Properties

Label 441.2.e.j.361.2
Level $441$
Weight $2$
Character 441.361
Analytic conductor $3.521$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
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 361.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 441.361
Dual form 441.2.e.j.226.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 1.50000i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.73205 - 3.00000i) q^{5} +1.73205 q^{8} +O(q^{10})\) \(q+(0.866025 + 1.50000i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.73205 - 3.00000i) q^{5} +1.73205 q^{8} +(3.00000 - 5.19615i) q^{10} +(1.73205 - 3.00000i) q^{11} +2.00000 q^{13} +(2.50000 + 4.33013i) q^{16} +(1.73205 - 3.00000i) q^{17} +(2.00000 + 3.46410i) q^{19} +3.46410 q^{20} +6.00000 q^{22} +(-1.73205 - 3.00000i) q^{23} +(-3.50000 + 6.06218i) q^{25} +(1.73205 + 3.00000i) q^{26} +(2.00000 - 3.46410i) q^{31} +(-2.59808 + 4.50000i) q^{32} +6.00000 q^{34} +(-1.00000 - 1.73205i) q^{37} +(-3.46410 + 6.00000i) q^{38} +(-3.00000 - 5.19615i) q^{40} -10.3923 q^{41} -4.00000 q^{43} +(1.73205 + 3.00000i) q^{44} +(3.00000 - 5.19615i) q^{46} +(3.46410 + 6.00000i) q^{47} -12.1244 q^{50} +(-1.00000 + 1.73205i) q^{52} +(-3.46410 + 6.00000i) q^{53} -12.0000 q^{55} +(-3.46410 + 6.00000i) q^{59} +(5.00000 + 8.66025i) q^{61} +6.92820 q^{62} +1.00000 q^{64} +(-3.46410 - 6.00000i) q^{65} +(2.00000 - 3.46410i) q^{67} +(1.73205 + 3.00000i) q^{68} +10.3923 q^{71} +(-7.00000 + 12.1244i) q^{73} +(1.73205 - 3.00000i) q^{74} -4.00000 q^{76} +(-4.00000 - 6.92820i) q^{79} +(8.66025 - 15.0000i) q^{80} +(-9.00000 - 15.5885i) q^{82} -12.0000 q^{85} +(-3.46410 - 6.00000i) q^{86} +(3.00000 - 5.19615i) q^{88} +(-1.73205 - 3.00000i) q^{89} +3.46410 q^{92} +(-6.00000 + 10.3923i) q^{94} +(6.92820 - 12.0000i) q^{95} +14.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{4} + O(q^{10}) \) \( 4q - 2q^{4} + 12q^{10} + 8q^{13} + 10q^{16} + 8q^{19} + 24q^{22} - 14q^{25} + 8q^{31} + 24q^{34} - 4q^{37} - 12q^{40} - 16q^{43} + 12q^{46} - 4q^{52} - 48q^{55} + 20q^{61} + 4q^{64} + 8q^{67} - 28q^{73} - 16q^{76} - 16q^{79} - 36q^{82} - 48q^{85} + 12q^{88} - 24q^{94} + 56q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 0.990839 + 0.135045i \(0.0431180\pi\)
−0.378467 + 0.925615i \(0.623549\pi\)
\(3\) 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 0
\(8\) 1.73205 0.612372
\(9\) 0 0
\(10\) 3.00000 5.19615i 0.948683 1.64317i
\(11\) 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
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.50000 + 4.33013i 0.625000 + 1.08253i
\(17\) 1.73205 3.00000i 0.420084 0.727607i −0.575863 0.817546i \(-0.695334\pi\)
0.995947 + 0.0899392i \(0.0286673\pi\)
\(18\) 0 0
\(19\) 2.00000 + 3.46410i 0.458831 + 0.794719i 0.998899 0.0469020i \(-0.0149348\pi\)
−0.540068 + 0.841621i \(0.681602\pi\)
\(20\) 3.46410 0.774597
\(21\) 0 0
\(22\) 6.00000 1.27920
\(23\) −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
\(26\) 1.73205 + 3.00000i 0.339683 + 0.588348i
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i \(-0.716379\pi\)
0.987829 + 0.155543i \(0.0497126\pi\)
\(32\) −2.59808 + 4.50000i −0.459279 + 0.795495i
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) 0 0
\(37\) −1.00000 1.73205i −0.164399 0.284747i 0.772043 0.635571i \(-0.219235\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(38\) −3.46410 + 6.00000i −0.561951 + 0.973329i
