Properties

Label 637.2.e.j.508.2
Level $637$
Weight $2$
Character 637.508
Analytic conductor $5.086$
Analytic rank $0$
Dimension $6$
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.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.2696112.1
Defining polynomial: \(x^{6} - x^{5} + 5 x^{4} + 18 x^{2} - 8 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 508.2
Root \(0.235342 + 0.407624i\) of defining polynomial
Character \(\chi\) \(=\) 637.508
Dual form 637.2.e.j.79.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.235342 - 0.407624i) q^{2} +(-1.12457 + 1.94781i) q^{3} +(0.889229 - 1.54019i) q^{4} +(-0.264658 - 0.458402i) q^{5} +1.05863 q^{6} -1.77846 q^{8} +(-1.02932 - 1.78283i) q^{9} +O(q^{10})\) \(q+(-0.235342 - 0.407624i) q^{2} +(-1.12457 + 1.94781i) q^{3} +(0.889229 - 1.54019i) q^{4} +(-0.264658 - 0.458402i) q^{5} +1.05863 q^{6} -1.77846 q^{8} +(-1.02932 - 1.78283i) q^{9} +(-0.124570 + 0.215762i) q^{10} +(1.12457 - 1.94781i) q^{11} +(2.00000 + 3.46410i) q^{12} +1.00000 q^{13} +1.19051 q^{15} +(-1.35991 - 2.35544i) q^{16} +(0.653887 - 1.13257i) q^{17} +(-0.484482 + 0.839148i) q^{18} +(0.735342 + 1.27365i) q^{19} -0.941367 q^{20} -1.05863 q^{22} +(-2.91855 - 5.05507i) q^{23} +(2.00000 - 3.46410i) q^{24} +(2.35991 - 4.08749i) q^{25} +(-0.235342 - 0.407624i) q^{26} -2.11727 q^{27} +5.22154 q^{29} +(-0.280176 - 0.485279i) q^{30} +(3.51380 - 6.08608i) q^{31} +(-2.41855 + 4.18904i) q^{32} +(2.52932 + 4.38090i) q^{33} -0.615547 q^{34} -3.66119 q^{36} +(1.18320 + 2.04937i) q^{37} +(0.346113 - 0.599486i) q^{38} +(-1.12457 + 1.94781i) q^{39} +(0.470683 + 0.815248i) q^{40} +6.49828 q^{41} +11.3940 q^{43} +(-2.00000 - 3.46410i) q^{44} +(-0.544834 + 0.943681i) q^{45} +(-1.37371 + 2.37934i) q^{46} +(-4.29226 - 7.43441i) q^{47} +6.11727 q^{48} -2.22154 q^{50} +(1.47068 + 2.54730i) q^{51} +(0.889229 - 1.54019i) q^{52} +(-5.63837 + 9.76594i) q^{53} +(0.498281 + 0.863048i) q^{54} -1.19051 q^{55} -3.30777 q^{57} +(-1.22885 - 2.12843i) q^{58} +(6.08623 - 10.5417i) q^{59} +(1.05863 - 1.83361i) q^{60} +(1.00000 + 1.73205i) q^{61} -3.30777 q^{62} -3.16291 q^{64} +(-0.264658 - 0.458402i) q^{65} +(1.19051 - 2.06202i) q^{66} +(7.96896 - 13.8027i) q^{67} +(-1.16291 - 2.01422i) q^{68} +13.1284 q^{69} +1.19051 q^{71} +(1.83060 + 3.17068i) q^{72} +(-3.82157 + 6.61916i) q^{73} +(0.556914 - 0.964604i) q^{74} +(5.30777 + 9.19333i) q^{75} +2.61555 q^{76} +1.05863 q^{78} +(0.669405 + 1.15944i) q^{79} +(-0.719824 + 1.24677i) q^{80} +(5.46896 - 9.47252i) q^{81} +(-1.52932 - 2.64885i) q^{82} -16.3500 q^{83} -0.692226 q^{85} +(-2.68148 - 4.64447i) q^{86} +(-5.87199 + 10.1706i) q^{87} +(-2.00000 + 3.46410i) q^{88} +(-3.45517 - 5.98452i) q^{89} +0.512889 q^{90} -10.3810 q^{92} +(7.90303 + 13.6884i) q^{93} +(-2.02029 + 3.49925i) q^{94} +(0.389229 - 0.674164i) q^{95} +(-5.43965 - 9.42175i) q^{96} -3.47068 q^{97} -4.63016 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{2} + 2q^{3} - 3q^{4} - 2q^{5} + 8q^{6} + 6q^{8} - 7q^{9} + O(q^{10}) \) \( 6q - q^{2} + 2q^{3} - 3q^{4} - 2q^{5} + 8q^{6} + 6q^{8} - 7q^{9} + 8q^{10} - 2q^{11} + 12q^{12} + 6q^{13} - 12q^{15} + q^{16} - 4q^{17} + 15q^{18} + 4q^{19} - 4q^{20} - 8q^{22} - 10q^{23} + 12q^{24} + 5q^{25} - q^{26} - 16q^{27} + 48q^{29} - 20q^{30} + 4q^{31} - 7q^{32} + 16q^{33} + 28q^{34} - 2q^{36} + 10q^{38} + 2q^{39} + 2q^{40} + 4q^{41} + 20q^{43} - 12q^{44} - 22q^{45} + 18q^{46} + 8q^{47} + 40q^{48} - 30q^{50} + 8q^{51} - 3q^{52} - 8q^{53} - 32q^{54} + 12q^{55} - 4q^{57} - 12q^{58} + 4q^{59} + 8q^{60} + 6q^{61} - 4q^{62} - 34q^{64} - 2q^{65} - 12q^{66} + 12q^{67} - 22q^{68} - 12q^{69} - 12q^{71} + q^{72} + 10q^{73} - 30q^{74} + 16q^{75} - 16q^{76} + 8q^{78} + 14q^{79} + 14q^{80} - 3q^{81} - 10q^{82} - 24q^{83} - 20q^{85} + 26q^{86} + 26q^{87} - 12q^{88} - 2q^{89} - 56q^{90} - 24q^{92} + 22q^{93} + 10q^{94} - 6q^{95} + 4q^{96} - 20q^{97} + 28q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.235342 0.407624i −0.166412 0.288234i 0.770744 0.637145i \(-0.219885\pi\)
−0.937156 + 0.348911i \(0.886551\pi\)
\(3\) −1.12457 + 1.94781i −0.649271 + 1.12457i 0.334026 + 0.942564i \(0.391593\pi\)
−0.983297 + 0.182007i \(0.941741\pi\)
\(4\) 0.889229 1.54019i 0.444614 0.770095i
\(5\) −0.264658 0.458402i −0.118359 0.205003i 0.800759 0.598987i \(-0.204430\pi\)
−0.919117 + 0.393984i \(0.871097\pi\)
\(6\) 1.05863 0.432185
\(7\) 0 0
\(8\) −1.77846 −0.628780
\(9\) −1.02932 1.78283i −0.343106 0.594276i
\(10\) −0.124570 + 0.215762i −0.0393926 + 0.0682299i
\(11\) 1.12457 1.94781i 0.339071 0.587288i −0.645187 0.764024i \(-0.723221\pi\)
0.984258 + 0.176737i \(0.0565541\pi\)
\(12\) 2.00000 + 3.46410i 0.577350 + 1.00000i
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 1.19051 0.307388
\(16\) −1.35991 2.35544i −0.339978 0.588859i
\(17\) 0.653887 1.13257i 0.158591 0.274687i −0.775770 0.631016i \(-0.782638\pi\)
0.934361 + 0.356328i \(0.115972\pi\)
\(18\) −0.484482 + 0.839148i −0.114194 + 0.197789i
\(19\) 0.735342 + 1.27365i 0.168699 + 0.292195i 0.937963 0.346736i \(-0.112710\pi\)
−0.769264 + 0.638931i \(0.779377\pi\)
\(20\) −0.941367 −0.210496
\(21\) 0 0
\(22\) −1.05863 −0.225701
\(23\) −2.91855 5.05507i −0.608559 1.05405i −0.991478 0.130273i \(-0.958415\pi\)
0.382919 0.923782i \(-0.374919\pi\)
\(24\) 2.00000 3.46410i 0.408248 0.707107i
\(25\) 2.35991 4.08749i 0.471982 0.817497i
