Properties

Label 567.2.f.j.379.2
Level $567$
Weight $2$
Character 567.379
Analytic conductor $4.528$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.f (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 379.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 567.379
Dual form 567.2.f.j.190.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 1.50000i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.73205 - 3.00000i) q^{5} +(-0.500000 + 0.866025i) q^{7} +1.73205 q^{8} +O(q^{10})\) \(q+(0.866025 - 1.50000i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.73205 - 3.00000i) q^{5} +(-0.500000 + 0.866025i) q^{7} +1.73205 q^{8} -6.00000 q^{10} +(1.73205 - 3.00000i) q^{11} +(-1.00000 - 1.73205i) q^{13} +(0.866025 + 1.50000i) q^{14} +(2.50000 - 4.33013i) q^{16} -3.46410 q^{17} -4.00000 q^{19} +(-1.73205 + 3.00000i) q^{20} +(-3.00000 - 5.19615i) q^{22} +(-1.73205 - 3.00000i) q^{23} +(-3.50000 + 6.06218i) q^{25} -3.46410 q^{26} +1.00000 q^{28} +(2.00000 + 3.46410i) q^{31} +(-2.59808 - 4.50000i) q^{32} +(-3.00000 + 5.19615i) q^{34} +3.46410 q^{35} +2.00000 q^{37} +(-3.46410 + 6.00000i) q^{38} +(-3.00000 - 5.19615i) q^{40} +(5.19615 + 9.00000i) q^{41} +(2.00000 - 3.46410i) q^{43} -3.46410 q^{44} -6.00000 q^{46} +(3.46410 - 6.00000i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(6.06218 + 10.5000i) q^{50} +(-1.00000 + 1.73205i) q^{52} +6.92820 q^{53} -12.0000 q^{55} +(-0.866025 + 1.50000i) q^{56} +(-3.46410 - 6.00000i) q^{59} +(5.00000 - 8.66025i) q^{61} +6.92820 q^{62} +1.00000 q^{64} +(-3.46410 + 6.00000i) q^{65} +(2.00000 + 3.46410i) q^{67} +(1.73205 + 3.00000i) q^{68} +(3.00000 - 5.19615i) q^{70} +10.3923 q^{71} +14.0000 q^{73} +(1.73205 - 3.00000i) q^{74} +(2.00000 + 3.46410i) q^{76} +(1.73205 + 3.00000i) q^{77} +(-4.00000 + 6.92820i) q^{79} -17.3205 q^{80} +18.0000 q^{82} +(6.00000 + 10.3923i) q^{85} +(-3.46410 - 6.00000i) q^{86} +(3.00000 - 5.19615i) q^{88} +3.46410 q^{89} +2.00000 q^{91} +(-1.73205 + 3.00000i) q^{92} +(-6.00000 - 10.3923i) q^{94} +(6.92820 + 12.0000i) q^{95} +(-7.00000 + 12.1244i) q^{97} -1.73205 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{4} - 2 q^{7} + O(q^{10}) \) \( 4 q - 2 q^{4} - 2 q^{7} - 24 q^{10} - 4 q^{13} + 10 q^{16} - 16 q^{19} - 12 q^{22} - 14 q^{25} + 4 q^{28} + 8 q^{31} - 12 q^{34} + 8 q^{37} - 12 q^{40} + 8 q^{43} - 24 q^{46} - 2 q^{49} - 4 q^{52} - 48 q^{55} + 20 q^{61} + 4 q^{64} + 8 q^{67} + 12 q^{70} + 56 q^{73} + 8 q^{76} - 16 q^{79} + 72 q^{82} + 24 q^{85} + 12 q^{88} + 8 q^{91} - 24 q^{94} - 28 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 1.50000i 0.612372 1.06066i −0.378467 0.925615i \(-0.623549\pi\)
0.990839 0.135045i \(-0.0431180\pi\)
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.73205 3.00000i −0.774597 1.34164i −0.935021 0.354593i \(-0.884620\pi\)
0.160424 0.987048i \(-0.448714\pi\)
\(6\) 0 0
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) 1.73205 0.612372
\(9\) 0 0
\(10\) −6.00000 −1.89737
\(11\) 1.73205 3.00000i 0.522233 0.904534i −0.477432 0.878668i \(-0.658432\pi\)
0.999665 0.0258656i \(-0.00823419\pi\)
\(12\) 0 0
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 0.866025 + 1.50000i 0.231455 + 0.400892i
\(15\) 0 0
\(16\) 2.50000 4.33013i 0.625000 1.08253i
\(17\) −3.46410 −0.840168 −0.420084 0.907485i \(-0.637999\pi\)
−0.420084 + 0.907485i \(0.637999\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) −1.73205 + 3.00000i −0.387298 + 0.670820i
\(21\) 0 0
\(22\) −3.00000 5.19615i −0.639602 1.10782i
\(23\) −1.73205 3.00000i −0.361158 0.625543i 0.626994 0.779024i \(-0.284285\pi\)
−0.988152 + 0.153481i \(0.950952\pi\)
\(24\) 0 0
\(25\) −3.50000 + 6.06218i −0.700000 + 1.21244i
\(26\) −3.46410 −0.679366
\(27\) 0 0
\(28\) 1.00000 0.188982
\(29\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(30\) 0 0
\(31\) 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −2.59808 4.50000i −0.459279 0.795495i
\(33\) 0 0
\(34\) −3.00000 + 5.19615i −0.514496 + 0.891133i
\(35\) 3.46410 0.585540
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −3.46410 + 6.00000i −0.561951 + 0.973329i
\(39\) 0 0
\(40\) −3.00000 5.19615i −0.474342 0.821584i
\(41\) 5.19615 + 9.00000i 0.811503 + 1.40556i 0.911812 + 0.410608i \(0.134683\pi\)
−0.100309 + 0.994956i \(0.531983\pi\)
\(42\) 0 0
\(43\) 2.00000 3.46410i 0.304997 0.528271i −0.672264 0.740312i \(-0.734678\pi\)
