Properties

Label 630.2.t.a.311.2
Level 630
Weight 2
Character 630.311
Analytic conductor 5.031
Analytic rank 0
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.03057532734\)
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 311.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 630.311
Dual form 630.2.t.a.551.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 - 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 - 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-0.866025 - 0.500000i) q^{10} -1.26795i q^{11} +1.73205 q^{12} +(3.00000 + 1.73205i) q^{13} +(1.73205 - 2.00000i) q^{14} +(-0.866025 + 1.50000i) q^{15} +(-0.500000 + 0.866025i) q^{16} -3.00000i q^{18} +(4.09808 - 2.36603i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-3.46410 - 3.00000i) q^{21} +(0.633975 - 1.09808i) q^{22} -9.46410i q^{23} +(1.50000 + 0.866025i) q^{24} +1.00000 q^{25} +(1.73205 + 3.00000i) q^{26} -5.19615 q^{27} +(2.50000 - 0.866025i) q^{28} +(-0.401924 + 0.232051i) q^{29} +(-1.50000 + 0.866025i) q^{30} +(-1.90192 + 1.09808i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.90192 - 1.09808i) q^{33} +(-0.500000 + 2.59808i) q^{35} +(1.50000 - 2.59808i) q^{36} +(2.09808 + 3.63397i) q^{37} +4.73205 q^{38} +(5.19615 - 3.00000i) q^{39} -1.00000i q^{40} +(-4.50000 + 7.79423i) q^{41} +(-1.50000 - 4.33013i) q^{42} +(3.59808 + 6.23205i) q^{43} +(1.09808 - 0.633975i) q^{44} +(1.50000 + 2.59808i) q^{45} +(4.73205 - 8.19615i) q^{46} +(-4.50000 + 7.79423i) q^{47} +(0.866025 + 1.50000i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(0.866025 + 0.500000i) q^{50} +3.46410i q^{52} +(9.29423 + 5.36603i) q^{53} +(-4.50000 - 2.59808i) q^{54} +1.26795i q^{55} +(2.59808 + 0.500000i) q^{56} -8.19615i q^{57} -0.464102 q^{58} +(-4.09808 - 7.09808i) q^{59} -1.73205 q^{60} +(0.803848 + 0.464102i) q^{61} -2.19615 q^{62} +(-7.50000 + 2.59808i) q^{63} -1.00000 q^{64} +(-3.00000 - 1.73205i) q^{65} +(-1.09808 - 1.90192i) q^{66} +(2.00000 + 3.46410i) q^{67} +(-14.1962 - 8.19615i) q^{69} +(-1.73205 + 2.00000i) q^{70} +1.26795i q^{71} +(2.59808 - 1.50000i) q^{72} +(6.00000 + 3.46410i) q^{73} +4.19615i q^{74} +(0.866025 - 1.50000i) q^{75} +(4.09808 + 2.36603i) q^{76} +(-3.29423 - 0.633975i) q^{77} +6.00000 q^{78} +(8.29423 - 14.3660i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-7.79423 + 4.50000i) q^{82} +(0.401924 + 0.696152i) q^{83} +(0.866025 - 4.50000i) q^{84} +7.19615i q^{86} +0.803848i q^{87} +1.26795 q^{88} +(8.19615 + 14.1962i) q^{89} +3.00000i q^{90} +(6.00000 - 6.92820i) q^{91} +(8.19615 - 4.73205i) q^{92} +3.80385i q^{93} +(-7.79423 + 4.50000i) q^{94} +(-4.09808 + 2.36603i) q^{95} +1.73205i q^{96} +(-13.3923 + 7.73205i) q^{97} +(-4.33013 - 5.50000i) q^{98} +(-3.29423 + 1.90192i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} - 4q^{5} + 6q^{6} + 2q^{7} - 6q^{9} + O(q^{10}) \) \( 4q + 2q^{4} - 4q^{5} + 6q^{6} + 2q^{7} - 6q^{9} + 12q^{13} - 2q^{16} + 6q^{19} - 2q^{20} + 6q^{22} + 6q^{24} + 4q^{25} + 10q^{28} - 12q^{29} - 6q^{30} - 18q^{31} - 18q^{33} - 2q^{35} + 6q^{36} - 2q^{37} + 12q^{38} - 18q^{41} - 6q^{42} + 4q^{43} - 6q^{44} + 6q^{45} + 12q^{46} - 18q^{47} - 26q^{49} + 6q^{53} - 18q^{54} + 12q^{58} - 6q^{59} + 24q^{61} + 12q^{62} - 30q^{63} - 4q^{64} - 12q^{65} + 6q^{66} + 8q^{67} - 36q^{69} + 24q^{73} + 6q^{76} + 18q^{77} + 24q^{78} + 2q^{79} + 2q^{80} - 18q^{81} + 12q^{83} + 12q^{88} + 12q^{89} + 24q^{91} + 12q^{92} - 6q^{95} - 12q^{97} + 18q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0.866025 1.50000i 0.500000 0.866025i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −1.00000 −0.447214
\(6\) 1.50000 0.866025i 0.612372 0.353553i
\(7\) 0.500000 2.59808i 0.188982 0.981981i
\(8\) 1.00000i 0.353553i
\(9\) −1.50000 2.59808i −0.500000 0.866025i
\(10\) −0.866025 0.500000i −0.273861 0.158114i
\(11\) 1.26795i 0.382301i −0.981561 0.191151i \(-0.938778\pi\)
0.981561 0.191151i \(-0.0612219\pi\)
\(12\) 1.73205 0.500000
\(13\) 3.00000 + 1.73205i 0.832050 + 0.480384i 0.854554 0.519362i \(-0.173830\pi\)
−0.0225039 + 0.999747i \(0.507164\pi\)
\(14\) 1.73205 2.00000i 0.462910 0.534522i
\(15\) −0.866025 + 1.50000i −0.223607 + 0.387298i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 3.00000i 0.707107i
\(19\) 4.09808 2.36603i 0.940163 0.542803i 0.0501517 0.998742i \(-0.484030\pi\)
0.890011 + 0.455938i \(0.150696\pi\)
\(20\) −0.500000 0.866025i −0.111803 0.193649i
\(21\) −3.46410 3.00000i −0.755929 0.654654i
\(22\) 0.633975 1.09808i 0.135164 0.234111i
\(23\) 9.46410i 1.97340i −0.162547 0.986701i \(-0.551971\pi\)
0.162547 0.986701i \(-0.448029\pi\)
\(24\) 1.50000 + 0.866025i 0.306186 + 0.176777i
\(25\) 1.00000 0.200000
\(26\) 1.73205 + 3.00000i 0.339683 + 0.588348i
\(27\) −5.19615 −1.00000
\(28\) 2.50000 0.866025i 0.472456 0.163663i
\(29\) −0.401924 + 0.232051i −0.0746354 + 0.0430908i −0.536853 0.843676i \(-0.680387\pi\)
0.462218 + 0.886766i \(0.347054\pi\)
\(30\) −1.50000 + 0.866025i −0.273861 + 0.158114i
\(31\) −1.90192 + 1.09808i −0.341596 + 0.197220i −0.660977 0.750406i \(-0.729858\pi\)
0.319382 + 0.947626i \(0.396525\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) −1.90192 1.09808i −0.331082 0.191151i
\(34\) 0 0
\(35\) −0.500000 + 2.59808i −0.0845154 + 0.439155i
\(36\) 1.50000 2.59808i 0.250000 0.433013i
\(37\) 2.09808 + 3.63397i 0.344922 + 0.597422i 0.985340 0.170605i \(-0.0545722\pi\)
−0.640418 + 0.768027i \(0.721239\pi\)
\(38\) 4.73205 0.767640
\(39\) 5.19615 3.00000i 0.832050 0.480384i
\(40\) 1.00000i 0.158114i
\(41\) −4.50000 + 7.79423i −0.702782 + 1.21725i 0.264704 + 0.964330i \(0.414726\pi\)
−0.967486 + 0.252924i \(0.918608\pi\)
