Properties

Label 560.2.ci.c.33.3
Level $560$
Weight $2$
Character 560.33
Analytic conductor $4.472$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.ci (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.47162251319\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 10 x^{14} + 61 x^{12} + 266 x^{10} + 852 x^{8} + 1438 x^{6} + 1933 x^{4} + 3038 x^{2} + 2401\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 33.3
Root \(-1.01089 - 0.750919i\) of defining polynomial
Character \(\chi\) \(=\) 560.33
Dual form 560.2.ci.c.17.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.279864 + 0.0749894i) q^{3} +(0.774197 + 2.09777i) q^{5} +(-2.64273 + 0.126334i) q^{7} +(-2.52538 - 1.45803i) q^{9} +O(q^{10})\) \(q+(0.279864 + 0.0749894i) q^{3} +(0.774197 + 2.09777i) q^{5} +(-2.64273 + 0.126334i) q^{7} +(-2.52538 - 1.45803i) q^{9} +(2.81288 + 4.87205i) q^{11} +(1.42962 - 1.42962i) q^{13} +(0.0593598 + 0.645146i) q^{15} +(-1.37400 + 5.12784i) q^{17} +(-1.94590 + 3.37040i) q^{19} +(-0.749081 - 0.162821i) q^{21} +(-1.08562 + 0.290892i) q^{23} +(-3.80124 + 3.24817i) q^{25} +(-1.21205 - 1.21205i) q^{27} +3.15502i q^{29} +(3.33287 - 1.92423i) q^{31} +(0.421872 + 1.57445i) q^{33} +(-2.31101 - 5.44603i) q^{35} +(-1.30444 - 4.86824i) q^{37} +(0.507306 - 0.292893i) q^{39} +7.21050i q^{41} +(-1.85669 - 1.85669i) q^{43} +(1.10346 - 6.42644i) q^{45} +(5.69475 - 1.52590i) q^{47} +(6.96808 - 0.667734i) q^{49} +(-0.769067 + 1.33206i) q^{51} +(-0.357978 + 1.33599i) q^{53} +(-8.04270 + 9.67269i) q^{55} +(-0.797333 + 0.797333i) q^{57} +(2.73923 + 4.74448i) q^{59} +(-3.99172 - 2.30462i) q^{61} +(6.85809 + 3.53413i) q^{63} +(4.10581 + 1.89220i) q^{65} +(0.816193 + 0.218698i) q^{67} -0.325641 q^{69} -4.77710 q^{71} +(5.42104 + 1.45256i) q^{73} +(-1.30741 + 0.623993i) q^{75} +(-8.04920 - 12.5202i) q^{77} +(5.41079 + 3.12392i) q^{79} +(4.12576 + 7.14603i) q^{81} +(5.67281 - 5.67281i) q^{83} +(-11.8207 + 1.08763i) q^{85} +(-0.236593 + 0.882976i) q^{87} +(5.96090 - 10.3246i) q^{89} +(-3.59749 + 3.95871i) q^{91} +(1.07705 - 0.288594i) q^{93} +(-8.57682 - 1.47269i) q^{95} +(6.63103 + 6.63103i) q^{97} -16.4050i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 12q^{5} - 8q^{7} + O(q^{10}) \) \( 16q - 12q^{5} - 8q^{7} + 12q^{11} - 16q^{15} - 36q^{17} - 28q^{21} + 4q^{23} + 12q^{25} - 24q^{31} + 48q^{33} - 8q^{35} + 4q^{37} + 8q^{43} - 12q^{45} - 12q^{47} + 16q^{51} - 28q^{53} + 8q^{57} - 12q^{61} + 36q^{63} - 8q^{65} - 32q^{67} - 16q^{71} - 12q^{73} + 48q^{75} + 16q^{77} + 24q^{85} + 24q^{87} + 16q^{91} + 28q^{93} - 20q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(351\) \(421\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

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
\(3\) 0.279864 + 0.0749894i 0.161580 + 0.0432952i 0.338702 0.940894i \(-0.390012\pi\)
−0.177122 + 0.984189i \(0.556679\pi\)
\(4\) 0 0
\(5\) 0.774197 + 2.09777i 0.346231 + 0.938149i
\(6\) 0 0
\(7\) −2.64273 + 0.126334i −0.998859 + 0.0477497i
\(8\) 0 0
\(9\) −2.52538 1.45803i −0.841792 0.486009i
\(10\) 0 0
\(11\) 2.81288 + 4.87205i 0.848115 + 1.46898i 0.882888 + 0.469583i \(0.155596\pi\)
−0.0347729 + 0.999395i \(0.511071\pi\)
\(12\) 0 0
\(13\) 1.42962 1.42962i 0.396505 0.396505i −0.480493 0.876998i \(-0.659542\pi\)
0.876998 + 0.480493i \(0.159542\pi\)
\(14\) 0 0
\(15\) 0.0593598 + 0.645146i 0.0153266 + 0.166576i
\(16\) 0 0
\(17\) −1.37400 + 5.12784i −0.333244 + 1.24368i 0.572516 + 0.819893i \(0.305967\pi\)
−0.905760 + 0.423790i \(0.860699\pi\)
\(18\) 0 0
\(19\) −1.94590 + 3.37040i −0.446420 + 0.773223i −0.998150 0.0608002i \(-0.980635\pi\)
0.551729 + 0.834023i \(0.313968\pi\)
\(20\) 0 0
\(21\) −0.749081 0.162821i −0.163463 0.0355304i
\(22\) 0 0
\(23\) −1.08562 + 0.290892i −0.226368 + 0.0606552i −0.370220 0.928944i \(-0.620718\pi\)
0.143852 + 0.989599i \(0.454051\pi\)
\(24\) 0 0
\(25\) −3.80124 + 3.24817i −0.760248 + 0.649633i
\(26\) 0 0
\(27\) −1.21205 1.21205i −0.233259 0.233259i
\(28\) 0 0
\(29\) 3.15502i 0.585872i 0.956132 + 0.292936i \(0.0946322\pi\)
−0.956132 + 0.292936i \(0.905368\pi\)
\(30\) 0 0
\(31\) 3.33287 1.92423i 0.598601 0.345602i −0.169890 0.985463i \(-0.554341\pi\)
0.768491 + 0.639861i \(0.221008\pi\)
\(32\) 0 0
\(33\) 0.421872 + 1.57445i 0.0734386 + 0.274076i
\(34\) 0 0
\(35\) −2.31101 5.44603i −0.390633 0.920547i
\(36\) 0 0
\(37\) −1.30444 4.86824i −0.214449 0.800334i −0.986360 0.164603i \(-0.947366\pi\)
0.771911 0.635731i \(-0.219301\pi\)
\(38\) 0 0
