Properties

Label 3822.2.c.d.883.2
Level $3822$
Weight $2$
Character 3822.883
Analytic conductor $30.519$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3822.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(30.5188236525\)
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 78)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 883.2
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 3822.883
Dual form 3822.2.c.d.883.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -2.00000i q^{5} -1.00000i q^{6} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -2.00000i q^{5} -1.00000i q^{6} -1.00000i q^{8} +1.00000 q^{9} +2.00000 q^{10} +1.00000 q^{12} +(3.00000 + 2.00000i) q^{13} +2.00000i q^{15} +1.00000 q^{16} +2.00000 q^{17} +1.00000i q^{18} +6.00000i q^{19} +2.00000i q^{20} +4.00000 q^{23} +1.00000i q^{24} +1.00000 q^{25} +(-2.00000 + 3.00000i) q^{26} -1.00000 q^{27} -10.0000 q^{29} -2.00000 q^{30} -10.0000i q^{31} +1.00000i q^{32} +2.00000i q^{34} -1.00000 q^{36} +8.00000i q^{37} -6.00000 q^{38} +(-3.00000 - 2.00000i) q^{39} -2.00000 q^{40} -10.0000i q^{41} +4.00000 q^{43} -2.00000i q^{45} +4.00000i q^{46} +12.0000i q^{47} -1.00000 q^{48} +1.00000i q^{50} -2.00000 q^{51} +(-3.00000 - 2.00000i) q^{52} -6.00000 q^{53} -1.00000i q^{54} -6.00000i q^{57} -10.0000i q^{58} -4.00000i q^{59} -2.00000i q^{60} -2.00000 q^{61} +10.0000 q^{62} -1.00000 q^{64} +(4.00000 - 6.00000i) q^{65} -2.00000i q^{67} -2.00000 q^{68} -4.00000 q^{69} -1.00000i q^{72} +4.00000i q^{73} -8.00000 q^{74} -1.00000 q^{75} -6.00000i q^{76} +(2.00000 - 3.00000i) q^{78} -2.00000i q^{80} +1.00000 q^{81} +10.0000 q^{82} +4.00000i q^{83} -4.00000i q^{85} +4.00000i q^{86} +10.0000 q^{87} +6.00000i q^{89} +2.00000 q^{90} -4.00000 q^{92} +10.0000i q^{93} -12.0000 q^{94} +12.0000 q^{95} -1.00000i q^{96} +12.0000i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{3} - 2 q^{4} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{3} - 2 q^{4} + 2 q^{9} + 4 q^{10} + 2 q^{12} + 6 q^{13} + 2 q^{16} + 4 q^{17} + 8 q^{23} + 2 q^{25} - 4 q^{26} - 2 q^{27} - 20 q^{29} - 4 q^{30} - 2 q^{36} - 12 q^{38} - 6 q^{39} - 4 q^{40} + 8 q^{43} - 2 q^{48} - 4 q^{51} - 6 q^{52} - 12 q^{53} - 4 q^{61} + 20 q^{62} - 2 q^{64} + 8 q^{65} - 4 q^{68} - 8 q^{69} - 16 q^{74} - 2 q^{75} + 4 q^{78} + 2 q^{81} + 20 q^{82} + 20 q^{87} + 4 q^{90} - 8 q^{92} - 24 q^{94} + 24 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3822\mathbb{Z}\right)^\times\).

\(n\) \(1471\) \(2549\) \(3433\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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
\(3\) −1.00000 −0.577350
\(4\) −1.00000 −0.500000
\(5\) 2.00000i 0.894427i −0.894427 0.447214i \(-0.852416\pi\)
0.894427 0.447214i \(-0.147584\pi\)
\(6\) 1.00000i 0.408248i
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 1.00000 0.333333
\(10\) 2.00000 0.632456
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 1.00000 0.288675
\(13\) 3.00000 + 2.00000i 0.832050 + 0.554700i
\(14\) 0 0
\(15\) 2.00000i 0.516398i
\(16\) 1.00000 0.250000
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 6.00000i 1.37649i 0.725476 + 0.688247i \(0.241620\pi\)
−0.725476 + 0.688247i \(0.758380\pi\)
\(20\) 2.00000i 0.447214i
\(21\) 0 0
\(22\) 0 0
\(23\) 4.00000 0.834058 0.417029 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 1.00000i 0.204124i
\(25\) 1.00000 0.200000
\(26\) −2.00000 + 3.00000i −0.392232 + 0.588348i
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −10.0000 −1.85695 −0.928477 0.371391i \(-0.878881\pi\)
−0.928477 + 0.371391i \(0.878881\pi\)
\(30\) −2.00000 −0.365148
\(31\) 10.0000i 1.79605i −0.439941 0.898027i \(-0.645001\pi\)
0.439941 0.898027i \(-0.354999\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 2.00000i 0.342997i
