Properties

Label 950.2.e.f.201.1
Level $950$
Weight $2$
Character 950.201
Analytic conductor $7.586$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 950.201
Dual form 950.2.e.f.501.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +5.00000 q^{11} +(1.00000 + 1.73205i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +3.00000 q^{18} +(-0.500000 + 4.33013i) q^{19} +(2.50000 - 4.33013i) q^{22} +(0.500000 + 0.866025i) q^{23} +2.00000 q^{26} +(0.500000 + 0.866025i) q^{28} +(-3.00000 - 5.19615i) q^{29} +4.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{36} +11.0000 q^{37} +(3.50000 + 2.59808i) q^{38} +(4.50000 - 7.79423i) q^{41} +(3.00000 - 5.19615i) q^{43} +(-2.50000 - 4.33013i) q^{44} +1.00000 q^{46} -6.00000 q^{49} +(1.00000 - 1.73205i) q^{52} +(2.50000 + 4.33013i) q^{53} +1.00000 q^{56} -6.00000 q^{58} +(2.00000 - 3.46410i) q^{62} +(-1.50000 - 2.59808i) q^{63} +1.00000 q^{64} +(6.00000 + 10.3923i) q^{67} +(-3.00000 + 5.19615i) q^{71} +(-1.50000 - 2.59808i) q^{72} +(7.00000 - 12.1244i) q^{73} +(5.50000 - 9.52628i) q^{74} +(4.00000 - 1.73205i) q^{76} -5.00000 q^{77} +(-5.00000 + 8.66025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-4.50000 - 7.79423i) q^{82} -14.0000 q^{83} +(-3.00000 - 5.19615i) q^{86} -5.00000 q^{88} +(3.50000 + 6.06218i) q^{89} +(-1.00000 - 1.73205i) q^{91} +(0.500000 - 0.866025i) q^{92} +(-1.00000 + 1.73205i) q^{97} +(-3.00000 + 5.19615i) q^{98} +(7.50000 + 12.9904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{4} - 2q^{7} - 2q^{8} + 3q^{9} + O(q^{10}) \) \( 2q + q^{2} - q^{4} - 2q^{7} - 2q^{8} + 3q^{9} + 10q^{11} + 2q^{13} - q^{14} - q^{16} + 6q^{18} - q^{19} + 5q^{22} + q^{23} + 4q^{26} + q^{28} - 6q^{29} + 8q^{31} + q^{32} + 3q^{36} + 22q^{37} + 7q^{38} + 9q^{41} + 6q^{43} - 5q^{44} + 2q^{46} - 12q^{49} + 2q^{52} + 5q^{53} + 2q^{56} - 12q^{58} + 4q^{62} - 3q^{63} + 2q^{64} + 12q^{67} - 6q^{71} - 3q^{72} + 14q^{73} + 11q^{74} + 8q^{76} - 10q^{77} - 10q^{79} - 9q^{81} - 9q^{82} - 28q^{83} - 6q^{86} - 10q^{88} + 7q^{89} - 2q^{91} + q^{92} - 2q^{97} - 6q^{98} + 15q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 0 0
\(11\) 5.00000 1.50756 0.753778 0.657129i \(-0.228229\pi\)
0.753778 + 0.657129i \(0.228229\pi\)
\(12\) 0 0
\(13\) 1.00000 + 1.73205i 0.277350 + 0.480384i 0.970725 0.240192i \(-0.0772105\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) −0.500000 + 0.866025i −0.133631 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 3.00000 0.707107
\(19\) −0.500000 + 4.33013i −0.114708 + 0.993399i
\(20\) 0 0
\(21\) 0 0
\(22\) 2.50000 4.33013i 0.533002 0.923186i
\(23\) 0.500000 + 0.866025i 0.104257 + 0.180579i 0.913434 0.406986i \(-0.133420\pi\)
−0.809177 + 0.587565i \(0.800087\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 2.00000 0.392232
\(27\) 0 0
\(28\) 0.500000 + 0.866025i 0.0944911 + 0.163663i
\(29\) −3.00000 5.19615i −0.557086 0.964901i −0.997738 0.0672232i \(-0.978586\pi\)
0.440652 0.897678i \(-0.354747\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 1.50000 2.59808i 0.250000 0.433013i
\(37\) 11.0000 1.80839 0.904194 0.427121i \(-0.140472\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) 3.50000 + 2.59808i 0.567775 + 0.421464i
\(39\) 0 0
\(40\) 0 0
\(41\) 4.50000 7.79423i 0.702782 1.21725i −0.264704 0.964330i \(-0.585274\pi\)
0.967486 0.252924i \(-0.0813924\pi\)
\(42\) 0 0
\(43\) 3.00000 5.19615i 0.457496 0.792406i −0.541332 0.840809i \(-0.682080\pi\)
0.998828 + 0.0484030i \(0.0154132\pi\)
\(44\) −2.50000 4.33013i −0.376889 0.652791i
\(45\) 0 0
\(46\) 1.00000 0.147442
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) 0 0
\(52\) 1.00000 1.73205i 0.138675 0.240192i
\(53\) 2.50000 + 4.33013i 0.343401 + 0.594789i 0.985062 0.172200i \(-0.0550875\pi\)
−0.641661 + 0.766989i \(0.721754\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) −6.00000 −0.787839
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 0 0
\(61\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(62\) 2.00000 3.46410i 0.254000 0.439941i
\(63\) −1.50000 2.59808i −0.188982 0.327327i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 6.00000 + 10.3923i 0.733017 + 1.26962i 0.955588 + 0.294706i \(0.0952216\pi\)
