Properties

Label 300.2.m.b.241.2
Level $300$
Weight $2$
Character 300.241
Analytic conductor $2.396$
Analytic rank $0$
Dimension $8$
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.m (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.26265625.1
Defining polynomial: \(x^{8} - 3 x^{7} + 2 x^{6} + x^{4} + 8 x^{2} - 24 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 241.2
Root \(-1.21700 - 0.720348i\) of defining polynomial
Character \(\chi\) \(=\) 300.241
Dual form 300.2.m.b.61.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.309017 - 0.951057i) q^{3} +(-0.962197 + 2.01846i) q^{5} +1.50430 q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.309017 - 0.951057i) q^{3} +(-0.962197 + 2.01846i) q^{5} +1.50430 q^{7} +(-0.809017 + 0.587785i) q^{9} +(4.99517 + 3.62921i) q^{11} +(2.87714 - 2.09036i) q^{13} +(2.21700 + 0.291365i) q^{15} +(0.153180 - 0.471439i) q^{17} +(0.0963126 - 0.296420i) q^{19} +(-0.464854 - 1.43067i) q^{21} +(2.47611 + 1.79900i) q^{23} +(-3.14835 - 3.88431i) q^{25} +(0.809017 + 0.587785i) q^{27} +(-0.0378031 - 0.116346i) q^{29} +(-0.909629 + 2.79955i) q^{31} +(1.90799 - 5.87218i) q^{33} +(-1.44743 + 3.03637i) q^{35} +(3.53298 - 2.56686i) q^{37} +(-2.87714 - 2.09036i) q^{39} +(-3.44096 + 2.50001i) q^{41} -3.62663 q^{43} +(-0.407987 - 2.19853i) q^{45} +(1.63227 + 5.02362i) q^{47} -4.73708 q^{49} -0.495700 q^{51} +(-2.65748 - 8.17888i) q^{53} +(-12.1317 + 6.59054i) q^{55} -0.311674 q^{57} +(-10.4222 + 7.57219i) q^{59} +(9.15882 + 6.65427i) q^{61} +(-1.21700 + 0.884205i) q^{63} +(1.45094 + 7.81873i) q^{65} +(4.09181 - 12.5933i) q^{67} +(0.945790 - 2.91084i) q^{69} +(1.00994 + 3.10827i) q^{71} +(-12.9174 - 9.38504i) q^{73} +(-2.72130 + 4.19458i) q^{75} +(7.51424 + 5.45941i) q^{77} +(-2.63513 - 8.11010i) q^{79} +(0.309017 - 0.951057i) q^{81} +(3.50367 - 10.7832i) q^{83} +(0.804191 + 0.762805i) q^{85} +(-0.0989699 + 0.0719058i) q^{87} +(-11.4335 - 8.30691i) q^{89} +(4.32808 - 3.14453i) q^{91} +2.94362 q^{93} +(0.505640 + 0.479617i) q^{95} +(-3.54837 - 10.9208i) q^{97} -6.17438 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{3} - 5q^{5} + 8q^{7} - 2q^{9} + O(q^{10}) \) \( 8q + 2q^{3} - 5q^{5} + 8q^{7} - 2q^{9} + 8q^{11} + 5q^{15} + 3q^{17} + 5q^{19} + 7q^{21} - 7q^{23} + 5q^{25} + 2q^{27} - 3q^{29} - 3q^{31} + 7q^{33} - 10q^{35} - q^{37} + 10q^{41} - 12q^{43} + 5q^{45} - 33q^{47} - 8q^{49} - 8q^{51} - 19q^{53} - 15q^{55} + 10q^{57} - 38q^{59} + 46q^{61} + 3q^{63} + 25q^{65} - 8q^{67} + 2q^{69} - 25q^{71} - 26q^{73} - 5q^{75} + 23q^{77} - 16q^{79} - 2q^{81} + 8q^{83} - 30q^{85} + 3q^{87} - 30q^{89} + 25q^{91} - 22q^{93} - 25q^{95} - 14q^{97} - 2q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\)

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
\(3\) −0.309017 0.951057i −0.178411 0.549093i
\(4\) 0 0
\(5\) −0.962197 + 2.01846i −0.430308 + 0.902682i
\(6\) 0 0
\(7\) 1.50430 0.568572 0.284286 0.958740i \(-0.408244\pi\)
0.284286 + 0.958740i \(0.408244\pi\)
\(8\) 0 0
\(9\) −0.809017 + 0.587785i −0.269672 + 0.195928i
\(10\) 0 0
\(11\) 4.99517 + 3.62921i 1.50610 + 1.09425i 0.967870 + 0.251450i \(0.0809074\pi\)
0.538231 + 0.842797i \(0.319093\pi\)
\(12\) 0 0
\(13\) 2.87714 2.09036i 0.797975 0.579763i −0.112344 0.993669i \(-0.535836\pi\)
0.910319 + 0.413906i \(0.135836\pi\)
\(14\) 0 0
\(15\) 2.21700 + 0.291365i 0.572428 + 0.0752302i
\(16\) 0 0
\(17\) 0.153180 0.471439i 0.0371516 0.114341i −0.930761 0.365629i \(-0.880854\pi\)
0.967912 + 0.251288i \(0.0808541\pi\)
\(18\) 0 0
\(19\) 0.0963126 0.296420i 0.0220956 0.0680034i −0.939401 0.342821i \(-0.888618\pi\)
0.961496 + 0.274818i \(0.0886175\pi\)
\(20\) 0 0
\(21\) −0.464854 1.43067i −0.101439 0.312199i
\(22\) 0 0
\(23\) 2.47611 + 1.79900i 0.516305 + 0.375117i 0.815210 0.579165i \(-0.196621\pi\)
−0.298905 + 0.954283i \(0.596621\pi\)
\(24\) 0 0
\(25\) −3.14835 3.88431i −0.629671 0.776862i
\(26\) 0 0
\(27\) 0.809017 + 0.587785i 0.155695 + 0.113119i
\(28\) 0 0
\(29\) −0.0378031 0.116346i −0.00701987 0.0216049i 0.947485 0.319800i \(-0.103616\pi\)
−0.954505 + 0.298195i \(0.903616\pi\)
\(30\) 0 0
\(31\) −0.909629 + 2.79955i −0.163374 + 0.502814i −0.998913 0.0466176i \(-0.985156\pi\)
0.835539 + 0.549432i \(0.185156\pi\)
\(32\) 0 0
\(33\) 1.90799 5.87218i 0.332138 1.02222i
\(34\) 0 0
\(35\) −1.44743 + 3.03637i −0.244661 + 0.513240i
\(36\) 0 0
\(37\) 3.53298 2.56686i 0.580818 0.421989i −0.258201 0.966091i \(-0.583130\pi\)
