Properties

Label 630.2.t.a.311.1
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 311.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 630.311
Dual form 630.2.t.a.551.1

$q$-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} +4.73205i 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} +(-1.09808 + 0.633975i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(3.46410 + 3.00000i) q^{21} +(2.36603 - 4.09808i) q^{22} +2.53590i 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} +(-5.59808 + 3.23205i) q^{29} +(-1.50000 + 0.866025i) q^{30} +(-7.09808 + 4.09808i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-7.09808 - 4.09808i) q^{33} +(-0.500000 + 2.59808i) q^{35} +(1.50000 - 2.59808i) q^{36} +(-3.09808 - 5.36603i) q^{37} +1.26795 q^{38} +(-5.19615 + 3.00000i) q^{39} +1.00000i q^{40} +(-4.50000 + 7.79423i) q^{41} +(-1.50000 - 4.33013i) q^{42} +(-1.59808 - 2.76795i) q^{43} +(-4.09808 + 2.36603i) q^{44} +(1.50000 + 2.59808i) q^{45} +(1.26795 - 2.19615i) 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} +(-6.29423 - 3.63397i) q^{53} +(-4.50000 - 2.59808i) q^{54} -4.73205i q^{55} +(-2.59808 - 0.500000i) q^{56} -2.19615i q^{57} +6.46410 q^{58} +(1.09808 + 1.90192i) q^{59} +1.73205 q^{60} +(11.1962 + 6.46410i) q^{61} +8.19615 q^{62} +(-7.50000 + 2.59808i) q^{63} -1.00000 q^{64} +(-3.00000 - 1.73205i) q^{65} +(4.09808 + 7.09808i) q^{66} +(2.00000 + 3.46410i) q^{67} +(-3.80385 - 2.19615i) q^{69} +(1.73205 - 2.00000i) q^{70} -4.73205i q^{71} +(-2.59808 + 1.50000i) q^{72} +(6.00000 + 3.46410i) q^{73} +6.19615i q^{74} +(-0.866025 + 1.50000i) q^{75} +(-1.09808 - 0.633975i) q^{76} +(12.2942 + 2.36603i) q^{77} +6.00000 q^{78} +(-7.29423 + 12.6340i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(7.79423 - 4.50000i) q^{82} +(5.59808 + 9.69615i) q^{83} +(-0.866025 + 4.50000i) q^{84} +3.19615i q^{86} -11.1962i q^{87} +4.73205 q^{88} +(-2.19615 - 3.80385i) q^{89} -3.00000i q^{90} +(6.00000 - 6.92820i) q^{91} +(-2.19615 + 1.26795i) q^{92} -14.1962i q^{93} +(7.79423 - 4.50000i) q^{94} +(1.09808 - 0.633975i) q^{95} +1.73205i q^{96} +(7.39230 - 4.26795i) q^{97} +(4.33013 + 5.50000i) q^{98} +(12.2942 - 7.09808i) 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
\(11\) 4.73205i 1.42677i 0.700774 + 0.713384i \(0.252838\pi\)
−0.700774 + 0.713384i \(0.747162\pi\)
\(12\) −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
\(19\) −1.09808 + 0.633975i −0.251916 + 0.145444i −0.620641 0.784095i \(-0.713128\pi\)
0.368725 + 0.929538i \(0.379794\pi\)
\(20\) −0.500000 0.866025i −0.111803 0.193649i
\(21\) 3.46410 + 3.00000i 0.755929 + 0.654654i
\(22\) 2.36603 4.09808i 0.504438 0.873713i
\(23\) 2.53590i 0.528771i 0.964417 + 0.264386i \(0.0851692\pi\)
−0.964417 + 0.264386i \(0.914831\pi\)
\(24\) 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
\(29\) −5.59808 + 3.23205i −1.03954 + 0.600177i −0.919702 0.392617i \(-0.871570\pi\)
−0.119835 + 0.992794i \(0.538236\pi\)
\(30\) −1.50000 + 0.866025i −0.273861 + 0.158114i
\(31\) −7.09808 + 4.09808i −1.27485 + 0.736036i −0.975897 0.218231i \(-0.929971\pi\)
−0.298955 + 0.954267i \(0.596638\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) −7.09808 4.09808i −1.23562 0.713384i
\(34\) 0 0
\(35\) −0.500000 + 2.59808i −0.0845154 + 0.439155i
\(36\) 1.50000 2.59808i 0.250000 0.433013i
\(37\) −3.09808 5.36603i −0.509321 0.882169i −0.999942 0.0107961i \(-0.996563\pi\)
0.490621 0.871373i \(-0.336770\pi\)
\(38\) 1.26795 0.205689
\(39\) −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
\(43\) −1.59808 2.76795i −0.243704 0.422108i 0.718062 0.695979i \(-0.245029\pi\)
−0.961767 + 0.273871i \(0.911696\pi\)
\(44\) −4.09808 + 2.36603i −0.617808 + 0.356692i
\(45\) 1.50000 + 2.59808i 0.223607 + 0.387298i
\(46\) 1.26795 2.19615i 0.186949 0.323805i
\(47\) −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
\(53\) −6.29423 3.63397i −0.864579 0.499165i 0.000964138 1.00000i \(-0.499693\pi\)
−0.865543 + 0.500835i \(0.833026\pi\)
\(54\) −4.50000 2.59808i −0.612372 0.353553i
\(55\) 4.73205i 0.638070i
\(56\) −2.59808 0.500000i −0.347183 0.0668153i
\(57\) 2.19615i 0.290887i
\(58\) 6.46410 0.848778
\(59\) 1.09808 + 1.90192i 0.142957 + 0.247609i 0.928609 0.371060i \(-0.121005\pi\)
−0.785652 + 0.618669i \(0.787672\pi\)
\(60\) 1.73205 0.223607
\(61\) 11.1962 + 6.46410i 1.43352 + 0.827643i 0.997387 0.0722388i \(-0.0230144\pi\)
0.436133 + 0.899882i \(0.356348\pi\)
\(62\) 8.19615 1.04091
\(63\) −7.50000 + 2.59808i −0.944911 + 0.327327i
\(64\) −1.00000 −0.125000
\(65\) −3.00000 1.73205i −0.372104 0.214834i
\(66\) 4.09808 + 7.09808i 0.504438 + 0.873713i
\(67\) 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
\(69\) −3.80385 2.19615i −0.457929 0.264386i
\(70\) 1.73205 2.00000i 0.207020 0.239046i
\(71\) 4.73205i 0.561591i −0.959768 0.280796i \(-0.909402\pi\)
0.959768 0.280796i \(-0.0905983\pi\)
\(72\) −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 \(0.533784\pi\)
\(74\) 6.19615i 0.720288i
\(75\) −0.866025 + 1.50000i −0.100000 + 0.173205i
\(76\) −1.09808 0.633975i −0.125958 0.0727219i