\(39\) 0 0
\(40\) −3.00000 5.19615i −0.474342 0.821584i
\(41\) −10.3923 −1.62301 −0.811503 0.584349i \(-0.801350\pi\)
−0.811503 + 0.584349i \(0.801350\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 1.73205 + 3.00000i 0.261116 + 0.452267i
\(45\) 0 0
\(46\) 3.00000 5.19615i 0.442326 0.766131i
\(47\) 3.46410 + 6.00000i 0.505291 + 0.875190i 0.999981 + 0.00612051i \(0.00194823\pi\)
−0.494690 + 0.869069i \(0.664718\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −12.1244 −1.71464
\(51\) 0 0
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) −3.46410 + 6.00000i −0.475831 + 0.824163i −0.999617 0.0276867i \(-0.991186\pi\)
0.523786 + 0.851850i \(0.324519\pi\)
\(54\) 0 0
\(55\) −12.0000 −1.61808
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.46410 + 6.00000i −0.450988 + 0.781133i −0.998448 0.0556984i \(-0.982261\pi\)
0.547460 + 0.836832i \(0.315595\pi\)
\(60\) 0 0
\(61\) 5.00000 + 8.66025i 0.640184 + 1.10883i 0.985391 + 0.170305i \(0.0544754\pi\)
−0.345207 + 0.938527i \(0.612191\pi\)
\(62\) 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 −0.717607 0.696449i \(-0.754762\pi\)
0.961946 + 0.273241i \(0.0880957\pi\)
\(68\) 1.73205 + 3.00000i 0.210042 + 0.363803i
\(69\) 0 0
\(70\) 0 0
\(71\) 10.3923 1.23334 0.616670 0.787222i \(-0.288481\pi\)
0.616670 + 0.787222i \(0.288481\pi\)
\(72\) 0 0
\(73\) −7.00000 + 12.1244i −0.819288 + 1.41905i 0.0869195 + 0.996215i \(0.472298\pi\)
−0.906208 + 0.422833i \(0.861036\pi\)
\(74\) 1.73205 3.00000i 0.201347 0.348743i
\(75\) 0 0
\(76\) −4.00000 −0.458831
\(77\) 0 0
\(78\) 0 0
\(79\) −4.00000 6.92820i −0.450035 0.779484i 0.548352 0.836247i \(-0.315255\pi\)
−0.998388 + 0.0567635i \(0.981922\pi\)
\(80\) 8.66025 15.0000i 0.968246 1.67705i
\(81\) 0 0
\(82\) −9.00000 15.5885i −0.993884 1.72146i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) −12.0000 −1.30158
\(86\) −3.46410 6.00000i −0.373544 0.646997i
\(87\) 0 0
\(88\) 3.00000 5.19615i 0.319801 0.553912i
\(89\) −1.73205 3.00000i −0.183597 0.317999i 0.759506 0.650500i \(-0.225441\pi\)
−0.943103 + 0.332501i \(0.892107\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 3.46410 0.361158
\(93\) 0 0
\(94\) −6.00000 + 10.3923i −0.618853 + 1.07188i
\(95\) 6.92820 12.0000i 0.710819 1.23117i
\(96\) 0 0
\(97\) 14.0000 1.42148 0.710742 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −3.50000 6.06218i −0.350000 0.606218i
\(101\) 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 \(0.770192\pi\)
\(104\) 3.46410 0.339683
\(105\) 0 0
\(106\) −12.0000 −1.16554
\(107\) 8.66025 + 15.0000i 0.837218 + 1.45010i 0.892211 + 0.451618i \(0.149153\pi\)
−0.0549930 + 0.998487i \(0.517514\pi\)
\(108\) 0 0
\(109\) −1.00000 + 1.73205i −0.0957826 + 0.165900i −0.909935 0.414751i \(-0.863869\pi\)
0.814152 + 0.580651i \(0.197202\pi\)
\(110\) −10.3923 18.0000i −0.990867 1.71623i
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) −6.00000 + 10.3923i −0.559503 + 0.969087i
\(116\) 0 0
\(117\) 0 0
\(118\) −12.0000 −1.10469
\(119\) 0 0
\(120\) 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
\(133\) 0 0
\(134\) 6.92820 0.598506
\(135\) 0 0
\(136\) 3.00000 5.19615i 0.257248 0.445566i
\(137\) −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
\(139\) −16.0000 −1.35710 −0.678551 0.734553i \(-0.737392\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 9.00000 + 15.5885i 0.755263 + 1.30815i
