Properties

Label 300.2.x.a.113.5
Level $300$
Weight $2$
Character 300.113
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 113.5
Character \(\chi\) \(=\) 300.113
Dual form 300.2.x.a.77.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.194059 + 1.72115i) q^{3} +(2.22337 + 0.237965i) q^{5} +(2.44386 - 2.44386i) q^{7} +(-2.92468 + 0.668006i) q^{9} +O(q^{10})\) \(q+(0.194059 + 1.72115i) q^{3} +(2.22337 + 0.237965i) q^{5} +(2.44386 - 2.44386i) q^{7} +(-2.92468 + 0.668006i) q^{9} +(0.626305 - 0.862035i) q^{11} +(4.64256 + 0.735309i) q^{13} +(0.0218922 + 3.87292i) q^{15} +(-5.63490 + 2.87112i) q^{17} +(-2.86859 - 0.932063i) q^{19} +(4.68049 + 3.73199i) q^{21} +(-4.44376 + 0.703822i) q^{23} +(4.88675 + 1.05817i) q^{25} +(-1.71730 - 4.90417i) q^{27} +(2.43550 + 7.49571i) q^{29} +(-0.586924 + 1.80637i) q^{31} +(1.60523 + 0.910677i) q^{33} +(6.01516 - 4.85205i) q^{35} +(0.993131 - 6.27038i) q^{37} +(-0.364645 + 8.13321i) q^{39} +(1.22959 + 1.69238i) q^{41} +(-8.27416 - 8.27416i) q^{43} +(-6.66161 + 0.789253i) q^{45} +(4.80234 - 9.42512i) q^{47} -4.94490i q^{49} +(-6.03512 - 9.14131i) q^{51} +(-9.25431 - 4.71531i) q^{53} +(1.59764 - 1.76758i) q^{55} +(1.04754 - 5.11814i) q^{57} +(-3.79924 + 2.76031i) q^{59} +(2.42074 + 1.75877i) q^{61} +(-5.51500 + 8.78003i) q^{63} +(10.1471 + 2.73963i) q^{65} +(2.94083 + 5.77171i) q^{67} +(-2.07373 - 7.51177i) q^{69} +(-0.855266 + 0.277893i) q^{71} +(-0.277586 - 1.75261i) q^{73} +(-0.872944 + 8.61615i) q^{75} +(-0.576091 - 3.63730i) q^{77} +(-8.30052 + 2.69700i) q^{79} +(8.10754 - 3.90741i) q^{81} +(-2.42816 - 4.76553i) q^{83} +(-13.2117 + 5.04266i) q^{85} +(-12.4286 + 5.64646i) q^{87} +(1.94640 + 1.41415i) q^{89} +(13.1428 - 9.54877i) q^{91} +(-3.22292 - 0.659641i) q^{93} +(-6.15615 - 2.75494i) q^{95} +(-4.23366 - 2.15716i) q^{97} +(-1.25590 + 2.93956i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 2q^{3} + 4q^{7} + O(q^{10}) \) \( 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{19}{20}\right)\)

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
\(3\) 0.194059 + 1.72115i 0.112040 + 0.993704i
\(4\) 0 0
\(5\) 2.22337 + 0.237965i 0.994321 + 0.106421i
\(6\) 0 0
\(7\) 2.44386 2.44386i 0.923692 0.923692i −0.0735960 0.997288i \(-0.523448\pi\)
0.997288 + 0.0735960i \(0.0234475\pi\)
\(8\) 0 0
\(9\) −2.92468 + 0.668006i −0.974894 + 0.222669i
\(10\) 0 0
\(11\) 0.626305 0.862035i 0.188838 0.259913i −0.704092 0.710109i \(-0.748646\pi\)
0.892930 + 0.450195i \(0.148646\pi\)
\(12\) 0 0
\(13\) 4.64256 + 0.735309i 1.28761 + 0.203938i 0.762441 0.647058i \(-0.224001\pi\)
0.525173 + 0.850996i \(0.324001\pi\)
\(14\) 0 0
\(15\) 0.0218922 + 3.87292i 0.00565253 + 0.999984i
\(16\) 0 0
\(17\) −5.63490 + 2.87112i −1.36666 + 0.696350i −0.974676 0.223621i \(-0.928212\pi\)
−0.391987 + 0.919971i \(0.628212\pi\)
\(18\) 0 0
\(19\) −2.86859 0.932063i −0.658101 0.213830i −0.0391181 0.999235i \(-0.512455\pi\)
−0.618983 + 0.785405i \(0.712455\pi\)
\(20\) 0 0
\(21\) 4.68049 + 3.73199i 1.02137 + 0.814386i
\(22\) 0 0
\(23\) −4.44376 + 0.703822i −0.926588 + 0.146757i −0.601451 0.798910i \(-0.705410\pi\)
−0.325137 + 0.945667i \(0.605410\pi\)
\(24\) 0 0
\(25\) 4.88675 + 1.05817i 0.977349 + 0.211633i
\(26\) 0 0
\(27\) −1.71730 4.90417i −0.330494 0.943808i
\(28\) 0 0
\(29\) 2.43550 + 7.49571i 0.452261 + 1.39192i 0.874320 + 0.485349i \(0.161307\pi\)
−0.422059 + 0.906568i \(0.638693\pi\)
\(30\) 0 0
\(31\) −0.586924 + 1.80637i −0.105415 + 0.324433i −0.989828 0.142272i \(-0.954559\pi\)
0.884413 + 0.466705i \(0.154559\pi\)
\(32\) 0 0
\(33\) 1.60523 + 0.910677i 0.279434 + 0.158529i
\(34\) 0 0
\(35\) 6.01516 4.85205i 1.01675 0.820146i
\(36\) 0 0
\(37\) 0.993131 6.27038i 0.163270 1.03084i −0.760902 0.648867i \(-0.775243\pi\)
0.924172 0.381977i \(-0.124757\pi\)
\(38\) 0 0
\(39\) −0.364645 + 8.13321i −0.0583900 + 1.30236i
\(40\) 0 0
\(41\) 1.22959 + 1.69238i 0.192029 + 0.264306i 0.894165 0.447737i \(-0.147770\pi\)
−0.702136 + 0.712043i \(0.747770\pi\)
\(42\) 0 0
\(43\) −8.27416 8.27416i −1.26180 1.26180i −0.950221 0.311576i \(-0.899143\pi\)
−0.311576 0.950221i \(-0.600857\pi\)
\(44\) 0 0
\(45\) −6.66161 + 0.789253i −0.993055 + 0.117655i
\(46\) 0 0
\(47\) 4.80234 9.42512i 0.700493 1.37480i −0.216655 0.976248i \(-0.569515\pi\)
0.917148 0.398547i \(-0.130485\pi\)
\(48\) 0 0
\(49\) 4.94490i 0.706414i
\(50\) 0 0
\(51\) −6.03512 9.14131i −0.845086 1.28004i
\(52\) 0 0
\(53\) −9.25431 4.71531i −1.27118 0.647697i −0.317423 0.948284i \(-0.602817\pi\)
