Properties

Label 637.2.q.e.491.2
Level $637$
Weight $2$
Character 637.491
Analytic conductor $5.086$
Analytic rank $0$
Dimension $4$
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.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-7})\)
Defining polynomial: \( x^{4} - x^{3} - x^{2} - 2x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 491.2
Root \(-0.895644 - 1.09445i\) of defining polynomial
Character \(\chi\) \(=\) 637.491
Dual form 637.2.q.e.589.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.89564 - 1.09445i) q^{2} +(0.895644 + 1.55130i) q^{3} +(1.39564 - 2.41733i) q^{4} +2.18890i q^{5} +(3.39564 + 1.96048i) q^{6} -1.73205i q^{8} +(-0.104356 + 0.180750i) q^{9} +O(q^{10})\) \(q+(1.89564 - 1.09445i) q^{2} +(0.895644 + 1.55130i) q^{3} +(1.39564 - 2.41733i) q^{4} +2.18890i q^{5} +(3.39564 + 1.96048i) q^{6} -1.73205i q^{8} +(-0.104356 + 0.180750i) q^{9} +(2.39564 + 4.14938i) q^{10} +(-1.10436 + 0.637600i) q^{11} +5.00000 q^{12} +(3.50000 + 0.866025i) q^{13} +(-3.39564 + 1.96048i) q^{15} +(0.895644 + 1.55130i) q^{16} +(-1.50000 + 2.59808i) q^{17} +0.456850i q^{18} +(-5.68693 - 3.28335i) q^{19} +(5.29129 + 3.05493i) q^{20} +(-1.39564 + 2.41733i) q^{22} +(-3.79129 - 6.56670i) q^{23} +(2.68693 - 1.55130i) q^{24} +0.208712 q^{25} +(7.58258 - 2.18890i) q^{26} +5.00000 q^{27} +(1.10436 + 1.91280i) q^{29} +(-4.29129 + 7.43273i) q^{30} -8.66025i q^{31} +(6.39564 + 3.69253i) q^{32} +(-1.97822 - 1.14213i) q^{33} +6.56670i q^{34} +(0.291288 + 0.504525i) q^{36} +(6.00000 - 3.46410i) q^{37} -14.3739 q^{38} +(1.79129 + 6.20520i) q^{39} +3.79129 q^{40} +(2.20871 - 1.27520i) q^{41} +(2.18693 - 3.78788i) q^{43} +3.55945i q^{44} +(-0.395644 - 0.228425i) q^{45} +(-14.3739 - 8.29875i) q^{46} +4.28245i q^{47} +(-1.60436 + 2.77883i) q^{48} +(0.395644 - 0.228425i) q^{50} -5.37386 q^{51} +(6.97822 - 7.25198i) q^{52} -12.1652 q^{53} +(9.47822 - 5.47225i) q^{54} +(-1.39564 - 2.41733i) q^{55} -11.7629i q^{57} +(4.18693 + 2.41733i) q^{58} +(-7.66515 - 4.42548i) q^{59} +10.9445i q^{60} +(-6.37386 + 11.0399i) q^{61} +(-9.47822 - 16.4168i) q^{62} +12.5826 q^{64} +(-1.89564 + 7.66115i) q^{65} -5.00000 q^{66} +(9.87386 - 5.70068i) q^{67} +(4.18693 + 7.25198i) q^{68} +(6.79129 - 11.7629i) q^{69} +(-0.791288 - 0.456850i) q^{71} +(0.313068 + 0.180750i) q^{72} +3.46410i q^{73} +(7.58258 - 13.1334i) q^{74} +(0.186932 + 0.323775i) q^{75} +(-15.8739 + 9.16478i) q^{76} +(10.1869 + 9.80238i) q^{78} -6.00000 q^{79} +(-3.39564 + 1.96048i) q^{80} +(4.79129 + 8.29875i) q^{81} +(2.79129 - 4.83465i) q^{82} -3.55945i q^{83} +(-5.68693 - 3.28335i) q^{85} -9.57395i q^{86} +(-1.97822 + 3.42638i) q^{87} +(1.10436 + 1.91280i) q^{88} +(-2.52178 + 1.45595i) q^{89} -1.00000 q^{90} -21.1652 q^{92} +(13.4347 - 7.75650i) q^{93} +(4.68693 + 8.11800i) q^{94} +(7.18693 - 12.4481i) q^{95} +13.2288i q^{96} +(-13.1869 - 7.61348i) q^{97} -0.266150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 3 q^{2} - q^{3} + q^{4} + 9 q^{6} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 3 q^{2} - q^{3} + q^{4} + 9 q^{6} - 5 q^{9} + 5 q^{10} - 9 q^{11} + 20 q^{12} + 14 q^{13} - 9 q^{15} - q^{16} - 6 q^{17} - 9 q^{19} + 12 q^{20} - q^{22} - 6 q^{23} - 3 q^{24} + 10 q^{25} + 12 q^{26} + 20 q^{27} + 9 q^{29} - 8 q^{30} + 21 q^{32} + 15 q^{33} - 8 q^{36} + 24 q^{37} - 30 q^{38} - 2 q^{39} + 6 q^{40} + 18 q^{41} - 5 q^{43} + 3 q^{45} - 30 q^{46} - 11 q^{48} - 3 q^{50} + 6 q^{51} + 5 q^{52} - 12 q^{53} + 15 q^{54} - q^{55} + 3 q^{58} + 6 q^{59} + 2 q^{61} - 15 q^{62} + 32 q^{64} - 3 q^{65} - 20 q^{66} + 12 q^{67} + 3 q^{68} + 18 q^{69} + 6 q^{71} + 15 q^{72} + 12 q^{74} - 13 q^{75} - 36 q^{76} + 27 q^{78} - 24 q^{79} - 9 q^{80} + 10 q^{81} + 2 q^{82} - 9 q^{85} + 15 q^{87} + 9 q^{88} - 33 q^{89} - 4 q^{90} - 48 q^{92} - 15 q^{93} + 5 q^{94} + 15 q^{95} - 39 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.89564 1.09445i 1.34042 0.773893i 0.353553 0.935414i \(-0.384973\pi\)
0.986869 + 0.161521i \(0.0516399\pi\)
\(3\) 0.895644 + 1.55130i 0.517100 + 0.895644i 0.999803 + 0.0198595i \(0.00632191\pi\)
−0.482703 + 0.875784i \(0.660345\pi\)
\(4\) 1.39564 2.41733i 0.697822 1.20866i
\(5\) 2.18890i 0.978906i 0.872030 + 0.489453i \(0.162804\pi\)
−0.872030 + 0.489453i \(0.837196\pi\)
\(6\) 3.39564 + 1.96048i 1.38627 + 0.800361i
\(7\) 0 0
\(8\) 1.73205i 0.612372i
\(9\) −0.104356 + 0.180750i −0.0347854 + 0.0602500i
\(10\) 2.39564 + 4.14938i 0.757569 + 1.31215i
\(11\) −1.10436 + 0.637600i −0.332976 + 0.192244i −0.657162 0.753750i \(-0.728243\pi\)
0.324186 + 0.945993i \(0.394910\pi\)
\(12\) 5.00000 1.44338
\(13\) 3.50000 + 0.866025i 0.970725 + 0.240192i
\(14\) 0 0
\(15\) −3.39564 + 1.96048i −0.876751 + 0.506193i
\(16\) 0.895644 + 1.55130i 0.223911 + 0.387825i
\(17\) −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 0.456850i 0.107681i
\(19\) −5.68693 3.28335i −1.30467 0.753253i −0.323470 0.946238i \(-0.604850\pi\)
−0.981202 + 0.192986i \(0.938183\pi\)
\(20\) 5.29129 + 3.05493i 1.18317 + 0.683102i
\(21\) 0 0
\(22\) −1.39564 + 2.41733i −0.297552 + 0.515376i
\(23\) −3.79129 6.56670i −0.790538 1.36925i −0.925634 0.378420i \(-0.876468\pi\)
0.135096 0.990833i \(-0.456866\pi\)
\(24\) 2.68693 1.55130i 0.548468 0.316658i
\(25\) 0.208712 0.0417424
\(26\) 7.58258 2.18890i 1.48707 0.429279i
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) 1.10436 + 1.91280i 0.205074 + 0.355198i 0.950156 0.311774i \(-0.100923\pi\)