0.839019 + 0.544102i \(0.183130\pi\)
\(38\) 0 0
\(39\) −2.87714 2.09036i −0.460711 0.334726i
\(40\) 0 0
\(41\) −3.44096 + 2.50001i −0.537388 + 0.390436i −0.823114 0.567876i \(-0.807765\pi\)
0.285726 + 0.958311i \(0.407765\pi\)
\(42\) 0 0
\(43\) −3.62663 −0.553056 −0.276528 0.961006i \(-0.589184\pi\)
−0.276528 + 0.961006i \(0.589184\pi\)
\(44\) 0 0
\(45\) −0.407987 2.19853i −0.0608191 0.327738i
\(46\) 0 0
\(47\) 1.63227 + 5.02362i 0.238091 + 0.732770i 0.996696 + 0.0812191i \(0.0258813\pi\)
−0.758605 + 0.651551i \(0.774119\pi\)
\(48\) 0 0
\(49\) −4.73708 −0.676726
\(50\) 0 0
\(51\) −0.495700 −0.0694120
\(52\) 0 0
\(53\) −2.65748 8.17888i −0.365033 1.12346i −0.949960 0.312370i \(-0.898877\pi\)
0.584928 0.811086i \(-0.301123\pi\)
\(54\) 0 0
\(55\) −12.1317 + 6.59054i −1.63584 + 0.888669i
\(56\) 0 0
\(57\) −0.311674 −0.0412823
\(58\) 0 0
\(59\) −10.4222 + 7.57219i −1.35686 + 0.985815i −0.358220 + 0.933637i \(0.616616\pi\)
−0.998638 + 0.0521781i \(0.983384\pi\)
\(60\) 0 0
\(61\) 9.15882 + 6.65427i 1.17267 + 0.851992i 0.991326 0.131428i \(-0.0419562\pi\)
0.181341 + 0.983420i \(0.441956\pi\)
\(62\) 0 0
\(63\) −1.21700 + 0.884205i −0.153328 + 0.111399i
\(64\) 0 0
\(65\) 1.45094 + 7.81873i 0.179967 + 0.969794i
\(66\) 0 0
\(67\) 4.09181 12.5933i 0.499894 1.53852i −0.309293 0.950967i \(-0.600092\pi\)
0.809188 0.587550i \(-0.199908\pi\)
\(68\) 0 0
\(69\) 0.945790 2.91084i 0.113860 0.350424i
\(70\) 0 0
\(71\) 1.00994 + 3.10827i 0.119858 + 0.368884i 0.992929 0.118708i \(-0.0378753\pi\)
−0.873071 + 0.487592i \(0.837875\pi\)
\(72\) 0 0
\(73\) −12.9174 9.38504i −1.51187 1.09844i −0.965340 0.260994i \(-0.915950\pi\)
−0.546527 0.837441i \(-0.684050\pi\)
\(74\) 0 0
\(75\) −2.72130 + 4.19458i −0.314229 + 0.484348i
\(76\) 0 0
\(77\) 7.51424 + 5.45941i 0.856327 + 0.622158i
\(78\) 0 0
\(79\) −2.63513 8.11010i −0.296475 0.912457i −0.982722 0.185088i \(-0.940743\pi\)
0.686247 0.727369i \(-0.259257\pi\)
\(80\) 0 0
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 0 0
\(83\) 3.50367 10.7832i 0.384578 1.18361i −0.552208 0.833706i \(-0.686215\pi\)
0.936786 0.349903i \(-0.113785\pi\)
\(84\) 0 0
\(85\) 0.804191 + 0.762805i 0.0872268 + 0.0827378i
\(86\) 0 0
\(87\) −0.0989699 + 0.0719058i −0.0106107 + 0.00770911i
\(88\) 0 0
\(89\) −11.4335 8.30691i −1.21195 0.880531i −0.216541 0.976274i \(-0.569477\pi\)
−0.995406 + 0.0957428i \(0.969477\pi\)
\(90\) 0 0
\(91\) 4.32808 3.14453i 0.453706 0.329637i
\(92\) 0 0
\(93\) 2.94362 0.305239
\(94\) 0 0
\(95\) 0.505640 + 0.479617i 0.0518775 + 0.0492077i
\(96\) 0 0
\(97\) −3.54837 10.9208i −0.360282 1.10884i −0.952883 0.303339i \(-0.901899\pi\)
0.592601 0.805497i \(-0.298101\pi\)
\(98\) 0 0
\(99\) −6.17438 −0.620548
\(100\) 0 0
\(101\) −14.8359 −1.47622 −0.738111 0.674679i \(-0.764282\pi\)
−0.738111 + 0.674679i \(0.764282\pi\)
\(102\) 0 0
\(103\) 5.95307 + 18.3217i 0.586574 + 1.80529i 0.592857 + 0.805308i \(0.298000\pi\)
−0.00628354 + 0.999980i \(0.502000\pi\)
\(104\) 0 0
\(105\) 3.33504 + 0.438301i 0.325466 + 0.0427738i
\(106\) 0 0
\(107\) 8.63523 0.834799 0.417400 0.908723i \(-0.362942\pi\)
0.417400 + 0.908723i \(0.362942\pi\)
\(108\) 0 0
\(109\) 15.1200 10.9853i 1.44823 1.05220i 0.461989 0.886886i \(-0.347136\pi\)
0.986241 0.165315i \(-0.0528641\pi\)
\(110\) 0 0
\(111\) −3.53298 2.56686i −0.335335 0.243635i
\(112\) 0 0
\(113\) −4.89971 + 3.55985i −0.460926 + 0.334883i −0.793894 0.608056i \(-0.791950\pi\)
0.332968 + 0.942938i \(0.391950\pi\)
\(114\) 0 0
\(115\) −6.01371 + 3.26694i −0.560782 + 0.304643i
\(116\) 0 0
\(117\) −1.09897 + 3.38228i −0.101600 + 0.312692i
\(118\) 0 0
\(119\) 0.230428 0.709186i 0.0211233 0.0650109i
\(120\) 0 0
\(121\) 8.38144 + 25.7954i 0.761949 + 2.34504i
\(122\) 0 0
\(123\) 3.44096 + 2.50001i 0.310261 + 0.225418i
\(124\) 0 0
\(125\) 10.8697 2.61735i 0.972212 0.234103i
\(126\) 0 0
\(127\) 7.47988 + 5.43445i 0.663732 + 0.482230i 0.867921 0.496702i \(-0.165456\pi\)
−0.204189 + 0.978931i \(0.565456\pi\)
\(128\) 0 0
\(129\) 1.12069 + 3.44913i 0.0986714 + 0.303679i
\(130\) 0 0
\(131\) 5.87613 18.0849i 0.513399 1.58008i −0.272776 0.962078i \(-0.587942\pi\)
0.786175 0.618003i \(-0.212058\pi\)
\(132\) 0 0
\(133\) 0.144883 0.445904i 0.0125630 0.0386648i
\(134\) 0 0
\(135\) −1.96485 + 1.06740i −0.169108 + 0.0918674i
\(136\) 0 0
\(137\) −6.36053 + 4.62120i −0.543417 + 0.394816i −0.825352 0.564618i \(-0.809024\pi\)
0.281936 + 0.959433i \(0.409024\pi\)
\(138\) 0 0