\(77\) 12.2942 + 2.36603i 1.40106 + 0.269634i
\(78\) 6.00000 0.679366
\(79\) −7.29423 + 12.6340i −0.820665 + 1.42143i 0.0845230 + 0.996422i \(0.473063\pi\)
−0.905188 + 0.425012i \(0.860270\pi\)
\(80\) 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
\(83\) 5.59808 + 9.69615i 0.614469 + 1.06429i 0.990477 + 0.137675i \(0.0439629\pi\)
−0.376009 + 0.926616i \(0.622704\pi\)
\(84\) −0.866025 + 4.50000i −0.0944911 + 0.490990i
\(85\) 0 0
\(86\) 3.19615i 0.344650i
\(87\) 11.1962i 1.20035i
\(88\) 4.73205 0.504438
\(89\) −2.19615 3.80385i −0.232792 0.403207i 0.725837 0.687867i \(-0.241453\pi\)
−0.958629 + 0.284660i \(0.908119\pi\)
\(90\) 3.00000i 0.316228i
\(91\) 6.00000 6.92820i 0.628971 0.726273i
\(92\) −2.19615 + 1.26795i −0.228965 + 0.132193i
\(93\) 14.1962i 1.47207i
\(94\) 7.79423 4.50000i 0.803913 0.464140i
\(95\) 1.09808 0.633975i 0.112660 0.0650444i
\(96\) 1.73205i 0.176777i
\(97\) 7.39230 4.26795i 0.750575 0.433345i −0.0753267 0.997159i \(-0.524000\pi\)
0.825902 + 0.563814i \(0.190667\pi\)
\(98\) 4.33013 + 5.50000i 0.437409 + 0.555584i
\(99\) 12.2942 7.09808i 1.23562 0.713384i
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) −11.1962 −1.11406 −0.557029 0.830493i \(-0.688059\pi\)
−0.557029 + 0.830493i \(0.688059\pi\)
\(102\) 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
\(106\) 3.63397 + 6.29423i 0.352963 + 0.611350i
\(107\) 13.7942 7.96410i 1.33354 0.769919i 0.347698 0.937606i \(-0.386963\pi\)
0.985840 + 0.167688i \(0.0536300\pi\)
\(108\) 2.59808 + 4.50000i 0.250000 + 0.433013i
\(109\) 3.59808 6.23205i 0.344633 0.596922i −0.640654 0.767830i \(-0.721337\pi\)
0.985287 + 0.170908i \(0.0546700\pi\)
\(110\) −2.36603 + 4.09808i −0.225592 + 0.390736i
\(111\) 10.7321 1.01864
\(112\) 2.00000 + 1.73205i 0.188982 + 0.163663i
\(113\) −10.9019 6.29423i −1.02557 0.592111i −0.109855 0.993948i \(-0.535039\pi\)
−0.915711 + 0.401836i \(0.868372\pi\)
\(114\) −1.09808 + 1.90192i −0.102844 + 0.178131i
\(115\) 2.53590i 0.236474i
\(116\) −5.59808 3.23205i −0.519768 0.300088i
\(117\) 10.3923i 0.960769i
\(118\) 2.19615i 0.202172i
\(119\) 0 0
\(120\) −1.50000 0.866025i −0.136931 0.0790569i
\(121\) −11.3923 −1.03566
\(122\) −6.46410 11.1962i −0.585232 1.01365i
\(123\) −7.79423 13.5000i −0.702782 1.21725i
\(124\) −7.09808 4.09808i −0.637426 0.368018i
\(125\) −1.00000 −0.0894427
\(126\) 7.79423 + 1.50000i 0.694365 + 0.133631i
\(127\) −11.3923 −1.01090 −0.505452 0.862855i \(-0.668674\pi\)
−0.505452 + 0.862855i \(0.668674\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 5.53590 0.487409
\(130\) 1.73205 + 3.00000i 0.151911 + 0.263117i
\(131\) 4.39230 0.383757 0.191879 0.981419i \(-0.438542\pi\)
0.191879 + 0.981419i \(0.438542\pi\)
\(132\) 8.19615i 0.713384i
\(133\) 1.09808 + 3.16987i 0.0952153 + 0.274863i
\(134\) 4.00000i 0.345547i
\(135\) −5.19615 −0.447214
\(136\) 0 0
\(137\) 7.26795i 0.620943i −0.950583 0.310471i \(-0.899513\pi\)
0.950583 0.310471i \(-0.100487\pi\)
\(138\) 2.19615 + 3.80385i 0.186949 + 0.323805i
\(139\) 19.0981 + 11.0263i 1.61988 + 0.935237i 0.986950 + 0.161026i \(0.0514802\pi\)
0.632927 + 0.774211i \(0.281853\pi\)
\(140\) −2.50000 + 0.866025i −0.211289 + 0.0731925i
\(141\) −7.79423 13.5000i −0.656392 1.13691i
\(142\) −2.36603 + 4.09808i −0.198552 + 0.343903i
\(143\) −8.19615 + 14.1962i −0.685397 + 1.18714i
\(144\) 3.00000 0.250000
\(145\) 5.59808 3.23205i 0.464895 0.268407i
\(146\) −3.46410 6.00000i −0.286691 0.496564i
\(147\) 9.52628 7.50000i 0.785714 0.618590i
\(148\) 3.09808 5.36603i 0.254660 0.441085i
\(149\) 12.0000i 0.983078i 0.870855 + 0.491539i \(0.163566\pi\)
−0.870855 + 0.491539i \(0.836434\pi\)
\(150\) 1.50000 0.866025i 0.122474 0.0707107i
\(151\) −4.19615 −0.341478 −0.170739 0.985316i \(-0.554616\pi\)
−0.170739 + 0.985316i \(0.554616\pi\)
\(152\) 0.633975 + 1.09808i 0.0514221 + 0.0890657i
\(153\) 0 0
\(154\) −9.46410 8.19615i −0.762639 0.660465i
\(155\) 7.09808 4.09808i 0.570131 0.329165i
\(156\) −5.19615 3.00000i −0.416025 0.240192i
\(157\) −15.2942 + 8.83013i −1.22061 + 0.704721i −0.965049 0.262071i \(-0.915594\pi\)
−0.255564 + 0.966792i \(0.582261\pi\)
\(158\) 12.6340 7.29423i 1.00511 0.580298i
\(159\) 10.9019 6.29423i 0.864579 0.499165i
\(160\) −0.866025 + 0.500000i −0.0684653 + 0.0395285i
\(161\) 6.58846 + 1.26795i 0.519243 + 0.0999284i
\(162\) 7.79423 4.50000i 0.612372 0.353553i
\(163\) 4.19615 + 7.26795i 0.328668 + 0.569270i 0.982248 0.187588i \(-0.0600669\pi\)
−0.653580 + 0.756858i \(0.726734\pi\)
\(164\) −9.00000 −0.702782
\(165\) 7.09808 + 4.09808i 0.552584 + 0.319035i
\(166\) 11.1962i 0.868990i
\(167\) 5.19615 9.00000i 0.402090 0.696441i −0.591888 0.806020i \(-0.701617\pi\)
0.993978 + 0.109580i \(0.0349504\pi\)
\(168\) 3.00000 3.46410i 0.231455 0.267261i
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) 0 0
\(171\) 3.29423 + 1.90192i 0.251916 + 0.145444i
\(172\) 1.59808 2.76795i 0.121852 0.211054i
\(173\) 4.09808 7.09808i 0.311571 0.539657i −0.667132 0.744940i \(-0.732478\pi\)
0.978703 + 0.205283i \(0.0658115\pi\)
\(174\) −5.59808 + 9.69615i −0.424389 + 0.735063i
