Properties

Label 300.2.o.a.229.4
Level $300$
Weight $2$
Character 300.229
Analytic conductor $2.396$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.o (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 229.4
Character \(\chi\) \(=\) 300.229
Dual form 300.2.o.a.169.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.587785 - 0.809017i) q^{3} +(-0.921600 + 2.03732i) q^{5} -4.41540i q^{7} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(0.587785 - 0.809017i) q^{3} +(-0.921600 + 2.03732i) q^{5} -4.41540i q^{7} +(-0.309017 - 0.951057i) q^{9} +(1.37568 - 4.23392i) q^{11} +(5.46646 - 1.77616i) q^{13} +(1.10652 + 1.94309i) q^{15} +(3.86196 + 5.31553i) q^{17} +(-2.25162 + 1.63590i) q^{19} +(-3.57213 - 2.59531i) q^{21} +(1.25059 + 0.406341i) q^{23} +(-3.30131 - 3.75518i) q^{25} +(-0.951057 - 0.309017i) q^{27} +(-3.91985 - 2.84794i) q^{29} +(0.159486 - 0.115873i) q^{31} +(-2.61671 - 3.60159i) q^{33} +(8.99556 + 4.06923i) q^{35} +(-7.80690 + 2.53662i) q^{37} +(1.77616 - 5.46646i) q^{39} +(2.42573 + 7.46564i) q^{41} -0.412792i q^{43} +(2.22239 + 0.246929i) q^{45} +(-4.58154 + 6.30595i) q^{47} -12.4958 q^{49} +6.57035 q^{51} +(-0.185420 + 0.255208i) q^{53} +(7.35800 + 6.70469i) q^{55} +2.78315i q^{57} +(-0.778419 - 2.39573i) q^{59} +(2.88348 - 8.87444i) q^{61} +(-4.19929 + 1.36443i) q^{63} +(-1.41929 + 12.7738i) q^{65} +(7.02151 + 9.66428i) q^{67} +(1.06382 - 0.772907i) q^{69} +(-0.411990 - 0.299328i) q^{71} +(14.9990 + 4.87346i) q^{73} +(-4.97846 + 0.463572i) q^{75} +(-18.6945 - 6.07420i) q^{77} +(-2.77617 - 2.01700i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(3.15732 + 4.34568i) q^{83} +(-14.3886 + 2.96923i) q^{85} +(-4.60806 + 1.49725i) q^{87} +(-3.50585 + 10.7899i) q^{89} +(-7.84246 - 24.1366i) q^{91} -0.197136i q^{93} +(-1.25774 - 6.09490i) q^{95} +(2.98572 - 4.10948i) q^{97} -4.45181 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 2q^{5} + 6q^{9} + O(q^{10}) \) \( 24q - 2q^{5} + 6q^{9} - 6q^{11} + 4q^{15} + 10q^{17} + 10q^{19} - 4q^{21} + 40q^{23} - 4q^{25} + 4q^{29} + 6q^{31} + 10q^{33} - 6q^{35} - 10q^{41} + 2q^{45} - 40q^{47} - 56q^{49} + 16q^{51} - 60q^{53} - 62q^{55} - 36q^{59} - 12q^{61} - 10q^{63} + 20q^{67} + 4q^{69} + 40q^{71} + 60q^{73} + 8q^{75} - 40q^{77} + 8q^{79} - 6q^{81} - 50q^{83} + 34q^{85} - 20q^{87} - 30q^{91} - 60q^{95} - 40q^{97} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{10}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.587785 0.809017i 0.339358 0.467086i
\(4\) 0 0
\(5\) −0.921600 + 2.03732i −0.412152 + 0.911115i
\(6\) 0 0
\(7\) 4.41540i 1.66886i −0.551111 0.834432i \(-0.685796\pi\)
0.551111 0.834432i \(-0.314204\pi\)
\(8\) 0 0
\(9\) −0.309017 0.951057i −0.103006 0.317019i
\(10\) 0 0
\(11\) 1.37568 4.23392i 0.414785 1.27658i −0.497659 0.867373i \(-0.665807\pi\)
0.912443 0.409203i \(-0.134193\pi\)
\(12\) 0 0
\(13\) 5.46646 1.77616i 1.51612 0.492619i 0.571452 0.820635i \(-0.306380\pi\)
0.944672 + 0.328017i \(0.106380\pi\)
\(14\) 0 0
\(15\) 1.10652 + 1.94309i 0.285702 + 0.501705i
\(16\) 0 0
\(17\) 3.86196 + 5.31553i 0.936662 + 1.28921i 0.957203 + 0.289416i \(0.0934611\pi\)
−0.0205412 + 0.999789i \(0.506539\pi\)
\(18\) 0 0
\(19\) −2.25162 + 1.63590i −0.516557 + 0.375301i −0.815305 0.579031i \(-0.803431\pi\)
0.298748 + 0.954332i \(0.403431\pi\)
\(20\) 0 0
\(21\) −3.57213 2.59531i −0.779503 0.566342i
\(22\) 0 0
\(23\) 1.25059 + 0.406341i 0.260766 + 0.0847280i 0.436482 0.899713i \(-0.356224\pi\)
−0.175716 + 0.984441i \(0.556224\pi\)
\(24\) 0 0
\(25\) −3.30131 3.75518i −0.660261 0.751036i
\(26\) 0 0
\(27\) −0.951057 0.309017i −0.183031 0.0594703i
\(28\) 0 0
\(29\) −3.91985 2.84794i −0.727899 0.528849i 0.160999 0.986954i \(-0.448528\pi\)
−0.888898 + 0.458105i \(0.848528\pi\)
\(30\) 0 0
\(31\) 0.159486 0.115873i 0.0286446 0.0208115i −0.573371 0.819296i \(-0.694365\pi\)
0.602015 + 0.798484i \(0.294365\pi\)
\(32\) 0 0
\(33\) −2.61671 3.60159i −0.455510 0.626956i
\(34\) 0 0
\(35\) 8.99556 + 4.06923i 1.52053 + 0.687826i
\(36\) 0 0
\(37\) −7.80690 + 2.53662i −1.28345 + 0.417017i −0.869793 0.493417i \(-0.835748\pi\)
−0.413654 + 0.910434i \(0.635748\pi\)
\(38\) 0 0
\(39\) 1.77616 5.46646i 0.284413 0.875335i
\(40\) 0 0
\(41\) 2.42573 + 7.46564i 0.378836 + 1.16594i 0.940854 + 0.338813i \(0.110025\pi\)
−0.562018 + 0.827125i \(0.689975\pi\)
\(42\) 0 0
\(43\) 0.412792i 0.0629502i −0.999505 0.0314751i \(-0.989980\pi\)