\(26\) −0.235342 0.407624i −0.0461543 0.0799416i
\(27\) −2.11727 −0.407468
\(28\) 0 0
\(29\) 5.22154 0.969616 0.484808 0.874621i \(-0.338889\pi\)
0.484808 + 0.874621i \(0.338889\pi\)
\(30\) −0.280176 0.485279i −0.0511529 0.0885994i
\(31\) 3.51380 6.08608i 0.631097 1.09309i −0.356231 0.934398i \(-0.615938\pi\)
0.987328 0.158694i \(-0.0507283\pi\)
\(32\) −2.41855 + 4.18904i −0.427542 + 0.740525i
\(33\) 2.52932 + 4.38090i 0.440298 + 0.762618i
\(34\) −0.615547 −0.105566
\(35\) 0 0
\(36\) −3.66119 −0.610198
\(37\) 1.18320 + 2.04937i 0.194517 + 0.336914i 0.946742 0.321992i \(-0.104353\pi\)
−0.752225 + 0.658907i \(0.771019\pi\)
\(38\) 0.346113 0.599486i 0.0561470 0.0972494i
\(39\) −1.12457 + 1.94781i −0.180075 + 0.311900i
\(40\) 0.470683 + 0.815248i 0.0744216 + 0.128902i
\(41\) 6.49828 1.01486 0.507431 0.861693i \(-0.330595\pi\)
0.507431 + 0.861693i \(0.330595\pi\)
\(42\) 0 0
\(43\) 11.3940 1.73757 0.868785 0.495190i \(-0.164902\pi\)
0.868785 + 0.495190i \(0.164902\pi\)
\(44\) −2.00000 3.46410i −0.301511 0.522233i
\(45\) −0.544834 + 0.943681i −0.0812191 + 0.140676i
\(46\) −1.37371 + 2.37934i −0.202543 + 0.350814i
\(47\) −4.29226 7.43441i −0.626090 1.08442i −0.988329 0.152334i \(-0.951321\pi\)
0.362239 0.932085i \(-0.382012\pi\)
\(48\) 6.11727 0.882951
\(49\) 0 0
\(50\) −2.22154 −0.314174
\(51\) 1.47068 + 2.54730i 0.205937 + 0.356693i
\(52\) 0.889229 1.54019i 0.123314 0.213586i
\(53\) −5.63837 + 9.76594i −0.774490 + 1.34146i 0.160591 + 0.987021i \(0.448660\pi\)
−0.935081 + 0.354434i \(0.884673\pi\)
\(54\) 0.498281 + 0.863048i 0.0678075 + 0.117446i
\(55\) −1.19051 −0.160528
\(56\) 0 0
\(57\) −3.30777 −0.438125
\(58\) −1.22885 2.12843i −0.161355 0.279476i
\(59\) 6.08623 10.5417i 0.792360 1.37241i −0.132142 0.991231i \(-0.542186\pi\)
0.924502 0.381177i \(-0.124481\pi\)
\(60\) 1.05863 1.83361i 0.136669 0.236718i
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) −3.30777 −0.420088
\(63\) 0 0
\(64\) −3.16291 −0.395364
\(65\) −0.264658 0.458402i −0.0328268 0.0568577i
\(66\) 1.19051 2.06202i 0.146541 0.253817i
\(67\) 7.96896 13.8027i 0.973564 1.68626i 0.288969 0.957338i \(-0.406687\pi\)
0.684595 0.728924i \(-0.259979\pi\)
\(68\) −1.16291 2.01422i −0.141024 0.244260i
\(69\) 13.1284 1.58048
\(70\) 0 0
\(71\) 1.19051 0.141287 0.0706436 0.997502i \(-0.477495\pi\)
0.0706436 + 0.997502i \(0.477495\pi\)
\(72\) 1.83060 + 3.17068i 0.215738 + 0.373669i
\(73\) −3.82157 + 6.61916i −0.447281 + 0.774714i −0.998208 0.0598398i \(-0.980941\pi\)
0.550927 + 0.834554i \(0.314274\pi\)
\(74\) 0.556914 0.964604i 0.0647400 0.112133i
\(75\) 5.30777 + 9.19333i 0.612889 + 1.06155i
\(76\) 2.61555 0.300024
\(77\) 0 0
\(78\) 1.05863 0.119867
\(79\) 0.669405 + 1.15944i 0.0753139 + 0.130448i 0.901223 0.433356i \(-0.142671\pi\)
−0.825909 + 0.563804i \(0.809337\pi\)
\(80\) −0.719824 + 1.24677i −0.0804788 + 0.139393i
\(81\) 5.46896 9.47252i 0.607663 1.05250i
\(82\) −1.52932 2.64885i −0.168885 0.292517i
\(83\) −16.3500 −1.79464 −0.897322 0.441377i \(-0.854490\pi\)
−0.897322 + 0.441377i \(0.854490\pi\)
\(84\) 0 0
\(85\) −0.692226 −0.0750825
\(86\) −2.68148 4.64447i −0.289152 0.500826i
\(87\) −5.87199 + 10.1706i −0.629544 + 1.09040i
\(88\) −2.00000 + 3.46410i −0.213201 + 0.369274i
\(89\) −3.45517 5.98452i −0.366247 0.634358i 0.622729 0.782438i \(-0.286024\pi\)
−0.988975 + 0.148080i \(0.952691\pi\)
\(90\) 0.512889 0.0540632
\(91\) 0 0
\(92\) −10.3810 −1.08230
\(93\) 7.90303 + 13.6884i 0.819506 + 1.41943i
\(94\) −2.02029 + 3.49925i −0.208377 + 0.360920i
\(95\) 0.389229 0.674164i 0.0399340 0.0691677i
\(96\) −5.43965 9.42175i −0.555182 0.961603i
\(97\) −3.47068 −0.352395 −0.176197 0.984355i \(-0.556380\pi\)
−0.176197 + 0.984355i \(0.556380\pi\)
\(98\) 0 0
\(99\) −4.63016 −0.465348
\(100\) −4.19700 7.26942i −0.419700 0.726942i
\(101\) −3.87543 + 6.71244i −0.385620 + 0.667913i −0.991855 0.127372i \(-0.959346\pi\)
0.606235 + 0.795285i \(0.292679\pi\)
\(102\) 0.692226 1.19897i 0.0685406 0.118716i
\(103\) 8.49828 + 14.7195i 0.837361 + 1.45035i 0.892094 + 0.451850i \(0.149236\pi\)
−0.0547334 + 0.998501i \(0.517431\pi\)
\(104\) −1.77846 −0.174392
\(105\) 0 0
\(106\) 5.30777 0.515537
\(107\) 2.77846 + 4.81243i 0.268604 + 0.465235i 0.968501 0.249008i \(-0.0801045\pi\)
−0.699898 + 0.714243i \(0.746771\pi\)
\(108\) −1.88273 + 3.26099i −0.181166 + 0.313789i
\(109\) −3.96166 + 6.86180i −0.379458 + 0.657241i −0.990984 0.133984i \(-0.957223\pi\)
0.611525 + 0.791225i \(0.290556\pi\)
\(110\) 0.280176 + 0.485279i 0.0267137 + 0.0462696i
\(111\) −5.32238 −0.505178
\(112\) 0 0
\(113\) −9.89229 −0.930588 −0.465294 0.885156i \(-0.654051\pi\)
−0.465294 + 0.885156i \(0.654051\pi\)
\(114\) 0.778457 + 1.34833i 0.0729092 + 0.126282i
\(115\) −1.54483 + 2.67573i −0.144057 + 0.249513i
\(116\) 4.64315 8.04216i 0.431105 0.746696i
\(117\) −1.02932 1.78283i −0.0951604 0.164823i
\(118\) −5.72938 −0.527432
\(119\) 0 0
\(120\) −2.11727 −0.193279
\(121\) 2.97068 + 5.14537i 0.270062 + 0.467761i
\(122\) 0.470683 0.815248i 0.0426137 0.0738090i
\(123\) −7.30777 + 12.6574i −0.658920 + 1.14128i
\(124\) −6.24914 10.8238i −0.561189 0.972009i
\(125\) −5.14486 −0.460171
\(126\) 0 0
\(127\) 0.824101 0.0731271 0.0365635 0.999331i \(-0.488359\pi\)
0.0365635 + 0.999331i \(0.488359\pi\)
\(128\) 5.58145 + 9.66736i 0.493336 + 0.854482i
\(129\) −12.8134 + 22.1934i −1.12815 + 1.95402i
