Properties

Label 300.2.x.a.17.9
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 17.9
Character \(\chi\) \(=\) 300.17
Dual form 300.2.x.a.53.9

$q$-expansion

\(f(q)\) \(=\) \(q+(1.29334 + 1.15207i) q^{3} +(1.99640 + 1.00718i) q^{5} +(0.814380 + 0.814380i) q^{7} +(0.345460 + 2.98004i) q^{9} +O(q^{10})\) \(q+(1.29334 + 1.15207i) q^{3} +(1.99640 + 1.00718i) q^{5} +(0.814380 + 0.814380i) q^{7} +(0.345460 + 2.98004i) q^{9} +(-3.46407 + 1.12554i) q^{11} +(-2.63271 - 5.16697i) q^{13} +(1.42168 + 3.60261i) q^{15} +(0.902627 - 0.142962i) q^{17} +(4.29919 - 5.91733i) q^{19} +(0.115046 + 1.99149i) q^{21} +(-3.05909 + 6.00381i) q^{23} +(2.97120 + 4.02144i) q^{25} +(-2.98643 + 4.25221i) q^{27} +(4.30536 - 3.12803i) q^{29} +(-1.78920 - 1.29993i) q^{31} +(-5.77692 - 2.53514i) q^{33} +(0.805601 + 2.44605i) q^{35} +(2.74637 - 1.39935i) q^{37} +(2.54774 - 9.71572i) q^{39} +(-2.66555 - 0.866089i) q^{41} +(-3.01283 + 3.01283i) q^{43} +(-2.31175 + 6.29729i) q^{45} +(0.998165 - 6.30217i) q^{47} -5.67357i q^{49} +(1.33211 + 0.854993i) q^{51} +(8.04180 + 1.27370i) q^{53} +(-8.04927 - 1.24189i) q^{55} +(12.3775 - 2.70014i) q^{57} +(-1.98388 + 6.10574i) q^{59} +(-4.21356 - 12.9680i) q^{61} +(-2.14555 + 2.70822i) q^{63} +(-0.0518720 - 12.9669i) q^{65} +(0.976557 + 6.16574i) q^{67} +(-10.8733 + 4.24068i) q^{69} +(-5.88318 - 8.09750i) q^{71} +(-8.26387 - 4.21065i) q^{73} +(-0.790225 + 8.62413i) q^{75} +(-3.73768 - 1.90445i) q^{77} +(4.29102 + 5.90609i) q^{79} +(-8.76132 + 2.05897i) q^{81} +(0.190258 + 1.20124i) q^{83} +(1.94599 + 0.623695i) q^{85} +(9.17202 + 0.914482i) q^{87} +(-3.41396 - 10.5071i) q^{89} +(2.06386 - 6.35190i) q^{91} +(-0.816433 - 3.74254i) q^{93} +(14.5427 - 7.48329i) q^{95} +(3.84712 + 0.609325i) q^{97} +(-4.55086 - 9.93423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 2q^{3} + 4q^{7} + O(q^{10}) \) \( 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) \)

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
\(3\) 1.29334 + 1.15207i 0.746711 + 0.665149i
\(4\) 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
\(9\) 0.345460 + 2.98004i 0.115153 + 0.993348i
\(10\) 0 0
\(11\) −3.46407 + 1.12554i −1.04446 + 0.339364i −0.780490 0.625168i \(-0.785030\pi\)
−0.263965 + 0.964532i \(0.585030\pi\)
\(12\) 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
\(15\) 1.42168 + 3.60261i 0.367077 + 0.930191i
\(16\) 0 0
\(17\) 0.902627 0.142962i 0.218919 0.0346734i −0.0460112 0.998941i \(-0.514651\pi\)
0.264930 + 0.964268i \(0.414651\pi\)
\(18\) 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
\(21\) 0.115046 + 1.99149i 0.0251051 + 0.434580i
\(22\) 0 0
\(23\) −3.05909 + 6.00381i −0.637865 + 1.25188i 0.315174 + 0.949034i \(0.397937\pi\)
−0.953039 + 0.302847i \(0.902063\pi\)
\(24\) 0 0
\(25\) 2.97120 + 4.02144i 0.594239 + 0.804289i
\(26\) 0 0
\(27\) −2.98643 + 4.25221i −0.574738 + 0.818337i
\(28\) 0 0
\(29\) 4.30536 3.12803i 0.799486 0.580861i −0.111277 0.993789i \(-0.535494\pi\)
0.910763 + 0.412929i \(0.135494\pi\)
\(30\) 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
\(33\) −5.77692 2.53514i −1.00563 0.441312i
