Properties

Label 600.2.d.e.349.1
Level 600
Weight 2
Character 600.349
Analytic conductor 4.791
Analytic rank 0
Dimension 6
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 600.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.79102412128\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.399424.1
Defining polynomial: \(x^{6} - 2 x^{5} + 3 x^{4} - 6 x^{3} + 6 x^{2} - 8 x + 8\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 349.1
Root \(-0.671462 - 1.24464i\) of defining polynomial
Character \(\chi\) \(=\) 600.349
Dual form 600.2.d.e.349.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.24464 - 0.671462i) q^{2} -1.00000 q^{3} +(1.09828 + 1.67146i) q^{4} +(1.24464 + 0.671462i) q^{6} +4.68585i q^{7} +(-0.244644 - 2.81783i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-1.24464 - 0.671462i) q^{2} -1.00000 q^{3} +(1.09828 + 1.67146i) q^{4} +(1.24464 + 0.671462i) q^{6} +4.68585i q^{7} +(-0.244644 - 2.81783i) q^{8} +1.00000 q^{9} +2.29273i q^{11} +(-1.09828 - 1.67146i) q^{12} -4.97858 q^{13} +(3.14637 - 5.83221i) q^{14} +(-1.58757 + 3.67146i) q^{16} -2.97858i q^{17} +(-1.24464 - 0.671462i) q^{18} -2.68585i q^{19} -4.68585i q^{21} +(1.53948 - 2.85363i) q^{22} -2.68585i q^{23} +(0.244644 + 2.81783i) q^{24} +(6.19656 + 3.34292i) q^{26} -1.00000 q^{27} +(-7.83221 + 5.14637i) q^{28} -2.00000i q^{29} -6.97858 q^{31} +(4.44120 - 3.50367i) q^{32} -2.29273i q^{33} +(-2.00000 + 3.70727i) q^{34} +(1.09828 + 1.67146i) q^{36} -4.39312 q^{37} +(-1.80344 + 3.34292i) q^{38} +4.97858 q^{39} -11.3717 q^{41} +(-3.14637 + 5.83221i) q^{42} +9.37169 q^{43} +(-3.83221 + 2.51806i) q^{44} +(-1.80344 + 3.34292i) q^{46} +7.27131i q^{47} +(1.58757 - 3.67146i) q^{48} -14.9572 q^{49} +2.97858i q^{51} +(-5.46787 - 8.32150i) q^{52} -2.00000 q^{53} +(1.24464 + 0.671462i) q^{54} +(13.2039 - 1.14637i) q^{56} +2.68585i q^{57} +(-1.34292 + 2.48929i) q^{58} -1.70727i q^{59} +4.58546i q^{61} +(8.68585 + 4.68585i) q^{62} +4.68585i q^{63} +(-7.88030 + 1.37873i) q^{64} +(-1.53948 + 2.85363i) q^{66} -4.00000 q^{67} +(4.97858 - 3.27131i) q^{68} +2.68585i q^{69} +0.585462 q^{71} +(-0.244644 - 2.81783i) q^{72} +6.00000i q^{73} +(5.46787 + 2.94981i) q^{74} +(4.48929 - 2.94981i) q^{76} -10.7434 q^{77} +(-6.19656 - 3.34292i) q^{78} -1.02142 q^{79} +1.00000 q^{81} +(14.1537 + 7.63565i) q^{82} -13.3717 q^{83} +(7.83221 - 5.14637i) q^{84} +(-11.6644 - 6.29273i) q^{86} +2.00000i q^{87} +(6.46052 - 0.560904i) q^{88} -3.37169 q^{89} -23.3288i q^{91} +(4.48929 - 2.94981i) q^{92} +6.97858 q^{93} +(4.88240 - 9.05019i) q^{94} +(-4.44120 + 3.50367i) q^{96} -3.95715i q^{97} +(18.6163 + 10.0432i) q^{98} +2.29273i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6q^{3} + 2q^{4} + 6q^{8} + 6q^{9} + O(q^{10}) \) \( 6q - 6q^{3} + 2q^{4} + 6q^{8} + 6q^{9} - 2q^{12} + 16q^{14} + 10q^{16} - 12q^{22} - 6q^{24} + 28q^{26} - 6q^{27} - 20q^{28} - 12q^{31} + 10q^{32} - 12q^{34} + 2q^{36} - 8q^{37} - 20q^{38} - 20q^{41} - 16q^{42} + 8q^{43} + 4q^{44} - 20q^{46} - 10q^{48} - 30q^{49} + 12q^{52} - 12q^{53} + 4q^{56} + 4q^{58} + 28q^{62} - 22q^{64} + 12q^{66} - 24q^{67} - 8q^{71} + 6q^{72} - 12q^{74} + 12q^{76} + 32q^{77} - 28q^{78} - 36q^{79} + 6q^{81} + 16q^{82} - 32q^{83} + 20q^{84} - 16q^{86} + 60q^{88} + 28q^{89} + 12q^{92} + 12q^{93} - 4q^{94} - 10q^{96} + 56q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).

\(n\) \(151\) \(301\) \(401\) \(577\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.24464 0.671462i −0.880096 0.474795i
\(3\) −1.00000 −0.577350
\(4\) 1.09828 + 1.67146i 0.549139 + 0.835731i
\(5\) 0 0
\(6\) 1.24464 + 0.671462i 0.508124 + 0.274123i
\(7\) 4.68585i 1.77108i 0.464560 + 0.885542i \(0.346213\pi\)
−0.464560 + 0.885542i \(0.653787\pi\)
\(8\) −0.244644 2.81783i −0.0864948 0.996252i
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 2.29273i 0.691284i 0.938366 + 0.345642i \(0.112339\pi\)
−0.938366 + 0.345642i \(0.887661\pi\)
\(12\) −1.09828 1.67146i −0.317046 0.482509i
\(13\) −4.97858 −1.38081 −0.690404 0.723424i \(-0.742567\pi\)
−0.690404 + 0.723424i \(0.742567\pi\)
\(14\) 3.14637 5.83221i 0.840902 1.55872i
\(15\) 0 0
\(16\) −1.58757 + 3.67146i −0.396892 + 0.917865i
\(17\) 2.97858i 0.722411i −0.932486 0.361206i \(-0.882365\pi\)
0.932486 0.361206i \(-0.117635\pi\)
\(18\) −1.24464 0.671462i −0.293365 0.158265i
\(19\) 2.68585i 0.616175i −0.951358 0.308088i \(-0.900311\pi\)
0.951358 0.308088i \(-0.0996890\pi\)
\(20\) 0 0
\(21\) 4.68585i 1.02254i
\(22\) 1.53948 2.85363i 0.328218 0.608397i
\(23\) 2.68585i 0.560038i −0.959995 0.280019i \(-0.909659\pi\)
0.959995 0.280019i \(-0.0903407\pi\)
\(24\) 0.244644 + 2.81783i 0.0499378 + 0.575187i
\(25\) 0 0
\(26\) 6.19656 + 3.34292i 1.21524 + 0.655601i
\(27\) −1.00000 −0.192450
\(28\) −7.83221 + 5.14637i −1.48015 + 0.972572i
\(29\) 2.00000i 0.371391i −0.982607 0.185695i \(-0.940546\pi\)
