Properties

Label 1440.2.q.i.481.3
Level $1440$
Weight $2$
Character 1440.481
Analytic conductor $11.498$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1440.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.4984578911\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.3010058496.1
Defining polynomial: \(x^{8} - 4 x^{7} + 6 x^{6} + 2 x^{5} - 17 x^{4} + 6 x^{3} + 54 x^{2} - 108 x + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 481.3
Root \(-1.54667 + 0.779618i\) of defining polynomial
Character \(\chi\) \(=\) 1440.481
Dual form 1440.2.q.i.961.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0981673 + 1.72927i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-0.0981673 - 0.170031i) q^{7} +(-2.98073 + 0.339515i) q^{9} +O(q^{10})\) \(q+(0.0981673 + 1.72927i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-0.0981673 - 0.170031i) q^{7} +(-2.98073 + 0.339515i) q^{9} +(-2.64484 - 4.58100i) q^{11} +(-1.28439 + 2.22463i) q^{13} +(1.54667 + 0.779618i) q^{15} -5.22524 q^{17} +6.89701 q^{19} +(0.284392 - 0.186449i) q^{21} +(3.66695 - 6.35135i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-0.879722 - 5.12114i) q^{27} +(-2.39701 - 4.15174i) q^{29} +(1.12028 - 1.94038i) q^{31} +(7.66213 - 5.02334i) q^{33} -0.196335 q^{35} -9.61791 q^{37} +(-3.97307 - 2.00267i) q^{39} +(2.50529 - 4.33929i) q^{41} +(-4.44851 - 7.70504i) q^{43} +(-1.19633 + 2.75114i) q^{45} +(6.44368 + 11.1608i) q^{47} +(3.48073 - 6.02879i) q^{49} +(-0.512948 - 9.03583i) q^{51} -7.53024 q^{53} -5.28968 q^{55} +(0.677061 + 11.9268i) q^{57} +(2.19633 - 3.80416i) q^{59} +(3.30895 + 5.73128i) q^{61} +(0.350338 + 0.473486i) q^{63} +(1.28439 + 2.22463i) q^{65} +(2.74301 - 4.75103i) q^{67} +(11.3431 + 5.71764i) q^{69} -5.49566 q^{71} -2.57936 q^{73} +(1.44851 - 0.949649i) q^{75} +(-0.519274 + 0.899408i) q^{77} +(-1.19633 - 2.07211i) q^{79} +(8.76946 - 2.02400i) q^{81} +(-2.38785 - 4.13587i) q^{83} +(-2.61262 + 4.52519i) q^{85} +(6.94416 - 4.55264i) q^{87} +15.5794 q^{89} +0.504341 q^{91} +(3.46541 + 1.74678i) q^{93} +(3.44851 - 5.97299i) q^{95} +(6.26946 + 10.8590i) q^{97} +(9.43886 + 12.7567i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{3} + 4 q^{5} + 2 q^{7} - 8 q^{9} + O(q^{10}) \) \( 8 q - 2 q^{3} + 4 q^{5} + 2 q^{7} - 8 q^{9} - 2 q^{11} - 4 q^{15} - 8 q^{17} + 28 q^{19} - 8 q^{21} + 6 q^{23} - 4 q^{25} - 14 q^{27} + 8 q^{29} + 2 q^{31} + 8 q^{33} + 4 q^{35} - 32 q^{37} - 6 q^{39} - 8 q^{41} - 22 q^{43} - 4 q^{45} + 8 q^{47} + 12 q^{49} + 14 q^{51} - 8 q^{53} - 4 q^{55} - 16 q^{57} + 12 q^{59} + 4 q^{61} - 8 q^{63} + 12 q^{69} - 60 q^{71} + 56 q^{73} - 2 q^{75} - 20 q^{77} - 4 q^{79} + 28 q^{81} + 22 q^{83} - 4 q^{85} + 58 q^{87} + 48 q^{89} - 12 q^{91} - 8 q^{93} + 14 q^{95} + 8 q^{97} + 2 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(641\) \(901\) \(991\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.0981673 + 1.72927i 0.0566769 + 0.998393i
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) −0.0981673 0.170031i −0.0371038 0.0642656i 0.846877 0.531789i \(-0.178480\pi\)
−0.883981 + 0.467523i \(0.845147\pi\)
\(8\) 0 0
\(9\) −2.98073 + 0.339515i −0.993575 + 0.113172i
\(10\) 0 0
\(11\) −2.64484 4.58100i −0.797449 1.38122i −0.921272 0.388918i \(-0.872849\pi\)
0.123823 0.992304i \(-0.460484\pi\)
\(12\) 0 0
\(13\) −1.28439 + 2.22463i −0.356226 + 0.617002i −0.987327 0.158699i \(-0.949270\pi\)
0.631101 + 0.775701i \(0.282603\pi\)
\(14\) 0 0
\(15\) 1.54667 + 0.779618i 0.399349 + 0.201296i
\(16\) 0 0
\(17\) −5.22524 −1.26731 −0.633653 0.773617i \(-0.718445\pi\)
−0.633653 + 0.773617i \(0.718445\pi\)
\(18\) 0 0
\(19\) 6.89701 1.58228 0.791141 0.611633i \(-0.209487\pi\)
0.791141 + 0.611633i \(0.209487\pi\)
\(20\) 0 0
\(21\) 0.284392 0.186449i 0.0620594 0.0406865i
\(22\) 0 0
\(23\) 3.66695 6.35135i 0.764612 1.32435i −0.175839 0.984419i \(-0.556264\pi\)
0.940451 0.339928i \(-0.110403\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) −0.879722 5.12114i −0.169303 0.985564i
\(28\) 0 0
\(29\) −2.39701 4.15174i −0.445114 0.770959i 0.552946 0.833217i \(-0.313503\pi\)
−0.998060 + 0.0622573i \(0.980170\pi\)
\(30\) 0 0
\(31\) 1.12028 1.94038i 0.201208 0.348502i −0.747710 0.664025i \(-0.768847\pi\)
0.948918 + 0.315523i \(0.102180\pi\)
\(32\) 0 0
\(33\) 7.66213 5.02334i 1.33381 0.874451i
\(34\) 0 0
\(35\) −0.196335 −0.0331866
\(36\) 0 0