−0.222571 + 0.974916i \(0.571445\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) −1.50000 2.59808i −0.176777 0.306186i
\(73\) 7.00000 12.1244i 0.819288 1.41905i −0.0869195 0.996215i \(-0.527702\pi\)
0.906208 0.422833i \(-0.138964\pi\)
\(74\) 5.50000 9.52628i 0.639362 1.10741i
\(75\) 0 0
\(76\) 4.00000 1.73205i 0.458831 0.198680i
\(77\) −5.00000 −0.569803
\(78\) 0 0
\(79\) −5.00000 + 8.66025i −0.562544 + 0.974355i 0.434730 + 0.900561i \(0.356844\pi\)
−0.997274 + 0.0737937i \(0.976489\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) −4.50000 7.79423i −0.496942 0.860729i
\(83\) −14.0000 −1.53670 −0.768350 0.640030i \(-0.778922\pi\)
−0.768350 + 0.640030i \(0.778922\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −3.00000 5.19615i −0.323498 0.560316i
\(87\) 0 0
\(88\) −5.00000 −0.533002
\(89\) 3.50000 + 6.06218i 0.370999 + 0.642590i 0.989720 0.143022i \(-0.0456819\pi\)
−0.618720 + 0.785611i \(0.712349\pi\)
\(90\) 0 0
\(91\) −1.00000 1.73205i −0.104828 0.181568i
\(92\) 0.500000 0.866025i 0.0521286 0.0902894i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i \(-0.865709\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) −3.00000 + 5.19615i −0.303046 + 0.524891i
\(99\) 7.50000 + 12.9904i 0.753778 + 1.30558i
\(100\) 0 0
\(101\) −5.00000 8.66025i −0.497519 0.861727i 0.502477 0.864590i \(-0.332422\pi\)
−0.999996 + 0.00286291i \(0.999089\pi\)
\(102\) 0 0
\(103\) −13.0000 −1.28093 −0.640464 0.767988i \(-0.721258\pi\)
−0.640464 + 0.767988i \(0.721258\pi\)
\(104\) −1.00000 1.73205i −0.0980581 0.169842i
\(105\) 0 0
\(106\) 5.00000 0.485643
\(107\) 4.00000 0.386695 0.193347 0.981130i \(-0.438066\pi\)
0.193347 + 0.981130i \(0.438066\pi\)
\(108\) 0 0
\(109\) −2.00000 + 3.46410i −0.191565 + 0.331801i −0.945769 0.324840i \(-0.894690\pi\)
0.754204 + 0.656640i \(0.228023\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.500000 0.866025i 0.0472456 0.0818317i
\(113\) 12.0000 1.12887 0.564433 0.825479i \(-0.309095\pi\)
0.564433 + 0.825479i \(0.309095\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −3.00000 + 5.19615i −0.278543 + 0.482451i
\(117\) −3.00000 + 5.19615i −0.277350 + 0.480384i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 14.0000 1.27273
\(122\) 0 0
\(123\) 0 0
\(124\) −2.00000 3.46410i −0.179605 0.311086i
\(125\) 0 0
\(126\) −3.00000 −0.267261
\(127\) −7.50000 12.9904i −0.665517 1.15271i −0.979145 0.203164i \(-0.934878\pi\)
0.313627 0.949546i \(-0.398456\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) −0.500000 + 0.866025i −0.0436852 + 0.0756650i −0.887041 0.461690i \(-0.847243\pi\)
0.843356 + 0.537355i \(0.180577\pi\)
\(132\) 0 0
\(133\) 0.500000 4.33013i 0.0433555 0.375470i
\(134\) 12.0000 1.03664
\(135\) 0 0
\(136\) 0 0
\(137\) 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i \(0.00465636\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(138\) 0 0
\(139\) −8.00000 13.8564i −0.678551 1.17529i −0.975417 0.220366i \(-0.929275\pi\)
0.296866 0.954919i \(-0.404058\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 3.00000 + 5.19615i 0.251754 + 0.436051i
\(143\) 5.00000 + 8.66025i 0.418121 + 0.724207i
\(144\) −3.00000 −0.250000
\(145\) 0 0
\(146\) −7.00000 12.1244i −0.579324 1.00342i
\(147\) 0 0
\(148\) −5.50000 9.52628i −0.452097 0.783055i
\(149\) 2.00000 3.46410i 0.163846 0.283790i −0.772399 0.635138i \(-0.780943\pi\)
0.936245 + 0.351348i \(0.114277\pi\)
\(150\) 0 0
\(151\) −16.0000 −1.30206 −0.651031 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) 0.500000 4.33013i 0.0405554 0.351220i
\(153\) 0 0
\(154\) −2.50000 + 4.33013i −0.201456 + 0.348932i
\(155\) 0 0
\(156\) 0 0
\(157\) −10.5000 + 18.1865i −0.837991 + 1.45144i 0.0535803 + 0.998564i \(0.482937\pi\)
−0.891572 + 0.452880i \(0.850397\pi\)
\(158\) 5.00000 + 8.66025i 0.397779 + 0.688973i
\(159\) 0 0
\(160\) 0 0
\(161\) −0.500000 0.866025i −0.0394055 0.0682524i
\(162\) 4.50000 + 7.79423i 0.353553 + 0.612372i
\(163\) −10.0000 −0.783260 −0.391630 0.920123i \(-0.628089\pi\)
−0.391630 + 0.920123i \(0.628089\pi\)
\(164\) −9.00000 −0.702782
\(165\) 0 0
\(166\) −7.00000 + 12.1244i −0.543305 + 0.941033i
\(167\) −2.50000 4.33013i −0.193456 0.335075i 0.752937 0.658092i \(-0.228636\pi\)
