Properties

Label 756.2.ba.a.575.20
Level $756$
Weight $2$
Character 756.575
Analytic conductor $6.037$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.ba (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 575.20
Character \(\chi\) \(=\) 756.575
Dual form 756.2.ba.a.71.20

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0405943 + 1.41363i) q^{2} +(-1.99670 + 0.114771i) q^{4} +(2.16781 - 1.25159i) q^{5} +(0.866025 + 0.500000i) q^{7} +(-0.243298 - 2.81794i) q^{8} +O(q^{10})\) \(q+(0.0405943 + 1.41363i) q^{2} +(-1.99670 + 0.114771i) q^{4} +(2.16781 - 1.25159i) q^{5} +(0.866025 + 0.500000i) q^{7} +(-0.243298 - 2.81794i) q^{8} +(1.85728 + 3.01367i) q^{10} +(0.351433 - 0.608700i) q^{11} +(1.55324 + 2.69030i) q^{13} +(-0.671660 + 1.24454i) q^{14} +(3.97366 - 0.458326i) q^{16} -7.91554i q^{17} -2.37413i q^{19} +(-4.18483 + 2.74785i) q^{20} +(0.874743 + 0.472087i) q^{22} +(0.346619 + 0.600362i) q^{23} +(0.632931 - 1.09627i) q^{25} +(-3.74003 + 2.30492i) q^{26} +(-1.78658 - 0.898958i) q^{28} +(8.70126 + 5.02368i) q^{29} +(7.34846 - 4.24264i) q^{31} +(0.809212 + 5.59868i) q^{32} +(11.1896 - 0.321326i) q^{34} +2.50317 q^{35} +2.85107 q^{37} +(3.35614 - 0.0963760i) q^{38} +(-4.05432 - 5.80426i) q^{40} +(-5.82034 + 3.36037i) q^{41} +(3.17043 + 1.83045i) q^{43} +(-0.631847 + 1.25573i) q^{44} +(-0.834620 + 0.514363i) q^{46} +(-3.67787 + 6.37026i) q^{47} +(0.500000 + 0.866025i) q^{49} +(1.57541 + 0.850229i) q^{50} +(-3.41013 - 5.19346i) q^{52} -0.889576i q^{53} -1.75939i q^{55} +(1.19827 - 2.56206i) q^{56} +(-6.74840 + 12.5043i) q^{58} +(-3.63052 - 6.28824i) q^{59} +(-2.39732 + 4.15228i) q^{61} +(6.29583 + 10.2158i) q^{62} +(-7.88161 + 1.37120i) q^{64} +(6.73427 + 3.88803i) q^{65} +(-7.40811 + 4.27707i) q^{67} +(0.908472 + 15.8050i) q^{68} +(0.101614 + 3.53856i) q^{70} -6.34514 q^{71} +8.20222 q^{73} +(0.115737 + 4.03035i) q^{74} +(0.272480 + 4.74043i) q^{76} +(0.608700 - 0.351433i) q^{77} +(2.27268 + 1.31214i) q^{79} +(8.04049 - 5.96693i) q^{80} +(-4.98660 - 8.09139i) q^{82} +(6.50432 - 11.2658i) q^{83} +(-9.90697 - 17.1594i) q^{85} +(-2.45887 + 4.55612i) q^{86} +(-1.80079 - 0.842223i) q^{88} -1.71842i q^{89} +3.10649i q^{91} +(-0.761000 - 1.15896i) q^{92} +(-9.15449 - 4.94056i) q^{94} +(-2.97142 - 5.14665i) q^{95} +(-6.81083 + 11.7967i) q^{97} +(-1.20394 + 0.741971i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0405943 + 1.41363i 0.0287045 + 0.999588i
\(3\) 0 0
\(4\) −1.99670 + 0.114771i −0.998352 + 0.0573853i
\(5\) 2.16781 1.25159i 0.969474 0.559726i 0.0703980 0.997519i \(-0.477573\pi\)
0.899076 + 0.437793i \(0.144240\pi\)
\(6\) 0 0
\(7\) 0.866025 + 0.500000i 0.327327 + 0.188982i
\(8\) −0.243298 2.81794i −0.0860189 0.996294i
\(9\) 0 0
\(10\) 1.85728 + 3.01367i 0.587324 + 0.953008i
\(11\) 0.351433 0.608700i 0.105961 0.183530i −0.808169 0.588950i \(-0.799541\pi\)
0.914130 + 0.405420i \(0.132875\pi\)
\(12\) 0 0
\(13\) 1.55324 + 2.69030i 0.430792 + 0.746154i 0.996942 0.0781487i \(-0.0249009\pi\)
−0.566150 + 0.824302i \(0.691568\pi\)
\(14\) −0.671660 + 1.24454i −0.179509 + 0.332617i
\(15\) 0 0
\(16\) 3.97366 0.458326i 0.993414 0.114582i
\(17\) 7.91554i 1.91980i −0.280343 0.959900i \(-0.590448\pi\)
0.280343 0.959900i \(-0.409552\pi\)
\(18\) 0 0
\(19\) 2.37413i 0.544662i −0.962204 0.272331i \(-0.912205\pi\)
0.962204 0.272331i \(-0.0877945\pi\)
\(20\) −4.18483 + 2.74785i −0.935756 + 0.614437i
\(21\) 0 0
\(22\) 0.874743 + 0.472087i 0.186496 + 0.100649i
\(23\) 0.346619 + 0.600362i 0.0722751 + 0.125184i 0.899898 0.436100i \(-0.143641\pi\)
−0.827623 + 0.561284i \(0.810307\pi\)
\(24\) 0 0
\(25\) 0.632931 1.09627i 0.126586 0.219254i
\(26\) −3.74003 + 2.30492i −0.733481 + 0.452033i
\(27\) 0 0
\(28\) −1.78658 0.898958i −0.337632 0.169887i
\(29\) 8.70126 + 5.02368i 1.61578 + 0.932873i 0.987994 + 0.154490i \(0.0493735\pi\)
0.627789 + 0.778383i \(0.283960\pi\)
\(30\) 0 0
\(31\) 7.34846 4.24264i 1.31982 0.762000i 0.336123 0.941818i \(-0.390884\pi\)
0.983700 + 0.179818i \(0.0575509\pi\)
\(32\) 0.809212 + 5.59868i 0.143050 + 0.989715i
\(33\) 0 0
\(34\) 11.1896 0.321326i 1.91901 0.0551069i
\(35\) 2.50317 0.423113
\(36\) 0 0
\(37\) 2.85107 0.468712 0.234356 0.972151i \(-0.424702\pi\)
0.234356 + 0.972151i \(0.424702\pi\)
\(38\) 3.35614 0.0963760i 0.544437 0.0156342i
\(39\) 0 0
\(40\) −4.05432 5.80426i −0.641044 0.917733i
\(41\) −5.82034 + 3.36037i −0.908984 + 0.524802i −0.880104 0.474781i \(-0.842527\pi\)
−0.0288798 + 0.999583i \(0.509194\pi\)
\(42\) 0 0
\(43\) 3.17043 + 1.83045i 0.483485 + 0.279140i 0.721868 0.692031i \(-0.243284\pi\)
−0.238383 + 0.971171i \(0.576617\pi\)
\(44\) −0.631847 + 1.25573i −0.0952545 + 0.189308i
\(45\) 0 0
\(46\) −0.834620 + 0.514363i −0.123058 + 0.0758387i
\(47\) −3.67787 + 6.37026i −0.536473 + 0.929198i 0.462618 + 0.886558i \(0.346910\pi\)
−0.999091 + 0.0426400i \(0.986423\pi\)
\(48\) 0 0
