Properties

Label 3528.2.s.o.3313.1
Level $3528$
Weight $2$
Character 3528.3313
Analytic conductor $28.171$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3528.s (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.1712218331\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 3313.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 3528.3313
Dual form 3528.2.s.o.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{5} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{11} -2.00000 q^{13} +(-1.50000 - 2.59808i) q^{17} +(2.50000 - 4.33013i) q^{19} +(-1.50000 + 2.59808i) q^{23} +(2.00000 + 3.46410i) q^{25} +6.00000 q^{29} +(-0.500000 - 0.866025i) q^{31} +(2.50000 - 4.33013i) q^{37} -10.0000 q^{41} -4.00000 q^{43} +(-0.500000 + 0.866025i) q^{47} +(-4.50000 - 7.79423i) q^{53} -1.00000 q^{55} +(-1.50000 - 2.59808i) q^{59} +(1.50000 - 2.59808i) q^{61} +(-1.00000 + 1.73205i) q^{65} +(-5.50000 - 9.52628i) q^{67} -16.0000 q^{71} +(3.50000 + 6.06218i) q^{73} +(5.50000 - 9.52628i) q^{79} -4.00000 q^{83} -3.00000 q^{85} +(4.50000 - 7.79423i) q^{89} +(-2.50000 - 4.33013i) q^{95} -6.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{5} + O(q^{10}) \) \( 2q + q^{5} - q^{11} - 4q^{13} - 3q^{17} + 5q^{19} - 3q^{23} + 4q^{25} + 12q^{29} - q^{31} + 5q^{37} - 20q^{41} - 8q^{43} - q^{47} - 9q^{53} - 2q^{55} - 3q^{59} + 3q^{61} - 2q^{65} - 11q^{67} - 32q^{71} + 7q^{73} + 11q^{79} - 8q^{83} - 6q^{85} + 9q^{89} - 5q^{95} - 12q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3528\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\) \(1765\) \(2647\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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 0
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i −0.732294 0.680989i \(-0.761550\pi\)
0.955901 + 0.293691i \(0.0948835\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.500000 0.866025i −0.150756 0.261116i 0.780750 0.624844i \(-0.214837\pi\)
−0.931505 + 0.363727i \(0.881504\pi\)
\(12\) 0 0
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 0 0
\(19\) 2.50000 4.33013i 0.573539 0.993399i −0.422659 0.906289i \(-0.638903\pi\)
0.996199 0.0871106i \(-0.0277634\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.50000 + 2.59808i −0.312772 + 0.541736i −0.978961 0.204046i \(-0.934591\pi\)
0.666190 + 0.745782i \(0.267924\pi\)
\(24\) 0 0
\(25\) 2.00000 + 3.46410i 0.400000 + 0.692820i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) −0.500000 0.866025i −0.0898027 0.155543i 0.817625 0.575751i \(-0.195290\pi\)
−0.907428 + 0.420208i \(0.861957\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.50000 4.33013i 0.410997 0.711868i −0.584002 0.811752i \(-0.698514\pi\)
0.994999 + 0.0998840i \(0.0318472\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −0.500000 + 0.866025i −0.0729325 + 0.126323i −0.900185 0.435507i \(-0.856569\pi\)
0.827253 + 0.561830i \(0.189902\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.50000 7.79423i −0.618123 1.07062i −0.989828 0.142269i \(-0.954560\pi\)
0.371706 0.928351i \(-0.378773\pi\)
\(54\) 0 0
\(55\) −1.00000 −0.134840
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.50000 2.59808i −0.195283 0.338241i 0.751710 0.659494i \(-0.229229\pi\)
−0.946993 + 0.321253i \(0.895896\pi\)
\(60\) 0 0
\(61\) 1.50000 2.59808i 0.192055 0.332650i −0.753876 0.657017i \(-0.771818\pi\)
0.945931 + 0.324367i \(0.105151\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.00000 + 1.73205i −0.124035 + 0.214834i
\(66\) 0 0
