Properties

Label 300.2.x.a.53.8
Level $300$
Weight $2$
Character 300.53
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 53.8
Character \(\chi\) \(=\) 300.53
Dual form 300.2.x.a.17.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.17077 + 1.27644i) q^{3} +(1.13602 + 1.92599i) q^{5} +(3.00936 - 3.00936i) q^{7} +(-0.258608 + 2.98883i) q^{9} +O(q^{10})\) \(q+(1.17077 + 1.27644i) q^{3} +(1.13602 + 1.92599i) q^{5} +(3.00936 - 3.00936i) q^{7} +(-0.258608 + 2.98883i) q^{9} +(-2.76163 - 0.897307i) q^{11} +(0.404807 - 0.794479i) q^{13} +(-1.12840 + 3.70496i) q^{15} +(-3.19333 - 0.505773i) q^{17} +(0.694208 + 0.955496i) q^{19} +(7.36453 + 0.318013i) q^{21} +(2.51796 + 4.94177i) q^{23} +(-2.41891 + 4.37594i) q^{25} +(-4.11784 + 3.16913i) q^{27} +(-6.77941 - 4.92553i) q^{29} +(6.19212 - 4.49884i) q^{31} +(-2.08786 - 4.57559i) q^{33} +(9.21471 + 2.37731i) q^{35} +(-8.57635 - 4.36987i) q^{37} +(1.48804 - 0.413437i) q^{39} +(8.73412 - 2.83789i) q^{41} +(-1.45614 - 1.45614i) q^{43} +(-6.05026 + 2.89730i) q^{45} +(1.10756 + 6.99286i) q^{47} -11.1125i q^{49} +(-3.09305 - 4.66824i) q^{51} +(-2.56331 + 0.405989i) q^{53} +(-1.40906 - 6.33824i) q^{55} +(-0.406879 + 2.00478i) q^{57} +(-3.44583 - 10.6052i) q^{59} +(-2.69549 + 8.29586i) q^{61} +(8.21623 + 9.77272i) q^{63} +(1.99003 - 0.122889i) q^{65} +(0.616819 - 3.89444i) q^{67} +(-3.35994 + 8.99969i) q^{69} +(0.265914 - 0.366000i) q^{71} +(-2.68754 + 1.36937i) q^{73} +(-8.41762 + 2.03561i) q^{75} +(-11.0110 + 5.61041i) q^{77} +(2.07296 - 2.85319i) q^{79} +(-8.86624 - 1.54587i) q^{81} +(2.20859 - 13.9445i) q^{83} +(-2.65357 - 6.72490i) q^{85} +(-1.64996 - 14.4202i) q^{87} +(2.41968 - 7.44701i) q^{89} +(-1.17266 - 3.60908i) q^{91} +(12.9920 + 2.63679i) q^{93} +(-1.05164 + 2.42251i) q^{95} +(-1.51448 + 0.239870i) q^{97} +(3.39608 - 8.02199i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 2q^{3} + 4q^{7} + O(q^{10}) \) \( 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.17077 + 1.27644i 0.675943 + 0.736954i
\(4\) 0 0
\(5\) 1.13602 + 1.92599i 0.508044 + 0.861331i
\(6\) 0 0
\(7\) 3.00936 3.00936i 1.13743 1.13743i 0.148522 0.988909i \(-0.452548\pi\)
0.988909 0.148522i \(-0.0474516\pi\)
\(8\) 0 0
\(9\) −0.258608 + 2.98883i −0.0862027 + 0.996278i
\(10\) 0 0
\(11\) −2.76163 0.897307i −0.832662 0.270548i −0.138496 0.990363i \(-0.544227\pi\)
−0.694166 + 0.719815i \(0.744227\pi\)
\(12\) 0 0
\(13\) 0.404807 0.794479i 0.112273 0.220349i −0.828032 0.560681i \(-0.810539\pi\)
0.940305 + 0.340332i \(0.110539\pi\)
\(14\) 0 0
\(15\) −1.12840 + 3.70496i −0.291352 + 0.956616i
\(16\) 0 0
\(17\) −3.19333 0.505773i −0.774496 0.122668i −0.243339 0.969941i \(-0.578243\pi\)
−0.531157 + 0.847273i \(0.678243\pi\)
\(18\) 0 0
\(19\) 0.694208 + 0.955496i 0.159262 + 0.219206i 0.881189 0.472763i \(-0.156743\pi\)
−0.721927 + 0.691969i \(0.756743\pi\)
\(20\) 0 0
\(21\) 7.36453 + 0.318013i 1.60707 + 0.0693962i
\(22\) 0 0
\(23\) 2.51796 + 4.94177i 0.525030 + 1.03043i 0.989458 + 0.144819i \(0.0462600\pi\)
−0.464428 + 0.885611i \(0.653740\pi\)
\(24\) 0 0
\(25\) −2.41891 + 4.37594i −0.483782 + 0.875189i
\(26\) 0 0
\(27\) −4.11784 + 3.16913i −0.792479 + 0.609899i
\(28\) 0 0
\(29\) −6.77941 4.92553i −1.25890 0.914648i −0.260201 0.965554i \(-0.583789\pi\)
−0.998703 + 0.0509065i \(0.983789\pi\)
\(30\) 0 0
\(31\) 6.19212 4.49884i 1.11214 0.808015i 0.129139 0.991627i \(-0.458779\pi\)
0.982999 + 0.183611i \(0.0587787\pi\)
\(32\) 0 0
\(33\) −2.08786 4.57559i −0.363450 0.796509i
\(34\) 0 0
\(35\) 9.21471 + 2.37731i 1.55757 + 0.401839i
\(36\) 0 0
\(37\) −8.57635 4.36987i −1.40994 0.718402i −0.427335 0.904093i \(-0.640548\pi\)
−0.982608 + 0.185691i \(0.940548\pi\)
\(38\) 0 0
\(39\) 1.48804 0.413437i 0.238277 0.0662029i
\(40\) 0 0
\(41\) 8.73412 2.83789i 1.36404 0.443204i 0.466651 0.884442i \(-0.345460\pi\)
0.897390 + 0.441238i \(0.145460\pi\)
\(42\) 0 0
\(43\) −1.45614 1.45614i −0.222059 0.222059i 0.587306 0.809365i \(-0.300188\pi\)
−0.809365 + 0.587306i \(0.800188\pi\)
\(44\) 0 0
\(45\) −6.05026 + 2.89730i −0.901920 + 0.431904i
\(46\) 0 0
\(47\) 1.10756 + 6.99286i 0.161554 + 1.02001i 0.926603 + 0.376041i \(0.122715\pi\)
−0.765049 + 0.643973i \(0.777285\pi\)
\(48\) 0 0
\(49\) 11.1125i 1.58750i
\(50\) 0 0
\(51\) −3.09305 4.66824i −0.433114 0.653684i
\(52\) 0 0
\(53\) −2.56331 + 0.405989i −0.352098 + 0.0557668i −0.329978 0.943989i \(-0.607041\pi\)
−0.0221195 + 0.999755i \(0.507041\pi\)