0.999505 0.0314751i \(-0.0100205\pi\)
\(44\) 0 0
\(45\) 2.22239 + 0.246929i 0.331295 + 0.0368100i
\(46\) 0 0
\(47\) −4.58154 + 6.30595i −0.668287 + 0.919818i −0.999720 0.0236610i \(-0.992468\pi\)
0.331433 + 0.943479i \(0.392468\pi\)
\(48\) 0 0
\(49\) −12.4958 −1.78511
\(50\) 0 0
\(51\) 6.57035 0.920034
\(52\) 0 0
\(53\) −0.185420 + 0.255208i −0.0254694 + 0.0350556i −0.821562 0.570120i \(-0.806897\pi\)
0.796092 + 0.605175i \(0.206897\pi\)
\(54\) 0 0
\(55\) 7.35800 + 6.70469i 0.992153 + 0.904060i
\(56\) 0 0
\(57\) 2.78315i 0.368638i
\(58\) 0 0
\(59\) −0.778419 2.39573i −0.101342 0.311897i 0.887513 0.460783i \(-0.152431\pi\)
−0.988854 + 0.148886i \(0.952431\pi\)
\(60\) 0 0
\(61\) 2.88348 8.87444i 0.369192 1.13626i −0.578123 0.815950i \(-0.696214\pi\)
0.947314 0.320305i \(-0.103786\pi\)
\(62\) 0 0
\(63\) −4.19929 + 1.36443i −0.529061 + 0.171902i
\(64\) 0 0
\(65\) −1.41929 + 12.7738i −0.176042 + 1.58440i
\(66\) 0 0
\(67\) 7.02151 + 9.66428i 0.857814 + 1.18068i 0.982086 + 0.188431i \(0.0603403\pi\)
−0.124273 + 0.992248i \(0.539660\pi\)
\(68\) 0 0
\(69\) 1.06382 0.772907i 0.128068 0.0930471i
\(70\) 0 0
\(71\) −0.411990 0.299328i −0.0488942 0.0355237i 0.563070 0.826409i \(-0.309620\pi\)
−0.611964 + 0.790886i \(0.709620\pi\)
\(72\) 0 0
\(73\) 14.9990 + 4.87346i 1.75549 + 0.570395i 0.996718 0.0809557i \(-0.0257972\pi\)
0.758777 + 0.651351i \(0.225797\pi\)
\(74\) 0 0
\(75\) −4.97846 + 0.463572i −0.574863 + 0.0535287i
\(76\) 0 0
\(77\) −18.6945 6.07420i −2.13043 0.692219i
\(78\) 0 0
\(79\) −2.77617 2.01700i −0.312343 0.226930i 0.420558 0.907266i \(-0.361834\pi\)
−0.732901 + 0.680335i \(0.761834\pi\)
\(80\) 0 0
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) 0 0
\(83\) 3.15732 + 4.34568i 0.346561 + 0.477000i 0.946343 0.323163i \(-0.104746\pi\)
−0.599783 + 0.800163i \(0.704746\pi\)
\(84\) 0 0
\(85\) −14.3886 + 2.96923i −1.56066 + 0.322058i
\(86\) 0 0
\(87\) −4.60806 + 1.49725i −0.494036 + 0.160522i
\(88\) 0 0
\(89\) −3.50585 + 10.7899i −0.371619 + 1.14373i 0.574112 + 0.818777i \(0.305347\pi\)
−0.945731 + 0.324950i \(0.894653\pi\)
\(90\) 0 0
\(91\) −7.84246 24.1366i −0.822114 2.53021i
\(92\) 0 0
\(93\) 0.197136i 0.0204420i
\(94\) 0 0
\(95\) −1.25774 6.09490i −0.129042 0.625324i
\(96\) 0 0
\(97\) 2.98572 4.10948i 0.303153 0.417255i −0.630077 0.776532i \(-0.716977\pi\)
0.933231 + 0.359277i \(0.116977\pi\)
\(98\) 0 0
\(99\) −4.45181 −0.447424
\(100\) 0 0
\(101\) −11.1860 −1.11305 −0.556525 0.830831i \(-0.687866\pi\)
−0.556525 + 0.830831i \(0.687866\pi\)
\(102\) 0 0
\(103\) −1.84898 + 2.54490i −0.182185 + 0.250757i −0.890335 0.455305i \(-0.849530\pi\)
0.708150 + 0.706062i \(0.249530\pi\)
\(104\) 0 0
\(105\) 8.57954 4.88573i 0.837277 0.476798i
\(106\) 0 0
\(107\) 7.74013i 0.748266i 0.927375 + 0.374133i \(0.122060\pi\)
−0.927375 + 0.374133i \(0.877940\pi\)
\(108\) 0 0
\(109\) 3.20477 + 9.86326i 0.306961 + 0.944729i 0.978938 + 0.204157i \(0.0654453\pi\)
−0.671977 + 0.740572i \(0.734555\pi\)
\(110\) 0 0
\(111\) −2.53662 + 7.80690i −0.240765 + 0.740998i
\(112\) 0 0
\(113\) 9.72574 3.16009i 0.914921 0.297276i 0.186539 0.982447i \(-0.440273\pi\)
0.728382 + 0.685172i \(0.240273\pi\)
\(114\) 0 0
\(115\) −1.98039 + 2.17336i −0.184672 + 0.202667i
\(116\) 0 0
\(117\) −3.37846 4.65005i −0.312339 0.429897i
\(118\) 0 0
\(119\) 23.4702 17.0521i 2.15151 1.56316i
\(120\) 0 0
\(121\) −7.13440 5.18344i −0.648582 0.471222i
\(122\) 0 0
\(123\) 7.46564 + 2.42573i 0.673154 + 0.218721i
\(124\) 0 0
\(125\) 10.6930 3.26502i 0.956408 0.292032i
\(126\) 0 0
\(127\) 10.7590 + 3.49582i 0.954709 + 0.310204i 0.744628 0.667480i \(-0.232627\pi\)
0.210081 + 0.977684i \(0.432627\pi\)
\(128\) 0 0
\(129\) −0.333956 0.242633i −0.0294031 0.0213626i
\(130\) 0 0
\(131\) 7.64816 5.55671i 0.668223 0.485492i −0.201207 0.979549i \(-0.564486\pi\)
0.869430 + 0.494056i \(0.164486\pi\)
\(132\) 0 0
\(133\) 7.22314 + 9.94180i 0.626326 + 0.862063i
\(134\) 0 0
\(135\) 1.50606 1.65281i 0.129621 0.142251i
\(136\) 0 0
\(137\) 7.99861 2.59891i 0.683367 0.222039i 0.0532983 0.998579i \(-0.483027\pi\)
0.630069 + 0.776539i \(0.283027\pi\)
\(138\) 0 0
\(139\) −3.65307 + 11.2430i −0.309849 + 0.953617i 0.667974 + 0.744185i \(0.267162\pi\)
−0.977823 + 0.209433i \(0.932838\pi\)
\(140\) 0 0
\(141\) 2.40866 + 7.41309i 0.202846 + 0.624295i
\(142\) 0 0
\(143\) 25.5880i 2.13978i
\(144\) 0 0
\(145\) 9.41469 5.36131i 0.781847 0.445233i