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 8.00000i 1.31519i 0.753371 + 0.657596i \(0.228427\pi\)
−0.753371 + 0.657596i \(0.771573\pi\)
\(38\) −6.00000 −0.973329
\(39\) −3.00000 2.00000i −0.480384 0.320256i
\(40\) −2.00000 −0.316228
\(41\) 10.0000i 1.56174i −0.624695 0.780869i \(-0.714777\pi\)
0.624695 0.780869i \(-0.285223\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) 2.00000i 0.298142i
\(46\) 4.00000i 0.589768i
\(47\) 12.0000i 1.75038i 0.483779 + 0.875190i \(0.339264\pi\)
−0.483779 + 0.875190i \(0.660736\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) 1.00000i 0.141421i
\(51\) −2.00000 −0.280056
\(52\) −3.00000 2.00000i −0.416025 0.277350i
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 0 0
\(56\) 0 0
\(57\) 6.00000i 0.794719i
\(58\) 10.0000i 1.31306i
\(59\) 4.00000i 0.520756i −0.965507 0.260378i \(-0.916153\pi\)
0.965507 0.260378i \(-0.0838471\pi\)
\(60\) 2.00000i 0.258199i
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 10.0000 1.27000
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 4.00000 6.00000i 0.496139 0.744208i
\(66\) 0 0
\(67\) 2.00000i 0.244339i −0.992509 0.122169i \(-0.961015\pi\)
0.992509 0.122169i \(-0.0389851\pi\)
\(68\) −2.00000 −0.242536
\(69\) −4.00000 −0.481543
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 4.00000i 0.468165i 0.972217 + 0.234082i \(0.0752085\pi\)
−0.972217 + 0.234082i \(0.924791\pi\)
\(74\) −8.00000 −0.929981
\(75\) −1.00000 −0.115470
\(76\) 6.00000i 0.688247i
\(77\) 0 0
\(78\) 2.00000 3.00000i 0.226455 0.339683i
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 2.00000i 0.223607i
\(81\) 1.00000 0.111111
\(82\) 10.0000 1.10432
\(83\) 4.00000i 0.439057i 0.975606 + 0.219529i \(0.0704519\pi\)
−0.975606 + 0.219529i \(0.929548\pi\)
\(84\) 0 0
\(85\) 4.00000i 0.433861i
\(86\) 4.00000i 0.431331i
\(87\) 10.0000 1.07211
\(88\) 0 0
\(89\) 6.00000i 0.635999i 0.948091 + 0.317999i \(0.103011\pi\)
−0.948091 + 0.317999i \(0.896989\pi\)
\(90\) 2.00000 0.210819
\(91\) 0 0
\(92\) −4.00000 −0.417029
\(93\) 10.0000i 1.03695i
\(94\) −12.0000 −1.23771
\(95\) 12.0000 1.23117
\(96\) 1.00000i 0.102062i
\(97\) 12.0000i 1.21842i 0.793011 + 0.609208i \(0.208512\pi\)
−0.793011 + 0.609208i \(0.791488\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −1.00000 −0.100000
\(101\) −2.00000 −0.199007 −0.0995037 0.995037i \(-0.531726\pi\)
−0.0995037 + 0.995037i \(0.531726\pi\)
\(102\) 2.00000i 0.198030i
\(103\) 16.0000 1.57653 0.788263 0.615338i \(-0.210980\pi\)
0.788263 + 0.615338i \(0.210980\pi\)
\(104\) 2.00000 3.00000i 0.196116 0.294174i
\(105\) 0 0
\(106\) 6.00000i 0.582772i
\(107\) 8.00000 0.773389 0.386695 0.922208i \(-0.373617\pi\)
0.386695 + 0.922208i \(0.373617\pi\)
\(108\) 1.00000 0.0962250
\(109\) 4.00000i 0.383131i 0.981480 + 0.191565i \(0.0613564\pi\)
−0.981480 + 0.191565i \(0.938644\pi\)
\(110\) 0 0
\(111\) 8.00000i 0.759326i
\(112\) 0 0
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 6.00000 0.561951
\(115\) 8.00000i 0.746004i
\(116\) 10.0000 0.928477
\(117\) 3.00000 + 2.00000i 0.277350 + 0.184900i
\(118\) 4.00000 0.368230
\(119\) 0 0
\(120\) 2.00000 0.182574
\(121\) 11.0000 1.00000
\(122\) 2.00000i 0.181071i
\(123\) 10.0000i 0.901670i
\(124\) 10.0000i 0.898027i
\(125\) 12.0000i 1.07331i
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −4.00000 −0.352180
\(130\) 6.00000 + 4.00000i 0.526235 + 0.350823i
\(131\) 8.00000 0.698963 0.349482 0.936943i \(-0.386358\pi\)
0.349482 + 0.936943i \(0.386358\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 2.00000 0.172774
\(135\) 2.00000i 0.172133i
\(136\) 2.00000i 0.171499i
\(137\) 2.00000i 0.170872i −0.996344 0.0854358i \(-0.972772\pi\)
0.996344 0.0854358i \(-0.0272282\pi\)
\(138\) 4.00000i 0.340503i
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 0 0