\(39\) 0.507306 0.292893i 0.0812340 0.0469005i
\(40\) 0 0
\(41\) 7.21050i 1.12609i 0.826426 + 0.563046i \(0.190371\pi\)
−0.826426 + 0.563046i \(0.809629\pi\)
\(42\) 0 0
\(43\) −1.85669 1.85669i −0.283143 0.283143i 0.551218 0.834361i \(-0.314163\pi\)
−0.834361 + 0.551218i \(0.814163\pi\)
\(44\) 0 0
\(45\) 1.10346 6.42644i 0.164494 0.957998i
\(46\) 0 0
\(47\) 5.69475 1.52590i 0.830665 0.222576i 0.181661 0.983361i \(-0.441853\pi\)
0.649004 + 0.760785i \(0.275186\pi\)
\(48\) 0 0
\(49\) 6.96808 0.667734i 0.995440 0.0953905i
\(50\) 0 0
\(51\) −0.769067 + 1.33206i −0.107691 + 0.186526i
\(52\) 0 0
\(53\) −0.357978 + 1.33599i −0.0491720 + 0.183512i −0.986144 0.165892i \(-0.946950\pi\)
0.936972 + 0.349405i \(0.113616\pi\)
\(54\) 0 0
\(55\) −8.04270 + 9.67269i −1.08448 + 1.30426i
\(56\) 0 0
\(57\) −0.797333 + 0.797333i −0.105609 + 0.105609i
\(58\) 0 0
\(59\) 2.73923 + 4.74448i 0.356617 + 0.617679i 0.987393 0.158286i \(-0.0505968\pi\)
−0.630776 + 0.775965i \(0.717263\pi\)
\(60\) 0 0
\(61\) −3.99172 2.30462i −0.511088 0.295077i 0.222193 0.975003i \(-0.428678\pi\)
−0.733281 + 0.679926i \(0.762012\pi\)
\(62\) 0 0
\(63\) 6.85809 + 3.53413i 0.864038 + 0.445259i
\(64\) 0 0
\(65\) 4.10581 + 1.89220i 0.509264 + 0.234699i
\(66\) 0 0
\(67\) 0.816193 + 0.218698i 0.0997138 + 0.0267182i 0.308331 0.951279i \(-0.400230\pi\)
−0.208617 + 0.977997i \(0.566896\pi\)
\(68\) 0 0
\(69\) −0.325641 −0.0392026
\(70\) 0 0
\(71\) −4.77710 −0.566937 −0.283469 0.958982i \(-0.591485\pi\)
−0.283469 + 0.958982i \(0.591485\pi\)
\(72\) 0 0
\(73\) 5.42104 + 1.45256i 0.634485 + 0.170010i 0.561704 0.827338i \(-0.310146\pi\)
0.0727807 + 0.997348i \(0.476813\pi\)
\(74\) 0 0
\(75\) −1.30741 + 0.623993i −0.150967 + 0.0720525i
\(76\) 0 0
\(77\) −8.04920 12.5202i −0.917291 1.42681i
\(78\) 0 0
\(79\) 5.41079 + 3.12392i 0.608761 + 0.351469i 0.772481 0.635038i \(-0.219016\pi\)
−0.163719 + 0.986507i \(0.552349\pi\)
\(80\) 0 0
\(81\) 4.12576 + 7.14603i 0.458418 + 0.794003i
\(82\) 0 0
\(83\) 5.67281 5.67281i 0.622672 0.622672i −0.323542 0.946214i \(-0.604874\pi\)
0.946214 + 0.323542i \(0.104874\pi\)
\(84\) 0 0
\(85\) −11.8207 + 1.08763i −1.28214 + 0.117970i
\(86\) 0 0
\(87\) −0.236593 + 0.882976i −0.0253654 + 0.0946650i
\(88\) 0 0
\(89\) 5.96090 10.3246i 0.631855 1.09440i −0.355318 0.934746i \(-0.615627\pi\)
0.987172 0.159659i \(-0.0510393\pi\)
\(90\) 0 0
\(91\) −3.59749 + 3.95871i −0.377120 + 0.414986i
\(92\) 0 0
\(93\) 1.07705 0.288594i 0.111685 0.0299258i
\(94\) 0 0
\(95\) −8.57682 1.47269i −0.879963 0.151095i
\(96\) 0 0
\(97\) 6.63103 + 6.63103i 0.673279 + 0.673279i 0.958471 0.285191i \(-0.0920572\pi\)
−0.285191 + 0.958471i \(0.592057\pi\)
\(98\) 0 0
\(99\) 16.4050i 1.64877i
\(100\) 0 0
\(101\) 13.9423 8.04960i 1.38731 0.800965i 0.394301 0.918981i \(-0.370987\pi\)
0.993012 + 0.118016i \(0.0376535\pi\)
\(102\) 0 0
\(103\) −5.09084 18.9993i −0.501616 1.87206i −0.489271 0.872132i \(-0.662737\pi\)
−0.0123445 0.999924i \(-0.503929\pi\)
\(104\) 0 0
\(105\) −0.238376 1.69745i −0.0232631 0.165654i
\(106\) 0 0
\(107\) −0.724955 2.70557i −0.0700840 0.261557i 0.921990 0.387214i \(-0.126563\pi\)
−0.992074 + 0.125657i \(0.959896\pi\)
\(108\) 0 0
\(109\) 5.11895 2.95543i 0.490306 0.283078i −0.234395 0.972141i \(-0.575311\pi\)
0.724701 + 0.689063i \(0.241978\pi\)
\(110\) 0 0
\(111\) 1.46027i 0.138602i
\(112\) 0 0
\(113\) −13.5818 13.5818i −1.27767 1.27767i −0.941970 0.335697i \(-0.891028\pi\)
−0.335697 0.941970i \(-0.608972\pi\)
\(114\) 0 0
\(115\) −1.45071 2.05218i −0.135279 0.191367i
\(116\) 0 0
\(117\) −5.69475 + 1.52590i −0.526480 + 0.141070i
\(118\) 0 0
\(119\) 2.98330 13.7251i 0.273478 1.25818i
\(120\) 0 0
\(121\) −10.3246 + 17.8827i −0.938599 + 1.62570i
\(122\) 0 0
\(123\) −0.540712 + 2.01796i −0.0487543 + 0.181954i
\(124\) 0 0
\(125\) −9.75680 5.45939i −0.872674 0.488303i
\(126\) 0 0
\(127\) −4.63487 + 4.63487i −0.411278 + 0.411278i −0.882184 0.470906i \(-0.843927\pi\)
0.470906 + 0.882184i \(0.343927\pi\)
\(128\) 0 0
\(129\) −0.380390 0.658854i −0.0334915 0.0580089i
\(130\) 0 0
\(131\) 6.66437 + 3.84768i 0.582269 + 0.336173i 0.762035 0.647536i \(-0.224201\pi\)
−0.179766 + 0.983709i \(0.557534\pi\)
\(132\) 0 0
\(133\) 4.71670 9.15290i 0.408990 0.793657i
\(134\) 0 0
\(135\) 1.60423 3.48096i 0.138070 0.299594i
\(136\) 0 0
\(137\) 8.53471 + 2.28687i 0.729170 + 0.195380i 0.604259 0.796788i \(-0.293469\pi\)
0.124910 + 0.992168i \(0.460136\pi\)
\(138\) 0 0
\(139\) 11.0631 0.938361 0.469180 0.883102i \(-0.344549\pi\)
