Properties

Label 300.2.o.a.229.3
Level $300$
Weight $2$
Character 300.229
Analytic conductor $2.396$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.o (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 229.3
Character \(\chi\) \(=\) 300.229
Dual form 300.2.o.a.169.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.587785 + 0.809017i) q^{3} +(1.99921 - 1.00158i) q^{5} +3.80992i q^{7} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.587785 + 0.809017i) q^{3} +(1.99921 - 1.00158i) q^{5} +3.80992i q^{7} +(-0.309017 - 0.951057i) q^{9} +(0.0589397 - 0.181398i) q^{11} +(1.59724 - 0.518974i) q^{13} +(-0.364813 + 2.20611i) q^{15} +(2.70572 + 3.72410i) q^{17} +(-2.13682 + 1.55249i) q^{19} +(-3.08229 - 2.23941i) q^{21} +(6.04461 + 1.96401i) q^{23} +(2.99369 - 4.00473i) q^{25} +(0.951057 + 0.309017i) q^{27} +(2.03878 + 1.48126i) q^{29} +(-3.03331 + 2.20383i) q^{31} +(0.112110 + 0.154306i) q^{33} +(3.81593 + 7.61682i) q^{35} +(-11.2820 + 3.66574i) q^{37} +(-0.518974 + 1.59724i) q^{39} +(-2.22169 - 6.83765i) q^{41} -9.22619i q^{43} +(-1.57035 - 1.59186i) q^{45} +(2.67353 - 3.67980i) q^{47} -7.51545 q^{49} -4.60324 q^{51} +(5.54285 - 7.62908i) q^{53} +(-0.0638510 - 0.421685i) q^{55} -2.64126i q^{57} +(-2.20656 - 6.79109i) q^{59} +(2.94497 - 9.06368i) q^{61} +(3.62344 - 1.17733i) q^{63} +(2.67342 - 2.63729i) q^{65} +(3.55709 + 4.89591i) q^{67} +(-5.14185 + 3.73577i) q^{69} +(-10.7586 - 7.81655i) q^{71} +(-4.95645 - 1.61045i) q^{73} +(1.48025 + 4.77586i) q^{75} +(0.691110 + 0.224555i) q^{77} +(-2.51740 - 1.82900i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-2.74988 - 3.78488i) q^{83} +(9.13928 + 4.73528i) q^{85} +(-2.39673 + 0.778746i) q^{87} +(-4.30840 + 13.2599i) q^{89} +(1.97725 + 6.08534i) q^{91} -3.74937i q^{93} +(-2.71702 + 5.24395i) q^{95} +(-3.93527 + 5.41643i) q^{97} -0.190733 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 2q^{5} + 6q^{9} + O(q^{10}) \) \( 24q - 2q^{5} + 6q^{9} - 6q^{11} + 4q^{15} + 10q^{17} + 10q^{19} - 4q^{21} + 40q^{23} - 4q^{25} + 4q^{29} + 6q^{31} + 10q^{33} - 6q^{35} - 10q^{41} + 2q^{45} - 40q^{47} - 56q^{49} + 16q^{51} - 60q^{53} - 62q^{55} - 36q^{59} - 12q^{61} - 10q^{63} + 20q^{67} + 4q^{69} + 40q^{71} + 60q^{73} + 8q^{75} - 40q^{77} + 8q^{79} - 6q^{81} - 50q^{83} + 34q^{85} - 20q^{87} - 30q^{91} - 60q^{95} - 40q^{97} - 4q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{10}\right)\)

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
\(3\) −0.587785 + 0.809017i −0.339358 + 0.467086i
\(4\) 0 0
\(5\) 1.99921 1.00158i 0.894074 0.447919i
\(6\) 0 0
\(7\) 3.80992i 1.44001i 0.693968 + 0.720006i \(0.255861\pi\)
−0.693968 + 0.720006i \(0.744139\pi\)
\(8\) 0 0
\(9\) −0.309017 0.951057i −0.103006 0.317019i
\(10\) 0 0
\(11\) 0.0589397 0.181398i 0.0177710 0.0546935i −0.941778 0.336236i \(-0.890846\pi\)
0.959549 + 0.281542i \(0.0908460\pi\)
\(12\) 0 0
\(13\) 1.59724 0.518974i 0.442994 0.143937i −0.0790227 0.996873i \(-0.525180\pi\)
0.522016 + 0.852935i \(0.325180\pi\)
\(14\) 0 0
\(15\) −0.364813 + 2.20611i −0.0941944 + 0.569615i
\(16\) 0 0
\(17\) 2.70572 + 3.72410i 0.656233 + 0.903227i 0.999349 0.0360656i \(-0.0114825\pi\)
−0.343116 + 0.939293i \(0.611483\pi\)
\(18\) 0 0
\(19\) −2.13682 + 1.55249i −0.490221 + 0.356166i −0.805269 0.592909i \(-0.797979\pi\)
0.315049 + 0.949076i \(0.397979\pi\)
\(20\) 0 0
\(21\) −3.08229 2.23941i −0.672610 0.488680i
\(22\) 0 0
\(23\) 6.04461 + 1.96401i 1.26039 + 0.409525i 0.861632 0.507533i \(-0.169442\pi\)
0.398755 + 0.917057i \(0.369442\pi\)
\(24\) 0 0
\(25\) 2.99369 4.00473i 0.598737 0.800946i
\(26\) 0 0
\(27\) 0.951057 + 0.309017i 0.183031 + 0.0594703i
\(28\) 0 0
\(29\) 2.03878 + 1.48126i 0.378593 + 0.275064i 0.760765 0.649027i \(-0.224824\pi\)
−0.382172 + 0.924091i \(0.624824\pi\)
\(30\) 0 0
\(31\) −3.03331 + 2.20383i −0.544798 + 0.395819i −0.825864 0.563870i \(-0.809312\pi\)
0.281066 + 0.959688i \(0.409312\pi\)
\(32\) 0 0
\(33\) 0.112110 + 0.154306i 0.0195158 + 0.0268612i
\(34\) 0 0
\(35\) 3.81593 + 7.61682i 0.645009 + 1.28748i
\(36\) 0 0
\(37\) −11.2820 + 3.66574i −1.85474 + 0.602643i −0.858839 + 0.512245i \(0.828814\pi\)
−0.995906 + 0.0903980i \(0.971186\pi\)
\(38\) 0 0
\(39\) −0.518974 + 1.59724i −0.0831023 + 0.255763i
\(40\) 0 0
\(41\) −2.22169 6.83765i −0.346969 1.06786i −0.960521 0.278207i \(-0.910260\pi\)
0.613552 0.789655i \(-0.289740\pi\)
\(42\) 0 0
