Properties

Label 637.2.k.d.569.2
Level $637$
Weight $2$
Character 637.569
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.k (of order \(6\), degree \(2\), not 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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 569.2
Root \(-0.895644 + 1.09445i\) of defining polynomial
Character \(\chi\) \(=\) 637.569
Dual form 637.2.k.d.459.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.18890i q^{2} +(0.895644 - 1.55130i) q^{3} -2.79129 q^{4} +(-1.89564 - 1.09445i) q^{5} +(3.39564 + 1.96048i) q^{6} -1.73205i q^{8} +(-0.104356 - 0.180750i) q^{9} +O(q^{10})\) \(q+2.18890i q^{2} +(0.895644 - 1.55130i) q^{3} -2.79129 q^{4} +(-1.89564 - 1.09445i) 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} +(-2.50000 + 4.33013i) q^{12} +(3.50000 + 0.866025i) q^{13} +(-3.39564 + 1.96048i) q^{15} -1.79129 q^{16} +3.00000 q^{17} +(0.395644 - 0.228425i) q^{18} +(5.68693 - 3.28335i) q^{19} +(5.29129 + 3.05493i) q^{20} +(-1.39564 + 2.41733i) q^{22} +7.58258 q^{23} +(-2.68693 - 1.55130i) q^{24} +(-0.104356 - 0.180750i) q^{25} +(-1.89564 + 7.66115i) q^{26} +5.00000 q^{27} +(1.10436 + 1.91280i) q^{29} +(-4.29129 - 7.43273i) q^{30} +(-7.50000 + 4.33013i) q^{31} -7.38505i q^{32} +(1.97822 - 1.14213i) q^{33} +6.56670i q^{34} +(0.291288 + 0.504525i) q^{36} +6.92820i q^{37} +(7.18693 + 12.4481i) q^{38} +(4.47822 - 4.65390i) q^{39} +(-1.89564 + 3.28335i) q^{40} +(2.20871 - 1.27520i) q^{41} +(2.18693 - 3.78788i) q^{43} +(-3.08258 - 1.77973i) q^{44} +0.456850i q^{45} +16.5975i q^{46} +(-3.70871 - 2.14123i) q^{47} +(-1.60436 + 2.77883i) q^{48} +(0.395644 - 0.228425i) q^{50} +(2.68693 - 4.65390i) q^{51} +(-9.76951 - 2.41733i) q^{52} +(6.08258 + 10.5353i) q^{53} +10.9445i q^{54} +(-1.39564 - 2.41733i) q^{55} -11.7629i q^{57} +(-4.18693 + 2.41733i) q^{58} +8.85095i q^{59} +(9.47822 - 5.47225i) q^{60} +(-6.37386 - 11.0399i) q^{61} +(-9.47822 - 16.4168i) q^{62} +12.5826 q^{64} +(-5.68693 - 5.47225i) q^{65} +(2.50000 + 4.33013i) q^{66} +(-9.87386 - 5.70068i) q^{67} -8.37386 q^{68} +(6.79129 - 11.7629i) q^{69} +(-0.791288 - 0.456850i) q^{71} +(-0.313068 + 0.180750i) q^{72} +(3.00000 - 1.73205i) q^{73} -15.1652 q^{74} -0.373864 q^{75} +(-15.8739 + 9.16478i) q^{76} +(10.1869 + 9.80238i) q^{78} +(3.00000 - 5.19615i) 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} +(8.29129 + 4.78698i) q^{86} +3.95644 q^{87} +(1.10436 - 1.91280i) q^{88} -2.91190i q^{89} -1.00000 q^{90} -21.1652 q^{92} +15.5130i q^{93} +(4.68693 - 8.11800i) q^{94} -14.3739 q^{95} +(-11.4564 - 6.61438i) q^{96} +(-13.1869 - 7.61348i) q^{97} -0.266150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{3} - 2 q^{4} - 3 q^{5} + 9 q^{6} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{3} - 2 q^{4} - 3 q^{5} + 9 q^{6} - 5 q^{9} + 5 q^{10} + 9 q^{11} - 10 q^{12} + 14 q^{13} - 9 q^{15} + 2 q^{16} + 12 q^{17} - 3 q^{18} + 9 q^{19} + 12 q^{20} - q^{22} + 12 q^{23} + 3 q^{24} - 5 q^{25} - 3 q^{26} + 20 q^{27} + 9 q^{29} - 8 q^{30} - 30 q^{31} - 15 q^{33} - 8 q^{36} + 15 q^{38} - 5 q^{39} - 3 q^{40} + 18 q^{41} - 5 q^{43} + 6 q^{44} - 24 q^{47} - 11 q^{48} - 3 q^{50} - 3 q^{51} - 7 q^{52} + 6 q^{53} - q^{55} - 3 q^{58} + 15 q^{60} + 2 q^{61} - 15 q^{62} + 32 q^{64} - 9 q^{65} + 10 q^{66} - 12 q^{67} - 6 q^{68} + 18 q^{69} + 6 q^{71} - 15 q^{72} + 12 q^{73} - 24 q^{74} + 26 q^{75} - 36 q^{76} + 27 q^{78} + 12 q^{79} + 9 q^{80} + 10 q^{81} + 2 q^{82} - 9 q^{85} + 24 q^{86} - 30 q^{87} + 9 q^{88} - 4 q^{90} - 48 q^{92} + 5 q^{94} - 30 q^{95} - 39 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.18890i 1.54779i 0.633316 + 0.773893i \(0.281693\pi\)
−0.633316 + 0.773893i \(0.718307\pi\)
\(3\) 0.895644 1.55130i 0.517100 0.895644i −0.482703 0.875784i \(-0.660345\pi\)
0.999803 0.0198595i \(-0.00632191\pi\)
\(4\) −2.79129 −1.39564
\(5\) −1.89564 1.09445i −0.847758 0.489453i 0.0121359 0.999926i \(-0.496137\pi\)
−0.859894 + 0.510473i \(0.829470\pi\)
\(6\) 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 \(-0.271757\pi\)
−0.324186 + 0.945993i \(0.605090\pi\)
\(12\) −2.50000 + 4.33013i −0.721688 + 1.25000i
\(13\) 3.50000 + 0.866025i 0.970725 + 0.240192i
