Properties

Label 3150.2.m.j.2843.1
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: 8.0.1698758656.6
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 630)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 2843.1
Root \(1.69230i\)
Character \(\chi\) = 3150.2843
Dual form 3150.2.m.j.1457.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} -6.36365i q^{11} +(1.69230 + 1.69230i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(0.979056 + 0.979056i) q^{17} +(-4.49978 + 4.49978i) q^{22} +(-1.38459 + 1.38459i) q^{23} -2.39327i q^{26} +(-0.707107 - 0.707107i) q^{28} +5.81975 q^{29} +2.36365 q^{31} +(0.707107 + 0.707107i) q^{32} -1.38459i q^{34} +(-0.157074 + 0.157074i) q^{37} -8.94944i q^{41} +(-5.88438 - 5.88438i) q^{43} +6.36365 q^{44} +1.95811 q^{46} +(3.05595 + 3.05595i) q^{47} -1.00000i q^{49} +(-1.69230 + 1.69230i) q^{52} +(0.192517 - 0.192517i) q^{53} +1.00000i q^{56} +(-4.11519 - 4.11519i) q^{58} -10.3842 q^{59} -0.979056 q^{61} +(-1.67135 - 1.67135i) q^{62} -1.00000i q^{64} +(-9.88438 + 9.88438i) q^{67} +(-0.979056 + 0.979056i) q^{68} +12.3423i q^{71} +(-4.71324 - 4.71324i) q^{73} +0.222136 q^{74} +(4.49978 + 4.49978i) q^{77} +6.68541i q^{79} +(-6.32821 + 6.32821i) q^{82} +(11.3427 - 11.3427i) q^{83} +8.32176i q^{86} +(-4.49978 - 4.49978i) q^{88} +11.8371 q^{89} -2.39327 q^{91} +(-1.38459 - 1.38459i) q^{92} -4.32176i q^{94} +(9.39866 - 9.39866i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q + 4q^{13} + 8q^{14} - 8q^{16} + 4q^{22} + 8q^{23} + 24q^{29} - 8q^{31} + 4q^{37} + 12q^{43} + 24q^{44} - 12q^{47} - 4q^{52} + 32q^{53} - 12q^{58} + 16q^{59} + 4q^{62} - 20q^{67} - 36q^{73} + 40q^{74} - 4q^{77} + 12q^{82} + 56q^{83} + 4q^{88} + 72q^{89} + 8q^{92} + 4q^{97} + O(q^{100}) \)

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
\(11\) 6.36365i 1.91871i −0.282197 0.959356i \(-0.591063\pi\)
0.282197 0.959356i \(-0.408937\pi\)
\(12\) 0 0
\(13\) 1.69230 + 1.69230i 0.469359 + 0.469359i 0.901707 0.432348i \(-0.142315\pi\)
−0.432348 + 0.901707i \(0.642315\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 0.979056 + 0.979056i 0.237456 + 0.237456i 0.815796 0.578340i \(-0.196299\pi\)
−0.578340 + 0.815796i \(0.696299\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −4.49978 + 4.49978i −0.959356 + 0.959356i
\(23\) −1.38459 + 1.38459i −0.288708 + 0.288708i −0.836569 0.547861i \(-0.815442\pi\)
0.547861 + 0.836569i \(0.315442\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 2.39327i 0.469359i
\(27\) 0 0
\(28\) −0.707107 0.707107i −0.133631 0.133631i
\(29\) 5.81975 1.08070 0.540350 0.841440i \(-0.318292\pi\)
0.540350 + 0.841440i \(0.318292\pi\)
\(30\) 0 0
\(31\) 2.36365 0.424524 0.212262 0.977213i \(-0.431917\pi\)
0.212262 + 0.977213i \(0.431917\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 0 0
\(34\) 1.38459i 0.237456i
\(35\) 0 0
\(36\) 0 0
\(37\) −0.157074 + 0.157074i −0.0258227 + 0.0258227i −0.719900 0.694078i \(-0.755812\pi\)
0.694078 + 0.719900i \(0.255812\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 8.94944i 1.39767i −0.715284 0.698834i \(-0.753703\pi\)
0.715284 0.698834i \(-0.246297\pi\)
\(42\) 0 0
\(43\) −5.88438 5.88438i −0.897359 0.897359i 0.0978430 0.995202i \(-0.468806\pi\)
−0.995202 + 0.0978430i \(0.968806\pi\)
\(44\) 6.36365 0.959356
\(45\) 0 0
\(46\) 1.95811 0.288708
\(47\) 3.05595 + 3.05595i 0.445756 + 0.445756i 0.893941 0.448185i \(-0.147929\pi\)
−0.448185 + 0.893941i \(0.647929\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) −1.69230 + 1.69230i −0.234679 + 0.234679i
\(53\) 0.192517 0.192517i 0.0264442 0.0264442i −0.693761 0.720205i \(-0.744048\pi\)
0.720205 + 0.693761i \(0.244048\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000i 0.133631i
\(57\) 0 0
\(58\) −4.11519 4.11519i −0.540350 0.540350i
\(59\) −10.3842 −1.35190 −0.675951 0.736947i \(-0.736267\pi\)
−0.675951 + 0.736947i \(0.736267\pi\)
\(60\) 0 0
\(61\) −0.979056 −0.125355 −0.0626777 0.998034i \(-0.519964\pi\)
−0.0626777 + 0.998034i \(0.519964\pi\)
