Properties

Label 1040.2.da.b.641.2
Level $1040$
Weight $2$
Character 1040.641
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 641.2
Root \(-1.27597 - 0.609843i\) of defining polynomial
Character \(\chi\) \(=\) 1040.641
Dual form 1040.2.da.b.881.2

$q$-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 \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).

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

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 −0.999057 0.0434075i \(-0.986179\pi\)
0.537121 + 0.843505i \(0.319512\pi\)
\(4\) 0 0
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 0.287734 0.166123i 0.108753 0.0627887i −0.444637 0.895711i \(-0.646667\pi\)
0.553390 + 0.832922i \(0.313334\pi\)
\(8\) 0 0
\(9\) 0.219687 + 0.380509i 0.0732290 + 0.126836i
\(10\) 0 0
\(11\) −4.65213 2.68591i −1.40267 0.809832i −0.408004 0.912980i \(-0.633775\pi\)
−0.994666 + 0.103149i \(0.967108\pi\)
\(12\) 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 −0.990535 0.137258i \(-0.956171\pi\)
0.376399 0.926458i \(-0.377162\pi\)
\(18\) 0 0
\(19\) 1.96410 1.13397i 0.450596 0.260152i −0.257486 0.966282i \(-0.582894\pi\)
0.708082 + 0.706130i \(0.249561\pi\)
\(20\) 0 0
\(21\) 0.531659i 0.116018i
\(22\) 0 0
\(23\) 1.41959 2.45880i 0.296005 0.512695i −0.679213 0.733941i \(-0.737679\pi\)
0.975218 + 0.221246i \(0.0710122\pi\)
\(24\) 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 −0.699173 0.714953i \(-0.746448\pi\)
0.968754 + 0.248025i \(0.0797815\pi\)
\(30\) 0 0
\(31\) 5.46410i 0.981382i 0.871334 + 0.490691i \(0.163256\pi\)
−0.871334 + 0.490691i \(0.836744\pi\)
\(32\) 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 0.0104803 0.999945i \(-0.496664\pi\)
−0.860738 + 0.509049i \(0.829997\pi\)
\(38\) 0 0
\(39\) 1.98340 5.41796i 0.317598 0.867568i
\(40\) 0 0
\(41\) 3.23205 + 1.86603i 0.504762 + 0.291424i 0.730678 0.682723i \(-0.239204\pi\)
−0.225916 + 0.974147i \(0.572538\pi\)
\(42\) 0 0
\(43\) 2.53215 + 4.38581i 0.386149 + 0.668830i 0.991928 0.126803i \(-0.0404717\pi\)
−0.605779 + 0.795633i \(0.707138\pi\)
\(44\) 0 0
\(45\) −0.380509 + 0.219687i −0.0567229 + 0.0327490i
\(46\) 0 0
\(47\) 8.34285i 1.21693i −0.793581 0.608465i \(-0.791786\pi\)
0.793581 0.608465i \(-0.208214\pi\)
\(48\) 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 −0.644795 0.764355i \(-0.723057\pi\)
0.339553 + 0.940587i \(0.389724\pi\)
\(60\) 0 0
\(61\) −7.05193 12.2143i −0.902908 1.56388i −0.823702 0.567023i \(-0.808095\pi\)
−0.0792059 0.996858i \(-0.525238\pi\)
\(62\) 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 −0.158752 0.987319i \(-0.550747\pi\)
−0.934419 + 0.356176i \(0.884080\pi\)
\(68\) 0 0
\(69\) 2.27162 + 3.93456i 0.273471 + 0.473666i
\(70\) 0 0
\(71\) 11.0828 6.39866i 1.31529 0.759382i 0.332321 0.943166i \(-0.392168\pi\)
0.982967 + 0.183785i \(0.0588349\pi\)
\(72\) 0 0
\(73\) 9.68922i 1.13404i −0.823705 0.567019i \(-0.808097\pi\)
0.823705 0.567019i \(-0.191903\pi\)
\(74\) 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 \(-0.924818\pi\)
0.972236 0.234001i \(-0.0751821\pi\)
\(84\) 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 0.344575 0.938759i \(-0.388023\pi\)
−0.640702 + 0.767790i \(0.721356\pi\)
\(90\) 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 −0.385669 0.922637i \(-0.626029\pi\)
0.606193 + 0.795318i \(0.292696\pi\)
\(98\) 0 0
\(99\) 2.36023i 0.237213i
\(100\) 0 0