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) 1.57541 + 0.850229i 0.222797 + 0.120241i
\(51\) 0 0
\(52\) −3.41013 5.19346i −0.472900 0.720203i
\(53\) 0.889576i 0.122193i −0.998132 0.0610964i \(-0.980540\pi\)
0.998132 0.0610964i \(-0.0194597\pi\)
\(54\) 0 0
\(55\) 1.75939i 0.237237i
\(56\) 1.19827 2.56206i 0.160125 0.342370i
\(57\) 0 0
\(58\) −6.74840 + 12.5043i −0.886109 + 1.64190i
\(59\) −3.63052 6.28824i −0.472653 0.818660i 0.526857 0.849954i \(-0.323370\pi\)
−0.999510 + 0.0312945i \(0.990037\pi\)
\(60\) 0 0
\(61\) −2.39732 + 4.15228i −0.306946 + 0.531645i −0.977693 0.210041i \(-0.932640\pi\)
0.670747 + 0.741686i \(0.265974\pi\)
\(62\) 6.29583 + 10.2158i 0.799571 + 1.29741i
\(63\) 0 0
\(64\) −7.88161 + 1.37120i −0.985201 + 0.171400i
\(65\) 6.73427 + 3.88803i 0.835283 + 0.482251i
\(66\) 0 0
\(67\) −7.40811 + 4.27707i −0.905044 + 0.522528i −0.878833 0.477129i \(-0.841677\pi\)
−0.0262109 + 0.999656i \(0.508344\pi\)
\(68\) 0.908472 + 15.8050i 0.110168 + 1.91664i
\(69\) 0 0
\(70\) 0.101614 + 3.53856i 0.0121452 + 0.422939i
\(71\) −6.34514 −0.753030 −0.376515 0.926411i \(-0.622878\pi\)
−0.376515 + 0.926411i \(0.622878\pi\)
\(72\) 0 0
\(73\) 8.20222 0.959998 0.479999 0.877269i \(-0.340637\pi\)
0.479999 + 0.877269i \(0.340637\pi\)
\(74\) 0.115737 + 4.03035i 0.0134542 + 0.468519i
\(75\) 0 0
\(76\) 0.272480 + 4.74043i 0.0312556 + 0.543764i
\(77\) 0.608700 0.351433i 0.0693678 0.0400495i
\(78\) 0 0
\(79\) 2.27268 + 1.31214i 0.255697 + 0.147627i 0.622370 0.782723i \(-0.286170\pi\)
−0.366673 + 0.930350i \(0.619503\pi\)
\(80\) 8.04049 5.96693i 0.898954 0.667123i
\(81\) 0 0
\(82\) −4.98660 8.09139i −0.550678 0.893545i
\(83\) 6.50432 11.2658i 0.713942 1.23658i −0.249425 0.968394i \(-0.580241\pi\)
0.963366 0.268189i \(-0.0864252\pi\)
\(84\) 0 0
\(85\) −9.90697 17.1594i −1.07456 1.86120i
\(86\) −2.45887 + 4.55612i −0.265147 + 0.491299i
\(87\) 0 0
\(88\) −1.80079 0.842223i −0.191964 0.0897813i
\(89\) 1.71842i 0.182152i −0.995844 0.0910760i \(-0.970969\pi\)
0.995844 0.0910760i \(-0.0290306\pi\)
\(90\) 0 0
\(91\) 3.10649i 0.325648i
\(92\) −0.761000 1.15896i −0.0793398 0.120830i
\(93\) 0 0
\(94\) −9.15449 4.94056i −0.944214 0.509579i
\(95\) −2.97142 5.14665i −0.304861 0.528035i
\(96\) 0 0
\(97\) −6.81083 + 11.7967i −0.691535 + 1.19777i 0.279800 + 0.960058i \(0.409732\pi\)
−0.971335 + 0.237716i \(0.923601\pi\)
\(98\) −1.20394 + 0.741971i −0.121617 + 0.0749504i
\(99\) 0 0
\(100\) −1.13796 + 2.26157i −0.113796 + 0.226157i
\(101\) −2.23784 1.29202i −0.222673 0.128560i 0.384514 0.923119i \(-0.374369\pi\)
−0.607187 + 0.794559i \(0.707702\pi\)
\(102\) 0 0
\(103\) 11.6579 6.73069i 1.14869 0.663195i 0.200120 0.979771i \(-0.435867\pi\)
0.948567 + 0.316576i \(0.102533\pi\)
\(104\) 7.20320 5.03149i 0.706332 0.493379i
\(105\) 0 0
\(106\) 1.25753 0.0361117i 0.122142 0.00350748i
\(107\) −17.0371 −1.64703 −0.823517 0.567291i \(-0.807991\pi\)
−0.823517 + 0.567291i \(0.807991\pi\)
\(108\) 0 0
\(109\) −2.43459 −0.233191 −0.116596 0.993179i \(-0.537198\pi\)
−0.116596 + 0.993179i \(0.537198\pi\)
\(110\) 2.48713 0.0714214i 0.237139 0.00680976i
\(111\) 0 0
\(112\) 3.67045 + 1.58991i 0.346825 + 0.150232i
\(113\) 4.13789 2.38901i 0.389260 0.224739i −0.292580 0.956241i \(-0.594514\pi\)
0.681839 + 0.731502i \(0.261180\pi\)
\(114\) 0 0
\(115\) 1.50281 + 0.867647i 0.140138 + 0.0809085i
\(116\) −17.9504 9.03215i −1.66665 0.838614i
\(117\) 0 0
\(118\) 8.74188 5.38748i 0.804755 0.495958i
\(119\) 3.95777 6.85506i 0.362808 0.628402i
\(120\) 0 0
\(121\) 5.25299 + 9.09844i 0.477544 + 0.827131i
\(122\) −5.96711 3.22037i −0.540237 0.291559i
\(123\) 0 0
\(124\) −14.1858 + 9.31468i −1.27392 + 0.836483i
\(125\) 9.34718i 0.836037i
\(126\) 0 0
\(127\) 4.91393i 0.436041i −0.975944 0.218020i \(-0.930040\pi\)
0.975944 0.218020i \(-0.0699599\pi\)
\(128\) −2.25832 11.0860i −0.199609 0.979876i
\(129\) 0 0
\(130\) −5.22287 + 9.67760i −0.458076 + 0.848782i
\(131\) 2.61968 + 4.53741i 0.228882 + 0.396435i 0.957477 0.288509i \(-0.0931596\pi\)
−0.728595 + 0.684945i \(0.759826\pi\)
\(132\) 0 0
\(133\) 1.18706 2.05605i 0.102931 0.178282i
\(134\) −6.34693 10.2987i −0.548291 0.889672i
\(135\) 0 0
\(136\) −22.3055 + 1.92584i −1.91268 + 0.165139i
\(137\) −9.03659 5.21728i −0.772048 0.445742i 0.0615566 0.998104i \(-0.480394\pi\)
−0.833605 + 0.552361i \(0.813727\pi\)
\(138\) 0 0
\(139\) 10.2848 5.93796i 0.872349 0.503651i 0.00422072 0.999991i \(-0.498656\pi\)
0.868128 + 0.496340i \(0.165323\pi\)
\(140\) −4.99809 + 0.287291i −0.422416 + 0.0242805i
\(141\) 0 0
\(142\) −0.257577 8.96969i −0.0216153 0.752719i
\(143\) 2.18344 0.182589
\(144\) 0 0
\(145\) 25.1502 2.08861
\(146\) 0.332963 + 11.5949i 0.0275563 + 0.959602i
\(147\) 0 0
\(148\) −5.69273 + 0.327219i −0.467940 + 0.0268972i
\(149\) −15.3300 + 8.85079i −1.25588 + 0.725085i −0.972272 0.233854i \(-0.924866\pi\)
−0.283612 + 0.958939i \(0.591533\pi\)
\(150\) 0 0
