Properties

Label 210.2.n.a.109.1
Level $210$
Weight $2$
Character 210.109
Analytic conductor $1.677$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.n (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.67685844245\)
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 109.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 210.109
Dual form 210.2.n.a.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.133975 - 2.23205i) q^{5} -1.00000 q^{6} +(1.73205 + 2.00000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.133975 - 2.23205i) q^{5} -1.00000 q^{6} +(1.73205 + 2.00000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.23205 + 1.86603i) q^{10} +(2.50000 - 4.33013i) q^{11} +(0.866025 - 0.500000i) q^{12} -1.00000i q^{13} +(-2.50000 - 0.866025i) q^{14} +(1.00000 - 2.00000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.73205 + 1.00000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(3.50000 + 6.06218i) q^{19} +(-2.00000 - 1.00000i) q^{20} +(0.500000 + 2.59808i) q^{21} +5.00000i q^{22} +(-2.59808 + 1.50000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-4.96410 + 0.598076i) q^{25} +(0.500000 + 0.866025i) q^{26} +1.00000i q^{27} +(2.59808 - 0.500000i) q^{28} +(0.133975 + 2.23205i) q^{30} +(3.00000 - 5.19615i) q^{31} +(0.866025 + 0.500000i) q^{32} +(4.33013 - 2.50000i) q^{33} -2.00000 q^{34} +(4.23205 - 4.13397i) q^{35} +1.00000 q^{36} +(-4.33013 + 2.50000i) q^{37} +(-6.06218 - 3.50000i) q^{38} +(0.500000 - 0.866025i) q^{39} +(2.23205 - 0.133975i) q^{40} -9.00000 q^{41} +(-1.73205 - 2.00000i) q^{42} -10.0000i q^{43} +(-2.50000 - 4.33013i) q^{44} +(1.86603 - 1.23205i) q^{45} +(1.50000 - 2.59808i) q^{46} +(-11.2583 + 6.50000i) q^{47} -1.00000i q^{48} +(-1.00000 + 6.92820i) q^{49} +(4.00000 - 3.00000i) q^{50} +(1.00000 + 1.73205i) q^{51} +(-0.866025 - 0.500000i) q^{52} +(-0.866025 - 0.500000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-10.0000 - 5.00000i) q^{55} +(-2.00000 + 1.73205i) q^{56} +7.00000i q^{57} +(2.00000 - 3.46410i) q^{59} +(-1.23205 - 1.86603i) q^{60} +(1.00000 + 1.73205i) q^{61} +6.00000i q^{62} +(-0.866025 + 2.50000i) q^{63} -1.00000 q^{64} +(-2.23205 + 0.133975i) q^{65} +(-2.50000 + 4.33013i) q^{66} +(-5.19615 - 3.00000i) q^{67} +(1.73205 - 1.00000i) q^{68} -3.00000 q^{69} +(-1.59808 + 5.69615i) q^{70} -2.00000 q^{71} +(-0.866025 + 0.500000i) q^{72} +(3.46410 + 2.00000i) q^{73} +(2.50000 - 4.33013i) q^{74} +(-4.59808 - 1.96410i) q^{75} +7.00000 q^{76} +(12.9904 - 2.50000i) q^{77} +1.00000i q^{78} +(-7.00000 - 12.1244i) q^{79} +(-1.86603 + 1.23205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(7.79423 - 4.50000i) q^{82} +10.0000i q^{83} +(2.50000 + 0.866025i) q^{84} +(2.00000 - 4.00000i) q^{85} +(5.00000 + 8.66025i) q^{86} +(4.33013 + 2.50000i) q^{88} +(5.00000 + 8.66025i) q^{89} +(-1.00000 + 2.00000i) q^{90} +(2.00000 - 1.73205i) q^{91} +3.00000i q^{92} +(5.19615 - 3.00000i) q^{93} +(6.50000 - 11.2583i) q^{94} +(13.0622 - 8.62436i) q^{95} +(0.500000 + 0.866025i) q^{96} +8.00000i q^{97} +(-2.59808 - 6.50000i) q^{98} +5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} - 4q^{5} - 4q^{6} + 2q^{9} + O(q^{10}) \) \( 4q + 2q^{4} - 4q^{5} - 4q^{6} + 2q^{9} - 2q^{10} + 10q^{11} - 10q^{14} + 4q^{15} - 2q^{16} + 14q^{19} - 8q^{20} + 2q^{21} - 2q^{24} - 6q^{25} + 2q^{26} + 4q^{30} + 12q^{31} - 8q^{34} + 10q^{35} + 4q^{36} + 2q^{39} + 2q^{40} - 36q^{41} - 10q^{44} + 4q^{45} + 6q^{46} - 4q^{49} + 16q^{50} + 4q^{51} - 2q^{54} - 40q^{55} - 8q^{56} + 8q^{59} + 2q^{60} + 4q^{61} - 4q^{64} - 2q^{65} - 10q^{66} - 12q^{69} + 4q^{70} - 8q^{71} + 10q^{74} - 8q^{75} + 28q^{76} - 28q^{79} - 4q^{80} - 2q^{81} + 10q^{84} + 8q^{85} + 20q^{86} + 20q^{89} - 4q^{90} + 8q^{91} + 26q^{94} + 28q^{95} + 2q^{96} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −0.133975 2.23205i −0.0599153 0.998203i
\(6\) −1.00000 −0.408248
\(7\) 1.73205 + 2.00000i 0.654654 + 0.755929i
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 1.23205 + 1.86603i 0.389609 + 0.590089i
\(11\) 2.50000 4.33013i 0.753778 1.30558i −0.192201 0.981356i \(-0.561563\pi\)
0.945979 0.324227i \(-0.105104\pi\)
\(12\) 0.866025 0.500000i 0.250000 0.144338i
\(13\) 1.00000i 0.277350i −0.990338 0.138675i \(-0.955716\pi\)
0.990338 0.138675i \(-0.0442844\pi\)
\(14\) −2.50000 0.866025i −0.668153 0.231455i
\(15\) 1.00000 2.00000i 0.258199 0.516398i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.73205 + 1.00000i 0.420084 + 0.242536i 0.695113 0.718900i \(-0.255354\pi\)
−0.275029 + 0.961436i \(0.588688\pi\)
\(18\) −0.866025 0.500000i −0.204124 0.117851i
\(19\) 3.50000 + 6.06218i 0.802955 + 1.39076i 0.917663 + 0.397360i \(0.130073\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) −2.00000 1.00000i −0.447214 0.223607i
\(21\) 0.500000 + 2.59808i 0.109109 + 0.566947i
\(22\) 5.00000i 1.06600i
\(23\) −2.59808 + 1.50000i −0.541736 + 0.312772i −0.745782 0.666190i \(-0.767924\pi\)
0.204046 + 0.978961i \(0.434591\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) −4.96410 + 0.598076i −0.992820 + 0.119615i
\(26\) 0.500000 + 0.866025i 0.0980581 + 0.169842i
\(27\) 1.00000i 0.192450i
\(28\) 2.59808 0.500000i 0.490990 0.0944911i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0.133975 + 2.23205i 0.0244603 + 0.407515i
\(31\) 3.00000 5.19615i 0.538816 0.933257i −0.460152 0.887840i \(-0.652205\pi\)
0.998968 0.0454165i \(-0.0144615\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 4.33013 2.50000i 0.753778 0.435194i
\(34\) −2.00000 −0.342997
\(35\) 4.23205 4.13397i 0.715347 0.698769i
\(36\) 1.00000 0.166667
\(37\) −4.33013 + 2.50000i −0.711868 + 0.410997i −0.811752 0.584002i \(-0.801486\pi\)
0.0998840 + 0.994999i \(0.468153\pi\)