\(43\) 9.22619i 1.40698i −0.710705 0.703491i \(-0.751624\pi\)
0.710705 0.703491i \(-0.248376\pi\)
\(44\) 0 0
\(45\) −1.57035 1.59186i −0.234093 0.237300i
\(46\) 0 0
\(47\) 2.67353 3.67980i 0.389975 0.536754i −0.568218 0.822878i \(-0.692367\pi\)
0.958193 + 0.286124i \(0.0923670\pi\)
\(48\) 0 0
\(49\) −7.51545 −1.07364
\(50\) 0 0
\(51\) −4.60324 −0.644583
\(52\) 0 0
\(53\) 5.54285 7.62908i 0.761369 1.04793i −0.235730 0.971819i \(-0.575748\pi\)
0.997099 0.0761162i \(-0.0242520\pi\)
\(54\) 0 0
\(55\) −0.0638510 0.421685i −0.00860967 0.0568600i
\(56\) 0 0
\(57\) 2.64126i 0.349843i
\(58\) 0 0
\(59\) −2.20656 6.79109i −0.287269 0.884124i −0.985709 0.168456i \(-0.946122\pi\)
0.698440 0.715669i \(-0.253878\pi\)
\(60\) 0 0
\(61\) 2.94497 9.06368i 0.377064 1.16049i −0.565011 0.825084i \(-0.691128\pi\)
0.942075 0.335402i \(-0.108872\pi\)
\(62\) 0 0
\(63\) 3.62344 1.17733i 0.456511 0.148329i
\(64\) 0 0
\(65\) 2.67342 2.63729i 0.331597 0.327116i
\(66\) 0 0
\(67\) 3.55709 + 4.89591i 0.434567 + 0.598131i 0.968994 0.247084i \(-0.0794724\pi\)
−0.534427 + 0.845215i \(0.679472\pi\)
\(68\) 0 0
\(69\) −5.14185 + 3.73577i −0.619006 + 0.449734i
\(70\) 0 0
\(71\) −10.7586 7.81655i −1.27681 0.927654i −0.277355 0.960768i \(-0.589458\pi\)
−0.999452 + 0.0331133i \(0.989458\pi\)
\(72\) 0 0
\(73\) −4.95645 1.61045i −0.580109 0.188489i 0.00424038 0.999991i \(-0.498650\pi\)
−0.584349 + 0.811502i \(0.698650\pi\)
\(74\) 0 0
\(75\) 1.48025 + 4.77586i 0.170924 + 0.551469i
\(76\) 0 0
\(77\) 0.691110 + 0.224555i 0.0787593 + 0.0255904i
\(78\) 0 0
\(79\) −2.51740 1.82900i −0.283230 0.205779i 0.437095 0.899415i \(-0.356007\pi\)
−0.720325 + 0.693637i \(0.756007\pi\)
\(80\) 0 0
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) 0 0
\(83\) −2.74988 3.78488i −0.301838 0.415445i 0.630976 0.775802i \(-0.282655\pi\)
−0.932814 + 0.360358i \(0.882655\pi\)
\(84\) 0 0
\(85\) 9.13928 + 4.73528i 0.991294 + 0.513613i
\(86\) 0 0
\(87\) −2.39673 + 0.778746i −0.256957 + 0.0834904i
\(88\) 0 0
\(89\) −4.30840 + 13.2599i −0.456690 + 1.40555i 0.412451 + 0.910980i \(0.364673\pi\)
−0.869140 + 0.494566i \(0.835327\pi\)
\(90\) 0 0
\(91\) 1.97725 + 6.08534i 0.207272 + 0.637917i
\(92\) 0 0
\(93\) 3.74937i 0.388792i
\(94\) 0 0
\(95\) −2.71702 + 5.24395i −0.278760 + 0.538018i
\(96\) 0 0
\(97\) −3.93527 + 5.41643i −0.399566 + 0.549955i −0.960635 0.277814i \(-0.910390\pi\)
0.561069 + 0.827769i \(0.310390\pi\)
\(98\) 0 0
\(99\) −0.190733 −0.0191694
\(100\) 0 0
\(101\) 10.5147 1.04625 0.523127 0.852255i \(-0.324765\pi\)
0.523127 + 0.852255i \(0.324765\pi\)
\(102\) 0 0
\(103\) −7.62055 + 10.4888i −0.750875 + 1.03349i 0.247044 + 0.969004i \(0.420541\pi\)
−0.997919 + 0.0644861i \(0.979459\pi\)
\(104\) 0 0
\(105\) −8.40508 1.38991i −0.820252 0.135641i
\(106\) 0 0
\(107\) 9.64606i 0.932520i 0.884648 + 0.466260i \(0.154399\pi\)
−0.884648 + 0.466260i \(0.845601\pi\)
\(108\) 0 0
\(109\) −6.31798 19.4447i −0.605153 1.86247i −0.495738 0.868472i \(-0.665102\pi\)
−0.109414 0.993996i \(-0.534898\pi\)
\(110\) 0 0
\(111\) 3.66574 11.2820i 0.347936 1.07084i
\(112\) 0 0
\(113\) 3.84623 1.24972i 0.361823 0.117564i −0.122463 0.992473i \(-0.539079\pi\)
0.484286 + 0.874910i \(0.339079\pi\)
\(114\) 0 0
\(115\) 14.0515 2.12767i 1.31031 0.198406i
\(116\) 0 0
\(117\) −0.987147 1.35869i −0.0912617 0.125611i
\(118\) 0 0
\(119\) −14.1885 + 10.3086i −1.30066 + 0.944984i
\(120\) 0 0
\(121\) 8.86976 + 6.44425i 0.806341 + 0.585841i
\(122\) 0 0
\(123\) 6.83765 + 2.22169i 0.616530 + 0.200323i
\(124\) 0 0
\(125\) 1.97396 11.0047i 0.176556 0.984291i
\(126\) 0 0
\(127\) 15.9338 + 5.17719i 1.41389 + 0.459401i 0.913656 0.406488i \(-0.133247\pi\)
0.500236 + 0.865889i \(0.333247\pi\)
\(128\) 0 0
\(129\) 7.46415 + 5.42302i 0.657181 + 0.477470i
\(130\) 0 0
\(131\) 2.67583 1.94410i 0.233788 0.169857i −0.464723 0.885456i \(-0.653846\pi\)
0.698511 + 0.715599i \(0.253846\pi\)
\(132\) 0 0
\(133\) −5.91486 8.14111i −0.512884 0.705924i
\(134\) 0 0
\(135\) 2.21087 0.334767i 0.190281 0.0288121i
\(136\) 0 0
\(137\) −1.99642 + 0.648677i −0.170566 + 0.0554202i −0.393055 0.919515i \(-0.628582\pi\)
0.222489 + 0.974935i \(0.428582\pi\)
\(138\) 0 0
\(139\) 4.10525 12.6347i 0.348203 1.07166i −0.611643 0.791134i \(-0.709491\pi\)
0.959847 0.280525i \(-0.0905087\pi\)
\(140\) 0 0
\(141\) 1.40556 + 4.32586i 0.118369 + 0.364303i
\(142\) 0 0
\(143\) 0.320323i 0.0267868i
\(144\) 0 0
\(145\) 5.55956 + 0.919357i 0.461696 + 0.0763484i