\(14\) 0 0
\(15\) −3.39564 + 1.96048i −0.876751 + 0.506193i
\(16\) −1.79129 −0.447822
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 0.395644 0.228425i 0.0932542 0.0538403i
\(19\) 5.68693 3.28335i 1.30467 0.753253i 0.323470 0.946238i \(-0.395150\pi\)
0.981202 + 0.192986i \(0.0618172\pi\)
\(20\) 5.29129 + 3.05493i 1.18317 + 0.683102i
\(21\) 0 0
\(22\) −1.39564 + 2.41733i −0.297552 + 0.515376i
\(23\) 7.58258 1.58108 0.790538 0.612413i \(-0.209801\pi\)
0.790538 + 0.612413i \(0.209801\pi\)
\(24\) −2.68693 1.55130i −0.548468 0.316658i
\(25\) −0.104356 0.180750i −0.0208712 0.0361500i
\(26\) −1.89564 + 7.66115i −0.371766 + 1.50248i
\(27\) 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
\(31\) −7.50000 + 4.33013i −1.34704 + 0.777714i −0.987829 0.155543i \(-0.950287\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 7.38505i 1.30551i
\(33\) 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
\(37\) 6.92820i 1.13899i 0.821995 + 0.569495i \(0.192861\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 7.18693 + 12.4481i 1.16587 + 2.01935i
\(39\) 4.47822 4.65390i 0.717089 0.745221i
\(40\) −1.89564 + 3.28335i −0.299728 + 0.519143i
\(41\) 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 \(0.0584356\pi\)
\(44\) −3.08258 1.77973i −0.464716 0.268304i
\(45\) 0.456850i 0.0681032i
\(46\) 16.5975i 2.44717i
\(47\) −3.70871 2.14123i −0.540971 0.312330i 0.204501 0.978866i \(-0.434443\pi\)
−0.745472 + 0.666536i \(0.767776\pi\)
\(48\) −1.60436 + 2.77883i −0.231569 + 0.401089i
\(49\) 0 0
\(50\) 0.395644 0.228425i 0.0559525 0.0323042i
\(51\) 2.68693 4.65390i 0.376246 0.651677i
\(52\) −9.76951 2.41733i −1.35479 0.335223i
\(53\) 6.08258 + 10.5353i 0.835506 + 1.44714i 0.893618 + 0.448829i \(0.148159\pi\)
−0.0581117 + 0.998310i \(0.518508\pi\)
\(54\) 10.9445i 1.48936i
\(55\) −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
\(59\) 8.85095i 1.15230i 0.817345 + 0.576148i \(0.195445\pi\)
−0.817345 + 0.576148i \(0.804555\pi\)
\(60\) 9.47822 5.47225i 1.22363 0.706465i
\(61\) −6.37386 11.0399i −0.816090 1.41351i −0.908543 0.417792i \(-0.862804\pi\)
0.0924533 0.995717i \(-0.470529\pi\)
\(62\) −9.47822 16.4168i −1.20374 2.08493i
\(63\) 0 0
\(64\) 12.5826 1.57282
\(65\) −5.68693 5.47225i −0.705377 0.678749i
\(66\) 2.50000 + 4.33013i 0.307729 + 0.533002i
\(67\) −9.87386 5.70068i −1.20628 0.696449i −0.244339 0.969690i \(-0.578571\pi\)
−0.961946 + 0.273241i \(0.911904\pi\)
\(68\) −8.37386 −1.01548
\(69\) 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
\(73\) 3.00000 1.73205i 0.351123 0.202721i −0.314057 0.949404i \(-0.601688\pi\)
0.665180 + 0.746683i \(0.268355\pi\)
\(74\) −15.1652 −1.76291
\(75\) −0.373864 −0.0431700
\(76\) −15.8739 + 9.16478i −1.82086 + 1.05127i
\(77\) 0 0
\(78\) 10.1869 + 9.80238i 1.15344 + 1.10990i
\(79\) 3.00000 5.19615i 0.337526 0.584613i −0.646440 0.762964i \(-0.723743\pi\)
0.983967 + 0.178352i \(0.0570765\pi\)
\(80\) 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
\(86\) 8.29129 + 4.78698i 0.894073 + 0.516193i
\(87\) 3.95644 0.424175
\(88\) 1.10436 1.91280i 0.117725 0.203905i
\(89\) 2.91190i 0.308661i −0.988019 0.154330i \(-0.950678\pi\)
0.988019 0.154330i \(-0.0493220\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) −21.1652 −2.20662
\(93\) 15.5130i 1.60862i
\(94\) 4.68693 8.11800i 0.483420 0.837308i
\(95\) −14.3739 −1.47473
\(96\) −11.4564 6.61438i −1.16927 0.675077i
\(97\) −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 −0.999891 0.0147923i \(-0.995291\pi\)
0.512756 + 0.858534i \(0.328625\pi\)
\(102\) 10.1869 + 5.88143i 1.00866 + 0.582348i
\(103\) 2.29129 3.96863i 0.225767 0.391040i −0.730782 0.682611i \(-0.760844\pi\)
0.956549 + 0.291570i \(0.0941778\pi\)
\(104\) 1.50000 6.06218i 0.147087 0.594445i
\(105\) 0 0
\(106\) −23.0608 + 13.3142i −2.23986 + 1.29319i
\(107\) −9.79129 −0.946560 −0.473280 0.880912i \(-0.656930\pi\)
−0.473280 + 0.880912i \(0.656930\pi\)
\(108\) −13.9564 −1.34296
\(109\) −6.87386 + 3.96863i −0.658397 + 0.380126i −0.791666 0.610954i \(-0.790786\pi\)
0.133269 + 0.991080i \(0.457453\pi\)
\(110\) 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 \(0.187904\pi\)
