Properties

Label 768.2.o.b.287.3
Level 768
Weight 2
Character 768.287
Analytic conductor 6.133
Analytic rank 0
Dimension 56
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 768.o (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.13251087523\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 287.3
Character \(\chi\) \(=\) 768.287
Dual form 768.2.o.b.479.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.44423 - 0.956131i) q^{3} +(-1.56013 + 3.76650i) q^{5} +(-0.838552 + 0.838552i) q^{7} +(1.17163 + 2.76175i) q^{9} +O(q^{10})\) \(q+(-1.44423 - 0.956131i) q^{3} +(-1.56013 + 3.76650i) q^{5} +(-0.838552 + 0.838552i) q^{7} +(1.17163 + 2.76175i) q^{9} +(0.249049 - 0.601256i) q^{11} +(2.05771 - 0.852332i) q^{13} +(5.85446 - 3.94801i) q^{15} -3.23677 q^{17} +(-1.47818 - 3.56865i) q^{19} +(2.01283 - 0.409300i) q^{21} +(-2.58369 + 2.58369i) q^{23} +(-8.21694 - 8.21694i) q^{25} +(0.948494 - 5.10885i) q^{27} +(-3.52027 + 1.45815i) q^{29} -7.63408i q^{31} +(-0.934564 + 0.630232i) q^{33} +(-1.85015 - 4.46665i) q^{35} +(-0.579146 - 0.239890i) q^{37} +(-3.78676 - 0.736474i) q^{39} +(-3.54554 - 3.54554i) q^{41} +(3.19595 + 1.32381i) q^{43} +(-12.2300 + 0.104223i) q^{45} +5.96658i q^{47} +5.59366i q^{49} +(4.67465 + 3.09477i) q^{51} +(0.762825 + 0.315973i) q^{53} +(1.87608 + 1.87608i) q^{55} +(-1.27725 + 6.56731i) q^{57} +(-5.86827 - 2.43072i) q^{59} +(-2.68247 - 6.47607i) q^{61} +(-3.29834 - 1.33340i) q^{63} +9.08011i q^{65} +(-4.78575 + 1.98232i) q^{67} +(6.20180 - 1.26111i) q^{69} +(-10.2094 - 10.2094i) q^{71} +(8.09458 - 8.09458i) q^{73} +(4.01072 + 19.7237i) q^{75} +(0.295345 + 0.713025i) q^{77} -11.5343 q^{79} +(-6.25458 + 6.47149i) q^{81} +(-0.998651 + 0.413655i) q^{83} +(5.04979 - 12.1913i) q^{85} +(6.47828 + 1.25994i) q^{87} +(10.4124 - 10.4124i) q^{89} +(-1.01077 + 2.44022i) q^{91} +(-7.29918 + 11.0254i) q^{93} +15.7475 q^{95} +9.21596 q^{97} +(1.95232 - 0.0166374i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + O(q^{10}) \) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + 8q^{13} - 8q^{15} + 8q^{19} + 4q^{21} - 8q^{25} + 28q^{27} - 8q^{33} + 8q^{37} - 28q^{39} + 8q^{43} + 4q^{45} + 16q^{51} + 24q^{55} - 4q^{57} + 40q^{61} - 56q^{67} + 4q^{69} - 8q^{73} - 16q^{75} + 16q^{79} + 48q^{85} + 52q^{87} - 40q^{91} - 8q^{93} - 16q^{97} - 60q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{8}\right)\)

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
\(3\) −1.44423 0.956131i −0.833829 0.552022i
\(4\) 0 0
\(5\) −1.56013 + 3.76650i −0.697713 + 1.68443i 0.0309186 + 0.999522i \(0.490157\pi\)
−0.728631 + 0.684906i \(0.759843\pi\)
\(6\) 0 0
\(7\) −0.838552 + 0.838552i −0.316943 + 0.316943i −0.847592 0.530649i \(-0.821948\pi\)
0.530649 + 0.847592i \(0.321948\pi\)
\(8\) 0 0
\(9\) 1.17163 + 2.76175i 0.390542 + 0.920585i
\(10\) 0 0
\(11\) 0.249049 0.601256i 0.0750910 0.181286i −0.881877 0.471480i \(-0.843720\pi\)
0.956968 + 0.290194i \(0.0937200\pi\)
\(12\) 0 0
\(13\) 2.05771 0.852332i 0.570706 0.236394i −0.0786194 0.996905i \(-0.525051\pi\)
0.649326 + 0.760510i \(0.275051\pi\)
\(14\) 0 0
\(15\) 5.85446 3.94801i 1.51162 1.01937i
\(16\) 0 0
\(17\) −3.23677 −0.785032 −0.392516 0.919745i \(-0.628395\pi\)
−0.392516 + 0.919745i \(0.628395\pi\)
\(18\) 0 0
\(19\) −1.47818 3.56865i −0.339119 0.818705i −0.997801 0.0662838i \(-0.978886\pi\)
0.658682 0.752421i \(-0.271114\pi\)
\(20\) 0 0
\(21\) 2.01283 0.409300i 0.439236 0.0893166i
\(22\) 0 0
\(23\) −2.58369 + 2.58369i −0.538737 + 0.538737i −0.923158 0.384421i \(-0.874401\pi\)
0.384421 + 0.923158i \(0.374401\pi\)
\(24\) 0 0
\(25\) −8.21694 8.21694i −1.64339 1.64339i
\(26\) 0 0
\(27\) 0.948494 5.10885i 0.182538 0.983199i
\(28\) 0 0
\(29\) −3.52027 + 1.45815i −0.653698 + 0.270771i −0.684784 0.728746i \(-0.740104\pi\)
0.0310857 + 0.999517i \(0.490104\pi\)
\(30\) 0 0
\(31\) 7.63408i 1.37112i −0.728015 0.685561i \(-0.759557\pi\)
0.728015 0.685561i \(-0.240443\pi\)
\(32\) 0 0
\(33\) −0.934564 + 0.630232i −0.162687 + 0.109709i
\(34\) 0 0
\(35\) −1.85015 4.46665i −0.312732 0.755002i
\(36\) 0 0
\(37\) −0.579146 0.239890i −0.0952110 0.0394377i 0.334570 0.942371i \(-0.391409\pi\)
−0.429781 + 0.902933i \(0.641409\pi\)
\(38\) 0 0
\(39\) −3.78676 0.736474i −0.606367 0.117930i
\(40\) 0 0
\(41\) −3.54554 3.54554i −0.553720 0.553720i 0.373792 0.927512i \(-0.378057\pi\)