\(42\) −1.50000 4.33013i −0.231455 0.668153i
\(43\) 3.59808 + 6.23205i 0.548701 + 0.950379i 0.998364 + 0.0571802i \(0.0182110\pi\)
−0.449662 + 0.893199i \(0.648456\pi\)
\(44\) 1.09808 0.633975i 0.165541 0.0955753i
\(45\) 1.50000 + 2.59808i 0.223607 + 0.387298i
\(46\) 4.73205 8.19615i 0.697703 1.20846i
\(47\) −4.50000 + 7.79423i −0.656392 + 1.13691i 0.325150 + 0.945662i \(0.394585\pi\)
−0.981543 + 0.191243i \(0.938748\pi\)
\(48\) 0.866025 + 1.50000i 0.125000 + 0.216506i
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) 0.866025 + 0.500000i 0.122474 + 0.0707107i
\(51\) 0 0
\(52\) 3.46410i 0.480384i
\(53\) 9.29423 + 5.36603i 1.27666 + 0.737080i 0.976233 0.216724i \(-0.0695373\pi\)
0.300428 + 0.953805i \(0.402871\pi\)
\(54\) −4.50000 2.59808i −0.612372 0.353553i
\(55\) 1.26795i 0.170970i
\(56\) 2.59808 + 0.500000i 0.347183 + 0.0668153i
\(57\) 8.19615i 1.08561i
\(58\) −0.464102 −0.0609395
\(59\) −4.09808 7.09808i −0.533524 0.924091i −0.999233 0.0391530i \(-0.987534\pi\)
0.465709 0.884938i \(-0.345799\pi\)
\(60\) −1.73205 −0.223607
\(61\) 0.803848 + 0.464102i 0.102922 + 0.0594221i 0.550578 0.834784i \(-0.314408\pi\)
−0.447655 + 0.894206i \(0.647741\pi\)
\(62\) −2.19615 −0.278912
\(63\) −7.50000 + 2.59808i −0.944911 + 0.327327i
\(64\) −1.00000 −0.125000
\(65\) −3.00000 1.73205i −0.372104 0.214834i
\(66\) −1.09808 1.90192i −0.135164 0.234111i
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) 0 0
\(69\) −14.1962 8.19615i −1.70902 0.986701i
\(70\) −1.73205 + 2.00000i −0.207020 + 0.239046i
\(71\) 1.26795i 0.150478i 0.997166 + 0.0752389i \(0.0239720\pi\)
−0.997166 + 0.0752389i \(0.976028\pi\)
\(72\) 2.59808 1.50000i 0.306186 0.176777i
\(73\) 6.00000 + 3.46410i 0.702247 + 0.405442i 0.808184 0.588930i \(-0.200451\pi\)
−0.105937 + 0.994373i \(0.533784\pi\)
\(74\) 4.19615i 0.487793i
\(75\) 0.866025 1.50000i 0.100000 0.173205i
\(76\) 4.09808 + 2.36603i 0.470082 + 0.271402i
\(77\) −3.29423 0.633975i −0.375412 0.0722481i
\(78\) 6.00000 0.679366
\(79\) 8.29423 14.3660i 0.933174 1.61630i 0.155315 0.987865i \(-0.450361\pi\)
0.777859 0.628439i \(-0.216306\pi\)
\(80\) 0.500000 0.866025i 0.0559017 0.0968246i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) −7.79423 + 4.50000i −0.860729 + 0.496942i
\(83\) 0.401924 + 0.696152i 0.0441169 + 0.0764127i 0.887241 0.461307i \(-0.152619\pi\)
−0.843124 + 0.537720i \(0.819286\pi\)
\(84\) 0.866025 4.50000i 0.0944911 0.490990i
\(85\) 0 0
\(86\) 7.19615i 0.775981i
\(87\) 0.803848i 0.0861815i
\(88\) 1.26795 0.135164
\(89\) 8.19615 + 14.1962i 0.868790 + 1.50479i 0.863234 + 0.504805i \(0.168435\pi\)
0.00555677 + 0.999985i \(0.498231\pi\)
\(90\) 3.00000i 0.316228i
\(91\) 6.00000 6.92820i 0.628971 0.726273i
\(92\) 8.19615 4.73205i 0.854508 0.493350i
\(93\) 3.80385i 0.394441i
\(94\) −7.79423 + 4.50000i −0.803913 + 0.464140i
\(95\) −4.09808 + 2.36603i −0.420454 + 0.242749i
\(96\) 1.73205i 0.176777i
\(97\) −13.3923 + 7.73205i −1.35978 + 0.785071i −0.989594 0.143886i \(-0.954040\pi\)
−0.370188 + 0.928957i \(0.620707\pi\)
\(98\) −4.33013 5.50000i −0.437409 0.555584i
\(99\) −3.29423 + 1.90192i −0.331082 + 0.191151i
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) −0.803848 −0.0799858 −0.0399929 0.999200i \(-0.512734\pi\)
−0.0399929 + 0.999200i \(0.512734\pi\)
\(102\) 0 0
\(103\) 12.1244i 1.19465i 0.802000 + 0.597324i \(0.203769\pi\)
−0.802000 + 0.597324i \(0.796231\pi\)
\(104\) −1.73205 + 3.00000i −0.169842 + 0.294174i
\(105\) 3.46410 + 3.00000i 0.338062 + 0.292770i
\(106\) 5.36603 + 9.29423i 0.521194 + 0.902735i
\(107\) −1.79423 + 1.03590i −0.173455 + 0.100144i −0.584214 0.811600i \(-0.698597\pi\)
0.410759 + 0.911744i \(0.365264\pi\)
\(108\) −2.59808 4.50000i −0.250000 0.433013i
\(109\) −1.59808 + 2.76795i −0.153068 + 0.265121i −0.932354 0.361547i \(-0.882249\pi\)
0.779286 + 0.626669i \(0.215582\pi\)
\(110\) −0.633975 + 1.09808i −0.0604471 + 0.104697i
\(111\) 7.26795 0.689843
\(112\) 2.00000 + 1.73205i 0.188982 + 0.163663i
\(113\) −16.0981 9.29423i −1.51438 0.874327i −0.999858 0.0168501i \(-0.994636\pi\)
−0.514522 0.857477i \(-0.672030\pi\)
\(114\) 4.09808 7.09808i 0.383820 0.664796i
\(115\) 9.46410i 0.882532i
\(116\) −0.401924 0.232051i −0.0373177 0.0215454i
\(117\) 10.3923i 0.960769i
\(118\) 8.19615i 0.754517i
\(119\) 0 0
\(120\) −1.50000 0.866025i −0.136931 0.0790569i
\(121\) 9.39230 0.853846
\(122\) 0.464102 + 0.803848i 0.0420178 + 0.0727769i
\(123\) 7.79423 + 13.5000i 0.702782 + 1.21725i
\(124\) −1.90192 1.09808i −0.170798 0.0986102i
\(125\) −1.00000 −0.0894427
\(126\) −7.79423 1.50000i −0.694365 0.133631i
\(127\) 9.39230 0.833432 0.416716 0.909037i \(-0.363181\pi\)
0.416716 + 0.909037i \(0.363181\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 12.4641 1.09740
\(130\) −1.73205 3.00000i −0.151911 0.263117i
\(131\) −16.3923 −1.43220 −0.716101 0.697997i \(-0.754075\pi\)
−0.716101 + 0.697997i \(0.754075\pi\)
\(132\) 2.19615i 0.191151i
\(133\) −4.09808 11.8301i −0.355348 1.02580i
\(134\) 4.00000i 0.345547i
\(135\) 5.19615 0.447214
\(136\) 0 0
\(137\) 10.7321i 0.916901i 0.888720 + 0.458450i \(0.151595\pi\)
−0.888720 + 0.458450i \(0.848405\pi\)
\(138\) −8.19615 14.1962i −0.697703 1.20846i
\(139\) 13.9019 + 8.02628i 1.17915 + 0.680780i 0.955817 0.293963i \(-0.0949742\pi\)
0.223329 + 0.974743i \(0.428308\pi\)
\(140\) −2.50000 + 0.866025i −0.211289 + 0.0731925i
\(141\) 7.79423 + 13.5000i 0.656392 + 1.13691i
\(142\) −0.633975 + 1.09808i −0.0532020 + 0.0921485i
\(143\) 2.19615 3.80385i 0.183651 0.318094i
\(144\) 3.00000 0.250000
\(145\) 0.401924 0.232051i 0.0333780 0.0192708i
\(146\) 3.46410 + 6.00000i 0.286691 + 0.496564i
