Properties

Label 729.2.i.a.685.7
Level $729$
Weight $2$
Character 729.685
Analytic conductor $5.821$
Analytic rank $0$
Dimension $1404$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.i (of order \(81\), degree \(54\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(1404\)
Relative dimension: \(26\) over \(\Q(\zeta_{81})\)
Twist minimal: no (minimal twist has level 243)
Sato-Tate group: $\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label 685.7
Character \(\chi\) \(=\) 729.685
Dual form 729.2.i.a.613.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.17597 - 0.327353i) q^{2} +(-0.436594 - 0.263486i) q^{4} +(-3.30824 + 0.128375i) q^{5} +(3.02899 + 0.473725i) q^{7} +(2.10253 + 2.22855i) q^{8} +O(q^{10})\) \(q+(-1.17597 - 0.327353i) q^{2} +(-0.436594 - 0.263486i) q^{4} +(-3.30824 + 0.128375i) q^{5} +(3.02899 + 0.473725i) q^{7} +(2.10253 + 2.22855i) q^{8} +(3.93241 + 0.931999i) q^{10} +(-0.345643 - 2.53055i) q^{11} +(-2.19930 + 3.20665i) q^{13} +(-3.40692 - 1.54863i) q^{14} +(-1.26768 - 2.40662i) q^{16} +(2.28530 - 1.14772i) q^{17} +(-0.0846874 - 1.45403i) q^{19} +(1.47818 + 0.815627i) q^{20} +(-0.421919 + 3.08900i) q^{22} +(-1.73750 + 4.50023i) q^{23} +(5.94303 - 0.461929i) q^{25} +(3.63601 - 3.05098i) q^{26} +(-1.19762 - 1.00492i) q^{28} +(4.11031 + 2.93787i) q^{29} +(5.18413 - 5.94035i) q^{31} +(-0.594320 - 2.74369i) q^{32} +(-3.06315 + 0.601583i) q^{34} +(-10.0814 - 1.17835i) q^{35} +(-5.96054 - 8.00640i) q^{37} +(-0.376390 + 1.73761i) q^{38} +(-7.24177 - 7.10268i) q^{40} +(1.91809 - 7.44647i) q^{41} +(-8.37244 - 7.59758i) q^{43} +(-0.515859 + 1.19590i) q^{44} +(3.51640 - 4.72335i) q^{46} +(-4.91942 - 5.63703i) q^{47} +(2.28463 + 0.732536i) q^{49} +(-7.14003 - 1.40226i) q^{50} +(1.80511 - 0.820522i) q^{52} +(0.683668 - 3.87727i) q^{53} +(1.46833 + 8.32732i) q^{55} +(5.31282 + 7.74628i) q^{56} +(-3.87187 - 4.80036i) q^{58} +(-1.90759 + 0.779338i) q^{59} +(7.42756 - 4.48255i) q^{61} +(-8.04096 + 5.28863i) q^{62} +(-0.515570 + 8.85200i) q^{64} +(6.86416 - 10.8907i) q^{65} +(-6.69805 + 4.78748i) q^{67} +(-1.30016 - 0.101056i) q^{68} +(11.4697 + 4.68590i) q^{70} +(-2.48512 - 8.30090i) q^{71} +(-2.45021 + 0.580711i) q^{73} +(4.38849 + 11.3665i) q^{74} +(-0.346141 + 0.657133i) q^{76} +(0.151839 - 7.82876i) q^{77} +(7.41722 - 7.27476i) q^{79} +(4.50273 + 7.79896i) q^{80} +(-4.69323 + 8.12892i) q^{82} +(2.15695 + 8.37379i) q^{83} +(-7.41300 + 4.09032i) q^{85} +(7.35863 + 11.6753i) q^{86} +(4.91275 - 6.09085i) q^{88} +(4.79498 - 16.0163i) q^{89} +(-8.18072 + 8.67106i) q^{91} +(1.94432 - 1.50697i) q^{92} +(3.93978 + 8.23936i) q^{94} +(0.466827 + 4.79940i) q^{95} +(-6.93251 - 0.269013i) q^{97} +(-2.44685 - 1.60932i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{81}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.17597 0.327353i −0.831535 0.231474i −0.173855 0.984771i \(-0.555622\pi\)
−0.657680 + 0.753298i \(0.728462\pi\)
\(3\) 0 0
\(4\) −0.436594 0.263486i −0.218297 0.131743i
\(5\) −3.30824 + 0.128375i −1.47949 + 0.0574110i −0.765813 0.643063i \(-0.777663\pi\)
−0.713678 + 0.700474i \(0.752972\pi\)
\(6\) 0 0
\(7\) 3.02899 + 0.473725i 1.14485 + 0.179051i 0.698367 0.715740i \(-0.253911\pi\)
0.446484 + 0.894792i \(0.352676\pi\)
\(8\) 2.10253 + 2.22855i 0.743357 + 0.787912i
\(9\) 0 0
\(10\) 3.93241 + 0.931999i 1.24354 + 0.294724i
\(11\) −0.345643 2.53055i −0.104215 0.762991i −0.966518 0.256598i \(-0.917398\pi\)
0.862303 0.506393i \(-0.169021\pi\)
\(12\) 0 0
\(13\) −2.19930 + 3.20665i −0.609975 + 0.889366i −0.999499 0.0316506i \(-0.989924\pi\)
0.389524 + 0.921016i \(0.372640\pi\)
\(14\) −3.40692 1.54863i −0.910537 0.413890i
\(15\) 0 0
\(16\) −1.26768 2.40662i −0.316919 0.601656i
\(17\) 2.28530 1.14772i 0.554267 0.278363i −0.149539 0.988756i \(-0.547779\pi\)
0.703806 + 0.710392i \(0.251483\pi\)
\(18\) 0 0
\(19\) −0.0846874 1.45403i −0.0194286 0.333577i −0.993991 0.109461i \(-0.965088\pi\)
0.974563 0.224116i \(-0.0719494\pi\)
\(20\) 1.47818 + 0.815627i 0.330532 + 0.182380i
\(21\) 0 0
\(22\) −0.421919 + 3.08900i −0.0899535 + 0.658576i
\(23\) −1.73750 + 4.50023i −0.362293 + 0.938362i 0.625167 + 0.780491i \(0.285031\pi\)
−0.987460 + 0.157871i \(0.949537\pi\)
\(24\) 0 0
\(25\) 5.94303 0.461929i 1.18861 0.0923858i
\(26\) 3.63601 3.05098i 0.713080 0.598345i
\(27\) 0 0
\(28\) −1.19762 1.00492i −0.226328 0.189912i
\(29\) 4.11031 + 2.93787i 0.763265 + 0.545549i 0.895176 0.445713i \(-0.147050\pi\)
−0.131911 + 0.991262i \(0.542111\pi\)
\(30\) 0 0
\(31\) 5.18413 5.94035i 0.931097 1.06692i −0.0665100 0.997786i \(-0.521186\pi\)
0.997607 0.0691335i \(-0.0220234\pi\)
\(32\) −0.594320 2.74369i −0.105062 0.485020i
\(33\) 0 0
\(34\) −3.06315 + 0.601583i −0.525326 + 0.103171i
\(35\) −10.0814 1.17835i −1.70408 0.199178i
\(36\) 0 0
\(37\) −5.96054 8.00640i −0.979907 1.31624i −0.948514 0.316736i \(-0.897413\pi\)
−0.0313935 0.999507i \(-0.509994\pi\)
\(38\) −0.376390 + 1.73761i −0.0610586 + 0.281878i
\(39\) 0 0
\(40\) −7.24177 7.10268i −1.14502 1.12303i
\(41\) 1.91809 7.44647i 0.299555 1.16294i −0.624606 0.780940i \(-0.714740\pi\)
0.924161 0.382003i \(-0.124766\pi\)
\(42\) 0 0
