Properties

Label 1183.2.e.j.508.4
Level $1183$
Weight $2$
Character 1183.508
Analytic conductor $9.446$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 508.4
Character \(\chi\) \(=\) 1183.508
Dual form 1183.2.e.j.170.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.672613 - 1.16500i) q^{2} +(-1.02505 + 1.77544i) q^{3} +(0.0951832 - 0.164862i) q^{4} +(-1.78389 - 3.08979i) q^{5} +2.75785 q^{6} +(2.62255 + 0.349630i) q^{7} -2.94654 q^{8} +(-0.601462 - 1.04176i) q^{9} +O(q^{10})\) \(q+(-0.672613 - 1.16500i) q^{2} +(-1.02505 + 1.77544i) q^{3} +(0.0951832 - 0.164862i) q^{4} +(-1.78389 - 3.08979i) q^{5} +2.75785 q^{6} +(2.62255 + 0.349630i) q^{7} -2.94654 q^{8} +(-0.601462 - 1.04176i) q^{9} +(-2.39973 + 4.15646i) q^{10} +(-0.639336 + 1.10736i) q^{11} +(0.195135 + 0.337984i) q^{12} +(-1.35664 - 3.29043i) q^{14} +7.31431 q^{15} +(1.79151 + 3.10299i) q^{16} +(-3.86960 + 6.70234i) q^{17} +(-0.809103 + 1.40141i) q^{18} +(0.471939 + 0.817422i) q^{19} -0.679185 q^{20} +(-3.30899 + 4.29779i) q^{21} +1.72010 q^{22} +(-0.823637 - 1.42658i) q^{23} +(3.02035 - 5.23141i) q^{24} +(-3.86451 + 6.69354i) q^{25} -3.68419 q^{27} +(0.307263 - 0.399080i) q^{28} +4.04484 q^{29} +(-4.91970 - 8.52117i) q^{30} +(2.57610 - 4.46193i) q^{31} +(-0.536547 + 0.929326i) q^{32} +(-1.31071 - 2.27021i) q^{33} +10.4110 q^{34} +(-3.59805 - 8.72681i) q^{35} -0.228996 q^{36} +(0.528041 + 0.914594i) q^{37} +(0.634865 - 1.09962i) q^{38} +(5.25629 + 9.10417i) q^{40} +4.19882 q^{41} +(7.23260 + 0.964227i) q^{42} +3.83065 q^{43} +(0.121708 + 0.210805i) q^{44} +(-2.14588 + 3.71678i) q^{45} +(-1.10798 + 1.91908i) q^{46} +(0.447109 + 0.774415i) q^{47} -7.34558 q^{48} +(6.75552 + 1.83384i) q^{49} +10.3973 q^{50} +(-7.93308 - 13.7405i) q^{51} +(0.0399961 - 0.0692754i) q^{53} +(2.47804 + 4.29208i) q^{54} +4.56202 q^{55} +(-7.72744 - 1.03020i) q^{56} -1.93505 q^{57} +(-2.72061 - 4.71224i) q^{58} +(-5.59237 + 9.68627i) q^{59} +(0.696200 - 1.20585i) q^{60} +(3.81196 + 6.60251i) q^{61} -6.93087 q^{62} +(-1.21313 - 2.94236i) q^{63} +8.60961 q^{64} +(-1.76319 + 3.05394i) q^{66} +(-3.16052 + 5.47418i) q^{67} +(0.736641 + 1.27590i) q^{68} +3.37708 q^{69} +(-7.74664 + 10.0615i) q^{70} +11.4240 q^{71} +(1.77223 + 3.06959i) q^{72} +(-0.380253 + 0.658617i) q^{73} +(0.710335 - 1.23034i) q^{74} +(-7.92265 - 13.7224i) q^{75} +0.179683 q^{76} +(-2.06386 + 2.68058i) q^{77} +(1.42765 + 2.47277i) q^{79} +(6.39172 - 11.0708i) q^{80} +(5.58087 - 9.66636i) q^{81} +(-2.82418 - 4.89163i) q^{82} -2.32483 q^{83} +(0.393583 + 0.954606i) q^{84} +27.6117 q^{85} +(-2.57654 - 4.46270i) q^{86} +(-4.14617 + 7.18137i) q^{87} +(1.88383 - 3.26289i) q^{88} +(3.78813 + 6.56124i) q^{89} +5.77339 q^{90} -0.313586 q^{92} +(5.28127 + 9.14742i) q^{93} +(0.601462 - 1.04176i) q^{94} +(1.68377 - 2.91638i) q^{95} +(-1.09998 - 1.90522i) q^{96} -0.478557 q^{97} +(-2.40742 - 9.10365i) q^{98} +1.53815 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 6q^{3} - 8q^{4} - 2q^{9} + O(q^{10}) \) \( 24q - 6q^{3} - 8q^{4} - 2q^{9} - 24q^{10} + 2q^{12} + 8q^{14} - 16q^{16} - 34q^{17} + 60q^{22} - 6q^{23} + 10q^{25} + 24q^{27} + 4q^{29} - 22q^{30} - 24q^{35} - 52q^{36} - 38q^{38} - 2q^{40} + 32q^{42} + 44q^{43} - 76q^{48} + 12q^{49} - 8q^{51} - 16q^{53} + 60q^{55} + 54q^{56} + 10q^{61} + 164q^{62} - 4q^{64} - 68q^{66} - 22q^{68} + 28q^{69} - 66q^{74} - 2q^{75} + 38q^{77} - 70q^{79} + 28q^{81} - 10q^{82} + 20q^{87} + 28q^{88} - 132q^{92} + 2q^{94} - 4q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.672613 1.16500i −0.475609 0.823779i 0.524000 0.851718i \(-0.324439\pi\)
−0.999610 + 0.0279386i \(0.991106\pi\)
\(3\) −1.02505 + 1.77544i −0.591814 + 1.02505i 0.402174 + 0.915563i \(0.368255\pi\)
−0.993988 + 0.109489i \(0.965079\pi\)
\(4\) 0.0951832 0.164862i 0.0475916 0.0824311i
\(5\) −1.78389 3.08979i −0.797779 1.38179i −0.921059 0.389422i \(-0.872675\pi\)
0.123280 0.992372i \(-0.460659\pi\)
\(6\) 2.75785 1.12589
\(7\) 2.62255 + 0.349630i 0.991230 + 0.132148i
\(8\) −2.94654 −1.04176
\(9\) −0.601462 1.04176i −0.200487 0.347254i
\(10\) −2.39973 + 4.15646i −0.758862 + 1.31439i
\(11\) −0.639336 + 1.10736i −0.192767 + 0.333882i −0.946166 0.323681i \(-0.895080\pi\)
0.753399 + 0.657563i \(0.228413\pi\)
\(12\) 0.195135 + 0.337984i 0.0563307 + 0.0975677i
\(13\) 0 0
\(14\) −1.35664 3.29043i −0.362578 0.879406i
\(15\) 7.31431 1.88855
\(16\) 1.79151 + 3.10299i 0.447878 + 0.775748i
\(17\) −3.86960 + 6.70234i −0.938515 + 1.62556i −0.170273 + 0.985397i \(0.554465\pi\)
−0.768242 + 0.640159i \(0.778868\pi\)
\(18\) −0.809103 + 1.40141i −0.190707 + 0.330315i
\(19\) 0.471939 + 0.817422i 0.108270 + 0.187530i 0.915070 0.403296i \(-0.132135\pi\)
−0.806799 + 0.590826i \(0.798802\pi\)
\(20\) −0.679185 −0.151870
\(21\) −3.30899 + 4.29779i −0.722082 + 0.937855i
\(22\) 1.72010 0.366727
\(23\) −0.823637 1.42658i −0.171740 0.297463i 0.767288 0.641303i \(-0.221606\pi\)
−0.939028 + 0.343840i \(0.888272\pi\)
\(24\) 3.02035 5.23141i 0.616527 1.06786i
\(25\) −3.86451 + 6.69354i −0.772903 + 1.33871i
\(26\) 0 0
\(27\) −3.68419 −0.709023
\(28\) 0.307263 0.399080i 0.0580673 0.0754190i
\(29\) 4.04484 0.751107 0.375554 0.926801i \(-0.377453\pi\)
0.375554 + 0.926801i \(0.377453\pi\)
\(30\) −4.91970 8.52117i −0.898210 1.55575i
\(31\) 2.57610 4.46193i 0.462681 0.801387i −0.536413 0.843956i \(-0.680221\pi\)
0.999094 + 0.0425691i \(0.0135543\pi\)
\(32\) −0.536547 + 0.929326i −0.0948490 + 0.164283i
\(33\) −1.31071 2.27021i −0.228164 0.395192i
\(34\) 10.4110 1.78547
\(35\) −3.59805 8.72681i −0.608182 1.47510i
\(36\) −0.228996 −0.0381661