\(62\) −1.67135 1.67135i −0.212262 0.212262i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 0 0
\(67\) −9.88438 + 9.88438i −1.20757 + 1.20757i −0.235756 + 0.971812i \(0.575757\pi\)
−0.971812 + 0.235756i \(0.924243\pi\)
\(68\) −0.979056 + 0.979056i −0.118728 + 0.118728i
\(69\) 0 0
\(70\) 0 0
\(71\) 12.3423i 1.46476i 0.680897 + 0.732379i \(0.261590\pi\)
−0.680897 + 0.732379i \(0.738410\pi\)
\(72\) 0 0
\(73\) −4.71324 4.71324i −0.551643 0.551643i 0.375272 0.926915i \(-0.377549\pi\)
−0.926915 + 0.375272i \(0.877549\pi\)
\(74\) 0.222136 0.0258227
\(75\) 0 0
\(76\) 0 0
\(77\) 4.49978 + 4.49978i 0.512798 + 0.512798i
\(78\) 0 0
\(79\) 6.68541i 0.752168i 0.926586 + 0.376084i \(0.122730\pi\)
−0.926586 + 0.376084i \(0.877270\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −6.32821 + 6.32821i −0.698834 + 0.698834i
\(83\) 11.3427 11.3427i 1.24502 1.24502i 0.287133 0.957891i \(-0.407298\pi\)
0.957891 0.287133i \(-0.0927022\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 8.32176i 0.897359i
\(87\) 0 0
\(88\) −4.49978 4.49978i −0.479678 0.479678i
\(89\) 11.8371 1.25473 0.627365 0.778725i \(-0.284133\pi\)
0.627365 + 0.778725i \(0.284133\pi\)
\(90\) 0 0
\(91\) −2.39327 −0.250883
\(92\) −1.38459 1.38459i −0.144354 0.144354i
\(93\) 0 0
\(94\) 4.32176i 0.445756i
\(95\) 0 0
\(96\) 0 0
\(97\) 9.39866 9.39866i 0.954289 0.954289i −0.0447111 0.999000i \(-0.514237\pi\)
0.999000 + 0.0447111i \(0.0142367\pi\)
\(98\) −0.707107 + 0.707107i −0.0714286 + 0.0714286i
\(99\) 0 0
\(100\) 0 0
\(101\) 16.0501i 1.59705i −0.601964 0.798524i \(-0.705615\pi\)
0.601964 0.798524i \(-0.294385\pi\)
\(102\) 0 0
\(103\) 0.706797 + 0.706797i 0.0696427 + 0.0696427i 0.741070 0.671428i \(-0.234319\pi\)
−0.671428 + 0.741070i \(0.734319\pi\)
\(104\) 2.39327 0.234679
\(105\) 0 0
\(106\) −0.272260 −0.0264442
\(107\) −9.51384 9.51384i −0.919738 0.919738i 0.0772723 0.997010i \(-0.475379\pi\)
−0.997010 + 0.0772723i \(0.975379\pi\)
\(108\) 0 0
\(109\) 14.9577i 1.43269i −0.697749 0.716343i \(-0.745815\pi\)
0.697749 0.716343i \(-0.254185\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.707107 0.707107i 0.0668153 0.0668153i
\(113\) 9.22170 9.22170i 0.867504 0.867504i −0.124691 0.992196i \(-0.539794\pi\)
0.992196 + 0.124691i \(0.0397941\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 5.81975i 0.540350i
\(117\) 0 0
\(118\) 7.34271 + 7.34271i 0.675951 + 0.675951i
\(119\) −1.38459 −0.126926
\(120\) 0 0
\(121\) −29.4961 −2.68146
\(122\) 0.692297 + 0.692297i 0.0626777 + 0.0626777i
\(123\) 0 0
\(124\) 2.36365i 0.212262i
\(125\) 0 0
\(126\) 0 0
\(127\) 5.38459 5.38459i 0.477806 0.477806i −0.426624 0.904429i \(-0.640297\pi\)
0.904429 + 0.426624i \(0.140297\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) 0 0
\(130\) 0 0
\(131\) 13.2718i 1.15956i −0.814772 0.579782i \(-0.803138\pi\)
0.814772 0.579782i \(-0.196862\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 13.9786 1.20757
\(135\) 0 0
\(136\) 1.38459 0.118728
\(137\) −3.56484 3.56484i −0.304565 0.304565i 0.538232 0.842797i \(-0.319092\pi\)
−0.842797 + 0.538232i \(0.819092\pi\)
\(138\) 0 0
\(139\) 1.41359i 0.119899i 0.998201 + 0.0599497i \(0.0190940\pi\)
−0.998201 + 0.0599497i \(0.980906\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 8.72730 8.72730i 0.732379 0.732379i
\(143\) 10.7692 10.7692i 0.900565 0.900565i
\(144\) 0 0
\(145\) 0 0
\(146\) 6.66553i 0.551643i
\(147\) 0 0
\(148\) −0.157074 0.157074i −0.0129114 0.0129114i
\(149\) 20.0609 1.64345 0.821726 0.569882i \(-0.193011\pi\)
0.821726 + 0.569882i \(0.193011\pi\)
\(150\) 0 0
\(151\) 8.81108 0.717035 0.358518 0.933523i \(-0.383282\pi\)
0.358518 + 0.933523i \(0.383282\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 6.36365i 0.512798i
\(155\) 0 0
\(156\) 0 0
\(157\) −15.2654 + 15.2654i −1.21831 + 1.21831i −0.250086 + 0.968224i \(0.580459\pi\)
−0.968224 + 0.250086i \(0.919541\pi\)
\(158\) 4.72730 4.72730i 0.376084 0.376084i
\(159\) 0 0
\(160\) 0 0
\(161\) 1.95811i 0.154321i
\(162\) 0 0
