Properties

Label 930.2.i.h.211.1
Level $930$
Weight $2$
Character 930.211
Analytic conductor $7.426$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 211.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 930.211
Dual form 930.2.i.h.811.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.00000 + 5.19615i) q^{13} +(1.50000 + 2.59808i) q^{14} +1.00000 q^{15} +1.00000 q^{16} +(-4.00000 - 6.92820i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(2.00000 + 3.46410i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.50000 + 2.59808i) q^{21} +(-2.50000 + 4.33013i) q^{22} +8.00000 q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-3.00000 + 5.19615i) q^{26} -1.00000 q^{27} +(1.50000 + 2.59808i) q^{28} -1.00000 q^{29} +1.00000 q^{30} +(3.50000 - 4.33013i) q^{31} +1.00000 q^{32} -5.00000 q^{33} +(-4.00000 - 6.92820i) q^{34} +3.00000 q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.00000 + 1.73205i) q^{37} +(2.00000 + 3.46410i) q^{38} -6.00000 q^{39} +(0.500000 - 0.866025i) q^{40} +(3.00000 - 5.19615i) q^{41} +(-1.50000 + 2.59808i) q^{42} +(-4.00000 - 6.92820i) q^{43} +(-2.50000 + 4.33013i) q^{44} +(0.500000 + 0.866025i) q^{45} +8.00000 q^{46} +12.0000 q^{47} +(0.500000 + 0.866025i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(4.00000 - 6.92820i) q^{51} +(-3.00000 + 5.19615i) q^{52} +(-2.50000 + 4.33013i) q^{53} -1.00000 q^{54} +(2.50000 + 4.33013i) q^{55} +(1.50000 + 2.59808i) q^{56} +(-2.00000 + 3.46410i) q^{57} -1.00000 q^{58} +(-5.50000 - 9.52628i) q^{59} +1.00000 q^{60} +12.0000 q^{61} +(3.50000 - 4.33013i) q^{62} -3.00000 q^{63} +1.00000 q^{64} +(3.00000 + 5.19615i) q^{65} -5.00000 q^{66} +(-5.00000 + 8.66025i) q^{67} +(-4.00000 - 6.92820i) q^{68} +(4.00000 + 6.92820i) q^{69} +3.00000 q^{70} +(-0.500000 + 0.866025i) q^{72} +(-3.00000 + 5.19615i) q^{73} +(1.00000 + 1.73205i) q^{74} +(0.500000 - 0.866025i) q^{75} +(2.00000 + 3.46410i) q^{76} -15.0000 q^{77} -6.00000 q^{78} +(-4.00000 - 6.92820i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} +(-1.50000 + 2.59808i) q^{83} +(-1.50000 + 2.59808i) q^{84} -8.00000 q^{85} +(-4.00000 - 6.92820i) q^{86} +(-0.500000 - 0.866025i) q^{87} +(-2.50000 + 4.33013i) q^{88} +(0.500000 + 0.866025i) q^{90} -18.0000 q^{91} +8.00000 q^{92} +(5.50000 + 0.866025i) q^{93} +12.0000 q^{94} +4.00000 q^{95} +(0.500000 + 0.866025i) q^{96} +13.0000 q^{97} +(-1.00000 + 1.73205i) q^{98} +(-2.50000 - 4.33013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + q^{5} + q^{6} + 3 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + q^{5} + q^{6} + 3 q^{7} + 2 q^{8} - q^{9} + q^{10} - 5 q^{11} + q^{12} - 6 q^{13} + 3 q^{14} + 2 q^{15} + 2 q^{16} - 8 q^{17} - q^{18} + 4 q^{19} + q^{20} - 3 q^{21} - 5 q^{22} + 16 q^{23} + q^{24} - q^{25} - 6 q^{26} - 2 q^{27} + 3 q^{28} - 2 q^{29} + 2 q^{30} + 7 q^{31} + 2 q^{32} - 10 q^{33} - 8 q^{34} + 6 q^{35} - q^{36} + 2 q^{37} + 4 q^{38} - 12 q^{39} + q^{40} + 6 q^{41} - 3 q^{42} - 8 q^{43} - 5 q^{44} + q^{45} + 16 q^{46} + 24 q^{47} + q^{48} - 2 q^{49} - q^{50} + 8 q^{51} - 6 q^{52} - 5 q^{53} - 2 q^{54} + 5 q^{55} + 3 q^{56} - 4 q^{57} - 2 q^{58} - 11 q^{59} + 2 q^{60} + 24 q^{61} + 7 q^{62} - 6 q^{63} + 2 q^{64} + 6 q^{65} - 10 q^{66} - 10 q^{67} - 8 q^{68} + 8 q^{69} + 6 q^{70} - q^{72} - 6 q^{73} + 2 q^{74} + q^{75} + 4 q^{76} - 30 q^{77} - 12 q^{78} - 8 q^{79} + q^{80} - q^{81} + 6 q^{82} - 3 q^{83} - 3 q^{84} - 16 q^{85} - 8 q^{86} - q^{87} - 5 q^{88} + q^{90} - 36 q^{91} + 16 q^{92} + 11 q^{93} + 24 q^{94} + 8 q^{95} + q^{96} + 26 q^{97} - 2 q^{98} - 5 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 1.00000 0.500000
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) 1.50000 + 2.59808i 0.566947 + 0.981981i 0.996866 + 0.0791130i \(0.0252088\pi\)
−0.429919 + 0.902867i \(0.641458\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) −2.50000 + 4.33013i −0.753778 + 1.30558i 0.192201 + 0.981356i \(0.438437\pi\)
−0.945979 + 0.324227i \(0.894896\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) −3.00000 + 5.19615i −0.832050 + 1.44115i 0.0643593 + 0.997927i \(0.479500\pi\)
−0.896410 + 0.443227i \(0.853834\pi\)
\(14\) 1.50000 + 2.59808i 0.400892 + 0.694365i
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) −4.00000 6.92820i −0.970143 1.68034i −0.695113 0.718900i \(-0.744646\pi\)
−0.275029 0.961436i \(-0.588688\pi\)
\(18\) −0.500000 + 0.866025i −0.117851 + 0.204124i
\(19\) 2.00000 + 3.46410i 0.458831 + 0.794719i 0.998899 0.0469020i \(-0.0149348\pi\)
−0.540068 + 0.841621i \(0.681602\pi\)
\(20\) 0.500000 0.866025i 0.111803 0.193649i
\(21\) −1.50000 + 2.59808i −0.327327 + 0.566947i
\(22\) −2.50000 + 4.33013i −0.533002 + 0.923186i
\(23\) 8.00000 1.66812 0.834058 0.551677i \(-0.186012\pi\)
0.834058 + 0.551677i \(0.186012\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −3.00000 + 5.19615i −0.588348 + 1.01905i
\(27\) −1.00000 −0.192450
\(28\) 1.50000 + 2.59808i 0.283473 + 0.490990i
\(29\) −1.00000 −0.185695 −0.0928477 0.995680i \(-0.529597\pi\)
−0.0928477 + 0.995680i \(0.529597\pi\)
\(30\) 1.00000 0.182574
\(31\) 3.50000 4.33013i 0.628619 0.777714i
\(32\) 1.00000 0.176777
\(33\) −5.00000 −0.870388
\(34\) −4.00000 6.92820i −0.685994 1.18818i
\(35\) 3.00000 0.507093
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 1.00000 + 1.73205i 0.164399 + 0.284747i 0.936442 0.350823i \(-0.114098\pi\)
−0.772043 + 0.635571i \(0.780765\pi\)
\(38\) 2.00000 + 3.46410i 0.324443 + 0.561951i
\(39\) −6.00000 −0.960769