\(175\) 0.500000 2.59808i 0.0377964 0.196396i
\(176\) −4.09808 2.36603i −0.308904 0.178346i
\(177\) −3.80385 −0.285915
\(178\) 4.39230i 0.329217i
\(179\) 21.2942 + 12.2942i 1.59161 + 0.918914i 0.993032 + 0.117846i \(0.0375989\pi\)
0.598573 + 0.801068i \(0.295734\pi\)
\(180\) −1.50000 + 2.59808i −0.111803 + 0.193649i
\(181\) 13.3923i 0.995442i −0.867337 0.497721i \(-0.834170\pi\)
0.867337 0.497721i \(-0.165830\pi\)
\(182\) −8.66025 + 3.00000i −0.641941 + 0.222375i
\(183\) −19.3923 + 11.1962i −1.43352 + 0.827643i
\(184\) 2.53590 0.186949
\(185\) 3.09808 + 5.36603i 0.227775 + 0.394518i
\(186\) −7.09808 + 12.2942i −0.520456 + 0.901457i
\(187\) 0 0
\(188\) −9.00000 −0.656392
\(189\) 2.59808 13.5000i 0.188982 0.981981i
\(190\) −1.26795 −0.0919867
\(191\) 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
\(193\) −6.90192 11.9545i −0.496811 0.860502i 0.503182 0.864181i \(-0.332163\pi\)
−0.999993 + 0.00367804i \(0.998829\pi\)
\(194\) −8.53590 −0.612842
\(195\) 5.19615 3.00000i 0.372104 0.214834i
\(196\) −1.00000 6.92820i −0.0714286 0.494872i
\(197\) 23.6603i 1.68572i −0.538130 0.842862i \(-0.680869\pi\)
0.538130 0.842862i \(-0.319131\pi\)
\(198\) −14.1962 −1.00888
\(199\) 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
\(202\) 9.69615 + 5.59808i 0.682219 + 0.393879i
\(203\) 5.59808 + 16.1603i 0.392908 + 1.13423i
\(204\) 0 0
\(205\) 4.50000 7.79423i 0.314294 0.544373i
\(206\) 6.06218 10.5000i 0.422372 0.731570i
\(207\) 6.58846 3.80385i 0.457929 0.264386i
\(208\) −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
\(211\) 10.2942 17.8301i 0.708684 1.22748i −0.256662 0.966501i \(-0.582623\pi\)
0.965345 0.260975i \(-0.0840441\pi\)
\(212\) 7.26795i 0.499165i
\(213\) 7.09808 + 4.09808i 0.486352 + 0.280796i
\(214\) −15.9282 −1.08883
\(215\) 1.59808 + 2.76795i 0.108988 + 0.188773i
\(216\) 5.19615i 0.353553i
\(217\) 7.09808 + 20.4904i 0.481849 + 1.39098i
\(218\) −6.23205 + 3.59808i −0.422088 + 0.243692i
\(219\) −10.3923 + 6.00000i −0.702247 + 0.405442i
\(220\) 4.09808 2.36603i 0.276292 0.159517i
\(221\) 0 0
\(222\) −9.29423 5.36603i −0.623788 0.360144i
\(223\) 11.8923 6.86603i 0.796368 0.459783i −0.0458318 0.998949i \(-0.514594\pi\)
0.842199 + 0.539166i \(0.181260\pi\)
\(224\) −0.866025 2.50000i −0.0578638 0.167038i
\(225\) −1.50000 2.59808i −0.100000 0.173205i
\(226\) 6.29423 + 10.9019i 0.418686 + 0.725185i
\(227\) −16.3923 −1.08800 −0.543998 0.839087i \(-0.683090\pi\)
−0.543998 + 0.839087i \(0.683090\pi\)
\(228\) 1.90192 1.09808i 0.125958 0.0727219i
\(229\) 14.0718i 0.929891i 0.885339 + 0.464945i \(0.153926\pi\)
−0.885339 + 0.464945i \(0.846074\pi\)
\(230\) −1.26795 + 2.19615i −0.0836061 + 0.144810i
\(231\) −14.1962 + 16.3923i −0.934038 + 1.07853i
\(232\) 3.23205 + 5.59808i 0.212195 + 0.367532i
\(233\) 1.09808 0.633975i 0.0719374 0.0415331i −0.463600 0.886045i \(-0.653442\pi\)
0.535537 + 0.844512i \(0.320109\pi\)
\(234\) −5.19615 + 9.00000i −0.339683 + 0.588348i
\(235\) 4.50000 7.79423i 0.293548 0.508439i
\(236\) −1.09808 + 1.90192i −0.0714787 + 0.123805i
\(237\) −12.6340 21.8827i −0.820665 1.42143i
\(238\) 0 0
\(239\) 2.70577 + 1.56218i 0.175022 + 0.101049i 0.584952 0.811068i \(-0.301113\pi\)
−0.409930 + 0.912117i \(0.634447\pi\)
\(240\) 0.866025 + 1.50000i 0.0559017 + 0.0968246i
\(241\) 3.33975i 0.215132i 0.994198 + 0.107566i \(0.0343057\pi\)
−0.994198 + 0.107566i \(0.965694\pi\)
\(242\) 9.86603 + 5.69615i 0.634212 + 0.366163i
\(243\) −7.79423 13.5000i −0.500000 0.866025i
\(244\) 12.9282i 0.827643i
\(245\) 6.50000 + 2.59808i 0.415270 + 0.165985i
\(246\) 15.5885i 0.993884i
\(247\) −4.39230 −0.279476
\(248\) 4.09808 + 7.09808i 0.260228 + 0.450728i
\(249\) −19.3923 −1.22894
\(250\) 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
\(254\) 9.86603 + 5.69615i 0.619049 + 0.357408i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 28.3923 1.77106 0.885532 0.464579i \(-0.153794\pi\)
0.885532 + 0.464579i \(0.153794\pi\)
\(258\) −4.79423 2.76795i −0.298476 0.172325i
\(259\) −15.4904 + 5.36603i −0.962525 + 0.333429i
\(260\) 3.46410i 0.214834i
\(261\) 16.7942 + 9.69615i 1.03954 + 0.600177i
\(262\) −3.80385 2.19615i −0.235002 0.135679i
\(263\) 13.7321i 0.846755i 0.905953 + 0.423377i \(0.139156\pi\)
−0.905953 + 0.423377i \(0.860844\pi\)
\(264\) −4.09808 + 7.09808i −0.252219 + 0.436856i
\(265\) 6.29423 + 3.63397i 0.386651 + 0.223233i
\(266\) 0.633975 3.29423i 0.0388715 0.201982i
\(267\) 7.60770 0.465583
\(268\) −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
\(271\) 5.70577 3.29423i 0.346601 0.200110i −0.316586 0.948564i \(-0.602537\pi\)
0.663187 + 0.748454i \(0.269203\pi\)
\(272\) 0 0
\(273\) 5.19615 + 15.0000i 0.314485 + 0.907841i
\(274\) −3.63397 + 6.29423i −0.219536 + 0.380248i
\(275\) 4.73205i 0.285353i
\(276\) 4.39230i 0.264386i
\(277\) −24.1962 −1.45381 −0.726903 0.686740i \(-0.759041\pi\)
−0.726903 + 0.686740i \(0.759041\pi\)
\(278\) −11.0263 19.0981i −0.661312 1.14543i
\(279\) 21.2942 + 12.2942i 1.27485 + 0.736036i
\(280\) 2.59808 + 0.500000i 0.155265 + 0.0298807i
\(281\) 12.6962 7.33013i 0.757389 0.437279i −0.0709685 0.997479i \(-0.522609\pi\)