\(146\) 0 0
\(147\) −7.34482 + 10.1093i −0.605791 + 0.833799i
\(148\) 0 0
\(149\) −10.6355 −0.871294 −0.435647 0.900118i \(-0.643480\pi\)
−0.435647 + 0.900118i \(0.643480\pi\)
\(150\) 0 0
\(151\) 4.41657 0.359415 0.179707 0.983720i \(-0.442485\pi\)
0.179707 + 0.983720i \(0.442485\pi\)
\(152\) 0 0
\(153\) 3.86196 5.31553i 0.312221 0.429735i
\(154\) 0 0
\(155\) 0.0890883 + 0.431713i 0.00715574 + 0.0346760i
\(156\) 0 0
\(157\) 13.5289i 1.07972i −0.841754 0.539861i \(-0.818477\pi\)
0.841754 0.539861i \(-0.181523\pi\)
\(158\) 0 0
\(159\) 0.0974809 + 0.300015i 0.00773074 + 0.0237928i
\(160\) 0 0
\(161\) 1.79416 5.52186i 0.141400 0.435183i
\(162\) 0 0
\(163\) −13.8458 + 4.49876i −1.08448 + 0.352370i −0.796112 0.605149i \(-0.793114\pi\)
−0.288371 + 0.957519i \(0.593114\pi\)
\(164\) 0 0
\(165\) 9.74913 2.01183i 0.758969 0.156621i
\(166\) 0 0
\(167\) −5.85918 8.06448i −0.453397 0.624048i 0.519726 0.854333i \(-0.326034\pi\)
−0.973123 + 0.230285i \(0.926034\pi\)
\(168\) 0 0
\(169\) 16.2103 11.7774i 1.24694 0.905957i
\(170\) 0 0
\(171\) 2.25162 + 1.63590i 0.172186 + 0.125100i
\(172\) 0 0
\(173\) −10.3427 3.36056i −0.786344 0.255499i −0.111798 0.993731i \(-0.535661\pi\)
−0.674547 + 0.738232i \(0.735661\pi\)
\(174\) 0 0
\(175\) −16.5806 + 14.5766i −1.25338 + 1.10189i
\(176\) 0 0
\(177\) −2.39573 0.778419i −0.180074 0.0585096i
\(178\) 0 0
\(179\) −20.3662 14.7969i −1.52224 1.10597i −0.960364 0.278749i \(-0.910080\pi\)
−0.561875 0.827222i \(-0.689920\pi\)
\(180\) 0 0
\(181\) 6.14184 4.46231i 0.456520 0.331681i −0.335645 0.941989i \(-0.608954\pi\)
0.792164 + 0.610308i \(0.208954\pi\)
\(182\) 0 0
\(183\) −5.48470 7.54905i −0.405441 0.558042i
\(184\) 0 0
\(185\) 2.02696 18.2429i 0.149025 1.34124i
\(186\) 0 0
\(187\) 27.8184 9.03874i 2.03428 0.660978i
\(188\) 0 0
\(189\) −1.36443 + 4.19929i −0.0992479 + 0.305454i
\(190\) 0 0
\(191\) −0.00373697 0.0115012i −0.000270398 0.000832198i 0.950921 0.309433i \(-0.100139\pi\)
−0.951192 + 0.308601i \(0.900139\pi\)
\(192\) 0 0
\(193\) 12.7841i 0.920219i 0.887862 + 0.460110i \(0.152190\pi\)
−0.887862 + 0.460110i \(0.847810\pi\)
\(194\) 0 0
\(195\) 9.50000 + 8.65650i 0.680309 + 0.619905i
\(196\) 0 0
\(197\) −5.79877 + 7.98132i −0.413145 + 0.568646i −0.963982 0.265967i \(-0.914309\pi\)
0.550837 + 0.834613i \(0.314309\pi\)
\(198\) 0 0
\(199\) 0.295640 0.0209573 0.0104787 0.999945i \(-0.496664\pi\)
0.0104787 + 0.999945i \(0.496664\pi\)
\(200\) 0 0
\(201\) 11.9457 0.842585
\(202\) 0 0
\(203\) −12.5748 + 17.3077i −0.882578 + 1.21476i
\(204\) 0 0
\(205\) −17.4454 1.93835i −1.21844 0.135381i
\(206\) 0 0
\(207\) 1.31495i 0.0913952i
\(208\) 0 0
\(209\) 3.82874 + 11.7837i 0.264840 + 0.815093i
\(210\) 0 0
\(211\) −3.90836 + 12.0287i −0.269062 + 0.828089i 0.721667 + 0.692240i \(0.243376\pi\)
−0.990730 + 0.135849i \(0.956624\pi\)
\(212\) 0 0
\(213\) −0.484323 + 0.157366i −0.0331853 + 0.0107826i
\(214\) 0 0
\(215\) 0.840987 + 0.380429i 0.0573548 + 0.0259450i
\(216\) 0 0
\(217\) −0.511628 0.704195i −0.0347315 0.0478039i
\(218\) 0 0
\(219\) 12.7589 9.26986i 0.862165 0.626399i
\(220\) 0 0
\(221\) 30.5525 + 22.1977i 2.05518 + 1.49318i
\(222\) 0 0
\(223\) 4.98335 + 1.61919i 0.333710 + 0.108429i 0.471079 0.882091i \(-0.343865\pi\)
−0.137369 + 0.990520i \(0.543865\pi\)
\(224\) 0 0
\(225\) −2.55123 + 4.30014i −0.170082 + 0.286676i
\(226\) 0 0
\(227\) −7.38873 2.40074i −0.490407 0.159343i 0.0533663 0.998575i \(-0.483005\pi\)
−0.543773 + 0.839232i \(0.683005\pi\)
\(228\) 0 0
\(229\) −4.84757 3.52196i −0.320336 0.232738i 0.415983 0.909373i \(-0.363438\pi\)
−0.736319 + 0.676635i \(0.763438\pi\)
\(230\) 0 0
\(231\) −15.9025 + 11.5538i −1.04630 + 0.760185i
\(232\) 0 0
\(233\) −8.73631 12.0245i −0.572334 0.787751i 0.420494 0.907295i \(-0.361857\pi\)
−0.992829 + 0.119544i \(0.961857\pi\)
\(234\) 0 0
\(235\) −8.62486 15.1456i −0.562624 0.987991i
\(236\) 0 0
\(237\) −3.26358 + 1.06040i −0.211992 + 0.0688804i
\(238\) 0 0
\(239\) 6.55140 20.1631i 0.423775 1.30424i −0.480388 0.877056i \(-0.659504\pi\)
0.904163 0.427188i \(-0.140496\pi\)
\(240\) 0 0
\(241\) 4.96162 + 15.2703i 0.319606 + 0.983647i 0.973817 + 0.227334i \(0.0730010\pi\)
−0.654210 + 0.756313i \(0.726999\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) 11.5161 25.4578i 0.735736 1.62644i
\(246\) 0 0
\(247\) −9.40278 + 12.9418i −0.598284 + 0.823468i
\(248\) 0 0
\(249\) 5.37155 0.340408
\(250\) 0 0
