Properties

Label 819.2.do.e.361.4
Level $819$
Weight $2$
Character 819.361
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 361.4
Root \(0.655911 - 1.25291i\) of defining polynomial
Character \(\chi\) \(=\) 819.361
Dual form 819.2.do.e.667.4

$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

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 0.554343 0.832288i \(-0.312970\pi\)
−0.443611 + 0.896219i \(0.646303\pi\)
\(3\) 0 0
\(4\) −0.983651 1.70373i −0.491826 0.851867i
\(5\) −2.32670 + 1.34332i −1.04053 + 0.600751i −0.919984 0.391956i \(-0.871799\pi\)
−0.120548 + 0.992708i \(0.538465\pi\)
\(6\) 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 \(0.133137\pi\)
−0.913796 + 0.406172i \(0.866863\pi\)
\(12\) 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 −0.995727 0.0923405i \(-0.970565\pi\)
0.417894 0.908496i \(-0.362768\pi\)
\(18\) 0 0
\(19\) 0.188424i 0.0432275i 0.999766 + 0.0216138i \(0.00688041\pi\)
−0.999766 + 0.0216138i \(0.993120\pi\)
\(20\) 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 −0.998890 0.0470977i \(-0.985003\pi\)
0.540233 + 0.841516i \(0.318336\pi\)
\(24\) 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 0.981163 + 0.193182i \(0.0618807\pi\)
−0.323281 + 0.946303i \(0.604786\pi\)
\(30\) 0 0
\(31\) 3.20369 + 1.84965i 0.575400 + 0.332207i 0.759303 0.650737i \(-0.225540\pi\)
−0.183903 + 0.982944i \(0.558873\pi\)
\(32\) −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 0.944552 0.328361i \(-0.106496\pi\)
0.187907 + 0.982187i \(0.439830\pi\)
\(38\) −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 −0.820013 0.572345i \(-0.806034\pi\)
0.0856594 + 0.996324i \(0.472700\pi\)
\(42\) 0 0
\(43\) −4.00533 + 6.93743i −0.610807 + 1.05795i 0.380298 + 0.924864i \(0.375821\pi\)
−0.991105 + 0.133084i \(0.957512\pi\)
\(44\) 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 −0.612212 0.790694i \(-0.709720\pi\)
0.378655 + 0.925538i \(0.376387\pi\)
\(48\) 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 −0.999866 0.0163917i \(-0.994782\pi\)
0.514128 + 0.857713i \(0.328115\pi\)
\(54\) 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 −0.00692130 0.999976i \(-0.502203\pi\)
0.862544 + 0.505982i \(0.168870\pi\)
\(60\) 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 \(0.245229\pi\)
−0.717626 + 0.696429i \(0.754771\pi\)
\(68\) −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 0.318162 0.948037i \(-0.396935\pi\)
−0.661943 + 0.749554i \(0.730268\pi\)
\(72\) 0 0
\(73\) −12.3112 7.10790i −1.44092 0.831917i −0.443011 0.896516i \(-0.646090\pi\)
−0.997911 + 0.0645994i \(0.979423\pi\)
\(74\) 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 −0.999895 0.0145069i \(-0.995382\pi\)
0.487384 0.873188i \(-0.337951\pi\)
\(80\) 10.2224i 1.14290i
\(81\) 0 0
\(82\) −0.981797 −0.108421
\(83\) 16.5866i 1.82061i −0.413934 0.910307i \(-0.635845\pi\)
0.413934 0.910307i \(-0.364155\pi\)
\(84\) 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 0.745421 0.666594i \(-0.232248\pi\)
−0.204577 + 0.978851i \(0.565582\pi\)
\(90\) 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 0.519702 0.854348i \(-0.326043\pi\)
−0.480036 + 0.877249i \(0.659376\pi\)
\(98\) −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 0.964647 0.263545i \(-0.0848918\pi\)
−0.710560 + 0.703636i \(0.751558\pi\)
\(104\) 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 −0.603935 0.797034i \(-0.706401\pi\)
0.992219 + 0.124506i \(0.0397345\pi\)
\(108\) 0 0
\(109\) −1.15490 0.666781i −0.110619 0.0638660i 0.443670 0.896190i \(-0.353676\pi\)
−0.554289 + 0.832324i \(0.687010\pi\)
\(110\) 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 −0.168296 + 0.985736i \(0.553827\pi\)
−0.769525 + 0.638617i \(0.779507\pi\)
\(114\) 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 0.633370 0.773849i \(-0.281671\pi\)
−0.986858 + 0.161590i \(0.948338\pi\)
\(128\) 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 0.997507 0.0705727i \(-0.0224827\pi\)
−0.559871 + 0.828580i \(0.689149\pi\)
