Properties

Label 3150.2.m.k.2843.4
Level 3150
Weight 2
Character 3150.2843
Analytic conductor 25.153
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{24})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 2843.4
Root \(-0.258819 + 0.965926i\)
Character \(\chi\) = 3150.2843
Dual form 3150.2.m.k.1457.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -3.41421i q^{11} +(2.02494 + 2.02494i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(-4.37101 - 4.37101i) q^{17} +4.87832i q^{19} +(2.41421 - 2.41421i) q^{22} +(-3.74238 + 3.74238i) q^{23} +2.86370i q^{26} +(-0.707107 - 0.707107i) q^{28} +5.21682 q^{29} -4.93942 q^{31} +(-0.707107 - 0.707107i) q^{32} -6.18154i q^{34} +(-6.87832 + 6.87832i) q^{37} +(-3.44949 + 3.44949i) q^{38} +8.77729i q^{41} +(-0.174857 - 0.174857i) q^{43} +3.41421 q^{44} -5.29253 q^{46} +(3.42883 + 3.42883i) q^{47} -1.00000i q^{49} +(-2.02494 + 2.02494i) q^{52} +(-6.43916 + 6.43916i) q^{53} -1.00000i q^{56} +(3.68885 + 3.68885i) q^{58} +2.22803 q^{59} -15.2526 q^{61} +(-3.49269 - 3.49269i) q^{62} -1.00000i q^{64} +(3.81382 - 3.81382i) q^{67} +(4.37101 - 4.37101i) q^{68} -10.9282i q^{71} +(-2.51059 - 2.51059i) q^{73} -9.72741 q^{74} -4.87832 q^{76} +(2.41421 + 2.41421i) q^{77} +9.98414i q^{79} +(-6.20648 + 6.20648i) q^{82} +(-2.35640 + 2.35640i) q^{83} -0.247285i q^{86} +(2.41421 + 2.41421i) q^{88} +4.07055 q^{89} -2.86370 q^{91} +(-3.74238 - 3.74238i) q^{92} +4.84909i q^{94} +(-5.64564 + 5.64564i) q^{97} +(0.707107 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q + 8q^{13} - 8q^{14} - 8q^{16} + 8q^{22} - 16q^{23} - 16q^{37} - 8q^{38} - 8q^{43} + 16q^{44} + 8q^{46} + 8q^{47} - 8q^{52} - 32q^{53} - 8q^{58} - 8q^{59} - 32q^{61} - 32q^{62} + 16q^{67} - 16q^{74} + 8q^{77} - 8q^{82} + 8q^{83} + 8q^{88} + 16q^{89} + 8q^{91} - 16q^{92} + 16q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) 0 0
\(4\) 1.00000i 0.500000i
\(5\) 0 0
\(6\) 0 0
\(7\) −0.707107 + 0.707107i −0.267261 + 0.267261i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 0 0
\(10\) 0 0
\(11\) 3.41421i 1.02942i −0.857363 0.514712i \(-0.827899\pi\)
0.857363 0.514712i \(-0.172101\pi\)
\(12\) 0 0
\(13\) 2.02494 + 2.02494i 0.561618 + 0.561618i 0.929767 0.368149i \(-0.120008\pi\)
−0.368149 + 0.929767i \(0.620008\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) −4.37101 4.37101i −1.06013 1.06013i −0.998073 0.0620526i \(-0.980235\pi\)
−0.0620526 0.998073i \(-0.519765\pi\)
\(18\) 0 0
\(19\) 4.87832i 1.11916i 0.828776 + 0.559581i \(0.189038\pi\)
−0.828776 + 0.559581i \(0.810962\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 2.41421 2.41421i 0.514712 0.514712i
\(23\) −3.74238 + 3.74238i −0.780341 + 0.780341i −0.979888 0.199547i \(-0.936053\pi\)
0.199547 + 0.979888i \(0.436053\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 2.86370i 0.561618i
\(27\) 0 0
\(28\) −0.707107 0.707107i −0.133631 0.133631i
\(29\) 5.21682 0.968739 0.484369 0.874864i \(-0.339049\pi\)
0.484369 + 0.874864i \(0.339049\pi\)
\(30\) 0 0
\(31\) −4.93942 −0.887145 −0.443573 0.896238i \(-0.646289\pi\)
−0.443573 + 0.896238i \(0.646289\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 0 0
\(34\) 6.18154i 1.06013i
\(35\) 0 0
\(36\) 0 0
\(37\) −6.87832 + 6.87832i −1.13079 + 1.13079i −0.140742 + 0.990046i \(0.544949\pi\)
−0.990046 + 0.140742i \(0.955051\pi\)
\(38\) −3.44949 + 3.44949i −0.559581 + 0.559581i
\(39\) 0 0
\(40\) 0 0
\(41\) 8.77729i 1.37078i 0.728175 + 0.685392i \(0.240369\pi\)
−0.728175 + 0.685392i \(0.759631\pi\)
\(42\) 0 0
\(43\) −0.174857 0.174857i −0.0266654 0.0266654i 0.693648 0.720314i \(-0.256002\pi\)
−0.720314 + 0.693648i \(0.756002\pi\)
\(44\) 3.41421 0.514712
\(45\) 0 0
\(46\) −5.29253 −0.780341
\(47\) 3.42883 + 3.42883i 0.500146 + 0.500146i 0.911483 0.411338i \(-0.134938\pi\)
−0.411338 + 0.911483i \(0.634938\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) −2.02494 + 2.02494i −0.280809 + 0.280809i
\(53\) −6.43916 + 6.43916i −0.884486 + 0.884486i −0.993987 0.109500i \(-0.965075\pi\)
0.109500 + 0.993987i \(0.465075\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000i 0.133631i
