Properties

Label 300.2.x.a.17.2
Level $300$
Weight $2$
Character 300.17
Analytic conductor $2.396$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.x (of order \(20\), degree \(8\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 17.2
Character \(\chi\) \(=\) 300.17
Dual form 300.2.x.a.53.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.58605 + 0.696021i) q^{3} +(-1.99640 - 1.00718i) q^{5} +(0.814380 + 0.814380i) q^{7} +(2.03111 - 2.20785i) q^{9} +O(q^{10})\) \(q+(-1.58605 + 0.696021i) q^{3} +(-1.99640 - 1.00718i) q^{5} +(0.814380 + 0.814380i) q^{7} +(2.03111 - 2.20785i) q^{9} +(3.46407 - 1.12554i) q^{11} +(-2.63271 - 5.16697i) q^{13} +(3.86740 + 0.207896i) q^{15} +(-0.902627 + 0.142962i) q^{17} +(4.29919 - 5.91733i) q^{19} +(-1.85847 - 0.724821i) q^{21} +(3.05909 - 6.00381i) q^{23} +(2.97120 + 4.02144i) q^{25} +(-1.68473 + 4.91545i) q^{27} +(-4.30536 + 3.12803i) q^{29} +(-1.78920 - 1.29993i) q^{31} +(-4.71078 + 4.19623i) q^{33} +(-0.805601 - 2.44605i) q^{35} +(2.74637 - 1.39935i) q^{37} +(7.77193 + 6.36266i) q^{39} +(2.66555 + 0.866089i) q^{41} +(-3.01283 + 3.01283i) q^{43} +(-6.27859 + 2.36206i) q^{45} +(-0.998165 + 6.30217i) q^{47} -5.67357i q^{49} +(1.33211 - 0.854993i) q^{51} +(-8.04180 - 1.27370i) q^{53} +(-8.04927 - 1.24189i) q^{55} +(-2.70014 + 12.3775i) q^{57} +(1.98388 - 6.10574i) q^{59} +(-4.21356 - 12.9680i) q^{61} +(3.45212 - 0.143935i) q^{63} +(0.0518720 + 12.9669i) q^{65} +(0.976557 + 6.16574i) q^{67} +(-0.673095 + 11.6515i) q^{69} +(5.88318 + 8.09750i) q^{71} +(-8.26387 - 4.21065i) q^{73} +(-7.51147 - 4.31019i) q^{75} +(3.73768 + 1.90445i) q^{77} +(4.29102 + 5.90609i) q^{79} +(-0.749199 - 8.96876i) q^{81} +(-0.190258 - 1.20124i) q^{83} +(1.94599 + 0.623695i) q^{85} +(4.65135 - 7.95784i) q^{87} +(3.41396 + 10.5071i) q^{89} +(2.06386 - 6.35190i) q^{91} +(3.74254 + 0.816433i) q^{93} +(-14.5427 + 7.48329i) q^{95} +(3.84712 + 0.609325i) q^{97} +(4.55086 - 9.93423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 2q^{3} + 4q^{7} + O(q^{10}) \) \( 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{13}{20}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.58605 + 0.696021i −0.915706 + 0.401848i
\(4\) 0 0
\(5\) −1.99640 1.00718i −0.892815 0.450423i
\(6\) 0 0
\(7\) 0.814380 + 0.814380i 0.307807 + 0.307807i 0.844058 0.536252i \(-0.180160\pi\)
−0.536252 + 0.844058i \(0.680160\pi\)
\(8\) 0 0
\(9\) 2.03111 2.20785i 0.677036 0.735950i
\(10\) 0 0
\(11\) 3.46407 1.12554i 1.04446 0.339364i 0.263965 0.964532i \(-0.414970\pi\)
0.780490 + 0.625168i \(0.214970\pi\)
\(12\) 0 0
\(13\) −2.63271 5.16697i −0.730181 1.43306i −0.894691 0.446686i \(-0.852604\pi\)
0.164510 0.986375i \(-0.447396\pi\)
\(14\) 0 0
\(15\) 3.86740 + 0.207896i 0.998558 + 0.0536785i
\(16\) 0 0
\(17\) −0.902627 + 0.142962i −0.218919 + 0.0346734i −0.264930 0.964268i \(-0.585349\pi\)
0.0460112 + 0.998941i \(0.485349\pi\)
\(18\) 0 0
\(19\) 4.29919 5.91733i 0.986302 1.35753i 0.0529373 0.998598i \(-0.483142\pi\)
0.933364 0.358930i \(-0.116858\pi\)
\(20\) 0 0
\(21\) −1.85847 0.724821i −0.405552 0.158169i
\(22\) 0 0
\(23\) 3.05909 6.00381i 0.637865 1.25188i −0.315174 0.949034i \(-0.602063\pi\)
0.953039 0.302847i \(-0.0979372\pi\)
\(24\) 0 0
\(25\) 2.97120 + 4.02144i 0.594239 + 0.804289i
\(26\) 0 0
\(27\) −1.68473 + 4.91545i −0.324226 + 0.945980i
\(28\) 0 0
\(29\) −4.30536 + 3.12803i −0.799486 + 0.580861i −0.910763 0.412929i \(-0.864506\pi\)
0.111277 + 0.993789i \(0.464506\pi\)
\(30\) 0 0
\(31\) −1.78920 1.29993i −0.321350 0.233475i 0.415401 0.909638i \(-0.363641\pi\)
−0.736751 + 0.676164i \(0.763641\pi\)
\(32\) 0 0
\(33\) −4.71078 + 4.19623i −0.820041 + 0.730470i
\(34\) 0 0
\(35\) −0.805601 2.44605i −0.136171 0.413458i
\(36\) 0 0
\(37\) 2.74637 1.39935i 0.451501 0.230051i −0.213427 0.976959i \(-0.568462\pi\)
0.664927 + 0.746908i \(0.268462\pi\)
\(38\) 0 0
\(39\) 7.77193 + 6.36266i 1.24450 + 1.01884i
\(40\) 0 0
\(41\) 2.66555 + 0.866089i 0.416289 + 0.135260i 0.509670 0.860370i \(-0.329768\pi\)
−0.0933813 + 0.995630i \(0.529768\pi\)
\(42\) 0 0
\(43\) −3.01283 + 3.01283i −0.459453 + 0.459453i −0.898476 0.439023i \(-0.855325\pi\)
0.439023 + 0.898476i \(0.355325\pi\)
\(44\) 0 0
\(45\) −6.27859 + 2.36206i −0.935957 + 0.352115i
\(46\) 0 0
\(47\) −0.998165 + 6.30217i −0.145597 + 0.919265i 0.801424 + 0.598096i \(0.204076\pi\)
−0.947022 + 0.321169i \(0.895924\pi\)
\(48\) 0 0
\(49\) 5.67357i 0.810510i
\(50\) 0 0
\(51\) 1.33211 0.854993i 0.186532 0.119723i