0.977261 + 0.212041i \(0.0680112\pi\)
\(44\) −3.46410 −0.522233
\(45\) 0 0
\(46\) −6.00000 −0.884652
\(47\) 3.46410 6.00000i 0.505291 0.875190i −0.494690 0.869069i \(-0.664718\pi\)
0.999981 0.00612051i \(-0.00194823\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 6.06218 + 10.5000i 0.857321 + 1.48492i
\(51\) 0 0
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) 6.92820 0.951662 0.475831 0.879537i \(-0.342147\pi\)
0.475831 + 0.879537i \(0.342147\pi\)
\(54\) 0 0
\(55\) −12.0000 −1.61808
\(56\) −0.866025 + 1.50000i −0.115728 + 0.200446i
\(57\) 0 0
\(58\) 0 0
\(59\) −3.46410 6.00000i −0.450988 0.781133i 0.547460 0.836832i \(-0.315595\pi\)
−0.998448 + 0.0556984i \(0.982261\pi\)
\(60\) 0 0
\(61\) 5.00000 8.66025i 0.640184 1.10883i −0.345207 0.938527i \(-0.612191\pi\)
0.985391 0.170305i \(-0.0544754\pi\)
\(62\) 6.92820 0.879883
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −3.46410 + 6.00000i −0.429669 + 0.744208i
\(66\) 0 0
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) 1.73205 + 3.00000i 0.210042 + 0.363803i
\(69\) 0 0
\(70\) 3.00000 5.19615i 0.358569 0.621059i
\(71\) 10.3923 1.23334 0.616670 0.787222i \(-0.288481\pi\)
0.616670 + 0.787222i \(0.288481\pi\)
\(72\) 0 0
\(73\) 14.0000 1.63858 0.819288 0.573382i \(-0.194369\pi\)
0.819288 + 0.573382i \(0.194369\pi\)
\(74\) 1.73205 3.00000i 0.201347 0.348743i
\(75\) 0 0
\(76\) 2.00000 + 3.46410i 0.229416 + 0.397360i
\(77\) 1.73205 + 3.00000i 0.197386 + 0.341882i
\(78\) 0 0
\(79\) −4.00000 + 6.92820i −0.450035 + 0.779484i −0.998388 0.0567635i \(-0.981922\pi\)
0.548352 + 0.836247i \(0.315255\pi\)
\(80\) −17.3205 −1.93649
\(81\) 0 0
\(82\) 18.0000 1.98777
\(83\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(84\) 0 0
\(85\) 6.00000 + 10.3923i 0.650791 + 1.12720i
\(86\) −3.46410 6.00000i −0.373544 0.646997i
\(87\) 0 0
\(88\) 3.00000 5.19615i 0.319801 0.553912i
\(89\) 3.46410 0.367194 0.183597 0.983002i \(-0.441226\pi\)
0.183597 + 0.983002i \(0.441226\pi\)
\(90\) 0 0
\(91\) 2.00000 0.209657
\(92\) −1.73205 + 3.00000i −0.180579 + 0.312772i
\(93\) 0 0
\(94\) −6.00000 10.3923i −0.618853 1.07188i
\(95\) 6.92820 + 12.0000i 0.710819 + 1.23117i
\(96\) 0 0
\(97\) −7.00000 + 12.1244i −0.710742 + 1.23104i 0.253837 + 0.967247i \(0.418307\pi\)
−0.964579 + 0.263795i \(0.915026\pi\)
\(98\) −1.73205 −0.174964
\(99\) 0 0
\(100\) 7.00000 0.700000
\(101\) 1.73205 3.00000i 0.172345 0.298511i −0.766894 0.641774i \(-0.778199\pi\)
0.939239 + 0.343263i \(0.111532\pi\)
\(102\) 0 0
\(103\) 2.00000 + 3.46410i 0.197066 + 0.341328i 0.947576 0.319531i \(-0.103525\pi\)
−0.750510 + 0.660859i \(0.770192\pi\)
\(104\) −1.73205 3.00000i −0.169842 0.294174i
\(105\) 0 0
\(106\) 6.00000 10.3923i 0.582772 1.00939i
\(107\) −17.3205 −1.67444 −0.837218 0.546869i \(-0.815820\pi\)
−0.837218 + 0.546869i \(0.815820\pi\)
\(108\) 0 0
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) −10.3923 + 18.0000i −0.990867 + 1.71623i
\(111\) 0 0
\(112\) 2.50000 + 4.33013i 0.236228 + 0.409159i
\(113\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(114\) 0 0
\(115\) −6.00000 + 10.3923i −0.559503 + 0.969087i
\(116\) 0 0
\(117\) 0 0
\(118\) −12.0000 −1.10469
\(119\) 1.73205 3.00000i 0.158777 0.275010i
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −8.66025 15.0000i −0.784063 1.35804i
\(123\) 0 0
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) 6.92820 0.619677
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 6.06218 10.5000i 0.535826 0.928078i
\(129\) 0 0
\(130\) 6.00000 + 10.3923i 0.526235 + 0.911465i
\(131\) −6.92820 12.0000i −0.605320 1.04844i −0.992001 0.126231i \(-0.959712\pi\)
0.386681 0.922214i \(-0.373621\pi\)
\(132\) 0 0
\(133\) 2.00000 3.46410i 0.173422 0.300376i
\(134\) 6.92820 0.598506
\(135\) 0 0
\(136\) −6.00000 −0.514496
\(137\) −3.46410 + 6.00000i −0.295958 + 0.512615i −0.975207 0.221293i \(-0.928972\pi\)
0.679249 + 0.733908i \(0.262306\pi\)
\(138\) 0 0
\(139\) 8.00000 + 13.8564i 0.678551 + 1.17529i 0.975417 + 0.220366i \(0.0707252\pi\)
−0.296866 + 0.954919i \(0.595942\pi\)
\(140\) −1.73205 3.00000i −0.146385 0.253546i
\(141\) 0 0
\(142\) 9.00000 15.5885i 0.755263 1.30815i
\(143\) −6.92820 −0.579365
\(144\) 0 0
\(145\) 0 0
\(146\) 12.1244 21.0000i 1.00342 1.73797i
\(147\) 0 0
\(148\) −1.00000 1.73205i −0.0821995 0.142374i
\(149\) 3.46410 + 6.00000i 0.283790 + 0.491539i 0.972315 0.233674i \(-0.0750747\pi\)
