Properties

Label 91.2.k.a.23.1
Level $91$
Weight $2$
Character 91.23
Analytic conductor $0.727$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.k (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 23.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 91.23
Dual form 91.2.k.a.4.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.73205i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(1.50000 + 0.866025i) q^{5} +(1.50000 + 0.866025i) q^{6} +(-2.00000 - 1.73205i) q^{7} +1.73205i q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+1.73205i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(1.50000 + 0.866025i) q^{5} +(1.50000 + 0.866025i) q^{6} +(-2.00000 - 1.73205i) q^{7} +1.73205i q^{8} +(1.00000 + 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(-4.50000 - 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-1.00000 - 3.46410i) q^{13} +(3.00000 - 3.46410i) q^{14} +(1.50000 - 0.866025i) q^{15} -5.00000 q^{16} +6.00000 q^{17} +(-3.00000 + 1.73205i) q^{18} +(-1.50000 + 0.866025i) q^{19} +(-1.50000 - 0.866025i) q^{20} +(-2.50000 + 0.866025i) q^{21} +(4.50000 - 7.79423i) q^{22} +(1.50000 + 0.866025i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(6.00000 - 1.73205i) q^{26} +5.00000 q^{27} +(2.00000 + 1.73205i) q^{28} +(-1.50000 - 2.59808i) q^{29} +(1.50000 + 2.59808i) q^{30} +(-1.50000 + 0.866025i) q^{31} -5.19615i q^{32} +(-4.50000 + 2.59808i) q^{33} +10.3923i q^{34} +(-1.50000 - 4.33013i) q^{35} +(-1.00000 - 1.73205i) q^{36} +(-1.50000 - 2.59808i) q^{38} +(-3.50000 - 0.866025i) q^{39} +(-1.50000 + 2.59808i) q^{40} +(-4.50000 + 2.59808i) q^{41} +(-1.50000 - 4.33013i) q^{42} +(-5.50000 + 9.52628i) q^{43} +(4.50000 + 2.59808i) q^{44} +3.46410i q^{45} +(7.50000 + 4.33013i) q^{47} +(-2.50000 + 4.33013i) q^{48} +(1.00000 + 6.92820i) q^{49} +(3.00000 - 1.73205i) q^{50} +(3.00000 - 5.19615i) q^{51} +(1.00000 + 3.46410i) q^{52} +(4.50000 + 7.79423i) q^{53} +8.66025i q^{54} +(-4.50000 - 7.79423i) q^{55} +(3.00000 - 3.46410i) q^{56} +1.73205i q^{57} +(4.50000 - 2.59808i) q^{58} -3.46410i q^{59} +(-1.50000 + 0.866025i) q^{60} +(-3.50000 - 6.06218i) q^{61} +(-1.50000 - 2.59808i) q^{62} +(1.00000 - 5.19615i) q^{63} -1.00000 q^{64} +(1.50000 - 6.06218i) q^{65} +(-4.50000 - 7.79423i) q^{66} +(7.50000 + 4.33013i) q^{67} -6.00000 q^{68} +(7.50000 - 2.59808i) q^{70} +(1.50000 + 0.866025i) q^{71} +(-3.00000 + 1.73205i) q^{72} +(7.50000 - 4.33013i) q^{73} -2.00000 q^{75} +(1.50000 - 0.866025i) q^{76} +(4.50000 + 12.9904i) q^{77} +(1.50000 - 6.06218i) q^{78} +(2.50000 - 4.33013i) q^{79} +(-7.50000 - 4.33013i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.50000 - 7.79423i) q^{82} +3.46410i q^{83} +(2.50000 - 0.866025i) q^{84} +(9.00000 + 5.19615i) q^{85} +(-16.5000 - 9.52628i) q^{86} -3.00000 q^{87} +(4.50000 - 7.79423i) q^{88} +6.92820i q^{89} -6.00000 q^{90} +(-4.00000 + 8.66025i) q^{91} +1.73205i q^{93} +(-7.50000 + 12.9904i) q^{94} -3.00000 