\(147\) −9.52628 + 7.50000i −0.785714 + 0.618590i
\(148\) −2.09808 + 3.63397i −0.172461 + 0.298711i
\(149\) 12.0000i 0.983078i −0.870855 0.491539i \(-0.836434\pi\)
0.870855 0.491539i \(-0.163566\pi\)
\(150\) 1.50000 0.866025i 0.122474 0.0707107i
\(151\) 6.19615 0.504236 0.252118 0.967697i \(-0.418873\pi\)
0.252118 + 0.967697i \(0.418873\pi\)
\(152\) 2.36603 + 4.09808i 0.191910 + 0.332398i
\(153\) 0 0
\(154\) −2.53590 2.19615i −0.204349 0.176971i
\(155\) 1.90192 1.09808i 0.152766 0.0881996i
\(156\) 5.19615 + 3.00000i 0.416025 + 0.240192i
\(157\) 0.294229 0.169873i 0.0234820 0.0135573i −0.488213 0.872724i \(-0.662351\pi\)
0.511695 + 0.859167i \(0.329018\pi\)
\(158\) 14.3660 8.29423i 1.14290 0.659853i
\(159\) 16.0981 9.29423i 1.27666 0.737080i
\(160\) 0.866025 0.500000i 0.0684653 0.0395285i
\(161\) −24.5885 4.73205i −1.93784 0.372938i
\(162\) −7.79423 + 4.50000i −0.612372 + 0.353553i
\(163\) −6.19615 10.7321i −0.485320 0.840599i 0.514538 0.857468i \(-0.327964\pi\)
−0.999858 + 0.0168687i \(0.994630\pi\)
\(164\) −9.00000 −0.702782
\(165\) 1.90192 + 1.09808i 0.148065 + 0.0854851i
\(166\) 0.803848i 0.0623907i
\(167\) −5.19615 + 9.00000i −0.402090 + 0.696441i −0.993978 0.109580i \(-0.965050\pi\)
0.591888 + 0.806020i \(0.298383\pi\)
\(168\) 3.00000 3.46410i 0.231455 0.267261i
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) 0 0
\(171\) −12.2942 7.09808i −0.940163 0.542803i
\(172\) −3.59808 + 6.23205i −0.274351 + 0.475189i
\(173\) −1.09808 + 1.90192i −0.0834852 + 0.144601i −0.904745 0.425954i \(-0.859938\pi\)
0.821260 + 0.570555i \(0.193272\pi\)
\(174\) −0.401924 + 0.696152i −0.0304698 + 0.0527752i
\(175\) 0.500000 2.59808i 0.0377964 0.196396i
\(176\) 1.09808 + 0.633975i 0.0827706 + 0.0477876i
\(177\) −14.1962 −1.06705
\(178\) 16.3923i 1.22866i
\(179\) 5.70577 + 3.29423i 0.426469 + 0.246222i 0.697841 0.716252i \(-0.254144\pi\)
−0.271372 + 0.962475i \(0.587477\pi\)
\(180\) −1.50000 + 2.59808i −0.111803 + 0.193649i
\(181\) 7.39230i 0.549466i −0.961521 0.274733i \(-0.911411\pi\)
0.961521 0.274733i \(-0.0885894\pi\)
\(182\) 8.66025 3.00000i 0.641941 0.222375i
\(183\) 1.39230 0.803848i 0.102922 0.0594221i
\(184\) 9.46410 0.697703
\(185\) −2.09808 3.63397i −0.154254 0.267175i
\(186\) −1.90192 + 3.29423i −0.139456 + 0.241545i
\(187\) 0 0
\(188\) −9.00000 −0.656392
\(189\) −2.59808 + 13.5000i −0.188982 + 0.981981i
\(190\) −4.73205 −0.343299
\(191\) 3.00000 + 1.73205i 0.217072 + 0.125327i 0.604594 0.796534i \(-0.293335\pi\)
−0.387522 + 0.921861i \(0.626669\pi\)
\(192\) −0.866025 + 1.50000i −0.0625000 + 0.108253i
\(193\) −12.0981 20.9545i −0.870839 1.50834i −0.861131 0.508384i \(-0.830243\pi\)
−0.00970797 0.999953i \(-0.503090\pi\)
\(194\) −15.4641 −1.11026
\(195\) −5.19615 + 3.00000i −0.372104 + 0.214834i
\(196\) −1.00000 6.92820i −0.0714286 0.494872i
\(197\) 6.33975i 0.451688i 0.974163 + 0.225844i \(0.0725140\pi\)
−0.974163 + 0.225844i \(0.927486\pi\)
\(198\) −3.80385 −0.270328
\(199\) 6.00000 + 3.46410i 0.425329 + 0.245564i 0.697355 0.716726i \(-0.254360\pi\)
−0.272026 + 0.962290i \(0.587694\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 6.92820 0.488678
\(202\) −0.696152 0.401924i −0.0489811 0.0282793i
\(203\) 0.401924 + 1.16025i 0.0282095 + 0.0814339i
\(204\) 0 0
\(205\) 4.50000 7.79423i 0.314294 0.544373i
\(206\) −6.06218 + 10.5000i −0.422372 + 0.731570i
\(207\) −24.5885 + 14.1962i −1.70902 + 0.986701i
\(208\) −3.00000 + 1.73205i −0.208013 + 0.120096i
\(209\) −3.00000 5.19615i −0.207514 0.359425i
\(210\) 1.50000 + 4.33013i 0.103510 + 0.298807i
\(211\) −5.29423 + 9.16987i −0.364470 + 0.631280i −0.988691 0.149968i \(-0.952083\pi\)
0.624221 + 0.781248i \(0.285416\pi\)
\(212\) 10.7321i 0.737080i
\(213\) 1.90192 + 1.09808i 0.130318 + 0.0752389i
\(214\) −2.07180 −0.141625
\(215\) −3.59808 6.23205i −0.245387 0.425022i
\(216\) 5.19615i 0.353553i
\(217\) 1.90192 + 5.49038i 0.129111 + 0.372711i
\(218\) −2.76795 + 1.59808i −0.187469 + 0.108235i
\(219\) 10.3923 6.00000i 0.702247 0.405442i
\(220\) −1.09808 + 0.633975i −0.0740323 + 0.0427426i
\(221\) 0 0
\(222\) 6.29423 + 3.63397i 0.422441 + 0.243896i
\(223\) −8.89230 + 5.13397i −0.595473 + 0.343796i −0.767259 0.641338i \(-0.778380\pi\)
0.171786 + 0.985134i \(0.445046\pi\)
\(224\) 0.866025 + 2.50000i 0.0578638 + 0.167038i
\(225\) −1.50000 2.59808i −0.100000 0.173205i
\(226\) −9.29423 16.0981i −0.618243 1.07083i
\(227\) 4.39230 0.291528 0.145764 0.989319i \(-0.453436\pi\)
0.145764 + 0.989319i \(0.453436\pi\)
\(228\) 7.09808 4.09808i 0.470082 0.271402i
\(229\) 27.9282i 1.84555i −0.385342 0.922774i \(-0.625917\pi\)
0.385342 0.922774i \(-0.374083\pi\)
\(230\) −4.73205 + 8.19615i −0.312022 + 0.540438i
\(231\) −3.80385 + 4.39230i −0.250275 + 0.288992i
\(232\) −0.232051 0.401924i −0.0152349 0.0263876i
\(233\) −4.09808 + 2.36603i −0.268474 + 0.155003i −0.628194 0.778057i \(-0.716206\pi\)
0.359720 + 0.933060i \(0.382872\pi\)
\(234\) 5.19615 9.00000i 0.339683 0.588348i
\(235\) 4.50000 7.79423i 0.293548 0.508439i
\(236\) 4.09808 7.09808i 0.266762 0.462045i
\(237\) −14.3660 24.8827i −0.933174 1.61630i
\(238\) 0 0
\(239\) 18.2942 + 10.5622i 1.18336 + 0.683210i 0.956788 0.290785i \(-0.0939165\pi\)
0.226567 + 0.973996i \(0.427250\pi\)
\(240\) −0.866025 1.50000i −0.0559017 0.0968246i
\(241\) 20.6603i 1.33084i −0.746467 0.665422i \(-0.768252\pi\)
0.746467 0.665422i \(-0.231748\pi\)
\(242\) 8.13397 + 4.69615i 0.522872 + 0.301880i
\(243\) 7.79423 + 13.5000i 0.500000 + 0.866025i
\(244\) 0.928203i 0.0594221i
\(245\) 6.50000 + 2.59808i 0.415270 + 0.165985i
\(246\) 15.5885i 0.993884i
\(247\) 16.3923 1.04302
