Properties

Label 1040.2.da.b.881.2
Level $1040$
Weight $2$
Character 1040.881
Analytic conductor $8.304$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1040.da (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.30444181021\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.22581504.2
Defining polynomial: \(x^{8} - 4 x^{7} + 5 x^{6} + 2 x^{5} - 11 x^{4} + 4 x^{3} + 20 x^{2} - 32 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 881.2
Root \(-1.27597 + 0.609843i\) of defining polynomial
Character \(\chi\) \(=\) 1040.881
Dual form 1040.2.da.b.641.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.800098 - 1.38581i) q^{3} -1.00000i q^{5} +(0.287734 + 0.166123i) q^{7} +(0.219687 - 0.380509i) q^{9} +O(q^{10})\) \(q+(-0.800098 - 1.38581i) q^{3} -1.00000i q^{5} +(0.287734 + 0.166123i) q^{7} +(0.219687 - 0.380509i) q^{9} +(-4.65213 + 2.68591i) q^{11} +(-3.55193 - 0.619491i) q^{13} +(-1.38581 + 0.800098i) q^{15} +(-2.53215 + 4.38581i) q^{17} +(1.96410 + 1.13397i) q^{19} -0.531659i q^{21} +(1.41959 + 2.45880i) q^{23} -1.00000 q^{25} -5.50367 q^{27} +(1.45174 + 2.51448i) q^{29} -5.46410i q^{31} +(7.44432 + 4.29798i) q^{33} +(0.166123 - 0.287734i) q^{35} +(-5.17191 + 2.98601i) q^{37} +(1.98340 + 5.41796i) q^{39} +(3.23205 - 1.86603i) q^{41} +(2.53215 - 4.38581i) q^{43} +(-0.380509 - 0.219687i) q^{45} +8.34285i q^{47} +(-3.44481 - 5.96658i) q^{49} +8.10387 q^{51} -1.56063 q^{53} +(2.68591 + 4.65213i) q^{55} -3.62916i q^{57} +(-2.34461 - 1.35366i) q^{59} +(-7.05193 + 12.2143i) q^{61} +(0.126423 - 0.0729902i) q^{63} +(-0.619491 + 3.55193i) q^{65} +(-8.94799 + 5.16612i) q^{67} +(2.27162 - 3.93456i) q^{69} +(11.0828 + 6.39866i) q^{71} +9.68922i q^{73} +(0.800098 + 1.38581i) q^{75} -1.78477 q^{77} -4.51851 q^{79} +(3.74441 + 6.48552i) q^{81} +4.26371i q^{83} +(4.38581 + 2.53215i) q^{85} +(2.32306 - 4.02367i) q^{87} +(-2.79366 + 1.61292i) q^{89} +(-0.919100 - 0.768307i) q^{91} +(-7.57221 + 4.37182i) q^{93} +(1.13397 - 1.96410i) q^{95} +(2.17191 + 1.25396i) q^{97} +2.36023i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{3} + 6q^{7} - 4q^{9} + O(q^{10}) \) \( 8q - 2q^{3} + 6q^{7} - 4q^{9} + 6q^{15} - 2q^{17} - 12q^{19} + 10q^{23} - 8q^{25} + 4q^{27} - 8q^{29} + 42q^{33} - 10q^{35} + 6q^{37} + 12q^{41} + 2q^{43} + 12q^{49} + 8q^{51} - 24q^{53} + 12q^{59} - 28q^{61} + 24q^{63} - 8q^{65} - 6q^{67} - 16q^{69} + 2q^{75} - 36q^{77} + 16q^{79} + 8q^{81} + 18q^{85} - 22q^{87} + 24q^{89} - 28q^{91} + 16q^{95} - 30q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(417\) \(561\) \(911\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.800098 1.38581i −0.461937 0.800098i 0.537121 0.843505i \(-0.319512\pi\)
−0.999057 + 0.0434075i \(0.986179\pi\)
\(4\) 0 0
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 0.287734 + 0.166123i 0.108753 + 0.0627887i 0.553390 0.832922i \(-0.313334\pi\)
−0.444637 + 0.895711i \(0.646667\pi\)
\(8\) 0 0
\(9\) 0.219687 0.380509i 0.0732290 0.126836i
\(10\) 0 0
\(11\) −4.65213 + 2.68591i −1.40267 + 0.809832i −0.994666 0.103149i \(-0.967108\pi\)
−0.408004 + 0.912980i \(0.633775\pi\)
\(12\) 0 0
\(13\) −3.55193 0.619491i −0.985129 0.171816i
\(14\) 0 0
\(15\) −1.38581 + 0.800098i −0.357815 + 0.206584i
\(16\) 0 0
\(17\) −2.53215 + 4.38581i −0.614136 + 1.06372i 0.376399 + 0.926458i \(0.377162\pi\)
−0.990535 + 0.137258i \(0.956171\pi\)
\(18\) 0 0
\(19\) 1.96410 + 1.13397i 0.450596 + 0.260152i 0.708082 0.706130i \(-0.249561\pi\)
−0.257486 + 0.966282i \(0.582894\pi\)
\(20\) 0 0
\(21\) 0.531659i 0.116018i
\(22\) 0 0
\(23\) 1.41959 + 2.45880i 0.296005 + 0.512695i 0.975218 0.221246i \(-0.0710122\pi\)
−0.679213 + 0.733941i \(0.737679\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) −5.50367 −1.05918
\(28\) 0 0
\(29\) 1.45174 + 2.51448i 0.269581 + 0.466928i 0.968754 0.248025i \(-0.0797815\pi\)
−0.699173 + 0.714953i \(0.746448\pi\)
\(30\) 0 0
\(31\) 5.46410i 0.981382i −0.871334 0.490691i \(-0.836744\pi\)
0.871334 0.490691i \(-0.163256\pi\)
\(32\) 0 0
\(33\) 7.44432 + 4.29798i 1.29589 + 0.748182i
\(34\) 0 0
\(35\) 0.166123 0.287734i 0.0280800 0.0486359i
\(36\) 0 0
\(37\) −5.17191 + 2.98601i −0.850257 + 0.490896i −0.860738 0.509049i \(-0.829997\pi\)
0.0104803 + 0.999945i \(0.496664\pi\)
\(38\) 0 0