\(57\) 0 0
\(58\) 3.68885 + 3.68885i 0.484369 + 0.484369i
\(59\) 2.22803 0.290065 0.145032 0.989427i \(-0.453671\pi\)
0.145032 + 0.989427i \(0.453671\pi\)
\(60\) 0 0
\(61\) −15.2526 −1.95290 −0.976448 0.215752i \(-0.930780\pi\)
−0.976448 + 0.215752i \(0.930780\pi\)
\(62\) −3.49269 3.49269i −0.443573 0.443573i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 0 0
\(67\) 3.81382 3.81382i 0.465932 0.465932i −0.434662 0.900594i \(-0.643132\pi\)
0.900594 + 0.434662i \(0.143132\pi\)
\(68\) 4.37101 4.37101i 0.530063 0.530063i
\(69\) 0 0
\(70\) 0 0
\(71\) 10.9282i 1.29694i −0.761241 0.648470i \(-0.775409\pi\)
0.761241 0.648470i \(-0.224591\pi\)
\(72\) 0 0
\(73\) −2.51059 2.51059i −0.293842 0.293842i 0.544754 0.838596i \(-0.316623\pi\)
−0.838596 + 0.544754i \(0.816623\pi\)
\(74\) −9.72741 −1.13079
\(75\) 0 0
\(76\) −4.87832 −0.559581
\(77\) 2.41421 + 2.41421i 0.275125 + 0.275125i
\(78\) 0 0
\(79\) 9.98414i 1.12330i 0.827374 + 0.561652i \(0.189834\pi\)
−0.827374 + 0.561652i \(0.810166\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −6.20648 + 6.20648i −0.685392 + 0.685392i
\(83\) −2.35640 + 2.35640i −0.258648 + 0.258648i −0.824504 0.565856i \(-0.808546\pi\)
0.565856 + 0.824504i \(0.308546\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.247285i 0.0266654i
\(87\) 0 0
\(88\) 2.41421 + 2.41421i 0.257356 + 0.257356i
\(89\) 4.07055 0.431478 0.215739 0.976451i \(-0.430784\pi\)
0.215739 + 0.976451i \(0.430784\pi\)
\(90\) 0 0
\(91\) −2.86370 −0.300198
\(92\) −3.74238 3.74238i −0.390170 0.390170i
\(93\) 0 0
\(94\) 4.84909i 0.500146i
\(95\) 0 0
\(96\) 0 0
\(97\) −5.64564 + 5.64564i −0.573228 + 0.573228i −0.933029 0.359801i \(-0.882845\pi\)
0.359801 + 0.933029i \(0.382845\pi\)
\(98\) 0.707107 0.707107i 0.0714286 0.0714286i
\(99\) 0 0
\(100\) 0 0
\(101\) 4.91484i 0.489044i −0.969644 0.244522i \(-0.921369\pi\)
0.969644 0.244522i \(-0.0786311\pi\)
\(102\) 0 0
\(103\) 8.07019 + 8.07019i 0.795179 + 0.795179i 0.982331 0.187152i \(-0.0599256\pi\)
−0.187152 + 0.982331i \(0.559926\pi\)
\(104\) −2.86370 −0.280809
\(105\) 0 0
\(106\) −9.10634 −0.884486
\(107\) −5.77729 5.77729i −0.558512 0.558512i 0.370372 0.928884i \(-0.379230\pi\)
−0.928884 + 0.370372i \(0.879230\pi\)
\(108\) 0 0
\(109\) 6.07712i 0.582083i −0.956710 0.291041i \(-0.905998\pi\)
0.956710 0.291041i \(-0.0940017\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.707107 0.707107i 0.0668153 0.0668153i
\(113\) −6.76733 + 6.76733i −0.636617 + 0.636617i −0.949719 0.313103i \(-0.898632\pi\)
0.313103 + 0.949719i \(0.398632\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 5.21682i 0.484369i
\(117\) 0 0
\(118\) 1.57545 + 1.57545i 0.145032 + 0.145032i
\(119\) 6.18154 0.566661
\(120\) 0 0
\(121\) −0.656854 −0.0597140
\(122\) −10.7852 10.7852i −0.976448 0.976448i
\(123\) 0 0
\(124\) 4.93942i 0.443573i
\(125\) 0 0
\(126\) 0 0
\(127\) −11.0345 + 11.0345i −0.979158 + 0.979158i −0.999787 0.0206295i \(-0.993433\pi\)
0.0206295 + 0.999787i \(0.493433\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 0 0
\(130\) 0 0
\(131\) 2.41370i 0.210886i −0.994425 0.105443i \(-0.966374\pi\)
0.994425 0.105443i \(-0.0336260\pi\)
\(132\) 0 0
\(133\) −3.44949 3.44949i −0.299109 0.299109i
\(134\) 5.39355 0.465932
\(135\) 0 0
\(136\) 6.18154 0.530063
\(137\) −9.39836 9.39836i −0.802956 0.802956i 0.180601 0.983557i \(-0.442196\pi\)
−0.983557 + 0.180601i \(0.942196\pi\)
\(138\) 0 0
\(139\) 11.2621i 0.955236i −0.878568 0.477618i \(-0.841500\pi\)
0.878568 0.477618i \(-0.158500\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 7.72741 7.72741i 0.648470 0.648470i
\(143\) 6.91359 6.91359i 0.578144 0.578144i
\(144\) 0 0
\(145\) 0 0
\(146\) 3.55051i 0.293842i
\(147\) 0 0
\(148\) −6.87832 6.87832i −0.565394 0.565394i
\(149\) 3.18759 0.261138 0.130569 0.991439i \(-0.458320\pi\)
0.130569 + 0.991439i \(0.458320\pi\)
\(150\) 0 0
\(151\) 1.80725 0.147072 0.0735359 0.997293i \(-0.476572\pi\)
0.0735359 + 0.997293i \(0.476572\pi\)
\(152\) −3.44949 3.44949i −0.279791 0.279791i
\(153\) 0 0
\(154\) 3.41421i 0.275125i
\(155\) 0 0
\(156\) 0 0