−0.953754 + 0.300587i \(0.902817\pi\)
\(54\) 0 0
\(55\) 1.59764 1.76758i 0.215426 0.238341i
\(56\) 0 0
\(57\) 1.04754 5.11814i 0.138750 0.677915i
\(58\) 0 0
\(59\) −3.79924 + 2.76031i −0.494619 + 0.359362i −0.806958 0.590609i \(-0.798888\pi\)
0.312339 + 0.949971i \(0.398888\pi\)
\(60\) 0 0
\(61\) 2.42074 + 1.75877i 0.309944 + 0.225188i 0.731873 0.681441i \(-0.238647\pi\)
−0.421928 + 0.906629i \(0.638647\pi\)
\(62\) 0 0
\(63\) −5.51500 + 8.78003i −0.694825 + 1.10618i
\(64\) 0 0
\(65\) 10.1471 + 2.73963i 1.25860 + 0.339809i
\(66\) 0 0
\(67\) 2.94083 + 5.77171i 0.359280 + 0.705126i 0.997926 0.0643744i \(-0.0205052\pi\)
−0.638646 + 0.769501i \(0.720505\pi\)
\(68\) 0 0
\(69\) −2.07373 7.51177i −0.249648 0.904311i
\(70\) 0 0
\(71\) −0.855266 + 0.277893i −0.101501 + 0.0329798i −0.359327 0.933212i \(-0.616994\pi\)
0.257826 + 0.966191i \(0.416994\pi\)
\(72\) 0 0
\(73\) −0.277586 1.75261i −0.0324890 0.205127i 0.966104 0.258152i \(-0.0831137\pi\)
−0.998593 + 0.0530251i \(0.983114\pi\)
\(74\) 0 0
\(75\) −0.872944 + 8.61615i −0.100799 + 0.994907i
\(76\) 0 0
\(77\) −0.576091 3.63730i −0.0656517 0.414508i
\(78\) 0 0
\(79\) −8.30052 + 2.69700i −0.933882 + 0.303437i −0.736149 0.676819i \(-0.763358\pi\)
−0.197733 + 0.980256i \(0.563358\pi\)
\(80\) 0 0
\(81\) 8.10754 3.90741i 0.900837 0.434157i
\(82\) 0 0
\(83\) −2.42816 4.76553i −0.266525 0.523085i 0.718493 0.695534i \(-0.244832\pi\)
−0.985018 + 0.172449i \(0.944832\pi\)
\(84\) 0 0
\(85\) −13.2117 + 5.04266i −1.43301 + 0.546954i
\(86\) 0 0
\(87\) −12.4286 + 5.64646i −1.33248 + 0.605364i
\(88\) 0 0
\(89\) 1.94640 + 1.41415i 0.206318 + 0.149899i 0.686146 0.727463i \(-0.259301\pi\)
−0.479828 + 0.877363i \(0.659301\pi\)
\(90\) 0 0
\(91\) 13.1428 9.54877i 1.37773 1.00098i
\(92\) 0 0
\(93\) −3.22292 0.659641i −0.334201 0.0684016i
\(94\) 0 0
\(95\) −6.15615 2.75494i −0.631607 0.282651i
\(96\) 0 0
\(97\) −4.23366 2.15716i −0.429864 0.219026i 0.225652 0.974208i \(-0.427549\pi\)
−0.655516 + 0.755182i \(0.727549\pi\)
\(98\) 0 0
\(99\) −1.25590 + 2.93956i −0.126223 + 0.295436i
\(100\) 0 0
\(101\) 19.4515i 1.93550i −0.251916 0.967749i \(-0.581061\pi\)
0.251916 0.967749i \(-0.418939\pi\)
\(102\) 0 0
\(103\) 2.61006 5.12254i 0.257177 0.504738i −0.725930 0.687768i \(-0.758591\pi\)
0.983107 + 0.183030i \(0.0585905\pi\)
\(104\) 0 0
\(105\) 9.51838 + 9.41137i 0.928899 + 0.918456i
\(106\) 0 0
\(107\) 7.71479 + 7.71479i 0.745817 + 0.745817i 0.973691 0.227874i \(-0.0731774\pi\)
−0.227874 + 0.973691i \(0.573177\pi\)
\(108\) 0 0
\(109\) 6.10072 + 8.39692i 0.584343 + 0.804279i 0.994163 0.107887i \(-0.0344086\pi\)
−0.409820 + 0.912166i \(0.634409\pi\)
\(110\) 0 0
\(111\) 10.9850 + 0.492501i 1.04265 + 0.0467461i
\(112\) 0 0
\(113\) −0.703338 + 4.44070i −0.0661645 + 0.417746i 0.932268 + 0.361769i \(0.117827\pi\)
−0.998432 + 0.0559766i \(0.982173\pi\)
\(114\) 0 0
\(115\) −10.0476 + 0.507399i −0.936944 + 0.0473152i
\(116\) 0 0
\(117\) −14.0692 + 0.950712i −1.30070 + 0.0878934i
\(118\) 0 0
\(119\) −6.75428 + 20.7875i −0.619163 + 1.90559i
\(120\) 0 0
\(121\) 3.04834 + 9.38183i 0.277122 + 0.852893i
\(122\) 0 0
\(123\) −2.67422 + 2.44472i −0.241127 + 0.220433i
\(124\) 0 0
\(125\) 10.6132 + 3.51557i 0.949277 + 0.314442i
\(126\) 0 0
\(127\) 9.50331 1.50518i 0.843283 0.133563i 0.280178 0.959948i \(-0.409607\pi\)
0.563105 + 0.826385i \(0.309607\pi\)
\(128\) 0 0
\(129\) 12.6354 15.8467i 1.11248 1.39522i
\(130\) 0 0
\(131\) −15.2113 4.94246i −1.32902 0.431825i −0.443436 0.896306i \(-0.646241\pi\)
−0.885583 + 0.464481i \(0.846241\pi\)
\(132\) 0 0
\(133\) −9.28827 + 4.73261i −0.805395 + 0.410369i
\(134\) 0 0
\(135\) −2.65116 11.3124i −0.228176 0.973620i
\(136\) 0 0
\(137\) 7.60492 + 1.20450i 0.649732 + 0.102907i 0.472596 0.881279i \(-0.343317\pi\)
0.177136 + 0.984186i \(0.443317\pi\)
\(138\) 0 0
\(139\) 5.03690 6.93270i 0.427224 0.588024i −0.540089 0.841608i \(-0.681609\pi\)
0.967313 + 0.253584i \(0.0816094\pi\)
\(140\) 0 0
\(141\) 17.1539 + 6.43650i 1.44462 + 0.542051i
\(142\) 0 0
\(143\) 3.54152 3.54152i 0.296157 0.296157i
\(144\) 0 0
\(145\) 3.63131 + 17.2453i 0.301564 + 1.43214i
\(146\) 0 0
\(147\) 8.51089 0.959600i 0.701966 0.0791465i
\(148\) 0 0
\(149\) 5.42628 0.444538 0.222269 0.974985i \(-0.428654\pi\)
0.222269 + 0.974985i \(0.428654\pi\)
\(150\) 0 0
\(151\) −15.4523 −1.25749 −0.628745 0.777611i \(-0.716431\pi\)
−0.628745 + 0.777611i \(0.716431\pi\)
\(152\) 0 0
