Properties

Label 570.2.d.c.229.3
Level $570$
Weight $2$
Character 570.229
Analytic conductor $4.551$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Defining polynomial: \(x^{6} - 2 x^{5} + 2 x^{4} + 2 x^{3} + 4 x^{2} - 4 x + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 229.3
Root \(1.45161 + 1.45161i\) of defining polynomial
Character \(\chi\) \(=\) 570.229
Dual form 570.2.d.c.229.6

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(2.21432 + 0.311108i) q^{5} -1.00000 q^{6} +4.42864i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(2.21432 + 0.311108i) q^{5} -1.00000 q^{6} +4.42864i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(0.311108 - 2.21432i) q^{10} +2.62222 q^{11} +1.00000i q^{12} +5.80642i q^{13} +4.42864 q^{14} +(0.311108 - 2.21432i) q^{15} +1.00000 q^{16} +3.80642i q^{17} +1.00000i q^{18} -1.00000 q^{19} +(-2.21432 - 0.311108i) q^{20} +4.42864 q^{21} -2.62222i q^{22} -2.62222i q^{23} +1.00000 q^{24} +(4.80642 + 1.37778i) q^{25} +5.80642 q^{26} +1.00000i q^{27} -4.42864i q^{28} -3.37778 q^{29} +(-2.21432 - 0.311108i) q^{30} -4.42864 q^{31} -1.00000i q^{32} -2.62222i q^{33} +3.80642 q^{34} +(-1.37778 + 9.80642i) q^{35} +1.00000 q^{36} -5.80642i q^{37} +1.00000i q^{38} +5.80642 q^{39} +(-0.311108 + 2.21432i) q^{40} +5.67307 q^{41} -4.42864i q^{42} -10.9906i q^{43} -2.62222 q^{44} +(-2.21432 - 0.311108i) q^{45} -2.62222 q^{46} -2.62222i q^{47} -1.00000i q^{48} -12.6128 q^{49} +(1.37778 - 4.80642i) q^{50} +3.80642 q^{51} -5.80642i q^{52} -6.00000i q^{53} +1.00000 q^{54} +(5.80642 + 0.815792i) q^{55} -4.42864 q^{56} +1.00000i q^{57} +3.37778i q^{58} +1.05086 q^{59} +(-0.311108 + 2.21432i) q^{60} +4.75557 q^{61} +4.42864i q^{62} -4.42864i q^{63} -1.00000 q^{64} +(-1.80642 + 12.8573i) q^{65} -2.62222 q^{66} -15.6128i q^{67} -3.80642i q^{68} -2.62222 q^{69} +(9.80642 + 1.37778i) q^{70} +15.6128 q^{71} -1.00000i q^{72} +11.6128i q^{73} -5.80642 q^{74} +(1.37778 - 4.80642i) q^{75} +1.00000 q^{76} +11.6128i q^{77} -5.80642i q^{78} -4.42864 q^{79} +(2.21432 + 0.311108i) q^{80} +1.00000 q^{81} -5.67307i q^{82} +11.9081i q^{83} -4.42864 q^{84} +(-1.18421 + 8.42864i) q^{85} -10.9906 q^{86} +3.37778i q^{87} +2.62222i q^{88} -12.4286 q^{89} +(-0.311108 + 2.21432i) q^{90} -25.7146 q^{91} +2.62222i q^{92} +4.42864i q^{93} -2.62222 q^{94} +(-2.21432 - 0.311108i) q^{95} -1.00000 q^{96} -7.37778i q^{97} +12.6128i q^{98} -2.62222 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6q^{4} - 6q^{6} - 6q^{9} + O(q^{10}) \) \( 6q - 6q^{4} - 6q^{6} - 6q^{9} + 2q^{10} + 16q^{11} + 2q^{15} + 6q^{16} - 6q^{19} + 6q^{24} + 2q^{25} + 8q^{26} - 20q^{29} - 4q^{34} - 8q^{35} + 6q^{36} + 8q^{39} - 2q^{40} + 8q^{41} - 16q^{44} - 16q^{46} - 22q^{49} + 8q^{50} - 4q^{51} + 6q^{54} + 8q^{55} - 20q^{59} - 2q^{60} + 28q^{61} - 6q^{64} + 16q^{65} - 16q^{66} - 16q^{69} + 32q^{70} + 40q^{71} - 8q^{74} + 8q^{75} + 6q^{76} + 6q^{81} + 20q^{85} - 12q^{86} - 48q^{89} - 2q^{90} - 48q^{91} - 16q^{94} - 6q^{96} - 16q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) 2.21432 + 0.311108i 0.990274 + 0.139132i
\(6\) −1.00000 −0.408248
\(7\) 4.42864i 1.67387i 0.547304 + 0.836934i \(0.315654\pi\)
−0.547304 + 0.836934i \(0.684346\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) 0.311108 2.21432i 0.0983809 0.700229i
\(11\) 2.62222 0.790628 0.395314 0.918546i \(-0.370636\pi\)
0.395314 + 0.918546i \(0.370636\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 5.80642i 1.61041i 0.592995 + 0.805206i \(0.297945\pi\)
−0.592995 + 0.805206i \(0.702055\pi\)
\(14\) 4.42864 1.18360
\(15\) 0.311108 2.21432i 0.0803277 0.571735i
\(16\) 1.00000 0.250000
\(17\) 3.80642i 0.923193i 0.887090 + 0.461597i \(0.152723\pi\)
−0.887090 + 0.461597i \(0.847277\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −1.00000 −0.229416
\(20\) −2.21432 0.311108i −0.495137 0.0695658i
\(21\) 4.42864 0.966408
\(22\) 2.62222i 0.559058i
\(23\) 2.62222i 0.546770i −0.961905 0.273385i \(-0.911857\pi\)
0.961905 0.273385i \(-0.0881433\pi\)
\(24\) 1.00000 0.204124
\(25\) 4.80642 + 1.37778i 0.961285 + 0.275557i
\(26\) 5.80642 1.13873
\(27\) 1.00000i 0.192450i
\(28\) 4.42864i 0.836934i
\(29\) −3.37778 −0.627239 −0.313619 0.949549i \(-0.601542\pi\)
−0.313619 + 0.949549i \(0.601542\pi\)
\(30\) −2.21432 0.311108i −0.404278 0.0568003i
\(31\) −4.42864 −0.795407 −0.397704 0.917514i \(-0.630193\pi\)
−0.397704 + 0.917514i \(0.630193\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.62222i 0.456469i
\(34\) 3.80642 0.652796
\(35\) −1.37778 + 9.80642i −0.232888 + 1.65759i
\(36\) 1.00000 0.166667
\(37\) 5.80642i 0.954570i −0.878749 0.477285i \(-0.841621\pi\)
0.878749 0.477285i \(-0.158379\pi\)
\(38\) 1.00000i 0.162221i
