Properties

Label 390.2.bb.a.121.1
Level $390$
Weight $2$
Character 390.121
Analytic conductor $3.114$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.bb (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.11416567883\)
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 121.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 390.121
Dual form 390.2.bb.a.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-0.866025 + 0.500000i) q^{6} +(-2.59808 + 1.50000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-0.866025 + 0.500000i) q^{6} +(-2.59808 + 1.50000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-3.23205 - 1.86603i) q^{11} +1.00000 q^{12} +(-0.866025 - 3.50000i) q^{13} +3.00000 q^{14} +(-0.866025 - 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +1.00000i q^{18} +(-1.96410 + 1.13397i) q^{19} +(0.866025 - 0.500000i) q^{20} +3.00000i q^{21} +(1.86603 + 3.23205i) q^{22} +(1.73205 - 3.00000i) q^{23} +(-0.866025 - 0.500000i) q^{24} -1.00000 q^{25} +(-1.00000 + 3.46410i) q^{26} -1.00000 q^{27} +(-2.59808 - 1.50000i) q^{28} +(2.73205 - 4.73205i) q^{29} +(0.500000 + 0.866025i) q^{30} +8.92820i q^{31} +(0.866025 - 0.500000i) q^{32} +(-3.23205 + 1.86603i) q^{33} +4.00000i q^{34} +(1.50000 + 2.59808i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-6.86603 - 3.96410i) q^{37} +2.26795 q^{38} +(-3.46410 - 1.00000i) q^{39} -1.00000 q^{40} +(3.46410 + 2.00000i) q^{41} +(1.50000 - 2.59808i) q^{42} +(-3.00000 - 5.19615i) q^{43} -3.73205i q^{44} +(-0.866025 + 0.500000i) q^{45} +(-3.00000 + 1.73205i) q^{46} -0.464102i q^{47} +(0.500000 + 0.866025i) q^{48} +(1.00000 - 1.73205i) q^{49} +(0.866025 + 0.500000i) q^{50} -4.00000 q^{51} +(2.59808 - 2.50000i) q^{52} -3.73205 q^{53} +(0.866025 + 0.500000i) q^{54} +(-1.86603 + 3.23205i) q^{55} +(1.50000 + 2.59808i) q^{56} +2.26795i q^{57} +(-4.73205 + 2.73205i) q^{58} +(3.92820 - 2.26795i) q^{59} -1.00000i q^{60} +(3.73205 + 6.46410i) q^{61} +(4.46410 - 7.73205i) q^{62} +(2.59808 + 1.50000i) q^{63} -1.00000 q^{64} +(-3.50000 + 0.866025i) q^{65} +3.73205 q^{66} +(4.73205 + 2.73205i) q^{67} +(2.00000 - 3.46410i) q^{68} +(-1.73205 - 3.00000i) q^{69} -3.00000i q^{70} +(-0.803848 + 0.464102i) q^{71} +(-0.866025 + 0.500000i) q^{72} -6.92820i q^{73} +(3.96410 + 6.86603i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(-1.96410 - 1.13397i) q^{76} +11.1962 q^{77} +(2.50000 + 2.59808i) q^{78} +16.9282 q^{79} +(0.866025 + 0.500000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.00000 - 3.46410i) q^{82} -2.53590i q^{83} +(-2.59808 + 1.50000i) q^{84} +(-3.46410 + 2.00000i) q^{85} +6.00000i q^{86} +(-2.73205 - 4.73205i) q^{87} +(-1.86603 + 3.23205i) q^{88} +(-8.76795 - 5.06218i) q^{89} +1.00000 q^{90} +(7.50000 + 7.79423i) q^{91} +3.46410 q^{92} +(7.73205 + 4.46410i) q^{93} +(-0.232051 + 0.401924i) q^{94} +(1.13397 + 1.96410i) q^{95} -1.00000i q^{96} +(10.7321 - 6.19615i) q^{97} +(-1.73205 + 1.00000i) q^{98} +3.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{3} + 2q^{4} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{3} + 2q^{4} - 2q^{9} - 2q^{10} - 6q^{11} + 4q^{12} + 12q^{14} - 2q^{16} - 8q^{17} + 6q^{19} + 4q^{22} - 4q^{25} - 4q^{26} - 4q^{27} + 4q^{29} + 2q^{30} - 6q^{33} + 6q^{35} + 2q^{36} - 24q^{37} + 16q^{38} - 4q^{40} + 6q^{42} - 12q^{43} - 12q^{46} + 2q^{48} + 4q^{49} - 16q^{51} - 8q^{53} - 4q^{55} + 6q^{56} - 12q^{58} - 12q^{59} + 8q^{61} + 4q^{62} - 4q^{64} - 14q^{65} + 8q^{66} + 12q^{67} + 8q^{68} - 24q^{71} + 2q^{74} - 2q^{75} + 6q^{76} + 24q^{77} + 10q^{78} + 40q^{79} - 2q^{81} - 8q^{82} - 4q^{87} - 4q^{88} - 42q^{89} + 4q^{90} + 30q^{91} + 24q^{93} + 6q^{94} + 8q^{95} + 36q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.00000i 0.447214i
\(6\) −0.866025 + 0.500000i −0.353553 + 0.204124i
\(7\) −2.59808 + 1.50000i −0.981981 + 0.566947i −0.902867 0.429919i \(-0.858542\pi\)
−0.0791130 + 0.996866i \(0.525209\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) −3.23205 1.86603i −0.974500 0.562628i −0.0738948 0.997266i \(-0.523543\pi\)
−0.900605 + 0.434638i \(0.856876\pi\)
\(12\) 1.00000 0.288675
\(13\) −0.866025 3.50000i −0.240192 0.970725i
\(14\) 3.00000 0.801784
\(15\) −0.866025 0.500000i −0.223607 0.129099i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.00000 3.46410i −0.485071 0.840168i 0.514782 0.857321i \(-0.327873\pi\)
−0.999853 + 0.0171533i \(0.994540\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −1.96410 + 1.13397i −0.450596 + 0.260152i −0.708082 0.706130i \(-0.750439\pi\)
0.257486 + 0.966282i \(0.417106\pi\)
\(20\) 0.866025 0.500000i 0.193649 0.111803i
\(21\) 3.00000i 0.654654i
\(22\) 1.86603 + 3.23205i 0.397838 + 0.689076i
\(23\) 1.73205 3.00000i 0.361158 0.625543i −0.626994 0.779024i \(-0.715715\pi\)
0.988152 + 0.153481i \(0.0490483\pi\)
\(24\) −0.866025 0.500000i −0.176777 0.102062i
\(25\) −1.00000 −0.200000
\(26\) −1.00000 + 3.46410i −0.196116 + 0.679366i
\(27\) −1.00000 −0.192450
\(28\) −2.59808 1.50000i −0.490990 0.283473i
\(29\) 2.73205 4.73205i 0.507329 0.878720i −0.492635 0.870236i \(-0.663966\pi\)
0.999964 0.00848369i \(-0.00270048\pi\)
\(30\) 0.500000 + 0.866025i 0.0912871 + 0.158114i
\(31\) 8.92820i 1.60355i 0.597624 + 0.801776i \(0.296111\pi\)
−0.597624 + 0.801776i \(0.703889\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) −3.23205 + 1.86603i −0.562628 + 0.324833i
\(34\) 4.00000i 0.685994i
\(35\) 1.50000 + 2.59808i 0.253546 + 0.439155i
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) −6.86603 3.96410i −1.12877 0.651694i −0.185143 0.982712i \(-0.559275\pi\)
−0.943625 + 0.331017i \(0.892608\pi\)
\(38\) 2.26795 0.367910
\(39\) −3.46410 1.00000i −0.554700 0.160128i
\(40\) −1.00000 −0.158114