\(34\) 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
\(39\) 2.54774 9.71572i 0.407965 1.55576i
\(40\) 0 0
\(41\) −2.66555 0.866089i −0.416289 0.135260i 0.0933813 0.995630i \(-0.470232\pi\)
−0.509670 + 0.860370i \(0.670232\pi\)
\(42\) 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
\(45\) −2.31175 + 6.29729i −0.344616 + 0.938744i
\(46\) 0 0
\(47\) 0.998165 6.30217i 0.145597 0.919265i −0.801424 0.598096i \(-0.795924\pi\)
0.947022 0.321169i \(-0.104076\pi\)
\(48\) 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 \(-0.261109\pi\)
0.422623 + 0.906305i \(0.361109\pi\)
\(54\) 0 0
\(55\) −8.04927 1.24189i −1.08536 0.167457i
\(56\) 0 0
\(57\) 12.3775 2.70014i 1.63944 0.357643i
\(58\) 0 0
\(59\) −1.98388 + 6.10574i −0.258279 + 0.794900i 0.734887 + 0.678189i \(0.237235\pi\)
−0.993166 + 0.116711i \(0.962765\pi\)
\(60\) 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
\(63\) −2.14555 + 2.70822i −0.270314 + 0.341204i
\(64\) 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
\(69\) −10.8733 + 4.24068i −1.30899 + 0.510517i
\(70\) 0 0
\(71\) −5.88318 8.09750i −0.698205 0.960996i −0.999971 0.00761427i \(-0.997576\pi\)
0.301766 0.953382i \(-0.402424\pi\)
\(72\) 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
\(75\) −0.790225 + 8.62413i −0.0912473 + 0.995828i
\(76\) 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
\(81\) −8.76132 + 2.05897i −0.973479 + 0.228774i
\(82\) 0 0
\(83\) 0.190258 + 1.20124i 0.0208835 + 0.131853i 0.995927 0.0901590i \(-0.0287375\pi\)
−0.975044 + 0.222012i \(0.928738\pi\)
\(84\) 0 0
\(85\) 1.94599 + 0.623695i 0.211072 + 0.0676492i
\(86\) 0 0
\(87\) 9.17202 + 0.914482i 0.983344 + 0.0980427i
\(88\) 0 0
\(89\) −3.41396 10.5071i −0.361879 1.11375i −0.951913 0.306369i \(-0.900886\pi\)
0.590034 0.807378i \(-0.299114\pi\)
\(90\) 0 0
\(91\) 2.06386 6.35190i 0.216351 0.665860i
\(92\) 0 0
\(93\) −0.816433 3.74254i −0.0846602 0.388084i
\(94\) 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 \(0.0290527\pi\)
−0.995838 + 0.0911450i \(0.970947\pi\)
\(102\) 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
\(105\) −1.77611 + 4.09168i −0.173330 + 0.399307i
\(106\) 0 0
\(107\) −12.7040 + 12.7040i −1.22814 + 1.22814i −0.263470 + 0.964668i \(0.584867\pi\)
−0.964668 + 0.263470i \(0.915133\pi\)
\(108\) 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
\(111\) 5.16414 + 1.35419i 0.490159 + 0.128534i
\(112\) 0 0
\(113\) −16.6927 + 8.50535i −1.57032 + 0.800116i −0.999776 0.0211535i \(-0.993266\pi\)
−0.570540 + 0.821270i \(0.693266\pi\)
\(114\) 0 0
\(115\) −12.1541 + 8.90494i −1.13337 + 0.830390i
\(116\) 0 0
\(117\) 14.4883 9.63056i 1.33945 0.890345i
\(118\) 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
\(123\) −2.44966 4.19105i −0.220879 0.377894i
\(124\) 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
\(129\) −7.36762 + 0.425618i −0.648683 + 0.0374736i
\(130\) 0 0
\(131\) 3.48009 4.78993i 0.304057 0.418498i −0.629460 0.777033i \(-0.716724\pi\)
0.933516 + 0.358535i \(0.116724\pi\)
\(132\) 0 0
\(133\) 8.32012 1.31778i 0.721446 0.114266i
\(134\) 0 0
