Properties

Label 768.2.o.b.287.6
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 287.6
Character \(\chi\) \(=\) 768.287
Dual form 768.2.o.b.479.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.345141 + 1.69731i) q^{3} +(1.56013 - 3.76650i) q^{5} +(-0.838552 + 0.838552i) q^{7} +(-2.76175 - 1.17163i) q^{9} +O(q^{10})\) \(q+(-0.345141 + 1.69731i) q^{3} +(1.56013 - 3.76650i) q^{5} +(-0.838552 + 0.838552i) q^{7} +(-2.76175 - 1.17163i) q^{9} +(-0.249049 + 0.601256i) q^{11} +(2.05771 - 0.852332i) q^{13} +(5.85446 + 3.94801i) q^{15} +3.23677 q^{17} +(-1.47818 - 3.56865i) q^{19} +(-1.13387 - 1.71271i) q^{21} +(2.58369 - 2.58369i) q^{23} +(-8.21694 - 8.21694i) q^{25} +(2.94182 - 4.28319i) q^{27} +(3.52027 - 1.45815i) q^{29} -7.63408i q^{31} +(-0.934564 - 0.630232i) q^{33} +(1.85015 + 4.46665i) q^{35} +(-0.579146 - 0.239890i) q^{37} +(0.736474 + 3.78676i) q^{39} +(3.54554 + 3.54554i) q^{41} +(3.19595 + 1.32381i) q^{43} +(-8.72163 + 8.57424i) q^{45} -5.96658i q^{47} +5.59366i q^{49} +(-1.11714 + 5.49382i) q^{51} +(-0.762825 - 0.315973i) q^{53} +(1.87608 + 1.87608i) q^{55} +(6.56731 - 1.27725i) q^{57} +(5.86827 + 2.43072i) q^{59} +(-2.68247 - 6.47607i) q^{61} +(3.29834 - 1.33340i) q^{63} -9.08011i q^{65} +(-4.78575 + 1.98232i) q^{67} +(3.49360 + 5.27708i) q^{69} +(10.2094 + 10.2094i) q^{71} +(8.09458 - 8.09458i) q^{73} +(16.7827 - 11.1107i) q^{75} +(-0.295345 - 0.713025i) q^{77} -11.5343 q^{79} +(6.25458 + 6.47149i) q^{81} +(0.998651 - 0.413655i) q^{83} +(5.04979 - 12.1913i) q^{85} +(1.25994 + 6.47828i) q^{87} +(-10.4124 + 10.4124i) q^{89} +(-1.01077 + 2.44022i) q^{91} +(12.9574 + 2.63484i) q^{93} -15.7475 q^{95} +9.21596 q^{97} +(1.39226 - 1.36873i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + O(q^{10}) \) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + 8q^{13} - 8q^{15} + 8q^{19} + 4q^{21} - 8q^{25} + 28q^{27} - 8q^{33} + 8q^{37} - 28q^{39} + 8q^{43} + 4q^{45} + 16q^{51} + 24q^{55} - 4q^{57} + 40q^{61} - 56q^{67} + 4q^{69} - 8q^{73} - 16q^{75} + 16q^{79} + 48q^{85} + 52q^{87} - 40q^{91} - 8q^{93} - 16q^{97} - 60q^{99} + O(q^{100}) \)

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
\(3\) −0.345141 + 1.69731i −0.199268 + 0.979945i
\(4\) 0 0
\(5\) 1.56013 3.76650i 0.697713 1.68443i −0.0309186 0.999522i \(-0.509843\pi\)
0.728631 0.684906i \(-0.240157\pi\)
\(6\) 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
\(9\) −2.76175 1.17163i −0.920585 0.390542i
\(10\) 0 0
\(11\) −0.249049 + 0.601256i −0.0750910 + 0.181286i −0.956968 0.290194i \(-0.906280\pi\)
0.881877 + 0.471480i \(0.156280\pi\)
\(12\) 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 \(-0.371605\pi\)
0.392516 + 0.919745i \(0.371605\pi\)
\(18\) 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
\(21\) −1.13387 1.71271i −0.247430 0.373743i
\(22\) 0 0
\(23\) 2.58369 2.58369i 0.538737 0.538737i −0.384421 0.923158i \(-0.625599\pi\)
0.923158 + 0.384421i \(0.125599\pi\)
\(24\) 0 0
\(25\) −8.21694 8.21694i −1.64339 1.64339i
\(26\) 0 0
\(27\) 2.94182 4.28319i 0.566153 0.824300i
\(28\) 0 0
\(29\) 3.52027 1.45815i 0.653698 0.270771i −0.0310857 0.999517i \(-0.509896\pi\)
0.684784 + 0.728746i \(0.259896\pi\)