\(37\) 0.528041 + 0.914594i 0.0868094 + 0.150358i 0.906161 0.422933i \(-0.139000\pi\)
−0.819351 + 0.573292i \(0.805666\pi\)
\(38\) 0.634865 1.09962i 0.102989 0.178382i
\(39\) 0 0
\(40\) 5.25629 + 9.10417i 0.831093 + 1.43950i
\(41\) 4.19882 0.655746 0.327873 0.944722i \(-0.393668\pi\)
0.327873 + 0.944722i \(0.393668\pi\)
\(42\) 7.23260 + 0.964227i 1.11601 + 0.148784i
\(43\) 3.83065 0.584168 0.292084 0.956393i \(-0.405651\pi\)
0.292084 + 0.956393i \(0.405651\pi\)
\(44\) 0.121708 + 0.210805i 0.0183482 + 0.0317800i
\(45\) −2.14588 + 3.71678i −0.319889 + 0.554064i
\(46\) −1.10798 + 1.91908i −0.163363 + 0.282952i
\(47\) 0.447109 + 0.774415i 0.0652175 + 0.112960i 0.896790 0.442456i \(-0.145893\pi\)
−0.831573 + 0.555416i \(0.812559\pi\)
\(48\) −7.34558 −1.06024
\(49\) 6.75552 + 1.83384i 0.965074 + 0.261977i
\(50\) 10.3973 1.47040
\(51\) −7.93308 13.7405i −1.11085 1.92405i
\(52\) 0 0
\(53\) 0.0399961 0.0692754i 0.00549389 0.00951570i −0.863265 0.504750i \(-0.831585\pi\)
0.868759 + 0.495235i \(0.164918\pi\)
\(54\) 2.47804 + 4.29208i 0.337218 + 0.584079i
\(55\) 4.56202 0.615142
\(56\) −7.72744 1.03020i −1.03262 0.137666i
\(57\) −1.93505 −0.256303
\(58\) −2.72061 4.71224i −0.357234 0.618747i
\(59\) −5.59237 + 9.68627i −0.728064 + 1.26104i 0.229636 + 0.973277i \(0.426246\pi\)
−0.957700 + 0.287768i \(0.907087\pi\)
\(60\) 0.696200 1.20585i 0.0898790 0.155675i
\(61\) 3.81196 + 6.60251i 0.488072 + 0.845365i 0.999906 0.0137195i \(-0.00436719\pi\)
−0.511834 + 0.859084i \(0.671034\pi\)
\(62\) −6.93087 −0.880221
\(63\) −1.21313 2.94236i −0.152840 0.370703i
\(64\) 8.60961 1.07620
\(65\) 0 0
\(66\) −1.76319 + 3.05394i −0.217034 + 0.375914i
\(67\) −3.16052 + 5.47418i −0.386119 + 0.668777i −0.991924 0.126836i \(-0.959518\pi\)
0.605805 + 0.795613i \(0.292851\pi\)
\(68\) 0.736641 + 1.27590i 0.0893309 + 0.154726i
\(69\) 3.37708 0.406553
\(70\) −7.74664 + 10.0615i −0.925900 + 1.20258i
\(71\) 11.4240 1.35578 0.677889 0.735165i \(-0.262895\pi\)
0.677889 + 0.735165i \(0.262895\pi\)
\(72\) 1.77223 + 3.06959i 0.208859 + 0.361755i
\(73\) −0.380253 + 0.658617i −0.0445052 + 0.0770853i −0.887420 0.460962i \(-0.847504\pi\)
0.842915 + 0.538047i \(0.180838\pi\)
\(74\) 0.710335 1.23034i 0.0825747 0.143024i
\(75\) −7.92265 13.7224i −0.914829 1.58453i
\(76\) 0.179683 0.0206110
\(77\) −2.06386 + 2.68058i −0.235198 + 0.305481i
\(78\) 0 0
\(79\) 1.42765 + 2.47277i 0.160624 + 0.278208i 0.935093 0.354404i \(-0.115316\pi\)
−0.774469 + 0.632612i \(0.781983\pi\)
\(80\) 6.39172 11.0708i 0.714616 1.23775i
\(81\) 5.58087 9.66636i 0.620097 1.07404i
\(82\) −2.82418 4.89163i −0.311879 0.540190i
\(83\) −2.32483 −0.255183 −0.127591 0.991827i \(-0.540725\pi\)
−0.127591 + 0.991827i \(0.540725\pi\)
\(84\) 0.393583 + 0.954606i 0.0429434 + 0.104156i
\(85\) 27.6117 2.99491
\(86\) −2.57654 4.46270i −0.277836 0.481226i
\(87\) −4.14617 + 7.18137i −0.444516 + 0.769924i
\(88\) 1.88383 3.26289i 0.200817 0.347825i
\(89\) 3.78813 + 6.56124i 0.401541 + 0.695490i 0.993912 0.110176i \(-0.0351414\pi\)
−0.592371 + 0.805665i \(0.701808\pi\)
\(90\) 5.77339 0.608569
\(91\) 0 0
\(92\) −0.313586 −0.0326936
\(93\) 5.28127 + 9.14742i 0.547642 + 0.948544i
\(94\) 0.601462 1.04176i 0.0620361 0.107450i
\(95\) 1.68377 2.91638i 0.172751 0.299214i
\(96\) −1.09998 1.90522i −0.112266 0.194450i
\(97\) −0.478557 −0.0485901 −0.0242951 0.999705i \(-0.507734\pi\)
−0.0242951 + 0.999705i \(0.507734\pi\)
\(98\) −2.40742 9.10365i −0.243187 0.919607i
\(99\) 1.53815 0.154589
\(100\) 0.735674 + 1.27422i 0.0735674 + 0.127422i
\(101\) −1.43918 + 2.49273i −0.143204 + 0.248036i −0.928701 0.370829i \(-0.879074\pi\)
0.785498 + 0.618865i \(0.212407\pi\)
\(102\) −10.6718 + 18.4841i −1.05666 + 1.83020i
\(103\) 5.66755 + 9.81649i 0.558441 + 0.967248i 0.997627 + 0.0688516i \(0.0219335\pi\)
−0.439186 + 0.898396i \(0.644733\pi\)
\(104\) 0 0
\(105\) 19.1821 + 2.55730i 1.87198 + 0.249567i
\(106\) −0.107608 −0.0104518
\(107\) 3.28603 + 5.69157i 0.317673 + 0.550225i 0.980002 0.198988i \(-0.0637653\pi\)
−0.662329 + 0.749213i \(0.730432\pi\)
\(108\) −0.350673 + 0.607384i −0.0337435 + 0.0584455i
\(109\) −2.91957 + 5.05684i −0.279644 + 0.484358i −0.971296 0.237873i \(-0.923550\pi\)
0.691652 + 0.722231i \(0.256883\pi\)
\(110\) −3.06847 5.31475i −0.292567 0.506741i
\(111\) −2.16508 −0.205500
\(112\) 3.61343 + 8.76412i 0.341437 + 0.828131i
\(113\) 6.53233 0.614510 0.307255 0.951627i \(-0.400590\pi\)
0.307255 + 0.951627i \(0.400590\pi\)
\(114\) 1.30154 + 2.25433i 0.121900 + 0.211137i
\(115\) −2.93855 + 5.08973i −0.274022 + 0.474619i
\(116\) 0.385001 0.666841i 0.0357464 0.0619146i
\(117\) 0 0
\(118\) 15.0460 1.38510
\(119\) −12.4915 + 16.2243i −1.14510 + 1.48728i
\(120\) −21.5519 −1.96741
\(121\) 4.68250 + 8.11033i 0.425682 + 0.737302i
\(122\) 5.12795 8.88187i 0.464263 0.804127i
\(123\) −4.30401 + 7.45477i −0.388080 + 0.672174i
\(124\) −0.490402 0.849402i −0.0440394 0.0762786i
\(125\) 9.73656 0.870865
\(126\) −2.61188 + 3.39237i −0.232685 + 0.302216i
\(127\) 14.7164 1.30586 0.652932 0.757416i \(-0.273539\pi\)
0.652932 + 0.757416i \(0.273539\pi\)
\(128\) −4.71784 8.17154i −0.417002 0.722269i
\(129\) −3.92661 + 6.80109i −0.345719 + 0.598802i
\(130\) 0 0
\(131\) −5.59335 9.68796i −0.488693 0.846441i 0.511222 0.859448i \(-0.329193\pi\)
−0.999915 + 0.0130074i \(0.995860\pi\)
\(132\) −0.499028 −0.0434349
\(133\) 0.951888 + 2.30873i 0.0825391 + 0.200193i
\(134\) 8.50322 0.734566
\(135\) 6.57219 + 11.3834i 0.565644 + 0.979724i
\(136\) 11.4019 19.7487i 0.977706 1.69344i
\(137\) 8.81541 15.2687i 0.753151 1.30450i −0.193137 0.981172i \(-0.561866\pi\)
