Properties

Label 2646.2.h.o.667.1
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(0.500000 + 1.41036i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.o.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.18194 q^{5} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.18194 q^{5} +1.00000 q^{8} +(1.59097 + 2.75564i) q^{10} -3.18194 q^{11} +(-2.85185 - 4.93955i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-0.760877 - 1.31788i) q^{17} +(0.641315 - 1.11079i) q^{19} +(1.59097 - 2.75564i) q^{20} +(1.59097 + 2.75564i) q^{22} -2.23912 q^{23} +5.12476 q^{25} +(-2.85185 + 4.93955i) q^{26} +(3.54063 - 6.13255i) q^{29} +(-4.71053 + 8.15888i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.760877 + 1.31788i) q^{34} +(0.500000 - 0.866025i) q^{37} -1.28263 q^{38} -3.18194 q^{40} +(-2.80150 - 4.85235i) q^{41} +(3.41423 - 5.91362i) q^{43} +(1.59097 - 2.75564i) q^{44} +(1.11956 + 1.93914i) q^{46} +(2.91423 + 5.04759i) q^{47} +(-2.56238 - 4.43818i) q^{50} +5.70370 q^{52} +(-1.02859 - 1.78157i) q^{53} +10.1248 q^{55} -7.08126 q^{58} +(0.562382 - 0.974074i) q^{59} +(1.56238 + 2.70612i) q^{61} +9.42107 q^{62} +1.00000 q^{64} +(9.07442 + 15.7174i) q^{65} +(-5.48345 + 9.49761i) q^{67} +1.52175 q^{68} -8.69002 q^{71} +(2.48345 + 4.30146i) q^{73} -1.00000 q^{74} +(0.641315 + 1.11079i) q^{76} +(2.06922 + 3.58399i) q^{79} +(1.59097 + 2.75564i) q^{80} +(-2.80150 + 4.85235i) q^{82} +(-4.03379 + 6.98673i) q^{83} +(2.42107 + 4.19341i) q^{85} -6.82846 q^{86} -3.18194 q^{88} +(0.112725 - 0.195246i) q^{89} +(1.11956 - 1.93914i) q^{92} +(2.91423 - 5.04759i) q^{94} +(-2.04063 + 3.53447i) q^{95} +(-7.42107 + 12.8537i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} - 3 q^{4} - 2 q^{5} + 6 q^{8} + O(q^{10}) \) \( 6 q - 3 q^{2} - 3 q^{4} - 2 q^{5} + 6 q^{8} + q^{10} - 2 q^{11} - 8 q^{13} - 3 q^{16} - 4 q^{17} + 3 q^{19} + q^{20} + q^{22} - 14 q^{23} - 4 q^{25} - 8 q^{26} + 5 q^{29} - 20 q^{31} - 3 q^{32} - 4 q^{34} + 3 q^{37} - 6 q^{38} - 2 q^{40} - 6 q^{43} + q^{44} + 7 q^{46} - 9 q^{47} + 2 q^{50} + 16 q^{52} - 15 q^{53} + 26 q^{55} - 10 q^{58} - 14 q^{59} - 8 q^{61} + 40 q^{62} + 6 q^{64} + 12 q^{65} + q^{67} + 8 q^{68} - 14 q^{71} - 19 q^{73} - 6 q^{74} + 3 q^{76} + 5 q^{79} + q^{80} + 2 q^{83} - 2 q^{85} + 12 q^{86} - 2 q^{88} - 9 q^{89} + 7 q^{92} - 9 q^{94} + 4 q^{95} - 28 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −3.18194 −1.42301 −0.711504 0.702682i \(-0.751986\pi\)
−0.711504 + 0.702682i \(0.751986\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 1.59097 + 2.75564i 0.503109 + 0.871411i
\(11\) −3.18194 −0.959392 −0.479696 0.877435i \(-0.659253\pi\)
−0.479696 + 0.877435i \(0.659253\pi\)
\(12\) 0 0
\(13\) −2.85185 4.93955i −0.790960 1.36998i −0.925373 0.379058i \(-0.876248\pi\)
0.134412 0.990925i \(-0.457085\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −0.760877 1.31788i −0.184540 0.319632i 0.758882 0.651229i \(-0.225746\pi\)
−0.943421 + 0.331596i \(0.892413\pi\)
\(18\) 0 0
\(19\) 0.641315 1.11079i 0.147128 0.254833i −0.783037 0.621975i \(-0.786330\pi\)
0.930165 + 0.367142i \(0.119664\pi\)
\(20\) 1.59097 2.75564i 0.355752 0.616181i
\(21\) 0 0
\(22\) 1.59097 + 2.75564i 0.339196 + 0.587505i
\(23\) −2.23912 −0.466889 −0.233445 0.972370i \(-0.575000\pi\)
−0.233445 + 0.972370i \(0.575000\pi\)
\(24\) 0 0
\(25\) 5.12476 1.02495
\(26\) −2.85185 + 4.93955i −0.559293 + 0.968725i
\(27\) 0 0
\(28\) 0 0
\(29\) 3.54063 6.13255i 0.657478 1.13879i −0.323788 0.946130i \(-0.604957\pi\)
0.981266 0.192656i \(-0.0617101\pi\)
\(30\) 0 0
\(31\) −4.71053 + 8.15888i −0.846037 + 1.46538i 0.0386810 + 0.999252i \(0.487684\pi\)
−0.884718 + 0.466127i \(0.845649\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −0.760877 + 1.31788i −0.130489 + 0.226014i
\(35\) 0 0
\(36\) 0 0
\(37\) 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) −1.28263 −0.208070
\(39\) 0 0
\(40\) −3.18194 −0.503109
\(41\) −2.80150 4.85235i −0.437522 0.757810i 0.559976 0.828509i \(-0.310810\pi\)
−0.997498 + 0.0706992i \(0.977477\pi\)
\(42\) 0 0
\(43\) 3.41423 5.91362i 0.520665 0.901819i −0.479046 0.877790i \(-0.659017\pi\)
0.999711 0.0240288i \(-0.00764935\pi\)
\(44\) 1.59097 2.75564i 0.239848 0.415429i
\(45\) 0 0
\(46\) 1.11956 + 1.93914i 0.165070 + 0.285910i
\(47\) 2.91423 + 5.04759i 0.425084 + 0.736267i 0.996428 0.0844432i \(-0.0269112\pi\)
