Properties

Label 1050.2.o.d.949.2
Level $1050$
Weight $2$
Character 1050.949
Analytic conductor $8.384$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 949.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1050.949
Dual form 1050.2.o.d.499.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-2.59808 + 0.500000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-2.59808 + 0.500000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.866025 + 0.500000i) q^{12} +5.00000i q^{13} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-5.19615 - 3.00000i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-3.50000 - 6.06218i) q^{19} +(2.50000 + 0.866025i) q^{21} +(-5.19615 + 3.00000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{26} -1.00000i q^{27} +(-0.866025 + 2.50000i) q^{28} +(-4.00000 + 6.92820i) q^{31} +(-0.866025 - 0.500000i) q^{32} -6.00000 q^{34} +1.00000 q^{36} +(0.866025 - 0.500000i) q^{37} +(-6.06218 - 3.50000i) q^{38} +(2.50000 - 4.33013i) q^{39} +(2.59808 - 0.500000i) q^{42} +8.00000i q^{43} +(-3.00000 + 5.19615i) q^{46} +(-5.19615 + 3.00000i) q^{47} +1.00000i q^{48} +(6.50000 - 2.59808i) q^{49} +(3.00000 + 5.19615i) q^{51} +(4.33013 + 2.50000i) q^{52} +(5.19615 + 3.00000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(0.500000 + 2.59808i) q^{56} +7.00000i q^{57} +(-3.00000 + 5.19615i) q^{59} +(0.500000 + 0.866025i) q^{61} +8.00000i q^{62} +(-1.73205 - 2.00000i) q^{63} -1.00000 q^{64} +(-11.2583 - 6.50000i) q^{67} +(-5.19615 + 3.00000i) q^{68} +6.00000 q^{69} +12.0000 q^{71} +(0.866025 - 0.500000i) q^{72} +(-4.33013 - 2.50000i) q^{73} +(0.500000 - 0.866025i) q^{74} -7.00000 q^{76} -5.00000i q^{78} +(-3.50000 - 6.06218i) q^{79} +(-0.500000 + 0.866025i) q^{81} -18.0000i q^{83} +(2.00000 - 1.73205i) q^{84} +(4.00000 + 6.92820i) q^{86} +(-3.00000 - 5.19615i) q^{89} +(-2.50000 - 12.9904i) q^{91} +6.00000i q^{92} +(6.92820 - 4.00000i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(0.500000 + 0.866025i) q^{96} +7.00000i q^{97} +(4.33013 - 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} - 4q^{6} + 2q^{9} + O(q^{10}) \) \( 4q + 2q^{4} - 4q^{6} + 2q^{9} - 8q^{14} - 2q^{16} - 14q^{19} + 10q^{21} - 2q^{24} + 10q^{26} - 16q^{31} - 24q^{34} + 4q^{36} + 10q^{39} - 12q^{46} + 26q^{49} + 12q^{51} - 2q^{54} + 2q^{56} - 12q^{59} + 2q^{61} - 4q^{64} + 24q^{69} + 48q^{71} + 2q^{74} - 28q^{76} - 14q^{79} - 2q^{81} + 8q^{84} + 16q^{86} - 12q^{89} - 10q^{91} - 12q^{94} + 2q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 0.500000i 0.612372 0.353553i
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) −1.00000 −0.408248
\(7\) −2.59808 + 0.500000i −0.981981 + 0.188982i
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(12\) −0.866025 + 0.500000i −0.250000 + 0.144338i
\(13\) 5.00000i 1.38675i 0.720577 + 0.693375i \(0.243877\pi\)
−0.720577 + 0.693375i \(0.756123\pi\)
\(14\) −2.00000 + 1.73205i −0.534522 + 0.462910i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −5.19615 3.00000i −1.26025 0.727607i −0.287129 0.957892i \(-0.592701\pi\)
−0.973123 + 0.230285i \(0.926034\pi\)
\(18\) 0.866025 + 0.500000i 0.204124 + 0.117851i
\(19\) −3.50000 6.06218i −0.802955 1.39076i −0.917663 0.397360i \(-0.869927\pi\)
0.114708 0.993399i \(-0.463407\pi\)
\(20\) 0 0
\(21\) 2.50000 + 0.866025i 0.545545 + 0.188982i
\(22\) 0 0
\(23\) −5.19615 + 3.00000i −1.08347 + 0.625543i −0.931831 0.362892i \(-0.881789\pi\)
−0.151642 + 0.988436i \(0.548456\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 0 0
\(26\) 2.50000 + 4.33013i 0.490290 + 0.849208i
\(27\) 1.00000i 0.192450i
\(28\) −0.866025 + 2.50000i −0.163663 + 0.472456i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) −4.00000 + 6.92820i −0.718421 + 1.24434i 0.243204 + 0.969975i \(0.421802\pi\)
−0.961625 + 0.274367i \(0.911532\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0 0
\(34\) −6.00000 −1.02899
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 0.866025 0.500000i 0.142374 0.0821995i −0.427121 0.904194i \(-0.640472\pi\)
0.569495 + 0.821995i \(0.307139\pi\)
\(38\) −6.06218 3.50000i −0.983415 0.567775i
\(39\) 2.50000 4.33013i 0.400320 0.693375i
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 2.59808 0.500000i 0.400892 0.0771517i
\(43\) 8.00000i 1.21999i 0.792406 + 0.609994i \(0.208828\pi\)
−0.792406 + 0.609994i \(0.791172\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −3.00000 + 5.19615i −0.442326 + 0.766131i
\(47\) −5.19615 + 3.00000i −0.757937 + 0.437595i −0.828554 0.559908i \(-0.810836\pi\)