\(38\) −6.06218 3.50000i −0.983415 0.567775i
\(39\) 0.500000 0.866025i 0.0800641 0.138675i
\(40\) 2.23205 0.133975i 0.352918 0.0211832i
\(41\) −9.00000 −1.40556 −0.702782 0.711405i \(-0.748059\pi\)
−0.702782 + 0.711405i \(0.748059\pi\)
\(42\) −1.73205 2.00000i −0.267261 0.308607i
\(43\) 10.0000i 1.52499i −0.646997 0.762493i \(-0.723975\pi\)
0.646997 0.762493i \(-0.276025\pi\)
\(44\) −2.50000 4.33013i −0.376889 0.652791i
\(45\) 1.86603 1.23205i 0.278171 0.183663i
\(46\) 1.50000 2.59808i 0.221163 0.383065i
\(47\) −11.2583 + 6.50000i −1.64220 + 0.948122i −0.662145 + 0.749375i \(0.730354\pi\)
−0.980051 + 0.198747i \(0.936313\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −1.00000 + 6.92820i −0.142857 + 0.989743i
\(50\) 4.00000 3.00000i 0.565685 0.424264i
\(51\) 1.00000 + 1.73205i 0.140028 + 0.242536i
\(52\) −0.866025 0.500000i −0.120096 0.0693375i
\(53\) −0.866025 0.500000i −0.118958 0.0686803i 0.439340 0.898321i \(-0.355212\pi\)
−0.558298 + 0.829640i \(0.688546\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) −10.0000 5.00000i −1.34840 0.674200i
\(56\) −2.00000 + 1.73205i −0.267261 + 0.231455i
\(57\) 7.00000i 0.927173i
\(58\) 0 0
\(59\) 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) −1.23205 1.86603i −0.159057 0.240903i
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) 6.00000i 0.762001i
\(63\) −0.866025 + 2.50000i −0.109109 + 0.314970i
\(64\) −1.00000 −0.125000
\(65\) −2.23205 + 0.133975i −0.276852 + 0.0166175i
\(66\) −2.50000 + 4.33013i −0.307729 + 0.533002i
\(67\) −5.19615 3.00000i −0.634811 0.366508i 0.147802 0.989017i \(-0.452780\pi\)
−0.782613 + 0.622509i \(0.786114\pi\)
\(68\) 1.73205 1.00000i 0.210042 0.121268i
\(69\) −3.00000 −0.361158
\(70\) −1.59808 + 5.69615i −0.191007 + 0.680820i
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 3.46410 + 2.00000i 0.405442 + 0.234082i 0.688830 0.724923i \(-0.258125\pi\)
−0.283387 + 0.959006i \(0.591458\pi\)
\(74\) 2.50000 4.33013i 0.290619 0.503367i
\(75\) −4.59808 1.96410i −0.530940 0.226795i
\(76\) 7.00000 0.802955
\(77\) 12.9904 2.50000i 1.48039 0.284901i
\(78\) 1.00000i 0.113228i
\(79\) −7.00000 12.1244i −0.787562 1.36410i −0.927457 0.373930i \(-0.878010\pi\)
0.139895 0.990166i \(-0.455323\pi\)
\(80\) −1.86603 + 1.23205i −0.208628 + 0.137747i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 7.79423 4.50000i 0.860729 0.496942i
\(83\) 10.0000i 1.09764i 0.835940 + 0.548821i \(0.184923\pi\)
−0.835940 + 0.548821i \(0.815077\pi\)
\(84\) 2.50000 + 0.866025i 0.272772 + 0.0944911i
\(85\) 2.00000 4.00000i 0.216930 0.433861i
\(86\) 5.00000 + 8.66025i 0.539164 + 0.933859i
\(87\) 0 0
\(88\) 4.33013 + 2.50000i 0.461593 + 0.266501i
\(89\) 5.00000 + 8.66025i 0.529999 + 0.917985i 0.999388 + 0.0349934i \(0.0111410\pi\)
−0.469389 + 0.882992i \(0.655526\pi\)
\(90\) −1.00000 + 2.00000i −0.105409 + 0.210819i
\(91\) 2.00000 1.73205i 0.209657 0.181568i
\(92\) 3.00000i 0.312772i
\(93\) 5.19615 3.00000i 0.538816 0.311086i
\(94\) 6.50000 11.2583i 0.670424 1.16121i
\(95\) 13.0622 8.62436i 1.34015 0.884840i
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 8.00000i 0.812277i 0.913812 + 0.406138i \(0.133125\pi\)
−0.913812 + 0.406138i \(0.866875\pi\)
\(98\) −2.59808 6.50000i −0.262445 0.656599i
\(99\) 5.00000 0.502519
\(100\) −1.96410 + 4.59808i −0.196410 + 0.459808i
\(101\) −4.00000 + 6.92820i −0.398015 + 0.689382i −0.993481 0.113998i \(-0.963634\pi\)
0.595466 + 0.803380i \(0.296967\pi\)
\(102\) −1.73205 1.00000i −0.171499 0.0990148i
\(103\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(104\) 1.00000 0.0980581
\(105\) 5.73205 1.46410i 0.559391 0.142882i
\(106\) 1.00000 0.0971286
\(107\) 10.3923 6.00000i 1.00466 0.580042i 0.0950377 0.995474i \(-0.469703\pi\)
0.909624 + 0.415432i \(0.136370\pi\)
\(108\) 0.866025 + 0.500000i 0.0833333 + 0.0481125i
\(109\) −9.00000 + 15.5885i −0.862044 + 1.49310i 0.00790932 + 0.999969i \(0.497482\pi\)
−0.869953 + 0.493135i \(0.835851\pi\)
\(110\) 11.1603 0.669873i 1.06409 0.0638699i
\(111\) −5.00000 −0.474579
\(112\) 0.866025 2.50000i 0.0818317 0.236228i
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) −3.50000 6.06218i −0.327805 0.567775i
\(115\) 3.69615 + 5.59808i 0.344668 + 0.522023i
\(116\) 0 0
\(117\) 0.866025 0.500000i 0.0800641 0.0462250i
\(118\) 4.00000i 0.368230i
\(119\) 1.00000 + 5.19615i 0.0916698 + 0.476331i
\(120\) 2.00000 + 1.00000i 0.182574 + 0.0912871i
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) −1.73205 1.00000i −0.156813 0.0905357i
\(123\) −7.79423 4.50000i −0.702782 0.405751i
\(124\) −3.00000 5.19615i −0.269408 0.466628i
\(125\) 2.00000 + 11.0000i 0.178885 + 0.983870i
\(126\) −0.500000 2.59808i −0.0445435 0.231455i
\(127\) 9.00000i 0.798621i 0.916816 + 0.399310i \(0.130750\pi\)
−0.916816 + 0.399310i \(0.869250\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 5.00000 8.66025i 0.440225 0.762493i
\(130\) 1.86603 1.23205i 0.163661 0.108058i
\(131\) 8.50000 + 14.7224i 0.742648 + 1.28630i 0.951285 + 0.308312i \(0.0997640\pi\)
−0.208637 + 0.977993i \(0.566903\pi\)
\(132\) 5.00000i 0.435194i
\(133\) −6.06218 + 17.5000i −0.525657 + 1.51744i
\(134\) 6.00000 0.518321
\(135\) 2.23205 0.133975i 0.192104 0.0115307i
\(136\) −1.00000 + 1.73205i −0.0857493 + 0.148522i
\(137\) 3.46410 + 2.00000i 0.295958 + 0.170872i 0.640626 0.767853i \(-0.278675\pi\)
−0.344668 + 0.938725i \(0.612008\pi\)
\(138\) 2.59808 1.50000i 0.221163 0.127688i
\(139\) 8.00000 0.678551 0.339276 0.940687i \(-0.389818\pi\)
0.339276 + 0.940687i \(0.389818\pi\)
\(140\) −1.46410 5.73205i −0.123739 0.484447i
\(141\) −13.0000 −1.09480
\(142\) 1.73205 1.00000i 0.145350 0.0839181i
\(143\) −4.33013 2.50000i −0.362103 0.209061i
