Properties

Label 1152.2.i.j.769.1
Level $1152$
Weight $2$
Character 1152.769
Analytic conductor $9.199$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 2 x^{11} + 3 x^{10} - 8 x^{9} + 22 x^{8} - 42 x^{7} + 51 x^{6} - 126 x^{5} + 198 x^{4} - 216 x^{3} + 243 x^{2} - 486 x + 729\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 769.1
Root \(0.952418 - 1.44669i\) of defining polynomial
Character \(\chi\) \(=\) 1152.769
Dual form 1152.2.i.j.385.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.72908 + 0.101475i) q^{3} +(1.24278 - 2.15256i) q^{5} +(0.909142 + 1.57468i) q^{7} +(2.97941 - 0.350917i) q^{9} +O(q^{10})\) \(q+(-1.72908 + 0.101475i) q^{3} +(1.24278 - 2.15256i) q^{5} +(0.909142 + 1.57468i) q^{7} +(2.97941 - 0.350917i) q^{9} +(-0.598407 - 1.03647i) q^{11} +(2.83342 - 4.90762i) q^{13} +(-1.93043 + 3.84805i) q^{15} -5.30021 q^{17} +4.55980 q^{19} +(-1.73177 - 2.63049i) q^{21} +(-2.01328 + 3.48711i) q^{23} +(-0.589008 - 1.02019i) q^{25} +(-5.11601 + 0.909098i) q^{27} +(3.01513 + 5.22236i) q^{29} +(2.81647 - 4.87827i) q^{31} +(1.13987 + 1.73141i) q^{33} +4.51946 q^{35} -5.18127 q^{37} +(-4.40119 + 8.77317i) q^{39} +(4.57620 - 7.92621i) q^{41} +(-3.99129 - 6.91313i) q^{43} +(2.94738 - 6.84946i) q^{45} +(1.39470 + 2.41570i) q^{47} +(1.84692 - 3.19896i) q^{49} +(9.16447 - 0.537841i) q^{51} +1.54470 q^{53} -2.97475 q^{55} +(-7.88424 + 0.462707i) q^{57} +(1.85725 - 3.21686i) q^{59} +(-4.01513 - 6.95441i) q^{61} +(3.26129 + 4.37258i) q^{63} +(-7.04263 - 12.1982i) q^{65} +(6.91372 - 11.9749i) q^{67} +(3.12726 - 6.23377i) q^{69} -11.1794 q^{71} +12.3969 q^{73} +(1.12196 + 1.70422i) q^{75} +(1.08807 - 1.88460i) q^{77} +(4.36480 + 7.56006i) q^{79} +(8.75371 - 2.09105i) q^{81} +(-8.89267 - 15.4025i) q^{83} +(-6.58700 + 11.4090i) q^{85} +(-5.74333 - 8.72390i) q^{87} -0.455297 q^{89} +10.3039 q^{91} +(-4.37486 + 8.72069i) q^{93} +(5.66683 - 9.81524i) q^{95} +(-1.01640 - 1.76045i) q^{97} +(-2.14661 - 2.87808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{3} + 2q^{5} + 6q^{7} - 2q^{9} + O(q^{10}) \) \( 12q - 4q^{3} + 2q^{5} + 6q^{7} - 2q^{9} - 4q^{11} - 10q^{13} + 4q^{15} + 4q^{17} - 4q^{19} - 2q^{21} + 8q^{23} - 14q^{25} + 14q^{27} + 2q^{29} + 8q^{31} - 10q^{33} - 8q^{35} + 22q^{39} - 2q^{41} + 2q^{43} - 10q^{45} - 14q^{47} - 18q^{49} + 38q^{51} - 24q^{53} - 16q^{55} - 38q^{57} - 6q^{59} - 14q^{61} - 16q^{63} - 8q^{65} - 4q^{67} + 50q^{69} - 28q^{71} + 60q^{73} - 50q^{75} - 2q^{77} + 16q^{79} + 22q^{81} - 24q^{83} - 16q^{85} - 36q^{87} - 48q^{89} + 52q^{91} - 42q^{93} - 20q^{95} - 14q^{97} - 68q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.72908 + 0.101475i −0.998282 + 0.0585868i
\(4\) 0 0
\(5\) 1.24278 2.15256i 0.555788 0.962654i −0.442053 0.896989i \(-0.645750\pi\)
0.997842 0.0656650i \(-0.0209169\pi\)
\(6\) 0 0
\(7\) 0.909142 + 1.57468i 0.343623 + 0.595173i 0.985103 0.171967i \(-0.0550123\pi\)
−0.641479 + 0.767140i \(0.721679\pi\)
\(8\) 0 0
\(9\) 2.97941 0.350917i 0.993135 0.116972i
\(10\) 0 0
\(11\) −0.598407 1.03647i −0.180426 0.312508i 0.761599 0.648048i \(-0.224414\pi\)
−0.942026 + 0.335540i \(0.891081\pi\)
\(12\) 0 0
\(13\) 2.83342 4.90762i 0.785848 1.36113i −0.142643 0.989774i \(-0.545560\pi\)
0.928491 0.371355i \(-0.121107\pi\)
\(14\) 0 0
\(15\) −1.93043 + 3.84805i −0.498435 + 0.993562i
\(16\) 0 0
\(17\) −5.30021 −1.28549 −0.642745 0.766080i \(-0.722205\pi\)
−0.642745 + 0.766080i \(0.722205\pi\)
\(18\) 0 0
\(19\) 4.55980 1.04609 0.523045 0.852305i \(-0.324796\pi\)
0.523045 + 0.852305i \(0.324796\pi\)
\(20\) 0 0
\(21\) −1.73177 2.63049i −0.377902 0.574019i
\(22\) 0 0
\(23\) −2.01328 + 3.48711i −0.419798 + 0.727112i −0.995919 0.0902526i \(-0.971233\pi\)
0.576120 + 0.817365i \(0.304566\pi\)
\(24\) 0 0
\(25\) −0.589008 1.02019i −0.117802 0.204038i
\(26\) 0 0
\(27\) −5.11601 + 0.909098i −0.984576 + 0.174956i
\(28\) 0 0
\(29\) 3.01513 + 5.22236i 0.559896 + 0.969768i 0.997505 + 0.0706027i \(0.0224923\pi\)
−0.437609 + 0.899166i \(0.644174\pi\)
\(30\) 0 0
\(31\) 2.81647 4.87827i 0.505853 0.876163i −0.494124 0.869391i \(-0.664511\pi\)
0.999977 0.00677135i \(-0.00215540\pi\)
\(32\) 0 0
\(33\) 1.13987 + 1.73141i 0.198425 + 0.301400i
\(34\) 0 0
\(35\) 4.51946 0.763928
\(36\) 0 0
\(37\) −5.18127 −0.851796 −0.425898 0.904771i \(-0.640042\pi\)
−0.425898 + 0.904771i \(0.640042\pi\)