\(151\) −18.1796 10.4960i −1.47944 0.854152i −0.479706 0.877429i \(-0.659257\pi\)
−0.999729 + 0.0232767i \(0.992590\pi\)
\(152\) −6.69015 + 0.577621i −0.542643 + 0.0468512i
\(153\) 0 0
\(154\) 0.521507 + 0.846211i 0.0420242 + 0.0681896i
\(155\) 10.6200 18.3945i 0.853022 1.47748i
\(156\) 0 0
\(157\) −0.841990 1.45837i −0.0671981 0.116391i 0.830469 0.557065i \(-0.188073\pi\)
−0.897667 + 0.440675i \(0.854739\pi\)
\(158\) −1.76262 + 3.26600i −0.140226 + 0.259829i
\(159\) 0 0
\(160\) 8.76144 + 11.1241i 0.692652 + 0.879435i
\(161\) 0.693239i 0.0546349i
\(162\) 0 0
\(163\) 14.9299i 1.16940i −0.811249 0.584700i \(-0.801212\pi\)
0.811249 0.584700i \(-0.198788\pi\)
\(164\) 11.2358 7.37767i 0.877370 0.576100i
\(165\) 0 0
\(166\) 16.1897 + 8.73738i 1.25657 + 0.678152i
\(167\) −1.17066 2.02764i −0.0905885 0.156904i 0.817170 0.576396i \(-0.195541\pi\)
−0.907759 + 0.419492i \(0.862208\pi\)
\(168\) 0 0
\(169\) 1.67487 2.90097i 0.128836 0.223151i
\(170\) 23.8549 14.7014i 1.82958 1.12754i
\(171\) 0 0
\(172\) −6.54048 3.29099i −0.498707 0.250935i
\(173\) −0.875908 0.505706i −0.0665940 0.0384481i 0.466333 0.884609i \(-0.345575\pi\)
−0.532927 + 0.846161i \(0.678908\pi\)
\(174\) 0 0
\(175\) 1.09627 0.632931i 0.0828702 0.0478451i
\(176\) 1.11749 2.57984i 0.0842341 0.194462i
\(177\) 0 0
\(178\) 2.42921 0.0697580i 0.182077 0.00522858i
\(179\) 11.8651 0.886837 0.443419 0.896315i \(-0.353765\pi\)
0.443419 + 0.896315i \(0.353765\pi\)
\(180\) 0 0
\(181\) −11.7216 −0.871262 −0.435631 0.900125i \(-0.643475\pi\)
−0.435631 + 0.900125i \(0.643475\pi\)
\(182\) −4.39142 + 0.126106i −0.325514 + 0.00934757i
\(183\) 0 0
\(184\) 1.60746 1.12282i 0.118503 0.0827754i
\(185\) 6.18057 3.56835i 0.454404 0.262350i
\(186\) 0 0
\(187\) −4.81819 2.78178i −0.352341 0.203424i
\(188\) 6.61250 13.1416i 0.482266 0.958452i
\(189\) 0 0
\(190\) 7.15484 4.40942i 0.519067 0.319893i
\(191\) −3.38132 + 5.85662i −0.244664 + 0.423770i −0.962037 0.272919i \(-0.912011\pi\)
0.717373 + 0.696689i \(0.245344\pi\)
\(192\) 0 0
\(193\) −1.38307 2.39554i −0.0995553 0.172435i 0.811945 0.583733i \(-0.198409\pi\)
−0.911501 + 0.411299i \(0.865075\pi\)
\(194\) −16.9527 9.14912i −1.21713 0.656869i
\(195\) 0 0
\(196\) −1.09775 1.67181i −0.0784105 0.119415i
\(197\) 17.2636i 1.22998i −0.788536 0.614989i \(-0.789161\pi\)
0.788536 0.614989i \(-0.210839\pi\)
\(198\) 0 0
\(199\) 14.4922i 1.02732i 0.857993 + 0.513662i \(0.171711\pi\)
−0.857993 + 0.513662i \(0.828289\pi\)
\(200\) −3.24322 1.51684i −0.229330 0.107257i
\(201\) 0 0
\(202\) 1.73559 3.21592i 0.122116 0.226272i
\(203\) 5.02368 + 8.70126i 0.352593 + 0.610709i
\(204\) 0 0
\(205\) −8.41159 + 14.5693i −0.587491 + 1.01756i
\(206\) 9.98796 + 16.2067i 0.695894 + 1.12918i
\(207\) 0 0
\(208\) 7.40509 + 9.97842i 0.513450 + 0.691879i
\(209\) −1.44513 0.834347i −0.0999618 0.0577130i
\(210\) 0 0
\(211\) −22.1795 + 12.8053i −1.52690 + 0.881555i −0.527407 + 0.849612i \(0.676836\pi\)
−0.999490 + 0.0319420i \(0.989831\pi\)
\(212\) 0.102097 + 1.77622i 0.00701207 + 0.121991i
\(213\) 0 0
\(214\) −0.691607 24.0841i −0.0472773 1.64636i
\(215\) 9.16384 0.624968
\(216\) 0 0
\(217\) 8.48527 0.576018
\(218\) −0.0988305 3.44161i −0.00669364 0.233095i
\(219\) 0 0
\(220\) 0.201927 + 3.51299i 0.0136139 + 0.236846i
\(221\) 21.2951 12.2948i 1.43247 0.827035i
\(222\) 0 0
\(223\) −13.2137 7.62891i −0.884853 0.510870i −0.0125973 0.999921i \(-0.504010\pi\)
−0.872255 + 0.489051i \(0.837343\pi\)
\(224\) −2.09854 + 5.25320i −0.140215 + 0.350994i
\(225\) 0 0
\(226\) 3.54515 + 5.75247i 0.235820 + 0.382648i
\(227\) −3.88279 + 6.72519i −0.257710 + 0.446367i −0.965628 0.259928i \(-0.916301\pi\)
0.707918 + 0.706295i \(0.249635\pi\)
\(228\) 0 0
\(229\) −5.70048 9.87351i −0.376698 0.652460i 0.613882 0.789398i \(-0.289607\pi\)
−0.990580 + 0.136938i \(0.956274\pi\)
\(230\) −1.16553 + 2.15964i −0.0768526 + 0.142402i
\(231\) 0 0
\(232\) 12.0394 25.7419i 0.790428 1.69004i
\(233\) 19.4113i 1.27167i 0.771824 + 0.635837i \(0.219345\pi\)
−0.771824 + 0.635837i \(0.780655\pi\)
\(234\) 0 0
\(235\) 18.4127i 1.20111i
\(236\) 7.97078 + 12.1391i 0.518853 + 0.790187i
\(237\) 0 0
\(238\) 9.85118 + 5.31655i 0.638557 + 0.344621i
\(239\) 3.57434 + 6.19093i 0.231205 + 0.400458i 0.958163 0.286224i \(-0.0924000\pi\)
−0.726958 + 0.686682i \(0.759067\pi\)
\(240\) 0 0
\(241\) −1.19735 + 2.07386i −0.0771279 + 0.133589i −0.902010 0.431716i \(-0.857908\pi\)
0.824882 + 0.565305i \(0.191242\pi\)
\(242\) −12.6486 + 7.79513i −0.813083 + 0.501090i
\(243\) 0 0
\(244\) 4.31018 8.56602i 0.275931 0.548383i
\(245\) 2.16781 + 1.25159i 0.138496 + 0.0799609i
\(246\) 0 0
\(247\) 6.38710 3.68759i 0.406401 0.234636i
\(248\) −13.7434 19.6753i −0.872705 1.24938i
\(249\) 0 0
\(250\) −13.2135 + 0.379442i −0.835693 + 0.0239980i
\(251\) 3.05973 0.193129 0.0965644 0.995327i \(-0.469215\pi\)
0.0965644 + 0.995327i \(0.469215\pi\)
\(252\) 0 0
\(253\) 0.487254 0.0306334
\(254\) 6.94648 0.199478i 0.435861 0.0125163i