\(37\) −9.61791 −1.58117 −0.790587 0.612350i \(-0.790224\pi\)
−0.790587 + 0.612350i \(0.790224\pi\)
\(38\) 0 0
\(39\) −3.97307 2.00267i −0.636200 0.320684i
\(40\) 0 0
\(41\) 2.50529 4.33929i 0.391260 0.677683i −0.601356 0.798981i \(-0.705373\pi\)
0.992616 + 0.121299i \(0.0387059\pi\)
\(42\) 0 0
\(43\) −4.44851 7.70504i −0.678391 1.17501i −0.975465 0.220153i \(-0.929344\pi\)
0.297075 0.954854i \(-0.403989\pi\)
\(44\) 0 0
\(45\) −1.19633 + 2.75114i −0.178339 + 0.410116i
\(46\) 0 0
\(47\) 6.44368 + 11.1608i 0.939908 + 1.62797i 0.765640 + 0.643270i \(0.222423\pi\)
0.174268 + 0.984698i \(0.444244\pi\)
\(48\) 0 0
\(49\) 3.48073 6.02879i 0.497247 0.861256i
\(50\) 0 0
\(51\) −0.512948 9.03583i −0.0718270 1.26527i
\(52\) 0 0
\(53\) −7.53024 −1.03436 −0.517179 0.855877i \(-0.673018\pi\)
−0.517179 + 0.855877i \(0.673018\pi\)
\(54\) 0 0
\(55\) −5.28968 −0.713260
\(56\) 0 0
\(57\) 0.677061 + 11.9268i 0.0896789 + 1.57974i
\(58\) 0 0
\(59\) 2.19633 3.80416i 0.285938 0.495260i −0.686898 0.726754i \(-0.741028\pi\)
0.972836 + 0.231494i \(0.0743614\pi\)
\(60\) 0 0
\(61\) 3.30895 + 5.73128i 0.423668 + 0.733815i 0.996295 0.0860015i \(-0.0274090\pi\)
−0.572627 + 0.819816i \(0.694076\pi\)
\(62\) 0 0
\(63\) 0.350338 + 0.473486i 0.0441384 + 0.0596536i
\(64\) 0 0
\(65\) 1.28439 + 2.22463i 0.159309 + 0.275932i
\(66\) 0 0
\(67\) 2.74301 4.75103i 0.335112 0.580430i −0.648395 0.761304i \(-0.724559\pi\)
0.983506 + 0.180874i \(0.0578926\pi\)
\(68\) 0 0
\(69\) 11.3431 + 5.71764i 1.36555 + 0.688323i
\(70\) 0 0
\(71\) −5.49566 −0.652215 −0.326107 0.945333i \(-0.605737\pi\)
−0.326107 + 0.945333i \(0.605737\pi\)
\(72\) 0 0
\(73\) −2.57936 −0.301891 −0.150946 0.988542i \(-0.548232\pi\)
−0.150946 + 0.988542i \(0.548232\pi\)
\(74\) 0 0
\(75\) 1.44851 0.949649i 0.167259 0.109656i
\(76\) 0 0
\(77\) −0.519274 + 0.899408i −0.0591767 + 0.102497i
\(78\) 0 0
\(79\) −1.19633 2.07211i −0.134598 0.233131i 0.790846 0.612016i \(-0.209641\pi\)
−0.925444 + 0.378885i \(0.876308\pi\)
\(80\) 0 0
\(81\) 8.76946 2.02400i 0.974384 0.224889i
\(82\) 0 0
\(83\) −2.38785 4.13587i −0.262100 0.453971i 0.704700 0.709506i \(-0.251082\pi\)
−0.966800 + 0.255535i \(0.917748\pi\)
\(84\) 0 0
\(85\) −2.61262 + 4.52519i −0.283378 + 0.490826i
\(86\) 0 0
\(87\) 6.94416 4.55264i 0.744493 0.488094i
\(88\) 0 0
\(89\) 15.5794 1.65141 0.825704 0.564103i \(-0.190778\pi\)
0.825704 + 0.564103i \(0.190778\pi\)
\(90\) 0 0
\(91\) 0.504341 0.0528693
\(92\) 0 0
\(93\) 3.46541 + 1.74678i 0.359346 + 0.181132i
\(94\) 0 0
\(95\) 3.44851 5.97299i 0.353809 0.612815i
\(96\) 0 0
\(97\) 6.26946 + 10.8590i 0.636567 + 1.10257i 0.986181 + 0.165673i \(0.0529795\pi\)
−0.349614 + 0.936894i \(0.613687\pi\)
\(98\) 0 0
\(99\) 9.43886 + 12.7567i 0.948641 + 1.28210i
\(100\) 0 0
\(101\) −9.55914 16.5569i −0.951170 1.64747i −0.742899 0.669403i \(-0.766550\pi\)
−0.208271 0.978071i \(-0.566783\pi\)
\(102\) 0 0
\(103\) −3.01729 + 5.22610i −0.297302 + 0.514943i −0.975518 0.219920i \(-0.929420\pi\)
0.678216 + 0.734863i \(0.262754\pi\)
\(104\) 0 0
\(105\) −0.0192736 0.339515i −0.00188091 0.0331333i
\(106\) 0 0
\(107\) −7.86147 −0.759997 −0.379999 0.924987i \(-0.624076\pi\)
−0.379999 + 0.924987i \(0.624076\pi\)
\(108\) 0 0
\(109\) −9.49169 −0.909139 −0.454569 0.890711i \(-0.650207\pi\)
−0.454569 + 0.890711i \(0.650207\pi\)
\(110\) 0 0
\(111\) −0.944164 16.6319i −0.0896161 1.57863i
\(112\) 0 0
\(113\) 8.05480 13.9513i 0.757732 1.31243i −0.186273 0.982498i \(-0.559641\pi\)
0.944005 0.329932i \(-0.107026\pi\)
\(114\) 0 0
\(115\) −3.66695 6.35135i −0.341945 0.592266i
\(116\) 0 0
\(117\) 3.07312 7.06709i 0.284110 0.653353i
\(118\) 0 0
\(119\) 0.512948 + 0.888451i 0.0470218 + 0.0814442i
\(120\) 0 0
\(121\) −8.49036 + 14.7057i −0.771850 + 1.33688i
\(122\) 0 0
\(123\) 7.74972 + 3.90633i 0.698769 + 0.352222i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 6.82956 0.606025 0.303013 0.952987i \(-0.402008\pi\)
0.303013 + 0.952987i \(0.402008\pi\)
\(128\) 0 0
\(129\) 12.8874 8.44903i 1.13467 0.743896i
\(130\) 0 0
\(131\) −2.42157 + 4.19429i −0.211574 + 0.366456i −0.952207 0.305453i \(-0.901192\pi\)
0.740633 + 0.671909i \(0.234526\pi\)
\(132\) 0 0
\(133\) −0.677061 1.17270i −0.0587086 0.101686i
\(134\) 0 0
\(135\) −4.87490 1.79871i −0.419565 0.154808i
\(136\) 0 0
\(137\) −5.59769 9.69548i −0.478243 0.828340i 0.521446 0.853284i \(-0.325393\pi\)