\(163\) −7.11519 7.11519i −0.557304 0.557304i 0.371235 0.928539i \(-0.378935\pi\)
−0.928539 + 0.371235i \(0.878935\pi\)
\(164\) 8.94944 0.698834
\(165\) 0 0
\(166\) −16.0410 −1.24502
\(167\) −16.7128 16.7128i −1.29328 1.29328i −0.932749 0.360527i \(-0.882597\pi\)
−0.360527 0.932749i \(-0.617403\pi\)
\(168\) 0 0
\(169\) 7.27226i 0.559405i
\(170\) 0 0
\(171\) 0 0
\(172\) 5.88438 5.88438i 0.448679 0.448679i
\(173\) 14.7843 14.7843i 1.12403 1.12403i 0.132901 0.991129i \(-0.457571\pi\)
0.991129 0.132901i \(-0.0424292\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 6.36365i 0.479678i
\(177\) 0 0
\(178\) −8.37010 8.37010i −0.627365 0.627365i
\(179\) −12.0205 −0.898455 −0.449227 0.893417i \(-0.648301\pi\)
−0.449227 + 0.893417i \(0.648301\pi\)
\(180\) 0 0
\(181\) 17.5236 1.30252 0.651259 0.758856i \(-0.274241\pi\)
0.651259 + 0.758856i \(0.274241\pi\)
\(182\) 1.69230 + 1.69230i 0.125441 + 0.125441i
\(183\) 0 0
\(184\) 1.95811i 0.144354i
\(185\) 0 0
\(186\) 0 0
\(187\) 6.23037 6.23037i 0.455610 0.455610i
\(188\) −3.05595 + 3.05595i −0.222878 + 0.222878i
\(189\) 0 0
\(190\) 0 0
\(191\) 6.30038i 0.455880i 0.973675 + 0.227940i \(0.0731989\pi\)
−0.973675 + 0.227940i \(0.926801\pi\)
\(192\) 0 0
\(193\) 11.6435 + 11.6435i 0.838119 + 0.838119i 0.988611 0.150492i \(-0.0480857\pi\)
−0.150492 + 0.988611i \(0.548086\pi\)
\(194\) −13.2917 −0.954289
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −1.92849 1.92849i −0.137399 0.137399i 0.635062 0.772461i \(-0.280975\pi\)
−0.772461 + 0.635062i \(0.780975\pi\)
\(198\) 0 0
\(199\) 5.67736i 0.402457i −0.979544 0.201229i \(-0.935507\pi\)
0.979544 0.201229i \(-0.0644934\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −11.3492 + 11.3492i −0.798524 + 0.798524i
\(203\) −4.11519 + 4.11519i −0.288829 + 0.288829i
\(204\) 0 0
\(205\) 0 0
\(206\) 0.999561i 0.0696427i
\(207\) 0 0
\(208\) −1.69230 1.69230i −0.117340 0.117340i
\(209\) 0 0
\(210\) 0 0
\(211\) 7.91622 0.544975 0.272488 0.962159i \(-0.412154\pi\)
0.272488 + 0.962159i \(0.412154\pi\)
\(212\) 0.192517 + 0.192517i 0.0132221 + 0.0132221i
\(213\) 0 0
\(214\) 13.4546i 0.919738i
\(215\) 0 0
\(216\) 0 0
\(217\) −1.67135 + 1.67135i −0.113459 + 0.113459i
\(218\) −10.5767 + 10.5767i −0.716343 + 0.716343i
\(219\) 0 0
\(220\) 0 0
\(221\) 3.31371i 0.222904i
\(222\) 0 0
\(223\) −8.34227 8.34227i −0.558640 0.558640i 0.370280 0.928920i \(-0.379262\pi\)
−0.928920 + 0.370280i \(0.879262\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) −13.0414 −0.867504
\(227\) −3.27270 3.27270i −0.217217 0.217217i 0.590108 0.807324i \(-0.299085\pi\)
−0.807324 + 0.590108i \(0.799085\pi\)
\(228\) 0 0
\(229\) 23.0901i 1.52584i −0.646496 0.762918i \(-0.723766\pi\)
0.646496 0.762918i \(-0.276234\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 4.11519 4.11519i 0.270175 0.270175i
\(233\) 5.23081 5.23081i 0.342682 0.342682i −0.514693 0.857375i \(-0.672094\pi\)
0.857375 + 0.514693i \(0.172094\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 10.3842i 0.675951i
\(237\) 0 0
\(238\) 0.979056 + 0.979056i 0.0634628 + 0.0634628i
\(239\) 5.27182 0.341006 0.170503 0.985357i \(-0.445461\pi\)
0.170503 + 0.985357i \(0.445461\pi\)
\(240\) 0 0
\(241\) −5.27270 −0.339644 −0.169822 0.985475i \(-0.554319\pi\)
−0.169822 + 0.985475i \(0.554319\pi\)
\(242\) 20.8569 + 20.8569i 1.34073 + 1.34073i
\(243\) 0 0
\(244\) 0.979056i 0.0626777i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 1.67135 1.67135i 0.106131 0.106131i
\(249\) 0 0
\(250\) 0 0
\(251\) 20.3423i 1.28399i 0.766708 + 0.641996i \(0.221894\pi\)
−0.766708 + 0.641996i \(0.778106\pi\)
\(252\) 0 0
\(253\) 8.81108 + 8.81108i 0.553948 + 0.553948i
\(254\) −7.61497 −0.477806
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 2.50201 + 2.50201i 0.156071 + 0.156071i 0.780823 0.624752i \(-0.214800\pi\)
−0.624752 + 0.780823i \(0.714800\pi\)
\(258\) 0 0
\(259\) 0.222136i 0.0138028i
\(260\) 0 0
\(261\) 0 0
\(262\) −9.38459 + 9.38459i −0.579782 + 0.579782i
\(263\) −12.6983 + 12.6983i −0.783011 + 0.783011i −0.980338 0.197327i \(-0.936774\pi\)