0.828357 + 0.560200i \(0.189276\pi\)
\(282\) 15.5885i 0.928279i
\(283\) −14.5981 + 8.42820i −0.867766 + 0.501005i −0.866605 0.498995i \(-0.833703\pi\)
−0.00116049 + 0.999999i \(0.500369\pi\)
\(284\) 4.09808 2.36603i 0.243176 0.140398i
\(285\) 2.19615i 0.130089i
\(286\) 14.1962 8.19615i 0.839436 0.484649i
\(287\) 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
\(290\) −6.46410 −0.379585
\(291\) 14.7846i 0.866689i
\(292\) 6.92820i 0.405442i
\(293\) −8.19615 + 14.1962i −0.478824 + 0.829348i −0.999705 0.0242813i \(-0.992270\pi\)
0.520881 + 0.853629i \(0.325604\pi\)
\(294\) −12.0000 + 1.73205i −0.699854 + 0.101015i
\(295\) −1.09808 1.90192i −0.0639325 0.110734i
\(296\) −5.36603 + 3.09808i −0.311894 + 0.180072i
\(297\) 24.5885i 1.42677i
\(298\) 6.00000 10.3923i 0.347571 0.602010i
\(299\) −4.39230 + 7.60770i −0.254014 + 0.439964i
\(300\) −1.73205 −0.100000
\(301\) −7.99038 + 2.76795i −0.460558 + 0.159542i
\(302\) 3.63397 + 2.09808i 0.209112 + 0.120731i
\(303\) 9.69615 16.7942i 0.557029 0.964803i
\(304\) 1.26795i 0.0727219i
\(305\) −11.1962 6.46410i −0.641090 0.370133i
\(306\) 0 0
\(307\) 23.7846i 1.35746i 0.734388 + 0.678730i \(0.237469\pi\)
−0.734388 + 0.678730i \(0.762531\pi\)
\(308\) 4.09808 + 11.8301i 0.233510 + 0.674084i
\(309\) −18.1865 10.5000i −1.03460 0.597324i
\(310\) −8.19615 −0.465510
\(311\) −7.90192 13.6865i −0.448077 0.776092i 0.550184 0.835044i \(-0.314558\pi\)
−0.998261 + 0.0589514i \(0.981224\pi\)
\(312\) 3.00000 + 5.19615i 0.169842 + 0.294174i
\(313\) −17.4904 10.0981i −0.988615 0.570777i −0.0837548 0.996486i \(-0.526691\pi\)
−0.904860 + 0.425709i \(0.860025\pi\)
\(314\) 17.6603 0.996626
\(315\) 7.50000 2.59808i 0.422577 0.146385i
\(316\) −14.5885 −0.820665
\(317\) 17.7846 + 10.2679i 0.998883 + 0.576705i 0.907918 0.419149i \(-0.137671\pi\)
0.0909655 + 0.995854i \(0.471005\pi\)
\(318\) −12.5885 −0.705926
\(319\) −15.2942 26.4904i −0.856312 1.48318i
\(320\) 1.00000 0.0559017
\(321\) 27.5885i 1.53984i
\(322\) −5.07180 4.39230i −0.282640 0.244774i
\(323\) 0 0
\(324\) −9.00000 −0.500000
\(325\) 3.00000 + 1.73205i 0.166410 + 0.0960769i
\(326\) 8.39230i 0.464807i
\(327\) 6.23205 + 10.7942i 0.344633 + 0.596922i
\(328\) 7.79423 + 4.50000i 0.430364 + 0.248471i
\(329\) 18.0000 + 15.5885i 0.992372 + 0.859419i
\(330\) −4.09808 7.09808i −0.225592 0.390736i
\(331\) 4.00000 6.92820i 0.219860 0.380808i −0.734905 0.678170i \(-0.762773\pi\)
0.954765 + 0.297361i \(0.0961066\pi\)
\(332\) −5.59808 + 9.69615i −0.307234 + 0.532145i
\(333\) −9.29423 + 16.0981i −0.509321 + 0.882169i
\(334\) −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
\(339\) 18.8827 10.9019i 1.02557 0.592111i
\(340\) 0 0
\(341\) −19.3923 33.5885i −1.05015 1.81892i
\(342\) −1.90192 3.29423i −0.102844 0.178131i
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) −2.76795 + 1.59808i −0.149238 + 0.0861625i
\(345\) 3.80385 + 2.19615i 0.204792 + 0.118237i
\(346\) −7.09808 + 4.09808i −0.381595 + 0.220314i
\(347\) 18.4019 10.6244i 0.987867 0.570345i 0.0832310 0.996530i \(-0.473476\pi\)
0.904636 + 0.426185i \(0.140143\pi\)
\(348\) 9.69615 5.59808i 0.519768 0.300088i
\(349\) 14.1962 8.19615i 0.759903 0.438730i −0.0693582 0.997592i \(-0.522095\pi\)
0.829261 + 0.558862i \(0.188762\pi\)
\(350\) −1.73205 + 2.00000i −0.0925820 + 0.106904i
\(351\) 15.5885 + 9.00000i 0.832050 + 0.480384i
\(352\) 2.36603 + 4.09808i 0.126110 + 0.218428i
\(353\) −0.588457 −0.0313204 −0.0156602 0.999877i \(-0.504985\pi\)
−0.0156602 + 0.999877i \(0.504985\pi\)
\(354\) 3.29423 + 1.90192i 0.175086 + 0.101086i
\(355\) 4.73205i 0.251151i
\(356\) 2.19615 3.80385i 0.116396 0.201604i
\(357\) 0 0
\(358\) −12.2942 21.2942i −0.649770 1.12543i
\(359\) −13.6865 + 7.90192i −0.722348 + 0.417048i −0.815616 0.578593i \(-0.803602\pi\)
0.0932685 + 0.995641i \(0.470268\pi\)
\(360\) 2.59808 1.50000i 0.136931 0.0790569i
\(361\) −8.69615 + 15.0622i −0.457692 + 0.792746i
\(362\) −6.69615 + 11.5981i −0.351942 + 0.609581i
\(363\) 9.86603 17.0885i 0.517832 0.896911i
\(364\) 9.00000 + 1.73205i 0.471728 + 0.0907841i
\(365\) −6.00000 3.46410i −0.314054 0.181319i
\(366\) 22.3923 1.17046
\(367\) 29.1962i 1.52403i −0.647561 0.762013i \(-0.724211\pi\)
0.647561 0.762013i \(-0.275789\pi\)
\(368\) −2.19615 1.26795i −0.114482 0.0660964i
\(369\) 27.0000 1.40556
\(370\) 6.19615i 0.322123i
\(371\) −12.5885 + 14.5359i −0.653560 + 0.754666i
\(372\) 12.2942 7.09808i 0.637426 0.368018i
\(373\) 10.1962 0.527937 0.263968 0.964531i \(-0.414969\pi\)
0.263968 + 0.964531i \(0.414969\pi\)
\(374\) 0 0
\(375\) 0.866025 1.50000i 0.0447214 0.0774597i
\(376\) 7.79423 + 4.50000i 0.401957 + 0.232070i
\(377\) −22.3923 −1.15326
\(378\) −9.00000 + 10.3923i −0.462910 + 0.534522i
\(379\) −9.60770 −0.493514 −0.246757 0.969077i \(-0.579365\pi\)
−0.246757 + 0.969077i \(0.579365\pi\)
\(380\) 1.09808 + 0.633975i 0.0563301 + 0.0325222i
\(381\) 9.86603 17.0885i 0.505452 0.875468i
\(382\) −1.73205 3.00000i −0.0886194 0.153493i
\(383\) 19.3923 0.990900 0.495450 0.868636i \(-0.335003\pi\)
0.495450 + 0.868636i \(0.335003\pi\)
