Properties

Label 882.2.f.k.295.1
Level $882$
Weight $2$
Character 882.295
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.f (of order \(3\), degree \(2\), 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 295.1
Root \(-1.18614 - 1.26217i\) of defining polynomial
Character \(\chi\) \(=\) 882.295
Dual form 882.2.f.k.589.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-1.18614 + 1.26217i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.686141 - 1.18843i) q^{5} +(0.500000 + 1.65831i) q^{6} -1.00000 q^{8} +(-0.186141 - 2.99422i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-1.18614 + 1.26217i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.686141 - 1.18843i) q^{5} +(0.500000 + 1.65831i) q^{6} -1.00000 q^{8} +(-0.186141 - 2.99422i) q^{9} -1.37228 q^{10} +(-2.18614 + 3.78651i) q^{11} +(1.68614 + 0.396143i) q^{12} +(1.00000 + 1.73205i) q^{13} +(2.31386 + 0.543620i) q^{15} +(-0.500000 + 0.866025i) q^{16} +4.37228 q^{17} +(-2.68614 - 1.33591i) q^{18} -5.00000 q^{19} +(-0.686141 + 1.18843i) q^{20} +(2.18614 + 3.78651i) q^{22} +(3.68614 + 6.38458i) q^{23} +(1.18614 - 1.26217i) q^{24} +(1.55842 - 2.69927i) q^{25} +2.00000 q^{26} +(4.00000 + 3.31662i) q^{27} +(-1.37228 + 2.37686i) q^{29} +(1.62772 - 1.73205i) q^{30} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.18614 - 7.25061i) q^{33} +(2.18614 - 3.78651i) q^{34} +(-2.50000 + 1.65831i) q^{36} +2.00000 q^{37} +(-2.50000 + 4.33013i) q^{38} +(-3.37228 - 0.792287i) q^{39} +(0.686141 + 1.18843i) q^{40} +(5.18614 + 8.98266i) q^{41} +(-4.55842 + 7.89542i) q^{43} +4.37228 q^{44} +(-3.43070 + 2.27567i) q^{45} +7.37228 q^{46} +(-0.500000 - 1.65831i) q^{48} +(-1.55842 - 2.69927i) q^{50} +(-5.18614 + 5.51856i) q^{51} +(1.00000 - 1.73205i) q^{52} +2.74456 q^{53} +(4.87228 - 1.80579i) q^{54} +6.00000 q^{55} +(5.93070 - 6.31084i) q^{57} +(1.37228 + 2.37686i) q^{58} +(3.55842 + 6.16337i) q^{59} +(-0.686141 - 2.27567i) q^{60} +(-7.05842 + 12.2255i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(1.37228 - 2.37686i) q^{65} +(-7.37228 - 1.73205i) q^{66} +(-7.55842 - 13.0916i) q^{67} +(-2.18614 - 3.78651i) q^{68} +(-12.4307 - 2.92048i) q^{69} +10.1168 q^{71} +(0.186141 + 2.99422i) q^{72} +5.11684 q^{73} +(1.00000 - 1.73205i) q^{74} +(1.55842 + 5.16870i) q^{75} +(2.50000 + 4.33013i) q^{76} +(-2.37228 + 2.52434i) q^{78} +(-6.05842 + 10.4935i) q^{79} +1.37228 q^{80} +(-8.93070 + 1.11469i) q^{81} +10.3723 q^{82} +(-2.74456 + 4.75372i) q^{83} +(-3.00000 - 5.19615i) q^{85} +(4.55842 + 7.89542i) q^{86} +(-1.37228 - 4.55134i) q^{87} +(2.18614 - 3.78651i) q^{88} -3.25544 q^{89} +(0.255437 + 4.10891i) q^{90} +(3.68614 - 6.38458i) q^{92} +(-3.37228 - 0.792287i) q^{93} +(3.43070 + 5.94215i) q^{95} +(-1.68614 - 0.396143i) q^{96} +(4.55842 - 7.89542i) q^{97} +(11.7446 + 5.84096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} + q^{3} - 2q^{4} + 3q^{5} + 2q^{6} - 4q^{8} + 5q^{9} + O(q^{10}) \) \( 4q + 2q^{2} + q^{3} - 2q^{4} + 3q^{5} + 2q^{6} - 4q^{8} + 5q^{9} + 6q^{10} - 3q^{11} + q^{12} + 4q^{13} + 15q^{15} - 2q^{16} + 6q^{17} - 5q^{18} - 20q^{19} + 3q^{20} + 3q^{22} + 9q^{23} - q^{24} - 11q^{25} + 8q^{26} + 16q^{27} + 6q^{29} + 18q^{30} + 4q^{31} + 2q^{32} - 3q^{33} + 3q^{34} - 10q^{36} + 8q^{37} - 10q^{38} - 2q^{39} - 3q^{40} + 15q^{41} - q^{43} + 6q^{44} + 15q^{45} + 18q^{46} - 2q^{48} + 11q^{50} - 15q^{51} + 4q^{52} - 12q^{53} + 8q^{54} + 24q^{55} - 5q^{57} - 6q^{58} - 3q^{59} + 3q^{60} - 11q^{61} + 8q^{62} + 4q^{64} - 6q^{65} - 18q^{66} - 13q^{67} - 3q^{68} - 21q^{69} + 6q^{71} - 5q^{72} - 14q^{73} + 4q^{74} - 11q^{75} + 10q^{76} + 2q^{78} - 7q^{79} - 6q^{80} - 7q^{81} + 30q^{82} + 12q^{83} - 12q^{85} + q^{86} + 6q^{87} + 3q^{88} - 36q^{89} + 24q^{90} + 9q^{92} - 2q^{93} - 15q^{95} - q^{96} + q^{97} + 24q^{99} + O(q^{100}) \)

Character values

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

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

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
\(5\) −0.686141 1.18843i −0.306851 0.531482i 0.670820 0.741620i \(-0.265942\pi\)
−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
\(10\) −1.37228 −0.433953
\(11\) −2.18614 + 3.78651i −0.659146 + 1.14167i 0.321691 + 0.946845i \(0.395749\pi\)
−0.980837 + 0.194830i \(0.937584\pi\)
\(12\) 1.68614 + 0.396143i 0.486747 + 0.114357i
\(13\) 1.00000 + 1.73205i 0.277350 + 0.480384i 0.970725 0.240192i \(-0.0772105\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 2.31386 + 0.543620i 0.597436 + 0.140362i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 4.37228 1.06043 0.530217 0.847862i \(-0.322110\pi\)
0.530217 + 0.847862i \(0.322110\pi\)
\(18\) −2.68614 1.33591i −0.633129 0.314876i
\(19\) −5.00000 −1.14708 −0.573539 0.819178i \(-0.694430\pi\)
−0.573539 + 0.819178i \(0.694430\pi\)
\(20\) −0.686141 + 1.18843i −0.153426 + 0.265741i
\(21\) 0 0
\(22\) 2.18614 + 3.78651i 0.466087 + 0.807286i
\(23\) 3.68614 + 6.38458i 0.768613 + 1.33128i 0.938315 + 0.345782i \(0.112386\pi\)
−0.169701 + 0.985496i \(0.554280\pi\)
\(24\) 1.18614 1.26217i 0.242120 0.257639i
\(25\) 1.55842 2.69927i 0.311684 0.539853i
\(26\) 2.00000 0.392232
\(27\) 4.00000 + 3.31662i 0.769800 + 0.638285i
\(28\) 0 0
\(29\) −1.37228 + 2.37686i −0.254826 + 0.441372i −0.964848 0.262807i \(-0.915352\pi\)
0.710022 + 0.704179i \(0.248685\pi\)
\(30\) 1.62772 1.73205i 0.297179 0.316228i
