Properties

Label 300.2.m.b.61.2
Level $300$
Weight $2$
Character 300.61
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 61.2
Root \(-1.21700 + 0.720348i\) of defining polynomial
Character \(\chi\) \(=\) 300.61
Dual form 300.2.m.b.241.2

$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\)

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 0.538231 0.842797i \(-0.319093\pi\)
0.967870 0.251450i \(-0.0809074\pi\)
\(12\) 0 0
\(13\) 2.87714 + 2.09036i 0.797975 + 0.579763i 0.910319 0.413906i \(-0.135836\pi\)
−0.112344 + 0.993669i \(0.535836\pi\)
\(14\) 0 0
\(15\) 2.21700 0.291365i 0.572428 0.0752302i
\(16\) 0 0
\(17\) 0.153180 + 0.471439i 0.0371516 + 0.114341i 0.967912 0.251288i \(-0.0808541\pi\)
−0.930761 + 0.365629i \(0.880854\pi\)
\(18\) 0 0
\(19\) 0.0963126 + 0.296420i 0.0220956 + 0.0680034i 0.961496 0.274818i \(-0.0886175\pi\)
−0.939401 + 0.342821i \(0.888618\pi\)
\(20\) 0 0
\(21\) −0.464854 + 1.43067i −0.101439 + 0.312199i
\(22\) 0 0
\(23\) 2.47611 1.79900i 0.516305 0.375117i −0.298905 0.954283i \(-0.596621\pi\)
0.815210 + 0.579165i \(0.196621\pi\)
\(24\) 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 −0.954505 0.298195i \(-0.903616\pi\)
0.947485 + 0.319800i \(0.103616\pi\)
\(30\) 0 0
\(31\) −0.909629 2.79955i −0.163374 0.502814i 0.835539 0.549432i \(-0.185156\pi\)
−0.998913 + 0.0466176i \(0.985156\pi\)
\(32\) 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 0.839019 0.544102i \(-0.183130\pi\)
−0.258201 + 0.966091i \(0.583130\pi\)
\(38\) 0 0
\(39\) −2.87714 + 2.09036i −0.460711 + 0.334726i
\(40\) 0 0
\(41\) −3.44096 2.50001i −0.537388 0.390436i 0.285726 0.958311i \(-0.407765\pi\)
−0.823114 + 0.567876i \(0.807765\pi\)
\(42\) 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 −0.758605 0.651551i \(-0.774119\pi\)
0.996696 0.0812191i \(-0.0258813\pi\)
\(48\) 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 0.584928 + 0.811086i \(0.301123\pi\)
−0.949960 + 0.312370i \(0.898877\pi\)
\(54\) 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 −0.998638 0.0521781i \(-0.983384\pi\)
−0.358220 0.933637i \(-0.616616\pi\)
\(60\) 0 0
\(61\) 9.15882 6.65427i 1.17267 0.851992i 0.181341 0.983420i \(-0.441956\pi\)
0.991326 + 0.131428i \(0.0419562\pi\)
\(62\) 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 0.809188 + 0.587550i \(0.199908\pi\)
−0.309293 + 0.950967i \(0.600092\pi\)
\(68\) 0 0
\(69\) 0.945790 + 2.91084i 0.113860 + 0.350424i
\(70\) 0 0
\(71\) 1.00994 3.10827i 0.119858 0.368884i −0.873071 0.487592i \(-0.837875\pi\)
0.992929 + 0.118708i \(0.0378753\pi\)
\(72\) 0 0
\(73\) −12.9174 + 9.38504i −1.51187 + 1.09844i −0.546527 + 0.837441i \(0.684050\pi\)
−0.965340 + 0.260994i \(0.915950\pi\)
\(74\) 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 0.686247 + 0.727369i \(0.259257\pi\)
−0.982722 + 0.185088i \(0.940743\pi\)
\(80\) 0 0
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 0 0
\(83\) 3.50367 + 10.7832i 0.384578 + 1.18361i 0.936786 + 0.349903i \(0.113785\pi\)
−0.552208 + 0.833706i \(0.686215\pi\)
\(84\) 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 −0.995406 0.0957428i \(-0.969477\pi\)
−0.216541 + 0.976274i \(0.569477\pi\)