\(135\) −10.2448 + 5.48123i −0.881733 + 0.471749i
\(136\) 0 0
\(137\) 2.92241 + 5.73556i 0.249679 + 0.490022i 0.981497 0.191478i \(-0.0613280\pi\)
−0.731818 + 0.681500i \(0.761328\pi\)
\(138\) 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
\(141\) 8.55152 7.00089i 0.720168 0.589581i
\(142\) 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
\(147\) 6.53636 7.33786i 0.539110 0.605216i
\(148\) 0 0
\(149\) 21.8247 1.78795 0.893974 0.448119i \(-0.147906\pi\)
0.893974 + 0.448119i \(0.147906\pi\)
\(150\) 0 0
\(151\) −7.79667 −0.634484 −0.317242 0.948345i \(-0.602757\pi\)
−0.317242 + 0.948345i \(0.602757\pi\)
\(152\) 0 0
\(153\) 0.737855 + 2.64048i 0.0596520 + 0.213470i
\(154\) 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
\(159\) 8.93339 + 10.9121i 0.708464 + 0.865382i
\(160\) 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
\(165\) −8.97969 10.8795i −0.699068 0.846970i
\(166\) 0 0
\(167\) 0.370295 0.0586489i 0.0286543 0.00453839i −0.142091 0.989854i \(-0.545383\pi\)
0.170745 + 0.985315i \(0.445383\pi\)
\(168\) 0 0
\(169\) −12.1253 + 16.6890i −0.932714 + 1.28377i
\(170\) 0 0
\(171\) 19.1191 + 10.7676i 1.46207 + 0.823417i
\(172\) 0 0
\(173\) −5.57182 + 10.9353i −0.423618 + 0.831397i 0.576282 + 0.817251i \(0.304503\pi\)
−0.999900 + 0.0141460i \(0.995497\pi\)
\(174\) 0 0
\(175\) −0.855300 + 5.69466i −0.0646546 + 0.430476i
\(176\) 0 0
\(177\) −9.60008 + 5.61124i −0.721586 + 0.421766i
\(178\) 0 0
\(179\) 4.46475 3.24383i 0.333711 0.242455i −0.408293 0.912851i \(-0.633876\pi\)
0.742004 + 0.670396i \(0.233876\pi\)
\(180\) 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
\(183\) 9.49052 21.6264i 0.701559 1.59867i
\(184\) 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
\(189\) −5.89500 + 1.03082i −0.428798 + 0.0749814i
\(190\) 0 0
\(191\) −9.80442 3.18565i −0.709423 0.230505i −0.0679914 0.997686i \(-0.521659\pi\)
−0.641431 + 0.767181i \(0.721659\pi\)
\(192\) 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
\(195\) 14.8717 16.8304i 1.06499 1.20525i
\(196\) 0 0
\(197\) 0.296468 1.87183i 0.0211225 0.133362i −0.974874 0.222759i \(-0.928494\pi\)
0.995996 + 0.0893965i \(0.0284938\pi\)
\(198\) 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
\(207\) −18.9484 7.04216i −1.31701 0.489464i
\(208\) 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
\(213\) 1.71995 17.2507i 0.117849 1.18200i
\(214\) 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
\(219\) −5.83702 14.9664i −0.394429 1.01133i
\(220\) 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
\(225\) −10.9576 + 10.2435i −0.730510 + 0.682902i
\(226\) 0 0
\(227\) −11.3411 5.77860i −0.752738 0.383539i 0.0351307 0.999383i \(-0.488815\pi\)
−0.787868 + 0.615844i \(0.788815\pi\)
\(228\) 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
\(231\) −2.64004 6.76918i −0.173702 0.445379i
\(232\) 0 0
\(233\) −0.939042 5.92888i −0.0615187 0.388414i −0.999166 0.0408262i \(-0.987001\pi\)
0.937648 0.347587i \(-0.112999\pi\)
\(234\) 0 0
\(235\) 8.34012 11.5763i 0.544049 0.755154i
\(236\) 0 0
\(237\) −1.25448 + 12.5821i −0.0814875 + 0.817298i