0.197327 + 0.980338i \(0.436774\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −9.88438 9.88438i −0.603784 0.603784i
\(269\) −26.9196 −1.64131 −0.820657 0.571421i \(-0.806392\pi\)
−0.820657 + 0.571421i \(0.806392\pi\)
\(270\) 0 0
\(271\) 23.1320 1.40517 0.702583 0.711601i \(-0.252030\pi\)
0.702583 + 0.711601i \(0.252030\pi\)
\(272\) −0.979056 0.979056i −0.0593640 0.0593640i
\(273\) 0 0
\(274\) 5.04145i 0.304565i
\(275\) 0 0
\(276\) 0 0
\(277\) −12.2271 + 12.2271i −0.734654 + 0.734654i −0.971538 0.236884i \(-0.923874\pi\)
0.236884 + 0.971538i \(0.423874\pi\)
\(278\) 0.999561 0.999561i 0.0599497 0.0599497i
\(279\) 0 0
\(280\) 0 0
\(281\) 10.4428i 0.622964i −0.950252 0.311482i \(-0.899175\pi\)
0.950252 0.311482i \(-0.100825\pi\)
\(282\) 0 0
\(283\) −22.9577 22.9577i −1.36469 1.36469i −0.867829 0.496863i \(-0.834485\pi\)
−0.496863 0.867829i \(-0.665515\pi\)
\(284\) −12.3423 −0.732379
\(285\) 0 0
\(286\) −15.2299 −0.900565
\(287\) 6.32821 + 6.32821i 0.373542 + 0.373542i
\(288\) 0 0
\(289\) 15.0829i 0.887229i
\(290\) 0 0
\(291\) 0 0
\(292\) 4.71324 4.71324i 0.275822 0.275822i
\(293\) −18.6413 + 18.6413i −1.08904 + 1.08904i −0.0934082 + 0.995628i \(0.529776\pi\)
−0.995628 + 0.0934082i \(0.970224\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.222136i 0.0129114i
\(297\) 0 0
\(298\) −14.1852 14.1852i −0.821726 0.821726i
\(299\) −4.68629 −0.271015
\(300\) 0 0
\(301\) 8.32176 0.479658
\(302\) −6.23037 6.23037i −0.358518 0.358518i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −0.727302 + 0.727302i −0.0415093 + 0.0415093i −0.727557 0.686047i \(-0.759344\pi\)
0.686047 + 0.727557i \(0.259344\pi\)
\(308\) −4.49978 + 4.49978i −0.256399 + 0.256399i
\(309\) 0 0
\(310\) 0 0
\(311\) 24.2295i 1.37393i −0.726691 0.686964i \(-0.758943\pi\)
0.726691 0.686964i \(-0.241057\pi\)
\(312\) 0 0
\(313\) −3.44054 3.44054i −0.194471 0.194471i 0.603154 0.797625i \(-0.293910\pi\)
−0.797625 + 0.603154i \(0.793910\pi\)
\(314\) 21.5885 1.21831
\(315\) 0 0
\(316\) −6.68541 −0.376084
\(317\) −12.9198 12.9198i −0.725649 0.725649i 0.244101 0.969750i \(-0.421507\pi\)
−0.969750 + 0.244101i \(0.921507\pi\)
\(318\) 0 0
\(319\) 37.0349i 2.07355i
\(320\) 0 0
\(321\) 0 0
\(322\) −1.38459 + 1.38459i −0.0771604 + 0.0771604i
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 10.0624i 0.557304i
\(327\) 0 0
\(328\) −6.32821 6.32821i −0.349417 0.349417i
\(329\) −4.32176 −0.238267
\(330\) 0 0
\(331\) 8.76831 0.481950 0.240975 0.970531i \(-0.422533\pi\)
0.240975 + 0.970531i \(0.422533\pi\)
\(332\) 11.3427 + 11.3427i 0.622512 + 0.622512i
\(333\) 0 0
\(334\) 23.6355i 1.29328i
\(335\) 0 0
\(336\) 0 0
\(337\) 12.3427 12.3427i 0.672350 0.672350i −0.285907 0.958257i \(-0.592295\pi\)
0.958257 + 0.285907i \(0.0922949\pi\)
\(338\) −5.14226 + 5.14226i −0.279702 + 0.279702i
\(339\) 0 0
\(340\) 0 0
\(341\) 15.0414i 0.814540i
\(342\) 0 0
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) −8.32176 −0.448679
\(345\) 0 0
\(346\) −20.9082 −1.12403
\(347\) −5.17157 5.17157i −0.277625 0.277625i 0.554535 0.832160i \(-0.312896\pi\)
−0.832160 + 0.554535i \(0.812896\pi\)
\(348\) 0 0
\(349\) 28.9363i 1.54892i 0.632620 + 0.774462i \(0.281979\pi\)
−0.632620 + 0.774462i \(0.718021\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 4.49978 4.49978i 0.239839 0.239839i
\(353\) −10.3637 + 10.3637i −0.551601 + 0.551601i −0.926903 0.375301i \(-0.877539\pi\)
0.375301 + 0.926903i \(0.377539\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 11.8371i 0.627365i
\(357\) 0 0
\(358\) 8.49978 + 8.49978i 0.449227 + 0.449227i
\(359\) −13.2308 −0.698295 −0.349148 0.937068i \(-0.613529\pi\)
−0.349148 + 0.937068i \(0.613529\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) −12.3910 12.3910i −0.651259 0.651259i
\(363\) 0 0
\(364\) 2.39327i 0.125441i
\(365\) 0 0
\(366\) 0 0
\(367\) 3.20943 3.20943i 0.167531 0.167531i −0.618362 0.785893i \(-0.712204\pi\)
0.785893 + 0.618362i \(0.212204\pi\)
\(368\) 1.38459 1.38459i 0.0721770 0.0721770i
\(369\) 0 0
\(370\) 0 0