\(41\) 3.46410 + 2.00000i 0.541002 + 0.312348i 0.745485 0.666523i \(-0.232218\pi\)
−0.204483 + 0.978870i \(0.565551\pi\)
\(42\) 1.50000 2.59808i 0.231455 0.400892i
\(43\) −3.00000 5.19615i −0.457496 0.792406i 0.541332 0.840809i \(-0.317920\pi\)
−0.998828 + 0.0484030i \(0.984587\pi\)
\(44\) 3.73205i 0.562628i
\(45\) −0.866025 + 0.500000i −0.129099 + 0.0745356i
\(46\) −3.00000 + 1.73205i −0.442326 + 0.255377i
\(47\) 0.464102i 0.0676962i −0.999427 0.0338481i \(-0.989224\pi\)
0.999427 0.0338481i \(-0.0107762\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) 1.00000 1.73205i 0.142857 0.247436i
\(50\) 0.866025 + 0.500000i 0.122474 + 0.0707107i
\(51\) −4.00000 −0.560112
\(52\) 2.59808 2.50000i 0.360288 0.346688i
\(53\) −3.73205 −0.512637 −0.256318 0.966592i \(-0.582510\pi\)
−0.256318 + 0.966592i \(0.582510\pi\)
\(54\) 0.866025 + 0.500000i 0.117851 + 0.0680414i
\(55\) −1.86603 + 3.23205i −0.251615 + 0.435810i
\(56\) 1.50000 + 2.59808i 0.200446 + 0.347183i
\(57\) 2.26795i 0.300397i
\(58\) −4.73205 + 2.73205i −0.621349 + 0.358736i
\(59\) 3.92820 2.26795i 0.511409 0.295262i −0.222004 0.975046i \(-0.571260\pi\)
0.733412 + 0.679784i \(0.237926\pi\)
\(60\) 1.00000i 0.129099i
\(61\) 3.73205 + 6.46410i 0.477840 + 0.827643i 0.999677 0.0254017i \(-0.00808648\pi\)
−0.521837 + 0.853045i \(0.674753\pi\)
\(62\) 4.46410 7.73205i 0.566941 0.981971i
\(63\) 2.59808 + 1.50000i 0.327327 + 0.188982i
\(64\) −1.00000 −0.125000
\(65\) −3.50000 + 0.866025i −0.434122 + 0.107417i
\(66\) 3.73205 0.459384
\(67\) 4.73205 + 2.73205i 0.578112 + 0.333773i 0.760383 0.649475i \(-0.225011\pi\)
−0.182271 + 0.983248i \(0.558345\pi\)
\(68\) 2.00000 3.46410i 0.242536 0.420084i
\(69\) −1.73205 3.00000i −0.208514 0.361158i
\(70\) 3.00000i 0.358569i
\(71\) −0.803848 + 0.464102i −0.0953992 + 0.0550787i −0.546941 0.837171i \(-0.684208\pi\)
0.451541 + 0.892250i \(0.350874\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 6.92820i 0.810885i −0.914121 0.405442i \(-0.867117\pi\)
0.914121 0.405442i \(-0.132883\pi\)
\(74\) 3.96410 + 6.86603i 0.460817 + 0.798159i
\(75\) −0.500000 + 0.866025i −0.0577350 + 0.100000i
\(76\) −1.96410 1.13397i −0.225298 0.130076i
\(77\) 11.1962 1.27592
\(78\) 2.50000 + 2.59808i 0.283069 + 0.294174i
\(79\) 16.9282 1.90457 0.952286 0.305208i \(-0.0987259\pi\)
0.952286 + 0.305208i \(0.0987259\pi\)
\(80\) 0.866025 + 0.500000i 0.0968246 + 0.0559017i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −2.00000 3.46410i −0.220863 0.382546i
\(83\) 2.53590i 0.278351i −0.990268 0.139176i \(-0.955555\pi\)
0.990268 0.139176i \(-0.0444452\pi\)
\(84\) −2.59808 + 1.50000i −0.283473 + 0.163663i
\(85\) −3.46410 + 2.00000i −0.375735 + 0.216930i
\(86\) 6.00000i 0.646997i
\(87\) −2.73205 4.73205i −0.292907 0.507329i
\(88\) −1.86603 + 3.23205i −0.198919 + 0.344538i
\(89\) −8.76795 5.06218i −0.929401 0.536590i −0.0427788 0.999085i \(-0.513621\pi\)
−0.886622 + 0.462495i \(0.846954\pi\)
\(90\) 1.00000 0.105409
\(91\) 7.50000 + 7.79423i 0.786214 + 0.817057i
\(92\) 3.46410 0.361158
\(93\) 7.73205 + 4.46410i 0.801776 + 0.462906i
\(94\) −0.232051 + 0.401924i −0.0239342 + 0.0414553i
\(95\) 1.13397 + 1.96410i 0.116343 + 0.201513i
\(96\) 1.00000i 0.102062i
\(97\) 10.7321 6.19615i 1.08967 0.629124i 0.156185 0.987728i \(-0.450080\pi\)
0.933490 + 0.358604i \(0.116747\pi\)
\(98\) −1.73205 + 1.00000i −0.174964 + 0.101015i
\(99\) 3.73205i 0.375085i
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 4.19615 7.26795i 0.417533 0.723188i −0.578158 0.815925i \(-0.696228\pi\)
0.995691 + 0.0927369i \(0.0295616\pi\)
\(102\) 3.46410 + 2.00000i 0.342997 + 0.198030i
\(103\) 19.5885 1.93011 0.965054 0.262051i \(-0.0843989\pi\)
0.965054 + 0.262051i \(0.0843989\pi\)
\(104\) −3.50000 + 0.866025i −0.343203 + 0.0849208i
\(105\) 3.00000 0.292770
\(106\) 3.23205 + 1.86603i 0.313925 + 0.181244i
\(107\) −0.464102 + 0.803848i −0.0448664 + 0.0777109i −0.887587 0.460641i \(-0.847620\pi\)
0.842720 + 0.538352i \(0.180953\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 10.3923i 0.995402i −0.867349 0.497701i \(-0.834178\pi\)
0.867349 0.497701i \(-0.165822\pi\)
\(110\) 3.23205 1.86603i 0.308164 0.177919i
\(111\) −6.86603 + 3.96410i −0.651694 + 0.376256i
\(112\) 3.00000i 0.283473i
\(113\) 6.00000 + 10.3923i 0.564433 + 0.977626i 0.997102 + 0.0760733i \(0.0242383\pi\)
−0.432670 + 0.901553i \(0.642428\pi\)
\(114\) 1.13397 1.96410i 0.106206 0.183955i
\(115\) −3.00000 1.73205i −0.279751 0.161515i
\(116\) 5.46410 0.507329
\(117\) −2.59808 + 2.50000i −0.240192 + 0.231125i
\(118\) −4.53590 −0.417563
\(119\) 10.3923 + 6.00000i 0.952661 + 0.550019i
\(120\) −0.500000 + 0.866025i −0.0456435 + 0.0790569i
\(121\) 1.46410 + 2.53590i 0.133100 + 0.230536i
\(122\) 7.46410i 0.675768i
\(123\) 3.46410 2.00000i 0.312348 0.180334i
\(124\) −7.73205 + 4.46410i −0.694359 + 0.400888i
\(125\) 1.00000i 0.0894427i
\(126\) −1.50000 2.59808i −0.133631 0.231455i
\(127\) −2.33013 + 4.03590i −0.206765 + 0.358128i −0.950694 0.310131i \(-0.899627\pi\)
0.743928 + 0.668259i \(0.232960\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) −6.00000 −0.528271
\(130\) 3.46410 + 1.00000i 0.303822 + 0.0877058i
\(131\) −20.3205 −1.77541 −0.887706 0.460412i \(-0.847702\pi\)
−0.887706 + 0.460412i \(0.847702\pi\)
\(132\) −3.23205 1.86603i −0.281314 0.162417i
\(133\) 3.40192 5.89230i 0.294984 0.510928i
\(134\) −2.73205 4.73205i −0.236013 0.408787i
\(135\) 1.00000i 0.0860663i
\(136\) −3.46410 + 2.00000i −0.297044 + 0.171499i
\(137\) −5.66025 + 3.26795i −0.483588 + 0.279200i −0.721911 0.691986i \(-0.756736\pi\)
0.238322 + 0.971186i \(0.423402\pi\)
\(138\) 3.46410i 0.294884i
\(139\) −10.8923 18.8660i −0.923873 1.60020i −0.793363 0.608748i \(-0.791672\pi\)
