Properties

Label 2790.2.d.f.559.1
Level $2790$
Weight $2$
Character 2790.559
Analytic conductor $22.278$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2790.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(22.2782621639\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 930)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 559.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 2790.559
Dual form 2790.2.d.f.559.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} +1.00000i q^{7} +1.00000i q^{8} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} +1.00000i q^{7} +1.00000i q^{8} +(-2.00000 - 1.00000i) q^{10} +3.00000 q^{11} +4.00000i q^{13} +1.00000 q^{14} +1.00000 q^{16} +1.00000 q^{19} +(-1.00000 + 2.00000i) q^{20} -3.00000i q^{22} +5.00000i q^{23} +(-3.00000 - 4.00000i) q^{25} +4.00000 q^{26} -1.00000i q^{28} +2.00000 q^{29} -1.00000 q^{31} -1.00000i q^{32} +(2.00000 + 1.00000i) q^{35} +4.00000i q^{37} -1.00000i q^{38} +(2.00000 + 1.00000i) q^{40} +10.0000 q^{41} +5.00000i q^{43} -3.00000 q^{44} +5.00000 q^{46} +8.00000i q^{47} +6.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} -4.00000i q^{52} +5.00000i q^{53} +(3.00000 - 6.00000i) q^{55} -1.00000 q^{56} -2.00000i q^{58} -6.00000 q^{59} -2.00000 q^{61} +1.00000i q^{62} -1.00000 q^{64} +(8.00000 + 4.00000i) q^{65} +2.00000i q^{67} +(1.00000 - 2.00000i) q^{70} +5.00000 q^{71} +7.00000i q^{73} +4.00000 q^{74} -1.00000 q^{76} +3.00000i q^{77} -3.00000 q^{79} +(1.00000 - 2.00000i) q^{80} -10.0000i q^{82} -2.00000i q^{83} +5.00000 q^{86} +3.00000i q^{88} +1.00000 q^{89} -4.00000 q^{91} -5.00000i q^{92} +8.00000 q^{94} +(1.00000 - 2.00000i) q^{95} -10.0000i q^{97} -6.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{4} + 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{4} + 2 q^{5} - 4 q^{10} + 6 q^{11} + 2 q^{14} + 2 q^{16} + 2 q^{19} - 2 q^{20} - 6 q^{25} + 8 q^{26} + 4 q^{29} - 2 q^{31} + 4 q^{35} + 4 q^{40} + 20 q^{41} - 6 q^{44} + 10 q^{46} + 12 q^{49} - 8 q^{50} + 6 q^{55} - 2 q^{56} - 12 q^{59} - 4 q^{61} - 2 q^{64} + 16 q^{65} + 2 q^{70} + 10 q^{71} + 8 q^{74} - 2 q^{76} - 6 q^{79} + 2 q^{80} + 10 q^{86} + 2 q^{89} - 8 q^{91} + 16 q^{94} + 2 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2790\mathbb{Z}\right)^\times\).

\(n\) \(1117\) \(1801\) \(2171\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) 1.00000 2.00000i 0.447214 0.894427i
\(6\) 0 0
\(7\) 1.00000i 0.377964i 0.981981 + 0.188982i \(0.0605189\pi\)
−0.981981 + 0.188982i \(0.939481\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −2.00000 1.00000i −0.632456 0.316228i
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 0 0
\(13\) 4.00000i 1.10940i 0.832050 + 0.554700i \(0.187167\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416 0.114708 0.993399i \(-0.463407\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) −1.00000 + 2.00000i −0.223607 + 0.447214i
\(21\) 0 0
\(22\) 3.00000i 0.639602i
\(23\) 5.00000i 1.04257i 0.853382 + 0.521286i \(0.174548\pi\)
−0.853382 + 0.521286i \(0.825452\pi\)
\(24\) 0 0
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) 4.00000 0.784465
\(27\) 0 0
\(28\) 1.00000i 0.188982i
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) −1.00000 −0.179605
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 0 0
\(35\) 2.00000 + 1.00000i 0.338062 + 0.169031i
\(36\) 0 0
\(37\) 4.00000i 0.657596i 0.944400 + 0.328798i \(0.106644\pi\)
−0.944400 + 0.328798i \(0.893356\pi\)
\(38\) 1.00000i 0.162221i
\(39\) 0 0
\(40\) 2.00000 + 1.00000i 0.316228 + 0.158114i
\(41\) 10.0000 1.56174 0.780869 0.624695i \(-0.214777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) 0 0
\(43\) 5.00000i 0.762493i 0.924473 + 0.381246i \(0.124505\pi\)
−0.924473 + 0.381246i \(0.875495\pi\)
\(44\) −3.00000 −0.452267
\(45\) 0 0