\(30\) 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
\(39\) 0.736474 + 3.78676i 0.117930 + 0.606367i
\(40\) 0 0
\(41\) 3.54554 + 3.54554i 0.553720 + 0.553720i 0.927512 0.373792i \(-0.121943\pi\)
−0.373792 + 0.927512i \(0.621943\pi\)
\(42\) 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
\(45\) −8.72163 + 8.57424i −1.30014 + 1.27817i
\(46\) 0 0
\(47\) 5.96658i 0.870315i −0.900354 0.435158i \(-0.856693\pi\)
0.900354 0.435158i \(-0.143307\pi\)
\(48\) 0 0
\(49\) 5.59366i 0.799095i
\(50\) 0 0
\(51\) −1.11714 + 5.49382i −0.156431 + 0.769288i
\(52\) 0 0
\(53\) −0.762825 0.315973i −0.104782 0.0434022i 0.329677 0.944094i \(-0.393060\pi\)
−0.434459 + 0.900692i \(0.643060\pi\)
\(54\) 0 0
\(55\) 1.87608 + 1.87608i 0.252971 + 0.252971i
\(56\) 0 0
\(57\) 6.56731 1.27725i 0.869862 0.169176i
\(58\) 0 0
\(59\) 5.86827 + 2.43072i 0.763984 + 0.316452i 0.730433 0.682985i \(-0.239318\pi\)
0.0335508 + 0.999437i \(0.489318\pi\)
\(60\) 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
\(69\) 3.49360 + 5.27708i 0.420580 + 0.635285i
\(70\) 0 0
\(71\) 10.2094 + 10.2094i 1.21163 + 1.21163i 0.970489 + 0.241145i \(0.0775229\pi\)
0.241145 + 0.970489i \(0.422477\pi\)
\(72\) 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
\(75\) 16.7827 11.1107i 1.93790 1.28296i
\(76\) 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 −0.327201 0.944955i \(-0.606106\pi\)
0.436818 + 0.899550i \(0.356106\pi\)
\(84\) 0 0
\(85\) 5.04979 12.1913i 0.547727 1.32233i
\(86\) 0 0
\(87\) 1.25994 + 6.47828i 0.135080 + 0.694544i
\(88\) 0 0
\(89\) −10.4124 + 10.4124i −1.10372 + 1.10372i −0.109759 + 0.993958i \(0.535008\pi\)
−0.993958 + 0.109759i \(0.964992\pi\)
\(90\) 0 0
\(91\) −1.01077 + 2.44022i −0.105958 + 0.255805i
\(92\) 0 0
\(93\) 12.9574 + 2.63484i 1.34362 + 0.273220i
\(94\) 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
\(99\) 1.39226 1.36873i 0.139927 0.137563i
\(100\) 0 0
\(101\) 1.61830 3.90691i 0.161026 0.388752i −0.822687 0.568494i \(-0.807526\pi\)
0.983714 + 0.179742i \(0.0575262\pi\)
\(102\) 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
\(105\) −8.21988 + 1.59866i −0.802178 + 0.156013i
\(106\) 0 0
\(107\) −2.82811 + 6.82767i −0.273404 + 0.660055i −0.999624 0.0274065i \(-0.991275\pi\)
0.726221 + 0.687462i \(0.241275\pi\)
\(108\) 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 \(-0.551572\pi\)
−0.161310 + 0.986904i \(0.551572\pi\)
\(114\) 0 0
\(115\) −5.70056 13.7624i −0.531580 1.28335i
\(116\) 0 0
\(117\) −6.68151 0.0569391i −0.617706 0.00526402i
\(118\) 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
\(123\) −7.24160 + 4.79418i −0.652953 + 0.432277i
\(124\) 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 0.848238 0.529616i \(-0.177664\pi\)
−0.974290 + 0.225299i \(0.927664\pi\)
\(132\) 0 0
\(133\) 4.23204 + 1.75297i 0.366964 + 0.152001i
\(134\) 0 0
\(135\) −11.5430 17.7627i −0.993462 1.52877i
\(136\) 0 0
\(137\) −2.20990 2.20990i −0.188805 0.188805i 0.606375 0.795179i \(-0.292623\pi\)
−0.795179 + 0.606375i \(0.792623\pi\)
\(138\) 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
\(141\) 10.1272 + 2.05931i 0.852861 + 0.173426i
\(142\) 0 0
\(143\) 1.44948i 0.121212i
\(144\) 0 0
\(145\) 15.5340i 1.29003i
\(146\) 0 0
