Properties

Label 729.2.i.a.685.16
Level $729$
Weight $2$
Character 729.685
Analytic conductor $5.821$
Analytic rank $0$
Dimension $1404$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.i (of order \(81\), degree \(54\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(1404\)
Relative dimension: \(26\) over \(\Q(\zeta_{81})\)
Twist minimal: no (minimal twist has level 243)
Sato-Tate group: $\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label 685.16
Character \(\chi\) \(=\) 729.685
Dual form 729.2.i.a.613.16

$q$-expansion

\(f(q)\) \(=\) \(q+(0.626870 + 0.174501i) q^{2} +(-1.34982 - 0.814620i) q^{4} +(-0.644276 + 0.0250008i) q^{5} +(-0.504626 - 0.0789220i) q^{7} +(-1.59709 - 1.69282i) q^{8} +O(q^{10})\) \(q+(0.626870 + 0.174501i) q^{2} +(-1.34982 - 0.814620i) q^{4} +(-0.644276 + 0.0250008i) q^{5} +(-0.504626 - 0.0789220i) q^{7} +(-1.59709 - 1.69282i) q^{8} +(-0.408240 - 0.0967545i) q^{10} +(0.486835 + 3.56426i) q^{11} +(0.0982538 - 0.143258i) q^{13} +(-0.302563 - 0.137532i) q^{14} +(0.763745 + 1.44993i) q^{16} +(-6.29666 + 3.16230i) q^{17} +(-0.433027 - 7.43479i) q^{19} +(0.890022 + 0.491093i) q^{20} +(-0.316785 + 2.31928i) q^{22} +(-2.32731 + 6.02788i) q^{23} +(-4.57050 + 0.355247i) q^{25} +(0.0865909 - 0.0726584i) q^{26} +(0.616862 + 0.517609i) q^{28} +(-3.25574 - 2.32706i) q^{29} +(-5.44489 + 6.23915i) q^{31} +(1.21115 + 5.59129i) q^{32} +(-4.49901 + 0.883576i) q^{34} +(0.327091 + 0.0382315i) q^{35} +(3.71264 + 4.98695i) q^{37} +(1.02593 - 4.73621i) q^{38} +(1.07129 + 1.05071i) q^{40} +(-0.706491 + 2.74277i) q^{41} +(-5.41027 - 4.90955i) q^{43} +(2.24638 - 5.20769i) q^{44} +(-2.51079 + 3.37258i) q^{46} +(5.10306 + 5.84745i) q^{47} +(-6.41732 - 2.05763i) q^{49} +(-2.92710 - 0.574863i) q^{50} +(-0.249325 + 0.113332i) q^{52} +(1.26021 - 7.14700i) q^{53} +(-0.402765 - 2.28419i) q^{55} +(0.672332 + 0.980284i) q^{56} +(-1.63485 - 2.02690i) q^{58} +(-0.549203 + 0.224374i) q^{59} +(3.13733 - 1.89339i) q^{61} +(-4.50198 + 2.96100i) q^{62} +(-0.0258795 + 0.444333i) q^{64} +(-0.0597210 + 0.0947538i) q^{65} +(5.50829 - 3.93709i) q^{67} +(11.0754 + 0.860850i) q^{68} +(0.198372 + 0.0810439i) q^{70} +(-3.45446 - 11.5387i) q^{71} +(8.73145 - 2.06939i) q^{73} +(1.45712 + 3.77402i) q^{74} +(-5.47202 + 10.3884i) q^{76} +(0.0356293 - 1.83704i) q^{77} +(0.340402 - 0.333864i) q^{79} +(-0.528312 - 0.915063i) q^{80} +(-0.921493 + 1.59607i) q^{82} +(0.138317 + 0.536978i) q^{83} +(3.97772 - 2.19481i) q^{85} +(-2.53481 - 4.02175i) q^{86} +(5.25612 - 6.51656i) q^{88} +(-3.77350 + 12.6044i) q^{89} +(-0.0608876 + 0.0645370i) q^{91} +(8.05187 - 6.24067i) q^{92} +(2.17856 + 4.55608i) q^{94} +(0.464865 + 4.77923i) q^{95} +(-6.14797 - 0.238569i) q^{97} +(-3.66376 - 2.40969i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{81}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.626870 + 0.174501i 0.443264 + 0.123391i 0.482611 0.875835i \(-0.339688\pi\)
−0.0393475 + 0.999226i \(0.512528\pi\)
\(3\) 0 0
\(4\) −1.34982 0.814620i −0.674909 0.407310i
\(5\) −0.644276 + 0.0250008i −0.288129 + 0.0111807i −0.182435 0.983218i \(-0.558398\pi\)
−0.105694 + 0.994399i \(0.533706\pi\)
\(6\) 0 0
\(7\) −0.504626 0.0789220i −0.190731 0.0298297i 0.0584320 0.998291i \(-0.481390\pi\)
−0.249163 + 0.968462i \(0.580155\pi\)
\(8\) −1.59709 1.69282i −0.564656 0.598501i
\(9\) 0 0
\(10\) −0.408240 0.0967545i −0.129097 0.0305965i
\(11\) 0.486835 + 3.56426i 0.146786 + 1.07466i 0.905835 + 0.423631i \(0.139245\pi\)
−0.759049 + 0.651034i \(0.774336\pi\)
\(12\) 0 0
\(13\) 0.0982538 0.143258i 0.0272507 0.0397325i −0.810810 0.585309i \(-0.800973\pi\)
0.838061 + 0.545576i \(0.183689\pi\)
\(14\) −0.302563 0.137532i −0.0808632 0.0367569i
\(15\) 0 0
\(16\) 0.763745 + 1.44993i 0.190936 + 0.362483i
\(17\) −6.29666 + 3.16230i −1.52716 + 0.766970i −0.996734 0.0807584i \(-0.974266\pi\)
−0.530430 + 0.847729i \(0.677969\pi\)
\(18\) 0 0
\(19\) −0.433027 7.43479i −0.0993433 1.70566i −0.568614 0.822604i \(-0.692520\pi\)
0.469271 0.883054i \(-0.344517\pi\)
\(20\) 0.890022 + 0.491093i 0.199015 + 0.109812i
\(21\) 0 0
\(22\) −0.316785 + 2.31928i −0.0675389 + 0.494472i
\(23\) −2.32731 + 6.02788i −0.485277 + 1.25690i 0.446798 + 0.894635i \(0.352564\pi\)
−0.932075 + 0.362265i \(0.882004\pi\)
\(24\) 0 0
\(25\) −4.57050 + 0.355247i −0.914100 + 0.0710495i
\(26\) 0.0865909 0.0726584i 0.0169819 0.0142495i
\(27\) 0 0
\(28\) 0.616862 + 0.517609i 0.116576 + 0.0978188i
\(29\) −3.25574 2.32706i −0.604576 0.432125i 0.237573 0.971370i \(-0.423648\pi\)
−0.842149 + 0.539245i \(0.818710\pi\)
\(30\) 0 0
\(31\) −5.44489 + 6.23915i −0.977931 + 1.12058i 0.0147587 + 0.999891i \(0.495302\pi\)
−0.992690 + 0.120694i \(0.961488\pi\)
\(32\) 1.21115 + 5.59129i 0.214103 + 0.988410i
\(33\) 0 0
\(34\) −4.49901 + 0.883576i −0.771573 + 0.151532i
\(35\) 0.327091 + 0.0382315i 0.0552885 + 0.00646230i
\(36\) 0 0
\(37\) 3.71264 + 4.98695i 0.610355 + 0.819849i 0.994644 0.103364i \(-0.0329607\pi\)
−0.384289 + 0.923213i \(0.625553\pi\)
\(38\) 1.02593 4.73621i 0.166427 0.768315i
\(39\) 0 0
\(40\) 1.07129 + 1.05071i 0.169385 + 0.166132i
\(41\) −0.706491 + 2.74277i −0.110335 + 0.428348i −0.999577 0.0290901i \(-0.990739\pi\)
0.889241 + 0.457438i \(0.151233\pi\)