\(238\) 0 0
\(239\) −3.44778 10.6112i −0.223019 0.686380i −0.998487 0.0549938i \(-0.982486\pi\)
0.775468 0.631387i \(-0.217514\pi\)
\(240\) 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
\(243\) −13.7034 7.43072i −0.879076 0.476681i
\(244\) 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
\(255\) 1.79829 + 3.04857i 0.112613 + 0.190909i
\(256\) 0 0
\(257\) −12.8233 + 12.8233i −0.799894 + 0.799894i −0.983079 0.183184i \(-0.941359\pi\)
0.183184 + 0.983079i \(0.441359\pi\)
\(258\) 0 0
\(259\) 3.37619 + 1.09699i 0.209786 + 0.0681637i
\(260\) 0 0
\(261\) 10.8090 + 11.7496i 0.669060 + 0.727280i
\(262\) 0 0
\(263\) 18.6904 9.52321i 1.15250 0.587226i 0.229984 0.973194i \(-0.426132\pi\)
0.922512 + 0.385968i \(0.126132\pi\)
\(264\) 0 0
\(265\) 14.7718 + 10.6423i 0.907423 + 0.653751i
\(266\) 0 0
\(267\) 7.68950 17.5223i 0.470590 1.07235i
\(268\) 0 0
\(269\) 10.9550 + 7.95929i 0.667940 + 0.485287i 0.869335 0.494223i \(-0.164548\pi\)
−0.201395 + 0.979510i \(0.564548\pi\)
\(270\) 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
\(273\) 9.98712 5.83746i 0.604448 0.353299i
\(274\) 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
\(279\) 3.25576 5.78097i 0.194917 0.346098i
\(280\) 0 0
\(281\) −3.75864 + 5.17333i −0.224222 + 0.308615i −0.906276 0.422687i \(-0.861087\pi\)
0.682054 + 0.731302i \(0.261087\pi\)
\(282\) 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
\(285\) 27.4299 + 7.07576i 1.62481 + 0.419132i
\(286\) 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
\(291\) 4.27366 + 5.22023i 0.250526 + 0.306015i
\(292\) 0 0
\(293\) −20.0058 20.0058i −1.16875 1.16875i −0.982503 0.186248i \(-0.940367\pi\)
−0.186248 0.982503i \(-0.559633\pi\)
\(294\) 0 0
\(295\) −10.1102 + 10.1914i −0.588636 + 0.593364i
\(296\) 0 0
\(297\) 5.55914 18.0913i 0.322574 1.04976i
\(298\) 0 0
\(299\) 39.0752 2.25978
\(300\) 0 0
\(301\) −4.90718 −0.282845
\(302\) 0 0
\(303\) −2.11059 + 2.36939i −0.121250 + 0.136118i
\(304\) 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
\(309\) −13.6442 + 11.1701i −0.776190 + 0.635445i
\(310\) 0 0
\(311\) 16.6707 5.41664i 0.945310 0.307150i 0.204501 0.978866i \(-0.434443\pi\)
0.740808 + 0.671717i \(0.234443\pi\)
\(312\) 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
\(315\) −7.01103 + 3.24574i −0.395027 + 0.182877i
\(316\) 0 0
\(317\) −10.0629 + 1.59380i −0.565187 + 0.0895168i −0.432488 0.901640i \(-0.642364\pi\)
−0.132699 + 0.991156i \(0.542364\pi\)
\(318\) 0 0
\(319\) −11.3933 + 15.6816i −0.637904 + 0.878000i
\(320\) 0 0
\(321\) −31.0664 + 1.79467i −1.73396 + 0.100169i
\(322\) 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
\(327\) 6.88232 + 11.7747i 0.380593 + 0.651144i
\(328\) 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
\(333\) 5.11887 + 7.70089i 0.280513 + 0.422006i
\(334\) 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
\(339\) −31.3881 8.23087i −1.70477 0.447039i
\(340\) 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
\(345\) −25.9785 2.48523i −1.39863 0.133800i
\(346\) 0 0
\(347\) −1.70896 + 10.7899i −0.0917415 + 0.579233i 0.898402 + 0.439175i \(0.144729\pi\)
