Properties

Label 300.2.o.a.169.2
Level $300$
Weight $2$
Character 300.169
Analytic conductor $2.396$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 169.2
Character \(\chi\) \(=\) 300.169
Dual form 300.2.o.a.229.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.587785 - 0.809017i) q^{3} +(-0.900274 - 2.04683i) q^{5} +0.957526i q^{7} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.587785 - 0.809017i) q^{3} +(-0.900274 - 2.04683i) q^{5} +0.957526i q^{7} +(-0.309017 + 0.951057i) q^{9} +(-1.67360 - 5.15082i) q^{11} +(-1.92371 - 0.625052i) q^{13} +(-1.12675 + 1.93143i) q^{15} +(0.377867 - 0.520090i) q^{17} +(-4.07829 - 2.96305i) q^{19} +(0.774655 - 0.562820i) q^{21} +(-3.34734 + 1.08762i) q^{23} +(-3.37901 + 3.68541i) q^{25} +(0.951057 - 0.309017i) q^{27} +(8.20405 - 5.96059i) q^{29} +(-2.98671 - 2.16997i) q^{31} +(-3.18338 + 4.38155i) q^{33} +(1.95989 - 0.862036i) q^{35} +(10.7615 + 3.49663i) q^{37} +(0.625052 + 1.92371i) q^{39} +(1.08859 - 3.35035i) q^{41} +0.766348i q^{43} +(2.22485 - 0.223707i) q^{45} +(2.90026 + 3.99186i) q^{47} +6.08314 q^{49} -0.642866 q^{51} +(-3.49517 - 4.81069i) q^{53} +(-9.03615 + 8.06273i) q^{55} +5.04105i q^{57} +(-1.45818 + 4.48783i) q^{59} +(1.34263 + 4.13219i) q^{61} +(-0.910662 - 0.295892i) q^{63} +(0.452494 + 4.50023i) q^{65} +(-5.59441 + 7.70005i) q^{67} +(2.84742 + 2.06877i) q^{69} +(9.66368 - 7.02107i) q^{71} +(5.16713 - 1.67890i) q^{73} +(4.96770 + 0.567448i) q^{75} +(4.93205 - 1.60252i) q^{77} +(9.58637 - 6.96491i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-0.819420 + 1.12784i) q^{83} +(-1.40472 - 0.305206i) q^{85} +(-9.64444 - 3.13367i) q^{87} +(0.527839 + 1.62452i) q^{89} +(0.598504 - 1.84200i) q^{91} +3.69178i q^{93} +(-2.39328 + 11.0151i) q^{95} +(8.57451 + 11.8018i) q^{97} +5.41590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 2q^{5} + 6q^{9} + O(q^{10}) \) \( 24q - 2q^{5} + 6q^{9} - 6q^{11} + 4q^{15} + 10q^{17} + 10q^{19} - 4q^{21} + 40q^{23} - 4q^{25} + 4q^{29} + 6q^{31} + 10q^{33} - 6q^{35} - 10q^{41} + 2q^{45} - 40q^{47} - 56q^{49} + 16q^{51} - 60q^{53} - 62q^{55} - 36q^{59} - 12q^{61} - 10q^{63} + 20q^{67} + 4q^{69} + 40q^{71} + 60q^{73} + 8q^{75} - 40q^{77} + 8q^{79} - 6q^{81} - 50q^{83} + 34q^{85} - 20q^{87} - 30q^{91} - 60q^{95} - 40q^{97} - 4q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{9}{10}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.587785 0.809017i −0.339358 0.467086i
\(4\) 0 0
\(5\) −0.900274 2.04683i −0.402615 0.915370i
\(6\) 0 0
\(7\) 0.957526i 0.361911i 0.983491 + 0.180955i \(0.0579190\pi\)
−0.983491 + 0.180955i \(0.942081\pi\)
\(8\) 0 0
\(9\) −0.309017 + 0.951057i −0.103006 + 0.317019i
\(10\) 0 0
\(11\) −1.67360 5.15082i −0.504611 1.55303i −0.801424 0.598096i \(-0.795924\pi\)
0.296814 0.954935i \(-0.404076\pi\)
\(12\) 0 0
\(13\) −1.92371 0.625052i −0.533542 0.173358i 0.0298404 0.999555i \(-0.490500\pi\)
−0.563382 + 0.826196i \(0.690500\pi\)
\(14\) 0 0
\(15\) −1.12675 + 1.93143i −0.290926 + 0.498694i
\(16\) 0 0
\(17\) 0.377867 0.520090i 0.0916463 0.126140i −0.760732 0.649067i \(-0.775160\pi\)
0.852378 + 0.522926i \(0.175160\pi\)
\(18\) 0 0
\(19\) −4.07829 2.96305i −0.935625 0.679771i 0.0117388 0.999931i \(-0.496263\pi\)
−0.947364 + 0.320160i \(0.896263\pi\)
\(20\) 0 0
\(21\) 0.774655 0.562820i 0.169044 0.122817i
\(22\) 0 0
\(23\) −3.34734 + 1.08762i −0.697969 + 0.226784i −0.636445 0.771322i \(-0.719596\pi\)
−0.0615235 + 0.998106i \(0.519596\pi\)
\(24\) 0 0
\(25\) −3.37901 + 3.68541i −0.675803 + 0.737083i
\(26\) 0 0
\(27\) 0.951057 0.309017i 0.183031 0.0594703i
\(28\) 0 0
\(29\) 8.20405 5.96059i 1.52345 1.10685i 0.563712 0.825972i \(-0.309373\pi\)
0.959742 0.280882i \(-0.0906271\pi\)
\(30\) 0 0
\(31\) −2.98671 2.16997i −0.536429 0.389738i 0.286328 0.958132i \(-0.407565\pi\)
−0.822757 + 0.568393i \(0.807565\pi\)
\(32\) 0 0
\(33\) −3.18338 + 4.38155i −0.554156 + 0.762730i
\(34\) 0 0
\(35\) 1.95989 0.862036i 0.331282 0.145711i
\(36\) 0 0
\(37\) 10.7615 + 3.49663i 1.76918 + 0.574842i 0.998084 0.0618753i \(-0.0197081\pi\)
0.771097 + 0.636717i \(0.219708\pi\)
\(38\) 0 0
\(39\) 0.625052 + 1.92371i 0.100088 + 0.308040i
\(40\) 0 0
\(41\) 1.08859 3.35035i 0.170010 0.523237i −0.829361 0.558714i \(-0.811295\pi\)
0.999370 + 0.0354770i \(0.0112950\pi\)
\(42\) 0 0
\(43\) 0.766348i 0.116867i 0.998291 + 0.0584335i \(0.0186106\pi\)
−0.998291 + 0.0584335i \(0.981389\pi\)