\(31\) 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
\(33\) −2.18614 7.25061i −0.380558 1.26217i
\(34\) 2.18614 3.78651i 0.374920 0.649381i
\(35\) 0 0
\(36\) −2.50000 + 1.65831i −0.416667 + 0.276385i
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −2.50000 + 4.33013i −0.405554 + 0.702439i
\(39\) −3.37228 0.792287i −0.539997 0.126867i
\(40\) 0.686141 + 1.18843i 0.108488 + 0.187907i
\(41\) 5.18614 + 8.98266i 0.809939 + 1.40286i 0.912906 + 0.408171i \(0.133833\pi\)
−0.102966 + 0.994685i \(0.532833\pi\)
\(42\) 0 0
\(43\) −4.55842 + 7.89542i −0.695153 + 1.20404i 0.274976 + 0.961451i \(0.411330\pi\)
−0.970129 + 0.242589i \(0.922003\pi\)
\(44\) 4.37228 0.659146
\(45\) −3.43070 + 2.27567i −0.511419 + 0.339237i
\(46\) 7.37228 1.08698
\(47\) 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
\(50\) −1.55842 2.69927i −0.220394 0.381734i
\(51\) −5.18614 + 5.51856i −0.726205 + 0.772753i
\(52\) 1.00000 1.73205i 0.138675 0.240192i
\(53\) 2.74456 0.376995 0.188497 0.982074i \(-0.439638\pi\)
0.188497 + 0.982074i \(0.439638\pi\)
\(54\) 4.87228 1.80579i 0.663034 0.245737i
\(55\) 6.00000 0.809040
\(56\) 0 0
\(57\) 5.93070 6.31084i 0.785541 0.835892i
\(58\) 1.37228 + 2.37686i 0.180189 + 0.312097i
\(59\) 3.55842 + 6.16337i 0.463267 + 0.802402i 0.999121 0.0419083i \(-0.0133437\pi\)
−0.535854 + 0.844310i \(0.680010\pi\)
\(60\) −0.686141 2.27567i −0.0885804 0.293788i
\(61\) −7.05842 + 12.2255i −0.903738 + 1.56532i −0.0811364 + 0.996703i \(0.525855\pi\)
−0.822602 + 0.568618i \(0.807478\pi\)
\(62\) 2.00000 0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.37228 2.37686i 0.170211 0.294813i
\(66\) −7.37228 1.73205i −0.907465 0.213201i
\(67\) −7.55842 13.0916i −0.923408 1.59939i −0.794101 0.607785i \(-0.792058\pi\)
−0.129307 0.991605i \(-0.541275\pi\)
\(68\) −2.18614 3.78651i −0.265108 0.459181i
\(69\) −12.4307 2.92048i −1.49648 0.351585i
\(70\) 0 0
\(71\) 10.1168 1.20065 0.600324 0.799757i \(-0.295038\pi\)
0.600324 + 0.799757i \(0.295038\pi\)
\(72\) 0.186141 + 2.99422i 0.0219369 + 0.352872i
\(73\) 5.11684 0.598881 0.299441 0.954115i \(-0.403200\pi\)
0.299441 + 0.954115i \(0.403200\pi\)
\(74\) 1.00000 1.73205i 0.116248 0.201347i
\(75\) 1.55842 + 5.16870i 0.179951 + 0.596830i
\(76\) 2.50000 + 4.33013i 0.286770 + 0.496700i
\(77\) 0 0
\(78\) −2.37228 + 2.52434i −0.268608 + 0.285825i
\(79\) −6.05842 + 10.4935i −0.681626 + 1.18061i 0.292859 + 0.956156i \(0.405393\pi\)
−0.974485 + 0.224455i \(0.927940\pi\)
\(80\) 1.37228 0.153426
\(81\) −8.93070 + 1.11469i −0.992300 + 0.123855i
\(82\) 10.3723 1.14543
\(83\) −2.74456 + 4.75372i −0.301255 + 0.521789i −0.976420 0.215877i \(-0.930739\pi\)
0.675166 + 0.737666i \(0.264072\pi\)
\(84\) 0 0
\(85\) −3.00000 5.19615i −0.325396 0.563602i
\(86\) 4.55842 + 7.89542i 0.491547 + 0.851385i
\(87\) −1.37228 4.55134i −0.147124 0.487955i
\(88\) 2.18614 3.78651i 0.233043 0.403643i
\(89\) −3.25544 −0.345076 −0.172538 0.985003i \(-0.555197\pi\)
−0.172538 + 0.985003i \(0.555197\pi\)
\(90\) 0.255437 + 4.10891i 0.0269255 + 0.433117i
\(91\) 0 0
\(92\) 3.68614 6.38458i 0.384307 0.665639i
\(93\) −3.37228 0.792287i −0.349689 0.0821563i
\(94\) 0 0
\(95\) 3.43070 + 5.94215i 0.351983 + 0.609652i
\(96\) −1.68614 0.396143i −0.172091 0.0404312i
\(97\) 4.55842 7.89542i 0.462838 0.801658i −0.536263 0.844051i \(-0.680165\pi\)
0.999101 + 0.0423924i \(0.0134980\pi\)
\(98\) 0 0
\(99\) 11.7446 + 5.84096i 1.18037 + 0.587039i
\(100\) −3.11684 −0.311684
\(101\) 3.68614 6.38458i 0.366785 0.635290i −0.622276 0.782798i \(-0.713792\pi\)
0.989061 + 0.147508i \(0.0471252\pi\)
\(102\) 2.18614 + 7.25061i 0.216460 + 0.717917i
\(103\) −5.00000 8.66025i −0.492665 0.853320i 0.507300 0.861770i \(-0.330644\pi\)
−0.999964 + 0.00844953i \(0.997310\pi\)
\(104\) −1.00000 1.73205i −0.0980581 0.169842i
\(105\) 0 0
\(106\) 1.37228 2.37686i 0.133288 0.230861i
\(107\) −1.62772 −0.157358 −0.0786788 0.996900i \(-0.525070\pi\)
−0.0786788 + 0.996900i \(0.525070\pi\)
\(108\) 0.872281 5.12241i 0.0839353 0.492905i
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 3.00000 5.19615i 0.286039 0.495434i
\(111\) −2.37228 + 2.52434i −0.225167 + 0.239600i
\(112\) 0 0
\(113\) −0.686141 1.18843i −0.0645467 0.111798i 0.831946 0.554856i \(-0.187227\pi\)
−0.896493 + 0.443058i \(0.853893\pi\)
\(114\) −2.50000 8.29156i −0.234146 0.776576i
\(115\) 5.05842 8.76144i 0.471700 0.817009i
\(116\) 2.74456 0.254826
\(117\) 5.00000 3.31662i 0.462250 0.306622i
\(118\) 7.11684 0.655159
\(119\) 0 0
\(120\) −2.31386 0.543620i −0.211225 0.0496255i
\(121\) −4.05842 7.02939i −0.368947 0.639036i
\(122\) 7.05842 + 12.2255i 0.639040 + 1.10685i
\(123\) −17.4891 4.10891i −1.57694 0.370488i
\(124\) 1.00000 1.73205i 0.0898027 0.155543i
\(125\) −11.1386 −0.996266
\(126\) 0 0
\(127\) −14.1168 −1.25267 −0.626334 0.779555i \(-0.715445\pi\)
−0.626334 + 0.779555i \(0.715445\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −4.55842 15.1186i −0.401347 1.33112i
\(130\) −1.37228 2.37686i −0.120357 0.208464i
\(131\) −3.68614 6.38458i −0.322060 0.557824i 0.658853 0.752271i \(-0.271042\pi\)
−0.980913 + 0.194448i \(0.937708\pi\)
\(132\) −5.18614 + 5.51856i −0.451396 + 0.480329i
\(133\) 0 0
\(134\) −15.1168 −1.30590
\(135\) 1.19702 7.02939i 0.103023 0.604994i
\(136\) −4.37228 −0.374920
\(137\) −8.18614 + 14.1788i −0.699389 + 1.21138i 0.269289 + 0.963059i \(0.413211\pi\)
