Properties

Label 300.2.x.a.17.4
Level $300$
Weight $2$
Character 300.17
Analytic conductor $2.396$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.x (of order \(20\), degree \(8\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 17.4
Character \(\chi\) \(=\) 300.17
Dual form 300.2.x.a.53.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.719024 - 1.57576i) q^{3} +(-1.13602 + 1.92599i) q^{5} +(3.00936 + 3.00936i) q^{7} +(-1.96601 + 2.26601i) q^{9} +O(q^{10})\) \(q+(-0.719024 - 1.57576i) q^{3} +(-1.13602 + 1.92599i) q^{5} +(3.00936 + 3.00936i) q^{7} +(-1.96601 + 2.26601i) q^{9} +(2.76163 - 0.897307i) q^{11} +(0.404807 + 0.794479i) q^{13} +(3.85172 + 0.405257i) q^{15} +(3.19333 - 0.505773i) q^{17} +(0.694208 - 0.955496i) q^{19} +(2.57821 - 6.90582i) q^{21} +(-2.51796 + 4.94177i) q^{23} +(-2.41891 - 4.37594i) q^{25} +(4.98429 + 1.46864i) q^{27} +(6.77941 - 4.92553i) q^{29} +(6.19212 + 4.49884i) q^{31} +(-3.39961 - 3.70646i) q^{33} +(-9.21471 + 2.37731i) q^{35} +(-8.57635 + 4.36987i) q^{37} +(0.960839 - 1.20913i) q^{39} +(-8.73412 - 2.83789i) q^{41} +(-1.45614 + 1.45614i) q^{43} +(-2.13089 - 6.36076i) q^{45} +(-1.10756 + 6.99286i) q^{47} +11.1125i q^{49} +(-3.09305 - 4.66824i) q^{51} +(2.56331 + 0.405989i) q^{53} +(-1.40906 + 6.33824i) q^{55} +(-2.00478 - 0.406879i) q^{57} +(3.44583 - 10.6052i) q^{59} +(-2.69549 - 8.29586i) q^{61} +(-12.7357 + 0.902808i) q^{63} +(-1.99003 - 0.122889i) q^{65} +(0.616819 + 3.89444i) q^{67} +(9.59749 + 0.414436i) q^{69} +(-0.265914 - 0.366000i) q^{71} +(-2.68754 - 1.36937i) q^{73} +(-5.15616 + 6.95802i) q^{75} +(11.0110 + 5.61041i) q^{77} +(2.07296 + 2.85319i) q^{79} +(-1.26961 - 8.91000i) q^{81} +(-2.20859 - 13.9445i) q^{83} +(-2.65357 + 6.72490i) q^{85} +(-12.6360 - 7.14112i) q^{87} +(-2.41968 - 7.44701i) q^{89} +(-1.17266 + 3.60908i) q^{91} +(2.63679 - 12.9920i) q^{93} +(1.05164 + 2.42251i) q^{95} +(-1.51448 - 0.239870i) q^{97} +(-3.39608 + 8.02199i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 2q^{3} + 4q^{7} + O(q^{10}) \) \( 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{13}{20}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.719024 1.57576i −0.415128 0.909763i
\(4\) 0 0
\(5\) −1.13602 + 1.92599i −0.508044 + 0.861331i
\(6\) 0 0
\(7\) 3.00936 + 3.00936i 1.13743 + 1.13743i 0.988909 + 0.148522i \(0.0474516\pi\)
0.148522 + 0.988909i \(0.452548\pi\)
\(8\) 0 0
\(9\) −1.96601 + 2.26601i −0.655337 + 0.755337i
\(10\) 0 0
\(11\) 2.76163 0.897307i 0.832662 0.270548i 0.138496 0.990363i \(-0.455773\pi\)
0.694166 + 0.719815i \(0.255773\pi\)
\(12\) 0 0
\(13\) 0.404807 + 0.794479i 0.112273 + 0.220349i 0.940305 0.340332i \(-0.110539\pi\)
−0.828032 + 0.560681i \(0.810539\pi\)
\(14\) 0 0
\(15\) 3.85172 + 0.405257i 0.994510 + 0.104637i
\(16\) 0 0
\(17\) 3.19333 0.505773i 0.774496 0.122668i 0.243339 0.969941i \(-0.421757\pi\)
0.531157 + 0.847273i \(0.321757\pi\)
\(18\) 0 0
\(19\) 0.694208 0.955496i 0.159262 0.219206i −0.721927 0.691969i \(-0.756743\pi\)
0.881189 + 0.472763i \(0.156743\pi\)
\(20\) 0 0
\(21\) 2.57821 6.90582i 0.562613 1.50697i
\(22\) 0 0
\(23\) −2.51796 + 4.94177i −0.525030 + 1.03043i 0.464428 + 0.885611i \(0.346260\pi\)
−0.989458 + 0.144819i \(0.953740\pi\)
\(24\) 0 0
\(25\) −2.41891 4.37594i −0.483782 0.875189i
\(26\) 0 0
\(27\) 4.98429 + 1.46864i 0.959226 + 0.282639i
\(28\) 0 0
\(29\) 6.77941 4.92553i 1.25890 0.914648i 0.260201 0.965554i \(-0.416211\pi\)
0.998703 + 0.0509065i \(0.0162111\pi\)
\(30\) 0 0
\(31\) 6.19212 + 4.49884i 1.11214 + 0.808015i 0.982999 0.183611i \(-0.0587787\pi\)
0.129139 + 0.991627i \(0.458779\pi\)
\(32\) 0 0
\(33\) −3.39961 3.70646i −0.591796 0.645213i
\(34\) 0 0
\(35\) −9.21471 + 2.37731i −1.55757 + 0.401839i
\(36\) 0 0
\(37\) −8.57635 + 4.36987i −1.40994 + 0.718402i −0.982608 0.185691i \(-0.940548\pi\)
−0.427335 + 0.904093i \(0.640548\pi\)
\(38\) 0 0
\(39\) 0.960839 1.20913i 0.153857 0.193615i
\(40\) 0 0
\(41\) −8.73412 2.83789i −1.36404 0.443204i −0.466651 0.884442i \(-0.654540\pi\)
−0.897390 + 0.441238i \(0.854540\pi\)
\(42\) 0 0