\(46\) 5.00000 0.737210
\(47\) 8.00000i 1.16692i 0.812142 + 0.583460i \(0.198301\pi\)
−0.812142 + 0.583460i \(0.801699\pi\)
\(48\) 0 0
\(49\) 6.00000 0.857143
\(50\) −4.00000 + 3.00000i −0.565685 + 0.424264i
\(51\) 0 0
\(52\) 4.00000i 0.554700i
\(53\) 5.00000i 0.686803i 0.939189 + 0.343401i \(0.111579\pi\)
−0.939189 + 0.343401i \(0.888421\pi\)
\(54\) 0 0
\(55\) 3.00000 6.00000i 0.404520 0.809040i
\(56\) −1.00000 −0.133631
\(57\) 0 0
\(58\) 2.00000i 0.262613i
\(59\) −6.00000 −0.781133 −0.390567 0.920575i \(-0.627721\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 1.00000i 0.127000i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 8.00000 + 4.00000i 0.992278 + 0.496139i
\(66\) 0 0
\(67\) 2.00000i 0.244339i 0.992509 + 0.122169i \(0.0389851\pi\)
−0.992509 + 0.122169i \(0.961015\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 1.00000 2.00000i 0.119523 0.239046i
\(71\) 5.00000 0.593391 0.296695 0.954972i \(-0.404115\pi\)
0.296695 + 0.954972i \(0.404115\pi\)
\(72\) 0 0
\(73\) 7.00000i 0.819288i 0.912245 + 0.409644i \(0.134347\pi\)
−0.912245 + 0.409644i \(0.865653\pi\)
\(74\) 4.00000 0.464991
\(75\) 0 0
\(76\) −1.00000 −0.114708
\(77\) 3.00000i 0.341882i
\(78\) 0 0
\(79\) −3.00000 −0.337526 −0.168763 0.985657i \(-0.553977\pi\)
−0.168763 + 0.985657i \(0.553977\pi\)
\(80\) 1.00000 2.00000i 0.111803 0.223607i
\(81\) 0 0
\(82\) 10.0000i 1.10432i
\(83\) 2.00000i 0.219529i −0.993958 0.109764i \(-0.964990\pi\)
0.993958 0.109764i \(-0.0350096\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 5.00000 0.539164
\(87\) 0 0
\(88\) 3.00000i 0.319801i
\(89\) 1.00000 0.106000 0.0529999 0.998595i \(-0.483122\pi\)
0.0529999 + 0.998595i \(0.483122\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) 5.00000i 0.521286i
\(93\) 0 0
\(94\) 8.00000 0.825137
\(95\) 1.00000 2.00000i 0.102598 0.205196i
\(96\) 0 0
\(97\) 10.0000i 1.01535i −0.861550 0.507673i \(-0.830506\pi\)
0.861550 0.507673i \(-0.169494\pi\)
\(98\) 6.00000i 0.606092i
\(99\) 0 0
\(100\) 3.00000 + 4.00000i 0.300000 + 0.400000i
\(101\) 15.0000 1.49256 0.746278 0.665635i \(-0.231839\pi\)
0.746278 + 0.665635i \(0.231839\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) 5.00000 0.485643
\(107\) 19.0000i 1.83680i −0.395654 0.918400i \(-0.629482\pi\)
0.395654 0.918400i \(-0.370518\pi\)
\(108\) 0 0
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) −6.00000 3.00000i −0.572078 0.286039i
\(111\) 0 0
\(112\) 1.00000i 0.0944911i
\(113\) 15.0000i 1.41108i −0.708669 0.705541i \(-0.750704\pi\)
0.708669 0.705541i \(-0.249296\pi\)
\(114\) 0 0
\(115\) 10.0000 + 5.00000i 0.932505 + 0.466252i
\(116\) −2.00000 −0.185695
\(117\) 0 0
\(118\) 6.00000i 0.552345i
\(119\) 0 0
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 2.00000i 0.181071i
\(123\) 0 0
\(124\) 1.00000 0.0898027
\(125\) −11.0000 + 2.00000i −0.983870 + 0.178885i
\(126\) 0 0
\(127\) 8.00000i 0.709885i 0.934888 + 0.354943i \(0.115500\pi\)
−0.934888 + 0.354943i \(0.884500\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 4.00000 8.00000i 0.350823 0.701646i
\(131\) 2.00000 0.174741 0.0873704 0.996176i \(-0.472154\pi\)
0.0873704 + 0.996176i \(0.472154\pi\)
\(132\) 0 0
\(133\) 1.00000i 0.0867110i
\(134\) 2.00000 0.172774
\(135\) 0 0
\(136\) 0 0
\(137\) 2.00000i 0.170872i −0.996344 0.0854358i \(-0.972772\pi\)
0.996344 0.0854358i \(-0.0272282\pi\)
\(138\) 0 0
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) −2.00000 1.00000i −0.169031 0.0845154i
\(141\) 0 0
\(142\) 5.00000i 0.419591i
\(143\) 12.0000i 1.00349i
\(144\) 0 0
\(145\) 2.00000 4.00000i 0.166091 0.332182i
\(146\) 7.00000 0.579324
\(147\) 0 0
\(148\) 4.00000i 0.328798i
\(149\) 15.0000 1.22885 0.614424 0.788976i \(-0.289388\pi\)
0.614424 + 0.788976i \(0.289388\pi\)
\(150\) 0 0
\(151\) −16.0000 −1.30206 −0.651031 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) 1.00000i 0.0811107i