\(143\) 3.46410 6.00000i 0.289683 0.501745i
\(144\) 0 0
\(145\) 0 0
\(146\) −24.2487 −2.00684
\(147\) 0 0
\(148\) 2.00000 0.164399
\(149\) 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 \(0.272204\pi\)
\(152\) 3.46410 + 6.00000i 0.280976 + 0.486664i
\(153\) 0 0
\(154\) 0 0
\(155\) −13.8564 −1.11297
\(156\) 0 0
\(157\) 5.00000 8.66025i 0.399043 0.691164i −0.594565 0.804048i \(-0.702676\pi\)
0.993608 + 0.112884i \(0.0360089\pi\)
\(158\) 6.92820 12.0000i 0.551178 0.954669i
\(159\) 0 0
\(160\) 18.0000 1.42302
\(161\) 0 0
\(162\) 0 0
\(163\) −10.0000 17.3205i −0.783260 1.35665i −0.930033 0.367477i \(-0.880222\pi\)
0.146772 0.989170i \(-0.453112\pi\)
\(164\) 5.19615 9.00000i 0.405751 0.702782i
\(165\) 0 0
\(166\) 0 0
\(167\) 20.7846 1.60836 0.804181 0.594385i \(-0.202604\pi\)
0.804181 + 0.594385i \(0.202604\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) −10.3923 18.0000i −0.797053 1.38054i
\(171\) 0 0
\(172\) 2.00000 3.46410i 0.152499 0.264135i
\(173\) 8.66025 + 15.0000i 0.658427 + 1.14043i 0.981023 + 0.193892i \(0.0621112\pi\)
−0.322596 + 0.946537i \(0.604555\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 17.3205 1.30558
\(177\) 0 0
\(178\) 3.00000 5.19615i 0.224860 0.389468i
\(179\) −8.66025 + 15.0000i −0.647298 + 1.12115i 0.336468 + 0.941695i \(0.390768\pi\)
−0.983766 + 0.179458i \(0.942566\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) 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 −0.854306 0.519771i \(-0.826017\pi\)
−0.0229818 0.999736i \(-0.507316\pi\)
\(192\) 0 0
\(193\) −7.00000 + 12.1244i −0.503871 + 0.872730i 0.496119 + 0.868255i \(0.334758\pi\)
−0.999990 + 0.00447566i \(0.998575\pi\)
\(194\) 12.1244 + 21.0000i 0.870478 + 1.50771i
\(195\) 0 0
\(196\) 0 0
\(197\) −20.7846 −1.48084 −0.740421 0.672143i \(-0.765374\pi\)
−0.740421 + 0.672143i \(0.765374\pi\)
\(198\) 0 0
\(199\) 8.00000 13.8564i 0.567105 0.982255i −0.429745 0.902950i \(-0.641397\pi\)
0.996850 0.0793045i \(-0.0252700\pi\)
\(200\) −6.06218 + 10.5000i −0.428661 + 0.742462i
\(201\) 0 0
\(202\) 6.00000 0.422159
\(203\) 0 0
\(204\) 0 0
\(205\) 18.0000 + 31.1769i 1.25717 + 2.17749i
\(206\) −3.46410 + 6.00000i −0.241355 + 0.418040i
\(207\) 0 0
\(208\) 5.00000 + 8.66025i 0.346688 + 0.600481i
\(209\) 13.8564 0.958468
\(210\) 0 0
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) −3.46410 6.00000i −0.237915 0.412082i
\(213\) 0 0
\(214\) −15.0000 + 25.9808i −1.02538 + 1.77601i
\(215\) 6.92820 + 12.0000i 0.472500 + 0.818393i
\(216\) 0 0
\(217\) 0 0
\(218\) −3.46410 −0.234619
\(219\) 0 0
\(220\) 6.00000 10.3923i 0.404520 0.700649i
\(221\) 3.46410 6.00000i 0.233021 0.403604i
\(222\) 0 0
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) 0 0
\(225\) 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 \(0.574293\pi\)
\(230\) −20.7846 −1.37050
\(231\) 0 0
\(232\) 0 0
\(233\) 3.46410 + 6.00000i 0.226941 + 0.393073i 0.956900 0.290418i \(-0.0937943\pi\)
−0.729959 + 0.683491i \(0.760461\pi\)
\(234\) 0 0
\(235\) 12.0000 20.7846i 0.782794 1.35584i
\(236\) −3.46410 6.00000i −0.225494 0.390567i
\(237\) 0 0
\(238\) 0 0
\(239\) −10.3923 −0.672222 −0.336111 0.941822i \(-0.609112\pi\)
−0.336111 + 0.941822i \(0.609112\pi\)
\(240\) 0 0
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) 0.866025 1.50000i 0.0556702 0.0964237i