q^{95} +(-4.50000 - 2.59808i) q^{96} +(-4.50000 - 2.59808i) q^{97} +(-12.0000 + 1.73205i) q^{98} -10.3923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{3} - 2q^{4} + 3q^{5} + 3q^{6} - 4q^{7} + 2q^{9} + O(q^{10}) \) \( 2q + q^{3} - 2q^{4} + 3q^{5} + 3q^{6} - 4q^{7} + 2q^{9} - 3q^{10} - 9q^{11} - q^{12} - 2q^{13} + 6q^{14} + 3q^{15} - 10q^{16} + 12q^{17} - 6q^{18} - 3q^{19} - 3q^{20} - 5q^{21} + 9q^{22} + 3q^{24} - 2q^{25} + 12q^{26} + 10q^{27} + 4q^{28} - 3q^{29} + 3q^{30} - 3q^{31} - 9q^{33} - 3q^{35} - 2q^{36} - 3q^{38} - 7q^{39} - 3q^{40} - 9q^{41} - 3q^{42} - 11q^{43} + 9q^{44} + 15q^{47} - 5q^{48} + 2q^{49} + 6q^{50} + 6q^{51} + 2q^{52} + 9q^{53} - 9q^{55} + 6q^{56} + 9q^{58} - 3q^{60} - 7q^{61} - 3q^{62} + 2q^{63} - 2q^{64} + 3q^{65} - 9q^{66} + 15q^{67} - 12q^{68} + 15q^{70} + 3q^{71} - 6q^{72} + 15q^{73} - 4q^{75} + 3q^{76} + 9q^{77} + 3q^{78} + 5q^{79} - 15q^{80} - q^{81} - 9q^{82} + 5q^{84} + 18q^{85} - 33q^{86} - 6q^{87} + 9q^{88} - 12q^{90} - 8q^{91} - 15q^{94} - 6q^{95} - 9q^{96} - 9q^{97} - 24q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.73205i 1.22474i 0.790569 + 0.612372i \(0.209785\pi\)
−0.790569 + 0.612372i \(0.790215\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i −0.684819 0.728714i \(-0.740119\pi\)
0.973494 + 0.228714i \(0.0734519\pi\)
\(4\) −1.00000 −0.500000
\(5\) 1.50000 + 0.866025i 0.670820 + 0.387298i 0.796387 0.604787i \(-0.206742\pi\)
−0.125567 + 0.992085i \(0.540075\pi\)
\(6\) 1.50000 + 0.866025i 0.612372 + 0.353553i
\(7\) −2.00000 1.73205i −0.755929 0.654654i
\(8\) 1.73205i 0.612372i
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) −1.50000 + 2.59808i −0.474342 + 0.821584i
\(11\) −4.50000 2.59808i −1.35680 0.783349i −0.367610 0.929980i \(-0.619824\pi\)
−0.989191 + 0.146631i \(0.953157\pi\)
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) −1.00000 3.46410i −0.277350 0.960769i
\(14\) 3.00000 3.46410i 0.801784 0.925820i
\(15\) 1.50000 0.866025i 0.387298 0.223607i
\(16\) −5.00000 −1.25000
\(17\) 6.00000 1.45521 0.727607 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) −3.00000 + 1.73205i −0.707107 + 0.408248i
\(19\) −1.50000 + 0.866025i −0.344124 + 0.198680i −0.662094 0.749421i \(-0.730332\pi\)
0.317970 + 0.948101i \(0.396999\pi\)
\(20\) −1.50000 0.866025i −0.335410 0.193649i
\(21\) −2.50000 + 0.866025i −0.545545 + 0.188982i
\(22\) 4.50000 7.79423i 0.959403 1.66174i
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 1.50000 + 0.866025i 0.306186 + 0.176777i
\(25\) −1.00000 1.73205i −0.200000 0.346410i
\(26\) 6.00000 1.73205i 1.17670 0.339683i
\(27\) 5.00000 0.962250
\(28\) 2.00000 + 1.73205i 0.377964 + 0.327327i
\(29\) −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) 1.50000 + 2.59808i 0.273861 + 0.474342i
\(31\) −1.50000 + 0.866025i −0.269408 + 0.155543i −0.628619 0.777714i \(-0.716379\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 5.19615i 0.918559i