\(38\) 0 0
\(39\) −4.40119 + 8.77317i −0.704754 + 1.40483i
\(40\) 0 0
\(41\) 4.57620 7.92621i 0.714682 1.23787i −0.248400 0.968658i \(-0.579905\pi\)
0.963082 0.269208i \(-0.0867619\pi\)
\(42\) 0 0
\(43\) −3.99129 6.91313i −0.608667 1.05424i −0.991460 0.130408i \(-0.958371\pi\)
0.382794 0.923834i \(-0.374962\pi\)
\(44\) 0 0
\(45\) 2.94738 6.84946i 0.439369 1.02106i
\(46\) 0 0
\(47\) 1.39470 + 2.41570i 0.203438 + 0.352366i 0.949634 0.313361i \(-0.101455\pi\)
−0.746196 + 0.665727i \(0.768122\pi\)
\(48\) 0 0
\(49\) 1.84692 3.19896i 0.263846 0.456994i
\(50\) 0 0
\(51\) 9.16447 0.537841i 1.28328 0.0753128i
\(52\) 0 0
\(53\) 1.54470 0.212181 0.106091 0.994356i \(-0.466167\pi\)
0.106091 + 0.994356i \(0.466167\pi\)
\(54\) 0 0
\(55\) −2.97475 −0.401116
\(56\) 0 0
\(57\) −7.88424 + 0.462707i −1.04429 + 0.0612871i
\(58\) 0 0
\(59\) 1.85725 3.21686i 0.241794 0.418799i −0.719431 0.694563i \(-0.755598\pi\)
0.961225 + 0.275764i \(0.0889309\pi\)
\(60\) 0 0
\(61\) −4.01513 6.95441i −0.514085 0.890421i −0.999866 0.0163411i \(-0.994798\pi\)
0.485781 0.874080i \(-0.338535\pi\)
\(62\) 0 0
\(63\) 3.26129 + 4.37258i 0.410883 + 0.550893i
\(64\) 0 0
\(65\) −7.04263 12.1982i −0.873531 1.51300i
\(66\) 0 0
\(67\) 6.91372 11.9749i 0.844645 1.46297i −0.0412836 0.999147i \(-0.513145\pi\)
0.885929 0.463821i \(-0.153522\pi\)
\(68\) 0 0
\(69\) 3.12726 6.23377i 0.376478 0.750458i
\(70\) 0 0
\(71\) −11.1794 −1.32675 −0.663376 0.748287i \(-0.730877\pi\)
−0.663376 + 0.748287i \(0.730877\pi\)
\(72\) 0 0
\(73\) 12.3969 1.45095 0.725473 0.688251i \(-0.241621\pi\)
0.725473 + 0.688251i \(0.241621\pi\)
\(74\) 0 0
\(75\) 1.12196 + 1.70422i 0.129553 + 0.196786i
\(76\) 0 0
\(77\) 1.08807 1.88460i 0.123998 0.214770i
\(78\) 0 0
\(79\) 4.36480 + 7.56006i 0.491079 + 0.850573i 0.999947 0.0102710i \(-0.00326940\pi\)
−0.508869 + 0.860844i \(0.669936\pi\)
\(80\) 0 0
\(81\) 8.75371 2.09105i 0.972635 0.232339i
\(82\) 0 0
\(83\) −8.89267 15.4025i −0.976097 1.69065i −0.676267 0.736657i \(-0.736403\pi\)
−0.299830 0.953993i \(-0.596930\pi\)
\(84\) 0 0
\(85\) −6.58700 + 11.4090i −0.714461 + 1.23748i
\(86\) 0 0
\(87\) −5.74333 8.72390i −0.615750 0.935300i
\(88\) 0 0
\(89\) −0.455297 −0.0482614 −0.0241307 0.999709i \(-0.507682\pi\)
−0.0241307 + 0.999709i \(0.507682\pi\)
\(90\) 0 0
\(91\) 10.3039 1.08014
\(92\) 0 0
\(93\) −4.37486 + 8.72069i −0.453652 + 0.904294i
\(94\) 0 0
\(95\) 5.66683 9.81524i 0.581405 1.00702i
\(96\) 0 0
\(97\) −1.01640 1.76045i −0.103199 0.178747i 0.809802 0.586704i \(-0.199575\pi\)
−0.913001 + 0.407957i \(0.866241\pi\)
\(98\) 0 0
\(99\) −2.14661 2.87808i −0.215743 0.289258i
\(100\) 0 0
\(101\) 3.06107 + 5.30192i 0.304587 + 0.527561i 0.977169 0.212462i \(-0.0681481\pi\)
−0.672582 + 0.740023i \(0.734815\pi\)
\(102\) 0 0
\(103\) 3.09086 5.35352i 0.304551 0.527498i −0.672610 0.739997i \(-0.734827\pi\)
0.977161 + 0.212499i \(0.0681602\pi\)
\(104\) 0 0
\(105\) −7.81448 + 0.458613i −0.762616 + 0.0447561i
\(106\) 0 0
\(107\) −16.2193 −1.56798 −0.783990 0.620774i \(-0.786818\pi\)
−0.783990 + 0.620774i \(0.786818\pi\)
\(108\) 0 0
\(109\) −2.08460 −0.199669 −0.0998344 0.995004i \(-0.531831\pi\)
−0.0998344 + 0.995004i \(0.531831\pi\)
\(110\) 0 0
\(111\) 8.95881 0.525771i 0.850333 0.0499040i
\(112\) 0 0
\(113\) 1.45933 2.52763i 0.137282 0.237779i −0.789185 0.614156i \(-0.789497\pi\)
0.926467 + 0.376376i \(0.122830\pi\)
\(114\) 0 0
\(115\) 5.00414 + 8.66742i 0.466638 + 0.808241i
\(116\) 0 0
\(117\) 6.71973 15.6161i 0.621239 1.44371i
\(118\) 0 0
\(119\) −4.81865 8.34614i −0.441725 0.765090i
\(120\) 0 0
\(121\) 4.78382 8.28582i 0.434893 0.753256i
\(122\) 0 0
\(123\) −7.10828 + 14.1694i −0.640932 + 1.27761i
\(124\) 0 0
\(125\) 9.49978 0.849686
\(126\) 0 0
\(127\) 15.0618 1.33652 0.668261 0.743926i \(-0.267039\pi\)
0.668261 + 0.743926i \(0.267039\pi\)
\(128\) 0 0
\(129\) 7.60276 + 11.5483i 0.669386 + 1.01677i
\(130\) 0 0
\(131\) −1.89311 + 3.27896i −0.165402 + 0.286484i −0.936798 0.349871i \(-0.886225\pi\)
0.771396 + 0.636355i \(0.219559\pi\)
\(132\) 0 0
\(133\) 4.14551 + 7.18023i 0.359461 + 0.622605i
\(134\) 0 0
\(135\) −4.40119 + 12.1423i −0.378794 + 1.04504i
\(136\) 0 0
\(137\) 6.39448 + 11.0756i 0.546317 + 0.946250i 0.998523 + 0.0543357i \(0.0173041\pi\)
−0.452205 + 0.891914i \(0.649363\pi\)
\(138\) 0 0
\(139\) −4.46539 + 7.73428i −0.378749 + 0.656013i −0.990881 0.134743i \(-0.956979\pi\)