−0.688525 + 0.725213i \(0.741741\pi\)
\(150\) 0 0
\(151\) −4.00000 + 6.92820i −0.325515 + 0.563809i −0.981617 0.190864i \(-0.938871\pi\)
0.656101 + 0.754673i \(0.272204\pi\)
\(152\) −6.92820 −0.561951
\(153\) 0 0
\(154\) 6.00000 0.483494
\(155\) 6.92820 12.0000i 0.556487 0.963863i
\(156\) 0 0
\(157\) 5.00000 + 8.66025i 0.399043 + 0.691164i 0.993608 0.112884i \(-0.0360089\pi\)
−0.594565 + 0.804048i \(0.702676\pi\)
\(158\) 6.92820 + 12.0000i 0.551178 + 0.954669i
\(159\) 0 0
\(160\) −9.00000 + 15.5885i −0.711512 + 1.23238i
\(161\) 3.46410 0.273009
\(162\) 0 0
\(163\) 20.0000 1.56652 0.783260 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) 5.19615 9.00000i 0.405751 0.702782i
\(165\) 0 0
\(166\) 0 0
\(167\) −10.3923 18.0000i −0.804181 1.39288i −0.916843 0.399248i \(-0.869271\pi\)
0.112662 0.993633i \(-0.464062\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 20.7846 1.59411
\(171\) 0 0
\(172\) −4.00000 −0.304997
\(173\) 8.66025 15.0000i 0.658427 1.14043i −0.322596 0.946537i \(-0.604555\pi\)
0.981023 0.193892i \(-0.0621112\pi\)
\(174\) 0 0
\(175\) −3.50000 6.06218i −0.264575 0.458258i
\(176\) −8.66025 15.0000i −0.652791 1.13067i
\(177\) 0 0
\(178\) 3.00000 5.19615i 0.224860 0.389468i
\(179\) 17.3205 1.29460 0.647298 0.762237i \(-0.275899\pi\)
0.647298 + 0.762237i \(0.275899\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 1.73205 3.00000i 0.128388 0.222375i
\(183\) 0 0
\(184\) −3.00000 5.19615i −0.221163 0.383065i
\(185\) −3.46410 6.00000i −0.254686 0.441129i
\(186\) 0 0
\(187\) −6.00000 + 10.3923i −0.438763 + 0.759961i
\(188\) −6.92820 −0.505291
\(189\) 0 0
\(190\) 24.0000 1.74114
\(191\) −12.1244 + 21.0000i −0.877288 + 1.51951i −0.0229818 + 0.999736i \(0.507316\pi\)
−0.854306 + 0.519771i \(0.826017\pi\)
\(192\) 0 0
\(193\) −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i \(-0.998575\pi\)
0.496119 0.868255i \(-0.334758\pi\)
\(194\) 12.1244 + 21.0000i 0.870478 + 1.50771i
\(195\) 0 0
\(196\) −0.500000 + 0.866025i −0.0357143 + 0.0618590i
\(197\) −20.7846 −1.48084 −0.740421 0.672143i \(-0.765374\pi\)
−0.740421 + 0.672143i \(0.765374\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) −6.06218 + 10.5000i −0.428661 + 0.742462i
\(201\) 0 0
\(202\) −3.00000 5.19615i −0.211079 0.365600i
\(203\) 0 0
\(204\) 0 0
\(205\) 18.0000 31.1769i 1.25717 2.17749i
\(206\) 6.92820 0.482711
\(207\) 0 0
\(208\) −10.0000 −0.693375
\(209\) −6.92820 + 12.0000i −0.479234 + 0.830057i
\(210\) 0 0
\(211\) −10.0000 17.3205i −0.688428 1.19239i −0.972346 0.233544i \(-0.924968\pi\)
0.283918 0.958849i \(-0.408366\pi\)
\(212\) −3.46410 6.00000i −0.237915 0.412082i
\(213\) 0 0
\(214\) −15.0000 + 25.9808i −1.02538 + 1.77601i
\(215\) −13.8564 −0.944999
\(216\) 0 0
\(217\) −4.00000 −0.271538
\(218\) 1.73205 3.00000i 0.117309 0.203186i
\(219\) 0 0
\(220\) 6.00000 + 10.3923i 0.404520 + 0.700649i
\(221\) 3.46410 + 6.00000i 0.233021 + 0.403604i
\(222\) 0 0
\(223\) −4.00000 + 6.92820i −0.267860 + 0.463947i −0.968309 0.249756i \(-0.919650\pi\)
0.700449 + 0.713702i \(0.252983\pi\)
\(224\) 5.19615 0.347183
\(225\) 0 0
\(226\) 0 0
\(227\) −3.46410 + 6.00000i −0.229920 + 0.398234i −0.957784 0.287488i \(-0.907180\pi\)
0.727864 + 0.685722i \(0.240513\pi\)
\(228\) 0 0
\(229\) 11.0000 + 19.0526i 0.726900 + 1.25903i 0.958187 + 0.286143i \(0.0923732\pi\)
−0.231287 + 0.972886i \(0.574293\pi\)
\(230\) 10.3923 + 18.0000i 0.685248 + 1.18688i
\(231\) 0 0
\(232\) 0 0
\(233\) −6.92820 −0.453882 −0.226941 0.973909i \(-0.572872\pi\)
−0.226941 + 0.973909i \(0.572872\pi\)
\(234\) 0 0
\(235\) −24.0000 −1.56559
\(236\) −3.46410 + 6.00000i −0.225494 + 0.390567i
\(237\) 0 0
\(238\) −3.00000 5.19615i −0.194461 0.336817i
\(239\) 5.19615 + 9.00000i 0.336111 + 0.582162i 0.983698 0.179830i \(-0.0575549\pi\)
−0.647586 + 0.761992i \(0.724222\pi\)
\(240\) 0 0
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) −1.73205 −0.111340
\(243\) 0 0
\(244\) −10.0000 −0.640184
\(245\) −1.73205 + 3.00000i −0.110657 + 0.191663i
\(246\) 0 0
\(247\) 4.00000 + 6.92820i 0.254514 + 0.440831i
\(248\) 3.46410 + 6.00000i 0.219971 + 0.381000i
\(249\) 0 0
\(250\) 6.00000 10.3923i 0.379473 0.657267i
\(251\) −20.7846 −1.31191 −0.655956 0.754799i \(-0.727735\pi\)
−0.655956 + 0.754799i \(0.727735\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) 6.92820 12.0000i 0.434714 0.752947i
\(255\) 0 0
\(256\) −9.50000 16.4545i −0.593750 1.02841i