\(33\) −4.50000 + 2.59808i −0.783349 + 0.452267i
\(34\) 10.3923i 1.78227i
\(35\) −1.50000 4.33013i −0.253546 0.731925i
\(36\) −1.00000 1.73205i −0.166667 0.288675i
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) −1.50000 2.59808i −0.243332 0.421464i
\(39\) −3.50000 0.866025i −0.560449 0.138675i
\(40\) −1.50000 + 2.59808i −0.237171 + 0.410792i
\(41\) −4.50000 + 2.59808i −0.702782 + 0.405751i −0.808383 0.588657i \(-0.799657\pi\)
0.105601 + 0.994409i \(0.466323\pi\)
\(42\) −1.50000 4.33013i −0.231455 0.668153i
\(43\) −5.50000 + 9.52628i −0.838742 + 1.45274i 0.0522047 + 0.998636i \(0.483375\pi\)
−0.890947 + 0.454108i \(0.849958\pi\)
\(44\) 4.50000 + 2.59808i 0.678401 + 0.391675i
\(45\) 3.46410i 0.516398i
\(46\) 0 0
\(47\) 7.50000 + 4.33013i 1.09399 + 0.631614i 0.934635 0.355608i \(-0.115726\pi\)
0.159352 + 0.987222i \(0.449059\pi\)
\(48\) −2.50000 + 4.33013i −0.360844 + 0.625000i
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 3.00000 1.73205i 0.424264 0.244949i
\(51\) 3.00000 5.19615i 0.420084 0.727607i
\(52\) 1.00000 + 3.46410i 0.138675 + 0.480384i
\(53\) 4.50000 + 7.79423i 0.618123 + 1.07062i 0.989828 + 0.142269i \(0.0454398\pi\)
−0.371706 + 0.928351i \(0.621227\pi\)
\(54\) 8.66025i 1.17851i
\(55\) −4.50000 7.79423i −0.606780 1.05097i
\(56\) 3.00000 3.46410i 0.400892 0.462910i
\(57\) 1.73205i 0.229416i
\(58\) 4.50000 2.59808i 0.590879 0.341144i
\(59\) 3.46410i 0.450988i −0.974245 0.225494i \(-0.927600\pi\)
0.974245 0.225494i \(-0.0723995\pi\)
\(60\) −1.50000 + 0.866025i −0.193649 + 0.111803i
\(61\) −3.50000 6.06218i −0.448129 0.776182i 0.550135 0.835076i \(-0.314576\pi\)
−0.998264 + 0.0588933i \(0.981243\pi\)
\(62\) −1.50000 2.59808i −0.190500 0.329956i
\(63\) 1.00000 5.19615i 0.125988 0.654654i
\(64\) −1.00000 −0.125000
\(65\) 1.50000 6.06218i 0.186052 0.751921i
\(66\) −4.50000 7.79423i −0.553912 0.959403i
\(67\) 7.50000 + 4.33013i 0.916271 + 0.529009i 0.882443 0.470418i \(-0.155897\pi\)
0.0338274 + 0.999428i \(0.489230\pi\)
\(68\) −6.00000 −0.727607
\(69\) 0 0
\(70\) 7.50000 2.59808i 0.896421 0.310530i
\(71\) 1.50000 + 0.866025i 0.178017 + 0.102778i 0.586361 0.810050i \(-0.300560\pi\)
−0.408344 + 0.912828i \(0.633893\pi\)
\(72\) −3.00000 + 1.73205i −0.353553 + 0.204124i
\(73\) 7.50000 4.33013i 0.877809 0.506803i 0.00787336 0.999969i \(-0.497494\pi\)
0.869935 + 0.493166i \(0.164160\pi\)
\(74\) 0 0
\(75\) −2.00000 −0.230940
\(76\) 1.50000 0.866025i 0.172062 0.0993399i
\(77\) 4.50000 + 12.9904i 0.512823 + 1.48039i
\(78\) 1.50000 6.06218i 0.169842 0.686406i
\(79\) 2.50000 4.33013i 0.281272 0.487177i −0.690426 0.723403i \(-0.742577\pi\)
0.971698 + 0.236225i \(0.0759104\pi\)
\(80\) −7.50000 4.33013i −0.838525 0.484123i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −4.50000 7.79423i −0.496942 0.860729i
\(83\) 3.46410i 0.380235i 0.981761 + 0.190117i \(0.0608868\pi\)
−0.981761 + 0.190117i \(0.939113\pi\)
\(84\) 2.50000 0.866025i 0.272772 0.0944911i