0.612131 + 0.790756i \(0.290312\pi\)
\(140\) 0 0
\(141\) −2.65668 4.03540i −0.223733 0.339842i
\(142\) 0 0
\(143\) −6.78214 −0.567151
\(144\) 0 0
\(145\) 14.9886 1.24473
\(146\) 0 0
\(147\) −2.86885 + 5.71866i −0.236619 + 0.471667i
\(148\) 0 0
\(149\) 4.65170 8.05698i 0.381082 0.660054i −0.610135 0.792297i \(-0.708885\pi\)
0.991217 + 0.132244i \(0.0422182\pi\)
\(150\) 0 0
\(151\) 7.83527 + 13.5711i 0.637625 + 1.10440i 0.985953 + 0.167026i \(0.0534164\pi\)
−0.348328 + 0.937373i \(0.613250\pi\)
\(152\) 0 0
\(153\) −15.7915 + 1.85993i −1.27667 + 0.150367i
\(154\) 0 0
\(155\) −7.00051 12.1252i −0.562294 0.973922i
\(156\) 0 0
\(157\) −9.75491 + 16.8960i −0.778526 + 1.34845i 0.154265 + 0.988030i \(0.450699\pi\)
−0.932791 + 0.360418i \(0.882634\pi\)
\(158\) 0 0
\(159\) −2.67091 + 0.156749i −0.211817 + 0.0124310i
\(160\) 0 0
\(161\) −7.32144 −0.577010
\(162\) 0 0
\(163\) 5.02888 0.393892 0.196946 0.980414i \(-0.436898\pi\)
0.196946 + 0.980414i \(0.436898\pi\)
\(164\) 0 0
\(165\) 5.14358 0.301864i 0.400427 0.0235001i
\(166\) 0 0
\(167\) 7.65066 13.2513i 0.592026 1.02542i −0.401933 0.915669i \(-0.631662\pi\)
0.993959 0.109750i \(-0.0350050\pi\)
\(168\) 0 0
\(169\) −9.55650 16.5523i −0.735115 1.27326i
\(170\) 0 0
\(171\) 13.5855 1.60011i 1.03891 0.122364i
\(172\) 0 0
\(173\) 5.30192 + 9.18320i 0.403098 + 0.698186i 0.994098 0.108486i \(-0.0346001\pi\)
−0.591000 + 0.806671i \(0.701267\pi\)
\(174\) 0 0
\(175\) 1.07098 1.85500i 0.0809588 0.140225i
\(176\) 0 0
\(177\) −2.88490 + 5.75066i −0.216842 + 0.432246i
\(178\) 0 0
\(179\) 9.27314 0.693107 0.346553 0.938030i \(-0.387352\pi\)
0.346553 + 0.938030i \(0.387352\pi\)
\(180\) 0 0
\(181\) 2.32975 0.173169 0.0865845 0.996245i \(-0.472405\pi\)
0.0865845 + 0.996245i \(0.472405\pi\)
\(182\) 0 0
\(183\) 7.64817 + 11.6173i 0.565369 + 0.858773i
\(184\) 0 0
\(185\) −6.43918 + 11.1530i −0.473418 + 0.819985i
\(186\) 0 0
\(187\) 3.17169 + 5.49352i 0.231937 + 0.401726i
\(188\) 0 0
\(189\) −6.08272 7.22958i −0.442453 0.525874i
\(190\) 0 0
\(191\) −8.54208 14.7953i −0.618083 1.07055i −0.989835 0.142219i \(-0.954576\pi\)
0.371752 0.928332i \(-0.378757\pi\)
\(192\) 0 0
\(193\) −12.1360 + 21.0202i −0.873568 + 1.51306i −0.0152882 + 0.999883i \(0.504867\pi\)
−0.858280 + 0.513182i \(0.828467\pi\)
\(194\) 0 0
\(195\) 13.4151 + 20.3769i 0.960672 + 1.45922i
\(196\) 0 0
\(197\) −15.6971 −1.11837 −0.559186 0.829042i \(-0.688886\pi\)
−0.559186 + 0.829042i \(0.688886\pi\)
\(198\) 0 0
\(199\) −14.4764 −1.02620 −0.513101 0.858328i \(-0.671503\pi\)
−0.513101 + 0.858328i \(0.671503\pi\)
\(200\) 0 0
\(201\) −10.7392 + 21.4071i −0.757484 + 1.50994i
\(202\) 0 0
\(203\) −5.48237 + 9.49574i −0.384787 + 0.666470i
\(204\) 0 0
\(205\) −11.3744 19.7011i −0.794424 1.37598i
\(206\) 0 0
\(207\) −4.77470 + 11.0960i −0.331865 + 0.771225i
\(208\) 0 0
\(209\) −2.72862 4.72610i −0.188742 0.326911i
\(210\) 0 0
\(211\) −3.21103 + 5.56167i −0.221056 + 0.382881i −0.955129 0.296190i \(-0.904284\pi\)
0.734073 + 0.679071i \(0.237617\pi\)
\(212\) 0 0
\(213\) 19.3300 1.13443i 1.32447 0.0777301i
\(214\) 0 0
\(215\) −19.8412 −1.35316
\(216\) 0 0
\(217\) 10.2423 0.695291
\(218\) 0 0
\(219\) −21.4351 + 1.25798i −1.44845 + 0.0850062i
\(220\) 0 0
\(221\) −15.0177 + 26.0114i −1.01020 + 1.74972i
\(222\) 0 0
\(223\) −7.90683 13.6950i −0.529481 0.917087i −0.999409 0.0343825i \(-0.989054\pi\)
0.469928 0.882705i \(-0.344280\pi\)
\(224\) 0 0
\(225\) −2.11290 2.83287i −0.140860 0.188858i
\(226\) 0 0
\(227\) 3.00928 + 5.21223i 0.199733 + 0.345948i 0.948442 0.316951i \(-0.102659\pi\)
−0.748709 + 0.662899i \(0.769326\pi\)
\(228\) 0 0
\(229\) −13.8177 + 23.9329i −0.913098 + 1.58153i −0.103436 + 0.994636i \(0.532984\pi\)
−0.809662 + 0.586896i \(0.800350\pi\)
\(230\) 0 0
\(231\) −1.69012 + 3.36903i −0.111202 + 0.221666i
\(232\) 0 0
\(233\) −12.1858 −0.798321 −0.399161 0.916881i \(-0.630698\pi\)
−0.399161 + 0.916881i \(0.630698\pi\)
\(234\) 0 0
\(235\) 6.93324 0.452275
\(236\) 0 0
\(237\) −8.31423 12.6290i −0.540068 0.820342i
\(238\) 0 0
\(239\) −7.82794 + 13.5584i −0.506347 + 0.877019i 0.493626 + 0.869674i \(0.335671\pi\)
−0.999973 + 0.00734451i \(0.997662\pi\)
\(240\) 0 0
\(241\) 9.39281 + 16.2688i 0.605044 + 1.04797i 0.992045 + 0.125887i \(0.0401778\pi\)
−0.387001 + 0.922079i \(0.626489\pi\)