−0.968678 + 0.248318i \(0.920122\pi\)
\(138\) −8.74456 + 9.30506i −0.744387 + 0.792100i
\(139\) −10.6168 18.3889i −0.900509 1.55973i −0.826835 0.562445i \(-0.809861\pi\)
−0.0736742 0.997282i \(-0.523472\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 5.05842 8.76144i 0.424493 0.735244i
\(143\) −8.74456 −0.731257
\(144\) 2.68614 + 1.33591i 0.223845 + 0.111326i
\(145\) 3.76631 0.312775
\(146\) 2.55842 4.43132i 0.211737 0.366738i
\(147\) 0 0
\(148\) −1.00000 1.73205i −0.0821995 0.142374i
\(149\) −7.37228 12.7692i −0.603961 1.04609i −0.992215 0.124538i \(-0.960255\pi\)
0.388254 0.921552i \(-0.373078\pi\)
\(150\) 5.25544 + 1.23472i 0.429105 + 0.100814i
\(151\) 4.05842 7.02939i 0.330270 0.572044i −0.652295 0.757965i \(-0.726194\pi\)
0.982565 + 0.185921i \(0.0595270\pi\)
\(152\) 5.00000 0.405554
\(153\) −0.813859 13.0916i −0.0657966 1.05839i
\(154\) 0 0
\(155\) 1.37228 2.37686i 0.110224 0.190914i
\(156\) 1.00000 + 3.31662i 0.0800641 + 0.265543i
\(157\) −4.05842 7.02939i −0.323897 0.561007i 0.657391 0.753549i \(-0.271660\pi\)
−0.981289 + 0.192543i \(0.938327\pi\)
\(158\) 6.05842 + 10.4935i 0.481982 + 0.834818i
\(159\) −3.25544 + 3.46410i −0.258173 + 0.274721i
\(160\) 0.686141 1.18843i 0.0542442 0.0939537i
\(161\) 0 0
\(162\) −3.50000 + 8.29156i −0.274986 + 0.651447i
\(163\) 16.2337 1.27152 0.635760 0.771887i \(-0.280687\pi\)
0.635760 + 0.771887i \(0.280687\pi\)
\(164\) 5.18614 8.98266i 0.404970 0.701428i
\(165\) −7.11684 + 7.57301i −0.554046 + 0.589558i
\(166\) 2.74456 + 4.75372i 0.213019 + 0.368960i
\(167\) 8.74456 + 15.1460i 0.676675 + 1.17203i 0.975976 + 0.217876i \(0.0699129\pi\)
−0.299302 + 0.954158i \(0.596754\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) −6.00000 −0.460179
\(171\) 0.930703 + 14.9711i 0.0711727 + 1.14487i
\(172\) 9.11684 0.695153
\(173\) −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i \(-0.906580\pi\)
0.729155 + 0.684349i \(0.239913\pi\)
\(174\) −4.62772 1.08724i −0.350826 0.0824235i
\(175\) 0 0
\(176\) −2.18614 3.78651i −0.164787 0.285419i
\(177\) −12.0000 2.81929i −0.901975 0.211911i
\(178\) −1.62772 + 2.81929i −0.122003 + 0.211315i
\(179\) 14.7446 1.10206 0.551030 0.834485i \(-0.314235\pi\)
0.551030 + 0.834485i \(0.314235\pi\)
\(180\) 3.68614 + 1.83324i 0.274749 + 0.136642i
\(181\) −18.1168 −1.34661 −0.673307 0.739363i \(-0.735127\pi\)
−0.673307 + 0.739363i \(0.735127\pi\)
\(182\) 0 0
\(183\) −7.05842 23.4101i −0.521774 1.73053i
\(184\) −3.68614 6.38458i −0.271746 0.470678i
\(185\) −1.37228 2.37686i −0.100892 0.174750i
\(186\) −2.37228 + 2.52434i −0.173944 + 0.185093i
\(187\) −9.55842 + 16.5557i −0.698981 + 1.21067i
\(188\) 0 0
\(189\) 0 0
\(190\) 6.86141 0.497779
\(191\) 0.941578 1.63086i 0.0681302 0.118005i −0.829948 0.557841i \(-0.811630\pi\)
0.898078 + 0.439836i \(0.144963\pi\)
\(192\) −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 \(0.752266\pi\)
\(194\) −4.55842 7.89542i −0.327276 0.566858i
\(195\) 1.37228 + 4.55134i 0.0982711 + 0.325928i
\(196\) 0 0
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 10.9307 7.25061i 0.776811 0.515278i
\(199\) 10.0000 0.708881 0.354441 0.935079i \(-0.384671\pi\)
0.354441 + 0.935079i \(0.384671\pi\)
\(200\) −1.55842 + 2.69927i −0.110197 + 0.190867i
\(201\) 25.4891 + 5.98844i 1.79786 + 0.422392i
\(202\) −3.68614 6.38458i −0.259356 0.449218i
\(203\) 0 0
\(204\) 7.37228 + 1.73205i 0.516163 + 0.121268i
\(205\) 7.11684 12.3267i 0.497062 0.860937i
\(206\) −10.0000 −0.696733
\(207\) 18.4307 12.2255i 1.28102 0.849734i
\(208\) −2.00000 −0.138675
\(209\) 10.9307 18.9325i 0.756093 1.30959i
\(210\) 0 0
\(211\) 8.00000 + 13.8564i 0.550743 + 0.953914i 0.998221 + 0.0596196i \(0.0189888\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) −1.37228 2.37686i −0.0942487 0.163243i
\(213\) −12.0000 + 12.7692i −0.822226 + 0.874929i
\(214\) −0.813859 + 1.40965i −0.0556343 + 0.0963614i
\(215\) 12.5109 0.853235
\(216\) −4.00000 3.31662i −0.272166 0.225668i
\(217\) 0 0
\(218\) 7.00000 12.1244i 0.474100 0.821165i
\(219\) −6.06930 + 6.45832i −0.410125 + 0.436413i
\(220\) −3.00000 5.19615i −0.202260 0.350325i
\(221\) 4.37228 + 7.57301i 0.294111 + 0.509416i
\(222\) 1.00000 + 3.31662i 0.0671156 + 0.222597i
\(223\) −2.00000 + 3.46410i −0.133930 + 0.231973i −0.925188 0.379509i \(-0.876093\pi\)
0.791258 + 0.611482i \(0.209426\pi\)
\(224\) 0 0
\(225\) −8.37228 4.16381i −0.558152 0.277588i
\(226\) −1.37228 −0.0912828
\(227\) −11.8723 + 20.5634i −0.787991 + 1.36484i 0.139205 + 0.990264i \(0.455545\pi\)
−0.927196 + 0.374577i \(0.877788\pi\)
\(228\) −8.43070 1.98072i −0.558337 0.131176i
\(229\) −10.0584 17.4217i −0.664679 1.15126i −0.979372 0.202065i \(-0.935235\pi\)
0.314693 0.949194i \(-0.398098\pi\)
\(230\) −5.05842 8.76144i −0.333542 0.577713i
\(231\) 0 0
\(232\) 1.37228 2.37686i 0.0900947 0.156049i
\(233\) −11.7446 −0.769412 −0.384706 0.923039i \(-0.625697\pi\)
−0.384706 + 0.923039i \(0.625697\pi\)
\(234\) −0.372281 5.98844i −0.0243368 0.391477i
\(235\) 0 0
\(236\) 3.55842 6.16337i 0.231634 0.401201i
\(237\) −6.05842 20.0935i −0.393537 1.30521i
\(238\) 0 0
\(239\) 9.43070 + 16.3345i 0.610021 + 1.05659i 0.991236 + 0.132102i \(0.0421725\pi\)
−0.381215 + 0.924487i \(0.624494\pi\)
\(240\) −1.62772 + 1.73205i −0.105069 + 0.111803i
\(241\) 0.441578 0.764836i 0.0284445 0.0492674i −0.851453 0.524431i \(-0.824278\pi\)
0.879897 + 0.475164i \(0.157611\pi\)