\(90\) 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 0.592601 + 0.805497i \(0.298101\pi\)
−0.952883 + 0.303339i \(0.901899\pi\)
\(98\) 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 −0.00628354 0.999980i \(-0.502000\pi\)
0.592857 0.805308i \(-0.298000\pi\)
\(104\) 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 0.986241 + 0.165315i \(0.0528641\pi\)
0.461989 + 0.886886i \(0.347136\pi\)
\(110\) 0 0
\(111\) −3.53298 + 2.56686i −0.335335 + 0.243635i
\(112\) 0 0
\(113\) −4.89971 3.55985i −0.460926 0.334883i 0.332968 0.942938i \(-0.391950\pi\)
−0.793894 + 0.608056i \(0.791950\pi\)
\(114\) 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 −0.204189 0.978931i \(-0.565456\pi\)
0.867921 + 0.496702i \(0.165456\pi\)
\(128\) 0 0
\(129\) 1.12069 3.44913i 0.0986714 0.303679i
\(130\) 0 0
\(131\) 5.87613 + 18.0849i 0.513399 + 1.58008i 0.786175 + 0.618003i \(0.212058\pi\)
−0.272776 + 0.962078i \(0.587942\pi\)
\(132\) 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 0.281936 0.959433i \(-0.409024\pi\)
−0.825352 + 0.564618i \(0.809024\pi\)
\(138\) 0 0
\(139\) 11.1647 8.11165i 0.946980 0.688021i −0.00311101 0.999995i \(-0.500990\pi\)
0.950091 + 0.311974i \(0.100990\pi\)
\(140\) 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 −0.0298692 0.999554i \(-0.509509\pi\)
−0.959862 + 0.280472i \(0.909509\pi\)
\(164\) 0 0
\(165\) 10.0169 9.50139i 0.779814 0.739682i
\(166\) 0 0
\(167\) 3.66014 + 11.2647i 0.283230 + 0.871692i 0.986924 + 0.161189i \(0.0515327\pi\)
−0.703694 + 0.710503i \(0.748467\pi\)
\(168\) 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 −0.941571 0.336814i \(-0.890651\pi\)
0.0293681 + 0.999569i \(0.490651\pi\)
\(174\) 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 −0.961505 0.274786i \(-0.911393\pi\)
0.939389 + 0.342852i \(0.111393\pi\)
\(180\) 0 0
\(181\) 1.27971 + 3.93855i 0.0951202 + 0.292750i 0.987285 0.158960i \(-0.0508141\pi\)
−0.892165 + 0.451710i \(0.850814\pi\)
\(182\) 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 0.968720 0.248156i \(-0.0798244\pi\)
0.0633410 + 0.997992i \(0.479824\pi\)
\(192\) 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 −0.971644 0.236449i \(-0.924016\pi\)
0.925058 + 0.379827i \(0.124016\pi\)
\(198\) 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 0.121950 0.992536i \(-0.461085\pi\)
0.981643 + 0.190729i \(0.0610853\pi\)
\(212\) 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 −0.751629 0.659586i \(-0.770732\pi\)
0.395037 + 0.918665i \(0.370732\pi\)
\(224\) 0 0
\(225\) 4.83021 1.29192i 0.322014 0.0861278i
\(226\) 0 0
\(227\) −9.53193 + 6.92535i −0.632656 + 0.459652i −0.857319 0.514785i \(-0.827872\pi\)
0.224663 + 0.974436i \(0.427872\pi\)
\(228\) 0 0
\(229\) 3.67417 11.3079i 0.242796 0.747250i −0.753195 0.657798i \(-0.771488\pi\)
0.995991 0.0894526i \(-0.0285117\pi\)
\(230\) 0 0
\(231\) 2.87018 + 8.83352i 0.188844 + 0.581203i
\(232\) 0 0
\(233\) −1.56054 4.80285i −0.102234 0.314645i 0.886837 0.462082i \(-0.152898\pi\)
−0.989071 + 0.147437i \(0.952898\pi\)
\(234\) 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 −0.655680 0.755039i \(-0.727618\pi\)
0.515468 + 0.856909i \(0.327618\pi\)
\(240\) 0 0