\(153\) 14.5624 12.1613i 1.17730 0.983181i
\(154\) 0 0
\(155\) −1.73480 + 3.87656i −0.139343 + 0.311372i
\(156\) 0 0
\(157\) −5.46444 + 5.46444i −0.436110 + 0.436110i −0.890700 0.454591i \(-0.849786\pi\)
0.454591 + 0.890700i \(0.349786\pi\)
\(158\) 0 0
\(159\) 6.31985 16.8431i 0.501197 1.33574i
\(160\) 0 0
\(161\) −9.13988 + 12.5800i −0.720324 + 0.991440i
\(162\) 0 0
\(163\) 12.1195 + 1.91953i 0.949270 + 0.150350i 0.611823 0.790995i \(-0.290437\pi\)
0.337447 + 0.941344i \(0.390437\pi\)
\(164\) 0 0
\(165\) 3.35231 + 2.40676i 0.260977 + 0.187366i
\(166\) 0 0
\(167\) 8.67164 4.41842i 0.671032 0.341908i −0.0850576 0.996376i \(-0.527107\pi\)
0.756090 + 0.654468i \(0.227107\pi\)
\(168\) 0 0
\(169\) 8.64893 + 2.81021i 0.665302 + 0.216170i
\(170\) 0 0
\(171\) 9.01235 + 0.809749i 0.689192 + 0.0619231i
\(172\) 0 0
\(173\) −16.7643 + 2.65520i −1.27456 + 0.201871i −0.756797 0.653650i \(-0.773237\pi\)
−0.517767 + 0.855522i \(0.673237\pi\)
\(174\) 0 0
\(175\) 14.5285 9.35651i 1.09825 0.707286i
\(176\) 0 0
\(177\) −5.48817 6.00339i −0.412516 0.451242i
\(178\) 0 0
\(179\) 3.51696 + 10.8241i 0.262870 + 0.809031i 0.992176 + 0.124843i \(0.0398429\pi\)
−0.729306 + 0.684187i \(0.760157\pi\)
\(180\) 0 0
\(181\) 0.864359 2.66022i 0.0642473 0.197733i −0.913780 0.406209i \(-0.866850\pi\)
0.978027 + 0.208476i \(0.0668504\pi\)
\(182\) 0 0
\(183\) −2.55734 + 4.50775i −0.189044 + 0.333223i
\(184\) 0 0
\(185\) 3.70023 13.7050i 0.272046 1.00762i
\(186\) 0 0
\(187\) −1.05416 + 6.65568i −0.0770875 + 0.486712i
\(188\) 0 0
\(189\) −16.1819 7.78828i −1.17706 0.566514i
\(190\) 0 0
\(191\) 7.23129 + 9.95302i 0.523238 + 0.720175i 0.986081 0.166265i \(-0.0531707\pi\)
−0.462843 + 0.886440i \(0.653171\pi\)
\(192\) 0 0
\(193\) −2.46367 2.46367i −0.177339 0.177339i 0.612856 0.790195i \(-0.290021\pi\)
−0.790195 + 0.612856i \(0.790021\pi\)
\(194\) 0 0
\(195\) −2.74616 + 17.9964i −0.196656 + 1.28875i
\(196\) 0 0
\(197\) −4.60438 + 9.03661i −0.328049 + 0.643832i −0.994845 0.101408i \(-0.967665\pi\)
0.666796 + 0.745240i \(0.267665\pi\)
\(198\) 0 0
\(199\) 13.8104i 0.978994i 0.872005 + 0.489497i \(0.162820\pi\)
−0.872005 + 0.489497i \(0.837180\pi\)
\(200\) 0 0
\(201\) −9.36325 + 6.18165i −0.660433 + 0.436020i
\(202\) 0 0
\(203\) 24.2705 + 12.3664i 1.70345 + 0.867953i
\(204\) 0 0
\(205\) 2.33110 + 4.05539i 0.162811 + 0.283241i
\(206\) 0 0
\(207\) 12.5264 5.02692i 0.870647 0.349395i
\(208\) 0 0
\(209\) −2.60009 + 1.88907i −0.179852 + 0.130670i
\(210\) 0 0
\(211\) −4.04500 2.93886i −0.278469 0.202320i 0.439780 0.898105i \(-0.355056\pi\)
−0.718249 + 0.695786i \(0.755056\pi\)
\(212\) 0 0
\(213\) −0.644265 1.41811i −0.0441443 0.0971672i
\(214\) 0 0
\(215\) −16.4276 20.3655i −1.12035 1.38891i
\(216\) 0 0
\(217\) 2.98015 + 5.84887i 0.202306 + 0.397047i
\(218\) 0 0
\(219\) 2.96262 0.817874i 0.200196 0.0552668i
\(220\) 0 0
\(221\) −28.2715 + 9.18597i −1.90175 + 0.617915i
\(222\) 0 0
\(223\) 2.86335 + 18.0785i 0.191744 + 1.21063i 0.876337 + 0.481699i \(0.159980\pi\)
−0.684592 + 0.728926i \(0.740020\pi\)
\(224\) 0 0
\(225\) −14.9990 + 0.169573i −0.999936 + 0.0113049i
\(226\) 0 0
\(227\) −0.316481 1.99819i −0.0210056 0.132624i 0.974957 0.222394i \(-0.0713870\pi\)
−0.995963 + 0.0897694i \(0.971387\pi\)
\(228\) 0 0
\(229\) −25.7555 + 8.36847i −1.70197 + 0.553004i −0.988965 0.148153i \(-0.952667\pi\)
−0.713007 + 0.701157i \(0.752667\pi\)
\(230\) 0 0
\(231\) 6.14852 1.69738i 0.404543 0.111680i
\(232\) 0 0
\(233\) −13.3461 26.1931i −0.874329 1.71597i −0.677491 0.735531i \(-0.736933\pi\)
−0.196838 0.980436i \(-0.563067\pi\)
\(234\) 0 0
\(235\) 12.9202 19.8127i 0.842822 1.29244i
\(236\) 0 0
\(237\) −6.25272 13.7630i −0.406158 0.894005i
\(238\) 0 0
\(239\) 3.18910 + 2.31702i 0.206286 + 0.149875i 0.686132 0.727477i \(-0.259307\pi\)
−0.479846 + 0.877353i \(0.659307\pi\)
\(240\) 0 0
\(241\) −8.48908 + 6.16768i −0.546830 + 0.397295i −0.826615 0.562768i \(-0.809737\pi\)
0.279786 + 0.960063i \(0.409737\pi\)
\(242\) 0 0
\(243\) 8.29856 + 13.1960i 0.532353 + 0.846523i
\(244\) 0 0
\(245\) 1.17671 10.9943i 0.0751774 0.702403i
\(246\) 0 0
\(247\) −12.6323 6.43646i −0.803772 0.409542i
\(248\) 0 0
\(249\) 7.73097 5.10401i 0.489930 0.323453i
\(250\) 0 0
\(251\) 1.17570i 0.0742098i −0.999311 0.0371049i \(-0.988186\pi\)
0.999311 0.0371049i \(-0.0118136\pi\)
\(252\) 0 0
\(253\) −2.17643 + 4.27149i −0.136831 + 0.268546i
\(254\) 0 0
\(255\) −11.2430 21.7607i −0.704064 1.36271i
\(256\) 0 0