−0.571344 + 0.820711i \(0.693578\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −2.56238 4.43818i −0.362375 0.627653i
\(51\) 0 0
\(52\) 5.70370 0.790960
\(53\) −1.02859 1.78157i −0.141288 0.244717i 0.786694 0.617343i \(-0.211791\pi\)
−0.927982 + 0.372626i \(0.878458\pi\)
\(54\) 0 0
\(55\) 10.1248 1.36522
\(56\) 0 0
\(57\) 0 0
\(58\) −7.08126 −0.929815
\(59\) 0.562382 0.974074i 0.0732159 0.126814i −0.827093 0.562065i \(-0.810007\pi\)
0.900309 + 0.435251i \(0.143340\pi\)
\(60\) 0 0
\(61\) 1.56238 + 2.70612i 0.200042 + 0.346484i 0.948542 0.316652i \(-0.102559\pi\)
−0.748499 + 0.663135i \(0.769225\pi\)
\(62\) 9.42107 1.19648
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 9.07442 + 15.7174i 1.12554 + 1.94950i
\(66\) 0 0
\(67\) −5.48345 + 9.49761i −0.669910 + 1.16032i 0.308019 + 0.951380i \(0.400334\pi\)
−0.977929 + 0.208938i \(0.932999\pi\)
\(68\) 1.52175 0.184540
\(69\) 0 0
\(70\) 0 0
\(71\) −8.69002 −1.03132 −0.515658 0.856794i \(-0.672452\pi\)
−0.515658 + 0.856794i \(0.672452\pi\)
\(72\) 0 0
\(73\) 2.48345 + 4.30146i 0.290666 + 0.503448i 0.973967 0.226689i \(-0.0727899\pi\)
−0.683302 + 0.730136i \(0.739457\pi\)
\(74\) −1.00000 −0.116248
\(75\) 0 0
\(76\) 0.641315 + 1.11079i 0.0735639 + 0.127416i
\(77\) 0 0
\(78\) 0 0
\(79\) 2.06922 + 3.58399i 0.232805 + 0.403231i 0.958633 0.284646i \(-0.0918762\pi\)
−0.725827 + 0.687877i \(0.758543\pi\)
\(80\) 1.59097 + 2.75564i 0.177876 + 0.308090i
\(81\) 0 0
\(82\) −2.80150 + 4.85235i −0.309374 + 0.535852i
\(83\) −4.03379 + 6.98673i −0.442766 + 0.766893i −0.997894 0.0648718i \(-0.979336\pi\)
0.555127 + 0.831765i \(0.312669\pi\)
\(84\) 0 0
\(85\) 2.42107 + 4.19341i 0.262602 + 0.454839i
\(86\) −6.82846 −0.736332
\(87\) 0 0
\(88\) −3.18194 −0.339196
\(89\) 0.112725 0.195246i 0.0119488 0.0206960i −0.859989 0.510312i \(-0.829530\pi\)
0.871938 + 0.489616i \(0.162863\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.11956 1.93914i 0.116722 0.202169i
\(93\) 0 0
\(94\) 2.91423 5.04759i 0.300580 0.520620i
\(95\) −2.04063 + 3.53447i −0.209364 + 0.362629i
\(96\) 0 0
\(97\) −7.42107 + 12.8537i −0.753495 + 1.30509i 0.192624 + 0.981273i \(0.438300\pi\)
−0.946119 + 0.323819i \(0.895033\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.56238 + 4.43818i −0.256238 + 0.443818i
\(101\) 18.5893 1.84971 0.924854 0.380322i \(-0.124187\pi\)
0.924854 + 0.380322i \(0.124187\pi\)
\(102\) 0 0
\(103\) 0.282630 0.0278484 0.0139242 0.999903i \(-0.495568\pi\)
0.0139242 + 0.999903i \(0.495568\pi\)
\(104\) −2.85185 4.93955i −0.279647 0.484362i
\(105\) 0 0
\(106\) −1.02859 + 1.78157i −0.0999055 + 0.173041i
\(107\) −5.68878 + 9.85326i −0.549955 + 0.952550i 0.448322 + 0.893872i \(0.352022\pi\)
−0.998277 + 0.0586780i \(0.981311\pi\)
\(108\) 0 0
\(109\) −2.21053 3.82876i −0.211731 0.366728i 0.740526 0.672028i \(-0.234577\pi\)
−0.952256 + 0.305300i \(0.901243\pi\)
\(110\) −5.06238 8.76830i −0.482679 0.836025i
\(111\) 0 0
\(112\) 0 0
\(113\) 1.60752 + 2.78431i 0.151223 + 0.261926i 0.931677 0.363287i \(-0.118345\pi\)
−0.780454 + 0.625213i \(0.785012\pi\)
\(114\) 0 0
\(115\) 7.12476 0.664388
\(116\) 3.54063 + 6.13255i 0.328739 + 0.569393i
\(117\) 0 0
\(118\) −1.12476 −0.103543
\(119\) 0 0
\(120\) 0 0
\(121\) −0.875237 −0.0795670
\(122\) 1.56238 2.70612i 0.141451 0.245001i
\(123\) 0 0
\(124\) −4.71053 8.15888i −0.423018 0.732689i
\(125\) −0.396990 −0.0355079
\(126\) 0 0
\(127\) 20.1053 1.78406 0.892030 0.451976i \(-0.149281\pi\)
0.892030 + 0.451976i \(0.149281\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 9.07442 15.7174i 0.795879 1.37850i
\(131\) 6.36389 0.556015 0.278008 0.960579i \(-0.410326\pi\)
0.278008 + 0.960579i \(0.410326\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 10.9669 0.947396
\(135\) 0 0
\(136\) −0.760877 1.31788i −0.0652446 0.113007i
\(137\) −2.74145 −0.234218 −0.117109 0.993119i \(-0.537363\pi\)
−0.117109 + 0.993119i \(0.537363\pi\)
\(138\) 0 0
\(139\) 3.98345 + 6.89953i 0.337872 + 0.585211i 0.984032 0.177991i \(-0.0569597\pi\)
−0.646161 + 0.763202i \(0.723626\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 4.34501 + 7.52578i 0.364625 + 0.631550i
\(143\) 9.07442 + 15.7174i 0.758841 + 1.31435i
\(144\) 0 0
\(145\) −11.2661 + 19.5134i −0.935597 + 1.62050i
\(146\) 2.48345 4.30146i 0.205532 0.355991i
\(147\) 0 0
\(148\) 0.500000 + 0.866025i 0.0410997 + 0.0711868i
\(149\) 23.2599 1.90553 0.952764 0.303712i \(-0.0982261\pi\)
0.952764 + 0.303712i \(0.0982261\pi\)
\(150\) 0 0