\(242\) −8.11684 −0.521770
\(243\) 9.18614 12.5942i 0.589291 0.807921i
\(244\) 14.1168 0.903738
\(245\) 0 0
\(246\) −12.3030 + 13.0916i −0.784410 + 0.834688i
\(247\) −5.00000 8.66025i −0.318142 0.551039i
\(248\) −1.00000 1.73205i −0.0635001 0.109985i
\(249\) −2.74456 9.10268i −0.173930 0.576859i
\(250\) −5.56930 + 9.64630i −0.352233 + 0.610086i
\(251\) 9.00000 0.568075 0.284037 0.958813i \(-0.408326\pi\)
0.284037 + 0.958813i \(0.408326\pi\)
\(252\) 0 0
\(253\) −32.2337 −2.02651
\(254\) −7.05842 + 12.2255i −0.442885 + 0.767099i
\(255\) 10.1168 + 2.37686i 0.633541 + 0.148845i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 10.9307 + 18.9325i 0.681839 + 1.18098i 0.974419 + 0.224738i \(0.0721527\pi\)
−0.292581 + 0.956241i \(0.594514\pi\)
\(258\) −15.3723 3.61158i −0.957036 0.224847i
\(259\) 0 0
\(260\) −2.74456 −0.170211
\(261\) 7.37228 + 3.66648i 0.456333 + 0.226949i
\(262\) −7.37228 −0.455461
\(263\) −6.68614 + 11.5807i −0.412285 + 0.714099i −0.995139 0.0984781i \(-0.968603\pi\)
0.582854 + 0.812577i \(0.301936\pi\)
\(264\) 2.18614 + 7.25061i 0.134548 + 0.446244i
\(265\) −1.88316 3.26172i −0.115681 0.200366i
\(266\) 0 0
\(267\) 3.86141 4.10891i 0.236314 0.251461i
\(268\) −7.55842 + 13.0916i −0.461704 + 0.799695i
\(269\) 7.37228 0.449496 0.224748 0.974417i \(-0.427844\pi\)
0.224748 + 0.974417i \(0.427844\pi\)
\(270\) −5.48913 4.55134i −0.334058 0.276986i
\(271\) 18.2337 1.10762 0.553809 0.832644i \(-0.313174\pi\)
0.553809 + 0.832644i \(0.313174\pi\)
\(272\) −2.18614 + 3.78651i −0.132554 + 0.229591i
\(273\) 0 0
\(274\) 8.18614 + 14.1788i 0.494543 + 0.856573i
\(275\) 6.81386 + 11.8020i 0.410891 + 0.711684i
\(276\) 3.68614 + 12.2255i 0.221880 + 0.735891i
\(277\) −11.1168 + 19.2549i −0.667946 + 1.15692i 0.310531 + 0.950563i \(0.399493\pi\)
−0.978477 + 0.206354i \(0.933840\pi\)
\(278\) −21.2337 −1.27351
\(279\) 5.00000 3.31662i 0.299342 0.198561i
\(280\) 0 0
\(281\) −5.31386 + 9.20387i −0.316998 + 0.549057i −0.979860 0.199685i \(-0.936008\pi\)
0.662862 + 0.748742i \(0.269342\pi\)
\(282\) 0 0
\(283\) 4.94158 + 8.55906i 0.293746 + 0.508784i 0.974692 0.223550i \(-0.0717646\pi\)
−0.680946 + 0.732333i \(0.738431\pi\)
\(284\) −5.05842 8.76144i −0.300162 0.519896i
\(285\) −11.5693 2.71810i −0.685306 0.161006i
\(286\) −4.37228 + 7.57301i −0.258538 + 0.447802i
\(287\) 0 0
\(288\) 2.50000 1.65831i 0.147314 0.0977170i
\(289\) 2.11684 0.124520
\(290\) 1.88316 3.26172i 0.110583 0.191535i
\(291\) 4.55842 + 15.1186i 0.267219 + 0.886267i
\(292\) −2.55842 4.43132i −0.149720 0.259323i
\(293\) −2.31386 4.00772i −0.135177 0.234134i 0.790488 0.612478i \(-0.209827\pi\)
−0.925665 + 0.378344i \(0.876494\pi\)
\(294\) 0 0
\(295\) 4.88316 8.45787i 0.284308 0.492436i
\(296\) −2.00000 −0.116248
\(297\) −21.3030 + 7.89542i −1.23612 + 0.458139i
\(298\) −14.7446 −0.854130
\(299\) −7.37228 + 12.7692i −0.426350 + 0.738460i
\(300\) 3.69702 3.93398i 0.213447 0.227129i
\(301\) 0 0
\(302\) −4.05842 7.02939i −0.233536 0.404496i
\(303\) 3.68614 + 12.2255i 0.211763 + 0.702339i
\(304\) 2.50000 4.33013i 0.143385 0.248350i
\(305\) 19.3723 1.10925
\(306\) −11.7446 5.84096i −0.671392 0.333906i
\(307\) 13.0000 0.741949 0.370975 0.928643i \(-0.379024\pi\)
0.370975 + 0.928643i \(0.379024\pi\)
\(308\) 0 0
\(309\) 16.8614 + 3.96143i 0.959212 + 0.225358i
\(310\) −1.37228 2.37686i −0.0779403 0.134997i
\(311\) −13.1168 22.7190i −0.743788 1.28828i −0.950759 0.309931i \(-0.899694\pi\)
0.206971 0.978347i \(-0.433639\pi\)
\(312\) 3.37228 + 0.792287i 0.190918 + 0.0448544i
\(313\) −1.44158 + 2.49689i −0.0814828 + 0.141132i −0.903887 0.427771i \(-0.859299\pi\)
0.822404 + 0.568904i \(0.192632\pi\)
\(314\) −8.11684 −0.458060
\(315\) 0 0
\(316\) 12.1168 0.681626
\(317\) 3.00000 5.19615i 0.168497 0.291845i −0.769395 0.638774i \(-0.779442\pi\)
0.937892 + 0.346929i \(0.112775\pi\)
\(318\) 1.37228 + 4.55134i 0.0769537 + 0.255227i
\(319\) −6.00000 10.3923i −0.335936 0.581857i
\(320\) −0.686141 1.18843i −0.0383564 0.0664353i
\(321\) 1.93070 2.05446i 0.107761 0.114669i
\(322\) 0 0
\(323\) −21.8614 −1.21640
\(324\) 5.43070 + 7.17687i 0.301706 + 0.398715i
\(325\) 6.23369 0.345783
\(326\) 8.11684 14.0588i 0.449550 0.778644i
\(327\) −16.6060 + 17.6704i −0.918312 + 0.977173i
\(328\) −5.18614 8.98266i −0.286357 0.495984i
\(329\) 0 0
\(330\) 3.00000 + 9.94987i 0.165145 + 0.547723i
\(331\) 6.11684 10.5947i 0.336212 0.582337i −0.647505 0.762061i \(-0.724187\pi\)
0.983717 + 0.179725i \(0.0575207\pi\)
\(332\) 5.48913 0.301255
\(333\) −0.372281 5.98844i −0.0204009 0.328164i
\(334\) 17.4891 0.956962
\(335\) −10.3723 + 17.9653i −0.566698 + 0.981550i
\(336\) 0 0
\(337\) −4.55842 7.89542i −0.248313 0.430091i 0.714745 0.699385i \(-0.246543\pi\)
−0.963058 + 0.269294i \(0.913210\pi\)
\(338\) −4.50000 7.79423i −0.244768 0.423950i
\(339\) 2.31386 + 0.543620i 0.125672 + 0.0295254i
\(340\) −3.00000 + 5.19615i −0.162698 + 0.281801i
\(341\) −8.74456 −0.473545
\(342\) 13.4307 + 6.67954i 0.726249 + 0.361188i
\(343\) 0 0
\(344\) 4.55842 7.89542i 0.245774 0.425692i
\(345\) 5.05842 + 16.7769i 0.272336 + 0.903237i
\(346\) 3.00000 + 5.19615i 0.161281 + 0.279347i
\(347\) −3.55842 6.16337i −0.191026 0.330867i 0.754564 0.656226i \(-0.227848\pi\)
−0.945591 + 0.325359i \(0.894515\pi\)
\(348\) −3.25544 + 3.46410i −0.174510 + 0.185695i
\(349\) −11.0000 + 19.0526i −0.588817 + 1.01986i 0.405571 + 0.914063i \(0.367073\pi\)