\(243\) 0 0
\(244\) −10.0000 −0.640184
\(245\) 0 0
\(246\) 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
\(259\) 0 0
\(260\) 6.92820 0.429669
\(261\) 0 0
\(262\) 12.0000 20.7846i 0.741362 1.28408i
\(263\) −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
\(265\) 24.0000 1.47431
\(266\) 0 0
\(267\) 0 0
\(268\) 2.00000 + 3.46410i 0.122169 + 0.211604i
\(269\) −8.66025 + 15.0000i −0.528025 + 0.914566i 0.471441 + 0.881897i \(0.343734\pi\)
−0.999466 + 0.0326687i \(0.989599\pi\)
\(270\) 0 0
\(271\) −10.0000 17.3205i −0.607457 1.05215i −0.991658 0.128897i \(-0.958856\pi\)
0.384201 0.923249i \(-0.374477\pi\)
\(272\) 17.3205 1.05021
\(273\) 0 0
\(274\) −12.0000 −0.724947
\(275\) 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 \(0.0695395\pi\)
\(278\) −13.8564 24.0000i −0.831052 1.43942i
\(279\) 0 0
\(280\) 0 0
\(281\) 20.7846 1.23991 0.619953 0.784639i \(-0.287152\pi\)
0.619953 + 0.784639i \(0.287152\pi\)
\(282\) 0 0
\(283\) 2.00000 3.46410i 0.118888 0.205919i −0.800439 0.599414i \(-0.795400\pi\)
0.919327 + 0.393494i \(0.128734\pi\)
\(284\) −5.19615 + 9.00000i −0.308335 + 0.534052i
\(285\) 0 0
\(286\) 12.0000 0.709575
\(287\) 0 0
\(288\) 0 0
\(289\) 2.50000 + 4.33013i 0.147059 + 0.254713i
\(290\) 0 0
\(291\) 0 0
\(292\) −7.00000 12.1244i −0.409644 0.709524i
\(293\) 10.3923 0.607125 0.303562 0.952812i \(-0.401824\pi\)
0.303562 + 0.952812i \(0.401824\pi\)
\(294\) 0 0
\(295\) 24.0000 1.39733
\(296\) −1.73205 3.00000i −0.100673 0.174371i
\(297\) 0 0
\(298\) −6.00000 + 10.3923i −0.347571 + 0.602010i
\(299\) −3.46410 6.00000i −0.200334 0.346989i
\(300\) 0 0
\(301\) 0 0
\(302\) −13.8564 −0.797347
\(303\) 0 0
\(304\) −10.0000 + 17.3205i −0.573539 + 0.993399i
\(305\) 17.3205 30.0000i 0.991769 1.71780i
\(306\) 0 0
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −12.0000 20.7846i −0.681554 1.18049i
\(311\) 17.3205 30.0000i 0.982156 1.70114i 0.328206 0.944606i \(-0.393556\pi\)
0.653950 0.756538i \(-0.273111\pi\)
\(312\) 0 0
\(313\) −1.00000 1.73205i −0.0565233 0.0979013i 0.836379 0.548151i \(-0.184668\pi\)
−0.892903 + 0.450250i \(0.851335\pi\)
\(314\) 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 \(-0.104338\pi\)
−0.752194 + 0.658942i \(0.771004\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.73205 3.00000i −0.0968246 0.167705i
\(321\) 0 0
\(322\) 0 0
\(323\) 13.8564 0.770991
\(324\) 0 0
\(325\) −7.00000 + 12.1244i −0.388290 + 0.672538i
\(326\) 17.3205 30.0000i 0.959294 1.66155i
\(327\) 0 0
\(328\) −18.0000 −0.993884
\(329\) 0 0
\(330\) 0 0
\(331\) −10.0000 17.3205i −0.549650 0.952021i −0.998298 0.0583130i \(-0.981428\pi\)
0.448649 0.893708i \(-0.351905\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 18.0000 + 31.1769i 0.984916 + 1.70592i
\(335\) −13.8564 −0.757056
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) −7.79423 13.5000i −0.423950 0.734303i
\(339\) 0 0
\(340\) 6.00000 10.3923i 0.325396 0.563602i
\(341\) −6.92820 12.0000i −0.375183 0.649836i
\(342\) 0 0
\(343\) 0 0
\(344\) −6.92820 −0.373544
\(345\) 0 0
\(346\) −15.0000 + 25.9808i −0.806405 + 1.39673i
\(347\) −8.66025 + 15.0000i −0.464907 + 0.805242i −0.999197 0.0400587i \(-0.987246\pi\)
0.534291 + 0.845301i \(0.320579\pi\)
\(348\) 0 0
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 9.00000 + 15.5885i 0.479702 + 0.830868i
\(353\) 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