\(54\) 0 0
\(55\) −1.40906 6.33824i −0.189998 0.854648i
\(56\) 0 0
\(57\) −0.406879 + 2.00478i −0.0538924 + 0.265540i
\(58\) 0 0
\(59\) −3.44583 10.6052i −0.448609 1.38068i −0.878477 0.477785i \(-0.841440\pi\)
0.429867 0.902892i \(-0.358560\pi\)
\(60\) 0 0
\(61\) −2.69549 + 8.29586i −0.345122 + 1.06218i 0.616397 + 0.787436i \(0.288592\pi\)
−0.961519 + 0.274740i \(0.911408\pi\)
\(62\) 0 0
\(63\) 8.21623 + 9.77272i 1.03515 + 1.23125i
\(64\) 0 0
\(65\) 1.99003 0.122889i 0.246833 0.0152425i
\(66\) 0 0
\(67\) 0.616819 3.89444i 0.0753564 0.475782i −0.920933 0.389720i \(-0.872572\pi\)
0.996290 0.0860617i \(-0.0274282\pi\)
\(68\) 0 0
\(69\) −3.35994 + 8.99969i −0.404489 + 1.08343i
\(70\) 0 0
\(71\) 0.265914 0.366000i 0.0315582 0.0434362i −0.792946 0.609292i \(-0.791454\pi\)
0.824505 + 0.565855i \(0.191454\pi\)
\(72\) 0 0
\(73\) −2.68754 + 1.36937i −0.314553 + 0.160273i −0.604139 0.796879i \(-0.706483\pi\)
0.289585 + 0.957152i \(0.406483\pi\)
\(74\) 0 0
\(75\) −8.41762 + 2.03561i −0.971983 + 0.235052i
\(76\) 0 0
\(77\) −11.0110 + 5.61041i −1.25483 + 0.639366i
\(78\) 0 0
\(79\) 2.07296 2.85319i 0.233227 0.321009i −0.676322 0.736606i \(-0.736427\pi\)
0.909549 + 0.415597i \(0.136427\pi\)
\(80\) 0 0
\(81\) −8.86624 1.54587i −0.985138 0.171764i
\(82\) 0 0
\(83\) 2.20859 13.9445i 0.242424 1.53060i −0.503161 0.864193i \(-0.667830\pi\)
0.745585 0.666411i \(-0.232170\pi\)
\(84\) 0 0
\(85\) −2.65357 6.72490i −0.287820 0.729418i
\(86\) 0 0
\(87\) −1.64996 14.4202i −0.176894 1.54600i
\(88\) 0 0
\(89\) 2.41968 7.44701i 0.256486 0.789382i −0.737048 0.675841i \(-0.763781\pi\)
0.993533 0.113541i \(-0.0362193\pi\)
\(90\) 0 0
\(91\) −1.17266 3.60908i −0.122928 0.378335i
\(92\) 0 0
\(93\) 12.9920 + 2.63679i 1.34721 + 0.273422i
\(94\) 0 0
\(95\) −1.05164 + 2.42251i −0.107896 + 0.248544i
\(96\) 0 0
\(97\) −1.51448 + 0.239870i −0.153772 + 0.0243551i −0.232846 0.972514i \(-0.574804\pi\)
0.0790736 + 0.996869i \(0.474804\pi\)
\(98\) 0 0
\(99\) 3.39608 8.02199i 0.341319 0.806240i
\(100\) 0 0
\(101\) 4.19521i 0.417439i −0.977976 0.208719i \(-0.933070\pi\)
0.977976 0.208719i \(-0.0669296\pi\)
\(102\) 0 0
\(103\) 2.94153 + 18.5721i 0.289838 + 1.82996i 0.516854 + 0.856074i \(0.327103\pi\)
−0.227016 + 0.973891i \(0.572897\pi\)
\(104\) 0 0
\(105\) 7.75378 + 14.5453i 0.756691 + 1.41948i
\(106\) 0 0
\(107\) −1.62455 1.62455i −0.157051 0.157051i 0.624208 0.781259i \(-0.285422\pi\)
−0.781259 + 0.624208i \(0.785422\pi\)
\(108\) 0 0
\(109\) −2.44163 + 0.793334i −0.233866 + 0.0759876i −0.423605 0.905847i \(-0.639236\pi\)
0.189740 + 0.981834i \(0.439236\pi\)
\(110\) 0 0
\(111\) −4.46303 16.0633i −0.423612 1.52466i
\(112\) 0 0
\(113\) 4.59551 + 2.34153i 0.432310 + 0.220273i 0.656583 0.754253i \(-0.272001\pi\)
−0.224274 + 0.974526i \(0.572001\pi\)
\(114\) 0 0
\(115\) −6.65736 + 10.4635i −0.620802 + 0.975729i
\(116\) 0 0
\(117\) 2.26988 + 1.41536i 0.209850 + 0.130850i
\(118\) 0 0
\(119\) −11.1319 + 8.08782i −1.02046 + 0.741409i
\(120\) 0 0
\(121\) −2.07776 1.50958i −0.188888 0.137235i
\(122\) 0 0
\(123\) 13.8480 + 7.82610i 1.24863 + 0.705655i
\(124\) 0 0
\(125\) −11.1760 + 0.312362i −0.999610 + 0.0279385i
\(126\) 0 0
\(127\) 6.30372 + 12.3717i 0.559364 + 1.09781i 0.981532 + 0.191297i \(0.0612693\pi\)
−0.422168 + 0.906518i \(0.638731\pi\)
\(128\) 0 0
\(129\) 0.153877 3.56347i 0.0135481 0.313746i
\(130\) 0 0
\(131\) 6.21317 + 8.55169i 0.542847 + 0.747165i 0.989020 0.147782i \(-0.0472134\pi\)
−0.446173 + 0.894947i \(0.647213\pi\)
\(132\) 0 0
\(133\) 4.96455 + 0.786308i 0.430481 + 0.0681815i
\(134\) 0 0
\(135\) −10.7817 4.33074i −0.927940 0.372731i
\(136\) 0 0
\(137\) −9.93006 + 19.4888i −0.848382 + 1.66504i −0.106701 + 0.994291i \(0.534029\pi\)
−0.741681 + 0.670752i \(0.765971\pi\)
\(138\) 0 0
\(139\) 13.6780 + 4.44425i 1.16015 + 0.376956i 0.824958 0.565193i \(-0.191198\pi\)
0.335193 + 0.942150i \(0.391198\pi\)
\(140\) 0 0
\(141\) −7.62929 + 9.60075i −0.642502 + 0.808529i
\(142\) 0 0
\(143\) −1.83082 + 1.83082i −0.153101 + 0.153101i
\(144\) 0 0
\(145\) 1.78499 18.6526i 0.148235 1.54902i
\(146\) 0 0
\(147\) 14.1845 13.0101i 1.16991 1.07306i
\(148\) 0 0
\(149\) 19.6307 1.60821 0.804106 0.594487i \(-0.202645\pi\)
0.804106 + 0.594487i \(0.202645\pi\)
\(150\) 0 0
\(151\) 7.05432 0.574072 0.287036 0.957920i \(-0.407330\pi\)
0.287036 + 0.957920i \(0.407330\pi\)
\(152\) 0 0
\(153\) 2.33749 9.41353i 0.188975 0.761038i
\(154\) 0 0
