Properties

Label 1323.2.g.d.667.3
Level $1323$
Weight $2$
Character 1323.667
Analytic conductor $10.564$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \(x^{6} - x^{3} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.3
Root \(-0.766044 + 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 1323.667
Dual form 1323.2.g.d.361.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.26604 + 2.19285i) q^{2} +(-2.20574 + 3.82045i) q^{4} +0.879385 q^{5} -6.10607 q^{8} +O(q^{10})\) \(q+(1.26604 + 2.19285i) q^{2} +(-2.20574 + 3.82045i) q^{4} +0.879385 q^{5} -6.10607 q^{8} +(1.11334 + 1.92836i) q^{10} -3.87939 q^{11} +(2.72668 + 4.72275i) q^{13} +(-3.31908 - 5.74881i) q^{16} +(0.826352 + 1.43128i) q^{17} +(-1.20574 + 2.08840i) q^{19} +(-1.93969 + 3.35965i) q^{20} +(-4.91147 - 8.50692i) q^{22} -3.16250 q^{23} -4.22668 q^{25} +(-6.90420 + 11.9584i) q^{26} +(-3.02481 + 5.23913i) q^{29} +(2.27719 - 3.94421i) q^{31} +(2.29813 - 3.98048i) q^{32} +(-2.09240 + 3.62414i) q^{34} +(2.27719 - 3.94421i) q^{37} -6.10607 q^{38} -5.36959 q^{40} +(-0.592396 - 1.02606i) q^{41} +(-0.0923963 + 0.160035i) q^{43} +(8.55690 - 14.8210i) q^{44} +(-4.00387 - 6.93491i) q^{46} +(-0.511144 - 0.885328i) q^{47} +(-5.35117 - 9.26849i) q^{50} -24.0574 q^{52} +(3.64543 + 6.31407i) q^{53} -3.41147 q^{55} -15.3182 q^{58} +(3.33022 - 5.76811i) q^{59} +(1.29813 + 2.24843i) q^{61} +11.5321 q^{62} -1.63816 q^{64} +(2.39780 + 4.15312i) q^{65} +(1.47906 - 2.56180i) q^{67} -7.29086 q^{68} +3.68004 q^{71} +(6.39053 + 11.0687i) q^{73} +11.5321 q^{74} +(-5.31908 - 9.21291i) q^{76} +(2.97906 + 5.15988i) q^{79} +(-2.91875 - 5.05542i) q^{80} +(1.50000 - 2.59808i) q^{82} +(-0.109470 + 0.189608i) q^{83} +(0.726682 + 1.25865i) q^{85} -0.467911 q^{86} +23.6878 q^{88} +(5.51367 - 9.54996i) q^{89} +(6.97565 - 12.0822i) q^{92} +(1.29426 - 2.24173i) q^{94} +(-1.06031 + 1.83651i) q^{95} +(-6.25150 + 10.8279i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 3q^{2} - 3q^{4} - 6q^{5} - 12q^{8} + O(q^{10}) \) \( 6q + 3q^{2} - 3q^{4} - 6q^{5} - 12q^{8} - 12q^{11} + 3q^{13} - 3q^{16} + 6q^{17} + 3q^{19} - 6q^{20} - 9q^{22} - 24q^{23} - 12q^{25} - 3q^{26} + 9q^{29} + 3q^{31} - 9q^{34} + 3q^{37} - 12q^{38} - 18q^{40} + 3q^{43} + 15q^{44} + 3q^{47} - 6q^{50} - 42q^{52} + 6q^{53} - 18q^{58} - 3q^{59} - 6q^{61} + 60q^{62} + 24q^{64} + 15q^{65} + 12q^{67} - 12q^{68} - 18q^{71} + 21q^{73} + 60q^{74} - 15q^{76} + 21q^{79} - 15q^{80} + 9q^{82} - 18q^{83} - 9q^{85} - 12q^{86} + 54q^{88} + 12q^{89} + 3q^{92} + 18q^{94} - 12q^{95} + 3q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.26604 + 2.19285i 0.895229 + 1.55058i 0.833521 + 0.552487i \(0.186321\pi\)
0.0617072 + 0.998094i \(0.480346\pi\)
\(3\) 0 0
\(4\) −2.20574 + 3.82045i −1.10287 + 1.91022i
\(5\) 0.879385 0.393273 0.196637 0.980476i \(-0.436998\pi\)
0.196637 + 0.980476i \(0.436998\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −6.10607 −2.15882
\(9\) 0 0
\(10\) 1.11334 + 1.92836i 0.352069 + 0.609802i
\(11\) −3.87939 −1.16968 −0.584839 0.811149i \(-0.698842\pi\)
−0.584839 + 0.811149i \(0.698842\pi\)
\(12\) 0 0
\(13\) 2.72668 + 4.72275i 0.756245 + 1.30986i 0.944753 + 0.327784i \(0.106302\pi\)
−0.188507 + 0.982072i \(0.560365\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −3.31908 5.74881i −0.829769 1.43720i
\(17\) 0.826352 + 1.43128i 0.200420 + 0.347137i 0.948664 0.316286i \(-0.102436\pi\)
−0.748244 + 0.663424i \(0.769103\pi\)
\(18\) 0 0
\(19\) −1.20574 + 2.08840i −0.276615 + 0.479111i −0.970541 0.240935i \(-0.922546\pi\)
0.693926 + 0.720046i \(0.255879\pi\)
\(20\) −1.93969 + 3.35965i −0.433728 + 0.751240i
\(21\) 0 0
\(22\) −4.91147 8.50692i −1.04713 1.81368i
\(23\) −3.16250 −0.659428 −0.329714 0.944081i \(-0.606952\pi\)
−0.329714 + 0.944081i \(0.606952\pi\)
\(24\) 0 0
\(25\) −4.22668 −0.845336
\(26\) −6.90420 + 11.9584i −1.35403 + 2.34524i
\(27\) 0 0
\(28\) 0 0
\(29\) −3.02481 + 5.23913i −0.561694 + 0.972883i 0.435655 + 0.900114i \(0.356517\pi\)
−0.997349 + 0.0727688i \(0.976816\pi\)
\(30\) 0 0
\(31\) 2.27719 3.94421i 0.408995 0.708400i −0.585782 0.810468i \(-0.699213\pi\)
0.994777 + 0.102068i \(0.0325459\pi\)
\(32\) 2.29813 3.98048i 0.406256 0.703657i
\(33\) 0 0
\(34\) −2.09240 + 3.62414i −0.358843 + 0.621534i
\(35\) 0 0
\(36\) 0 0
\(37\) 2.27719 3.94421i 0.374368 0.648424i −0.615865 0.787852i \(-0.711193\pi\)
0.990232 + 0.139428i \(0.0445265\pi\)
\(38\) −6.10607 −0.990535
\(39\) 0 0
\(40\) −5.36959 −0.849006