\(371\) 0.272260i 0.0141350i
\(372\) 0 0
\(373\) 2.26897 + 2.26897i 0.117483 + 0.117483i 0.763404 0.645921i \(-0.223527\pi\)
−0.645921 + 0.763404i \(0.723527\pi\)
\(374\) −8.81108 −0.455610
\(375\) 0 0
\(376\) 4.32176 0.222878
\(377\) 9.84875 + 9.84875i 0.507236 + 0.507236i
\(378\) 0 0
\(379\) 2.39792i 0.123173i −0.998102 0.0615865i \(-0.980384\pi\)
0.998102 0.0615865i \(-0.0196160\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 4.45504 4.45504i 0.227940 0.227940i
\(383\) 16.6838 16.6838i 0.852503 0.852503i −0.137938 0.990441i \(-0.544048\pi\)
0.990441 + 0.137938i \(0.0440476\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 16.4664i 0.838119i
\(387\) 0 0
\(388\) 9.39866 + 9.39866i 0.477144 + 0.477144i
\(389\) 22.0782 1.11941 0.559706 0.828691i \(-0.310914\pi\)
0.559706 + 0.828691i \(0.310914\pi\)
\(390\) 0 0
\(391\) −2.71119 −0.137111
\(392\) −0.707107 0.707107i −0.0357143 0.0357143i
\(393\) 0 0
\(394\) 2.72730i 0.137399i
\(395\) 0 0
\(396\) 0 0
\(397\) −20.9717 + 20.9717i −1.05254 + 1.05254i −0.0540003 + 0.998541i \(0.517197\pi\)
−0.998541 + 0.0540003i \(0.982803\pi\)
\(398\) −4.01450 + 4.01450i −0.201229 + 0.201229i
\(399\) 0 0
\(400\) 0 0
\(401\) 9.29574i 0.464207i −0.972691 0.232103i \(-0.925439\pi\)
0.972691 0.232103i \(-0.0745608\pi\)
\(402\) 0 0
\(403\) 4.00000 + 4.00000i 0.199254 + 0.199254i
\(404\) 16.0501 0.798524
\(405\) 0 0
\(406\) 5.81975 0.288829
\(407\) 0.999561 + 0.999561i 0.0495464 + 0.0495464i
\(408\) 0 0
\(409\) 34.2367i 1.69289i 0.532472 + 0.846447i \(0.321263\pi\)
−0.532472 + 0.846447i \(0.678737\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −0.706797 + 0.706797i −0.0348214 + 0.0348214i
\(413\) 7.34271 7.34271i 0.361311 0.361311i
\(414\) 0 0
\(415\) 0 0
\(416\) 2.39327i 0.117340i
\(417\) 0 0
\(418\) 0 0
\(419\) −13.7753 −0.672969 −0.336484 0.941689i \(-0.609238\pi\)
−0.336484 + 0.941689i \(0.609238\pi\)
\(420\) 0 0
\(421\) 10.6283 0.517991 0.258996 0.965878i \(-0.416608\pi\)
0.258996 + 0.965878i \(0.416608\pi\)
\(422\) −5.59762 5.59762i −0.272488 0.272488i
\(423\) 0 0
\(424\) 0.272260i 0.0132221i
\(425\) 0 0
\(426\) 0 0
\(427\) 0.692297 0.692297i 0.0335026 0.0335026i
\(428\) 9.51384 9.51384i 0.459869 0.459869i
\(429\) 0 0
\(430\) 0 0
\(431\) 18.8877i 0.909787i 0.890546 + 0.454893i \(0.150323\pi\)
−0.890546 + 0.454893i \(0.849677\pi\)
\(432\) 0 0
\(433\) 19.3697 + 19.3697i 0.930846 + 0.930846i 0.997759 0.0669125i \(-0.0213149\pi\)
−0.0669125 + 0.997759i \(0.521315\pi\)
\(434\) 2.36365 0.113459
\(435\) 0 0
\(436\) 14.9577 0.716343
\(437\) 0 0
\(438\) 0 0
\(439\) 4.86628i 0.232255i −0.993234 0.116127i \(-0.962952\pi\)
0.993234 0.116127i \(-0.0370481\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 2.34315 2.34315i 0.111452 0.111452i
\(443\) 7.17070 7.17070i 0.340690 0.340690i −0.515937 0.856627i \(-0.672556\pi\)
0.856627 + 0.515937i \(0.172556\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 11.7977i 0.558640i
\(447\) 0 0
\(448\) 0.707107 + 0.707107i 0.0334077 + 0.0334077i
\(449\) 8.87093 0.418645 0.209323 0.977847i \(-0.432874\pi\)
0.209323 + 0.977847i \(0.432874\pi\)
\(450\) 0 0
\(451\) −56.9511 −2.68172
\(452\) 9.22170 + 9.22170i 0.433752 + 0.433752i
\(453\) 0 0
\(454\) 4.62829i 0.217217i
\(455\) 0 0
\(456\) 0 0
\(457\) −4.27270 + 4.27270i −0.199868 + 0.199868i −0.799944 0.600075i \(-0.795137\pi\)
0.600075 + 0.799944i \(0.295137\pi\)
\(458\) −16.3271 + 16.3271i −0.762918 + 0.762918i
\(459\) 0 0
\(460\) 0 0
\(461\) 0.771724i 0.0359428i 0.999839 + 0.0179714i \(0.00572077\pi\)
−0.999839 + 0.0179714i \(0.994279\pi\)
\(462\) 0 0
\(463\) 19.6150 + 19.6150i 0.911585 + 0.911585i 0.996397 0.0848121i \(-0.0270290\pi\)
−0.0848121 + 0.996397i \(0.527029\pi\)
\(464\) −5.81975 −0.270175
\(465\) 0 0
\(466\) −7.39748 −0.342682
\(467\) −8.18848 8.18848i −0.378918 0.378918i 0.491794 0.870712i \(-0.336341\pi\)
−0.870712 + 0.491794i \(0.836341\pi\)
\(468\) 0 0
\(469\) 13.9786i 0.645473i
\(470\) 0 0
\(471\) 0 0
\(472\) −7.34271 + 7.34271i −0.337975 + 0.337975i