\(151\) −8.12476 −0.661184 −0.330592 0.943774i \(-0.607248\pi\)
−0.330592 + 0.943774i \(0.607248\pi\)
\(152\) 0.641315 1.11079i 0.0520175 0.0900970i
\(153\) 0 0
\(154\) 0 0
\(155\) 14.9887 25.9611i 1.20392 2.08525i
\(156\) 0 0
\(157\) −5.63160 + 9.75422i −0.449451 + 0.778471i −0.998350 0.0574170i \(-0.981714\pi\)
0.548900 + 0.835888i \(0.315047\pi\)
\(158\) 2.06922 3.58399i 0.164618 0.285127i
\(159\) 0 0
\(160\) 1.59097 2.75564i 0.125777 0.217853i
\(161\) 0 0
\(162\) 0 0
\(163\) −1.99028 + 3.44727i −0.155891 + 0.270011i −0.933383 0.358881i \(-0.883158\pi\)
0.777492 + 0.628893i \(0.216492\pi\)
\(164\) 5.60301 0.437522
\(165\) 0 0
\(166\) 8.06758 0.626166
\(167\) 2.61956 + 4.53721i 0.202708 + 0.351100i 0.949400 0.314070i \(-0.101693\pi\)
−0.746692 + 0.665170i \(0.768359\pi\)
\(168\) 0 0
\(169\) −9.76608 + 16.9153i −0.751237 + 1.30118i
\(170\) 2.42107 4.19341i 0.185687 0.321620i
\(171\) 0 0
\(172\) 3.41423 + 5.91362i 0.260333 + 0.450909i
\(173\) −1.27579 2.20974i −0.0969968 0.168003i 0.813443 0.581644i \(-0.197590\pi\)
−0.910440 + 0.413641i \(0.864257\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.59097 + 2.75564i 0.119924 + 0.207714i
\(177\) 0 0
\(178\) −0.225450 −0.0168982
\(179\) −3.51887 6.09487i −0.263013 0.455552i 0.704028 0.710172i \(-0.251383\pi\)
−0.967041 + 0.254620i \(0.918050\pi\)
\(180\) 0 0
\(181\) 12.9669 0.963822 0.481911 0.876220i \(-0.339943\pi\)
0.481911 + 0.876220i \(0.339943\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −2.23912 −0.165070
\(185\) −1.59097 + 2.75564i −0.116971 + 0.202599i
\(186\) 0 0
\(187\) 2.42107 + 4.19341i 0.177046 + 0.306653i
\(188\) −5.82846 −0.425084
\(189\) 0 0
\(190\) 4.08126 0.296085
\(191\) 0.990285 + 1.71522i 0.0716545 + 0.124109i 0.899627 0.436660i \(-0.143839\pi\)
−0.827972 + 0.560769i \(0.810505\pi\)
\(192\) 0 0
\(193\) 2.27292 3.93680i 0.163608 0.283377i −0.772552 0.634951i \(-0.781020\pi\)
0.936160 + 0.351574i \(0.114353\pi\)
\(194\) 14.8421 1.06560
\(195\) 0 0
\(196\) 0 0
\(197\) 21.8148 1.55424 0.777120 0.629353i \(-0.216680\pi\)
0.777120 + 0.629353i \(0.216680\pi\)
\(198\) 0 0
\(199\) −6.14132 10.6371i −0.435346 0.754042i 0.561978 0.827152i \(-0.310041\pi\)
−0.997324 + 0.0731106i \(0.976707\pi\)
\(200\) 5.12476 0.362375
\(201\) 0 0
\(202\) −9.29467 16.0988i −0.653971 1.13271i
\(203\) 0 0
\(204\) 0 0
\(205\) 8.91423 + 15.4399i 0.622597 + 1.07837i
\(206\) −0.141315 0.244765i −0.00984589 0.0170536i
\(207\) 0 0
\(208\) −2.85185 + 4.93955i −0.197740 + 0.342496i
\(209\) −2.04063 + 3.53447i −0.141153 + 0.244485i
\(210\) 0 0
\(211\) −8.32846 14.4253i −0.573355 0.993080i −0.996218 0.0868863i \(-0.972308\pi\)
0.422863 0.906193i \(-0.361025\pi\)
\(212\) 2.05718 0.141288
\(213\) 0 0
\(214\) 11.3776 0.777754
\(215\) −10.8639 + 18.8168i −0.740911 + 1.28330i
\(216\) 0 0
\(217\) 0 0
\(218\) −2.21053 + 3.82876i −0.149716 + 0.259316i
\(219\) 0 0
\(220\) −5.06238 + 8.76830i −0.341306 + 0.591159i
\(221\) −4.33981 + 7.51677i −0.291927 + 0.505633i
\(222\) 0 0
\(223\) 5.32846 9.22916i 0.356820 0.618031i −0.630608 0.776102i \(-0.717194\pi\)
0.987428 + 0.158071i \(0.0505276\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1.60752 2.78431i 0.106931 0.185210i
\(227\) −14.5081 −0.962935 −0.481468 0.876464i \(-0.659896\pi\)
−0.481468 + 0.876464i \(0.659896\pi\)
\(228\) 0 0
\(229\) −10.2495 −0.677308 −0.338654 0.940911i \(-0.609972\pi\)
−0.338654 + 0.940911i \(0.609972\pi\)
\(230\) −3.56238 6.17023i −0.234896 0.406853i
\(231\) 0 0
\(232\) 3.54063 6.13255i 0.232454 0.402622i
\(233\) −0.540628 + 0.936396i −0.0354177 + 0.0613453i −0.883191 0.469014i \(-0.844610\pi\)
0.847773 + 0.530359i \(0.177943\pi\)
\(234\) 0 0
\(235\) −9.27292 16.0612i −0.604898 1.04771i
\(236\) 0.562382 + 0.974074i 0.0366079 + 0.0634068i
\(237\) 0 0
\(238\) 0 0
\(239\) 6.16019 + 10.6698i 0.398470 + 0.690170i 0.993537 0.113506i \(-0.0362081\pi\)
−0.595068 + 0.803676i \(0.702875\pi\)
\(240\) 0 0
\(241\) 13.0000 0.837404 0.418702 0.908124i \(-0.362485\pi\)
0.418702 + 0.908124i \(0.362485\pi\)
\(242\) 0.437618 + 0.757977i 0.0281312 + 0.0487246i
\(243\) 0 0
\(244\) −3.12476 −0.200042
\(245\) 0 0
\(246\) 0 0
\(247\) −7.31573 −0.465489
\(248\) −4.71053 + 8.15888i −0.299119 + 0.518090i
\(249\) 0 0
\(250\) 0.198495 + 0.343803i 0.0125539 + 0.0217440i
\(251\) 5.11109 0.322609 0.161305 0.986905i \(-0.448430\pi\)
0.161305 + 0.986905i \(0.448430\pi\)
\(252\) 0 0