\(44\) 0 0
\(45\) 2.22485 0.223707i 0.331661 0.0333482i
\(46\) 0 0
\(47\) 2.90026 + 3.99186i 0.423046 + 0.582273i 0.966340 0.257270i \(-0.0828229\pi\)
−0.543293 + 0.839543i \(0.682823\pi\)
\(48\) 0 0
\(49\) 6.08314 0.869021
\(50\) 0 0
\(51\) −0.642866 −0.0900193
\(52\) 0 0
\(53\) −3.49517 4.81069i −0.480099 0.660799i 0.498425 0.866933i \(-0.333912\pi\)
−0.978524 + 0.206134i \(0.933912\pi\)
\(54\) 0 0
\(55\) −9.03615 + 8.06273i −1.21843 + 1.08718i
\(56\) 0 0
\(57\) 5.04105i 0.667703i
\(58\) 0 0
\(59\) −1.45818 + 4.48783i −0.189839 + 0.584265i −0.999998 0.00194529i \(-0.999381\pi\)
0.810159 + 0.586210i \(0.199381\pi\)
\(60\) 0 0
\(61\) 1.34263 + 4.13219i 0.171906 + 0.529073i 0.999479 0.0322858i \(-0.0102787\pi\)
−0.827572 + 0.561359i \(0.810279\pi\)
\(62\) 0 0
\(63\) −0.910662 0.295892i −0.114733 0.0372789i
\(64\) 0 0
\(65\) 0.452494 + 4.50023i 0.0561249 + 0.558184i
\(66\) 0 0
\(67\) −5.59441 + 7.70005i −0.683466 + 0.940711i −0.999969 0.00788103i \(-0.997491\pi\)
0.316503 + 0.948592i \(0.397491\pi\)
\(68\) 0 0
\(69\) 2.84742 + 2.06877i 0.342789 + 0.249051i
\(70\) 0 0
\(71\) 9.66368 7.02107i 1.14687 0.833248i 0.158806 0.987310i \(-0.449235\pi\)
0.988061 + 0.154062i \(0.0492354\pi\)
\(72\) 0 0
\(73\) 5.16713 1.67890i 0.604766 0.196500i 0.00940128 0.999956i \(-0.497007\pi\)
0.595365 + 0.803455i \(0.297007\pi\)
\(74\) 0 0
\(75\) 4.96770 + 0.567448i 0.573620 + 0.0655233i
\(76\) 0 0
\(77\) 4.93205 1.60252i 0.562059 0.182624i
\(78\) 0 0
\(79\) 9.58637 6.96491i 1.07855 0.783613i 0.101122 0.994874i \(-0.467757\pi\)
0.977430 + 0.211261i \(0.0677569\pi\)
\(80\) 0 0
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) 0 0
\(83\) −0.819420 + 1.12784i −0.0899431 + 0.123796i −0.851617 0.524164i \(-0.824378\pi\)
0.761674 + 0.647960i \(0.224378\pi\)
\(84\) 0 0
\(85\) −1.40472 0.305206i −0.152363 0.0331043i
\(86\) 0 0
\(87\) −9.64444 3.13367i −1.03399 0.335965i
\(88\) 0 0
\(89\) 0.527839 + 1.62452i 0.0559508 + 0.172199i 0.975127 0.221649i \(-0.0711438\pi\)
−0.919176 + 0.393847i \(0.871144\pi\)
\(90\) 0 0
\(91\) 0.598504 1.84200i 0.0627402 0.193095i
\(92\) 0 0
\(93\) 3.69178i 0.382819i
\(94\) 0 0
\(95\) −2.39328 + 11.0151i −0.245545 + 1.13013i
\(96\) 0 0
\(97\) 8.57451 + 11.8018i 0.870610 + 1.19829i 0.978934 + 0.204176i \(0.0654514\pi\)
−0.108325 + 0.994116i \(0.534549\pi\)
\(98\) 0 0
\(99\) 5.41590 0.544318
\(100\) 0 0
\(101\) −10.2832 −1.02322 −0.511610 0.859218i \(-0.670951\pi\)
−0.511610 + 0.859218i \(0.670951\pi\)
\(102\) 0 0
\(103\) −8.22008 11.3140i −0.809949 1.11480i −0.991331 0.131386i \(-0.958057\pi\)
0.181383 0.983413i \(-0.441943\pi\)
\(104\) 0 0
\(105\) −1.84940 1.07889i −0.180483 0.105289i
\(106\) 0 0
\(107\) 9.06727i 0.876566i −0.898837 0.438283i \(-0.855587\pi\)
0.898837 0.438283i \(-0.144413\pi\)
\(108\) 0 0
\(109\) −0.734025 + 2.25910i −0.0703068 + 0.216382i −0.980036 0.198820i \(-0.936289\pi\)
0.909729 + 0.415202i \(0.136289\pi\)
\(110\) 0 0
\(111\) −3.49663 10.7615i −0.331885 1.02144i
\(112\) 0 0
\(113\) −12.7797 4.15238i −1.20221 0.390623i −0.361638 0.932318i \(-0.617782\pi\)
−0.840575 + 0.541696i \(0.817782\pi\)
\(114\) 0 0
\(115\) 5.23969 + 5.87228i 0.488604 + 0.547593i
\(116\) 0 0
\(117\) 1.18892 1.63641i 0.109916 0.151286i
\(118\) 0 0
\(119\) 0.498000 + 0.361818i 0.0456515 + 0.0331678i
\(120\) 0 0
\(121\) −14.8308 + 10.7752i −1.34826 + 0.979567i
\(122\) 0 0
\(123\) −3.35035 + 1.08859i −0.302091 + 0.0981553i
\(124\) 0 0
\(125\) 10.5854 + 3.59838i 0.946791 + 0.321849i
\(126\) 0 0
\(127\) 13.5648 4.40749i 1.20369 0.391101i 0.362570 0.931957i \(-0.381899\pi\)
0.841116 + 0.540855i \(0.181899\pi\)
\(128\) 0 0
\(129\) 0.619989 0.450448i 0.0545869 0.0396597i
\(130\) 0 0
\(131\) 0.104093 + 0.0756282i 0.00909468 + 0.00660767i 0.592323 0.805700i \(-0.298211\pi\)
−0.583229 + 0.812308i \(0.698211\pi\)
\(132\) 0 0
\(133\) 2.83720 3.90507i 0.246017 0.338613i
\(134\) 0 0
\(135\) −1.48872 1.66845i −0.128128 0.143597i
\(136\) 0 0
\(137\) −13.0316 4.23423i −1.11337 0.361754i −0.306133 0.951989i \(-0.599035\pi\)
−0.807232 + 0.590234i \(0.799035\pi\)
\(138\) 0 0
\(139\) −7.25318 22.3230i −0.615206 1.89341i −0.398475 0.917179i \(-0.630461\pi\)
−0.216731 0.976231i \(-0.569539\pi\)
\(140\) 0 0
\(141\) 1.52476 4.69272i 0.128408 0.395198i
\(142\) 0 0
\(143\) 10.9548i 0.916086i
\(144\) 0 0
\(145\) −19.5862 11.4261i −1.62655 0.948888i
\(146\) 0 0
\(147\) −3.57558 4.92137i −0.294909 0.405907i