\(144\) 0.500000 0.866025i 0.0416667 0.0721688i
\(145\) 0 0
\(146\) −4.00000 −0.331042
\(147\) −4.33013 + 5.50000i −0.357143 + 0.453632i
\(148\) 5.00000i 0.410997i
\(149\) −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) 4.96410 0.598076i 0.405317 0.0488327i
\(151\) 11.0000 19.0526i 0.895167 1.55048i 0.0615699 0.998103i \(-0.480389\pi\)
0.833597 0.552372i \(-0.186277\pi\)
\(152\) −6.06218 + 3.50000i −0.491708 + 0.283887i
\(153\) 2.00000i 0.161690i
\(154\) −10.0000 + 8.66025i −0.805823 + 0.697863i
\(155\) −12.0000 6.00000i −0.963863 0.481932i
\(156\) −0.500000 0.866025i −0.0400320 0.0693375i
\(157\) −11.2583 6.50000i −0.898513 0.518756i −0.0217953 0.999762i \(-0.506938\pi\)
−0.876717 + 0.481006i \(0.840272\pi\)
\(158\) 12.1244 + 7.00000i 0.964562 + 0.556890i
\(159\) −0.500000 0.866025i −0.0396526 0.0686803i
\(160\) 1.00000 2.00000i 0.0790569 0.158114i
\(161\) −7.50000 2.59808i −0.591083 0.204757i
\(162\) 1.00000i 0.0785674i
\(163\) 10.3923 6.00000i 0.813988 0.469956i −0.0343508 0.999410i \(-0.510936\pi\)
0.848339 + 0.529454i \(0.177603\pi\)
\(164\) −4.50000 + 7.79423i −0.351391 + 0.608627i
\(165\) −6.16025 9.33013i −0.479575 0.726349i
\(166\) −5.00000 8.66025i −0.388075 0.672166i
\(167\) 19.0000i 1.47026i −0.677924 0.735132i \(-0.737120\pi\)
0.677924 0.735132i \(-0.262880\pi\)
\(168\) −2.59808 + 0.500000i −0.200446 + 0.0385758i
\(169\) 12.0000 0.923077
\(170\) 0.267949 + 4.46410i 0.0205508 + 0.342381i
\(171\) −3.50000 + 6.06218i −0.267652 + 0.463586i
\(172\) −8.66025 5.00000i −0.660338 0.381246i
\(173\) −6.06218 + 3.50000i −0.460899 + 0.266100i −0.712422 0.701751i \(-0.752402\pi\)
0.251523 + 0.967851i \(0.419068\pi\)
\(174\) 0 0
\(175\) −9.79423 8.89230i −0.740374 0.672195i
\(176\) −5.00000 −0.376889
\(177\) 3.46410 2.00000i 0.260378 0.150329i
\(178\) −8.66025 5.00000i −0.649113 0.374766i
\(179\) −5.50000 + 9.52628i −0.411089 + 0.712028i −0.995009 0.0997838i \(-0.968185\pi\)
0.583920 + 0.811811i \(0.301518\pi\)
\(180\) −0.133975 2.23205i −0.00998588 0.166367i
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) −0.866025 + 2.50000i −0.0641941 + 0.185312i
\(183\) 2.00000i 0.147844i
\(184\) −1.50000 2.59808i −0.110581 0.191533i
\(185\) 6.16025 + 9.33013i 0.452911 + 0.685965i
\(186\) −3.00000 + 5.19615i −0.219971 + 0.381000i
\(187\) 8.66025 5.00000i 0.633300 0.365636i
\(188\) 13.0000i 0.948122i
\(189\) −2.00000 + 1.73205i −0.145479 + 0.125988i
\(190\) −7.00000 + 14.0000i −0.507833 + 1.01567i
\(191\) 8.00000 + 13.8564i 0.578860 + 1.00261i 0.995610 + 0.0935936i \(0.0298354\pi\)
−0.416751 + 0.909021i \(0.636831\pi\)
\(192\) −0.866025 0.500000i −0.0625000 0.0360844i
\(193\) −15.5885 9.00000i −1.12208 0.647834i −0.180150 0.983639i \(-0.557658\pi\)
−0.941932 + 0.335805i \(0.890992\pi\)
\(194\) −4.00000 6.92820i −0.287183 0.497416i
\(195\) −2.00000 1.00000i −0.143223 0.0716115i
\(196\) 5.50000 + 4.33013i 0.392857 + 0.309295i
\(197\) 27.0000i 1.92367i −0.273629 0.961835i \(-0.588224\pi\)
0.273629 0.961835i \(-0.411776\pi\)
\(198\) −4.33013 + 2.50000i −0.307729 + 0.177667i
\(199\) −7.00000 + 12.1244i −0.496217 + 0.859473i −0.999990 0.00436292i \(-0.998611\pi\)
0.503774 + 0.863836i \(0.331945\pi\)
\(200\) −0.598076 4.96410i −0.0422904 0.351015i
\(201\) −3.00000 5.19615i −0.211604 0.366508i
\(202\) 8.00000i 0.562878i
\(203\) 0 0
\(204\) 2.00000 0.140028
\(205\) 1.20577 + 20.0885i 0.0842147 + 1.40304i
\(206\) 0 0
\(207\) −2.59808 1.50000i −0.180579 0.104257i
\(208\) −0.866025 + 0.500000i −0.0600481 + 0.0346688i
\(209\) 35.0000 2.42100
\(210\) −4.23205 + 4.13397i −0.292039 + 0.285271i
\(211\) 19.0000 1.30801 0.654007 0.756489i \(-0.273087\pi\)
0.654007 + 0.756489i \(0.273087\pi\)
\(212\) −0.866025 + 0.500000i −0.0594789 + 0.0343401i
\(213\) −1.73205 1.00000i −0.118678 0.0685189i
\(214\) −6.00000 + 10.3923i −0.410152 + 0.710403i
\(215\) −22.3205 + 1.33975i −1.52225 + 0.0913699i
\(216\) −1.00000 −0.0680414
\(217\) 15.5885 3.00000i 1.05821 0.203653i
\(218\) 18.0000i 1.21911i
\(219\) 2.00000 + 3.46410i 0.135147 + 0.234082i
\(220\) −9.33013 + 6.16025i −0.629037 + 0.415324i
\(221\) 1.00000 1.73205i 0.0672673 0.116510i
\(222\) 4.33013 2.50000i 0.290619 0.167789i
\(223\) 16.0000i 1.07144i −0.844396 0.535720i \(-0.820040\pi\)
0.844396 0.535720i \(-0.179960\pi\)
\(224\) 0.500000 + 2.59808i 0.0334077 + 0.173591i
\(225\) −3.00000 4.00000i −0.200000 0.266667i
\(226\) 3.00000 + 5.19615i 0.199557 + 0.345643i
\(227\) −12.1244 7.00000i −0.804722 0.464606i 0.0403978 0.999184i \(-0.487137\pi\)
−0.845120 + 0.534577i \(0.820471\pi\)
\(228\) 6.06218 + 3.50000i 0.401478 + 0.231793i
\(229\) −2.00000 3.46410i −0.132164 0.228914i 0.792347 0.610071i \(-0.208859\pi\)
−0.924510 + 0.381157i \(0.875526\pi\)
\(230\) −6.00000 3.00000i −0.395628 0.197814i
\(231\) 12.5000 + 4.33013i 0.822440 + 0.284901i
\(232\) 0 0
\(233\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(234\) −0.500000 + 0.866025i −0.0326860 + 0.0566139i
\(235\) 16.0167 + 24.2583i 1.04481 + 1.58244i
\(236\) −2.00000 3.46410i −0.130189 0.225494i
\(237\) 14.0000i 0.909398i
\(238\) −3.46410 4.00000i −0.224544 0.259281i
\(239\) −20.0000 −1.29369 −0.646846 0.762620i \(-0.723912\pi\)
−0.646846 + 0.762620i \(0.723912\pi\)
\(240\) −2.23205 + 0.133975i −0.144078 + 0.00864802i
\(241\) 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i \(-0.823079\pi\)
0.881680 + 0.471848i \(0.156413\pi\)
\(242\) 12.1244 + 7.00000i 0.779383 + 0.449977i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) 2.00000 0.128037
\(245\) 15.5981 + 1.30385i 0.996525 + 0.0832998i
\(246\) 9.00000 0.573819
\(247\) 6.06218 3.50000i 0.385727 0.222700i
\(248\) 5.19615 + 3.00000i 0.329956 + 0.190500i