−0.927512 + 0.373792i \(0.878057\pi\)
\(42\) 0 0
\(43\) 3.19595 + 1.32381i 0.487378 + 0.201879i 0.612820 0.790222i \(-0.290035\pi\)
−0.125442 + 0.992101i \(0.540035\pi\)
\(44\) 0 0
\(45\) −12.2300 + 0.104223i −1.82315 + 0.0155366i
\(46\) 0 0
\(47\) 5.96658i 0.870315i 0.900354 + 0.435158i \(0.143307\pi\)
−0.900354 + 0.435158i \(0.856693\pi\)
\(48\) 0 0
\(49\) 5.59366i 0.799095i
\(50\) 0 0
\(51\) 4.67465 + 3.09477i 0.654582 + 0.433355i
\(52\) 0 0
\(53\) 0.762825 + 0.315973i 0.104782 + 0.0434022i 0.434459 0.900692i \(-0.356940\pi\)
−0.329677 + 0.944094i \(0.606940\pi\)
\(54\) 0 0
\(55\) 1.87608 + 1.87608i 0.252971 + 0.252971i
\(56\) 0 0
\(57\) −1.27725 + 6.56731i −0.169176 + 0.869862i
\(58\) 0 0
\(59\) −5.86827 2.43072i −0.763984 0.316452i −0.0335508 0.999437i \(-0.510682\pi\)
−0.730433 + 0.682985i \(0.760682\pi\)
\(60\) 0 0
\(61\) −2.68247 6.47607i −0.343456 0.829175i −0.997361 0.0725992i \(-0.976871\pi\)
0.653906 0.756576i \(-0.273129\pi\)
\(62\) 0 0
\(63\) −3.29834 1.33340i −0.415552 0.167993i
\(64\) 0 0
\(65\) 9.08011i 1.12625i
\(66\) 0 0
\(67\) −4.78575 + 1.98232i −0.584673 + 0.242179i −0.655357 0.755319i \(-0.727482\pi\)
0.0706842 + 0.997499i \(0.477482\pi\)
\(68\) 0 0
\(69\) 6.20180 1.26111i 0.746609 0.151820i
\(70\) 0 0
\(71\) −10.2094 10.2094i −1.21163 1.21163i −0.970489 0.241145i \(-0.922477\pi\)
−0.241145 0.970489i \(1.42248\pi\)
\(72\) 0 0
\(73\) 8.09458 8.09458i 0.947399 0.947399i −0.0512851 0.998684i \(-0.516332\pi\)
0.998684 + 0.0512851i \(0.0163317\pi\)
\(74\) 0 0
\(75\) 4.01072 + 19.7237i 0.463118 + 2.27749i
\(76\) 0 0
\(77\) 0.295345 + 0.713025i 0.0336576 + 0.0812567i
\(78\) 0 0
\(79\) −11.5343 −1.29771 −0.648857 0.760910i \(-0.724753\pi\)
−0.648857 + 0.760910i \(0.724753\pi\)
\(80\) 0 0
\(81\) −6.25458 + 6.47149i −0.694953 + 0.719055i
\(82\) 0 0
\(83\) −0.998651 + 0.413655i −0.109616 + 0.0454045i −0.436818 0.899550i \(-0.643894\pi\)
0.327201 + 0.944955i \(0.393894\pi\)
\(84\) 0 0
\(85\) 5.04979 12.1913i 0.547727 1.32233i
\(86\) 0 0
\(87\) 6.47828 + 1.25994i 0.694544 + 0.135080i
\(88\) 0 0
\(89\) 10.4124 10.4124i 1.10372 1.10372i 0.109759 0.993958i \(-0.464992\pi\)
0.993958 0.109759i \(-0.0350078\pi\)
\(90\) 0 0
\(91\) −1.01077 + 2.44022i −0.105958 + 0.255805i
\(92\) 0 0
\(93\) −7.29918 + 11.0254i −0.756890 + 1.14328i
\(94\) 0 0
\(95\) 15.7475 1.61566
\(96\) 0 0
\(97\) 9.21596 0.935739 0.467870 0.883797i \(-0.345022\pi\)
0.467870 + 0.883797i \(0.345022\pi\)
\(98\) 0 0
\(99\) 1.95232 0.0166374i 0.196215 0.00167212i
\(100\) 0 0
\(101\) −1.61830 + 3.90691i −0.161026 + 0.388752i −0.983714 0.179742i \(-0.942474\pi\)
0.822687 + 0.568494i \(0.192474\pi\)
\(102\) 0 0
\(103\) −4.29846 + 4.29846i −0.423540 + 0.423540i −0.886421 0.462881i \(-0.846816\pi\)
0.462881 + 0.886421i \(0.346816\pi\)
\(104\) 0 0
\(105\) −1.59866 + 8.21988i −0.156013 + 0.802178i
\(106\) 0 0
\(107\) 2.82811 6.82767i 0.273404 0.660055i −0.726221 0.687462i \(-0.758725\pi\)
0.999624 + 0.0274065i \(0.00872486\pi\)
\(108\) 0 0
\(109\) −12.4025 + 5.13729i −1.18794 + 0.492063i −0.887085 0.461606i \(-0.847273\pi\)
−0.300859 + 0.953669i \(0.597273\pi\)
\(110\) 0 0
\(111\) 0.607056 + 0.900196i 0.0576192 + 0.0854429i
\(112\) 0 0
\(113\) 3.42949 0.322619 0.161310 0.986904i \(-0.448428\pi\)
0.161310 + 0.986904i \(0.448428\pi\)
\(114\) 0 0
\(115\) −5.70056 13.7624i −0.531580 1.28335i
\(116\) 0 0
\(117\) 4.76480 + 4.68428i 0.440506 + 0.433062i
\(118\) 0 0
\(119\) 2.71420 2.71420i 0.248810 0.248810i
\(120\) 0 0
\(121\) 7.47869 + 7.47869i 0.679881 + 0.679881i
\(122\) 0 0
\(123\) 1.73059 + 8.51059i 0.156042 + 0.767374i
\(124\) 0 0
\(125\) 24.9361 10.3289i 2.23035 0.923842i
\(126\) 0 0
\(127\) 0.724490i 0.0642881i −0.999483 0.0321441i \(-0.989766\pi\)
0.999483 0.0321441i \(-0.0102335\pi\)
\(128\) 0 0
\(129\) −3.34997 4.96764i −0.294949 0.437376i
\(130\) 0 0
\(131\) 1.44273 + 3.48306i 0.126052 + 0.304317i 0.974290 0.225299i \(-0.0723360\pi\)
−0.848238 + 0.529616i \(0.822336\pi\)
\(132\) 0 0
\(133\) 4.23204 + 1.75297i 0.366964 + 0.152001i
\(134\) 0 0
\(135\) 17.7627 + 11.5430i 1.52877 + 0.993462i
\(136\) 0 0
\(137\) 2.20990 + 2.20990i 0.188805 + 0.188805i 0.795179 0.606375i \(-0.207377\pi\)
−0.606375 + 0.795179i \(0.707377\pi\)
\(138\) 0 0
\(139\) −4.01991 1.66510i −0.340964 0.141232i 0.205629 0.978630i \(-0.434076\pi\)