\(43\) −8.37244 7.59758i −1.27679 1.15862i −0.978972 0.203997i \(-0.934607\pi\)
−0.297814 0.954624i \(-0.596257\pi\)
\(44\) −0.515859 + 1.19590i −0.0777687 + 0.180288i
\(45\) 0 0
\(46\) 3.51640 4.72335i 0.518465 0.696420i
\(47\) −4.91942 5.63703i −0.717572 0.822246i 0.272596 0.962128i \(-0.412118\pi\)
−0.990168 + 0.139883i \(0.955327\pi\)
\(48\) 0 0
\(49\) 2.28463 + 0.732536i 0.326375 + 0.104648i
\(50\) −7.14003 1.40226i −1.00975 0.198309i
\(51\) 0 0
\(52\) 1.80511 0.820522i 0.250323 0.113786i
\(53\) 0.683668 3.87727i 0.0939090 0.532585i −0.901167 0.433472i \(-0.857288\pi\)
0.995076 0.0991128i \(-0.0316005\pi\)
\(54\) 0 0
\(55\) 1.46833 + 8.32732i 0.197990 + 1.12286i
\(56\) 5.31282 + 7.74628i 0.709956 + 1.03514i
\(57\) 0 0
\(58\) −3.87187 4.80036i −0.508401 0.630318i
\(59\) −1.90759 + 0.779338i −0.248348 + 0.101461i −0.498956 0.866627i \(-0.666283\pi\)
0.250608 + 0.968089i \(0.419369\pi\)
\(60\) 0 0
\(61\) 7.42756 4.48255i 0.951001 0.573932i 0.0458161 0.998950i \(-0.485411\pi\)
0.905185 + 0.425018i \(0.139732\pi\)
\(62\) −8.04096 + 5.28863i −1.02120 + 0.671656i
\(63\) 0 0
\(64\) −0.515570 + 8.85200i −0.0644463 + 1.10650i
\(65\) 6.86416 10.8907i 0.851394 1.35083i
\(66\) 0 0
\(67\) −6.69805 + 4.78748i −0.818297 + 0.584884i −0.911753 0.410740i \(-0.865270\pi\)
0.0934555 + 0.995623i \(0.470209\pi\)
\(68\) −1.30016 0.101056i −0.157667 0.0122549i
\(69\) 0 0
\(70\) 11.4697 + 4.68590i 1.37089 + 0.560072i
\(71\) −2.48512 8.30090i −0.294930 0.985135i −0.969123 0.246579i \(-0.920693\pi\)
0.674193 0.738556i \(-0.264492\pi\)
\(72\) 0 0
\(73\) −2.45021 + 0.580711i −0.286776 + 0.0679671i −0.371486 0.928439i \(-0.621152\pi\)
0.0847104 + 0.996406i \(0.473003\pi\)
\(74\) 4.38849 + 11.3665i 0.510151 + 1.32132i
\(75\) 0 0
\(76\) −0.346141 + 0.657133i −0.0397051 + 0.0753783i
\(77\) 0.151839 7.82876i 0.0173036 0.892170i
\(78\) 0 0
\(79\) 7.41722 7.27476i 0.834503 0.818475i −0.150929 0.988545i \(-0.548227\pi\)
0.985432 + 0.170070i \(0.0543994\pi\)
\(80\) 4.50273 + 7.79896i 0.503421 + 0.871950i
\(81\) 0 0
\(82\) −4.69323 + 8.12892i −0.518281 + 0.897689i
\(83\) 2.15695 + 8.37379i 0.236756 + 0.919143i 0.970771 + 0.240009i \(0.0771504\pi\)
−0.734015 + 0.679133i \(0.762356\pi\)
\(84\) 0 0
\(85\) −7.41300 + 4.09032i −0.804053 + 0.443657i
\(86\) 7.35863 + 11.6753i 0.793501 + 1.25898i
\(87\) 0 0
\(88\) 4.91275 6.09085i 0.523700 0.649287i
\(89\) 4.79498 16.0163i 0.508267 1.69773i −0.189909 0.981802i \(-0.560819\pi\)
0.698175 0.715927i \(-0.253996\pi\)
\(90\) 0 0
\(91\) −8.18072 + 8.67106i −0.857573 + 0.908974i
\(92\) 1.94432 1.50697i 0.202710 0.157112i
\(93\) 0 0
\(94\) 3.93978 + 8.23936i 0.406358 + 0.849825i
\(95\) 0.466827 + 4.79940i 0.0478955 + 0.492408i
\(96\) 0 0
\(97\) −6.93251 0.269013i −0.703890 0.0273141i −0.315654 0.948874i \(-0.602224\pi\)
−0.388235 + 0.921560i \(0.626915\pi\)
\(98\) −2.44685 1.60932i −0.247169 0.162566i
\(99\) 0 0
\(100\) −2.71640 1.36423i −0.271640 0.136423i
\(101\) 0.357227 + 18.4185i 0.0355454 + 1.83271i 0.417666 + 0.908600i \(0.362848\pi\)
−0.382121 + 0.924112i \(0.624806\pi\)
\(102\) 0 0
\(103\) 3.17391 + 2.45997i 0.312735 + 0.242388i 0.756860 0.653577i \(-0.226732\pi\)
−0.444125 + 0.895965i \(0.646485\pi\)
\(104\) −11.7703 + 1.84084i −1.15417 + 0.180509i
\(105\) 0 0
\(106\) −2.07321 + 4.33575i −0.201368 + 0.421125i
\(107\) 1.07822 + 0.392441i 0.104236 + 0.0379387i 0.393612 0.919277i \(-0.371226\pi\)
−0.289376 + 0.957216i \(0.593448\pi\)
\(108\) 0 0
\(109\) 4.52259 1.64609i 0.433185 0.157666i −0.116218 0.993224i \(-0.537077\pi\)
0.549403 + 0.835557i \(0.314855\pi\)
\(110\) 0.999263 10.2733i 0.0952760 0.979522i
\(111\) 0 0
\(112\) −2.69970 7.89017i −0.255098 0.745551i
\(113\) 8.02980 7.28665i 0.755380 0.685471i −0.200347 0.979725i \(-0.564207\pi\)
0.955727 + 0.294254i \(0.0950712\pi\)
\(114\) 0 0
\(115\) 5.17034 15.1109i 0.482137 1.40910i
\(116\) −1.02045 2.36566i −0.0947461 0.219646i
\(117\) 0 0
\(118\) 2.49839 0.292020i 0.229995 0.0268826i
\(119\) 7.46586 2.39383i 0.684394 0.219442i
\(120\) 0 0
\(121\) 4.31285 1.20056i 0.392077 0.109142i
\(122\) −10.2019 + 2.83990i −0.923641 + 0.257113i
\(123\) 0 0
\(124\) −3.82856 + 1.22758i −0.343815 + 0.110240i
\(125\) −3.15996 + 0.369346i −0.282635 + 0.0330353i
\(126\) 0 0
\(127\) 1.30665 + 3.02914i 0.115946 + 0.268793i 0.966300 0.257418i \(-0.0828716\pi\)
−0.850354 + 0.526211i \(0.823612\pi\)
\(128\) 1.68637 4.92861i 0.149056 0.435632i
\(129\) 0 0
\(130\) −11.6371 + 10.5601i −1.02064 + 0.926186i
\(131\) −6.30110 18.4157i −0.550530 1.60898i −0.773250 0.634101i \(-0.781370\pi\)
0.222720 0.974882i \(-0.428506\pi\)
\(132\) 0 0
\(133\) 0.432292 4.44435i 0.0374845 0.385374i
\(134\) 9.44389 3.43729i 0.815828 0.296937i
\(135\) 0 0
\(136\) 7.36268 + 2.67979i 0.631344 + 0.229791i
\(137\) 3.01475 6.30481i 0.257567 0.538656i −0.732244 0.681043i \(-0.761527\pi\)
0.989811 + 0.142386i \(0.0454775\pi\)
\(138\) 0 0
\(139\) −8.84337 + 1.38308i −0.750084 + 0.117311i −0.517995 0.855383i \(-0.673322\pi\)
−0.232089 + 0.972695i \(0.574556\pi\)
\(140\) 4.09102 + 3.17078i 0.345754 + 0.267980i
\(141\) 0 0
\(142\) 0.205104 + 10.5751i 0.0172119 + 0.887443i