\(42\) 0 0
\(43\) −5.41027 4.90955i −0.825058 0.748700i 0.145554 0.989350i \(-0.453504\pi\)
−0.970612 + 0.240650i \(0.922639\pi\)
\(44\) 2.24638 5.20769i 0.338654 0.785089i
\(45\) 0 0
\(46\) −2.51079 + 3.37258i −0.370196 + 0.497259i
\(47\) 5.10306 + 5.84745i 0.744357 + 0.852939i 0.993298 0.115580i \(-0.0368726\pi\)
−0.248941 + 0.968519i \(0.580082\pi\)
\(48\) 0 0
\(49\) −6.41732 2.05763i −0.916760 0.293947i
\(50\) −2.92710 0.574863i −0.413954 0.0812979i
\(51\) 0 0
\(52\) −0.249325 + 0.113332i −0.0345752 + 0.0157164i
\(53\) 1.26021 7.14700i 0.173103 0.981716i −0.767208 0.641399i \(-0.778354\pi\)
0.940311 0.340317i \(-0.110534\pi\)
\(54\) 0 0
\(55\) −0.402765 2.28419i −0.0543088 0.308001i
\(56\) 0.672332 + 0.980284i 0.0898441 + 0.130996i
\(57\) 0 0
\(58\) −1.63485 2.02690i −0.214666 0.266145i
\(59\) −0.549203 + 0.224374i −0.0715002 + 0.0292110i −0.413668 0.910428i \(-0.635753\pi\)
0.342168 + 0.939639i \(0.388839\pi\)
\(60\) 0 0
\(61\) 3.13733 1.89339i 0.401694 0.242424i −0.301434 0.953487i \(-0.597465\pi\)
0.703128 + 0.711063i \(0.251786\pi\)
\(62\) −4.50198 + 2.96100i −0.571751 + 0.376047i
\(63\) 0 0
\(64\) −0.0258795 + 0.444333i −0.00323493 + 0.0555417i
\(65\) −0.0597210 + 0.0947538i −0.00740747 + 0.0117528i
\(66\) 0 0
\(67\) 5.50829 3.93709i 0.672945 0.480992i −0.192956 0.981207i \(-0.561807\pi\)
0.865901 + 0.500215i \(0.166746\pi\)
\(68\) 11.0754 + 0.860850i 1.34309 + 0.104393i
\(69\) 0 0
\(70\) 0.198372 + 0.0810439i 0.0237100 + 0.00968660i
\(71\) −3.45446 11.5387i −0.409969 1.36939i −0.875011 0.484104i \(-0.839146\pi\)
0.465041 0.885289i \(-0.346040\pi\)
\(72\) 0 0
\(73\) 8.73145 2.06939i 1.02194 0.242204i 0.314709 0.949188i \(-0.398093\pi\)
0.707229 + 0.706984i \(0.249945\pi\)
\(74\) 1.45712 + 3.77402i 0.169386 + 0.438721i
\(75\) 0 0
\(76\) −5.47202 + 10.3884i −0.627684 + 1.19163i
\(77\) 0.0356293 1.83704i 0.00406034 0.209350i
\(78\) 0 0
\(79\) 0.340402 0.333864i 0.0382982 0.0375626i −0.680816 0.732454i \(-0.738375\pi\)
0.719115 + 0.694892i \(0.244548\pi\)
\(80\) −0.528312 0.915063i −0.0590670 0.102307i
\(81\) 0 0
\(82\) −0.921493 + 1.59607i −0.101762 + 0.176257i
\(83\) 0.138317 + 0.536978i 0.0151822 + 0.0589410i 0.975533 0.219855i \(-0.0705585\pi\)
−0.960350 + 0.278796i \(0.910065\pi\)
\(84\) 0 0
\(85\) 3.97772 2.19481i 0.431445 0.238061i
\(86\) −2.53481 4.02175i −0.273335 0.433676i
\(87\) 0 0
\(88\) 5.25612 6.51656i 0.560304 0.694668i
\(89\) −3.77350 + 12.6044i −0.399990 + 1.33606i 0.486649 + 0.873598i \(0.338219\pi\)
−0.886639 + 0.462462i \(0.846966\pi\)
\(90\) 0 0
\(91\) −0.0608876 + 0.0645370i −0.00638275 + 0.00676532i
\(92\) 8.05187 6.24067i 0.839466 0.650635i
\(93\) 0 0
\(94\) 2.17856 + 4.55608i 0.224702 + 0.469924i
\(95\) 0.464865 + 4.77923i 0.0476941 + 0.490339i
\(96\) 0 0
\(97\) −6.14797 0.238569i −0.624232 0.0242231i −0.275281 0.961364i \(-0.588771\pi\)
−0.348951 + 0.937141i \(0.613462\pi\)
\(98\) −3.66376 2.40969i −0.370096 0.243416i
\(99\) 0 0
\(100\) 6.45874 + 3.24370i 0.645874 + 0.324370i
\(101\) −0.0688430 3.54953i −0.00685013 0.353191i −0.987518 0.157509i \(-0.949654\pi\)
0.980667 0.195682i \(-0.0626920\pi\)
\(102\) 0 0
\(103\) 1.80465 + 1.39871i 0.177817 + 0.137819i 0.697621 0.716467i \(-0.254242\pi\)
−0.519804 + 0.854286i \(0.673995\pi\)
\(104\) −0.399429 + 0.0624695i −0.0391672 + 0.00612564i
\(105\) 0 0
\(106\) 2.03715 4.26033i 0.197865 0.413800i
\(107\) −3.27909 1.19349i −0.317001 0.115379i 0.178619 0.983918i \(-0.442837\pi\)
−0.495620 + 0.868539i \(0.665059\pi\)
\(108\) 0 0
\(109\) 10.3333 3.76102i 0.989752 0.360240i 0.204128 0.978944i \(-0.434564\pi\)
0.785624 + 0.618704i \(0.212342\pi\)
\(110\) 0.146113 1.50218i 0.0139313 0.143227i
\(111\) 0 0
\(112\) −0.270974 0.791950i −0.0256046 0.0748322i
\(113\) −0.339501 + 0.308081i −0.0319375 + 0.0289818i −0.687820 0.725881i \(-0.741432\pi\)
0.655883 + 0.754863i \(0.272297\pi\)
\(114\) 0 0
\(115\) 1.34873 3.94180i 0.125769 0.367575i
\(116\) 2.49899 + 5.79331i 0.232025 + 0.537895i
\(117\) 0 0
\(118\) −0.383432 + 0.0448168i −0.0352978 + 0.00412572i
\(119\) 3.42703 1.09883i 0.314155 0.100730i
\(120\) 0 0
\(121\) −1.86986 + 0.520512i −0.169988 + 0.0473193i
\(122\) 2.29710 0.639441i 0.207969 0.0578923i
\(123\) 0 0
\(124\) 12.4322 3.98621i 1.11644 0.357972i
\(125\) 6.13778 0.717404i 0.548980 0.0641666i
\(126\) 0 0
\(127\) −8.64840 20.0493i −0.767422 1.77908i −0.611386 0.791332i \(-0.709388\pi\)
−0.156036 0.987751i \(-0.549871\pi\)
\(128\) 3.61038 10.5517i 0.319115 0.932650i
\(129\) 0 0
\(130\) −0.0539719 + 0.0489769i −0.00473365 + 0.00429556i
\(131\) −1.14497 3.34631i −0.100037 0.292368i 0.884769 0.466031i \(-0.154316\pi\)
−0.984805 + 0.173662i \(0.944440\pi\)
\(132\) 0 0
\(133\) −0.368252 + 3.78596i −0.0319315 + 0.328285i
\(134\) 4.14001 1.50684i 0.357642 0.130171i
\(135\) 0 0
\(136\) 15.4095 + 5.60860i 1.32135 + 0.480934i
\(137\) −2.42613 + 5.07382i −0.207278 + 0.433485i −0.979384 0.202009i \(-0.935253\pi\)
0.772106 + 0.635494i \(0.219204\pi\)
\(138\) 0 0
\(139\) −18.3237 + 2.86577i −1.55419 + 0.243071i −0.872517 0.488583i \(-0.837514\pi\)
−0.681676 + 0.731654i \(0.738748\pi\)
\(140\) −0.410370 0.318061i −0.0346826 0.0268810i
\(141\) 0 0
\(142\) −0.151980 7.83607i −0.0127539 0.657589i