\(132\) 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 −0.675598 0.737270i \(-0.736114\pi\)
0.300696 + 0.953720i \(0.402781\pi\)
\(138\) 0 0
\(139\) −3.86289 + 6.69073i −0.327646 + 0.567500i −0.982044 0.188650i \(-0.939589\pi\)
0.654398 + 0.756150i \(0.272922\pi\)
\(140\) 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 \(-0.800502\pi\)
0.809944 0.586507i \(-0.199498\pi\)
\(150\) 0 0
\(151\) −5.60534 3.23624i −0.456156 0.263362i 0.254271 0.967133i \(-0.418165\pi\)
−0.710427 + 0.703771i \(0.751498\pi\)
\(152\) 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 0.351240 + 0.936285i \(0.385760\pi\)
−0.986467 + 0.163960i \(0.947573\pi\)
\(158\) 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 \(-0.940038\pi\)
0.982310 0.187263i \(-0.0599616\pi\)
\(164\) 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 −0.406424 0.913685i \(-0.633224\pi\)
0.588062 + 0.808816i \(0.299891\pi\)
\(168\) 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 \(0.213422\pi\)
−0.783521 + 0.621365i \(0.786578\pi\)
\(194\) 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 −0.339224 0.940705i \(-0.610165\pi\)
0.645063 + 0.764130i \(0.276831\pi\)
\(198\) 0 0
\(199\) 3.59097 + 6.21975i 0.254557 + 0.440906i 0.964775 0.263076i \(-0.0847369\pi\)
−0.710218 + 0.703982i \(0.751404\pi\)
\(200\) −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 0.991962 + 0.126539i \(0.0403868\pi\)
−0.386395 + 0.922333i \(0.626280\pi\)
\(212\) 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 −0.0317129 0.999497i \(-0.510096\pi\)
0.849733 + 0.527213i \(0.176763\pi\)
\(224\) 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 −0.580178 0.814490i \(-0.697017\pi\)
0.415280 + 0.909694i \(0.363684\pi\)
\(228\) 0 0
\(229\) −7.59860 + 4.38706i −0.502130 + 0.289905i −0.729593 0.683882i \(-0.760290\pi\)
0.227463 + 0.973787i \(0.426957\pi\)
\(230\) 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 0.770170 0.637839i \(-0.220171\pi\)
−0.937469 + 0.348068i \(0.886838\pi\)
\(234\) 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 \(-0.974256\pi\)
0.996731 0.0807901i \(-0.0257443\pi\)
\(240\) 0 0
\(241\) 6.91532 3.99256i 0.445455 0.257183i −0.260454 0.965486i \(-0.583872\pi\)
0.705909 + 0.708303i \(0.250539\pi\)
\(242\) 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 0.124389 + 0.992234i \(0.460303\pi\)
−0.921494 + 0.388393i \(0.873030\pi\)
\(252\) 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 −0.808608 0.588348i \(-0.799778\pi\)
0.913828 + 0.406101i \(0.133112\pi\)
\(258\) 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 −0.964435 0.264318i \(-0.914853\pi\)
0.253311 0.967385i \(-0.418480\pi\)
\(270\) 0 0
\(271\) 10.2373 + 5.91049i 0.621870 + 0.359037i 0.777597 0.628763i \(-0.216439\pi\)
−0.155727 + 0.987800i \(0.549772\pi\)
\(272\) 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 −0.904107 0.427306i \(-0.859463\pi\)
0.0819961 0.996633i \(-0.473870\pi\)
\(278\) −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 \(0.324140\pi\)
−0.524801 + 0.851225i \(0.675860\pi\)
\(282\) 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 0.0735896 0.997289i \(-0.476554\pi\)
−0.826882 + 0.562375i \(0.809888\pi\)
\(294\) 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 \(0.234164\pi\)
−0.741396 + 0.671068i \(0.765836\pi\)
\(308\) −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 −0.888219 0.459420i \(-0.848057\pi\)
0.841979 + 0.539510i \(0.181391\pi\)
\(312\) 0 0
\(313\) 0.348367 + 0.603389i 0.0196909 + 0.0341056i 0.875703 0.482850i \(-0.160398\pi\)
−0.856012 + 0.516956i \(0.827065\pi\)
\(314\) −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 0.121826 0.992551i \(-0.461125\pi\)
0.920488 + 0.390771i \(0.127792\pi\)
\(318\) 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 \(-0.986695\pi\)
0.999127 0.0417861i \(-0.0133048\pi\)
\(332\) −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 0.954710 0.297539i \(-0.0961659\pi\)
−0.735031 + 0.678033i \(0.762833\pi\)
\(348\) 0 0
\(349\) −18.9220 + 10.9246i −1.01287 + 0.584782i −0.912031 0.410120i \(-0.865487\pi\)