0.982607 0.185695i \(-0.0594537\pi\)
\(30\) 0 0
\(31\) −6.97858 −1.25339 −0.626695 0.779265i \(-0.715593\pi\)
−0.626695 + 0.779265i \(0.715593\pi\)
\(32\) 4.44120 3.50367i 0.785101 0.619368i
\(33\) 2.29273i 0.399113i
\(34\) −2.00000 + 3.70727i −0.342997 + 0.635791i
\(35\) 0 0
\(36\) 1.09828 + 1.67146i 0.183046 + 0.278577i
\(37\) −4.39312 −0.722224 −0.361112 0.932523i \(-0.617603\pi\)
−0.361112 + 0.932523i \(0.617603\pi\)
\(38\) −1.80344 + 3.34292i −0.292557 + 0.542294i
\(39\) 4.97858 0.797210
\(40\) 0 0
\(41\) −11.3717 −1.77596 −0.887980 0.459882i \(-0.847892\pi\)
−0.887980 + 0.459882i \(0.847892\pi\)
\(42\) −3.14637 + 5.83221i −0.485495 + 0.899930i
\(43\) 9.37169 1.42917 0.714585 0.699549i \(-0.246616\pi\)
0.714585 + 0.699549i \(0.246616\pi\)
\(44\) −3.83221 + 2.51806i −0.577728 + 0.379611i
\(45\) 0 0
\(46\) −1.80344 + 3.34292i −0.265903 + 0.492887i
\(47\) 7.27131i 1.06063i 0.847801 + 0.530315i \(0.177926\pi\)
−0.847801 + 0.530315i \(0.822074\pi\)
\(48\) 1.58757 3.67146i 0.229146 0.529930i
\(49\) −14.9572 −2.13674
\(50\) 0 0
\(51\) 2.97858i 0.417084i
\(52\) −5.46787 8.32150i −0.758257 1.15398i
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 1.24464 + 0.671462i 0.169375 + 0.0913743i
\(55\) 0 0
\(56\) 13.2039 1.14637i 1.76445 0.153190i
\(57\) 2.68585i 0.355749i
\(58\) −1.34292 + 2.48929i −0.176334 + 0.326860i
\(59\) 1.70727i 0.222267i −0.993805 0.111134i \(-0.964552\pi\)
0.993805 0.111134i \(-0.0354482\pi\)
\(60\) 0 0
\(61\) 4.58546i 0.587108i 0.955942 + 0.293554i \(0.0948381\pi\)
−0.955942 + 0.293554i \(0.905162\pi\)
\(62\) 8.68585 + 4.68585i 1.10310 + 0.595103i
\(63\) 4.68585i 0.590361i
\(64\) −7.88030 + 1.37873i −0.985037 + 0.172341i
\(65\) 0 0
\(66\) −1.53948 + 2.85363i −0.189497 + 0.351258i
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 4.97858 3.27131i 0.603741 0.396704i
\(69\) 2.68585i 0.323338i
\(70\) 0 0
\(71\) 0.585462 0.0694816 0.0347408 0.999396i \(-0.488939\pi\)
0.0347408 + 0.999396i \(0.488939\pi\)
\(72\) −0.244644 2.81783i −0.0288316 0.332084i
\(73\) 6.00000i 0.702247i 0.936329 + 0.351123i \(0.114200\pi\)
−0.936329 + 0.351123i \(0.885800\pi\)
\(74\) 5.46787 + 2.94981i 0.635626 + 0.342908i
\(75\) 0 0
\(76\) 4.48929 2.94981i 0.514957 0.338366i
\(77\) −10.7434 −1.22432
\(78\) −6.19656 3.34292i −0.701622 0.378512i
\(79\) −1.02142 −0.114919 −0.0574595 0.998348i \(-0.518300\pi\)
−0.0574595 + 0.998348i \(0.518300\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 14.1537 + 7.63565i 1.56302 + 0.843217i
\(83\) −13.3717 −1.46773 −0.733867 0.679293i \(-0.762286\pi\)
−0.733867 + 0.679293i \(0.762286\pi\)
\(84\) 7.83221 5.14637i 0.854564 0.561515i
\(85\) 0 0
\(86\) −11.6644 6.29273i −1.25781 0.678563i
\(87\) 2.00000i 0.214423i
\(88\) 6.46052 0.560904i 0.688694 0.0597925i
\(89\) −3.37169 −0.357399 −0.178699 0.983904i \(-0.557189\pi\)
−0.178699 + 0.983904i \(0.557189\pi\)
\(90\) 0 0
\(91\) 23.3288i 2.44553i
\(92\) 4.48929 2.94981i 0.468041 0.307539i
\(93\) 6.97858 0.723645
\(94\) 4.88240 9.05019i 0.503581 0.933456i
\(95\) 0 0
\(96\) −4.44120 + 3.50367i −0.453278 + 0.357592i
\(97\) 3.95715i 0.401788i −0.979613 0.200894i \(-0.935615\pi\)
0.979613 0.200894i \(-0.0643847\pi\)
\(98\) 18.6163 + 10.0432i 1.88053 + 1.01451i
\(99\) 2.29273i 0.230428i
\(100\) 0 0
\(101\) 2.00000i 0.199007i −0.995037 0.0995037i \(-0.968274\pi\)
0.995037 0.0995037i \(-0.0317255\pi\)
\(102\) 2.00000 3.70727i 0.198030 0.367074i
\(103\) 14.6430i 1.44282i 0.692509 + 0.721409i \(0.256505\pi\)
−0.692509 + 0.721409i \(0.743495\pi\)
\(104\) 1.21798 + 14.0288i 0.119433 + 1.37563i
\(105\) 0 0
\(106\) 2.48929 + 1.34292i 0.241781 + 0.130436i
\(107\) 11.3288 1.09520 0.547600 0.836740i \(-0.315541\pi\)
0.547600 + 0.836740i \(0.315541\pi\)
\(108\) −1.09828 1.67146i −0.105682 0.160836i
\(109\) 9.37169i 0.897645i 0.893621 + 0.448823i \(0.148157\pi\)
−0.893621 + 0.448823i \(0.851843\pi\)
\(110\) 0 0
\(111\) 4.39312 0.416976
\(112\) −17.2039 7.43910i −1.62562 0.702929i
\(113\) 19.7648i 1.85932i −0.368423 0.929658i \(-0.620102\pi\)
0.368423 0.929658i \(-0.379898\pi\)
\(114\) 1.80344 3.34292i 0.168908 0.313093i
\(115\) 0 0
\(116\) 3.34292 2.19656i 0.310383 0.203945i
\(117\) −4.97858 −0.460270
\(118\) −1.14637 + 2.12494i −0.105531 + 0.195617i
\(119\) 13.9572 1.27945
\(120\) 0 0
\(121\) 5.74338 0.522126
\(122\) 3.07896 5.70727i 0.278756 0.516712i
\(123\) 11.3717 1.02535
\(124\) −7.66442 11.6644i −0.688286 1.04750i
\(125\) 0 0
\(126\) 3.14637 5.83221i 0.280301 0.519575i
\(127\) 6.64300i 0.589471i 0.955579 + 0.294735i \(0.0952315\pi\)
−0.955579 + 0.294735i \(0.904768\pi\)
\(128\) 10.7339 + 3.57529i 0.948755 + 0.316014i
\(129\) −9.37169 −0.825132
\(130\) 0 0
\(131\) 7.07896i 0.618492i 0.950982 + 0.309246i \(0.100077\pi\)
−0.950982 + 0.309246i \(0.899923\pi\)
\(132\) 3.83221 2.51806i 0.333551 0.219169i
\(133\) 12.5855 1.09130
\(134\) 4.97858 + 2.68585i 0.430084 + 0.232022i