\(241\) −10.2390 7.43906i −0.659551 0.479192i 0.206960 0.978349i \(-0.433643\pi\)
−0.866511 + 0.499157i \(0.833643\pi\)
\(242\) 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 0.256010 0.966674i \(-0.417592\pi\)
−0.840250 + 0.542198i \(0.817592\pi\)
\(264\) 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 0.982830 0.184513i \(-0.0590709\pi\)
−0.903580 + 0.428419i \(0.859071\pi\)
\(270\) 0 0
\(271\) −3.88308 + 11.9509i −0.235880 + 0.725965i 0.761123 + 0.648608i \(0.224648\pi\)
−0.997003 + 0.0773578i \(0.975352\pi\)
\(272\) 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 −0.604543 + 0.796573i \(0.706644\pi\)
−0.944400 + 0.328800i \(0.893356\pi\)
\(278\) 0 0
\(279\) −0.909629 + 2.79955i −0.0544581 + 0.167605i
\(280\) 0 0
\(281\) 5.03691 + 15.5020i 0.300477 + 0.924773i 0.981326 + 0.192350i \(0.0616108\pi\)
−0.680849 + 0.732423i \(0.738389\pi\)
\(282\) 0 0
\(283\) −4.21205 12.9634i −0.250381 0.770592i −0.994705 0.102774i \(-0.967228\pi\)
0.744324 0.667819i \(-0.232772\pi\)
\(284\) 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 −0.868594 0.495524i \(-0.834976\pi\)
0.202861 + 0.979208i \(0.434976\pi\)
\(312\) 0 0
\(313\) −17.7334 12.8841i −1.00235 0.728250i −0.0397589 0.999209i \(-0.512659\pi\)
−0.962591 + 0.270960i \(0.912659\pi\)
\(314\) 0 0
\(315\) −0.613734 + 3.30725i −0.0345800 + 0.186343i
\(316\) 0 0
\(317\) −10.4194 32.0675i −0.585210 1.80109i −0.598426 0.801178i \(-0.704207\pi\)
0.0132156 0.999913i \(-0.495793\pi\)
\(318\) 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 0.650645 + 0.759382i \(0.274498\pi\)
−0.0800299 + 0.996792i \(0.525502\pi\)
\(332\) 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 0.517723 0.855548i \(-0.326780\pi\)
−0.653690 + 0.756763i \(0.726780\pi\)
\(338\) 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 −0.790959 0.611869i \(-0.790418\pi\)
0.999547 0.0300984i \(-0.00958206\pi\)
\(348\) 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 −0.999960 0.00895265i \(-0.997150\pi\)
0.814247 + 0.580519i \(0.197150\pi\)
\(354\) 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 0.0905254 0.995894i \(-0.471145\pi\)
−0.919178 + 0.393843i \(0.871145\pi\)
\(360\) 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 0.986868 + 0.161526i \(0.0516417\pi\)
−0.703450 + 0.710744i \(0.748358\pi\)
\(368\) 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 0.189204 0.981938i \(-0.439409\pi\)
0.992346 + 0.123492i \(0.0394093\pi\)
\(374\) 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 −0.918123 0.396296i \(-0.870295\pi\)
0.975714 + 0.219049i \(0.0702954\pi\)
\(380\) 0 0
\(381\) 2.85706 + 8.79313i 0.146372 + 0.450486i
\(382\) 0 0
\(383\) −4.27519 13.1577i −0.218452 0.672326i −0.998890 0.0470934i \(-0.985004\pi\)
0.780439 0.625232i \(-0.214996\pi\)
\(384\) 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 −0.0698138 0.997560i \(-0.522241\pi\)
0.927162 + 0.374660i \(0.122241\pi\)
\(390\) 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 0.756821 + 0.653622i \(0.226752\pi\)
−0.996471 + 0.0839436i \(0.973248\pi\)
\(398\) 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 0.633463 0.773773i \(-0.281633\pi\)
−0.540151 + 0.841568i \(0.681633\pi\)