\(473\) −37.4461 + 37.4461i −1.72177 + 1.72177i
\(474\) 0 0
\(475\) 0 0
\(476\) 1.38459i 0.0634628i
\(477\) 0 0
\(478\) −3.72774 3.72774i −0.170503 0.170503i
\(479\) −21.0833 −0.963322 −0.481661 0.876358i \(-0.659966\pi\)
−0.481661 + 0.876358i \(0.659966\pi\)
\(480\) 0 0
\(481\) −0.531630 −0.0242403
\(482\) 3.72836 + 3.72836i 0.169822 + 0.169822i
\(483\) 0 0
\(484\) 29.4961i 1.34073i
\(485\) 0 0
\(486\) 0 0
\(487\) 20.6983 20.6983i 0.937930 0.937930i −0.0602535 0.998183i \(-0.519191\pi\)
0.998183 + 0.0602535i \(0.0191909\pi\)
\(488\) −0.692297 + 0.692297i −0.0313388 + 0.0313388i
\(489\) 0 0
\(490\) 0 0
\(491\) 10.2799i 0.463924i −0.972725 0.231962i \(-0.925485\pi\)
0.972725 0.231962i \(-0.0745146\pi\)
\(492\) 0 0
\(493\) 5.69786 + 5.69786i 0.256619 + 0.256619i
\(494\) 0 0
\(495\) 0 0
\(496\) −2.36365 −0.106131
\(497\) −8.72730 8.72730i −0.391473 0.391473i
\(498\) 0 0
\(499\) 5.16711i 0.231312i 0.993289 + 0.115656i \(0.0368970\pi\)
−0.993289 + 0.115656i \(0.963103\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 14.3842 14.3842i 0.641996 0.641996i
\(503\) 0.741801 0.741801i 0.0330753 0.0330753i −0.690376 0.723451i \(-0.742555\pi\)
0.723451 + 0.690376i \(0.242555\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 12.4607i 0.553948i
\(507\) 0 0
\(508\) 5.38459 + 5.38459i 0.238903 + 0.238903i
\(509\) −1.96723 −0.0871958 −0.0435979 0.999049i \(-0.513882\pi\)
−0.0435979 + 0.999049i \(0.513882\pi\)
\(510\) 0 0
\(511\) 6.66553 0.294866
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 0 0
\(514\) 3.53838i 0.156071i
\(515\) 0 0
\(516\) 0 0
\(517\) 19.4470 19.4470i 0.855278 0.855278i
\(518\) −0.157074 + 0.157074i −0.00690142 + 0.00690142i
\(519\) 0 0
\(520\) 0 0
\(521\) 5.19146i 0.227442i 0.993513 + 0.113721i \(0.0362770\pi\)
−0.993513 + 0.113721i \(0.963723\pi\)
\(522\) 0 0
\(523\) 28.2295 + 28.2295i 1.23439 + 1.23439i 0.962261 + 0.272129i \(0.0877277\pi\)
0.272129 + 0.962261i \(0.412272\pi\)
\(524\) 13.2718 0.579782
\(525\) 0 0
\(526\) 17.9581 0.783011
\(527\) 2.31415 + 2.31415i 0.100806 + 0.100806i
\(528\) 0 0
\(529\) 19.1658i 0.833295i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 15.1451 15.1451i 0.656007 0.656007i
\(534\) 0 0
\(535\) 0 0
\(536\) 13.9786i 0.603784i
\(537\) 0 0
\(538\) 19.0350 + 19.0350i 0.820657 + 0.820657i
\(539\) −6.36365 −0.274102
\(540\) 0 0
\(541\) −14.9167 −0.641317 −0.320659 0.947195i \(-0.603904\pi\)
−0.320659 + 0.947195i \(0.603904\pi\)
\(542\) −16.3568 16.3568i −0.702583 0.702583i
\(543\) 0 0
\(544\) 1.38459i 0.0593640i
\(545\) 0 0
\(546\) 0 0
\(547\) 14.8839 14.8839i 0.636391 0.636391i −0.313272 0.949663i \(-0.601425\pi\)
0.949663 + 0.313272i \(0.101425\pi\)
\(548\) 3.56484 3.56484i 0.152283 0.152283i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −4.72730 4.72730i −0.201025 0.201025i
\(554\) 17.2917 0.734654
\(555\) 0 0
\(556\) −1.41359 −0.0599497
\(557\) 16.1925 + 16.1925i 0.686099 + 0.686099i 0.961367 0.275268i \(-0.0887667\pi\)
−0.275268 + 0.961367i \(0.588767\pi\)
\(558\) 0 0
\(559\) 19.9162i 0.842367i
\(560\) 0 0
\(561\) 0 0
\(562\) −7.38416 + 7.38416i −0.311482 + 0.311482i
\(563\) 4.69830 4.69830i 0.198010 0.198010i −0.601136 0.799146i \(-0.705285\pi\)
0.799146 + 0.601136i \(0.205285\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 32.4671i 1.36469i
\(567\) 0 0
\(568\) 8.72730 + 8.72730i 0.366189 + 0.366189i
\(569\) −38.1643 −1.59993 −0.799965 0.600046i \(-0.795149\pi\)
−0.799965 + 0.600046i \(0.795149\pi\)
\(570\) 0 0
\(571\) −24.6008 −1.02951 −0.514755 0.857337i \(-0.672117\pi\)
−0.514755 + 0.857337i \(0.672117\pi\)
\(572\) 10.7692 + 10.7692i 0.450282 + 0.450282i
\(573\) 0 0
\(574\) 8.94944i 0.373542i
\(575\) 0 0
\(576\) 0 0
\(577\) 8.01318 8.01318i 0.333593 0.333593i −0.520356 0.853949i \(-0.674201\pi\)
0.853949 + 0.520356i \(0.174201\pi\)
\(578\) −10.6652 + 10.6652i −0.443615 + 0.443615i
\(579\) 0 0
\(580\) 0 0
\(581\) 16.0410i 0.665493i
\(582\) 0 0
\(583\) −1.22511 1.22511i −0.0507388 0.0507388i
\(584\) −6.66553 −0.275822
\(585\) 0 0