\(130\) −0.124570 + 0.215762i −0.0109255 + 0.0189236i
\(131\) −5.30777 9.19333i −0.463742 0.803225i 0.535401 0.844598i \(-0.320160\pi\)
−0.999144 + 0.0413724i \(0.986827\pi\)
\(132\) 8.99656 0.783050
\(133\) 0 0
\(134\) −7.50172 −0.648050
\(135\) 0.560352 + 0.970558i 0.0482274 + 0.0835324i
\(136\) −1.16291 + 2.01422i −0.0997187 + 0.172718i
\(137\) −5.68148 + 9.84062i −0.485402 + 0.840741i −0.999859 0.0167751i \(-0.994660\pi\)
0.514457 + 0.857516i \(0.327993\pi\)
\(138\) −3.08967 5.35146i −0.263010 0.455547i
\(139\) −13.9233 −1.18096 −0.590480 0.807052i \(-0.701062\pi\)
−0.590480 + 0.807052i \(0.701062\pi\)
\(140\) 0 0
\(141\) 19.3078 1.62601
\(142\) −0.280176 0.485279i −0.0235119 0.0407237i
\(143\) 1.12457 1.94781i 0.0940413 0.162884i
\(144\) −2.79956 + 4.84898i −0.233297 + 0.404082i
\(145\) −1.38192 2.39356i −0.114763 0.198775i
\(146\) 3.59750 0.297731
\(147\) 0 0
\(148\) 4.20855 0.345941
\(149\) −4.65389 8.06077i −0.381261 0.660364i 0.609982 0.792416i \(-0.291177\pi\)
−0.991243 + 0.132052i \(0.957844\pi\)
\(150\) 2.49828 4.32715i 0.203984 0.353310i
\(151\) −3.53662 + 6.12561i −0.287806 + 0.498495i −0.973286 0.229597i \(-0.926259\pi\)
0.685480 + 0.728092i \(0.259593\pi\)
\(152\) −1.30777 2.26513i −0.106074 0.183726i
\(153\) −2.69223 −0.217654
\(154\) 0 0
\(155\) −3.71982 −0.298783
\(156\) 2.00000 + 3.46410i 0.160128 + 0.277350i
\(157\) 3.02029 5.23130i 0.241046 0.417503i −0.719967 0.694009i \(-0.755843\pi\)
0.961012 + 0.276505i \(0.0891763\pi\)
\(158\) 0.315078 0.545730i 0.0250662 0.0434160i
\(159\) −12.6815 21.9650i −1.00571 1.74194i
\(160\) 2.56035 0.202414
\(161\) 0 0
\(162\) −5.14830 −0.404489
\(163\) −3.19051 5.52612i −0.249900 0.432839i 0.713598 0.700555i \(-0.247064\pi\)
−0.963498 + 0.267716i \(0.913731\pi\)
\(164\) 5.77846 10.0086i 0.451222 0.781539i
\(165\) 1.33881 2.31889i 0.104226 0.180525i
\(166\) 3.84783 + 6.66464i 0.298650 + 0.517276i
\(167\) −16.5845 −1.28335 −0.641674 0.766977i \(-0.721760\pi\)
−0.641674 + 0.766977i \(0.721760\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0.162910 + 0.282168i 0.0124946 + 0.0216413i
\(171\) 1.51380 2.62198i 0.115763 0.200508i
\(172\) 10.1319 17.5489i 0.772548 1.33809i
\(173\) 11.6504 + 20.1792i 0.885767 + 1.53419i 0.844832 + 0.535032i \(0.179700\pi\)
0.0409355 + 0.999162i \(0.486966\pi\)
\(174\) 5.52770 0.419054
\(175\) 0 0
\(176\) −6.11727 −0.461106
\(177\) 13.6888 + 23.7097i 1.02891 + 1.78213i
\(178\) −1.62629 + 2.81682i −0.121896 + 0.211129i
\(179\) −10.5211 + 18.2231i −0.786384 + 1.36206i 0.141785 + 0.989898i \(0.454716\pi\)
−0.928169 + 0.372160i \(0.878617\pi\)
\(180\) 0.968964 + 1.67830i 0.0722223 + 0.125093i
\(181\) 16.7474 1.24483 0.622413 0.782689i \(-0.286152\pi\)
0.622413 + 0.782689i \(0.286152\pi\)
\(182\) 0 0
\(183\) −4.49828 −0.332523
\(184\) 5.19051 + 8.99022i 0.382649 + 0.662768i
\(185\) 0.626289 1.08476i 0.0460457 0.0797535i
\(186\) 3.71982 6.44292i 0.272751 0.472418i
\(187\) −1.47068 2.54730i −0.107547 0.186277i
\(188\) −15.2672 −1.11347
\(189\) 0 0
\(190\) −0.366407 −0.0265819
\(191\) 3.71982 + 6.44292i 0.269157 + 0.466194i 0.968644 0.248451i \(-0.0799216\pi\)
−0.699487 + 0.714645i \(0.746588\pi\)
\(192\) 3.55691 6.16076i 0.256698 0.444614i
\(193\) 0.750859 1.30053i 0.0540480 0.0936140i −0.837736 0.546076i \(-0.816121\pi\)
0.891784 + 0.452462i \(0.149454\pi\)
\(194\) 0.816797 + 1.41473i 0.0586426 + 0.101572i
\(195\) 1.19051 0.0852540
\(196\) 0 0
\(197\) 23.9931 1.70944 0.854720 0.519090i \(-0.173729\pi\)
0.854720 + 0.519090i \(0.173729\pi\)
\(198\) 1.08967 + 1.88736i 0.0774394 + 0.134129i
\(199\) 1.00730 1.74470i 0.0714059 0.123679i −0.828112 0.560563i \(-0.810585\pi\)
0.899518 + 0.436884i \(0.143918\pi\)
\(200\) −4.19700 + 7.26942i −0.296773 + 0.514026i
\(201\) 17.9233 + 31.0441i 1.26421 + 2.18968i
\(202\) 3.64820 0.256687
\(203\) 0 0
\(204\) 5.23109 0.366250
\(205\) −1.71982 2.97882i −0.120118 0.208050i
\(206\) 4.00000 6.92820i 0.278693 0.482711i
\(207\) −6.00821 + 10.4065i −0.417600 + 0.723304i
\(208\) −1.35991 2.35544i −0.0942929 0.163320i
\(209\) 3.30777 0.228803
\(210\) 0 0
\(211\) 10.1008 0.695370 0.347685 0.937611i \(-0.386968\pi\)
0.347685 + 0.937611i \(0.386968\pi\)
\(212\) 10.0276 + 17.3683i 0.688698 + 1.19286i
\(213\) −1.33881 + 2.31889i −0.0917337 + 0.158887i
\(214\) 1.30777 2.26513i 0.0893976 0.154841i
\(215\) −3.01552 5.22303i −0.205657 0.356208i
\(216\) 3.76547 0.256208
\(217\) 0 0
\(218\) 3.72938 0.252585
\(219\) −8.59525 14.8874i −0.580813 1.00600i
\(220\) −1.05863 + 1.83361i −0.0713730 + 0.123622i
\(221\) 0.653887 1.13257i 0.0439852 0.0761846i
\(222\) 1.25258 + 2.16953i 0.0840676 + 0.145609i
\(223\) 10.1414 0.679120 0.339560 0.940584i \(-0.389722\pi\)
0.339560 + 0.940584i \(0.389722\pi\)
\(224\) 0 0
\(225\) −9.71639 −0.647759
\(226\) 2.32807 + 4.03233i 0.154861 + 0.268227i
\(227\) 2.69223 4.66307i 0.178689 0.309499i −0.762743 0.646702i \(-0.776148\pi\)
0.941432 + 0.337203i \(0.109481\pi\)
\(228\) −2.94137 + 5.09460i −0.194797 + 0.337398i
\(229\) −1.66119 2.87727i −0.109775 0.190135i 0.805904 0.592046i \(-0.201680\pi\)
−0.915679 + 0.401911i \(0.868346\pi\)
\(230\) 1.45426 0.0958908
\(231\) 0 0
\(232\) −9.28629 −0.609675
\(233\) −6.85991 11.8817i −0.449408 0.778397i 0.548940 0.835862i \(-0.315032\pi\)
−0.998348 + 0.0574648i \(0.981698\pi\)
\(234\) −0.484482 + 0.839148i −0.0316716 + 0.0548568i