\(248\) −1.09808 1.90192i −0.0697279 0.120772i
\(249\) 1.39230 0.0882337
\(250\) −0.866025 0.500000i −0.0547723 0.0316228i
\(251\) −18.0000 −1.13615 −0.568075 0.822977i \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) −6.00000 5.19615i −0.377964 0.327327i
\(253\) −12.0000 −0.754434
\(254\) 8.13397 + 4.69615i 0.510371 + 0.294663i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 7.60770 0.474555 0.237277 0.971442i \(-0.423745\pi\)
0.237277 + 0.971442i \(0.423745\pi\)
\(258\) 10.7942 + 6.23205i 0.672019 + 0.387991i
\(259\) 10.4904 3.63397i 0.651841 0.225804i
\(260\) 3.46410i 0.214834i
\(261\) 1.20577 + 0.696152i 0.0746354 + 0.0430908i
\(262\) −14.1962 8.19615i −0.877041 0.506360i
\(263\) 10.2679i 0.633149i −0.948568 0.316574i \(-0.897467\pi\)
0.948568 0.316574i \(-0.102533\pi\)
\(264\) 1.09808 1.90192i 0.0675819 0.117055i
\(265\) −9.29423 5.36603i −0.570940 0.329632i
\(266\) 2.36603 12.2942i 0.145070 0.753808i
\(267\) 28.3923 1.73758
\(268\) −2.00000 + 3.46410i −0.122169 + 0.211604i
\(269\) 9.00000 15.5885i 0.548740 0.950445i −0.449622 0.893219i \(-0.648441\pi\)
0.998361 0.0572259i \(-0.0182255\pi\)
\(270\) 4.50000 + 2.59808i 0.273861 + 0.158114i
\(271\) 21.2942 12.2942i 1.29353 0.746821i 0.314254 0.949339i \(-0.398246\pi\)
0.979279 + 0.202518i \(0.0649124\pi\)
\(272\) 0 0
\(273\) −5.19615 15.0000i −0.314485 0.907841i
\(274\) −5.36603 + 9.29423i −0.324173 + 0.561485i
\(275\) 1.26795i 0.0764602i
\(276\) 16.3923i 0.986701i
\(277\) −13.8038 −0.829393 −0.414696 0.909960i \(-0.636112\pi\)
−0.414696 + 0.909960i \(0.636112\pi\)
\(278\) 8.02628 + 13.9019i 0.481384 + 0.833782i
\(279\) 5.70577 + 3.29423i 0.341596 + 0.197220i
\(280\) −2.59808 0.500000i −0.155265 0.0298807i
\(281\) 2.30385 1.33013i 0.137436 0.0793487i −0.429705 0.902969i \(-0.641383\pi\)
0.567141 + 0.823620i \(0.308049\pi\)
\(282\) 15.5885i 0.928279i
\(283\) −9.40192 + 5.42820i −0.558886 + 0.322673i −0.752698 0.658365i \(-0.771248\pi\)
0.193812 + 0.981039i \(0.437915\pi\)
\(284\) −1.09808 + 0.633975i −0.0651588 + 0.0376195i
\(285\) 8.19615i 0.485498i
\(286\) 3.80385 2.19615i 0.224926 0.129861i
\(287\) 18.0000 + 15.5885i 1.06251 + 0.920158i
\(288\) 2.59808 + 1.50000i 0.153093 + 0.0883883i
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) 0.464102 0.0272530
\(291\) 26.7846i 1.57014i
\(292\) 6.92820i 0.405442i
\(293\) 2.19615 3.80385i 0.128301 0.222223i −0.794718 0.606979i \(-0.792381\pi\)
0.923018 + 0.384756i \(0.125714\pi\)
\(294\) −12.0000 + 1.73205i −0.699854 + 0.101015i
\(295\) 4.09808 + 7.09808i 0.238599 + 0.413266i
\(296\) −3.63397 + 2.09808i −0.211220 + 0.121948i
\(297\) 6.58846i 0.382301i
\(298\) 6.00000 10.3923i 0.347571 0.602010i
\(299\) 16.3923 28.3923i 0.947991 1.64197i
\(300\) 1.73205 0.100000
\(301\) 17.9904 6.23205i 1.03695 0.359209i
\(302\) 5.36603 + 3.09808i 0.308780 + 0.178274i
\(303\) −0.696152 + 1.20577i −0.0399929 + 0.0692698i
\(304\) 4.73205i 0.271402i
\(305\) −0.803848 0.464102i −0.0460282 0.0265744i
\(306\) 0 0
\(307\) 17.7846i 1.01502i 0.861645 + 0.507511i \(0.169434\pi\)
−0.861645 + 0.507511i \(0.830566\pi\)
\(308\) −1.09808 3.16987i −0.0625687 0.180620i
\(309\) 18.1865 + 10.5000i 1.03460 + 0.597324i
\(310\) 2.19615 0.124733
\(311\) −13.0981 22.6865i −0.742724 1.28644i −0.951251 0.308419i \(-0.900200\pi\)
0.208527 0.978017i \(-0.433133\pi\)
\(312\) 3.00000 + 5.19615i 0.169842 + 0.294174i
\(313\) 8.49038 + 4.90192i 0.479905 + 0.277073i 0.720377 0.693583i \(-0.243969\pi\)
−0.240472 + 0.970656i \(0.577302\pi\)
\(314\) 0.339746 0.0191730
\(315\) 7.50000 2.59808i 0.422577 0.146385i
\(316\) 16.5885 0.933174
\(317\) −23.7846 13.7321i −1.33588 0.771269i −0.349684 0.936868i \(-0.613711\pi\)
−0.986193 + 0.165599i \(0.947044\pi\)
\(318\) 18.5885 1.04239
\(319\) 0.294229 + 0.509619i 0.0164736 + 0.0285332i
\(320\) 1.00000 0.0559017
\(321\) 3.58846i 0.200288i
\(322\) −18.9282 16.3923i −1.05483 0.913507i
\(323\) 0 0
\(324\) −9.00000 −0.500000
\(325\) 3.00000 + 1.73205i 0.166410 + 0.0960769i
\(326\) 12.3923i 0.686346i
\(327\) 2.76795 + 4.79423i 0.153068 + 0.265121i
\(328\) −7.79423 4.50000i −0.430364 0.248471i
\(329\) 18.0000 + 15.5885i 0.992372 + 0.859419i
\(330\) 1.09808 + 1.90192i 0.0604471 + 0.104697i
\(331\) 4.00000 6.92820i 0.219860 0.380808i −0.734905 0.678170i \(-0.762773\pi\)
0.954765 + 0.297361i \(0.0961066\pi\)
\(332\) −0.401924 + 0.696152i −0.0220584 + 0.0382063i
\(333\) 6.29423 10.9019i 0.344922 0.597422i
\(334\) −9.00000 + 5.19615i −0.492458 + 0.284321i
\(335\) −2.00000 3.46410i −0.109272 0.189264i
\(336\) 4.33013 1.50000i 0.236228 0.0818317i
\(337\) −5.00000 + 8.66025i −0.272367 + 0.471754i −0.969468 0.245220i \(-0.921140\pi\)
0.697100 + 0.716974i \(0.254473\pi\)
\(338\) 1.00000i 0.0543928i
\(339\) −27.8827 + 16.0981i −1.51438 + 0.874327i
\(340\) 0 0
\(341\) 1.39230 + 2.41154i 0.0753975 + 0.130592i
\(342\) −7.09808 12.2942i −0.383820 0.664796i
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) −6.23205 + 3.59808i −0.336010 + 0.193995i
\(345\) 14.1962 + 8.19615i 0.764295 + 0.441266i
\(346\) −1.90192 + 1.09808i −0.102248 + 0.0590329i
\(347\) 23.5981 13.6244i 1.26681 0.731394i 0.292428 0.956288i \(-0.405537\pi\)
0.974383 + 0.224894i \(0.0722035\pi\)
\(348\) −0.696152 + 0.401924i −0.0373177 + 0.0215454i
\(349\) 3.80385 2.19615i 0.203615 0.117557i −0.394725 0.918799i \(-0.629160\pi\)
0.598341 + 0.801242i \(0.295827\pi\)
\(350\) 1.73205 2.00000i 0.0925820 0.106904i
\(351\) −15.5885 9.00000i −0.832050 0.480384i
\(352\) 0.633975 + 1.09808i 0.0337910 + 0.0585277i
\(353\) 30.5885 1.62806 0.814030 0.580823i \(-0.197269\pi\)
0.814030 + 0.580823i \(0.197269\pi\)