−0.990143 + 0.140059i \(0.955271\pi\)
\(348\) 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 0.0770944 0.997024i \(-0.475436\pi\)
−0.234776 + 0.972049i \(0.575436\pi\)
\(354\) 0 0
\(355\) −3.58955 22.0912i −0.190513 1.17248i
\(356\) 0 0
\(357\) 0.388552 + 1.78113i 0.0205644 + 0.0942674i
\(358\) 0 0
\(359\) −9.84389 + 30.2964i −0.519540 + 1.59898i 0.255325 + 0.966855i \(0.417817\pi\)
−0.774866 + 0.632126i \(0.782183\pi\)
\(360\) 0 0
\(361\) −10.6604 32.8093i −0.561074 1.72681i
\(362\) 0 0
\(363\) 3.90649 + 0.389491i 0.205038 + 0.0204430i
\(364\) 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
\(369\) 1.66014 8.24265i 0.0864236 0.429095i
\(370\) 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
\(375\) −10.2636 + 16.4213i −0.530011 + 0.847991i
\(376\) 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
\(381\) 11.7459 4.58099i 0.601758 0.234691i
\(382\) 0 0
\(383\) 4.01050 + 25.3213i 0.204927 + 1.29386i 0.848795 + 0.528722i \(0.177329\pi\)
−0.643868 + 0.765137i \(0.722671\pi\)
\(384\) 0 0
\(385\) −5.54379 7.56653i −0.282538 0.385626i
\(386\) 0 0
\(387\) −10.0192 7.93756i −0.509304 0.403489i
\(388\) 0 0
\(389\) 3.42204 + 10.5320i 0.173504 + 0.533991i 0.999562 0.0295942i \(-0.00942151\pi\)
−0.826058 + 0.563586i \(0.809422\pi\)
\(390\) 0 0
\(391\) −1.90291 + 5.85654i −0.0962341 + 0.296178i
\(392\) 0 0
\(393\) 10.0193 2.18570i 0.505406 0.110254i
\(394\) 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 \(0.249561\pi\)
−0.708081 + 0.706131i \(0.750439\pi\)
\(402\) 0 0
\(403\) −2.00627 + 12.6671i −0.0999395 + 0.630993i
\(404\) 0 0
\(405\) −19.5648 4.71366i −0.972183 0.234224i
\(406\) 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
\(411\) −2.82810 + 10.7849i −0.139500 + 0.531978i
\(412\) 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
\(417\) −4.46386 1.95892i −0.218596 0.0959287i
\(418\) 0 0
\(419\) −28.4906 20.6996i −1.39186 1.01124i −0.995659 0.0930769i \(-0.970330\pi\)
−0.396197 0.918166i \(-0.629670\pi\)
\(420\) 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
\(423\) 19.1256 + 0.797431i 0.929916 + 0.0387724i
\(424\) 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
\(429\) 2.10992 + 36.5235i 0.101868 + 1.76337i
\(430\) 0 0
\(431\) 3.75782 5.17220i 0.181008 0.249136i −0.708865 0.705344i \(-0.750793\pi\)
0.889873 + 0.456208i \(0.150793\pi\)
\(432\) 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
\(435\) 17.3899 + 11.0635i 0.833784 + 0.530454i
\(436\) 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
\(441\) 16.9075 1.95999i 0.805118 0.0933328i
\(442\) 0 0
\(443\) 6.75410 + 6.75410i 0.320897 + 0.320897i 0.849111 0.528214i \(-0.177138\pi\)
−0.528214 + 0.849111i \(0.677138\pi\)
\(444\) 0 0
\(445\) 3.76686 24.4147i 0.178566 1.15737i
\(446\) 0 0
\(447\) 28.2268 + 25.1436i 1.33508 + 1.18925i
\(448\) 0 0
\(449\) 24.0642 1.13566 0.567830 0.823146i \(-0.307783\pi\)
0.567830 + 0.823146i \(0.307783\pi\)
\(450\) 0 0
\(451\) 10.2085 0.480697
\(452\) 0 0
\(453\) −10.0838 8.98233i −0.473776 0.422027i
\(454\) 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