−0.994388 + 0.105797i \(0.966261\pi\)
\(350\) 0 0
\(351\) −1.74456 + 10.2448i −0.0931179 + 0.546828i
\(352\) −4.37228 −0.233043
\(353\) −3.81386 + 6.60580i −0.202991 + 0.351591i −0.949491 0.313795i \(-0.898400\pi\)
0.746500 + 0.665386i \(0.231733\pi\)
\(354\) −8.44158 + 8.98266i −0.448665 + 0.477423i
\(355\) −6.94158 12.0232i −0.368421 0.638123i
\(356\) 1.62772 + 2.81929i 0.0862689 + 0.149422i
\(357\) 0 0
\(358\) 7.37228 12.7692i 0.389637 0.674871i
\(359\) −6.86141 −0.362131 −0.181066 0.983471i \(-0.557955\pi\)
−0.181066 + 0.983471i \(0.557955\pi\)
\(360\) 3.43070 2.27567i 0.180814 0.119938i
\(361\) 6.00000 0.315789
\(362\) −9.05842 + 15.6896i −0.476100 + 0.824630i
\(363\) 13.6861 + 3.21543i 0.718336 + 0.168767i
\(364\) 0 0
\(365\) −3.51087 6.08101i −0.183768 0.318295i
\(366\) −23.8030 5.59230i −1.24420 0.292314i
\(367\) 11.1168 19.2549i 0.580295 1.00510i −0.415150 0.909753i \(-0.636271\pi\)
0.995444 0.0953465i \(-0.0303959\pi\)
\(368\) −7.37228 −0.384307
\(369\) 25.9307 17.2005i 1.34990 0.895421i
\(370\) −2.74456 −0.142683
\(371\) 0 0
\(372\) 1.00000 + 3.31662i 0.0518476 + 0.171959i
\(373\) 5.00000 + 8.66025i 0.258890 + 0.448411i 0.965945 0.258748i \(-0.0833099\pi\)
−0.707055 + 0.707159i \(0.749977\pi\)
\(374\) 9.55842 + 16.5557i 0.494254 + 0.856073i
\(375\) 13.2119 14.0588i 0.682262 0.725993i
\(376\) 0 0
\(377\) −5.48913 −0.282704
\(378\) 0 0
\(379\) 9.11684 0.468301 0.234150 0.972200i \(-0.424769\pi\)
0.234150 + 0.972200i \(0.424769\pi\)
\(380\) 3.43070 5.94215i 0.175991 0.304826i
\(381\) 16.7446 17.8178i 0.857850 0.912836i
\(382\) −0.941578 1.63086i −0.0481753 0.0834421i
\(383\) −10.6277 18.4077i −0.543051 0.940592i −0.998727 0.0504462i \(-0.983936\pi\)
0.455676 0.890146i \(-0.349398\pi\)
\(384\) 0.500000 + 1.65831i 0.0255155 + 0.0846254i
\(385\) 0 0
\(386\) 7.00000 0.356291
\(387\) 24.4891 + 12.1793i 1.24485 + 0.619107i
\(388\) −9.11684 −0.462838
\(389\) 17.4891 30.2921i 0.886734 1.53587i 0.0430204 0.999074i \(-0.486302\pi\)
0.843713 0.536794i \(-0.180365\pi\)
\(390\) 4.62772 + 1.08724i 0.234334 + 0.0550546i
\(391\) 16.1168 + 27.9152i 0.815064 + 1.41173i
\(392\) 0 0
\(393\) 12.4307 + 2.92048i 0.627046 + 0.147319i
\(394\) −3.00000 + 5.19615i −0.151138 + 0.261778i
\(395\) 16.6277 0.836631
\(396\) −0.813859 13.0916i −0.0408980 0.657876i
\(397\) 22.0000 1.10415 0.552074 0.833795i \(-0.313837\pi\)
0.552074 + 0.833795i \(0.313837\pi\)
\(398\) 5.00000 8.66025i 0.250627 0.434099i
\(399\) 0 0
\(400\) 1.55842 + 2.69927i 0.0779211 + 0.134963i
\(401\) 0.127719 + 0.221215i 0.00637797 + 0.0110470i 0.869197 0.494466i \(-0.164636\pi\)
−0.862819 + 0.505513i \(0.831303\pi\)
\(402\) 17.9307 19.0800i 0.894302 0.951624i
\(403\) −2.00000 + 3.46410i −0.0996271 + 0.172559i
\(404\) −7.37228 −0.366785
\(405\) 7.45245 + 9.84868i 0.370315 + 0.489385i
\(406\) 0 0
\(407\) −4.37228 + 7.57301i −0.216726 + 0.375380i
\(408\) 5.18614 5.51856i 0.256752 0.273209i
\(409\) 14.6753 + 25.4183i 0.725645 + 1.25685i 0.958708 + 0.284393i \(0.0917919\pi\)
−0.233063 + 0.972462i \(0.574875\pi\)
\(410\) −7.11684 12.3267i −0.351476 0.608774i
\(411\) −8.18614 27.1504i −0.403793 1.33923i
\(412\) −5.00000 + 8.66025i −0.246332 + 0.426660i
\(413\) 0 0
\(414\) −1.37228 22.0742i −0.0674439 1.08489i
\(415\) 7.53262 0.369762
\(416\) −1.00000 + 1.73205i −0.0490290 + 0.0849208i
\(417\) 35.8030 + 8.41159i 1.75328 + 0.411917i
\(418\) −10.9307 18.9325i −0.534638 0.926020i
\(419\) 13.8030 + 23.9075i 0.674320 + 1.16796i 0.976667 + 0.214759i \(0.0688964\pi\)
−0.302347 + 0.953198i \(0.597770\pi\)
\(420\) 0 0
\(421\) 0.116844 0.202380i 0.00569463 0.00986338i −0.863164 0.504924i \(-0.831521\pi\)
0.868859 + 0.495060i \(0.164854\pi\)
\(422\) 16.0000 0.778868
\(423\) 0 0
\(424\) −2.74456 −0.133288
\(425\) 6.81386 11.8020i 0.330521 0.572479i
\(426\) 5.05842 + 16.7769i 0.245081 + 0.812843i
\(427\) 0 0
\(428\) 0.813859 + 1.40965i 0.0393394 + 0.0681378i
\(429\) 10.3723 11.0371i 0.500778 0.532877i
\(430\) 6.25544 10.8347i 0.301664 0.522497i
\(431\) −29.4891 −1.42044 −0.710221 0.703979i \(-0.751405\pi\)
−0.710221 + 0.703979i \(0.751405\pi\)
\(432\) −4.87228 + 1.80579i −0.234418 + 0.0868811i
\(433\) 2.88316 0.138556 0.0692778 0.997597i \(-0.477931\pi\)
0.0692778 + 0.997597i \(0.477931\pi\)
\(434\) 0 0
\(435\) −4.46738 + 4.75372i −0.214194 + 0.227924i
\(436\) −7.00000 12.1244i −0.335239 0.580651i
\(437\) −18.4307 31.9229i −0.881660 1.52708i
\(438\) 2.55842 + 8.48533i 0.122246 + 0.405445i
\(439\) 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
\(442\) 8.74456 0.415936
\(443\) 11.4416 19.8174i 0.543606 0.941553i −0.455087 0.890447i \(-0.650392\pi\)
0.998693 0.0511061i \(-0.0162747\pi\)
\(444\) 3.37228 + 0.792287i 0.160041 + 0.0376003i
\(445\) 2.23369 + 3.86886i 0.105887 + 0.183402i
\(446\) 2.00000 + 3.46410i 0.0947027 + 0.164030i
\(447\) 24.8614 + 5.84096i 1.17590 + 0.276268i
\(448\) 0 0
\(449\) 33.0000 1.55737 0.778683 0.627417i \(-0.215888\pi\)
0.778683 + 0.627417i \(0.215888\pi\)
\(450\) −7.79211 + 5.16870i −0.367324 + 0.243655i
\(451\) −45.3505 −2.13547
\(452\) −0.686141 + 1.18843i −0.0322733 + 0.0558991i
\(453\) 4.05842 + 13.4603i 0.190681 + 0.632418i
\(454\) 11.8723 + 20.5634i 0.557194 + 0.965088i
\(455\) 0 0
\(456\) −5.93070 + 6.31084i −0.277731 + 0.295532i
\(457\) −16.7337 + 28.9836i −0.782769 + 1.35580i 0.147554 + 0.989054i \(0.452860\pi\)