\(257\) 18.9675 + 18.9675i 1.18316 + 1.18316i 0.978921 + 0.204237i \(0.0654714\pi\)
0.204237 + 0.978921i \(0.434529\pi\)
\(258\) 0 0
\(259\) −12.8969 17.7510i −0.801372 1.10299i
\(260\) 0 0
\(261\) −12.1302 20.2956i −0.750843 1.25627i
\(262\) 0 0
\(263\) 3.31659 20.9401i 0.204510 1.29122i −0.645216 0.764000i \(-0.723233\pi\)
0.849726 0.527224i \(-0.176767\pi\)
\(264\) 0 0
\(265\) −19.4537 12.6861i −1.19503 0.779299i
\(266\) 0 0
\(267\) −2.05623 + 3.62447i −0.125839 + 0.221814i
\(268\) 0 0
\(269\) 6.34707 19.5343i 0.386988 1.19103i −0.548040 0.836452i \(-0.684626\pi\)
0.935028 0.354574i \(-0.115374\pi\)
\(270\) 0 0
\(271\) 8.54780 + 26.3074i 0.519242 + 1.59806i 0.775429 + 0.631435i \(0.217534\pi\)
−0.256187 + 0.966627i \(0.582466\pi\)
\(272\) 0 0
\(273\) 18.9853 + 20.7676i 1.14904 + 1.25691i
\(274\) 0 0
\(275\) 3.97277 3.54981i 0.239567 0.214062i
\(276\) 0 0
\(277\) −17.2867 + 2.73795i −1.03866 + 0.164507i −0.652393 0.757880i \(-0.726235\pi\)
−0.386265 + 0.922388i \(0.626235\pi\)
\(278\) 0 0
\(279\) 0.509903 5.67512i 0.0305271 0.339761i
\(280\) 0 0
\(281\) 22.5521 + 7.32761i 1.34534 + 0.437129i 0.891123 0.453761i \(-0.149918\pi\)
0.454220 + 0.890890i \(0.349918\pi\)
\(282\) 0 0
\(283\) −22.7567 + 11.5951i −1.35275 + 0.689258i −0.971903 0.235382i \(-0.924366\pi\)
−0.380843 + 0.924640i \(0.624366\pi\)
\(284\) 0 0
\(285\) 3.54701 11.1302i 0.210107 0.659299i
\(286\) 0 0
\(287\) 7.14088 + 1.13100i 0.421513 + 0.0667611i
\(288\) 0 0
\(289\) 13.5164 18.6037i 0.795081 1.09433i
\(290\) 0 0
\(291\) 2.89121 7.70537i 0.169486 0.451697i
\(292\) 0 0
\(293\) 14.6342 14.6342i 0.854941 0.854941i −0.135796 0.990737i \(-0.543359\pi\)
0.990737 + 0.135796i \(0.0433590\pi\)
\(294\) 0 0
\(295\) −9.10398 + 5.23311i −0.530054 + 0.304683i
\(296\) 0 0
\(297\) −5.30312 1.59114i −0.307718 0.0923272i
\(298\) 0 0
\(299\) −21.1479 −1.22302
\(300\) 0 0
\(301\) −40.4418 −2.33102
\(302\) 0 0
\(303\) 33.4789 3.77473i 1.92331 0.216853i
\(304\) 0 0
\(305\) 4.96368 + 4.48645i 0.284219 + 0.256894i
\(306\) 0 0
\(307\) −0.692742 + 0.692742i −0.0395369 + 0.0395369i −0.726599 0.687062i \(-0.758900\pi\)
0.687062 + 0.726599i \(0.258900\pi\)
\(308\) 0 0
\(309\) 9.32313 + 3.49822i 0.530375 + 0.199007i
\(310\) 0 0
\(311\) −8.16369 + 11.2364i −0.462920 + 0.637155i −0.975111 0.221716i \(-0.928834\pi\)
0.512191 + 0.858872i \(0.328834\pi\)
\(312\) 0 0
\(313\) 24.8253 + 3.93194i 1.40321 + 0.222246i 0.811711 0.584060i \(-0.198537\pi\)
0.591498 + 0.806306i \(0.298537\pi\)
\(314\) 0 0
\(315\) −14.3512 + 18.2089i −0.808600 + 1.02595i
\(316\) 0 0
\(317\) 0.679335 0.346138i 0.0381552 0.0194411i −0.434809 0.900523i \(-0.643184\pi\)
0.472964 + 0.881082i \(0.343184\pi\)
\(318\) 0 0
\(319\) 7.98693 + 2.59511i 0.447182 + 0.145298i
\(320\) 0 0
\(321\) −11.7812 + 14.7754i −0.657560 + 0.824682i
\(322\) 0 0
\(323\) 18.8403 2.98401i 1.04830 0.166035i
\(324\) 0 0
\(325\) 21.9089 + 8.50587i 1.21529 + 0.471821i
\(326\) 0 0
\(327\) −13.2684 + 12.1297i −0.733745 + 0.670775i
\(328\) 0 0
\(329\) −11.2974 34.7699i −0.622848 1.91693i
\(330\) 0 0
\(331\) 10.5348 32.4227i 0.579043 1.78211i −0.0429352 0.999078i \(-0.513671\pi\)
0.621979 0.783034i \(-0.286329\pi\)
\(332\) 0 0
\(333\) 1.28406 + 19.0023i 0.0703661 + 1.04132i
\(334\) 0 0
\(335\) 5.16509 + 13.5325i 0.282199 + 0.739357i
\(336\) 0 0
\(337\) 1.01297 6.39561i 0.0551797 0.348391i −0.944616 0.328178i \(-0.893565\pi\)
0.999796 0.0202133i \(-0.00643454\pi\)
\(338\) 0 0
\(339\) −7.77958 0.348791i −0.422529 0.0189437i
\(340\) 0 0
\(341\) 1.18956 + 1.63729i 0.0644182 + 0.0886641i
\(342\) 0 0
\(343\) 5.02238 + 5.02238i 0.271183 + 0.271183i
\(344\) 0 0
\(345\) −2.82313 17.1949i −0.151992 0.925744i
\(346\) 0 0
\(347\) −1.98524 + 3.89625i −0.106573 + 0.209162i −0.938134 0.346272i \(-0.887448\pi\)
0.831561 + 0.555433i \(0.187448\pi\)
\(348\) 0 0
\(349\) 1.78658i 0.0956333i 0.998856 + 0.0478167i \(0.0152263\pi\)
−0.998856 + 0.0478167i \(0.984774\pi\)
\(350\) 0 0
\(351\) −4.36656 24.0306i −0.233070 1.28266i
\(352\) 0 0
\(353\) −21.0739 10.7377i −1.12165 0.571511i −0.208050 0.978118i \(-0.566712\pi\)
−0.913603 + 0.406607i \(0.866712\pi\)
\(354\) 0 0
\(355\) −1.96770 + 0.414335i −0.104435 + 0.0219906i
\(356\) 0 0
\(357\) −37.0891 7.59109i −1.96296 0.401763i
\(358\) 0 0
\(359\) −0.704752 + 0.512032i −0.0371954 + 0.0270240i −0.606228 0.795291i \(-0.707318\pi\)
0.569032 + 0.822315i \(0.307318\pi\)
\(360\) 0 0
\(361\) −8.01123 5.82050i −0.421644 0.306342i