−0.946393 + 0.323017i \(0.895303\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 0 0
\(171\) −12.0000 + 5.19615i −0.917663 + 0.397360i
\(172\) −6.00000 −0.457496
\(173\) 0.500000 0.866025i 0.0380143 0.0658427i −0.846392 0.532560i \(-0.821230\pi\)
0.884407 + 0.466717i \(0.154563\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −2.50000 + 4.33013i −0.188445 + 0.326396i
\(177\) 0 0
\(178\) 7.00000 0.524672
\(179\) 19.0000 1.42013 0.710063 0.704138i \(-0.248666\pi\)
0.710063 + 0.704138i \(0.248666\pi\)
\(180\) 0 0
\(181\) −1.00000 1.73205i −0.0743294 0.128742i 0.826465 0.562988i \(-0.190348\pi\)
−0.900794 + 0.434246i \(0.857015\pi\)
\(182\) −2.00000 −0.148250
\(183\) 0 0
\(184\) −0.500000 0.866025i −0.0368605 0.0638442i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −18.0000 −1.30243 −0.651217 0.758891i \(-0.725741\pi\)
−0.651217 + 0.758891i \(0.725741\pi\)
\(192\) 0 0
\(193\) 2.00000 3.46410i 0.143963 0.249351i −0.785022 0.619467i \(-0.787349\pi\)
0.928986 + 0.370116i \(0.120682\pi\)
\(194\) 1.00000 + 1.73205i 0.0717958 + 0.124354i
\(195\) 0 0
\(196\) 3.00000 + 5.19615i 0.214286 + 0.371154i
\(197\) −23.0000 −1.63868 −0.819341 0.573306i \(-0.805660\pi\)
−0.819341 + 0.573306i \(0.805660\pi\)
\(198\) 15.0000 1.06600
\(199\) −12.0000 20.7846i −0.850657 1.47338i −0.880616 0.473831i \(-0.842871\pi\)
0.0299585 0.999551i \(-0.490462\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −10.0000 −0.703598
\(203\) 3.00000 + 5.19615i 0.210559 + 0.364698i
\(204\) 0 0
\(205\) 0 0
\(206\) −6.50000 + 11.2583i −0.452876 + 0.784405i
\(207\) −1.50000 + 2.59808i −0.104257 + 0.180579i
\(208\) −2.00000 −0.138675
\(209\) −2.50000 + 21.6506i −0.172929 + 1.49761i
\(210\) 0 0
\(211\) −6.50000 + 11.2583i −0.447478 + 0.775055i −0.998221 0.0596196i \(-0.981011\pi\)
0.550743 + 0.834675i \(0.314345\pi\)
\(212\) 2.50000 4.33013i 0.171701 0.297394i
\(213\) 0 0
\(214\) 2.00000 3.46410i 0.136717 0.236801i
\(215\) 0 0
\(216\) 0 0
\(217\) −4.00000 −0.271538
\(218\) 2.00000 + 3.46410i 0.135457 + 0.234619i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −11.5000 + 19.9186i −0.770097 + 1.33385i 0.167412 + 0.985887i \(0.446459\pi\)
−0.937509 + 0.347960i \(0.886874\pi\)
\(224\) −0.500000 0.866025i −0.0334077 0.0578638i
\(225\) 0 0
\(226\) 6.00000 10.3923i 0.399114 0.691286i
\(227\) 10.0000 0.663723 0.331862 0.943328i \(-0.392323\pi\)
0.331862 + 0.943328i \(0.392323\pi\)
\(228\) 0 0
\(229\) 6.00000 0.396491 0.198246 0.980152i \(-0.436476\pi\)
0.198246 + 0.980152i \(0.436476\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 3.00000 + 5.19615i 0.196960 + 0.341144i
\(233\) 5.00000 8.66025i 0.327561 0.567352i −0.654466 0.756091i \(-0.727107\pi\)
0.982027 + 0.188739i \(0.0604400\pi\)
\(234\) 3.00000 + 5.19615i 0.196116 + 0.339683i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 16.0000 1.03495 0.517477 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) 0 0
\(241\) 9.00000 + 15.5885i 0.579741 + 1.00414i 0.995509 + 0.0946700i \(0.0301796\pi\)
−0.415768 + 0.909471i \(0.636487\pi\)
\(242\) 7.00000 12.1244i 0.449977 0.779383i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −8.00000 + 3.46410i −0.509028 + 0.220416i
\(248\) −4.00000 −0.254000
\(249\) 0 0
\(250\) 0 0
\(251\) 6.00000 + 10.3923i 0.378717 + 0.655956i 0.990876 0.134778i \(-0.0430322\pi\)
−0.612159 + 0.790735i \(0.709699\pi\)
\(252\) −1.50000 + 2.59808i −0.0944911 + 0.163663i
\(253\) 2.50000 + 4.33013i 0.157174 + 0.272233i
\(254\) −15.0000 −0.941184
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −7.00000 12.1244i −0.436648 0.756297i 0.560781 0.827964i \(-0.310501\pi\)
−0.997429 + 0.0716680i \(0.977168\pi\)
\(258\) 0 0
\(259\) −11.0000 −0.683507
\(260\) 0 0
\(261\) 9.00000 15.5885i 0.557086 0.964901i
\(262\) 0.500000 + 0.866025i 0.0308901 + 0.0535032i
\(263\) 5.50000 9.52628i 0.339145 0.587416i −0.645128 0.764075i \(-0.723196\pi\)
0.984272 + 0.176659i \(0.0565291\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −3.50000 2.59808i −0.214599 0.159298i
\(267\) 0 0
\(268\) 6.00000 10.3923i 0.366508 0.634811i
\(269\) 14.0000 24.2487i 0.853595 1.47847i −0.0243472 0.999704i \(-0.507751\pi\)