0.469180 + 0.883102i \(0.344549\pi\)
\(140\) 0 0
\(141\) 1.70818 0.143855
\(142\) 0 0
\(143\) 10.9865 + 2.94383i 0.918740 + 0.246176i
\(144\) 0 0
\(145\) −6.61848 + 2.44260i −0.549635 + 0.202847i
\(146\) 0 0
\(147\) 2.00019 + 0.335657i 0.164973 + 0.0276846i
\(148\) 0 0
\(149\) 4.37243 + 2.52443i 0.358204 + 0.206809i 0.668293 0.743899i \(-0.267025\pi\)
−0.310089 + 0.950708i \(0.600359\pi\)
\(150\) 0 0
\(151\) 6.72142 + 11.6418i 0.546981 + 0.947399i 0.998479 + 0.0551270i \(0.0175564\pi\)
−0.451498 + 0.892272i \(0.649110\pi\)
\(152\) 0 0
\(153\) 10.9464 10.9464i 0.884963 0.884963i
\(154\) 0 0
\(155\) 6.61688 + 5.50184i 0.531481 + 0.441918i
\(156\) 0 0
\(157\) −0.285443 + 1.06529i −0.0227808 + 0.0850191i −0.976380 0.216059i \(-0.930680\pi\)
0.953600 + 0.301078i \(0.0973464\pi\)
\(158\) 0 0
\(159\) −0.200370 + 0.347052i −0.0158904 + 0.0275230i
\(160\) 0 0
\(161\) 2.83227 0.905902i 0.223214 0.0713951i
\(162\) 0 0
\(163\) −12.7899 + 3.42705i −1.00179 + 0.268428i −0.722193 0.691691i \(-0.756866\pi\)
−0.279592 + 0.960119i \(0.590199\pi\)
\(164\) 0 0
\(165\) −2.97621 + 2.10392i −0.231698 + 0.163790i
\(166\) 0 0
\(167\) −4.70680 4.70680i −0.364223 0.364223i 0.501142 0.865365i \(-0.332913\pi\)
−0.865365 + 0.501142i \(0.832913\pi\)
\(168\) 0 0
\(169\) 8.91237i 0.685567i
\(170\) 0 0
\(171\) 9.82827 5.67435i 0.751586 0.433929i
\(172\) 0 0
\(173\) −1.82586 6.81421i −0.138818 0.518075i −0.999953 0.00969875i \(-0.996913\pi\)
0.861135 0.508376i \(-0.169754\pi\)
\(174\) 0 0
\(175\) 9.63531 9.06426i 0.728361 0.685194i
\(176\) 0 0
\(177\) 0.410826 + 1.53322i 0.0308796 + 0.115244i
\(178\) 0 0
\(179\) 1.91075 1.10317i 0.142816 0.0824550i −0.426889 0.904304i \(-0.640391\pi\)
0.569706 + 0.821849i \(0.307057\pi\)
\(180\) 0 0
\(181\) 4.11867i 0.306139i −0.988215 0.153069i \(-0.951084\pi\)
0.988215 0.153069i \(-0.0489158\pi\)
\(182\) 0 0
\(183\) −0.944318 0.944318i −0.0698060 0.0698060i
\(184\) 0 0
\(185\) 9.20253 6.50539i 0.676584 0.478286i
\(186\) 0 0
\(187\) −28.8480 + 7.72980i −2.10957 + 0.565259i
\(188\) 0 0
\(189\) 3.35625 + 3.05000i 0.244131 + 0.221855i
\(190\) 0 0
\(191\) −8.60117 + 14.8977i −0.622359 + 1.07796i 0.366686 + 0.930345i \(0.380492\pi\)
−0.989045 + 0.147613i \(0.952841\pi\)
\(192\) 0 0
\(193\) −3.12327 + 11.6562i −0.224818 + 0.839032i 0.757659 + 0.652650i \(0.226343\pi\)
−0.982477 + 0.186382i \(0.940324\pi\)
\(194\) 0 0
\(195\) 1.00718 + 0.837452i 0.0721254 + 0.0599712i
\(196\) 0 0
\(197\) 14.3135 14.3135i 1.01979 1.01979i 0.0199932 0.999800i \(-0.493636\pi\)
0.999800 0.0199932i \(-0.00636444\pi\)
\(198\) 0 0
\(199\) −3.76653 6.52383i −0.267002 0.462462i 0.701084 0.713079i \(-0.252700\pi\)
−0.968086 + 0.250617i \(0.919367\pi\)
\(200\) 0 0
\(201\) 0.212023 + 0.122412i 0.0149550 + 0.00863425i
\(202\) 0 0
\(203\) −0.398585 8.33786i −0.0279752 0.585203i
\(204\) 0 0
\(205\) −15.1259 + 5.58235i −1.05644 + 0.389888i
\(206\) 0 0
\(207\) 3.16574 + 0.848257i 0.220034 + 0.0589579i
\(208\) 0 0
\(209\) −21.8944 −1.51446
\(210\) 0 0
\(211\) −19.5766 −1.34771 −0.673854 0.738865i \(-0.735362\pi\)
−0.673854 + 0.738865i \(0.735362\pi\)
\(212\) 0 0
\(213\) −1.33694 0.358232i −0.0916056 0.0245456i
\(214\) 0 0
\(215\) 2.45746 5.33235i 0.167597 0.363663i
\(216\) 0 0
\(217\) −8.56478 + 5.50629i −0.581415 + 0.373791i
\(218\) 0 0
\(219\) 1.40823 + 0.813041i 0.0951593 + 0.0549402i
\(220\) 0 0
\(221\) 5.36656 + 9.29516i 0.360994 + 0.625260i
\(222\) 0 0
\(223\) 1.46027 1.46027i 0.0977867 0.0977867i −0.656521 0.754308i \(-0.727973\pi\)
0.754308 + 0.656521i \(0.227973\pi\)
\(224\) 0 0
\(225\) 14.3355 2.66053i 0.955698 0.177369i
\(226\) 0 0
\(227\) 4.82525 18.0081i 0.320263 1.19524i −0.598726 0.800954i \(-0.704326\pi\)
0.918989 0.394283i \(-0.129007\pi\)
\(228\) 0 0
\(229\) 2.00384 3.47074i 0.132417 0.229353i −0.792191 0.610274i \(-0.791059\pi\)
0.924608 + 0.380920i \(0.124393\pi\)
\(230\) 0 0
\(231\) −1.31380 4.10755i −0.0864419 0.270257i
\(232\) 0 0
\(233\) 13.2637 3.55400i 0.868934 0.232830i 0.203307 0.979115i \(-0.434831\pi\)
0.665627 + 0.746285i \(0.268164\pi\)
\(234\) 0 0
\(235\) 7.60984 + 10.7649i 0.496412 + 0.702225i
\(236\) 0 0
\(237\) 1.28003 + 1.28003i 0.0831466 + 0.0831466i
\(238\) 0 0
\(239\) 19.6621i 1.27183i 0.771758 + 0.635916i \(0.219378\pi\)
−0.771758 + 0.635916i \(0.780622\pi\)
\(240\) 0 0
\(241\) −5.09667 + 2.94256i −0.328305 + 0.189547i −0.655088 0.755552i \(-0.727369\pi\)
0.326783 + 0.945099i \(0.394035\pi\)
\(242\) 0 0