\(147\) −9.49420 1.93060i −0.783069 0.159234i
\(148\) 0 0
\(149\) 5.47285 + 2.26693i 0.448353 + 0.185714i 0.595423 0.803412i \(-0.296984\pi\)
−0.147070 + 0.989126i \(0.546984\pi\)
\(150\) 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
\(153\) −8.93916 3.79229i −0.722688 0.306588i
\(154\) 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
\(165\) −3.83181 + 2.53679i −0.298306 + 0.197489i
\(166\) 0 0
\(167\) −6.72756 6.72756i −0.520594 0.520594i 0.397157 0.917751i \(-0.369997\pi\)
−0.917751 + 0.397157i \(0.869997\pi\)
\(168\) 0 0
\(169\) −5.68468 + 5.68468i −0.437283 + 0.437283i
\(170\) 0 0
\(171\) −0.0987485 + 11.5876i −0.00755148 + 0.886128i
\(172\) 0 0
\(173\) 0.275804 + 0.665850i 0.0209690 + 0.0506236i 0.934017 0.357228i \(-0.116278\pi\)
−0.913048 + 0.407852i \(0.866278\pi\)
\(174\) 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 0.110203 0.993909i \(-0.464850\pi\)
0.780725 + 0.624875i \(0.214850\pi\)
\(180\) 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
\(183\) 11.9178 2.31784i 0.880986 0.171340i
\(184\) 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
\(189\) 1.12481 + 6.05854i 0.0818180 + 0.440694i
\(190\) 0 0
\(191\) 1.62308 0.117442 0.0587210 0.998274i \(-0.481298\pi\)
0.0587210 + 0.998274i \(0.481298\pi\)
\(192\) 0 0
\(193\) −10.3575 −0.745548 −0.372774 0.927922i \(-0.621593\pi\)
−0.372774 + 0.927922i \(0.621593\pi\)
\(194\) 0 0
\(195\) 15.4118 + 3.13392i 1.10366 + 0.224425i
\(196\) 0 0
\(197\) −0.784033 + 1.89282i −0.0558601 + 0.134858i −0.949346 0.314234i \(-0.898252\pi\)
0.893486 + 0.449092i \(0.148252\pi\)
\(198\) 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
\(201\) −1.71287 8.80711i −0.120816 0.621206i
\(202\) 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
\(213\) −20.8523 + 13.8049i −1.42877 + 0.945896i
\(214\) 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
\(219\) 10.9453 + 16.5328i 0.739613 + 1.11718i
\(220\) 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 \(-0.811079\pi\)
0.190710 0.981646i \(1.56108\pi\)
\(228\) 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
\(231\) 1.31216 0.255198i 0.0863340 0.0167908i
\(232\) 0 0
\(233\) 13.5410 + 13.5410i 0.887101 + 0.887101i 0.994244 0.107143i \(-0.0341701\pi\)
−0.107143 + 0.994244i \(0.534170\pi\)
\(234\) 0 0
\(235\) −22.4731 9.30866i −1.46598 0.607230i
\(236\) 0 0
\(237\) 3.98098 19.5774i 0.258592 1.27169i
\(238\) 0 0
\(239\) 19.1168i 1.23657i −0.785956 0.618283i \(-0.787829\pi\)
0.785956 0.618283i \(-0.212171\pi\)
\(240\) 0 0
\(241\) 1.71219i 0.110292i 0.998478 + 0.0551460i \(0.0175624\pi\)
−0.998478 + 0.0551460i \(0.982438\pi\)
\(242\) 0 0
\(243\) −13.1429 + 8.38241i −0.843116 + 0.537732i
\(244\) 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
\(249\) 0.357427 + 1.83780i 0.0226510 + 0.116466i
\(250\) 0 0
\(251\) 25.5253 + 10.5729i 1.61115 + 0.667358i 0.992936 0.118655i \(-0.0378582\pi\)
0.618210 + 0.786013i \(0.287858\pi\)
\(252\) 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 \(-0.765697\pi\)
0.741104 0.671391i \(-0.234303\pi\)
\(258\) 0 0
\(259\) 0.686804 0.284483i 0.0426759 0.0176769i
\(260\) 0 0
\(261\) −11.4305 0.0974097i −0.707532 0.00602951i
\(262\) 0 0