0.877942 0.478766i \(-0.158916\pi\)
\(270\) 0 0
\(271\) 3.00000 5.19615i 0.182237 0.315644i −0.760405 0.649449i \(-0.775000\pi\)
0.942642 + 0.333805i \(0.108333\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 12.0000 0.724947
\(275\) 0 0
\(276\) 0 0
\(277\) 2.00000 0.120168 0.0600842 0.998193i \(-0.480863\pi\)
0.0600842 + 0.998193i \(0.480863\pi\)
\(278\) −16.0000 −0.959616
\(279\) 6.00000 + 10.3923i 0.359211 + 0.622171i
\(280\) 0 0
\(281\) 7.50000 + 12.9904i 0.447412 + 0.774941i 0.998217 0.0596933i \(-0.0190123\pi\)
−0.550804 + 0.834634i \(0.685679\pi\)
\(282\) 0 0
\(283\) −7.00000 + 12.1244i −0.416107 + 0.720718i −0.995544 0.0942988i \(-0.969939\pi\)
0.579437 + 0.815017i \(0.303272\pi\)
\(284\) 6.00000 0.356034
\(285\) 0 0
\(286\) 10.0000 0.591312
\(287\) −4.50000 + 7.79423i −0.265627 + 0.460079i
\(288\) −1.50000 + 2.59808i −0.0883883 + 0.153093i
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) 0 0
\(291\) 0 0
\(292\) −14.0000 −0.819288
\(293\) 21.0000 1.22683 0.613417 0.789760i \(-0.289795\pi\)
0.613417 + 0.789760i \(0.289795\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −11.0000 −0.639362
\(297\) 0 0
\(298\) −2.00000 3.46410i −0.115857 0.200670i
\(299\) −1.00000 + 1.73205i −0.0578315 + 0.100167i
\(300\) 0 0
\(301\) −3.00000 + 5.19615i −0.172917 + 0.299501i
\(302\) −8.00000 + 13.8564i −0.460348 + 0.797347i
\(303\) 0 0
\(304\) −3.50000 2.59808i −0.200739 0.149010i
\(305\) 0 0
\(306\) 0 0
\(307\) −1.00000 + 1.73205i −0.0570730 + 0.0988534i −0.893150 0.449758i \(-0.851510\pi\)
0.836077 + 0.548612i \(0.184843\pi\)
\(308\) 2.50000 + 4.33013i 0.142451 + 0.246732i
\(309\) 0 0
\(310\) 0 0
\(311\) 4.00000 0.226819 0.113410 0.993548i \(-0.463823\pi\)
0.113410 + 0.993548i \(0.463823\pi\)
\(312\) 0 0
\(313\) −14.0000 24.2487i −0.791327 1.37062i −0.925146 0.379612i \(-0.876057\pi\)
0.133819 0.991006i \(-0.457276\pi\)
\(314\) 10.5000 + 18.1865i 0.592549 + 1.02633i
\(315\) 0 0
\(316\) 10.0000 0.562544
\(317\) −13.5000 23.3827i −0.758236 1.31330i −0.943750 0.330661i \(-0.892728\pi\)
0.185514 0.982642i \(-0.440605\pi\)
\(318\) 0 0
\(319\) −15.0000 25.9808i −0.839839 1.45464i
\(320\) 0 0
\(321\) 0 0
\(322\) −1.00000 −0.0557278
\(323\) 0 0
\(324\) 9.00000 0.500000
\(325\) 0 0
\(326\) −5.00000 + 8.66025i −0.276924 + 0.479647i
\(327\) 0 0
\(328\) −4.50000 + 7.79423i −0.248471 + 0.430364i
\(329\) 0 0
\(330\) 0 0
\(331\) −25.0000 −1.37412 −0.687062 0.726599i \(-0.741100\pi\)
−0.687062 + 0.726599i \(0.741100\pi\)
\(332\) 7.00000 + 12.1244i 0.384175 + 0.665410i
\(333\) 16.5000 + 28.5788i 0.904194 + 1.56611i
\(334\) −5.00000 −0.273588
\(335\) 0 0
\(336\) 0 0
\(337\) 3.00000 5.19615i 0.163420 0.283052i −0.772673 0.634804i \(-0.781081\pi\)
0.936093 + 0.351752i \(0.114414\pi\)
\(338\) −4.50000 7.79423i −0.244768 0.423950i
\(339\) 0 0
\(340\) 0 0
\(341\) 20.0000 1.08306
\(342\) −1.50000 + 12.9904i −0.0811107 + 0.702439i
\(343\) 13.0000 0.701934
\(344\) −3.00000 + 5.19615i −0.161749 + 0.280158i
\(345\) 0 0
\(346\) −0.500000 0.866025i −0.0268802 0.0465578i
\(347\) 9.00000 15.5885i 0.483145 0.836832i −0.516667 0.856186i \(-0.672828\pi\)
0.999813 + 0.0193540i \(0.00616095\pi\)
\(348\) 0 0
\(349\) −28.0000 −1.49881 −0.749403 0.662114i \(-0.769659\pi\)
−0.749403 + 0.662114i \(0.769659\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 2.50000 + 4.33013i 0.133250 + 0.230797i
\(353\) −4.00000 −0.212899 −0.106449 0.994318i \(-0.533948\pi\)
−0.106449 + 0.994318i \(0.533948\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 3.50000 6.06218i 0.185500 0.321295i
\(357\) 0 0
\(358\) 9.50000 16.4545i 0.502091 0.869646i
\(359\) −5.00000 + 8.66025i −0.263890 + 0.457071i −0.967272 0.253741i \(-0.918339\pi\)
0.703382 + 0.710812i \(0.251672\pi\)
\(360\) 0 0
\(361\) −18.5000 4.33013i −0.973684 0.227901i
\(362\) −2.00000 −0.105118
\(363\) 0 0
\(364\) −1.00000 + 1.73205i −0.0524142 + 0.0907841i
\(365\) 0 0
\(366\) 0 0
\(367\) −2.00000 3.46410i −0.104399 0.180825i 0.809093 0.587680i \(-0.199959\pi\)
−0.913493 + 0.406855i \(0.866625\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 27.0000 1.40556
\(370\) 0 0
\(371\) −2.50000 4.33013i −0.129794 0.224809i
\(372\) 0 0
