Properties

Label 1050.2.o.d.949.1
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 949.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1050.949
Dual form 1050.2.o.d.499.1

$q$-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 \(-0.756123\pi\)
0.720577 0.693375i \(-0.243877\pi\)
\(14\) −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 0.973123 0.230285i \(-0.0739659\pi\)
0.287129 + 0.957892i \(0.407299\pi\)
\(18\) −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 0.151642 0.988436i \(-0.451544\pi\)
0.931831 + 0.362892i \(0.118211\pi\)
\(24\) −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 −0.569495 0.821995i \(-0.692861\pi\)
0.427121 + 0.904194i \(0.359528\pi\)
\(38\) 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 \(-0.791172\pi\)
0.792406 0.609994i \(-0.208828\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −3.00000 + 5.19615i −0.442326 + 0.766131i
\(47\) 5.19615 3.00000i 0.757937 0.437595i −0.0706177 0.997503i \(-0.522497\pi\)
0.828554 + 0.559908i \(0.189164\pi\)
\(48\) 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 0.0987002 0.995117i \(-0.468532\pi\)
−0.812447 + 0.583036i \(0.801865\pi\)
\(54\) −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 0.991605 0.129307i \(-0.0412752\pi\)
0.383819 + 0.923408i \(0.374609\pi\)
\(68\) 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 0.731519 0.681822i \(-0.238812\pi\)
−0.224716 + 0.974424i \(0.572145\pi\)
\(74\) 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 \(0.450388\pi\)
−0.155230 + 0.987878i \(0.549612\pi\)
\(84\) 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 \(-0.884354\pi\)
0.934725 0.355371i \(-0.115646\pi\)
\(98\) −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 0.170664 0.985329i \(-0.445409\pi\)
0.938652 + 0.344865i \(0.112075\pi\)
\(104\) 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 \(0.669255\pi\)
−0.999967 + 0.00813215i \(0.997411\pi\)
\(108\) 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 \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) 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 \(0.162290\pi\)
−0.872818 + 0.488046i \(0.837710\pi\)
\(128\) 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 0.985577 0.169226i \(-0.0541268\pi\)
0.346235 + 0.938148i \(0.387460\pi\)
\(138\) −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 0.534160 0.845383i \(-0.320628\pi\)
−0.465044 + 0.885288i \(0.653961\pi\)
\(158\) 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 −0.465700 0.884943i \(-0.654198\pi\)
0.533533 + 0.845780i \(0.320864\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −9.00000 15.5885i −0.698535 1.20990i
\(167\) 6.00000i 0.464294i −0.972681 0.232147i \(-0.925425\pi\)
0.972681 0.232147i \(-0.0745750\pi\)
\(168\) −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 −0.957205 0.289412i \(-0.906540\pi\)
−0.227964 + 0.973670i \(0.573207\pi\)
\(174\) 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 0.154805 0.987945i \(-0.450525\pi\)
−0.778183 + 0.628037i \(0.783859\pi\)
\(194\) 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 \(-0.859401\pi\)
0.904024 0.427482i \(-0.140599\pi\)
\(198\) 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 \(-0.807252\pi\)
0.822198 0.569202i \(-0.192748\pi\)
\(224\) 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 0.113761 0.993508i \(-0.463710\pi\)
−0.803523 + 0.595274i \(0.797043\pi\)
\(228\) −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 −0.989843 0.142166i \(-0.954593\pi\)
−0.371802 + 0.928312i \(0.621260\pi\)
\(234\) −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 −0.979799 0.199983i \(-0.935911\pi\)
−0.316709 + 0.948523i \(0.602578\pi\)
\(258\) 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 0.904872 0.425684i \(-0.139967\pi\)
0.0837823 + 0.996484i \(0.473300\pi\)
\(278\) 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 0.623148 0.782104i \(-0.285854\pi\)
−0.365748 + 0.930714i \(0.619187\pi\)
\(284\) 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 \(0.247284\pi\)
−0.713115 + 0.701047i \(0.752716\pi\)
\(294\) −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 \(-0.705351\pi\)
0.601302 0.799022i \(-0.294649\pi\)
\(308\) 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 −0.801852 0.597522i \(-0.796152\pi\)
0.116543 + 0.993186i \(0.462819\pi\)
\(314\) −1.00000 −0.0564333
\(315\) 0 0
\(316\) −7.00000 −0.393781
\(317\) −15.5885 + 9.00000i −0.875535 + 0.505490i −0.869184 0.494489i \(-0.835355\pi\)
−0.00635137 + 0.999980i \(0.502022\pi\)