−0.930323 + 0.366742i \(0.880473\pi\)
\(458\) −20.1168 −0.939998
\(459\) 17.4891 + 14.5012i 0.816322 + 0.676859i
\(460\) −10.1168 −0.471700
\(461\) 15.4307 26.7268i 0.718680 1.24479i −0.242844 0.970065i \(-0.578080\pi\)
0.961523 0.274724i \(-0.0885865\pi\)
\(462\) 0 0
\(463\) 2.94158 + 5.09496i 0.136707 + 0.236783i 0.926248 0.376914i \(-0.123015\pi\)
−0.789541 + 0.613697i \(0.789682\pi\)
\(464\) −1.37228 2.37686i −0.0637066 0.110343i
\(465\) 1.37228 + 4.55134i 0.0636380 + 0.211063i
\(466\) −5.87228 + 10.1711i −0.272028 + 0.471167i
\(467\) 30.0951 1.39263 0.696317 0.717734i \(-0.254821\pi\)
0.696317 + 0.717734i \(0.254821\pi\)
\(468\) −5.37228 2.67181i −0.248334 0.123505i
\(469\) 0 0
\(470\) 0 0
\(471\) 13.6861 + 3.21543i 0.630624 + 0.148159i
\(472\) −3.55842 6.16337i −0.163790 0.283692i
\(473\) −19.9307 34.5210i −0.916415 1.58728i
\(474\) −20.4307 4.80001i −0.938413 0.220472i
\(475\) −7.79211 + 13.4963i −0.357527 + 0.619254i
\(476\) 0 0
\(477\) −0.510875 8.21782i −0.0233913 0.376268i
\(478\) 18.8614 0.862701
\(479\) 10.6277 18.4077i 0.485593 0.841072i −0.514270 0.857628i \(-0.671937\pi\)
0.999863 + 0.0165568i \(0.00527043\pi\)
\(480\) 0.686141 + 2.27567i 0.0313179 + 0.103870i
\(481\) 2.00000 + 3.46410i 0.0911922 + 0.157949i
\(482\) −0.441578 0.764836i −0.0201133 0.0348373i
\(483\) 0 0
\(484\) −4.05842 + 7.02939i −0.184474 + 0.319518i
\(485\) −12.5109 −0.568090
\(486\) −6.31386 14.2525i −0.286402 0.646509i
\(487\) −16.3505 −0.740913 −0.370457 0.928850i \(-0.620799\pi\)
−0.370457 + 0.928850i \(0.620799\pi\)
\(488\) 7.05842 12.2255i 0.319520 0.553424i
\(489\) −19.2554 + 20.4897i −0.870761 + 0.926574i
\(490\) 0 0
\(491\) 9.81386 + 16.9981i 0.442893 + 0.767114i 0.997903 0.0647303i \(-0.0206187\pi\)
−0.555010 + 0.831844i \(0.687285\pi\)
\(492\) 5.18614 + 17.2005i 0.233809 + 0.775458i
\(493\) −6.00000 + 10.3923i −0.270226 + 0.468046i
\(494\) −10.0000 −0.449921
\(495\) −1.11684 17.9653i −0.0501984 0.807481i
\(496\) −2.00000 −0.0898027
\(497\) 0 0
\(498\) −9.25544 2.17448i −0.414746 0.0974408i
\(499\) −0.441578 0.764836i −0.0197677 0.0342387i 0.855972 0.517022i \(-0.172959\pi\)
−0.875740 + 0.482783i \(0.839626\pi\)
\(500\) 5.56930 + 9.64630i 0.249067 + 0.431396i
\(501\) −29.4891 6.92820i −1.31748 0.309529i
\(502\) 4.50000 7.79423i 0.200845 0.347873i
\(503\) −2.23369 −0.0995952 −0.0497976 0.998759i \(-0.515858\pi\)
−0.0497976 + 0.998759i \(0.515858\pi\)
\(504\) 0 0
\(505\) −10.1168 −0.450194
\(506\) −16.1168 + 27.9152i −0.716481 + 1.24098i
\(507\) 4.50000 + 14.9248i 0.199852 + 0.662834i
\(508\) 7.05842 + 12.2255i 0.313167 + 0.542421i
\(509\) 8.48913 + 14.7036i 0.376274 + 0.651725i 0.990517 0.137392i \(-0.0438718\pi\)
−0.614243 + 0.789117i \(0.710539\pi\)
\(510\) 7.11684 7.57301i 0.315139 0.335339i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −20.0000 16.5831i −0.883022 0.732163i
\(514\) 21.8614 0.964265
\(515\) −6.86141 + 11.8843i −0.302350 + 0.523685i
\(516\) −10.8139 + 11.5070i −0.476054 + 0.506567i
\(517\) 0 0
\(518\) 0 0
\(519\) −3.00000 9.94987i −0.131685 0.436751i
\(520\) −1.37228 + 2.37686i −0.0601785 + 0.104232i
\(521\) −3.86141 −0.169171 −0.0845856 0.996416i \(-0.526957\pi\)
−0.0845856 + 0.996416i \(0.526957\pi\)
\(522\) 6.86141 4.55134i 0.300316 0.199207i
\(523\) 17.8832 0.781976 0.390988 0.920396i \(-0.372133\pi\)
0.390988 + 0.920396i \(0.372133\pi\)
\(524\) −3.68614 + 6.38458i −0.161030 + 0.278912i
\(525\) 0 0
\(526\) 6.68614 + 11.5807i 0.291530 + 0.504944i
\(527\) 4.37228 + 7.57301i 0.190460 + 0.329886i
\(528\) 7.37228 + 1.73205i 0.320837 + 0.0753778i
\(529\) −15.6753 + 27.1504i −0.681533 + 1.18045i
\(530\) −3.76631 −0.163598
\(531\) 17.7921 11.8020i 0.772112 0.512161i
\(532\) 0 0
\(533\) −10.3723 + 17.9653i −0.449273 + 0.778164i
\(534\) −1.62772 5.39853i −0.0704383 0.233617i
\(535\) 1.11684 + 1.93443i 0.0482854 + 0.0836327i
\(536\) 7.55842 + 13.0916i 0.326474 + 0.565470i
\(537\) −17.4891 + 18.6101i −0.754711 + 0.803086i
\(538\) 3.68614 6.38458i 0.158921 0.275259i
\(539\) 0 0
\(540\) −6.68614 + 2.47805i −0.287726 + 0.106638i
\(541\) 28.2337 1.21386 0.606931 0.794755i \(-0.292401\pi\)
0.606931 + 0.794755i \(0.292401\pi\)
\(542\) 9.11684 15.7908i 0.391602 0.678275i
\(543\) 21.4891 22.8665i 0.922187 0.981296i
\(544\) 2.18614 + 3.78651i 0.0937300 + 0.162345i
\(545\) −9.60597 16.6380i −0.411475 0.712695i
\(546\) 0 0
\(547\) −0.441578 + 0.764836i −0.0188805 + 0.0327020i −0.875311 0.483560i \(-0.839344\pi\)
0.856431 + 0.516262i \(0.172677\pi\)
\(548\) 16.3723 0.699389
\(549\) 37.9198 + 18.8588i 1.61838 + 0.804874i
\(550\) 13.6277 0.581088
\(551\) 6.86141 11.8843i 0.292306 0.506288i
\(552\) 12.4307 + 2.92048i 0.529086 + 0.124304i
\(553\) 0 0
\(554\) 11.1168 + 19.2549i 0.472309 + 0.818064i
\(555\) 4.62772 + 1.08724i 0.196436 + 0.0461508i
\(556\) −10.6168 + 18.3889i −0.450254 + 0.779864i
\(557\) 6.51087 0.275875 0.137937 0.990441i \(-0.455953\pi\)
0.137937 + 0.990441i \(0.455953\pi\)
\(558\) −0.372281 5.98844i −0.0157599 0.253511i
\(559\) −18.2337 −0.771203
\(560\) 0 0
\(561\) −9.55842 31.7017i −0.403557 1.33845i
\(562\) 5.31386 + 9.20387i 0.224152 + 0.388242i
\(563\) 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
\(565\) −0.941578 + 1.63086i −0.0396125 + 0.0686108i
\(566\) 9.88316 0.415420
\(567\) 0 0
\(568\) −10.1168 −0.424493
\(569\) 0.558422 0.967215i 0.0234103 0.0405478i −0.854083 0.520137i \(-0.825881\pi\)