\(459\) −2.08773 + 4.26510i −0.0974468 + 0.199078i
\(460\) 0 0
\(461\) 8.27650 2.68920i 0.385475 0.125248i −0.109867 0.993946i \(-0.535043\pi\)
0.495342 + 0.868698i \(0.335043\pi\)
\(462\) 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
\(465\) 2.13948 8.29389i 0.0992158 0.384620i
\(466\) 0 0
\(467\) 32.4831 5.14481i 1.50314 0.238074i 0.650070 0.759874i \(-0.274739\pi\)
0.853067 + 0.521801i \(0.174739\pi\)
\(468\) 0 0
\(469\) −4.22596 + 5.81654i −0.195137 + 0.268583i
\(470\) 0 0
\(471\) 1.46813 + 25.4139i 0.0676478 + 1.17101i
\(472\) 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
\(477\) −1.01755 + 24.4049i −0.0465905 + 1.11742i
\(478\) 0 0
\(479\) −22.4708 + 16.3260i −1.02672 + 0.745953i −0.967649 0.252301i \(-0.918813\pi\)
−0.0590677 + 0.998254i \(0.518813\pi\)
\(480\) 0 0
\(481\) −14.4608 10.5064i −0.659355 0.479049i
\(482\) 0 0
\(483\) −12.3085 5.40146i −0.560056 0.245775i
\(484\) 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
\(489\) −3.42349 + 13.0554i −0.154816 + 0.590384i
\(490\) 0 0
\(491\) −11.6547 3.78683i −0.525968 0.170897i 0.0339840 0.999422i \(-0.489180\pi\)
−0.559952 + 0.828525i \(0.689180\pi\)
\(492\) 0 0
\(493\) 3.43895 3.43895i 0.154883 0.154883i
\(494\) 0 0
\(495\) 0.920195 24.4162i 0.0413597 1.09743i
\(496\) 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 −0.546995 0.837136i \(-0.684228\pi\)
−0.778913 + 0.627132i \(0.784228\pi\)
\(504\) 0 0
\(505\) −1.84514 + 3.65738i −0.0821076 + 0.162751i
\(506\) 0 0
\(507\) −34.9091 + 7.61539i −1.55037 + 0.338211i
\(508\) 0 0
\(509\) 10.5395 32.4372i 0.467155 1.43776i −0.389097 0.921197i \(-0.627213\pi\)
0.856252 0.516559i \(-0.172787\pi\)
\(510\) 0 0
\(511\) −3.30086 10.1590i −0.146021 0.449407i
\(512\) 0 0
\(513\) 12.3225 + 35.9527i 0.544050 + 1.58735i
\(514\) 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
\(519\) −19.8045 + 7.72395i −0.869323 + 0.339044i
\(520\) 0 0
\(521\) −7.87830 10.8435i −0.345154 0.475064i 0.600784 0.799412i \(-0.294855\pi\)
−0.945938 + 0.324347i \(0.894855\pi\)
\(522\) 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
\(525\) −7.66686 + 6.37977i −0.334609 + 0.278436i
\(526\) 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
\(531\) −18.8807 3.80275i −0.819354 0.165025i
\(532\) 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
\(537\) 9.51156 + 0.948335i 0.410454 + 0.0409237i
\(538\) 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
\(543\) 3.67323 + 16.8382i 0.157634 + 0.722595i
\(544\) 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
\(555\) 8.94577 + 7.90469i 0.379727 + 0.335535i
\(556\) 0 0
\(557\) 19.5853 19.5853i 0.829857 0.829857i −0.157639 0.987497i \(-0.550388\pi\)
0.987497 + 0.157639i \(0.0503884\pi\)
\(558\) 0 0
\(559\) 23.4991 + 7.63533i 0.993908 + 0.322940i
\(560\) 0 0
\(561\) −5.57684 1.46241i −0.235454 0.0617429i
\(562\) 0 0
\(563\) 14.2772 7.27459i 0.601712 0.306587i −0.126471 0.991970i \(-0.540365\pi\)
0.728183 + 0.685383i \(0.240365\pi\)
\(564\) 0 0
\(565\) −41.8916 + 0.167580i −1.76239 + 0.00705015i
\(566\) 0 0
\(567\) −8.81182 5.45826i −0.370062 0.229225i