\(384\) −1.50000 + 0.866025i −0.0765466 + 0.0441942i
\(385\) −12.2942 2.36603i −0.626572 0.120584i
\(386\) 13.8038i 0.702597i
\(387\) −4.79423 + 8.30385i −0.243704 + 0.422108i
\(388\) 7.39230 + 4.26795i 0.375287 + 0.216672i
\(389\) 24.7128i 1.25299i −0.779426 0.626495i \(-0.784489\pi\)
0.779426 0.626495i \(-0.215511\pi\)
\(390\) −6.00000 −0.303822
\(391\) 0 0
\(392\) −2.59808 + 6.50000i −0.131223 + 0.328300i
\(393\) −3.80385 + 6.58846i −0.191879 + 0.332344i
\(394\) −11.8301 + 20.4904i −0.595993 + 1.03229i
\(395\) 7.29423 12.6340i 0.367012 0.635684i
\(396\) 12.2942 + 7.09808i 0.617808 + 0.356692i
\(397\) −26.4904 + 15.2942i −1.32951 + 0.767595i −0.985224 0.171268i \(-0.945214\pi\)
−0.344290 + 0.938863i \(0.611880\pi\)
\(398\) −3.46410 6.00000i −0.173640 0.300753i
\(399\) −5.70577 1.09808i −0.285646 0.0549726i
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) 3.58846i 0.179199i 0.995978 + 0.0895995i \(0.0285587\pi\)
−0.995978 + 0.0895995i \(0.971441\pi\)
\(402\) 6.00000 + 3.46410i 0.299253 + 0.172774i
\(403\) −28.3923 −1.41432
\(404\) −5.59808 9.69615i −0.278515 0.482402i
\(405\) 4.50000 7.79423i 0.223607 0.387298i
\(406\) 3.23205 16.7942i 0.160404 0.833484i
\(407\) 25.3923 14.6603i 1.25865 0.726682i
\(408\) 0 0
\(409\) −9.10770 + 5.25833i −0.450347 + 0.260008i −0.707977 0.706236i \(-0.750392\pi\)
0.257630 + 0.966244i \(0.417058\pi\)
\(410\) −7.79423 + 4.50000i −0.384930 + 0.222239i
\(411\) 10.9019 + 6.29423i 0.537752 + 0.310471i
\(412\) −10.5000 + 6.06218i −0.517298 + 0.298662i
\(413\) 5.49038 1.90192i 0.270164 0.0935876i
\(414\) −7.60770 −0.373898
\(415\) −5.59808 9.69615i −0.274799 0.475965i
\(416\) 3.46410 0.169842
\(417\) −33.0788 + 19.0981i −1.61988 + 0.935237i
\(418\) 6.00000i 0.293470i
\(419\) 5.19615 9.00000i 0.253849 0.439679i −0.710734 0.703461i \(-0.751637\pi\)
0.964582 + 0.263783i \(0.0849701\pi\)
\(420\) 0.866025 4.50000i 0.0422577 0.219578i
\(421\) 14.9904 + 25.9641i 0.730586 + 1.26541i 0.956633 + 0.291296i \(0.0940866\pi\)
−0.226046 + 0.974117i \(0.572580\pi\)
\(422\) −17.8301 + 10.2942i −0.867957 + 0.501115i
\(423\) 27.0000 1.31278
\(424\) −3.63397 + 6.29423i −0.176481 + 0.305675i
\(425\) 0 0
\(426\) −4.09808 7.09808i −0.198552 0.343903i
\(427\) 22.3923 25.8564i 1.08364 1.25128i
\(428\) 13.7942 + 7.96410i 0.666769 + 0.384959i
\(429\) −14.1962 24.5885i −0.685397 1.18714i
\(430\) 3.19615i 0.154132i
\(431\) −33.5885 19.3923i −1.61790 0.934094i −0.987463 0.157854i \(-0.949543\pi\)
−0.630437 0.776241i \(-0.717124\pi\)
\(432\) −2.59808 + 4.50000i −0.125000 + 0.216506i
\(433\) 18.0000i 0.865025i −0.901628 0.432512i \(-0.857627\pi\)
0.901628 0.432512i \(-0.142373\pi\)
\(434\) 4.09808 21.2942i 0.196714 1.02216i
\(435\) 11.1962i 0.536814i
\(436\) 7.19615 0.344633
\(437\) −1.60770 2.78461i −0.0769065 0.133206i
\(438\) 12.0000 0.573382
\(439\) 25.6865 + 14.8301i 1.22595 + 0.707803i 0.966180 0.257867i \(-0.0830196\pi\)
0.259771 + 0.965670i \(0.416353\pi\)
\(440\) −4.73205 −0.225592
\(441\) 3.00000 + 20.7846i 0.142857 + 0.989743i
\(442\) 0 0
\(443\) 7.79423 + 4.50000i 0.370315 + 0.213801i 0.673596 0.739100i \(-0.264749\pi\)
−0.303281 + 0.952901i \(0.598082\pi\)
\(444\) 5.36603 + 9.29423i 0.254660 + 0.441085i
\(445\) 2.19615 + 3.80385i 0.104108 + 0.180320i
\(446\) −13.7321 −0.650231
\(447\) −18.0000 10.3923i −0.851371 0.491539i
\(448\) −0.500000 + 2.59808i −0.0236228 + 0.122748i
\(449\) 9.58846i 0.452507i 0.974068 + 0.226254i \(0.0726478\pi\)
−0.974068 + 0.226254i \(0.927352\pi\)
\(450\) 3.00000i 0.141421i
\(451\) −36.8827 21.2942i −1.73674 1.00271i
\(452\) 12.5885i 0.592111i
\(453\) 3.63397 6.29423i 0.170739 0.295729i
\(454\) 14.1962 + 8.19615i 0.666258 + 0.384664i
\(455\) −6.00000 + 6.92820i −0.281284 + 0.324799i
\(456\) −2.19615 −0.102844
\(457\) −1.19615 + 2.07180i −0.0559537 + 0.0969146i −0.892645 0.450759i \(-0.851153\pi\)
0.836692 + 0.547674i \(0.184487\pi\)
\(458\) 7.03590 12.1865i 0.328766 0.569439i
\(459\) 0 0
\(460\) 2.19615 1.26795i 0.102396 0.0591184i
\(461\) −2.59808 4.50000i −0.121004 0.209586i 0.799160 0.601119i \(-0.205278\pi\)
−0.920164 + 0.391533i \(0.871945\pi\)
\(462\) 20.4904 7.09808i 0.953299 0.330232i
\(463\) 1.30385 2.25833i 0.0605949 0.104954i −0.834137 0.551558i \(-0.814034\pi\)
0.894731 + 0.446604i \(0.147367\pi\)
\(464\) 6.46410i 0.300088i
\(465\) 14.1962i 0.658331i
\(466\) −1.26795 −0.0587366
\(467\) 3.40192 + 5.89230i 0.157422 + 0.272663i 0.933938 0.357434i \(-0.116348\pi\)
−0.776516 + 0.630097i \(0.783015\pi\)
\(468\) 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
\(471\) 30.5885i 1.40944i
\(472\) 1.90192 1.09808i 0.0875431 0.0505431i
\(473\) 13.0981 7.56218i 0.602250 0.347709i
\(474\) 25.2679i 1.16060i
\(475\) −1.09808 + 0.633975i −0.0503832 + 0.0290887i
\(476\) 0 0
\(477\) 21.8038i 0.998330i
\(478\) −1.56218 2.70577i −0.0714524 0.123759i
\(479\) −10.3923 −0.474837 −0.237418 0.971408i \(-0.576301\pi\)
−0.237418 + 0.971408i \(0.576301\pi\)
\(480\) 1.73205i 0.0790569i
\(481\) 21.4641i 0.978679i
\(482\) 1.66987 2.89230i 0.0760606 0.131741i
