Properties

Label 637.2.u.e.361.1
Level $637$
Weight $2$
Character 637.361
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.u (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 361.1
Root \(-0.895644 + 1.09445i\) of defining polynomial
Character \(\chi\) \(=\) 637.361
Dual form 637.2.u.e.30.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.89564 - 1.09445i) q^{2} -1.79129 q^{3} +(1.39564 + 2.41733i) q^{4} +(1.89564 - 1.09445i) q^{5} +(3.39564 + 1.96048i) q^{6} -1.73205i q^{8} +0.208712 q^{9} +O(q^{10})\) \(q+(-1.89564 - 1.09445i) q^{2} -1.79129 q^{3} +(1.39564 + 2.41733i) q^{4} +(1.89564 - 1.09445i) q^{5} +(3.39564 + 1.96048i) q^{6} -1.73205i q^{8} +0.208712 q^{9} -4.79129 q^{10} -1.27520i q^{11} +(-2.50000 - 4.33013i) 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} +(-0.395644 - 0.228425i) q^{18} +6.56670i q^{19} +(5.29129 + 3.05493i) q^{20} +(-1.39564 + 2.41733i) q^{22} +(-3.79129 + 6.56670i) q^{23} +3.10260i q^{24} +(-0.104356 + 0.180750i) q^{25} +(-5.68693 - 5.47225i) q^{26} +5.00000 q^{27} +(1.10436 + 1.91280i) q^{29} +8.58258 q^{30} +(7.50000 + 4.33013i) q^{31} +(-6.39564 + 3.69253i) q^{32} +2.28425i q^{33} +6.56670i q^{34} +(0.291288 + 0.504525i) q^{36} +(-6.00000 - 3.46410i) q^{37} +(7.18693 - 12.4481i) q^{38} +(-6.26951 - 1.55130i) 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} +(0.395644 - 0.228425i) q^{45} +(14.3739 - 8.29875i) 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} +(2.79129 + 9.66930i) q^{52} +(6.08258 - 10.5353i) q^{53} +(-9.47822 - 5.47225i) q^{54} +(-1.39564 - 2.41733i) q^{55} -11.7629i q^{57} -4.83465i q^{58} +(7.66515 - 4.42548i) q^{59} +(-9.47822 - 5.47225i) q^{60} +12.7477 q^{61} +(-9.47822 - 16.4168i) q^{62} +12.5826 q^{64} +(7.58258 - 2.18890i) q^{65} +(2.50000 - 4.33013i) q^{66} +11.4014i q^{67} +(4.18693 - 7.25198i) q^{68} +(6.79129 - 11.7629i) q^{69} +(-0.791288 - 0.456850i) q^{71} -0.361500i q^{72} +(-3.00000 - 1.73205i) 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} +(3.00000 + 5.19615i) q^{79} -3.92095i q^{80} -9.58258 q^{81} -5.58258 q^{82} -3.55945i q^{83} +(-5.68693 - 3.28335i) q^{85} +(-8.29129 + 4.78698i) q^{86} +(-1.97822 - 3.42638i) q^{87} -2.20871 q^{88} +(2.52178 + 1.45595i) q^{89} -1.00000 q^{90} -21.1652 q^{92} +(-13.4347 - 7.75650i) q^{93} -9.37386 q^{94} +(7.18693 + 12.4481i) q^{95} +(11.4564 - 6.61438i) q^{96} +(-13.1869 - 7.61348i) q^{97} -0.266150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 3 q^{2} + 2 q^{3} + q^{4} + 3 q^{5} + 9 q^{6} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 3 q^{2} + 2 q^{3} + q^{4} + 3 q^{5} + 9 q^{6} + 10 q^{9} - 10 q^{10} - 10 q^{12} + 14 q^{13} - 9 q^{15} - q^{16} - 6 q^{17} + 3 q^{18} + 12 q^{20} - q^{22} - 6 q^{23} - 5 q^{25} - 9 q^{26} + 20 q^{27} + 9 q^{29} + 16 q^{30} + 30 q^{31} - 21 q^{32} - 8 q^{36} - 24 q^{37} + 15 q^{38} + 7 q^{39} - 3 q^{40} + 18 q^{41} - 5 q^{43} - 6 q^{44} - 3 q^{45} + 30 q^{46} + 24 q^{47} - 11 q^{48} - 3 q^{50} - 3 q^{51} + 2 q^{52} + 6 q^{53} - 15 q^{54} - q^{55} - 6 q^{59} - 15 q^{60} - 4 q^{61} - 15 q^{62} + 32 q^{64} + 12 q^{65} + 10 q^{66} + 3 q^{68} + 18 q^{69} + 6 q^{71} - 12 q^{73} + 12 q^{74} - 13 q^{75} - 36 q^{76} + 27 q^{78} + 12 q^{79} - 20 q^{81} - 4 q^{82} - 9 q^{85} - 24 q^{86} + 15 q^{87} - 18 q^{88} + 33 q^{89} - 4 q^{90} - 48 q^{92} + 15 q^{93} - 10 q^{94} + 15 q^{95} - 39 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.89564 1.09445i −1.34042 0.773893i −0.353553 0.935414i \(-0.615027\pi\)
−0.986869 + 0.161521i \(0.948360\pi\)
\(3\) −1.79129 −1.03420 −0.517100 0.855925i \(-0.672989\pi\)
−0.517100 + 0.855925i \(0.672989\pi\)
\(4\) 1.39564 + 2.41733i 0.697822 + 1.20866i
\(5\) 1.89564 1.09445i 0.847758 0.489453i −0.0121359 0.999926i \(-0.503863\pi\)
0.859894 + 0.510473i \(0.170530\pi\)
\(6\) 3.39564 + 1.96048i 1.38627 + 0.800361i
\(7\) 0 0
\(8\) 1.73205i 0.612372i