\(568\) 0 0
\(569\) −29.7086 21.5845i −1.24545 0.904871i −0.247499 0.968888i \(-0.579609\pi\)
−0.997949 + 0.0640170i \(0.979609\pi\)
\(570\) 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
\(573\) −9.01035 15.4155i −0.376413 0.643993i
\(574\) 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
\(579\) −0.582873 + 0.0336718i −0.0242234 + 0.00139935i
\(580\) 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
\(585\) 38.6241 4.63413i 1.59691 0.191598i
\(586\) 0 0
\(587\) −0.114338 0.224402i −0.00471925 0.00926205i 0.888635 0.458615i \(-0.151654\pi\)
−0.893354 + 0.449353i \(0.851654\pi\)
\(588\) 0 0
\(589\) −15.3842 + 4.99864i −0.633897 + 0.205966i
\(590\) 0 0
\(591\) 2.53991 2.07936i 0.104478 0.0855333i
\(592\) 0 0
\(593\) 14.4925 + 14.4925i 0.595137 + 0.595137i 0.939014 0.343878i \(-0.111741\pi\)
−0.343878 + 0.939014i \(0.611741\pi\)
\(594\) 0 0
\(595\) 1.07685 + 2.09270i 0.0441466 + 0.0857923i
\(596\) 0 0
\(597\) 21.4744 24.1076i 0.878889 0.986659i
\(598\) 0 0
\(599\) −16.6754 −0.681340 −0.340670 0.940183i \(-0.610654\pi\)
−0.340670 + 0.940183i \(0.610654\pi\)
\(600\) 0 0
\(601\) −21.5251 −0.878028 −0.439014 0.898480i \(-0.644672\pi\)
−0.439014 + 0.898480i \(0.644672\pi\)
\(602\) 0 0
\(603\) −18.0368 + 5.04019i −0.734515 + 0.205253i
\(604\) 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
\(609\) 6.72477 + 8.21424i 0.272501 + 0.332858i
\(610\) 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
\(615\) −0.669376 10.8342i −0.0269918 0.436879i
\(616\) 0 0
\(617\) −9.79635 + 1.55159i −0.394386 + 0.0624646i −0.350478 0.936571i \(-0.613981\pi\)
−0.0439081 + 0.999036i \(0.513981\pi\)
\(618\) 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
\(621\) −16.3937 30.9378i −0.657855 1.24149i
\(622\) 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
\(627\) −39.8374 + 23.2849i −1.59095 + 0.929909i
\(628\) 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
\(633\) −17.5044 + 39.8879i −0.695737 + 1.58540i
\(634\) 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
\(639\) 22.0985 20.3295i 0.874203 0.804222i
\(640\) 0 0
\(641\) 16.9921 + 5.52105i 0.671146 + 0.218068i 0.624715 0.780853i \(-0.285215\pi\)
0.0464310 + 0.998922i \(0.485215\pi\)
\(642\) 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
\(645\) −15.1374 6.57079i −0.596033 0.258724i
\(646\) 0 0
\(647\) 5.84782 36.9217i 0.229902 1.45154i −0.554963 0.831875i \(-0.687268\pi\)
0.784865 0.619667i \(-0.212732\pi\)
\(648\) 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 \(-0.672994\pi\)
−0.756298 + 0.654227i \(0.772994\pi\)
\(654\) 0 0
\(655\) 11.7719 6.05753i 0.459967 0.236687i
\(656\) 0 0
\(657\) 9.69309 26.0813i 0.378163 1.01753i
\(658\) 0 0
\(659\) 5.58239 17.1808i 0.217459 0.669270i −0.781511 0.623892i \(-0.785551\pi\)
0.998970 0.0453785i \(-0.0144494\pi\)
\(660\) 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
\(663\) 0.910682 9.13391i 0.0353680 0.354732i
\(664\) 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
\(669\) 3.02684 + 7.76095i 0.117024 + 0.300056i
\(670\) 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