\(373\) −31.0000 −1.60512 −0.802560 0.596572i \(-0.796529\pi\)
−0.802560 + 0.596572i \(0.796529\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 6.00000 10.3923i 0.309016 0.535231i
\(378\) 0 0
\(379\) −12.0000 −0.616399 −0.308199 0.951322i \(-0.599726\pi\)
−0.308199 + 0.951322i \(0.599726\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −9.00000 + 15.5885i −0.460480 + 0.797575i
\(383\) 4.00000 6.92820i 0.204390 0.354015i −0.745548 0.666452i \(-0.767812\pi\)
0.949938 + 0.312437i \(0.101145\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −2.00000 3.46410i −0.101797 0.176318i
\(387\) 18.0000 0.914991
\(388\) 2.00000 0.101535
\(389\) −13.0000 22.5167i −0.659126 1.14164i −0.980842 0.194804i \(-0.937593\pi\)
0.321716 0.946836i \(-0.395740\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 6.00000 0.303046
\(393\) 0 0
\(394\) −11.5000 + 19.9186i −0.579362 + 1.00348i
\(395\) 0 0
\(396\) 7.50000 12.9904i 0.376889 0.652791i
\(397\) 14.5000 25.1147i 0.727734 1.26047i −0.230105 0.973166i \(-0.573907\pi\)
0.957839 0.287307i \(-0.0927599\pi\)
\(398\) −24.0000 −1.20301
\(399\) 0 0
\(400\) 0 0
\(401\) 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i \(-0.684957\pi\)
0.998350 + 0.0574304i \(0.0182907\pi\)
\(402\) 0 0
\(403\) 4.00000 + 6.92820i 0.199254 + 0.345118i
\(404\) −5.00000 + 8.66025i −0.248759 + 0.430864i
\(405\) 0 0
\(406\) 6.00000 0.297775
\(407\) 55.0000 2.72625
\(408\) 0 0
\(409\) 5.50000 + 9.52628i 0.271957 + 0.471044i 0.969363 0.245633i \(-0.0789957\pi\)
−0.697406 + 0.716677i \(0.745662\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 6.50000 + 11.2583i 0.320232 + 0.554658i
\(413\) 0 0
\(414\) 1.50000 + 2.59808i 0.0737210 + 0.127688i
\(415\) 0 0
\(416\) −1.00000 + 1.73205i −0.0490290 + 0.0849208i
\(417\) 0 0
\(418\) 17.5000 + 12.9904i 0.855953 + 0.635380i
\(419\) −7.00000 −0.341972 −0.170986 0.985273i \(-0.554695\pi\)
−0.170986 + 0.985273i \(0.554695\pi\)
\(420\) 0 0
\(421\) 4.00000 6.92820i 0.194948 0.337660i −0.751935 0.659237i \(-0.770879\pi\)
0.946883 + 0.321577i \(0.104213\pi\)
\(422\) 6.50000 + 11.2583i 0.316415 + 0.548047i
\(423\) 0 0
\(424\) −2.50000 4.33013i −0.121411 0.210290i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −2.00000 3.46410i −0.0966736 0.167444i
\(429\) 0 0
\(430\) 0 0
\(431\) −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i \(-0.259993\pi\)
−0.973574 + 0.228373i \(0.926659\pi\)
\(432\) 0 0
\(433\) 1.00000 + 1.73205i 0.0480569 + 0.0832370i 0.889053 0.457804i \(-0.151364\pi\)
−0.840996 + 0.541041i \(0.818030\pi\)
\(434\) −2.00000 + 3.46410i −0.0960031 + 0.166282i
\(435\) 0 0
\(436\) 4.00000 0.191565
\(437\) −4.00000 + 1.73205i −0.191346 + 0.0828552i
\(438\) 0 0
\(439\) −4.00000 + 6.92820i −0.190910 + 0.330665i −0.945552 0.325471i \(-0.894477\pi\)
0.754642 + 0.656136i \(0.227810\pi\)
\(440\) 0 0
\(441\) −9.00000 15.5885i −0.428571 0.742307i
\(442\) 0 0
\(443\) 18.0000 + 31.1769i 0.855206 + 1.48126i 0.876454 + 0.481486i \(0.159903\pi\)
−0.0212481 + 0.999774i \(0.506764\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 11.5000 + 19.9186i 0.544541 + 0.943172i
\(447\) 0 0
\(448\) −1.00000 −0.0472456
\(449\) −19.0000 −0.896665 −0.448333 0.893867i \(-0.647982\pi\)
−0.448333 + 0.893867i \(0.647982\pi\)
\(450\) 0 0
\(451\) 22.5000 38.9711i 1.05948 1.83508i
\(452\) −6.00000 10.3923i −0.282216 0.488813i
\(453\) 0 0
\(454\) 5.00000 8.66025i 0.234662 0.406446i
\(455\) 0 0
\(456\) 0 0
\(457\) 32.0000 1.49690 0.748448 0.663193i \(-0.230799\pi\)
0.748448 + 0.663193i \(0.230799\pi\)
\(458\) 3.00000 5.19615i 0.140181 0.242800i
\(459\) 0 0
\(460\) 0 0
\(461\) 15.0000 25.9808i 0.698620 1.21004i −0.270326 0.962769i \(-0.587131\pi\)
0.968945 0.247276i \(-0.0795353\pi\)
\(462\) 0 0
\(463\) −37.0000 −1.71954 −0.859768 0.510685i \(-0.829392\pi\)
−0.859768 + 0.510685i \(0.829392\pi\)
\(464\) 6.00000 0.278543
\(465\) 0 0
\(466\) −5.00000 8.66025i −0.231621 0.401179i
\(467\) −34.0000 −1.57333 −0.786666 0.617379i \(-0.788195\pi\)
−0.786666 + 0.617379i \(0.788195\pi\)
\(468\) 6.00000 0.277350
\(469\) −6.00000 10.3923i −0.277054 0.479872i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 15.0000 25.9808i 0.689701 1.19460i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −7.50000 + 12.9904i −0.343401 + 0.594789i
