Properties

Label 300.2.x.a.53.2
Level $300$
Weight $2$
Character 300.53
Analytic conductor $2.396$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

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 53.2
Character \(\chi\) \(=\) 300.53
Dual form 300.2.x.a.17.2

$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{7}{20}\right)\)

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 −0.536252 0.844058i \(-0.680160\pi\)
0.844058 + 0.536252i \(0.180160\pi\)
\(8\) 0 0
\(9\) 2.03111 + 2.20785i 0.677036 + 0.735950i
\(10\) 0 0
\(11\) 3.46407 + 1.12554i 1.04446 + 0.339364i 0.780490 0.625168i \(-0.214970\pi\)
0.263965 + 0.964532i \(0.414970\pi\)
\(12\) 0 0
\(13\) −2.63271 + 5.16697i −0.730181 + 1.43306i 0.164510 + 0.986375i \(0.447396\pi\)
−0.894691 + 0.446686i \(0.852604\pi\)
\(14\) 0 0
\(15\) 3.86740 0.207896i 0.998558 0.0536785i
\(16\) 0 0
\(17\) −0.902627 0.142962i −0.218919 0.0346734i 0.0460112 0.998941i \(-0.485349\pi\)
−0.264930 + 0.964268i \(0.585349\pi\)
\(18\) 0 0
\(19\) 4.29919 + 5.91733i 0.986302 + 1.35753i 0.933364 + 0.358930i \(0.116858\pi\)
0.0529373 + 0.998598i \(0.483142\pi\)
\(20\) 0 0
\(21\) −1.85847 + 0.724821i −0.405552 + 0.158169i
\(22\) 0 0
\(23\) 3.05909 + 6.00381i 0.637865 + 1.25188i 0.953039 + 0.302847i \(0.0979372\pi\)
−0.315174 + 0.949034i \(0.602063\pi\)
\(24\) 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 0.111277 0.993789i \(-0.464506\pi\)
−0.910763 + 0.412929i \(0.864506\pi\)
\(30\) 0 0
\(31\) −1.78920 + 1.29993i −0.321350 + 0.233475i −0.736751 0.676164i \(-0.763641\pi\)
0.415401 + 0.909638i \(0.363641\pi\)
\(32\) 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 0.664927 0.746908i \(-0.268462\pi\)
−0.213427 + 0.976959i \(0.568462\pi\)
\(38\) 0 0
\(39\) 7.77193 6.36266i 1.24450 1.01884i
\(40\) 0 0
\(41\) 2.66555 0.866089i 0.416289 0.135260i −0.0933813 0.995630i \(-0.529768\pi\)
0.509670 + 0.860370i \(0.329768\pi\)
\(42\) 0 0
\(43\) −3.01283 3.01283i −0.459453 0.459453i 0.439023 0.898476i \(-0.355325\pi\)
−0.898476 + 0.439023i \(0.855325\pi\)
\(44\) 0 0
\(45\) −6.27859 2.36206i −0.935957 0.352115i
\(46\) 0 0
\(47\) −0.998165 6.30217i −0.145597 0.919265i −0.947022 0.321169i \(-0.895924\pi\)
0.801424 0.598096i \(-0.204076\pi\)
\(48\) 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 −0.682002 0.731350i \(-0.738891\pi\)
−0.422623 + 0.906305i \(0.638891\pi\)
\(54\) 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 0.993166 + 0.116711i \(0.0372350\pi\)
−0.734887 + 0.678189i \(0.762765\pi\)
\(60\) 0 0
\(61\) −4.21356 + 12.9680i −0.539492 + 1.66038i 0.194247 + 0.980953i \(0.437774\pi\)
−0.733739 + 0.679432i \(0.762226\pi\)
\(62\) 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 −0.853406 0.521247i \(-0.825467\pi\)
0.972712 0.232018i \(-0.0745328\pi\)
\(68\) 0 0
\(69\) −0.673095 11.6515i −0.0810311 1.40268i
\(70\) 0 0
\(71\) 5.88318 8.09750i 0.698205 0.960996i −0.301766 0.953382i \(-0.597576\pi\)
0.999971 0.00761427i \(-0.00242372\pi\)
\(72\) 0 0
\(73\) −8.26387 + 4.21065i −0.967212 + 0.492819i −0.864906 0.501934i \(-0.832622\pi\)
−0.102306 + 0.994753i \(0.532622\pi\)
\(74\) 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 −0.496258 0.868175i \(-0.665293\pi\)
0.979036 + 0.203689i \(0.0652930\pi\)
\(80\) 0 0
\(81\) −0.749199 + 8.96876i −0.0832444 + 0.996529i
