Properties

Label 882.2.h.m.79.2
Level $882$
Weight $2$
Character 882.79
Analytic conductor $7.043$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
Defining polynomial: \(x^{4} - x^{3} - 2 x^{2} - 3 x + 9\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.2
Root \(-1.18614 - 1.26217i\) of defining polynomial
Character \(\chi\) \(=\) 882.79
Dual form 882.2.h.m.67.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(1.18614 + 1.26217i) q^{3} +(-0.500000 + 0.866025i) q^{4} +4.37228 q^{5} +(-0.500000 + 1.65831i) q^{6} -1.00000 q^{8} +(-0.186141 + 2.99422i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(1.18614 + 1.26217i) q^{3} +(-0.500000 + 0.866025i) q^{4} +4.37228 q^{5} +(-0.500000 + 1.65831i) q^{6} -1.00000 q^{8} +(-0.186141 + 2.99422i) q^{9} +(2.18614 + 3.78651i) q^{10} -1.37228 q^{11} +(-1.68614 + 0.396143i) q^{12} +(-1.00000 - 1.73205i) q^{13} +(5.18614 + 5.51856i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.686141 - 1.18843i) q^{17} +(-2.68614 + 1.33591i) q^{18} +(-2.50000 + 4.33013i) q^{19} +(-2.18614 + 3.78651i) q^{20} +(-0.686141 - 1.18843i) q^{22} -1.62772 q^{23} +(-1.18614 - 1.26217i) q^{24} +14.1168 q^{25} +(1.00000 - 1.73205i) q^{26} +(-4.00000 + 3.31662i) q^{27} +(4.37228 - 7.57301i) q^{29} +(-2.18614 + 7.25061i) q^{30} +(-1.00000 + 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.62772 - 1.73205i) q^{33} +(0.686141 - 1.18843i) q^{34} +(-2.50000 - 1.65831i) q^{36} +(-1.00000 + 1.73205i) q^{37} -5.00000 q^{38} +(1.00000 - 3.31662i) q^{39} -4.37228 q^{40} +(-2.31386 - 4.00772i) q^{41} +(4.05842 - 7.02939i) q^{43} +(0.686141 - 1.18843i) q^{44} +(-0.813859 + 13.0916i) q^{45} +(-0.813859 - 1.40965i) q^{46} +(0.500000 - 1.65831i) q^{48} +(7.05842 + 12.2255i) q^{50} +(0.686141 - 2.27567i) q^{51} +2.00000 q^{52} +(4.37228 + 7.57301i) q^{53} +(-4.87228 - 1.80579i) q^{54} -6.00000 q^{55} +(-8.43070 + 1.98072i) q^{57} +8.74456 q^{58} +(5.05842 - 8.76144i) q^{59} +(-7.37228 + 1.73205i) q^{60} +(-1.55842 - 2.69927i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(-4.37228 - 7.57301i) q^{65} +(0.686141 - 2.27567i) q^{66} +(1.05842 - 1.83324i) q^{67} +1.37228 q^{68} +(-1.93070 - 2.05446i) q^{69} -7.11684 q^{71} +(0.186141 - 2.99422i) q^{72} +(-6.05842 - 10.4935i) q^{73} -2.00000 q^{74} +(16.7446 + 17.8178i) q^{75} +(-2.50000 - 4.33013i) q^{76} +(3.37228 - 0.792287i) q^{78} +(2.55842 + 4.43132i) q^{79} +(-2.18614 - 3.78651i) q^{80} +(-8.93070 - 1.11469i) q^{81} +(2.31386 - 4.00772i) q^{82} +(-8.74456 + 15.1460i) q^{83} +(-3.00000 - 5.19615i) q^{85} +8.11684 q^{86} +(14.7446 - 3.46410i) q^{87} +1.37228 q^{88} +(-7.37228 + 12.7692i) q^{89} +(-11.7446 + 5.84096i) q^{90} +(0.813859 - 1.40965i) q^{92} +(-3.37228 + 0.792287i) q^{93} +(-10.9307 + 18.9325i) q^{95} +(1.68614 - 0.396143i) q^{96} +(4.05842 - 7.02939i) q^{97} +(0.255437 - 4.10891i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - q^{3} - 2q^{4} + 6q^{5} - 2q^{6} - 4q^{8} + 5q^{9} + O(q^{10}) \) \( 4q + 2q^{2} - q^{3} - 2q^{4} + 6q^{5} - 2q^{6} - 4q^{8} + 5q^{9} + 3q^{10} + 6q^{11} - q^{12} - 4q^{13} + 15q^{15} - 2q^{16} + 3q^{17} - 5q^{18} - 10q^{19} - 3q^{20} + 3q^{22} - 18q^{23} + q^{24} + 22q^{25} + 4q^{26} - 16q^{27} + 6q^{29} - 3q^{30} - 4q^{31} + 2q^{32} - 18q^{33} - 3q^{34} - 10q^{36} - 4q^{37} - 20q^{38} + 4q^{39} - 6q^{40} - 15q^{41} - q^{43} - 3q^{44} - 9q^{45} - 9q^{46} + 2q^{48} + 11q^{50} - 3q^{51} + 8q^{52} + 6q^{53} - 8q^{54} - 24q^{55} - 5q^{57} + 12q^{58} + 3q^{59} - 18q^{60} + 11q^{61} - 8q^{62} + 4q^{64} - 6q^{65} - 3q^{66} - 13q^{67} - 6q^{68} + 21q^{69} + 6q^{71} - 5q^{72} - 7q^{73} - 8q^{74} + 44q^{75} - 10q^{76} + 2q^{78} - 7q^{79} - 3q^{80} - 7q^{81} + 15q^{82} - 12q^{83} - 12q^{85} - 2q^{86} + 36q^{87} - 6q^{88} - 18q^{89} - 24q^{90} + 9q^{92} - 2q^{93} - 15q^{95} + q^{96} - q^{97} + 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 1.18614 + 1.26217i 0.684819 + 0.728714i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 4.37228 1.95534 0.977672 0.210138i \(-0.0673912\pi\)
0.977672 + 0.210138i \(0.0673912\pi\)
\(6\) −0.500000 + 1.65831i −0.204124 + 0.677003i
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −0.186141 + 2.99422i −0.0620469 + 0.998073i
\(10\) 2.18614 + 3.78651i 0.691318 + 1.19740i
\(11\) −1.37228 −0.413758 −0.206879 0.978366i \(-0.566331\pi\)
−0.206879 + 0.978366i \(0.566331\pi\)
\(12\) −1.68614 + 0.396143i −0.486747 + 0.114357i
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 0 0
\(15\) 5.18614 + 5.51856i 1.33906 + 1.42489i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −0.686141 1.18843i −0.166414 0.288237i 0.770743 0.637146i \(-0.219885\pi\)
−0.937156 + 0.348910i \(0.886552\pi\)
\(18\) −2.68614 + 1.33591i −0.633129 + 0.314876i
\(19\) −2.50000 + 4.33013i −0.573539 + 0.993399i 0.422659 + 0.906289i \(0.361097\pi\)
−0.996199 + 0.0871106i \(0.972237\pi\)
\(20\) −2.18614 + 3.78651i −0.488836 + 0.846689i
\(21\) 0 0
\(22\) −0.686141 1.18843i −0.146286 0.253374i
\(23\) −1.62772 −0.339403 −0.169701 0.985496i \(-0.554280\pi\)
−0.169701 + 0.985496i \(0.554280\pi\)
\(24\) −1.18614 1.26217i −0.242120 0.257639i
\(25\) 14.1168 2.82337
\(26\) 1.00000 1.73205i 0.196116 0.339683i
\(27\) −4.00000 + 3.31662i −0.769800 + 0.638285i
\(28\) 0 0
\(29\) 4.37228 7.57301i 0.811912 1.40627i −0.0996117 0.995026i \(-0.531760\pi\)
0.911524 0.411247i \(-0.134907\pi\)
\(30\) −2.18614 + 7.25061i −0.399133 + 1.32377i