\(39\) 5.80642 0.929772
\(40\) −0.311108 + 2.21432i −0.0491905 + 0.350115i
\(41\) 5.67307 0.885985 0.442992 0.896525i \(-0.353917\pi\)
0.442992 + 0.896525i \(0.353917\pi\)
\(42\) 4.42864i 0.683354i
\(43\) 10.9906i 1.67606i −0.545627 0.838028i \(-0.683709\pi\)
0.545627 0.838028i \(-0.316291\pi\)
\(44\) −2.62222 −0.395314
\(45\) −2.21432 0.311108i −0.330091 0.0463772i
\(46\) −2.62222 −0.386625
\(47\) 2.62222i 0.382489i −0.981542 0.191245i \(-0.938748\pi\)
0.981542 0.191245i \(-0.0612524\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −12.6128 −1.80184
\(50\) 1.37778 4.80642i 0.194848 0.679731i
\(51\) 3.80642 0.533006
\(52\) 5.80642i 0.805206i
\(53\) 6.00000i 0.824163i −0.911147 0.412082i \(-0.864802\pi\)
0.911147 0.412082i \(-0.135198\pi\)
\(54\) 1.00000 0.136083
\(55\) 5.80642 + 0.815792i 0.782938 + 0.110001i
\(56\) −4.42864 −0.591802
\(57\) 1.00000i 0.132453i
\(58\) 3.37778i 0.443525i
\(59\) 1.05086 0.136810 0.0684048 0.997658i \(-0.478209\pi\)
0.0684048 + 0.997658i \(0.478209\pi\)
\(60\) −0.311108 + 2.21432i −0.0401638 + 0.285867i
\(61\) 4.75557 0.608888 0.304444 0.952530i \(-0.401529\pi\)
0.304444 + 0.952530i \(0.401529\pi\)
\(62\) 4.42864i 0.562438i
\(63\) 4.42864i 0.557956i
\(64\) −1.00000 −0.125000
\(65\) −1.80642 + 12.8573i −0.224059 + 1.59475i
\(66\) −2.62222 −0.322772
\(67\) 15.6128i 1.90741i −0.300739 0.953706i \(-0.597233\pi\)
0.300739 0.953706i \(-0.402767\pi\)
\(68\) 3.80642i 0.461597i
\(69\) −2.62222 −0.315678
\(70\) 9.80642 + 1.37778i 1.17209 + 0.164677i
\(71\) 15.6128 1.85290 0.926452 0.376413i \(-0.122843\pi\)
0.926452 + 0.376413i \(0.122843\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 11.6128i 1.35918i 0.733592 + 0.679591i \(0.237843\pi\)
−0.733592 + 0.679591i \(0.762157\pi\)
\(74\) −5.80642 −0.674983
\(75\) 1.37778 4.80642i 0.159093 0.554998i
\(76\) 1.00000 0.114708
\(77\) 11.6128i 1.32341i
\(78\) 5.80642i 0.657448i
\(79\) −4.42864 −0.498261 −0.249130 0.968470i \(-0.580145\pi\)
−0.249130 + 0.968470i \(0.580145\pi\)
\(80\) 2.21432 + 0.311108i 0.247568 + 0.0347829i
\(81\) 1.00000 0.111111
\(82\) 5.67307i 0.626486i
\(83\) 11.9081i 1.30709i 0.756889 + 0.653544i \(0.226718\pi\)
−0.756889 + 0.653544i \(0.773282\pi\)
\(84\) −4.42864 −0.483204
\(85\) −1.18421 + 8.42864i −0.128445 + 0.914214i
\(86\) −10.9906 −1.18515
\(87\) 3.37778i 0.362136i
\(88\) 2.62222i 0.279529i
\(89\) −12.4286 −1.31743 −0.658717 0.752391i \(-0.728900\pi\)
−0.658717 + 0.752391i \(0.728900\pi\)
\(90\) −0.311108 + 2.21432i −0.0327936 + 0.233410i
\(91\) −25.7146 −2.69562
\(92\) 2.62222i 0.273385i
\(93\) 4.42864i 0.459229i
\(94\) −2.62222 −0.270461
\(95\) −2.21432 0.311108i −0.227184 0.0319190i
\(96\) −1.00000 −0.102062
\(97\) 7.37778i 0.749101i −0.927207 0.374550i \(-0.877797\pi\)
0.927207 0.374550i \(-0.122203\pi\)
\(98\) 12.6128i 1.27409i
\(99\) −2.62222 −0.263543
\(100\) −4.80642 1.37778i −0.480642 0.137778i
\(101\) 17.6731 1.75854 0.879268 0.476327i \(-0.158032\pi\)
0.879268 + 0.476327i \(0.158032\pi\)
\(102\) 3.80642i 0.376892i
\(103\) 1.18421i 0.116684i −0.998297 0.0583418i \(-0.981419\pi\)
0.998297 0.0583418i \(-0.0185813\pi\)
\(104\) −5.80642 −0.569367
\(105\) 9.80642 + 1.37778i 0.957009 + 0.134458i
\(106\) −6.00000 −0.582772
\(107\) 4.85728i 0.469571i −0.972047 0.234785i \(-0.924561\pi\)
0.972047 0.234785i \(-0.0754388\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 6.04149 0.578670 0.289335 0.957228i \(-0.406566\pi\)
0.289335 + 0.957228i \(0.406566\pi\)
\(110\) 0.815792 5.80642i 0.0777827 0.553621i
\(111\) −5.80642 −0.551121
\(112\) 4.42864i 0.418467i
\(113\) 9.34614i 0.879211i 0.898191 + 0.439606i \(0.144882\pi\)
−0.898191 + 0.439606i \(0.855118\pi\)
\(114\) 1.00000 0.0936586
\(115\) 0.815792 5.80642i 0.0760730 0.541452i
\(116\) 3.37778 0.313619
\(117\) 5.80642i 0.536804i
\(118\) 1.05086i 0.0967391i
\(119\) −16.8573 −1.54530
\(120\) 2.21432 + 0.311108i 0.202139 + 0.0284001i
\(121\) −4.12399 −0.374908
\(122\) 4.75557i 0.430549i
\(123\) 5.67307i 0.511524i
\(124\) 4.42864 0.397704
\(125\) 10.2143 + 4.54617i 0.913597 + 0.406622i
\(126\) −4.42864 −0.394535
\(127\) 6.42864i 0.570450i −0.958461 0.285225i \(-0.907932\pi\)
0.958461 0.285225i \(-0.0920682\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −10.9906 −0.967671
\(130\) 12.8573 + 1.80642i 1.12766 + 0.158434i
\(131\) −15.0923 −1.31862 −0.659312 0.751869i \(-0.729152\pi\)
−0.659312 + 0.751869i \(0.729152\pi\)
\(132\) 2.62222i 0.228235i
\(133\) 4.42864i 0.384012i
\(134\) −15.6128 −1.34874
\(135\) −0.311108 + 2.21432i −0.0267759 + 0.190578i
\(136\) −3.80642 −0.326398
\(137\) 7.53972i 0.644162i 0.946712 + 0.322081i \(0.104382\pi\)
−0.946712 + 0.322081i \(0.895618\pi\)