\(141\) 12.0000i 1.01058i
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 20.0000i 1.66091i
\(146\) −4.00000 −0.331042
\(147\) 0 0
\(148\) 8.00000i 0.657596i
\(149\) 14.0000i 1.14692i 0.819232 + 0.573462i \(0.194400\pi\)
−0.819232 + 0.573462i \(0.805600\pi\)
\(150\) 1.00000i 0.0816497i
\(151\) 10.0000i 0.813788i 0.913475 + 0.406894i \(0.133388\pi\)
−0.913475 + 0.406894i \(0.866612\pi\)
\(152\) 6.00000 0.486664
\(153\) 2.00000 0.161690
\(154\) 0 0
\(155\) −20.0000 −1.60644
\(156\) 3.00000 + 2.00000i 0.240192 + 0.160128i
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) 0 0
\(159\) 6.00000 0.475831
\(160\) 2.00000 0.158114
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 14.0000i 1.09656i −0.836293 0.548282i \(-0.815282\pi\)
0.836293 0.548282i \(-0.184718\pi\)
\(164\) 10.0000i 0.780869i
\(165\) 0 0
\(166\) −4.00000 −0.310460
\(167\) 12.0000i 0.928588i 0.885681 + 0.464294i \(0.153692\pi\)
−0.885681 + 0.464294i \(0.846308\pi\)
\(168\) 0 0
\(169\) 5.00000 + 12.0000i 0.384615 + 0.923077i
\(170\) 4.00000 0.306786
\(171\) 6.00000i 0.458831i
\(172\) −4.00000 −0.304997
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 10.0000i 0.758098i
\(175\) 0 0
\(176\) 0 0
\(177\) 4.00000i 0.300658i
\(178\) −6.00000 −0.449719
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 2.00000i 0.149071i
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) 4.00000i 0.294884i
\(185\) 16.0000 1.17634
\(186\) −10.0000 −0.733236
\(187\) 0 0
\(188\) 12.0000i 0.875190i
\(189\) 0 0
\(190\) 12.0000i 0.870572i
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 1.00000 0.0721688
\(193\) 16.0000i 1.15171i 0.817554 + 0.575853i \(0.195330\pi\)
−0.817554 + 0.575853i \(0.804670\pi\)
\(194\) −12.0000 −0.861550
\(195\) −4.00000 + 6.00000i −0.286446 + 0.429669i
\(196\) 0 0
\(197\) 22.0000i 1.56744i −0.621117 0.783718i \(-0.713321\pi\)
0.621117 0.783718i \(-0.286679\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 2.00000i 0.141069i
\(202\) 2.00000i 0.140720i
\(203\) 0 0
\(204\) 2.00000 0.140028
\(205\) −20.0000 −1.39686
\(206\) 16.0000i 1.11477i
\(207\) 4.00000 0.278019
\(208\) 3.00000 + 2.00000i 0.208013 + 0.138675i
\(209\) 0 0
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) 6.00000 0.412082
\(213\) 0 0
\(214\) 8.00000i 0.546869i
\(215\) 8.00000i 0.545595i
\(216\) 1.00000i 0.0680414i
\(217\) 0 0
\(218\) −4.00000 −0.270914
\(219\) 4.00000i 0.270295i
\(220\) 0 0
\(221\) 6.00000 + 4.00000i 0.403604 + 0.269069i
\(222\) 8.00000 0.536925
\(223\) 14.0000i 0.937509i 0.883328 + 0.468755i \(0.155297\pi\)
−0.883328 + 0.468755i \(0.844703\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 14.0000i 0.931266i
\(227\) 8.00000i 0.530979i −0.964114 0.265489i \(-0.914466\pi\)
0.964114 0.265489i \(-0.0855335\pi\)
\(228\) 6.00000i 0.397360i
\(229\) 4.00000i 0.264327i −0.991228 0.132164i \(-0.957808\pi\)
0.991228 0.132164i \(-0.0421925\pi\)
\(230\) 8.00000 0.527504
\(231\) 0 0
\(232\) 10.0000i 0.656532i
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) −2.00000 + 3.00000i −0.130744 + 0.196116i
\(235\) 24.0000 1.56559
\(236\) 4.00000i 0.260378i
\(237\) 0 0
\(238\) 0 0
\(239\) 16.0000i 1.03495i −0.855697 0.517477i \(-0.826871\pi\)
0.855697 0.517477i \(-0.173129\pi\)
\(240\) 2.00000i 0.129099i
\(241\) 20.0000i 1.28831i −0.764894 0.644157i \(-0.777208\pi\)
0.764894 0.644157i \(-0.222792\pi\)
\(242\) 11.0000i 0.707107i
\(243\) −1.00000 −0.0641500
\(244\) 2.00000 0.128037
\(245\) 0 0
\(246\) −10.0000 −0.637577
\(247\) −12.0000 + 18.0000i −0.763542 + 1.14531i
\(248\) −10.0000 −0.635001
\(249\) 4.00000i 0.253490i
\(250\) 12.0000 0.758947
\(251\) 28.0000 1.76734 0.883672 0.468106i \(-0.155064\pi\)
0.883672 + 0.468106i \(0.155064\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 8.00000i 0.501965i
\(255\) 4.00000i 0.250490i