\(85\) 9.00000 + 5.19615i 0.976187 + 0.563602i
\(86\) −16.5000 9.52628i −1.77924 1.02725i
\(87\) −3.00000 −0.321634
\(88\) 4.50000 7.79423i 0.479702 0.830868i
\(89\) 6.92820i 0.734388i 0.930144 + 0.367194i \(0.119682\pi\)
−0.930144 + 0.367194i \(0.880318\pi\)
\(90\) −6.00000 −0.632456
\(91\) −4.00000 + 8.66025i −0.419314 + 0.907841i
\(92\) 0 0
\(93\) 1.73205i 0.179605i
\(94\) −7.50000 + 12.9904i −0.773566 + 1.33986i
\(95\) −3.00000 −0.307794
\(96\) −4.50000 2.59808i −0.459279 0.265165i
\(97\) −4.50000 2.59808i −0.456906 0.263795i 0.253837 0.967247i \(-0.418307\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) −12.0000 + 1.73205i −1.21218 + 0.174964i
\(99\) 10.3923i 1.04447i
\(100\) 1.00000 + 1.73205i 0.100000 + 0.173205i
\(101\) 4.50000 7.79423i 0.447767 0.775555i −0.550474 0.834853i \(-0.685553\pi\)
0.998240 + 0.0592978i \(0.0188862\pi\)
\(102\) 9.00000 + 5.19615i 0.891133 + 0.514496i
\(103\) 6.50000 11.2583i 0.640464 1.10932i −0.344865 0.938652i \(-0.612075\pi\)
0.985329 0.170664i \(-0.0545913\pi\)
\(104\) 6.00000 1.73205i 0.588348 0.169842i
\(105\) −4.50000 0.866025i −0.439155 0.0845154i
\(106\) −13.5000 + 7.79423i −1.31124 + 0.757042i
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) −5.00000 −0.481125
\(109\) −4.50000 + 2.59808i −0.431022 + 0.248851i −0.699782 0.714357i \(-0.746719\pi\)
0.268760 + 0.963207i \(0.413386\pi\)
\(110\) 13.5000 7.79423i 1.28717 0.743151i
\(111\) 0 0
\(112\) 10.0000 + 8.66025i 0.944911 + 0.818317i
\(113\) −7.50000 + 12.9904i −0.705541 + 1.22203i 0.260955 + 0.965351i \(0.415962\pi\)
−0.966496 + 0.256681i \(0.917371\pi\)
\(114\) −3.00000 −0.280976
\(115\) 0 0
\(116\) 1.50000 + 2.59808i 0.139272 + 0.241225i
\(117\) 5.00000 5.19615i 0.462250 0.480384i
\(118\) 6.00000 0.552345
\(119\) −12.0000 10.3923i −1.10004 0.952661i
\(120\) 1.50000 + 2.59808i 0.136931 + 0.237171i
\(121\) 8.00000 + 13.8564i 0.727273 + 1.25967i
\(122\) 10.5000 6.06218i 0.950625 0.548844i
\(123\) 5.19615i 0.468521i
\(124\) 1.50000 0.866025i 0.134704 0.0777714i
\(125\) 12.1244i 1.08444i
\(126\) 9.00000 + 1.73205i 0.801784 + 0.154303i
\(127\) −6.50000 11.2583i −0.576782 0.999015i −0.995846 0.0910585i \(-0.970975\pi\)
0.419064 0.907957i \(-0.362358\pi\)
\(128\) 12.1244i 1.07165i
\(129\) 5.50000 + 9.52628i 0.484248 + 0.838742i
\(130\) 10.5000 + 2.59808i 0.920911 + 0.227866i
\(131\) −7.50000 + 12.9904i −0.655278 + 1.13497i 0.326546 + 0.945181i \(0.394115\pi\)
−0.981824 + 0.189794i \(0.939218\pi\)
\(132\) 4.50000 2.59808i 0.391675 0.226134i
\(133\) 4.50000 + 0.866025i 0.390199 + 0.0750939i
\(134\) −7.50000 + 12.9904i −0.647901 + 1.12220i
\(135\) 7.50000 + 4.33013i 0.645497 + 0.372678i
\(136\) 10.3923i 0.891133i
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 6.50000 11.2583i 0.551323 0.954919i −0.446857 0.894606i \(-0.647457\pi\)
0.998179 0.0603135i \(-0.0192101\pi\)
\(140\) 1.50000 + 4.33013i 0.126773 + 0.365963i
\(141\) 7.50000 4.33013i 0.631614 0.364662i