\(483\) −7.60770 + 8.78461i −0.346162 + 0.399714i
\(484\) −5.69615 9.86603i −0.258916 0.448456i
\(485\) −7.39230 + 4.26795i −0.335667 + 0.193798i
\(486\) 15.5885i 0.707107i
\(487\) −17.0000 + 29.4449i −0.770344 + 1.33427i 0.167031 + 0.985952i \(0.446582\pi\)
−0.937375 + 0.348323i \(0.886751\pi\)
\(488\) 6.46410 11.1962i 0.292616 0.506826i
\(489\) −14.5359 −0.657336
\(490\) −4.33013 5.50000i −0.195615 0.248465i
\(491\) −23.4904 13.5622i −1.06011 0.612053i −0.134644 0.990894i \(-0.542989\pi\)
−0.925462 + 0.378841i \(0.876323\pi\)
\(492\) 7.79423 13.5000i 0.351391 0.608627i
\(493\) 0 0
\(494\) 3.80385 + 2.19615i 0.171143 + 0.0988096i
\(495\) −12.2942 + 7.09808i −0.552584 + 0.319035i
\(496\) 8.19615i 0.368018i
\(497\) −12.2942 2.36603i −0.551472 0.106131i
\(498\) 16.7942 + 9.69615i 0.752567 + 0.434495i
\(499\) −16.1962 −0.725039 −0.362520 0.931976i \(-0.618083\pi\)
−0.362520 + 0.931976i \(0.618083\pi\)
\(500\) −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
\(503\) −7.39230 −0.329607 −0.164803 0.986326i \(-0.552699\pi\)
−0.164803 + 0.986326i \(0.552699\pi\)
\(504\) 2.59808 + 7.50000i 0.115728 + 0.334077i
\(505\) 11.1962 0.498222
\(506\) 10.3923 + 6.00000i 0.461994 + 0.266733i
\(507\) 1.73205 0.0769231
\(508\) −5.69615 9.86603i −0.252726 0.437734i
\(509\) 9.58846 0.425001 0.212500 0.977161i \(-0.431839\pi\)
0.212500 + 0.977161i \(0.431839\pi\)
\(510\) 0 0
\(511\) 12.0000 13.8564i 0.530849 0.612971i
\(512\) 1.00000i 0.0441942i
\(513\) −5.70577 + 3.29423i −0.251916 + 0.145444i
\(514\) −24.5885 14.1962i −1.08455 0.626165i
\(515\) 12.1244i 0.534263i
\(516\) 2.76795 + 4.79423i 0.121852 + 0.211054i
\(517\) −36.8827 21.2942i −1.62210 0.936519i
\(518\) 16.0981 + 3.09808i 0.707309 + 0.136122i
\(519\) 7.09808 + 12.2942i 0.311571 + 0.539657i
\(520\) −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 \(0.0145113\pi\)
\(522\) −9.69615 16.7942i −0.424389 0.735063i
\(523\) 28.5788 16.5000i 1.24967 0.721495i 0.278623 0.960401i \(-0.410122\pi\)
0.971043 + 0.238906i \(0.0767888\pi\)
\(524\) 2.19615 + 3.80385i 0.0959394 + 0.166172i
\(525\) 3.46410 + 3.00000i 0.151186 + 0.130931i
\(526\) 6.86603 11.8923i 0.299373 0.518529i
\(527\) 0 0
\(528\) 7.09808 4.09808i 0.308904 0.178346i
\(529\) 16.5692 0.720401
\(530\) −3.63397 6.29423i −0.157850 0.273404i
\(531\) 3.29423 5.70577i 0.142957 0.247609i
\(532\) −2.19615 + 2.53590i −0.0952153 + 0.109945i
\(533\) −27.0000 + 15.5885i −1.16950 + 0.675211i
\(534\) −6.58846 3.80385i −0.285110 0.164609i
\(535\) −13.7942 + 7.96410i −0.596377 + 0.344318i
\(536\) 3.46410 2.00000i 0.149626 0.0863868i
\(537\) −36.8827 + 21.2942i −1.59161 + 0.918914i
\(538\) −15.5885 + 9.00000i −0.672066 + 0.388018i
\(539\) 12.2942 30.7583i 0.529550 1.32486i
\(540\) −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 \(0.888348\pi\)
\(542\) −6.58846 −0.282998
\(543\) 20.0885 + 11.5981i 0.862078 + 0.497721i
\(544\) 0 0
\(545\) −3.59808 + 6.23205i −0.154125 + 0.266952i
\(546\) 3.00000 15.5885i 0.128388 0.667124i
\(547\) −2.79423 4.83975i −0.119473 0.206933i 0.800086 0.599885i \(-0.204787\pi\)
−0.919559 + 0.392952i \(0.871454\pi\)
\(548\) 6.29423 3.63397i 0.268876 0.155236i
\(549\) 38.7846i 1.65529i
\(550\) 2.36603 4.09808i 0.100888 0.174743i
\(551\) 4.09808 7.09808i 0.174584 0.302388i
\(552\) −2.19615 + 3.80385i −0.0934745 + 0.161903i
\(553\) 29.1769 + 25.2679i 1.24073 + 1.07450i
\(554\) 20.9545 + 12.0981i 0.890271 + 0.513998i
\(555\) −10.7321 −0.455550
\(556\) 22.0526i 0.935237i
\(557\) 28.3923 + 16.3923i 1.20302 + 0.694564i 0.961226 0.275763i \(-0.0889305\pi\)
0.241795 + 0.970327i \(0.422264\pi\)
\(558\) −12.2942 21.2942i −0.520456 0.901457i
\(559\) 11.0718i 0.468287i
\(560\) −2.00000 1.73205i −0.0845154 0.0731925i
\(561\) 0 0
\(562\) −14.6603 −0.618405
\(563\) −6.80385 11.7846i −0.286748 0.496662i 0.686284 0.727334i \(-0.259241\pi\)
−0.973032 + 0.230672i \(0.925908\pi\)
\(564\) 7.79423 13.5000i 0.328196 0.568453i
\(565\) 10.9019 + 6.29423i 0.458647 + 0.264800i
\(566\) 16.8564 0.708528
\(567\) 18.0000 + 15.5885i 0.755929 + 0.654654i
\(568\) −4.73205 −0.198552
\(569\) −5.19615 3.00000i −0.217834 0.125767i 0.387113 0.922032i \(-0.373472\pi\)
−0.604947 + 0.796266i \(0.706806\pi\)
\(570\) 1.09808 1.90192i 0.0459934 0.0796628i
\(571\) −10.8038 18.7128i −0.452127 0.783107i 0.546391 0.837530i \(-0.316001\pi\)
−0.998518 + 0.0544234i \(0.982668\pi\)
\(572\) −16.3923 −0.685397
\(573\) −5.19615 + 3.00000i −0.217072 + 0.125327i
\(574\) −7.79423 22.5000i −0.325325 0.939132i
\(575\) 2.53590i 0.105754i
\(576\) 1.50000 + 2.59808i 0.0625000 + 0.108253i
\(577\) 20.7846 + 12.0000i 0.865275 + 0.499567i 0.865775 0.500433i \(-0.166826\pi\)
−0.000500448 1.00000i \(0.500159\pi\)
\(578\) 17.0000i 0.707107i
\(579\) 23.9090 0.993623
\(580\) 5.59808 + 3.23205i 0.232447 + 0.134204i
\(581\) 27.9904 9.69615i 1.16124 0.402264i
\(582\) 7.39230 12.8038i 0.306421 0.530737i
\(583\) 17.1962 29.7846i 0.712192 1.23355i
\(584\) 3.46410 6.00000i 0.143346 0.248282i
\(585\) 10.3923i 0.429669i
\(586\) 14.1962 8.19615i 0.586438 0.338580i