0.877493 + 0.479589i \(0.159214\pi\)
\(570\) −8.13859 + 8.66025i −0.340888 + 0.362738i
\(571\) −14.6753 25.4183i −0.614141 1.06372i −0.990535 0.137263i \(-0.956169\pi\)
0.376394 0.926460i \(-0.377164\pi\)
\(572\) 4.37228 + 7.57301i 0.182814 + 0.316644i
\(573\) 0.941578 + 3.12286i 0.0393350 + 0.130459i
\(574\) 0 0
\(575\) 22.9783 0.958259
\(576\) −0.186141 2.99422i −0.00775586 0.124759i
\(577\) −27.1168 −1.12889 −0.564444 0.825471i \(-0.690910\pi\)
−0.564444 + 0.825471i \(0.690910\pi\)
\(578\) 1.05842 1.83324i 0.0440246 0.0762528i
\(579\) −11.8030 2.77300i −0.490515 0.115242i
\(580\) −1.88316 3.26172i −0.0781938 0.135436i
\(581\) 0 0
\(582\) 15.3723 + 3.61158i 0.637202 + 0.149705i
\(583\) −6.00000 + 10.3923i −0.248495 + 0.430405i
\(584\) −5.11684 −0.211737
\(585\) −7.37228 3.66648i −0.304806 0.151590i
\(586\) −4.62772 −0.191169
\(587\) −4.24456 + 7.35180i −0.175192 + 0.303441i −0.940228 0.340547i \(-0.889388\pi\)
0.765036 + 0.643988i \(0.222721\pi\)
\(588\) 0 0
\(589\) −5.00000 8.66025i −0.206021 0.356840i
\(590\) −4.88316 8.45787i −0.201036 0.348205i
\(591\) 7.11684 7.57301i 0.292748 0.311512i
\(592\) −1.00000 + 1.73205i −0.0410997 + 0.0711868i
\(593\) −3.25544 −0.133685 −0.0668424 0.997764i \(-0.521292\pi\)
−0.0668424 + 0.997764i \(0.521292\pi\)
\(594\) −3.81386 + 22.3966i −0.156485 + 0.918945i
\(595\) 0 0
\(596\) −7.37228 + 12.7692i −0.301980 + 0.523045i
\(597\) −11.8614 + 12.6217i −0.485455 + 0.516571i
\(598\) 7.37228 + 12.7692i 0.301475 + 0.522170i
\(599\) −12.0000 20.7846i −0.490307 0.849236i 0.509631 0.860393i \(-0.329782\pi\)
−0.999938 + 0.0111569i \(0.996449\pi\)
\(600\) −1.55842 5.16870i −0.0636223 0.211011i
\(601\) 3.44158 5.96099i 0.140385 0.243154i −0.787257 0.616625i \(-0.788499\pi\)
0.927642 + 0.373472i \(0.121833\pi\)
\(602\) 0 0
\(603\) −37.7921 + 25.0684i −1.53901 + 1.02087i
\(604\) −8.11684 −0.330270
\(605\) −5.56930 + 9.64630i −0.226424 + 0.392178i
\(606\) 12.4307 + 2.92048i 0.504963 + 0.118636i
\(607\) −6.11684 10.5947i −0.248275 0.430025i 0.714772 0.699357i \(-0.246530\pi\)
−0.963047 + 0.269332i \(0.913197\pi\)
\(608\) −2.50000 4.33013i −0.101388 0.175610i
\(609\) 0 0
\(610\) 9.68614 16.7769i 0.392180 0.679276i
\(611\) 0 0
\(612\) −10.9307 + 7.25061i −0.441847 + 0.293088i
\(613\) −1.76631 −0.0713407 −0.0356703 0.999364i \(-0.511357\pi\)
−0.0356703 + 0.999364i \(0.511357\pi\)
\(614\) 6.50000 11.2583i 0.262319 0.454349i
\(615\) 7.11684 + 23.6039i 0.286979 + 0.951801i
\(616\) 0 0
\(617\) 4.93070 + 8.54023i 0.198503 + 0.343817i 0.948043 0.318142i \(-0.103059\pi\)
−0.749540 + 0.661959i \(0.769725\pi\)
\(618\) 11.8614 12.6217i 0.477136 0.507719i
\(619\) −11.7337 + 20.3233i −0.471617 + 0.816864i −0.999473 0.0324697i \(-0.989663\pi\)
0.527856 + 0.849334i \(0.322996\pi\)
\(620\) −2.74456 −0.110224
\(621\) −6.43070 + 37.7639i −0.258055 + 1.51541i
\(622\) −26.2337 −1.05188
\(623\) 0 0
\(624\) 2.37228 2.52434i 0.0949673 0.101054i
\(625\) −0.149468 0.258886i −0.00597872 0.0103555i
\(626\) 1.44158 + 2.49689i 0.0576170 + 0.0997956i
\(627\) 10.9307 + 36.2530i 0.436530 + 1.44781i
\(628\) −4.05842 + 7.02939i −0.161949 + 0.280503i
\(629\) 8.74456 0.348669
\(630\) 0 0
\(631\) 14.3505 0.571286 0.285643 0.958336i \(-0.407793\pi\)
0.285643 + 0.958336i \(0.407793\pi\)
\(632\) 6.05842 10.4935i 0.240991 0.417409i
\(633\) −26.9783 6.33830i −1.07229 0.251925i
\(634\) −3.00000 5.19615i −0.119145 0.206366i
\(635\) 9.68614 + 16.7769i 0.384383 + 0.665770i
\(636\) 4.62772 + 1.08724i 0.183501 + 0.0431119i
\(637\) 0 0
\(638\) −12.0000 −0.475085
\(639\) −1.88316 30.2921i −0.0744965 1.19834i
\(640\) −1.37228 −0.0542442
\(641\) 23.1060 40.0207i 0.912631 1.58072i 0.102298 0.994754i \(-0.467381\pi\)
0.810333 0.585969i \(-0.199286\pi\)
\(642\) −0.813859 2.69927i −0.0321205 0.106532i
\(643\) −12.6753 21.9542i −0.499864 0.865789i 0.500136 0.865947i \(-0.333283\pi\)
−1.00000 0.000157386i \(0.999950\pi\)
\(644\) 0 0
\(645\) −14.8397 + 15.7908i −0.584311 + 0.621764i
\(646\) −10.9307 + 18.9325i −0.430063 + 0.744891i
\(647\) 17.4891 0.687568 0.343784 0.939049i \(-0.388291\pi\)
0.343784 + 0.939049i \(0.388291\pi\)
\(648\) 8.93070 1.11469i 0.350831 0.0437892i
\(649\) −31.1168 −1.22144
\(650\) 3.11684 5.39853i 0.122253 0.211748i
\(651\) 0 0
\(652\) −8.11684 14.0588i −0.317880 0.550585i
\(653\) 7.62772 + 13.2116i 0.298496 + 0.517010i 0.975792 0.218701i \(-0.0701818\pi\)
−0.677296 + 0.735710i \(0.736848\pi\)
\(654\) 7.00000 + 23.2164i 0.273722 + 0.907832i
\(655\) −5.05842 + 8.76144i −0.197649 + 0.342338i
\(656\) −10.3723 −0.404970
\(657\) −0.952453 15.3210i −0.0371587 0.597727i
\(658\) 0 0
\(659\) 4.62772 8.01544i 0.180270 0.312237i −0.761702 0.647927i \(-0.775636\pi\)
0.941973 + 0.335690i \(0.108969\pi\)
\(660\) 10.1168 + 2.37686i 0.393798 + 0.0925192i
\(661\) 4.94158 + 8.55906i 0.192205 + 0.332909i 0.945981 0.324223i \(-0.105103\pi\)
−0.753776 + 0.657132i \(0.771769\pi\)
\(662\) −6.11684 10.5947i −0.237738 0.411774i
\(663\) −14.7446 3.46410i −0.572631 0.134535i
\(664\) 2.74456 4.75372i 0.106510 0.184480i
\(665\) 0 0
\(666\) −5.37228 2.67181i −0.208172 0.103531i
\(667\) −20.2337 −0.783452
\(668\) 8.74456 15.1460i 0.338337 0.586017i
\(669\) −2.00000 6.63325i −0.0773245 0.256456i
\(670\) 10.3723 + 17.9653i 0.400716 + 0.694061i
\(671\) −30.8614 53.4535i −1.19139 2.06355i
\(672\) 0 0