−0.100841 + 0.994903i \(0.532153\pi\)
\(350\) −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 \(-0.995195\pi\)
0.999886 0.0150940i \(-0.00480474\pi\)
\(354\) 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 −0.999771 0.0214184i \(-0.993182\pi\)
−0.481336 + 0.876536i \(0.659848\pi\)
\(360\) 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 −0.146545 0.989204i \(-0.546815\pi\)
0.783404 + 0.621513i \(0.213482\pi\)
\(380\) −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 \(-0.777479\pi\)
0.765441 0.643507i \(-0.222521\pi\)
\(384\) 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 0.251524 + 0.967851i \(0.419068\pi\)
−0.963946 + 0.266099i \(0.914265\pi\)
\(390\) 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 \(-0.815973\pi\)
0.837482 0.546465i \(-0.184027\pi\)
\(398\) 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 0.873229 0.487310i \(-0.162022\pi\)
0.0145918 + 0.999894i \(0.495355\pi\)
\(402\) 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 −0.359741 0.933052i \(-0.617135\pi\)
0.628177 + 0.778071i \(0.283801\pi\)
\(410\) 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 0.894439 + 0.447189i \(0.147575\pi\)
−0.0599424 + 0.998202i \(0.519092\pi\)
\(420\) 0 0
\(421\) 11.5233i 0.561613i 0.959764 + 0.280806i \(0.0906019\pi\)
−0.959764 + 0.280806i \(0.909398\pi\)
\(422\) 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 \(-0.932257\pi\)
0.977439 0.211218i \(-0.0677431\pi\)
\(432\) 0 0
\(433\) 11.0535 19.1452i 0.531196 0.920058i −0.468141 0.883654i \(-0.655076\pi\)
0.999337 0.0364046i \(-0.0115905\pi\)
\(434\) 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 −0.962828 0.270114i \(-0.912939\pi\)
0.715339 + 0.698777i \(0.246272\pi\)
\(440\) −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 0.880506 + 0.474036i \(0.157203\pi\)
−0.0297257 + 0.999558i \(0.509463\pi\)
\(444\) 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 0.886751 0.462247i \(-0.152957\pi\)
0.0430575 + 0.999073i \(0.486290\pi\)
\(450\) 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 −0.293949 0.955821i \(-0.594969\pi\)
−0.974740 + 0.223344i \(0.928303\pi\)
\(458\) −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 0.659881 0.751370i \(-0.270607\pi\)
−0.320765 + 0.947159i \(0.603940\pi\)
\(462\) 0 0
\(463\) 10.0392i 0.466563i −0.972409 0.233281i \(-0.925054\pi\)
0.972409 0.233281i \(-0.0749463\pi\)
\(464\) −26.9599 −1.25158
\(465\) 0 0
\(466\) 0.923545i 0.0427824i
\(467\) 13.1756 + 22.8209i 0.609696 + 1.05602i 0.991290 + 0.131695i \(0.0420418\pi\)
−0.381594 + 0.924330i \(0.624625\pi\)
\(468\) 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 \(-0.937169\pi\)
0.980582 0.196110i \(-0.0628309\pi\)
\(480\) 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 −0.0211110 0.999777i \(-0.506720\pi\)
0.855277 + 0.518171i \(0.173387\pi\)
\(488\) 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 0.999970 + 0.00770409i \(0.00245231\pi\)
−0.493313 + 0.869852i \(0.664214\pi\)
\(492\) 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 0.507284 0.861779i \(-0.330650\pi\)
0.999964 0.00843082i \(-0.00268365\pi\)
\(500\) −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 −0.798764 0.601645i \(-0.794512\pi\)
0.920422 + 0.390927i \(0.127846\pi\)
\(504\) 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 0.276154 0.961113i \(-0.410940\pi\)
−0.694271 + 0.719713i \(0.744273\pi\)
\(510\) 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 −0.379985 0.924993i \(-0.624071\pi\)
0.991060 0.133419i \(-0.0425957\pi\)
\(522\) 0 0
\(523\) −8.36180 + 14.4831i −0.365636 + 0.633300i −0.988878 0.148729i \(-0.952482\pi\)
0.623242 + 0.782029i \(0.285815\pi\)
\(524\) 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 −0.693169 0.720776i \(-0.743786\pi\)
0.277626 + 0.960689i \(0.410453\pi\)
\(542\) 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 \(-0.752839\pi\)
0.713386 0.700772i \(-0.247161\pi\)
\(558\) 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 0.615309 0.788286i \(-0.289031\pi\)
−0.990330 + 0.138730i \(0.955698\pi\)