−0.999689 + 0.0249436i \(0.992059\pi\)
\(138\) 0 0
\(139\) −1.43122 + 2.47894i −0.121394 + 0.210261i −0.920318 0.391172i \(-0.872070\pi\)
0.798924 + 0.601433i \(0.205403\pi\)
\(140\) 0 0
\(141\) −18.6674 + 12.2385i −1.57208 + 1.03067i
\(142\) 0 0
\(143\) 13.5880 1.13629
\(144\) 0 0
\(145\) −4.79402 −0.398122
\(146\) 0 0
\(147\) 10.7671 + 5.42727i 0.888054 + 0.447634i
\(148\) 0 0
\(149\) 0.112619 0.195061i 0.00922608 0.0159800i −0.861376 0.507969i \(-0.830397\pi\)
0.870602 + 0.491989i \(0.163730\pi\)
\(150\) 0 0
\(151\) −2.14050 3.70745i −0.174191 0.301708i 0.765690 0.643210i \(-0.222398\pi\)
−0.939881 + 0.341502i \(0.889064\pi\)
\(152\) 0 0
\(153\) 15.5750 1.77405i 1.25916 0.143423i
\(154\) 0 0
\(155\) −1.12028 1.94038i −0.0899829 0.155855i
\(156\) 0 0
\(157\) −3.38302 + 5.85957i −0.269995 + 0.467645i −0.968860 0.247609i \(-0.920355\pi\)
0.698865 + 0.715253i \(0.253689\pi\)
\(158\) 0 0
\(159\) −0.739223 13.0218i −0.0586242 1.03269i
\(160\) 0 0
\(161\) −1.43990 −0.113480
\(162\) 0 0
\(163\) −2.97410 −0.232950 −0.116475 0.993194i \(-0.537159\pi\)
−0.116475 + 0.993194i \(0.537159\pi\)
\(164\) 0 0
\(165\) −0.519274 9.14727i −0.0404254 0.712114i
\(166\) 0 0
\(167\) 7.20313 12.4762i 0.557395 0.965436i −0.440318 0.897842i \(-0.645134\pi\)
0.997713 0.0675941i \(-0.0215323\pi\)
\(168\) 0 0
\(169\) 3.20068 + 5.54373i 0.246206 + 0.426441i
\(170\) 0 0
\(171\) −20.5581 + 2.34164i −1.57212 + 0.179070i
\(172\) 0 0
\(173\) 10.2511 + 17.7555i 0.779379 + 1.34992i 0.932300 + 0.361686i \(0.117799\pi\)
−0.152921 + 0.988238i \(0.548868\pi\)
\(174\) 0 0
\(175\) −0.0981673 + 0.170031i −0.00742075 + 0.0128531i
\(176\) 0 0
\(177\) 6.79402 + 3.42460i 0.510670 + 0.257409i
\(178\) 0 0
\(179\) −1.84789 −0.138118 −0.0690588 0.997613i \(-0.522000\pi\)
−0.0690588 + 0.997613i \(0.522000\pi\)
\(180\) 0 0
\(181\) 10.0087 0.743939 0.371970 0.928245i \(-0.378683\pi\)
0.371970 + 0.928245i \(0.378683\pi\)
\(182\) 0 0
\(183\) −9.58607 + 6.28469i −0.708623 + 0.464577i
\(184\) 0 0
\(185\) −4.80895 + 8.32935i −0.353561 + 0.612386i
\(186\) 0 0
\(187\) 13.8199 + 23.9368i 1.01061 + 1.75043i
\(188\) 0 0
\(189\) −0.784392 + 0.652308i −0.0570561 + 0.0474485i
\(190\) 0 0
\(191\) −0.689062 1.19349i −0.0498588 0.0863579i 0.840019 0.542557i \(-0.182544\pi\)
−0.889878 + 0.456199i \(0.849210\pi\)
\(192\) 0 0
\(193\) −7.01397 + 12.1486i −0.504877 + 0.874472i 0.495107 + 0.868832i \(0.335129\pi\)
−0.999984 + 0.00564022i \(0.998205\pi\)
\(194\) 0 0
\(195\) −3.72090 + 2.43944i −0.266459 + 0.174692i
\(196\) 0 0
\(197\) −4.26378 −0.303782 −0.151891 0.988397i \(-0.548536\pi\)
−0.151891 + 0.988397i \(0.548536\pi\)
\(198\) 0 0
\(199\) −0.691031 −0.0489859 −0.0244930 0.999700i \(-0.507797\pi\)
−0.0244930 + 0.999700i \(0.507797\pi\)
\(200\) 0 0
\(201\) 8.48507 + 4.27700i 0.598491 + 0.301676i
\(202\) 0 0
\(203\) −0.470616 + 0.815131i −0.0330308 + 0.0572110i
\(204\) 0 0
\(205\) −2.50529 4.33929i −0.174977 0.303069i
\(206\) 0 0
\(207\) −8.77380 + 20.1766i −0.609821 + 1.40237i
\(208\) 0 0
\(209\) −18.2415 31.5952i −1.26179 2.18548i
\(210\) 0 0
\(211\) 11.3359 19.6343i 0.780394 1.35168i −0.151319 0.988485i \(-0.548352\pi\)
0.931713 0.363196i \(-0.118315\pi\)
\(212\) 0 0
\(213\) −0.539494 9.50346i −0.0369655 0.651166i
\(214\) 0 0
\(215\) −8.89701 −0.606771
\(216\) 0 0
\(217\) −0.439899 −0.0298623
\(218\) 0 0
\(219\) −0.253209 4.46040i −0.0171103 0.301406i
\(220\) 0 0
\(221\) 6.71125 11.6242i 0.451448 0.781930i
\(222\) 0 0
\(223\) 7.07123 + 12.2477i 0.473525 + 0.820169i 0.999541 0.0303057i \(-0.00964807\pi\)
−0.526016 + 0.850475i \(0.676315\pi\)
\(224\) 0 0
\(225\) 1.78439 + 2.41163i 0.118959 + 0.160775i
\(226\) 0 0
\(227\) 4.22327 + 7.31491i 0.280308 + 0.485508i 0.971461 0.237201i \(-0.0762300\pi\)
−0.691152 + 0.722709i \(0.742897\pi\)
\(228\) 0 0
\(229\) −10.2555 + 17.7630i −0.677701 + 1.17381i 0.297971 + 0.954575i \(0.403690\pi\)
−0.975672 + 0.219237i \(0.929643\pi\)
\(230\) 0 0
\(231\) −1.60629 0.809670i −0.105686 0.0532724i
\(232\) 0 0
\(233\) −6.40325 −0.419491 −0.209745 0.977756i \(-0.567263\pi\)
−0.209745 + 0.977756i \(0.567263\pi\)
\(234\) 0 0
\(235\) 12.8874 0.840679
\(236\) 0 0
\(237\) 3.46579 2.27220i 0.225128 0.147595i
\(238\) 0 0
\(239\) −8.14814 + 14.1130i −0.527060 + 0.912894i 0.472443 + 0.881361i \(0.343372\pi\)
−0.999503 + 0.0315328i \(0.989961\pi\)
\(240\) 0 0