\(52\) 0 0
\(53\) −8.04180 1.27370i −1.10463 0.174956i −0.422623 0.906305i \(-0.638891\pi\)
−0.682002 + 0.731350i \(0.738891\pi\)
\(54\) 0 0
\(55\) −8.04927 1.24189i −1.08536 0.167457i
\(56\) 0 0
\(57\) −2.70014 + 12.3775i −0.357643 + 1.63944i
\(58\) 0 0
\(59\) 1.98388 6.10574i 0.258279 0.794900i −0.734887 0.678189i \(-0.762765\pi\)
0.993166 0.116711i \(-0.0372350\pi\)
\(60\) 0 0
\(61\) −4.21356 12.9680i −0.539492 1.66038i −0.733739 0.679432i \(-0.762226\pi\)
0.194247 0.980953i \(-0.437774\pi\)
\(62\) 0 0
\(63\) 3.45212 0.143935i 0.434926 0.0181341i
\(64\) 0 0
\(65\) 0.0518720 + 12.9669i 0.00643393 + 1.60835i
\(66\) 0 0
\(67\) 0.976557 + 6.16574i 0.119305 + 0.753265i 0.972712 + 0.232018i \(0.0745328\pi\)
−0.853406 + 0.521247i \(0.825467\pi\)
\(68\) 0 0
\(69\) −0.673095 + 11.6515i −0.0810311 + 1.40268i
\(70\) 0 0
\(71\) 5.88318 + 8.09750i 0.698205 + 0.960996i 0.999971 + 0.00761427i \(0.00242372\pi\)
−0.301766 + 0.953382i \(0.597576\pi\)
\(72\) 0 0
\(73\) −8.26387 4.21065i −0.967212 0.492819i −0.102306 0.994753i \(-0.532622\pi\)
−0.864906 + 0.501934i \(0.832622\pi\)
\(74\) 0 0
\(75\) −7.51147 4.31019i −0.867350 0.497698i
\(76\) 0 0
\(77\) 3.73768 + 1.90445i 0.425949 + 0.217032i
\(78\) 0 0
\(79\) 4.29102 + 5.90609i 0.482778 + 0.664487i 0.979036 0.203689i \(-0.0652930\pi\)
−0.496258 + 0.868175i \(0.665293\pi\)
\(80\) 0 0
\(81\) −0.749199 8.96876i −0.0832444 0.996529i
\(82\) 0 0
\(83\) −0.190258 1.20124i −0.0208835 0.131853i 0.975044 0.222012i \(-0.0712625\pi\)
−0.995927 + 0.0901590i \(0.971262\pi\)
\(84\) 0 0
\(85\) 1.94599 + 0.623695i 0.211072 + 0.0676492i
\(86\) 0 0
\(87\) 4.65135 7.95784i 0.498677 0.853170i
\(88\) 0 0
\(89\) 3.41396 + 10.5071i 0.361879 + 1.11375i 0.951913 + 0.306369i \(0.0991143\pi\)
−0.590034 + 0.807378i \(0.700886\pi\)
\(90\) 0 0
\(91\) 2.06386 6.35190i 0.216351 0.665860i
\(92\) 0 0
\(93\) 3.74254 + 0.816433i 0.388084 + 0.0846602i
\(94\) 0 0
\(95\) −14.5427 + 7.48329i −1.49205 + 0.767769i
\(96\) 0 0
\(97\) 3.84712 + 0.609325i 0.390616 + 0.0618675i 0.348654 0.937252i \(-0.386639\pi\)
0.0419626 + 0.999119i \(0.486639\pi\)
\(98\) 0 0
\(99\) 4.55086 9.93423i 0.457379 0.998428i
\(100\) 0 0
\(101\) 1.83199i 0.182290i −0.995838 0.0911450i \(-0.970947\pi\)
0.995838 0.0911450i \(-0.0290527\pi\)
\(102\) 0 0
\(103\) −1.59260 + 10.0553i −0.156923 + 0.990775i 0.776009 + 0.630722i \(0.217241\pi\)
−0.932932 + 0.360053i \(0.882759\pi\)
\(104\) 0 0
\(105\) 2.98023 + 3.31884i 0.290840 + 0.323885i
\(106\) 0 0
\(107\) 12.7040 12.7040i 1.22814 1.22814i 0.263470 0.964668i \(-0.415133\pi\)
0.964668 0.263470i \(-0.0848669\pi\)
\(108\) 0 0
\(109\) 7.48884 + 2.43327i 0.717301 + 0.233065i 0.644853 0.764307i \(-0.276919\pi\)
0.0724482 + 0.997372i \(0.476919\pi\)
\(110\) 0 0
\(111\) −3.38191 + 4.13097i −0.320996 + 0.392094i
\(112\) 0 0
\(113\) 16.6927 8.50535i 1.57032 0.800116i 0.570540 0.821270i \(-0.306734\pi\)
0.999776 + 0.0211535i \(0.00673389\pi\)
\(114\) 0 0
\(115\) −12.1541 + 8.90494i −1.13337 + 0.830390i
\(116\) 0 0
\(117\) −16.7552 4.68207i −1.54902 0.432857i
\(118\) 0 0
\(119\) −0.851507 0.618656i −0.0780575 0.0567121i
\(120\) 0 0
\(121\) 1.83371 1.33227i 0.166701 0.121116i
\(122\) 0 0
\(123\) −4.83051 + 0.481618i −0.435552 + 0.0434261i
\(124\) 0 0
\(125\) −1.88138 11.0209i −0.168276 0.985740i
\(126\) 0 0
\(127\) 3.30459 6.48562i 0.293235 0.575505i −0.696645 0.717416i \(-0.745325\pi\)
0.989879 + 0.141911i \(0.0453246\pi\)
\(128\) 0 0
\(129\) 2.68151 6.87550i 0.236094 0.605354i
\(130\) 0 0
\(131\) −3.48009 + 4.78993i −0.304057 + 0.418498i −0.933516 0.358535i \(-0.883276\pi\)
0.629460 + 0.777033i \(0.283276\pi\)
\(132\) 0 0
\(133\) 8.32012 1.31778i 0.721446 0.114266i
\(134\) 0 0
\(135\) 8.31411 8.11638i 0.715565 0.698547i
\(136\) 0 0
\(137\) −2.92241 5.73556i −0.249679 0.490022i 0.731818 0.681500i \(-0.238672\pi\)
−0.981497 + 0.191478i \(0.938672\pi\)
\(138\) 0 0
\(139\) −2.67670 + 0.869713i −0.227035 + 0.0737681i −0.420325 0.907373i \(-0.638084\pi\)
0.193290 + 0.981142i \(0.438084\pi\)
\(140\) 0 0
\(141\) −2.80330 10.6903i −0.236081 0.900285i
\(142\) 0 0
\(143\) −14.9355 14.9355i −1.24897 1.24897i
\(144\) 0 0
\(145\) 11.7457 1.90853i 0.975426 0.158495i
\(146\) 0 0
\(147\) 3.94893 + 8.99857i 0.325702 + 0.742189i
\(148\) 0 0
\(149\) −21.8247 −1.78795 −0.893974 0.448119i \(-0.852094\pi\)
−0.893974 + 0.448119i \(0.852094\pi\)
\(150\) 0 0
\(151\) −7.79667 −0.634484 −0.317242 0.948345i \(-0.602757\pi\)
−0.317242 + 0.948345i \(0.602757\pi\)