−0.546594 + 0.837398i \(0.684076\pi\)
\(140\) 0 0
\(141\) 5.70483 8.61714i 0.480434 0.725694i
\(142\) 0 0
\(143\) 1.44948i 0.121212i
\(144\) 0 0
\(145\) 15.5340i 1.29003i
\(146\) 0 0
\(147\) 5.34827 8.07856i 0.441118 0.666308i
\(148\) 0 0
\(149\) −5.47285 2.26693i −0.448353 0.185714i 0.147070 0.989126i \(-0.453016\pi\)
−0.595423 + 0.803412i \(0.703016\pi\)
\(150\) 0 0
\(151\) −5.81381 5.81381i −0.473121 0.473121i 0.429802 0.902923i \(-0.358583\pi\)
−0.902923 + 0.429802i \(0.858583\pi\)
\(152\) 0 0
\(153\) −3.79229 8.93916i −0.306588 0.722688i
\(154\) 0 0
\(155\) 28.7537 + 11.9102i 2.30956 + 0.956649i
\(156\) 0 0
\(157\) 3.37305 + 8.14326i 0.269199 + 0.649903i 0.999446 0.0332797i \(-0.0105952\pi\)
−0.730247 + 0.683183i \(0.760595\pi\)
\(158\) 0 0
\(159\) −0.799588 1.18570i −0.0634114 0.0940321i
\(160\) 0 0
\(161\) 4.33312i 0.341498i
\(162\) 0 0
\(163\) −13.8401 + 5.73275i −1.08404 + 0.449024i −0.851924 0.523665i \(-0.824564\pi\)
−0.232114 + 0.972688i \(0.574564\pi\)
\(164\) 0 0
\(165\) −0.915722 4.50328i −0.0712889 0.350580i
\(166\) 0 0
\(167\) 6.72756 + 6.72756i 0.520594 + 0.520594i 0.917751 0.397157i \(-0.130003\pi\)
−0.397157 + 0.917751i \(0.630003\pi\)
\(168\) 0 0
\(169\) −5.68468 + 5.68468i −0.437283 + 0.437283i
\(170\) 0 0
\(171\) 8.12386 8.26352i 0.621247 0.631927i
\(172\) 0 0
\(173\) −0.275804 0.665850i −0.0209690 0.0506236i 0.913048 0.407852i \(-0.133722\pi\)
−0.934017 + 0.357228i \(0.883722\pi\)
\(174\) 0 0
\(175\) 13.7807 1.04172
\(176\) 0 0
\(177\) 6.15107 + 9.12136i 0.462343 + 0.685603i
\(178\) 0 0
\(179\) −11.9198 + 4.93735i −0.890928 + 0.369035i −0.780725 0.624875i \(-0.785150\pi\)
−0.110203 + 0.993909i \(0.535150\pi\)
\(180\) 0 0
\(181\) 2.66842 6.44214i 0.198342 0.478841i −0.793147 0.609030i \(-0.791559\pi\)
0.991489 + 0.130190i \(0.0415587\pi\)
\(182\) 0 0
\(183\) −2.31784 + 11.9178i −0.171340 + 0.880986i
\(184\) 0 0
\(185\) 1.80709 1.80709i 0.132860 0.132860i
\(186\) 0 0
\(187\) −0.806113 + 1.94613i −0.0589488 + 0.142315i
\(188\) 0 0
\(189\) 3.48867 + 5.07940i 0.253764 + 0.369472i
\(190\) 0 0
\(191\) −1.62308 −0.117442 −0.0587210 0.998274i \(-0.518702\pi\)
−0.0587210 + 0.998274i \(0.518702\pi\)
\(192\) 0 0
\(193\) −10.3575 −0.745548 −0.372774 0.927922i \(-0.621593\pi\)
−0.372774 + 0.927922i \(0.621593\pi\)
\(194\) 0 0
\(195\) 8.68177 13.1138i 0.621715 0.939099i
\(196\) 0 0
\(197\) 0.784033 1.89282i 0.0558601 0.134858i −0.893486 0.449092i \(-0.851748\pi\)
0.949346 + 0.314234i \(0.101748\pi\)
\(198\) 0 0
\(199\) −8.78498 + 8.78498i −0.622751 + 0.622751i −0.946234 0.323483i \(-0.895146\pi\)
0.323483 + 0.946234i \(0.395146\pi\)
\(200\) 0 0
\(201\) 8.80711 + 1.71287i 0.621206 + 0.120816i
\(202\) 0 0
\(203\) 1.72920 4.17466i 0.121366 0.293004i
\(204\) 0 0
\(205\) 18.8858 7.82274i 1.31904 0.546364i
\(206\) 0 0
\(207\) −10.1626 4.10840i −0.706353 0.285553i
\(208\) 0 0
\(209\) −2.51382 −0.173884
\(210\) 0 0
\(211\) 9.81540 + 23.6965i 0.675720 + 1.63133i 0.771729 + 0.635951i \(0.219392\pi\)
−0.0960096 + 0.995380i \(0.530608\pi\)
\(212\) 0 0
\(213\) 4.98325 + 24.5063i 0.341447 + 1.67915i
\(214\) 0 0
\(215\) −9.97223 + 9.97223i −0.680100 + 0.680100i
\(216\) 0 0
\(217\) 6.40157 + 6.40157i 0.434567 + 0.434567i
\(218\) 0 0
\(219\) −19.4300 + 3.95099i −1.31295 + 0.266983i
\(220\) 0 0
\(221\) −6.66034 + 2.75880i −0.448023 + 0.185577i
\(222\) 0 0
\(223\) 16.3840i 1.09715i 0.836101 + 0.548576i \(0.184830\pi\)
−0.836101 + 0.548576i \(0.815170\pi\)
\(224\) 0 0
\(225\) 13.0660 32.3204i 0.871065 2.15469i
\(226\) 0 0
\(227\) 9.61652 + 23.2163i 0.638271 + 1.54092i 0.828981 + 0.559276i \(0.188921\pi\)
−0.190710 + 0.981646i \(0.561079\pi\)
\(228\) 0 0
\(229\) 11.2556 + 4.66223i 0.743792 + 0.308089i 0.722206 0.691678i \(-0.243128\pi\)
0.0215864 + 0.999767i \(0.493128\pi\)
\(230\) 0 0
\(231\) 0.255198 1.31216i 0.0167908 0.0863340i
\(232\) 0 0
\(233\) −13.5410 13.5410i −0.887101 0.887101i 0.107143 0.994244i \(-0.465830\pi\)
−0.994244 + 0.107143i \(0.965830\pi\)
\(234\) 0 0
\(235\) −22.4731 9.30866i −1.46598 0.607230i
\(236\) 0 0
\(237\) 16.6583 + 11.0283i 1.08207 + 0.716367i
\(238\) 0 0
\(239\) 19.1168i 1.23657i 0.785956 + 0.618283i \(0.212171\pi\)
−0.785956 + 0.618283i \(0.787829\pi\)
\(240\) 0 0
\(241\) 1.71219i 0.110292i 0.998478 + 0.0551460i \(0.0175624\pi\)
−0.998478 + 0.0551460i \(0.982438\pi\)