\(242\) 0 0
\(243\) −14.9236 + 4.50386i −0.957352 + 0.288923i
\(244\) 0 0
\(245\) −4.59064 7.95121i −0.293285 0.507984i
\(246\) 0 0
\(247\) 12.9198 22.3778i 0.822068 1.42386i
\(248\) 0 0
\(249\) 16.9391 + 25.7298i 1.07347 + 1.63056i
\(250\) 0 0
\(251\) −11.1684 −0.704942 −0.352471 0.935823i \(-0.614658\pi\)
−0.352471 + 0.935823i \(0.614658\pi\)
\(252\) 0 0
\(253\) 4.81905 0.302971
\(254\) 0 0
\(255\) 10.2317 20.3955i 0.640734 1.27722i
\(256\) 0 0
\(257\) 3.19941 5.54154i 0.199574 0.345672i −0.748817 0.662777i \(-0.769378\pi\)
0.948390 + 0.317106i \(0.102711\pi\)
\(258\) 0 0
\(259\) −4.71051 8.15885i −0.292697 0.506966i
\(260\) 0 0
\(261\) 10.8159 + 14.5015i 0.669488 + 0.897619i
\(262\) 0 0
\(263\) 6.71632 + 11.6330i 0.414146 + 0.717322i 0.995338 0.0964440i \(-0.0307469\pi\)
−0.581192 + 0.813766i \(0.697414\pi\)
\(264\) 0 0
\(265\) 1.91973 3.32507i 0.117928 0.204257i
\(266\) 0 0
\(267\) 0.787243 0.0462014i 0.0481785 0.00282748i
\(268\) 0 0
\(269\) 26.6295 1.62363 0.811814 0.583916i \(-0.198480\pi\)
0.811814 + 0.583916i \(0.198480\pi\)
\(270\) 0 0
\(271\) 14.9630 0.908936 0.454468 0.890763i \(-0.349829\pi\)
0.454468 + 0.890763i \(0.349829\pi\)
\(272\) 0 0
\(273\) −17.8162 + 1.04559i −1.07829 + 0.0632821i
\(274\) 0 0
\(275\) −0.704933 + 1.22098i −0.0425091 + 0.0736278i
\(276\) 0 0
\(277\) −8.36861 14.4949i −0.502821 0.870912i −0.999995 0.00326057i \(-0.998962\pi\)
0.497174 0.867651i \(-0.334371\pi\)
\(278\) 0 0
\(279\) 6.67954 15.5227i 0.399893 0.929319i
\(280\) 0 0
\(281\) −2.80547 4.85922i −0.167361 0.289877i 0.770131 0.637886i \(-0.220191\pi\)
−0.937491 + 0.348009i \(0.886858\pi\)
\(282\) 0 0
\(283\) −6.41074 + 11.1037i −0.381079 + 0.660048i −0.991217 0.132247i \(-0.957781\pi\)
0.610138 + 0.792295i \(0.291114\pi\)
\(284\) 0 0
\(285\) −8.80238 + 17.5463i −0.521408 + 1.03936i
\(286\) 0 0
\(287\) 16.6417 0.982326
\(288\) 0 0
\(289\) 11.0923 0.652487
\(290\) 0 0
\(291\) 1.93607 + 2.94081i 0.113494 + 0.172393i
\(292\) 0 0
\(293\) −7.24047 + 12.5409i −0.422993 + 0.732645i −0.996231 0.0867441i \(-0.972354\pi\)
0.573238 + 0.819389i \(0.305687\pi\)
\(294\) 0 0
\(295\) −4.61632 7.99570i −0.268772 0.465528i
\(296\) 0 0
\(297\) 4.00371 + 4.75858i 0.232319 + 0.276121i
\(298\) 0 0
\(299\) 11.4089 + 19.7609i 0.659796 + 1.14280i
\(300\) 0 0
\(301\) 7.25731 12.5700i 0.418304 0.724524i
\(302\) 0 0
\(303\) −5.83083 8.85680i −0.334972 0.508810i
\(304\) 0 0
\(305\) −19.9597 −1.14289
\(306\) 0 0
\(307\) 19.4320 1.10905 0.554523 0.832169i \(-0.312901\pi\)
0.554523 + 0.832169i \(0.312901\pi\)
\(308\) 0 0
\(309\) −4.80108 + 9.57029i −0.273124 + 0.544435i
\(310\) 0 0
\(311\) 3.47547 6.01968i 0.197076 0.341345i −0.750503 0.660867i \(-0.770189\pi\)
0.947579 + 0.319522i \(0.103522\pi\)
\(312\) 0 0
\(313\) −2.19252 3.79756i −0.123929 0.214651i 0.797385 0.603471i \(-0.206216\pi\)
−0.921314 + 0.388820i \(0.872883\pi\)
\(314\) 0 0
\(315\) 13.4653 1.58595i 0.758684 0.0893584i
\(316\) 0 0
\(317\) 15.6742 + 27.1485i 0.880350 + 1.52481i 0.850952 + 0.525244i \(0.176026\pi\)
0.0293983 + 0.999568i \(0.490641\pi\)
\(318\) 0 0
\(319\) 3.60855 6.25020i 0.202040 0.349944i
\(320\) 0 0
\(321\) 28.0444 1.64586i 1.56529 0.0918629i
\(322\) 0 0
\(323\) −24.1679 −1.34474
\(324\) 0 0
\(325\) −6.67562 −0.370297
\(326\) 0 0
\(327\) 3.60444 0.211536i 0.199326 0.0116979i
\(328\) 0 0
\(329\) −2.53597 + 4.39243i −0.139812 + 0.242162i
\(330\) 0 0
\(331\) −11.1515 19.3150i −0.612943 1.06165i −0.990742 0.135760i \(-0.956652\pi\)
0.377799 0.925888i \(-0.376681\pi\)
\(332\) 0 0
\(333\) −15.4371 + 1.81820i −0.845948 + 0.0996365i
\(334\) 0 0
\(335\) −17.1845 29.7644i −0.938888 1.62620i
\(336\) 0 0
\(337\) −10.4077 + 18.0266i −0.566943 + 0.981974i 0.429923 + 0.902866i \(0.358541\pi\)
−0.996866 + 0.0791086i \(0.974793\pi\)
\(338\) 0 0
\(339\) −2.26679 + 4.51855i −0.123115 + 0.245414i
\(340\) 0 0
\(341\) −6.74158 −0.365077
\(342\) 0 0
\(343\) 19.4444 1.04990
\(344\) 0 0
\(345\) −9.53206 14.4788i −0.513189 0.779514i
\(346\) 0 0
\(347\) 14.4912 25.0995i 0.777929 1.34741i −0.155204 0.987882i \(-0.549604\pi\)
0.933133 0.359530i \(-0.117063\pi\)
\(348\) 0 0
\(349\) 7.60709 + 13.1759i 0.407198 + 0.705288i 0.994575 0.104026i \(-0.0331725\pi\)
−0.587377 + 0.809314i \(0.699839\pi\)
\(350\) 0 0
\(351\) −10.0343 + 27.6833i −0.535590 + 1.47762i
\(352\) 0 0
