Properties

Label 300.2.o.a.229.2
Level $300$
Weight $2$
Character 300.229
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 229.2
Character \(\chi\) \(=\) 300.229
Dual form 300.2.o.a.169.2

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

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

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 \(-0.942081\pi\)
0.983491 0.180955i \(-0.0579190\pi\)
\(8\) 0 0
\(9\) −0.309017 0.951057i −0.103006 0.317019i
\(10\) 0 0
\(11\) −1.67360 + 5.15082i −0.504611 + 1.55303i 0.296814 + 0.954935i \(0.404076\pi\)
−0.801424 + 0.598096i \(0.795924\pi\)
\(12\) 0 0
\(13\) −1.92371 + 0.625052i −0.533542 + 0.173358i −0.563382 0.826196i \(-0.690500\pi\)
0.0298404 + 0.999555i \(0.490500\pi\)
\(14\) 0 0
\(15\) −1.12675 1.93143i −0.290926 0.498694i
\(16\) 0 0
\(17\) 0.377867 + 0.520090i 0.0916463 + 0.126140i 0.852378 0.522926i \(-0.175160\pi\)
−0.760732 + 0.649067i \(0.775160\pi\)
\(18\) 0 0
\(19\) −4.07829 + 2.96305i −0.935625 + 0.679771i −0.947364 0.320160i \(-0.896263\pi\)
0.0117388 + 0.999931i \(0.496263\pi\)
\(20\) 0 0
\(21\) 0.774655 + 0.562820i 0.169044 + 0.122817i
\(22\) 0 0
\(23\) −3.34734 1.08762i −0.697969 0.226784i −0.0615235 0.998106i \(-0.519596\pi\)
−0.636445 + 0.771322i \(0.719596\pi\)
\(24\) 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 0.959742 + 0.280882i \(0.0906271\pi\)
0.563712 + 0.825972i \(0.309373\pi\)
\(30\) 0 0
\(31\) −2.98671 + 2.16997i −0.536429 + 0.389738i −0.822757 0.568393i \(-0.807565\pi\)
0.286328 + 0.958132i \(0.407565\pi\)
\(32\) 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 0.771097 0.636717i \(-0.219708\pi\)
0.998084 + 0.0618753i \(0.0197081\pi\)
\(38\) 0 0
\(39\) 0.625052 1.92371i 0.100088 0.308040i
\(40\) 0 0
\(41\) 1.08859 + 3.35035i 0.170010 + 0.523237i 0.999370 0.0354770i \(-0.0112950\pi\)
−0.829361 + 0.558714i \(0.811295\pi\)
\(42\) 0 0
\(43\) 0.766348i 0.116867i −0.998291 0.0584335i \(-0.981389\pi\)
0.998291 0.0584335i \(-0.0186106\pi\)
\(44\) 0 0
\(45\) 2.22485 + 0.223707i 0.331661 + 0.0333482i
\(46\) 0 0
\(47\) 2.90026 3.99186i 0.423046 0.582273i −0.543293 0.839543i \(-0.682823\pi\)
0.966340 + 0.257270i \(0.0828229\pi\)
\(48\) 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 −0.978524 0.206134i \(-0.933912\pi\)
0.498425 + 0.866933i \(0.333912\pi\)
\(54\) 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 0.810159 0.586210i \(-0.199381\pi\)
−0.999998 + 0.00194529i \(0.999381\pi\)
\(60\) 0 0
\(61\) 1.34263 4.13219i 0.171906 0.529073i −0.827572 0.561359i \(-0.810279\pi\)
0.999479 + 0.0322858i \(0.0102787\pi\)
\(62\) 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 0.316503 0.948592i \(-0.397491\pi\)
−0.999969 + 0.00788103i \(0.997491\pi\)
\(68\) 0 0
\(69\) 2.84742 2.06877i 0.342789 0.249051i
\(70\) 0 0
\(71\) 9.66368 + 7.02107i 1.14687 + 0.833248i 0.988061 0.154062i \(-0.0492354\pi\)
0.158806 + 0.987310i \(0.449235\pi\)
\(72\) 0 0
\(73\) 5.16713 + 1.67890i 0.604766 + 0.196500i 0.595365 0.803455i \(-0.297007\pi\)
0.00940128 + 0.999956i \(0.497007\pi\)