\(142\) −1.50000 + 2.59808i −0.125877 + 0.218026i
\(143\) −4.50000 + 18.1865i −0.376309 + 1.52083i
\(144\) −5.00000 8.66025i −0.416667 0.721688i
\(145\) 5.19615i 0.431517i
\(146\) 7.50000 + 12.9904i 0.620704 + 1.07509i
\(147\) 6.50000 + 2.59808i 0.536111 + 0.214286i
\(148\) 0 0
\(149\) −16.5000 + 9.52628i −1.35173 + 0.780423i −0.988492 0.151272i \(-0.951663\pi\)
−0.363241 + 0.931695i \(0.618330\pi\)
\(150\) 3.46410i 0.282843i
\(151\) 10.5000 6.06218i 0.854478 0.493333i −0.00768132 0.999970i \(-0.502445\pi\)
0.862159 + 0.506637i \(0.169112\pi\)
\(152\) −1.50000 2.59808i −0.121666 0.210732i
\(153\) 6.00000 + 10.3923i 0.485071 + 0.840168i
\(154\) −22.5000 + 7.79423i −1.81310 + 0.628077i
\(155\) −3.00000 −0.240966
\(156\) 3.50000 + 0.866025i 0.280224 + 0.0693375i
\(157\) −11.5000 19.9186i −0.917800 1.58968i −0.802749 0.596316i \(-0.796630\pi\)
−0.115050 0.993360i \(-0.536703\pi\)
\(158\) 7.50000 + 4.33013i 0.596668 + 0.344486i
\(159\) 9.00000 0.713746
\(160\) 4.50000 7.79423i 0.355756 0.616188i
\(161\) 0 0
\(162\) −1.50000 0.866025i −0.117851 0.0680414i
\(163\) 10.5000 6.06218i 0.822423 0.474826i −0.0288280 0.999584i \(-0.509178\pi\)
0.851251 + 0.524758i \(0.175844\pi\)
\(164\) 4.50000 2.59808i 0.351391 0.202876i
\(165\) −9.00000 −0.700649
\(166\) −6.00000 −0.465690
\(167\) −1.50000 + 0.866025i −0.116073 + 0.0670151i −0.556913 0.830571i \(-0.688014\pi\)
0.440839 + 0.897586i \(0.354681\pi\)
\(168\) −1.50000 4.33013i −0.115728 0.334077i
\(169\) −11.0000 + 6.92820i −0.846154 + 0.532939i
\(170\) −9.00000 + 15.5885i −0.690268 + 1.19558i
\(171\) −3.00000 1.73205i −0.229416 0.132453i
\(172\) 5.50000 9.52628i 0.419371 0.726372i
\(173\) −7.50000 12.9904i −0.570214 0.987640i −0.996544 0.0830722i \(-0.973527\pi\)
0.426329 0.904568i \(-0.359807\pi\)
\(174\) 5.19615i 0.393919i
\(175\) −1.00000 + 5.19615i −0.0755929 + 0.392792i
\(176\) 22.5000 + 12.9904i 1.69600 + 0.979187i
\(177\) −3.00000 1.73205i −0.225494 0.130189i
\(178\) −12.0000 −0.899438
\(179\) −1.50000 + 2.59808i −0.112115 + 0.194189i −0.916623 0.399753i \(-0.869096\pi\)
0.804508 + 0.593942i \(0.202429\pi\)
\(180\) 3.46410i 0.258199i
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) −15.0000 6.92820i −1.11187 0.513553i
\(183\) −7.00000 −0.517455
\(184\) 0 0
\(185\) 0 0
\(186\) −3.00000 −0.219971
\(187\) −27.0000 15.5885i −1.97444 1.13994i
\(188\) −7.50000 4.33013i −0.546994 0.315807i
\(189\) −10.0000 8.66025i −0.727393 0.629941i
\(190\) 5.19615i 0.376969i
\(191\) 7.50000 + 12.9904i 0.542681 + 0.939951i 0.998749 + 0.0500060i \(0.0159241\pi\)
−0.456068 + 0.889945i \(0.650743\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) 1.50000 + 0.866025i 0.107972 + 0.0623379i 0.553014 0.833172i \(-0.313478\pi\)
−0.445041 + 0.895510i \(0.646811\pi\)
\(194\) 4.50000 7.79423i 0.323081 0.559593i
\(195\) −4.50000 4.33013i −0.322252 0.310087i
\(196\) −1.00000 6.92820i −0.0714286 0.494872i
\(197\) 19.5000 11.2583i 1.38932 0.802123i 0.396079 0.918216i \(-0.370371\pi\)