−0.130510 0.991447i \(-0.541661\pi\)
\(140\) −1.50000 + 2.59808i −0.126773 + 0.219578i
\(141\) −0.401924 0.232051i −0.0338481 0.0195422i
\(142\) 0.928203 0.0778931
\(143\) −3.73205 + 12.9282i −0.312090 + 1.08111i
\(144\) 1.00000 0.0833333
\(145\) −4.73205 2.73205i −0.392975 0.226884i
\(146\) −3.46410 + 6.00000i −0.286691 + 0.496564i
\(147\) −1.00000 1.73205i −0.0824786 0.142857i
\(148\) 7.92820i 0.651694i
\(149\) 19.7321 11.3923i 1.61651 0.933294i 0.628700 0.777648i \(-0.283587\pi\)
0.987813 0.155646i \(-0.0497458\pi\)
\(150\) 0.866025 0.500000i 0.0707107 0.0408248i
\(151\) 18.7846i 1.52867i 0.644819 + 0.764335i \(0.276933\pi\)
−0.644819 + 0.764335i \(0.723067\pi\)
\(152\) 1.13397 + 1.96410i 0.0919775 + 0.159310i
\(153\) −2.00000 + 3.46410i −0.161690 + 0.280056i
\(154\) −9.69615 5.59808i −0.781338 0.451106i
\(155\) 8.92820 0.717131
\(156\) −0.866025 3.50000i −0.0693375 0.280224i
\(157\) 10.8038 0.862241 0.431120 0.902294i \(-0.358118\pi\)
0.431120 + 0.902294i \(0.358118\pi\)
\(158\) −14.6603 8.46410i −1.16631 0.673368i
\(159\) −1.86603 + 3.23205i −0.147985 + 0.256318i
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) 10.3923i 0.819028i
\(162\) 0.866025 0.500000i 0.0680414 0.0392837i
\(163\) −9.46410 + 5.46410i −0.741286 + 0.427981i −0.822537 0.568712i \(-0.807442\pi\)
0.0812509 + 0.996694i \(0.474108\pi\)
\(164\) 4.00000i 0.312348i
\(165\) 1.86603 + 3.23205i 0.145270 + 0.251615i
\(166\) −1.26795 + 2.19615i −0.0984119 + 0.170454i
\(167\) −5.59808 3.23205i −0.433192 0.250104i 0.267513 0.963554i \(-0.413798\pi\)
−0.700706 + 0.713451i \(0.747131\pi\)
\(168\) 3.00000 0.231455
\(169\) −11.5000 + 6.06218i −0.884615 + 0.466321i
\(170\) 4.00000 0.306786
\(171\) 1.96410 + 1.13397i 0.150199 + 0.0867172i
\(172\) 3.00000 5.19615i 0.228748 0.396203i
\(173\) −11.0622 19.1603i −0.841042 1.45673i −0.889015 0.457879i \(-0.848609\pi\)
0.0479730 0.998849i \(-0.484724\pi\)
\(174\) 5.46410i 0.414232i
\(175\) 2.59808 1.50000i 0.196396 0.113389i
\(176\) 3.23205 1.86603i 0.243625 0.140657i
\(177\) 4.53590i 0.340939i
\(178\) 5.06218 + 8.76795i 0.379426 + 0.657186i
\(179\) −11.4641 + 19.8564i −0.856867 + 1.48414i 0.0180347 + 0.999837i \(0.494259\pi\)
−0.874902 + 0.484300i \(0.839074\pi\)
\(180\) −0.866025 0.500000i −0.0645497 0.0372678i
\(181\) 3.07180 0.228325 0.114162 0.993462i \(-0.463582\pi\)
0.114162 + 0.993462i \(0.463582\pi\)
\(182\) −2.59808 10.5000i −0.192582 0.778312i
\(183\) 7.46410 0.551762
\(184\) −3.00000 1.73205i −0.221163 0.127688i
\(185\) −3.96410 + 6.86603i −0.291447 + 0.504800i
\(186\) −4.46410 7.73205i −0.327324 0.566941i
\(187\) 14.9282i 1.09166i
\(188\) 0.401924 0.232051i 0.0293133 0.0169240i
\(189\) 2.59808 1.50000i 0.188982 0.109109i
\(190\) 2.26795i 0.164534i
\(191\) −8.66025 15.0000i −0.626634 1.08536i −0.988222 0.153024i \(-0.951099\pi\)
0.361588 0.932338i \(-0.382235\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −15.4641 8.92820i −1.11313 0.642666i −0.173492 0.984835i \(-0.555505\pi\)
−0.939638 + 0.342169i \(0.888838\pi\)
\(194\) −12.3923 −0.889716
\(195\) −1.00000 + 3.46410i −0.0716115 + 0.248069i
\(196\) 2.00000 0.142857
\(197\) −8.13397 4.69615i −0.579522 0.334587i 0.181422 0.983405i \(-0.441930\pi\)
−0.760943 + 0.648818i \(0.775263\pi\)
\(198\) 1.86603 3.23205i 0.132613 0.229692i
\(199\) 5.53590 + 9.58846i 0.392429 + 0.679708i 0.992769 0.120037i \(-0.0383014\pi\)
−0.600340 + 0.799745i \(0.704968\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 4.73205 2.73205i 0.333773 0.192704i
\(202\) −7.26795 + 4.19615i −0.511371 + 0.295240i
\(203\) 16.3923i 1.15051i
\(204\) −2.00000 3.46410i −0.140028 0.242536i
\(205\) 2.00000 3.46410i 0.139686 0.241943i
\(206\) −16.9641 9.79423i −1.18194 0.682396i
\(207\) −3.46410 −0.240772
\(208\) 3.46410 + 1.00000i 0.240192 + 0.0693375i
\(209\) 8.46410 0.585474
\(210\) −2.59808 1.50000i −0.179284 0.103510i
\(211\) 10.9641 18.9904i 0.754800 1.30735i −0.190674 0.981653i \(-0.561067\pi\)
0.945474 0.325698i \(-0.105599\pi\)
\(212\) −1.86603 3.23205i −0.128159 0.221978i
\(213\) 0.928203i 0.0635994i
\(214\) 0.803848 0.464102i 0.0549499 0.0317253i
\(215\) −5.19615 + 3.00000i −0.354375 + 0.204598i
\(216\) 1.00000i 0.0680414i
\(217\) −13.3923 23.1962i −0.909129 1.57466i
\(218\) −5.19615 + 9.00000i −0.351928 + 0.609557i
\(219\) −6.00000 3.46410i −0.405442 0.234082i
\(220\) −3.73205 −0.251615
\(221\) −10.3923 + 10.0000i −0.699062 + 0.672673i
\(222\) 7.92820 0.532106
\(223\) −7.66987 4.42820i −0.513613 0.296534i 0.220705 0.975341i \(-0.429164\pi\)
−0.734317 + 0.678806i \(0.762498\pi\)
\(224\) −1.50000 + 2.59808i −0.100223 + 0.173591i
\(225\) 0.500000 + 0.866025i 0.0333333 + 0.0577350i
\(226\) 12.0000i 0.798228i
\(227\) −11.6603 + 6.73205i −0.773918 + 0.446822i −0.834271 0.551355i \(-0.814111\pi\)
0.0603523 + 0.998177i \(0.480778\pi\)
\(228\) −1.96410 + 1.13397i −0.130076 + 0.0750993i
\(229\) 11.4641i 0.757569i −0.925485 0.378785i \(-0.876342\pi\)
0.925485 0.378785i \(-0.123658\pi\)
\(230\) 1.73205 + 3.00000i 0.114208 + 0.197814i
\(231\) 5.59808 9.69615i 0.368326 0.637960i
\(232\) −4.73205 2.73205i −0.310674 0.179368i
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 3.50000 0.866025i 0.228802 0.0566139i
\(235\) −0.464102 −0.0302747
\(236\) 3.92820 + 2.26795i 0.255704 + 0.147631i
\(237\) 8.46410 14.6603i 0.549802 0.952286i
\(238\) −6.00000 10.3923i −0.388922 0.673633i
\(239\) 3.46410i 0.224074i −0.993704 0.112037i \(-0.964262\pi\)
0.993704 0.112037i \(-0.0357375\pi\)
\(240\) 0.866025 0.500000i 0.0559017 0.0322749i
\(241\) 12.8205 7.40192i 0.825842 0.476800i −0.0265852 0.999647i \(-0.508463\pi\)
0.852427 + 0.522847i \(0.175130\pi\)
\(242\) 2.92820i 0.188232i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −3.73205 + 6.46410i −0.238920 + 0.413822i