\(43\) −1.45614 + 1.45614i −0.222059 + 0.222059i −0.809365 0.587306i \(-0.800188\pi\)
0.587306 + 0.809365i \(0.300188\pi\)
\(44\) 0 0
\(45\) −2.13089 6.36076i −0.317655 0.948206i
\(46\) 0 0
\(47\) −1.10756 + 6.99286i −0.161554 + 1.02001i 0.765049 + 0.643973i \(0.222715\pi\)
−0.926603 + 0.376041i \(0.877285\pi\)
\(48\) 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 \(-0.392959\pi\)
0.0221195 + 0.999755i \(0.492959\pi\)
\(54\) 0 0
\(55\) −1.40906 + 6.33824i −0.189998 + 0.854648i
\(56\) 0 0
\(57\) −2.00478 0.406879i −0.265540 0.0538924i
\(58\) 0 0
\(59\) 3.44583 10.6052i 0.448609 1.38068i −0.429867 0.902892i \(-0.641440\pi\)
0.878477 0.477785i \(-0.158560\pi\)
\(60\) 0 0
\(61\) −2.69549 8.29586i −0.345122 1.06218i −0.961519 0.274740i \(-0.911408\pi\)
0.616397 0.787436i \(-0.288592\pi\)
\(62\) 0 0
\(63\) −12.7357 + 0.902808i −1.60454 + 0.113743i
\(64\) 0 0
\(65\) −1.99003 0.122889i −0.246833 0.0152425i
\(66\) 0 0
\(67\) 0.616819 + 3.89444i 0.0753564 + 0.475782i 0.996290 + 0.0860617i \(0.0274282\pi\)
−0.920933 + 0.389720i \(0.872572\pi\)
\(68\) 0 0
\(69\) 9.59749 + 0.414436i 1.15540 + 0.0498923i
\(70\) 0 0
\(71\) −0.265914 0.366000i −0.0315582 0.0434362i 0.792946 0.609292i \(-0.208546\pi\)
−0.824505 + 0.565855i \(0.808546\pi\)
\(72\) 0 0
\(73\) −2.68754 1.36937i −0.314553 0.160273i 0.289585 0.957152i \(-0.406483\pi\)
−0.604139 + 0.796879i \(0.706483\pi\)
\(74\) 0 0
\(75\) −5.15616 + 6.95802i −0.595383 + 0.803442i
\(76\) 0 0
\(77\) 11.0110 + 5.61041i 1.25483 + 0.639366i
\(78\) 0 0
\(79\) 2.07296 + 2.85319i 0.233227 + 0.321009i 0.909549 0.415597i \(-0.136427\pi\)
−0.676322 + 0.736606i \(0.736427\pi\)
\(80\) 0 0
\(81\) −1.26961 8.91000i −0.141067 0.990000i
\(82\) 0 0
\(83\) −2.20859 13.9445i −0.242424 1.53060i −0.745585 0.666411i \(-0.767830\pi\)
0.503161 0.864193i \(-0.332170\pi\)
\(84\) 0 0
\(85\) −2.65357 + 6.72490i −0.287820 + 0.729418i
\(86\) 0 0
\(87\) −12.6360 7.14112i −1.35472 0.765608i
\(88\) 0 0
\(89\) −2.41968 7.44701i −0.256486 0.789382i −0.993533 0.113541i \(-0.963781\pi\)
0.737048 0.675841i \(-0.236219\pi\)
\(90\) 0 0
\(91\) −1.17266 + 3.60908i −0.122928 + 0.378335i
\(92\) 0 0
\(93\) 2.63679 12.9920i 0.273422 1.34721i
\(94\) 0 0
\(95\) 1.05164 + 2.42251i 0.107896 + 0.248544i
\(96\) 0 0
\(97\) −1.51448 0.239870i −0.153772 0.0243551i 0.0790736 0.996869i \(-0.474804\pi\)
−0.232846 + 0.972514i \(0.574804\pi\)
\(98\) 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 −0.227016 0.973891i \(-0.572897\pi\)
0.516854 0.856074i \(-0.327103\pi\)
\(104\) 0 0
\(105\) 10.3717 + 12.8108i 1.01217 + 1.25020i
\(106\) 0 0
\(107\) 1.62455 1.62455i 0.157051 0.157051i −0.624208 0.781259i \(-0.714578\pi\)
0.781259 + 0.624208i \(0.214578\pi\)
\(108\) 0 0
\(109\) −2.44163 0.793334i −0.233866 0.0759876i 0.189740 0.981834i \(-0.439236\pi\)
−0.423605 + 0.905847i \(0.639236\pi\)
\(110\) 0 0
\(111\) 13.0524 + 10.3722i 1.23888 + 0.984485i
\(112\) 0 0
\(113\) −4.59551 + 2.34153i −0.432310 + 0.220273i −0.656583 0.754253i \(-0.727999\pi\)
0.224274 + 0.974526i \(0.427999\pi\)
\(114\) 0 0
\(115\) −6.65736 10.4635i −0.620802 0.975729i
\(116\) 0 0
\(117\) −2.59615 0.644657i −0.240014 0.0595985i
\(118\) 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
\(123\) 1.80822 + 15.8034i 0.163042 + 1.42494i
\(124\) 0 0
\(125\) 11.1760 + 0.312362i 0.999610 + 0.0279385i
\(126\) 0 0
\(127\) 6.30372 12.3717i 0.559364 1.09781i −0.422168 0.906518i \(-0.638731\pi\)
0.981532 0.191297i \(-0.0612693\pi\)
\(128\) 0 0
\(129\) 3.34151 + 1.24752i 0.294204 + 0.109838i
\(130\) 0 0
\(131\) −6.21317 + 8.55169i −0.542847 + 0.747165i −0.989020 0.147782i \(-0.952787\pi\)
0.446173 + 0.894947i \(0.352787\pi\)
\(132\) 0 0
\(133\) 4.96455 0.786308i 0.430481 0.0681815i
\(134\) 0 0
\(135\) −8.49084 + 7.93130i −0.730775 + 0.682618i
\(136\) 0 0
\(137\) 9.93006 + 19.4888i 0.848382 + 1.66504i 0.741681 + 0.670752i \(0.234029\pi\)
0.106701 + 0.994291i \(0.465971\pi\)
\(138\) 0 0
\(139\) 13.6780 4.44425i 1.16015 0.376956i 0.335193 0.942150i \(-0.391198\pi\)
0.824958 + 0.565193i \(0.191198\pi\)
\(140\) 0 0