\(242\) 0 0
\(243\) 15.2207 3.36616i 0.976407 0.215939i
\(244\) 0 0
\(245\) −21.0685 8.72686i −1.34602 0.557539i
\(246\) 0 0
\(247\) −6.08335 6.08335i −0.387075 0.387075i
\(248\) 0 0
\(249\) 1.83780 + 0.357427i 0.116466 + 0.0226510i
\(250\) 0 0
\(251\) −25.5253 10.5729i −1.61115 0.667358i −0.618210 0.786013i \(-0.712142\pi\)
−0.992936 + 0.118655i \(0.962142\pi\)
\(252\) 0 0
\(253\) 0.909996 + 2.19693i 0.0572110 + 0.138120i
\(254\) 0 0
\(255\) −18.9495 + 12.7788i −1.18667 + 0.800239i
\(256\) 0 0
\(257\) 21.5264i 1.34278i 0.741104 + 0.671391i \(0.234303\pi\)
−0.741104 + 0.671391i \(0.765697\pi\)
\(258\) 0 0
\(259\) 0.686804 0.284483i 0.0426759 0.0176769i
\(260\) 0 0
\(261\) −8.15149 8.01373i −0.504564 0.496037i
\(262\) 0 0
\(263\) −10.4924 10.4924i −0.646988 0.646988i 0.305276 0.952264i \(-0.401251\pi\)
−0.952264 + 0.305276i \(0.901251\pi\)
\(264\) 0 0
\(265\) −2.38022 + 2.38022i −0.146216 + 0.146216i
\(266\) 0 0
\(267\) −24.9937 + 5.08235i −1.52959 + 0.311035i
\(268\) 0 0
\(269\) −4.94856 11.9469i −0.301719 0.728414i −0.999922 0.0125138i \(-0.996017\pi\)
0.698203 0.715900i \(1.74602\pi\)
\(270\) 0 0
\(271\) 7.03570 0.427388 0.213694 0.976901i \(-0.431450\pi\)
0.213694 + 0.976901i \(0.431450\pi\)
\(272\) 0 0
\(273\) 3.79296 2.55782i 0.229561 0.154806i
\(274\) 0 0
\(275\) −6.98690 + 2.89407i −0.421326 + 0.174519i
\(276\) 0 0
\(277\) −9.40456 + 22.7046i −0.565065 + 1.36419i 0.340606 + 0.940206i \(0.389368\pi\)
−0.905671 + 0.423982i \(0.860632\pi\)
\(278\) 0 0
\(279\) 21.0835 8.94430i 1.26223 0.535481i
\(280\) 0 0
\(281\) −13.7076 + 13.7076i −0.817727 + 0.817727i −0.985778 0.168051i \(-0.946253\pi\)
0.168051 + 0.985778i \(0.446253\pi\)
\(282\) 0 0
\(283\) 11.3422 27.3825i 0.674224 1.62772i −0.100134 0.994974i \(-0.531927\pi\)
0.774358 0.632747i \(-0.218073\pi\)
\(284\) 0 0
\(285\) −22.7431 15.0567i −1.34718 0.891879i
\(286\) 0 0
\(287\) 5.94623 0.350995
\(288\) 0 0
\(289\) −6.52333 −0.383725
\(290\) 0 0
\(291\) −13.3100 8.81167i −0.780247 0.516549i
\(292\) 0 0
\(293\) 4.07927 9.84823i 0.238314 0.575340i −0.758795 0.651329i \(-0.774212\pi\)
0.997109 + 0.0759896i \(0.0242116\pi\)
\(294\) 0 0
\(295\) 18.3106 18.3106i 1.06608 1.06608i
\(296\) 0 0
\(297\) −2.83551 1.84264i −0.164533 0.106921i
\(298\) 0 0
\(299\) −3.11433 + 7.51865i −0.180106 + 0.434815i
\(300\) 0 0
\(301\) −3.79005 + 1.56989i −0.218455 + 0.0904871i
\(302\) 0 0
\(303\) 6.07272 4.09520i 0.348869 0.235263i
\(304\) 0 0
\(305\) 28.5771 1.63632
\(306\) 0 0
\(307\) 8.04114 + 19.4130i 0.458932 + 1.10796i 0.968830 + 0.247725i \(0.0796830\pi\)
−0.509898 + 0.860235i \(0.670317\pi\)
\(308\) 0 0
\(309\) 10.3179 2.09809i 0.586963 0.119356i
\(310\) 0 0
\(311\) 20.9205 20.9205i 1.18629 1.18629i 0.208210 0.978084i \(-0.433236\pi\)
0.978084 0.208210i \(-0.0667638\pi\)
\(312\) 0 0
\(313\) −8.91198 8.91198i −0.503735 0.503735i 0.408861 0.912596i \(-0.365926\pi\)
−0.912596 + 0.408861i \(0.865926\pi\)
\(314\) 0 0
\(315\) 10.1681 10.3429i 0.572909 0.582757i
\(316\) 0 0
\(317\) 0.482452 0.199838i 0.0270972 0.0112240i −0.369094 0.929392i \(-0.620332\pi\)
0.396191 + 0.918168i \(0.370332\pi\)
\(318\) 0 0
\(319\) 2.47974i 0.138839i
\(320\) 0 0
\(321\) −10.6126 + 7.15671i −0.592337 + 0.399448i
\(322\) 0 0
\(323\) 4.78454 + 11.5509i 0.266219 + 0.642710i
\(324\) 0 0
\(325\) −23.9116 9.90452i −1.32638 0.549404i
\(326\) 0 0
\(327\) 22.8240 + 4.43897i 1.26217 + 0.245476i
\(328\) 0 0
\(329\) −5.00329 5.00329i −0.275840 0.275840i
\(330\) 0 0
\(331\) 19.5132 + 8.08262i 1.07254 + 0.444261i 0.847887 0.530177i \(-0.177875\pi\)
0.224654 + 0.974439i \(0.427875\pi\)
\(332\) 0 0
\(333\) −0.0160256 1.88052i −0.000878196 0.103052i
\(334\) 0 0
\(335\) 21.1182i 1.15381i
\(336\) 0 0
\(337\) 10.2626i 0.559037i −0.960140 0.279519i \(-0.909825\pi\)
0.960140 0.279519i \(-0.0901749\pi\)
\(338\) 0 0
\(339\) −4.95299 3.27904i −0.269009 0.178093i
\(340\) 0 0
\(341\) −4.59004 1.90126i −0.248565 0.102959i
\(342\) 0 0
\(343\) −10.5604 10.5604i −0.570210 0.570210i
\(344\) 0 0
\(345\) −4.92568 + 25.3266i −0.265190 + 1.36354i
\(346\) 0 0
\(347\) 4.24383 + 1.75785i 0.227821 + 0.0943665i 0.493674 0.869647i \(-0.335654\pi\)
−0.265853 + 0.964014i \(0.585654\pi\)
\(348\) 0 0
\(349\) −13.7021 33.0798i −0.733457 1.77072i −0.630716 0.776014i \(-0.717239\pi\)
−0.102741 0.994708i \(-0.532761\pi\)
\(350\) 0 0