\(245\) −1.73205 1.00000i −0.110657 0.0638877i
\(246\) −4.00000 −0.255031
\(247\) 5.66987 + 5.89230i 0.360765 + 0.374918i
\(248\) 8.92820 0.566941
\(249\) −2.19615 1.26795i −0.139176 0.0803530i
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) −13.2321 22.9186i −0.835200 1.44661i −0.893868 0.448331i \(-0.852019\pi\)
0.0586681 0.998278i \(-0.481315\pi\)
\(252\) 3.00000i 0.188982i
\(253\) −11.1962 + 6.46410i −0.703896 + 0.406395i
\(254\) 4.03590 2.33013i 0.253235 0.146205i
\(255\) 4.00000i 0.250490i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −10.7321 + 18.5885i −0.669447 + 1.15952i 0.308612 + 0.951188i \(0.400136\pi\)
−0.978059 + 0.208328i \(0.933198\pi\)
\(258\) 5.19615 + 3.00000i 0.323498 + 0.186772i
\(259\) 23.7846 1.47790
\(260\) −2.50000 2.59808i −0.155043 0.161126i
\(261\) −5.46410 −0.338219
\(262\) 17.5981 + 10.1603i 1.08721 + 0.627703i
\(263\) −10.2583 + 17.7679i −0.632556 + 1.09562i 0.354472 + 0.935067i \(0.384661\pi\)
−0.987027 + 0.160552i \(0.948673\pi\)
\(264\) 1.86603 + 3.23205i 0.114846 + 0.198919i
\(265\) 3.73205i 0.229258i
\(266\) −5.89230 + 3.40192i −0.361280 + 0.208585i
\(267\) −8.76795 + 5.06218i −0.536590 + 0.309800i
\(268\) 5.46410i 0.333773i
\(269\) 15.4641 + 26.7846i 0.942863 + 1.63309i 0.759975 + 0.649953i \(0.225211\pi\)
0.182888 + 0.983134i \(0.441455\pi\)
\(270\) 0.500000 0.866025i 0.0304290 0.0527046i
\(271\) −3.12436 1.80385i −0.189791 0.109576i 0.402094 0.915599i \(-0.368283\pi\)
−0.591885 + 0.806023i \(0.701616\pi\)
\(272\) 4.00000 0.242536
\(273\) 10.5000 2.59808i 0.635489 0.157243i
\(274\) 6.53590 0.394848
\(275\) 3.23205 + 1.86603i 0.194900 + 0.112526i
\(276\) 1.73205 3.00000i 0.104257 0.180579i
\(277\) 9.79423 + 16.9641i 0.588478 + 1.01927i 0.994432 + 0.105380i \(0.0336060\pi\)
−0.405954 + 0.913894i \(0.633061\pi\)
\(278\) 21.7846i 1.30655i
\(279\) 7.73205 4.46410i 0.462906 0.267259i
\(280\) 2.59808 1.50000i 0.155265 0.0896421i
\(281\) 6.92820i 0.413302i −0.978415 0.206651i \(-0.933744\pi\)
0.978415 0.206651i \(-0.0662565\pi\)
\(282\) 0.232051 + 0.401924i 0.0138184 + 0.0239342i
\(283\) −7.19615 + 12.4641i −0.427767 + 0.740914i −0.996674 0.0814876i \(-0.974033\pi\)
0.568907 + 0.822402i \(0.307366\pi\)
\(284\) −0.803848 0.464102i −0.0476996 0.0275394i
\(285\) 2.26795 0.134342
\(286\) 9.69615 9.33013i 0.573346 0.551702i
\(287\) −12.0000 −0.708338
\(288\) −0.866025 0.500000i −0.0510310 0.0294628i
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 2.73205 + 4.73205i 0.160432 + 0.277876i
\(291\) 12.3923i 0.726450i
\(292\) 6.00000 3.46410i 0.351123 0.202721i
\(293\) 16.6699 9.62436i 0.973864 0.562261i 0.0734522 0.997299i \(-0.476598\pi\)
0.900412 + 0.435038i \(0.143265\pi\)
\(294\) 2.00000i 0.116642i
\(295\) −2.26795 3.92820i −0.132045 0.228709i
\(296\) −3.96410 + 6.86603i −0.230409 + 0.399080i
\(297\) 3.23205 + 1.86603i 0.187543 + 0.108278i
\(298\) −22.7846 −1.31988
\(299\) −12.0000 3.46410i −0.693978 0.200334i
\(300\) −1.00000 −0.0577350
\(301\) 15.5885 + 9.00000i 0.898504 + 0.518751i
\(302\) 9.39230 16.2679i 0.540466 0.936115i
\(303\) −4.19615 7.26795i −0.241063 0.417533i
\(304\) 2.26795i 0.130076i
\(305\) 6.46410 3.73205i 0.370133 0.213697i
\(306\) 3.46410 2.00000i 0.198030 0.114332i
\(307\) 20.2487i 1.15565i 0.816159 + 0.577827i \(0.196099\pi\)
−0.816159 + 0.577827i \(0.803901\pi\)
\(308\) 5.59808 + 9.69615i 0.318980 + 0.552490i
\(309\) 9.79423 16.9641i 0.557174 0.965054i
\(310\) −7.73205 4.46410i −0.439151 0.253544i
\(311\) 5.07180 0.287595 0.143798 0.989607i \(-0.454069\pi\)
0.143798 + 0.989607i \(0.454069\pi\)
\(312\) −1.00000 + 3.46410i −0.0566139 + 0.196116i
\(313\) 1.32051 0.0746395 0.0373198 0.999303i \(-0.488118\pi\)
0.0373198 + 0.999303i \(0.488118\pi\)
\(314\) −9.35641 5.40192i −0.528013 0.304848i
\(315\) 1.50000 2.59808i 0.0845154 0.146385i
\(316\) 8.46410 + 14.6603i 0.476143 + 0.824704i
\(317\) 23.5359i 1.32191i 0.750427 + 0.660954i \(0.229848\pi\)
−0.750427 + 0.660954i \(0.770152\pi\)
\(318\) 3.23205 1.86603i 0.181244 0.104642i
\(319\) −17.6603 + 10.1962i −0.988784 + 0.570875i
\(320\) 1.00000i 0.0559017i
\(321\) 0.464102 + 0.803848i 0.0259036 + 0.0448664i
\(322\) 5.19615 9.00000i 0.289570 0.501550i
\(323\) 7.85641 + 4.53590i 0.437142 + 0.252384i
\(324\) −1.00000 −0.0555556
\(325\) 0.866025 + 3.50000i 0.0480384 + 0.194145i
\(326\) 10.9282 0.605257
\(327\) −9.00000 5.19615i −0.497701 0.287348i
\(328\) 2.00000 3.46410i 0.110432 0.191273i
\(329\) 0.696152 + 1.20577i 0.0383801 + 0.0664763i
\(330\) 3.73205i 0.205443i
\(331\) 5.53590 3.19615i 0.304280 0.175676i −0.340084 0.940395i \(-0.610455\pi\)
0.644364 + 0.764719i \(0.277122\pi\)
\(332\) 2.19615 1.26795i 0.120530 0.0695878i
\(333\) 7.92820i 0.434463i
\(334\) 3.23205 + 5.59808i 0.176850 + 0.306313i
\(335\) 2.73205 4.73205i 0.149268 0.258540i
\(336\) −2.59808 1.50000i −0.141737 0.0818317i
\(337\) −5.60770 −0.305471 −0.152735 0.988267i \(-0.548808\pi\)
−0.152735 + 0.988267i \(0.548808\pi\)
\(338\) 12.9904 + 0.500000i 0.706584 + 0.0271964i
\(339\) 12.0000 0.651751
\(340\) −3.46410 2.00000i −0.187867 0.108465i
\(341\) 16.6603 28.8564i 0.902203 1.56266i
\(342\) −1.13397 1.96410i −0.0613183 0.106206i
\(343\) 15.0000i 0.809924i
\(344\) −5.19615 + 3.00000i −0.280158 + 0.161749i
\(345\) −3.00000 + 1.73205i −0.161515 + 0.0932505i
\(346\) 22.1244i 1.18941i
\(347\) 8.19615 + 14.1962i 0.439993 + 0.762089i 0.997688 0.0679560i \(-0.0216478\pi\)
−0.557696 + 0.830045i \(0.688314\pi\)
\(348\) 2.73205 4.73205i 0.146453 0.253665i
\(349\) 15.1244 + 8.73205i 0.809588 + 0.467416i 0.846813 0.531891i \(-0.178518\pi\)
−0.0372247 + 0.999307i \(0.511852\pi\)
\(350\) −3.00000 −0.160357