−0.745082 + 0.666972i \(0.767590\pi\)
\(30\) −4.29129 + 7.43273i −0.783478 + 1.35702i
\(31\) 8.66025i 1.55543i −0.628619 0.777714i \(-0.716379\pi\)
0.628619 0.777714i \(-0.283621\pi\)
\(32\) 6.39564 + 3.69253i 1.13060 + 0.652753i
\(33\) −1.97822 1.14213i −0.344364 0.198819i
\(34\) 6.56670i 1.12618i
\(35\) 0 0
\(36\) 0.291288 + 0.504525i 0.0485480 + 0.0840876i
\(37\) 6.00000 3.46410i 0.986394 0.569495i 0.0821995 0.996616i \(-0.473806\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) −14.3739 −2.33175
\(39\) 1.79129 + 6.20520i 0.286836 + 0.993628i
\(40\) 3.79129 0.599455
\(41\) 2.20871 1.27520i 0.344943 0.199153i −0.317513 0.948254i \(-0.602848\pi\)
0.662456 + 0.749101i \(0.269514\pi\)
\(42\) 0 0
\(43\) 2.18693 3.78788i 0.333504 0.577646i −0.649692 0.760197i \(-0.725102\pi\)
0.983196 + 0.182551i \(0.0584356\pi\)
\(44\) 3.55945i 0.536608i
\(45\) −0.395644 0.228425i −0.0589791 0.0340516i
\(46\) −14.3739 8.29875i −2.11931 1.22358i
\(47\) 4.28245i 0.624660i 0.949974 + 0.312330i \(0.101109\pi\)
−0.949974 + 0.312330i \(0.898891\pi\)
\(48\) −1.60436 + 2.77883i −0.231569 + 0.401089i
\(49\) 0 0
\(50\) 0.395644 0.228425i 0.0559525 0.0323042i
\(51\) −5.37386 −0.752491
\(52\) 6.97822 7.25198i 0.967705 1.00567i
\(53\) −12.1652 −1.67101 −0.835506 0.549481i \(-0.814825\pi\)
−0.835506 + 0.549481i \(0.814825\pi\)
\(54\) 9.47822 5.47225i 1.28982 0.744679i
\(55\) −1.39564 2.41733i −0.188189 0.325952i
\(56\) 0 0
\(57\) 11.7629i 1.55803i
\(58\) 4.18693 + 2.41733i 0.549771 + 0.317410i
\(59\) −7.66515 4.42548i −0.997918 0.576148i −0.0902862 0.995916i \(-0.528778\pi\)
−0.907632 + 0.419768i \(0.862112\pi\)
\(60\) 10.9445i 1.41293i
\(61\) −6.37386 + 11.0399i −0.816090 + 1.41351i 0.0924533 + 0.995717i \(0.470529\pi\)
−0.908543 + 0.417792i \(0.862804\pi\)
\(62\) −9.47822 16.4168i −1.20374 2.08493i
\(63\) 0 0
\(64\) 12.5826 1.57282
\(65\) −1.89564 + 7.66115i −0.235126 + 0.950249i
\(66\) −5.00000 −0.615457
\(67\) 9.87386 5.70068i 1.20628 0.696449i 0.244339 0.969690i \(-0.421429\pi\)
0.961946 + 0.273241i \(0.0880957\pi\)
\(68\) 4.18693 + 7.25198i 0.507740 + 0.879432i
\(69\) 6.79129 11.7629i 0.817575 1.41608i
\(70\) 0 0
\(71\) −0.791288 0.456850i −0.0939086 0.0542181i 0.452310 0.891861i \(-0.350600\pi\)
−0.546219 + 0.837643i \(0.683933\pi\)
\(72\) 0.313068 + 0.180750i 0.0368954 + 0.0213016i
\(73\) 3.46410i 0.405442i 0.979236 + 0.202721i \(0.0649785\pi\)
−0.979236 + 0.202721i \(0.935021\pi\)
\(74\) 7.58258 13.1334i 0.881457 1.52673i
\(75\) 0.186932 + 0.323775i 0.0215850 + 0.0373864i
\(76\) −15.8739 + 9.16478i −1.82086 + 1.05127i
\(77\) 0 0
\(78\) 10.1869 + 9.80238i 1.15344 + 1.10990i
\(79\) −6.00000 −0.675053 −0.337526 0.941316i \(-0.609590\pi\)
−0.337526 + 0.941316i \(0.609590\pi\)
\(80\) −3.39564 + 1.96048i −0.379645 + 0.219188i
\(81\) 4.79129 + 8.29875i 0.532365 + 0.922084i
\(82\) 2.79129 4.83465i 0.308246 0.533898i
\(83\) 3.55945i 0.390701i −0.980734 0.195350i \(-0.937416\pi\)
0.980734 0.195350i \(-0.0625844\pi\)
\(84\) 0 0
\(85\) −5.68693 3.28335i −0.616834 0.356129i
\(86\) 9.57395i 1.03239i
\(87\) −1.97822 + 3.42638i −0.212087 + 0.367346i
\(88\) 1.10436 + 1.91280i 0.117725 + 0.203905i
\(89\) −2.52178 + 1.45595i −0.267308 + 0.154330i −0.627664 0.778485i \(-0.715989\pi\)
0.360356 + 0.932815i \(0.382655\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) −21.1652 −2.20662
\(93\) 13.4347 7.75650i 1.39311 0.804312i
\(94\) 4.68693 + 8.11800i 0.483420 + 0.837308i
\(95\) 7.18693 12.4481i 0.737364 1.27715i
\(96\) 13.2288i 1.35015i
\(97\) −13.1869 7.61348i −1.33893 0.773032i −0.352281 0.935894i \(-0.614594\pi\)
−0.986649 + 0.162863i \(0.947927\pi\)
\(98\) 0 0
\(99\) 0.266150i 0.0267491i
\(100\) 0.291288 0.504525i 0.0291288 0.0504525i
\(101\) −4.89564 8.47950i −0.487135 0.843742i 0.512756 0.858534i \(-0.328625\pi\)
−0.999891 + 0.0147923i \(0.995291\pi\)
\(102\) −10.1869 + 5.88143i −1.00866 + 0.582348i
\(103\) −4.58258 −0.451535 −0.225767 0.974181i \(-0.572489\pi\)
−0.225767 + 0.974181i \(0.572489\pi\)
\(104\) 1.50000 6.06218i 0.147087 0.594445i
\(105\) 0 0
\(106\) −23.0608 + 13.3142i −2.23986 + 1.29319i
\(107\) 4.89564 + 8.47950i 0.473280 + 0.819745i 0.999532 0.0305838i \(-0.00973664\pi\)
−0.526252 + 0.850328i \(0.676403\pi\)
\(108\) 6.97822 12.0866i 0.671479 1.16304i
\(109\) 7.93725i 0.760251i −0.924935 0.380126i \(-0.875881\pi\)
0.924935 0.380126i \(-0.124119\pi\)
\(110\) −5.29129 3.05493i −0.504505 0.291276i
\(111\) 10.7477 + 6.20520i 1.02013 + 0.588972i
\(112\) 0 0
\(113\) −0.708712 + 1.22753i −0.0666700 + 0.115476i −0.897434 0.441150i \(-0.854571\pi\)
0.830764 + 0.556625i \(0.187904\pi\)
\(114\) −12.8739 22.2982i −1.20575 2.08842i
\(115\) 14.3739 8.29875i 1.34037 0.773863i
\(116\) 6.16515 0.572420
\(117\) −0.521780 + 0.542250i −0.0482386 + 0.0501310i
\(118\) −19.3739 −1.78351
\(119\) 0 0
\(120\) 3.39564 + 5.88143i 0.309978 + 0.536898i
\(121\) −4.68693 + 8.11800i −0.426085 + 0.738000i
\(122\) 27.9035i 2.52627i
\(123\) 3.95644 + 2.28425i 0.356740 + 0.205964i
\(124\) −20.9347 12.0866i −1.87999 1.08541i
\(125\) 11.4014i 1.01977i
\(126\) 0 0
\(127\) 7.97822 + 13.8187i 0.707953 + 1.22621i 0.965615 + 0.259975i \(0.0837143\pi\)
−0.257663 + 0.966235i \(0.582952\pi\)
\(128\) 11.0608 6.38595i 0.977645 0.564444i
\(129\) 7.83485 0.689820