\(114\) 25.7477 2.41150
\(115\) −14.3739 8.29875i −1.34037 0.773863i
\(116\) −3.08258 5.33918i −0.286210 0.495730i
\(117\) −0.208712 0.723000i −0.0192954 0.0668414i
\(118\) −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
\(122\) 24.1652 13.9518i 2.18781 1.26313i
\(123\) 4.56850i 0.411928i
\(124\) 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 \(0.582952\pi\)
\(128\) 12.7719i 1.12889i
\(129\) −3.91742 6.78518i −0.344910 0.597402i
\(130\) 11.9782 12.4481i 1.05056 1.09177i
\(131\) 1.81307 3.14033i 0.158409 0.274372i −0.775886 0.630873i \(-0.782697\pi\)
0.934295 + 0.356501i \(0.116030\pi\)
\(132\) −5.52178 + 3.18800i −0.480609 + 0.277480i
\(133\) 0 0
\(134\) 12.4782 21.6129i 1.07795 1.86707i
\(135\) −9.47822 5.47225i −0.815755 0.470977i
\(136\) 5.19615i 0.445566i
\(137\) 17.1497i 1.46520i 0.680660 + 0.732599i \(0.261693\pi\)
−0.680660 + 0.732599i \(0.738307\pi\)
\(138\) 25.7477 + 14.8655i 2.19179 + 1.26543i
\(139\) 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
\(142\) 1.00000 1.73205i 0.0839181 0.145350i
\(143\) 3.31307 + 3.18800i 0.277053 + 0.266594i
\(144\) 0.186932 + 0.323775i 0.0155776 + 0.0269813i
\(145\) 4.83465i 0.401496i
\(146\) 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 \(-0.695245\pi\)
0.420338 + 0.907368i \(0.361912\pi\)
\(150\) 0.818350i 0.0668180i
\(151\) 10.5000 6.06218i 0.854478 0.493333i −0.00768132 0.999970i \(-0.502445\pi\)
0.862159 + 0.506637i \(0.169112\pi\)
\(152\) −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
\(156\) −12.5000 + 12.9904i −1.00080 + 1.04006i
\(157\) −10.9782 19.0148i −0.876157 1.51755i −0.855525 0.517762i \(-0.826765\pi\)
−0.0206325 0.999787i \(-0.506568\pi\)
\(158\) 11.3739 + 6.56670i 0.904856 + 0.522419i
\(159\) 21.7913 1.72816
\(160\) −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 \(-0.754130\pi\)
0.246265 + 0.969202i \(0.420797\pi\)
\(164\) −6.16515 + 3.55945i −0.481417 + 0.277946i
\(165\) −5.00000 −0.389249
\(166\) 7.79129 0.604721
\(167\) 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
\(170\) 7.18693 12.4481i 0.551213 0.954728i
\(171\) −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 0.974874 0.222756i \(-0.0715054\pi\)
−0.680350 + 0.732888i \(0.738172\pi\)
\(174\) 8.66025i 0.656532i
\(175\) 0 0
\(176\) −1.97822 1.14213i −0.149114 0.0860910i
\(177\) 13.7305 + 7.92730i 1.03205 + 0.595853i
\(178\) 6.37386 0.477741
\(179\) 4.50000 7.79423i 0.336346 0.582568i −0.647397 0.762153i \(-0.724142\pi\)
0.983742 + 0.179585i \(0.0574756\pi\)
\(180\) 1.27520i 0.0950478i
\(181\) 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
\(184\) 13.1334i 0.968208i
\(185\) 7.58258 13.1334i 0.557482 0.965587i
\(186\) −33.9564 −2.48981
\(187\) 3.31307 + 1.91280i 0.242276 + 0.139878i
\(188\) 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 0.877130 0.480254i \(-0.159455\pi\)
−0.854477 + 0.519490i \(0.826122\pi\)
\(192\) 11.2695 19.5194i 0.813307 1.40869i
\(193\) 10.7477 + 6.20520i 0.773638 + 0.446660i 0.834171 0.551506i \(-0.185947\pi\)
−0.0605327 + 0.998166i \(0.519280\pi\)
\(194\) 16.6652 28.8649i 1.19649 2.07238i
\(195\) −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 \(0.460817\pi\)
\(198\) 0.582576 0.0414019
\(199\) −11.0000 −0.779769 −0.389885 0.920864i \(-0.627485\pi\)
−0.389885 + 0.920864i \(0.627485\pi\)
\(200\) −0.313068 + 0.180750i −0.0221373 + 0.0127810i
\(201\) −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
\(205\) −5.58258 −0.389904
\(206\) 8.68693 + 5.01540i 0.605247 + 0.349440i
\(207\) −0.791288 1.37055i −0.0549983 0.0952599i
\(208\) −6.26951 1.55130i −0.434712 0.107563i
\(209\) 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
\(213\) −1.41742 + 0.818350i −0.0971203 + 0.0560724i
\(214\) 21.4322i 1.46507i
\(215\) −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
\(219\) 6.20520i 0.419309i
\(220\) 3.89564 + 6.74745i 0.262644 + 0.454913i
\(221\) 10.5000 + 2.59808i 0.706306 + 0.174766i
\(222\) −13.5826 + 23.5257i −0.911603 + 1.57894i
\(223\) −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
\(226\) −2.68693 1.55130i −0.178732 0.103191i
\(227\) 12.3151i 0.817379i −0.912673 0.408689i \(-0.865986\pi\)