\(362\) 0 0
\(363\) −15.5559 + 7.06726i −0.816475 + 0.370935i
\(364\) 0 0
\(365\) −0.200117 3.96275i −0.0104746 0.207420i
\(366\) 0 0
\(367\) −4.22786 8.29765i −0.220693 0.433134i 0.753940 0.656943i \(-0.228151\pi\)
−0.974633 + 0.223809i \(0.928151\pi\)
\(368\) 0 0
\(369\) −4.72667 4.12831i −0.246061 0.214911i
\(370\) 0 0
\(371\) −34.1398 + 11.0927i −1.77245 + 0.575904i
\(372\) 0 0
\(373\) −1.84063 11.6213i −0.0953042 0.601727i −0.988401 0.151864i \(-0.951473\pi\)
0.893097 0.449864i \(-0.148527\pi\)
\(374\) 0 0
\(375\) −3.99122 + 18.9491i −0.206106 + 0.978530i
\(376\) 0 0
\(377\) 5.79530 + 36.5901i 0.298473 + 1.88449i
\(378\) 0 0
\(379\) 33.6144 10.9220i 1.72666 0.561024i 0.733696 0.679478i \(-0.237794\pi\)
0.992960 + 0.118453i \(0.0377936\pi\)
\(380\) 0 0
\(381\) 4.43483 + 16.0645i 0.227203 + 0.823009i
\(382\) 0 0
\(383\) 0.430527 + 0.844956i 0.0219989 + 0.0431753i 0.901744 0.432270i \(-0.142287\pi\)
−0.879746 + 0.475445i \(0.842287\pi\)
\(384\) 0 0
\(385\) −0.415315 8.22414i −0.0211664 0.419141i
\(386\) 0 0
\(387\) 29.7265 + 18.6721i 1.51108 + 0.949156i
\(388\) 0 0
\(389\) 11.4768 + 8.33838i 0.581897 + 0.422773i 0.839407 0.543503i \(-0.182902\pi\)
−0.257511 + 0.966275i \(0.582902\pi\)
\(390\) 0 0
\(391\) 23.0194 16.7246i 1.16414 0.845797i
\(392\) 0 0
\(393\) 5.55480 27.1400i 0.280203 1.36903i
\(394\) 0 0
\(395\) −19.0969 + 4.02120i −0.960871 + 0.202329i
\(396\) 0 0
\(397\) 15.5654 + 7.93097i 0.781205 + 0.398044i 0.798644 0.601804i \(-0.205551\pi\)
−0.0174386 + 0.999848i \(0.505551\pi\)
\(398\) 0 0
\(399\) −9.94798 15.0681i −0.498022 0.754347i
\(400\) 0 0
\(401\) 25.5008i 1.27345i 0.771092 + 0.636724i \(0.219711\pi\)
−0.771092 + 0.636724i \(0.780289\pi\)
\(402\) 0 0
\(403\) −4.05307 + 7.95459i −0.201898 + 0.396247i
\(404\) 0 0
\(405\) 18.9559 6.75831i 0.941925 0.335823i
\(406\) 0 0
\(407\) −4.78329 4.78329i −0.237099 0.237099i
\(408\) 0 0
\(409\) 14.7468 + 20.2972i 0.729183 + 1.00363i 0.999169 + 0.0407700i \(0.0129811\pi\)
−0.269985 + 0.962864i \(0.587019\pi\)
\(410\) 0 0
\(411\) −0.597321 + 13.3229i −0.0294637 + 0.657171i
\(412\) 0 0
\(413\) −2.53900 + 16.0306i −0.124936 + 0.788816i
\(414\) 0 0
\(415\) −4.26467 11.1734i −0.209344 0.548478i
\(416\) 0 0
\(417\) 12.9096 + 7.32389i 0.632188 + 0.358652i
\(418\) 0 0
\(419\) 0.988493 3.04227i 0.0482910 0.148625i −0.924003 0.382385i \(-0.875103\pi\)
0.972294 + 0.233760i \(0.0751030\pi\)
\(420\) 0 0
\(421\) 5.67396 + 17.4626i 0.276532 + 0.851077i 0.988810 + 0.149180i \(0.0476634\pi\)
−0.712278 + 0.701897i \(0.752337\pi\)
\(422\) 0 0
\(423\) −7.74928 + 30.7735i −0.376783 + 1.49626i
\(424\) 0 0
\(425\) −30.5744 + 8.06779i −1.48308 + 0.391345i
\(426\) 0 0
\(427\) 10.2141 1.61776i 0.494297 0.0782890i
\(428\) 0 0
\(429\) 6.78273 + 5.40821i 0.327473 + 0.261111i
\(430\) 0 0
\(431\) 1.65426 + 0.537501i 0.0796828 + 0.0258905i 0.348587 0.937276i \(-0.386662\pi\)
−0.268904 + 0.963167i \(0.586662\pi\)
\(432\) 0 0
\(433\) 23.5980 12.0238i 1.13405 0.577825i 0.216827 0.976210i \(-0.430429\pi\)
0.917218 + 0.398385i \(0.130429\pi\)
\(434\) 0 0
\(435\) −28.9770 + 9.59661i −1.38934 + 0.460122i
\(436\) 0 0
\(437\) 13.4034 + 2.12288i 0.641169 + 0.101551i
\(438\) 0 0
\(439\) −5.66588 + 7.79842i −0.270418 + 0.372198i −0.922531 0.385924i \(-0.873883\pi\)
0.652113 + 0.758122i \(0.273883\pi\)
\(440\) 0 0
\(441\) 3.30322 + 14.4623i 0.157296 + 0.688679i
\(442\) 0 0
\(443\) −2.72820 + 2.72820i −0.129621 + 0.129621i −0.768941 0.639320i \(-0.779216\pi\)
0.639320 + 0.768941i \(0.279216\pi\)
\(444\) 0 0
\(445\) 3.99106 + 3.60734i 0.189194 + 0.171004i
\(446\) 0 0
\(447\) 1.05302 + 9.33941i 0.0498059 + 0.441739i
\(448\) 0 0
\(449\) 21.4808 1.01374 0.506870 0.862022i \(-0.330802\pi\)
0.506870 + 0.862022i \(0.330802\pi\)
\(450\) 0 0
\(451\) 2.22899 0.104959
\(452\) 0 0
\(453\) −2.99865 26.5957i −0.140889 1.24957i
\(454\) 0 0
\(455\) 31.4935 18.1029i 1.47644 0.848678i
\(456\) 0 0
\(457\) −4.66772 + 4.66772i −0.218347 + 0.218347i −0.807801 0.589455i \(-0.799343\pi\)
0.589455 + 0.807801i \(0.299343\pi\)
\(458\) 0 0
\(459\) 23.7573 + 22.7039i 1.10889 + 1.05973i
\(460\) 0 0
\(461\) 8.79509 12.1054i 0.409628 0.563805i −0.553499 0.832850i \(-0.686708\pi\)
0.963128 + 0.269045i \(0.0867079\pi\)
\(462\) 0 0
\(463\) 25.9007 + 4.10227i 1.20371 + 0.190648i 0.725890 0.687811i \(-0.241428\pi\)
0.477817 + 0.878459i \(0.341428\pi\)
\(464\) 0 0
\(465\) −7.00877 2.23357i −0.325024 0.103579i
\(466\) 0 0