\(241\) −8.41194 14.5699i −0.541861 0.938531i −0.998797 0.0490312i \(-0.984387\pi\)
0.456936 0.889499i \(-0.348947\pi\)
\(242\) 0 0
\(243\) 4.36091 + 14.9660i 0.279753 + 0.960072i
\(244\) 0 0
\(245\) −3.48073 6.02879i −0.222375 0.385166i
\(246\) 0 0
\(247\) −8.85846 + 15.3433i −0.563651 + 0.976271i
\(248\) 0 0
\(249\) 6.91762 4.53523i 0.438386 0.287409i
\(250\) 0 0
\(251\) −23.6053 −1.48995 −0.744975 0.667092i \(-0.767539\pi\)
−0.744975 + 0.667092i \(0.767539\pi\)
\(252\) 0 0
\(253\) −38.7940 −2.43896
\(254\) 0 0
\(255\) −8.08173 4.07369i −0.506098 0.255104i
\(256\) 0 0
\(257\) 2.04912 3.54919i 0.127821 0.221392i −0.795011 0.606595i \(-0.792535\pi\)
0.922832 + 0.385203i \(0.125868\pi\)
\(258\) 0 0
\(259\) 0.944164 + 1.63534i 0.0586675 + 0.101615i
\(260\) 0 0
\(261\) 8.55441 + 11.5614i 0.529505 + 0.715632i
\(262\) 0 0
\(263\) 12.1309 + 21.0113i 0.748021 + 1.29561i 0.948770 + 0.315967i \(0.102329\pi\)
−0.200750 + 0.979643i \(0.564338\pi\)
\(264\) 0 0
\(265\) −3.76512 + 6.52138i −0.231289 + 0.400605i
\(266\) 0 0
\(267\) 1.52938 + 26.9409i 0.0935968 + 1.64875i
\(268\) 0 0
\(269\) −11.1357 −0.678954 −0.339477 0.940614i \(-0.610250\pi\)
−0.339477 + 0.940614i \(0.610250\pi\)
\(270\) 0 0
\(271\) −27.8804 −1.69361 −0.846806 0.531901i \(-0.821478\pi\)
−0.846806 + 0.531901i \(0.821478\pi\)
\(272\) 0 0
\(273\) 0.0495098 + 0.872140i 0.00299647 + 0.0527843i
\(274\) 0 0
\(275\) −2.64484 + 4.58100i −0.159490 + 0.276245i
\(276\) 0 0
\(277\) −2.74150 4.74842i −0.164721 0.285305i 0.771835 0.635823i \(-0.219339\pi\)
−0.936556 + 0.350518i \(0.886006\pi\)
\(278\) 0 0
\(279\) −2.68046 + 6.16409i −0.160475 + 0.369034i
\(280\) 0 0
\(281\) −2.14152 3.70922i −0.127752 0.221274i 0.795053 0.606540i \(-0.207443\pi\)
−0.922805 + 0.385266i \(0.874110\pi\)
\(282\) 0 0
\(283\) −0.338724 + 0.586687i −0.0201350 + 0.0348749i −0.875917 0.482461i \(-0.839743\pi\)
0.855782 + 0.517336i \(0.173076\pi\)
\(284\) 0 0
\(285\) 10.6674 + 5.37703i 0.631883 + 0.318508i
\(286\) 0 0
\(287\) −0.983750 −0.0580689
\(288\) 0 0
\(289\) 10.3031 0.606065
\(290\) 0 0
\(291\) −18.1627 + 11.9076i −1.06472 + 0.698034i
\(292\) 0 0
\(293\) 3.32294 5.75550i 0.194128 0.336240i −0.752486 0.658608i \(-0.771146\pi\)
0.946614 + 0.322368i \(0.104479\pi\)
\(294\) 0 0
\(295\) −2.19633 3.80416i −0.127876 0.221487i
\(296\) 0 0
\(297\) −21.1332 + 17.5746i −1.22627 + 1.01978i
\(298\) 0 0
\(299\) 9.41960 + 16.3152i 0.544750 + 0.943534i
\(300\) 0 0
\(301\) −0.873396 + 1.51277i −0.0503417 + 0.0871944i
\(302\) 0 0
\(303\) 27.6929 18.1556i 1.59092 1.04301i
\(304\) 0 0
\(305\) 6.61791 0.378940
\(306\) 0 0
\(307\) 4.89323 0.279271 0.139636 0.990203i \(-0.455407\pi\)
0.139636 + 0.990203i \(0.455407\pi\)
\(308\) 0 0
\(309\) −9.33351 4.70466i −0.530965 0.267639i
\(310\) 0 0
\(311\) 12.8113 22.1898i 0.726463 1.25827i −0.231906 0.972738i \(-0.574496\pi\)
0.958369 0.285532i \(-0.0921704\pi\)
\(312\) 0 0
\(313\) −14.9571 25.9065i −0.845425 1.46432i −0.885252 0.465113i \(-0.846014\pi\)
0.0398265 0.999207i \(-0.487319\pi\)
\(314\) 0 0
\(315\) 0.585220 0.0666585i 0.0329734 0.00375578i
\(316\) 0 0
\(317\) −10.3883 17.9931i −0.583466 1.01059i −0.995065 0.0992273i \(-0.968363\pi\)
0.411599 0.911365i \(-0.364970\pi\)
\(318\) 0 0
\(319\) −12.6794 + 21.9614i −0.709911 + 1.22960i
\(320\) 0 0
\(321\) −0.771739 13.5946i −0.0430743 0.758775i
\(322\) 0 0
\(323\) −36.0385 −2.00524
\(324\) 0 0
\(325\) 2.56878 0.142490
\(326\) 0 0
\(327\) −0.931774 16.4137i −0.0515272 0.907678i
\(328\) 0 0
\(329\) 1.26512 2.19125i 0.0697482 0.120807i
\(330\) 0 0
\(331\) −11.4456 19.8243i −0.629106 1.08964i −0.987732 0.156162i \(-0.950088\pi\)
0.358626 0.933481i \(-0.383245\pi\)
\(332\) 0 0
\(333\) 28.6683 3.26542i 1.57102 0.178944i
\(334\) 0 0
\(335\) −2.74301 4.75103i −0.149866 0.259576i
\(336\) 0 0
\(337\) −11.8787 + 20.5745i −0.647073 + 1.12076i 0.336745 + 0.941596i \(0.390674\pi\)
−0.983819 + 0.179168i \(0.942660\pi\)
\(338\) 0 0
\(339\) 24.9163 + 12.5593i 1.35327 + 0.682129i
\(340\) 0 0
\(341\) −11.8518 −0.641812
\(342\) 0 0
\(343\) −2.74112 −0.148006
\(344\) 0 0
\(345\) 10.6232 6.96463i 0.571934 0.374963i
\(346\) 0 0
\(347\) 2.66506 4.61602i 0.143068 0.247801i −0.785583 0.618757i \(-0.787637\pi\)
0.928650 + 0.370956i \(0.120970\pi\)
\(348\) 0 0
\(349\) 10.0505 + 17.4079i 0.537989 + 0.931824i 0.999012 + 0.0444357i \(0.0141490\pi\)
−0.461024 + 0.887388i \(0.652518\pi\)