0.0706177 + 0.997503i \(0.477503\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 6.50000 2.59808i 0.928571 0.371154i
\(50\) 0 0
\(51\) 3.00000 + 5.19615i 0.420084 + 0.727607i
\(52\) 4.33013 + 2.50000i 0.600481 + 0.346688i
\(53\) 5.19615 + 3.00000i 0.713746 + 0.412082i 0.812447 0.583036i \(-0.198135\pi\)
−0.0987002 + 0.995117i \(0.531468\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 0 0
\(56\) 0.500000 + 2.59808i 0.0668153 + 0.347183i
\(57\) 7.00000i 0.927173i
\(58\) 0 0
\(59\) −3.00000 + 5.19615i −0.390567 + 0.676481i −0.992524 0.122047i \(-0.961054\pi\)
0.601958 + 0.798528i \(0.294388\pi\)
\(60\) 0 0
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) 8.00000i 1.01600i
\(63\) −1.73205 2.00000i −0.218218 0.251976i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −11.2583 6.50000i −1.37542 0.794101i −0.383819 0.923408i \(-0.625391\pi\)
−0.991605 + 0.129307i \(0.958725\pi\)
\(68\) −5.19615 + 3.00000i −0.630126 + 0.363803i
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) −4.33013 2.50000i −0.506803 0.292603i 0.224716 0.974424i \(-0.427855\pi\)
−0.731519 + 0.681822i \(0.761188\pi\)
\(74\) 0.500000 0.866025i 0.0581238 0.100673i
\(75\) 0 0
\(76\) −7.00000 −0.802955
\(77\) 0 0
\(78\) 5.00000i 0.566139i
\(79\) −3.50000 6.06218i −0.393781 0.682048i 0.599164 0.800626i \(-0.295500\pi\)
−0.992945 + 0.118578i \(0.962166\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 18.0000i 1.97576i −0.155230 0.987878i \(-0.549612\pi\)
0.155230 0.987878i \(-0.450388\pi\)
\(84\) 2.00000 1.73205i 0.218218 0.188982i
\(85\) 0 0
\(86\) 4.00000 + 6.92820i 0.431331 + 0.747087i
\(87\) 0 0
\(88\) 0 0
\(89\) −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) 0 0
\(91\) −2.50000 12.9904i −0.262071 1.36176i
\(92\) 6.00000i 0.625543i
\(93\) 6.92820 4.00000i 0.718421 0.414781i
\(94\) −3.00000 + 5.19615i −0.309426 + 0.535942i
\(95\) 0 0
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 7.00000i 0.710742i 0.934725 + 0.355371i \(0.115646\pi\)
−0.934725 + 0.355371i \(0.884354\pi\)
\(98\) 4.33013 5.50000i 0.437409 0.555584i
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 5.19615 + 3.00000i 0.514496 + 0.297044i
\(103\) −11.2583 + 6.50000i −1.10932 + 0.640464i −0.938652 0.344865i \(-0.887925\pi\)
−0.170664 + 0.985329i \(0.554591\pi\)
\(104\) 5.00000 0.490290
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) 15.5885 9.00000i 1.50699 0.870063i 0.507026 0.861931i \(-0.330745\pi\)
0.999967 0.00813215i \(-0.00258857\pi\)
\(108\) −0.866025 0.500000i −0.0833333 0.0481125i
\(109\) −3.50000 + 6.06218i −0.335239 + 0.580651i −0.983531 0.180741i \(-0.942150\pi\)
0.648292 + 0.761392i \(0.275484\pi\)
\(110\) 0 0
\(111\) −1.00000 −0.0949158
\(112\) 1.73205 + 2.00000i 0.163663 + 0.188982i
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) 3.50000 + 6.06218i 0.327805 + 0.567775i
\(115\) 0 0
\(116\) 0 0
\(117\) −4.33013 + 2.50000i −0.400320 + 0.231125i
\(118\) 6.00000i 0.552345i
\(119\) 15.0000 + 5.19615i 1.37505 + 0.476331i
\(120\) 0 0
\(121\) 5.50000 + 9.52628i 0.500000 + 0.866025i
\(122\) 0.866025 + 0.500000i 0.0784063 + 0.0452679i
\(123\) 0 0
\(124\) 4.00000 + 6.92820i 0.359211 + 0.622171i
\(125\) 0 0
\(126\) −2.50000 0.866025i −0.222718 0.0771517i
\(127\) 11.0000i 0.976092i −0.872818 0.488046i \(-0.837710\pi\)
0.872818 0.488046i \(-0.162290\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 4.00000 6.92820i 0.352180 0.609994i
\(130\) 0 0
\(131\) −3.00000 5.19615i −0.262111 0.453990i 0.704692 0.709514i \(-0.251085\pi\)
−0.966803 + 0.255524i \(0.917752\pi\)
\(132\) 0 0
\(133\) 12.1244 + 14.0000i 1.05131 + 1.21395i
\(134\) −13.0000 −1.12303
\(135\) 0 0
\(136\) −3.00000 + 5.19615i −0.257248 + 0.445566i
\(137\) −15.5885 9.00000i −1.33181 0.768922i −0.346235 0.938148i \(-0.612540\pi\)
−0.985577 + 0.169226i \(0.945873\pi\)
\(138\) 5.19615 3.00000i 0.442326 0.255377i
\(139\) −11.0000 −0.933008 −0.466504 0.884519i \(-0.654487\pi\)
−0.466504 + 0.884519i \(0.654487\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 10.3923 6.00000i 0.872103 0.503509i
\(143\) 0 0
\(144\) 0.500000 0.866025i 0.0416667 0.0721688i
\(145\) 0 0
\(146\) −5.00000 −0.413803
\(147\) −6.92820 1.00000i −0.571429 0.0824786i
\(148\) 1.00000i 0.0821995i
\(149\) 6.00000 + 10.3923i 0.491539 + 0.851371i 0.999953 0.00974235i \(-0.00310113\pi\)
−0.508413 + 0.861113i \(0.669768\pi\)
\(150\) 0 0
\(151\) 0.500000 0.866025i 0.0406894 0.0704761i −0.844963 0.534824i \(-0.820378\pi\)
0.885653 + 0.464348i \(0.153711\pi\)
\(152\) −6.06218 + 3.50000i −0.491708 + 0.283887i
\(153\) 6.00000i 0.485071i
\(154\) 0 0
\(155\) 0 0
\(156\) −2.50000 4.33013i −0.200160 0.346688i
