Properties

Label 432.2.be.b.335.4
Level $432$
Weight $2$
Character 432.335
Analytic conductor $3.450$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.be (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 335.4
Character \(\chi\) \(=\) 432.335
Dual form 432.2.be.b.383.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0760859 - 1.73038i) q^{3} +(-1.38279 + 3.79919i) q^{5} +(1.08929 + 0.192071i) q^{7} +(-2.98842 - 0.263315i) q^{9} +O(q^{10})\) \(q+(0.0760859 - 1.73038i) q^{3} +(-1.38279 + 3.79919i) q^{5} +(1.08929 + 0.192071i) q^{7} +(-2.98842 - 0.263315i) q^{9} +(-5.69507 + 2.07284i) q^{11} +(-2.30399 + 1.93328i) q^{13} +(6.46883 + 2.68182i) q^{15} +(-2.73425 + 1.57862i) q^{17} +(3.28561 + 1.89695i) q^{19} +(0.415234 - 1.87026i) q^{21} +(-0.347216 - 1.96916i) q^{23} +(-8.69152 - 7.29305i) q^{25} +(-0.683011 + 5.15107i) q^{27} +(2.14987 - 2.56211i) q^{29} +(3.05409 - 0.538519i) q^{31} +(3.15348 + 10.0123i) q^{33} +(-2.23597 + 3.87281i) q^{35} +(4.96790 + 8.60465i) q^{37} +(3.17000 + 4.13387i) q^{39} +(5.58989 + 6.66177i) q^{41} +(-1.77028 - 4.86379i) q^{43} +(5.13275 - 10.9895i) q^{45} +(-0.132939 + 0.753937i) q^{47} +(-5.42820 - 1.97570i) q^{49} +(2.52358 + 4.85141i) q^{51} +3.19332i q^{53} -24.5030i q^{55} +(3.53243 - 5.54102i) q^{57} +(7.48972 + 2.72603i) q^{59} +(-1.13739 + 6.45044i) q^{61} +(-3.20467 - 0.860813i) q^{63} +(-4.15895 - 11.4266i) q^{65} +(-3.17844 - 3.78791i) q^{67} +(-3.43381 + 0.450990i) q^{69} +(-4.30646 - 7.45900i) q^{71} +(4.12714 - 7.14841i) q^{73} +(-13.2810 + 14.4847i) q^{75} +(-6.60169 + 1.16406i) q^{77} +(-4.29080 + 5.11358i) q^{79} +(8.86133 + 1.57379i) q^{81} +(-9.12222 - 7.65445i) q^{83} +(-2.21658 - 12.5709i) q^{85} +(-4.26985 - 3.91503i) q^{87} +(10.9332 + 6.31231i) q^{89} +(-2.88103 + 1.66336i) q^{91} +(-0.699469 - 5.32571i) q^{93} +(-11.7502 + 9.85957i) q^{95} +(-6.13725 + 2.23378i) q^{97} +(17.5651 - 4.69491i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 3 q^{5} + 6 q^{9} + O(q^{10}) \) \( 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{13}{18}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.0760859 1.73038i 0.0439282 0.999035i
\(4\) 0 0
\(5\) −1.38279 + 3.79919i −0.618404 + 1.69905i 0.0924566 + 0.995717i \(0.470528\pi\)
−0.710860 + 0.703333i \(0.751694\pi\)
\(6\) 0 0
\(7\) 1.08929 + 0.192071i 0.411711 + 0.0725958i 0.375668 0.926754i \(-0.377413\pi\)
0.0360436 + 0.999350i \(0.488524\pi\)
\(8\) 0 0
\(9\) −2.98842 0.263315i −0.996141 0.0877716i
\(10\) 0 0
\(11\) −5.69507 + 2.07284i −1.71713 + 0.624984i −0.997585 0.0694631i \(-0.977871\pi\)
−0.719544 + 0.694447i \(0.755649\pi\)
\(12\) 0 0
\(13\) −2.30399 + 1.93328i −0.639011 + 0.536194i −0.903714 0.428136i \(-0.859170\pi\)
0.264703 + 0.964330i \(0.414726\pi\)
\(14\) 0 0
\(15\) 6.46883 + 2.68182i 1.67024 + 0.692443i
\(16\) 0 0
\(17\) −2.73425 + 1.57862i −0.663154 + 0.382872i −0.793478 0.608599i \(-0.791732\pi\)
0.130324 + 0.991472i \(0.458398\pi\)
\(18\) 0 0
\(19\) 3.28561 + 1.89695i 0.753770 + 0.435190i 0.827055 0.562122i \(-0.190015\pi\)
−0.0732842 + 0.997311i \(0.523348\pi\)
\(20\) 0 0
\(21\) 0.415234 1.87026i 0.0906115 0.408125i
\(22\) 0 0
\(23\) −0.347216 1.96916i −0.0723995 0.410598i −0.999371 0.0354658i \(-0.988709\pi\)
0.926971 0.375132i \(-0.122403\pi\)
\(24\) 0 0
\(25\) −8.69152 7.29305i −1.73830 1.45861i
\(26\) 0 0
\(27\) −0.683011 + 5.15107i −0.131445 + 0.991323i
\(28\) 0 0
\(29\) 2.14987 2.56211i 0.399220 0.475772i −0.528562 0.848895i \(-0.677268\pi\)
0.927782 + 0.373123i \(0.121713\pi\)
\(30\) 0 0
\(31\) 3.05409 0.538519i 0.548531 0.0967209i 0.107488 0.994206i \(-0.465719\pi\)
0.441044 + 0.897486i \(0.354608\pi\)
\(32\) 0 0
\(33\) 3.15348 + 10.0123i 0.548950 + 1.74293i
\(34\) 0 0
\(35\) −2.23597 + 3.87281i −0.377948 + 0.654625i
\(36\) 0 0
\(37\) 4.96790 + 8.60465i 0.816717 + 1.41460i 0.908088 + 0.418779i \(0.137542\pi\)
−0.0913713 + 0.995817i \(0.529125\pi\)
\(38\) 0 0
\(39\) 3.17000 + 4.13387i 0.507606 + 0.661949i
\(40\) 0 0
\(41\) 5.58989 + 6.66177i 0.872994 + 1.04039i 0.998831 + 0.0483427i \(0.0153940\pi\)
−0.125837 + 0.992051i \(0.540162\pi\)
\(42\) 0 0
\(43\) −1.77028 4.86379i −0.269965 0.741722i −0.998397 0.0566037i \(-0.981973\pi\)
0.728432 0.685118i \(-0.240249\pi\)
\(44\) 0 0
\(45\) 5.13275 10.9895i 0.765145 1.63821i
\(46\) 0 0
\(47\) −0.132939 + 0.753937i −0.0193912 + 0.109973i −0.992967 0.118391i \(-0.962226\pi\)
0.973576 + 0.228364i \(0.0733376\pi\)
\(48\) 0 0