\(351\) −2.40271 11.3210i −0.128247 0.604269i
\(352\) 0 0
\(353\) 4.53983i 0.241631i 0.992675 + 0.120815i \(0.0385509\pi\)
−0.992675 + 0.120815i \(0.961449\pi\)
\(354\) 0 0
\(355\) 54.3817 22.5257i 2.88628 1.19554i
\(356\) 0 0
\(357\) −6.51507 + 1.32481i −0.344814 + 0.0701164i
\(358\) 0 0
\(359\) −2.86633 2.86633i −0.151279 0.151279i 0.627410 0.778689i \(-0.284115\pi\)
−0.778689 + 0.627410i \(0.784115\pi\)
\(360\) 0 0
\(361\) 2.88477 2.88477i 0.151830 0.151830i
\(362\) 0 0
\(363\) −3.65038 17.9516i −0.191595 0.942214i
\(364\) 0 0
\(365\) 17.8596 + 43.1168i 0.934813 + 2.25684i
\(366\) 0 0
\(367\) −28.9994 −1.51376 −0.756878 0.653557i \(-0.773276\pi\)
−0.756878 + 0.653557i \(0.773276\pi\)
\(368\) 0 0
\(369\) 5.63786 13.9460i 0.293495 0.725997i
\(370\) 0 0
\(371\) −0.904628 + 0.374709i −0.0469659 + 0.0194539i
\(372\) 0 0
\(373\) −7.55879 + 18.2485i −0.391379 + 0.944873i 0.598261 + 0.801302i \(0.295859\pi\)
−0.989640 + 0.143572i \(0.954141\pi\)
\(374\) 0 0
\(375\) −45.8893 8.92486i −2.36971 0.460878i
\(376\) 0 0
\(377\) −6.00088 + 6.00088i −0.309061 + 0.309061i
\(378\) 0 0
\(379\) −7.21366 + 17.4153i −0.370541 + 0.894564i 0.623118 + 0.782128i \(0.285866\pi\)
−0.993659 + 0.112437i \(0.964134\pi\)
\(380\) 0 0
\(381\) −0.692708 + 1.04633i −0.0354885 + 0.0536053i
\(382\) 0 0
\(383\) −18.2276 −0.931388 −0.465694 0.884946i \(-0.654195\pi\)
−0.465694 + 0.884946i \(0.654195\pi\)
\(384\) 0 0
\(385\) −3.14638 −0.160354
\(386\) 0 0
\(387\) 0.0884355 + 10.3775i 0.00449543 + 0.527515i
\(388\) 0 0
\(389\) 0.747968 1.80575i 0.0379235 0.0915554i −0.903783 0.427991i \(-0.859221\pi\)
0.941706 + 0.336436i \(0.109221\pi\)
\(390\) 0 0
\(391\) 8.36281 8.36281i 0.422926 0.422926i
\(392\) 0 0
\(393\) 1.24662 6.40980i 0.0628837 0.323332i
\(394\) 0 0
\(395\) 17.9951 43.4440i 0.905432 2.18591i
\(396\) 0 0
\(397\) 7.44786 3.08500i 0.373797 0.154832i −0.187872 0.982193i \(-0.560159\pi\)
0.561670 + 0.827361i \(0.310159\pi\)
\(398\) 0 0
\(399\) −4.43599 6.57807i −0.222077 0.329316i
\(400\) 0 0
\(401\) −33.1951 −1.65768 −0.828842 0.559482i \(-0.811000\pi\)
−0.828842 + 0.559482i \(0.811000\pi\)
\(402\) 0 0
\(403\) −6.50677 15.7087i −0.324125 0.782508i
\(404\) 0 0
\(405\) −14.6169 33.6542i −0.726318 1.67229i
\(406\) 0 0
\(407\) −0.288471 + 0.288471i −0.0142990 + 0.0142990i
\(408\) 0 0
\(409\) 24.3278 + 24.3278i 1.20293 + 1.20293i 0.973270 + 0.229664i \(0.0737629\pi\)
0.229664 + 0.973270i \(0.426237\pi\)
\(410\) 0 0
\(411\) −1.07866 5.30457i −0.0532064 0.261655i
\(412\) 0 0
\(413\) 6.95913 2.88257i 0.342436 0.141842i
\(414\) 0 0
\(415\) 4.40677i 0.216320i
\(416\) 0 0
\(417\) 4.21364 + 6.24836i 0.206343 + 0.305983i
\(418\) 0 0
\(419\) −8.96150 21.6350i −0.437798 1.05694i −0.976708 0.214574i \(-0.931164\pi\)
0.538910 0.842363i \(1.68116\pi\)
\(420\) 0 0
\(421\) −15.8146 6.55062i −0.770756 0.319258i −0.0375773 0.999294i \(-0.511964\pi\)
−0.733179 + 0.680036i \(0.761964\pi\)
\(422\) 0 0
\(423\) −16.4782 + 6.99061i −0.801199 + 0.339895i
\(424\) 0 0
\(425\) 26.5963 + 26.5963i 1.29011 + 1.29011i
\(426\) 0 0
\(427\) 7.67991 + 3.18112i 0.371657 + 0.153945i
\(428\) 0 0
\(429\) −1.38590 + 2.09340i −0.0669117 + 0.101070i
\(430\) 0 0
\(431\) 21.2060i 1.02146i −0.859742 0.510729i \(-0.829375\pi\)
0.859742 0.510729i \(-0.170625\pi\)
\(432\) 0 0
\(433\) 7.73016i 0.371488i 0.982598 + 0.185744i \(0.0594695\pi\)
−0.982598 + 0.185744i \(0.940531\pi\)
\(434\) 0 0
\(435\) −14.8525 + 22.4347i −0.712124 + 1.07566i
\(436\) 0 0
\(437\) 13.0395 + 5.40113i 0.623763 + 0.258371i
\(438\) 0 0
\(439\) 25.4093 + 25.4093i 1.21272 + 1.21272i 0.970128 + 0.242594i \(0.0779983\pi\)
0.242594 + 0.970128i \(0.422002\pi\)
\(440\) 0 0
\(441\) −15.4483 + 6.55369i −0.735634 + 0.312080i
\(442\) 0 0
\(443\) −4.74325 1.96472i −0.225359 0.0933467i 0.267147 0.963656i \(-0.413919\pi\)
−0.492506 + 0.870309i \(0.663919\pi\)
\(444\) 0 0
\(445\) 22.9736 + 55.4632i 1.08905 + 2.62921i
\(446\) 0 0
\(447\) 5.73660 + 8.50674i 0.271332 + 0.402355i
\(448\) 0 0
\(449\) 13.4003i 0.632399i 0.948693 + 0.316199i \(0.102407\pi\)
−0.948693 + 0.316199i \(0.897593\pi\)
\(450\) 0 0
\(451\) −3.01479 + 1.24877i −0.141961 + 0.0588021i
\(452\) 0 0
\(453\) 2.83774 + 13.9553i 0.133329 + 0.655676i
\(454\) 0 0
\(455\) −7.61414 7.61414i −0.356957 0.356957i
\(456\) 0 0