\(101\) 6.22336 10.7792i 0.619247 1.07257i −0.370376 0.928882i \(-0.620771\pi\)
0.989623 0.143686i \(-0.0458955\pi\)
\(102\) 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 0.355761 + 0.934577i \(0.384222\pi\)
−0.987248 + 0.159190i \(0.949112\pi\)
\(108\) 0 0
\(109\) 11.2325i 1.07587i 0.842985 + 0.537937i \(0.180796\pi\)
−0.842985 + 0.537937i \(0.819204\pi\)
\(110\) 0 0
\(111\) 8.27607 4.77819i 0.785530 0.453526i
\(112\) 0 0
\(113\) 9.17191 + 15.8862i 0.862821 + 1.49445i 0.869195 + 0.494470i \(0.164638\pi\)
−0.00637349 + 0.999980i \(0.502029\pi\)
\(114\) 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 −0.928906 0.370316i \(-0.879249\pi\)
0.785156 + 0.619298i \(0.212583\pi\)
\(128\) 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 −0.985383 0.170353i \(-0.945509\pi\)
−0.345162 + 0.938543i \(0.612176\pi\)
\(138\) 0 0
\(139\) 5.99307 + 10.3803i 0.508325 + 0.880445i 0.999954 + 0.00964021i \(0.00306862\pi\)
−0.491628 + 0.870805i \(0.663598\pi\)
\(140\) 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 −0.374117 0.927381i \(-0.622054\pi\)
0.616077 + 0.787686i \(0.288721\pi\)
\(150\) 0 0
\(151\) 7.96141i 0.647890i −0.946076 0.323945i \(-0.894991\pi\)
0.946076 0.323945i \(-0.105009\pi\)
\(152\) 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 −0.962301 0.271986i \(-0.912320\pi\)
−0.245604 + 0.969370i \(0.578986\pi\)
\(164\) 0 0
\(165\) 4.29798 + 7.44432i 0.334597 + 0.579539i
\(166\) 0 0
\(167\) −5.45047 3.14683i −0.421770 0.243509i 0.274064 0.961711i \(-0.411632\pi\)
−0.695834 + 0.718202i \(0.744965\pi\)
\(168\) 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 0.991686 + 0.128679i \(0.0410738\pi\)
−0.384404 + 0.923165i \(0.625593\pi\)
\(174\) 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 −0.0342123 + 0.999415i \(0.510892\pi\)
−0.848412 + 0.529336i \(0.822441\pi\)
\(180\) 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 0.827254 0.561828i \(-0.189902\pi\)
−0.900184 + 0.435509i \(0.856568\pi\)
\(192\) 0 0
\(193\) −19.7636 11.4105i −1.42262 0.821348i −0.426095 0.904678i \(-0.640111\pi\)
−0.996522 + 0.0833298i \(0.973445\pi\)
\(194\) 0 0
\(195\) 5.41796 + 1.98340i 0.387988 + 0.142034i
\(196\) 0 0
\(197\) −0.556877 0.321513i −0.0396758 0.0229068i 0.480031 0.877252i \(-0.340625\pi\)
−0.519707 + 0.854345i \(0.673959\pi\)
\(198\) 0 0
\(199\) −1.53342 2.65596i −0.108701 0.188276i 0.806543 0.591175i \(-0.201336\pi\)
−0.915244 + 0.402899i \(0.868003\pi\)
\(200\) 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 −0.971943 0.235215i \(-0.924420\pi\)
0.689674 + 0.724120i \(0.257754\pi\)
\(212\) 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 0.172620 0.984989i \(-0.444777\pi\)
−0.766715 + 0.641987i \(0.778110\pi\)
\(224\) 0 0
\(225\) −0.219687 0.380509i −0.0146458 0.0253673i
\(226\) 0 0
\(227\) 6.10012 3.52190i 0.404879 0.233757i −0.283708 0.958911i \(-0.591565\pi\)
0.688587 + 0.725154i \(0.258231\pi\)
\(228\) 0 0
\(229\) 1.32899i 0.0878219i 0.999035 + 0.0439109i \(0.0139818\pi\)
−0.999035 + 0.0439109i \(0.986018\pi\)
\(230\) 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 \(-0.895796\pi\)
0.946893 0.321549i \(-0.104204\pi\)
\(240\) 0 0
\(241\) −19.5608 + 11.2934i −1.26002 + 0.727475i −0.973079 0.230472i \(-0.925973\pi\)
−0.286944 + 0.957947i \(0.592640\pi\)
\(242\) 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 0.952841 0.303470i \(-0.0981453\pi\)
−0.739233 + 0.673449i \(0.764812\pi\)