\(243\) 1.94970 + 7.27638i 0.125073 + 0.466780i
\(244\) 0 0
\(245\) 6.79541 + 14.1004i 0.434143 + 0.900844i
\(246\) 0 0
\(247\) 2.03649 + 7.60029i 0.129579 + 0.483595i
\(248\) 0 0
\(249\) 2.01302 1.16222i 0.127570 0.0736525i
\(250\) 0 0
\(251\) 7.09950i 0.448116i 0.974576 + 0.224058i \(0.0719306\pi\)
−0.974576 + 0.224058i \(0.928069\pi\)
\(252\) 0 0
\(253\) −4.47097 4.47097i −0.281088 0.281088i
\(254\) 0 0
\(255\) −3.38977 0.582044i −0.212275 0.0364490i
\(256\) 0 0
\(257\) −9.54998 + 2.55891i −0.595711 + 0.159620i −0.544062 0.839045i \(-0.683114\pi\)
−0.0516491 + 0.998665i \(0.516448\pi\)
\(258\) 0 0
\(259\) 4.06231 + 12.7007i 0.252420 + 0.789181i
\(260\) 0 0
\(261\) 4.60010 7.96760i 0.284739 0.493182i
\(262\) 0 0
\(263\) −3.55829 + 13.2797i −0.219413 + 0.818861i 0.765153 + 0.643849i \(0.222663\pi\)
−0.984566 + 0.175013i \(0.944003\pi\)
\(264\) 0 0
\(265\) −3.07974 + 0.283366i −0.189187 + 0.0174071i
\(266\) 0 0
\(267\) 2.44248 2.44248i 0.149477 0.149477i
\(268\) 0 0
\(269\) 13.2510 + 22.9514i 0.807928 + 1.39937i 0.914296 + 0.405046i \(0.132745\pi\)
−0.106368 + 0.994327i \(0.533922\pi\)
\(270\) 0 0
\(271\) 11.0824 + 6.39844i 0.673209 + 0.388678i 0.797292 0.603594i \(-0.206265\pi\)
−0.124082 + 0.992272i \(0.539599\pi\)
\(272\) 0 0
\(273\) −1.30367 + 0.838129i −0.0789018 + 0.0507259i
\(274\) 0 0
\(275\) −26.5177 9.38313i −1.59908 0.565824i
\(276\) 0 0
\(277\) −19.4184 5.20313i −1.16674 0.312626i −0.377083 0.926180i \(-0.623073\pi\)
−0.789653 + 0.613554i \(0.789739\pi\)
\(278\) 0 0
\(279\) −11.2223 −0.671863
\(280\) 0 0
\(281\) −14.1498 −0.844107 −0.422054 0.906571i \(-0.638691\pi\)
−0.422054 + 0.906571i \(0.638691\pi\)
\(282\) 0 0
\(283\) 26.1454 + 7.00563i 1.55418 + 0.416442i 0.930816 0.365489i \(-0.119098\pi\)
0.623366 + 0.781930i \(0.285765\pi\)
\(284\) 0 0
\(285\) −2.28991 1.05532i −0.135643 0.0625121i
\(286\) 0 0
\(287\) −0.910931 19.0554i −0.0537706 1.12481i
\(288\) 0 0
\(289\) −9.68442 5.59130i −0.569672 0.328900i
\(290\) 0 0
\(291\) 1.35853 + 2.35305i 0.0796385 + 0.137938i
\(292\) 0 0
\(293\) −17.1191 + 17.1191i −1.00011 + 1.00011i −0.000106876 1.00000i \(0.500034\pi\)
−1.00000 0.000106876i \(0.999966\pi\)
\(294\) 0 0
\(295\) −7.83211 + 9.41941i −0.456003 + 0.548420i
\(296\) 0 0
\(297\) 2.49582 9.31453i 0.144822 0.540484i
\(298\) 0 0
\(299\) −1.13616 + 1.96790i −0.0657061 + 0.113806i
\(300\) 0 0
\(301\) 5.14131 + 4.67218i 0.296340 + 0.269300i
\(302\) 0 0
\(303\) 4.50559 1.20727i 0.258840 0.0693558i
\(304\) 0 0
\(305\) 1.74418 10.1579i 0.0998713 0.581641i
\(306\) 0 0
\(307\) 17.2974 + 17.2974i 0.987217 + 0.987217i 0.999919 0.0127019i \(-0.00404326\pi\)
−0.0127019 + 0.999919i \(0.504043\pi\)
\(308\) 0 0
\(309\) 5.69898i 0.324204i
\(310\) 0 0
\(311\) 9.51095 5.49115i 0.539316 0.311374i −0.205486 0.978660i \(-0.565877\pi\)
0.744802 + 0.667286i \(0.232544\pi\)
\(312\) 0 0
\(313\) 7.61212 + 28.4088i 0.430262 + 1.60576i 0.752156 + 0.658985i \(0.229014\pi\)
−0.321893 + 0.946776i \(0.604319\pi\)
\(314\) 0 0
\(315\) −2.10427 + 17.1228i −0.118562 + 0.964760i
\(316\) 0 0
\(317\) 1.11136 + 4.14766i 0.0624203 + 0.232956i 0.990087 0.140453i \(-0.0448558\pi\)
−0.927667 + 0.373408i \(0.878189\pi\)
\(318\) 0 0
\(319\) −15.3714 + 8.87468i −0.860633 + 0.496887i
\(320\) 0 0
\(321\) 0.811556i 0.0452966i
\(322\) 0 0
\(323\) −14.6092 14.6092i −0.812878 0.812878i
\(324\) 0 0
\(325\) −0.790684 + 10.0780i −0.0438593 + 0.559025i
\(326\) 0 0
\(327\) 1.65424 0.443251i 0.0914795 0.0245119i
\(328\) 0 0
\(329\) −14.8569 + 4.75200i −0.819089 + 0.261986i
\(330\) 0 0
\(331\) 17.7249 30.7005i 0.974250 1.68745i 0.291863 0.956460i \(-0.405725\pi\)
0.682387 0.730991i \(-0.260942\pi\)
\(332\) 0 0
\(333\) −3.80382 + 14.1960i −0.208448 + 0.777939i
\(334\) 0 0
\(335\) 0.173116 + 1.88150i 0.00945835 + 0.102797i
\(336\) 0 0
\(337\) −12.1473 + 12.1473i −0.661708 + 0.661708i −0.955782 0.294075i \(-0.904989\pi\)
0.294075 + 0.955782i \(0.404989\pi\)
\(338\) 0 0
\(339\) −2.78257 4.81955i −0.151128 0.261762i
\(340\) 0 0
\(341\) 18.7499 + 10.8253i 1.01536 + 0.586221i
\(342\) 0 0
\(343\) −18.3304 + 2.64495i −0.989750 + 0.142814i
\(344\) 0 0
\(345\) −0.252110 0.683119i −0.0135732 0.0367779i
\(346\) 0 0
\(347\) 8.67040 + 2.32323i 0.465452 + 0.124717i 0.483920 0.875112i \(-0.339212\pi\)
−0.0184687 + 0.999829i \(0.505879\pi\)
\(348\) 0 0
\(349\) 26.0251 1.39309 0.696546 0.717512i \(-0.254719\pi\)
0.696546 + 0.717512i \(0.254719\pi\)
\(350\) 0 0
\(351\) −3.46554 −0.184977
\(352\) 0 0