\(467\) 15.6353 7.96659i 0.723516 0.368650i −0.0531298 0.998588i \(-0.516920\pi\)
0.776645 + 0.629938i \(0.216920\pi\)
\(468\) 0 0
\(469\) 21.2922 + 6.91826i 0.983184 + 0.319456i
\(470\) 0 0
\(471\) −10.4655 8.34467i −0.482226 0.384502i
\(472\) 0 0
\(473\) −12.3148 + 1.95047i −0.566233 + 0.0896825i
\(474\) 0 0
\(475\) −13.0318 7.59021i −0.597941 0.348263i
\(476\) 0 0
\(477\) 30.2158 + 7.60884i 1.38349 + 0.348385i
\(478\) 0 0
\(479\) 4.12695 + 12.7015i 0.188565 + 0.580345i 0.999992 0.00411038i \(-0.00130838\pi\)
−0.811426 + 0.584455i \(0.801308\pi\)
\(480\) 0 0
\(481\) 9.22133 28.3804i 0.420457 1.29403i
\(482\) 0 0
\(483\) −23.4256 13.2898i −1.06590 0.604707i
\(484\) 0 0
\(485\) −8.89967 5.80363i −0.404113 0.263529i
\(486\) 0 0
\(487\) −3.73244 + 23.5657i −0.169133 + 1.06786i 0.746364 + 0.665538i \(0.231798\pi\)
−0.915497 + 0.402325i \(0.868202\pi\)
\(488\) 0 0
\(489\) −0.951912 + 21.2319i −0.0430469 + 0.960138i
\(490\) 0 0
\(491\) −2.44616 3.36685i −0.110393 0.151944i 0.750245 0.661160i \(-0.229935\pi\)
−0.860639 + 0.509216i \(0.829935\pi\)
\(492\) 0 0
\(493\) −35.2449 35.2449i −1.58735 1.58735i
\(494\) 0 0
\(495\) −3.49184 + 6.23686i −0.156946 + 0.280326i
\(496\) 0 0
\(497\) −1.41102 + 2.76928i −0.0632928 + 0.124219i
\(498\) 0 0
\(499\) 3.23858i 0.144979i 0.997369 + 0.0724894i \(0.0230943\pi\)
−0.997369 + 0.0724894i \(0.976906\pi\)
\(500\) 0 0
\(501\) 9.28755 + 14.0677i 0.414937 + 0.628500i
\(502\) 0 0
\(503\) 16.4890 + 8.40155i 0.735207 + 0.374607i 0.781155 0.624337i \(-0.214631\pi\)
−0.0459478 + 0.998944i \(0.514631\pi\)
\(504\) 0 0
\(505\) 4.62878 43.2479i 0.205978 1.92451i
\(506\) 0 0
\(507\) −3.15838 + 15.4314i −0.140268 + 0.685333i
\(508\) 0 0
\(509\) −5.30145 + 3.85173i −0.234982 + 0.170725i −0.699045 0.715078i \(-0.746391\pi\)
0.464063 + 0.885802i \(0.346391\pi\)
\(510\) 0 0
\(511\) −4.96151 3.60475i −0.219484 0.159465i
\(512\) 0 0
\(513\) 0.355229 + 15.6687i 0.0156837 + 0.691790i
\(514\) 0 0
\(515\) 7.02212 10.7682i 0.309431 0.474503i
\(516\) 0 0
\(517\) −5.11706 10.0428i −0.225048 0.441681i
\(518\) 0 0
\(519\) −7.82323 28.3385i −0.343402 1.24392i
\(520\) 0 0
\(521\) 5.03678 1.63655i 0.220666 0.0716986i −0.196598 0.980484i \(-0.562989\pi\)
0.417263 + 0.908786i \(0.362989\pi\)
\(522\) 0 0
\(523\) −3.33523 21.0578i −0.145839 0.920794i −0.946741 0.321997i \(-0.895646\pi\)
0.800901 0.598797i \(-0.204354\pi\)
\(524\) 0 0
\(525\) 18.9233 + 23.1900i 0.825880 + 1.01209i
\(526\) 0 0
\(527\) −1.87905 11.8638i −0.0818525 0.516797i
\(528\) 0 0
\(529\) −2.62266 + 0.852155i −0.114029 + 0.0370502i
\(530\) 0 0
\(531\) 9.26768 10.6110i 0.402183 0.460476i
\(532\) 0 0
\(533\) 4.46401 + 8.76111i 0.193358 + 0.379486i
\(534\) 0 0
\(535\) 15.3170 + 18.9887i 0.662211 + 0.820952i
\(536\) 0 0
\(537\) −17.9473 + 8.15371i −0.774485 + 0.351859i
\(538\) 0 0
\(539\) −4.26268 3.09702i −0.183607 0.133398i
\(540\) 0 0
\(541\) 23.2705 16.9070i 1.00048 0.726890i 0.0382880 0.999267i \(-0.487810\pi\)
0.962191 + 0.272376i \(0.0878096\pi\)
\(542\) 0 0
\(543\) 4.74637 + 0.971449i 0.203686 + 0.0416888i
\(544\) 0 0
\(545\) 11.5660 + 20.1212i 0.495432 + 0.861898i
\(546\) 0 0
\(547\) 20.6603 + 10.5270i 0.883372 + 0.450100i 0.835970 0.548776i \(-0.184906\pi\)
0.0474020 + 0.998876i \(0.484906\pi\)
\(548\) 0 0
\(549\) −8.25477 3.52678i −0.352305 0.150519i
\(550\) 0 0
\(551\) 23.7722i 1.01273i
\(552\) 0 0
\(553\) −13.6942 + 26.8764i −0.582337 + 1.14290i
\(554\) 0 0
\(555\) 24.3064 + 3.70905i 1.03175 + 0.157440i
\(556\) 0 0
\(557\) −29.9868 29.9868i −1.27058 1.27058i −0.945784 0.324797i \(-0.894704\pi\)
−0.324797 0.945784i \(-0.605296\pi\)
\(558\) 0 0
\(559\) −32.3292 44.4973i −1.36738 1.88204i
\(560\) 0 0
\(561\) −11.6600 0.522764i −0.492284 0.0220711i
\(562\) 0 0
\(563\) −5.14467 + 32.4822i −0.216822 + 1.36896i 0.603639 + 0.797258i \(0.293717\pi\)
−0.820461 + 0.571702i \(0.806283\pi\)
\(564\) 0 0
\(565\) −2.62051 + 9.70595i −0.110246 + 0.408332i
\(566\) 0 0
\(567\) 10.2645 29.3628i 0.431069 1.23312i
\(568\) 0 0
\(569\) 4.11085 12.6519i 0.172336 0.530395i −0.827166 0.561958i \(-0.810048\pi\)
0.999502 + 0.0315628i \(0.0100484\pi\)
\(570\) 0 0
\(571\) 3.97739 + 12.2411i 0.166449 + 0.512276i 0.999140 0.0414611i \(-0.0132013\pi\)
−0.832692 + 0.553737i \(0.813201\pi\)
\(572\) 0 0
\(573\) −15.7273 + 14.3776i −0.657018 + 0.600632i
\(574\) 0 0
\(575\) −22.4603 1.26284i −0.936659 0.0526641i
\(576\) 0 0
\(577\) 8.34723 1.32207i 0.347500 0.0550386i 0.0197550 0.999805i \(-0.493711\pi\)