\(251\) −24.1371 −1.52352 −0.761761 0.647858i \(-0.775665\pi\)
−0.761761 + 0.647858i \(0.775665\pi\)
\(252\) 0 0
\(253\) 3.44084 4.73590i 0.216323 0.297744i
\(254\) 0 0
\(255\) −6.05524 + 13.3859i −0.379194 + 0.838256i
\(256\) 0 0
\(257\) 4.22940i 0.263823i −0.991262 0.131911i \(-0.957889\pi\)
0.991262 0.131911i \(-0.0421114\pi\)
\(258\) 0 0
\(259\) 11.2002 + 34.4706i 0.695945 + 2.14190i
\(260\) 0 0
\(261\) −1.49725 + 4.60806i −0.0926775 + 0.285232i
\(262\) 0 0
\(263\) −7.97729 + 2.59198i −0.491901 + 0.159828i −0.544455 0.838790i \(-0.683264\pi\)
0.0525547 + 0.998618i \(0.483264\pi\)
\(264\) 0 0
\(265\) −0.349057 0.612958i −0.0214424 0.0376537i
\(266\) 0 0
\(267\) 6.66852 + 9.17843i 0.408107 + 0.561711i
\(268\) 0 0
\(269\) −4.47812 + 3.25354i −0.273036 + 0.198372i −0.715874 0.698229i \(-0.753972\pi\)
0.442838 + 0.896601i \(0.353972\pi\)
\(270\) 0 0
\(271\) −12.8227 9.31623i −0.778923 0.565921i 0.125733 0.992064i \(-0.459872\pi\)
−0.904656 + 0.426144i \(0.859872\pi\)
\(272\) 0 0
\(273\) −24.1366 7.84246i −1.46081 0.474647i
\(274\) 0 0
\(275\) −20.4407 + 8.81152i −1.23262 + 0.531355i
\(276\) 0 0
\(277\) 8.26699 + 2.68611i 0.496715 + 0.161393i 0.546652 0.837360i \(-0.315902\pi\)
−0.0499369 + 0.998752i \(0.515902\pi\)
\(278\) 0 0
\(279\) −0.159486 0.115873i −0.00954819 0.00693716i
\(280\) 0 0
\(281\) −8.72120 + 6.33633i −0.520263 + 0.377994i −0.816703 0.577058i \(-0.804201\pi\)
0.296440 + 0.955052i \(0.404201\pi\)
\(282\) 0 0
\(283\) −5.78686 7.96493i −0.343993 0.473466i 0.601609 0.798791i \(-0.294527\pi\)
−0.945602 + 0.325324i \(0.894527\pi\)
\(284\) 0 0
\(285\) −5.67016 2.56496i −0.335871 0.151935i
\(286\) 0 0
\(287\) 32.9638 10.7106i 1.94579 0.632226i
\(288\) 0 0
\(289\) −8.08684 + 24.8887i −0.475696 + 1.46404i
\(290\) 0 0
\(291\) −1.56968 4.83099i −0.0920165 0.283198i
\(292\) 0 0
\(293\) 9.77733i 0.571198i 0.958349 + 0.285599i \(0.0921925\pi\)
−0.958349 + 0.285599i \(0.907808\pi\)
\(294\) 0 0
\(295\) 5.59824 + 0.622019i 0.325942 + 0.0362153i
\(296\) 0 0
\(297\) −2.61671 + 3.60159i −0.151837 + 0.208985i
\(298\) 0 0
\(299\) 7.55803 0.437092
\(300\) 0 0
\(301\) −1.82264 −0.105055
\(302\) 0 0
\(303\) −6.57497 + 9.04967i −0.377722 + 0.519890i
\(304\) 0 0
\(305\) 15.4226 + 14.0532i 0.883096 + 0.804686i
\(306\) 0 0
\(307\) 32.7301i 1.86801i −0.357265 0.934003i \(-0.616291\pi\)
0.357265 0.934003i \(-0.383709\pi\)
\(308\) 0 0
\(309\) 0.972067 + 2.99171i 0.0552989 + 0.170193i
\(310\) 0 0
\(311\) −7.60939 + 23.4193i −0.431489 + 1.32799i 0.465153 + 0.885230i \(0.345999\pi\)
−0.896642 + 0.442756i \(0.854001\pi\)
\(312\) 0 0
\(313\) 21.4458 6.96817i 1.21219 0.393864i 0.367957 0.929843i \(-0.380057\pi\)
0.844232 + 0.535979i \(0.180057\pi\)
\(314\) 0 0
\(315\) 1.09029 9.81275i 0.0614309 0.552886i
\(316\) 0 0
\(317\) 0.954767 + 1.31412i 0.0536251 + 0.0738086i 0.834987 0.550269i \(-0.185475\pi\)
−0.781362 + 0.624078i \(0.785475\pi\)
\(318\) 0 0
\(319\) −17.4504 + 12.6785i −0.977037 + 0.709859i
\(320\) 0 0
\(321\) 6.26189 + 4.54953i 0.349505 + 0.253930i
\(322\) 0 0
\(323\) −17.3913 5.65078i −0.967679 0.314418i
\(324\) 0 0
\(325\) −24.7163 14.6639i −1.37101 0.813407i
\(326\) 0 0
\(327\) 9.86326 + 3.20477i 0.545440 + 0.177224i
\(328\) 0 0
\(329\) 27.8433 + 20.2293i 1.53505 + 1.11528i
\(330\) 0 0
\(331\) 7.29178 5.29779i 0.400793 0.291193i −0.369071 0.929401i \(-0.620324\pi\)
0.769864 + 0.638208i \(0.220324\pi\)
\(332\) 0 0
\(333\) 4.82493 + 6.64095i 0.264405 + 0.363922i
\(334\) 0 0
\(335\) −26.1602 + 5.39842i −1.42928 + 0.294947i
\(336\) 0 0
\(337\) 25.6482 8.33361i 1.39715 0.453961i 0.488880 0.872351i \(-0.337406\pi\)
0.908267 + 0.418390i \(0.137406\pi\)
\(338\) 0 0
\(339\) 3.16009 9.72574i 0.171632 0.528230i
\(340\) 0 0
\(341\) −0.271197 0.834657i −0.0146861 0.0451992i
\(342\) 0 0
\(343\) 24.2660i 1.31024i
\(344\) 0 0
\(345\) 0.594243 + 2.87964i 0.0319929 + 0.155035i
\(346\) 0 0
\(347\) 15.4263 21.2325i 0.828127 1.13982i −0.160142 0.987094i \(-0.551195\pi\)
0.988269 0.152725i \(-0.0488048\pi\)
\(348\) 0 0
\(349\) −18.2310 −0.975885 −0.487943 0.872876i \(-0.662252\pi\)
−0.487943 + 0.872876i \(0.662252\pi\)
\(350\) 0 0
\(351\) −5.74778 −0.306794
\(352\) 0 0
\(353\) 2.61542 3.59982i 0.139205 0.191599i −0.733723 0.679449i \(-0.762219\pi\)
0.872927 + 0.487850i \(0.162219\pi\)
\(354\) 0 0
\(355\) 0.989516 0.563492i 0.0525181 0.0299071i
\(356\) 0 0
\(357\) 29.0107i 1.53541i
\(358\) 0 0