\(410\) 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 0.905771 0.423768i \(-0.139293\pi\)
−0.981869 + 0.189563i \(0.939293\pi\)
\(420\) 0 0
\(421\) 3.99823 12.3053i 0.194862 0.599724i −0.805116 0.593117i \(-0.797897\pi\)
0.999978 0.00660640i \(-0.00210290\pi\)
\(422\) 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 0.962028 0.272950i \(-0.0879994\pi\)
−0.938733 + 0.344645i \(0.887999\pi\)
\(432\) 0 0
\(433\) 7.99517 + 24.6066i 0.384224 + 1.18252i 0.937042 + 0.349217i \(0.113552\pi\)
−0.552818 + 0.833302i \(0.686448\pi\)
\(434\) 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 −0.857138 0.515087i \(-0.827760\pi\)
0.225006 + 0.974357i \(0.427760\pi\)
\(440\) 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 −0.433499 0.901154i \(-0.642721\pi\)
0.723090 + 0.690754i \(0.242721\pi\)
\(462\) 0 0
\(463\) −15.4555 11.2291i −0.718279 0.521860i 0.167555 0.985863i \(-0.446413\pi\)
−0.885834 + 0.464002i \(0.846413\pi\)
\(464\) 0 0
\(465\) −2.83234 5.94158i −0.131347 0.275534i
\(466\) 0 0
\(467\) −1.98372 6.10525i −0.0917955 0.282517i 0.894610 0.446848i \(-0.147454\pi\)
−0.986405 + 0.164331i \(0.947454\pi\)
\(468\) 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 −0.373633 0.927577i \(-0.621888\pi\)
0.847491 0.530810i \(-0.178112\pi\)
\(480\) 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 0.784298 0.620384i \(-0.213023\pi\)
−0.347659 + 0.937621i \(0.613023\pi\)
\(488\) 0 0
\(489\) 12.6360 9.18062i 0.571422 0.415162i
\(490\) 0 0
\(491\) −12.6312 9.17712i −0.570039 0.414158i 0.265080 0.964226i \(-0.414602\pi\)
−0.835119 + 0.550069i \(0.814602\pi\)
\(492\) 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 −0.472732 0.881206i \(-0.656732\pi\)
0.900408 0.435046i \(-0.143268\pi\)
\(504\) 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 0.800729 0.599027i \(-0.204446\pi\)
−0.322269 + 0.946648i \(0.604446\pi\)
\(510\) 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 −0.594649 0.803985i \(-0.702709\pi\)
0.953652 0.300912i \(-0.0972910\pi\)
\(522\) 0 0
\(523\) 14.0888 10.2361i 0.616060 0.447594i −0.235483 0.971878i \(-0.575667\pi\)
0.851543 + 0.524285i \(0.175667\pi\)
\(524\) 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 0.488638 0.872487i \(-0.337494\pi\)
−0.678787 + 0.734335i \(0.737494\pi\)
\(542\) 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 −0.700099 0.714046i \(-0.746861\pi\)
0.986098 0.166167i \(-0.0531391\pi\)
\(548\) 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 0.194493 0.980904i \(-0.437694\pi\)
−0.872794 + 0.488089i \(0.837694\pi\)
\(564\) 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 0.907587 + 0.419865i \(0.137923\pi\)
−0.487463 + 0.873144i \(0.662077\pi\)
\(570\) 0 0
\(571\) 4.23915 13.0468i 0.177403 0.545990i −0.822332 0.569008i \(-0.807327\pi\)
0.999735 + 0.0230176i \(0.00732739\pi\)
\(572\) 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 −0.919553 0.392965i \(-0.871449\pi\)
0.0895741 + 0.995980i \(0.471449\pi\)
\(578\) 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 0.440115 0.897941i \(-0.354938\pi\)
−0.717990 + 0.696054i \(0.754938\pi\)
\(588\) 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 0.850804 0.525484i \(-0.176116\pi\)
