Properties

Label 1183.2.e.j.170.4
Level $1183$
Weight $2$
Character 1183.170
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 170.4
Character \(\chi\) \(=\) 1183.170
Dual form 1183.2.e.j.508.4

$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

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

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 −0.999610 0.0279386i \(-0.991106\pi\)
0.524000 + 0.851718i \(0.324439\pi\)
\(3\) −1.02505 1.77544i −0.591814 1.02505i −0.993988 0.109489i \(-0.965079\pi\)
0.402174 0.915563i \(-0.368255\pi\)
\(4\) 0.0951832 + 0.164862i 0.0475916 + 0.0824311i
\(5\) −1.78389 + 3.08979i −0.797779 + 1.38179i 0.123280 + 0.992372i \(0.460659\pi\)
−0.921059 + 0.389422i \(0.872675\pi\)
\(6\) 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 0.753399 0.657563i \(-0.228413\pi\)
−0.946166 + 0.323681i \(0.895080\pi\)
\(12\) 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 −0.768242 0.640159i \(-0.778868\pi\)
−0.170273 0.985397i \(-0.554465\pi\)
\(18\) −0.809103 1.40141i −0.190707 0.330315i
\(19\) 0.471939 0.817422i 0.108270 0.187530i −0.806799 0.590826i \(-0.798802\pi\)
0.915070 + 0.403296i \(0.132135\pi\)
\(20\) −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 −0.939028 0.343840i \(-0.888272\pi\)
0.767288 + 0.641303i \(0.221606\pi\)
\(24\) 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 0.999094 0.0425691i \(-0.0135543\pi\)
−0.536413 + 0.843956i \(0.680221\pi\)
\(32\) −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 −0.819351 0.573292i \(-0.805666\pi\)
0.906161 + 0.422933i \(0.139000\pi\)
\(38\) 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 −0.831573 0.555416i \(-0.812559\pi\)
0.896790 + 0.442456i \(0.145893\pi\)
\(48\) −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 0.868759 0.495235i \(-0.164918\pi\)
−0.863265 + 0.504750i \(0.831585\pi\)
\(54\) 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 −0.957700 0.287768i \(-0.907087\pi\)
0.229636 0.973277i \(-0.426246\pi\)
\(60\) 0.696200 + 1.20585i 0.0898790 + 0.155675i
\(61\) 3.81196 6.60251i 0.488072 0.845365i −0.511834 0.859084i \(-0.671034\pi\)
0.999906 + 0.0137195i \(0.00436719\pi\)
\(62\) −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 0.605805 0.795613i \(-0.292851\pi\)
−0.991924 + 0.126836i \(0.959518\pi\)
\(68\) 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 0.842915 0.538047i \(-0.180838\pi\)
−0.887420 + 0.460962i \(0.847504\pi\)
\(74\) 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 −0.774469 0.632612i \(-0.781983\pi\)
0.935093 + 0.354404i \(0.115316\pi\)
\(80\) 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 −0.592371 0.805665i \(-0.701808\pi\)
0.993912 + 0.110176i \(0.0351414\pi\)
\(90\) 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 0.785498 0.618865i \(-0.212407\pi\)
−0.928701 + 0.370829i \(0.879074\pi\)
\(102\) −10.6718 18.4841i −1.05666 1.83020i
\(103\) 5.66755 9.81649i 0.558441 0.967248i −0.439186 0.898396i \(-0.644733\pi\)
0.997627 0.0688516i \(-0.0219335\pi\)
\(104\) 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 −0.662329 0.749213i \(-0.730432\pi\)
0.980002 + 0.198988i \(0.0637653\pi\)
\(108\) −0.350673 0.607384i −0.0337435 0.0584455i
\(109\) −2.91957 5.05684i −0.279644 0.484358i 0.691652 0.722231i \(-0.256883\pi\)
−0.971296 + 0.237873i \(0.923550\pi\)
\(110\) −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 −0.999915 0.0130074i \(-0.995860\pi\)
0.511222 + 0.859448i \(0.329193\pi\)
\(132\) −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 0.946288 + 0.323324i \(0.104800\pi\)
−0.193137 + 0.981172i \(0.561866\pi\)
\(138\) −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 −0.567570 0.823325i \(-0.692116\pi\)
0.996805 + 0.0798677i \(0.0254498\pi\)
\(150\) −10.6578 18.4598i −0.870203 1.50724i
\(151\) 2.35703 + 4.08249i 0.191812 + 0.332229i 0.945851 0.324602i \(-0.105230\pi\)
−0.754039 + 0.656830i \(0.771897\pi\)
\(152\) −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 0.628608 0.777722i \(-0.283625\pi\)
−0.987831 + 0.155530i \(0.950291\pi\)
\(158\) 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 −0.999458 0.0329144i \(-0.989521\pi\)
0.528234 + 0.849099i \(0.322854\pi\)
\(164\) 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 0.451875 + 0.892081i \(0.350755\pi\)
−0.998503 + 0.0547049i \(0.982578\pi\)
\(174\) 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 0.746642 0.665226i \(-0.231665\pi\)
−0.949424 + 0.313998i \(0.898331\pi\)