\(155\) 15.6991 + 6.81521i 1.26098 + 0.547411i
\(156\) 0 0
\(157\) −12.4751 + 12.4751i −0.995620 + 0.995620i −0.999990 0.00437087i \(-0.998609\pi\)
0.00437087 + 0.999990i \(0.498609\pi\)
\(158\) 0 0
\(159\) −3.51926 2.79660i −0.279096 0.221785i
\(160\) 0 0
\(161\) 22.4490 + 7.29412i 1.76923 + 0.574857i
\(162\) 0 0
\(163\) 4.70822 9.24039i 0.368776 0.723764i −0.629820 0.776741i \(-0.716871\pi\)
0.998596 + 0.0529778i \(0.0168712\pi\)
\(164\) 0 0
\(165\) 6.44071 9.21919i 0.501409 0.717713i
\(166\) 0 0
\(167\) 4.64134 + 0.735116i 0.359158 + 0.0568850i 0.333406 0.942783i \(-0.391802\pi\)
0.0257518 + 0.999668i \(0.491802\pi\)
\(168\) 0 0
\(169\) 7.17388 + 9.87400i 0.551837 + 0.759538i
\(170\) 0 0
\(171\) −3.03534 + 1.82777i −0.232119 + 0.139773i
\(172\) 0 0
\(173\) −5.89408 11.5678i −0.448119 0.879483i −0.998992 0.0448938i \(-0.985705\pi\)
0.550873 0.834589i \(-0.314295\pi\)
\(174\) 0 0
\(175\) 5.88942 + 20.4482i 0.445198 + 1.54574i
\(176\) 0 0
\(177\) 9.50263 16.8146i 0.714262 1.26386i
\(178\) 0 0
\(179\) −9.64168 7.00509i −0.720653 0.523585i 0.165940 0.986136i \(-0.446934\pi\)
−0.886593 + 0.462551i \(0.846934\pi\)
\(180\) 0 0
\(181\) 2.03092 1.47555i 0.150957 0.109677i −0.509743 0.860327i \(-0.670259\pi\)
0.660700 + 0.750650i \(0.270259\pi\)
\(182\) 0 0
\(183\) −13.7450 + 6.27188i −1.01606 + 0.463631i
\(184\) 0 0
\(185\) −1.32658 21.4823i −0.0975320 1.57941i
\(186\) 0 0
\(187\) 8.36495 + 4.26215i 0.611705 + 0.311679i
\(188\) 0 0
\(189\) −2.85502 + 21.9291i −0.207672 + 1.59511i
\(190\) 0 0
\(191\) −4.35419 + 1.41476i −0.315058 + 0.102369i −0.462278 0.886735i \(-0.652968\pi\)
0.147219 + 0.989104i \(0.452968\pi\)
\(192\) 0 0
\(193\) −0.834752 0.834752i −0.0600868 0.0600868i 0.676425 0.736512i \(-0.263528\pi\)
−0.736512 + 0.676425i \(0.763528\pi\)
\(194\) 0 0
\(195\) 2.48673 + 2.39629i 0.178078 + 0.171602i
\(196\) 0 0
\(197\) 3.31070 + 20.9029i 0.235878 + 1.48927i 0.766819 + 0.641863i \(0.221838\pi\)
−0.530941 + 0.847409i \(0.678162\pi\)
\(198\) 0 0
\(199\) 12.1010i 0.857815i −0.903348 0.428908i \(-0.858899\pi\)
0.903348 0.428908i \(-0.141101\pi\)
\(200\) 0 0
\(201\) 5.69318 3.77215i 0.401566 0.266067i
\(202\) 0 0
\(203\) −35.2244 + 5.57899i −2.47227 + 0.391569i
\(204\) 0 0
\(205\) 15.3879 + 13.5980i 1.07474 + 0.949723i
\(206\) 0 0
\(207\) −15.4213 + 6.24777i −1.07185 + 0.434250i
\(208\) 0 0
\(209\) −1.05977 3.26164i −0.0733059 0.225612i
\(210\) 0 0
\(211\) −6.11917 + 18.8329i −0.421261 + 1.29651i 0.485269 + 0.874365i \(0.338722\pi\)
−0.906530 + 0.422142i \(0.861278\pi\)
\(212\) 0 0
\(213\) 0.778501 0.0890762i 0.0533420 0.00610340i
\(214\) 0 0
\(215\) 1.15031 4.45871i 0.0784503 0.304082i
\(216\) 0 0
\(217\) 5.09569 32.1729i 0.345918 2.18404i
\(218\) 0 0
\(219\) −4.89441 1.82728i −0.330734 0.123476i
\(220\) 0 0
\(221\) −1.69451 + 2.33229i −0.113985 + 0.156887i
\(222\) 0 0
\(223\) −6.45454 + 3.28875i −0.432228 + 0.220231i −0.656548 0.754285i \(-0.727984\pi\)
0.224320 + 0.974516i \(0.427984\pi\)
\(224\) 0 0
\(225\) −12.4534 8.36137i −0.830228 0.557425i
\(226\) 0 0
\(227\) 1.65327 0.842383i 0.109731 0.0559109i −0.398263 0.917271i \(-0.630387\pi\)
0.507995 + 0.861360i \(0.330387\pi\)
\(228\) 0 0
\(229\) −13.9886 + 19.2537i −0.924394 + 1.27232i 0.0376122 + 0.999292i \(0.488025\pi\)
−0.962006 + 0.273027i \(0.911975\pi\)
\(230\) 0 0
\(231\) −20.0527 7.48648i −1.31937 0.492574i
\(232\) 0 0
\(233\) −0.810240 + 5.11565i −0.0530806 + 0.335138i 0.946830 + 0.321735i \(0.104266\pi\)
−0.999910 + 0.0134021i \(0.995734\pi\)
\(234\) 0 0
\(235\) −12.2100 + 10.0772i −0.796493 + 0.657364i
\(236\) 0 0
\(237\) 6.06889 0.694403i 0.394217 0.0451063i
\(238\) 0 0
\(239\) 1.51663 4.66771i 0.0981026 0.301929i −0.889947 0.456064i \(-0.849259\pi\)
0.988050 + 0.154135i \(0.0492590\pi\)
\(240\) 0 0
\(241\) 1.76890 + 5.44413i 0.113945 + 0.350687i 0.991726 0.128376i \(-0.0409765\pi\)
−0.877780 + 0.479063i \(0.840976\pi\)
\(242\) 0 0
\(243\) −8.40709 13.1271i −0.539315 0.842104i
\(244\) 0 0
\(245\) 21.4026 12.6240i 1.36736 0.806520i
\(246\) 0 0
\(247\) 1.04014 0.164742i 0.0661827 0.0104823i
\(248\) 0 0
\(249\) 20.3850 13.5066i 1.29185 0.855945i
\(250\) 0 0
\(251\) 20.3411i 1.28392i 0.766738 + 0.641961i \(0.221879\pi\)
−0.766738 + 0.641961i \(0.778121\pi\)
\(252\) 0 0
\(253\) −2.51937 15.9067i −0.158392 1.00005i
\(254\) 0 0
\(255\) 5.47723 11.2604i 0.342997 0.705155i
\(256\) 0 0
\(257\) −16.9061 16.9061i −1.05458 1.05458i −0.998422 0.0561541i \(-0.982116\pi\)