\(49\) −5.42820 1.97570i −0.775457 0.282243i
\(50\) 0 0
\(51\) 2.52358 + 4.85141i 0.353371 + 0.679333i
\(52\) 0 0
\(53\) 3.19332i 0.438636i 0.975653 + 0.219318i \(0.0703832\pi\)
−0.975653 + 0.219318i \(0.929617\pi\)
\(54\) 0 0
\(55\) 24.5030i 3.30398i
\(56\) 0 0
\(57\) 3.53243 5.54102i 0.467881 0.733926i
\(58\) 0 0
\(59\) 7.48972 + 2.72603i 0.975078 + 0.354899i 0.779925 0.625873i \(-0.215257\pi\)
0.195153 + 0.980773i \(0.437480\pi\)
\(60\) 0 0
\(61\) −1.13739 + 6.45044i −0.145627 + 0.825894i 0.821234 + 0.570592i \(0.193286\pi\)
−0.966861 + 0.255302i \(0.917825\pi\)
\(62\) 0 0
\(63\) −3.20467 0.860813i −0.403751 0.108452i
\(64\) 0 0
\(65\) −4.15895 11.4266i −0.515854 1.41730i
\(66\) 0 0
\(67\) −3.17844 3.78791i −0.388308 0.462767i 0.536110 0.844148i \(-0.319893\pi\)
−0.924418 + 0.381381i \(0.875449\pi\)
\(68\) 0 0
\(69\) −3.43381 + 0.450990i −0.413382 + 0.0542928i
\(70\) 0 0
\(71\) −4.30646 7.45900i −0.511082 0.885220i −0.999918 0.0128443i \(-0.995911\pi\)
0.488835 0.872376i \(-0.337422\pi\)
\(72\) 0 0
\(73\) 4.12714 7.14841i 0.483045 0.836658i −0.516766 0.856127i \(-0.672864\pi\)
0.999810 + 0.0194687i \(0.00619746\pi\)
\(74\) 0 0
\(75\) −13.2810 + 14.4847i −1.53356 + 1.67255i
\(76\) 0 0
\(77\) −6.60169 + 1.16406i −0.752333 + 0.132657i
\(78\) 0 0
\(79\) −4.29080 + 5.11358i −0.482753 + 0.575322i −0.951359 0.308085i \(-0.900312\pi\)
0.468606 + 0.883407i \(0.344756\pi\)
\(80\) 0 0
\(81\) 8.86133 + 1.57379i 0.984592 + 0.174866i
\(82\) 0 0
\(83\) −9.12222 7.65445i −1.00129 0.840185i −0.0141306 0.999900i \(-0.504498\pi\)
−0.987163 + 0.159715i \(0.948943\pi\)
\(84\) 0 0
\(85\) −2.21658 12.5709i −0.240422 1.36350i
\(86\) 0 0
\(87\) −4.26985 3.91503i −0.457776 0.419735i
\(88\) 0 0
\(89\) 10.9332 + 6.31231i 1.15892 + 0.669104i 0.951045 0.309051i \(-0.100012\pi\)
0.207876 + 0.978155i \(0.433345\pi\)
\(90\) 0 0
\(91\) −2.88103 + 1.66336i −0.302014 + 0.174368i
\(92\) 0 0
\(93\) −0.699469 5.32571i −0.0725315 0.552251i
\(94\) 0 0
\(95\) −11.7502 + 9.85957i −1.20554 + 1.01157i
\(96\) 0 0
\(97\) −6.13725 + 2.23378i −0.623144 + 0.226806i −0.634244 0.773133i \(-0.718689\pi\)
0.0111006 + 0.999938i \(0.496466\pi\)
\(98\) 0 0
\(99\) 17.5651 4.69491i 1.76536 0.471857i
\(100\) 0 0
\(101\) −0.0682784 0.0120393i −0.00679396 0.00119796i 0.170250 0.985401i \(-0.445542\pi\)
−0.177044 + 0.984203i \(0.556654\pi\)
\(102\) 0 0
\(103\) 2.61896 7.19554i 0.258054 0.708998i −0.741233 0.671248i \(-0.765759\pi\)
0.999287 0.0377502i \(-0.0120191\pi\)
\(104\) 0 0
\(105\) 6.53131 + 4.16374i 0.637390 + 0.406339i
\(106\) 0 0
\(107\) −8.77523 −0.848333 −0.424167 0.905584i \(-0.639433\pi\)
−0.424167 + 0.905584i \(0.639433\pi\)
\(108\) 0 0
\(109\) −7.10766 −0.680790 −0.340395 0.940283i \(-0.610561\pi\)
−0.340395 + 0.940283i \(0.610561\pi\)
\(110\) 0 0
\(111\) 15.2673 7.94165i 1.44911 0.753788i
\(112\) 0 0
\(113\) −1.52252 + 4.18309i −0.143227 + 0.393512i −0.990476 0.137683i \(-0.956035\pi\)
0.847250 + 0.531195i \(0.178257\pi\)
\(114\) 0 0
\(115\) 7.96133 + 1.40380i 0.742398 + 0.130905i
\(116\) 0 0
\(117\) 7.39435 5.17077i 0.683608 0.478038i
\(118\) 0 0
\(119\) −3.28159 + 1.19440i −0.300823 + 0.109491i
\(120\) 0 0
\(121\) 19.7107 16.5392i 1.79188 1.50357i
\(122\) 0 0
\(123\) 11.9527 9.16576i 1.07774 0.826449i
\(124\) 0 0
\(125\) 22.2195 12.8284i 1.98737 1.14741i
\(126\) 0 0
\(127\) 18.8491 + 10.8825i 1.67259 + 0.965668i 0.966183 + 0.257859i \(0.0830170\pi\)
0.706404 + 0.707809i \(0.250316\pi\)
\(128\) 0 0
\(129\) −8.55090 + 2.69318i −0.752865 + 0.237122i
\(130\) 0 0
\(131\) −0.293030 1.66185i −0.0256021 0.145197i 0.969327 0.245774i \(-0.0790422\pi\)
−0.994929 + 0.100577i \(0.967931\pi\)
\(132\) 0 0
\(133\) 3.21462 + 2.69739i 0.278743 + 0.233893i
\(134\) 0 0
\(135\) −18.6254 9.71775i −1.60302 0.836370i
\(136\) 0 0
\(137\) −7.85456 + 9.36070i −0.671060 + 0.799738i −0.988928 0.148397i \(-0.952589\pi\)
0.317868 + 0.948135i \(0.397033\pi\)
\(138\) 0 0
\(139\) −18.6597 + 3.29020i −1.58269 + 0.279071i −0.894707 0.446654i \(-0.852616\pi\)
−0.687985 + 0.725725i \(0.741504\pi\)
\(140\) 0 0
\(141\) 1.29448 + 0.287399i 0.109015 + 0.0242034i
\(142\) 0 0
\(143\) 9.11401 15.7859i 0.762152 1.32009i
\(144\) 0 0
\(145\) 6.76113 + 11.7106i 0.561482 + 0.972515i
\(146\) 0 0
\(147\) −3.83172 + 9.24251i −0.316035 + 0.762310i
\(148\) 0 0
\(149\) 2.05041 + 2.44358i 0.167976 + 0.200186i 0.843465 0.537184i \(-0.180512\pi\)
−0.675489 + 0.737370i \(0.736067\pi\)