\(41\) −0.592396 1.02606i −0.0925168 0.160244i 0.816053 0.577977i \(-0.196158\pi\)
−0.908570 + 0.417734i \(0.862825\pi\)
\(42\) 0 0
\(43\) −0.0923963 + 0.160035i −0.0140903 + 0.0244051i −0.872985 0.487748i \(-0.837819\pi\)
0.858894 + 0.512153i \(0.171152\pi\)
\(44\) 8.55690 14.8210i 1.29000 2.23435i
\(45\) 0 0
\(46\) −4.00387 6.93491i −0.590338 1.02250i
\(47\) −0.511144 0.885328i −0.0745581 0.129138i 0.826336 0.563178i \(-0.190421\pi\)
−0.900894 + 0.434039i \(0.857088\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −5.35117 9.26849i −0.756769 1.31076i
\(51\) 0 0
\(52\) −24.0574 −3.33616
\(53\) 3.64543 + 6.31407i 0.500738 + 0.867304i 1.00000 0.000852699i \(0.000271423\pi\)
−0.499261 + 0.866451i \(0.666395\pi\)
\(54\) 0 0
\(55\) −3.41147 −0.460003
\(56\) 0 0
\(57\) 0 0
\(58\) −15.3182 −2.01138
\(59\) 3.33022 5.76811i 0.433558 0.750944i −0.563619 0.826035i \(-0.690591\pi\)
0.997177 + 0.0750906i \(0.0239246\pi\)
\(60\) 0 0
\(61\) 1.29813 + 2.24843i 0.166209 + 0.287882i 0.937084 0.349104i \(-0.113514\pi\)
−0.770875 + 0.636986i \(0.780181\pi\)
\(62\) 11.5321 1.46458
\(63\) 0 0
\(64\) −1.63816 −0.204769
\(65\) 2.39780 + 4.15312i 0.297411 + 0.515131i
\(66\) 0 0
\(67\) 1.47906 2.56180i 0.180695 0.312974i −0.761422 0.648256i \(-0.775499\pi\)
0.942118 + 0.335283i \(0.108832\pi\)
\(68\) −7.29086 −0.884147
\(69\) 0 0
\(70\) 0 0
\(71\) 3.68004 0.436741 0.218370 0.975866i \(-0.429926\pi\)
0.218370 + 0.975866i \(0.429926\pi\)
\(72\) 0 0
\(73\) 6.39053 + 11.0687i 0.747955 + 1.29550i 0.948801 + 0.315873i \(0.102297\pi\)
−0.200847 + 0.979623i \(0.564369\pi\)
\(74\) 11.5321 1.34058
\(75\) 0 0
\(76\) −5.31908 9.21291i −0.610140 1.05679i
\(77\) 0 0
\(78\) 0 0
\(79\) 2.97906 + 5.15988i 0.335170 + 0.580531i 0.983517 0.180813i \(-0.0578729\pi\)
−0.648348 + 0.761345i \(0.724540\pi\)
\(80\) −2.91875 5.05542i −0.326326 0.565213i
\(81\) 0 0
\(82\) 1.50000 2.59808i 0.165647 0.286910i
\(83\) −0.109470 + 0.189608i −0.0120159 + 0.0208122i −0.871971 0.489558i \(-0.837158\pi\)
0.859955 + 0.510370i \(0.170492\pi\)
\(84\) 0 0
\(85\) 0.726682 + 1.25865i 0.0788197 + 0.136520i
\(86\) −0.467911 −0.0504562
\(87\) 0 0
\(88\) 23.6878 2.52513
\(89\) 5.51367 9.54996i 0.584448 1.01229i −0.410496 0.911862i \(-0.634644\pi\)
0.994944 0.100431i \(-0.0320222\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 6.97565 12.0822i 0.727262 1.25965i
\(93\) 0 0
\(94\) 1.29426 2.24173i 0.133493 0.231217i
\(95\) −1.06031 + 1.83651i −0.108785 + 0.188422i
\(96\) 0 0
\(97\) −6.25150 + 10.8279i −0.634743 + 1.09941i 0.351826 + 0.936065i \(0.385561\pi\)
−0.986569 + 0.163342i \(0.947773\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 9.32295 16.1478i 0.932295 1.61478i
\(101\) 9.71688 0.966866 0.483433 0.875381i \(-0.339390\pi\)
0.483433 + 0.875381i \(0.339390\pi\)
\(102\) 0 0
\(103\) 6.59627 0.649949 0.324975 0.945723i \(-0.394644\pi\)
0.324975 + 0.945723i \(0.394644\pi\)
\(104\) −16.6493 28.8374i −1.63260 2.82774i
\(105\) 0 0
\(106\) −9.23055 + 15.9878i −0.896550 + 1.55287i
\(107\) 1.19459 2.06910i 0.115486 0.200027i −0.802488 0.596668i \(-0.796491\pi\)
0.917974 + 0.396641i \(0.129824\pi\)
\(108\) 0 0
\(109\) −1.97906 3.42782i −0.189559 0.328326i 0.755544 0.655098i \(-0.227373\pi\)
−0.945103 + 0.326772i \(0.894039\pi\)
\(110\) −4.31908 7.48086i −0.411808 0.713272i
\(111\) 0 0
\(112\) 0 0
\(113\) 8.22668 + 14.2490i 0.773901 + 1.34044i 0.935410 + 0.353565i \(0.115031\pi\)
−0.161509 + 0.986871i \(0.551636\pi\)
\(114\) 0 0
\(115\) −2.78106 −0.259335
\(116\) −13.3439 23.1123i −1.23895 2.14592i
\(117\) 0 0
\(118\) 16.8648 1.55253
\(119\) 0 0
\(120\) 0 0
\(121\) 4.04963 0.368148
\(122\) −3.28699 + 5.69323i −0.297590 + 0.515441i
\(123\) 0 0
\(124\) 10.0458 + 17.3998i 0.902136 + 1.56255i
\(125\) −8.11381 −0.725721
\(126\) 0 0
\(127\) 17.6536 1.56651 0.783253 0.621702i \(-0.213559\pi\)
0.783253 + 0.621702i \(0.213559\pi\)
\(128\) −6.67024 11.5532i −0.589572 1.02117i
\(129\) 0 0
\(130\) −6.07145 + 10.5161i −0.532502 + 0.922320i
\(131\) 19.1976 1.67730 0.838650 0.544670i \(-0.183345\pi\)
0.838650 + 0.544670i \(0.183345\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 7.49020 0.647055
\(135\) 0 0
\(136\) −5.04576 8.73951i −0.432670 0.749407i
\(137\) −18.1557 −1.55115 −0.775573 0.631258i \(-0.782539\pi\)
−0.775573 + 0.631258i \(0.782539\pi\)
\(138\) 0 0
\(139\) −11.0287 19.1022i −0.935441 1.62023i −0.773846 0.633374i \(-0.781670\pi\)