−0.0561541 0.998422i \(-0.517884\pi\)
\(258\) 0 0
\(259\) −38.9598 + 12.6588i −2.42085 + 0.786581i
\(260\) 0 0
\(261\) 16.4748 18.9887i 1.01976 1.17537i
\(262\) 0 0
\(263\) −9.39006 4.78447i −0.579016 0.295023i 0.139850 0.990173i \(-0.455338\pi\)
−0.718865 + 0.695150i \(0.755338\pi\)
\(264\) 0 0
\(265\) −3.69391 4.47571i −0.226915 0.274941i
\(266\) 0 0
\(267\) 12.3386 5.63014i 0.755108 0.344559i
\(268\) 0 0
\(269\) 6.24078 4.53419i 0.380507 0.276454i −0.381048 0.924555i \(-0.624437\pi\)
0.761554 + 0.648101i \(0.224437\pi\)
\(270\) 0 0
\(271\) −16.4232 11.9322i −0.997641 0.724828i −0.0360598 0.999350i \(-0.511481\pi\)
−0.961581 + 0.274521i \(0.911481\pi\)
\(272\) 0 0
\(273\) 3.23387 5.72223i 0.195723 0.346325i
\(274\) 0 0
\(275\) 10.6067 9.91422i 0.639607 0.597850i
\(276\) 0 0
\(277\) 8.84515 + 17.3596i 0.531453 + 1.04304i 0.988161 + 0.153419i \(0.0490285\pi\)
−0.456708 + 0.889617i \(0.650971\pi\)
\(278\) 0 0
\(279\) 11.8449 + 19.6707i 0.709138 + 1.17765i
\(280\) 0 0
\(281\) 1.43495 + 1.97505i 0.0856022 + 0.117821i 0.849670 0.527314i \(-0.176801\pi\)
−0.764068 + 0.645136i \(0.776801\pi\)
\(282\) 0 0
\(283\) −8.06450 1.27729i −0.479385 0.0759271i −0.0879343 0.996126i \(-0.528027\pi\)
−0.391450 + 0.920199i \(0.628027\pi\)
\(284\) 0 0
\(285\) −4.32342 + 1.49383i −0.256097 + 0.0884867i
\(286\) 0 0
\(287\) 17.7439 34.8244i 1.04739 2.05562i
\(288\) 0 0
\(289\) −6.22643 2.02309i −0.366260 0.119005i
\(290\) 0 0
\(291\) −2.07929 1.65232i −0.121890 0.0968605i
\(292\) 0 0
\(293\) −11.2030 + 11.2030i −0.654488 + 0.654488i −0.954070 0.299582i \(-0.903153\pi\)
0.299582 + 0.954070i \(0.403153\pi\)
\(294\) 0 0
\(295\) 16.5110 18.6844i 0.961307 1.08785i
\(296\) 0 0
\(297\) 14.2156 5.05698i 0.824874 0.293436i
\(298\) 0 0
\(299\) 4.94542 0.286001
\(300\) 0 0
\(301\) −8.76407 −0.505153
\(302\) 0 0
\(303\) 5.35494 4.91161i 0.307633 0.282165i
\(304\) 0 0
\(305\) −19.0399 + 4.23278i −1.09022 + 0.242368i
\(306\) 0 0
\(307\) −2.43888 + 2.43888i −0.139194 + 0.139194i −0.773270 0.634076i \(-0.781380\pi\)
0.634076 + 0.773270i \(0.281380\pi\)
\(308\) 0 0
\(309\) −20.2624 + 25.4983i −1.15269 + 1.45055i
\(310\) 0 0
\(311\) −9.68418 3.14658i −0.549139 0.178426i 0.0212893 0.999773i \(-0.493223\pi\)
−0.570429 + 0.821347i \(0.693223\pi\)
\(312\) 0 0
\(313\) −1.29485 + 2.54128i −0.0731892 + 0.143642i −0.924702 0.380692i \(-0.875686\pi\)
0.851513 + 0.524334i \(0.175686\pi\)
\(314\) 0 0
\(315\) −9.48839 + 26.9264i −0.534610 + 1.51713i
\(316\) 0 0
\(317\) 23.8744 + 3.78133i 1.34092 + 0.212381i 0.785331 0.619076i \(-0.212493\pi\)
0.555589 + 0.831457i \(0.312493\pi\)
\(318\) 0 0
\(319\) 14.3025 + 19.6857i 0.800786 + 1.10219i
\(320\) 0 0
\(321\) 0.171674 3.97561i 0.00958189 0.221897i
\(322\) 0 0
\(323\) −1.73357 3.40232i −0.0964584 0.189310i
\(324\) 0 0
\(325\) 2.49740 + 3.69319i 0.138531 + 0.204861i
\(326\) 0 0
\(327\) −3.87122 2.18779i −0.214079 0.120985i
\(328\) 0 0
\(329\) 24.3771 + 17.7110i 1.34395 + 0.976439i
\(330\) 0 0
\(331\) 6.91086 5.02103i 0.379855 0.275981i −0.381431 0.924397i \(-0.624568\pi\)
0.761286 + 0.648417i \(0.224568\pi\)
\(332\) 0 0
\(333\) 15.2787 24.5032i 0.837269 1.34277i
\(334\) 0 0
\(335\) 8.20139 3.23618i 0.448090 0.176811i
\(336\) 0 0
\(337\) −3.29999 1.68143i −0.179762 0.0915932i 0.361794 0.932258i \(-0.382164\pi\)
−0.541556 + 0.840665i \(0.682164\pi\)
\(338\) 0 0
\(339\) 2.39145 + 8.60729i 0.129886 + 0.467484i
\(340\) 0 0
\(341\) −21.1372 + 6.86788i −1.14464 + 0.371917i
\(342\) 0 0
\(343\) −12.3760 12.3760i −0.668240 0.668240i
\(344\) 0 0
\(345\) −21.1503 + 3.75262i −1.13869 + 0.202034i
\(346\) 0 0
\(347\) −1.58515 10.0082i −0.0850953 0.537270i −0.993002 0.118098i \(-0.962320\pi\)
0.907907 0.419172i \(-0.137680\pi\)
\(348\) 0 0
\(349\) 10.8302i 0.579729i −0.957068 0.289864i \(-0.906390\pi\)
0.957068 0.289864i \(-0.0936102\pi\)
\(350\) 0 0
\(351\) 0.850874 + 4.55443i 0.0454163 + 0.243097i
\(352\) 0 0
\(353\) 13.1776 2.08713i 0.701375 0.111087i 0.204445 0.978878i \(-0.434461\pi\)
0.496929 + 0.867791i \(0.334461\pi\)
\(354\) 0 0
\(355\) 1.00700 + 0.0963659i 0.0534459 + 0.00511457i
\(356\) 0 0
\(357\) −23.3565 4.74031i −1.23616 0.250884i
\(358\) 0 0
\(359\) −10.0379 30.8935i −0.529781 1.63050i −0.754663 0.656113i \(-0.772200\pi\)
0.224882 0.974386i \(-0.427800\pi\)
\(360\) 0 0
\(361\) 5.44028 16.7434i 0.286330 0.881234i
\(362\) 0 0
\(363\) −0.505681 4.41951i −0.0265414 0.231964i