\(587\) 15.4019 + 26.6769i 0.635705 + 1.10107i 0.986365 + 0.164571i \(0.0526240\pi\)
−0.350660 + 0.936503i \(0.614043\pi\)
\(588\) 11.2583 + 4.50000i 0.464286 + 0.185577i
\(589\) 5.19615 9.00000i 0.214104 0.370839i
\(590\) 2.19615i 0.0904142i
\(591\) 35.4904 + 20.4904i 1.45988 + 0.842862i
\(592\) 6.19615 0.254660
\(593\) −13.3923 23.1962i −0.549956 0.952552i −0.998277 0.0586791i \(-0.981311\pi\)
0.448321 0.893873i \(-0.352022\pi\)
\(594\) 12.2942 21.2942i 0.504438 0.873713i
\(595\) 0 0
\(596\) −10.3923 + 6.00000i −0.425685 + 0.245770i
\(597\) −10.3923 + 6.00000i −0.425329 + 0.245564i
\(598\) 7.60770 4.39230i 0.311102 0.179615i
\(599\) 3.80385 2.19615i 0.155421 0.0897324i −0.420272 0.907398i \(-0.638066\pi\)
0.575693 + 0.817666i \(0.304732\pi\)
\(600\) 1.50000 + 0.866025i 0.0612372 + 0.0353553i
\(601\) 27.5885 15.9282i 1.12536 0.649725i 0.182594 0.983188i \(-0.441551\pi\)
0.942763 + 0.333464i \(0.108217\pi\)
\(602\) 8.30385 + 1.59808i 0.338440 + 0.0651327i
\(603\) 6.00000 10.3923i 0.244339 0.423207i
\(604\) −2.09808 3.63397i −0.0853695 0.147864i
\(605\) 11.3923 0.463163
\(606\) −16.7942 + 9.69615i −0.682219 + 0.393879i
\(607\) 6.12436i 0.248580i 0.992246 + 0.124290i \(0.0396653\pi\)
−0.992246 + 0.124290i \(0.960335\pi\)
\(608\) −0.633975 + 1.09808i −0.0257111 + 0.0445329i
\(609\) −29.0885 5.59808i −1.17872 0.226845i
\(610\) 6.46410 + 11.1962i 0.261724 + 0.453319i
\(611\) −27.0000 + 15.5885i −1.09230 + 0.630641i
\(612\) 0 0
\(613\) 3.39230 5.87564i 0.137014 0.237315i −0.789351 0.613942i \(-0.789583\pi\)
0.926365 + 0.376627i \(0.122916\pi\)
\(614\) 11.8923 20.5981i 0.479934 0.831271i
\(615\) 7.79423 + 13.5000i 0.314294 + 0.544373i
\(616\) 2.36603 12.2942i 0.0953299 0.495349i
\(617\) 15.8038 + 9.12436i 0.636239 + 0.367333i 0.783164 0.621815i \(-0.213604\pi\)
−0.146925 + 0.989148i \(0.546938\pi\)
\(618\) 10.5000 + 18.1865i 0.422372 + 0.731570i
\(619\) 16.3923i 0.658862i 0.944180 + 0.329431i \(0.106857\pi\)
−0.944180 + 0.329431i \(0.893143\pi\)
\(620\) 7.09808 + 4.09808i 0.285066 + 0.164583i
\(621\) 13.1769i 0.528771i
\(622\) 15.8038i 0.633677i
\(623\) −10.9808 + 3.80385i −0.439935 + 0.152398i
\(624\) 6.00000i 0.240192i
\(625\) 1.00000 0.0400000
\(626\) 10.0981 + 17.4904i 0.403600 + 0.699056i
\(627\) 10.3923 0.415029
\(628\) −15.2942 8.83013i −0.610306 0.352360i
\(629\) 0 0
\(630\) −7.79423 1.50000i −0.310530 0.0597614i
\(631\) 12.3923 0.493330 0.246665 0.969101i \(-0.420665\pi\)
0.246665 + 0.969101i \(0.420665\pi\)
\(632\) 12.6340 + 7.29423i 0.502553 + 0.290149i
\(633\) 17.8301 + 30.8827i 0.708684 + 1.22748i
\(634\) −10.2679 17.7846i −0.407792 0.706317i
\(635\) 11.3923 0.452090
\(636\) 10.9019 + 6.29423i 0.432289 + 0.249582i
\(637\) −15.0000 19.0526i −0.594322 0.754890i
\(638\) 30.5885i 1.21101i
\(639\) −12.2942 + 7.09808i −0.486352 + 0.280796i
\(640\) −0.866025 0.500000i −0.0342327 0.0197642i
\(641\) 3.21539i 0.127000i −0.997982 0.0635001i \(-0.979774\pi\)
0.997982 0.0635001i \(-0.0202263\pi\)
\(642\) 13.7942 23.8923i 0.544415 0.942954i
\(643\) 16.2058 + 9.35641i 0.639093 + 0.368981i 0.784265 0.620426i \(-0.213040\pi\)
−0.145172 + 0.989406i \(0.546374\pi\)
\(644\) 2.19615 + 6.33975i 0.0865405 + 0.249821i
\(645\) −5.53590 −0.217976
\(646\) 0 0
\(647\) 2.30385 3.99038i 0.0905736 0.156878i −0.817179 0.576384i \(-0.804463\pi\)
0.907753 + 0.419506i \(0.137797\pi\)
\(648\) 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
\(651\) −36.8827 7.09808i −1.44555 0.278196i
\(652\) −4.19615 + 7.26795i −0.164334 + 0.284635i
\(653\) 49.8564i 1.95103i −0.219929 0.975516i \(-0.570582\pi\)
0.219929 0.975516i \(-0.429418\pi\)
\(654\) 12.4641i 0.487385i
\(655\) −4.39230 −0.171622
\(656\) −4.50000 7.79423i −0.175695 0.304314i
\(657\) 20.7846i 0.810885i
\(658\) −7.79423 22.5000i −0.303851 0.877141i
\(659\) −33.2942 + 19.2224i −1.29696 + 0.748800i −0.979878 0.199599i \(-0.936036\pi\)
−0.317081 + 0.948398i \(0.602703\pi\)
\(660\) 8.19615i 0.319035i
\(661\) 11.3827 6.57180i 0.442735 0.255613i −0.262022 0.965062i \(-0.584389\pi\)
0.704757 + 0.709449i \(0.251056\pi\)
\(662\) −6.92820 + 4.00000i −0.269272 + 0.155464i
\(663\) 0 0
\(664\) 9.69615 5.59808i 0.376284 0.217247i
\(665\) −1.09808 3.16987i −0.0425816 0.122922i
\(666\) 16.0981 9.29423i 0.623788 0.360144i
\(667\) −8.19615 14.1962i −0.317356 0.549677i
\(668\) 10.3923 0.402090
\(669\) 23.7846i 0.919566i
\(670\) 4.00000i 0.154533i
\(671\) −30.5885 + 52.9808i −1.18085 + 2.04530i
\(672\) 4.50000 + 0.866025i 0.173591 + 0.0334077i
\(673\) 12.4904 + 21.6340i 0.481469 + 0.833928i 0.999774 0.0212674i \(-0.00677013\pi\)
−0.518305 + 0.855196i \(0.673437\pi\)
\(674\) 8.66025 5.00000i 0.333581 0.192593i
\(675\) 5.19615 0.200000
\(676\) 0.500000 0.866025i 0.0192308 0.0333087i
\(677\) 11.4904 19.9019i 0.441611 0.764893i −0.556198 0.831050i \(-0.687740\pi\)
0.997809 + 0.0661567i \(0.0210737\pi\)
\(678\) −21.8038 −0.837372
\(679\) −7.39230 21.3397i −0.283691 0.818944i
\(680\) 0 0
\(681\) 14.1962 24.5885i 0.543998 0.942232i
\(682\) 38.7846i 1.48514i
\(683\) 30.7750 + 17.7679i 1.17757 + 0.679872i 0.955452 0.295148i \(-0.0953688\pi\)