\(143\) 8.87478 + 4.45708i 0.742147 + 0.372720i
\(144\) 0 0
\(145\) −13.9750 9.19153i −1.16056 0.763315i
\(146\) 3.07147 + 0.119187i 0.254197 + 0.00986398i
\(147\) 0 0
\(148\) 0.492764 + 5.06606i 0.0405050 + 0.416427i
\(149\) 1.89172 + 3.95620i 0.154976 + 0.324104i 0.964982 0.262317i \(-0.0844867\pi\)
−0.810006 + 0.586422i \(0.800536\pi\)
\(150\) 0 0
\(151\) 1.51381 1.17329i 0.123192 0.0954812i −0.549141 0.835729i \(-0.685045\pi\)
0.672334 + 0.740248i \(0.265292\pi\)
\(152\) 3.06232 3.24587i 0.248387 0.263274i
\(153\) 0 0
\(154\) −2.74133 + 9.15666i −0.220902 + 0.737865i
\(155\) −16.3878 + 20.3177i −1.31630 + 1.63195i
\(156\) 0 0
\(157\) 6.80388 + 10.7951i 0.543008 + 0.861542i 0.999604 0.0281327i \(-0.00895609\pi\)
−0.456596 + 0.889674i \(0.650931\pi\)
\(158\) −11.1038 + 6.12683i −0.883373 + 0.487425i
\(159\) 0 0
\(160\) 2.31838 + 9.00049i 0.183284 + 0.711551i
\(161\) −7.39473 + 12.8080i −0.582786 + 1.00942i
\(162\) 0 0
\(163\) 9.03528 + 15.6496i 0.707698 + 1.22577i 0.965709 + 0.259627i \(0.0835996\pi\)
−0.258011 + 0.966142i \(0.583067\pi\)
\(164\) −2.79946 + 2.74569i −0.218601 + 0.214403i
\(165\) 0 0
\(166\) 0.204683 10.5534i 0.0158865 0.819102i
\(167\) 4.94500 9.38786i 0.382656 0.726454i −0.615437 0.788186i \(-0.711020\pi\)
0.998093 + 0.0617319i \(0.0196624\pi\)
\(168\) 0 0
\(169\) −0.763411 1.97728i −0.0587239 0.152099i
\(170\) 10.0564 2.38342i 0.771293 0.182800i
\(171\) 0 0
\(172\) 1.65350 + 5.52307i 0.126078 + 0.421130i
\(173\) −8.25690 3.37332i −0.627761 0.256469i 0.0419160 0.999121i \(-0.486654\pi\)
−0.669677 + 0.742653i \(0.733567\pi\)
\(174\) 0 0
\(175\) 18.2202 + 1.41619i 1.37732 + 0.107054i
\(176\) −5.65193 + 4.03976i −0.426030 + 0.304508i
\(177\) 0 0
\(178\) −10.8817 + 17.2650i −0.815621 + 1.29407i
\(179\) 0.748157 12.8454i 0.0559199 0.960108i −0.847350 0.531035i \(-0.821803\pi\)
0.903270 0.429073i \(-0.141160\pi\)
\(180\) 0 0
\(181\) 12.2749 8.07335i 0.912389 0.600088i −0.00416824 0.999991i \(-0.501327\pi\)
0.916557 + 0.399904i \(0.130956\pi\)
\(182\) 12.4588 7.51890i 0.923505 0.557338i
\(183\) 0 0
\(184\) −13.6821 + 5.58976i −1.00866 + 0.412083i
\(185\) 20.7467 + 25.7219i 1.52533 + 1.89111i
\(186\) 0 0
\(187\) −3.69427 5.38638i −0.270152 0.393891i
\(188\) 0.662512 + 3.75729i 0.0483186 + 0.274029i
\(189\) 0 0
\(190\) 1.02213 5.79676i 0.0741528 0.420541i
\(191\) −12.9951 + 5.90702i −0.940296 + 0.427417i −0.824504 0.565857i \(-0.808546\pi\)
−0.115792 + 0.993273i \(0.536941\pi\)
\(192\) 0 0
\(193\) 2.58441 + 0.507562i 0.186030 + 0.0365351i 0.284860 0.958569i \(-0.408053\pi\)
−0.0988295 + 0.995104i \(0.531510\pi\)
\(194\) 8.06434 + 2.58573i 0.578986 + 0.185644i
\(195\) 0 0
\(196\) −0.804441 0.921787i −0.0574600 0.0658419i
\(197\) −2.23653 + 3.00418i −0.159346 + 0.214039i −0.874625 0.484800i \(-0.838892\pi\)
0.715279 + 0.698839i \(0.246300\pi\)
\(198\) 0 0
\(199\) 2.56811 5.95355i 0.182048 0.422036i −0.802616 0.596496i \(-0.796559\pi\)
0.984664 + 0.174461i \(0.0558182\pi\)
\(200\) 13.5248 + 12.2731i 0.956350 + 0.867842i
\(201\) 0 0
\(202\) 5.60927 21.7765i 0.394667 1.53219i
\(203\) 11.0583 + 10.8459i 0.776143 + 0.761235i
\(204\) 0 0
\(205\) −5.38956 + 24.8810i −0.376423 + 1.73776i
\(206\) −2.92714 3.93183i −0.203944 0.273944i
\(207\) 0 0
\(208\) 10.5052 + 1.22788i 0.728405 + 0.0851384i
\(209\) −3.65022 + 0.716880i −0.252491 + 0.0495876i
\(210\) 0 0
\(211\) −2.36564 10.9210i −0.162858 0.751835i −0.983575 0.180500i \(-0.942228\pi\)
0.820717 0.571334i \(-0.193574\pi\)
\(212\) −1.32009 + 1.51266i −0.0906642 + 0.103890i
\(213\) 0 0
\(214\) −1.13949 0.814457i −0.0778938 0.0556752i
\(215\) 28.6734 + 24.0598i 1.95551 + 1.64087i
\(216\) 0 0
\(217\) 18.5168 15.5374i 1.25700 1.05475i
\(218\) −5.85727 + 0.455263i −0.396704 + 0.0308343i
\(219\) 0 0
\(220\) 1.55306 4.02254i 0.104708 0.271199i
\(221\) −1.34571 + 9.85236i −0.0905224 + 0.662741i
\(222\) 0 0
\(223\) 20.7325 + 11.4397i 1.38835 + 0.766059i 0.988600 0.150565i \(-0.0481091\pi\)
0.399750 + 0.916624i \(0.369097\pi\)
\(224\) −0.500435 8.59214i −0.0334367 0.574087i
\(225\) 0 0
\(226\) −11.8281 + 5.94029i −0.786793 + 0.395142i
\(227\) −5.10294 9.68769i −0.338694 0.642994i 0.654936 0.755684i \(-0.272695\pi\)
−0.993630 + 0.112690i \(0.964053\pi\)
\(228\) 0 0
\(229\) −9.27442 4.21574i −0.612871 0.278584i 0.0832272 0.996531i \(-0.473477\pi\)
−0.696098 + 0.717946i \(0.745082\pi\)
\(230\) −11.0268 + 16.0774i −0.727083 + 1.06011i
\(231\) 0 0
\(232\) 2.09485 + 15.3370i 0.137533 + 1.00692i
\(233\) −8.52260 2.01989i −0.558334 0.132328i −0.0582462 0.998302i \(-0.518551\pi\)
−0.500088 + 0.865975i \(0.666699\pi\)
\(234\) 0 0
\(235\) 16.9983 + 18.0172i 1.10885 + 1.17531i
\(236\) 1.03819 + 0.162370i 0.0675803 + 0.0105694i
\(237\) 0 0
\(238\) −9.56324 + 0.371097i −0.619893 + 0.0240547i
\(239\) −10.5333 6.35687i −0.681341 0.411191i 0.133364 0.991067i \(-0.457422\pi\)
−0.814705 + 0.579876i \(0.803101\pi\)
\(240\) 0 0
\(241\) −24.6524 6.86248i −1.58800 0.442051i −0.642133 0.766593i \(-0.721950\pi\)
−0.945871 + 0.324542i \(0.894790\pi\)
\(242\) −5.46478 −0.351289
\(243\) 0 0
\(244\) −4.42391 −0.283212
\(245\) −7.65214 2.13012i −0.488877 0.136088i
\(246\) 0 0