\(257\) −1.73205 3.00000i −0.108042 0.187135i 0.806935 0.590641i \(-0.201125\pi\)
−0.914977 + 0.403506i \(0.867792\pi\)
\(258\) 0 0
\(259\) −1.00000 + 1.73205i −0.0621370 + 0.107624i
\(260\) 6.92820 0.429669
\(261\) 0 0
\(262\) −24.0000 −1.48272
\(263\) −8.66025 + 15.0000i −0.534014 + 0.924940i 0.465196 + 0.885208i \(0.345984\pi\)
−0.999210 + 0.0397320i \(0.987350\pi\)
\(264\) 0 0
\(265\) −12.0000 20.7846i −0.737154 1.27679i
\(266\) −3.46410 6.00000i −0.212398 0.367884i
\(267\) 0 0
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) 17.3205 1.05605 0.528025 0.849229i \(-0.322933\pi\)
0.528025 + 0.849229i \(0.322933\pi\)
\(270\) 0 0
\(271\) 20.0000 1.21491 0.607457 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) −8.66025 + 15.0000i −0.525105 + 0.909509i
\(273\) 0 0
\(274\) 6.00000 + 10.3923i 0.362473 + 0.627822i
\(275\) 12.1244 + 21.0000i 0.731126 + 1.26635i
\(276\) 0 0
\(277\) 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i \(-0.736206\pi\)
0.976231 + 0.216731i \(0.0695395\pi\)
\(278\) 27.7128 1.66210
\(279\) 0 0
\(280\) 6.00000 0.358569
\(281\) −10.3923 + 18.0000i −0.619953 + 1.07379i 0.369541 + 0.929214i \(0.379515\pi\)
−0.989494 + 0.144575i \(0.953818\pi\)
\(282\) 0 0
\(283\) 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) −5.19615 9.00000i −0.308335 0.534052i
\(285\) 0 0
\(286\) −6.00000 + 10.3923i −0.354787 + 0.614510i
\(287\) −10.3923 −0.613438
\(288\) 0 0
\(289\) −5.00000 −0.294118
\(290\) 0 0
\(291\) 0 0
\(292\) −7.00000 12.1244i −0.409644 0.709524i
\(293\) −5.19615 9.00000i −0.303562 0.525786i 0.673378 0.739299i \(-0.264843\pi\)
−0.976940 + 0.213513i \(0.931509\pi\)
\(294\) 0 0
\(295\) −12.0000 + 20.7846i −0.698667 + 1.21013i
\(296\) 3.46410 0.201347
\(297\) 0 0
\(298\) 12.0000 0.695141
\(299\) −3.46410 + 6.00000i −0.200334 + 0.346989i
\(300\) 0 0
\(301\) 2.00000 + 3.46410i 0.115278 + 0.199667i
\(302\) 6.92820 + 12.0000i 0.398673 + 0.690522i
\(303\) 0 0
\(304\) −10.0000 + 17.3205i −0.573539 + 0.993399i
\(305\) −34.6410 −1.98354
\(306\) 0 0
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 1.73205 3.00000i 0.0986928 0.170941i
\(309\) 0 0
\(310\) −12.0000 20.7846i −0.681554 1.18049i
\(311\) 17.3205 + 30.0000i 0.982156 + 1.70114i 0.653950 + 0.756538i \(0.273111\pi\)
0.328206 + 0.944606i \(0.393556\pi\)
\(312\) 0 0
\(313\) −1.00000 + 1.73205i −0.0565233 + 0.0979013i −0.892903 0.450250i \(-0.851335\pi\)
0.836379 + 0.548151i \(0.184668\pi\)
\(314\) 17.3205 0.977453
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) 3.46410 6.00000i 0.194563 0.336994i −0.752194 0.658942i \(-0.771004\pi\)
0.946757 + 0.321948i \(0.104338\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.73205 3.00000i −0.0968246 0.167705i
\(321\) 0 0
\(322\) 3.00000 5.19615i 0.167183 0.289570i
\(323\) 13.8564 0.770991
\(324\) 0 0
\(325\) 14.0000 0.776580
\(326\) 17.3205 30.0000i 0.959294 1.66155i
\(327\) 0 0
\(328\) 9.00000 + 15.5885i 0.496942 + 0.860729i
\(329\) 3.46410 + 6.00000i 0.190982 + 0.330791i
\(330\) 0 0
\(331\) −10.0000 + 17.3205i −0.549650 + 0.952021i 0.448649 + 0.893708i \(0.351905\pi\)
−0.998298 + 0.0583130i \(0.981428\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −36.0000 −1.96983
\(335\) 6.92820 12.0000i 0.378528 0.655630i
\(336\) 0 0
\(337\) −7.00000 12.1244i −0.381314 0.660456i 0.609936 0.792451i \(-0.291195\pi\)
−0.991250 + 0.131995i \(0.957862\pi\)
\(338\) −7.79423 13.5000i −0.423950 0.734303i
\(339\) 0 0
\(340\) 6.00000 10.3923i 0.325396 0.563602i
\(341\) 13.8564 0.750366
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 3.46410 6.00000i 0.186772 0.323498i
\(345\) 0 0
\(346\) −15.0000 25.9808i −0.806405 1.39673i
\(347\) −8.66025 15.0000i −0.464907 0.805242i 0.534291 0.845301i \(-0.320579\pi\)
−0.999197 + 0.0400587i \(0.987246\pi\)
\(348\) 0 0
\(349\) −7.00000 + 12.1244i −0.374701 + 0.649002i −0.990282 0.139072i \(-0.955588\pi\)
0.615581 + 0.788074i \(0.288921\pi\)
\(350\) −12.1244 −0.648074
\(351\) 0 0
\(352\) −18.0000 −0.959403
\(353\) 1.73205 3.00000i 0.0921878 0.159674i −0.816244 0.577708i \(-0.803947\pi\)
0.908431 + 0.418034i \(0.137281\pi\)
\(354\) 0 0
\(355\) −18.0000 31.1769i −0.955341 1.65470i
\(356\) −1.73205 3.00000i −0.0917985 0.159000i
\(357\) 0 0
\(358\) 15.0000 25.9808i 0.792775 1.37313i
\(359\) 24.2487 1.27980 0.639899 0.768459i \(-0.278976\pi\)
0.639899 + 0.768459i \(0.278976\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 1.73205 3.00000i 0.0910346 0.157676i
