Properties

Label 912.2.q.l.577.3
Level $912$
Weight $2$
Character 912.577
Analytic conductor $7.282$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.954288.1
Defining polynomial: \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: no (minimal twist has level 57)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 577.3
Root \(-1.62241 + 0.606458i\) of defining polynomial
Character \(\chi\) \(=\) 912.577
Dual form 912.2.q.l.49.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} +(1.33641 + 2.31473i) q^{5} +3.67282 q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} +(1.33641 + 2.31473i) q^{5} +3.67282 q^{7} +(-0.500000 + 0.866025i) q^{9} +3.81681 q^{11} +(-0.0719933 + 0.124696i) q^{13} +(-1.33641 + 2.31473i) q^{15} +(-4.24482 + 0.990721i) q^{19} +(1.83641 + 3.18076i) q^{21} +(3.76442 - 6.52016i) q^{23} +(-1.07199 + 1.85675i) q^{25} -1.00000 q^{27} +(2.67282 - 4.62947i) q^{29} -8.81681 q^{31} +(1.90841 + 3.30545i) q^{33} +(4.90841 + 8.50161i) q^{35} -1.00000 q^{37} -0.143987 q^{39} +(-2.67282 - 4.62947i) q^{41} +(1.40841 + 2.43943i) q^{43} -2.67282 q^{45} +(-3.00000 + 5.19615i) q^{47} +6.48963 q^{49} +(-4.00924 + 6.94420i) q^{53} +(5.10083 + 8.83490i) q^{55} +(-2.98040 - 3.18076i) q^{57} +(1.90841 + 3.30545i) q^{59} +(-5.74482 + 9.95031i) q^{61} +(-1.83641 + 3.18076i) q^{63} -0.384851 q^{65} +(2.69243 - 4.66342i) q^{67} +7.52884 q^{69} +(-6.81681 - 11.8071i) q^{71} +(0.172824 + 0.299339i) q^{73} -2.14399 q^{75} +14.0185 q^{77} +(3.26442 + 5.65414i) q^{79} +(-0.500000 - 0.866025i) q^{81} +2.28797 q^{83} +5.34565 q^{87} +(4.33641 - 7.51089i) q^{89} +(-0.264419 + 0.457986i) q^{91} +(-4.40841 - 7.63558i) q^{93} +(-7.96608 - 8.50161i) q^{95} +(2.95684 + 5.12140i) q^{97} +(-1.90841 + 3.30545i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 3 q^{9} + q^{13} + 2 q^{15} - 4 q^{19} + q^{21} + 14 q^{23} - 5 q^{25} - 6 q^{27} - 4 q^{29} - 30 q^{31} + 18 q^{35} - 6 q^{37} + 2 q^{39} + 4 q^{41} - 3 q^{43} + 4 q^{45} - 18 q^{47} - 4 q^{49} + 6 q^{53} + 12 q^{55} - 5 q^{57} - 13 q^{61} - q^{63} + 12 q^{65} + 9 q^{67} + 28 q^{69} - 18 q^{71} - 19 q^{73} - 10 q^{75} + 24 q^{77} + 11 q^{79} - 3 q^{81} + 8 q^{83} - 8 q^{87} + 16 q^{89} + 7 q^{91} - 15 q^{93} - 2 q^{95} + 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0 0
\(5\) 1.33641 + 2.31473i 0.597662 + 1.03518i 0.993165 + 0.116716i \(0.0372367\pi\)
−0.395504 + 0.918464i \(0.629430\pi\)
\(6\) 0 0
\(7\) 3.67282 1.38820 0.694098 0.719880i \(-0.255803\pi\)
0.694098 + 0.719880i \(0.255803\pi\)
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 3.81681 1.15081 0.575406 0.817868i \(-0.304844\pi\)
0.575406 + 0.817868i \(0.304844\pi\)
\(12\) 0 0
\(13\) −0.0719933 + 0.124696i −0.0199673 + 0.0345844i −0.875836 0.482608i \(-0.839690\pi\)
0.855869 + 0.517193i \(0.173023\pi\)
\(14\) 0 0
\(15\) −1.33641 + 2.31473i −0.345060 + 0.597662i
\(16\) 0 0
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) −4.24482 + 0.990721i −0.973828 + 0.227287i
\(20\) 0 0
\(21\) 1.83641 + 3.18076i 0.400738 + 0.694098i
\(22\) 0 0
\(23\) 3.76442 6.52016i 0.784936 1.35955i −0.144102 0.989563i \(-0.546029\pi\)
0.929038 0.369985i \(-0.120637\pi\)
\(24\) 0 0
\(25\) −1.07199 + 1.85675i −0.214399 + 0.371349i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 2.67282 4.62947i 0.496331 0.859670i −0.503660 0.863902i \(-0.668014\pi\)
0.999991 + 0.00423154i \(0.00134695\pi\)
\(30\) 0 0
\(31\) −8.81681 −1.58355 −0.791773 0.610816i \(-0.790842\pi\)
−0.791773 + 0.610816i \(0.790842\pi\)
\(32\) 0 0
\(33\) 1.90841 + 3.30545i 0.332211 + 0.575406i
\(34\) 0 0
\(35\) 4.90841 + 8.50161i 0.829672 + 1.43703i
\(36\) 0 0
\(37\) −1.00000 −0.164399 −0.0821995 0.996616i \(-0.526194\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) 0 0
\(39\) −0.143987 −0.0230563
\(40\) 0 0
\(41\) −2.67282 4.62947i −0.417425 0.723001i 0.578255 0.815856i \(-0.303734\pi\)
−0.995680 + 0.0928551i \(0.970401\pi\)
\(42\) 0 0
\(43\) 1.40841 + 2.43943i 0.214780 + 0.372009i 0.953204 0.302327i \(-0.0977633\pi\)
−0.738425 + 0.674336i \(0.764430\pi\)
\(44\) 0 0
\(45\) −2.67282 −0.398441
\(46\) 0 0