\(353\) −6.78818 11.7575i −0.361298 0.625787i 0.626877 0.779119i \(-0.284333\pi\)
−0.988175 + 0.153332i \(0.951000\pi\)
\(354\) 0 0
\(355\) −13.8935 + 24.0643i −0.737393 + 1.27720i
\(356\) 0 0
\(357\) 9.17874 + 13.9421i 0.485790 + 0.737896i
\(358\) 0 0
\(359\) 31.6623 1.67107 0.835536 0.549436i \(-0.185158\pi\)
0.835536 + 0.549436i \(0.185158\pi\)
\(360\) 0 0
\(361\) 1.79179 0.0943046
\(362\) 0 0
\(363\) −7.43078 + 14.8122i −0.390015 + 0.777441i
\(364\) 0 0
\(365\) 15.4066 26.6850i 0.806419 1.39676i
\(366\) 0 0
\(367\) 4.90625 + 8.49788i 0.256104 + 0.443585i 0.965195 0.261532i \(-0.0842276\pi\)
−0.709091 + 0.705117i \(0.750894\pi\)
\(368\) 0 0
\(369\) 10.8529 25.2212i 0.564980 1.31297i
\(370\) 0 0
\(371\) 1.40435 + 2.43241i 0.0729105 + 0.126285i
\(372\) 0 0
\(373\) −4.98487 + 8.63404i −0.258107 + 0.447054i −0.965735 0.259531i \(-0.916432\pi\)
0.707628 + 0.706585i \(0.249765\pi\)
\(374\) 0 0
\(375\) −16.4258 + 0.963992i −0.848226 + 0.0497804i
\(376\) 0 0
\(377\) 34.1725 1.75997
\(378\) 0 0
\(379\) 30.2351 1.55307 0.776537 0.630072i \(-0.216974\pi\)
0.776537 + 0.630072i \(0.216974\pi\)
\(380\) 0 0
\(381\) −26.0431 + 1.52841i −1.33423 + 0.0783026i
\(382\) 0 0
\(383\) −9.86835 + 17.0925i −0.504249 + 0.873386i 0.495739 + 0.868472i \(0.334897\pi\)
−0.999988 + 0.00491371i \(0.998436\pi\)
\(384\) 0 0
\(385\) −2.70447 4.68429i −0.137833 0.238733i
\(386\) 0 0
\(387\) −14.3176 19.1964i −0.727805 0.975807i
\(388\) 0 0
\(389\) −3.60577 6.24537i −0.182820 0.316653i 0.760020 0.649900i \(-0.225189\pi\)
−0.942840 + 0.333247i \(0.891856\pi\)
\(390\) 0 0
\(391\) 10.6708 18.4824i 0.539647 0.934696i
\(392\) 0 0
\(393\) 2.94060 5.86168i 0.148333 0.295683i
\(394\) 0 0
\(395\) 21.6980 1.09174
\(396\) 0 0
\(397\) 20.8930 1.04859 0.524296 0.851536i \(-0.324329\pi\)
0.524296 + 0.851536i \(0.324329\pi\)
\(398\) 0 0
\(399\) −7.89651 11.9945i −0.395320 0.600476i
\(400\) 0 0
\(401\) −1.59174 + 2.75697i −0.0794877 + 0.137677i −0.903029 0.429580i \(-0.858662\pi\)
0.823541 + 0.567256i \(0.191995\pi\)
\(402\) 0 0
\(403\) −15.9605 27.6443i −0.795047 1.37706i
\(404\) 0 0
\(405\) 6.37784 21.4416i 0.316918 1.06544i
\(406\) 0 0
\(407\) 3.10051 + 5.37024i 0.153687 + 0.266193i
\(408\) 0 0
\(409\) 11.5046 19.9265i 0.568865 0.985302i −0.427814 0.903867i \(-0.640716\pi\)
0.996679 0.0814356i \(-0.0259505\pi\)
\(410\) 0 0
\(411\) −12.1804 18.5016i −0.600817 0.912617i
\(412\) 0 0
\(413\) 6.75403 0.332344
\(414\) 0 0
\(415\) −44.2065 −2.17001
\(416\) 0 0
\(417\) 6.93616 13.8263i 0.339665 0.677076i
\(418\) 0 0
\(419\) 1.36640 2.36667i 0.0667528 0.115619i −0.830717 0.556694i \(-0.812069\pi\)
0.897470 + 0.441075i \(0.145403\pi\)
\(420\) 0 0
\(421\) 2.98079 + 5.16288i 0.145275 + 0.251624i 0.929475 0.368884i \(-0.120260\pi\)
−0.784201 + 0.620507i \(0.786927\pi\)
\(422\) 0 0
\(423\) 5.00310 + 6.70792i 0.243259 + 0.326150i
\(424\) 0 0
\(425\) 3.12187 + 5.40724i 0.151433 + 0.262289i
\(426\) 0 0
\(427\) 7.30065 12.6451i 0.353303 0.611939i
\(428\) 0 0
\(429\) 11.7268 0.688220i 0.566177 0.0332276i
\(430\) 0 0
\(431\) 20.5125 0.988051 0.494026 0.869447i \(-0.335525\pi\)
0.494026 + 0.869447i \(0.335525\pi\)
\(432\) 0 0
\(433\) −41.5464 −1.99659 −0.998295 0.0583639i \(-0.981412\pi\)
−0.998295 + 0.0583639i \(0.981412\pi\)
\(434\) 0 0
\(435\) −25.9164 + 1.52097i −1.24260 + 0.0729250i
\(436\) 0 0
\(437\) −9.18017 + 15.9005i −0.439147 + 0.760625i
\(438\) 0 0
\(439\) 15.0834 + 26.1253i 0.719894 + 1.24689i 0.961042 + 0.276404i \(0.0891428\pi\)
−0.241148 + 0.970488i \(0.577524\pi\)
\(440\) 0 0
\(441\) 4.38016 10.1791i 0.208579 0.484720i
\(442\) 0 0
\(443\) 9.67554 + 16.7585i 0.459699 + 0.796222i 0.998945 0.0459267i \(-0.0146241\pi\)
−0.539246 + 0.842148i \(0.681291\pi\)
\(444\) 0 0
\(445\) −0.565834 + 0.980054i −0.0268231 + 0.0464590i
\(446\) 0 0
\(447\) −7.22556 + 14.4032i −0.341757 + 0.681246i
\(448\) 0 0
\(449\) 13.4220 0.633424 0.316712 0.948522i \(-0.397421\pi\)
0.316712 + 0.948522i \(0.397421\pi\)
\(450\) 0 0
\(451\) −10.9537 −0.515790
\(452\) 0 0
\(453\) −14.9249 22.6703i −0.701233 1.06515i
\(454\) 0 0
\(455\) 12.8055 22.1798i 0.600331 1.03980i
\(456\) 0 0
\(457\) −3.06037 5.30072i −0.143158 0.247957i 0.785526 0.618828i \(-0.212392\pi\)
−0.928684 + 0.370871i \(0.879059\pi\)
\(458\) 0 0
\(459\) 27.1159 4.81841i 1.26566 0.224904i
\(460\) 0 0