\(146\) 0 0
\(147\) 4.41747 6.08013i 0.364347 0.501481i
\(148\) 0 0
\(149\) 2.79913 0.229313 0.114657 0.993405i \(-0.463423\pi\)
0.114657 + 0.993405i \(0.463423\pi\)
\(150\) 0 0
\(151\) −6.71330 −0.546320 −0.273160 0.961969i \(-0.588069\pi\)
−0.273160 + 0.961969i \(0.588069\pi\)
\(152\) 0 0
\(153\) 2.70572 3.72410i 0.218744 0.301076i
\(154\) 0 0
\(155\) −3.85692 + 7.44401i −0.309795 + 0.597917i
\(156\) 0 0
\(157\) 13.9495i 1.11329i 0.830750 + 0.556646i \(0.187912\pi\)
−0.830750 + 0.556646i \(0.812088\pi\)
\(158\) 0 0
\(159\) 2.91405 + 8.96852i 0.231099 + 0.711250i
\(160\) 0 0
\(161\) −7.48272 + 23.0294i −0.589721 + 1.81497i
\(162\) 0 0
\(163\) −8.44065 + 2.74253i −0.661123 + 0.214812i −0.620312 0.784355i \(-0.712994\pi\)
−0.0408107 + 0.999167i \(0.512994\pi\)
\(164\) 0 0
\(165\) 0.378681 + 0.196204i 0.0294803 + 0.0152744i
\(166\) 0 0
\(167\) −14.4563 19.8973i −1.11866 1.53970i −0.808003 0.589178i \(-0.799452\pi\)
−0.310655 0.950523i \(-0.600548\pi\)
\(168\) 0 0
\(169\) −8.23539 + 5.98336i −0.633492 + 0.460259i
\(170\) 0 0
\(171\) 2.13682 + 1.55249i 0.163407 + 0.118722i
\(172\) 0 0
\(173\) 16.1062 + 5.23322i 1.22453 + 0.397874i 0.848730 0.528826i \(-0.177368\pi\)
0.375801 + 0.926701i \(0.377368\pi\)
\(174\) 0 0
\(175\) 15.2577 + 11.4057i 1.15337 + 0.862189i
\(176\) 0 0
\(177\) 6.79109 + 2.20656i 0.510449 + 0.165855i
\(178\) 0 0
\(179\) 11.9328 + 8.66966i 0.891897 + 0.648001i 0.936372 0.351010i \(-0.114162\pi\)
−0.0444751 + 0.999010i \(0.514162\pi\)
\(180\) 0 0
\(181\) 8.89013 6.45906i 0.660798 0.480098i −0.206134 0.978524i \(-0.566088\pi\)
0.866932 + 0.498426i \(0.166088\pi\)
\(182\) 0 0
\(183\) 5.60166 + 7.71003i 0.414087 + 0.569941i
\(184\) 0 0
\(185\) −18.8835 + 18.6283i −1.38834 + 1.36958i
\(186\) 0 0
\(187\) 0.835018 0.271314i 0.0610625 0.0198404i
\(188\) 0 0
\(189\) −1.17733 + 3.62344i −0.0856380 + 0.263567i
\(190\) 0 0
\(191\) −7.42739 22.8591i −0.537427 1.65403i −0.738346 0.674422i \(-0.764393\pi\)
0.200919 0.979608i \(-0.435607\pi\)
\(192\) 0 0
\(193\) 7.50843i 0.540469i 0.962795 + 0.270234i \(0.0871012\pi\)
−0.962795 + 0.270234i \(0.912899\pi\)
\(194\) 0 0
\(195\) 0.562219 + 3.71300i 0.0402613 + 0.265894i
\(196\) 0 0
\(197\) 7.37799 10.1549i 0.525660 0.723509i −0.460801 0.887503i \(-0.652438\pi\)
0.986461 + 0.163995i \(0.0524380\pi\)
\(198\) 0 0
\(199\) 19.7618 1.40088 0.700440 0.713711i \(-0.252987\pi\)
0.700440 + 0.713711i \(0.252987\pi\)
\(200\) 0 0
\(201\) −6.05168 −0.426852
\(202\) 0 0
\(203\) −5.64349 + 7.76760i −0.396095 + 0.545178i
\(204\) 0 0
\(205\) −11.2901 11.4447i −0.788532 0.799333i
\(206\) 0 0
\(207\) 6.35567i 0.441750i
\(208\) 0 0
\(209\) 0.155675 + 0.479118i 0.0107683 + 0.0331413i
\(210\) 0 0
\(211\) −3.47579 + 10.6974i −0.239283 + 0.736437i 0.757241 + 0.653135i \(0.226547\pi\)
−0.996524 + 0.0833021i \(0.973453\pi\)
\(212\) 0 0
\(213\) 12.6474 4.10941i 0.866589 0.281572i
\(214\) 0 0
\(215\) −9.24075 18.4451i −0.630214 1.25795i
\(216\) 0 0
\(217\) −8.39639 11.5566i −0.569984 0.784516i
\(218\) 0 0
\(219\) 4.21621 3.06326i 0.284905 0.206996i
\(220\) 0 0
\(221\) 6.25438 + 4.54407i 0.420715 + 0.305668i
\(222\) 0 0
\(223\) −6.91605 2.24716i −0.463133 0.150481i 0.0681508 0.997675i \(-0.478290\pi\)
−0.531284 + 0.847194i \(0.678290\pi\)
\(224\) 0 0
\(225\) −4.73382 1.60963i −0.315588 0.107309i
\(226\) 0 0
\(227\) −9.00583 2.92617i −0.597738 0.194217i −0.00550660 0.999985i \(-0.501753\pi\)
−0.592231 + 0.805768i \(0.701753\pi\)
\(228\) 0 0
\(229\) 17.1755 + 12.4787i 1.13499 + 0.824617i 0.986413 0.164284i \(-0.0525315\pi\)
0.148575 + 0.988901i \(0.452531\pi\)
\(230\) 0 0
\(231\) −0.587893 + 0.427129i −0.0386805 + 0.0281030i
\(232\) 0 0
\(233\) −4.16700 5.73538i −0.272989 0.375737i 0.650407 0.759586i \(-0.274598\pi\)
−0.923396 + 0.383849i \(0.874598\pi\)
\(234\) 0 0
\(235\) 1.65935 10.0344i 0.108244 0.654575i
\(236\) 0 0
\(237\) 2.95939 0.961563i 0.192233 0.0624602i
\(238\) 0 0
\(239\) 6.18395 19.0323i 0.400007 1.23109i −0.524987 0.851110i \(-0.675930\pi\)
0.924993 0.379983i \(-0.124070\pi\)
\(240\) 0 0
\(241\) 6.43498 + 19.8048i 0.414513 + 1.27574i 0.912686 + 0.408662i \(0.134005\pi\)
−0.498172 + 0.867078i \(0.665995\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) −15.0250 + 7.52731i −0.959910 + 0.480902i
\(246\) 0 0
\(247\) −2.60731 + 3.58865i −0.165899 + 0.228340i
\(248\) 0 0
\(249\) 4.67837 0.296480
\(250\) 0 0