\(354\) −12.2942 7.09808i −0.653431 0.377258i
\(355\) 1.26795i 0.0672958i
\(356\) −8.19615 + 14.1962i −0.434395 + 0.752395i
\(357\) 0 0
\(358\) 3.29423 + 5.70577i 0.174105 + 0.301559i
\(359\) 22.6865 13.0981i 1.19735 0.691290i 0.237386 0.971415i \(-0.423709\pi\)
0.959963 + 0.280125i \(0.0903760\pi\)
\(360\) −2.59808 + 1.50000i −0.136931 + 0.0790569i
\(361\) 1.69615 2.93782i 0.0892712 0.154622i
\(362\) 3.69615 6.40192i 0.194265 0.336478i
\(363\) 8.13397 14.0885i 0.426923 0.739452i
\(364\) 9.00000 + 1.73205i 0.471728 + 0.0907841i
\(365\) −6.00000 3.46410i −0.314054 0.181319i
\(366\) 1.60770 0.0840356
\(367\) 18.8038i 0.981553i 0.871286 + 0.490776i \(0.163287\pi\)
−0.871286 + 0.490776i \(0.836713\pi\)
\(368\) 8.19615 + 4.73205i 0.427254 + 0.246675i
\(369\) 27.0000 1.40556
\(370\) 4.19615i 0.218148i
\(371\) 18.5885 21.4641i 0.965065 1.11436i
\(372\) −3.29423 + 1.90192i −0.170798 + 0.0986102i
\(373\) −0.196152 −0.0101564 −0.00507819 0.999987i \(-0.501616\pi\)
−0.00507819 + 0.999987i \(0.501616\pi\)
\(374\) 0 0
\(375\) −0.866025 + 1.50000i −0.0447214 + 0.0774597i
\(376\) −7.79423 4.50000i −0.401957 0.232070i
\(377\) −1.60770 −0.0828005
\(378\) −9.00000 + 10.3923i −0.462910 + 0.534522i
\(379\) −30.3923 −1.56115 −0.780574 0.625063i \(-0.785073\pi\)
−0.780574 + 0.625063i \(0.785073\pi\)
\(380\) −4.09808 2.36603i −0.210227 0.121375i
\(381\) 8.13397 14.0885i 0.416716 0.721774i
\(382\) 1.73205 + 3.00000i 0.0886194 + 0.153493i
\(383\) −1.39230 −0.0711435 −0.0355717 0.999367i \(-0.511325\pi\)
−0.0355717 + 0.999367i \(0.511325\pi\)
\(384\) −1.50000 + 0.866025i −0.0765466 + 0.0441942i
\(385\) 3.29423 + 0.633975i 0.167889 + 0.0323103i
\(386\) 24.1962i 1.23155i
\(387\) 10.7942 18.6962i 0.548701 0.950379i
\(388\) −13.3923 7.73205i −0.679891 0.392535i
\(389\) 30.7128i 1.55720i −0.627520 0.778601i \(-0.715930\pi\)
0.627520 0.778601i \(-0.284070\pi\)
\(390\) −6.00000 −0.303822
\(391\) 0 0
\(392\) 2.59808 6.50000i 0.131223 0.328300i
\(393\) −14.1962 + 24.5885i −0.716101 + 1.24032i
\(394\) −3.16987 + 5.49038i −0.159696 + 0.276601i
\(395\) −8.29423 + 14.3660i −0.417328 + 0.722833i
\(396\) −3.29423 1.90192i −0.165541 0.0955753i
\(397\) −0.509619 + 0.294229i −0.0255770 + 0.0147669i −0.512734 0.858548i \(-0.671367\pi\)
0.487157 + 0.873314i \(0.338034\pi\)
\(398\) 3.46410 + 6.00000i 0.173640 + 0.300753i
\(399\) −21.2942 4.09808i −1.06604 0.205160i
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) 27.5885i 1.37770i 0.724903 + 0.688851i \(0.241885\pi\)
−0.724903 + 0.688851i \(0.758115\pi\)
\(402\) 6.00000 + 3.46410i 0.299253 + 0.172774i
\(403\) −7.60770 −0.378966
\(404\) −0.401924 0.696152i −0.0199965 0.0346349i
\(405\) 4.50000 7.79423i 0.223607 0.387298i
\(406\) −0.232051 + 1.20577i −0.0115165 + 0.0598414i
\(407\) 4.60770 2.66025i 0.228395 0.131864i
\(408\) 0 0
\(409\) −29.8923 + 17.2583i −1.47808 + 0.853370i −0.999693 0.0247799i \(-0.992111\pi\)
−0.478386 + 0.878149i \(0.658778\pi\)
\(410\) 7.79423 4.50000i 0.384930 0.222239i
\(411\) 16.0981 + 9.29423i 0.794060 + 0.458450i
\(412\) −10.5000 + 6.06218i −0.517298 + 0.298662i
\(413\) −20.4904 + 7.09808i −1.00827 + 0.349273i
\(414\) −28.3923 −1.39541
\(415\) −0.401924 0.696152i −0.0197297 0.0341728i
\(416\) −3.46410 −0.169842
\(417\) 24.0788 13.9019i 1.17915 0.680780i
\(418\) 6.00000i 0.293470i
\(419\) −5.19615 + 9.00000i −0.253849 + 0.439679i −0.964582 0.263783i \(-0.915030\pi\)
0.710734 + 0.703461i \(0.248363\pi\)
\(420\) −0.866025 + 4.50000i −0.0422577 + 0.219578i
\(421\) −10.9904 19.0359i −0.535638 0.927753i −0.999132 0.0416527i \(-0.986738\pi\)
0.463494 0.886100i \(-0.346596\pi\)
\(422\) −9.16987 + 5.29423i −0.446382 + 0.257719i
\(423\) 27.0000 1.31278
\(424\) −5.36603 + 9.29423i −0.260597 + 0.451368i
\(425\) 0 0
\(426\) 1.09808 + 1.90192i 0.0532020 + 0.0921485i
\(427\) 1.60770 1.85641i 0.0778018 0.0898378i
\(428\) −1.79423 1.03590i −0.0867273 0.0500720i
\(429\) −3.80385 6.58846i −0.183651 0.318094i
\(430\) 7.19615i 0.347029i
\(431\) −2.41154 1.39230i −0.116160 0.0670650i 0.440794 0.897608i \(-0.354697\pi\)
−0.556954 + 0.830543i \(0.688030\pi\)
\(432\) 2.59808 4.50000i 0.125000 0.216506i
\(433\) 18.0000i 0.865025i 0.901628 + 0.432512i \(0.142373\pi\)
−0.901628 + 0.432512i \(0.857627\pi\)
\(434\) −1.09808 + 5.70577i −0.0527093 + 0.273886i
\(435\) 0.803848i 0.0385415i
\(436\) −3.19615 −0.153068
\(437\) −22.3923 38.7846i −1.07117 1.85532i
\(438\) 12.0000 0.573382
\(439\) −10.6865 6.16987i −0.510040 0.294472i 0.222810 0.974862i \(-0.428477\pi\)
−0.732850 + 0.680390i \(0.761810\pi\)
\(440\) −1.26795 −0.0604471
\(441\) 3.00000 + 20.7846i 0.142857 + 0.989743i
\(442\) 0 0
\(443\) −7.79423 4.50000i −0.370315 0.213801i 0.303281 0.952901i \(-0.401918\pi\)
−0.673596 + 0.739100i \(0.735251\pi\)
\(444\) 3.63397 + 6.29423i 0.172461 + 0.298711i
\(445\) −8.19615 14.1962i −0.388535 0.672962i
\(446\) −10.2679 −0.486201
\(447\) −18.0000 10.3923i −0.851371 0.491539i
\(448\) −0.500000 + 2.59808i −0.0236228 + 0.122748i
\(449\) 21.5885i 1.01882i 0.860523 + 0.509411i \(0.170137\pi\)
−0.860523 + 0.509411i \(0.829863\pi\)
\(450\) 3.00000i 0.141421i
\(451\) 9.88269 + 5.70577i 0.465358 + 0.268674i
\(452\) 18.5885i 0.874327i
\(453\) 5.36603 9.29423i 0.252118 0.436681i
\(454\) 3.80385 + 2.19615i 0.178523 + 0.103071i
\(455\) −6.00000 + 6.92820i −0.281284 + 0.324799i
\(456\) 8.19615 0.383820
\(457\) 9.19615 15.9282i 0.430178 0.745090i −0.566710 0.823917i \(-0.691784\pi\)
0.996888 + 0.0788271i \(0.0251175\pi\)
\(458\) 13.9641 24.1865i 0.652500 1.13016i
\(459\) 0 0
\(460\) −8.19615 + 4.73205i −0.382148 + 0.220633i
\(461\) 2.59808 + 4.50000i 0.121004 + 0.209586i 0.920164 0.391533i \(-0.128055\pi\)