\(141\) 11.8154 3.28279i 0.995037 0.276461i
\(142\) 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
\(147\) 17.5106 7.99014i 1.44425 0.659016i
\(148\) 0 0
\(149\) −19.6307 −1.60821 −0.804106 0.594487i \(-0.797355\pi\)
−0.804106 + 0.594487i \(0.797355\pi\)
\(150\) 0 0
\(151\) 7.05432 0.574072 0.287036 0.957920i \(-0.407330\pi\)
0.287036 + 0.957920i \(0.407330\pi\)
\(152\) 0 0
\(153\) −5.13203 + 8.23047i −0.414900 + 0.665394i
\(154\) 0 0
\(155\) −15.6991 + 6.81521i −1.26098 + 0.547411i
\(156\) 0 0
\(157\) −12.4751 12.4751i −0.995620 0.995620i 0.00437087 0.999990i \(-0.498609\pi\)
−0.999990 + 0.00437087i \(0.998609\pi\)
\(158\) 0 0
\(159\) −1.20334 4.33107i −0.0954312 0.343476i
\(160\) 0 0
\(161\) −22.4490 + 7.29412i −1.76923 + 0.574857i
\(162\) 0 0
\(163\) 4.70822 + 9.24039i 0.368776 + 0.723764i 0.998596 0.0529778i \(-0.0168712\pi\)
−0.629820 + 0.776741i \(0.716871\pi\)
\(164\) 0 0
\(165\) 11.0007 2.33701i 0.856400 0.181936i
\(166\) 0 0
\(167\) −4.64134 + 0.735116i −0.359158 + 0.0568850i −0.333406 0.942783i \(-0.608198\pi\)
−0.0257518 + 0.999668i \(0.508198\pi\)
\(168\) 0 0
\(169\) 7.17388 9.87400i 0.551837 0.759538i
\(170\) 0 0
\(171\) 0.800343 + 3.45160i 0.0612037 + 0.263950i
\(172\) 0 0
\(173\) 5.89408 11.5678i 0.448119 0.879483i −0.550873 0.834589i \(-0.685705\pi\)
0.998992 0.0448938i \(-0.0142949\pi\)
\(174\) 0 0
\(175\) 5.88942 20.4482i 0.445198 1.54574i
\(176\) 0 0
\(177\) −19.1888 + 2.19559i −1.44232 + 0.165030i
\(178\) 0 0
\(179\) 9.64168 7.00509i 0.720653 0.523585i −0.165940 0.986136i \(-0.553066\pi\)
0.886593 + 0.462551i \(0.153066\pi\)
\(180\) 0 0
\(181\) 2.03092 + 1.47555i 0.150957 + 0.109677i 0.660700 0.750650i \(-0.270259\pi\)
−0.509743 + 0.860327i \(0.670259\pi\)
\(182\) 0 0
\(183\) −11.1341 + 10.2123i −0.823058 + 0.754918i
\(184\) 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
\(189\) 10.5799 + 19.4192i 0.769571 + 1.41254i
\(190\) 0 0
\(191\) 4.35419 + 1.41476i 0.315058 + 0.102369i 0.462278 0.886735i \(-0.347032\pi\)
−0.147219 + 0.989104i \(0.547032\pi\)
\(192\) 0 0
\(193\) −0.834752 + 0.834752i −0.0600868 + 0.0600868i −0.736512 0.676425i \(-0.763528\pi\)
0.676425 + 0.736512i \(0.263528\pi\)
\(194\) 0 0
\(195\) 1.23724 + 3.22416i 0.0886004 + 0.230887i
\(196\) 0 0
\(197\) −3.31070 + 20.9029i −0.235878 + 1.48927i 0.530941 + 0.847409i \(0.321838\pi\)
−0.766819 + 0.641863i \(0.778162\pi\)
\(198\) 0 0
\(199\) 12.1010i 0.857815i 0.903348 + 0.428908i \(0.141101\pi\)
−0.903348 + 0.428908i \(0.858899\pi\)
\(200\) 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
\(207\) −6.24777 15.4213i −0.434250 1.07185i
\(208\) 0 0
\(209\) 1.05977 3.26164i 0.0733059 0.225612i
\(210\) 0 0
\(211\) −6.11917 18.8329i −0.421261 1.29651i −0.906530 0.422142i \(-0.861278\pi\)
0.485269 0.874365i \(-0.338722\pi\)
\(212\) 0 0
\(213\) −0.385527 + 0.682179i −0.0264159 + 0.0467421i
\(214\) 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
\(219\) −0.225388 + 5.21952i −0.0152303 + 0.352703i
\(220\) 0 0
\(221\) 1.69451 + 2.33229i 0.113985 + 0.156887i
\(222\) 0 0
\(223\) −6.45454 3.28875i −0.432228 0.220231i 0.224320 0.974516i \(-0.427984\pi\)
−0.656548 + 0.754285i \(0.727984\pi\)
\(224\) 0 0
\(225\) 14.6715 + 3.12188i 0.978102 + 0.208125i
\(226\) 0 0
\(227\) −1.65327 0.842383i −0.109731 0.0559109i 0.398263 0.917271i \(-0.369613\pi\)
−0.507995 + 0.861360i \(0.669613\pi\)
\(228\) 0 0
\(229\) −13.9886 19.2537i −0.924394 1.27232i −0.962006 0.273027i \(-0.911975\pi\)
0.0376122 0.999292i \(-0.488025\pi\)
\(230\) 0 0
\(231\) 0.923430 21.3847i 0.0607573 1.40701i
\(232\) 0 0
\(233\) 0.810240 + 5.11565i 0.0530806 + 0.335138i 0.999910 + 0.0134021i \(0.00426616\pi\)
−0.946830 + 0.321735i \(0.895734\pi\)
\(234\) 0 0
\(235\) −12.2100 10.0772i −0.796493 0.657364i
\(236\) 0 0
\(237\) 3.00542 5.31800i 0.195223 0.345441i
\(238\) 0 0
\(239\) −1.51663 4.66771i −0.0981026 0.301929i 0.889947 0.456064i \(-0.150741\pi\)
−0.988050 + 0.154135i \(0.950741\pi\)
\(240\) 0 0
\(241\) 1.76890 5.44413i 0.113945 0.350687i −0.877780 0.479063i \(-0.840976\pi\)
0.991726 + 0.128376i \(0.0409765\pi\)