\(364\) 0 0
\(365\) −5.69051 3.62056i −0.297855 0.189509i
\(366\) 0 0
\(367\) −1.65984 + 10.4798i −0.0866430 + 0.547042i 0.905738 + 0.423837i \(0.139317\pi\)
−0.992381 + 0.123205i \(0.960683\pi\)
\(368\) 0 0
\(369\) 6.22326 + 26.8387i 0.323970 + 1.39717i
\(370\) 0 0
\(371\) −6.49216 + 8.93569i −0.337056 + 0.463918i
\(372\) 0 0
\(373\) 14.2945 7.28340i 0.740140 0.377120i −0.0429097 0.999079i \(-0.513663\pi\)
0.783050 + 0.621959i \(0.213663\pi\)
\(374\) 0 0
\(375\) −13.4832 13.8998i −0.696268 0.717782i
\(376\) 0 0
\(377\) −6.65759 + 3.39221i −0.342883 + 0.174708i
\(378\) 0 0
\(379\) 18.2024 25.0535i 0.934995 1.28691i −0.0228835 0.999738i \(-0.507285\pi\)
0.957879 0.287173i \(-0.0927153\pi\)
\(380\) 0 0
\(381\) −8.41163 + 22.5308i −0.430941 + 1.15429i
\(382\) 0 0
\(383\) −4.80077 + 30.3108i −0.245308 + 1.54881i 0.490391 + 0.871503i \(0.336854\pi\)
−0.735698 + 0.677309i \(0.763146\pi\)
\(384\) 0 0
\(385\) −23.3144 14.8337i −1.18821 0.755994i
\(386\) 0 0
\(387\) 4.72872 3.97558i 0.240374 0.202090i
\(388\) 0 0
\(389\) −7.88532 + 24.2685i −0.399802 + 1.23046i 0.525357 + 0.850882i \(0.323932\pi\)
−0.925159 + 0.379581i \(0.876068\pi\)
\(390\) 0 0
\(391\) −5.54125 17.0542i −0.280233 0.862468i
\(392\) 0 0
\(393\) −3.64157 + 17.9428i −0.183693 + 0.905094i
\(394\) 0 0
\(395\) 7.85016 + 0.751231i 0.394984 + 0.0377985i
\(396\) 0 0
\(397\) 8.20587 1.29968i 0.411841 0.0652292i 0.0529236 0.998599i \(-0.483146\pi\)
0.358917 + 0.933369i \(0.383146\pi\)
\(398\) 0 0
\(399\) 4.80866 + 7.25755i 0.240734 + 0.363332i
\(400\) 0 0
\(401\) 17.6021i 0.879008i 0.898241 + 0.439504i \(0.144846\pi\)
−0.898241 + 0.439504i \(0.855154\pi\)
\(402\) 0 0
\(403\) −1.06762 6.74067i −0.0531818 0.335777i
\(404\) 0 0
\(405\) −7.09490 18.8325i −0.352549 0.935794i
\(406\) 0 0
\(407\) 19.7636 + 19.7636i 0.979644 + 0.979644i
\(408\) 0 0
\(409\) −14.6004 + 4.74394i −0.721941 + 0.234573i −0.646865 0.762605i \(-0.723920\pi\)
−0.0750765 + 0.997178i \(0.523920\pi\)
\(410\) 0 0
\(411\) −36.5022 + 10.1417i −1.80052 + 0.500255i
\(412\) 0 0
\(413\) −42.2846 21.5451i −2.08069 1.06016i
\(414\) 0 0
\(415\) 29.3660 11.5875i 1.44152 0.568807i
\(416\) 0 0
\(417\) 10.3409 + 22.6623i 0.506397 + 1.10978i
\(418\) 0 0
\(419\) 7.27149 5.28305i 0.355236 0.258094i −0.395827 0.918325i \(-0.629542\pi\)
0.751062 + 0.660232i \(0.229542\pi\)
\(420\) 0 0
\(421\) 22.8808 + 16.6239i 1.11514 + 0.810199i 0.983466 0.181093i \(-0.0579636\pi\)
0.131678 + 0.991293i \(0.457964\pi\)
\(422\) 0 0
\(423\) −21.1869 + 1.50190i −1.03014 + 0.0730250i
\(424\) 0 0
\(425\) 9.93760 12.7504i 0.482045 0.618485i
\(426\) 0 0
\(427\) 16.8535 + 33.0769i 0.815599 + 1.60070i
\(428\) 0 0
\(429\) −4.48040 0.193471i −0.216316 0.00934088i
\(430\) 0 0
\(431\) 18.6234 + 25.6329i 0.897059 + 1.23470i 0.971397 + 0.237462i \(0.0763156\pi\)
−0.0743381 + 0.997233i \(0.523684\pi\)
\(432\) 0 0
\(433\) 8.79670 + 1.39326i 0.422743 + 0.0669559i 0.364182 0.931328i \(-0.381349\pi\)
0.0585611 + 0.998284i \(0.481349\pi\)
\(434\) 0 0
\(435\) 25.8988 19.5594i 1.24175 0.937803i
\(436\) 0 0
\(437\) −2.97385 + 5.83651i −0.142259 + 0.279198i
\(438\) 0 0
\(439\) 35.2858 + 11.4651i 1.68410 + 0.547198i 0.985700 0.168509i \(-0.0538953\pi\)
0.698401 + 0.715707i \(0.253895\pi\)
\(440\) 0 0
\(441\) 33.2134 + 2.87378i 1.58159 + 0.136847i
\(442\) 0 0
\(443\) 0.101009 0.101009i 0.00479907 0.00479907i −0.704703 0.709502i \(-0.748920\pi\)
0.709502 + 0.704703i \(0.248920\pi\)
\(444\) 0 0
\(445\) 17.0917 3.79968i 0.810225 0.180122i
\(446\) 0 0
\(447\) 22.9830 + 25.0575i 1.08706 + 1.18518i
\(448\) 0 0
\(449\) 5.09561 0.240477 0.120238 0.992745i \(-0.461634\pi\)
0.120238 + 0.992745i \(0.461634\pi\)
\(450\) 0 0
\(451\) −26.6669 −1.25569
\(452\) 0 0
\(453\) 8.25897 + 9.00443i 0.388040 + 0.423065i
\(454\) 0 0
\(455\) 5.61891 6.35854i 0.263418 0.298093i
\(456\) 0 0
\(457\) 9.17964 9.17964i 0.429406 0.429406i −0.459020 0.888426i \(-0.651799\pi\)
0.888426 + 0.459020i \(0.151799\pi\)
\(458\) 0 0
\(459\) 14.7525 8.03737i 0.688587 0.375152i
\(460\) 0 0
\(461\) −2.89432 0.940423i −0.134802 0.0437999i 0.240839 0.970565i \(-0.422577\pi\)
−0.375641 + 0.926765i \(0.622577\pi\)
\(462\) 0 0
\(463\) 3.81952 7.49623i 0.177508 0.348380i −0.785060 0.619420i \(-0.787368\pi\)
0.962568 + 0.271041i \(0.0873678\pi\)
\(464\) 0 0
\(465\) 9.68080 + 28.0180i 0.448936 + 1.29931i
\(466\) 0 0
\(467\) 3.67547 + 0.582137i 0.170080 + 0.0269381i 0.240894 0.970551i \(-0.422559\pi\)