0.946288 0.323324i \(-0.104800\pi\)
\(138\) −2.27147 3.93430i −0.193360 0.334910i
\(139\) −5.85710 −0.496793 −0.248396 0.968658i \(-0.579904\pi\)
−0.248396 + 0.968658i \(0.579904\pi\)
\(140\) −1.78119 0.237463i −0.150538 0.0200693i
\(141\) −1.83324 −0.154386
\(142\) −7.68392 13.3089i −0.644820 1.11686i
\(143\) 0 0
\(144\) 2.15506 3.73267i 0.179588 0.311055i
\(145\) −7.21554 12.4977i −0.599218 1.03788i
\(146\) 1.02305 0.0846684
\(147\) −10.1806 + 10.1142i −0.839685 + 0.834209i
\(148\) 0.201043 0.0165256
\(149\) 5.23948 + 9.07505i 0.429235 + 0.743457i 0.996805 0.0798677i \(-0.0254498\pi\)
−0.567570 + 0.823325i \(0.692116\pi\)
\(150\) −10.6578 + 18.4598i −0.870203 + 1.50724i
\(151\) 2.35703 4.08249i 0.191812 0.332229i −0.754039 0.656830i \(-0.771897\pi\)
0.945851 + 0.324602i \(0.105230\pi\)
\(152\) −1.39059 2.40857i −0.112791 0.195361i
\(153\) 9.30967 0.752642
\(154\) 4.51105 + 0.601399i 0.363511 + 0.0484621i
\(155\) −18.3819 −1.47647
\(156\) 0 0
\(157\) −4.50105 + 7.79604i −0.359223 + 0.622192i −0.987831 0.155530i \(-0.950291\pi\)
0.628608 + 0.777722i \(0.283625\pi\)
\(158\) 1.92052 3.32643i 0.152788 0.264637i
\(159\) 0.0819962 + 0.142022i 0.00650272 + 0.0112630i
\(160\) 3.82856 0.302674
\(161\) −1.66125 4.02925i −0.130925 0.317549i
\(162\) −15.0151 −1.17970
\(163\) −6.01619 10.4203i −0.471224 0.816185i 0.528234 0.849099i \(-0.322854\pi\)
−0.999458 + 0.0329144i \(0.989521\pi\)
\(164\) 0.399657 0.692227i 0.0312080 0.0540538i
\(165\) −4.67630 + 8.09959i −0.364050 + 0.630553i
\(166\) 1.56371 + 2.70842i 0.121367 + 0.210214i
\(167\) −19.4220 −1.50292 −0.751459 0.659780i \(-0.770650\pi\)
−0.751459 + 0.659780i \(0.770650\pi\)
\(168\) 9.75008 12.6636i 0.752235 0.977019i
\(169\) 0 0
\(170\) −18.5720 32.1677i −1.42441 2.46715i
\(171\) 0.567707 0.983297i 0.0434136 0.0751946i
\(172\) 0.364613 0.631528i 0.0278015 0.0481536i
\(173\) −7.18976 12.4530i −0.546627 0.946786i −0.998503 0.0547049i \(-0.982578\pi\)
0.451875 0.892081i \(-0.350755\pi\)
\(174\) 11.1551 0.845663
\(175\) −12.4751 + 16.2030i −0.943031 + 1.22483i
\(176\) −4.58152 −0.345345
\(177\) −11.4649 19.8578i −0.861757 1.49261i
\(178\) 5.09589 8.82635i 0.381953 0.661563i
\(179\) −2.71303 + 4.69911i −0.202781 + 0.351228i −0.949424 0.313998i \(-0.898331\pi\)
0.746642 + 0.665226i \(0.231665\pi\)
\(180\) 0.408504 + 0.707550i 0.0304481 + 0.0527376i
\(181\) 15.4902 1.15138 0.575688 0.817669i \(-0.304734\pi\)
0.575688 + 0.817669i \(0.304734\pi\)
\(182\) 0 0
\(183\) −15.6298 −1.15539
\(184\) 2.42688 + 4.20348i 0.178912 + 0.309885i
\(185\) 1.88393 3.26307i 0.138509 0.239905i
\(186\) 7.10450 12.3054i 0.520927 0.902272i
\(187\) −4.94795 8.57010i −0.361830 0.626707i
\(188\) 0.170229 0.0124152
\(189\) −9.66197 1.28810i −0.702805 0.0936957i
\(190\) −4.53011 −0.328649
\(191\) −2.37311 4.11035i −0.171712 0.297414i 0.767306 0.641281i \(-0.221597\pi\)
−0.939019 + 0.343866i \(0.888263\pi\)
\(192\) −8.82529 + 15.2859i −0.636911 + 1.10316i
\(193\) 10.5196 18.2204i 0.757215 1.31154i −0.187050 0.982350i \(-0.559893\pi\)
0.944266 0.329185i \(-0.106774\pi\)
\(194\) 0.321884 + 0.557519i 0.0231099 + 0.0400276i
\(195\) 0 0
\(196\) 0.945343 0.939178i 0.0675245 0.0670842i
\(197\) −5.81209 −0.414094 −0.207047 0.978331i \(-0.566385\pi\)
−0.207047 + 0.978331i \(0.566385\pi\)
\(198\) −1.03458 1.79194i −0.0735242 0.127348i
\(199\) −5.30909 + 9.19562i −0.376352 + 0.651860i −0.990528 0.137309i \(-0.956155\pi\)
0.614177 + 0.789168i \(0.289488\pi\)
\(200\) 11.3869 19.7228i 0.805178 1.39461i
\(201\) −6.47939 11.2226i −0.457021 0.791583i
\(202\) 3.87204 0.272436
\(203\) 10.6078 + 1.41420i 0.744520 + 0.0992571i
\(204\) −3.02038 −0.211469
\(205\) −7.49023 12.9735i −0.523140 0.906106i
\(206\) 7.62414 13.2054i 0.531199 0.920064i
\(207\) −0.990773 + 1.71607i −0.0688635 + 0.119275i
\(208\) 0 0
\(209\) −1.20691 −0.0834837
\(210\) −9.92290 24.0673i −0.684745 1.66080i
\(211\) −4.66549 −0.321186 −0.160593 0.987021i \(-0.551341\pi\)
−0.160593 + 0.987021i \(0.551341\pi\)
\(212\) −0.00761392 0.0131877i −0.000522926 0.000905735i
\(213\) −11.7102 + 20.2826i −0.802368 + 1.38974i
\(214\) 4.42046 7.65645i 0.302176 0.523384i
\(215\) −6.83344 11.8359i −0.466037 0.807200i
\(216\) 10.8556 0.738631
\(217\) 8.31596 10.8010i 0.564524 0.733216i
\(218\) 7.85497 0.532005
\(219\) −0.779558 1.35023i −0.0526776 0.0912403i
\(220\) 0.434227 0.752104i 0.0292756 0.0507068i
\(221\) 0 0
\(222\) 1.45626 + 2.52232i 0.0977377 + 0.169287i
\(223\) −24.2254 −1.62225 −0.811126 0.584871i \(-0.801145\pi\)
−0.811126 + 0.584871i \(0.801145\pi\)
\(224\) −1.73204 + 2.24961i −0.115727 + 0.150308i
\(225\) 9.29744 0.619829
\(226\) −4.39373 7.61017i −0.292267 0.506221i
\(227\) −7.68764 + 13.3154i −0.510247 + 0.883773i 0.489683 + 0.871901i \(0.337113\pi\)
−0.999930 + 0.0118726i \(0.996221\pi\)
\(228\) −0.184184 + 0.319016i −0.0121979 + 0.0211274i
\(229\) −8.17573 14.1608i −0.540268 0.935771i −0.998888 0.0471389i \(-0.984990\pi\)
0.458621 0.888632i \(-0.348344\pi\)
\(230\) 7.90604 0.521309
\(231\) −2.64366 6.41199i −0.173940 0.421878i
\(232\) −11.9183 −0.782473
\(233\) 14.5554 + 25.2106i 0.953554 + 1.65160i 0.737643 + 0.675191i \(0.235939\pi\)
0.215911 + 0.976413i \(0.430728\pi\)
\(234\) 0 0
\(235\) 1.59518 2.76294i 0.104058 0.180234i
\(236\) 1.06460 + 1.84394i 0.0692995 + 0.120030i
\(237\) −5.85368 −0.380237
\(238\) 27.3033 + 3.63998i 1.76981 + 0.235945i
\(239\) 8.65409 0.559787 0.279893 0.960031i \(-0.409701\pi\)
0.279893 + 0.960031i \(0.409701\pi\)
\(240\) 13.1037 + 22.6963i 0.845840 + 1.46504i
\(241\) −9.09909 + 15.7601i −0.586124 + 1.01520i 0.408611 + 0.912709i \(0.366013\pi\)