\(235\) −2.27196 + 3.93515i −0.148206 + 0.256701i
\(236\) −10.8241 18.7479i −0.704589 1.22038i
\(237\) −3.01117 −0.195597
\(238\) 0 0
\(239\) −3.50172 −0.226507 −0.113254 0.993566i \(-0.536127\pi\)
−0.113254 + 0.993566i \(0.536127\pi\)
\(240\) −1.61899 2.80416i −0.104505 0.181008i
\(241\) −0.793975 + 1.37520i −0.0511444 + 0.0885847i −0.890464 0.455053i \(-0.849620\pi\)
0.839320 + 0.543638i \(0.182954\pi\)
\(242\) 1.39825 2.42184i 0.0898830 0.155682i
\(243\) 9.12457 + 15.8042i 0.585341 + 1.01384i
\(244\) 3.55691 0.227708
\(245\) 0 0
\(246\) 6.87930 0.438608
\(247\) 0.735342 + 1.27365i 0.0467887 + 0.0810404i
\(248\) −6.24914 + 10.8238i −0.396821 + 0.687314i
\(249\) 18.3867 31.8467i 1.16521 2.01820i
\(250\) 1.21080 + 2.09717i 0.0765778 + 0.132637i
\(251\) −4.92676 −0.310974 −0.155487 0.987838i \(-0.549695\pi\)
−0.155487 + 0.987838i \(0.549695\pi\)
\(252\) 0 0
\(253\) −13.1284 −0.825378
\(254\) −0.193945 0.335923i −0.0121692 0.0210777i
\(255\) 0.778457 1.34833i 0.0487489 0.0844355i
\(256\) −0.535811 + 0.928053i −0.0334882 + 0.0580033i
\(257\) 4.00730 + 6.94085i 0.249969 + 0.432959i 0.963517 0.267648i \(-0.0862463\pi\)
−0.713548 + 0.700606i \(0.752913\pi\)
\(258\) 12.0621 0.750952
\(259\) 0 0
\(260\) −0.941367 −0.0583811
\(261\) −5.37462 9.30912i −0.332681 0.576220i
\(262\) −2.49828 + 4.32715i −0.154344 + 0.267332i
\(263\) −0.801279 + 1.38786i −0.0494090 + 0.0855788i −0.889672 0.456600i \(-0.849067\pi\)
0.840263 + 0.542179i \(0.182400\pi\)
\(264\) −4.49828 7.79125i −0.276850 0.479518i
\(265\) 5.96896 0.366671
\(266\) 0 0
\(267\) 15.5423 0.951174
\(268\) −14.1725 24.5474i −0.865721 1.49947i
\(269\) 5.91033 10.2370i 0.360359 0.624161i −0.627661 0.778487i \(-0.715987\pi\)
0.988020 + 0.154327i \(0.0493208\pi\)
\(270\) 0.263748 0.456826i 0.0160512 0.0278015i
\(271\) −10.9414 18.9510i −0.664641 1.15119i −0.979383 0.202014i \(-0.935251\pi\)
0.314742 0.949177i \(-0.398082\pi\)
\(272\) −3.55691 −0.215670
\(273\) 0 0
\(274\) 5.34836 0.323106
\(275\) −5.30777 9.19333i −0.320071 0.554379i
\(276\) 11.6742 20.2203i 0.702703 1.21712i
\(277\) 5.10905 8.84914i 0.306973 0.531693i −0.670725 0.741706i \(-0.734017\pi\)
0.977699 + 0.210012i \(0.0673505\pi\)
\(278\) 3.27674 + 5.67548i 0.196526 + 0.340392i
\(279\) −14.4672 −0.866131
\(280\) 0 0
\(281\) 1.54231 0.0920063 0.0460031 0.998941i \(-0.485352\pi\)
0.0460031 + 0.998941i \(0.485352\pi\)
\(282\) −4.54392 7.87031i −0.270587 0.468670i
\(283\) −7.92332 + 13.7236i −0.470993 + 0.815783i −0.999449 0.0331771i \(-0.989437\pi\)
0.528457 + 0.848960i \(0.322771\pi\)
\(284\) 1.05863 1.83361i 0.0628183 0.108805i
\(285\) 0.875430 + 1.51629i 0.0518560 + 0.0898172i
\(286\) −1.05863 −0.0625983
\(287\) 0 0
\(288\) 9.95779 0.586769
\(289\) 7.64486 + 13.2413i 0.449698 + 0.778900i
\(290\) −0.650449 + 1.12661i −0.0381957 + 0.0661569i
\(291\) 3.90303 6.76024i 0.228800 0.396292i
\(292\) 6.79650 + 11.7719i 0.397735 + 0.688898i
\(293\) 11.0828 0.647464 0.323732 0.946149i \(-0.395062\pi\)
0.323732 + 0.946149i \(0.395062\pi\)
\(294\) 0 0
\(295\) −6.44309 −0.375131
\(296\) −2.10428 3.64471i −0.122309 0.211845i
\(297\) −2.38101 + 4.12404i −0.138160 + 0.239301i
\(298\) −2.19051 + 3.79407i −0.126893 + 0.219785i
\(299\) −2.91855 5.05507i −0.168784 0.292342i
\(300\) 18.8793 1.09000
\(301\) 0 0
\(302\) 3.32926 0.191577
\(303\) −8.71639 15.0972i −0.500743 0.867313i
\(304\) 2.00000 3.46410i 0.114708 0.198680i
\(305\) 0.529317 0.916803i 0.0303086 0.0524960i
\(306\) 0.633593 + 1.09742i 0.0362201 + 0.0627351i
\(307\) 20.4121 1.16498 0.582489 0.812839i \(-0.302079\pi\)
0.582489 + 0.812839i \(0.302079\pi\)
\(308\) 0 0
\(309\) −38.2277 −2.17470
\(310\) 0.875430 + 1.51629i 0.0497211 + 0.0861194i
\(311\) 0.961661 1.66564i 0.0545308 0.0944501i −0.837471 0.546481i \(-0.815967\pi\)
0.892002 + 0.452031i \(0.149300\pi\)
\(312\) 2.00000 3.46410i 0.113228 0.196116i
\(313\) 7.18320 + 12.4417i 0.406019 + 0.703245i 0.994439 0.105310i \(-0.0335835\pi\)
−0.588421 + 0.808555i \(0.700250\pi\)
\(314\) −2.84320 −0.160451
\(315\) 0 0
\(316\) 2.38101 0.133943
\(317\) −7.77846 13.4727i −0.436882 0.756701i 0.560565 0.828110i \(-0.310584\pi\)
−0.997447 + 0.0714089i \(0.977250\pi\)
\(318\) −5.96896 + 10.3385i −0.334723 + 0.579757i
\(319\) 5.87199 10.1706i 0.328768 0.569444i
\(320\) 0.837090 + 1.44988i 0.0467948 + 0.0810509i
\(321\) −12.4983 −0.697586
\(322\) 0 0
\(323\) 1.92332 0.107016
\(324\) −9.72632 16.8465i −0.540351 0.935915i
\(325\) 2.35991 4.08749i 0.130904 0.226733i
\(326\) −1.50172 + 2.60105i −0.0831725 + 0.144059i
\(327\) −8.91033 15.4331i −0.492742 0.853455i
\(328\) −11.5569 −0.638124
\(329\) 0 0
\(330\) −1.26031 −0.0693778
\(331\) −15.7750 27.3231i −0.867073 1.50182i −0.864974 0.501818i \(-0.832665\pi\)
−0.00209996 0.999998i \(-0.500668\pi\)
\(332\) −14.5389 + 25.1821i −0.797924 + 1.38205i
\(333\) 2.43578 4.21890i 0.133480 0.231194i
\(334\) 3.90303 + 6.76024i 0.213564 + 0.369904i
\(335\) −8.43621 −0.460919
\(336\) 0 0
\(337\) −8.42666 −0.459029 −0.229515 0.973305i \(-0.573714\pi\)
−0.229515 + 0.973305i \(0.573714\pi\)
\(338\) −0.235342 0.407624i −0.0128009 0.0221718i
\(339\) 11.1246 19.2683i 0.604204 1.04651i
\(340\) −0.615547 + 1.06616i −0.0333827 + 0.0578206i
\(341\) −7.90303 13.6884i −0.427973 0.741271i
\(342\) −1.42504 −0.0770573
\(343\) 0 0
\(344\) −20.2637 −1.09255
\(345\) −3.47455 6.01810i −0.187063 0.324003i
