Properties

Label 882.2.e.l.373.1
Level $882$
Weight $2$
Character 882.373
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.e (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: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.1
Root \(-1.18614 - 1.26217i\) of defining polynomial
Character \(\chi\) \(=\) 882.373
Dual form 882.2.e.l.655.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(0.500000 - 1.65831i) q^{3} +1.00000 q^{4} +(0.686141 + 1.18843i) q^{5} +(-0.500000 + 1.65831i) q^{6} -1.00000 q^{8} +(-2.50000 - 1.65831i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(0.500000 - 1.65831i) q^{3} +1.00000 q^{4} +(0.686141 + 1.18843i) q^{5} +(-0.500000 + 1.65831i) q^{6} -1.00000 q^{8} +(-2.50000 - 1.65831i) q^{9} +(-0.686141 - 1.18843i) q^{10} +(-2.18614 + 3.78651i) q^{11} +(0.500000 - 1.65831i) q^{12} +(-1.00000 + 1.73205i) q^{13} +(2.31386 - 0.543620i) q^{15} +1.00000 q^{16} +(2.18614 + 3.78651i) q^{17} +(2.50000 + 1.65831i) q^{18} +(-2.50000 + 4.33013i) q^{19} +(0.686141 + 1.18843i) q^{20} +(2.18614 - 3.78651i) q^{22} +(3.68614 + 6.38458i) q^{23} +(-0.500000 + 1.65831i) q^{24} +(1.55842 - 2.69927i) q^{25} +(1.00000 - 1.73205i) q^{26} +(-4.00000 + 3.31662i) q^{27} +(-1.37228 - 2.37686i) q^{29} +(-2.31386 + 0.543620i) q^{30} +2.00000 q^{31} -1.00000 q^{32} +(5.18614 + 5.51856i) q^{33} +(-2.18614 - 3.78651i) q^{34} +(-2.50000 - 1.65831i) q^{36} +(-1.00000 + 1.73205i) q^{37} +(2.50000 - 4.33013i) q^{38} +(2.37228 + 2.52434i) q^{39} +(-0.686141 - 1.18843i) q^{40} +(-5.18614 + 8.98266i) q^{41} +(-4.55842 - 7.89542i) q^{43} +(-2.18614 + 3.78651i) q^{44} +(0.255437 - 4.10891i) q^{45} +(-3.68614 - 6.38458i) q^{46} +(0.500000 - 1.65831i) q^{48} +(-1.55842 + 2.69927i) q^{50} +(7.37228 - 1.73205i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-1.37228 - 2.37686i) q^{53} +(4.00000 - 3.31662i) q^{54} -6.00000 q^{55} +(5.93070 + 6.31084i) q^{57} +(1.37228 + 2.37686i) q^{58} +7.11684 q^{59} +(2.31386 - 0.543620i) q^{60} -14.1168 q^{61} -2.00000 q^{62} +1.00000 q^{64} -2.74456 q^{65} +(-5.18614 - 5.51856i) q^{66} +15.1168 q^{67} +(2.18614 + 3.78651i) q^{68} +(12.4307 - 2.92048i) q^{69} +10.1168 q^{71} +(2.50000 + 1.65831i) q^{72} +(2.55842 + 4.43132i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-3.69702 - 3.93398i) q^{75} +(-2.50000 + 4.33013i) q^{76} +(-2.37228 - 2.52434i) q^{78} +12.1168 q^{79} +(0.686141 + 1.18843i) q^{80} +(3.50000 + 8.29156i) q^{81} +(5.18614 - 8.98266i) q^{82} +(2.74456 + 4.75372i) q^{83} +(-3.00000 + 5.19615i) q^{85} +(4.55842 + 7.89542i) q^{86} +(-4.62772 + 1.08724i) q^{87} +(2.18614 - 3.78651i) q^{88} +(-1.62772 + 2.81929i) q^{89} +(-0.255437 + 4.10891i) q^{90} +(3.68614 + 6.38458i) q^{92} +(1.00000 - 3.31662i) q^{93} -6.86141 q^{95} +(-0.500000 + 1.65831i) q^{96} +(-4.55842 - 7.89542i) q^{97} +(11.7446 - 5.84096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{2} + 2q^{3} + 4q^{4} - 3q^{5} - 2q^{6} - 4q^{8} - 10q^{9} + O(q^{10}) \) \( 4q - 4q^{2} + 2q^{3} + 4q^{4} - 3q^{5} - 2q^{6} - 4q^{8} - 10q^{9} + 3q^{10} - 3q^{11} + 2q^{12} - 4q^{13} + 15q^{15} + 4q^{16} + 3q^{17} + 10q^{18} - 10q^{19} - 3q^{20} + 3q^{22} + 9q^{23} - 2q^{24} - 11q^{25} + 4q^{26} - 16q^{27} + 6q^{29} - 15q^{30} + 8q^{31} - 4q^{32} + 15q^{33} - 3q^{34} - 10q^{36} - 4q^{37} + 10q^{38} - 2q^{39} + 3q^{40} - 15q^{41} - q^{43} - 3q^{44} + 24q^{45} - 9q^{46} + 2q^{48} + 11q^{50} + 18q^{51} - 4q^{52} + 6q^{53} + 16q^{54} - 24q^{55} - 5q^{57} - 6q^{58} - 6q^{59} + 15q^{60} - 22q^{61} - 8q^{62} + 4q^{64} + 12q^{65} - 15q^{66} + 26q^{67} + 3q^{68} + 21q^{69} + 6q^{71} + 10q^{72} - 7q^{73} + 4q^{74} - 55q^{75} - 10q^{76} + 2q^{78} + 14q^{79} - 3q^{80} + 14q^{81} + 15q^{82} - 12q^{83} - 12q^{85} + q^{86} - 30q^{87} + 3q^{88} - 18q^{89} - 24q^{90} + 9q^{92} + 4q^{93} + 30q^{95} - 2q^{96} - q^{97} + 24q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.500000 1.65831i 0.288675 0.957427i
\(4\) 1.00000 0.500000
\(5\) 0.686141 + 1.18843i 0.306851 + 0.531482i 0.977672 0.210138i \(-0.0673912\pi\)
−0.670820 + 0.741620i \(0.734058\pi\)
\(6\) −0.500000 + 1.65831i −0.204124 + 0.677003i
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −2.50000 1.65831i −0.833333 0.552771i
\(10\) −0.686141 1.18843i −0.216977 0.375815i
\(11\) −2.18614 + 3.78651i −0.659146 + 1.14167i 0.321691 + 0.946845i \(0.395749\pi\)
−0.980837 + 0.194830i \(0.937584\pi\)
\(12\) 0.500000 1.65831i 0.144338 0.478714i
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 0 0
\(15\) 2.31386 0.543620i 0.597436 0.140362i
\(16\) 1.00000 0.250000
\(17\) 2.18614 + 3.78651i 0.530217 + 0.918363i 0.999379 + 0.0352504i \(0.0112229\pi\)
−0.469162 + 0.883112i \(0.655444\pi\)
\(18\) 2.50000 + 1.65831i 0.589256 + 0.390868i
\(19\) −2.50000 + 4.33013i −0.573539 + 0.993399i 0.422659 + 0.906289i \(0.361097\pi\)
−0.996199 + 0.0871106i \(0.972237\pi\)
\(20\) 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 \(0.554280\pi\)
\(24\) −0.500000 + 1.65831i −0.102062 + 0.338502i