\(457\) −21.8591 + 21.8591i −1.02253 + 1.02253i −0.0227865 + 0.999740i \(0.507254\pi\)
−0.999740 + 0.0227865i \(0.992746\pi\)
\(458\) 0 0
\(459\) −3.07006 + 16.5362i −0.143298 + 0.771842i
\(460\) 0 0
\(461\) −8.39897 20.2769i −0.391179 0.944389i −0.989684 0.143270i \(-0.954238\pi\)
0.598505 0.801119i \(1.70424\pi\)
\(462\) 0 0
\(463\) 24.1790 1.12369 0.561847 0.827241i \(-0.310091\pi\)
0.561847 + 0.827241i \(0.310091\pi\)
\(464\) 0 0
\(465\) −30.1394 44.6934i −1.39768 2.07261i
\(466\) 0 0
\(467\) −22.1546 + 9.17674i −1.02519 + 0.424649i −0.830975 0.556309i \(-0.812217\pi\)
−0.194218 + 0.980958i \(0.562217\pi\)
\(468\) 0 0
\(469\) 2.35082 5.67538i 0.108551 0.262065i
\(470\) 0 0
\(471\) 2.91455 14.9859i 0.134295 0.690512i
\(472\) 0 0
\(473\) 1.59190 1.59190i 0.0731954 0.0731954i
\(474\) 0 0
\(475\) −17.1772 + 41.4695i −0.788146 + 1.90275i
\(476\) 0 0
\(477\) 0.0211082 + 2.47694i 0.000966478 + 0.113411i
\(478\) 0 0
\(479\) −23.6803 −1.08198 −0.540991 0.841028i \(-0.681951\pi\)
−0.540991 + 0.841028i \(0.681951\pi\)
\(480\) 0 0
\(481\) −1.39618 −0.0636603
\(482\) 0 0
\(483\) −4.14303 + 6.25804i −0.188514 + 0.284751i
\(484\) 0 0
\(485\) −14.3781 + 34.7119i −0.652877 + 1.57619i
\(486\) 0 0
\(487\) 15.7774 15.7774i 0.714942 0.714942i −0.252623 0.967565i \(-0.581293\pi\)
0.967565 + 0.252623i \(0.0812931\pi\)
\(488\) 0 0
\(489\) 25.4696 + 4.95349i 1.15177 + 0.224005i
\(490\) 0 0
\(491\) −1.45911 + 3.52259i −0.0658486 + 0.158972i −0.953378 0.301778i \(-0.902420\pi\)
0.887530 + 0.460751i \(0.152420\pi\)
\(492\) 0 0
\(493\) 11.3943 4.71968i 0.513174 0.212564i
\(494\) 0 0
\(495\) −2.98321 + 7.37934i −0.134085 + 0.331677i
\(496\) 0 0
\(497\) 17.1222 0.768037
\(498\) 0 0
\(499\) −12.0066 28.9865i −0.537490 1.29761i −0.926470 0.376369i \(-0.877173\pi\)
0.388980 0.921246i \(-0.372827\pi\)
\(500\) 0 0
\(501\) −3.28375 16.1486i −0.146707 0.721466i
\(502\) 0 0
\(503\) −9.02060 + 9.02060i −0.402208 + 0.402208i −0.879011 0.476802i \(-0.841796\pi\)
0.476802 + 0.879011i \(0.341796\pi\)
\(504\) 0 0
\(505\) −12.1906 12.1906i −0.542475 0.542475i
\(506\) 0 0
\(507\) 13.6453 2.77471i 0.606010 0.123229i
\(508\) 0 0
\(509\) 13.9019 5.75836i 0.616192 0.255235i −0.0526815 0.998611i \(-0.516777\pi\)
0.668873 + 0.743376i \(0.266777\pi\)
\(510\) 0 0
\(511\) 13.5754i 0.600543i
\(512\) 0 0
\(513\) −19.6338 + 4.16698i −0.866852 + 0.183977i
\(514\) 0 0
\(515\) −9.48396 22.8963i −0.417913 1.00893i
\(516\) 0 0
\(517\) 3.58745 + 1.48597i 0.157776 + 0.0653528i
\(518\) 0 0
\(519\) −0.238314 + 1.22535i −0.0104608 + 0.0537868i
\(520\) 0 0
\(521\) −24.3052 24.3052i −1.06483 1.06483i −0.997747 0.0670849i \(-0.978630\pi\)
−0.0670849 0.997747i \(1.47863\pi\)
\(522\) 0 0
\(523\) −11.5224 4.77273i −0.503839 0.208697i 0.116262 0.993219i \(-0.462909\pi\)
−0.620102 + 0.784522i \(0.712909\pi\)
\(524\) 0 0
\(525\) −19.9025 13.1761i −0.868616 0.575053i
\(526\) 0 0
\(527\) 24.7098i 1.07637i
\(528\) 0 0
\(529\) 9.64908i 0.419525i
\(530\) 0 0
\(531\) −0.162381 19.0546i −0.00704675 0.826900i
\(532\) 0 0
\(533\) −10.3177 4.27372i −0.446908 0.185115i
\(534\) 0 0
\(535\) 21.3041 + 21.3041i 0.921058 + 0.921058i
\(536\) 0 0
\(537\) 21.9357 + 4.26621i 0.946597 + 0.184101i
\(538\) 0 0
\(539\) 3.36323 + 1.39309i 0.144864 + 0.0600048i
\(540\) 0 0
\(541\) −11.0650 26.7133i −0.475722 1.14849i −0.961597 0.274466i \(-0.911499\pi\)
0.485875 0.874028i \(-0.338501\pi\)
\(542\) 0 0
\(543\) −10.0134 + 6.75260i −0.429714 + 0.289782i
\(544\) 0 0
\(545\) 54.7288i 2.34433i
\(546\) 0 0
\(547\) −5.80786 + 2.40569i −0.248326 + 0.102860i −0.503375 0.864068i \(-0.667909\pi\)
0.255049 + 0.966928i \(0.417909\pi\)
\(548\) 0 0
\(549\) 14.7424 14.9959i 0.629192 0.640008i
\(550\) 0 0
\(551\) 10.4072 + 10.4072i 0.443363 + 0.443363i
\(552\) 0 0
\(553\) 9.67214 9.67214i 0.411301 0.411301i
\(554\) 0 0
\(555\) −4.33767 + 0.882047i −0.184124 + 0.0374408i
\(556\) 0 0
\(557\) 7.71096 + 18.6159i 0.326724 + 0.788781i 0.998832 + 0.0483277i \(0.0153892\pi\)
−0.672108 + 0.740453i \(0.734611\pi\)
\(558\) 0 0
\(559\) 7.70467 0.325873
\(560\) 0 0
\(561\) 3.02497 2.03992i 0.127714 0.0861253i
\(562\) 0 0
\(563\) 11.4466 4.74136i 0.482419 0.199824i −0.128201 0.991748i \(-0.540920\pi\)
0.610620 + 0.791924i \(0.290920\pi\)
\(564\) 0 0
\(565\) −5.35046 + 12.9172i −0.225096 + 0.543429i
\(566\) 0 0
\(567\) −0.181895 10.6715i −0.00763889 0.448160i