\(180\) 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 −0.939019 0.343866i \(-0.888263\pi\)
0.767306 + 0.641281i \(0.221597\pi\)
\(192\) −8.82529 15.2859i −0.636911 1.10316i
\(193\) 10.5196 + 18.2204i 0.757215 + 1.31154i 0.944266 + 0.329185i \(0.106774\pi\)
−0.187050 + 0.982350i \(0.559893\pi\)
\(194\) 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 0.614177 0.789168i \(-0.289488\pi\)
−0.990528 + 0.137309i \(0.956155\pi\)
\(200\) 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 −0.999930 0.0118726i \(-0.996221\pi\)
0.489683 0.871901i \(-0.337113\pi\)
\(228\) −0.184184 0.319016i −0.0121979 0.0211274i
\(229\) −8.17573 + 14.1608i −0.540268 + 0.935771i 0.458621 + 0.888632i \(0.348344\pi\)
−0.998888 + 0.0471389i \(0.984990\pi\)
\(230\) 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 0.215911 0.976413i \(-0.430728\pi\)
0.737643 0.675191i \(-0.235939\pi\)
\(234\) 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 −0.994734 0.102487i \(-0.967320\pi\)
0.408611 0.912709i \(-0.366013\pi\)
\(242\) 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 −0.184769 0.982782i \(-0.559154\pi\)
0.943499 0.331376i \(-0.107513\pi\)
\(258\) 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 0.523751 0.851872i \(-0.324532\pi\)
−0.999618 + 0.0276456i \(0.991199\pi\)
\(264\) 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 0.993423 0.114499i \(-0.0365261\pi\)
−0.595870 + 0.803081i \(0.703193\pi\)
\(270\) 8.84108 + 15.3132i 0.538051 + 0.931931i
\(271\) 13.4853 23.3572i 0.819174 1.41885i −0.0871168 0.996198i \(-0.527765\pi\)
0.906291 0.422654i \(-0.138901\pi\)
\(272\) −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 0.609710 0.792625i \(-0.291286\pi\)
−0.991288 + 0.131712i \(0.957953\pi\)
\(278\) 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 0.559380 0.828911i \(-0.311039\pi\)
−0.997548 + 0.0699819i \(0.977706\pi\)
\(284\) 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 0.868153 0.496296i \(-0.165307\pi\)
−0.863882 + 0.503695i \(0.831974\pi\)
\(312\) 0 0
\(313\) 5.26057 9.11157i 0.297345 0.515016i −0.678183 0.734893i \(-0.737232\pi\)
0.975528 + 0.219877i \(0.0705656\pi\)
\(314\) 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 −0.886407 0.462907i \(-0.846806\pi\)
0.844093 + 0.536197i \(0.180140\pi\)
\(318\) 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 0.276574 + 0.960993i \(0.410801\pi\)
−0.970531 + 0.240976i \(0.922533\pi\)
\(332\) −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 −0.979368 0.202085i \(-0.935228\pi\)
0.314673 0.949200i \(-0.398105\pi\)
\(348\) 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 0.999183 + 0.0404237i \(0.0128708\pi\)
−0.464583 + 0.885529i \(0.653796\pi\)
\(354\) −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 −0.596196 0.802839i \(-0.703322\pi\)
0.993377 + 0.114901i \(0.0366551\pi\)
\(360\) 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 0.724279 0.689507i \(-0.242173\pi\)
−0.959270 + 0.282491i \(0.908839\pi\)
\(368\) 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 −0.577896 0.816110i \(-0.696126\pi\)
0.995720 + 0.0924174i \(0.0294594\pi\)
\(374\) −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 −0.358345 0.933589i \(-0.616659\pi\)
0.987685 0.156459i \(-0.0500078\pi\)
\(384\) 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 0.999683 0.0251791i \(-0.00801560\pi\)
−0.521647 + 0.853161i \(0.674682\pi\)
\(390\) 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 −0.624664 0.780894i \(-0.714764\pi\)
0.988606 + 0.150528i \(0.0480973\pi\)
\(398\) 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 −0.475539 0.879695i \(-0.657747\pi\)
0.999607 0.0280189i \(-0.00891986\pi\)
\(402\) −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 −0.999397 0.0347148i \(-0.988948\pi\)
0.469635 0.882861i \(-0.344386\pi\)
\(410\) −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 0.788645 0.614849i \(-0.210783\pi\)
−0.926797 + 0.375561i \(0.877450\pi\)
\(432\) −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 −0.0170416 + 0.999855i \(0.505425\pi\)
−0.857379 + 0.514686i \(0.827909\pi\)
\(440\) −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 0.340996 + 0.940065i \(0.389236\pi\)
−0.984618 + 0.174721i \(0.944098\pi\)
\(444\) −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 0.140539 0.990075i \(-0.455116\pi\)
0.787161 0.616748i \(-0.211550\pi\)
\(458\) −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 0.211383 + 0.977403i \(0.432203\pi\)
