Properties

Label 882.2.h.n.67.1
Level $882$
Weight $2$
Character 882.67
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 67.1
Root \(-1.18614 - 1.26217i\) of defining polynomial
Character \(\chi\) \(=\) 882.67
Dual form 882.2.h.n.79.1

$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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 \(-0.932609\pi\)
−0.977672 + 0.210138i \(0.932609\pi\)
\(6\) 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 \(-0.743877\pi\)
0.970725 + 0.240192i \(0.0772105\pi\)
\(14\) 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 \(-0.780115\pi\)
0.937156 + 0.348910i \(0.113448\pi\)
\(18\) −2.68614 1.33591i −0.633129 0.314876i
\(19\) 2.50000 + 4.33013i 0.573539 + 0.993399i 0.996199 + 0.0871106i \(0.0277634\pi\)
−0.422659 + 0.906289i \(0.638903\pi\)
\(20\) 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 0.911524 + 0.411247i \(0.134907\pi\)
−0.0996117 + 0.995026i \(0.531760\pi\)
\(30\) −2.18614 7.25061i −0.399133 1.32377i
\(31\) 1.00000 + 1.73205i 0.179605 + 0.311086i 0.941745 0.336327i \(-0.109185\pi\)
−0.762140 + 0.647412i \(0.775851\pi\)
\(32\) 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 0.772043 0.635571i \(-0.219235\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(38\) 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 \(-0.715644\pi\)
0.988186 + 0.153262i \(0.0489778\pi\)
\(42\) 0 0
\(43\) 4.05842 + 7.02939i 0.618904 + 1.07197i 0.989686 + 0.143253i \(0.0457562\pi\)
−0.370783 + 0.928720i \(0.620910\pi\)
\(44\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) −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 −0.392154 0.919899i \(-0.628270\pi\)
0.992733 0.120334i \(-0.0383965\pi\)
\(54\) 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 −0.980991 0.194053i \(-0.937837\pi\)
0.322441 0.946590i \(-0.395497\pi\)
\(60\) −7.37228 1.73205i −0.951757 0.223607i
\(61\) 1.55842 2.69927i 0.199535 0.345606i −0.748842 0.662748i \(-0.769390\pi\)
0.948378 + 0.317142i \(0.102723\pi\)
\(62\) 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 0.923408 0.383819i \(-0.125391\pi\)
−0.794101 + 0.607785i \(0.792058\pi\)
\(68\) −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 −0.256112 0.966647i \(-0.582442\pi\)
0.965197 0.261524i \(-0.0842249\pi\)
\(74\) −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 −0.685450 0.728120i \(-0.740395\pi\)
0.973295 + 0.229557i \(0.0737279\pi\)
\(80\) 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 0.722881 + 0.690973i \(0.242818\pi\)
0.236960 + 0.971519i \(0.423849\pi\)
\(84\) 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 0.931091 + 0.364787i \(0.118858\pi\)
−0.149631 + 0.988742i \(0.547808\pi\)
\(90\) 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 \(-0.301861\pi\)
−0.995116 + 0.0987127i \(0.968528\pi\)
\(98\) 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 \(-0.525806\pi\)
−0.0809820 + 0.996716i \(0.525806\pi\)
\(102\) 2.31386 + 0.543620i 0.229106 + 0.0538264i
\(103\) 10.0000 0.985329 0.492665 0.870219i \(-0.336023\pi\)
0.492665 + 0.870219i \(0.336023\pi\)
\(104\) −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 0.987348 0.158565i \(-0.0506868\pi\)
−0.630996 + 0.775786i \(0.717354\pi\)
\(108\) 0.872281 5.12241i 0.0839353 0.492905i
\(109\) −7.00000 + 12.1244i −0.670478 + 1.16130i 0.307290 + 0.951616i \(0.400578\pi\)
−0.977769 + 0.209687i \(0.932756\pi\)
\(110\) 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 −0.744686 0.667415i \(-0.767401\pi\)
0.950341 + 0.311210i \(0.100734\pi\)
\(114\) −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 \(-0.477347\pi\)
0.0711072 + 0.997469i \(0.477347\pi\)
\(132\) −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 −0.436156 0.899871i \(-0.643660\pi\)
0.997389 0.0722136i \(-0.0230063\pi\)
\(140\) 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 \(-0.0481453\pi\)