\(152\) 0 0
\(153\) −1.51770 + 2.28324i −0.122698 + 0.184589i
\(154\) 0 0
\(155\) 2.26270 + 4.39722i 0.181744 + 0.353193i
\(156\) 0 0
\(157\) 10.3925 + 10.3925i 0.829410 + 0.829410i 0.987435 0.158025i \(-0.0505126\pi\)
−0.158025 + 0.987435i \(0.550513\pi\)
\(158\) 0 0
\(159\) 13.6412 3.57712i 1.08182 0.283684i
\(160\) 0 0
\(161\) 7.38065 2.39812i 0.581677 0.188998i
\(162\) 0 0
\(163\) 3.53766 + 6.94305i 0.277091 + 0.543822i 0.987048 0.160423i \(-0.0512859\pi\)
−0.709957 + 0.704245i \(0.751286\pi\)
\(164\) 0 0
\(165\) 13.6309 3.63276i 1.06117 0.282810i
\(166\) 0 0
\(167\) −0.370295 + 0.0586489i −0.0286543 + 0.00453839i −0.170745 0.985315i \(-0.554617\pi\)
0.142091 + 0.989854i \(0.454617\pi\)
\(168\) 0 0
\(169\) −12.1253 + 16.6890i −0.932714 + 1.28377i
\(170\) 0 0
\(171\) −4.33245 21.5107i −0.331311 1.64496i
\(172\) 0 0
\(173\) 5.57182 10.9353i 0.423618 0.831397i −0.576282 0.817251i \(-0.695497\pi\)
0.999900 0.0141460i \(-0.00450296\pi\)
\(174\) 0 0
\(175\) −0.855300 + 5.69466i −0.0646546 + 0.430476i
\(176\) 0 0
\(177\) 1.10320 + 11.0648i 0.0829217 + 0.831684i
\(178\) 0 0
\(179\) −4.46475 + 3.24383i −0.333711 + 0.242455i −0.742004 0.670396i \(-0.766124\pi\)
0.408293 + 0.912851i \(0.366124\pi\)
\(180\) 0 0
\(181\) 8.04985 + 5.84856i 0.598340 + 0.434720i 0.845289 0.534309i \(-0.179428\pi\)
−0.246949 + 0.969028i \(0.579428\pi\)
\(182\) 0 0
\(183\) 15.7089 + 17.6352i 1.16124 + 1.30363i
\(184\) 0 0
\(185\) −6.89223 + 0.0275712i −0.506727 + 0.00202708i
\(186\) 0 0
\(187\) −2.96585 + 1.51118i −0.216884 + 0.110508i
\(188\) 0 0
\(189\) −5.37506 + 2.63104i −0.390978 + 0.191380i
\(190\) 0 0
\(191\) 9.80442 + 3.18565i 0.709423 + 0.230505i 0.641431 0.767181i \(-0.278341\pi\)
0.0679914 + 0.997686i \(0.478341\pi\)
\(192\) 0 0
\(193\) −0.238354 + 0.238354i −0.0171571 + 0.0171571i −0.715633 0.698476i \(-0.753862\pi\)
0.698476 + 0.715633i \(0.253862\pi\)
\(194\) 0 0
\(195\) −9.10753 20.5301i −0.652204 1.47019i
\(196\) 0 0
\(197\) −0.296468 + 1.87183i −0.0211225 + 0.133362i −0.995996 0.0893965i \(-0.971506\pi\)
0.974874 + 0.222759i \(0.0715062\pi\)
\(198\) 0 0
\(199\) 18.6398i 1.32134i −0.750676 0.660670i \(-0.770272\pi\)
0.750676 0.660670i \(-0.229728\pi\)
\(200\) 0 0
\(201\) −5.84035 9.09946i −0.411947 0.641826i
\(202\) 0 0
\(203\) −6.05361 0.958797i −0.424880 0.0672944i
\(204\) 0 0
\(205\) −4.44919 4.41373i −0.310745 0.308268i
\(206\) 0 0
\(207\) −7.04216 18.9484i −0.489464 1.31701i
\(208\) 0 0
\(209\) 8.23247 25.3369i 0.569452 1.75259i
\(210\) 0 0
\(211\) 7.77153 + 23.9183i 0.535014 + 1.64660i 0.743618 + 0.668604i \(0.233108\pi\)
−0.208604 + 0.978000i \(0.566892\pi\)
\(212\) 0 0
\(213\) −14.9670 8.74822i −1.02552 0.599418i
\(214\) 0 0
\(215\) 9.04926 2.98036i 0.617155 0.203259i
\(216\) 0 0
\(217\) −0.398452 2.51573i −0.0270487 0.170779i
\(218\) 0 0
\(219\) 16.0376 + 0.926472i 1.08372 + 0.0626052i
\(220\) 0 0
\(221\) 3.11503 + 4.28748i 0.209540 + 0.288407i
\(222\) 0 0
\(223\) 4.28530 + 2.18347i 0.286965 + 0.146216i 0.591548 0.806270i \(-0.298517\pi\)
−0.304583 + 0.952486i \(0.598517\pi\)
\(224\) 0 0
\(225\) 14.9136 + 1.60803i 0.994237 + 0.107202i
\(226\) 0 0
\(227\) 11.3411 + 5.77860i 0.752738 + 0.383539i 0.787868 0.615844i \(-0.211185\pi\)
−0.0351307 + 0.999383i \(0.511185\pi\)
\(228\) 0 0
\(229\) 0.0954879 + 0.131428i 0.00631002 + 0.00868500i 0.812160 0.583434i \(-0.198291\pi\)
−0.805850 + 0.592119i \(0.798291\pi\)
\(230\) 0 0
\(231\) −7.25369 0.419037i −0.477258 0.0275706i
\(232\) 0 0
\(233\) 0.939042 + 5.92888i 0.0615187 + 0.388414i 0.999166 + 0.0408262i \(0.0129990\pi\)
−0.937648 + 0.347587i \(0.887001\pi\)
\(234\) 0 0
\(235\) 8.34012 11.5763i 0.544049 0.755154i
\(236\) 0 0
\(237\) −10.9165 6.38070i −0.709105 0.414471i
\(238\) 0 0
\(239\) 3.44778 + 10.6112i 0.223019 + 0.686380i 0.998487 + 0.0549938i \(0.0175139\pi\)
−0.775468 + 0.631387i \(0.782486\pi\)
\(240\) 0 0
\(241\) −8.68635 + 26.7338i −0.559537 + 1.72208i 0.124114 + 0.992268i \(0.460391\pi\)
−0.683650 + 0.729810i \(0.739609\pi\)
\(242\) 0 0
\(243\) 7.43072 + 13.7034i 0.476681 + 0.879076i
\(244\) 0 0
\(245\) −5.71428 + 11.3267i −0.365072 + 0.723636i
\(246\) 0 0
\(247\) −41.8932 6.63523i −2.66560 0.422189i
\(248\) 0 0
\(249\) 1.13785 + 1.77280i 0.0721081 + 0.112347i
\(250\) 0 0
\(251\) 28.1347i 1.77585i 0.459991 + 0.887924i \(0.347853\pi\)
−0.459991 + 0.887924i \(0.652147\pi\)
\(252\) 0 0
\(253\) 3.83936 24.2407i 0.241378 1.52400i
\(254\) 0 0
\(255\) −3.52054 + 0.365239i −0.220465 + 0.0228722i