\(255\) 0 0
\(256\) 15.5799 3.64246i 0.973742 0.227654i
\(257\) −17.1928 + 9.92624i −1.07245 + 0.619182i −0.928851 0.370453i \(-0.879202\pi\)
−0.143603 + 0.989635i \(0.545869\pi\)
\(258\) 0 0
\(259\) 2.46909 + 1.42553i 0.153422 + 0.0885783i
\(260\) −13.8926 6.99035i −0.861581 0.433523i
\(261\) 0 0
\(262\) −6.30788 + 3.88745i −0.389702 + 0.240167i
\(263\) −9.51239 + 16.4759i −0.586559 + 1.01595i 0.408120 + 0.912928i \(0.366184\pi\)
−0.994679 + 0.103022i \(0.967149\pi\)
\(264\) 0 0
\(265\) −1.11338 1.92843i −0.0683944 0.118463i
\(266\) 2.95469 + 1.59460i 0.181164 + 0.0977715i
\(267\) 0 0
\(268\) 14.3009 9.39028i 0.873567 0.573603i
\(269\) 27.0790i 1.65103i −0.564378 0.825517i \(-0.690884\pi\)
0.564378 0.825517i \(-0.309116\pi\)
\(270\) 0 0
\(271\) 29.1249i 1.76921i 0.466337 + 0.884607i \(0.345573\pi\)
−0.466337 + 0.884607i \(0.654427\pi\)
\(272\) −3.62790 31.4536i −0.219974 1.90716i
\(273\) 0 0
\(274\) 7.00847 12.9862i 0.423397 0.784525i
\(275\) −0.444866 0.770531i −0.0268264 0.0464648i
\(276\) 0 0
\(277\) 8.22279 14.2423i 0.494060 0.855737i −0.505917 0.862582i \(-0.668846\pi\)
0.999977 + 0.00684565i \(0.00217905\pi\)
\(278\) 8.81158 + 14.2979i 0.528484 + 0.857532i
\(279\) 0 0
\(280\) −0.609017 7.05379i −0.0363957 0.421545i
\(281\) −5.47490 3.16093i −0.326605 0.188566i 0.327728 0.944772i \(-0.393717\pi\)
−0.654333 + 0.756207i \(0.727050\pi\)
\(282\) 0 0
\(283\) 7.14839 4.12712i 0.424927 0.245332i −0.272256 0.962225i \(-0.587770\pi\)
0.697183 + 0.716893i \(0.254436\pi\)
\(284\) 12.6694 0.728236i 0.751789 0.0432129i
\(285\) 0 0
\(286\) 0.0886354 + 3.08658i 0.00524112 + 0.182514i
\(287\) −6.72075 −0.396713
\(288\) 0 0
\(289\) −45.6557 −2.68563
\(290\) 1.02096 + 35.5531i 0.0599526 + 2.08775i
\(291\) 0 0
\(292\) −16.3774 + 0.941375i −0.958416 + 0.0550898i
\(293\) −6.70404 + 3.87058i −0.391654 + 0.226122i −0.682877 0.730534i \(-0.739271\pi\)
0.291222 + 0.956655i \(0.405938\pi\)
\(294\) 0 0
\(295\) −15.7405 9.08781i −0.916450 0.529113i
\(296\) −0.693659 8.03414i −0.0403181 0.466975i
\(297\) 0 0
\(298\) −13.1341 21.3117i −0.760836 1.23455i
\(299\) −1.07677 + 1.86502i −0.0622711 + 0.107857i
\(300\) 0 0
\(301\) 1.83045 + 3.17043i 0.105505 + 0.182740i
\(302\) 14.0995 26.1253i 0.811334 1.50334i
\(303\) 0 0
\(304\) −1.08812 9.43396i −0.0624082 0.541075i
\(305\) 12.0018i 0.687222i
\(306\) 0 0
\(307\) 14.7032i 0.839154i 0.907720 + 0.419577i \(0.137822\pi\)
−0.907720 + 0.419577i \(0.862178\pi\)
\(308\) −1.17506 + 0.771569i −0.0669553 + 0.0439642i
\(309\) 0 0
\(310\) 26.4341 + 14.2661i 1.50135 + 0.810261i
\(311\) 6.26710 + 10.8549i 0.355375 + 0.615527i 0.987182 0.159599i \(-0.0510200\pi\)
−0.631807 + 0.775125i \(0.717687\pi\)
\(312\) 0 0
\(313\) −11.6110 + 20.1108i −0.656292 + 1.13673i 0.325276 + 0.945619i \(0.394543\pi\)
−0.981568 + 0.191112i \(0.938790\pi\)
\(314\) 2.02742 1.24946i 0.114414 0.0705113i
\(315\) 0 0
\(316\) −4.68847 2.35911i −0.263747 0.132710i
\(317\) −5.93134 3.42446i −0.333137 0.192337i 0.324096 0.946024i \(-0.394940\pi\)
−0.657233 + 0.753687i \(0.728273\pi\)
\(318\) 0 0
\(319\) 6.11582 3.53097i 0.342420 0.197697i
\(320\) −15.3697 + 12.8370i −0.859190 + 0.717611i
\(321\) 0 0
\(322\) −0.979983 + 0.0281415i −0.0546123 + 0.00156827i
\(323\) −18.7925 −1.04564
\(324\) 0 0
\(325\) 3.93239 0.218129
\(326\) 21.1054 0.606069i 1.16892 0.0335671i
\(327\) 0 0
\(328\) 10.8854 + 15.5838i 0.601047 + 0.860472i
\(329\) −6.37026 + 3.67787i −0.351204 + 0.202768i
\(330\) 0 0
\(331\) −6.98234 4.03126i −0.383784 0.221578i 0.295679 0.955287i \(-0.404454\pi\)
−0.679463 + 0.733709i \(0.737787\pi\)
\(332\) −11.6942 + 23.2410i −0.641803 + 1.27552i
\(333\) 0 0
\(334\) 2.81882 1.73719i 0.154239 0.0950550i
\(335\) −10.7062 + 18.5438i −0.584944 + 1.01315i
\(336\) 0 0
\(337\) −8.08375 14.0015i −0.440350 0.762708i 0.557365 0.830267i \(-0.311812\pi\)
−0.997715 + 0.0675590i \(0.978479\pi\)
\(338\) 4.16888 + 2.24989i 0.226757 + 0.122378i
\(339\) 0 0
\(340\) 21.7507 + 33.1252i 1.17960 + 1.79646i
\(341\) 5.96401i 0.322969i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 4.38673 9.37942i 0.236517 0.505705i
\(345\) 0 0
\(346\) 0.679324 1.25874i 0.0365207 0.0676702i
\(347\) 3.82900 + 6.63203i 0.205552 + 0.356026i 0.950308 0.311310i \(-0.100768\pi\)
−0.744757 + 0.667336i \(0.767434\pi\)
\(348\) 0 0
\(349\) 4.40927 7.63708i 0.236023 0.408803i −0.723547 0.690275i \(-0.757489\pi\)
0.959569 + 0.281472i \(0.0908227\pi\)
\(350\) 0.939234 + 1.52403i 0.0502042 + 0.0814627i
\(351\) 0 0
\(352\) 3.69230 + 1.47499i 0.196800 + 0.0786174i
\(353\) 2.81435 + 1.62487i 0.149793 + 0.0864830i 0.573023 0.819539i \(-0.305771\pi\)
−0.423230 + 0.906022i \(0.639104\pi\)
\(354\) 0 0
\(355\) −13.7551 + 7.94149i −0.730043 + 0.421490i
\(356\) 0.197224 + 3.43117i 0.0104529 + 0.181852i
\(357\) 0 0
\(358\) 0.481654 + 16.7728i 0.0254562 + 0.886472i
\(359\) 28.4033 1.49907 0.749533 0.661967i \(-0.230278\pi\)