\(138\) 2.62222i 0.223218i
\(139\) −0.387152 −0.0328378 −0.0164189 0.999865i \(-0.505227\pi\)
−0.0164189 + 0.999865i \(0.505227\pi\)
\(140\) 1.37778 9.80642i 0.116444 0.828794i
\(141\) −2.62222 −0.220830
\(142\) 15.6128i 1.31020i
\(143\) 15.2257i 1.27324i
\(144\) −1.00000 −0.0833333
\(145\) −7.47949 1.05086i −0.621138 0.0872688i
\(146\) 11.6128 0.961086
\(147\) 12.6128i 1.04029i
\(148\) 5.80642i 0.477285i
\(149\) 14.5303 1.19037 0.595186 0.803588i \(-0.297078\pi\)
0.595186 + 0.803588i \(0.297078\pi\)
\(150\) −4.80642 1.37778i −0.392443 0.112496i
\(151\) 4.69535 0.382102 0.191051 0.981580i \(-0.438810\pi\)
0.191051 + 0.981580i \(0.438810\pi\)
\(152\) 1.00000i 0.0811107i
\(153\) 3.80642i 0.307731i
\(154\) 11.6128 0.935790
\(155\) −9.80642 1.37778i −0.787671 0.110666i
\(156\) −5.80642 −0.464886
\(157\) 21.5210i 1.71756i 0.512343 + 0.858781i \(0.328778\pi\)
−0.512343 + 0.858781i \(0.671222\pi\)
\(158\) 4.42864i 0.352324i
\(159\) −6.00000 −0.475831
\(160\) 0.311108 2.21432i 0.0245952 0.175057i
\(161\) 11.6128 0.915221
\(162\) 1.00000i 0.0785674i
\(163\) 8.23506i 0.645020i −0.946566 0.322510i \(-0.895473\pi\)
0.946566 0.322510i \(-0.104527\pi\)
\(164\) −5.67307 −0.442992
\(165\) 0.815792 5.80642i 0.0635093 0.452029i
\(166\) 11.9081 0.924250
\(167\) 8.47013i 0.655438i −0.944775 0.327719i \(-0.893720\pi\)
0.944775 0.327719i \(-0.106280\pi\)
\(168\) 4.42864i 0.341677i
\(169\) −20.7146 −1.59343
\(170\) 8.42864 + 1.18421i 0.646447 + 0.0908246i
\(171\) 1.00000 0.0764719
\(172\) 10.9906i 0.838028i
\(173\) 22.4701i 1.70837i −0.519967 0.854186i \(-0.674056\pi\)
0.519967 0.854186i \(-0.325944\pi\)
\(174\) 3.37778 0.256069
\(175\) −6.10171 + 21.2859i −0.461246 + 1.60906i
\(176\) 2.62222 0.197657
\(177\) 1.05086i 0.0789871i
\(178\) 12.4286i 0.931566i
\(179\) 2.94914 0.220429 0.110215 0.993908i \(-0.464846\pi\)
0.110215 + 0.993908i \(0.464846\pi\)
\(180\) 2.21432 + 0.311108i 0.165046 + 0.0231886i
\(181\) 22.8988 1.70205 0.851026 0.525124i \(-0.175981\pi\)
0.851026 + 0.525124i \(0.175981\pi\)
\(182\) 25.7146i 1.90609i
\(183\) 4.75557i 0.351542i
\(184\) 2.62222 0.193312
\(185\) 1.80642 12.8573i 0.132811 0.945286i
\(186\) 4.42864 0.324724
\(187\) 9.98126i 0.729902i
\(188\) 2.62222i 0.191245i
\(189\) −4.42864 −0.322136
\(190\) −0.311108 + 2.21432i −0.0225701 + 0.160644i
\(191\) −9.05086 −0.654897 −0.327448 0.944869i \(-0.606189\pi\)
−0.327448 + 0.944869i \(0.606189\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 18.7239i 1.34778i 0.738833 + 0.673889i \(0.235377\pi\)
−0.738833 + 0.673889i \(0.764623\pi\)
\(194\) −7.37778 −0.529694
\(195\) 12.8573 + 1.80642i 0.920729 + 0.129361i
\(196\) 12.6128 0.900918
\(197\) 0.888922i 0.0633331i −0.999498 0.0316665i \(-0.989919\pi\)
0.999498 0.0316665i \(-0.0100815\pi\)
\(198\) 2.62222i 0.186353i
\(199\) −21.7146 −1.53930 −0.769652 0.638464i \(-0.779570\pi\)
−0.769652 + 0.638464i \(0.779570\pi\)
\(200\) −1.37778 + 4.80642i −0.0974241 + 0.339865i
\(201\) −15.6128 −1.10125
\(202\) 17.6731i 1.24347i
\(203\) 14.9590i 1.04992i
\(204\) −3.80642 −0.266503
\(205\) 12.5620 + 1.76494i 0.877368 + 0.123269i
\(206\) −1.18421 −0.0825077
\(207\) 2.62222i 0.182257i
\(208\) 5.80642i 0.402603i
\(209\) −2.62222 −0.181382
\(210\) 1.37778 9.80642i 0.0950762 0.676708i
\(211\) −3.61285 −0.248719 −0.124359 0.992237i \(-0.539688\pi\)
−0.124359 + 0.992237i \(0.539688\pi\)
\(212\) 6.00000i 0.412082i
\(213\) 15.6128i 1.06977i
\(214\) −4.85728 −0.332037
\(215\) 3.41927 24.3368i 0.233192 1.65975i
\(216\) −1.00000 −0.0680414
\(217\) 19.6128i 1.33141i
\(218\) 6.04149i 0.409181i
\(219\) 11.6128 0.784724
\(220\) −5.80642 0.815792i −0.391469 0.0550007i
\(221\) −22.1017 −1.48672
\(222\) 5.80642i 0.389702i
\(223\) 21.3876i 1.43222i −0.697987 0.716111i \(-0.745921\pi\)
0.697987 0.716111i \(-0.254079\pi\)
\(224\) 4.42864 0.295901
\(225\) −4.80642 1.37778i −0.320428 0.0918523i
\(226\) 9.34614 0.621696
\(227\) 8.47013i 0.562182i −0.959681 0.281091i \(-0.909304\pi\)
0.959681 0.281091i \(-0.0906963\pi\)
\(228\) 1.00000i 0.0662266i
\(229\) 16.9590 1.12068 0.560341 0.828262i \(-0.310670\pi\)
0.560341 + 0.828262i \(0.310670\pi\)
\(230\) −5.80642 0.815792i −0.382864 0.0537917i
\(231\) 11.6128 0.764069
\(232\) 3.37778i 0.221762i
\(233\) 17.9081i 1.17320i −0.809876 0.586600i \(-0.800466\pi\)
0.809876 0.586600i \(-0.199534\pi\)
\(234\) −5.80642 −0.379578
\(235\) 0.815792 5.80642i 0.0532164 0.378769i
\(236\) −1.05086 −0.0684048
\(237\) 4.42864i 0.287671i
\(238\) 16.8573i 1.09270i
\(239\) 28.2766 1.82906 0.914529 0.404520i \(-0.132562\pi\)
0.914529 + 0.404520i \(0.132562\pi\)
\(240\) 0.311108 2.21432i 0.0200819 0.142934i
\(241\) −11.5111 −0.741498 −0.370749 0.928733i \(-0.620899\pi\)