\(150\) 0 0
\(151\) 7.21676 + 19.8279i 0.587291 + 1.61357i 0.775434 + 0.631428i \(0.217531\pi\)
−0.188143 + 0.982142i \(0.560247\pi\)
\(152\) 0 0
\(153\) 8.58678 3.99762i 0.694200 0.323189i
\(154\) 0 0
\(155\) −2.17724 + 12.3477i −0.174880 + 0.991795i
\(156\) 0 0
\(157\) 10.1291 + 3.68669i 0.808390 + 0.294230i 0.712959 0.701206i \(-0.247355\pi\)
0.0954313 + 0.995436i \(0.469577\pi\)
\(158\) 0 0
\(159\) 5.52565 + 0.242966i 0.438213 + 0.0192685i
\(160\) 0 0
\(161\) 2.21167i 0.174304i
\(162\) 0 0
\(163\) 9.46792i 0.741585i 0.928716 + 0.370792i \(0.120914\pi\)
−0.928716 + 0.370792i \(0.879086\pi\)
\(164\) 0 0
\(165\) −42.3994 1.86433i −3.30079 0.145138i
\(166\) 0 0
\(167\) 4.31832 + 1.57174i 0.334161 + 0.121625i 0.503651 0.863907i \(-0.331990\pi\)
−0.169490 + 0.985532i \(0.554212\pi\)
\(168\) 0 0
\(169\) −0.686620 + 3.89401i −0.0528169 + 0.299539i
\(170\) 0 0
\(171\) −9.31929 6.53403i −0.712664 0.499670i
\(172\) 0 0
\(173\) −1.18374 3.25230i −0.0899981 0.247268i 0.886525 0.462681i \(-0.153112\pi\)
−0.976523 + 0.215413i \(0.930890\pi\)
\(174\) 0 0
\(175\) −8.06677 9.61360i −0.609790 0.726720i
\(176\) 0 0
\(177\) 5.28693 12.7526i 0.397390 0.958547i
\(178\) 0 0
\(179\) −0.297137 0.514656i −0.0222090 0.0384672i 0.854707 0.519110i \(-0.173737\pi\)
−0.876916 + 0.480643i \(0.840403\pi\)
\(180\) 0 0
\(181\) −3.23404 + 5.60152i −0.240384 + 0.416358i −0.960824 0.277160i \(-0.910607\pi\)
0.720439 + 0.693518i \(0.243940\pi\)
\(182\) 0 0
\(183\) 11.0752 + 2.45890i 0.818700 + 0.181767i
\(184\) 0 0
\(185\) −39.5603 + 6.97554i −2.90853 + 0.512852i
\(186\) 0 0
\(187\) 12.2995 14.6580i 0.899432 1.07190i
\(188\) 0 0
\(189\) −1.73336 + 5.47980i −0.126084 + 0.398597i
\(190\) 0 0
\(191\) 17.0734 + 14.3263i 1.23539 + 1.03661i 0.997870 + 0.0652317i \(0.0207786\pi\)
0.237519 + 0.971383i \(0.423666\pi\)
\(192\) 0 0
\(193\) −1.58626 8.99614i −0.114182 0.647557i −0.987152 0.159783i \(-0.948920\pi\)
0.872970 0.487773i \(-0.162191\pi\)
\(194\) 0 0
\(195\) −20.0888 + 6.32715i −1.43859 + 0.453097i
\(196\) 0 0
\(197\) 16.9561 + 9.78961i 1.20807 + 0.697481i 0.962338 0.271856i \(-0.0876375\pi\)
0.245735 + 0.969337i \(0.420971\pi\)
\(198\) 0 0
\(199\) −11.3321 + 6.54259i −0.803311 + 0.463792i −0.844627 0.535355i \(-0.820178\pi\)
0.0413169 + 0.999146i \(0.486845\pi\)
\(200\) 0 0
\(201\) −6.79636 + 5.21169i −0.479378 + 0.367605i
\(202\) 0 0
\(203\) 2.83393 2.37795i 0.198903 0.166899i
\(204\) 0 0
\(205\) −33.0390 + 12.0252i −2.30754 + 0.839877i
\(206\) 0 0
\(207\) 0.519119 + 5.97610i 0.0360812 + 0.415368i
\(208\) 0 0
\(209\) −22.6438 3.99272i −1.56631 0.276182i
\(210\) 0 0
\(211\) −2.90364 + 7.97769i −0.199895 + 0.549207i −0.998622 0.0524872i \(-0.983285\pi\)
0.798727 + 0.601694i \(0.205507\pi\)
\(212\) 0 0
\(213\) −13.2346 + 6.88428i −0.906817 + 0.471703i
\(214\) 0 0
\(215\) 20.9264 1.42717
\(216\) 0 0
\(217\) 3.43021 0.232858
\(218\) 0 0
\(219\) −12.0554 7.68540i −0.814631 0.519331i
\(220\) 0 0
\(221\) 3.24778 8.92320i 0.218469 0.600239i
\(222\) 0 0
\(223\) −4.40925 0.777470i −0.295265 0.0520633i 0.0240532 0.999711i \(-0.492343\pi\)
−0.319319 + 0.947647i \(0.603454\pi\)
\(224\) 0 0
\(225\) 24.0536 + 24.0833i 1.60357 + 1.60555i
\(226\) 0 0
\(227\) −4.95239 + 1.80252i −0.328702 + 0.119638i −0.501099 0.865390i \(-0.667071\pi\)
0.172397 + 0.985027i \(0.444849\pi\)
\(228\) 0 0
\(229\) −3.50504 + 2.94107i −0.231619 + 0.194352i −0.751209 0.660064i \(-0.770529\pi\)
0.519590 + 0.854416i \(0.326085\pi\)
\(230\) 0 0
\(231\) 1.51196 + 11.5120i 0.0994799 + 0.757434i
\(232\) 0 0
\(233\) 7.68478 4.43681i 0.503447 0.290665i −0.226689 0.973967i \(-0.572790\pi\)
0.730136 + 0.683302i \(0.239457\pi\)
\(234\) 0 0
\(235\) −2.68052 1.54760i −0.174858 0.100954i
\(236\) 0 0
\(237\) 8.52196 + 7.81378i 0.553561 + 0.507560i
\(238\) 0 0
\(239\) −2.00688 11.3816i −0.129815 0.736215i −0.978331 0.207046i \(-0.933615\pi\)
0.848517 0.529169i \(-0.177496\pi\)
\(240\) 0 0
\(241\) 13.7462 + 11.5344i 0.885471 + 0.742998i 0.967296 0.253649i \(-0.0816307\pi\)
−0.0818259 + 0.996647i \(0.526075\pi\)
\(242\) 0 0
\(243\) 3.39748 15.2137i 0.217948 0.975960i
\(244\) 0 0
\(245\) 15.0121 17.8908i 0.959090 1.14300i
\(246\) 0 0
\(247\) −11.2373 + 1.98144i −0.715014 + 0.126076i
\(248\) 0 0
\(249\) −13.9392 + 15.2025i −0.883359 + 0.963419i
\(250\) 0 0
\(251\) 11.4327 19.8020i 0.721625 1.24989i −0.238724 0.971088i \(-0.576729\pi\)
0.960348 0.278803i \(-0.0899377\pi\)
\(252\) 0 0
