Properties

Label 819.2.do.e.667.4
Level $819$
Weight $2$
Character 819.667
Analytic conductor $6.540$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.do (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.2346760387617129.1
Defining polynomial: \(x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 667.4
Root \(0.655911 + 1.25291i\) of defining polynomial
Character \(\chi\) \(=\) 819.667
Dual form 819.2.do.e.361.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.156598 - 0.0904119i) q^{2} +(-0.983651 + 1.70373i) q^{4} +(-2.32670 - 1.34332i) q^{5} +(-0.393717 + 2.61629i) q^{7} +0.717383i q^{8} +O(q^{10})\) \(q+(0.156598 - 0.0904119i) q^{2} +(-0.983651 + 1.70373i) q^{4} +(-2.32670 - 1.34332i) q^{5} +(-0.393717 + 2.61629i) q^{7} +0.717383i q^{8} -0.485809 q^{10} -2.69424i q^{11} +(1.92153 - 3.05086i) q^{13} +(0.174889 + 0.445303i) q^{14} +(-1.90244 - 3.29513i) q^{16} +(-2.38247 + 4.12655i) q^{17} -0.188424i q^{19} +(4.57732 - 2.64272i) q^{20} +(-0.243592 - 0.421913i) q^{22} +(-2.19964 - 3.80989i) q^{23} +(1.10902 + 1.92088i) q^{25} +(0.0250743 - 0.651487i) q^{26} +(-4.07019 - 3.24431i) q^{28} +(3.54280 - 6.13631i) q^{29} +(3.20369 - 1.84965i) q^{31} +(-1.83838 - 1.06139i) q^{32} +0.861613i q^{34} +(4.43058 - 5.55844i) q^{35} +(6.88848 - 3.97707i) q^{37} +(-0.0170358 - 0.0295069i) q^{38} +(0.963675 - 1.66913i) q^{40} +(-4.70215 - 2.71479i) q^{41} +(-4.00533 - 6.93743i) q^{43} +(4.59027 + 2.65020i) q^{44} +(-0.688919 - 0.397748i) q^{46} +(-1.60118 - 0.924445i) q^{47} +(-6.68997 - 2.06016i) q^{49} +(0.347341 + 0.200538i) q^{50} +(3.30773 + 6.27476i) q^{52} +(-3.53622 - 6.12491i) q^{53} +(-3.61923 + 6.26869i) q^{55} +(-1.87688 - 0.282446i) q^{56} -1.28125i q^{58} +(6.57216 + 3.79444i) q^{59} -0.411564 q^{61} +(0.334461 - 0.579304i) q^{62} +7.22592 q^{64} +(-8.56910 + 4.51719i) q^{65} -11.4010i q^{67} +(-4.68703 - 8.11818i) q^{68} +(0.191271 - 1.27102i) q^{70} +(-2.89675 + 1.67244i) q^{71} +(-12.3112 + 7.10790i) q^{73} +(0.719148 - 1.24560i) q^{74} +(0.321025 + 0.185344i) q^{76} +(7.04893 + 1.06077i) q^{77} +(-4.55529 + 7.89000i) q^{79} +10.2224i q^{80} -0.981797 q^{82} +16.5866i q^{83} +(11.0866 - 6.40083i) q^{85} +(-1.25445 - 0.724258i) q^{86} +1.93280 q^{88} +(5.10232 - 2.94582i) q^{89} +(7.22539 + 6.22846i) q^{91} +8.65473 q^{92} -0.334323 q^{94} +(-0.253115 + 0.438407i) q^{95} +(0.390659 - 0.225547i) q^{97} +(-1.23390 + 0.282236i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 4q^{4} - 3q^{5} + 3q^{7} + O(q^{10}) \) \( 12q + 4q^{4} - 3q^{5} + 3q^{7} - 24q^{10} - 2q^{13} - 4q^{14} - 8q^{16} - 17q^{17} + 3q^{20} - 15q^{22} - 3q^{23} - 5q^{25} + 9q^{26} + 27q^{28} + q^{29} - 18q^{31} - 18q^{32} - 18q^{35} + 15q^{37} - 19q^{38} - q^{40} + 6q^{41} + 11q^{43} - 33q^{44} - 30q^{46} - 15q^{47} + 9q^{49} - 18q^{50} + 47q^{52} + 8q^{53} - 15q^{55} - 27q^{59} - 10q^{61} - 41q^{62} + 2q^{64} + 3q^{65} + 11q^{68} - 3q^{70} - 30q^{71} - 42q^{73} + 33q^{74} - 45q^{76} + 19q^{77} - 35q^{79} - 10q^{82} - 21q^{85} - 57q^{86} + 28q^{88} - 48q^{89} - 16q^{91} + 66q^{92} - 2q^{94} - 2q^{95} - 3q^{97} + 36q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.156598 0.0904119i 0.110731 0.0639308i −0.443611 0.896219i \(-0.646303\pi\)
0.554343 + 0.832288i \(0.312970\pi\)
\(3\) 0 0
\(4\) −0.983651 + 1.70373i −0.491826 + 0.851867i
\(5\) −2.32670 1.34332i −1.04053 0.600751i −0.120548 0.992708i \(-0.538465\pi\)
−0.919984 + 0.391956i \(0.871799\pi\)
\(6\) 0 0
\(7\) −0.393717 + 2.61629i −0.148811 + 0.988866i
\(8\) 0.717383i 0.253633i
\(9\) 0 0
\(10\) −0.485809 −0.153626
\(11\) 2.69424i 0.812345i −0.913796 0.406172i \(-0.866863\pi\)
0.913796 0.406172i \(-0.133137\pi\)
\(12\) 0 0
\(13\) 1.92153 3.05086i 0.532937 0.846155i
\(14\) 0.174889 + 0.445303i 0.0467409 + 0.119012i
\(15\) 0 0
\(16\) −1.90244 3.29513i −0.475611 0.823782i
\(17\) −2.38247 + 4.12655i −0.577833 + 1.00084i 0.417894 + 0.908496i \(0.362768\pi\)
−0.995727 + 0.0923405i \(0.970565\pi\)
\(18\) 0 0
\(19\) 0.188424i 0.0432275i −0.999766 0.0216138i \(-0.993120\pi\)
0.999766 0.0216138i \(-0.00688041\pi\)
\(20\) 4.57732 2.64272i 1.02352 0.590930i
\(21\) 0 0
\(22\) −0.243592 0.421913i −0.0519339 0.0899521i
\(23\) −2.19964 3.80989i −0.458657 0.794418i 0.540233 0.841516i \(-0.318336\pi\)
−0.998890 + 0.0470977i \(0.985003\pi\)
\(24\) 0 0
\(25\) 1.10902 + 1.92088i 0.221804 + 0.384177i
\(26\) 0.0250743 0.651487i 0.00491747 0.127767i
\(27\) 0 0
\(28\) −4.07019 3.24431i −0.769193 0.613117i
\(29\) 3.54280 6.13631i 0.657882 1.13948i −0.323281 0.946303i \(-0.604786\pi\)
0.981163 0.193182i \(-0.0618807\pi\)
\(30\) 0 0
\(31\) 3.20369 1.84965i 0.575400 0.332207i −0.183903 0.982944i \(-0.558873\pi\)
0.759303 + 0.650737i \(0.225540\pi\)
\(32\) −1.83838 1.06139i −0.324983 0.187629i
\(33\) 0 0
\(34\) 0.861613i 0.147765i
\(35\) 4.43058 5.55844i 0.748905 0.939548i
\(36\) 0 0