\(568\) 0 0
\(569\) 27.9002 27.9002i 1.16964 1.16964i 0.187343 0.982295i \(-0.440013\pi\)
0.982295 0.187343i \(-0.0599874\pi\)
\(570\) 0 0
\(571\) 9.45224 22.8197i 0.395564 0.954976i −0.593141 0.805099i \(-0.702112\pi\)
0.988705 0.149877i \(-0.0478878\pi\)
\(572\) 0 0
\(573\) 2.34411 + 1.55188i 0.0979266 + 0.0648307i
\(574\) 0 0
\(575\) 42.4601 1.77071
\(576\) 0 0
\(577\) −16.6076 −0.691383 −0.345691 0.938348i \(-0.612356\pi\)
−0.345691 + 0.938348i \(0.612356\pi\)
\(578\) 0 0
\(579\) 14.9586 + 9.90310i 0.621659 + 0.411559i
\(580\) 0 0
\(581\) 0.490550 1.18429i 0.0203514 0.0491327i
\(582\) 0 0
\(583\) 0.379961 0.379961i 0.0157364 0.0157364i
\(584\) 0 0
\(585\) −25.0770 + 10.6385i −1.03681 + 0.439848i
\(586\) 0 0
\(587\) −5.82661 + 14.0667i −0.240490 + 0.580594i −0.997332 0.0730041i \(-0.976741\pi\)
0.756842 + 0.653598i \(0.226741\pi\)
\(588\) 0 0
\(589\) −27.2434 + 11.2846i −1.12254 + 0.464973i
\(590\) 0 0
\(591\) −2.94212 + 1.98404i −0.121022 + 0.0816126i
\(592\) 0 0
\(593\) 0.760076 0.0312126 0.0156063 0.999878i \(-0.495032\pi\)
0.0156063 + 0.999878i \(0.495032\pi\)
\(594\) 0 0
\(595\) 5.98850 + 14.4575i 0.245505 + 0.592701i
\(596\) 0 0
\(597\) 21.0872 4.28798i 0.863041 0.175495i
\(598\) 0 0
\(599\) −18.9662 + 18.9662i −0.774937 + 0.774937i −0.978965 0.204028i \(-0.934597\pi\)
0.204028 + 0.978965i \(0.434597\pi\)
\(600\) 0 0
\(601\) −15.3756 15.3756i −0.627183 0.627183i 0.320175 0.947358i \(-0.396258\pi\)
−0.947358 + 0.320175i \(0.896258\pi\)
\(602\) 0 0
\(603\) −11.0818 10.8945i −0.451286 0.443660i
\(604\) 0 0
\(605\) −39.8362 + 16.5007i −1.61957 + 0.670849i
\(606\) 0 0
\(607\) 8.77741i 0.356264i −0.984007 0.178132i \(-0.942995\pi\)
0.984007 0.178132i \(-0.0570054\pi\)
\(608\) 0 0
\(609\) −6.48890 + 4.37585i −0.262943 + 0.177318i
\(610\) 0 0
\(611\) 5.08551 + 12.2775i 0.205738 + 0.496695i
\(612\) 0 0
\(613\) 4.08951 + 1.69393i 0.165174 + 0.0684172i 0.463738 0.885972i \(-0.346508\pi\)
−0.298564 + 0.954389i \(0.596508\pi\)
\(614\) 0 0
\(615\) −34.7550 6.75939i −1.40146 0.272565i
\(616\) 0 0
\(617\) −10.3859 10.3859i −0.418123 0.418123i 0.466434 0.884556i \(-0.345539\pi\)
−0.884556 + 0.466434i \(0.845539\pi\)
\(618\) 0 0
\(619\) 20.6486 + 8.55293i 0.829937 + 0.343771i 0.756878 0.653556i \(-0.226724\pi\)
0.0730593 + 0.997328i \(0.476724\pi\)
\(620\) 0 0
\(621\) 10.7491 + 15.6503i 0.431346 + 0.628025i
\(622\) 0 0
\(623\) 17.4628i 0.699630i
\(624\) 0 0
\(625\) 51.9336i 2.07734i
\(626\) 0 0
\(627\) 3.63054 + 2.40354i 0.144990 + 0.0959880i
\(628\) 0 0
\(629\) 1.87456 + 0.776468i 0.0747436 + 0.0309598i
\(630\) 0 0
\(631\) 13.2657 + 13.2657i 0.528098 + 0.528098i 0.920005 0.391907i \(-0.128185\pi\)
−0.391907 + 0.920005i \(0.628185\pi\)
\(632\) 0 0
\(633\) 8.48118 43.6081i 0.337097 1.73326i
\(634\) 0 0
\(635\) 2.72879 + 1.13030i 0.108289 + 0.0448546i
\(636\) 0 0
\(637\) 4.76766 + 11.5101i 0.188901 + 0.456048i
\(638\) 0 0
\(639\) 16.2343 40.1575i 0.642218 1.58861i
\(640\) 0 0
\(641\) 3.60149i 0.142250i 0.997467 + 0.0711252i \(0.0226590\pi\)
−0.997467 + 0.0711252i \(0.977341\pi\)
\(642\) 0 0
\(643\) −16.5202 + 6.84287i −0.651492 + 0.269857i −0.683853 0.729620i \(-0.739697\pi\)
0.0323617 + 0.999476i \(0.489697\pi\)
\(644\) 0 0
\(645\) 23.9370 4.86748i 0.942518 0.191657i
\(646\) 0 0
\(647\) 23.6599 + 23.6599i 0.930167 + 0.930167i 0.997716 0.0675491i \(-0.0215179\pi\)
−0.0675491 + 0.997716i \(0.521518\pi\)
\(648\) 0 0
\(649\) −2.92297 + 2.92297i −0.114737 + 0.114737i
\(650\) 0 0
\(651\) −3.12463 15.3661i −0.122464 0.602246i
\(652\) 0 0
\(653\) −12.1760 29.3955i −0.476484 1.15033i −0.961247 0.275689i \(-0.911094\pi\)
0.484763 0.874646i \(1.66109\pi\)
\(654\) 0 0
\(655\) −15.3698 −0.600547
\(656\) 0 0
\(657\) 31.8391 + 12.8714i 1.24216 + 0.502162i
\(658\) 0 0
\(659\) 41.6508 17.2523i 1.62248 0.672055i 0.628123 0.778114i \(-0.283823\pi\)
0.994360 + 0.106059i \(0.0338233\pi\)
\(660\) 0 0
\(661\) −2.34448 + 5.66007i −0.0911896 + 0.220151i −0.962893 0.269882i \(-0.913015\pi\)
0.871704 + 0.490033i \(0.163015\pi\)
\(662\) 0 0
\(663\) 12.2569 + 2.38380i 0.476017 + 0.0925790i
\(664\) 0 0
\(665\) −13.2051 + 13.2051i −0.512071 + 0.512071i
\(666\) 0 0
\(667\) 5.32790 12.8627i 0.206297 0.498046i
\(668\) 0 0
\(669\) 15.6652 23.6623i 0.605652 0.914837i
\(670\) 0 0
\(671\) −4.56184 −0.176108
\(672\) 0 0