\(242\) 0 0
\(243\) −13.1271 + 8.40709i −0.842104 + 0.539315i
\(244\) 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
\(255\) 12.5048 0.653980i 0.783080 0.0409538i
\(256\) 0 0
\(257\) 16.9061 16.9061i 1.05458 1.05458i 0.0561541 0.998422i \(-0.482116\pi\)
0.998422 0.0561541i \(-0.0178838\pi\)
\(258\) 0 0
\(259\) −38.9598 12.6588i −2.42085 0.786581i
\(260\) 0 0
\(261\) −2.16709 + 25.0459i −0.134139 + 1.55030i
\(262\) 0 0
\(263\) 9.39006 4.78447i 0.579016 0.295023i −0.139850 0.990173i \(-0.544662\pi\)
0.718865 + 0.695150i \(0.244662\pi\)
\(264\) 0 0
\(265\) −3.69391 + 4.47571i −0.226915 + 0.274941i
\(266\) 0 0
\(267\) −9.99486 + 9.16740i −0.611676 + 0.561036i
\(268\) 0 0
\(269\) −6.24078 4.53419i −0.380507 0.276454i 0.381048 0.924555i \(-0.375563\pi\)
−0.761554 + 0.648101i \(0.775563\pi\)
\(270\) 0 0
\(271\) −16.4232 + 11.9322i −0.997641 + 0.724828i −0.961581 0.274521i \(-0.911481\pi\)
−0.0360598 + 0.999350i \(0.511481\pi\)
\(272\) 0 0
\(273\) 6.53021 0.747187i 0.395226 0.0452218i
\(274\) 0 0
\(275\) −10.6067 9.91422i −0.639607 0.597850i
\(276\) 0 0
\(277\) 8.84515 17.3596i 0.531453 1.04304i −0.456708 0.889617i \(-0.650971\pi\)
0.988161 0.153419i \(-0.0490285\pi\)
\(278\) 0 0
\(279\) −22.3682 + 5.18665i −1.33915 + 0.310516i
\(280\) 0 0
\(281\) −1.43495 + 1.97505i −0.0856022 + 0.117821i −0.849670 0.527314i \(-0.823199\pi\)
0.764068 + 0.645136i \(0.223199\pi\)
\(282\) 0 0
\(283\) −8.06450 + 1.27729i −0.479385 + 0.0759271i −0.391450 0.920199i \(-0.628027\pi\)
−0.0879343 + 0.996126i \(0.528027\pi\)
\(284\) 0 0
\(285\) 3.06112 3.39897i 0.181325 0.201338i
\(286\) 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
\(291\) 0.710971 + 2.55892i 0.0416779 + 0.150007i
\(292\) 0 0
\(293\) 11.2030 + 11.2030i 0.654488 + 0.654488i 0.954070 0.299582i \(-0.0968473\pi\)
−0.299582 + 0.954070i \(0.596847\pi\)
\(294\) 0 0
\(295\) 16.5110 + 18.6844i 0.961307 + 1.08785i
\(296\) 0 0
\(297\) 15.0826 0.416608i 0.875179 0.0241741i
\(298\) 0 0
\(299\) −4.94542 −0.286001
\(300\) 0 0
\(301\) −8.76407 −0.505153
\(302\) 0 0
\(303\) −6.61062 + 3.01645i −0.379770 + 0.173291i
\(304\) 0 0
\(305\) 19.0399 + 4.23278i 1.09022 + 0.242368i
\(306\) 0 0
\(307\) −2.43888 2.43888i −0.139194 0.139194i 0.634076 0.773270i \(-0.281380\pi\)
−0.773270 + 0.634076i \(0.781380\pi\)
\(308\) 0 0
\(309\) −31.3801 + 8.71865i −1.78515 + 0.495987i
\(310\) 0 0
\(311\) 9.68418 3.14658i 0.549139 0.178426i −0.0212893 0.999773i \(-0.506777\pi\)
0.570429 + 0.821347i \(0.306777\pi\)
\(312\) 0 0
\(313\) −1.29485 2.54128i −0.0731892 0.143642i 0.851513 0.524334i \(-0.175686\pi\)
−0.924702 + 0.380692i \(0.875686\pi\)
\(314\) 0 0
\(315\) 12.7292 25.5544i 0.717209 1.43983i
\(316\) 0 0
\(317\) −23.8744 + 3.78133i −1.34092 + 0.212381i −0.785331 0.619076i \(-0.787507\pi\)
−0.555589 + 0.831457i \(0.687507\pi\)
\(318\) 0 0
\(319\) 14.3025 19.6857i 0.800786 1.10219i
\(320\) 0 0
\(321\) −3.72798 1.39180i −0.208075 0.0776828i
\(322\) 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
\(327\) 0.505489 + 4.41784i 0.0279536 + 0.244307i
\(328\) 0 0
\(329\) −24.3771 + 17.7110i −1.34395 + 0.976439i
\(330\) 0 0
\(331\) 6.91086 + 5.02103i 0.379855 + 0.275981i 0.761286 0.648417i \(-0.224568\pi\)
−0.381431 + 0.924397i \(0.624568\pi\)
\(332\) 0 0
\(333\) 6.95903 28.0253i 0.381352 1.53578i
\(334\) 0 0
\(335\) −8.20139 3.23618i −0.448090 0.176811i
\(336\) 0 0
\(337\) −3.29999 + 1.68143i −0.179762 + 0.0915932i −0.541556 0.840665i \(-0.682164\pi\)
0.361794 + 0.932258i \(0.382164\pi\)
\(338\) 0 0
\(339\) 6.99396 + 5.55779i 0.379860 + 0.301858i
\(340\) 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
\(345\) −11.7012 + 18.0139i −0.629969 + 0.969836i
\(346\) 0 0
\(347\) 1.58515 10.0082i 0.0850953 0.537270i −0.907907 0.419172i \(-0.862320\pi\)
0.993002 0.118098i \(-0.0376797\pi\)
\(348\) 0 0
\(349\) 10.8302i 0.579729i 0.957068 + 0.289864i \(0.0936102\pi\)
−0.957068 + 0.289864i \(0.906390\pi\)
\(350\) 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 \(-0.565539\pi\)
−0.496929 + 0.867791i \(0.665539\pi\)
\(354\) 0 0