\(143\) 0.558440 + 0.280459i 0.0466991 + 0.0234532i
\(144\) 0 0
\(145\) 2.15577 + 1.41787i 0.179027 + 0.117748i
\(146\) 5.83459 + 0.226409i 0.482874 + 0.0187377i
\(147\) 0 0
\(148\) −0.948931 9.75587i −0.0780017 0.801927i
\(149\) 2.35692 + 4.92907i 0.193086 + 0.403805i 0.975828 0.218542i \(-0.0701299\pi\)
−0.782742 + 0.622347i \(0.786179\pi\)
\(150\) 0 0
\(151\) −2.04726 + 1.58675i −0.166604 + 0.129128i −0.692491 0.721427i \(-0.743487\pi\)
0.525887 + 0.850555i \(0.323734\pi\)
\(152\) −11.8942 + 12.6071i −0.964743 + 1.02257i
\(153\) 0 0
\(154\) 0.342900 1.14537i 0.0276317 0.0922963i
\(155\) 3.35203 4.15586i 0.269241 0.333807i
\(156\) 0 0
\(157\) 4.17066 + 6.61720i 0.332855 + 0.528110i 0.970149 0.242511i \(-0.0779710\pi\)
−0.637294 + 0.770621i \(0.719946\pi\)
\(158\) 0.271647 0.149889i 0.0216111 0.0119245i
\(159\) 0 0
\(160\) −0.920101 3.57205i −0.0727404 0.282395i
\(161\) 1.65015 2.85815i 0.130050 0.225253i
\(162\) 0 0
\(163\) 12.6789 + 21.9605i 0.993087 + 1.72008i 0.598199 + 0.801348i \(0.295883\pi\)
0.394888 + 0.918729i \(0.370783\pi\)
\(164\) 3.18795 3.12671i 0.248937 0.244155i
\(165\) 0 0
\(166\) −0.00699677 + 0.360752i −0.000543055 + 0.0279998i
\(167\) 1.25701 2.38638i 0.0972706 0.184664i −0.831296 0.555831i \(-0.812400\pi\)
0.928566 + 0.371167i \(0.121042\pi\)
\(168\) 0 0
\(169\) 4.67144 + 12.0993i 0.359342 + 0.930718i
\(170\) 2.87651 0.681746i 0.220618 0.0522875i
\(171\) 0 0
\(172\) 3.30346 + 11.0343i 0.251886 + 0.841359i
\(173\) −9.50885 3.88479i −0.722944 0.295355i −0.0132963 0.999912i \(-0.504232\pi\)
−0.709648 + 0.704556i \(0.751146\pi\)
\(174\) 0 0
\(175\) 2.33443 + 0.181446i 0.176466 + 0.0137160i
\(176\) −4.79612 + 3.42806i −0.361521 + 0.258400i
\(177\) 0 0
\(178\) −4.56497 + 7.24281i −0.342159 + 0.542872i
\(179\) 1.23862 21.2663i 0.0925788 1.58952i −0.557846 0.829945i \(-0.688372\pi\)
0.650424 0.759571i \(-0.274591\pi\)
\(180\) 0 0
\(181\) −13.5943 + 8.94110i −1.01045 + 0.664587i −0.942882 0.333128i \(-0.891896\pi\)
−0.0675731 + 0.997714i \(0.521526\pi\)
\(182\) −0.0494303 + 0.0298314i −0.00366402 + 0.00221125i
\(183\) 0 0
\(184\) 13.9210 5.68736i 1.02627 0.419277i
\(185\) −2.51664 3.12015i −0.185027 0.229398i
\(186\) 0 0
\(187\) −14.3367 20.9034i −1.04840 1.52861i
\(188\) −2.12475 12.0501i −0.154963 0.878841i
\(189\) 0 0
\(190\) −0.542571 + 3.07707i −0.0393622 + 0.223234i
\(191\) −23.0457 + 10.4756i −1.66753 + 0.757986i −0.667622 + 0.744500i \(0.732688\pi\)
−0.999909 + 0.0134859i \(0.995707\pi\)
\(192\) 0 0
\(193\) 5.26100 + 1.03323i 0.378695 + 0.0743733i 0.378438 0.925627i \(-0.376461\pi\)
0.000257145 1.00000i \(0.499918\pi\)
\(194\) −3.81235 1.22238i −0.273711 0.0877618i
\(195\) 0 0
\(196\) 6.98603 + 8.00510i 0.499002 + 0.571793i
\(197\) −1.20356 + 1.61666i −0.0857498 + 0.115182i −0.842928 0.538026i \(-0.819170\pi\)
0.757178 + 0.653208i \(0.226577\pi\)
\(198\) 0 0
\(199\) 2.47144 5.72945i 0.175196 0.406150i −0.807880 0.589346i \(-0.799385\pi\)
0.983076 + 0.183197i \(0.0586446\pi\)
\(200\) 7.90086 + 7.16965i 0.558675 + 0.506971i
\(201\) 0 0
\(202\) 0.576241 2.23710i 0.0405441 0.157402i
\(203\) 1.45927 + 1.43125i 0.102421 + 0.100454i
\(204\) 0 0
\(205\) 0.386603 1.78476i 0.0270015 0.124653i
\(206\) 0.887204 + 1.19172i 0.0618144 + 0.0830312i
\(207\) 0 0
\(208\) 0.282755 + 0.0330493i 0.0196055 + 0.00229156i
\(209\) 26.2887 5.16294i 1.81843 0.357128i
\(210\) 0 0
\(211\) 5.18300 + 23.9274i 0.356813 + 1.64723i 0.704562 + 0.709643i \(0.251144\pi\)
−0.347749 + 0.937588i \(0.613054\pi\)
\(212\) −7.52314 + 8.62056i −0.516692 + 0.592063i
\(213\) 0 0
\(214\) −1.84729 1.32037i −0.126278 0.0902584i
\(215\) 3.60845 + 3.02785i 0.246094 + 0.206497i
\(216\) 0 0
\(217\) 3.24004 2.71871i 0.219948 0.184558i
\(218\) 7.13394 0.554494i 0.483172 0.0375551i
\(219\) 0 0
\(220\) −1.31709 + 3.41135i −0.0887982 + 0.229993i
\(221\) −0.165647 + 1.21275i −0.0111426 + 0.0815785i
\(222\) 0 0
\(223\) 4.41345 + 2.43524i 0.295547 + 0.163076i 0.623955 0.781460i \(-0.285525\pi\)
−0.328409 + 0.944536i \(0.606512\pi\)
\(224\) −0.169901 2.91709i −0.0113520 0.194907i
\(225\) 0 0
\(226\) −0.266583 + 0.133883i −0.0177328 + 0.00890577i
\(227\) −5.70573 10.8321i −0.378702 0.718949i 0.619093 0.785318i \(-0.287500\pi\)
−0.997795 + 0.0663691i \(0.978859\pi\)
\(228\) 0 0
\(229\) 4.66696 + 2.12139i 0.308401 + 0.140186i 0.562032 0.827116i \(-0.310020\pi\)
−0.253631 + 0.967301i \(0.581625\pi\)
\(230\) 1.53332 2.23564i 0.101104 0.147414i
\(231\) 0 0
\(232\) 1.26042 + 9.22790i 0.0827506 + 0.605841i
\(233\) 10.4270 + 2.47125i 0.683098 + 0.161897i 0.557491 0.830183i \(-0.311764\pi\)
0.125607 + 0.992080i \(0.459912\pi\)
\(234\) 0 0
\(235\) −3.43397 3.63979i −0.224007 0.237434i
\(236\) 0.924105 + 0.144527i 0.0601541 + 0.00940793i
\(237\) 0 0
\(238\) 2.34005 0.0908045i 0.151683 0.00588598i
\(239\) 1.76602 + 1.06580i 0.114234 + 0.0689406i 0.572665 0.819789i \(-0.305909\pi\)
−0.458431 + 0.888730i \(0.651588\pi\)
\(240\) 0 0
\(241\) −11.5630 3.21878i −0.744839 0.207340i −0.125095 0.992145i \(-0.539924\pi\)
−0.619743 + 0.784805i \(0.712763\pi\)
\(242\) −1.26299 −0.0811881
\(243\) 0 0
\(244\) −5.77722 −0.369849
\(245\) 4.18596 + 1.16524i 0.267431 + 0.0744446i
\(246\) 0 0