\(251\) −29.7741 −1.87932 −0.939662 0.342104i \(-0.888861\pi\)
−0.939662 + 0.342104i \(0.888861\pi\)
\(252\) 0 0
\(253\) 0.712534 0.980719i 0.0447966 0.0616573i
\(254\) 0 0
\(255\) −9.20285 + 4.61050i −0.576305 + 0.288721i
\(256\) 0 0
\(257\) 21.2853i 1.32774i 0.747849 + 0.663869i \(0.231087\pi\)
−0.747849 + 0.663869i \(0.768913\pi\)
\(258\) 0 0
\(259\) −13.9661 42.9834i −0.867814 2.67086i
\(260\) 0 0
\(261\) 0.778746 2.39673i 0.0482032 0.148354i
\(262\) 0 0
\(263\) −20.7951 + 6.75674i −1.28228 + 0.416638i −0.869383 0.494139i \(-0.835483\pi\)
−0.412898 + 0.910777i \(0.635483\pi\)
\(264\) 0 0
\(265\) 3.44021 20.8037i 0.211331 1.27796i
\(266\) 0 0
\(267\) −8.19506 11.2795i −0.501530 0.690297i
\(268\) 0 0
\(269\) −3.69018 + 2.68108i −0.224995 + 0.163468i −0.694572 0.719423i \(-0.744406\pi\)
0.469578 + 0.882891i \(0.344406\pi\)
\(270\) 0 0
\(271\) 10.4519 + 7.59377i 0.634909 + 0.461288i 0.858097 0.513487i \(-0.171646\pi\)
−0.223188 + 0.974775i \(0.571646\pi\)
\(272\) 0 0
\(273\) −6.08534 1.97725i −0.368301 0.119668i
\(274\) 0 0
\(275\) −0.550002 0.779085i −0.0331663 0.0469806i
\(276\) 0 0
\(277\) −8.40278 2.73023i −0.504874 0.164044i 0.0454957 0.998965i \(-0.485513\pi\)
−0.550370 + 0.834921i \(0.685513\pi\)
\(278\) 0 0
\(279\) 3.03331 + 2.20383i 0.181599 + 0.131940i
\(280\) 0 0
\(281\) −0.0247151 + 0.0179566i −0.00147438 + 0.00107120i −0.588522 0.808481i \(-0.700290\pi\)
0.587048 + 0.809552i \(0.300290\pi\)
\(282\) 0 0
\(283\) 2.82560 + 3.88910i 0.167964 + 0.231183i 0.884699 0.466163i \(-0.154364\pi\)
−0.716735 + 0.697346i \(0.754364\pi\)
\(284\) 0 0
\(285\) −2.64542 5.28043i −0.156701 0.312786i
\(286\) 0 0
\(287\) 26.0509 8.46444i 1.53773 0.499640i
\(288\) 0 0
\(289\) −1.29473 + 3.98478i −0.0761607 + 0.234399i
\(290\) 0 0
\(291\) −2.06889 6.36739i −0.121281 0.373263i
\(292\) 0 0
\(293\) 14.9705i 0.874587i 0.899319 + 0.437294i \(0.144063\pi\)
−0.899319 + 0.437294i \(0.855937\pi\)
\(294\) 0 0
\(295\) −11.2132 11.3668i −0.652856 0.661799i
\(296\) 0 0
\(297\) 0.112110 0.154306i 0.00650528 0.00895375i
\(298\) 0 0
\(299\) 10.6739 0.617290
\(300\) 0 0
\(301\) 35.1510 2.02607
\(302\) 0 0
\(303\) −6.18040 + 8.50659i −0.355055 + 0.488691i
\(304\) 0 0
\(305\) −3.19037 21.0698i −0.182680 1.20645i
\(306\) 0 0
\(307\) 4.47622i 0.255472i 0.991808 + 0.127736i \(0.0407710\pi\)
−0.991808 + 0.127736i \(0.959229\pi\)
\(308\) 0 0
\(309\) −4.00636 12.3303i −0.227914 0.701446i
\(310\) 0 0
\(311\) 0.0915043 0.281621i 0.00518873 0.0159693i −0.948429 0.316991i \(-0.897328\pi\)
0.953617 + 0.301021i \(0.0973276\pi\)
\(312\) 0 0
\(313\) −20.1214 + 6.53785i −1.13733 + 0.369541i −0.816357 0.577547i \(-0.804010\pi\)
−0.320973 + 0.947088i \(0.604010\pi\)
\(314\) 0 0
\(315\) 6.06484 5.98289i 0.341715 0.337098i
\(316\) 0 0
\(317\) −15.2334 20.9670i −0.855594 1.17762i −0.982602 0.185723i \(-0.940537\pi\)
0.127008 0.991902i \(-0.459463\pi\)
\(318\) 0 0
\(319\) 0.388863 0.282526i 0.0217722 0.0158184i
\(320\) 0 0
\(321\) −7.80383 5.66981i −0.435567 0.316458i
\(322\) 0 0
\(323\) −11.5633 3.75714i −0.643398 0.209053i
\(324\) 0 0
\(325\) 2.70328 7.95014i 0.149951 0.440995i
\(326\) 0 0
\(327\) 19.4447 + 6.31798i 1.07530 + 0.349385i
\(328\) 0 0
\(329\) 14.0197 + 10.1859i 0.772932 + 0.561568i
\(330\) 0 0
\(331\) 2.48400 1.80473i 0.136533 0.0991969i −0.517423 0.855730i \(-0.673108\pi\)
0.653955 + 0.756533i \(0.273108\pi\)
\(332\) 0 0
\(333\) 6.97264 + 9.59702i 0.382098 + 0.525913i
\(334\) 0 0
\(335\) 12.0150 + 6.22526i 0.656450 + 0.340122i
\(336\) 0 0
\(337\) −26.8694 + 8.73038i −1.46367 + 0.475574i −0.929188 0.369607i \(-0.879492\pi\)
−0.534479 + 0.845182i \(0.679492\pi\)
\(338\) 0 0
\(339\) −1.24972 + 3.84623i −0.0678753 + 0.208899i
\(340\) 0 0
\(341\) 0.220987 + 0.680128i 0.0119671 + 0.0368310i
\(342\) 0 0
\(343\) 1.96383i 0.106037i
\(344\) 0 0
\(345\) −6.53797 + 12.6186i −0.351993 + 0.679360i
\(346\) 0 0
\(347\) 17.9869 24.7568i 0.965586 1.32901i 0.0213401 0.999772i \(-0.493207\pi\)
0.944245 0.329242i \(-0.106793\pi\)
\(348\) 0 0
\(349\) 16.1178 0.862764 0.431382 0.902169i \(-0.358026\pi\)
0.431382 + 0.902169i \(0.358026\pi\)
\(350\) 0 0
\(351\) 1.67943 0.0896416
\(352\) 0 0
\(353\) 0.253341 0.348695i 0.0134840 0.0185591i −0.802222 0.597026i \(-0.796349\pi\)
0.815706 + 0.578467i \(0.196349\pi\)
\(354\) 0 0
\(355\) −29.3375 4.85140i −1.55707 0.257486i
\(356\) 0 0
\(357\) 17.5380i 0.928207i
\(358\) 0 0