\(139\) 11.1647 + 8.11165i 0.946980 + 0.688021i 0.950091 0.311974i \(-0.100990\pi\)
−0.00311101 + 0.999995i \(0.500990\pi\)
\(140\) 0 0
\(141\) 4.27335 3.10477i 0.359881 0.261469i
\(142\) 0 0
\(143\) 21.9582 1.83624
\(144\) 0 0
\(145\) 0.271214 + 0.0356438i 0.0225231 + 0.00296005i
\(146\) 0 0
\(147\) 1.46384 + 4.50523i 0.120735 + 0.371585i
\(148\) 0 0
\(149\) 5.12168 0.419585 0.209792 0.977746i \(-0.432721\pi\)
0.209792 + 0.977746i \(0.432721\pi\)
\(150\) 0 0
\(151\) −12.9476 −1.05366 −0.526829 0.849972i \(-0.676619\pi\)
−0.526829 + 0.849972i \(0.676619\pi\)
\(152\) 0 0
\(153\) 0.153180 + 0.471439i 0.0123839 + 0.0381136i
\(154\) 0 0
\(155\) −4.77554 4.52977i −0.383580 0.363840i
\(156\) 0 0
\(157\) −4.02750 −0.321429 −0.160715 0.987001i \(-0.551380\pi\)
−0.160715 + 0.987001i \(0.551380\pi\)
\(158\) 0 0
\(159\) −6.95737 + 5.05483i −0.551755 + 0.400874i
\(160\) 0 0
\(161\) 3.72481 + 2.70623i 0.293556 + 0.213281i
\(162\) 0 0
\(163\) −12.6360 + 9.18062i −0.989732 + 0.719082i −0.959862 0.280472i \(-0.909509\pi\)
−0.0298692 + 0.999554i \(0.509509\pi\)
\(164\) 0 0
\(165\) 10.0169 + 9.50139i 0.779814 + 0.739682i
\(166\) 0 0
\(167\) 3.66014 11.2647i 0.283230 0.871692i −0.703694 0.710503i \(-0.748467\pi\)
0.986924 0.161189i \(-0.0515327\pi\)
\(168\) 0 0
\(169\) −0.108909 + 0.335187i −0.00837761 + 0.0257836i
\(170\) 0 0
\(171\) 0.0963126 + 0.296420i 0.00736521 + 0.0226678i
\(172\) 0 0
\(173\) −11.9982 8.71717i −0.912203 0.662754i 0.0293681 0.999569i \(-0.490651\pi\)
−0.941571 + 0.336814i \(0.890651\pi\)
\(174\) 0 0
\(175\) −4.73607 5.84317i −0.358013 0.441702i
\(176\) 0 0
\(177\) 10.4222 + 7.57219i 0.783382 + 0.569161i
\(178\) 0 0
\(179\) −0.295895 0.910670i −0.0221162 0.0680667i 0.939389 0.342852i \(-0.111393\pi\)
−0.961505 + 0.274786i \(0.911393\pi\)
\(180\) 0 0
\(181\) 1.27971 3.93855i 0.0951202 0.292750i −0.892165 0.451710i \(-0.850814\pi\)
0.987285 + 0.158960i \(0.0508141\pi\)
\(182\) 0 0
\(183\) 3.49836 10.7668i 0.258606 0.795908i
\(184\) 0 0
\(185\) 1.78168 + 9.60099i 0.130992 + 0.705879i
\(186\) 0 0
\(187\) 2.47611 1.79900i 0.181071 0.131556i
\(188\) 0 0
\(189\) 1.21700 + 0.884205i 0.0885240 + 0.0643165i
\(190\) 0 0
\(191\) 14.2634 10.3629i 1.03206 0.749836i 0.0633410 0.997992i \(-0.479824\pi\)
0.968720 + 0.248156i \(0.0798244\pi\)
\(192\) 0 0
\(193\) 5.25392 0.378185 0.189093 0.981959i \(-0.439445\pi\)
0.189093 + 0.981959i \(0.439445\pi\)
\(194\) 0 0
\(195\) 6.98769 3.79605i 0.500399 0.271841i
\(196\) 0 0
\(197\) −0.653870 2.01240i −0.0465863 0.143378i 0.925058 0.379827i \(-0.124016\pi\)
−0.971644 + 0.236449i \(0.924016\pi\)
\(198\) 0 0
\(199\) 9.07029 0.642976 0.321488 0.946914i \(-0.395817\pi\)
0.321488 + 0.946914i \(0.395817\pi\)
\(200\) 0 0
\(201\) −13.2414 −0.933975
\(202\) 0 0
\(203\) −0.0568672 0.175019i −0.00399130 0.0122840i
\(204\) 0 0
\(205\) −1.73528 9.35095i −0.121197 0.653098i
\(206\) 0 0
\(207\) −3.06064 −0.212729
\(208\) 0 0
\(209\) 1.55687 1.13113i 0.107691 0.0782419i
\(210\) 0 0
\(211\) 16.0306 + 11.6469i 1.10359 + 0.801807i 0.981643 0.190729i \(-0.0610853\pi\)
0.121950 + 0.992536i \(0.461085\pi\)
\(212\) 0 0
\(213\) 2.64405 1.92102i 0.181168 0.131626i
\(214\) 0 0
\(215\) 3.48953 7.32021i 0.237984 0.499234i
\(216\) 0 0
\(217\) −1.36835 + 4.21136i −0.0928900 + 0.285886i
\(218\) 0 0
\(219\) −4.93401 + 15.1853i −0.333409 + 1.02613i
\(220\) 0 0
\(221\) −0.544760 1.67660i −0.0366445 0.112780i
\(222\) 0 0
\(223\) −5.32506 3.86888i −0.356593 0.259080i 0.395037 0.918665i \(-0.370732\pi\)
−0.751629 + 0.659586i \(0.770732\pi\)
\(224\) 0 0
\(225\) 4.83021 + 1.29192i 0.322014 + 0.0861278i
\(226\) 0 0
\(227\) −9.53193 6.92535i −0.632656 0.459652i 0.224663 0.974436i \(-0.427872\pi\)
−0.857319 + 0.514785i \(0.827872\pi\)
\(228\) 0 0
\(229\) 3.67417 + 11.3079i 0.242796 + 0.747250i 0.995991 + 0.0894526i \(0.0285117\pi\)
−0.753195 + 0.657798i \(0.771488\pi\)
\(230\) 0 0
\(231\) 2.87018 8.83352i 0.188844 0.581203i
\(232\) 0 0
\(233\) −1.56054 + 4.80285i −0.102234 + 0.314645i −0.989071 0.147437i \(-0.952898\pi\)
0.886837 + 0.462082i \(0.152898\pi\)
\(234\) 0 0
\(235\) −11.7105 1.53903i −0.763911 0.100396i
\(236\) 0 0
\(237\) −6.89886 + 5.01232i −0.448129 + 0.325585i
\(238\) 0 0
\(239\) −2.16762 1.57487i −0.140212 0.101870i 0.515468 0.856909i \(-0.327618\pi\)
−0.655680 + 0.755039i \(0.727618\pi\)
\(240\) 0 0
\(241\) −10.2390 + 7.43906i −0.659551 + 0.479192i −0.866511 0.499157i \(-0.833643\pi\)