\(256\) 0 0
\(257\) 12.8233 12.8233i 0.799894 0.799894i −0.183184 0.983079i \(-0.558641\pi\)
0.983079 + 0.183184i \(0.0586405\pi\)
\(258\) 0 0
\(259\) 3.37619 + 1.09699i 0.209786 + 0.0681637i
\(260\) 0 0
\(261\) −1.83844 + 15.8590i −0.113797 + 0.981645i
\(262\) 0 0
\(263\) −18.6904 + 9.52321i −1.15250 + 0.587226i −0.922512 0.385968i \(-0.873868\pi\)
−0.229984 + 0.973194i \(0.573868\pi\)
\(264\) 0 0
\(265\) 14.7718 + 10.6423i 0.907423 + 0.653751i
\(266\) 0 0
\(267\) −12.7279 14.2886i −0.778932 0.874446i
\(268\) 0 0
\(269\) −10.9550 7.95929i −0.667940 0.485287i 0.201395 0.979510i \(-0.435452\pi\)
−0.869335 + 0.494223i \(0.835452\pi\)
\(270\) 0 0
\(271\) 1.95011 1.41684i 0.118461 0.0860669i −0.526977 0.849879i \(-0.676675\pi\)
0.645438 + 0.763812i \(0.276675\pi\)
\(272\) 0 0
\(273\) 1.14768 + 11.5109i 0.0694607 + 0.696673i
\(274\) 0 0
\(275\) 14.8187 + 10.5863i 0.893602 + 0.638380i
\(276\) 0 0
\(277\) −4.61588 + 9.05917i −0.277341 + 0.544313i −0.987095 0.160137i \(-0.948806\pi\)
0.709753 + 0.704450i \(0.248806\pi\)
\(278\) 0 0
\(279\) −6.50412 + 1.30999i −0.389391 + 0.0784269i
\(280\) 0 0
\(281\) 3.75864 5.17333i 0.224222 0.308615i −0.682054 0.731302i \(-0.738913\pi\)
0.906276 + 0.422687i \(0.138913\pi\)
\(282\) 0 0
\(283\) −12.2845 + 1.94568i −0.730239 + 0.115658i −0.510472 0.859894i \(-0.670529\pi\)
−0.219766 + 0.975553i \(0.570529\pi\)
\(284\) 0 0
\(285\) 17.8569 21.9909i 1.05775 1.30263i
\(286\) 0 0
\(287\) 1.46544 + 2.87609i 0.0865024 + 0.169770i
\(288\) 0 0
\(289\) −15.3737 + 4.99521i −0.904333 + 0.293836i
\(290\) 0 0
\(291\) −6.52583 + 1.71126i −0.382551 + 0.100316i
\(292\) 0 0
\(293\) 20.0058 + 20.0058i 1.16875 + 1.16875i 0.982503 + 0.186248i \(0.0596329\pi\)
0.186248 + 0.982503i \(0.440367\pi\)
\(294\) 0 0
\(295\) −10.1102 + 10.1914i −0.588636 + 0.593364i
\(296\) 0 0
\(297\) −0.303452 + 18.9237i −0.0176081 + 1.09806i
\(298\) 0 0
\(299\) −39.0752 −2.25978
\(300\) 0 0
\(301\) −4.90718 −0.282845
\(302\) 0 0
\(303\) 1.27511 + 2.90563i 0.0732529 + 0.166924i
\(304\) 0 0
\(305\) −4.64913 + 30.1331i −0.266208 + 1.72542i
\(306\) 0 0
\(307\) 1.67900 + 1.67900i 0.0958255 + 0.0958255i 0.753394 0.657569i \(-0.228415\pi\)
−0.657569 + 0.753394i \(0.728415\pi\)
\(308\) 0 0
\(309\) −4.47274 17.0566i −0.254445 0.970318i
\(310\) 0 0
\(311\) −16.6707 + 5.41664i −0.945310 + 0.307150i −0.740808 0.671717i \(-0.765557\pi\)
−0.204501 + 0.978866i \(0.565557\pi\)
\(312\) 0 0
\(313\) 7.60246 + 14.9207i 0.429716 + 0.843366i 0.999763 + 0.0217538i \(0.00692499\pi\)
−0.570047 + 0.821612i \(0.693075\pi\)
\(314\) 0 0
\(315\) −7.03677 3.18954i −0.396477 0.179710i
\(316\) 0 0
\(317\) 10.0629 1.59380i 0.565187 0.0895168i 0.132699 0.991156i \(-0.457636\pi\)
0.432488 + 0.901640i \(0.357636\pi\)
\(318\) 0 0
\(319\) −11.3933 + 15.6816i −0.637904 + 0.878000i
\(320\) 0 0
\(321\) −11.3069 + 28.9913i −0.631088 + 1.61814i
\(322\) 0 0
\(323\) −3.03461 + 5.95576i −0.168850 + 0.331388i
\(324\) 0 0
\(325\) 12.9564 25.9394i 0.718692 1.43886i
\(326\) 0 0
\(327\) −13.5713 + 1.35310i −0.750494 + 0.0748268i
\(328\) 0 0
\(329\) −5.94524 + 4.31947i −0.327772 + 0.238140i
\(330\) 0 0
\(331\) 21.8809 + 15.8974i 1.20268 + 0.873801i 0.994546 0.104298i \(-0.0332597\pi\)
0.208138 + 0.978099i \(0.433260\pi\)
\(332\) 0 0
\(333\) 2.48863 8.90580i 0.136376 0.488035i
\(334\) 0 0
\(335\) 4.26038 13.2928i 0.232770 0.726264i
\(336\) 0 0
\(337\) 13.4244 6.84007i 0.731273 0.372602i −0.0483675 0.998830i \(-0.515402\pi\)
0.779640 + 0.626227i \(0.215402\pi\)
\(338\) 0 0
\(339\) −20.5555 + 25.1084i −1.11642 + 1.36370i
\(340\) 0 0
\(341\) −7.66104 2.48922i −0.414869 0.134799i
\(342\) 0 0
\(343\) 10.3211 10.3211i 0.557287 0.557287i
\(344\) 0 0
\(345\) 13.0789 22.5832i 0.704145 1.21584i
\(346\) 0 0
\(347\) 1.70896 10.7899i 0.0917415 0.579233i −0.898402 0.439175i \(-0.855271\pi\)
0.990143 0.140059i \(-0.0447291\pi\)
\(348\) 0 0
\(349\) 4.93794i 0.264322i 0.991228 + 0.132161i \(0.0421916\pi\)
−0.991228 + 0.132161i \(0.957808\pi\)
\(350\) 0 0
\(351\) 29.8334 4.23600i 1.59239 0.226101i
\(352\) 0 0
\(353\) 2.96257 + 0.469225i 0.157682 + 0.0249744i 0.234776 0.972049i \(-0.424564\pi\)
−0.0770944 + 0.997024i \(0.524564\pi\)
\(354\) 0 0
\(355\) −3.58955 22.0912i −0.190513 1.17248i
\(356\) 0 0
\(357\) 1.78113 + 0.388552i 0.0942674 + 0.0205644i
\(358\) 0 0
\(359\) 9.84389 30.2964i 0.519540 1.59898i −0.255325 0.966855i \(-0.582183\pi\)
0.774866 0.632126i \(-0.217817\pi\)
\(360\) 0 0
