19\) 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 \(-0.100278\pi\)
−0.743728 + 0.668482i \(0.766944\pi\)
\(24\) 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 −0.501155 0.865357i \(-0.667092\pi\)
0.999999 + 0.00133469i \(0.000424845\pi\)
\(30\) −2.16354 −0.395006
\(31\) 9.07425 5.23902i 1.62978 0.940956i 0.645627 0.763653i \(-0.276596\pi\)
0.984156 0.177303i \(-0.0567372\pi\)
\(32\) 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 −0.0122297 0.999925i \(-0.503893\pi\)
0.859846 + 0.510554i \(0.170560\pi\)
\(38\) −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 0.920295 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
\(45\) 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 0.565158 0.824983i \(-0.308815\pi\)
−0.431877 + 0.901933i \(0.642148\pi\)
\(48\) 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 0.500991 0.865453i \(-0.332969\pi\)
−0.999999 + 0.00114437i \(0.999636\pi\)
\(54\) −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 0.978302 0.207183i \(-0.0664297\pi\)
0.309725 + 0.950826i \(0.399763\pi\)
\(60\) 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 \(0.311455\pi\)
−0.558296 + 0.829642i \(0.688545\pi\)
\(68\) 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 −0.428958 0.903324i \(-0.641119\pi\)
0.567823 + 0.823151i \(0.307786\pi\)
\(72\) 19.0949i 2.25036i
\(73\) −7.88374 + 4.55168i −0.922721 + 0.532733i −0.884502 0.466536i \(-0.845502\pi\)
−0.0382192 + 0.999269i \(0.512169\pi\)
\(74\) −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 −0.636988 0.770874i \(-0.719820\pi\)
0.986090 + 0.166211i \(0.0531532\pi\)
\(80\) 14.0189i 1.56736i
\(81\) 6.65300 0.739222
\(82\) −19.9361 −2.20158
\(83\) 2.69672i 0.296003i −0.988987 0.148002i \(-0.952716\pi\)
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
\(87\) −1.39278 + 2.41237i −0.149322 + 0.258633i
\(88\) −18.9115 −2.01597
\(89\) −1.52410 + 0.879938i −0.161554 + 0.0932732i −0.578597 0.815613i \(-0.696400\pi\)
0.417043 + 0.908887i \(0.363066\pi\)
\(90\) −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 0.371555 0.928411i \(-0.378825\pi\)
0.989805 + 0.142430i \(0.0454915\pi\)
\(98\) 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 −0.432098 0.901827i \(-0.642227\pi\)
0.997054 0.0767054i \(-0.0244401\pi\)
\(104\) 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 \(-0.0868205\pi\)
−0.714811 + 0.699318i \(0.753487\pi\)
\(108\) 6.98412 12.0969i 0.672048 1.16402i
\(109\) −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
\(111\) −2.67313 + 1.54333i −0.253722 + 0.146487i
\(112\) 0 0
\(113\) 4.29556 + 7.44014i 0.404093 + 0.699909i 0.994215 0.107404i \(-0.0342540\pi\)
−0.590123 + 0.807314i \(0.700921\pi\)
\(114\) 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 −0.926971 0.375133i \(-0.877597\pi\)
0.788361 + 0.615214i \(0.210930\pi\)
\(128\) −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 −0.552130 0.833758i \(-0.686185\pi\)
0.998121 + 0.0612793i \(0.0195180\pi\)
\(132\) −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 0.821832 0.569729i \(-0.192952\pi\)
−0.0824839 + 0.996592i \(0.526285\pi\)
\(138\) 2.30836 + 1.33273i 0.196501 + 0.113450i
\(139\) −0.832100 1.44124i −0.0705778 0.122244i 0.828577 0.559875i \(-0.189151\pi\)
−0.899155 + 0.437631i \(0.855818\pi\)
\(140\) 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 \(-0.698946\pi\)
0.585103 0.810959i \(-0.301054\pi\)
\(150\) −2.79100 1.61138i −0.227884 0.131569i
\(151\) 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
\(153\) 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 0.997594 + 0.0693309i \(0.0220864\pi\)
−0.438755 + 0.898607i \(0.644580\pi\)
\(158\) 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 \(-0.909401\pi\)
0.959767 0.280797i \(-0.0905987\pi\)
\(164\) 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 −0.243312 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