\(253\) 6.05916 + 10.4948i 0.380936 + 0.659801i
\(254\) 0 0
\(255\) −21.9210 + 2.87906i −1.37275 + 0.180294i
\(256\) 0 0
\(257\) −3.51480 4.18877i −0.219247 0.261288i 0.645198 0.764015i \(-0.276775\pi\)
−0.864445 + 0.502727i \(0.832330\pi\)
\(258\) 0 0
\(259\) 3.75876 + 10.3271i 0.233558 + 0.641695i
\(260\) 0 0
\(261\) −7.09935 + 7.09058i −0.439439 + 0.438896i
\(262\) 0 0
\(263\) 2.70605 15.3468i 0.166862 0.946324i −0.780261 0.625454i \(-0.784914\pi\)
0.947123 0.320870i \(-0.103975\pi\)
\(264\) 0 0
\(265\) −12.1320 4.41570i −0.745264 0.271254i
\(266\) 0 0
\(267\) 11.7546 18.4384i 0.719367 1.12841i
\(268\) 0 0
\(269\) 3.32950i 0.203003i −0.994835 0.101502i \(-0.967635\pi\)
0.994835 0.101502i \(-0.0323647\pi\)
\(270\) 0 0
\(271\) 7.46821i 0.453661i −0.973934 0.226831i \(-0.927164\pi\)
0.973934 0.226831i \(-0.0728364\pi\)
\(272\) 0 0
\(273\) 2.65904 + 5.11183i 0.160932 + 0.309382i
\(274\) 0 0
\(275\) 64.6161 + 23.5183i 3.89650 + 1.41821i
\(276\) 0 0
\(277\) −0.0646551 + 0.366677i −0.00388475 + 0.0220315i −0.986689 0.162622i \(-0.948005\pi\)
0.982804 + 0.184653i \(0.0591161\pi\)
\(278\) 0 0
\(279\) −9.26872 + 0.805134i −0.554904 + 0.0482021i
\(280\) 0 0
\(281\) −0.756825 2.07936i −0.0451484 0.124044i 0.915069 0.403296i \(-0.132136\pi\)
−0.960218 + 0.279252i \(0.909913\pi\)
\(282\) 0 0
\(283\) 8.02980 + 9.56954i 0.477322 + 0.568850i 0.949946 0.312414i \(-0.101138\pi\)
−0.472624 + 0.881264i \(0.656693\pi\)
\(284\) 0 0
\(285\) 16.1668 + 21.0824i 0.957637 + 1.24882i
\(286\) 0 0
\(287\) 4.80946 + 8.33023i 0.283893 + 0.491718i
\(288\) 0 0
\(289\) −3.51590 + 6.08972i −0.206818 + 0.358219i
\(290\) 0 0
\(291\) 3.39832 + 10.7897i 0.199213 + 0.632505i
\(292\) 0 0
\(293\) 17.2687 3.04493i 1.00885 0.177887i 0.355283 0.934759i \(-0.384384\pi\)
0.653563 + 0.756872i \(0.273273\pi\)
\(294\) 0 0
\(295\) −20.7134 + 24.6853i −1.20598 + 1.43724i
\(296\) 0 0
\(297\) −6.78753 30.7515i −0.393852 1.78438i
\(298\) 0 0
\(299\) 4.60690 + 3.86565i 0.266424 + 0.223556i
\(300\) 0 0
\(301\) −0.994146 5.63808i −0.0573016 0.324974i
\(302\) 0 0
\(303\) −0.0260276 + 0.117232i −0.00149525 + 0.00673477i
\(304\) 0 0
\(305\) −22.9337 13.2408i −1.31318 0.758164i
\(306\) 0 0
\(307\) 8.25491 4.76598i 0.471133 0.272009i −0.245581 0.969376i \(-0.578979\pi\)
0.716714 + 0.697367i \(0.245645\pi\)
\(308\) 0 0
\(309\) −12.2518 5.07928i −0.696978 0.288950i
\(310\) 0 0
\(311\) −24.6382 + 20.6739i −1.39711 + 1.17231i −0.434741 + 0.900556i \(0.643160\pi\)
−0.962366 + 0.271756i \(0.912396\pi\)
\(312\) 0 0
\(313\) 2.99538 1.09023i 0.169309 0.0616234i −0.255975 0.966683i \(-0.582396\pi\)
0.425284 + 0.905060i \(0.360174\pi\)
\(314\) 0 0
\(315\) 7.70179 10.9848i 0.433947 0.618925i
\(316\) 0 0
\(317\) −6.86086 1.20975i −0.385344 0.0679466i −0.0223797 0.999750i \(-0.507124\pi\)
−0.362965 + 0.931803i \(0.618235\pi\)
\(318\) 0 0
\(319\) −6.93281 + 19.0477i −0.388163 + 1.06647i
\(320\) 0 0
\(321\) −0.667671 + 15.1845i −0.0372657 + 0.847515i
\(322\) 0 0
\(323\) −11.9783 −0.666488
\(324\) 0 0
\(325\) 34.1246 1.89289
\(326\) 0 0
\(327\) −0.540792 + 12.2989i −0.0299059 + 0.680133i
\(328\) 0 0
\(329\) −0.289618 + 0.795719i −0.0159672 + 0.0438694i
\(330\) 0 0
\(331\) −16.2725 2.86928i −0.894419 0.157710i −0.292498 0.956266i \(-0.594487\pi\)
−0.601921 + 0.798556i \(0.705598\pi\)
\(332\) 0 0
\(333\) −12.5804 27.0224i −0.689404 1.48082i
\(334\) 0 0
\(335\) 18.7861 6.83759i 1.02640 0.373578i
\(336\) 0 0
\(337\) 17.6769 14.8327i 0.962925 0.807990i −0.0185019 0.999829i \(-0.505890\pi\)
0.981426 + 0.191839i \(0.0614452\pi\)
\(338\) 0 0
\(339\) 7.12249 + 2.95281i 0.386840 + 0.160375i
\(340\) 0 0
\(341\) −16.2770 + 9.39754i −0.881450 + 0.508905i
\(342\) 0 0
\(343\) −12.2387 7.06602i −0.660828 0.381529i
\(344\) 0 0
\(345\) 3.03485 13.6693i 0.163391 0.735931i
\(346\) 0 0
\(347\) −5.24439 29.7424i −0.281534 1.59666i −0.717411 0.696650i \(-0.754673\pi\)
0.435878 0.900006i \(-0.356438\pi\)
\(348\) 0 0
\(349\) −6.03314 5.06240i −0.322946 0.270984i 0.466872 0.884325i \(-0.345381\pi\)
−0.789819 + 0.613341i \(0.789825\pi\)
\(350\) 0 0
\(351\) −8.38478 13.1884i −0.447547 0.703947i
\(352\) 0 0
\(353\) 7.94108 9.46381i 0.422661 0.503708i −0.512129 0.858909i \(-0.671143\pi\)
0.934790 + 0.355201i \(0.115587\pi\)
\(354\) 0 0
\(355\) 34.2931 6.04680i 1.82009 0.320931i
\(356\) 0 0
\(357\) 1.81708 + 5.76927i 0.0961703 + 0.305342i
\(358\) 0 0
\(359\) −17.4551 + 30.2332i −0.921247 + 1.59565i −0.123760 + 0.992312i \(0.539495\pi\)