\(359\) −5.70871 17.5696i −0.301294 0.927288i −0.981034 0.193835i \(-0.937907\pi\)
0.679740 0.733453i \(-0.262093\pi\)
\(360\) 0 0
\(361\) −3.71555 + 11.4353i −0.195555 + 0.601857i
\(362\) 0 0
\(363\) −10.4270 + 3.38795i −0.547277 + 0.177821i
\(364\) 0 0
\(365\) −11.5220 + 1.74465i −0.603088 + 0.0913189i
\(366\) 0 0
\(367\) −6.03990 8.31320i −0.315280 0.433946i 0.621739 0.783225i \(-0.286427\pi\)
−0.937019 + 0.349279i \(0.886427\pi\)
\(368\) 0 0
\(369\) −5.81645 + 4.22590i −0.302792 + 0.219992i
\(370\) 0 0
\(371\) 29.0662 + 21.1178i 1.50904 + 1.09638i
\(372\) 0 0
\(373\) −13.9266 4.52503i −0.721092 0.234297i −0.0745954 0.997214i \(-0.523767\pi\)
−0.646497 + 0.762917i \(0.723767\pi\)
\(374\) 0 0
\(375\) 7.74273 + 8.06537i 0.399833 + 0.416494i
\(376\) 0 0
\(377\) 4.02516 + 1.30785i 0.207306 + 0.0673579i
\(378\) 0 0
\(379\) −8.66061 6.29230i −0.444866 0.323214i 0.342700 0.939445i \(-0.388659\pi\)
−0.787565 + 0.616231i \(0.788659\pi\)
\(380\) 0 0
\(381\) −13.5541 + 9.84760i −0.694396 + 0.504508i
\(382\) 0 0
\(383\) 15.4690 + 21.2912i 0.790428 + 1.08793i 0.994055 + 0.108882i \(0.0347270\pi\)
−0.203627 + 0.979049i \(0.565273\pi\)
\(384\) 0 0
\(385\) 1.60658 0.243267i 0.0818791 0.0123980i
\(386\) 0 0
\(387\) −8.77463 + 2.85105i −0.446040 + 0.144927i
\(388\) 0 0
\(389\) −0.0901650 + 0.277499i −0.00457155 + 0.0140698i −0.953316 0.301974i \(-0.902355\pi\)
0.948745 + 0.316043i \(0.102355\pi\)
\(390\) 0 0
\(391\) 9.04082 + 27.8248i 0.457214 + 1.40716i
\(392\) 0 0
\(393\) 3.30750i 0.166841i
\(394\) 0 0
\(395\) −6.86471 1.13518i −0.345401 0.0571173i
\(396\) 0 0
\(397\) 1.18504 1.63106i 0.0594753 0.0818608i −0.778243 0.627963i \(-0.783889\pi\)
0.837719 + 0.546102i \(0.183889\pi\)
\(398\) 0 0
\(399\) 10.0630 0.503778
\(400\) 0 0
\(401\) 9.88760 0.493763 0.246882 0.969046i \(-0.420594\pi\)
0.246882 + 0.969046i \(0.420594\pi\)
\(402\) 0 0
\(403\) −3.70118 + 5.09424i −0.184369 + 0.253762i
\(404\) 0 0
\(405\) −1.02868 + 1.98540i −0.0511157 + 0.0986553i
\(406\) 0 0
\(407\) 2.26258i 0.112152i
\(408\) 0 0
\(409\) 11.6440 + 35.8367i 0.575761 + 1.77201i 0.633573 + 0.773683i \(0.281587\pi\)
−0.0578124 + 0.998327i \(0.518413\pi\)
\(410\) 0 0
\(411\) 0.648677 1.99642i 0.0319969 0.0984762i
\(412\) 0 0
\(413\) 25.8735 8.40680i 1.27315 0.413672i
\(414\) 0 0
\(415\) −9.28843 4.81256i −0.455951 0.236239i
\(416\) 0 0
\(417\) 7.80866 + 10.7477i 0.382392 + 0.526317i
\(418\) 0 0
\(419\) −12.6641 + 9.20102i −0.618682 + 0.449499i −0.852461 0.522791i \(-0.824891\pi\)
0.233779 + 0.972290i \(0.424891\pi\)
\(420\) 0 0
\(421\) −11.7531 8.53916i −0.572813 0.416173i 0.263313 0.964711i \(-0.415185\pi\)
−0.836126 + 0.548537i \(0.815185\pi\)
\(422\) 0 0
\(423\) −4.32586 1.40556i −0.210331 0.0683406i
\(424\) 0 0
\(425\) 23.0141 + 0.313121i 1.11635 + 0.0151886i
\(426\) 0 0
\(427\) 34.5318 + 11.2201i 1.67111 + 0.542978i
\(428\) 0 0
\(429\) 0.259147 + 0.188281i 0.0125117 + 0.00909030i
\(430\) 0 0
\(431\) 10.2150 7.42161i 0.492038 0.357486i −0.313930 0.949446i \(-0.601646\pi\)
0.805967 + 0.591960i \(0.201646\pi\)
\(432\) 0 0
\(433\) −2.05145 2.82358i −0.0985864 0.135693i 0.756874 0.653561i \(-0.226726\pi\)
−0.855460 + 0.517868i \(0.826726\pi\)
\(434\) 0 0
\(435\) −4.01160 + 3.95739i −0.192342 + 0.189742i
\(436\) 0 0
\(437\) −15.9654 + 5.18746i −0.763727 + 0.248150i
\(438\) 0 0
\(439\) 6.04528 18.6055i 0.288526 0.887991i −0.696794 0.717271i \(-0.745391\pi\)
0.985320 0.170719i \(-0.0546092\pi\)
\(440\) 0 0
\(441\) 2.32240 + 7.14762i 0.110591 + 0.340363i
\(442\) 0 0
\(443\) 2.77485i 0.131837i 0.997825 + 0.0659185i \(0.0209977\pi\)
−0.997825 + 0.0659185i \(0.979002\pi\)
\(444\) 0 0
\(445\) 4.66741 + 30.8245i 0.221257 + 1.46122i
\(446\) 0 0
\(447\) −1.64529 + 2.26454i −0.0778194 + 0.107109i
\(448\) 0 0
\(449\) 38.4261 1.81344 0.906721 0.421732i \(-0.138578\pi\)
0.906721 + 0.421732i \(0.138578\pi\)
\(450\) 0 0
\(451\) −1.37128 −0.0645710
\(452\) 0 0
\(453\) 3.94598 5.43117i 0.185398 0.255179i
\(454\) 0 0
\(455\) 10.0479 + 10.1855i 0.471051 + 0.477504i
\(456\) 0 0
\(457\) 36.0296i 1.68539i −0.538389 0.842696i \(-0.680967\pi\)
0.538389 0.842696i \(-0.319033\pi\)
\(458\) 0 0
\(459\) 1.42248 + 4.37794i 0.0663957 + 0.204345i
\(460\) 0 0
\(461\) 0.265011 0.815619i 0.0123428 0.0379871i −0.944695 0.327949i \(-0.893643\pi\)
0.957038 + 0.289962i \(0.0936426\pi\)
\(462\) 0 0
\(463\) 9.89742 3.21587i 0.459972 0.149454i −0.0698596 0.997557i \(-0.522255\pi\)