\(130\) 4.79129 + 16.5975i 0.420224 + 1.45570i
\(131\) −3.62614 −0.316817 −0.158409 0.987374i \(-0.550636\pi\)
−0.158409 + 0.987374i \(0.550636\pi\)
\(132\) −5.52178 + 3.18800i −0.480609 + 0.277480i
\(133\) 0 0
\(134\) 12.4782 21.6129i 1.07795 1.86707i
\(135\) 10.9445i 0.941953i
\(136\) 4.50000 + 2.59808i 0.385872 + 0.222783i
\(137\) −14.8521 8.57485i −1.26890 0.732599i −0.294119 0.955769i \(-0.595026\pi\)
−0.974780 + 0.223169i \(0.928360\pi\)
\(138\) 29.7309i 2.53086i
\(139\) 0.395644 0.685275i 0.0335581 0.0581243i −0.848759 0.528781i \(-0.822649\pi\)
0.882317 + 0.470656i \(0.155983\pi\)
\(140\) 0 0
\(141\) −6.64337 + 3.83555i −0.559473 + 0.323012i
\(142\) −2.00000 −0.167836
\(143\) −4.41742 + 1.27520i −0.369404 + 0.106638i
\(144\) −0.373864 −0.0311553
\(145\) −4.18693 + 2.41733i −0.347706 + 0.200748i
\(146\) 3.79129 + 6.56670i 0.313769 + 0.543464i
\(147\) 0 0
\(148\) 19.3386i 1.58962i
\(149\) 1.89564 + 1.09445i 0.155297 + 0.0896609i 0.575635 0.817707i \(-0.304755\pi\)
−0.420338 + 0.907368i \(0.638088\pi\)
\(150\) 0.708712 + 0.409175i 0.0578661 + 0.0334090i
\(151\) 12.1244i 0.986666i 0.869841 + 0.493333i \(0.164222\pi\)
−0.869841 + 0.493333i \(0.835778\pi\)
\(152\) −5.68693 + 9.85005i −0.461271 + 0.798945i
\(153\) −0.313068 0.542250i −0.0253101 0.0438383i
\(154\) 0 0
\(155\) 18.9564 1.52262
\(156\) 17.5000 + 4.33013i 1.40112 + 0.346688i
\(157\) 21.9564 1.75231 0.876157 0.482025i \(-0.160099\pi\)
0.876157 + 0.482025i \(0.160099\pi\)
\(158\) −11.3739 + 6.56670i −0.904856 + 0.522419i
\(159\) −10.8956 18.8718i −0.864081 1.49663i
\(160\) −8.08258 + 13.9994i −0.638984 + 1.10675i
\(161\) 0 0
\(162\) 18.1652 + 10.4877i 1.42719 + 0.823988i
\(163\) 6.00000 + 3.46410i 0.469956 + 0.271329i 0.716221 0.697873i \(-0.245870\pi\)
−0.246265 + 0.969202i \(0.579203\pi\)
\(164\) 7.11890i 0.555893i
\(165\) 2.50000 4.33013i 0.194625 0.337100i
\(166\) −3.89564 6.74745i −0.302361 0.523704i
\(167\) 17.2913 9.98313i 1.33804 0.772518i 0.351523 0.936179i \(-0.385664\pi\)
0.986517 + 0.163661i \(0.0523304\pi\)
\(168\) 0 0
\(169\) 11.5000 + 6.06218i 0.884615 + 0.466321i
\(170\) −14.3739 −1.10243
\(171\) 1.18693 0.685275i 0.0907669 0.0524043i
\(172\) −6.10436 10.5731i −0.465453 0.806188i
\(173\) 3.87386 6.70973i 0.294524 0.510131i −0.680350 0.732888i \(-0.738172\pi\)
0.974874 + 0.222756i \(0.0715054\pi\)
\(174\) 8.66025i 0.656532i
\(175\) 0 0
\(176\) −1.97822 1.14213i −0.149114 0.0860910i
\(177\) 15.8546i 1.19171i
\(178\) −3.18693 + 5.51993i −0.238871 + 0.413736i
\(179\) 4.50000 + 7.79423i 0.336346 + 0.582568i 0.983742 0.179585i \(-0.0574756\pi\)
−0.647397 + 0.762153i \(0.724142\pi\)
\(180\) −1.10436 + 0.637600i −0.0823138 + 0.0475239i
\(181\) 9.16515 0.681240 0.340620 0.940201i \(-0.389363\pi\)
0.340620 + 0.940201i \(0.389363\pi\)
\(182\) 0 0
\(183\) −22.8348 −1.68800
\(184\) −11.3739 + 6.56670i −0.838492 + 0.484104i
\(185\) 7.58258 + 13.1334i 0.557482 + 0.965587i
\(186\) 16.9782 29.4071i 1.24490 2.15624i
\(187\) 3.82560i 0.279756i
\(188\) 10.3521 + 5.97678i 0.755003 + 0.435901i
\(189\) 0 0
\(190\) 31.4630i 2.28256i
\(191\) 0.313068 0.542250i 0.0226528 0.0392358i −0.854477 0.519490i \(-0.826122\pi\)
0.877130 + 0.480254i \(0.159455\pi\)
\(192\) 11.2695 + 19.5194i 0.813307 + 1.40869i
\(193\) −10.7477 + 6.20520i −0.773638 + 0.446660i −0.834171 0.551506i \(-0.814053\pi\)
0.0605327 + 0.998166i \(0.480720\pi\)
\(194\) −33.3303 −2.39298
\(195\) −13.5826 + 3.92095i −0.972668 + 0.280785i
\(196\) 0 0
\(197\) −9.47822 + 5.47225i −0.675295 + 0.389882i −0.798080 0.602551i \(-0.794151\pi\)
0.122785 + 0.992433i \(0.460817\pi\)
\(198\) −0.291288 0.504525i −0.0207009 0.0358551i
\(199\) 5.50000 9.52628i 0.389885 0.675300i −0.602549 0.798082i \(-0.705848\pi\)
0.992434 + 0.122782i \(0.0391815\pi\)
\(200\) 0.361500i 0.0255619i
\(201\) 17.6869 + 10.2116i 1.24754 + 0.720268i
\(202\) −18.5608 10.7161i −1.30593 0.753981i
\(203\) 0 0
\(204\) −7.50000 + 12.9904i −0.525105 + 0.909509i
\(205\) 2.79129 + 4.83465i 0.194952 + 0.337667i
\(206\) −8.68693 + 5.01540i −0.605247 + 0.349440i
\(207\) 1.58258 0.109997
\(208\) 1.79129 + 6.20520i 0.124203 + 0.430253i
\(209\) 8.37386 0.579232
\(210\) 0 0
\(211\) −0.708712 1.22753i −0.0487898 0.0845063i 0.840599 0.541658i \(-0.182203\pi\)
−0.889389 + 0.457151i \(0.848870\pi\)
\(212\) −16.9782 + 29.4071i −1.16607 + 2.01969i
\(213\) 1.63670i 0.112145i
\(214\) 18.5608 + 10.7161i 1.26879 + 0.732536i
\(215\) 8.29129 + 4.78698i 0.565461 + 0.326469i
\(216\) 8.66025i 0.589256i
\(217\) 0 0
\(218\) −8.68693 15.0462i −0.588353 1.01906i
\(219\) −5.37386 + 3.10260i −0.363132 + 0.209654i
\(220\) −7.79129 −0.525289
\(221\) −7.50000 + 7.79423i −0.504505 + 0.524297i
\(222\) 27.1652 1.82321
\(223\) −17.9347 + 10.3546i −1.20099 + 0.693394i −0.960776 0.277325i \(-0.910552\pi\)
−0.240217 + 0.970719i \(0.577219\pi\)
\(224\) 0 0
\(225\) −0.0217804 + 0.0377247i −0.00145203 + 0.00251498i
\(226\) 3.10260i 0.206382i
\(227\) 10.6652 + 6.15753i 0.707871 + 0.408689i 0.810272 0.586054i \(-0.199319\pi\)
−0.102401 + 0.994743i \(0.532653\pi\)
\(228\) −28.4347 16.4168i −1.88313 1.08723i
\(229\) 6.92820i 0.457829i 0.973447 + 0.228914i \(0.0735176\pi\)
−0.973447 + 0.228914i \(0.926482\pi\)
\(230\) 18.1652 31.4630i 1.19777 2.07461i
\(231\) 0 0
\(232\) 3.31307 1.91280i 0.217514 0.125582i
\(233\) −6.95644 −0.455731 −0.227866 0.973693i \(-0.573175\pi\)