\(148\) 0 0
\(149\) 10.6938 0.876071 0.438035 0.898958i \(-0.355674\pi\)
0.438035 + 0.898958i \(0.355674\pi\)
\(150\) 0 0
\(151\) 7.37520 0.600185 0.300092 0.953910i \(-0.402982\pi\)
0.300092 + 0.953910i \(0.402982\pi\)
\(152\) 0 0
\(153\) 0.377867 + 0.520090i 0.0305488 + 0.0420468i
\(154\) 0 0
\(155\) −1.75270 + 8.06685i −0.140780 + 0.647945i
\(156\) 0 0
\(157\) 13.0329i 1.04014i −0.854124 0.520070i \(-0.825906\pi\)
0.854124 0.520070i \(-0.174094\pi\)
\(158\) 0 0
\(159\) −1.83752 + 5.65531i −0.145725 + 0.448495i
\(160\) 0 0
\(161\) −1.04142 3.20517i −0.0820755 0.252603i
\(162\) 0 0
\(163\) 7.03403 + 2.28549i 0.550948 + 0.179014i 0.571244 0.820780i \(-0.306461\pi\)
−0.0202964 + 0.999794i \(0.506461\pi\)
\(164\) 0 0
\(165\) 11.8342 + 2.57124i 0.921292 + 0.200171i
\(166\) 0 0
\(167\) −11.8301 + 16.2827i −0.915438 + 1.25999i 0.0498368 + 0.998757i \(0.484130\pi\)
−0.965275 + 0.261235i \(0.915870\pi\)
\(168\) 0 0
\(169\) −7.20724 5.23637i −0.554403 0.402798i
\(170\) 0 0
\(171\) 4.07829 2.96305i 0.311875 0.226590i
\(172\) 0 0
\(173\) 2.11241 0.686365i 0.160604 0.0521833i −0.227612 0.973752i \(-0.573092\pi\)
0.388215 + 0.921569i \(0.373092\pi\)
\(174\) 0 0
\(175\) −3.52888 3.23549i −0.266758 0.244580i
\(176\) 0 0
\(177\) 4.48783 1.45818i 0.337326 0.109604i
\(178\) 0 0
\(179\) −0.0312215 + 0.0226837i −0.00233360 + 0.00169546i −0.588951 0.808168i \(-0.700459\pi\)
0.586618 + 0.809864i \(0.300459\pi\)
\(180\) 0 0
\(181\) −0.118881 0.0863720i −0.00883634 0.00641998i 0.583358 0.812215i \(-0.301738\pi\)
−0.592195 + 0.805795i \(0.701738\pi\)
\(182\) 0 0
\(183\) 2.55384 3.51505i 0.188785 0.259840i
\(184\) 0 0
\(185\) −2.53131 25.1749i −0.186106 1.85089i
\(186\) 0 0
\(187\) −3.31129 1.07590i −0.242146 0.0786779i
\(188\) 0 0
\(189\) 0.295892 + 0.910662i 0.0215230 + 0.0662409i
\(190\) 0 0
\(191\) −0.142049 + 0.437183i −0.0102783 + 0.0316335i −0.956064 0.293158i \(-0.905294\pi\)
0.945786 + 0.324791i \(0.105294\pi\)
\(192\) 0 0
\(193\) 19.0231i 1.36932i −0.728864 0.684658i \(-0.759952\pi\)
0.728864 0.684658i \(-0.240048\pi\)
\(194\) 0 0
\(195\) 3.37479 3.01124i 0.241674 0.215640i
\(196\) 0 0
\(197\) 7.12107 + 9.80131i 0.507355 + 0.698315i 0.983471 0.181068i \(-0.0579555\pi\)
−0.476115 + 0.879383i \(0.657955\pi\)
\(198\) 0 0
\(199\) −16.4872 −1.16875 −0.584375 0.811484i \(-0.698660\pi\)
−0.584375 + 0.811484i \(0.698660\pi\)
\(200\) 0 0
\(201\) 9.51778 0.671333
\(202\) 0 0
\(203\) 5.70742 + 7.85559i 0.400583 + 0.551355i
\(204\) 0 0
\(205\) −7.83763 + 0.788066i −0.547404 + 0.0550409i
\(206\) 0 0
\(207\) 3.51960i 0.244629i
\(208\) 0 0
\(209\) −8.43672 + 25.9656i −0.583580 + 1.79607i
\(210\) 0 0
\(211\) 5.61985 + 17.2961i 0.386887 + 1.19071i 0.935102 + 0.354378i \(0.115307\pi\)
−0.548216 + 0.836337i \(0.684693\pi\)
\(212\) 0 0
\(213\) −11.3603 3.69120i −0.778397 0.252917i
\(214\) 0 0
\(215\) 1.56858 0.689923i 0.106976 0.0470524i
\(216\) 0 0
\(217\) 2.07780 2.85985i 0.141051 0.194139i
\(218\) 0 0
\(219\) −4.39542 3.19346i −0.297015 0.215794i
\(220\) 0 0
\(221\) −1.05199 + 0.764316i −0.0707646 + 0.0514135i
\(222\) 0 0
\(223\) 22.3596 7.26507i 1.49731 0.486505i 0.558077 0.829789i \(-0.311539\pi\)
0.939231 + 0.343284i \(0.111539\pi\)
\(224\) 0 0
\(225\) −2.46086 4.35249i −0.164058 0.290166i
\(226\) 0 0
\(227\) −18.7171 + 6.08155i −1.24230 + 0.403647i −0.855154 0.518373i \(-0.826538\pi\)
−0.387142 + 0.922020i \(0.626538\pi\)
\(228\) 0 0
\(229\) 4.29343 3.11936i 0.283718 0.206133i −0.436819 0.899549i \(-0.643895\pi\)
0.720538 + 0.693416i \(0.243895\pi\)
\(230\) 0 0
\(231\) −4.19545 3.04817i −0.276040 0.200555i
\(232\) 0 0
\(233\) −13.6774 + 18.8253i −0.896034 + 1.23329i 0.0756813 + 0.997132i \(0.475887\pi\)
−0.971716 + 0.236154i \(0.924113\pi\)
\(234\) 0 0
\(235\) 5.55963 9.53010i 0.362670 0.621675i
\(236\) 0 0
\(237\) −11.2695 3.66167i −0.732030 0.237851i
\(238\) 0 0
\(239\) 4.65842 + 14.3371i 0.301328 + 0.927392i 0.981022 + 0.193897i \(0.0621126\pi\)
−0.679694 + 0.733496i \(0.737887\pi\)
\(240\) 0 0
\(241\) −5.84454 + 17.9877i −0.376480 + 1.15869i 0.565995 + 0.824409i \(0.308492\pi\)
−0.942475 + 0.334278i \(0.891508\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) −5.47650 12.4512i −0.349880 0.795475i
\(246\) 0 0
\(247\) 5.99340 + 8.24921i 0.381351 + 0.524885i
\(248\) 0 0
\(249\) 1.39408 0.0883463
\(250\) 0 0
\(251\) −4.56761 −0.288305 −0.144153 0.989555i \(-0.546046\pi\)