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) 3.00000 5.19615i 0.468521 0.811503i −0.530831 0.847477i \(-0.678120\pi\)
0.999353 + 0.0359748i \(0.0114536\pi\)
\(42\) −1.50000 + 2.59808i −0.231455 + 0.400892i
\(43\) −4.00000 6.92820i −0.609994 1.05654i −0.991241 0.132068i \(-0.957838\pi\)
0.381246 0.924473i \(-0.375495\pi\)
\(44\) −2.50000 + 4.33013i −0.376889 + 0.652791i
\(45\) 0.500000 + 0.866025i 0.0745356 + 0.129099i
\(46\) 8.00000 1.17954
\(47\) 12.0000 1.75038 0.875190 0.483779i \(-0.160736\pi\)
0.875190 + 0.483779i \(0.160736\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) −1.00000 + 1.73205i −0.142857 + 0.247436i
\(50\) −0.500000 0.866025i −0.0707107 0.122474i
\(51\) 4.00000 6.92820i 0.560112 0.970143i
\(52\) −3.00000 + 5.19615i −0.416025 + 0.720577i
\(53\) −2.50000 + 4.33013i −0.343401 + 0.594789i −0.985062 0.172200i \(-0.944912\pi\)
0.641661 + 0.766989i \(0.278246\pi\)
\(54\) −1.00000 −0.136083
\(55\) 2.50000 + 4.33013i 0.337100 + 0.583874i
\(56\) 1.50000 + 2.59808i 0.200446 + 0.347183i
\(57\) −2.00000 + 3.46410i −0.264906 + 0.458831i
\(58\) −1.00000 −0.131306
\(59\) −5.50000 9.52628i −0.716039 1.24022i −0.962557 0.271078i \(-0.912620\pi\)
0.246518 0.969138i \(-0.420713\pi\)
\(60\) 1.00000 0.129099
\(61\) 12.0000 1.53644 0.768221 0.640184i \(-0.221142\pi\)
0.768221 + 0.640184i \(0.221142\pi\)
\(62\) 3.50000 4.33013i 0.444500 0.549927i
\(63\) −3.00000 −0.377964
\(64\) 1.00000 0.125000
\(65\) 3.00000 + 5.19615i 0.372104 + 0.644503i
\(66\) −5.00000 −0.615457
\(67\) −5.00000 + 8.66025i −0.610847 + 1.05802i 0.380251 + 0.924883i \(0.375838\pi\)
−0.991098 + 0.133135i \(0.957496\pi\)
\(68\) −4.00000 6.92820i −0.485071 0.840168i
\(69\) 4.00000 + 6.92820i 0.481543 + 0.834058i
\(70\) 3.00000 0.358569
\(71\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) −3.00000 + 5.19615i −0.351123 + 0.608164i −0.986447 0.164083i \(-0.947534\pi\)
0.635323 + 0.772246i \(0.280867\pi\)
\(74\) 1.00000 + 1.73205i 0.116248 + 0.201347i
\(75\) 0.500000 0.866025i 0.0577350 0.100000i
\(76\) 2.00000 + 3.46410i 0.229416 + 0.397360i
\(77\) −15.0000 −1.70941
\(78\) −6.00000 −0.679366
\(79\) −4.00000 6.92820i −0.450035 0.779484i 0.548352 0.836247i \(-0.315255\pi\)
−0.998388 + 0.0567635i \(0.981922\pi\)
\(80\) 0.500000 0.866025i 0.0559017 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 3.00000 5.19615i 0.331295 0.573819i
\(83\) −1.50000 + 2.59808i −0.164646 + 0.285176i −0.936530 0.350588i \(-0.885982\pi\)
0.771883 + 0.635764i \(0.219315\pi\)
\(84\) −1.50000 + 2.59808i −0.163663 + 0.283473i
\(85\) −8.00000 −0.867722
\(86\) −4.00000 6.92820i −0.431331 0.747087i
\(87\) −0.500000 0.866025i −0.0536056 0.0928477i
\(88\) −2.50000 + 4.33013i −0.266501 + 0.461593i
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0.500000 + 0.866025i 0.0527046 + 0.0912871i
\(91\) −18.0000 −1.88691
\(92\) 8.00000 0.834058
\(93\) 5.50000 + 0.866025i 0.570323 + 0.0898027i
\(94\) 12.0000 1.23771
\(95\) 4.00000 0.410391
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 13.0000 1.31995 0.659975 0.751288i \(-0.270567\pi\)
0.659975 + 0.751288i \(0.270567\pi\)
\(98\) −1.00000 + 1.73205i −0.101015 + 0.174964i
\(99\) −2.50000 4.33013i −0.251259 0.435194i
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) −1.00000 −0.0995037 −0.0497519 0.998762i \(-0.515843\pi\)
−0.0497519 + 0.998762i \(0.515843\pi\)
\(102\) 4.00000 6.92820i 0.396059 0.685994i
\(103\) 3.50000 6.06218i 0.344865 0.597324i −0.640464 0.767988i \(-0.721258\pi\)
0.985329 + 0.170664i \(0.0545913\pi\)
\(104\) −3.00000 + 5.19615i −0.294174 + 0.509525i
\(105\) 1.50000 + 2.59808i 0.146385 + 0.253546i
\(106\) −2.50000 + 4.33013i −0.242821 + 0.420579i
\(107\) 2.50000 + 4.33013i 0.241684 + 0.418609i 0.961194 0.275873i \(-0.0889669\pi\)
−0.719510 + 0.694482i \(0.755634\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −12.0000 −1.14939 −0.574696 0.818367i \(-0.694880\pi\)
−0.574696 + 0.818367i \(0.694880\pi\)
\(110\) 2.50000 + 4.33013i 0.238366 + 0.412861i
\(111\) −1.00000 + 1.73205i −0.0949158 + 0.164399i
\(112\) 1.50000 + 2.59808i 0.141737 + 0.245495i
\(113\) 5.00000 8.66025i 0.470360 0.814688i −0.529065 0.848581i \(-0.677457\pi\)
0.999425 + 0.0338931i \(0.0107906\pi\)
\(114\) −2.00000 + 3.46410i −0.187317 + 0.324443i
\(115\) 4.00000 6.92820i 0.373002 0.646058i
\(116\) −1.00000 −0.0928477
\(117\) −3.00000 5.19615i −0.277350 0.480384i
\(118\) −5.50000 9.52628i −0.506316 0.876965i
\(119\) 12.0000 20.7846i 1.10004 1.90532i
\(120\) 1.00000 0.0912871
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) 12.0000 1.08643
\(123\) 6.00000 0.541002
\(124\) 3.50000 4.33013i 0.314309 0.388857i
\(125\) −1.00000 −0.0894427
\(126\) −3.00000 −0.267261
\(127\) −3.50000 6.06218i −0.310575 0.537931i 0.667912 0.744240i \(-0.267188\pi\)
−0.978487 + 0.206309i \(0.933855\pi\)
\(128\) 1.00000 0.0883883
\(129\) 4.00000 6.92820i 0.352180 0.609994i
\(130\) 3.00000 + 5.19615i 0.263117 + 0.455733i
\(131\) 8.00000 + 13.8564i 0.698963 + 1.21064i 0.968826 + 0.247741i \(0.0796882\pi\)
−0.269863 + 0.962899i \(0.586978\pi\)
\(132\) −5.00000 −0.435194
\(133\) −6.00000 + 10.3923i −0.520266 + 0.901127i
\(134\) −5.00000 + 8.66025i −0.431934 + 0.748132i
\(135\) −0.500000 + 0.866025i −0.0430331 + 0.0745356i
\(136\) −4.00000 6.92820i −0.342997 0.594089i
\(137\) 3.00000 5.19615i 0.256307 0.443937i −0.708942 0.705266i \(-0.750827\pi\)
0.965250 + 0.261329i \(0.0841608\pi\)
\(138\) 4.00000 + 6.92820i 0.340503 + 0.589768i
