Properties

Label 567.2.f.j.379.1
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 379.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 567.379
Dual form 567.2.f.j.190.1

$q$-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 \(0.376451\pi\)
−0.990839 + 0.135045i \(0.956882\pi\)
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.73205 + 3.00000i 0.774597 + 1.34164i 0.935021 + 0.354593i \(0.115380\pi\)
−0.160424 + 0.987048i \(0.551286\pi\)
\(6\) 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 \(0.341568\pi\)
−0.999665 + 0.0258656i \(0.991766\pi\)
\(12\) 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 \(-0.362001\pi\)
0.420084 + 0.907485i \(0.362001\pi\)
\(18\) 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 0.988152 0.153481i \(-0.0490483\pi\)
−0.626994 + 0.779024i \(0.715715\pi\)
\(24\) 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 \(-0.865317\pi\)
0.100309 0.994956i \(-0.468017\pi\)
\(42\) 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 \(0.335282\pi\)
−0.999981 + 0.00612051i \(0.998052\pi\)
\(48\) 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 \(-0.657853\pi\)
−0.475831 + 0.879537i \(0.657853\pi\)
\(54\) 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 0.998448 0.0556984i \(-0.0177385\pi\)
−0.547460 + 0.836832i \(0.684405\pi\)
\(60\) 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 \(-0.711519\pi\)
−0.616670 + 0.787222i \(0.711519\pi\)
\(72\) 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 \(-0.558774\pi\)
−0.183597 + 0.983002i \(0.558774\pi\)
\(90\) 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 −0.939239 0.343263i \(-0.888468\pi\)
0.766894 + 0.641774i \(0.221801\pi\)
\(102\) 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 \(-0.184180\pi\)
0.837218 + 0.546869i \(0.184180\pi\)
\(108\) 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 \(0.0402882\pi\)
−0.386681 + 0.922214i \(0.626379\pi\)
\(132\) 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 −0.679249 0.733908i \(-0.737694\pi\)
0.975207 + 0.221293i \(0.0710278\pi\)
\(138\) 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 0.688525 0.725213i \(-0.258259\pi\)
−0.972315 + 0.233674i \(0.924925\pi\)
\(150\) 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 \(0.130729\pi\)
−0.112662 + 0.993633i \(0.535938\pi\)
\(168\) 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 \(0.395445\pi\)
−0.981023 + 0.193892i \(0.937889\pi\)
\(174\) 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 \(-0.724101\pi\)
−0.647298 + 0.762237i \(0.724101\pi\)
\(180\) 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 \(-0.492684\pi\)
0.854306 0.519771i \(-0.173983\pi\)
\(192\) 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 \(-0.234626\pi\)
0.740421 + 0.672143i \(0.234626\pi\)
\(198\) 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 −0.727864 0.685722i \(-0.759487\pi\)
0.957784 + 0.287488i \(0.0928200\pi\)
\(228\) 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 \(-0.427128\pi\)
0.226941 + 0.973909i \(0.427128\pi\)
\(234\) 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 0.647586 0.761992i \(-0.275778\pi\)
−0.983698 + 0.179830i \(0.942445\pi\)
\(240\) 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 \(-0.272265\pi\)
0.655956 + 0.754799i \(0.272265\pi\)
\(252\) 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 0.914977 0.403506i \(-0.132208\pi\)
−0.806935 + 0.590641i \(0.798875\pi\)
\(258\) 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 \(-0.654016\pi\)
0.999210 0.0397320i \(-0.0126504\pi\)
\(264\) 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 \(-0.677067\pi\)
−0.528025 + 0.849229i \(0.677067\pi\)
\(270\) 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 \(-0.620485\pi\)
0.989494 0.144575i \(-0.0461817\pi\)
\(282\) 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 0.976940 0.213513i \(-0.0684906\pi\)
−0.673378 + 0.739299i \(0.735157\pi\)
\(294\) 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 \(-0.726889\pi\)
−0.328206 0.944606i \(-0.606444\pi\)
\(312\) 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 −0.946757 0.321948i \(-0.895662\pi\)
0.752194 + 0.658942i \(0.228996\pi\)