\(247\) −1.10764 0.668462i −0.0704772 0.0425332i
\(248\) 19.2577 0.747287i 1.22287 0.0474528i
\(249\) 0 0
\(250\) 3.97278 + 0.621331i 0.251261 + 0.0392964i
\(251\) 5.77741 + 6.12370i 0.364667 + 0.386524i 0.883562 0.468313i \(-0.155138\pi\)
−0.518896 + 0.854838i \(0.673657\pi\)
\(252\) 0 0
\(253\) −22.6179 5.36055i −1.42198 0.337015i
\(254\) −1.92281 14.0774i −0.120648 0.883296i
\(255\) 0 0
\(256\) 4.60801 6.71865i 0.288001 0.419916i
\(257\) 6.10772 + 2.77630i 0.380989 + 0.173181i 0.595144 0.803619i \(-0.297095\pi\)
−0.214155 + 0.976800i \(0.568700\pi\)
\(258\) 0 0
\(259\) −1.47992 2.80955i −0.0919575 0.174577i
\(260\) 0.157801 0.0792505i 0.00978639 0.00491491i
\(261\) 0 0
\(262\) −0.133814 2.29750i −0.00826706 0.141940i
\(263\) −19.4326 10.7225i −1.19827 0.661177i −0.246843 0.969056i \(-0.579393\pi\)
−0.951426 + 0.307879i \(0.900381\pi\)
\(264\) 0 0
\(265\) −0.633241 + 4.63614i −0.0388997 + 0.284796i
\(266\) −0.891501 + 2.30905i −0.0546614 + 0.141577i
\(267\) 0 0
\(268\) −10.6424 + 0.827195i −0.650090 + 0.0505290i
\(269\) 5.58686 4.68794i 0.340637 0.285829i −0.456380 0.889785i \(-0.650854\pi\)
0.797017 + 0.603956i \(0.206410\pi\)
\(270\) 0 0
\(271\) −17.8077 14.9425i −1.08174 0.907690i −0.0856784 0.996323i \(-0.527306\pi\)
−0.996064 + 0.0886329i \(0.971750\pi\)
\(272\) −9.39416 6.71454i −0.569605 0.407129i
\(273\) 0 0
\(274\) −2.40625 + 2.75726i −0.145367 + 0.166572i
\(275\) −3.49127 16.1175i −0.210532 0.971922i
\(276\) 0 0
\(277\) 13.0158 2.55621i 0.782042 0.153588i 0.214271 0.976774i \(-0.431263\pi\)
0.567771 + 0.823186i \(0.307806\pi\)
\(278\) −11.9866 1.40104i −0.718910 0.0840286i
\(279\) 0 0
\(280\) −0.457675 0.614764i −0.0273513 0.0367392i
\(281\) 2.13065 9.83618i 0.127104 0.586777i −0.868706 0.495328i \(-0.835048\pi\)
0.995810 0.0914489i \(-0.0291498\pi\)
\(282\) 0 0
\(283\) 2.26446 + 2.22097i 0.134608 + 0.132023i 0.764403 0.644739i \(-0.223034\pi\)
−0.629795 + 0.776762i \(0.716861\pi\)
\(284\) −4.73676 + 18.3892i −0.281075 + 1.09120i
\(285\) 0 0
\(286\) 0.301129 + 0.273260i 0.0178061 + 0.0161582i
\(287\) 0.572978 1.32831i 0.0338218 0.0784078i
\(288\) 0 0
\(289\) 19.4961 26.1877i 1.14683 1.54046i
\(290\) 1.10397 + 1.26501i 0.0648273 + 0.0742838i
\(291\) 0 0
\(292\) −13.4716 4.31951i −0.788368 0.252780i
\(293\) −29.6963 5.83216i −1.73488 0.340719i −0.777351 0.629068i \(-0.783437\pi\)
−0.957525 + 0.288349i \(0.906894\pi\)
\(294\) 0 0
\(295\) 0.348229 0.158289i 0.0202747 0.00921596i
\(296\) 2.51256 14.2494i 0.146039 0.828231i
\(297\) 0 0
\(298\) 0.617351 + 3.50117i 0.0357622 + 0.202817i
\(299\) 0.634872 + 0.925666i 0.0367156 + 0.0535326i
\(300\) 0 0
\(301\) 2.34269 + 2.90448i 0.135030 + 0.167411i
\(302\) −1.56026 + 0.637435i −0.0897827 + 0.0366803i
\(303\) 0 0
\(304\) 10.4492 6.30615i 0.599305 0.361682i
\(305\) −1.97397 + 1.29830i −0.113029 + 0.0743405i
\(306\) 0 0
\(307\) −0.469867 + 8.06731i −0.0268167 + 0.460426i 0.957993 + 0.286791i \(0.0925884\pi\)
−0.984810 + 0.173635i \(0.944449\pi\)
\(308\) −1.54458 + 2.45065i −0.0880107 + 0.139639i
\(309\) 0 0
\(310\) 2.82649 2.02025i 0.160534 0.114743i
\(311\) 1.48194 + 0.115185i 0.0840331 + 0.00653157i 0.119440 0.992841i \(-0.461890\pi\)
−0.0354070 + 0.999373i \(0.511273\pi\)
\(312\) 0 0
\(313\) 21.4867 + 8.77827i 1.21450 + 0.496177i 0.892709 0.450634i \(-0.148802\pi\)
0.321790 + 0.946811i \(0.395716\pi\)
\(314\) 1.45975 + 4.87590i 0.0823784 + 0.275163i
\(315\) 0 0
\(316\) −0.731453 + 0.173358i −0.0411475 + 0.00975213i
\(317\) 11.3360 + 29.3610i 0.636694 + 1.64908i 0.754704 + 0.656066i \(0.227781\pi\)
−0.118010 + 0.993012i \(0.537652\pi\)
\(318\) 0 0
\(319\) 6.70926 12.7372i 0.375646 0.713147i
\(320\) 0.00556481 0.286920i 0.000311082 0.0160393i
\(321\) 0 0
\(322\) 1.53318 1.50373i 0.0854408 0.0837997i
\(323\) 26.2377 + 45.4450i 1.45990 + 2.52863i
\(324\) 0 0
\(325\) −0.398177 + 0.689663i −0.0220869 + 0.0382556i
\(326\) 4.11588 + 15.9788i 0.227958 + 0.884986i
\(327\) 0 0
\(328\) 5.77132 3.18448i 0.318668 0.175834i
\(329\) −2.11364 3.35352i −0.116529 0.184886i
\(330\) 0 0
\(331\) −13.3685 + 16.5743i −0.734799 + 0.911008i −0.998564 0.0535788i \(-0.982937\pi\)
0.263764 + 0.964587i \(0.415036\pi\)
\(332\) 0.250731 0.837499i 0.0137606 0.0459637i
\(333\) 0 0
\(334\) 1.20441 1.27660i 0.0659023 0.0698524i
\(335\) −3.45043 + 2.67428i −0.188517 + 0.146112i
\(336\) 0 0
\(337\) −0.699507 1.46289i −0.0381046 0.0796889i 0.882235 0.470810i \(-0.156038\pi\)
−0.920339 + 0.391121i \(0.872088\pi\)
\(338\) 0.817037 + 8.39988i 0.0444410 + 0.456893i
\(339\) 0 0
\(340\) −7.15714 0.277730i −0.388151 0.0150620i
\(341\) −24.8887 16.3696i −1.34780 0.886462i
\(342\) 0 0
\(343\) 6.27097 + 3.14940i 0.338601 + 0.170052i
\(344\) 0.329707 + 16.9996i 0.0177766 + 0.916556i
\(345\) 0 0
\(346\) −5.28291 4.09456i −0.284011 0.220125i
\(347\) −12.8947 + 2.01669i −0.692223 + 0.108262i −0.490839 0.871251i \(-0.663310\pi\)
−0.201385 + 0.979512i \(0.564544\pi\)
\(348\) 0 0
\(349\) −4.80981 + 10.0589i −0.257463 + 0.538439i −0.989793 0.142511i \(-0.954482\pi\)
0.732330 + 0.680950i \(0.238433\pi\)
\(350\) 1.43172 + 0.521103i 0.0765286 + 0.0278541i
\(351\) 0 0
\(352\) −19.3392 + 7.03889i −1.03078 + 0.375174i