\(586\) 26.3628 1.08904
\(587\) −7.42648 7.42648i −0.306524 0.306524i 0.537036 0.843559i \(-0.319544\pi\)
−0.843559 + 0.537036i \(0.819544\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0.157074 0.157074i 0.00645568 0.00645568i
\(593\) 13.8157 13.8157i 0.567344 0.567344i −0.364040 0.931383i \(-0.618603\pi\)
0.931383 + 0.364040i \(0.118603\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 20.0609i 0.821726i
\(597\) 0 0
\(598\) 3.31371 + 3.31371i 0.135508 + 0.135508i
\(599\) 0.643527 0.0262938 0.0131469 0.999914i \(-0.495815\pi\)
0.0131469 + 0.999914i \(0.495815\pi\)
\(600\) 0 0
\(601\) 20.0548 0.818051 0.409026 0.912523i \(-0.365869\pi\)
0.409026 + 0.912523i \(0.365869\pi\)
\(602\) −5.88438 5.88438i −0.239829 0.239829i
\(603\) 0 0
\(604\) 8.81108i 0.358518i
\(605\) 0 0
\(606\) 0 0
\(607\) 16.3423 16.3423i 0.663312 0.663312i −0.292847 0.956159i \(-0.594603\pi\)
0.956159 + 0.292847i \(0.0946027\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 10.3431i 0.418439i
\(612\) 0 0
\(613\) −6.29797 6.29797i −0.254373 0.254373i 0.568388 0.822761i \(-0.307567\pi\)
−0.822761 + 0.568388i \(0.807567\pi\)
\(614\) 1.02856 0.0415093
\(615\) 0 0
\(616\) 6.36365 0.256399
\(617\) 15.3632 + 15.3632i 0.618500 + 0.618500i 0.945146 0.326647i \(-0.105919\pi\)
−0.326647 + 0.945146i \(0.605919\pi\)
\(618\) 0 0
\(619\) 35.1462i 1.41264i 0.707891 + 0.706322i \(0.249647\pi\)
−0.707891 + 0.706322i \(0.750353\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −17.1328 + 17.1328i −0.686964 + 0.686964i
\(623\) −8.37010 + 8.37010i −0.335341 + 0.335341i
\(624\) 0 0
\(625\) 0 0
\(626\) 4.86566i 0.194471i
\(627\) 0 0
\(628\) −15.2654 15.2654i −0.609155 0.609155i
\(629\) −0.307568 −0.0122635
\(630\) 0 0
\(631\) 22.5864 0.899151 0.449575 0.893242i \(-0.351575\pi\)
0.449575 + 0.893242i \(0.351575\pi\)
\(632\) 4.72730 + 4.72730i 0.188042 + 0.188042i
\(633\) 0 0
\(634\) 18.2714i 0.725649i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.69230 1.69230i 0.0670513 0.0670513i
\(638\) −26.1876 + 26.1876i −1.03678 + 1.03678i
\(639\) 0 0
\(640\) 0 0
\(641\) 6.90352i 0.272673i 0.990663 + 0.136336i \(0.0435328\pi\)
−0.990663 + 0.136336i \(0.956467\pi\)
\(642\) 0 0
\(643\) −30.4542 30.4542i −1.20100 1.20100i −0.973864 0.227131i \(-0.927066\pi\)
−0.227131 0.973864i \(-0.572934\pi\)
\(644\) 1.95811 0.0771604
\(645\) 0 0
\(646\) 0 0
\(647\) 13.9726 + 13.9726i 0.549320 + 0.549320i 0.926244 0.376924i \(-0.123018\pi\)
−0.376924 + 0.926244i \(0.623018\pi\)
\(648\) 0 0
\(649\) 66.0811i 2.59391i
\(650\) 0 0
\(651\) 0 0
\(652\) 7.11519 7.11519i 0.278652 0.278652i
\(653\) −7.99597 + 7.99597i −0.312906 + 0.312906i −0.846035 0.533128i \(-0.821016\pi\)
0.533128 + 0.846035i \(0.321016\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 8.94944i 0.349417i
\(657\) 0 0
\(658\) 3.05595 + 3.05595i 0.119133 + 0.119133i
\(659\) −27.9020 −1.08691 −0.543454 0.839439i \(-0.682884\pi\)
−0.543454 + 0.839439i \(0.682884\pi\)
\(660\) 0 0
\(661\) −0.294519 −0.0114555 −0.00572774 0.999984i \(-0.501823\pi\)
−0.00572774 + 0.999984i \(0.501823\pi\)
\(662\) −6.20013 6.20013i −0.240975 0.240975i
\(663\) 0 0
\(664\) 16.0410i 0.622512i
\(665\) 0 0
\(666\) 0 0
\(667\) −8.05800 + 8.05800i −0.312007 + 0.312007i
\(668\) 16.7128 16.7128i 0.646638 0.646638i
\(669\) 0 0
\(670\) 0 0
\(671\) 6.23037i 0.240521i
\(672\) 0 0
\(673\) 24.6569 + 24.6569i 0.950452 + 0.950452i 0.998829 0.0483773i \(-0.0154050\pi\)
−0.0483773 + 0.998829i \(0.515405\pi\)
\(674\) −17.4552 −0.672350
\(675\) 0 0
\(676\) 7.27226 0.279702
\(677\) −28.7195 28.7195i −1.10378 1.10378i −0.993950 0.109831i \(-0.964969\pi\)
−0.109831 0.993950i \(-0.535031\pi\)
\(678\) 0 0
\(679\) 13.2917i 0.510089i
\(680\) 0 0
\(681\) 0 0
\(682\) −10.6359 + 10.6359i −0.407270 + 0.407270i
\(683\) 0.221515 0.221515i 0.00847605 0.00847605i −0.702856 0.711332i \(-0.748092\pi\)
0.711332 + 0.702856i \(0.248092\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000i 0.0381802i
\(687\) 0 0
\(688\) 5.88438 + 5.88438i 0.224340 + 0.224340i
