Properties

Label 1152.2.p.g.959.8
Level $1152$
Weight $2$
Character 1152.959
Analytic conductor $9.199$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 959.8
Character \(\chi\) \(=\) 1152.959
Dual form 1152.2.p.g.191.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.765007 + 1.55395i) q^{3} +(0.781546 - 1.35368i) q^{5} +(-0.954503 + 0.551083i) q^{7} +(-1.82953 + 2.37757i) q^{9} +O(q^{10})\) \(q+(0.765007 + 1.55395i) q^{3} +(0.781546 - 1.35368i) q^{5} +(-0.954503 + 0.551083i) q^{7} +(-1.82953 + 2.37757i) q^{9} +(-2.15418 + 1.24372i) q^{11} +(5.48986 + 3.16957i) q^{13} +(2.70144 + 0.178912i) q^{15} +0.874622i q^{17} -6.45410 q^{19} +(-1.58656 - 1.06167i) q^{21} +(-1.52981 + 2.64970i) q^{23} +(1.27837 + 2.21421i) q^{25} +(-5.09422 - 1.02415i) q^{27} +(-0.767807 - 1.32988i) q^{29} +(6.29677 + 3.63544i) q^{31} +(-3.58063 - 2.39604i) q^{33} +1.72279i q^{35} -1.74638i q^{37} +(-0.725582 + 10.9557i) q^{39} +(7.45339 + 4.30322i) q^{41} +(2.66223 + 4.61112i) q^{43} +(1.78859 + 4.33477i) q^{45} +(1.73458 + 3.00438i) q^{47} +(-2.89262 + 5.01016i) q^{49} +(-1.35912 + 0.669092i) q^{51} -11.1315 q^{53} +3.88808i q^{55} +(-4.93743 - 10.0294i) q^{57} +(-1.76786 - 1.02067i) q^{59} +(6.23086 - 3.59739i) q^{61} +(0.436057 - 3.27762i) q^{63} +(8.58115 - 4.95433i) q^{65} +(1.14096 - 1.97621i) q^{67} +(-5.28782 - 0.350205i) q^{69} +13.1244 q^{71} -4.92960 q^{73} +(-2.46281 + 3.68041i) q^{75} +(1.37078 - 2.37426i) q^{77} +(3.31959 - 1.91656i) q^{79} +(-2.30564 - 8.69966i) q^{81} +(-11.2198 + 6.47775i) q^{83} +(1.18396 + 0.683557i) q^{85} +(1.47919 - 2.21050i) q^{87} -13.3358i q^{89} -6.98679 q^{91} +(-0.832229 + 12.5660i) q^{93} +(-5.04418 + 8.73677i) q^{95} +(4.65272 + 8.05875i) q^{97} +(0.984118 - 7.39712i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 12q^{7} - 4q^{9} + O(q^{10}) \) \( 24q + 12q^{7} - 4q^{9} + 20q^{15} - 12q^{23} - 12q^{25} - 36q^{31} + 4q^{33} + 20q^{39} - 12q^{41} + 12q^{47} + 12q^{49} + 4q^{57} - 92q^{63} - 48q^{65} + 24q^{73} + 84q^{79} - 20q^{81} + 68q^{87} + 24q^{95} - 12q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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
\(3\) 0.765007 + 1.55395i 0.441677 + 0.897174i
\(4\) 0 0
\(5\) 0.781546 1.35368i 0.349518 0.605383i −0.636646 0.771156i \(-0.719679\pi\)
0.986164 + 0.165774i \(0.0530121\pi\)
\(6\) 0 0
\(7\) −0.954503 + 0.551083i −0.360768 + 0.208290i −0.669418 0.742886i \(-0.733456\pi\)
0.308649 + 0.951176i \(0.400123\pi\)
\(8\) 0 0
\(9\) −1.82953 + 2.37757i −0.609843 + 0.792522i
\(10\) 0 0
\(11\) −2.15418 + 1.24372i −0.649509 + 0.374994i −0.788268 0.615332i \(-0.789022\pi\)
0.138759 + 0.990326i \(0.455689\pi\)
\(12\) 0 0
\(13\) 5.48986 + 3.16957i 1.52261 + 0.879081i 0.999643 + 0.0267307i \(0.00850965\pi\)
0.522971 + 0.852351i \(0.324824\pi\)
\(14\) 0 0
\(15\) 2.70144 + 0.178912i 0.697508 + 0.0461950i
\(16\) 0 0
\(17\) 0.874622i 0.212127i 0.994359 + 0.106064i \(0.0338247\pi\)
−0.994359 + 0.106064i \(0.966175\pi\)
\(18\) 0 0
\(19\) −6.45410 −1.48067 −0.740337 0.672236i \(-0.765334\pi\)
−0.740337 + 0.672236i \(0.765334\pi\)
\(20\) 0 0
\(21\) −1.58656 1.06167i −0.346215 0.231675i
\(22\) 0 0
\(23\) −1.52981 + 2.64970i −0.318987 + 0.552501i −0.980277 0.197629i \(-0.936676\pi\)
0.661290 + 0.750130i \(0.270009\pi\)
\(24\) 0 0
\(25\) 1.27837 + 2.21421i 0.255675 + 0.442841i
\(26\) 0 0
\(27\) −5.09422 1.02415i −0.980384 0.197097i
\(28\) 0 0
\(29\) −0.767807 1.32988i −0.142578 0.246953i 0.785889 0.618368i \(-0.212206\pi\)
−0.928467 + 0.371415i \(0.878873\pi\)
\(30\) 0 0
\(31\) 6.29677 + 3.63544i 1.13093 + 0.652945i 0.944169 0.329460i \(-0.106867\pi\)
0.186764 + 0.982405i \(0.440200\pi\)
\(32\) 0 0
\(33\) −3.58063 2.39604i −0.623309 0.417097i
\(34\) 0 0
\(35\) 1.72279i 0.291204i
\(36\) 0 0
\(37\) 1.74638i 0.287103i −0.989643 0.143551i \(-0.954148\pi\)
0.989643 0.143551i \(-0.0458522\pi\)
\(38\) 0 0
\(39\) −0.725582 + 10.9557i −0.116186 + 1.75432i
\(40\) 0 0
\(41\) 7.45339 + 4.30322i 1.16402 + 0.672049i 0.952265 0.305273i \(-0.0987476\pi\)
0.211759 + 0.977322i \(0.432081\pi\)
\(42\) 0 0
\(43\) 2.66223 + 4.61112i 0.405986 + 0.703189i 0.994436 0.105345i \(-0.0335947\pi\)
−0.588449 + 0.808534i \(0.700261\pi\)
\(44\) 0 0
\(45\) 1.78859 + 4.33477i 0.266628 + 0.646189i
\(46\) 0 0