\(346\) 5.48367 9.49800i 0.294804 0.510616i
\(347\) −9.67418 + 16.7562i −0.519337 + 0.899518i 0.480410 + 0.877044i \(0.340488\pi\)
−0.999747 + 0.0224745i \(0.992846\pi\)
\(348\) 10.4431 + 18.0880i 0.559808 + 0.969616i
\(349\) 27.2553 1.45894 0.729470 0.684013i \(-0.239767\pi\)
0.729470 + 0.684013i \(0.239767\pi\)
\(350\) 0 0
\(351\) −2.11727 −0.113011
\(352\) 5.43965 + 9.42175i 0.289934 + 0.502181i
\(353\) 12.8371 22.2345i 0.683249 1.18342i −0.290734 0.956804i \(-0.593900\pi\)
0.973984 0.226619i \(-0.0727671\pi\)
\(354\) 6.44309 11.1598i 0.342446 0.593134i
\(355\) −0.315078 0.545730i −0.0167226 0.0289644i
\(356\) −12.2897 −0.651354
\(357\) 0 0
\(358\) 9.90422 0.523454
\(359\) 11.7091 + 20.2807i 0.617982 + 1.07038i 0.989854 + 0.142092i \(0.0453828\pi\)
−0.371872 + 0.928284i \(0.621284\pi\)
\(360\) 0.968964 1.67830i 0.0510689 0.0884540i
\(361\) 8.41855 14.5813i 0.443081 0.767439i
\(362\) −3.94137 6.82665i −0.207154 0.358801i
\(363\) −13.3630 −0.701374
\(364\) 0 0
\(365\) 4.04564 0.211759
\(366\) 1.05863 + 1.83361i 0.0553356 + 0.0958441i
\(367\) 7.34268 12.7179i 0.383285 0.663868i −0.608245 0.793749i \(-0.708126\pi\)
0.991530 + 0.129881i \(0.0414595\pi\)
\(368\) −7.93793 + 13.7489i −0.413793 + 0.716711i
\(369\) −6.68879 11.5853i −0.348204 0.603108i
\(370\) −0.589568 −0.0306502
\(371\) 0 0
\(372\) 28.1104 1.45746
\(373\) 11.8337 + 20.4965i 0.612723 + 1.06127i 0.990779 + 0.135485i \(0.0432593\pi\)
−0.378056 + 0.925783i \(0.623407\pi\)
\(374\) −0.692226 + 1.19897i −0.0357942 + 0.0619973i
\(375\) 5.78576 10.0212i 0.298775 0.517494i
\(376\) 7.63359 + 13.2218i 0.393673 + 0.681861i
\(377\) 5.22154 0.268923
\(378\) 0 0
\(379\) −32.7405 −1.68177 −0.840884 0.541215i \(-0.817965\pi\)
−0.840884 + 0.541215i \(0.817965\pi\)
\(380\) −0.692226 1.19897i −0.0355105 0.0615059i
\(381\) −0.926759 + 1.60519i −0.0474793 + 0.0822366i
\(382\) 1.75086 3.03258i 0.0895818 0.155160i
\(383\) 11.3078 + 19.5856i 0.577800 + 1.00078i 0.995731 + 0.0923006i \(0.0294221\pi\)
−0.417931 + 0.908479i \(0.637245\pi\)
\(384\) −25.1070 −1.28123
\(385\) 0 0
\(386\) −0.706834 −0.0359769
\(387\) −11.7280 20.3136i −0.596170 1.03260i
\(388\) −3.08623 + 5.34551i −0.156680 + 0.271377i
\(389\) −19.0242 + 32.9508i −0.964563 + 1.67067i −0.253779 + 0.967262i \(0.581674\pi\)
−0.710784 + 0.703410i \(0.751660\pi\)
\(390\) −0.280176 0.485279i −0.0141873 0.0245731i
\(391\) −7.63359 −0.386047
\(392\) 0 0
\(393\) 23.8759 1.20438
\(394\) −5.64658 9.78017i −0.284471 0.492718i
\(395\) 0.354327 0.613712i 0.0178281 0.0308792i
\(396\) −4.11727 + 7.13131i −0.206900 + 0.358362i
\(397\) 5.85261 + 10.1370i 0.293734 + 0.508762i 0.974690 0.223563i \(-0.0717687\pi\)
−0.680956 + 0.732325i \(0.738435\pi\)
\(398\) −0.948243 −0.0475311
\(399\) 0 0
\(400\) −12.8371 −0.641855
\(401\) −1.77846 3.08038i −0.0888119 0.153827i 0.818197 0.574938i \(-0.194974\pi\)
−0.907009 + 0.421111i \(0.861640\pi\)
\(402\) 8.43621 14.6119i 0.420760 0.728778i
\(403\) 3.51380 6.08608i 0.175035 0.303169i
\(404\) 6.89229 + 11.9378i 0.342904 + 0.593927i
\(405\) −5.78963 −0.287689
\(406\) 0 0
\(407\) 5.32238 0.263821
\(408\) −2.61555 4.53026i −0.129489 0.224281i
\(409\) −2.63107 + 4.55714i −0.130098 + 0.225336i −0.923714 0.383083i \(-0.874862\pi\)
0.793616 + 0.608419i \(0.208196\pi\)
\(410\) −0.809493 + 1.40208i −0.0399780 + 0.0692439i
\(411\) −12.7785 22.1329i −0.630315 1.09174i
\(412\) 30.2277 1.48921
\(413\) 0 0
\(414\) 5.65593 0.277974
\(415\) 4.32716 + 7.49486i 0.212412 + 0.367908i
\(416\) −2.41855 + 4.18904i −0.118579 + 0.205385i
\(417\) 15.6578 27.1200i 0.766763 1.32807i
\(418\) −0.778457 1.34833i −0.0380756 0.0659488i
\(419\) 26.0337 1.27183 0.635915 0.771759i \(-0.280623\pi\)
0.635915 + 0.771759i \(0.280623\pi\)
\(420\) 0 0
\(421\) 22.2423 1.08402 0.542011 0.840372i \(-0.317663\pi\)
0.542011 + 0.840372i \(0.317663\pi\)
\(422\) −2.37715 4.11734i −0.115718 0.200429i
\(423\) −8.83618 + 15.3047i −0.429630 + 0.744141i
\(424\) 10.0276 17.3683i 0.486983 0.843480i
\(425\) −3.08623 5.34551i −0.149704 0.259295i
\(426\) 1.26031 0.0610622
\(427\) 0 0
\(428\) 9.88273 0.477700
\(429\) 2.52932 + 4.38090i 0.122117 + 0.211512i
\(430\) −1.41935 + 2.45839i −0.0684473 + 0.118554i
\(431\) −13.8371 + 23.9665i −0.666509 + 1.15443i 0.312365 + 0.949962i \(0.398879\pi\)
−0.978874 + 0.204465i \(0.934454\pi\)
\(432\) 2.87930 + 4.98709i 0.138530 + 0.239941i
\(433\) −12.7880 −0.614552 −0.307276 0.951620i \(-0.599418\pi\)
−0.307276 + 0.951620i \(0.599418\pi\)
\(434\) 0 0
\(435\) 6.21629 0.298048
\(436\) 7.04564 + 12.2034i 0.337425 + 0.584437i
\(437\) 4.29226 7.43441i 0.205326 0.355636i
\(438\) −4.04564 + 7.00726i −0.193308 + 0.334820i
\(439\) 9.08279 + 15.7319i 0.433498 + 0.750841i 0.997172 0.0751569i \(-0.0239458\pi\)
−0.563674 + 0.825998i \(0.690612\pi\)
\(440\) 2.11727 0.100937
\(441\) 0 0
\(442\) −0.615547 −0.0292786
\(443\) −0.0538572 0.0932834i −0.00255883 0.00443203i 0.864743 0.502214i \(-0.167481\pi\)
−0.867302 + 0.497782i \(0.834148\pi\)
\(444\) −4.73281 + 8.19747i −0.224609 + 0.389035i
\(445\) −1.82888 + 3.16771i −0.0866971 + 0.150164i
\(446\) −2.38670 4.13389i −0.113014 0.195745i
\(447\) 20.9345 0.990167
\(448\) 0 0
\(449\) −22.1725 −1.04638 −0.523192 0.852215i \(-0.675259\pi\)
−0.523192 + 0.852215i \(0.675259\pi\)
\(450\) 2.28667 + 3.96063i 0.107795 + 0.186706i
\(451\) 7.30777 12.6574i 0.344110 0.596015i