\(74\) 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 0.977430 0.211261i \(-0.0677569\pi\)
0.101122 + 0.994874i \(0.467757\pi\)
\(80\) 0 0
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) 0 0
\(83\) −0.819420 1.12784i −0.0899431 0.123796i 0.761674 0.647960i \(-0.224378\pi\)
−0.851617 + 0.524164i \(0.824378\pi\)
\(84\) 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 −0.919176 0.393847i \(-0.871144\pi\)
0.975127 + 0.221649i \(0.0711438\pi\)
\(90\) 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 −0.108325 0.994116i \(-0.534549\pi\)
0.978934 0.204176i \(-0.0654514\pi\)
\(98\) 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 0.181383 + 0.983413i \(0.441943\pi\)
−0.991331 + 0.131386i \(0.958057\pi\)
\(104\) 0 0
\(105\) −1.84940 + 1.07889i −0.180483 + 0.105289i
\(106\) 0 0
\(107\) 9.06727i 0.876566i 0.898837 + 0.438283i \(0.144413\pi\)
−0.898837 + 0.438283i \(0.855587\pi\)
\(108\) 0 0
\(109\) −0.734025 2.25910i −0.0703068 0.216382i 0.909729 0.415202i \(-0.136289\pi\)
−0.980036 + 0.198820i \(0.936289\pi\)
\(110\) 0 0
\(111\) −3.49663 + 10.7615i −0.331885 + 1.02144i
\(112\) 0 0
\(113\) −12.7797 + 4.15238i −1.20221 + 0.390623i −0.840575 0.541696i \(-0.817782\pi\)
−0.361638 + 0.932318i \(0.617782\pi\)
\(114\) 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 0.841116 0.540855i \(-0.181899\pi\)
0.362570 + 0.931957i \(0.381899\pi\)
\(128\) 0 0
\(129\) 0.619989 + 0.450448i 0.0545869 + 0.0396597i
\(130\) 0 0
\(131\) 0.104093 0.0756282i 0.00909468 0.00660767i −0.583229 0.812308i \(-0.698211\pi\)
0.592323 + 0.805700i \(0.298211\pi\)
\(132\) 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 −0.807232 0.590234i \(-0.799035\pi\)
−0.306133 + 0.951989i \(0.599035\pi\)
\(138\) 0 0
\(139\) −7.25318 + 22.3230i −0.615206 + 1.89341i −0.216731 + 0.976231i \(0.569539\pi\)
−0.398475 + 0.917179i \(0.630461\pi\)
\(140\) 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 \(0.174094\pi\)
−0.854124 + 0.520070i \(0.825906\pi\)
\(158\) 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 −0.0202964 0.999794i \(-0.506461\pi\)
0.571244 + 0.820780i \(0.306461\pi\)
\(164\) 0 0
\(165\) 11.8342 2.57124i 0.921292 0.200171i
\(166\) 0 0
\(167\) −11.8301 16.2827i −0.915438 1.25999i −0.965275 0.261235i \(-0.915870\pi\)
0.0498368 0.998757i \(-0.484130\pi\)
\(168\) 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 0.388215 0.921569i \(-0.373092\pi\)
−0.227612 + 0.973752i \(0.573092\pi\)
\(174\) 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 0.586618 0.809864i \(-0.300459\pi\)
−0.588951 + 0.808168i \(0.700459\pi\)
\(180\) 0 0
\(181\) −0.118881 + 0.0863720i −0.00883634 + 0.00641998i −0.592195 0.805795i \(-0.701738\pi\)
0.583358 + 0.812215i \(0.301738\pi\)
\(182\) 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 0.945786 0.324791i \(-0.105294\pi\)
−0.956064 + 0.293158i \(0.905294\pi\)
\(192\) 0 0
\(193\) 19.0231i 1.36932i 0.728864 + 0.684658i \(0.240048\pi\)
−0.728864 + 0.684658i \(0.759952\pi\)
\(194\) 0 0
\(195\) 3.37479 + 3.01124i 0.241674 + 0.215640i
\(196\) 0 0