\(355\) 1.00700 0.0963659i 0.0534459 0.00511457i
\(356\) 0 0
\(357\) 4.74031 23.3565i 0.250884 1.23616i
\(358\) 0 0
\(359\) 10.0379 30.8935i 0.529781 1.63050i −0.224882 0.974386i \(-0.572200\pi\)
0.754663 0.656113i \(-0.227800\pi\)
\(360\) 0 0
\(361\) 5.44028 + 16.7434i 0.286330 + 0.881234i
\(362\) 0 0
\(363\) 3.87269 + 2.18862i 0.203264 + 0.114873i
\(364\) 0 0
\(365\) 5.69051 3.62056i 0.297855 0.189509i
\(366\) 0 0
\(367\) −1.65984 10.4798i −0.0866430 0.547042i −0.992381 0.123205i \(-0.960683\pi\)
0.905738 0.423837i \(-0.139317\pi\)
\(368\) 0 0
\(369\) 23.6021 14.2123i 1.22867 0.739863i
\(370\) 0 0
\(371\) 6.49216 + 8.93569i 0.337056 + 0.463918i
\(372\) 0 0
\(373\) 14.2945 + 7.28340i 0.740140 + 0.377120i 0.783050 0.621959i \(-0.213663\pi\)
−0.0429097 + 0.999079i \(0.513663\pi\)
\(374\) 0 0
\(375\) −7.54358 17.8352i −0.389549 0.921006i
\(376\) 0 0
\(377\) 6.65759 + 3.39221i 0.342883 + 0.174708i
\(378\) 0 0
\(379\) 18.2024 + 25.0535i 0.934995 + 1.28691i 0.957879 + 0.287173i \(0.0927153\pi\)
−0.0228835 + 0.999738i \(0.507285\pi\)
\(380\) 0 0
\(381\) −24.0274 1.03754i −1.23096 0.0531550i
\(382\) 0 0
\(383\) 4.80077 + 30.3108i 0.245308 + 1.54881i 0.735698 + 0.677309i \(0.236854\pi\)
−0.490391 + 0.871503i \(0.663146\pi\)
\(384\) 0 0
\(385\) −23.3144 + 14.8337i −1.18821 + 0.755994i
\(386\) 0 0
\(387\) −0.436841 6.16240i −0.0222059 0.313252i
\(388\) 0 0
\(389\) 7.88532 + 24.2685i 0.399802 + 1.23046i 0.925159 + 0.379581i \(0.123932\pi\)
−0.525357 + 0.850882i \(0.676068\pi\)
\(390\) 0 0
\(391\) −5.54125 + 17.0542i −0.280233 + 0.862468i
\(392\) 0 0
\(393\) 17.9428 + 3.64157i 0.905094 + 0.183693i
\(394\) 0 0
\(395\) −7.85016 + 0.751231i −0.394984 + 0.0377985i
\(396\) 0 0
\(397\) 8.20587 + 1.29968i 0.411841 + 0.0652292i 0.358917 0.933369i \(-0.383146\pi\)
0.0529236 + 0.998599i \(0.483146\pi\)
\(398\) 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
\(405\) 18.6029 + 7.67670i 0.924386 + 0.381458i
\(406\) 0 0
\(407\) −19.7636 + 19.7636i −0.979644 + 0.979644i
\(408\) 0 0
\(409\) −14.6004 4.74394i −0.721941 0.234573i −0.0750765 0.997178i \(-0.523920\pi\)
−0.646865 + 0.762605i \(0.723920\pi\)
\(410\) 0 0
\(411\) 23.5697 29.6603i 1.16261 1.46303i
\(412\) 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
\(417\) −16.8378 18.3576i −0.824552 0.898977i
\(418\) 0 0
\(419\) −7.27149 5.28305i −0.355236 0.258094i 0.395827 0.918325i \(-0.370458\pi\)
−0.751062 + 0.660232i \(0.770458\pi\)
\(420\) 0 0
\(421\) 22.8808 16.6239i 1.11514 0.810199i 0.131678 0.991293i \(-0.457964\pi\)
0.983466 + 0.181093i \(0.0579636\pi\)
\(422\) 0 0
\(423\) −13.6684 16.2578i −0.664582 0.790481i
\(424\) 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
\(429\) 1.56852 4.20132i 0.0757289 0.202842i
\(430\) 0 0
\(431\) −18.6234 + 25.6329i −0.897059 + 1.23470i 0.0743381 + 0.997233i \(0.476316\pi\)
−0.971397 + 0.237462i \(0.923684\pi\)
\(432\) 0 0
\(433\) 8.79670 1.39326i 0.422743 0.0669559i 0.0585611 0.998284i \(-0.481349\pi\)
0.364182 + 0.931328i \(0.381349\pi\)
\(434\) 0 0
\(435\) 28.1085 16.2244i 1.34770 0.777899i
\(436\) 0 0
\(437\) 2.97385 + 5.83651i 0.142259 + 0.279198i
\(438\) 0 0
\(439\) 35.2858 11.4651i 1.68410 0.547198i 0.698401 0.715707i \(-0.253895\pi\)
0.985700 + 0.168509i \(0.0538953\pi\)
\(440\) 0 0
\(441\) −25.1810 21.8473i −1.19910 1.04035i
\(442\) 0 0
\(443\) −0.101009 0.101009i −0.00479907 0.00479907i 0.704703 0.709502i \(-0.251080\pi\)
−0.709502 + 0.704703i \(0.751080\pi\)
\(444\) 0 0
\(445\) 17.0917 + 3.79968i 0.810225 + 0.180122i
\(446\) 0 0
\(447\) 14.1149 + 30.9332i 0.667614 + 1.46309i
\(448\) 0 0
\(449\) −5.09561 −0.240477 −0.120238 0.992745i \(-0.538366\pi\)
−0.120238 + 0.992745i \(0.538366\pi\)
\(450\) 0 0
\(451\) −26.6669 −1.25569
\(452\) 0 0
\(453\) −5.07222 11.1159i −0.238314 0.522270i
\(454\) 0 0
\(455\) −5.61891 6.35854i −0.263418 0.298093i
\(456\) 0 0
\(457\) 9.17964 + 9.17964i 0.429406 + 0.429406i 0.888426 0.459020i \(-0.151799\pi\)
−0.459020 + 0.888426i \(0.651799\pi\)
\(458\) 0 0
\(459\) 16.6593 + 2.16892i 0.777587 + 0.101236i
\(460\) 0 0