\(256\) 1.00000 0.0625000
\(257\) −18.0000 −1.12281 −0.561405 0.827541i \(-0.689739\pi\)
−0.561405 + 0.827541i \(0.689739\pi\)
\(258\) 4.00000i 0.249029i
\(259\) 0 0
\(260\) −4.00000 + 6.00000i −0.248069 + 0.372104i
\(261\) −10.0000 −0.618984
\(262\) 8.00000i 0.494242i
\(263\) 24.0000 1.47990 0.739952 0.672660i \(-0.234848\pi\)
0.739952 + 0.672660i \(0.234848\pi\)
\(264\) 0 0
\(265\) 12.0000i 0.737154i
\(266\) 0 0
\(267\) 6.00000i 0.367194i
\(268\) 2.00000i 0.122169i
\(269\) 10.0000 0.609711 0.304855 0.952399i \(-0.401392\pi\)
0.304855 + 0.952399i \(0.401392\pi\)
\(270\) −2.00000 −0.121716
\(271\) 10.0000i 0.607457i 0.952759 + 0.303728i \(0.0982315\pi\)
−0.952759 + 0.303728i \(0.901768\pi\)
\(272\) 2.00000 0.121268
\(273\) 0 0
\(274\) 2.00000 0.120824
\(275\) 0 0
\(276\) 4.00000 0.240772
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) 20.0000i 1.19952i
\(279\) 10.0000i 0.598684i
\(280\) 0 0
\(281\) 10.0000i 0.596550i −0.954480 0.298275i \(-0.903589\pi\)
0.954480 0.298275i \(-0.0964112\pi\)
\(282\) 12.0000 0.714590
\(283\) −4.00000 −0.237775 −0.118888 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) 0 0
\(285\) −12.0000 −0.710819
\(286\) 0 0
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) −13.0000 −0.764706
\(290\) −20.0000 −1.17444
\(291\) 12.0000i 0.703452i
\(292\) 4.00000i 0.234082i
\(293\) 14.0000i 0.817889i 0.912559 + 0.408944i \(0.134103\pi\)
−0.912559 + 0.408944i \(0.865897\pi\)
\(294\) 0 0
\(295\) −8.00000 −0.465778
\(296\) 8.00000 0.464991
\(297\) 0 0
\(298\) −14.0000 −0.810998
\(299\) 12.0000 + 8.00000i 0.693978 + 0.462652i
\(300\) 1.00000 0.0577350
\(301\) 0 0
\(302\) −10.0000 −0.575435
\(303\) 2.00000 0.114897
\(304\) 6.00000i 0.344124i
\(305\) 4.00000i 0.229039i
\(306\) 2.00000i 0.114332i
\(307\) 2.00000i 0.114146i 0.998370 + 0.0570730i \(0.0181768\pi\)
−0.998370 + 0.0570730i \(0.981823\pi\)
\(308\) 0 0
\(309\) −16.0000 −0.910208
\(310\) 20.0000i 1.13592i
\(311\) 28.0000 1.58773 0.793867 0.608091i \(-0.208065\pi\)
0.793867 + 0.608091i \(0.208065\pi\)
\(312\) −2.00000 + 3.00000i −0.113228 + 0.169842i
\(313\) 26.0000 1.46961 0.734803 0.678280i \(-0.237274\pi\)
0.734803 + 0.678280i \(0.237274\pi\)
\(314\) 2.00000i 0.112867i
\(315\) 0 0
\(316\) 0 0
\(317\) 18.0000i 1.01098i 0.862832 + 0.505490i \(0.168688\pi\)
−0.862832 + 0.505490i \(0.831312\pi\)
\(318\) 6.00000i 0.336463i
\(319\) 0 0
\(320\) 2.00000i 0.111803i
\(321\) −8.00000 −0.446516
\(322\) 0 0
\(323\) 12.0000i 0.667698i
\(324\) −1.00000 −0.0555556
\(325\) 3.00000 + 2.00000i 0.166410 + 0.110940i
\(326\) 14.0000 0.775388
\(327\) 4.00000i 0.221201i
\(328\) −10.0000 −0.552158
\(329\) 0 0
\(330\) 0 0
\(331\) 10.0000i 0.549650i −0.961494 0.274825i \(-0.911380\pi\)
0.961494 0.274825i \(-0.0886199\pi\)
\(332\) 4.00000i 0.219529i
\(333\) 8.00000i 0.438397i
\(334\) −12.0000 −0.656611
\(335\) −4.00000 −0.218543
\(336\) 0 0
\(337\) −2.00000 −0.108947 −0.0544735 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) −12.0000 + 5.00000i −0.652714 + 0.271964i
\(339\) −14.0000 −0.760376
\(340\) 4.00000i 0.216930i
\(341\) 0 0
\(342\) −6.00000 −0.324443
\(343\) 0 0
\(344\) 4.00000i 0.215666i
\(345\) 8.00000i 0.430706i
\(346\) 6.00000i 0.322562i
\(347\) −12.0000 −0.644194 −0.322097 0.946707i \(-0.604388\pi\)
−0.322097 + 0.946707i \(0.604388\pi\)
\(348\) −10.0000 −0.536056
\(349\) 16.0000i 0.856460i 0.903670 + 0.428230i \(0.140863\pi\)
−0.903670 + 0.428230i \(0.859137\pi\)
\(350\) 0 0
\(351\) −3.00000 2.00000i −0.160128 0.106752i
\(352\) 0 0
\(353\) 26.0000i 1.38384i −0.721974 0.691920i \(-0.756765\pi\)
0.721974 0.691920i \(-0.243235\pi\)
\(354\) −4.00000 −0.212598
\(355\) 0 0
\(356\) 6.00000i 0.317999i
\(357\) 0 0
\(358\) 0 0
\(359\) 4.00000i 0.211112i 0.994413 + 0.105556i \(0.0336622\pi\)
−0.994413 + 0.105556i \(0.966338\pi\)