−0.144153 + 0.989555i \(0.546046\pi\)
\(252\) 0 0
\(253\) 11.2042 + 15.4213i 0.704405 + 0.969530i
\(254\) 0 0
\(255\) 0.578756 + 1.31584i 0.0362431 + 0.0824009i
\(256\) 0 0
\(257\) 20.2556i 1.26351i −0.775169 0.631754i \(-0.782335\pi\)
0.775169 0.631754i \(-0.217665\pi\)
\(258\) 0 0
\(259\) −3.34811 + 10.3044i −0.208042 + 0.640286i
\(260\) 0 0
\(261\) 3.13367 + 9.64444i 0.193969 + 0.596976i
\(262\) 0 0
\(263\) 29.2724 + 9.51119i 1.80502 + 0.586485i 0.999977 0.00673789i \(-0.00214475\pi\)
0.805038 + 0.593223i \(0.202145\pi\)
\(264\) 0 0
\(265\) −6.70005 + 11.4850i −0.411581 + 0.705515i
\(266\) 0 0
\(267\) 1.00401 1.38190i 0.0614443 0.0845709i
\(268\) 0 0
\(269\) −21.5796 15.6785i −1.31573 0.955936i −0.999975 0.00709610i \(-0.997741\pi\)
−0.315758 0.948840i \(-0.602259\pi\)
\(270\) 0 0
\(271\) 4.47342 3.25013i 0.271741 0.197431i −0.443566 0.896242i \(-0.646287\pi\)
0.715307 + 0.698810i \(0.246287\pi\)
\(272\) 0 0
\(273\) −1.84200 + 0.598504i −0.111483 + 0.0362231i
\(274\) 0 0
\(275\) 24.6380 + 11.2368i 1.48573 + 0.677603i
\(276\) 0 0
\(277\) 29.4098 9.55583i 1.76706 0.574154i 0.769172 0.639041i \(-0.220669\pi\)
0.997893 + 0.0648872i \(0.0206688\pi\)
\(278\) 0 0
\(279\) 2.98671 2.16997i 0.178810 0.129913i
\(280\) 0 0
\(281\) 13.6310 + 9.90352i 0.813159 + 0.590795i 0.914745 0.404032i \(-0.132392\pi\)
−0.101586 + 0.994827i \(0.532392\pi\)
\(282\) 0 0
\(283\) 6.62008 9.11176i 0.393523 0.541638i −0.565581 0.824693i \(-0.691348\pi\)
0.959104 + 0.283055i \(0.0913480\pi\)
\(284\) 0 0
\(285\) 10.3182 4.53832i 0.611195 0.268827i
\(286\) 0 0
\(287\) 3.20805 + 1.04236i 0.189365 + 0.0615285i
\(288\) 0 0
\(289\) 5.12558 + 15.7749i 0.301505 + 0.927936i
\(290\) 0 0
\(291\) 4.50789 13.8738i 0.264257 0.813299i
\(292\) 0 0
\(293\) 11.1995i 0.654284i 0.944975 + 0.327142i \(0.106086\pi\)
−0.944975 + 0.327142i \(0.893914\pi\)
\(294\) 0 0
\(295\) 10.4986 1.05562i 0.611251 0.0614607i
\(296\) 0 0
\(297\) −3.18338 4.38155i −0.184719 0.254243i
\(298\) 0 0
\(299\) 7.11914 0.411710
\(300\) 0 0
\(301\) −0.733798 −0.0422954
\(302\) 0 0
\(303\) 6.04433 + 8.31931i 0.347238 + 0.477932i
\(304\) 0 0
\(305\) 7.24916 6.46824i 0.415086 0.370371i
\(306\) 0 0
\(307\) 24.1289i 1.37711i 0.725185 + 0.688554i \(0.241754\pi\)
−0.725185 + 0.688554i \(0.758246\pi\)
\(308\) 0 0
\(309\) −4.32155 + 13.3004i −0.245844 + 0.756632i
\(310\) 0 0
\(311\) 0.640628 + 1.97165i 0.0363267 + 0.111802i 0.967576 0.252582i \(-0.0812797\pi\)
−0.931249 + 0.364384i \(0.881280\pi\)
\(312\) 0 0
\(313\) 8.10268 + 2.63272i 0.457991 + 0.148810i 0.528921 0.848671i \(-0.322597\pi\)
−0.0709303 + 0.997481i \(0.522597\pi\)
\(314\) 0 0
\(315\) 0.214205 + 2.13035i 0.0120691 + 0.120032i
\(316\) 0 0
\(317\) 7.99798 11.0083i 0.449211 0.618286i −0.523017 0.852322i \(-0.675194\pi\)
0.972228 + 0.234036i \(0.0751935\pi\)
\(318\) 0 0
\(319\) −44.4323 32.2819i −2.48773 1.80744i
\(320\) 0 0
\(321\) −7.33558 + 5.32961i −0.409432 + 0.297470i
\(322\) 0 0
\(323\) −3.08211 + 1.00144i −0.171493 + 0.0557215i
\(324\) 0 0
\(325\) 8.80382 4.97761i 0.488348 0.276108i
\(326\) 0 0
\(327\) 2.25910 0.734025i 0.124928 0.0405917i
\(328\) 0 0
\(329\) −3.82231 + 2.77707i −0.210731 + 0.153105i
\(330\) 0 0
\(331\) 18.3097 + 13.3028i 1.00639 + 0.731187i 0.963449 0.267891i \(-0.0863266\pi\)
0.0429430 + 0.999078i \(0.486327\pi\)
\(332\) 0 0
\(333\) −6.65098 + 9.15429i −0.364471 + 0.501652i
\(334\) 0 0
\(335\) 20.7972 + 4.51865i 1.13627 + 0.246880i
\(336\) 0 0
\(337\) −34.2285 11.1215i −1.86455 0.605828i −0.993385 0.114831i \(-0.963367\pi\)
−0.871161 0.490997i \(-0.836633\pi\)
\(338\) 0 0
\(339\) 4.15238 + 12.7797i 0.225526 + 0.694098i
\(340\) 0 0
\(341\) −6.17857 + 19.0157i −0.334588 + 1.02976i
\(342\) 0 0
\(343\) 12.5275i 0.676419i
\(344\) 0 0
\(345\) 1.67096 7.69064i 0.0899616 0.414050i
\(346\) 0 0
\(347\) −5.26858 7.25158i −0.282832 0.389285i 0.643837 0.765162i \(-0.277341\pi\)
−0.926669 + 0.375877i \(0.877341\pi\)
\(348\) 0 0
\(349\) 11.8276 0.633114 0.316557 0.948573i \(-0.397473\pi\)
0.316557 + 0.948573i \(0.397473\pi\)
\(350\) 0 0
\(351\) −2.02271 −0.107964
\(352\) 0 0
\(353\) −13.5712 18.6791i −0.722320 0.994188i −0.999444 0.0333537i \(-0.989381\pi\)
0.277124 0.960834i \(-0.410619\pi\)
\(354\) 0 0
\(355\) −23.0709 13.4590i −1.22448 0.714330i
\(356\) 0 0
\(357\) 0.615561i 0.0325790i
\(358\) 0 0
\(359\) −6.52607 + 20.0852i −0.344433 + 1.06005i 0.617454 + 0.786607i \(0.288164\pi\)