−0.994734 + 0.102487i \(0.967320\pi\)
\(242\) 6.29902 10.9102i 0.404916 0.701336i
\(243\) 5.91508 + 10.2452i 0.379453 + 0.657231i
\(244\) 1.45134 0.0929124
\(245\) −6.38491 24.1445i −0.407917 1.54253i
\(246\) 11.5797 0.738297
\(247\) 0 0
\(248\) −7.59057 + 13.1473i −0.482002 + 0.834851i
\(249\) 2.38307 4.12759i 0.151021 0.261576i
\(250\) −6.54894 11.3431i −0.414191 0.717400i
\(251\) 15.8720 1.00183 0.500915 0.865497i \(-0.332997\pi\)
0.500915 + 0.865497i \(0.332997\pi\)
\(252\) −0.600554 0.0800639i −0.0378313 0.00504355i
\(253\) 2.10632 0.132423
\(254\) −9.89841 17.1446i −0.621082 1.07574i
\(255\) −28.3034 + 49.0230i −1.77243 + 3.06994i
\(256\) 2.26304 3.91971i 0.141440 0.244982i
\(257\) 12.1634 + 21.0676i 0.758730 + 1.31416i 0.943499 + 0.331376i \(0.107513\pi\)
−0.184769 + 0.982782i \(0.559154\pi\)
\(258\) 10.5644 0.657708
\(259\) 1.06504 + 2.58319i 0.0661786 + 0.160511i
\(260\) 0 0
\(261\) −2.43282 4.21376i −0.150588 0.260825i
\(262\) −7.52432 + 13.0325i −0.464854 + 0.805150i
\(263\) −7.71727 + 13.3667i −0.475867 + 0.824226i −0.999618 0.0276456i \(-0.991199\pi\)
0.523751 + 0.851872i \(0.324532\pi\)
\(264\) 3.86204 + 6.68925i 0.237692 + 0.411695i
\(265\) −0.285395 −0.0175317
\(266\) 2.04942 2.66183i 0.125658 0.163207i
\(267\) −15.5321 −0.950550
\(268\) 0.601656 + 1.04210i 0.0367520 + 0.0636563i
\(269\) 6.52035 11.2936i 0.397553 0.688582i −0.595870 0.803081i \(-0.703193\pi\)
0.993423 + 0.114499i \(0.0365261\pi\)
\(270\) 8.84108 15.3132i 0.538051 0.931931i
\(271\) 13.4853 + 23.3572i 0.819174 + 1.41885i 0.906291 + 0.422654i \(0.138901\pi\)
−0.0871168 + 0.996198i \(0.527765\pi\)
\(272\) −27.7298 −1.68136
\(273\) 0 0
\(274\) −23.7174 −1.43282
\(275\) −4.94145 8.55884i −0.297980 0.516117i
\(276\) 0.321442 0.556753i 0.0193485 0.0335126i
\(277\) −6.35073 + 10.9998i −0.381578 + 0.660913i −0.991288 0.131712i \(-0.957953\pi\)
0.609710 + 0.792625i \(0.291286\pi\)
\(278\) 3.93956 + 6.82352i 0.236279 + 0.409248i
\(279\) −6.19770 −0.371047
\(280\) 10.6018 + 25.7139i 0.633579 + 1.53670i
\(281\) −26.7216 −1.59408 −0.797038 0.603930i \(-0.793601\pi\)
−0.797038 + 0.603930i \(0.793601\pi\)
\(282\) 1.23306 + 2.13572i 0.0734276 + 0.127180i
\(283\) −7.37113 + 12.7672i −0.438168 + 0.758929i −0.997548 0.0699819i \(-0.977706\pi\)
0.559380 + 0.828911i \(0.311039\pi\)
\(284\) 1.08737 1.88338i 0.0645236 0.111758i
\(285\) 3.45191 + 5.97888i 0.204473 + 0.354158i
\(286\) 0 0
\(287\) 11.0116 + 1.46803i 0.649995 + 0.0866553i
\(288\) 1.29085 0.0760641
\(289\) −21.4476 37.1483i −1.26162 2.18519i
\(290\) −9.70653 + 16.8122i −0.569987 + 0.987247i
\(291\) 0.490546 0.849651i 0.0287563 0.0498074i
\(292\) 0.0723874 + 0.125379i 0.00423615 + 0.00733723i
\(293\) 11.5831 0.676689 0.338345 0.941022i \(-0.390133\pi\)
0.338345 + 0.941022i \(0.390133\pi\)
\(294\) 18.6307 + 5.05747i 1.08657 + 0.294957i
\(295\) 39.9046 2.32334
\(296\) −1.55589 2.69489i −0.0904344 0.156637i
\(297\) 2.35544 4.07974i 0.136676 0.236730i
\(298\) 7.04829 12.2080i 0.408297 0.707190i
\(299\) 0 0
\(300\) −3.01641 −0.174153
\(301\) 10.0461 + 1.33931i 0.579045 + 0.0771964i
\(302\) −6.34147 −0.364911
\(303\) −2.95047 5.11036i −0.169500 0.293582i
\(304\) −1.69097 + 2.92885i −0.0969838 + 0.167981i
\(305\) 13.6002 23.5563i 0.778746 1.34883i
\(306\) −6.26180 10.8458i −0.357963 0.620011i
\(307\) −29.3335 −1.67415 −0.837076 0.547086i \(-0.815737\pi\)
−0.837076 + 0.547086i \(0.815737\pi\)
\(308\) 0.245482 + 0.595398i 0.0139876 + 0.0339260i
\(309\) −23.2381 −1.32197
\(310\) 12.3639 + 21.4149i 0.702222 + 1.21628i
\(311\) 0.0753271 0.130470i 0.00427141 0.00739830i −0.863882 0.503695i \(-0.831974\pi\)
0.868153 + 0.496296i \(0.165307\pi\)
\(312\) 0 0
\(313\) 5.26057 + 9.11157i 0.297345 + 0.515016i 0.975528 0.219877i \(-0.0705656\pi\)
−0.678183 + 0.734893i \(0.737232\pi\)
\(314\) 12.1099 0.683399
\(315\) −6.92718 + 8.99716i −0.390302 + 0.506933i
\(316\) 0.543555 0.0305773
\(317\) −0.753380 1.30489i −0.0423140 0.0732901i 0.844093 0.536197i \(-0.180140\pi\)
−0.886407 + 0.462907i \(0.846806\pi\)
\(318\) 0.110303 0.191051i 0.00618551 0.0107136i
\(319\) −2.58601 + 4.47910i −0.144789 + 0.250782i
\(320\) −15.3586 26.6018i −0.858571 1.48709i
\(321\) −13.4734 −0.752012
\(322\) −3.57669 + 4.64549i −0.199321 + 0.258883i
\(323\) −7.30486 −0.406453
\(324\) −1.06241 1.84015i −0.0590228 0.102231i
\(325\) 0 0
\(326\) −8.09314 + 14.0177i −0.448237 + 0.776370i
\(327\) −5.98542 10.3671i −0.330995 0.573299i
\(328\) −12.3720 −0.683129
\(329\) 0.901805 + 2.18726i 0.0497181 + 0.120588i
\(330\) 12.5814 0.692582
\(331\) −12.6254 21.8679i −0.693957 1.20197i −0.970531 0.240976i \(-0.922533\pi\)
0.276574 0.960993i \(-0.410801\pi\)
\(332\) −0.221284 + 0.383276i −0.0121446 + 0.0210350i
\(333\) 0.635193 1.10019i 0.0348084 0.0602899i
\(334\) 13.0635 + 22.6266i 0.714802 + 1.23807i
\(335\) 22.5520 1.23215
\(336\) −19.2641 2.56823i −1.05094 0.140109i
\(337\) −32.1811 −1.75302 −0.876509 0.481386i \(-0.840134\pi\)
−0.876509 + 0.481386i \(0.840134\pi\)
\(338\) 0 0
\(339\) −6.69598 + 11.5978i −0.363676 + 0.629905i
\(340\) 2.62817 4.55213i 0.142533 0.246874i
\(341\) 3.29398 + 5.70535i 0.178379 + 0.308962i
\(342\) −1.52739 −0.0825917
\(343\) 17.0755 + 7.17127i 0.921991 + 0.387212i
\(344\) −11.2871 −0.608562
\(345\) −6.02434 10.4345i −0.324340 0.561773i
\(346\) −9.67185 + 16.7521i −0.519962 + 0.900600i
\(347\) −12.3819 + 21.4461i −0.664695 + 1.15128i 0.314673 + 0.949200i \(0.398105\pi\)
−0.979368 + 0.202085i \(0.935228\pi\)
\(348\) 0.789291 + 1.36709i 0.0423104 + 0.0732838i