−0.624781 + 0.780800i \(0.714812\pi\)
\(158\) −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 0.963311 + 0.268388i \(0.0864909\pi\)
−0.249225 + 0.968446i \(0.580176\pi\)
\(164\) −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 \(-0.901455\pi\)
0.740078 + 0.672521i \(0.234788\pi\)
\(168\) 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 \(-0.906580\pi\)
0.729155 + 0.684349i \(0.239913\pi\)
\(174\) −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 −0.920423 0.390924i \(-0.872156\pi\)
0.798762 + 0.601648i \(0.205489\pi\)
\(180\) 10.9307 7.25061i 0.814727 0.540428i
\(181\) −0.883156 −0.0656445 −0.0328222 0.999461i \(-0.510450\pi\)
−0.0328222 + 0.999461i \(0.510450\pi\)
\(182\) 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 −0.279683 0.960092i \(-0.590229\pi\)
0.971306 0.237834i \(-0.0764374\pi\)
\(192\) −1.18614 + 1.26217i −0.0856023 + 0.0910892i
\(193\) 3.50000 + 6.06218i 0.251936 + 0.436365i 0.964059 0.265689i \(-0.0855996\pi\)
−0.712123 + 0.702055i \(0.752266\pi\)
\(194\) −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 \(-0.948662\pi\)
0.632581 + 0.774494i \(0.281995\pi\)
\(200\) −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 −0.447478 0.894295i \(-0.647678\pi\)
0.998221 0.0596196i \(-0.0189888\pi\)
\(212\) −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 \(-0.209426\pi\)
−0.925188 + 0.379509i \(0.876093\pi\)
\(224\) 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 \(-0.366676\pi\)
0.406711 + 0.913557i \(0.366676\pi\)
\(228\) 2.50000 + 8.29156i 0.165567 + 0.549122i
\(229\) 2.88316 0.190524 0.0952622 0.995452i \(-0.469631\pi\)
0.0952622 + 0.995452i \(0.469631\pi\)
\(230\) 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 0.870179 0.492736i \(-0.164003\pi\)
−0.861812 + 0.507229i \(0.830670\pi\)
\(234\) −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 −0.980267 0.197677i \(-0.936660\pi\)
0.661327 + 0.750098i \(0.269994\pi\)
\(240\) 2.18614 + 7.25061i 0.141115 + 0.468025i
\(241\) −18.1168 −1.16701 −0.583504 0.812110i \(-0.698319\pi\)
−0.583504 + 0.812110i \(0.698319\pi\)
\(242\) −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 \(-0.408326\pi\)
0.284037 + 0.958813i \(0.408326\pi\)
\(252\) 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 \(-0.431350\pi\)
0.214001 + 0.976833i \(0.431350\pi\)
\(258\) −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 \(-0.849135\pi\)
0.840148 + 0.542358i \(0.182468\pi\)
\(270\) −21.3030 + 7.89542i −1.29646 + 0.480500i
\(271\) 8.11684 + 14.0588i 0.493063 + 0.854010i 0.999968 0.00799154i \(-0.00254381\pi\)
−0.506905 + 0.862002i \(0.669210\pi\)
\(272\) 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 0.511566 0.859244i \(-0.329066\pi\)
−0.999910 + 0.0134071i \(0.995732\pi\)
\(282\) 0 0
\(283\) 13.5584 + 23.4839i 0.805965 + 1.39597i 0.915638 + 0.402004i \(0.131686\pi\)
−0.109673 + 0.993968i \(0.534981\pi\)
\(284\) 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 \(-0.931314\pi\)
0.673831 + 0.738885i \(0.264647\pi\)
\(294\) 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 \(-0.379024\pi\)
0.370975 + 0.928643i \(0.379024\pi\)
\(308\) 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 \(-0.0916668\pi\)
−0.725375 + 0.688354i \(0.758334\pi\)
\(312\) −1.00000 3.31662i −0.0566139 0.187767i
\(313\) −10.0584 + 17.4217i −0.568536 + 0.984733i 0.428175 + 0.903696i \(0.359157\pi\)
−0.996711 + 0.0810370i \(0.974177\pi\)
\(314\) 9.11684 0.514493
\(315\) 0 0
\(316\) −5.11684 −0.287845
\(317\) 3.00000 5.19615i 0.168497 0.291845i −0.769395 0.638774i \(-0.779442\pi\)
0.937892 + 0.346929i \(0.112775\pi\)
\(318\) 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 0.380029 + 0.924975i \(0.375914\pi\)
−0.991066 + 0.133373i \(0.957419\pi\)
\(332\) 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 −0.734059 0.679086i \(-0.762376\pi\)
0.955135 + 0.296171i \(0.0957097\pi\)