\(47\) −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i \(-0.977503\pi\)
0.559908 + 0.828554i \(0.310836\pi\)
\(48\) 0 0
\(49\) 6.48963 0.927091
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.00924 + 6.94420i −0.550711 + 0.953859i 0.447513 + 0.894278i \(0.352310\pi\)
−0.998223 + 0.0595815i \(0.981023\pi\)
\(54\) 0 0
\(55\) 5.10083 + 8.83490i 0.687796 + 1.19130i
\(56\) 0 0
\(57\) −2.98040 3.18076i −0.394763 0.421302i
\(58\) 0 0
\(59\) 1.90841 + 3.30545i 0.248453 + 0.430334i 0.963097 0.269155i \(-0.0867445\pi\)
−0.714644 + 0.699489i \(0.753411\pi\)
\(60\) 0 0
\(61\) −5.74482 + 9.95031i −0.735548 + 1.27401i 0.218934 + 0.975740i \(0.429742\pi\)
−0.954482 + 0.298268i \(0.903591\pi\)
\(62\) 0 0
\(63\) −1.83641 + 3.18076i −0.231366 + 0.400738i
\(64\) 0 0
\(65\) −0.384851 −0.0477348
\(66\) 0 0
\(67\) 2.69243 4.66342i 0.328932 0.569727i −0.653368 0.757040i \(-0.726645\pi\)
0.982300 + 0.187313i \(0.0599779\pi\)
\(68\) 0 0
\(69\) 7.52884 0.906365
\(70\) 0 0
\(71\) −6.81681 11.8071i −0.809007 1.40124i −0.913553 0.406720i \(-0.866672\pi\)
0.104546 0.994520i \(-0.466661\pi\)
\(72\) 0 0
\(73\) 0.172824 + 0.299339i 0.0202275 + 0.0350350i 0.875962 0.482380i \(-0.160228\pi\)
−0.855734 + 0.517415i \(0.826894\pi\)
\(74\) 0 0
\(75\) −2.14399 −0.247566
\(76\) 0 0
\(77\) 14.0185 1.59755
\(78\) 0 0
\(79\) 3.26442 + 5.65414i 0.367276 + 0.636140i 0.989139 0.146986i \(-0.0469572\pi\)
−0.621863 + 0.783126i \(0.713624\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 2.28797 0.251138 0.125569 0.992085i \(-0.459924\pi\)
0.125569 + 0.992085i \(0.459924\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 5.34565 0.573114
\(88\) 0 0
\(89\) 4.33641 7.51089i 0.459659 0.796152i −0.539284 0.842124i \(-0.681305\pi\)
0.998943 + 0.0459717i \(0.0146384\pi\)
\(90\) 0 0
\(91\) −0.264419 + 0.457986i −0.0277186 + 0.0480100i
\(92\) 0 0
\(93\) −4.40841 7.63558i −0.457130 0.791773i
\(94\) 0 0
\(95\) −7.96608 8.50161i −0.817303 0.872246i
\(96\) 0 0
\(97\) 2.95684 + 5.12140i 0.300222 + 0.520000i 0.976186 0.216935i \(-0.0696059\pi\)
−0.675964 + 0.736935i \(0.736273\pi\)
\(98\) 0 0
\(99\) −1.90841 + 3.30545i −0.191802 + 0.332211i
\(100\) 0 0
\(101\) −4.14399 + 7.17760i −0.412342 + 0.714197i −0.995145 0.0984158i \(-0.968622\pi\)
0.582803 + 0.812613i \(0.301956\pi\)
\(102\) 0 0
\(103\) −14.6521 −1.44371 −0.721857 0.692043i \(-0.756711\pi\)
−0.721857 + 0.692043i \(0.756711\pi\)
\(104\) 0 0
\(105\) −4.90841 + 8.50161i −0.479011 + 0.829672i
\(106\) 0 0
\(107\) 16.6913 1.61361 0.806804 0.590819i \(-0.201195\pi\)
0.806804 + 0.590819i \(0.201195\pi\)
\(108\) 0 0
\(109\) −3.91764 6.78555i −0.375242 0.649938i 0.615121 0.788432i \(-0.289107\pi\)
−0.990363 + 0.138494i \(0.955774\pi\)
\(110\) 0 0
\(111\) −0.500000 0.866025i −0.0474579 0.0821995i
\(112\) 0 0
\(113\) −6.38485 −0.600636 −0.300318 0.953839i \(-0.597093\pi\)
−0.300318 + 0.953839i \(0.597093\pi\)
\(114\) 0 0
\(115\) 20.1233 1.87650
\(116\) 0 0
\(117\) −0.0719933 0.124696i −0.00665578 0.0115281i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 3.56804 0.324367
\(122\) 0 0
\(123\) 2.67282 4.62947i 0.241000 0.417425i
\(124\) 0 0
\(125\) 7.63362 0.682772
\(126\) 0 0
\(127\) 1.32718 2.29874i 0.117768 0.203980i −0.801115 0.598511i \(-0.795759\pi\)
0.918883 + 0.394531i \(0.129093\pi\)
\(128\) 0 0
\(129\) −1.40841 + 2.43943i −0.124003 + 0.214780i
\(130\) 0 0
\(131\) −5.67282 9.82562i −0.495637 0.858468i 0.504350 0.863499i \(-0.331732\pi\)
−0.999987 + 0.00503076i \(0.998399\pi\)
\(132\) 0 0
\(133\) −15.5905 + 3.63875i −1.35186 + 0.315519i
\(134\) 0 0
\(135\) −1.33641 2.31473i −0.115020 0.199221i
\(136\) 0 0
\(137\) 0.816810 1.41476i 0.0697848 0.120871i −0.829022 0.559216i \(-0.811102\pi\)
0.898806 + 0.438346i \(0.144435\pi\)
\(138\) 0 0
\(139\) 3.75405 6.50221i 0.318415 0.551510i −0.661743 0.749731i \(-0.730183\pi\)
0.980157 + 0.198221i \(0.0635163\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) −0.274785 + 0.475941i −0.0229786 + 0.0398002i
\(144\) 0 0
\(145\) 14.2880 1.18655
\(146\) 0 0
\(147\) 3.24482 + 5.62019i 0.267628 + 0.463545i
\(148\) 0 0
\(149\) −7.00924 12.1404i −0.574219 0.994576i −0.996126 0.0879373i \(-0.971972\pi\)