\(673\) 45.2206 1.74313 0.871563 0.490283i \(-0.163107\pi\)
0.871563 + 0.490283i \(0.163107\pi\)
\(674\) 0 0
\(675\) −49.7728 + 34.1854i −1.91576 + 1.31580i
\(676\) 0 0
\(677\) 19.1300 46.1838i 0.735224 1.77499i 0.110886 0.993833i \(-0.464631\pi\)
0.624338 0.781155i \(-0.285369\pi\)
\(678\) 0 0
\(679\) −7.72806 + 7.72806i −0.296576 + 0.296576i
\(680\) 0 0
\(681\) 8.30935 42.7245i 0.318415 1.63721i
\(682\) 0 0
\(683\) −14.1282 + 34.1085i −0.540600 + 1.30512i 0.383700 + 0.923458i \(0.374650\pi\)
−0.924300 + 0.381666i \(0.875350\pi\)
\(684\) 0 0
\(685\) −11.7713 + 4.87584i −0.449759 + 0.186296i
\(686\) 0 0
\(687\) −11.7981 17.4952i −0.450124 0.667484i
\(688\) 0 0
\(689\) 1.83899 0.0700599
\(690\) 0 0
\(691\) 1.84991 + 4.46608i 0.0703740 + 0.169898i 0.955153 0.296113i \(-0.0956906\pi\)
−0.884779 + 0.466011i \(0.845691\pi\)
\(692\) 0 0
\(693\) −1.62317 + 1.65107i −0.0616590 + 0.0627189i
\(694\) 0 0
\(695\) 12.5432 12.5432i 0.475791 0.475791i
\(696\) 0 0
\(697\) 11.4761 + 11.4761i 0.434688 + 0.434688i
\(698\) 0 0
\(699\) 6.60942 + 32.5034i 0.249991 + 1.22939i
\(700\) 0 0
\(701\) −9.68643 + 4.01225i −0.365851 + 0.151541i −0.558033 0.829819i \(-0.688444\pi\)
0.192182 + 0.981359i \(0.438444\pi\)
\(702\) 0 0
\(703\) 2.42137i 0.0913238i
\(704\) 0 0
\(705\) 23.5561 + 34.9311i 0.887175 + 1.31558i
\(706\) 0 0
\(707\) −1.91912 4.63317i −0.0721761 0.174248i
\(708\) 0 0
\(709\) 38.1564 + 15.8049i 1.43299 + 0.593565i 0.958088 0.286473i \(-0.0924827\pi\)
0.474904 + 0.880038i \(0.342483\pi\)
\(710\) 0 0
\(711\) −13.5139 31.8550i −0.506812 1.19466i
\(712\) 0 0
\(713\) 19.7241 + 19.7241i 0.738674 + 0.738674i
\(714\) 0 0
\(715\) 5.45948 + 2.26139i 0.204173 + 0.0845711i
\(716\) 0 0
\(717\) 18.2782 27.6092i 0.682612 1.03108i
\(718\) 0 0
\(719\) 46.6233i 1.73876i 0.494147 + 0.869378i \(0.335481\pi\)
−0.494147 + 0.869378i \(0.664519\pi\)
\(720\) 0 0
\(721\) 7.20896i 0.268476i
\(722\) 0 0
\(723\) 1.63708 2.47281i 0.0608837 0.0919647i
\(724\) 0 0
\(725\) 40.9074 + 16.9444i 1.51926 + 0.629298i
\(726\) 0 0
\(727\) −25.2103 25.2103i −0.934997 0.934997i 0.0630153 0.998013i \(-0.479928\pi\)
−0.998013 + 0.0630153i \(0.979928\pi\)
\(728\) 0 0
\(729\) −25.2007 9.69143i −0.933360 0.358942i
\(730\) 0 0
\(731\) −10.3446 4.28486i −0.382608 0.158481i
\(732\) 0 0
\(733\) 2.25020 + 5.43246i 0.0831129 + 0.200652i 0.959973 0.280094i \(-0.0903657\pi\)
−0.876860 + 0.480747i \(0.840366\pi\)
\(734\) 0 0
\(735\) 22.0838 + 32.7479i 0.814575 + 1.20792i
\(736\) 0 0
\(737\) 3.37116i 0.124178i
\(738\) 0 0
\(739\) −10.5170 + 4.35630i −0.386876 + 0.160249i −0.567639 0.823277i \(-0.692143\pi\)
0.180763 + 0.983527i \(0.442143\pi\)
\(740\) 0 0
\(741\) 2.96931 + 14.6023i 0.109080 + 0.536428i
\(742\) 0 0
\(743\) 15.4609 + 15.4609i 0.567205 + 0.567205i 0.931345 0.364139i \(-0.118637\pi\)
−0.364139 + 0.931345i \(0.618637\pi\)
\(744\) 0 0
\(745\) 17.0768 17.0768i 0.625644 0.625644i
\(746\) 0 0
\(747\) −2.31246 2.27338i −0.0846085 0.0831787i
\(748\) 0 0
\(749\) 3.35383 + 8.09687i 0.122546 + 0.295853i
\(750\) 0 0
\(751\) 34.5867 1.26209 0.631043 0.775748i \(-0.282627\pi\)
0.631043 + 0.775748i \(0.282627\pi\)
\(752\) 0 0
\(753\) 26.7555 + 39.6754i 0.975023 + 1.44585i
\(754\) 0 0
\(755\) 30.9680 12.8274i 1.12704 0.466836i
\(756\) 0 0
\(757\) 6.82795 16.4841i 0.248166 0.599126i −0.749882 0.661571i \(-0.769890\pi\)
0.998048 + 0.0624455i \(0.0198900\pi\)
\(758\) 0 0
\(759\) 0.786300 4.04295i 0.0285409 0.146750i
\(760\) 0 0
\(761\) −10.6555 + 10.6555i −0.386261 + 0.386261i −0.873352 0.487090i \(-0.838058\pi\)
0.487090 + 0.873352i \(0.338058\pi\)
\(762\) 0 0
\(763\) 6.09226 14.7080i 0.220555 0.532466i
\(764\) 0 0
\(765\) 39.5858 0.337346i 1.43123 0.0121968i
\(766\) 0 0
\(767\) −14.1470 −0.510818
\(768\) 0 0
\(769\) 4.53950 0.163699 0.0818493 0.996645i \(-0.473917\pi\)
0.0818493 + 0.996645i \(0.473917\pi\)
\(770\) 0 0
\(771\) 20.5821 31.0892i 0.741245 1.11965i
\(772\) 0 0
\(773\) −10.7578 + 25.9715i −0.386929 + 0.934130i 0.603657 + 0.797244i \(0.293710\pi\)
−0.990587 + 0.136886i \(0.956290\pi\)
\(774\) 0 0
\(775\) −62.7288 + 62.7288i −2.25328 + 2.25328i
\(776\) 0 0
\(777\) −1.26391 0.245814i −0.0453425 0.00881851i
\(778\) 0 0
\(779\) −7.41183 + 17.8938i −0.265557 + 0.641110i
\(780\) 0 0
\(781\) −8.68111 + 3.59583i −0.310635 + 0.128669i
\(782\) 0 0
\(783\) 4.11049 + 19.3676i 0.146897 <