\(9\) 0.208712 0.0695707
\(10\) −4.79129 −1.51514
\(11\) 1.27520i 0.384487i −0.981347 0.192244i \(-0.938424\pi\)
0.981347 0.192244i \(-0.0615764\pi\)
\(12\) −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
\(16\) 0.895644 1.55130i 0.223911 0.387825i
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) −0.395644 0.228425i −0.0932542 0.0538403i
\(19\) 6.56670i 1.50651i 0.657731 + 0.753253i \(0.271516\pi\)
−0.657731 + 0.753253i \(0.728484\pi\)
\(20\) 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 0.135096 + 0.990833i \(0.456866\pi\)
−0.925634 + 0.378420i \(0.876468\pi\)
\(24\) 3.10260i 0.633316i
\(25\) −0.104356 + 0.180750i −0.0208712 + 0.0361500i
\(26\) −5.68693 5.47225i −1.11530 1.07320i
\(27\) 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 \(0.767590\pi\)
\(30\) 8.58258 1.56696
\(31\) 7.50000 + 4.33013i 1.34704 + 0.777714i 0.987829 0.155543i \(-0.0497126\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) −6.39564 + 3.69253i −1.13060 + 0.652753i
\(33\) 2.28425i 0.397637i
\(34\) 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 \(-0.526194\pi\)
−0.904194 + 0.427121i \(0.859528\pi\)
\(38\) 7.18693 12.4481i 1.16587 2.01935i
\(39\) −6.26951 1.55130i −1.00392 0.248407i
\(40\) −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
\(45\) 0.395644 0.228425i 0.0589791 0.0340516i
\(46\) 14.3739 8.29875i 2.11931 1.22358i
\(47\) 3.70871 2.14123i 0.540971 0.312330i −0.204501 0.978866i \(-0.565557\pi\)
0.745472 + 0.666536i \(0.232224\pi\)
\(48\) −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
\(52\) 2.79129 + 9.66930i 0.387082 + 1.34089i
\(53\) 6.08258 10.5353i 0.835506 1.44714i −0.0581117 0.998310i \(-0.518508\pi\)
0.893618 0.448829i \(-0.148159\pi\)
\(54\) −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
\(58\) 4.83465i 0.634821i
\(59\) 7.66515 4.42548i 0.997918 0.576148i 0.0902862 0.995916i \(-0.471222\pi\)
0.907632 + 0.419768i \(0.137888\pi\)
\(60\) −9.47822 5.47225i −1.22363 0.706465i
\(61\) 12.7477 1.63218 0.816090 0.577925i \(-0.196138\pi\)
0.816090 + 0.577925i \(0.196138\pi\)
\(62\) −9.47822 16.4168i −1.20374 2.08493i
\(63\) 0 0
\(64\) 12.5826 1.57282
\(65\) 7.58258 2.18890i 0.940503 0.271500i
\(66\) 2.50000 4.33013i 0.307729 0.533002i
\(67\) 11.4014i 1.39290i 0.717607 + 0.696449i \(0.245238\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) 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 \(0.683933\pi\)
\(72\) 0.361500i 0.0426032i
\(73\) −3.00000 1.73205i −0.351123 0.202721i 0.314057 0.949404i \(-0.398312\pi\)
−0.665180 + 0.746683i \(0.731645\pi\)
\(74\) 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
\(79\) 3.00000 + 5.19615i 0.337526 + 0.584613i 0.983967 0.178352i \(-0.0570765\pi\)
−0.646440 + 0.762964i \(0.723743\pi\)
\(80\) 3.92095i 0.438376i
\(81\) −9.58258 −1.06473
\(82\) −5.58258 −0.616492
\(83\) 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
\(87\) −1.97822 3.42638i −0.212087 0.367346i
\(88\) −2.20871 −0.235450
\(89\) 2.52178 + 1.45595i 0.267308 + 0.154330i 0.627664 0.778485i \(-0.284011\pi\)
−0.360356 + 0.932815i \(0.617345\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) −21.1652 −2.20662
\(93\) −13.4347 7.75650i −1.39311 0.804312i
\(94\) −9.37386 −0.966840
\(95\) 7.18693 + 12.4481i 0.737364 + 1.27715i
\(96\) 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
\(100\) −0.582576 −0.0582576
\(101\) 9.79129 0.974270 0.487135 0.873327i \(-0.338042\pi\)
0.487135 + 0.873327i \(0.338042\pi\)
\(102\) 11.7629i 1.16470i
\(103\) 2.29129 + 3.96863i 0.225767 + 0.391040i 0.956549 0.291570i \(-0.0941778\pi\)
−0.730782 + 0.682611i \(0.760844\pi\)
\(104\) 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 −0.526252 0.850328i \(-0.676403\pi\)
0.999532 + 0.0305838i \(0.00973664\pi\)
\(108\) 6.97822 + 12.0866i 0.671479 + 1.16304i