−0.227866 + 0.973693i \(0.573175\pi\)
\(234\) −0.395644 + 1.59898i −0.0258641 + 0.104528i
\(235\) −9.37386 −0.611483
\(236\) −21.3956 + 12.3528i −1.39274 + 0.804098i
\(237\) −5.37386 9.30780i −0.349070 0.604607i
\(238\) 0 0
\(239\) 13.2288i 0.855697i 0.903850 + 0.427849i \(0.140728\pi\)
−0.903850 + 0.427849i \(0.859272\pi\)
\(240\) −6.08258 3.51178i −0.392629 0.226684i
\(241\) −3.56080 2.05583i −0.229371 0.132427i 0.380911 0.924612i \(-0.375610\pi\)
−0.610282 + 0.792184i \(0.708944\pi\)
\(242\) 20.5185i 1.31898i
\(243\) −1.08258 + 1.87508i −0.0694473 + 0.120286i
\(244\) 17.7913 + 30.8154i 1.13897 + 1.97275i
\(245\) 0 0
\(246\) 10.0000 0.637577
\(247\) −17.0608 16.4168i −1.08555 1.04457i
\(248\) −15.0000 −0.952501
\(249\) 5.52178 3.18800i 0.349929 0.202031i
\(250\) 12.4782 + 21.6129i 0.789192 + 1.36692i
\(251\) −10.5826 + 18.3296i −0.667966 + 1.15695i 0.310506 + 0.950572i \(0.399502\pi\)
−0.978472 + 0.206380i \(0.933832\pi\)
\(252\) 0 0
\(253\) 8.37386 + 4.83465i 0.526460 + 0.303952i
\(254\) 30.2477 + 17.4635i 1.89791 + 1.09576i
\(255\) 11.7629i 0.736619i
\(256\) 1.39564 2.41733i 0.0872277 0.151083i
\(257\) 13.9782 + 24.2110i 0.871937 + 1.51024i 0.859990 + 0.510311i \(0.170470\pi\)
0.0119476 + 0.999929i \(0.496197\pi\)
\(258\) 14.8521 8.57485i 0.924650 0.533847i
\(259\) 0 0
\(260\) 15.8739 + 15.2746i 0.984455 + 0.947292i
\(261\) −0.460985 −0.0285343
\(262\) −6.87386 + 3.96863i −0.424669 + 0.245183i
\(263\) 13.6652 + 23.6687i 0.842629 + 1.45948i 0.887664 + 0.460491i \(0.152327\pi\)
−0.0450348 + 0.998985i \(0.514340\pi\)
\(264\) −1.97822 + 3.42638i −0.121751 + 0.210879i
\(265\) 26.6283i 1.63576i
\(266\) 0 0
\(267\) −4.51723 2.60803i −0.276450 0.159609i
\(268\) 31.8245i 1.94399i
\(269\) −5.60436 + 9.70703i −0.341704 + 0.591848i −0.984749 0.173980i \(-0.944337\pi\)
0.643046 + 0.765828i \(0.277671\pi\)
\(270\) 11.9782 + 20.7469i 0.728971 + 1.26262i
\(271\) 24.8739 14.3609i 1.51098 0.872364i 0.511062 0.859544i \(-0.329252\pi\)
0.999918 0.0128205i \(-0.00408101\pi\)
\(272\) −5.37386 −0.325838
\(273\) 0 0
\(274\) −37.5390 −2.26781
\(275\) −0.230493 + 0.133075i −0.0138992 + 0.00802472i
\(276\) −18.9564 32.8335i −1.14104 1.97635i
\(277\) 7.87386 13.6379i 0.473095 0.819424i −0.526431 0.850218i \(-0.676470\pi\)
0.999526 + 0.0307939i \(0.00980354\pi\)
\(278\) 1.73205i 0.103882i
\(279\) 1.56534 + 0.903750i 0.0937145 + 0.0541061i
\(280\) 0 0
\(281\) 6.39590i 0.381548i 0.981634 + 0.190774i \(0.0610997\pi\)
−0.981634 + 0.190774i \(0.938900\pi\)
\(282\) −8.39564 + 14.5417i −0.499953 + 0.865945i
\(283\) −12.3739 21.4322i −0.735550 1.27401i −0.954482 0.298270i \(-0.903591\pi\)
0.218932 0.975740i \(-0.429743\pi\)
\(284\) −2.20871 + 1.27520i −0.131063 + 0.0756692i
\(285\) 25.7477 1.52516
\(286\) −6.97822 + 7.25198i −0.412631 + 0.428818i
\(287\) 0 0
\(288\) −1.33485 + 0.770675i −0.0786567 + 0.0454125i
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) −5.29129 + 9.16478i −0.310715 + 0.538174i
\(291\) 27.2759i 1.59894i
\(292\) 8.37386 + 4.83465i 0.490043 + 0.282927i
\(293\) −6.79129 3.92095i −0.396751 0.229064i 0.288330 0.957531i \(-0.406900\pi\)
−0.685081 + 0.728467i \(0.740233\pi\)
\(294\) 0 0
\(295\) 9.68693 16.7783i 0.563995 0.976868i
\(296\) −6.00000 10.3923i −0.348743 0.604040i
\(297\) −5.52178 + 3.18800i −0.320406 + 0.184987i
\(298\) 4.79129 0.277552
\(299\) −7.58258 26.2668i −0.438512 1.51905i
\(300\) 1.04356 0.0602500
\(301\) 0 0
\(302\) 13.2695 + 22.9835i 0.763574 + 1.32255i
\(303\) 8.76951 15.1892i 0.503795 0.872599i
\(304\) 11.7629i 0.674646i
\(305\) −24.1652 13.9518i −1.38369 0.798875i
\(306\) −1.18693 0.685275i −0.0678524 0.0391746i
\(307\) 24.1733i 1.37964i −0.723980 0.689820i \(-0.757689\pi\)
0.723980 0.689820i \(-0.242311\pi\)
\(308\) 0 0
\(309\) −4.10436 7.10895i −0.233489 0.404414i
\(310\) 35.9347 20.7469i 2.04095 1.17834i
\(311\) 5.53901 0.314089 0.157044 0.987592i \(-0.449803\pi\)
0.157044 + 0.987592i \(0.449803\pi\)
\(312\) 10.7477 3.10260i 0.608470 0.175650i
\(313\) −20.7477 −1.17273 −0.586365 0.810047i \(-0.699442\pi\)
−0.586365 + 0.810047i \(0.699442\pi\)
\(314\) 41.6216 24.0302i 2.34884 1.35610i
\(315\) 0 0
\(316\) −8.37386 + 14.5040i −0.471067 + 0.815911i
\(317\) 18.5203i 1.04020i −0.854105 0.520101i \(-0.825894\pi\)
0.854105 0.520101i \(-0.174106\pi\)
\(318\) −41.3085 23.8495i −2.31647 1.33741i
\(319\) −2.43920 1.40828i −0.136569 0.0788483i
\(320\) 27.5420i 1.53965i
\(321\) −8.76951 + 15.1892i −0.489466 + 0.847780i
\(322\) 0 0
\(323\) 17.0608 9.85005i 0.949288 0.548072i
\(324\) 26.7477 1.48598
\(325\) 0.730493 + 0.180750i 0.0405204 + 0.0100262i
\(326\) 15.1652 0.839920
\(327\) 12.3131 7.10895i 0.680914 0.393126i
\(328\) −2.20871 3.82560i −0.121956 0.211234i
\(329\) 0 0
\(330\) 10.9445i 0.602475i
\(331\) 0.939205 + 0.542250i 0.0516234 + 0.0298048i 0.525590 0.850738i \(-0.323845\pi\)
−0.473966 + 0.880543i \(0.657178\pi\)
\(332\) −8.60436 4.96773i −0.472225 0.272639i
\(333\) 1.44600i 0.0792403i
\(334\) 21.8521 37.8489i 1.19569 2.07100i
\(335\) 12.4782 + 21.6129i 0.681758 + 1.18084i
\(336\) 0 0
\(337\) −12.9564 −0.705782 −0.352891 0.935664i \(-0.614801\pi\)
−0.352891 + 0.935664i \(0.614801\pi\)
\(338\) 28.4347 1.09445i 1.54664 0.0595303i
\(339\) −2.53901 −0.137900
\(340\) −15.8739 + 9.16478i −0.860881 + 0.497030i
\(341\) 5.52178 + 9.56400i 0.299021 + 0.517920i
\(342\) 1.50000 2.59808i 0.0811107 0.140488i