\(157\) −12.8577 + 12.8577i −1.02615 + 1.02615i −0.0265035 + 0.999649i \(0.508437\pi\)
−0.999649 + 0.0265035i \(0.991563\pi\)
\(158\) −7.05986 + 7.05986i −0.561652 + 0.561652i
\(159\) 0 0
\(160\) 0 0
\(161\) 5.29253i 0.417110i
\(162\) 0 0
\(163\) −10.0884 10.0884i −0.790188 0.790188i 0.191336 0.981525i \(-0.438718\pi\)
−0.981525 + 0.191336i \(0.938718\pi\)
\(164\) −8.77729 −0.685392
\(165\) 0 0
\(166\) −3.33245 −0.258648
\(167\) −3.31319 3.31319i −0.256383 0.256383i 0.567199 0.823581i \(-0.308027\pi\)
−0.823581 + 0.567199i \(0.808027\pi\)
\(168\) 0 0
\(169\) 4.79920i 0.369169i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.174857 0.174857i 0.0133327 0.0133327i
\(173\) −8.88437 + 8.88437i −0.675466 + 0.675466i −0.958971 0.283505i \(-0.908503\pi\)
0.283505 + 0.958971i \(0.408503\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 3.41421i 0.257356i
\(177\) 0 0
\(178\) 2.87832 + 2.87832i 0.215739 + 0.215739i
\(179\) 24.6556 1.84285 0.921423 0.388560i \(-0.127027\pi\)
0.921423 + 0.388560i \(0.127027\pi\)
\(180\) 0 0
\(181\) −13.2432 −0.984356 −0.492178 0.870495i \(-0.663799\pi\)
−0.492178 + 0.870495i \(0.663799\pi\)
\(182\) −2.02494 2.02494i −0.150099 0.150099i
\(183\) 0 0
\(184\) 5.29253i 0.390170i
\(185\) 0 0
\(186\) 0 0
\(187\) −14.9236 + 14.9236i −1.09132 + 1.09132i
\(188\) −3.42883 + 3.42883i −0.250073 + 0.250073i
\(189\) 0 0
\(190\) 0 0
\(191\) 19.7228i 1.42709i −0.700610 0.713545i \(-0.747089\pi\)
0.700610 0.713545i \(-0.252911\pi\)
\(192\) 0 0
\(193\) 7.01461 + 7.01461i 0.504923 + 0.504923i 0.912964 0.408041i \(-0.133788\pi\)
−0.408041 + 0.912964i \(0.633788\pi\)
\(194\) −7.98414 −0.573228
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 17.5394 + 17.5394i 1.24963 + 1.24963i 0.955882 + 0.293752i \(0.0949041\pi\)
0.293752 + 0.955882i \(0.405096\pi\)
\(198\) 0 0
\(199\) 15.9683i 1.13196i 0.824418 + 0.565981i \(0.191502\pi\)
−0.824418 + 0.565981i \(0.808498\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 3.47531 3.47531i 0.244522 0.244522i
\(203\) −3.68885 + 3.68885i −0.258906 + 0.258906i
\(204\) 0 0
\(205\) 0 0
\(206\) 11.4130i 0.795179i
\(207\) 0 0
\(208\) −2.02494 2.02494i −0.140405 0.140405i
\(209\) 16.6556 1.15209
\(210\) 0 0
\(211\) −26.2686 −1.80841 −0.904203 0.427102i \(-0.859535\pi\)
−0.904203 + 0.427102i \(0.859535\pi\)
\(212\) −6.43916 6.43916i −0.442243 0.442243i
\(213\) 0 0
\(214\) 8.17033i 0.558512i
\(215\) 0 0
\(216\) 0 0
\(217\) 3.49269 3.49269i 0.237100 0.237100i
\(218\) 4.29717 4.29717i 0.291041 0.291041i
\(219\) 0 0
\(220\) 0 0
\(221\) 17.7021i 1.19077i
\(222\) 0 0
\(223\) 12.6061 + 12.6061i 0.844166 + 0.844166i 0.989398 0.145232i \(-0.0463928\pi\)
−0.145232 + 0.989398i \(0.546393\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) −9.57045 −0.636617
\(227\) −3.02786 3.02786i −0.200966 0.200966i 0.599448 0.800414i \(-0.295387\pi\)
−0.800414 + 0.599448i \(0.795387\pi\)
\(228\) 0 0
\(229\) 3.50543i 0.231645i 0.993270 + 0.115823i \(0.0369504\pi\)
−0.993270 + 0.115823i \(0.963050\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −3.68885 + 3.68885i −0.242185 + 0.242185i
\(233\) 8.98074 8.98074i 0.588348 0.588348i −0.348836 0.937184i \(-0.613423\pi\)
0.937184 + 0.348836i \(0.113423\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 2.22803i 0.145032i
\(237\) 0 0
\(238\) 4.37101 + 4.37101i 0.283330 + 0.283330i
\(239\) −16.4853 −1.06634 −0.533172 0.846007i \(-0.679000\pi\)
−0.533172 + 0.846007i \(0.679000\pi\)
\(240\) 0 0
\(241\) 27.8179 1.79191 0.895954 0.444147i \(-0.146493\pi\)
0.895954 + 0.444147i \(0.146493\pi\)
\(242\) −0.464466 0.464466i −0.0298570 0.0298570i
\(243\) 0 0
\(244\) 15.2526i 0.976448i
\(245\) 0 0
\(246\) 0 0
\(247\) −9.87832 + 9.87832i −0.628542 + 0.628542i
\(248\) 3.49269 3.49269i 0.221786 0.221786i
\(249\) 0 0
\(250\) 0 0
\(251\) 8.43969i 0.532708i −0.963875 0.266354i \(-0.914181\pi\)
0.963875 0.266354i \(-0.0858191\pi\)
\(252\) 0 0
\(253\) 12.7773 + 12.7773i 0.803302 + 0.803302i
\(254\) −15.6052 −0.979158
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 14.7275 + 14.7275i 0.918678 + 0.918678i 0.996933 0.0782557i \(-0.0249351\pi\)