\(25\) 1.55842 2.69927i 0.311684 0.539853i
\(26\) 1.00000 1.73205i 0.196116 0.339683i
\(27\) −4.00000 + 3.31662i −0.769800 + 0.638285i
\(28\) 0 0
\(29\) −1.37228 2.37686i −0.254826 0.441372i 0.710022 0.704179i \(-0.248685\pi\)
−0.964848 + 0.262807i \(0.915352\pi\)
\(30\) −2.31386 + 0.543620i −0.422451 + 0.0992510i
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) −1.00000 −0.176777
\(33\) 5.18614 + 5.51856i 0.902791 + 0.960658i
\(34\) −2.18614 3.78651i −0.374920 0.649381i
\(35\) 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 \(0.219235\pi\)
\(38\) 2.50000 4.33013i 0.405554 0.702439i
\(39\) 2.37228 + 2.52434i 0.379869 + 0.404218i
\(40\) −0.686141 1.18843i −0.108488 0.187907i
\(41\) −5.18614 + 8.98266i −0.809939 + 1.40286i 0.102966 + 0.994685i \(0.467167\pi\)
−0.912906 + 0.408171i \(0.866167\pi\)
\(42\) 0 0
\(43\) −4.55842 7.89542i −0.695153 1.20404i −0.970129 0.242589i \(-0.922003\pi\)
0.274976 0.961451i \(-0.411330\pi\)
\(44\) −2.18614 + 3.78651i −0.329573 + 0.570837i
\(45\) 0.255437 4.10891i 0.0380784 0.612520i
\(46\) −3.68614 6.38458i −0.543492 0.941355i
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0.500000 1.65831i 0.0721688 0.239357i
\(49\) 0 0
\(50\) −1.55842 + 2.69927i −0.220394 + 0.381734i
\(51\) 7.37228 1.73205i 1.03233 0.242536i
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) −1.37228 2.37686i −0.188497 0.326487i 0.756252 0.654280i \(-0.227028\pi\)
−0.944749 + 0.327793i \(0.893695\pi\)
\(54\) 4.00000 3.31662i 0.544331 0.451335i
\(55\) −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
\(59\) 7.11684 0.926534 0.463267 0.886219i \(-0.346677\pi\)
0.463267 + 0.886219i \(0.346677\pi\)
\(60\) 2.31386 0.543620i 0.298718 0.0701811i
\(61\) −14.1168 −1.80748 −0.903738 0.428085i \(-0.859188\pi\)
−0.903738 + 0.428085i \(0.859188\pi\)
\(62\) −2.00000 −0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −2.74456 −0.340421
\(66\) −5.18614 5.51856i −0.638370 0.679287i
\(67\) 15.1168 1.84682 0.923408 0.383819i \(-0.125391\pi\)
0.923408 + 0.383819i \(0.125391\pi\)
\(68\) 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 \(0.295038\pi\)
\(72\) 2.50000 + 1.65831i 0.294628 + 0.195434i
\(73\) 2.55842 + 4.43132i 0.299441 + 0.518646i 0.976008 0.217734i \(-0.0698666\pi\)
−0.676567 + 0.736381i \(0.736533\pi\)
\(74\) 1.00000 1.73205i 0.116248 0.201347i
\(75\) −3.69702 3.93398i −0.426895 0.454257i
\(76\) −2.50000 + 4.33013i −0.286770 + 0.496700i
\(77\) 0 0
\(78\) −2.37228 2.52434i −0.268608 0.285825i
\(79\) 12.1168 1.36325 0.681626 0.731701i \(-0.261273\pi\)
0.681626 + 0.731701i \(0.261273\pi\)
\(80\) 0.686141 + 1.18843i 0.0767129 + 0.132871i
\(81\) 3.50000 + 8.29156i 0.388889 + 0.921285i
\(82\) 5.18614 8.98266i 0.572713 0.991969i
\(83\) 2.74456 + 4.75372i 0.301255 + 0.521789i 0.976420 0.215877i \(-0.0692612\pi\)
−0.675166 + 0.737666i \(0.735928\pi\)
\(84\) 0 0
\(85\) −3.00000 + 5.19615i −0.325396 + 0.563602i
\(86\) 4.55842 + 7.89542i 0.491547 + 0.851385i
\(87\) −4.62772 + 1.08724i −0.496144 + 0.116564i
\(88\) 2.18614 3.78651i 0.233043 0.403643i
\(89\) −1.62772 + 2.81929i −0.172538 + 0.298844i −0.939306 0.343079i \(-0.888530\pi\)
0.766769 + 0.641924i \(0.221863\pi\)
\(90\) −0.255437 + 4.10891i −0.0269255 + 0.433117i
\(91\) 0 0
\(92\) 3.68614 + 6.38458i 0.384307 + 0.665639i
\(93\) 1.00000 3.31662i 0.103695 0.343918i
\(94\) 0 0
\(95\) −6.86141 −0.703965
\(96\) −0.500000 + 1.65831i −0.0510310 + 0.169251i
\(97\) −4.55842 7.89542i −0.462838 0.801658i 0.536263 0.844051i \(-0.319835\pi\)
−0.999101 + 0.0423924i \(0.986502\pi\)
\(98\) 0 0
\(99\) 11.7446 5.84096i 1.18037 0.587039i
\(100\) 1.55842 2.69927i 0.155842 0.269927i
\(101\) −3.68614 + 6.38458i −0.366785 + 0.635290i −0.989061 0.147508i \(-0.952875\pi\)
0.622276 + 0.782798i \(0.286208\pi\)
\(102\) −7.37228 + 1.73205i −0.729965 + 0.171499i
\(103\) 5.00000 + 8.66025i 0.492665 + 0.853320i 0.999964 0.00844953i \(-0.00268960\pi\)
−0.507300 + 0.861770i \(0.669356\pi\)
\(104\) 1.00000 1.73205i 0.0980581 0.169842i
\(105\) 0 0
\(106\) 1.37228 + 2.37686i 0.133288 + 0.230861i
\(107\) 0.813859 1.40965i 0.0786788 0.136276i −0.824001 0.566588i \(-0.808263\pi\)
0.902680 + 0.430312i \(0.141597\pi\)
\(108\) −4.00000 + 3.31662i −0.384900 + 0.319142i
\(109\) −7.00000 12.1244i −0.670478 1.16130i −0.977769 0.209687i \(-0.932756\pi\)
0.307290 0.951616i \(-0.400578\pi\)
\(110\) 6.00000 0.572078
\(111\) 2.37228 + 2.52434i 0.225167 + 0.239600i
\(112\) 0 0
\(113\) −0.686141 + 1.18843i −0.0645467 + 0.111798i −0.896493 0.443058i \(-0.853893\pi\)
0.831946 + 0.554856i \(0.187227\pi\)
\(114\) −5.93070 6.31084i −0.555461 0.591065i
\(115\) −5.05842 + 8.76144i −0.471700 + 0.817009i
\(116\) −1.37228 2.37686i −0.127413 0.220686i
\(117\) 5.37228 2.67181i 0.496668 0.247009i
\(118\) −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
\(122\) 14.1168 1.27808
\(123\) 12.3030 + 13.0916i 1.10932 + 1.18043i
\(124\) 2.00000 0.179605
\(125\) 11.1386 0.996266
\(126\) 0 0
\(127\) −14.1168 −1.25267 −0.626334 0.779555i \(-0.715445\pi\)