\(675\) −25.9733 + 0.624383i −0.999711 + 0.0240325i
\(676\) 0 0
\(677\) −13.4384 6.84718i −0.516478 0.263159i 0.176266 0.984343i \(-0.443598\pi\)
−0.692744 + 0.721184i \(0.743598\pi\)
\(678\) 0 0
\(679\) 2.63680 + 3.62924i 0.101191 + 0.139278i
\(680\) 0 0
\(681\) −8.01059 20.5395i −0.306966 0.787075i
\(682\) 0 0
\(683\) −2.11149 13.3314i −0.0807939 0.510113i −0.994585 0.103928i \(-0.966859\pi\)
0.913791 0.406185i \(-0.133141\pi\)
\(684\) 0 0
\(685\) 0.0575801 + 14.3938i 0.00220002 + 0.549960i
\(686\) 0 0
\(687\) −0.0279160 + 0.279990i −0.00106506 + 0.0106823i
\(688\) 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
\(693\) 4.38411 11.7964i 0.166539 0.448107i
\(694\) 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
\(705\) 24.1233 5.36367i 0.908538 0.202007i
\(706\) 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
\(711\) −16.1180 + 14.8277i −0.604473 + 0.556084i
\(712\) 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
\(717\) 7.76569 17.6960i 0.290015 0.660868i
\(718\) 0 0
\(719\) 18.6310 + 13.5362i 0.694820 + 0.504816i 0.878241 0.478218i \(-0.158717\pi\)
−0.183421 + 0.983034i \(0.558717\pi\)
\(720\) 0 0
\(721\) −9.48579 + 6.89183i −0.353269 + 0.256665i
\(722\) 0 0
\(723\) −42.0337 + 24.5687i −1.56325 + 0.913718i
\(724\) 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
\(729\) −9.16250 25.3978i −0.339352 0.940660i
\(730\) 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
\(735\) 20.4397 8.06601i 0.753929 0.297519i
\(736\) 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
\(741\) −46.5379 56.8456i −1.70961 2.08827i
\(742\) 0 0
\(743\) −7.06750 7.06750i −0.259281 0.259281i 0.565480 0.824762i \(-0.308691\pi\)
−0.824762 + 0.565480i \(0.808691\pi\)
\(744\) 0 0
\(745\) 43.5707 + 21.9813i 1.59631 + 0.805332i
\(746\) 0 0
\(747\) −3.51402 + 0.981955i −0.128571 + 0.0359279i
\(748\) 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
\(753\) 32.4132 36.3878i 1.18120 1.32604i
\(754\) 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
\(759\) 32.8927 26.9283i 1.19393 0.977436i
\(760\) 0 0
\(761\) 36.8728 11.9807i 1.33664 0.434300i 0.448460 0.893803i \(-0.351973\pi\)
0.888176 + 0.459503i \(0.151973\pi\)
\(762\) 0 0
\(763\) 4.11715 + 8.08037i 0.149051 + 0.292529i
\(764\) 0 0
\(765\) −1.18638 + 6.01460i −0.0428936 + 0.217458i
\(766\) 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
\(771\) −31.3582 + 1.81152i −1.12934 + 0.0652405i
\(772\) 0 0
\(773\) 10.0630 19.7497i 0.361940 0.710347i −0.636186 0.771535i \(-0.719489\pi\)
0.998126 + 0.0611885i \(0.0194891\pi\)
\(774\) 0 0
\(775\) −0.0884689 11.0575i −0.00317790 0.397198i
\(776\) 0 0
\(777\) 3.10275 + 5.30840i 0.111311 + 0.190438i
\(778\) 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
\(783\) 0.443366 + 27.6489i 0.0158446 + 0.988092i
\(784\) 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
\(789\) 35.1444 + 9.21588i 1.25117 + 0.328094i
\(790\) 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
\(795\) 6.84424 + 30.7823i 0.242740 + 1.09173i
\(796\) 0 0
\(797\) −3.19808 + 20.1919i −0.113282