\(135\) 0 0
\(136\) −8.39312 + 0.728692i −0.719704 + 0.0624848i
\(137\) 14.9786i 1.27971i −0.768497 0.639853i \(-0.778995\pi\)
0.768497 0.639853i \(-0.221005\pi\)
\(138\) 1.80344 3.34292i 0.153519 0.284569i
\(139\) 4.64300i 0.393814i −0.980422 0.196907i \(-0.936910\pi\)
0.980422 0.196907i \(-0.0630897\pi\)
\(140\) 0 0
\(141\) 7.27131i 0.612355i
\(142\) −0.728692 0.393115i −0.0611505 0.0329895i
\(143\) 11.4145i 0.954532i
\(144\) −1.58757 + 3.67146i −0.132297 + 0.305955i
\(145\) 0 0
\(146\) 4.02877 7.46787i 0.333423 0.618045i
\(147\) 14.9572 1.23365
\(148\) −4.82487 7.34292i −0.396601 0.603585i
\(149\) 2.00000i 0.163846i −0.996639 0.0819232i \(-0.973894\pi\)
0.996639 0.0819232i \(-0.0261062\pi\)
\(150\) 0 0
\(151\) −8.35027 −0.679535 −0.339768 0.940509i \(-0.610348\pi\)
−0.339768 + 0.940509i \(0.610348\pi\)
\(152\) −7.56825 + 0.657077i −0.613866 + 0.0532960i
\(153\) 2.97858i 0.240804i
\(154\) 13.3717 + 7.21377i 1.07752 + 0.581302i
\(155\) 0 0
\(156\) 5.46787 + 8.32150i 0.437780 + 0.666253i
\(157\) 22.3503 1.78375 0.891873 0.452286i \(-0.149391\pi\)
0.891873 + 0.452286i \(0.149391\pi\)
\(158\) 1.27131 + 0.685846i 0.101140 + 0.0545630i
\(159\) 2.00000 0.158610
\(160\) 0 0
\(161\) 12.5855 0.991873
\(162\) −1.24464 0.671462i −0.0977885 0.0527550i
\(163\) −1.37169 −0.107439 −0.0537196 0.998556i \(-0.517108\pi\)
−0.0537196 + 0.998556i \(0.517108\pi\)
\(164\) −12.4893 19.0073i −0.975250 1.48422i
\(165\) 0 0
\(166\) 16.6430 + 8.97858i 1.29175 + 0.696873i
\(167\) 11.2713i 0.872200i 0.899898 + 0.436100i \(0.143641\pi\)
−0.899898 + 0.436100i \(0.856359\pi\)
\(168\) −13.2039 + 1.14637i −1.01870 + 0.0884440i
\(169\) 11.7862 0.906633
\(170\) 0 0
\(171\) 2.68585i 0.205392i
\(172\) 10.2927 + 15.6644i 0.784813 + 1.19440i
\(173\) −10.7862 −0.820062 −0.410031 0.912072i \(-0.634482\pi\)
−0.410031 + 0.912072i \(0.634482\pi\)
\(174\) 1.34292 2.48929i 0.101807 0.188712i
\(175\) 0 0
\(176\) −8.41767 3.63986i −0.634506 0.274365i
\(177\) 1.70727i 0.128326i
\(178\) 4.19656 + 2.26396i 0.314545 + 0.169691i
\(179\) 3.66442i 0.273892i −0.990579 0.136946i \(-0.956271\pi\)
0.990579 0.136946i \(-0.0437287\pi\)
\(180\) 0 0
\(181\) 6.62831i 0.492678i −0.969184 0.246339i \(-0.920772\pi\)
0.969184 0.246339i \(-0.0792277\pi\)
\(182\) −15.6644 + 29.0361i −1.16112 + 2.15230i
\(183\) 4.58546i 0.338967i
\(184\) −7.56825 + 0.657077i −0.557939 + 0.0484404i
\(185\) 0 0
\(186\) −8.68585 4.68585i −0.636877 0.343583i
\(187\) 6.82908 0.499392
\(188\) −12.1537 + 7.98592i −0.886401 + 0.582433i
\(189\) 4.68585i 0.340845i
\(190\) 0 0
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) 7.88030 1.37873i 0.568712 0.0995013i
\(193\) 1.21377i 0.0873690i −0.999045 0.0436845i \(-0.986090\pi\)
0.999045 0.0436845i \(-0.0139096\pi\)
\(194\) −2.65708 + 4.92525i −0.190767 + 0.353612i
\(195\) 0 0
\(196\) −16.4271 25.0003i −1.17337 1.78574i
\(197\) −23.9572 −1.70688 −0.853438 0.521194i \(-0.825487\pi\)
−0.853438 + 0.521194i \(0.825487\pi\)
\(198\) 1.53948 2.85363i 0.109406 0.202799i
\(199\) −0.350269 −0.0248299 −0.0124150 0.999923i \(-0.503952\pi\)
−0.0124150 + 0.999923i \(0.503952\pi\)
\(200\) 0 0
\(201\) 4.00000 0.282138
\(202\) −1.34292 + 2.48929i −0.0944877 + 0.175146i
\(203\) 9.37169 0.657764
\(204\) −4.97858 + 3.27131i −0.348570 + 0.229037i
\(205\) 0 0
\(206\) 9.83221 18.2253i 0.685043 1.26982i
\(207\) 2.68585i 0.186679i
\(208\) 7.90383 18.2787i 0.548032 1.26740i
\(209\) 6.15792 0.425952
\(210\) 0 0
\(211\) 14.1004i 0.970710i 0.874317 + 0.485355i \(0.161310\pi\)
−0.874317 + 0.485355i \(0.838690\pi\)
\(212\) −2.19656 3.34292i −0.150860 0.229593i
\(213\) −0.585462 −0.0401152
\(214\) −14.1004 7.60688i −0.963882 0.519996i
\(215\) 0 0
\(216\) 0.244644 + 2.81783i 0.0166459 + 0.191729i
\(217\) 32.7005i 2.21986i
\(218\) 6.29273 11.6644i 0.426198 0.790014i
\(219\) 6.00000i 0.405442i
\(220\) 0 0
\(221\) 14.8291i 0.997512i
\(222\) −5.46787 2.94981i −0.366979 0.197978i
\(223\) 6.72869i 0.450587i 0.974291 + 0.225293i \(0.0723340\pi\)
−0.974291 + 0.225293i \(0.927666\pi\)
\(224\) 16.4177 + 20.8108i 1.09695 + 1.39048i
\(225\) 0 0
\(226\) −13.2713 + 24.6002i −0.882794 + 1.63638i
\(227\) −9.95715 −0.660880 −0.330440 0.943827i \(-0.607197\pi\)
−0.330440 + 0.943827i \(0.607197\pi\)
\(228\) −4.48929 + 2.94981i −0.297310 + 0.195356i
\(229\) 11.3288i 0.748631i 0.927301 + 0.374316i \(0.122122\pi\)
−0.927301 + 0.374316i \(0.877878\pi\)
\(230\) 0 0
\(231\) 10.7434 0.706863
\(232\) −5.63565 + 0.489289i −0.369999 + 0.0321234i
\(233\) 18.9786i 1.24333i 0.783284 + 0.621664i \(0.213543\pi\)
−0.783284 + 0.621664i \(0.786457\pi\)
\(234\) 6.19656 + 3.34292i 0.405082 + 0.218534i
\(235\) 0 0
\(236\) 2.85363 1.87506i 0.185756 0.122056i
\(237\) 1.02142 0.0663485
\(238\) −17.3717 9.37169i −1.12604 0.607477i
\(239\) −2.62831 −0.170011 −0.0850055 0.996380i \(-0.527091\pi\)
−0.0850055 + 0.996380i \(0.527091\pi\)