−0.0708133 + 0.997490i \(0.522559\pi\)
\(468\) 0 0
\(469\) −9.86354 13.5760i −0.455456 0.626882i
\(470\) 0 0
\(471\) −30.5291 1.31830i −1.40671 0.0607441i
\(472\) 0 0
\(473\) 2.71470 + 5.32791i 0.124822 + 0.244977i
\(474\) 0 0
\(475\) −5.86042 + 0.726559i −0.268895 + 0.0333368i
\(476\) 0 0
\(477\) −0.550539 7.76630i −0.0252074 0.355594i
\(478\) 0 0
\(479\) −19.2357 13.9755i −0.878900 0.638558i 0.0540606 0.998538i \(-0.482784\pi\)
−0.932960 + 0.359980i \(0.882784\pi\)
\(480\) 0 0
\(481\) −6.94354 + 5.04478i −0.316598 + 0.230022i
\(482\) 0 0
\(483\) 16.9720 + 37.1946i 0.772254 + 1.69241i
\(484\) 0 0
\(485\) −2.18247 2.64439i −0.0991010 0.120075i
\(486\) 0 0
\(487\) −36.1675 18.4282i −1.63890 0.835063i −0.997707 0.0676872i \(-0.978438\pi\)
−0.641197 0.767376i \(-0.721562\pi\)
\(488\) 0 0
\(489\) 17.3071 4.80859i 0.782652 0.217452i
\(490\) 0 0
\(491\) 22.0112 7.15186i 0.993350 0.322759i 0.233145 0.972442i \(-0.425098\pi\)
0.760205 + 0.649683i \(0.225098\pi\)
\(492\) 0 0
\(493\) 19.1577 + 19.1577i 0.862818 + 0.862818i
\(494\) 0 0
\(495\) 19.3083 2.57232i 0.867845 0.115617i
\(496\) 0 0
\(497\) −0.301193 1.90166i −0.0135103 0.0853010i
\(498\) 0 0
\(499\) 35.2669i 1.57876i −0.613904 0.789381i \(-0.710402\pi\)
0.613904 0.789381i \(-0.289598\pi\)
\(500\) 0 0
\(501\) 4.49560 + 6.78505i 0.200848 + 0.303134i
\(502\) 0 0
\(503\) 25.0737 3.97129i 1.11798 0.177071i 0.430021 0.902819i \(-0.358506\pi\)
0.687961 + 0.725748i \(0.258506\pi\)
\(504\) 0 0
\(505\) 8.07995 4.76585i 0.359553 0.212078i
\(506\) 0 0
\(507\) −4.20464 + 20.7172i −0.186735 + 0.920083i
\(508\) 0 0
\(509\) −1.80435 5.55322i −0.0799765 0.246142i 0.903072 0.429490i \(-0.141307\pi\)
−0.983048 + 0.183348i \(0.941307\pi\)
\(510\) 0 0
\(511\) −3.96685 + 12.2087i −0.175483 + 0.540082i
\(512\) 0 0
\(513\) −5.88673 1.73454i −0.259905 0.0765820i
\(514\) 0 0
\(515\) −32.4281 + 26.7637i −1.42895 + 1.17935i
\(516\) 0 0
\(517\) 3.21608 20.3055i 0.141443 0.893035i
\(518\) 0 0
\(519\) 7.86501 21.0666i 0.345236 0.924723i
\(520\) 0 0
\(521\) 5.69171 7.83396i 0.249358 0.343212i −0.665928 0.746016i \(-0.731964\pi\)
0.915286 + 0.402804i \(0.131964\pi\)
\(522\) 0 0
\(523\) −0.993315 + 0.506119i −0.0434346 + 0.0221310i −0.475573 0.879676i \(-0.657759\pi\)
0.432138 + 0.901807i \(0.357759\pi\)
\(524\) 0 0
\(525\) −19.2057 + 31.4575i −0.838207 + 1.37292i
\(526\) 0 0
\(527\) −22.0489 + 11.2345i −0.960464 + 0.489381i
\(528\) 0 0
\(529\) −4.56191 + 6.27893i −0.198344 + 0.272997i
\(530\) 0 0
\(531\) 32.5882 7.55643i 1.41421 0.327921i
\(532\) 0 0
\(533\) 1.28099 8.08788i 0.0554860 0.350325i
\(534\) 0 0
\(535\) 1.28335 4.97439i 0.0554840 0.215062i
\(536\) 0 0
\(537\) −2.34657 20.5084i −0.101262 0.885002i
\(538\) 0 0
\(539\) −9.97132 + 30.6886i −0.429495 + 1.32185i
\(540\) 0 0
\(541\) −9.75500 30.0228i −0.419400 1.29078i −0.908255 0.418417i \(-0.862585\pi\)
0.488855 0.872365i \(-0.337415\pi\)
\(542\) 0 0
\(543\) 4.26120 + 0.864828i 0.182865 + 0.0371133i
\(544\) 0 0
\(545\) −4.30170 3.80132i −0.184265 0.162831i
\(546\) 0 0
\(547\) −30.7784 + 4.87482i −1.31599 + 0.208432i −0.774660 0.632378i \(-0.782079\pi\)
−0.541330 + 0.840810i \(0.682079\pi\)
\(548\) 0 0
\(549\) −24.0978 10.2017i −1.02847 0.435399i
\(550\) 0 0
\(551\) 9.89704i 0.421628i
\(552\) 0 0
\(553\) −2.34798 14.8246i −0.0998463 0.630405i
\(554\) 0 0
\(555\) 25.8678 26.8440i 1.09803 1.13947i
\(556\) 0 0
\(557\) 11.9164 + 11.9164i 0.504915 + 0.504915i 0.912961 0.408046i \(-0.133790\pi\)
−0.408046 + 0.912961i \(0.633790\pi\)
\(558\) 0 0
\(559\) −1.74632 + 0.567415i −0.0738616 + 0.0239991i
\(560\) 0 0
\(561\) 4.35301 + 15.6674i 0.183784 + 0.661476i
\(562\) 0 0
\(563\) 16.5294 + 8.42215i 0.696631 + 0.354951i 0.766179 0.642627i \(-0.222156\pi\)
−0.0695477 + 0.997579i \(0.522156\pi\)
\(564\) 0 0
\(565\) 0.710828 + 11.5110i 0.0299047 + 0.484270i
\(566\) 0 0
\(567\) −31.3338 + 22.0296i −1.31590 + 0.925157i
\(568\) 0 0
\(569\) 1.23297 0.895803i 0.0516887 0.0375540i −0.561641 0.827381i \(-0.689830\pi\)
0.613330 + 0.789827i \(0.289830\pi\)
\(570\) 0 0
\(571\) 24.3901 + 17.7205i 1.02070 + 0.741579i 0.966425 0.256948i \(-0.0827168\pi\)
0.0542700 + 0.998526i \(0.482717\pi\)
\(572\) 0 0
\(573\) −6.90361 3.90152i −0.288402 0.162988i
\(574\) 0 0
\(575\) −27.7156 0.935252i −1.15582 0.0390027i
\(576\) 0 0
\(577\) 16.3743 + 32.1363i 0.681669 + 1.33785i 0.929419 + 0.369027i \(0.120309\pi\)
−0.247749 + 0.968824i \(0.579691\pi\)