\(461\) 2.89432 0.940423i 0.134802 0.0437999i −0.240839 0.970565i \(-0.577423\pi\)
0.375641 + 0.926765i \(0.377423\pi\)
\(462\) 0 0
\(463\) 3.81952 + 7.49623i 0.177508 + 0.348380i 0.962568 0.271041i \(-0.0873678\pi\)
−0.785060 + 0.619420i \(0.787368\pi\)
\(464\) 0 0
\(465\) 22.0271 + 19.8377i 1.02148 + 0.919951i
\(466\) 0 0
\(467\) −3.67547 + 0.582137i −0.170080 + 0.0269381i −0.240894 0.970551i \(-0.577441\pi\)
0.0708133 + 0.997490i \(0.477441\pi\)
\(468\) 0 0
\(469\) −9.86354 + 13.5760i −0.455456 + 0.626882i
\(470\) 0 0
\(471\) −10.6878 + 28.6275i −0.492468 + 1.31909i
\(472\) 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
\(477\) −5.95947 + 5.01031i −0.272865 + 0.229406i
\(478\) 0 0
\(479\) 19.2357 13.9755i 0.878900 0.638558i −0.0540606 0.998538i \(-0.517216\pi\)
0.932960 + 0.359980i \(0.117216\pi\)
\(480\) 0 0
\(481\) −6.94354 5.04478i −0.316598 0.230022i
\(482\) 0 0
\(483\) 27.6351 + 30.1295i 1.25744 + 1.37094i
\(484\) 0 0
\(485\) 2.18247 2.64439i 0.0991010 0.120075i
\(486\) 0 0
\(487\) −36.1675 + 18.4282i −1.63890 + 0.835063i −0.641197 + 0.767376i \(0.721562\pi\)
−0.997707 + 0.0676872i \(0.978438\pi\)
\(488\) 0 0
\(489\) 11.1753 14.0631i 0.505364 0.635953i
\(490\) 0 0
\(491\) −22.0112 7.15186i −0.993350 0.322759i −0.233145 0.972442i \(-0.574902\pi\)
−0.760205 + 0.649683i \(0.774902\pi\)
\(492\) 0 0
\(493\) 19.1577 19.1577i 0.862818 0.862818i
\(494\) 0 0
\(495\) −11.5923 15.6540i −0.521035 0.703594i
\(496\) 0 0
\(497\) 0.301193 1.90166i 0.0135103 0.0853010i
\(498\) 0 0
\(499\) 35.2669i 1.57876i 0.613904 + 0.789381i \(0.289598\pi\)
−0.613904 + 0.789381i \(0.710402\pi\)
\(500\) 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 \(-0.641494\pi\)
−0.687961 + 0.725748i \(0.741494\pi\)
\(504\) 0 0
\(505\) 8.07995 + 4.76585i 0.359553 + 0.212078i
\(506\) 0 0
\(507\) −20.7172 4.20464i −0.920083 0.186735i
\(508\) 0 0
\(509\) 1.80435 5.55322i 0.0799765 0.246142i −0.903072 0.429490i \(-0.858693\pi\)
0.983048 + 0.183348i \(0.0586934\pi\)
\(510\) 0 0
\(511\) −3.96685 12.2087i −0.175483 0.540082i
\(512\) 0 0
\(513\) 4.86341 3.74292i 0.214725 0.165254i
\(514\) 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
\(519\) −22.4660 0.970121i −0.986148 0.0425836i
\(520\) 0 0
\(521\) −5.69171 7.83396i −0.249358 0.343212i 0.665928 0.746016i \(-0.268036\pi\)
−0.915286 + 0.402804i \(0.868036\pi\)
\(522\) 0 0
\(523\) −0.993315 0.506119i −0.0434346 0.0221310i 0.432138 0.901807i \(-0.357759\pi\)
−0.475573 + 0.879676i \(0.657759\pi\)
\(524\) 0 0
\(525\) −36.4559 + 5.42242i −1.59107 + 0.236654i
\(526\) 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
\(531\) 17.2569 + 28.6582i 0.748886 + 1.24366i
\(532\) 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
\(537\) −17.9709 10.1561i −0.775502 0.438268i
\(538\) 0 0
\(539\) 9.97132 + 30.6886i 0.429495 + 1.32185i
\(540\) 0 0
\(541\) −9.75500 + 30.0228i −0.419400 + 1.29078i 0.488855 + 0.872365i \(0.337415\pi\)
−0.908255 + 0.418417i \(0.862585\pi\)
\(542\) 0 0
\(543\) 0.864828 4.26120i 0.0371133 0.182865i
\(544\) 0 0
\(545\) 4.30170 3.80132i 0.184265 0.162831i
\(546\) 0 0
\(547\) −30.7784 4.87482i −1.31599 0.208432i −0.541330 0.840810i \(-0.682079\pi\)
−0.774660 + 0.632378i \(0.782079\pi\)
\(548\) 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
\(555\) −34.8046 + 13.3559i −1.47738 + 0.566926i
\(556\) 0 0
\(557\) −11.9164 + 11.9164i −0.504915 + 0.504915i −0.912961 0.408046i \(-0.866210\pi\)
0.408046 + 0.912961i \(0.366210\pi\)
\(558\) 0 0
\(559\) −1.74632 0.567415i −0.0738616 0.0239991i
\(560\) 0 0
\(561\) −12.7307 10.1165i −0.537491 0.427120i
\(562\) 0 0
\(563\) −16.5294 + 8.42215i −0.696631 + 0.354951i −0.766179 0.642627i \(-0.777844\pi\)
0.0695477 + 0.997579i \(0.477844\pi\)
\(564\) 0 0
\(565\) 0.710828 11.5110i 0.0299047 0.484270i
\(566\) 0 0
\(567\) 22.9927 30.6341i 0.965602 1.28651i
\(568\) 0 0
\(569\) −1.23297 0.895803i −0.0516887 0.0375540i 0.561641 0.827381i \(-0.310170\pi\)
−0.613330 + 0.789827i \(0.710170\pi\)
\(570\) 0 0
\(571\) 24.3901 17.7205i 1.02070 0.741579i 0.0542700 0.998526i \(-0.482717\pi\)