\(252\) 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 −0.980448 0.196779i \(-0.936952\pi\)
0.660640 + 0.750703i \(0.270285\pi\)
\(258\) 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 −0.420798 0.907154i \(-0.638250\pi\)
0.996018 0.0891555i \(-0.0284168\pi\)
\(264\) 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 −0.998448 0.0556934i \(-0.982263\pi\)
0.450992 0.892528i \(-0.351070\pi\)
\(270\) 0 0
\(271\) 26.7582 + 15.4488i 1.62544 + 0.938450i 0.985429 + 0.170086i \(0.0544047\pi\)
0.640014 + 0.768363i \(0.278929\pi\)
\(272\) 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 0.922042 + 0.387089i \(0.126519\pi\)
−0.125792 + 0.992057i \(0.540147\pi\)
\(278\) 0 0
\(279\) −2.07914 + 1.20039i −0.124475 + 0.0718656i
\(280\) 0 0
\(281\) 4.97766i 0.296942i 0.988917 + 0.148471i \(0.0474352\pi\)
−0.988917 + 0.148471i \(0.952565\pi\)
\(282\) 0 0
\(283\) 6.29317 10.9001i 0.374090 0.647943i −0.616100 0.787668i \(-0.711288\pi\)
0.990190 + 0.139725i \(0.0446218\pi\)
\(284\) 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 −0.00672072 0.999977i \(-0.502139\pi\)
0.862645 + 0.505809i \(0.168806\pi\)
\(294\) 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 \(0.0391965\pi\)
−0.992428 + 0.122828i \(0.960803\pi\)
\(308\) 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 \(0.00287522\pi\)
−0.999959 + 0.00903266i \(0.997125\pi\)
\(318\) 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 −0.0488600 0.998806i \(-0.515559\pi\)
0.840561 + 0.541717i \(0.182225\pi\)
\(332\) 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 0.769463 0.638692i \(-0.220524\pi\)
−0.937855 + 0.347028i \(0.887191\pi\)
\(348\) 0 0
\(349\) −6.12275 3.53497i −0.327743 0.189223i 0.327095 0.944991i \(-0.393930\pi\)
−0.654839 + 0.755769i \(0.727263\pi\)
\(350\) 0 0
\(351\) 19.5487 3.40948i 1.04343 0.181984i
\(352\) 0 0
\(353\) −18.8705 10.8949i −1.00438 0.579878i −0.0948371 0.995493i \(-0.530233\pi\)
−0.909541 + 0.415615i \(0.863566\pi\)
\(354\) 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 \(-0.781971\pi\)
0.774444 0.632642i \(-0.218029\pi\)
\(360\) 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 −0.770485 0.637458i \(-0.779986\pi\)
0.937297 + 0.348531i \(0.113319\pi\)
\(368\) 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 0.999734 + 0.0230798i \(0.00734719\pi\)
−0.479879 + 0.877335i \(0.659319\pi\)
\(374\) 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 0.616540 0.787324i \(-0.288534\pi\)
−0.373572 + 0.927601i \(0.621867\pi\)
\(380\) 0 0
\(381\) −2.59229 4.48997i −0.132807 0.230028i
\(382\) 0 0
\(383\) −4.90842 + 2.83388i −0.250808 + 0.144804i −0.620134 0.784496i \(-0.712922\pi\)
0.369326 + 0.929300i \(0.379589\pi\)
\(384\) 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 0.253884 0.967235i \(-0.418292\pi\)
0.964592 + 0.263748i \(0.0849586\pi\)
\(398\) 0 0
\(399\) 0.602888 + 1.04423i 0.0301822 + 0.0522770i
\(400\) 0 0
\(401\) 19.4979 + 11.2571i 0.973680 + 0.562155i 0.900356 0.435154i \(-0.143306\pi\)
0.0733241 + 0.997308i \(0.476639\pi\)
\(402\) 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 −0.588988 0.808142i \(-0.700473\pi\)
0.405378 + 0.914149i \(0.367140\pi\)
\(410\) 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 −0.564466 0.825456i \(-0.690918\pi\)
0.997099 + 0.0761137i \(0.0242512\pi\)
\(420\) 0 0
\(421\) 12.8787i 0.627672i −0.949477 0.313836i \(-0.898386\pi\)