\(157\) −0.866025 0.500000i −0.0691164 0.0399043i 0.465044 0.885288i \(-0.346039\pi\)
−0.534160 + 0.845383i \(0.679372\pi\)
\(158\) −6.06218 3.50000i −0.482281 0.278445i
\(159\) −3.00000 5.19615i −0.237915 0.412082i
\(160\) 0 0
\(161\) 12.0000 10.3923i 0.945732 0.819028i
\(162\) 1.00000i 0.0785674i
\(163\) −0.866025 + 0.500000i −0.0678323 + 0.0391630i −0.533533 0.845780i \(-0.679136\pi\)
0.465700 + 0.884943i \(0.345802\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −9.00000 15.5885i −0.698535 1.20990i
\(167\) 6.00000i 0.464294i 0.972681 + 0.232147i \(0.0745750\pi\)
−0.972681 + 0.232147i \(0.925425\pi\)
\(168\) 0.866025 2.50000i 0.0668153 0.192879i
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 3.50000 6.06218i 0.267652 0.463586i
\(172\) 6.92820 + 4.00000i 0.528271 + 0.304997i
\(173\) 15.5885 9.00000i 1.18517 0.684257i 0.227964 0.973670i \(-0.426793\pi\)
0.957205 + 0.289412i \(0.0934598\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 5.19615 3.00000i 0.390567 0.225494i
\(178\) −5.19615 3.00000i −0.389468 0.224860i
\(179\) 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i \(-0.685306\pi\)
0.998286 + 0.0585225i \(0.0186389\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) −8.66025 10.0000i −0.641941 0.741249i
\(183\) 1.00000i 0.0739221i
\(184\) 3.00000 + 5.19615i 0.221163 + 0.383065i
\(185\) 0 0
\(186\) 4.00000 6.92820i 0.293294 0.508001i
\(187\) 0 0
\(188\) 6.00000i 0.437595i
\(189\) 0.500000 + 2.59808i 0.0363696 + 0.188982i
\(190\) 0 0
\(191\) −12.0000 20.7846i −0.868290 1.50392i −0.863743 0.503932i \(-0.831886\pi\)
−0.00454614 0.999990i \(-0.501447\pi\)
\(192\) 0.866025 + 0.500000i 0.0625000 + 0.0360844i
\(193\) 8.66025 + 5.00000i 0.623379 + 0.359908i 0.778183 0.628037i \(-0.216141\pi\)
−0.154805 + 0.987945i \(0.549475\pi\)
\(194\) 3.50000 + 6.06218i 0.251285 + 0.435239i
\(195\) 0 0
\(196\) 1.00000 6.92820i 0.0714286 0.494872i
\(197\) 12.0000i 0.854965i 0.904024 + 0.427482i \(0.140599\pi\)
−0.904024 + 0.427482i \(0.859401\pi\)
\(198\) 0 0
\(199\) 5.50000 9.52628i 0.389885 0.675300i −0.602549 0.798082i \(-0.705848\pi\)
0.992434 + 0.122782i \(0.0391815\pi\)
\(200\) 0 0
\(201\) 6.50000 + 11.2583i 0.458475 + 0.794101i
\(202\) 0 0
\(203\) 0 0
\(204\) 6.00000 0.420084
\(205\) 0 0
\(206\) −6.50000 + 11.2583i −0.452876 + 0.784405i
\(207\) −5.19615 3.00000i −0.361158 0.208514i
\(208\) 4.33013 2.50000i 0.300240 0.173344i
\(209\) 0 0
\(210\) 0 0
\(211\) −13.0000 −0.894957 −0.447478 0.894295i \(-0.647678\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) 5.19615 3.00000i 0.356873 0.206041i
\(213\) −10.3923 6.00000i −0.712069 0.411113i
\(214\) 9.00000 15.5885i 0.615227 1.06561i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 6.92820 20.0000i 0.470317 1.35769i
\(218\) 7.00000i 0.474100i
\(219\) 2.50000 + 4.33013i 0.168934 + 0.292603i
\(220\) 0 0
\(221\) 15.0000 25.9808i 1.00901 1.74766i
\(222\) −0.866025 + 0.500000i −0.0581238 + 0.0335578i
\(223\) 17.0000i 1.13840i 0.822198 + 0.569202i \(0.192748\pi\)
−0.822198 + 0.569202i \(0.807252\pi\)
\(224\) 2.50000 + 0.866025i 0.167038 + 0.0578638i
\(225\) 0 0
\(226\) −3.00000 5.19615i −0.199557 0.345643i
\(227\) 10.3923 + 6.00000i 0.689761 + 0.398234i 0.803523 0.595274i \(-0.202957\pi\)
−0.113761 + 0.993508i \(0.536290\pi\)
\(228\) 6.06218 + 3.50000i 0.401478 + 0.231793i
\(229\) 2.50000 + 4.33013i 0.165205 + 0.286143i 0.936728 0.350058i \(-0.113838\pi\)
−0.771523 + 0.636201i \(0.780505\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 20.7846 12.0000i 1.36165 0.786146i 0.371802 0.928312i \(-0.378740\pi\)
0.989843 + 0.142166i \(0.0454066\pi\)
\(234\) −2.50000 + 4.33013i −0.163430 + 0.283069i
\(235\) 0 0
\(236\) 3.00000 + 5.19615i 0.195283 + 0.338241i
\(237\) 7.00000i 0.454699i
\(238\) 15.5885 3.00000i 1.01045 0.194461i
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0 0
\(241\) −2.50000 + 4.33013i −0.161039 + 0.278928i −0.935242 0.354010i \(-0.884818\pi\)
0.774202 + 0.632938i \(0.218151\pi\)
\(242\) 9.52628 + 5.50000i 0.612372 + 0.353553i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) 1.00000 0.0640184
\(245\) 0 0
\(246\) 0 0
\(247\) 30.3109 17.5000i 1.92864 1.11350i
\(248\) 6.92820 + 4.00000i 0.439941 + 0.254000i
\(249\) −9.00000 + 15.5885i −0.570352 + 0.987878i
\(250\) 0 0
\(251\) −24.0000 −1.51487 −0.757433 0.652913i \(-0.773547\pi\)
−0.757433 + 0.652913i \(0.773547\pi\)
\(252\) −2.59808 + 0.500000i −0.163663 + 0.0314970i
\(253\) 0 0
\(254\) −5.50000 9.52628i −0.345101 0.597732i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 20.7846 12.0000i 1.29651 0.748539i 0.316709 0.948523i \(-0.397422\pi\)