\(37\) 6.88848 3.97707i 1.13246 0.653826i 0.187907 0.982187i \(-0.439830\pi\)
0.944552 + 0.328361i \(0.106496\pi\)
\(38\) −0.0170358 0.0295069i −0.00276357 0.00478665i
\(39\) 0 0
\(40\) 0.963675 1.66913i 0.152370 0.263913i
\(41\) −4.70215 2.71479i −0.734353 0.423979i 0.0856594 0.996324i \(-0.472700\pi\)
−0.820013 + 0.572345i \(0.806034\pi\)
\(42\) 0 0
\(43\) −4.00533 6.93743i −0.610807 1.05795i −0.991105 0.133084i \(-0.957512\pi\)
0.380298 0.924864i \(-0.375821\pi\)
\(44\) 4.59027 + 2.65020i 0.692010 + 0.399532i
\(45\) 0 0
\(46\) −0.688919 0.397748i −0.101576 0.0586447i
\(47\) −1.60118 0.924445i −0.233557 0.134844i 0.378655 0.925538i \(-0.376387\pi\)
−0.612212 + 0.790694i \(0.709720\pi\)
\(48\) 0 0
\(49\) −6.68997 2.06016i −0.955710 0.294308i
\(50\) 0.347341 + 0.200538i 0.0491215 + 0.0283603i
\(51\) 0 0
\(52\) 3.30773 + 6.27476i 0.458700 + 0.870152i
\(53\) −3.53622 6.12491i −0.485737 0.841321i 0.514128 0.857713i \(-0.328115\pi\)
−0.999866 + 0.0163917i \(0.994782\pi\)
\(54\) 0 0
\(55\) −3.61923 + 6.26869i −0.488017 + 0.845271i
\(56\) −1.87688 0.282446i −0.250809 0.0377434i
\(57\) 0 0
\(58\) 1.28125i 0.168236i
\(59\) 6.57216 + 3.79444i 0.855623 + 0.493994i 0.862544 0.505982i \(-0.168870\pi\)
−0.00692130 + 0.999976i \(0.502203\pi\)
\(60\) 0 0
\(61\) −0.411564 −0.0526954 −0.0263477 0.999653i \(-0.508388\pi\)
−0.0263477 + 0.999653i \(0.508388\pi\)
\(62\) 0.334461 0.579304i 0.0424766 0.0735716i
\(63\) 0 0
\(64\) 7.22592 0.903240
\(65\) −8.56910 + 4.51719i −1.06287 + 0.560289i
\(66\) 0 0
\(67\) 11.4010i 1.39286i −0.717626 0.696429i \(-0.754771\pi\)
0.717626 0.696429i \(-0.245229\pi\)
\(68\) −4.68703 8.11818i −0.568386 0.984474i
\(69\) 0 0
\(70\) 0.191271 1.27102i 0.0228613 0.151916i
\(71\) −2.89675 + 1.67244i −0.343781 + 0.198482i −0.661943 0.749554i \(-0.730268\pi\)
0.318162 + 0.948037i \(0.396935\pi\)
\(72\) 0 0
\(73\) −12.3112 + 7.10790i −1.44092 + 0.831917i −0.997911 0.0645994i \(-0.979423\pi\)
−0.443011 + 0.896516i \(0.646090\pi\)
\(74\) 0.719148 1.24560i 0.0835993 0.144798i
\(75\) 0 0
\(76\) 0.321025 + 0.185344i 0.0368241 + 0.0212604i
\(77\) 7.04893 + 1.06077i 0.803300 + 0.120886i
\(78\) 0 0
\(79\) −4.55529 + 7.89000i −0.512511 + 0.887695i 0.487384 + 0.873188i \(0.337951\pi\)
−0.999895 + 0.0145069i \(0.995382\pi\)
\(80\) 10.2224i 1.14290i
\(81\) 0 0
\(82\) −0.981797 −0.108421
\(83\) 16.5866i 1.82061i 0.413934 + 0.910307i \(0.364155\pi\)
−0.413934 + 0.910307i \(0.635845\pi\)
\(84\) 0 0
\(85\) 11.0866 6.40083i 1.20251 0.694268i
\(86\) −1.25445 0.724258i −0.135271 0.0780988i
\(87\) 0 0
\(88\) 1.93280 0.206037
\(89\) 5.10232 2.94582i 0.540844 0.312257i −0.204577 0.978851i \(-0.565582\pi\)
0.745421 + 0.666594i \(0.232248\pi\)
\(90\) 0 0
\(91\) 7.22539 + 6.22846i 0.757427 + 0.652920i
\(92\) 8.65473 0.902318
\(93\) 0 0
\(94\) −0.334323 −0.0344828
\(95\) −0.253115 + 0.438407i −0.0259690 + 0.0449796i
\(96\) 0 0
\(97\) 0.390659 0.225547i 0.0396654 0.0229008i −0.480036 0.877249i \(-0.659376\pi\)
0.519702 + 0.854348i \(0.326043\pi\)
\(98\) −1.23390 + 0.282236i −0.124643 + 0.0285102i
\(99\) 0 0
\(100\) −4.36356 −0.436356
\(101\) −7.65680 −0.761880 −0.380940 0.924600i \(-0.624400\pi\)
−0.380940 + 0.924600i \(0.624400\pi\)
\(102\) 0 0
\(103\) 2.57870 4.46644i 0.254087 0.440091i −0.710560 0.703636i \(-0.751558\pi\)
0.964647 + 0.263545i \(0.0848918\pi\)
\(104\) 2.18863 + 1.37847i 0.214613 + 0.135170i
\(105\) 0 0
\(106\) −1.10753 0.639433i −0.107573 0.0621072i
\(107\) 4.01644 + 6.95669i 0.388284 + 0.672528i 0.992219 0.124506i \(-0.0397345\pi\)
−0.603935 + 0.797034i \(0.706401\pi\)
\(108\) 0 0
\(109\) −1.15490 + 0.666781i −0.110619 + 0.0638660i −0.554289 0.832324i \(-0.687010\pi\)
0.443670 + 0.896190i \(0.353676\pi\)
\(110\) 1.30889i 0.124797i
\(111\) 0 0
\(112\) 9.37004 3.68000i 0.885386 0.347727i
\(113\) −9.96917 17.2671i −0.937821 1.62435i −0.769525 0.638617i \(-0.779507\pi\)
−0.168296 0.985736i \(-0.553827\pi\)
\(114\) 0 0
\(115\) 11.8193i 1.10216i
\(116\) 6.96976 + 12.0720i 0.647126 + 1.12086i
\(117\) 0 0
\(118\) 1.37225 0.126326
\(119\) −9.85825 7.85792i −0.903704 0.720335i
\(120\) 0 0
\(121\) 3.74106 0.340096
\(122\) −0.0644501 + 0.0372103i −0.00583503 + 0.00336886i
\(123\) 0 0
\(124\) 7.27765i 0.653553i
\(125\) 7.47412i 0.668505i
\(126\) 0 0
\(127\) −3.98361 + 6.89981i −0.353488 + 0.612259i −0.986858 0.161590i \(-0.948338\pi\)
0.633370 + 0.773849i \(0.281671\pi\)
\(128\) 4.80833 2.77609i 0.425000 0.245374i
\(129\) 0 0
\(130\) −0.933496 + 1.48213i −0.0818730 + 0.129992i
\(131\) 5.00897 8.67579i 0.437636 0.758007i −0.559871 0.828580i \(-0.689149\pi\)
0.997507 + 0.0705727i \(0.0224827\pi\)
\(132\) 0 0
\(133\) 0.492974 + 0.0741860i 0.0427462 + 0.00643274i
\(134\) −1.03079 1.78538i −0.0890465 0.154233i
\(135\) 0 0
\(136\) −2.96032 1.70914i −0.253845 0.146558i
\(137\) −4.38811 2.53348i −0.374902 0.216450i 0.300696 0.953720i \(-0.402781\pi\)