0.206960 + 0.978349i \(0.433643\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 4.55801 9.56161i 0.291200 0.610869i
\(246\) 0 0
\(247\) −0.342521 1.05417i −0.0217941 0.0670752i
\(248\) 0 0
\(249\) −11.3381 −0.718524
\(250\) 0 0
\(251\) −22.9068 −1.44586 −0.722932 0.690919i \(-0.757206\pi\)
−0.722932 + 0.690919i \(0.757206\pi\)
\(252\) 0 0
\(253\) 5.83966 + 17.9726i 0.367136 + 1.12993i
\(254\) 0 0
\(255\) 0.476961 1.00055i 0.0298685 0.0626569i
\(256\) 0 0
\(257\) −27.7764 −1.73264 −0.866322 0.499486i \(-0.833522\pi\)
−0.866322 + 0.499486i \(0.833522\pi\)
\(258\) 0 0
\(259\) 5.31466 3.86132i 0.330237 0.239931i
\(260\) 0 0
\(261\) 0.0989699 + 0.0719058i 0.00612608 + 0.00445086i
\(262\) 0 0
\(263\) −9.47479 + 6.88384i −0.584241 + 0.424476i −0.840250 0.542198i \(-0.817592\pi\)
0.256010 + 0.966674i \(0.417592\pi\)
\(264\) 0 0
\(265\) 19.0658 + 2.50568i 1.17120 + 0.153923i
\(266\) 0 0
\(267\) −4.36720 + 13.4409i −0.267268 + 0.822568i
\(268\) 0 0
\(269\) 1.29979 4.00034i 0.0792496 0.243905i −0.903580 0.428419i \(-0.859071\pi\)
0.982830 + 0.184513i \(0.0590709\pi\)
\(270\) 0 0
\(271\) −3.88308 11.9509i −0.235880 0.725965i −0.997003 0.0773578i \(-0.975352\pi\)
0.761123 0.648608i \(-0.224648\pi\)
\(272\) 0 0
\(273\) −4.32808 3.14453i −0.261947 0.190316i
\(274\) 0 0
\(275\) −1.62962 30.8288i −0.0982695 1.85905i
\(276\) 0 0
\(277\) −25.7795 18.7299i −1.54894 1.12537i −0.944400 0.328800i \(-0.893356\pi\)
−0.604543 0.796573i \(-0.706644\pi\)
\(278\) 0 0
\(279\) −0.909629 2.79955i −0.0544581 0.167605i
\(280\) 0 0
\(281\) 5.03691 15.5020i 0.300477 0.924773i −0.680849 0.732423i \(-0.738389\pi\)
0.981326 0.192350i \(-0.0616108\pi\)
\(282\) 0 0
\(283\) −4.21205 + 12.9634i −0.250381 + 0.770592i 0.744324 + 0.667819i \(0.232772\pi\)
−0.994705 + 0.102774i \(0.967228\pi\)
\(284\) 0 0
\(285\) 0.299892 0.629102i 0.0177641 0.0372648i
\(286\) 0 0
\(287\) −5.17624 + 3.76076i −0.305544 + 0.221991i
\(288\) 0 0
\(289\) 13.5545 + 9.84792i 0.797323 + 0.579289i
\(290\) 0 0
\(291\) −9.28975 + 6.74940i −0.544575 + 0.395657i
\(292\) 0 0
\(293\) 25.2652 1.47601 0.738004 0.674796i \(-0.235768\pi\)
0.738004 + 0.674796i \(0.235768\pi\)
\(294\) 0 0
\(295\) −5.25592 28.3228i −0.306012 1.64902i
\(296\) 0 0
\(297\) 1.90799 + 5.87218i 0.110713 + 0.340738i
\(298\) 0 0
\(299\) 10.8847 0.629477
\(300\) 0 0
\(301\) −5.45554 −0.314452
\(302\) 0 0
\(303\) 4.58453 + 14.1097i 0.263374 + 0.810583i
\(304\) 0 0
\(305\) −22.2440 + 12.0840i −1.27369 + 0.691927i
\(306\) 0 0
\(307\) −7.01023 −0.400095 −0.200047 0.979786i \(-0.564110\pi\)
−0.200047 + 0.979786i \(0.564110\pi\)
\(308\) 0 0
\(309\) 15.5853 11.3234i 0.886619 0.644167i
\(310\) 0 0
\(311\) −11.7403 8.52985i −0.665733 0.483683i 0.202861 0.979208i \(-0.434976\pi\)
−0.868594 + 0.495524i \(0.834976\pi\)
\(312\) 0 0
\(313\) −17.7334 + 12.8841i −1.00235 + 0.728250i −0.962591 0.270960i \(-0.912659\pi\)
−0.0397589 + 0.999209i \(0.512659\pi\)
\(314\) 0 0
\(315\) −0.613734 3.30725i −0.0345800 0.186343i
\(316\) 0 0
\(317\) −10.4194 + 32.0675i −0.585210 + 1.80109i 0.0132156 + 0.999913i \(0.495793\pi\)
−0.598426 + 0.801178i \(0.704207\pi\)
\(318\) 0 0
\(319\) 0.233411 0.718364i 0.0130685 0.0402207i
\(320\) 0 0
\(321\) −2.66843 8.21259i −0.148937 0.458382i
\(322\) 0 0
\(323\) −0.124991 0.0908111i −0.00695467 0.00505286i
\(324\) 0 0
\(325\) −17.1779 4.59450i −0.952858 0.254857i
\(326\) 0 0
\(327\) −15.1200 10.9853i −0.836136 0.607488i
\(328\) 0 0
\(329\) 2.45543 + 7.55703i 0.135372 + 0.416632i
\(330\) 0 0
\(331\) 10.3814 31.9508i 0.570616 1.75617i −0.0800299 0.996792i \(-0.525502\pi\)
0.650645 0.759382i \(-0.274498\pi\)
\(332\) 0 0
\(333\) −1.34948 + 4.15326i −0.0739509 + 0.227597i
\(334\) 0 0
\(335\) 21.4819 + 20.3764i 1.17368 + 1.11328i
\(336\) 0 0
\(337\) −2.49603 + 1.81347i −0.135967 + 0.0987859i −0.653690 0.756763i \(-0.726780\pi\)
0.517723 + 0.855548i \(0.326780\pi\)
\(338\) 0 0
\(339\) 4.89971 + 3.55985i 0.266116 + 0.193345i
\(340\) 0 0
\(341\) −14.7039 + 10.6830i −0.796261 + 0.578518i
\(342\) 0 0
\(343\) −17.6561 −0.953339
\(344\) 0 0
\(345\) 4.96538 + 4.70984i 0.267327 + 0.253569i
\(346\) 0 0
\(347\) 3.88556 + 11.9585i 0.208588 + 0.641967i 0.999547 + 0.0300984i \(0.00958206\pi\)
−0.790959 + 0.611869i \(0.790418\pi\)
\(348\) 0 0
\(349\) 13.3100 0.712466 0.356233 0.934397i \(-0.384061\pi\)
0.356233 + 0.934397i \(0.384061\pi\)
\(350\) 0 0
\(351\) 3.55634 0.189823
\(352\) 0 0
\(353\) −3.48923 10.7388i −0.185713 0.571566i 0.814247 0.580519i \(-0.197150\pi\)