\(82\) 0 0
\(83\) −0.190258 + 1.20124i −0.0208835 + 0.131853i −0.995927 0.0901590i \(-0.971262\pi\)
0.975044 + 0.222012i \(0.0712625\pi\)
\(84\) 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 −0.590034 0.807378i \(-0.700886\pi\)
0.951913 0.306369i \(-0.0991143\pi\)
\(90\) 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 0.0419626 0.999119i \(-0.486639\pi\)
0.348654 + 0.937252i \(0.386639\pi\)
\(98\) 0 0
\(99\) 4.55086 + 9.93423i 0.457379 + 0.998428i
\(100\) 0 0
\(101\) 1.83199i 0.182290i 0.995838 + 0.0911450i \(0.0290527\pi\)
−0.995838 + 0.0911450i \(0.970947\pi\)
\(102\) 0 0
\(103\) −1.59260 10.0553i −0.156923 0.990775i −0.932932 0.360053i \(-0.882759\pi\)
0.776009 0.630722i \(-0.217241\pi\)
\(104\) 0 0
\(105\) 2.98023 3.31884i 0.290840 0.323885i
\(106\) 0 0
\(107\) 12.7040 + 12.7040i 1.22814 + 1.22814i 0.964668 + 0.263470i \(0.0848669\pi\)
0.263470 + 0.964668i \(0.415133\pi\)
\(108\) 0 0
\(109\) 7.48884 2.43327i 0.717301 0.233065i 0.0724482 0.997372i \(-0.476919\pi\)
0.644853 + 0.764307i \(0.276919\pi\)
\(110\) 0 0
\(111\) −3.38191 4.13097i −0.320996 0.392094i
\(112\) 0 0
\(113\) 16.6927 + 8.50535i 1.57032 + 0.800116i 0.999776 0.0211535i \(-0.00673389\pi\)
0.570540 + 0.821270i \(0.306734\pi\)
\(114\) 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 0.989879 0.141911i \(-0.0453246\pi\)
−0.696645 + 0.717416i \(0.745325\pi\)
\(128\) 0 0
\(129\) 2.68151 + 6.87550i 0.236094 + 0.605354i
\(130\) 0 0
\(131\) −3.48009 4.78993i −0.304057 0.418498i 0.629460 0.777033i \(-0.283276\pi\)
−0.933516 + 0.358535i \(0.883276\pi\)
\(132\) 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 −0.981497 0.191478i \(-0.938672\pi\)
0.731818 + 0.681500i \(0.238672\pi\)
\(138\) 0 0
\(139\) −2.67670 0.869713i −0.227035 0.0737681i 0.193290 0.981142i \(-0.438084\pi\)
−0.420325 + 0.907373i \(0.638084\pi\)
\(140\) 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 −0.158025 0.987435i \(-0.550513\pi\)
0.987435 + 0.158025i \(0.0505126\pi\)
\(158\) 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 −0.709957 0.704245i \(-0.751286\pi\)
0.987048 + 0.160423i \(0.0512859\pi\)
\(164\) 0 0
\(165\) 13.6309 + 3.63276i 1.06117 + 0.282810i
\(166\) 0 0
\(167\) −0.370295 0.0586489i −0.0286543 0.00453839i 0.142091 0.989854i \(-0.454617\pi\)
−0.170745 + 0.985315i \(0.554617\pi\)
\(168\) 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 0.999900 + 0.0141460i \(0.00450296\pi\)
−0.576282 + 0.817251i \(0.695497\pi\)
\(174\) 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 0.408293 0.912851i \(-0.366124\pi\)
−0.742004 + 0.670396i \(0.766124\pi\)
\(180\) 0 0
\(181\) 8.04985 5.84856i 0.598340 0.434720i −0.246949 0.969028i \(-0.579428\pi\)
0.845289 + 0.534309i \(0.179428\pi\)
\(182\) 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 0.0679914 0.997686i \(-0.478341\pi\)
0.641431 + 0.767181i \(0.278341\pi\)
\(192\) 0 0
\(193\) −0.238354 0.238354i −0.0171571 0.0171571i 0.698476 0.715633i \(-0.253862\pi\)
−0.715633 + 0.698476i \(0.753862\pi\)
\(194\) 0 0
\(195\) −9.10753 + 20.5301i −0.652204 + 1.47019i
\(196\) 0 0
\(197\) −0.296468 1.87183i −0.0211225 0.133362i 0.974874 0.222759i \(-0.0715062\pi\)
−0.995996 + 0.0893965i \(0.971506\pi\)
\(198\) 0 0
\(199\) 18.6398i 1.32134i 0.750676 + 0.660670i \(0.229728\pi\)