\(171\) 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 \(0.0346559\pi\)
−0.994079 + 0.108660i \(0.965344\pi\)
\(194\) −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 0.636546 0.771238i \(-0.280362\pi\)
−0.349639 + 0.936885i \(0.613696\pi\)
\(198\) 9.56198 + 16.5618i 0.679540 + 1.17700i
\(199\) −0.205360 + 0.355694i −0.0145576 + 0.0252145i −0.873212 0.487340i \(-0.837967\pi\)
0.858655 + 0.512554i \(0.171301\pi\)
\(200\) 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 −0.707186 0.707028i \(-0.750035\pi\)
0.965897 + 0.258927i \(0.0833688\pi\)
\(212\) −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 0.982006 0.188852i \(-0.0604766\pi\)
0.327452 + 0.944868i \(0.393810\pi\)
\(224\) 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 0.0526478 0.998613i \(-0.483234\pi\)
−0.838500 + 0.544901i \(0.816567\pi\)
\(228\) −7.77057 4.48634i −0.514618 0.297115i
\(229\) 6.86832 + 3.96543i 0.453872 + 0.262043i 0.709464 0.704742i \(-0.248937\pi\)
−0.255592 + 0.966785i \(0.582270\pi\)
\(230\) 4.14383 + 7.17733i 0.273236 + 0.473259i
\(231\) 0 0
\(232\) 32.5305 + 18.7815i 2.13573 + 1.23306i
\(233\) −3.28585 + 5.69127i −0.215263 + 0.372847i −0.953354 0.301854i \(-0.902394\pi\)
0.738091 + 0.674702i \(0.235728\pi\)
\(234\) −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 \(0.0982508\pi\)
−0.952740 + 0.303786i \(0.901749\pi\)
\(240\) 7.26833i 0.469169i
\(241\) −8.73460 5.04292i −0.562645 0.324843i 0.191562 0.981481i \(-0.438645\pi\)
−0.754206 + 0.656637i \(0.771978\pi\)
\(242\) −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 0.981834 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
\(255\) −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 0.714180 0.699962i \(-0.246800\pi\)
−0.963275 + 0.268517i \(0.913466\pi\)
\(258\) −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 −0.572823 0.819679i \(-0.694152\pi\)
0.996274 + 0.0862400i \(0.0274852\pi\)
\(270\) 12.3997 0.754619
\(271\) 7.21158 4.16361i 0.438072 0.252921i −0.264707 0.964329i \(-0.585275\pi\)
0.702780 + 0.711408i \(0.251942\pi\)
\(272\) 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 0.272066 + 0.962279i \(0.412293\pi\)
−0.969391 + 0.245523i \(0.921040\pi\)
\(278\) 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 \(0.300587\pi\)
−0.586292 + 0.810100i \(0.699413\pi\)
\(282\) 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 −0.0814609 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
\(297\) 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 \(0.0824750\pi\)
−0.966620 + 0.256213i \(0.917525\pi\)
\(308\) 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 0.640045 0.768338i \(-0.278916\pi\)
−0.985422 + 0.170126i \(0.945583\pi\)
\(312\) −9.85436 + 8.58502i −0.557893 + 0.486031i
\(313\) 6.56198 11.3657i 0.370905 0.642427i −0.618800 0.785549i \(-0.712381\pi\)
0.989705 + 0.143122i \(0.0457141\pi\)
\(314\) −31.3951 18.1260i −1.77173 1.02291i
\(315\) 0 0
\(316\) −14.5862 25.2641i −0.820540 1.42122i
\(317\) −14.4761 8.35775i −0.813056 0.469418i 0.0349599 0.999389i \(-0.488870\pi\)
−0.848016 + 0.529971i \(0.822203\pi\)
\(318\) −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 \(0.0347691\pi\)
−0.994040 + 0.109013i \(0.965231\pi\)
\(332\) −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 −0.256837 0.966455i \(-0.582680\pi\)
0.965393 0.260800i \(-0.0839863\pi\)
\(348\) 6.54727 + 11.3402i 0.350971 + 0.607899i
\(349\) 4.23507 + 2.44512i 0.226698 + 0.130884i 0.609048 0.793133i \(-0.291552\pi\)
−0.382350 + 0.924018i \(0.624885\pi\)
\(350\) 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 \(0.117497\pi\)
−0.932642 + 0.360802i \(0.882503\pi\)
\(354\) 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 0.290785 0.956789i \(-0.406084\pi\)
−0.683211 + 0.730221i \(0.739417\pi\)