\(47\) 1.73458 + 3.00438i 0.253015 + 0.438234i 0.964354 0.264614i \(-0.0852446\pi\)
−0.711340 + 0.702848i \(0.751911\pi\)
\(48\) 0 0
\(49\) −2.89262 + 5.01016i −0.413231 + 0.715737i
\(50\) 0 0
\(51\) −1.35912 + 0.669092i −0.190315 + 0.0936916i
\(52\) 0 0
\(53\) −11.1315 −1.52903 −0.764514 0.644607i \(-0.777021\pi\)
−0.764514 + 0.644607i \(0.777021\pi\)
\(54\) 0 0
\(55\) 3.88808i 0.524269i
\(56\) 0 0
\(57\) −4.93743 10.0294i −0.653979 1.32842i
\(58\) 0 0
\(59\) −1.76786 1.02067i −0.230155 0.132880i 0.380488 0.924786i \(-0.375756\pi\)
−0.610644 + 0.791905i \(0.709089\pi\)
\(60\) 0 0
\(61\) 6.23086 3.59739i 0.797780 0.460599i −0.0449142 0.998991i \(-0.514301\pi\)
0.842694 + 0.538392i \(0.180968\pi\)
\(62\) 0 0
\(63\) 0.436057 3.27762i 0.0549380 0.412941i
\(64\) 0 0
\(65\) 8.58115 4.95433i 1.06436 0.614509i
\(66\) 0 0
\(67\) 1.14096 1.97621i 0.139391 0.241432i −0.787875 0.615835i \(-0.788819\pi\)
0.927266 + 0.374403i \(0.122152\pi\)
\(68\) 0 0
\(69\) −5.28782 0.350205i −0.636579 0.0421597i
\(70\) 0 0
\(71\) 13.1244 1.55758 0.778788 0.627287i \(-0.215835\pi\)
0.778788 + 0.627287i \(0.215835\pi\)
\(72\) 0 0
\(73\) −4.92960 −0.576966 −0.288483 0.957485i \(-0.593151\pi\)
−0.288483 + 0.957485i \(0.593151\pi\)
\(74\) 0 0
\(75\) −2.46281 + 3.68041i −0.284380 + 0.424977i
\(76\) 0 0
\(77\) 1.37078 2.37426i 0.156215 0.270572i
\(78\) 0 0
\(79\) 3.31959 1.91656i 0.373483 0.215630i −0.301496 0.953467i \(-0.597486\pi\)
0.674979 + 0.737837i \(0.264153\pi\)
\(80\) 0 0
\(81\) −2.30564 8.69966i −0.256182 0.966628i
\(82\) 0 0
\(83\) −11.2198 + 6.47775i −1.23153 + 0.711026i −0.967349 0.253447i \(-0.918436\pi\)
−0.264183 + 0.964472i \(0.585102\pi\)
\(84\) 0 0
\(85\) 1.18396 + 0.683557i 0.128418 + 0.0741422i
\(86\) 0 0
\(87\) 1.47919 2.21050i 0.158586 0.236991i
\(88\) 0 0
\(89\) 13.3358i 1.41359i −0.707416 0.706797i \(-0.750139\pi\)
0.707416 0.706797i \(-0.249861\pi\)
\(90\) 0 0
\(91\) −6.98679 −0.732414
\(92\) 0 0
\(93\) −0.832229 + 12.5660i −0.0862982 + 1.30303i
\(94\) 0 0
\(95\) −5.04418 + 8.73677i −0.517522 + 0.896374i
\(96\) 0 0
\(97\) 4.65272 + 8.05875i 0.472412 + 0.818242i 0.999502 0.0315680i \(-0.0100501\pi\)
−0.527089 + 0.849810i \(0.676717\pi\)
\(98\) 0 0
\(99\) 0.984118 7.39712i 0.0989076 0.743438i
\(100\) 0 0
\(101\) −9.15459 15.8562i −0.910916 1.57775i −0.812773 0.582581i \(-0.802043\pi\)
−0.0981434 0.995172i \(-0.531290\pi\)
\(102\) 0 0
\(103\) −14.0766 8.12710i −1.38700 0.800787i −0.394028 0.919098i \(-0.628919\pi\)
−0.992977 + 0.118311i \(0.962252\pi\)
\(104\) 0 0
\(105\) −2.67712 + 1.31794i −0.261261 + 0.128618i
\(106\) 0 0
\(107\) 5.80067i 0.560772i −0.959887 0.280386i \(-0.909538\pi\)
0.959887 0.280386i \(-0.0904624\pi\)
\(108\) 0 0
\(109\) 7.34771i 0.703783i 0.936041 + 0.351892i \(0.114461\pi\)
−0.936041 + 0.351892i \(0.885539\pi\)
\(110\) 0 0
\(111\) 2.71379 1.33599i 0.257581 0.126807i
\(112\) 0 0
\(113\) −0.260651 0.150487i −0.0245200 0.0141566i 0.487690 0.873017i \(-0.337840\pi\)
−0.512210 + 0.858860i \(0.671173\pi\)
\(114\) 0 0
\(115\) 2.39123 + 4.14173i 0.222983 + 0.386218i
\(116\) 0 0
\(117\) −17.5797 + 7.25368i −1.62525 + 0.670603i
\(118\) 0 0
\(119\) −0.481989 0.834830i −0.0441839 0.0765287i
\(120\) 0 0
\(121\) −2.40634 + 4.16791i −0.218758 + 0.378901i
\(122\) 0 0
\(123\) −0.985097 + 14.8742i −0.0888232 + 1.34116i
\(124\) 0 0
\(125\) 11.8119 1.05649
\(126\) 0 0
\(127\) 18.6505i 1.65497i 0.561490 + 0.827484i \(0.310228\pi\)
−0.561490 + 0.827484i \(0.689772\pi\)
\(128\) 0 0
\(129\) −5.12883 + 7.66451i −0.451568 + 0.674823i
\(130\) 0 0
\(131\) 7.75570 + 4.47775i 0.677618 + 0.391223i 0.798957 0.601388i \(-0.205385\pi\)
−0.121339 + 0.992611i \(0.538719\pi\)
\(132\) 0 0
\(133\) 6.16046 3.55675i 0.534180 0.308409i
\(134\) 0 0
\(135\) −5.36773 + 6.09552i −0.461981 + 0.524618i
\(136\) 0 0
\(137\) 8.59826 4.96421i 0.734599 0.424121i −0.0855034 0.996338i \(-0.527250\pi\)
0.820102 + 0.572217i \(0.193917\pi\)
\(138\) 0 0
\(139\) 0.970830 1.68153i 0.0823448 0.142625i −0.821912 0.569615i \(-0.807092\pi\)
0.904257 + 0.426989i \(0.140426\pi\)
\(140\) 0 0
\(141\) −3.34170 + 4.99383i −0.281422 + 0.420556i
\(142\) 0 0
\(143\) −15.7682 −1.31860
\(144\) 0 0
\(145\) −2.40030 −0.199334
\(146\) 0 0
\(147\) −9.99841 0.662181i −0.824655 0.0546158i
\(148\) 0 0
\(149\) 9.65962 16.7310i 0.791347 1.37065i −0.133786 0.991010i \(-0.542713\pi\)