−0.236852 + 0.971546i \(0.576116\pi\)
\(614\) 0 0
\(615\) −8.35705 4.53995i −0.336989 0.183068i
\(616\) 0 0
\(617\) 12.1530 + 37.4030i 0.489260 + 1.50579i 0.825715 + 0.564087i \(0.190772\pi\)
−0.336456 + 0.941699i \(0.609228\pi\)
\(618\) 0 0
\(619\) −4.95554 15.2516i −0.199180 0.613013i −0.999902 0.0139774i \(-0.995551\pi\)
0.800722 0.599036i \(-0.204449\pi\)
\(620\) 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 0.976346 0.216213i \(-0.0693705\pi\)
−0.916967 + 0.398962i \(0.869371\pi\)
\(632\) 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 0.990816 0.135220i \(-0.0431742\pi\)
0.177577 + 0.984107i \(0.443174\pi\)
\(642\) 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 0.309743 + 0.950820i \(0.399757\pi\)
−0.809465 + 0.587167i \(0.800243\pi\)
\(648\) 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 0.726236 + 0.687446i \(0.241268\pi\)
−0.991608 + 0.129285i \(0.958732\pi\)
\(654\) 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 0.201179 0.979554i \(-0.435523\pi\)
−0.869444 + 0.494032i \(0.835523\pi\)
\(660\) 0 0
\(661\) −14.5172 + 10.5473i −0.564652 + 0.410244i −0.833159 0.553034i \(-0.813470\pi\)
0.268507 + 0.963278i \(0.413470\pi\)
\(662\) 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 −0.975858 0.218404i \(-0.929915\pi\)
−0.0938421 + 0.995587i \(0.529915\pi\)
\(674\) 0 0
\(675\) −0.263932 + 4.99303i −0.0101587 + 0.192182i
\(676\) 0 0
\(677\) 3.35495 2.43752i 0.128941 0.0936814i −0.521445 0.853285i \(-0.674607\pi\)
0.650387 + 0.759603i \(0.274607\pi\)
\(678\) 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 0.962799 0.270218i \(-0.0870956\pi\)
−0.937751 + 0.347309i \(0.887096\pi\)
\(684\) 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 0.647264 0.762266i \(-0.275913\pi\)
−0.524942 + 0.851138i \(0.675913\pi\)
\(692\) 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 0.0334959 0.999439i \(-0.489336\pi\)
−0.940172 + 0.340700i \(0.889336\pi\)
\(710\) 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 0.984712 0.174191i \(-0.0557311\pi\)
−0.899036 + 0.437875i \(0.855731\pi\)
\(720\) 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 −0.322759 0.946481i \(-0.604610\pi\)
0.800419 + 0.599441i \(0.204610\pi\)
\(728\) 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 0.959197 + 0.282738i \(0.0912428\pi\)
−0.609817 + 0.792542i \(0.708757\pi\)
\(734\) 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 −0.902542 0.430602i \(-0.858301\pi\)
0.130626 + 0.991432i \(0.458301\pi\)
\(740\) 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 −0.595418 0.803416i \(-0.703014\pi\)
0.580100 + 0.814546i \(0.303014\pi\)
\(762\) 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 −0.903632 0.428310i \(-0.859109\pi\)
0.479299 0.877651i \(-0.340891\pi\)
\(770\) 0 0
\(771\) 8.58338 26.4169i 0.309123 0.951382i
\(772\) 0 0
\(773\) 18.3577 13.3376i 0.660280 0.479721i −0.206478 0.978451i \(-0.566200\pi\)
0.866757 + 0.498730i \(0.166200\pi\)
\(774\) 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 0.554437 0.832226i \(-0.312934\pi\)
−0.620163 + 0.784473i \(0.712934\pi\)
\(788\) 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