\(356\) 3.46410 0.183597
\(357\) 0 0
\(358\) −30.0000 −1.58555
\(359\) −12.1244 21.0000i −0.639899 1.10834i −0.985455 0.169939i \(-0.945643\pi\)
0.345556 0.938398i \(-0.387690\pi\)
\(360\) 0 0
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) 1.73205 + 3.00000i 0.0910346 + 0.157676i
\(363\) 0 0
\(364\) 0 0
\(365\) 48.4974 2.53847
\(366\) 0 0
\(367\) 8.00000 13.8564i 0.417597 0.723299i −0.578101 0.815966i \(-0.696206\pi\)
0.995697 + 0.0926670i \(0.0295392\pi\)
\(368\) 8.66025 15.0000i 0.451447 0.781929i
\(369\) 0 0
\(370\) −12.0000 −0.623850
\(371\) 0 0
\(372\) 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
\(385\) 0 0
\(386\) −24.2487 −1.23423
\(387\) 0 0
\(388\) −7.00000 + 12.1244i −0.355371 + 0.615521i
\(389\) 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
\(391\) −12.0000 −0.606866
\(392\) 0 0
\(393\) 0 0
\(394\) −18.0000 31.1769i −0.906827 1.57067i
\(395\) −13.8564 + 24.0000i −0.697191 + 1.20757i
\(396\) 0 0
\(397\) −19.0000 32.9090i −0.953583 1.65165i −0.737579 0.675261i \(-0.764031\pi\)
−0.216004 0.976392i \(-0.569302\pi\)
\(398\) 27.7128 1.38912
\(399\) 0 0
\(400\) −35.0000 −1.75000
\(401\) 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
\(404\) 1.73205 + 3.00000i 0.0861727 + 0.149256i
\(405\) 0 0
\(406\) 0 0
\(407\) −6.92820 −0.343418
\(408\) 0 0
\(409\) −7.00000 + 12.1244i −0.346128 + 0.599511i −0.985558 0.169338i \(-0.945837\pi\)
0.639430 + 0.768849i \(0.279170\pi\)
\(410\) −31.1769 + 54.0000i −1.53972 + 2.66687i
\(411\) 0 0
\(412\) −4.00000 −0.197066
\(413\) 0 0
\(414\) 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
\(419\) −20.7846 −1.01539 −0.507697 0.861536i \(-0.669503\pi\)
−0.507697 + 0.861536i \(0.669503\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 17.3205 + 30.0000i 0.843149 + 1.46038i
\(423\) 0 0
\(424\) −6.00000 + 10.3923i −0.291386 + 0.504695i
\(425\) 12.1244 + 21.0000i 0.588118 + 1.01865i
\(426\) 0 0
\(427\) 0 0
\(428\) −17.3205 −0.837218
\(429\) 0 0
\(430\) −12.0000 + 20.7846i −0.578691 + 1.00232i
\(431\) 1.73205 3.00000i 0.0834300 0.144505i −0.821291 0.570509i \(-0.806746\pi\)
0.904721 + 0.426004i \(0.140079\pi\)
\(432\) 0 0
\(433\) 26.0000 1.24948 0.624740 0.780833i \(-0.285205\pi\)
0.624740 + 0.780833i \(0.285205\pi\)
\(434\) 0 0
\(435\) 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 0.991322 0.131453i \(-0.0419644\pi\)
−0.609503 + 0.792784i \(0.708631\pi\)
\(440\) −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 \(-0.192891\pi\)
−0.904234 + 0.427037i \(0.859557\pi\)
\(444\) 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 0
\(449\) −41.5692 −1.96177 −0.980886 0.194581i \(-0.937665\pi\)
−0.980886 + 0.194581i \(0.937665\pi\)
\(450\) 0 0
\(451\) −18.0000 + 31.1769i −0.847587 + 1.46806i
\(452\) 0 0
\(453\) 0 0
\(454\) −12.0000 −0.563188
\(455\) 0 0
\(456\) 0 0
\(457\) 5.00000 + 8.66025i 0.233890 + 0.405110i 0.958950 0.283577i \(-0.0915211\pi\)
−0.725059 + 0.688686i \(0.758188\pi\)
\(458\) −19.0526 + 33.0000i −0.890268 + 1.54199i
\(459\) 0 0
\(460\) −6.00000 10.3923i −0.279751 0.484544i
\(461\) −31.1769 −1.45205 −0.726027 0.687666i \(-0.758635\pi\)
−0.726027 + 0.687666i \(0.758635\pi\)
\(462\) 0 0
\(463\) 32.0000 1.48717 0.743583 0.668644i \(-0.233125\pi\)
0.743583 + 0.668644i \(0.233125\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −6.00000 + 10.3923i −0.277945 + 0.481414i