\(109\) 6.87386 + 3.96863i 0.658397 + 0.380126i 0.791666 0.610954i \(-0.209214\pi\)
−0.133269 + 0.991080i \(0.542547\pi\)
\(110\) 6.10985i 0.582552i
\(111\) 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
\(115\) 16.5975i 1.54773i
\(116\) −3.08258 + 5.33918i −0.286210 + 0.495730i
\(117\) 0.730493 + 0.180750i 0.0675341 + 0.0167103i
\(118\) −19.3739 −1.78351
\(119\) 0 0
\(120\) 3.39564 + 5.88143i 0.309978 + 0.536898i
\(121\) 9.37386 0.852169
\(122\) −24.1652 13.9518i −2.18781 1.26313i
\(123\) −3.95644 + 2.28425i −0.356740 + 0.205964i
\(124\) 24.1733i 2.17082i
\(125\) 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
\(129\) −3.91742 + 6.78518i −0.344910 + 0.597402i
\(130\) −16.7695 4.14938i −1.47078 0.363924i
\(131\) 1.81307 + 3.14033i 0.158409 + 0.274372i 0.934295 0.356501i \(-0.116030\pi\)
−0.775886 + 0.630873i \(0.782697\pi\)
\(132\) −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
\(136\) −4.50000 + 2.59808i −0.385872 + 0.222783i
\(137\) 14.8521 8.57485i 1.26890 0.732599i 0.294119 0.955769i \(-0.404974\pi\)
0.974780 + 0.223169i \(0.0716403\pi\)
\(138\) −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
\(143\) 1.10436 4.46320i 0.0923509 0.373232i
\(144\) 0.186932 0.323775i 0.0155776 0.0269813i
\(145\) 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
\(149\) 2.18890i 0.179322i −0.995972 0.0896609i \(-0.971422\pi\)
0.995972 0.0896609i \(-0.0285783\pi\)
\(150\) −0.708712 + 0.409175i −0.0578661 + 0.0334090i
\(151\) −10.5000 6.06218i −0.854478 0.493333i 0.00768132 0.999970i \(-0.497555\pi\)
−0.862159 + 0.506637i \(0.830888\pi\)
\(152\) 11.3739 0.922542
\(153\) −0.313068 0.542250i −0.0253101 0.0438383i
\(154\) 0 0
\(155\) 18.9564 1.52262
\(156\) −5.00000 17.3205i −0.400320 1.38675i
\(157\) −10.9782 + 19.0148i −0.876157 + 1.51755i −0.0206325 + 0.999787i \(0.506568\pi\)
−0.855525 + 0.517762i \(0.826765\pi\)
\(158\) 13.1334i 1.04484i
\(159\) −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
\(163\) 6.92820i 0.542659i −0.962487 0.271329i \(-0.912537\pi\)
0.962487 0.271329i \(-0.0874633\pi\)
\(164\) 6.16515 + 3.55945i 0.481417 + 0.277946i
\(165\) 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
\(170\) 7.18693 + 12.4481i 0.551213 + 0.954728i
\(171\) 1.37055i 0.104809i
\(172\) 12.2087 0.930906
\(173\) −7.74773 −0.589049 −0.294524 0.955644i \(-0.595161\pi\)
−0.294524 + 0.955644i \(0.595161\pi\)
\(174\) 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
\(178\) −3.18693 5.51993i −0.238871 0.413736i
\(179\) −9.00000 −0.672692 −0.336346 0.941739i \(-0.609191\pi\)
−0.336346 + 0.941739i \(0.609191\pi\)
\(180\) 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
\(185\) −15.1652 −1.11496
\(186\) 16.9782 + 29.4071i 1.24490 + 2.15624i
\(187\) −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
\(191\) −0.626136 −0.0453056 −0.0226528 0.999743i \(-0.507211\pi\)
−0.0226528 + 0.999743i \(0.507211\pi\)
\(192\) −22.5390 −1.62661
\(193\) 12.4104i 0.893321i −0.894704 0.446660i \(-0.852613\pi\)
0.894704 0.446660i \(-0.147387\pi\)
\(194\) 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 \(0.460817\pi\)
\(198\) −0.291288 + 0.504525i −0.0207009 + 0.0358551i
\(199\) 5.50000 + 9.52628i 0.389885 + 0.675300i 0.992434 0.122782i \(-0.0391815\pi\)
−0.602549 + 0.798082i \(0.705848\pi\)
\(200\) 0.313068 + 0.180750i 0.0221373 + 0.0127810i
\(201\) 20.4231i 1.44054i
\(202\) −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
\(206\) 10.0308i 0.698879i
\(207\) −0.791288 + 1.37055i −0.0549983 + 0.0952599i
\(208\) 4.47822 4.65390i 0.310509 0.322690i
\(209\) 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 \(0.848870\pi\)
\(212\) 33.9564 2.33214
\(213\) 1.41742 + 0.818350i 0.0971203 + 0.0560724i
\(214\) −18.5608 + 10.7161i −1.26879 + 0.732536i
\(215\) 9.57395i 0.652938i
\(216\) 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
\(220\) 3.89564 6.74745i 0.262644 0.454913i