0.912673 0.408689i \(-0.134014\pi\)
\(228\) 32.8335i 2.17445i
\(229\) −6.00000 3.46410i −0.396491 0.228914i 0.288478 0.957487i \(-0.406851\pi\)
−0.684969 + 0.728572i \(0.740184\pi\)
\(230\) 18.1652 31.4630i 1.19777 2.07461i
\(231\) 0 0
\(232\) 3.31307 1.91280i 0.217514 0.125582i
\(233\) 3.47822 6.02445i 0.227866 0.394675i −0.729310 0.684184i \(-0.760159\pi\)
0.957175 + 0.289509i \(0.0934919\pi\)
\(234\) 1.58258 0.456850i 0.103456 0.0298652i
\(235\) 4.68693 + 8.11800i 0.305742 + 0.529560i
\(236\) 24.7056i 1.60820i
\(237\) −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
\(241\) 4.11165i 0.264855i 0.991193 + 0.132427i \(0.0422771\pi\)
−0.991193 + 0.132427i \(0.957723\pi\)
\(242\) 17.7695 10.2592i 1.14227 0.659488i
\(243\) −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
\(247\) 22.7477 6.56670i 1.44740 0.417829i
\(248\) 7.50000 + 12.9904i 0.476250 + 0.824890i
\(249\) −5.52178 3.18800i −0.349929 0.202031i
\(250\) −24.9564 −1.57838
\(251\) −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
\(255\) −10.1869 + 5.88143i −0.637930 + 0.368309i
\(256\) −2.79129 −0.174455
\(257\) −27.9564 −1.74387 −0.871937 0.489617i \(-0.837136\pi\)
−0.871937 + 0.489617i \(0.837136\pi\)
\(258\) 14.8521 8.57485i 0.924650 0.533847i
\(259\) 0 0
\(260\) 15.8739 + 15.2746i 0.984455 + 0.947292i
\(261\) 0.230493 0.399225i 0.0142671 0.0247114i
\(262\) 6.87386 + 3.96863i 0.424669 + 0.245183i
\(263\) 13.6652 23.6687i 0.842629 1.45948i −0.0450348 0.998985i \(-0.514340\pi\)
0.887664 0.460491i \(-0.152327\pi\)
\(264\) −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
\(268\) 27.5608 + 15.9122i 1.68354 + 0.971994i
\(269\) 11.2087 0.683407 0.341704 0.939808i \(-0.388996\pi\)
0.341704 + 0.939808i \(0.388996\pi\)
\(270\) 11.9782 20.7469i 0.728971 1.26262i
\(271\) 28.7219i 1.74473i 0.488856 + 0.872364i \(0.337414\pi\)
−0.488856 + 0.872364i \(0.662586\pi\)
\(272\) −5.37386 −0.325838
\(273\) 0 0
\(274\) −37.5390 −2.26781
\(275\) 0.266150i 0.0160494i
\(276\) −18.9564 + 32.8335i −1.14104 + 1.97635i
\(277\) −15.7477 −0.946189 −0.473095 0.881012i \(-0.656863\pi\)
−0.473095 + 0.881012i \(0.656863\pi\)
\(278\) 1.50000 + 0.866025i 0.0899640 + 0.0519408i
\(279\) 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 0.218932 + 0.975740i \(0.429743\pi\)
−0.954482 + 0.298270i \(0.903591\pi\)
\(284\) 2.20871 + 1.27520i 0.131063 + 0.0756692i
\(285\) −12.8739 + 22.2982i −0.762582 + 1.32083i
\(286\) −6.97822 + 7.25198i −0.412631 + 0.428818i
\(287\) 0 0
\(288\) −1.33485 + 0.770675i −0.0786567 + 0.0454125i
\(289\) −8.00000 −0.470588
\(290\) 10.5826 0.621430
\(291\) −23.6216 + 13.6379i −1.38472 + 0.799470i
\(292\) −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
\(296\) 12.0000 0.697486
\(297\) 5.52178 + 3.18800i 0.320406 + 0.184987i
\(298\) −2.39564 4.14938i −0.138776 0.240367i
\(299\) 26.5390 + 6.56670i 1.53479 + 0.379762i
\(300\) 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
\(304\) −10.1869 + 5.88143i −0.584261 + 0.337323i
\(305\) 27.9035i 1.59775i
\(306\) 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
\(310\) 41.4938i 2.35669i
\(311\) −2.76951 4.79693i −0.157044 0.272009i 0.776757 0.629800i \(-0.216863\pi\)
−0.933802 + 0.357791i \(0.883530\pi\)
\(312\) −8.06080 7.75650i −0.456353 0.439126i
\(313\) 10.3739 17.9681i 0.586365 1.01561i −0.408338 0.912831i \(-0.633892\pi\)
0.994704 0.102784i \(-0.0327751\pi\)
\(314\) 41.6216 24.0302i 2.34884 1.35610i
\(315\) 0 0
\(316\) −8.37386 + 14.5040i −0.471067 + 0.815911i
\(317\) 16.0390 + 9.26013i 0.900841 + 0.520101i 0.877473 0.479626i \(-0.159228\pi\)
0.0233679 + 0.999727i \(0.492561\pi\)
\(318\) 47.6990i 2.67483i
\(319\) 2.81655i 0.157697i
\(320\) −23.8521 13.7710i −1.33337 0.769823i
\(321\) −8.76951 + 15.1892i −0.489466 + 0.847780i
\(322\) 0 0
\(323\) 17.0608 9.85005i 0.949288 0.548072i
\(324\) −13.3739 + 23.1642i −0.742992 + 1.28690i
\(325\) −0.208712 0.723000i −0.0115773 0.0401048i
\(326\) −7.58258 13.1334i −0.419960 0.727392i
\(327\) 14.2179i 0.786252i
\(328\) −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 \(-0.676155\pi\)
0.473966 + 0.880543i \(0.342822\pi\)
\(332\) 9.93545i 0.545279i