\(461\) −5.80084 10.0473i −0.270172 0.467952i 0.698734 0.715382i \(-0.253747\pi\)
−0.968906 + 0.247430i \(0.920414\pi\)
\(462\) 0 0
\(463\) 4.42830 7.67005i 0.205801 0.356457i −0.744587 0.667526i \(-0.767353\pi\)
0.950388 + 0.311068i \(0.100687\pi\)
\(464\) 0 0
\(465\) 13.3348 + 20.2551i 0.618387 + 0.939306i
\(466\) 0 0
\(467\) 7.20231 0.333283 0.166642 0.986018i \(-0.446708\pi\)
0.166642 + 0.986018i \(0.446708\pi\)
\(468\) 0 0
\(469\) 25.1422 1.16096
\(470\) 0 0
\(471\) 15.1524 30.2043i 0.698188 1.39174i
\(472\) 0 0
\(473\) −4.77684 + 8.27372i −0.219639 + 0.380426i
\(474\) 0 0
\(475\) −2.68576 4.65187i −0.123231 0.213443i
\(476\) 0 0
\(477\) 4.60230 0.542062i 0.210725 0.0248193i
\(478\) 0 0
\(479\) 12.2521 + 21.2213i 0.559815 + 0.969628i 0.997511 + 0.0705051i \(0.0224611\pi\)
−0.437696 + 0.899123i \(0.644206\pi\)
\(480\) 0 0
\(481\) −14.6807 + 25.4277i −0.669382 + 1.15940i
\(482\) 0 0
\(483\) 12.6593 0.742945i 0.576019 0.0338052i
\(484\) 0 0
\(485\) −5.05263 −0.229428
\(486\) 0 0
\(487\) −37.7200 −1.70926 −0.854629 0.519239i \(-0.826215\pi\)
−0.854629 + 0.519239i \(0.826215\pi\)
\(488\) 0 0
\(489\) −8.69531 + 0.510307i −0.393215 + 0.0230769i
\(490\) 0 0
\(491\) 0.203651 0.352734i 0.00919063 0.0159186i −0.861394 0.507938i \(-0.830408\pi\)
0.870584 + 0.492020i \(0.163741\pi\)
\(492\) 0 0
\(493\) −15.9808 27.6796i −0.719741 1.24663i
\(494\) 0 0
\(495\) −8.86300 + 1.04389i −0.398362 + 0.0469194i
\(496\) 0 0
\(497\) −10.1637 17.6040i −0.455903 0.789647i
\(498\) 0 0
\(499\) 3.73644 6.47171i 0.167266 0.289714i −0.770192 0.637813i \(-0.779839\pi\)
0.937458 + 0.348099i \(0.113173\pi\)
\(500\) 0 0
\(501\) −11.8839 + 23.6889i −0.530933 + 1.05834i
\(502\) 0 0
\(503\) −34.5169 −1.53903 −0.769517 0.638626i \(-0.779503\pi\)
−0.769517 + 0.638626i \(0.779503\pi\)
\(504\) 0 0
\(505\) 15.2169 0.677145
\(506\) 0 0
\(507\) 18.2036 + 27.6505i 0.808449 + 1.22800i
\(508\) 0 0
\(509\) −1.41136 + 2.44454i −0.0625572 + 0.108352i −0.895608 0.444845i \(-0.853259\pi\)
0.833051 + 0.553197i \(0.186592\pi\)
\(510\) 0 0
\(511\) 11.2705 + 19.5211i 0.498579 + 0.863564i
\(512\) 0 0
\(513\) −23.3280 + 4.14531i −1.02996 + 0.183020i
\(514\) 0 0
\(515\) −7.68252 13.3065i −0.338532 0.586355i
\(516\) 0 0
\(517\) 1.66920 2.89114i 0.0734114 0.127152i
\(518\) 0 0
\(519\) −10.0993 15.3404i −0.443310 0.673370i
\(520\) 0 0
\(521\) 9.11300 0.399248 0.199624 0.979873i \(-0.436028\pi\)
0.199624 + 0.979873i \(0.436028\pi\)
\(522\) 0 0
\(523\) −1.96313 −0.0858418 −0.0429209 0.999078i \(-0.513666\pi\)
−0.0429209 + 0.999078i \(0.513666\pi\)
\(524\) 0 0
\(525\) −1.66358 + 3.31611i −0.0726044 + 0.144727i
\(526\) 0 0
\(527\) −14.9279 + 25.8559i −0.650269 + 1.12630i
\(528\) 0 0
\(529\) 3.39339 + 5.87752i 0.147539 + 0.255544i
\(530\) 0 0
\(531\) 4.40466 10.2361i 0.191146 0.444207i
\(532\) 0 0
\(533\) −25.9325 44.9165i −1.12326 1.94555i
\(534\) 0 0
\(535\) −20.1570 + 34.9130i −0.871465 + 1.50942i
\(536\) 0 0
\(537\) −16.0340 + 0.940994i −0.691916 + 0.0406069i
\(538\) 0 0
\(539\) −4.42084 −0.190419
\(540\) 0 0
\(541\) −3.46053 −0.148780 −0.0743899 0.997229i \(-0.523701\pi\)
−0.0743899 + 0.997229i \(0.523701\pi\)
\(542\) 0 0
\(543\) −4.02832 + 0.236412i −0.172872 + 0.0101454i
\(544\) 0 0
\(545\) −2.59070 + 4.48723i −0.110974 + 0.192212i
\(546\) 0 0
\(547\) 4.80884 + 8.32915i 0.205611 + 0.356129i 0.950327 0.311252i \(-0.100748\pi\)
−0.744716 + 0.667381i \(0.767415\pi\)
\(548\) 0 0
\(549\) −14.4031 19.3110i −0.614711 0.824175i
\(550\) 0 0
\(551\) 13.7484 + 23.8129i 0.585702 + 1.01447i
\(552\) 0 0
\(553\) −7.93645 + 13.7463i −0.337492 + 0.584554i
\(554\) 0 0
\(555\) 10.0021 19.9378i 0.424565 0.846312i
\(556\) 0 0
\(557\) −9.47602 −0.401512 −0.200756 0.979641i \(-0.564340\pi\)
−0.200756 + 0.979641i \(0.564340\pi\)
\(558\) 0 0
\(559\) −45.2360 −1.91328
\(560\) 0 0
\(561\) −6.04154 9.17686i −0.255074 0.387447i
\(562\) 0 0
\(563\) −20.8982 + 36.1967i −0.880753 + 1.52551i −0.0302481 + 0.999542i \(0.509630\pi\)
−0.850505 + 0.525967i \(0.823704\pi\)
\(564\) 0 0
\(565\) −3.62725 6.28257i −0.152599 0.264310i
\(566\) 0 0
\(567\) 11.2511 + 11.8832i 0.472502 + 0.499049i
\(568\) 0 0
\(569\) 9.74041 + 16.8709i 0.408339 + 0.707265i 0.994704 0.102783i \(-0.0327747\pi\)
−0.586364 + 0.810047i \(0.699441\pi\)
\(570\) 0 0
\(571\) −9.27352 + 16.0622i −0.388085 + 0.672182i −0.992192 0.124721i \(-0.960197\pi\)