\(39\) 1.98340 + 5.41796i 0.317598 + 0.867568i
\(40\) 0 0
\(41\) 3.23205 1.86603i 0.504762 0.291424i −0.225916 0.974147i \(-0.572538\pi\)
0.730678 + 0.682723i \(0.239204\pi\)
\(42\) 0 0
\(43\) 2.53215 4.38581i 0.386149 0.668830i −0.605779 0.795633i \(-0.707138\pi\)
0.991928 + 0.126803i \(0.0404717\pi\)
\(44\) 0 0
\(45\) −0.380509 0.219687i −0.0567229 0.0327490i
\(46\) 0 0
\(47\) 8.34285i 1.21693i 0.793581 + 0.608465i \(0.208214\pi\)
−0.793581 + 0.608465i \(0.791786\pi\)
\(48\) 0 0
\(49\) −3.44481 5.96658i −0.492115 0.852368i
\(50\) 0 0
\(51\) 8.10387 1.13477
\(52\) 0 0
\(53\) −1.56063 −0.214369 −0.107184 0.994239i \(-0.534183\pi\)
−0.107184 + 0.994239i \(0.534183\pi\)
\(54\) 0 0
\(55\) 2.68591 + 4.65213i 0.362168 + 0.627293i
\(56\) 0 0
\(57\) 3.62916i 0.480694i
\(58\) 0 0
\(59\) −2.34461 1.35366i −0.305242 0.176232i 0.339553 0.940587i \(-0.389724\pi\)
−0.644795 + 0.764355i \(0.723057\pi\)
\(60\) 0 0
\(61\) −7.05193 + 12.2143i −0.902908 + 1.56388i −0.0792059 + 0.996858i \(0.525238\pi\)
−0.823702 + 0.567023i \(0.808095\pi\)
\(62\) 0 0
\(63\) 0.126423 0.0729902i 0.0159278 0.00919590i
\(64\) 0 0
\(65\) −0.619491 + 3.55193i −0.0768384 + 0.440563i
\(66\) 0 0
\(67\) −8.94799 + 5.16612i −1.09317 + 0.631142i −0.934419 0.356176i \(-0.884080\pi\)
−0.158752 + 0.987319i \(0.550747\pi\)
\(68\) 0 0
\(69\) 2.27162 3.93456i 0.273471 0.473666i
\(70\) 0 0
\(71\) 11.0828 + 6.39866i 1.31529 + 0.759382i 0.982967 0.183785i \(-0.0588349\pi\)
0.332321 + 0.943166i \(0.392168\pi\)
\(72\) 0 0
\(73\) 9.68922i 1.13404i 0.823705 + 0.567019i \(0.191903\pi\)
−0.823705 + 0.567019i \(0.808097\pi\)
\(74\) 0 0
\(75\) 0.800098 + 1.38581i 0.0923873 + 0.160020i
\(76\) 0 0
\(77\) −1.78477 −0.203393
\(78\) 0 0
\(79\) −4.51851 −0.508372 −0.254186 0.967155i \(-0.581808\pi\)
−0.254186 + 0.967155i \(0.581808\pi\)
\(80\) 0 0
\(81\) 3.74441 + 6.48552i 0.416046 + 0.720613i
\(82\) 0 0
\(83\) 4.26371i 0.468003i 0.972236 + 0.234001i \(0.0751821\pi\)
−0.972236 + 0.234001i \(0.924818\pi\)
\(84\) 0 0
\(85\) 4.38581 + 2.53215i 0.475708 + 0.274650i
\(86\) 0 0
\(87\) 2.32306 4.02367i 0.249059 0.431382i
\(88\) 0 0
\(89\) −2.79366 + 1.61292i −0.296127 + 0.170969i −0.640702 0.767790i \(-0.721356\pi\)
0.344575 + 0.938759i \(0.388023\pi\)
\(90\) 0 0
\(91\) −0.919100 0.768307i −0.0963478 0.0805405i
\(92\) 0 0
\(93\) −7.57221 + 4.37182i −0.785201 + 0.453336i
\(94\) 0 0
\(95\) 1.13397 1.96410i 0.116343 0.201513i
\(96\) 0 0
\(97\) 2.17191 + 1.25396i 0.220524 + 0.127320i 0.606193 0.795318i \(-0.292696\pi\)
−0.385669 + 0.922637i \(0.626029\pi\)
\(98\) 0 0
\(99\) 2.36023i 0.237213i
\(100\) 0 0
\(101\) 6.22336 + 10.7792i 0.619247 + 1.07257i 0.989623 + 0.143686i \(0.0458955\pi\)
−0.370376 + 0.928882i \(0.620771\pi\)
\(102\) 0 0
\(103\) −15.0247 −1.48043 −0.740215 0.672370i \(-0.765276\pi\)
−0.740215 + 0.672370i \(0.765276\pi\)
\(104\) 0 0
\(105\) −0.531659 −0.0518846
\(106\) 0 0
\(107\) −6.53215 11.3140i −0.631487 1.09377i −0.987248 0.159190i \(-0.949112\pi\)
0.355761 0.934577i \(-0.384222\pi\)
\(108\) 0 0
\(109\) 11.2325i 1.07587i −0.842985 0.537937i \(-0.819204\pi\)
0.842985 0.537937i \(-0.180796\pi\)
\(110\) 0 0
\(111\) 8.27607 + 4.77819i 0.785530 + 0.453526i
\(112\) 0 0
\(113\) 9.17191 15.8862i 0.862821 1.49445i −0.00637349 0.999980i \(-0.502029\pi\)
0.869195 0.494470i \(-0.164638\pi\)
\(114\) 0 0
\(115\) 2.45880 1.41959i 0.229284 0.132377i
\(116\) 0 0
\(117\) −1.01603 + 1.21545i −0.0939325 + 0.112368i
\(118\) 0 0
\(119\) −1.45717 + 0.841298i −0.133579 + 0.0771216i
\(120\) 0 0
\(121\) 8.92820 15.4641i 0.811655 1.40583i
\(122\) 0 0
\(123\) −5.17191 2.98601i −0.466336 0.269239i
\(124\) 0 0
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) −1.61998 2.80589i −0.143750 0.248982i 0.785156 0.619298i \(-0.212583\pi\)
−0.928906 + 0.370316i \(0.879249\pi\)
\(128\) 0 0
\(129\) −8.10387 −0.713506
\(130\) 0 0
\(131\) −0.175664 −0.0153478 −0.00767390 0.999971i \(-0.502443\pi\)
−0.00767390 + 0.999971i \(0.502443\pi\)
\(132\) 0 0
\(133\) 0.376759 + 0.652566i 0.0326692 + 0.0565846i
\(134\) 0 0
\(135\) 5.50367i 0.473681i
\(136\) 0 0
\(137\) −15.5736 8.99144i −1.33054 0.768190i −0.345162 0.938543i \(-0.612176\pi\)
−0.985383 + 0.170353i \(0.945509\pi\)
\(138\) 0 0
\(139\) 5.99307 10.3803i 0.508325 0.880445i −0.491628 0.870805i \(-0.663598\pi\)