\(361\) −10.6604 32.8093i −0.561074 1.72681i
\(362\) 0 0
\(363\) −1.98107 + 3.38935i −0.103979 + 0.177895i
\(364\) 0 0
\(365\) 12.2571 + 16.7293i 0.641565 + 0.875651i
\(366\) 0 0
\(367\) −4.72166 29.8114i −0.246469 1.55614i −0.731621 0.681712i \(-0.761236\pi\)
0.485152 0.874430i \(-0.338764\pi\)
\(368\) 0 0
\(369\) 7.32621 4.12601i 0.381387 0.214791i
\(370\) 0 0
\(371\) −5.51180 7.58635i −0.286159 0.393864i
\(372\) 0 0
\(373\) 17.7102 + 9.02378i 0.916998 + 0.467234i 0.847768 0.530367i \(-0.177946\pi\)
0.0692297 + 0.997601i \(0.477946\pi\)
\(374\) 0 0
\(375\) 10.6548 + 16.1702i 0.550209 + 0.835027i
\(376\) 0 0
\(377\) 27.4972 + 14.0105i 1.41618 + 0.721579i
\(378\) 0 0
\(379\) −8.60609 11.8453i −0.442065 0.608450i 0.528604 0.848868i \(-0.322716\pi\)
−0.970669 + 0.240418i \(0.922716\pi\)
\(380\) 0 0
\(381\) −0.727111 + 12.5866i −0.0372510 + 0.644830i
\(382\) 0 0
\(383\) −4.01050 25.3213i −0.204927 1.29386i −0.848795 0.528722i \(-0.822671\pi\)
0.643868 0.765137i \(-0.277329\pi\)
\(384\) 0 0
\(385\) −5.54379 7.56653i −0.282538 0.385626i
\(386\) 0 0
\(387\) 0.532493 + 12.7713i 0.0270681 + 0.649200i
\(388\) 0 0
\(389\) −3.42204 10.5320i −0.173504 0.533991i 0.826058 0.563586i \(-0.190578\pi\)
−0.999562 + 0.0295942i \(0.990578\pi\)
\(390\) 0 0
\(391\) −1.90291 + 5.85654i −0.0962341 + 0.296178i
\(392\) 0 0
\(393\) 2.18570 10.0193i 0.110254 0.505406i
\(394\) 0 0
\(395\) −2.61812 16.1127i −0.131732 0.810718i
\(396\) 0 0
\(397\) −34.8560 5.52065i −1.74937 0.277074i −0.802029 0.597286i \(-0.796246\pi\)
−0.947346 + 0.320212i \(0.896246\pi\)
\(398\) 0 0
\(399\) −12.2789 + 7.88105i −0.614715 + 0.394546i
\(400\) 0 0
\(401\) 28.2805i 1.41226i −0.708081 0.706131i \(-0.750439\pi\)
0.708081 0.706131i \(-0.249561\pi\)
\(402\) 0 0
\(403\) −2.00627 + 12.6671i −0.0999395 + 0.630993i
\(404\) 0 0
\(405\) −7.53742 + 18.6598i −0.374537 + 0.927212i
\(406\) 0 0
\(407\) 7.93859 7.93859i 0.393501 0.393501i
\(408\) 0 0
\(409\) 15.1592 + 4.92552i 0.749574 + 0.243551i 0.658798 0.752320i \(-0.271065\pi\)
0.0907761 + 0.995871i \(0.471065\pi\)
\(410\) 0 0
\(411\) 8.62717 + 7.06282i 0.425547 + 0.348383i
\(412\) 0 0
\(413\) 6.58802 3.35676i 0.324175 0.165176i
\(414\) 0 0
\(415\) −0.830029 + 2.58977i −0.0407445 + 0.127127i
\(416\) 0 0
\(417\) 3.64004 3.24245i 0.178254 0.158784i
\(418\) 0 0
\(419\) 28.4906 + 20.6996i 1.39186 + 1.01124i 0.995659 + 0.0930769i \(0.0296702\pi\)
0.396197 + 0.918166i \(0.370330\pi\)
\(420\) 0 0
\(421\) −1.21908 + 0.885714i −0.0594143 + 0.0431670i −0.617096 0.786888i \(-0.711691\pi\)
0.557682 + 0.830055i \(0.311691\pi\)
\(422\) 0 0
\(423\) 11.8869 + 15.0042i 0.577959 + 0.729528i
\(424\) 0 0
\(425\) −3.25680 3.20510i −0.157978 0.155470i
\(426\) 0 0
\(427\) 7.12945 13.9923i 0.345018 0.677137i
\(428\) 0 0
\(429\) 34.0839 + 13.2930i 1.64559 + 0.641794i
\(430\) 0 0
\(431\) −3.75782 + 5.17220i −0.181008 + 0.249136i −0.889873 0.456208i \(-0.849207\pi\)
0.708865 + 0.705344i \(0.249207\pi\)
\(432\) 0 0
\(433\) 22.5721 3.57506i 1.08474 0.171807i 0.411634 0.911349i \(-0.364958\pi\)
0.673110 + 0.739542i \(0.264958\pi\)
\(434\) 0 0
\(435\) −17.3009 + 11.2023i −0.829513 + 0.537108i
\(436\) 0 0
\(437\) −22.3749 43.9132i −1.07034 2.10065i
\(438\) 0 0
\(439\) −1.74365 + 0.566545i −0.0832197 + 0.0270397i −0.350331 0.936626i \(-0.613931\pi\)
0.267111 + 0.963666i \(0.413931\pi\)
\(440\) 0 0
\(441\) −12.5264 11.5236i −0.596495 0.548745i
\(442\) 0 0
\(443\) −6.75410 6.75410i −0.320897 0.320897i 0.528214 0.849111i \(-0.322862\pi\)
−0.849111 + 0.528214i \(0.822862\pi\)
\(444\) 0 0
\(445\) 3.76686 24.4147i 0.178566 1.15737i
\(446\) 0 0
\(447\) 34.6150 15.1905i 1.63724 0.718484i
\(448\) 0 0
\(449\) −24.0642 −1.13566 −0.567830 0.823146i \(-0.692217\pi\)
−0.567830 + 0.823146i \(0.692217\pi\)
\(450\) 0 0
\(451\) 10.2085 0.480697
\(452\) 0 0
\(453\) 12.3659 5.42665i 0.581001 0.254966i
\(454\) 0 0
\(455\) −10.5178 + 10.6022i −0.493080 + 0.497041i
\(456\) 0 0
\(457\) 15.7146 + 15.7146i 0.735097 + 0.735097i 0.971625 0.236528i \(-0.0760095\pi\)
−0.236528 + 0.971625i \(0.576010\pi\)
\(458\) 0 0
\(459\) 0.817958 4.67768i 0.0381790 0.218335i
\(460\) 0 0
\(461\) −8.27650 + 2.68920i −0.385475 + 0.125248i −0.495342 0.868698i \(-0.664957\pi\)
0.109867 + 0.993946i \(0.464957\pi\)
\(462\) 0 0
\(463\) −6.79566 13.3372i −0.315821 0.619834i 0.677460 0.735560i \(-0.263081\pi\)
−0.993281 + 0.115726i \(0.963081\pi\)
\(464\) 0 0
\(465\) −6.64931 5.39932i −0.308354 0.250388i
\(466\) 0 0