\(31\) −1.00000 + 1.73205i −0.179605 + 0.311086i −0.941745 0.336327i \(-0.890815\pi\)
0.762140 + 0.647412i \(0.224149\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −1.62772 1.73205i −0.283349 0.301511i
\(34\) 0.686141 1.18843i 0.117672 0.203814i
\(35\) 0 0
\(36\) −2.50000 1.65831i −0.416667 0.276385i
\(37\) −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i \(-0.885902\pi\)
0.772043 + 0.635571i \(0.219235\pi\)
\(38\) −5.00000 −0.811107
\(39\) 1.00000 3.31662i 0.160128 0.531085i
\(40\) −4.37228 −0.691318
\(41\) −2.31386 4.00772i −0.361364 0.625901i 0.626821 0.779163i \(-0.284356\pi\)
−0.988186 + 0.153262i \(0.951022\pi\)
\(42\) 0 0
\(43\) 4.05842 7.02939i 0.618904 1.07197i −0.370783 0.928720i \(-0.620910\pi\)
0.989686 0.143253i \(-0.0457562\pi\)
\(44\) 0.686141 1.18843i 0.103440 0.179163i
\(45\) −0.813859 + 13.0916i −0.121323 + 1.95158i
\(46\) −0.813859 1.40965i −0.119997 0.207841i
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0.500000 1.65831i 0.0721688 0.239357i
\(49\) 0 0
\(50\) 7.05842 + 12.2255i 0.998212 + 1.72895i
\(51\) 0.686141 2.27567i 0.0960789 0.318658i
\(52\) 2.00000 0.277350
\(53\) 4.37228 + 7.57301i 0.600579 + 1.04023i 0.992733 + 0.120334i \(0.0383965\pi\)
−0.392154 + 0.919899i \(0.628270\pi\)
\(54\) −4.87228 1.80579i −0.663034 0.245737i
\(55\) −6.00000 −0.809040
\(56\) 0 0
\(57\) −8.43070 + 1.98072i −1.11667 + 0.262352i
\(58\) 8.74456 1.14822
\(59\) 5.05842 8.76144i 0.658550 1.14064i −0.322441 0.946590i \(-0.604503\pi\)
0.980991 0.194053i \(-0.0621634\pi\)
\(60\) −7.37228 + 1.73205i −0.951757 + 0.223607i
\(61\) −1.55842 2.69927i −0.199535 0.345606i 0.748842 0.662748i \(-0.230610\pi\)
−0.948378 + 0.317142i \(0.897277\pi\)
\(62\) −2.00000 −0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −4.37228 7.57301i −0.542315 0.939317i
\(66\) 0.686141 2.27567i 0.0844581 0.280116i
\(67\) 1.05842 1.83324i 0.129307 0.223966i −0.794101 0.607785i \(-0.792058\pi\)
0.923408 + 0.383819i \(0.125391\pi\)
\(68\) 1.37228 0.166414
\(69\) −1.93070 2.05446i −0.232429 0.247327i
\(70\) 0 0
\(71\) −7.11684 −0.844614 −0.422307 0.906453i \(-0.638780\pi\)
−0.422307 + 0.906453i \(0.638780\pi\)
\(72\) 0.186141 2.99422i 0.0219369 0.352872i
\(73\) −6.05842 10.4935i −0.709085 1.22817i −0.965197 0.261524i \(-0.915775\pi\)
0.256112 0.966647i \(-0.417558\pi\)
\(74\) −2.00000 −0.232495
\(75\) 16.7446 + 17.8178i 1.93350 + 2.05743i
\(76\) −2.50000 4.33013i −0.286770 0.496700i
\(77\) 0 0
\(78\) 3.37228 0.792287i 0.381836 0.0897088i
\(79\) 2.55842 + 4.43132i 0.287845 + 0.498562i 0.973295 0.229557i \(-0.0737279\pi\)
−0.685450 + 0.728120i \(0.740395\pi\)
\(80\) −2.18614 3.78651i −0.244418 0.423344i
\(81\) −8.93070 1.11469i −0.992300 0.123855i
\(82\) 2.31386 4.00772i 0.255523 0.442579i
\(83\) −8.74456 + 15.1460i −0.959840 + 1.66249i −0.236960 + 0.971519i \(0.576151\pi\)
−0.722881 + 0.690973i \(0.757182\pi\)
\(84\) 0 0
\(85\) −3.00000 5.19615i −0.325396 0.563602i
\(86\) 8.11684 0.875262
\(87\) 14.7446 3.46410i 1.58078 0.371391i
\(88\) 1.37228 0.146286
\(89\) −7.37228 + 12.7692i −0.781460 + 1.35353i 0.149631 + 0.988742i \(0.452192\pi\)
−0.931091 + 0.364787i \(0.881142\pi\)
\(90\) −11.7446 + 5.84096i −1.23799 + 0.615692i
\(91\) 0 0
\(92\) 0.813859 1.40965i 0.0848507 0.146966i
\(93\) −3.37228 + 0.792287i −0.349689 + 0.0821563i
\(94\) 0 0
\(95\) −10.9307 + 18.9325i −1.12147 + 1.94244i
\(96\) 1.68614 0.396143i 0.172091 0.0404312i
\(97\) 4.05842 7.02939i 0.412070 0.713727i −0.583046 0.812439i \(-0.698139\pi\)
0.995116 + 0.0987127i \(0.0314725\pi\)
\(98\) 0 0
\(99\) 0.255437 4.10891i 0.0256724 0.412961i
\(100\) −7.05842 + 12.2255i −0.705842 + 1.22255i
\(101\) 1.62772 0.161964 0.0809820 0.996716i \(-0.474194\pi\)
0.0809820 + 0.996716i \(0.474194\pi\)
\(102\) 2.31386 0.543620i 0.229106 0.0538264i
\(103\) −10.0000 −0.985329 −0.492665 0.870219i \(-0.663977\pi\)
−0.492665 + 0.870219i \(0.663977\pi\)
\(104\) 1.00000 + 1.73205i 0.0980581 + 0.169842i
\(105\) 0 0
\(106\) −4.37228 + 7.57301i −0.424674 + 0.735556i
\(107\) 3.68614 6.38458i 0.356353 0.617221i −0.630996 0.775786i \(-0.717354\pi\)
0.987348 + 0.158565i \(0.0506868\pi\)
\(108\) −0.872281 5.12241i −0.0839353 0.492905i
\(109\) −7.00000 12.1244i −0.670478 1.16130i −0.977769 0.209687i \(-0.932756\pi\)
0.307290 0.951616i \(-0.400578\pi\)
\(110\) −3.00000 5.19615i −0.286039 0.495434i
\(111\) −3.37228 + 0.792287i −0.320083 + 0.0752006i
\(112\) 0 0
\(113\) 2.18614 + 3.78651i 0.205655 + 0.356205i 0.950341 0.311210i \(-0.100734\pi\)
−0.744686 + 0.667415i \(0.767401\pi\)
\(114\) −5.93070 6.31084i −0.555461 0.591065i
\(115\) −7.11684 −0.663649
\(116\) 4.37228 + 7.57301i 0.405956 + 0.703137i
\(117\) 5.37228 2.67181i 0.496668 0.247009i
\(118\) 10.1168 0.931331
\(119\) 0 0
\(120\) −5.18614 5.51856i −0.473428 0.503773i
\(121\) −9.11684 −0.828804
\(122\) 1.55842 2.69927i 0.141093 0.244380i
\(123\) 2.31386 7.67420i 0.208634 0.691960i
\(124\) −1.00000 1.73205i −0.0898027 0.155543i
\(125\) 39.8614 3.56531
\(126\) 0 0
\(127\) 3.11684 0.276575 0.138288 0.990392i \(-0.455840\pi\)
0.138288 + 0.990392i \(0.455840\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 13.6861 3.21543i 1.20500 0.283103i
\(130\) 4.37228 7.57301i 0.383474 0.664197i
\(131\) −1.62772 −0.142214 −0.0711072 0.997469i \(-0.522653\pi\)
−0.0711072 + 0.997469i \(0.522653\pi\)
\(132\) 2.31386 0.543620i 0.201396 0.0473161i
\(133\) 0 0
\(134\) 2.11684 0.182867