\(359\) 9.98964 + 30.7449i 0.527233 + 1.62266i 0.759858 + 0.650089i \(0.225269\pi\)
−0.232625 + 0.972567i \(0.574731\pi\)
\(360\) 0 0
\(361\) −3.47769 + 10.7032i −0.183036 + 0.563328i
\(362\) 0 0
\(363\) −8.38699 + 2.72510i −0.440203 + 0.143031i
\(364\) 0 0
\(365\) −23.7518 + 26.0662i −1.24323 + 1.36437i
\(366\) 0 0
\(367\) −3.37390 4.64378i −0.176116 0.242403i 0.711829 0.702353i \(-0.247867\pi\)
−0.887945 + 0.459950i \(0.847867\pi\)
\(368\) 0 0
\(369\) 6.35066 4.61402i 0.330602 0.240196i
\(370\) 0 0
\(371\) 1.12685 + 0.818702i 0.0585030 + 0.0425049i
\(372\) 0 0
\(373\) 0.990868 + 0.321953i 0.0513052 + 0.0166701i 0.334557 0.942375i \(-0.391413\pi\)
−0.283252 + 0.959046i \(0.591413\pi\)
\(374\) 0 0
\(375\) 3.64371 10.5699i 0.188160 0.545829i
\(376\) 0 0
\(377\) −26.4861 8.60587i −1.36411 0.443225i
\(378\) 0 0
\(379\) −3.84230 2.79159i −0.197366 0.143395i 0.484713 0.874673i \(-0.338924\pi\)
−0.682079 + 0.731279i \(0.738924\pi\)
\(380\) 0 0
\(381\) 9.15217 6.64944i 0.468880 0.340661i
\(382\) 0 0
\(383\) −6.47739 8.91536i −0.330979 0.455553i 0.610801 0.791784i \(-0.290848\pi\)
−0.941780 + 0.336231i \(0.890848\pi\)
\(384\) 0 0
\(385\) 29.6039 32.4885i 1.50875 1.65577i
\(386\) 0 0
\(387\) −0.392588 + 0.127560i −0.0199564 + 0.00648422i
\(388\) 0 0
\(389\) 10.2628 31.5856i 0.520344 1.60145i −0.253000 0.967466i \(-0.581417\pi\)
0.773344 0.633987i \(-0.218583\pi\)
\(390\) 0 0
\(391\) 2.66981 + 8.21682i 0.135018 + 0.415542i
\(392\) 0 0
\(393\) 9.45365i 0.476873i
\(394\) 0 0
\(395\) 6.66778 3.79705i 0.335493 0.191050i
\(396\) 0 0
\(397\) −1.61299 + 2.22008i −0.0809534 + 0.111423i −0.847573 0.530678i \(-0.821937\pi\)
0.766620 + 0.642101i \(0.221937\pi\)
\(398\) 0 0
\(399\) 12.2887 0.615207
\(400\) 0 0
\(401\) −2.11503 −0.105619 −0.0528097 0.998605i \(-0.516818\pi\)
−0.0528097 + 0.998605i \(0.516818\pi\)
\(402\) 0 0
\(403\) 0.666015 0.916691i 0.0331766 0.0456636i
\(404\) 0 0
\(405\) −0.451913 2.18993i −0.0224558 0.108818i
\(406\) 0 0
\(407\) 36.5434i 1.81139i
\(408\) 0 0
\(409\) 2.03102 + 6.25083i 0.100427 + 0.309084i 0.988630 0.150368i \(-0.0480459\pi\)
−0.888203 + 0.459452i \(0.848046\pi\)
\(410\) 0 0
\(411\) 2.59891 7.99861i 0.128195 0.394542i
\(412\) 0 0
\(413\) −10.5781 + 3.43703i −0.520514 + 0.169125i
\(414\) 0 0
\(415\) −11.7633 + 2.42748i −0.577438 + 0.119160i
\(416\) 0 0
\(417\) 6.94855 + 9.56385i 0.340272 + 0.468344i
\(418\) 0 0
\(419\) 28.5125 20.7155i 1.39293 1.01202i 0.397389 0.917650i \(-0.369916\pi\)
0.995537 0.0943704i \(-0.0300838\pi\)
\(420\) 0 0
\(421\) −5.07520 3.68735i −0.247350 0.179710i 0.457201 0.889363i \(-0.348852\pi\)
−0.704552 + 0.709653i \(0.748852\pi\)
\(422\) 0 0
\(423\) 7.41309 + 2.40866i 0.360437 + 0.117113i
\(424\) 0 0
\(425\) 7.21127 32.0505i 0.349798 1.55468i
\(426\) 0 0
\(427\) −39.1842 12.7317i −1.89626 0.616131i
\(428\) 0 0
\(429\) −20.7011 15.0403i −0.999461 0.726151i
\(430\) 0 0
\(431\) 11.0609 8.03624i 0.532787 0.387092i −0.288612 0.957446i \(-0.593194\pi\)
0.821399 + 0.570354i \(0.193194\pi\)
\(432\) 0 0
\(433\) 3.98412 + 5.48367i 0.191465 + 0.263529i 0.893947 0.448173i \(-0.147925\pi\)
−0.702482 + 0.711701i \(0.747925\pi\)
\(434\) 0 0
\(435\) 1.19642 10.7679i 0.0573641 0.516283i
\(436\) 0 0
\(437\) −3.48059 + 1.13091i −0.166499 + 0.0540988i
\(438\) 0 0
\(439\) 5.23618 16.1153i 0.249909 0.769142i −0.744881 0.667197i \(-0.767494\pi\)
0.994790 0.101944i \(-0.0325063\pi\)
\(440\) 0 0
\(441\) 3.86140 + 11.8842i 0.183876 + 0.565913i
\(442\) 0 0
\(443\) 23.8927i 1.13517i 0.823313 + 0.567587i \(0.192123\pi\)
−0.823313 + 0.567587i \(0.807877\pi\)
\(444\) 0 0
\(445\) −18.7514 17.0865i −0.888902 0.809977i
\(446\) 0 0
\(447\) −6.25139 + 8.60430i −0.295681 + 0.406969i
\(448\) 0 0
\(449\) −6.39281 −0.301695 −0.150848 0.988557i \(-0.548200\pi\)
−0.150848 + 0.988557i \(0.548200\pi\)
\(450\) 0 0
\(451\) 34.9460 1.64554
\(452\) 0 0
\(453\) 2.59599 3.57308i 0.121970 0.167878i
\(454\) 0 0
\(455\) 56.4015 + 6.26675i 2.64414 + 0.293790i
\(456\) 0 0
\(457\) 5.89482i 0.275748i 0.990450 + 0.137874i \(0.0440269\pi\)
−0.990450 + 0.137874i \(0.955973\pi\)
\(458\) 0 0
\(459\) −2.03035 6.24878i −0.0947687 0.291668i
\(460\) 0 0
\(461\) −7.60801 + 23.4151i −0.354340 + 1.09055i 0.602050 + 0.798458i \(0.294351\pi\)
−0.956391 + 0.292090i \(0.905649\pi\)
\(462\) 0 0
\(463\) −28.3995 + 9.22757i −1.31984 + 0.428842i −0.882440 0.470426i \(-0.844100\pi\)
−0.437399 + 0.899267i \(0.644100\pi\)