0.949477 0.313836i \(-0.101614\pi\)
\(422\) 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 0.288627 0.957442i \(-0.406801\pi\)
−0.684855 + 0.728679i \(0.740134\pi\)
\(432\) 0 0
\(433\) −0.698141 1.20922i −0.0335505 0.0581112i 0.848763 0.528774i \(-0.177348\pi\)
−0.882313 + 0.470663i \(0.844015\pi\)
\(434\) 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 −0.911402 0.411518i \(-0.864999\pi\)
0.812086 + 0.583538i \(0.198332\pi\)
\(440\) 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 0.0144310 0.999896i \(-0.495406\pi\)
0.873151 + 0.487450i \(0.162073\pi\)
\(450\) 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 0.592599 0.805498i \(-0.298102\pi\)
−0.401282 + 0.915955i \(0.631435\pi\)
\(458\) 0 0
\(459\) 13.9361 + 24.1381i 0.650482 + 1.12667i
\(460\) 0 0
\(461\) 1.54283 0.890753i 0.0718568 0.0414865i −0.463641 0.886023i \(-0.653457\pi\)
0.535498 + 0.844537i \(0.320124\pi\)
\(462\) 0 0
\(463\) 6.80200i 0.316116i −0.987430 0.158058i \(-0.949477\pi\)
0.987430 0.158058i \(-0.0505232\pi\)
\(464\) 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 −0.398544 0.917149i \(-0.630485\pi\)
−0.993547 + 0.113425i \(0.963818\pi\)
\(480\) 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 −0.688365 0.725364i \(-0.741671\pi\)
0.284002 + 0.958824i \(0.408338\pi\)
\(488\) 0 0
\(489\) 28.4950i 1.28859i
\(490\) 0 0
\(491\) −4.66599 + 8.08174i −0.210573 + 0.364724i −0.951894 0.306427i \(-0.900866\pi\)
0.741321 + 0.671151i \(0.234200\pi\)
\(492\) 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 \(0.180026\pi\)
−0.844283 + 0.535897i \(0.819974\pi\)
\(500\) 0 0
\(501\) 8.72181 5.03554i 0.389662 0.224971i
\(502\) 0 0
\(503\) 21.0721 + 36.4980i 0.939560 + 1.62737i 0.766294 + 0.642490i \(0.222099\pi\)
0.173266 + 0.984875i \(0.444568\pi\)
\(504\) 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 −0.309899 0.950770i \(-0.600295\pi\)
−0.978340 + 0.207005i \(0.933629\pi\)
\(510\) 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 −0.921239 0.388998i \(-0.872821\pi\)
0.797501 + 0.603317i \(0.206155\pi\)
\(524\) 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 \(-0.892054\pi\)
0.943047 0.332660i \(-0.107946\pi\)
\(542\) 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 −0.997812 0.0661194i \(-0.978938\pi\)
−0.556167 0.831071i \(-0.687728\pi\)
\(558\) 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 −0.999999 0.00153173i \(-0.999512\pi\)
0.498673 0.866790i \(-0.333821\pi\)
\(564\) 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 0.436906 + 0.899507i \(0.356074\pi\)
−0.997449 + 0.0713817i \(0.977259\pi\)
\(570\) 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 \(0.141625\pi\)
−0.902642 + 0.430393i \(0.858375\pi\)
\(578\) 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 0.0799116 0.996802i \(-0.474536\pi\)
−0.823300 + 0.567606i \(0.807870\pi\)
\(588\) 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 \(-0.851928\pi\)
0.893740 0.448585i \(-0.148072\pi\)
\(594\) 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 −0.997329 0.0730352i \(-0.976731\pi\)
0.561915 + 0.827195i \(0.310065\pi\)
\(602\) 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 0.830598 0.556872i \(-0.187999\pi\)
−0.897565 + 0.440883i \(0.854665\pi\)
\(608\) 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 0.662838 0.748763i \(-0.269352\pi\)
−0.317029 + 0.948416i \(0.602685\pi\)