−0.797488 + 0.603335i \(0.793838\pi\)
\(360\) 0 0
\(361\) −2.30318 3.98923i −0.121220 0.209959i
\(362\) 0 0
\(363\) −27.1194 35.3654i −1.42340 1.85620i
\(364\) 0 0
\(365\) 21.4512 + 25.5646i 1.12281 + 1.33811i
\(366\) 0 0
\(367\) 4.42147 + 12.1479i 0.230799 + 0.634114i 0.999988 0.00490680i \(-0.00156189\pi\)
−0.769189 + 0.639021i \(0.779340\pi\)
\(368\) 0 0
\(369\) −14.9508 21.3801i −0.778308 1.11300i
\(370\) 0 0
\(371\) −0.613342 + 3.47844i −0.0318431 + 0.180591i
\(372\) 0 0
\(373\) 25.1002 + 9.13573i 1.29964 + 0.473030i 0.896879 0.442275i \(-0.145828\pi\)
0.402761 + 0.915305i \(0.368051\pi\)
\(374\) 0 0
\(375\) −20.5075 39.4242i −1.05900 2.03586i
\(376\) 0 0
\(377\) 10.0594i 0.518083i
\(378\) 0 0
\(379\) 25.2149i 1.29520i 0.761980 + 0.647600i \(0.224227\pi\)
−0.761980 + 0.647600i \(0.775773\pi\)
\(380\) 0 0
\(381\) 20.2650 31.7881i 1.03821 1.62855i
\(382\) 0 0
\(383\) 7.57778 + 2.75809i 0.387206 + 0.140932i 0.528286 0.849067i \(-0.322835\pi\)
−0.141079 + 0.989998i \(0.545057\pi\)
\(384\) 0 0
\(385\) 4.70630 26.6907i 0.239855 1.36029i
\(386\) 0 0
\(387\) 4.00962 + 15.0012i 0.203821 + 0.762554i
\(388\) 0 0
\(389\) −9.34231 25.6678i −0.473674 1.30141i −0.914780 0.403953i \(-0.867636\pi\)
0.441106 0.897455i \(-0.354586\pi\)
\(390\) 0 0
\(391\) 4.05793 + 4.83606i 0.205218 + 0.244570i
\(392\) 0 0
\(393\) −2.89793 + 0.380609i −0.146181 + 0.0191992i
\(394\) 0 0
\(395\) −13.4942 23.3726i −0.678965 1.17600i
\(396\) 0 0
\(397\) −0.561110 + 0.971871i −0.0281613 + 0.0487768i −0.879763 0.475413i \(-0.842299\pi\)
0.851601 + 0.524190i \(0.175632\pi\)
\(398\) 0 0
\(399\) 4.91209 5.35728i 0.245912 0.268199i
\(400\) 0 0
\(401\) −3.05033 + 0.537855i −0.152326 + 0.0268592i −0.249291 0.968429i \(-0.580198\pi\)
0.0969651 + 0.995288i \(0.469086\pi\)
\(402\) 0 0
\(403\) −5.99549 + 7.14515i −0.298657 + 0.355925i
\(404\) 0 0
\(405\) −18.2325 + 31.4897i −0.905981 + 1.56473i
\(406\) 0 0
\(407\) −46.1285 38.7064i −2.28651 1.91861i
\(408\) 0 0
\(409\) 3.12881 + 17.7443i 0.154710 + 0.877402i 0.959051 + 0.283234i \(0.0914073\pi\)
−0.804341 + 0.594168i \(0.797482\pi\)
\(410\) 0 0
\(411\) 15.5999 + 14.3036i 0.769488 + 0.705543i
\(412\) 0 0
\(413\) 7.63485 + 4.40798i 0.375687 + 0.216903i
\(414\) 0 0
\(415\) 41.6949 24.0725i 2.04672 1.18167i
\(416\) 0 0
\(417\) 4.27356 + 32.5386i 0.209277 + 1.59342i
\(418\) 0 0
\(419\) 7.33380 6.15379i 0.358279 0.300632i −0.445825 0.895120i \(-0.647090\pi\)
0.804105 + 0.594488i \(0.202645\pi\)
\(420\) 0 0
\(421\) 27.5246 10.0181i 1.34147 0.488254i 0.431193 0.902260i \(-0.358093\pi\)
0.910275 + 0.414005i \(0.135870\pi\)
\(422\) 0 0
\(423\) 0.595802 2.21808i 0.0289689 0.107847i
\(424\) 0 0
\(425\) 35.2778 + 6.22043i 1.71122 + 0.301735i
\(426\) 0 0
\(427\) −2.47788 + 6.80791i −0.119913 + 0.329458i
\(428\) 0 0
\(429\) −26.6222 16.9718i −1.28533 0.819405i
\(430\) 0 0
\(431\) 4.22604 0.203561 0.101781 0.994807i \(-0.467546\pi\)
0.101781 + 0.994807i \(0.467546\pi\)
\(432\) 0 0
\(433\) 24.7833 1.19101 0.595504 0.803352i \(-0.296952\pi\)
0.595504 + 0.803352i \(0.296952\pi\)
\(434\) 0 0
\(435\) 20.7782 10.8083i 0.996241 0.518219i
\(436\) 0 0
\(437\) 2.59457 7.12853i 0.124115 0.341004i
\(438\) 0 0
\(439\) 7.08050 + 1.24848i 0.337934 + 0.0595868i 0.340040 0.940411i \(-0.389559\pi\)
−0.00210632 + 0.999998i \(0.500670\pi\)
\(440\) 0 0
\(441\) 15.7015 + 7.33355i 0.747691 + 0.349217i
\(442\) 0 0
\(443\) −13.4625 + 4.89994i −0.639621 + 0.232803i −0.641414 0.767195i \(-0.721652\pi\)
0.00179224 + 0.999998i \(0.499430\pi\)
\(444\) 0 0
\(445\) −39.1001 + 32.8089i −1.85352 + 1.55529i
\(446\) 0 0
\(447\) 4.38433 3.36207i 0.207372 0.159020i
\(448\) 0 0
\(449\) 1.65721 0.956788i 0.0782084 0.0451536i −0.460386 0.887719i \(-0.652289\pi\)
0.538594 + 0.842565i \(0.318956\pi\)
\(450\) 0 0
\(451\) −45.6436 26.3523i −2.14927 1.24088i
\(452\) 0 0
\(453\) 34.8588 10.9791i 1.63781 0.515843i
\(454\) 0 0
\(455\) −2.33557 13.2457i −0.109493 0.620966i
\(456\) 0 0
\(457\) −25.4947 21.3926i −1.19259 1.00070i −0.999811 0.0194611i \(-0.993805\pi\)
−0.192781 0.981242i \(-0.561751\pi\)
\(458\) 0 0
\(459\) −6.26407 15.1625i −0.292382 0.707727i
\(460\) 0 0
\(461\) 8.78283 10.4670i 0.409057 0.487495i −0.521702 0.853128i \(-0.674703\pi\)
0.930759 + 0.365632i \(0.119147\pi\)
\(462\) 0 0
\(463\) −26.9189 + 4.74653i −1.25103 + 0.220590i −0.759636 0.650349i \(-0.774623\pi\)
−0.491392 + 0.870939i \(0.663512\pi\)