0.999954 0.00964021i \(-0.00306862\pi\)
\(140\) 0 0
\(141\) 11.5616 6.67510i 0.973663 0.562144i
\(142\) 0 0
\(143\) 18.1879 6.65821i 1.52095 0.556788i
\(144\) 0 0
\(145\) 2.51448 1.45174i 0.208816 0.120560i
\(146\) 0 0
\(147\) −5.51236 + 9.54769i −0.454652 + 0.787481i
\(148\) 0 0
\(149\) 2.95350 + 1.70520i 0.241960 + 0.139696i 0.616077 0.787686i \(-0.288721\pi\)
−0.374117 + 0.927381i \(0.622054\pi\)
\(150\) 0 0
\(151\) 7.96141i 0.647890i 0.946076 + 0.323945i \(0.105009\pi\)
−0.946076 + 0.323945i \(0.894991\pi\)
\(152\) 0 0
\(153\) 1.11256 + 1.92701i 0.0899451 + 0.155790i
\(154\) 0 0
\(155\) −5.46410 −0.438887
\(156\) 0 0
\(157\) −16.4329 −1.31148 −0.655742 0.754985i \(-0.727644\pi\)
−0.655742 + 0.754985i \(0.727644\pi\)
\(158\) 0 0
\(159\) 1.24865 + 2.16273i 0.0990247 + 0.171516i
\(160\) 0 0
\(161\) 0.943307i 0.0743430i
\(162\) 0 0
\(163\) −15.4215 8.90361i −1.20791 0.697384i −0.245604 0.969370i \(-0.578986\pi\)
−0.962301 + 0.271986i \(0.912320\pi\)
\(164\) 0 0
\(165\) 4.29798 7.44432i 0.334597 0.579539i
\(166\) 0 0
\(167\) −5.45047 + 3.14683i −0.421770 + 0.243509i −0.695834 0.718202i \(-0.744965\pi\)
0.274064 + 0.961711i \(0.411632\pi\)
\(168\) 0 0
\(169\) 12.2325 + 4.40078i 0.940959 + 0.338522i
\(170\) 0 0
\(171\) 0.862975 0.498239i 0.0659933 0.0381013i
\(172\) 0 0
\(173\) 7.98756 13.8349i 0.607283 1.05184i −0.384404 0.923165i \(-0.625593\pi\)
0.991686 0.128679i \(-0.0410738\pi\)
\(174\) 0 0
\(175\) −0.287734 0.166123i −0.0217506 0.0125577i
\(176\) 0 0
\(177\) 4.33225i 0.325632i
\(178\) 0 0
\(179\) −11.8087 20.4533i −0.882625 1.52875i −0.848412 0.529336i \(-0.822441\pi\)
−0.0342123 0.999415i \(-0.510892\pi\)
\(180\) 0 0
\(181\) 2.62590 0.195182 0.0975909 0.995227i \(-0.468886\pi\)
0.0975909 + 0.995227i \(0.468886\pi\)
\(182\) 0 0
\(183\) 22.5689 1.66834
\(184\) 0 0
\(185\) 2.98601 + 5.17191i 0.219536 + 0.380247i
\(186\) 0 0
\(187\) 27.2045i 1.98939i
\(188\) 0 0
\(189\) −1.58359 0.914288i −0.115189 0.0665046i
\(190\) 0 0
\(191\) −1.00791 + 1.74575i −0.0729298 + 0.126318i −0.900184 0.435509i \(-0.856568\pi\)
0.827254 + 0.561828i \(0.189902\pi\)
\(192\) 0 0
\(193\) −19.7636 + 11.4105i −1.42262 + 0.821348i −0.996522 0.0833298i \(-0.973445\pi\)
−0.426095 + 0.904678i \(0.640111\pi\)
\(194\) 0 0
\(195\) 5.41796 1.98340i 0.387988 0.142034i
\(196\) 0 0
\(197\) −0.556877 + 0.321513i −0.0396758 + 0.0229068i −0.519707 0.854345i \(-0.673959\pi\)
0.480031 + 0.877252i \(0.340625\pi\)
\(198\) 0 0
\(199\) −1.53342 + 2.65596i −0.108701 + 0.188276i −0.915244 0.402899i \(-0.868003\pi\)
0.806543 + 0.591175i \(0.201336\pi\)
\(200\) 0 0
\(201\) 14.3185 + 8.26681i 1.00995 + 0.583096i
\(202\) 0 0
\(203\) 0.964670i 0.0677065i
\(204\) 0 0
\(205\) −1.86603 3.23205i −0.130329 0.225736i
\(206\) 0 0
\(207\) 1.24746 0.0867045
\(208\) 0 0
\(209\) −12.1830 −0.842716
\(210\) 0 0
\(211\) −4.10020 7.10175i −0.282269 0.488904i 0.689674 0.724120i \(-0.257754\pi\)
−0.971943 + 0.235215i \(0.924420\pi\)
\(212\) 0 0
\(213\) 20.4782i 1.40314i
\(214\) 0 0
\(215\) −4.38581 2.53215i −0.299110 0.172691i
\(216\) 0 0
\(217\) 0.907714 1.57221i 0.0616197 0.106728i
\(218\) 0 0
\(219\) 13.4274 7.75232i 0.907341 0.523854i
\(220\) 0 0
\(221\) 11.7110 14.0095i 0.787767 0.942378i
\(222\) 0 0
\(223\) −8.87174 + 5.12210i −0.594095 + 0.343001i −0.766715 0.641987i \(-0.778110\pi\)
0.172620 + 0.984989i \(0.444777\pi\)
\(224\) 0 0
\(225\) −0.219687 + 0.380509i −0.0146458 + 0.0253673i
\(226\) 0 0
\(227\) 6.10012 + 3.52190i 0.404879 + 0.233757i 0.688587 0.725154i \(-0.258231\pi\)
−0.283708 + 0.958911i \(0.591565\pi\)
\(228\) 0 0
\(229\) 1.32899i 0.0878219i −0.999035 0.0439109i \(-0.986018\pi\)
0.999035 0.0439109i \(-0.0139818\pi\)
\(230\) 0 0
\(231\) 1.42799 + 2.47335i 0.0939547 + 0.162734i
\(232\) 0 0
\(233\) 1.24746 0.0817238 0.0408619 0.999165i \(-0.486990\pi\)
0.0408619 + 0.999165i \(0.486990\pi\)
\(234\) 0 0
\(235\) 8.34285 0.544227
\(236\) 0 0
\(237\) 3.61525 + 6.26180i 0.234836 + 0.406748i
\(238\) 0 0
\(239\) 9.94207i 0.643099i 0.946893 + 0.321549i \(0.104204\pi\)
−0.946893 + 0.321549i \(0.895796\pi\)
\(240\) 0 0
\(241\) −19.5608 11.2934i −1.26002 0.727475i −0.286944 0.957947i \(-0.592640\pi\)
−0.973079 + 0.230472i \(0.925973\pi\)
\(242\) 0 0
\(243\) −2.26371 + 3.92086i −0.145217 + 0.251523i