\(353\) 9.62659 + 2.57944i 0.512372 + 0.137290i 0.505736 0.862688i \(-0.331221\pi\)
0.00663577 + 0.999978i \(0.497888\pi\)
\(354\) 0 0
\(355\) −3.69841 10.0212i −0.196291 0.531872i
\(356\) 0 0
\(357\) 1.86416 3.61745i 0.0986615 0.191456i
\(358\) 0 0
\(359\) 10.0235 + 5.78705i 0.529019 + 0.305429i 0.740617 0.671928i \(-0.234533\pi\)
−0.211598 + 0.977357i \(0.567867\pi\)
\(360\) 0 0
\(361\) 1.92693 + 3.33754i 0.101417 + 0.175660i
\(362\) 0 0
\(363\) −4.23050 + 4.23050i −0.222044 + 0.222044i
\(364\) 0 0
\(365\) 1.14981 + 12.4966i 0.0601840 + 0.654104i
\(366\) 0 0
\(367\) −4.32083 + 16.1256i −0.225545 + 0.841747i 0.756640 + 0.653832i \(0.226840\pi\)
−0.982185 + 0.187915i \(0.939827\pi\)
\(368\) 0 0
\(369\) 10.5131 18.2092i 0.547290 0.947935i
\(370\) 0 0
\(371\) 0.777258 3.57589i 0.0403532 0.185651i
\(372\) 0 0
\(373\) −3.07061 + 0.822767i −0.158990 + 0.0426013i −0.337436 0.941348i \(-0.609560\pi\)
0.178446 + 0.983950i \(0.442893\pi\)
\(374\) 0 0
\(375\) −2.32118 2.25954i −0.119865 0.116682i
\(376\) 0 0
\(377\) 4.51047 + 4.51047i 0.232301 + 0.232301i
\(378\) 0 0
\(379\) 7.15349i 0.367450i 0.982978 + 0.183725i \(0.0588156\pi\)
−0.982978 + 0.183725i \(0.941184\pi\)
\(380\) 0 0
\(381\) −1.64470 + 0.949568i −0.0842605 + 0.0486478i
\(382\) 0 0
\(383\) 3.77704 + 14.0961i 0.192998 + 0.720278i 0.992776 + 0.119982i \(0.0382837\pi\)
−0.799778 + 0.600296i \(0.795050\pi\)
\(384\) 0 0
\(385\) 20.0327 26.5784i 1.02096 1.35456i
\(386\) 0 0
\(387\) 1.98174 + 7.39595i 0.100737 + 0.375957i
\(388\) 0 0
\(389\) −5.36634 + 3.09826i −0.272084 + 0.157088i −0.629834 0.776729i \(-0.716877\pi\)
0.357750 + 0.933817i \(0.383544\pi\)
\(390\) 0 0
\(391\) 5.96659i 0.301744i
\(392\) 0 0
\(393\) 1.57658 + 1.57658i 0.0795282 + 0.0795282i
\(394\) 0 0
\(395\) −2.36424 + 13.7691i −0.118958 + 0.692798i
\(396\) 0 0
\(397\) 2.81652 0.754685i 0.141357 0.0378766i −0.187447 0.982275i \(-0.560021\pi\)
0.328804 + 0.944398i \(0.393354\pi\)
\(398\) 0 0
\(399\) 2.00641 2.20787i 0.100446 0.110532i
\(400\) 0 0
\(401\) 9.98528 17.2950i 0.498641 0.863672i −0.501358 0.865240i \(-0.667166\pi\)
0.999999 + 0.00156835i \(0.000499221\pi\)
\(402\) 0 0
\(403\) 2.01381 7.51565i 0.100315 0.374381i
\(404\) 0 0
\(405\) −11.7965 + 14.1873i −0.586175 + 0.704973i
\(406\) 0 0
\(407\) 20.0491 20.0491i 0.993796 0.993796i
\(408\) 0 0
\(409\) −17.1791 29.7550i −0.849451 1.47129i −0.881699 0.471812i \(-0.843600\pi\)
0.0322484 0.999480i \(-0.489733\pi\)
\(410\) 0 0
\(411\) 2.21707 + 1.28003i 0.109360 + 0.0631390i
\(412\) 0 0
\(413\) −7.83843 12.1923i −0.385704 0.599946i
\(414\) 0 0
\(415\) 16.2921 + 7.50836i 0.799748 + 0.368571i
\(416\) 0 0
\(417\) 3.09617 + 0.829616i 0.151620 + 0.0406265i
\(418\) 0 0
\(419\) −31.1360 −1.52109 −0.760547 0.649283i \(-0.775069\pi\)
−0.760547 + 0.649283i \(0.775069\pi\)
\(420\) 0 0
\(421\) −33.6728 −1.64111 −0.820555 0.571567i \(-0.806336\pi\)
−0.820555 + 0.571567i \(0.806336\pi\)
\(422\) 0 0
\(423\) −16.6062 4.44962i −0.807421 0.216348i
\(424\) 0 0
\(425\) −11.4332 23.9551i −0.554590 1.16199i
\(426\) 0 0
\(427\) 10.8402 + 5.58621i 0.524594 + 0.270336i
\(428\) 0 0
\(429\) 2.85398 + 1.64775i 0.137792 + 0.0795540i
\(430\) 0 0
\(431\) −7.37284 12.7701i −0.355137 0.615116i 0.632004 0.774965i \(-0.282233\pi\)
−0.987141 + 0.159849i \(0.948899\pi\)
\(432\) 0 0
\(433\) 9.98256 9.98256i 0.479731 0.479731i −0.425315 0.905046i \(-0.639837\pi\)
0.905046 + 0.425315i \(0.139837\pi\)
\(434\) 0 0
\(435\) −2.03545 + 0.187281i −0.0975922 + 0.00897944i
\(436\) 0 0
\(437\) 1.13210 4.22504i 0.0541555 0.202111i
\(438\) 0 0
\(439\) 19.2142 33.2800i 0.917046 1.58837i 0.113167 0.993576i \(-0.463900\pi\)
0.803878 0.594794i \(-0.202766\pi\)
\(440\) 0 0
\(441\) −18.5706 8.47336i −0.884314 0.403494i
\(442\) 0 0
\(443\) 5.54016 1.48448i 0.263221 0.0705299i −0.124795 0.992183i \(-0.539827\pi\)
0.388016 + 0.921653i \(0.373161\pi\)
\(444\) 0 0
\(445\) 26.2735 + 4.51132i 1.24548 + 0.213857i
\(446\) 0 0
\(447\) 1.03438 + 1.03438i 0.0489247 + 0.0489247i
\(448\) 0 0
\(449\) 7.30267i 0.344635i −0.985042 0.172317i \(-0.944875\pi\)
0.985042 0.172317i \(-0.0551254\pi\)
\(450\) 0 0
\(451\) −35.1299 + 20.2823i −1.65420 + 0.955055i
\(452\) 0 0
\(453\) 1.00807 + 3.76217i 0.0473633 + 0.176762i
\(454\) 0 0
\(455\) −11.0896 4.48188i −0.519889 0.210114i
\(456\) 0 0
\(457\) 1.33183 + 4.97047i 0.0623006 + 0.232509i 0.990055 0.140683i \(-0.0449299\pi\)
−0.927754 + 0.373192i \(0.878263\pi\)
\(458\) 0 0
\(459\) 7.88056 4.54984i 0.367833 0.212368i
\(460\) 0 0