−0.675598 + 0.737270i \(0.736114\pi\)
\(138\) 0 0
\(139\) −3.86289 6.69073i −0.327646 0.567500i 0.654398 0.756150i \(-0.272922\pi\)
−0.982044 + 0.188650i \(0.939589\pi\)
\(140\) 5.11195 + 13.0161i 0.432039 + 1.10006i
\(141\) 0 0
\(142\) −0.302417 + 0.523802i −0.0253783 + 0.0439565i
\(143\) −8.21974 5.17707i −0.687370 0.432928i
\(144\) 0 0
\(145\) −16.4861 + 9.51824i −1.36909 + 0.790447i
\(146\) −1.28528 + 2.22617i −0.106370 + 0.184239i
\(147\) 0 0
\(148\) 15.6482i 1.28627i
\(149\) 14.3185i 1.17301i 0.809944 + 0.586507i \(0.199498\pi\)
−0.809944 + 0.586507i \(0.800502\pi\)
\(150\) 0 0
\(151\) −5.60534 + 3.23624i −0.456156 + 0.263362i −0.710427 0.703771i \(-0.751498\pi\)
0.254271 + 0.967133i \(0.418165\pi\)
\(152\) 0.135172 0.0109639
\(153\) 0 0
\(154\) 1.19975 0.471192i 0.0966789 0.0379698i
\(155\) −9.93871 −0.798296
\(156\) 0 0
\(157\) −7.95937 13.7860i −0.635227 1.10025i −0.986467 0.163960i \(-0.947573\pi\)
0.351240 0.936285i \(-0.385760\pi\)
\(158\) 1.64741i 0.131061i
\(159\) 0 0
\(160\) 2.85157 + 4.93907i 0.225437 + 0.390468i
\(161\) 10.8338 4.25489i 0.853826 0.335332i
\(162\) 0 0
\(163\) 4.78162i 0.374525i 0.982310 + 0.187263i \(0.0599616\pi\)
−0.982310 + 0.187263i \(0.940038\pi\)
\(164\) 9.25056 5.34081i 0.722348 0.417048i
\(165\) 0 0
\(166\) 1.49962 + 2.59743i 0.116393 + 0.201599i
\(167\) 2.34729 + 1.35521i 0.181639 + 0.104869i 0.588062 0.808816i \(-0.299891\pi\)
−0.406424 + 0.913685i \(0.633224\pi\)
\(168\) 0 0
\(169\) −5.61544 11.7246i −0.431957 0.901894i
\(170\) 1.15742 2.00472i 0.0887703 0.153755i
\(171\) 0 0
\(172\) 15.7594 1.20164
\(173\) −0.899816 −0.0684118 −0.0342059 0.999415i \(-0.510890\pi\)
−0.0342059 + 0.999415i \(0.510890\pi\)
\(174\) 0 0
\(175\) −5.46223 + 2.14524i −0.412906 + 0.162165i
\(176\) −8.87787 + 5.12564i −0.669195 + 0.386360i
\(177\) 0 0
\(178\) 0.532675 0.922620i 0.0399257 0.0691533i
\(179\) −11.0558 −0.826351 −0.413175 0.910651i \(-0.635580\pi\)
−0.413175 + 0.910651i \(0.635580\pi\)
\(180\) 0 0
\(181\) −3.52898 −0.262307 −0.131153 0.991362i \(-0.541868\pi\)
−0.131153 + 0.991362i \(0.541868\pi\)
\(182\) 1.69461 + 0.322103i 0.125613 + 0.0238759i
\(183\) 0 0
\(184\) 2.73315 1.57799i 0.201491 0.116331i
\(185\) −21.3699 −1.57115
\(186\) 0 0
\(187\) 11.1179 + 6.41894i 0.813024 + 0.469400i
\(188\) 3.15002 1.81866i 0.229738 0.132640i
\(189\) 0 0
\(190\) 0.0915382i 0.00664088i
\(191\) 20.4004 1.47612 0.738059 0.674736i \(-0.235742\pi\)
0.738059 + 0.674736i \(0.235742\pi\)
\(192\) 0 0
\(193\) 17.2646i 1.24273i −0.783521 0.621365i \(-0.786578\pi\)
0.783521 0.621365i \(-0.213422\pi\)
\(194\) 0.0407842 0.0706403i 0.00292814 0.00507168i
\(195\) 0 0
\(196\) 10.0906 9.37146i 0.720755 0.669390i
\(197\) 4.29264 + 2.47836i 0.305838 + 0.176576i 0.645063 0.764130i \(-0.276831\pi\)
−0.339224 + 0.940705i \(0.610165\pi\)
\(198\) 0 0
\(199\) 3.59097 6.21975i 0.254557 0.440906i −0.710218 0.703982i \(-0.751404\pi\)
0.964775 + 0.263076i \(0.0847369\pi\)
\(200\) −1.37801 + 0.795593i −0.0974399 + 0.0562569i
\(201\) 0 0
\(202\) −1.19904 + 0.692265i −0.0843641 + 0.0487076i
\(203\) 14.6595 + 11.6850i 1.02890 + 0.820125i
\(204\) 0 0
\(205\) 7.29367 + 12.6330i 0.509412 + 0.882327i
\(206\) 0.932580i 0.0649759i
\(207\) 0 0
\(208\) −13.7086 0.527611i −0.950518 0.0365833i
\(209\) −0.507661 −0.0351157
\(210\) 0 0
\(211\) 8.79636 15.2357i 0.605566 1.04887i −0.386395 0.922333i \(-0.626280\pi\)
0.991962 0.126539i \(-0.0403868\pi\)
\(212\) 13.9136 0.955592
\(213\) 0 0
\(214\) 1.25793 + 0.726269i 0.0859906 + 0.0496467i
\(215\) 21.5218i 1.46777i
\(216\) 0 0
\(217\) 3.57788 + 9.11004i 0.242883 + 0.618430i
\(218\) −0.120570 + 0.208833i −0.00816602 + 0.0141440i
\(219\) 0 0
\(220\) −7.12013 12.3324i −0.480039 0.831452i
\(221\) 8.01153 + 15.1979i 0.538914 + 1.02232i
\(222\) 0 0
\(223\) 12.2157 + 7.05271i 0.818020 + 0.472284i 0.849733 0.527213i \(-0.176763\pi\)
−0.0317129 + 0.999497i \(0.510096\pi\)
\(224\) 3.50071 4.39185i 0.233901 0.293443i
\(225\) 0 0
\(226\) −3.12230 1.80266i −0.207693 0.119911i
\(227\) −2.48443 1.43439i −0.164897 0.0952035i 0.415280 0.909694i \(-0.363684\pi\)
−0.580178 + 0.814490i \(0.697017\pi\)
\(228\) 0 0
\(229\) −7.59860 4.38706i −0.502130 0.289905i 0.227463 0.973787i \(-0.426957\pi\)
−0.729593 + 0.683882i \(0.760290\pi\)
\(230\) 1.06861 + 1.85088i 0.0704618 + 0.122043i
\(231\) 0 0
\(232\) 4.40208 + 2.54154i 0.289011 + 0.166861i
\(233\) −2.55371 + 4.42316i −0.167299 + 0.289771i −0.937469 0.348068i \(-0.886838\pi\)
0.770170 + 0.637839i \(0.220171\pi\)
\(234\) 0 0
\(235\) 2.48365 + 4.30181i 0.162016 + 0.280619i
\(236\) −12.9294 + 7.46481i −0.841634 + 0.485918i
\(237\) 0 0
\(238\) −2.25423 0.339232i −0.146120 0.0219891i
\(239\) 2.49797i 0.161580i 0.996731 + 0.0807901i \(0.0257443\pi\)
−0.996731 + 0.0807901i \(0.974256\pi\)
\(240\) 0 0
\(241\) 6.91532 + 3.99256i 0.445455 + 0.257183i 0.705909 0.708303i \(-0.250539\pi\)