\(333\) 1.25227 0.723000i 0.0686241 0.0396202i
\(334\) 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 \(0.614801\pi\)
\(338\) −13.2695 + 25.1724i −0.721766 + 1.36920i
\(339\) 1.26951 + 2.19885i 0.0689502 + 0.119425i
\(340\) 15.8739 + 9.16478i 0.860881 + 0.497030i
\(341\) −11.0436 −0.598042
\(342\) 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
\(346\) −14.6869 + 8.47950i −0.789574 + 0.455861i
\(347\) −4.41742 −0.237140 −0.118570 0.992946i \(-0.537831\pi\)
−0.118570 + 0.992946i \(0.537831\pi\)
\(348\) −11.0436 −0.591997
\(349\) −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
\(352\) 4.70871 8.15573i 0.250975 0.434702i
\(353\) −23.2259 13.4095i −1.23619 0.713716i −0.267879 0.963453i \(-0.586323\pi\)
−0.968314 + 0.249737i \(0.919656\pi\)
\(354\) −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
\(359\) 10.9782 + 6.33828i 0.579408 + 0.334522i 0.760898 0.648871i \(-0.224759\pi\)
−0.181490 + 0.983393i \(0.558092\pi\)
\(360\) 0.791288 0.0417045
\(361\) 12.0608 20.8899i 0.634779 1.09947i
\(362\) 20.0616i 1.05441i
\(363\) −16.7913 −0.881314
\(364\) 0 0
\(365\) −7.58258 −0.396890
\(366\) 49.9832i 2.61266i
\(367\) −9.00000 + 15.5885i −0.469796 + 0.813711i −0.999404 0.0345320i \(-0.989006\pi\)
0.529607 + 0.848243i \(0.322339\pi\)
\(368\) −13.5826 −0.708041
\(369\) −0.460985 0.266150i −0.0239979 0.0138552i
\(370\) 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 −0.740009 0.672596i \(-0.765179\pi\)
−0.212481 0.977165i \(-0.568154\pi\)
\(374\) −4.18693 + 7.25198i −0.216501 + 0.374991i
\(375\) 17.6869 + 10.2116i 0.913349 + 0.527322i
\(376\) −3.70871 + 6.42368i −0.191262 + 0.331276i
\(377\) 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 \(0.370604\pi\)
\(380\) 40.1216 2.05819
\(381\) 28.5826 1.46433
\(382\) −1.18693 + 0.685275i −0.0607287 + 0.0350617i
\(383\) 3.39564 1.96048i 0.173509 0.100176i −0.410730 0.911757i \(-0.634726\pi\)
0.584240 + 0.811581i \(0.301393\pi\)
\(384\) 19.8131 + 11.4391i 1.01108 + 0.583748i
\(385\) 0 0
\(386\) −13.5826 + 23.5257i −0.691335 + 1.19743i
\(387\) −0.912878 −0.0464042
\(388\) 36.8085 + 21.2514i 1.86867 + 1.07888i
\(389\) −18.1652 31.4630i −0.921010 1.59524i −0.797856 0.602848i \(-0.794033\pi\)
−0.123154 0.992388i \(-0.539301\pi\)
\(390\) −8.58258 29.7309i −0.434596 1.50548i
\(391\) 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
\(395\) −11.3739 + 6.56670i −0.572281 + 0.330407i
\(396\) 0.742901i 0.0373322i
\(397\) −13.1216 + 7.57575i −0.658554 + 0.380216i −0.791726 0.610877i \(-0.790817\pi\)
0.133172 + 0.991093i \(0.457484\pi\)
\(398\) 24.0779i 1.20692i
\(399\) 0 0
\(400\) 0.186932 + 0.323775i 0.00934659 + 0.0161888i
\(401\) 29.5601i 1.47616i −0.674712 0.738081i \(-0.735732\pi\)
0.674712 0.738081i \(-0.264268\pi\)
\(402\) −22.3521 38.7149i −1.11482 1.93093i
\(403\) −30.0000 + 8.66025i −1.49441 + 0.431398i
\(404\) 13.6652 23.6687i 0.679867 1.17756i
\(405\) −18.1652 + 10.4877i −0.902634 + 0.521136i
\(406\) 0 0
\(407\) −4.41742 + 7.65120i −0.218964 + 0.379256i
\(408\) −8.06080 4.65390i −0.399069 0.230402i
\(409\) 0.361500i 0.0178750i 0.999960 + 0.00893751i \(0.00284494\pi\)
−0.999960 + 0.00893751i \(0.997155\pi\)
\(410\) 12.2197i 0.603488i
\(411\) 26.6044 + 15.3600i 1.31230 + 0.757655i
\(412\) −6.39564 + 11.0776i −0.315091 + 0.545753i
\(413\) 0 0
\(414\) 3.00000 1.73205i 0.147442 0.0851257i
\(415\) −3.89564 + 6.74745i −0.191230 + 0.331219i
\(416\) 6.39564 25.8477i 0.313572 1.26729i
\(417\) −0.708712 1.22753i −0.0347058 0.0601122i
\(418\) 18.3296i 0.896528i
\(419\) 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
\(423\) 0.893800i 0.0434580i
\(424\) 18.2477 10.5353i 0.886188 0.511641i
\(425\) −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
\(429\) 7.91288 2.28425i 0.382037 0.110285i
\(430\) −10.4782 18.1488i −0.505305 0.875213i
\(431\) 13.5172 + 7.80418i 0.651102 + 0.375914i 0.788878 0.614549i \(-0.210662\pi\)
−0.137776 + 0.990463i \(0.543995\pi\)
\(432\) −8.95644 −0.430917
\(433\) 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
\(437\) 43.1216 24.8963i 2.06279 1.19095i
\(438\) 13.5826 0.649001
\(439\) −11.5390 −0.550727 −0.275364 0.961340i \(-0.588798\pi\)