−0.626334 + 0.779555i \(0.715445\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −15.3723 + 3.61158i −1.35345 + 0.317982i
\(130\) 2.74456 0.240714
\(131\) 3.68614 + 6.38458i 0.322060 + 0.557824i 0.980913 0.194448i \(-0.0622915\pi\)
−0.658853 + 0.752271i \(0.728958\pi\)
\(132\) 5.18614 + 5.51856i 0.451396 + 0.480329i
\(133\) 0 0
\(134\) −15.1168 −1.30590
\(135\) −6.68614 2.47805i −0.575451 0.213277i
\(136\) −2.18614 3.78651i −0.187460 0.324690i
\(137\) −8.18614 + 14.1788i −0.699389 + 1.21138i 0.269289 + 0.963059i \(0.413211\pi\)
−0.968678 + 0.248318i \(0.920122\pi\)
\(138\) −12.4307 + 2.92048i −1.05817 + 0.248608i
\(139\) 10.6168 18.3889i 0.900509 1.55973i 0.0736742 0.997282i \(-0.476528\pi\)
0.826835 0.562445i \(-0.190139\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −10.1168 −0.848987
\(143\) −4.37228 7.57301i −0.365629 0.633287i
\(144\) −2.50000 1.65831i −0.208333 0.138193i
\(145\) 1.88316 3.26172i 0.156388 0.270871i
\(146\) −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 \(-0.373078\pi\)
\(150\) 3.69702 + 3.93398i 0.301860 + 0.321208i
\(151\) 4.05842 7.02939i 0.330270 0.572044i −0.652295 0.757965i \(-0.726194\pi\)
0.982565 + 0.185921i \(0.0595270\pi\)
\(152\) 2.50000 4.33013i 0.202777 0.351220i
\(153\) 0.813859 13.0916i 0.0657966 1.05839i
\(154\) 0 0
\(155\) 1.37228 + 2.37686i 0.110224 + 0.190914i
\(156\) 2.37228 + 2.52434i 0.189935 + 0.202109i
\(157\) −8.11684 −0.647795 −0.323897 0.946092i \(-0.604993\pi\)
−0.323897 + 0.946092i \(0.604993\pi\)
\(158\) −12.1168 −0.963964
\(159\) −4.62772 + 1.08724i −0.367002 + 0.0862238i
\(160\) −0.686141 1.18843i −0.0542442 0.0939537i
\(161\) 0 0
\(162\) −3.50000 8.29156i −0.274986 0.651447i
\(163\) −8.11684 + 14.0588i −0.635760 + 1.10117i 0.350593 + 0.936528i \(0.385980\pi\)
−0.986354 + 0.164641i \(0.947353\pi\)
\(164\) −5.18614 + 8.98266i −0.404970 + 0.701428i
\(165\) −3.00000 + 9.94987i −0.233550 + 0.774597i
\(166\) −2.74456 4.75372i −0.213019 0.368960i
\(167\) −8.74456 + 15.1460i −0.676675 + 1.17203i 0.299302 + 0.954158i \(0.403246\pi\)
−0.975976 + 0.217876i \(0.930087\pi\)
\(168\) 0 0
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) 3.00000 5.19615i 0.230089 0.398527i
\(171\) 13.4307 6.67954i 1.02707 0.510797i
\(172\) −4.55842 7.89542i −0.347576 0.602020i
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 4.62772 1.08724i 0.350826 0.0824235i
\(175\) 0 0
\(176\) −2.18614 + 3.78651i −0.164787 + 0.285419i
\(177\) 3.55842 11.8020i 0.267467 0.887089i
\(178\) 1.62772 2.81929i 0.122003 0.211315i
\(179\) −7.37228 12.7692i −0.551030 0.954412i −0.998201 0.0599635i \(-0.980902\pi\)
0.447170 0.894449i \(-0.352432\pi\)
\(180\) 0.255437 4.10891i 0.0190392 0.306260i
\(181\) 18.1168 1.34661 0.673307 0.739363i \(-0.264873\pi\)
0.673307 + 0.739363i \(0.264873\pi\)
\(182\) 0 0
\(183\) −7.05842 + 23.4101i −0.521774 + 1.73053i
\(184\) −3.68614 6.38458i −0.271746 0.470678i
\(185\) −2.74456 −0.201784
\(186\) −1.00000 + 3.31662i −0.0733236 + 0.243187i
\(187\) −19.1168 −1.39796
\(188\) 0 0
\(189\) 0 0
\(190\) 6.86141 0.497779
\(191\) −1.88316 −0.136260 −0.0681302 0.997676i \(-0.521703\pi\)
−0.0681302 + 0.997676i \(0.521703\pi\)
\(192\) 0.500000 1.65831i 0.0360844 0.119678i
\(193\) −7.00000 −0.503871 −0.251936 0.967744i \(-0.581067\pi\)
−0.251936 + 0.967744i \(0.581067\pi\)
\(194\) 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 \(0.568565\pi\)
\(198\) −11.7446 + 5.84096i −0.834650 + 0.415099i
\(199\) 5.00000 + 8.66025i 0.354441 + 0.613909i 0.987022 0.160585i \(-0.0513380\pi\)
−0.632581 + 0.774494i \(0.718005\pi\)
\(200\) −1.55842 + 2.69927i −0.110197 + 0.190867i
\(201\) 7.55842 25.0684i 0.533130 1.76819i
\(202\) 3.68614 6.38458i 0.259356 0.449218i
\(203\) 0 0
\(204\) 7.37228 1.73205i 0.516163 0.121268i
\(205\) −14.2337 −0.994124
\(206\) −5.00000 8.66025i −0.348367 0.603388i
\(207\) 1.37228 22.0742i 0.0953801 1.53427i
\(208\) −1.00000 + 1.73205i −0.0693375 + 0.120096i
\(209\) −10.9307 18.9325i −0.756093 1.30959i
\(210\) 0 0
\(211\) 8.00000 13.8564i 0.550743 0.953914i −0.447478 0.894295i \(-0.647678\pi\)
0.998221 0.0596196i \(-0.0189888\pi\)
\(212\) −1.37228 2.37686i −0.0942487 0.163243i
\(213\) 5.05842 16.7769i 0.346597 1.14953i
\(214\) −0.813859 + 1.40965i −0.0556343 + 0.0963614i
\(215\) 6.25544 10.8347i 0.426617 0.738923i
\(216\) 4.00000 3.31662i 0.272166 0.225668i
\(217\) 0 0
\(218\) 7.00000 + 12.1244i 0.474100 + 0.821165i
\(219\) 8.62772 2.02700i 0.583007 0.136972i
\(220\) −6.00000 −0.404520
\(221\) −8.74456 −0.588223
\(222\) −2.37228 2.52434i −0.159217 0.169422i
\(223\) 2.00000 + 3.46410i 0.133930 + 0.231973i 0.925188 0.379509i \(-0.123907\pi\)
−0.791258 + 0.611482i \(0.790574\pi\)
\(224\) 0 0
\(225\) −8.37228 + 4.16381i −0.558152 + 0.277588i
\(226\) 0.686141 1.18843i 0.0456414 0.0790532i
\(227\) 11.8723 20.5634i 0.787991 1.36484i −0.139205 0.990264i \(-0.544455\pi\)
0.927196 0.374577i \(-0.122212\pi\)
\(228\) 5.93070 + 6.31084i 0.392770 + 0.417946i