\(338\) 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 0.969259 0.246043i \(-0.0791303\pi\)
−0.697709 + 0.716382i \(0.745797\pi\)
\(348\) 4.37228 + 14.5012i 0.234379 + 0.777347i
\(349\) −11.0000 19.0526i −0.588817 1.01986i −0.994388 0.105797i \(-0.966261\pi\)
0.405571 0.914063i \(-0.367073\pi\)
\(350\) 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 \(-0.384185\pi\)
0.355867 + 0.934536i \(0.384185\pi\)
\(354\) 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 −0.995832 0.0912032i \(-0.970929\pi\)
0.418932 0.908018i \(-0.362405\pi\)
\(360\) −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 \(-0.396553\pi\)
0.319297 + 0.947655i \(0.396553\pi\)
\(368\) 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 \(-0.184549\pi\)
0.836584 + 0.547838i \(0.184549\pi\)
\(384\) 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 −0.998125 0.0612128i \(-0.980503\pi\)
0.446051 0.895008i \(-0.352830\pi\)
\(398\) 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 −0.998087 0.0618200i \(-0.980310\pi\)
0.445506 0.895279i \(-0.353024\pi\)
\(410\) 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 \(-0.932967\pi\)
0.669986 + 0.742373i \(0.266300\pi\)
\(420\) 0 0
\(421\) −17.1168 29.6472i −0.834224 1.44492i −0.894661 0.446746i \(-0.852583\pi\)
0.0604368 0.998172i \(-0.480751\pi\)
\(422\) −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 −0.776907 0.629615i \(-0.783213\pi\)
0.933716 + 0.358014i \(0.116546\pi\)
\(432\) −4.87228 + 1.80579i −0.234418 + 0.0868811i
\(433\) 20.1168 0.966754 0.483377 0.875412i \(-0.339410\pi\)
0.483377 + 0.875412i \(0.339410\pi\)
\(434\) 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 \(-0.772190\pi\)
0.945552 + 0.325471i \(0.105523\pi\)
\(440\) −6.00000 −0.286039
\(441\) 0 0
\(442\) −2.74456 −0.130546
\(443\) 20.0584 34.7422i 0.953004 1.65065i 0.214134 0.976804i \(-0.431307\pi\)
0.738870 0.673848i \(-0.235360\pi\)
\(444\) −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 −0.0688472 0.997627i \(-0.521932\pi\)
0.898394 0.439190i \(-0.144735\pi\)
\(458\) 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 \(-0.150808\pi\)
−0.840050 + 0.542509i \(0.817474\pi\)
\(462\) 0 0
\(463\) 11.5584 20.0198i 0.537165 0.930398i −0.461890 0.886937i \(-0.652828\pi\)
0.999055 0.0434604i \(-0.0138382\pi\)
\(464\) −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 0.939860 + 0.341559i \(0.110955\pi\)
−0.174131 + 0.984722i \(0.555712\pi\)
\(468\) 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 \(-0.769019\pi\)
−0.748069 + 0.663621i \(0.769019\pi\)
\(480\) 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 0.118053 + 0.993007i \(0.462335\pi\)
−0.918996 + 0.394266i \(0.870999\pi\)
\(488\) −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 −0.423789 0.905761i \(-0.639300\pi\)
0.996306 0.0858685i \(-0.0273665\pi\)
\(492\) 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 \(-0.244777\pi\)
0.718615 + 0.695409i \(0.244777\pi\)
\(504\) 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 \(-0.278014\pi\)
0.642219 + 0.766521i \(0.278014\pi\)
\(510\) −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 0.454033 + 0.890985i \(0.349985\pi\)
−0.998632 + 0.0522883i \(0.983349\pi\)
\(522\) −1.62772 26.1831i −0.0712433 1.14600i
\(523\) −17.5584 30.4121i −0.767776 1.32983i −0.938766 0.344555i \(-0.888030\pi\)
0.170990 0.985273i \(-0.445303\pi\)
\(524\) −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 0.925216 0.379440i \(-0.123883\pi\)
−0.791213 + 0.611541i \(0.790550\pi\)
\(542\) 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 0.604777 0.796395i \(-0.293262\pi\)
−0.992087 + 0.125554i \(0.959929\pi\)
\(548\) −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 0.363843 + 0.931460i \(0.381465\pi\)
−0.988590 + 0.150633i \(0.951869\pi\)
\(558\) −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 \(-0.146530\pi\)
