Properties

Label 882.2.e.k.373.2
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 373.2
Root \(-1.18614 - 1.26217i\) of defining polynomial
Character \(\chi\) \(=\) 882.373
Dual form 882.2.e.k.655.1

$q$-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 0.670820 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
\(9\) −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 −0.693375 0.720577i \(-0.743877\pi\)
0.970725 + 0.240192i \(0.0772105\pi\)
\(14\) 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 \(-0.988777\pi\)
0.469162 0.883112i \(-0.344556\pi\)
\(18\) 2.50000 + 1.65831i 0.589256 + 0.390868i
\(19\) 2.50000 4.33013i 0.573539 0.993399i −0.422659 0.906289i \(-0.638903\pi\)
0.996199 0.0871106i \(-0.0277634\pi\)
\(20\) −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 \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) −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 \(-0.532833\pi\)
0.912906 0.408171i \(-0.133833\pi\)
\(42\) 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 \(-0.653323\pi\)
−0.463267 + 0.886219i \(0.653323\pi\)
\(60\) 2.31386 0.543620i 0.298718 0.0701811i
\(61\) 14.1168 1.80748 0.903738 0.428085i \(-0.140812\pi\)
0.903738 + 0.428085i \(0.140812\pi\)
\(62\) 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 0.676567 0.736381i \(-0.263467\pi\)
−0.976008 + 0.217734i \(0.930133\pi\)
\(74\) 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 0.675166 0.737666i \(-0.264072\pi\)
−0.976420 + 0.215877i \(0.930739\pi\)
\(84\) 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 −0.766769 0.641924i \(-0.778137\pi\)
0.939306 + 0.343079i \(0.111470\pi\)
\(90\) 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 0.999101 0.0423924i \(-0.0134980\pi\)
−0.536263 + 0.844051i \(0.680165\pi\)
\(98\) 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 −0.622276 0.782798i \(-0.713792\pi\)
0.989061 + 0.147508i \(0.0471252\pi\)
\(102\) −7.37228 + 1.73205i −0.729965 + 0.171499i
\(103\) −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
\(107\) 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 0.658853 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
\(135\) −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 \(0.523472\pi\)
−0.826835 + 0.562445i \(0.809861\pi\)
\(140\) 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 \(-0.395007\pi\)
0.323897 + 0.946092i \(0.395007\pi\)
\(158\) −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 \(-0.596754\pi\)
0.975976 0.217876i \(-0.0699129\pi\)
\(168\) 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 \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) −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 \(-0.735127\pi\)
−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
\(185\) 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 0.632581 0.774494i \(-0.281995\pi\)
−0.987022 + 0.160585i \(0.948662\pi\)
\(200\) −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 0.791258 0.611482i \(-0.209426\pi\)
−0.925188 + 0.379509i \(0.876093\pi\)
\(224\) 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 \(0.455545\pi\)
−0.927196 + 0.374577i \(0.877788\pi\)
\(228\) 5.93070 + 6.31084i 0.392770 + 0.417946i
\(229\) −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
\(233\) 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 −0.851453 0.524431i \(-0.824278\pi\)
0.879897 + 0.475164i \(0.157611\pi\)
\(242\) 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 \(-0.408326\pi\)
0.284037 + 0.958813i \(0.408326\pi\)
\(252\) 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 \(0.0721527\pi\)
−0.292581 + 0.956241i \(0.594514\pi\)
\(258\) −15.3723 + 3.61158i −0.957036 + 0.224847i
\(259\) 0 0
\(260\) −2.74456 −0.170211
\(261\) −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 0.731496 0.681846i \(-0.238823\pi\)
−0.956244 + 0.292571i \(0.905489\pi\)
\(270\) 6.68614 + 2.47805i 0.406906 + 0.150809i
\(271\) −9.11684 + 15.7908i −0.553809 + 0.959225i 0.444186 + 0.895934i \(0.353493\pi\)
−0.997995 + 0.0632906i \(0.979841\pi\)
\(272\) −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 \(-0.594902\pi\)
−0.293746 + 0.955883i \(0.594902\pi\)
\(284\) 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 −0.925665 0.378344i \(-0.876494\pi\)
0.790488 + 0.612478i \(0.209827\pi\)
\(294\) 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 \(-0.379024\pi\)
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
\(311\) 26.2337 1.48758 0.743788 0.668416i \(-0.233027\pi\)
0.743788 + 0.668416i \(0.233027\pi\)
\(312\) −2.37228 2.52434i −0.134304 0.142912i
\(313\) 2.88316 0.162966 0.0814828 0.996675i \(-0.474034\pi\)