−0.275364 + 0.961340i \(0.588798\pi\)
\(440\) −4.18693 + 2.41733i −0.199604 + 0.115242i
\(441\) 0 0
\(442\) −5.68693 + 22.9835i −0.270500 + 1.09321i
\(443\) −1.58258 + 2.74110i −0.0751904 + 0.130234i −0.901169 0.433468i \(-0.857290\pi\)
0.825979 + 0.563701i \(0.190623\pi\)
\(444\) −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 \(0.822010\pi\)
\(450\) −0.0825757 0.0476751i −0.00389266 0.00224743i
\(451\) 3.25227 0.153144
\(452\) 1.97822 3.42638i 0.0930476 0.161163i
\(453\) 21.7182i 1.02041i
\(454\) 26.9564 1.26513
\(455\) 0 0
\(456\) −20.3739 −0.954094
\(457\) 8.94630i 0.418490i −0.977863 0.209245i \(-0.932899\pi\)
0.977863 0.209245i \(-0.0671007\pi\)
\(458\) 7.58258 13.1334i 0.354310 0.613684i
\(459\) 15.0000 0.700140
\(460\) 40.1216 + 23.1642i 1.87068 + 1.08004i
\(461\) −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
\(467\) 5.91742 10.2493i 0.273826 0.474280i −0.696012 0.718030i \(-0.745044\pi\)
0.969838 + 0.243750i \(0.0783775\pi\)
\(468\) 0.582576 + 2.01810i 0.0269296 + 0.0932868i
\(469\) 0 0
\(470\) −17.7695 + 10.2592i −0.819646 + 0.473223i
\(471\) −39.3303 −1.81224
\(472\) 15.3303 0.705634
\(473\) 4.83030 2.78878i 0.222098 0.128228i
\(474\) 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
\(478\) −28.9564 −1.32444
\(479\) 8.85208 + 5.11075i 0.404462 + 0.233516i 0.688407 0.725324i \(-0.258310\pi\)
−0.283945 + 0.958840i \(0.591643\pi\)
\(480\) 14.4782 + 25.0770i 0.660837 + 1.14460i
\(481\) −6.00000 + 24.2487i −0.273576 + 1.10565i
\(482\) −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
\(486\) 4.10436 2.36965i 0.186177 0.107490i
\(487\) 10.3169i 0.467501i 0.972297 + 0.233751i \(0.0750999\pi\)
−0.972297 + 0.233751i \(0.924900\pi\)
\(488\) −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 \(-0.482730\pi\)
\(492\) 12.7520i 0.574905i
\(493\) 3.31307 + 5.73840i 0.149213 + 0.258445i
\(494\) 14.3739 + 49.7925i 0.646711 + 2.24027i
\(495\) −0.291288 + 0.504525i −0.0130924 + 0.0226767i
\(496\) 13.4347 7.75650i 0.603234 0.348277i
\(497\) 0 0
\(498\) 6.97822 12.0866i 0.312701 0.541615i
\(499\) 36.5608 + 21.1084i 1.63669 + 0.944941i 0.981963 + 0.189072i \(0.0605479\pi\)
0.654723 + 0.755869i \(0.272785\pi\)
\(500\) 31.8245i 1.42323i
\(501\) 35.7653i 1.59788i
\(502\) −40.1216 23.1642i −1.79071 1.03387i
\(503\) −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
\(506\) −10.5826 + 18.3296i −0.470453 + 0.814848i
\(507\) 19.7042 12.4104i 0.875093 0.551165i
\(508\) −22.2695 38.5719i −0.988050 1.71135i
\(509\) 21.9844i 0.974440i −0.873279 0.487220i \(-0.838011\pi\)
0.873279 0.487220i \(-0.161989\pi\)
\(510\) −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
\(514\) 61.1939i 2.69915i
\(515\) −8.68693 + 5.01540i −0.382792 + 0.221005i
\(516\) 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
\(520\) −9.47822 + 9.85005i −0.415647 + 0.431953i
\(521\) 12.7913 + 22.1552i 0.560396 + 0.970635i 0.997462 + 0.0712054i \(0.0226846\pi\)
−0.437065 + 0.899430i \(0.643982\pi\)
\(522\) 0.873864 + 0.504525i 0.0382480 + 0.0220825i
\(523\) 12.3303 0.539166 0.269583 0.962977i \(-0.413114\pi\)
0.269583 + 0.962977i \(0.413114\pi\)
\(524\) −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
\(528\) −3.54356 + 2.04588i −0.154214 + 0.0890353i
\(529\) 34.4955 1.49980
\(530\) 58.2867 2.53181
\(531\) 1.59981 0.923651i 0.0694259 0.0400830i
\(532\) 0 0
\(533\) 8.83485 2.55040i 0.382680 0.110470i
\(534\) 5.70871 9.88778i 0.247040 0.427886i
\(535\) 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
\(541\) 26.0608 + 15.0462i 1.12044 + 0.646887i 0.941513 0.336975i \(-0.109404\pi\)
0.178928 + 0.983862i \(0.442737\pi\)
\(542\) −62.8693 −2.70047
\(543\) 8.20871 14.2179i 0.352270 0.610149i
\(544\) 22.1552i 0.949895i
\(545\) 17.3739 0.744215
\(546\) 0 0
\(547\) 15.7477 0.673324 0.336662 0.941626i \(-0.390702\pi\)
0.336662 + 0.941626i \(0.390702\pi\)
\(548\) 47.8698i 2.04490i
\(549\) −1.33030 + 2.30415i −0.0567759 + 0.0983388i
\(550\) 0.582576 0.0248411
\(551\) 12.5608 + 7.25198i 0.535108 + 0.308945i
\(552\) −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 \(-0.534031\pi\)
−0.914434 + 0.404734i \(0.867364\pi\)