0.925133 0.379643i \(-0.123953\pi\)
\(150\) 0 0
\(151\) 9.90266 5.71730i 0.805867 0.465267i −0.0396516 0.999214i \(-0.512625\pi\)
0.845519 + 0.533946i \(0.179291\pi\)
\(152\) 0 0
\(153\) −2.07947 1.60015i −0.168115 0.129364i
\(154\) 0 0
\(155\) 9.84243 5.68253i 0.790563 0.456432i
\(156\) 0 0
\(157\) 15.2905 + 8.82799i 1.22032 + 0.704551i 0.964986 0.262303i \(-0.0844820\pi\)
0.255332 + 0.966854i \(0.417815\pi\)
\(158\) 0 0
\(159\) −8.51566 17.2978i −0.675336 1.37180i
\(160\) 0 0
\(161\) 3.37220i 0.265767i
\(162\) 0 0
\(163\) 5.64209 0.441922 0.220961 0.975283i \(-0.429081\pi\)
0.220961 + 0.975283i \(0.429081\pi\)
\(164\) 0 0
\(165\) −6.04189 + 2.97441i −0.470361 + 0.231557i
\(166\) 0 0
\(167\) 11.6305 20.1446i 0.899993 1.55883i 0.0724922 0.997369i \(-0.476905\pi\)
0.827501 0.561465i \(-0.189762\pi\)
\(168\) 0 0
\(169\) 13.5924 + 23.5427i 1.04557 + 1.81098i
\(170\) 0 0
\(171\) 11.8080 15.3451i 0.902979 1.17347i
\(172\) 0 0
\(173\) −5.69231 9.85937i −0.432778 0.749594i 0.564333 0.825547i \(-0.309133\pi\)
−0.997111 + 0.0759531i \(0.975800\pi\)
\(174\) 0 0
\(175\) −2.44042 1.40898i −0.184479 0.106509i
\(176\) 0 0
\(177\) 0.233654 3.52799i 0.0175625 0.265180i
\(178\) 0 0
\(179\) 10.6783i 0.798133i −0.916922 0.399066i \(-0.869334\pi\)
0.916922 0.399066i \(-0.130666\pi\)
\(180\) 0 0
\(181\) 5.74638i 0.427125i −0.976929 0.213562i \(-0.931493\pi\)
0.976929 0.213562i \(-0.0685067\pi\)
\(182\) 0 0
\(183\) 10.3568 + 6.93043i 0.765598 + 0.512312i
\(184\) 0 0
\(185\) −2.36403 1.36487i −0.173807 0.100348i
\(186\) 0 0
\(187\) −1.08778 1.88409i −0.0795464 0.137778i
\(188\) 0 0
\(189\) 5.42684 1.82979i 0.394745 0.133097i
\(190\) 0 0
\(191\) −8.87439 15.3709i −0.642129 1.11220i −0.984957 0.172801i \(-0.944718\pi\)
0.342828 0.939398i \(-0.388615\pi\)
\(192\) 0 0
\(193\) −10.5823 + 18.3291i −0.761732 + 1.31936i 0.180225 + 0.983625i \(0.442317\pi\)
−0.941957 + 0.335733i \(0.891016\pi\)
\(194\) 0 0
\(195\) 14.2634 + 9.54460i 1.02143 + 0.683503i
\(196\) 0 0
\(197\) −5.51688 −0.393061 −0.196531 0.980498i \(-0.562968\pi\)
−0.196531 + 0.980498i \(0.562968\pi\)
\(198\) 0 0
\(199\) 6.90420i 0.489426i −0.969596 0.244713i \(-0.921306\pi\)
0.969596 0.244713i \(-0.0786938\pi\)
\(200\) 0 0
\(201\) 3.94377 + 0.261191i 0.278172 + 0.0184230i
\(202\) 0 0
\(203\) 1.46575 + 0.846250i 0.102875 + 0.0593951i
\(204\) 0 0
\(205\) 11.6503 6.72632i 0.813694 0.469786i
\(206\) 0 0
\(207\) −3.50102 8.48493i −0.243338 0.589743i
\(208\) 0 0
\(209\) 13.9033 8.02707i 0.961711 0.555244i
\(210\) 0 0
\(211\) 3.74236 6.48196i 0.257635 0.446237i −0.707973 0.706240i \(-0.750390\pi\)
0.965608 + 0.260003i \(0.0837235\pi\)
\(212\) 0 0
\(213\) 10.0402 + 20.3946i 0.687946 + 1.39742i
\(214\) 0 0
\(215\) 8.32262 0.567598
\(216\) 0 0
\(217\) −8.01372 −0.544007
\(218\) 0 0
\(219\) −3.77117 7.66035i −0.254832 0.517639i
\(220\) 0 0
\(221\) −2.77218 + 4.80155i −0.186477 + 0.322987i
\(222\) 0 0
\(223\) 17.3052 9.99117i 1.15884 0.669058i 0.207816 0.978168i \(-0.433364\pi\)
0.951026 + 0.309110i \(0.100031\pi\)
\(224\) 0 0
\(225\) −7.60324 1.01154i −0.506883 0.0674361i
\(226\) 0 0
\(227\) 18.3301 10.5829i 1.21661 0.702409i 0.252417 0.967618i \(-0.418774\pi\)
0.964191 + 0.265209i \(0.0854410\pi\)
\(228\) 0 0
\(229\) 3.97745 + 2.29638i 0.262838 + 0.151749i 0.625628 0.780121i \(-0.284843\pi\)
−0.362791 + 0.931871i \(0.618176\pi\)
\(230\) 0 0
\(231\) 4.73814 + 0.313801i 0.311747 + 0.0206466i
\(232\) 0 0
\(233\) 19.1408i 1.25396i 0.779037 + 0.626979i \(0.215709\pi\)
−0.779037 + 0.626979i \(0.784291\pi\)
\(234\) 0 0
\(235\) 5.42262 0.353733
\(236\) 0 0
\(237\) 5.51775 + 3.69229i 0.358416 + 0.239840i
\(238\) 0 0
\(239\) −12.0889 + 20.9385i −0.781964 + 1.35440i 0.148832 + 0.988862i \(0.452449\pi\)
−0.930796 + 0.365539i \(0.880885\pi\)
\(240\) 0 0
\(241\) −5.04705 8.74174i −0.325109 0.563105i 0.656426 0.754391i \(-0.272068\pi\)
−0.981534 + 0.191286i \(0.938734\pi\)
\(242\) 0 0
\(243\) 11.7550 10.2381i 0.754084 0.656778i
\(244\) 0 0
\(245\) 4.52142 + 7.83133i 0.288863 + 0.500325i
\(246\) 0 0
\(247\) −35.4321 20.4568i −2.25449 1.30163i
\(248\) 0 0
\(249\) −18.6493 12.4795i −1.18185 0.790856i
\(250\) 0 0
\(251\) 17.6233i 1.11237i 0.831057 + 0.556187i \(0.187736\pi\)
−0.831057 + 0.556187i \(0.812264\pi\)
\(252\) 0 0