\(263\) 10.4924 + 10.4924i 0.646988 + 0.646988i 0.952264 0.305276i \(-0.0987488\pi\)
−0.305276 + 0.952264i \(0.598749\pi\)
\(264\) 0 0
\(265\) −2.38022 + 2.38022i −0.146216 + 0.146216i
\(266\) 0 0
\(267\) −14.0794 21.2670i −0.861647 1.30152i
\(268\) 0 0
\(269\) 4.94856 + 11.9469i 0.301719 + 0.728414i 0.999922 + 0.0125138i \(0.00398337\pi\)
−0.698203 + 0.715900i \(0.746017\pi\)
\(270\) 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
\(279\) −8.94430 + 21.0835i −0.535481 + 1.26223i
\(280\) 0 0
\(281\) 13.7076 13.7076i 0.817727 0.817727i −0.168051 0.985778i \(-0.553747\pi\)
0.985778 + 0.168051i \(0.0537473\pi\)
\(282\) 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
\(285\) 5.43511 26.7284i 0.321948 1.58326i
\(286\) 0 0
\(287\) −5.94623 −0.350995
\(288\) 0 0
\(289\) −6.52333 −0.383725
\(290\) 0 0
\(291\) −3.18081 + 15.6424i −0.186462 + 0.916973i
\(292\) 0 0
\(293\) −4.07927 + 9.84823i −0.238314 + 0.575340i −0.997109 0.0759896i \(-0.975788\pi\)
0.758795 + 0.651329i \(0.225788\pi\)
\(294\) 0 0
\(295\) 18.3106 18.3106i 1.06608 1.06608i
\(296\) 0 0
\(297\) 1.84264 + 2.83551i 0.106921 + 0.164533i
\(298\) 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
\(309\) −5.81226 8.77941i −0.330648 0.499443i
\(310\) 0 0
\(311\) −20.9205 + 20.9205i −1.18629 + 1.18629i −0.208210 + 0.978084i \(0.566764\pi\)
−0.978084 + 0.208210i \(0.933236\pi\)
\(312\) 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
\(315\) 0.123597 14.5035i 0.00696391 0.817179i
\(316\) 0 0
\(317\) −0.482452 + 0.199838i −0.0270972 + 0.0112240i −0.396191 0.918168i \(-0.629668\pi\)
0.369094 + 0.929392i \(0.379668\pi\)
\(318\) 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
\(327\) −4.43897 22.8240i −0.245476 1.26217i
\(328\) 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
\(333\) 1.31840 + 1.34106i 0.0722477 + 0.0734896i
\(334\) 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
\(339\) 1.18366 5.82092i 0.0642875 0.316149i
\(340\) 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
\(345\) 25.3266 4.92568i 1.36354 0.265190i
\(346\) 0 0
\(347\) −4.24383 1.75785i −0.227821 0.0943665i 0.265853 0.964014i \(-0.414346\pi\)
−0.493674 + 0.869647i \(0.664346\pi\)
\(348\) 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 \(-0.961449\pi\)
0.992675 0.120815i \(-0.0385509\pi\)
\(354\) 0 0
\(355\) 54.3817 22.5257i 2.88628 1.19554i
\(356\) 0 0
\(357\) −3.67007 5.54363i −0.194241 0.293400i
\(358\) 0 0
\(359\) 2.86633 + 2.86633i 0.151279 + 0.151279i 0.778689 0.627410i \(-0.215885\pi\)
−0.627410 + 0.778689i \(0.715885\pi\)
\(360\) 0 0
\(361\) 2.88477 2.88477i 0.151830 0.151830i
\(362\) 0 0
\(363\) −15.2749 + 10.1125i −0.801724 + 0.530768i
\(364\) 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
\(375\) −8.92486 45.8893i −0.460878 2.36971i
\(376\) 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
\(381\) 1.22969 + 0.250052i 0.0629988 + 0.0128105i
\(382\) 0 0
\(383\) 18.2276 0.931388 0.465694 0.884946i \(-0.345805\pi\)
0.465694 + 0.884946i \(0.345805\pi\)
\(384\) 0 0
\(385\) −3.14638 −0.160354
\(386\) 0 0
\(387\) −7.27543 7.40050i −0.369831 0.376189i
\(388\) 0 0
\(389\) −0.747968 + 1.80575i −0.0379235 + 0.0915554i −0.941706 0.336436i \(-0.890779\pi\)
0.903783 + 0.427991i \(0.140779\pi\)