−0.161595 0.986857i \(-0.551664\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 4.65910 + 8.06980i 0.390983 + 0.677202i
\(143\) −10.5778 18.3214i −0.884564 1.53211i
\(144\) 0 0
\(145\) −2.65998 + 4.60722i −0.220899 + 0.382608i
\(146\) −16.1814 + 28.0270i −1.33918 + 2.31953i
\(147\) 0 0
\(148\) 10.0458 + 17.3998i 0.825756 + 1.43025i
\(149\) 15.1557 1.24160 0.620802 0.783968i \(-0.286807\pi\)
0.620802 + 0.783968i \(0.286807\pi\)
\(150\) 0 0
\(151\) −18.9564 −1.54265 −0.771323 0.636444i \(-0.780405\pi\)
−0.771323 + 0.636444i \(0.780405\pi\)
\(152\) 7.36231 12.7519i 0.597162 1.03432i
\(153\) 0 0
\(154\) 0 0
\(155\) 2.00253 3.46848i 0.160847 0.278595i
\(156\) 0 0
\(157\) 9.02869 15.6381i 0.720568 1.24806i −0.240205 0.970722i \(-0.577215\pi\)
0.960773 0.277337i \(-0.0894520\pi\)
\(158\) −7.54323 + 13.0653i −0.600107 + 1.03942i
\(159\) 0 0
\(160\) 2.02094 3.50038i 0.159770 0.276729i
\(161\) 0 0
\(162\) 0 0
\(163\) −0.479055 + 0.829748i −0.0375225 + 0.0649909i −0.884177 0.467152i \(-0.845280\pi\)
0.846654 + 0.532143i \(0.178613\pi\)
\(164\) 5.22668 0.408135
\(165\) 0 0
\(166\) −0.554378 −0.0430280
\(167\) 9.91921 + 17.1806i 0.767572 + 1.32947i 0.938876 + 0.344255i \(0.111869\pi\)
−0.171304 + 0.985218i \(0.554798\pi\)
\(168\) 0 0
\(169\) −8.36959 + 14.4965i −0.643814 + 1.11512i
\(170\) −1.84002 + 3.18701i −0.141123 + 0.244433i
\(171\) 0 0
\(172\) −0.407604 0.705990i −0.0310795 0.0538313i
\(173\) 11.3414 + 19.6438i 0.862268 + 1.49349i 0.869734 + 0.493520i \(0.164290\pi\)
−0.00746626 + 0.999972i \(0.502377\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 12.8760 + 22.3019i 0.970564 + 1.68107i
\(177\) 0 0
\(178\) 27.9222 2.09286
\(179\) −3.67365 6.36295i −0.274581 0.475589i 0.695448 0.718576i \(-0.255206\pi\)
−0.970029 + 0.242988i \(0.921873\pi\)
\(180\) 0 0
\(181\) −3.44562 −0.256111 −0.128056 0.991767i \(-0.540874\pi\)
−0.128056 + 0.991767i \(0.540874\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 19.3105 1.42359
\(185\) 2.00253 3.46848i 0.147229 0.255008i
\(186\) 0 0
\(187\) −3.20574 5.55250i −0.234427 0.406039i
\(188\) 4.50980 0.328911
\(189\) 0 0
\(190\) −5.36959 −0.389551
\(191\) 2.82888 + 4.89976i 0.204690 + 0.354534i 0.950034 0.312146i \(-0.101048\pi\)
−0.745344 + 0.666680i \(0.767715\pi\)
\(192\) 0 0
\(193\) −4.79813 + 8.31061i −0.345377 + 0.598211i −0.985422 0.170127i \(-0.945582\pi\)
0.640045 + 0.768337i \(0.278916\pi\)
\(194\) −31.6587 −2.27296
\(195\) 0 0
\(196\) 0 0
\(197\) −8.31996 −0.592772 −0.296386 0.955068i \(-0.595782\pi\)
−0.296386 + 0.955068i \(0.595782\pi\)
\(198\) 0 0
\(199\) −3.29813 5.71253i −0.233798 0.404951i 0.725124 0.688618i \(-0.241782\pi\)
−0.958923 + 0.283667i \(0.908449\pi\)
\(200\) 25.8084 1.82493
\(201\) 0 0
\(202\) 12.3020 + 21.3077i 0.865566 + 1.49920i
\(203\) 0 0
\(204\) 0 0
\(205\) −0.520945 0.902302i −0.0363843 0.0630195i
\(206\) 8.35117 + 14.4646i 0.581853 + 1.00780i
\(207\) 0 0
\(208\) 18.1001 31.3504i 1.25502 2.17376i
\(209\) 4.67752 8.10170i 0.323551 0.560406i
\(210\) 0 0
\(211\) 1.68479 + 2.91815i 0.115986 + 0.200893i 0.918173 0.396179i \(-0.129664\pi\)
−0.802188 + 0.597072i \(0.796331\pi\)
\(212\) −32.1634 −2.20899
\(213\) 0 0
\(214\) 6.04963 0.413544
\(215\) −0.0812519 + 0.140732i −0.00554133 + 0.00959787i
\(216\) 0 0
\(217\) 0 0
\(218\) 5.01114 8.67956i 0.339398 0.587854i
\(219\) 0 0
\(220\) 7.52481 13.0334i 0.507323 0.878709i
\(221\) −4.50640 + 7.80531i −0.303133 + 0.525042i
\(222\) 0 0
\(223\) 3.13816 5.43545i 0.210146 0.363984i −0.741614 0.670827i \(-0.765939\pi\)
0.951760 + 0.306843i \(0.0992726\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −20.8307 + 36.0798i −1.38564 + 2.39999i
\(227\) 6.16250 0.409020 0.204510 0.978865i \(-0.434440\pi\)
0.204510 + 0.978865i \(0.434440\pi\)
\(228\) 0 0
\(229\) 23.3851 1.54533 0.772664 0.634815i \(-0.218924\pi\)
0.772664 + 0.634815i \(0.218924\pi\)
\(230\) −3.52094 6.09845i −0.232164 0.402120i
\(231\) 0 0
\(232\) 18.4697 31.9905i 1.21260 2.10028i
\(233\) −4.26264 + 7.38311i −0.279255 + 0.483684i −0.971200 0.238267i \(-0.923421\pi\)
0.691945 + 0.721950i \(0.256754\pi\)
\(234\) 0 0
\(235\) −0.449493 0.778544i −0.0293217 0.0507866i
\(236\) 14.6912 + 25.4459i 0.956315 + 1.65639i
\(237\) 0 0
\(238\) 0 0
\(239\) 7.28106 + 12.6112i 0.470973 + 0.815748i 0.999449 0.0331997i \(-0.0105697\pi\)
−0.528476 + 0.848948i \(0.677236\pi\)
\(240\) 0 0
\(241\) −5.40373 −0.348085 −0.174043 0.984738i \(-0.555683\pi\)
−0.174043 + 0.984738i \(0.555683\pi\)