\(564\) 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 −0.766911 0.641754i \(-0.778207\pi\)
0.939231 + 0.343287i \(0.111540\pi\)
\(570\) 0 0
\(571\) −12.8776 + 22.3047i −0.538912 + 0.933424i 0.460051 + 0.887893i \(0.347831\pi\)
−0.998963 + 0.0455309i \(0.985502\pi\)
\(572\) 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 0.513805 0.857907i \(-0.328235\pi\)
−0.486066 + 0.873922i \(0.661569\pi\)
\(578\) −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 −0.268051 0.963405i \(-0.586380\pi\)
0.700307 + 0.713841i \(0.253046\pi\)
\(588\) 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 −0.756018 0.654551i \(-0.772858\pi\)
0.188848 + 0.982006i \(0.439525\pi\)
\(594\) 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 −0.929469 0.368900i \(-0.879734\pi\)
0.784211 + 0.620494i \(0.213068\pi\)
\(600\) 0 0
\(601\) −10.3953 18.0051i −0.424032 0.734445i 0.572297 0.820046i \(-0.306052\pi\)
−0.996329 + 0.0856011i \(0.972719\pi\)
\(602\) 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 \(0.135428\pi\)
−0.910850 + 0.412738i \(0.864572\pi\)
\(614\) −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 0.578010 0.816030i \(-0.303829\pi\)
−0.417697 + 0.908586i \(0.637163\pi\)
\(618\) 0 0
\(619\) 8.70599 + 5.02641i 0.349923 + 0.202028i 0.664651 0.747154i \(-0.268580\pi\)
−0.314728 + 0.949182i \(0.601913\pi\)
\(620\) 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 0.369348 0.929291i \(-0.379581\pi\)
−0.620116 + 0.784510i \(0.712914\pi\)
\(632\) −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 0.825498 0.564404i \(-0.190894\pi\)
−0.901538 + 0.432700i \(0.857561\pi\)
\(642\) 0 0
\(643\) 2.49163 + 1.43855i 0.0982605 + 0.0567307i 0.548325 0.836265i \(-0.315266\pi\)
−0.450065 + 0.892996i \(0.648599\pi\)
\(644\) −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 −0.599679 0.800240i \(-0.704705\pi\)
0.992868 + 0.119218i \(0.0380386\pi\)
\(654\) 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 −0.753223 0.657766i \(-0.771502\pi\)
0.946253 + 0.323427i \(0.104835\pi\)
\(660\) 0 0
\(661\) 47.2266i 1.83690i −0.395537 0.918450i \(-0.629442\pi\)
0.395537 0.918450i \(-0.370558\pi\)
\(662\) 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 0.924952 0.380084i \(-0.124105\pi\)
−0.791639 + 0.610990i \(0.790772\pi\)
\(674\) −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 0.722908 0.690945i \(-0.242805\pi\)
−0.959830 + 0.280584i \(0.909472\pi\)
\(678\) 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 −0.848023 0.529960i \(-0.822207\pi\)
0.0349470 + 0.999389i \(0.488874\pi\)
\(684\) 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 0.342423 0.939546i \(-0.388753\pi\)
−0.642459 + 0.766320i \(0.722086\pi\)
\(692\) 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 \(0.113473\pi\)
−0.937129 + 0.348984i \(0.886527\pi\)
\(710\) 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 −0.650413 0.759580i \(-0.725404\pi\)
0.332609 + 0.943065i \(0.392071\pi\)
\(734\) −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 \(0.0612784\pi\)
−0.981527 + 0.191325i \(0.938722\pi\)
\(740\) 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 −0.472612 0.881271i \(-0.656689\pi\)
0.526897 + 0.849929i \(0.323355\pi\)
\(744\) 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 −0.451462 0.892290i \(-0.649097\pi\)
0.998477 0.0551673i \(-0.0175692\pi\)
\(752\) 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 0.779497 0.626406i \(-0.215475\pi\)
−0.932232 + 0.361861i \(0.882141\pi\)
\(758\) 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 \(-0.623692\pi\)
0.378885 0.925444i \(-0.376308\pi\)
\(762\) 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 −0.510959 0.859605i \(-0.670710\pi\)
0.488960 + 0.872306i \(0.337376\pi\)
\(770\) −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 −0.480166 0.877178i \(-0.659423\pi\)
0.519575 + 0.854425i \(0.326090\pi\)
\(774\) 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 0.363497 0.931595i \(-0.381583\pi\)
0.988534 + 0.151000i \(0.0482494\pi\)
\(788\) −8.44493