−0.260454 + 0.965486i \(0.583872\pi\)
\(242\) 0.585842 0.338236i 0.0376593 0.0217426i
\(243\) 0 0
\(244\) 0.404835 0.701195i 0.0259169 0.0448894i
\(245\) 12.7981 + 13.7802i 0.817641 + 0.880382i
\(246\) 0 0
\(247\) −0.574856 0.362063i −0.0365772 0.0230375i
\(248\) 1.32691 + 2.29827i 0.0842588 + 0.145941i
\(249\) 0 0
\(250\) 0.675749 + 1.17043i 0.0427381 + 0.0740246i
\(251\) −12.6285 21.8732i −0.797105 1.38063i −0.921494 0.388393i \(-0.873030\pi\)
0.124389 0.992234i \(-0.460303\pi\)
\(252\) 0 0
\(253\) −10.2648 + 5.92637i −0.645341 + 0.372588i
\(254\) 1.44066i 0.0903952i
\(255\) 0 0
\(256\) −6.72394 + 11.6462i −0.420246 + 0.727888i
\(257\) 1.68682 + 2.92165i 0.105221 + 0.182248i 0.913828 0.406101i \(-0.133112\pi\)
−0.808608 + 0.588348i \(0.799778\pi\)
\(258\) 0 0
\(259\) 7.69305 + 19.5881i 0.478023 + 1.21715i
\(260\) 0.732915 19.0428i 0.0454535 1.18099i
\(261\) 0 0
\(262\) 1.81148i 0.111914i
\(263\) 0.158935 0.00980037 0.00490019 0.999988i \(-0.498440\pi\)
0.00490019 + 0.999988i \(0.498440\pi\)
\(264\) 0 0
\(265\) 19.0011i 1.16723i
\(266\) 0.0839059 0.0329533i 0.00514460 0.00202050i
\(267\) 0 0
\(268\) 19.4243 + 11.2146i 1.18653 + 0.685043i
\(269\) −11.6633 + 20.2014i −0.711124 + 1.23170i 0.253311 + 0.967385i \(0.418480\pi\)
−0.964435 + 0.264318i \(0.914853\pi\)
\(270\) 0 0
\(271\) 10.2373 5.91049i 0.621870 0.359037i −0.155727 0.987800i \(-0.549772\pi\)
0.777597 + 0.628763i \(0.216439\pi\)
\(272\) 18.1300 1.09929
\(273\) 0 0
\(274\) −0.916226 −0.0553513
\(275\) 5.17532 2.98797i 0.312084 0.180182i
\(276\) 0 0
\(277\) −13.6827 + 23.6991i −0.822111 + 1.42394i 0.0819961 + 0.996633i \(0.473870\pi\)
−0.904107 + 0.427306i \(0.859463\pi\)
\(278\) −1.20984 0.698503i −0.0725615 0.0418934i
\(279\) 0 0
\(280\) 3.98753 + 3.17842i 0.238300 + 0.189947i
\(281\) 28.5383i 1.70245i −0.524801 0.851225i \(-0.675860\pi\)
0.524801 0.851225i \(-0.324140\pi\)
\(282\) 0 0
\(283\) −17.9721 −1.06833 −0.534165 0.845380i \(-0.679374\pi\)
−0.534165 + 0.845380i \(0.679374\pi\)
\(284\) 6.58040i 0.390475i
\(285\) 0 0
\(286\) −1.75526 0.0675561i −0.103791 0.00399468i
\(287\) 8.95400 11.2334i 0.528538 0.663084i
\(288\) 0 0
\(289\) −2.85229 4.94032i −0.167782 0.290607i
\(290\) −1.72112 + 2.98107i −0.101068 + 0.175055i
\(291\) 0 0
\(292\) 27.9668i 1.63663i
\(293\) −12.8943 + 7.44453i −0.753293 + 0.434914i −0.826882 0.562375i \(-0.809888\pi\)
0.0735896 + 0.997289i \(0.476554\pi\)
\(294\) 0 0
\(295\) −10.1943 17.6570i −0.593535 1.02803i
\(296\) 2.85308 + 4.94168i 0.165832 + 0.287229i
\(297\) 0 0
\(298\) 1.29456 + 2.24224i 0.0749918 + 0.129890i
\(299\) −15.8501 0.610035i −0.916636 0.0352792i
\(300\) 0 0
\(301\) 19.7273 7.74772i 1.13706 0.446571i
\(302\) −0.585190 + 1.01358i −0.0336739 + 0.0583249i
\(303\) 0 0
\(304\) −0.620883 + 0.358467i −0.0356101 + 0.0205595i
\(305\) 0.957586 + 0.552862i 0.0548312 + 0.0316568i
\(306\) 0 0
\(307\) 23.5161i 1.34214i −0.741396 0.671068i \(-0.765836\pi\)
0.741396 0.671068i \(-0.234164\pi\)
\(308\) −8.74096 + 10.9661i −0.498062 + 0.624850i
\(309\) 0 0
\(310\) −1.55638 + 0.898577i −0.0883965 + 0.0510358i
\(311\) −0.815450 1.41240i −0.0462399 0.0800899i 0.841979 0.539510i \(-0.181391\pi\)
−0.888219 + 0.459420i \(0.848057\pi\)
\(312\) 0 0
\(313\) 0.348367 0.603389i 0.0196909 0.0341056i −0.856012 0.516956i \(-0.827065\pi\)
0.875703 + 0.482850i \(0.160398\pi\)
\(314\) −2.49284 1.43924i −0.140679 0.0812212i
\(315\) 0 0
\(316\) −8.96164 15.5220i −0.504132 0.873182i
\(317\) 18.5579 + 10.7144i 1.04231 + 0.601780i 0.920488 0.390771i \(-0.127792\pi\)
0.121826 + 0.992551i \(0.461125\pi\)
\(318\) 0 0
\(319\) −16.5327 9.54517i −0.925654 0.534427i
\(320\) −16.8126 9.70673i −0.939850 0.542623i
\(321\) 0 0
\(322\) 1.31186 1.64581i 0.0731073 0.0917177i
\(323\) 0.777544 + 0.448915i 0.0432637 + 0.0249783i
\(324\) 0 0
\(325\) 7.99136 + 0.307569i 0.443281 + 0.0170609i
\(326\) 0.432315 + 0.748792i 0.0239437 + 0.0414717i
\(327\) 0 0
\(328\) 1.94754 3.37324i 0.107535 0.186256i
\(329\) 3.04903 3.82520i 0.168099 0.210890i
\(330\) 0 0
\(331\) 1.52046i 0.0835722i 0.999127 + 0.0417861i \(0.0133048\pi\)
−0.999127 + 0.0417861i \(0.986695\pi\)
\(332\) −28.2591 16.3154i −1.55092 0.895425i
\(333\) 0 0
\(334\) 0.490108 0.0268175
\(335\) −15.3152 + 26.5268i −0.836761 + 1.44931i
\(336\) 0 0
\(337\) −32.2304 −1.75570 −0.877850 0.478936i \(-0.841023\pi\)
−0.877850 + 0.478936i \(0.841023\pi\)
\(338\) −1.93941 1.32835i −0.105490 0.0722527i
\(339\) 0 0
\(340\) 25.1848i 1.36584i
\(341\) −4.98341 8.63153i −0.269867 0.467423i
\(342\) 0 0
\(343\) 8.02394 16.6918i 0.433252 0.901273i
\(344\) 4.97679 2.87335i 0.268331 0.154921i
\(345\) 0 0
\(346\) −0.140909 + 0.0813541i −0.00757534 + 0.00437362i
\(347\) 4.09215 7.08782i 0.219678 0.380494i −0.735031 0.678033i \(-0.762833\pi\)
0.954710 + 0.297539i \(0.0961659\pi\)
\(348\) 0 0