\(247\) 4.84881 + 2.92627i 0.308523 + 0.186194i
\(248\) 24.1382 0.936671i 1.53278 0.0594787i
\(249\) 0 0
\(250\) 3.83692 + 0.600083i 0.242668 + 0.0379526i
\(251\) 14.8878 + 15.7802i 0.939710 + 0.996035i 0.999998 0.00214620i \(-0.000683156\pi\)
−0.0602873 + 0.998181i \(0.519202\pi\)
\(252\) 0 0
\(253\) 11.9886 + 2.84136i 0.753718 + 0.178634i
\(254\) −0.544973 3.98991i −0.0341947 0.250349i
\(255\) 0 0
\(256\) 6.43395 9.38094i 0.402122 0.586308i
\(257\) −13.4868 6.13049i −0.841281 0.382409i −0.0536528 0.998560i \(-0.517086\pi\)
−0.787629 + 0.616150i \(0.788691\pi\)
\(258\) 0 0
\(259\) −14.2616 27.0750i −0.886172 1.68236i
\(260\) −5.86640 + 2.94622i −0.363819 + 0.182717i
\(261\) 0 0
\(262\) 1.38147 + 23.7189i 0.0853474 + 1.46536i
\(263\) −3.12526 1.72444i −0.192711 0.106334i 0.383822 0.923407i \(-0.374607\pi\)
−0.576534 + 0.817073i \(0.695595\pi\)
\(264\) 0 0
\(265\) −1.76400 + 12.9147i −0.108361 + 0.793346i
\(266\) −1.96323 + 5.08490i −0.120374 + 0.311775i
\(267\) 0 0
\(268\) 4.18576 0.325343i 0.255686 0.0198735i
\(269\) −2.46549 + 2.06879i −0.150324 + 0.126137i −0.714848 0.699280i \(-0.753504\pi\)
0.564524 + 0.825416i \(0.309060\pi\)
\(270\) 0 0
\(271\) 4.01195 + 3.36643i 0.243709 + 0.204496i 0.756458 0.654043i \(-0.226928\pi\)
−0.512749 + 0.858539i \(0.671373\pi\)
\(272\) −5.65916 4.04492i −0.343137 0.245260i
\(273\) 0 0
\(274\) −5.60915 + 6.42737i −0.338861 + 0.388292i
\(275\) −3.22310 14.8795i −0.194360 0.897268i
\(276\) 0 0
\(277\) −21.4061 + 4.20402i −1.28617 + 0.252595i −0.788641 0.614854i \(-0.789215\pi\)
−0.497526 + 0.867449i \(0.665758\pi\)
\(278\) 10.8523 + 1.26845i 0.650876 + 0.0760765i
\(279\) 0 0
\(280\) −18.5705 24.9446i −1.10980 1.49072i
\(281\) −1.35679 + 6.26364i −0.0809393 + 0.373657i −0.999780 0.0209711i \(-0.993324\pi\)
0.918841 + 0.394628i \(0.129127\pi\)
\(282\) 0 0
\(283\) −12.6431 12.4003i −0.751554 0.737119i 0.219595 0.975591i \(-0.429526\pi\)
−0.971149 + 0.238472i \(0.923353\pi\)
\(284\) −1.10218 + 4.27891i −0.0654022 + 0.253907i
\(285\) 0 0
\(286\) −8.97742 8.14657i −0.530846 0.481717i
\(287\) 9.33745 21.6466i 0.551172 1.27776i
\(288\) 0 0
\(289\) −6.24635 + 8.39031i −0.367433 + 0.493548i
\(290\) 13.4253 + 15.3837i 0.788362 + 0.903363i
\(291\) 0 0
\(292\) 1.22276 + 0.392061i 0.0715564 + 0.0229436i
\(293\) 20.3778 + 4.00207i 1.19049 + 0.233804i 0.748448 0.663193i \(-0.230799\pi\)
0.442037 + 0.896997i \(0.354256\pi\)
\(294\) 0 0
\(295\) 6.21074 2.82313i 0.361603 0.164369i
\(296\) 5.31045 30.1171i 0.308664 1.75052i
\(297\) 0 0
\(298\) −0.929529 5.27162i −0.0538462 0.305377i
\(299\) −10.6094 15.4689i −0.613558 0.894589i
\(300\) 0 0
\(301\) −21.7609 26.9792i −1.25428 1.55506i
\(302\) −2.16427 + 0.884203i −0.124540 + 0.0508802i
\(303\) 0 0
\(304\) −3.39194 + 2.04705i −0.194541 + 0.117406i
\(305\) −23.9967 + 15.7829i −1.37405 + 0.903726i
\(306\) 0 0
\(307\) 1.46209 25.1030i 0.0834457 1.43271i −0.653588 0.756851i \(-0.726737\pi\)
0.737034 0.675856i \(-0.236226\pi\)
\(308\) −2.12906 + 3.37798i −0.121314 + 0.192478i
\(309\) 0 0
\(310\) 25.9225 18.5283i 1.47230 1.05234i
\(311\) 6.96503 + 0.541365i 0.394951 + 0.0306980i 0.273432 0.961891i \(-0.411841\pi\)
0.121518 + 0.992589i \(0.461224\pi\)
\(312\) 0 0
\(313\) −9.13195 3.73081i −0.516168 0.210878i 0.105121 0.994459i \(-0.466477\pi\)
−0.621289 + 0.783582i \(0.713391\pi\)
\(314\) −4.46734 14.9219i −0.252106 0.842094i
\(315\) 0 0
\(316\) −5.15511 + 1.22178i −0.289997 + 0.0687306i
\(317\) 1.01277 + 2.62314i 0.0568829 + 0.147330i 0.958412 0.285388i \(-0.0921224\pi\)
−0.901529 + 0.432718i \(0.857554\pi\)
\(318\) 0 0
\(319\) 6.01374 11.4168i 0.336705 0.639218i
\(320\) 0.569257 29.3508i 0.0318225 1.64076i
\(321\) 0 0
\(322\) 12.8887 12.6412i 0.718260 0.704464i
\(323\) −1.86235 3.22569i −0.103624 0.179482i
\(324\) 0 0
\(325\) −11.5892 + 20.0732i −0.642856 + 1.11346i
\(326\) −5.50227 21.3611i −0.304742 1.18308i
\(327\) 0 0
\(328\) 20.6277 11.3819i 1.13897 0.628459i
\(329\) −12.2305 19.4050i −0.674288 1.06983i
\(330\) 0 0
\(331\) −3.51777 + 4.36135i −0.193354 + 0.239721i −0.865758 0.500463i \(-0.833163\pi\)
0.672404 + 0.740185i \(0.265262\pi\)
\(332\) 1.26466 4.22427i 0.0694074 0.231837i
\(333\) 0 0
\(334\) −8.88831 + 9.42106i −0.486347 + 0.515497i
\(335\) 21.5442 16.6980i 1.17708 0.912310i
\(336\) 0 0
\(337\) 6.08010 + 12.7155i 0.331204 + 0.692655i 0.998647 0.0520062i \(-0.0165616\pi\)
−0.667442 + 0.744661i \(0.732611\pi\)
\(338\) 0.250477 + 2.57513i 0.0136241 + 0.140068i
\(339\) 0 0
\(340\) 4.31421 + 0.167411i 0.233971 + 0.00907913i
\(341\) −16.8242 11.0655i −0.911084 0.599229i
\(342\) 0 0
\(343\) −12.6049 6.33040i −0.680599 0.341810i
\(344\) −0.671698 34.6326i −0.0362155 1.86726i
\(345\) 0 0
\(346\) 8.60559 + 6.66983i 0.462639 + 0.358573i
\(347\) −27.2531 + 4.26230i −1.46302 + 0.228812i −0.835372 0.549685i \(-0.814748\pi\)
−0.627648 + 0.778497i \(0.715982\pi\)
\(348\) 0 0
\(349\) 8.39323 17.5530i 0.449279 0.939588i −0.545555 0.838075i \(-0.683681\pi\)
0.994834 0.101513i \(-0.0323683\pi\)
\(350\) −20.9628 7.62983i −1.12051 0.407832i
\(351\) 0 0
\(352\) −6.73762 + 2.45229i −0.359117 + 0.130708i