0.421907 0.906639i \(-0.361361\pi\)
\(150\) 0 0
\(151\) −11.0577 −0.899861 −0.449930 0.893064i \(-0.648551\pi\)
−0.449930 + 0.893064i \(0.648551\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −11.7829 20.4086i −0.946424 1.63926i
\(156\) 0 0
\(157\) −7.02884 12.1743i −0.560962 0.971615i −0.997413 0.0718869i \(-0.977098\pi\)
0.436451 0.899728i \(-0.356235\pi\)
\(158\) 0 0
\(159\) −8.01847 −0.635906
\(160\) 0 0
\(161\) 13.8260 23.9474i 1.08965 1.88732i
\(162\) 0 0
\(163\) −4.61515 −0.361486 −0.180743 0.983530i \(-0.557850\pi\)
−0.180743 + 0.983530i \(0.557850\pi\)
\(164\) 0 0
\(165\) −5.10083 + 8.83490i −0.397099 + 0.687796i
\(166\) 0 0
\(167\) −6.11007 + 10.5829i −0.472811 + 0.818933i −0.999516 0.0311155i \(-0.990094\pi\)
0.526705 + 0.850048i \(0.323427\pi\)
\(168\) 0 0
\(169\) 6.48963 + 11.2404i 0.499203 + 0.864644i
\(170\) 0 0
\(171\) 1.26442 4.17148i 0.0966925 0.319001i
\(172\) 0 0
\(173\) −7.52884 13.0403i −0.572407 0.991438i −0.996318 0.0857340i \(-0.972676\pi\)
0.423911 0.905704i \(-0.360657\pi\)
\(174\) 0 0
\(175\) −3.93724 + 6.81950i −0.297628 + 0.515506i
\(176\) 0 0
\(177\) −1.90841 + 3.30545i −0.143445 + 0.248453i
\(178\) 0 0
\(179\) 15.1625 1.13330 0.566648 0.823960i \(-0.308240\pi\)
0.566648 + 0.823960i \(0.308240\pi\)
\(180\) 0 0
\(181\) −6.10083 + 10.5669i −0.453471 + 0.785435i −0.998599 0.0529179i \(-0.983148\pi\)
0.545128 + 0.838353i \(0.316481\pi\)
\(182\) 0 0
\(183\) −11.4896 −0.849338
\(184\) 0 0
\(185\) −1.33641 2.31473i −0.0982550 0.170183i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −3.67282 −0.267159
\(190\) 0 0
\(191\) −5.45043 −0.394379 −0.197190 0.980365i \(-0.563181\pi\)
−0.197190 + 0.980365i \(0.563181\pi\)
\(192\) 0 0
\(193\) 0.255183 + 0.441990i 0.0183685 + 0.0318151i 0.875064 0.484008i \(-0.160819\pi\)
−0.856695 + 0.515823i \(0.827486\pi\)
\(194\) 0 0
\(195\) −0.192425 0.333290i −0.0137799 0.0238674i
\(196\) 0 0
\(197\) 22.9608 1.63589 0.817945 0.575297i \(-0.195114\pi\)
0.817945 + 0.575297i \(0.195114\pi\)
\(198\) 0 0
\(199\) −0.0627577 + 0.108700i −0.00444878 + 0.00770551i −0.868241 0.496142i \(-0.834749\pi\)
0.863792 + 0.503848i \(0.168083\pi\)
\(200\) 0 0
\(201\) 5.38485 0.379818
\(202\) 0 0
\(203\) 9.81681 17.0032i 0.689005 1.19339i
\(204\) 0 0
\(205\) 7.14399 12.3737i 0.498958 0.864220i
\(206\) 0 0
\(207\) 3.76442 + 6.52016i 0.261645 + 0.453183i
\(208\) 0 0
\(209\) −16.2017 + 3.78140i −1.12069 + 0.261565i
\(210\) 0 0
\(211\) 12.4269 + 21.5240i 0.855501 + 1.48177i 0.876179 + 0.481986i \(0.160084\pi\)
−0.0206776 + 0.999786i \(0.506582\pi\)
\(212\) 0 0
\(213\) 6.81681 11.8071i 0.467080 0.809007i
\(214\) 0 0
\(215\) −3.76442 + 6.52016i −0.256731 + 0.444672i
\(216\) 0 0
\(217\) −32.3826 −2.19827
\(218\) 0 0
\(219\) −0.172824 + 0.299339i −0.0116783 + 0.0202275i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −11.8980 20.6080i −0.796752 1.38001i −0.921721 0.387854i \(-0.873217\pi\)
0.124969 0.992161i \(-0.460117\pi\)
\(224\) 0 0
\(225\) −1.07199 1.85675i −0.0714662 0.123783i
\(226\) 0 0
\(227\) −9.81681 −0.651565 −0.325782 0.945445i \(-0.605628\pi\)
−0.325782 + 0.945445i \(0.605628\pi\)
\(228\) 0 0
\(229\) 0.143987 0.00951490 0.00475745 0.999989i \(-0.498486\pi\)
0.00475745 + 0.999989i \(0.498486\pi\)
\(230\) 0 0
\(231\) 7.00924 + 12.1404i 0.461174 + 0.798777i
\(232\) 0 0
\(233\) −5.28797 9.15904i −0.346427 0.600029i 0.639185 0.769053i \(-0.279272\pi\)
−0.985612 + 0.169024i \(0.945938\pi\)
\(234\) 0 0
\(235\) −16.0369 −1.04613
\(236\) 0 0
\(237\) −3.26442 + 5.65414i −0.212047 + 0.367276i
\(238\) 0 0
\(239\) 9.81681 0.634997 0.317498 0.948259i \(-0.397157\pi\)
0.317498 + 0.948259i \(0.397157\pi\)
\(240\) 0 0
\(241\) −0.971163 + 1.68210i −0.0625581 + 0.108354i −0.895608 0.444844i \(-0.853259\pi\)
0.833050 + 0.553198i \(0.186593\pi\)
\(242\) 0 0
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) 8.67282 + 15.0218i 0.554086 + 0.959706i
\(246\) 0 0
\(247\) 0.182059 0.600637i 0.0115842 0.0382176i
\(248\) 0 0
\(249\) 1.14399 + 1.98144i 0.0724972 + 0.125569i
\(250\) 0 0