\(351\) 0.866025 + 3.50000i 0.0462250 + 0.186816i
\(352\) −3.73205 −0.198919
\(353\) −24.5885 14.1962i −1.30871 0.755585i −0.326830 0.945083i \(-0.605981\pi\)
−0.981881 + 0.189498i \(0.939314\pi\)
\(354\) −2.26795 + 3.92820i −0.120540 + 0.208782i
\(355\) 0.464102 + 0.803848i 0.0246320 + 0.0426638i
\(356\) 10.1244i 0.536590i
\(357\) 10.3923 6.00000i 0.550019 0.317554i
\(358\) 19.8564 11.4641i 1.04944 0.605897i
\(359\) 12.9282i 0.682324i −0.940004 0.341162i \(-0.889179\pi\)
0.940004 0.341162i \(-0.110821\pi\)
\(360\) 0.500000 + 0.866025i 0.0263523 + 0.0456435i
\(361\) −6.92820 + 12.0000i −0.364642 + 0.631579i
\(362\) −2.66025 1.53590i −0.139820 0.0807250i
\(363\) 2.92820 0.153691
\(364\) −3.00000 + 10.3923i −0.157243 + 0.544705i
\(365\) −6.92820 −0.362639
\(366\) −6.46410 3.73205i −0.337884 0.195077i
\(367\) 6.66025 11.5359i 0.347662 0.602169i −0.638171 0.769894i \(-0.720309\pi\)
0.985834 + 0.167725i \(0.0536422\pi\)
\(368\) 1.73205 + 3.00000i 0.0902894 + 0.156386i
\(369\) 4.00000i 0.208232i
\(370\) 6.86603 3.96410i 0.356948 0.206084i
\(371\) 9.69615 5.59808i 0.503399 0.290638i
\(372\) 8.92820i 0.462906i
\(373\) −11.4641 19.8564i −0.593589 1.02813i −0.993744 0.111679i \(-0.964377\pi\)
0.400156 0.916447i \(-0.368956\pi\)
\(374\) 7.46410 12.9282i 0.385960 0.668501i
\(375\) 0.866025 + 0.500000i 0.0447214 + 0.0258199i
\(376\) −0.464102 −0.0239342
\(377\) −18.9282 5.46410i −0.974852 0.281416i
\(378\) −3.00000 −0.154303
\(379\) 5.42820 + 3.13397i 0.278828 + 0.160981i 0.632893 0.774239i \(-0.281867\pi\)
−0.354065 + 0.935221i \(0.615201\pi\)
\(380\) −1.13397 + 1.96410i −0.0581717 + 0.100756i
\(381\) 2.33013 + 4.03590i 0.119376 + 0.206765i
\(382\) 17.3205i 0.886194i
\(383\) 31.8564 18.3923i 1.62779 0.939803i 0.643035 0.765837i \(-0.277675\pi\)
0.984752 0.173966i \(-0.0556582\pi\)
\(384\) 0.866025 0.500000i 0.0441942 0.0255155i
\(385\) 11.1962i 0.570609i
\(386\) 8.92820 + 15.4641i 0.454434 + 0.787102i
\(387\) −3.00000 + 5.19615i −0.152499 + 0.264135i
\(388\) 10.7321 + 6.19615i 0.544837 + 0.314562i
\(389\) −9.85641 −0.499740 −0.249870 0.968279i \(-0.580388\pi\)
−0.249870 + 0.968279i \(0.580388\pi\)
\(390\) 2.59808 2.50000i 0.131559 0.126592i
\(391\) −13.8564 −0.700749
\(392\) −1.73205 1.00000i −0.0874818 0.0505076i
\(393\) −10.1603 + 17.5981i −0.512517 + 0.887706i
\(394\) 4.69615 + 8.13397i 0.236589 + 0.409784i
\(395\) 16.9282i 0.851750i
\(396\) −3.23205 + 1.86603i −0.162417 + 0.0937713i
\(397\) −6.86603 + 3.96410i −0.344596 + 0.198953i −0.662303 0.749237i \(-0.730421\pi\)
0.317707 + 0.948189i \(0.397087\pi\)
\(398\) 11.0718i 0.554979i
\(399\) −3.40192 5.89230i −0.170309 0.294984i
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) −1.83975 1.06218i −0.0918725 0.0530426i 0.453360 0.891328i \(-0.350225\pi\)
−0.545232 + 0.838285i \(0.683559\pi\)
\(402\) −5.46410 −0.272525
\(403\) 31.2487 7.73205i 1.55661 0.385161i
\(404\) 8.39230 0.417533
\(405\) 0.866025 + 0.500000i 0.0430331 + 0.0248452i
\(406\) 8.19615 14.1962i 0.406768 0.704543i
\(407\) 14.7942 + 25.6244i 0.733323 + 1.27015i
\(408\) 4.00000i 0.198030i
\(409\) 0.820508 0.473721i 0.0405715 0.0234240i −0.479577 0.877500i \(-0.659210\pi\)
0.520149 + 0.854076i \(0.325877\pi\)
\(410\) −3.46410 + 2.00000i −0.171080 + 0.0987730i
\(411\) 6.53590i 0.322392i
\(412\) 9.79423 + 16.9641i 0.482527 + 0.835761i
\(413\) −6.80385 + 11.7846i −0.334795 + 0.579883i
\(414\) 3.00000 + 1.73205i 0.147442 + 0.0851257i
\(415\) −2.53590 −0.124482
\(416\) −2.50000 2.59808i −0.122573 0.127381i
\(417\) −21.7846 −1.06680
\(418\) −7.33013 4.23205i −0.358528 0.206996i
\(419\) 8.92820 15.4641i 0.436171 0.755471i −0.561219 0.827667i \(-0.689668\pi\)
0.997390 + 0.0721964i \(0.0230008\pi\)
\(420\) 1.50000 + 2.59808i 0.0731925 + 0.126773i
\(421\) 5.85641i 0.285424i −0.989764 0.142712i \(-0.954418\pi\)
0.989764 0.142712i \(-0.0455822\pi\)
\(422\) −18.9904 + 10.9641i −0.924437 + 0.533724i
\(423\) −0.401924 + 0.232051i −0.0195422 + 0.0112827i
\(424\) 3.73205i 0.181244i
\(425\) 2.00000 + 3.46410i 0.0970143 + 0.168034i
\(426\) 0.464102 0.803848i 0.0224858 0.0389465i
\(427\) −19.3923 11.1962i −0.938459 0.541820i
\(428\) −0.928203 −0.0448664
\(429\) 9.33013 + 9.69615i 0.450463 + 0.468135i
\(430\) 6.00000 0.289346
\(431\) −12.0000 6.92820i −0.578020 0.333720i 0.182326 0.983238i \(-0.441637\pi\)
−0.760346 + 0.649518i \(0.774971\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −16.3923 28.3923i −0.787764 1.36445i −0.927334 0.374235i \(-0.877905\pi\)
0.139570 0.990212i \(-0.455428\pi\)
\(434\) 26.7846i 1.28570i
\(435\) −4.73205 + 2.73205i −0.226884 + 0.130992i
\(436\) 9.00000 5.19615i 0.431022 0.248851i
\(437\) 7.85641i 0.375823i
\(438\) 3.46410 + 6.00000i 0.165521 + 0.286691i
\(439\) −10.6603 + 18.4641i −0.508786 + 0.881243i 0.491162 + 0.871068i \(0.336572\pi\)
−0.999948 + 0.0101753i \(0.996761\pi\)
\(440\) 3.23205 + 1.86603i 0.154082 + 0.0889593i
\(441\) −2.00000 −0.0952381
\(442\) 14.0000 3.46410i 0.665912 0.164771i
\(443\) 7.85641 0.373269 0.186635 0.982429i \(-0.440242\pi\)
0.186635 + 0.982429i \(0.440242\pi\)
\(444\) −6.86603 3.96410i −0.325847 0.188128i
\(445\) −5.06218 + 8.76795i −0.239970 + 0.415641i
\(446\) 4.42820 + 7.66987i 0.209682 + 0.363179i
\(447\) 22.7846i 1.07768i
\(448\) 2.59808 1.50000i 0.122748 0.0708683i
\(449\) −15.6962 + 9.06218i −0.740747 + 0.427671i −0.822341 0.568995i \(-0.807332\pi\)
0.0815937 + 0.996666i \(0.473999\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) −7.46410 12.9282i −0.351471 0.608765i
\(452\) −6.00000 + 10.3923i −0.282216 + 0.488813i
\(453\) 16.2679 + 9.39230i 0.764335 + 0.441289i
\(454\) 13.4641 0.631902
\(455\) 7.79423 7.50000i 0.365399 0.351605i
\(456\) 2.26795 0.106206