\(343\) 0 0
\(344\) −6.56080 3.78788i −0.353734 0.204229i
\(345\) 25.7477 + 14.8655i 1.38621 + 0.800329i
\(346\) 16.9590i 0.911722i
\(347\) 2.20871 3.82560i 0.118570 0.205369i −0.800631 0.599157i \(-0.795502\pi\)
0.919201 + 0.393788i \(0.128836\pi\)
\(348\) 5.52178 + 9.56400i 0.295998 + 0.512684i
\(349\) −9.24773 + 5.33918i −0.495019 + 0.285800i −0.726654 0.687003i \(-0.758926\pi\)
0.231635 + 0.972803i \(0.425593\pi\)
\(350\) 0 0
\(351\) 17.5000 + 4.33013i 0.934081 + 0.231125i
\(352\) −9.41742 −0.501950
\(353\) 23.2259 13.4095i 1.23619 0.713716i 0.267879 0.963453i \(-0.413677\pi\)
0.968314 + 0.249737i \(0.0803441\pi\)
\(354\) −17.3521 30.0547i −0.922253 1.59739i
\(355\) 1.00000 1.73205i 0.0530745 0.0919277i
\(356\) 8.12795i 0.430781i
\(357\) 0 0
\(358\) 17.0608 + 9.85005i 0.901691 + 0.520592i
\(359\) 12.6766i 0.669043i −0.942388 0.334522i \(-0.891425\pi\)
0.942388 0.334522i \(-0.108575\pi\)
\(360\) −0.395644 + 0.685275i −0.0208523 + 0.0361172i
\(361\) 12.0608 + 20.8899i 0.634779 + 1.09947i
\(362\) 17.3739 10.0308i 0.913150 0.527207i
\(363\) −16.7913 −0.881314
\(364\) 0 0
\(365\) −7.58258 −0.396890
\(366\) −43.2867 + 24.9916i −2.26263 + 1.30633i
\(367\) −9.00000 15.5885i −0.469796 0.813711i 0.529607 0.848243i \(-0.322339\pi\)
−0.999404 + 0.0345320i \(0.989006\pi\)
\(368\) 6.79129 11.7629i 0.354020 0.613181i
\(369\) 0.532300i 0.0277104i
\(370\) 28.7477 + 16.5975i 1.49452 + 0.862863i
\(371\) 0 0
\(372\) 43.3013i 2.24507i
\(373\) −18.3956 + 31.8622i −0.952490 + 1.64976i −0.212481 + 0.977165i \(0.568154\pi\)
−0.740009 + 0.672596i \(0.765179\pi\)
\(374\) −4.18693 7.25198i −0.216501 0.374991i
\(375\) −17.6869 + 10.2116i −0.913349 + 0.527322i
\(376\) 7.41742 0.382524
\(377\) 2.20871 + 7.65120i 0.113754 + 0.394057i
\(378\) 0 0
\(379\) −3.93920 + 2.27430i −0.202343 + 0.116823i −0.597748 0.801684i \(-0.703938\pi\)
0.395405 + 0.918507i \(0.370604\pi\)
\(380\) −20.0608 34.7463i −1.02910 1.78245i
\(381\) −14.2913 + 24.7532i −0.732165 + 1.26815i
\(382\) 1.37055i 0.0701235i
\(383\) −3.39564 1.96048i −0.173509 0.100176i 0.410730 0.911757i \(-0.365274\pi\)
−0.584240 + 0.811581i \(0.698607\pi\)
\(384\) 19.8131 + 11.4391i 1.01108 + 0.583748i
\(385\) 0 0
\(386\) −13.5826 + 23.5257i −0.691335 + 1.19743i
\(387\) 0.456439 + 0.790576i 0.0232021 + 0.0401872i
\(388\) −36.8085 + 21.2514i −1.86867 + 1.07888i
\(389\) 36.3303 1.84202 0.921010 0.389540i \(-0.127366\pi\)
0.921010 + 0.389540i \(0.127366\pi\)
\(390\) −21.4564 + 22.2982i −1.08649 + 1.12911i
\(391\) 22.7477 1.15040
\(392\) 0 0
\(393\) −3.24773 5.62523i −0.163826 0.283755i
\(394\) −11.9782 + 20.7469i −0.603454 + 1.04521i
\(395\) 13.1334i 0.660813i
\(396\) −0.643371 0.371450i −0.0323306 0.0186661i
\(397\) 13.1216 + 7.57575i 0.658554 + 0.380216i 0.791726 0.610877i \(-0.209183\pi\)
−0.133172 + 0.991093i \(0.542516\pi\)
\(398\) 24.0779i 1.20692i
\(399\) 0 0
\(400\) 0.186932 + 0.323775i 0.00934659 + 0.0161888i
\(401\) −25.5998 + 14.7801i −1.27839 + 0.738081i −0.976553 0.215278i \(-0.930934\pi\)
−0.301841 + 0.953358i \(0.597601\pi\)
\(402\) 44.7042 2.22964
\(403\) 7.50000 30.3109i 0.373602 1.50989i
\(404\) −27.3303 −1.35973
\(405\) −18.1652 + 10.4877i −0.902634 + 0.521136i
\(406\) 0 0
\(407\) −4.41742 + 7.65120i −0.218964 + 0.379256i
\(408\) 9.30780i 0.460805i
\(409\) −0.313068 0.180750i −0.0154802 0.00893751i 0.492240 0.870460i \(-0.336178\pi\)
−0.507720 + 0.861522i \(0.669512\pi\)
\(410\) 10.5826 + 6.10985i 0.522636 + 0.301744i
\(411\) 30.7201i 1.51531i
\(412\) −6.39564 + 11.0776i −0.315091 + 0.545753i
\(413\) 0 0
\(414\) 3.00000 1.73205i 0.147442 0.0851257i
\(415\) 7.79129 0.382459
\(416\) 19.1869 + 18.4626i 0.940717 + 0.905205i
\(417\) 1.41742 0.0694116
\(418\) 15.8739 9.16478i 0.776416 0.448264i
\(419\) 12.8739 + 22.2982i 0.628929 + 1.08934i 0.987767 + 0.155938i \(0.0498399\pi\)
−0.358838 + 0.933400i \(0.616827\pi\)
\(420\) 0 0
\(421\) 20.0616i 0.977743i −0.872356 0.488872i \(-0.837409\pi\)
0.872356 0.488872i \(-0.162591\pi\)
\(422\) −2.68693 1.55130i −0.130798 0.0755161i
\(423\) −0.774053 0.446900i −0.0376358 0.0217290i
\(424\) 21.0707i 1.02328i
\(425\) −0.313068 + 0.542250i −0.0151860 + 0.0263030i
\(426\) −1.79129 3.10260i −0.0867882 0.150322i
\(427\) 0 0
\(428\) 27.3303 1.32106
\(429\) −5.93466 5.71063i −0.286528 0.275712i
\(430\) 20.9564 1.01061
\(431\) −13.5172 + 7.80418i −0.651102 + 0.375914i −0.788878 0.614549i \(-0.789338\pi\)
0.137776 + 0.990463i \(0.456005\pi\)
\(432\) 4.47822 + 7.75650i 0.215458 + 0.373185i
\(433\) 11.2477 19.4816i 0.540531 0.936228i −0.458342 0.888776i \(-0.651557\pi\)
0.998874 0.0474518i \(-0.0151101\pi\)
\(434\) 0 0
\(435\) −7.50000 4.33013i −0.359597 0.207614i
\(436\) −19.1869 11.0776i −0.918887 0.530520i
\(437\) 49.7925i 2.38190i
\(438\) −6.79129 + 11.7629i −0.324500 + 0.562051i
\(439\) 5.76951 + 9.99308i 0.275364 + 0.476944i 0.970227 0.242198i \(-0.0778684\pi\)
−0.694863 + 0.719142i \(0.744535\pi\)
\(440\) −4.18693 + 2.41733i −0.199604 + 0.115242i
\(441\) 0 0
\(442\) −5.68693 + 22.9835i −0.270500 + 1.09321i
\(443\) 3.16515 0.150381 0.0751904 0.997169i \(-0.476044\pi\)
0.0751904 + 0.997169i \(0.476044\pi\)
\(444\) 30.0000 17.3205i 1.42374 0.821995i
\(445\) −3.18693 5.51993i −0.151075 0.261670i
\(446\) −22.6652 + 39.2572i −1.07323 + 1.85888i
\(447\) 3.92095i 0.185455i
\(448\) 0 0