\(689\) 0.651591 0.0248236
\(690\) 0 0
\(691\) −36.2648 −1.37958 −0.689789 0.724010i \(-0.742297\pi\)
−0.689789 + 0.724010i \(0.742297\pi\)
\(692\) 14.7843 + 14.7843i 0.562015 + 0.562015i
\(693\) 0 0
\(694\) 7.31371i 0.277625i
\(695\) 0 0
\(696\) 0 0
\(697\) 8.76200 8.76200i 0.331885 0.331885i
\(698\) 20.4610 20.4610i 0.774462 0.774462i
\(699\) 0 0
\(700\) 0 0
\(701\) 21.0497i 0.795036i 0.917594 + 0.397518i \(0.130128\pi\)
−0.917594 + 0.397518i \(0.869872\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −6.36365 −0.239839
\(705\) 0 0
\(706\) 14.6564 0.551601
\(707\) 11.3492 + 11.3492i 0.426829 + 0.426829i
\(708\) 0 0
\(709\) 14.3617i 0.539366i 0.962949 + 0.269683i \(0.0869190\pi\)
−0.962949 + 0.269683i \(0.913081\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 8.37010 8.37010i 0.313683 0.313683i
\(713\) −3.27270 + 3.27270i −0.122564 + 0.122564i
\(714\) 0 0
\(715\) 0 0
\(716\) 12.0205i 0.449227i
\(717\) 0 0
\(718\) 9.35560 + 9.35560i 0.349148 + 0.349148i
\(719\) 16.9706 0.632895 0.316448 0.948610i \(-0.397510\pi\)
0.316448 + 0.948610i \(0.397510\pi\)
\(720\) 0 0
\(721\) −0.999561 −0.0372256
\(722\) −13.4350 13.4350i −0.500000 0.500000i
\(723\) 0 0
\(724\) 17.5236i 0.651259i
\(725\) 0 0
\(726\) 0 0
\(727\) 2.42692 2.42692i 0.0900095 0.0900095i −0.660668 0.750678i \(-0.729727\pi\)
0.750678 + 0.660668i \(0.229727\pi\)
\(728\) −1.69230 + 1.69230i −0.0627207 + 0.0627207i
\(729\) 0 0
\(730\) 0 0
\(731\) 11.5223i 0.426167i
\(732\) 0 0
\(733\) 14.3701 + 14.3701i 0.530772 + 0.530772i 0.920802 0.390030i \(-0.127536\pi\)
−0.390030 + 0.920802i \(0.627536\pi\)
\(734\) −4.53882 −0.167531
\(735\) 0 0
\(736\) −1.95811 −0.0721770
\(737\) 62.9007 + 62.9007i 2.31698 + 2.31698i
\(738\) 0 0
\(739\) 38.0886i 1.40111i −0.713598 0.700556i \(-0.752935\pi\)
0.713598 0.700556i \(-0.247065\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.192517 0.192517i 0.00706751 0.00706751i
\(743\) −31.4965 + 31.4965i −1.15549 + 1.15549i −0.170061 + 0.985434i \(0.554396\pi\)
−0.985434 + 0.170061i \(0.945604\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 3.20881i 0.117483i
\(747\) 0 0
\(748\) 6.23037 + 6.23037i 0.227805 + 0.227805i
\(749\) 13.4546 0.491621
\(750\) 0 0
\(751\) 16.9511 0.618554 0.309277 0.950972i \(-0.399913\pi\)
0.309277 + 0.950972i \(0.399913\pi\)
\(752\) −3.05595 3.05595i −0.111439 0.111439i
\(753\) 0 0
\(754\) 13.9282i 0.507236i
\(755\) 0 0
\(756\) 0 0
\(757\) 2.34644 2.34644i 0.0852826 0.0852826i −0.663179 0.748461i \(-0.730793\pi\)
0.748461 + 0.663179i \(0.230793\pi\)
\(758\) −1.69559 + 1.69559i −0.0615865 + 0.0615865i
\(759\) 0 0
\(760\) 0 0
\(761\) 3.07510i 0.111472i −0.998446 0.0557361i \(-0.982249\pi\)
0.998446 0.0557361i \(-0.0177506\pi\)
\(762\) 0 0
\(763\) 10.5767 + 10.5767i 0.382901 + 0.382901i
\(764\) −6.30038 −0.227940
\(765\) 0 0
\(766\) −23.5945 −0.852503
\(767\) −17.5731 17.5731i −0.634527 0.634527i
\(768\) 0 0
\(769\) 17.4666i 0.629862i 0.949115 + 0.314931i \(0.101981\pi\)
−0.949115 + 0.314931i \(0.898019\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −11.6435 + 11.6435i −0.419060 + 0.419060i
\(773\) 38.6076 38.6076i 1.38862 1.38862i 0.560395 0.828225i \(-0.310649\pi\)
0.828225 0.560395i \(-0.189351\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 13.2917i 0.477144i
\(777\) 0 0
\(778\) −15.6117 15.6117i −0.559706 0.559706i
\(779\) 0 0
\(780\) 0 0
\(781\) 78.5419 2.81045
\(782\) 1.91710 + 1.91710i 0.0685554 + 0.0685554i
\(783\) 0 0
\(784\) 1.00000i 0.0357143i
\(785\) 0 0
\(786\) 0 0
\(787\) 12.3076 12.3076i 0.438717 0.438717i −0.452863 0.891580i \(-0.649597\pi\)
0.891580 + 0.452863i \(0.149597\pi\)
\(788\) 1.92849 1.92849i 0.0686997 0.0686997i
\(789\) 0 0
\(790\) 0 0
\(791\) 13.0414i 0.463701i
\(792\) 0 0
\(793\) −1.65685 1.65685i −0.0588366 0.0588366i
\(794\) 29.6585 1.05254
\(795\) 0 0
\(796\) 5.67736 0.201229
\(797\) −4.88543 4.88543i −0.173051 0.173051i 0.615267 0.788318i \(-0.289048\pi\)
−0.788318 + 0.615267i \(0.789048\pi\)
\(798\) 0 0
\(799\) 5.98389i 0.211695i