\(457\) 0.464102 + 0.267949i 0.0217098 + 0.0125341i 0.510816 0.859690i \(-0.329343\pi\)
−0.489106 + 0.872224i \(0.662677\pi\)
\(458\) −5.73205 + 9.92820i −0.267841 + 0.463914i
\(459\) 2.00000 + 3.46410i 0.0933520 + 0.161690i
\(460\) 3.46410i 0.161515i
\(461\) 28.0526 16.1962i 1.30654 0.754330i 0.325021 0.945707i \(-0.394629\pi\)
0.981517 + 0.191377i \(0.0612952\pi\)
\(462\) −9.69615 + 5.59808i −0.451106 + 0.260446i
\(463\) 0.784610i 0.0364639i 0.999834 + 0.0182320i \(0.00580373\pi\)
−0.999834 + 0.0182320i \(0.994196\pi\)
\(464\) 2.73205 + 4.73205i 0.126832 + 0.219680i
\(465\) 4.46410 7.73205i 0.207018 0.358565i
\(466\) −15.5885 9.00000i −0.722121 0.416917i
\(467\) 3.60770 0.166944 0.0834721 0.996510i \(-0.473399\pi\)
0.0834721 + 0.996510i \(0.473399\pi\)
\(468\) −3.46410 1.00000i −0.160128 0.0462250i
\(469\) −16.3923 −0.756926
\(470\) 0.401924 + 0.232051i 0.0185394 + 0.0107037i
\(471\) 5.40192 9.35641i 0.248908 0.431120i
\(472\) −2.26795 3.92820i −0.104391 0.180810i
\(473\) 22.3923i 1.02960i
\(474\) −14.6603 + 8.46410i −0.673368 + 0.388769i
\(475\) 1.96410 1.13397i 0.0901192 0.0520303i
\(476\) 12.0000i 0.550019i
\(477\) 1.86603 + 3.23205i 0.0854394 + 0.147985i
\(478\) −1.73205 + 3.00000i −0.0792222 + 0.137217i
\(479\) −22.7321 13.1244i −1.03865 0.599667i −0.119202 0.992870i \(-0.538034\pi\)
−0.919452 + 0.393203i \(0.871367\pi\)
\(480\) −1.00000 −0.0456435
\(481\) −7.92820 + 27.4641i −0.361495 + 1.25226i
\(482\) −14.8038 −0.674297
\(483\) 9.00000 + 5.19615i 0.409514 + 0.236433i
\(484\) −1.46410 + 2.53590i −0.0665501 + 0.115268i
\(485\) −6.19615 10.7321i −0.281353 0.487317i
\(486\) 1.00000i 0.0453609i
\(487\) −18.1865 + 10.5000i −0.824110 + 0.475800i −0.851832 0.523815i \(-0.824508\pi\)
0.0277214 + 0.999616i \(0.491175\pi\)
\(488\) 6.46410 3.73205i 0.292616 0.168942i
\(489\) 10.9282i 0.494190i
\(490\) 1.00000 + 1.73205i 0.0451754 + 0.0782461i
\(491\) 7.69615 13.3301i 0.347322 0.601580i −0.638450 0.769663i \(-0.720424\pi\)
0.985773 + 0.168083i \(0.0537576\pi\)
\(492\) 3.46410 + 2.00000i 0.156174 + 0.0901670i
\(493\) −21.8564 −0.984363
\(494\) −1.96410 7.93782i −0.0883691 0.357140i
\(495\) 3.73205 0.167743
\(496\) −7.73205 4.46410i −0.347179 0.200444i
\(497\) 1.39230 2.41154i 0.0624534 0.108172i
\(498\) 1.26795 + 2.19615i 0.0568182 + 0.0984119i
\(499\) 1.32051i 0.0591141i −0.999563 0.0295570i \(-0.990590\pi\)
0.999563 0.0295570i \(-0.00940967\pi\)
\(500\) −0.866025 + 0.500000i −0.0387298 + 0.0223607i
\(501\) −5.59808 + 3.23205i −0.250104 + 0.144397i
\(502\) 26.4641i 1.18115i
\(503\) −0.133975 0.232051i −0.00597363 0.0103466i 0.863023 0.505164i \(-0.168568\pi\)
−0.868997 + 0.494818i \(0.835235\pi\)
\(504\) 1.50000 2.59808i 0.0668153 0.115728i
\(505\) −7.26795 4.19615i −0.323419 0.186726i
\(506\) 12.9282 0.574729
\(507\) −0.500000 + 12.9904i −0.0222058 + 0.576923i
\(508\) −4.66025 −0.206765
\(509\) 4.60770 + 2.66025i 0.204232 + 0.117914i 0.598628 0.801027i \(-0.295713\pi\)
−0.394396 + 0.918941i \(0.629046\pi\)
\(510\) 2.00000 3.46410i 0.0885615 0.153393i
\(511\) 10.3923 + 18.0000i 0.459728 + 0.796273i
\(512\) 1.00000i 0.0441942i
\(513\) 1.96410 1.13397i 0.0867172 0.0500662i
\(514\) 18.5885 10.7321i 0.819902 0.473370i
\(515\) 19.5885i 0.863171i
\(516\) −3.00000 5.19615i −0.132068 0.228748i
\(517\) −0.866025 + 1.50000i −0.0380878 + 0.0659699i
\(518\) −20.5981 11.8923i −0.905028 0.522518i
\(519\) −22.1244 −0.971151
\(520\) 0.866025 + 3.50000i 0.0379777 + 0.153485i
\(521\) −27.3923 −1.20008 −0.600039 0.799970i \(-0.704848\pi\)
−0.600039 + 0.799970i \(0.704848\pi\)
\(522\) 4.73205 + 2.73205i 0.207116 + 0.119579i
\(523\) −6.85641 + 11.8756i −0.299810 + 0.519286i −0.976092 0.217357i \(-0.930257\pi\)
0.676283 + 0.736642i \(0.263590\pi\)
\(524\) −10.1603 17.5981i −0.443853 0.768776i
\(525\) 3.00000i 0.130931i
\(526\) 17.7679 10.2583i 0.774719 0.447284i
\(527\) 30.9282 17.8564i 1.34725 0.777837i
\(528\) 3.73205i 0.162417i
\(529\) 5.50000 + 9.52628i 0.239130 + 0.414186i
\(530\) 1.86603 3.23205i 0.0810550 0.140391i
\(531\) −3.92820 2.26795i −0.170470 0.0984206i
\(532\) 6.80385 0.294984
\(533\) 4.00000 13.8564i 0.173259 0.600188i
\(534\) 10.1244 0.438124
\(535\) 0.803848 + 0.464102i 0.0347534 + 0.0200649i
\(536\) 2.73205 4.73205i 0.118007 0.204393i
\(537\) 11.4641 + 19.8564i 0.494713 + 0.856867i
\(538\) 30.9282i 1.33341i
\(539\) −6.46410 + 3.73205i −0.278429 + 0.160751i
\(540\) −0.866025 + 0.500000i −0.0372678 + 0.0215166i
\(541\) 26.7846i 1.15156i −0.817605 0.575780i \(-0.804698\pi\)
0.817605 0.575780i \(-0.195302\pi\)
\(542\) 1.80385 + 3.12436i 0.0774819 + 0.134203i
\(543\) 1.53590 2.66025i 0.0659117 0.114162i
\(544\) −3.46410 2.00000i −0.148522 0.0857493i
\(545\) −10.3923 −0.445157
\(546\) −10.3923 3.00000i −0.444750 0.128388i
\(547\) 29.3205 1.25365 0.626827 0.779158i \(-0.284353\pi\)
0.626827 + 0.779158i \(0.284353\pi\)
\(548\) −5.66025 3.26795i −0.241794 0.139600i
\(549\) 3.73205 6.46410i 0.159280 0.275881i
\(550\) −1.86603 3.23205i −0.0795676 0.137815i
\(551\) 12.3923i 0.527930i
\(552\) −3.00000 + 1.73205i −0.127688 + 0.0737210i
\(553\) −43.9808 + 25.3923i −1.87025 + 1.07979i
\(554\) 19.5885i 0.832234i
\(555\) 3.96410 + 6.86603i 0.168267 + 0.291447i
\(556\) 10.8923 18.8660i 0.461937 0.800098i
\(557\) 37.5788 + 21.6962i 1.59227 + 0.919295i 0.992917 + 0.118808i \(0.0379072\pi\)
0.599349 + 0.800488i \(0.295426\pi\)
\(558\) −8.92820 −0.377961
\(559\) −15.5885 + 15.0000i −0.659321 + 0.634432i
\(560\) −3.00000 −0.126773
\(561\) 12.9282 + 7.46410i 0.545829 + 0.315135i
\(562\) −3.46410 + 6.00000i −0.146124 + 0.253095i
\(563\) −9.66025 16.7321i −0.407131 0.705172i 0.587436 0.809271i \(-0.300137\pi\)
−0.994567 + 0.104099i \(0.966804\pi\)
\(564\) 0.464102i 0.0195422i