\(240\) 0 0
\(241\) 10.7862 0.694802 0.347401 0.937717i \(-0.387064\pi\)
0.347401 + 0.937717i \(0.387064\pi\)
\(242\) −7.14847 3.85646i −0.459521 0.247903i
\(243\) −1.00000 −0.0641500
\(244\) −7.66442 + 5.03612i −0.490664 + 0.322404i
\(245\) 0 0
\(246\) −14.1537 7.63565i −0.902408 0.486832i
\(247\) 13.3717i 0.850820i
\(248\) 1.70727 + 19.6644i 0.108412 + 1.24869i
\(249\) 13.3717 0.847397
\(250\) 0 0
\(251\) 30.9933i 1.95628i 0.207952 + 0.978139i \(0.433320\pi\)
−0.207952 + 0.978139i \(0.566680\pi\)
\(252\) −7.83221 + 5.14637i −0.493383 + 0.324191i
\(253\) 6.15792 0.387145
\(254\) 4.46052 8.26817i 0.279878 0.518791i
\(255\) 0 0
\(256\) −10.9593 11.6574i −0.684954 0.728587i
\(257\) 20.9357i 1.30594i 0.757386 + 0.652968i \(0.226476\pi\)
−0.757386 + 0.652968i \(0.773524\pi\)
\(258\) 11.6644 + 6.29273i 0.726195 + 0.391768i
\(259\) 20.5855i 1.27912i
\(260\) 0 0
\(261\) 2.00000i 0.123797i
\(262\) 4.75325 8.81079i 0.293657 0.544332i
\(263\) 19.2713i 1.18832i 0.804347 + 0.594160i \(0.202515\pi\)
−0.804347 + 0.594160i \(0.797485\pi\)
\(264\) −6.46052 + 0.560904i −0.397617 + 0.0345212i
\(265\) 0 0
\(266\) −15.6644 8.45065i −0.960447 0.518143i
\(267\) 3.37169 0.206344
\(268\) −4.39312 6.68585i −0.268352 0.408403i
\(269\) 24.7434i 1.50863i 0.656512 + 0.754315i \(0.272031\pi\)
−0.656512 + 0.754315i \(0.727969\pi\)
\(270\) 0 0
\(271\) 27.5640 1.67440 0.837198 0.546900i \(-0.184192\pi\)
0.837198 + 0.546900i \(0.184192\pi\)
\(272\) 10.9357 + 4.72869i 0.663076 + 0.286719i
\(273\) 23.3288i 1.41193i
\(274\) −10.0575 + 18.6430i −0.607598 + 1.12626i
\(275\) 0 0
\(276\) −4.48929 + 2.94981i −0.270223 + 0.177558i
\(277\) 20.3074 1.22015 0.610077 0.792342i \(-0.291138\pi\)
0.610077 + 0.792342i \(0.291138\pi\)
\(278\) −3.11760 + 5.77888i −0.186981 + 0.346594i
\(279\) −6.97858 −0.417796
\(280\) 0 0
\(281\) −10.7862 −0.643453 −0.321726 0.946833i \(-0.604263\pi\)
−0.321726 + 0.946833i \(0.604263\pi\)
\(282\) −4.88240 + 9.05019i −0.290743 + 0.538931i
\(283\) −20.0000 −1.18888 −0.594438 0.804141i \(-0.702626\pi\)
−0.594438 + 0.804141i \(0.702626\pi\)
\(284\) 0.643000 + 0.978577i 0.0381551 + 0.0580679i
\(285\) 0 0
\(286\) −7.66442 + 14.2070i −0.453207 + 0.840080i
\(287\) 53.2860i 3.14537i
\(288\) 4.44120 3.50367i 0.261700 0.206456i
\(289\) 8.12808 0.478122
\(290\) 0 0
\(291\) 3.95715i 0.231972i
\(292\) −10.0288 + 6.58967i −0.586889 + 0.385631i
\(293\) −21.9143 −1.28025 −0.640124 0.768272i \(-0.721117\pi\)
−0.640124 + 0.768272i \(0.721117\pi\)
\(294\) −18.6163 10.0432i −1.08573 0.585729i
\(295\) 0 0
\(296\) 1.07475 + 12.3790i 0.0624686 + 0.719517i
\(297\) 2.29273i 0.133038i
\(298\) −1.34292 + 2.48929i −0.0777934 + 0.144201i
\(299\) 13.3717i 0.773305i
\(300\) 0 0
\(301\) 43.9143i 2.53118i
\(302\) 10.3931 + 5.60688i 0.598057 + 0.322640i
\(303\) 2.00000i 0.114897i
\(304\) 9.86098 + 4.26396i 0.565566 + 0.244555i
\(305\) 0 0
\(306\) −2.00000 + 3.70727i −0.114332 + 0.211930i
\(307\) −26.5426 −1.51487 −0.757434 0.652912i \(-0.773547\pi\)
−0.757434 + 0.652912i \(0.773547\pi\)
\(308\) −11.7992 17.9572i −0.672324 1.02320i
\(309\) 14.6430i 0.833011i
\(310\) 0 0
\(311\) 12.2008 0.691842 0.345921 0.938264i \(-0.387566\pi\)
0.345921 + 0.938264i \(0.387566\pi\)
\(312\) −1.21798 14.0288i −0.0689546 0.794223i
\(313\) 15.9572i 0.901952i −0.892536 0.450976i \(-0.851076\pi\)
0.892536 0.450976i \(-0.148924\pi\)
\(314\) −27.8181 15.0073i −1.56987 0.846914i
\(315\) 0 0
\(316\) −1.12181 1.70727i −0.0631066 0.0960414i
\(317\) 33.5296 1.88321 0.941605 0.336718i \(-0.109317\pi\)
0.941605 + 0.336718i \(0.109317\pi\)
\(318\) −2.48929 1.34292i −0.139592 0.0753074i
\(319\) 4.58546 0.256737
\(320\) 0 0
\(321\) −11.3288 −0.632315
\(322\) −15.6644 8.45065i −0.872944 0.470937i
\(323\) −8.00000 −0.445132
\(324\) 1.09828 + 1.67146i 0.0610155 + 0.0928590i
\(325\) 0 0
\(326\) 1.70727 + 0.921039i 0.0945569 + 0.0510116i
\(327\) 9.37169i 0.518256i
\(328\) 2.78202 + 32.0435i 0.153611 + 1.76930i
\(329\) −34.0722 −1.87846
\(330\) 0 0
\(331\) 19.8568i 1.09143i −0.837972 0.545713i \(-0.816259\pi\)
0.837972 0.545713i \(-0.183741\pi\)
\(332\) −14.6858 22.3503i −0.805991 1.22663i
\(333\) −4.39312 −0.240741
\(334\) 7.56825 14.0288i 0.414116 0.767620i
\(335\) 0 0
\(336\) 17.2039 + 7.43910i 0.938550 + 0.405836i
\(337\) 7.17092i 0.390625i 0.980741 + 0.195313i \(0.0625721\pi\)
−0.980741 + 0.195313i \(0.937428\pi\)
\(338\) −14.6697 7.91400i −0.797925 0.430465i
\(339\) 19.7648i 1.07348i
\(340\) 0 0
\(341\) 16.0000i 0.866449i
\(342\) −1.80344 + 3.34292i −0.0975190 + 0.180765i
\(343\) 37.2860i 2.01325i
\(344\) −2.29273 26.4078i −0.123616 1.42381i
\(345\) 0 0
\(346\) 13.4250 + 7.24254i 0.721734 + 0.389361i
\(347\) −0.786230 −0.0422071 −0.0211035 0.999777i \(-0.506718\pi\)
−0.0211035 + 0.999777i \(0.506718\pi\)
\(348\) −3.34292 + 2.19656i −0.179199 + 0.117748i
\(349\) 6.15792i 0.329626i −0.986325 0.164813i \(-0.947298\pi\)