\(349\) −18.9220 10.9246i −1.01287 0.584782i −0.100841 0.994903i \(-0.532153\pi\)
−0.912031 + 0.410120i \(0.865487\pi\)
\(350\) −0.661419 + 0.829791i −0.0353543 + 0.0443542i
\(351\) 0 0
\(352\) −2.85964 + 4.95304i −0.152419 + 0.263998i
\(353\) 0.567179i 0.0301879i 0.999886 + 0.0150940i \(0.00480474\pi\)
−0.999886 + 0.0150940i \(0.995195\pi\)
\(354\) 0 0
\(355\) 8.98650 0.476954
\(356\) 11.5907i 0.614303i
\(357\) 0 0
\(358\) −1.73132 + 0.999577i −0.0915030 + 0.0528293i
\(359\) −28.0630 16.2022i −1.48111 0.855118i −0.481336 0.876536i \(-0.659848\pi\)
−0.999771 + 0.0214184i \(0.993182\pi\)
\(360\) 0 0
\(361\) 18.9645 0.998131
\(362\) −0.552631 + 0.319061i −0.0290456 + 0.0167695i
\(363\) 0 0
\(364\) −17.7189 + 6.18351i −0.928723 + 0.324104i
\(365\) 38.1928 1.99910
\(366\) 0 0
\(367\) −7.86888 −0.410752 −0.205376 0.978683i \(-0.565842\pi\)
−0.205376 + 0.978683i \(0.565842\pi\)
\(368\) −8.36939 + 14.4962i −0.436285 + 0.755667i
\(369\) 0 0
\(370\) −3.34648 + 1.93209i −0.173975 + 0.100445i
\(371\) 17.4168 6.84030i 0.904237 0.355131i
\(372\) 0 0
\(373\) −2.09163 −0.108300 −0.0541502 0.998533i \(-0.517245\pi\)
−0.0541502 + 0.998533i \(0.517245\pi\)
\(374\) 2.32139 0.120036
\(375\) 0 0
\(376\) 0.663180 1.14866i 0.0342009 0.0592377i
\(377\) −11.9134 22.5997i −0.613571 1.16394i
\(378\) 0 0
\(379\) 12.3983 + 7.15817i 0.636859 + 0.367691i 0.783404 0.621513i \(-0.213482\pi\)
−0.146545 + 0.989204i \(0.546815\pi\)
\(380\) −0.497953 0.862480i −0.0255444 0.0442443i
\(381\) 0 0
\(382\) 3.19466 1.84444i 0.163453 0.0943695i
\(383\) 25.1873i 1.28701i 0.765441 + 0.643507i \(0.222521\pi\)
−0.765441 + 0.643507i \(0.777479\pi\)
\(384\) 0 0
\(385\) −14.9758 11.9371i −0.763237 0.608369i
\(386\) −1.56092 2.70359i −0.0794488 0.137609i
\(387\) 0 0
\(388\) 0.887438i 0.0450528i
\(389\) −14.0512 24.3373i −0.712422 1.23395i −0.963946 0.266099i \(-0.914265\pi\)
0.251524 0.967851i \(-0.419068\pi\)
\(390\) 0 0
\(391\) 20.9623 1.06011
\(392\) 1.47792 4.79927i 0.0746463 0.242400i
\(393\) 0 0
\(394\) 0.896292 0.0451546
\(395\) 21.1976 12.2384i 1.06657 0.615783i
\(396\) 0 0
\(397\) 21.7765i 1.09293i 0.837482 + 0.546465i \(0.184027\pi\)
−0.837482 + 0.546465i \(0.815973\pi\)
\(398\) 1.29867i 0.0650963i
\(399\) 0 0
\(400\) 4.21970 7.30874i 0.210985 0.365437i
\(401\) 17.7786 10.2645i 0.887821 0.512584i 0.0145918 0.999894i \(-0.495355\pi\)
0.873229 + 0.487310i \(0.162022\pi\)
\(402\) 0 0
\(403\) 0.512971 13.3282i 0.0255529 0.663923i
\(404\) 7.53162 13.0451i 0.374712 0.649020i
\(405\) 0 0
\(406\) 3.35211 + 0.504448i 0.166363 + 0.0250354i
\(407\) −10.7152 18.5592i −0.531132 0.919947i
\(408\) 0 0
\(409\) 5.42879 + 3.13431i 0.268436 + 0.154982i 0.628177 0.778071i \(-0.283801\pi\)
−0.359741 + 0.933052i \(0.617135\pi\)
\(410\) 2.28435 + 1.31887i 0.112816 + 0.0651343i
\(411\) 0 0
\(412\) 5.07308 + 8.78683i 0.249933 + 0.432896i
\(413\) −12.5149 + 15.7008i −0.615820 + 0.772584i
\(414\) 0 0
\(415\) 22.2811 38.5920i 1.09374 1.89441i
\(416\) −6.77065 + 3.56914i −0.331958 + 0.174991i
\(417\) 0 0
\(418\) −0.0794987 + 0.0458986i −0.00388841 + 0.00224497i
\(419\) 17.0817 29.5864i 0.834497 1.44539i −0.0599424 0.998202i \(-0.519092\pi\)
0.894439 0.447189i \(-0.147575\pi\)
\(420\) 0 0
\(421\) 11.5233i 0.561613i −0.959764 0.280806i \(-0.909398\pi\)
0.959764 0.280806i \(-0.0906019\pi\)
\(422\) 3.18118i 0.154858i
\(423\) 0 0
\(424\) 4.39391 2.53682i 0.213387 0.123199i
\(425\) −10.5688 −0.512664
\(426\) 0 0
\(427\) 0.162040 1.07677i 0.00784165 0.0521086i
\(428\) −15.8031 −0.763873
\(429\) 0 0
\(430\) 1.94582 + 3.37026i 0.0938359 + 0.162529i
\(431\) 8.77001i 0.422436i 0.977439 + 0.211218i \(0.0677431\pi\)
−0.977439 + 0.211218i \(0.932257\pi\)
\(432\) 0 0
\(433\) 11.0535 + 19.1452i 0.531196 + 0.920058i 0.999337 + 0.0364046i \(0.0115905\pi\)
−0.468141 + 0.883654i \(0.655076\pi\)
\(434\) 1.38394 + 1.10313i 0.0664315 + 0.0529519i
\(435\) 0 0
\(436\) 2.62352i 0.125644i
\(437\) −0.717877 + 0.414467i −0.0343407 + 0.0198266i
\(438\) 0 0
\(439\) −5.18547 8.98150i −0.247489 0.428664i 0.715339 0.698777i \(-0.246272\pi\)
−0.962828 + 0.270114i \(0.912939\pi\)
\(440\) −4.49705 2.59637i −0.214389 0.123777i
\(441\) 0 0
\(442\) 2.62866 + 1.65562i 0.125032 + 0.0787496i
\(443\) 17.9068 31.0156i 0.850780 1.47359i −0.0297257 0.999558i \(-0.509463\pi\)
0.880506 0.474036i \(-0.157203\pi\)
\(444\) 0 0
\(445\) −15.8287 −0.750354
\(446\) 2.55059 0.120774
\(447\) 0 0
\(448\) −2.84497 + 18.9051i −0.134412 + 0.893183i
\(449\) 19.7023 11.3751i 0.929809 0.536825i 0.0430575 0.999073i \(-0.486290\pi\)
0.886751 + 0.462247i \(0.152957\pi\)
\(450\) 0 0
\(451\) −7.31430 + 12.6687i −0.344417 + 0.596548i
\(452\) 39.2248 1.84498
\(453\) 0 0
\(454\) −0.518742 −0.0243458
\(455\) −8.44449 24.1978i −0.395884 1.13441i
\(456\) 0 0
\(457\) −27.1215 + 15.6586i −1.26869 + 0.732478i −0.974740 0.223344i \(-0.928303\pi\)
−0.293949 + 0.955821i \(0.594969\pi\)