−0.0782557 + 0.996933i \(0.524935\pi\)
\(258\) 0 0
\(259\) 9.72741i 0.604432i
\(260\) 0 0
\(261\) 0 0
\(262\) 1.70674 1.70674i 0.105443 0.105443i
\(263\) 3.42919 3.42919i 0.211453 0.211453i −0.593432 0.804884i \(-0.702227\pi\)
0.804884 + 0.593432i \(0.202227\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 4.87832i 0.299109i
\(267\) 0 0
\(268\) 3.81382 + 3.81382i 0.232966 + 0.232966i
\(269\) 5.33510 0.325287 0.162643 0.986685i \(-0.447998\pi\)
0.162643 + 0.986685i \(0.447998\pi\)
\(270\) 0 0
\(271\) 17.0479 1.03559 0.517794 0.855506i \(-0.326754\pi\)
0.517794 + 0.855506i \(0.326754\pi\)
\(272\) 4.37101 + 4.37101i 0.265031 + 0.265031i
\(273\) 0 0
\(274\) 13.2913i 0.802956i
\(275\) 0 0
\(276\) 0 0
\(277\) −6.36360 + 6.36360i −0.382351 + 0.382351i −0.871949 0.489597i \(-0.837144\pi\)
0.489597 + 0.871949i \(0.337144\pi\)
\(278\) 7.96348 7.96348i 0.477618 0.477618i
\(279\) 0 0
\(280\) 0 0
\(281\) 6.14214i 0.366409i 0.983075 + 0.183205i \(0.0586471\pi\)
−0.983075 + 0.183205i \(0.941353\pi\)
\(282\) 0 0
\(283\) 14.4600 + 14.4600i 0.859556 + 0.859556i 0.991286 0.131730i \(-0.0420530\pi\)
−0.131730 + 0.991286i \(0.542053\pi\)
\(284\) 10.9282 0.648470
\(285\) 0 0
\(286\) 9.77729 0.578144
\(287\) −6.20648 6.20648i −0.366357 0.366357i
\(288\) 0 0
\(289\) 21.2114i 1.24773i
\(290\) 0 0
\(291\) 0 0
\(292\) 2.51059 2.51059i 0.146921 0.146921i
\(293\) −3.55708 + 3.55708i −0.207807 + 0.207807i −0.803335 0.595528i \(-0.796943\pi\)
0.595528 + 0.803335i \(0.296943\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 9.72741i 0.565394i
\(297\) 0 0
\(298\) 2.25397 + 2.25397i 0.130569 + 0.130569i
\(299\) −15.1562 −0.876508
\(300\) 0 0
\(301\) 0.247285 0.0142533
\(302\) 1.27792 + 1.27792i 0.0735359 + 0.0735359i
\(303\) 0 0
\(304\) 4.87832i 0.279791i
\(305\) 0 0
\(306\) 0 0
\(307\) 4.32729 4.32729i 0.246971 0.246971i −0.572755 0.819727i \(-0.694125\pi\)
0.819727 + 0.572755i \(0.194125\pi\)
\(308\) −2.41421 + 2.41421i −0.137563 + 0.137563i
\(309\) 0 0
\(310\) 0 0
\(311\) 3.69537i 0.209545i 0.994496 + 0.104773i \(0.0334114\pi\)
−0.994496 + 0.104773i \(0.966589\pi\)
\(312\) 0 0
\(313\) −13.3390 13.3390i −0.753966 0.753966i 0.221251 0.975217i \(-0.428986\pi\)
−0.975217 + 0.221251i \(0.928986\pi\)
\(314\) −18.1835 −1.02615
\(315\) 0 0
\(316\) −9.98414 −0.561652
\(317\) −13.5601 13.5601i −0.761612 0.761612i 0.215002 0.976614i \(-0.431024\pi\)
−0.976614 + 0.215002i \(0.931024\pi\)
\(318\) 0 0
\(319\) 17.8113i 0.997243i
\(320\) 0 0
\(321\) 0 0
\(322\) 3.74238 3.74238i 0.208555 0.208555i
\(323\) 21.3232 21.3232i 1.18645 1.18645i
\(324\) 0 0
\(325\) 0 0
\(326\) 14.2672i 0.790188i
\(327\) 0 0
\(328\) −6.20648 6.20648i −0.342696 0.342696i
\(329\) −4.84909 −0.267339
\(330\) 0 0
\(331\) 12.1849 0.669745 0.334872 0.942263i \(-0.391307\pi\)
0.334872 + 0.942263i \(0.391307\pi\)
\(332\) −2.35640 2.35640i −0.129324 0.129324i
\(333\) 0 0
\(334\) 4.68556i 0.256383i
\(335\) 0 0
\(336\) 0 0
\(337\) 14.8403 14.8403i 0.808401 0.808401i −0.175991 0.984392i \(-0.556313\pi\)
0.984392 + 0.175991i \(0.0563129\pi\)
\(338\) 3.39355 3.39355i 0.184585 0.184585i
\(339\) 0 0
\(340\) 0 0
\(341\) 16.8642i 0.913249i
\(342\) 0 0
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) 0.247285 0.0133327
\(345\) 0 0
\(346\) −12.5644 −0.675466
\(347\) 13.5731 + 13.5731i 0.728642 + 0.728642i 0.970349 0.241707i \(-0.0777073\pi\)
−0.241707 + 0.970349i \(0.577707\pi\)
\(348\) 0 0
\(349\) 23.9467i 1.28184i 0.767608 + 0.640920i \(0.221447\pi\)
−0.767608 + 0.640920i \(0.778553\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −2.41421 + 2.41421i −0.128678 + 0.128678i
\(353\) −17.0693 + 17.0693i −0.908508 + 0.908508i −0.996152 0.0876442i \(-0.972066\pi\)
0.0876442 + 0.996152i \(0.472066\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 4.07055i 0.215739i
\(357\) 0 0
\(358\) 17.4341 + 17.4341i 0.921423 + 0.921423i
\(359\) −11.9223 −0.629236 −0.314618 0.949218i \(-0.601876\pi\)
−0.314618 + 0.949218i \(0.601876\pi\)
\(360\) 0 0
\(361\) −4.79796 −0.252524
\(362\) −9.36433 9.36433i −0.492178 0.492178i
\(363\) 0 0