−0.370749 + 0.928733i \(0.620899\pi\)
\(242\) 4.12399i 0.265100i
\(243\) 1.00000i 0.0641500i
\(244\) −4.75557 −0.304444
\(245\) −27.9289 3.92396i −1.78431 0.250692i
\(246\) −5.67307 −0.361702
\(247\) 5.80642i 0.369454i
\(248\) 4.42864i 0.281219i
\(249\) 11.9081 0.754647
\(250\) 4.54617 10.2143i 0.287525 0.646010i
\(251\) −7.74620 −0.488936 −0.244468 0.969657i \(-0.578613\pi\)
−0.244468 + 0.969657i \(0.578613\pi\)
\(252\) 4.42864i 0.278978i
\(253\) 6.87601i 0.432291i
\(254\) −6.42864 −0.403369
\(255\) 8.42864 + 1.18421i 0.527822 + 0.0741580i
\(256\) 1.00000 0.0625000
\(257\) 13.8796i 0.865783i 0.901446 + 0.432891i \(0.142507\pi\)
−0.901446 + 0.432891i \(0.857493\pi\)
\(258\) 10.9906i 0.684247i
\(259\) 25.7146 1.59782
\(260\) 1.80642 12.8573i 0.112030 0.797375i
\(261\) 3.37778 0.209080
\(262\) 15.0923i 0.932408i
\(263\) 18.6222i 1.14830i −0.818752 0.574148i \(-0.805334\pi\)
0.818752 0.574148i \(-0.194666\pi\)
\(264\) 2.62222 0.161386
\(265\) 1.86665 13.2859i 0.114667 0.816147i
\(266\) −4.42864 −0.271537
\(267\) 12.4286i 0.760620i
\(268\) 15.6128i 0.953706i
\(269\) −15.8479 −0.966264 −0.483132 0.875547i \(-0.660501\pi\)
−0.483132 + 0.875547i \(0.660501\pi\)
\(270\) 2.21432 + 0.311108i 0.134759 + 0.0189334i
\(271\) 1.51114 0.0917951 0.0458975 0.998946i \(-0.485385\pi\)
0.0458975 + 0.998946i \(0.485385\pi\)
\(272\) 3.80642i 0.230798i
\(273\) 25.7146i 1.55632i
\(274\) 7.53972 0.455491
\(275\) 12.6035 + 3.61285i 0.760018 + 0.217863i
\(276\) 2.62222 0.157839
\(277\) 1.05086i 0.0631398i −0.999502 0.0315699i \(-0.989949\pi\)
0.999502 0.0315699i \(-0.0100507\pi\)
\(278\) 0.387152i 0.0232199i
\(279\) 4.42864 0.265136
\(280\) −9.80642 1.37778i −0.586046 0.0823384i
\(281\) 3.45091 0.205864 0.102932 0.994688i \(-0.467178\pi\)
0.102932 + 0.994688i \(0.467178\pi\)
\(282\) 2.62222i 0.156151i
\(283\) 15.5812i 0.926206i 0.886304 + 0.463103i \(0.153264\pi\)
−0.886304 + 0.463103i \(0.846736\pi\)
\(284\) −15.6128 −0.926452
\(285\) −0.311108 + 2.21432i −0.0184284 + 0.131165i
\(286\) 15.2257 0.900314
\(287\) 25.1240i 1.48302i
\(288\) 1.00000i 0.0589256i
\(289\) 2.51114 0.147714
\(290\) −1.05086 + 7.47949i −0.0617083 + 0.439211i
\(291\) −7.37778 −0.432493
\(292\) 11.6128i 0.679591i
\(293\) 7.12399i 0.416188i 0.978109 + 0.208094i \(0.0667259\pi\)
−0.978109 + 0.208094i \(0.933274\pi\)
\(294\) 12.6128 0.735596
\(295\) 2.32693 + 0.326929i 0.135479 + 0.0190346i
\(296\) 5.80642 0.337492
\(297\) 2.62222i 0.152156i
\(298\) 14.5303i 0.841721i
\(299\) 15.2257 0.880525
\(300\) −1.37778 + 4.80642i −0.0795464 + 0.277499i
\(301\) 48.6735 2.80550
\(302\) 4.69535i 0.270187i
\(303\) 17.6731i 1.01529i
\(304\) −1.00000 −0.0573539
\(305\) 10.5303 + 1.47949i 0.602966 + 0.0847156i
\(306\) −3.80642 −0.217599
\(307\) 1.12399i 0.0641492i −0.999485 0.0320746i \(-0.989789\pi\)
0.999485 0.0320746i \(-0.0102114\pi\)
\(308\) 11.6128i 0.661703i
\(309\) −1.18421 −0.0673673
\(310\) −1.37778 + 9.80642i −0.0782529 + 0.556967i
\(311\) 14.9491 0.847688 0.423844 0.905735i \(-0.360680\pi\)
0.423844 + 0.905735i \(0.360680\pi\)
\(312\) 5.80642i 0.328724i
\(313\) 3.14272i 0.177637i 0.996048 + 0.0888185i \(0.0283091\pi\)
−0.996048 + 0.0888185i \(0.971691\pi\)
\(314\) 21.5210 1.21450
\(315\) 1.37778 9.80642i 0.0776294 0.552529i
\(316\) 4.42864 0.249130
\(317\) 10.5906i 0.594826i −0.954749 0.297413i \(-0.903876\pi\)
0.954749 0.297413i \(-0.0961238\pi\)
\(318\) 6.00000i 0.336463i
\(319\) −8.85728 −0.495912
\(320\) −2.21432 0.311108i −0.123784 0.0173915i
\(321\) −4.85728 −0.271107
\(322\) 11.6128i 0.647159i
\(323\) 3.80642i 0.211795i
\(324\) −1.00000 −0.0555556
\(325\) −8.00000 + 27.9081i −0.443760 + 1.54806i
\(326\) −8.23506 −0.456098
\(327\) 6.04149i 0.334095i
\(328\) 5.67307i 0.313243i
\(329\) 11.6128 0.640237
\(330\) −5.80642 0.815792i −0.319633 0.0449079i
\(331\) −15.1427 −0.832319 −0.416160 0.909292i \(-0.636624\pi\)
−0.416160 + 0.909292i \(0.636624\pi\)
\(332\) 11.9081i 0.653544i
\(333\) 5.80642i 0.318190i
\(334\) −8.47013 −0.463465
\(335\) 4.85728 34.5718i 0.265381 1.88886i
\(336\) 4.42864 0.241602
\(337\) 11.1111i 0.605259i −0.953108 0.302629i \(-0.902136\pi\)
0.953108 0.302629i \(-0.0978645\pi\)
\(338\) 20.7146i 1.12672i
\(339\) 9.34614 0.507613
\(340\) 1.18421 8.42864i 0.0642227 0.457107i
\(341\) −11.6128 −0.628871
\(342\) 1.00000i 0.0540738i
\(343\) 24.8573i 1.34217i
\(344\) 10.9906 0.592575
\(345\) −5.80642 0.815792i −0.312607 0.0439208i
\(346\) −22.4701 −1.20800
\(347\) 14.1936i 0.761951i 0.924585 + 0.380976i \(0.124412\pi\)
−0.924585 + 0.380976i \(0.875588\pi\)
\(348\) 3.37778i 0.181068i
\(349\) −32.3684 −1.73264 −0.866321 0.499488i \(-0.833521\pi\)
−0.866321 + 0.499488i \(0.833521\pi\)