\(390\) 0 0
\(391\) 8.36281 8.36281i 0.422926 0.422926i
\(392\) 0 0
\(393\) 6.40980 1.24662i 0.323332 0.0628837i
\(394\) 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 \(-0.189000\pi\)
0.828842 + 0.559482i \(0.189000\pi\)
\(402\) 0 0
\(403\) −6.50677 15.7087i −0.324125 0.782508i
\(404\) 0 0
\(405\) 34.1328 13.4614i 1.69607 0.668905i
\(406\) 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
\(411\) 4.51363 2.98817i 0.222641 0.147396i
\(412\) 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 \(0.0688363\pi\)
−0.538910 + 0.842363i \(0.681164\pi\)
\(420\) 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
\(423\) −6.99061 + 16.4782i −0.339895 + 0.801199i
\(424\) 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
\(429\) −2.46023 0.500277i −0.118781 0.0241536i
\(430\) 0 0
\(431\) 21.2060i 1.02146i 0.859742 + 0.510729i \(0.170625\pi\)
−0.859742 + 0.510729i \(0.829375\pi\)
\(432\) 0 0
\(433\) 7.73016i 0.371488i 0.982598 + 0.185744i \(0.0594695\pi\)
−0.982598 + 0.185744i \(0.940531\pi\)
\(434\) 0 0
\(435\) 26.3661 + 5.36143i 1.26416 + 0.257061i
\(436\) 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
\(441\) 6.55369 15.4483i 0.312080 0.735634i
\(442\) 0 0
\(443\) 4.74325 + 1.96472i 0.225359 + 0.0933467i 0.492506 0.870309i \(-0.336081\pi\)
−0.267147 + 0.963656i \(0.586081\pi\)
\(444\) 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 \(-0.897593\pi\)
0.948693 0.316199i \(-0.102407\pi\)
\(450\) 0 0
\(451\) −3.01479 + 1.24877i −0.141961 + 0.0588021i
\(452\) 0 0
\(453\) 11.8745 7.86128i 0.557911 0.369355i
\(454\) 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
\(459\) 9.52198 13.8637i 0.444448 0.647102i
\(460\) 0 0
\(461\) 8.39897 + 20.2769i 0.391179 + 0.944389i 0.989684 + 0.143270i \(0.0457618\pi\)
−0.598505 + 0.801119i \(0.704238\pi\)
\(462\) 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 0.194218 0.980958i \(-0.437783\pi\)
0.830975 + 0.556309i \(0.187783\pi\)
\(468\) 0 0
\(469\) 2.35082 5.67538i 0.108551 0.262065i
\(470\) 0 0
\(471\) −14.9859 + 2.91455i −0.690512 + 0.134295i
\(472\) 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
\(477\) 1.73653 + 1.76639i 0.0795105 + 0.0808773i
\(478\) 0 0
\(479\) 23.6803 1.08198 0.540991 0.841028i \(-0.318049\pi\)
0.540991 + 0.841028i \(0.318049\pi\)
\(480\) 0 0
\(481\) −1.39618 −0.0636603
\(482\) 0 0
\(483\) −7.35467 1.49554i −0.334649 0.0680494i
\(484\) 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
\(489\) −4.95349 25.4696i −0.224005 1.15177i
\(490\) 0 0
\(491\) 1.45911 3.52259i 0.0658486 0.158972i −0.887530 0.460751i \(-0.847580\pi\)
0.953378 + 0.301778i \(0.0975802\pi\)
\(492\) 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
\(501\) 13.7407 9.09682i 0.613891 0.406416i
\(502\) 0 0
\(503\) 9.02060 9.02060i 0.402208 0.402208i −0.476802 0.879011i \(-0.658204\pi\)
0.879011 + 0.476802i \(0.158204\pi\)
\(504\) 0 0
\(505\) −12.1906 12.1906i −0.542475 0.542475i
\(506\) 0 0
\(507\) −7.68668 11.6107i −0.341377 0.515650i
\(508\) 0 0
\(509\) −13.9019 + 5.75836i −0.616192 + 0.255235i −0.668873 0.743376i \(-0.733223\pi\)
0.0526815 + 0.998611i \(0.483223\pi\)
\(510\) 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