\(363\) 0 0
\(364\) −1.00000 1.73205i −0.0524142 0.0907841i
\(365\) −24.2487 42.0000i −1.26924 2.19838i
\(366\) 0 0
\(367\) 8.00000 13.8564i 0.417597 0.723299i −0.578101 0.815966i \(-0.696206\pi\)
0.995697 + 0.0926670i \(0.0295392\pi\)
\(368\) −17.3205 −0.902894
\(369\) 0 0
\(370\) −12.0000 −0.623850
\(371\) −3.46410 + 6.00000i −0.179847 + 0.311504i
\(372\) 0 0
\(373\) 5.00000 + 8.66025i 0.258890 + 0.448411i 0.965945 0.258748i \(-0.0833099\pi\)
−0.707055 + 0.707159i \(0.749977\pi\)
\(374\) 10.3923 + 18.0000i 0.537373 + 0.930758i
\(375\) 0 0
\(376\) 6.00000 10.3923i 0.309426 0.535942i
\(377\) 0 0
\(378\) 0 0
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) 6.92820 12.0000i 0.355409 0.615587i
\(381\) 0 0
\(382\) 21.0000 + 36.3731i 1.07445 + 1.86101i
\(383\) −6.92820 12.0000i −0.354015 0.613171i 0.632934 0.774206i \(-0.281850\pi\)
−0.986949 + 0.161034i \(0.948517\pi\)
\(384\) 0 0
\(385\) 6.00000 10.3923i 0.305788 0.529641i
\(386\) −24.2487 −1.23423
\(387\) 0 0
\(388\) 14.0000 0.710742
\(389\) 6.92820 12.0000i 0.351274 0.608424i −0.635199 0.772348i \(-0.719082\pi\)
0.986473 + 0.163924i \(0.0524153\pi\)
\(390\) 0 0
\(391\) 6.00000 + 10.3923i 0.303433 + 0.525561i
\(392\) −0.866025 1.50000i −0.0437409 0.0757614i
\(393\) 0 0
\(394\) −18.0000 + 31.1769i −0.906827 + 1.57067i
\(395\) 27.7128 1.39438
\(396\) 0 0
\(397\) 38.0000 1.90717 0.953583 0.301131i \(-0.0973643\pi\)
0.953583 + 0.301131i \(0.0973643\pi\)
\(398\) −13.8564 + 24.0000i −0.694559 + 1.20301i
\(399\) 0 0
\(400\) 17.5000 + 30.3109i 0.875000 + 1.51554i
\(401\) 3.46410 + 6.00000i 0.172989 + 0.299626i 0.939463 0.342649i \(-0.111324\pi\)
−0.766475 + 0.642275i \(0.777991\pi\)
\(402\) 0 0
\(403\) 4.00000 6.92820i 0.199254 0.345118i
\(404\) −3.46410 −0.172345
\(405\) 0 0
\(406\) 0 0
\(407\) 3.46410 6.00000i 0.171709 0.297409i
\(408\) 0 0
\(409\) −7.00000 12.1244i −0.346128 0.599511i 0.639430 0.768849i \(-0.279170\pi\)
−0.985558 + 0.169338i \(0.945837\pi\)
\(410\) −31.1769 54.0000i −1.53972 2.66687i
\(411\) 0 0
\(412\) 2.00000 3.46410i 0.0985329 0.170664i
\(413\) 6.92820 0.340915
\(414\) 0 0
\(415\) 0 0
\(416\) −5.19615 + 9.00000i −0.254762 + 0.441261i
\(417\) 0 0
\(418\) 12.0000 + 20.7846i 0.586939 + 1.01661i
\(419\) 10.3923 + 18.0000i 0.507697 + 0.879358i 0.999960 + 0.00891102i \(0.00283650\pi\)
−0.492263 + 0.870447i \(0.663830\pi\)
\(420\) 0 0
\(421\) 5.00000 8.66025i 0.243685 0.422075i −0.718076 0.695965i \(-0.754977\pi\)
0.961761 + 0.273890i \(0.0883103\pi\)
\(422\) −34.6410 −1.68630
\(423\) 0 0
\(424\) 12.0000 0.582772
\(425\) 12.1244 21.0000i 0.588118 1.01865i
\(426\) 0 0
\(427\) 5.00000 + 8.66025i 0.241967 + 0.419099i
\(428\) 8.66025 + 15.0000i 0.418609 + 0.725052i
\(429\) 0 0
\(430\) −12.0000 + 20.7846i −0.578691 + 1.00232i
\(431\) −3.46410 −0.166860 −0.0834300 0.996514i \(-0.526587\pi\)
−0.0834300 + 0.996514i \(0.526587\pi\)
\(432\) 0 0
\(433\) 26.0000 1.24948 0.624740 0.780833i \(-0.285205\pi\)
0.624740 + 0.780833i \(0.285205\pi\)
\(434\) −3.46410 + 6.00000i −0.166282 + 0.288009i
\(435\) 0 0
\(436\) −1.00000 1.73205i −0.0478913 0.0829502i
\(437\) 6.92820 + 12.0000i 0.331421 + 0.574038i
\(438\) 0 0
\(439\) 8.00000 13.8564i 0.381819 0.661330i −0.609503 0.792784i \(-0.708631\pi\)
0.991322 + 0.131453i \(0.0419644\pi\)
\(440\) −20.7846 −0.990867
\(441\) 0 0
\(442\) 12.0000 0.570782
\(443\) −1.73205 + 3.00000i −0.0822922 + 0.142534i −0.904234 0.427037i \(-0.859557\pi\)
0.821942 + 0.569571i \(0.192891\pi\)
\(444\) 0 0
\(445\) −6.00000 10.3923i −0.284427 0.492642i
\(446\) 6.92820 + 12.0000i 0.328060 + 0.568216i
\(447\) 0 0
\(448\) −0.500000 + 0.866025i −0.0236228 + 0.0409159i
\(449\) −41.5692 −1.96177 −0.980886 0.194581i \(-0.937665\pi\)
−0.980886 + 0.194581i \(0.937665\pi\)
\(450\) 0 0
\(451\) 36.0000 1.69517
\(452\) 0 0
\(453\) 0 0
\(454\) 6.00000 + 10.3923i 0.281594 + 0.487735i
\(455\) −3.46410 6.00000i −0.162400 0.281284i
\(456\) 0 0
\(457\) 5.00000 8.66025i 0.233890 0.405110i −0.725059 0.688686i \(-0.758188\pi\)
0.958950 + 0.283577i \(0.0915211\pi\)
\(458\) 38.1051 1.78054
\(459\) 0 0
\(460\) 12.0000 0.559503
\(461\) 15.5885 27.0000i 0.726027 1.25752i −0.232523 0.972591i \(-0.574698\pi\)
0.958550 0.284925i \(-0.0919685\pi\)
\(462\) 0 0
\(463\) −16.0000 27.7128i −0.743583 1.28792i −0.950854 0.309640i \(-0.899791\pi\)