\(364\) 2.86370i 0.150099i
\(365\) 0 0
\(366\) 0 0
\(367\) −17.6572 + 17.6572i −0.921699 + 0.921699i −0.997150 0.0754503i \(-0.975961\pi\)
0.0754503 + 0.997150i \(0.475961\pi\)
\(368\) 3.74238 3.74238i 0.195085 0.195085i
\(369\) 0 0
\(370\) 0 0
\(371\) 9.10634i 0.472778i
\(372\) 0 0
\(373\) −16.7980 16.7980i −0.869765 0.869765i 0.122681 0.992446i \(-0.460851\pi\)
−0.992446 + 0.122681i \(0.960851\pi\)
\(374\) −21.1051 −1.09132
\(375\) 0 0
\(376\) −4.84909 −0.250073
\(377\) 10.5638 + 10.5638i 0.544061 + 0.544061i
\(378\) 0 0
\(379\) 14.7821i 0.759306i −0.925129 0.379653i \(-0.876043\pi\)
0.925129 0.379653i \(-0.123957\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 13.9461 13.9461i 0.713545 0.713545i
\(383\) 19.2573 19.2573i 0.984000 0.984000i −0.0158744 0.999874i \(-0.505053\pi\)
0.999874 + 0.0158744i \(0.00505318\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 9.92016i 0.504923i
\(387\) 0 0
\(388\) −5.64564 5.64564i −0.286614 0.286614i
\(389\) 7.50397 0.380466 0.190233 0.981739i \(-0.439076\pi\)
0.190233 + 0.981739i \(0.439076\pi\)
\(390\) 0 0
\(391\) 32.7160 1.65452
\(392\) 0.707107 + 0.707107i 0.0357143 + 0.0357143i
\(393\) 0 0
\(394\) 24.8045i 1.24963i
\(395\) 0 0
\(396\) 0 0
\(397\) −7.67324 + 7.67324i −0.385109 + 0.385109i −0.872939 0.487830i \(-0.837789\pi\)
0.487830 + 0.872939i \(0.337789\pi\)
\(398\) −11.2913 + 11.2913i −0.565981 + 0.565981i
\(399\) 0 0
\(400\) 0 0
\(401\) 1.80828i 0.0903011i −0.998980 0.0451506i \(-0.985623\pi\)
0.998980 0.0451506i \(-0.0143768\pi\)
\(402\) 0 0
\(403\) −10.0020 10.0020i −0.498237 0.498237i
\(404\) 4.91484 0.244522
\(405\) 0 0
\(406\) −5.21682 −0.258906
\(407\) 23.4840 + 23.4840i 1.16406 + 1.16406i
\(408\) 0 0
\(409\) 35.3440i 1.74765i 0.486243 + 0.873824i \(0.338367\pi\)
−0.486243 + 0.873824i \(0.661633\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −8.07019 + 8.07019i −0.397590 + 0.397590i
\(413\) −1.57545 + 1.57545i −0.0775230 + 0.0775230i
\(414\) 0 0
\(415\) 0 0
\(416\) 2.86370i 0.140405i
\(417\) 0 0
\(418\) 11.7773 + 11.7773i 0.576046 + 0.576046i
\(419\) 27.4979 1.34336 0.671681 0.740841i \(-0.265573\pi\)
0.671681 + 0.740841i \(0.265573\pi\)
\(420\) 0 0
\(421\) −5.86194 −0.285694 −0.142847 0.989745i \(-0.545626\pi\)
−0.142847 + 0.989745i \(0.545626\pi\)
\(422\) −18.5747 18.5747i −0.904203 0.904203i
\(423\) 0 0
\(424\) 9.10634i 0.442243i
\(425\) 0 0
\(426\) 0 0
\(427\) 10.7852 10.7852i 0.521934 0.521934i
\(428\) 5.77729 5.77729i 0.279256 0.279256i
\(429\) 0 0
\(430\) 0 0
\(431\) 21.4794i 1.03463i −0.855796 0.517313i \(-0.826932\pi\)
0.855796 0.517313i \(-0.173068\pi\)
\(432\) 0 0
\(433\) 16.0406 + 16.0406i 0.770862 + 0.770862i 0.978257 0.207395i \(-0.0664986\pi\)
−0.207395 + 0.978257i \(0.566499\pi\)
\(434\) 4.93942 0.237100
\(435\) 0 0
\(436\) 6.07712 0.291041
\(437\) −18.2565 18.2565i −0.873328 0.873328i
\(438\) 0 0
\(439\) 11.8583i 0.565967i 0.959125 + 0.282984i \(0.0913242\pi\)
−0.959125 + 0.282984i \(0.908676\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 12.5173 12.5173i 0.595386 0.595386i
\(443\) −19.9223 + 19.9223i −0.946538 + 0.946538i −0.998642 0.0521039i \(-0.983407\pi\)
0.0521039 + 0.998642i \(0.483407\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 17.8277i 0.844166i
\(447\) 0 0
\(448\) 0.707107 + 0.707107i 0.0334077 + 0.0334077i
\(449\) 23.6138 1.11440 0.557201 0.830377i \(-0.311875\pi\)
0.557201 + 0.830377i \(0.311875\pi\)
\(450\) 0 0
\(451\) 29.9676 1.41112
\(452\) −6.76733 6.76733i −0.318308 0.318308i
\(453\) 0 0
\(454\) 4.28205i 0.200966i
\(455\) 0 0
\(456\) 0 0
\(457\) 19.4150 19.4150i 0.908196 0.908196i −0.0879308 0.996127i \(-0.528025\pi\)
0.996127 + 0.0879308i \(0.0280254\pi\)
\(458\) −2.47871 + 2.47871i −0.115823 + 0.115823i
\(459\) 0 0
\(460\) 0 0
\(461\) 29.8406i 1.38981i −0.719100 0.694906i \(-0.755446\pi\)
0.719100 0.694906i \(-0.244554\pi\)
\(462\) 0 0
\(463\) −9.13505 9.13505i −0.424542 0.424542i 0.462222 0.886764i \(-0.347052\pi\)
−0.886764 + 0.462222i \(0.847052\pi\)
\(464\) −5.21682 −0.242185
\(465\) 0 0
\(466\) 12.7007 0.588348