0.966425 + 0.256948i \(0.0827168\pi\)
\(572\) 0 0
\(573\) −0.901447 7.87839i −0.0376585 0.329125i
\(574\) 0 0
\(575\) 27.7156 0.935252i 1.15582 0.0390027i
\(576\) 0 0
\(577\) 16.3743 32.1363i 0.681669 1.33785i −0.247749 0.968824i \(-0.579691\pi\)
0.929419 0.369027i \(-0.120309\pi\)
\(578\) 0 0
\(579\) 1.91557 + 0.715159i 0.0796085 + 0.0297210i
\(580\) 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
\(585\) 4.19089 4.26783i 0.173272 0.176453i
\(586\) 0 0
\(587\) −7.58856 14.8934i −0.313213 0.614716i 0.679709 0.733482i \(-0.262106\pi\)
−0.992922 + 0.118766i \(0.962106\pi\)
\(588\) 0 0
\(589\) 8.59724 2.79341i 0.354243 0.115101i
\(590\) 0 0
\(591\) 35.3184 9.81285i 1.45280 0.403647i
\(592\) 0 0
\(593\) −17.3573 17.3573i −0.712780 0.712780i 0.254336 0.967116i \(-0.418143\pi\)
−0.967116 + 0.254336i \(0.918143\pi\)
\(594\) 0 0
\(595\) −28.2232 + 12.2521i −1.15704 + 0.502287i
\(596\) 0 0
\(597\) 19.0682 8.70088i 0.780408 0.356103i
\(598\) 0 0
\(599\) −14.4303 −0.589605 −0.294802 0.955558i \(-0.595254\pi\)
−0.294802 + 0.955558i \(0.595254\pi\)
\(600\) 0 0
\(601\) −40.6930 −1.65990 −0.829951 0.557837i \(-0.811632\pi\)
−0.829951 + 0.557837i \(0.811632\pi\)
\(602\) 0 0
\(603\) −10.0375 6.25879i −0.408759 0.254878i
\(604\) 0 0
\(605\) −0.547065 5.71668i −0.0222413 0.232416i
\(606\) 0 0
\(607\) 31.1483 + 31.1483i 1.26427 + 1.26427i 0.949003 + 0.315266i \(0.102094\pi\)
0.315266 + 0.949003i \(0.397906\pi\)
\(608\) 0 0
\(609\) −16.5360 59.5164i −0.670074 2.41173i
\(610\) 0 0
\(611\) −6.00403 + 1.95083i −0.242897 + 0.0789221i
\(612\) 0 0
\(613\) −16.5958 32.5711i −0.670299 1.31554i −0.936177 0.351529i \(-0.885662\pi\)
0.265878 0.964007i \(-0.414338\pi\)
\(614\) 0 0
\(615\) −32.4913 14.4703i −1.31018 0.583500i
\(616\) 0 0
\(617\) 34.4877 5.46232i 1.38842 0.219905i 0.582936 0.812518i \(-0.301904\pi\)
0.805487 + 0.592613i \(0.201904\pi\)
\(618\) 0 0
\(619\) 3.48931 4.80263i 0.140247 0.193034i −0.733115 0.680104i \(-0.761934\pi\)
0.873363 + 0.487070i \(0.161934\pi\)
\(620\) 0 0
\(621\) −19.8079 + 20.9332i −0.794863 + 0.840021i
\(622\) 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
\(627\) −5.90155 + 0.675256i −0.235685 + 0.0269671i
\(628\) 0 0
\(629\) −25.1769 + 18.2921i −1.00387 + 0.729354i
\(630\) 0 0
\(631\) 21.9450 + 15.9440i 0.873616 + 0.634719i 0.931555 0.363601i \(-0.118453\pi\)
−0.0579392 + 0.998320i \(0.518453\pi\)
\(632\) 0 0
\(633\) −25.2762 + 23.1836i −1.00464 + 0.921464i
\(634\) 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
\(639\) 1.35215 + 0.116995i 0.0534902 + 0.00462823i
\(640\) 0 0
\(641\) −6.43772 2.09174i −0.254275 0.0826188i 0.179106 0.983830i \(-0.442679\pi\)
−0.433381 + 0.901211i \(0.642679\pi\)
\(642\) 0 0
\(643\) −1.88726 + 1.88726i −0.0744264 + 0.0744264i −0.743340 0.668914i \(-0.766760\pi\)
0.668914 + 0.743340i \(0.266760\pi\)
\(644\) 0 0
\(645\) −6.19874 + 5.01852i −0.244075 + 0.197604i
\(646\) 0 0
\(647\) 1.80177 11.3759i 0.0708349 0.447234i −0.926624 0.375989i \(-0.877303\pi\)
0.997459 0.0712445i \(-0.0226971\pi\)
\(648\) 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 \(-0.754013\pi\)
−0.896659 + 0.442722i \(0.854013\pi\)
\(654\) 0 0
\(655\) −9.41222 21.6814i −0.367766 0.847164i
\(656\) 0 0
\(657\) 8.38675 3.39780i 0.327198 0.132561i
\(658\) 0 0
\(659\) 0.104879 0.322784i 0.00408550 0.0125739i −0.948993 0.315297i \(-0.897896\pi\)
0.953078 + 0.302723i \(0.0978958\pi\)
\(660\) 0 0
\(661\) 4.25007 + 13.0804i 0.165308 + 0.508767i 0.999059 0.0433745i \(-0.0138109\pi\)
−0.833750 + 0.552141i \(0.813811\pi\)
\(662\) 0 0
\(663\) 2.45673 4.34710i 0.0954115 0.168828i
\(664\) 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
\(669\) −0.541303 + 12.5355i −0.0209280 + 0.484649i
\(670\) 0 0
\(671\) −14.8879 20.4914i −0.574739 0.791061i
\(672\) 0 0
\(673\) −8.28693 4.22240i −0.319438 0.162762i 0.286918 0.957955i \(-0.407369\pi\)
−0.606356 + 0.795193i \(0.707369\pi\)
\(674\) 0 0
\(675\) −5.62986 25.3635i −0.216694 0.976240i
\(676\) 0 0
\(677\) 3.29687 + 1.67984i 0.126709 + 0.0645615i 0.516196 0.856470i \(-0.327348\pi\)