\(197\) 7.12107 9.80131i 0.507355 0.698315i −0.476115 0.879383i \(-0.657955\pi\)
0.983471 + 0.181068i \(0.0579555\pi\)
\(198\) 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 −0.548216 0.836337i \(-0.684693\pi\)
0.935102 0.354378i \(-0.115307\pi\)
\(212\) 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 0.939231 0.343284i \(-0.111539\pi\)
0.558077 + 0.829789i \(0.311539\pi\)
\(224\) 0 0
\(225\) −2.46086 + 4.35249i −0.164058 + 0.290166i
\(226\) 0 0
\(227\) −18.7171 6.08155i −1.24230 0.403647i −0.387142 0.922020i \(-0.626538\pi\)
−0.855154 + 0.518373i \(0.826538\pi\)
\(228\) 0 0
\(229\) 4.29343 + 3.11936i 0.283718 + 0.206133i 0.720538 0.693416i \(-0.243895\pi\)
−0.436819 + 0.899549i \(0.643895\pi\)
\(230\) 0 0
\(231\) −4.19545 + 3.04817i −0.276040 + 0.200555i
\(232\) 0 0
\(233\) −13.6774 18.8253i −0.896034 1.23329i −0.971716 0.236154i \(-0.924113\pi\)
0.0756813 0.997132i \(-0.475887\pi\)
\(234\) 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 −0.679694 0.733496i \(-0.737887\pi\)
0.981022 0.193897i \(-0.0621126\pi\)
\(240\) 0 0
\(241\) −5.84454 17.9877i −0.376480 1.15869i −0.942475 0.334278i \(-0.891508\pi\)
0.565995 0.824409i \(-0.308492\pi\)
\(242\) 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 \(0.217665\pi\)
−0.775169 + 0.631754i \(0.782335\pi\)
\(258\) 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 0.805038 0.593223i \(-0.202145\pi\)
0.999977 + 0.00673789i \(0.00214475\pi\)
\(264\) 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 −0.315758 + 0.948840i \(0.602259\pi\)
−0.999975 + 0.00709610i \(0.997741\pi\)
\(270\) 0 0
\(271\) 4.47342 + 3.25013i 0.271741 + 0.197431i 0.715307 0.698810i \(-0.246287\pi\)
−0.443566 + 0.896242i \(0.646287\pi\)
\(272\) 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 0.997893 0.0648872i \(-0.0206688\pi\)
0.769172 + 0.639041i \(0.220669\pi\)
\(278\) 0 0
\(279\) 2.98671 + 2.16997i 0.178810 + 0.129913i
\(280\) 0 0
\(281\) 13.6310 9.90352i 0.813159 0.590795i −0.101586 0.994827i \(-0.532392\pi\)
0.914745 + 0.404032i \(0.132392\pi\)
\(282\) 0 0
\(283\) 6.62008 + 9.11176i 0.393523 + 0.541638i 0.959104 0.283055i \(-0.0913480\pi\)
−0.565581 + 0.824693i \(0.691348\pi\)
\(284\) 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 \(-0.893914\pi\)
0.944975 0.327142i \(-0.106086\pi\)
\(294\) 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 \(-0.758246\pi\)
0.725185 0.688554i \(-0.241754\pi\)
\(308\) 0 0
\(309\) −4.32155 13.3004i −0.245844 0.756632i
\(310\) 0 0
\(311\) 0.640628 1.97165i 0.0363267 0.111802i −0.931249 0.364384i \(-0.881280\pi\)
0.967576 + 0.252582i \(0.0812797\pi\)
\(312\) 0 0
\(313\) 8.10268 2.63272i 0.457991 0.148810i −0.0709303 0.997481i \(-0.522597\pi\)
0.528921 + 0.848671i \(0.322597\pi\)
\(314\) 0 0
\(315\) 0.214205 2.13035i 0.0120691 0.120032i
\(316\) 0 0
\(317\) 7.99798 + 11.0083i 0.449211 + 0.618286i 0.972228 0.234036i \(-0.0751935\pi\)
−0.523017 + 0.852322i \(0.675194\pi\)
\(318\) 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 0.0429430 0.999078i \(-0.486327\pi\)
0.963449 + 0.267891i \(0.0863266\pi\)