\(449\) −17.2087 9.93545i −0.812129 0.468883i 0.0355654 0.999367i \(-0.488677\pi\)
−0.847695 + 0.530484i \(0.822010\pi\)
\(450\) 0.0953502i 0.00449485i
\(451\) −1.62614 + 2.81655i −0.0765718 + 0.132626i
\(452\) 1.97822 + 3.42638i 0.0930476 + 0.161163i
\(453\) −18.8085 + 10.8591i −0.883701 + 0.510205i
\(454\) 26.9564 1.26513
\(455\) 0 0
\(456\) −20.3739 −0.954094
\(457\) −7.74773 + 4.47315i −0.362423 + 0.209245i −0.670143 0.742232i \(-0.733767\pi\)
0.307720 + 0.951477i \(0.400434\pi\)
\(458\) 7.58258 + 13.1334i 0.354310 + 0.613684i
\(459\) −7.50000 + 12.9904i −0.350070 + 0.606339i
\(460\) 46.3284i 2.16007i
\(461\) −15.4782 8.93635i −0.720893 0.416208i 0.0941885 0.995554i \(-0.469974\pi\)
−0.815081 + 0.579347i \(0.803308\pi\)
\(462\) 0 0
\(463\) 7.93725i 0.368875i 0.982844 + 0.184438i \(0.0590464\pi\)
−0.982844 + 0.184438i \(0.940954\pi\)
\(464\) −1.97822 + 3.42638i −0.0918365 + 0.159066i
\(465\) 16.9782 + 29.4071i 0.787346 + 1.36372i
\(466\) −13.1869 + 7.61348i −0.610873 + 0.352688i
\(467\) −11.8348 −0.547651 −0.273826 0.961779i \(-0.588289\pi\)
−0.273826 + 0.961779i \(0.588289\pi\)
\(468\) 0.582576 + 2.01810i 0.0269296 + 0.0932868i
\(469\) 0 0
\(470\) −17.7695 + 10.2592i −0.819646 + 0.473223i
\(471\) 19.6652 + 34.0610i 0.906122 + 1.56945i
\(472\) −7.66515 + 13.2764i −0.352817 + 0.611097i
\(473\) 5.57755i 0.256456i
\(474\) −20.3739 11.7629i −0.935803 0.540286i
\(475\) −1.18693 0.685275i −0.0544602 0.0314426i
\(476\) 0 0
\(477\) 1.26951 2.19885i 0.0581268 0.100678i
\(478\) 14.4782 + 25.0770i 0.662218 + 1.14700i
\(479\) −8.85208 + 5.11075i −0.404462 + 0.233516i −0.688407 0.725324i \(-0.741690\pi\)
0.283945 + 0.958840i \(0.408357\pi\)
\(480\) −28.9564 −1.32167
\(481\) 24.0000 6.92820i 1.09431 0.315899i
\(482\) −9.00000 −0.409939
\(483\) 0 0
\(484\) 13.0826 + 22.6597i 0.594663 + 1.02999i
\(485\) 16.6652 28.8649i 0.756726 1.31069i
\(486\) 4.73930i 0.214979i
\(487\) −8.93466 5.15843i −0.404868 0.233751i 0.283714 0.958909i \(-0.408433\pi\)
−0.688582 + 0.725158i \(0.741767\pi\)
\(488\) 19.1216 + 11.0399i 0.865594 + 0.499751i
\(489\) 12.4104i 0.561218i
\(490\) 0 0
\(491\) −18.5608 32.1482i −0.837637 1.45083i −0.891865 0.452301i \(-0.850603\pi\)
0.0542283 0.998529i \(-0.482730\pi\)
\(492\) 11.0436 6.37600i 0.497882 0.287452i
\(493\) −6.62614 −0.298426
\(494\) −50.3085 12.4481i −2.26349 0.560068i
\(495\) 0.582576 0.0261848
\(496\) 13.4347 7.75650i 0.603234 0.348277i
\(497\) 0 0
\(498\) 6.97822 12.0866i 0.312701 0.541615i
\(499\) 42.2168i 1.88988i −0.327240 0.944941i \(-0.606119\pi\)
0.327240 0.944941i \(-0.393881\pi\)
\(500\) 27.5608 + 15.9122i 1.23256 + 0.711617i
\(501\) 30.9737 + 17.8827i 1.38380 + 0.798938i
\(502\) 46.3284i 2.06774i
\(503\) −11.0608 + 19.1579i −0.493176 + 0.854207i −0.999969 0.00786127i \(-0.997498\pi\)
0.506793 + 0.862068i \(0.330831\pi\)
\(504\) 0 0
\(505\) 18.5608 10.7161i 0.825945 0.476859i
\(506\) 21.1652 0.940906
\(507\) 0.895644 + 23.2695i 0.0397769 + 1.03344i
\(508\) 44.5390 1.97610
\(509\) −19.0390 + 10.9922i −0.843890 + 0.487220i −0.858584 0.512672i \(-0.828656\pi\)
0.0146949 + 0.999892i \(0.495322\pi\)
\(510\) −12.8739 22.2982i −0.570064 0.987380i
\(511\) 0 0
\(512\) 19.4340i 0.858868i
\(513\) −28.4347 16.4168i −1.25542 0.724818i
\(514\) 52.9955 + 30.5969i 2.33753 + 1.34957i
\(515\) 10.0308i 0.442010i
\(516\) 10.9347 18.9394i 0.481372 0.833760i
\(517\) −2.73049 4.72935i −0.120087 0.207997i
\(518\) 0 0
\(519\) 13.8784 0.609195
\(520\) 13.2695 + 3.28335i 0.581906 + 0.143984i
\(521\) −25.5826 −1.12079 −0.560396 0.828224i \(-0.689351\pi\)
−0.560396 + 0.828224i \(0.689351\pi\)
\(522\) −0.873864 + 0.504525i −0.0382480 + 0.0220825i
\(523\) −6.16515 10.6784i −0.269583 0.466932i 0.699171 0.714954i \(-0.253553\pi\)
−0.968754 + 0.248023i \(0.920219\pi\)
\(524\) −5.06080 + 8.76555i −0.221082 + 0.382925i
\(525\) 0 0
\(526\) 51.8085 + 29.9117i 2.25896 + 1.30421i
\(527\) 22.5000 + 12.9904i 0.980115 + 0.565870i
\(528\) 4.09175i 0.178071i
\(529\) −17.2477 + 29.8739i −0.749901 + 1.29887i
\(530\) −29.1434 50.4778i −1.26591 2.19262i
\(531\) 1.59981 0.923651i 0.0694259 0.0400830i
\(532\) 0 0
\(533\) 8.83485 2.55040i 0.382680 0.110470i
\(534\) −11.4174 −0.494080
\(535\) −18.5608 + 10.7161i −0.802453 + 0.463297i
\(536\) −9.87386 17.1020i −0.426486 0.738695i
\(537\) −8.06080 + 13.9617i −0.347849 + 0.602492i
\(538\) 24.5348i 1.05777i
\(539\) 0 0
\(540\) 26.4564 + 15.2746i 1.13850 + 0.657316i
\(541\) 30.0924i 1.29377i −0.762586 0.646887i \(-0.776071\pi\)
0.762586 0.646887i \(-0.223929\pi\)
\(542\) 31.4347 54.4464i 1.35023 2.33867i
\(543\) 8.20871 + 14.2179i 0.352270 + 0.610149i
\(544\) −19.1869 + 11.0776i −0.822633 + 0.474947i
\(545\) 17.3739 0.744215
\(546\) 0 0
\(547\) 15.7477 0.673324 0.336662 0.941626i \(-0.390702\pi\)
0.336662 + 0.941626i \(0.390702\pi\)
\(548\) −41.4564 + 23.9349i −1.77093 + 1.02245i
\(549\) −1.33030 2.30415i −0.0567759 0.0983388i
\(550\) −0.291288 + 0.504525i −0.0124206 + 0.0215130i
\(551\) 14.5040i 0.617889i
\(552\) −20.3739 11.7629i −0.867169 0.500660i
\(553\) 0 0
\(554\) 34.4702i 1.46450i
\(555\) −13.5826 + 23.5257i −0.576548 + 0.998611i
\(556\) −1.10436 1.91280i −0.0468351 0.0811208i
\(557\) 24.0998 13.9140i 1.02114 0.589556i 0.106707 0.994290i \(-0.465969\pi\)
0.914434 + 0.404734i \(0.132636\pi\)
\(558\) 3.95644 0.167489
\(559\) 10.9347 11.3636i 0.462487 0.480630i
\(560\) 0 0