\(467\) −32.4831 + 5.14481i −1.50314 + 0.238074i −0.853067 0.521801i \(-0.825261\pi\)
−0.650070 + 0.759874i \(0.725261\pi\)
\(468\) 0 0
\(469\) −4.22596 + 5.81654i −0.195137 + 0.268583i
\(470\) 0 0
\(471\) −23.7164 9.24960i −1.09279 0.426199i
\(472\) 0 0
\(473\) −7.04558 + 13.8277i −0.323956 + 0.635800i
\(474\) 0 0
\(475\) 36.5699 0.292588i 1.67794 0.0134249i
\(476\) 0 0
\(477\) −19.1459 + 15.1681i −0.876630 + 0.694498i
\(478\) 0 0
\(479\) 22.4708 16.3260i 1.02672 0.745953i 0.0590677 0.998254i \(-0.481187\pi\)
0.967649 + 0.252301i \(0.0811872\pi\)
\(480\) 0 0
\(481\) −14.4608 10.5064i −0.659355 0.479049i
\(482\) 0 0
\(483\) −10.0369 + 8.94062i −0.456696 + 0.406812i
\(484\) 0 0
\(485\) −7.06669 5.09118i −0.320882 0.231179i
\(486\) 0 0
\(487\) 28.0023 14.2679i 1.26891 0.646540i 0.315700 0.948859i \(-0.397761\pi\)
0.953207 + 0.302319i \(0.0977607\pi\)
\(488\) 0 0
\(489\) −10.4434 8.54973i −0.472268 0.386632i
\(490\) 0 0
\(491\) 11.6547 + 3.78683i 0.525968 + 0.170897i 0.559952 0.828525i \(-0.310820\pi\)
−0.0339840 + 0.999422i \(0.510820\pi\)
\(492\) 0 0
\(493\) 3.43895 3.43895i 0.154883 0.154883i
\(494\) 0 0
\(495\) −19.0908 + 15.2492i −0.858069 + 0.685398i
\(496\) 0 0
\(497\) −1.80330 + 11.3856i −0.0808890 + 0.510713i
\(498\) 0 0
\(499\) 2.58376i 0.115665i −0.998326 0.0578324i \(-0.981581\pi\)
0.998326 0.0578324i \(-0.0184189\pi\)
\(500\) 0 0
\(501\) 0.546485 0.350753i 0.0244151 0.0156705i
\(502\) 0 0
\(503\) 29.7370 + 4.70988i 1.32591 + 0.210003i 0.778913 0.627132i \(-0.215772\pi\)
0.546995 + 0.837136i \(0.315772\pi\)
\(504\) 0 0
\(505\) −1.84514 + 3.65738i −0.0821076 + 0.162751i
\(506\) 0 0
\(507\) 7.61539 34.9091i 0.338211 1.55037i
\(508\) 0 0
\(509\) −10.5395 + 32.4372i −0.467155 + 1.43776i 0.389097 + 0.921197i \(0.372787\pi\)
−0.856252 + 0.516559i \(0.827213\pi\)
\(510\) 0 0
\(511\) −3.30086 10.1590i −0.146021 0.449407i
\(512\) 0 0
\(513\) 21.8434 + 31.1016i 0.964409 + 1.37317i
\(514\) 0 0
\(515\) 13.3069 18.4703i 0.586371 0.813898i
\(516\) 0 0
\(517\) 3.63565 + 22.9546i 0.159896 + 1.00954i
\(518\) 0 0
\(519\) −1.22597 + 21.2221i −0.0538142 + 0.931545i
\(520\) 0 0
\(521\) 7.87830 + 10.8435i 0.345154 + 0.475064i 0.945938 0.324347i \(-0.105145\pi\)
−0.600784 + 0.799412i \(0.705145\pi\)
\(522\) 0 0
\(523\) 11.1465 + 5.67941i 0.487401 + 0.248343i 0.680380 0.732860i \(-0.261815\pi\)
−0.192979 + 0.981203i \(0.561815\pi\)
\(524\) 0 0
\(525\) −2.60706 9.62733i −0.113781 0.420171i
\(526\) 0 0
\(527\) 1.80082 + 0.917566i 0.0784451 + 0.0399698i
\(528\) 0 0
\(529\) −13.1686 18.1251i −0.572549 0.788046i
\(530\) 0 0
\(531\) −9.45109 16.7815i −0.410143 0.728256i
\(532\) 0 0
\(533\) −2.54254 16.0530i −0.110130 0.695332i
\(534\) 0 0
\(535\) −38.1572 + 12.5670i −1.64968 + 0.543319i
\(536\) 0 0
\(537\) 4.82354 8.25243i 0.208151 0.356119i
\(538\) 0 0
\(539\) −6.38585 19.6536i −0.275058 0.846541i
\(540\) 0 0
\(541\) 1.14874 3.53545i 0.0493881 0.152001i −0.923321 0.384029i \(-0.874536\pi\)
0.972709 + 0.232028i \(0.0745362\pi\)
\(542\) 0 0
\(543\) −16.8382 3.67323i −0.722595 0.157634i
\(544\) 0 0
\(545\) −12.5000 12.4003i −0.535439 0.531173i
\(546\) 0 0
\(547\) −2.64836 0.419459i −0.113236 0.0179348i 0.0995594 0.995032i \(-0.468257\pi\)
−0.212795 + 0.977097i \(0.568257\pi\)
\(548\) 0 0
\(549\) −37.1896 17.0365i −1.58722 0.727101i
\(550\) 0 0
\(551\) 38.9242i 1.65823i
\(552\) 0 0
\(553\) −1.31527 + 8.30432i −0.0559312 + 0.353136i
\(554\) 0 0
\(555\) 10.9122 4.84087i 0.463199 0.205484i
\(556\) 0 0
\(557\) −19.5853 + 19.5853i −0.829857 + 0.829857i −0.987497 0.157639i \(-0.949612\pi\)
0.157639 + 0.987497i \(0.449612\pi\)
\(558\) 0 0
\(559\) 23.4991 + 7.63533i 0.993908 + 0.322940i
\(560\) 0 0
\(561\) 3.65218 4.46110i 0.154195 0.188348i
\(562\) 0 0
\(563\) −14.2772 + 7.27459i −0.601712 + 0.306587i −0.728183 0.685383i \(-0.759635\pi\)
0.126471 + 0.991970i \(0.459635\pi\)
\(564\) 0 0
\(565\) −41.8916 + 0.167580i −1.76239 + 0.00705015i
\(566\) 0 0
\(567\) 6.69385 7.91411i 0.281115 0.332361i
\(568\) 0 0
\(569\) 29.7086 + 21.5845i 1.24545 + 0.904871i 0.997949 0.0640170i \(-0.0203912\pi\)
0.247499 + 0.968888i \(0.420391\pi\)
\(570\) 0 0
\(571\) 34.0496 24.7385i 1.42493 1.03527i 0.433997 0.900914i \(-0.357103\pi\)
0.990933 0.134358i \(-0.0428971\pi\)
\(572\) 0 0
\(573\) −17.7676 + 1.77149i −0.742251 + 0.0740050i
\(574\) 0 0
\(575\) 33.2332 5.53652i 1.38592 0.230889i
\(576\) 0 0
\(577\) 19.4132 38.1006i 0.808182 1.58615i −0.00202117 0.999998i \(-0.500643\pi\)