0.207271 0.978284i \(-0.433542\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −6.00000 + 10.3923i −0.277945 + 0.481414i
\(467\) −6.92820 −0.320599 −0.160300 0.987068i \(-0.551246\pi\)
−0.160300 + 0.987068i \(0.551246\pi\)
\(468\) 0 0
\(469\) −4.00000 −0.184703
\(470\) −20.7846 + 36.0000i −0.958723 + 1.66056i
\(471\) 0 0
\(472\) −6.00000 10.3923i −0.276172 0.478345i
\(473\) −6.92820 12.0000i −0.318559 0.551761i
\(474\) 0 0
\(475\) 14.0000 24.2487i 0.642364 1.11261i
\(476\) −3.46410 −0.158777
\(477\) 0 0
\(478\) 18.0000 0.823301
\(479\) −3.46410 + 6.00000i −0.158279 + 0.274147i −0.934248 0.356624i \(-0.883928\pi\)
0.775969 + 0.630771i \(0.217261\pi\)
\(480\) 0 0
\(481\) −2.00000 3.46410i −0.0911922 0.157949i
\(482\) −8.66025 15.0000i −0.394464 0.683231i
\(483\) 0 0
\(484\) −0.500000 + 0.866025i −0.0227273 + 0.0393648i
\(485\) 48.4974 2.20215
\(486\) 0 0
\(487\) −40.0000 −1.81257 −0.906287 0.422664i \(-0.861095\pi\)
−0.906287 + 0.422664i \(0.861095\pi\)
\(488\) 8.66025 15.0000i 0.392031 0.679018i
\(489\) 0 0
\(490\) 3.00000 + 5.19615i 0.135526 + 0.234738i
\(491\) 5.19615 + 9.00000i 0.234499 + 0.406164i 0.959127 0.282976i \(-0.0913217\pi\)
−0.724628 + 0.689140i \(0.757988\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 13.8564 0.623429
\(495\) 0 0
\(496\) 20.0000 0.898027
\(497\) −5.19615 + 9.00000i −0.233079 + 0.403705i
\(498\) 0 0
\(499\) 2.00000 + 3.46410i 0.0895323 + 0.155074i 0.907314 0.420455i \(-0.138129\pi\)
−0.817781 + 0.575529i \(0.804796\pi\)
\(500\) −3.46410 6.00000i −0.154919 0.268328i
\(501\) 0 0
\(502\) −18.0000 + 31.1769i −0.803379 + 1.39149i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) −12.0000 −0.533993
\(506\) −10.3923 + 18.0000i −0.461994 + 0.800198i
\(507\) 0 0
\(508\) −4.00000 6.92820i −0.177471 0.307389i
\(509\) −1.73205 3.00000i −0.0767718 0.132973i 0.825084 0.565011i \(-0.191128\pi\)
−0.901855 + 0.432038i \(0.857795\pi\)
\(510\) 0 0
\(511\) −7.00000 + 12.1244i −0.309662 + 0.536350i
\(512\) −8.66025 −0.382733
\(513\) 0 0
\(514\) −6.00000 −0.264649
\(515\) 6.92820 12.0000i 0.305293 0.528783i
\(516\) 0 0
\(517\) −12.0000 20.7846i −0.527759 0.914106i
\(518\) 1.73205 + 3.00000i 0.0761019 + 0.131812i
\(519\) 0 0
\(520\) −6.00000 + 10.3923i −0.263117 + 0.455733i
\(521\) −3.46410 −0.151765 −0.0758825 0.997117i \(-0.524177\pi\)
−0.0758825 + 0.997117i \(0.524177\pi\)
\(522\) 0 0
\(523\) −16.0000 −0.699631 −0.349816 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) −6.92820 + 12.0000i −0.302660 + 0.524222i
\(525\) 0 0
\(526\) 15.0000 + 25.9808i 0.654031 + 1.13282i
\(527\) −6.92820 12.0000i −0.301797 0.522728i
\(528\) 0 0
\(529\) 5.50000 9.52628i 0.239130 0.414186i
\(530\) −41.5692 −1.80565
\(531\) 0 0
\(532\) −4.00000 −0.173422
\(533\) 10.3923 18.0000i 0.450141 0.779667i
\(534\) 0 0
\(535\) 30.0000 + 51.9615i 1.29701 + 2.24649i
\(536\) 3.46410 + 6.00000i 0.149626 + 0.259161i
\(537\) 0 0
\(538\) 15.0000 25.9808i 0.646696 1.12011i
\(539\) −3.46410 −0.149209
\(540\) 0 0
\(541\) 14.0000 0.601907 0.300954 0.953639i \(-0.402695\pi\)
0.300954 + 0.953639i \(0.402695\pi\)
\(542\) 17.3205 30.0000i 0.743980 1.28861i
\(543\) 0 0
\(544\) 9.00000 + 15.5885i 0.385872 + 0.668350i
\(545\) −3.46410 6.00000i −0.148386 0.257012i
\(546\) 0 0
\(547\) 2.00000 3.46410i 0.0855138 0.148114i −0.820096 0.572226i \(-0.806080\pi\)
0.905610 + 0.424111i \(0.139413\pi\)
\(548\) 6.92820 0.295958
\(549\) 0 0
\(550\) 42.0000 1.79089
\(551\) 0 0
\(552\) 0 0
\(553\) −4.00000 6.92820i −0.170097 0.294617i
\(554\) −8.66025 15.0000i −0.367939 0.637289i
\(555\) 0 0
\(556\) 8.00000 13.8564i 0.339276 0.587643i
\(557\) 6.92820 0.293557 0.146779 0.989169i \(-0.453109\pi\)
0.146779 + 0.989169i \(0.453109\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 8.66025 15.0000i 0.365963 0.633866i
\(561\) 0 0
\(562\) 18.0000 + 31.1769i 0.759284 + 1.31512i
\(563\) 17.3205 + 30.0000i 0.729972 + 1.26435i 0.956894 + 0.290436i \(0.0938004\pi\)
−0.226922 + 0.973913i \(0.572866\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 6.92820 0.291214
\(567\) 0 0
\(568\) 18.0000 0.755263
\(569\) 3.46410 6.00000i 0.145223 0.251533i −0.784233 0.620466i \(-0.786943\pi\)
0.929456 + 0.368933i \(0.120277\pi\)
\(570\) 0 0
\(571\) 14.0000 + 24.2487i 0.585882 + 1.01478i 0.994765 + 0.102190i \(0.0325850\pi\)
−0.408883 + 0.912587i \(0.634082\pi\)
\(572\) 3.46410 + 6.00000i 0.144841 + 0.250873i
\(573\) 0 0