\(242\) 5.12701 + 8.88024i 0.329577 + 0.570844i
\(243\) 0 0
\(244\) −11.4534 −0.733226
\(245\) 0 0
\(246\) 0 0
\(247\) −13.1506 −0.836755
\(248\) −13.9047 + 24.0836i −0.882947 + 1.52931i
\(249\) 0 0
\(250\) −10.2724 17.7924i −0.649686 1.12529i
\(251\) 12.0669 0.761654 0.380827 0.924646i \(-0.375639\pi\)
0.380827 + 0.924646i \(0.375639\pi\)
\(252\) 0 0
\(253\) 12.2686 0.771318
\(254\) 22.3503 + 38.7118i 1.40238 + 2.42900i
\(255\) 0 0
\(256\) 15.2515 26.4164i 0.953219 1.65102i
\(257\) −10.5662 −0.659104 −0.329552 0.944137i \(-0.606898\pi\)
−0.329552 + 0.944137i \(0.606898\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −21.1557 −1.31202
\(261\) 0 0
\(262\) 24.3050 + 42.0975i 1.50157 + 2.60079i
\(263\) 28.3533 1.74834 0.874169 0.485622i \(-0.161407\pi\)
0.874169 + 0.485622i \(0.161407\pi\)
\(264\) 0 0
\(265\) 3.20574 + 5.55250i 0.196927 + 0.341087i
\(266\) 0 0
\(267\) 0 0
\(268\) 6.52481 + 11.3013i 0.398567 + 0.690337i
\(269\) 3.74170 + 6.48081i 0.228135 + 0.395142i 0.957255 0.289244i \(-0.0934038\pi\)
−0.729120 + 0.684386i \(0.760070\pi\)
\(270\) 0 0
\(271\) −6.81908 + 11.8110i −0.414229 + 0.717467i −0.995347 0.0963530i \(-0.969282\pi\)
0.581118 + 0.813819i \(0.302616\pi\)
\(272\) 5.48545 9.50108i 0.332604 0.576088i
\(273\) 0 0
\(274\) −22.9859 39.8128i −1.38863 2.40518i
\(275\) 16.3969 0.988772
\(276\) 0 0
\(277\) −6.15064 −0.369556 −0.184778 0.982780i \(-0.559157\pi\)
−0.184778 + 0.982780i \(0.559157\pi\)
\(278\) 27.9256 48.3686i 1.67487 2.90095i
\(279\) 0 0
\(280\) 0 0
\(281\) 1.65611 2.86846i 0.0987951 0.171118i −0.812391 0.583113i \(-0.801835\pi\)
0.911186 + 0.411995i \(0.135168\pi\)
\(282\) 0 0
\(283\) −14.5116 + 25.1348i −0.862626 + 1.49411i 0.00675974 + 0.999977i \(0.497848\pi\)
−0.869385 + 0.494134i \(0.835485\pi\)
\(284\) −8.11721 + 14.0594i −0.481668 + 0.834273i
\(285\) 0 0
\(286\) 26.7841 46.3913i 1.58377 2.74318i
\(287\) 0 0
\(288\) 0 0
\(289\) 7.13429 12.3569i 0.419664 0.726879i
\(290\) −13.4706 −0.791021
\(291\) 0 0
\(292\) −56.3833 −3.29958
\(293\) −4.20961 7.29125i −0.245928 0.425960i 0.716464 0.697624i \(-0.245759\pi\)
−0.962392 + 0.271664i \(0.912426\pi\)
\(294\) 0 0
\(295\) 2.92855 5.07239i 0.170507 0.295326i
\(296\) −13.9047 + 24.0836i −0.808192 + 1.39983i
\(297\) 0 0
\(298\) 19.1878 + 33.2342i 1.11152 + 1.92521i
\(299\) −8.62314 14.9357i −0.498689 0.863755i
\(300\) 0 0
\(301\) 0 0
\(302\) −23.9996 41.5685i −1.38102 2.39200i
\(303\) 0 0
\(304\) 16.0077 0.918107
\(305\) 1.14156 + 1.97724i 0.0653655 + 0.113216i
\(306\) 0 0
\(307\) −12.6878 −0.724130 −0.362065 0.932153i \(-0.617928\pi\)
−0.362065 + 0.932153i \(0.617928\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 10.1411 0.575979
\(311\) −8.24510 + 14.2809i −0.467537 + 0.809797i −0.999312 0.0370881i \(-0.988192\pi\)
0.531775 + 0.846886i \(0.321525\pi\)
\(312\) 0 0
\(313\) −14.2592 24.6977i −0.805980 1.39600i −0.915628 0.402027i \(-0.868306\pi\)
0.109648 0.993970i \(-0.465028\pi\)
\(314\) 45.7229 2.58029
\(315\) 0 0
\(316\) −26.2841 −1.47859
\(317\) −12.9474 22.4256i −0.727200 1.25955i −0.958062 0.286561i \(-0.907488\pi\)
0.230862 0.972987i \(-0.425846\pi\)
\(318\) 0 0
\(319\) 11.7344 20.3246i 0.657002 1.13796i
\(320\) −1.44057 −0.0805303
\(321\) 0 0
\(322\) 0 0
\(323\) −3.98545 −0.221756
\(324\) 0 0
\(325\) −11.5248 19.9616i −0.639282 1.10727i
\(326\) −2.42602 −0.134365
\(327\) 0 0
\(328\) 3.61721 + 6.26519i 0.199727 + 0.345937i
\(329\) 0 0
\(330\) 0 0
\(331\) −4.10947 7.11781i −0.225877 0.391230i 0.730705 0.682693i \(-0.239191\pi\)
−0.956582 + 0.291463i \(0.905858\pi\)
\(332\) −0.482926 0.836452i −0.0265040 0.0459063i
\(333\) 0 0
\(334\) −25.1163 + 43.5028i −1.37430 + 2.38037i
\(335\) 1.30066 2.25281i 0.0710626 0.123084i
\(336\) 0 0
\(337\) −2.28564 3.95885i −0.124507 0.215652i 0.797033 0.603936i \(-0.206402\pi\)
−0.921540 + 0.388283i \(0.873068\pi\)
\(338\) −42.3851 −2.30544
\(339\) 0 0
\(340\) −6.41147 −0.347711
\(341\) −8.83409 + 15.3011i −0.478393 + 0.828601i
\(342\) 0 0
\(343\) 0 0
\(344\) 0.564178 0.977185i 0.0304184 0.0526863i
\(345\) 0 0
\(346\) −28.7173 + 49.7399i −1.54385 + 2.67403i
\(347\) 11.2331 19.4563i 0.603023 1.04447i −0.389337 0.921095i \(-0.627296\pi\)
0.992361 0.123372i \(-0.0393707\pi\)
\(348\) 0 0
\(349\) −13.0496 + 22.6026i −0.698531 + 1.20989i 0.270445 + 0.962735i \(0.412829\pi\)
−0.968976 + 0.247155i \(0.920504\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −8.91534 + 15.4418i −0.475189 + 0.823052i