\(350\) 21.2859 + 6.10171i 1.13778 + 0.326150i
\(351\) −5.80642 −0.309924
\(352\) 2.62222i 0.139765i
\(353\) 11.8064i 0.628393i −0.949358 0.314196i \(-0.898265\pi\)
0.949358 0.314196i \(-0.101735\pi\)
\(354\) −1.05086 −0.0558523
\(355\) 34.5718 + 4.85728i 1.83488 + 0.257798i
\(356\) 12.4286 0.658717
\(357\) 16.8573i 0.892182i
\(358\) 2.94914i 0.155867i
\(359\) 10.8287 0.571517 0.285758 0.958302i \(-0.407755\pi\)
0.285758 + 0.958302i \(0.407755\pi\)
\(360\) 0.311108 2.21432i 0.0163968 0.116705i
\(361\) 1.00000 0.0526316
\(362\) 22.8988i 1.20353i
\(363\) 4.12399i 0.216453i
\(364\) 25.7146 1.34781
\(365\) −3.61285 + 25.7146i −0.189105 + 1.34596i
\(366\) −4.75557 −0.248578
\(367\) 1.46965i 0.0767151i 0.999264 + 0.0383576i \(0.0122126\pi\)
−0.999264 + 0.0383576i \(0.987787\pi\)
\(368\) 2.62222i 0.136692i
\(369\) −5.67307 −0.295328
\(370\) −12.8573 1.80642i −0.668418 0.0939115i
\(371\) 26.5718 1.37954
\(372\) 4.42864i 0.229614i
\(373\) 24.3783i 1.26226i 0.775678 + 0.631129i \(0.217408\pi\)
−0.775678 + 0.631129i \(0.782592\pi\)
\(374\) 9.98126 0.516119
\(375\) 4.54617 10.2143i 0.234763 0.527465i
\(376\) 2.62222 0.135230
\(377\) 19.6128i 1.01011i
\(378\) 4.42864i 0.227785i
\(379\) −18.9590 −0.973858 −0.486929 0.873442i \(-0.661883\pi\)
−0.486929 + 0.873442i \(0.661883\pi\)
\(380\) 2.21432 + 0.311108i 0.113592 + 0.0159595i
\(381\) −6.42864 −0.329349
\(382\) 9.05086i 0.463082i
\(383\) 26.1017i 1.33374i −0.745176 0.666868i \(-0.767635\pi\)
0.745176 0.666868i \(-0.232365\pi\)
\(384\) 1.00000 0.0510310
\(385\) −3.61285 + 25.7146i −0.184128 + 1.31054i
\(386\) 18.7239 0.953023
\(387\) 10.9906i 0.558685i
\(388\) 7.37778i 0.374550i
\(389\) 3.57136 0.181075 0.0905376 0.995893i \(-0.471141\pi\)
0.0905376 + 0.995893i \(0.471141\pi\)
\(390\) 1.80642 12.8573i 0.0914718 0.651054i
\(391\) 9.98126 0.504774
\(392\) 12.6128i 0.637045i
\(393\) 15.0923i 0.761308i
\(394\) −0.888922 −0.0447832
\(395\) −9.80642 1.37778i −0.493415 0.0693239i
\(396\) 2.62222 0.131771
\(397\) 31.4193i 1.57689i −0.615107 0.788444i \(-0.710887\pi\)
0.615107 0.788444i \(-0.289113\pi\)
\(398\) 21.7146i 1.08845i
\(399\) −4.42864 −0.221709
\(400\) 4.80642 + 1.37778i 0.240321 + 0.0688892i
\(401\) 12.0415 0.601323 0.300662 0.953731i \(-0.402793\pi\)
0.300662 + 0.953731i \(0.402793\pi\)
\(402\) 15.6128i 0.778698i
\(403\) 25.7146i 1.28093i
\(404\) −17.6731 −0.879268
\(405\) 2.21432 + 0.311108i 0.110030 + 0.0154591i
\(406\) −14.9590 −0.742402
\(407\) 15.2257i 0.754710i
\(408\) 3.80642i 0.188446i
\(409\) −26.4701 −1.30886 −0.654432 0.756121i \(-0.727092\pi\)
−0.654432 + 0.756121i \(0.727092\pi\)
\(410\) 1.76494 12.5620i 0.0871640 0.620393i
\(411\) 7.53972 0.371907
\(412\) 1.18421i 0.0583418i
\(413\) 4.65386i 0.229001i
\(414\) 2.62222 0.128875
\(415\) −3.70471 + 26.3684i −0.181857 + 1.29437i
\(416\) 5.80642 0.284683
\(417\) 0.387152i 0.0189589i
\(418\) 2.62222i 0.128257i
\(419\) 25.9684 1.26864 0.634319 0.773072i \(-0.281281\pi\)
0.634319 + 0.773072i \(0.281281\pi\)
\(420\) −9.80642 1.37778i −0.478504 0.0672290i
\(421\) −29.2672 −1.42640 −0.713198 0.700963i \(-0.752754\pi\)
−0.713198 + 0.700963i \(0.752754\pi\)
\(422\) 3.61285i 0.175871i
\(423\) 2.62222i 0.127496i
\(424\) 6.00000 0.291386
\(425\) −5.24443 + 18.2953i −0.254392 + 0.887452i
\(426\) −15.6128 −0.756445
\(427\) 21.0607i 1.01920i
\(428\) 4.85728i 0.234785i
\(429\) 15.2257 0.735104
\(430\) −24.3368 3.41927i −1.17362 0.164892i
\(431\) 14.8385 0.714747 0.357374 0.933961i \(-0.383672\pi\)
0.357374 + 0.933961i \(0.383672\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 5.27607i 0.253552i −0.991931 0.126776i \(-0.959537\pi\)
0.991931 0.126776i \(-0.0404629\pi\)
\(434\) −19.6128 −0.941447
\(435\) −1.05086 + 7.47949i −0.0503846 + 0.358614i
\(436\) −6.04149 −0.289335
\(437\) 2.62222i 0.125438i
\(438\) 11.6128i 0.554883i
\(439\) −31.8578 −1.52049 −0.760244 0.649638i \(-0.774921\pi\)
−0.760244 + 0.649638i \(0.774921\pi\)
\(440\) −0.815792 + 5.80642i −0.0388913 + 0.276810i
\(441\) 12.6128 0.600612
\(442\) 22.1017i 1.05127i
\(443\) 4.94914i 0.235141i −0.993065 0.117570i \(-0.962489\pi\)
0.993065 0.117570i \(-0.0375106\pi\)
\(444\) 5.80642 0.275561
\(445\) −27.5210 3.86665i −1.30462 0.183297i
\(446\) −21.3876 −1.01273
\(447\) 14.5303i 0.687262i
\(448\) 4.42864i 0.209234i
\(449\) −9.75605 −0.460416 −0.230208 0.973141i \(-0.573941\pi\)
−0.230208 + 0.973141i \(0.573941\pi\)
\(450\) −1.37778 + 4.80642i −0.0649494 + 0.226577i
\(451\) 14.8760 0.700484
\(452\) 9.34614i 0.439606i
\(453\) 4.69535i 0.220607i
\(454\) −8.47013 −0.397523
\(455\) −56.9403 8.00000i −2.66940 0.375046i
\(456\) −1.00000 −0.0468293
\(457\) 8.00000i 0.374224i −0.982339 0.187112i \(-0.940087\pi\)