\(464\) 0 0
\(465\) 0.401628 + 0.181680i 0.0186250 + 0.00842522i
\(466\) 0 0
\(467\) 15.3714 + 21.1569i 0.711301 + 0.979022i 0.999768 + 0.0215325i \(0.00685454\pi\)
−0.288467 + 0.957490i \(0.593145\pi\)
\(468\) 0 0
\(469\) 42.6716 31.0028i 1.97039 1.43157i
\(470\) 0 0
\(471\) −10.9451 7.95207i −0.504323 0.366412i
\(472\) 0 0
\(473\) −1.74773 0.567871i −0.0803606 0.0261108i
\(474\) 0 0
\(475\) 13.5764 + 3.05464i 0.622927 + 0.140157i
\(476\) 0 0
\(477\) 0.300015 + 0.0974809i 0.0137368 + 0.00446334i
\(478\) 0 0
\(479\) 1.25147 + 0.909247i 0.0571812 + 0.0415446i 0.616009 0.787739i \(-0.288749\pi\)
−0.558827 + 0.829284i \(0.688749\pi\)
\(480\) 0 0
\(481\) −38.1707 + 27.7326i −1.74043 + 1.26450i
\(482\) 0 0
\(483\) −3.41269 4.69717i −0.155283 0.213729i
\(484\) 0 0
\(485\) 5.62068 + 9.87015i 0.255222 + 0.448180i
\(486\) 0 0
\(487\) 11.8681 3.85619i 0.537797 0.174741i −0.0275101 0.999622i \(-0.508758\pi\)
0.565307 + 0.824881i \(0.308758\pi\)
\(488\) 0 0
\(489\) −4.49876 + 13.8458i −0.203441 + 0.626126i
\(490\) 0 0
\(491\) −5.46864 16.8307i −0.246796 0.759561i −0.995336 0.0964706i \(-0.969245\pi\)
0.748540 0.663090i \(-0.230755\pi\)
\(492\) 0 0
\(493\) 31.8347i 1.43376i
\(494\) 0 0
\(495\) 4.10279 9.06974i 0.184407 0.407654i
\(496\) 0 0
\(497\) −1.32165 + 1.81910i −0.0592843 + 0.0815978i
\(498\) 0 0
\(499\) 30.9281 1.38453 0.692267 0.721642i \(-0.256612\pi\)
0.692267 + 0.721642i \(0.256612\pi\)
\(500\) 0 0
\(501\) −9.96824 −0.445348
\(502\) 0 0
\(503\) 18.5467 25.5273i 0.826956 1.13821i −0.161526 0.986868i \(-0.551642\pi\)
0.988482 0.151338i \(-0.0483583\pi\)
\(504\) 0 0
\(505\) 10.3090 22.7894i 0.458746 1.01412i
\(506\) 0 0
\(507\) 20.0370i 0.889873i
\(508\) 0 0
\(509\) 2.23276 + 6.87172i 0.0989652 + 0.304583i 0.988267 0.152738i \(-0.0488090\pi\)
−0.889302 + 0.457321i \(0.848809\pi\)
\(510\) 0 0
\(511\) 21.5183 66.2264i 0.951912 2.92968i
\(512\) 0 0
\(513\) 2.64694 0.860042i 0.116865 0.0379718i
\(514\) 0 0
\(515\) −3.48075 6.11234i −0.153380 0.269342i
\(516\) 0 0
\(517\) 20.3962 + 28.0729i 0.897022 + 1.23464i
\(518\) 0 0
\(519\) −8.79806 + 6.39217i −0.386192 + 0.280585i
\(520\) 0 0
\(521\) 7.67413 + 5.57558i 0.336210 + 0.244271i 0.743061 0.669224i \(-0.233373\pi\)
−0.406851 + 0.913494i \(0.633373\pi\)
\(522\) 0 0
\(523\) −19.3589 6.29007i −0.846504 0.275046i −0.146523 0.989207i \(-0.546808\pi\)
−0.699981 + 0.714162i \(0.746808\pi\)
\(524\) 0 0
\(525\) 2.04686 + 21.9819i 0.0893321 + 0.959369i
\(526\) 0 0
\(527\) 1.23186 + 0.400255i 0.0536606 + 0.0174354i
\(528\) 0 0
\(529\) −17.2085 12.5027i −0.748197 0.543597i
\(530\) 0 0
\(531\) −2.03793 + 1.48064i −0.0884385 + 0.0642544i
\(532\) 0 0
\(533\) 26.5204 + 36.5022i 1.14873 + 1.58108i
\(534\) 0 0
\(535\) −15.7691 7.13330i −0.681757 0.308400i
\(536\) 0 0
\(537\) −23.9419 + 7.77918i −1.03317 + 0.335697i
\(538\) 0 0
\(539\) −17.1902 + 52.9061i −0.740435 + 2.27883i
\(540\) 0 0
\(541\) 9.54086 + 29.3638i 0.410194 + 1.26245i 0.916480 + 0.400081i \(0.131018\pi\)
−0.506286 + 0.862366i \(0.668982\pi\)
\(542\) 0 0
\(543\) 7.59173i 0.325792i
\(544\) 0 0
\(545\) −23.0481 2.56086i −0.987271 0.109695i
\(546\) 0 0
\(547\) 9.01637 12.4100i 0.385512 0.530612i −0.571522 0.820587i \(-0.693647\pi\)
0.957034 + 0.289975i \(0.0936469\pi\)
\(548\) 0 0
\(549\) −9.33114 −0.398243
\(550\) 0 0
\(551\) 13.4850 0.574478
\(552\) 0 0
\(553\) −8.90587 + 12.2579i −0.378716 + 0.521258i
\(554\) 0 0
\(555\) −13.5674 12.3627i −0.575903 0.524769i
\(556\) 0 0
\(557\) 28.6722i 1.21488i −0.794365 0.607441i \(-0.792196\pi\)
0.794365 0.607441i \(-0.207804\pi\)
\(558\) 0 0
\(559\) −0.733185 2.25651i −0.0310104 0.0954403i
\(560\) 0 0
\(561\) 9.03874 27.8184i 0.381616 1.17449i
\(562\) 0 0
\(563\) −6.99026 + 2.27127i −0.294604 + 0.0957227i −0.452590 0.891719i \(-0.649500\pi\)
0.157986 + 0.987441i \(0.449500\pi\)
\(564\) 0 0
\(565\) −2.52516 + 22.7267i −0.106234 + 0.956121i
\(566\) 0 0
\(567\) 2.59531 + 3.57213i 0.108993 + 0.150016i
\(568\) 0 0
\(569\) −25.1830 + 18.2965i −1.05572 + 0.767029i −0.973293 0.229568i \(-0.926269\pi\)
−0.0824322 + 0.996597i \(0.526269\pi\)
\(570\) 0 0
\(571\) −10.5055 7.63268i −0.439641 0.319418i 0.345851 0.938289i \(-0.387590\pi\)
−0.785492 + 0.618872i \(0.787590\pi\)
\(572\) 0 0
\(573\) −0.0115012 0.00373697i −0.000480470 0.000156114i
\(574\) 0 0
\(575\) −2.60269 6.03765i −0.108540 0.251787i
\(576\) 0 0