\(349\) −11.5556 −0.618559 −0.309280 0.950971i \(-0.600088\pi\)
−0.309280 + 0.950971i \(0.600088\pi\)
\(350\) 27.2674 + 3.63520i 1.45750 + 0.194310i
\(351\) 0 0
\(352\) −0.686067 1.18830i −0.0365675 0.0633368i
\(353\) 10.0442 17.3971i 0.534599 0.925953i −0.464583 0.885529i \(-0.653796\pi\)
0.999183 0.0404237i \(-0.0128708\pi\)
\(354\) −15.4229 + 26.7133i −0.819719 + 1.41980i
\(355\) −20.3791 35.2977i −1.08161 1.87340i
\(356\) 1.44227 0.0764399
\(357\) −16.0008 38.8087i −0.846852 2.05398i
\(358\) 7.29928 0.385779
\(359\) 7.52551 + 13.0346i 0.397181 + 0.687938i 0.993377 0.114901i \(-0.0366551\pi\)
−0.596196 + 0.802839i \(0.703322\pi\)
\(360\) 6.32292 10.9516i 0.333247 0.577201i
\(361\) 9.05455 15.6829i 0.476555 0.825418i
\(362\) −10.4189 18.0461i −0.547606 0.948481i
\(363\) −19.1992 −1.00770
\(364\) 0 0
\(365\) 2.71331 0.142021
\(366\) 10.5128 + 18.2087i 0.549514 + 0.951787i
\(367\) −4.50178 + 7.79731i −0.234991 + 0.407016i −0.959270 0.282491i \(-0.908839\pi\)
0.724279 + 0.689507i \(0.242173\pi\)
\(368\) 2.95112 5.11148i 0.153838 0.266454i
\(369\) −2.52543 4.37418i −0.131469 0.227711i
\(370\) −5.06863 −0.263506
\(371\) 0.129113 0.167694i 0.00670319 0.00870624i
\(372\) 2.01075 0.104253
\(373\) 8.06953 + 13.9768i 0.417824 + 0.723693i 0.995720 0.0924174i \(-0.0294594\pi\)
−0.577896 + 0.816110i \(0.696126\pi\)
\(374\) −6.65611 + 11.5287i −0.344179 + 0.596136i
\(375\) −9.98048 + 17.2867i −0.515390 + 0.892681i
\(376\) −1.31742 2.28184i −0.0679409 0.117677i
\(377\) 0 0
\(378\) 4.99813 + 12.1226i 0.257076 + 0.623519i
\(379\) 15.6655 0.804685 0.402342 0.915489i \(-0.368196\pi\)
0.402342 + 0.915489i \(0.368196\pi\)
\(380\) −0.320534 0.555181i −0.0164430 0.0284802i
\(381\) −15.0850 + 26.1280i −0.772829 + 1.33858i
\(382\) −3.19237 + 5.52935i −0.163336 + 0.282906i
\(383\) 12.3164 + 21.3327i 0.629339 + 1.09005i 0.987685 + 0.156459i \(0.0500078\pi\)
−0.358345 + 0.933589i \(0.616659\pi\)
\(384\) 19.3441 0.987151
\(385\) 11.9641 + 1.59502i 0.609747 + 0.0812896i
\(386\) −28.3024 −1.44055
\(387\) −2.30399 3.99062i −0.117118 0.202855i
\(388\) −0.0455506 + 0.0788960i −0.00231248 + 0.00400534i
\(389\) 9.42834 16.3304i 0.478036 0.827982i −0.521647 0.853161i \(-0.674682\pi\)
0.999683 + 0.0251791i \(0.00801560\pi\)
\(390\) 0 0
\(391\) 12.7486 0.644724
\(392\) −19.9054 5.40348i −1.00537 0.272917i
\(393\) 22.9339 1.15686
\(394\) 3.90929 + 6.77108i 0.196947 + 0.341122i
\(395\) 5.09355 8.82229i 0.256284 0.443897i
\(396\) 0.146406 0.253582i 0.00735716 0.0127430i
\(397\) 7.25149 + 12.5600i 0.363942 + 0.630366i 0.988606 0.150528i \(-0.0480973\pi\)
−0.624664 + 0.780894i \(0.714764\pi\)
\(398\) 14.2839 0.715985
\(399\) −5.07476 0.676550i −0.254056 0.0338699i
\(400\) −27.6933 −1.38467
\(401\) 10.4945 + 18.1770i 0.524069 + 0.907714i 0.999607 + 0.0280189i \(0.00891986\pi\)
−0.475539 + 0.879695i \(0.657747\pi\)
\(402\) −8.71624 + 15.0970i −0.434727 + 0.752968i
\(403\) 0 0
\(404\) 0.273971 + 0.474532i 0.0136306 + 0.0236089i
\(405\) −39.8226 −1.97880
\(406\) −5.48739 13.3093i −0.272335 0.660528i
\(407\) −1.35038 −0.0669360
\(408\) 23.3751 + 40.4869i 1.15724 + 2.00440i
\(409\) −10.7138 + 18.5568i −0.529763 + 0.917576i 0.469635 + 0.882861i \(0.344386\pi\)
−0.999397 + 0.0347148i \(0.988948\pi\)
\(410\) −10.0761 + 17.4522i −0.497621 + 0.861905i
\(411\) 18.0725 + 31.3025i 0.891451 + 1.54404i
\(412\) 2.15782 0.106308
\(413\) −18.0529 + 23.4474i −0.888323 + 1.15377i
\(414\) 2.66563 0.131009
\(415\) 4.14723 + 7.18321i 0.203580 + 0.352610i
\(416\) 0 0
\(417\) 6.00383 10.3989i 0.294009 0.509238i
\(418\) 0.811784 + 1.40605i 0.0397056 + 0.0687722i
\(419\) 7.96406 0.389070 0.194535 0.980896i \(-0.437680\pi\)
0.194535 + 0.980896i \(0.437680\pi\)
\(420\) 2.24742 2.91900i 0.109663 0.142432i
\(421\) −2.81786 −0.137334 −0.0686670 0.997640i \(-0.521875\pi\)
−0.0686670 + 0.997640i \(0.521875\pi\)
\(422\) 3.13807 + 5.43530i 0.152759 + 0.264586i
\(423\) 0.537838 0.931562i 0.0261506 0.0452941i
\(424\) −0.117850 + 0.204122i −0.00572331 + 0.00991306i
\(425\) −29.9082 51.8026i −1.45076 2.51279i
\(426\) 31.5057 1.52645
\(427\) 7.68862 + 18.6482i 0.372078 + 0.902448i
\(428\) 1.25110 0.0604742
\(429\) 0 0
\(430\) −9.19253 + 15.9219i −0.443303 + 0.767823i
\(431\) −2.86813 + 4.96775i −0.138153 + 0.239288i −0.926797 0.375561i \(-0.877450\pi\)
0.788645 + 0.614849i \(0.210783\pi\)
\(432\) −6.60028 11.4320i −0.317556 0.550023i
\(433\) −24.5257 −1.17863 −0.589314 0.807904i \(-0.700602\pi\)
−0.589314 + 0.807904i \(0.700602\pi\)
\(434\) −18.1765 2.42324i −0.872502 0.116319i
\(435\) 29.5852 1.41850
\(436\) 0.555788 + 0.962653i 0.0266174 + 0.0461027i
\(437\) 0.777413 1.34652i 0.0371887 0.0644128i
\(438\) −1.04868 + 1.81637i −0.0501079 + 0.0867895i
\(439\) −18.3211 31.7332i −0.874420 1.51454i −0.857379 0.514686i \(-0.827909\pi\)
−0.0170416 0.999855i \(-0.505425\pi\)
\(440\) −13.4422 −0.640830
\(441\) −2.15276 8.14063i −0.102512 0.387649i
\(442\) 0 0
\(443\) −13.5467 23.4635i −0.643622 1.11479i −0.984618 0.174721i \(-0.944098\pi\)
0.340996 0.940065i \(-0.389236\pi\)
\(444\) −0.206079 + 0.356939i −0.00978008 + 0.0169396i
\(445\) 13.5152 23.4090i 0.640682 1.10969i
\(446\) 16.2943 + 28.2226i 0.771558 + 1.33638i
\(447\) −21.4830 −1.01611
\(448\) 22.5791 + 3.01018i 1.06676 + 0.142217i
\(449\) −27.4324 −1.29461 −0.647307 0.762229i \(-0.724105\pi\)
−0.647307 + 0.762229i \(0.724105\pi\)
\(450\) −6.25358 10.8315i −0.294796 0.510602i
\(451\) −2.68446 + 4.64962i −0.126406 + 0.218942i
\(452\) 0.621768 1.07693i 0.0292455 0.0506547i
\(453\) 4.83215 + 8.36953i 0.227034 + 0.393235i
\(454\) 20.6832 0.970712