\(221\) −3.00000 10.3923i −0.201802 0.699062i
\(222\) −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
\(227\) −10.6652 + 6.15753i −0.707871 + 0.408689i −0.810272 0.586054i \(-0.800681\pi\)
0.102401 + 0.994743i \(0.467347\pi\)
\(228\) 28.4347 16.4168i 1.88313 1.08723i
\(229\) 6.00000 3.46410i 0.396491 0.228914i −0.288478 0.957487i \(-0.593149\pi\)
0.684969 + 0.728572i \(0.259816\pi\)
\(230\) 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 0.957175 0.289509i \(-0.0934919\pi\)
−0.729310 + 0.684184i \(0.760159\pi\)
\(234\) −1.18693 1.14213i −0.0775922 0.0746631i
\(235\) 4.68693 8.11800i 0.305742 0.529560i
\(236\) 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 \(0.859272\pi\)
\(240\) 7.02355i 0.453368i
\(241\) 3.56080 2.05583i 0.229371 0.132427i −0.380911 0.924612i \(-0.624390\pi\)
0.610282 + 0.792184i \(0.291056\pi\)
\(242\) −17.7695 10.2592i −1.14227 0.659488i
\(243\) 2.16515 0.138895
\(244\) 17.7913 + 30.8154i 1.13897 + 1.97275i
\(245\) 0 0
\(246\) 10.0000 0.637577
\(247\) −5.68693 + 22.9835i −0.361851 + 1.46240i
\(248\) 7.50000 12.9904i 0.476250 0.824890i
\(249\) 6.37600i 0.404063i
\(250\) 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
\(254\) 34.9271i 2.19152i
\(255\) 10.1869 + 5.88143i 0.637930 + 0.368309i
\(256\) 1.39564 + 2.41733i 0.0872277 + 0.151083i
\(257\) 13.9782 24.2110i 0.871937 1.51024i 0.0119476 0.999929i \(-0.496197\pi\)
0.859990 0.510311i \(-0.170470\pi\)
\(258\) 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
\(262\) 7.93725i 0.490365i
\(263\) −27.3303 −1.68526 −0.842629 0.538494i \(-0.818993\pi\)
−0.842629 + 0.538494i \(0.818993\pi\)
\(264\) 3.95644 0.243502
\(265\) 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
\(269\) −5.60436 9.70703i −0.341704 0.591848i 0.643046 0.765828i \(-0.277671\pi\)
−0.984749 + 0.173980i \(0.944337\pi\)
\(270\) −23.9564 −1.45794
\(271\) −24.8739 14.3609i −1.51098 0.872364i −0.999918 0.0128205i \(-0.995919\pi\)
−0.511062 0.859544i \(-0.670748\pi\)
\(272\) −5.37386 −0.325838
\(273\) 0 0
\(274\) −37.5390 −2.26781
\(275\) 0.230493 + 0.133075i 0.0138992 + 0.00802472i
\(276\) 37.9129 2.28209
\(277\) 7.87386 + 13.6379i 0.473095 + 0.819424i 0.999526 0.0307939i \(-0.00980354\pi\)
−0.526431 + 0.850218i \(0.676470\pi\)
\(278\) −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 \(0.938900\pi\)
\(282\) 16.7913 0.999907
\(283\) 24.7477 1.47110 0.735550 0.677471i \(-0.236924\pi\)
0.735550 + 0.677471i \(0.236924\pi\)
\(284\) 2.55040i 0.151338i
\(285\) −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
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) −5.29129 9.16478i −0.310715 0.538174i
\(291\) 23.6216 + 13.6379i 1.38472 + 0.799470i
\(292\) 9.66930i 0.565853i
\(293\) −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
\(297\) 6.37600i 0.369973i
\(298\) −2.39564 + 4.14938i −0.138776 + 0.240367i
\(299\) −18.9564 + 19.7001i −1.09628 + 1.13929i
\(300\) 1.04356 0.0602500
\(301\) 0 0
\(302\) 13.2695 + 22.9835i 0.763574 + 1.32255i
\(303\) −17.5390 −1.00759
\(304\) 10.1869 + 5.88143i 0.584261 + 0.337323i
\(305\) 24.1652 13.9518i 1.38369 0.798875i
\(306\) 1.37055i 0.0783492i
\(307\) 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
\(311\) −2.76951 + 4.79693i −0.157044 + 0.272009i −0.933802 0.357791i \(-0.883530\pi\)
0.776757 + 0.629800i \(0.216863\pi\)
\(312\) −2.68693 + 10.8591i −0.152118 + 0.614776i
\(313\) 10.3739 + 17.9681i 0.586365 + 1.01561i 0.994704 + 0.102784i \(0.0327751\pi\)
−0.408338 + 0.912831i \(0.633892\pi\)
\(314\) 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 \(-0.840772\pi\)
−0.0233679 + 0.999727i \(0.507439\pi\)
\(318\) 41.3085 23.8495i 2.31647 1.33741i
\(319\) 2.43920 1.40828i 0.136569 0.0788483i
\(320\) 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
\(325\) −0.521780 + 0.542250i −0.0289432 + 0.0300786i
\(326\) −7.58258 + 13.1334i −0.419960 + 0.727392i