\(135\) −17.4891 + 14.5012i −1.50522 + 1.24807i
\(136\) 0.686141 + 1.18843i 0.0588361 + 0.101907i
\(137\) 10.6277 0.907987 0.453994 0.891005i \(-0.349999\pi\)
0.453994 + 0.891005i \(0.349999\pi\)
\(138\) 0.813859 2.69927i 0.0692803 0.229777i
\(139\) −6.61684 11.4607i −0.561233 0.972085i −0.997389 0.0722136i \(-0.976994\pi\)
0.436156 0.899871i \(-0.356340\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −3.55842 6.16337i −0.298616 0.517218i
\(143\) 1.37228 + 2.37686i 0.114756 + 0.198763i
\(144\) 2.68614 1.33591i 0.223845 0.111326i
\(145\) 19.1168 33.1113i 1.58757 2.74975i
\(146\) 6.05842 10.4935i 0.501399 0.868448i
\(147\) 0 0
\(148\) −1.00000 1.73205i −0.0821995 0.142374i
\(149\) 3.25544 0.266696 0.133348 0.991069i \(-0.457427\pi\)
0.133348 + 0.991069i \(0.457427\pi\)
\(150\) −7.05842 + 23.4101i −0.576318 + 1.91143i
\(151\) 9.11684 0.741918 0.370959 0.928649i \(-0.379029\pi\)
0.370959 + 0.928649i \(0.379029\pi\)
\(152\) 2.50000 4.33013i 0.202777 0.351220i
\(153\) 3.68614 1.83324i 0.298007 0.148209i
\(154\) 0 0
\(155\) −4.37228 + 7.57301i −0.351190 + 0.608279i
\(156\) 2.37228 + 2.52434i 0.189935 + 0.202109i
\(157\) −4.55842 + 7.89542i −0.363802 + 0.630123i −0.988583 0.150677i \(-0.951855\pi\)
0.624781 + 0.780800i \(0.285188\pi\)
\(158\) −2.55842 + 4.43132i −0.203537 + 0.352537i
\(159\) −4.37228 + 14.5012i −0.346744 + 1.15002i
\(160\) 2.18614 3.78651i 0.172830 0.299350i
\(161\) 0 0
\(162\) −3.50000 8.29156i −0.274986 0.651447i
\(163\) 9.11684 15.7908i 0.714086 1.23683i −0.249225 0.968446i \(-0.580176\pi\)
0.963311 0.268388i \(-0.0864909\pi\)
\(164\) 4.62772 0.361364
\(165\) −7.11684 7.57301i −0.554046 0.589558i
\(166\) −17.4891 −1.35742
\(167\) 2.74456 + 4.75372i 0.212381 + 0.367854i 0.952459 0.304666i \(-0.0985450\pi\)
−0.740078 + 0.672521i \(0.765212\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 3.00000 5.19615i 0.230089 0.398527i
\(171\) −12.5000 8.29156i −0.955899 0.634072i
\(172\) 4.05842 + 7.02939i 0.309452 + 0.535986i
\(173\) 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 10.3723 + 11.0371i 0.786321 + 0.836722i
\(175\) 0 0
\(176\) 0.686141 + 1.18843i 0.0517198 + 0.0895813i
\(177\) 17.0584 4.00772i 1.28219 0.301239i
\(178\) −14.7446 −1.10515
\(179\) −1.62772 2.81929i −0.121661 0.210724i 0.798762 0.601648i \(-0.205489\pi\)
−0.920423 + 0.390924i \(0.872156\pi\)
\(180\) −10.9307 7.25061i −0.814727 0.540428i
\(181\) 0.883156 0.0656445 0.0328222 0.999461i \(-0.489550\pi\)
0.0328222 + 0.999461i \(0.489550\pi\)
\(182\) 0 0
\(183\) 1.55842 5.16870i 0.115202 0.382081i
\(184\) 1.62772 0.119997
\(185\) −4.37228 + 7.57301i −0.321457 + 0.556779i
\(186\) −2.37228 2.52434i −0.173944 0.185093i
\(187\) 0.941578 + 1.63086i 0.0688550 + 0.119260i
\(188\) 0 0
\(189\) 0 0
\(190\) −21.8614 −1.58599
\(191\) 9.55842 + 16.5557i 0.691623 + 1.19793i 0.971306 + 0.237834i \(0.0764374\pi\)
−0.279683 + 0.960092i \(0.590229\pi\)
\(192\) 1.18614 + 1.26217i 0.0856023 + 0.0910892i
\(193\) 3.50000 6.06218i 0.251936 0.436365i −0.712123 0.702055i \(-0.752266\pi\)
0.964059 + 0.265689i \(0.0855996\pi\)
\(194\) 8.11684 0.582755
\(195\) 4.37228 14.5012i 0.313106 1.03845i
\(196\) 0 0
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 3.68614 1.83324i 0.261963 0.130283i
\(199\) 5.00000 + 8.66025i 0.354441 + 0.613909i 0.987022 0.160585i \(-0.0513380\pi\)
−0.632581 + 0.774494i \(0.718005\pi\)
\(200\) −14.1168 −0.998212
\(201\) 3.56930 0.838574i 0.251759 0.0591484i
\(202\) 0.813859 + 1.40965i 0.0572629 + 0.0991823i
\(203\) 0 0
\(204\) 1.62772 + 1.73205i 0.113963 + 0.121268i
\(205\) −10.1168 17.5229i −0.706591 1.22385i
\(206\) −5.00000 8.66025i −0.348367 0.603388i
\(207\) 0.302985 4.87375i 0.0210589 0.338749i
\(208\) −1.00000 + 1.73205i −0.0693375 + 0.120096i
\(209\) 3.43070 5.94215i 0.237307 0.411027i
\(210\) 0 0
\(211\) 8.00000 + 13.8564i 0.550743 + 0.953914i 0.998221 + 0.0596196i \(0.0189888\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) −8.74456 −0.600579
\(213\) −8.44158 8.98266i −0.578407 0.615482i
\(214\) 7.37228 0.503959
\(215\) 17.7446 30.7345i 1.21017 2.09607i
\(216\) 4.00000 3.31662i 0.272166 0.225668i
\(217\) 0 0
\(218\) 7.00000 12.1244i 0.474100 0.821165i
\(219\) 6.05842 20.0935i 0.409390 1.35779i
\(220\) 3.00000 5.19615i 0.202260 0.350325i
\(221\) −1.37228 + 2.37686i −0.0923096 + 0.159885i
\(222\) −2.37228 2.52434i −0.159217 0.169422i
\(223\) 2.00000 3.46410i 0.133930 0.231973i −0.791258 0.611482i \(-0.790574\pi\)
0.925188 + 0.379509i \(0.123907\pi\)
\(224\) 0 0
\(225\) −2.62772 + 42.2689i −0.175181 + 2.81793i
\(226\) −2.18614 + 3.78651i −0.145420 + 0.251875i
\(227\) −12.2554 −0.813422 −0.406711 0.913557i \(-0.633324\pi\)
−0.406711 + 0.913557i \(0.633324\pi\)
\(228\) 2.50000 8.29156i 0.165567 0.549122i
\(229\) −2.88316 −0.190524 −0.0952622 0.995452i \(-0.530369\pi\)
−0.0952622 + 0.995452i \(0.530369\pi\)
\(230\) −3.55842 6.16337i −0.234635 0.406400i
\(231\) 0 0
\(232\) −4.37228 + 7.57301i −0.287054 + 0.497193i
\(233\) 0.127719 0.221215i 0.00836713 0.0144923i −0.861812 0.507229i \(-0.830670\pi\)
0.870179 + 0.492736i \(0.164003\pi\)
\(234\) 5.00000 + 3.31662i 0.326860 + 0.216815i
\(235\) 0 0
\(236\) 5.05842 + 8.76144i 0.329275 + 0.570321i
\(237\) −2.55842 + 8.48533i −0.166187 + 0.551181i
\(238\) 0 0
\(239\) −4.93070 8.54023i −0.318941 0.552421i 0.661327 0.750098i \(-0.269994\pi\)
−0.980267 + 0.197677i \(0.936660\pi\)