\(458\) −1.58657 −0.0741354
\(459\) 0 0
\(460\) −20.1370 11.6261i −0.938891 0.542069i
\(461\) 7.28113 4.20376i 0.339116 0.195789i −0.320765 0.947159i \(-0.603940\pi\)
0.659881 + 0.751370i \(0.270607\pi\)
\(462\) 0 0
\(463\) 10.0392i 0.466563i 0.972409 + 0.233281i \(0.0749463\pi\)
−0.972409 + 0.233281i \(0.925054\pi\)
\(464\) −26.9599 −1.25158
\(465\) 0 0
\(466\) 0.923545i 0.0427824i
\(467\) 13.1756 22.8209i 0.609696 1.05602i −0.381594 0.924330i \(-0.624625\pi\)
0.991290 0.131695i \(-0.0420418\pi\)
\(468\) 0 0
\(469\) 29.8284 + 4.48878i 1.37735 + 0.207273i
\(470\) 0.777869 + 0.449103i 0.0358804 + 0.0207156i
\(471\) 0 0
\(472\) −2.72206 + 4.71475i −0.125293 + 0.217014i
\(473\) −18.6911 + 10.7913i −0.859418 + 0.496185i
\(474\) 0 0
\(475\) 0.361941 0.208967i 0.0166070 0.00958806i
\(476\) 23.0849 9.06638i 1.05809 0.415557i
\(477\) 0 0
\(478\) 0.225846 + 0.391177i 0.0103300 + 0.0178920i
\(479\) 8.58414i 0.392220i 0.980582 + 0.196110i \(0.0628309\pi\)
−0.980582 + 0.196110i \(0.937169\pi\)
\(480\) 0 0
\(481\) 1.10297 28.6578i 0.0502913 1.30668i
\(482\) 1.44390 0.0657678
\(483\) 0 0
\(484\) −3.67990 + 6.37377i −0.167268 + 0.289717i
\(485\) −1.21193 −0.0550308
\(486\) 0 0
\(487\) 18.4084 + 10.6281i 0.834166 + 0.481606i 0.855277 0.518171i \(-0.173387\pi\)
−0.0211110 + 0.999777i \(0.506720\pi\)
\(488\) 0.295249i 0.0133653i
\(489\) 0 0
\(490\) 3.25005 + 1.00084i 0.146822 + 0.0452135i
\(491\) 11.2268 19.4453i 0.506657 0.877556i −0.493313 0.869852i \(-0.664214\pi\)
0.999970 0.00770409i \(-0.00245231\pi\)
\(492\) 0 0
\(493\) 16.8812 + 29.2391i 0.760292 + 1.31686i
\(494\) −0.122756 0.00472460i −0.00552306 0.000212570i
\(495\) 0 0
\(496\) −12.1897 7.03772i −0.547333 0.316003i
\(497\) −3.23509 8.23722i −0.145114 0.369490i
\(498\) 0 0
\(499\) 33.6694 + 19.4390i 1.50725 + 0.870210i 0.999964 + 0.00843082i \(0.00268365\pi\)
0.507284 + 0.861779i \(0.330650\pi\)
\(500\) −12.7339 7.35193i −0.569478 0.328788i
\(501\) 0 0
\(502\) −3.95520 2.28354i −0.176529 0.101919i
\(503\) 2.72850 + 4.72591i 0.121658 + 0.210718i 0.920422 0.390927i \(-0.127846\pi\)
−0.798764 + 0.601645i \(0.794512\pi\)
\(504\) 0 0
\(505\) 17.8151 + 10.2855i 0.792760 + 0.457700i
\(506\) −1.07163 + 1.85612i −0.0476397 + 0.0825144i
\(507\) 0 0
\(508\) −7.83697 13.5740i −0.347709 0.602250i
\(509\) −9.43315 + 5.44623i −0.418117 + 0.241400i −0.694271 0.719713i \(-0.744273\pi\)
0.276154 + 0.961113i \(0.410940\pi\)
\(510\) 0 0
\(511\) −13.7492 35.0083i −0.608229 1.54868i
\(512\) 13.5360i 0.598214i
\(513\) 0 0
\(514\) 0.528304 + 0.305017i 0.0233025 + 0.0134537i
\(515\) −11.9997 + 6.92804i −0.528771 + 0.305286i
\(516\) 0 0
\(517\) −2.49068 + 4.31398i −0.109540 + 0.189729i
\(518\) 2.97572 + 2.37192i 0.130745 + 0.104216i
\(519\) 0 0
\(520\) −3.24056 6.14733i −0.142108 0.269578i
\(521\) 13.9480 + 24.1587i 0.611074 + 1.05841i 0.991060 + 0.133419i \(0.0425957\pi\)
−0.379985 + 0.924993i \(0.624071\pi\)
\(522\) 0 0
\(523\) −8.36180 14.4831i −0.365636 0.633300i 0.623242 0.782029i \(-0.285815\pi\)
−0.988878 + 0.148729i \(0.952482\pi\)
\(524\) 9.85416 + 17.0679i 0.430481 + 0.745615i
\(525\) 0 0
\(526\) 0.0248890 0.0143696i 0.00108521 0.000626546i
\(527\) 17.6269i 0.767842i
\(528\) 0 0
\(529\) 1.82314 3.15777i 0.0792668 0.137294i
\(530\) 1.71793 + 2.97554i 0.0746219 + 0.129249i
\(531\) 0 0
\(532\) −0.611307 + 0.766923i −0.0265035 + 0.0332503i
\(533\) −17.3178 + 9.12904i −0.750116 + 0.395423i
\(534\) 0 0
\(535\) 21.5815i 0.933049i
\(536\) 8.17890 0.353275
\(537\) 0 0
\(538\) 4.21800i 0.181851i
\(539\) −5.55057 + 18.0244i −0.239080 + 0.776366i
\(540\) 0 0
\(541\) −9.66528 5.58025i −0.415543 0.239914i 0.277626 0.960689i \(-0.410453\pi\)
−0.693169 + 0.720776i \(0.743786\pi\)
\(542\) 1.06876 1.85114i 0.0459070 0.0795133i
\(543\) 0 0
\(544\) 8.75976 5.05745i 0.375572 0.216836i
\(545\) 3.58280 0.153470
\(546\) 0 0
\(547\) 36.6556 1.56728 0.783640 0.621215i \(-0.213361\pi\)
0.783640 + 0.621215i \(0.213361\pi\)
\(548\) 8.63275 4.98412i 0.368773 0.212911i
\(549\) 0 0
\(550\) 0.540297 0.935821i 0.0230383 0.0399036i
\(551\) −1.15623 0.667551i −0.0492571 0.0284386i
\(552\) 0 0
\(553\) −18.8491 15.0244i −0.801543 0.638903i
\(554\) 4.94830i 0.210233i
\(555\) 0 0
\(556\) 15.1990 0.644579
\(557\) 33.0776i 1.40154i 0.713386 + 0.700772i \(0.247161\pi\)
−0.713386 + 0.700772i \(0.752839\pi\)
\(558\) 0 0
\(559\) −28.8615 1.11081i −1.22071 0.0469823i
\(560\) −26.7447 4.02472i −1.13017 0.170076i
\(561\) 0 0
\(562\) −2.58020 4.46903i −0.108839 0.188515i
\(563\) −8.89836 + 15.4124i −0.375021 + 0.649556i −0.990330 0.138730i \(-0.955698\pi\)
0.615309 + 0.788286i \(0.289031\pi\)
\(564\) 0 0
\(565\) 53.5672i 2.25359i
\(566\) −2.81439 + 1.62489i −0.118298 + 0.0682992i
\(567\) 0 0
\(568\) −1.19978 2.07808i −0.0503417 0.0871943i
\(569\) 4.11047 + 7.11954i 0.172320 + 0.298467i 0.939231 0.343287i \(-0.111540\pi\)