0.986325 0.164813i \(-0.0527021\pi\)
\(350\) 0 0
\(351\) 4.97858 0.265737
\(352\) 8.03298 + 10.1825i 0.428159 + 0.542728i
\(353\) 21.7220i 1.15614i −0.815986 0.578072i \(-0.803805\pi\)
0.815986 0.578072i \(-0.196195\pi\)
\(354\) 1.14637 2.12494i 0.0609286 0.112939i
\(355\) 0 0
\(356\) −3.70306 5.63565i −0.196262 0.298689i
\(357\) −13.9572 −0.738691
\(358\) −2.46052 + 4.56090i −0.130042 + 0.241051i
\(359\) −0.585462 −0.0308995 −0.0154498 0.999881i \(-0.504918\pi\)
−0.0154498 + 0.999881i \(0.504918\pi\)
\(360\) 0 0
\(361\) 11.7862 0.620328
\(362\) −4.45065 + 8.24989i −0.233921 + 0.433604i
\(363\) −5.74338 −0.301450
\(364\) 38.9933 25.6216i 2.04380 1.34294i
\(365\) 0 0
\(366\) −3.07896 + 5.70727i −0.160940 + 0.298324i
\(367\) 0.485078i 0.0253209i −0.999920 0.0126604i \(-0.995970\pi\)
0.999920 0.0126604i \(-0.00403005\pi\)
\(368\) 9.86098 + 4.26396i 0.514039 + 0.222274i
\(369\) −11.3717 −0.591987
\(370\) 0 0
\(371\) 9.37169i 0.486554i
\(372\) 7.66442 + 11.6644i 0.397382 + 0.604772i
\(373\) −12.3931 −0.641691 −0.320846 0.947132i \(-0.603967\pi\)
−0.320846 + 0.947132i \(0.603967\pi\)
\(374\) −8.49977 4.58546i −0.439513 0.237109i
\(375\) 0 0
\(376\) 20.4893 1.77888i 1.05665 0.0917389i
\(377\) 9.95715i 0.512820i
\(378\) −3.14637 + 5.83221i −0.161832 + 0.299977i
\(379\) 26.0147i 1.33629i 0.744033 + 0.668143i \(0.232910\pi\)
−0.744033 + 0.668143i \(0.767090\pi\)
\(380\) 0 0
\(381\) 6.64300i 0.340331i
\(382\) 9.95715 + 5.37169i 0.509452 + 0.274840i
\(383\) 6.68585i 0.341631i −0.985303 0.170815i \(-0.945360\pi\)
0.985303 0.170815i \(-0.0546402\pi\)
\(384\) −10.7339 3.57529i −0.547764 0.182451i
\(385\) 0 0
\(386\) −0.815000 + 1.51071i −0.0414824 + 0.0768932i
\(387\) 9.37169 0.476390
\(388\) 6.61423 4.34606i 0.335787 0.220638i
\(389\) 29.9143i 1.51672i −0.651838 0.758358i \(-0.726002\pi\)
0.651838 0.758358i \(-0.273998\pi\)
\(390\) 0 0
\(391\) −8.00000 −0.404577
\(392\) 3.65918 + 42.1467i 0.184817 + 2.12873i
\(393\) 7.07896i 0.357086i
\(394\) 29.8181 + 16.0863i 1.50222 + 0.810416i
\(395\) 0 0
\(396\) −3.83221 + 2.51806i −0.192576 + 0.126537i
\(397\) −9.76481 −0.490082 −0.245041 0.969513i \(-0.578801\pi\)
−0.245041 + 0.969513i \(0.578801\pi\)
\(398\) 0.435961 + 0.235192i 0.0218527 + 0.0117891i
\(399\) −12.5855 −0.630061
\(400\) 0 0
\(401\) −6.58546 −0.328862 −0.164431 0.986389i \(-0.552579\pi\)
−0.164431 + 0.986389i \(0.552579\pi\)
\(402\) −4.97858 2.68585i −0.248309 0.133958i
\(403\) 34.7434 1.73069
\(404\) 3.34292 2.19656i 0.166317 0.109283i
\(405\) 0 0
\(406\) −11.6644 6.29273i −0.578896 0.312303i
\(407\) 10.0722i 0.499262i
\(408\) 8.39312 0.728692i 0.415521 0.0360756i
\(409\) 25.9143 1.28138 0.640690 0.767800i \(-0.278648\pi\)
0.640690 + 0.767800i \(0.278648\pi\)
\(410\) 0 0
\(411\) 14.9786i 0.738839i
\(412\) −24.4752 + 16.0821i −1.20581 + 0.792308i
\(413\) 8.00000 0.393654
\(414\) −1.80344 + 3.34292i −0.0886344 + 0.164296i
\(415\) 0 0
\(416\) −22.1109 + 17.4433i −1.08407 + 0.855229i
\(417\) 4.64300i 0.227369i
\(418\) −7.66442 4.13481i −0.374879 0.202240i
\(419\) 12.2499i 0.598446i 0.954183 + 0.299223i \(0.0967275\pi\)
−0.954183 + 0.299223i \(0.903273\pi\)
\(420\) 0 0
\(421\) 4.67115i 0.227658i −0.993500 0.113829i \(-0.963688\pi\)
0.993500 0.113829i \(-0.0363116\pi\)
\(422\) 9.46787 17.5500i 0.460888 0.854319i
\(423\) 7.27131i 0.353543i
\(424\) 0.489289 + 5.63565i 0.0237620 + 0.273692i
\(425\) 0 0
\(426\) 0.728692 + 0.393115i 0.0353052 + 0.0190465i
\(427\) −21.4868 −1.03982
\(428\) 12.4422 + 18.9357i 0.601418 + 0.915293i
\(429\) 11.4145i 0.551099i
\(430\) 0 0
\(431\) 0.585462 0.0282007 0.0141004 0.999901i \(-0.495512\pi\)
0.0141004 + 0.999901i \(0.495512\pi\)
\(432\) 1.58757 3.67146i 0.0763819 0.176643i
\(433\) 21.9143i 1.05313i 0.850133 + 0.526567i \(0.176521\pi\)
−0.850133 + 0.526567i \(0.823479\pi\)
\(434\) −21.9572 + 40.7005i −1.05398 + 1.95369i
\(435\) 0 0
\(436\) −15.6644 + 10.2927i −0.750190 + 0.492932i
\(437\) −7.21377 −0.345081
\(438\) −4.02877 + 7.46787i −0.192502 + 0.356828i
\(439\) 2.39312 0.114217 0.0571086 0.998368i \(-0.481812\pi\)
0.0571086 + 0.998368i \(0.481812\pi\)
\(440\) 0 0
\(441\) −14.9572 −0.712245
\(442\) 9.95715 18.4569i 0.473614 0.877906i
\(443\) −20.7005 −0.983512 −0.491756 0.870733i \(-0.663645\pi\)
−0.491756 + 0.870733i \(0.663645\pi\)
\(444\) 4.82487 + 7.34292i 0.228978 + 0.348480i
\(445\) 0 0
\(446\) 4.51806 8.37483i 0.213936 0.396560i
\(447\) 2.00000i 0.0945968i
\(448\) −6.46052 36.9259i −0.305231 1.74458i
\(449\) 37.9143 1.78929 0.894643 0.446781i \(-0.147430\pi\)
0.894643 + 0.446781i \(0.147430\pi\)
\(450\) 0 0
\(451\) 26.0722i 1.22769i
\(452\) 33.0361 21.7073i 1.55389 1.02102i
\(453\) 8.35027 0.392330
\(454\) 12.3931 + 6.68585i 0.581638 + 0.313782i
\(455\) 0 0
\(456\) 7.56825 0.657077i 0.354416 0.0307704i
\(457\) 38.7005i 1.81033i 0.425055 + 0.905167i \(0.360255\pi\)