0.529832 + 0.848103i \(0.322255\pi\)
\(464\) 0 0
\(465\) −3.75529 7.49579i −0.174147 0.347609i
\(466\) 0 0
\(467\) 12.0910 + 16.6419i 0.559506 + 0.770094i 0.991264 0.131895i \(-0.0421063\pi\)
−0.431757 + 0.901990i \(0.642106\pi\)
\(468\) 0 0
\(469\) −18.6530 + 13.5522i −0.861316 + 0.625782i
\(470\) 0 0
\(471\) −11.2854 8.19931i −0.520003 0.377804i
\(472\) 0 0
\(473\) −1.67361 0.543789i −0.0769527 0.0250034i
\(474\) 0 0
\(475\) −0.179663 + 13.2051i −0.00824351 + 0.605890i
\(476\) 0 0
\(477\) −8.96852 2.91405i −0.410640 0.133425i
\(478\) 0 0
\(479\) 25.8384 + 18.7727i 1.18059 + 0.857747i 0.992238 0.124355i \(-0.0396861\pi\)
0.188350 + 0.982102i \(0.439686\pi\)
\(480\) 0 0
\(481\) −16.1176 + 11.7101i −0.734898 + 0.533934i
\(482\) 0 0
\(483\) −14.2330 19.5900i −0.647623 0.891376i
\(484\) 0 0
\(485\) −2.44245 + 14.7701i −0.110906 + 0.670674i
\(486\) 0 0
\(487\) −14.9140 + 4.84587i −0.675820 + 0.219587i −0.626764 0.779209i \(-0.715621\pi\)
−0.0490554 + 0.998796i \(0.515621\pi\)
\(488\) 0 0
\(489\) 2.74253 8.44065i 0.124022 0.381699i
\(490\) 0 0
\(491\) 5.09354 + 15.6763i 0.229868 + 0.707462i 0.997761 + 0.0668834i \(0.0213055\pi\)
−0.767892 + 0.640579i \(0.778694\pi\)
\(492\) 0 0
\(493\) 11.6005i 0.522461i
\(494\) 0 0
\(495\) −0.381315 + 0.191034i −0.0171388 + 0.00858633i
\(496\) 0 0
\(497\) 29.7804 40.9892i 1.33583 1.83862i
\(498\) 0 0
\(499\) −12.4339 −0.556618 −0.278309 0.960492i \(-0.589774\pi\)
−0.278309 + 0.960492i \(0.589774\pi\)
\(500\) 0 0
\(501\) 24.5944 1.09880
\(502\) 0 0
\(503\) −2.54703 + 3.50569i −0.113567 + 0.156311i −0.862016 0.506881i \(-0.830799\pi\)
0.748450 + 0.663191i \(0.230799\pi\)
\(504\) 0 0
\(505\) 21.0211 10.5313i 0.935428 0.468637i
\(506\) 0 0
\(507\) 10.1795i 0.452088i
\(508\) 0 0
\(509\) −4.32995 13.3262i −0.191922 0.590674i −0.999999 0.00159734i \(-0.999492\pi\)
0.808077 0.589077i \(-0.200508\pi\)
\(510\) 0 0
\(511\) 6.13568 18.8837i 0.271426 0.835364i
\(512\) 0 0
\(513\) −2.51198 + 0.816193i −0.110907 + 0.0360358i
\(514\) 0 0
\(515\) −4.72975 + 28.6019i −0.208418 + 1.26035i
\(516\) 0 0
\(517\) −0.509930 0.701859i −0.0224267 0.0308677i
\(518\) 0 0
\(519\) −13.7007 + 9.95417i −0.601396 + 0.436940i
\(520\) 0 0
\(521\) −1.56002 1.13342i −0.0683458 0.0496561i 0.553088 0.833123i \(-0.313449\pi\)
−0.621434 + 0.783467i \(0.713449\pi\)
\(522\) 0 0
\(523\) 1.86306 + 0.605344i 0.0814659 + 0.0264699i 0.349466 0.936949i \(-0.386363\pi\)
−0.268001 + 0.963419i \(0.586363\pi\)
\(524\) 0 0
\(525\) −18.1956 + 5.63962i −0.794122 + 0.246133i
\(526\) 0 0
\(527\) −16.4145 5.33341i −0.715029 0.232327i
\(528\) 0 0
\(529\) 14.0725 + 10.2243i 0.611849 + 0.444534i
\(530\) 0 0
\(531\) −5.77684 + 4.19712i −0.250694 + 0.182140i
\(532\) 0 0
\(533\) −7.09712 9.76835i −0.307410 0.423114i
\(534\) 0 0
\(535\) 9.66128 + 19.2845i 0.417693 + 0.833742i
\(536\) 0 0
\(537\) −14.0278 + 4.55791i −0.605345 + 0.196688i
\(538\) 0 0
\(539\) −0.442958 + 1.36329i −0.0190796 + 0.0587209i
\(540\) 0 0
\(541\) −10.6961 32.9191i −0.459860 1.41530i −0.865333 0.501197i \(-0.832893\pi\)
0.405473 0.914107i \(-0.367107\pi\)
\(542\) 0 0
\(543\) 10.9888i 0.471575i
\(544\) 0 0
\(545\) −32.1064 32.5462i −1.37529 1.39413i
\(546\) 0 0
\(547\) 9.37482 12.9033i 0.400838 0.551706i −0.560116 0.828414i \(-0.689243\pi\)
0.960954 + 0.276708i \(0.0892434\pi\)
\(548\) 0 0
\(549\) −9.53012 −0.406735
\(550\) 0 0
\(551\) −6.65617 −0.283562
\(552\) 0 0
\(553\) 6.96834 9.59110i 0.296324 0.407855i
\(554\) 0 0
\(555\) −3.97119 26.2266i −0.168568 1.11326i
\(556\) 0 0
\(557\) 43.0343i 1.82342i 0.410831 + 0.911711i \(0.365239\pi\)
−0.410831 + 0.911711i \(0.634761\pi\)
\(558\) 0 0
\(559\) −4.78815 14.7364i −0.202517 0.623284i
\(560\) 0 0
\(561\) −0.271314 + 0.835018i −0.0114549 + 0.0352545i
\(562\) 0 0
\(563\) 17.9331 5.82682i 0.755791 0.245571i 0.0943197 0.995542i \(-0.469932\pi\)
0.661471 + 0.749971i \(0.269932\pi\)
\(564\) 0 0
\(565\) 6.43774 6.35075i 0.270838 0.267178i
\(566\) 0 0
\(567\) −2.23941 3.08229i −0.0940465 0.129444i
\(568\) 0 0
\(569\) −19.7119 + 14.3215i −0.826364 + 0.600389i −0.918528 0.395355i \(-0.870621\pi\)
0.0921644 + 0.995744i \(0.470621\pi\)
\(570\) 0 0
\(571\) −12.4096 9.01612i −0.519327 0.377313i 0.297023 0.954870i \(-0.404006\pi\)
−0.816350 + 0.577557i \(0.804006\pi\)
\(572\) 0 0
\(573\) 22.8591 + 7.42739i 0.954955 + 0.310284i
\(574\) 0 0
\(575\) 25.9610 18.3274i 1.08265 0.764304i