\(229\) 10.0584 + 17.4217i 0.664679 + 1.15126i 0.979372 + 0.202065i \(0.0647651\pi\)
−0.314693 + 0.949194i \(0.601902\pi\)
\(230\) 5.05842 8.76144i 0.333542 0.577713i
\(231\) 0 0
\(232\) 1.37228 + 2.37686i 0.0900947 + 0.156049i
\(233\) 5.87228 10.1711i 0.384706 0.666330i −0.607022 0.794685i \(-0.707636\pi\)
0.991728 + 0.128354i \(0.0409695\pi\)
\(234\) −5.37228 + 2.67181i −0.351197 + 0.174662i
\(235\) 0 0
\(236\) 7.11684 0.463267
\(237\) 6.05842 20.0935i 0.393537 1.30521i
\(238\) 0 0
\(239\) 9.43070 16.3345i 0.610021 1.05659i −0.381215 0.924487i \(-0.624494\pi\)
0.991236 0.132102i \(-0.0421725\pi\)
\(240\) 2.31386 0.543620i 0.149359 0.0350905i
\(241\) −0.441578 + 0.764836i −0.0284445 + 0.0492674i −0.879897 0.475164i \(-0.842389\pi\)
0.851453 + 0.524431i \(0.175722\pi\)
\(242\) 4.05842 + 7.02939i 0.260885 + 0.451867i
\(243\) 15.5000 1.65831i 0.994325 0.106381i
\(244\) −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
\(248\) −2.00000 −0.127000
\(249\) 9.25544 2.17448i 0.586540 0.137802i
\(250\) −11.1386 −0.704467
\(251\) −9.00000 −0.568075 −0.284037 0.958813i \(-0.591674\pi\)
−0.284037 + 0.958813i \(0.591674\pi\)
\(252\) 0 0
\(253\) −32.2337 −2.02651
\(254\) 14.1168 0.885770
\(255\) 7.11684 + 7.57301i 0.445674 + 0.474240i
\(256\) 1.00000 0.0625000
\(257\) −10.9307 18.9325i −0.681839 1.18098i −0.974419 0.224738i \(-0.927847\pi\)
0.292581 0.956241i \(-0.405486\pi\)
\(258\) 15.3723 3.61158i 0.957036 0.224847i
\(259\) 0 0
\(260\) −2.74456 −0.170211
\(261\) −0.510875 + 8.21782i −0.0316224 + 0.508671i
\(262\) −3.68614 6.38458i −0.227731 0.394441i
\(263\) −6.68614 + 11.5807i −0.412285 + 0.714099i −0.995139 0.0984781i \(-0.968603\pi\)
0.582854 + 0.812577i \(0.301936\pi\)
\(264\) −5.18614 5.51856i −0.319185 0.339644i
\(265\) 1.88316 3.26172i 0.115681 0.200366i
\(266\) 0 0
\(267\) 3.86141 + 4.10891i 0.236314 + 0.251461i
\(268\) 15.1168 0.923408
\(269\) 3.68614 + 6.38458i 0.224748 + 0.389275i 0.956244 0.292571i \(-0.0945108\pi\)
−0.731496 + 0.681846i \(0.761177\pi\)
\(270\) 6.68614 + 2.47805i 0.406906 + 0.150809i
\(271\) 9.11684 15.7908i 0.553809 0.959225i −0.444186 0.895934i \(-0.646507\pi\)
0.997995 0.0632906i \(-0.0201595\pi\)
\(272\) 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
\(276\) 12.4307 2.92048i 0.748240 0.175792i
\(277\) −11.1168 + 19.2549i −0.667946 + 1.15692i 0.310531 + 0.950563i \(0.399493\pi\)
−0.978477 + 0.206354i \(0.933840\pi\)
\(278\) −10.6168 + 18.3889i −0.636756 + 1.10289i
\(279\) −5.00000 3.31662i −0.299342 0.198561i
\(280\) 0 0
\(281\) −5.31386 9.20387i −0.316998 0.549057i 0.662862 0.748742i \(-0.269342\pi\)
−0.979860 + 0.199685i \(0.936008\pi\)
\(282\) 0 0
\(283\) 9.88316 0.587493 0.293746 0.955883i \(-0.405098\pi\)
0.293746 + 0.955883i \(0.405098\pi\)
\(284\) 10.1168 0.600324
\(285\) −3.43070 + 11.3784i −0.203217 + 0.673996i
\(286\) 4.37228 + 7.57301i 0.258538 + 0.447802i
\(287\) 0 0
\(288\) 2.50000 + 1.65831i 0.147314 + 0.0977170i
\(289\) −1.05842 + 1.83324i −0.0622601 + 0.107838i
\(290\) −1.88316 + 3.26172i −0.110583 + 0.191535i
\(291\) −15.3723 + 3.61158i −0.901139 + 0.211714i
\(292\) 2.55842 + 4.43132i 0.149720 + 0.259323i
\(293\) 2.31386 4.00772i 0.135177 0.234134i −0.790488 0.612478i \(-0.790173\pi\)
0.925665 + 0.378344i \(0.123506\pi\)
\(294\) 0 0
\(295\) 4.88316 + 8.45787i 0.284308 + 0.492436i
\(296\) 1.00000 1.73205i 0.0581238 0.100673i
\(297\) −3.81386 22.3966i −0.221303 1.29958i
\(298\) 7.37228 + 12.7692i 0.427065 + 0.739698i
\(299\) −14.7446 −0.852700
\(300\) −3.69702 3.93398i −0.213447 0.227129i
\(301\) 0 0
\(302\) −4.05842 + 7.02939i −0.233536 + 0.404496i
\(303\) 8.74456 + 9.30506i 0.502362 + 0.534562i
\(304\) −2.50000 + 4.33013i −0.143385 + 0.248350i
\(305\) −9.68614 16.7769i −0.554627 0.960642i
\(306\) −0.813859 + 13.0916i −0.0465252 + 0.748395i
\(307\) −13.0000 −0.741949 −0.370975 0.928643i \(-0.620976\pi\)
−0.370975 + 0.928643i \(0.620976\pi\)
\(308\) 0 0
\(309\) 16.8614 3.96143i 0.959212 0.225358i
\(310\) −1.37228 2.37686i −0.0779403 0.134997i
\(311\) −26.2337 −1.48758 −0.743788 0.668416i \(-0.766973\pi\)
−0.743788 + 0.668416i \(0.766973\pi\)
\(312\) −2.37228 2.52434i −0.134304 0.142912i
\(313\) −2.88316 −0.162966 −0.0814828 0.996675i \(-0.525966\pi\)
−0.0814828 + 0.996675i \(0.525966\pi\)
\(314\) 8.11684 0.458060
\(315\) 0 0
\(316\) 12.1168 0.681626
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) 4.62772 1.08724i 0.259510 0.0609694i
\(319\) 12.0000 0.671871
\(320\) 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
\(324\) 3.50000 + 8.29156i 0.194444 + 0.460642i
\(325\) 3.11684 + 5.39853i 0.172891 + 0.299457i
\(326\) 8.11684 14.0588i 0.449550 0.778644i
\(327\) −23.6060 + 5.54601i −1.30541 + 0.306695i
\(328\) 5.18614 8.98266i 0.286357 0.495984i
\(329\) 0 0
\(330\) 3.00000 9.94987i 0.165145 0.547723i
\(331\) −12.2337 −0.672424 −0.336212 0.941786i \(-0.609146\pi\)
−0.336212 + 0.941786i \(0.609146\pi\)
\(332\) 2.74456 + 4.75372i 0.150627 + 0.260894i
\(333\) 5.37228 2.67181i 0.294399 0.146415i
\(334\) 8.74456 15.1460i 0.478481 0.828754i