\(67\) −5.50000 9.52628i −0.671932 1.16382i −0.977356 0.211604i \(-0.932131\pi\)
0.305424 0.952217i \(-0.401202\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −16.0000 −1.89885 −0.949425 0.313993i \(-0.898333\pi\)
−0.949425 + 0.313993i \(0.898333\pi\)
\(72\) 0 0
\(73\) 3.50000 + 6.06218i 0.409644 + 0.709524i 0.994850 0.101361i \(-0.0323196\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 5.50000 9.52628i 0.618798 1.07179i −0.370907 0.928670i \(-0.620953\pi\)
0.989705 0.143120i \(-0.0457135\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) −3.00000 −0.325396
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 4.50000 7.79423i 0.476999 0.826187i −0.522654 0.852545i \(-0.675058\pi\)
0.999653 + 0.0263586i \(0.00839118\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.50000 4.33013i −0.256495 0.444262i
\(96\) 0 0
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 6.50000 + 11.2583i 0.646774 + 1.12025i 0.983889 + 0.178782i \(0.0572157\pi\)
−0.337115 + 0.941464i \(0.609451\pi\)
\(102\) 0 0
\(103\) 2.50000 4.33013i 0.246332 0.426660i −0.716173 0.697923i \(-0.754108\pi\)
0.962505 + 0.271263i \(0.0874412\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.50000 + 2.59808i −0.145010 + 0.251166i −0.929377 0.369132i \(-0.879655\pi\)
0.784366 + 0.620298i \(0.212988\pi\)
\(108\) 0 0
\(109\) −5.50000 9.52628i −0.526804 0.912452i −0.999512 0.0312328i \(-0.990057\pi\)
0.472708 0.881219i \(-0.343277\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 10.0000 0.940721 0.470360 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) 0 0
\(115\) 1.50000 + 2.59808i 0.139876 + 0.242272i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −8.50000 + 14.7224i −0.742648 + 1.28630i 0.208637 + 0.977993i \(0.433097\pi\)
−0.951285 + 0.308312i \(0.900236\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.50000 + 2.59808i 0.128154 + 0.221969i 0.922961 0.384893i \(-0.125762\pi\)
−0.794808 + 0.606861i \(0.792428\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1.00000 + 1.73205i 0.0836242 + 0.144841i
\(144\) 0 0
\(145\) 3.00000 5.19615i 0.249136 0.431517i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 7.50000 12.9904i 0.614424 1.06421i −0.376061 0.926595i \(-0.622722\pi\)
0.990485 0.137619i \(-0.0439449\pi\)
\(150\) 0 0
\(151\) −7.50000 12.9904i −0.610341 1.05714i −0.991183 0.132502i \(-0.957699\pi\)
0.380841 0.924640i \(-0.375634\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.00000 −0.0803219
\(156\) 0 0
\(157\) 7.50000 + 12.9904i 0.598565 + 1.03675i 0.993033 + 0.117836i \(0.0375956\pi\)
−0.394468 + 0.918910i \(0.629071\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −4.50000 + 7.79423i −0.352467 + 0.610491i −0.986681 0.162667i \(-0.947991\pi\)
0.634214 + 0.773158i \(0.281324\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −20.0000 −1.54765 −0.773823 0.633402i \(-0.781658\pi\)
−0.773823 + 0.633402i \(0.781658\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 10.5000 18.1865i 0.798300 1.38270i −0.122422 0.992478i \(-0.539066\pi\)
0.920722 0.390218i \(-0.127601\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −0.500000 0.866025i −0.0373718 0.0647298i 0.846735 0.532016i \(-0.178565\pi\)
−0.884106 + 0.467286i \(0.845232\pi\)
\(180\) 0 0
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2.50000 4.33013i −0.183804 0.318357i
\(186\) 0 0
\(187\) −1.50000 + 2.59808i −0.109691 + 0.189990i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 8.50000 14.7224i 0.615038 1.06528i −0.375339 0.926887i \(-0.622474\pi\)