\(673\) 10.0584 17.4217i 0.387724 0.671557i −0.604419 0.796666i \(-0.706595\pi\)
0.992143 + 0.125109i \(0.0399281\pi\)
\(674\) −9.11684 −0.351168
\(675\) 15.1861 5.62836i 0.584515 0.216636i
\(676\) −9.00000 −0.346154
\(677\) −17.2337 + 29.8496i −0.662344 + 1.14721i 0.317654 + 0.948207i \(0.397105\pi\)
−0.979998 + 0.199007i \(0.936228\pi\)
\(678\) 1.62772 1.73205i 0.0625122 0.0665190i
\(679\) 0 0
\(680\) 3.00000 + 5.19615i 0.115045 + 0.199263i
\(681\) −11.8723 39.3759i −0.454947 1.50889i
\(682\) −4.37228 + 7.57301i −0.167423 + 0.289986i
\(683\) −44.8397 −1.71574 −0.857871 0.513865i \(-0.828213\pi\)
−0.857871 + 0.513865i \(0.828213\pi\)
\(684\) 12.5000 8.29156i 0.477949 0.317036i
\(685\) 22.4674 0.858434
\(686\) 0 0
\(687\) 33.9198 + 7.96916i 1.29412 + 0.304042i
\(688\) −4.55842 7.89542i −0.173788 0.301010i
\(689\) 2.74456 + 4.75372i 0.104560 + 0.181102i
\(690\) 17.0584 + 4.00772i 0.649403 + 0.152571i
\(691\) −2.94158 + 5.09496i −0.111903 + 0.193822i −0.916537 0.399949i \(-0.869028\pi\)
0.804635 + 0.593770i \(0.202361\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −7.11684 −0.270152
\(695\) −14.5693 + 25.2348i −0.552645 + 0.957209i
\(696\) 1.37228 + 4.55134i 0.0520162 + 0.172518i
\(697\) 22.6753 + 39.2747i 0.858887 + 1.48764i
\(698\) 11.0000 + 19.0526i 0.416356 + 0.721150i
\(699\) 13.9307 14.8236i 0.526908 0.560681i
\(700\) 0 0
\(701\) −3.76631 −0.142252 −0.0711258 0.997467i \(-0.522659\pi\)
−0.0711258 + 0.997467i \(0.522659\pi\)
\(702\) 8.00000 + 6.63325i 0.301941 + 0.250356i
\(703\) −10.0000 −0.377157
\(704\) −2.18614 + 3.78651i −0.0823933 + 0.142709i
\(705\) 0 0
\(706\) 3.81386 + 6.60580i 0.143536 + 0.248612i
\(707\) 0 0
\(708\) 3.55842 + 11.8020i 0.133734 + 0.443544i
\(709\) −22.0000 + 38.1051i −0.826227 + 1.43107i 0.0747503 + 0.997202i \(0.476184\pi\)
−0.900978 + 0.433865i \(0.857149\pi\)
\(710\) −13.8832 −0.521026
\(711\) 32.5475 + 16.1870i 1.22063 + 0.607059i
\(712\) 3.25544 0.122003
\(713\) −7.37228 + 12.7692i −0.276094 + 0.478209i
\(714\) 0 0
\(715\) 6.00000 + 10.3923i 0.224387 + 0.388650i
\(716\) −7.37228 12.7692i −0.275515 0.477206i
\(717\) −31.8030 7.47182i −1.18770 0.279040i
\(718\) −3.43070 + 5.94215i −0.128033 + 0.221759i
\(719\) 8.74456 0.326117 0.163059 0.986616i \(-0.447864\pi\)
0.163059 + 0.986616i \(0.447864\pi\)
\(720\) −0.255437 4.10891i −0.00951959 0.153130i
\(721\) 0 0
\(722\) 3.00000 5.19615i 0.111648 0.193381i
\(723\) 0.441578 + 1.46455i 0.0164225 + 0.0544671i
\(724\) 9.05842 + 15.6896i 0.336654 + 0.583101i
\(725\) 4.27719 + 7.40830i 0.158851 + 0.275138i
\(726\) 9.62772 10.2448i 0.357318 0.380221i
\(727\) −0.883156 + 1.52967i −0.0327544 + 0.0567324i −0.881938 0.471366i \(-0.843761\pi\)
0.849183 + 0.528098i \(0.177095\pi\)
\(728\) 0 0
\(729\) 5.00000 + 26.5330i 0.185185 + 0.982704i
\(730\) −7.02175 −0.259887
\(731\) −19.9307 + 34.5210i −0.737164 + 1.27680i
\(732\) −16.7446 + 17.8178i −0.618897 + 0.658566i
\(733\) −11.9416 20.6834i −0.441072 0.763960i 0.556697 0.830716i \(-0.312068\pi\)
−0.997769 + 0.0667560i \(0.978735\pi\)
\(734\) −11.1168 19.2549i −0.410330 0.710713i
\(735\) 0 0
\(736\) −3.68614 + 6.38458i −0.135873 + 0.235339i
\(737\) 66.0951 2.43464
\(738\) −1.93070 31.0569i −0.0710702 1.14322i
\(739\) 9.11684 0.335369 0.167684 0.985841i \(-0.446371\pi\)
0.167684 + 0.985841i \(0.446371\pi\)
\(740\) −1.37228 + 2.37686i −0.0504461 + 0.0873751i
\(741\) 16.8614 + 3.96143i 0.619419 + 0.145527i
\(742\) 0 0
\(743\) −21.8614 37.8651i −0.802017 1.38913i −0.918286 0.395917i \(-0.870427\pi\)
0.116269 0.993218i \(-0.462906\pi\)
\(744\) 3.37228 + 0.792287i 0.123634 + 0.0290467i
\(745\) −10.1168 + 17.5229i −0.370652 + 0.641989i
\(746\) 10.0000 0.366126
\(747\) 14.7446 + 7.33296i 0.539475 + 0.268299i
\(748\) 19.1168 0.698981
\(749\) 0 0
\(750\) −5.56930 18.4713i −0.203362 0.674475i
\(751\) −0.0584220 0.101190i −0.00213185 0.00369247i 0.864958 0.501845i \(-0.167345\pi\)
−0.867089 + 0.498153i \(0.834012\pi\)
\(752\) 0 0
\(753\) −10.6753 + 11.3595i −0.389028 + 0.413964i
\(754\) −2.74456 + 4.75372i −0.0999511 + 0.173120i
\(755\) −11.1386 −0.405375
\(756\) 0 0
\(757\) 11.7663 0.427654 0.213827 0.976872i \(-0.431407\pi\)
0.213827 + 0.976872i \(0.431407\pi\)
\(758\) 4.55842 7.89542i 0.165569 0.286775i
\(759\) 38.2337 40.6844i 1.38779 1.47675i
\(760\) −3.43070 5.94215i −0.124445 0.215545i
\(761\) 6.25544 + 10.8347i 0.226759 + 0.392759i 0.956846 0.290596i \(-0.0938536\pi\)
−0.730086 + 0.683355i \(0.760520\pi\)
\(762\) −7.05842 23.4101i −0.255700 0.848060i
\(763\) 0 0
\(764\) −1.88316 −0.0681302
\(765\) −15.0000 + 9.94987i −0.542326 + 0.359738i
\(766\) −21.2554 −0.767990
\(767\) −7.11684 + 12.3267i −0.256974 + 0.445093i
\(768\) 1.68614 + 0.396143i 0.0608434 + 0.0142946i
\(769\) −5.00000 8.66025i −0.180305 0.312297i 0.761680 0.647954i \(-0.224375\pi\)
−0.941984 + 0.335657i \(0.891042\pi\)
\(770\) 0 0
\(771\) −36.8614 8.66025i −1.32753 0.311891i
\(772\) 3.50000 6.06218i 0.125968 0.218183i
\(773\) 11.1386 0.400627 0.200314 0.979732i \(-0.435804\pi\)
0.200314 + 0.979732i \(0.435804\pi\)
\(774\) 22.7921 15.1186i 0.819245 0.543426i
\(775\) 6.23369 0.223921
\(776\) −4.55842 + 7.89542i −0.163638 + 0.283429i
\(777\) 0 0
\(778\) −17.4891 30.2921i −0.627016 1.08602i
\(779\) −25.9307 44.9133i −0.929064 1.60919i
\(780\) 3.25544 3.46410i 0.116563 0.124035i
\(781\) −22.1168 + 38.3075i −0.791403 + 1.37075i