\(240\) 2.18614 7.25061i 0.141115 0.468025i
\(241\) 18.1168 1.16701 0.583504 0.812110i \(-0.301681\pi\)
0.583504 + 0.812110i \(0.301681\pi\)
\(242\) −4.55842 7.89542i −0.293026 0.507537i
\(243\) −9.18614 12.5942i −0.589291 0.807921i
\(244\) 3.11684 0.199535
\(245\) 0 0
\(246\) 7.80298 1.83324i 0.497500 0.116883i
\(247\) 10.0000 0.636285
\(248\) 1.00000 1.73205i 0.0635001 0.109985i
\(249\) −29.4891 + 6.92820i −1.86880 + 0.439057i
\(250\) 19.9307 + 34.5210i 1.26053 + 2.18330i
\(251\) −9.00000 −0.568075 −0.284037 0.958813i \(-0.591674\pi\)
−0.284037 + 0.958813i \(0.591674\pi\)
\(252\) 0 0
\(253\) 2.23369 0.140431
\(254\) 1.55842 + 2.69927i 0.0977841 + 0.169367i
\(255\) 3.00000 9.94987i 0.187867 0.623085i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −6.86141 −0.428003 −0.214001 0.976833i \(-0.568650\pi\)
−0.214001 + 0.976833i \(0.568650\pi\)
\(258\) 9.62772 + 10.2448i 0.599396 + 0.637815i
\(259\) 0 0
\(260\) 8.74456 0.542315
\(261\) 21.8614 + 14.5012i 1.35319 + 0.897603i
\(262\) −0.813859 1.40965i −0.0502804 0.0870882i
\(263\) 7.62772 0.470345 0.235173 0.971954i \(-0.424434\pi\)
0.235173 + 0.971954i \(0.424434\pi\)
\(264\) 1.62772 + 1.73205i 0.100179 + 0.106600i
\(265\) 19.1168 + 33.1113i 1.17434 + 2.03401i
\(266\) 0 0
\(267\) −24.8614 + 5.84096i −1.52149 + 0.357461i
\(268\) 1.05842 + 1.83324i 0.0646534 + 0.111983i
\(269\) 0.813859 + 1.40965i 0.0496219 + 0.0859476i 0.889769 0.456410i \(-0.150865\pi\)
−0.840148 + 0.542358i \(0.817532\pi\)
\(270\) −21.3030 7.89542i −1.29646 0.480500i
\(271\) −8.11684 + 14.0588i −0.493063 + 0.854010i −0.999968 0.00799154i \(-0.997456\pi\)
0.506905 + 0.862002i \(0.330790\pi\)
\(272\) −0.686141 + 1.18843i −0.0416034 + 0.0720592i
\(273\) 0 0
\(274\) 5.31386 + 9.20387i 0.321022 + 0.556026i
\(275\) −19.3723 −1.16819
\(276\) 2.74456 0.644810i 0.165203 0.0388130i
\(277\) −12.2337 −0.735051 −0.367526 0.930013i \(-0.619795\pi\)
−0.367526 + 0.930013i \(0.619795\pi\)
\(278\) 6.61684 11.4607i 0.396852 0.687368i
\(279\) −5.00000 3.31662i −0.299342 0.198561i
\(280\) 0 0
\(281\) −8.18614 + 14.1788i −0.488344 + 0.845837i −0.999910 0.0134071i \(-0.995732\pi\)
0.511566 + 0.859244i \(0.329066\pi\)
\(282\) 0 0
\(283\) −13.5584 + 23.4839i −0.805965 + 1.39597i 0.109673 + 0.993968i \(0.465019\pi\)
−0.915638 + 0.402004i \(0.868314\pi\)
\(284\) 3.55842 6.16337i 0.211153 0.365729i
\(285\) −36.8614 + 8.66025i −2.18348 + 0.512989i
\(286\) −1.37228 + 2.37686i −0.0811447 + 0.140547i
\(287\) 0 0
\(288\) 2.50000 + 1.65831i 0.147314 + 0.0977170i
\(289\) 7.55842 13.0916i 0.444613 0.770092i
\(290\) 38.2337 2.24516
\(291\) 13.6861 3.21543i 0.802296 0.188492i
\(292\) 12.1168 0.709085
\(293\) 5.18614 + 8.98266i 0.302978 + 0.524773i 0.976809 0.214113i \(-0.0686859\pi\)
−0.673831 + 0.738885i \(0.735353\pi\)
\(294\) 0 0
\(295\) 22.1168 38.3075i 1.28769 2.23035i
\(296\) 1.00000 1.73205i 0.0581238 0.100673i
\(297\) 5.48913 4.55134i 0.318511 0.264096i
\(298\) 1.62772 + 2.81929i 0.0942912 + 0.163317i
\(299\) 1.62772 + 2.81929i 0.0941334 + 0.163044i
\(300\) −23.8030 + 5.59230i −1.37427 + 0.322871i
\(301\) 0 0
\(302\) 4.55842 + 7.89542i 0.262308 + 0.454330i
\(303\) 1.93070 + 2.05446i 0.110916 + 0.118025i
\(304\) 5.00000 0.286770
\(305\) −6.81386 11.8020i −0.390160 0.675778i
\(306\) 3.43070 + 2.27567i 0.196120 + 0.130091i
\(307\) −13.0000 −0.741949 −0.370975 0.928643i \(-0.620976\pi\)
−0.370975 + 0.928643i \(0.620976\pi\)
\(308\) 0 0
\(309\) −11.8614 12.6217i −0.674772 0.718023i
\(310\) −8.74456 −0.496658
\(311\) −4.11684 + 7.13058i −0.233445 + 0.404338i −0.958820 0.284016i \(-0.908333\pi\)
0.725375 + 0.688354i \(0.241666\pi\)
\(312\) −1.00000 + 3.31662i −0.0566139 + 0.187767i
\(313\) 10.0584 + 17.4217i 0.568536 + 0.984733i 0.996711 + 0.0810370i \(0.0258232\pi\)
−0.428175 + 0.903696i \(0.640843\pi\)
\(314\) −9.11684 −0.514493
\(315\) 0 0
\(316\) −5.11684 −0.287845
\(317\) 3.00000 + 5.19615i 0.168497 + 0.291845i 0.937892 0.346929i \(-0.112775\pi\)
−0.769395 + 0.638774i \(0.779442\pi\)
\(318\) −14.7446 + 3.46410i −0.826834 + 0.194257i
\(319\) −6.00000 + 10.3923i −0.335936 + 0.581857i
\(320\) 4.37228 0.244418
\(321\) 12.4307 2.92048i 0.693814 0.163005i
\(322\) 0 0
\(323\) 6.86141 0.381779
\(324\) 5.43070 7.17687i 0.301706 0.398715i
\(325\) −14.1168 24.4511i −0.783062 1.35630i
\(326\) 18.2337 1.00987
\(327\) 7.00000 23.2164i 0.387101 1.28387i
\(328\) 2.31386 + 4.00772i 0.127762 + 0.221289i
\(329\) 0 0
\(330\) 3.00000 9.94987i 0.165145 0.547723i
\(331\) −11.1168 19.2549i −0.611037 1.05835i −0.991066 0.133373i \(-0.957419\pi\)
0.380029 0.924975i \(-0.375914\pi\)
\(332\) −8.74456 15.1460i −0.479920 0.831246i
\(333\) −5.00000 3.31662i −0.273998 0.181750i
\(334\) −2.74456 + 4.75372i −0.150176 + 0.260112i
\(335\) 4.62772 8.01544i 0.252839 0.437930i
\(336\) 0 0
\(337\) 4.05842 + 7.02939i 0.221076 + 0.382915i 0.955135 0.296171i \(-0.0957097\pi\)
−0.734059 + 0.679086i \(0.762376\pi\)
\(338\) 9.00000 0.489535
\(339\) −2.18614 + 7.25061i −0.118735 + 0.393799i
\(340\) 6.00000 0.325396
\(341\) 1.37228 2.37686i 0.0743132 0.128714i
\(342\) 0.930703 14.9711i 0.0503267 0.809544i
\(343\) 0 0
\(344\) −4.05842 + 7.02939i −0.218815 + 0.378999i
\(345\) −8.44158 8.98266i −0.454479 0.483610i
\(346\) −3.00000 + 5.19615i −0.161281 + 0.279347i
\(347\) 5.05842 8.76144i 0.271550 0.470339i −0.697709 0.716382i \(-0.745797\pi\)
0.969259 + 0.246043i \(0.0791303\pi\)