−0.389487 + 0.921032i \(0.627348\pi\)
\(678\) 0 0
\(679\) −3.83576 5.27948i −0.147203 0.202608i
\(680\) 0 0
\(681\) −0.138650 + 3.21084i −0.00531307 + 0.123040i
\(682\) 0 0
\(683\) −1.53600 9.69792i −0.0587734 0.371081i −0.999491 0.0318908i \(-0.989847\pi\)
0.940718 0.339190i \(-0.110153\pi\)
\(684\) 0 0
\(685\) −48.8161 3.01451i −1.86517 0.115178i
\(686\) 0 0
\(687\) −20.2810 + 35.8865i −0.773767 + 1.36916i
\(688\) 0 0
\(689\) 0.715098 + 2.20084i 0.0272430 + 0.0838455i
\(690\) 0 0
\(691\) −5.28572 + 16.2678i −0.201078 + 0.618855i 0.798773 + 0.601632i \(0.205483\pi\)
−0.999852 + 0.0172234i \(0.994517\pi\)
\(692\) 0 0
\(693\) −34.3611 + 13.9210i −1.30527 + 0.528816i
\(694\) 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
\(705\) −7.09993 + 26.4857i −0.267399 + 0.997510i
\(706\) 0 0
\(707\) 12.6249 12.6249i 0.474808 0.474808i
\(708\) 0 0
\(709\) 12.9358 + 4.20308i 0.485813 + 0.157850i 0.541674 0.840588i \(-0.317791\pi\)
−0.0558616 + 0.998439i \(0.517791\pi\)
\(710\) 0 0
\(711\) −10.5408 0.912043i −0.395312 0.0342043i
\(712\) 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
\(717\) −6.26467 + 5.74603i −0.233958 + 0.214589i
\(718\) 0 0
\(719\) 29.7221 + 21.5944i 1.10845 + 0.805335i 0.982419 0.186692i \(-0.0597766\pi\)
0.126030 + 0.992026i \(0.459777\pi\)
\(720\) 0 0
\(721\) 64.7423 47.0380i 2.41113 1.75179i
\(722\) 0 0
\(723\) −9.85050 + 1.12710i −0.366344 + 0.0419171i
\(724\) 0 0
\(725\) −37.9526 17.7519i −1.40952 0.659289i
\(726\) 0 0
\(727\) −4.12344 + 8.09270i −0.152930 + 0.300142i −0.954742 0.297434i \(-0.903869\pi\)
0.801813 + 0.597576i \(0.203869\pi\)
\(728\) 0 0
\(729\) 22.6862 + 14.6402i 0.840230 + 0.542230i
\(730\) 0 0
\(731\) −3.91344 + 5.38639i −0.144744 + 0.199223i
\(732\) 0 0
\(733\) −9.91162 + 1.56985i −0.366094 + 0.0579836i −0.336771 0.941586i \(-0.609335\pi\)
−0.0293225 + 0.999570i \(0.509335\pi\)
\(734\) 0 0
\(735\) −4.50342 + 42.8022i −0.166111 + 1.57878i
\(736\) 0 0
\(737\) 5.19793 + 10.2015i 0.191468 + 0.375778i
\(738\) 0 0
\(739\) −47.6656 + 15.4875i −1.75341 + 0.569717i −0.996484 0.0837861i \(-0.973299\pi\)
−0.756924 + 0.653503i \(0.773299\pi\)
\(740\) 0 0
\(741\) −0.488293 1.75746i −0.0179379 0.0645620i
\(742\) 0 0
\(743\) 0.668282 + 0.668282i 0.0245169 + 0.0245169i 0.719259 0.694742i \(-0.244481\pi\)
−0.694742 + 0.719259i \(0.744481\pi\)
\(744\) 0 0
\(745\) 22.3009 37.8087i 0.817043 1.38520i
\(746\) 0 0
\(747\) 35.9404 + 22.4103i 1.31499 + 0.819949i
\(748\) 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
\(753\) 32.0527 14.6258i 1.16806 0.532992i
\(754\) 0 0
\(755\) −8.01386 + 13.5866i −0.291654 + 0.494466i
\(756\) 0 0
\(757\) −14.6049 14.6049i −0.530826 0.530826i 0.389992 0.920818i \(-0.372478\pi\)
−0.920818 + 0.389992i \(0.872478\pi\)
\(758\) 0 0
\(759\) 26.8766 7.46738i 0.975557 0.271049i
\(760\) 0 0
\(761\) 21.2600 6.90779i 0.770674 0.250407i 0.102821 0.994700i \(-0.467213\pi\)
0.667854 + 0.744293i \(0.267213\pi\)
\(762\) 0 0
\(763\) −4.96032 9.73517i −0.179575 0.352437i
\(764\) 0 0
\(765\) −10.0217 19.2342i −0.362337 0.695416i
\(766\) 0 0
\(767\) 9.82050 1.55541i 0.354598 0.0561627i
\(768\) 0 0
\(769\) −2.03314 + 2.79838i −0.0733169 + 0.100912i −0.844101 0.536185i \(-0.819865\pi\)
0.770784 + 0.637097i \(0.219865\pi\)
\(770\) 0 0
\(771\) −38.7959 14.4840i −1.39720 0.521630i
\(772\) 0 0
\(773\) −15.1556 + 29.7445i −0.545109 + 1.06984i 0.440015 + 0.897990i \(0.354973\pi\)
−0.985124 + 0.171846i \(0.945027\pi\)
\(774\) 0 0
\(775\) 4.70849 37.9787i 0.169134 1.36423i
\(776\) 0 0
\(777\) 8.06584 + 70.4932i 0.289360 + 2.52893i
\(778\) 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
\(783\) 41.0243 14.5938i 1.46609 0.521538i
\(784\) 0 0
\(785\) 38.1989 9.85497i 1.36338 0.351739i
\(786\) 0 0
\(787\) 18.0985 9.22165i 0.645142 0.328716i −0.100624 0.994925i \(-0.532084\pi\)
0.745766 + 0.666208i \(0.232084\pi\)
\(788\) 0 0
\(789\) −14.2908 11.3563i −0.508767 0.404294i
\(790\) 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
\(795\) 9.70863 + 2.60256i 0.344330 + 0.0923031i
\(796\) 0 0