\(139\) −10.0000 −0.848189 −0.424094 0.905618i \(-0.639408\pi\)
−0.424094 + 0.905618i \(0.639408\pi\)
\(140\) 3.00000 0.253546
\(141\) 6.00000 + 10.3923i 0.505291 + 0.875190i
\(142\) 0 0
\(143\) −15.0000 25.9808i −1.25436 2.17262i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) −0.500000 + 0.866025i −0.0415227 + 0.0719195i
\(146\) −3.00000 + 5.19615i −0.248282 + 0.430037i
\(147\) −2.00000 −0.164957
\(148\) 1.00000 + 1.73205i 0.0821995 + 0.142374i
\(149\) −6.50000 11.2583i −0.532501 0.922318i −0.999280 0.0379444i \(-0.987919\pi\)
0.466779 0.884374i \(-0.345414\pi\)
\(150\) 0.500000 0.866025i 0.0408248 0.0707107i
\(151\) −5.00000 −0.406894 −0.203447 0.979086i \(-0.565214\pi\)
−0.203447 + 0.979086i \(0.565214\pi\)
\(152\) 2.00000 + 3.46410i 0.162221 + 0.280976i
\(153\) 8.00000 0.646762
\(154\) −15.0000 −1.20873
\(155\) −2.00000 5.19615i −0.160644 0.417365i
\(156\) −6.00000 −0.480384
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) −4.00000 6.92820i −0.318223 0.551178i
\(159\) −5.00000 −0.396526
\(160\) 0.500000 0.866025i 0.0395285 0.0684653i
\(161\) 12.0000 + 20.7846i 0.945732 + 1.63806i
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 3.00000 5.19615i 0.234261 0.405751i
\(165\) −2.50000 + 4.33013i −0.194625 + 0.337100i
\(166\) −1.50000 + 2.59808i −0.116423 + 0.201650i
\(167\) 9.00000 + 15.5885i 0.696441 + 1.20627i 0.969693 + 0.244328i \(0.0785675\pi\)
−0.273252 + 0.961943i \(0.588099\pi\)
\(168\) −1.50000 + 2.59808i −0.115728 + 0.200446i
\(169\) −11.5000 19.9186i −0.884615 1.53220i
\(170\) −8.00000 −0.613572
\(171\) −4.00000 −0.305888
\(172\) −4.00000 6.92820i −0.304997 0.528271i
\(173\) 2.50000 4.33013i 0.190071 0.329213i −0.755202 0.655492i \(-0.772461\pi\)
0.945274 + 0.326278i \(0.105795\pi\)
\(174\) −0.500000 0.866025i −0.0379049 0.0656532i
\(175\) 1.50000 2.59808i 0.113389 0.196396i
\(176\) −2.50000 + 4.33013i −0.188445 + 0.326396i
\(177\) 5.50000 9.52628i 0.413405 0.716039i
\(178\) 0 0
\(179\) −5.50000 9.52628i −0.411089 0.712028i 0.583920 0.811811i \(-0.301518\pi\)
−0.995009 + 0.0997838i \(0.968185\pi\)
\(180\) 0.500000 + 0.866025i 0.0372678 + 0.0645497i
\(181\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(182\) −18.0000 −1.33425
\(183\) 6.00000 + 10.3923i 0.443533 + 0.768221i
\(184\) 8.00000 0.589768
\(185\) 2.00000 0.147043
\(186\) 5.50000 + 0.866025i 0.403280 + 0.0635001i
\(187\) 40.0000 2.92509
\(188\) 12.0000 0.875190
\(189\) −1.50000 2.59808i −0.109109 0.188982i
\(190\) 4.00000 0.290191
\(191\) 13.0000 22.5167i 0.940647 1.62925i 0.176406 0.984317i \(-0.443553\pi\)
0.764241 0.644931i \(-0.223114\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 6.50000 + 11.2583i 0.467880 + 0.810392i 0.999326 0.0366998i \(-0.0116845\pi\)
−0.531446 + 0.847092i \(0.678351\pi\)
\(194\) 13.0000 0.933346
\(195\) −3.00000 + 5.19615i −0.214834 + 0.372104i
\(196\) −1.00000 + 1.73205i −0.0714286 + 0.123718i
\(197\) 5.00000 8.66025i 0.356235 0.617018i −0.631093 0.775707i \(-0.717394\pi\)
0.987329 + 0.158689i \(0.0507268\pi\)
\(198\) −2.50000 4.33013i −0.177667 0.307729i
\(199\) −9.50000 + 16.4545i −0.673437 + 1.16643i 0.303486 + 0.952836i \(0.401849\pi\)
−0.976923 + 0.213591i \(0.931484\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) −10.0000 −0.705346
\(202\) −1.00000 −0.0703598
\(203\) −1.50000 2.59808i −0.105279 0.182349i
\(204\) 4.00000 6.92820i 0.280056 0.485071i
\(205\) −3.00000 5.19615i −0.209529 0.362915i
\(206\) 3.50000 6.06218i 0.243857 0.422372i
\(207\) −4.00000 + 6.92820i −0.278019 + 0.481543i
\(208\) −3.00000 + 5.19615i −0.208013 + 0.360288i
\(209\) −20.0000 −1.38343
\(210\) 1.50000 + 2.59808i 0.103510 + 0.179284i
\(211\) 8.00000 + 13.8564i 0.550743 + 0.953914i 0.998221 + 0.0596196i \(0.0189888\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) −2.50000 + 4.33013i −0.171701 + 0.297394i
\(213\) 0 0
\(214\) 2.50000 + 4.33013i 0.170896 + 0.296001i
\(215\) −8.00000 −0.545595
\(216\) −1.00000 −0.0680414
\(217\) 16.5000 + 2.59808i 1.12009 + 0.176369i
\(218\) −12.0000 −0.812743
\(219\) −6.00000 −0.405442
\(220\) 2.50000 + 4.33013i 0.168550 + 0.291937i
\(221\) 48.0000 3.22883
\(222\) −1.00000 + 1.73205i −0.0671156 + 0.116248i
\(223\) −0.500000 0.866025i −0.0334825 0.0579934i 0.848799 0.528716i \(-0.177326\pi\)
−0.882281 + 0.470723i \(0.843993\pi\)
\(224\) 1.50000 + 2.59808i 0.100223 + 0.173591i
\(225\) 1.00000 0.0666667
\(226\) 5.00000 8.66025i 0.332595 0.576072i
\(227\) 12.5000 21.6506i 0.829654 1.43700i −0.0686556 0.997640i \(-0.521871\pi\)
0.898310 0.439363i \(-0.144796\pi\)
\(228\) −2.00000 + 3.46410i −0.132453 + 0.229416i
\(229\) 1.00000 + 1.73205i 0.0660819 + 0.114457i 0.897173 0.441679i \(-0.145617\pi\)
−0.831092 + 0.556136i \(0.812283\pi\)
\(230\) 4.00000 6.92820i 0.263752 0.456832i
\(231\) −7.50000 12.9904i −0.493464 0.854704i
\(232\) −1.00000 −0.0656532
\(233\) −14.0000 −0.917170 −0.458585 0.888650i \(-0.651644\pi\)
−0.458585 + 0.888650i \(0.651644\pi\)
\(234\) −3.00000 5.19615i −0.196116 0.339683i
\(235\) 6.00000 10.3923i 0.391397 0.677919i
\(236\) −5.50000 9.52628i −0.358020 0.620108i
\(237\) 4.00000 6.92820i 0.259828 0.450035i
\(238\) 12.0000 20.7846i 0.777844 1.34727i
\(239\) −3.00000 + 5.19615i −0.194054 + 0.336111i −0.946590 0.322440i \(-0.895497\pi\)
0.752536 + 0.658551i \(0.228830\pi\)
\(240\) 1.00000 0.0645497
\(241\) 2.50000 + 4.33013i 0.161039 + 0.278928i 0.935242 0.354010i \(-0.115182\pi\)
−0.774202 + 0.632938i \(0.781849\pi\)