\(348\) −4.37228 + 14.5012i −0.234379 + 0.777347i
\(349\) 11.0000 19.0526i 0.588817 1.01986i −0.405571 0.914063i \(-0.632927\pi\)
0.994388 0.105797i \(-0.0337393\pi\)
\(350\) 0 0
\(351\) 9.74456 + 3.61158i 0.520126 + 0.192772i
\(352\) −0.686141 + 1.18843i −0.0365714 + 0.0633436i
\(353\) −13.3723 −0.711735 −0.355867 0.934536i \(-0.615815\pi\)
−0.355867 + 0.934536i \(0.615815\pi\)
\(354\) 12.0000 + 12.7692i 0.637793 + 0.678674i
\(355\) −31.1168 −1.65151
\(356\) −7.37228 12.7692i −0.390730 0.676764i
\(357\) 0 0
\(358\) 1.62772 2.81929i 0.0860276 0.149004i
\(359\) −10.9307 + 18.9325i −0.576900 + 0.999221i 0.418932 + 0.908018i \(0.362405\pi\)
−0.995832 + 0.0912032i \(0.970929\pi\)
\(360\) 0.813859 13.0916i 0.0428942 0.689986i
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) 0.441578 + 0.764836i 0.0232088 + 0.0401989i
\(363\) −10.8139 11.5070i −0.567580 0.603961i
\(364\) 0 0
\(365\) −26.4891 45.8805i −1.38650 2.40150i
\(366\) 5.25544 1.23472i 0.274706 0.0645397i
\(367\) −12.2337 −0.638593 −0.319297 0.947655i \(-0.603447\pi\)
−0.319297 + 0.947655i \(0.603447\pi\)
\(368\) 0.813859 + 1.40965i 0.0424254 + 0.0734829i
\(369\) 12.4307 6.18220i 0.647117 0.321833i
\(370\) −8.74456 −0.454608
\(371\) 0 0
\(372\) 1.00000 3.31662i 0.0518476 0.171959i
\(373\) −10.0000 −0.517780 −0.258890 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) −0.941578 + 1.63086i −0.0486878 + 0.0843298i
\(375\) 47.2812 + 50.3118i 2.44159 + 2.59809i
\(376\) 0 0
\(377\) −17.4891 −0.900736
\(378\) 0 0
\(379\) −8.11684 −0.416934 −0.208467 0.978029i \(-0.566847\pi\)
−0.208467 + 0.978029i \(0.566847\pi\)
\(380\) −10.9307 18.9325i −0.560733 0.971218i
\(381\) 3.69702 + 3.93398i 0.189404 + 0.201544i
\(382\) −9.55842 + 16.5557i −0.489051 + 0.847062i
\(383\) −32.7446 −1.67317 −0.836584 0.547838i \(-0.815451\pi\)
−0.836584 + 0.547838i \(0.815451\pi\)
\(384\) −0.500000 + 1.65831i −0.0255155 + 0.0846254i
\(385\) 0 0
\(386\) 7.00000 0.356291
\(387\) 20.2921 + 13.4603i 1.03151 + 0.684224i
\(388\) 4.05842 + 7.02939i 0.206035 + 0.356863i
\(389\) 10.9783 0.556619 0.278310 0.960491i \(-0.410226\pi\)
0.278310 + 0.960491i \(0.410226\pi\)
\(390\) 14.7446 3.46410i 0.746620 0.175412i
\(391\) 1.11684 + 1.93443i 0.0564812 + 0.0978284i
\(392\) 0 0
\(393\) −1.93070 2.05446i −0.0973911 0.103634i
\(394\) −3.00000 5.19615i −0.151138 0.261778i
\(395\) 11.1861 + 19.3750i 0.562836 + 0.974860i
\(396\) 3.43070 + 2.27567i 0.172399 + 0.114357i
\(397\) 11.0000 19.0526i 0.552074 0.956221i −0.446051 0.895008i \(-0.647170\pi\)
0.998125 0.0612128i \(-0.0194968\pi\)
\(398\) −5.00000 + 8.66025i −0.250627 + 0.434099i
\(399\) 0 0
\(400\) −7.05842 12.2255i −0.352921 0.611277i
\(401\) −11.7446 −0.586495 −0.293248 0.956036i \(-0.594736\pi\)
−0.293248 + 0.956036i \(0.594736\pi\)
\(402\) 2.51087 + 2.67181i 0.125231 + 0.133258i
\(403\) 4.00000 0.199254
\(404\) −0.813859 + 1.40965i −0.0404910 + 0.0701325i
\(405\) −39.0475 4.87375i −1.94029 0.242178i
\(406\) 0 0
\(407\) 1.37228 2.37686i 0.0680215 0.117817i
\(408\) −0.686141 + 2.27567i −0.0339690 + 0.112663i
\(409\) 11.1753 19.3561i 0.552581 0.957099i −0.445506 0.895279i \(-0.646976\pi\)
0.998087 0.0618200i \(-0.0196905\pi\)
\(410\) 10.1168 17.5229i 0.499635 0.865394i
\(411\) 12.6060 + 13.4140i 0.621807 + 0.661663i
\(412\) 5.00000 8.66025i 0.246332 0.426660i
\(413\) 0 0
\(414\) 4.37228 2.17448i 0.214886 0.106870i
\(415\) −38.2337 + 66.2227i −1.87682 + 3.25074i
\(416\) −2.00000 −0.0980581
\(417\) 6.61684 21.9456i 0.324028 1.07468i
\(418\) 6.86141 0.335602
\(419\) 6.30298 + 10.9171i 0.307921 + 0.533335i 0.977907 0.209039i \(-0.0670334\pi\)
−0.669986 + 0.742373i \(0.733700\pi\)
\(420\) 0 0
\(421\) −17.1168 + 29.6472i −0.834224 + 1.44492i 0.0604368 + 0.998172i \(0.480751\pi\)
−0.894661 + 0.446746i \(0.852583\pi\)
\(422\) −8.00000 + 13.8564i −0.389434 + 0.674519i
\(423\) 0 0
\(424\) −4.37228 7.57301i −0.212337 0.367778i
\(425\) −9.68614 16.7769i −0.469847 0.813799i
\(426\) 3.55842 11.8020i 0.172406 0.571806i
\(427\) 0 0
\(428\) 3.68614 + 6.38458i 0.178176 + 0.308610i
\(429\) −1.37228 + 4.55134i −0.0662544 + 0.219741i
\(430\) 35.4891 1.71144
\(431\) 3.25544 + 5.63858i 0.156809 + 0.271601i 0.933716 0.358014i \(-0.116546\pi\)
−0.776907 + 0.629615i \(0.783213\pi\)
\(432\) 4.87228 + 1.80579i 0.234418 + 0.0868811i
\(433\) −20.1168 −0.966754 −0.483377 0.875412i \(-0.660590\pi\)
−0.483377 + 0.875412i \(0.660590\pi\)
\(434\) 0 0
\(435\) 64.4674 15.1460i 3.09097 0.726196i
\(436\) 14.0000 0.670478
\(437\) 4.06930 7.04823i 0.194661 0.337162i
\(438\) 20.4307 4.80001i 0.976217 0.229353i
\(439\) −4.00000 6.92820i −0.190910 0.330665i 0.754642 0.656136i \(-0.227810\pi\)
−0.945552 + 0.325471i \(0.894477\pi\)
\(440\) 6.00000 0.286039
\(441\) 0 0
\(442\) −2.74456 −0.130546
\(443\) 20.0584 + 34.7422i 0.953004 + 1.65065i 0.738870 + 0.673848i \(0.235360\pi\)
0.214134 + 0.976804i \(0.431307\pi\)
\(444\) 1.00000 3.31662i 0.0474579 0.157400i
\(445\) −32.2337 + 55.8304i −1.52802 + 2.64661i
\(446\) 4.00000 0.189405
\(447\) 3.86141 + 4.10891i 0.182638 + 0.194345i
\(448\) 0 0
\(449\) 33.0000 1.55737 0.778683 0.627417i \(-0.215888\pi\)
0.778683 + 0.627417i \(0.215888\pi\)
\(450\) −37.9198 + 18.8588i −1.78756 + 0.889012i
\(451\) 3.17527 + 5.49972i 0.149517 + 0.258972i
\(452\) −4.37228 −0.205655
\(453\) 10.8139 + 11.5070i 0.508079 + 0.540646i
\(454\) −6.12772 10.6135i −0.287588 0.498117i
\(455\) 0 0