0.749533 + 0.661967i \(0.230278\pi\)
\(360\) 0 0
\(361\) 13.3635 0.703343
\(362\) −0.475831 16.5701i −0.0250091 0.870903i
\(363\) 0 0
\(364\) −0.356534 6.20273i −0.0186874 0.325112i
\(365\) 17.7809 10.2658i 0.930692 0.537336i
\(366\) 0 0
\(367\) 4.00164 + 2.31035i 0.208884 + 0.120599i 0.600793 0.799405i \(-0.294852\pi\)
−0.391909 + 0.920004i \(0.628185\pi\)
\(368\) 1.65251 + 2.22677i 0.0861429 + 0.116078i
\(369\) 0 0
\(370\) 5.29523 + 8.59218i 0.275286 + 0.446686i
\(371\) 0.444788 0.770396i 0.0230923 0.0399970i
\(372\) 0 0
\(373\) −13.7859 23.8779i −0.713808 1.23635i −0.963417 0.268005i \(-0.913636\pi\)
0.249609 0.968347i \(-0.419698\pi\)
\(374\) 3.73682 6.92406i 0.193226 0.358035i
\(375\) 0 0
\(376\) 18.8458 + 8.81416i 0.971900 + 0.454556i
\(377\) 31.2120i 1.60750i
\(378\) 0 0
\(379\) 20.5766i 1.05695i 0.848949 + 0.528475i \(0.177236\pi\)
−0.848949 + 0.528475i \(0.822764\pi\)
\(380\) 6.52373 + 9.93531i 0.334660 + 0.509671i
\(381\) 0 0
\(382\) −8.41636 4.54219i −0.430618 0.232399i
\(383\) 0.0457558 + 0.0792514i 0.00233801 + 0.00404955i 0.867192 0.497974i \(-0.165922\pi\)
−0.864854 + 0.502023i \(0.832589\pi\)
\(384\) 0 0
\(385\) 0.879697 1.52368i 0.0448335 0.0776539i
\(386\) 3.33027 2.05239i 0.169506 0.104464i
\(387\) 0 0
\(388\) 12.2453 24.3362i 0.621661 1.23548i
\(389\) 1.65481 + 0.955404i 0.0839021 + 0.0484409i 0.541364 0.840788i \(-0.317908\pi\)
−0.457462 + 0.889229i \(0.651241\pi\)
\(390\) 0 0
\(391\) 4.75219 2.74368i 0.240329 0.138754i
\(392\) 2.31876 1.61967i 0.117115 0.0818059i
\(393\) 0 0
\(394\) 24.4043 0.700802i 1.22947 0.0353059i
\(395\) 6.56900 0.330522
\(396\) 0 0
\(397\) 30.4353 1.52750 0.763751 0.645511i \(-0.223355\pi\)
0.763751 + 0.645511i \(0.223355\pi\)
\(398\) −20.4866 + 0.588300i −1.02690 + 0.0294888i
\(399\) 0 0
\(400\) 2.01260 4.64629i 0.100630 0.232314i
\(401\) −18.9221 + 10.9247i −0.944922 + 0.545551i −0.891500 0.453021i \(-0.850346\pi\)
−0.0534223 + 0.998572i \(0.517013\pi\)
\(402\) 0 0
\(403\) 22.8279 + 13.1797i 1.13714 + 0.656527i
\(404\) 4.61658 + 2.32294i 0.229684 + 0.115570i
\(405\) 0 0
\(406\) −12.0964 + 7.45484i −0.600336 + 0.369978i
\(407\) 1.00196 1.73544i 0.0496653 0.0860228i
\(408\) 0 0
\(409\) 2.23786 + 3.87609i 0.110655 + 0.191660i 0.916035 0.401099i \(-0.131372\pi\)
−0.805379 + 0.592760i \(0.798038\pi\)
\(410\) −20.9371 11.2994i −1.03401 0.558040i
\(411\) 0 0
\(412\) −22.5049 + 14.7772i −1.10874 + 0.728020i
\(413\) 7.26104i 0.357292i
\(414\) 0 0
\(415\) 32.5628i 1.59845i
\(416\) −13.8052 + 10.8731i −0.676855 + 0.533099i
\(417\) 0 0
\(418\) 1.12079 2.07675i 0.0548198 0.101577i
\(419\) 11.4022 + 19.7492i 0.557033 + 0.964809i 0.997742 + 0.0671595i \(0.0213936\pi\)
−0.440709 + 0.897650i \(0.645273\pi\)
\(420\) 0 0
\(421\) −14.0510 + 24.3370i −0.684803 + 1.18611i 0.288696 + 0.957421i \(0.406778\pi\)
−0.973499 + 0.228693i \(0.926555\pi\)
\(422\) −19.0024 30.8337i −0.925020 1.50096i
\(423\) 0 0
\(424\) −2.50678 + 0.216432i −0.121740 + 0.0105109i
\(425\) −8.67756 5.00999i −0.420924 0.243020i
\(426\) 0 0
\(427\) −4.15228 + 2.39732i −0.200943 + 0.116015i
\(428\) 34.0180 1.95535i 1.64432 0.0945156i
\(429\) 0 0
\(430\) 0.371999 + 12.9543i 0.0179394 + 0.624711i
\(431\) 0.610755 0.0294190 0.0147095 0.999892i \(-0.495318\pi\)
0.0147095 + 0.999892i \(0.495318\pi\)
\(432\) 0 0
\(433\) 10.5169 0.505410 0.252705 0.967543i \(-0.418680\pi\)
0.252705 + 0.967543i \(0.418680\pi\)
\(434\) 0.344454 + 11.9950i 0.0165343 + 0.575781i
\(435\) 0 0
\(436\) 4.86116 0.279420i 0.232807 0.0133818i
\(437\) 1.42534 0.822918i 0.0681830 0.0393655i
\(438\) 0 0
\(439\) 32.6334 + 18.8409i 1.55751 + 0.899227i 0.997495 + 0.0707423i \(0.0225368\pi\)
0.560012 + 0.828485i \(0.310797\pi\)
\(440\) −4.95787 + 0.428057i −0.236357 + 0.0204068i
\(441\) 0 0
\(442\) 18.2447 + 29.6044i 0.867812 + 1.40814i
\(443\) −20.7455 + 35.9322i −0.985647 + 1.70719i −0.346622 + 0.938005i \(0.612671\pi\)
−0.639025 + 0.769186i \(0.720662\pi\)
\(444\) 0 0
\(445\) −2.15075 3.72520i −0.101955 0.176592i
\(446\) 10.2481 18.9889i 0.485260 0.899152i
\(447\) 0 0
\(448\) −7.51128 2.75331i −0.354874 0.130082i
\(449\) 31.9656i 1.50855i 0.656559 + 0.754275i \(0.272011\pi\)
−0.656559 + 0.754275i \(0.727989\pi\)
\(450\) 0 0
\(451\) 4.72379i 0.222434i
\(452\) −7.98795 + 5.24506i −0.375722 + 0.246707i
\(453\) 0 0
\(454\) −9.66456 5.21583i −0.453580 0.244791i
\(455\) 3.88803 + 6.73427i 0.182274 + 0.315707i
\(456\) 0 0
\(457\) −14.8515 + 25.7236i −0.694724 + 1.20330i 0.275549 + 0.961287i \(0.411140\pi\)
−0.970274 + 0.242011i \(0.922193\pi\)
\(458\) 13.7261 8.45918i 0.641378 0.395271i
\(459\) 0 0
\(460\) −3.10025 1.55996i −0.144550 0.0727333i
\(461\) 8.96753 + 5.17741i 0.417659 + 0.241136i 0.694075 0.719902i \(-0.255813\pi\)
−0.276416 + 0.961038i \(0.589147\pi\)
\(462\) 0 0
\(463\) 13.7219 7.92236i 0.637712 0.368183i −0.146021 0.989282i \(-0.546647\pi\)