−0.999960 + 0.00895265i \(0.997150\pi\)
\(354\) 0 0
\(355\) −7.24568 0.952250i −0.384561 0.0505402i
\(356\) 0 0
\(357\) −0.745682 −0.0394657
\(358\) 0 0
\(359\) −15.7007 + 11.4072i −0.828652 + 0.602051i −0.919178 0.393843i \(-0.871145\pi\)
0.0905254 + 0.995894i \(0.471145\pi\)
\(360\) 0 0
\(361\) 15.2927 + 11.1108i 0.804881 + 0.584780i
\(362\) 0 0
\(363\) 21.9429 15.9424i 1.15170 0.836761i
\(364\) 0 0
\(365\) 31.3724 17.0430i 1.64211 0.892071i
\(366\) 0 0
\(367\) 5.42951 16.7103i 0.283418 0.872271i −0.703450 0.710744i \(-0.748358\pi\)
0.986868 0.161526i \(-0.0516417\pi\)
\(368\) 0 0
\(369\) 1.31433 4.04510i 0.0684214 0.210579i
\(370\) 0 0
\(371\) −3.99764 12.3035i −0.207547 0.638765i
\(372\) 0 0
\(373\) 22.8195 + 16.5793i 1.18155 + 0.858446i 0.992346 0.123492i \(-0.0394093\pi\)
0.189204 + 0.981938i \(0.439409\pi\)
\(374\) 0 0
\(375\) −5.84816 9.52885i −0.301998 0.492068i
\(376\) 0 0
\(377\) −0.351971 0.255722i −0.0181274 0.0131703i
\(378\) 0 0
\(379\) 1.12118 + 3.45064i 0.0575912 + 0.177247i 0.975714 0.219049i \(-0.0702954\pi\)
−0.918123 + 0.396296i \(0.870295\pi\)
\(380\) 0 0
\(381\) 2.85706 8.79313i 0.146372 0.450486i
\(382\) 0 0
\(383\) −4.27519 + 13.1577i −0.218452 + 0.672326i 0.780439 + 0.625232i \(0.214996\pi\)
−0.998890 + 0.0470934i \(0.985004\pi\)
\(384\) 0 0
\(385\) −18.2498 + 9.91415i −0.930095 + 0.505272i
\(386\) 0 0
\(387\) 2.93401 2.13168i 0.149144 0.108359i
\(388\) 0 0
\(389\) 16.9096 + 12.2855i 0.857348 + 0.622900i 0.927162 0.374660i \(-0.122241\pi\)
−0.0698138 + 0.997560i \(0.522241\pi\)
\(390\) 0 0
\(391\) 1.22741 0.891765i 0.0620727 0.0450985i
\(392\) 0 0
\(393\) −19.0155 −0.959207
\(394\) 0 0
\(395\) 18.9054 + 2.48461i 0.951235 + 0.125014i
\(396\) 0 0
\(397\) −4.77499 14.6959i −0.239650 0.737566i −0.996471 0.0839436i \(-0.973248\pi\)
0.756821 0.653622i \(-0.226752\pi\)
\(398\) 0 0
\(399\) −0.468851 −0.0234719
\(400\) 0 0
\(401\) 2.25590 0.112654 0.0563271 0.998412i \(-0.482061\pi\)
0.0563271 + 0.998412i \(0.482061\pi\)
\(402\) 0 0
\(403\) 3.23495 + 9.95616i 0.161144 + 0.495952i
\(404\) 0 0
\(405\) 1.62233 + 1.53884i 0.0806144 + 0.0764657i
\(406\) 0 0
\(407\) 26.9635 1.33653
\(408\) 0 0
\(409\) 1.88712 1.37107i 0.0933119 0.0677951i −0.540151 0.841568i \(-0.681633\pi\)
0.633463 + 0.773773i \(0.281633\pi\)
\(410\) 0 0
\(411\) 6.36053 + 4.62120i 0.313742 + 0.227947i
\(412\) 0 0
\(413\) −15.6781 + 11.3908i −0.771471 + 0.560507i
\(414\) 0 0
\(415\) 18.3942 + 17.4476i 0.902936 + 0.856468i
\(416\) 0 0
\(417\) 4.26455 13.1249i 0.208836 0.642730i
\(418\) 0 0
\(419\) −1.55768 + 4.79405i −0.0760977 + 0.234205i −0.981869 0.189563i \(-0.939293\pi\)
0.905771 + 0.423768i \(0.139293\pi\)
\(420\) 0 0
\(421\) 3.99823 + 12.3053i 0.194862 + 0.599724i 0.999978 + 0.00660640i \(0.00210290\pi\)
−0.805116 + 0.593117i \(0.797897\pi\)
\(422\) 0 0
\(423\) −4.27335 3.10477i −0.207777 0.150959i
\(424\) 0 0
\(425\) −2.31348 + 0.889259i −0.112220 + 0.0431354i
\(426\) 0 0
\(427\) 13.7776 + 10.0100i 0.666745 + 0.484419i
\(428\) 0 0
\(429\) −6.78545 20.8835i −0.327605 1.00826i
\(430\) 0 0
\(431\) 0.483616 1.48842i 0.0232950 0.0716945i −0.938733 0.344645i \(-0.887999\pi\)
0.962028 + 0.272950i \(0.0879994\pi\)
\(432\) 0 0
\(433\) 7.99517 24.6066i 0.384224 1.18252i −0.552818 0.833302i \(-0.686448\pi\)
0.937042 0.349217i \(-0.113552\pi\)
\(434\) 0 0
\(435\) −0.0499105 0.268954i −0.00239302 0.0128954i
\(436\) 0 0
\(437\) 0.771740 0.560702i 0.0369173 0.0268220i
\(438\) 0 0
\(439\) −13.2446 9.62279i −0.632132 0.459271i 0.225006 0.974357i \(-0.427760\pi\)
−0.857138 + 0.515087i \(0.827760\pi\)
\(440\) 0 0
\(441\) 3.83238 2.78439i 0.182494 0.132590i
\(442\) 0 0
\(443\) 28.1180 1.33593 0.667963 0.744194i \(-0.267166\pi\)
0.667963 + 0.744194i \(0.267166\pi\)
\(444\) 0 0
\(445\) 27.7684 15.0851i 1.31635 0.715104i
\(446\) 0 0
\(447\) −1.58269 4.87101i −0.0748585 0.230391i
\(448\) 0 0
\(449\) −2.65681 −0.125383 −0.0626914 0.998033i \(-0.519968\pi\)
−0.0626914 + 0.998033i \(0.519968\pi\)
\(450\) 0 0
\(451\) −26.2613 −1.23659
\(452\) 0 0
\(453\) 4.00101 + 12.3139i 0.187984 + 0.578556i
\(454\) 0 0
\(455\) 2.18265 + 11.7617i 0.102324 + 0.551398i
\(456\) 0 0
\(457\) −0.321574 −0.0150426 −0.00752129 0.999972i \(-0.502394\pi\)
−0.00752129 + 0.999972i \(0.502394\pi\)
\(458\) 0 0
\(459\) 0.401030 0.291365i 0.0187185 0.0135998i
\(460\) 0 0
\(461\) 6.21780 + 4.51749i 0.289592 + 0.210401i 0.723090 0.690754i \(-0.242721\pi\)