\(253\) 7.61058i 0.478473i
\(254\) 0 0
\(255\) −0.156481 + 2.36273i −0.00979920 + 0.147960i
\(256\) 0 0
\(257\) 16.6994 + 9.64142i 1.04168 + 0.601415i 0.920309 0.391192i \(-0.127937\pi\)
0.121372 + 0.992607i \(0.461271\pi\)
\(258\) 0 0
\(259\) 0.962399 + 1.66692i 0.0598005 + 0.103578i
\(260\) 0 0
\(261\) 4.56660 + 0.607544i 0.282666 + 0.0376061i
\(262\) 0 0
\(263\) 0.912358 + 1.58025i 0.0562584 + 0.0974424i 0.892783 0.450487i \(-0.148750\pi\)
−0.836525 + 0.547929i \(0.815416\pi\)
\(264\) 0 0
\(265\) −8.69977 + 15.0684i −0.534422 + 0.925647i
\(266\) 0 0
\(267\) 20.7232 10.2020i 1.26824 0.624352i
\(268\) 0 0
\(269\) −2.48843 −0.151722 −0.0758610 0.997118i \(-0.524171\pi\)
−0.0758610 + 0.997118i \(0.524171\pi\)
\(270\) 0 0
\(271\) 8.04111i 0.488463i 0.969717 + 0.244231i \(0.0785356\pi\)
−0.969717 + 0.244231i \(0.921464\pi\)
\(272\) 0 0
\(273\) −5.34494 10.8571i −0.323490 0.657103i
\(274\) 0 0
\(275\) −5.50769 3.17987i −0.332126 0.191753i
\(276\) 0 0
\(277\) 4.27917 2.47058i 0.257110 0.148443i −0.365905 0.930652i \(-0.619241\pi\)
0.623016 + 0.782209i \(0.285907\pi\)
\(278\) 0 0
\(279\) −20.1636 + 8.31984i −1.20717 + 0.498096i
\(280\) 0 0
\(281\) 12.4468 7.18614i 0.742511 0.428689i −0.0804703 0.996757i \(-0.525642\pi\)
0.822982 + 0.568068i \(0.192309\pi\)
\(282\) 0 0
\(283\) 16.3639 28.3432i 0.972736 1.68483i 0.285522 0.958372i \(-0.407833\pi\)
0.687214 0.726455i \(-0.258833\pi\)
\(284\) 0 0
\(285\) −17.4353 1.15472i −1.03278 0.0683996i
\(286\) 0 0
\(287\) −9.48571 −0.559924
\(288\) 0 0
\(289\) 16.2350 0.955002
\(290\) 0 0
\(291\) −8.96354 + 13.3951i −0.525452 + 0.785234i
\(292\) 0 0
\(293\) −2.68074 + 4.64317i −0.156610 + 0.271257i −0.933644 0.358202i \(-0.883390\pi\)
0.777034 + 0.629459i \(0.216723\pi\)
\(294\) 0 0
\(295\) −2.76332 + 1.59540i −0.160887 + 0.0928880i
\(296\) 0 0
\(297\) 12.2476 4.12957i 0.710679 0.239622i
\(298\) 0 0
\(299\) −16.7969 + 9.69767i −0.971387 + 0.560831i
\(300\) 0 0
\(301\) −5.08222 2.93422i −0.292934 0.169126i
\(302\) 0 0
\(303\) 17.6365 26.3559i 1.01319 1.51411i
\(304\) 0 0
\(305\) 11.2461i 0.643950i
\(306\) 0 0
\(307\) −11.1124 −0.634219 −0.317110 0.948389i \(-0.602712\pi\)
−0.317110 + 0.948389i \(0.602712\pi\)
\(308\) 0 0
\(309\) 1.86047 28.0916i 0.105838 1.59807i
\(310\) 0 0
\(311\) 10.4892 18.1679i 0.594790 1.03021i −0.398787 0.917044i \(-0.630569\pi\)
0.993576 0.113163i \(-0.0360981\pi\)
\(312\) 0 0
\(313\) −11.3679 19.6898i −0.642553 1.11293i −0.984861 0.173347i \(-0.944542\pi\)
0.342308 0.939588i \(-0.388791\pi\)
\(314\) 0 0
\(315\) −4.09604 3.15189i −0.230785 0.177589i
\(316\) 0 0
\(317\) −14.6224 25.3267i −0.821276 1.42249i −0.904733 0.425980i \(-0.859930\pi\)
0.0834573 0.996511i \(-0.473404\pi\)
\(318\) 0 0
\(319\) 3.30799 + 1.90987i 0.185212 + 0.106932i
\(320\) 0 0
\(321\) 9.01396 4.43755i 0.503110 0.247680i
\(322\) 0 0
\(323\) 5.64490i 0.314091i
\(324\) 0 0
\(325\) 16.2076i 0.899035i
\(326\) 0 0
\(327\) −11.4180 + 5.62105i −0.631416 + 0.310845i
\(328\) 0 0
\(329\) −3.31133 1.91180i −0.182559 0.105401i
\(330\) 0 0
\(331\) 13.2737 + 22.9908i 0.729591 + 1.26369i 0.957056 + 0.289903i \(0.0936229\pi\)
−0.227465 + 0.973786i \(0.573044\pi\)
\(332\) 0 0
\(333\) 4.15213 + 3.19505i 0.227535 + 0.175088i
\(334\) 0 0
\(335\) −1.78343 3.08899i −0.0974392 0.168770i
\(336\) 0 0
\(337\) 4.28240 7.41733i 0.233277 0.404048i −0.725493 0.688229i \(-0.758388\pi\)
0.958771 + 0.284181i \(0.0917217\pi\)
\(338\) 0 0
\(339\) 0.0344497 0.520163i 0.00187105 0.0282514i
\(340\) 0 0
\(341\) −18.0858 −0.979402
\(342\) 0 0
\(343\) 14.0914i 0.760866i
\(344\) 0 0
\(345\) −4.60674 + 6.88430i −0.248019 + 0.370638i
\(346\) 0 0
\(347\) 11.8860 + 6.86239i 0.638075 + 0.368393i 0.783872 0.620922i \(-0.213242\pi\)
−0.145798 + 0.989314i \(0.546575\pi\)
\(348\) 0 0
\(349\) −11.2390 + 6.48885i −0.601611 + 0.347340i −0.769675 0.638436i \(-0.779582\pi\)
0.168064 + 0.985776i \(0.446248\pi\)
\(350\) 0 0
\(351\) −24.7205 21.7689i −1.31948 1.16194i
\(352\) 0 0
\(353\) −22.9788 + 13.2668i −1.22304 + 0.706120i −0.965564 0.260166i \(-0.916223\pi\)
−0.257472 + 0.966286i \(0.582889\pi\)
\(354\) 0 0
\(355\) 10.2573 17.7662i 0.544401 0.942930i
\(356\) 0 0
\(357\) 0.928560 1.38764i 0.0491446 0.0734416i
\(358\) 0 0
\(359\) −5.61198 −0.296189 −0.148095 0.988973i \(-0.547314\pi\)