\(558\) −1.97822 + 3.42638i −0.0837447 + 0.145050i
\(559\) 10.9347 11.3636i 0.462487 0.480630i
\(560\) 0 0
\(561\) 5.93466 3.42638i 0.250561 0.144662i
\(562\) −14.0000 −0.590554
\(563\) 0.330303 0.0139206 0.00696030 0.999976i \(-0.497784\pi\)
0.00696030 + 0.999976i \(0.497784\pi\)
\(564\) 18.5436 10.7061i 0.780825 0.450809i
\(565\) 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
\(569\) −10.7477 −0.450568 −0.225284 0.974293i \(-0.572331\pi\)
−0.225284 + 0.974293i \(0.572331\pi\)
\(570\) −48.8085 28.1796i −2.04436 1.18031i
\(571\) 12.4782 + 21.6129i 0.522197 + 0.904472i 0.999667 + 0.0258237i \(0.00822085\pi\)
−0.477469 + 0.878648i \(0.658446\pi\)
\(572\) −9.24773 8.89863i −0.386667 0.372070i
\(573\) 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
\(577\) 17.1261 9.88778i 0.712970 0.411634i −0.0991895 0.995069i \(-0.531625\pi\)
0.812160 + 0.583435i \(0.198292\pi\)
\(578\) 17.5112i 0.728370i
\(579\) 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
\(583\) 15.5130i 0.642483i
\(584\) −3.00000 5.19615i −0.124141 0.215018i
\(585\) −0.395644 + 1.59898i −0.0163579 + 0.0661095i
\(586\) 8.58258 14.8655i 0.354543 0.614086i
\(587\) −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
\(590\) 36.7259 + 21.2037i 1.51198 + 0.872944i
\(591\) 19.6048i 0.806432i
\(592\) 12.4104i 0.510065i
\(593\) −16.9782 9.80238i −0.697212 0.402535i 0.109096 0.994031i \(-0.465204\pi\)
−0.806308 + 0.591496i \(0.798538\pi\)
\(594\) −6.97822 + 12.0866i −0.286320 + 0.495920i
\(595\) 0 0
\(596\) 5.29129 3.05493i 0.216740 0.125135i
\(597\) −9.85208 + 17.0643i −0.403219 + 0.698396i
\(598\) −14.3739 + 58.0913i −0.587791 + 2.37553i
\(599\) 10.1869 + 17.6443i 0.416227 + 0.720926i 0.995556 0.0941675i \(-0.0300189\pi\)
−0.579330 + 0.815093i \(0.696686\pi\)
\(600\) 0.647551i 0.0264361i
\(601\) 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
\(605\) 20.5185i 0.834194i
\(606\) −33.2477 + 19.1956i −1.35060 + 0.779767i
\(607\) 3.87386 + 6.70973i 0.157235 + 0.272339i 0.933871 0.357611i \(-0.116409\pi\)
−0.776635 + 0.629950i \(0.783075\pi\)
\(608\) −24.2477 41.9983i −0.983375 1.70326i
\(609\) 0 0
\(610\) −61.0780 −2.47298
\(611\) −11.1261 10.7061i −0.450115 0.433124i
\(612\) 0.873864 + 1.51358i 0.0353238 + 0.0611827i
\(613\) −32.3085 18.6533i −1.30493 0.753401i −0.323684 0.946165i \(-0.604921\pi\)
−0.981245 + 0.192764i \(0.938255\pi\)
\(614\) 52.9129 2.13539
\(615\) −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
\(619\) −10.7477 + 6.20520i −0.431988 + 0.249408i −0.700193 0.713954i \(-0.746903\pi\)
0.268205 + 0.963362i \(0.413569\pi\)
\(620\) −52.9129 −2.12503
\(621\) 37.9129 1.52139
\(622\) 10.5000 6.06218i 0.421012 0.243071i
\(623\) 0 0
\(624\) −8.02178 + 8.33648i −0.321128 + 0.333726i
\(625\) 11.9564 20.7092i 0.478258 0.828366i
\(626\) 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 \(0.743758\pi\)
\(632\) −9.00000 5.19615i −0.358001 0.206692i
\(633\) −2.53901 −0.100917
\(634\) −20.2695 + 35.1078i −0.805005 + 1.39431i
\(635\) 34.9271i 1.38604i
\(636\) −60.8258 −2.41190
\(637\) 0 0
\(638\) −6.16515 −0.244081
\(639\) 0.190700i 0.00754399i
\(640\) 13.9782 24.2110i 0.552538 0.957023i
\(641\) 15.6261 0.617195 0.308598 0.951193i \(-0.400140\pi\)
0.308598 + 0.951193i \(0.400140\pi\)
\(642\) −33.2477 19.1956i −1.31218 0.757589i
\(643\) −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 0.424816 + 0.905280i \(0.360339\pi\)
−0.996403 + 0.0847389i \(0.972994\pi\)
\(648\) −14.3739 8.29875i −0.564659 0.326006i
\(649\) −5.64337 + 9.77461i −0.221522 + 0.383687i
\(650\) 1.58258 0.456850i 0.0620737 0.0179191i
\(651\) 0 0
\(652\) 16.7477 9.66930i 0.655892 0.378679i
\(653\) 11.2087 0.438631 0.219315 0.975654i \(-0.429618\pi\)
0.219315 + 0.975654i \(0.429618\pi\)
\(654\) −31.1216 −1.21695
\(655\) −6.87386 + 3.96863i −0.268584 + 0.155067i
\(656\) −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 \(0.203951\pi\)
\(660\) 13.9564 0.543254
\(661\) −16.2523 9.38325i −0.632140 0.364966i 0.149440 0.988771i \(-0.452253\pi\)
−0.781580 + 0.623804i \(0.785586\pi\)
\(662\) −1.18693 2.05583i −0.0461314 0.0799020i
\(663\) 13.4347 13.9617i 0.521759 0.542228i