\(455\) 0 0
\(456\) 5.70169 0.267006
\(457\) 19.8320 + 34.3500i 0.927700 + 1.60682i 0.787161 + 0.616748i \(0.211550\pi\)
0.140539 + 0.990075i \(0.455116\pi\)
\(458\) −10.9982 + 19.0495i −0.513913 + 0.890123i
\(459\) 14.2563 24.6927i 0.665429 1.15256i
\(460\) 0.559402 + 0.968913i 0.0260823 + 0.0451758i
\(461\) −4.89580 −0.228020 −0.114010 0.993480i \(-0.536370\pi\)
−0.114010 + 0.993480i \(0.536370\pi\)
\(462\) −5.69181 + 7.39265i −0.264807 + 0.343937i
\(463\) −4.71193 −0.218982 −0.109491 0.993988i \(-0.534922\pi\)
−0.109491 + 0.993988i \(0.534922\pi\)
\(464\) 7.24638 + 12.5511i 0.336405 + 0.582670i
\(465\) 18.8424 32.6360i 0.873794 1.51346i
\(466\) 19.5803 33.9140i 0.907038 1.57104i
\(467\) −16.0081 27.7268i −0.740765 1.28304i −0.952147 0.305639i \(-0.901130\pi\)
0.211383 0.977403i \(-0.432203\pi\)
\(468\) 0 0
\(469\) −10.2025 + 13.2513i −0.471110 + 0.611887i
\(470\) −4.29176 −0.197964
\(471\) −9.22761 15.9827i −0.425186 0.736444i
\(472\) 16.4781 28.5410i 0.758467 1.31370i
\(473\) −2.44907 + 4.24191i −0.112608 + 0.195043i
\(474\) 3.93726 + 6.81953i 0.180844 + 0.313232i
\(475\) −7.29526 −0.334730
\(476\) 1.48578 + 3.60366i 0.0681008 + 0.165174i
\(477\) −0.0962247 −0.00440582
\(478\) −5.82086 10.0820i −0.266240 0.461141i
\(479\) 9.01224 15.6097i 0.411780 0.713224i −0.583305 0.812254i \(-0.698241\pi\)
0.995084 + 0.0990298i \(0.0315739\pi\)
\(480\) −3.92447 + 6.79738i −0.179127 + 0.310257i
\(481\) 0 0
\(482\) 24.4807 1.11506
\(483\) 8.85657 + 1.18073i 0.402988 + 0.0537250i
\(484\) 1.78278 0.0810355
\(485\) 0.853693 + 1.47864i 0.0387642 + 0.0671416i
\(486\) 7.95712 13.7821i 0.360942 0.625170i
\(487\) −8.80020 + 15.2424i −0.398775 + 0.690699i −0.993575 0.113175i \(-0.963898\pi\)
0.594800 + 0.803874i \(0.297231\pi\)
\(488\) −11.2321 19.4545i −0.508453 0.880666i
\(489\) 24.6676 1.11551
\(490\) −23.8337 + 23.6783i −1.07670 + 1.06968i
\(491\) 3.86360 0.174362 0.0871810 0.996192i \(-0.472214\pi\)
0.0871810 + 0.996192i \(0.472214\pi\)
\(492\) 0.819339 + 1.41914i 0.0369387 + 0.0639796i
\(493\) −15.6519 + 27.1099i −0.704926 + 1.22097i
\(494\) 0 0
\(495\) −2.74388 4.75254i −0.123328 0.213611i
\(496\) 18.4605 0.828899
\(497\) 29.9599 + 3.99416i 1.34389 + 0.179163i
\(498\) −6.41153 −0.287308
\(499\) 6.32363 + 10.9528i 0.283084 + 0.490317i 0.972143 0.234389i \(-0.0753090\pi\)
−0.689058 + 0.724706i \(0.741976\pi\)
\(500\) 0.926757 1.60519i 0.0414458 0.0717863i
\(501\) 19.9085 34.4826i 0.889448 1.54057i
\(502\) −10.6757 18.4908i −0.476480 0.825287i
\(503\) 22.0360 0.982537 0.491268 0.871008i \(-0.336533\pi\)
0.491268 + 0.871008i \(0.336533\pi\)
\(504\) 3.57454 + 8.66978i 0.159223 + 0.386183i
\(505\) 10.2693 0.456980
\(506\) −1.41674 2.45387i −0.0629818 0.109088i
\(507\) 0 0
\(508\) 1.40075 2.42617i 0.0621482 0.107644i
\(509\) 7.83509 + 13.5708i 0.347284 + 0.601514i 0.985766 0.168123i \(-0.0537706\pi\)
−0.638482 + 0.769637i \(0.720437\pi\)
\(510\) 76.1491 3.37194
\(511\) −1.22750 + 1.59431i −0.0543016 + 0.0705280i
\(512\) −24.9600 −1.10309
\(513\) −1.73871 3.01154i −0.0767661 0.132963i
\(514\) 16.3625 28.3406i 0.721718 1.25005i
\(515\) 20.2206 35.0230i 0.891025 1.54330i
\(516\) 0.747495 + 1.29470i 0.0329066 + 0.0569959i
\(517\) −1.14341 −0.0502871
\(518\) 2.29305 2.97826i 0.100751 0.130857i
\(519\) 29.4795 1.29401
\(520\) 0 0
\(521\) 12.6207 21.8598i 0.552925 0.957694i −0.445137 0.895463i \(-0.646845\pi\)
0.998062 0.0622317i \(-0.0198218\pi\)
\(522\) −3.27269 + 5.66846i −0.143242 + 0.248102i
\(523\) 6.62383 + 11.4728i 0.289640 + 0.501671i 0.973724 0.227733i \(-0.0731312\pi\)
−0.684084 + 0.729403i \(0.739798\pi\)
\(524\) −2.12957 −0.0930307
\(525\) −15.9798 38.7578i −0.697414 1.69153i
\(526\) 20.7629 0.905307
\(527\) 19.9369 + 34.5318i 0.868466 + 1.50423i
\(528\) 4.69629 8.13422i 0.204380 0.353996i
\(529\) 10.1432 17.5686i 0.441011 0.763853i
\(530\) 0.191960 + 0.332485i 0.00833822 + 0.0144422i
\(531\) 13.4544 0.583871
\(532\) 0.471226 + 0.0628224i 0.0204303 + 0.00272370i
\(533\) 0 0
\(534\) 10.4471 + 18.0949i 0.452091 + 0.783044i
\(535\) 11.7238 20.3063i 0.506865 0.877916i
\(536\) 9.31258 16.1299i 0.402242 0.696704i
\(537\) −5.56200 9.63366i −0.240018 0.415723i
\(538\) −17.5427 −0.756320
\(539\) −6.34977 + 6.30837i −0.273504 + 0.271721i
\(540\) 2.50225 0.107680
\(541\) −7.20170 12.4737i −0.309625 0.536287i 0.668655 0.743573i \(-0.266870\pi\)
−0.978280 + 0.207286i \(0.933537\pi\)
\(542\) 18.1408 31.4208i 0.779214 1.34964i
\(543\) −15.8782 + 27.5019i −0.681401 + 1.18022i
\(544\) −4.15244 7.19224i −0.178034 0.308365i
\(545\) 20.8328 0.892377
\(546\) 0 0
\(547\) 2.00679 0.0858042 0.0429021 0.999079i \(-0.486340\pi\)
0.0429021 + 0.999079i \(0.486340\pi\)
\(548\) −1.67816 2.90665i −0.0716873 0.124166i
\(549\) 4.58550 7.94232i 0.195704 0.338970i
\(550\) −6.64736 + 11.5136i −0.283445 + 0.490940i
\(551\) 1.90892 + 3.30634i 0.0813226 + 0.140855i
\(552\) −9.95071 −0.423530
\(553\) 2.87954 + 6.98411i 0.122450 + 0.296994i
\(554\) 17.0863 0.725928
\(555\) 3.86226 + 6.68962i 0.163944 + 0.283959i
\(556\) −0.557497 + 0.965614i −0.0236432 + 0.0409512i
\(557\) −4.28958 + 7.42977i −0.181755 + 0.314810i −0.942478 0.334267i \(-0.891511\pi\)
0.760723 + 0.649077i \(0.224845\pi\)
\(558\) 4.16865 + 7.22032i 0.176473 + 0.305661i
\(559\) 0 0
\(560\) 20.6333 26.7989i 0.871915 1.13246i
\(561\) 20.2876 0.856543
\(562\) 17.9733 + 31.1306i 0.758157 + 1.31317i
\(563\) 6.38718 11.0629i 0.269188 0.466247i −0.699465 0.714667i \(-0.746578\pi\)
0.968652 + 0.248421i \(0.0799115\pi\)
\(564\) −0.174493 + 0.302231i −0.00734750 + 0.0127262i
\(565\) −11.6530 20.1835i −0.490243 0.849126i