−0.148095 + 0.988973i \(0.547314\pi\)
\(360\) 0 0
\(361\) 22.6555 1.19239
\(362\) 0 0
\(363\) −8.31759 0.550863i −0.436560 0.0289128i
\(364\) 0 0
\(365\) −3.85270 + 6.67308i −0.201660 + 0.349285i
\(366\) 0 0
\(367\) 20.8358 12.0295i 1.08762 0.627937i 0.154677 0.987965i \(-0.450566\pi\)
0.932941 + 0.360029i \(0.117233\pi\)
\(368\) 0 0
\(369\) −23.8674 + 9.84806i −1.24249 + 0.512670i
\(370\) 0 0
\(371\) 10.6250 6.13437i 0.551625 0.318481i
\(372\) 0 0
\(373\) 14.8743 + 8.58769i 0.770163 + 0.444654i 0.832933 0.553374i \(-0.186660\pi\)
−0.0627699 + 0.998028i \(0.519993\pi\)
\(374\) 0 0
\(375\) 9.03617 + 18.3551i 0.466626 + 0.947853i
\(376\) 0 0
\(377\) 9.73448i 0.501351i
\(378\) 0 0
\(379\) −30.5262 −1.56803 −0.784013 0.620745i \(-0.786830\pi\)
−0.784013 + 0.620745i \(0.786830\pi\)
\(380\) 0 0
\(381\) −28.9820 + 14.2678i −1.48479 + 0.730961i
\(382\) 0 0
\(383\) 8.10743 14.0425i 0.414270 0.717537i −0.581081 0.813846i \(-0.697370\pi\)
0.995352 + 0.0963082i \(0.0307034\pi\)
\(384\) 0 0
\(385\) −2.14266 3.71119i −0.109200 0.189140i
\(386\) 0 0
\(387\) −15.8339 2.10655i −0.804881 0.107082i
\(388\) 0 0
\(389\) 12.8869 + 22.3207i 0.653391 + 1.13171i 0.982295 + 0.187343i \(0.0599877\pi\)
−0.328903 + 0.944364i \(0.606679\pi\)
\(390\) 0 0
\(391\) −2.31749 1.33800i −0.117200 0.0676657i
\(392\) 0 0
\(393\) −1.02505 + 15.4775i −0.0517070 + 0.780736i
\(394\) 0 0
\(395\) 5.99153i 0.301466i
\(396\) 0 0
\(397\) 9.36711i 0.470122i 0.971981 + 0.235061i \(0.0755290\pi\)
−0.971981 + 0.235061i \(0.924471\pi\)
\(398\) 0 0
\(399\) 10.2398 + 6.85213i 0.512631 + 0.343035i
\(400\) 0 0
\(401\) −4.16389 2.40402i −0.207935 0.120051i 0.392416 0.919788i \(-0.371639\pi\)
−0.600351 + 0.799736i \(0.704973\pi\)
\(402\) 0 0
\(403\) 23.0456 + 39.9161i 1.14798 + 1.98836i
\(404\) 0 0
\(405\) −13.5785 3.67809i −0.674720 0.182766i
\(406\) 0 0
\(407\) 2.17200 + 3.76201i 0.107662 + 0.186476i
\(408\) 0 0
\(409\) 18.1532 31.4422i 0.897616 1.55472i 0.0670820 0.997747i \(-0.478631\pi\)
0.830534 0.556968i \(-0.188036\pi\)
\(410\) 0 0
\(411\) 14.2919 + 9.56363i 0.704966 + 0.471739i
\(412\) 0 0
\(413\) 2.24990 0.110710
\(414\) 0 0
\(415\) 20.2506i 0.994065i
\(416\) 0 0
\(417\) 3.35570 + 0.222244i 0.164330 + 0.0108833i
\(418\) 0 0
\(419\) −7.72947 4.46261i −0.377609 0.218013i 0.299168 0.954200i \(-0.403291\pi\)
−0.676778 + 0.736188i \(0.736624\pi\)
\(420\) 0 0
\(421\) −0.670604 + 0.387173i −0.0326832 + 0.0188697i −0.516253 0.856436i \(-0.672673\pi\)
0.483569 + 0.875306i \(0.339340\pi\)
\(422\) 0 0
\(423\) −10.3166 1.37253i −0.501610 0.0667345i
\(424\) 0 0
\(425\) −1.93659 + 1.11809i −0.0939386 + 0.0542355i
\(426\) 0 0
\(427\) −3.96492 + 6.86744i −0.191876 + 0.332339i
\(428\) 0 0
\(429\) −12.0628 24.5030i −0.582396 1.18302i
\(430\) 0 0
\(431\) −20.8535 −1.00448 −0.502238 0.864730i \(-0.667490\pi\)
−0.502238 + 0.864730i \(0.667490\pi\)
\(432\) 0 0
\(433\) −5.02013 −0.241252 −0.120626 0.992698i \(-0.538490\pi\)
−0.120626 + 0.992698i \(0.538490\pi\)
\(434\) 0 0
\(435\) −1.83625 3.72996i −0.0880414 0.178838i
\(436\) 0 0
\(437\) 9.87354 17.1015i 0.472315 0.818074i
\(438\) 0 0
\(439\) −22.7559 + 13.1381i −1.08608 + 0.627049i −0.932530 0.361092i \(-0.882404\pi\)
−0.153550 + 0.988141i \(0.549071\pi\)
\(440\) 0 0
\(441\) −6.61985 16.0436i −0.315231 0.763982i
\(442\) 0 0
\(443\) 25.6178 14.7905i 1.21714 0.702716i 0.252835 0.967509i \(-0.418637\pi\)
0.964305 + 0.264793i \(0.0853037\pi\)
\(444\) 0 0
\(445\) −18.0524 10.4226i −0.855765 0.494076i
\(446\) 0 0
\(447\) 33.3888 + 2.21129i 1.57923 + 0.104591i
\(448\) 0 0
\(449\) 1.43585i 0.0677617i −0.999426 0.0338809i \(-0.989213\pi\)
0.999426 0.0338809i \(-0.0107867\pi\)
\(450\) 0 0
\(451\) −21.4079 −1.00806
\(452\) 0 0
\(453\) 16.4600 + 11.0145i 0.773359 + 0.517505i
\(454\) 0 0
\(455\) −5.46049 + 9.45785i −0.255992 + 0.443391i
\(456\) 0 0
\(457\) 2.66816 + 4.62138i 0.124811 + 0.216179i 0.921659 0.388001i \(-0.126834\pi\)
−0.796848 + 0.604180i \(0.793501\pi\)
\(458\) 0 0
\(459\) 0.895741 4.45552i 0.0418096 0.207966i
\(460\) 0 0
\(461\) −4.71373 8.16442i −0.219540 0.380255i 0.735127 0.677929i \(-0.237122\pi\)
−0.954668 + 0.297674i \(0.903789\pi\)
\(462\) 0 0
\(463\) 13.0444 + 7.53117i 0.606223 + 0.350003i 0.771486 0.636246i \(-0.219514\pi\)
−0.165262 + 0.986250i \(0.552847\pi\)
\(464\) 0 0