\(467\) 2.03591 + 2.03591i 0.0942106 + 0.0942106i 0.752641 0.658431i \(-0.228779\pi\)
−0.658431 + 0.752641i \(0.728779\pi\)
\(468\) 0 0
\(469\) 5.39355i 0.249051i
\(470\) 0 0
\(471\) 0 0
\(472\) −1.57545 + 1.57545i −0.0725162 + 0.0725162i
\(473\) −0.596999 + 0.596999i −0.0274500 + 0.0274500i
\(474\) 0 0
\(475\) 0 0
\(476\) 6.18154i 0.283330i
\(477\) 0 0
\(478\) −11.6569 11.6569i −0.533172 0.533172i
\(479\) −38.9202 −1.77831 −0.889154 0.457608i \(-0.848706\pi\)
−0.889154 + 0.457608i \(0.848706\pi\)
\(480\) 0 0
\(481\) −27.8564 −1.27014
\(482\) 19.6702 + 19.6702i 0.895954 + 0.895954i
\(483\) 0 0
\(484\) 0.656854i 0.0298570i
\(485\) 0 0
\(486\) 0 0
\(487\) 23.6040 23.6040i 1.06960 1.06960i 0.0722080 0.997390i \(-0.476995\pi\)
0.997390 0.0722080i \(-0.0230045\pi\)
\(488\) 10.7852 10.7852i 0.488224 0.488224i
\(489\) 0 0
\(490\) 0 0
\(491\) 26.4735i 1.19473i −0.801969 0.597366i \(-0.796214\pi\)
0.801969 0.597366i \(-0.203786\pi\)
\(492\) 0 0
\(493\) −22.8028 22.8028i −1.02698 1.02698i
\(494\) −13.9700 −0.628542
\(495\) 0 0
\(496\) 4.93942 0.221786
\(497\) 7.72741 + 7.72741i 0.346622 + 0.346622i
\(498\) 0 0
\(499\) 40.3855i 1.80790i −0.427634 0.903952i \(-0.640653\pi\)
0.427634 0.903952i \(-0.359347\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 5.96776 5.96776i 0.266354 0.266354i
\(503\) 18.8113 18.8113i 0.838756 0.838756i −0.149940 0.988695i \(-0.547908\pi\)
0.988695 + 0.149940i \(0.0479079\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 18.0698i 0.803302i
\(507\) 0 0
\(508\) −11.0345 11.0345i −0.489579 0.489579i
\(509\) −28.6793 −1.27119 −0.635594 0.772024i \(-0.719245\pi\)
−0.635594 + 0.772024i \(0.719245\pi\)
\(510\) 0 0
\(511\) 3.55051 0.157065
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) 20.8279i 0.918678i
\(515\) 0 0
\(516\) 0 0
\(517\) 11.7067 11.7067i 0.514862 0.514862i
\(518\) 6.87832 6.87832i 0.302216 0.302216i
\(519\) 0 0
\(520\) 0 0
\(521\) 16.4916i 0.722509i 0.932467 + 0.361254i \(0.117651\pi\)
−0.932467 + 0.361254i \(0.882349\pi\)
\(522\) 0 0
\(523\) 22.8596 + 22.8596i 0.999579 + 0.999579i 1.00000 0.000420508i \(-0.000133852\pi\)
−0.000420508 1.00000i \(0.500134\pi\)
\(524\) 2.41370 0.105443
\(525\) 0 0
\(526\) 4.84961 0.211453
\(527\) 21.5902 + 21.5902i 0.940485 + 0.940485i
\(528\) 0 0
\(529\) 5.01086i 0.217863i
\(530\) 0 0
\(531\) 0 0
\(532\) 3.44949 3.44949i 0.149554 0.149554i
\(533\) −17.7735 + 17.7735i −0.769857 + 0.769857i
\(534\) 0 0
\(535\) 0 0
\(536\) 5.39355i 0.232966i
\(537\) 0 0
\(538\) 3.77249 + 3.77249i 0.162643 + 0.162643i
\(539\) −3.41421 −0.147061
\(540\) 0 0
\(541\) 30.4412 1.30877 0.654385 0.756161i \(-0.272927\pi\)
0.654385 + 0.756161i \(0.272927\pi\)
\(542\) 12.0547 + 12.0547i 0.517794 + 0.517794i
\(543\) 0 0
\(544\) 6.18154i 0.265031i
\(545\) 0 0
\(546\) 0 0
\(547\) 22.9103 22.9103i 0.979574 0.979574i −0.0202215 0.999796i \(-0.506437\pi\)
0.999796 + 0.0202215i \(0.00643715\pi\)
\(548\) 9.39836 9.39836i 0.401478 0.401478i
\(549\) 0 0
\(550\) 0 0
\(551\) 25.4493i 1.08418i
\(552\) 0 0
\(553\) −7.05986 7.05986i −0.300216 0.300216i
\(554\) −8.99948 −0.382351
\(555\) 0 0
\(556\) 11.2621 0.477618
\(557\) 4.43612 + 4.43612i 0.187965 + 0.187965i 0.794816 0.606851i \(-0.207568\pi\)
−0.606851 + 0.794816i \(0.707568\pi\)
\(558\) 0 0
\(559\) 0.708151i 0.0299516i
\(560\) 0 0
\(561\) 0 0
\(562\) −4.34315 + 4.34315i −0.183205 + 0.183205i
\(563\) 8.80589 8.80589i 0.371124 0.371124i −0.496763 0.867886i \(-0.665478\pi\)
0.867886 + 0.496763i \(0.165478\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 20.4495i 0.859556i
\(567\) 0 0
\(568\) 7.72741 + 7.72741i 0.324235 + 0.324235i
\(569\) −17.6654 −0.740573 −0.370286 0.928918i \(-0.620740\pi\)
−0.370286 + 0.928918i \(0.620740\pi\)
\(570\) 0 0
\(571\) 30.9852 1.29669 0.648345 0.761347i \(-0.275462\pi\)
0.648345 + 0.761347i \(0.275462\pi\)
\(572\) 6.91359 + 6.91359i 0.289072 + 0.289072i
\(573\) 0 0
\(574\) 8.77729i 0.366357i
\(575\) 0 0
\(576\) 0 0
\(577\) −16.4860 + 16.4860i −0.686322 + 0.686322i −0.961417 0.275095i \(-0.911291\pi\)
0.275095 + 0.961417i \(0.411291\pi\)
\(578\) −14.9988 + 14.9988i −0.623866 + 0.623866i