\(327\) −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
\(331\) 1.08450i 0.0596095i −0.999556 0.0298048i \(-0.990511\pi\)
0.999556 0.0298048i \(-0.00948855\pi\)
\(332\) 8.60436 4.96773i 0.472225 0.272639i
\(333\) −1.25227 0.723000i −0.0686241 0.0396202i
\(334\) −43.7042 −2.39139
\(335\) 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 \(0.614801\pi\)
\(338\) −15.1652 24.0779i −0.824875 1.30967i
\(339\) 1.26951 2.19885i 0.0689502 0.119425i
\(340\) 18.3296i 0.994060i
\(341\) 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
\(345\) 29.7309i 1.60066i
\(346\) 14.6869 + 8.47950i 0.789574 + 0.455861i
\(347\) 2.20871 + 3.82560i 0.118570 + 0.205369i 0.919201 0.393788i \(-0.128836\pi\)
−0.800631 + 0.599157i \(0.795502\pi\)
\(348\) 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
\(352\) 4.70871 + 8.15573i 0.250975 + 0.434702i
\(353\) 26.8190i 1.42743i 0.700435 + 0.713716i \(0.252989\pi\)
−0.700435 + 0.713716i \(0.747011\pi\)
\(354\) 34.7042 1.84451
\(355\) −2.00000 −0.106149
\(356\) 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 \(-0.775241\pi\)
0.181490 + 0.983393i \(0.441908\pi\)
\(360\) −0.395644 0.685275i −0.0208523 0.0361172i
\(361\) −24.1216 −1.26956
\(362\) −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
\(367\) 18.0000 0.939592 0.469796 0.882775i \(-0.344327\pi\)
0.469796 + 0.882775i \(0.344327\pi\)
\(368\) 6.79129 + 11.7629i 0.354020 + 0.613181i
\(369\) 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
\(373\) 36.7913 1.90498 0.952490 0.304569i \(-0.0985124\pi\)
0.952490 + 0.304569i \(0.0985124\pi\)
\(374\) 8.37386 0.433002
\(375\) 20.4231i 1.05464i
\(376\) −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 \(0.370604\pi\)
\(380\) −20.0608 + 34.7463i −1.02910 + 1.78245i
\(381\) −14.2913 24.7532i −0.732165 1.26815i
\(382\) 1.18693 + 0.685275i 0.0607287 + 0.0350617i
\(383\) 3.92095i 0.200351i 0.994970 + 0.100176i \(0.0319405\pi\)
−0.994970 + 0.100176i \(0.968060\pi\)
\(384\) 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
\(388\) 42.5028i 2.15775i
\(389\) −18.1652 + 31.4630i −0.921010 + 1.59524i −0.123154 + 0.992388i \(0.539301\pi\)
−0.797856 + 0.602848i \(0.794033\pi\)
\(390\) 30.0390 + 7.43273i 1.52108 + 0.376371i
\(391\) 22.7477 1.15040
\(392\) 0 0
\(393\) −3.24773 5.62523i −0.163826 0.283755i
\(394\) 23.9564 1.20691
\(395\) 11.3739 + 6.56670i 0.572281 + 0.330407i
\(396\) 0.643371 0.371450i 0.0323306 0.0186661i
\(397\) 15.1515i 0.760432i −0.924898 0.380216i \(-0.875850\pi\)
0.924898 0.380216i \(-0.124150\pi\)
\(398\) 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 \(-0.0690656\pi\)
0.301841 + 0.953358i \(0.402399\pi\)
\(402\) −22.3521 + 38.7149i −1.11482 + 1.93093i
\(403\) 22.5000 + 21.6506i 1.12080 + 1.07849i
\(404\) 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
\(409\) 0.313068 0.180750i 0.0154802 0.00893751i −0.492240 0.870460i \(-0.663822\pi\)
0.507720 + 0.861522i \(0.330488\pi\)
\(410\) −10.5826 + 6.10985i −0.522636 + 0.301744i
\(411\) −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
\(416\) −25.5826 + 7.38505i −1.25429 + 0.362082i
\(417\) −0.708712 + 1.22753i −0.0347058 + 0.0601122i
\(418\) −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 \(-0.162591\pi\)
\(422\) 3.10260i 0.151032i
\(423\) 0.774053 0.446900i 0.0376358 0.0217290i
\(424\) −18.2477 10.5353i −0.886188 0.511641i
\(425\) 0.626136 0.0303721
\(426\) −1.79129 3.10260i −0.0867882 0.150322i
\(427\) 0 0
\(428\) 27.3303 1.32106
\(429\) −1.97822 + 7.99488i −0.0955093 + 0.385996i
\(430\) −10.4782 + 18.1488i −0.505305 + 0.875213i
\(431\) 15.6084i 0.751828i −0.926655 0.375914i \(-0.877329\pi\)
0.926655 0.375914i \(-0.122671\pi\)
\(432\) 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
\(436\) 22.1552i 1.06104i
\(437\) −43.1216 24.8963i −2.06279 1.19095i
\(438\) −6.79129 11.7629i −0.324500 0.562051i