\(353\) 0.355037 0.0188967 0.00944836 0.999955i \(-0.496992\pi\)
0.00944836 + 0.999955i \(0.496992\pi\)
\(354\) 0 0
\(355\) 3.23618 0.171758
\(356\) 24.3234 + 42.1294i 1.28914 + 2.23285i
\(357\) 0 0
\(358\) 9.30200 16.1115i 0.491626 0.851522i
\(359\) 2.72803 4.72508i 0.143980 0.249380i −0.785012 0.619480i \(-0.787343\pi\)
0.928992 + 0.370100i \(0.120677\pi\)
\(360\) 0 0
\(361\) 6.59240 + 11.4184i 0.346968 + 0.600967i
\(362\) −4.36231 7.55574i −0.229278 0.397121i
\(363\) 0 0
\(364\) 0 0
\(365\) 5.61974 + 9.73367i 0.294150 + 0.509484i
\(366\) 0 0
\(367\) 10.9240 0.570226 0.285113 0.958494i \(-0.407969\pi\)
0.285113 + 0.958494i \(0.407969\pi\)
\(368\) 10.4966 + 18.1806i 0.547173 + 0.947731i
\(369\) 0 0
\(370\) 10.1411 0.527213
\(371\) 0 0
\(372\) 0 0
\(373\) 1.73143 0.0896500 0.0448250 0.998995i \(-0.485727\pi\)
0.0448250 + 0.998995i \(0.485727\pi\)
\(374\) 8.11721 14.0594i 0.419731 0.726995i
\(375\) 0 0
\(376\) 3.12108 + 5.40587i 0.160957 + 0.278787i
\(377\) −32.9908 −1.69911
\(378\) 0 0
\(379\) −12.1334 −0.623251 −0.311626 0.950205i \(-0.600873\pi\)
−0.311626 + 0.950205i \(0.600873\pi\)
\(380\) −4.67752 8.10170i −0.239952 0.415608i
\(381\) 0 0
\(382\) −7.16297 + 12.4066i −0.366489 + 0.634778i
\(383\) 8.71183 0.445154 0.222577 0.974915i \(-0.428553\pi\)
0.222577 + 0.974915i \(0.428553\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −24.2986 −1.23677
\(387\) 0 0
\(388\) −27.5783 47.7670i −1.40008 2.42500i
\(389\) −3.64321 −0.184718 −0.0923590 0.995726i \(-0.529441\pi\)
−0.0923590 + 0.995726i \(0.529441\pi\)
\(390\) 0 0
\(391\) −2.61334 4.52644i −0.132162 0.228912i
\(392\) 0 0
\(393\) 0 0
\(394\) −10.5334 18.2444i −0.530667 0.919142i
\(395\) 2.61974 + 4.53752i 0.131813 + 0.228307i
\(396\) 0 0
\(397\) 7.72281 13.3763i 0.387597 0.671337i −0.604529 0.796583i \(-0.706639\pi\)
0.992126 + 0.125246i \(0.0399720\pi\)
\(398\) 8.35117 14.4646i 0.418606 0.725047i
\(399\) 0 0
\(400\) 14.0287 + 24.2984i 0.701434 + 1.21492i
\(401\) −18.4219 −0.919946 −0.459973 0.887933i \(-0.652141\pi\)
−0.459973 + 0.887933i \(0.652141\pi\)
\(402\) 0 0
\(403\) 24.8367 1.23720
\(404\) −21.4329 + 37.1228i −1.06633 + 1.84693i
\(405\) 0 0
\(406\) 0 0
\(407\) −8.83409 + 15.3011i −0.437890 + 0.758447i
\(408\) 0 0
\(409\) 14.3182 24.7999i 0.707989 1.22627i −0.257612 0.966248i \(-0.582936\pi\)
0.965602 0.260025i \(-0.0837309\pi\)
\(410\) 1.31908 2.28471i 0.0651446 0.112834i
\(411\) 0 0
\(412\) −14.5496 + 25.2007i −0.716809 + 1.24155i
\(413\) 0 0
\(414\) 0 0
\(415\) −0.0962667 + 0.166739i −0.00472554 + 0.00818488i
\(416\) 25.0651 1.22892
\(417\) 0 0
\(418\) 23.6878 1.15861
\(419\) −17.3478 30.0472i −0.847494 1.46790i −0.883438 0.468548i \(-0.844777\pi\)
0.0359442 0.999354i \(-0.488556\pi\)
\(420\) 0 0
\(421\) 13.7010 23.7308i 0.667745 1.15657i −0.310788 0.950479i \(-0.600593\pi\)
0.978533 0.206090i \(-0.0660738\pi\)
\(422\) −4.26604 + 7.38901i −0.207668 + 0.359691i
\(423\) 0 0
\(424\) −22.2592 38.5541i −1.08100 1.87235i
\(425\) −3.49273 6.04958i −0.169422 0.293448i
\(426\) 0 0
\(427\) 0 0
\(428\) 5.26991 + 9.12776i 0.254731 + 0.441207i
\(429\) 0 0
\(430\) −0.411474 −0.0198430
\(431\) 13.2961 + 23.0295i 0.640449 + 1.10929i 0.985333 + 0.170645i \(0.0545852\pi\)
−0.344883 + 0.938646i \(0.612081\pi\)
\(432\) 0 0
\(433\) 37.1830 1.78690 0.893451 0.449160i \(-0.148277\pi\)
0.893451 + 0.449160i \(0.148277\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 17.4611 0.836235
\(437\) 3.81315 6.60457i 0.182408 0.315939i
\(438\) 0 0
\(439\) −12.5373 21.7152i −0.598373 1.03641i −0.993061 0.117597i \(-0.962481\pi\)
0.394689 0.918815i \(-0.370853\pi\)
\(440\) 20.8307 0.993064
\(441\) 0 0
\(442\) −22.8212 −1.08549
\(443\) 1.02229 + 1.77066i 0.0485704 + 0.0841264i 0.889288 0.457347i \(-0.151200\pi\)
−0.840718 + 0.541473i \(0.817867\pi\)
\(444\) 0 0
\(445\) 4.84864 8.39809i 0.229848 0.398108i
\(446\) 15.8922 0.752516
\(447\) 0 0
\(448\) 0 0
\(449\) 10.2344 0.482992 0.241496 0.970402i \(-0.422362\pi\)
0.241496 + 0.970402i \(0.422362\pi\)
\(450\) 0 0
\(451\) 2.29813 + 3.98048i 0.108215 + 0.187434i
\(452\) −72.5836 −3.41404
\(453\) 0 0
\(454\) 7.80200 + 13.5135i 0.366166 + 0.634218i
\(455\) 0 0
\(456\) 0 0
\(457\) 21.2973 + 36.8879i 0.996244 + 1.72554i 0.573115 + 0.819475i \(0.305735\pi\)
0.423129 + 0.906070i \(0.360932\pi\)
\(458\) 29.6065 + 51.2800i 1.38342 + 2.39616i
\(459\) 0 0
\(460\) 6.13429 10.6249i 0.286013 0.495388i