\(478\) 8.00000 13.8564i 0.365911 0.633777i
\(479\) 9.00000 + 15.5885i 0.411220 + 0.712255i 0.995023 0.0996406i \(-0.0317693\pi\)
−0.583803 + 0.811895i \(0.698436\pi\)
\(480\) 0 0
\(481\) 11.0000 + 19.0526i 0.501557 + 0.868722i
\(482\) 18.0000 0.819878
\(483\) 0 0
\(484\) −7.00000 12.1244i −0.318182 0.551107i
\(485\) 0 0
\(486\) 0 0
\(487\) 23.0000 1.04223 0.521115 0.853487i \(-0.325516\pi\)
0.521115 + 0.853487i \(0.325516\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −13.5000 + 23.3827i −0.609246 + 1.05525i 0.382118 + 0.924113i \(0.375195\pi\)
−0.991365 + 0.131132i \(0.958139\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −1.00000 + 8.66025i −0.0449921 + 0.389643i
\(495\) 0 0
\(496\) −2.00000 + 3.46410i −0.0898027 + 0.155543i
\(497\) 3.00000 5.19615i 0.134568 0.233079i
\(498\) 0 0
\(499\) 19.5000 33.7750i 0.872940 1.51198i 0.0139987 0.999902i \(-0.495544\pi\)
0.858941 0.512074i \(-0.171123\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 12.0000 0.535586
\(503\) −16.5000 28.5788i −0.735699 1.27427i −0.954416 0.298479i \(-0.903521\pi\)
0.218718 0.975788i \(-0.429813\pi\)
\(504\) 1.50000 + 2.59808i 0.0668153 + 0.115728i
\(505\) 0 0
\(506\) 5.00000 0.222277
\(507\) 0 0
\(508\) −7.50000 + 12.9904i −0.332759 + 0.576355i
\(509\) −7.00000 12.1244i −0.310270 0.537403i 0.668151 0.744026i \(-0.267086\pi\)
−0.978421 + 0.206623i \(0.933753\pi\)
\(510\) 0 0
\(511\) −7.00000 + 12.1244i −0.309662 + 0.536350i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −14.0000 −0.617514
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) −5.50000 + 9.52628i −0.241656 + 0.418561i
\(519\) 0 0
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) −9.00000 15.5885i −0.393919 0.682288i
\(523\) −21.0000 36.3731i −0.918266 1.59048i −0.802048 0.597259i \(-0.796256\pi\)
−0.116218 0.993224i \(-0.537077\pi\)
\(524\) 1.00000 0.0436852
\(525\) 0 0
\(526\) −5.50000 9.52628i −0.239811 0.415366i
\(527\) 0 0
\(528\) 0 0
\(529\) 11.0000 19.0526i 0.478261 0.828372i
\(530\) 0 0
\(531\) 0 0
\(532\) −4.00000 + 1.73205i −0.173422 + 0.0750939i
\(533\) 18.0000 0.779667
\(534\) 0 0
\(535\) 0 0
\(536\) −6.00000 10.3923i −0.259161 0.448879i
\(537\) 0 0
\(538\) −14.0000 24.2487i −0.603583 1.04544i
\(539\) −30.0000 −1.29219
\(540\) 0 0
\(541\) 10.0000 + 17.3205i 0.429934 + 0.744667i 0.996867 0.0790969i \(-0.0252036\pi\)
−0.566933 + 0.823764i \(0.691870\pi\)
\(542\) −3.00000 5.19615i −0.128861 0.223194i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −11.0000 19.0526i −0.470326 0.814629i 0.529098 0.848561i \(-0.322530\pi\)
−0.999424 + 0.0339321i \(0.989197\pi\)
\(548\) 6.00000 10.3923i 0.256307 0.443937i
\(549\) 0 0
\(550\) 0 0
\(551\) 24.0000 10.3923i 1.02243 0.442727i
\(552\) 0 0
\(553\) 5.00000 8.66025i 0.212622 0.368271i
\(554\) 1.00000 1.73205i 0.0424859 0.0735878i
\(555\) 0 0
\(556\) −8.00000 + 13.8564i −0.339276 + 0.587643i
\(557\) −4.50000 7.79423i −0.190671 0.330252i 0.754802 0.655953i \(-0.227733\pi\)
−0.945473 + 0.325701i \(0.894400\pi\)
\(558\) 12.0000 0.508001
\(559\) 12.0000 0.507546
\(560\) 0 0
\(561\) 0 0
\(562\) 15.0000 0.632737
\(563\) −32.0000 −1.34864 −0.674320 0.738440i \(-0.735563\pi\)
−0.674320 + 0.738440i \(0.735563\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 7.00000 + 12.1244i 0.294232 + 0.509625i
\(567\) 4.50000 7.79423i 0.188982 0.327327i
\(568\) 3.00000 5.19615i 0.125877 0.218026i
\(569\) 45.0000 1.88650 0.943249 0.332086i \(-0.107752\pi\)
0.943249 + 0.332086i \(0.107752\pi\)
\(570\) 0 0
\(571\) 12.0000 0.502184 0.251092 0.967963i \(-0.419210\pi\)
0.251092 + 0.967963i \(0.419210\pi\)
\(572\) 5.00000 8.66025i 0.209061 0.362103i
\(573\) 0 0
\(574\) 4.50000 + 7.79423i 0.187826 + 0.325325i
\(575\) 0 0
\(576\) 1.50000 + 2.59808i 0.0625000 + 0.108253i
\(577\) −32.0000 −1.33218 −0.666089 0.745873i \(-0.732033\pi\)
−0.666089 + 0.745873i \(0.732033\pi\)
\(578\) 17.0000 0.707107
\(579\) 0 0
\(580\) 0 0
\(581\) 14.0000 0.580818
\(582\) 0 0
\(583\) 12.5000 + 21.6506i 0.517697 + 0.896678i
\(584\) −7.00000 + 12.1244i −0.289662 + 0.501709i
\(585\) 0 0