\(335\) 10.3723 + 17.9653i 0.566698 + 0.981550i
\(336\) 0 0
\(337\) −4.55842 + 7.89542i −0.248313 + 0.430091i −0.963058 0.269294i \(-0.913210\pi\)
0.714745 + 0.699385i \(0.246543\pi\)
\(338\) −4.50000 7.79423i −0.244768 0.423950i
\(339\) 1.62772 + 1.73205i 0.0884055 + 0.0940721i
\(340\) −3.00000 + 5.19615i −0.162698 + 0.281801i
\(341\) −4.37228 + 7.57301i −0.236772 + 0.410102i
\(342\) −13.4307 + 6.67954i −0.726249 + 0.361188i
\(343\) 0 0
\(344\) 4.55842 + 7.89542i 0.245774 + 0.425692i
\(345\) 12.0000 + 12.7692i 0.646058 + 0.687469i
\(346\) 6.00000 0.322562
\(347\) 7.11684 0.382052 0.191026 0.981585i \(-0.438818\pi\)
0.191026 + 0.981585i \(0.438818\pi\)
\(348\) −4.62772 + 1.08724i −0.248072 + 0.0582822i
\(349\) 11.0000 + 19.0526i 0.588817 + 1.01986i 0.994388 + 0.105797i \(0.0337393\pi\)
−0.405571 + 0.914063i \(0.632927\pi\)
\(350\) 0 0
\(351\) −1.74456 10.2448i −0.0931179 0.546828i
\(352\) 2.18614 3.78651i 0.116522 0.201821i
\(353\) 3.81386 6.60580i 0.202991 0.351591i −0.746500 0.665386i \(-0.768267\pi\)
0.949491 + 0.313795i \(0.101600\pi\)
\(354\) −3.55842 + 11.8020i −0.189128 + 0.627267i
\(355\) 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
\(359\) 3.43070 5.94215i 0.181066 0.313615i −0.761178 0.648543i \(-0.775379\pi\)
0.942244 + 0.334928i \(0.108712\pi\)
\(360\) −0.255437 + 4.10891i −0.0134627 + 0.216559i
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) −18.1168 −0.952200
\(363\) −13.6861 + 3.21543i −0.718336 + 0.168767i
\(364\) 0 0
\(365\) −3.51087 + 6.08101i −0.183768 + 0.318295i
\(366\) 7.05842 23.4101i 0.368950 1.22367i
\(367\) −11.1168 + 19.2549i −0.580295 + 1.00510i 0.415150 + 0.909753i \(0.363729\pi\)
−0.995444 + 0.0953465i \(0.969604\pi\)
\(368\) 3.68614 + 6.38458i 0.192153 + 0.332819i
\(369\) 27.8614 13.8564i 1.45041 0.721336i
\(370\) 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 \(0.749977\pi\)
\(374\) 19.1168 0.988508
\(375\) 5.56930 18.4713i 0.287597 0.953852i
\(376\) 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 \(0.424769\pi\)
\(380\) −6.86141 −0.351983
\(381\) −7.05842 + 23.4101i −0.361614 + 1.19934i
\(382\) 1.88316 0.0963506
\(383\) 10.6277 + 18.4077i 0.543051 + 0.940592i 0.998727 + 0.0504462i \(0.0160643\pi\)
−0.455676 + 0.890146i \(0.650602\pi\)
\(384\) −0.500000 + 1.65831i −0.0255155 + 0.0846254i
\(385\) 0 0
\(386\) 7.00000 0.356291
\(387\) −1.69702 + 27.2978i −0.0862641 + 1.38763i
\(388\) −4.55842 7.89542i −0.231419 0.400829i
\(389\) 17.4891 30.2921i 0.886734 1.53587i 0.0430204 0.999074i \(-0.486302\pi\)
0.843713 0.536794i \(-0.180365\pi\)
\(390\) 1.37228 4.55134i 0.0694882 0.230466i
\(391\) −16.1168 + 27.9152i −0.815064 + 1.41173i
\(392\) 0 0
\(393\) 12.4307 2.92048i 0.627046 0.147319i
\(394\) 6.00000 0.302276
\(395\) 8.31386 + 14.4000i 0.418316 + 0.724544i
\(396\) 11.7446 5.84096i 0.590186 0.293519i
\(397\) 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
\(400\) 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 \(0.831303\pi\)
\(402\) −7.55842 + 25.0684i −0.376980 + 1.25030i
\(403\) −2.00000 + 3.46410i −0.0996271 + 0.172559i
\(404\) −3.68614 + 6.38458i −0.183392 + 0.317645i
\(405\) −7.45245 + 9.84868i −0.370315 + 0.489385i
\(406\) 0 0
\(407\) −4.37228 7.57301i −0.216726 0.375380i
\(408\) −7.37228 + 1.73205i −0.364982 + 0.0857493i
\(409\) 29.3505 1.45129 0.725645 0.688069i \(-0.241541\pi\)
0.725645 + 0.688069i \(0.241541\pi\)
\(410\) 14.2337 0.702952
\(411\) 19.4198 + 20.6646i 0.957910 + 1.01931i
\(412\) 5.00000 + 8.66025i 0.246332 + 0.426660i
\(413\) 0 0
\(414\) −1.37228 + 22.0742i −0.0674439 + 1.08489i
\(415\) −3.76631 + 6.52344i −0.184881 + 0.320223i
\(416\) 1.00000 1.73205i 0.0490290 0.0849208i
\(417\) −25.1861 26.8005i −1.23337 1.31243i
\(418\) 10.9307 + 18.9325i 0.534638 + 0.926020i
\(419\) −13.8030 + 23.9075i −0.674320 + 1.16796i 0.302347 + 0.953198i \(0.402230\pi\)
−0.976667 + 0.214759i \(0.931104\pi\)
\(420\) 0 0
\(421\) 0.116844 + 0.202380i 0.00569463 + 0.00986338i 0.868859 0.495060i \(-0.164854\pi\)
−0.863164 + 0.504924i \(0.831521\pi\)
\(422\) −8.00000 + 13.8564i −0.389434 + 0.674519i
\(423\) 0 0
\(424\) 1.37228 + 2.37686i 0.0666439 + 0.115431i
\(425\) 13.6277 0.661041
\(426\) −5.05842 + 16.7769i −0.245081 + 0.812843i
\(427\) 0 0
\(428\) 0.813859 1.40965i 0.0393394 0.0681378i
\(429\) −14.7446 + 3.46410i −0.711874 + 0.167248i
\(430\) −6.25544 + 10.8347i −0.301664 + 0.522497i
\(431\) 14.7446 + 25.5383i 0.710221 + 1.23014i 0.964774 + 0.263079i \(0.0847381\pi\)
−0.254554 + 0.967059i \(0.581929\pi\)
\(432\) −4.00000 + 3.31662i −0.192450 + 0.159571i
\(433\) −2.88316 −0.138556 −0.0692778 0.997597i \(-0.522069\pi\)
−0.0692778 + 0.997597i \(0.522069\pi\)
\(434\) 0 0
\(435\) −4.46738 4.75372i −0.214194 0.227924i
\(436\) −7.00000 12.1244i −0.335239 0.580651i
\(437\) −36.8614 −1.76332
\(438\) −8.62772 + 2.02700i −0.412248 + 0.0968540i
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 6.00000 0.286039
\(441\) 0 0
\(442\) 8.74456 0.415936