\(251\) 6.81681 11.8071i 0.430273 0.745255i −0.566623 0.823977i \(-0.691751\pi\)
0.996897 + 0.0787218i \(0.0250839\pi\)
\(252\) 0 0
\(253\) 14.3681 24.8862i 0.903313 1.56458i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.29721 10.9071i 0.392809 0.680365i −0.600010 0.799993i \(-0.704837\pi\)
0.992819 + 0.119627i \(0.0381700\pi\)
\(258\) 0 0
\(259\) −3.67282 −0.228218
\(260\) 0 0
\(261\) 2.67282 + 4.62947i 0.165444 + 0.286557i
\(262\) 0 0
\(263\) −0.816810 1.41476i −0.0503667 0.0872376i 0.839743 0.542984i \(-0.182706\pi\)
−0.890110 + 0.455747i \(0.849372\pi\)
\(264\) 0 0
\(265\) −21.4320 −1.31655
\(266\) 0 0
\(267\) 8.67282 0.530768
\(268\) 0 0
\(269\) 10.8260 + 18.7513i 0.660076 + 1.14328i 0.980595 + 0.196043i \(0.0628091\pi\)
−0.320520 + 0.947242i \(0.603858\pi\)
\(270\) 0 0
\(271\) −10.7776 18.6674i −0.654693 1.13396i −0.981971 0.189033i \(-0.939465\pi\)
0.327278 0.944928i \(-0.393869\pi\)
\(272\) 0 0
\(273\) −0.528837 −0.0320067
\(274\) 0 0
\(275\) −4.09159 + 7.08685i −0.246732 + 0.427353i
\(276\) 0 0
\(277\) 7.62571 0.458185 0.229092 0.973405i \(-0.426424\pi\)
0.229092 + 0.973405i \(0.426424\pi\)
\(278\) 0 0
\(279\) 4.40841 7.63558i 0.263924 0.457130i
\(280\) 0 0
\(281\) 0.846778 1.46666i 0.0505145 0.0874937i −0.839663 0.543109i \(-0.817247\pi\)
0.890177 + 0.455615i \(0.150581\pi\)
\(282\) 0 0
\(283\) 5.14399 + 8.90965i 0.305778 + 0.529623i 0.977434 0.211240i \(-0.0677500\pi\)
−0.671656 + 0.740863i \(0.734417\pi\)
\(284\) 0 0
\(285\) 3.37957 11.1496i 0.200188 0.660447i
\(286\) 0 0
\(287\) −9.81681 17.0032i −0.579468 1.00367i
\(288\) 0 0
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) 0 0
\(291\) −2.95684 + 5.12140i −0.173333 + 0.300222i
\(292\) 0 0
\(293\) 12.1153 0.707786 0.353893 0.935286i \(-0.384858\pi\)
0.353893 + 0.935286i \(0.384858\pi\)
\(294\) 0 0
\(295\) −5.10083 + 8.83490i −0.296982 + 0.514388i
\(296\) 0 0
\(297\) −3.81681 −0.221474
\(298\) 0 0
\(299\) 0.542026 + 0.938816i 0.0313461 + 0.0542931i
\(300\) 0 0
\(301\) 5.17282 + 8.95959i 0.298157 + 0.516422i
\(302\) 0 0
\(303\) −8.28797 −0.476132
\(304\) 0 0
\(305\) −30.7098 −1.75844
\(306\) 0 0
\(307\) −2.24482 3.88814i −0.128118 0.221908i 0.794829 0.606833i \(-0.207560\pi\)
−0.922948 + 0.384926i \(0.874227\pi\)
\(308\) 0 0
\(309\) −7.32605 12.6891i −0.416764 0.721857i
\(310\) 0 0
\(311\) −0.759136 −0.0430466 −0.0215233 0.999768i \(-0.506852\pi\)
−0.0215233 + 0.999768i \(0.506852\pi\)
\(312\) 0 0
\(313\) −5.71598 + 9.90037i −0.323086 + 0.559602i −0.981123 0.193384i \(-0.938054\pi\)
0.658037 + 0.752986i \(0.271387\pi\)
\(314\) 0 0
\(315\) −9.81681 −0.553115
\(316\) 0 0
\(317\) 5.80757 10.0590i 0.326186 0.564971i −0.655566 0.755138i \(-0.727570\pi\)
0.981752 + 0.190168i \(0.0609031\pi\)
\(318\) 0 0
\(319\) 10.2017 17.6698i 0.571183 0.989319i
\(320\) 0 0
\(321\) 8.34565 + 14.4551i 0.465809 + 0.806804i
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −0.154353 0.267347i −0.00856194 0.0148297i
\(326\) 0 0
\(327\) 3.91764 6.78555i 0.216646 0.375242i
\(328\) 0 0
\(329\) −11.0185 + 19.0846i −0.607468 + 1.05217i
\(330\) 0 0
\(331\) 11.4712 0.630512 0.315256 0.949007i \(-0.397910\pi\)
0.315256 + 0.949007i \(0.397910\pi\)
\(332\) 0 0
\(333\) 0.500000 0.866025i 0.0273998 0.0474579i
\(334\) 0 0
\(335\) 14.3928 0.786360
\(336\) 0 0
\(337\) −3.78402 6.55412i −0.206129 0.357025i 0.744363 0.667775i \(-0.232753\pi\)
−0.950492 + 0.310750i \(0.899420\pi\)
\(338\) 0 0
\(339\) −3.19243 5.52944i −0.173389 0.300318i
\(340\) 0 0
\(341\) −33.6521 −1.82236
\(342\) 0 0
\(343\) −1.87448 −0.101213
\(344\) 0 0
\(345\) 10.0616 + 17.4272i 0.541700 + 0.938252i
\(346\) 0 0
\(347\) 10.9084 + 18.8939i 0.585594 + 1.01428i 0.994801 + 0.101837i \(0.0324720\pi\)
−0.409207 + 0.912441i \(0.634195\pi\)
\(348\) 0 0
\(349\) −4.54731 −0.243412 −0.121706 0.992566i \(-0.538836\pi\)
−0.121706 + 0.992566i \(0.538836\pi\)
\(350\) 0 0
\(351\) 0.0719933 0.124696i 0.00384272 0.00665578i
\(352\) 0 0
\(353\) −8.99774 −0.478901 −0.239451 0.970909i \(-0.576967\pi\)
−0.239451 + 0.970909i \(0.576967\pi\)
\(354\) 0 0
\(355\) 18.2201 31.5582i 0.967024 1.67494i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6.48963 + 11.2404i 0.342510 + 0.593244i 0.984898 0.173135i \(-0.0553897\pi\)