\(586\) 10.5000 18.1865i 0.433751 0.751279i
\(587\) 6.00000 10.3923i 0.247647 0.428936i −0.715226 0.698893i \(-0.753676\pi\)
0.962872 + 0.269957i \(0.0870095\pi\)
\(588\) 0 0
\(589\) −2.00000 + 17.3205i −0.0824086 + 0.713679i
\(590\) 0 0
\(591\) 0 0
\(592\) −5.50000 + 9.52628i −0.226049 + 0.391528i
\(593\) 21.0000 + 36.3731i 0.862367 + 1.49366i 0.869638 + 0.493689i \(0.164352\pi\)
−0.00727173 + 0.999974i \(0.502315\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −4.00000 −0.163846
\(597\) 0 0
\(598\) 1.00000 + 1.73205i 0.0408930 + 0.0708288i
\(599\) 22.0000 + 38.1051i 0.898896 + 1.55693i 0.828908 + 0.559385i \(0.188963\pi\)
0.0699877 + 0.997548i \(0.477704\pi\)
\(600\) 0 0
\(601\) 21.0000 0.856608 0.428304 0.903635i \(-0.359111\pi\)
0.428304 + 0.903635i \(0.359111\pi\)
\(602\) 3.00000 + 5.19615i 0.122271 + 0.211779i
\(603\) −18.0000 + 31.1769i −0.733017 + 1.26962i
\(604\) 8.00000 + 13.8564i 0.325515 + 0.563809i
\(605\) 0 0
\(606\) 0 0
\(607\) −13.0000 −0.527654 −0.263827 0.964570i \(-0.584985\pi\)
−0.263827 + 0.964570i \(0.584985\pi\)
\(608\) −4.00000 + 1.73205i −0.162221 + 0.0702439i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 12.5000 21.6506i 0.504870 0.874461i −0.495114 0.868828i \(-0.664874\pi\)
0.999984 0.00563283i \(-0.00179300\pi\)
\(614\) 1.00000 + 1.73205i 0.0403567 + 0.0698999i
\(615\) 0 0
\(616\) 5.00000 0.201456
\(617\) 10.0000 + 17.3205i 0.402585 + 0.697297i 0.994037 0.109043i \(-0.0347785\pi\)
−0.591452 + 0.806340i \(0.701445\pi\)
\(618\) 0 0
\(619\) −45.0000 −1.80870 −0.904351 0.426789i \(-0.859645\pi\)
−0.904351 + 0.426789i \(0.859645\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 2.00000 3.46410i 0.0801927 0.138898i
\(623\) −3.50000 6.06218i −0.140225 0.242876i
\(624\) 0 0
\(625\) 0 0
\(626\) −28.0000 −1.11911
\(627\) 0 0
\(628\) 21.0000 0.837991
\(629\) 0 0
\(630\) 0 0
\(631\) 11.0000 + 19.0526i 0.437903 + 0.758470i 0.997528 0.0702759i \(-0.0223880\pi\)
−0.559625 + 0.828746i \(0.689055\pi\)
\(632\) 5.00000 8.66025i 0.198889 0.344486i
\(633\) 0 0
\(634\) −27.0000 −1.07231
\(635\) 0 0
\(636\) 0 0
\(637\) −6.00000 10.3923i −0.237729 0.411758i
\(638\) −30.0000 −1.18771
\(639\) −18.0000 −0.712069
\(640\) 0 0
\(641\) 5.00000 8.66025i 0.197488 0.342059i −0.750225 0.661182i \(-0.770055\pi\)
0.947713 + 0.319123i \(0.103388\pi\)
\(642\) 0 0
\(643\) −8.00000 + 13.8564i −0.315489 + 0.546443i −0.979541 0.201243i \(-0.935502\pi\)
0.664052 + 0.747686i \(0.268835\pi\)
\(644\) −0.500000 + 0.866025i −0.0197028 + 0.0341262i
\(645\) 0 0
\(646\) 0 0
\(647\) 3.00000 0.117942 0.0589711 0.998260i \(-0.481218\pi\)
0.0589711 + 0.998260i \(0.481218\pi\)
\(648\) 4.50000 7.79423i 0.176777 0.306186i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 5.00000 + 8.66025i 0.195815 + 0.339162i
\(653\) 25.0000 0.978326 0.489163 0.872192i \(-0.337302\pi\)
0.489163 + 0.872192i \(0.337302\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 4.50000 + 7.79423i 0.175695 + 0.304314i
\(657\) 42.0000 1.63858
\(658\) 0 0
\(659\) 7.50000 + 12.9904i 0.292159 + 0.506033i 0.974320 0.225168i \(-0.0722932\pi\)
−0.682161 + 0.731202i \(0.738960\pi\)
\(660\) 0 0
\(661\) −12.0000 20.7846i −0.466746 0.808428i 0.532533 0.846410i \(-0.321240\pi\)
−0.999278 + 0.0379819i \(0.987907\pi\)
\(662\) −12.5000 + 21.6506i −0.485826 + 0.841476i
\(663\) 0 0
\(664\) 14.0000 0.543305
\(665\) 0 0
\(666\) 33.0000 1.27872
\(667\) 3.00000 5.19615i 0.116160 0.201196i
\(668\) −2.50000 + 4.33013i −0.0967279 + 0.167538i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −16.0000 −0.616755 −0.308377 0.951264i \(-0.599786\pi\)
−0.308377 + 0.951264i \(0.599786\pi\)
\(674\) −3.00000 5.19615i −0.115556 0.200148i
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) −27.0000 −1.03769 −0.518847 0.854867i \(-0.673639\pi\)
−0.518847 + 0.854867i \(0.673639\pi\)
\(678\) 0 0
\(679\) 1.00000 1.73205i 0.0383765 0.0664700i
\(680\) 0 0
\(681\) 0 0
\(682\) 10.0000 17.3205i 0.382920 0.663237i
\(683\) 44.0000 1.68361 0.841807 0.539779i \(-0.181492\pi\)
0.841807 + 0.539779i \(0.181492\pi\)
\(684\) 10.5000 + 7.79423i 0.401478 + 0.298020i
\(685\) 0 0
\(686\) 6.50000 11.2583i 0.248171 0.429845i
\(687\) 0 0