\(353\) −1.36546 + 14.0382i −0.0726761 + 0.747175i 0.886191 + 0.463320i \(0.153342\pi\)
−0.958867 + 0.283855i \(0.908386\pi\)
\(354\) 0 0
\(355\) 9.28703 + 27.1424i 0.492904 + 1.44057i
\(356\) −6.31353 + 5.72922i −0.334616 + 0.303648i
\(357\) 0 0
\(358\) −5.08478 + 14.8608i −0.268739 + 0.785419i
\(359\) −8.27755 19.1895i −0.436872 1.01278i −0.984392 0.175991i \(-0.943687\pi\)
0.547519 0.836793i \(-0.315572\pi\)
\(360\) 0 0
\(361\) 16.7645 1.95949i 0.882343 0.103131i
\(362\) −17.0778 + 5.47577i −0.897588 + 0.287800i
\(363\) 0 0
\(364\) 5.85635 1.63023i 0.306956 0.0854471i
\(365\) 8.03135 2.23568i 0.420380 0.117021i
\(366\) 0 0
\(367\) 31.2825 10.0303i 1.63293 0.523579i 0.659336 0.751849i \(-0.270838\pi\)
0.973598 + 0.228270i \(0.0733068\pi\)
\(368\) 13.0329 1.52333i 0.679389 0.0794092i
\(369\) 0 0
\(370\) −15.9774 37.0397i −0.830623 1.92560i
\(371\) 3.90759 11.4204i 0.202872 0.592915i
\(372\) 0 0
\(373\) −27.1921 + 24.6755i −1.40795 + 1.27765i −0.495419 + 0.868654i \(0.664985\pi\)
−0.912536 + 0.408996i \(0.865879\pi\)
\(374\) 2.58110 + 7.54354i 0.133465 + 0.390067i
\(375\) 0 0
\(376\) 2.21919 22.8152i 0.114446 1.17661i
\(377\) −18.4605 + 6.71908i −0.950765 + 0.346050i
\(378\) 0 0
\(379\) 17.8517 + 6.49750i 0.916981 + 0.333754i 0.757037 0.653372i \(-0.226646\pi\)
0.159944 + 0.987126i \(0.448868\pi\)
\(380\) 1.06076 2.21839i 0.0544158 0.113801i
\(381\) 0 0
\(382\) 17.2156 2.69246i 0.880824 0.137758i
\(383\) 6.08943 + 4.71966i 0.311155 + 0.241163i 0.756194 0.654348i \(-0.227057\pi\)
−0.445038 + 0.895512i \(0.646810\pi\)
\(384\) 0 0
\(385\) 0.502697 + 25.9189i 0.0256198 + 1.32095i
\(386\) −2.87303 1.44289i −0.146234 0.0734413i
\(387\) 0 0
\(388\) 2.95581 + 1.94407i 0.150058 + 0.0986950i
\(389\) −4.79877 0.186214i −0.243307 0.00944143i −0.0831666 0.996536i \(-0.526503\pi\)
−0.160141 + 0.987094i \(0.551195\pi\)
\(390\) 0 0
\(391\) 1.19431 + 12.2785i 0.0603987 + 0.620953i
\(392\) 3.17100 + 6.63159i 0.160160 + 0.334946i
\(393\) 0 0
\(394\) 3.61351 2.80068i 0.182046 0.141096i
\(395\) −23.6041 + 25.0189i −1.18765 + 1.25884i
\(396\) 0 0
\(397\) 9.89224 33.0424i 0.496477 1.65835i −0.231566 0.972819i \(-0.574385\pi\)
0.728044 0.685531i \(-0.240430\pi\)
\(398\) −4.96892 + 6.16050i −0.249070 + 0.308798i
\(399\) 0 0
\(400\) −8.64553 13.7171i −0.432277 0.685853i
\(401\) 1.86142 1.02709i 0.0929547 0.0512903i −0.435954 0.899969i \(-0.643589\pi\)
0.528909 + 0.848679i \(0.322601\pi\)
\(402\) 0 0
\(403\) 7.64722 + 29.6883i 0.380935 + 1.47888i
\(404\) 4.69706 8.13554i 0.233687 0.404758i
\(405\) 0 0
\(406\) −9.45379 16.3744i −0.469184 0.812650i
\(407\) −18.2004 + 17.8508i −0.902160 + 0.884833i
\(408\) 0 0
\(409\) −0.206616 + 10.6530i −0.0102165 + 0.526759i 0.959389 + 0.282086i \(0.0910263\pi\)
−0.969606 + 0.244673i \(0.921319\pi\)
\(410\) 14.4828 27.4949i 0.715255 1.35788i
\(411\) 0 0
\(412\) −0.737544 1.91029i −0.0363362 0.0941131i
\(413\) −6.14728 + 1.45693i −0.302488 + 0.0716909i
\(414\) 0 0
\(415\) −8.21070 27.4256i −0.403047 1.34627i
\(416\) 10.1051 + 4.12840i 0.495445 + 0.202412i
\(417\) 0 0
\(418\) 4.52721 + 0.351883i 0.221433 + 0.0172112i
\(419\) 12.3746 8.84481i 0.604537 0.432097i −0.237598 0.971364i \(-0.576360\pi\)
0.842135 + 0.539266i \(0.181298\pi\)
\(420\) 0 0
\(421\) −18.6538 + 29.5962i −0.909130 + 1.44243i −0.0123661 + 0.999924i \(0.503936\pi\)
−0.896764 + 0.442509i \(0.854088\pi\)
\(422\) −0.793110 + 13.6172i −0.0386080 + 0.662874i
\(423\) 0 0
\(424\) 10.0781 6.62850i 0.489438 0.321908i
\(425\) 13.0515 7.87660i 0.633089 0.382071i
\(426\) 0 0
\(427\) 24.6215 10.0590i 1.19152 0.486788i
\(428\) −0.367343 0.455433i −0.0177562 0.0220142i
\(429\) 0 0
\(430\) −25.8429 37.6799i −1.24626 1.81709i
\(431\) 5.82480 + 33.0341i 0.280571 + 1.59119i 0.720691 + 0.693256i \(0.243825\pi\)
−0.440121 + 0.897939i \(0.645064\pi\)
\(432\) 0 0
\(433\) −3.13975 + 17.8064i −0.150887 + 0.855720i 0.811564 + 0.584264i \(0.198617\pi\)
−0.962451 + 0.271457i \(0.912495\pi\)
\(434\) −26.8614 + 12.2100i −1.28939 + 0.586098i
\(435\) 0 0
\(436\) −2.40825 0.472965i −0.115334 0.0226509i
\(437\) 6.69059 + 2.14525i 0.320055 + 0.102621i
\(438\) 0 0
\(439\) −20.6122 23.6190i −0.983767 1.12727i −0.991864 0.127304i \(-0.959368\pi\)
0.00809698 0.999967i \(-0.497423\pi\)
\(440\) −15.4706 + 20.7807i −0.737534 + 0.990680i
\(441\) 0 0
\(442\) 4.80771 11.1455i 0.228680 0.530139i
\(443\) −6.00236 5.44685i −0.285181 0.258788i 0.516842 0.856081i \(-0.327107\pi\)
−0.802023 + 0.597293i \(0.796243\pi\)
\(444\) 0 0
\(445\) −13.8069 + 53.6015i −0.654508 + 2.54096i
\(446\) −20.6359 20.2396i −0.977139 0.958371i
\(447\) 0 0
\(448\) −5.75507 + 26.5684i −0.271902 + 1.25524i
\(449\) 22.6491 + 30.4231i 1.06888 + 1.43575i 0.892287 + 0.451470i \(0.149100\pi\)
0.176592 + 0.984284i \(0.443493\pi\)
\(450\) 0 0
\(451\) −19.5067 2.28000i −0.918533 0.107361i
\(452\) −5.42569 + 1.06557i −0.255203 + 0.0501202i
\(453\) 0 0
\(454\) 2.82960 + 13.0629i 0.132800 + 0.613071i
\(455\) 25.9507 29.7362i 1.21659 1.39405i
\(456\) 0 0
\(457\) 21.1619 + 15.1256i 0.989911 + 0.707546i 0.956451 0.291894i \(-0.0942856\pi\)
0.0334602 + 0.999440i \(0.489347\pi\)
\(458\) 9.52639 + 7.99359i 0.445139 + 0.373516i