−0.642388 + 0.766379i \(0.722056\pi\)
\(360\) 0 0
\(361\) 17.0369 8.41086i 0.896681 0.442677i
\(362\) 0 0
\(363\) 1.78402 + 3.09001i 0.0936368 + 0.162184i
\(364\) 0 0
\(365\) −0.461927 + 0.800082i −0.0241784 + 0.0418782i
\(366\) 0 0
\(367\) −2.02355 + 3.50490i −0.105629 + 0.182954i −0.913995 0.405726i \(-0.867019\pi\)
0.808366 + 0.588680i \(0.200352\pi\)
\(368\) 0 0
\(369\) 5.34565 0.278283
\(370\) 0 0
\(371\) −14.7252 + 25.5048i −0.764495 + 1.32414i
\(372\) 0 0
\(373\) 3.79834 0.196671 0.0983353 0.995153i \(-0.468648\pi\)
0.0983353 + 0.995153i \(0.468648\pi\)
\(374\) 0 0
\(375\) 3.81681 + 6.61091i 0.197099 + 0.341386i
\(376\) 0 0
\(377\) 0.384851 + 0.666581i 0.0198208 + 0.0343307i
\(378\) 0 0
\(379\) −4.89522 −0.251450 −0.125725 0.992065i \(-0.540126\pi\)
−0.125725 + 0.992065i \(0.540126\pi\)
\(380\) 0 0
\(381\) 2.65435 0.135987
\(382\) 0 0
\(383\) 17.0709 + 29.5676i 0.872280 + 1.51083i 0.859632 + 0.510914i \(0.170693\pi\)
0.0126484 + 0.999920i \(0.495974\pi\)
\(384\) 0 0
\(385\) 18.7345 + 32.4490i 0.954796 + 1.65376i
\(386\) 0 0
\(387\) −2.81681 −0.143187
\(388\) 0 0
\(389\) −13.4412 + 23.2808i −0.681496 + 1.18039i 0.293029 + 0.956104i \(0.405337\pi\)
−0.974524 + 0.224281i \(0.927997\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 5.67282 9.82562i 0.286156 0.495637i
\(394\) 0 0
\(395\) −8.72522 + 15.1125i −0.439013 + 0.760393i
\(396\) 0 0
\(397\) −12.6193 21.8573i −0.633345 1.09699i −0.986863 0.161558i \(-0.948348\pi\)
0.353519 0.935427i \(-0.384985\pi\)
\(398\) 0 0
\(399\) −10.9465 11.6824i −0.548009 0.584850i
\(400\) 0 0
\(401\) 1.66359 + 2.88142i 0.0830756 + 0.143891i 0.904570 0.426326i \(-0.140192\pi\)
−0.821494 + 0.570217i \(0.806859\pi\)
\(402\) 0 0
\(403\) 0.634751 1.09942i 0.0316192 0.0547661i
\(404\) 0 0
\(405\) 1.33641 2.31473i 0.0664068 0.115020i
\(406\) 0 0
\(407\) −3.81681 −0.189192
\(408\) 0 0
\(409\) −17.0616 + 29.5516i −0.843643 + 1.46123i 0.0431512 + 0.999069i \(0.486260\pi\)
−0.886794 + 0.462164i \(0.847073\pi\)
\(410\) 0 0
\(411\) 1.63362 0.0805806
\(412\) 0 0
\(413\) 7.00924 + 12.1404i 0.344902 + 0.597388i
\(414\) 0 0
\(415\) 3.05767 + 5.29605i 0.150095 + 0.259973i
\(416\) 0 0
\(417\) 7.50811 0.367673
\(418\) 0 0
\(419\) 9.16246 0.447615 0.223808 0.974633i \(-0.428151\pi\)
0.223808 + 0.974633i \(0.428151\pi\)
\(420\) 0 0
\(421\) 7.91764 + 13.7138i 0.385882 + 0.668368i 0.991891 0.127090i \(-0.0405638\pi\)
−0.606009 + 0.795458i \(0.707230\pi\)
\(422\) 0 0
\(423\) −3.00000 5.19615i −0.145865 0.252646i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −21.0997 + 36.5458i −1.02109 + 1.76857i
\(428\) 0 0
\(429\) −0.549569 −0.0265335
\(430\) 0 0
\(431\) −4.63362 + 8.02567i −0.223194 + 0.386583i −0.955776 0.294096i \(-0.904982\pi\)
0.732582 + 0.680678i \(0.238315\pi\)
\(432\) 0 0
\(433\) 9.90727 17.1599i 0.476113 0.824652i −0.523512 0.852018i \(-0.675379\pi\)
0.999625 + 0.0273658i \(0.00871190\pi\)
\(434\) 0 0
\(435\) 7.14399 + 12.3737i 0.342528 + 0.593276i
\(436\) 0 0
\(437\) −9.51960 + 31.4064i −0.455384 + 1.50237i
\(438\) 0 0
\(439\) 3.45156 + 5.97828i 0.164734 + 0.285328i 0.936561 0.350505i \(-0.113990\pi\)
−0.771827 + 0.635833i \(0.780657\pi\)
\(440\) 0 0
\(441\) −3.24482 + 5.62019i −0.154515 + 0.267628i
\(442\) 0 0
\(443\) −9.81681 + 17.0032i −0.466411 + 0.807847i −0.999264 0.0383606i \(-0.987786\pi\)
0.532853 + 0.846208i \(0.321120\pi\)
\(444\) 0 0
\(445\) 23.1809 1.09888
\(446\) 0 0
\(447\) 7.00924 12.1404i 0.331525 0.574219i
\(448\) 0 0
\(449\) 29.0162 1.36936 0.684680 0.728844i \(-0.259942\pi\)
0.684680 + 0.728844i \(0.259942\pi\)
\(450\) 0 0
\(451\) −10.2017 17.6698i −0.480377 0.832038i
\(452\) 0 0
\(453\) −5.52884 9.57623i −0.259767 0.449930i
\(454\) 0 0
\(455\) −1.41349 −0.0662654
\(456\) 0 0
\(457\) 32.5473 1.52250 0.761249 0.648459i \(-0.224586\pi\)
0.761249 + 0.648459i \(0.224586\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4.82605 + 8.35896i 0.224771 + 0.389315i 0.956251 0.292548i \(-0.0945031\pi\)
−0.731479 + 0.681863i \(0.761170\pi\)
\(462\) 0 0