\(576\) 0 0
\(577\) 13.6382 + 4.43133i 0.567767 + 0.184479i 0.578813 0.815460i \(-0.303516\pi\)
−0.0110462 + 0.999939i \(0.503516\pi\)
\(578\) 0 0
\(579\) −6.07445 4.41335i −0.252446 0.183412i
\(580\) 0 0
\(581\) 14.4201 10.4768i 0.598245 0.434651i
\(582\) 0 0
\(583\) −1.05720 1.45512i −0.0437849 0.0602648i
\(584\) 0 0
\(585\) −3.33435 1.72760i −0.137858 0.0714277i
\(586\) 0 0
\(587\) 10.1788 3.30729i 0.420123 0.136506i −0.0913234 0.995821i \(-0.529110\pi\)
0.511447 + 0.859315i \(0.329110\pi\)
\(588\) 0 0
\(589\) 3.06021 9.41837i 0.126094 0.388077i
\(590\) 0 0
\(591\) 3.87884 + 11.9378i 0.159554 + 0.491057i
\(592\) 0 0
\(593\) 23.5756i 0.968135i −0.875031 0.484067i \(-0.839159\pi\)
0.875031 0.484067i \(-0.160841\pi\)
\(594\) 0 0
\(595\) −18.0410 + 34.8199i −0.739609 + 1.42748i
\(596\) 0 0
\(597\) −11.6157 + 15.9877i −0.475400 + 0.654332i
\(598\) 0 0
\(599\) −13.8055 −0.564078 −0.282039 0.959403i \(-0.591011\pi\)
−0.282039 + 0.959403i \(0.591011\pi\)
\(600\) 0 0
\(601\) 9.61536 0.392219 0.196109 0.980582i \(-0.437169\pi\)
0.196109 + 0.980582i \(0.437169\pi\)
\(602\) 0 0
\(603\) 3.55709 4.89591i 0.144856 0.199377i
\(604\) 0 0
\(605\) 24.1869 + 3.99967i 0.983338 + 0.162610i
\(606\) 0 0
\(607\) 23.7884i 0.965539i 0.875747 + 0.482770i \(0.160369\pi\)
−0.875747 + 0.482770i \(0.839631\pi\)
\(608\) 0 0
\(609\) −2.96696 9.13136i −0.120227 0.370021i
\(610\) 0 0
\(611\) 2.36054 7.26500i 0.0954973 0.293911i
\(612\) 0 0
\(613\) −15.2850 + 4.96640i −0.617356 + 0.200591i −0.600966 0.799275i \(-0.705217\pi\)
−0.0163900 + 0.999866i \(0.505217\pi\)
\(614\) 0 0
\(615\) 15.8951 2.40682i 0.640952 0.0970522i
\(616\) 0 0
\(617\) 5.49341 + 7.56104i 0.221157 + 0.304396i 0.905150 0.425092i \(-0.139758\pi\)
−0.683994 + 0.729488i \(0.739758\pi\)
\(618\) 0 0
\(619\) −14.9480 + 10.8604i −0.600813 + 0.436516i −0.846167 0.532917i \(-0.821096\pi\)
0.245354 + 0.969433i \(0.421096\pi\)
\(620\) 0 0
\(621\) 5.14185 + 3.73577i 0.206335 + 0.149911i
\(622\) 0 0
\(623\) −50.5191 16.4146i −2.02400 0.657639i
\(624\) 0 0
\(625\) −7.07570 23.9778i −0.283028 0.959112i
\(626\) 0 0
\(627\) −0.479118 0.155675i −0.0191341 0.00621706i
\(628\) 0 0
\(629\) −44.1774 32.0968i −1.76147 1.27978i
\(630\) 0 0
\(631\) −31.2030 + 22.6703i −1.24217 + 0.902491i −0.997741 0.0671762i \(-0.978601\pi\)
−0.244431 + 0.969667i \(0.578601\pi\)
\(632\) 0 0
\(633\) −6.61134 9.09973i −0.262777 0.361682i
\(634\) 0 0
\(635\) 37.0403 5.60860i 1.46990 0.222570i
\(636\) 0 0
\(637\) −12.0040 + 3.90032i −0.475614 + 0.154536i
\(638\) 0 0
\(639\) −4.10941 + 12.6474i −0.162566 + 0.500325i
\(640\) 0 0
\(641\) −3.96965 12.2173i −0.156792 0.482556i 0.841546 0.540185i \(-0.181646\pi\)
−0.998338 + 0.0576293i \(0.981646\pi\)
\(642\) 0 0
\(643\) 20.1030i 0.792784i 0.918081 + 0.396392i \(0.129738\pi\)
−0.918081 + 0.396392i \(0.870262\pi\)
\(644\) 0 0
\(645\) 20.3540 + 3.36584i 0.801437 + 0.132530i
\(646\) 0 0
\(647\) −23.0350 + 31.7050i −0.905600 + 1.24645i 0.0630466 + 0.998011i \(0.479918\pi\)
−0.968647 + 0.248441i \(0.920082\pi\)
\(648\) 0 0
\(649\) −1.36194 −0.0534609
\(650\) 0 0
\(651\) 14.2848 0.559865
\(652\) 0 0
\(653\) 15.2762 21.0259i 0.597804 0.822806i −0.397701 0.917515i \(-0.630192\pi\)
0.995505 + 0.0947087i \(0.0301920\pi\)
\(654\) 0 0
\(655\) 3.40237 6.56671i 0.132942 0.256583i
\(656\) 0 0
\(657\) 5.21152i 0.203321i
\(658\) 0 0
\(659\) 1.98499 + 6.10917i 0.0773242 + 0.237980i 0.982246 0.187599i \(-0.0600706\pi\)
−0.904921 + 0.425579i \(0.860071\pi\)
\(660\) 0 0
\(661\) 6.67091 20.5310i 0.259468 0.798562i −0.733448 0.679746i \(-0.762090\pi\)
0.992916 0.118816i \(-0.0379098\pi\)
\(662\) 0 0
\(663\) −7.35247 + 2.38896i −0.285546 + 0.0927796i
\(664\) 0 0
\(665\) −19.9790 10.3516i −0.774753 0.401418i
\(666\) 0 0
\(667\) 9.41443 + 12.9578i 0.364528 + 0.501730i
\(668\) 0 0
\(669\) 5.88314 4.27435i 0.227455 0.165256i
\(670\) 0 0
\(671\) −1.47055 1.06842i −0.0567701 0.0412459i
\(672\) 0 0
\(673\) 5.64965 + 1.83568i 0.217778 + 0.0707604i 0.415874 0.909422i \(-0.363476\pi\)
−0.198096 + 0.980183i \(0.563476\pi\)
\(674\) 0 0
\(675\) 4.08469 2.88362i 0.157220 0.110991i
\(676\) 0 0
\(677\) −35.3587 11.4888i −1.35895 0.441549i −0.463256 0.886225i \(-0.653319\pi\)
−0.895691 + 0.444676i \(0.853319\pi\)
\(678\) 0 0
\(679\) −20.6361 14.9930i −0.791942 0.575380i
\(680\) 0 0
\(681\) 7.66082 5.56591i 0.293563 0.213286i
\(682\) 0 0