\(439\) 5.76951 9.99308i 0.275364 0.476944i −0.694863 0.719142i \(-0.744535\pi\)
0.970227 + 0.242198i \(0.0778684\pi\)
\(440\) −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 0.825979 0.563701i \(-0.190623\pi\)
−0.901169 + 0.433468i \(0.857290\pi\)
\(444\) 34.6410i 1.64399i
\(445\) 6.37386 0.302150
\(446\) 45.3303 2.14645
\(447\) 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
\(451\) −1.62614 2.81655i −0.0765718 0.132626i
\(452\) −3.95644 −0.186095
\(453\) 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 \(-0.266233\pi\)
−0.307720 + 0.951477i \(0.599566\pi\)
\(458\) −15.1652 −0.708621
\(459\) −7.50000 12.9904i −0.350070 0.606339i
\(460\) −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 \(0.940954\pi\)
\(464\) 3.95644 0.183673
\(465\) −33.9564 −1.57469
\(466\) 15.2270i 0.705375i
\(467\) 5.91742 + 10.2493i 0.273826 + 0.474280i 0.969838 0.243750i \(-0.0783775\pi\)
−0.696012 + 0.718030i \(0.745044\pi\)
\(468\) 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
\(473\) −4.83030 2.78878i −0.222098 0.128228i
\(474\) 23.5257i 1.08057i
\(475\) −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
\(479\) 10.2215i 0.467032i −0.972353 0.233516i \(-0.924977\pi\)
0.972353 0.233516i \(-0.0750232\pi\)
\(480\) 14.4782 25.0770i 0.660837 1.14460i
\(481\) −18.0000 17.3205i −0.820729 0.789747i
\(482\) −9.00000 −0.409939
\(483\) 0 0
\(484\) 13.0826 + 22.6597i 0.594663 + 1.02999i
\(485\) −33.3303 −1.51345
\(486\) −4.10436 2.36965i −0.186177 0.107490i
\(487\) 8.93466 5.15843i 0.404868 0.233751i −0.283714 0.958909i \(-0.591567\pi\)
0.688582 + 0.725158i \(0.258233\pi\)
\(488\) 22.0797i 0.999502i
\(489\) 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
\(493\) 3.31307 5.73840i 0.149213 0.258445i
\(494\) 35.9347 37.3444i 1.61678 1.68020i
\(495\) −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 −0.654723 + 0.755869i \(0.727215\pi\)
−0.981963 + 0.189072i \(0.939452\pi\)
\(500\) −27.5608 + 15.9122i −1.23256 + 0.711617i
\(501\) −30.9737 + 17.8827i −1.38380 + 0.798938i
\(502\) 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
\(507\) −20.5998 10.8591i −0.914870 0.482270i
\(508\) −22.2695 + 38.5719i −0.988050 + 1.71135i
\(509\) 19.0390 + 10.9922i 0.843890 + 0.487220i 0.858584 0.512672i \(-0.171344\pi\)
−0.0146949 + 0.999892i \(0.504678\pi\)
\(510\) −12.8739 22.2982i −0.570064 0.987380i
\(511\) 0 0
\(512\) 19.4340i 0.858868i
\(513\) 32.8335i 1.44964i
\(514\) −52.9955 + 30.5969i −2.33753 + 1.34957i
\(515\) 8.68693 + 5.01540i 0.382792 + 0.221005i
\(516\) −21.8693 −0.962743
\(517\) −2.73049 4.72935i −0.120087 0.207997i
\(518\) 0 0
\(519\) 13.8784 0.609195
\(520\) −3.79129 13.1334i −0.166259 0.575938i
\(521\) 12.7913 22.1552i 0.560396 0.970635i −0.437065 0.899430i \(-0.643982\pi\)
0.997462 0.0712054i \(-0.0226846\pi\)
\(522\) 1.00905i 0.0441649i
\(523\) −6.16515 + 10.6784i −0.269583 + 0.466932i −0.968754 0.248023i \(-0.920219\pi\)
0.699171 + 0.714954i \(0.253553\pi\)
\(524\) −5.06080 + 8.76555i −0.221082 + 0.382925i
\(525\) 0 0
\(526\) 51.8085 + 29.9117i 2.25896 + 1.30421i
\(527\) 25.9808i 1.13174i
\(528\) 3.54356 + 2.04588i 0.154214 + 0.0890353i
\(529\) −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
\(534\) 5.70871 + 9.88778i 0.247040 + 0.427886i
\(535\) 21.4322i 0.926593i
\(536\) 19.7477 0.852972
\(537\) 16.1216 0.695698
\(538\) 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 \(-0.890596\pi\)
−0.178928 + 0.983862i \(0.557263\pi\)
\(542\) 31.4347 + 54.4464i 1.35023 + 2.33867i
\(543\) −16.4174 −0.704539
\(544\) 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
\(549\) 2.66061 0.113552
\(550\) −0.291288 0.504525i −0.0124206 0.0215130i
\(551\) −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
\(555\) 27.1652 1.15310
\(556\) 2.20871 0.0936703
\(557\) 27.8281i 1.17911i 0.807727 + 0.589556i \(0.200697\pi\)