\(464\) 0 0
\(465\) 21.2006 + 4.70694i 0.983155 + 0.218279i
\(466\) 0 0
\(467\) 3.55751 6.16179i 0.164622 0.285134i −0.771899 0.635745i \(-0.780693\pi\)
0.936521 + 0.350612i \(0.114026\pi\)
\(468\) 0 0
\(469\) −2.73468 4.73661i −0.126276 0.218716i
\(470\) 0 0
\(471\) 7.15005 17.2467i 0.329457 0.794684i
\(472\) 0 0
\(473\) 20.1637 + 24.0302i 0.927128 + 1.10491i
\(474\) 0 0
\(475\) −14.7224 40.4495i −0.675510 1.85595i
\(476\) 0 0
\(477\) 0.840847 9.54298i 0.0384998 0.436943i
\(478\) 0 0
\(479\) −4.10239 + 23.2658i −0.187443 + 1.06304i 0.735334 + 0.677705i \(0.237026\pi\)
−0.922776 + 0.385336i \(0.874086\pi\)
\(480\) 0 0
\(481\) −28.0811 10.2207i −1.28039 0.466024i
\(482\) 0 0
\(483\) −3.82702 0.168276i −0.174135 0.00765684i
\(484\) 0 0
\(485\) 26.4055i 1.19901i
\(486\) 0 0
\(487\) 32.5422i 1.47463i 0.675551 + 0.737314i \(0.263906\pi\)
−0.675551 + 0.737314i \(0.736094\pi\)
\(488\) 0 0
\(489\) 16.3831 + 0.720375i 0.740869 + 0.0325765i
\(490\) 0 0
\(491\) −24.0124 8.73980i −1.08366 0.394422i −0.262394 0.964961i \(-0.584512\pi\)
−0.821270 + 0.570539i \(0.806734\pi\)
\(492\) 0 0
\(493\) −1.83368 + 10.3993i −0.0825846 + 0.468361i
\(494\) 0 0
\(495\) −6.45199 + 73.2252i −0.289995 + 3.29123i
\(496\) 0 0
\(497\) −3.25831 8.95213i −0.146155 0.401558i
\(498\) 0 0
\(499\) 3.15334 + 3.75800i 0.141163 + 0.168231i 0.831994 0.554785i \(-0.187200\pi\)
−0.690831 + 0.723016i \(0.742755\pi\)
\(500\) 0 0
\(501\) 3.04827 7.35274i 0.136187 0.328496i
\(502\) 0 0
\(503\) 17.7556 + 30.7537i 0.791685 + 1.37124i 0.924923 + 0.380155i \(0.124129\pi\)
−0.133238 + 0.991084i \(0.542537\pi\)
\(504\) 0 0
\(505\) 0.140155 0.242755i 0.00623680 0.0108025i
\(506\) 0 0
\(507\) 6.68588 + 1.48439i 0.296930 + 0.0659241i
\(508\) 0 0
\(509\) −31.5798 + 5.56837i −1.39975 + 0.246814i −0.822040 0.569429i \(-0.807164\pi\)
−0.577709 + 0.816243i \(0.696053\pi\)
\(510\) 0 0
\(511\) 5.86863 6.99396i 0.259613 0.309395i
\(512\) 0 0
\(513\) −12.0154 + 15.6288i −0.530493 + 0.690027i
\(514\) 0 0
\(515\) 23.7158 + 19.8999i 1.04504 + 0.876894i
\(516\) 0 0
\(517\) −0.805688 4.56929i −0.0354341 0.200957i
\(518\) 0 0
\(519\) −5.71777 + 1.80086i −0.250982 + 0.0790492i
\(520\) 0 0
\(521\) −0.881959 0.509200i −0.0386393 0.0223084i 0.480556 0.876964i \(-0.340435\pi\)
−0.519195 + 0.854656i \(0.673768\pi\)
\(522\) 0 0
\(523\) 2.29961 1.32768i 0.100555 0.0580555i −0.448879 0.893592i \(-0.648177\pi\)
0.549434 + 0.835537i \(0.314843\pi\)
\(524\) 0 0
\(525\) −17.2489 + 13.2271i −0.752805 + 0.577278i
\(526\) 0 0
\(527\) −7.50055 + 6.29371i −0.326729 + 0.274158i
\(528\) 0 0
\(529\) 17.8559 6.49902i 0.776344 0.282566i
\(530\) 0 0
\(531\) −21.6646 10.1187i −0.940165 0.439114i
\(532\) 0 0
\(533\) −25.7581 4.54184i −1.11571 0.196729i
\(534\) 0 0
\(535\) 12.1343 33.3388i 0.524612 1.44136i
\(536\) 0 0
\(537\) −0.913157 + 0.475001i −0.0394057 + 0.0204978i
\(538\) 0 0
\(539\) 35.0093 1.50796
\(540\) 0 0
\(541\) −9.39810 −0.404056 −0.202028 0.979380i \(-0.564753\pi\)
−0.202028 + 0.979380i \(0.564753\pi\)
\(542\) 0 0
\(543\) 9.44669 + 6.02231i 0.405396 + 0.258442i
\(544\) 0 0
\(545\) 9.82842 27.0034i 0.421003 1.15670i
\(546\) 0 0
\(547\) 18.0711 + 3.18642i 0.772663 + 0.136241i 0.546060 0.837746i \(-0.316127\pi\)
0.226603 + 0.973987i \(0.427238\pi\)
\(548\) 0 0
\(549\) 5.09749 18.9771i 0.217555 0.809925i
\(550\) 0 0
\(551\) 11.9238 4.33991i 0.507972 0.184887i
\(552\) 0 0
\(553\) −5.65608 + 4.74601i −0.240521 + 0.201821i
\(554\) 0 0
\(555\) 9.06036 + 68.9850i 0.384591 + 2.92825i
\(556\) 0 0
\(557\) −22.3343 + 12.8947i −0.946334 + 0.546366i −0.891940 0.452153i \(-0.850656\pi\)
−0.0543940 + 0.998520i \(0.517323\pi\)
\(558\) 0 0
\(559\) 13.4818 + 7.78369i 0.570217 + 0.329215i
\(560\) 0 0
\(561\) −24.4281 22.3981i −1.03136 0.945651i
\(562\) 0 0
\(563\) −4.51280 25.5933i −0.190192 1.07863i −0.919102 0.394021i \(-0.871084\pi\)
0.728910 0.684610i \(-0.240027\pi\)
\(564\) 0 0
\(565\) −13.7870 11.5687i −0.580025 0.486699i
\(566\) 0 0
\(567\) 9.35024 + 3.41631i 0.392673 + 0.143471i
\(568\) 0 0
\(569\) −22.4714 + 26.7804i −0.942050 + 1.12269i 0.0502374 + 0.998737i \(0.484002\pi\)
−0.992288 + 0.123955i \(0.960442\pi\)
\(570\) 0 0
\(571\) 16.7380 2.95137i 0.700466 0.123511i 0.187937 0.982181i \(-0.439820\pi\)
0.512529 + 0.858670i \(0.328709\pi\)
\(572\) 0 0
\(573\) 26.0890 28.4535i 1.08988 1.18866i
\(574\) 0 0
\(575\) −11.3433 + 19.6472i −0.473050 + 0.819346i
\(576\) 0 0