\(614\) 0 0
\(615\) −2.98601 5.17191i −0.120407 0.208552i
\(616\) 0 0
\(617\) 39.5920 22.8584i 1.59391 0.920246i 0.601287 0.799033i \(-0.294655\pi\)
0.992626 0.121213i \(-0.0386785\pi\)
\(618\) 0 0
\(619\) 19.9143i 0.800425i −0.916422 0.400212i \(-0.868936\pi\)
0.916422 0.400212i \(-0.131064\pi\)
\(620\) 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 −0.730036 0.683409i \(-0.760497\pi\)
0.226832 + 0.973934i \(0.427163\pi\)
\(632\) 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 0.691598 0.722282i \(-0.256907\pi\)
−0.971314 + 0.237801i \(0.923573\pi\)
\(642\) 0 0
\(643\) 14.5246 8.38581i 0.572796 0.330704i −0.185469 0.982650i \(-0.559380\pi\)
0.758265 + 0.651946i \(0.226047\pi\)
\(644\) 0 0
\(645\) 8.10387i 0.319089i
\(646\) 0 0
\(647\) 1.49584 2.59087i 0.0588075 0.101858i −0.835123 0.550063i \(-0.814604\pi\)
0.893930 + 0.448206i \(0.147937\pi\)
\(648\) 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 −0.729053 0.684457i \(-0.760039\pi\)
0.957284 + 0.289150i \(0.0933727\pi\)
\(654\) 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 0.847855 0.530228i \(-0.177894\pi\)
−0.883118 + 0.469150i \(0.844560\pi\)
\(660\) 0 0
\(661\) 10.6872 + 6.17028i 0.415686 + 0.239996i 0.693230 0.720717i \(-0.256187\pi\)
−0.277544 + 0.960713i \(0.589520\pi\)
\(662\) 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 −0.762805 0.646628i \(-0.776178\pi\)
0.941399 + 0.337295i \(0.109512\pi\)
\(674\) 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 0.279678 0.960094i \(-0.409772\pi\)
0.971305 + 0.237838i \(0.0764388\pi\)
\(684\) 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 0.526981 0.849877i \(-0.323324\pi\)
−0.472525 + 0.881317i \(0.656657\pi\)
\(692\) 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 −0.0987679 0.995110i \(-0.531490\pi\)
0.812407 + 0.583091i \(0.198157\pi\)
\(710\) 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 −0.959227 0.282636i \(-0.908791\pi\)
0.234844 0.972033i \(-0.424542\pi\)
\(720\) 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 \(-0.851298\pi\)
0.892850 0.450355i \(-0.148702\pi\)
\(734\) 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 0.964802 0.262977i \(-0.0847044\pi\)
0.254656 + 0.967032i \(0.418038\pi\)
\(740\) 0 0
\(741\) −2.24823 12.8905i −0.0825909 0.473546i
\(742\) 0 0
\(743\) 34.6479 + 20.0040i 1.27111 + 0.733874i 0.975196 0.221342i \(-0.0710437\pi\)
0.295910 + 0.955216i \(0.404377\pi\)
\(744\) 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 −0.999294 0.0375648i \(-0.988040\pi\)
0.532179 + 0.846632i \(0.321373\pi\)
\(752\) 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 −0.848741 0.528809i \(-0.822639\pi\)
0.882333 + 0.470626i \(0.155972\pi\)
\(758\) 0 0
\(759\) 24.4055i 0.885862i
\(760\) 0 0
\(761\) 22.7006 13.1062i 0.822896 0.475099i −0.0285179 0.999593i \(-0.509079\pi\)
0.851414 + 0.524494i \(0.175745\pi\)
\(762\) 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 −0.392271 0.919850i \(-0.628310\pi\)
−0.992749 + 0.120208i \(0.961644\pi\)
\(770\) 0 0
\(771\) −8.20406 14.2099i −0.295462 0.511755i
\(772\) 0 0
\(773\) 20.1471 11.6319i 0.724640 0.418371i −0.0918181 0.995776i \(-0.529268\pi\)
0.816458 + 0.577405i \(0.195935\pi\)
\(774\) 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 0.479387 0.877604i \(-0.340859\pi\)
0.999721 + 0.0236408i \(0.00752582\pi\)
\(788\) 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