\(242\) −7.00000 12.1244i −0.449977 0.779383i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 12.0000 0.768221
\(245\) 1.00000 + 1.73205i 0.0638877 + 0.110657i
\(246\) 6.00000 0.382546
\(247\) −24.0000 −1.52708
\(248\) 3.50000 4.33013i 0.222250 0.274963i
\(249\) −3.00000 −0.190117
\(250\) −1.00000 −0.0632456
\(251\) −10.0000 17.3205i −0.631194 1.09326i −0.987308 0.158818i \(-0.949232\pi\)
0.356113 0.934443i \(-0.384102\pi\)
\(252\) −3.00000 −0.188982
\(253\) −20.0000 + 34.6410i −1.25739 + 2.17786i
\(254\) −3.50000 6.06218i −0.219610 0.380375i
\(255\) −4.00000 6.92820i −0.250490 0.433861i
\(256\) 1.00000 0.0625000
\(257\) −8.00000 + 13.8564i −0.499026 + 0.864339i −0.999999 0.00112398i \(-0.999642\pi\)
0.500973 + 0.865463i \(0.332976\pi\)
\(258\) 4.00000 6.92820i 0.249029 0.431331i
\(259\) −3.00000 + 5.19615i −0.186411 + 0.322873i
\(260\) 3.00000 + 5.19615i 0.186052 + 0.322252i
\(261\) 0.500000 0.866025i 0.0309492 0.0536056i
\(262\) 8.00000 + 13.8564i 0.494242 + 0.856052i
\(263\) −6.00000 −0.369976 −0.184988 0.982741i \(-0.559225\pi\)
−0.184988 + 0.982741i \(0.559225\pi\)
\(264\) −5.00000 −0.307729
\(265\) 2.50000 + 4.33013i 0.153574 + 0.265998i
\(266\) −6.00000 + 10.3923i −0.367884 + 0.637193i
\(267\) 0 0
\(268\) −5.00000 + 8.66025i −0.305424 + 0.529009i
\(269\) 9.00000 15.5885i 0.548740 0.950445i −0.449622 0.893219i \(-0.648441\pi\)
0.998361 0.0572259i \(-0.0182255\pi\)
\(270\) −0.500000 + 0.866025i −0.0304290 + 0.0527046i
\(271\) −17.0000 −1.03268 −0.516338 0.856385i \(-0.672705\pi\)
−0.516338 + 0.856385i \(0.672705\pi\)
\(272\) −4.00000 6.92820i −0.242536 0.420084i
\(273\) −9.00000 15.5885i −0.544705 0.943456i
\(274\) 3.00000 5.19615i 0.181237 0.313911i
\(275\) 5.00000 0.301511
\(276\) 4.00000 + 6.92820i 0.240772 + 0.417029i
\(277\) −24.0000 −1.44202 −0.721010 0.692925i \(-0.756322\pi\)
−0.721010 + 0.692925i \(0.756322\pi\)
\(278\) −10.0000 −0.599760
\(279\) 2.00000 + 5.19615i 0.119737 + 0.311086i
\(280\) 3.00000 0.179284
\(281\) −8.00000 −0.477240 −0.238620 0.971113i \(-0.576695\pi\)
−0.238620 + 0.971113i \(0.576695\pi\)
\(282\) 6.00000 + 10.3923i 0.357295 + 0.618853i
\(283\) −6.00000 −0.356663 −0.178331 0.983970i \(-0.557070\pi\)
−0.178331 + 0.983970i \(0.557070\pi\)
\(284\) 0 0
\(285\) 2.00000 + 3.46410i 0.118470 + 0.205196i
\(286\) −15.0000 25.9808i −0.886969 1.53627i
\(287\) 18.0000 1.06251
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) −23.5000 + 40.7032i −1.38235 + 2.39431i
\(290\) −0.500000 + 0.866025i −0.0293610 + 0.0508548i
\(291\) 6.50000 + 11.2583i 0.381037 + 0.659975i
\(292\) −3.00000 + 5.19615i −0.175562 + 0.304082i
\(293\) −4.50000 7.79423i −0.262893 0.455344i 0.704117 0.710084i \(-0.251343\pi\)
−0.967009 + 0.254741i \(0.918010\pi\)
\(294\) −2.00000 −0.116642
\(295\) −11.0000 −0.640445
\(296\) 1.00000 + 1.73205i 0.0581238 + 0.100673i
\(297\) 2.50000 4.33013i 0.145065 0.251259i
\(298\) −6.50000 11.2583i −0.376535 0.652178i
\(299\) −24.0000 + 41.5692i −1.38796 + 2.40401i
\(300\) 0.500000 0.866025i 0.0288675 0.0500000i
\(301\) 12.0000 20.7846i 0.691669 1.19800i
\(302\) −5.00000 −0.287718
\(303\) −0.500000 0.866025i −0.0287242 0.0497519i
\(304\) 2.00000 + 3.46410i 0.114708 + 0.198680i
\(305\) 6.00000 10.3923i 0.343559 0.595062i
\(306\) 8.00000 0.457330
\(307\) −1.00000 1.73205i −0.0570730 0.0988534i 0.836077 0.548612i \(-0.184843\pi\)
−0.893150 + 0.449758i \(0.851510\pi\)
\(308\) −15.0000 −0.854704
\(309\) 7.00000 0.398216
\(310\) −2.00000 5.19615i −0.113592 0.295122i
\(311\) −22.0000 −1.24751 −0.623753 0.781622i \(-0.714393\pi\)
−0.623753 + 0.781622i \(0.714393\pi\)
\(312\) −6.00000 −0.339683
\(313\) 0.500000 + 0.866025i 0.0282617 + 0.0489506i 0.879810 0.475325i \(-0.157669\pi\)
−0.851549 + 0.524276i \(0.824336\pi\)
\(314\) 0 0
\(315\) −1.50000 + 2.59808i −0.0845154 + 0.146385i
\(316\) −4.00000 6.92820i −0.225018 0.389742i
\(317\) 15.5000 + 26.8468i 0.870567 + 1.50787i 0.861411 + 0.507908i \(0.169581\pi\)
0.00915525 + 0.999958i \(0.497086\pi\)
\(318\) −5.00000 −0.280386
\(319\) 2.50000 4.33013i 0.139973 0.242441i
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) −2.50000 + 4.33013i −0.139536 + 0.241684i
\(322\) 12.0000 + 20.7846i 0.668734 + 1.15828i
\(323\) 16.0000 27.7128i 0.890264 1.54198i
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 6.00000 0.332820
\(326\) 0 0
\(327\) −6.00000 10.3923i −0.331801 0.574696i
\(328\) 3.00000 5.19615i 0.165647 0.286910i
\(329\) 18.0000 + 31.1769i 0.992372 + 1.71884i
\(330\) −2.50000 + 4.33013i −0.137620 + 0.238366i
\(331\) 6.00000 10.3923i 0.329790 0.571213i −0.652680 0.757634i \(-0.726355\pi\)
0.982470 + 0.186421i \(0.0596888\pi\)
\(332\) −1.50000 + 2.59808i −0.0823232 + 0.142588i
\(333\) −2.00000 −0.109599
\(334\) 9.00000 + 15.5885i 0.492458 + 0.852962i
\(335\) 5.00000 + 8.66025i 0.273179 + 0.473160i
\(336\) −1.50000 + 2.59808i −0.0818317 + 0.141737i
\(337\) 23.0000 1.25289 0.626445 0.779466i \(-0.284509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(338\) −11.5000 19.9186i −0.625518 1.08343i
\(339\) 10.0000 0.543125
\(340\) −8.00000 −0.433861
\(341\) 10.0000 + 25.9808i 0.541530 + 1.40694i
\(342\) −4.00000 −0.216295
\(343\) 15.0000 0.809924
\(344\) −4.00000 6.92820i −0.215666 0.373544i
\(345\) 8.00000 0.430706
\(346\) 2.50000 4.33013i 0.134401 0.232789i
\(347\) −2.50000 4.33013i −0.134207 0.232453i 0.791087 0.611703i \(-0.209515\pi\)
−0.925294 + 0.379250i \(0.876182\pi\)
\(348\) −0.500000 0.866025i −0.0268028 0.0464238i
\(349\) −20.0000 −1.07058 −0.535288 0.844670i \(-0.679797\pi\)