\(350\) 0 0
\(351\) 12.5226 + 4.62049i 0.668405 + 0.246624i
\(352\) 0 0
\(353\) 13.5880 + 23.5352i 0.723218 + 1.25265i 0.959703 + 0.281016i \(0.0906714\pi\)
−0.236485 + 0.971635i \(0.575995\pi\)
\(354\) 0 0
\(355\) −2.74783 + 4.75938i −0.145840 + 0.252602i
\(356\) 0 0
\(357\) −1.48601 + 0.974240i −0.0786482 + 0.0515622i
\(358\) 0 0
\(359\) 19.8497 1.04763 0.523815 0.851832i \(-0.324508\pi\)
0.523815 + 0.851832i \(0.324508\pi\)
\(360\) 0 0
\(361\) 28.5688 1.50362
\(362\) 0 0
\(363\) −26.2636 13.2385i −1.37848 0.694839i
\(364\) 0 0
\(365\) −1.28968 + 2.23379i −0.0675049 + 0.116922i
\(366\) 0 0
\(367\) 2.18472 + 3.78405i 0.114041 + 0.197526i 0.917396 0.397975i \(-0.130287\pi\)
−0.803355 + 0.595501i \(0.796954\pi\)
\(368\) 0 0
\(369\) −5.99433 + 13.7848i −0.312052 + 0.717608i
\(370\) 0 0
\(371\) 0.739223 + 1.28037i 0.0383785 + 0.0664736i
\(372\) 0 0
\(373\) 0.363767 0.630062i 0.0188351 0.0326234i −0.856454 0.516223i \(-0.827338\pi\)
0.875289 + 0.483600i \(0.160671\pi\)
\(374\) 0 0
\(375\) −0.0981673 1.72927i −0.00506934 0.0892989i
\(376\) 0 0
\(377\) 12.3148 0.634245
\(378\) 0 0
\(379\) 3.04912 0.156623 0.0783115 0.996929i \(-0.475047\pi\)
0.0783115 + 0.996929i \(0.475047\pi\)
\(380\) 0 0
\(381\) 0.670440 + 11.8101i 0.0343477 + 0.605051i
\(382\) 0 0
\(383\) −10.3070 + 17.8522i −0.526661 + 0.912204i 0.472856 + 0.881140i \(0.343223\pi\)
−0.999517 + 0.0310647i \(0.990110\pi\)
\(384\) 0 0
\(385\) 0.519274 + 0.899408i 0.0264646 + 0.0458381i
\(386\) 0 0
\(387\) 15.8758 + 21.4563i 0.807010 + 1.09068i
\(388\) 0 0
\(389\) 5.58806 + 9.67880i 0.283326 + 0.490735i 0.972202 0.234145i \(-0.0752289\pi\)
−0.688876 + 0.724879i \(0.741896\pi\)
\(390\) 0 0
\(391\) −19.1607 + 33.1873i −0.968998 + 1.67835i
\(392\) 0 0
\(393\) −7.49076 3.77580i −0.377859 0.190464i
\(394\) 0 0
\(395\) −2.39267 −0.120388
\(396\) 0 0
\(397\) 15.6863 0.787272 0.393636 0.919266i \(-0.371217\pi\)
0.393636 + 0.919266i \(0.371217\pi\)
\(398\) 0 0
\(399\) 1.96145 1.28594i 0.0981955 0.0643775i
\(400\) 0 0
\(401\) 11.7997 20.4377i 0.589249 1.02061i −0.405082 0.914280i \(-0.632757\pi\)
0.994331 0.106328i \(-0.0339095\pi\)
\(402\) 0 0
\(403\) 2.87775 + 4.98441i 0.143351 + 0.248291i
\(404\) 0 0
\(405\) 2.63189 8.60658i 0.130780 0.427664i
\(406\) 0 0
\(407\) 25.4378 + 44.0596i 1.26091 + 2.18395i
\(408\) 0 0
\(409\) −5.17611 + 8.96529i −0.255942 + 0.443305i −0.965151 0.261693i \(-0.915719\pi\)
0.709209 + 0.704999i \(0.249052\pi\)
\(410\) 0 0
\(411\) 16.2166 10.6317i 0.799904 0.524422i
\(412\) 0 0
\(413\) −0.862433 −0.0424376
\(414\) 0 0
\(415\) −4.77569 −0.234430
\(416\) 0 0
\(417\) −4.42725 2.23160i −0.216803 0.109282i
\(418\) 0 0
\(419\) 4.14050 7.17155i 0.202277 0.350353i −0.746985 0.664841i \(-0.768499\pi\)
0.949262 + 0.314488i \(0.101833\pi\)
\(420\) 0 0
\(421\) 11.7555 + 20.3611i 0.572927 + 0.992338i 0.996263 + 0.0863658i \(0.0275254\pi\)
−0.423337 + 0.905972i \(0.639141\pi\)
\(422\) 0 0
\(423\) −22.9961 31.0795i −1.11811 1.51114i
\(424\) 0 0
\(425\) 2.61262 + 4.52519i 0.126731 + 0.219504i
\(426\) 0 0
\(427\) 0.649662 1.12525i 0.0314394 0.0544546i
\(428\) 0 0
\(429\) 1.33390 + 23.4973i 0.0644014 + 1.13446i
\(430\) 0 0
\(431\) −1.73622 −0.0836306 −0.0418153 0.999125i \(-0.513314\pi\)
−0.0418153 + 0.999125i \(0.513314\pi\)
\(432\) 0 0
\(433\) −10.0797 −0.484401 −0.242200 0.970226i \(-0.577869\pi\)
−0.242200 + 0.970226i \(0.577869\pi\)
\(434\) 0 0
\(435\) −0.470616 8.29014i −0.0225643 0.397482i
\(436\) 0 0
\(437\) 25.2910 43.8053i 1.20983 2.09549i
\(438\) 0 0
\(439\) 2.53024 + 4.38250i 0.120762 + 0.209165i 0.920068 0.391758i \(-0.128133\pi\)
−0.799307 + 0.600923i \(0.794800\pi\)
\(440\) 0 0
\(441\) −8.32823 + 19.1519i −0.396582 + 0.911997i
\(442\) 0 0
\(443\) 5.61111 + 9.71874i 0.266592 + 0.461751i 0.967980 0.251029i \(-0.0807690\pi\)
−0.701387 + 0.712780i \(0.747436\pi\)
\(444\) 0 0
\(445\) 7.78968 13.4921i 0.369266 0.639588i
\(446\) 0 0
\(447\) 0.348368 + 0.175599i 0.0164773 + 0.00830555i
\(448\) 0 0
\(449\) −15.7056 −0.741192 −0.370596 0.928794i \(-0.620847\pi\)
−0.370596 + 0.928794i \(0.620847\pi\)
\(450\) 0 0
\(451\) −26.5043 −1.24804
\(452\) 0 0
\(453\) 6.20105 4.06544i 0.291351 0.191011i
\(454\) 0 0
\(455\) 0.252171 0.436772i 0.0118219 0.0204762i
\(456\) 0 0
\(457\) 6.31519 + 10.9382i 0.295412 + 0.511669i 0.975081 0.221851i \(-0.0712097\pi\)
−0.679669 + 0.733519i \(0.737876\pi\)