\(360\) −2.00000 −0.105409
\(361\) −17.0000 −0.894737
\(362\) 22.0000i 1.15629i
\(363\) −11.0000 −0.577350
\(364\) 0 0
\(365\) 8.00000 0.418739
\(366\) 2.00000i 0.104542i
\(367\) −8.00000 −0.417597 −0.208798 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) 4.00000 0.208514
\(369\) 10.0000i 0.520579i
\(370\) 16.0000i 0.831800i
\(371\) 0 0
\(372\) 10.0000i 0.518476i
\(373\) −6.00000 −0.310668 −0.155334 0.987862i \(-0.549645\pi\)
−0.155334 + 0.987862i \(0.549645\pi\)
\(374\) 0 0
\(375\) 12.0000i 0.619677i
\(376\) 12.0000 0.618853
\(377\) −30.0000 20.0000i −1.54508 1.03005i
\(378\) 0 0
\(379\) 34.0000i 1.74646i 0.487306 + 0.873231i \(0.337980\pi\)
−0.487306 + 0.873231i \(0.662020\pi\)
\(380\) −12.0000 −0.615587
\(381\) −8.00000 −0.409852
\(382\) 12.0000i 0.613973i
\(383\) 4.00000i 0.204390i 0.994764 + 0.102195i \(0.0325866\pi\)
−0.994764 + 0.102195i \(0.967413\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 0 0
\(386\) −16.0000 −0.814379
\(387\) 4.00000 0.203331
\(388\) 12.0000i 0.609208i
\(389\) 30.0000 1.52106 0.760530 0.649303i \(-0.224939\pi\)
0.760530 + 0.649303i \(0.224939\pi\)
\(390\) −6.00000 4.00000i −0.303822 0.202548i
\(391\) 8.00000 0.404577
\(392\) 0 0
\(393\) −8.00000 −0.403547
\(394\) 22.0000 1.10834
\(395\) 0 0
\(396\) 0 0
\(397\) 8.00000i 0.401508i −0.979642 0.200754i \(-0.935661\pi\)
0.979642 0.200754i \(-0.0643393\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 30.0000i 1.49813i −0.662497 0.749064i \(-0.730503\pi\)
0.662497 0.749064i \(-0.269497\pi\)
\(402\) −2.00000 −0.0997509
\(403\) 20.0000 30.0000i 0.996271 1.49441i
\(404\) 2.00000 0.0995037
\(405\) 2.00000i 0.0993808i
\(406\) 0 0
\(407\) 0 0
\(408\) 2.00000i 0.0990148i
\(409\) 4.00000i 0.197787i −0.995098 0.0988936i \(-0.968470\pi\)
0.995098 0.0988936i \(-0.0315304\pi\)
\(410\) 20.0000i 0.987730i
\(411\) 2.00000i 0.0986527i
\(412\) −16.0000 −0.788263
\(413\) 0 0
\(414\) 4.00000i 0.196589i
\(415\) 8.00000 0.392705
\(416\) −2.00000 + 3.00000i −0.0980581 + 0.147087i
\(417\) −20.0000 −0.979404
\(418\) 0 0
\(419\) −40.0000 −1.95413 −0.977064 0.212946i \(-0.931694\pi\)
−0.977064 + 0.212946i \(0.931694\pi\)
\(420\) 0 0
\(421\) 20.0000i 0.974740i 0.873195 + 0.487370i \(0.162044\pi\)
−0.873195 + 0.487370i \(0.837956\pi\)
\(422\) 12.0000i 0.584151i
\(423\) 12.0000i 0.583460i
\(424\) 6.00000i 0.291386i
\(425\) 2.00000 0.0970143
\(426\) 0 0
\(427\) 0 0
\(428\) −8.00000 −0.386695
\(429\) 0 0
\(430\) 8.00000 0.385794
\(431\) 20.0000i 0.963366i −0.876346 0.481683i \(-0.840026\pi\)
0.876346 0.481683i \(-0.159974\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 26.0000 1.24948 0.624740 0.780833i \(-0.285205\pi\)
0.624740 + 0.780833i \(0.285205\pi\)
\(434\) 0 0
\(435\) 20.0000i 0.958927i
\(436\) 4.00000i 0.191565i
\(437\) 24.0000i 1.14808i
\(438\) 4.00000 0.191127
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −4.00000 + 6.00000i −0.190261 + 0.285391i
\(443\) −16.0000 −0.760183 −0.380091 0.924949i \(-0.624107\pi\)
−0.380091 + 0.924949i \(0.624107\pi\)
\(444\) 8.00000i 0.379663i
\(445\) 12.0000 0.568855
\(446\) −14.0000 −0.662919
\(447\) 14.0000i 0.662177i
\(448\) 0 0
\(449\) 6.00000i 0.283158i −0.989927 0.141579i \(-0.954782\pi\)
0.989927 0.141579i \(-0.0452178\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) 0 0
\(452\) −14.0000 −0.658505
\(453\) 10.0000i 0.469841i
\(454\) 8.00000 0.375459
\(455\) 0 0
\(456\) −6.00000 −0.280976
\(457\) 28.0000i 1.30978i 0.755722 + 0.654892i \(0.227286\pi\)
−0.755722 + 0.654892i \(0.772714\pi\)
\(458\) 4.00000 0.186908
\(459\) −2.00000 −0.0933520
\(460\) 8.00000i 0.373002i
\(461\) 30.0000i 1.39724i 0.715493 + 0.698620i \(0.246202\pi\)
−0.715493 + 0.698620i \(0.753798\pi\)
\(462\) 0 0
\(463\) 6.00000i 0.278844i 0.990233 + 0.139422i \(0.0445244\pi\)