−0.535288 + 0.844670i \(0.679797\pi\)
\(350\) 1.50000 2.59808i 0.0801784 0.138873i
\(351\) 3.00000 5.19615i 0.160128 0.277350i
\(352\) −2.50000 + 4.33013i −0.133250 + 0.230797i
\(353\) 9.00000 + 15.5885i 0.479022 + 0.829690i 0.999711 0.0240566i \(-0.00765819\pi\)
−0.520689 + 0.853746i \(0.674325\pi\)
\(354\) 5.50000 9.52628i 0.292322 0.506316i
\(355\) 0 0
\(356\) 0 0
\(357\) 24.0000 1.27021
\(358\) −5.50000 9.52628i −0.290684 0.503480i
\(359\) −2.00000 + 3.46410i −0.105556 + 0.182828i −0.913965 0.405793i \(-0.866996\pi\)
0.808409 + 0.588621i \(0.200329\pi\)
\(360\) 0.500000 + 0.866025i 0.0263523 + 0.0456435i
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) 0 0
\(363\) 7.00000 12.1244i 0.367405 0.636364i
\(364\) −18.0000 −0.943456
\(365\) 3.00000 + 5.19615i 0.157027 + 0.271979i
\(366\) 6.00000 + 10.3923i 0.313625 + 0.543214i
\(367\) −2.00000 + 3.46410i −0.104399 + 0.180825i −0.913493 0.406855i \(-0.866625\pi\)
0.809093 + 0.587680i \(0.199959\pi\)
\(368\) 8.00000 0.417029
\(369\) 3.00000 + 5.19615i 0.156174 + 0.270501i
\(370\) 2.00000 0.103975
\(371\) −15.0000 −0.778761
\(372\) 5.50000 + 0.866025i 0.285162 + 0.0449013i
\(373\) 4.00000 0.207112 0.103556 0.994624i \(-0.466978\pi\)
0.103556 + 0.994624i \(0.466978\pi\)
\(374\) 40.0000 2.06835
\(375\) −0.500000 0.866025i −0.0258199 0.0447214i
\(376\) 12.0000 0.618853
\(377\) 3.00000 5.19615i 0.154508 0.267615i
\(378\) −1.50000 2.59808i −0.0771517 0.133631i
\(379\) −14.0000 24.2487i −0.719132 1.24557i −0.961344 0.275349i \(-0.911206\pi\)
0.242213 0.970223i \(-0.422127\pi\)
\(380\) 4.00000 0.205196
\(381\) 3.50000 6.06218i 0.179310 0.310575i
\(382\) 13.0000 22.5167i 0.665138 1.15205i
\(383\) −11.0000 + 19.0526i −0.562074 + 0.973540i 0.435242 + 0.900314i \(0.356663\pi\)
−0.997315 + 0.0732266i \(0.976670\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) −7.50000 + 12.9904i −0.382235 + 0.662051i
\(386\) 6.50000 + 11.2583i 0.330841 + 0.573034i
\(387\) 8.00000 0.406663
\(388\) 13.0000 0.659975
\(389\) −15.0000 25.9808i −0.760530 1.31728i −0.942578 0.333987i \(-0.891606\pi\)
0.182047 0.983290i \(-0.441728\pi\)
\(390\) −3.00000 + 5.19615i −0.151911 + 0.263117i
\(391\) −32.0000 55.4256i −1.61831 2.80299i
\(392\) −1.00000 + 1.73205i −0.0505076 + 0.0874818i
\(393\) −8.00000 + 13.8564i −0.403547 + 0.698963i
\(394\) 5.00000 8.66025i 0.251896 0.436297i
\(395\) −8.00000 −0.402524
\(396\) −2.50000 4.33013i −0.125630 0.217597i
\(397\) 10.0000 + 17.3205i 0.501886 + 0.869291i 0.999998 + 0.00217869i \(0.000693499\pi\)
−0.498112 + 0.867113i \(0.665973\pi\)
\(398\) −9.50000 + 16.4545i −0.476192 + 0.824789i
\(399\) −12.0000 −0.600751
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) 2.00000 0.0998752 0.0499376 0.998752i \(-0.484098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) −10.0000 −0.498755
\(403\) 12.0000 + 31.1769i 0.597763 + 1.55303i
\(404\) −1.00000 −0.0497519
\(405\) −1.00000 −0.0496904
\(406\) −1.50000 2.59808i −0.0744438 0.128940i
\(407\) −10.0000 −0.495682
\(408\) 4.00000 6.92820i 0.198030 0.342997i
\(409\) 4.50000 + 7.79423i 0.222511 + 0.385400i 0.955570 0.294765i \(-0.0952414\pi\)
−0.733059 + 0.680165i \(0.761908\pi\)
\(410\) −3.00000 5.19615i −0.148159 0.256620i
\(411\) 6.00000 0.295958
\(412\) 3.50000 6.06218i 0.172433 0.298662i
\(413\) 16.5000 28.5788i 0.811912 1.40627i
\(414\) −4.00000 + 6.92820i −0.196589 + 0.340503i
\(415\) 1.50000 + 2.59808i 0.0736321 + 0.127535i
\(416\) −3.00000 + 5.19615i −0.147087 + 0.254762i
\(417\) −5.00000 8.66025i −0.244851 0.424094i
\(418\) −20.0000 −0.978232
\(419\) −27.0000 −1.31904 −0.659518 0.751689i \(-0.729240\pi\)
−0.659518 + 0.751689i \(0.729240\pi\)
\(420\) 1.50000 + 2.59808i 0.0731925 + 0.126773i
\(421\) −16.0000 + 27.7128i −0.779792 + 1.35064i 0.152269 + 0.988339i \(0.451342\pi\)
−0.932061 + 0.362301i \(0.881991\pi\)
\(422\) 8.00000 + 13.8564i 0.389434 + 0.674519i
\(423\) −6.00000 + 10.3923i −0.291730 + 0.505291i
\(424\) −2.50000 + 4.33013i −0.121411 + 0.210290i
\(425\) −4.00000 + 6.92820i −0.194029 + 0.336067i
\(426\) 0 0
\(427\) 18.0000 + 31.1769i 0.871081 + 1.50876i
\(428\) 2.50000 + 4.33013i 0.120842 + 0.209305i
\(429\) 15.0000 25.9808i 0.724207 1.25436i
\(430\) −8.00000 −0.385794
\(431\) 15.0000 + 25.9808i 0.722525 + 1.25145i 0.959985 + 0.280052i \(0.0903517\pi\)
−0.237460 + 0.971397i \(0.576315\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 16.5000 + 2.59808i 0.792025 + 0.124712i
\(435\) −1.00000 −0.0479463
\(436\) −12.0000 −0.574696
\(437\) 16.0000 + 27.7128i 0.765384 + 1.32568i
\(438\) −6.00000 −0.286691
\(439\) 2.50000 4.33013i 0.119318 0.206666i −0.800179 0.599761i \(-0.795262\pi\)
0.919498 + 0.393095i \(0.128596\pi\)
\(440\) 2.50000 + 4.33013i 0.119183 + 0.206431i
\(441\) −1.00000 1.73205i −0.0476190 0.0824786i
\(442\) 48.0000 2.28313
\(443\) 8.00000 13.8564i 0.380091 0.658338i −0.610984 0.791643i \(-0.709226\pi\)
0.991075 + 0.133306i \(0.0425592\pi\)
\(444\) −1.00000 + 1.73205i −0.0474579 + 0.0821995i
\(445\) 0 0
\(446\) −0.500000 0.866025i −0.0236757 0.0410075i
\(447\) 6.50000 11.2583i 0.307439 0.532501i
\(448\) 1.50000 + 2.59808i 0.0708683 + 0.122748i
\(449\) −24.0000 −1.13263 −0.566315 0.824189i \(-0.691631\pi\)
−0.566315 + 0.824189i \(0.691631\pi\)
\(450\) 1.00000 0.0471405
\(451\) 15.0000 + 25.9808i 0.706322 + 1.22339i
\(452\) 5.00000 8.66025i 0.235180 0.407344i
\(453\) −2.50000 4.33013i −0.117460 0.203447i
\(454\) 12.5000 21.6506i 0.586654 1.01611i