\(574\) −9.00000 + 15.5885i −0.375653 + 0.650650i
\(575\) 24.2487 1.01124
\(576\) 0 0
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) −4.33013 + 7.50000i −0.180110 + 0.311959i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 12.0000 20.7846i 0.496989 0.860811i
\(584\) 24.2487 1.00342
\(585\) 0 0
\(586\) −18.0000 −0.743573
\(587\) −10.3923 + 18.0000i −0.428936 + 0.742940i −0.996779 0.0801976i \(-0.974445\pi\)
0.567843 + 0.823137i \(0.307778\pi\)
\(588\) 0 0
\(589\) −8.00000 13.8564i −0.329634 0.570943i
\(590\) 20.7846 + 36.0000i 0.855689 + 1.48210i
\(591\) 0 0
\(592\) 5.00000 8.66025i 0.205499 0.355934i
\(593\) 24.2487 0.995775 0.497888 0.867242i \(-0.334109\pi\)
0.497888 + 0.867242i \(0.334109\pi\)
\(594\) 0 0
\(595\) −12.0000 −0.491952
\(596\) 3.46410 6.00000i 0.141895 0.245770i
\(597\) 0 0
\(598\) 6.00000 + 10.3923i 0.245358 + 0.424973i
\(599\) 22.5167 + 39.0000i 0.920006 + 1.59350i 0.799402 + 0.600796i \(0.205150\pi\)
0.120603 + 0.992701i \(0.461517\pi\)
\(600\) 0 0
\(601\) 11.0000 19.0526i 0.448699 0.777170i −0.549602 0.835426i \(-0.685221\pi\)
0.998302 + 0.0582563i \(0.0185541\pi\)
\(602\) 6.92820 0.282372
\(603\) 0 0
\(604\) 8.00000 0.325515
\(605\) −1.73205 + 3.00000i −0.0704179 + 0.121967i
\(606\) 0 0
\(607\) −4.00000 6.92820i −0.162355 0.281207i 0.773358 0.633970i \(-0.218576\pi\)
−0.935713 + 0.352763i \(0.885242\pi\)
\(608\) 10.3923 + 18.0000i 0.421464 + 0.729996i
\(609\) 0 0
\(610\) −30.0000 + 51.9615i −1.21466 + 2.10386i
\(611\) −13.8564 −0.560570
\(612\) 0 0
\(613\) 38.0000 1.53481 0.767403 0.641165i \(-0.221549\pi\)
0.767403 + 0.641165i \(0.221549\pi\)
\(614\) −24.2487 + 42.0000i −0.978598 + 1.69498i
\(615\) 0 0
\(616\) 3.00000 + 5.19615i 0.120873 + 0.209359i
\(617\) −10.3923 18.0000i −0.418378 0.724653i 0.577398 0.816463i \(-0.304068\pi\)
−0.995777 + 0.0918100i \(0.970735\pi\)
\(618\) 0 0
\(619\) −4.00000 + 6.92820i −0.160774 + 0.278468i −0.935146 0.354262i \(-0.884732\pi\)
0.774373 + 0.632730i \(0.218066\pi\)
\(620\) −13.8564 −0.556487
\(621\) 0 0
\(622\) 60.0000 2.40578
\(623\) −1.73205 + 3.00000i −0.0693932 + 0.120192i
\(624\) 0 0
\(625\) 5.50000 + 9.52628i 0.220000 + 0.381051i
\(626\) 1.73205 + 3.00000i 0.0692267 + 0.119904i
\(627\) 0 0
\(628\) 5.00000 8.66025i 0.199522 0.345582i
\(629\) −6.92820 −0.276246
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) −6.92820 + 12.0000i −0.275589 + 0.477334i
\(633\) 0 0
\(634\) −6.00000 10.3923i −0.238290 0.412731i
\(635\) −13.8564 24.0000i −0.549875 0.952411i
\(636\) 0 0
\(637\) −1.00000 + 1.73205i −0.0396214 + 0.0686264i
\(638\) 0 0
\(639\) 0 0
\(640\) −42.0000 −1.66020
\(641\) −24.2487 + 42.0000i −0.957767 + 1.65890i −0.229860 + 0.973224i \(0.573827\pi\)
−0.727906 + 0.685677i \(0.759506\pi\)
\(642\) 0 0
\(643\) −10.0000 17.3205i −0.394362 0.683054i 0.598658 0.801005i \(-0.295701\pi\)
−0.993019 + 0.117951i \(0.962368\pi\)
\(644\) −1.73205 3.00000i −0.0682524 0.118217i
\(645\) 0 0
\(646\) 12.0000 20.7846i 0.472134 0.817760i
\(647\) 6.92820 0.272376 0.136188 0.990683i \(-0.456515\pi\)
0.136188 + 0.990683i \(0.456515\pi\)
\(648\) 0 0
\(649\) −24.0000 −0.942082
\(650\) 12.1244 21.0000i 0.475556 0.823688i
\(651\) 0 0
\(652\) −10.0000 17.3205i −0.391630 0.678323i
\(653\) 13.8564 + 24.0000i 0.542243 + 0.939193i 0.998775 + 0.0494855i \(0.0157581\pi\)
−0.456532 + 0.889707i \(0.650909\pi\)
\(654\) 0 0
\(655\) −24.0000 + 41.5692i −0.937758 + 1.62424i
\(656\) 51.9615 2.02876
\(657\) 0 0
\(658\) 12.0000 0.467809
\(659\) −5.19615 + 9.00000i −0.202413 + 0.350590i −0.949306 0.314355i \(-0.898212\pi\)
0.746892 + 0.664945i \(0.231545\pi\)
\(660\) 0 0
\(661\) 5.00000 + 8.66025i 0.194477 + 0.336845i 0.946729 0.322031i \(-0.104366\pi\)
−0.752252 + 0.658876i \(0.771032\pi\)
\(662\) 17.3205 + 30.0000i 0.673181 + 1.16598i
\(663\) 0 0
\(664\) 0 0
\(665\) −13.8564 −0.537328
\(666\) 0 0
\(667\) 0 0
\(668\) −10.3923 + 18.0000i −0.402090 + 0.696441i
\(669\) 0 0
\(670\) −12.0000 20.7846i −0.463600 0.802980i
\(671\) −17.3205 30.0000i −0.668651 1.15814i
\(672\) 0 0
\(673\) 5.00000 8.66025i 0.192736 0.333828i −0.753420 0.657539i \(-0.771597\pi\)
0.946156 + 0.323711i \(0.104931\pi\)
\(674\) −24.2487 −0.934025
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) −12.1244 + 21.0000i −0.465977 + 0.807096i −0.999245 0.0388507i \(-0.987630\pi\)
0.533268 + 0.845946i \(0.320964\pi\)
\(678\) 0 0
\(679\) −7.00000 12.1244i −0.268635 0.465290i