\(360\) −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 −0.409775 0.912187i \(-0.634393\pi\)
−0.994864 + 0.101218i \(0.967726\pi\)
\(380\) −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 \(-0.696618\pi\)
0.579156 0.815217i \(-0.303382\pi\)
\(384\) 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 −0.984464 0.175589i \(-0.943817\pi\)
0.340168 0.940365i \(-0.389516\pi\)
\(390\) 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 \(-0.966719\pi\)
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 \(-0.829459\pi\)
0.0121716 + 0.999926i \(0.496126\pi\)
\(402\) 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 0.827539 0.561409i \(-0.189740\pi\)
−0.0724249 + 0.997374i \(0.523074\pi\)
\(410\) 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 −0.226688 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
\(423\) −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 \(0.0693172\pi\)
−0.976382 + 0.216049i \(0.930683\pi\)
\(432\) −12.9202 22.3785i −0.621625 1.07669i
\(433\) 1.72531 + 2.98833i 0.0829132 + 0.143610i 0.904500 0.426473i \(-0.140244\pi\)
−0.821587 + 0.570083i \(0.806911\pi\)
\(434\) 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 0.800792 + 0.598943i \(0.204412\pi\)
0.118304 + 0.992977i \(0.462254\pi\)
\(440\) 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 \(-0.717036\pi\)
0.987506 + 0.157580i \(0.0503693\pi\)
\(444\) 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 0.597646 0.801760i \(-0.296103\pi\)
0.993168 0.116696i \(-0.0372304\pi\)
\(450\) −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 −0.755033 0.655687i \(-0.772379\pi\)
0.190325 + 0.981721i \(0.439046\pi\)
\(458\) −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 −0.511167 + 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
\(465\) 8.75749 0.406119
\(466\) 17.0115i 0.788044i
\(467\) −2.52516 + 4.37371i −0.116851 + 0.202391i −0.918518 0.395379i \(-0.870613\pi\)
0.801667 + 0.597770i \(0.203947\pi\)
\(468\) 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 \(-0.930711\pi\)
0.976401 0.215964i \(-0.0692892\pi\)
\(480\) 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 0.996201 + 0.0870831i \(0.0277546\pi\)
0.573517 + 0.819194i \(0.305579\pi\)
\(488\) 20.4504i 0.925748i
\(489\) 3.71737i 0.168105i
\(490\) 0 0
\(491\) −3.38049 + 5.85517i −0.152559 + 0.264240i −0.932168 0.362027i \(-0.882085\pi\)
0.779608 + 0.626267i \(0.215418\pi\)
\(492\) −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 0.703732 0.710466i \(-0.251516\pi\)
−0.263416 + 0.964682i \(0.584849\pi\)
\(500\) 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 0.667955 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
\(507\) 0.923570 6.67648i 0.0410172 0.296513i
\(508\) 7.34301 + 12.7185i 0.325793 + 0.564290i
\(509\) −17.1602 + 9.90746i −0.760614 + 0.439141i −0.829516 0.558483i \(-0.811384\pi\)
0.0689022 + 0.997623i \(0.478050\pi\)
\(510\) 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 −0.974630 0.223823i \(-0.928146\pi\)
0.293479 0.955966i \(-0.405187\pi\)
\(522\) 37.9849i 1.66255i
\(523\) 11.3601 + 19.6763i 0.496742 + 0.860383i 0.999993 0.00375758i \(-0.00119608\pi\)
−0.503251 + 0.864140i \(0.667863\pi\)
\(524\) −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 0.460420 0.887701i \(-0.347699\pi\)
−0.538562 + 0.842586i \(0.681032\pi\)
\(542\) −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 \(-0.613159\pi\)
0.348058 0.937473i \(-0.386841\pi\)
\(558\) 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 −0.0865108 0.996251i \(-0.527572\pi\)
0.906034 0.423205i \(-0.139095\pi\)
\(564\) −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 0.702687 + 0.711499i \(0.251983\pi\)
0.264832 + 0.964294i \(0.414683\pi\)
\(570\) 7.96508i 0.333620i
\(571\) 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
\(573\) −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 0.0317671 0.999495i \(-0.489887\pi\)