\(458\) 0 0
\(459\) 4.59675 + 26.7592i 0.214558 + 1.24901i
\(460\) 0 0
\(461\) −4.86280 8.42262i −0.226483 0.392281i 0.730280 0.683148i \(-0.239390\pi\)
−0.956763 + 0.290867i \(0.906056\pi\)
\(462\) 0 0
\(463\) 11.3714 19.6959i 0.528474 0.915344i −0.470975 0.882147i \(-0.656098\pi\)
0.999449 0.0331975i \(-0.0105690\pi\)
\(464\) 0 0
\(465\) 3.24546 2.12774i 0.150505 0.0986717i
\(466\) 0 0
\(467\) 3.40722 0.157667 0.0788336 0.996888i \(-0.474880\pi\)
0.0788336 + 0.996888i \(0.474880\pi\)
\(468\) 0 0
\(469\) −1.07709 −0.0497356
\(470\) 0 0
\(471\) −10.4649 5.27493i −0.482195 0.243056i
\(472\) 0 0
\(473\) −23.5312 + 40.7572i −1.08196 + 1.87402i
\(474\) 0 0
\(475\) −3.44851 5.97299i −0.158228 0.274059i
\(476\) 0 0
\(477\) 22.4456 2.55663i 1.02771 0.117060i
\(478\) 0 0
\(479\) 9.87679 + 17.1071i 0.451282 + 0.781643i 0.998466 0.0553690i \(-0.0176335\pi\)
−0.547184 + 0.837012i \(0.684300\pi\)
\(480\) 0 0
\(481\) 12.3532 21.3963i 0.563256 0.975587i
\(482\) 0 0
\(483\) −0.141351 2.48997i −0.00643169 0.113298i
\(484\) 0 0
\(485\) 12.5389 0.569363
\(486\) 0 0
\(487\) 14.9182 0.676006 0.338003 0.941145i \(-0.390249\pi\)
0.338003 + 0.941145i \(0.390249\pi\)
\(488\) 0 0
\(489\) −0.291960 5.14302i −0.0132029 0.232575i
\(490\) 0 0
\(491\) 17.2984 29.9616i 0.780664 1.35215i −0.150891 0.988550i \(-0.548214\pi\)
0.931555 0.363600i \(-0.118452\pi\)
\(492\) 0 0
\(493\) 12.5249 + 21.6938i 0.564095 + 0.977042i
\(494\) 0 0
\(495\) 15.7671 1.79593i 0.708678 0.0807208i
\(496\) 0 0
\(497\) 0.539494 + 0.934431i 0.0241996 + 0.0419150i
\(498\) 0 0
\(499\) 10.2358 17.7289i 0.458218 0.793657i −0.540649 0.841248i \(-0.681821\pi\)
0.998867 + 0.0475916i \(0.0151546\pi\)
\(500\) 0 0
\(501\) 22.2818 + 11.2314i 0.995475 + 0.501781i
\(502\) 0 0
\(503\) −19.3878 −0.864458 −0.432229 0.901764i \(-0.642273\pi\)
−0.432229 + 0.901764i \(0.642273\pi\)
\(504\) 0 0
\(505\) −19.1183 −0.850752
\(506\) 0 0
\(507\) −9.27239 + 6.07904i −0.411801 + 0.269979i
\(508\) 0 0
\(509\) −17.7415 + 30.7292i −0.786378 + 1.36205i 0.141795 + 0.989896i \(0.454713\pi\)
−0.928173 + 0.372150i \(0.878621\pi\)
\(510\) 0 0
\(511\) 0.253209 + 0.438570i 0.0112013 + 0.0194012i
\(512\) 0 0
\(513\) −6.06745 35.3206i −0.267884 1.55944i
\(514\) 0 0
\(515\) 3.01729 + 5.22610i 0.132958 + 0.230289i
\(516\) 0 0
\(517\) 34.0850 59.0370i 1.49906 2.59644i
\(518\) 0 0
\(519\) −29.6976 + 19.4699i −1.30358 + 0.854636i
\(520\) 0 0
\(521\) −39.6081 −1.73526 −0.867631 0.497209i \(-0.834358\pi\)
−0.867631 + 0.497209i \(0.834358\pi\)
\(522\) 0 0
\(523\) 43.2415 1.89082 0.945408 0.325888i \(-0.105663\pi\)
0.945408 + 0.325888i \(0.105663\pi\)
\(524\) 0 0
\(525\) −0.303665 0.153066i −0.0132530 0.00668035i
\(526\) 0 0
\(527\) −5.85372 + 10.1389i −0.254992 + 0.441659i
\(528\) 0 0
\(529\) −15.3931 26.6616i −0.669263 1.15920i
\(530\) 0 0
\(531\) −5.25510 + 12.0849i −0.228052 + 0.524438i
\(532\) 0 0
\(533\) 6.43554 + 11.1467i 0.278754 + 0.482817i
\(534\) 0 0
\(535\) −3.93074 + 6.80823i −0.169941 + 0.294346i
\(536\) 0 0
\(537\) −0.181402 3.19549i −0.00782808 0.137896i
\(538\) 0 0
\(539\) −36.8239 −1.58612
\(540\) 0 0
\(541\) −10.2340 −0.439992 −0.219996 0.975501i \(-0.570604\pi\)
−0.219996 + 0.975501i \(0.570604\pi\)
\(542\) 0 0
\(543\) 0.982525 + 17.3077i 0.0421642 + 0.742744i
\(544\) 0 0
\(545\) −4.74584 + 8.22004i −0.203290 + 0.352108i
\(546\) 0 0
\(547\) −13.7709 23.8518i −0.588800 1.01983i −0.994390 0.105776i \(-0.966267\pi\)
0.405590 0.914055i \(-0.367066\pi\)
\(548\) 0 0
\(549\) −11.8089 15.9599i −0.503993 0.681153i
\(550\) 0 0
\(551\) −16.5322 28.6346i −0.704296 1.21988i
\(552\) 0 0
\(553\) −0.234882 + 0.406827i −0.00998819 + 0.0173001i
\(554\) 0 0
\(555\) −14.8758 7.49829i −0.631440 0.318285i
\(556\) 0 0
\(557\) 4.73355 0.200567 0.100283 0.994959i \(-0.468025\pi\)
0.100283 + 0.994959i \(0.468025\pi\)
\(558\) 0 0
\(559\) 22.8545 0.966642
\(560\) 0 0
\(561\) −40.0364 + 26.2481i −1.69034 + 1.10820i
\(562\) 0 0
\(563\) 10.6497 18.4458i 0.448830 0.777396i −0.549480 0.835507i \(-0.685174\pi\)
0.998310 + 0.0581107i \(0.0185076\pi\)
\(564\) 0 0
\(565\) −8.05480 13.9513i −0.338868 0.586936i
\(566\) 0 0
\(567\) −1.20502 1.29239i −0.0506060 0.0542752i
\(568\) 0 0
\(569\) 2.13757 + 3.70237i 0.0896115 + 0.155212i 0.907347 0.420383i \(-0.138104\pi\)
−0.817735 + 0.575594i \(0.804771\pi\)
\(570\) 0 0