\(561\) 5.93466 3.42638i 0.250561 0.144662i
\(562\) 7.00000 + 12.1244i 0.295277 + 0.511435i
\(563\) −0.165151 + 0.286051i −0.00696030 + 0.0120556i −0.869485 0.493960i \(-0.835549\pi\)
0.862524 + 0.506016i \(0.168882\pi\)
\(564\) 21.4123i 0.901619i
\(565\) −2.68693 1.55130i −0.113040 0.0652637i
\(566\) −46.9129 27.0852i −1.97190 1.13847i
\(567\) 0 0
\(568\) −0.791288 + 1.37055i −0.0332017 + 0.0575070i
\(569\) 5.37386 + 9.30780i 0.225284 + 0.390203i 0.956405 0.292045i \(-0.0943356\pi\)
−0.731121 + 0.682248i \(0.761002\pi\)
\(570\) 48.8085 28.1796i 2.04436 1.18031i
\(571\) −24.9564 −1.04439 −0.522197 0.852825i \(-0.674888\pi\)
−0.522197 + 0.852825i \(0.674888\pi\)
\(572\) −3.08258 + 12.4581i −0.128889 + 0.520899i
\(573\) 1.12159 0.0468551
\(574\) 0 0
\(575\) −0.791288 1.37055i −0.0329990 0.0571559i
\(576\) −1.31307 + 2.27430i −0.0547112 + 0.0947625i
\(577\) 19.7756i 0.823267i 0.911349 + 0.411634i \(0.135042\pi\)
−0.911349 + 0.411634i \(0.864958\pi\)
\(578\) 15.1652 + 8.75560i 0.630787 + 0.364185i
\(579\) −19.2523 11.1153i −0.800097 0.461936i
\(580\) 13.4949i 0.560345i
\(581\) 0 0
\(582\) −29.8521 51.7053i −1.23741 2.14325i
\(583\) 13.4347 7.75650i 0.556407 0.321242i
\(584\) 6.00000 0.248282
\(585\) −1.18693 1.14213i −0.0490736 0.0472211i
\(586\) −17.1652 −0.709086
\(587\) −30.7259 + 17.7396i −1.26820 + 0.732193i −0.974646 0.223751i \(-0.928170\pi\)
−0.293549 + 0.955944i \(0.594836\pi\)
\(588\) 0 0
\(589\) −28.4347 + 49.2503i −1.17163 + 2.02932i
\(590\) 42.4075i 1.74589i
\(591\) −16.9782 9.80238i −0.698391 0.403216i
\(592\) 10.7477 + 6.20520i 0.441729 + 0.255032i
\(593\) 19.6048i 0.805071i 0.915404 + 0.402535i \(0.131871\pi\)
−0.915404 + 0.402535i \(0.868129\pi\)
\(594\) −6.97822 + 12.0866i −0.286320 + 0.495920i
\(595\) 0 0
\(596\) 5.29129 3.05493i 0.216740 0.125135i
\(597\) 19.7042 0.806438
\(598\) −43.1216 41.4938i −1.76337 1.69681i
\(599\) −20.3739 −0.832453 −0.416227 0.909261i \(-0.636648\pi\)
−0.416227 + 0.909261i \(0.636648\pi\)
\(600\) 0.560795 0.323775i 0.0228944 0.0132181i
\(601\) 0.686932 + 1.18980i 0.0280205 + 0.0485330i 0.879696 0.475537i \(-0.157746\pi\)
−0.851675 + 0.524070i \(0.824413\pi\)
\(602\) 0 0
\(603\) 2.37960i 0.0969049i
\(604\) 29.3085 + 16.9213i 1.19255 + 0.688517i
\(605\) −17.7695 10.2592i −0.722433 0.417097i
\(606\) 38.3912i 1.55953i
\(607\) 3.87386 6.70973i 0.157235 0.272339i −0.776635 0.629950i \(-0.783075\pi\)
0.933871 + 0.357611i \(0.116409\pi\)
\(608\) −24.2477 41.9983i −0.983375 1.70326i
\(609\) 0 0
\(610\) −61.0780 −2.47298
\(611\) −3.70871 + 14.9886i −0.150038 + 0.606373i
\(612\) −1.74773 −0.0706477
\(613\) 32.3085 18.6533i 1.30493 0.753401i 0.323684 0.946165i \(-0.395079\pi\)
0.981245 + 0.192764i \(0.0617453\pi\)
\(614\) −26.4564 45.8239i −1.06769 1.84930i
\(615\) −5.00000 + 8.66025i −0.201619 + 0.349215i
\(616\) 0 0
\(617\) −24.0826 13.9041i −0.969528 0.559757i −0.0704357 0.997516i \(-0.522439\pi\)
−0.899092 + 0.437759i \(0.855772\pi\)
\(618\) −15.5608 8.98403i −0.625947 0.361391i
\(619\) 12.4104i 0.498816i −0.968398 0.249408i \(-0.919764\pi\)
0.968398 0.249408i \(-0.0802361\pi\)
\(620\) 26.4564 45.8239i 1.06252 1.84033i
\(621\) −18.9564 32.8335i −0.760696 1.31756i
\(622\) 10.5000 6.06218i 0.421012 0.243071i
\(623\) 0 0
\(624\) −8.02178 + 8.33648i −0.321128 + 0.333726i
\(625\) −23.9129 −0.956515
\(626\) −39.3303 + 22.7074i −1.57196 + 0.907569i
\(627\) 7.50000 + 12.9904i 0.299521 + 0.518786i
\(628\) 30.6434 53.0759i 1.22280 2.11796i
\(629\) 20.7846i 0.828737i
\(630\) 0 0
\(631\) −10.4347 6.02445i −0.415397 0.239830i 0.277709 0.960665i \(-0.410425\pi\)
−0.693106 + 0.720836i \(0.743758\pi\)
\(632\) 10.3923i 0.413384i
\(633\) 1.26951 2.19885i 0.0504584 0.0873965i
\(634\) −20.2695 35.1078i −0.805005 1.39431i
\(635\) −30.2477 + 17.4635i −1.20034 + 0.693019i
\(636\) −60.8258 −2.41190
\(637\) 0 0
\(638\) −6.16515 −0.244081
\(639\) 0.165151 0.0953502i 0.00653329 0.00377200i
\(640\) 13.9782 + 24.2110i 0.552538 + 0.957023i
\(641\) −7.81307 + 13.5326i −0.308598 + 0.534507i −0.978056 0.208343i \(-0.933193\pi\)
0.669458 + 0.742850i \(0.266526\pi\)
\(642\) 38.3912i 1.51518i
\(643\) −11.7523 6.78518i −0.463464 0.267581i 0.250035 0.968237i \(-0.419558\pi\)
−0.713500 + 0.700655i \(0.752891\pi\)
\(644\) 0 0
\(645\) 17.1497i 0.675269i
\(646\) 21.5608 37.3444i 0.848298 1.46930i
\(647\) −14.5390 25.1823i −0.571588 0.990019i −0.996403 0.0847389i \(-0.972994\pi\)
0.424816 0.905280i \(-0.360339\pi\)
\(648\) 14.3739 8.29875i 0.564659 0.326006i
\(649\) 11.2867 0.443043
\(650\) 1.58258 0.456850i 0.0620737 0.0179191i
\(651\) 0 0
\(652\) 16.7477 9.66930i 0.655892 0.378679i
\(653\) −5.60436 9.70703i −0.219315 0.379865i 0.735283 0.677760i \(-0.237049\pi\)
−0.954599 + 0.297894i \(0.903716\pi\)
\(654\) 15.5608 26.9521i 0.608475 1.05391i
\(655\) 7.93725i 0.310134i
\(656\) 3.95644 + 2.28425i 0.154473 + 0.0891850i
\(657\) −0.626136 0.361500i −0.0244279 0.0141035i
\(658\) 0 0
\(659\) −3.00000 + 5.19615i −0.116863 + 0.202413i −0.918523 0.395367i \(-0.870617\pi\)
0.801660 + 0.597781i \(0.203951\pi\)
\(660\) −6.97822 12.0866i −0.271627 0.470471i
\(661\) 16.2523 9.38325i 0.632140 0.364966i −0.149440 0.988771i \(-0.547747\pi\)
0.781580 + 0.623804i \(0.214414\pi\)
\(662\) 2.37386 0.0922628
\(663\) −18.8085 4.65390i −0.730462 0.180743i
\(664\) −6.16515 −0.239254
\(665\) 0 0
\(666\) 1.58258 + 2.74110i 0.0613236 + 0.106216i