−0.961887 + 0.273448i \(0.911836\pi\)
\(360\) 0 0
\(361\) 1.98147 + 6.09833i 0.104288 + 0.320965i
\(362\) 0 0
\(363\) 17.4347 + 5.66488i 0.915085 + 0.297329i
\(364\) 0 0
\(365\) −8.08825 9.06475i −0.423358 0.474471i
\(366\) 0 0
\(367\) −4.93178 + 6.78801i −0.257437 + 0.354331i −0.918098 0.396353i \(-0.870276\pi\)
0.660662 + 0.750684i \(0.270276\pi\)
\(368\) 0 0
\(369\) 2.84998 + 2.07063i 0.148364 + 0.107793i
\(370\) 0 0
\(371\) 4.60636 3.34672i 0.239150 0.173753i
\(372\) 0 0
\(373\) −6.01888 + 1.95565i −0.311646 + 0.101260i −0.460664 0.887575i \(-0.652389\pi\)
0.149018 + 0.988834i \(0.452389\pi\)
\(374\) 0 0
\(375\) −3.31082 10.6789i −0.170970 0.551455i
\(376\) 0 0
\(377\) −19.5079 + 6.33850i −1.00471 + 0.326450i
\(378\) 0 0
\(379\) 12.1990 8.86310i 0.626621 0.455267i −0.228607 0.973519i \(-0.573417\pi\)
0.855228 + 0.518252i \(0.173417\pi\)
\(380\) 0 0
\(381\) −11.5389 8.38354i −0.591158 0.429502i
\(382\) 0 0
\(383\) 19.1490 26.3563i 0.978466 1.34674i 0.0408145 0.999167i \(-0.487005\pi\)
0.937652 0.347576i \(-0.112995\pi\)
\(384\) 0 0
\(385\) −7.72028 8.65235i −0.393462 0.440965i
\(386\) 0 0
\(387\) −0.728840 0.236815i −0.0370490 0.0120380i
\(388\) 0 0
\(389\) 1.69084 + 5.20388i 0.0857292 + 0.263847i 0.984727 0.174106i \(-0.0557035\pi\)
−0.898998 + 0.437953i \(0.855704\pi\)
\(390\) 0 0
\(391\) −0.699192 + 2.15189i −0.0353597 + 0.108826i
\(392\) 0 0
\(393\) 0.128666i 0.00649036i
\(394\) 0 0
\(395\) −22.8863 13.3513i −1.15154 0.671779i
\(396\) 0 0
\(397\) −8.38686 11.5435i −0.420925 0.579353i 0.544916 0.838491i \(-0.316562\pi\)
−0.965840 + 0.259138i \(0.916562\pi\)
\(398\) 0 0
\(399\) −4.82694 −0.241649
\(400\) 0 0
\(401\) 17.8291 0.890342 0.445171 0.895446i \(-0.353143\pi\)
0.445171 + 0.895446i \(0.353143\pi\)
\(402\) 0 0
\(403\) 4.38923 + 6.04125i 0.218643 + 0.300936i
\(404\) 0 0
\(405\) −0.474759 + 2.18509i −0.0235909 + 0.108578i
\(406\) 0 0
\(407\) 61.2826i 3.03767i
\(408\) 0 0
\(409\) −7.42964 + 22.8661i −0.367372 + 1.13065i 0.581110 + 0.813825i \(0.302618\pi\)
−0.948482 + 0.316830i \(0.897382\pi\)
\(410\) 0 0
\(411\) 4.23423 + 13.0316i 0.208859 + 0.642802i
\(412\) 0 0
\(413\) −4.29721 1.39625i −0.211452 0.0687049i
\(414\) 0 0
\(415\) 3.04619 + 0.661852i 0.149531 + 0.0324890i
\(416\) 0 0
\(417\) −13.7964 + 18.9891i −0.675611 + 0.929898i
\(418\) 0 0
\(419\) −22.7180 16.5056i −1.10984 0.806349i −0.127206 0.991876i \(-0.540601\pi\)
−0.982639 + 0.185527i \(0.940601\pi\)
\(420\) 0 0
\(421\) −16.3383 + 11.8704i −0.796278 + 0.578530i −0.909820 0.415003i \(-0.863780\pi\)
0.113542 + 0.993533i \(0.463780\pi\)
\(422\) 0 0
\(423\) −4.69272 + 1.52476i −0.228168 + 0.0741362i
\(424\) 0 0
\(425\) 0.639926 + 3.14999i 0.0310410 + 0.152797i
\(426\) 0 0
\(427\) −3.95668 + 1.28560i −0.191477 + 0.0622148i
\(428\) 0 0
\(429\) 8.86261 6.43907i 0.427891 0.310881i
\(430\) 0 0
\(431\) 3.35912 + 2.44055i 0.161803 + 0.117557i 0.665741 0.746183i \(-0.268116\pi\)
−0.503937 + 0.863740i \(0.668116\pi\)
\(432\) 0 0
\(433\) 17.8217 24.5295i 0.856456 1.17881i −0.125947 0.992037i \(-0.540197\pi\)
0.982403 0.186773i \(-0.0598030\pi\)
\(434\) 0 0
\(435\) 2.26856 + 22.5617i 0.108769 + 1.08175i
\(436\) 0 0
\(437\) 16.8741 + 5.48273i 0.807198 + 0.262275i
\(438\) 0 0
\(439\) 0.984067 + 3.02865i 0.0469670 + 0.144549i 0.971790 0.235849i \(-0.0757870\pi\)
−0.924823 + 0.380398i \(0.875787\pi\)
\(440\) 0 0
\(441\) −1.87979 + 5.78541i −0.0895140 + 0.275496i
\(442\) 0 0
\(443\) 30.4607i 1.44723i −0.690204 0.723615i \(-0.742479\pi\)
0.690204 0.723615i \(-0.257521\pi\)
\(444\) 0 0
\(445\) 2.84992 2.54291i 0.135099 0.120545i
\(446\) 0 0
\(447\) −6.28566 8.65147i −0.297302 0.409201i
\(448\) 0 0
\(449\) −1.35787 −0.0640820 −0.0320410 0.999487i \(-0.510201\pi\)
−0.0320410 + 0.999487i \(0.510201\pi\)
\(450\) 0 0
\(451\) −19.0789 −0.898392
\(452\) 0 0
\(453\) −4.33503 5.96666i −0.203678 0.280338i
\(454\) 0 0
\(455\) −4.30909 + 0.433275i −0.202013 + 0.0203122i
\(456\) 0 0
\(457\) 9.89208i 0.462732i 0.972867 + 0.231366i \(0.0743195\pi\)
−0.972867 + 0.231366i \(0.925680\pi\)
\(458\) 0 0
\(459\) 0.198657 0.611402i 0.00927250 0.0285378i
\(460\) 0 0
\(461\) −6.51515 20.0516i −0.303441 0.933894i −0.980255 0.197740i \(-0.936640\pi\)
0.676814 0.736154i \(-0.263360\pi\)
\(462\) 0 0
\(463\) 0.488978 + 0.158879i 0.0227248 + 0.00738372i 0.320357 0.947297i \(-0.396197\pi\)
−0.297633 + 0.954681i \(0.596197\pi\)