\(244\) 0 0
\(245\) −5.96658 + 3.44481i −0.381191 + 0.220081i
\(246\) 0 0
\(247\) −6.27387 5.24455i −0.399197 0.333702i
\(248\) 0 0
\(249\) 5.90869 3.41139i 0.374448 0.216188i
\(250\) 0 0
\(251\) 3.38418 5.86157i 0.213608 0.369979i −0.739233 0.673449i \(-0.764812\pi\)
0.952841 + 0.303470i \(0.0981453\pi\)
\(252\) 0 0
\(253\) −13.2082 7.62577i −0.830394 0.479428i
\(254\) 0 0
\(255\) 8.10387i 0.507484i
\(256\) 0 0
\(257\) −5.12691 8.88007i −0.319808 0.553924i 0.660640 0.750703i \(-0.270285\pi\)
−0.980448 + 0.196779i \(0.936952\pi\)
\(258\) 0 0
\(259\) −1.98418 −0.123291
\(260\) 0 0
\(261\) 1.27571 0.0789645
\(262\) 0 0
\(263\) 9.32850 + 16.1574i 0.575220 + 0.996310i 0.996018 + 0.0891555i \(0.0284168\pi\)
−0.420798 + 0.907154i \(0.638250\pi\)
\(264\) 0 0
\(265\) 1.56063i 0.0958685i
\(266\) 0 0
\(267\) 4.47040 + 2.58098i 0.273584 + 0.157954i
\(268\) 0 0
\(269\) −8.97894 + 15.5520i −0.547456 + 0.948221i 0.450992 + 0.892528i \(0.351070\pi\)
−0.998448 + 0.0556934i \(0.982263\pi\)
\(270\) 0 0
\(271\) 26.7582 15.4488i 1.62544 0.938450i 0.640014 0.768363i \(-0.278929\pi\)
0.985429 0.170086i \(-0.0544047\pi\)
\(272\) 0 0
\(273\) −0.329358 + 1.88842i −0.0199337 + 0.114292i
\(274\) 0 0
\(275\) 4.65213 2.68591i 0.280534 0.161966i
\(276\) 0 0
\(277\) 13.2522 22.9536i 0.796250 1.37915i −0.125792 0.992057i \(-0.540147\pi\)
0.922042 0.387089i \(-0.126519\pi\)
\(278\) 0 0
\(279\) −2.07914 1.20039i −0.124475 0.0718656i
\(280\) 0 0
\(281\) 4.97766i 0.296942i −0.988917 0.148471i \(-0.952565\pi\)
0.988917 0.148471i \(-0.0474352\pi\)
\(282\) 0 0
\(283\) 6.29317 + 10.9001i 0.374090 + 0.647943i 0.990190 0.139725i \(-0.0446218\pi\)
−0.616100 + 0.787668i \(0.711288\pi\)
\(284\) 0 0
\(285\) −3.62916 −0.214973
\(286\) 0 0
\(287\) 1.23996 0.0731926
\(288\) 0 0
\(289\) −4.32355 7.48861i −0.254327 0.440507i
\(290\) 0 0
\(291\) 4.01315i 0.235255i
\(292\) 0 0
\(293\) 14.6511 + 8.45880i 0.855925 + 0.494168i 0.862645 0.505809i \(-0.168806\pi\)
−0.00672072 + 0.999977i \(0.502139\pi\)
\(294\) 0 0
\(295\) −1.35366 + 2.34461i −0.0788132 + 0.136508i
\(296\) 0 0
\(297\) 25.6038 14.7824i 1.48568 0.857759i
\(298\) 0 0
\(299\) −3.51908 9.61292i −0.203514 0.555929i
\(300\) 0 0
\(301\) 1.45717 0.841298i 0.0839899 0.0484916i
\(302\) 0 0
\(303\) 9.95859 17.2488i 0.572106 0.990917i
\(304\) 0 0
\(305\) 12.2143 + 7.05193i 0.699389 + 0.403793i
\(306\) 0 0
\(307\) 4.30426i 0.245657i −0.992428 0.122828i \(-0.960803\pi\)
0.992428 0.122828i \(-0.0391965\pi\)
\(308\) 0 0
\(309\) 12.0213 + 20.8214i 0.683865 + 1.18449i
\(310\) 0 0
\(311\) −2.22512 −0.126175 −0.0630875 0.998008i \(-0.520095\pi\)
−0.0630875 + 0.998008i \(0.520095\pi\)
\(312\) 0 0
\(313\) 7.20887 0.407469 0.203735 0.979026i \(-0.434692\pi\)
0.203735 + 0.979026i \(0.434692\pi\)
\(314\) 0 0
\(315\) −0.0729902 0.126423i −0.00411253 0.00712311i
\(316\) 0 0
\(317\) 0.321644i 0.0180653i −0.999959 0.00903266i \(-0.997125\pi\)
0.999959 0.00903266i \(-0.00287522\pi\)
\(318\) 0 0
\(319\) −13.5073 7.79847i −0.756266 0.436630i
\(320\) 0 0
\(321\) −10.4527 + 18.1046i −0.583414 + 1.01050i
\(322\) 0 0
\(323\) −9.94679 + 5.74278i −0.553454 + 0.319537i
\(324\) 0 0
\(325\) 3.55193 + 0.619491i 0.197026 + 0.0343632i
\(326\) 0 0
\(327\) −15.5661 + 8.98707i −0.860805 + 0.496986i
\(328\) 0 0
\(329\) −1.38594 + 2.40052i −0.0764094 + 0.132345i
\(330\) 0 0
\(331\) 14.4037 + 8.31600i 0.791701 + 0.457089i 0.840561 0.541717i \(-0.182225\pi\)
−0.0488600 + 0.998806i \(0.515559\pi\)
\(332\) 0 0
\(333\) 2.62395i 0.143791i
\(334\) 0 0
\(335\) 5.16612 + 8.94799i 0.282255 + 0.488881i
\(336\) 0 0
\(337\) −24.2186 −1.31927 −0.659636 0.751586i \(-0.729289\pi\)
−0.659636 + 0.751586i \(0.729289\pi\)
\(338\) 0 0
\(339\) −29.3537 −1.59427
\(340\) 0 0
\(341\) 14.6761 + 25.4197i 0.794754 + 1.37655i
\(342\) 0 0
\(343\) 4.61478i 0.249174i
\(344\) 0 0
\(345\) −3.93456 2.27162i −0.211830 0.122300i
\(346\) 0 0
\(347\) −3.13680 + 5.43309i −0.168392 + 0.291664i −0.937855 0.347028i \(-0.887191\pi\)
0.769463 + 0.638692i \(0.220524\pi\)
\(348\) 0 0
\(349\) −6.12275 + 3.53497i −0.327743 + 0.189223i −0.654839 0.755769i \(-0.727263\pi\)
0.327095 + 0.944991i \(0.393930\pi\)
\(350\) 0 0
\(351\) 19.5487 + 3.40948i 1.04343 + 0.181984i
\(352\) 0 0