−0.990233 + 0.139422i \(0.955476\pi\)
\(464\) −10.0000 −0.464238
\(465\) 20.0000 0.927478
\(466\) 6.00000i 0.277945i
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) −3.00000 2.00000i −0.138675 0.0924500i
\(469\) 0 0
\(470\) 24.0000i 1.10704i
\(471\) −2.00000 −0.0921551
\(472\) −4.00000 −0.184115
\(473\) 0 0
\(474\) 0 0
\(475\) 6.00000i 0.275299i
\(476\) 0 0
\(477\) −6.00000 −0.274721
\(478\) 16.0000 0.731823
\(479\) 24.0000i 1.09659i −0.836286 0.548294i \(-0.815277\pi\)
0.836286 0.548294i \(-0.184723\pi\)
\(480\) −2.00000 −0.0912871
\(481\) −16.0000 + 24.0000i −0.729537 + 1.09431i
\(482\) 20.0000 0.910975
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) 24.0000 1.08978
\(486\) 1.00000i 0.0453609i
\(487\) 18.0000i 0.815658i 0.913058 + 0.407829i \(0.133714\pi\)
−0.913058 + 0.407829i \(0.866286\pi\)
\(488\) 2.00000i 0.0905357i
\(489\) 14.0000i 0.633102i
\(490\) 0 0
\(491\) −28.0000 −1.26362 −0.631811 0.775122i \(-0.717688\pi\)
−0.631811 + 0.775122i \(0.717688\pi\)
\(492\) 10.0000i 0.450835i
\(493\) −20.0000 −0.900755
\(494\) −18.0000 12.0000i −0.809858 0.539906i
\(495\) 0 0
\(496\) 10.0000i 0.449013i
\(497\) 0 0
\(498\) 4.00000 0.179244
\(499\) 14.0000i 0.626726i 0.949633 + 0.313363i \(0.101456\pi\)
−0.949633 + 0.313363i \(0.898544\pi\)
\(500\) 12.0000i 0.536656i
\(501\) 12.0000i 0.536120i
\(502\) 28.0000i 1.24970i
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 0 0
\(505\) 4.00000i 0.177998i
\(506\) 0 0
\(507\) −5.00000 12.0000i −0.222058 0.532939i
\(508\) −8.00000 −0.354943
\(509\) 6.00000i 0.265945i 0.991120 + 0.132973i \(0.0424523\pi\)
−0.991120 + 0.132973i \(0.957548\pi\)
\(510\) −4.00000 −0.177123
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 6.00000i 0.264906i
\(514\) 18.0000i 0.793946i
\(515\) 32.0000i 1.41009i
\(516\) 4.00000 0.176090
\(517\) 0 0
\(518\) 0 0
\(519\) −6.00000 −0.263371
\(520\) −6.00000 4.00000i −0.263117 0.175412i
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 10.0000i 0.437688i
\(523\) −4.00000 −0.174908 −0.0874539 0.996169i \(-0.527873\pi\)
−0.0874539 + 0.996169i \(0.527873\pi\)
\(524\) −8.00000 −0.349482
\(525\) 0 0
\(526\) 24.0000i 1.04645i
\(527\) 20.0000i 0.871214i
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) −12.0000 −0.521247
\(531\) 4.00000i 0.173585i
\(532\) 0 0
\(533\) 20.0000 30.0000i 0.866296 1.29944i
\(534\) 6.00000 0.259645
\(535\) 16.0000i 0.691740i
\(536\) −2.00000 −0.0863868
\(537\) 0 0
\(538\) 10.0000i 0.431131i
\(539\) 0 0
\(540\) 2.00000i 0.0860663i
\(541\) 20.0000i 0.859867i −0.902861 0.429934i \(-0.858537\pi\)
0.902861 0.429934i \(-0.141463\pi\)
\(542\) −10.0000 −0.429537
\(543\) 22.0000 0.944110
\(544\) 2.00000i 0.0857493i
\(545\) 8.00000 0.342682
\(546\) 0 0
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) 2.00000i 0.0854358i
\(549\) −2.00000 −0.0853579
\(550\) 0 0
\(551\) 60.0000i 2.55609i
\(552\) 4.00000i 0.170251i
\(553\) 0 0
\(554\) 2.00000i 0.0849719i
\(555\) −16.0000 −0.679162
\(556\) −20.0000 −0.848189
\(557\) 18.0000i 0.762684i 0.924434 + 0.381342i \(0.124538\pi\)
−0.924434 + 0.381342i \(0.875462\pi\)
\(558\) 10.0000 0.423334
\(559\) 12.0000 + 8.00000i 0.507546 + 0.338364i
\(560\) 0 0
\(561\) 0 0
\(562\) 10.0000 0.421825
\(563\) 16.0000 0.674320 0.337160 0.941447i \(-0.390534\pi\)
0.337160 + 0.941447i \(0.390534\pi\)
\(564\) 12.0000i 0.505291i
\(565\) 28.0000i 1.17797i
\(566\) 4.00000i 0.168133i
\(567\) 0 0
\(568\) 0 0
\(569\) 10.0000 0.419222 0.209611 0.977785i \(-0.432780\pi\)
0.209611 + 0.977785i \(0.432780\pi\)
\(570\) 12.0000i 0.502625i
\(571\) −28.0000 −1.17176 −0.585882 0.810397i \(-0.699252\pi\)
−0.585882 + 0.810397i \(0.699252\pi\)
\(572\) 0 0
\(573\) −12.0000 −0.501307
\(574\) 0 0
\(575\) 4.00000 0.166812
\(576\) −1.00000 −0.0416667