\(579\) 0 0
\(580\) 0 0
\(581\) 3.33245i 0.138253i
\(582\) 0 0
\(583\) 21.9847 + 21.9847i 0.910512 + 0.910512i
\(584\) 3.55051 0.146921
\(585\) 0 0
\(586\) −5.03047 −0.207807
\(587\) 29.4681 + 29.4681i 1.21628 + 1.21628i 0.968926 + 0.247351i \(0.0795602\pi\)
0.247351 + 0.968926i \(0.420440\pi\)
\(588\) 0 0
\(589\) 24.0960i 0.992859i
\(590\) 0 0
\(591\) 0 0
\(592\) 6.87832 6.87832i 0.282697 0.282697i
\(593\) 22.7874 22.7874i 0.935767 0.935767i −0.0622906 0.998058i \(-0.519841\pi\)
0.998058 + 0.0622906i \(0.0198406\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 3.18759i 0.130569i
\(597\) 0 0
\(598\) −10.7171 10.7171i −0.438254 0.438254i
\(599\) 34.9314 1.42726 0.713629 0.700524i \(-0.247050\pi\)
0.713629 + 0.700524i \(0.247050\pi\)
\(600\) 0 0
\(601\) −39.8254 −1.62451 −0.812256 0.583301i \(-0.801761\pi\)
−0.812256 + 0.583301i \(0.801761\pi\)
\(602\) 0.174857 + 0.174857i 0.00712663 + 0.00712663i
\(603\) 0 0
\(604\) 1.80725i 0.0735359i
\(605\) 0 0
\(606\) 0 0
\(607\) −22.7675 + 22.7675i −0.924104 + 0.924104i −0.997316 0.0732124i \(-0.976675\pi\)
0.0732124 + 0.997316i \(0.476675\pi\)
\(608\) 3.44949 3.44949i 0.139895 0.139895i
\(609\) 0 0
\(610\) 0 0
\(611\) 13.8864i 0.561782i
\(612\) 0 0
\(613\) −3.99446 3.99446i −0.161335 0.161335i 0.621823 0.783158i \(-0.286392\pi\)
−0.783158 + 0.621823i \(0.786392\pi\)
\(614\) 6.11971 0.246971
\(615\) 0 0
\(616\) −3.41421 −0.137563
\(617\) −1.46002 1.46002i −0.0587783 0.0587783i 0.677107 0.735885i \(-0.263234\pi\)
−0.735885 + 0.677107i \(0.763234\pi\)
\(618\) 0 0
\(619\) 47.4138i 1.90572i 0.303407 + 0.952861i \(0.401876\pi\)
−0.303407 + 0.952861i \(0.598124\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −2.61302 + 2.61302i −0.104773 + 0.104773i
\(623\) −2.87832 + 2.87832i −0.115317 + 0.115317i
\(624\) 0 0
\(625\) 0 0
\(626\) 18.8642i 0.753966i
\(627\) 0 0
\(628\) −12.8577 12.8577i −0.513076 0.513076i
\(629\) 60.1304 2.39755
\(630\) 0 0
\(631\) 4.98665 0.198515 0.0992577 0.995062i \(-0.468353\pi\)
0.0992577 + 0.995062i \(0.468353\pi\)
\(632\) −7.05986 7.05986i −0.280826 0.280826i
\(633\) 0 0
\(634\) 19.1769i 0.761612i
\(635\) 0 0
\(636\) 0 0
\(637\) 2.02494 2.02494i 0.0802312 0.0802312i
\(638\) 12.5945 12.5945i 0.498621 0.498621i
\(639\) 0 0
\(640\) 0 0
\(641\) 37.4961i 1.48101i 0.672052 + 0.740504i \(0.265413\pi\)
−0.672052 + 0.740504i \(0.734587\pi\)
\(642\) 0 0
\(643\) −4.58970 4.58970i −0.181000 0.181000i 0.610791 0.791792i \(-0.290851\pi\)
−0.791792 + 0.610791i \(0.790851\pi\)
\(644\) 5.29253 0.208555
\(645\) 0 0
\(646\) 30.1555 1.18645
\(647\) −27.4412 27.4412i −1.07883 1.07883i −0.996615 0.0822112i \(-0.973802\pi\)
−0.0822112 0.996615i \(-0.526198\pi\)
\(648\) 0 0
\(649\) 7.60697i 0.298600i
\(650\) 0 0
\(651\) 0 0
\(652\) 10.0884 10.0884i 0.395094 0.395094i
\(653\) −13.3212 + 13.3212i −0.521300 + 0.521300i −0.917964 0.396664i \(-0.870168\pi\)
0.396664 + 0.917964i \(0.370168\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 8.77729i 0.342696i
\(657\) 0 0
\(658\) −3.42883 3.42883i −0.133670 0.133670i
\(659\) 13.9355 0.542851 0.271425 0.962459i \(-0.412505\pi\)
0.271425 + 0.962459i \(0.412505\pi\)
\(660\) 0 0
\(661\) 38.5879 1.50089 0.750447 0.660930i \(-0.229838\pi\)
0.750447 + 0.660930i \(0.229838\pi\)
\(662\) 8.61605 + 8.61605i 0.334872 + 0.334872i
\(663\) 0 0
\(664\) 3.33245i 0.129324i
\(665\) 0 0
\(666\) 0 0
\(667\) −19.5233 + 19.5233i −0.755946 + 0.755946i
\(668\) 3.31319 3.31319i 0.128191 0.128191i
\(669\) 0 0
\(670\) 0 0
\(671\) 52.0757i 2.01036i
\(672\) 0 0
\(673\) −28.1223 28.1223i −1.08403 1.08403i −0.996129 0.0879048i \(-0.971983\pi\)
−0.0879048 0.996129i \(-0.528017\pi\)
\(674\) 20.9873 0.808401
\(675\) 0 0
\(676\) 4.79920 0.184585
\(677\) 22.7408 + 22.7408i 0.873999 + 0.873999i 0.992905 0.118907i \(-0.0379389\pi\)
−0.118907 + 0.992905i \(0.537939\pi\)
\(678\) 0 0
\(679\) 7.98414i 0.306403i
\(680\) 0 0
\(681\) 0 0
\(682\) −11.9248 + 11.9248i −0.456624 + 0.456624i
\(683\) 11.9549 11.9549i 0.457442 0.457442i −0.440373 0.897815i \(-0.645154\pi\)
0.897815 + 0.440373i \(0.145154\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000i 0.0381802i