\(332\) 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 −0.871161 + 0.490997i \(0.836633\pi\)
−0.993385 + 0.114831i \(0.963367\pi\)
\(338\) 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 −0.926669 0.375877i \(-0.877341\pi\)
0.643837 + 0.765162i \(0.277341\pi\)
\(348\) 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 0.277124 + 0.960834i \(0.410619\pi\)
−0.999444 + 0.0333537i \(0.989381\pi\)
\(354\) 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 −0.961887 0.273448i \(-0.911836\pi\)
0.617454 0.786607i \(-0.288164\pi\)
\(360\) 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 0.660662 0.750684i \(-0.270276\pi\)
−0.918098 + 0.396353i \(0.870276\pi\)
\(368\) 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 0.149018 0.988834i \(-0.452389\pi\)
−0.460664 + 0.887575i \(0.652389\pi\)
\(374\) 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 0.855228 0.518252i \(-0.173417\pi\)
−0.228607 + 0.973519i \(0.573417\pi\)
\(380\) 0 0
\(381\) −11.5389 + 8.38354i −0.591158 + 0.429502i
\(382\) 0 0
\(383\) 19.1490 + 26.3563i 0.978466 + 1.34674i 0.937652 + 0.347576i \(0.112995\pi\)
0.0408145 + 0.999167i \(0.487005\pi\)
\(384\) 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 −0.898998 0.437953i \(-0.855704\pi\)
0.984727 + 0.174106i \(0.0557035\pi\)
\(390\) 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 −0.965840 0.259138i \(-0.916562\pi\)
0.544916 + 0.838491i \(0.316562\pi\)
\(398\) 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 −0.948482 0.316830i \(-0.897382\pi\)
0.581110 0.813825i \(-0.302618\pi\)
\(410\) 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 −0.982639 0.185527i \(-0.940601\pi\)
−0.127206 + 0.991876i \(0.540601\pi\)
\(420\) 0 0
\(421\) −16.3383 11.8704i −0.796278 0.578530i 0.113542 0.993533i \(-0.463780\pi\)
−0.909820 + 0.415003i \(0.863780\pi\)
\(422\) 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 −0.503937 0.863740i \(-0.668116\pi\)
0.665741 + 0.746183i \(0.268116\pi\)
\(432\) 0 0
\(433\) 17.8217 + 24.5295i 0.856456 + 1.17881i 0.982403 + 0.186773i \(0.0598030\pi\)
−0.125947 + 0.992037i \(0.540197\pi\)
\(434\) 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 −0.924823 0.380398i \(-0.875787\pi\)
0.971790 + 0.235849i \(0.0757870\pi\)
\(440\) 0 0
\(441\) −1.87979 5.78541i −0.0895140 0.275496i
\(442\) 0 0
\(443\) 30.4607i 1.44723i 0.690204 + 0.723615i \(0.257521\pi\)
−0.690204 + 0.723615i \(0.742479\pi\)
\(444\) 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 \(-0.925680\pi\)
0.972867 0.231366i \(-0.0743195\pi\)
\(458\) 0 0
\(459\) 0.198657 + 0.611402i 0.00927250 + 0.0285378i
\(460\) 0 0
\(461\) −6.51515 + 20.0516i −0.303441 + 0.933894i 0.676814 + 0.736154i \(0.263360\pi\)
−0.980255 + 0.197740i \(0.936640\pi\)
\(462\) 0 0
\(463\) 0.488978 0.158879i 0.0227248 0.00738372i −0.297633 0.954681i \(-0.596197\pi\)
0.320357 + 0.947297i \(0.396197\pi\)
\(464\) 0 0
\(465\) 7.55643 + 3.32361i 0.350421 + 0.154129i
\(466\) 0 0
\(467\) −10.9175 15.0267i −0.505202 0.695352i 0.477899 0.878415i \(-0.341399\pi\)
−0.983101 + 0.183063i \(0.941399\pi\)