\(456\) 8.43070 1.98072i 0.394804 0.0927556i
\(457\) 17.7337 + 30.7156i 0.829547 + 1.43682i 0.898394 + 0.439190i \(0.144735\pi\)
−0.0688472 + 0.997627i \(0.521932\pi\)
\(458\) −1.44158 2.49689i −0.0673605 0.116672i
\(459\) 6.68614 + 2.47805i 0.312082 + 0.115666i
\(460\) 3.55842 6.16337i 0.165912 0.287368i
\(461\) −1.06930 + 1.85208i −0.0498021 + 0.0862598i −0.889852 0.456250i \(-0.849192\pi\)
0.840050 + 0.542509i \(0.182526\pi\)
\(462\) 0 0
\(463\) 11.5584 + 20.0198i 0.537165 + 0.930398i 0.999055 + 0.0434604i \(0.0138382\pi\)
−0.461890 + 0.886937i \(0.652828\pi\)
\(464\) −8.74456 −0.405956
\(465\) −14.7446 + 3.46410i −0.683763 + 0.160644i
\(466\) 0.255437 0.0118329
\(467\) −16.5475 + 28.6612i −0.765729 + 1.32628i 0.174131 + 0.984722i \(0.444288\pi\)
−0.939860 + 0.341559i \(0.889045\pi\)
\(468\) −0.372281 + 5.98844i −0.0172087 + 0.276816i
\(469\) 0 0
\(470\) 0 0
\(471\) −15.3723 + 3.61158i −0.708317 + 0.166413i
\(472\) −5.05842 + 8.76144i −0.232833 + 0.403278i
\(473\) −5.56930 + 9.64630i −0.256077 + 0.443538i
\(474\) −8.62772 + 2.02700i −0.396284 + 0.0931034i
\(475\) −35.2921 + 61.1277i −1.61931 + 2.80473i
\(476\) 0 0
\(477\) −23.4891 + 11.6819i −1.07549 + 0.534879i
\(478\) 4.93070 8.54023i 0.225525 0.390621i
\(479\) 32.7446 1.49614 0.748069 0.663621i \(-0.230981\pi\)
0.748069 + 0.663621i \(0.230981\pi\)
\(480\) 7.37228 1.73205i 0.336497 0.0790569i
\(481\) 4.00000 0.182384
\(482\) 9.05842 + 15.6896i 0.412600 + 0.714644i
\(483\) 0 0
\(484\) 4.55842 7.89542i 0.207201 0.358883i
\(485\) 17.7446 30.7345i 0.805739 1.39558i
\(486\) 6.31386 14.2525i 0.286402 0.646509i
\(487\) −17.6753 30.6145i −0.800943 1.38727i −0.918996 0.394266i \(-0.870999\pi\)
0.118053 0.993007i \(-0.462335\pi\)
\(488\) 1.55842 + 2.69927i 0.0705464 + 0.122190i
\(489\) 30.7446 7.22316i 1.39032 0.326642i
\(490\) 0 0
\(491\) 12.6861 + 21.9730i 0.572518 + 0.991629i 0.996306 + 0.0858685i \(0.0273665\pi\)
−0.423789 + 0.905761i \(0.639300\pi\)
\(492\) 5.48913 + 5.84096i 0.247469 + 0.263331i
\(493\) −12.0000 −0.540453
\(494\) 5.00000 + 8.66025i 0.224961 + 0.389643i
\(495\) 1.11684 17.9653i 0.0501984 0.807481i
\(496\) 2.00000 0.0898027
\(497\) 0 0
\(498\) −20.7446 22.0742i −0.929586 0.989170i
\(499\) 18.1168 0.811021 0.405511 0.914090i \(-0.367094\pi\)
0.405511 + 0.914090i \(0.367094\pi\)
\(500\) −19.9307 + 34.5210i −0.891328 + 1.54383i
\(501\) −2.74456 + 9.10268i −0.122618 + 0.406678i
\(502\) −4.50000 7.79423i −0.200845 0.347873i
\(503\) −32.2337 −1.43723 −0.718615 0.695409i \(-0.755223\pi\)
−0.718615 + 0.695409i \(0.755223\pi\)
\(504\) 0 0
\(505\) 7.11684 0.316695
\(506\) 1.11684 + 1.93443i 0.0496498 + 0.0859959i
\(507\) 15.1753 3.56529i 0.673957 0.158340i
\(508\) −1.55842 + 2.69927i −0.0691438 + 0.119761i
\(509\) −28.9783 −1.28444 −0.642219 0.766521i \(-0.721986\pi\)
−0.642219 + 0.766521i \(0.721986\pi\)
\(510\) 10.1168 2.37686i 0.447981 0.105249i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −4.36141 25.6121i −0.192561 1.13080i
\(514\) −3.43070 5.94215i −0.151322 0.262097i
\(515\) −43.7228 −1.92666
\(516\) −4.05842 + 13.4603i −0.178662 + 0.592555i
\(517\) 0 0
\(518\) 0 0
\(519\) −3.00000 + 9.94987i −0.131685 + 0.436751i
\(520\) 4.37228 + 7.57301i 0.191737 + 0.332099i
\(521\) 12.4307 + 21.5306i 0.544599 + 0.943273i 0.998632 + 0.0522883i \(0.0166515\pi\)
−0.454033 + 0.890985i \(0.650015\pi\)
\(522\) −1.62772 + 26.1831i −0.0712433 + 1.14600i
\(523\) 17.5584 30.4121i 0.767776 1.32983i −0.170990 0.985273i \(-0.554697\pi\)
0.938766 0.344555i \(-0.111970\pi\)
\(524\) 0.813859 1.40965i 0.0355536 0.0615807i
\(525\) 0 0
\(526\) 3.81386 + 6.60580i 0.166292 + 0.288026i
\(527\) 2.74456 0.119555
\(528\) −0.686141 + 2.27567i −0.0298604 + 0.0990359i
\(529\) −20.3505 −0.884806
\(530\) −19.1168 + 33.1113i −0.830383 + 1.43826i
\(531\) 25.2921 + 16.7769i 1.09758 + 0.728055i
\(532\) 0 0
\(533\) −4.62772 + 8.01544i −0.200449 + 0.347187i
\(534\) −17.4891 18.6101i −0.756828 0.805339i
\(535\) 16.1168 27.9152i 0.696792 1.20688i
\(536\) −1.05842 + 1.83324i −0.0457169 + 0.0791839i
\(537\) 1.62772 5.39853i 0.0702412 0.232964i
\(538\) −0.813859 + 1.40965i −0.0350880 + 0.0607741i
\(539\) 0 0
\(540\) −3.81386 22.3966i −0.164122 0.963798i
\(541\) 3.11684 5.39853i 0.134004 0.232101i −0.791213 0.611541i \(-0.790550\pi\)
0.925216 + 0.379440i \(0.123883\pi\)
\(542\) −16.2337 −0.697297
\(543\) 1.04755 + 1.11469i 0.0449546 + 0.0478360i
\(544\) −1.37228 −0.0588361
\(545\) −30.6060 53.0111i −1.31102 2.27075i
\(546\) 0 0
\(547\) −9.05842 + 15.6896i −0.387310 + 0.670841i −0.992087 0.125554i \(-0.959929\pi\)
0.604777 + 0.796395i \(0.293262\pi\)
\(548\) −5.31386 + 9.20387i −0.226997 + 0.393170i
\(549\) 8.37228 4.16381i 0.357320 0.177707i
\(550\) −9.68614 16.7769i −0.413018 0.715369i
\(551\) 21.8614 + 37.8651i 0.931327 + 1.61311i
\(552\) 1.93070 + 2.05446i 0.0821762 + 0.0874434i
\(553\) 0 0
\(554\) −6.11684 10.5947i −0.259880 0.450125i
\(555\) −14.7446 + 3.46410i −0.625872 + 0.147043i
\(556\) 13.2337 0.561233
\(557\) −14.7446 25.5383i −0.624747 1.08209i −0.988590 0.150633i \(-0.951869\pi\)
0.363843 0.931460i \(-0.381465\pi\)
\(558\) 0.372281 5.98844i 0.0157599 0.253511i
\(559\) −16.2337 −0.686612
\(560\) 0 0
\(561\) −0.941578 + 3.12286i −0.0397535 + 0.131847i
\(562\) −16.3723 −0.690623
\(563\) −1.50000 + 2.59808i −0.0632175 + 0.109496i −0.895902 0.444252i \(-0.853470\pi\)
0.832684 + 0.553748i \(0.186803\pi\)
\(564\) 0 0