−0.952147 + 0.305639i \(0.901130\pi\)
\(468\) 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 0.995084 0.0990298i \(-0.0315739\pi\)
−0.583305 + 0.812254i \(0.698241\pi\)
\(480\) −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 0.594800 0.803874i \(-0.297231\pi\)
−0.993575 + 0.113175i \(0.963898\pi\)
\(488\) −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 −0.689058 0.724706i \(-0.741976\pi\)
0.972143 + 0.234389i \(0.0753090\pi\)
\(500\) 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 −0.638482 0.769637i \(-0.720437\pi\)
0.985766 + 0.168123i \(0.0537706\pi\)
\(510\) 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 0.998062 + 0.0622317i \(0.0198218\pi\)
−0.445137 + 0.895463i \(0.646845\pi\)
\(522\) −3.27269 5.66846i −0.143242 0.248102i
\(523\) 6.62383 11.4728i 0.289640 0.501671i −0.684084 0.729403i \(-0.739798\pi\)
0.973724 + 0.227733i \(0.0731312\pi\)
\(524\) −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 −0.978280 0.207286i \(-0.933537\pi\)
0.668655 + 0.743573i \(0.266870\pi\)
\(542\) 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 0.760723 0.649077i \(-0.224845\pi\)
−0.942478 + 0.334267i \(0.891511\pi\)
\(558\) 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 0.968652 0.248421i \(-0.0799115\pi\)
−0.699465 + 0.714667i \(0.746578\pi\)
\(564\) −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 −0.798927 0.601429i \(-0.794598\pi\)
0.920316 + 0.391176i \(0.127932\pi\)
\(570\) 4.64360 + 8.04295i 0.194499 + 0.336882i
\(571\) 22.0666 + 38.2204i 0.923458 + 1.59948i 0.794023 + 0.607888i \(0.207983\pi\)
0.129435 + 0.991588i \(0.458684\pi\)
\(572\) 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 0.963079 0.269220i \(-0.0867658\pi\)
−0.714691 + 0.699441i \(0.753432\pi\)
\(578\) −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 −0.616787 0.787130i \(-0.711566\pi\)
0.990068 + 0.140588i \(0.0448991\pi\)
\(594\) −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 0.930894 + 0.365290i \(0.119030\pi\)
−0.149096 + 0.988823i \(0.547636\pi\)
\(600\) 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 −0.754709 0.656059i \(-0.772222\pi\)
0.945519 + 0.325568i \(0.105555\pi\)
\(608\) −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 0.700066 0.714078i \(-0.253154\pi\)
−0.968443 + 0.249236i \(0.919820\pi\)
\(614\) 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 0.944114 0.329619i \(-0.106920\pi\)
−0.757515 + 0.652817i \(0.773587\pi\)
\(620\) −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 0.681174 0.732122i \(-0.261470\pi\)
−0.974623 + 0.223853i \(0.928137\pi\)
\(642\) 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 0.776639 0.629946i \(-0.216923\pi\)
−0.933869 + 0.357616i \(0.883590\pi\)
\(648\) −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 −0.902370 0.430962i \(-0.858174\pi\)
0.824409 + 0.565995i \(0.191508\pi\)
\(654\) −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 0.925928 0.377700i \(-0.123285\pi\)
−0.790062 + 0.613027i \(0.789952\pi\)
\(662\) −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 0.333903 + 0.942607i \(0.391634\pi\)
−0.983273 + 0.182135i \(0.941699\pi\)
\(678\) 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 0.959360 0.282185i \(-0.0910591\pi\)
−0.724059 + 0.689738i \(0.757726\pi\)
\(684\) −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 −0.952008 0.306075i \(-0.900984\pi\)
0.741072 + 0.671425i \(0.234318\pi\)
\(692\) −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 0.176178 + 0.984358i \(0.443627\pi\)
−0.940568 + 0.339605i \(0.889707\pi\)
\(710\) −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 −0.760377 0.649482i \(-0.774986\pi\)
0.942657 + 0.333764i \(0.108319\pi\)
\(720\) −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 −0.583003 0.812470i \(-0.698123\pi\)
0.995121 + 0.0986608i \(0.0314559\pi\)
\(734\) 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 −0.932313 0.361653i \(-0.882213\pi\)
0.152956 0.988233i \(-0.451121\pi\)
\(740\) −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 −0.995078 0.0990930i \(-0.968406\pi\)
0.583356 + 0.812216i \(0.301739\pi\)
\(752\) −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 −0.459696 0.888076i \(-0.652042\pi\)
0.998945 0.0459296i \(-0.0146250\pi\)
\(762\) 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 0.950133 + 0.311845i \(0.100947\pi\)
−0.205001 + 0.978762i \(0.565720\pi\)
\(774\) −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.