\(353\) −18.8705 + 10.8949i −1.00438 + 0.579878i −0.909541 0.415615i \(-0.863566\pi\)
−0.0948371 + 0.995493i \(0.530233\pi\)
\(354\) 0 0
\(355\) 6.39866 11.0828i 0.339606 0.588214i
\(356\) 0 0
\(357\) 2.33176 + 1.34624i 0.123410 + 0.0712506i
\(358\) 0 0
\(359\) 23.9737i 1.26528i 0.774444 + 0.632642i \(0.218029\pi\)
−0.774444 + 0.632642i \(0.781971\pi\)
\(360\) 0 0
\(361\) −6.92820 12.0000i −0.364642 0.631579i
\(362\) 0 0
\(363\) −28.5737 −1.49973
\(364\) 0 0
\(365\) 9.68922 0.507157
\(366\) 0 0
\(367\) 3.19566 + 5.53505i 0.166812 + 0.288927i 0.937297 0.348531i \(-0.113319\pi\)
−0.770485 + 0.637458i \(0.779986\pi\)
\(368\) 0 0
\(369\) 1.63977i 0.0853628i
\(370\) 0 0
\(371\) −0.449045 0.259256i −0.0233133 0.0134599i
\(372\) 0 0
\(373\) 10.0401 17.3899i 0.519855 0.900414i −0.479879 0.877335i \(-0.659319\pi\)
0.999734 0.0230798i \(-0.00734719\pi\)
\(374\) 0 0
\(375\) 1.38581 0.800098i 0.0715629 0.0413169i
\(376\) 0 0
\(377\) −3.59878 9.83062i −0.185346 0.506302i
\(378\) 0 0
\(379\) 4.73007 2.73091i 0.242968 0.140277i −0.373572 0.927601i \(-0.621867\pi\)
0.616540 + 0.787324i \(0.288534\pi\)
\(380\) 0 0
\(381\) −2.59229 + 4.48997i −0.132807 + 0.230028i
\(382\) 0 0
\(383\) −4.90842 2.83388i −0.250808 0.144804i 0.369326 0.929300i \(-0.379589\pi\)
−0.620134 + 0.784496i \(0.712922\pi\)
\(384\) 0 0
\(385\) 1.78477i 0.0909602i
\(386\) 0 0
\(387\) −1.11256 1.92701i −0.0565546 0.0979554i
\(388\) 0 0
\(389\) −10.6174 −0.538325 −0.269162 0.963095i \(-0.586747\pi\)
−0.269162 + 0.963095i \(0.586747\pi\)
\(390\) 0 0
\(391\) −14.3784 −0.727149
\(392\) 0 0
\(393\) 0.140548 + 0.243436i 0.00708971 + 0.0122797i
\(394\) 0 0
\(395\) 4.51851i 0.227351i
\(396\) 0 0
\(397\) 24.2780 + 14.0169i 1.21848 + 0.703487i 0.964592 0.263748i \(-0.0849586\pi\)
0.253884 + 0.967235i \(0.418292\pi\)
\(398\) 0 0
\(399\) 0.602888 1.04423i 0.0301822 0.0522770i
\(400\) 0 0
\(401\) 19.4979 11.2571i 0.973680 0.562155i 0.0733241 0.997308i \(-0.476639\pi\)
0.900356 + 0.435154i \(0.143306\pi\)
\(402\) 0 0
\(403\) −3.38496 + 19.4081i −0.168617 + 0.966788i
\(404\) 0 0
\(405\) 6.48552 3.74441i 0.322268 0.186061i
\(406\) 0 0
\(407\) 16.0403 27.7826i 0.795087 1.37713i
\(408\) 0 0
\(409\) −3.71328 2.14386i −0.183610 0.106007i 0.405378 0.914149i \(-0.367140\pi\)
−0.588988 + 0.808142i \(0.700473\pi\)
\(410\) 0 0
\(411\) 28.7761i 1.41942i
\(412\) 0 0
\(413\) −0.449749 0.778989i −0.0221307 0.0383315i
\(414\) 0 0
\(415\) 4.26371 0.209297
\(416\) 0 0
\(417\) −19.1802 −0.939257
\(418\) 0 0
\(419\) 8.85578 + 15.3387i 0.432633 + 0.749343i 0.997099 0.0761137i \(-0.0242512\pi\)
−0.564466 + 0.825456i \(0.690918\pi\)
\(420\) 0 0
\(421\) 12.8787i 0.627672i 0.949477 + 0.313836i \(0.101614\pi\)
−0.949477 + 0.313836i \(0.898386\pi\)
\(422\) 0 0
\(423\) 3.17453 + 1.83281i 0.154351 + 0.0891145i
\(424\) 0 0
\(425\) 2.53215 4.38581i 0.122827 0.212743i
\(426\) 0 0
\(427\) −4.05816 + 2.34298i −0.196388 + 0.113385i
\(428\) 0 0
\(429\) −23.7792 19.8778i −1.14807 0.959710i
\(430\) 0 0
\(431\) −8.22590 + 4.74923i −0.396228 + 0.228762i −0.684855 0.728679i \(-0.740134\pi\)
0.288627 + 0.957442i \(0.406801\pi\)
\(432\) 0 0
\(433\) −0.698141 + 1.20922i −0.0335505 + 0.0581112i −0.882313 0.470663i \(-0.844015\pi\)
0.848763 + 0.528774i \(0.177348\pi\)
\(434\) 0 0
\(435\) −4.02367 2.32306i −0.192920 0.111382i
\(436\) 0 0
\(437\) 6.43911i 0.308024i
\(438\) 0 0
\(439\) −2.08090 3.60422i −0.0993159 0.172020i 0.812086 0.583538i \(-0.198332\pi\)
−0.911402 + 0.411518i \(0.864999\pi\)
\(440\) 0 0
\(441\) −3.02711 −0.144148
\(442\) 0 0
\(443\) −9.54563 −0.453526 −0.226763 0.973950i \(-0.572814\pi\)
−0.226763 + 0.973950i \(0.572814\pi\)
\(444\) 0 0
\(445\) 1.61292 + 2.79366i 0.0764596 + 0.132432i
\(446\) 0 0
\(447\) 5.45732i 0.258122i
\(448\) 0 0
\(449\) 18.8075 + 10.8585i 0.887582 + 0.512446i 0.873151 0.487450i \(-0.162073\pi\)
0.0144310 + 0.999896i \(0.495406\pi\)
\(450\) 0 0
\(451\) −10.0239 + 17.3620i −0.472009 + 0.817544i
\(452\) 0 0
\(453\) 11.0330 6.36991i 0.518376 0.299284i
\(454\) 0 0
\(455\) −0.768307 + 0.919100i −0.0360188 + 0.0430881i
\(456\) 0 0
\(457\) 4.08989 2.36130i 0.191317 0.110457i −0.401282 0.915955i \(-0.631435\pi\)
0.592599 + 0.805498i \(0.298102\pi\)
\(458\) 0 0
\(459\) 13.9361 24.1381i 0.650482 1.12667i
\(460\) 0 0