−0.425055 + 0.905167i \(0.639745\pi\)
\(458\) 7.60688 14.1004i 0.355446 0.658868i
\(459\) 2.97858i 0.139028i
\(460\) 0 0
\(461\) 4.74338i 0.220921i −0.993880 0.110461i \(-0.964767\pi\)
0.993880 0.110461i \(-0.0352326\pi\)
\(462\) −13.3717 7.21377i −0.622107 0.335615i
\(463\) 15.3142i 0.711709i −0.934541 0.355855i \(-0.884190\pi\)
0.934541 0.355855i \(-0.115810\pi\)
\(464\) 7.34292 + 3.17513i 0.340887 + 0.147402i
\(465\) 0 0
\(466\) 12.7434 23.6216i 0.590326 1.09425i
\(467\) 30.5426 1.41334 0.706672 0.707541i \(-0.250196\pi\)
0.706672 + 0.707541i \(0.250196\pi\)
\(468\) −5.46787 8.32150i −0.252752 0.384661i
\(469\) 18.7434i 0.865489i
\(470\) 0 0
\(471\) −22.3503 −1.02985
\(472\) −4.81079 + 0.417674i −0.221435 + 0.0192250i
\(473\) 21.4868i 0.987963i
\(474\) −1.27131 0.685846i −0.0583931 0.0315020i
\(475\) 0 0
\(476\) 15.3288 + 23.3288i 0.702597 + 1.06928i
\(477\) −2.00000 −0.0915737
\(478\) 3.27131 + 1.76481i 0.149626 + 0.0807204i
\(479\) −3.32885 −0.152099 −0.0760494 0.997104i \(-0.524231\pi\)
−0.0760494 + 0.997104i \(0.524231\pi\)
\(480\) 0 0
\(481\) 21.8715 0.997253
\(482\) −13.4250 7.24254i −0.611493 0.329889i
\(483\) −12.5855 −0.572658
\(484\) 6.30784 + 9.59985i 0.286720 + 0.436357i
\(485\) 0 0
\(486\) 1.24464 + 0.671462i 0.0564582 + 0.0304581i
\(487\) 12.1004i 0.548321i −0.961684 0.274160i \(-0.911600\pi\)
0.961684 0.274160i \(-0.0883999\pi\)
\(488\) 12.9210 1.12181i 0.584908 0.0507818i
\(489\) 1.37169 0.0620301
\(490\) 0 0
\(491\) 14.2927i 0.645022i 0.946566 + 0.322511i \(0.104527\pi\)
−0.946566 + 0.322511i \(0.895473\pi\)
\(492\) 12.4893 + 19.0073i 0.563061 + 0.856917i
\(493\) −5.95715 −0.268297
\(494\) 8.97858 16.6430i 0.403965 0.748804i
\(495\) 0 0
\(496\) 11.0790 25.6216i 0.497460 1.15044i
\(497\) 2.74338i 0.123058i
\(498\) −16.6430 8.97858i −0.745791 0.402340i
\(499\) 9.22846i 0.413123i 0.978434 + 0.206561i \(0.0662273\pi\)
−0.978434 + 0.206561i \(0.933773\pi\)
\(500\) 0 0
\(501\) 11.2713i 0.503565i
\(502\) 20.8108 38.5756i 0.928831 1.72171i
\(503\) 14.1004i 0.628705i 0.949306 + 0.314353i \(0.101787\pi\)
−0.949306 + 0.314353i \(0.898213\pi\)
\(504\) 13.2039 1.14637i 0.588149 0.0510632i
\(505\) 0 0
\(506\) −7.66442 4.13481i −0.340725 0.183815i
\(507\) −11.7862 −0.523445
\(508\) −11.1035 + 7.29587i −0.492639 + 0.323702i
\(509\) 43.4011i 1.92372i −0.273544 0.961859i \(-0.588196\pi\)
0.273544 0.961859i \(-0.411804\pi\)
\(510\) 0 0
\(511\) −28.1151 −1.24374
\(512\) 5.81289 + 21.8680i 0.256896 + 0.966439i
\(513\) 2.68585i 0.118583i
\(514\) 14.0575 26.0575i 0.620051 1.14935i
\(515\) 0 0
\(516\) −10.2927 15.6644i −0.453112 0.689588i
\(517\) −16.6712 −0.733196
\(518\) −13.8223 + 25.6216i −0.607319 + 1.12575i
\(519\) 10.7862 0.473463
\(520\) 0 0
\(521\) 10.0000 0.438108 0.219054 0.975713i \(-0.429703\pi\)
0.219054 + 0.975713i \(0.429703\pi\)
\(522\) −1.34292 + 2.48929i −0.0587781 + 0.108953i
\(523\) −13.5725 −0.593482 −0.296741 0.954958i \(-0.595900\pi\)
−0.296741 + 0.954958i \(0.595900\pi\)
\(524\) −11.8322 + 7.77467i −0.516893 + 0.339638i
\(525\) 0 0
\(526\) 12.9399 23.9859i 0.564208 1.04584i
\(527\) 20.7862i 0.905462i
\(528\) 8.41767 + 3.63986i 0.366332 + 0.158405i
\(529\) 15.7862 0.686358
\(530\) 0 0
\(531\) 1.70727i 0.0740892i
\(532\) 13.8223 + 21.0361i 0.599275 + 0.912031i
\(533\) 56.6148 2.45226
\(534\) −4.19656 2.26396i −0.181603 0.0979712i
\(535\) 0 0
\(536\) 0.978577 + 11.2713i 0.0422681 + 0.486846i
\(537\) 3.66442i 0.158132i
\(538\) 16.6142 30.7967i 0.716290 1.32774i
\(539\) 34.2927i 1.47709i
\(540\) 0 0
\(541\) 37.2860i 1.60305i 0.597961 + 0.801525i \(0.295978\pi\)
−0.597961 + 0.801525i \(0.704022\pi\)
\(542\) −34.3074 18.5082i −1.47363 0.794995i
\(543\) 6.62831i 0.284448i
\(544\) −10.4360 13.2285i −0.447438 0.567166i
\(545\) 0 0
\(546\) 15.6644 29.0361i 0.670375 1.24263i
\(547\) −0.200768 −0.00858424 −0.00429212 0.999991i \(-0.501366\pi\)
−0.00429212 + 0.999991i \(0.501366\pi\)
\(548\) 25.0361 16.4507i 1.06949 0.702737i
\(549\) 4.58546i 0.195703i
\(550\) 0 0
\(551\) −5.37169 −0.228842
\(552\) 7.56825 0.657077i 0.322126 0.0279671i
\(553\) 4.78623i 0.203531i
\(554\) −25.2755 13.6357i −1.07385 0.579323i
\(555\) 0 0
\(556\) 7.76060 5.09931i 0.329123 0.216259i
\(557\) 9.21377 0.390400 0.195200 0.980763i \(-0.437464\pi\)
0.195200 + 0.980763i \(0.437464\pi\)
\(558\) 8.68585 + 4.68585i 0.367701 + 0.198368i
\(559\) −46.6577 −1.97341
\(560\) 0 0
\(561\) −6.82908 −0.288324
\(562\) 13.4250 + 7.24254i 0.566300 + 0.305508i
\(563\) 36.7005 1.54674 0.773372 0.633953i \(-0.218569\pi\)
0.773372 + 0.633953i \(0.218569\pi\)
\(564\) 12.1537 7.98592i 0.511764 0.336268i
\(565\) 0 0
\(566\) 24.8929 + 13.4292i 1.04633 + 0.564473i
\(567\) 4.68585i 0.196787i
\(568\) −0.143230 1.64973i −0.00600979 0.0692212i
\(569\) −13.4145 −0.562367 −0.281183 0.959654i \(-0.590727\pi\)
−0.281183 + 0.959654i \(0.590727\pi\)
\(570\) 0 0