0.990378 0.138390i \(-0.0441928\pi\)
\(192\) 0 0
\(193\) 2.50000 + 4.33013i 0.179954 + 0.311689i 0.941865 0.335993i \(-0.109072\pi\)
−0.761911 + 0.647682i \(0.775738\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) −4.50000 7.79423i −0.318997 0.552518i 0.661282 0.750137i \(-0.270013\pi\)
−0.980279 + 0.197619i \(0.936679\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −5.00000 + 8.66025i −0.349215 + 0.604858i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −5.00000 −0.345857
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2.00000 + 3.46410i −0.136399 + 0.236250i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 3.00000 + 5.19615i 0.201802 + 0.349531i
\(222\) 0 0
\(223\) −24.0000 −1.60716 −0.803579 0.595198i \(-0.797074\pi\)
−0.803579 + 0.595198i \(0.797074\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −3.50000 6.06218i −0.232303 0.402361i 0.726182 0.687502i \(-0.241293\pi\)
−0.958485 + 0.285141i \(0.907959\pi\)
\(228\) 0 0
\(229\) 3.50000 6.06218i 0.231287 0.400600i −0.726900 0.686743i \(-0.759040\pi\)
0.958187 + 0.286143i \(0.0923732\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −6.50000 + 11.2583i −0.425829 + 0.737558i −0.996497 0.0836229i \(-0.973351\pi\)
0.570668 + 0.821181i \(0.306684\pi\)
\(234\) 0 0
\(235\) 0.500000 + 0.866025i 0.0326164 + 0.0564933i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4.00000 0.258738 0.129369 0.991596i \(-0.458705\pi\)
0.129369 + 0.991596i \(0.458705\pi\)
\(240\) 0 0
\(241\) −8.50000 14.7224i −0.547533 0.948355i −0.998443 0.0557856i \(-0.982234\pi\)
0.450910 0.892570i \(-0.351100\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −5.00000 + 8.66025i −0.318142 + 0.551039i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 24.0000 1.51487 0.757433 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 0 0
\(253\) 3.00000 0.188608
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.50000 11.2583i 0.405459 0.702275i −0.588916 0.808194i \(-0.700445\pi\)
0.994375 + 0.105919i \(0.0337784\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.50000 + 2.59808i 0.0924940 + 0.160204i 0.908560 0.417755i \(-0.137183\pi\)
−0.816066 + 0.577959i \(0.803849\pi\)
\(264\) 0 0
\(265\) −9.00000 −0.552866
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 8.50000 + 14.7224i 0.518254 + 0.897643i 0.999775 + 0.0212079i \(0.00675120\pi\)
−0.481521 + 0.876435i \(0.659915\pi\)
\(270\) 0 0
\(271\) −1.50000 + 2.59808i −0.0911185 + 0.157822i −0.907982 0.419009i \(-0.862378\pi\)
0.816864 + 0.576831i \(0.195711\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.00000 3.46410i 0.120605 0.208893i
\(276\) 0 0
\(277\) −3.50000 6.06218i −0.210295 0.364241i 0.741512 0.670940i \(-0.234109\pi\)
−0.951807 + 0.306699i \(0.900776\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 0 0
\(283\) −8.50000 14.7224i −0.505273 0.875158i −0.999981 0.00609896i \(-0.998059\pi\)
0.494709 0.869059i \(-0.335275\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 0 0
\(295\) −3.00000 −0.174667
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3.00000 5.19615i 0.173494 0.300501i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.50000 2.59808i −0.0858898 0.148765i
\(306\) 0 0
\(307\) −4.00000 −0.228292 −0.114146 0.993464i \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −5.50000 9.52628i −0.311876 0.540186i 0.666892 0.745154i \(-0.267624\pi\)
−0.978769 + 0.204968i \(0.934291\pi\)
\(312\) 0 0
\(313\) 15.5000 26.8468i 0.876112 1.51747i 0.0205381 0.999789i \(-0.493462\pi\)