0.979799 + 0.199983i \(0.0640888\pi\)
\(258\) 8.00000i 0.498058i
\(259\) −2.00000 + 1.73205i −0.124274 + 0.107624i
\(260\) 0 0
\(261\) 0 0
\(262\) −5.19615 3.00000i −0.321019 0.185341i
\(263\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 17.5000 + 6.06218i 1.07299 + 0.371696i
\(267\) 6.00000i 0.367194i
\(268\) −11.2583 + 6.50000i −0.687712 + 0.397051i
\(269\) −12.0000 + 20.7846i −0.731653 + 1.26726i 0.224523 + 0.974469i \(0.427917\pi\)
−0.956176 + 0.292791i \(0.905416\pi\)
\(270\) 0 0
\(271\) −10.0000 17.3205i −0.607457 1.05215i −0.991658 0.128897i \(-0.958856\pi\)
0.384201 0.923249i \(-0.374477\pi\)
\(272\) 6.00000i 0.363803i
\(273\) −4.33013 + 12.5000i −0.262071 + 0.756534i
\(274\) −18.0000 −1.08742
\(275\) 0 0
\(276\) 3.00000 5.19615i 0.180579 0.312772i
\(277\) −16.4545 9.50000i −0.988654 0.570800i −0.0837823 0.996484i \(-0.526700\pi\)
−0.904872 + 0.425684i \(0.860033\pi\)
\(278\) −9.52628 + 5.50000i −0.571348 + 0.329868i
\(279\) −8.00000 −0.478947
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 5.19615 3.00000i 0.309426 0.178647i
\(283\) −4.33013 2.50000i −0.257399 0.148610i 0.365748 0.930714i \(-0.380813\pi\)
−0.623148 + 0.782104i \(0.714146\pi\)
\(284\) 6.00000 10.3923i 0.356034 0.616670i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) 9.50000 + 16.4545i 0.558824 + 0.967911i
\(290\) 0 0
\(291\) 3.50000 6.06218i 0.205174 0.355371i
\(292\) −4.33013 + 2.50000i −0.253402 + 0.146301i
\(293\) 24.0000i 1.40209i −0.713115 0.701047i \(-0.752716\pi\)
0.713115 0.701047i \(-0.247284\pi\)
\(294\) −6.50000 + 2.59808i −0.379088 + 0.151523i
\(295\) 0 0
\(296\) −0.500000 0.866025i −0.0290619 0.0503367i
\(297\) 0 0
\(298\) 10.3923 + 6.00000i 0.602010 + 0.347571i
\(299\) −15.0000 25.9808i −0.867472 1.50251i
\(300\) 0 0
\(301\) −4.00000 20.7846i −0.230556 1.19800i
\(302\) 1.00000i 0.0575435i
\(303\) 0 0
\(304\) −3.50000 + 6.06218i −0.200739 + 0.347690i
\(305\) 0 0
\(306\) −3.00000 5.19615i −0.171499 0.297044i
\(307\) 28.0000i 1.59804i 0.601302 + 0.799022i \(0.294649\pi\)
−0.601302 + 0.799022i \(0.705351\pi\)
\(308\) 0 0
\(309\) 13.0000 0.739544
\(310\) 0 0
\(311\) −9.00000 + 15.5885i −0.510343 + 0.883940i 0.489585 + 0.871956i \(0.337148\pi\)
−0.999928 + 0.0119847i \(0.996185\pi\)
\(312\) −4.33013 2.50000i −0.245145 0.141535i
\(313\) 12.1244 7.00000i 0.685309 0.395663i −0.116543 0.993186i \(-0.537181\pi\)
0.801852 + 0.597522i \(0.203848\pi\)
\(314\) −1.00000 −0.0564333
\(315\) 0 0
\(316\) −7.00000 −0.393781
\(317\) 15.5885 9.00000i 0.875535 0.505490i 0.00635137 0.999980i \(-0.497978\pi\)
0.869184 + 0.494489i \(0.164645\pi\)
\(318\) −5.19615 3.00000i −0.291386 0.168232i
\(319\) 0 0
\(320\) 0 0
\(321\) −18.0000 −1.00466
\(322\) 5.19615 15.0000i 0.289570 0.835917i
\(323\) 42.0000i 2.33694i
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) −0.500000 + 0.866025i −0.0276924 + 0.0479647i
\(327\) 6.06218 3.50000i 0.335239 0.193550i
\(328\) 0 0
\(329\) 12.0000 10.3923i 0.661581 0.572946i
\(330\) 0 0
\(331\) 9.50000 + 16.4545i 0.522167 + 0.904420i 0.999667 + 0.0257885i \(0.00820965\pi\)
−0.477500 + 0.878632i \(0.658457\pi\)
\(332\) −15.5885 9.00000i −0.855528 0.493939i
\(333\) 0.866025 + 0.500000i 0.0474579 + 0.0273998i
\(334\) 3.00000 + 5.19615i 0.164153 + 0.284321i
\(335\) 0 0
\(336\) −0.500000 2.59808i −0.0272772 0.141737i
\(337\) 34.0000i 1.85210i 0.377403 + 0.926049i \(0.376817\pi\)
−0.377403 + 0.926049i \(0.623183\pi\)
\(338\) −10.3923 + 6.00000i −0.565267 + 0.326357i
\(339\) −3.00000 + 5.19615i −0.162938 + 0.282216i
\(340\) 0 0
\(341\) 0 0
\(342\) 7.00000i 0.378517i
\(343\) −15.5885 + 10.0000i −0.841698 + 0.539949i
\(344\) 8.00000 0.431331
\(345\) 0 0
\(346\) 9.00000 15.5885i 0.483843 0.838041i
\(347\) 15.5885 + 9.00000i 0.836832 + 0.483145i 0.856186 0.516667i \(-0.172828\pi\)
−0.0193540 + 0.999813i \(0.506161\pi\)
\(348\) 0 0
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 0 0
\(351\) 5.00000 0.266880
\(352\) 0 0
\(353\) 20.7846 + 12.0000i 1.10625 + 0.638696i 0.937856 0.347024i \(-0.112808\pi\)
0.168397 + 0.985719i \(0.446141\pi\)
\(354\) 3.00000 5.19615i 0.159448 0.276172i
\(355\) 0 0
\(356\) −6.00000 −0.317999
\(357\) −10.3923 12.0000i −0.550019 0.635107i
\(358\) 12.0000i 0.634220i
\(359\) 15.0000 + 25.9808i 0.791670 + 1.37121i 0.924932 + 0.380131i \(0.124121\pi\)
−0.133263 + 0.991081i \(0.542545\pi\)
\(360\) 0 0
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) −8.66025 + 5.00000i −0.455173 + 0.262794i
\(363\) 11.0000i 0.577350i