\(249\) −5.00000 + 8.66025i −0.316862 + 0.548821i
\(250\) −7.23205 8.52628i −0.457395 0.539249i
\(251\) −3.00000 −0.189358 −0.0946792 0.995508i \(-0.530183\pi\)
−0.0946792 + 0.995508i \(0.530183\pi\)
\(252\) 1.73205 + 2.00000i 0.109109 + 0.125988i
\(253\) 15.0000i 0.943042i
\(254\) −4.50000 7.79423i −0.282355 0.489053i
\(255\) 3.73205 2.46410i 0.233710 0.154308i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −8.66025 + 5.00000i −0.540212 + 0.311891i −0.745165 0.666880i \(-0.767629\pi\)
0.204953 + 0.978772i \(0.434296\pi\)
\(258\) 10.0000i 0.622573i
\(259\) −12.5000 4.33013i −0.776712 0.269061i
\(260\) −1.00000 + 2.00000i −0.0620174 + 0.124035i
\(261\) 0 0
\(262\) −14.7224 8.50000i −0.909555 0.525132i
\(263\) 20.7846 + 12.0000i 1.28163 + 0.739952i 0.977147 0.212565i \(-0.0681817\pi\)
0.304487 + 0.952517i \(0.401515\pi\)
\(264\) 2.50000 + 4.33013i 0.153864 + 0.266501i
\(265\) −1.00000 + 2.00000i −0.0614295 + 0.122859i
\(266\) −3.50000 18.1865i −0.214599 1.11509i
\(267\) 10.0000i 0.611990i
\(268\) −5.19615 + 3.00000i −0.317406 + 0.183254i
\(269\) 7.00000 12.1244i 0.426798 0.739235i −0.569789 0.821791i \(-0.692975\pi\)
0.996586 + 0.0825561i \(0.0263084\pi\)
\(270\) −1.86603 + 1.23205i −0.113563 + 0.0749802i
\(271\) −4.00000 6.92820i −0.242983 0.420858i 0.718580 0.695444i \(-0.244792\pi\)
−0.961563 + 0.274586i \(0.911459\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 2.59808 0.500000i 0.157243 0.0302614i
\(274\) −4.00000 −0.241649
\(275\) −9.82051 + 22.9904i −0.592199 + 1.38637i
\(276\) −1.50000 + 2.59808i −0.0902894 + 0.156386i
\(277\) −1.73205 1.00000i −0.104069 0.0600842i 0.447062 0.894503i \(-0.352470\pi\)
−0.551131 + 0.834419i \(0.685804\pi\)
\(278\) −6.92820 + 4.00000i −0.415526 + 0.239904i
\(279\) 6.00000 0.359211
\(280\) 4.13397 + 4.23205i 0.247052 + 0.252913i
\(281\) −11.0000 −0.656205 −0.328102 0.944642i \(-0.606409\pi\)
−0.328102 + 0.944642i \(0.606409\pi\)
\(282\) 11.2583 6.50000i 0.670424 0.387069i
\(283\) 22.5167 + 13.0000i 1.33848 + 0.772770i 0.986581 0.163270i \(-0.0522041\pi\)
0.351895 + 0.936039i \(0.385537\pi\)
\(284\) −1.00000 + 1.73205i −0.0593391 + 0.102778i
\(285\) 15.6244 0.937822i 0.925507 0.0555518i
\(286\) 5.00000 0.295656
\(287\) −15.5885 18.0000i −0.920158 1.06251i
\(288\) 1.00000i 0.0589256i
\(289\) −6.50000 11.2583i −0.382353 0.662255i
\(290\) 0 0
\(291\) −4.00000 + 6.92820i −0.234484 + 0.406138i
\(292\) 3.46410 2.00000i 0.202721 0.117041i
\(293\) 1.00000i 0.0584206i −0.999573 0.0292103i \(-0.990701\pi\)
0.999573 0.0292103i \(-0.00929925\pi\)
\(294\) 1.00000 6.92820i 0.0583212 0.404061i
\(295\) −8.00000 4.00000i −0.465778 0.232889i
\(296\) −2.50000 4.33013i −0.145310 0.251684i
\(297\) 4.33013 + 2.50000i 0.251259 + 0.145065i
\(298\) 5.19615 + 3.00000i 0.301005 + 0.173785i
\(299\) 1.50000 + 2.59808i 0.0867472 + 0.150251i
\(300\) −4.00000 + 3.00000i −0.230940 + 0.173205i
\(301\) 20.0000 17.3205i 1.15278 0.998337i
\(302\) 22.0000i 1.26596i
\(303\) −6.92820 + 4.00000i −0.398015 + 0.229794i
\(304\) 3.50000 6.06218i 0.200739 0.347690i
\(305\) 3.73205 2.46410i 0.213697 0.141094i
\(306\) −1.00000 1.73205i −0.0571662 0.0990148i
\(307\) 2.00000i 0.114146i 0.998370 + 0.0570730i \(0.0181768\pi\)
−0.998370 + 0.0570730i \(0.981823\pi\)
\(308\) 4.33013 12.5000i 0.246732 0.712254i
\(309\) 0 0
\(310\) 13.3923 0.803848i 0.760632 0.0456555i
\(311\) 13.0000 22.5167i 0.737162 1.27680i −0.216606 0.976259i \(-0.569499\pi\)
0.953768 0.300544i \(-0.0971681\pi\)
\(312\) 0.866025 + 0.500000i 0.0490290 + 0.0283069i
\(313\) 8.66025 5.00000i 0.489506 0.282617i −0.234863 0.972028i \(-0.575464\pi\)
0.724370 + 0.689412i \(0.242131\pi\)
\(314\) 13.0000 0.733632
\(315\) 5.69615 + 1.59808i 0.320942 + 0.0900414i
\(316\) −14.0000 −0.787562
\(317\) 1.73205 1.00000i 0.0972817 0.0561656i −0.450570 0.892741i \(-0.648779\pi\)
0.547852 + 0.836576i \(0.315446\pi\)
\(318\) 0.866025 + 0.500000i 0.0485643 + 0.0280386i
\(319\) 0 0
\(320\) 0.133975 + 2.23205i 0.00748941 + 0.124775i
\(321\) 12.0000 0.669775
\(322\) 7.79423 1.50000i 0.434355 0.0835917i
\(323\) 14.0000i 0.778981i
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 0.598076 + 4.96410i 0.0331753 + 0.275359i
\(326\) −6.00000 + 10.3923i −0.332309 + 0.575577i
\(327\) −15.5885 + 9.00000i −0.862044 + 0.497701i
\(328\) 9.00000i 0.496942i
\(329\) −32.5000 11.2583i −1.79178 0.620692i
\(330\) 10.0000 + 5.00000i 0.550482 + 0.275241i
\(331\) 7.50000 + 12.9904i 0.412237 + 0.714016i 0.995134 0.0985303i \(-0.0314141\pi\)
−0.582897 + 0.812546i \(0.698081\pi\)
\(332\) 8.66025 + 5.00000i 0.475293 + 0.274411i
\(333\) −4.33013 2.50000i −0.237289 0.136999i
\(334\) 9.50000 + 16.4545i 0.519817 + 0.900349i
\(335\) −6.00000 + 12.0000i −0.327815 + 0.655630i
\(336\) 2.00000 1.73205i 0.109109 0.0944911i
\(337\) 14.0000i 0.762629i −0.924445 0.381314i \(-0.875472\pi\)
0.924445 0.381314i \(-0.124528\pi\)
\(338\) −10.3923 + 6.00000i −0.565267 + 0.326357i
\(339\) 3.00000 5.19615i 0.162938 0.282216i
\(340\) −2.46410 3.73205i −0.133635 0.202399i
\(341\) −15.0000 25.9808i −0.812296 1.40694i
\(342\) 7.00000i 0.378517i
\(343\) −15.5885 + 10.0000i −0.841698 + 0.539949i
\(344\) 10.0000 0.539164
\(345\) 0.401924 + 6.69615i 0.0216388 + 0.360509i
\(346\) 3.50000 6.06218i 0.188161 0.325905i
\(347\) 13.8564 + 8.00000i 0.743851 + 0.429463i 0.823468 0.567363i \(-0.192036\pi\)
−0.0796169 + 0.996826i \(0.525370\pi\)
\(348\) 0 0
\(349\) 24.0000 1.28469 0.642345 0.766415i \(-0.277962\pi\)
0.642345 + 0.766415i \(0.277962\pi\)
\(350\) 12.9282 + 2.80385i 0.691042 + 0.149872i
\(351\) 1.00000 0.0533761
\(352\) 4.33013 2.50000i 0.230797 0.133250i