\(463\) 31.0554 1.44327 0.721634 0.692275i \(-0.243392\pi\)
0.721634 + 0.692275i \(0.243392\pi\)
\(464\) 0 0
\(465\) 11.7829 20.4086i 0.546418 0.946424i
\(466\) 0 0
\(467\) −8.61289 −0.398557 −0.199278 0.979943i \(-0.563860\pi\)
−0.199278 + 0.979943i \(0.563860\pi\)
\(468\) 0 0
\(469\) 9.88880 17.1279i 0.456623 0.790893i
\(470\) 0 0
\(471\) 7.02884 12.1743i 0.323872 0.560962i
\(472\) 0 0
\(473\) 5.37562 + 9.31084i 0.247171 + 0.428113i
\(474\) 0 0
\(475\) 2.71090 8.94360i 0.124384 0.410360i
\(476\) 0 0
\(477\) −4.00924 6.94420i −0.183570 0.317953i
\(478\) 0 0
\(479\) 8.73050 15.1217i 0.398907 0.690927i −0.594685 0.803959i \(-0.702723\pi\)
0.993591 + 0.113032i \(0.0360564\pi\)
\(480\) 0 0
\(481\) 0.0719933 0.124696i 0.00328261 0.00568565i
\(482\) 0 0
\(483\) 27.6521 1.25821
\(484\) 0 0
\(485\) −7.90312 + 13.6886i −0.358862 + 0.621568i
\(486\) 0 0
\(487\) 11.6336 0.527170 0.263585 0.964636i \(-0.415095\pi\)
0.263585 + 0.964636i \(0.415095\pi\)
\(488\) 0 0
\(489\) −2.30757 3.99684i −0.104352 0.180743i
\(490\) 0 0
\(491\) −12.1625 21.0660i −0.548884 0.950695i −0.998351 0.0573983i \(-0.981720\pi\)
0.449467 0.893297i \(-0.351614\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −10.2017 −0.458531
\(496\) 0 0
\(497\) −25.0369 43.3653i −1.12306 1.94520i
\(498\) 0 0
\(499\) 19.0565 + 33.0069i 0.853088 + 1.47759i 0.878407 + 0.477912i \(0.158606\pi\)
−0.0253194 + 0.999679i \(0.508060\pi\)
\(500\) 0 0
\(501\) −12.2201 −0.545955
\(502\) 0 0
\(503\) 2.18319 3.78140i 0.0973436 0.168604i −0.813241 0.581927i \(-0.802299\pi\)
0.910584 + 0.413323i \(0.135632\pi\)
\(504\) 0 0
\(505\) −22.1523 −0.985764
\(506\) 0 0
\(507\) −6.48963 + 11.2404i −0.288215 + 0.499203i
\(508\) 0 0
\(509\) 7.85601 13.6070i 0.348212 0.603120i −0.637720 0.770268i \(-0.720122\pi\)
0.985932 + 0.167148i \(0.0534557\pi\)
\(510\) 0 0
\(511\) 0.634751 + 1.09942i 0.0280797 + 0.0486355i
\(512\) 0 0
\(513\) 4.24482 0.990721i 0.187413 0.0437414i
\(514\) 0 0
\(515\) −19.5812 33.9157i −0.862852 1.49450i
\(516\) 0 0
\(517\) −11.4504 + 19.8327i −0.503589 + 0.872242i
\(518\) 0 0
\(519\) 7.52884 13.0403i 0.330479 0.572407i
\(520\) 0 0
\(521\) 33.4425 1.46514 0.732572 0.680690i \(-0.238320\pi\)
0.732572 + 0.680690i \(0.238320\pi\)
\(522\) 0 0
\(523\) −14.7109 + 25.4800i −0.643263 + 1.11416i 0.341437 + 0.939905i \(0.389086\pi\)
−0.984700 + 0.174259i \(0.944247\pi\)
\(524\) 0 0
\(525\) −7.87448 −0.343671
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −16.8417 29.1707i −0.732248 1.26829i
\(530\) 0 0
\(531\) −3.81681 −0.165635
\(532\) 0 0
\(533\) 0.769701 0.0333395
\(534\) 0 0
\(535\) 22.3064 + 38.6359i 0.964392 + 1.67038i
\(536\) 0 0
\(537\) 7.58123 + 13.1311i 0.327154 + 0.566648i
\(538\) 0 0
\(539\) 24.7697 1.06691
\(540\) 0 0
\(541\) −13.0865 + 22.6665i −0.562633 + 0.974509i 0.434632 + 0.900608i \(0.356878\pi\)
−0.997266 + 0.0739012i \(0.976455\pi\)
\(542\) 0 0
\(543\) −12.2017 −0.523623
\(544\) 0 0
\(545\) 10.4712 18.1366i 0.448535 0.776886i
\(546\) 0 0
\(547\) 10.9557 18.9759i 0.468432 0.811349i −0.530917 0.847424i \(-0.678152\pi\)
0.999349 + 0.0360752i \(0.0114856\pi\)
\(548\) 0 0
\(549\) −5.74482 9.95031i −0.245183 0.424669i
\(550\) 0 0
\(551\) −6.75914 + 22.2993i −0.287949 + 0.949980i
\(552\) 0 0
\(553\) 11.9896 + 20.7667i 0.509851 + 0.883088i
\(554\) 0 0
\(555\) 1.33641 2.31473i 0.0567275 0.0982550i
\(556\) 0 0
\(557\) −17.0185 + 29.4769i −0.721096 + 1.24897i 0.239465 + 0.970905i \(0.423028\pi\)
−0.960561 + 0.278070i \(0.910305\pi\)
\(558\) 0 0
\(559\) −0.405583 −0.0171543
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −11.5552 −0.486994 −0.243497 0.969902i \(-0.578295\pi\)
−0.243497 + 0.969902i \(0.578295\pi\)
\(564\) 0 0
\(565\) −8.53279 14.7792i −0.358977 0.621767i
\(566\) 0 0
\(567\) −1.83641 3.18076i −0.0771220 0.133579i
\(568\) 0 0
\(569\) 39.7075 1.66463 0.832313 0.554307i \(-0.187016\pi\)
0.832313 + 0.554307i \(0.187016\pi\)
\(570\) 0 0
\(571\) −14.6521 −0.613171 −0.306585 0.951843i \(-0.599187\pi\)
−0.306585 + 0.951843i \(0.599187\pi\)
\(572\) 0 0
\(573\) −2.72522 4.72021i −0.113848 0.197190i
\(574\) 0 0
\(575\) 8.07086 + 13.9791i 0.336578 + 0.582971i