\(464\) 0 0
\(465\) 7.55643 3.32361i 0.350421 0.154129i
\(466\) 0 0
\(467\) −10.9175 + 15.0267i −0.505202 + 0.695352i −0.983101 0.183063i \(-0.941399\pi\)
0.477899 + 0.878415i \(0.341399\pi\)
\(468\) 0 0
\(469\) −7.37300 5.35680i −0.340453 0.247354i
\(470\) 0 0
\(471\) −10.5439 + 7.66056i −0.485835 + 0.352980i
\(472\) 0 0
\(473\) 3.94732 1.28256i 0.181498 0.0589723i
\(474\) 0 0
\(475\) 24.7007 5.01800i 1.13335 0.230241i
\(476\) 0 0
\(477\) 5.65531 1.83752i 0.258939 0.0841343i
\(478\) 0 0
\(479\) 18.3847 13.3573i 0.840017 0.610308i −0.0823581 0.996603i \(-0.526245\pi\)
0.922376 + 0.386294i \(0.126245\pi\)
\(480\) 0 0
\(481\) −18.5165 13.4530i −0.844279 0.613404i
\(482\) 0 0
\(483\) −1.98090 + 2.72648i −0.0901342 + 0.124059i
\(484\) 0 0
\(485\) 16.4369 28.1754i 0.746359 1.27938i
\(486\) 0 0
\(487\) −25.2840 8.21528i −1.14573 0.372270i −0.326196 0.945302i \(-0.605767\pi\)
−0.819533 + 0.573032i \(0.805767\pi\)
\(488\) 0 0
\(489\) −2.28549 7.03403i −0.103354 0.318090i
\(490\) 0 0
\(491\) 1.66601 5.12746i 0.0751860 0.231399i −0.906400 0.422421i \(-0.861180\pi\)
0.981586 + 0.191022i \(0.0611803\pi\)
\(492\) 0 0
\(493\) 6.51915i 0.293608i
\(494\) 0 0
\(495\) −4.87579 11.0854i −0.219150 0.498252i
\(496\) 0 0
\(497\) 6.72286 + 9.25323i 0.301562 + 0.415064i
\(498\) 0 0
\(499\) 14.5574 0.651677 0.325839 0.945425i \(-0.394353\pi\)
0.325839 + 0.945425i \(0.394353\pi\)
\(500\) 0 0
\(501\) 20.1265 0.899187
\(502\) 0 0
\(503\) 19.9353 + 27.4386i 0.888873 + 1.22343i 0.973883 + 0.227049i \(0.0729076\pi\)
−0.0850104 + 0.996380i \(0.527092\pi\)
\(504\) 0 0
\(505\) 9.25773 + 21.0480i 0.411963 + 0.936624i
\(506\) 0 0
\(507\) 8.90864i 0.395647i
\(508\) 0 0
\(509\) 5.18882 15.9695i 0.229990 0.707838i −0.767756 0.640742i \(-0.778627\pi\)
0.997747 0.0670956i \(-0.0213733\pi\)
\(510\) 0 0
\(511\) 1.60759 + 4.94766i 0.0711157 + 0.218872i
\(512\) 0 0
\(513\) −4.79432 1.55777i −0.211674 0.0687772i
\(514\) 0 0
\(515\) −15.7574 + 27.0108i −0.694355 + 1.19024i
\(516\) 0 0
\(517\) 15.7075 21.6195i 0.690815 0.950825i
\(518\) 0 0
\(519\) −1.79693 1.30554i −0.0788763 0.0573070i
\(520\) 0 0
\(521\) 13.8271 10.0460i 0.605777 0.440123i −0.242148 0.970239i \(-0.577852\pi\)
0.847925 + 0.530117i \(0.177852\pi\)
\(522\) 0 0
\(523\) −19.6398 + 6.38135i −0.858788 + 0.279037i −0.705122 0.709086i \(-0.749108\pi\)
−0.153666 + 0.988123i \(0.549108\pi\)
\(524\) 0 0
\(525\) −0.543347 + 4.75670i −0.0237136 + 0.207599i
\(526\) 0 0
\(527\) −2.25716 + 0.733396i −0.0983234 + 0.0319472i
\(528\) 0 0
\(529\) −8.58561 + 6.23781i −0.373287 + 0.271209i
\(530\) 0 0
\(531\) −3.81757 2.77363i −0.165669 0.120365i
\(532\) 0 0
\(533\) −4.18829 + 5.76468i −0.181415 + 0.249696i
\(534\) 0 0
\(535\) −18.5591 + 8.16303i −0.802382 + 0.352918i
\(536\) 0 0
\(537\) 0.0367031 + 0.0119255i 0.00158385 + 0.000514625i
\(538\) 0 0
\(539\) −10.1808 31.3332i −0.438517 1.34962i
\(540\) 0 0
\(541\) −3.75968 + 11.5711i −0.161641 + 0.497480i −0.998773 0.0495207i \(-0.984231\pi\)
0.837132 + 0.547001i \(0.184231\pi\)
\(542\) 0 0
\(543\) 0.146945i 0.00630600i
\(544\) 0 0
\(545\) 5.28481 0.531383i 0.226376 0.0227619i
\(546\) 0 0
\(547\) 6.56378 + 9.03427i 0.280647 + 0.386278i 0.925948 0.377651i \(-0.123268\pi\)
−0.645301 + 0.763928i \(0.723268\pi\)
\(548\) 0 0
\(549\) −4.34485 −0.185434
\(550\) 0 0
\(551\) −51.1201 −2.17779
\(552\) 0 0
\(553\) 6.66908 + 9.17921i 0.283598 + 0.390340i
\(554\) 0 0
\(555\) −18.8790 + 16.8453i −0.801371 + 0.715043i
\(556\) 0 0
\(557\) 12.9282i 0.547787i −0.961760 0.273894i \(-0.911688\pi\)
0.961760 0.273894i \(-0.0883116\pi\)
\(558\) 0 0
\(559\) 0.479007 1.47423i 0.0202598 0.0623534i
\(560\) 0 0
\(561\) 1.07590 + 3.31129i 0.0454247 + 0.139803i
\(562\) 0 0
\(563\) −30.1722 9.80354i −1.27161 0.413170i −0.405989 0.913878i \(-0.633073\pi\)
−0.865616 + 0.500708i \(0.833073\pi\)
\(564\) 0 0
\(565\) 3.00603 + 29.8961i 0.126465 + 1.25774i
\(566\) 0 0
\(567\) 0.562820 0.774655i 0.0236362 0.0325325i
\(568\) 0 0
\(569\) 23.3050 + 16.9321i 0.976997 + 0.709830i 0.957036 0.289971i \(-0.0936455\pi\)
0.0199619 + 0.999801i \(0.493646\pi\)
\(570\) 0 0
\(571\) 14.6999 10.6801i 0.615173 0.446950i −0.236059 0.971739i \(-0.575856\pi\)
0.851232 + 0.524789i \(0.175856\pi\)
\(572\) 0 0
\(573\) 0.437183 0.142049i 0.0182636 0.00593420i
\(574\) 0 0
\(575\) 7.30239 16.0114i 0.304531 0.667722i
\(576\) 0 0