\(461\) 0.252374 0.437124i 0.0117542 0.0203589i −0.860088 0.510145i \(-0.829592\pi\)
0.871843 + 0.489786i \(0.162925\pi\)
\(462\) 0 0
\(463\) −1.34002 2.32099i −0.0622761 0.107865i 0.833206 0.552962i \(-0.186503\pi\)
−0.895482 + 0.445097i \(0.853169\pi\)
\(464\) 40.1584 1.86431
\(465\) 0 0
\(466\) −21.5868 −0.999988
\(467\) −15.7083 + 27.2075i −0.726892 + 1.25901i 0.231299 + 0.972883i \(0.425702\pi\)
−0.958191 + 0.286131i \(0.907631\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 1.13816 1.97134i 0.0524992 0.0909313i
\(471\) 0 0
\(472\) −20.3346 + 35.2205i −0.935974 + 1.62115i
\(473\) 0.358441 0.620838i 0.0164811 0.0285461i
\(474\) 0 0
\(475\) 5.09627 8.82699i 0.233833 0.405010i
\(476\) 0 0
\(477\) 0 0
\(478\) −18.4363 + 31.9326i −0.843256 + 1.46056i
\(479\) 16.4406 0.751189 0.375594 0.926784i \(-0.377439\pi\)
0.375594 + 0.926784i \(0.377439\pi\)
\(480\) 0 0
\(481\) 24.8367 1.13245
\(482\) −6.84137 11.8496i −0.311616 0.539734i
\(483\) 0 0
\(484\) −8.93242 + 15.4714i −0.406019 + 0.703246i
\(485\) −5.49747 + 9.52190i −0.249627 + 0.432367i
\(486\) 0 0
\(487\) 1.48767 + 2.57673i 0.0674129 + 0.116763i 0.897762 0.440481i \(-0.145192\pi\)
−0.830349 + 0.557244i \(0.811859\pi\)
\(488\) −7.92649 13.7291i −0.358815 0.621486i
\(489\) 0 0
\(490\) 0 0
\(491\) −13.2430 22.9376i −0.597650 1.03516i −0.993167 0.116702i \(-0.962768\pi\)
0.395517 0.918459i \(-0.370565\pi\)
\(492\) 0 0
\(493\) −9.99825 −0.450298
\(494\) −16.6493 28.8374i −0.749087 1.29746i
\(495\) 0 0
\(496\) −30.2327 −1.35749
\(497\) 0 0
\(498\) 0 0
\(499\) −13.4439 −0.601830 −0.300915 0.953651i \(-0.597292\pi\)
−0.300915 + 0.953651i \(0.597292\pi\)
\(500\) 17.8969 30.9984i 0.800375 1.38629i
\(501\) 0 0
\(502\) 15.2772 + 26.4609i 0.681854 + 1.18101i
\(503\) 22.6631 1.01050 0.505250 0.862973i \(-0.331400\pi\)
0.505250 + 0.862973i \(0.331400\pi\)
\(504\) 0 0
\(505\) 8.54488 0.380242
\(506\) 15.5326 + 26.9032i 0.690506 + 1.19599i
\(507\) 0 0
\(508\) −38.9393 + 67.4448i −1.72765 + 2.99238i
\(509\) −9.54757 −0.423189 −0.211594 0.977358i \(-0.567866\pi\)
−0.211594 + 0.977358i \(0.567866\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 50.5553 2.23425
\(513\) 0 0
\(514\) −13.3773 23.1702i −0.590049 1.02199i
\(515\) 5.80066 0.255608
\(516\) 0 0
\(517\) 1.98293 + 3.43453i 0.0872090 + 0.151050i
\(518\) 0 0
\(519\) 0 0
\(520\) −14.6411 25.3592i −0.642057 1.11208i
\(521\) −1.55644 2.69583i −0.0681887 0.118106i 0.829915 0.557889i \(-0.188389\pi\)
−0.898104 + 0.439783i \(0.855055\pi\)
\(522\) 0 0
\(523\) 8.07444 13.9853i 0.353071 0.611537i −0.633715 0.773567i \(-0.718471\pi\)
0.986786 + 0.162030i \(0.0518041\pi\)
\(524\) −42.3448 + 73.3434i −1.84984 + 3.20402i
\(525\) 0 0
\(526\) 35.8965 + 62.1746i 1.56516 + 2.71094i
\(527\) 7.52704 0.327883
\(528\) 0 0
\(529\) −12.9986 −0.565155
\(530\) −8.11721 + 14.0594i −0.352589 + 0.610702i
\(531\) 0 0
\(532\) 0 0
\(533\) 3.23055 5.59548i 0.139931 0.242367i
\(534\) 0 0
\(535\) 1.05051 1.81953i 0.0454174 0.0786652i
\(536\) −9.03121 + 15.6425i −0.390089 + 0.675654i
\(537\) 0 0
\(538\) −9.47431 + 16.4100i −0.408466 + 0.707485i
\(539\) 0 0
\(540\) 0 0
\(541\) 2.50774 4.34353i 0.107816 0.186743i −0.807069 0.590457i \(-0.798948\pi\)
0.914885 + 0.403714i \(0.132281\pi\)
\(542\) −34.5330 −1.48332
\(543\) 0 0
\(544\) 7.59627 0.325687
\(545\) −1.74035 3.01438i −0.0745485 0.129122i
\(546\) 0 0
\(547\) −8.23901 + 14.2704i −0.352275 + 0.610157i −0.986648 0.162870i \(-0.947925\pi\)
0.634373 + 0.773027i \(0.281258\pi\)
\(548\) 40.0467 69.3629i 1.71071 2.96304i
\(549\) 0 0
\(550\) 20.7592 + 35.9561i 0.885177 + 1.53317i
\(551\) −7.29426 12.6340i −0.310746 0.538228i
\(552\) 0 0
\(553\) 0 0
\(554\) −7.78699 13.4875i −0.330837 0.573027i
\(555\) 0 0
\(556\) 97.3055 4.12667
\(557\) −17.2815 29.9325i −0.732242 1.26828i −0.955923 0.293618i \(-0.905141\pi\)
0.223681 0.974662i \(-0.428193\pi\)
\(558\) 0 0
\(559\) −1.00774 −0.0426229
\(560\) 0 0
\(561\) 0 0
\(562\) 8.38682 0.353777
\(563\) −18.6052 + 32.2251i −0.784115 + 1.35813i 0.145411 + 0.989371i \(0.453550\pi\)
−0.929526 + 0.368756i \(0.879784\pi\)
\(564\) 0 0
\(565\) 7.23442 + 12.5304i 0.304354 + 0.527157i
\(566\) −73.4894 −3.08899
\(567\) 0 0
\(568\) −22.4706 −0.942845
\(569\) 0.202333 + 0.350452i 0.00848226 + 0.0146917i 0.870235 0.492636i \(-0.163967\pi\)
−0.861753 + 0.507328i \(0.830633\pi\)
\(570\) 0 0
\(571\) 18.8897 32.7178i 0.790507 1.36920i −0.135146 0.990826i \(-0.543150\pi\)
0.925653 0.378373i \(-0.123516\pi\)