\(571\) 18.6858i 0.781978i −0.920395 0.390989i \(-0.872133\pi\)
0.920395 0.390989i \(-0.127867\pi\)
\(572\) 19.0790 12.5363i 0.797731 0.524171i
\(573\) 8.00000 0.334205
\(574\) −35.7795 + 66.3221i −1.49341 + 2.76823i
\(575\) 0 0
\(576\) −7.88030 + 1.37873i −0.328346 + 0.0574471i
\(577\) 2.78623i 0.115992i −0.998317 0.0579961i \(-0.981529\pi\)
0.998317 0.0579961i \(-0.0184711\pi\)
\(578\) −10.1166 5.45769i −0.420794 0.227010i
\(579\) 1.21377i 0.0504425i
\(580\) 0 0
\(581\) 62.6577i 2.59948i
\(582\) 2.65708 4.92525i 0.110139 0.204158i
\(583\) 4.58546i 0.189910i
\(584\) 16.9070 1.46787i 0.699615 0.0607407i
\(585\) 0 0
\(586\) 27.2755 + 14.7146i 1.12674 + 0.607855i
\(587\) −27.3288 −1.12798 −0.563991 0.825781i \(-0.690735\pi\)
−0.563991 + 0.825781i \(0.690735\pi\)
\(588\) 16.4271 + 25.0003i 0.677443 + 1.03100i
\(589\) 18.7434i 0.772308i
\(590\) 0 0
\(591\) 23.9572 0.985466
\(592\) 6.97437 16.1292i 0.286645 0.662904i
\(593\) 6.97858i 0.286576i 0.989681 + 0.143288i \(0.0457675\pi\)
−0.989681 + 0.143288i \(0.954233\pi\)
\(594\) −1.53948 + 2.85363i −0.0631657 + 0.117086i
\(595\) 0 0
\(596\) 3.34292 2.19656i 0.136931 0.0899745i
\(597\) 0.350269 0.0143356
\(598\) 8.97858 16.6430i 0.367161 0.680583i
\(599\) −36.4998 −1.49134 −0.745670 0.666315i \(-0.767870\pi\)
−0.745670 + 0.666315i \(0.767870\pi\)
\(600\) 0 0
\(601\) −15.5725 −0.635214 −0.317607 0.948222i \(-0.602879\pi\)
−0.317607 + 0.948222i \(0.602879\pi\)
\(602\) 29.4868 54.6577i 1.20179 2.22768i
\(603\) −4.00000 −0.162893
\(604\) −9.17092 13.9572i −0.373160 0.567909i
\(605\) 0 0
\(606\) 1.34292 2.48929i 0.0545525 0.101120i
\(607\) 31.2285i 1.26752i −0.773528 0.633762i \(-0.781510\pi\)
0.773528 0.633762i \(-0.218490\pi\)
\(608\) −9.41033 11.9284i −0.381639 0.483760i
\(609\) −9.37169 −0.379760
\(610\) 0 0
\(611\) 36.2008i 1.46453i
\(612\) 4.97858 3.27131i 0.201247 0.132235i
\(613\) 0.978577 0.0395244 0.0197622 0.999805i \(-0.493709\pi\)
0.0197622 + 0.999805i \(0.493709\pi\)
\(614\) 33.0361 + 17.8223i 1.33323 + 0.719251i
\(615\) 0 0
\(616\) 2.62831 + 30.2730i 0.105898 + 1.21973i
\(617\) 32.9357i 1.32594i 0.748645 + 0.662971i \(0.230705\pi\)
−0.748645 + 0.662971i \(0.769295\pi\)
\(618\) −9.83221 + 18.2253i −0.395510 + 0.733130i
\(619\) 3.35700i 0.134929i 0.997722 + 0.0674646i \(0.0214910\pi\)
−0.997722 + 0.0674646i \(0.978509\pi\)
\(620\) 0 0
\(621\) 2.68585i 0.107779i
\(622\) −15.1856 8.19235i −0.608888 0.328483i
\(623\) 15.7992i 0.632983i
\(624\) −7.90383 + 18.2787i −0.316406 + 0.731732i
\(625\) 0 0
\(626\) −10.7146 + 19.8610i −0.428242 + 0.793804i
\(627\) −6.15792 −0.245924
\(628\) 24.5468 + 37.3576i 0.979525 + 1.49073i
\(629\) 13.0852i 0.521742i
\(630\) 0 0
\(631\) −27.7648 −1.10530 −0.552650 0.833414i \(-0.686383\pi\)
−0.552650 + 0.833414i \(0.686383\pi\)
\(632\) 0.249885 + 2.87819i 0.00993990 + 0.114488i
\(633\) 14.1004i 0.560440i
\(634\) −41.7324 22.5138i −1.65741 0.894139i
\(635\) 0 0
\(636\) 2.19656 + 3.34292i 0.0870992 + 0.132556i
\(637\) 74.4653 2.95042
\(638\) −5.70727 3.07896i −0.225953 0.121897i
\(639\) 0.585462 0.0231605
\(640\) 0 0
\(641\) −21.1281 −0.834509 −0.417254 0.908790i \(-0.637008\pi\)
−0.417254 + 0.908790i \(0.637008\pi\)
\(642\) 14.1004 + 7.60688i 0.556498 + 0.300220i
\(643\) 29.2860 1.15493 0.577464 0.816416i \(-0.304043\pi\)
0.577464 + 0.816416i \(0.304043\pi\)
\(644\) 13.8223 + 21.0361i 0.544677 + 0.828939i
\(645\) 0 0
\(646\) 9.95715 + 5.37169i 0.391759 + 0.211346i
\(647\) 15.6728i 0.616163i 0.951360 + 0.308082i \(0.0996870\pi\)
−0.951360 + 0.308082i \(0.900313\pi\)
\(648\) −0.244644 2.81783i −0.00961054 0.110695i
\(649\) 3.91431 0.153650
\(650\) 0 0
\(651\) 32.7005i 1.28164i
\(652\) −1.50650 2.29273i −0.0589991 0.0897903i
\(653\) 17.5296 0.685987 0.342993 0.939338i \(-0.388559\pi\)
0.342993 + 0.939338i \(0.388559\pi\)
\(654\) −6.29273 + 11.6644i −0.246065 + 0.456115i
\(655\) 0 0
\(656\) 18.0533 41.7507i 0.704864 1.63009i
\(657\) 6.00000i 0.234082i
\(658\) 42.4078 + 22.8782i 1.65323 + 0.891885i
\(659\) 23.8652i 0.929656i 0.885401 + 0.464828i \(0.153884\pi\)
−0.885401 + 0.464828i \(0.846116\pi\)
\(660\) 0 0
\(661\) 30.1579i 1.17301i −0.809947 0.586504i \(-0.800504\pi\)
0.809947 0.586504i \(-0.199496\pi\)
\(662\) −13.3331 + 24.7146i −0.518204 + 0.960561i
\(663\) 14.8291i 0.575914i
\(664\) 3.27131 + 37.6791i 0.126951 + 1.46223i
\(665\) 0 0
\(666\) 5.46787 + 2.94981i 0.211875 + 0.114303i
\(667\) −5.37169 −0.207993
\(668\) −18.8396 + 12.3790i −0.728924 + 0.478959i
\(669\) 6.72869i 0.260146i
\(670\) 0 0
\(671\) −10.5132 −0.405859
\(672\) −16.4177 20.8108i −0.633326 0.802794i
\(673\) 18.0000i 0.693849i 0.937893 + 0.346925i \(0.112774\pi\)
−0.937893 + 0.346925i \(0.887226\pi\)
\(674\) 4.81500 8.92525i 0.185467 0.343788i
\(675\) 0 0
\(676\) 12.9446 + 19.7002i 0.497868 + 0.757701i
\(677\) −9.61531 −0.369546 −0.184773 0.982781i \(-0.559155\pi\)
−0.184773 + 0.982781i \(0.559155\pi\)