\(153\) 0 0
\(154\) 3.00000 0.241747
\(155\) −1.00000 + 2.00000i −0.0803219 + 0.160644i
\(156\) 0 0
\(157\) 9.00000i 0.718278i 0.933284 + 0.359139i \(0.116930\pi\)
−0.933284 + 0.359139i \(0.883070\pi\)
\(158\) 3.00000i 0.238667i
\(159\) 0 0
\(160\) −2.00000 1.00000i −0.158114 0.0790569i
\(161\) −5.00000 −0.394055
\(162\) 0 0
\(163\) 4.00000i 0.313304i 0.987654 + 0.156652i \(0.0500701\pi\)
−0.987654 + 0.156652i \(0.949930\pi\)
\(164\) −10.0000 −0.780869
\(165\) 0 0
\(166\) −2.00000 −0.155230
\(167\) 21.0000i 1.62503i −0.582941 0.812514i \(-0.698098\pi\)
0.582941 0.812514i \(-0.301902\pi\)
\(168\) 0 0
\(169\) −3.00000 −0.230769
\(170\) 0 0
\(171\) 0 0
\(172\) 5.00000i 0.381246i
\(173\) 2.00000i 0.152057i −0.997106 0.0760286i \(-0.975776\pi\)
0.997106 0.0760286i \(-0.0242240\pi\)
\(174\) 0 0
\(175\) 4.00000 3.00000i 0.302372 0.226779i
\(176\) 3.00000 0.226134
\(177\) 0 0
\(178\) 1.00000i 0.0749532i
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) −5.00000 −0.371647 −0.185824 0.982583i \(-0.559495\pi\)
−0.185824 + 0.982583i \(0.559495\pi\)
\(182\) 4.00000i 0.296500i
\(183\) 0 0
\(184\) −5.00000 −0.368605
\(185\) 8.00000 + 4.00000i 0.588172 + 0.294086i
\(186\) 0 0
\(187\) 0 0
\(188\) 8.00000i 0.583460i
\(189\) 0 0
\(190\) −2.00000 1.00000i −0.145095 0.0725476i
\(191\) 16.0000 1.15772 0.578860 0.815427i \(-0.303498\pi\)
0.578860 + 0.815427i \(0.303498\pi\)
\(192\) 0 0
\(193\) 10.0000i 0.719816i 0.932988 + 0.359908i \(0.117192\pi\)
−0.932988 + 0.359908i \(0.882808\pi\)
\(194\) −10.0000 −0.717958
\(195\) 0 0
\(196\) −6.00000 −0.428571
\(197\) 18.0000i 1.28245i −0.767354 0.641223i \(-0.778427\pi\)
0.767354 0.641223i \(-0.221573\pi\)
\(198\) 0 0
\(199\) 21.0000 1.48865 0.744325 0.667817i \(-0.232771\pi\)
0.744325 + 0.667817i \(0.232771\pi\)
\(200\) 4.00000 3.00000i 0.282843 0.212132i
\(201\) 0 0
\(202\) 15.0000i 1.05540i
\(203\) 2.00000i 0.140372i
\(204\) 0 0
\(205\) 10.0000 20.0000i 0.698430 1.39686i
\(206\) 0 0
\(207\) 0 0
\(208\) 4.00000i 0.277350i
\(209\) 3.00000 0.207514
\(210\) 0 0
\(211\) 7.00000 0.481900 0.240950 0.970538i \(-0.422541\pi\)
0.240950 + 0.970538i \(0.422541\pi\)
\(212\) 5.00000i 0.343401i
\(213\) 0 0
\(214\) −19.0000 −1.29881
\(215\) 10.0000 + 5.00000i 0.681994 + 0.340997i
\(216\) 0 0
\(217\) 1.00000i 0.0678844i
\(218\) 2.00000i 0.135457i
\(219\) 0 0
\(220\) −3.00000 + 6.00000i −0.202260 + 0.404520i
\(221\) 0 0
\(222\) 0 0
\(223\) 20.0000i 1.33930i 0.742677 + 0.669650i \(0.233556\pi\)
−0.742677 + 0.669650i \(0.766444\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) −15.0000 −0.997785
\(227\) 9.00000i 0.597351i 0.954355 + 0.298675i \(0.0965448\pi\)
−0.954355 + 0.298675i \(0.903455\pi\)
\(228\) 0 0
\(229\) −15.0000 −0.991228 −0.495614 0.868543i \(-0.665057\pi\)
−0.495614 + 0.868543i \(0.665057\pi\)
\(230\) 5.00000 10.0000i 0.329690 0.659380i
\(231\) 0 0
\(232\) 2.00000i 0.131306i
\(233\) 21.0000i 1.37576i −0.725826 0.687878i \(-0.758542\pi\)
0.725826 0.687878i \(-0.241458\pi\)
\(234\) 0 0
\(235\) 16.0000 + 8.00000i 1.04372 + 0.521862i
\(236\) 6.00000 0.390567
\(237\) 0 0
\(238\) 0 0
\(239\) −14.0000 −0.905585 −0.452792 0.891616i \(-0.649572\pi\)
−0.452792 + 0.891616i \(0.649572\pi\)
\(240\) 0 0
\(241\) −12.0000 −0.772988 −0.386494 0.922292i \(-0.626314\pi\)
−0.386494 + 0.922292i \(0.626314\pi\)
\(242\) 2.00000i 0.128565i
\(243\) 0 0
\(244\) 2.00000 0.128037
\(245\) 6.00000 12.0000i 0.383326 0.766652i
\(246\) 0 0
\(247\) 4.00000i 0.254514i
\(248\) 1.00000i 0.0635001i
\(249\) 0 0
\(250\) 2.00000 + 11.0000i 0.126491 + 0.695701i
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) 15.0000i 0.943042i
\(254\) 8.00000 0.501965
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 5.00000i 0.311891i −0.987766 0.155946i \(-0.950158\pi\)