\(577\) −22.4525 38.8889i −0.934711 1.61897i −0.775149 0.631779i \(-0.782325\pi\)
−0.159562 0.987188i \(-0.551008\pi\)
\(578\) 0 0
\(579\) −15.6874 + 2.06036i −0.651947 + 0.0856255i
\(580\) 0 0
\(581\) −8.46651 10.0900i −0.351250 0.418604i
\(582\) 0 0
\(583\) −6.61923 18.1862i −0.274140 0.753194i
\(584\) 0 0
\(585\) 9.41989 + 35.2426i 0.389465 + 1.45710i
\(586\) 0 0
\(587\) −0.297968 + 1.68986i −0.0122985 + 0.0697481i −0.990339 0.138665i \(-0.955719\pi\)
0.978041 + 0.208413i \(0.0668299\pi\)
\(588\) 0 0
\(589\) 11.0561 + 4.02409i 0.455559 + 0.165810i
\(590\) 0 0
\(591\) 18.2299 28.5956i 0.749876 1.17627i
\(592\) 0 0
\(593\) 6.04981i 0.248436i 0.992255 + 0.124218i \(0.0396422\pi\)
−0.992255 + 0.124218i \(0.960358\pi\)
\(594\) 0 0
\(595\) 14.1190i 0.578823i
\(596\) 0 0
\(597\) 10.4589 + 20.1066i 0.428056 + 0.822909i
\(598\) 0 0
\(599\) 24.8844 + 9.05720i 1.01675 + 0.370067i 0.796022 0.605268i \(-0.206934\pi\)
0.220729 + 0.975335i \(0.429156\pi\)
\(600\) 0 0
\(601\) −5.02900 + 28.5209i −0.205137 + 1.16339i 0.692086 + 0.721815i \(0.256692\pi\)
−0.897224 + 0.441577i \(0.854419\pi\)
\(602\) 0 0
\(603\) 8.50110 + 12.1568i 0.346191 + 0.495064i
\(604\) 0 0
\(605\) 35.5799 + 97.7550i 1.44653 + 3.97431i
\(606\) 0 0
\(607\) −31.4425 37.4717i −1.27621 1.52093i −0.730394 0.683026i \(-0.760663\pi\)
−0.545818 0.837904i \(-0.683781\pi\)
\(608\) 0 0
\(609\) −3.89913 5.08469i −0.158001 0.206042i
\(610\) 0 0
\(611\) −1.15128 1.99407i −0.0465757 0.0806714i
\(612\) 0 0
\(613\) −16.3748 + 28.3620i −0.661371 + 1.14553i 0.318884 + 0.947794i \(0.396692\pi\)
−0.980255 + 0.197735i \(0.936641\pi\)
\(614\) 0 0
\(615\) 18.2944 + 58.0849i 0.737700 + 2.34221i
\(616\) 0 0
\(617\) 21.7419 3.83369i 0.875296 0.154338i 0.282089 0.959388i \(-0.408973\pi\)
0.593207 + 0.805050i \(0.297861\pi\)
\(618\) 0 0
\(619\) 13.2926 15.8415i 0.534276 0.636725i −0.429618 0.903011i \(-0.641352\pi\)
0.963894 + 0.266285i \(0.0857964\pi\)
\(620\) 0 0
\(621\) 10.3804 0.443575i 0.416552 0.0178001i
\(622\) 0 0
\(623\) 10.6970 + 8.97587i 0.428567 + 0.359610i
\(624\) 0 0
\(625\) 8.16167 + 46.2871i 0.326467 + 1.85149i
\(626\) 0 0
\(627\) −8.63179 + 38.8786i −0.344721 + 1.55266i
\(628\) 0 0
\(629\) −27.1670 15.6849i −1.08322 0.625397i
\(630\) 0 0
\(631\) 17.6889 10.2127i 0.704182 0.406560i −0.104721 0.994502i \(-0.533395\pi\)
0.808903 + 0.587942i \(0.200062\pi\)
\(632\) 0 0
\(633\) 13.5835 + 5.63139i 0.539896 + 0.223828i
\(634\) 0 0
\(635\) −67.4092 + 56.5630i −2.67505 + 2.24464i
\(636\) 0 0
\(637\) 16.3261 5.94220i 0.646863 0.235439i
\(638\) 0 0
\(639\) 10.9054 + 23.4246i 0.431413 + 0.926663i
\(640\) 0 0
\(641\) 28.5691 + 5.03751i 1.12841 + 0.198970i 0.706532 0.707681i \(-0.250259\pi\)
0.421882 + 0.906651i \(0.361370\pi\)
\(642\) 0 0
\(643\) 9.33983 25.6610i 0.368327 1.01197i −0.607671 0.794189i \(-0.707896\pi\)
0.975998 0.217781i \(-0.0698818\pi\)
\(644\) 0 0
\(645\) 1.59220 36.2106i 0.0626930 1.42579i
\(646\) 0 0
\(647\) −30.2231 −1.18819 −0.594096 0.804394i \(-0.702490\pi\)
−0.594096 + 0.804394i \(0.702490\pi\)
\(648\) 0 0
\(649\) −48.3051 −1.89614
\(650\) 0 0
\(651\) 0.260991 5.93557i 0.0102290 0.232633i
\(652\) 0 0
\(653\) 8.57540 23.5607i 0.335581 0.922002i −0.651050 0.759035i \(-0.725671\pi\)
0.986631 0.162968i \(-0.0521066\pi\)
\(654\) 0 0
\(655\) 6.71890 + 1.18472i 0.262529 + 0.0462910i
\(656\) 0 0
\(657\) −14.2159 + 20.2757i −0.554615 + 0.791032i
\(658\) 0 0
\(659\) −4.97059 + 1.80915i −0.193627 + 0.0704744i −0.437013 0.899455i \(-0.643964\pi\)
0.243387 + 0.969929i \(0.421742\pi\)
\(660\) 0 0
\(661\) 6.96047 5.84053i 0.270731 0.227170i −0.497307 0.867575i \(-0.665678\pi\)
0.768038 + 0.640405i \(0.221233\pi\)
\(662\) 0 0
\(663\) −15.1934 6.29881i −0.590063 0.244626i
\(664\) 0 0
\(665\) −14.6930 + 8.48303i −0.569772 + 0.328958i
\(666\) 0 0
\(667\) −5.79167 3.34382i −0.224254 0.129473i
\(668\) 0 0
\(669\) −1.68080 + 7.57052i −0.0649835 + 0.292693i
\(670\) 0 0
\(671\) −6.89321 39.0933i −0.266109 1.50918i
\(672\) 0 0
\(673\) 21.6889 + 18.1991i 0.836045 + 0.701525i 0.956670 0.291173i \(-0.0940456\pi\)
−0.120626 + 0.992698i \(0.538490\pi\)
\(674\) 0 0
\(675\) 43.5034 39.7894i 1.67445 1.53149i
\(676\) 0 0
\(677\) −13.8249 + 16.4759i −0.531335 + 0.633221i −0.963222 0.268707i \(-0.913404\pi\)
0.431887 + 0.901928i \(0.357848\pi\)
\(678\) 0 0
\(679\) −7.11427 + 1.25444i −0.273021 + 0.0481409i
\(680\) 0 0
\(681\) 2.74224 + 8.70667i 0.105083 + 0.333640i
\(682\) 0 0