0.810203 0.586149i \(-0.199357\pi\)
\(578\) 0 0
\(579\) 0.212141 0.543940i 0.00881630 0.0226054i
\(580\) 0 0
\(581\) 0.823323 1.13321i 0.0341572 0.0470133i
\(582\) 0 0
\(583\) −29.2909 + 4.63922i −1.21311 + 0.192137i
\(584\) 0 0
\(585\) 28.7344 + 26.2227i 1.18802 + 1.08418i
\(586\) 0 0
\(587\) 0.114338 + 0.224402i 0.00471925 + 0.00926205i 0.893354 0.449353i \(-0.148346\pi\)
−0.888635 + 0.458615i \(0.848346\pi\)
\(588\) 0 0
\(589\) −15.3842 + 4.99864i −0.633897 + 0.205966i
\(590\) 0 0
\(591\) −0.832618 3.17516i −0.0342493 0.130609i
\(592\) 0 0
\(593\) −14.4925 14.4925i −0.595137 0.595137i 0.343878 0.939014i \(-0.388259\pi\)
−0.939014 + 0.343878i \(0.888259\pi\)
\(594\) 0 0
\(595\) 1.07685 + 2.09270i 0.0441466 + 0.0857923i
\(596\) 0 0
\(597\) 12.9737 + 29.5637i 0.530978 + 1.20996i
\(598\) 0 0
\(599\) 16.6754 0.681340 0.340670 0.940183i \(-0.389346\pi\)
0.340670 + 0.940183i \(0.389346\pi\)
\(600\) 0 0
\(601\) −21.5251 −0.878028 −0.439014 0.898480i \(-0.644672\pi\)
−0.439014 + 0.898480i \(0.644672\pi\)
\(602\) 0 0
\(603\) 15.5965 + 10.3672i 0.635139 + 0.422184i
\(604\) 0 0
\(605\) −5.00265 + 0.812870i −0.203387 + 0.0330479i
\(606\) 0 0
\(607\) 7.49042 + 7.49042i 0.304027 + 0.304027i 0.842587 0.538560i \(-0.181032\pi\)
−0.538560 + 0.842587i \(0.681032\pi\)
\(608\) 0 0
\(609\) 10.2687 2.69274i 0.416107 0.109115i
\(610\) 0 0
\(611\) 35.1910 11.4343i 1.42368 0.462580i
\(612\) 0 0
\(613\) −9.77730 19.1890i −0.394902 0.775038i 0.604872 0.796323i \(-0.293224\pi\)
−0.999773 + 0.0212848i \(0.993224\pi\)
\(614\) 0 0
\(615\) 10.1287 + 3.90367i 0.408428 + 0.157411i
\(616\) 0 0
\(617\) 9.79635 1.55159i 0.394386 0.0624646i 0.0439081 0.999036i \(-0.486019\pi\)
0.350478 + 0.936571i \(0.386019\pi\)
\(618\) 0 0
\(619\) 4.81151 6.62247i 0.193391 0.266180i −0.701299 0.712867i \(-0.747396\pi\)
0.894690 + 0.446687i \(0.147396\pi\)
\(620\) 0 0
\(621\) 24.3577 + 25.1516i 0.977442 + 1.00930i
\(622\) 0 0
\(623\) −5.77649 + 11.3370i −0.231430 + 0.454208i
\(624\) 0 0
\(625\) −7.34400 + 23.8970i −0.293760 + 0.955879i
\(626\) 0 0
\(627\) 4.57794 + 45.9156i 0.182825 + 1.83369i
\(628\) 0 0
\(629\) −2.27890 + 1.65572i −0.0908656 + 0.0660177i
\(630\) 0 0
\(631\) −0.620208 0.450607i −0.0246901 0.0179384i 0.575372 0.817892i \(-0.304857\pi\)
−0.600062 + 0.799954i \(0.704857\pi\)
\(632\) 0 0
\(633\) −28.9737 32.5265i −1.15160 1.29281i
\(634\) 0 0
\(635\) −13.1294 + 9.61956i −0.521025 + 0.381741i
\(636\) 0 0
\(637\) −29.3152 + 14.9368i −1.16151 + 0.591819i
\(638\) 0 0
\(639\) 29.8274 + 3.45772i 1.17995 + 0.136785i
\(640\) 0 0
\(641\) −16.9921 5.52105i −0.671146 0.218068i −0.0464310 0.998922i \(-0.514785\pi\)
−0.624715 + 0.780853i \(0.714785\pi\)
\(642\) 0 0
\(643\) 5.47671 5.47671i 0.215980 0.215980i −0.590822 0.806802i \(-0.701196\pi\)
0.806802 + 0.590822i \(0.201196\pi\)
\(644\) 0 0
\(645\) −12.2782 + 11.0255i −0.483453 + 0.434128i
\(646\) 0 0
\(647\) −5.84782 + 36.9217i −0.229902 + 1.45154i 0.554963 + 0.831875i \(0.312732\pi\)
−0.784865 + 0.619667i \(0.787268\pi\)
\(648\) 0 0
\(649\) 23.3836i 0.917888i
\(650\) 0 0
\(651\) 2.38297 + 3.71274i 0.0933958 + 0.145514i
\(652\) 0 0
\(653\) 32.5406 + 5.15393i 1.27341 + 0.201689i 0.756298 0.654227i \(-0.227006\pi\)
0.517115 + 0.855916i \(0.327006\pi\)
\(654\) 0 0
\(655\) 11.7719 6.05753i 0.459967 0.236687i
\(656\) 0 0
\(657\) −26.0813 + 9.69309i −1.01753 + 0.378163i
\(658\) 0 0
\(659\) −5.58239 + 17.1808i −0.217459 + 0.669270i 0.781511 + 0.623892i \(0.214449\pi\)
−0.998970 + 0.0453785i \(0.985551\pi\)
\(660\) 0 0
\(661\) 5.43861 + 16.7383i 0.211537 + 0.651045i 0.999381 + 0.0351703i \(0.0111974\pi\)
−0.787844 + 0.615875i \(0.788803\pi\)
\(662\) 0 0
\(663\) −7.92477 4.63202i −0.307773 0.179893i
\(664\) 0 0
\(665\) −17.9375 5.74902i −0.695586 0.222937i
\(666\) 0 0
\(667\) 5.60959 + 35.4175i 0.217204 + 1.37137i
\(668\) 0 0
\(669\) −8.31644 0.480431i −0.321532 0.0185745i
\(670\) 0 0
\(671\) −29.1921 40.1795i −1.12695 1.55111i
\(672\) 0 0
\(673\) −44.4567 22.6518i −1.71368 0.873164i −0.981354 0.192211i \(-0.938434\pi\)
−0.732327 0.680953i \(-0.761566\pi\)
\(674\) 0 0
\(675\) −24.7729 + 7.82974i −0.953508 + 0.301367i
\(676\) 0 0
\(677\) 13.4384 + 6.84718i 0.516478 + 0.263159i 0.692744 0.721184i \(-0.256402\pi\)
−0.176266 + 0.984343i \(0.556402\pi\)
\(678\) 0 0
\(679\) 2.63680 + 3.62924i 0.101191 + 0.139278i
\(680\) 0 0
\(681\) −22.0096 1.27147i −0.843411 0.0487228i
\(682\) 0 0
\(683\) 2.11149 + 13.3314i 0.0807939 + 0.510113i 0.994585 + 0.103928i \(0.0331411\pi\)