\(664\) −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
\(668\) −48.2650 + 27.8658i −1.86743 + 1.07816i
\(669\) 37.0961i 1.43422i
\(670\) −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 \(0.648262\pi\)
\(674\) 28.3604i 1.09240i
\(675\) −0.521780 0.903750i −0.0200833 0.0347854i
\(676\) −32.0998 16.9213i −1.23461 0.650819i
\(677\) −16.8956 + 29.2641i −0.649352 + 1.12471i 0.333925 + 0.942599i \(0.391627\pi\)
−0.983278 + 0.182112i \(0.941707\pi\)
\(678\) −4.81307 + 2.77883i −0.184845 + 0.106720i
\(679\) 0 0
\(680\) −5.68693 + 9.85005i −0.218084 + 0.377732i
\(681\) −19.1044 11.0299i −0.732081 0.422667i
\(682\) 24.1733i 0.925642i
\(683\) 25.0671i 0.959164i −0.877497 0.479582i \(-0.840788\pi\)
0.877497 0.479582i \(-0.159212\pi\)
\(684\) 3.31307 + 1.91280i 0.126678 + 0.0731378i
\(685\) 18.7695 32.5097i 0.717146 1.24213i
\(686\) 0 0
\(687\) −10.7477 + 6.20520i −0.410051 + 0.236743i
\(688\) −3.91742 + 6.78518i −0.149350 + 0.258682i
\(689\) 12.1652 + 42.1413i 0.463455 + 1.60546i
\(690\) −32.5390 56.3592i −1.23874 2.14556i
\(691\) 29.3694i 1.11727i −0.829415 0.558633i \(-0.811326\pi\)
0.829415 0.558633i \(-0.188674\pi\)
\(692\) −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
\(696\) 6.85275i 0.259753i
\(697\) 6.62614 3.82560i 0.250983 0.144905i
\(698\) −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 \(0.294105\pi\)
\(702\) −9.47822 + 38.3058i −0.357732 + 1.44576i
\(703\) 22.7477 + 39.4002i 0.857947 + 1.48601i
\(704\) 13.8956 + 8.02265i 0.523712 + 0.302365i
\(705\) 16.7913 0.632396
\(706\) 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 \(-0.622957\pi\)
0.613840 + 0.789431i \(0.289624\pi\)
\(710\) −3.79129 + 2.18890i −0.142284 + 0.0821480i
\(711\) −1.25227 −0.0469639
\(712\) −5.04356 −0.189015
\(713\) −56.8693 + 32.8335i −2.12977 + 1.22962i
\(714\) 0 0
\(715\) −2.79129 9.66930i −0.104388 0.361611i
\(716\) −12.5608 + 21.7559i −0.469419 + 0.813057i
\(717\) 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 0.915285 0.402807i \(-0.131965\pi\)
−0.806483 + 0.591257i \(0.798632\pi\)
\(720\) 0.818350i 0.0304981i
\(721\) 0 0
\(722\) 45.7259 + 26.3999i 1.70174 + 0.982502i
\(723\) 6.37841 + 3.68258i 0.237216 + 0.136956i
\(724\) −25.5826 −0.950769
\(725\) 0.230493 0.399225i 0.00856028 0.0148268i
\(726\) 36.7545i 1.36409i
\(727\) 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
\(730\) 16.5975i 0.614301i
\(731\) 6.56080 11.3636i 0.242660 0.420299i
\(732\) 63.7386 2.35585
\(733\) −7.81307 4.51088i −0.288582 0.166613i 0.348720 0.937227i \(-0.386616\pi\)
−0.637302 + 0.770614i \(0.719950\pi\)
\(734\) −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 \(-0.260029\pi\)
−0.289119 + 0.957293i \(0.593362\pi\)
\(740\) −21.1652 + 36.6591i −0.778046 + 1.34762i
\(741\) 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 \(0.301946\pi\)
\(744\) 26.8693 0.985077
\(745\) 4.79129 0.175539
\(746\) 69.7432 40.2662i 2.55348 1.47425i
\(747\) −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
\(751\) −3.74773 −0.136757 −0.0683783 0.997659i \(-0.521782\pi\)
−0.0683783 + 0.997659i \(0.521782\pi\)
\(752\) 6.64337 + 3.83555i 0.242259 + 0.139868i
\(753\) 18.9564 + 32.8335i 0.690811 + 1.19652i
\(754\) −16.7477 + 4.83465i −0.609916 + 0.176068i
\(755\) −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
\(759\) 15.0000 8.66025i 0.544466 0.314347i
\(760\) 24.8963i 0.903082i
\(761\) −27.7259 + 16.0076i −1.00506 + 0.580274i −0.909743 0.415172i \(-0.863721\pi\)
−0.0953219 + 0.995447i \(0.530388\pi\)
\(762\) 62.5644i 2.26647i
\(763\) 0 0
\(764\) −0.873864 1.51358i −0.0316153 0.0547593i
\(765\) 1.37055i 0.0495524i
\(766\) 4.29129 + 7.43273i 0.155051 + 0.268555i
\(767\) −7.66515 + 30.9783i −0.276773 + 1.11856i
\(768\) −2.50000 + 4.33013i −0.0902110 + 0.156250i
\(769\) 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
\(772\) −30.0000 17.3205i −1.07972 0.623379i
\(773\) 22.8981i 0.823586i −0.911277 0.411793i \(-0.864903\pi\)
0.911277 0.411793i \(-0.135097\pi\)
\(774\) 1.99820i 0.0718238i
\(775\) 1.56534 + 0.903750i 0.0562287 + 0.0324637i
\(776\) −13.1869 + 22.8404i −0.473383 + 0.819924i
\(777\) 0 0
\(778\)