\(455\) −9.00000 + 15.5885i −0.421927 + 0.730798i
\(456\) −2.00000 + 3.46410i −0.0936586 + 0.162221i
\(457\) −22.0000 −1.02912 −0.514558 0.857455i \(-0.672044\pi\)
−0.514558 + 0.857455i \(0.672044\pi\)
\(458\) 1.00000 + 1.73205i 0.0467269 + 0.0809334i
\(459\) 4.00000 + 6.92820i 0.186704 + 0.323381i
\(460\) 4.00000 6.92820i 0.186501 0.323029i
\(461\) 1.00000 0.0465746 0.0232873 0.999729i \(-0.492587\pi\)
0.0232873 + 0.999729i \(0.492587\pi\)
\(462\) −7.50000 12.9904i −0.348932 0.604367i
\(463\) 27.0000 1.25480 0.627398 0.778699i \(-0.284120\pi\)
0.627398 + 0.778699i \(0.284120\pi\)
\(464\) −1.00000 −0.0464238
\(465\) 3.50000 4.33013i 0.162309 0.200805i
\(466\) −14.0000 −0.648537
\(467\) 23.0000 1.06431 0.532157 0.846646i \(-0.321382\pi\)
0.532157 + 0.846646i \(0.321382\pi\)
\(468\) −3.00000 5.19615i −0.138675 0.240192i
\(469\) −30.0000 −1.38527
\(470\) 6.00000 10.3923i 0.276759 0.479361i
\(471\) 0 0
\(472\) −5.50000 9.52628i −0.253158 0.438483i
\(473\) 40.0000 1.83920
\(474\) 4.00000 6.92820i 0.183726 0.318223i
\(475\) 2.00000 3.46410i 0.0917663 0.158944i
\(476\) 12.0000 20.7846i 0.550019 0.952661i
\(477\) −2.50000 4.33013i −0.114467 0.198263i
\(478\) −3.00000 + 5.19615i −0.137217 + 0.237666i
\(479\) −6.00000 10.3923i −0.274147 0.474837i 0.695773 0.718262i \(-0.255062\pi\)
−0.969920 + 0.243426i \(0.921729\pi\)
\(480\) 1.00000 0.0456435
\(481\) −12.0000 −0.547153
\(482\) 2.50000 + 4.33013i 0.113872 + 0.197232i
\(483\) −12.0000 + 20.7846i −0.546019 + 0.945732i
\(484\) −7.00000 12.1244i −0.318182 0.551107i
\(485\) 6.50000 11.2583i 0.295150 0.511214i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) −8.50000 + 14.7224i −0.385172 + 0.667137i −0.991793 0.127854i \(-0.959191\pi\)
0.606621 + 0.794991i \(0.292524\pi\)
\(488\) 12.0000 0.543214
\(489\) 0 0
\(490\) 1.00000 + 1.73205i 0.0451754 + 0.0782461i
\(491\) 3.50000 6.06218i 0.157953 0.273582i −0.776178 0.630514i \(-0.782844\pi\)
0.934130 + 0.356932i \(0.116177\pi\)
\(492\) 6.00000 0.270501
\(493\) 4.00000 + 6.92820i 0.180151 + 0.312031i
\(494\) −24.0000 −1.07981
\(495\) −5.00000 −0.224733
\(496\) 3.50000 4.33013i 0.157155 0.194428i
\(497\) 0 0
\(498\) −3.00000 −0.134433
\(499\) 19.0000 + 32.9090i 0.850557 + 1.47321i 0.880707 + 0.473662i \(0.157068\pi\)
−0.0301498 + 0.999545i \(0.509598\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −9.00000 + 15.5885i −0.402090 + 0.696441i
\(502\) −10.0000 17.3205i −0.446322 0.773052i
\(503\) −7.00000 12.1244i −0.312115 0.540598i 0.666705 0.745321i \(-0.267704\pi\)
−0.978820 + 0.204723i \(0.934371\pi\)
\(504\) −3.00000 −0.133631
\(505\) −0.500000 + 0.866025i −0.0222497 + 0.0385376i
\(506\) −20.0000 + 34.6410i −0.889108 + 1.53998i
\(507\) 11.5000 19.9186i 0.510733 0.884615i
\(508\) −3.50000 6.06218i −0.155287 0.268966i
\(509\) 10.5000 18.1865i 0.465404 0.806104i −0.533815 0.845601i \(-0.679242\pi\)
0.999220 + 0.0394971i \(0.0125756\pi\)
\(510\) −4.00000 6.92820i −0.177123 0.306786i
\(511\) −18.0000 −0.796273
\(512\) 1.00000 0.0441942
\(513\) −2.00000 3.46410i −0.0883022 0.152944i
\(514\) −8.00000 + 13.8564i −0.352865 + 0.611180i
\(515\) −3.50000 6.06218i −0.154228 0.267131i
\(516\) 4.00000 6.92820i 0.176090 0.304997i
\(517\) −30.0000 + 51.9615i −1.31940 + 2.28527i
\(518\) −3.00000 + 5.19615i −0.131812 + 0.228306i
\(519\) 5.00000 0.219476
\(520\) 3.00000 + 5.19615i 0.131559 + 0.227866i
\(521\) 1.00000 + 1.73205i 0.0438108 + 0.0758825i 0.887099 0.461579i \(-0.152717\pi\)
−0.843288 + 0.537461i \(0.819383\pi\)
\(522\) 0.500000 0.866025i 0.0218844 0.0379049i
\(523\) 20.0000 0.874539 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) 8.00000 + 13.8564i 0.349482 + 0.605320i
\(525\) 3.00000 0.130931
\(526\) −6.00000 −0.261612
\(527\) −44.0000 6.92820i −1.91667 0.301797i
\(528\) −5.00000 −0.217597
\(529\) 41.0000 1.78261
\(530\) 2.50000 + 4.33013i 0.108593 + 0.188089i
\(531\) 11.0000 0.477359
\(532\) −6.00000 + 10.3923i −0.260133 + 0.450564i
\(533\) 18.0000 + 31.1769i 0.779667 + 1.35042i
\(534\) 0 0
\(535\) 5.00000 0.216169
\(536\) −5.00000 + 8.66025i −0.215967 + 0.374066i
\(537\) 5.50000 9.52628i 0.237343 0.411089i
\(538\) 9.00000 15.5885i 0.388018 0.672066i
\(539\) −5.00000 8.66025i −0.215365 0.373024i
\(540\) −0.500000 + 0.866025i −0.0215166 + 0.0372678i
\(541\) −4.00000 6.92820i −0.171973 0.297867i 0.767136 0.641484i \(-0.221681\pi\)
−0.939110 + 0.343617i \(0.888348\pi\)
\(542\) −17.0000 −0.730213
\(543\) 0 0
\(544\) −4.00000 6.92820i −0.171499 0.297044i
\(545\) −6.00000 + 10.3923i −0.257012 + 0.445157i
\(546\) −9.00000 15.5885i −0.385164 0.667124i
\(547\) 16.0000 27.7128i 0.684111 1.18491i −0.289605 0.957146i \(-0.593524\pi\)
0.973715 0.227768i \(-0.0731428\pi\)
\(548\) 3.00000 5.19615i 0.128154 0.221969i
\(549\) −6.00000 + 10.3923i −0.256074 + 0.443533i
\(550\) 5.00000 0.213201
\(551\) −2.00000 3.46410i −0.0852029 0.147576i
\(552\) 4.00000 + 6.92820i 0.170251 + 0.294884i
\(553\) 12.0000 20.7846i 0.510292 0.883852i
\(554\) −24.0000 −1.01966
\(555\) 1.00000 + 1.73205i 0.0424476 + 0.0735215i
\(556\) −10.0000 −0.424094
\(557\) −21.0000 −0.889799 −0.444899 0.895581i \(-0.646761\pi\)
−0.444899 + 0.895581i \(0.646761\pi\)
\(558\) 2.00000 + 5.19615i 0.0846668 + 0.219971i
\(559\) 48.0000 2.03018
\(560\) 3.00000 0.126773
\(561\) 20.0000 + 34.6410i 0.844401 + 1.46254i
\(562\) −8.00000 −0.337460
\(563\) −22.5000 + 38.9711i −0.948262 + 1.64244i −0.199177 + 0.979963i \(0.563827\pi\)
−0.749085 + 0.662474i \(0.769506\pi\)
\(564\) 6.00000 + 10.3923i 0.252646 + 0.437595i