\(318\) 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 \(-0.623183\pi\)
0.377403 0.926049i \(-0.376817\pi\)
\(338\) 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 0.0193540 0.999813i \(-0.493839\pi\)
−0.856186 + 0.516667i \(0.827172\pi\)
\(348\) 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 −0.168397 0.985719i \(-0.553859\pi\)
−0.937856 + 0.347024i \(0.887192\pi\)
\(354\) 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 0.308155 0.951336i \(-0.400289\pi\)
−0.669804 + 0.742538i \(0.733622\pi\)
\(368\) −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 −0.179364 0.983783i \(-0.557404\pi\)
0.762299 + 0.647225i \(0.224071\pi\)
\(374\) 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 −0.361335 0.932436i \(-0.617679\pi\)
0.626846 + 0.779143i \(0.284346\pi\)
\(384\) 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 −0.163876 0.986481i \(-0.552400\pi\)
0.772380 + 0.635161i \(0.219066\pi\)
\(398\) 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 \(0.304347\pi\)
−0.576683 + 0.816968i \(0.695653\pi\)
\(434\) −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 \(-0.188070\pi\)
0.897664 0.440681i \(-0.145263\pi\)
\(444\) −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 0.220008 0.975498i \(-0.429392\pi\)
0.954810 + 0.297217i \(0.0960584\pi\)
\(458\) −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 \(0.256017\pi\)
−0.693615 + 0.720346i \(0.743983\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 12.0000 20.7846i 0.555889 0.962828i
\(467\) 25.9808 15.0000i 1.20225 0.694117i 0.241192 0.970477i \(-0.422462\pi\)
0.961054 + 0.276360i \(0.0891283\pi\)
\(468\) 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 \(0.0277618\pi\)
0.573535 + 0.819181i \(0.305572\pi\)
\(488\) −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 −0.963150 0.268963i \(-0.913319\pi\)
−0.248646 + 0.968594i \(0.579986\pi\)
\(524\) −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 \(-0.795725\pi\)
0.801050 0.598597i \(-0.204275\pi\)
\(548\) 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 0.703740 0.710457i \(-0.251512\pi\)
−0.263404 + 0.964686i \(0.584845\pi\)
\(558\) 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 0.264758 0.964315i \(-0.414708\pi\)
−0.702742 + 0.711445i \(0.748041\pi\)
\(564\) 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 0.225927 0.974144i \(-0.427459\pi\)
−0.730670 + 0.682730i \(0.760792\pi\)
\(578\) −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 \(-0.787491\pi\)
0.785299 0.619116i \(-0.212509\pi\)
\(588\) 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 −0.389501 0.921026i \(-0.627353\pi\)
0.602881 + 0.797831i \(0.294019\pi\)
\(594\) 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 \(0.670939\pi\)
−0.999910 + 0.0134214i \(0.995728\pi\)
\(608\) 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 0.985173 0.171564i \(-0.0548821\pi\)
0.344008 + 0.938967i \(0.388215\pi\)
\(614\) 14.0000 + 24.2487i 0.564994 + 0.978598i
\(615\) 0 0
\(616\) 0 0
\(617\) 48.0000i 1.93241i 0.257780 + 0.966204i \(0.417009\pi\)
−0.257780 + 0.966204i \(0.582991\pi\)
\(618\) −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 \(-0.930406\pi\)
0.976194 0.216899i \(-0.0695942\pi\)
\(644\) −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 0.690172 0.723645i \(-0.257535\pi\)
−0.281609 + 0.959529i \(0.590868\pi\)
\(648\) −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 0.255119 0.966910i \(-0.417885\pi\)
0.964928 + 0.262515i \(0.0845520\pi\)
\(654\) 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 \(0.00613535\pi\)
−0.999814 + 0.0192736i \(0.993865\pi\)
\(674\) 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 0.403755 0.914867i \(-0.367705\pi\)
0.994176 + 0.107772i \(0.0343715\pi\)
\(678\) 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 0.841825 0.539750i \(-0.181481\pi\)
−0.0465244 + 0.998917i \(0.514815\pi\)
\(684\) −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 \(-0.759309\pi\)
0.727482 0.686127i \(-0.240691\pi\)
\(728\) 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 −0.982342 0.187096i \(-0.940092\pi\)
−0.329141 + 0.944281i \(0.606759\pi\)
\(734\) 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 \(-0.814515\pi\)
0.834969 0.550297i \(-0.185485\pi\)
\(744\) −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 \(0.176688\pi\)
−0.849858 + 0.527011i \(0.823312\pi\)
\(758\) 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 0.101048 0.994882i \(-0.467780\pi\)
−0.811069 + 0.584951i \(0.801114\pi\)
\(788\) −10.3923 6.00000i −0.370211 0.213741i
\(789\)