\(461\) 1.54283 + 0.890753i 0.0718568 + 0.0414865i 0.535498 0.844537i \(-0.320124\pi\)
−0.463641 + 0.886023i \(0.653457\pi\)
\(462\) 0 0
\(463\) 6.80200i 0.316116i 0.987430 + 0.158058i \(0.0505232\pi\)
−0.987430 + 0.158058i \(0.949477\pi\)
\(464\) 0 0
\(465\) 4.37182 + 7.57221i 0.202738 + 0.351153i
\(466\) 0 0
\(467\) 18.2374 0.843927 0.421963 0.906613i \(-0.361341\pi\)
0.421963 + 0.906613i \(0.361341\pi\)
\(468\) 0 0
\(469\) −3.43285 −0.158514
\(470\) 0 0
\(471\) 13.1479 + 22.7728i 0.605823 + 1.04932i
\(472\) 0 0
\(473\) 27.2045i 1.25086i
\(474\) 0 0
\(475\) −1.96410 1.13397i −0.0901192 0.0520303i
\(476\) 0 0
\(477\) −0.342849 + 0.593832i −0.0156980 + 0.0271897i
\(478\) 0 0
\(479\) −30.4674 + 17.5904i −1.39209 + 0.803724i −0.993547 0.113425i \(-0.963818\pi\)
−0.398544 + 0.917149i \(0.630485\pi\)
\(480\) 0 0
\(481\) 20.2201 7.40214i 0.921957 0.337508i
\(482\) 0 0
\(483\) 1.30724 0.754738i 0.0594817 0.0343418i
\(484\) 0 0
\(485\) 1.25396 2.17191i 0.0569392 0.0986215i
\(486\) 0 0
\(487\) −8.92352 5.15200i −0.404363 0.233459i 0.284002 0.958824i \(-0.408338\pi\)
−0.688365 + 0.725364i \(0.741671\pi\)
\(488\) 0 0
\(489\) 28.4950i 1.28859i
\(490\) 0 0
\(491\) −4.66599 8.08174i −0.210573 0.364724i 0.741321 0.671151i \(-0.234200\pi\)
−0.951894 + 0.306427i \(0.900866\pi\)
\(492\) 0 0
\(493\) −14.7041 −0.662238
\(494\) 0 0
\(495\) 2.36023 0.106085
\(496\) 0 0
\(497\) 2.12593 + 3.68222i 0.0953611 + 0.165170i
\(498\) 0 0
\(499\) 23.9421i 1.07179i −0.844283 0.535897i \(-0.819974\pi\)
0.844283 0.535897i \(-0.180026\pi\)
\(500\) 0 0
\(501\) 8.72181 + 5.03554i 0.389662 + 0.224971i
\(502\) 0 0
\(503\) 21.0721 36.4980i 0.939560 1.62737i 0.173266 0.984875i \(-0.444568\pi\)
0.766294 0.642490i \(-0.222099\pi\)
\(504\) 0 0
\(505\) 10.7792 6.22336i 0.479667 0.276936i
\(506\) 0 0
\(507\) −3.68852 20.4729i −0.163813 0.909235i
\(508\) 0 0
\(509\) −29.0640 + 16.7801i −1.28824 + 0.743765i −0.978340 0.207005i \(-0.933629\pi\)
−0.309899 + 0.950770i \(0.600295\pi\)
\(510\) 0 0
\(511\) −1.60960 + 2.78792i −0.0712047 + 0.123330i
\(512\) 0 0
\(513\) −10.8098 6.24102i −0.477263 0.275548i
\(514\) 0 0
\(515\) 15.0247i 0.662069i
\(516\) 0 0
\(517\) −22.4081 38.8120i −0.985508 1.70695i
\(518\) 0 0
\(519\) −25.5633 −1.12210
\(520\) 0 0
\(521\) 12.4649 0.546098 0.273049 0.962000i \(-0.411968\pi\)
0.273049 + 0.962000i \(0.411968\pi\)
\(522\) 0 0
\(523\) −2.82978 4.90132i −0.123738 0.214320i 0.797501 0.603317i \(-0.206155\pi\)
−0.921239 + 0.388998i \(0.872821\pi\)
\(524\) 0 0
\(525\) 0.531659i 0.0232035i
\(526\) 0 0
\(527\) 23.9645 + 13.8359i 1.04391 + 0.602702i
\(528\) 0 0
\(529\) 7.46953 12.9376i 0.324762 0.562505i
\(530\) 0 0
\(531\) −1.03016 + 0.594763i −0.0447051 + 0.0258105i
\(532\) 0 0
\(533\) −12.6360 + 4.62577i −0.547327 + 0.200364i
\(534\) 0 0
\(535\) −11.3140 + 6.53215i −0.489147 + 0.282409i
\(536\) 0 0
\(537\) −18.8963 + 32.7293i −0.815433 + 1.41237i
\(538\) 0 0
\(539\) 32.0514 + 18.5049i 1.38055 + 0.797061i
\(540\) 0 0
\(541\) 15.4750i 0.665321i 0.943047 + 0.332660i \(0.107946\pi\)
−0.943047 + 0.332660i \(0.892054\pi\)
\(542\) 0 0
\(543\) −2.10098 3.63900i −0.0901616 0.156165i
\(544\) 0 0
\(545\) −11.2325 −0.481146
\(546\) 0 0
\(547\) −25.1765 −1.07647 −0.538234 0.842795i \(-0.680908\pi\)
−0.538234 + 0.842795i \(0.680908\pi\)
\(548\) 0 0
\(549\) 3.09843 + 5.36665i 0.132238 + 0.229043i
\(550\) 0 0
\(551\) 6.58493i 0.280528i
\(552\) 0 0
\(553\) −1.30013 0.750630i −0.0552871 0.0319200i
\(554\) 0 0
\(555\) 4.77819 8.27607i 0.202823 0.351300i
\(556\) 0 0
\(557\) −36.6752 + 21.1744i −1.55398 + 0.897190i −0.556167 + 0.831071i \(0.687728\pi\)
−0.997812 + 0.0661194i \(0.978938\pi\)
\(558\) 0 0
\(559\) −11.7110 + 14.0095i −0.495322 + 0.592537i
\(560\) 0 0
\(561\) −37.7002 + 21.7662i −1.59171 + 0.918971i
\(562\) 0 0
\(563\) −11.8953 + 20.6032i −0.501326 + 0.868322i 0.498673 + 0.866790i \(0.333821\pi\)
−0.999999 + 0.00153173i \(0.999512\pi\)
\(564\) 0 0
\(565\) −15.8862 9.17191i −0.668338 0.385865i
\(566\) 0 0
\(567\) 2.48814i 0.104492i
\(568\) 0 0
\(569\) −13.3710 23.1593i −0.560543 0.970889i −0.997449 0.0713817i \(-0.977259\pi\)
0.436906 0.899507i \(-0.356074\pi\)
\(570\) 0 0
\(571\) −16.7159 −0.699539 −0.349769 0.936836i \(-0.613740\pi\)
−0.349769 + 0.936836i \(0.613740\pi\)
\(572\) 0 0
\(573\) 3.22571 0.134756