0.222121 + 0.975019i \(0.428702\pi\)
\(684\) 3.80385i 0.145444i
\(685\) 7.26795i 0.277694i
\(686\) 16.4545 8.50000i 0.628235 0.324532i
\(687\) −21.1077 12.1865i −0.805309 0.464945i
\(688\) 3.19615 0.121852
\(689\) −12.5885 21.8038i −0.479582 0.830660i
\(690\) −2.19615 3.80385i −0.0836061 0.144810i
\(691\) −4.39230 2.53590i −0.167091 0.0964701i 0.414122 0.910221i \(-0.364089\pi\)
−0.581214 + 0.813751i \(0.697422\pi\)
\(692\) 8.19615 0.311571
\(693\) −12.2942 35.4904i −0.467019 1.34817i
\(694\) −21.2487 −0.806590
\(695\) −19.0981 11.0263i −0.724431 0.418251i
\(696\) −11.1962 −0.424389
\(697\) 0 0
\(698\) −16.3923 −0.620458
\(699\) 2.19615i 0.0830661i
\(700\) 2.50000 0.866025i 0.0944911 0.0327327i
\(701\) 44.3205i 1.67396i 0.547232 + 0.836981i \(0.315682\pi\)
−0.547232 + 0.836981i \(0.684318\pi\)
\(702\) −9.00000 15.5885i −0.339683 0.588348i
\(703\) 6.80385 + 3.92820i 0.256612 + 0.148155i
\(704\) 4.73205i 0.178346i
\(705\) 7.79423 + 13.5000i 0.293548 + 0.508439i
\(706\) 0.509619 + 0.294229i 0.0191798 + 0.0110734i
\(707\) −5.59808 + 29.0885i −0.210537 + 1.09398i
\(708\) −1.90192 3.29423i −0.0714787 0.123805i
\(709\) 23.3923 40.5167i 0.878516 1.52164i 0.0255474 0.999674i \(-0.491867\pi\)
0.852969 0.521962i \(-0.174800\pi\)
\(710\) 2.36603 4.09808i 0.0887954 0.153798i
\(711\) 43.7654 1.64133
\(712\) −3.80385 + 2.19615i −0.142555 + 0.0823043i
\(713\) −10.3923 18.0000i −0.389195 0.674105i
\(714\) 0 0
\(715\) 8.19615 14.1962i 0.306519 0.530906i
\(716\) 24.5885i 0.918914i
\(717\) −4.68653 + 2.70577i −0.175022 + 0.101049i
\(718\) 15.8038 0.589794
\(719\) 20.7846 + 36.0000i 0.775135 + 1.34257i 0.934718 + 0.355389i \(0.115652\pi\)
−0.159583 + 0.987184i \(0.551015\pi\)
\(720\) −3.00000 −0.111803
\(721\) 31.5000 + 6.06218i 1.17312 + 0.225767i
\(722\) 15.0622 8.69615i 0.560556 0.323637i
\(723\) −5.00962 2.89230i −0.186310 0.107566i
\(724\) 11.5981 6.69615i 0.431039 0.248861i
\(725\) −5.59808 + 3.23205i −0.207907 + 0.120035i
\(726\) −17.0885 + 9.86603i −0.634212 + 0.366163i
\(727\) −41.7846 + 24.1244i −1.54971 + 0.894723i −0.551542 + 0.834147i \(0.685960\pi\)
−0.998164 + 0.0605756i \(0.980706\pi\)
\(728\) −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
\(732\) −19.3923 11.1962i −0.716760 0.413822i
\(733\) 34.0526i 1.25776i 0.777502 + 0.628880i \(0.216486\pi\)
−0.777502 + 0.628880i \(0.783514\pi\)
\(734\) −14.5981 + 25.2846i −0.538825 + 0.933272i
\(735\) −9.52628 + 7.50000i −0.351382 + 0.276642i
\(736\) 1.26795 + 2.19615i 0.0467372 + 0.0809513i
\(737\) −16.3923 + 9.46410i −0.603818 + 0.348615i
\(738\) −23.3827 13.5000i −0.860729 0.496942i
\(739\) −16.5885 + 28.7321i −0.610216 + 1.05693i 0.380987 + 0.924580i \(0.375584\pi\)
−0.991204 + 0.132345i \(0.957749\pi\)
\(740\) −3.09808 + 5.36603i −0.113888 + 0.197259i
\(741\) 3.80385 6.58846i 0.139738 0.242033i
\(742\) 18.1699 6.29423i 0.667037 0.231068i
\(743\) −23.6769 13.6699i −0.868622 0.501499i −0.00173176 0.999999i \(-0.500551\pi\)
−0.866890 + 0.498499i \(0.833885\pi\)
\(744\) −14.1962 −0.520456
\(745\) 12.0000i 0.439646i
\(746\) −8.83013 5.09808i −0.323294 0.186654i
\(747\) 16.7942 29.0885i 0.614469 1.06429i
\(748\) 0 0
\(749\) −13.7942 39.8205i −0.504030 1.45501i
\(750\) −1.50000 + 0.866025i −0.0547723 + 0.0316228i
\(751\) −21.6077 −0.788476 −0.394238 0.919008i \(-0.628991\pi\)
−0.394238 + 0.919008i \(0.628991\pi\)
\(752\) −4.50000 7.79423i −0.164098 0.284226i
\(753\) 15.5885 27.0000i 0.568075 0.983935i
\(754\) 19.3923 + 11.1962i 0.706226 + 0.407740i
\(755\) 4.19615 0.152714
\(756\) 12.9904 4.50000i 0.472456 0.163663i
\(757\) −8.58846 −0.312153 −0.156076 0.987745i \(-0.549885\pi\)
−0.156076 + 0.987745i \(0.549885\pi\)
\(758\) 8.32051 + 4.80385i 0.302214 + 0.174484i
\(759\) 10.3923 18.0000i 0.377217 0.653359i
\(760\) −0.633975 1.09808i −0.0229967 0.0398314i
\(761\) −33.0000 −1.19625 −0.598125 0.801403i \(-0.704087\pi\)
−0.598125 + 0.801403i \(0.704087\pi\)
\(762\) −17.0885 + 9.86603i −0.619049 + 0.357408i
\(763\) −14.3923 12.4641i −0.521036 0.451231i
\(764\) 3.46410i 0.125327i
\(765\) 0 0
\(766\) −16.7942 9.69615i −0.606800 0.350336i
\(767\) 7.60770i 0.274698i
\(768\) 1.73205 0.0625000
\(769\) 13.5000 + 7.79423i 0.486822 + 0.281067i 0.723255 0.690581i \(-0.242645\pi\)
−0.236433 + 0.971648i \(0.575978\pi\)
\(770\) 9.46410 + 8.19615i 0.341063 + 0.295369i
\(771\) −24.5885 + 42.5885i −0.885532 + 1.53379i
\(772\) 6.90192 11.9545i 0.248406 0.430251i
\(773\) −9.00000 + 15.5885i −0.323708 + 0.560678i −0.981250 0.192740i \(-0.938263\pi\)
0.657542 + 0.753418i \(0.271596\pi\)
\(774\) 8.30385 4.79423i 0.298476 0.172325i
\(775\) −7.09808 + 4.09808i −0.254970 + 0.147207i
\(776\) −4.26795 7.39230i −0.153210 0.265368i
\(777\) 5.36603 27.8827i 0.192505 1.00029i
\(778\) −12.3564 + 21.4019i −0.442999 + 0.767296i
\(779\) 11.4115i 0.408861i
\(780\) 5.19615 + 3.00000i 0.186052 + 0.107417i
\(781\) 22.3923 0.801260
\(782\) 0 0
\(783\) −29.0885 + 16.7942i −1.03954 + 0.600177i
\(784\) 5.50000 4.33013i 0.196429 0.154647i
\(785\) 15.2942 8.83013i 0.545874 0.315161i
\(786\) 6.58846 3.80385i 0.235002 0.135679i