\(468\) 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 0.922376 0.386294i \(-0.126245\pi\)
−0.0823581 + 0.996603i \(0.526245\pi\)
\(480\) 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 −0.819533 0.573032i \(-0.805767\pi\)
−0.326196 + 0.945302i \(0.605767\pi\)
\(488\) 0 0
\(489\) −2.28549 + 7.03403i −0.103354 + 0.318090i
\(490\) 0 0
\(491\) 1.66601 + 5.12746i 0.0751860 + 0.231399i 0.981586 0.191022i \(-0.0611803\pi\)
−0.906400 + 0.422421i \(0.861180\pi\)
\(492\) 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 −0.0850104 0.996380i \(-0.527092\pi\)
0.973883 0.227049i \(-0.0729076\pi\)
\(504\) 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 0.997747 + 0.0670956i \(0.0213733\pi\)
−0.767756 + 0.640742i \(0.778627\pi\)
\(510\) 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 0.847925 0.530117i \(-0.177852\pi\)
−0.242148 + 0.970239i \(0.577852\pi\)
\(522\) 0 0
\(523\) −19.6398 6.38135i −0.858788 0.279037i −0.153666 0.988123i \(-0.549108\pi\)
−0.705122 + 0.709086i \(0.749108\pi\)
\(524\) 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 0.837132 0.547001i \(-0.184231\pi\)
−0.998773 + 0.0495207i \(0.984231\pi\)
\(542\) 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 −0.645301 0.763928i \(-0.723268\pi\)
0.925948 + 0.377651i \(0.123268\pi\)
\(548\) 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 \(0.0883116\pi\)
−0.961760 + 0.273894i \(0.911688\pi\)
\(558\) 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 −0.865616 0.500708i \(-0.833073\pi\)
−0.405989 + 0.913878i \(0.633073\pi\)
\(564\) 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 0.0199619 0.999801i \(-0.493646\pi\)
0.957036 + 0.289971i \(0.0936455\pi\)
\(570\) 0 0
\(571\) 14.6999 + 10.6801i 0.615173 + 0.446950i 0.851232 0.524789i \(-0.175856\pi\)
−0.236059 + 0.971739i \(0.575856\pi\)
\(572\) 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 0.970808 0.239859i \(-0.0771014\pi\)
0.644414 + 0.764677i \(0.277101\pi\)
\(578\) 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 −0.122725 0.992441i \(-0.539163\pi\)
0.484056 + 0.875037i \(0.339163\pi\)
\(588\) 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 \(0.0818474\pi\)
−0.967124 + 0.254307i \(0.918153\pi\)
\(594\) 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 \(-0.940432\pi\)
0.982541 0.186048i \(-0.0595680\pi\)
\(608\) 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 −0.566237 0.824242i \(-0.691601\pi\)
0.0263819 + 0.999652i \(0.491601\pi\)
\(614\) 0 0
\(615\) 5.24440 5.87756i 0.211475 0.237006i
\(616\) 0 0
\(617\) −21.2980 29.3141i −0.857424 1.18014i −0.982178 0.187955i \(-0.939814\pi\)
0.124754 0.992188i \(-0.460186\pi\)
\(618\) 0 0
\(619\) 20.7716 15.0915i 0.834882 0.606577i −0.0860542 0.996290i \(-0.527426\pi\)
0.920936 + 0.389713i \(0.127426\pi\)
\(620\) 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 −0.114719 0.993398i \(-0.536597\pi\)
0.909327 + 0.416081i \(0.136597\pi\)
\(632\) 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 −0.949728 0.313077i \(-0.898640\pi\)
0.584324 0.811520i \(-0.301360\pi\)