\(318\) 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 0.999197 0.0400587i \(-0.0127545\pi\)
−0.534291 + 0.845301i \(0.679421\pi\)
\(348\) 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 −0.908431 0.418034i \(-0.862719\pi\)
0.816244 + 0.577708i \(0.196053\pi\)
\(354\) 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 \(-0.721024\pi\)
−0.639899 + 0.768459i \(0.721024\pi\)
\(360\) 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 0.986949 0.161034i \(-0.0514830\pi\)
−0.632934 + 0.774206i \(0.718150\pi\)
\(384\) 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 −0.986473 0.163924i \(-0.947585\pi\)
0.635199 + 0.772348i \(0.280918\pi\)
\(390\) 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 0.766475 0.642275i \(-0.222009\pi\)
−0.939463 + 0.342649i \(0.888676\pi\)
\(402\) 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 \(-0.997163\pi\)
0.492263 0.870447i \(-0.336170\pi\)
\(420\) 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 \(-0.473413\pi\)
0.0834300 + 0.996514i \(0.473413\pi\)
\(432\) 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 −0.821942 0.569571i \(-0.807109\pi\)
0.904234 + 0.427037i \(0.140443\pi\)
\(444\) 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 \(-0.0623348\pi\)
0.980886 + 0.194581i \(0.0623348\pi\)
\(450\) 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 \(0.425302\pi\)
−0.958550 + 0.284925i \(0.908031\pi\)
\(462\) 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 \(-0.448754\pi\)
0.160300 + 0.987068i \(0.448754\pi\)
\(468\) 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 −0.775969 0.630771i \(-0.782739\pi\)
0.934248 + 0.356624i \(0.116072\pi\)
\(480\) 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 0.724628 0.689140i \(-0.242012\pi\)
−0.959127 + 0.282976i \(0.908678\pi\)
\(492\) 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 0.901855 0.432038i \(-0.142205\pi\)
−0.825084 + 0.565011i \(0.808872\pi\)
\(510\) 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 \(-0.475823\pi\)
0.0758825 + 0.997117i \(0.475823\pi\)
\(522\) 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 \(-0.546891\pi\)
−0.146779 + 0.989169i \(0.546891\pi\)
\(558\) 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 \(-0.906200\pi\)
0.226922 0.973913i \(-0.427134\pi\)
\(564\) 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 −0.929456 0.368933i \(-0.879723\pi\)
0.784233 + 0.620466i \(0.213057\pi\)
\(570\) 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 −0.567843 0.823137i \(-0.692222\pi\)
0.996779 + 0.0801976i \(0.0255551\pi\)
\(588\) 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 \(-0.665891\pi\)
−0.497888 + 0.867242i \(0.665891\pi\)
\(594\) 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 \(-0.794850\pi\)
−0.120603 0.992701i \(-0.538483\pi\)
\(600\) 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 0.995777 0.0918100i \(-0.0292653\pi\)
−0.577398 + 0.816463i \(0.695932\pi\)
\(618\) 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 \(-0.426173\pi\)
0.727906 0.685677i \(-0.240494\pi\)
\(642\) 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 \(-0.543485\pi\)
−0.136188 + 0.990683i \(0.543485\pi\)
\(648\) 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 \(-0.984242\pi\)
0.456532 0.889707i \(-0.349091\pi\)
\(654\) 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 −0.746892 0.664945i \(-0.768455\pi\)
0.949306 + 0.314355i \(0.101788\pi\)
\(660\) 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 −0.533268 0.845946i \(-0.679036\pi\)
0.999245 + 0.0388507i \(0.0123697\pi\)
\(678\) 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 \(-0.346441\pi\)
0.463926 + 0.885874i \(0.346441\pi\)
\(684\) 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 \(-0.327139\pi\)
0.516757 + 0.856132i \(0.327139\pi\)
\(720\) 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 0.945459 0.325742i \(-0.105614\pi\)
−0.754830 + 0.655920i \(0.772281\pi\)
\(744\) 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 \(-0.923989\pi\)
0.280969 0.959717i \(-0.409344\pi\)
\(762\) 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 \(-0.199539\pi\)
0.809868 + 0.586612i \(0.199539\pi\)
\(774\) 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