\(574\) 0 0
\(575\) −1.41959 2.45880i −0.0592010 0.102539i
\(576\) 0 0
\(577\) 20.6768i 0.860786i −0.902642 0.430393i \(-0.858375\pi\)
0.902642 0.430393i \(-0.141625\pi\)
\(578\) 0 0
\(579\) 31.6257 + 18.2591i 1.31432 + 0.758822i
\(580\) 0 0
\(581\) −0.708301 + 1.22681i −0.0293853 + 0.0508968i
\(582\) 0 0
\(583\) 7.26023 4.19170i 0.300688 0.173602i
\(584\) 0 0
\(585\) 1.21545 + 1.01603i 0.0502526 + 0.0420079i
\(586\) 0 0
\(587\) −18.0109 + 10.3986i −0.743388 + 0.429196i −0.823300 0.567606i \(-0.807870\pi\)
0.0799116 + 0.996802i \(0.474536\pi\)
\(588\) 0 0
\(589\) 6.19615 10.7321i 0.255308 0.442206i
\(590\) 0 0
\(591\) 0.891111 + 0.514483i 0.0366554 + 0.0211630i
\(592\) 0 0
\(593\) 21.8475i 0.897169i 0.893740 + 0.448585i \(0.148072\pi\)
−0.893740 + 0.448585i \(0.851928\pi\)
\(594\) 0 0
\(595\) 0.841298 + 1.45717i 0.0344898 + 0.0597381i
\(596\) 0 0
\(597\) 4.90755 0.200853
\(598\) 0 0
\(599\) 3.58040 0.146291 0.0731456 0.997321i \(-0.476696\pi\)
0.0731456 + 0.997321i \(0.476696\pi\)
\(600\) 0 0
\(601\) −10.6743 18.4885i −0.435414 0.754160i 0.561915 0.827195i \(-0.310065\pi\)
−0.997329 + 0.0730352i \(0.976731\pi\)
\(602\) 0 0
\(603\) 4.53972i 0.184872i
\(604\) 0 0
\(605\) −15.4641 8.92820i −0.628705 0.362983i
\(606\) 0 0
\(607\) −1.64988 + 2.85767i −0.0669665 + 0.115989i −0.897565 0.440883i \(-0.854665\pi\)
0.830598 + 0.556872i \(0.187999\pi\)
\(608\) 0 0
\(609\) 1.33685 0.771830i 0.0541718 0.0312761i
\(610\) 0 0
\(611\) 5.16832 29.6332i 0.209088 1.19883i
\(612\) 0 0
\(613\) 8.56183 4.94318i 0.345809 0.199653i −0.317029 0.948416i \(-0.602685\pi\)
0.662838 + 0.748763i \(0.269352\pi\)
\(614\) 0 0
\(615\) −2.98601 + 5.17191i −0.120407 + 0.208552i
\(616\) 0 0
\(617\) 39.5920 + 22.8584i 1.59391 + 0.920246i 0.992626 + 0.121213i \(0.0386785\pi\)
0.601287 + 0.799033i \(0.294655\pi\)
\(618\) 0 0
\(619\) 19.9143i 0.800425i 0.916422 + 0.400212i \(0.131064\pi\)
−0.916422 + 0.400212i \(0.868936\pi\)
\(620\) 0 0
\(621\) −7.81295 13.5324i −0.313523 0.543038i
\(622\) 0 0
\(623\) −1.07177 −0.0429397
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 9.74760 + 16.8833i 0.389282 + 0.674255i
\(628\) 0 0
\(629\) 30.2440i 1.20591i
\(630\) 0 0
\(631\) −12.6403 7.29790i −0.503204 0.290525i 0.226832 0.973934i \(-0.427163\pi\)
−0.730036 + 0.683409i \(0.760497\pi\)
\(632\) 0 0
\(633\) −6.56112 + 11.3642i −0.260781 + 0.451686i
\(634\) 0 0
\(635\) −2.80589 + 1.61998i −0.111348 + 0.0642870i
\(636\) 0 0
\(637\) 8.53948 + 23.3269i 0.338346 + 0.924246i
\(638\) 0 0
\(639\) 4.86950 2.81140i 0.192634 0.111217i
\(640\) 0 0
\(641\) −7.08183 + 12.2661i −0.279716 + 0.484482i −0.971314 0.237801i \(-0.923573\pi\)
0.691598 + 0.722282i \(0.256907\pi\)
\(642\) 0 0
\(643\) 14.5246 + 8.38581i 0.572796 + 0.330704i 0.758265 0.651946i \(-0.226047\pi\)
−0.185469 + 0.982650i \(0.559380\pi\)
\(644\) 0 0
\(645\) 8.10387i 0.319089i
\(646\) 0 0
\(647\) 1.49584 + 2.59087i 0.0588075 + 0.101858i 0.893930 0.448206i \(-0.147937\pi\)
−0.835123 + 0.550063i \(0.814604\pi\)
\(648\) 0 0
\(649\) 14.5432 0.570872
\(650\) 0 0
\(651\) −2.90504 −0.113858
\(652\) 0 0
\(653\) 5.83217 + 10.1016i 0.228230 + 0.395307i 0.957284 0.289150i \(-0.0933727\pi\)
−0.729053 + 0.684457i \(0.760039\pi\)
\(654\) 0 0
\(655\) 0.175664i 0.00686374i
\(656\) 0 0
\(657\) 3.68683 + 2.12859i 0.143837 + 0.0830444i
\(658\) 0 0
\(659\) −0.905237 + 1.56792i −0.0352630 + 0.0610773i −0.883118 0.469150i \(-0.844560\pi\)
0.847855 + 0.530228i \(0.177894\pi\)
\(660\) 0 0
\(661\) 10.6872 6.17028i 0.415686 0.239996i −0.277544 0.960713i \(-0.589520\pi\)
0.693230 + 0.720717i \(0.256187\pi\)
\(662\) 0 0
\(663\) −28.7844 5.02027i −1.11789 0.194971i
\(664\) 0 0
\(665\) 0.652566 0.376759i 0.0253054 0.0146101i
\(666\) 0 0
\(667\) −4.12174 + 7.13907i −0.159594 + 0.276426i
\(668\) 0 0
\(669\) 14.1965 + 8.19636i 0.548869 + 0.316890i
\(670\) 0 0
\(671\) 75.7634i 2.92481i
\(672\) 0 0
\(673\) 4.63313 + 8.02481i 0.178594 + 0.309334i 0.941399 0.337295i \(-0.109512\pi\)
−0.762805 + 0.646628i \(0.776178\pi\)
\(674\) 0 0
\(675\) 5.50367 0.211836
\(676\) 0 0
\(677\) 13.8984 0.534158 0.267079 0.963675i \(-0.413941\pi\)
0.267079 + 0.963675i \(0.413941\pi\)
\(678\) 0 0
\(679\) 0.416622 + 0.721611i 0.0159885 + 0.0276929i
\(680\) 0 0
\(681\) 11.2715i 0.431924i