\(353\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(354\) −2.00000 + 3.46410i −0.106299 + 0.184115i
\(355\) 0.267949 + 4.46410i 0.0142213 + 0.236930i
\(356\) 10.0000 0.529999
\(357\) −1.73205 + 5.00000i −0.0916698 + 0.264628i
\(358\) 11.0000i 0.581368i
\(359\) −14.0000 24.2487i −0.738892 1.27980i −0.952995 0.302987i \(-0.902016\pi\)
0.214103 0.976811i \(-0.431317\pi\)
\(360\) 1.23205 + 1.86603i 0.0649348 + 0.0983482i
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) 1.73205 1.00000i 0.0910346 0.0525588i
\(363\) 14.0000i 0.734809i
\(364\) −0.500000 2.59808i −0.0262071 0.136176i
\(365\) 4.00000 8.00000i 0.209370 0.418739i
\(366\) −1.00000 1.73205i −0.0522708 0.0905357i
\(367\) 32.0429 + 18.5000i 1.67263 + 0.965692i 0.966159 + 0.257948i \(0.0830464\pi\)
0.706469 + 0.707744i \(0.250287\pi\)
\(368\) 2.59808 + 1.50000i 0.135434 + 0.0781929i
\(369\) −4.50000 7.79423i −0.234261 0.405751i
\(370\) −10.0000 5.00000i −0.519875 0.259938i
\(371\) −0.500000 2.59808i −0.0259587 0.134885i
\(372\) 6.00000i 0.311086i
\(373\) −5.19615 + 3.00000i −0.269047 + 0.155334i −0.628454 0.777847i \(-0.716312\pi\)
0.359408 + 0.933181i \(0.382979\pi\)
\(374\) −5.00000 + 8.66025i −0.258544 + 0.447811i
\(375\) −3.76795 + 10.5263i −0.194576 + 0.543575i
\(376\) −6.50000 11.2583i −0.335212 0.580604i
\(377\) 0 0
\(378\) 0.866025 2.50000i 0.0445435 0.128586i
\(379\) 1.00000 0.0513665 0.0256833 0.999670i \(-0.491824\pi\)
0.0256833 + 0.999670i \(0.491824\pi\)
\(380\) −0.937822 15.6244i −0.0481093 0.801513i
\(381\) −4.50000 + 7.79423i −0.230542 + 0.399310i
\(382\) −13.8564 8.00000i −0.708955 0.409316i
\(383\) 7.79423 4.50000i 0.398266 0.229939i −0.287469 0.957790i \(-0.592814\pi\)
0.685736 + 0.727851i \(0.259481\pi\)
\(384\) 1.00000 0.0510310
\(385\) −7.32051 28.6603i −0.373088 1.46066i
\(386\) 18.0000 0.916176
\(387\) 8.66025 5.00000i 0.440225 0.254164i
\(388\) 6.92820 + 4.00000i 0.351726 + 0.203069i
\(389\) 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i \(-0.784728\pi\)
0.932002 + 0.362454i \(0.118061\pi\)
\(390\) 2.23205 0.133975i 0.113024 0.00678407i
\(391\) −6.00000 −0.303433
\(392\) −6.92820 1.00000i −0.349927 0.0505076i
\(393\) 17.0000i 0.857537i
\(394\) 13.5000 + 23.3827i 0.680120 + 1.17800i
\(395\) −26.1244 + 17.2487i −1.31446 + 0.867877i
\(396\) 2.50000 4.33013i 0.125630 0.217597i
\(397\) −1.73205 + 1.00000i −0.0869291 + 0.0501886i −0.542834 0.839840i \(-0.682649\pi\)
0.455905 + 0.890028i \(0.349316\pi\)
\(398\) 14.0000i 0.701757i
\(399\) −14.0000 + 12.1244i −0.700877 + 0.606977i
\(400\) 3.00000 + 4.00000i 0.150000 + 0.200000i
\(401\) 13.5000 + 23.3827i 0.674158 + 1.16768i 0.976714 + 0.214544i \(0.0688266\pi\)
−0.302556 + 0.953131i \(0.597840\pi\)
\(402\) 5.19615 + 3.00000i 0.259161 + 0.149626i
\(403\) −5.19615 3.00000i −0.258839 0.149441i
\(404\) 4.00000 + 6.92820i 0.199007 + 0.344691i
\(405\) 2.00000 + 1.00000i 0.0993808 + 0.0496904i
\(406\) 0 0
\(407\) 25.0000i 1.23920i
\(408\) −1.73205 + 1.00000i −0.0857493 + 0.0495074i
\(409\) 5.00000 8.66025i 0.247234 0.428222i −0.715523 0.698589i \(-0.753812\pi\)
0.962757 + 0.270367i \(0.0871450\pi\)
\(410\) −11.0885 16.7942i −0.547620 0.829408i
\(411\) 2.00000 + 3.46410i 0.0986527 + 0.170872i
\(412\) 0 0
\(413\) 10.3923 2.00000i 0.511372 0.0984136i
\(414\) 3.00000 0.147442
\(415\) 22.3205 1.33975i 1.09567 0.0657655i
\(416\) 0.500000 0.866025i 0.0245145 0.0424604i
\(417\) 6.92820 + 4.00000i 0.339276 + 0.195881i
\(418\) −30.3109 + 17.5000i −1.48255 + 0.855953i
\(419\) −3.00000 −0.146560 −0.0732798 0.997311i \(-0.523347\pi\)
−0.0732798 + 0.997311i \(0.523347\pi\)
\(420\) 1.59808 5.69615i 0.0779781 0.277944i
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) −16.4545 + 9.50000i −0.800992 + 0.462453i
\(423\) −11.2583 6.50000i −0.547399 0.316041i
\(424\) 0.500000 0.866025i 0.0242821 0.0420579i
\(425\) −9.19615 3.92820i −0.446079 0.190546i
\(426\) 2.00000 0.0969003
\(427\) −1.73205 + 5.00000i −0.0838198 + 0.241967i
\(428\) 12.0000i 0.580042i
\(429\) −2.50000 4.33013i −0.120701 0.209061i
\(430\) 18.6603 12.3205i 0.899877 0.594148i
\(431\) −9.00000 + 15.5885i −0.433515 + 0.750870i −0.997173 0.0751385i \(-0.976060\pi\)
0.563658 + 0.826008i \(0.309393\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) 4.00000i 0.192228i −0.995370 0.0961139i \(-0.969359\pi\)
0.995370 0.0961139i \(-0.0306413\pi\)
\(434\) −12.0000 + 10.3923i −0.576018 + 0.498847i
\(435\) 0 0
\(436\) 9.00000 + 15.5885i 0.431022 + 0.746552i
\(437\) −18.1865 10.5000i −0.869980 0.502283i
\(438\) −3.46410 2.00000i −0.165521 0.0955637i
\(439\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 5.00000 10.0000i 0.238366 0.476731i
\(441\) −6.50000 + 2.59808i −0.309524 + 0.123718i
\(442\) 2.00000i 0.0951303i
\(443\) 5.19615 3.00000i 0.246877 0.142534i −0.371457 0.928450i \(-0.621142\pi\)
0.618333 + 0.785916i \(0.287808\pi\)
\(444\) −2.50000 + 4.33013i −0.118645 + 0.205499i
\(445\) 18.6603 12.3205i 0.884581 0.584048i
\(446\) 8.00000 + 13.8564i 0.378811 + 0.656120i
\(447\) 6.00000i 0.283790i
\(448\) −1.73205 2.00000i −0.0818317 0.0944911i
\(449\) −9.00000 −0.424736 −0.212368 0.977190i \(-0.568118\pi\)
−0.212368 + 0.977190i \(0.568118\pi\)
\(450\) 4.59808 + 1.96410i 0.216755 + 0.0925886i
\(451\) −22.5000 + 38.9711i −1.05948 + 1.83508i
\(452\) −5.19615 3.00000i −0.244406 0.141108i
\(453\) 19.0526 11.0000i 0.895167 0.516825i
\(454\) 14.0000 0.657053
\(455\) −4.13397 4.23205i −0.193804 0.198402i
\(456\) −7.00000 −0.327805
\(457\) −32.9090 + 19.0000i −1.53942 + 0.888783i −0.540544 + 0.841316i \(0.681781\pi\)
−0.998873 + 0.0474665i \(0.984885\pi\)
\(458\) 3.46410 + 2.00000i 0.161867 + 0.0934539i
\(459\) −1.00000 + 1.73205i −0.0466760 + 0.0808452i
\(460\) 6.69615 0.401924i 0.312210 0.0187398i