0.783733 + 0.621098i \(0.213313\pi\)
\(464\) 36.8783 + 15.9743i 1.71203 + 0.741590i
\(465\) 0 0
\(466\) −27.4403 + 0.787986i −1.27115 + 0.0365028i
\(467\) 27.9844 1.29496 0.647481 0.762081i \(-0.275822\pi\)
0.647481 + 0.762081i \(0.275822\pi\)
\(468\) 0 0
\(469\) −8.55414 −0.394994
\(470\) −26.0287 + 0.747450i −1.20062 + 0.0344773i
\(471\) 0 0
\(472\) −16.8366 + 11.7605i −0.774968 + 0.541322i
\(473\) 2.22839 1.28656i 0.102461 0.0591560i
\(474\) 0 0
\(475\) −2.60268 1.50266i −0.119419 0.0689467i
\(476\) −7.11573 + 14.1418i −0.326149 + 0.648186i
\(477\) 0 0
\(478\) −8.60659 + 5.30411i −0.393656 + 0.242604i
\(479\) −11.5844 + 20.0648i −0.529306 + 0.916785i 0.470110 + 0.882608i \(0.344214\pi\)
−0.999416 + 0.0341768i \(0.989119\pi\)
\(480\) 0 0
\(481\) 4.42840 + 7.67021i 0.201918 + 0.349731i
\(482\) −2.98028 1.60842i −0.135748 0.0732615i
\(483\) 0 0
\(484\) −11.5329 17.5640i −0.524223 0.798364i
\(485\) 34.0973i 1.54828i
\(486\) 0 0
\(487\) 13.8456i 0.627406i 0.949521 + 0.313703i \(0.101570\pi\)
−0.949521 + 0.313703i \(0.898430\pi\)
\(488\) 12.2842 + 5.74527i 0.556078 + 0.260076i
\(489\) 0 0
\(490\) −1.68128 + 3.11529i −0.0759524 + 0.140734i
\(491\) −1.97999 3.42944i −0.0893557 0.154769i 0.817883 0.575384i \(-0.195147\pi\)
−0.907239 + 0.420616i \(0.861814\pi\)
\(492\) 0 0
\(493\) 39.7651 68.8752i 1.79093 3.10198i
\(494\) 5.47218 + 8.87931i 0.246205 + 0.399499i
\(495\) 0 0
\(496\) 27.2557 20.2268i 1.22382 0.908209i
\(497\) −5.49505 3.17257i −0.246487 0.142309i
\(498\) 0 0
\(499\) −18.6834 + 10.7868i −0.836382 + 0.482886i −0.856033 0.516921i \(-0.827078\pi\)
0.0196506 + 0.999807i \(0.493745\pi\)
\(500\) −1.07278 18.6636i −0.0479763 0.834660i
\(501\) 0 0
\(502\) 0.124208 + 4.32534i 0.00554366 + 0.193049i
\(503\) −24.7621 −1.10409 −0.552044 0.833815i \(-0.686152\pi\)
−0.552044 + 0.833815i \(0.686152\pi\)
\(504\) 0 0
\(505\) −6.46827 −0.287834
\(506\) 0.0197797 + 0.688797i 0.000879317 + 0.0306208i
\(507\) 0 0
\(508\) 0.563975 + 9.81166i 0.0250224 + 0.435322i
\(509\) 22.5133 12.9980i 0.997882 0.576128i 0.0902614 0.995918i \(-0.471230\pi\)
0.907621 + 0.419790i \(0.137896\pi\)
\(510\) 0 0
\(511\) 7.10333 + 4.10111i 0.314233 + 0.181422i
\(512\) 5.78155 + 21.8763i 0.255511 + 0.966806i
\(513\) 0 0
\(514\) −14.7300 23.9013i −0.649711 1.05424i
\(515\) 16.8481 29.1817i 0.742415 1.28590i
\(516\) 0 0
\(517\) 2.58505 + 4.47744i 0.113690 + 0.196918i
\(518\) −1.91495 + 3.54826i −0.0841379 + 0.155901i
\(519\) 0 0
\(520\) 9.31782 19.9227i 0.408613 0.873670i
\(521\) 16.4772i 0.721880i −0.932589 0.360940i \(-0.882456\pi\)
0.932589 0.360940i \(-0.117544\pi\)
\(522\) 0 0
\(523\) 35.6352i 1.55822i −0.626888 0.779110i \(-0.715671\pi\)
0.626888 0.779110i \(-0.284329\pi\)
\(524\) −5.75148 8.75921i −0.251255 0.382648i
\(525\) 0 0
\(526\) −23.6770 12.7782i −1.03237 0.557155i
\(527\) −33.5827 58.1670i −1.46289 2.53380i
\(528\) 0 0
\(529\) 11.2597 19.5024i 0.489553 0.847930i
\(530\) 2.68089 1.65219i 0.116451 0.0717667i
\(531\) 0 0
\(532\) −2.13424 + 4.24157i −0.0925310 + 0.183895i
\(533\) −18.0808 10.4390i −0.783166 0.452161i
\(534\) 0 0
\(535\) −36.9331 + 21.3233i −1.59676 + 0.921888i
\(536\) 13.8549 + 19.8350i 0.598442 + 0.856742i
\(537\) 0 0
\(538\) 38.2796 1.09925i 1.65035 0.0473921i
\(539\) 0.702866 0.0302746
\(540\) 0 0
\(541\) 16.0235 0.688903 0.344452 0.938804i \(-0.388065\pi\)
0.344452 + 0.938804i \(0.388065\pi\)
\(542\) −41.1719 + 1.18231i −1.76849 + 0.0507844i
\(543\) 0 0
\(544\) 44.3165 6.40535i 1.90006 0.274627i
\(545\) −5.27773 + 3.04710i −0.226073 + 0.130523i
\(546\) 0 0
\(547\) −9.75181 5.63021i −0.416957 0.240730i 0.276817 0.960923i \(-0.410720\pi\)
−0.693775 + 0.720192i \(0.744054\pi\)
\(548\) 18.6422 + 9.38023i 0.796355 + 0.400703i
\(549\) 0 0
\(550\) 1.07119 0.660156i 0.0456756 0.0281491i
\(551\) 11.9268 20.6579i 0.508100 0.880056i
\(552\) 0 0
\(553\) 1.31214 + 2.27268i 0.0557977 + 0.0966444i
\(554\) 20.4671 + 11.0458i 0.869566 + 0.469293i
\(555\) 0 0
\(556\) −19.8543 + 13.0367i −0.842009 + 0.552881i
\(557\) 25.2666i 1.07058i −0.844669 0.535289i \(-0.820203\pi\)
0.844669 0.535289i \(-0.179797\pi\)
\(558\) 0 0
\(559\) 11.3725i 0.481006i
\(560\) 9.94674 1.14727i 0.420326 0.0484810i
\(561\) 0 0
\(562\) 4.24614 7.86780i 0.179113 0.331883i
\(563\) −6.29010 10.8948i −0.265096 0.459160i 0.702493 0.711691i \(-0.252070\pi\)
−0.967589 + 0.252531i \(0.918737\pi\)
\(564\) 0 0
\(565\) 5.98010 10.3578i 0.251585 0.435758i
\(566\) 6.12441 + 9.93764i 0.257428 + 0.417710i
\(567\) 0 0
\(568\) 1.54376 + 17.8803i 0.0647748 + 0.750239i
\(569\) 9.64118 + 5.56634i 0.404179 + 0.233353i 0.688286 0.725440i \(-0.258364\pi\)
−0.284107 + 0.958793i \(0.591697\pi\)
\(570\) 0 0
\(571\) 38.6886 22.3369i 1.61907 0.934769i 0.631906 0.775045i \(-0.282273\pi\)
0.987162 0.159724i \(-0.0510605\pi\)
\(572\) −4.35969 + 0.250595i −0.182288 + 0.0104779i
\(573\) 0 0
\(574\) −0.272824 9.50065i −0.0113875 0.396550i