\(577\) 20.7231 + 6.73333i 0.862712 + 0.280312i 0.706761 0.707453i \(-0.250156\pi\)
0.155951 + 0.987765i \(0.450156\pi\)
\(578\) 0 0
\(579\) 10.3426 + 7.51430i 0.429822 + 0.312284i
\(580\) 0 0
\(581\) 19.1879 13.9408i 0.796048 0.578363i
\(582\) 0 0
\(583\) 0.825453 + 1.13614i 0.0341868 + 0.0470541i
\(584\) 0 0
\(585\) 12.5872 2.59750i 0.520417 0.107393i
\(586\) 0 0
\(587\) −25.3208 + 8.22724i −1.04510 + 0.339575i −0.780745 0.624850i \(-0.785160\pi\)
−0.264358 + 0.964425i \(0.585160\pi\)
\(588\) 0 0
\(589\) −0.169545 + 0.521806i −0.00698598 + 0.0215006i
\(590\) 0 0
\(591\) 3.04859 + 9.38261i 0.125402 + 0.385949i
\(592\) 0 0
\(593\) 5.23169i 0.214840i −0.994214 0.107420i \(-0.965741\pi\)
0.994214 0.107420i \(-0.0342589\pi\)
\(594\) 0 0
\(595\) 13.1103 + 63.5314i 0.537472 + 2.60453i
\(596\) 0 0
\(597\) 0.173773 0.239178i 0.00711204 0.00978889i
\(598\) 0 0
\(599\) −39.5405 −1.61558 −0.807790 0.589471i \(-0.799336\pi\)
−0.807790 + 0.589471i \(0.799336\pi\)
\(600\) 0 0
\(601\) −45.5789 −1.85920 −0.929602 0.368565i \(-0.879849\pi\)
−0.929602 + 0.368565i \(0.879849\pi\)
\(602\) 0 0
\(603\) 7.02151 9.66428i 0.285938 0.393560i
\(604\) 0 0
\(605\) 17.1354 9.75796i 0.696652 0.396717i
\(606\) 0 0
\(607\) 18.6524i 0.757078i −0.925585 0.378539i \(-0.876427\pi\)
0.925585 0.378539i \(-0.123573\pi\)
\(608\) 0 0
\(609\) 6.61096 + 20.3464i 0.267890 + 0.824480i
\(610\) 0 0
\(611\) −13.8444 + 42.6088i −0.560086 + 1.72377i
\(612\) 0 0
\(613\) 10.1837 3.30887i 0.411314 0.133644i −0.0960485 0.995377i \(-0.530620\pi\)
0.507363 + 0.861733i \(0.330620\pi\)
\(614\) 0 0
\(615\) −11.8223 + 12.9743i −0.476722 + 0.523175i
\(616\) 0 0
\(617\) 9.83565 + 13.5376i 0.395968 + 0.545004i 0.959726 0.280936i \(-0.0906449\pi\)
−0.563758 + 0.825940i \(0.690645\pi\)
\(618\) 0 0
\(619\) 18.5531 13.4796i 0.745711 0.541791i −0.148783 0.988870i \(-0.547536\pi\)
0.894495 + 0.447079i \(0.147536\pi\)
\(620\) 0 0
\(621\) −1.06382 0.772907i −0.0426894 0.0310157i
\(622\) 0 0
\(623\) 47.6417 + 15.4797i 1.90872 + 0.620182i
\(624\) 0 0
\(625\) −3.20277 + 24.7940i −0.128111 + 0.991760i
\(626\) 0 0
\(627\) 11.7837 + 3.82874i 0.470594 + 0.152905i
\(628\) 0 0
\(629\) −43.6334 31.7015i −1.73978 1.26402i
\(630\) 0 0
\(631\) −11.7443 + 8.53273i −0.467533 + 0.339683i −0.796479 0.604666i \(-0.793307\pi\)
0.328946 + 0.944349i \(0.393307\pi\)
\(632\) 0 0
\(633\) 7.43414 + 10.2322i 0.295481 + 0.406694i
\(634\) 0 0
\(635\) −17.0376 + 18.6978i −0.676117 + 0.741999i
\(636\) 0 0
\(637\) −68.3076 + 22.1945i −2.70645 + 0.879377i
\(638\) 0 0
\(639\) −0.157366 + 0.484323i −0.00622531 + 0.0191595i
\(640\) 0 0
\(641\) −9.81208 30.1985i −0.387554 1.19277i −0.934611 0.355672i \(-0.884252\pi\)
0.547057 0.837095i \(-0.315748\pi\)
\(642\) 0 0
\(643\) 3.63816i 0.143475i 0.997424 + 0.0717376i \(0.0228544\pi\)
−0.997424 + 0.0717376i \(0.977146\pi\)
\(644\) 0 0
\(645\) 0.802093 0.456762i 0.0315824 0.0179850i
\(646\) 0 0
\(647\) 6.60932 9.09695i 0.259839 0.357638i −0.659088 0.752066i \(-0.729057\pi\)
0.918927 + 0.394428i \(0.129057\pi\)
\(648\) 0 0
\(649\) −11.2142 −0.440195
\(650\) 0 0
\(651\) −0.870433 −0.0341150
\(652\) 0 0
\(653\) −1.18866 + 1.63604i −0.0465157 + 0.0640233i −0.831641 0.555313i \(-0.812598\pi\)
0.785126 + 0.619337i \(0.212598\pi\)
\(654\) 0 0
\(655\) 4.27223 + 20.7028i 0.166930 + 0.808925i
\(656\) 0 0
\(657\) 15.7708i 0.615279i
\(658\) 0 0
\(659\) 0.245610 + 0.755909i 0.00956760 + 0.0294460i 0.955726 0.294257i \(-0.0950721\pi\)
−0.946159 + 0.323703i \(0.895072\pi\)
\(660\) 0 0
\(661\) 12.6628 38.9722i 0.492527 1.51584i −0.328249 0.944591i \(-0.606459\pi\)
0.820776 0.571250i \(-0.193541\pi\)
\(662\) 0 0
\(663\) 35.9166 11.6700i 1.39489 0.453226i
\(664\) 0 0
\(665\) −26.9114 + 5.55345i −1.04358 + 0.215353i
\(666\) 0 0
\(667\) −3.74489 5.15440i −0.145003 0.199579i
\(668\) 0 0
\(669\) 4.23909 3.07988i 0.163893 0.119075i
\(670\) 0 0
\(671\) −33.6069 24.4169i −1.29738 0.942602i
\(672\) 0 0
\(673\) −33.3834 10.8469i −1.28683 0.418118i −0.415852 0.909432i \(-0.636517\pi\)
−0.870982 + 0.491314i \(0.836517\pi\)
\(674\) 0 0
\(675\) 1.97931 + 4.59155i 0.0761838 + 0.176729i
\(676\) 0 0
\(677\) −36.5079 11.8621i −1.40311 0.455899i −0.492916 0.870077i \(-0.664069\pi\)
−0.910196 + 0.414178i \(0.864069\pi\)
\(678\) 0 0
\(679\) −18.1450 13.1831i −0.696342 0.505922i
\(680\) 0 0
\(681\) −6.28523 + 4.56649i −0.240850 + 0.174988i
\(682\) 0 0