0.327745 + 0.944766i \(0.393711\pi\)
\(578\) 0 0
\(579\) 3.76224 4.71843i 0.156353 0.196091i
\(580\) 0 0
\(581\) −17.5804 5.71221i −0.729357 0.236982i
\(582\) 0 0
\(583\) −9.86078 + 5.02432i −0.408392 + 0.208086i
\(584\) 0 0
\(585\) −31.5073 1.23419i −1.30267 0.0510274i
\(586\) 0 0
\(587\) −22.1842 3.51364i −0.915641 0.145023i −0.319207 0.947685i \(-0.603416\pi\)
−0.596434 + 0.802662i \(0.703416\pi\)
\(588\) 0 0
\(589\) 3.36730 4.63469i 0.138747 0.190969i
\(590\) 0 0
\(591\) −16.4468 6.17118i −0.676532 0.253848i
\(592\) 0 0
\(593\) 12.6961 12.6961i 0.521368 0.521368i −0.396616 0.917984i \(-0.629816\pi\)
0.917984 + 0.396616i \(0.129816\pi\)
\(594\) 0 0
\(595\) −19.9639 + 44.6111i −0.818442 + 1.82888i
\(596\) 0 0
\(597\) −23.7697 + 2.68003i −0.972830 + 0.109686i
\(598\) 0 0
\(599\) −20.3237 −0.830405 −0.415202 0.909729i \(-0.636289\pi\)
−0.415202 + 0.909729i \(0.636289\pi\)
\(600\) 0 0
\(601\) −19.3802 −0.790537 −0.395268 0.918566i \(-0.629348\pi\)
−0.395268 + 0.918566i \(0.629348\pi\)
\(602\) 0 0
\(603\) −12.4565 14.9159i −0.507269 0.607423i
\(604\) 0 0
\(605\) 4.54504 + 21.5847i 0.184782 + 0.877542i
\(606\) 0 0
\(607\) −4.21561 + 4.21561i −0.171106 + 0.171106i −0.787465 0.616359i \(-0.788607\pi\)
0.616359 + 0.787465i \(0.288607\pi\)
\(608\) 0 0
\(609\) −16.5745 + 44.1728i −0.671633 + 1.78997i
\(610\) 0 0
\(611\) 29.2255 40.2255i 1.18234 1.62735i
\(612\) 0 0
\(613\) 26.2327 + 4.15485i 1.05953 + 0.167813i 0.661793 0.749687i \(-0.269796\pi\)
0.397736 + 0.917500i \(0.369796\pi\)
\(614\) 0 0
\(615\) −6.52754 + 4.79915i −0.263216 + 0.193520i
\(616\) 0 0
\(617\) 21.7016 11.0575i 0.873673 0.445159i 0.0411527 0.999153i \(-0.486897\pi\)
0.832521 + 0.553994i \(0.186897\pi\)
\(618\) 0 0
\(619\) −1.60460 0.521366i −0.0644943 0.0209555i 0.276592 0.960987i \(-0.410795\pi\)
−0.341086 + 0.940032i \(0.610795\pi\)
\(620\) 0 0
\(621\) 11.0829 + 20.5843i 0.444742 + 0.826019i
\(622\) 0 0
\(623\) 8.21271 1.30077i 0.329035 0.0521141i
\(624\) 0 0
\(625\) 22.7606 + 10.3420i 0.910423 + 0.413679i
\(626\) 0 0
\(627\) −3.75594 4.10854i −0.149998 0.164079i
\(628\) 0 0
\(629\) 12.4069 + 38.1844i 0.494694 + 1.52251i
\(630\) 0 0
\(631\) −12.4398 + 38.2857i −0.495219 + 1.52413i 0.321395 + 0.946945i \(0.395848\pi\)
−0.816615 + 0.577183i \(0.804152\pi\)
\(632\) 0 0
\(633\) 4.27324 7.53234i 0.169846 0.299384i
\(634\) 0 0
\(635\) 21.4876 1.08511i 0.852708 0.0430613i
\(636\) 0 0
\(637\) 3.63603 22.9570i 0.144065 0.909589i
\(638\) 0 0
\(639\) 2.31575 1.38407i 0.0916095 0.0547530i
\(640\) 0 0
\(641\) −2.73450 3.76371i −0.108006 0.148658i 0.751592 0.659628i \(-0.229286\pi\)
−0.859598 + 0.510970i \(0.829286\pi\)
\(642\) 0 0
\(643\) −23.9228 23.9228i −0.943425 0.943425i 0.0550581 0.998483i \(-0.482466\pi\)
−0.998483 + 0.0550581i \(0.982466\pi\)
\(644\) 0 0
\(645\) 31.8640 32.2263i 1.25464 1.26891i
\(646\) 0 0
\(647\) −7.38947 + 14.5027i −0.290510 + 0.570158i −0.989425 0.145047i \(-0.953667\pi\)
0.698915 + 0.715205i \(0.253667\pi\)
\(648\) 0 0
\(649\) 5.00388i 0.196419i
\(650\) 0 0
\(651\) −9.48843 + 6.26429i −0.371881 + 0.245517i
\(652\) 0 0
\(653\) 5.02081 + 2.55823i 0.196479 + 0.100111i 0.549462 0.835519i \(-0.314833\pi\)
−0.352983 + 0.935630i \(0.614833\pi\)
\(654\) 0 0
\(655\) −32.6443 14.6087i −1.27552 0.570808i
\(656\) 0 0
\(657\) 1.98260 + 4.94039i 0.0773487 + 0.192743i
\(658\) 0 0
\(659\) 13.2174 9.60298i 0.514875 0.374079i −0.299794 0.954004i \(-0.596918\pi\)
0.814670 + 0.579925i \(0.196918\pi\)
\(660\) 0 0
\(661\) 31.5545 + 22.9257i 1.22733 + 0.891706i 0.996687 0.0813326i \(-0.0259176\pi\)
0.230641 + 0.973039i \(0.425918\pi\)
\(662\) 0 0
\(663\) −21.2967 46.8767i −0.827096 1.82054i
\(664\) 0 0
\(665\) −21.7775 + 8.31206i −0.844494 + 0.322328i
\(666\) 0 0
\(667\) −16.0984 31.5950i −0.623334 1.22336i
\(668\) 0 0
\(669\) −30.5600 + 8.43653i −1.18152 + 0.326175i
\(670\) 0 0
\(671\) 3.03225 0.985237i 0.117059 0.0380347i
\(672\) 0 0
\(673\) −2.05812 12.9944i −0.0793346 0.500899i −0.995075 0.0991277i \(-0.968395\pi\)
0.915740 0.401771i \(-0.131605\pi\)
\(674\) 0 0
\(675\) −3.20255 25.7826i −0.123266 0.992374i
\(676\) 0 0
\(677\) 1.37035 + 8.65208i 0.0526670 + 0.332526i 0.999927 + 0.0120611i \(0.00383925\pi\)
−0.947260 + 0.320465i \(0.896161\pi\)
\(678\) 0 0
\(679\) −15.6183 + 5.07469i −0.599375 + 0.194749i
\(680\) 0 0
\(681\) 3.37775 0.932476i 0.129436 0.0357325i
\(682\) 0 0
\(683\) 0.144185 + 0.282980i 0.00551710 + 0.0108279i 0.893749 0.448568i \(-0.148066\pi\)