\(575\) 0.877545 0.0365962
\(576\) 0 0
\(577\) 0.773772 0.0322125 0.0161063 0.999870i \(-0.494873\pi\)
0.0161063 + 0.999870i \(0.494873\pi\)
\(578\) −1.85336 64.5404i −0.0770897 2.68452i
\(579\) 0 0
\(580\) −50.2176 + 2.88651i −2.08517 + 0.119856i
\(581\) 11.2658 6.50432i 0.467385 0.269845i
\(582\) 0 0
\(583\) −0.541485 0.312627i −0.0224260 0.0129477i
\(584\) −1.99559 23.1134i −0.0825779 0.956439i
\(585\) 0 0
\(586\) −5.74372 9.31992i −0.237271 0.385002i
\(587\) 3.95356 6.84776i 0.163181 0.282637i −0.772827 0.634617i \(-0.781158\pi\)
0.936008 + 0.351979i \(0.114491\pi\)
\(588\) 0 0
\(589\) −10.0726 17.4462i −0.415032 0.718857i
\(590\) 12.2078 22.6202i 0.502588 0.931260i
\(591\) 0 0
\(592\) 11.3292 1.30672i 0.465625 0.0537058i
\(593\) 13.0459i 0.535732i −0.963456 0.267866i \(-0.913682\pi\)
0.963456 0.267866i \(-0.0863184\pi\)
\(594\) 0 0
\(595\) 19.8139i 0.812292i
\(596\) 29.5937 19.4319i 1.21221 0.795960i
\(597\) 0 0
\(598\) −2.68016 1.44644i −0.109600 0.0591495i
\(599\) 5.35898 + 9.28202i 0.218962 + 0.379253i 0.954491 0.298240i \(-0.0963996\pi\)
−0.735529 + 0.677493i \(0.763066\pi\)
\(600\) 0 0
\(601\) −2.22698 + 3.85725i −0.0908406 + 0.157341i −0.907865 0.419262i \(-0.862289\pi\)
0.817024 + 0.576603i \(0.195622\pi\)
\(602\) −4.40750 + 2.71628i −0.179636 + 0.110707i
\(603\) 0 0
\(604\) 37.5039 + 18.8709i 1.52601 + 0.767847i
\(605\) 22.7750 + 13.1491i 0.925934 + 0.534588i
\(606\) 0 0
\(607\) −29.7000 + 17.1473i −1.20549 + 0.695988i −0.961770 0.273858i \(-0.911700\pi\)
−0.243717 + 0.969846i \(0.578367\pi\)
\(608\) 13.2920 1.92117i 0.539060 0.0779138i
\(609\) 0 0
\(610\) −16.9661 + 0.487205i −0.686938 + 0.0197264i
\(611\) −22.8505 −0.924433
\(612\) 0 0
\(613\) −27.5606 −1.11316 −0.556581 0.830794i \(-0.687887\pi\)
−0.556581 + 0.830794i \(0.687887\pi\)
\(614\) −20.7849 + 0.596865i −0.838808 + 0.0240875i
\(615\) 0 0
\(616\) −1.13841 1.62978i −0.0458680 0.0656657i
\(617\) −21.8157 + 12.5953i −0.878268 + 0.507068i −0.870087 0.492899i \(-0.835937\pi\)
−0.00818075 + 0.999967i \(0.502604\pi\)
\(618\) 0 0
\(619\) −2.44808 1.41340i −0.0983968 0.0568094i 0.449994 0.893032i \(-0.351426\pi\)
−0.548391 + 0.836222i \(0.684759\pi\)
\(620\) −19.0939 + 37.9472i −0.766831 + 1.52399i
\(621\) 0 0
\(622\) −15.0905 + 9.30001i −0.605072 + 0.372897i
\(623\) 0.859209 1.48819i 0.0344235 0.0596232i
\(624\) 0 0
\(625\) 14.8635 + 25.7443i 0.594538 + 1.02977i
\(626\) −28.9006 15.5973i −1.15510 0.623393i
\(627\) 0 0
\(628\) 1.84858 + 2.81530i 0.0737665 + 0.112343i
\(629\) 22.5677i 0.899834i
\(630\) 0 0
\(631\) 35.3279i 1.40638i −0.711002 0.703190i \(-0.751758\pi\)
0.711002 0.703190i \(-0.248242\pi\)
\(632\) 3.14458 6.72354i 0.125085 0.267448i
\(633\) 0 0
\(634\) 4.60015 8.52374i 0.182695 0.338521i
\(635\) −6.15020 10.6525i −0.244063 0.422730i
\(636\) 0 0
\(637\) −1.55324 + 2.69030i −0.0615417 + 0.106593i
\(638\) 5.23976 + 8.50218i 0.207444 + 0.336605i
\(639\) 0 0
\(640\) −18.7707 21.2059i −0.741978 0.838237i
\(641\) −17.8094 10.2823i −0.703431 0.406126i 0.105193 0.994452i \(-0.466454\pi\)
−0.808624 + 0.588326i \(0.799787\pi\)
\(642\) 0 0
\(643\) 16.6218 9.59659i 0.655499 0.378453i −0.135061 0.990837i \(-0.543123\pi\)
0.790560 + 0.612385i \(0.209790\pi\)
\(644\) −0.0795635 1.38419i −0.00313524 0.0545448i
\(645\) 0 0
\(646\) −0.762868 26.5656i −0.0300146 1.04521i
\(647\) 30.9160 1.21544 0.607718 0.794153i \(-0.292085\pi\)
0.607718 + 0.794153i \(0.292085\pi\)
\(648\) 0 0
\(649\) −5.10354 −0.200331
\(650\) 0.159632 + 5.55894i 0.00626130 + 0.218040i
\(651\) 0 0
\(652\) 1.71352 + 29.8106i 0.0671064 + 1.16747i
\(653\) 14.2740 8.24109i 0.558584 0.322499i −0.193993 0.981003i \(-0.562144\pi\)
0.752577 + 0.658504i \(0.228810\pi\)
\(654\) 0 0
\(655\) 11.3579 + 6.55749i 0.443790 + 0.256222i
\(656\) −21.5879 + 16.0206i −0.842864 + 0.625498i
\(657\) 0 0
\(658\) −5.45775 8.85589i −0.212765 0.345239i
\(659\) −13.7838 + 23.8743i −0.536942 + 0.930010i 0.462125 + 0.886815i \(0.347087\pi\)
−0.999067 + 0.0431955i \(0.986246\pi\)
\(660\) 0 0
\(661\) 5.86138 + 10.1522i 0.227981 + 0.394875i 0.957210 0.289395i \(-0.0934542\pi\)
−0.729229 + 0.684270i \(0.760121\pi\)
\(662\) 5.41527 10.0341i 0.210470 0.389986i
\(663\) 0 0
\(664\) −33.3289 15.5879i −1.29341 0.604926i
\(665\) 5.94284i 0.230454i
\(666\) 0 0
\(667\) 6.96521i 0.269694i
\(668\) 2.57018 + 3.91425i 0.0994432 + 0.151447i
\(669\) 0 0
\(670\) −26.6486 14.3819i −1.02953 0.555621i
\(671\) 1.68500 + 2.91850i 0.0650486 + 0.112667i
\(672\) 0 0
\(673\) −3.04565 + 5.27522i −0.117401 + 0.203345i −0.918737 0.394870i \(-0.870790\pi\)
0.801336 + 0.598215i \(0.204123\pi\)
\(674\) 19.4647 11.9958i 0.749754 0.462062i
\(675\) 0 0
\(676\) −3.01128 + 5.98460i −0.115818 + 0.230177i
\(677\) −25.8756 14.9393i −0.994481 0.574164i −0.0878702 0.996132i \(-0.528006\pi\)
−0.906611 + 0.421968i \(0.861339\pi\)
\(678\) 0 0
\(679\) −11.7967 + 6.81083i −0.452716 + 0.261376i