0.987766 0.155946i \(-0.0498425\pi\)
\(258\) 0 0
\(259\) −4.00000 −0.248548
\(260\) −8.00000 4.00000i −0.496139 0.248069i
\(261\) 0 0
\(262\) 2.00000i 0.123560i
\(263\) 24.0000i 1.47990i 0.672660 + 0.739952i \(0.265152\pi\)
−0.672660 + 0.739952i \(0.734848\pi\)
\(264\) 0 0
\(265\) 10.0000 + 5.00000i 0.614295 + 0.307148i
\(266\) 1.00000 0.0613139
\(267\) 0 0
\(268\) 2.00000i 0.122169i
\(269\) 2.00000 0.121942 0.0609711 0.998140i \(-0.480580\pi\)
0.0609711 + 0.998140i \(0.480580\pi\)
\(270\) 0 0
\(271\) 9.00000 0.546711 0.273356 0.961913i \(-0.411866\pi\)
0.273356 + 0.961913i \(0.411866\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) −9.00000 12.0000i −0.542720 0.723627i
\(276\) 0 0
\(277\) 2.00000i 0.120168i 0.998193 + 0.0600842i \(0.0191369\pi\)
−0.998193 + 0.0600842i \(0.980863\pi\)
\(278\) 20.0000i 1.19952i
\(279\) 0 0
\(280\) −1.00000 + 2.00000i −0.0597614 + 0.119523i
\(281\) 32.0000 1.90896 0.954480 0.298275i \(-0.0964112\pi\)
0.954480 + 0.298275i \(0.0964112\pi\)
\(282\) 0 0
\(283\) 14.0000i 0.832214i −0.909316 0.416107i \(-0.863394\pi\)
0.909316 0.416107i \(-0.136606\pi\)
\(284\) −5.00000 −0.296695
\(285\) 0 0
\(286\) 12.0000 0.709575
\(287\) 10.0000i 0.590281i
\(288\) 0 0
\(289\) 17.0000 1.00000
\(290\) −4.00000 2.00000i −0.234888 0.117444i
\(291\) 0 0
\(292\) 7.00000i 0.409644i
\(293\) 18.0000i 1.05157i −0.850617 0.525786i \(-0.823771\pi\)
0.850617 0.525786i \(-0.176229\pi\)
\(294\) 0 0
\(295\) −6.00000 + 12.0000i −0.349334 + 0.698667i
\(296\) −4.00000 −0.232495
\(297\) 0 0
\(298\) 15.0000i 0.868927i
\(299\) −20.0000 −1.15663
\(300\) 0 0
\(301\) −5.00000 −0.288195
\(302\) 16.0000i 0.920697i
\(303\) 0 0
\(304\) 1.00000 0.0573539
\(305\) −2.00000 + 4.00000i −0.114520 + 0.229039i
\(306\) 0 0
\(307\) 4.00000i 0.228292i −0.993464 0.114146i \(-0.963587\pi\)
0.993464 0.114146i \(-0.0364132\pi\)
\(308\) 3.00000i 0.170941i
\(309\) 0 0
\(310\) 2.00000 + 1.00000i 0.113592 + 0.0567962i
\(311\) −16.0000 −0.907277 −0.453638 0.891186i \(-0.649874\pi\)
−0.453638 + 0.891186i \(0.649874\pi\)
\(312\) 0 0
\(313\) 6.00000i 0.339140i 0.985518 + 0.169570i \(0.0542379\pi\)
−0.985518 + 0.169570i \(0.945762\pi\)
\(314\) 9.00000 0.507899
\(315\) 0 0
\(316\) 3.00000 0.168763
\(317\) 18.0000i 1.01098i −0.862832 0.505490i \(-0.831312\pi\)
0.862832 0.505490i \(-0.168688\pi\)
\(318\) 0 0
\(319\) 6.00000 0.335936
\(320\) −1.00000 + 2.00000i −0.0559017 + 0.111803i
\(321\) 0 0
\(322\) 5.00000i 0.278639i
\(323\) 0 0
\(324\) 0 0
\(325\) 16.0000 12.0000i 0.887520 0.665640i
\(326\) 4.00000 0.221540
\(327\) 0 0
\(328\) 10.0000i 0.552158i
\(329\) −8.00000 −0.441054
\(330\) 0 0
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 2.00000i 0.109764i
\(333\) 0 0
\(334\) −21.0000 −1.14907
\(335\) 4.00000 + 2.00000i 0.218543 + 0.109272i
\(336\) 0 0
\(337\) 34.0000i 1.85210i −0.377403 0.926049i \(-0.623183\pi\)
0.377403 0.926049i \(-0.376817\pi\)
\(338\) 3.00000i 0.163178i
\(339\) 0 0
\(340\) 0 0
\(341\) −3.00000 −0.162459
\(342\) 0 0
\(343\) 13.0000i 0.701934i
\(344\) −5.00000 −0.269582
\(345\) 0 0
\(346\) −2.00000 −0.107521
\(347\) 22.0000i 1.18102i 0.807030 + 0.590511i \(0.201074\pi\)
−0.807030 + 0.590511i \(0.798926\pi\)
\(348\) 0 0
\(349\) −20.0000 −1.07058 −0.535288 0.844670i \(-0.679797\pi\)
−0.535288 + 0.844670i \(0.679797\pi\)
\(350\) −3.00000 4.00000i −0.160357 0.213809i
\(351\) 0 0
\(352\) 3.00000i 0.159901i
\(353\) 24.0000i 1.27739i 0.769460 + 0.638696i \(0.220526\pi\)
−0.769460 + 0.638696i \(0.779474\pi\)
\(354\) 0 0
\(355\) 5.00000 10.0000i 0.265372 0.530745i
\(356\) −1.00000 −0.0529999
\(357\) 0 0
\(358\) 0 0
\(359\) 3.00000 0.158334 0.0791670 0.996861i \(-0.474774\pi\)
0.0791670 + 0.996861i \(0.474774\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) 5.00000i 0.262794i
\(363\) 0 0
\(364\) 4.00000 0.209657