−0.799160 + 0.601119i \(0.794722\pi\)
\(462\) −5.49038 + 1.90192i −0.255436 + 0.0884855i
\(463\) 11.6962 20.2583i 0.543566 0.941484i −0.455129 0.890425i \(-0.650407\pi\)
0.998696 0.0510591i \(-0.0162597\pi\)
\(464\) 0.464102i 0.0215454i
\(465\) 3.80385i 0.176399i
\(466\) −4.73205 −0.219208
\(467\) 8.59808 + 14.8923i 0.397872 + 0.689134i 0.993463 0.114154i \(-0.0364156\pi\)
−0.595592 + 0.803287i \(0.703082\pi\)
\(468\) 9.00000 5.19615i 0.416025 0.240192i
\(469\) 10.0000 3.46410i 0.461757 0.159957i
\(470\) 7.79423 4.50000i 0.359521 0.207570i
\(471\) 0.588457i 0.0271147i
\(472\) 7.09808 4.09808i 0.326715 0.188629i
\(473\) 7.90192 4.56218i 0.363331 0.209769i
\(474\) 28.7321i 1.31971i
\(475\) 4.09808 2.36603i 0.188033 0.108561i
\(476\) 0 0
\(477\) 32.1962i 1.47416i
\(478\) 10.5622 + 18.2942i 0.483103 + 0.836759i
\(479\) 10.3923 0.474837 0.237418 0.971408i \(-0.423699\pi\)
0.237418 + 0.971408i \(0.423699\pi\)
\(480\) 1.73205i 0.0790569i
\(481\) 14.5359i 0.662780i
\(482\) 10.3301 17.8923i 0.470524 0.814972i
\(483\) −28.3923 + 32.7846i −1.29189 + 1.49175i
\(484\) 4.69615 + 8.13397i 0.213461 + 0.369726i
\(485\) 13.3923 7.73205i 0.608113 0.351094i
\(486\) 15.5885i 0.707107i
\(487\) −17.0000 + 29.4449i −0.770344 + 1.33427i 0.167031 + 0.985952i \(0.446582\pi\)
−0.937375 + 0.348323i \(0.886751\pi\)
\(488\) −0.464102 + 0.803848i −0.0210089 + 0.0363885i
\(489\) −21.4641 −0.970640
\(490\) 4.33013 + 5.50000i 0.195615 + 0.248465i
\(491\) 2.49038 + 1.43782i 0.112389 + 0.0648880i 0.555141 0.831756i \(-0.312664\pi\)
−0.442752 + 0.896644i \(0.645998\pi\)
\(492\) −7.79423 + 13.5000i −0.351391 + 0.608627i
\(493\) 0 0
\(494\) 14.1962 + 8.19615i 0.638715 + 0.368762i
\(495\) 3.29423 1.90192i 0.148065 0.0854851i
\(496\) 2.19615i 0.0986102i
\(497\) 3.29423 + 0.633975i 0.147766 + 0.0284376i
\(498\) 1.20577 + 0.696152i 0.0540319 + 0.0311953i
\(499\) −5.80385 −0.259816 −0.129908 0.991526i \(-0.541468\pi\)
−0.129908 + 0.991526i \(0.541468\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) 9.00000 + 15.5885i 0.402090 + 0.696441i
\(502\) −15.5885 9.00000i −0.695747 0.401690i
\(503\) 13.3923 0.597133 0.298567 0.954389i \(-0.403491\pi\)
0.298567 + 0.954389i \(0.403491\pi\)
\(504\) −2.59808 7.50000i −0.115728 0.334077i
\(505\) 0.803848 0.0357707
\(506\) −10.3923 6.00000i −0.461994 0.266733i
\(507\) −1.73205 −0.0769231
\(508\) 4.69615 + 8.13397i 0.208358 + 0.360887i
\(509\) −21.5885 −0.956892 −0.478446 0.878117i \(-0.658800\pi\)
−0.478446 + 0.878117i \(0.658800\pi\)
\(510\) 0 0
\(511\) 12.0000 13.8564i 0.530849 0.612971i
\(512\) 1.00000i 0.0441942i
\(513\) −21.2942 + 12.2942i −0.940163 + 0.542803i
\(514\) 6.58846 + 3.80385i 0.290604 + 0.167781i
\(515\) 12.1244i 0.534263i
\(516\) 6.23205 + 10.7942i 0.274351 + 0.475189i
\(517\) 9.88269 + 5.70577i 0.434640 + 0.250940i
\(518\) 10.9019 + 2.09808i 0.479003 + 0.0921842i
\(519\) 1.90192 + 3.29423i 0.0834852 + 0.144601i
\(520\) 1.73205 3.00000i 0.0759555 0.131559i
\(521\) 10.5000 18.1865i 0.460013 0.796766i −0.538948 0.842339i \(-0.681178\pi\)
0.998961 + 0.0455727i \(0.0145113\pi\)
\(522\) 0.696152 + 1.20577i 0.0304698 + 0.0527752i
\(523\) −28.5788 + 16.5000i −1.24967 + 0.721495i −0.971043 0.238906i \(-0.923211\pi\)
−0.278623 + 0.960401i \(0.589878\pi\)
\(524\) −8.19615 14.1962i −0.358051 0.620162i
\(525\) −3.46410 3.00000i −0.151186 0.130931i
\(526\) 5.13397 8.89230i 0.223852 0.387723i
\(527\) 0 0
\(528\) 1.90192 1.09808i 0.0827706 0.0477876i
\(529\) −66.5692 −2.89431
\(530\) −5.36603 9.29423i −0.233085 0.403715i
\(531\) −12.2942 + 21.2942i −0.533524 + 0.924091i
\(532\) 8.19615 9.46410i 0.355348 0.410321i
\(533\) −27.0000 + 15.5885i −1.16950 + 0.675211i
\(534\) 24.5885 + 14.1962i 1.06405 + 0.614328i
\(535\) 1.79423 1.03590i 0.0775713 0.0447858i
\(536\) −3.46410 + 2.00000i −0.149626 + 0.0863868i
\(537\) 9.88269 5.70577i 0.426469 0.246222i
\(538\) 15.5885 9.00000i 0.672066 0.388018i
\(539\) −3.29423 + 8.24167i −0.141892 + 0.354994i
\(540\) 2.59808 + 4.50000i 0.111803 + 0.193649i
\(541\) −4.00000 6.92820i −0.171973 0.297867i 0.767136 0.641484i \(-0.221681\pi\)
−0.939110 + 0.343617i \(0.888348\pi\)
\(542\) 24.5885 1.05616
\(543\) −11.0885 6.40192i −0.475851 0.274733i
\(544\) 0 0
\(545\) 1.59808 2.76795i 0.0684541 0.118566i
\(546\) 3.00000 15.5885i 0.128388 0.667124i
\(547\) 12.7942 + 22.1603i 0.547042 + 0.947504i 0.998475 + 0.0551993i \(0.0175794\pi\)
−0.451434 + 0.892305i \(0.649087\pi\)
\(548\) −9.29423 + 5.36603i −0.397030 + 0.229225i
\(549\) 2.78461i 0.118844i
\(550\) 0.633975 1.09808i 0.0270328 0.0468221i
\(551\) −1.09808 + 1.90192i −0.0467796 + 0.0810247i
\(552\) 8.19615 14.1962i 0.348851 0.604228i
\(553\) −33.1769 28.7321i −1.41083 1.22181i
\(554\) −11.9545 6.90192i −0.507897 0.293235i
\(555\) −7.26795 −0.308507
\(556\) 16.0526i 0.680780i
\(557\) 7.60770 + 4.39230i 0.322348 + 0.186108i 0.652439 0.757841i \(-0.273746\pi\)
−0.330090 + 0.943949i \(0.607079\pi\)
\(558\) 3.29423 + 5.70577i 0.139456 + 0.241545i
\(559\) 24.9282i 1.05435i
\(560\) −2.00000 1.73205i −0.0845154 0.0731925i
\(561\) 0 0
\(562\) 2.66025 0.112216
\(563\) −17.1962 29.7846i −0.724731 1.25527i −0.959084 0.283120i \(-0.908631\pi\)
0.234353 0.972152i \(-0.424703\pi\)
\(564\) −7.79423 + 13.5000i −0.328196 + 0.568453i
\(565\) 16.0981 + 9.29423i 0.677251 + 0.391011i
\(566\) −10.8564 −0.456329
\(567\) 18.0000 + 15.5885i 0.755929 + 0.654654i
\(568\) −1.26795 −0.0532020
\(569\) 5.19615 + 3.00000i 0.217834 + 0.125767i 0.604947 0.796266i \(-0.293194\pi\)
−0.387113 + 0.922032i \(0.626528\pi\)
\(570\) −4.09808 + 7.09808i −0.171650 + 0.297306i