0.982339 0.187112i \(-0.0599128\pi\)
\(458\) 16.9590i 0.792442i
\(459\) −3.80642 −0.177669
\(460\) −0.815792 + 5.80642i −0.0380365 + 0.270726i
\(461\) −36.1245 −1.68248 −0.841242 0.540659i \(-0.818175\pi\)
−0.841242 + 0.540659i \(0.818175\pi\)
\(462\) 11.6128i 0.540279i
\(463\) 35.1209i 1.63221i 0.577905 + 0.816104i \(0.303870\pi\)
−0.577905 + 0.816104i \(0.696130\pi\)
\(464\) −3.37778 −0.156810
\(465\) −1.37778 + 9.80642i −0.0638932 + 0.454762i
\(466\) −17.9081 −0.829578
\(467\) 4.56199i 0.211104i 0.994414 + 0.105552i \(0.0336609\pi\)
−0.994414 + 0.105552i \(0.966339\pi\)
\(468\) 5.80642i 0.268402i
\(469\) 69.1437 3.19276
\(470\) −5.80642 0.815792i −0.267830 0.0376297i
\(471\) 21.5210 0.991634
\(472\) 1.05086i 0.0483695i
\(473\) 28.8198i 1.32514i
\(474\) 4.42864 0.203414
\(475\) −4.80642 1.37778i −0.220534 0.0632171i
\(476\) 16.8573 0.772652
\(477\) 6.00000i 0.274721i
\(478\) 28.2766i 1.29334i
\(479\) −37.4005 −1.70887 −0.854437 0.519555i \(-0.826098\pi\)
−0.854437 + 0.519555i \(0.826098\pi\)
\(480\) −2.21432 0.311108i −0.101069 0.0142001i
\(481\) 33.7146 1.53725
\(482\) 11.5111i 0.524318i
\(483\) 11.6128i 0.528403i
\(484\) 4.12399 0.187454
\(485\) 2.29529 16.3368i 0.104224 0.741815i
\(486\) −1.00000 −0.0453609
\(487\) 20.9175i 0.947862i 0.880562 + 0.473931i \(0.157165\pi\)
−0.880562 + 0.473931i \(0.842835\pi\)
\(488\) 4.75557i 0.215274i
\(489\) −8.23506 −0.372402
\(490\) −3.92396 + 27.9289i −0.177266 + 1.26170i
\(491\) −15.8666 −0.716052 −0.358026 0.933712i \(-0.616550\pi\)
−0.358026 + 0.933712i \(0.616550\pi\)
\(492\) 5.67307i 0.255762i
\(493\) 12.8573i 0.579063i
\(494\) −5.80642 −0.261243
\(495\) −5.80642 0.815792i −0.260979 0.0366671i
\(496\) −4.42864 −0.198852
\(497\) 69.1437i 3.10152i
\(498\) 11.9081i 0.533616i
\(499\) −16.7368 −0.749244 −0.374622 0.927178i \(-0.622227\pi\)
−0.374622 + 0.927178i \(0.622227\pi\)
\(500\) −10.2143 4.54617i −0.456798 0.203311i
\(501\) −8.47013 −0.378417
\(502\) 7.74620i 0.345730i
\(503\) 21.9684i 0.979521i 0.871857 + 0.489760i \(0.162916\pi\)
−0.871857 + 0.489760i \(0.837084\pi\)
\(504\) 4.42864 0.197267
\(505\) 39.1338 + 5.49823i 1.74143 + 0.244668i
\(506\) −6.87601 −0.305676
\(507\) 20.7146i 0.919966i
\(508\) 6.42864i 0.285225i
\(509\) 15.2573 0.676270 0.338135 0.941098i \(-0.390204\pi\)
0.338135 + 0.941098i \(0.390204\pi\)
\(510\) 1.18421 8.42864i 0.0524376 0.373226i
\(511\) −51.4291 −2.27509
\(512\) 1.00000i 0.0441942i
\(513\) 1.00000i 0.0441511i
\(514\) 13.8796 0.612201
\(515\) 0.368416 2.62222i 0.0162344 0.115549i
\(516\) 10.9906 0.483836
\(517\) 6.87601i 0.302407i
\(518\) 25.7146i 1.12983i
\(519\) −22.4701 −0.986329
\(520\) −12.8573 1.80642i −0.563829 0.0792169i
\(521\) −18.3269 −0.802917 −0.401459 0.915877i \(-0.631497\pi\)
−0.401459 + 0.915877i \(0.631497\pi\)
\(522\) 3.37778i 0.147842i
\(523\) 24.8573i 1.08693i 0.839431 + 0.543466i \(0.182888\pi\)
−0.839431 + 0.543466i \(0.817112\pi\)
\(524\) 15.0923 0.659312
\(525\) 21.2859 + 6.10171i 0.928994 + 0.266300i
\(526\) −18.6222 −0.811967
\(527\) 16.8573i 0.734315i
\(528\) 2.62222i 0.114117i
\(529\) 16.1240 0.701043
\(530\) −13.2859 1.86665i −0.577103 0.0810820i
\(531\) −1.05086 −0.0456032
\(532\) 4.42864i 0.192006i
\(533\) 32.9403i 1.42680i
\(534\) 12.4286 0.537840
\(535\) 1.51114 10.7556i 0.0653322 0.465004i
\(536\) 15.6128 0.674372
\(537\) 2.94914i 0.127265i
\(538\) 15.8479i 0.683252i
\(539\) −33.0736 −1.42458
\(540\) 0.311108 2.21432i 0.0133879 0.0952891i
\(541\) −1.34614 −0.0578751 −0.0289376 0.999581i \(-0.509212\pi\)
−0.0289376 + 0.999581i \(0.509212\pi\)
\(542\) 1.51114i 0.0649089i
\(543\) 22.8988i 0.982680i
\(544\) 3.80642 0.163199
\(545\) 13.3778 + 1.87955i 0.573041 + 0.0805112i
\(546\) 25.7146 1.10048
\(547\) 8.59057i 0.367306i 0.982991 + 0.183653i \(0.0587923\pi\)
−0.982991 + 0.183653i \(0.941208\pi\)
\(548\) 7.53972i 0.322081i
\(549\) −4.75557 −0.202963
\(550\) 3.61285 12.6035i 0.154052 0.537414i
\(551\) 3.37778 0.143898
\(552\) 2.62222i 0.111609i
\(553\) 19.6128i 0.834023i
\(554\) −1.05086 −0.0446466
\(555\) −12.8573 1.80642i −0.545761 0.0766784i
\(556\) 0.387152 0.0164189
\(557\) 5.86665i 0.248578i 0.992246 + 0.124289i \(0.0396650\pi\)
−0.992246 + 0.124289i \(0.960335\pi\)
\(558\) 4.42864i 0.187479i
\(559\) 63.8163 2.69914
\(560\) −1.37778 + 9.80642i −0.0582220 + 0.414397i
\(561\) 9.98126 0.421409
\(562\) 3.45091i 0.145568i
\(563\) 31.4291i 1.32458i 0.749248 + 0.662290i \(0.230415\pi\)
−0.749248 + 0.662290i \(0.769585\pi\)
\(564\) 2.62222 0.110415
\(565\) −2.90766 + 20.6953i −0.122326 + 0.870660i
\(566\) 15.5812 0.654927
\(567\) 4.42864i 0.185985i
\(568\) 15.6128i 0.655101i
\(569\) 7.95851 0.333638 0.166819 0.985988i \(-0.446650\pi\)