\(571\) 18.5495 32.1287i 0.776272 1.34454i −0.157805 0.987470i \(-0.550442\pi\)
0.934077 0.357072i \(-0.116225\pi\)
\(572\) 0 0
\(573\) 1.99622 1.30873i 0.0833932 0.0546731i
\(574\) 0 0
\(575\) −7.33390 −0.305845
\(576\) 0 0
\(577\) 32.7354 1.36279 0.681396 0.731914i \(-0.261373\pi\)
0.681396 + 0.731914i \(0.261373\pi\)
\(578\) 0 0
\(579\) −21.6966 10.9364i −0.901681 0.454503i
\(580\) 0 0
\(581\) −0.468817 + 0.812015i −0.0194498 + 0.0336881i
\(582\) 0 0
\(583\) 19.9163 + 34.4960i 0.824848 + 1.42868i
\(584\) 0 0
\(585\) −4.58372 6.19495i −0.189513 0.256130i
\(586\) 0 0
\(587\) −14.7796 25.5989i −0.610017 1.05658i −0.991237 0.132097i \(-0.957829\pi\)
0.381219 0.924485i \(-0.375504\pi\)
\(588\) 0 0
\(589\) 7.72657 13.3828i 0.318368 0.551429i
\(590\) 0 0
\(591\) −0.418564 7.37322i −0.0172174 0.303294i
\(592\) 0 0
\(593\) 33.1251 1.36028 0.680142 0.733081i \(-0.261918\pi\)
0.680142 + 0.733081i \(0.261918\pi\)
\(594\) 0 0
\(595\) 1.02590 0.0420576
\(596\) 0 0
\(597\) −0.0678367 1.19498i −0.00277637 0.0489072i
\(598\) 0 0
\(599\) 19.0249 32.9522i 0.777338 1.34639i −0.156134 0.987736i \(-0.549903\pi\)
0.933471 0.358652i \(-0.116764\pi\)
\(600\) 0 0
\(601\) 22.2232 + 38.4916i 0.906502 + 1.57011i 0.818889 + 0.573952i \(0.194591\pi\)
0.0876129 + 0.996155i \(0.472076\pi\)
\(602\) 0 0
\(603\) −6.56311 + 15.0928i −0.267270 + 0.614627i
\(604\) 0 0
\(605\) 8.49036 + 14.7057i 0.345182 + 0.597873i
\(606\) 0 0
\(607\) 6.66024 11.5359i 0.270331 0.468227i −0.698616 0.715497i \(-0.746200\pi\)
0.968946 + 0.247270i \(0.0795336\pi\)
\(608\) 0 0
\(609\) −1.45578 0.733802i −0.0589911 0.0297351i
\(610\) 0 0
\(611\) −33.1049 −1.33928
\(612\) 0 0
\(613\) −28.1780 −1.13810 −0.569049 0.822304i \(-0.692688\pi\)
−0.569049 + 0.822304i \(0.692688\pi\)
\(614\) 0 0
\(615\) 7.25785 4.75829i 0.292665 0.191873i
\(616\) 0 0
\(617\) −13.7910 + 23.8867i −0.555205 + 0.961644i 0.442682 + 0.896679i \(0.354027\pi\)
−0.997888 + 0.0649652i \(0.979306\pi\)
\(618\) 0 0
\(619\) 9.99800 + 17.3170i 0.401854 + 0.696031i 0.993950 0.109837i \(-0.0350328\pi\)
−0.592096 + 0.805867i \(0.701699\pi\)
\(620\) 0 0
\(621\) −35.7520 13.1916i −1.43468 0.529359i
\(622\) 0 0
\(623\) −1.52938 2.64897i −0.0612735 0.106129i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 52.8458 34.6460i 2.11046 1.38363i
\(628\) 0 0
\(629\) 50.2558 2.00383
\(630\) 0 0
\(631\) −22.0423 −0.877490 −0.438745 0.898612i \(-0.644577\pi\)
−0.438745 + 0.898612i \(0.644577\pi\)
\(632\) 0 0
\(633\) 35.0658 + 17.6753i 1.39374 + 0.702530i
\(634\) 0 0
\(635\) 3.41478 5.91457i 0.135511 0.234713i
\(636\) 0 0
\(637\) 8.94123 + 15.4867i 0.354265 + 0.613604i
\(638\) 0 0
\(639\) 16.3811 1.86586i 0.648025 0.0738122i
\(640\) 0 0
\(641\) −9.49564 16.4469i −0.375055 0.649615i 0.615280 0.788309i \(-0.289043\pi\)
−0.990335 + 0.138694i \(0.955710\pi\)
\(642\) 0 0
\(643\) 4.67366 8.09502i 0.184311 0.319237i −0.759033 0.651052i \(-0.774328\pi\)
0.943344 + 0.331816i \(0.107661\pi\)
\(644\) 0 0
\(645\) −0.873396 15.3853i −0.0343899 0.605796i
\(646\) 0 0
\(647\) 33.6708 1.32373 0.661867 0.749621i \(-0.269764\pi\)
0.661867 + 0.749621i \(0.269764\pi\)
\(648\) 0 0
\(649\) −23.2358 −0.912085
\(650\) 0 0
\(651\) −0.0431837 0.760702i −0.00169250 0.0298143i
\(652\) 0 0
\(653\) −20.8887 + 36.1803i −0.817437 + 1.41584i 0.0901271 + 0.995930i \(0.471273\pi\)
−0.907564 + 0.419913i \(0.862061\pi\)
\(654\) 0 0
\(655\) 2.42157 + 4.19429i 0.0946186 + 0.163884i
\(656\) 0 0
\(657\) 7.68836 0.875731i 0.299952 0.0341655i
\(658\) 0 0
\(659\) −7.09902 12.2959i −0.276539 0.478979i 0.693984 0.719991i \(-0.255854\pi\)
−0.970522 + 0.241012i \(0.922521\pi\)
\(660\) 0 0
\(661\) 17.2984 29.9616i 0.672828 1.16537i −0.304270 0.952586i \(-0.598413\pi\)
0.977099 0.212787i \(-0.0682541\pi\)
\(662\) 0 0
\(663\) 20.7602 + 10.4644i 0.806260 + 0.406405i
\(664\) 0 0
\(665\) −1.35412 −0.0525106
\(666\) 0 0
\(667\) −35.1589 −1.36136
\(668\) 0 0
\(669\) −20.4854 + 13.4304i −0.792013 + 0.519248i
\(670\) 0 0
\(671\) 17.5033 30.3166i 0.675708 1.17036i
\(672\) 0 0
\(673\) −16.2594 28.1622i −0.626755 1.08557i −0.988199 0.153177i \(-0.951049\pi\)
0.361444 0.932394i \(-0.382284\pi\)
\(674\) 0 0
\(675\) −3.99518 + 3.32243i −0.153774 + 0.127880i
\(676\) 0 0
\(677\) −0.0149325 0.0258638i −0.000573903 0.000994028i 0.865738 0.500497i \(-0.166849\pi\)
−0.866312 + 0.499503i \(0.833516\pi\)
\(678\) 0 0