\(571\) −21.1962 36.7128i −0.887031 1.53638i −0.843368 0.537337i \(-0.819430\pi\)
−0.0436638 0.999046i \(-0.513903\pi\)
\(572\) 4.39230 0.183651
\(573\) 5.19615 3.00000i 0.217072 0.125327i
\(574\) 7.79423 + 22.5000i 0.325325 + 0.939132i
\(575\) 9.46410i 0.394680i
\(576\) 1.50000 + 2.59808i 0.0625000 + 0.108253i
\(577\) −20.7846 12.0000i −0.865275 0.499567i 0.000500448 1.00000i \(-0.499841\pi\)
−0.865775 + 0.500433i \(0.833174\pi\)
\(578\) 17.0000i 0.707107i
\(579\) −41.9090 −1.74168
\(580\) 0.401924 + 0.232051i 0.0166890 + 0.00963539i
\(581\) 2.00962 0.696152i 0.0833730 0.0288813i
\(582\) −13.3923 + 23.1962i −0.555129 + 0.961511i
\(583\) 6.80385 11.7846i 0.281787 0.488069i
\(584\) −3.46410 + 6.00000i −0.143346 + 0.248282i
\(585\) 10.3923i 0.429669i
\(586\) 3.80385 2.19615i 0.157135 0.0907222i
\(587\) 20.5981 + 35.6769i 0.850174 + 1.47254i 0.881051 + 0.473021i \(0.156836\pi\)
−0.0308777 + 0.999523i \(0.509830\pi\)
\(588\) −11.2583 4.50000i −0.464286 0.185577i
\(589\) −5.19615 + 9.00000i −0.214104 + 0.370839i
\(590\) 8.19615i 0.337430i
\(591\) 9.50962 + 5.49038i 0.391173 + 0.225844i
\(592\) −4.19615 −0.172461
\(593\) 7.39230 + 12.8038i 0.303566 + 0.525791i 0.976941 0.213510i \(-0.0684895\pi\)
−0.673375 + 0.739301i \(0.735156\pi\)
\(594\) −3.29423 + 5.70577i −0.135164 + 0.234111i
\(595\) 0 0
\(596\) 10.3923 6.00000i 0.425685 0.245770i
\(597\) 10.3923 6.00000i 0.425329 0.245564i
\(598\) 28.3923 16.3923i 1.16105 0.670331i
\(599\) 14.1962 8.19615i 0.580039 0.334886i −0.181110 0.983463i \(-0.557969\pi\)
0.761149 + 0.648577i \(0.224636\pi\)
\(600\) 1.50000 + 0.866025i 0.0612372 + 0.0353553i
\(601\) −3.58846 + 2.07180i −0.146376 + 0.0845104i −0.571399 0.820672i \(-0.693599\pi\)
0.425023 + 0.905182i \(0.360266\pi\)
\(602\) 18.6962 + 3.59808i 0.761998 + 0.146647i
\(603\) 6.00000 10.3923i 0.244339 0.423207i
\(604\) 3.09808 + 5.36603i 0.126059 + 0.218340i
\(605\) −9.39230 −0.381851
\(606\) −1.20577 + 0.696152i −0.0489811 + 0.0282793i
\(607\) 18.1244i 0.735645i 0.929896 + 0.367822i \(0.119897\pi\)
−0.929896 + 0.367822i \(0.880103\pi\)
\(608\) −2.36603 + 4.09808i −0.0959550 + 0.166199i
\(609\) 2.08846 + 0.401924i 0.0846286 + 0.0162868i
\(610\) −0.464102 0.803848i −0.0187909 0.0325468i
\(611\) −27.0000 + 15.5885i −1.09230 + 0.630641i
\(612\) 0 0
\(613\) −17.3923 + 30.1244i −0.702469 + 1.21671i 0.265129 + 0.964213i \(0.414586\pi\)
−0.967597 + 0.252498i \(0.918748\pi\)
\(614\) −8.89230 + 15.4019i −0.358864 + 0.621571i
\(615\) −7.79423 13.5000i −0.314294 0.544373i
\(616\) 0.633975 3.29423i 0.0255436 0.132728i
\(617\) 26.1962 + 15.1244i 1.05462 + 0.608884i 0.923938 0.382541i \(-0.124951\pi\)
0.130679 + 0.991425i \(0.458284\pi\)
\(618\) 10.5000 + 18.1865i 0.422372 + 0.731570i
\(619\) 4.39230i 0.176542i 0.996097 + 0.0882708i \(0.0281341\pi\)
−0.996097 + 0.0882708i \(0.971866\pi\)
\(620\) 1.90192 + 1.09808i 0.0763831 + 0.0440998i
\(621\) 49.1769i 1.97340i
\(622\) 26.1962i 1.05037i
\(623\) 40.9808 14.1962i 1.64186 0.568757i
\(624\) 6.00000i 0.240192i
\(625\) 1.00000 0.0400000
\(626\) 4.90192 + 8.49038i 0.195920 + 0.339344i
\(627\) −10.3923 −0.415029
\(628\) 0.294229 + 0.169873i 0.0117410 + 0.00677867i
\(629\) 0 0
\(630\) 7.79423 + 1.50000i 0.310530 + 0.0597614i
\(631\) −8.39230 −0.334092 −0.167046 0.985949i \(-0.553423\pi\)
−0.167046 + 0.985949i \(0.553423\pi\)
\(632\) 14.3660 + 8.29423i 0.571450 + 0.329927i
\(633\) 9.16987 + 15.8827i 0.364470 + 0.631280i
\(634\) −13.7321 23.7846i −0.545369 0.944608i
\(635\) −9.39230 −0.372722
\(636\) 16.0981 + 9.29423i 0.638330 + 0.368540i
\(637\) −15.0000 19.0526i −0.594322 0.754890i
\(638\) 0.588457i 0.0232972i
\(639\) 3.29423 1.90192i 0.130318 0.0752389i
\(640\) 0.866025 + 0.500000i 0.0342327 + 0.0197642i
\(641\) 44.7846i 1.76889i 0.466648 + 0.884443i \(0.345461\pi\)
−0.466648 + 0.884443i \(0.654539\pi\)
\(642\) −1.79423 + 3.10770i −0.0708126 + 0.122651i
\(643\) 31.7942 + 18.3564i 1.25384 + 0.723906i 0.971870 0.235517i \(-0.0756782\pi\)
0.281972 + 0.959423i \(0.409012\pi\)
\(644\) −8.19615 23.6603i −0.322974 0.932345i
\(645\) −12.4641 −0.490774
\(646\) 0 0
\(647\) 12.6962 21.9904i 0.499137 0.864531i −0.500862 0.865527i \(-0.666984\pi\)
1.00000 0.000995924i \(0.000317013\pi\)
\(648\) −7.79423 4.50000i −0.306186 0.176777i
\(649\) −9.00000 + 5.19615i −0.353281 + 0.203967i
\(650\) 1.73205 + 3.00000i 0.0679366 + 0.117670i
\(651\) 9.88269 + 1.90192i 0.387333 + 0.0745423i
\(652\) 6.19615 10.7321i 0.242660 0.420300i
\(653\) 22.1436i 0.866546i 0.901263 + 0.433273i \(0.142641\pi\)
−0.901263 + 0.433273i \(0.857359\pi\)
\(654\) 5.53590i 0.216471i
\(655\) 16.3923 0.640500
\(656\) −4.50000 7.79423i −0.175695 0.304314i
\(657\) 20.7846i 0.810885i
\(658\) 7.79423 + 22.5000i 0.303851 + 0.877141i
\(659\) −17.7058 + 10.2224i −0.689719 + 0.398209i −0.803507 0.595296i \(-0.797035\pi\)
0.113788 + 0.993505i \(0.463702\pi\)
\(660\) 2.19615i 0.0854851i
\(661\) −35.3827 + 20.4282i −1.37623 + 0.794565i −0.991703 0.128550i \(-0.958968\pi\)
−0.384524 + 0.923115i \(0.625634\pi\)
\(662\) 6.92820 4.00000i 0.269272 0.155464i
\(663\) 0 0
\(664\) −0.696152 + 0.401924i −0.0270160 + 0.0155977i
\(665\) 4.09808 + 11.8301i 0.158917 + 0.458753i
\(666\) 10.9019 6.29423i 0.422441 0.243896i
\(667\) 2.19615 + 3.80385i 0.0850354 + 0.147286i
\(668\) −10.3923 −0.402090
\(669\) 17.7846i 0.687593i
\(670\) 4.00000i 0.154533i
\(671\) 0.588457 1.01924i 0.0227171 0.0393472i
\(672\) 4.50000 + 0.866025i 0.173591 + 0.0334077i
\(673\) −13.4904 23.3660i −0.520016 0.900694i −0.999729 0.0232688i \(-0.992593\pi\)
0.479713 0.877425i \(-0.340741\pi\)
\(674\) −8.66025 + 5.00000i −0.333581 + 0.192593i