\(365\) 14.0000 + 7.00000i 0.732793 + 0.366397i
\(366\) 0 0
\(367\) 14.0000i 0.730794i 0.930852 + 0.365397i \(0.119067\pi\)
−0.930852 + 0.365397i \(0.880933\pi\)
\(368\) 5.00000i 0.260643i
\(369\) 0 0
\(370\) 4.00000 8.00000i 0.207950 0.415900i
\(371\) −5.00000 −0.259587
\(372\) 0 0
\(373\) 11.0000i 0.569558i 0.958593 + 0.284779i \(0.0919203\pi\)
−0.958593 + 0.284779i \(0.908080\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −8.00000 −0.412568
\(377\) 8.00000i 0.412021i
\(378\) 0 0
\(379\) 15.0000 0.770498 0.385249 0.922813i \(-0.374116\pi\)
0.385249 + 0.922813i \(0.374116\pi\)
\(380\) −1.00000 + 2.00000i −0.0512989 + 0.102598i
\(381\) 0 0
\(382\) 16.0000i 0.818631i
\(383\) 28.0000i 1.43073i 0.698749 + 0.715367i \(0.253740\pi\)
−0.698749 + 0.715367i \(0.746260\pi\)
\(384\) 0 0
\(385\) 6.00000 + 3.00000i 0.305788 + 0.152894i
\(386\) 10.0000 0.508987
\(387\) 0 0
\(388\) 10.0000i 0.507673i
\(389\) −28.0000 −1.41966 −0.709828 0.704375i \(-0.751227\pi\)
−0.709828 + 0.704375i \(0.751227\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 6.00000i 0.303046i
\(393\) 0 0
\(394\) −18.0000 −0.906827
\(395\) −3.00000 + 6.00000i −0.150946 + 0.301893i
\(396\) 0 0
\(397\) 31.0000i 1.55585i −0.628360 0.777923i \(-0.716273\pi\)
0.628360 0.777923i \(-0.283727\pi\)
\(398\) 21.0000i 1.05263i
\(399\) 0 0
\(400\) −3.00000 4.00000i −0.150000 0.200000i
\(401\) −5.00000 −0.249688 −0.124844 0.992176i \(-0.539843\pi\)
−0.124844 + 0.992176i \(0.539843\pi\)
\(402\) 0 0
\(403\) 4.00000i 0.199254i
\(404\) −15.0000 −0.746278
\(405\) 0 0
\(406\) 2.00000 0.0992583
\(407\) 12.0000i 0.594818i
\(408\) 0 0
\(409\) −4.00000 −0.197787 −0.0988936 0.995098i \(-0.531530\pi\)
−0.0988936 + 0.995098i \(0.531530\pi\)
\(410\) −20.0000 10.0000i −0.987730 0.493865i
\(411\) 0 0
\(412\) 0 0
\(413\) 6.00000i 0.295241i
\(414\) 0 0
\(415\) −4.00000 2.00000i −0.196352 0.0981761i
\(416\) 4.00000 0.196116
\(417\) 0 0
\(418\) 3.00000i 0.146735i
\(419\) −18.0000 −0.879358 −0.439679 0.898155i \(-0.644908\pi\)
−0.439679 + 0.898155i \(0.644908\pi\)
\(420\) 0 0
\(421\) −14.0000 −0.682318 −0.341159 0.940006i \(-0.610819\pi\)
−0.341159 + 0.940006i \(0.610819\pi\)
\(422\) 7.00000i 0.340755i
\(423\) 0 0
\(424\) −5.00000 −0.242821
\(425\) 0 0
\(426\) 0 0
\(427\) 2.00000i 0.0967868i
\(428\) 19.0000i 0.918400i
\(429\) 0 0
\(430\) 5.00000 10.0000i 0.241121 0.482243i
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 19.0000i 0.913082i −0.889702 0.456541i \(-0.849088\pi\)
0.889702 0.456541i \(-0.150912\pi\)
\(434\) −1.00000 −0.0480015
\(435\) 0 0
\(436\) 2.00000 0.0957826
\(437\) 5.00000i 0.239182i
\(438\) 0 0
\(439\) −20.0000 −0.954548 −0.477274 0.878755i \(-0.658375\pi\)
−0.477274 + 0.878755i \(0.658375\pi\)
\(440\) 6.00000 + 3.00000i 0.286039 + 0.143019i
\(441\) 0 0
\(442\) 0 0
\(443\) 29.0000i 1.37783i 0.724841 + 0.688916i \(0.241913\pi\)
−0.724841 + 0.688916i \(0.758087\pi\)
\(444\) 0 0
\(445\) 1.00000 2.00000i 0.0474045 0.0948091i
\(446\) 20.0000 0.947027
\(447\) 0 0
\(448\) 1.00000i 0.0472456i
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) 0 0
\(451\) 30.0000 1.41264
\(452\) 15.0000i 0.705541i
\(453\) 0 0
\(454\) 9.00000 0.422391
\(455\) −4.00000 + 8.00000i −0.187523 + 0.375046i
\(456\) 0 0
\(457\) 30.0000i 1.40334i 0.712502 + 0.701670i \(0.247562\pi\)
−0.712502 + 0.701670i \(0.752438\pi\)
\(458\) 15.0000i 0.700904i
\(459\) 0 0
\(460\) −10.0000 5.00000i −0.466252 0.233126i
\(461\) −16.0000 −0.745194 −0.372597 0.927993i \(-0.621533\pi\)
−0.372597 + 0.927993i \(0.621533\pi\)
\(462\) 0 0
\(463\) 14.0000i 0.650635i 0.945605 + 0.325318i \(0.105471\pi\)
−0.945605 + 0.325318i \(0.894529\pi\)
\(464\) 2.00000 0.0928477
\(465\) 0 0
\(466\) −21.0000 −0.972806
\(467\) 28.0000i 1.29569i −0.761774 0.647843i \(-0.775671\pi\)
0.761774 0.647843i \(-0.224329\pi\)