−0.433499 + 0.901154i \(0.642721\pi\)
\(462\) 0 0
\(463\) −15.4555 + 11.2291i −0.718279 + 0.521860i −0.885834 0.464002i \(-0.846413\pi\)
0.167555 + 0.985863i \(0.446413\pi\)
\(464\) 0 0
\(465\) −2.83234 + 5.94158i −0.131347 + 0.275534i
\(466\) 0 0
\(467\) −1.98372 + 6.10525i −0.0917955 + 0.282517i −0.986405 0.164331i \(-0.947454\pi\)
0.894610 + 0.446848i \(0.147454\pi\)
\(468\) 0 0
\(469\) 6.15531 18.9441i 0.284226 0.874757i
\(470\) 0 0
\(471\) 1.24457 + 3.83038i 0.0573466 + 0.176495i
\(472\) 0 0
\(473\) −18.1157 13.1618i −0.832959 0.605180i
\(474\) 0 0
\(475\) −1.45461 + 0.559126i −0.0667422 + 0.0256545i
\(476\) 0 0
\(477\) 6.95737 + 5.05483i 0.318556 + 0.231445i
\(478\) 0 0
\(479\) 10.3709 + 31.9183i 0.473858 + 1.45839i 0.847491 + 0.530810i \(0.178112\pi\)
−0.373633 + 0.927577i \(0.621888\pi\)
\(480\) 0 0
\(481\) 4.79920 14.7704i 0.218825 0.673473i
\(482\) 0 0
\(483\) 1.42275 4.37878i 0.0647374 0.199241i
\(484\) 0 0
\(485\) 25.4573 + 3.34568i 1.15596 + 0.151920i
\(486\) 0 0
\(487\) 9.63578 7.00080i 0.436639 0.317237i −0.347659 0.937621i \(-0.613023\pi\)
0.784298 + 0.620384i \(0.213023\pi\)
\(488\) 0 0
\(489\) 12.6360 + 9.18062i 0.571422 + 0.415162i
\(490\) 0 0
\(491\) −12.6312 + 9.17712i −0.570039 + 0.414158i −0.835119 0.550069i \(-0.814602\pi\)
0.265080 + 0.964226i \(0.414602\pi\)
\(492\) 0 0
\(493\) −0.0606408 −0.00273112
\(494\) 0 0
\(495\) 5.94096 12.4627i 0.267026 0.560158i
\(496\) 0 0
\(497\) 1.51925 + 4.67577i 0.0681477 + 0.209737i
\(498\) 0 0
\(499\) 30.9130 1.38386 0.691929 0.721966i \(-0.256761\pi\)
0.691929 + 0.721966i \(0.256761\pi\)
\(500\) 0 0
\(501\) −11.8445 −0.529171
\(502\) 0 0
\(503\) 9.59178 + 29.5204i 0.427676 + 1.31625i 0.900408 + 0.435046i \(0.143268\pi\)
−0.472732 + 0.881206i \(0.656732\pi\)
\(504\) 0 0
\(505\) 14.2750 29.9456i 0.635230 1.33256i
\(506\) 0 0
\(507\) 0.352437 0.0156523
\(508\) 0 0
\(509\) 10.7945 7.84269i 0.478460 0.347621i −0.322269 0.946648i \(-0.604446\pi\)
0.800729 + 0.599027i \(0.204446\pi\)
\(510\) 0 0
\(511\) −19.4316 14.1179i −0.859605 0.624540i
\(512\) 0 0
\(513\) 0.252150 0.183198i 0.0111327 0.00808837i
\(514\) 0 0
\(515\) −42.7096 5.61302i −1.88201 0.247339i
\(516\) 0 0
\(517\) −10.0783 + 31.0177i −0.443242 + 1.36416i
\(518\) 0 0
\(519\) −4.58289 + 14.1047i −0.201166 + 0.619127i
\(520\) 0 0
\(521\) 8.19439 + 25.2197i 0.359003 + 1.10490i 0.953652 + 0.300912i \(0.0972910\pi\)
−0.594649 + 0.803985i \(0.702709\pi\)
\(522\) 0 0
\(523\) 14.0888 + 10.2361i 0.616060 + 0.447594i 0.851543 0.524285i \(-0.175667\pi\)
−0.235483 + 0.971878i \(0.575667\pi\)
\(524\) 0 0
\(525\) −4.09366 + 6.30991i −0.178662 + 0.275387i
\(526\) 0 0
\(527\) 1.18048 + 0.857670i 0.0514226 + 0.0373607i
\(528\) 0 0
\(529\) −4.21267 12.9653i −0.183159 0.563707i
\(530\) 0 0
\(531\) 3.98094 12.2521i 0.172758 0.531694i
\(532\) 0 0
\(533\) −4.67421 + 14.3857i −0.202463 + 0.623116i
\(534\) 0 0
\(535\) −8.30879 + 17.4299i −0.359220 + 0.753559i
\(536\) 0 0
\(537\) −0.774662 + 0.562825i −0.0334291 + 0.0242877i
\(538\) 0 0
\(539\) −23.6626 17.1919i −1.01922 0.740506i
\(540\) 0 0
\(541\) −4.42275 + 3.21332i −0.190149 + 0.138151i −0.678787 0.734335i \(-0.737494\pi\)
0.488638 + 0.872487i \(0.337494\pi\)
\(542\) 0 0
\(543\) −4.14123 −0.177717
\(544\) 0 0
\(545\) 7.62499 + 41.0890i 0.326619 + 1.76006i
\(546\) 0 0
\(547\) 6.68894 + 20.5864i 0.285998 + 0.880212i 0.986098 + 0.166167i \(0.0531391\pi\)
−0.700099 + 0.714046i \(0.746861\pi\)
\(548\) 0 0
\(549\) −11.3209 −0.483165
\(550\) 0 0
\(551\) −0.0381282 −0.00162432
\(552\) 0 0
\(553\) −3.96403 12.2000i −0.168568 0.518798i
\(554\) 0 0
\(555\) 8.58052 4.66135i 0.364223 0.197863i
\(556\) 0 0
\(557\) −2.58830 −0.109670 −0.0548349 0.998495i \(-0.517463\pi\)
−0.0548349 + 0.998495i \(0.517463\pi\)
\(558\) 0 0
\(559\) −10.4343 + 7.58099i −0.441325 + 0.320642i
\(560\) 0 0
\(561\) −2.47611 1.79900i −0.104541 0.0759538i
\(562\) 0 0
\(563\) −16.0945 + 11.6933i −0.678301 + 0.492815i −0.872794 0.488089i \(-0.837694\pi\)
0.194493 + 0.980904i \(0.437694\pi\)
\(564\) 0 0
\(565\) −2.47092 13.3151i −0.103953 0.560172i
\(566\) 0 0
\(567\) 0.464854 1.43067i 0.0195220 0.0600827i
\(568\) 0 0
\(569\) 10.0215 30.8431i 0.420124 1.29301i −0.487463 0.873144i \(-0.662077\pi\)
0.907587 0.419865i \(-0.137923\pi\)
\(570\) 0 0
\(571\) 4.23915 + 13.0468i 0.177403 + 0.545990i 0.999735 0.0230176i \(-0.00732739\pi\)
−0.822332 + 0.569008i \(0.807327\pi\)
\(572\) 0 0