\(578\) 0 0
\(579\) 0.0882122 2.04281i 0.00366598 0.0848964i
\(580\) 0 0
\(581\) −35.3175 48.6103i −1.46522 2.01670i
\(582\) 0 0
\(583\) 7.44321 + 1.17889i 0.308266 + 0.0488245i
\(584\) 0 0
\(585\) −0.147344 + 5.97965i −0.00609194 + 0.247228i
\(586\) 0 0
\(587\) 7.58856 14.8934i 0.313213 0.614716i −0.679709 0.733482i \(-0.737894\pi\)
0.992922 + 0.118766i \(0.0378939\pi\)
\(588\) 0 0
\(589\) 8.59724 + 2.79341i 0.354243 + 0.115101i
\(590\) 0 0
\(591\) −22.8053 + 28.6984i −0.938085 + 1.18049i
\(592\) 0 0
\(593\) 17.3573 17.3573i 0.712780 0.712780i −0.254336 0.967116i \(-0.581857\pi\)
0.967116 + 0.254336i \(0.0818568\pi\)
\(594\) 0 0
\(595\) −28.2232 12.2521i −1.15704 0.502287i
\(596\) 0 0
\(597\) 15.4462 14.1674i 0.632170 0.579834i
\(598\) 0 0
\(599\) 14.4303 0.589605 0.294802 0.955558i \(-0.404746\pi\)
0.294802 + 0.955558i \(0.404746\pi\)
\(600\) 0 0
\(601\) −40.6930 −1.65990 −0.829951 0.557837i \(-0.811632\pi\)
−0.829951 + 0.557837i \(0.811632\pi\)
\(602\) 0 0
\(603\) 11.4803 + 2.85070i 0.467515 + 0.116090i
\(604\) 0 0
\(605\) 0.547065 5.71668i 0.0222413 0.232416i
\(606\) 0 0
\(607\) 31.1483 31.1483i 1.26427 1.26427i 0.315266 0.949003i \(-0.397906\pi\)
0.949003 0.315266i \(-0.102094\pi\)
\(608\) 0 0
\(609\) −48.3608 38.4302i −1.95968 1.55727i
\(610\) 0 0
\(611\) 6.00403 + 1.95083i 0.242897 + 0.0789221i
\(612\) 0 0
\(613\) −16.5958 + 32.5711i −0.670299 + 1.31554i 0.265878 + 0.964007i \(0.414338\pi\)
−0.936177 + 0.351529i \(0.885662\pi\)
\(614\) 0 0
\(615\) 0.658644 + 35.5618i 0.0265591 + 1.43399i
\(616\) 0 0
\(617\) −34.4877 5.46232i −1.38842 0.219905i −0.582936 0.812518i \(-0.698096\pi\)
−0.805487 + 0.592613i \(0.798096\pi\)
\(618\) 0 0
\(619\) 3.48931 + 4.80263i 0.140247 + 0.193034i 0.873363 0.487070i \(-0.161934\pi\)
−0.733115 + 0.680104i \(0.761934\pi\)
\(620\) 0 0
\(621\) −26.0297 12.3697i −1.04453 0.496379i
\(622\) 0 0
\(623\) −15.1291 29.6924i −0.606133 1.18960i
\(624\) 0 0
\(625\) −13.2978 21.1700i −0.531910 0.846801i
\(626\) 0 0
\(627\) 2.92255 5.17136i 0.116715 0.206524i
\(628\) 0 0
\(629\) 25.1769 + 18.2921i 1.00387 + 0.729354i
\(630\) 0 0
\(631\) 21.9450 15.9440i 0.873616 0.634719i −0.0579392 0.998320i \(-0.518453\pi\)
0.931555 + 0.363601i \(0.118453\pi\)
\(632\) 0 0
\(633\) −31.2032 + 14.2381i −1.24021 + 0.565915i
\(634\) 0 0
\(635\) −16.6667 + 26.1955i −0.661400 + 1.03954i
\(636\) 0 0
\(637\) −8.82864 4.49842i −0.349804 0.178234i
\(638\) 0 0
\(639\) 1.02514 + 0.889424i 0.0405541 + 0.0351851i
\(640\) 0 0
\(641\) 6.43772 2.09174i 0.254275 0.0826188i −0.179106 0.983830i \(-0.557321\pi\)
0.433381 + 0.901211i \(0.357321\pi\)
\(642\) 0 0
\(643\) −1.88726 1.88726i −0.0744264 0.0744264i 0.668914 0.743340i \(-0.266760\pi\)
−0.743340 + 0.668914i \(0.766760\pi\)
\(644\) 0 0
\(645\) 7.03803 3.75181i 0.277122 0.147727i
\(646\) 0 0
\(647\) −1.80177 11.3759i −0.0708349 0.447234i −0.997459 0.0712445i \(-0.977303\pi\)
0.926624 0.375989i \(-0.122697\pi\)
\(648\) 0 0
\(649\) 32.3795i 1.27101i
\(650\) 0 0
\(651\) 47.0328 31.1627i 1.84336 1.22136i
\(652\) 0 0
\(653\) 41.2088 6.52683i 1.61262 0.255414i 0.715965 0.698136i \(-0.245987\pi\)
0.896659 + 0.442722i \(0.145987\pi\)
\(654\) 0 0
\(655\) −9.41222 + 21.6814i −0.367766 + 0.847164i
\(656\) 0 0
\(657\) −3.39780 8.38675i −0.132561 0.327198i
\(658\) 0 0
\(659\) −0.104879 0.322784i −0.00408550 0.0125739i 0.948993 0.315297i \(-0.102104\pi\)
−0.953078 + 0.302723i \(0.902104\pi\)
\(660\) 0 0
\(661\) 4.25007 13.0804i 0.165308 0.508767i −0.833750 0.552141i \(-0.813811\pi\)
0.999059 + 0.0433745i \(0.0138109\pi\)
\(662\) 0 0
\(663\) −4.96091 + 0.567628i −0.192666 + 0.0220448i
\(664\) 0 0
\(665\) 4.12542 + 10.4550i 0.159977 + 0.405426i
\(666\) 0 0
\(667\) 7.27057 45.9045i 0.281517 1.77743i
\(668\) 0 0
\(669\) −11.7547 4.38848i −0.454461 0.169668i
\(670\) 0 0
\(671\) 14.8879 20.4914i 0.574739 0.791061i
\(672\) 0 0
\(673\) −8.28693 + 4.22240i −0.319438 + 0.162762i −0.606356 0.795193i \(-0.707369\pi\)
0.286918 + 0.957955i \(0.407369\pi\)
\(674\) 0 0
\(675\) −3.90724 25.6853i −0.150390 0.988627i
\(676\) 0 0
\(677\) −3.29687 + 1.67984i −0.126709 + 0.0645615i −0.516196 0.856470i \(-0.672652\pi\)
0.389487 + 0.921032i \(0.372652\pi\)
\(678\) 0 0
\(679\) −3.83576 + 5.27948i −0.147203 + 0.202608i
\(680\) 0 0
\(681\) 3.01085 + 1.12407i 0.115376 + 0.0430744i
\(682\) 0 0
\(683\) 1.53600 9.69792i 0.0587734 0.371081i −0.940718 0.339190i \(-0.889847\pi\)