\(353\) −2.14673 + 22.0703i −0.114259 + 1.17468i 0.746398 + 0.665500i \(0.231781\pi\)
−0.860657 + 0.509185i \(0.829947\pi\)
\(354\) 0 0
\(355\) 2.51410 + 7.34775i 0.133435 + 0.389978i
\(356\) 15.3613 13.9396i 0.814148 0.738800i
\(357\) 0 0
\(358\) 4.48744 13.1150i 0.237169 0.693151i
\(359\) 8.10950 + 18.7999i 0.428003 + 0.992222i 0.986656 + 0.162821i \(0.0520592\pi\)
−0.558653 + 0.829402i \(0.688682\pi\)
\(360\) 0 0
\(361\) −36.2171 + 4.23317i −1.90616 + 0.222799i
\(362\) −10.0821 + 3.23269i −0.529902 + 0.169906i
\(363\) 0 0
\(364\) 0.134760 0.0375131i 0.00706336 0.00196622i
\(365\) −5.57372 + 1.55155i −0.291742 + 0.0812119i
\(366\) 0 0
\(367\) −26.6265 + 8.53744i −1.38989 + 0.445650i −0.903686 0.428195i \(-0.859150\pi\)
−0.486204 + 0.873845i \(0.661619\pi\)
\(368\) −10.5175 + 1.22932i −0.548262 + 0.0640827i
\(369\) 0 0
\(370\) −1.03314 2.39508i −0.0537103 0.124514i
\(371\) −1.19999 + 3.50710i −0.0623004 + 0.182080i
\(372\) 0 0
\(373\) 13.1262 11.9114i 0.679649 0.616749i −0.257252 0.966344i \(-0.582817\pi\)
0.936901 + 0.349596i \(0.113681\pi\)
\(374\) −5.33957 15.6055i −0.276103 0.806940i
\(375\) 0 0
\(376\) 1.74863 17.9774i 0.0901785 0.927116i
\(377\) −0.653258 + 0.237767i −0.0336445 + 0.0122456i
\(378\) 0 0
\(379\) −2.58185 0.939718i −0.132621 0.0482701i 0.274857 0.961485i \(-0.411369\pi\)
−0.407478 + 0.913215i \(0.633592\pi\)
\(380\) 3.26577 6.82978i 0.167531 0.350361i
\(381\) 0 0
\(382\) −16.2747 + 2.54531i −0.832685 + 0.130230i
\(383\) −19.0919 14.7973i −0.975550 0.756109i −0.00574371 0.999984i \(-0.501828\pi\)
−0.969807 + 0.243875i \(0.921581\pi\)
\(384\) 0 0
\(385\) 0.0229724 + 1.18445i 0.00117078 + 0.0603652i
\(386\) 3.11766 + 1.56575i 0.158685 + 0.0796945i
\(387\) 0 0
\(388\) 8.10431 + 5.33029i 0.411434 + 0.270604i
\(389\) −26.5747 1.03122i −1.34739 0.0522850i −0.645059 0.764133i \(-0.723167\pi\)
−0.702334 + 0.711848i \(0.747859\pi\)
\(390\) 0 0
\(391\) −4.40770 45.3151i −0.222907 2.29168i
\(392\) 6.76584 + 14.1496i 0.341727 + 0.714660i
\(393\) 0 0
\(394\) −1.03658 + 0.803411i −0.0522222 + 0.0404753i
\(395\) −0.210966 + 0.223611i −0.0106148 + 0.0112511i
\(396\) 0 0
\(397\) −1.54280 + 5.15331i −0.0774309 + 0.258637i −0.987937 0.154859i \(-0.950508\pi\)
0.910506 + 0.413497i \(0.135693\pi\)
\(398\) 2.54907 3.16035i 0.127773 0.158414i
\(399\) 0 0
\(400\) −4.00578 6.35560i −0.200289 0.317780i
\(401\) 25.0443 13.8189i 1.25065 0.690081i 0.287178 0.957877i \(-0.407283\pi\)
0.963476 + 0.267796i \(0.0862953\pi\)
\(402\) 0 0
\(403\) 0.358824 + 1.39304i 0.0178743 + 0.0693923i
\(404\) −2.79859 + 4.84730i −0.139235 + 0.241162i
\(405\) 0 0
\(406\) 0.665021 + 1.15185i 0.0330044 + 0.0571653i
\(407\) −15.9673 + 15.6606i −0.791471 + 0.776269i
\(408\) 0 0
\(409\) −0.00864957 + 0.445969i −0.000427694 + 0.0220518i −0.999965 0.00836427i \(-0.997338\pi\)
0.999537 + 0.0304160i \(0.00968322\pi\)
\(410\) 0.553792 1.05135i 0.0273499 0.0519224i
\(411\) 0 0
\(412\) −1.29653 3.35811i −0.0638756 0.165442i
\(413\) 0.294850 0.0698808i 0.0145086 0.00343861i
\(414\) 0 0
\(415\) −0.102539 0.342504i −0.00503344 0.0168129i
\(416\) 0.919994 + 0.375859i 0.0451064 + 0.0184280i
\(417\) 0 0
\(418\) 17.3805 + 1.35092i 0.850110 + 0.0660758i
\(419\) −18.2218 + 13.0241i −0.890192 + 0.636271i −0.931843 0.362861i \(-0.881800\pi\)
0.0416512 + 0.999132i \(0.486738\pi\)
\(420\) 0 0
\(421\) −15.3697 + 24.3857i −0.749074 + 1.18849i 0.227599 + 0.973755i \(0.426913\pi\)
−0.976673 + 0.214732i \(0.931112\pi\)
\(422\) −0.926291 + 15.9038i −0.0450911 + 0.774185i
\(423\) 0 0
\(424\) −14.1112 + 9.28110i −0.685301 + 0.450730i
\(425\) 27.6555 16.6902i 1.34149 0.809592i
\(426\) 0 0
\(427\) −1.73261 + 0.707849i −0.0838468 + 0.0342552i
\(428\) 3.45393 + 4.28220i 0.166952 + 0.206988i
\(429\) 0 0
\(430\) 1.73366 + 2.52774i 0.0836046 + 0.121899i
\(431\) 0.232346 + 1.31770i 0.0111917 + 0.0634713i 0.989892 0.141822i \(-0.0452962\pi\)
−0.978700 + 0.205294i \(0.934185\pi\)
\(432\) 0 0
\(433\) 2.48760 14.1079i 0.119546 0.677982i −0.864852 0.502027i \(-0.832588\pi\)
0.984398 0.175955i \(-0.0563012\pi\)
\(434\) 2.50550 1.13889i 0.120268 0.0546684i
\(435\) 0 0
\(436\) −17.0119 3.34103i −0.814722 0.160006i
\(437\) 45.8238 + 14.6928i 2.19205 + 0.702853i
\(438\) 0 0
\(439\) −11.0688 12.6835i −0.528286 0.605349i 0.425823 0.904806i \(-0.359985\pi\)
−0.954110 + 0.299457i \(0.903194\pi\)
\(440\) −3.22347 + 4.32987i −0.153673 + 0.206418i
\(441\) 0 0
\(442\) −0.315466 + 0.731331i −0.0150052 + 0.0347859i
\(443\) −7.29332 6.61833i −0.346516 0.314447i 0.480099 0.877214i \(-0.340601\pi\)
−0.826615 + 0.562768i \(0.809737\pi\)
\(444\) 0 0
\(445\) 2.11605 8.21503i 0.100311 0.389430i
\(446\) 2.34171 + 2.29673i 0.110883 + 0.108753i
\(447\) 0 0
\(448\) 0.0481271 0.222180i 0.00227379 0.0104970i
\(449\) 13.5411 + 18.1889i 0.639046 + 0.858388i 0.997162 0.0752894i \(-0.0239880\pi\)
−0.358116 + 0.933677i \(0.616581\pi\)
\(450\) 0 0
\(451\) −10.1199 1.18284i −0.476526 0.0556979i
\(452\) 0.709233 0.139289i 0.0333595 0.00655160i
\(453\) 0 0
\(454\) −1.68654 7.78594i −0.0791533 0.365412i
\(455\) 0.0376149 0.0431019i 0.00176341 0.00202065i
\(456\) 0 0
\(457\) 14.3979 + 10.2910i 0.673503 + 0.481391i 0.866090 0.499889i \(-0.166626\pi\)
−0.192586 + 0.981280i \(0.561688\pi\)