\(468\) 0 0
\(469\) −2.00000 −0.0923514
\(470\) 8.00000 16.0000i 0.369012 0.738025i
\(471\) 0 0
\(472\) 6.00000i 0.276172i
\(473\) 15.0000i 0.689701i
\(474\) 0 0
\(475\) −3.00000 4.00000i −0.137649 0.183533i
\(476\) 0 0
\(477\) 0 0
\(478\) 14.0000i 0.640345i
\(479\) −25.0000 −1.14228 −0.571140 0.820853i \(-0.693499\pi\)
−0.571140 + 0.820853i \(0.693499\pi\)
\(480\) 0 0
\(481\) −16.0000 −0.729537
\(482\) 12.0000i 0.546585i
\(483\) 0 0
\(484\) 2.00000 0.0909091
\(485\) −20.0000 10.0000i −0.908153 0.454077i
\(486\) 0 0
\(487\) 4.00000i 0.181257i −0.995885 0.0906287i \(-0.971112\pi\)
0.995885 0.0906287i \(-0.0288876\pi\)
\(488\) 2.00000i 0.0905357i
\(489\) 0 0
\(490\) −12.0000 6.00000i −0.542105 0.271052i
\(491\) −33.0000 −1.48927 −0.744635 0.667472i \(-0.767376\pi\)
−0.744635 + 0.667472i \(0.767376\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 4.00000 0.179969
\(495\) 0 0
\(496\) −1.00000 −0.0449013
\(497\) 5.00000i 0.224281i
\(498\) 0 0
\(499\) −22.0000 −0.984855 −0.492428 0.870353i \(-0.663890\pi\)
−0.492428 + 0.870353i \(0.663890\pi\)
\(500\) 11.0000 2.00000i 0.491935 0.0894427i
\(501\) 0 0
\(502\) 12.0000i 0.535586i
\(503\) 14.0000i 0.624229i 0.950044 + 0.312115i \(0.101037\pi\)
−0.950044 + 0.312115i \(0.898963\pi\)
\(504\) 0 0
\(505\) 15.0000 30.0000i 0.667491 1.33498i
\(506\) 15.0000 0.666831
\(507\) 0 0
\(508\) 8.00000i 0.354943i
\(509\) 32.0000 1.41838 0.709188 0.705020i \(-0.249062\pi\)
0.709188 + 0.705020i \(0.249062\pi\)
\(510\) 0 0
\(511\) −7.00000 −0.309662
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −5.00000 −0.220541
\(515\) 0 0
\(516\) 0 0
\(517\) 24.0000i 1.05552i
\(518\) 4.00000i 0.175750i
\(519\) 0 0
\(520\) −4.00000 + 8.00000i −0.175412 + 0.350823i
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 0 0
\(523\) 19.0000i 0.830812i −0.909636 0.415406i \(-0.863640\pi\)
0.909636 0.415406i \(-0.136360\pi\)
\(524\) −2.00000 −0.0873704
\(525\) 0 0
\(526\) 24.0000 1.04645
\(527\) 0 0
\(528\) 0 0
\(529\) −2.00000 −0.0869565
\(530\) 5.00000 10.0000i 0.217186 0.434372i
\(531\) 0 0
\(532\) 1.00000i 0.0433555i
\(533\) 40.0000i 1.73259i
\(534\) 0 0
\(535\) −38.0000 19.0000i −1.64288 0.821442i
\(536\) −2.00000 −0.0863868
\(537\) 0 0
\(538\) 2.00000i 0.0862261i
\(539\) 18.0000 0.775315
\(540\) 0 0
\(541\) 24.0000 1.03184 0.515920 0.856637i \(-0.327450\pi\)
0.515920 + 0.856637i \(0.327450\pi\)
\(542\) 9.00000i 0.386583i
\(543\) 0 0
\(544\) 0 0
\(545\) −2.00000 + 4.00000i −0.0856706 + 0.171341i
\(546\) 0 0
\(547\) 28.0000i 1.19719i 0.801050 + 0.598597i \(0.204275\pi\)
−0.801050 + 0.598597i \(0.795725\pi\)
\(548\) 2.00000i 0.0854358i
\(549\) 0 0
\(550\) −12.0000 + 9.00000i −0.511682 + 0.383761i
\(551\) 2.00000 0.0852029
\(552\) 0 0
\(553\) 3.00000i 0.127573i
\(554\) 2.00000 0.0849719
\(555\) 0 0
\(556\) −20.0000 −0.848189
\(557\) 9.00000i 0.381342i −0.981654 0.190671i \(-0.938934\pi\)
0.981654 0.190671i \(-0.0610664\pi\)
\(558\) 0 0
\(559\) −20.0000 −0.845910
\(560\) 2.00000 + 1.00000i 0.0845154 + 0.0422577i
\(561\) 0 0
\(562\) 32.0000i 1.34984i
\(563\) 36.0000i 1.51722i 0.651546 + 0.758610i \(0.274121\pi\)
−0.651546 + 0.758610i \(0.725879\pi\)
\(564\) 0 0
\(565\) −30.0000 15.0000i −1.26211 0.631055i
\(566\) −14.0000 −0.588464
\(567\) 0 0
\(568\) 5.00000i 0.209795i
\(569\) −39.0000 −1.63497 −0.817483 0.575953i \(-0.804631\pi\)
−0.817483 + 0.575953i \(0.804631\pi\)
\(570\) 0 0
\(571\) 26.0000 1.08807 0.544033 0.839064i \(-0.316897\pi\)
0.544033 + 0.839064i \(0.316897\pi\)
\(572\) 12.0000i 0.501745i
\(573\) 0 0
\(574\) 10.0000 0.417392
\(575\) 20.0000 15.0000i 0.834058 0.625543i
\(576\) 0 0
\(577\) 34.0000i 1.41544i −0.706494 0.707719i \(-0.749724\pi\)
0.706494 0.707719i \(-0.250276\pi\)
\(578\) 17.0000i 0.707107i
\(579\) 0 0
\(580\) −2.00000 + 4.00000i −0.0830455 + 0.166091i