−0.807727 + 0.589556i \(0.799303\pi\)
\(558\) −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
\(562\) 7.00000 12.1244i 0.295277 0.511435i
\(563\) −0.165151 0.286051i −0.00696030 0.0120556i 0.862524 0.506016i \(-0.168882\pi\)
−0.869485 + 0.493960i \(0.835549\pi\)
\(564\) −18.5436 10.7061i −0.780825 0.450809i
\(565\) 3.10260i 0.130527i
\(566\) −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 −0.731121 0.682248i \(-0.761002\pi\)
0.956405 + 0.292045i \(0.0943356\pi\)
\(570\) 56.3592i 2.36063i
\(571\) 12.4782 21.6129i 0.522197 0.904472i −0.477469 0.878648i \(-0.658446\pi\)
0.999667 0.0258237i \(-0.00822085\pi\)
\(572\) 12.3303 3.55945i 0.515556 0.148828i
\(573\) 1.12159 0.0468551
\(574\) 0 0
\(575\) −0.791288 1.37055i −0.0329990 0.0571559i
\(576\) 2.62614 0.109422
\(577\) −17.1261 9.88778i −0.712970 0.411634i 0.0991895 0.995069i \(-0.468375\pi\)
−0.812160 + 0.583435i \(0.801708\pi\)
\(578\) −15.1652 + 8.75560i −0.630787 + 0.364185i
\(579\) 22.2306i 0.923873i
\(580\) 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
\(584\) −3.00000 + 5.19615i −0.124141 + 0.215018i
\(585\) 1.58258 0.456850i 0.0654315 0.0188884i
\(586\) 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
\(591\) 16.9782 9.80238i 0.698391 0.403216i
\(592\) −10.7477 + 6.20520i −0.441729 + 0.255032i
\(593\) 16.9782 9.80238i 0.697212 0.402535i −0.109096 0.994031i \(-0.534796\pi\)
0.806308 + 0.591496i \(0.201462\pi\)
\(594\) −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
\(598\) 57.4955 16.5975i 2.35116 0.678723i
\(599\) 10.1869 17.6443i 0.416227 0.720926i −0.579330 0.815093i \(-0.696686\pi\)
0.995556 + 0.0941675i \(0.0300189\pi\)
\(600\) −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
\(604\) 33.8426i 1.37703i
\(605\) 17.7695 10.2592i 0.722433 0.417097i
\(606\) 33.2477 + 19.1956i 1.35060 + 0.779767i
\(607\) −7.74773 −0.314471 −0.157235 0.987561i \(-0.550258\pi\)
−0.157235 + 0.987561i \(0.550258\pi\)
\(608\) −24.2477 41.9983i −0.983375 1.70326i
\(609\) 0 0
\(610\) −61.0780 −2.47298
\(611\) 14.8348 4.28245i 0.600154 0.173249i
\(612\) 0.873864 1.51358i 0.0353238 0.0611827i
\(613\) 37.3067i 1.50680i 0.657561 + 0.753401i \(0.271588\pi\)
−0.657561 + 0.753401i \(0.728412\pi\)
\(614\) −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 \(0.855772\pi\)
\(618\) 17.9681i 0.722781i
\(619\) 10.7477 + 6.20520i 0.431988 + 0.249408i 0.700193 0.713954i \(-0.253097\pi\)
−0.268205 + 0.963362i \(0.586431\pi\)
\(620\) 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
\(625\) 11.9564 + 20.7092i 0.478258 + 0.828366i
\(626\) 45.4147i 1.81514i
\(627\) −15.0000 −0.599042
\(628\) −61.2867 −2.44561
\(629\) 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
\(633\) 1.26951 + 2.19885i 0.0504584 + 0.0873965i
\(634\) 40.5390 1.61001
\(635\) 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
\(640\) −27.9564 −1.10508
\(641\) −7.81307 13.5326i −0.308598 0.534507i 0.669458 0.742850i \(-0.266526\pi\)
−0.978056 + 0.208343i \(0.933193\pi\)
\(642\) 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
\(646\) −43.1216 −1.69660
\(647\) 29.0780 1.14318 0.571588 0.820541i \(-0.306328\pi\)
0.571588 + 0.820541i \(0.306328\pi\)
\(648\) 16.5975i 0.652012i
\(649\) −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
\(653\) −5.60436 + 9.70703i −0.219315 + 0.379865i −0.954599 0.297894i \(-0.903716\pi\)
0.735283 + 0.677760i \(0.237049\pi\)
\(654\) 15.5608 + 26.9521i 0.608475 + 1.05391i
\(655\) 6.87386 + 3.96863i 0.268584 + 0.155067i
\(656\) 4.56850i 0.178370i
\(657\) −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
\(661\) 18.7665i 0.729933i 0.931021 + 0.364966i \(0.118919\pi\)
−0.931021 + 0.364966i \(0.881081\pi\)
\(662\) −1.18693 + 2.05583i −0.0461314 + 0.0799020i
\(663\) 5.37386 + 18.6156i 0.208704 + 0.722970i
\(664\) −6.16515 −0.239254
\(665\) 0 0
\(666\) 1.58258 + 2.74110i 0.0613236 + 0.106216i