\(364\) −12.5000 4.33013i −0.655178 0.226960i
\(365\) 0 0
\(366\) −0.500000 0.866025i −0.0261354 0.0452679i
\(367\) 6.92820 + 4.00000i 0.361649 + 0.208798i 0.669804 0.742538i \(-0.266378\pi\)
−0.308155 + 0.951336i \(0.599711\pi\)
\(368\) 5.19615 + 3.00000i 0.270868 + 0.156386i
\(369\) 0 0
\(370\) 0 0
\(371\) −15.0000 5.19615i −0.778761 0.269771i
\(372\) 8.00000i 0.414781i
\(373\) −11.2583 + 6.50000i −0.582934 + 0.336557i −0.762299 0.647225i \(-0.775929\pi\)
0.179364 + 0.983783i \(0.442596\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 3.00000 + 5.19615i 0.154713 + 0.267971i
\(377\) 0 0
\(378\) 1.73205 + 2.00000i 0.0890871 + 0.102869i
\(379\) −11.0000 −0.565032 −0.282516 0.959263i \(-0.591169\pi\)
−0.282516 + 0.959263i \(0.591169\pi\)
\(380\) 0 0
\(381\) −5.50000 + 9.52628i −0.281774 + 0.488046i
\(382\) −20.7846 12.0000i −1.06343 0.613973i
\(383\) −5.19615 + 3.00000i −0.265511 + 0.153293i −0.626846 0.779143i \(-0.715654\pi\)
0.361335 + 0.932436i \(0.382321\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 10.0000 0.508987
\(387\) −6.92820 + 4.00000i −0.352180 + 0.203331i
\(388\) 6.06218 + 3.50000i 0.307760 + 0.177686i
\(389\) −6.00000 + 10.3923i −0.304212 + 0.526911i −0.977086 0.212847i \(-0.931726\pi\)
0.672874 + 0.739758i \(0.265060\pi\)
\(390\) 0 0
\(391\) 36.0000 1.82060
\(392\) −2.59808 6.50000i −0.131223 0.328300i
\(393\) 6.00000i 0.302660i
\(394\) 6.00000 + 10.3923i 0.302276 + 0.523557i
\(395\) 0 0
\(396\) 0 0
\(397\) −12.1244 + 7.00000i −0.608504 + 0.351320i −0.772380 0.635161i \(-0.780934\pi\)
0.163876 + 0.986481i \(0.447600\pi\)
\(398\) 11.0000i 0.551380i
\(399\) −3.50000 18.1865i −0.175219 0.910465i
\(400\) 0 0
\(401\) 18.0000 + 31.1769i 0.898877 + 1.55690i 0.828932 + 0.559350i \(0.188949\pi\)
0.0699455 + 0.997551i \(0.477717\pi\)
\(402\) 11.2583 + 6.50000i 0.561514 + 0.324191i
\(403\) −34.6410 20.0000i −1.72559 0.996271i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 5.19615 3.00000i 0.257248 0.148522i
\(409\) 2.50000 4.33013i 0.123617 0.214111i −0.797574 0.603220i \(-0.793884\pi\)
0.921192 + 0.389109i \(0.127217\pi\)
\(410\) 0 0
\(411\) 9.00000 + 15.5885i 0.443937 + 0.768922i
\(412\) 13.0000i 0.640464i
\(413\) 5.19615 15.0000i 0.255686 0.738102i
\(414\) −6.00000 −0.294884
\(415\) 0 0
\(416\) 2.50000 4.33013i 0.122573 0.212302i
\(417\) 9.52628 + 5.50000i 0.466504 + 0.269336i
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 5.00000 0.243685 0.121843 0.992549i \(-0.461120\pi\)
0.121843 + 0.992549i \(0.461120\pi\)
\(422\) −11.2583 + 6.50000i −0.548047 + 0.316415i
\(423\) −5.19615 3.00000i −0.252646 0.145865i
\(424\) 3.00000 5.19615i 0.145693 0.252347i
\(425\) 0 0
\(426\) −12.0000 −0.581402
\(427\) −1.73205 2.00000i −0.0838198 0.0967868i
\(428\) 18.0000i 0.870063i
\(429\) 0 0
\(430\) 0 0
\(431\) 9.00000 15.5885i 0.433515 0.750870i −0.563658 0.826008i \(-0.690607\pi\)
0.997173 + 0.0751385i \(0.0239399\pi\)
\(432\) −0.866025 + 0.500000i −0.0416667 + 0.0240563i
\(433\) 34.0000i 1.63394i −0.576683 0.816968i \(-0.695653\pi\)
0.576683 0.816968i \(-0.304347\pi\)
\(434\) −4.00000 20.7846i −0.192006 0.997693i
\(435\) 0 0
\(436\) 3.50000 + 6.06218i 0.167620 + 0.290326i
\(437\) 36.3731 + 21.0000i 1.73996 + 1.00457i
\(438\) 4.33013 + 2.50000i 0.206901 + 0.119455i
\(439\) 2.50000 + 4.33013i 0.119318 + 0.206666i 0.919498 0.393095i \(-0.128596\pi\)
−0.800179 + 0.599761i \(0.795262\pi\)
\(440\) 0 0
\(441\) 5.50000 + 4.33013i 0.261905 + 0.206197i
\(442\) 30.0000i 1.42695i
\(443\) −36.3731 + 21.0000i −1.72814 + 0.997740i −0.830473 + 0.557059i \(0.811930\pi\)
−0.897664 + 0.440681i \(0.854737\pi\)
\(444\) −0.500000 + 0.866025i −0.0237289 + 0.0410997i
\(445\) 0 0
\(446\) 8.50000 + 14.7224i 0.402487 + 0.697127i
\(447\) 12.0000i 0.567581i
\(448\) 2.59808 0.500000i 0.122748 0.0236228i
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −5.19615 3.00000i −0.244406 0.141108i
\(453\) −0.866025 + 0.500000i −0.0406894 + 0.0234920i
\(454\) 12.0000 0.563188
\(455\) 0 0
\(456\) 7.00000 0.327805
\(457\) −25.1147 + 14.5000i −1.17482 + 0.678281i −0.954810 0.297217i \(-0.903942\pi\)
−0.220008 + 0.975498i \(0.570608\pi\)
\(458\) 4.33013 + 2.50000i 0.202334 + 0.116817i
\(459\) −3.00000 + 5.19615i −0.140028 + 0.242536i
\(460\) 0 0
\(461\) 6.00000 0.279448 0.139724 0.990190i \(-0.455378\pi\)
0.139724 + 0.990190i \(0.455378\pi\)
\(462\) 0 0
\(463\) 31.0000i 1.44069i −0.693615 0.720346i \(-0.743983\pi\)
0.693615 0.720346i \(-0.256017\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 12.0000 20.7846i 0.555889 0.962828i
\(467\) −25.9808 + 15.0000i −1.20225 + 0.694117i −0.961054 0.276360i \(-0.910872\pi\)