\(577\) 8.00000i 0.333044i −0.986038 0.166522i \(-0.946746\pi\)
0.986038 0.166522i \(-0.0532537\pi\)
\(578\) 13.0000i 0.540729i
\(579\) 16.0000i 0.664937i
\(580\) 20.0000i 0.830455i
\(581\) 0 0
\(582\) 12.0000 0.497416
\(583\) 0 0
\(584\) 4.00000 0.165521
\(585\) 4.00000 6.00000i 0.165380 0.248069i
\(586\) −14.0000 −0.578335
\(587\) 28.0000i 1.15568i −0.816149 0.577842i \(-0.803895\pi\)
0.816149 0.577842i \(-0.196105\pi\)
\(588\) 0 0
\(589\) 60.0000 2.47226
\(590\) 8.00000i 0.329355i
\(591\) 22.0000i 0.904959i
\(592\) 8.00000i 0.328798i
\(593\) 26.0000i 1.06769i −0.845582 0.533846i \(-0.820746\pi\)
0.845582 0.533846i \(-0.179254\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 14.0000i 0.573462i
\(597\) 0 0
\(598\) −8.00000 + 12.0000i −0.327144 + 0.490716i
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 1.00000i 0.0408248i
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 0 0
\(603\) 2.00000i 0.0814463i
\(604\) 10.0000i 0.406894i
\(605\) 22.0000i 0.894427i
\(606\) 2.00000i 0.0812444i
\(607\) 32.0000 1.29884 0.649420 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) −6.00000 −0.243332
\(609\) 0 0
\(610\) −4.00000 −0.161955
\(611\) −24.0000 + 36.0000i −0.970936 + 1.45640i
\(612\) −2.00000 −0.0808452
\(613\) 16.0000i 0.646234i 0.946359 + 0.323117i \(0.104731\pi\)
−0.946359 + 0.323117i \(0.895269\pi\)
\(614\) −2.00000 −0.0807134
\(615\) 20.0000 0.806478
\(616\) 0 0
\(617\) 22.0000i 0.885687i −0.896599 0.442843i \(-0.853970\pi\)
0.896599 0.442843i \(-0.146030\pi\)
\(618\) 16.0000i 0.643614i
\(619\) 26.0000i 1.04503i 0.852631 + 0.522514i \(0.175006\pi\)
−0.852631 + 0.522514i \(0.824994\pi\)
\(620\) 20.0000 0.803219
\(621\) −4.00000 −0.160514
\(622\) 28.0000i 1.12270i
\(623\) 0 0
\(624\) −3.00000 2.00000i −0.120096 0.0800641i
\(625\) −19.0000 −0.760000
\(626\) 26.0000i 1.03917i
\(627\) 0 0
\(628\) −2.00000 −0.0798087
\(629\) 16.0000i 0.637962i
\(630\) 0 0
\(631\) 10.0000i 0.398094i 0.979990 + 0.199047i \(0.0637846\pi\)
−0.979990 + 0.199047i \(0.936215\pi\)
\(632\) 0 0
\(633\) −12.0000 −0.476957
\(634\) −18.0000 −0.714871
\(635\) 16.0000i 0.634941i
\(636\) −6.00000 −0.237915
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −2.00000 −0.0790569
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) 8.00000i 0.315735i
\(643\) 6.00000i 0.236617i −0.992977 0.118308i \(-0.962253\pi\)
0.992977 0.118308i \(-0.0377472\pi\)
\(644\) 0 0
\(645\) 8.00000i 0.315000i
\(646\) −12.0000 −0.472134
\(647\) 32.0000 1.25805 0.629025 0.777385i \(-0.283454\pi\)
0.629025 + 0.777385i \(0.283454\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 0 0
\(650\) −2.00000 + 3.00000i −0.0784465 + 0.117670i
\(651\) 0 0
\(652\) 14.0000i 0.548282i
\(653\) −26.0000 −1.01746 −0.508729 0.860927i \(-0.669885\pi\)
−0.508729 + 0.860927i \(0.669885\pi\)
\(654\) 4.00000 0.156412
\(655\) 16.0000i 0.625172i
\(656\) 10.0000i 0.390434i
\(657\) 4.00000i 0.156055i
\(658\) 0 0
\(659\) 20.0000 0.779089 0.389545 0.921008i \(-0.372632\pi\)
0.389545 + 0.921008i \(0.372632\pi\)
\(660\) 0 0
\(661\) 40.0000i 1.55582i 0.628376 + 0.777910i \(0.283720\pi\)
−0.628376 + 0.777910i \(0.716280\pi\)
\(662\) 10.0000 0.388661
\(663\) −6.00000 4.00000i −0.233021 0.155347i
\(664\) 4.00000 0.155230
\(665\) 0 0
\(666\) −8.00000 −0.309994
\(667\) −40.0000 −1.54881
\(668\) 12.0000i 0.464294i
\(669\) 14.0000i 0.541271i
\(670\) 4.00000i 0.154533i
\(671\) 0 0
\(672\) 0 0
\(673\) −6.00000 −0.231283 −0.115642 0.993291i \(-0.536892\pi\)
−0.115642 + 0.993291i \(0.536892\pi\)
\(674\) 2.00000i 0.0770371i
\(675\) −1.00000 −0.0384900
\(676\) −5.00000 12.0000i −0.192308 0.461538i
\(677\) −18.0000 −0.691796 −0.345898 0.938272i \(-0.612426\pi\)
−0.345898 + 0.938272i \(0.612426\pi\)
\(678\) 14.0000i 0.537667i
\(679\) 0 0
\(680\) −4.00000 −0.153393
\(681\) 8.00000i 0.306561i
\(682\) 0 0