\(458\) 2.55539 + 2.14423i 0.119405 + 0.100193i
\(459\) 0 0
\(460\) −5.03160 + 4.22202i −0.234600 + 0.196853i
\(461\) −22.3499 + 1.73717i −1.04094 + 0.0809082i −0.586565 0.809902i \(-0.699520\pi\)
−0.454375 + 0.890811i \(0.650137\pi\)
\(462\) 0 0
\(463\) 4.91504 12.7303i 0.228421 0.591626i −0.770530 0.637403i \(-0.780008\pi\)
0.998952 + 0.0457771i \(0.0145764\pi\)
\(464\) 0.887533 6.49789i 0.0412027 0.301657i
\(465\) 0 0
\(466\) 6.10516 + 3.36868i 0.282816 + 0.156051i
\(467\) 0.292077 + 5.01477i 0.0135157 + 0.232056i 0.998300 + 0.0582771i \(0.0185607\pi\)
−0.984785 + 0.173779i \(0.944402\pi\)
\(468\) 0 0
\(469\) −3.09035 + 1.55203i −0.142699 + 0.0716662i
\(470\) −1.51750 2.88091i −0.0699971 0.132886i
\(471\) 0 0
\(472\) 1.25695 + 0.571354i 0.0578558 + 0.0262987i
\(473\) 14.8650 21.6737i 0.683495 0.996560i
\(474\) 0 0
\(475\) 4.62034 + 33.8269i 0.211996 + 1.55208i
\(476\) −5.52100 1.30850i −0.253055 0.0599751i
\(477\) 0 0
\(478\) 0.921079 + 0.976287i 0.0421292 + 0.0446543i
\(479\) −23.6168 3.69359i −1.07908 0.168765i −0.410095 0.912043i \(-0.634504\pi\)
−0.668982 + 0.743278i \(0.733270\pi\)
\(480\) 0 0
\(481\) 1.07920 0.0418778i 0.0492072 0.00190946i
\(482\) −6.68682 4.03551i −0.304576 0.183813i
\(483\) 0 0
\(484\) 2.94800 + 0.820631i 0.134000 + 0.0373014i
\(485\) 3.96695 0.180130
\(486\) 0 0
\(487\) 31.8858 1.44489 0.722443 0.691431i \(-0.243019\pi\)
0.722443 + 0.691431i \(0.243019\pi\)
\(488\) −8.21576 2.28701i −0.371910 0.103528i
\(489\) 0 0
\(490\) 2.42072 + 1.46091i 0.109357 + 0.0659972i
\(491\) −27.0288 + 1.04884i −1.21979 + 0.0473335i −0.640611 0.767865i \(-0.721319\pi\)
−0.579181 + 0.815199i \(0.696628\pi\)
\(492\) 0 0
\(493\) 27.8592 + 4.35709i 1.25471 + 0.196234i
\(494\) −0.577696 0.612322i −0.0259918 0.0275497i
\(495\) 0 0
\(496\) −13.2049 3.12961i −0.592916 0.140524i
\(497\) 0.832553 + 6.09536i 0.0373451 + 0.273414i
\(498\) 0 0
\(499\) −2.98994 + 4.35945i −0.133848 + 0.195156i −0.885806 0.464056i \(-0.846394\pi\)
0.751958 + 0.659211i \(0.229110\pi\)
\(500\) −8.86931 4.03160i −0.396648 0.180298i
\(501\) 0 0
\(502\) 2.55309 + 4.84692i 0.113950 + 0.216329i
\(503\) 19.4887 9.78761i 0.868960 0.436408i 0.0422967 0.999105i \(-0.486533\pi\)
0.826663 + 0.562697i \(0.190236\pi\)
\(504\) 0 0
\(505\) 0.133095 + 2.28515i 0.00592265 + 0.101688i
\(506\) −13.2431 7.30722i −0.588727 0.324846i
\(507\) 0 0
\(508\) −4.65874 + 34.1080i −0.206698 + 1.51330i
\(509\) −2.45242 + 6.35194i −0.108702 + 0.281545i −0.976552 0.215281i \(-0.930933\pi\)
0.867850 + 0.496826i \(0.165501\pi\)
\(510\) 0 0
\(511\) −4.56943 + 0.355164i −0.202140 + 0.0157116i
\(512\) −13.0253 + 10.9295i −0.575642 + 0.483021i
\(513\) 0 0
\(514\) 3.34428 + 2.80618i 0.147510 + 0.123775i
\(515\) −1.19766 0.856036i −0.0527752 0.0377215i
\(516\) 0 0
\(517\) −18.3575 + 21.0354i −0.807362 + 0.925134i
\(518\) −0.437444 2.01947i −0.0192202 0.0887304i
\(519\) 0 0
\(520\) 0.255780 0.0502336i 0.0112167 0.00220289i
\(521\) 24.3561 + 2.84683i 1.06706 + 0.124722i 0.631453 0.775414i \(-0.282459\pi\)
0.435609 + 0.900136i \(0.356533\pi\)
\(522\) 0 0
\(523\) −0.401997 0.539976i −0.0175781 0.0236115i 0.793247 0.608900i \(-0.208389\pi\)
−0.810825 + 0.585288i \(0.800981\pi\)
\(524\) −1.18046 + 5.44963i −0.0515688 + 0.238068i
\(525\) 0 0
\(526\) −10.3107 10.1126i −0.449566 0.440931i
\(527\) 14.5545 56.5042i 0.634006 2.46136i
\(528\) 0 0
\(529\) −13.8864 12.6013i −0.603758 0.547881i
\(530\) −1.20597 + 2.79576i −0.0523841 + 0.121440i
\(531\) 0 0
\(532\) 3.58119 4.81038i 0.155264 0.208556i
\(533\) 0.323506 + 0.370697i 0.0140126 + 0.0160567i
\(534\) 0 0
\(535\) 2.14247 + 0.686956i 0.0926272 + 0.0296997i
\(536\) −15.4620 3.03664i −0.667857 0.131163i
\(537\) 0 0
\(538\) 4.32029 1.96381i 0.186261 0.0846659i
\(539\) 4.20976 23.8747i 0.181327 1.02836i
\(540\) 0 0
\(541\) 1.32479 + 7.51323i 0.0569570 + 0.323019i 0.999952 0.00978743i \(-0.00311549\pi\)
−0.942995 + 0.332807i \(0.892004\pi\)
\(542\) −8.55565 12.4744i −0.367497 0.535823i
\(543\) 0 0
\(544\) −25.3075 31.3764i −1.08505 1.34525i
\(545\) −6.56347 + 2.68147i −0.281148 + 0.114862i
\(546\) 0 0
\(547\) 25.2876 15.2612i 1.08122 0.652520i 0.139945 0.990159i \(-0.455307\pi\)
0.941276 + 0.337639i \(0.109628\pi\)
\(548\) 7.40806 4.87236i 0.316457 0.208137i
\(549\) 0 0
\(550\) 0.623950 10.7128i 0.0266053 0.456795i
\(551\) −15.8914 + 25.2135i −0.676997 + 1.07413i
\(552\) 0 0
\(553\) −0.198125 + 0.141611i −0.00842512 + 0.00602192i
\(554\) 8.60525 + 0.668853i 0.365602 + 0.0284168i
\(555\) 0 0
\(556\) 27.0681 + 11.0586i 1.14794 + 0.468987i
\(557\) 7.00518 + 23.3989i 0.296819 + 0.991444i 0.968168 + 0.250303i \(0.0805301\pi\)
−0.671349 + 0.741142i \(0.734285\pi\)
\(558\) 0 0
\(559\) −1.23491 + 0.292679i −0.0522311 + 0.0123790i
\(560\) 0.194381 + 0.503460i 0.00821410 + 0.0212751i
\(561\) 0 0
\(562\) 3.05207 5.79420i 0.128744 0.244414i
\(563\) 0.326358 16.8269i 0.0137543 0.709170i −0.927946 0.372716i \(-0.878427\pi\)
0.941700 0.336454i \(-0.109228\pi\)
\(564\) 0 0
\(565\) 0.211030 0.206977i 0.00887809 0.00870757i
\(566\) 1.03196 + 1.78741i 0.0433766 + 0.0751304i
\(567\) 0 0
\(568\) −14.0158 + 24.2761i −0.588091 + 1.01860i
\(569\) 1.46214 + 5.67639i 0.0612962 + 0.237967i 0.991701 0.128568i \(-0.0410380\pi\)