\(467\) 3.46410 + 6.00000i 0.160300 + 0.277647i 0.934976 0.354711i \(-0.115421\pi\)
−0.774677 + 0.632358i \(0.782087\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 41.5692 1.91745
\(471\) 0 0
\(472\) −6.00000 + 10.3923i −0.276172 + 0.478345i
\(473\) −6.92820 + 12.0000i −0.318559 + 0.551761i
\(474\) 0 0
\(475\) −28.0000 −1.28473
\(476\) 0 0
\(477\) 0 0
\(478\) −9.00000 15.5885i −0.411650 0.712999i
\(479\) −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
\(482\) 17.3205 0.788928
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −24.2487 42.0000i −1.10108 1.90712i
\(486\) 0 0
\(487\) 20.0000 34.6410i 0.906287 1.56973i 0.0871056 0.996199i \(-0.472238\pi\)
0.819181 0.573535i \(-0.194428\pi\)
\(488\) 8.66025 + 15.0000i 0.392031 + 0.679018i
\(489\) 0 0
\(490\) 0 0
\(491\) −10.3923 −0.468998 −0.234499 0.972116i \(-0.575345\pi\)
−0.234499 + 0.972116i \(0.575345\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −6.92820 + 12.0000i −0.311715 + 0.539906i
\(495\) 0 0
\(496\) 20.0000 0.898027
\(497\) 0 0
\(498\) 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
\(511\) 0 0
\(512\) −8.66025 −0.382733
\(513\) 0 0
\(514\) 3.00000 5.19615i 0.132324 0.229192i
\(515\) 6.92820 12.0000i 0.305293 0.528783i
\(516\) 0 0
\(517\) 24.0000 1.05552
\(518\) 0 0
\(519\) 0 0
\(520\) −6.00000 10.3923i −0.263117 0.455733i
\(521\) 1.73205 3.00000i 0.0758825 0.131432i −0.825587 0.564275i \(-0.809156\pi\)
0.901470 + 0.432842i \(0.142489\pi\)
\(522\) 0 0
\(523\) 8.00000 + 13.8564i 0.349816 + 0.605898i 0.986216 0.165460i \(-0.0529109\pi\)
−0.636401 + 0.771358i \(0.719578\pi\)
\(524\) 13.8564 0.605320
\(525\) 0 0
\(526\) −30.0000 −1.30806
\(527\) −6.92820 12.0000i −0.301797 0.522728i
\(528\) 0 0
\(529\) 5.50000 9.52628i 0.239130 0.414186i
\(530\) 20.7846 + 36.0000i 0.902826 + 1.56374i
\(531\) 0 0
\(532\) 0 0
\(533\) −20.7846 −0.900281
\(534\) 0 0
\(535\) 30.0000 51.9615i 1.29701 2.24649i
\(536\) 3.46410 6.00000i 0.149626 0.259161i
\(537\) 0 0
\(538\) −30.0000 −1.29339
\(539\) 0 0
\(540\) 0 0
\(541\) −7.00000 12.1244i −0.300954 0.521267i 0.675399 0.737453i \(-0.263972\pi\)
−0.976352 + 0.216186i \(0.930638\pi\)
\(542\) 17.3205 30.0000i 0.743980 1.28861i
\(543\) 0 0
\(544\) 9.00000 + 15.5885i 0.385872 + 0.668350i
\(545\) 6.92820 0.296772
\(546\) 0 0
\(547\) −4.00000 −0.171028 −0.0855138 0.996337i \(-0.527253\pi\)
−0.0855138 + 0.996337i \(0.527253\pi\)
\(548\) −3.46410 6.00000i −0.147979 0.256307i
\(549\) 0 0
\(550\) −21.0000 + 36.3731i −0.895443 + 1.55095i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 17.3205 0.735878
\(555\) 0 0
\(556\) 8.00000 13.8564i 0.339276 0.587643i
\(557\) −3.46410 + 6.00000i −0.146779 + 0.254228i −0.930035 0.367471i \(-0.880224\pi\)
0.783256 + 0.621699i \(0.213557\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) 18.0000 + 31.1769i 0.759284 + 1.31512i
\(563\) 17.3205 30.0000i 0.729972 1.26435i −0.226922 0.973913i \(-0.572866\pi\)
0.956894 0.290436i \(-0.0938004\pi\)
\(564\) 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 \(-0.120277\pi\)
−0.784233 + 0.620466i \(0.786943\pi\)
\(570\) 0 0
\(571\) 14.0000 24.2487i 0.585882 1.01478i −0.408883 0.912587i \(-0.634082\pi\)
0.994765 0.102190i \(-0.0325850\pi\)
\(572\) 3.46410 + 6.00000i 0.144841 + 0.250873i
\(573\) 0 0
\(574\) 0 0
\(575\) 24.2487 1.01124
\(576\) 0 0