\(443\) −22.8832 −1.08721 −0.543606 0.839341i \(-0.682941\pi\)
−0.543606 + 0.839341i \(0.682941\pi\)
\(444\) 2.37228 + 2.52434i 0.112583 + 0.119800i
\(445\) −4.46738 −0.211774
\(446\) −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 \(0.215888\pi\)
\(450\) 8.37228 4.16381i 0.394673 0.196284i
\(451\) −22.6753 39.2747i −1.06774 1.84937i
\(452\) −0.686141 + 1.18843i −0.0322733 + 0.0558991i
\(453\) −9.62772 10.2448i −0.452350 0.481344i
\(454\) −11.8723 + 20.5634i −0.557194 + 0.965088i
\(455\) 0 0
\(456\) −5.93070 6.31084i −0.277731 0.295532i
\(457\) 33.4674 1.56554 0.782769 0.622312i \(-0.213807\pi\)
0.782769 + 0.622312i \(0.213807\pi\)
\(458\) −10.0584 17.4217i −0.469999 0.814062i
\(459\) −21.3030 7.89542i −0.994338 0.368527i
\(460\) −5.05842 + 8.76144i −0.235850 + 0.408504i
\(461\) −15.4307 26.7268i −0.718680 1.24479i −0.961523 0.274724i \(-0.911414\pi\)
0.242844 0.970065i \(-0.421920\pi\)
\(462\) 0 0
\(463\) 2.94158 5.09496i 0.136707 0.236783i −0.789541 0.613697i \(-0.789682\pi\)
0.926248 + 0.376914i \(0.123015\pi\)
\(464\) −1.37228 2.37686i −0.0637066 0.110343i
\(465\) 4.62772 1.08724i 0.214605 0.0504196i
\(466\) −5.87228 + 10.1711i −0.272028 + 0.471167i
\(467\) 15.0475 26.0631i 0.696317 1.20606i −0.273417 0.961896i \(-0.588154\pi\)
0.969735 0.244162i \(-0.0785127\pi\)
\(468\) 5.37228 2.67181i 0.248334 0.123505i
\(469\) 0 0
\(470\) 0 0
\(471\) −4.05842 + 13.4603i −0.187002 + 0.620216i
\(472\) −7.11684 −0.327579
\(473\) 39.8614 1.83283
\(474\) −6.05842 + 20.0935i −0.278273 + 0.922926i
\(475\) 7.79211 + 13.4963i 0.357527 + 0.619254i
\(476\) 0 0
\(477\) −0.510875 + 8.21782i −0.0233913 + 0.376268i
\(478\) −9.43070 + 16.3345i −0.431350 + 0.747121i
\(479\) −10.6277 + 18.4077i −0.485593 + 0.841072i −0.999863 0.0165568i \(-0.994730\pi\)
0.514270 + 0.857628i \(0.328063\pi\)
\(480\) −2.31386 + 0.543620i −0.105613 + 0.0248128i
\(481\) −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
\(485\) 6.25544 10.8347i 0.284045 0.491980i
\(486\) −15.5000 + 1.65831i −0.703094 + 0.0752226i
\(487\) 8.17527 + 14.1600i 0.370457 + 0.641650i 0.989636 0.143600i \(-0.0458679\pi\)
−0.619179 + 0.785250i \(0.712535\pi\)
\(488\) 14.1168 0.639040
\(489\) 19.2554 + 20.4897i 0.870761 + 0.926574i
\(490\) 0 0
\(491\) 9.81386 16.9981i 0.442893 0.767114i −0.555010 0.831844i \(-0.687285\pi\)
0.997903 + 0.0647303i \(0.0206187\pi\)
\(492\) 12.3030 + 13.0916i 0.554661 + 0.590214i
\(493\) 6.00000 10.3923i 0.270226 0.468046i
\(494\) 5.00000 + 8.66025i 0.224961 + 0.389643i
\(495\) 15.0000 + 9.94987i 0.674200 + 0.447214i
\(496\) 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 \(0.839626\pi\)
\(500\) 11.1386 0.498133
\(501\) 20.7446 + 22.0742i 0.926799 + 0.986204i
\(502\) 9.00000 0.401690
\(503\) 2.23369 0.0995952 0.0497976 0.998759i \(-0.484142\pi\)
0.0497976 + 0.998759i \(0.484142\pi\)
\(504\) 0 0
\(505\) −10.1168 −0.450194
\(506\) 32.2337 1.43296
\(507\) 15.1753 3.56529i 0.673957 0.158340i
\(508\) −14.1168 −0.626334
\(509\) −8.48913 14.7036i −0.376274 0.651725i 0.614243 0.789117i \(-0.289461\pi\)
−0.990517 + 0.137392i \(0.956128\pi\)
\(510\) −7.11684 7.57301i −0.315139 0.335339i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −4.36141 25.6121i −0.192561 1.13080i
\(514\) 10.9307 + 18.9325i 0.482133 + 0.835078i
\(515\) −6.86141 + 11.8843i −0.302350 + 0.523685i
\(516\) −15.3723 + 3.61158i −0.676727 + 0.158991i
\(517\) 0 0
\(518\) 0 0
\(519\) −3.00000 + 9.94987i −0.131685 + 0.436751i
\(520\) 2.74456 0.120357
\(521\) −1.93070 3.34408i −0.0845856 0.146507i 0.820629 0.571461i \(-0.193623\pi\)
−0.905215 + 0.424955i \(0.860290\pi\)
\(522\) 0.510875 8.21782i 0.0223604 0.359684i
\(523\) 8.94158 15.4873i 0.390988 0.677211i −0.601592 0.798803i \(-0.705467\pi\)
0.992580 + 0.121592i \(0.0388001\pi\)
\(524\) 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
\(528\) 5.18614 + 5.51856i 0.225698 + 0.240164i
\(529\) −15.6753 + 27.1504i −0.681533 + 1.18045i
\(530\) −1.88316 + 3.26172i −0.0817991 + 0.141680i
\(531\) −17.7921 11.8020i −0.772112 0.512161i
\(532\) 0 0
\(533\) −10.3723 17.9653i −0.449273 0.778164i
\(534\) −3.86141 4.10891i −0.167099 0.177810i
\(535\) 2.23369 0.0965708
\(536\) −15.1168 −0.652948
\(537\) −24.8614 + 5.84096i −1.07285 + 0.252056i
\(538\) −3.68614 6.38458i −0.158921 0.275259i
\(539\) 0 0
\(540\) −6.68614 2.47805i −0.287726 0.106638i
\(541\) −14.1168 + 24.4511i −0.606931 + 1.05123i 0.384813 + 0.922995i \(0.374266\pi\)
−0.991743 + 0.128240i \(0.959067\pi\)
\(542\) −9.11684 + 15.7908i −0.391602 + 0.678275i
\(543\) 9.05842 30.0434i 0.388734 1.28929i
\(544\) −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 0.856431 0.516262i \(-0.172677\pi\)
−0.875311 + 0.483560i \(0.839344\pi\)
\(548\) −8.18614 + 14.1788i −0.349695 + 0.605689i
\(549\) 35.2921 + 23.4101i 1.50623 + 0.999120i
\(550\) −6.81386 11.8020i −0.290544 0.503237i
\(551\) 13.7228 0.584611
\(552\) −12.4307 + 2.92048i −0.529086 + 0.124304i
\(553\) 0 0
\(554\) 11.1168 19.2549i 0.472309 0.818064i
\(555\) −1.37228 + 4.55134i −0.0582501 + 0.193194i