\(519\) −1.22535 + 0.238314i −0.0537868 + 0.0104608i
\(520\) 0 0
\(521\) 24.3052 + 24.3052i 1.06483 + 1.06483i 0.997747 + 0.0670849i \(0.0213698\pi\)
0.0670849 + 0.997747i \(0.478630\pi\)
\(522\) 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
\(525\) −4.75627 + 23.3901i −0.207581 + 1.02083i
\(526\) 0 0
\(527\) 24.7098i 1.07637i
\(528\) 0 0
\(529\) 9.64908i 0.419525i
\(530\) 0 0
\(531\) −13.3588 13.5885i −0.579724 0.589689i
\(532\) 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
\(537\) 4.26621 + 21.9357i 0.184101 + 0.946597i
\(538\) 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
\(549\) −0.179200 + 21.0282i −0.00764806 + 0.897460i
\(550\) 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
\(555\) −2.44350 3.69090i −0.103721 0.156670i
\(556\) 0 0
\(557\) −7.71096 18.6159i −0.326724 0.788781i −0.998832 0.0483277i \(-0.984611\pi\)
0.672108 0.740453i \(1.73461\pi\)
\(558\) 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 −0.610620 0.791924i \(-0.709080\pi\)
0.128201 + 0.991748i \(0.459080\pi\)
\(564\) 0 0
\(565\) −5.35046 + 12.9172i −0.225096 + 0.543429i
\(566\) 0 0
\(567\) −10.6715 0.181895i −0.448160 0.00763889i
\(568\) 0 0
\(569\) −27.9002 + 27.9002i −1.16964 + 1.16964i −0.187343 + 0.982295i \(0.559987\pi\)
−0.982295 + 0.187343i \(0.940013\pi\)
\(570\) 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
\(573\) −0.560193 + 2.75488i −0.0234024 + 0.115087i
\(574\) 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
\(579\) 3.57479 17.5799i 0.148563 0.730596i
\(580\) 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
\(585\) −10.6385 + 25.0770i −0.439848 + 1.03681i
\(586\) 0 0
\(587\) 5.82661 14.0667i 0.240490 0.580594i −0.756842 0.653598i \(-0.773259\pi\)
0.997332 + 0.0730041i \(0.0232586\pi\)
\(588\) 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 \(-0.504968\pi\)
−0.0156063 + 0.999878i \(0.504968\pi\)
\(594\) 0 0
\(595\) 5.98850 + 14.4575i 0.245505 + 0.592701i
\(596\) 0 0
\(597\) −11.8788 17.9429i −0.486168 0.734356i
\(598\) 0 0
\(599\) 18.9662 18.9662i 0.774937 0.774937i −0.204028 0.978965i \(-0.565403\pi\)
0.978965 + 0.204028i \(0.0654033\pi\)
\(600\) 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
\(603\) 15.5396 + 0.132427i 0.632822 + 0.00539284i
\(604\) 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
\(615\) 6.75939 + 34.7550i 0.272565 + 1.40146i
\(616\) 0 0
\(617\) 10.3859 + 10.3859i 0.418123 + 0.418123i 0.884556 0.466434i \(-0.154461\pi\)
−0.466434 + 0.884556i \(0.654461\pi\)
\(618\) 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
\(621\) −3.46570 18.6672i −0.139074 0.749088i
\(622\) 0 0
\(623\) 17.4628i 0.699630i
\(624\) 0 0
\(625\) 51.9336i 2.07734i
\(626\) 0 0
\(627\) −0.867622 + 4.26674i −0.0346495 + 0.170397i
\(628\) 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
\(633\) −43.6081 + 8.48118i −1.73326 + 0.337097i
\(634\) 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 \(-0.977341\pi\)
0.997467 0.0711252i \(-0.0226590\pi\)
\(642\) 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
\(645\) 13.4842 + 20.3678i 0.530939 + 0.801983i
\(646\) 0 0
\(647\) −23.6599 23.6599i −0.930167 0.930167i 0.0675491 0.997716i \(-0.478482\pi\)