\(465\) 16.3599 + 10.9475i 0.758672 + 0.507677i
\(466\) 0 0
\(467\) 22.9660i 1.06274i 0.847140 + 0.531369i \(0.178322\pi\)
−0.847140 + 0.531369i \(0.821678\pi\)
\(468\) 0 0
\(469\) 2.51506i 0.116135i
\(470\) 0 0
\(471\) −2.02091 + 30.5142i −0.0931188 + 1.40602i
\(472\) 0 0
\(473\) −11.4698 6.62212i −0.527384 0.304485i
\(474\) 0 0
\(475\) −8.25075 14.2907i −0.378571 0.655703i
\(476\) 0 0
\(477\) 20.3654 26.4658i 0.932467 1.21179i
\(478\) 0 0
\(479\) 15.2716 + 26.4512i 0.697779 + 1.20859i 0.969235 + 0.246137i \(0.0791614\pi\)
−0.271456 + 0.962451i \(0.587505\pi\)
\(480\) 0 0
\(481\) 5.53527 9.58737i 0.252387 0.437146i
\(482\) 0 0
\(483\) 5.24024 2.57976i 0.238439 0.117383i
\(484\) 0 0
\(485\) 14.5453 0.660466
\(486\) 0 0
\(487\) 25.2482i 1.14411i 0.820217 + 0.572053i \(0.193853\pi\)
−0.820217 + 0.572053i \(0.806147\pi\)
\(488\) 0 0
\(489\) 4.31623 + 8.76753i 0.195187 + 0.396481i
\(490\) 0 0
\(491\) −28.5831 16.5025i −1.28994 0.744746i −0.311295 0.950313i \(-0.600763\pi\)
−0.978643 + 0.205568i \(0.934096\pi\)
\(492\) 0 0
\(493\) 1.16314 0.671541i 0.0523853 0.0302447i
\(494\) 0 0
\(495\) −9.24417 7.11336i −0.415495 0.319722i
\(496\) 0 0
\(497\) −12.5273 + 7.23262i −0.561924 + 0.324427i
\(498\) 0 0
\(499\) 8.61075 14.9143i 0.385470 0.667654i −0.606364 0.795187i \(-0.707373\pi\)
0.991834 + 0.127533i \(0.0407060\pi\)
\(500\) 0 0
\(501\) 40.2011 + 2.66246i 1.79605 + 0.118950i
\(502\) 0 0
\(503\) 39.7159 1.77084 0.885421 0.464789i \(-0.153870\pi\)
0.885421 + 0.464789i \(0.153870\pi\)
\(504\) 0 0
\(505\) −28.6189 −1.27353
\(506\) 0 0
\(507\) −26.1859 + 39.1322i −1.16296 + 1.73792i
\(508\) 0 0
\(509\) −16.7472 + 29.0071i −0.742309 + 1.28572i 0.209133 + 0.977887i \(0.432936\pi\)
−0.951442 + 0.307829i \(0.900398\pi\)
\(510\) 0 0
\(511\) 4.70532 2.71662i 0.208151 0.120176i
\(512\) 0 0
\(513\) 32.8787 + 6.60995i 1.45163 + 0.291836i
\(514\) 0 0
\(515\) −22.0029 + 12.7034i −0.969566 + 0.559779i
\(516\) 0 0
\(517\) −7.47320 4.31465i −0.328671 0.189758i
\(518\) 0 0
\(519\) 10.9663 16.3881i 0.481368 0.719356i
\(520\) 0 0
\(521\) 19.2115i 0.841671i 0.907137 + 0.420836i \(0.138263\pi\)
−0.907137 + 0.420836i \(0.861737\pi\)
\(522\) 0 0
\(523\) −21.9153 −0.958290 −0.479145 0.877736i \(-0.659053\pi\)
−0.479145 + 0.877736i \(0.659053\pi\)
\(524\) 0 0
\(525\) 0.322545 4.87018i 0.0140770 0.212552i
\(526\) 0 0
\(527\) −3.17964 + 5.50729i −0.138507 + 0.239901i
\(528\) 0 0
\(529\) 6.81938 + 11.8115i 0.296495 + 0.513544i
\(530\) 0 0
\(531\) 5.66106 2.33585i 0.245669 0.101367i
\(532\) 0 0
\(533\) 27.2787 + 47.2481i 1.18157 + 2.04654i
\(534\) 0 0
\(535\) −7.85223 4.53349i −0.339481 0.196000i
\(536\) 0 0
\(537\) 16.5935 8.16896i 0.716064 0.352517i
\(538\) 0 0
\(539\) 14.3904i 0.619837i
\(540\) 0 0
\(541\) 18.1171i 0.778913i −0.921045 0.389456i \(-0.872663\pi\)
0.921045 0.389456i \(-0.127337\pi\)
\(542\) 0 0
\(543\) 8.92959 4.39602i 0.383205 0.188651i
\(544\) 0 0
\(545\) 9.94643 + 5.74257i 0.426058 + 0.245985i
\(546\) 0 0
\(547\) −4.95910 8.58941i −0.212036 0.367257i 0.740316 0.672259i \(-0.234676\pi\)
−0.952352 + 0.305003i \(0.901343\pi\)
\(548\) 0 0
\(549\) −2.84652 + 21.3958i −0.121486 + 0.913151i
\(550\) 0 0
\(551\) 4.95551 + 8.58319i 0.211112 + 0.365656i
\(552\) 0 0
\(553\) −2.11237 + 3.65873i −0.0898271 + 0.155585i
\(554\) 0 0
\(555\) 0.312448 4.71773i 0.0132627 0.200256i
\(556\) 0 0
\(557\) 9.59817 0.406687 0.203344 0.979107i \(-0.434819\pi\)
0.203344 + 0.979107i \(0.434819\pi\)
\(558\) 0 0
\(559\) 33.7525i 1.42758i
\(560\) 0 0
\(561\) 2.09563 3.13170i 0.0884775 0.132221i
\(562\) 0 0
\(563\) −13.9909 8.07768i −0.589648 0.340433i 0.175310 0.984513i \(-0.443907\pi\)
−0.764958 + 0.644080i \(0.777240\pi\)
\(564\) 0 0
\(565\) −0.407422 + 0.235225i −0.0171404 + 0.00989599i
\(566\) 0 0
\(567\) 6.99497 + 7.03325i 0.293761 + 0.295369i
\(568\) 0 0
\(569\) −22.7099 + 13.1116i −0.952048 + 0.549665i −0.893717 0.448632i \(-0.851911\pi\)
−0.0583315 + 0.998297i \(0.518578\pi\)
\(570\) 0 0
\(571\) 3.52667 6.10837i 0.147587 0.255628i −0.782748 0.622338i \(-0.786183\pi\)
0.930335 + 0.366711i \(0.119516\pi\)
\(572\) 0 0
\(573\) 17.0967 25.5492i 0.714223 1.06733i
\(574\) 0 0
\(575\) −7.82266 −0.326227
\(576\) 0 0
\(577\) −19.1200 −0.795978 −0.397989 0.917390i \(-0.630292\pi\)
−0.397989 + 0.917390i \(0.630292\pi\)
