Properties

Label 1323.2.g.e.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.e.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 \(-0.563002\pi\)
−0.196637 + 0.980476i \(0.563002\pi\)
\(6\) 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 \(-0.893698\pi\)
0.188507 0.982072i \(-0.439635\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −3.31908 5.74881i −0.829769 1.43720i
\(17\) −0.826352 1.43128i −0.200420 0.347137i 0.748244 0.663424i \(-0.230897\pi\)
−0.948664 + 0.316286i \(0.897564\pi\)
\(18\) 0 0
\(19\) 1.20574 2.08840i 0.276615 0.479111i −0.693926 0.720046i \(-0.744121\pi\)
0.970541 + 0.240935i \(0.0774540\pi\)
\(20\) 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 −0.994777 0.102068i \(-0.967454\pi\)
0.585782 + 0.810468i \(0.300787\pi\)
\(32\) 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 0.908570 0.417734i \(-0.137175\pi\)
−0.816053 + 0.577977i \(0.803842\pi\)
\(42\) 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 0.900894 0.434039i \(-0.142912\pi\)
−0.826336 + 0.563178i \(0.809579\pi\)
\(48\) 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 −0.997177 0.0750906i \(-0.976075\pi\)
0.563619 + 0.826035i \(0.309409\pi\)
\(60\) 0 0
\(61\) −1.29813 2.24843i −0.166209 0.287882i 0.770875 0.636986i \(-0.219819\pi\)
−0.937084 + 0.349104i \(0.886486\pi\)
\(62\) −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 \(-0.897703\pi\)
0.200847 0.979623i \(-0.435631\pi\)
\(74\) 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 −0.859955 0.510370i \(-0.829508\pi\)
0.871971 + 0.489558i \(0.162842\pi\)
\(84\) 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 \(0.365356\pi\)
−0.994944 + 0.100431i \(0.967978\pi\)
\(90\) 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 \(-0.614439\pi\)
0.986569 0.163342i \(-0.0522275\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 9.32295 16.1478i 0.932295 1.61478i
\(101\) −9.71688 −0.966866 −0.483433 0.875381i \(-0.660610\pi\)
−0.483433 + 0.875381i \(0.660610\pi\)
\(102\) 0 0
\(103\) −6.59627 −0.649949 −0.324975 0.945723i \(-0.605356\pi\)
−0.324975 + 0.945723i \(0.605356\pi\)
\(104\) 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 \(-0.816655\pi\)
−0.838650 + 0.544670i \(0.816655\pi\)
\(132\) 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 \(0.218330\pi\)
0.161595 + 0.986857i \(0.448336\pi\)
\(140\) 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 \(0.422785\pi\)
−0.960773 + 0.277337i \(0.910548\pi\)
\(158\) −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 \(-0.888131\pi\)
0.171304 0.985218i \(-0.445202\pi\)
\(168\) 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 \(-0.835710\pi\)
0.00746626 0.999972i \(-0.497623\pi\)
\(174\) 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 \(-0.459126\pi\)
0.128056 + 0.991767i \(0.459126\pi\)
\(182\) 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 0.958923 0.283667i \(-0.0915511\pi\)
−0.725124 + 0.688618i \(0.758218\pi\)
\(200\) 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 −0.951760 0.306843i \(-0.900727\pi\)
0.741614 + 0.670827i \(0.234061\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −20.8307 + 36.0798i −1.38564 + 2.39999i
\(227\) −6.16250 −0.409020 −0.204510 0.978865i \(-0.565560\pi\)
−0.204510 + 0.978865i \(0.565560\pi\)
\(228\) 0 0
\(229\) −23.3851 −1.54533 −0.772664 0.634815i \(-0.781076\pi\)
−0.772664 + 0.634815i \(0.781076\pi\)
\(230\) 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 \(-0.444317\pi\)
0.174043 + 0.984738i \(0.444317\pi\)
\(242\) 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 \(-0.624361\pi\)
−0.380827 + 0.924646i \(0.624361\pi\)
\(252\) 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 \(-0.393102\pi\)
0.329552 + 0.944137i \(0.393102\pi\)
\(258\) 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 0.729120 0.684386i \(-0.239930\pi\)
−0.957255 + 0.289244i \(0.906596\pi\)
\(270\) 0 0
\(271\) 6.81908 11.8110i 0.414229 0.717467i −0.581118 0.813819i \(-0.697384\pi\)
0.995347 + 0.0963530i \(0.0307178\pi\)
\(272\) −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 \(-0.502152\pi\)
0.869385 0.494134i \(-0.164515\pi\)
\(284\) −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 0.962392 0.271664i \(-0.0875740\pi\)
−0.716464 + 0.697624i \(0.754241\pi\)
\(294\) 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 \(-0.382072\pi\)
0.362065 + 0.932153i \(0.382072\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 10.1411 0.575979
\(311\) 8.24510 14.2809i 0.467537 0.809797i −0.531775 0.846886i \(-0.678475\pi\)
0.999312 + 0.0370881i \(0.0118082\pi\)
\(312\) 0 0
\(313\) 14.2592 + 24.6977i 0.805980 + 1.39600i 0.915628 + 0.402027i \(0.131694\pi\)