\(682\) 0 0
\(683\) 32.6935 + 18.8756i 1.25098 + 0.722255i 0.971305 0.237838i \(-0.0764388\pi\)
0.279678 + 0.960094i \(0.409772\pi\)
\(684\) 0 0
\(685\) −8.99144 + 15.5736i −0.343545 + 0.595038i
\(686\) 0 0
\(687\) −1.84172 + 1.06332i −0.0702661 + 0.0405681i
\(688\) 0 0
\(689\) 5.54324 + 0.966794i 0.211181 + 0.0368319i
\(690\) 0 0
\(691\) 1.43146 0.826456i 0.0544554 0.0314399i −0.472525 0.881317i \(-0.656657\pi\)
0.526981 + 0.849877i \(0.323324\pi\)
\(692\) 0 0
\(693\) −0.392090 + 0.679120i −0.0148943 + 0.0257976i
\(694\) 0 0
\(695\) −10.3803 5.99307i −0.393747 0.227330i
\(696\) 0 0
\(697\) 18.9002i 0.715897i
\(698\) 0 0
\(699\) −0.998090 1.72874i −0.0377512 0.0653871i
\(700\) 0 0
\(701\) −20.4819 −0.773590 −0.386795 0.922166i \(-0.626418\pi\)
−0.386795 + 0.922166i \(0.626418\pi\)
\(702\) 0 0
\(703\) −13.5442 −0.510830
\(704\) 0 0
\(705\) −6.67510 11.5616i −0.251399 0.435435i
\(706\) 0 0
\(707\) 4.13538i 0.155527i
\(708\) 0 0
\(709\) 19.0021 + 10.9709i 0.713639 + 0.412020i 0.812407 0.583091i \(-0.198157\pi\)
−0.0987679 + 0.995110i \(0.531490\pi\)
\(710\) 0 0
\(711\) −0.992658 + 1.71933i −0.0372276 + 0.0644801i
\(712\) 0 0
\(713\) 13.4351 7.75678i 0.503150 0.290494i
\(714\) 0 0
\(715\) −6.65821 18.1879i −0.249003 0.680191i
\(716\) 0 0
\(717\) 13.7778 7.95463i 0.514542 0.297071i
\(718\) 0 0
\(719\) −19.4237 + 33.6429i −0.724384 + 1.25467i 0.234844 + 0.972033i \(0.424542\pi\)
−0.959227 + 0.282636i \(0.908791\pi\)
\(720\) 0 0
\(721\) −4.32312 2.49596i −0.161002 0.0929543i
\(722\) 0 0
\(723\) 36.1434i 1.34419i
\(724\) 0 0
\(725\) −1.45174 2.51448i −0.0539162 0.0933856i
\(726\) 0 0
\(727\) −30.6598 −1.13711 −0.568555 0.822645i \(-0.692497\pi\)
−0.568555 + 0.822645i \(0.692497\pi\)
\(728\) 0 0
\(729\) 29.7112 1.10042
\(730\) 0 0
\(731\) 12.8236 + 22.2110i 0.474296 + 0.821505i
\(732\) 0 0
\(733\) 24.3858i 0.900709i 0.892850 + 0.450355i \(0.148702\pi\)
−0.892850 + 0.450355i \(0.851298\pi\)
\(734\) 0 0
\(735\) 9.54769 + 5.51236i 0.352172 + 0.203327i
\(736\) 0 0
\(737\) 27.7515 48.0669i 1.02224 1.77057i
\(738\) 0 0
\(739\) 33.1504 19.1394i 1.21946 0.704054i 0.254656 0.967032i \(-0.418038\pi\)
0.964802 + 0.262977i \(0.0847044\pi\)
\(740\) 0 0
\(741\) −2.24823 + 12.8905i −0.0825909 + 0.473546i
\(742\) 0 0
\(743\) 34.6479 20.0040i 1.27111 0.733874i 0.295910 0.955216i \(-0.404377\pi\)
0.975196 + 0.221342i \(0.0710437\pi\)
\(744\) 0 0
\(745\) 1.70520 2.95350i 0.0624738 0.108208i
\(746\) 0 0
\(747\) 1.62238 + 0.936681i 0.0593598 + 0.0342714i
\(748\) 0 0
\(749\) 4.34057i 0.158601i
\(750\) 0 0
\(751\) −12.8010 22.1720i −0.467115 0.809067i 0.532179 0.846632i \(-0.321373\pi\)
−0.999294 + 0.0375648i \(0.988040\pi\)
\(752\) 0 0
\(753\) −10.8307 −0.394693
\(754\) 0 0
\(755\) 7.96141 0.289745
\(756\) 0 0
\(757\) 0.924239 + 1.60083i 0.0335920 + 0.0581831i 0.882333 0.470626i \(-0.155972\pi\)
−0.848741 + 0.528809i \(0.822639\pi\)
\(758\) 0 0
\(759\) 24.4055i 0.885862i
\(760\) 0 0
\(761\) 22.7006 + 13.1062i 0.822896 + 0.475099i 0.851414 0.524494i \(-0.175745\pi\)
−0.0285179 + 0.999593i \(0.509079\pi\)
\(762\) 0 0
\(763\) 1.86597 3.23196i 0.0675528 0.117005i
\(764\) 0 0
\(765\) 1.92701 1.11256i 0.0696712 0.0402247i
\(766\) 0 0
\(767\) 7.48932 + 6.26058i 0.270424 + 0.226056i
\(768\) 0 0
\(769\) −38.4078 + 22.1747i −1.38502 + 0.799641i −0.992749 0.120208i \(-0.961644\pi\)
−0.392271 + 0.919850i \(0.628310\pi\)
\(770\) 0 0
\(771\) −8.20406 + 14.2099i −0.295462 + 0.511755i
\(772\) 0 0
\(773\) 20.1471 + 11.6319i 0.724640 + 0.418371i 0.816458 0.577405i \(-0.195935\pi\)
−0.0918181 + 0.995776i \(0.529268\pi\)
\(774\) 0 0
\(775\) 5.46410i 0.196276i
\(776\) 0 0
\(777\) 1.58754 + 2.74970i 0.0569526 + 0.0986448i
\(778\) 0 0
\(779\) 8.46410 0.303258
\(780\) 0 0
\(781\) −68.7449 −2.45989
\(782\) 0 0
\(783\) −7.98989 13.8389i −0.285535 0.494562i
\(784\) 0 0
\(785\) 16.4329i 0.586514i
\(786\) 0 0
\(787\) 41.4942 + 23.9567i 1.47911 + 0.853963i 0.999721 0.0236408i \(-0.00752582\pi\)
0.479387 + 0.877604i \(0.340859\pi\)
\(788\) 0 0
\(789\) 14.9274 25.8551i 0.531430 0.920464i
\(790\) 0 0
\(791\) 5.27814 3.04734i 0.187669 0.108351i
\(792\) 0 0
\(793\) 32.6147 39.0158i 1.15818 1.38549i
\(794\) 0 0
\(795\) 2.16273 1.24865i 0.0767042 0.0442852i
\(796\) 0 0
\(797\) −10.3476 + 17.9225i