\(683\) 24.0000i 0.918334i −0.888350 0.459167i \(-0.848148\pi\)
0.888350 0.459167i \(-0.151852\pi\)
\(684\) 6.00000i 0.229416i
\(685\) −4.00000 −0.152832
\(686\) 0 0
\(687\) 4.00000i 0.152610i
\(688\) 4.00000 0.152499
\(689\) −18.0000 12.0000i −0.685745 0.457164i
\(690\) −8.00000 −0.304555
\(691\) 10.0000i 0.380418i 0.981744 + 0.190209i \(0.0609166\pi\)
−0.981744 + 0.190209i \(0.939083\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) 12.0000i 0.455514i
\(695\) 40.0000i 1.51729i
\(696\) 10.0000i 0.379049i
\(697\) 20.0000i 0.757554i
\(698\) −16.0000 −0.605609
\(699\) 6.00000 0.226941
\(700\) 0 0
\(701\) 22.0000 0.830929 0.415464 0.909610i \(-0.363619\pi\)
0.415464 + 0.909610i \(0.363619\pi\)
\(702\) 2.00000 3.00000i 0.0754851 0.113228i
\(703\) −48.0000 −1.81035
\(704\) 0 0
\(705\) −24.0000 −0.903892
\(706\) 26.0000 0.978523
\(707\) 0 0
\(708\) 4.00000i 0.150329i
\(709\) 36.0000i 1.35201i −0.736898 0.676004i \(-0.763710\pi\)
0.736898 0.676004i \(-0.236290\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 6.00000 0.224860
\(713\) 40.0000i 1.49801i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 16.0000i 0.597531i
\(718\) −4.00000 −0.149279
\(719\) −20.0000 −0.745874 −0.372937 0.927857i \(-0.621649\pi\)
−0.372937 + 0.927857i \(0.621649\pi\)
\(720\) 2.00000i 0.0745356i
\(721\) 0 0
\(722\) 17.0000i 0.632674i
\(723\) 20.0000i 0.743808i
\(724\) 22.0000 0.817624
\(725\) −10.0000 −0.371391
\(726\) 11.0000i 0.408248i
\(727\) −8.00000 −0.296704 −0.148352 0.988935i \(-0.547397\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 8.00000i 0.296093i
\(731\) 8.00000 0.295891
\(732\) −2.00000 −0.0739221
\(733\) 44.0000i 1.62518i 0.582838 + 0.812589i \(0.301942\pi\)
−0.582838 + 0.812589i \(0.698058\pi\)
\(734\) 8.00000i 0.295285i
\(735\) 0 0
\(736\) 4.00000i 0.147442i
\(737\) 0 0
\(738\) 10.0000 0.368105
\(739\) 26.0000i 0.956425i −0.878244 0.478213i \(-0.841285\pi\)
0.878244 0.478213i \(-0.158715\pi\)
\(740\) −16.0000 −0.588172
\(741\) 12.0000 18.0000i 0.440831 0.661247i
\(742\) 0 0
\(743\) 16.0000i 0.586983i 0.955962 + 0.293492i \(0.0948173\pi\)
−0.955962 + 0.293492i \(0.905183\pi\)
\(744\) 10.0000 0.366618
\(745\) 28.0000 1.02584
\(746\) 6.00000i 0.219676i
\(747\) 4.00000i 0.146352i
\(748\) 0 0
\(749\) 0 0
\(750\) −12.0000 −0.438178
\(751\) 32.0000 1.16770 0.583848 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) 12.0000i 0.437595i
\(753\) −28.0000 −1.02038
\(754\) 20.0000 30.0000i 0.728357 1.09254i
\(755\) 20.0000 0.727875
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) −34.0000 −1.23494
\(759\) 0 0
\(760\) 12.0000i 0.435286i
\(761\) 30.0000i 1.08750i −0.839248 0.543750i \(-0.817004\pi\)
0.839248 0.543750i \(-0.182996\pi\)
\(762\) 8.00000i 0.289809i
\(763\) 0 0
\(764\) −12.0000 −0.434145
\(765\) 4.00000i 0.144620i
\(766\) −4.00000 −0.144526
\(767\) 8.00000 12.0000i 0.288863 0.433295i
\(768\) −1.00000 −0.0360844
\(769\) 24.0000i 0.865462i −0.901523 0.432731i \(-0.857550\pi\)
0.901523 0.432731i \(-0.142450\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) 16.0000i 0.575853i
\(773\) 6.00000i 0.215805i −0.994161 0.107903i \(-0.965587\pi\)
0.994161 0.107903i \(-0.0344134\pi\)
\(774\) 4.00000i 0.143777i
\(775\) 10.0000i 0.359211i
\(776\) 12.0000 0.430775
\(777\) 0 0
\(778\) 30.0000i 1.07555i
\(779\) 60.0000 2.14972
\(780\) 4.00000 6.00000i 0.143223 0.214834i
\(781\) 0 0
\(782\) 8.00000i 0.286079i
\(783\) 10.0000 0.357371
\(784\) 0 0
\(785\) 4.00000i 0.142766i
\(786\) 8.00000i 0.285351i
\(787\) 38.0000i 1.35455i −0.735728 0.677277i \(-0.763160\pi\)
0.735728 0.677277i \(-0.236840\pi\)
\(788\) 22.0000i 0.783718i
\(789\) −24.0000 −0.854423
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −6.00000 4.00000i −0.213066 0.142044i
\(794\) 8.00000 0.283909
\(795\) 12.0000i