\(459\) 0 0
\(460\) −6.23884 + 5.23501i −0.290888 + 0.244084i
\(461\) −3.39406 + 0.263808i −0.158077 + 0.0122867i −0.156287 0.987712i \(-0.549953\pi\)
−0.00179016 + 0.999998i \(0.500570\pi\)
\(462\) 0 0
\(463\) 9.57547 24.8011i 0.445010 1.15260i −0.511080 0.859533i \(-0.670755\pi\)
0.956090 0.293072i \(-0.0946775\pi\)
\(464\) 1.85981 13.6162i 0.0863396 0.632118i
\(465\) 0 0
\(466\) 9.36109 + 5.16523i 0.433644 + 0.239275i
\(467\) 1.03712 + 17.8066i 0.0479921 + 0.823992i 0.933325 + 0.359034i \(0.116894\pi\)
−0.885332 + 0.464959i \(0.846069\pi\)
\(468\) 0 0
\(469\) −22.5563 + 11.3282i −1.04155 + 0.523087i
\(470\) −14.0915 26.7520i −0.649992 1.23398i
\(471\) 0 0
\(472\) −5.74757 2.61259i −0.264553 0.120254i
\(473\) −16.3322 + 23.8130i −0.750956 + 1.09492i
\(474\) 0 0
\(475\) −1.17496 8.60221i −0.0539107 0.394696i
\(476\) −3.89029 0.922015i −0.178311 0.0422605i
\(477\) 0 0
\(478\) 10.3059 + 10.9236i 0.471379 + 0.499632i
\(479\) −5.20291 0.813720i −0.237727 0.0371798i 0.0345329 0.999404i \(-0.489006\pi\)
−0.272260 + 0.962224i \(0.587771\pi\)
\(480\) 0 0
\(481\) 38.7828 1.50495i 1.76834 0.0686197i
\(482\) 26.7440 + 16.1401i 1.21816 + 0.735162i
\(483\) 0 0
\(484\) −2.19929 0.612215i −0.0999678 0.0278279i
\(485\) 22.9690 1.04297
\(486\) 0 0
\(487\) −9.85734 −0.446679 −0.223339 0.974741i \(-0.571696\pi\)
−0.223339 + 0.974741i \(0.571696\pi\)
\(488\) 25.6063 + 7.12799i 1.15914 + 0.322669i
\(489\) 0 0
\(490\) 8.30137 + 5.00990i 0.375018 + 0.226324i
\(491\) 24.7853 0.961783i 1.11855 0.0434047i 0.527140 0.849779i \(-0.323265\pi\)
0.591406 + 0.806374i \(0.298573\pi\)
\(492\) 0 0
\(493\) 12.7652 + 1.99643i 0.574914 + 0.0899148i
\(494\) −4.74412 5.02848i −0.213448 0.226242i
\(495\) 0 0
\(496\) −20.8680 4.94581i −0.937001 0.222073i
\(497\) −3.59507 26.3206i −0.161261 1.18064i
\(498\) 0 0
\(499\) 10.8296 15.7899i 0.484799 0.706855i −0.502703 0.864459i \(-0.667661\pi\)
0.987502 + 0.157604i \(0.0503771\pi\)
\(500\) 1.47694 + 0.671350i 0.0660506 + 0.0300237i
\(501\) 0 0
\(502\) −12.3419 23.4305i −0.550846 1.04576i
\(503\) 18.4176 9.24969i 0.821202 0.412423i 0.0119817 0.999928i \(-0.496186\pi\)
0.809221 + 0.587505i \(0.199890\pi\)
\(504\) 0 0
\(505\) −3.54627 60.8871i −0.157807 2.70944i
\(506\) −13.1681 7.26585i −0.585394 0.323007i
\(507\) 0 0
\(508\) 0.227663 1.66679i 0.0101009 0.0739517i
\(509\) 9.13202 23.6525i 0.404770 1.04838i −0.569300 0.822130i \(-0.692786\pi\)
0.974069 0.226250i \(-0.0726465\pi\)
\(510\) 0 0
\(511\) −7.69677 + 0.598240i −0.340485 + 0.0264646i
\(512\) −18.6179 + 15.6222i −0.822801 + 0.690412i
\(513\) 0 0
\(514\) 13.8532 + 11.6242i 0.611037 + 0.512721i
\(515\) −10.8159 7.73073i −0.476605 0.340656i
\(516\) 0 0
\(517\) −12.5645 + 14.3973i −0.552584 + 0.633191i
\(518\) 7.90810 + 36.5078i 0.347462 + 1.60406i
\(519\) 0 0
\(520\) 38.7027 7.60095i 1.69722 0.333324i
\(521\) −38.6517 4.51773i −1.69336 0.197925i −0.785985 0.618246i \(-0.787844\pi\)
−0.907376 + 0.420321i \(0.861918\pi\)
\(522\) 0 0
\(523\) 3.04581 + 4.09123i 0.133184 + 0.178897i 0.863712 0.503986i \(-0.168134\pi\)
−0.730528 + 0.682882i \(0.760726\pi\)
\(524\) −2.10124 + 9.70041i −0.0917931 + 0.423764i
\(525\) 0 0
\(526\) 3.11070 + 3.05095i 0.135633 + 0.133028i
\(527\) 5.02943 19.5254i 0.219085 0.850542i
\(528\) 0 0
\(529\) −0.200643 0.182074i −0.00872359 0.00791624i
\(530\) 6.30208 14.6099i 0.273745 0.634612i
\(531\) 0 0
\(532\) −1.35976 + 1.82647i −0.0589530 + 0.0791876i
\(533\) 19.6598 + 22.5276i 0.851561 + 0.975781i
\(534\) 0 0
\(535\) −3.61740 1.15987i −0.156394 0.0501457i
\(536\) −24.7520 4.86113i −1.06912 0.209969i
\(537\) 0 0
\(538\) 3.57656 1.62575i 0.154197 0.0700910i
\(539\) 1.06406 6.03456i 0.0458322 0.259927i
\(540\) 0 0
\(541\) −3.06868 17.4033i −0.131933 0.748228i −0.976947 0.213484i \(-0.931519\pi\)
0.845014 0.534744i \(-0.179592\pi\)
\(542\) −3.61592 5.27214i −0.155317 0.226458i
\(543\) 0 0
\(544\) −4.50719 5.58804i −0.193244 0.239585i
\(545\) −14.7505 + 6.02624i −0.631842 + 0.258136i
\(546\) 0 0
\(547\) −12.7700 + 7.70674i −0.546006 + 0.329517i −0.762731 0.646716i \(-0.776142\pi\)
0.216724 + 0.976233i \(0.430463\pi\)
\(548\) −2.97745 + 1.95830i −0.127190 + 0.0836543i
\(549\) 0 0
\(550\) −1.08058 + 18.5529i −0.0460762 + 0.791098i
\(551\) 3.92365 6.22530i 0.167153 0.265206i
\(552\) 0 0
\(553\) 25.9129 18.5214i 1.10193 0.787612i
\(554\) 26.5491 + 2.06356i 1.12796 + 0.0876721i
\(555\) 0 0
\(556\) 4.22538 + 1.72626i 0.179196 + 0.0732096i
\(557\) 3.91581 + 13.0797i 0.165918 + 0.554206i 0.999997 + 0.00255997i \(0.000814866\pi\)
−0.834078 + 0.551646i \(0.814000\pi\)
\(558\) 0 0
\(559\) 42.7763 10.1382i 1.80925 0.428799i
\(560\) 9.94416 + 25.7560i 0.420218 + 1.08839i
\(561\) 0 0
\(562\) 3.64596 6.92169i 0.153796 0.291974i
\(563\) 0.0259795 1.33950i 0.00109491 0.0564531i −0.998866 0.0476102i \(-0.984839\pi\)
0.999961 0.00884295i \(-0.00281484\pi\)
\(564\) 0 0
\(565\) −25.6291 + 25.1369i −1.07822 + 1.05752i
\(566\) 10.8086 + 18.7211i 0.454320 + 0.786905i
\(567\) 0 0
\(568\) 13.2739 22.9911i 0.556962 0.964686i
\(569\) 10.3496 + 40.1796i 0.433878 + 1.68442i 0.694918 + 0.719089i \(0.255441\pi\)