0.855574 0.517681i \(-0.173205\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 13.5000 23.3827i 0.758236 1.31330i −0.185514 0.982642i \(-0.559395\pi\)
0.943750 0.330661i \(-0.107272\pi\)
\(318\) 0 0
\(319\) −3.00000 5.19615i −0.167968 0.290929i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −15.0000 −0.834622
\(324\) 0 0
\(325\) −4.00000 6.92820i −0.221880 0.384308i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 3.50000 6.06218i 0.192377 0.333207i −0.753660 0.657264i \(-0.771714\pi\)
0.946038 + 0.324057i \(0.105047\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −11.0000 −0.600994
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −0.500000 + 0.866025i −0.0270765 + 0.0468979i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.50000 + 2.59808i 0.0805242 + 0.139472i 0.903475 0.428640i \(-0.141007\pi\)
−0.822951 + 0.568112i \(0.807674\pi\)
\(348\) 0 0
\(349\) 6.00000 0.321173 0.160586 0.987022i \(-0.448662\pi\)
0.160586 + 0.987022i \(0.448662\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.50000 + 4.33013i 0.133062 + 0.230469i 0.924855 0.380319i \(-0.124186\pi\)
−0.791794 + 0.610789i \(0.790853\pi\)
\(354\) 0 0
\(355\) −8.00000 + 13.8564i −0.424596 + 0.735422i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −7.50000 + 12.9904i −0.395835 + 0.685606i −0.993207 0.116358i \(-0.962878\pi\)
0.597372 + 0.801964i \(0.296211\pi\)
\(360\) 0 0
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 7.00000 0.366397
\(366\) 0 0
\(367\) 9.50000 + 16.4545i 0.495896 + 0.858917i 0.999989 0.00473247i \(-0.00150640\pi\)
−0.504093 + 0.863649i \(0.668173\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −9.50000 + 16.4545i −0.491891 + 0.851981i −0.999956 0.00933789i \(-0.997028\pi\)
0.508065 + 0.861319i \(0.330361\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −4.50000 + 7.79423i −0.229939 + 0.398266i −0.957790 0.287469i \(-0.907186\pi\)
0.727851 + 0.685736i \(0.240519\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 9.50000 + 16.4545i 0.481669 + 0.834275i 0.999779 0.0210389i \(-0.00669738\pi\)
−0.518110 + 0.855314i \(0.673364\pi\)
\(390\) 0 0
\(391\) 9.00000 0.455150
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −5.50000 9.52628i −0.276735 0.479319i
\(396\) 0 0
\(397\) −8.50000 + 14.7224i −0.426603 + 0.738898i −0.996569 0.0827707i \(-0.973623\pi\)
0.569966 + 0.821668i \(0.306956\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.50000 2.59808i 0.0749064 0.129742i −0.826139 0.563466i \(-0.809468\pi\)
0.901046 + 0.433724i \(0.142801\pi\)
\(402\) 0 0
\(403\) 1.00000 + 1.73205i 0.0498135 + 0.0862796i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −5.00000 −0.247841
\(408\) 0 0
\(409\) 9.50000 + 16.4545i 0.469745 + 0.813622i 0.999402 0.0345902i \(-0.0110126\pi\)
−0.529657 + 0.848212i \(0.677679\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −2.00000 + 3.46410i −0.0981761 + 0.170046i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 20.0000 0.977064 0.488532 0.872546i \(-0.337533\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 6.00000 10.3923i 0.291043 0.504101i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −20.5000 35.5070i −0.987450 1.71031i −0.630497 0.776192i \(-0.717149\pi\)
−0.356953 0.934122i \(-0.616185\pi\)
\(432\) 0 0
\(433\) 26.0000 1.24948 0.624740 0.780833i \(-0.285205\pi\)
0.624740 + 0.780833i \(0.285205\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.50000 + 12.9904i 0.358774 + 0.621414i
\(438\) 0 0