0.604107 + 0.796903i \(0.293530\pi\)
\(572\) 0 0
\(573\) 16.2713 + 24.7154i 0.679742 + 1.03250i
\(574\) 0 0
\(575\) 4.74336 0.197812
\(576\) 0 0
\(577\) 28.5458 1.18838 0.594188 0.804326i \(-0.297473\pi\)
0.594188 + 0.804326i \(0.297473\pi\)
\(578\) 0 0
\(579\) 18.8510 37.5770i 0.783422 1.56165i
\(580\) 0 0
\(581\) 16.1694 28.0062i 0.670820 1.16189i
\(582\) 0 0
\(583\) −0.924361 1.60104i −0.0382831 0.0663083i
\(584\) 0 0
\(585\) −25.2634 33.8720i −1.04451 1.40043i
\(586\) 0 0
\(587\) −1.49840 2.59531i −0.0618457 0.107120i 0.833445 0.552603i \(-0.186365\pi\)
−0.895290 + 0.445483i \(0.853032\pi\)
\(588\) 0 0
\(589\) 12.8425 22.2439i 0.529168 0.916545i
\(590\) 0 0
\(591\) 27.1415 1.59287i 1.11645 0.0655218i
\(592\) 0 0
\(593\) 24.7528 1.01648 0.508238 0.861216i \(-0.330297\pi\)
0.508238 + 0.861216i \(0.330297\pi\)
\(594\) 0 0
\(595\) −23.9541 −0.982022
\(596\) 0 0
\(597\) 25.0307 1.46899i 1.02444 0.0601219i
\(598\) 0 0
\(599\) −19.2808 + 33.3954i −0.787794 + 1.36450i 0.139522 + 0.990219i \(0.455443\pi\)
−0.927316 + 0.374280i \(0.877890\pi\)
\(600\) 0 0
\(601\) −15.4398 26.7426i −0.629804 1.09085i −0.987591 0.157050i \(-0.949802\pi\)
0.357786 0.933803i \(-0.383532\pi\)
\(602\) 0 0
\(603\) 16.3966 38.1043i 0.667720 1.55173i
\(604\) 0 0
\(605\) −11.8905 20.5949i −0.483417 0.837302i
\(606\) 0 0
\(607\) −14.1298 + 24.4736i −0.573512 + 0.993352i 0.422689 + 0.906275i \(0.361086\pi\)
−0.996202 + 0.0870777i \(0.972247\pi\)
\(608\) 0 0
\(609\) 8.51585 16.9752i 0.345079 0.687869i
\(610\) 0 0
\(611\) 15.8071 0.639487
\(612\) 0 0
\(613\) 28.6419 1.15684 0.578419 0.815740i \(-0.303670\pi\)
0.578419 + 0.815740i \(0.303670\pi\)
\(614\) 0 0
\(615\) 21.6664 + 32.9104i 0.873674 + 1.32708i
\(616\) 0 0
\(617\) 1.80372 3.12413i 0.0726150 0.125773i −0.827432 0.561566i \(-0.810199\pi\)
0.900047 + 0.435794i \(0.143532\pi\)
\(618\) 0 0
\(619\) −4.76132 8.24686i −0.191374 0.331469i 0.754332 0.656493i \(-0.227961\pi\)
−0.945706 + 0.325024i \(0.894628\pi\)
\(620\) 0 0
\(621\) 7.12985 19.6703i 0.286111 0.789344i
\(622\) 0 0
\(623\) −0.413930 0.716947i −0.0165837 0.0287239i
\(624\) 0 0
\(625\) 14.7512 25.5498i 0.590047 1.02199i
\(626\) 0 0
\(627\) 5.19757 + 7.89490i 0.207571 + 0.315292i
\(628\) 0 0
\(629\) 27.4619 1.09498
\(630\) 0 0
\(631\) 30.5885 1.21771 0.608855 0.793281i \(-0.291629\pi\)
0.608855 + 0.793281i \(0.291629\pi\)
\(632\) 0 0
\(633\) 4.98774 9.94238i 0.198245 0.395174i
\(634\) 0 0
\(635\) 18.7186 32.4215i 0.742824 1.28661i
\(636\) 0 0
\(637\) −10.4662 18.1280i −0.414686 0.718257i
\(638\) 0 0
\(639\) −33.3080 + 3.92304i −1.31764 + 0.155193i
\(640\) 0 0
\(641\) 4.09007 + 7.08420i 0.161548 + 0.279809i 0.935424 0.353528i \(-0.115018\pi\)
−0.773876 + 0.633337i \(0.781685\pi\)
\(642\) 0 0
\(643\) −13.0611 + 22.6225i −0.515079 + 0.892144i 0.484768 + 0.874643i \(0.338904\pi\)
−0.999847 + 0.0175005i \(0.994429\pi\)
\(644\) 0 0
\(645\) 34.3070 2.01339i 1.35084 0.0792773i
\(646\) 0 0
\(647\) 22.0170 0.865577 0.432789 0.901495i \(-0.357530\pi\)
0.432789 + 0.901495i \(0.357530\pi\)
\(648\) 0 0
\(649\) −4.44557 −0.174504
\(650\) 0 0
\(651\) −17.7097 + 1.03934i −0.694097 + 0.0407349i
\(652\) 0 0
\(653\) −1.14611 + 1.98512i −0.0448508 + 0.0776839i −0.887579 0.460655i \(-0.847615\pi\)
0.842729 + 0.538339i \(0.180948\pi\)
\(654\) 0 0
\(655\) 4.70544 + 8.15006i 0.183857 + 0.318449i
\(656\) 0 0
\(657\) 36.9353 4.35028i 1.44098 0.169720i
\(658\) 0 0
\(659\) −3.29926 5.71449i −0.128521 0.222605i 0.794583 0.607156i \(-0.207690\pi\)
−0.923104 + 0.384551i \(0.874356\pi\)
\(660\) 0 0
\(661\) −2.88305 + 4.99359i −0.112138 + 0.194228i −0.916632 0.399732i \(-0.869103\pi\)
0.804494 + 0.593960i \(0.202436\pi\)
\(662\) 0 0
\(663\) 23.3272 46.4997i 0.905955 1.80590i
\(664\) 0 0
\(665\) 20.6078 0.799137
\(666\) 0 0
\(667\) −24.2813 −0.940174
\(668\) 0 0
\(669\) 15.0612 + 22.8774i 0.582300 + 0.884491i
\(670\) 0 0
\(671\) −4.80537 + 8.32314i −0.185509 + 0.321311i
\(672\) 0 0
\(673\) −22.6226 39.1835i −0.872038 1.51041i −0.859885 0.510488i \(-0.829465\pi\)
−0.0121528 0.999926i \(-0.503868\pi\)
\(674\) 0 0
\(675\) 3.94082 + 4.68384i 0.151682 + 0.180281i
\(676\) 0 0
\(677\) −3.70089 6.41013i −0.142237 0.246361i 0.786102 0.618097i \(-0.212096\pi\)
−0.928339 + 0.371736i \(0.878763\pi\)
\(678\) 0 0
\(679\) 1.84810 3.20100i 0.0709235 0.122843i