\(565\) −5.00000 8.66025i −0.210352 0.364340i
\(566\) −6.00000 −0.252199
\(567\) 1.50000 2.59808i 0.0629941 0.109109i
\(568\) 0 0
\(569\) −21.0000 + 36.3731i −0.880366 + 1.52484i −0.0294311 + 0.999567i \(0.509370\pi\)
−0.850935 + 0.525271i \(0.823964\pi\)
\(570\) 2.00000 + 3.46410i 0.0837708 + 0.145095i
\(571\) 22.0000 38.1051i 0.920671 1.59465i 0.122292 0.992494i \(-0.460975\pi\)
0.798379 0.602155i \(-0.205691\pi\)
\(572\) −15.0000 25.9808i −0.627182 1.08631i
\(573\) 26.0000 1.08617
\(574\) 18.0000 0.751305
\(575\) −4.00000 6.92820i −0.166812 0.288926i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 15.0000 + 25.9808i 0.624458 + 1.08159i 0.988645 + 0.150268i \(0.0480135\pi\)
−0.364187 + 0.931326i \(0.618653\pi\)
\(578\) −23.5000 + 40.7032i −0.977471 + 1.69303i
\(579\) −6.50000 + 11.2583i −0.270131 + 0.467880i
\(580\) −0.500000 + 0.866025i −0.0207614 + 0.0359597i
\(581\) −9.00000 −0.373383
\(582\) 6.50000 + 11.2583i 0.269434 + 0.466673i
\(583\) −12.5000 21.6506i −0.517697 0.896678i
\(584\) −3.00000 + 5.19615i −0.124141 + 0.215018i
\(585\) −6.00000 −0.248069
\(586\) −4.50000 7.79423i −0.185893 0.321977i
\(587\) 37.0000 1.52715 0.763577 0.645717i \(-0.223441\pi\)
0.763577 + 0.645717i \(0.223441\pi\)
\(588\) −2.00000 −0.0824786
\(589\) 22.0000 + 3.46410i 0.906494 + 0.142736i
\(590\) −11.0000 −0.452863
\(591\) 10.0000 0.411345
\(592\) 1.00000 + 1.73205i 0.0410997 + 0.0711868i
\(593\) −34.0000 −1.39621 −0.698106 0.715994i \(-0.745974\pi\)
−0.698106 + 0.715994i \(0.745974\pi\)
\(594\) 2.50000 4.33013i 0.102576 0.177667i
\(595\) −12.0000 20.7846i −0.491952 0.852086i
\(596\) −6.50000 11.2583i −0.266250 0.461159i
\(597\) −19.0000 −0.777618
\(598\) −24.0000 + 41.5692i −0.981433 + 1.69989i
\(599\) 8.00000 13.8564i 0.326871 0.566157i −0.655018 0.755613i \(-0.727339\pi\)
0.981889 + 0.189456i \(0.0606724\pi\)
\(600\) 0.500000 0.866025i 0.0204124 0.0353553i
\(601\) −11.0000 19.0526i −0.448699 0.777170i 0.549602 0.835426i \(-0.314779\pi\)
−0.998302 + 0.0582563i \(0.981446\pi\)
\(602\) 12.0000 20.7846i 0.489083 0.847117i
\(603\) −5.00000 8.66025i −0.203616 0.352673i
\(604\) −5.00000 −0.203447
\(605\) −14.0000 −0.569181
\(606\) −0.500000 0.866025i −0.0203111 0.0351799i
\(607\) 12.0000 20.7846i 0.487065 0.843621i −0.512824 0.858494i \(-0.671401\pi\)
0.999889 + 0.0148722i \(0.00473415\pi\)
\(608\) 2.00000 + 3.46410i 0.0811107 + 0.140488i
\(609\) 1.50000 2.59808i 0.0607831 0.105279i
\(610\) 6.00000 10.3923i 0.242933 0.420772i
\(611\) −36.0000 + 62.3538i −1.45640 + 2.52257i
\(612\) 8.00000 0.323381
\(613\) −8.00000 13.8564i −0.323117 0.559655i 0.658012 0.753007i \(-0.271397\pi\)
−0.981129 + 0.193352i \(0.938064\pi\)
\(614\) −1.00000 1.73205i −0.0403567 0.0698999i
\(615\) 3.00000 5.19615i 0.120972 0.209529i
\(616\) −15.0000 −0.604367
\(617\) 16.0000 + 27.7128i 0.644136 + 1.11568i 0.984500 + 0.175382i \(0.0561162\pi\)
−0.340365 + 0.940294i \(0.610551\pi\)
\(618\) 7.00000 0.281581
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) −2.00000 5.19615i −0.0803219 0.208683i
\(621\) −8.00000 −0.321029
\(622\) −22.0000 −0.882120
\(623\) 0 0
\(624\) −6.00000 −0.240192
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0.500000 + 0.866025i 0.0199840 + 0.0346133i
\(627\) −10.0000 17.3205i −0.399362 0.691714i
\(628\) 0 0
\(629\) 8.00000 13.8564i 0.318981 0.552491i
\(630\) −1.50000 + 2.59808i −0.0597614 + 0.103510i
\(631\) 18.5000 32.0429i 0.736473 1.27561i −0.217601 0.976038i \(-0.569823\pi\)
0.954074 0.299571i \(-0.0968437\pi\)
\(632\) −4.00000 6.92820i −0.159111 0.275589i
\(633\) −8.00000 + 13.8564i −0.317971 + 0.550743i
\(634\) 15.5000 + 26.8468i 0.615584 + 1.06622i
\(635\) −7.00000 −0.277787
\(636\) −5.00000 −0.198263
\(637\) −6.00000 10.3923i −0.237729 0.411758i
\(638\) 2.50000 4.33013i 0.0989759 0.171431i
\(639\) 0 0
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) 6.00000 10.3923i 0.236986 0.410471i −0.722862 0.690992i \(-0.757174\pi\)
0.959848 + 0.280521i \(0.0905072\pi\)
\(642\) −2.50000 + 4.33013i −0.0986671 + 0.170896i
\(643\) 40.0000 1.57745 0.788723 0.614749i \(-0.210743\pi\)
0.788723 + 0.614749i \(0.210743\pi\)
\(644\) 12.0000 + 20.7846i 0.472866 + 0.819028i
\(645\) −4.00000 6.92820i −0.157500 0.272798i
\(646\) 16.0000 27.7128i 0.629512 1.09035i
\(647\) −12.0000 −0.471769 −0.235884 0.971781i \(-0.575799\pi\)
−0.235884 + 0.971781i \(0.575799\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) 55.0000 2.15894
\(650\) 6.00000 0.235339
\(651\) 6.00000 + 15.5885i 0.235159 + 0.610960i
\(652\) 0 0
\(653\) −9.00000 −0.352197 −0.176099 0.984373i \(-0.556348\pi\)
−0.176099 + 0.984373i \(0.556348\pi\)
\(654\) −6.00000 10.3923i −0.234619 0.406371i
\(655\) 16.0000 0.625172
\(656\) 3.00000 5.19615i 0.117130 0.202876i
\(657\) −3.00000 5.19615i −0.117041 0.202721i
\(658\) 18.0000 + 31.1769i 0.701713 + 1.21540i
\(659\) 15.0000 0.584317 0.292159 0.956370i \(-0.405627\pi\)
0.292159 + 0.956370i \(0.405627\pi\)
\(660\) −2.50000 + 4.33013i −0.0973124 + 0.168550i
\(661\) −4.00000 + 6.92820i −0.155582 + 0.269476i −0.933271 0.359174i \(-0.883059\pi\)
0.777689 + 0.628649i \(0.216392\pi\)
\(662\) 6.00000 10.3923i 0.233197 0.403908i
\(663\) 24.0000 + 41.5692i 0.932083 + 1.61441i
\(664\) −1.50000 + 2.59808i −0.0582113 + 0.100825i
\(665\) 6.00000 + 10.3923i 0.232670 + 0.402996i
\(666\) −2.00000 −0.0774984
\(667\) −8.00000 −0.309761
\(668\) 9.00000 + 15.5885i 0.348220 + 0.603136i
\(669\) 0.500000 0.866025i 0.0193311 0.0334825i