\(683\) 26.5106 + 36.4886i 1.01440 + 1.39620i 0.916058 + 0.401046i \(0.131353\pi\)
0.0983404 + 0.995153i \(0.468647\pi\)
\(684\) 0 0
\(685\) −3.34157 + 3.29641i −0.127675 + 0.125949i
\(686\) 0 0
\(687\) −20.1910 + 6.56045i −0.770334 + 0.250297i
\(688\) 0 0
\(689\) 4.89395 15.0620i 0.186445 0.573818i
\(690\) 0 0
\(691\) −8.82903 27.1730i −0.335872 1.03371i −0.966291 0.257453i \(-0.917117\pi\)
0.630419 0.776255i \(-0.282883\pi\)
\(692\) 0 0
\(693\) 0.726676i 0.0276041i
\(694\) 0 0
\(695\) −4.44734 29.3711i −0.168697 1.11411i
\(696\) 0 0
\(697\) 19.4528 26.7745i 0.736829 1.01416i
\(698\) 0 0
\(699\) 7.08932 0.268143
\(700\) 0 0
\(701\) −44.2636 −1.67181 −0.835907 0.548871i \(-0.815058\pi\)
−0.835907 + 0.548871i \(0.815058\pi\)
\(702\) 0 0
\(703\) 18.4165 25.3482i 0.694593 0.956025i
\(704\) 0 0
\(705\) 7.14269 + 7.24054i 0.269009 + 0.272694i
\(706\) 0 0
\(707\) 40.0602i 1.50662i
\(708\) 0 0
\(709\) −5.25711 16.1797i −0.197435 0.607643i −0.999940 0.0109965i \(-0.996500\pi\)
0.802505 0.596646i \(-0.203500\pi\)
\(710\) 0 0
\(711\) −0.961563 + 2.95939i −0.0360614 + 0.110986i
\(712\) 0 0
\(713\) −22.6635 + 7.36381i −0.848754 + 0.275777i
\(714\) 0 0
\(715\) −0.320828 0.640393i −0.0119983 0.0239494i
\(716\) 0 0
\(717\) 11.7626 + 16.1898i 0.439282 + 0.604619i
\(718\) 0 0
\(719\) 6.71076 4.87565i 0.250269 0.181831i −0.455577 0.890196i \(-0.650567\pi\)
0.705846 + 0.708365i \(0.250567\pi\)
\(720\) 0 0
\(721\) −39.9614 29.0336i −1.48824 1.08127i
\(722\) 0 0
\(723\) −19.8048 6.43498i −0.736549 0.239319i
\(724\) 0 0
\(725\) 12.0355 3.73034i 0.446989 0.138541i
\(726\) 0 0
\(727\) 7.09791 + 2.30625i 0.263247 + 0.0855342i 0.437667 0.899137i \(-0.355805\pi\)
−0.174420 + 0.984671i \(0.555805\pi\)
\(728\) 0 0
\(729\) 0.809017 + 0.587785i 0.0299636 + 0.0217698i
\(730\) 0 0
\(731\) 34.3593 24.9635i 1.27082 0.923308i
\(732\) 0 0
\(733\) 7.06525 + 9.72449i 0.260961 + 0.359182i 0.919312 0.393529i \(-0.128746\pi\)
−0.658351 + 0.752711i \(0.728746\pi\)
\(734\) 0 0
\(735\) 2.74174 16.5799i 0.101130 0.611559i
\(736\) 0 0
\(737\) 1.09776 0.356684i 0.0404365 0.0131386i
\(738\) 0 0
\(739\) −7.82848 + 24.0936i −0.287975 + 0.886297i 0.697516 + 0.716570i \(0.254289\pi\)
−0.985491 + 0.169728i \(0.945711\pi\)
\(740\) 0 0
\(741\) −1.37074 4.21871i −0.0503555 0.154978i
\(742\) 0 0
\(743\) 21.0959i 0.773935i −0.922093 0.386968i \(-0.873523\pi\)
0.922093 0.386968i \(-0.126477\pi\)
\(744\) 0 0
\(745\) 5.59605 2.80354i 0.205023 0.102714i
\(746\) 0 0
\(747\) −2.74988 + 3.78488i −0.100613 + 0.138482i
\(748\) 0 0
\(749\) −36.7507 −1.34284
\(750\) 0 0
\(751\) −34.3897 −1.25490 −0.627449 0.778658i \(-0.715901\pi\)
−0.627449 + 0.778658i \(0.715901\pi\)
\(752\) 0 0
\(753\) 17.5008 24.0877i 0.637764 0.877806i
\(754\) 0 0
\(755\) −13.4213 + 6.72389i −0.488451 + 0.244707i
\(756\) 0 0
\(757\) 33.9762i 1.23488i −0.786616 0.617442i \(-0.788169\pi\)
0.786616 0.617442i \(-0.211831\pi\)
\(758\) 0 0
\(759\) 0.374601 + 1.15290i 0.0135972 + 0.0418478i
\(760\) 0 0
\(761\) −4.13686 + 12.7319i −0.149961 + 0.461533i −0.997616 0.0690159i \(-0.978014\pi\)
0.847654 + 0.530549i \(0.178014\pi\)
\(762\) 0 0
\(763\) 74.0828 24.0710i 2.68198 0.871427i
\(764\) 0 0
\(765\) 1.67932 10.1552i 0.0607161 0.367164i
\(766\) 0 0
\(767\) −7.04879 9.70183i −0.254517 0.350313i
\(768\) 0 0
\(769\) −4.80948 + 3.49429i −0.173434 + 0.126007i −0.671116 0.741352i \(-0.734185\pi\)
0.497682 + 0.867360i \(0.334185\pi\)
\(770\) 0 0
\(771\) −17.2201 12.5112i −0.620168 0.450579i
\(772\) 0 0
\(773\) 32.4278 + 10.5364i 1.16635 + 0.378969i 0.827278 0.561793i \(-0.189888\pi\)
0.339068 + 0.940762i \(0.389888\pi\)
\(774\) 0 0
\(775\) −0.255039 + 18.7451i −0.00916127 + 0.673345i
\(776\) 0 0
\(777\) 42.9834 + 13.9661i 1.54202 + 0.501032i
\(778\) 0 0
\(779\) 15.3628 + 11.1617i 0.550428 + 0.399909i
\(780\) 0 0
\(781\) −2.05201 + 1.49087i −0.0734267 + 0.0533476i
\(782\) 0 0
\(783\) 1.48126 + 2.03878i 0.0529360 + 0.0728602i
\(784\) 0 0
\(785\) 13.9715 + 27.8880i 0.498665 + 0.995365i
\(786\) 0 0
\(787\) −1.87644 + 0.609693i −0.0668879 + 0.0217332i −0.342270 0.939602i \(-0.611196\pi\)
0.275382 + 0.961335i \(0.411196\pi\)
\(788\) 0 0
\(789\) 6.75674 20.7951i 0.240546 0.740325i
\(790\) 0 0
\(791\) 4.76132 + 14.6538i 0.169293 + 0.521030i
\(792\) 0 0
\(793\) 16.0052i 0.568361i
\(794\) 0 0
\(795\) 14.8085 + 15.0113i 0.525202 + 0.532397i
\(796\) 0 0
\(797\) −17.3698 + 23.9075i −0.615269 + 0.846845i