\(680\) −45.9438 + 32.0921i −1.76186 + 1.23068i
\(681\) 0 0
\(682\) 8.43091 0.242105i 0.322836 0.00927068i
\(683\) −5.57818 −0.213443 −0.106722 0.994289i \(-0.534035\pi\)
−0.106722 + 0.994289i \(0.534035\pi\)
\(684\) 0 0
\(685\) −26.1195 −0.997974
\(686\) −1.41363 + 0.0405943i −0.0539727 + 0.00154990i
\(687\) 0 0
\(688\) 13.4371 + 5.82047i 0.512285 + 0.221903i
\(689\) 2.39322 1.38173i 0.0911745 0.0526396i
\(690\) 0 0
\(691\) 6.59535 + 3.80783i 0.250899 + 0.144857i 0.620176 0.784463i \(-0.287061\pi\)
−0.369277 + 0.929319i \(0.620395\pi\)
\(692\) 1.80697 + 0.909216i 0.0686907 + 0.0345632i
\(693\) 0 0
\(694\) −9.21981 + 5.68202i −0.349979 + 0.215687i
\(695\) 14.8637 25.7447i 0.563813 0.976553i
\(696\) 0 0
\(697\) 26.5992 + 46.0711i 1.00751 + 1.74507i
\(698\) 10.9750 + 5.92306i 0.415410 + 0.224191i
\(699\) 0 0
\(700\) −2.11628 + 1.38960i −0.0799880 + 0.0525218i
\(701\) 13.6591i 0.515896i 0.966159 + 0.257948i \(0.0830463\pi\)
−0.966159 + 0.257948i \(0.916954\pi\)
\(702\) 0 0
\(703\) 6.76879i 0.255290i
\(704\) −1.93521 + 5.27942i −0.0729360 + 0.198976i
\(705\) 0 0
\(706\) −2.18272 + 4.04442i −0.0821476 + 0.152214i
\(707\) −1.29202 2.23784i −0.0485913 0.0841625i
\(708\) 0 0
\(709\) −11.1244 + 19.2680i −0.417784 + 0.723624i −0.995716 0.0924613i \(-0.970527\pi\)
0.577932 + 0.816085i \(0.303860\pi\)
\(710\) −11.7847 19.1222i −0.442272 0.717643i
\(711\) 0 0
\(712\) −4.84241 + 0.418088i −0.181477 + 0.0156685i
\(713\) 5.09424 + 2.94116i 0.190781 + 0.110147i
\(714\) 0 0
\(715\) 4.73329 2.73277i 0.177015 0.102200i
\(716\) −23.6910 + 1.36176i −0.885376 + 0.0508915i
\(717\) 0 0
\(718\) 1.15301 + 40.1517i 0.0430299 + 1.49845i
\(719\) 17.7827 0.663184 0.331592 0.943423i \(-0.392414\pi\)
0.331592 + 0.943423i \(0.392414\pi\)
\(720\) 0 0
\(721\) 13.4614 0.501328
\(722\) 0.542483 + 18.8911i 0.0201891 + 0.703054i
\(723\) 0 0
\(724\) 23.4046 1.34530i 0.869826 0.0499977i
\(725\) 11.0146 6.35929i 0.409072 0.236178i
\(726\) 0 0
\(727\) −45.2123 26.1034i −1.67683 0.968120i −0.963660 0.267131i \(-0.913924\pi\)
−0.713173 0.700988i \(-0.752742\pi\)
\(728\) 8.75390 0.755802i 0.324441 0.0280119i
\(729\) 0 0
\(730\) 15.2338 + 24.7188i 0.563829 + 0.914885i
\(731\) 14.4890 25.0956i 0.535894 0.928195i
\(732\) 0 0
\(733\) −5.30936 9.19609i −0.196106 0.339665i 0.751157 0.660124i \(-0.229496\pi\)
−0.947262 + 0.320459i \(0.896163\pi\)
\(734\) −3.10354 + 5.75063i −0.114554 + 0.212260i
\(735\) 0 0
\(736\) −3.08075 + 2.42643i −0.113558 + 0.0894394i
\(737\) 6.01242i 0.221470i
\(738\) 0 0
\(739\) 25.7536i 0.947362i −0.880696 0.473681i \(-0.842925\pi\)
0.880696 0.473681i \(-0.157075\pi\)
\(740\) −11.9312 + 7.83429i −0.438600 + 0.287994i
\(741\) 0 0
\(742\) 1.10711 + 0.597493i 0.0406433 + 0.0219346i
\(743\) −1.97016 3.41241i −0.0722780 0.125189i 0.827621 0.561287i \(-0.189694\pi\)
−0.899899 + 0.436098i \(0.856360\pi\)
\(744\) 0 0
\(745\) −22.1550 + 38.3737i −0.811698 + 1.40590i
\(746\) 33.1949 20.4575i 1.21535 0.749003i
\(747\) 0 0
\(748\) 9.93976 + 5.00141i 0.363434 + 0.182870i
\(749\) −14.7545 8.51853i −0.539119 0.311260i
\(750\) 0 0
\(751\) 10.3540 5.97786i 0.377821 0.218135i −0.299049 0.954238i \(-0.596669\pi\)
0.676870 + 0.736103i \(0.263336\pi\)
\(752\) −11.6949 + 26.9989i −0.426470 + 0.984548i
\(753\) 0 0
\(754\) −44.1222 + 1.26703i −1.60684 + 0.0461424i
\(755\) −52.5466 −1.91237
\(756\) 0 0
\(757\) 1.73758 0.0631534 0.0315767 0.999501i \(-0.489947\pi\)
0.0315767 + 0.999501i \(0.489947\pi\)
\(758\) −29.0877 + 0.835293i −1.05651 + 0.0303392i
\(759\) 0 0
\(760\) −13.7800 + 9.62547i −0.499854 + 0.349152i
\(761\) 25.7786 14.8833i 0.934473 0.539518i 0.0462496 0.998930i \(-0.485273\pi\)
0.888223 + 0.459412i \(0.151940\pi\)
\(762\) 0 0
\(763\) −2.10842 1.21729i −0.0763298 0.0440690i
\(764\) 6.07933 12.0820i 0.219942 0.437112i
\(765\) 0 0
\(766\) −0.110175 + 0.0678989i −0.00398077 + 0.00245329i
\(767\) 11.2782 19.5343i 0.407231 0.705344i
\(768\) 0 0
\(769\) 11.5167 + 19.9475i 0.415303 + 0.719327i 0.995460 0.0951782i \(-0.0303421\pi\)
−0.580157 + 0.814505i \(0.697009\pi\)
\(770\) 2.18963 + 1.18171i 0.0789089 + 0.0425860i
\(771\) 0 0
\(772\) 3.03651 + 4.62445i 0.109287 + 0.166438i
\(773\) 1.33102i 0.0478734i −0.999713 0.0239367i \(-0.992380\pi\)
0.999713 0.0239367i \(-0.00762002\pi\)
\(774\) 0 0
\(775\) 10.7412i 0.385835i
\(776\) 34.8995 + 16.3224i 1.25282 + 0.585941i
\(777\) 0 0
\(778\) −1.28341 + 2.37807i −0.0460126 + 0.0852580i
\(779\) 7.97795 + 13.8182i 0.285840 + 0.495089i
\(780\) 0 0
\(781\) −2.22989 + 3.86229i −0.0797919 + 0.138204i
\(782\) 4.07146 + 6.60646i 0.145595 + 0.236247i
\(783\) 0 0
\(784\) 2.38375 + 3.21212i 0.0851339 + 0.114719i
\(785\) −3.65055 2.10764i −0.130294 0.0752250i
\(786\) 0 0
\(787\) 1.23901 0.715343i 0.0441659 0.0254992i −0.477754 0.878493i \(-0.658549\pi\)
0.521920 + 0.852994i \(0.325216\pi\)
\(788\) 1.98135 + 34.4702i 0.0705827 + 1.22795i
\(789\) 0