\(461\) −12.0000 −0.558896 −0.279448 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) −12.9904 + 2.50000i −0.604367 + 0.116311i
\(463\) 15.0000i 0.697109i 0.937288 + 0.348555i \(0.113327\pi\)
−0.937288 + 0.348555i \(0.886673\pi\)
\(464\) 0 0
\(465\) −7.39230 11.1962i −0.342810 0.519209i
\(466\) 0 0
\(467\) 1.73205 1.00000i 0.0801498 0.0462745i −0.459390 0.888235i \(-0.651932\pi\)
0.539539 + 0.841960i \(0.318598\pi\)
\(468\) 1.00000i 0.0462250i
\(469\) −3.00000 15.5885i −0.138527 0.719808i
\(470\) −26.0000 13.0000i −1.19929 0.599645i
\(471\) −6.50000 11.2583i −0.299504 0.518756i
\(472\) 3.46410 + 2.00000i 0.159448 + 0.0920575i
\(473\) −43.3013 25.0000i −1.99099 1.14950i
\(474\) 7.00000 + 12.1244i 0.321521 + 0.556890i
\(475\) −21.0000 28.0000i −0.963546 1.28473i
\(476\) 5.00000 + 1.73205i 0.229175 + 0.0793884i
\(477\) 1.00000i 0.0457869i
\(478\) 17.3205 10.0000i 0.792222 0.457389i
\(479\) 4.00000 6.92820i 0.182765 0.316558i −0.760056 0.649857i \(-0.774829\pi\)
0.942821 + 0.333300i \(0.108162\pi\)
\(480\) 1.86603 1.23205i 0.0851720 0.0562352i
\(481\) 2.50000 + 4.33013i 0.113990 + 0.197437i
\(482\) 1.00000i 0.0455488i
\(483\) −5.19615 6.00000i −0.236433 0.273009i
\(484\) −14.0000 −0.636364
\(485\) 17.8564 1.07180i 0.810818 0.0486678i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) −20.7846 12.0000i −0.941841 0.543772i −0.0513038 0.998683i \(-0.516338\pi\)
−0.890537 + 0.454911i \(0.849671\pi\)
\(488\) −1.73205 + 1.00000i −0.0784063 + 0.0452679i
\(489\) 12.0000 0.542659
\(490\) −14.1603 + 6.66987i −0.639695 + 0.301314i
\(491\) 24.0000 1.08310 0.541552 0.840667i \(-0.317837\pi\)
0.541552 + 0.840667i \(0.317837\pi\)
\(492\) −7.79423 + 4.50000i −0.351391 + 0.202876i
\(493\) 0 0
\(494\) −3.50000 + 6.06218i −0.157472 + 0.272750i
\(495\) −0.669873 11.1603i −0.0301086 0.501616i
\(496\) −6.00000 −0.269408
\(497\) −3.46410 4.00000i −0.155386 0.179425i
\(498\) 10.0000i 0.448111i
\(499\) −14.0000 24.2487i −0.626726 1.08552i −0.988204 0.153141i \(-0.951061\pi\)
0.361478 0.932381i \(-0.382272\pi\)
\(500\) 10.5263 + 3.76795i 0.470750 + 0.168508i
\(501\) 9.50000 16.4545i 0.424429 0.735132i
\(502\) 2.59808 1.50000i 0.115958 0.0669483i
\(503\) 24.0000i 1.07011i −0.844818 0.535054i \(-0.820291\pi\)
0.844818 0.535054i \(-0.179709\pi\)
\(504\) −2.50000 0.866025i −0.111359 0.0385758i
\(505\) 16.0000 + 8.00000i 0.711991 + 0.355995i
\(506\) −7.50000 12.9904i −0.333416 0.577493i
\(507\) 10.3923 + 6.00000i 0.461538 + 0.266469i
\(508\) 7.79423 + 4.50000i 0.345813 + 0.199655i
\(509\) 7.00000 + 12.1244i 0.310270 + 0.537403i 0.978421 0.206623i \(-0.0662474\pi\)
−0.668151 + 0.744026i \(0.732914\pi\)
\(510\) −2.00000 + 4.00000i −0.0885615 + 0.177123i
\(511\) 2.00000 + 10.3923i 0.0884748 + 0.459728i
\(512\) 1.00000i 0.0441942i
\(513\) −6.06218 + 3.50000i −0.267652 + 0.154529i
\(514\) 5.00000 8.66025i 0.220541 0.381987i
\(515\) 0 0
\(516\) −5.00000 8.66025i −0.220113 0.381246i
\(517\) 65.0000i 2.85870i
\(518\) 12.9904 2.50000i 0.570765 0.109844i
\(519\) −7.00000 −0.307266
\(520\) −0.133975 2.23205i −0.00587517 0.0978819i
\(521\) 7.50000 12.9904i 0.328581 0.569119i −0.653650 0.756797i \(-0.726763\pi\)
0.982231 + 0.187678i \(0.0600963\pi\)
\(522\) 0 0
\(523\) −10.3923 + 6.00000i −0.454424 + 0.262362i −0.709697 0.704507i \(-0.751168\pi\)
0.255273 + 0.966869i \(0.417835\pi\)
\(524\) 17.0000 0.742648
\(525\) −4.03590 12.5981i −0.176141 0.549825i
\(526\) −24.0000 −1.04645
\(527\) 10.3923 6.00000i 0.452696 0.261364i
\(528\) −4.33013 2.50000i −0.188445 0.108799i
\(529\) −7.00000 + 12.1244i −0.304348 + 0.527146i
\(530\) −0.133975 2.23205i −0.00581948 0.0969541i
\(531\) 4.00000 0.173585
\(532\) 12.1244 + 14.0000i 0.525657 + 0.606977i
\(533\) 9.00000i 0.389833i
\(534\) −5.00000 8.66025i −0.216371 0.374766i
\(535\) −14.7846 22.3923i −0.639194 0.968104i
\(536\) 3.00000 5.19615i 0.129580 0.224440i
\(537\) −9.52628 + 5.50000i −0.411089 + 0.237343i
\(538\) 14.0000i 0.603583i
\(539\) 27.5000 + 21.6506i 1.18451 + 0.932559i
\(540\) 1.00000 2.00000i 0.0430331 0.0860663i
\(541\) −2.00000 3.46410i −0.0859867 0.148933i 0.819825 0.572615i \(-0.194071\pi\)
−0.905811 + 0.423681i \(0.860738\pi\)
\(542\) 6.92820 + 4.00000i 0.297592 + 0.171815i
\(543\) −1.73205 1.00000i −0.0743294 0.0429141i
\(544\) 1.00000 + 1.73205i 0.0428746 + 0.0742611i
\(545\) 36.0000 + 18.0000i 1.54207 + 0.771035i
\(546\) −2.00000 + 1.73205i −0.0855921 + 0.0741249i
\(547\) 14.0000i 0.598597i −0.954160 0.299298i \(-0.903247\pi\)
0.954160 0.299298i \(-0.0967526\pi\)
\(548\) 3.46410 2.00000i 0.147979 0.0854358i
\(549\) −1.00000 + 1.73205i −0.0426790 + 0.0739221i
\(550\) −2.99038 24.8205i −0.127510 1.05835i
\(551\) 0 0
\(552\) 3.00000i 0.127688i
\(553\) 12.1244 35.0000i 0.515580 1.48835i
\(554\) 2.00000 0.0849719
\(555\) 0.669873 + 11.1603i 0.0284345 + 0.473726i
\(556\) 4.00000 6.92820i 0.169638 0.293821i
\(557\) 33.7750 + 19.5000i 1.43109 + 0.826242i 0.997204 0.0747252i \(-0.0238080\pi\)
0.433888 + 0.900967i \(0.357141\pi\)
\(558\) −5.19615 + 3.00000i −0.219971 + 0.127000i
\(559\) −10.0000 −0.422955
\(560\) −5.69615 1.59808i −0.240706 0.0675310i
\(561\) 10.0000 0.422200
\(562\) 9.52628 5.50000i 0.401842 0.232003i
\(563\) 25.9808 + 15.0000i 1.09496 + 0.632175i 0.934892 0.354932i \(-0.115496\pi\)
0.160066 + 0.987106i \(0.448829\pi\)
\(564\) −6.50000 + 11.2583i −0.273699 + 0.474061i
\(565\) −13.3923 + 0.803848i −0.563418 + 0.0338181i
\(566\) −26.0000 −1.09286
\(567\) −2.59808 + 0.500000i −0.109109 + 0.0209980i
\(568\) 2.00000i 0.0839181i
\(569\) −1.50000 2.59808i −0.0628833 0.108917i 0.832870 0.553469i \(-0.186696\pi\)
−0.895753 + 0.444552i \(0.853363\pi\)