\(253\) 7.12476 0.447930
\(254\) −10.0527 17.4117i −0.630760 1.09251i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 7.66019 0.477830 0.238915 0.971041i \(-0.423208\pi\)
0.238915 + 0.971041i \(0.423208\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −18.1488 −1.12554
\(261\) 0 0
\(262\) −3.18194 5.51129i −0.196581 0.340488i
\(263\) 3.09493 0.190842 0.0954208 0.995437i \(-0.469580\pi\)
0.0954208 + 0.995437i \(0.469580\pi\)
\(264\) 0 0
\(265\) 3.27292 + 5.66886i 0.201054 + 0.348235i
\(266\) 0 0
\(267\) 0 0
\(268\) −5.48345 9.49761i −0.334955 0.580159i
\(269\) −13.4451 23.2877i −0.819765 1.41987i −0.905855 0.423587i \(-0.860771\pi\)
0.0860906 0.996287i \(-0.472563\pi\)
\(270\) 0 0
\(271\) 11.1082 19.2400i 0.674776 1.16875i −0.301759 0.953384i \(-0.597574\pi\)
0.976534 0.215362i \(-0.0690930\pi\)
\(272\) −0.760877 + 1.31788i −0.0461349 + 0.0799080i
\(273\) 0 0
\(274\) 1.37072 + 2.37416i 0.0828084 + 0.143428i
\(275\) −16.3067 −0.983331
\(276\) 0 0
\(277\) −14.6375 −0.879482 −0.439741 0.898125i \(-0.644930\pi\)
−0.439741 + 0.898125i \(0.644930\pi\)
\(278\) 3.98345 6.89953i 0.238911 0.413807i
\(279\) 0 0
\(280\) 0 0
\(281\) −11.6992 + 20.2636i −0.697915 + 1.20882i 0.271273 + 0.962502i \(0.412555\pi\)
−0.969188 + 0.246322i \(0.920778\pi\)
\(282\) 0 0
\(283\) −13.0624 + 22.6247i −0.776478 + 1.34490i 0.157482 + 0.987522i \(0.449662\pi\)
−0.933960 + 0.357377i \(0.883671\pi\)
\(284\) 4.34501 7.52578i 0.257829 0.446573i
\(285\) 0 0
\(286\) 9.07442 15.7174i 0.536582 0.929387i
\(287\) 0 0
\(288\) 0 0
\(289\) 7.34213 12.7169i 0.431890 0.748056i
\(290\) 22.5322 1.32313
\(291\) 0 0
\(292\) −4.96690 −0.290666
\(293\) 12.9315 + 22.3980i 0.755465 + 1.30850i 0.945143 + 0.326657i \(0.105922\pi\)
−0.189678 + 0.981846i \(0.560745\pi\)
\(294\) 0 0
\(295\) −1.78947 + 3.09945i −0.104187 + 0.180457i
\(296\) 0.500000 0.866025i 0.0290619 0.0503367i
\(297\) 0 0
\(298\) −11.6300 20.1437i −0.673706 1.16689i
\(299\) 6.38564 + 11.0603i 0.369291 + 0.639631i
\(300\) 0 0
\(301\) 0 0
\(302\) 4.06238 + 7.03625i 0.233764 + 0.404891i
\(303\) 0 0
\(304\) −1.28263 −0.0735639
\(305\) −4.97141 8.61073i −0.284662 0.493049i
\(306\) 0 0
\(307\) −3.53216 −0.201591 −0.100795 0.994907i \(-0.532139\pi\)
−0.100795 + 0.994907i \(0.532139\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −29.9773 −1.70260
\(311\) −0.851848 + 1.47544i −0.0483039 + 0.0836648i −0.889166 0.457584i \(-0.848715\pi\)
0.840863 + 0.541249i \(0.182048\pi\)
\(312\) 0 0
\(313\) −1.42107 2.46136i −0.0803234 0.139124i 0.823065 0.567947i \(-0.192262\pi\)
−0.903389 + 0.428822i \(0.858929\pi\)
\(314\) 11.2632 0.635619
\(315\) 0 0
\(316\) −4.13844 −0.232805
\(317\) −12.4601 21.5815i −0.699827 1.21214i −0.968526 0.248911i \(-0.919927\pi\)
0.268700 0.963224i \(-0.413406\pi\)
\(318\) 0 0
\(319\) −11.2661 + 19.5134i −0.630779 + 1.09254i
\(320\) −3.18194 −0.177876
\(321\) 0 0
\(322\) 0 0
\(323\) −1.95185 −0.108604
\(324\) 0 0
\(325\) −14.6150 25.3140i −0.810697 1.40417i
\(326\) 3.98057 0.220463
\(327\) 0 0
\(328\) −2.80150 4.85235i −0.154687 0.267926i
\(329\) 0 0
\(330\) 0 0
\(331\) 3.58577 + 6.21074i 0.197092 + 0.341373i 0.947584 0.319506i \(-0.103517\pi\)
−0.750492 + 0.660879i \(0.770184\pi\)
\(332\) −4.03379 6.98673i −0.221383 0.383447i
\(333\) 0 0
\(334\) 2.61956 4.53721i 0.143336 0.248265i
\(335\) 17.4480 30.2209i 0.953287 1.65114i
\(336\) 0 0
\(337\) −10.9211 18.9158i −0.594908 1.03041i −0.993560 0.113309i \(-0.963855\pi\)
0.398651 0.917103i \(-0.369478\pi\)
\(338\) 19.5322 1.06241
\(339\) 0 0
\(340\) −4.84213 −0.262602
\(341\) 14.9887 25.9611i 0.811681 1.40587i
\(342\) 0 0
\(343\) 0 0
\(344\) 3.41423 5.91362i 0.184083 0.318841i
\(345\) 0 0
\(346\) −1.27579 + 2.20974i −0.0685871 + 0.118796i
\(347\) −1.05555 + 1.82826i −0.0566646 + 0.0981460i −0.892966 0.450124i \(-0.851380\pi\)
0.836302 + 0.548270i \(0.184713\pi\)
\(348\) 0 0
\(349\) −18.1082 + 31.3643i −0.969310 + 1.67889i −0.271751 + 0.962368i \(0.587603\pi\)
−0.697559 + 0.716527i \(0.745731\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.59097 2.75564i 0.0847991 0.146876i
\(353\) −10.4887 −0.558255 −0.279127 0.960254i \(-0.590045\pi\)
−0.279127 + 0.960254i \(0.590045\pi\)
\(354\) 0 0
\(355\) 27.6512 1.46757
\(356\) 0.112725 + 0.195246i 0.00597442 + 0.0103480i
\(357\) 0 0
\(358\) −3.51887 + 6.09487i −0.185978 + 0.322124i
\(359\) −16.2209 + 28.0955i −0.856108 + 1.48282i 0.0195047 + 0.999810i \(0.493791\pi\)