\(452\) −8.79650 + 15.2360i −0.413753 + 0.716641i
\(453\) −7.95436 13.7773i −0.373728 0.647316i
\(454\) −2.53437 −0.118944
\(455\) 0 0
\(456\) 5.88273 0.275484
\(457\) −2.17977 3.77546i −0.101965 0.176609i 0.810529 0.585698i \(-0.199180\pi\)
−0.912494 + 0.409090i \(0.865846\pi\)
\(458\) −0.781895 + 1.35428i −0.0365356 + 0.0632814i
\(459\) −1.38445 + 2.39794i −0.0646207 + 0.111926i
\(460\) 2.74742 + 4.75867i 0.128099 + 0.221874i
\(461\) 32.3810 1.50813 0.754067 0.656797i \(-0.228089\pi\)
0.754067 + 0.656797i \(0.228089\pi\)
\(462\) 0 0
\(463\) 8.36641 0.388820 0.194410 0.980920i \(-0.437721\pi\)
0.194410 + 0.980920i \(0.437721\pi\)
\(464\) −7.10084 12.2990i −0.329648 0.570967i
\(465\) 4.18320 7.24552i 0.193991 0.336003i
\(466\) −3.22885 + 5.59253i −0.149573 + 0.259069i
\(467\) 9.77115 + 16.9241i 0.452155 + 0.783156i 0.998520 0.0543919i \(-0.0173220\pi\)
−0.546365 + 0.837547i \(0.683989\pi\)
\(468\) −3.66119 −0.169239
\(469\) 0 0
\(470\) 2.13875 0.0986532
\(471\) 6.79307 + 11.7659i 0.313008 + 0.542146i
\(472\) −10.8241 + 18.7479i −0.498220 + 0.862942i
\(473\) 12.8134 22.1934i 0.589159 1.02045i
\(474\) 0.708654 + 1.22742i 0.0325496 + 0.0563775i
\(475\) 6.94137 0.318492
\(476\) 0 0
\(477\) 23.2147 1.06293
\(478\) 0.824101 + 1.42738i 0.0376935 + 0.0652870i
\(479\) 14.2612 24.7012i 0.651612 1.12862i −0.331120 0.943589i \(-0.607426\pi\)
0.982732 0.185036i \(-0.0592402\pi\)
\(480\) −2.87930 + 4.98709i −0.131421 + 0.227628i
\(481\) 1.18320 + 2.04937i 0.0539494 + 0.0934432i
\(482\) 0.747422 0.0340441
\(483\) 0 0
\(484\) 10.5665 0.480294
\(485\) 0.918545 + 1.59097i 0.0417090 + 0.0722421i
\(486\) 4.29478 7.43878i 0.194815 0.337430i
\(487\) −12.4121 + 21.4983i −0.562444 + 0.974181i 0.434839 + 0.900508i \(0.356805\pi\)
−0.997282 + 0.0736727i \(0.976528\pi\)
\(488\) −1.77846 3.08038i −0.0805070 0.139442i
\(489\) 14.3518 0.649011
\(490\) 0 0
\(491\) 29.1690 1.31638 0.658190 0.752852i \(-0.271322\pi\)
0.658190 + 0.752852i \(0.271322\pi\)
\(492\) 12.9966 + 22.5107i 0.585930 + 1.01486i
\(493\) 3.41430 5.91374i 0.153772 0.266341i
\(494\) 0.346113 0.599486i 0.0155724 0.0269721i
\(495\) 1.22541 + 2.12247i 0.0550780 + 0.0953980i
\(496\) −19.1138 −0.858236
\(497\) 0 0
\(498\) −17.3086 −0.775618
\(499\) 16.6504 + 28.8394i 0.745376 + 1.29103i 0.950019 + 0.312193i \(0.101064\pi\)
−0.204642 + 0.978837i \(0.565603\pi\)
\(500\) −4.57496 + 7.92406i −0.204598 + 0.354375i
\(501\) 18.6504 32.3035i 0.833241 1.44322i
\(502\) 1.15947 + 2.00826i 0.0517498 + 0.0896332i
\(503\) −12.3258 −0.549581 −0.274791 0.961504i \(-0.588609\pi\)
−0.274791 + 0.961504i \(0.588609\pi\)
\(504\) 0 0
\(505\) 4.10266 0.182566
\(506\) 3.08967 + 5.35146i 0.137353 + 0.237902i
\(507\) −1.12457 + 1.94781i −0.0499439 + 0.0865054i
\(508\) 0.732814 1.26927i 0.0325134 0.0563148i
\(509\) −11.8526 20.5293i −0.525358 0.909946i −0.999564 0.0295323i \(-0.990598\pi\)
0.474206 0.880414i \(-0.342735\pi\)
\(510\) −0.732814 −0.0324495
\(511\) 0 0
\(512\) 22.8302 1.00896
\(513\) −1.55691 2.69665i −0.0687394 0.119060i
\(514\) 1.88617 3.26694i 0.0831955 0.144099i
\(515\) 4.49828 7.79125i 0.198218 0.343324i
\(516\) 22.7880 + 39.4700i 1.00319 + 1.73757i
\(517\) −19.3078 −0.849155
\(518\) 0 0
\(519\) −52.4070 −2.30041
\(520\) 0.470683 + 0.815248i 0.0206408 + 0.0357510i
\(521\) −21.9509 + 38.0201i −0.961687 + 1.66569i −0.243424 + 0.969920i \(0.578270\pi\)
−0.718264 + 0.695771i \(0.755063\pi\)
\(522\) −2.52974 + 4.38165i −0.110724 + 0.191779i
\(523\) −18.7164 32.4177i −0.818410 1.41753i −0.906853 0.421447i \(-0.861522\pi\)
0.0884425 0.996081i \(-0.471811\pi\)
\(524\) −18.8793 −0.824746
\(525\) 0 0
\(526\) 0.754297 0.0328889
\(527\) −4.59525 7.95921i −0.200172 0.346709i
\(528\) 6.87930 11.9153i 0.299383 0.518546i
\(529\) −5.53581 + 9.58831i −0.240687 + 0.416883i
\(530\) −1.40475 2.43309i −0.0610183 0.105687i
\(531\) −25.0586 −1.08745
\(532\) 0 0
\(533\) 6.49828 0.281472
\(534\) −3.65775 6.33541i −0.158286 0.274160i
\(535\) 1.47068 2.54730i 0.0635832 0.110129i
\(536\) −14.1725 + 24.5474i −0.612157 + 1.06029i
\(537\) −23.6634 40.9863i −1.02115 1.76869i
\(538\) −5.56379 −0.239872
\(539\) 0 0
\(540\) 1.99312 0.0857704
\(541\) 17.4875 + 30.2893i 0.751848 + 1.30224i 0.946926 + 0.321451i \(0.104171\pi\)
−0.195078 + 0.980788i \(0.562496\pi\)
\(542\) −5.14992 + 8.91992i −0.221208 + 0.383144i
\(543\) −18.8337 + 32.6208i −0.808229 + 1.39989i
\(544\) 3.16291 + 5.47832i 0.135609 + 0.234881i
\(545\) 4.19395 0.179649
\(546\) 0 0
\(547\) 6.50783 0.278255 0.139127 0.990274i \(-0.455570\pi\)
0.139127 + 0.990274i \(0.455570\pi\)
\(548\) 10.1043 + 17.5011i 0.431633 + 0.747611i
\(549\) 2.05863 3.56566i 0.0878603 0.152179i
\(550\) −2.49828 + 4.32715i −0.106527 + 0.184510i
\(551\) 3.83962 + 6.65041i 0.163573 + 0.283317i
\(552\) −23.3484 −0.993772
\(553\) 0 0
\(554\) −4.80949 −0.204336
\(555\) 1.40861 + 2.43979i 0.0597923 + 0.103563i
\(556\) −12.3810 + 21.4445i −0.525072 + 0.909451i
\(557\) 21.7164 37.6139i 0.920153 1.59375i 0.120976 0.992655i \(-0.461398\pi\)
0.799177 0.601096i \(-0.205269\pi\)
\(558\) 3.40475 + 5.89719i 0.144134 + 0.249648i
\(559\) 11.3940 0.481915
\(560\) 0 0
\(561\) 6.61555 0.279309
\(562\) −0.362969 0.628681i −0.0153109 0.0265193i
\(563\) 16.9414 29.3433i 0.713993 1.23667i −0.249353 0.968413i \(-0.580218\pi\)
0.963346 0.268260i \(-0.0864487\pi\)