\(577\) −1.00000 + 1.73205i −0.0416305 + 0.0721062i −0.886090 0.463513i \(-0.846589\pi\)
0.844459 + 0.535620i \(0.179922\pi\)
\(578\) −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
\(584\) −12.1244 + 21.0000i −0.501709 + 0.868986i
\(585\) 0 0
\(586\) 9.00000 + 15.5885i 0.371787 + 0.643953i
\(587\) 20.7846 0.857873 0.428936 0.903335i \(-0.358888\pi\)
0.428936 + 0.903335i \(0.358888\pi\)
\(588\) 0 0
\(589\) 16.0000 0.659269
\(590\) 20.7846 + 36.0000i 0.855689 + 1.48210i
\(591\) 0 0
\(592\) 5.00000 8.66025i 0.205499 0.355934i
\(593\) −12.1244 21.0000i −0.497888 0.862367i 0.502109 0.864804i \(-0.332557\pi\)
−0.999997 + 0.00243746i \(0.999224\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −6.92820 −0.283790
\(597\) 0 0
\(598\) 6.00000 10.3923i 0.245358 0.424973i
\(599\) 22.5167 39.0000i 0.920006 1.59350i 0.120603 0.992701i \(-0.461517\pi\)
0.799402 0.600796i \(-0.205150\pi\)
\(600\) 0 0
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −4.00000 6.92820i −0.162758 0.281905i
\(605\) −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 \(0.885242\pi\)
\(608\) −20.7846 −0.842927
\(609\) 0 0
\(610\) 60.0000 2.42933
\(611\) 6.92820 + 12.0000i 0.280285 + 0.485468i
\(612\) 0 0
\(613\) −19.0000 + 32.9090i −0.767403 + 1.32918i 0.171564 + 0.985173i \(0.445118\pi\)
−0.938967 + 0.344008i \(0.888215\pi\)
\(614\) −24.2487 42.0000i −0.978598 1.69498i
\(615\) 0 0
\(616\) 0 0
\(617\) 20.7846 0.836757 0.418378 0.908273i \(-0.362599\pi\)
0.418378 + 0.908273i \(0.362599\pi\)
\(618\) 0 0
\(619\) −4.00000 + 6.92820i −0.160774 + 0.278468i −0.935146 0.354262i \(-0.884732\pi\)
0.774373 + 0.632730i \(0.218066\pi\)
\(620\) 6.92820 12.0000i 0.278243 0.481932i
\(621\) 0 0
\(622\) 60.0000 2.40578
\(623\) 0 0
\(624\) 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
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 21.0000 36.3731i 0.830098 1.43777i
\(641\) −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
\(643\) 20.0000 0.788723 0.394362 0.918955i \(-0.370966\pi\)
0.394362 + 0.918955i \(0.370966\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 12.0000 + 20.7846i 0.472134 + 0.817760i
\(647\) −3.46410 + 6.00000i −0.136188 + 0.235884i −0.926051 0.377399i \(-0.876818\pi\)
0.789863 + 0.613284i \(0.210152\pi\)
\(648\) 0 0
\(649\) 12.0000 + 20.7846i 0.471041 + 0.815867i
\(650\) −24.2487 −0.951113
\(651\) 0 0
\(652\) 20.0000 0.783260
\(653\) 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
\(656\) −25.9808 45.0000i −1.01438 1.75695i
\(657\) 0 0
\(658\) 0 0
\(659\) 10.3923 0.404827 0.202413 0.979300i \(-0.435122\pi\)
0.202413 + 0.979300i \(0.435122\pi\)
\(660\) 0 0
\(661\) 5.00000 8.66025i 0.194477 0.336845i −0.752252 0.658876i \(-0.771032\pi\)
0.946729 + 0.322031i \(0.104366\pi\)
\(662\) 17.3205 30.0000i 0.673181 1.16598i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 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
\(671\) 34.6410 1.33730
\(672\) 0 0
\(673\) −10.0000 −0.385472 −0.192736 0.981251i \(-0.561736\pi\)
−0.192736 + 0.981251i \(0.561736\pi\)
\(674\) 12.1244 + 21.0000i 0.467013 + 0.808890i
\(675\) 0 0
\(676\) 4.50000 7.79423i 0.173077 0.299778i
\(677\) −12.1244 21.0000i −0.465977 0.807096i 0.533268 0.845946i \(-0.320964\pi\)
−0.999245 + 0.0388507i \(0.987630\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −20.7846 −0.797053
\(681\) 0 0