\(578\) 0 0
\(579\) −36.5781 2.42252i −1.52013 0.100676i
\(580\) 0 0
\(581\) 7.13956 12.3661i 0.296199 0.513031i
\(582\) 0 0
\(583\) 23.9792 13.8444i 0.993118 0.573377i
\(584\) 0 0
\(585\) −3.92023 + 29.4664i −0.162081 + 1.21828i
\(586\) 0 0
\(587\) −20.9418 + 12.0908i −0.864361 + 0.499039i −0.865470 0.500960i \(-0.832980\pi\)
0.00110929 + 0.999999i \(0.499647\pi\)
\(588\) 0 0
\(589\) −40.6400 23.4635i −1.67454 0.966798i
\(590\) 0 0
\(591\) −4.22045 8.57296i −0.173606 0.352644i
\(592\) 0 0
\(593\) 15.8938i 0.652681i 0.945252 + 0.326340i \(0.105816\pi\)
−0.945252 + 0.326340i \(0.894184\pi\)
\(594\) 0 0
\(595\) −1.50679 −0.0617722
\(596\) 0 0
\(597\) 10.7288 5.28176i 0.439100 0.216168i
\(598\) 0 0
\(599\) −0.540573 + 0.936300i −0.0220872 + 0.0382562i −0.876858 0.480750i \(-0.840364\pi\)
0.854771 + 0.519006i \(0.173698\pi\)
\(600\) 0 0
\(601\) −7.09881 12.2955i −0.289566 0.501544i 0.684140 0.729351i \(-0.260178\pi\)
−0.973706 + 0.227807i \(0.926844\pi\)
\(602\) 0 0
\(603\) 2.61113 + 6.32824i 0.106334 + 0.257706i
\(604\) 0 0
\(605\) 3.76133 + 6.51482i 0.152920 + 0.264865i
\(606\) 0 0
\(607\) −3.34733 1.93258i −0.135864 0.0784411i 0.430527 0.902578i \(-0.358328\pi\)
−0.566391 + 0.824136i \(0.691661\pi\)
\(608\) 0 0
\(609\) −0.193725 + 2.92509i −0.00785011 + 0.118531i
\(610\) 0 0
\(611\) 21.9915i 0.889682i
\(612\) 0 0
\(613\) 5.87436i 0.237263i −0.992938 0.118632i \(-0.962149\pi\)
0.992938 0.118632i \(-0.0378507\pi\)
\(614\) 0 0
\(615\) 19.3649 + 12.9584i 0.780870 + 0.522532i
\(616\) 0 0
\(617\) 21.7236 + 12.5421i 0.874559 + 0.504927i 0.868860 0.495057i \(-0.164853\pi\)
0.00569811 + 0.999984i \(0.498186\pi\)
\(618\) 0 0
\(619\) 18.8316 + 32.6172i 0.756904 + 1.31100i 0.944422 + 0.328735i \(0.106622\pi\)
−0.187518 + 0.982261i \(0.560044\pi\)
\(620\) 0 0
\(621\) 10.5069 11.9314i 0.421626 0.478792i
\(622\) 0 0
\(623\) 7.34914 + 12.7291i 0.294437 + 0.509980i
\(624\) 0 0
\(625\) 2.83966 4.91844i 0.113586 0.196737i
\(626\) 0 0
\(627\) 23.1098 + 15.4643i 0.922916 + 0.617584i
\(628\) 0 0
\(629\) 1.52742 0.0609022
\(630\) 0 0
\(631\) 1.34576i 0.0535740i −0.999641 0.0267870i \(-0.991472\pi\)
0.999641 0.0267870i \(-0.00852759\pi\)
\(632\) 0 0
\(633\) 12.9356 + 0.856706i 0.514143 + 0.0340510i
\(634\) 0 0
\(635\) 25.2468 + 14.5762i 1.00189 + 0.578441i
\(636\) 0 0
\(637\) −31.7601 + 18.3367i −1.25838 + 0.726527i
\(638\) 0 0
\(639\) −24.0114 + 31.2041i −0.949878 + 1.23441i
\(640\) 0 0
\(641\) −12.5197 + 7.22823i −0.494497 + 0.285498i −0.726438 0.687232i \(-0.758826\pi\)
0.231941 + 0.972730i \(0.425492\pi\)
\(642\) 0 0
\(643\) −12.0008 + 20.7861i −0.473267 + 0.819722i −0.999532 0.0305983i \(-0.990259\pi\)
0.526265 + 0.850321i \(0.323592\pi\)
\(644\) 0 0
\(645\) 6.36686 + 12.9329i 0.250695 + 0.509234i
\(646\) 0 0
\(647\) −8.55443 −0.336309 −0.168155 0.985761i \(-0.553781\pi\)
−0.168155 + 0.985761i \(0.553781\pi\)
\(648\) 0 0
\(649\) 5.07771 0.199317
\(650\) 0 0
\(651\) −6.13055 12.4529i −0.240275 0.488069i
\(652\) 0 0
\(653\) −6.58668 + 11.4085i −0.257757 + 0.446448i −0.965641 0.259881i \(-0.916317\pi\)
0.707884 + 0.706329i \(0.249650\pi\)
\(654\) 0 0
\(655\) 12.1229 6.99914i 0.473679 0.273479i
\(656\) 0 0
\(657\) 9.01884 11.7204i 0.351859 0.457258i
\(658\) 0 0
\(659\) −10.6191 + 6.13093i −0.413661 + 0.238827i −0.692361 0.721551i \(-0.743430\pi\)
0.278701 + 0.960378i \(0.410096\pi\)
\(660\) 0 0
\(661\) −12.6734 7.31697i −0.492937 0.284597i 0.232855 0.972511i \(-0.425193\pi\)
−0.725792 + 0.687914i \(0.758526\pi\)
\(662\) 0 0
\(663\) −9.58211 0.634610i −0.372138 0.0246462i
\(664\) 0 0
\(665\) 11.1190i 0.431178i
\(666\) 0 0
\(667\) 4.69838 0.181922
\(668\) 0 0
\(669\) 28.7644 + 19.2482i 1.11210 + 0.744177i
\(670\) 0 0
\(671\) −8.94826 + 15.4988i −0.345444 + 0.598326i
\(672\) 0 0
\(673\) −6.35891 11.0140i −0.245118 0.424557i 0.717047 0.697025i \(-0.245493\pi\)
−0.962165 + 0.272468i \(0.912160\pi\)
\(674\) 0 0
\(675\) −4.24465 12.5889i −0.163376 0.484547i
\(676\) 0 0
\(677\) 13.3262 + 23.0816i 0.512167 + 0.887099i 0.999901 + 0.0141062i \(0.00449029\pi\)
−0.487734 + 0.872992i \(0.662176\pi\)
\(678\) 0 0
\(679\) −8.88207 5.12807i −0.340863 0.196797i
\(680\) 0 0
\(681\) 30.4679 + 20.3881i 1.16753 + 0.781272i
\(682\) 0 0
\(683\) 22.4974i 0.860841i 0.902629 + 0.430420i \(0.141635\pi\)