−0.832684 + 0.553748i \(0.813197\pi\)
\(564\) 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 −0.984024 0.178038i \(-0.943025\pi\)
0.646197 + 0.763171i \(0.276358\pi\)
\(570\) 25.9307 27.5928i 1.08612 1.15573i
\(571\) 11.1753 + 19.3561i 0.467670 + 0.810029i 0.999318 0.0369371i \(-0.0117601\pi\)
−0.531647 + 0.846966i \(0.678427\pi\)
\(572\) 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 \(-0.767380\pi\)
0.950362 + 0.311146i \(0.100713\pi\)
\(578\) 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 \(-0.0700086\pi\)
−0.676896 + 0.736079i \(0.736675\pi\)
\(588\) 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 \(-0.0687642\pi\)
−0.674013 + 0.738719i \(0.735431\pi\)
\(594\) −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 0.509631 0.860393i \(-0.329782\pi\)
−0.999938 + 0.0111569i \(0.996449\pi\)
\(600\) 16.7446 17.8178i 0.683594 0.727410i
\(601\) 12.0584 + 20.8858i 0.491873 + 0.851950i 0.999956 0.00935863i \(-0.00297899\pi\)
−0.508083 + 0.861308i \(0.669646\pi\)
\(602\) 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 \(-0.649011\pi\)
−0.451219 + 0.892413i \(0.649011\pi\)
\(608\) −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 −0.224410 0.974495i \(-0.572045\pi\)
0.956142 0.292903i \(-0.0946213\pi\)
\(614\) 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 −0.991014 0.133762i \(-0.957294\pi\)
0.611348 + 0.791362i \(0.290628\pi\)
\(618\) 5.00000 + 16.5831i 0.201129 + 0.667071i
\(619\) −45.4674 −1.82749 −0.913744 0.406290i \(-0.866822\pi\)
−0.913744 + 0.406290i \(0.866822\pi\)
\(620\) −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 −0.480159 0.877181i \(-0.659421\pi\)
0.999741 0.0227606i \(-0.00724556\pi\)
\(644\) 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 \(-0.798921\pi\)
0.914919 + 0.403637i \(0.132254\pi\)
\(648\) 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 0.994210 0.107454i \(-0.0342700\pi\)
−0.590163 + 0.807284i \(0.700937\pi\)
\(660\) 10.1168 + 2.37686i 0.393798 + 0.0925192i
\(661\) 13.5584 + 23.4839i 0.527361 + 0.913417i 0.999491 + 0.0318879i \(0.0101520\pi\)
−0.472130 + 0.881529i \(0.656515\pi\)
\(662\) 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 0.892472 0.451103i \(-0.148969\pi\)
−0.836903 + 0.547351i \(0.815636\pi\)
\(674\) −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 −0.317654 0.948207i \(-0.602895\pi\)
0.979998 0.199007i \(-0.0637718\pi\)
\(678\) 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 0.425583 + 0.904919i \(0.360069\pi\)
−0.996475 + 0.0838936i \(0.973264\pi\)
\(684\) −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 \(-0.978250\pi\)
0.557963 + 0.829866i \(0.311583\pi\)
\(692\) 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 0.0747503 + 0.997202i \(0.476184\pi\)
−0.900978 + 0.433865i \(0.857149\pi\)
\(710\) 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 \(-0.150369\pi\)
−0.839302 + 0.543666i \(0.817036\pi\)
\(720\) −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 −0.977360 0.211583i \(-0.932138\pi\)
0.305443 0.952210i \(-0.401195\pi\)
\(728\) 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 \(-0.225521\pi\)
0.759343 + 0.650691i \(0.225521\pi\)
\(734\) 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 −0.781674 0.623687i \(-0.785634\pi\)
0.930966 + 0.365106i \(0.118967\pi\)
\(740\) 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 −0.712279 0.701896i \(-0.752337\pi\)
0.964000 + 0.265904i \(0.0856703\pi\)
\(744\) 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 \(-0.722410\pi\)
−0.643240 + 0.765665i \(0.722410\pi\)
\(762\) 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 \(-0.891042\pi\)
0.761680 + 0.647954i \(0.224375\pi\)
\(770\) 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 0.245381 + 0.969427i \(0.421087\pi\)
−0.962239 + 0.272207i \(0.912246\pi\)
\(774\) −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