−0.261040 + 0.965328i \(0.584066\pi\)
\(570\) 0 0
\(571\) −27.4309 + 15.1357i −1.14795 + 0.633411i −0.938796 0.344472i \(-0.888058\pi\)
−0.209152 + 0.977883i \(0.567070\pi\)
\(572\) −2.70030 4.28431i −0.112905 0.179136i
\(573\) 0 0
\(574\) −18.0666 + 22.3991i −0.754087 + 0.934921i
\(575\) −8.24721 + 27.5476i −0.343932 + 1.14881i
\(576\) 0 0
\(577\) −20.6977 + 21.9383i −0.861656 + 0.913301i −0.996992 0.0774982i \(-0.975307\pi\)
0.135337 + 0.990800i \(0.456788\pi\)
\(578\) 10.0921 7.82197i 0.419776 0.325351i
\(579\) 0 0
\(580\) 3.67958 + 7.69519i 0.152786 + 0.319525i
\(581\) 2.56650 + 26.3859i 0.106476 + 1.09467i
\(582\) 0 0
\(583\) −10.0480 0.389906i −0.416144 0.0161483i
\(584\) −6.44579 4.23946i −0.266729 0.175430i
\(585\) 0 0
\(586\) −22.6536 11.3771i −0.935810 0.469982i
\(587\) −0.481861 24.8446i −0.0198885 1.02545i −0.868279 0.496076i \(-0.834774\pi\)
0.848390 0.529371i \(-0.177572\pi\)
\(588\) 0 0
\(589\) −9.07646 7.03479i −0.373989 0.289863i
\(590\) −8.22779 + 1.28680i −0.338733 + 0.0529768i
\(591\) 0 0
\(592\) −11.7124 + 24.4943i −0.481375 + 1.00671i
\(593\) −0.393101 0.143077i −0.0161427 0.00587547i 0.333936 0.942596i \(-0.391623\pi\)
−0.350079 + 0.936720i \(0.613845\pi\)
\(594\) 0 0
\(595\) −24.3916 + 8.87781i −0.999957 + 0.363955i
\(596\) 0.216488 2.22569i 0.00886770 0.0911679i
\(597\) 0 0
\(598\) 7.41253 + 21.6639i 0.303121 + 0.885904i
\(599\) −4.67664 + 4.24382i −0.191082 + 0.173398i −0.761933 0.647656i \(-0.775749\pi\)
0.570851 + 0.821054i \(0.306614\pi\)
\(600\) 0 0
\(601\) 6.75238 19.7346i 0.275435 0.804990i −0.718550 0.695475i \(-0.755194\pi\)
0.993985 0.109514i \(-0.0349296\pi\)
\(602\) 16.7583 + 38.8502i 0.683019 + 1.58342i
\(603\) 0 0
\(604\) −0.970066 + 0.113384i −0.0394714 + 0.00461355i
\(605\) −14.1138 + 4.52542i −0.573809 + 0.183984i
\(606\) 0 0
\(607\) 4.00460 1.11476i 0.162542 0.0452466i −0.185946 0.982560i \(-0.559535\pi\)
0.348487 + 0.937313i \(0.386695\pi\)
\(608\) −3.93906 + 1.09651i −0.159750 + 0.0444695i
\(609\) 0 0
\(610\) 33.3859 10.7048i 1.35176 0.433424i
\(611\) 28.8953 3.37738i 1.16898 0.136634i
\(612\) 0 0
\(613\) 1.06973 + 2.47990i 0.0432058 + 0.100162i 0.938452 0.345409i \(-0.112260\pi\)
−0.895246 + 0.445571i \(0.853001\pi\)
\(614\) −9.93692 + 29.0418i −0.401022 + 1.17203i
\(615\) 0 0
\(616\) 17.7660 16.1218i 0.715814 0.649567i
\(617\) −3.76006 10.9892i −0.151374 0.442408i 0.844240 0.535966i \(-0.180052\pi\)
−0.995614 + 0.0935582i \(0.970176\pi\)
\(618\) 0 0
\(619\) 2.62607 26.9984i 0.105551 1.08516i −0.781632 0.623740i \(-0.785613\pi\)
0.887183 0.461418i \(-0.152659\pi\)
\(620\) 12.5082 4.55262i 0.502342 0.182837i
\(621\) 0 0
\(622\) −8.01343 2.91665i −0.321309 0.116947i
\(623\) 22.1113 46.2418i 0.885870 1.85264i
\(624\) 0 0
\(625\) −19.0403 + 2.97785i −0.761613 + 0.119114i
\(626\) 9.51758 + 7.37668i 0.380399 + 0.294832i
\(627\) 0 0
\(628\) −0.126180 6.50579i −0.00503512 0.259609i
\(629\) −22.8108 11.4560i −0.909524 0.456780i
\(630\) 0 0
\(631\) 32.0455 + 21.0766i 1.27571 + 0.839048i 0.992763 0.120088i \(-0.0383176\pi\)
0.282947 + 0.959136i \(0.408688\pi\)
\(632\) 31.8071 + 1.23426i 1.26522 + 0.0490963i
\(633\) 0 0
\(634\) −0.332293 3.41627i −0.0131970 0.135677i
\(635\) −4.71157 9.85341i −0.186973 0.391021i
\(636\) 0 0
\(637\) −7.37356 + 5.71494i −0.292151 + 0.226434i
\(638\) −10.8093 + 11.4572i −0.427944 + 0.453594i
\(639\) 0 0
\(640\) −4.94623 + 16.5215i −0.195517 + 0.653072i
\(641\) 12.4768 15.4688i 0.492803 0.610980i −0.469509 0.882928i \(-0.655569\pi\)
0.962312 + 0.271947i \(0.0876677\pi\)
\(642\) 0 0
\(643\) 19.5807 + 31.0669i 0.772187 + 1.22516i 0.969566 + 0.244831i \(0.0787326\pi\)
−0.197378 + 0.980327i \(0.563243\pi\)
\(644\) 6.60323 3.64351i 0.260204 0.143574i
\(645\) 0 0
\(646\) 1.13413 + 4.40296i 0.0446217 + 0.173232i
\(647\) 13.2270 22.9098i 0.520006 0.900677i −0.479723 0.877420i \(-0.659263\pi\)
0.999730 0.0232575i \(-0.00740376\pi\)
\(648\) 0 0
\(649\) 2.63150 + 4.55790i 0.103296 + 0.178913i
\(650\) 20.1996 19.8116i 0.792293 0.777076i
\(651\) 0 0
\(652\) 0.178689 9.21317i 0.00699801 0.360816i
\(653\) −1.38260 + 2.62480i −0.0541053 + 0.102716i −0.910323 0.413899i \(-0.864166\pi\)
0.856217 + 0.516616i \(0.172808\pi\)
\(654\) 0 0
\(655\) 23.2097 + 60.1146i 0.906877 + 2.34887i
\(656\) −20.3524 + 4.82360i −0.794627 + 0.188330i
\(657\) 0 0
\(658\) 8.03037 + 26.8233i 0.313056 + 1.04568i
\(659\) −12.6577 5.17125i −0.493075 0.201443i 0.118004 0.993013i \(-0.462350\pi\)
−0.611079 + 0.791570i \(0.709264\pi\)
\(660\) 0 0
\(661\) 29.5777 + 2.29896i 1.15044 + 0.0894191i 0.638513 0.769611i \(-0.279550\pi\)
0.511925 + 0.859030i \(0.328933\pi\)
\(662\) 5.56448 3.97725i 0.216270 0.154580i
\(663\) 0 0
\(664\) −14.1264 + 22.4130i −0.548210 + 0.869794i
\(665\) −0.859584 + 14.7585i −0.0333332 + 0.572310i
\(666\) 0 0
\(667\) −20.3627 + 13.3928i −0.788448 + 0.518570i
\(668\) −4.63252 + 2.79574i −0.179238 + 0.108170i
\(669\) 0 0
\(670\) −30.8014 + 12.5838i −1.18996 + 0.486153i
\(671\) −13.9106 17.2465i −0.537014 0.665792i
\(672\) 0 0
\(673\) 2.31905 + 3.38126i 0.0893929 + 0.130338i 0.866792 0.498669i \(-0.166178\pi\)
−0.777400 + 0.629007i \(0.783462\pi\)