−0.766911 + 0.641754i \(0.778207\pi\)
\(570\) 0 0
\(571\) −12.8776 22.3047i −0.538912 0.933424i −0.998963 0.0455309i \(-0.985502\pi\)
0.460051 0.887893i \(-0.347831\pi\)
\(572\) 16.9057 8.91183i 0.706863 0.372622i
\(573\) 0 0
\(574\) 0.386550 2.56867i 0.0161343 0.107214i
\(575\) 4.87891 8.45051i 0.203464 0.352411i
\(576\) 0 0
\(577\) 0.666314 0.384697i 0.0277390 0.0160151i −0.486066 0.873922i \(-0.661569\pi\)
0.513805 + 0.857907i \(0.328235\pi\)
\(578\) −0.893326 0.515762i −0.0371575 0.0214529i
\(579\) 0 0
\(580\) 37.4505i 1.55505i
\(581\) −43.3954 6.53042i −1.80034 0.270928i
\(582\) 0 0
\(583\) −16.5020 + 9.52743i −0.683443 + 0.394586i
\(584\) −5.09908 8.83187i −0.211002 0.365465i
\(585\) 0 0
\(586\) −1.34615 + 2.33159i −0.0556088 + 0.0963173i
\(587\) 10.4727 + 6.04644i 0.432256 + 0.249563i 0.700307 0.713841i \(-0.253046\pi\)
−0.268051 + 0.963405i \(0.586380\pi\)
\(588\) 0 0
\(589\) −0.348520 0.603654i −0.0143605 0.0248731i
\(590\) −3.19281 1.84337i −0.131446 0.0758904i
\(591\) 0 0
\(592\) −26.2099 15.1323i −1.07722 0.621933i
\(593\) −13.8115 7.97406i −0.567170 0.327456i 0.188848 0.982006i \(-0.439525\pi\)
−0.756018 + 0.654551i \(0.772858\pi\)
\(594\) 0 0
\(595\) 12.3815 + 31.5258i 0.507591 + 1.29243i
\(596\) −24.3949 14.0844i −0.999253 0.576919i
\(597\) 0 0
\(598\) −2.53725 + 1.33751i −0.103756 + 0.0546948i
\(599\) −3.55511 6.15763i −0.145258 0.251594i 0.784211 0.620494i \(-0.213068\pi\)
−0.929469 + 0.368900i \(0.879734\pi\)
\(600\) 0 0
\(601\) −10.3953 + 18.0051i −0.424032 + 0.734445i −0.996329 0.0856011i \(-0.972719\pi\)
0.572297 + 0.820046i \(0.306052\pi\)
\(602\) 2.38877 2.99686i 0.0973590 0.122143i
\(603\) 0 0
\(604\) 12.7333i 0.518112i
\(605\) −8.70432 5.02544i −0.353881 0.204313i
\(606\) 0 0
\(607\) −7.71405 −0.313104 −0.156552 0.987670i \(-0.550038\pi\)
−0.156552 + 0.987670i \(0.550038\pi\)
\(608\) −0.199992 + 0.346396i −0.00811074 + 0.0140482i
\(609\) 0 0
\(610\) 0.199941 0.00809539
\(611\) −5.89707 + 3.10864i −0.238570 + 0.125762i
\(612\) 0 0
\(613\) 20.4378i 0.825476i −0.910850 0.412738i \(-0.864572\pi\)
0.910850 0.412738i \(-0.135428\pi\)
\(614\) −2.12614 3.68257i −0.0858038 0.148617i
\(615\) 0 0
\(616\) −0.760978 + 5.05678i −0.0306607 + 0.203743i
\(617\) 3.98209 2.29906i 0.160313 0.0925567i −0.417697 0.908586i \(-0.637163\pi\)
0.578010 + 0.816030i \(0.303829\pi\)
\(618\) 0 0
\(619\) 8.70599 5.02641i 0.349923 0.202028i −0.314728 0.949182i \(-0.601913\pi\)
0.664651 + 0.747154i \(0.268580\pi\)
\(620\) 9.77623 16.9329i 0.392623 0.680042i
\(621\) 0 0
\(622\) −0.255396 0.147453i −0.0102404 0.00591232i
\(623\) 5.69827 + 14.5090i 0.228296 + 0.581290i
\(624\) 0 0
\(625\) 15.5853 26.9944i 0.623410 1.07978i
\(626\) 0.125986i 0.00503541i
\(627\) 0 0
\(628\) 31.3170 1.24968
\(629\) 37.9009i 1.51121i
\(630\) 0 0
\(631\) −6.29923 + 3.63686i −0.250768 + 0.144781i −0.620116 0.784510i \(-0.712914\pi\)
0.369348 + 0.929291i \(0.379581\pi\)
\(632\) −5.66015 3.26789i −0.225149 0.129990i
\(633\) 0 0
\(634\) 3.87483 0.153889
\(635\) 18.5373 10.7025i 0.735631 0.424717i
\(636\) 0 0
\(637\) −19.1402 + 16.4515i −0.758364 + 0.651831i
\(638\) −3.45199 −0.136665
\(639\) 0 0
\(640\) −14.9167 −0.589635
\(641\) −1.92516 + 3.33448i −0.0760394 + 0.131704i −0.901538 0.432700i \(-0.857561\pi\)
0.825498 + 0.564404i \(0.190894\pi\)
\(642\) 0 0
\(643\) 2.49163 1.43855i 0.0982605 0.0567307i −0.450065 0.892996i \(-0.648599\pi\)
0.548325 + 0.836265i \(0.315266\pi\)
\(644\) −3.40752 + 22.6433i −0.134275 + 0.892271i
\(645\) 0 0
\(646\) 0.162349 0.00638754
\(647\) 37.1001 1.45856 0.729278 0.684218i \(-0.239856\pi\)
0.729278 + 0.684218i \(0.239856\pi\)
\(648\) 0 0
\(649\) 10.2231 17.7070i 0.401293 0.695061i
\(650\) 1.27924 0.674349i 0.0501758 0.0264501i
\(651\) 0 0
\(652\) −8.14661 4.70345i −0.319046 0.184201i
\(653\) 10.0475 + 17.4028i 0.393189 + 0.681023i 0.992868 0.119218i \(-0.0380386\pi\)
−0.599679 + 0.800240i \(0.704705\pi\)
\(654\) 0 0
\(655\) −23.3087 + 13.4573i −0.910748 + 0.525820i
\(656\) 20.6589i 0.806596i
\(657\) 0 0
\(658\) 0.131629 0.874687i 0.00513142 0.0340988i
\(659\) 4.95529 + 8.58281i 0.193031 + 0.334339i 0.946253 0.323427i \(-0.104835\pi\)
−0.753223 + 0.657766i \(0.771502\pi\)
\(660\) 0 0
\(661\) 47.2266i 1.83690i 0.395537 + 0.918450i \(0.370558\pi\)
−0.395537 + 0.918450i \(0.629442\pi\)
\(662\) 0.137468 + 0.238102i 0.00534284 + 0.00925408i
\(663\) 0 0
\(664\) −11.8989 −0.461768
\(665\) −1.04735 0.834830i −0.0406143 0.0323733i
\(666\) 0 0
\(667\) −31.1716 −1.20697
\(668\) −4.61783 + 2.66611i −0.178669 + 0.103155i
\(669\) 0 0
\(670\) 5.53872i 0.213979i
\(671\) 1.10885i 0.0428068i
\(672\) 0 0
\(673\) 3.45845 5.99020i 0.133313 0.230905i −0.791639 0.610990i \(-0.790772\pi\)
0.924952 + 0.380084i \(0.124105\pi\)
\(674\) −5.04721 + 2.91401i −0.194411 + 0.112243i
\(675\) 0 0
\(676\) 25.4993 + 1.96573i 0.980742 + 0.0756050i