−0.109648 + 0.993970i \(0.534972\pi\)
\(314\) −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 \(-0.587171\pi\)
0.968976 0.247155i \(-0.0794958\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −8.91534 + 15.4418i −0.475189 + 0.823052i
\(353\) −0.355037 −0.0188967 −0.00944836 0.999955i \(-0.503008\pi\)
−0.00944836 + 0.999955i \(0.503008\pi\)
\(354\) 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 \(-0.592031\pi\)
−0.285113 + 0.958494i \(0.592031\pi\)
\(368\) 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 \(-0.571447\pi\)
−0.222577 + 0.974915i \(0.571447\pi\)
\(384\) 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 −0.992126 0.125246i \(-0.960028\pi\)
0.604529 + 0.796583i \(0.293361\pi\)
\(398\) −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 \(0.417064\pi\)
−0.965602 + 0.260025i \(0.916269\pi\)
\(410\) 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 \(0.155223\pi\)
−0.0359442 + 0.999354i \(0.511444\pi\)
\(420\) 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 \(-0.851723\pi\)
−0.893451 + 0.449160i \(0.851723\pi\)
\(434\) 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 \(0.0375192\pi\)
−0.394689 + 0.918815i \(0.629147\pi\)
\(440\) −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 −0.871843 0.489786i \(-0.837075\pi\)
0.860088 + 0.510145i \(0.170408\pi\)
\(462\) 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 \(-0.574298\pi\)
0.958191 0.286131i \(-0.0923691\pi\)
\(468\) 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 \(-0.622561\pi\)
−0.375594 + 0.926784i \(0.622561\pi\)
\(480\) 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 \(-0.668600\pi\)
−0.505250 + 0.862973i \(0.668600\pi\)
\(504\) 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 \(-0.432134\pi\)
0.211594 + 0.977358i \(0.432134\pi\)
\(510\) 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 0.898104 0.439783i \(-0.144945\pi\)
−0.829915 + 0.557889i \(0.811611\pi\)
\(522\) 0 0
\(523\) −8.07444 + 13.9853i −0.353071 + 0.611537i −0.986786 0.162030i \(-0.948196\pi\)
0.633715 + 0.773567i \(0.281529\pi\)
\(524\) 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 \(-0.546450\pi\)
0.929526 0.368756i \(-0.120216\pi\)
\(564\) 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 0.842094 0.539330i \(-0.181323\pi\)
−0.888121 + 0.459610i \(0.847989\pi\)
\(578\) 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 −1.00000 0.000436347i \(-0.999861\pi\)
0.500378 + 0.865807i \(0.333194\pi\)
\(588\) 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 −0.963881 0.266334i \(-0.914188\pi\)
0.712592 + 0.701578i \(0.247521\pi\)
\(594\) 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 \(0.376310\pi\)
−0.990899 + 0.134605i \(0.957024\pi\)
\(602\) 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 \(-0.370598\pi\)
0.395422 + 0.918499i \(0.370598\pi\)
\(608\) −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 \(-0.140635\pi\)
0.903976 + 0.427583i \(0.140635\pi\)
\(620\) 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 0.881478 0.472225i \(-0.156549\pi\)
−0.849698 + 0.527270i \(0.823216\pi\)
\(644\) 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 \(0.133542\pi\)
−0.103876 + 0.994590i \(0.533125\pi\)
\(648\) 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 −0.598269 0.801296i \(-0.704144\pi\)
0.993077 + 0.117468i \(0.0374778\pi\)
\(662\) 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 0.742516 0.669828i \(-0.233632\pi\)
−0.951346 + 0.308124i \(0.900299\pi\)
\(678\) 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 0.972677 0.232162i \(-0.0745801\pi\)
−0.687397 + 0.726282i \(0.741247\pi\)
\(692\) 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 −0.999998 0.00179839i \(-0.999428\pi\)
0.501557 + 0.865125i \(0.332761\pi\)
\(720\) 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 \(0.487916\pi\)
−0.884379 + 0.466770i \(0.845418\pi\)
\(728\) 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 \(-0.535196\pi\)
−0.110346 + 0.993893i \(0.535196\pi\)
\(734\) −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 \(-0.456552\pi\)
0.136072 + 0.990699i \(0.456552\pi\)
\(762\) 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 0.883861 0.467749i \(-0.154935\pi\)
−0.847013 + 0.531572i \(0.821602\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −21.1668 36.6620i −0.761811 1.31950i
\(773\) 12.4709 + 21.6002i 0.448547 + 0.776907i 0.998292 0.0584263i \(-0.0186083\pi\)
−0.549744 + 0.835333i \(0.685275\pi\)
\(774\) 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 −0.795715 0.605671i \(-0.792905\pi\)
0.922384 + 0.386274i \(0.126238\pi\)
\(788\) 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