\(570\) −13.0622 + 8.62436i −0.547114 + 0.361235i
\(571\) 4.00000 6.92820i 0.167395 0.289936i −0.770108 0.637913i \(-0.779798\pi\)
0.937503 + 0.347977i \(0.113131\pi\)
\(572\) −4.33013 + 2.50000i −0.181052 + 0.104530i
\(573\) 16.0000i 0.668410i
\(574\) 22.5000 + 7.79423i 0.939132 + 0.325325i
\(575\) 12.0000 9.00000i 0.500435 0.375326i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −20.7846 12.0000i −0.865275 0.499567i 0.000500448 1.00000i \(-0.499841\pi\)
−0.865775 + 0.500433i \(0.833174\pi\)
\(578\) 11.2583 + 6.50000i 0.468285 + 0.270364i
\(579\) −9.00000 15.5885i −0.374027 0.647834i
\(580\) 0 0
\(581\) −20.0000 + 17.3205i −0.829740 + 0.718576i
\(582\) 8.00000i 0.331611i
\(583\) −4.33013 + 2.50000i −0.179336 + 0.103539i
\(584\) −2.00000 + 3.46410i −0.0827606 + 0.143346i
\(585\) −1.23205 1.86603i −0.0509390 0.0771507i
\(586\) 0.500000 + 0.866025i 0.0206548 + 0.0357752i
\(587\) 2.00000i 0.0825488i 0.999148 + 0.0412744i \(0.0131418\pi\)
−0.999148 + 0.0412744i \(0.986858\pi\)
\(588\) 2.59808 + 6.50000i 0.107143 + 0.268055i
\(589\) 42.0000 1.73058
\(590\) 8.92820 0.535898i 0.367568 0.0220626i
\(591\) 13.5000 23.3827i 0.555316 0.961835i
\(592\) 4.33013 + 2.50000i 0.177967 + 0.102749i
\(593\) 29.4449 17.0000i 1.20916 0.698106i 0.246581 0.969122i \(-0.420693\pi\)
0.962575 + 0.271016i \(0.0873596\pi\)
\(594\) −5.00000 −0.205152
\(595\) 11.4641 2.92820i 0.469982 0.120045i
\(596\) −6.00000 −0.245770
\(597\) −12.1244 + 7.00000i −0.496217 + 0.286491i
\(598\) −2.59808 1.50000i −0.106243 0.0613396i
\(599\) −14.0000 + 24.2487i −0.572024 + 0.990775i 0.424333 + 0.905506i \(0.360508\pi\)
−0.996358 + 0.0852695i \(0.972825\pi\)
\(600\) 1.96410 4.59808i 0.0801841 0.187716i
\(601\) −30.0000 −1.22373 −0.611863 0.790964i \(-0.709580\pi\)
−0.611863 + 0.790964i \(0.709580\pi\)
\(602\) −8.66025 + 25.0000i −0.352966 + 1.01892i
\(603\) 6.00000i 0.244339i
\(604\) −11.0000 19.0526i −0.447584 0.775238i
\(605\) −26.1244 + 17.2487i −1.06211 + 0.701260i
\(606\) 4.00000 6.92820i 0.162489 0.281439i
\(607\) 11.2583 6.50000i 0.456962 0.263827i −0.253804 0.967256i \(-0.581682\pi\)
0.710766 + 0.703429i \(0.248349\pi\)
\(608\) 7.00000i 0.283887i
\(609\) 0 0
\(610\) −2.00000 + 4.00000i −0.0809776 + 0.161955i
\(611\) 6.50000 + 11.2583i 0.262962 + 0.455463i
\(612\) 1.73205 + 1.00000i 0.0700140 + 0.0404226i
\(613\) 16.4545 + 9.50000i 0.664590 + 0.383701i 0.794024 0.607887i \(-0.207983\pi\)
−0.129433 + 0.991588i \(0.541316\pi\)
\(614\) −1.00000 1.73205i −0.0403567 0.0698999i
\(615\) −9.00000 + 18.0000i −0.362915 + 0.725830i
\(616\) 2.50000 + 12.9904i 0.100728 + 0.523397i
\(617\) 30.0000i 1.20775i 0.797077 + 0.603877i \(0.206378\pi\)
−0.797077 + 0.603877i \(0.793622\pi\)
\(618\) 0 0
\(619\) 7.50000 12.9904i 0.301450 0.522127i −0.675014 0.737805i \(-0.735863\pi\)
0.976465 + 0.215677i \(0.0691959\pi\)
\(620\) −11.1962 + 7.39230i −0.449648 + 0.296882i
\(621\) −1.50000 2.59808i −0.0601929 0.104257i
\(622\) 26.0000i 1.04251i
\(623\) −8.66025 + 25.0000i −0.346966 + 1.00160i
\(624\) −1.00000 −0.0400320
\(625\) 24.2846 5.93782i 0.971384 0.237513i
\(626\) −5.00000 + 8.66025i −0.199840 + 0.346133i
\(627\) 30.3109 + 17.5000i 1.21050 + 0.698883i
\(628\) −11.2583 + 6.50000i −0.449256 + 0.259378i
\(629\) −10.0000 −0.398726
\(630\) −5.73205 + 1.46410i −0.228370 + 0.0583312i
\(631\) 18.0000 0.716569 0.358284 0.933613i \(-0.383362\pi\)
0.358284 + 0.933613i \(0.383362\pi\)
\(632\) 12.1244 7.00000i 0.482281 0.278445i
\(633\) 16.4545 + 9.50000i 0.654007 + 0.377591i
\(634\) −1.00000 + 1.73205i −0.0397151 + 0.0687885i
\(635\) 20.0885 1.20577i 0.797186 0.0478496i
\(636\) −1.00000 −0.0396526
\(637\) 6.92820 + 1.00000i 0.274505 + 0.0396214i
\(638\) 0 0
\(639\) −1.00000 1.73205i −0.0395594 0.0685189i
\(640\) −1.23205 1.86603i −0.0487011 0.0737611i
\(641\) 16.5000 28.5788i 0.651711 1.12880i −0.330997 0.943632i \(-0.607385\pi\)
0.982708 0.185164i \(-0.0592817\pi\)
\(642\) −10.3923 + 6.00000i −0.410152 + 0.236801i
\(643\) 38.0000i 1.49857i −0.662246 0.749287i \(-0.730396\pi\)
0.662246 0.749287i \(-0.269604\pi\)
\(644\) −6.00000 + 5.19615i −0.236433 + 0.204757i
\(645\) −20.0000 10.0000i −0.787499 0.393750i
\(646\) −7.00000 12.1244i −0.275411 0.477026i
\(647\) 0.866025 + 0.500000i 0.0340470 + 0.0196570i 0.516927 0.856030i \(-0.327076\pi\)
−0.482880 + 0.875687i \(0.660409\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) −10.0000 17.3205i −0.392534 0.679889i
\(650\) −3.00000 4.00000i −0.117670 0.156893i
\(651\) 15.0000 + 5.19615i 0.587896 + 0.203653i
\(652\) 12.0000i 0.469956i
\(653\) −4.33013 + 2.50000i −0.169451 + 0.0978326i −0.582327 0.812955i \(-0.697858\pi\)
0.412876 + 0.910787i \(0.364524\pi\)
\(654\) 9.00000 15.5885i 0.351928 0.609557i
\(655\) 31.7224 20.9449i 1.23950 0.818384i
\(656\) 4.50000 + 7.79423i 0.175695 + 0.304314i
\(657\) 4.00000i 0.156055i
\(658\) 33.7750 6.50000i 1.31669 0.253396i
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) −11.1603 + 0.669873i −0.434412 + 0.0260748i
\(661\) −20.0000 + 34.6410i −0.777910 + 1.34738i 0.155235 + 0.987878i \(0.450387\pi\)
−0.933144 + 0.359502i \(0.882947\pi\)
\(662\) −12.9904 7.50000i −0.504885 0.291496i
\(663\) 1.73205 1.00000i 0.0672673 0.0388368i
\(664\) −10.0000 −0.388075
\(665\) 39.8731 + 11.1865i 1.54621 + 0.433795i
\(666\) 5.00000 0.193746
\(667\) 0 0
\(668\) −16.4545 9.50000i −0.636643 0.367566i
\(669\) 8.00000 13.8564i 0.309298 0.535720i
\(670\) −0.803848 13.3923i −0.0310553 0.517390i
\(671\) 10.0000 0.386046
\(672\) −0.866025 + 2.50000i −0.0334077 + 0.0964396i
\(673\) 36.0000i 1.38770i −0.720121 0.693849i \(-0.755914\pi\)
0.720121 0.693849i \(-0.244086\pi\)
\(674\) 7.00000 + 12.1244i 0.269630 + 0.467013i