\(642\) 0 0
\(643\) 10.1343i 0.399658i −0.979831 0.199829i \(-0.935961\pi\)
0.979831 0.199829i \(-0.0640387\pi\)
\(644\) 0 0
\(645\) −1.48015 + 0.863484i −0.0582808 + 0.0339996i
\(646\) 0 0
\(647\) 26.6027 36.6155i 1.04586 1.43950i 0.153518 0.988146i \(-0.450940\pi\)
0.892343 0.451358i \(-0.149060\pi\)
\(648\) 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 −0.238609 0.971116i \(-0.576691\pi\)
0.997320 0.0731608i \(-0.0233086\pi\)
\(654\) 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 0.934503 0.355954i \(-0.115844\pi\)
−0.965254 + 0.261314i \(0.915844\pi\)
\(660\) 0 0
\(661\) −14.0332 + 43.1898i −0.545829 + 1.67989i 0.173182 + 0.984890i \(0.444595\pi\)
−0.719011 + 0.694999i \(0.755405\pi\)
\(662\) 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 0.0936282 0.995607i \(-0.470153\pi\)
−0.509456 + 0.860496i \(0.670153\pi\)
\(674\) 0 0
\(675\) −2.07478 4.54921i −0.0798582 0.175099i
\(676\) 0 0
\(677\) −14.7113 4.78000i −0.565402 0.183710i 0.0123484 0.999924i \(-0.496069\pi\)
−0.577750 + 0.816213i \(0.696069\pi\)
\(678\) 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 0.878546 0.477657i \(-0.158514\pi\)
−0.725765 + 0.687943i \(0.758514\pi\)
\(684\) 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 0.813041 + 0.582206i \(0.197810\pi\)
−0.315552 + 0.948908i \(0.602190\pi\)
\(692\) 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 0.962802 0.270209i \(-0.0870927\pi\)
−0.937748 + 0.347317i \(0.887093\pi\)
\(710\) 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 −0.563517 0.826104i \(-0.690552\pi\)
0.611535 + 0.791217i \(0.290552\pi\)
\(720\) 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 0.285292 0.958441i \(-0.407909\pi\)
−0.332551 + 0.943085i \(0.607909\pi\)
\(728\) 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 −0.950627 0.310335i \(-0.899559\pi\)
−0.00138578 0.999999i \(-0.500441\pi\)
\(734\) 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 0.790747 + 0.612143i \(0.209692\pi\)
−0.999536 + 0.0304443i \(0.990308\pi\)
\(740\) 0 0
\(741\) 3.15092 + 9.69753i 0.115752 + 0.356248i
\(742\) 0 0
\(743\) 21.5051i 0.788947i −0.918907 0.394474i \(-0.870927\pi\)
0.918907 0.394474i \(-0.129073\pi\)
\(744\) 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 \(-0.968750\pi\)
0.995185 0.0980171i \(-0.0312500\pi\)
\(758\) 0 0
\(759\) 5.89042 + 18.1289i 0.213809 + 0.658036i
\(760\) 0 0
\(761\) −6.22670 + 19.1638i −0.225718 + 0.694688i 0.772500 + 0.635014i \(0.219006\pi\)
−0.998218 + 0.0596731i \(0.980994\pi\)
\(762\) 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 −0.0370088 0.999315i \(-0.511783\pi\)
0.938969 + 0.344003i \(0.111783\pi\)
\(770\) 0 0
\(771\) −16.3871 11.9059i −0.590167 0.428781i
\(772\) 0 0
\(773\) −30.4255 9.88584i −1.09433 0.355569i −0.294411 0.955679i \(-0.595124\pi\)
−0.799918 + 0.600110i \(0.795124\pi\)
\(774\) 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 0.135764 0.990741i \(-0.456651\pi\)
0.692178 + 0.721726i \(0.256651\pi\)
\(788\) 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 0.131184