\(461\) 29.4110i 1.36981i −0.728634 0.684903i \(-0.759845\pi\)
0.728634 0.684903i \(-0.240155\pi\)
\(462\) 0 0
\(463\) 4.04625 + 4.04625i 0.188045 + 0.188045i 0.794851 0.606805i \(-0.207549\pi\)
−0.606805 + 0.794851i \(0.707549\pi\)
\(464\) 0 0
\(465\) 1.43925 + 2.03596i 0.0667436 + 0.0944156i
\(466\) 0 0
\(467\) −16.0757 + 4.30747i −0.743894 + 0.199326i −0.610808 0.791779i \(-0.709155\pi\)
−0.133086 + 0.991105i \(0.542489\pi\)
\(468\) 0 0
\(469\) −2.18461 0.474848i −0.100876 0.0219264i
\(470\) 0 0
\(471\) −0.159770 + 0.276731i −0.00736184 + 0.0127511i
\(472\) 0 0
\(473\) 3.82325 14.2686i 0.175793 0.656069i
\(474\) 0 0
\(475\) −3.55078 19.1323i −0.162921 0.877851i
\(476\) 0 0
\(477\) 2.85194 2.85194i 0.130581 0.130581i
\(478\) 0 0
\(479\) 7.69460 + 13.3274i 0.351575 + 0.608946i 0.986526 0.163607i \(-0.0523128\pi\)
−0.634950 + 0.772553i \(0.718979\pi\)
\(480\) 0 0
\(481\) −8.82459 5.09488i −0.402367 0.232306i
\(482\) 0 0
\(483\) 0.860583 0.0411396i 0.0391579 0.00187191i
\(484\) 0 0
\(485\) −8.77662 + 19.0441i −0.398526 + 0.864747i
\(486\) 0 0
\(487\) −34.7656 9.31541i −1.57538 0.422122i −0.637888 0.770129i \(-0.720192\pi\)
−0.937492 + 0.348007i \(0.886858\pi\)
\(488\) 0 0
\(489\) −3.83644 −0.173490
\(490\) 0 0
\(491\) 15.2823 0.689680 0.344840 0.938661i \(-0.387933\pi\)
0.344840 + 0.938661i \(0.387933\pi\)
\(492\) 0 0
\(493\) −16.1784 4.33499i −0.728639 0.195238i
\(494\) 0 0
\(495\) 34.4139 12.7007i 1.54679 0.570854i
\(496\) 0 0
\(497\) 12.6246 0.603509i 0.566290 0.0270711i
\(498\) 0 0
\(499\) −27.3534 15.7925i −1.22451 0.706969i −0.258630 0.965976i \(-0.583271\pi\)
−0.965875 + 0.259008i \(0.916604\pi\)
\(500\) 0 0
\(501\) −0.964305 1.67023i −0.0430820 0.0746202i
\(502\) 0 0
\(503\) 16.9777 16.9777i 0.756997 0.756997i −0.218778 0.975775i \(-0.570207\pi\)
0.975775 + 0.218778i \(0.0702070\pi\)
\(504\) 0 0
\(505\) 27.6803 + 23.0157i 1.23176 + 1.02419i
\(506\) 0 0
\(507\) −0.668334 + 2.49426i −0.0296817 + 0.110774i
\(508\) 0 0
\(509\) −10.7571 + 18.6318i −0.476799 + 0.825840i −0.999647 0.0265865i \(-0.991536\pi\)
0.522848 + 0.852426i \(0.324870\pi\)
\(510\) 0 0
\(511\) −14.5099 3.15388i −0.641879 0.139519i
\(512\) 0 0
\(513\) 6.44363 1.72657i 0.284493 0.0762297i
\(514\) 0 0
\(515\) 35.9147 25.3886i 1.58259 1.11875i
\(516\) 0 0
\(517\) 23.4529 + 23.4529i 1.03146 + 1.03146i
\(518\) 0 0
\(519\) 2.04397i 0.0897205i
\(520\) 0 0
\(521\) 11.4657 6.61973i 0.502322 0.290016i −0.227350 0.973813i \(-0.573006\pi\)
0.729672 + 0.683798i \(0.239673\pi\)
\(522\) 0 0
\(523\) 6.97006 + 26.0126i 0.304779 + 1.13745i 0.933135 + 0.359526i \(0.117062\pi\)
−0.628356 + 0.777926i \(0.716272\pi\)
\(524\) 0 0
\(525\) 3.37630 1.81422i 0.147354 0.0791789i
\(526\) 0 0
\(527\) 5.28779 + 19.7343i 0.230340 + 0.859640i
\(528\) 0 0
\(529\) −18.8246 + 10.8684i −0.818462 + 0.472539i
\(530\) 0 0
\(531\) 15.9755i 0.693276i
\(532\) 0 0
\(533\) 10.3083 + 10.3083i 0.446501 + 0.446501i
\(534\) 0 0
\(535\) 5.11439 3.61543i 0.221114 0.156309i
\(536\) 0 0
\(537\) 0.617477 0.165453i 0.0266461 0.00713980i
\(538\) 0 0
\(539\) 22.8536 + 32.0706i 0.984374 + 1.38138i
\(540\) 0 0
\(541\) 5.66491 9.81190i 0.243553 0.421847i −0.718171 0.695867i \(-0.755020\pi\)
0.961724 + 0.274020i \(0.0883536\pi\)
\(542\) 0 0
\(543\) 0.308857 1.15267i 0.0132543 0.0494658i
\(544\) 0 0
\(545\) 10.1629 + 8.45027i 0.435329 + 0.361970i
\(546\) 0 0
\(547\) 30.9149 30.9149i 1.32182 1.32182i 0.409527 0.912298i \(-0.365694\pi\)
0.912298 0.409527i \(-0.134306\pi\)
\(548\) 0 0
\(549\) 6.72040 + 11.6401i 0.286820 + 0.496786i
\(550\) 0 0
\(551\) −10.6337 6.13935i −0.453009 0.261545i
\(552\) 0 0
\(553\) −14.6939 7.57212i −0.624850 0.321999i
\(554\) 0 0
\(555\) 3.06330 1.13053i 0.130030 0.0479885i
\(556\) 0 0
\(557\) 25.5003 + 6.83277i 1.08048 + 0.289514i 0.754793 0.655963i \(-0.227737\pi\)
0.325688 + 0.945477i \(0.394404\pi\)
\(558\) 0 0
\(559\) −5.30873 −0.224535
\(560\) 0 0
\(561\) −8.65318 −0.365337
\(562\) 0 0
\(563\) −19.5055 5.22648i −0.822058 0.220270i −0.176812 0.984245i \(-0.556578\pi\)
−0.645246 + 0.763975i \(0.723245\pi\)
\(564\) 0 0
\(565\) 17.9764 39.0064i 0.756274 1.64101i
\(566\) 0 0
\(567\) −11.8061 18.3638i −0.495808 0.771208i
\(568\) 0 0
\(569\) −21.4890 12.4067i −0.900867 0.520116i −0.0233856 0.999727i \(-0.507445\pi\)
−0.877481 + 0.479611i \(0.840778\pi\)
\(570\) 0 0
\(571\) 2.29029 + 3.96690i 0.0958458 + 0.166010i 0.909961 0.414693i \(-0.136111\pi\)
−0.814116 + 0.580703i \(0.802778\pi\)
\(572\) 0 0