\(667\) −16.7477 −0.648475
\(668\) 48.2650 + 27.8658i 1.86743 + 1.07816i
\(669\) 32.1261 18.5480i 1.24207 0.717108i
\(670\) 54.6272i 2.11043i
\(671\) 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
\(675\) −0.521780 + 0.903750i −0.0200833 + 0.0347854i
\(676\) 1.39564 + 36.2599i 0.0536786 + 1.39461i
\(677\) −16.8956 29.2641i −0.649352 1.12471i −0.983278 0.182112i \(-0.941707\pi\)
0.333925 0.942599i \(-0.391627\pi\)
\(678\) −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
\(682\) −20.9347 + 12.0866i −0.801630 + 0.462821i
\(683\) −21.7087 + 12.5335i −0.830661 + 0.479582i −0.854079 0.520144i \(-0.825878\pi\)
0.0234181 + 0.999726i \(0.492545\pi\)
\(684\) −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
\(689\) 30.4129 31.6060i 1.15864 1.20409i
\(690\) −32.5390 + 56.3592i −1.23874 + 2.14556i
\(691\) 25.4347 + 14.6847i 0.967580 + 0.558633i 0.898498 0.438978i \(-0.144660\pi\)
0.0690824 + 0.997611i \(0.477993\pi\)
\(692\) −10.8131 18.7288i −0.411051 0.711962i
\(693\) 0 0
\(694\) 9.66930i 0.367042i
\(695\) 1.73205i 0.0657004i
\(696\) −5.93466 + 3.42638i −0.224953 + 0.129876i
\(697\) −6.62614 3.82560i −0.250983 0.144905i
\(698\) 23.3739 0.884714
\(699\) −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 \(0.294105\pi\)
\(702\) −28.4347 27.3613i −1.07320 1.03268i
\(703\) 22.7477 39.4002i 0.857947 1.48601i
\(704\) 16.0453i 0.604730i
\(705\) −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
\(709\) 7.28970i 0.273771i 0.990587 + 0.136885i \(0.0437092\pi\)
−0.990587 + 0.136885i \(0.956291\pi\)
\(710\) 3.79129 + 2.18890i 0.142284 + 0.0821480i
\(711\) 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
\(716\) −12.5608 21.7559i −0.469419 0.813057i
\(717\) 23.6965i 0.884962i
\(718\) 27.7477 1.03554
\(719\) −5.83485 −0.217603 −0.108802 0.994063i \(-0.534701\pi\)
−0.108802 + 0.994063i \(0.534701\pi\)
\(720\) 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
\(724\) 12.7913 + 22.1552i 0.475384 + 0.823390i
\(725\) −0.460985 −0.0171206
\(726\) 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
\(731\) −13.1216 −0.485320
\(732\) −31.8693 55.1993i −1.17792 2.04022i
\(733\) 7.81307 4.51088i 0.288582 0.166613i −0.348720 0.937227i \(-0.613384\pi\)
0.637302 + 0.770614i \(0.280050\pi\)
\(734\) −34.1216 19.7001i −1.25945 0.727144i
\(735\) 0 0
\(736\) 55.9977i 2.06410i
\(737\) 14.5390 0.535551
\(738\) −1.16515 −0.0428898
\(739\) 12.4104i 0.456524i −0.973600 0.228262i \(-0.926696\pi\)
0.973600 0.228262i \(-0.0733043\pi\)
\(740\) −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 \(0.301946\pi\)
\(744\) −13.4347 + 23.2695i −0.492538 + 0.853102i
\(745\) −2.39564 4.14938i −0.0877696 0.152021i
\(746\) −69.7432 40.2662i −2.55348 1.47425i
\(747\) 0.742901i 0.0271813i
\(748\) −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 −0.829809 0.558047i \(-0.811551\pi\)
0.898188 + 0.439612i \(0.144884\pi\)
\(752\) 7.67110i 0.279736i
\(753\) 18.9564 32.8335i 0.690811 1.19652i
\(754\) 4.18693 16.9213i 0.152479 0.616237i
\(755\) −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 \(0.868110\pi\)
\(758\) 9.95644 0.361634
\(759\) −15.0000 8.66025i −0.544466 0.314347i
\(760\) 21.5608 12.4481i 0.782092 0.451541i
\(761\) 32.0152i 1.16055i −0.814421 0.580274i \(-0.802945\pi\)
0.814421 0.580274i \(-0.197055\pi\)
\(762\) 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
\(766\) 4.29129 7.43273i 0.155051 0.268555i
\(767\) 30.6606 8.85095i 1.10709 0.319589i
\(768\) −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
\(773\) −19.8303 + 11.4490i −0.713246 + 0.411793i −0.812262 0.583293i \(-0.801764\pi\)
0.0990155 + 0.995086i \(0.468431\pi\)
\(774\) −1.73049 + 0.999100i −0.0622013 + 0.0359119i
\(775\) −1.56534 + 0.903750i −0.0562287 + 0.0324637i
\(776\) −13.1869 + 22.8404i −0.473383 + 0.819924i
\(777\) 0 0
\(778\) 68.8693 39.7617i 2.46908