−0.241192 + 0.970477i \(0.577538\pi\)
\(468\) 5.00000i 0.231125i
\(469\) 32.5000 + 11.2583i 1.50071 + 0.519861i
\(470\) 0 0
\(471\) 0.500000 + 0.866025i 0.0230388 + 0.0399043i
\(472\) 5.19615 + 3.00000i 0.239172 + 0.138086i
\(473\) 0 0
\(474\) 3.50000 + 6.06218i 0.160760 + 0.278445i
\(475\) 0 0
\(476\) 12.0000 10.3923i 0.550019 0.476331i
\(477\) 6.00000i 0.274721i
\(478\) 10.3923 6.00000i 0.475333 0.274434i
\(479\) 9.00000 15.5885i 0.411220 0.712255i −0.583803 0.811895i \(-0.698436\pi\)
0.995023 + 0.0996406i \(0.0317693\pi\)
\(480\) 0 0
\(481\) 2.50000 + 4.33013i 0.113990 + 0.197437i
\(482\) 5.00000i 0.227744i
\(483\) −15.5885 + 3.00000i −0.709299 + 0.136505i
\(484\) 11.0000 0.500000
\(485\) 0 0
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) −34.6410 20.0000i −1.56973 0.906287i −0.996199 0.0871056i \(-0.972238\pi\)
−0.573535 0.819181i \(-0.694428\pi\)
\(488\) 0.866025 0.500000i 0.0392031 0.0226339i
\(489\) 1.00000 0.0452216
\(490\) 0 0
\(491\) −6.00000 −0.270776 −0.135388 0.990793i \(-0.543228\pi\)
−0.135388 + 0.990793i \(0.543228\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 17.5000 30.3109i 0.787362 1.36375i
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) −31.1769 + 6.00000i −1.39848 + 0.269137i
\(498\) 18.0000i 0.806599i
\(499\) 2.50000 + 4.33013i 0.111915 + 0.193843i 0.916542 0.399937i \(-0.130968\pi\)
−0.804627 + 0.593780i \(0.797635\pi\)
\(500\) 0 0
\(501\) 3.00000 5.19615i 0.134030 0.232147i
\(502\) −20.7846 + 12.0000i −0.927663 + 0.535586i
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) −2.00000 + 1.73205i −0.0890871 + 0.0771517i
\(505\) 0 0
\(506\) 0 0
\(507\) 10.3923 + 6.00000i 0.461538 + 0.266469i
\(508\) −9.52628 5.50000i −0.422660 0.244023i
\(509\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(510\) 0 0
\(511\) 12.5000 + 4.33013i 0.552967 + 0.191554i
\(512\) 1.00000i 0.0441942i
\(513\) −6.06218 + 3.50000i −0.267652 + 0.154529i
\(514\) 12.0000 20.7846i 0.529297 0.916770i
\(515\) 0 0
\(516\) −4.00000 6.92820i −0.176090 0.304997i
\(517\) 0 0
\(518\) −0.866025 + 2.50000i −0.0380510 + 0.109844i
\(519\) −18.0000 −0.790112
\(520\) 0 0
\(521\) −21.0000 + 36.3731i −0.920027 + 1.59353i −0.120656 + 0.992694i \(0.538500\pi\)
−0.799370 + 0.600839i \(0.794833\pi\)
\(522\) 0 0
\(523\) 27.7128 16.0000i 1.21180 0.699631i 0.248646 0.968594i \(-0.420014\pi\)
0.963150 + 0.268963i \(0.0866810\pi\)
\(524\) −6.00000 −0.262111
\(525\) 0 0
\(526\) 0 0
\(527\) 41.5692 24.0000i 1.81078 1.04546i
\(528\) 0 0
\(529\) 6.50000 11.2583i 0.282609 0.489493i
\(530\) 0 0
\(531\) −6.00000 −0.260378
\(532\) 18.1865 3.50000i 0.788486 0.151744i
\(533\) 0 0
\(534\) 3.00000 + 5.19615i 0.129823 + 0.224860i
\(535\) 0 0
\(536\) −6.50000 + 11.2583i −0.280757 + 0.486286i
\(537\) −10.3923 + 6.00000i −0.448461 + 0.258919i
\(538\) 24.0000i 1.03471i
\(539\) 0 0
\(540\) 0 0
\(541\) 21.5000 + 37.2391i 0.924357 + 1.60103i 0.792592 + 0.609753i \(0.208731\pi\)
0.131765 + 0.991281i \(0.457935\pi\)
\(542\) −17.3205 10.0000i −0.743980 0.429537i
\(543\) 8.66025 + 5.00000i 0.371647 + 0.214571i
\(544\) 3.00000 + 5.19615i 0.128624 + 0.222783i
\(545\) 0 0
\(546\) 2.50000 + 12.9904i 0.106990 + 0.555937i
\(547\) 28.0000i 1.19719i 0.801050 + 0.598597i \(0.204275\pi\)
−0.801050 + 0.598597i \(0.795725\pi\)
\(548\) −15.5885 + 9.00000i −0.665906 + 0.384461i
\(549\) −0.500000 + 0.866025i −0.0213395 + 0.0369611i
\(550\) 0 0
\(551\) 0 0
\(552\) 6.00000i 0.255377i
\(553\) 12.1244 + 14.0000i 0.515580 + 0.595341i
\(554\) −19.0000 −0.807233
\(555\) 0 0
\(556\) −5.50000 + 9.52628i −0.233252 + 0.404004i
\(557\) −10.3923 6.00000i −0.440336 0.254228i 0.263404 0.964686i \(-0.415155\pi\)
−0.703740 + 0.710457i \(0.748488\pi\)
\(558\) −6.92820 + 4.00000i −0.293294 + 0.169334i
\(559\) −40.0000 −1.69182
\(560\) 0 0
\(561\) 0 0
\(562\) −15.5885 + 9.00000i −0.657559 + 0.379642i
\(563\) 10.3923 + 6.00000i 0.437983 + 0.252870i 0.702742 0.711445i \(-0.251959\pi\)
−0.264758 + 0.964315i \(0.585292\pi\)
\(564\) 3.00000 5.19615i 0.126323 0.218797i
\(565\) 0 0
\(566\) −5.00000 −0.210166
\(567\) 0.866025 2.50000i 0.0363696 0.104990i
\(568\) 12.0000i 0.503509i
\(569\) −18.0000 31.1769i −0.754599 1.30700i −0.945573 0.325409i \(-0.894498\pi\)
0.190974 0.981595i \(-0.438835\pi\)
\(570\) 0 0
\(571\) −2.50000 + 4.33013i −0.104622 + 0.181210i −0.913584 0.406651i \(-0.866697\pi\)
0.808962 + 0.587861i \(0.200030\pi\)
\(572\) 0 0
\(573\) 24.0000i 1.00261i
\(574\) 0 0
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 12.1244 + 7.00000i 0.504744 + 0.291414i 0.730670 0.682730i \(-0.239208\pi\)