\(674\) −2.98756 16.9433i −0.115077 0.652632i
\(675\) 0 0
\(676\) −0.187686 + 1.06442i −0.00721867 + 0.0409391i
\(677\) 4.80039 2.18204i 0.184494 0.0838628i −0.319434 0.947609i \(-0.603493\pi\)
0.503928 + 0.863746i \(0.331888\pi\)
\(678\) 0 0
\(679\) −20.8711 4.09894i −0.800958 0.157303i
\(680\) −24.7015 7.92023i −0.947261 0.303727i
\(681\) 0 0
\(682\) 16.1625 + 18.5201i 0.618892 + 0.709172i
\(683\) −4.01138 + 5.38821i −0.153491 + 0.206174i −0.872217 0.489119i \(-0.837318\pi\)
0.718726 + 0.695294i \(0.244726\pi\)
\(684\) 0 0
\(685\) −9.16414 + 21.2449i −0.350144 + 0.811725i
\(686\) 12.7506 + 11.5706i 0.486822 + 0.441767i
\(687\) 0 0
\(688\) −7.67099 + 29.7806i −0.292454 + 1.13537i
\(689\) 10.9295 + 10.7196i 0.416380 + 0.408383i
\(690\) 0 0
\(691\) 5.36891 24.7856i 0.204243 0.942890i −0.753987 0.656890i \(-0.771872\pi\)
0.958230 0.286000i \(-0.0923258\pi\)
\(692\) 2.71609 + 3.64834i 0.103250 + 0.138689i
\(693\) 0 0
\(694\) 33.4440 + 3.90904i 1.26952 + 0.148385i
\(695\) 29.0785 5.71082i 1.10301 0.216624i
\(696\) 0 0
\(697\) −4.16307 19.2189i −0.157688 0.727967i
\(698\) −15.6162 + 17.8942i −0.591081 + 0.677304i
\(699\) 0 0
\(700\) −7.58168 5.41906i −0.286561 0.204821i
\(701\) 3.24535 + 2.72317i 0.122575 + 0.102853i 0.702015 0.712162i \(-0.252284\pi\)
−0.579440 + 0.815015i \(0.696729\pi\)
\(702\) 0 0
\(703\) −11.1367 + 9.34483i −0.420030 + 0.352447i
\(704\) 22.5787 1.75495i 0.850965 0.0661423i
\(705\) 0 0
\(706\) 6.20117 16.0614i 0.233384 0.604480i
\(707\) −7.64329 + 55.9588i −0.287455 + 2.10455i
\(708\) 0 0
\(709\) −30.2843 16.7102i −1.13735 0.627564i −0.201335 0.979522i \(-0.564528\pi\)
−0.936016 + 0.351959i \(0.885516\pi\)
\(710\) −2.03611 34.9587i −0.0764139 1.31198i
\(711\) 0 0
\(712\) 45.7748 22.9890i 1.71548 0.861549i
\(713\) 17.7255 + 33.6511i 0.663827 + 1.26024i
\(714\) 0 0
\(715\) −29.9321 13.6058i −1.11940 0.508829i
\(716\) −3.71121 + 5.41108i −0.138694 + 0.202221i
\(717\) 0 0
\(718\) 3.45239 + 25.2759i 0.128842 + 0.943290i
\(719\) −5.63418 1.33533i −0.210120 0.0497993i 0.124208 0.992256i \(-0.460361\pi\)
−0.334328 + 0.942457i \(0.608509\pi\)
\(720\) 0 0
\(721\) 8.44840 + 8.95478i 0.314635 + 0.333494i
\(722\) −20.3560 3.18361i −0.757571 0.118482i
\(723\) 0 0
\(724\) −7.48637 + 0.290505i −0.278229 + 0.0107965i
\(725\) 25.7848 + 15.5612i 0.957622 + 0.577928i
\(726\) 0 0
\(727\) 4.33694 + 1.20727i 0.160848 + 0.0447752i 0.347661 0.937620i \(-0.386976\pi\)
−0.186812 + 0.982396i \(0.559816\pi\)
\(728\) −36.5241 −1.35367
\(729\) 0 0
\(730\) −10.1765 −0.376648
\(731\) −27.8535 7.75354i −1.03020 0.286775i
\(732\) 0 0
\(733\) −6.97842 4.21150i −0.257754 0.155555i 0.381935 0.924189i \(-0.375258\pi\)
−0.639689 + 0.768634i \(0.720937\pi\)
\(734\) −40.0707 + 1.55492i −1.47904 + 0.0573933i
\(735\) 0 0
\(736\) 13.3798 + 2.09257i 0.493188 + 0.0771331i
\(737\) 14.4301 + 15.2950i 0.531540 + 0.563399i
\(738\) 0 0
\(739\) 0.537844 + 0.127471i 0.0197849 + 0.00468911i 0.240496 0.970650i \(-0.422690\pi\)
−0.220711 + 0.975339i \(0.570838\pi\)
\(740\) −2.28054 16.6965i −0.0838343 0.613775i
\(741\) 0 0
\(742\) −8.33368 + 12.1508i −0.305939 + 0.446070i
\(743\) 21.0887 + 9.58599i 0.773669 + 0.351676i 0.761428 0.648249i \(-0.224498\pi\)
0.0122412 + 0.999925i \(0.496103\pi\)
\(744\) 0 0
\(745\) −6.76615 12.8452i −0.247893 0.470612i
\(746\) 40.0547 20.1162i 1.46651 0.736507i
\(747\) 0 0
\(748\) 0.193662 + 3.32505i 0.00708098 + 0.121576i
\(749\) 3.08002 + 1.69948i 0.112541 + 0.0620977i
\(750\) 0 0
\(751\) −3.62518 + 26.5410i −0.132285 + 0.968494i 0.798259 + 0.602314i \(0.205754\pi\)
−0.930544 + 0.366180i \(0.880665\pi\)
\(752\) −7.32999 + 18.9851i −0.267297 + 0.692317i
\(753\) 0 0
\(754\) 23.9085 1.85831i 0.870696 0.0676758i
\(755\) −4.85743 + 4.07587i −0.176780 + 0.148336i
\(756\) 0 0
\(757\) −39.7575 33.3605i −1.44501 1.21251i −0.936121 0.351677i \(-0.885612\pi\)
−0.508890 0.860832i \(-0.669944\pi\)
\(758\) −18.8661 13.4847i −0.685247 0.489785i
\(759\) 0 0
\(760\) −9.71420 + 11.1312i −0.352371 + 0.403772i
\(761\) 7.00265 + 32.3279i 0.253846 + 1.17188i 0.909134 + 0.416504i \(0.136745\pi\)
−0.655288 + 0.755379i \(0.727453\pi\)
\(762\) 0 0
\(763\) 14.4787 2.84352i 0.524163 0.102942i
\(764\) 7.23001 + 0.845067i 0.261573 + 0.0305735i
\(765\) 0 0
\(766\) −5.61597 7.54356i −0.202913 0.272560i
\(767\) 1.69630 7.83099i 0.0612498 0.282761i
\(768\) 0 0
\(769\) −16.7863 16.4639i −0.605331 0.593705i 0.331513 0.943450i \(-0.392441\pi\)
−0.936845 + 0.349746i \(0.886268\pi\)
\(770\) 7.89349 30.6444i 0.284462 1.10435i
\(771\) 0 0
\(772\) −0.994603 0.902554i −0.0357965 0.0324836i
\(773\) 0.391986 0.908725i 0.0140987 0.0326846i −0.911021 0.412359i \(-0.864705\pi\)
0.925120 + 0.379675i \(0.123964\pi\)
\(774\) 0 0
\(775\) 28.0654 37.6984i 1.00814 1.35417i
\(776\) −13.9763 16.0151i −0.501720 0.574907i
\(777\) 0 0
\(778\) 5.58224 + 1.78987i 0.200133 + 0.0641700i
\(779\) −10.9898 2.15833i −0.393751 0.0773301i
\(780\) 0 0
\(781\) −20.1469 + 9.15789i −0.720913 + 0.327695i
\(782\) 2.61495 14.8301i 0.0935105 0.530324i
\(783\) 0 0
\(784\) −1.13323 6.42686i −0.0404724 0.229531i
\(785\) −23.8947 34.8393i −0.852838 1.24347i
\(786\) 0 0