\(581\) 2.00000 0.0829740
\(582\) 0 0
\(583\) 15.0000i 0.621237i
\(584\) −7.00000 −0.289662
\(585\) 0 0
\(586\) −18.0000 −0.743573
\(587\) 6.00000i 0.247647i −0.992304 0.123823i \(-0.960484\pi\)
0.992304 0.123823i \(-0.0395156\pi\)
\(588\) 0 0
\(589\) −1.00000 −0.0412043
\(590\) 12.0000 + 6.00000i 0.494032 + 0.247016i
\(591\) 0 0
\(592\) 4.00000i 0.164399i
\(593\) 6.00000i 0.246390i 0.992382 + 0.123195i \(0.0393141\pi\)
−0.992382 + 0.123195i \(0.960686\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −15.0000 −0.614424
\(597\) 0 0
\(598\) 20.0000i 0.817861i
\(599\) 13.0000 0.531166 0.265583 0.964088i \(-0.414436\pi\)
0.265583 + 0.964088i \(0.414436\pi\)
\(600\) 0 0
\(601\) −44.0000 −1.79480 −0.897399 0.441221i \(-0.854546\pi\)
−0.897399 + 0.441221i \(0.854546\pi\)
\(602\) 5.00000i 0.203785i
\(603\) 0 0
\(604\) 16.0000 0.651031
\(605\) −2.00000 + 4.00000i −0.0813116 + 0.162623i
\(606\) 0 0
\(607\) 27.0000i 1.09590i −0.836512 0.547948i \(-0.815409\pi\)
0.836512 0.547948i \(-0.184591\pi\)
\(608\) 1.00000i 0.0405554i
\(609\) 0 0
\(610\) 4.00000 + 2.00000i 0.161955 + 0.0809776i
\(611\) −32.0000 −1.29458
\(612\) 0 0
\(613\) 24.0000i 0.969351i −0.874694 0.484675i \(-0.838938\pi\)
0.874694 0.484675i \(-0.161062\pi\)
\(614\) −4.00000 −0.161427
\(615\) 0 0
\(616\) −3.00000 −0.120873
\(617\) 5.00000i 0.201292i −0.994922 0.100646i \(-0.967909\pi\)
0.994922 0.100646i \(-0.0320910\pi\)
\(618\) 0 0
\(619\) 12.0000 0.482321 0.241160 0.970485i \(-0.422472\pi\)
0.241160 + 0.970485i \(0.422472\pi\)
\(620\) 1.00000 2.00000i 0.0401610 0.0803219i
\(621\) 0 0
\(622\) 16.0000i 0.641542i
\(623\) 1.00000i 0.0400642i
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 6.00000 0.239808
\(627\) 0 0
\(628\) 9.00000i 0.359139i
\(629\) 0 0
\(630\) 0 0
\(631\) 25.0000 0.995234 0.497617 0.867397i \(-0.334208\pi\)
0.497617 + 0.867397i \(0.334208\pi\)
\(632\) 3.00000i 0.119334i
\(633\) 0 0
\(634\) −18.0000 −0.714871
\(635\) 16.0000 + 8.00000i 0.634941 + 0.317470i
\(636\) 0 0
\(637\) 24.0000i 0.950915i
\(638\) 6.00000i 0.237542i
\(639\) 0 0
\(640\) 2.00000 + 1.00000i 0.0790569 + 0.0395285i
\(641\) −50.0000 −1.97488 −0.987441 0.157991i \(-0.949498\pi\)
−0.987441 + 0.157991i \(0.949498\pi\)
\(642\) 0 0
\(643\) 7.00000i 0.276053i 0.990429 + 0.138027i \(0.0440759\pi\)
−0.990429 + 0.138027i \(0.955924\pi\)
\(644\) 5.00000 0.197028
\(645\) 0 0
\(646\) 0 0
\(647\) 7.00000i 0.275198i −0.990488 0.137599i \(-0.956061\pi\)
0.990488 0.137599i \(-0.0439386\pi\)
\(648\) 0 0
\(649\) −18.0000 −0.706562
\(650\) −12.0000 16.0000i −0.470679 0.627572i
\(651\) 0 0
\(652\) 4.00000i 0.156652i
\(653\) 42.0000i 1.64359i −0.569785 0.821794i \(-0.692974\pi\)
0.569785 0.821794i \(-0.307026\pi\)
\(654\) 0 0
\(655\) 2.00000 4.00000i 0.0781465 0.156293i
\(656\) 10.0000 0.390434
\(657\) 0 0
\(658\) 8.00000i 0.311872i
\(659\) 6.00000 0.233727 0.116863 0.993148i \(-0.462716\pi\)
0.116863 + 0.993148i \(0.462716\pi\)
\(660\) 0 0
\(661\) 36.0000 1.40024 0.700119 0.714026i \(-0.253130\pi\)
0.700119 + 0.714026i \(0.253130\pi\)
\(662\) 8.00000i 0.310929i
\(663\) 0 0
\(664\) 2.00000 0.0776151
\(665\) 2.00000 + 1.00000i 0.0775567 + 0.0387783i
\(666\) 0 0
\(667\) 10.0000i 0.387202i
\(668\) 21.0000i 0.812514i
\(669\) 0 0
\(670\) 2.00000 4.00000i 0.0772667 0.154533i
\(671\) −6.00000 −0.231627
\(672\) 0 0
\(673\) 30.0000i 1.15642i 0.815890 + 0.578208i \(0.196248\pi\)
−0.815890 + 0.578208i \(0.803752\pi\)
\(674\) −34.0000 −1.30963
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) 13.0000i 0.499631i −0.968294 0.249815i \(-0.919630\pi\)
0.968294 0.249815i \(-0.0803699\pi\)
\(678\) 0 0
\(679\) 10.0000 0.383765
\(680\) 0 0
\(681\) 0 0
\(682\) 3.00000i 0.114876i
\(683\) 35.0000i 1.33924i 0.742705 + 0.669619i \(0.233543\pi\)
−0.742705 + 0.669619i \(0.766457\pi\)