\(566\) 19.8317 0.833587
\(567\) 18.0158 23.3992i 0.756591 0.982676i
\(568\) −33.6612 −1.41239
\(569\) 2.89558 + 5.01530i 0.121389 + 0.210252i 0.920316 0.391176i \(-0.127932\pi\)
−0.798927 + 0.601429i \(0.794598\pi\)
\(570\) 4.64360 8.04295i 0.194499 0.336882i
\(571\) 22.0666 38.2204i 0.923458 1.59948i 0.129435 0.991588i \(-0.458684\pi\)
0.794023 0.607888i \(-0.207983\pi\)
\(572\) 0 0
\(573\) 9.73025 0.406487
\(574\) −5.69630 13.8160i −0.237759 0.576667i
\(575\) 12.7318 0.530954
\(576\) −5.17835 8.96917i −0.215765 0.373715i
\(577\) 5.96649 10.3343i 0.248388 0.430221i −0.714691 0.699441i \(-0.753432\pi\)
0.963079 + 0.269220i \(0.0867658\pi\)
\(578\) −28.8518 + 49.9729i −1.20008 + 2.07860i
\(579\) 21.5662 + 37.3538i 0.896261 + 1.55237i
\(580\) −2.74719 −0.114071
\(581\) −6.09697 0.812829i −0.252945 0.0337218i
\(582\) −1.31979 −0.0547071
\(583\) 0.0511420 + 0.0885805i 0.00211808 + 0.00366863i
\(584\) 1.12043 1.94064i 0.0463637 0.0803043i
\(585\) 0 0
\(586\) −7.79091 13.4943i −0.321840 0.557443i
\(587\) −20.3516 −0.840000 −0.420000 0.907524i \(-0.637970\pi\)
−0.420000 + 0.907524i \(0.637970\pi\)
\(588\) 0.698431 + 2.64111i 0.0288028 + 0.108917i
\(589\) 4.86304 0.200378
\(590\) −26.8404 46.4889i −1.10500 1.91392i
\(591\) 5.95769 10.3190i 0.245067 0.424468i
\(592\) −1.89199 + 3.27701i −0.0777601 + 0.134684i
\(593\) 9.09000 + 15.7443i 0.373282 + 0.646543i 0.990068 0.140588i \(-0.0448991\pi\)
−0.616787 + 0.787130i \(0.711566\pi\)
\(594\) −6.33719 −0.260018
\(595\) 72.4131 + 9.65388i 2.96865 + 0.395770i
\(596\) 1.99484 0.0817120
\(597\) −10.8842 18.8520i −0.445460 0.771560i
\(598\) 0 0
\(599\) 19.1341 33.1412i 0.781797 1.35411i −0.149096 0.988823i \(-0.547636\pi\)
0.930894 0.365290i \(-0.119030\pi\)
\(600\) 23.3444 + 40.4337i 0.953031 + 1.65070i
\(601\) −26.8719 −1.09613 −0.548064 0.836436i \(-0.684635\pi\)
−0.548064 + 0.836436i \(0.684635\pi\)
\(602\) −5.19681 12.6045i −0.211806 0.513721i
\(603\) 7.60372 0.309648
\(604\) −0.448699 0.777170i −0.0182573 0.0316226i
\(605\) 16.7061 28.9358i 0.679200 1.17641i
\(606\) −3.96904 + 6.87459i −0.161231 + 0.279261i
\(607\) 4.70105 + 8.14245i 0.190810 + 0.330492i 0.945519 0.325568i \(-0.105555\pi\)
−0.754709 + 0.656059i \(0.772222\pi\)
\(608\) −1.01287 −0.0410773
\(609\) −13.3843 + 17.3839i −0.542361 + 0.704430i
\(610\) −36.5908 −1.48152
\(611\) 0 0
\(612\) 0.886124 1.53481i 0.0358194 0.0620411i
\(613\) −6.64469 + 11.5089i −0.268376 + 0.464842i −0.968443 0.249236i \(-0.919820\pi\)
0.700066 + 0.714078i \(0.253154\pi\)
\(614\) 19.7301 + 34.1735i 0.796242 + 1.37913i
\(615\) 30.7115 1.23841
\(616\) 6.08123 7.89843i 0.245020 0.318237i
\(617\) −11.2261 −0.451947 −0.225973 0.974133i \(-0.572556\pi\)
−0.225973 + 0.974133i \(0.572556\pi\)
\(618\) 15.6303 + 27.0724i 0.628742 + 1.08901i
\(619\) 4.64253 8.04109i 0.186599 0.323199i −0.757515 0.652817i \(-0.773587\pi\)
0.944114 + 0.329619i \(0.106920\pi\)
\(620\) −1.74965 + 3.03048i −0.0702675 + 0.121707i
\(621\) 3.03444 + 5.25580i 0.121768 + 0.210908i
\(622\) −0.202664 −0.00812608
\(623\) 7.64055 + 18.5316i 0.306112 + 0.742453i
\(624\) 0 0
\(625\) 1.95363 + 3.38379i 0.0781452 + 0.135351i
\(626\) 7.07665 12.2571i 0.282840 0.489893i
\(627\) 1.23715 2.14280i 0.0494068 0.0855752i
\(628\) 0.856848 + 1.48410i 0.0341920 + 0.0592222i
\(629\) −8.17322 −0.325888
\(630\) 15.1410 + 2.01855i 0.603232 + 0.0804210i
\(631\) −10.4026 −0.414122 −0.207061 0.978328i \(-0.566390\pi\)
−0.207061 + 0.978328i \(0.566390\pi\)
\(632\) −4.20664 7.28611i −0.167331 0.289826i
\(633\) 4.78237 8.28331i 0.190082 0.329232i
\(634\) −1.01347 + 1.75538i −0.0402499 + 0.0697149i
\(635\) −26.2523 45.4704i −1.04179 1.80444i
\(636\) 0.0312187 0.00123790
\(637\) 0 0
\(638\) 6.95754 0.275452
\(639\) −6.87109 11.9011i −0.271816 0.470800i
\(640\) −16.8322 + 29.1542i −0.665351 + 1.15242i
\(641\) −7.42955 + 12.8684i −0.293449 + 0.508269i −0.974623 0.223853i \(-0.928137\pi\)
0.681174 + 0.732122i \(0.261470\pi\)
\(642\) 9.06239 + 15.6965i 0.357664 + 0.619492i
\(643\) 2.29722 0.0905935 0.0452968 0.998974i \(-0.485577\pi\)
0.0452968 + 0.998974i \(0.485577\pi\)
\(644\) −0.822394 0.109639i −0.0324069 0.00432038i
\(645\) 28.0185 1.10323
\(646\) 4.91334 + 8.51016i 0.193313 + 0.334828i
\(647\) −3.99932 + 6.92703i −0.157230 + 0.272330i −0.933869 0.357616i \(-0.883590\pi\)
0.776639 + 0.629946i \(0.216923\pi\)
\(648\) −16.4443 + 28.4823i −0.645991 + 1.11889i
\(649\) −7.15081 12.3856i −0.280694 0.486176i
\(650\) 0 0
\(651\) 10.6522 + 25.8360i 0.417491 + 1.01259i
\(652\) −2.29056 −0.0897053
\(653\) −1.99222 3.45062i −0.0779615 0.135033i 0.824409 0.565995i \(-0.191508\pi\)
−0.902370 + 0.430962i \(0.858174\pi\)
\(654\) −8.05175 + 13.9460i −0.314848 + 0.545333i
\(655\) −19.9558 + 34.5645i −0.779738 + 1.35055i
\(656\) 7.52225 + 13.0289i 0.293695 + 0.508694i
\(657\) 0.914831 0.0356910
\(658\) 1.94159 2.52178i 0.0756912 0.0983094i
\(659\) −27.5003 −1.07126 −0.535629 0.844453i \(-0.679925\pi\)
−0.535629 + 0.844453i \(0.679925\pi\)
\(660\) 0.890211 + 1.54189i 0.0346514 + 0.0600180i
\(661\) 3.49310 6.05023i 0.135866 0.235327i −0.790062 0.613027i \(-0.789952\pi\)
0.925928 + 0.377700i \(0.123285\pi\)
\(662\) −16.9841 + 29.4173i −0.660105 + 1.14333i
\(663\) 0 0
\(664\) 6.85019 0.265839
\(665\) 5.43543 7.05965i 0.210777 0.273762i
\(666\) −1.70896 −0.0662207
\(667\) −3.33148 5.77029i −0.128995 0.223427i
\(668\) −1.84865 + 3.20195i −0.0715263 + 0.123887i
\(669\) 24.8323 43.0108i 0.960071 1.66289i
\(670\) −15.1688 26.2731i −0.586022 1.01502i
\(671\) −9.74849 −0.376336