\(667\) 8.37386 14.5040i 0.324237 0.561595i
\(668\) 55.7316i 2.15632i
\(669\) −32.1261 18.5480i −1.24207 0.717108i
\(670\) 47.3085 + 27.3136i 1.82769 + 1.05522i
\(671\) 16.2559i 0.627552i
\(672\) 0 0
\(673\) 14.2477 + 24.6778i 0.549210 + 0.951259i 0.998329 + 0.0577870i \(0.0184044\pi\)
−0.449119 + 0.893472i \(0.648262\pi\)
\(674\) −24.5608 + 14.1802i −0.946046 + 0.546200i
\(675\) 1.04356 0.0401667
\(676\) 30.7042 19.3386i 1.18093 0.743793i
\(677\) 33.7913 1.29870 0.649352 0.760488i \(-0.275040\pi\)
0.649352 + 0.760488i \(0.275040\pi\)
\(678\) −4.81307 + 2.77883i −0.184845 + 0.106720i
\(679\) 0 0
\(680\) −5.68693 + 9.85005i −0.218084 + 0.377732i
\(681\) 22.0598i 0.845334i
\(682\) 20.9347 + 12.0866i 0.801630 + 0.462821i
\(683\) 21.7087 + 12.5335i 0.830661 + 0.479582i 0.854079 0.520144i \(-0.174122\pi\)
−0.0234181 + 0.999726i \(0.507455\pi\)
\(684\) 3.82560i 0.146276i
\(685\) 18.7695 32.5097i 0.717146 1.24213i
\(686\) 0 0
\(687\) −10.7477 + 6.20520i −0.410051 + 0.236743i
\(688\) 7.83485 0.298701
\(689\) −42.5780 10.5353i −1.62209 0.401364i
\(690\) 65.0780 2.47748
\(691\) −25.4347 + 14.6847i −0.967580 + 0.558633i −0.898498 0.438978i \(-0.855340\pi\)
−0.0690824 + 0.997611i \(0.522007\pi\)
\(692\) −10.8131 18.7288i −0.411051 0.711962i
\(693\) 0 0
\(694\) 9.66930i 0.367042i
\(695\) 1.50000 + 0.866025i 0.0568982 + 0.0328502i
\(696\) 5.93466 + 3.42638i 0.224953 + 0.129876i
\(697\) 7.65120i 0.289810i
\(698\) −11.6869 + 20.2424i −0.442357 + 0.766185i
\(699\) −6.23049 10.7915i −0.235659 0.408173i
\(700\) 0 0
\(701\) 31.9129 1.20533 0.602666 0.797993i \(-0.294105\pi\)
0.602666 + 0.797993i \(0.294105\pi\)
\(702\) 37.9129 10.9445i 1.43093 0.413074i
\(703\) −45.4955 −1.71589
\(704\) −13.8956 + 8.02265i −0.523712 + 0.302365i
\(705\) −8.39564 14.5417i −0.316198 0.547671i
\(706\) 29.3521 50.8393i 1.10468 1.91336i
\(707\) 0 0
\(708\) −38.3258 22.1274i −1.44037 0.831598i
\(709\) −6.31307 3.64485i −0.237092 0.136885i 0.376747 0.926316i \(-0.377043\pi\)
−0.613840 + 0.789431i \(0.710376\pi\)
\(710\) 4.37780i 0.164296i
\(711\) 0.626136 1.08450i 0.0234820 0.0406719i
\(712\) 2.52178 + 4.36785i 0.0945077 + 0.163692i
\(713\) −56.8693 + 32.8335i −2.12977 + 1.22962i
\(714\) 0 0
\(715\) −2.79129 9.66930i −0.104388 0.361611i
\(716\) 25.1216 0.938838
\(717\) −20.5218 + 11.8483i −0.766400 + 0.442481i
\(718\) −13.8739 24.0302i −0.517768 0.896800i
\(719\) 2.91742 5.05313i 0.108802 0.188450i −0.806483 0.591257i \(-0.798632\pi\)
0.915285 + 0.402807i \(0.131965\pi\)
\(720\) 0.818350i 0.0304981i
\(721\) 0 0
\(722\) 45.7259 + 26.3999i 1.70174 + 0.982502i
\(723\) 7.36515i 0.273913i
\(724\) 12.7913 22.1552i 0.475384 0.823390i
\(725\) 0.230493 + 0.399225i 0.00856028 + 0.0148268i
\(726\) −31.8303 + 18.3772i −1.18133 + 0.682043i
\(727\) 27.7477 1.02911 0.514553 0.857459i \(-0.327958\pi\)
0.514553 + 0.857459i \(0.327958\pi\)
\(728\) 0 0
\(729\) 24.8693 0.921086
\(730\) −14.3739 + 8.29875i −0.532001 + 0.307151i
\(731\) 6.56080 + 11.3636i 0.242660 + 0.420299i
\(732\) −31.8693 + 55.1993i −1.17792 + 2.04022i
\(733\) 9.02175i 0.333226i 0.986022 + 0.166613i \(0.0532831\pi\)
−0.986022 + 0.166613i \(0.946717\pi\)
\(734\) −34.1216 19.7001i −1.25945 0.727144i
\(735\) 0 0
\(736\) 55.9977i 2.06410i
\(737\) −7.26951 + 12.5912i −0.267776 + 0.463801i
\(738\) 0.582576 + 1.00905i 0.0214449 + 0.0371437i
\(739\) −10.7477 + 6.20520i −0.395362 + 0.228262i −0.684481 0.729031i \(-0.739971\pi\)
0.289119 + 0.957293i \(0.406638\pi\)
\(740\) 42.3303 1.55609
\(741\) 10.1869 41.1700i 0.374226 1.51242i
\(742\) 0 0
\(743\) 4.64792 2.68348i 0.170516 0.0984472i −0.412313 0.911042i \(-0.635279\pi\)
0.582829 + 0.812595i \(0.301946\pi\)
\(744\) −13.4347 23.2695i −0.492538 0.853102i
\(745\) −2.39564 + 4.14938i −0.0877696 + 0.152021i
\(746\) 80.5325i 2.94850i
\(747\) 0.643371 + 0.371450i 0.0235397 + 0.0135907i
\(748\) −9.24773 5.33918i −0.338130 0.195220i
\(749\) 0 0
\(750\) −22.3521 + 38.7149i −0.816183 + 1.41367i
\(751\) 1.87386 + 3.24563i 0.0683783 + 0.118435i 0.898188 0.439612i \(-0.144884\pi\)
−0.829809 + 0.558047i \(0.811551\pi\)
\(752\) −6.64337 + 3.83555i −0.242259 + 0.139868i
\(753\) −37.9129 −1.38162
\(754\) 12.5608 + 12.0866i 0.457437 + 0.440169i
\(755\) −26.5390 −0.965854
\(756\) 0 0
\(757\) −3.00000 5.19615i −0.109037 0.188857i 0.806343 0.591448i \(-0.201443\pi\)
−0.915380 + 0.402590i \(0.868110\pi\)
\(758\) −4.97822 + 8.62253i −0.180817 + 0.313184i
\(759\) 17.3205i 0.628695i
\(760\) −21.5608 12.4481i −0.782092 0.451541i
\(761\) 27.7259 + 16.0076i 1.00506 + 0.580274i 0.909743 0.415172i \(-0.136279\pi\)
0.0953219 + 0.995447i \(0.469612\pi\)
\(762\) 62.5644i 2.26647i
\(763\) 0 0
\(764\) −0.873864 1.51358i −0.0316153 0.0547593i
\(765\) 1.18693 0.685275i 0.0429136 0.0247762i
\(766\) −8.58258 −0.310101
\(767\) −22.9955 22.1274i −0.830318 0.798974i
\(768\) 5.00000 0.180422
\(769\) 21.8739 12.6289i 0.788792 0.455409i −0.0507453 0.998712i \(-0.516160\pi\)
0.839537 + 0.543303i \(0.182826\pi\)
\(770\) 0 0
\(771\) −25.0390 + 43.3688i −0.901758 + 1.56189i
\(772\) 34.6410i 1.24676i
\(773\) 19.8303 + 11.4490i 0.713246 + 0.411793i 0.812262 0.583293i \(-0.198236\pi\)
−0.0990155 + 0.995086i \(0.531569\pi\)
\(774\) 1.73049 + 0.999100i 0.0622013 + 0.0359119i
\(775\) 1.80750i 0.0649273i
\(776\) −13.1869 + 22.8404i −0.473383 + 0.819924i
\(777\) 0 0
\(778\)