\(677\) −6.16453 + 10.6773i −0.236922 + 0.410361i −0.959830 0.280584i \(-0.909472\pi\)
0.722908 + 0.690945i \(0.242805\pi\)
\(678\) 0 0
\(679\) 0.436287 + 1.11088i 0.0167432 + 0.0426316i
\(680\) 4.59185 + 7.95331i 0.176089 + 0.304996i
\(681\) 0 0
\(682\) −1.56078 0.901120i −0.0597655 0.0345057i
\(683\) −21.2491 12.2682i −0.813076 0.469430i 0.0349470 0.999389i \(-0.488874\pi\)
−0.848023 + 0.529960i \(0.822207\pi\)
\(684\) 0 0
\(685\) 6.80655 + 11.7893i 0.260065 + 0.450446i
\(686\) −0.252606 3.33936i −0.00964453 0.127497i
\(687\) 0 0
\(688\) −15.2398 + 26.3961i −0.581012 + 1.00634i
\(689\) −25.4812 0.980713i −0.970756 0.0373622i
\(690\) 0 0
\(691\) −7.88703 + 4.55358i −0.300037 + 0.173226i −0.642459 0.766320i \(-0.722086\pi\)
0.342423 + 0.939546i \(0.388753\pi\)
\(692\) 0.885106 1.53305i 0.0336467 0.0582777i
\(693\) 0 0
\(694\) 1.47992i 0.0561769i
\(695\) 20.7564i 0.787336i
\(696\) 0 0
\(697\) 22.4055 12.9358i 0.848667 0.489978i
\(698\) −3.95087 −0.149542
\(699\) 0 0
\(700\) 1.71801 11.4164i 0.0649347 0.431498i
\(701\) −0.286950 −0.0108380 −0.00541898 0.999985i \(-0.501725\pi\)
−0.00541898 + 0.999985i \(0.501725\pi\)
\(702\) 0 0
\(703\) −0.749377 1.29796i −0.0282633 0.0489534i
\(704\) 19.4684i 0.733742i
\(705\) 0 0
\(706\) 0.0512797 + 0.0888191i 0.00192994 + 0.00334275i
\(707\) 3.01461 20.0324i 0.113376 0.753397i
\(708\) 0 0
\(709\) 18.5848i 0.697967i −0.937129 0.348984i \(-0.886527\pi\)
0.937129 0.348984i \(-0.113473\pi\)
\(710\) 1.40727 0.812486i 0.0528138 0.0304921i
\(711\) 0 0
\(712\) 2.11328 + 3.66031i 0.0791986 + 0.137176i
\(713\) −14.0940 8.13715i −0.527823 0.304739i
\(714\) 0 0
\(715\) 12.1704 + 23.0872i 0.455148 + 0.863414i
\(716\) 10.8751 18.8362i 0.406421 0.703941i
\(717\) 0 0
\(718\) −5.85947 −0.218674
\(719\) 41.6949 1.55496 0.777479 0.628909i \(-0.216498\pi\)
0.777479 + 0.628909i \(0.216498\pi\)
\(720\) 0 0
\(721\) 10.6702 + 8.50514i 0.397380 + 0.316748i
\(722\) 2.96980 1.71462i 0.110525 0.0638114i
\(723\) 0 0
\(724\) 3.47128 6.01244i 0.129009 0.223451i
\(725\) 15.7162 0.583684
\(726\) 0 0
\(727\) 32.7039 1.21292 0.606461 0.795113i \(-0.292589\pi\)
0.606461 + 0.795113i \(0.292589\pi\)
\(728\) −4.46819 + 5.18337i −0.165602 + 0.192108i
\(729\) 0 0
\(730\) 5.98091 3.45308i 0.221363 0.127804i
\(731\) 38.1702 1.41178
\(732\) 0 0
\(733\) −8.60423 4.96765i −0.317804 0.183484i 0.332609 0.943065i \(-0.392071\pi\)
−0.650413 + 0.759580i \(0.725404\pi\)
\(734\) −1.23225 + 0.711440i −0.0454832 + 0.0262597i
\(735\) 0 0
\(736\) 9.33871i 0.344230i
\(737\) −30.7171 −1.13148
\(738\) 0 0
\(739\) 10.4022i 0.382649i −0.981527 0.191325i \(-0.938722\pi\)
0.981527 0.191325i \(-0.0612784\pi\)
\(740\) 21.0205 36.4086i 0.772730 1.33841i
\(741\) 0 0
\(742\) 2.10900 2.64587i 0.0774237 0.0971328i
\(743\) 1.47972 + 0.854317i 0.0542857 + 0.0313419i 0.526897 0.849929i \(-0.323355\pi\)
−0.472612 + 0.881271i \(0.656689\pi\)
\(744\) 0 0
\(745\) 19.2343 33.3148i 0.704690 1.22056i
\(746\) −0.327545 + 0.189108i −0.0119923 + 0.00692374i
\(747\) 0 0
\(748\) −21.8723 + 12.6280i −0.799732 + 0.461726i
\(749\) −19.7821 + 7.76923i −0.722821 + 0.283881i
\(750\) 0 0
\(751\) 14.9906 + 25.9645i 0.547015 + 0.947458i 0.998477 + 0.0551673i \(0.0175692\pi\)
−0.451462 + 0.892290i \(0.649097\pi\)
\(752\) 7.03481i 0.256533i
\(753\) 0 0
\(754\) −3.90890 2.46195i −0.142354 0.0896590i
\(755\) 17.3893 0.632860
\(756\) 0 0
\(757\) −4.20229 + 7.27858i −0.152735 + 0.264545i −0.932232 0.361861i \(-0.882141\pi\)
0.779497 + 0.626406i \(0.215475\pi\)
\(758\) 2.58874 0.0940271
\(759\) 0 0
\(760\) −0.314506 0.181580i −0.0114083 0.00658660i
\(761\) 51.0590i 1.85089i 0.378885 + 0.925444i \(0.376308\pi\)
−0.378885 + 0.925444i \(0.623692\pi\)
\(762\) 0 0
\(763\) −1.28979 3.28407i −0.0466935 0.118891i
\(764\) −20.0668 + 34.7568i −0.725993 + 1.25746i
\(765\) 0 0
\(766\) 2.27723 + 3.94429i 0.0822798 + 0.142513i
\(767\) 24.2049 12.7596i 0.873988 0.460722i
\(768\) 0 0
\(769\) −0.610062 0.352220i −0.0219994 0.0127014i 0.488960 0.872306i \(-0.337376\pi\)
−0.510959 + 0.859605i \(0.670710\pi\)
\(770\) −3.42443 0.515331i −0.123408 0.0185712i
\(771\) 0 0
\(772\) 29.4142 + 16.9823i 1.05864 + 0.611206i
\(773\) 1.09571 + 0.632607i 0.0394099 + 0.0227533i 0.519575 0.854425i \(-0.326090\pi\)
−0.480166 + 0.877178i \(0.659423\pi\)
\(774\) 0 0
\(775\) 7.10593 + 4.10261i 0.255253 + 0.147370i
\(776\) 0.161803 + 0.280252i 0.00580840 + 0.0100604i
\(777\) 0 0
\(778\) −4.40076 2.54078i −0.157775 0.0910914i
\(779\) −0.511533 + 0.886001i −0.0183276 + 0.0317443i
\(780\) 0 0
\(781\) 4.50596 + 7.80456i 0.161236 + 0.279269i
\(782\) 3.28265 1.89524i 0.117387 0.0677737i
\(783\) 0 0
\(784\) 5.93881 + 25.9637i 0.212100 + 0.927273i
\(785\) 42.7679i 1.52645i
\(786\) 0 0
\(787\) 37.9292 + 21.8984i 1.35203 + 0.780595i 0.988534 0.151000i \(-0.0482494\pi\)
0.363497 + 0.931595i \(0.381583\pi\)
\(788\) −8.44493 +