\(680\) 10.3923 + 18.0000i 0.398527 + 0.690268i
\(681\) 0 0
\(682\) 12.0000 20.7846i 0.459504 0.795884i
\(683\) −24.2487 −0.927851 −0.463926 0.885874i \(-0.653559\pi\)
−0.463926 + 0.885874i \(0.653559\pi\)
\(684\) 0 0
\(685\) 24.0000 0.916993
\(686\) 0.866025 1.50000i 0.0330650 0.0572703i
\(687\) 0 0
\(688\) −10.0000 17.3205i −0.381246 0.660338i
\(689\) −6.92820 12.0000i −0.263944 0.457164i
\(690\) 0 0
\(691\) −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i \(-0.881959\pi\)
0.779857 + 0.625958i \(0.215292\pi\)
\(692\) −17.3205 −0.658427
\(693\) 0 0
\(694\) −30.0000 −1.13878
\(695\) 27.7128 48.0000i 1.05121 1.82074i
\(696\) 0 0
\(697\) −18.0000 31.1769i −0.681799 1.18091i
\(698\) 12.1244 + 21.0000i 0.458914 + 0.794862i
\(699\) 0 0
\(700\) −3.50000 + 6.06218i −0.132288 + 0.229129i
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) −8.00000 −0.301726
\(704\) 1.73205 3.00000i 0.0652791 0.113067i
\(705\) 0 0
\(706\) −3.00000 5.19615i −0.112906 0.195560i
\(707\) 1.73205 + 3.00000i 0.0651405 + 0.112827i
\(708\) 0 0
\(709\) −13.0000 + 22.5167i −0.488225 + 0.845631i −0.999908 0.0135434i \(-0.995689\pi\)
0.511683 + 0.859174i \(0.329022\pi\)
\(710\) −62.3538 −2.34010
\(711\) 0 0
\(712\) 6.00000 0.224860
\(713\) 6.92820 12.0000i 0.259463 0.449404i
\(714\) 0 0
\(715\) 12.0000 + 20.7846i 0.448775 + 0.777300i
\(716\) −8.66025 15.0000i −0.323649 0.560576i
\(717\) 0 0
\(718\) 21.0000 36.3731i 0.783713 1.35743i
\(719\) −27.7128 −1.03351 −0.516757 0.856132i \(-0.672861\pi\)
−0.516757 + 0.856132i \(0.672861\pi\)
\(720\) 0 0
\(721\) −4.00000 −0.148968
\(722\) −2.59808 + 4.50000i −0.0966904 + 0.167473i
\(723\) 0 0
\(724\) −1.00000 1.73205i −0.0371647 0.0643712i
\(725\) 0 0
\(726\) 0 0
\(727\) 2.00000 3.46410i 0.0741759 0.128476i −0.826552 0.562861i \(-0.809701\pi\)
0.900728 + 0.434384i \(0.143034\pi\)
\(728\) 3.46410 0.128388
\(729\) 0 0
\(730\) −84.0000 −3.10898
\(731\) −6.92820 + 12.0000i −0.256249 + 0.443836i
\(732\) 0 0
\(733\) 11.0000 + 19.0526i 0.406294 + 0.703722i 0.994471 0.105010i \(-0.0334875\pi\)
−0.588177 + 0.808732i \(0.700154\pi\)
\(734\) −13.8564 24.0000i −0.511449 0.885856i
\(735\) 0 0
\(736\) −9.00000 + 15.5885i −0.331744 + 0.574598i
\(737\) 13.8564 0.510407
\(738\) 0 0
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) −3.46410 + 6.00000i −0.127343 + 0.220564i
\(741\) 0 0
\(742\) 6.00000 + 10.3923i 0.220267 + 0.381514i
\(743\) −5.19615 9.00000i −0.190628 0.330178i 0.754830 0.655920i \(-0.227719\pi\)
−0.945459 + 0.325742i \(0.894386\pi\)
\(744\) 0 0
\(745\) 12.0000 20.7846i 0.439646 0.761489i
\(746\) 17.3205 0.634149
\(747\) 0 0
\(748\) 12.0000 0.438763
\(749\) 8.66025 15.0000i 0.316439 0.548088i
\(750\) 0 0
\(751\) −4.00000 6.92820i −0.145962 0.252814i 0.783769 0.621052i \(-0.213294\pi\)
−0.929731 + 0.368238i \(0.879961\pi\)
\(752\) −17.3205 30.0000i −0.631614 1.09399i
\(753\) 0 0
\(754\) 0 0
\(755\) 27.7128 1.00857
\(756\) 0 0
\(757\) 26.0000 0.944986 0.472493 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) −24.2487 + 42.0000i −0.880753 + 1.52551i
\(759\) 0 0
\(760\) 12.0000 + 20.7846i 0.435286 + 0.753937i
\(761\) 19.0526 + 33.0000i 0.690655 + 1.19625i 0.971624 + 0.236532i \(0.0760109\pi\)
−0.280969 + 0.959717i \(0.590656\pi\)
\(762\) 0 0
\(763\) −1.00000 + 1.73205i −0.0362024 + 0.0627044i
\(764\) 24.2487 0.877288
\(765\) 0 0
\(766\) −24.0000 −0.867155
\(767\) −6.92820 + 12.0000i −0.250163 + 0.433295i
\(768\) 0 0
\(769\) 11.0000 + 19.0526i 0.396670 + 0.687053i 0.993313 0.115454i \(-0.0368323\pi\)
−0.596643 + 0.802507i \(0.703499\pi\)
\(770\) −10.3923 18.0000i −0.374513 0.648675i
\(771\) 0 0
\(772\) −7.00000 + 12.1244i −0.251936 + 0.436365i
\(773\) −45.0333 −1.61974 −0.809868 0.586612i \(-0.800461\pi\)
−0.809868 + 0.586612i \(0.800461\pi\)
\(774\) 0 0
\(775\) −28.0000 −1.00579
\(776\) −12.1244 + 21.0000i −0.435239 + 0.753856i
\(777\) 0 0
\(778\) −12.0000 20.7846i −0.430221 0.745164i
\(779\) −20.7846 36.0000i −0.744686 1.28983i
\(780\) 0 0
\(781\) 18.0000 31.1769i 0.644091 1.11560i
\(782\) 20.7846 0.743256
\(783\) 0 0
\(784\) −5.00000 −0.178571
\(785\) 17.3205 30.0000i 0.618195 1.07075i
\(786\) 0 0
\(787\) −16.0000 27.7128i −0.570338 0.987855i −0.996531 0.0832226i \(-0.973479\pi\)
0.426193 0.904632i \(-0.359855\pi\)
\(788\) 10.3923 + 18.0000i 0.370211 + 0.641223i
\(789\) 0 0
\(790\) 24.0000 41.5692i 0.853882 1.47897i
\(791\) 0 0