\(576\) 0 0
\(577\) 20.8145 0.866521 0.433261 0.901269i \(-0.357363\pi\)
0.433261 + 0.901269i \(0.357363\pi\)
\(578\) 0 0
\(579\) −0.255183 + 0.441990i −0.0106050 + 0.0183685i
\(580\) 0 0
\(581\) 8.40332 0.348629
\(582\) 0 0
\(583\) −15.3025 + 26.5047i −0.633764 + 1.09771i
\(584\) 0 0
\(585\) 0.192425 0.333290i 0.00795581 0.0137799i
\(586\) 0 0
\(587\) 9.82209 + 17.0124i 0.405401 + 0.702175i 0.994368 0.105982i \(-0.0337985\pi\)
−0.588967 + 0.808157i \(0.700465\pi\)
\(588\) 0 0
\(589\) 37.4257 8.73500i 1.54210 0.359920i
\(590\) 0 0
\(591\) 11.4804 + 19.8846i 0.472240 + 0.817945i
\(592\) 0 0
\(593\) −10.8260 + 18.7513i −0.444572 + 0.770022i −0.998022 0.0628605i \(-0.979978\pi\)
0.553450 + 0.832882i \(0.313311\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −0.125515 −0.00513700
\(598\) 0 0
\(599\) −5.88993 + 10.2017i −0.240656 + 0.416829i −0.960901 0.276891i \(-0.910696\pi\)
0.720245 + 0.693720i \(0.244029\pi\)
\(600\) 0 0
\(601\) −11.4112 −0.465474 −0.232737 0.972540i \(-0.574768\pi\)
−0.232737 + 0.972540i \(0.574768\pi\)
\(602\) 0 0
\(603\) 2.69243 + 4.66342i 0.109644 + 0.189909i
\(604\) 0 0
\(605\) 4.76837 + 8.25906i 0.193862 + 0.335779i
\(606\) 0 0
\(607\) 1.10478 0.0448418 0.0224209 0.999749i \(-0.492863\pi\)
0.0224209 + 0.999749i \(0.492863\pi\)
\(608\) 0 0
\(609\) 19.6336 0.795594
\(610\) 0 0
\(611\) −0.431960 0.748176i −0.0174752 0.0302680i
\(612\) 0 0
\(613\) −2.38880 4.13753i −0.0964829 0.167113i 0.813744 0.581224i \(-0.197426\pi\)
−0.910227 + 0.414111i \(0.864093\pi\)
\(614\) 0 0
\(615\) 14.2880 0.576147
\(616\) 0 0
\(617\) −18.7397 + 32.4582i −0.754433 + 1.30672i 0.191222 + 0.981547i \(0.438755\pi\)
−0.945656 + 0.325170i \(0.894578\pi\)
\(618\) 0 0
\(619\) 0.615149 0.0247249 0.0123625 0.999924i \(-0.496065\pi\)
0.0123625 + 0.999924i \(0.496065\pi\)
\(620\) 0 0
\(621\) −3.76442 + 6.52016i −0.151061 + 0.261645i
\(622\) 0 0
\(623\) 15.9269 27.5862i 0.638097 1.10522i
\(624\) 0 0
\(625\) 15.5616 + 26.9535i 0.622465 + 1.07814i
\(626\) 0 0
\(627\) −11.3756 12.1404i −0.454298 0.484839i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 10.6532 18.4519i 0.424098 0.734559i −0.572238 0.820088i \(-0.693925\pi\)
0.996336 + 0.0855284i \(0.0272578\pi\)
\(632\) 0 0
\(633\) −12.4269 + 21.5240i −0.493924 + 0.855501i
\(634\) 0 0
\(635\) 7.09462 0.281541
\(636\) 0 0
\(637\) −0.467210 + 0.809231i −0.0185115 + 0.0320629i
\(638\) 0 0
\(639\) 13.6336 0.539338
\(640\) 0 0
\(641\) −19.9608 34.5731i −0.788404 1.36556i −0.926944 0.375199i \(-0.877574\pi\)
0.138540 0.990357i \(-0.455759\pi\)
\(642\) 0 0
\(643\) −18.6924 32.3762i −0.737157 1.27679i −0.953770 0.300536i \(-0.902834\pi\)
0.216613 0.976258i \(-0.430499\pi\)
\(644\) 0 0
\(645\) −7.52884 −0.296448
\(646\) 0 0
\(647\) −16.0369 −0.630477 −0.315239 0.949012i \(-0.602085\pi\)
−0.315239 + 0.949012i \(0.602085\pi\)
\(648\) 0 0
\(649\) 7.28402 + 12.6163i 0.285923 + 0.495233i
\(650\) 0 0
\(651\) −16.1913 28.0441i −0.634587 1.09914i
\(652\) 0 0
\(653\) 13.4241 0.525324 0.262662 0.964888i \(-0.415400\pi\)
0.262662 + 0.964888i \(0.415400\pi\)
\(654\) 0 0
\(655\) 15.1625 26.2621i 0.592446 1.02615i
\(656\) 0 0
\(657\) −0.345647 −0.0134850
\(658\) 0 0
\(659\) −9.27252 + 16.0605i −0.361206 + 0.625628i −0.988160 0.153429i \(-0.950968\pi\)
0.626953 + 0.779057i \(0.284302\pi\)
\(660\) 0 0
\(661\) −3.28797 + 5.69494i −0.127887 + 0.221507i −0.922858 0.385141i \(-0.874153\pi\)
0.794971 + 0.606648i \(0.207486\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −29.2580 31.2249i −1.13458 1.21085i
\(666\) 0 0
\(667\) −20.1233 34.8545i −0.779176 1.34957i
\(668\) 0 0
\(669\) 11.8980 20.6080i 0.460005 0.796752i
\(670\) 0 0
\(671\) −21.9269 + 37.9785i −0.846478 + 1.46614i
\(672\) 0 0
\(673\) −39.2386 −1.51254 −0.756268 0.654261i \(-0.772980\pi\)
−0.756268 + 0.654261i \(0.772980\pi\)
\(674\) 0 0
\(675\) 1.07199 1.85675i 0.0412610 0.0714662i
\(676\) 0 0
\(677\) −25.8432 −0.993234 −0.496617 0.867970i \(-0.665425\pi\)
−0.496617 + 0.867970i \(0.665425\pi\)
\(678\) 0 0
\(679\) 10.8600 + 18.8100i 0.416767 + 0.721862i
\(680\) 0 0
\(681\) −4.90841 8.50161i −0.188090 0.325782i