\(573\) −14.2634 10.3629i −0.595861 0.432918i
\(574\) 0 0
\(575\) −0.807801 15.2819i −0.0336876 0.637298i
\(576\) 0 0
\(577\) −19.9368 14.4849i −0.829979 0.603015i 0.0895741 0.995980i \(-0.471449\pi\)
−0.919553 + 0.392965i \(0.871449\pi\)
\(578\) 0 0
\(579\) −1.62355 4.99677i −0.0674724 0.207659i
\(580\) 0 0
\(581\) 5.27057 16.2212i 0.218660 0.672967i
\(582\) 0 0
\(583\) 16.4083 50.4995i 0.679561 2.09147i
\(584\) 0 0
\(585\) −5.76957 5.47265i −0.238542 0.226266i
\(586\) 0 0
\(587\) −6.73236 + 4.89134i −0.277874 + 0.201887i −0.717990 0.696054i \(-0.754938\pi\)
0.440115 + 0.897941i \(0.354938\pi\)
\(588\) 0 0
\(589\) 0.742234 + 0.539264i 0.0305832 + 0.0222200i
\(590\) 0 0
\(591\) −1.71185 + 1.24373i −0.0704162 + 0.0511604i
\(592\) 0 0
\(593\) 21.7904 0.894826 0.447413 0.894328i \(-0.352346\pi\)
0.447413 + 0.894328i \(0.352346\pi\)
\(594\) 0 0
\(595\) 1.20974 + 1.14749i 0.0495947 + 0.0470424i
\(596\) 0 0
\(597\) −2.80287 8.62636i −0.114714 0.353053i
\(598\) 0 0
\(599\) 10.6482 0.435074 0.217537 0.976052i \(-0.430198\pi\)
0.217537 + 0.976052i \(0.430198\pi\)
\(600\) 0 0
\(601\) 2.60740 0.106358 0.0531791 0.998585i \(-0.483065\pi\)
0.0531791 + 0.998585i \(0.483065\pi\)
\(602\) 0 0
\(603\) 4.09181 + 12.5933i 0.166631 + 0.512839i
\(604\) 0 0
\(605\) −60.1316 7.90268i −2.44470 0.321290i
\(606\) 0 0
\(607\) 32.9820 1.33870 0.669349 0.742948i \(-0.266573\pi\)
0.669349 + 0.742948i \(0.266573\pi\)
\(608\) 0 0
\(609\) −0.148880 + 0.108168i −0.00603294 + 0.00438318i
\(610\) 0 0
\(611\) 15.1975 + 11.0416i 0.614824 + 0.446696i
\(612\) 0 0
\(613\) 15.2007 11.0440i 0.613951 0.446062i −0.236852 0.971546i \(-0.576116\pi\)
0.850804 + 0.525484i \(0.176116\pi\)
\(614\) 0 0
\(615\) −8.35705 + 4.53995i −0.336989 + 0.183068i
\(616\) 0 0
\(617\) 12.1530 37.4030i 0.489260 1.50579i −0.336456 0.941699i \(-0.609228\pi\)
0.825715 0.564087i \(-0.190772\pi\)
\(618\) 0 0
\(619\) −4.95554 + 15.2516i −0.199180 + 0.613013i 0.800722 + 0.599036i \(0.204449\pi\)
−0.999902 + 0.0139774i \(0.995551\pi\)
\(620\) 0 0
\(621\) 0.945790 + 2.91084i 0.0379532 + 0.116808i
\(622\) 0 0
\(623\) −17.1994 12.4961i −0.689079 0.500645i
\(624\) 0 0
\(625\) −5.17573 + 24.4584i −0.207029 + 0.978335i
\(626\) 0 0
\(627\) −1.55687 1.13113i −0.0621753 0.0451730i
\(628\) 0 0
\(629\) −0.668937 2.05878i −0.0266722 0.0820887i
\(630\) 0 0
\(631\) 1.49158 4.59061i 0.0593788 0.182749i −0.916967 0.398962i \(-0.869371\pi\)
0.976346 + 0.216213i \(0.0693705\pi\)
\(632\) 0 0
\(633\) 6.12315 18.8451i 0.243373 0.749026i
\(634\) 0 0
\(635\) −18.1663 + 9.86883i −0.720909 + 0.391632i
\(636\) 0 0
\(637\) −13.6293 + 9.90223i −0.540011 + 0.392341i
\(638\) 0 0
\(639\) −2.64405 1.92102i −0.104597 0.0759943i
\(640\) 0 0
\(641\) 29.5813 21.4921i 1.16839 0.848887i 0.177577 0.984107i \(-0.443174\pi\)
0.990816 + 0.135220i \(0.0431742\pi\)
\(642\) 0 0
\(643\) −18.3769 −0.724714 −0.362357 0.932039i \(-0.618028\pi\)
−0.362357 + 0.932039i \(0.618028\pi\)
\(644\) 0 0
\(645\) −8.04026 1.05668i −0.316585 0.0416066i
\(646\) 0 0
\(647\) −12.7110 39.1206i −0.499723 1.53799i −0.809465 0.587167i \(-0.800243\pi\)
0.309743 0.950820i \(-0.399757\pi\)
\(648\) 0 0
\(649\) −79.5419 −3.12229
\(650\) 0 0
\(651\) 4.42809 0.173550
\(652\) 0 0
\(653\) −6.78128 20.8706i −0.265372 0.816731i −0.991608 0.129285i \(-0.958732\pi\)
0.726236 0.687446i \(-0.241268\pi\)
\(654\) 0 0
\(655\) 30.8496 + 29.2619i 1.20539 + 1.14336i
\(656\) 0 0
\(657\) 15.9668 0.622924
\(658\) 0 0
\(659\) −17.1550 + 12.4638i −0.668264 + 0.485522i −0.869444 0.494032i \(-0.835523\pi\)
0.201179 + 0.979554i \(0.435523\pi\)
\(660\) 0 0
\(661\) −14.5172 10.5473i −0.564652 0.410244i 0.268507 0.963278i \(-0.413470\pi\)
−0.833159 + 0.553034i \(0.813470\pi\)
\(662\) 0 0
\(663\) −1.42620 + 1.03619i −0.0553890 + 0.0402425i
\(664\) 0 0
\(665\) 0.760633 + 0.721488i 0.0294961 + 0.0279781i
\(666\) 0 0
\(667\) 0.115702 0.356094i 0.00447999 0.0137880i
\(668\) 0 0
\(669\) −2.03399 + 6.25999i −0.0786387 + 0.242025i
\(670\) 0 0
\(671\) 21.6002 + 66.4785i 0.833865 + 2.56637i
\(672\) 0 0
\(673\) −27.7504 20.1619i −1.06970 0.777183i −0.0938421 0.995587i \(-0.529915\pi\)
−0.975858 + 0.218404i \(0.929915\pi\)
\(674\) 0 0
\(675\) −0.263932 4.99303i −0.0101587 0.192182i
\(676\) 0 0
\(677\) 3.35495 + 2.43752i 0.128941 + 0.0936814i 0.650387 0.759603i \(-0.274607\pi\)
−0.521445 + 0.853285i \(0.674607\pi\)
\(678\) 0 0
\(679\) −5.33781 16.4281i −0.204846 0.630452i
\(680\) 0 0