0.881472 + 0.472237i \(0.156553\pi\)
\(578\) −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 0.434970 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
\(591\) −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 0.877738 0.479141i \(-0.159052\pi\)
0.0239212 + 0.999714i \(0.492385\pi\)
\(594\) −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 0.732633 0.680624i \(-0.238291\pi\)
−0.955754 + 0.294166i \(0.904958\pi\)
\(600\) −7.53807 + 4.35211i −0.307740 + 0.177674i
\(601\) 12.1282 21.0067i 0.494720 0.856880i −0.505262 0.862966i \(-0.668604\pi\)
0.999981 + 0.00608649i \(0.00193740\pi\)
\(602\) 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 \(-0.976342\pi\)
0.997239 0.0742540i \(-0.0236575\pi\)
\(614\) −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 −0.136231 0.990677i \(-0.543499\pi\)
0.789836 + 0.613318i \(0.210166\pi\)
\(618\) 15.3903i 0.619090i
\(619\) 13.7650 7.94725i 0.553264 0.319427i −0.197174 0.980369i \(-0.563176\pi\)
0.750437 + 0.660942i \(0.229843\pi\)
\(620\) −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 −0.800130 0.599826i \(-0.795236\pi\)
0.119400 + 0.992846i \(0.461903\pi\)
\(632\) 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 0.406390 + 0.913699i \(0.366787\pi\)
−0.994482 + 0.104905i \(0.966546\pi\)
\(642\) 5.96867 + 3.44601i 0.235565 + 0.136003i
\(643\) −10.0220 + 5.78623i −0.395231 + 0.228187i −0.684424 0.729084i \(-0.739946\pi\)
0.289193 + 0.957271i \(0.406613\pi\)
\(644\) 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 0.854452 + 0.519530i \(0.173893\pi\)
0.0227004 + 0.999742i \(0.492774\pi\)
\(654\) −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 −0.918335 0.395805i \(-0.870466\pi\)
0.116390 0.993204i \(-0.462868\pi\)
\(660\) 5.31382 + 9.20380i 0.206840 + 0.358258i
\(661\) 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
\(663\) −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 −0.285189 0.958471i \(-0.592056\pi\)
0.972655 0.232254i \(-0.0746102\pi\)
\(674\) 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 −0.840428 0.541923i \(-0.817697\pi\)
0.889533 + 0.456871i \(0.151030\pi\)
\(678\) 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 −0.227320 0.973820i \(-0.572996\pi\)
−0.957013 + 0.290045i \(0.906330\pi\)
\(684\) −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 −0.863186 0.504885i \(-0.831535\pi\)
0.00565028 + 0.999984i \(0.498201\pi\)
\(692\) −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 \(0.0362421\pi\)
−0.993525 + 0.113612i \(0.963758\pi\)
\(710\) 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 −0.449658 0.893201i \(-0.648454\pi\)
−0.998364 + 0.0571848i \(0.981788\pi\)
\(734\) −3.72861 + 2.15271i −0.137625 + 0.0794581i
\(735\) 0 0
\(736\) 16.9378i 0.624335i
\(737\) −36.7382 −1.35327
\(738\) 54.4494 2.00431
\(739\) 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
\(741\) −5.18905 + 4.52065i −0.190624 + 0.166070i
\(742\) 0 0
\(743\) 30.2115 + 17.4426i 1.10835 + 0.639908i 0.938402 0.345545i \(-0.112306\pi\)
0.169951 + 0.985453i \(0.445639\pi\)
\(744\) −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 0.543193 0.839608i \(-0.317215\pi\)
−0.998718 + 0.0506146i \(0.983882\pi\)
\(752\) 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 −0.753431 0.657527i \(-0.771602\pi\)
0.946151 + 0.323726i \(0.104936\pi\)
\(758\) 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 \(0.201495\pi\)
−0.806248 + 0.591578i \(0.798505\pi\)
\(762\) 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 0.984267 + 0.176686i \(0.0565378\pi\)
0.645148 + 0.764057i \(0.276796\pi\)
\(770\) 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 0.939396 0.342835i \(-0.111387\pi\)
0.172794 + 0.984958i \(0.444721\pi\)
\(774\) −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
\(781\) 1.82735 + 3.16506i 0.0653876 + 0.113255i