−0.902629 + 0.430420i \(0.858365\pi\)
\(684\) 0 0
\(685\) 15.5190i 0.592951i
\(686\) 0 0
\(687\) −0.525691 + 7.93752i −0.0200564 + 0.302835i
\(688\) 0 0
\(689\) −61.1103 35.2821i −2.32812 1.34414i
\(690\) 0 0
\(691\) −5.25993 9.11047i −0.200097 0.346579i 0.748462 0.663177i \(-0.230793\pi\)
−0.948560 + 0.316599i \(0.897459\pi\)
\(692\) 0 0
\(693\) 3.13708 + 7.60290i 0.119168 + 0.288810i
\(694\) 0 0
\(695\) −1.51750 2.62838i −0.0575619 0.0997002i
\(696\) 0 0
\(697\) −3.76369 + 6.51890i −0.142560 + 0.246921i
\(698\) 0 0
\(699\) −29.7439 + 14.6429i −1.12502 + 0.553844i
\(700\) 0 0
\(701\) 30.8786 1.16627 0.583134 0.812376i \(-0.301826\pi\)
0.583134 + 0.812376i \(0.301826\pi\)
\(702\) 0 0
\(703\) 11.2713i 0.425105i
\(704\) 0 0
\(705\) 4.14834 + 8.42648i 0.156235 + 0.317360i
\(706\) 0 0
\(707\) 17.4762 + 10.0899i 0.657259 + 0.379469i
\(708\) 0 0
\(709\) −8.71948 + 5.03419i −0.327467 + 0.189063i −0.654716 0.755875i \(-0.727212\pi\)
0.327249 + 0.944938i \(0.393878\pi\)
\(710\) 0 0
\(711\) −1.51652 + 11.3989i −0.0568741 + 0.427494i
\(712\) 0 0
\(713\) −19.2657 + 11.1230i −0.721506 + 0.416561i
\(714\) 0 0
\(715\) −12.3236 + 21.3450i −0.460875 + 0.798259i
\(716\) 0 0
\(717\) −41.7855 2.76740i −1.56051 0.103350i
\(718\) 0 0
\(719\) 2.52664 0.0942280 0.0471140 0.998890i \(-0.484998\pi\)
0.0471140 + 0.998890i \(0.484998\pi\)
\(720\) 0 0
\(721\) 17.9148 0.667183
\(722\) 0 0
\(723\) 9.72322 14.5304i 0.361610 0.540390i
\(724\) 0 0
\(725\) 1.96309 3.40017i 0.0729072 0.126279i
\(726\) 0 0
\(727\) 30.9471 17.8673i 1.14776 0.662662i 0.199423 0.979914i \(-0.436093\pi\)
0.948341 + 0.317252i \(0.102760\pi\)
\(728\) 0 0
\(729\) 24.9022 + 10.4345i 0.922305 + 0.386462i
\(730\) 0 0
\(731\) −4.03299 + 2.32845i −0.149165 + 0.0861207i
\(732\) 0 0
\(733\) 3.78054 + 2.18269i 0.139637 + 0.0806196i 0.568191 0.822897i \(-0.307643\pi\)
−0.428554 + 0.903516i \(0.640977\pi\)
\(734\) 0 0
\(735\) −8.71059 + 13.0171i −0.321295 + 0.480143i
\(736\) 0 0
\(737\) 5.67614i 0.209083i
\(738\) 0 0
\(739\) −40.4265 −1.48711 −0.743556 0.668674i \(-0.766862\pi\)
−0.743556 + 0.668674i \(0.766862\pi\)
\(740\) 0 0
\(741\) 4.68298 70.7094i 0.172034 2.59757i
\(742\) 0 0
\(743\) 9.83837 17.0406i 0.360935 0.625158i −0.627180 0.778874i \(-0.715791\pi\)
0.988115 + 0.153717i \(0.0491243\pi\)
\(744\) 0 0
\(745\) −15.0989 26.1520i −0.553180 0.958136i
\(746\) 0 0
\(747\) 5.12567 38.5270i 0.187538 1.40963i
\(748\) 0 0
\(749\) 3.19665 + 5.53676i 0.116803 + 0.202309i
\(750\) 0 0
\(751\) −26.3391 15.2069i −0.961126 0.554906i −0.0646065 0.997911i \(-0.520579\pi\)
−0.896519 + 0.443005i \(0.853913\pi\)
\(752\) 0 0
\(753\) −27.3858 + 13.4820i −0.997994 + 0.491310i
\(754\) 0 0
\(755\) 17.8733i 0.650477i
\(756\) 0 0
\(757\) 5.71127i 0.207580i 0.994599 + 0.103790i \(0.0330969\pi\)
−0.994599 + 0.103790i \(0.966903\pi\)
\(758\) 0 0
\(759\) 11.8265 5.82214i 0.429274 0.211330i
\(760\) 0 0
\(761\) −32.8500 18.9660i −1.19081 0.687516i −0.232322 0.972639i \(-0.574632\pi\)
−0.958491 + 0.285123i \(0.907966\pi\)
\(762\) 0 0
\(763\) −4.04920 7.01342i −0.146591 0.253903i
\(764\) 0 0
\(765\) −3.79128 + 1.56434i −0.137074 + 0.0565590i
\(766\) 0 0
\(767\) −6.47019 11.2067i −0.233625 0.404651i
\(768\) 0 0
\(769\) 20.7986 36.0243i 0.750018 1.29907i −0.197795 0.980243i \(-0.563378\pi\)
0.947813 0.318826i \(-0.103289\pi\)
\(770\) 0 0
\(771\) −2.20712 + 33.3258i −0.0794876 + 1.20020i
\(772\) 0 0
\(773\) −20.0762 −0.722090 −0.361045 0.932548i \(-0.617580\pi\)
−0.361045 + 0.932548i \(0.617580\pi\)
\(774\) 0 0
\(775\) 18.5898i 0.667765i
\(776\) 0 0
\(777\) −1.85408 + 2.77073i −0.0665146 + 0.0993993i
\(778\) 0 0
\(779\) −48.1049 27.7734i −1.72354 0.995085i
\(780\) 0 0
\(781\) −28.2723 + 16.3230i −1.01166 + 0.584083i
\(782\) 0 0
\(783\) 2.54939 + 7.56106i 0.0911077 + 0.270210i
\(784\) 0 0
\(785\) 23.9005 13.7990i 0.853045 0.492506i
\(786\) 0 0
\(787\) −4.62218 + 8.00585i −0.164763 + 0.285378i −0.936571 0.350478i \(-0.886019\pi\)
0.771808 + 0.635855i \(0.219353\pi\)
\(788\) 0 0
\(789\) −1.75767 + 2.62666i −0.0625748 + 0.0935116i
\(790\) 0 0
\(791\) 0.331723 0.0117947
\(792\) 0 0
\(793\) 45.6088 1.61961
\(794\) 0 0
\(795\) −30.0710 1.99156i −1.06651 0.0706334i
\(796\) 0 0
\(797\) −5.18050 + 8.97288i −0.183503 + 0.317836i −0.943071 0.332592i \(-0.892077\pi\)