\(675\) −0.598076 4.96410i −0.0230200 0.191068i
\(676\) 6.00000 10.3923i 0.230769 0.399704i
\(677\) 28.5788 16.5000i 1.09837 0.634147i 0.162581 0.986695i \(-0.448018\pi\)
0.935793 + 0.352549i \(0.114685\pi\)
\(678\) 6.00000i 0.230429i
\(679\) −16.0000 + 13.8564i −0.614024 + 0.531760i
\(680\) 4.00000 + 2.00000i 0.153393 + 0.0766965i
\(681\) −7.00000 12.1244i −0.268241 0.464606i
\(682\) 25.9808 + 15.0000i 0.994855 + 0.574380i
\(683\) −3.46410 2.00000i −0.132550 0.0765279i 0.432259 0.901750i \(-0.357717\pi\)
−0.564809 + 0.825222i \(0.691050\pi\)
\(684\) 3.50000 + 6.06218i 0.133826 + 0.231793i
\(685\) 4.00000 8.00000i 0.152832 0.305664i
\(686\) 8.50000 16.4545i 0.324532 0.628235i
\(687\) 4.00000i 0.152610i
\(688\) −8.66025 + 5.00000i −0.330169 + 0.190623i
\(689\) −0.500000 + 0.866025i −0.0190485 + 0.0329929i
\(690\) −3.69615 5.59808i −0.140710 0.213115i
\(691\) 10.0000 + 17.3205i 0.380418 + 0.658903i 0.991122 0.132956i \(-0.0424468\pi\)
−0.610704 + 0.791859i \(0.709113\pi\)
\(692\) 7.00000i 0.266100i
\(693\) 8.66025 + 10.0000i 0.328976 + 0.379869i
\(694\) −16.0000 −0.607352
\(695\) −1.07180 17.8564i −0.0406556 0.677332i
\(696\) 0 0
\(697\) −15.5885 9.00000i −0.590455 0.340899i
\(698\) −20.7846 + 12.0000i −0.786709 + 0.454207i
\(699\) 0 0
\(700\) −12.5981 + 4.03590i −0.476163 + 0.152543i
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) −0.866025 + 0.500000i −0.0326860 + 0.0188713i
\(703\) −30.3109 17.5000i −1.14320 0.660025i
\(704\) −2.50000 + 4.33013i −0.0942223 + 0.163198i
\(705\) 1.74167 + 29.0167i 0.0655951 + 1.09283i
\(706\) 0 0
\(707\) −20.7846 + 4.00000i −0.781686 + 0.150435i
\(708\) 4.00000i 0.150329i
\(709\) 8.00000 + 13.8564i 0.300446 + 0.520388i 0.976237 0.216705i \(-0.0695310\pi\)
−0.675791 + 0.737093i \(0.736198\pi\)
\(710\) −2.46410 3.73205i −0.0924761 0.140061i
\(711\) 7.00000 12.1244i 0.262521 0.454699i
\(712\) −8.66025 + 5.00000i −0.324557 + 0.187383i
\(713\) 18.0000i 0.674105i
\(714\) −1.00000 5.19615i −0.0374241 0.194461i
\(715\) −5.00000 + 10.0000i −0.186989 + 0.373979i
\(716\) 5.50000 + 9.52628i 0.205545 + 0.356014i
\(717\) −17.3205 10.0000i −0.646846 0.373457i
\(718\) 24.2487 + 14.0000i 0.904954 + 0.522475i
\(719\) −1.00000 1.73205i −0.0372937 0.0645946i 0.846776 0.531949i \(-0.178540\pi\)
−0.884070 + 0.467355i \(0.845207\pi\)
\(720\) −2.00000 1.00000i −0.0745356 0.0372678i
\(721\) 0 0
\(722\) 30.0000i 1.11648i
\(723\) 0.866025 0.500000i 0.0322078 0.0185952i
\(724\) −1.00000 + 1.73205i −0.0371647 + 0.0643712i
\(725\) 0 0
\(726\) 7.00000 + 12.1244i 0.259794 + 0.449977i
\(727\) 53.0000i 1.96566i 0.184510 + 0.982831i \(0.440930\pi\)
−0.184510 + 0.982831i \(0.559070\pi\)
\(728\) 1.73205 + 2.00000i 0.0641941 + 0.0741249i
\(729\) −1.00000 −0.0370370
\(730\) 0.535898 + 8.92820i 0.0198345 + 0.330448i
\(731\) 10.0000 17.3205i 0.369863 0.640622i
\(732\) 1.73205 + 1.00000i 0.0640184 + 0.0369611i
\(733\) 18.1865 10.5000i 0.671735 0.387826i −0.124999 0.992157i \(-0.539893\pi\)
0.796734 + 0.604331i \(0.206559\pi\)
\(734\) −37.0000 −1.36569
\(735\) 12.8564 + 8.92820i 0.474216 + 0.329322i
\(736\) −3.00000 −0.110581
\(737\) −25.9808 + 15.0000i −0.957014 + 0.552532i
\(738\) 7.79423 + 4.50000i 0.286910 + 0.165647i
\(739\) 23.5000 40.7032i 0.864461 1.49729i −0.00311943 0.999995i \(-0.500993\pi\)
0.867581 0.497296i \(-0.165674\pi\)
\(740\) 11.1603 0.669873i 0.410259 0.0246250i
\(741\) 7.00000 0.257151
\(742\) 1.73205 + 2.00000i 0.0635856 + 0.0734223i
\(743\) 31.0000i 1.13728i 0.822587 + 0.568640i \(0.192530\pi\)
−0.822587 + 0.568640i \(0.807470\pi\)
\(744\) 3.00000 + 5.19615i 0.109985 + 0.190500i
\(745\) −11.1962 + 7.39230i −0.410195 + 0.270833i
\(746\) 3.00000 5.19615i 0.109838 0.190245i
\(747\) −8.66025 + 5.00000i −0.316862 + 0.182940i
\(748\) 10.0000i 0.365636i
\(749\) 30.0000 + 10.3923i 1.09618 + 0.379727i
\(750\) −2.00000 11.0000i −0.0730297 0.401663i
\(751\) −2.00000 3.46410i −0.0729810 0.126407i 0.827225 0.561870i \(-0.189918\pi\)
−0.900207 + 0.435463i \(0.856585\pi\)
\(752\) 11.2583 + 6.50000i 0.410549 + 0.237031i
\(753\) −2.59808 1.50000i −0.0946792 0.0546630i
\(754\) 0 0
\(755\) −44.0000 22.0000i −1.60132 0.800662i
\(756\) 0.500000 + 2.59808i 0.0181848 + 0.0944911i
\(757\) 26.0000i 0.944986i −0.881334 0.472493i \(-0.843354\pi\)
0.881334 0.472493i \(-0.156646\pi\)
\(758\) −0.866025 + 0.500000i −0.0314555 + 0.0181608i
\(759\) −7.50000 + 12.9904i −0.272233 + 0.471521i
\(760\) 8.62436 + 13.0622i 0.312838 + 0.473815i
\(761\) 1.50000 + 2.59808i 0.0543750 + 0.0941802i 0.891932 0.452170i \(-0.149350\pi\)
−0.837557 + 0.546350i \(0.816017\pi\)
\(762\) 9.00000i 0.326036i
\(763\) −46.7654 + 9.00000i −1.69302 + 0.325822i
\(764\) 16.0000 0.578860
\(765\) 4.46410 0.267949i 0.161400 0.00968772i
\(766\) −4.50000 + 7.79423i −0.162592 + 0.281617i
\(767\) −3.46410 2.00000i −0.125081 0.0722158i
\(768\) −0.866025 + 0.500000i −0.0312500 + 0.0180422i
\(769\) −51.0000 −1.83911 −0.919554 0.392965i \(-0.871449\pi\)
−0.919554 + 0.392965i \(0.871449\pi\)
\(770\) 20.6699 + 21.1603i 0.744891 + 0.762563i
\(771\) −10.0000 −0.360141
\(772\) −15.5885 + 9.00000i −0.561041 + 0.323917i
\(773\) −32.0429 18.5000i −1.15250 0.665399i −0.203008 0.979177i \(-0.565072\pi\)
−0.949496 + 0.313778i \(0.898405\pi\)
\(774\) −5.00000 + 8.66025i −0.179721 + 0.311286i
\(775\) −11.7846 + 27.5885i −0.423316 + 0.991007i
\(776\) −8.00000 −0.287183
\(777\) −8.66025 10.0000i −0.310685 0.358748i
\(778\) 6.00000i 0.215110i
\(779\) −31.5000 54.5596i −1.12860 1.95480i
\(780\) −1.86603 + 1.23205i −0.0668144 + 0.0441145i
\(781\) −5.00000 + 8.66025i −0.178914 + 0.309888i
\(782\) 5.19615 3.00000i 0.185814 0.107280i
\(783\) 0 0
\(784\) 6.50000 2.59808i 0.232143