0.999491 0.0318908i \(-0.0101529\pi\)
\(684\) 0 0
\(685\) −48.8161 + 3.01451i −1.86517 + 0.115178i
\(686\) 0 0
\(687\) −40.9536 + 4.68592i −1.56248 + 0.178779i
\(688\) 0 0
\(689\) −0.715098 + 2.20084i −0.0272430 + 0.0838455i
\(690\) 0 0
\(691\) −5.28572 16.2678i −0.201078 0.618855i −0.999852 0.0172234i \(-0.994517\pi\)
0.798773 0.601632i \(-0.205483\pi\)
\(692\) 0 0
\(693\) −13.9210 34.3611i −0.528816 1.30527i
\(694\) 0 0
\(695\) 6.97889 + 31.3925i 0.264725 + 1.19078i
\(696\) 0 0
\(697\) −29.3262 + 4.64482i −1.11081 + 0.175935i
\(698\) 0 0
\(699\) −7.47844 + 4.95501i −0.282860 + 0.187416i
\(700\) 0 0
\(701\) 33.4650i 1.26396i −0.774986 0.631979i \(-0.782243\pi\)
0.774986 0.631979i \(-0.217757\pi\)
\(702\) 0 0
\(703\) −1.77838 11.2283i −0.0670730 0.423482i
\(704\) 0 0
\(705\) −27.1580 3.78730i −1.02283 0.142638i
\(706\) 0 0
\(707\) −12.6249 12.6249i −0.474808 0.474808i
\(708\) 0 0
\(709\) 12.9358 4.20308i 0.485813 0.157850i −0.0558616 0.998439i \(-0.517791\pi\)
0.541674 + 0.840588i \(0.317791\pi\)
\(710\) 0 0
\(711\) 7.99162 + 6.93360i 0.299709 + 0.260030i
\(712\) 0 0
\(713\) 37.8237 + 19.2721i 1.41651 + 0.721748i
\(714\) 0 0
\(715\) −5.60600 1.44630i −0.209652 0.0540884i
\(716\) 0 0
\(717\) 7.73368 3.52891i 0.288819 0.131789i
\(718\) 0 0
\(719\) −29.7221 + 21.5944i −1.10845 + 0.805335i −0.982419 0.186692i \(-0.940223\pi\)
−0.126030 + 0.992026i \(0.540223\pi\)
\(720\) 0 0
\(721\) 64.7423 + 47.0380i 2.41113 + 1.75179i
\(722\) 0 0
\(723\) −4.87814 + 8.63171i −0.181420 + 0.321017i
\(724\) 0 0
\(725\) 37.9526 17.7519i 1.40952 0.659289i
\(726\) 0 0
\(727\) −4.12344 8.09270i −0.152930 0.300142i 0.801813 0.597576i \(-0.203869\pi\)
−0.954742 + 0.297434i \(0.903869\pi\)
\(728\) 0 0
\(729\) 6.91324 26.0999i 0.256046 0.966665i
\(730\) 0 0
\(731\) 3.91344 + 5.38639i 0.144744 + 0.199223i
\(732\) 0 0
\(733\) −9.91162 1.56985i −0.366094 0.0579836i −0.0293225 0.999570i \(-0.509335\pi\)
−0.336771 + 0.941586i \(0.609335\pi\)
\(734\) 0 0
\(735\) 41.1713 + 12.5394i 1.51863 + 0.462522i
\(736\) 0 0
\(737\) −5.19793 + 10.2015i −0.191468 + 0.375778i
\(738\) 0 0
\(739\) −47.6656 15.4875i −1.75341 0.569717i −0.756924 0.653503i \(-0.773299\pi\)
−0.996484 + 0.0837861i \(0.973299\pi\)
\(740\) 0 0
\(741\) 1.42805 + 1.13481i 0.0524607 + 0.0416881i
\(742\) 0 0
\(743\) −0.668282 + 0.668282i −0.0245169 + 0.0245169i −0.719259 0.694742i \(-0.755519\pi\)
0.694742 + 0.719259i \(0.255519\pi\)
\(744\) 0 0
\(745\) 22.3009 + 37.8087i 0.817043 + 1.38520i
\(746\) 0 0
\(747\) 41.1065 + 10.2072i 1.50401 + 0.373464i
\(748\) 0 0
\(749\) −9.77769 −0.357269
\(750\) 0 0
\(751\) 16.7359 0.610702 0.305351 0.952240i \(-0.401226\pi\)
0.305351 + 0.952240i \(0.401226\pi\)
\(752\) 0 0
\(753\) −25.9643 + 23.8147i −0.946191 + 0.867857i
\(754\) 0 0
\(755\) 8.01386 + 13.5866i 0.291654 + 0.494466i
\(756\) 0 0
\(757\) −14.6049 + 14.6049i −0.530826 + 0.530826i −0.920818 0.389992i \(-0.872478\pi\)
0.389992 + 0.920818i \(0.372478\pi\)
\(758\) 0 0
\(759\) 17.3544 21.8389i 0.629924 0.792701i
\(760\) 0 0
\(761\) −21.2600 6.90779i −0.770674 0.250407i −0.102821 0.994700i \(-0.532787\pi\)
−0.667854 + 0.744293i \(0.732787\pi\)
\(762\) 0 0
\(763\) −4.96032 + 9.73517i −0.179575 + 0.352437i
\(764\) 0 0
\(765\) 20.7858 6.19197i 0.751514 0.223871i
\(766\) 0 0
\(767\) −9.82050 1.55541i −0.354598 0.0561627i
\(768\) 0 0
\(769\) −2.03314 2.79838i −0.0733169 0.100912i 0.770784 0.637097i \(-0.219865\pi\)
−0.844101 + 0.536185i \(0.819865\pi\)
\(770\) 0 0
\(771\) 1.78655 41.3729i 0.0643411 1.49001i
\(772\) 0 0
\(773\) 15.1556 + 29.7445i 0.545109 + 1.06984i 0.985124 + 0.171846i \(0.0549731\pi\)
−0.440015 + 0.897990i \(0.645027\pi\)
\(774\) 0 0
\(775\) 4.70849 + 37.9787i 0.169134 + 1.36423i
\(776\) 0 0
\(777\) −61.7711 34.9094i −2.21603 1.25237i
\(778\) 0 0
\(779\) 8.77489 + 6.37533i 0.314393 + 0.228420i
\(780\) 0 0
\(781\) −1.06277 + 0.772148i −0.0380289 + 0.0276296i
\(782\) 0 0
\(783\) 43.5262 1.20227i 1.55550 0.0429658i
\(784\) 0 0
\(785\) −38.1989 9.85497i −1.36338 0.351739i
\(786\) 0 0
\(787\) 18.0985 + 9.22165i 0.645142 + 0.328716i 0.745766 0.666208i \(-0.232084\pi\)
−0.100624 + 0.994925i \(0.532084\pi\)
\(788\) 0 0
\(789\) −4.88647 17.5874i −0.173963 0.626127i
\(790\) 0 0
\(791\) 20.8761 6.78304i 0.742267 0.241177i
\(792\) 0 0
\(793\) 5.49973 + 5.49973i 0.195301 + 0.195301i
\(794\) 0 0
\(795\) 1.38828 9.95508i 0.0492371 0.353070i
\(796\) 0 0
\(797\) 5.53887 + 34.9710i