\(565\) 10.3923 6.00000i 0.437208 0.252422i
\(566\) 12.4641 7.19615i 0.523905 0.302477i
\(567\) 3.00000i 0.125988i
\(568\) 0.464102 + 0.803848i 0.0194733 + 0.0337287i
\(569\) −9.16025 + 15.8660i −0.384018 + 0.665138i −0.991632 0.129094i \(-0.958793\pi\)
0.607615 + 0.794232i \(0.292127\pi\)
\(570\) −1.96410 1.13397i −0.0822672 0.0474970i
\(571\) −16.8564 −0.705419 −0.352709 0.935733i \(-0.614740\pi\)
−0.352709 + 0.935733i \(0.614740\pi\)
\(572\) −13.0622 + 3.23205i −0.546157 + 0.135139i
\(573\) −17.3205 −0.723575
\(574\) 10.3923 + 6.00000i 0.433766 + 0.250435i
\(575\) −1.73205 + 3.00000i −0.0722315 + 0.125109i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 25.3205i 1.05411i 0.849832 + 0.527053i \(0.176703\pi\)
−0.849832 + 0.527053i \(0.823297\pi\)
\(578\) −0.866025 + 0.500000i −0.0360219 + 0.0207973i
\(579\) −15.4641 + 8.92820i −0.642666 + 0.371043i
\(580\) 5.46410i 0.226884i
\(581\) 3.80385 + 6.58846i 0.157810 + 0.273335i
\(582\) −6.19615 + 10.7321i −0.256839 + 0.444858i
\(583\) 12.0622 + 6.96410i 0.499564 + 0.288424i
\(584\) −6.92820 −0.286691
\(585\) 2.50000 + 2.59808i 0.103362 + 0.107417i
\(586\) −19.2487 −0.795157
\(587\) −4.26795 2.46410i −0.176157 0.101704i 0.409329 0.912387i \(-0.365763\pi\)
−0.585486 + 0.810683i \(0.699096\pi\)
\(588\) 1.00000 1.73205i 0.0412393 0.0714286i
\(589\) −10.1244 17.5359i −0.417167 0.722554i
\(590\) 4.53590i 0.186740i
\(591\) −8.13397 + 4.69615i −0.334587 + 0.193174i
\(592\) 6.86603 3.96410i 0.282192 0.162924i
\(593\) 3.21539i 0.132040i −0.997818 0.0660201i \(-0.978970\pi\)
0.997818 0.0660201i \(-0.0210302\pi\)
\(594\) −1.86603 3.23205i −0.0765639 0.132613i
\(595\) 6.00000 10.3923i 0.245976 0.426043i
\(596\) 19.7321 + 11.3923i 0.808256 + 0.466647i
\(597\) 11.0718 0.453138
\(598\) 8.66025 + 9.00000i 0.354144 + 0.368037i
\(599\) 15.0718 0.615817 0.307908 0.951416i \(-0.400371\pi\)
0.307908 + 0.951416i \(0.400371\pi\)
\(600\) 0.866025 + 0.500000i 0.0353553 + 0.0204124i
\(601\) 12.3564 21.4019i 0.504028 0.873003i −0.495961 0.868345i \(-0.665184\pi\)
0.999989 0.00465778i \(-0.00148262\pi\)
\(602\) −9.00000 15.5885i −0.366813 0.635338i
\(603\) 5.46410i 0.222515i
\(604\) −16.2679 + 9.39230i −0.661933 + 0.382167i
\(605\) 2.53590 1.46410i 0.103099 0.0595242i
\(606\) 8.39230i 0.340914i
\(607\) −18.7224 32.4282i −0.759920 1.31622i −0.942891 0.333102i \(-0.891905\pi\)
0.182971 0.983118i \(-0.441429\pi\)
\(608\) −1.13397 + 1.96410i −0.0459887 + 0.0796548i
\(609\) 14.1962 + 8.19615i 0.575257 + 0.332125i
\(610\) −7.46410 −0.302213
\(611\) −1.62436 + 0.401924i −0.0657144 + 0.0162601i
\(612\) −4.00000 −0.161690
\(613\) −38.9711 22.5000i −1.57403 0.908766i −0.995667 0.0929864i \(-0.970359\pi\)
−0.578362 0.815780i \(-0.696308\pi\)
\(614\) 10.1244 17.5359i 0.408586 0.707691i
\(615\) −2.00000 3.46410i −0.0806478 0.139686i
\(616\) 11.1962i 0.451106i
\(617\) 24.7128 14.2679i 0.994900 0.574406i 0.0881649 0.996106i \(-0.471900\pi\)
0.906735 + 0.421700i \(0.138566\pi\)
\(618\) −16.9641 + 9.79423i −0.682396 + 0.393982i
\(619\) 42.5167i 1.70889i −0.519543 0.854444i \(-0.673898\pi\)
0.519543 0.854444i \(-0.326102\pi\)
\(620\) 4.46410 + 7.73205i 0.179283 + 0.310527i
\(621\) −1.73205 + 3.00000i −0.0695048 + 0.120386i
\(622\) −4.39230 2.53590i −0.176115 0.101680i
\(623\) 30.3731 1.21687
\(624\) 2.59808 2.50000i 0.104006 0.100080i
\(625\) 1.00000 0.0400000
\(626\) −1.14359 0.660254i −0.0457072 0.0263891i
\(627\) 4.23205 7.33013i 0.169012 0.292737i
\(628\) 5.40192 + 9.35641i 0.215560 + 0.373361i
\(629\) 31.7128i 1.26447i
\(630\) −2.59808 + 1.50000i −0.103510 + 0.0597614i
\(631\) 6.92820 4.00000i 0.275807 0.159237i −0.355716 0.934594i \(-0.615763\pi\)
0.631524 + 0.775356i \(0.282430\pi\)
\(632\) 16.9282i 0.673368i
\(633\) −10.9641 18.9904i −0.435784 0.754800i
\(634\) 11.7679 20.3827i 0.467365 0.809500i
\(635\) 4.03590 + 2.33013i 0.160160 + 0.0924683i
\(636\) −3.73205 −0.147985
\(637\) −6.92820 2.00000i −0.274505 0.0792429i
\(638\) 20.3923 0.807339
\(639\) 0.803848 + 0.464102i 0.0317997 + 0.0183596i
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) −3.76795 6.52628i −0.148825 0.257773i 0.781968 0.623318i \(-0.214216\pi\)
−0.930793 + 0.365546i \(0.880882\pi\)
\(642\) 0.928203i 0.0366333i
\(643\) 24.9282 14.3923i 0.983072 0.567577i 0.0798761 0.996805i \(-0.474548\pi\)
0.903196 + 0.429228i \(0.141214\pi\)
\(644\) −9.00000 + 5.19615i −0.354650 + 0.204757i
\(645\) 6.00000i 0.236250i
\(646\) −4.53590 7.85641i −0.178463 0.309106i
\(647\) 16.1340 27.9449i 0.634292 1.09863i −0.352373 0.935860i \(-0.614625\pi\)
0.986665 0.162766i \(-0.0520416\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) −16.9282 −0.664490
\(650\) 1.00000 3.46410i 0.0392232 0.135873i
\(651\) −26.7846 −1.04977
\(652\) −9.46410 5.46410i −0.370643 0.213991i
\(653\) −14.7942 + 25.6244i −0.578943 + 1.00276i 0.416658 + 0.909063i \(0.363201\pi\)
−0.995601 + 0.0936952i \(0.970132\pi\)
\(654\) 5.19615 + 9.00000i 0.203186 + 0.351928i
\(655\) 20.3205i 0.793988i
\(656\) −3.46410 + 2.00000i −0.135250 + 0.0780869i
\(657\) −6.00000 + 3.46410i −0.234082 + 0.135147i
\(658\) 1.39230i 0.0542777i
\(659\) −7.85641 13.6077i −0.306042 0.530081i 0.671451 0.741049i \(-0.265672\pi\)
−0.977493 + 0.210969i \(0.932338\pi\)
\(660\) −1.86603 + 3.23205i −0.0726349 + 0.125807i
\(661\) 36.7128 + 21.1962i 1.42796 + 0.824435i 0.996960 0.0779157i \(-0.0248265\pi\)
0.431003 + 0.902351i \(0.358160\pi\)
\(662\) −6.39230 −0.248444
\(663\) 3.46410 + 14.0000i 0.134535 + 0.543715i
\(664\) −2.53590 −0.0984119
\(665\) −5.89230 3.40192i −0.228494 0.131921i
\(666\) 3.96410 6.86603i 0.153606 0.266053i
\(667\) −9.46410 16.3923i −0.366451 0.634713i
\(668\) 6.46410i 0.250104i
\(669\) −7.66987 + 4.42820i −0.296534 + 0.171204i