\(577\) 38.7990 12.6065i 1.61522 0.524817i 0.644414 0.764677i \(-0.277101\pi\)
0.970808 + 0.239859i \(0.0771014\pi\)
\(578\) 0 0
\(579\) −15.3900 + 11.1815i −0.639589 + 0.464688i
\(580\) 0 0
\(581\) −1.07993 0.784616i −0.0448031 0.0325514i
\(582\) 0 0
\(583\) −18.9295 + 26.0542i −0.783979 + 1.07905i
\(584\) 0 0
\(585\) −4.41980 0.960299i −0.182736 0.0397035i
\(586\) 0 0
\(587\) 8.75436 + 2.84446i 0.361331 + 0.117404i 0.484056 0.875037i \(-0.339163\pi\)
−0.122725 + 0.992441i \(0.539163\pi\)
\(588\) 0 0
\(589\) 5.75094 + 17.6996i 0.236963 + 0.729298i
\(590\) 0 0
\(591\) 3.74377 11.5221i 0.153998 0.473957i
\(592\) 0 0
\(593\) 12.3856i 0.508614i −0.967124 0.254307i \(-0.918153\pi\)
0.967124 0.254307i \(-0.0818474\pi\)
\(594\) 0 0
\(595\) 0.292243 1.34505i 0.0119808 0.0551419i
\(596\) 0 0
\(597\) 9.69096 + 13.3385i 0.396625 + 0.545907i
\(598\) 0 0
\(599\) 18.1732 0.742536 0.371268 0.928526i \(-0.378923\pi\)
0.371268 + 0.928526i \(0.378923\pi\)
\(600\) 0 0
\(601\) 29.8155 1.21620 0.608099 0.793861i \(-0.291932\pi\)
0.608099 + 0.793861i \(0.291932\pi\)
\(602\) 0 0
\(603\) −5.59441 7.70005i −0.227822 0.313570i
\(604\) 0 0
\(605\) 35.4069 + 20.6555i 1.43950 + 0.839767i
\(606\) 0 0
\(607\) 9.16747i 0.372096i 0.982541 + 0.186048i \(0.0595680\pi\)
−0.982541 + 0.186048i \(0.940432\pi\)
\(608\) 0 0
\(609\) 3.00057 9.23480i 0.121589 0.374213i
\(610\) 0 0
\(611\) −3.08414 9.49201i −0.124771 0.384006i
\(612\) 0 0
\(613\) −13.3662 4.34294i −0.539855 0.175410i 0.0263819 0.999652i \(-0.491601\pi\)
−0.566237 + 0.824242i \(0.691601\pi\)
\(614\) 0 0
\(615\) 5.24440 + 5.87756i 0.211475 + 0.237006i
\(616\) 0 0
\(617\) −21.2980 + 29.3141i −0.857424 + 1.18014i 0.124754 + 0.992188i \(0.460186\pi\)
−0.982178 + 0.187955i \(0.939814\pi\)
\(618\) 0 0
\(619\) 20.7716 + 15.0915i 0.834882 + 0.606577i 0.920936 0.389713i \(-0.127426\pi\)
−0.0860542 + 0.996290i \(0.527426\pi\)
\(620\) 0 0
\(621\) −2.84742 + 2.06877i −0.114263 + 0.0830169i
\(622\) 0 0
\(623\) −1.55552 + 0.505419i −0.0623206 + 0.0202492i
\(624\) 0 0
\(625\) −2.16453 24.9061i −0.0865814 0.996245i
\(626\) 0 0
\(627\) 25.9656 8.43672i 1.03696 0.336930i
\(628\) 0 0
\(629\) 5.88498 4.27569i 0.234650 0.170483i
\(630\) 0 0
\(631\) 19.9603 + 14.5020i 0.794608 + 0.577317i 0.909327 0.416081i \(-0.136597\pi\)
−0.114719 + 0.993398i \(0.536597\pi\)
\(632\) 0 0
\(633\) 10.6896 14.7130i 0.424873 0.584788i
\(634\) 0 0
\(635\) −21.2334 23.7970i −0.842624 0.944354i
\(636\) 0 0
\(637\) −11.7022 3.80228i −0.463659 0.150652i
\(638\) 0 0
\(639\) 3.69120 + 11.3603i 0.146021 + 0.449408i
\(640\) 0 0
\(641\) −9.25128 + 28.4725i −0.365404 + 1.12460i 0.584324 + 0.811520i \(0.301360\pi\)
−0.949728 + 0.313077i \(0.898640\pi\)
\(642\) 0 0
\(643\) 10.1343i 0.399658i 0.979831 + 0.199829i \(0.0640387\pi\)
−0.979831 + 0.199829i \(0.935961\pi\)
\(644\) 0 0
\(645\) −1.48015 0.863484i −0.0582808 0.0339996i
\(646\) 0 0
\(647\) 26.6027 + 36.6155i 1.04586 + 1.43950i 0.892343 + 0.451358i \(0.149060\pi\)
0.153518 + 0.988146i \(0.450940\pi\)
\(648\) 0 0
\(649\) 25.5564 1.00318
\(650\) 0 0
\(651\) −3.53497 −0.138547
\(652\) 0 0
\(653\) 19.3880 + 26.6853i 0.758711 + 1.04428i 0.997320 + 0.0731608i \(0.0233086\pi\)
−0.238609 + 0.971116i \(0.576691\pi\)
\(654\) 0 0
\(655\) 0.0610855 0.281147i 0.00238681 0.0109853i
\(656\) 0 0
\(657\) 5.43304i 0.211963i
\(658\) 0 0
\(659\) −0.789392 + 2.42950i −0.0307504 + 0.0946398i −0.965254 0.261314i \(-0.915844\pi\)
0.934503 + 0.355954i \(0.115844\pi\)
\(660\) 0 0
\(661\) −14.0332 43.1898i −0.545829 1.67989i −0.719011 0.694999i \(-0.755405\pi\)
0.173182 0.984890i \(-0.444595\pi\)
\(662\) 0 0
\(663\) 1.23669 + 0.401825i 0.0480290 + 0.0156056i
\(664\) 0 0
\(665\) −10.5473 2.29163i −0.409006 0.0888656i
\(666\) 0 0
\(667\) −20.9789 + 28.8750i −0.812307 + 1.11804i
\(668\) 0 0
\(669\) −19.0202 13.8190i −0.735363 0.534273i
\(670\) 0 0
\(671\) 19.0372 13.8313i 0.734922 0.533952i
\(672\) 0 0
\(673\) −10.7875 + 3.50508i −0.415828 + 0.135111i −0.509456 0.860496i \(-0.670153\pi\)
0.0936282 + 0.995607i \(0.470153\pi\)
\(674\) 0 0
\(675\) −2.07478 + 4.54921i −0.0798582 + 0.175099i
\(676\) 0 0
\(677\) −14.7113 + 4.78000i −0.565402 + 0.183710i −0.577750 0.816213i \(-0.696069\pi\)
0.0123484 + 0.999924i \(0.496069\pi\)
\(678\) 0 0
\(679\) −11.3005 + 8.21032i −0.433675 + 0.315083i
\(680\) 0 0
\(681\) 15.9217 + 11.5678i 0.610121 + 0.443279i
\(682\) 0 0