\(573\) −3.52433 + 3.52433i −0.147231 + 0.147231i
\(574\) 0 0
\(575\) 3.18185 4.63204i 0.132692 0.193169i
\(576\) 0 0
\(577\) −5.11957 + 19.1065i −0.213131 + 0.795414i 0.773686 + 0.633570i \(0.218411\pi\)
−0.986816 + 0.161845i \(0.948256\pi\)
\(578\) 0 0
\(579\) −1.74818 + 3.02794i −0.0726520 + 0.125837i
\(580\) 0 0
\(581\) −14.2751 + 15.7084i −0.592229 + 0.651694i
\(582\) 0 0
\(583\) −7.51596 + 2.01390i −0.311279 + 0.0834071i
\(584\) 0 0
\(585\) −7.60984 10.7649i −0.314628 0.445074i
\(586\) 0 0
\(587\) 19.3782 + 19.3782i 0.799824 + 0.799824i 0.983068 0.183244i \(-0.0586597\pi\)
−0.183244 + 0.983068i \(0.558660\pi\)
\(588\) 0 0
\(589\) 14.9775i 0.617136i
\(590\) 0 0
\(591\) 5.07919 2.93247i 0.208930 0.120626i
\(592\) 0 0
\(593\) 0.837988 + 3.12741i 0.0344121 + 0.128428i 0.980995 0.194033i \(-0.0621568\pi\)
−0.946583 + 0.322460i \(0.895490\pi\)
\(594\) 0 0
\(595\) 31.1017 4.36767i 1.27504 0.179057i
\(596\) 0 0
\(597\) −0.564900 2.10824i −0.0231198 0.0862844i
\(598\) 0 0
\(599\) 6.75802 3.90174i 0.276125 0.159421i −0.355543 0.934660i \(-0.615704\pi\)
0.631668 + 0.775239i \(0.282371\pi\)
\(600\) 0 0
\(601\) 31.7170i 1.29377i −0.762590 0.646883i \(-0.776072\pi\)
0.762590 0.646883i \(-0.223928\pi\)
\(602\) 0 0
\(603\) −1.74233 1.74233i −0.0709530 0.0709530i
\(604\) 0 0
\(605\) −45.5070 7.81383i −1.85012 0.317677i
\(606\) 0 0
\(607\) −0.743495 + 0.199219i −0.0301775 + 0.00808604i −0.273876 0.961765i \(-0.588306\pi\)
0.243699 + 0.969851i \(0.421639\pi\)
\(608\) 0 0
\(609\) 0.513702 2.36336i 0.0208162 0.0957682i
\(610\) 0 0
\(611\) 5.95987 10.3228i 0.241110 0.417615i
\(612\) 0 0
\(613\) 9.05898 33.8086i 0.365889 1.36552i −0.500323 0.865839i \(-0.666786\pi\)
0.866212 0.499676i \(-0.166548\pi\)
\(614\) 0 0
\(615\) −4.65183 + 0.428014i −0.187580 + 0.0172592i
\(616\) 0 0
\(617\) 21.5403 21.5403i 0.867179 0.867179i −0.124980 0.992159i \(-0.539887\pi\)
0.992159 + 0.124980i \(0.0398866\pi\)
\(618\) 0 0
\(619\) −21.6707 37.5348i −0.871021 1.50865i −0.860942 0.508703i \(-0.830125\pi\)
−0.0100783 0.999949i \(-0.503208\pi\)
\(620\) 0 0
\(621\) 1.66841 + 0.963256i 0.0669509 + 0.0386541i
\(622\) 0 0
\(623\) −14.4487 + 28.0382i −0.578876 + 1.12333i
\(624\) 0 0
\(625\) 3.89884 24.6941i 0.155953 0.987764i
\(626\) 0 0
\(627\) −6.12745 1.64184i −0.244707 0.0655690i
\(628\) 0 0
\(629\) 26.7559 1.06683
\(630\) 0 0
\(631\) −7.53463 −0.299949 −0.149974 0.988690i \(-0.547919\pi\)
−0.149974 + 0.988690i \(0.547919\pi\)
\(632\) 0 0
\(633\) −5.47879 1.46804i −0.217762 0.0583492i
\(634\) 0 0
\(635\) −13.3112 6.13457i −0.528237 0.243443i
\(636\) 0 0
\(637\) 9.00710 10.9163i 0.356874 0.432520i
\(638\) 0 0
\(639\) 12.0640 + 6.96513i 0.477243 + 0.275536i
\(640\) 0 0
\(641\) −12.1657 21.0717i −0.480518 0.832281i 0.519233 0.854633i \(-0.326218\pi\)
−0.999750 + 0.0223521i \(0.992885\pi\)
\(642\) 0 0
\(643\) −6.21713 + 6.21713i −0.245180 + 0.245180i −0.818989 0.573809i \(-0.805465\pi\)
0.573809 + 0.818989i \(0.305465\pi\)
\(644\) 0 0
\(645\) 1.08763 1.30805i 0.0428252 0.0515045i
\(646\) 0 0
\(647\) −5.33869 + 19.9243i −0.209886 + 0.783304i 0.778019 + 0.628241i \(0.216225\pi\)
−0.987905 + 0.155063i \(0.950442\pi\)
\(648\) 0 0
\(649\) −15.4102 + 26.6913i −0.604905 + 1.04773i
\(650\) 0 0
\(651\) −2.80989 + 0.898745i −0.110128 + 0.0352246i
\(652\) 0 0
\(653\) −25.2490 + 6.76544i −0.988069 + 0.264752i −0.716439 0.697650i \(-0.754229\pi\)
−0.271630 + 0.962402i \(0.587563\pi\)
\(654\) 0 0
\(655\) −2.91199 + 16.9591i −0.113781 + 0.662649i
\(656\) 0 0
\(657\) −11.5723 11.5723i −0.451478 0.451478i
\(658\) 0 0
\(659\) 24.2448i 0.944443i 0.881480 + 0.472222i \(0.156548\pi\)
−0.881480 + 0.472222i \(0.843452\pi\)
\(660\) 0 0
\(661\) 15.5301 8.96630i 0.604050 0.348749i −0.166583 0.986027i \(-0.553273\pi\)
0.770633 + 0.637279i \(0.219940\pi\)
\(662\) 0 0
\(663\) 0.804871 + 3.00382i 0.0312586 + 0.116659i
\(664\) 0 0
\(665\) 22.8523 + 2.80839i 0.886174 + 0.108905i
\(666\) 0 0
\(667\) −0.917769 3.42516i −0.0355362 0.132623i
\(668\) 0 0
\(669\) 0.518181 0.299172i 0.0200340 0.0115667i
\(670\) 0 0
\(671\) 25.9305i 1.00104i
\(672\) 0 0
\(673\) −4.85386 4.85386i −0.187103 0.187103i 0.607340 0.794442i \(-0.292237\pi\)
−0.794442 + 0.607340i \(0.792237\pi\)
\(674\) 0 0
\(675\) 8.54424 + 0.670353i 0.328868 + 0.0258019i
\(676\) 0 0
\(677\) −17.8506 + 4.78306i −0.686055 + 0.183828i −0.584976 0.811051i \(-0.698896\pi\)
−0.101079 + 0.994878i \(0.532229\pi\)
\(678\) 0 0
\(679\) −18.3618 16.6863i −0.704660 0.640362i