−0.875613 + 0.483013i \(0.839542\pi\)
\(360\) 0 0
\(361\) 8.67743 + 15.0297i 0.456707 + 0.791039i
\(362\) −6.48345 11.2297i −0.340762 0.590218i
\(363\) 0 0
\(364\) 0 0
\(365\) −7.90219 13.6870i −0.413620 0.716410i
\(366\) 0 0
\(367\) 18.1111 0.945391 0.472696 0.881226i \(-0.343281\pi\)
0.472696 + 0.881226i \(0.343281\pi\)
\(368\) 1.11956 + 1.93914i 0.0583612 + 0.101085i
\(369\) 0 0
\(370\) 3.18194 0.165421
\(371\) 0 0
\(372\) 0 0
\(373\) −11.6706 −0.604280 −0.302140 0.953263i \(-0.597701\pi\)
−0.302140 + 0.953263i \(0.597701\pi\)
\(374\) 2.42107 4.19341i 0.125190 0.216836i
\(375\) 0 0
\(376\) 2.91423 + 5.04759i 0.150290 + 0.260310i
\(377\) −40.3893 −2.08016
\(378\) 0 0
\(379\) 14.2690 0.732947 0.366474 0.930428i \(-0.380565\pi\)
0.366474 + 0.930428i \(0.380565\pi\)
\(380\) −2.04063 3.53447i −0.104682 0.181315i
\(381\) 0 0
\(382\) 0.990285 1.71522i 0.0506674 0.0877585i
\(383\) −1.64979 −0.0843001 −0.0421501 0.999111i \(-0.513421\pi\)
−0.0421501 + 0.999111i \(0.513421\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −4.54583 −0.231377
\(387\) 0 0
\(388\) −7.42107 12.8537i −0.376748 0.652546i
\(389\) 32.0676 1.62589 0.812946 0.582340i \(-0.197863\pi\)
0.812946 + 0.582340i \(0.197863\pi\)
\(390\) 0 0
\(391\) 1.70370 + 2.95089i 0.0861596 + 0.149233i
\(392\) 0 0
\(393\) 0 0
\(394\) −10.9074 18.8922i −0.549507 0.951773i
\(395\) −6.58414 11.4041i −0.331284 0.573800i
\(396\) 0 0
\(397\) 18.9669 32.8516i 0.951921 1.64878i 0.210660 0.977559i \(-0.432439\pi\)
0.741261 0.671217i \(-0.234228\pi\)
\(398\) −6.14132 + 10.6371i −0.307836 + 0.533188i
\(399\) 0 0
\(400\) −2.56238 4.43818i −0.128119 0.221909i
\(401\) −10.6192 −0.530296 −0.265148 0.964208i \(-0.585421\pi\)
−0.265148 + 0.964208i \(0.585421\pi\)
\(402\) 0 0
\(403\) 53.7349 2.67673
\(404\) −9.29467 + 16.0988i −0.462427 + 0.800947i
\(405\) 0 0
\(406\) 0 0
\(407\) −1.59097 + 2.75564i −0.0788615 + 0.136592i
\(408\) 0 0
\(409\) 2.77292 4.80283i 0.137112 0.237485i −0.789290 0.614020i \(-0.789551\pi\)
0.926402 + 0.376535i \(0.122885\pi\)
\(410\) 8.91423 15.4399i 0.440242 0.762522i
\(411\) 0 0
\(412\) −0.141315 + 0.244765i −0.00696209 + 0.0120587i
\(413\) 0 0
\(414\) 0 0
\(415\) 12.8353 22.2314i 0.630060 1.09130i
\(416\) 5.70370 0.279647
\(417\) 0 0
\(418\) 4.08126 0.199621
\(419\) 2.77455 + 4.80566i 0.135546 + 0.234772i 0.925806 0.378000i \(-0.123388\pi\)
−0.790260 + 0.612772i \(0.790055\pi\)
\(420\) 0 0
\(421\) −3.42107 + 5.92546i −0.166733 + 0.288789i −0.937269 0.348606i \(-0.886655\pi\)
0.770537 + 0.637396i \(0.219988\pi\)
\(422\) −8.32846 + 14.4253i −0.405423 + 0.702213i
\(423\) 0 0
\(424\) −1.02859 1.78157i −0.0499527 0.0865207i
\(425\) −3.89931 6.75381i −0.189144 0.327608i
\(426\) 0 0
\(427\) 0 0
\(428\) −5.68878 9.85326i −0.274978 0.476275i
\(429\) 0 0
\(430\) 21.7278 1.04781
\(431\) −16.5539 28.6722i −0.797374 1.38109i −0.921321 0.388803i \(-0.872889\pi\)
0.123947 0.992289i \(-0.460445\pi\)
\(432\) 0 0
\(433\) 12.1111 0.582022 0.291011 0.956720i \(-0.406008\pi\)
0.291011 + 0.956720i \(0.406008\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 4.42107 0.211731
\(437\) −1.43598 + 2.48720i −0.0686924 + 0.118979i
\(438\) 0 0
\(439\) −4.41711 7.65066i −0.210817 0.365146i 0.741153 0.671336i \(-0.234279\pi\)
−0.951970 + 0.306190i \(0.900946\pi\)
\(440\) 10.1248 0.482679
\(441\) 0 0
\(442\) 8.67962 0.412847
\(443\) 8.75924 + 15.1715i 0.416164 + 0.720817i 0.995550 0.0942360i \(-0.0300408\pi\)
−0.579386 + 0.815053i \(0.696708\pi\)
\(444\) 0 0
\(445\) −0.358685 + 0.621261i −0.0170033 + 0.0294506i
\(446\) −10.6569 −0.504620
\(447\) 0 0
\(448\) 0 0
\(449\) −31.2301 −1.47384 −0.736920 0.675980i \(-0.763720\pi\)
−0.736920 + 0.675980i \(0.763720\pi\)
\(450\) 0 0
\(451\) 8.91423 + 15.4399i 0.419755 + 0.727036i
\(452\) −3.21505 −0.151223
\(453\) 0 0
\(454\) 7.25404 + 12.5644i 0.340449 + 0.589675i
\(455\) 0 0
\(456\) 0 0
\(457\) 16.0624 + 27.8209i 0.751367 + 1.30140i 0.947161 + 0.320760i \(0.103938\pi\)
−0.195794 + 0.980645i \(0.562728\pi\)
\(458\) 5.12476 + 8.87635i 0.239464 + 0.414765i
\(459\) 0 0
\(460\) −3.56238 + 6.17023i −0.166097 + 0.287688i
\(461\) 1.23229 2.13438i 0.0573933 0.0994081i −0.835901 0.548880i \(-0.815054\pi\)
0.893295 + 0.449472i \(0.148388\pi\)
\(462\) 0 0
\(463\) 15.1735 + 26.2812i 0.705171 + 1.22139i 0.966630 + 0.256177i \(0.0824631\pi\)
−0.261459 + 0.965215i \(0.584204\pi\)