0.166819 + 0.985988i \(0.446650\pi\)
\(570\) 2.21432 + 0.311108i 0.0927476 + 0.0130309i
\(571\) −30.8385 −1.29055 −0.645276 0.763949i \(-0.723258\pi\)
−0.645276 + 0.763949i \(0.723258\pi\)
\(572\) 15.2257i 0.636618i
\(573\) 9.05086i 0.378105i
\(574\) 25.1240 1.04865
\(575\) 3.61285 12.6035i 0.150666 0.525601i
\(576\) 1.00000 0.0416667
\(577\) 32.0000i 1.33218i −0.745873 0.666089i \(-0.767967\pi\)
0.745873 0.666089i \(-0.232033\pi\)
\(578\) 2.51114i 0.104450i
\(579\) 18.7239 0.778140
\(580\) 7.47949 + 1.05086i 0.310569 + 0.0436344i
\(581\) −52.7368 −2.18789
\(582\) 7.37778i 0.305819i
\(583\) 15.7333i 0.651606i
\(584\) −11.6128 −0.480543
\(585\) 1.80642 12.8573i 0.0746864 0.531583i
\(586\) 7.12399 0.294289
\(587\) 17.8064i 0.734950i −0.930033 0.367475i \(-0.880222\pi\)
0.930033 0.367475i \(-0.119778\pi\)
\(588\) 12.6128i 0.520145i
\(589\) 4.42864 0.182479
\(590\) 0.326929 2.32693i 0.0134595 0.0957982i
\(591\) −0.888922 −0.0365654
\(592\) 5.80642i 0.238643i
\(593\) 13.3176i 0.546887i −0.961888 0.273443i \(-0.911837\pi\)
0.961888 0.273443i \(-0.0881626\pi\)
\(594\) 2.62222 0.107591
\(595\) −37.3274 5.24443i −1.53027 0.215001i
\(596\) −14.5303 −0.595186
\(597\) 21.7146i 0.888718i
\(598\) 15.2257i 0.622625i
\(599\) 43.8163 1.79028 0.895142 0.445781i \(-0.147074\pi\)
0.895142 + 0.445781i \(0.147074\pi\)
\(600\) 4.80642 + 1.37778i 0.196221 + 0.0562478i
\(601\) −9.73329 −0.397029 −0.198515 0.980098i \(-0.563612\pi\)
−0.198515 + 0.980098i \(0.563612\pi\)
\(602\) 48.6735i 1.98379i
\(603\) 15.6128i 0.635804i
\(604\) −4.69535 −0.191051
\(605\) −9.13182 1.28300i −0.371261 0.0521615i
\(606\) −17.6731 −0.717919
\(607\) 31.9398i 1.29640i 0.761472 + 0.648198i \(0.224477\pi\)
−0.761472 + 0.648198i \(0.775523\pi\)
\(608\) 1.00000i 0.0405554i
\(609\) −14.9590 −0.606169
\(610\) 1.47949 10.5303i 0.0599030 0.426361i
\(611\) 15.2257 0.615966
\(612\) 3.80642i 0.153866i
\(613\) 11.8064i 0.476857i 0.971160 + 0.238428i \(0.0766323\pi\)
−0.971160 + 0.238428i \(0.923368\pi\)
\(614\) −1.12399 −0.0453603
\(615\) 1.76494 12.5620i 0.0711691 0.506548i
\(616\) −11.6128 −0.467895
\(617\) 26.5620i 1.06935i −0.845059 0.534673i \(-0.820435\pi\)
0.845059 0.534673i \(-0.179565\pi\)
\(618\) 1.18421i 0.0476358i
\(619\) −7.34614 −0.295266 −0.147633 0.989042i \(-0.547166\pi\)
−0.147633 + 0.989042i \(0.547166\pi\)
\(620\) 9.80642 + 1.37778i 0.393835 + 0.0553332i
\(621\) 2.62222 0.105226
\(622\) 14.9491i 0.599406i
\(623\) 55.0420i 2.20521i
\(624\) 5.80642 0.232443
\(625\) 21.2034 + 13.2444i 0.848137 + 0.529777i
\(626\) 3.14272 0.125608
\(627\) 2.62222i 0.104721i
\(628\) 21.5210i 0.858781i
\(629\) 22.1017 0.881253
\(630\) −9.80642 1.37778i −0.390697 0.0548922i
\(631\) −30.7556 −1.22436 −0.612180 0.790718i \(-0.709707\pi\)
−0.612180 + 0.790718i \(0.709707\pi\)
\(632\) 4.42864i 0.176162i
\(633\) 3.61285i 0.143598i
\(634\) −10.5906 −0.420605
\(635\) 2.00000 14.2351i 0.0793676 0.564901i
\(636\) 6.00000 0.237915
\(637\) 73.2355i 2.90170i
\(638\) 8.85728i 0.350663i
\(639\) −15.6128 −0.617635
\(640\) −0.311108 + 2.21432i −0.0122976 + 0.0875287i
\(641\) −39.3876 −1.55572 −0.777859 0.628439i \(-0.783694\pi\)
−0.777859 + 0.628439i \(0.783694\pi\)
\(642\) 4.85728i 0.191702i
\(643\) 24.1146i 0.950988i 0.879719 + 0.475494i \(0.157731\pi\)
−0.879719 + 0.475494i \(0.842269\pi\)
\(644\) −11.6128 −0.457610
\(645\) −24.3368 3.41927i −0.958260 0.134634i
\(646\) −3.80642 −0.149762
\(647\) 47.6829i 1.87461i 0.348512 + 0.937304i \(0.386687\pi\)
−0.348512 + 0.937304i \(0.613313\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 2.75557 0.108166
\(650\) 27.9081 + 8.00000i 1.09465 + 0.313786i
\(651\) −19.6128 −0.768688
\(652\) 8.23506i 0.322510i
\(653\) 21.7462i 0.850995i 0.904960 + 0.425497i \(0.139901\pi\)
−0.904960 + 0.425497i \(0.860099\pi\)
\(654\) −6.04149 −0.236241
\(655\) −33.4193 4.69535i −1.30580 0.183462i
\(656\) 5.67307 0.221496
\(657\) 11.6128i 0.453060i
\(658\) 11.6128i 0.452716i
\(659\) 16.1936 0.630812 0.315406 0.948957i \(-0.397859\pi\)
0.315406 + 0.948957i \(0.397859\pi\)
\(660\) −0.815792 + 5.80642i −0.0317547 + 0.226015i
\(661\) −22.5116 −0.875600 −0.437800 0.899072i \(-0.644242\pi\)
−0.437800 + 0.899072i \(0.644242\pi\)
\(662\) 15.1427i 0.588539i
\(663\) 22.1017i 0.858359i
\(664\) −11.9081 −0.462125
\(665\) 1.37778 9.80642i 0.0534282 0.380277i
\(666\) 5.80642 0.224994
\(667\) 8.85728i 0.342955i
\(668\) 8.47013i 0.327719i
\(669\) −21.3876 −0.826893
\(670\) −34.5718 4.85728i −1.33563 0.187653i
\(671\) 12.4701 0.481404
\(672\) 4.42864i 0.170838i
\(673\) 9.66323i 0.372490i 0.982503 + 0.186245i \(0.0596318\pi\)
−0.982503 + 0.186245i \(0.940368\pi\)
\(674\) −11.1111 −0.427983
\(675\) −1.37778 + 4.80642i −0.0530309 + 0.184999i