−0.913791 + 0.406185i \(0.866859\pi\)
\(684\) 0 0
\(685\) 0.0575801 + 14.3938i 0.00220002 + 0.549960i
\(686\) 0 0
\(687\) −0.242925 0.141989i −0.00926818 0.00541724i
\(688\) 0 0
\(689\) 14.5905 + 44.9050i 0.555855 + 1.71075i
\(690\) 0 0
\(691\) −1.08757 + 3.34720i −0.0413731 + 0.127333i −0.969610 0.244657i \(-0.921325\pi\)
0.928237 + 0.371991i \(0.121325\pi\)
\(692\) 0 0
\(693\) 11.7964 4.38411i 0.448107 0.166539i
\(694\) 0 0
\(695\) 6.21971 + 0.959617i 0.235927 + 0.0364003i
\(696\) 0 0
\(697\) −2.52981 0.400683i −0.0958236 0.0151770i
\(698\) 0 0
\(699\) −5.61599 8.74990i −0.212416 0.330952i
\(700\) 0 0
\(701\) 40.9855i 1.54800i −0.633184 0.774001i \(-0.718253\pi\)
0.633184 0.774001i \(-0.281747\pi\)
\(702\) 0 0
\(703\) 3.52678 22.2672i 0.133015 0.839825i
\(704\) 0 0
\(705\) −5.17050 + 24.1655i −0.194732 + 0.910125i
\(706\) 0 0
\(707\) 1.49194 1.49194i 0.0561101 0.0561101i
\(708\) 0 0
\(709\) 12.6101 + 4.09726i 0.473581 + 0.153876i 0.536076 0.844170i \(-0.319906\pi\)
−0.0624957 + 0.998045i \(0.519906\pi\)
\(710\) 0 0
\(711\) 21.7553 + 2.52197i 0.815887 + 0.0945811i
\(712\) 0 0
\(713\) −13.2779 + 6.76542i −0.497261 + 0.253367i
\(714\) 0 0
\(715\) 14.7745 + 44.8599i 0.552536 + 1.67766i
\(716\) 0 0
\(717\) −12.8540 14.4301i −0.480040 0.538903i
\(718\) 0 0
\(719\) −18.6310 13.5362i −0.694820 0.504816i 0.183421 0.983034i \(-0.441283\pi\)
−0.878241 + 0.478218i \(0.841283\pi\)
\(720\) 0 0
\(721\) −9.48579 + 6.89183i −0.353269 + 0.256665i
\(722\) 0 0
\(723\) −4.83034 48.4471i −0.179642 1.80177i
\(724\) 0 0
\(725\) −25.3713 8.01979i −0.942265 0.297847i
\(726\) 0 0
\(727\) −10.3618 + 20.3362i −0.384299 + 0.754229i −0.999415 0.0342075i \(-0.989109\pi\)
0.615116 + 0.788437i \(0.289109\pi\)
\(728\) 0 0
\(729\) −21.3234 16.5624i −0.789755 0.613422i
\(730\) 0 0
\(731\) 2.28875 3.15019i 0.0846523 0.116514i
\(732\) 0 0
\(733\) −13.2294 + 2.09532i −0.488638 + 0.0773926i −0.395892 0.918297i \(-0.629564\pi\)
−0.0927459 + 0.995690i \(0.529564\pi\)
\(734\) 0 0
\(735\) 1.17951 21.9420i 0.0435070 0.809342i
\(736\) 0 0
\(737\) 10.3227 + 20.2594i 0.380240 + 0.746263i
\(738\) 0 0
\(739\) 15.0540 4.89134i 0.553770 0.179931i −0.0187462 0.999824i \(-0.505967\pi\)
0.572516 + 0.819894i \(0.305967\pi\)
\(740\) 0 0
\(741\) 71.0629 18.6348i 2.61056 0.684565i
\(742\) 0 0
\(743\) 7.06750 + 7.06750i 0.259281 + 0.259281i 0.824762 0.565480i \(-0.191309\pi\)
−0.565480 + 0.824762i \(0.691309\pi\)
\(744\) 0 0
\(745\) 43.5707 + 21.9813i 1.59631 + 0.805332i
\(746\) 0 0
\(747\) −3.03859 2.01979i −0.111176 0.0739001i
\(748\) 0 0
\(749\) 20.6917 0.756058
\(750\) 0 0
\(751\) −51.2590 −1.87047 −0.935234 0.354031i \(-0.884811\pi\)
−0.935234 + 0.354031i \(0.884811\pi\)
\(752\) 0 0
\(753\) −19.5824 44.6231i −0.713621 1.62615i
\(754\) 0 0
\(755\) 15.5652 + 7.85262i 0.566477 + 0.285786i
\(756\) 0 0
\(757\) 10.5818 + 10.5818i 0.384604 + 0.384604i 0.872758 0.488154i \(-0.162330\pi\)
−0.488154 + 0.872758i \(0.662330\pi\)
\(758\) 0 0
\(759\) 10.7827 + 41.1193i 0.391386 + 1.49254i
\(760\) 0 0
\(761\) −36.8728 + 11.9807i −1.33664 + 0.434300i −0.888176 0.459503i \(-0.848027\pi\)
−0.448460 + 0.893803i \(0.648027\pi\)
\(762\) 0 0
\(763\) 4.11715 + 8.08037i 0.149051 + 0.292529i
\(764\) 0 0
\(765\) 5.32954 3.02966i 0.192690 0.109538i
\(766\) 0 0
\(767\) −36.7712 + 5.82398i −1.32773 + 0.210292i
\(768\) 0 0
\(769\) 30.1156 41.4506i 1.08600 1.49475i 0.233252 0.972416i \(-0.425063\pi\)
0.852744 0.522329i \(-0.174937\pi\)
\(770\) 0 0
\(771\) −11.4131 + 29.2636i −0.411032 + 1.05390i
\(772\) 0 0
\(773\) −10.0630 + 19.7497i −0.361940 + 0.710347i −0.998126 0.0611885i \(-0.980511\pi\)
0.636186 + 0.771535i \(0.280511\pi\)
\(774\) 0 0
\(775\) −0.0884689 11.0575i −0.00317790 0.397198i
\(776\) 0 0
\(777\) −6.11833 + 0.610019i −0.219494 + 0.0218843i
\(778\) 0 0
\(779\) 16.5846 12.0494i 0.594206 0.431716i
\(780\) 0 0
\(781\) 29.4938 + 21.4285i 1.05537 + 0.766772i
\(782\) 0 0
\(783\) −8.12232 26.4327i −0.290268 0.944628i
\(784\) 0 0
\(785\) −10.2805 31.2146i −0.366925 1.11410i
\(786\) 0 0
\(787\) 7.51983 3.83155i 0.268053 0.136580i −0.314798 0.949159i \(-0.601937\pi\)
0.582852 + 0.812579i \(0.301937\pi\)
\(788\) 0 0
\(789\) 23.0155 28.1132i 0.819373 1.00086i
\(790\) 0 0
\(791\) 20.5208 + 6.66761i 0.729635 + 0.237073i
\(792\) 0 0
\(793\) −55.9124 + 55.9124i −1.98551 + 1.98551i
\(794\) 0 0
\(795\) −30.8360 6.59775i −1.09364 0.233998i
\(796\) 0 0
\(797\) 3.19808 20.1919i 0.113282