−0.750676 + 0.660670i \(0.770272\pi\)
\(200\) 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 −0.208604 0.978000i \(-0.566892\pi\)
0.743618 0.668604i \(-0.233108\pi\)
\(212\) 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 −0.304583 0.952486i \(-0.598517\pi\)
0.591548 + 0.806270i \(0.298517\pi\)
\(224\) 0 0
\(225\) 14.9136 1.60803i 0.994237 0.107202i
\(226\) 0 0
\(227\) 11.3411 5.77860i 0.752738 0.383539i −0.0351307 0.999383i \(-0.511185\pi\)
0.787868 + 0.615844i \(0.211185\pi\)
\(228\) 0 0
\(229\) 0.0954879 0.131428i 0.00631002 0.00868500i −0.805850 0.592119i \(-0.798291\pi\)
0.812160 + 0.583434i \(0.198291\pi\)
\(230\) 0 0
\(231\) −7.25369 + 0.419037i −0.477258 + 0.0275706i
\(232\) 0 0
\(233\) 0.939042 5.92888i 0.0615187 0.388414i −0.937648 0.347587i \(-0.887001\pi\)
0.999166 0.0408262i \(-0.0129990\pi\)
\(234\) 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 −0.775468 0.631387i \(-0.782486\pi\)
0.998487 0.0549938i \(-0.0175139\pi\)
\(240\) 0 0
\(241\) −8.68635 26.7338i −0.559537 1.72208i −0.683650 0.729810i \(-0.739609\pi\)
0.124114 0.992268i \(-0.460391\pi\)
\(242\) 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 \(-0.652147\pi\)
0.459991 0.887924i \(-0.347853\pi\)
\(252\) 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 0.983079 0.183184i \(-0.0586405\pi\)
−0.183184 + 0.983079i \(0.558641\pi\)
\(258\) 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 −0.229984 0.973194i \(-0.573868\pi\)
−0.922512 + 0.385968i \(0.873868\pi\)
\(264\) 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 −0.869335 0.494223i \(-0.835452\pi\)
0.201395 + 0.979510i \(0.435452\pi\)
\(270\) 0 0
\(271\) 1.95011 + 1.41684i 0.118461 + 0.0860669i 0.645438 0.763812i \(-0.276675\pi\)
−0.526977 + 0.849879i \(0.676675\pi\)
\(272\) 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 0.709753 0.704450i \(-0.248806\pi\)
−0.987095 + 0.160137i \(0.948806\pi\)
\(278\) 0 0
\(279\) −6.50412 1.30999i −0.389391 0.0784269i
\(280\) 0 0
\(281\) 3.75864 + 5.17333i 0.224222 + 0.308615i 0.906276 0.422687i \(-0.138913\pi\)
−0.682054 + 0.731302i \(0.738913\pi\)
\(282\) 0 0
\(283\) −12.2845 1.94568i −0.730239 0.115658i −0.219766 0.975553i \(-0.570529\pi\)
−0.510472 + 0.859894i \(0.670529\pi\)
\(284\) 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 0.186248 0.982503i \(-0.440367\pi\)
0.982503 0.186248i \(-0.0596329\pi\)
\(294\) 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 −0.657569 0.753394i \(-0.728415\pi\)
0.753394 + 0.657569i \(0.228415\pi\)
\(308\) 0 0
\(309\) −4.47274 + 17.0566i −0.254445 + 0.970318i
\(310\) 0 0
\(311\) −16.6707 5.41664i −0.945310 0.307150i −0.204501 0.978866i \(-0.565557\pi\)
−0.740808 + 0.671717i \(0.765557\pi\)
\(312\) 0 0
\(313\) 7.60246 14.9207i 0.429716 0.843366i −0.570047 0.821612i \(-0.693075\pi\)
0.999763 0.0217538i \(-0.00692499\pi\)
\(314\) 0 0
\(315\) −7.03677 + 3.18954i −0.396477 + 0.179710i
\(316\) 0 0
\(317\) 10.0629 + 1.59380i 0.565187 + 0.0895168i 0.432488 0.901640i \(-0.357636\pi\)
0.132699 + 0.991156i \(0.457636\pi\)
\(318\) 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 0.208138 0.978099i \(-0.433260\pi\)
0.994546 + 0.104298i \(0.0332597\pi\)
\(332\) 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 0.779640 0.626227i \(-0.215402\pi\)