\(688\) 3.00000 + 5.19615i 0.114374 + 0.198101i
\(689\) −5.00000 + 8.66025i −0.190485 + 0.329929i
\(690\) 0 0
\(691\) −15.0000 −0.570627 −0.285313 0.958434i \(-0.592098\pi\)
−0.285313 + 0.958434i \(0.592098\pi\)
\(692\) −1.00000 −0.0380143
\(693\) −7.50000 12.9904i −0.284901 0.493464i
\(694\) −9.00000 15.5885i −0.341635 0.591730i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −14.0000 + 24.2487i −0.529908 + 0.917827i
\(699\) 0 0
\(700\) 0 0
\(701\) −3.00000 + 5.19615i −0.113308 + 0.196256i −0.917102 0.398652i \(-0.869478\pi\)
0.803794 + 0.594908i \(0.202811\pi\)
\(702\) 0 0
\(703\) −5.50000 + 47.6314i −0.207436 + 1.79645i
\(704\) 5.00000 0.188445
\(705\) 0 0
\(706\) −2.00000 + 3.46410i −0.0752710 + 0.130373i
\(707\) 5.00000 + 8.66025i 0.188044 + 0.325702i
\(708\) 0 0
\(709\) −4.00000 6.92820i −0.150223 0.260194i 0.781086 0.624423i \(-0.214666\pi\)
−0.931309 + 0.364229i \(0.881333\pi\)
\(710\) 0 0
\(711\) −30.0000 −1.12509
\(712\) −3.50000 6.06218i −0.131168 0.227190i
\(713\) 2.00000 + 3.46410i 0.0749006 + 0.129732i
\(714\) 0 0
\(715\) 0 0
\(716\) −9.50000 16.4545i −0.355032 0.614933i
\(717\) 0 0
\(718\) 5.00000 + 8.66025i 0.186598 + 0.323198i
\(719\) 24.0000 41.5692i 0.895049 1.55027i 0.0613050 0.998119i \(-0.480474\pi\)
0.833744 0.552151i \(-0.186193\pi\)
\(720\) 0 0
\(721\) 13.0000 0.484145
\(722\) −13.0000 + 13.8564i −0.483810 + 0.515682i
\(723\) 0 0
\(724\) −1.00000 + 1.73205i −0.0371647 + 0.0643712i
\(725\) 0 0
\(726\) 0 0
\(727\) −8.00000 + 13.8564i −0.296704 + 0.513906i −0.975380 0.220532i \(-0.929221\pi\)
0.678676 + 0.734438i \(0.262554\pi\)
\(728\) 1.00000 + 1.73205i 0.0370625 + 0.0641941i
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 15.0000 0.554038 0.277019 0.960864i \(-0.410654\pi\)
0.277019 + 0.960864i \(0.410654\pi\)
\(734\) −4.00000 −0.147643
\(735\) 0 0
\(736\) −0.500000 + 0.866025i −0.0184302 + 0.0319221i
\(737\) 30.0000 + 51.9615i 1.10506 + 1.91403i
\(738\) 13.5000 23.3827i 0.496942 0.860729i
\(739\) 15.5000 26.8468i 0.570177 0.987575i −0.426371 0.904549i \(-0.640208\pi\)
0.996547 0.0830265i \(-0.0264586\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −5.00000 −0.183556
\(743\) −7.50000 + 12.9904i −0.275148 + 0.476571i −0.970173 0.242415i \(-0.922060\pi\)
0.695024 + 0.718986i \(0.255394\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −15.5000 + 26.8468i −0.567495 + 0.982931i
\(747\) −21.0000 36.3731i −0.768350 1.33082i
\(748\) 0 0
\(749\) −4.00000 −0.146157
\(750\) 0 0
\(751\) 10.0000 + 17.3205i 0.364905 + 0.632034i 0.988761 0.149505i \(-0.0477681\pi\)
−0.623856 + 0.781540i \(0.714435\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −6.00000 10.3923i −0.218507 0.378465i
\(755\) 0 0
\(756\) 0 0
\(757\) −7.50000 + 12.9904i −0.272592 + 0.472143i −0.969525 0.244993i \(-0.921214\pi\)
0.696933 + 0.717137i \(0.254548\pi\)
\(758\) −6.00000 + 10.3923i −0.217930 + 0.377466i
\(759\) 0 0
\(760\) 0 0
\(761\) −43.0000 −1.55875 −0.779374 0.626559i \(-0.784463\pi\)
−0.779374 + 0.626559i \(0.784463\pi\)
\(762\) 0 0
\(763\) 2.00000 3.46410i 0.0724049 0.125409i
\(764\) 9.00000 + 15.5885i 0.325609 + 0.563971i
\(765\) 0 0
\(766\) −4.00000 6.92820i −0.144526 0.250326i
\(767\) 0 0
\(768\) 0 0
\(769\) 13.0000 + 22.5167i 0.468792 + 0.811972i 0.999364 0.0356685i \(-0.0113561\pi\)
−0.530572 + 0.847640i \(0.678023\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −4.00000 −0.143963
\(773\) 22.5000 + 38.9711i 0.809269 + 1.40169i 0.913371 + 0.407128i \(0.133470\pi\)
−0.104102 + 0.994567i \(0.533197\pi\)
\(774\) 9.00000 15.5885i 0.323498 0.560316i
\(775\) 0 0
\(776\) 1.00000 1.73205i 0.0358979 0.0621770i
\(777\) 0 0
\(778\) −26.0000 −0.932145
\(779\) 31.5000 + 23.3827i 1.12860 + 0.837772i
\(780\) 0 0
\(781\) −15.0000 + 25.9808i −0.536742 + 0.929665i
\(782\) 0 0
\(783\) 0 0
\(784\) 3.00000 5.19615i 0.107143 0.185577i
\(785\) 0 0
\(786\) 0 0
\(787\) −18.0000 −0.641631 −0.320815 0.947142i \(-0.603957\pi\)
−0.320815 + 0.947142i \(0.603957\pi\)
\(788\) 11.5000 + 19.9186i 0.409671 + 0.709570i
\(789\) 0 0
\(790\) 0 0
\(791\) −12.0000 −0.426671
\(792\) −7.50000 12.9904i −0.266501 0.461593i
\(793\) 0 0
\(794\) −14.5000 25.1147i −0.514586 0.891289i
\(795\) 0