\(464\) −7.08126 −0.328739
\(465\) 0 0
\(466\) 1.08126 0.0500882
\(467\) −7.98181 + 13.8249i −0.369354 + 0.639740i −0.989465 0.144774i \(-0.953754\pi\)
0.620110 + 0.784515i \(0.287088\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −9.27292 + 16.0612i −0.427728 + 0.740846i
\(471\) 0 0
\(472\) 0.562382 0.974074i 0.0258857 0.0448354i
\(473\) −10.8639 + 18.8168i −0.499522 + 0.865198i
\(474\) 0 0
\(475\) 3.28659 5.69254i 0.150799 0.261192i
\(476\) 0 0
\(477\) 0 0
\(478\) 6.16019 10.6698i 0.281761 0.488024i
\(479\) −23.1729 −1.05880 −0.529399 0.848373i \(-0.677582\pi\)
−0.529399 + 0.848373i \(0.677582\pi\)
\(480\) 0 0
\(481\) −5.70370 −0.260066
\(482\) −6.50000 11.2583i −0.296067 0.512803i
\(483\) 0 0
\(484\) 0.437618 0.757977i 0.0198917 0.0344535i
\(485\) 23.6134 40.8996i 1.07223 1.85716i
\(486\) 0 0
\(487\) 1.70658 + 2.95588i 0.0773323 + 0.133943i 0.902098 0.431531i \(-0.142026\pi\)
−0.824766 + 0.565474i \(0.808693\pi\)
\(488\) 1.56238 + 2.70612i 0.0707257 + 0.122500i
\(489\) 0 0
\(490\) 0 0
\(491\) 9.58414 + 16.6002i 0.432526 + 0.749157i 0.997090 0.0762323i \(-0.0242890\pi\)
−0.564564 + 0.825389i \(0.690956\pi\)
\(492\) 0 0
\(493\) −10.7759 −0.485323
\(494\) 3.65787 + 6.33561i 0.164575 + 0.285053i
\(495\) 0 0
\(496\) 9.42107 0.423018
\(497\) 0 0
\(498\) 0 0
\(499\) 41.1696 1.84301 0.921503 0.388371i \(-0.126962\pi\)
0.921503 + 0.388371i \(0.126962\pi\)
\(500\) 0.198495 0.343803i 0.00887697 0.0153754i
\(501\) 0 0
\(502\) −2.55555 4.42633i −0.114060 0.197557i
\(503\) −26.4542 −1.17953 −0.589767 0.807574i \(-0.700780\pi\)
−0.589767 + 0.807574i \(0.700780\pi\)
\(504\) 0 0
\(505\) −59.1502 −2.63215
\(506\) −3.56238 6.17023i −0.158367 0.274300i
\(507\) 0 0
\(508\) −10.0527 + 17.4117i −0.446015 + 0.772521i
\(509\) 12.7713 0.566077 0.283039 0.959109i \(-0.408658\pi\)
0.283039 + 0.959109i \(0.408658\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −3.83009 6.63392i −0.168938 0.292610i
\(515\) −0.899313 −0.0396285
\(516\) 0 0
\(517\) −9.27292 16.0612i −0.407822 0.706369i
\(518\) 0 0
\(519\) 0 0
\(520\) 9.07442 + 15.7174i 0.397940 + 0.689252i
\(521\) −3.40615 5.89962i −0.149226 0.258467i 0.781716 0.623635i \(-0.214345\pi\)
−0.930942 + 0.365168i \(0.881012\pi\)
\(522\) 0 0
\(523\) −14.7535 + 25.5538i −0.645125 + 1.11739i 0.339148 + 0.940733i \(0.389861\pi\)
−0.984273 + 0.176656i \(0.943472\pi\)
\(524\) −3.18194 + 5.51129i −0.139004 + 0.240762i
\(525\) 0 0
\(526\) −1.54746 2.68029i −0.0674727 0.116866i
\(527\) 14.3365 0.624510
\(528\) 0 0
\(529\) −17.9863 −0.782014
\(530\) 3.27292 5.66886i 0.142166 0.246239i
\(531\) 0 0
\(532\) 0 0
\(533\) −15.9789 + 27.6763i −0.692125 + 1.19879i
\(534\) 0 0
\(535\) 18.1014 31.3525i 0.782591 1.35549i
\(536\) −5.48345 + 9.49761i −0.236849 + 0.410234i
\(537\) 0 0
\(538\) −13.4451 + 23.2877i −0.579661 + 1.00400i
\(539\) 0 0
\(540\) 0 0
\(541\) 14.7008 25.4626i 0.632038 1.09472i −0.355097 0.934829i \(-0.615552\pi\)
0.987135 0.159892i \(-0.0511145\pi\)
\(542\) −22.2164 −0.954277
\(543\) 0 0
\(544\) 1.52175 0.0652446
\(545\) 7.03379 + 12.1829i 0.301295 + 0.521857i
\(546\) 0 0
\(547\) 17.6150 30.5102i 0.753165 1.30452i −0.193116 0.981176i \(-0.561859\pi\)
0.946281 0.323344i \(-0.104807\pi\)
\(548\) 1.37072 2.37416i 0.0585544 0.101419i
\(549\) 0 0
\(550\) 8.15335 + 14.1220i 0.347660 + 0.602165i
\(551\) −4.54132 7.86579i −0.193467 0.335094i
\(552\) 0 0
\(553\) 0 0
\(554\) 7.31875 + 12.6764i 0.310944 + 0.538570i
\(555\) 0 0
\(556\) −7.96690 −0.337872
\(557\) 3.36909 + 5.83543i 0.142753 + 0.247255i 0.928532 0.371252i \(-0.121071\pi\)
−0.785779 + 0.618507i \(0.787738\pi\)
\(558\) 0 0
\(559\) −38.9475 −1.64730
\(560\) 0 0
\(561\) 0 0
\(562\) 23.3984 0.987001
\(563\) 0.729964 1.26433i 0.0307643 0.0532853i −0.850233 0.526406i \(-0.823539\pi\)
0.880998 + 0.473121i \(0.156873\pi\)
\(564\) 0 0
\(565\) −5.11505 8.85952i −0.215192 0.372723i
\(566\) 26.1248 1.09811
\(567\) 0 0
\(568\) −8.69002 −0.364625
\(569\) 9.78263 + 16.9440i 0.410109 + 0.710330i 0.994901 0.100853i \(-0.0321573\pi\)
−0.584792 + 0.811183i \(0.698824\pi\)
\(570\) 0 0
\(571\) 10.9629 18.9884i 0.458785 0.794638i −0.540112 0.841593i \(-0.681618\pi\)
0.998897 + 0.0469545i \(0.0149516\pi\)
\(572\) −18.1488 −0.758841
\(573\) 0 0
\(574\) 0 0
\(575\) −11.4750 −0.478540
\(576\) 0 0
\(577\) −12.3655 21.4177i −0.514783 0.891631i −0.999853 0.0171554i \(-0.994539\pi\)
0.485069 0.874476i \(-0.338794\pi\)