−0.0483675 + 0.998830i \(0.515402\pi\)
\(338\) 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 0.990143 + 0.140059i \(0.0447291\pi\)
−0.898402 + 0.439175i \(0.855271\pi\)
\(348\) 0 0
\(349\) 4.93794i 0.264322i −0.991228 0.132161i \(-0.957808\pi\)
0.991228 0.132161i \(-0.0421916\pi\)
\(350\) 0 0
\(351\) 29.8334 + 4.23600i 1.59239 + 0.226101i
\(352\) 0 0
\(353\) 2.96257 0.469225i 0.157682 0.0249744i −0.0770944 0.997024i \(-0.524564\pi\)
0.234776 + 0.972049i \(0.424564\pi\)
\(354\) 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 0.774866 + 0.632126i \(0.217817\pi\)
−0.255325 + 0.966855i \(0.582183\pi\)
\(360\) 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 0.485152 + 0.874430i \(0.338764\pi\)
−0.731621 + 0.681712i \(0.761236\pi\)
\(368\) 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 0.0692297 0.997601i \(-0.477946\pi\)
0.847768 + 0.530367i \(0.177946\pi\)
\(374\) 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 −0.970669 0.240418i \(-0.922716\pi\)
0.528604 + 0.848868i \(0.322716\pi\)
\(380\) 0 0
\(381\) −0.727111 12.5866i −0.0372510 0.644830i
\(382\) 0 0
\(383\) −4.01050 + 25.3213i −0.204927 + 1.29386i 0.643868 + 0.765137i \(0.277329\pi\)
−0.848795 + 0.528722i \(0.822671\pi\)
\(384\) 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 −0.999562 0.0295942i \(-0.990578\pi\)
0.826058 + 0.563586i \(0.190578\pi\)
\(390\) 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 −0.947346 0.320212i \(-0.896246\pi\)
−0.802029 + 0.597286i \(0.796246\pi\)
\(398\) 0 0
\(399\) −12.2789 7.88105i −0.614715 0.394546i
\(400\) 0 0
\(401\) 28.2805i 1.41226i 0.708081 + 0.706131i \(0.249561\pi\)
−0.708081 + 0.706131i \(0.750439\pi\)
\(402\) 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 0.0907761 0.995871i \(-0.471065\pi\)
0.658798 + 0.752320i \(0.271065\pi\)
\(410\) 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 0.396197 0.918166i \(-0.370330\pi\)
0.995659 0.0930769i \(-0.0296702\pi\)
\(420\) 0 0
\(421\) −1.21908 0.885714i −0.0594143 0.0431670i 0.557682 0.830055i \(-0.311691\pi\)
−0.617096 + 0.786888i \(0.711691\pi\)
\(422\) 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 0.708865 0.705344i \(-0.249207\pi\)
−0.889873 + 0.456208i \(0.849207\pi\)
\(432\) 0 0
\(433\) 22.5721 + 3.57506i 1.08474 + 0.171807i 0.673110 0.739542i \(-0.264958\pi\)
0.411634 + 0.911349i \(0.364958\pi\)
\(434\) 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 0.267111 0.963666i \(-0.413931\pi\)
−0.350331 + 0.936626i \(0.613931\pi\)
\(440\) 0 0
\(441\) −12.5264 + 11.5236i −0.596495 + 0.548745i
\(442\) 0 0
\(443\) −6.75410 + 6.75410i −0.320897 + 0.320897i −0.849111 0.528214i \(-0.822862\pi\)
0.528214 + 0.849111i \(0.322862\pi\)
\(444\) 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 −0.236528 0.971625i \(-0.576010\pi\)
0.971625 + 0.236528i \(0.0760095\pi\)
\(458\) 0 0
\(459\) 0.817958 + 4.67768i 0.0381790 + 0.218335i
\(460\) 0 0
\(461\) −8.27650 2.68920i −0.385475 0.125248i 0.109867 0.993946i \(-0.464957\pi\)
−0.495342 + 0.868698i \(0.664957\pi\)
\(462\) 0 0
\(463\) −6.79566 + 13.3372i −0.315821 + 0.619834i −0.993281 0.115726i \(-0.963081\pi\)
0.677460 + 0.735560i \(0.263081\pi\)
\(464\) 0 0
\(465\) −6.64931 + 5.39932i −0.308354 + 0.250388i
\(466\) 0 0
\(467\) −32.4831 5.14481i −1.50314 0.238074i −0.650070 0.759874i \(-0.725261\pi\)