\(670\) 5.00000 + 8.66025i 0.193167 + 0.334575i
\(671\) −30.0000 + 51.9615i −1.15814 + 2.00595i
\(672\) −1.50000 + 2.59808i −0.0578638 + 0.100223i
\(673\) 2.50000 4.33013i 0.0963679 0.166914i −0.813811 0.581130i \(-0.802611\pi\)
0.910179 + 0.414216i \(0.135944\pi\)
\(674\) 23.0000 0.885927
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) −11.5000 19.9186i −0.442308 0.766099i
\(677\) −19.5000 + 33.7750i −0.749446 + 1.29808i 0.198643 + 0.980072i \(0.436347\pi\)
−0.948089 + 0.318006i \(0.896987\pi\)
\(678\) 10.0000 0.384048
\(679\) 19.5000 + 33.7750i 0.748341 + 1.29617i
\(680\) −8.00000 −0.306786
\(681\) 25.0000 0.958002
\(682\) 10.0000 + 25.9808i 0.382920 + 0.994855i
\(683\) 9.00000 0.344375 0.172188 0.985064i \(-0.444916\pi\)
0.172188 + 0.985064i \(0.444916\pi\)
\(684\) −4.00000 −0.152944
\(685\) −3.00000 5.19615i −0.114624 0.198535i
\(686\) 15.0000 0.572703
\(687\) −1.00000 + 1.73205i −0.0381524 + 0.0660819i
\(688\) −4.00000 6.92820i −0.152499 0.264135i
\(689\) −15.0000 25.9808i −0.571454 0.989788i
\(690\) 8.00000 0.304555
\(691\) −5.00000 + 8.66025i −0.190209 + 0.329452i −0.945319 0.326146i \(-0.894250\pi\)
0.755110 + 0.655598i \(0.227583\pi\)
\(692\) 2.50000 4.33013i 0.0950357 0.164607i
\(693\) 7.50000 12.9904i 0.284901 0.493464i
\(694\) −2.50000 4.33013i −0.0948987 0.164369i
\(695\) −5.00000 + 8.66025i −0.189661 + 0.328502i
\(696\) −0.500000 0.866025i −0.0189525 0.0328266i
\(697\) −48.0000 −1.81813
\(698\) −20.0000 −0.757011
\(699\) −7.00000 12.1244i −0.264764 0.458585i
\(700\) 1.50000 2.59808i 0.0566947 0.0981981i
\(701\) −15.5000 26.8468i −0.585427 1.01399i −0.994822 0.101632i \(-0.967594\pi\)
0.409395 0.912357i \(-0.365740\pi\)
\(702\) 3.00000 5.19615i 0.113228 0.196116i
\(703\) −4.00000 + 6.92820i −0.150863 + 0.261302i
\(704\) −2.50000 + 4.33013i −0.0942223 + 0.163198i
\(705\) 12.0000 0.451946
\(706\) 9.00000 + 15.5885i 0.338719 + 0.586679i
\(707\) −1.50000 2.59808i −0.0564133 0.0977107i
\(708\) 5.50000 9.52628i 0.206703 0.358020i
\(709\) −22.0000 −0.826227 −0.413114 0.910679i \(-0.635559\pi\)
−0.413114 + 0.910679i \(0.635559\pi\)
\(710\) 0 0
\(711\) 8.00000 0.300023
\(712\) 0 0
\(713\) 28.0000 34.6410i 1.04861 1.29732i
\(714\) 24.0000 0.898177
\(715\) −30.0000 −1.12194
\(716\) −5.50000 9.52628i −0.205545 0.356014i
\(717\) −6.00000 −0.224074
\(718\) −2.00000 + 3.46410i −0.0746393 + 0.129279i
\(719\) 3.00000 + 5.19615i 0.111881 + 0.193784i 0.916529 0.399969i \(-0.130979\pi\)
−0.804648 + 0.593753i \(0.797646\pi\)
\(720\) 0.500000 + 0.866025i 0.0186339 + 0.0322749i
\(721\) 21.0000 0.782081
\(722\) 1.50000 2.59808i 0.0558242 0.0966904i
\(723\) −2.50000 + 4.33013i −0.0929760 + 0.161039i
\(724\) 0 0
\(725\) 0.500000 + 0.866025i 0.0185695 + 0.0321634i
\(726\) 7.00000 12.1244i 0.259794 0.449977i
\(727\) −9.50000 16.4545i −0.352335 0.610263i 0.634323 0.773068i \(-0.281279\pi\)
−0.986658 + 0.162805i \(0.947946\pi\)
\(728\) −18.0000 −0.667124
\(729\) 1.00000 0.0370370
\(730\) 3.00000 + 5.19615i 0.111035 + 0.192318i
\(731\) −32.0000 + 55.4256i −1.18356 + 2.04999i
\(732\) 6.00000 + 10.3923i 0.221766 + 0.384111i
\(733\) 23.0000 39.8372i 0.849524 1.47142i −0.0321090 0.999484i \(-0.510222\pi\)
0.881633 0.471935i \(-0.156444\pi\)
\(734\) −2.00000 + 3.46410i −0.0738213 + 0.127862i
\(735\) −1.00000 + 1.73205i −0.0368856 + 0.0638877i
\(736\) 8.00000 0.294884
\(737\) −25.0000 43.3013i −0.920887 1.59502i
\(738\) 3.00000 + 5.19615i 0.110432 + 0.191273i
\(739\) 5.00000 8.66025i 0.183928 0.318573i −0.759287 0.650756i \(-0.774452\pi\)
0.943215 + 0.332184i \(0.107785\pi\)
\(740\) 2.00000 0.0735215
\(741\) −12.0000 20.7846i −0.440831 0.763542i
\(742\) −15.0000 −0.550667
\(743\) −24.0000 −0.880475 −0.440237 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) 5.50000 + 0.866025i 0.201640 + 0.0317500i
\(745\) −13.0000 −0.476283
\(746\) 4.00000 0.146450
\(747\) −1.50000 2.59808i −0.0548821 0.0950586i
\(748\) 40.0000 1.46254
\(749\) −7.50000 + 12.9904i −0.274044 + 0.474658i
\(750\) −0.500000 0.866025i −0.0182574 0.0316228i
\(751\) −7.50000 12.9904i −0.273679 0.474026i 0.696122 0.717923i \(-0.254907\pi\)
−0.969801 + 0.243898i \(0.921574\pi\)
\(752\) 12.0000 0.437595
\(753\) 10.0000 17.3205i 0.364420 0.631194i
\(754\) 3.00000 5.19615i 0.109254 0.189233i
\(755\) −2.50000 + 4.33013i −0.0909843 + 0.157589i
\(756\) −1.50000 2.59808i −0.0545545 0.0944911i
\(757\) −18.0000 + 31.1769i −0.654221 + 1.13314i 0.327867 + 0.944724i \(0.393670\pi\)
−0.982088 + 0.188420i \(0.939663\pi\)
\(758\) −14.0000 24.2487i −0.508503 0.880753i
\(759\) −40.0000 −1.45191
\(760\) 4.00000 0.145095
\(761\) 7.00000 + 12.1244i 0.253750 + 0.439508i 0.964555 0.263881i \(-0.0850027\pi\)
−0.710805 + 0.703389i \(0.751669\pi\)
\(762\) 3.50000 6.06218i 0.126792 0.219610i
\(763\) −18.0000 31.1769i −0.651644 1.12868i
\(764\) 13.0000 22.5167i 0.470323 0.814624i
\(765\) 4.00000 6.92820i 0.144620 0.250490i
\(766\) −11.0000 + 19.0526i −0.397446 + 0.688397i
\(767\) 66.0000 2.38312
\(768\) 0.500000 + 0.866025i 0.0180422 + 0.0312500i
\(769\) 11.5000 + 19.9186i 0.414701 + 0.718283i 0.995397 0.0958377i \(-0.0305530\pi\)
−0.580696 + 0.814120i \(0.697220\pi\)
\(770\) −7.50000 + 12.9904i −0.270281 + 0.468141i
\(771\) −16.0000 −0.576226
\(772\) 6.50000 + 11.2583i 0.233940 + 0.405196i
\(773\) 14.0000 0.503545 0.251773 0.967786i \(-0.418987\pi\)
0.251773 + 0.967786i \(0.418987\pi\)
\(774\) 8.00000 0.287554
\(775\) −5.50000 0.866025i −0.197566 0.0311086i
\(776\) 13.0000 0.466673