\(684\) 0 0
\(685\) −4.00000 2.00000i −0.152832 0.0764161i
\(686\) 13.0000 0.496342
\(687\) 0 0
\(688\) 5.00000i 0.190623i
\(689\) −20.0000 −0.761939
\(690\) 0 0
\(691\) −41.0000 −1.55971 −0.779857 0.625958i \(-0.784708\pi\)
−0.779857 + 0.625958i \(0.784708\pi\)
\(692\) 2.00000i 0.0760286i
\(693\) 0 0
\(694\) 22.0000 0.835109
\(695\) 20.0000 40.0000i 0.758643 1.51729i
\(696\) 0 0
\(697\) 0 0
\(698\) 20.0000i 0.757011i
\(699\) 0 0
\(700\) −4.00000 + 3.00000i −0.151186 + 0.113389i
\(701\) 35.0000 1.32193 0.660966 0.750416i \(-0.270147\pi\)
0.660966 + 0.750416i \(0.270147\pi\)
\(702\) 0 0
\(703\) 4.00000i 0.150863i
\(704\) −3.00000 −0.113067
\(705\) 0 0
\(706\) 24.0000 0.903252
\(707\) 15.0000i 0.564133i
\(708\) 0 0
\(709\) −5.00000 −0.187779 −0.0938895 0.995583i \(-0.529930\pi\)
−0.0938895 + 0.995583i \(0.529930\pi\)
\(710\) −10.0000 5.00000i −0.375293 0.187647i
\(711\) 0 0
\(712\) 1.00000i 0.0374766i
\(713\) 5.00000i 0.187251i
\(714\) 0 0
\(715\) 24.0000 + 12.0000i 0.897549 + 0.448775i
\(716\) 0 0
\(717\) 0 0
\(718\) 3.00000i 0.111959i
\(719\) 10.0000 0.372937 0.186469 0.982461i \(-0.440296\pi\)
0.186469 + 0.982461i \(0.440296\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 18.0000i 0.669891i
\(723\) 0 0
\(724\) 5.00000 0.185824
\(725\) −6.00000 8.00000i −0.222834 0.297113i
\(726\) 0 0
\(727\) 49.0000i 1.81731i 0.417548 + 0.908655i \(0.362889\pi\)
−0.417548 + 0.908655i \(0.637111\pi\)
\(728\) 4.00000i 0.148250i
\(729\) 0 0
\(730\) 7.00000 14.0000i 0.259082 0.518163i
\(731\) 0 0
\(732\) 0 0
\(733\) 22.0000i 0.812589i 0.913742 + 0.406294i \(0.133179\pi\)
−0.913742 + 0.406294i \(0.866821\pi\)
\(734\) 14.0000 0.516749
\(735\) 0 0
\(736\) 5.00000 0.184302
\(737\) 6.00000i 0.221013i
\(738\) 0 0
\(739\) 18.0000 0.662141 0.331070 0.943606i \(-0.392590\pi\)
0.331070 + 0.943606i \(0.392590\pi\)
\(740\) −8.00000 4.00000i −0.294086 0.147043i
\(741\) 0 0
\(742\) 5.00000i 0.183556i
\(743\) 15.0000i 0.550297i 0.961402 + 0.275148i \(0.0887270\pi\)
−0.961402 + 0.275148i \(0.911273\pi\)
\(744\) 0 0
\(745\) 15.0000 30.0000i 0.549557 1.09911i
\(746\) 11.0000 0.402739
\(747\) 0 0
\(748\) 0 0
\(749\) 19.0000 0.694245
\(750\) 0 0
\(751\) 22.0000 0.802791 0.401396 0.915905i \(-0.368525\pi\)
0.401396 + 0.915905i \(0.368525\pi\)
\(752\) 8.00000i 0.291730i
\(753\) 0 0
\(754\) 8.00000 0.291343
\(755\) −16.0000 + 32.0000i −0.582300 + 1.16460i
\(756\) 0 0
\(757\) 20.0000i 0.726912i 0.931611 + 0.363456i \(0.118403\pi\)
−0.931611 + 0.363456i \(0.881597\pi\)
\(758\) 15.0000i 0.544825i
\(759\) 0 0
\(760\) 2.00000 + 1.00000i 0.0725476 + 0.0362738i
\(761\) −21.0000 −0.761249 −0.380625 0.924730i \(-0.624291\pi\)
−0.380625 + 0.924730i \(0.624291\pi\)
\(762\) 0 0
\(763\) 2.00000i 0.0724049i
\(764\) −16.0000 −0.578860
\(765\) 0 0
\(766\) 28.0000 1.01168
\(767\) 24.0000i 0.866590i
\(768\) 0 0
\(769\) −45.0000 −1.62274 −0.811371 0.584532i \(-0.801278\pi\)
−0.811371 + 0.584532i \(0.801278\pi\)
\(770\) 3.00000 6.00000i 0.108112 0.216225i
\(771\) 0 0
\(772\) 10.0000i 0.359908i
\(773\) 29.0000i 1.04306i −0.853234 0.521529i \(-0.825362\pi\)
0.853234 0.521529i \(-0.174638\pi\)
\(774\) 0 0
\(775\) 3.00000 + 4.00000i 0.107763 + 0.143684i
\(776\) 10.0000 0.358979
\(777\) 0 0
\(778\) 28.0000i 1.00385i
\(779\) 10.0000 0.358287
\(780\) 0 0
\(781\) 15.0000 0.536742
\(782\) 0 0
\(783\) 0 0
\(784\) 6.00000 0.214286
\(785\) 18.0000 + 9.00000i 0.642448 + 0.321224i
\(786\) 0 0
\(787\) 27.0000i 0.962446i 0.876598 + 0.481223i \(0.159807\pi\)
−0.876598 + 0.481223i \(0.840193\pi\)
\(788\) 18.0000i 0.641223i
\(789\) 0 0
\(790\) 6.00000 + 3.00000i 0.213470 + 0.106735i
\(791\) 15.0000 0.533339
\(792\) 0 0
\(793\) 8.00000i 0.284088i
\(794\) −31.0000 −1.10015
\(795\) 0 0
\(796\) −21.0000 −0.744325
\(797\) 22.0000i 0.779280i 0.920967 + 0.389640i \(0.127401\pi\)