−0.853067 + 0.521801i \(0.825261\pi\)
\(468\) 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 0.967649 0.252301i \(-0.0811872\pi\)
0.0590677 + 0.998254i \(0.481187\pi\)
\(480\) 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 0.953207 0.302319i \(-0.0977607\pi\)
0.315700 + 0.948859i \(0.397761\pi\)
\(488\) 0 0
\(489\) −10.4434 + 8.54973i −0.472268 + 0.386632i
\(490\) 0 0
\(491\) 11.6547 3.78683i 0.525968 0.170897i −0.0339840 0.999422i \(-0.510820\pi\)
0.559952 + 0.828525i \(0.310820\pi\)
\(492\) 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 \(0.0184189\pi\)
−0.998326 + 0.0578324i \(0.981581\pi\)
\(500\) 0 0
\(501\) 0.546485 + 0.350753i 0.0244151 + 0.0156705i
\(502\) 0 0
\(503\) 29.7370 4.70988i 1.32591 0.210003i 0.546995 0.837136i \(-0.315772\pi\)
0.778913 + 0.627132i \(0.215772\pi\)
\(504\) 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 −0.856252 0.516559i \(-0.827213\pi\)
0.389097 0.921197i \(-0.372787\pi\)
\(510\) 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 −0.600784 0.799412i \(-0.705145\pi\)
0.945938 + 0.324347i \(0.105145\pi\)
\(522\) 0 0
\(523\) 11.1465 5.67941i 0.487401 0.248343i −0.192979 0.981203i \(-0.561815\pi\)
0.680380 + 0.732860i \(0.261815\pi\)
\(524\) 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 0.972709 0.232028i \(-0.0745362\pi\)
−0.923321 + 0.384029i \(0.874536\pi\)
\(542\) 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 −0.212795 0.977097i \(-0.568257\pi\)
0.0995594 + 0.995032i \(0.468257\pi\)
\(548\) 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 0.157639 0.987497i \(-0.449612\pi\)
−0.987497 + 0.157639i \(0.949612\pi\)
\(558\) 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 0.126471 0.991970i \(-0.459635\pi\)
−0.728183 + 0.685383i \(0.759635\pi\)
\(564\) 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 0.247499 0.968888i \(-0.420391\pi\)
0.997949 + 0.0640170i \(0.0203912\pi\)
\(570\) 0 0
\(571\) 34.0496 + 24.7385i 1.42493 + 1.03527i 0.990933 + 0.134358i \(0.0428971\pi\)
0.433997 + 0.900914i \(0.357103\pi\)
\(572\) 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 0.810203 + 0.586149i \(0.199357\pi\)
−0.00202117 + 0.999998i \(0.500643\pi\)
\(578\) 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 −0.888635 0.458615i \(-0.848346\pi\)
0.893354 + 0.449353i \(0.148346\pi\)
\(588\) 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 −0.939014 0.343878i \(-0.888259\pi\)
0.343878 + 0.939014i \(0.388259\pi\)
\(594\) 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 −0.538560 0.842587i \(-0.681032\pi\)
0.842587 + 0.538560i \(0.181032\pi\)
\(608\) 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 −0.999773 0.0212848i \(-0.993224\pi\)
0.604872 + 0.796323i \(0.293224\pi\)
\(614\) 0 0
\(615\) 10.1287 3.90367i 0.408428 0.157411i
\(616\) 0 0
\(617\) 9.79635 + 1.55159i 0.394386 + 0.0624646i 0.350478 0.936571i \(-0.386019\pi\)
0.0439081 + 0.999036i \(0.486019\pi\)
\(618\) 0 0
\(619\) 4.81151 + 6.62247i 0.193391 + 0.266180i 0.894690 0.446687i \(-0.147396\pi\)
−0.701299 + 0.712867i \(0.747396\pi\)
\(620\) 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 −0.600062 0.799954i \(-0.704857\pi\)
0.575372 + 0.817892i \(0.304857\pi\)