\(572\) 93.3278 3.90223
\(573\) 0 0
\(574\) 0 0
\(575\) 13.3669 0.557438
\(576\) 0 0
\(577\) 1.10560 + 1.91496i 0.0460267 + 0.0797206i 0.888121 0.459610i \(-0.152011\pi\)
−0.842094 + 0.539330i \(0.818677\pi\)
\(578\) 36.1293 1.50278
\(579\) 0 0
\(580\) −11.7344 20.3246i −0.487245 0.843934i
\(581\) 0 0
\(582\) 0 0
\(583\) −14.1420 24.4947i −0.585703 1.01447i
\(584\) −39.0210 67.5864i −1.61470 2.79674i
\(585\) 0 0
\(586\) 10.6591 18.4621i 0.440323 0.762662i
\(587\) 12.1049 20.9663i 0.499622 0.865371i −0.500378 0.865807i \(-0.666806\pi\)
1.00000 0.000436347i \(0.000138894\pi\)
\(588\) 0 0
\(589\) 5.49138 + 9.51135i 0.226268 + 0.391908i
\(590\) 14.8307 0.610570
\(591\) 0 0
\(592\) −30.2327 −1.24255
\(593\) 6.11927 10.5989i 0.251288 0.435244i −0.712592 0.701578i \(-0.752479\pi\)
0.963881 + 0.266334i \(0.0858124\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −33.4295 + 57.9016i −1.36932 + 2.37174i
\(597\) 0 0
\(598\) 21.8346 37.8186i 0.892882 1.54652i
\(599\) 19.8084 34.3092i 0.809349 1.40183i −0.103966 0.994581i \(-0.533153\pi\)
0.913315 0.407253i \(-0.133513\pi\)
\(600\) 0 0
\(601\) 15.0039 25.9875i 0.612021 1.06005i −0.378879 0.925446i \(-0.623690\pi\)
0.990899 0.134605i \(-0.0429764\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 41.8127 72.4218i 1.70134 2.94680i
\(605\) 3.56118 0.144783
\(606\) 0 0
\(607\) −19.4843 −0.790844 −0.395422 0.918499i \(-0.629402\pi\)
−0.395422 + 0.918499i \(0.629402\pi\)
\(608\) 5.54189 + 9.59883i 0.224753 + 0.389284i
\(609\) 0 0
\(610\) −2.89053 + 5.00654i −0.117034 + 0.202709i
\(611\) 2.78746 4.82802i 0.112768 0.195321i
\(612\) 0 0
\(613\) 9.26382 + 16.0454i 0.374162 + 0.648068i 0.990201 0.139648i \(-0.0445970\pi\)
−0.616039 + 0.787716i \(0.711264\pi\)
\(614\) −16.0633 27.8225i −0.648262 1.12282i
\(615\) 0 0
\(616\) 0 0
\(617\) 13.9201 + 24.1103i 0.560402 + 0.970644i 0.997461 + 0.0712118i \(0.0226866\pi\)
−0.437059 + 0.899433i \(0.643980\pi\)
\(618\) 0 0
\(619\) −44.9813 −1.80795 −0.903976 0.427583i \(-0.859365\pi\)
−0.903976 + 0.427583i \(0.859365\pi\)
\(620\) 8.83409 + 15.3011i 0.354786 + 0.614507i
\(621\) 0 0
\(622\) −41.7547 −1.67421
\(623\) 0 0
\(624\) 0 0
\(625\) 13.9982 0.559930
\(626\) 36.1057 62.5368i 1.44307 2.49947i
\(627\) 0 0
\(628\) 39.8298 + 68.9873i 1.58938 + 2.75289i
\(629\) 7.52704 0.300123
\(630\) 0 0
\(631\) 9.43613 0.375646 0.187823 0.982203i \(-0.439857\pi\)
0.187823 + 0.982203i \(0.439857\pi\)
\(632\) −18.1903 31.5065i −0.723572 1.25326i
\(633\) 0 0
\(634\) 32.7841 56.7836i 1.30202 2.25517i
\(635\) 15.5243 0.616065
\(636\) 0 0
\(637\) 0 0
\(638\) 59.4252 2.35267
\(639\) 0 0
\(640\) −5.86571 10.1597i −0.231863 0.401598i
\(641\) −37.3901 −1.47682 −0.738410 0.674352i \(-0.764423\pi\)
−0.738410 + 0.674352i \(0.764423\pi\)
\(642\) 0 0
\(643\) −0.805874 1.39581i −0.0317806 0.0550456i 0.849698 0.527270i \(-0.176784\pi\)
−0.881478 + 0.472225i \(0.843451\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −5.04576 8.73951i −0.198523 0.343851i
\(647\) −20.5881 35.6597i −0.809402 1.40193i −0.913278 0.407336i \(-0.866458\pi\)
0.103876 0.994590i \(-0.466875\pi\)
\(648\) 0 0
\(649\) −12.9192 + 22.3767i −0.507124 + 0.878364i
\(650\) 29.1819 50.5445i 1.14461 1.98252i
\(651\) 0 0
\(652\) −2.11334 3.66041i −0.0827648 0.143353i
\(653\) −3.05199 −0.119434 −0.0597169 0.998215i \(-0.519020\pi\)
−0.0597169 + 0.998215i \(0.519020\pi\)
\(654\) 0 0
\(655\) 16.8821 0.659637
\(656\) −3.93242 + 6.81115i −0.153535 + 0.265931i
\(657\) 0 0
\(658\) 0 0
\(659\) 20.8175 36.0569i 0.810934 1.40458i −0.101277 0.994858i \(-0.532293\pi\)
0.912211 0.409721i \(-0.134374\pi\)
\(660\) 0 0
\(661\) −10.1505 + 17.5812i −0.394808 + 0.683828i −0.993077 0.117468i \(-0.962522\pi\)
0.598269 + 0.801296i \(0.295856\pi\)
\(662\) 10.4055 18.0229i 0.404423 0.700481i
\(663\) 0 0
\(664\) 0.668434 1.15776i 0.0259403 0.0449298i
\(665\) 0 0
\(666\) 0 0
\(667\) 9.56599 16.5688i 0.370397 0.641546i
\(668\) −87.5167 −3.38612
\(669\) 0 0
\(670\) 6.58677 0.254469
\(671\) −5.03596 8.72254i −0.194411 0.336730i
\(672\) 0 0
\(673\) 0.415345 0.719398i 0.0160104 0.0277307i −0.857909 0.513801i \(-0.828237\pi\)
0.873920 + 0.486071i \(0.161570\pi\)
\(674\) 5.78746 10.0242i 0.222924 0.386117i
\(675\) 0 0
\(676\) −36.9222 63.9511i −1.42008 2.45966i
\(677\) 5.43360 + 9.41127i 0.208830 + 0.361705i 0.951346 0.308124i \(-0.0997011\pi\)
−0.742516 + 0.669828i \(0.766368\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −4.43717 7.68540i −0.170158 0.294722i