\(681\) −3.64087 + 11.2055i −0.139519 + 0.429394i
\(682\) 0 0
\(683\) 0.654621 2.01472i 0.0250484 0.0770910i −0.937751 0.347309i \(-0.887096\pi\)
0.962799 + 0.270218i \(0.0870956\pi\)
\(684\) 0 0
\(685\) −3.20761 17.2850i −0.122557 0.660425i
\(686\) 0 0
\(687\) 9.61911 6.98869i 0.366992 0.266635i
\(688\) 0 0
\(689\) −24.7428 17.9767i −0.942625 0.684857i
\(690\) 0 0
\(691\) 3.21546 2.33617i 0.122322 0.0888721i −0.524942 0.851138i \(-0.675913\pi\)
0.647264 + 0.762266i \(0.275913\pi\)
\(692\) 0 0
\(693\) −9.28811 −0.352826
\(694\) 0 0
\(695\) −27.1157 + 14.7305i −1.02856 + 0.558761i
\(696\) 0 0
\(697\) 0.651515 + 2.00516i 0.0246779 + 0.0759507i
\(698\) 0 0
\(699\) 5.05001 0.191009
\(700\) 0 0
\(701\) −10.1954 −0.385076 −0.192538 0.981289i \(-0.561672\pi\)
−0.192538 + 0.981289i \(0.561672\pi\)
\(702\) 0 0
\(703\) −0.420597 1.29447i −0.0158631 0.0488217i
\(704\) 0 0
\(705\) 2.15505 + 11.6130i 0.0811637 + 0.437370i
\(706\) 0 0
\(707\) −22.3176 −0.839338
\(708\) 0 0
\(709\) −24.1421 + 17.5403i −0.906676 + 0.658739i −0.940172 0.340700i \(-0.889336\pi\)
0.0334959 + 0.999439i \(0.489336\pi\)
\(710\) 0 0
\(711\) 6.89886 + 5.01232i 0.258728 + 0.187977i
\(712\) 0 0
\(713\) −7.28873 + 5.29557i −0.272965 + 0.198321i
\(714\) 0 0
\(715\) −21.1281 + 44.3217i −0.790146 + 1.65754i
\(716\) 0 0
\(717\) −0.827957 + 2.54819i −0.0309206 + 0.0951639i
\(718\) 0 0
\(719\) 2.29734 7.07047i 0.0856762 0.263684i −0.899036 0.437875i \(-0.855731\pi\)
0.984712 + 0.174191i \(0.0557311\pi\)
\(720\) 0 0
\(721\) 8.95520 + 27.5613i 0.333509 + 1.02644i
\(722\) 0 0
\(723\) 10.2390 + 7.43906i 0.380792 + 0.276662i
\(724\) 0 0
\(725\) −0.332907 + 0.513138i −0.0123638 + 0.0190575i
\(726\) 0 0
\(727\) 12.8791 + 9.35722i 0.477660 + 0.347040i 0.800419 0.599441i \(-0.204610\pi\)
−0.322759 + 0.946481i \(0.604610\pi\)
\(728\) 0 0
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) 0 0
\(731\) −0.555527 + 1.70974i −0.0205469 + 0.0632369i
\(732\) 0 0
\(733\) 9.45910 29.1121i 0.349380 1.07528i −0.609817 0.792542i \(-0.708757\pi\)
0.959197 0.282738i \(-0.0912428\pi\)
\(734\) 0 0
\(735\) −10.5021 1.38022i −0.387377 0.0509103i
\(736\) 0 0
\(737\) 66.1430 48.0557i 2.43641 1.77015i
\(738\) 0 0
\(739\) −20.9842 15.2459i −0.771917 0.560830i 0.130626 0.991432i \(-0.458301\pi\)
−0.902542 + 0.430602i \(0.858301\pi\)
\(740\) 0 0
\(741\) −0.896731 + 0.651513i −0.0329422 + 0.0239339i
\(742\) 0 0
\(743\) 17.2136 0.631504 0.315752 0.948842i \(-0.397743\pi\)
0.315752 + 0.948842i \(0.397743\pi\)
\(744\) 0 0
\(745\) −4.92807 + 10.3379i −0.180550 + 0.378752i
\(746\) 0 0
\(747\) 3.50367 + 10.7832i 0.128193 + 0.394536i
\(748\) 0 0
\(749\) 12.9900 0.474643
\(750\) 0 0
\(751\) 10.4020 0.379576 0.189788 0.981825i \(-0.439220\pi\)
0.189788 + 0.981825i \(0.439220\pi\)
\(752\) 0 0
\(753\) 7.07859 + 21.7857i 0.257958 + 0.793913i
\(754\) 0 0
\(755\) 12.4581 26.1341i 0.453397 0.951118i
\(756\) 0 0
\(757\) −16.9118 −0.614669 −0.307335 0.951601i \(-0.599437\pi\)
−0.307335 + 0.951601i \(0.599437\pi\)
\(758\) 0 0
\(759\) 15.2884 11.1077i 0.554935 0.403184i
\(760\) 0 0
\(761\) −0.422588 0.307028i −0.0153188 0.0111297i 0.580100 0.814546i \(-0.303014\pi\)
−0.595418 + 0.803416i \(0.703014\pi\)
\(762\) 0 0
\(763\) 22.7450 16.5252i 0.823423 0.598252i
\(764\) 0 0
\(765\) −1.09897 0.144430i −0.0397333 0.00522188i
\(766\) 0 0
\(767\) −14.1576 + 43.5725i −0.511200 + 1.57331i
\(768\) 0 0
\(769\) −11.7671 + 36.2154i −0.424333 + 1.30596i 0.479299 + 0.877651i \(0.340891\pi\)
−0.903632 + 0.428310i \(0.859109\pi\)
\(770\) 0 0
\(771\) 8.58338 + 26.4169i 0.309123 + 0.951382i
\(772\) 0 0
\(773\) 18.3577 + 13.3376i 0.660280 + 0.479721i 0.866757 0.498730i \(-0.166200\pi\)
−0.206478 + 0.978451i \(0.566200\pi\)
\(774\) 0 0
\(775\) 13.7382 5.28070i 0.493489 0.189688i
\(776\) 0 0
\(777\) −5.31466 3.86132i −0.190662 0.138524i
\(778\) 0 0
\(779\) 0.409643 + 1.26075i 0.0146770 + 0.0451711i
\(780\) 0 0
\(781\) −6.23574 + 19.1916i −0.223132 + 0.686731i
\(782\) 0 0
\(783\) 0.0378031 0.116346i 0.00135097 0.00415787i
\(784\) 0 0
\(785\) 3.87525 8.12934i 0.138314 0.290149i
\(786\) 0 0
\(787\) −1.84384 + 1.33963i −0.0657257 + 0.0477525i −0.620163 0.784473i \(-0.712934\pi\)
0.554437 + 0.832226i \(0.312934\pi\)
\(788\) 0 0
\(789\) 9.47479 + 6.88384i 0.337312 + 0.245071i
\(790\) 0 0
\(791\) −7.37064 + 5.35508i −0.262070 + 0.190405i
\(792\) 0 0
\(793\) 40.2611 1.42971
\(794\) 0 0
\(795\) −3.50860 18.9069i −0.124437 0.670559i