\(565\) 9.55842 + 16.5557i 0.402126 + 0.696502i
\(566\) −27.1168 −1.13981
\(567\) 0 0
\(568\) 7.11684 0.298616
\(569\) −8.05842 13.9576i −0.337827 0.585133i 0.646197 0.763171i \(-0.276358\pi\)
−0.984024 + 0.178038i \(0.943025\pi\)
\(570\) −25.9307 27.5928i −1.08612 1.15573i
\(571\) 11.1753 19.3561i 0.467670 0.810029i −0.531647 0.846966i \(-0.678427\pi\)
0.999318 + 0.0369371i \(0.0117601\pi\)
\(572\) −2.74456 −0.114756
\(573\) −9.55842 + 31.7017i −0.399309 + 1.32436i
\(574\) 0 0
\(575\) −22.9783 −0.958259
\(576\) −0.186141 + 2.99422i −0.00775586 + 0.124759i
\(577\) −4.94158 8.55906i −0.205721 0.356319i 0.744641 0.667465i \(-0.232620\pi\)
−0.950362 + 0.311146i \(0.899287\pi\)
\(578\) 15.1168 0.628778
\(579\) 11.8030 2.77300i 0.490515 0.115242i
\(580\) 19.1168 + 33.1113i 0.793784 + 1.37487i
\(581\) 0 0
\(582\) 9.62772 + 10.2448i 0.399082 + 0.424662i
\(583\) −6.00000 10.3923i −0.248495 0.430405i
\(584\) 6.05842 + 10.4935i 0.250699 + 0.434224i
\(585\) 23.4891 11.6819i 0.971156 0.482988i
\(586\) −5.18614 + 8.98266i −0.214237 + 0.371070i
\(587\) −7.24456 + 12.5480i −0.299015 + 0.517909i −0.975911 0.218170i \(-0.929991\pi\)
0.676896 + 0.736079i \(0.263325\pi\)
\(588\) 0 0
\(589\) −5.00000 8.66025i −0.206021 0.356840i
\(590\) 44.2337 1.82107
\(591\) −7.11684 7.57301i −0.292748 0.311512i
\(592\) 2.00000 0.0821995
\(593\) −7.37228 + 12.7692i −0.302743 + 0.524367i −0.976756 0.214353i \(-0.931236\pi\)
0.674013 + 0.738719i \(0.264569\pi\)
\(594\) 6.68614 + 2.47805i 0.274336 + 0.101676i
\(595\) 0 0
\(596\) −1.62772 + 2.81929i −0.0666740 + 0.115483i
\(597\) −5.00000 + 16.5831i −0.204636 + 0.678702i
\(598\) −1.62772 + 2.81929i −0.0665624 + 0.115289i
\(599\) −12.0000 + 20.7846i −0.490307 + 0.849236i −0.999938 0.0111569i \(-0.996449\pi\)
0.509631 + 0.860393i \(0.329782\pi\)
\(600\) −16.7446 17.8178i −0.683594 0.727410i
\(601\) −12.0584 + 20.8858i −0.491873 + 0.851950i −0.999956 0.00935863i \(-0.997021\pi\)
0.508083 + 0.861308i \(0.330354\pi\)
\(602\) 0 0
\(603\) 5.29211 + 3.51039i 0.215511 + 0.142954i
\(604\) −4.55842 + 7.89542i −0.185480 + 0.321260i
\(605\) −39.8614 −1.62060
\(606\) −0.813859 + 2.69927i −0.0330608 + 0.109650i
\(607\) 22.2337 0.902438 0.451219 0.892413i \(-0.350989\pi\)
0.451219 + 0.892413i \(0.350989\pi\)
\(608\) 2.50000 + 4.33013i 0.101388 + 0.175610i
\(609\) 0 0
\(610\) 6.81386 11.8020i 0.275885 0.477847i
\(611\) 0 0
\(612\) −0.255437 + 4.10891i −0.0103254 + 0.166093i
\(613\) 18.1168 + 31.3793i 0.731732 + 1.26740i 0.956142 + 0.292903i \(0.0946213\pi\)
−0.224410 + 0.974495i \(0.572045\pi\)
\(614\) −6.50000 11.2583i −0.262319 0.454349i
\(615\) 10.1168 33.5538i 0.407951 1.35302i
\(616\) 0 0
\(617\) −9.43070 16.3345i −0.379666 0.657600i 0.611348 0.791362i \(-0.290628\pi\)
−0.991014 + 0.133762i \(0.957294\pi\)
\(618\) 5.00000 16.5831i 0.201129 0.667071i
\(619\) 45.4674 1.82749 0.913744 0.406290i \(-0.133178\pi\)
0.913744 + 0.406290i \(0.133178\pi\)
\(620\) −4.37228 7.57301i −0.175595 0.304140i
\(621\) 6.51087 5.39853i 0.261272 0.216636i
\(622\) −8.23369 −0.330141
\(623\) 0 0
\(624\) −3.37228 + 0.792287i −0.134999 + 0.0317169i
\(625\) 103.701 4.14804
\(626\) −10.0584 + 17.4217i −0.402015 + 0.696311i
\(627\) 11.5693 2.71810i 0.462033 0.108551i
\(628\) −4.55842 7.89542i −0.181901 0.315061i
\(629\) 2.74456 0.109433
\(630\) 0 0
\(631\) −37.3505 −1.48690 −0.743451 0.668791i \(-0.766812\pi\)
−0.743451 + 0.668791i \(0.766812\pi\)
\(632\) −2.55842 4.43132i −0.101769 0.176268i
\(633\) −8.00000 + 26.5330i −0.317971 + 1.05459i
\(634\) −3.00000 + 5.19615i −0.119145 + 0.206366i
\(635\) 13.6277 0.540800
\(636\) −10.3723 11.0371i −0.411288 0.437650i
\(637\) 0 0
\(638\) −12.0000 −0.475085
\(639\) 1.32473 21.3094i 0.0524057 0.842987i
\(640\) 2.18614 + 3.78651i 0.0864148 + 0.149675i
\(641\) 34.2119 1.35129 0.675645 0.737227i \(-0.263865\pi\)
0.675645 + 0.737227i \(0.263865\pi\)
\(642\) 8.74456 + 9.30506i 0.345120 + 0.367242i
\(643\) −13.1753 22.8202i −0.519582 0.899942i −0.999741 0.0227606i \(-0.992754\pi\)
0.480159 0.877181i \(-0.340579\pi\)
\(644\) 0 0
\(645\) 59.8397 14.0588i 2.35618 0.553564i
\(646\) 3.43070 + 5.94215i 0.134979 + 0.233791i
\(647\) −2.74456 4.75372i −0.107900 0.186888i 0.807019 0.590525i \(-0.201079\pi\)
−0.914919 + 0.403637i \(0.867746\pi\)
\(648\) 8.93070 + 1.11469i 0.350831 + 0.0437892i
\(649\) −6.94158 + 12.0232i −0.272481 + 0.471951i
\(650\) 14.1168 24.4511i 0.553708 0.959051i
\(651\) 0 0
\(652\) 9.11684 + 15.7908i 0.357043 + 0.618417i
\(653\) −26.7446 −1.04660 −0.523298 0.852150i \(-0.675298\pi\)
−0.523298 + 0.852150i \(0.675298\pi\)
\(654\) 23.6060 5.54601i 0.923066 0.216866i
\(655\) −7.11684 −0.278078
\(656\) −2.31386 + 4.00772i −0.0903410 + 0.156475i
\(657\) 32.5475 16.1870i 1.26980 0.631514i
\(658\) 0 0
\(659\) 10.3723 17.9653i 0.404047 0.699829i −0.590163 0.807284i \(-0.700937\pi\)
0.994210 + 0.107454i \(0.0342700\pi\)
\(660\) 10.1168 2.37686i 0.393798 0.0925192i
\(661\) −13.5584 + 23.4839i −0.527361 + 0.913417i 0.472130 + 0.881529i \(0.343485\pi\)
−0.999491 + 0.0318879i \(0.989848\pi\)
\(662\) 11.1168 19.2549i 0.432068 0.748364i
\(663\) −4.62772 + 1.08724i −0.179726 + 0.0422249i
\(664\) 8.74456 15.1460i 0.339355 0.587780i
\(665\) 0 0
\(666\) 0.372281 5.98844i 0.0144256 0.232047i
\(667\) −7.11684 + 12.3267i −0.275565 + 0.477293i
\(668\) −5.48913 −0.212381
\(669\) 6.74456 1.58457i 0.260760 0.0612632i
\(670\) 9.25544 0.357569