\(676\) 20.7146 0.796714
\(677\) 6.85728i 0.263547i 0.991280 + 0.131773i \(0.0420671\pi\)
−0.991280 + 0.131773i \(0.957933\pi\)
\(678\) 9.34614i 0.358936i
\(679\) 32.6735 1.25390
\(680\) −8.42864 1.18421i −0.323224 0.0454123i
\(681\) −8.47013 −0.324576
\(682\) 11.6128i 0.444679i
\(683\) 30.3051i 1.15959i 0.814761 + 0.579797i \(0.196868\pi\)
−0.814761 + 0.579797i \(0.803132\pi\)
\(684\) −1.00000 −0.0382360
\(685\) −2.34567 + 16.6953i −0.0896233 + 0.637896i
\(686\) −24.8573 −0.949055
\(687\) 16.9590i 0.647026i
\(688\) 10.9906i 0.419014i
\(689\) 34.8385 1.32724
\(690\) −0.815792 + 5.80642i −0.0310567 + 0.221047i
\(691\) 7.61285 0.289606 0.144803 0.989460i \(-0.453745\pi\)
0.144803 + 0.989460i \(0.453745\pi\)
\(692\) 22.4701i 0.854186i
\(693\) 11.6128i 0.441136i
\(694\) 14.1936 0.538781
\(695\) −0.857279 0.120446i −0.0325184 0.00456878i
\(696\) −3.37778 −0.128035
\(697\) 21.5941i 0.817935i
\(698\) 32.3684i 1.22516i
\(699\) −17.9081 −0.677348
\(700\) 6.10171 21.2859i 0.230623 0.804532i
\(701\) −32.3654 −1.22242 −0.611211 0.791467i \(-0.709317\pi\)
−0.611211 + 0.791467i \(0.709317\pi\)
\(702\) 5.80642i 0.219149i
\(703\) 5.80642i 0.218993i
\(704\) −2.62222 −0.0988285
\(705\) −5.80642 0.815792i −0.218683 0.0307245i
\(706\) −11.8064 −0.444341
\(707\) 78.2677i 2.94356i
\(708\) 1.05086i 0.0394936i
\(709\) 49.8992 1.87401 0.937003 0.349322i \(-0.113588\pi\)
0.937003 + 0.349322i \(0.113588\pi\)
\(710\) 4.85728 34.5718i 0.182290 1.29746i
\(711\) 4.42864 0.166087
\(712\) 12.4286i 0.465783i
\(713\) 11.6128i 0.434905i
\(714\) 16.8573 0.630868
\(715\) −4.73683 + 33.7146i −0.177148 + 1.26085i
\(716\) −2.94914 −0.110215
\(717\) 28.2766i 1.05601i
\(718\) 10.8287i 0.404123i
\(719\) 26.4415 0.986103 0.493052 0.870000i \(-0.335881\pi\)
0.493052 + 0.870000i \(0.335881\pi\)
\(720\) −2.21432 0.311108i −0.0825228 0.0115943i
\(721\) 5.24443 0.195313
\(722\) 1.00000i 0.0372161i
\(723\) 11.5111i 0.428104i
\(724\) −22.8988 −0.851026
\(725\) −16.2351 4.65386i −0.602955 0.172840i
\(726\) 4.12399 0.153055
\(727\) 48.1245i 1.78484i −0.451208 0.892419i \(-0.649007\pi\)
0.451208 0.892419i \(-0.350993\pi\)
\(728\) 25.7146i 0.953045i
\(729\) −1.00000 −0.0370370
\(730\) 25.7146 + 3.61285i 0.951738 + 0.133717i
\(731\) 41.8350 1.54732
\(732\) 4.75557i 0.175771i
\(733\) 14.0286i 0.518157i −0.965856 0.259079i \(-0.916581\pi\)
0.965856 0.259079i \(-0.0834189\pi\)
\(734\) 1.46965 0.0542458
\(735\) −3.92396 + 27.9289i −0.144737 + 1.03017i
\(736\) −2.62222 −0.0966562
\(737\) 40.9403i 1.50805i
\(738\) 5.67307i 0.208829i
\(739\) −10.1847 −0.374650 −0.187325 0.982298i \(-0.559982\pi\)
−0.187325 + 0.982298i \(0.559982\pi\)
\(740\) −1.80642 + 12.8573i −0.0664055 + 0.472643i
\(741\) −5.80642 −0.213304
\(742\) 26.5718i 0.975483i
\(743\) 42.9590i 1.57601i −0.615667 0.788006i \(-0.711113\pi\)
0.615667 0.788006i \(-0.288887\pi\)
\(744\) −4.42864 −0.162362
\(745\) 32.1748 + 4.52051i 1.17879 + 0.165619i
\(746\) 24.3783 0.892552
\(747\) 11.9081i 0.435696i
\(748\) 9.98126i 0.364951i
\(749\) 21.5111 0.786000
\(750\) −10.2143 4.54617i −0.372974 0.166003i
\(751\) −7.18421 −0.262155 −0.131078 0.991372i \(-0.541844\pi\)
−0.131078 + 0.991372i \(0.541844\pi\)
\(752\) 2.62222i 0.0956224i
\(753\) 7.74620i 0.282287i
\(754\) −19.6128 −0.714258
\(755\) 10.3970 + 1.46076i 0.378385 + 0.0531625i
\(756\) 4.42864 0.161068
\(757\) 41.2543i 1.49941i −0.661771 0.749706i \(-0.730195\pi\)
0.661771 0.749706i \(-0.269805\pi\)
\(758\) 18.9590i 0.688621i
\(759\) −6.87601 −0.249584
\(760\) 0.311108 2.21432i 0.0112851 0.0803218i
\(761\) 44.3051 1.60606 0.803030 0.595939i \(-0.203220\pi\)
0.803030 + 0.595939i \(0.203220\pi\)
\(762\) 6.42864i 0.232885i
\(763\) 26.7556i 0.968617i
\(764\) 9.05086 0.327448
\(765\) 1.18421 8.42864i 0.0428151 0.304738i
\(766\) −26.1017 −0.943093
\(767\) 6.10171i 0.220320i
\(768\) 1.00000i 0.0360844i
\(769\) 6.59057 0.237662 0.118831 0.992914i \(-0.462085\pi\)
0.118831 + 0.992914i \(0.462085\pi\)
\(770\) 25.7146 + 3.61285i 0.926688 + 0.130198i
\(771\) 13.8796 0.499860
\(772\) 18.7239i 0.673889i
\(773\) 8.83854i 0.317900i −0.987287 0.158950i \(-0.949189\pi\)
0.987287 0.158950i \(-0.0508109\pi\)
\(774\) 10.9906 0.395050
\(775\) −21.2859 6.10171i −0.764613 0.219180i
\(776\) 7.37778 0.264847
\(777\) 25.7146i 0.922505i
\(778\) 3.57136i 0.128039i
\(779\) −5.67307 −0.203259
\(780\) −12.8573 1.80642i −0.460364 0.0646803i
\(781\) 40.9403 1.46496
\(782\) 9.98126i 0.356929i
\(783\) 3.37778i 0.120712i
\(784\) −12.6128 −0.450459
\(785\) −6.69535 + 47.6543i −0.238967 + 1.70086i
\(786\) 15.0923 0.538326
\(787\) 16.9403i 0.603855i 0.953331 + 0.301927i \(0.0976300\pi\)
−0.953331 + 0.301927i \(0.902370\pi\)
\(788\)