\(679\) 1.23091 2.13200i 0.0472381 0.0818187i
\(680\) 0 0
\(681\) −12.2349 + 8.02124i −0.468841 + 0.307375i
\(682\) 0 0
\(683\) 11.1241 0.425653 0.212827 0.977090i \(-0.431733\pi\)
0.212827 + 0.977090i \(0.431733\pi\)
\(684\) 0 0
\(685\) −11.1954 −0.427753
\(686\) 0 0
\(687\) −31.7237 15.9907i −1.21034 0.610083i
\(688\) 0 0
\(689\) 9.67177 16.7520i 0.368465 0.638200i
\(690\) 0 0
\(691\) 0.299324 + 0.518445i 0.0113868 + 0.0197226i 0.871663 0.490106i \(-0.163042\pi\)
−0.860276 + 0.509829i \(0.829709\pi\)
\(692\) 0 0
\(693\) 1.24245 2.85719i 0.0471968 0.108536i
\(694\) 0 0
\(695\) 1.43122 + 2.47894i 0.0542891 + 0.0940315i
\(696\) 0 0
\(697\) −13.0907 + 22.6738i −0.495847 + 0.858831i
\(698\) 0 0
\(699\) −0.628589 11.0729i −0.0237754 0.418816i
\(700\) 0 0
\(701\) 15.6784 0.592164 0.296082 0.955162i \(-0.404320\pi\)
0.296082 + 0.955162i \(0.404320\pi\)
\(702\) 0 0
\(703\) −66.3348 −2.50186
\(704\) 0 0
\(705\) 1.26512 + 22.2857i 0.0476471 + 0.839328i
\(706\) 0 0
\(707\) −1.87679 + 3.25070i −0.0705840 + 0.122255i
\(708\) 0 0
\(709\) −1.37112 2.37484i −0.0514933 0.0891890i 0.839130 0.543931i \(-0.183065\pi\)
−0.890623 + 0.454742i \(0.849731\pi\)
\(710\) 0 0
\(711\) 4.26946 + 5.77023i 0.160117 + 0.216400i
\(712\) 0 0
\(713\) −8.21601 14.2305i −0.307692 0.532938i
\(714\) 0 0
\(715\) 6.79402 11.7676i 0.254082 0.440083i
\(716\) 0 0
\(717\) −25.2050 12.7049i −0.941299 0.474472i
\(718\) 0 0
\(719\) −17.7056 −0.660307 −0.330153 0.943927i \(-0.607100\pi\)
−0.330153 + 0.943927i \(0.607100\pi\)
\(720\) 0 0
\(721\) 1.18480 0.0441241
\(722\) 0 0
\(723\) 24.3695 15.9768i 0.906311 0.594183i
\(724\) 0 0
\(725\) −2.39701 + 4.15174i −0.0890227 + 0.154192i
\(726\) 0 0
\(727\) 5.24167 + 9.07885i 0.194403 + 0.336716i 0.946705 0.322103i \(-0.104390\pi\)
−0.752302 + 0.658819i \(0.771056\pi\)
\(728\) 0 0
\(729\) −25.4522 + 9.01036i −0.942673 + 0.333717i
\(730\) 0 0
\(731\) 23.2445 + 40.2606i 0.859729 + 1.48909i
\(732\) 0 0
\(733\) −7.20012 + 12.4710i −0.265942 + 0.460626i −0.967810 0.251682i \(-0.919016\pi\)
0.701868 + 0.712307i \(0.252350\pi\)
\(734\) 0 0
\(735\) 10.0837 6.61093i 0.371943 0.243848i
\(736\) 0 0
\(737\) −29.0193 −1.06894
\(738\) 0 0
\(739\) 18.8564 0.693645 0.346822 0.937931i \(-0.387261\pi\)
0.346822 + 0.937931i \(0.387261\pi\)
\(740\) 0 0
\(741\) −27.4023 13.8124i −1.00665 0.507412i
\(742\) 0 0
\(743\) 22.9413 39.7355i 0.841635 1.45775i −0.0468766 0.998901i \(-0.514927\pi\)
0.888512 0.458854i \(-0.151740\pi\)
\(744\) 0 0
\(745\) −0.112619 0.195061i −0.00412603 0.00714649i
\(746\) 0 0
\(747\) 8.52171 + 11.5172i 0.311793 + 0.421392i
\(748\) 0 0
\(749\) 0.771739 + 1.33669i 0.0281987 + 0.0488417i
\(750\) 0 0
\(751\) 10.5178 18.2174i 0.383802 0.664764i −0.607800 0.794090i \(-0.707948\pi\)
0.991602 + 0.129326i \(0.0412813\pi\)
\(752\) 0 0
\(753\) −2.31726 40.8198i −0.0844458 1.48756i
\(754\) 0 0
\(755\) −4.28100 −0.155801
\(756\) 0 0
\(757\) 38.8360 1.41152 0.705759 0.708452i \(-0.250606\pi\)
0.705759 + 0.708452i \(0.250606\pi\)
\(758\) 0 0
\(759\) −3.80830 67.0852i −0.138233 2.43504i
\(760\) 0 0
\(761\) 12.6425 21.8974i 0.458289 0.793780i −0.540582 0.841292i \(-0.681796\pi\)
0.998871 + 0.0475116i \(0.0151291\pi\)
\(762\) 0 0
\(763\) 0.931774 + 1.61388i 0.0337325 + 0.0584264i
\(764\) 0 0
\(765\) 6.25113 14.3754i 0.226010 0.519743i
\(766\) 0 0
\(767\) 5.64191 + 9.77207i 0.203717 + 0.352849i
\(768\) 0 0
\(769\) 11.5249 19.9618i 0.415600 0.719840i −0.579891 0.814694i \(-0.696905\pi\)
0.995491 + 0.0948539i \(0.0302384\pi\)
\(770\) 0 0
\(771\) 6.33864 + 3.19507i 0.228281 + 0.115068i
\(772\) 0 0
\(773\) 7.02605 0.252709 0.126355 0.991985i \(-0.459672\pi\)
0.126355 + 0.991985i \(0.459672\pi\)
\(774\) 0 0
\(775\) −2.24056 −0.0804832
\(776\) 0 0
\(777\) −2.73525 + 1.79325i −0.0981267 + 0.0643324i
\(778\) 0 0
\(779\) 17.2790 29.9281i 0.619084 1.07229i
\(780\) 0 0
\(781\) 14.5351 + 25.1756i 0.520108 + 0.900854i
\(782\) 0 0
\(783\) −19.1530 + 15.9278i −0.684471 + 0.569213i
\(784\) 0 0
\(785\) 3.38302 + 5.85957i 0.120745 + 0.209137i
\(786\) 0 0
\(787\) −7.73818 + 13.4029i −0.275837 + 0.477763i −0.970346 0.241721i \(-0.922288\pi\)
0.694509 + 0.719484i \(0.255622\pi\)
\(788\) 0 0
\(789\) −35.1432 + 23.0401i −1.25113 + 0.820249i
\(790\) 0 0
\(791\) −3.16287 −0.112459
\(792\) 0 0
\(793\) −17.0000 −0.603687
\(794\) 0 0
\(795\) −11.6468 5.87071i −0.413070 0.208213i