\(671\) 2.13859 + 3.70415i 0.0825595 + 0.142997i
\(672\) 0 0
\(673\) 1.44158 2.49689i 0.0555687 0.0962479i −0.836903 0.547351i \(-0.815636\pi\)
0.892472 + 0.451103i \(0.148969\pi\)
\(674\) −4.05842 + 7.02939i −0.156325 + 0.270762i
\(675\) −56.4674 + 46.8203i −2.17343 + 1.80211i
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) −17.2337 29.8496i −0.662344 1.14721i −0.979998 0.199007i \(-0.936228\pi\)
0.317654 0.948207i \(-0.397105\pi\)
\(678\) −7.37228 + 1.73205i −0.283131 + 0.0665190i
\(679\) 0 0
\(680\) 3.00000 + 5.19615i 0.115045 + 0.199263i
\(681\) −14.5367 15.4684i −0.557047 0.592752i
\(682\) 2.74456 0.105095
\(683\) −14.9198 25.8419i −0.570891 0.988813i −0.996475 0.0838936i \(-0.973264\pi\)
0.425583 0.904919i \(-0.360069\pi\)
\(684\) 13.4307 6.67954i 0.513536 0.255398i
\(685\) 46.4674 1.77543
\(686\) 0 0
\(687\) −3.41983 3.63903i −0.130475 0.138838i
\(688\) −8.11684 −0.309452
\(689\) 8.74456 15.1460i 0.333141 0.577018i
\(690\) 3.55842 11.8020i 0.135467 0.449293i
\(691\) 11.5584 + 20.0198i 0.439703 + 0.761588i 0.997666 0.0682775i \(-0.0217503\pi\)
−0.557963 + 0.829866i \(0.688417\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) 10.1168 0.384030
\(695\) −28.9307 50.1094i −1.09740 1.90076i
\(696\) −14.7446 + 3.46410i −0.558891 + 0.131306i
\(697\) −3.17527 + 5.49972i −0.120272 + 0.208317i
\(698\) 22.0000 0.832712
\(699\) 0.430703 0.101190i 0.0162907 0.00382735i
\(700\) 0 0
\(701\) −38.2337 −1.44407 −0.722033 0.691858i \(-0.756792\pi\)
−0.722033 + 0.691858i \(0.756792\pi\)
\(702\) 1.74456 + 10.2448i 0.0658443 + 0.386666i
\(703\) −5.00000 8.66025i −0.188579 0.326628i
\(704\) −1.37228 −0.0517198
\(705\) 0 0
\(706\) −6.68614 11.5807i −0.251636 0.435847i
\(707\) 0 0
\(708\) −5.05842 + 16.7769i −0.190107 + 0.630514i
\(709\) −22.0000 38.1051i −0.826227 1.43107i −0.900978 0.433865i \(-0.857149\pi\)
0.0747503 0.997202i \(-0.476184\pi\)
\(710\) −15.5584 26.9480i −0.583897 1.01134i
\(711\) −13.7446 + 6.83563i −0.515461 + 0.256356i
\(712\) 7.37228 12.7692i 0.276288 0.478545i
\(713\) 1.62772 2.81929i 0.0609585 0.105583i
\(714\) 0 0
\(715\) 6.00000 + 10.3923i 0.224387 + 0.388650i
\(716\) 3.25544 0.121661
\(717\) 4.93070 16.3533i 0.184140 0.610725i
\(718\) −21.8614 −0.815860
\(719\) −1.37228 + 2.37686i −0.0511775 + 0.0886420i −0.890479 0.455024i \(-0.849631\pi\)
0.839302 + 0.543666i \(0.182964\pi\)
\(720\) 11.7446 5.84096i 0.437694 0.217680i
\(721\) 0 0
\(722\) 3.00000 5.19615i 0.111648 0.193381i
\(723\) 21.4891 + 22.8665i 0.799189 + 0.850415i
\(724\) −0.441578 + 0.764836i −0.0164111 + 0.0284249i
\(725\) 61.7228 106.907i 2.29233 3.97043i
\(726\) 4.55842 15.1186i 0.169179 0.561103i
\(727\) 18.1168 31.3793i 0.671917 1.16379i −0.305443 0.952210i \(-0.598805\pi\)
0.977360 0.211583i \(-0.0678620\pi\)
\(728\) 0 0
\(729\) 5.00000 26.5330i 0.185185 0.982704i
\(730\) 26.4891 45.8805i 0.980407 1.69811i
\(731\) −11.1386 −0.411976
\(732\) 3.69702 + 3.93398i 0.136646 + 0.145404i
\(733\) −41.1168 −1.51869 −0.759343 0.650691i \(-0.774479\pi\)
−0.759343 + 0.650691i \(0.774479\pi\)
\(734\) −6.11684 10.5947i −0.225777 0.391057i
\(735\) 0 0
\(736\) −0.813859 + 1.40965i −0.0299993 + 0.0519602i
\(737\) −1.45245 + 2.51572i −0.0535018 + 0.0926678i
\(738\) 11.5693 + 7.67420i 0.425872 + 0.282491i
\(739\) 4.05842 + 7.02939i 0.149291 + 0.258580i 0.930966 0.365106i \(-0.118967\pi\)
−0.781674 + 0.623687i \(0.785634\pi\)
\(740\) −4.37228 7.57301i −0.160728 0.278390i
\(741\) 11.8614 + 12.6217i 0.435740 + 0.463669i
\(742\) 0 0
\(743\) 6.86141 + 11.8843i 0.251721 + 0.435993i 0.964000 0.265904i \(-0.0856703\pi\)
−0.712279 + 0.701896i \(0.752337\pi\)
\(744\) 3.37228 0.792287i 0.123634 0.0290467i
\(745\) 14.2337 0.521482
\(746\) −5.00000 8.66025i −0.183063 0.317074i
\(747\) −43.7228 29.0024i −1.59973 1.06114i
\(748\) −1.88316 −0.0688550
\(749\) 0 0
\(750\) −19.9307 + 66.1027i −0.727766 + 2.41373i
\(751\) −17.1168 −0.624603 −0.312301 0.949983i \(-0.601100\pi\)
−0.312301 + 0.949983i \(0.601100\pi\)
\(752\) 0 0
\(753\) −10.6753 11.3595i −0.389028 0.413964i
\(754\) −8.74456 15.1460i −0.318458 0.551586i
\(755\) 39.8614 1.45071
\(756\) 0 0
\(757\) 46.2337 1.68039 0.840196 0.542283i \(-0.182440\pi\)
0.840196 + 0.542283i \(0.182440\pi\)
\(758\) −4.05842 7.02939i −0.147409 0.255319i
\(759\) 2.64947 + 2.81929i 0.0961696 + 0.102334i
\(760\) 10.9307 18.9325i 0.396498 0.686755i
\(761\) 35.4891 1.28648 0.643240 0.765665i \(-0.277590\pi\)
0.643240 + 0.765665i \(0.277590\pi\)
\(762\) −1.55842 + 5.16870i −0.0564557 + 0.187242i
\(763\) 0 0
\(764\) −19.1168 −0.691623
\(765\) 16.1168 8.01544i 0.582706 0.289799i
\(766\) −16.3723 28.3576i −0.591555 1.02460i
\(767\) −20.2337 −0.730596
\(768\) −1.68614 + 0.396143i −0.0608434 + 0.0142946i
\(769\) 5.00000 + 8.66025i 0.180305 + 0.312297i 0.941984 0.335657i \(-0.108958\pi\)
−0.761680 + 0.647954i \(0.775625\pi\)
\(770\) 0 0
\(771\) −8.13859 8.66025i −0.293104 0.311891i
\(772\) 3.50000 + 6.06218i 0.125968 + 0.218183i
\(773\) 19.9307 + 34.5210i 0.716858 + 1.24163i 0.962239 + 0.272207i \(0.0877536\pi\)
−0.245381 + 0.969427i \(0.578913\pi\)
\(774\) −1.51087 + 24.3036i −0.0543073 + 0.873575i
\(775\) −14.1168 + 24.4511i −0.507092 + 0.878309i
\(776\) −4.05842 + 7.02939i −0.145689 + 0.252341i
\(777\) 0 0
\(778\) 5.48913 + 9.50744i 0.196795 + 0.340858i
\(779\) 23.1386 0.829026
\(780\) 10.3723 + 11.0371i 0.371387 + 0.395192i
\(781\) 9.76631