\(556\) 10.6168 18.3889i 0.450254 0.779864i
\(557\) −3.25544 5.63858i −0.137937 0.238914i 0.788778 0.614678i \(-0.210714\pi\)
−0.926716 + 0.375763i \(0.877381\pi\)
\(558\) 5.00000 + 3.31662i 0.211667 + 0.140404i
\(559\) 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
\(563\) 3.00000 0.126435 0.0632175 0.998000i \(-0.479864\pi\)
0.0632175 + 0.998000i \(0.479864\pi\)
\(564\) 0 0
\(565\) −1.88316 −0.0792250
\(566\) −9.88316 −0.415420
\(567\) 0 0
\(568\) −10.1168 −0.424493
\(569\) −1.11684 −0.0468205 −0.0234103 0.999726i \(-0.507452\pi\)
−0.0234103 + 0.999726i \(0.507452\pi\)
\(570\) 3.43070 11.3784i 0.143696 0.476587i
\(571\) 29.3505 1.22828 0.614141 0.789197i \(-0.289503\pi\)
0.614141 + 0.789197i \(0.289503\pi\)
\(572\) −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
\(576\) −2.50000 1.65831i −0.104167 0.0690963i
\(577\) −13.5584 23.4839i −0.564444 0.977647i −0.997101 0.0760878i \(-0.975757\pi\)
0.432657 0.901559i \(-0.357576\pi\)
\(578\) 1.05842 1.83324i 0.0440246 0.0762528i
\(579\) −3.50000 + 11.6082i −0.145455 + 0.482420i
\(580\) 1.88316 3.26172i 0.0781938 0.135436i
\(581\) 0 0
\(582\) 15.3723 3.61158i 0.637202 0.149705i
\(583\) 12.0000 0.496989
\(584\) −2.55842 4.43132i −0.105868 0.183369i
\(585\) 6.86141 + 4.55134i 0.283684 + 0.188175i
\(586\) −2.31386 + 4.00772i −0.0955846 + 0.165557i
\(587\) 4.24456 + 7.35180i 0.175192 + 0.303441i 0.940228 0.340547i \(-0.110612\pi\)
−0.765036 + 0.643988i \(0.777279\pi\)
\(588\) 0 0
\(589\) −5.00000 + 8.66025i −0.206021 + 0.356840i
\(590\) −4.88316 8.45787i −0.201036 0.348205i
\(591\) −3.00000 + 9.94987i −0.123404 + 0.409283i
\(592\) −1.00000 + 1.73205i −0.0410997 + 0.0711868i
\(593\) −1.62772 + 2.81929i −0.0668424 + 0.115774i −0.897510 0.440995i \(-0.854626\pi\)
0.830667 + 0.556769i \(0.187959\pi\)
\(594\) 3.81386 + 22.3966i 0.156485 + 0.918945i
\(595\) 0 0
\(596\) −7.37228 12.7692i −0.301980 0.523045i
\(597\) 16.8614 3.96143i 0.690091 0.162131i
\(598\) 14.7446 0.602950
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 3.69702 + 3.93398i 0.150930 + 0.160604i
\(601\) −3.44158 5.96099i −0.140385 0.243154i 0.787257 0.616625i \(-0.211501\pi\)
−0.927642 + 0.373472i \(0.878167\pi\)
\(602\) 0 0
\(603\) −37.7921 25.0684i −1.53901 1.02087i
\(604\) 4.05842 7.02939i 0.165135 0.286022i
\(605\) 5.56930 9.64630i 0.226424 0.392178i
\(606\) −8.74456 9.30506i −0.355224 0.377992i
\(607\) 6.11684 + 10.5947i 0.248275 + 0.430025i 0.963047 0.269332i \(-0.0868030\pi\)
−0.714772 + 0.699357i \(0.753470\pi\)
\(608\) 2.50000 4.33013i 0.101388 0.175610i
\(609\) 0 0
\(610\) 9.68614 + 16.7769i 0.392180 + 0.679276i
\(611\) 0 0
\(612\) 0.813859 13.0916i 0.0328983 0.529195i
\(613\) 0.883156 + 1.52967i 0.0356703 + 0.0617828i 0.883309 0.468790i \(-0.155310\pi\)
−0.847639 + 0.530573i \(0.821977\pi\)
\(614\) 13.0000 0.524637
\(615\) −7.11684 + 23.6039i −0.286979 + 0.951801i
\(616\) 0 0
\(617\) 4.93070 8.54023i 0.198503 0.343817i −0.749540 0.661959i \(-0.769725\pi\)
0.948043 + 0.318142i \(0.103059\pi\)
\(618\) −16.8614 + 3.96143i −0.678265 + 0.159352i
\(619\) 11.7337 20.3233i 0.471617 0.816864i −0.527856 0.849334i \(-0.677004\pi\)
0.999473 + 0.0324697i \(0.0103373\pi\)
\(620\) 1.37228 + 2.37686i 0.0551121 + 0.0954570i
\(621\) −35.9198 13.3128i −1.44141 0.534224i
\(622\) 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
\(626\) 2.88316 0.115234
\(627\) −36.8614 + 8.66025i −1.47210 + 0.345857i
\(628\) −8.11684 −0.323897
\(629\) −8.74456 −0.348669
\(630\) 0 0
\(631\) 14.3505 0.571286 0.285643 0.958336i \(-0.407793\pi\)
0.285643 + 0.958336i \(0.407793\pi\)
\(632\) −12.1168 −0.481982
\(633\) −18.9783 20.1947i −0.754318 0.802667i
\(634\) 6.00000 0.238290
\(635\) −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
\(639\) −25.2921 16.7769i −1.00054 0.663683i
\(640\) −0.686141 1.18843i −0.0271221 0.0469768i
\(641\) 23.1060 40.0207i 0.912631 1.58072i 0.102298 0.994754i \(-0.467381\pi\)
0.810333 0.585969i \(-0.199286\pi\)
\(642\) 1.93070 + 2.05446i 0.0761988 + 0.0810829i
\(643\) 12.6753 21.9542i 0.499864 0.865789i −0.500136 0.865947i \(-0.666717\pi\)
1.00000 0.000157386i \(5.00974e-5\pi\)
\(644\) 0 0
\(645\) −14.8397 15.7908i −0.584311 0.621764i
\(646\) 21.8614 0.860126
\(647\) 8.74456 + 15.1460i 0.343784 + 0.595452i 0.985132 0.171798i \(-0.0549578\pi\)
−0.641348 + 0.767250i \(0.721624\pi\)
\(648\) −3.50000 8.29156i −0.137493 0.325723i
\(649\) −15.5584 + 26.9480i −0.610721 + 1.05780i
\(650\) −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 \(0.736848\pi\)
\(654\) 23.6060 5.54601i 0.923066 0.216866i
\(655\) −5.05842 + 8.76144i −0.197649 + 0.342338i
\(656\) −5.18614 + 8.98266i −0.202485 + 0.350714i
\(657\) 0.952453 15.3210i 0.0371587 0.597727i
\(658\) 0 0
\(659\) 4.62772 + 8.01544i 0.180270 + 0.312237i 0.941973 0.335690i \(-0.108969\pi\)
−0.761702 + 0.647927i \(0.775636\pi\)
\(660\) −3.00000 + 9.94987i −0.116775 + 0.387298i
\(661\) 9.88316 0.384410 0.192205 0.981355i \(-0.438436\pi\)
0.192205 + 0.981355i \(0.438436\pi\)