−0.997716 + 0.0675491i \(0.978482\pi\)
\(648\) 0 0
\(649\) −2.92297 + 2.92297i −0.114737 + 0.114737i
\(650\) 0 0
\(651\) −13.0749 + 8.65604i −0.512447 + 0.339257i
\(652\) 0 0
\(653\) 12.1760 + 29.3955i 0.476484 + 1.15033i 0.961247 + 0.275689i \(0.0889058\pi\)
−0.484763 + 0.874646i \(0.661094\pi\)
\(654\) 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 −0.994360 0.106059i \(-0.966177\pi\)
−0.628123 + 0.778114i \(0.716177\pi\)
\(660\) 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
\(663\) 2.38380 + 12.2569i 0.0925790 + 0.476017i
\(664\) 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
\(669\) −27.8087 5.65478i −1.07515 0.218627i
\(670\) 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
\(675\) −59.3674 + 11.0220i −2.28505 + 0.424236i
\(676\) 0 0
\(677\) −19.1300 + 46.1838i −0.735224 + 1.77499i −0.110886 + 0.993833i \(0.535369\pi\)
−0.624338 + 0.781155i \(0.714631\pi\)
\(678\) 0 0
\(679\) −7.72806 + 7.72806i −0.296576 + 0.296576i
\(680\) 0 0
\(681\) 42.7245 8.30935i 1.63721 0.318415i
\(682\) 0 0
\(683\) 14.1282 34.1085i 0.540600 1.30512i −0.383700 0.923458i \(-0.625350\pi\)
0.924300 0.381666i \(-0.124650\pi\)
\(684\) 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
\(693\) −0.0197302 + 2.31523i −0.000749487 + 0.0879485i
\(694\) 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
\(699\) −27.6569 + 18.3098i −1.04608 + 0.692540i
\(700\) 0 0
\(701\) 9.68643 4.01225i 0.365851 0.151541i −0.192182 0.981359i \(-0.561556\pi\)
0.558033 + 0.829819i \(0.311556\pi\)
\(702\) 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
\(711\) 31.8550 + 13.5139i 1.19466 + 0.506812i
\(712\) 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
\(717\) 32.4473 + 6.59802i 1.21177 + 0.246407i
\(718\) 0 0
\(719\) 46.6233i 1.73876i −0.494147 0.869378i \(-0.664519\pi\)
0.494147 0.869378i \(-0.335481\pi\)
\(720\) 0 0
\(721\) 7.20896i 0.268476i
\(722\) 0 0
\(723\) −2.90613 0.590948i −0.108080 0.0219776i
\(724\) 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
\(729\) −9.69143 25.2007i −0.358942 0.933360i
\(730\) 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
\(741\) 12.4250 8.22575i 0.456443 0.302180i
\(742\) 0 0
\(743\) −15.4609 15.4609i −0.567205 0.567205i 0.364139 0.931345i \(-0.381363\pi\)
−0.931345 + 0.364139i \(0.881363\pi\)
\(744\) 0 0
\(745\) 17.0768 17.0768i 0.625644 0.625644i
\(746\) 0 0
\(747\) −3.24268 0.0276338i −0.118643 0.00101107i
\(748\) 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
\(759\) −4.04295 + 0.786300i −0.146750 + 0.0285409i
\(760\) 0 0
\(761\) 10.6555 10.6555i 0.386261 0.386261i −0.487090 0.873352i \(-0.661942\pi\)
0.873352 + 0.487090i \(0.161942\pi\)
\(762\) 0 0
\(763\) 6.09226 14.7080i 0.220555 0.532466i
\(764\) 0 0
\(765\) −28.2299 + 27.7528i −1.02065 + 1.00341i
\(766\) 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
\(771\) 36.5371 + 7.42966i 1.31585 + 0.267573i
\(772\) 0 0
\(773\) 10.7578 25.9715i 0.386929 0.934130i −0.603657 0.797244i \(-0.706290\pi\)
0.990587 0.136886i \(-0.0437095\pi\)
\(774\) 0 0
\(775\) −62.7288 + 62.7288i −2.25328 + 2.25328i
\(776\) 0 0
\(777\) 0.245814 + 1.26391i 0.00881851 + 0.0453425i
\(778\) 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