\(680\) 0 0
\(681\) 2.70083 4.67797i 0.103496 0.179260i
\(682\) 0 0
\(683\) 6.93661 25.8878i 0.265422 0.990569i −0.696569 0.717489i \(-0.745291\pi\)
0.961992 0.273079i \(-0.0880421\pi\)
\(684\) 0 0
\(685\) 1.81023 + 19.6743i 0.0691653 + 0.751717i
\(686\) 0 0
\(687\) 0.821071 0.821071i 0.0313258 0.0313258i
\(688\) 0 0
\(689\) 1.39819 + 2.42173i 0.0532667 + 0.0922606i
\(690\) 0 0
\(691\) −25.1773 14.5361i −0.957790 0.552980i −0.0622976 0.998058i \(-0.519843\pi\)
−0.895492 + 0.445077i \(0.853176\pi\)
\(692\) 0 0
\(693\) 2.07251 + 43.3541i 0.0787281 + 1.64689i
\(694\) 0 0
\(695\) 8.56502 + 23.2078i 0.324890 + 0.880323i
\(696\) 0 0
\(697\) −36.9743 9.90723i −1.40050 0.375263i
\(698\) 0 0
\(699\) 3.97855 0.150483
\(700\) 0 0
\(701\) 25.4462 0.961089 0.480545 0.876970i \(-0.340439\pi\)
0.480545 + 0.876970i \(0.340439\pi\)
\(702\) 0 0
\(703\) 18.9462 + 5.07663i 0.714571 + 0.191469i
\(704\) 0 0
\(705\) 1.32247 + 3.58337i 0.0498071 + 0.134957i
\(706\) 0 0
\(707\) −35.8289 + 23.0343i −1.34748 + 0.866295i
\(708\) 0 0
\(709\) 27.1994 + 15.7036i 1.02150 + 0.589760i 0.914537 0.404503i \(-0.132555\pi\)
0.106958 + 0.994263i \(0.465889\pi\)
\(710\) 0 0
\(711\) −9.10952 15.7781i −0.341634 0.591727i
\(712\) 0 0
\(713\) −3.05850 + 3.05850i −0.114542 + 0.114542i
\(714\) 0 0
\(715\) 2.33027 + 25.3263i 0.0871470 + 0.947149i
\(716\) 0 0
\(717\) −1.47445 + 5.50271i −0.0550642 + 0.205502i
\(718\) 0 0
\(719\) −5.40214 + 9.35678i −0.201466 + 0.348949i −0.949001 0.315273i \(-0.897904\pi\)
0.747535 + 0.664222i \(0.231237\pi\)
\(720\) 0 0
\(721\) 15.8540 + 49.5669i 0.590434 + 1.84597i
\(722\) 0 0
\(723\) −1.64704 + 0.441322i −0.0612539 + 0.0164129i
\(724\) 0 0
\(725\) −10.2480 11.9930i −0.380602 0.445408i
\(726\) 0 0
\(727\) 33.6108 + 33.6108i 1.24656 + 1.24656i 0.957231 + 0.289326i \(0.0934311\pi\)
0.289326 + 0.957231i \(0.406569\pi\)
\(728\) 0 0
\(729\) 22.5720i 0.835998i
\(730\) 0 0
\(731\) 12.0719 6.96972i 0.446496 0.257785i
\(732\) 0 0
\(733\) 6.66658 + 24.8800i 0.246236 + 0.918964i 0.972758 + 0.231822i \(0.0744686\pi\)
−0.726523 + 0.687143i \(0.758865\pi\)
\(734\) 0 0
\(735\) 0.844410 + 4.45579i 0.0311465 + 0.164354i
\(736\) 0 0
\(737\) 1.23034 + 4.59170i 0.0453203 + 0.169138i
\(738\) 0 0
\(739\) 10.4948 6.05920i 0.386059 0.222891i −0.294392 0.955685i \(-0.595117\pi\)
0.680451 + 0.732793i \(0.261784\pi\)
\(740\) 0 0
\(741\) 2.27977i 0.0837493i
\(742\) 0 0
\(743\) −23.2618 23.2618i −0.853393 0.853393i 0.137157 0.990549i \(-0.456204\pi\)
−0.990549 + 0.137157i \(0.956204\pi\)
\(744\) 0 0
\(745\) −1.91053 + 11.1267i −0.0699964 + 0.407652i
\(746\) 0 0
\(747\) −22.5971 + 6.05487i −0.826784 + 0.221536i
\(748\) 0 0
\(749\) 2.25767 + 7.05851i 0.0824934 + 0.257912i
\(750\) 0 0
\(751\) 6.98887 12.1051i 0.255028 0.441721i −0.709875 0.704327i \(-0.751249\pi\)
0.964903 + 0.262607i \(0.0845821\pi\)
\(752\) 0 0
\(753\) −0.532387 + 1.98690i −0.0194013 + 0.0724065i
\(754\) 0 0
\(755\) −19.2181 + 23.1130i −0.699420 + 0.841169i
\(756\) 0 0
\(757\) 17.5547 17.5547i 0.638036 0.638036i −0.312035 0.950071i \(-0.601010\pi\)
0.950071 + 0.312035i \(0.101010\pi\)
\(758\) 0 0
\(759\) −0.915990 1.58654i −0.0332483 0.0575878i
\(760\) 0 0
\(761\) 18.9372 + 10.9334i 0.686471 + 0.396334i 0.802289 0.596936i \(-0.203615\pi\)
−0.115817 + 0.993271i \(0.536949\pi\)
\(762\) 0 0
\(763\) −13.1546 + 8.45710i −0.476230 + 0.306168i
\(764\) 0 0
\(765\) 31.4376 + 14.4883i 1.13663 + 0.523826i
\(766\) 0 0
\(767\) 10.6989 + 2.86675i 0.386313 + 0.103512i
\(768\) 0 0
\(769\) −31.0506 −1.11971 −0.559857 0.828589i \(-0.689144\pi\)
−0.559857 + 0.828589i \(0.689144\pi\)
\(770\) 0 0
\(771\) −2.86459 −0.103166
\(772\) 0 0
\(773\) −5.86173 1.57065i −0.210832 0.0564922i 0.151857 0.988402i \(-0.451475\pi\)
−0.362689 + 0.931910i \(0.618141\pi\)
\(774\) 0 0
\(775\) −6.41880 + 18.1402i −0.230570 + 0.651614i
\(776\) 0 0
\(777\) 0.184481 + 3.85909i 0.00661822 + 0.138444i
\(778\) 0 0
\(779\) −24.3023 14.0309i −0.870720 0.502710i
\(780\) 0 0
\(781\) −13.4374 23.2743i −0.480828 0.832819i
\(782\) 0 0
\(783\) 3.82404 3.82404i 0.136660 0.136660i
\(784\) 0 0
\(785\) −2.45571 + 0.225950i −0.0876481 + 0.00806449i
\(786\) 0 0
\(787\) 5.78752 21.5993i 0.206303 0.769932i −0.782746 0.622342i \(-0.786182\pi\)
0.989049 0.147591i \(-0.0471518\pi\)
\(788\) 0 0
\(789\) −1.99167 + 3.44968i −0.0709055 + 0.122812i
\(790\) 0 0
\(791\) 37.6089 + 34.1772i 1.33722 + 1.21520i
\(792\) 0 0
\(793\) −9.00138 + 2.41191i −0.319648 + 0.0856495i