\(439\) −7.50000 + 12.9904i −0.357955 + 0.619997i −0.987619 0.156871i \(-0.949859\pi\)
0.629664 + 0.776868i \(0.283193\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −13.5000 + 23.3827i −0.641404 + 1.11094i 0.343715 + 0.939074i \(0.388315\pi\)
−0.985119 + 0.171871i \(0.945019\pi\)
\(444\) 0 0
\(445\) −4.50000 7.79423i −0.213320 0.369482i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) 0 0
\(451\) 5.00000 + 8.66025i 0.235441 + 0.407795i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 8.50000 14.7224i 0.397613 0.688686i −0.595818 0.803120i \(-0.703172\pi\)
0.993431 + 0.114433i \(0.0365053\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −6.00000 −0.279448 −0.139724 0.990190i \(-0.544622\pi\)
−0.139724 + 0.990190i \(0.544622\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −12.5000 + 21.6506i −0.578431 + 1.00187i 0.417229 + 0.908802i \(0.363001\pi\)
−0.995660 + 0.0930703i \(0.970332\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2.00000 + 3.46410i 0.0919601 + 0.159280i
\(474\) 0 0
\(475\) 20.0000 0.917663
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 10.5000 + 18.1865i 0.479757 + 0.830964i 0.999730 0.0232187i \(-0.00739140\pi\)
−0.519973 + 0.854183i \(0.674058\pi\)
\(480\) 0 0
\(481\) −5.00000 + 8.66025i −0.227980 + 0.394874i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −3.00000 + 5.19615i −0.136223 + 0.235945i
\(486\) 0 0
\(487\) 6.50000 + 11.2583i 0.294543 + 0.510164i 0.974879 0.222737i \(-0.0714992\pi\)
−0.680335 + 0.732901i \(0.738166\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) −9.00000 15.5885i −0.405340 0.702069i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 3.50000 6.06218i 0.156682 0.271380i −0.776989 0.629515i \(-0.783254\pi\)
0.933670 + 0.358134i \(0.116587\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 16.0000 0.713405 0.356702 0.934218i \(-0.383901\pi\)
0.356702 + 0.934218i \(0.383901\pi\)
\(504\) 0 0
\(505\) 13.0000 0.578492
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −3.50000 + 6.06218i −0.155135 + 0.268701i −0.933108 0.359596i \(-0.882915\pi\)
0.777973 + 0.628297i \(0.216248\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2.50000 4.33013i −0.110163 0.190808i
\(516\) 0 0
\(517\) 1.00000 0.0439799
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −7.50000 12.9904i −0.328581 0.569119i 0.653650 0.756797i \(-0.273237\pi\)
−0.982231 + 0.187678i \(0.939904\pi\)
\(522\) 0 0
\(523\) 6.50000 11.2583i 0.284225 0.492292i −0.688196 0.725525i \(-0.741597\pi\)
0.972421 + 0.233233i \(0.0749303\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.50000 + 2.59808i −0.0653410 + 0.113174i
\(528\) 0 0
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 20.0000 0.866296
\(534\) 0 0
\(535\) 1.50000 + 2.59808i 0.0648507 + 0.112325i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 12.5000 21.6506i 0.537417 0.930834i −0.461625 0.887075i \(-0.652733\pi\)
0.999042 0.0437584i \(-0.0139332\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −11.0000 −0.471188
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 15.0000 25.9808i 0.639021 1.10682i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 5.50000 + 9.52628i 0.233042 + 0.403641i 0.958702 0.284413i \(-0.0917985\pi\)
−0.725660 + 0.688054i \(0.758465\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −5.50000 9.52628i −0.231797 0.401485i 0.726540 0.687124i \(-0.241127\pi\)
−0.958337 + 0.285640i \(0.907794\pi\)
\(564\) 0 0