\(683\) 3.99284 5.49567i 0.152782 0.210286i −0.725765 0.687943i \(-0.758514\pi\)
0.878546 + 0.477657i \(0.158514\pi\)
\(684\) 0 0
\(685\) 3.06528 + 30.4854i 0.117118 + 1.16479i
\(686\) 0 0
\(687\) −5.04724 1.63995i −0.192564 0.0625678i
\(688\) 0 0
\(689\) 3.71677 + 11.4390i 0.141598 + 0.435793i
\(690\) 0 0
\(691\) 13.0774 40.2482i 0.497489 1.53111i −0.315552 0.948908i \(-0.602190\pi\)
0.813041 0.582206i \(-0.197810\pi\)
\(692\) 0 0
\(693\) 5.18586i 0.196995i
\(694\) 0 0
\(695\) −39.1615 + 34.9428i −1.48548 + 1.32546i
\(696\) 0 0
\(697\) −1.33114 1.83215i −0.0504205 0.0693978i
\(698\) 0 0
\(699\) 23.2693 0.880127
\(700\) 0 0
\(701\) 32.2924 1.21967 0.609834 0.792529i \(-0.291236\pi\)
0.609834 + 0.792529i \(0.291236\pi\)
\(702\) 0 0
\(703\) −33.5279 46.1472i −1.26453 1.74047i
\(704\) 0 0
\(705\) −10.9779 + 1.10382i −0.413451 + 0.0415721i
\(706\) 0 0
\(707\) 9.84647i 0.370314i
\(708\) 0 0
\(709\) 0.667116 2.05317i 0.0250541 0.0771085i −0.937748 0.347317i \(-0.887093\pi\)
0.962802 + 0.270209i \(0.0870927\pi\)
\(710\) 0 0
\(711\) 3.66167 + 11.2695i 0.137323 + 0.422638i
\(712\) 0 0
\(713\) 12.3576 + 4.01524i 0.462797 + 0.150372i
\(714\) 0 0
\(715\) 22.4226 9.86231i 0.838557 0.368830i
\(716\) 0 0
\(717\) 8.86084 12.1959i 0.330914 0.455464i
\(718\) 0 0
\(719\) 1.28757 + 0.935472i 0.0480181 + 0.0348872i 0.611535 0.791217i \(-0.290552\pi\)
−0.563517 + 0.826104i \(0.690552\pi\)
\(720\) 0 0
\(721\) 10.8334 7.87094i 0.403458 0.293129i
\(722\) 0 0
\(723\) 17.9877 5.84454i 0.668968 0.217361i
\(724\) 0 0
\(725\) −5.75436 + 50.3762i −0.213711 + 1.87093i
\(726\) 0 0
\(727\) −1.27424 + 0.414026i −0.0472589 + 0.0153554i −0.332551 0.943085i \(-0.607909\pi\)
0.285292 + 0.958441i \(0.407909\pi\)
\(728\) 0 0
\(729\) 0.809017 0.587785i 0.0299636 0.0217698i
\(730\) 0 0
\(731\) 0.398570 + 0.289578i 0.0147416 + 0.0107104i
\(732\) 0 0
\(733\) −25.7748 + 35.4759i −0.952013 + 1.31033i −0.00138578 + 0.999999i \(0.500441\pi\)
−0.950627 + 0.310335i \(0.899559\pi\)
\(734\) 0 0
\(735\) −6.85419 + 11.7492i −0.252821 + 0.433375i
\(736\) 0 0
\(737\) 49.0244 + 15.9290i 1.80584 + 0.586752i
\(738\) 0 0
\(739\) −5.67584 17.4684i −0.208789 0.642587i −0.999536 0.0304443i \(-0.990308\pi\)
0.790747 0.612143i \(-0.209692\pi\)
\(740\) 0 0
\(741\) 3.15092 9.69753i 0.115752 0.356248i
\(742\) 0 0
\(743\) 21.5051i 0.788947i 0.918907 + 0.394474i \(0.129073\pi\)
−0.918907 + 0.394474i \(0.870927\pi\)
\(744\) 0 0
\(745\) −9.62736 21.8884i −0.352719 0.801929i
\(746\) 0 0
\(747\) −0.819420 1.12784i −0.0299810 0.0412653i
\(748\) 0 0
\(749\) 8.68215 0.317239
\(750\) 0 0
\(751\) −7.02810 −0.256459 −0.128230 0.991745i \(-0.540929\pi\)
−0.128230 + 0.991745i \(0.540929\pi\)
\(752\) 0 0
\(753\) 2.68477 + 3.69528i 0.0978386 + 0.134663i
\(754\) 0 0
\(755\) −6.63970 15.0958i −0.241643 0.549391i
\(756\) 0 0
\(757\) 5.39361i 0.196034i 0.995185 + 0.0980171i \(0.0312500\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(758\) 0 0
\(759\) 5.89042 18.1289i 0.213809 0.658036i
\(760\) 0 0
\(761\) −6.22670 19.1638i −0.225718 0.694688i −0.998218 0.0596731i \(-0.980994\pi\)
0.772500 0.635014i \(-0.219006\pi\)
\(762\) 0 0
\(763\) −2.16314 0.702848i −0.0783111 0.0254448i
\(764\) 0 0
\(765\) 0.724350 1.24165i 0.0261889 0.0448920i
\(766\) 0 0
\(767\) 5.61025 7.72184i 0.202574 0.278820i
\(768\) 0 0
\(769\) 25.0121 + 18.1724i 0.901960 + 0.655312i 0.938969 0.344003i \(-0.111783\pi\)
−0.0370088 + 0.999315i \(0.511783\pi\)
\(770\) 0 0
\(771\) −16.3871 + 11.9059i −0.590167 + 0.428781i
\(772\) 0 0
\(773\) −30.4255 + 9.88584i −1.09433 + 0.355569i −0.799918 0.600110i \(-0.795124\pi\)
−0.294411 + 0.955679i \(0.595124\pi\)
\(774\) 0 0
\(775\) 18.0894 3.67489i 0.649790 0.132006i
\(776\) 0 0
\(777\) 10.3044 3.34811i 0.369669 0.120113i
\(778\) 0 0
\(779\) −14.3669 + 10.4381i −0.514747 + 0.373985i
\(780\) 0 0
\(781\) −52.3375 38.0254i −1.87278 1.36066i
\(782\) 0 0
\(783\) 5.96059 8.20405i 0.213014 0.293189i
\(784\) 0 0
\(785\) −26.6761 + 11.7332i −0.952112 + 0.418776i
\(786\) 0 0
\(787\) 23.2267 + 7.54681i 0.827942 + 0.269015i 0.692178 0.721726i \(-0.256651\pi\)
0.135764 + 0.990741i \(0.456651\pi\)
\(788\) 0 0
\(789\) −9.51119 29.2724i −0.338607 1.04213i
\(790\) 0 0
\(791\) 3.97601 12.2369i 0.141371 0.435094i
\(792\) 0 0
\(793\) 8.78837i 0.312084i
\(794\) 0 0
\(795\) 13.2297 1.33024i 0.469210 0.0471786i
\(796\) 0 0
\(797\) 29.1765 + 40.1580i 1.03348 + 1.42247i 0.902300 + 0.431110