\(680\) 0 0
\(681\) −5.73219 8.70698i −0.219658 0.333652i
\(682\) 0 0
\(683\) −9.88608 −0.378281 −0.189140 0.981950i \(-0.560570\pi\)
−0.189140 + 0.981950i \(0.560570\pi\)
\(684\) 0 0
\(685\) 31.7878 1.21455
\(686\) 0 0
\(687\) 21.4632 42.7840i 0.818873 1.63231i
\(688\) 0 0
\(689\) 4.37679 7.58082i 0.166742 0.288806i
\(690\) 0 0
\(691\) 4.43367 + 7.67934i 0.168665 + 0.292136i 0.937951 0.346769i \(-0.112721\pi\)
−0.769286 + 0.638905i \(0.779388\pi\)
\(692\) 0 0
\(693\) 2.58048 5.99681i 0.0980242 0.227800i
\(694\) 0 0
\(695\) 11.0990 + 19.2240i 0.421009 + 0.729209i
\(696\) 0 0
\(697\) −24.2548 + 42.0106i −0.918717 + 1.59126i
\(698\) 0 0
\(699\) 21.0703 1.23656i 0.796950 0.0467711i
\(700\) 0 0
\(701\) −38.9889 −1.47259 −0.736296 0.676660i \(-0.763427\pi\)
−0.736296 + 0.676660i \(0.763427\pi\)
\(702\) 0 0
\(703\) −23.6256 −0.891055
\(704\) 0 0
\(705\) −11.9881 + 0.703553i −0.451498 + 0.0264973i
\(706\) 0 0
\(707\) −5.56589 + 9.64040i −0.209327 + 0.362564i
\(708\) 0 0
\(709\) 5.12709 + 8.88039i 0.192552 + 0.333510i 0.946095 0.323888i \(-0.104990\pi\)
−0.753543 + 0.657398i \(0.771657\pi\)
\(710\) 0 0
\(711\) 15.6575 + 20.9928i 0.587201 + 0.787292i
\(712\) 0 0
\(713\) 11.3407 + 19.6427i 0.424712 + 0.735623i
\(714\) 0 0
\(715\) −8.42872 + 14.5990i −0.315216 + 0.545970i
\(716\) 0 0
\(717\) 12.1593 24.2378i 0.454096 0.905178i
\(718\) 0 0
\(719\) −16.8003 −0.626545 −0.313272 0.949663i \(-0.601425\pi\)
−0.313272 + 0.949663i \(0.601425\pi\)
\(720\) 0 0
\(721\) 11.2401 0.418604
\(722\) 0 0
\(723\) −17.8918 27.1769i −0.665402 1.01072i
\(724\) 0 0
\(725\) 3.55187 6.15203i 0.131913 0.228481i
\(726\) 0 0
\(727\) 9.98309 + 17.2912i 0.370252 + 0.641296i 0.989604 0.143818i \(-0.0459379\pi\)
−0.619352 + 0.785113i \(0.712605\pi\)
\(728\) 0 0
\(729\) 25.3471 9.30190i 0.938781 0.344515i
\(730\) 0 0
\(731\) 21.1547 + 36.6410i 0.782436 + 1.35522i
\(732\) 0 0
\(733\) 2.98307 5.16683i 0.110182 0.190841i −0.805661 0.592376i \(-0.798190\pi\)
0.915844 + 0.401535i \(0.131523\pi\)
\(734\) 0 0
\(735\) 8.74441 + 13.2824i 0.322542 + 0.489929i
\(736\) 0 0
\(737\) −16.5489 −0.609585
\(738\) 0 0
\(739\) −0.673830 −0.0247872 −0.0123936 0.999923i \(-0.503945\pi\)
−0.0123936 + 0.999923i \(0.503945\pi\)
\(740\) 0 0
\(741\) −20.0685 + 40.0039i −0.737237 + 1.46958i
\(742\) 0 0
\(743\) 15.4737 26.8013i 0.567676 0.983244i −0.429119 0.903248i \(-0.641176\pi\)
0.996795 0.0799963i \(-0.0254909\pi\)
\(744\) 0 0
\(745\) −11.5621 20.0261i −0.423602 0.733700i
\(746\) 0 0
\(747\) −31.8999 42.7699i −1.16716 1.56487i
\(748\) 0 0
\(749\) −14.7457 25.5402i −0.538794 0.933219i
\(750\) 0 0
\(751\) 0.0124745 0.0216064i 0.000455200 0.000788429i −0.865798 0.500394i \(-0.833188\pi\)
0.866253 + 0.499606i \(0.166522\pi\)
\(752\) 0 0
\(753\) 19.3110 1.13331i 0.703731 0.0413003i
\(754\) 0 0
\(755\) 38.9501 1.41754
\(756\) 0 0
\(757\) 2.61883 0.0951829 0.0475914 0.998867i \(-0.484845\pi\)
0.0475914 + 0.998867i \(0.484845\pi\)
\(758\) 0 0
\(759\) −8.33250 + 0.489014i −0.302451 + 0.0177501i
\(760\) 0 0
\(761\) 4.19437 7.26486i 0.152046 0.263351i −0.779934 0.625862i \(-0.784747\pi\)
0.931979 + 0.362511i \(0.118081\pi\)
\(762\) 0 0
\(763\) −1.89520 3.28258i −0.0686109 0.118837i
\(764\) 0 0
\(765\) −15.6217 + 36.3036i −0.564805 + 1.31256i
\(766\) 0 0
\(767\) −10.5247 18.2294i −0.380027 0.658225i
\(768\) 0 0
\(769\) −1.00513 + 1.74094i −0.0362460 + 0.0627800i −0.883579 0.468281i \(-0.844873\pi\)
0.847333 + 0.531061i \(0.178207\pi\)
\(770\) 0 0
\(771\) −4.96969 + 9.90640i −0.178979 + 0.356770i
\(772\) 0 0
\(773\) −10.2064 −0.367099 −0.183550 0.983010i \(-0.558759\pi\)
−0.183550 + 0.983010i \(0.558759\pi\)
\(774\) 0 0
\(775\) −6.63569 −0.238361
\(776\) 0 0
\(777\) 8.97275 + 13.6293i 0.321896 + 0.488947i
\(778\) 0 0
\(779\) 20.8666 36.1419i 0.747622 1.29492i
\(780\) 0 0
\(781\) 6.68983 + 11.5871i 0.239381 + 0.414620i
\(782\) 0 0
\(783\) −20.1731 23.9766i −0.720927 0.856854i
\(784\) 0 0
\(785\) 24.2464 + 41.9960i 0.865392 + 1.49890i
\(786\) 0 0
\(787\) −13.6213 + 23.5928i −0.485547 + 0.840991i −0.999862 0.0166097i \(-0.994713\pi\)
0.514315 + 0.857601i \(0.328046\pi\)
\(788\) 0 0
\(789\) −12.7935 19.4328i −0.455461 0.691827i
\(790\) 0 0
\(791\) 5.30694 0.188693
\(792\) 0 0
\(793\) −45.5062 −1.61597
\(794\) 0 0
\(795\) −2.98194 + 5.94409i −0.105759 + 0.210815i
\(796\) 0 0