−0.888232 + 0.459396i \(0.848066\pi\)
\(684\) 0 0
\(685\) 16.6219 + 4.48775i 0.635091 + 0.171468i
\(686\) 0 0
\(687\) −19.4014 42.7050i −0.740211 1.62930i
\(688\) 0 0
\(689\) −39.4965 28.6959i −1.50470 1.09323i
\(690\) 0 0
\(691\) −24.5745 + 17.8544i −0.934857 + 0.679214i −0.947177 0.320711i \(-0.896078\pi\)
0.0123200 + 0.999924i \(0.496078\pi\)
\(692\) 0 0
\(693\) 4.11462 + 10.2531i 0.156301 + 0.389483i
\(694\) 0 0
\(695\) 12.8486 14.2154i 0.487376 0.539219i
\(696\) 0 0
\(697\) −11.7876 6.00610i −0.446489 0.227497i
\(698\) 0 0
\(699\) 42.4922 28.0535i 1.60720 1.06108i
\(700\) 0 0
\(701\) 35.6884i 1.34793i −0.738763 0.673965i \(-0.764590\pi\)
0.738763 0.673965i \(-0.235410\pi\)
\(702\) 0 0
\(703\) −8.69328 + 17.0615i −0.327873 + 0.643488i
\(704\) 0 0
\(705\) 36.6079 + 18.3927i 1.37873 + 0.692711i
\(706\) 0 0
\(707\) −47.5368 47.5368i −1.78780 1.78780i
\(708\) 0 0
\(709\) −16.4858 22.6908i −0.619137 0.852169i 0.378153 0.925743i \(-0.376559\pi\)
−0.997290 + 0.0735741i \(0.976559\pi\)
\(710\) 0 0
\(711\) 22.4748 13.4327i 0.842870 0.503765i
\(712\) 0 0
\(713\) 1.33679 8.44015i 0.0500631 0.316086i
\(714\) 0 0
\(715\) 8.71687 7.03135i 0.325992 0.262958i
\(716\) 0 0
\(717\) −3.36905 + 5.93854i −0.125820 + 0.221779i
\(718\) 0 0
\(719\) −15.8013 + 48.6313i −0.589288 + 1.81364i −0.00796379 + 0.999968i \(0.502535\pi\)
−0.581324 + 0.813672i \(0.697465\pi\)
\(720\) 0 0
\(721\) −6.14013 18.8974i −0.228670 0.703775i
\(722\) 0 0
\(723\) −12.2628 13.4140i −0.456060 0.498874i
\(724\) 0 0
\(725\) 3.96997 + 39.2068i 0.147441 + 1.45610i
\(726\) 0 0
\(727\) −28.2055 + 4.46731i −1.04608 + 0.165684i −0.655741 0.754986i \(-0.727644\pi\)
−0.390343 + 0.920669i \(0.627644\pi\)
\(728\) 0 0
\(729\) −21.1018 + 16.8438i −0.781548 + 0.623845i
\(730\) 0 0
\(731\) 70.3802 + 22.8679i 2.60310 + 0.845800i
\(732\) 0 0
\(733\) −9.46545 + 4.82289i −0.349615 + 0.178138i −0.619975 0.784622i \(-0.712857\pi\)
0.270360 + 0.962759i \(0.412857\pi\)
\(734\) 0 0
\(735\) 19.1512 0.108255i 0.706403 0.00399303i
\(736\) 0 0
\(737\) 6.81727 + 1.07975i 0.251117 + 0.0397731i
\(738\) 0 0
\(739\) −22.5311 + 31.0114i −0.828820 + 1.14077i 0.159321 + 0.987227i \(0.449070\pi\)
−0.988141 + 0.153547i \(0.950930\pi\)
\(740\) 0 0
\(741\) 8.62668 22.9910i 0.316909 0.844596i
\(742\) 0 0
\(743\) −21.5734 + 21.5734i −0.791451 + 0.791451i −0.981730 0.190279i \(-0.939061\pi\)
0.190279 + 0.981730i \(0.439061\pi\)
\(744\) 0 0
\(745\) 12.0646 + 1.29126i 0.442014 + 0.0473082i
\(746\) 0 0
\(747\) 10.2850 + 12.3156i 0.376308 + 0.450606i
\(748\) 0 0
\(749\) 37.7077 1.37781
\(750\) 0 0
\(751\) 18.5240 0.675951 0.337975 0.941155i \(-0.390258\pi\)
0.337975 + 0.941155i \(0.390258\pi\)
\(752\) 0 0
\(753\) 2.02356 0.228155i 0.0737425 0.00831445i
\(754\) 0 0
\(755\) −34.3562 3.67710i −1.25035 0.133824i
\(756\) 0 0
\(757\) 26.4091 26.4091i 0.959855 0.959855i −0.0393695 0.999225i \(-0.512535\pi\)
0.999225 + 0.0393695i \(0.0125349\pi\)
\(758\) 0 0
\(759\) −7.77420 2.91703i −0.282186 0.105882i
\(760\) 0 0
\(761\) 6.87014 9.45593i 0.249042 0.342777i −0.666133 0.745833i \(-0.732052\pi\)
0.915176 + 0.403055i \(0.132052\pi\)
\(762\) 0 0
\(763\) 35.4302 + 5.61159i 1.28266 + 0.203153i
\(764\) 0 0
\(765\) 35.2715 23.5737i 1.27524 0.852308i
\(766\) 0 0
\(767\) −19.6679 + 10.0213i −0.710166 + 0.361848i
\(768\) 0 0
\(769\) −27.7100 9.00353i −0.999249 0.324676i −0.236683 0.971587i \(-0.576060\pi\)
−0.762565 + 0.646911i \(0.776060\pi\)
\(770\) 0 0
\(771\) −28.9650 + 36.3266i −1.04315 + 1.30827i
\(772\) 0 0
\(773\) −31.5458 + 4.99637i −1.13462 + 0.179707i −0.695368 0.718654i \(-0.744758\pi\)
−0.439257 + 0.898361i \(0.644758\pi\)
\(774\) 0 0
\(775\) −4.77959 + 8.20619i −0.171688 + 0.294775i
\(776\) 0 0
\(777\) 28.0493 25.6421i 1.00626 0.919905i
\(778\) 0 0
\(779\) −1.94978 6.00081i −0.0698582 0.215001i
\(780\) 0 0
\(781\) −0.296104 + 0.911315i −0.0105954 + 0.0326094i
\(782\) 0 0
\(783\) 32.5777 24.8165i 1.16423 0.886868i
\(784\) 0 0
\(785\) −13.4498 + 10.8491i −0.480044 + 0.387222i
\(786\) 0 0
\(787\) 0.919135 5.80319i 0.0327636 0.206861i −0.965876 0.259005i \(-0.916605\pi\)
0.998640 + 0.0521437i \(0.0166054\pi\)
\(788\) 0 0
\(789\) 36.6846 + 1.64472i 1.30601 + 0.0585537i
\(790\) 0 0
\(791\) 9.13359 + 12.5713i 0.324753 + 0.446984i
\(792\) 0 0
\(793\) 9.94520 + 9.94520i 0.353164 + 0.353164i
\(794\) 0 0
\(795\) 18.0594 35.9444i 0.640502 1.27482i
\(796\) 0 0
\(797\)