\(564\) 17.1690 29.7376i 0.722946 1.25218i
\(565\) 2.61808 + 4.53464i 0.110143 + 0.190774i
\(566\) 7.45875 0.313515
\(567\) 0 0
\(568\) −2.11727 −0.0888385
\(569\) −9.60733 16.6404i −0.402760 0.697601i 0.591298 0.806453i \(-0.298616\pi\)
−0.994058 + 0.108852i \(0.965283\pi\)
\(570\) 0.412050 0.713692i 0.0172589 0.0298933i
\(571\) −10.4134 + 18.0365i −0.435787 + 0.754805i −0.997359 0.0726226i \(-0.976863\pi\)
0.561573 + 0.827427i \(0.310196\pi\)
\(572\) −2.00000 3.46410i −0.0836242 0.144841i
\(573\) −16.7328 −0.699023
\(574\) 0 0
\(575\) −27.5500 −1.14892
\(576\) 3.25564 + 5.63893i 0.135651 + 0.234955i
\(577\) −14.3224 + 24.8071i −0.596249 + 1.03273i 0.397121 + 0.917766i \(0.370009\pi\)
−0.993369 + 0.114966i \(0.963324\pi\)
\(578\) 3.59831 6.23246i 0.149670 0.259236i
\(579\) 1.68879 + 2.92507i 0.0701837 + 0.121562i
\(580\) −4.91539 −0.204100
\(581\) 0 0
\(582\) −3.67418 −0.152300
\(583\) 12.6815 + 21.9650i 0.525213 + 0.909696i
\(584\) 6.79650 11.7719i 0.281241 0.487124i
\(585\) −0.544834 + 0.943681i −0.0225261 + 0.0390164i
\(586\) −2.60824 4.51761i −0.107746 0.186621i
\(587\) −4.32076 −0.178337 −0.0891685 0.996017i \(-0.528421\pi\)
−0.0891685 + 0.996017i \(0.528421\pi\)
\(588\) 0 0
\(589\) 10.3354 0.425862
\(590\) 1.51633 + 2.62636i 0.0624262 + 0.108125i
\(591\) −26.9820 + 46.7341i −1.10989 + 1.92238i
\(592\) 3.21811 5.57392i 0.132263 0.229087i
\(593\) 7.98448 + 13.8295i 0.327883 + 0.567911i 0.982092 0.188404i \(-0.0603314\pi\)
−0.654208 + 0.756314i \(0.726998\pi\)
\(594\) 2.24141 0.0919661
\(595\) 0 0
\(596\) −16.5535 −0.678057
\(597\) 2.26557 + 3.92408i 0.0927235 + 0.160602i
\(598\) −1.37371 + 2.37934i −0.0561752 + 0.0972983i
\(599\) 8.43487 14.6096i 0.344640 0.596933i −0.640649 0.767834i \(-0.721334\pi\)
0.985288 + 0.170901i \(0.0546678\pi\)
\(600\) −9.43965 16.3499i −0.385372 0.667484i
\(601\) −15.3415 −0.625792 −0.312896 0.949787i \(-0.601299\pi\)
−0.312896 + 0.949787i \(0.601299\pi\)
\(602\) 0 0
\(603\) −32.8103 −1.33614
\(604\) 6.28973 + 10.8941i 0.255925 + 0.443276i
\(605\) 1.57243 2.72353i 0.0639285 0.110727i
\(606\) −4.10266 + 7.10601i −0.166659 + 0.288662i
\(607\) −17.9176 31.0343i −0.727254 1.25964i −0.958039 0.286637i \(-0.907463\pi\)
0.230785 0.973005i \(-0.425871\pi\)
\(608\) −7.11383 −0.288504
\(609\) 0 0
\(610\) −0.498281 −0.0201748
\(611\) −4.29226 7.43441i −0.173646 0.300764i
\(612\) −2.39400 + 4.14654i −0.0967719 + 0.167614i
\(613\) −9.83365 + 17.0324i −0.397177 + 0.687932i −0.993376 0.114905i \(-0.963344\pi\)
0.596199 + 0.802837i \(0.296677\pi\)
\(614\) −4.80381 8.32044i −0.193866 0.335786i
\(615\) 7.73625 0.311956
\(616\) 0 0
\(617\) −41.4588 −1.66907 −0.834533 0.550958i \(-0.814263\pi\)
−0.834533 + 0.550958i \(0.814263\pi\)
\(618\) 8.99656 + 15.5825i 0.361895 + 0.626820i
\(619\) −5.43965 + 9.42175i −0.218638 + 0.378692i −0.954392 0.298557i \(-0.903495\pi\)
0.735754 + 0.677249i \(0.236828\pi\)
\(620\) −3.30777 + 5.72923i −0.132843 + 0.230091i
\(621\) 6.17934 + 10.7029i 0.247968 + 0.429494i
\(622\) −0.905275 −0.0362982
\(623\) 0 0
\(624\) 6.11727 0.244887
\(625\) −10.4379 18.0790i −0.417517 0.723161i
\(626\) 3.38101 5.85609i 0.135133 0.234056i
\(627\) −3.71982 + 6.44292i −0.148555 + 0.257306i
\(628\) −5.37146 9.30365i −0.214345 0.371256i
\(629\) 3.09472 0.123395
\(630\) 0 0
\(631\) −31.4396 −1.25159 −0.625796 0.779987i \(-0.715226\pi\)
−0.625796 + 0.779987i \(0.715226\pi\)
\(632\) −1.19051 2.06202i −0.0473558 0.0820227i
\(633\) −11.3591 + 19.6745i −0.451484 + 0.781993i
\(634\) −3.66119 + 6.34137i −0.145404 + 0.251848i
\(635\) −0.218105 0.377769i −0.00865523 0.0149913i
\(636\) −45.1070 −1.78861
\(637\) 0 0
\(638\) −5.52770 −0.218844
\(639\) −1.22541 2.12247i −0.0484764 0.0839636i
\(640\) 2.95436 5.11710i 0.116781 0.202271i
\(641\) −1.52110 + 2.63463i −0.0600799 + 0.104062i −0.894501 0.447066i \(-0.852469\pi\)
0.834421 + 0.551128i \(0.185802\pi\)
\(642\) 2.94137 + 5.09460i 0.116086 + 0.201068i
\(643\) 8.02922 0.316641 0.158321 0.987388i \(-0.449392\pi\)
0.158321 + 0.987388i \(0.449392\pi\)
\(644\) 0 0
\(645\) 13.5646 0.534107
\(646\) −0.452638 0.783991i −0.0178088 0.0308457i
\(647\) −3.53662 + 6.12561i −0.139039 + 0.240822i −0.927133 0.374732i \(-0.877735\pi\)
0.788094 + 0.615555i \(0.211068\pi\)
\(648\) −9.72632 + 16.8465i −0.382086 + 0.661792i
\(649\) −13.6888 23.7097i −0.537332 0.930686i
\(650\) −2.22154 −0.0871361
\(651\) 0 0
\(652\) −11.3484 −0.444436
\(653\) 7.87930 + 13.6473i 0.308341 + 0.534062i 0.978000 0.208607i \(-0.0668930\pi\)
−0.669659 + 0.742669i \(0.733560\pi\)
\(654\) −4.19395 + 7.26413i −0.163996 + 0.284050i
\(655\) −2.80949 + 4.86618i −0.109776 + 0.190138i
\(656\) −8.83709 15.3063i −0.345030 0.597610i
\(657\) 15.7344 0.613859
\(658\) 0 0
\(659\) −12.2181 −0.475950 −0.237975 0.971271i \(-0.576484\pi\)
−0.237975 + 0.971271i \(0.576484\pi\)
\(660\) −2.38101 4.12404i −0.0926809 0.160528i
\(661\) −1.86722 + 3.23411i −0.0726263 + 0.125792i −0.900052 0.435783i \(-0.856471\pi\)
0.827425 + 0.561576i \(0.189805\pi\)
\(662\) −7.42504 + 12.8605i −0.288582 + 0.499839i
\(663\) 1.47068 + 2.54730i 0.0571166 + 0.0989289i
\(664\) 29.0777 1.12844
\(665\) 0 0
\(666\) −2.29296 −0.0888506
\(667\) −15.2393 26.3953i −0.590068 1.02203i
\(668\) −14.7474 + 25.5433i −0.570595 + 0.988299i
\(669\) −11.4047 + 19.7536i −0.440933 + 0.763718i
\(670\) 1.98539 + 3.43880i 0.0767024 + 0.132852i