−0.930404 + 0.366534i \(0.880544\pi\)
\(570\) 0 0
\(571\) 34.2089 18.8757i 1.43160 0.789922i 0.437584 0.899178i \(-0.355834\pi\)
0.994014 + 0.109256i \(0.0348468\pi\)
\(572\) −0.525326 0.833486i −0.0219650 0.0348498i
\(573\) 0 0
\(574\) 0.590974 0.732693i 0.0246668 0.0305820i
\(575\) 8.49557 28.3772i 0.354290 1.18341i
\(576\) 0 0
\(577\) −16.7706 + 17.7758i −0.698170 + 0.740017i −0.975317 0.220811i \(-0.929130\pi\)
0.277147 + 0.960828i \(0.410611\pi\)
\(578\) 16.7913 13.0142i 0.698425 0.541320i
\(579\) 0 0
\(580\) −1.75488 3.67001i −0.0728672 0.152389i
\(581\) −0.0274187 0.281889i −0.00113752 0.0116947i
\(582\) 0 0
\(583\) 26.0873 + 1.01231i 1.08042 + 0.0419254i
\(584\) −17.4480 11.4757i −0.722003 0.474869i
\(585\) 0 0
\(586\) −17.5980 8.83804i −0.726966 0.365096i
\(587\) 0.305945 + 15.7744i 0.0126277 + 0.651081i 0.951643 + 0.307206i \(0.0993940\pi\)
−0.939015 + 0.343875i \(0.888260\pi\)
\(588\) 0 0
\(589\) 48.7446 + 37.7799i 2.00849 + 1.55669i
\(590\) 0.245916 0.0384605i 0.0101242 0.00158339i
\(591\) 0 0
\(592\) −4.39523 + 9.19184i −0.180643 + 0.377782i
\(593\) 2.73296 + 0.994717i 0.112229 + 0.0408481i 0.397524 0.917592i \(-0.369869\pi\)
−0.285295 + 0.958440i \(0.592092\pi\)
\(594\) 0 0
\(595\) −2.18048 + 0.793630i −0.0893910 + 0.0325357i
\(596\) 0.833910 8.57335i 0.0341583 0.351178i
\(597\) 0 0
\(598\) 0.236452 + 0.691058i 0.00966925 + 0.0282595i
\(599\) 22.6653 20.5676i 0.926078 0.840371i −0.0614027 0.998113i \(-0.519557\pi\)
0.987480 + 0.157743i \(0.0504216\pi\)
\(600\) 0 0
\(601\) −15.0681 + 44.0383i −0.614642 + 1.79636i −0.00988457 + 0.999951i \(0.503146\pi\)
−0.604758 + 0.796409i \(0.706730\pi\)
\(602\) 0.961725 + 2.22953i 0.0391970 + 0.0908689i
\(603\) 0 0
\(604\) 4.05603 0.474082i 0.165038 0.0192901i
\(605\) 1.19169 0.382101i 0.0484493 0.0155346i
\(606\) 0 0
\(607\) −45.1959 + 12.5811i −1.83445 + 0.510653i −0.999229 0.0392661i \(-0.987498\pi\)
−0.835218 + 0.549919i \(0.814658\pi\)
\(608\) 41.0456 11.4258i 1.66462 0.463379i
\(609\) 0 0
\(610\) −1.46398 + 0.469406i −0.0592747 + 0.0190057i
\(611\) 1.33909 0.156517i 0.0541736 0.00633199i
\(612\) 0 0
\(613\) 4.84480 + 11.2315i 0.195680 + 0.453636i 0.987601 0.156987i \(-0.0501781\pi\)
−0.791921 + 0.610624i \(0.790919\pi\)
\(614\) −1.70230 + 4.97516i −0.0686992 + 0.200781i
\(615\) 0 0
\(616\) −3.16667 + 2.87360i −0.127589 + 0.115781i
\(617\) 1.53206 + 4.47761i 0.0616784 + 0.180262i 0.972685 0.232131i \(-0.0745697\pi\)
−0.911006 + 0.412393i \(0.864693\pi\)
\(618\) 0 0
\(619\) 1.81255 18.6347i 0.0728527 0.748991i −0.885734 0.464192i \(-0.846345\pi\)
0.958587 0.284799i \(-0.0919269\pi\)
\(620\) −7.91007 + 2.87903i −0.317676 + 0.115625i
\(621\) 0 0
\(622\) 0.908883 + 0.330806i 0.0364429 + 0.0132641i
\(623\) 2.89897 6.06267i 0.116145 0.242896i
\(624\) 0 0
\(625\) 18.7096 2.92613i 0.748386 0.117045i
\(626\) 11.9375 + 9.25228i 0.477119 + 0.369795i
\(627\) 0 0
\(628\) −0.239131 12.3295i −0.00954235 0.492001i
\(629\) −39.1475 19.6606i −1.56091 0.783919i
\(630\) 0 0
\(631\) −6.34784 4.17504i −0.252703 0.166206i 0.416837 0.908981i \(-0.363139\pi\)
−0.669540 + 0.742776i \(0.733509\pi\)
\(632\) −1.10882 0.0430274i −0.0441066 0.00171154i
\(633\) 0 0
\(634\) 1.98267 + 20.3837i 0.0787420 + 0.809539i
\(635\) 6.07320 + 12.7010i 0.241008 + 0.504025i
\(636\) 0 0
\(637\) −0.925297 + 0.717159i −0.0366616 + 0.0284149i
\(638\) 6.42848 6.81380i 0.254506 0.269761i
\(639\) 0 0
\(640\) −2.06228 + 6.88849i −0.0815187 + 0.272291i
\(641\) −11.1667 + 13.8446i −0.441060 + 0.546828i −0.949294 0.314391i \(-0.898200\pi\)
0.508234 + 0.861219i \(0.330299\pi\)
\(642\) 0 0
\(643\) −10.1458 16.0974i −0.400112 0.634821i 0.584127 0.811662i \(-0.301437\pi\)
−0.984239 + 0.176841i \(0.943412\pi\)
\(644\) −4.55571 + 2.51373i −0.179520 + 0.0990550i
\(645\) 0 0
\(646\) 8.51740 + 33.0666i 0.335113 + 1.30099i
\(647\) 21.5111 37.2583i 0.845687 1.46477i −0.0393360 0.999226i \(-0.512524\pi\)
0.885023 0.465547i \(-0.154142\pi\)
\(648\) 0 0
\(649\) −1.06710 1.84827i −0.0418873 0.0725509i
\(650\) −0.369952 + 0.362846i −0.0145107 + 0.0142320i
\(651\) 0 0
\(652\) 0.775239 39.9711i 0.0303607 1.56539i
\(653\) 15.9189 30.2212i 0.622954 1.18265i −0.346656 0.937992i \(-0.612683\pi\)
0.969610 0.244656i \(-0.0786750\pi\)
\(654\) 0 0
\(655\) 0.821338 + 2.12732i 0.0320923 + 0.0831213i
\(656\) −4.51641 + 1.07041i −0.176336 + 0.0417924i
\(657\) 0 0
\(658\) −0.739785 2.47105i −0.0288398 0.0963317i
\(659\) 12.7828 + 5.22233i 0.497946 + 0.203433i 0.613238 0.789898i \(-0.289867\pi\)
−0.115292 + 0.993332i \(0.536780\pi\)
\(660\) 0 0
\(661\) 20.0298 + 1.55684i 0.779071 + 0.0605542i 0.460868 0.887469i \(-0.347538\pi\)
0.318203 + 0.948023i \(0.396921\pi\)
\(662\) −11.2726 + 8.05714i −0.438120 + 0.313149i
\(663\) 0 0
\(664\) 0.688101 1.09175i 0.0267035 0.0423680i
\(665\) 0.142604 2.44841i 0.00552993 0.0949453i
\(666\) 0 0
\(667\) 21.6044 14.2094i 0.836525 0.550191i
\(668\) −3.64073 + 2.19719i −0.140864 + 0.0850120i
\(669\) 0 0
\(670\) −2.62964 + 1.07432i −0.101592 + 0.0415048i
\(671\) 8.27590 + 10.2605i 0.319488 + 0.396102i
\(672\) 0 0
\(673\) 0.681188 + 0.993197i 0.0262579 + 0.0382849i 0.837582 0.546312i \(-0.183969\pi\)