\(683\) −4.91673 6.76730i −0.188134 0.258944i 0.704523 0.709681i \(-0.251161\pi\)
−0.892657 + 0.450738i \(0.851161\pi\)
\(684\) 0 0
\(685\) −2.07673 + 18.6908i −0.0793479 + 0.714140i
\(686\) 0 0
\(687\) −5.69866 + 1.85161i −0.217417 + 0.0706432i
\(688\) 0 0
\(689\) −0.560299 + 1.72442i −0.0213457 + 0.0656953i
\(690\) 0 0
\(691\) 1.80183 + 5.54547i 0.0685450 + 0.210960i 0.979462 0.201631i \(-0.0646241\pi\)
−0.910917 + 0.412590i \(0.864624\pi\)
\(692\) 0 0
\(693\) 19.6565i 0.746689i
\(694\) 0 0
\(695\) −19.5388 17.8040i −0.741150 0.675344i
\(696\) 0 0
\(697\) −30.3158 + 41.7261i −1.14829 + 1.58049i
\(698\) 0 0
\(699\) −14.8631 −0.562174
\(700\) 0 0
\(701\) 50.6649 1.91359 0.956793 0.290770i \(-0.0939114\pi\)
0.956793 + 0.290770i \(0.0939114\pi\)
\(702\) 0 0
\(703\) 13.4285 18.4828i 0.506467 0.697091i
\(704\) 0 0
\(705\) −17.3226 1.92471i −0.652408 0.0724888i
\(706\) 0 0
\(707\) 49.3907i 1.85753i
\(708\) 0 0
\(709\) 3.00734 + 9.25565i 0.112943 + 0.347603i 0.991512 0.130012i \(-0.0415015\pi\)
−0.878569 + 0.477615i \(0.841501\pi\)
\(710\) 0 0
\(711\) −1.06040 + 3.26358i −0.0397681 + 0.122394i
\(712\) 0 0
\(713\) 0.246536 0.0801044i 0.00923285 0.00299993i
\(714\) 0 0
\(715\) 52.1309 + 23.5819i 1.94958 + 0.881914i
\(716\) 0 0
\(717\) −12.4615 17.1518i −0.465383 0.640545i
\(718\) 0 0
\(719\) 15.1579 11.0129i 0.565294 0.410710i −0.268099 0.963391i \(-0.586395\pi\)
0.833393 + 0.552681i \(0.186395\pi\)
\(720\) 0 0
\(721\) 11.2368 + 8.16399i 0.418479 + 0.304043i
\(722\) 0 0
\(723\) 15.2703 + 4.96162i 0.567909 + 0.184525i
\(724\) 0 0
\(725\) 2.24610 + 24.1217i 0.0834181 + 0.895857i
\(726\) 0 0
\(727\) 36.1247 + 11.7376i 1.33979 + 0.435324i 0.889246 0.457430i \(-0.151230\pi\)
0.450544 + 0.892754i \(0.351230\pi\)
\(728\) 0 0
\(729\) 0.809017 + 0.587785i 0.0299636 + 0.0217698i
\(730\) 0 0
\(731\) 2.19421 1.59418i 0.0811557 0.0589630i
\(732\) 0 0
\(733\) 15.4951 + 21.3271i 0.572323 + 0.787735i 0.992828 0.119555i \(-0.0381469\pi\)
−0.420505 + 0.907290i \(0.638147\pi\)
\(734\) 0 0
\(735\) −13.8268 24.2804i −0.510009 0.895597i
\(736\) 0 0
\(737\) 50.5772 16.4335i 1.86303 0.605337i
\(738\) 0 0
\(739\) 10.2081 31.4174i 0.375513 1.15571i −0.567619 0.823291i \(-0.692136\pi\)
0.943132 0.332418i \(-0.107864\pi\)
\(740\) 0 0
\(741\) 4.94333 + 15.2140i 0.181598 + 0.558901i
\(742\) 0 0
\(743\) 40.2017i 1.47486i 0.675425 + 0.737428i \(0.263960\pi\)
−0.675425 + 0.737428i \(0.736040\pi\)
\(744\) 0 0
\(745\) 9.80168 21.6679i 0.359106 0.793849i
\(746\) 0 0
\(747\) 3.15732 4.34568i 0.115520 0.159000i
\(748\) 0 0
\(749\) 34.1758 1.24876
\(750\) 0 0
\(751\) 30.5937 1.11638 0.558190 0.829713i \(-0.311496\pi\)
0.558190 + 0.829713i \(0.311496\pi\)
\(752\) 0 0
\(753\) −14.1875 + 19.5274i −0.517020 + 0.711617i
\(754\) 0 0
\(755\) −4.07031 + 8.99793i −0.148134 + 0.327468i
\(756\) 0 0
\(757\) 24.4003i 0.886845i 0.896313 + 0.443422i \(0.146236\pi\)
−0.896313 + 0.443422i \(0.853764\pi\)
\(758\) 0 0
\(759\) −1.80895 5.56739i −0.0656609 0.202083i
\(760\) 0 0
\(761\) 8.75574 26.9474i 0.317395 0.976842i −0.657362 0.753575i \(-0.728328\pi\)
0.974757 0.223267i \(-0.0716723\pi\)
\(762\) 0 0
\(763\) 43.5502 14.1503i 1.57662 0.512276i
\(764\) 0 0
\(765\) 7.27022 + 12.7668i 0.262856 + 0.461585i
\(766\) 0 0
\(767\) −8.51040 11.7136i −0.307293 0.422952i
\(768\) 0 0
\(769\) −33.2679 + 24.1706i −1.19967 + 0.871613i −0.994252 0.107061i \(-0.965856\pi\)
−0.205420 + 0.978674i \(0.565856\pi\)
\(770\) 0 0
\(771\) −3.42166 2.48598i −0.123228 0.0895304i
\(772\) 0 0
\(773\) 4.58131 + 1.48856i 0.164778 + 0.0535397i 0.390244 0.920711i \(-0.372391\pi\)
−0.225466 + 0.974251i \(0.572391\pi\)
\(774\) 0 0
\(775\) −0.961638 0.216366i −0.0345431 0.00777208i
\(776\) 0 0
\(777\) 34.4706 + 11.2002i 1.23663 + 0.401804i
\(778\) 0 0
\(779\) −17.6749 12.8415i −0.633268 0.460096i
\(780\) 0 0
\(781\) −1.83410 + 1.33255i −0.0656293 + 0.0476825i
\(782\) 0 0
\(783\) 2.84794 + 3.91985i 0.101777 + 0.140084i
\(784\) 0 0
\(785\) 27.5626 + 12.4682i 0.983751 + 0.445010i
\(786\) 0 0
\(787\) −38.3447 + 12.4590i −1.36684 + 0.444114i −0.898321 0.439339i \(-0.855213\pi\)
−0.468520 + 0.883453i \(0.655213\pi\)
\(788\) 0 0
\(789\) −2.59198 + 7.97729i −0.0922769 + 0.283999i
\(790\) 0 0
\(791\) −13.9530 42.9430i −0.496113 1.52688i
\(792\) 0 0
\(793\) 53.6333i 1.90457i
\(794\) 0 0
\(795\) −0.701064 0.0778950i −0.0248642 0.00276265i
\(796\) 0 0
\(797\) 17.7487 24.4289i 0.628690 0.865318i