\(565\) 5.00000 8.66025i 0.210352 0.364340i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −0.500000 + 0.866025i −0.0209611 + 0.0363057i −0.876316 0.481737i \(-0.840006\pi\)
0.855355 + 0.518043i \(0.173339\pi\)
\(570\) 0 0
\(571\) 8.50000 + 14.7224i 0.355714 + 0.616115i 0.987240 0.159240i \(-0.0509044\pi\)
−0.631526 + 0.775355i \(0.717571\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −12.0000 −0.500435
\(576\) 0 0
\(577\) 15.5000 + 26.8468i 0.645273 + 1.11765i 0.984238 + 0.176847i \(0.0565899\pi\)
−0.338965 + 0.940799i \(0.610077\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −4.50000 + 7.79423i −0.186371 + 0.322804i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 0 0
\(589\) −5.00000 −0.206021
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −21.5000 + 37.2391i −0.882899 + 1.52923i −0.0347964 + 0.999394i \(0.511078\pi\)
−0.848103 + 0.529832i \(0.822255\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −10.5000 18.1865i −0.429018 0.743082i 0.567768 0.823189i \(-0.307807\pi\)
−0.996786 + 0.0801071i \(0.974474\pi\)
\(600\) 0 0
\(601\) 34.0000 1.38689 0.693444 0.720510i \(-0.256092\pi\)
0.693444 + 0.720510i \(0.256092\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −5.00000 8.66025i −0.203279 0.352089i
\(606\) 0 0
\(607\) −3.50000 + 6.06218i −0.142061 + 0.246056i −0.928272 0.371901i \(-0.878706\pi\)
0.786212 + 0.617957i \(0.212039\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.00000 1.73205i 0.0404557 0.0700713i
\(612\) 0 0
\(613\) 10.5000 + 18.1865i 0.424091 + 0.734547i 0.996335 0.0855362i \(-0.0272603\pi\)
−0.572244 + 0.820083i \(0.693927\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −22.0000 −0.885687 −0.442843 0.896599i \(-0.646030\pi\)
−0.442843 + 0.896599i \(0.646030\pi\)
\(618\) 0 0
\(619\) −2.50000 4.33013i −0.100483 0.174042i 0.811400 0.584491i \(-0.198706\pi\)
−0.911884 + 0.410448i \(0.865372\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −5.50000 + 9.52628i −0.220000 + 0.381051i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −15.0000 −0.598089
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −4.00000 + 6.92820i −0.158735 + 0.274937i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 7.50000 + 12.9904i 0.296232 + 0.513089i 0.975271 0.221013i \(-0.0709364\pi\)
−0.679039 + 0.734103i \(0.737603\pi\)
\(642\) 0 0
\(643\) 44.0000 1.73519 0.867595 0.497271i \(-0.165665\pi\)
0.867595 + 0.497271i \(0.165665\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −21.5000 37.2391i −0.845252 1.46402i −0.885402 0.464826i \(-0.846117\pi\)
0.0401498 0.999194i \(-0.487216\pi\)
\(648\) 0 0
\(649\) −1.50000 + 2.59808i −0.0588802 + 0.101983i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −2.50000 + 4.33013i −0.0978326 + 0.169451i −0.910787 0.412876i \(-0.864524\pi\)
0.812955 + 0.582327i \(0.197858\pi\)
\(654\) 0 0
\(655\) 8.50000 + 14.7224i 0.332122 + 0.575253i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0 0
\(661\) −0.500000 0.866025i −0.0194477 0.0336845i 0.856138 0.516748i \(-0.172857\pi\)
−0.875585 + 0.483063i \(0.839524\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −9.00000 + 15.5885i −0.348481 + 0.603587i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −3.00000 −0.115814
\(672\) 0 0
\(673\) −2.00000 −0.0770943 −0.0385472 0.999257i \(-0.512273\pi\)
−0.0385472 + 0.999257i \(0.512273\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.50000 7.79423i 0.172949 0.299557i −0.766501 0.642244i \(-0.778004\pi\)
0.939450 + 0.342687i \(0.111337\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 19.5000 + 33.7750i 0.746147 + 1.29236i 0.949657 + 0.313291i \(0.101432\pi\)