\(682\) 0 0
\(683\) −42.9898 −1.64496 −0.822480 0.568794i \(-0.807410\pi\)
−0.822480 + 0.568794i \(0.807410\pi\)
\(684\) 0 0
\(685\) 4.36638 0.166831
\(686\) 0 0
\(687\) 0.0719933 + 0.124696i 0.00274671 + 0.00475745i
\(688\) 0 0
\(689\) −0.577276 0.999871i −0.0219925 0.0380921i
\(690\) 0 0
\(691\) 48.4033 1.84135 0.920675 0.390331i \(-0.127639\pi\)
0.920675 + 0.390331i \(0.127639\pi\)
\(692\) 0 0
\(693\) −7.00924 + 12.1404i −0.266259 + 0.461174i
\(694\) 0 0
\(695\) 20.0678 0.761217
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 5.28797 9.15904i 0.200010 0.346427i
\(700\) 0 0
\(701\) 1.60591 + 2.78152i 0.0606545 + 0.105057i 0.894758 0.446551i \(-0.147348\pi\)
−0.834104 + 0.551608i \(0.814015\pi\)
\(702\) 0 0
\(703\) 4.24482 0.990721i 0.160096 0.0373658i
\(704\) 0 0
\(705\) −8.01847 13.8884i −0.301993 0.523067i
\(706\) 0 0
\(707\) −15.2201 + 26.3620i −0.572412 + 0.991447i
\(708\) 0 0
\(709\) −11.0328 + 19.1094i −0.414345 + 0.717667i −0.995359 0.0962265i \(-0.969323\pi\)
0.581014 + 0.813893i \(0.302656\pi\)
\(710\) 0 0
\(711\) −6.52884 −0.244851
\(712\) 0 0
\(713\) −33.1902 + 57.4871i −1.24298 + 2.15291i
\(714\) 0 0
\(715\) −1.46890 −0.0549338
\(716\) 0 0
\(717\) 4.90841 + 8.50161i 0.183308 + 0.317498i
\(718\) 0 0
\(719\) 8.83000 + 15.2940i 0.329303 + 0.570370i 0.982374 0.186927i \(-0.0598528\pi\)
−0.653070 + 0.757297i \(0.726519\pi\)
\(720\) 0 0
\(721\) −53.8145 −2.00416
\(722\) 0 0
\(723\) −1.94233 −0.0722359
\(724\) 0 0
\(725\) 5.73050 + 9.92551i 0.212825 + 0.368624i
\(726\) 0 0
\(727\) −20.1966 34.9815i −0.749050 1.29739i −0.948279 0.317439i \(-0.897177\pi\)
0.199229 0.979953i \(-0.436156\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −17.9137 −0.661657 −0.330829 0.943691i \(-0.607328\pi\)
−0.330829 + 0.943691i \(0.607328\pi\)
\(734\) 0 0
\(735\) −8.67282 + 15.0218i −0.319902 + 0.554086i
\(736\) 0 0
\(737\) 10.2765 17.7994i 0.378539 0.655649i
\(738\) 0 0
\(739\) −8.48850 14.7025i −0.312255 0.540841i 0.666595 0.745420i \(-0.267751\pi\)
−0.978850 + 0.204579i \(0.934418\pi\)
\(740\) 0 0
\(741\) 0.611196 0.142651i 0.0224529 0.00524040i
\(742\) 0 0
\(743\) −25.3588 43.9228i −0.930325 1.61137i −0.782765 0.622318i \(-0.786191\pi\)
−0.147561 0.989053i \(-0.547142\pi\)
\(744\) 0 0
\(745\) 18.7345 32.4490i 0.686377 1.18884i
\(746\) 0 0
\(747\) −1.14399 + 1.98144i −0.0418563 + 0.0724972i
\(748\) 0 0
\(749\) 61.3042 2.24001
\(750\) 0 0
\(751\) −12.7972 + 22.1654i −0.466977 + 0.808828i −0.999288 0.0377210i \(-0.987990\pi\)
0.532312 + 0.846549i \(0.321324\pi\)
\(752\) 0 0
\(753\) 13.6336 0.496837
\(754\) 0 0
\(755\) −14.7776 25.5956i −0.537812 0.931518i
\(756\) 0 0
\(757\) −22.8681 39.6087i −0.831154 1.43960i −0.897124 0.441780i \(-0.854347\pi\)
0.0659694 0.997822i \(-0.478986\pi\)
\(758\) 0 0
\(759\) 28.7361 1.04306
\(760\) 0 0
\(761\) −44.1338 −1.59985 −0.799925 0.600100i \(-0.795127\pi\)
−0.799925 + 0.600100i \(0.795127\pi\)
\(762\) 0 0
\(763\) −14.3888 24.9221i −0.520910 0.902242i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −0.549569 −0.0198438
\(768\) 0 0
\(769\) 22.0473 38.1871i 0.795046 1.37706i −0.127764 0.991805i \(-0.540780\pi\)
0.922810 0.385256i \(-0.125887\pi\)
\(770\) 0 0
\(771\) 12.5944 0.453577
\(772\) 0 0
\(773\) −2.45043 + 4.24427i −0.0881359 + 0.152656i −0.906723 0.421726i \(-0.861424\pi\)
0.818587 + 0.574382i \(0.194758\pi\)
\(774\) 0 0
\(775\) 9.45156 16.3706i 0.339510 0.588049i
\(776\) 0 0
\(777\) −1.83641 3.18076i −0.0658809 0.114109i
\(778\) 0 0
\(779\) 15.9322 + 17.0032i 0.570829 + 0.609203i
\(780\) 0 0
\(781\) −26.0185 45.0653i −0.931014 1.61256i
\(782\) 0 0
\(783\) −2.67282 + 4.62947i −0.0955189 + 0.165444i
\(784\) 0 0
\(785\) 18.7868 32.5398i 0.670531 1.16139i
\(786\) 0 0
\(787\) −35.0554 −1.24959 −0.624795 0.780789i \(-0.714818\pi\)
−0.624795 + 0.780789i \(0.714818\pi\)
\(788\) 0 0
\(789\) 0.816810 1.41476i 0.0290792 0.0503667i
\(790\) 0 0
\(791\) −23.4504 −0.833801
\(792\) 0 0
\(793\) −0.827176 1.43271i −0.0293739 0.0508771i
\(794\) 0 0
\(795\) −10.7160 18.5606i −0.380057 0.658277i
\(796\) 0 0
\(797\) −5.67056 −0.200862 −0.100431 0.994944i \(-0.532022\pi\)