\(578\) −14.6843 −0.610785
\(579\) 0 0
\(580\) −11.2661 19.5134i −0.467798 0.810251i
\(581\) 0 0
\(582\) 0 0
\(583\) 3.27292 + 5.66886i 0.135550 + 0.234780i
\(584\) 2.48345 + 4.30146i 0.102766 + 0.177996i
\(585\) 0 0
\(586\) 12.9315 22.3980i 0.534194 0.925251i
\(587\) −18.0796 + 31.3148i −0.746226 + 1.29250i 0.203394 + 0.979097i \(0.434803\pi\)
−0.949620 + 0.313404i \(0.898531\pi\)
\(588\) 0 0
\(589\) 6.04187 + 10.4648i 0.248951 + 0.431196i
\(590\) 3.57893 0.147342
\(591\) 0 0
\(592\) −1.00000 −0.0410997
\(593\) −7.55391 + 13.0838i −0.310202 + 0.537285i −0.978406 0.206693i \(-0.933730\pi\)
0.668204 + 0.743978i \(0.267063\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −11.6300 + 20.1437i −0.476382 + 0.825118i
\(597\) 0 0
\(598\) 6.38564 11.0603i 0.261128 0.452287i
\(599\) −2.72708 + 4.72345i −0.111426 + 0.192995i −0.916345 0.400389i \(-0.868875\pi\)
0.804920 + 0.593384i \(0.202208\pi\)
\(600\) 0 0
\(601\) 3.36840 5.83424i 0.137400 0.237984i −0.789112 0.614250i \(-0.789459\pi\)
0.926512 + 0.376266i \(0.122792\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 4.06238 7.03625i 0.165296 0.286301i
\(605\) 2.78495 0.113224
\(606\) 0 0
\(607\) −6.67059 −0.270751 −0.135376 0.990794i \(-0.543224\pi\)
−0.135376 + 0.990794i \(0.543224\pi\)
\(608\) 0.641315 + 1.11079i 0.0260088 + 0.0450485i
\(609\) 0 0
\(610\) −4.97141 + 8.61073i −0.201287 + 0.348638i
\(611\) 16.6219 28.7899i 0.672449 1.16472i
\(612\) 0 0
\(613\) 0.654988 + 1.13447i 0.0264547 + 0.0458209i 0.878950 0.476915i \(-0.158245\pi\)
−0.852495 + 0.522735i \(0.824912\pi\)
\(614\) 1.76608 + 3.05894i 0.0712731 + 0.123449i
\(615\) 0 0
\(616\) 0 0
\(617\) −17.2483 29.8749i −0.694390 1.20272i −0.970386 0.241560i \(-0.922341\pi\)
0.275996 0.961159i \(-0.410992\pi\)
\(618\) 0 0
\(619\) 16.4484 0.661118 0.330559 0.943785i \(-0.392763\pi\)
0.330559 + 0.943785i \(0.392763\pi\)
\(620\) 14.9887 + 25.9611i 0.601959 + 1.04262i
\(621\) 0 0
\(622\) 1.70370 0.0683120
\(623\) 0 0
\(624\) 0 0
\(625\) −24.3606 −0.974425
\(626\) −1.42107 + 2.46136i −0.0567972 + 0.0983757i
\(627\) 0 0
\(628\) −5.63160 9.75422i −0.224725 0.389236i
\(629\) −1.52175 −0.0606763
\(630\) 0 0
\(631\) −30.0118 −1.19475 −0.597375 0.801962i \(-0.703790\pi\)
−0.597375 + 0.801962i \(0.703790\pi\)
\(632\) 2.06922 + 3.58399i 0.0823091 + 0.142564i
\(633\) 0 0
\(634\) −12.4601 + 21.5815i −0.494852 + 0.857109i
\(635\) −63.9740 −2.53873
\(636\) 0 0
\(637\) 0 0
\(638\) 22.5322 0.892057
\(639\) 0 0
\(640\) 1.59097 + 2.75564i 0.0628887 + 0.108926i
\(641\) −27.8993 −1.10196 −0.550978 0.834520i \(-0.685745\pi\)
−0.550978 + 0.834520i \(0.685745\pi\)
\(642\) 0 0
\(643\) −14.2524 24.6859i −0.562060 0.973516i −0.997317 0.0732100i \(-0.976676\pi\)
0.435257 0.900306i \(-0.356658\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.975923 + 1.69035i 0.0383972 + 0.0665059i
\(647\) 8.35705 + 14.4748i 0.328550 + 0.569065i 0.982224 0.187711i \(-0.0601069\pi\)
−0.653675 + 0.756776i \(0.726774\pi\)
\(648\) 0 0
\(649\) −1.78947 + 3.09945i −0.0702427 + 0.121664i
\(650\) −14.6150 + 25.3140i −0.573249 + 0.992897i
\(651\) 0 0
\(652\) −1.99028 3.44727i −0.0779456 0.135006i
\(653\) −38.1650 −1.49351 −0.746756 0.665098i \(-0.768390\pi\)
−0.746756 + 0.665098i \(0.768390\pi\)
\(654\) 0 0
\(655\) −20.2495 −0.791214
\(656\) −2.80150 + 4.85235i −0.109380 + 0.189452i
\(657\) 0 0
\(658\) 0 0
\(659\) −4.37072 + 7.57031i −0.170259 + 0.294898i −0.938510 0.345251i \(-0.887794\pi\)
0.768251 + 0.640148i \(0.221127\pi\)
\(660\) 0 0
\(661\) −10.0419 + 17.3930i −0.390584 + 0.676511i −0.992527 0.122028i \(-0.961060\pi\)
0.601943 + 0.798539i \(0.294393\pi\)
\(662\) 3.58577 6.21074i 0.139365 0.241387i
\(663\) 0 0
\(664\) −4.03379 + 6.98673i −0.156541 + 0.271138i
\(665\) 0 0
\(666\) 0 0
\(667\) −7.92790 + 13.7315i −0.306970 + 0.531687i
\(668\) −5.23912 −0.202708
\(669\) 0 0
\(670\) −34.8960 −1.34815
\(671\) −4.97141 8.61073i −0.191919 0.332414i
\(672\) 0 0
\(673\) −17.0264 + 29.4906i −0.656319 + 1.13678i 0.325242 + 0.945631i \(0.394554\pi\)
−0.981561 + 0.191148i \(0.938779\pi\)
\(674\) −10.9211 + 18.9158i −0.420664 + 0.728611i
\(675\) 0 0
\(676\) −9.76608 16.9153i −0.375618 0.650590i
\(677\) 0.358685 + 0.621261i 0.0137854 + 0.0238770i 0.872836 0.488014i \(-0.162279\pi\)
−0.859050 + 0.511891i \(0.828945\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 2.42107 + 4.19341i 0.0928437 + 0.160810i
\(681\) 0 0