\(687\) 0 0
\(688\) 0.174857 + 0.174857i 0.00666635 + 0.00666635i
\(689\) −26.0779 −0.993488
\(690\) 0 0
\(691\) 6.79167 0.258367 0.129184 0.991621i \(-0.458764\pi\)
0.129184 + 0.991621i \(0.458764\pi\)
\(692\) −8.88437 8.88437i −0.337733 0.337733i
\(693\) 0 0
\(694\) 19.1953i 0.728642i
\(695\) 0 0
\(696\) 0 0
\(697\) 38.3656 38.3656i 1.45320 1.45320i
\(698\) −16.9329 + 16.9329i −0.640920 + 0.640920i
\(699\) 0 0
\(700\) 0 0
\(701\) 40.7354i 1.53855i 0.638915 + 0.769277i \(0.279383\pi\)
−0.638915 + 0.769277i \(0.720617\pi\)
\(702\) 0 0
\(703\) −33.5546 33.5546i −1.26554 1.26554i
\(704\) −3.41421 −0.128678
\(705\) 0 0
\(706\) −24.1396 −0.908508
\(707\) 3.47531 + 3.47531i 0.130703 + 0.130703i
\(708\) 0 0
\(709\) 30.8035i 1.15685i 0.815735 + 0.578425i \(0.196333\pi\)
−0.815735 + 0.578425i \(0.803667\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −2.87832 + 2.87832i −0.107869 + 0.107869i
\(713\) 18.4852 18.4852i 0.692276 0.692276i
\(714\) 0 0
\(715\) 0 0
\(716\) 24.6556i 0.921423i
\(717\) 0 0
\(718\) −8.43035 8.43035i −0.314618 0.314618i
\(719\) 13.0945 0.488341 0.244170 0.969732i \(-0.421484\pi\)
0.244170 + 0.969732i \(0.421484\pi\)
\(720\) 0 0
\(721\) −11.4130 −0.425041
\(722\) −3.39267 3.39267i −0.126262 0.126262i
\(723\) 0 0
\(724\) 13.2432i 0.492178i
\(725\) 0 0
\(726\) 0 0
\(727\) 34.4418 34.4418i 1.27738 1.27738i 0.335246 0.942131i \(-0.391181\pi\)
0.942131 0.335246i \(-0.108819\pi\)
\(728\) 2.02494 2.02494i 0.0750494 0.0750494i
\(729\) 0 0
\(730\) 0 0
\(731\) 1.52860i 0.0565374i
\(732\) 0 0
\(733\) −20.9524 20.9524i −0.773895 0.773895i 0.204890 0.978785i \(-0.434316\pi\)
−0.978785 + 0.204890i \(0.934316\pi\)
\(734\) −24.9711 −0.921699
\(735\) 0 0
\(736\) 5.29253 0.195085
\(737\) −13.0212 13.0212i −0.479641 0.479641i
\(738\) 0 0
\(739\) 51.0850i 1.87919i 0.342288 + 0.939595i \(0.388798\pi\)
−0.342288 + 0.939595i \(0.611202\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 6.43916 6.43916i 0.236389 0.236389i
\(743\) −23.2763 + 23.2763i −0.853925 + 0.853925i −0.990614 0.136689i \(-0.956354\pi\)
0.136689 + 0.990614i \(0.456354\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 23.7559i 0.869765i
\(747\) 0 0
\(748\) −14.9236 14.9236i −0.545659 0.545659i
\(749\) 8.17033 0.298537
\(750\) 0 0
\(751\) 16.7035 0.609520 0.304760 0.952429i \(-0.401424\pi\)
0.304760 + 0.952429i \(0.401424\pi\)
\(752\) −3.42883 3.42883i −0.125036 0.125036i
\(753\) 0 0
\(754\) 14.9394i 0.544061i
\(755\) 0 0
\(756\) 0 0
\(757\) 6.56461 6.56461i 0.238595 0.238595i −0.577673 0.816268i \(-0.696039\pi\)
0.816268 + 0.577673i \(0.196039\pi\)
\(758\) 10.4525 10.4525i 0.379653 0.379653i
\(759\) 0 0
\(760\) 0 0
\(761\) 46.4642i 1.68433i 0.539223 + 0.842163i \(0.318718\pi\)
−0.539223 + 0.842163i \(0.681282\pi\)
\(762\) 0 0
\(763\) 4.29717 + 4.29717i 0.155568 + 0.155568i
\(764\) 19.7228 0.713545
\(765\) 0 0
\(766\) 27.2339 0.984000
\(767\) 4.51163 + 4.51163i 0.162906 + 0.162906i
\(768\) 0 0
\(769\) 39.1177i 1.41062i −0.708898 0.705311i \(-0.750807\pi\)
0.708898 0.705311i \(-0.249193\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −7.01461 + 7.01461i −0.252461 + 0.252461i
\(773\) 4.88918 4.88918i 0.175851 0.175851i −0.613693 0.789545i \(-0.710317\pi\)
0.789545 + 0.613693i \(0.210317\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 7.98414i 0.286614i
\(777\) 0 0
\(778\) 5.30611 + 5.30611i 0.190233 + 0.190233i
\(779\) −42.8184 −1.53413
\(780\) 0 0
\(781\) −37.3112 −1.33510
\(782\) 23.1337 + 23.1337i 0.827259 + 0.827259i
\(783\) 0 0
\(784\) 1.00000i 0.0357143i
\(785\) 0 0
\(786\) 0 0
\(787\) 10.6549 10.6549i 0.379805 0.379805i −0.491226 0.871032i \(-0.663451\pi\)
0.871032 + 0.491226i \(0.163451\pi\)
\(788\) −17.5394 + 17.5394i −0.624817 + 0.624817i
\(789\) 0 0
\(790\) 0 0
\(791\) 9.57045i 0.340286i
\(792\) 0 0
\(793\) −30.8857 30.8857i −1.09678 1.09678i
\(794\) −10.8516 −0.385109
\(795\) 0 0
\(796\) −15.9683 −0.565981
\(797\) −8.27135 8.27135i −0.292986 0.292986i 0.545273 0.838259i \(-0.316426\pi\)
−0.838259 + 0.545273i \(0.816426\pi\)
\(798\) 0 0
\(799\)