\(632\) 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 −0.624715 0.780853i \(-0.714785\pi\)
−0.0464310 + 0.998922i \(0.514785\pi\)
\(642\) 0 0
\(643\) 5.47671 + 5.47671i 0.215980 + 0.215980i 0.806802 0.590822i \(-0.201196\pi\)
−0.590822 + 0.806802i \(0.701196\pi\)
\(644\) 0 0
\(645\) −12.2782 11.0255i −0.483453 0.434128i
\(646\) 0 0
\(647\) −5.84782 36.9217i −0.229902 1.45154i −0.784865 0.619667i \(-0.787268\pi\)
0.554963 0.831875i \(-0.312732\pi\)
\(648\) 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 0.517115 0.855916i \(-0.327006\pi\)
0.756298 + 0.654227i \(0.227006\pi\)
\(654\) 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 −0.998970 0.0453785i \(-0.985551\pi\)
0.781511 0.623892i \(-0.214449\pi\)
\(660\) 0 0
\(661\) 5.43861 16.7383i 0.211537 0.651045i −0.787844 0.615875i \(-0.788803\pi\)
0.999381 0.0351703i \(-0.0111974\pi\)
\(662\) 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 −0.732327 + 0.680953i \(0.761566\pi\)
−0.981354 + 0.192211i \(0.938434\pi\)
\(674\) 0 0
\(675\) −24.7729 7.82974i −0.953508 0.301367i
\(676\) 0 0
\(677\) 13.4384 6.84718i 0.516478 0.263159i −0.176266 0.984343i \(-0.556402\pi\)
0.692744 + 0.721184i \(0.256402\pi\)
\(678\) 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 −0.913791 0.406185i \(-0.866859\pi\)
0.994585 0.103928i \(-0.0331411\pi\)
\(684\) 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 0.928237 0.371991i \(-0.121325\pi\)
−0.969610 + 0.244657i \(0.921325\pi\)
\(692\) 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 \(0.281747\pi\)
−0.633184 + 0.774001i \(0.718253\pi\)
\(702\) 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 −0.0624957 0.998045i \(-0.519906\pi\)
0.536076 + 0.844170i \(0.319906\pi\)
\(710\) 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 −0.878241 0.478218i \(-0.841283\pi\)
0.183421 + 0.983034i \(0.441283\pi\)
\(720\) 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 0.615116 0.788437i \(-0.289109\pi\)
−0.999415 + 0.0342075i \(0.989109\pi\)
\(728\) 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 −0.0927459 0.995690i \(-0.529564\pi\)
−0.395892 + 0.918297i \(0.629564\pi\)
\(734\) 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 0.572516 0.819894i \(-0.305967\pi\)
−0.0187462 + 0.999824i \(0.505967\pi\)
\(740\) 0 0
\(741\) 71.0629 + 18.6348i 2.61056 + 0.684565i
\(742\) 0 0
\(743\) 7.06750 7.06750i 0.259281 0.259281i −0.565480 0.824762i \(-0.691309\pi\)
0.824762 + 0.565480i \(0.191309\pi\)
\(744\) 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 −0.488154 0.872758i \(-0.662330\pi\)
0.872758 + 0.488154i \(0.162330\pi\)
\(758\) 0 0
\(759\) 10.7827 41.1193i 0.391386 1.49254i
\(760\) 0 0
\(761\) −36.8728 11.9807i −1.33664 0.434300i −0.448460 0.893803i \(-0.648027\pi\)
−0.888176 + 0.459503i \(0.848027\pi\)
\(762\) 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 0.852744 + 0.522329i \(0.174937\pi\)
0.233252 + 0.972416i \(0.425063\pi\)
\(770\) 0 0
\(771\) −11.4131 29.2636i −0.411032 1.05390i
\(772\) 0 0
\(773\) −10.0630 19.7497i −0.361940 0.710347i 0.636186 0.771535i \(-0.280511\pi\)
−0.998126 + 0.0611885i \(0.980511\pi\)
\(774\) 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 0.582852 0.812579i \(-0.301937\pi\)
−0.314798 + 0.949159i \(0.601937\pi\)
\(788\) 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 +