\(662\) 12.2337 0.475476
\(663\) −4.37228 + 14.5012i −0.169805 + 0.563181i
\(664\) −2.74456 4.75372i −0.106510 0.184480i
\(665\) 0 0
\(666\) −5.37228 + 2.67181i −0.208172 + 0.103531i
\(667\) 10.1168 17.5229i 0.391726 0.678489i
\(668\) −8.74456 + 15.1460i −0.338337 + 0.586017i
\(669\) 6.74456 1.58457i 0.260760 0.0612632i
\(670\) −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 0.992143 0.125109i \(-0.0399281\pi\)
−0.604419 + 0.796666i \(0.706595\pi\)
\(674\) 4.55842 7.89542i 0.175584 0.304120i
\(675\) 2.71876 + 15.9658i 0.104645 + 0.614523i
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) −34.4674 −1.32469 −0.662344 0.749199i \(-0.730438\pi\)
−0.662344 + 0.749199i \(0.730438\pi\)
\(678\) −1.62772 1.73205i −0.0625122 0.0665190i
\(679\) 0 0
\(680\) 3.00000 5.19615i 0.115045 0.199263i
\(681\) −28.1644 29.9696i −1.07926 1.14844i
\(682\) 4.37228 7.57301i 0.167423 0.289986i
\(683\) 22.4198 + 38.8323i 0.857871 + 1.48588i 0.873956 + 0.486005i \(0.161546\pi\)
−0.0160849 + 0.999871i \(0.505120\pi\)
\(684\) 13.4307 6.67954i 0.513536 0.255398i
\(685\) −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
\(689\) 5.48913 0.209119
\(690\) −12.0000 12.7692i −0.456832 0.486114i
\(691\) −5.88316 −0.223806 −0.111903 0.993719i \(-0.535695\pi\)
−0.111903 + 0.993719i \(0.535695\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) −7.11684 −0.270152
\(695\) 29.1386 1.10529
\(696\) 4.62772 1.08724i 0.175413 0.0412118i
\(697\) −45.3505 −1.71777
\(698\) −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 \(0.522659\pi\)
\(702\) 1.74456 + 10.2448i 0.0658443 + 0.386666i
\(703\) −5.00000 8.66025i −0.188579 0.326628i
\(704\) −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
\(709\) 44.0000 1.65245 0.826227 0.563337i \(-0.190483\pi\)
0.826227 + 0.563337i \(0.190483\pi\)
\(710\) −6.94158 12.0232i −0.260513 0.451221i
\(711\) −30.2921 20.0935i −1.13604 0.753566i
\(712\) 1.62772 2.81929i 0.0610013 0.105657i
\(713\) 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
\(717\) −22.3723 23.8063i −0.835508 0.889062i
\(718\) −3.43070 + 5.94215i −0.128033 + 0.221759i
\(719\) 4.37228 7.57301i 0.163059 0.282426i −0.772906 0.634521i \(-0.781197\pi\)
0.935964 + 0.352095i \(0.114531\pi\)
\(720\) 0.255437 4.10891i 0.00951959 0.153130i
\(721\) 0 0
\(722\) 3.00000 + 5.19615i 0.111648 + 0.193381i
\(723\) 1.04755 + 1.11469i 0.0389587 + 0.0414558i
\(724\) 18.1168 0.673307
\(725\) −8.55437 −0.317701
\(726\) 13.6861 3.21543i 0.507940 0.119336i
\(727\) 0.883156 + 1.52967i 0.0327544 + 0.0567324i 0.881938 0.471366i \(-0.156239\pi\)
−0.849183 + 0.528098i \(0.822905\pi\)
\(728\) 0 0
\(729\) 5.00000 26.5330i 0.185185 0.982704i
\(730\) 3.51087 6.08101i 0.129943 0.225068i
\(731\) 19.9307 34.5210i 0.737164 1.27680i
\(732\) −7.05842 + 23.4101i −0.260887 + 0.865264i
\(733\) 11.9416 + 20.6834i 0.441072 + 0.763960i 0.997769 0.0667560i \(-0.0212649\pi\)
−0.556697 + 0.830716i \(0.687932\pi\)
\(734\) 11.1168 19.2549i 0.410330 0.710713i
\(735\) 0 0
\(736\) −3.68614 6.38458i −0.135873 0.235339i
\(737\) −33.0475 + 57.2400i −1.21732 + 2.10846i
\(738\) −27.8614 + 13.8564i −1.02559 + 0.510061i
\(739\) −4.55842 7.89542i −0.167684 0.290438i 0.769921 0.638139i \(-0.220296\pi\)
−0.937605 + 0.347702i \(0.886962\pi\)
\(740\) −2.74456 −0.100892
\(741\) −16.8614 + 3.96143i −0.619419 + 0.145527i
\(742\) 0 0
\(743\) −21.8614 + 37.8651i −0.802017 + 1.38913i 0.116269 + 0.993218i \(0.462906\pi\)
−0.918286 + 0.395917i \(0.870427\pi\)
\(744\) −1.00000 + 3.31662i −0.0366618 + 0.121593i
\(745\) 10.1168 17.5229i 0.370652 0.641989i
\(746\) −5.00000 8.66025i −0.183063 0.317074i
\(747\) 1.02175 16.4356i 0.0373839 0.601349i
\(748\) −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
\(753\) −4.50000 + 14.9248i −0.163989 + 0.543890i
\(754\) −5.48913 −0.199902
\(755\) 11.1386 0.405375
\(756\) 0 0
\(757\) 11.7663 0.427654 0.213827 0.976872i \(-0.431407\pi\)
0.213827 + 0.976872i \(0.431407\pi\)
\(758\) −9.11684 −0.331139
\(759\) −16.1168 + 53.4535i −0.585004 + 1.94024i
\(760\) 6.86141 0.248889
\(761\) −6.25544 10.8347i −0.226759 0.392759i 0.730086 0.683355i \(-0.239480\pi\)
−0.956846 + 0.290596i \(0.906146\pi\)
\(762\) 7.05842 23.4101i 0.255700 0.848060i
\(763\) 0 0
\(764\) −1.88316 −0.0681302
\(765\) 16.1168 8.01544i 0.582706 0.289799i
\(766\) −10.6277 18.4077i −0.383995 0.665099i
\(767\) −7.11684 + 12.3267i −0.256974 + 0.445093i
\(768\) 0.500000 1.65831i 0.0180422 0.0598392i
\(769\) 5.00000 8.66025i 0.180305 0.312297i −0.761680 0.647954i \(-0.775625\pi\)
0.941984 + 0.335657i \(0.108958\pi\)
\(770\) 0 0
\(771\) −36.8614 + 8.66025i −1.32753 + 0.311891i
\(772\) −7.00000 −0.251936
\(773\) 5.56930 + 9.64630i 0.200314 + 0.346953i 0.948629 0.316389i \(-0.102471\pi\)
−0.748316 + 0.663343i \(0.769137\pi\)
\(774\) 1.69702 27.2978i 0.0609980 0.981200i
\(775\) 3.11684 5.39853i 0.111960 0.193921i
\(776\) 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
\(780\) −1.37228 + 4.55134i −0.0491356 + 0.162964i