0.0814828 + 0.996675i \(0.474034\pi\)
\(314\) −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 \(-0.966261\pi\)
0.405571 0.914063i \(-0.367073\pi\)
\(350\) 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 −0.949491 0.313795i \(-0.898400\pi\)
0.746500 + 0.665386i \(0.231733\pi\)
\(354\) −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 \(-0.636271\pi\)
0.995444 0.0953465i \(-0.0303959\pi\)
\(368\) 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 \(-0.983936\pi\)
0.455676 0.890146i \(-0.349398\pi\)
\(384\) 0.500000 1.65831i 0.0255155 0.0846254i
\(385\) 0 0
\(386\) 7.00000 0.356291
\(387\) −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 \(0.352830\pi\)
−0.998125 + 0.0612128i \(0.980503\pi\)
\(398\) 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 \(-0.758459\pi\)
−0.725645 + 0.688069i \(0.758459\pi\)
\(410\) 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 \(-0.597770\pi\)
0.976667 0.214759i \(-0.0688964\pi\)
\(420\) 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 \(-0.477931\pi\)
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
\(437\) 36.8614 1.76332
\(438\) −8.62772 + 2.02700i −0.412248 + 0.0968540i
\(439\) −8.00000 −0.381819 −0.190910 0.981608i \(-0.561144\pi\)
−0.190910 + 0.981608i \(0.561144\pi\)
\(440\) −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 \(0.0885865\pi\)
−0.242844 + 0.970065i \(0.578080\pi\)
\(462\) 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 \(0.411846\pi\)
−0.969735 + 0.244162i \(0.921487\pi\)
\(468\) −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 −0.514270 0.857628i \(-0.671937\pi\)
0.999863 + 0.0165568i \(0.00527043\pi\)
\(480\) −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 \(-0.515858\pi\)
−0.0497976 + 0.998759i \(0.515858\pi\)
\(504\) 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 0.990517 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
\(513\) −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 0.905215 0.424955i \(-0.139710\pi\)
−0.820629 + 0.571461i \(0.806377\pi\)
\(522\) 0.510875 8.21782i 0.0223604 0.359684i
\(523\) −8.94158 + 15.4873i −0.390988 + 0.677211i −0.992580 0.121592i \(-0.961200\pi\)
0.601592 + 0.798803i \(0.294533\pi\)
\(524\) −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 \(-0.520136\pi\)
−0.0632175 + 0.998000i \(0.520136\pi\)
\(564\) 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 \(0.0242429\pi\)
−0.432657 + 0.901559i \(0.642424\pi\)
\(578\) 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 0.765036 0.643988i \(-0.222721\pi\)
−0.940228 + 0.340547i \(0.889388\pi\)
\(588\) 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 −0.830667 0.556769i \(-0.812041\pi\)
0.897510 + 0.440995i \(0.145374\pi\)
\(594\) −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 0.927642 0.373472i \(-0.121833\pi\)
−0.787257 + 0.616625i \(0.788499\pi\)
\(602\) 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 0.714772 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
\(612\) −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 −0.999473 0.0324697i \(-0.989663\pi\)
0.527856 + 0.849334i \(0.322996\pi\)
\(620\) 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 −1.00000 0.000157386i \(-0.999950\pi\)
0.500136 + 0.865947i \(0.333283\pi\)
\(644\) 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 0.641348 0.767250i \(-0.278376\pi\)
−0.985132 + 0.171798i \(0.945042\pi\)
\(648\) −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 \(-0.561564\pi\)
−0.192205 + 0.981355i \(0.561564\pi\)
\(662\) 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 \(-0.269562\pi\)
0.662344 + 0.749199i \(0.269562\pi\)
\(678\) 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 \(-0.464305\pi\)
0.111903 + 0.993719i \(0.464305\pi\)
\(692\) 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 −0.935964 0.352095i \(-0.885469\pi\)
0.772906 + 0.634521i \(0.218803\pi\)
\(720\) −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 0.849183 0.528098i \(-0.177095\pi\)
−0.881938 + 0.471366i \(0.843761\pi\)
\(728\) 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 0.556697 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
\(737\) −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 0.956846 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
\(765\) 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 −0.941984 0.335657i \(-0.891042\pi\)
0.761680 + 0.647954i \(0.224375\pi\)
\(770\) 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 0.748316 0.663343i \(-0.230863\pi\)
−0.948629 + 0.316389i \(0.897529\pi\)
\(774\) 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