\(672\) −2.21862 5.38110i −0.0855852 0.207581i
\(673\) 5.45566 0.210300 0.105150 0.994456i \(-0.466468\pi\)
0.105150 + 0.994456i \(0.466468\pi\)
\(674\) 21.6455 + 37.4910i 0.833752 + 1.44410i
\(675\) 14.2376 24.6603i 0.548006 0.949174i
\(676\) 0 0
\(677\) −16.8961 29.2649i −0.649371 1.12474i −0.983273 0.182135i \(-0.941699\pi\)
0.333903 0.942607i \(-0.391634\pi\)
\(678\) 18.0152 0.691870
\(679\) −1.25504 0.167318i −0.0481640 0.00642107i
\(680\) −81.3590 −3.11997
\(681\) −15.7605 27.2979i −0.603942 1.04606i
\(682\) 4.43115 7.67498i 0.169678 0.293890i
\(683\) 6.14942 10.6511i 0.235301 0.407553i −0.724059 0.689738i \(-0.757726\pi\)
0.959360 + 0.282185i \(0.0910591\pi\)
\(684\) −0.108072 0.187187i −0.00413225 0.00715726i
\(685\) −62.9028 −2.40339
\(686\) −3.13068 24.7165i −0.119530 0.943679i
\(687\) 33.5222 1.27895
\(688\) 6.86265 + 11.8865i 0.261636 + 0.453167i
\(689\) 0 0
\(690\) −8.10410 + 14.0367i −0.308518 + 0.534369i
\(691\) −5.54483 9.60393i −0.210935 0.365351i 0.741072 0.671425i \(-0.234318\pi\)
−0.952008 + 0.306075i \(0.900984\pi\)
\(692\) −2.73738 −0.104059
\(693\) 4.03386 + 0.537781i 0.153234 + 0.0204286i
\(694\) 33.3129 1.26454
\(695\) 10.4484 + 18.0972i 0.396331 + 0.686465i
\(696\) 12.2168 21.1602i 0.463078 0.802075i
\(697\) −16.2478 + 28.1419i −0.615428 + 1.06595i
\(698\) 7.77247 + 13.4623i 0.294193 + 0.509556i
\(699\) −59.6800 −2.25731
\(700\) 1.48383 + 3.59893i 0.0560836 + 0.136027i
\(701\) −10.6470 −0.402133 −0.201066 0.979578i \(-0.564441\pi\)
−0.201066 + 0.979578i \(0.564441\pi\)
\(702\) 0 0
\(703\) −0.498406 + 0.863265i −0.0187977 + 0.0325587i
\(704\) −5.50443 + 9.53396i −0.207456 + 0.359325i
\(705\) 3.27029 + 5.66431i 0.123166 + 0.213330i
\(706\) −27.0235 −1.01704
\(707\) −4.64585 + 6.03413i −0.174725 + 0.226937i
\(708\) −4.36508 −0.164050
\(709\) −20.3535 35.2532i −0.764391 1.32396i −0.940568 0.339605i \(-0.889707\pi\)
0.176178 0.984358i \(-0.443627\pi\)
\(710\) −27.4145 + 47.4833i −1.02885 + 1.78202i
\(711\) 1.71736 2.97455i 0.0644060 0.111554i
\(712\) −11.1619 19.3329i −0.418309 0.724532i
\(713\) −8.48708 −0.317844
\(714\) −34.4498 + 44.7442i −1.28925 + 1.67451i
\(715\) 0 0
\(716\) 0.516470 + 0.894552i 0.0193014 + 0.0334310i
\(717\) −8.87089 + 15.3648i −0.331290 + 0.573810i
\(718\) 10.1235 17.5344i 0.377806 0.654380i
\(719\) 4.88769 + 8.46572i 0.182280 + 0.315718i 0.942657 0.333764i \(-0.108319\pi\)
−0.760377 + 0.649482i \(0.774986\pi\)
\(720\) −15.3775 −0.573086
\(721\) 11.4313 + 27.7258i 0.425724 + 1.03256i
\(722\) −24.3608 −0.906616
\(723\) −18.6541 32.3098i −0.693752 1.20161i
\(724\) 1.47441 2.55375i 0.0547959 0.0949092i
\(725\) −15.6313 + 27.0743i −0.580533 + 1.00551i
\(726\) 12.9136 + 22.3671i 0.479270 + 0.830120i
\(727\) 12.2091 0.452811 0.226406 0.974033i \(-0.427303\pi\)
0.226406 + 0.974033i \(0.427303\pi\)
\(728\) 0 0
\(729\) 9.23219 0.341933
\(730\) −1.82501 3.16101i −0.0675467 0.116994i
\(731\) −14.8231 + 25.6743i −0.548251 + 0.949598i
\(732\) −1.48770 + 2.57677i −0.0549869 + 0.0952400i
\(733\) 11.1577 + 19.3256i 0.412118 + 0.713809i 0.995121 0.0986608i \(-0.0314559\pi\)
−0.583003 + 0.812470i \(0.698123\pi\)
\(734\) 12.1118 0.447055
\(735\) 49.4120 + 13.4133i 1.82259 + 0.494757i
\(736\) 1.76768 0.0651576
\(737\) −4.04126 6.99968i −0.148862 0.257836i
\(738\) −3.39728 + 5.88426i −0.125056 + 0.216603i
\(739\) −21.1865 + 36.6960i −0.779357 + 1.34989i 0.152956 + 0.988233i \(0.451121\pi\)
−0.932313 + 0.361653i \(0.882213\pi\)
\(740\) −0.358637 0.621178i −0.0131838 0.0228350i
\(741\) 0 0
\(742\) −0.282206 0.0376229i −0.0103601 0.00138118i
\(743\) 30.9801 1.13655 0.568276 0.822838i \(-0.307611\pi\)
0.568276 + 0.822838i \(0.307611\pi\)
\(744\) −15.5615 26.9532i −0.570511 0.988153i
\(745\) 18.6933 32.3778i 0.684870 1.18623i
\(746\) 10.8553 18.8020i 0.397442 0.688390i
\(747\) 1.39830 + 2.42192i 0.0511609 + 0.0886133i
\(748\) −1.88385 −0.0688802
\(749\) 6.62783 + 16.0753i 0.242176 + 0.587379i
\(750\) 26.8520 0.980497
\(751\) −11.2830 19.5427i −0.411722 0.713123i 0.583356 0.812216i \(-0.301739\pi\)
−0.995078 + 0.0990930i \(0.968406\pi\)
\(752\) −1.60200 + 2.77475i −0.0584190 + 0.101185i
\(753\) −16.2696 + 28.1798i −0.592897 + 1.02693i
\(754\) 0 0
\(755\) −16.8187 −0.612095
\(756\) −1.13202 + 1.47029i −0.0411710 + 0.0534738i
\(757\) 32.2808 1.17327 0.586633 0.809853i \(-0.300453\pi\)
0.586633 + 0.809853i \(0.300453\pi\)
\(758\) −10.5368 18.2504i −0.382716 0.662883i
\(759\) −2.15909 + 3.73966i −0.0783701 + 0.135741i
\(760\) −4.96130 + 8.59323i −0.179965 + 0.311709i
\(761\) 14.8758 + 25.7657i 0.539249 + 0.934006i 0.998945 + 0.0459296i \(0.0146250\pi\)
−0.459696 + 0.888076i \(0.652042\pi\)
\(762\) 40.5855 1.47026
\(763\) −9.42474 + 12.2411i −0.341198 + 0.443156i
\(764\) −0.903521 −0.0326883
\(765\) −16.6074 28.7649i −0.600442 1.04000i
\(766\) 16.5684 28.6972i 0.598639 1.03687i
\(767\) 0 0
\(768\) 4.63947 + 8.03581i 0.167413 + 0.289967i
\(769\) 41.8105 1.50773 0.753863 0.657032i \(-0.228188\pi\)
0.753863 + 0.657032i \(0.228188\pi\)
\(770\) −6.18902 15.0110i −0.223037 0.540959i
\(771\) −49.8723 −1.79611
\(772\) −2.00257 3.46856i −0.0720742 0.124836i
\(773\) 20.7168 35.8826i 0.745132 1.29061i −0.205001 0.978762i \(-0.565720\pi\)
0.950133 0.311845i \(-0.100947\pi\)
\(774\) −3.09938 + 5.36829i −0.111405 + 0.192959i
\(775\) 19.9107 + 34.4864i 0.715215 + 1.23879i
\(776\) 1.41009 0.0506192
\(777\) −5.67802 0.756975i −0.203698 0.0271563i
\(778\) −25.3665 −0.909433
\(779\) 1.98159 + 3.43221i 0.0709978 + 0.122972i
\(780\) 0 0
\(781\) −7.30376 + 12.6505i −0.261349 + 0.452670i
\(782\) −8.57486 14.8521i −0.306637