\(675\) −5.19615 −0.200000
\(676\) 0.500000 0.866025i 0.0192308 0.0333087i
\(677\) −14.4904 + 25.0981i −0.556911 + 0.964597i 0.440842 + 0.897585i \(0.354680\pi\)
−0.997752 + 0.0670125i \(0.978653\pi\)
\(678\) −32.1962 −1.23649
\(679\) 13.3923 + 38.6603i 0.513949 + 1.48364i
\(680\) 0 0
\(681\) 3.80385 6.58846i 0.145764 0.252470i
\(682\) 2.78461i 0.106628i
\(683\) −36.7750 21.2321i −1.40716 0.812422i −0.412043 0.911164i \(-0.635185\pi\)
−0.995113 + 0.0987426i \(0.968518\pi\)
\(684\) 14.1962i 0.542803i
\(685\) 10.7321i 0.410051i
\(686\) −16.4545 + 8.50000i −0.628235 + 0.324532i
\(687\) −41.8923 24.1865i −1.59829 0.922774i
\(688\) −7.19615 −0.274351
\(689\) 18.5885 + 32.1962i 0.708164 + 1.22658i
\(690\) 8.19615 + 14.1962i 0.312022 + 0.540438i
\(691\) 16.3923 + 9.46410i 0.623593 + 0.360031i 0.778266 0.627934i \(-0.216099\pi\)
−0.154674 + 0.987966i \(0.549433\pi\)
\(692\) −2.19615 −0.0834852
\(693\) 3.29423 + 9.50962i 0.125137 + 0.361241i
\(694\) 27.2487 1.03435
\(695\) −13.9019 8.02628i −0.527330 0.304454i
\(696\) −0.803848 −0.0304698
\(697\) 0 0
\(698\) 4.39230 0.166251
\(699\) 8.19615i 0.310007i
\(700\) 2.50000 0.866025i 0.0944911 0.0327327i
\(701\) 9.67949i 0.365589i −0.983151 0.182795i \(-0.941486\pi\)
0.983151 0.182795i \(-0.0585144\pi\)
\(702\) −9.00000 15.5885i −0.339683 0.588348i
\(703\) 17.1962 + 9.92820i 0.648565 + 0.374449i
\(704\) 1.26795i 0.0477876i
\(705\) −7.79423 13.5000i −0.293548 0.508439i
\(706\) 26.4904 + 15.2942i 0.996979 + 0.575606i
\(707\) −0.401924 + 2.08846i −0.0151159 + 0.0785445i
\(708\) −7.09808 12.2942i −0.266762 0.462045i
\(709\) 2.60770 4.51666i 0.0979340 0.169627i −0.812895 0.582410i \(-0.802110\pi\)
0.910829 + 0.412783i \(0.135443\pi\)
\(710\) 0.633975 1.09808i 0.0237926 0.0412101i
\(711\) −49.7654 −1.86635
\(712\) −14.1962 + 8.19615i −0.532023 + 0.307164i
\(713\) 10.3923 + 18.0000i 0.389195 + 0.674105i
\(714\) 0 0
\(715\) −2.19615 + 3.80385i −0.0821314 + 0.142256i
\(716\) 6.58846i 0.246222i
\(717\) 31.6865 18.2942i 1.18336 0.683210i
\(718\) 26.1962 0.977632
\(719\) −20.7846 36.0000i −0.775135 1.34257i −0.934718 0.355389i \(-0.884348\pi\)
0.159583 0.987184i \(-0.448985\pi\)
\(720\) −3.00000 −0.111803
\(721\) 31.5000 + 6.06218i 1.17312 + 0.225767i
\(722\) 2.93782 1.69615i 0.109334 0.0631243i
\(723\) −30.9904 17.8923i −1.15254 0.665422i
\(724\) 6.40192 3.69615i 0.237926 0.137366i
\(725\) −0.401924 + 0.232051i −0.0149271 + 0.00861815i
\(726\) 14.0885 8.13397i 0.522872 0.301880i
\(727\) −0.215390 + 0.124356i −0.00798838 + 0.00461210i −0.503989 0.863710i \(-0.668135\pi\)
0.496000 + 0.868322i \(0.334801\pi\)
\(728\) 6.92820 + 6.00000i 0.256776 + 0.222375i
\(729\) 27.0000 1.00000
\(730\) −3.46410 6.00000i −0.128212 0.222070i
\(731\) 0 0
\(732\) 1.39230 + 0.803848i 0.0514611 + 0.0297111i
\(733\) 4.05256i 0.149685i 0.997195 + 0.0748423i \(0.0238454\pi\)
−0.997195 + 0.0748423i \(0.976155\pi\)
\(734\) −9.40192 + 16.2846i −0.347031 + 0.601076i
\(735\) 9.52628 7.50000i 0.351382 0.276642i
\(736\) 4.73205 + 8.19615i 0.174426 + 0.302114i
\(737\) 4.39230 2.53590i 0.161793 0.0934110i
\(738\) 23.3827 + 13.5000i 0.860729 + 0.496942i
\(739\) 14.5885 25.2679i 0.536645 0.929497i −0.462437 0.886652i \(-0.653025\pi\)
0.999082 0.0428442i \(-0.0136419\pi\)
\(740\) 2.09808 3.63397i 0.0771268 0.133588i
\(741\) 14.1962 24.5885i 0.521509 0.903280i
\(742\) 26.8301 9.29423i 0.984965 0.341202i
\(743\) 38.6769 + 22.3301i 1.41892 + 0.819213i 0.996204 0.0870500i \(-0.0277440\pi\)
0.422714 + 0.906263i \(0.361077\pi\)
\(744\) −3.80385 −0.139456
\(745\) 12.0000i 0.439646i
\(746\) −0.169873 0.0980762i −0.00621949 0.00359083i
\(747\) 1.20577 2.08846i 0.0441169 0.0764127i
\(748\) 0 0
\(749\) 1.79423 + 5.17949i 0.0655597 + 0.189255i
\(750\) −1.50000 + 0.866025i −0.0547723 + 0.0316228i
\(751\) −42.3923 −1.54692 −0.773459 0.633847i \(-0.781475\pi\)
−0.773459 + 0.633847i \(0.781475\pi\)
\(752\) −4.50000 7.79423i −0.164098 0.284226i
\(753\) −15.5885 + 27.0000i −0.568075 + 0.983935i
\(754\) −1.39230 0.803848i −0.0507048 0.0292744i
\(755\) −6.19615 −0.225501
\(756\) −12.9904 + 4.50000i −0.472456 + 0.163663i
\(757\) 22.5885 0.820991 0.410496 0.911863i \(-0.365356\pi\)
0.410496 + 0.911863i \(0.365356\pi\)
\(758\) −26.3205 15.1962i −0.956004 0.551949i
\(759\) −10.3923 + 18.0000i −0.377217 + 0.653359i
\(760\) −2.36603 4.09808i −0.0858248 0.148653i
\(761\) −33.0000 −1.19625 −0.598125 0.801403i \(-0.704087\pi\)
−0.598125 + 0.801403i \(0.704087\pi\)
\(762\) 14.0885 8.13397i 0.510371 0.294663i
\(763\) 6.39230 + 5.53590i 0.231417 + 0.200413i
\(764\) 3.46410i 0.125327i
\(765\) 0 0
\(766\) −1.20577 0.696152i −0.0435663 0.0251530i
\(767\) 28.3923i 1.02519i
\(768\) −1.73205 −0.0625000
\(769\) 13.5000 + 7.79423i 0.486822 + 0.281067i 0.723255 0.690581i \(-0.242645\pi\)
−0.236433 + 0.971648i \(0.575978\pi\)
\(770\) 2.53590 + 2.19615i 0.0913874 + 0.0791438i
\(771\) 6.58846 11.4115i 0.237277 0.410977i
\(772\) 12.0981 20.9545i 0.435419 0.754168i
\(773\) −9.00000 + 15.5885i −0.323708 + 0.560678i −0.981250 0.192740i \(-0.938263\pi\)
0.657542 + 0.753418i \(0.271596\pi\)
\(774\) 18.6962 10.7942i 0.672019 0.387991i
\(775\) −1.90192 + 1.09808i −0.0683191 + 0.0394441i
\(776\) −7.73205 13.3923i −0.277564 0.480756i
\(777\) 3.63397 18.8827i 0.130368 0.677413i
\(778\) 15.3564 26.5981i 0.550554 0.953587i
\(779\) 42.5885i 1.52589i
\(780\) −5.19615 3.00000i −0.186052 0.107417i
\(781\) 1.60770 0.0575279
\(782\) 0 0
\(783\) 2.08846 1.20577i 0.0746354 0.0430908i
\(784\) 5.50000 4.33013i 0.196429 0.154647i
\(785\) −0.294229 + 0.169873i −0.0105015 + 0.00606303i
\(786\) −24.5885 + 14.1962i −0.877041 + 0.506360i