\(681\) 0 0
\(682\) −44.7374 −1.71308
\(683\) 16.3473 + 28.3143i 0.625512 + 1.08342i 0.988442 + 0.151602i \(0.0484432\pi\)
−0.362930 + 0.931817i \(0.618223\pi\)
\(684\) 0 0
\(685\) −15.9659 −0.610024
\(686\) 0 0
\(687\) 0 0
\(688\) 1.22668 0.0467668
\(689\) −19.8799 + 34.4329i −0.757362 + 1.31179i
\(690\) 0 0
\(691\) −7.49912 12.9889i −0.285280 0.494120i 0.687397 0.726282i \(-0.258753\pi\)
−0.972677 + 0.232162i \(0.925420\pi\)
\(692\) −100.064 −3.80387
\(693\) 0 0
\(694\) 56.8863 2.15937
\(695\) −9.69846 16.7982i −0.367884 0.637193i
\(696\) 0 0
\(697\) 0.979055 1.69577i 0.0370844 0.0642320i
\(698\) −66.0856 −2.50138
\(699\) 0 0
\(700\) 0 0
\(701\) −26.4688 −0.999714 −0.499857 0.866108i \(-0.666614\pi\)
−0.499857 + 0.866108i \(0.666614\pi\)
\(702\) 0 0
\(703\) 5.49138 + 9.51135i 0.207111 + 0.358727i
\(704\) 6.35504 0.239514
\(705\) 0 0
\(706\) 0.449493 + 0.778544i 0.0169169 + 0.0293009i
\(707\) 0 0
\(708\) 0 0
\(709\) −7.68004 13.3022i −0.288430 0.499576i 0.685005 0.728538i \(-0.259800\pi\)
−0.973435 + 0.228963i \(0.926467\pi\)
\(710\) 4.09714 + 7.09646i 0.153763 + 0.266325i
\(711\) 0 0
\(712\) −33.6668 + 58.3127i −1.26172 + 2.18536i
\(713\) −7.20162 + 12.4736i −0.269703 + 0.467139i
\(714\) 0 0
\(715\) −9.30200 16.1115i −0.347875 0.602538i
\(716\) 32.4124 1.21131
\(717\) 0 0
\(718\) 13.8152 0.515579
\(719\) 13.3653 23.1494i 0.498442 0.863326i −0.501557 0.865125i \(-0.667239\pi\)
0.999998 + 0.00179839i \(0.000572447\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −16.6925 + 28.9123i −0.621232 + 1.07600i
\(723\) 0 0
\(724\) 7.60014 13.1638i 0.282457 0.489230i
\(725\) 12.7849 22.1441i 0.474820 0.822413i
\(726\) 0 0
\(727\) 22.8221 39.5290i 0.846424 1.46605i −0.0379552 0.999279i \(-0.512084\pi\)
0.884379 0.466770i \(-0.154582\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −14.2297 + 24.6465i −0.526664 + 0.912209i
\(731\) −0.305407 −0.0112959
\(732\) 0 0
\(733\) 5.97502 0.220693 0.110346 0.993893i \(-0.464804\pi\)
0.110346 + 0.993893i \(0.464804\pi\)
\(734\) 13.8302 + 23.9546i 0.510483 + 0.884182i
\(735\) 0 0
\(736\) −7.26786 + 12.5883i −0.267897 + 0.464011i
\(737\) −5.73783 + 9.93821i −0.211356 + 0.366079i
\(738\) 0 0
\(739\) 17.7981 + 30.8273i 0.654715 + 1.13400i 0.981965 + 0.189062i \(0.0605447\pi\)
−0.327250 + 0.944938i \(0.606122\pi\)
\(740\) 8.83409 + 15.3011i 0.324748 + 0.562480i
\(741\) 0 0
\(742\) 0 0
\(743\) −14.6544 25.3821i −0.537616 0.931178i −0.999032 0.0439943i \(-0.985992\pi\)
0.461416 0.887184i \(-0.347342\pi\)
\(744\) 0 0
\(745\) 13.3277 0.488289
\(746\) 2.19207 + 3.79677i 0.0802573 + 0.139010i
\(747\) 0 0
\(748\) 28.2841 1.03417
\(749\) 0 0
\(750\) 0 0
\(751\) −17.3337 −0.632515 −0.316258 0.948673i \(-0.602426\pi\)
−0.316258 + 0.948673i \(0.602426\pi\)
\(752\) −3.39306 + 5.87695i −0.123732 + 0.214310i
\(753\) 0 0
\(754\) −41.7679 72.3440i −1.52110 2.63461i
\(755\) −16.6699 −0.606681
\(756\) 0 0
\(757\) −2.77156 −0.100734 −0.0503671 0.998731i \(-0.516039\pi\)
−0.0503671 + 0.998731i \(0.516039\pi\)
\(758\) −15.3614 26.6068i −0.557952 0.966402i
\(759\) 0 0
\(760\) 6.47431 11.2138i 0.234848 0.406768i
\(761\) −7.50744 −0.272144 −0.136072 0.990699i \(-0.543448\pi\)
−0.136072 + 0.990699i \(0.543448\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −24.9590 −0.902987
\(765\) 0 0
\(766\) 11.0296 + 19.1038i 0.398514 + 0.690247i
\(767\) 36.3218 1.31150
\(768\) 0 0
\(769\) −1.02182 1.76985i −0.0368478 0.0638223i 0.847013 0.531572i \(-0.178398\pi\)
−0.883861 + 0.467749i \(0.845065\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −21.1668 36.6620i −0.761811 1.31950i
\(773\) −12.4709 21.6002i −0.448547 0.776907i 0.549744 0.835333i \(-0.314725\pi\)
−0.998292 + 0.0584263i \(0.981392\pi\)
\(774\) 0 0
\(775\) −9.62495 + 16.6709i −0.345738 + 0.598837i
\(776\) 38.1721 66.1159i 1.37030 2.37342i
\(777\) 0 0
\(778\) −4.61246 7.98902i −0.165365 0.286420i
\(779\) 2.85710 0.102366
\(780\) 0 0
\(781\) −14.2763 −0.510847
\(782\) 6.61721 11.4613i 0.236631 0.409857i
\(783\) 0 0
\(784\) 0 0
\(785\) 7.93969 13.7520i 0.283380 0.490828i
\(786\) 0 0
\(787\) −3.55350 + 6.15484i −0.126669 + 0.219396i −0.922384 0.386274i \(-0.873762\pi\)
0.795715 + 0.605671i \(0.207095\pi\)
\(788\) 18.3516 31.7860i 0.653750 1.13233i
\(789\) 0 0
\(790\) −6.63341 + 11.4894i −0.236006 + 0.408774i
\(791\) 0 0
\(792\) 0 0
\(793\) −7.07919 + 12.2615i −0.251389 + 0.435419i
\(794\) 39.1097 1.38795