\(671\) 4.49828 0.173654
\(672\) 0 0
\(673\) −5.65775 −0.218090 −0.109045 0.994037i \(-0.534779\pi\)
−0.109045 + 0.994037i \(0.534779\pi\)
\(674\) 1.98314 + 3.43491i 0.0763879 + 0.132308i
\(675\) −4.99656 + 8.65430i −0.192318 + 0.333104i
\(676\) 0.889229 1.54019i 0.0342011 0.0592380i
\(677\) −4.69953 8.13983i −0.180618 0.312839i 0.761473 0.648196i \(-0.224476\pi\)
−0.942091 + 0.335357i \(0.891143\pi\)
\(678\) −10.4723 −0.402186
\(679\) 0 0
\(680\) 1.23109 0.0472103
\(681\) 6.05520 + 10.4879i 0.232036 + 0.401897i
\(682\) −3.71982 + 6.44292i −0.142439 + 0.246712i
\(683\) 10.3664 17.9551i 0.396660 0.687034i −0.596652 0.802500i \(-0.703503\pi\)
0.993311 + 0.115466i \(0.0368360\pi\)
\(684\) −2.69223 4.66307i −0.102940 0.178297i
\(685\) 6.01461 0.229806
\(686\) 0 0
\(687\) 7.47250 0.285094
\(688\) −15.4948 26.8379i −0.590735 1.02318i
\(689\) −5.63837 + 9.76594i −0.214805 + 0.372053i
\(690\) −1.63541 + 2.83262i −0.0622591 + 0.107836i
\(691\) −8.04312 13.9311i −0.305975 0.529963i 0.671503 0.741002i \(-0.265649\pi\)
−0.977478 + 0.211038i \(0.932316\pi\)
\(692\) 41.4396 1.57530
\(693\) 0 0
\(694\) 9.10695 0.345695
\(695\) 3.68492 + 6.38247i 0.139777 + 0.242101i
\(696\) 10.4431 18.0880i 0.395844 0.685622i
\(697\) 4.24914 7.35973i 0.160948 0.278770i
\(698\) −6.41430 11.1099i −0.242785 0.420516i
\(699\) 30.8578 1.16715
\(700\) 0 0
\(701\) −6.98013 −0.263636 −0.131818 0.991274i \(-0.542081\pi\)
−0.131818 + 0.991274i \(0.542081\pi\)
\(702\) 0.498281 + 0.863048i 0.0188064 + 0.0325737i
\(703\) −1.74012 + 3.01397i −0.0656298 + 0.113674i
\(704\) −3.55691 + 6.16076i −0.134056 + 0.232192i
\(705\) −5.10996 8.85071i −0.192452 0.333337i
\(706\) −12.0844 −0.454803
\(707\) 0 0
\(708\) 48.6898 1.82988
\(709\) −4.19619 7.26802i −0.157591 0.272956i 0.776408 0.630230i \(-0.217040\pi\)
−0.934000 + 0.357274i \(0.883706\pi\)
\(710\) −0.148302 + 0.256866i −0.00556567 + 0.00964002i
\(711\) 1.37806 2.38687i 0.0516812 0.0895145i
\(712\) 6.14486 + 10.6432i 0.230289 + 0.398871i
\(713\) −41.0207 −1.53624
\(714\) 0 0
\(715\) −1.19051 −0.0445225
\(716\) 18.7113 + 32.4090i 0.699275 + 1.21118i
\(717\) 3.93793 6.82069i 0.147065 0.254723i
\(718\) 5.51127 9.54580i 0.205679 0.356246i
\(719\) 2.58065 + 4.46981i 0.0962418 + 0.166696i 0.910126 0.414331i \(-0.135984\pi\)
−0.813884 + 0.581027i \(0.802651\pi\)
\(720\) 2.96371 0.110451
\(721\) 0 0
\(722\) −7.92494 −0.294936
\(723\) −1.78576 3.09303i −0.0664132 0.115031i
\(724\) 14.8923 25.7942i 0.553467 0.958634i
\(725\) 12.3224 21.3430i 0.457642 0.792659i
\(726\) 3.14486 + 5.44706i 0.116717 + 0.202160i
\(727\) −40.4362 −1.49970 −0.749848 0.661610i \(-0.769873\pi\)
−0.749848 + 0.661610i \(0.769873\pi\)
\(728\) 0 0
\(729\) −8.23109 −0.304855
\(730\) −0.952109 1.64910i −0.0352391 0.0610359i
\(731\) 7.45039 12.9045i 0.275563 0.477288i
\(732\) −4.00000 + 6.92820i −0.147844 + 0.256074i
\(733\) 19.5656 + 33.8885i 0.722670 + 1.25170i 0.959926 + 0.280254i \(0.0904188\pi\)
−0.237255 + 0.971447i \(0.576248\pi\)
\(734\) −6.91215 −0.255132
\(735\) 0 0
\(736\) 28.2345 1.04074
\(737\) −17.9233 31.0441i −0.660214 1.14352i
\(738\) −3.14830 + 5.45302i −0.115891 + 0.200728i
\(739\) 3.56766 6.17936i 0.131238 0.227311i −0.792916 0.609331i \(-0.791438\pi\)
0.924154 + 0.382020i \(0.124771\pi\)
\(740\) −1.11383 1.92921i −0.0409451 0.0709191i
\(741\) −3.30777 −0.121514
\(742\) 0 0
\(743\) 13.8827 0.509308 0.254654 0.967032i \(-0.418038\pi\)
0.254654 + 0.967032i \(0.418038\pi\)
\(744\) −14.0552 24.3443i −0.515288 0.892506i
\(745\) −2.46338 + 4.26670i −0.0902512 + 0.156320i
\(746\) 5.56990 9.64736i 0.203929 0.353215i
\(747\) 16.8293 + 29.1492i 0.615752 + 1.06651i
\(748\) −5.23109 −0.191268
\(749\) 0 0
\(750\) −5.44652 −0.198879
\(751\) 18.6625 + 32.3244i 0.681005 + 1.17954i 0.974674 + 0.223629i \(0.0717903\pi\)
−0.293669 + 0.955907i \(0.594876\pi\)
\(752\) −11.6742 + 20.2203i −0.425714 + 0.737358i
\(753\) 5.54049 9.59640i 0.201907 0.349712i
\(754\) −1.22885 2.12843i −0.0447520 0.0775127i
\(755\) 3.74398 0.136258
\(756\) 0 0
\(757\) −7.10428 −0.258209 −0.129105 0.991631i \(-0.541210\pi\)
−0.129105 + 0.991631i \(0.541210\pi\)
\(758\) 7.70522 + 13.3458i 0.279866 + 0.484742i
\(759\) 14.7638 25.5717i 0.535894 0.928195i
\(760\) −0.692226 + 1.19897i −0.0251097 + 0.0434913i
\(761\) 12.9810 + 22.4838i 0.470562 + 0.815038i 0.999433 0.0336643i \(-0.0107177\pi\)
−0.528871 + 0.848702i \(0.677384\pi\)
\(762\) 0.872420 0.0316044
\(763\) 0 0
\(764\) 13.2311 0.478684
\(765\) 0.712520 + 1.23412i 0.0257612 + 0.0446197i
\(766\) 5.32238 9.21864i 0.192305 0.333083i
\(767\) 6.08623 10.5417i 0.219761 0.380637i
\(768\) −1.20512 2.08732i −0.0434859 0.0753197i
\(769\) −21.4638 −0.774005 −0.387002 0.922079i \(-0.626489\pi\)
−0.387002 + 0.922079i \(0.626489\pi\)
\(770\) 0 0
\(771\) −18.0260 −0.649190
\(772\) −1.33537 2.31293i −0.0480611 0.0832442i
\(773\) 20.2457 35.0666i 0.728187 1.26126i −0.229461 0.973318i \(-0.573696\pi\)
0.957649 0.287940i \(-0.0929702\pi\)
\(774\) −5.52019 + 9.56125i −0.198419 + 0.343672i
\(775\) −16.5845 28.7252i −0.595733 1.03184i
\(776\) 6.17246 0.221578
\(777\) 0 0
\(778\) 17.9087 0.642058
\(779\) 4.77846 + 8.27653i 0.171206 + 0.296537i
\(780\) 1.05863 1.83361i 0.0379051 0.0656536i
\(781\) 1.33881 2.31889i 0.0479064 0.0829762i
\(782\) 1.79650 + 3.11163i 0.0642428 + 0.111272i
\(783\) −11.0554 −0.395088