−0.225927 + 0.974144i \(0.572541\pi\)
\(578\) 16.4545 + 9.50000i 0.684416 + 0.395148i
\(579\) −5.00000 8.66025i −0.207793 0.359908i
\(580\) 0 0
\(581\) 9.00000 + 46.7654i 0.373383 + 1.94015i
\(582\) 7.00000i 0.290159i
\(583\) 0 0
\(584\) −2.50000 + 4.33013i −0.103451 + 0.179182i
\(585\) 0 0
\(586\) −12.0000 20.7846i −0.495715 0.858604i
\(587\) 30.0000i 1.23823i 0.785299 + 0.619116i \(0.212509\pi\)
−0.785299 + 0.619116i \(0.787491\pi\)
\(588\) −4.33013 + 5.50000i −0.178571 + 0.226816i
\(589\) 56.0000 2.30744
\(590\) 0 0
\(591\) 6.00000 10.3923i 0.246807 0.427482i
\(592\) −0.866025 0.500000i −0.0355934 0.0205499i
\(593\) −5.19615 + 3.00000i −0.213380 + 0.123195i −0.602881 0.797831i \(-0.705981\pi\)
0.389501 + 0.921026i \(0.372647\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 12.0000 0.491539
\(597\) −9.52628 + 5.50000i −0.389885 + 0.225100i
\(598\) −25.9808 15.0000i −1.06243 0.613396i
\(599\) −15.0000 + 25.9808i −0.612883 + 1.06155i 0.377869 + 0.925859i \(0.376657\pi\)
−0.990752 + 0.135686i \(0.956676\pi\)
\(600\) 0 0
\(601\) 35.0000 1.42768 0.713840 0.700309i \(-0.246954\pi\)
0.713840 + 0.700309i \(0.246954\pi\)
\(602\) −13.8564 16.0000i −0.564745 0.652111i
\(603\) 13.0000i 0.529401i
\(604\) −0.500000 0.866025i −0.0203447 0.0352381i
\(605\) 0 0
\(606\) 0 0
\(607\) 37.2391 21.5000i 1.51149 0.872658i 0.511578 0.859237i \(-0.329061\pi\)
0.999910 0.0134214i \(-0.00427228\pi\)
\(608\) 7.00000i 0.283887i
\(609\) 0 0
\(610\) 0 0
\(611\) −15.0000 25.9808i −0.606835 1.05107i
\(612\) −5.19615 3.00000i −0.210042 0.121268i
\(613\) −32.9090 19.0000i −1.32918 0.767403i −0.344008 0.938967i \(-0.611785\pi\)
−0.985173 + 0.171564i \(0.945118\pi\)
\(614\) 14.0000 + 24.2487i 0.564994 + 0.978598i
\(615\) 0 0
\(616\) 0 0
\(617\) 48.0000i 1.93241i −0.257780 0.966204i \(-0.582991\pi\)
0.257780 0.966204i \(-0.417009\pi\)
\(618\) 11.2583 6.50000i 0.452876 0.261468i
\(619\) 10.0000 17.3205i 0.401934 0.696170i −0.592025 0.805919i \(-0.701671\pi\)
0.993959 + 0.109749i \(0.0350048\pi\)
\(620\) 0 0
\(621\) 3.00000 + 5.19615i 0.120386 + 0.208514i
\(622\) 18.0000i 0.721734i
\(623\) 10.3923 + 12.0000i 0.416359 + 0.480770i
\(624\) −5.00000 −0.200160
\(625\) 0 0
\(626\) 7.00000 12.1244i 0.279776 0.484587i
\(627\) 0 0
\(628\) −0.866025 + 0.500000i −0.0345582 + 0.0199522i
\(629\) −6.00000 −0.239236
\(630\) 0 0
\(631\) −19.0000 −0.756378 −0.378189 0.925728i \(-0.623453\pi\)
−0.378189 + 0.925728i \(0.623453\pi\)
\(632\) −6.06218 + 3.50000i −0.241140 + 0.139223i
\(633\) 11.2583 + 6.50000i 0.447478 + 0.258352i
\(634\) 9.00000 15.5885i 0.357436 0.619097i
\(635\) 0 0
\(636\) −6.00000 −0.237915
\(637\) 12.9904 + 32.5000i 0.514698 + 1.28770i
\(638\) 0 0
\(639\) 6.00000 + 10.3923i 0.237356 + 0.411113i
\(640\) 0 0
\(641\) 12.0000 20.7846i 0.473972 0.820943i −0.525584 0.850741i \(-0.676153\pi\)
0.999556 + 0.0297987i \(0.00948663\pi\)
\(642\) −15.5885 + 9.00000i −0.615227 + 0.355202i
\(643\) 11.0000i 0.433798i 0.976194 + 0.216899i \(0.0695942\pi\)
−0.976194 + 0.216899i \(0.930406\pi\)
\(644\) −3.00000 15.5885i −0.118217 0.614271i
\(645\) 0 0
\(646\) 21.0000 + 36.3731i 0.826234 + 1.43108i
\(647\) −10.3923 6.00000i −0.408564 0.235884i 0.281609 0.959529i \(-0.409132\pi\)
−0.690172 + 0.723645i \(0.742465\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) 0 0
\(650\) 0 0
\(651\) −16.0000 + 13.8564i −0.627089 + 0.543075i
\(652\) 1.00000i 0.0391630i
\(653\) −31.1769 + 18.0000i −1.22005 + 0.704394i −0.964928 0.262515i \(-0.915448\pi\)
−0.255119 + 0.966910i \(0.582115\pi\)
\(654\) 3.50000 6.06218i 0.136861 0.237050i
\(655\) 0 0
\(656\) 0 0
\(657\) 5.00000i 0.195069i
\(658\) 5.19615 15.0000i 0.202567 0.584761i
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −17.5000 + 30.3109i −0.680671 + 1.17896i 0.294105 + 0.955773i \(0.404978\pi\)
−0.974776 + 0.223184i \(0.928355\pi\)
\(662\) 16.4545 + 9.50000i 0.639522 + 0.369228i
\(663\) −25.9808 + 15.0000i −1.00901 + 0.582552i
\(664\) −18.0000 −0.698535
\(665\) 0 0
\(666\) 1.00000 0.0387492
\(667\) 0 0
\(668\) 5.19615 + 3.00000i 0.201045 + 0.116073i
\(669\) 8.50000 14.7224i 0.328629 0.569202i
\(670\) 0 0
\(671\) 0 0
\(672\) −1.73205 2.00000i −0.0668153 0.0771517i
\(673\) 1.00000i 0.0385472i −0.999814 0.0192736i \(-0.993865\pi\)
0.999814 0.0192736i \(-0.00613535\pi\)
\(674\) 17.0000 + 29.4449i 0.654816 + 1.13417i
\(675\) 0 0
\(676\) −6.00000 + 10.3923i −0.230769 + 0.399704i
\(677\) −36.3731 + 21.0000i −1.39793 + 0.807096i −0.994176 0.107772i \(-0.965628\pi\)
−0.403755 + 0.914867i \(0.632295\pi\)