\(682\) −29.9773 −1.14789
\(683\) 10.5270 + 18.2332i 0.402803 + 0.697675i 0.994063 0.108806i \(-0.0347027\pi\)
−0.591260 + 0.806481i \(0.701369\pi\)
\(684\) 0 0
\(685\) 8.72313 0.333294
\(686\) 0 0
\(687\) 0 0
\(688\) −6.82846 −0.260333
\(689\) −5.86677 + 10.1615i −0.223506 + 0.387124i
\(690\) 0 0
\(691\) 2.92395 + 5.06442i 0.111232 + 0.192660i 0.916267 0.400567i \(-0.131187\pi\)
−0.805035 + 0.593227i \(0.797854\pi\)
\(692\) 2.55159 0.0969968
\(693\) 0 0
\(694\) 2.11109 0.0801359
\(695\) −12.6751 21.9539i −0.480794 0.832760i
\(696\) 0 0
\(697\) −4.26320 + 7.38408i −0.161480 + 0.279692i
\(698\) 36.2164 1.37081
\(699\) 0 0
\(700\) 0 0
\(701\) −10.2711 −0.387935 −0.193967 0.981008i \(-0.562136\pi\)
−0.193967 + 0.981008i \(0.562136\pi\)
\(702\) 0 0
\(703\) −0.641315 1.11079i −0.0241877 0.0418942i
\(704\) −3.18194 −0.119924
\(705\) 0 0
\(706\) 5.24433 + 9.08344i 0.197373 + 0.341860i
\(707\) 0 0
\(708\) 0 0
\(709\) −21.7427 37.6594i −0.816564 1.41433i −0.908200 0.418538i \(-0.862543\pi\)
0.0916356 0.995793i \(-0.470790\pi\)
\(710\) −13.8256 23.9466i −0.518865 0.898700i
\(711\) 0 0
\(712\) 0.112725 0.195246i 0.00422455 0.00731714i
\(713\) 10.5475 18.2687i 0.395006 0.684170i
\(714\) 0 0
\(715\) −28.8743 50.0117i −1.07984 1.87033i
\(716\) 7.03775 0.263013
\(717\) 0 0
\(718\) 32.4419 1.21072
\(719\) 25.4412 44.0654i 0.948796 1.64336i 0.200830 0.979626i \(-0.435636\pi\)
0.747966 0.663737i \(-0.231031\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 8.67743 15.0297i 0.322941 0.559349i
\(723\) 0 0
\(724\) −6.48345 + 11.2297i −0.240955 + 0.417347i
\(725\) 18.1449 31.4279i 0.673884 1.16720i
\(726\) 0 0
\(727\) −6.07210 + 10.5172i −0.225202 + 0.390061i −0.956380 0.292126i \(-0.905637\pi\)
0.731178 + 0.682186i \(0.238971\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −7.90219 + 13.6870i −0.292473 + 0.506579i
\(731\) −10.3912 −0.384334
\(732\) 0 0
\(733\) 46.1696 1.70531 0.852657 0.522470i \(-0.174989\pi\)
0.852657 + 0.522470i \(0.174989\pi\)
\(734\) −9.05555 15.6847i −0.334246 0.578932i
\(735\) 0 0
\(736\) 1.11956 1.93914i 0.0412676 0.0714776i
\(737\) 17.4480 30.2209i 0.642706 1.11320i
\(738\) 0 0
\(739\) −2.49604 4.32327i −0.0918184 0.159034i 0.816458 0.577405i \(-0.195935\pi\)
−0.908276 + 0.418371i \(0.862601\pi\)
\(740\) −1.59097 2.75564i −0.0584853 0.101299i
\(741\) 0 0
\(742\) 0 0
\(743\) 15.7060 + 27.2036i 0.576198 + 0.998004i 0.995910 + 0.0903470i \(0.0287976\pi\)
−0.419712 + 0.907657i \(0.637869\pi\)
\(744\) 0 0
\(745\) −74.0118 −2.71158
\(746\) 5.83530 + 10.1070i 0.213645 + 0.370045i
\(747\) 0 0
\(748\) −4.84213 −0.177046
\(749\) 0 0
\(750\) 0 0
\(751\) 3.29630 0.120284 0.0601419 0.998190i \(-0.480845\pi\)
0.0601419 + 0.998190i \(0.480845\pi\)
\(752\) 2.91423 5.04759i 0.106271 0.184067i
\(753\) 0 0
\(754\) 20.1947 + 34.9782i 0.735447 + 1.27383i
\(755\) 25.8525 0.940870
\(756\) 0 0
\(757\) −10.1384 −0.368488 −0.184244 0.982881i \(-0.558984\pi\)
−0.184244 + 0.982881i \(0.558984\pi\)
\(758\) −7.13448 12.3573i −0.259136 0.448837i
\(759\) 0 0
\(760\) −2.04063 + 3.53447i −0.0740214 + 0.128209i
\(761\) 14.0676 0.509950 0.254975 0.966948i \(-0.417933\pi\)
0.254975 + 0.966948i \(0.417933\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −1.98057 −0.0716545
\(765\) 0 0
\(766\) 0.824893 + 1.42876i 0.0298046 + 0.0516231i
\(767\) −6.41531 −0.231643
\(768\) 0 0
\(769\) −11.3461 19.6520i −0.409151 0.708669i 0.585644 0.810568i \(-0.300842\pi\)
−0.994795 + 0.101899i \(0.967508\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 2.27292 + 3.93680i 0.0818040 + 0.141689i
\(773\) 0.327772 + 0.567717i 0.0117891 + 0.0204194i 0.871860 0.489756i \(-0.162914\pi\)
−0.860071 + 0.510175i \(0.829581\pi\)
\(774\) 0 0
\(775\) −24.1404 + 41.8123i −0.867148 + 1.50194i
\(776\) −7.42107 + 12.8537i −0.266401 + 0.461420i
\(777\) 0 0
\(778\) −16.0338 27.7713i −0.574839 0.995651i
\(779\) −7.18659 −0.257486
\(780\) 0 0
\(781\) 27.6512 0.989436
\(782\) 1.70370 2.95089i 0.0609241 0.105524i
\(783\) 0 0
\(784\) 0 0
\(785\) 17.9194 31.0374i 0.639572 1.10777i
\(786\) 0 0
\(787\) 0.270036 0.467717i 0.00962576 0.0166723i −0.861172 0.508313i \(-0.830269\pi\)
0.870798 + 0.491641i \(0.163603\pi\)
\(788\) −10.9074 + 18.8922i −0.388560 + 0.673005i
\(789\) 0 0
\(790\) −6.58414 + 11.4041i −0.234253 + 0.405738i
\(791\) 0 0
\(792\) 0 0
\(793\) 8.91135 15.4349i 0.316451 0.548110i
\(794\) −37.9338 −1.34622
\(795\)