\(678\) 13.2713 24.6002i 0.509682 0.944763i
\(679\) 18.5426 0.711600
\(680\) 0 0
\(681\) 9.95715 0.381559
\(682\) −10.7434 + 19.9143i −0.411385 + 0.762558i
\(683\) 18.6283 0.712792 0.356396 0.934335i \(-0.384005\pi\)
0.356396 + 0.934335i \(0.384005\pi\)
\(684\) 4.48929 2.94981i 0.171652 0.112789i
\(685\) 0 0
\(686\) −25.0361 + 46.4078i −0.955883 + 1.77186i
\(687\) 11.3288i 0.432222i
\(688\) −14.8782 + 34.4078i −0.567226 + 1.31179i
\(689\) 9.95715 0.379337
\(690\) 0 0
\(691\) 13.4292i 0.510872i −0.966826 0.255436i \(-0.917781\pi\)
0.966826 0.255436i \(-0.0822190\pi\)
\(692\) −11.8463 18.0288i −0.450328 0.685351i
\(693\) −10.7434 −0.408107
\(694\) 0.978577 + 0.527923i 0.0371463 + 0.0200397i
\(695\) 0 0
\(696\) 5.63565 0.489289i 0.213619 0.0185464i
\(697\) 33.8715i 1.28297i
\(698\) −4.13481 + 7.66442i −0.156505 + 0.290103i
\(699\) 18.9786i 0.717836i
\(700\) 0 0
\(701\) 19.1709i 0.724076i 0.932163 + 0.362038i \(0.117919\pi\)
−0.932163 + 0.362038i \(0.882081\pi\)
\(702\) −6.19656 3.34292i −0.233874 0.126171i
\(703\) 11.7992i 0.445016i
\(704\) −3.16106 18.0674i −0.119137 0.680941i
\(705\) 0 0
\(706\) −14.5855 + 27.0361i −0.548931 + 1.01752i
\(707\) 9.37169 0.352459
\(708\) −2.85363 + 1.87506i −0.107246 + 0.0704690i
\(709\) 15.4145i 0.578905i −0.957192 0.289453i \(-0.906527\pi\)
0.957192 0.289453i \(-0.0934732\pi\)
\(710\) 0 0
\(711\) −1.02142 −0.0383063
\(712\) 0.824865 + 9.50085i 0.0309131 + 0.356059i
\(713\) 18.7434i 0.701945i
\(714\) 17.3717 + 9.37169i 0.650119 + 0.350727i
\(715\) 0 0
\(716\) 6.12494 4.02456i 0.228900 0.150405i
\(717\) 2.62831 0.0981559
\(718\) 0.728692 + 0.393115i 0.0271945 + 0.0146709i
\(719\) −20.7862 −0.775196 −0.387598 0.921829i \(-0.626695\pi\)
−0.387598 + 0.921829i \(0.626695\pi\)
\(720\) 0 0
\(721\) −68.6148 −2.55535
\(722\) −14.6697 7.91400i −0.545948 0.294529i
\(723\) −10.7862 −0.401144
\(724\) 11.0790 7.27973i 0.411746 0.270549i
\(725\) 0 0
\(726\) 7.14847 + 3.85646i 0.265305 + 0.143127i
\(727\) 12.3012i 0.456224i 0.973635 + 0.228112i \(0.0732553\pi\)
−0.973635 + 0.228112i \(0.926745\pi\)
\(728\) −65.7367 + 5.70727i −2.43636 + 0.211525i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 27.9143i 1.03245i
\(732\) 7.66442 5.03612i 0.283285 0.186140i
\(733\) −35.9227 −1.32684 −0.663418 0.748249i \(-0.730895\pi\)
−0.663418 + 0.748249i \(0.730895\pi\)
\(734\) −0.325711 + 0.603749i −0.0120222 + 0.0222848i
\(735\) 0 0
\(736\) −9.41033 11.9284i −0.346869 0.439686i
\(737\) 9.17092i 0.337815i
\(738\) 14.1537 + 7.63565i 0.521005 + 0.281072i
\(739\) 29.0277i 1.06780i −0.845547 0.533900i \(-0.820726\pi\)
0.845547 0.533900i \(-0.179274\pi\)
\(740\) 0 0
\(741\) 13.3717i 0.491221i
\(742\) −6.29273 + 11.6644i −0.231013 + 0.428214i
\(743\) 2.60015i 0.0953904i −0.998862 0.0476952i \(-0.984812\pi\)
0.998862 0.0476952i \(-0.0151876\pi\)
\(744\) −1.70727 19.6644i −0.0625915 0.720933i
\(745\) 0 0
\(746\) 15.4250 + 8.32150i 0.564750 + 0.304672i
\(747\) −13.3717 −0.489245
\(748\) 7.50023 + 11.4145i 0.274236 + 0.417357i
\(749\) 53.0852i 1.93969i
\(750\) 0 0
\(751\) −10.8929 −0.397487 −0.198744 0.980052i \(-0.563686\pi\)
−0.198744 + 0.980052i \(0.563686\pi\)
\(752\) −26.6963 11.5437i −0.973515 0.420955i
\(753\) 30.9933i 1.12946i
\(754\) 6.68585 12.3931i 0.243484 0.451331i
\(755\) 0 0
\(756\) 7.83221 5.14637i 0.284855 0.187172i
\(757\) −34.3503 −1.24848 −0.624241 0.781232i \(-0.714592\pi\)
−0.624241 + 0.781232i \(0.714592\pi\)
\(758\) 17.4679 32.3790i 0.634461 1.17606i
\(759\) −6.15792 −0.223518
\(760\) 0 0
\(761\) −19.0852 −0.691839 −0.345920 0.938264i \(-0.612433\pi\)
−0.345920 + 0.938264i \(0.612433\pi\)
\(762\) −4.46052 + 8.26817i −0.161588 + 0.299524i
\(763\) −43.9143 −1.58980
\(764\) −8.78623 13.3717i −0.317875 0.483771i
\(765\) 0 0
\(766\) −4.48929 + 8.32150i −0.162205 + 0.300668i
\(767\) 8.49977i 0.306909i
\(768\) 10.9593 + 11.6574i 0.395458 + 0.420650i
\(769\) −31.8715 −1.14931 −0.574657 0.818394i \(-0.694865\pi\)
−0.574657 + 0.818394i \(0.694865\pi\)
\(770\) 0 0
\(771\) 20.9357i 0.753982i
\(772\) 2.02877 1.33306i 0.0730170 0.0479778i
\(773\) −11.9572 −0.430069 −0.215034 0.976606i \(-0.568986\pi\)
−0.215034 + 0.976606i \(0.568986\pi\)
\(774\) −11.6644 6.29273i −0.419269 0.226188i
\(775\) 0 0
\(776\) −11.1506 + 0.968095i −0.400282 + 0.0347526i
\(777\) 20.5855i 0.738499i
\(778\) −20.0863 + 37.2327i −0.720129 + 1.33486i
\(779\) 30.5426i 1.09430i
\(780\) 0 0
\(781\) 1.34231i 0.0480315i
\(782\) 9.95715 + 5.37169i 0.356067 + 0.192091i
\(783\) 2.00000i 0.0714742i
\(784\) 23.7455 54.9146i 0.848053 1.96124i
\(785\) 0 0
\(786\) −4.75325 + 8.81079i −0.169543 + 0.314270i
\(787\) −33.0852 −1.17936 −0.589681 0.807637i \(-0.700746\pi\)
−0.589681 + 0.807637i \(0.700746\pi\)
\(788\) −26.3116 40.0435i −0.937313 1.42649i
\(789\) 19.2713i 0.686077i
\(790\) 0 0
\(791\) 92.6148 3.29300
\(792\) 6.46052 0.560904i