\(670\) −4.73205 + 2.73205i −0.182815 + 0.105548i
\(671\) 27.8564i 1.07538i
\(672\) 1.50000 + 2.59808i 0.0578638 + 0.100223i
\(673\) −12.3923 + 21.4641i −0.477688 + 0.827380i −0.999673 0.0255746i \(-0.991858\pi\)
0.521985 + 0.852955i \(0.325192\pi\)
\(674\) 4.85641 + 2.80385i 0.187062 + 0.108000i
\(675\) 1.00000 0.0384900
\(676\) −11.0000 6.92820i −0.423077 0.266469i
\(677\) −2.92820 −0.112540 −0.0562700 0.998416i \(-0.517921\pi\)
−0.0562700 + 0.998416i \(0.517921\pi\)
\(678\) −10.3923 6.00000i −0.399114 0.230429i
\(679\) −18.5885 + 32.1962i −0.713360 + 1.23557i
\(680\) 2.00000 + 3.46410i 0.0766965 + 0.132842i
\(681\) 13.4641i 0.515945i
\(682\) −28.8564 + 16.6603i −1.10497 + 0.637954i
\(683\) −5.78461 + 3.33975i −0.221342 + 0.127792i −0.606571 0.795029i \(-0.707456\pi\)
0.385230 + 0.922821i \(0.374122\pi\)
\(684\) 2.26795i 0.0867172i
\(685\) 3.26795 + 5.66025i 0.124862 + 0.216267i
\(686\) −7.50000 + 12.9904i −0.286351 + 0.495975i
\(687\) −9.92820 5.73205i −0.378785 0.218691i
\(688\) 6.00000 0.228748
\(689\) 3.23205 + 13.0622i 0.123131 + 0.497629i
\(690\) 3.46410 0.131876
\(691\) 19.9641 + 11.5263i 0.759470 + 0.438480i 0.829106 0.559092i \(-0.188850\pi\)
−0.0696353 + 0.997573i \(0.522184\pi\)
\(692\) 11.0622 19.1603i 0.420521 0.728364i
\(693\) −5.59808 9.69615i −0.212653 0.368326i
\(694\) 16.3923i 0.622243i
\(695\) −18.8660 + 10.8923i −0.715629 + 0.413169i
\(696\) −4.73205 + 2.73205i −0.179368 + 0.103558i
\(697\) 16.0000i 0.606043i
\(698\) −8.73205 15.1244i −0.330513 0.572465i
\(699\) 9.00000 15.5885i 0.340411 0.589610i
\(700\) 2.59808 + 1.50000i 0.0981981 + 0.0566947i
\(701\) 16.3923 0.619129 0.309564 0.950878i \(-0.399817\pi\)
0.309564 + 0.950878i \(0.399817\pi\)
\(702\) 1.00000 3.46410i 0.0377426 0.130744i
\(703\) 17.9808 0.678157
\(704\) 3.23205 + 1.86603i 0.121812 + 0.0703285i
\(705\) −0.232051 + 0.401924i −0.00873954 + 0.0151373i
\(706\) 14.1962 + 24.5885i 0.534279 + 0.925399i
\(707\) 25.1769i 0.946875i
\(708\) 3.92820 2.26795i 0.147631 0.0852348i
\(709\) −6.33975 + 3.66025i −0.238094 + 0.137464i −0.614300 0.789072i \(-0.710562\pi\)
0.376206 + 0.926536i \(0.377228\pi\)
\(710\) 0.928203i 0.0348348i
\(711\) −8.46410 14.6603i −0.317429 0.549802i
\(712\) −5.06218 + 8.76795i −0.189713 + 0.328593i
\(713\) 26.7846 + 15.4641i 1.00309 + 0.579135i
\(714\) −12.0000 −0.449089
\(715\) 12.9282 + 3.73205i 0.483487 + 0.139571i
\(716\) −22.9282 −0.856867
\(717\) −3.00000 1.73205i −0.112037 0.0646846i
\(718\) −6.46410 + 11.1962i −0.241238 + 0.417837i
\(719\) −8.00000 13.8564i −0.298350 0.516757i 0.677409 0.735607i \(-0.263103\pi\)
−0.975759 + 0.218850i \(0.929769\pi\)
\(720\) 1.00000i 0.0372678i
\(721\) −50.8923 + 29.3827i −1.89533 + 1.09427i
\(722\) 12.0000 6.92820i 0.446594 0.257841i
\(723\) 14.8038i 0.550561i
\(724\) 1.53590 + 2.66025i 0.0570812 + 0.0988676i
\(725\) −2.73205 + 4.73205i −0.101466 + 0.175744i
\(726\) −2.53590 1.46410i −0.0941160 0.0543379i
\(727\) 12.6603 0.469543 0.234771 0.972051i \(-0.424566\pi\)
0.234771 + 0.972051i \(0.424566\pi\)
\(728\) 7.79423 7.50000i 0.288873 0.277968i
\(729\) 1.00000 0.0370370
\(730\) 6.00000 + 3.46410i 0.222070 + 0.128212i
\(731\) −12.0000 + 20.7846i −0.443836 + 0.768747i
\(732\) 3.73205 + 6.46410i 0.137941 + 0.238920i
\(733\) 6.85641i 0.253247i −0.991951 0.126624i \(-0.959586\pi\)
0.991951 0.126624i \(-0.0404140\pi\)
\(734\) −11.5359 + 6.66025i −0.425798 + 0.245834i
\(735\) −1.73205 + 1.00000i −0.0638877 + 0.0368856i
\(736\) 3.46410i 0.127688i
\(737\) −10.1962 17.6603i −0.375580 0.650524i
\(738\) −2.00000 + 3.46410i −0.0736210 + 0.127515i
\(739\) 37.9641 + 21.9186i 1.39653 + 0.806288i 0.994028 0.109130i \(-0.0348064\pi\)
0.402505 + 0.915418i \(0.368140\pi\)
\(740\) −7.92820 −0.291447
\(741\) 7.93782 1.96410i 0.291603 0.0721531i
\(742\) −11.1962 −0.411024
\(743\) −2.53590 1.46410i −0.0930331 0.0537127i 0.452762 0.891632i \(-0.350439\pi\)
−0.545795 + 0.837919i \(0.683772\pi\)
\(744\) 4.46410 7.73205i 0.163662 0.283471i
\(745\) −11.3923 19.7321i −0.417382 0.722926i
\(746\) 22.9282i 0.839461i
\(747\) −2.19615 + 1.26795i −0.0803530 + 0.0463918i
\(748\) −12.9282 + 7.46410i −0.472702 + 0.272915i
\(749\) 2.78461i 0.101747i
\(750\) −0.500000 0.866025i −0.0182574 0.0316228i
\(751\) −20.5885 + 35.6603i −0.751283 + 1.30126i 0.195917 + 0.980620i \(0.437232\pi\)
−0.947201 + 0.320641i \(0.896102\pi\)
\(752\) 0.401924 + 0.232051i 0.0146567 + 0.00846202i
\(753\) −26.4641 −0.964405
\(754\) 13.6603 + 14.1962i 0.497477 + 0.516993i
\(755\) 18.7846 0.683642
\(756\) 2.59808 + 1.50000i 0.0944911 + 0.0545545i
\(757\) −9.13397 + 15.8205i −0.331980 + 0.575006i −0.982900 0.184140i \(-0.941050\pi\)
0.650920 + 0.759146i \(0.274383\pi\)
\(758\) −3.13397 5.42820i −0.113831 0.197161i
\(759\) 12.9282i 0.469264i
\(760\) 1.96410 1.13397i 0.0712455 0.0411336i
\(761\) 38.0885 21.9904i 1.38071 0.797151i 0.388463 0.921465i \(-0.373006\pi\)
0.992243 + 0.124314i \(0.0396730\pi\)
\(762\) 4.66025i 0.168823i
\(763\) 15.5885 + 27.0000i 0.564340 + 0.977466i
\(764\) 8.66025 15.0000i 0.313317 0.542681i
\(765\) 3.46410 + 2.00000i 0.125245 + 0.0723102i
\(766\) −36.7846 −1.32908
\(767\) −11.3397 11.7846i −0.409454 0.425518i
\(768\) −1.00000 −0.0360844
\(769\) 34.3923 + 19.8564i 1.24022 + 0.716040i 0.969139 0.246517i \(-0.0792860\pi\)
0.271080 + 0.962557i \(0.412619\pi\)
\(770\) −5.59808 + 9.69615i −0.201741 + 0.349425i
\(771\) 10.7321 + 18.5885i 0.386505 + 0.669447i
\(772\) 17.8564i 0.642666i
\(773\) 46.2391 26.6962i 1.66310 0.960194i 0.691885 0.722008i \(-0.256780\pi\)
0.971220 0.238186i \(-0.0765528\pi\)
\(774\) 5.19615 3.00000i 0.186772 0.107833i
\(775\) 8.92820i 0.320711i
\(776\) −6.19615 10.7321i −0.222429 0.385258i