\(682\) 12.0000 20.7846i 0.459504 0.795884i
\(683\) 12.1244 21.0000i 0.463926 0.803543i −0.535227 0.844708i \(-0.679774\pi\)
0.999152 + 0.0411658i \(0.0131072\pi\)
\(684\) 0 0
\(685\) 24.0000 0.916993
\(686\) 0 0
\(687\) 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 0.779857 0.625958i \(-0.215292\pi\)
−0.932024 + 0.362397i \(0.881959\pi\)
\(692\) −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
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 4.00000 6.92820i 0.150863 0.261302i
\(704\) 1.73205 3.00000i 0.0652791 0.113067i
\(705\) 0 0
\(706\) 6.00000 0.225813
\(707\) 0 0
\(708\) 0 0
\(709\) −13.0000 22.5167i −0.488225 0.845631i 0.511683 0.859174i \(-0.329022\pi\)
−0.999908 + 0.0135434i \(0.995689\pi\)
\(710\) 31.1769 54.0000i 1.17005 2.02658i
\(711\) 0 0
\(712\) −3.00000 5.19615i −0.112430 0.194734i
\(713\) −13.8564 −0.518927
\(714\) 0 0
\(715\) −24.0000 −0.897549
\(716\) −8.66025 15.0000i −0.323649 0.560576i
\(717\) 0 0
\(718\) 21.0000 36.3731i 0.783713 1.35743i
\(719\) 13.8564 + 24.0000i 0.516757 + 0.895049i 0.999811 + 0.0194584i \(0.00619418\pi\)
−0.483054 + 0.875591i \(0.660472\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 5.19615 0.193381
\(723\) 0 0
\(724\) −1.00000 + 1.73205i −0.0371647 + 0.0643712i
\(725\) 0 0
\(726\) 0 0
\(727\) −4.00000 −0.148352 −0.0741759 0.997245i \(-0.523633\pi\)
−0.0741759 + 0.997245i \(0.523633\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 42.0000 + 72.7461i 1.55449 + 2.69246i
\(731\) −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 \(0.700154\pi\)
\(734\) 27.7128 1.02290
\(735\) 0 0
\(736\) 18.0000 0.663489
\(737\) −6.92820 12.0000i −0.255204 0.442026i
\(738\) 0 0
\(739\) −10.0000 + 17.3205i −0.367856 + 0.637145i −0.989230 0.146369i \(-0.953241\pi\)
0.621374 + 0.783514i \(0.286575\pi\)
\(740\) −3.46410 6.00000i −0.127343 0.220564i
\(741\) 0 0
\(742\) 0 0
\(743\) 10.3923 0.381257 0.190628 0.981662i \(-0.438947\pi\)
0.190628 + 0.981662i \(0.438947\pi\)
\(744\) 0 0
\(745\) 12.0000 20.7846i 0.439646 0.761489i
\(746\) −8.66025 + 15.0000i −0.317074 + 0.549189i
\(747\) 0 0
\(748\) 12.0000 0.438763
\(749\) 0 0
\(750\) 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
\(763\) 0 0
\(764\) 24.2487 0.877288
\(765\) 0 0
\(766\) 12.0000 20.7846i 0.433578 0.750978i
\(767\) −6.92820 + 12.0000i −0.250163 + 0.433295i
\(768\) 0 0
\(769\) −22.0000 −0.793340 −0.396670 0.917961i \(-0.629834\pi\)
−0.396670 + 0.917961i \(0.629834\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −7.00000 12.1244i −0.251936 0.436365i
\(773\) 22.5167 39.0000i 0.809868 1.40273i −0.103087 0.994672i \(-0.532872\pi\)
0.912955 0.408060i \(-0.133795\pi\)
\(774\) 0 0
\(775\) 14.0000 + 24.2487i 0.502895 + 0.871039i
\(776\) 24.2487 0.870478
\(777\) 0 0
\(778\) 24.0000 0.860442
\(779\) −20.7846 36.0000i −0.744686 1.28983i
\(780\) 0 0
\(781\) 18.0000 31.1769i 0.644091 1.11560i
\(782\) −10.3923 18.0000i −0.371628 0.643679i
\(783\) 0 0
\(784\) 0 0
\(785\) −34.6410 −1.23639
\(786\) 0 0
\(787\) −16.0000 + 27.7128i −0.570338 + 0.987855i 0.426193 + 0.904632i \(0.359855\pi\)
−0.996531 + 0.0832226i \(0.973479\pi\)
\(788\) 10.3923 18.0000i 0.370211 0.641223i
\(789\) 0 0
\(790\) −48.0000 −1.70776
\(791\) 0 0
\(792\) 0 0
\(793\) 10.0000 + 17.3205i 0.355110 + 0.615069i
\(794\) 32.9090 57.0000i 1.16790 2.02285i
\(795\) 0 0
\(796\) 8.00000 + 13.8564i 0.283552