−0.811324 + 0.584597i \(0.801253\pi\)
\(674\) −0.183223 1.03911i −0.00705748 0.0400250i
\(675\) 0 0
\(676\) 3.55076 20.1374i 0.136568 0.774514i
\(677\) −1.64786 + 0.749044i −0.0633324 + 0.0287881i −0.445226 0.895418i \(-0.646877\pi\)
0.381894 + 0.924206i \(0.375272\pi\)
\(678\) 0 0
\(679\) 3.08360 + 0.605599i 0.118338 + 0.0232407i
\(680\) −10.0682 3.22824i −0.386098 0.123797i
\(681\) 0 0
\(682\) −12.7455 14.6047i −0.488050 0.559243i
\(683\) −27.1997 + 36.5355i −1.04077 + 1.39799i −0.126930 + 0.991912i \(0.540512\pi\)
−0.913837 + 0.406081i \(0.866895\pi\)
\(684\) 0 0
\(685\) 1.43625 3.32959i 0.0548761 0.127217i
\(686\) 3.38151 + 3.06856i 0.129107 + 0.117158i
\(687\) 0 0
\(688\) 2.98647 11.5942i 0.113858 0.442024i
\(689\) −0.900041 0.882754i −0.0342888 0.0336303i
\(690\) 0 0
\(691\) 4.81635 22.2347i 0.183222 0.845849i −0.789477 0.613780i \(-0.789648\pi\)
0.972699 0.232069i \(-0.0745494\pi\)
\(692\) 9.67059 + 12.9899i 0.367621 + 0.493800i
\(693\) 0 0
\(694\) −8.43520 0.985934i −0.320196 0.0374255i
\(695\) 11.7338 2.30445i 0.445090 0.0874129i
\(696\) 0 0
\(697\) −4.22492 19.5044i −0.160030 0.738781i
\(698\) −4.77041 + 5.46628i −0.180563 + 0.206902i
\(699\) 0 0
\(700\) −3.00325 2.14659i −0.113512 0.0811335i
\(701\) 32.4765 + 27.2510i 1.22662 + 1.02926i 0.998451 + 0.0556356i \(0.0177185\pi\)
0.228170 + 0.973621i \(0.426726\pi\)
\(702\) 0 0
\(703\) 35.4692 29.7622i 1.33775 1.12250i
\(704\) −1.59632 + 0.124076i −0.0601635 + 0.00467628i
\(705\) 0 0
\(706\) −5.19701 + 13.4606i −0.195592 + 0.506597i
\(707\) −0.245396 + 1.79662i −0.00922906 + 0.0675687i
\(708\) 0 0
\(709\) 19.1837 + 10.5851i 0.720460 + 0.397533i 0.800559 0.599254i \(-0.204536\pi\)
−0.0800991 + 0.996787i \(0.525524\pi\)
\(710\) 0.293826 + 5.04479i 0.0110271 + 0.189328i
\(711\) 0 0
\(712\) 27.3635 13.7425i 1.02549 0.515020i
\(713\) −24.9369 47.3416i −0.933895 1.77296i
\(714\) 0 0
\(715\) −0.366801 0.166732i −0.0137176 0.00623541i
\(716\) −18.9958 + 27.6966i −0.709908 + 1.03507i
\(717\) 0 0
\(718\) 1.80299 + 13.2002i 0.0672870 + 0.492628i
\(719\) −15.7132 3.72411i −0.586005 0.138886i −0.0730905 0.997325i \(-0.523286\pi\)
−0.512915 + 0.858440i \(0.671434\pi\)
\(720\) 0 0
\(721\) −0.800284 0.848251i −0.0298041 0.0315905i
\(722\) −23.4421 3.66628i −0.872425 0.136445i
\(723\) 0 0
\(724\) 25.6334 0.994693i 0.952658 0.0369675i
\(725\) 15.7070 + 9.47925i 0.583345 + 0.352051i
\(726\) 0 0
\(727\) 22.1458 + 6.16472i 0.821344 + 0.228637i 0.653258 0.757136i \(-0.273402\pi\)
0.168086 + 0.985772i \(0.446241\pi\)
\(728\) 0.206492 0.00765311
\(729\) 0 0
\(730\) −3.76475 −0.139339
\(731\) 49.5921 + 13.8049i 1.83423 + 0.510593i
\(732\) 0 0
\(733\) −0.139415 0.0841376i −0.00514943 0.00310769i 0.514122 0.857717i \(-0.328118\pi\)
−0.519272 + 0.854609i \(0.673797\pi\)
\(734\) −18.1811 + 0.705510i −0.671077 + 0.0260409i
\(735\) 0 0
\(736\) −36.5223 5.71199i −1.34623 0.210547i
\(737\) 16.7145 + 17.7163i 0.615685 + 0.652588i
\(738\) 0 0
\(739\) 9.96919 + 2.36274i 0.366723 + 0.0869149i 0.409846 0.912155i \(-0.365583\pi\)
−0.0431229 + 0.999070i \(0.513731\pi\)
\(740\) 0.855278 + 6.26174i 0.0314406 + 0.230186i
\(741\) 0 0
\(742\) −1.36423 + 1.98910i −0.0500825 + 0.0730220i
\(743\) −32.7431 14.8836i −1.20123 0.546025i −0.289641 0.957135i \(-0.593536\pi\)
−0.911585 + 0.411111i \(0.865141\pi\)
\(744\) 0 0
\(745\) −1.64173 3.11676i −0.0601485 0.114189i
\(746\) 10.3070 5.17636i 0.377365 0.189520i
\(747\) 0 0
\(748\) 2.32361 + 39.8948i 0.0849594 + 1.45870i
\(749\) 1.56052 + 0.861058i 0.0570201 + 0.0314624i
\(750\) 0 0
\(751\) 4.19443 30.7086i 0.153057 1.12057i −0.740640 0.671902i \(-0.765478\pi\)
0.893697 0.448672i \(-0.148103\pi\)
\(752\) −4.58099 + 11.8651i −0.167051 + 0.432674i
\(753\) 0 0
\(754\) −0.450998 + 0.0350544i −0.0164244 + 0.00127660i
\(755\) 1.27933 1.07349i 0.0465597 0.0390682i
\(756\) 0 0
\(757\) 2.63307 + 2.20941i 0.0957004 + 0.0803022i 0.689383 0.724397i \(-0.257882\pi\)
−0.593682 + 0.804700i \(0.702326\pi\)
\(758\) −1.45450 1.03962i −0.0528300 0.0377606i
\(759\) 0 0
\(760\) 7.34793 8.41979i 0.266537 0.305418i
\(761\) 5.41614 + 25.0037i 0.196335 + 0.906384i 0.964077 + 0.265624i \(0.0855780\pi\)
−0.767742 + 0.640760i \(0.778620\pi\)
\(762\) 0 0
\(763\) −5.51128 + 1.08238i −0.199522 + 0.0391848i
\(764\) 39.6412 + 4.63339i 1.43417 + 0.167630i
\(765\) 0 0
\(766\) −9.38598 12.6076i −0.339129 0.455530i
\(767\) −0.0218180 + 0.100723i −0.000787802 + 0.00363690i
\(768\) 0 0
\(769\) 33.3022 + 32.6626i 1.20091 + 1.17784i 0.979237 + 0.202721i \(0.0649784\pi\)
0.221671 + 0.975121i \(0.428849\pi\)
\(770\) −0.192287 + 0.746505i −0.00692955 + 0.0269022i
\(771\) 0 0
\(772\) −6.25971 5.68038i −0.225292 0.204441i
\(773\) 16.1201 37.3706i 0.579800 1.34413i −0.335761 0.941947i \(-0.608993\pi\)
0.915561 0.402180i \(-0.131747\pi\)
\(774\) 0 0
\(775\) 22.6694 30.4503i 0.814310 1.09381i
\(776\) 9.41501 + 10.7884i 0.337979 + 0.387281i
\(777\) 0 0
\(778\) −16.4789 5.28376i −0.590799 0.189432i
\(779\) 20.6978 + 4.06492i 0.741576 + 0.145641i
\(780\) 0 0
\(781\) 39.4452 17.9300i 1.41146 0.641588i
\(782\) 5.14448 29.1758i 0.183966 1.04333i
\(783\) 0 0
\(784\) −1.91777 10.8762i −0.0684916 0.388435i
\(785\) −2.85249 4.15903i −0.101810 0.148442i
\(786\) 0 0