\(683\) −1.83973 + 3.18651i −0.0703953 + 0.121928i −0.899075 0.437795i \(-0.855759\pi\)
0.828679 + 0.559724i \(0.189093\pi\)
\(684\) 0 0
\(685\) −24.7019 42.7849i −0.943809 1.63473i
\(686\) 0 0
\(687\) 4.82249 + 6.28881i 0.183989 + 0.239933i
\(688\) 0 0
\(689\) −6.17356 7.35737i −0.235194 0.280293i
\(690\) 0 0
\(691\) 0.481097 + 1.32180i 0.0183018 + 0.0502837i 0.948507 0.316756i \(-0.102594\pi\)
−0.930205 + 0.367040i \(0.880371\pi\)
\(692\) 0 0
\(693\) 20.0352 1.74037i 0.761073 0.0661112i
\(694\) 0 0
\(695\) 13.3023 75.4413i 0.504586 2.86165i
\(696\) 0 0
\(697\) −25.8006 9.39065i −0.977267 0.355696i
\(698\) 0 0
\(699\) −7.09266 13.6352i −0.268269 0.515729i
\(700\) 0 0
\(701\) 26.9701i 1.01865i 0.860575 + 0.509323i \(0.170104\pi\)
−0.860575 + 0.509323i \(0.829896\pi\)
\(702\) 0 0
\(703\) 37.6953i 1.42171i
\(704\) 0 0
\(705\) −2.88188 + 4.52057i −0.108538 + 0.170254i
\(706\) 0 0
\(707\) −0.0720623 0.0262285i −0.00271018 0.000986426i
\(708\) 0 0
\(709\) −5.47277 + 31.0376i −0.205534 + 1.16564i 0.691063 + 0.722795i \(0.257143\pi\)
−0.896597 + 0.442847i \(0.853968\pi\)
\(710\) 0 0
\(711\) 14.1692 14.1517i 0.531387 0.530730i
\(712\) 0 0
\(713\) −2.12086 5.82701i −0.0794267 0.218223i
\(714\) 0 0
\(715\) 47.3710 + 56.4545i 1.77157 + 2.11128i
\(716\) 0 0
\(717\) −19.8472 + 2.60669i −0.741207 + 0.0973486i
\(718\) 0 0
\(719\) −3.71854 6.44071i −0.138678 0.240198i 0.788318 0.615268i \(-0.210952\pi\)
−0.926997 + 0.375070i \(0.877619\pi\)
\(720\) 0 0
\(721\) 4.23485 7.33498i 0.157714 0.273169i
\(722\) 0 0
\(723\) 21.0048 22.9085i 0.781178 0.851977i
\(724\) 0 0
\(725\) −37.3712 + 6.58955i −1.38793 + 0.244730i
\(726\) 0 0
\(727\) 24.3792 29.0539i 0.904173 1.07755i −0.0924731 0.995715i \(-0.529477\pi\)
0.996646 0.0818359i \(-0.0260784\pi\)
\(728\) 0 0
\(729\) −26.0670 7.03647i −0.965444 0.260610i
\(730\) 0 0
\(731\) 12.5185 + 10.5043i 0.463013 + 0.388514i
\(732\) 0 0
\(733\) −7.08394 40.1750i −0.261651 1.48390i −0.778404 0.627764i \(-0.783970\pi\)
0.516752 0.856135i \(-0.327141\pi\)
\(734\) 0 0
\(735\) −29.8156 27.3379i −1.09976 1.00837i
\(736\) 0 0
\(737\) 25.9532 + 14.9841i 0.955997 + 0.551945i
\(738\) 0 0
\(739\) −37.5716 + 21.6920i −1.38210 + 0.797953i −0.992407 0.122994i \(-0.960750\pi\)
−0.389688 + 0.920947i \(0.627417\pi\)
\(740\) 0 0
\(741\) 2.57365 + 19.5956i 0.0945453 + 0.719862i
\(742\) 0 0
\(743\) −23.6176 + 19.8175i −0.866444 + 0.727033i −0.963346 0.268261i \(-0.913551\pi\)
0.0969021 + 0.995294i \(0.469107\pi\)
\(744\) 0 0
\(745\) −12.1189 + 4.41093i −0.444003 + 0.161604i
\(746\) 0 0
\(747\) 25.2455 + 25.2767i 0.923685 + 0.924828i
\(748\) 0 0
\(749\) −9.55873 1.68546i −0.349269 0.0615855i
\(750\) 0 0
\(751\) −6.94105 + 19.0704i −0.253283 + 0.695888i 0.746260 + 0.665654i \(0.231847\pi\)
−0.999543 + 0.0302340i \(0.990375\pi\)
\(752\) 0 0
\(753\) −33.3951 21.2895i −1.21698 0.775834i
\(754\) 0 0
\(755\) −85.3092 −3.10472
\(756\) 0 0
\(757\) −45.5588 −1.65586 −0.827931 0.560830i \(-0.810482\pi\)
−0.827931 + 0.560830i \(0.810482\pi\)
\(758\) 0 0
\(759\) 18.6209 9.68614i 0.675898 0.351585i
\(760\) 0 0
\(761\) 12.2329 33.6096i 0.443443 1.21835i −0.493771 0.869592i \(-0.664382\pi\)
0.937213 0.348756i \(-0.113396\pi\)
\(762\) 0 0
\(763\) −7.74227 1.36517i −0.280289 0.0494225i
\(764\) 0 0
\(765\) 3.31399 + 38.1507i 0.119818 + 1.37934i
\(766\) 0 0
\(767\) −22.5264 + 8.19894i −0.813381 + 0.296046i
\(768\) 0 0
\(769\) 8.79701 7.38157i 0.317228 0.266186i −0.470244 0.882537i \(-0.655834\pi\)
0.787472 + 0.616350i \(0.211390\pi\)
\(770\) 0 0
\(771\) −7.51559 + 5.76322i −0.270667 + 0.207557i
\(772\) 0 0
\(773\) 31.0680 17.9371i 1.11744 0.645153i 0.176693 0.984266i \(-0.443460\pi\)
0.940746 + 0.339113i \(0.110127\pi\)
\(774\) 0 0
\(775\) −30.4722 17.5931i −1.09459 0.631963i
\(776\) 0 0
\(777\) 18.1558 5.71833i 0.651336 0.205144i
\(778\) 0 0
\(779\) 5.72916 + 32.4917i 0.205269 + 1.16414i
\(780\) 0 0
\(781\) 39.9869 + 33.5530i 1.43084 + 1.20062i
\(782\) 0 0
\(783\) 11.7292 + 12.8241i 0.419168 + 0.458295i
\(784\) 0 0
\(785\) −28.0129 + 33.3844i −0.999822 + 1.19154i
\(786\) 0 0
\(787\) 53.8788 9.50029i 1.92057 0.338649i 0.921778 0.387719i \(-0.126737\pi\)
0.998795 + 0.0490696i \(0.0156256\pi\)
\(788\) 0 0
\(789\) −26.3499 5.85017i −0.938080 0.208272i
\(790\) 0 0
\(791\) −2.46191 + 4.26415i −0.0875354 + 0.151616i
\(792\) 0 0
\(793\) −9.84995 17.0606i −0.349782 0.605840i
\(794\) 0 0
\(795\) −8.56390 + 20.6570i −0.303730 + 0.732629i
\(796\)