−0.203510 + 0.979073i \(0.565235\pi\)
\(684\) 0 0
\(685\) 3.00000 0.114624
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 9.00000 + 15.5885i 0.342873 + 0.593873i
\(690\) 0 0
\(691\) −23.5000 + 40.7032i −0.893982 + 1.54842i −0.0589228 + 0.998263i \(0.518767\pi\)
−0.835059 + 0.550160i \(0.814567\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.00000 + 3.46410i −0.0758643 + 0.131401i
\(696\) 0 0
\(697\) 15.0000 + 25.9808i 0.568166 + 0.984092i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) −12.5000 21.6506i −0.471446 0.816569i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −13.5000 + 23.3827i −0.507003 + 0.878155i 0.492964 + 0.870050i \(0.335913\pi\)
−0.999967 + 0.00810550i \(0.997420\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 3.00000 0.112351
\(714\) 0 0
\(715\) 2.00000 0.0747958
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −14.5000 + 25.1147i −0.540759 + 0.936622i 0.458102 + 0.888900i \(0.348529\pi\)
−0.998861 + 0.0477220i \(0.984804\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 12.0000 + 20.7846i 0.445669 + 0.771921i
\(726\) 0 0
\(727\) −16.0000 −0.593407 −0.296704 0.954970i \(-0.595887\pi\)
−0.296704 + 0.954970i \(0.595887\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 6.00000 + 10.3923i 0.221918 + 0.384373i
\(732\) 0 0
\(733\) 5.50000 9.52628i 0.203147 0.351861i −0.746394 0.665505i \(-0.768216\pi\)
0.949541 + 0.313644i \(0.101550\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −5.50000 + 9.52628i −0.202595 + 0.350905i
\(738\) 0 0
\(739\) 20.5000 + 35.5070i 0.754105 + 1.30615i 0.945818 + 0.324697i \(0.105262\pi\)
−0.191714 + 0.981451i \(0.561404\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −32.0000 −1.17397 −0.586983 0.809599i \(-0.699684\pi\)
−0.586983 + 0.809599i \(0.699684\pi\)
\(744\) 0 0
\(745\) −7.50000 12.9904i −0.274779 0.475931i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 23.5000 40.7032i 0.857527 1.48528i −0.0167534 0.999860i \(-0.505333\pi\)
0.874281 0.485421i \(-0.161334\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −15.0000 −0.545906
\(756\) 0 0
\(757\) 34.0000 1.23575 0.617876 0.786276i \(-0.287994\pi\)
0.617876 + 0.786276i \(0.287994\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −13.5000 + 23.3827i −0.489375 + 0.847622i −0.999925 0.0122260i \(-0.996108\pi\)
0.510551 + 0.859848i \(0.329442\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3.00000 + 5.19615i 0.108324 + 0.187622i
\(768\) 0 0
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −17.5000 30.3109i −0.629431 1.09021i −0.987666 0.156575i \(-0.949955\pi\)
0.358235 0.933632i \(-0.383379\pi\)
\(774\) 0 0
\(775\) 2.00000 3.46410i 0.0718421 0.124434i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −25.0000 + 43.3013i −0.895718 + 1.55143i
\(780\) 0 0
\(781\) 8.00000 + 13.8564i 0.286263 + 0.495821i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 15.0000 0.535373
\(786\) 0 0
\(787\) −6.50000 11.2583i −0.231700 0.401316i 0.726609 0.687052i \(-0.241095\pi\)
−0.958308 + 0.285736i \(0.907762\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −3.00000 + 5.19615i −0.106533 + 0.184521i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 42.0000 1.48772 0.743858 0.668338i \(-0.232994\pi\)
0.743858 + 0.668338i \(0.232994\pi\)
\(798\) 0 0
\(799\) 3.00000 0.106132
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 3.50000 6.06218i 0.123512 0.213930i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\)