\(678\) 6.00000i 0.230429i
\(679\) −3.50000 18.1865i −0.134318 0.697935i
\(680\) 0 0
\(681\) −6.00000 10.3923i −0.229920 0.398234i
\(682\) 0 0
\(683\) −20.7846 12.0000i −0.795301 0.459167i 0.0465244 0.998917i \(-0.485185\pi\)
−0.841825 + 0.539750i \(0.818519\pi\)
\(684\) −3.50000 6.06218i −0.133826 0.231793i
\(685\) 0 0
\(686\) −8.50000 + 16.4545i −0.324532 + 0.628235i
\(687\) 5.00000i 0.190762i
\(688\) 6.92820 4.00000i 0.264135 0.152499i
\(689\) −15.0000 + 25.9808i −0.571454 + 0.989788i
\(690\) 0 0
\(691\) 3.50000 + 6.06218i 0.133146 + 0.230616i 0.924888 0.380240i \(-0.124159\pi\)
−0.791742 + 0.610856i \(0.790825\pi\)
\(692\) 18.0000i 0.684257i
\(693\) 0 0
\(694\) 18.0000 0.683271
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −22.5167 + 13.0000i −0.852268 + 0.492057i
\(699\) −24.0000 −0.907763
\(700\) 0 0
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 4.33013 2.50000i 0.163430 0.0943564i
\(703\) −6.06218 3.50000i −0.228639 0.132005i
\(704\) 0 0
\(705\) 0 0
\(706\) 24.0000 0.903252
\(707\) 0 0
\(708\) 6.00000i 0.225494i
\(709\) −3.50000 6.06218i −0.131445 0.227670i 0.792789 0.609497i \(-0.208628\pi\)
−0.924234 + 0.381827i \(0.875295\pi\)
\(710\) 0 0
\(711\) 3.50000 6.06218i 0.131260 0.227349i
\(712\) −5.19615 + 3.00000i −0.194734 + 0.112430i
\(713\) 48.0000i 1.79761i
\(714\) −15.0000 5.19615i −0.561361 0.194461i
\(715\) 0 0
\(716\) −6.00000 10.3923i −0.224231 0.388379i
\(717\) −10.3923 6.00000i −0.388108 0.224074i
\(718\) 25.9808 + 15.0000i 0.969593 + 0.559795i
\(719\) −18.0000 31.1769i −0.671287 1.16270i −0.977539 0.210752i \(-0.932409\pi\)
0.306253 0.951950i \(-0.400925\pi\)
\(720\) 0 0
\(721\) 26.0000 22.5167i 0.968291 0.838564i
\(722\) 30.0000i 1.11648i
\(723\) 4.33013 2.50000i 0.161039 0.0929760i
\(724\) −5.00000 + 8.66025i −0.185824 + 0.321856i
\(725\) 0 0
\(726\) −5.50000 9.52628i −0.204124 0.353553i
\(727\) 37.0000i 1.37225i 0.727482 + 0.686127i \(0.240691\pi\)
−0.727482 + 0.686127i \(0.759309\pi\)
\(728\) −12.9904 + 2.50000i −0.481456 + 0.0926562i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 24.0000 41.5692i 0.887672 1.53749i
\(732\) −0.866025 0.500000i −0.0320092 0.0184805i
\(733\) 35.5070 20.5000i 1.31148 0.757185i 0.329141 0.944281i \(-0.393241\pi\)
0.982342 + 0.187096i \(0.0599076\pi\)
\(734\) 8.00000 0.295285
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) 0 0
\(738\) 0 0
\(739\) −12.5000 + 21.6506i −0.459820 + 0.796431i −0.998951 0.0457903i \(-0.985419\pi\)
0.539131 + 0.842222i \(0.318753\pi\)
\(740\) 0 0
\(741\) −35.0000 −1.28576
\(742\) −15.5885 + 3.00000i −0.572270 + 0.110133i
\(743\) 30.0000i 1.10059i 0.834969 + 0.550297i \(0.185485\pi\)
−0.834969 + 0.550297i \(0.814515\pi\)
\(744\) −4.00000 6.92820i −0.146647 0.254000i
\(745\) 0 0
\(746\) −6.50000 + 11.2583i −0.237982 + 0.412197i
\(747\) 15.5885 9.00000i 0.570352 0.329293i
\(748\) 0 0
\(749\) −36.0000 + 31.1769i −1.31541 + 1.13918i
\(750\) 0 0
\(751\) 12.5000 + 21.6506i 0.456131 + 0.790043i 0.998752 0.0499348i \(-0.0159013\pi\)
−0.542621 + 0.839978i \(0.682568\pi\)
\(752\) 5.19615 + 3.00000i 0.189484 + 0.109399i
\(753\) 20.7846 + 12.0000i 0.757433 + 0.437304i
\(754\) 0 0
\(755\) 0 0
\(756\) 2.50000 + 0.866025i 0.0909241 + 0.0314970i
\(757\) 29.0000i 1.05402i −0.849858 0.527011i \(-0.823312\pi\)
0.849858 0.527011i \(-0.176688\pi\)
\(758\) −9.52628 + 5.50000i −0.346010 + 0.199769i
\(759\) 0 0
\(760\) 0 0
\(761\) −9.00000 15.5885i −0.326250 0.565081i 0.655515 0.755182i \(-0.272452\pi\)
−0.981764 + 0.190101i \(0.939118\pi\)
\(762\) 11.0000i 0.398488i
\(763\) 6.06218 17.5000i 0.219466 0.633543i
\(764\) −24.0000 −0.868290
\(765\) 0 0
\(766\) −3.00000 + 5.19615i −0.108394 + 0.187745i
\(767\) −25.9808 15.0000i −0.938111 0.541619i
\(768\) 0.866025 0.500000i 0.0312500 0.0180422i
\(769\) 10.0000 0.360609 0.180305 0.983611i \(-0.442292\pi\)
0.180305 + 0.983611i \(0.442292\pi\)
\(770\) 0 0
\(771\) −24.0000 −0.864339
\(772\) 8.66025 5.00000i 0.311689 0.179954i
\(773\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(774\) −4.00000 + 6.92820i −0.143777 + 0.249029i
\(775\) 0 0
\(776\) 7.00000 0.251285
\(777\) 2.59808 0.500000i 0.0932055 0.0179374i
\(778\) 12.0000i 0.430221i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 31.1769 18.0000i 1.11488 0.643679i
\(783\) 0 0
\(784\) −5.50000 4.33013i −0.196429 0.154647i
\(785\) 0 0
\(786\) 3.00000 + 5.19615i 0.107006 + 0.185341i
\(787\) 19.9186 + 11.5000i 0.710021 + 0.409931i 0.811069 0.584951i \(-0.198886\pi\)
−0.101048 + 0.994882i \(0.532220\pi\)
\(788\) 10.3923 + 6.00000i 0.370211 + 0.213741i
\(789\)