0.993238 + 0.116094i \(0.0370372\pi\)
\(198\) 18.0000 1.27920
\(199\) 4.00000 0.283552 0.141776 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) 3.00000 1.73205i 0.212132 0.122474i
\(201\) 7.50000 4.33013i 0.529009 0.305424i
\(202\) 13.5000 + 7.79423i 0.949857 + 0.548400i
\(203\) −1.50000 + 7.79423i −0.105279 + 0.547048i
\(204\) −3.00000 + 5.19615i −0.210042 + 0.363803i
\(205\) −9.00000 −0.628587
\(206\) 19.5000 + 11.2583i 1.35863 + 0.784405i
\(207\) 0 0
\(208\) 5.00000 + 17.3205i 0.346688 + 1.20096i
\(209\) 9.00000 0.622543
\(210\) 1.50000 7.79423i 0.103510 0.537853i
\(211\) −6.50000 11.2583i −0.447478 0.775055i 0.550743 0.834675i \(-0.314345\pi\)
−0.998221 + 0.0596196i \(0.981011\pi\)
\(212\) −4.50000 7.79423i −0.309061 0.535310i
\(213\) 1.50000 0.866025i 0.102778 0.0593391i
\(214\) 0 0
\(215\) −16.5000 + 9.52628i −1.12529 + 0.649687i
\(216\) 8.66025i 0.589256i
\(217\) 4.50000 + 0.866025i 0.305480 + 0.0587896i
\(218\) −4.50000 7.79423i −0.304778 0.527892i
\(219\) 8.66025i 0.585206i
\(220\) 4.50000 + 7.79423i 0.303390 + 0.525487i
\(221\) −6.00000 20.7846i −0.403604 1.39812i
\(222\) 0 0
\(223\) 4.50000 2.59808i 0.301342 0.173980i −0.341703 0.939808i \(-0.611004\pi\)
0.643046 + 0.765828i \(0.277671\pi\)
\(224\) −9.00000 + 10.3923i −0.601338 + 0.694365i
\(225\) 2.00000 3.46410i 0.133333 0.230940i
\(226\) −22.5000 12.9904i −1.49668 0.864107i
\(227\) 17.3205i 1.14960i −0.818293 0.574801i \(-0.805079\pi\)
0.818293 0.574801i \(-0.194921\pi\)
\(228\) 1.73205i 0.114708i
\(229\) −10.5000 6.06218i −0.693860 0.400600i 0.111197 0.993798i \(-0.464532\pi\)
−0.805056 + 0.593198i \(0.797865\pi\)
\(230\) 0 0
\(231\) 13.5000 + 2.59808i 0.888235 + 0.170941i
\(232\) 4.50000 2.59808i 0.295439 0.170572i
\(233\) −1.50000 + 2.59808i −0.0982683 + 0.170206i −0.910968 0.412477i \(-0.864664\pi\)
0.812700 + 0.582683i \(0.197997\pi\)
\(234\) 9.00000 + 8.66025i 0.588348 + 0.566139i
\(235\) 7.50000 + 12.9904i 0.489246 + 0.847399i
\(236\) 3.46410i 0.225494i
\(237\) −2.50000 4.33013i −0.162392 0.281272i
\(238\) 18.0000 20.7846i 1.16677 1.34727i
\(239\) 10.3923i 0.672222i 0.941822 + 0.336111i \(0.109112\pi\)
−0.941822 + 0.336111i \(0.890888\pi\)
\(240\) −7.50000 + 4.33013i −0.484123 + 0.279508i
\(241\) 6.92820i 0.446285i −0.974786 0.223142i \(-0.928369\pi\)
0.974786 0.223142i \(-0.0716315\pi\)
\(242\) −24.0000 + 13.8564i −1.54278 + 0.890724i
\(243\) 8.00000 + 13.8564i 0.513200 + 0.888889i
\(244\) 3.50000 + 6.06218i 0.224065 + 0.388091i
\(245\) −4.50000 + 11.2583i −0.287494 + 0.719268i
\(246\) −9.00000 −0.573819
\(247\) 4.50000 + 4.33013i 0.286328 + 0.275519i
\(248\) −1.50000 2.59808i −0.0952501 0.164978i
\(249\) 3.00000 + 1.73205i 0.190117 + 0.109764i
\(250\) 21.0000 1.32816
\(251\) −1.50000 + 2.59808i −0.0946792 + 0.163989i −0.909475 0.415759i \(-0.863516\pi\)
0.814795 + 0.579748i \(0.196849\pi\)
\(252\) −1.00000 + 5.19615i −0.0629941 + 0.327327i
\(253\) 0 0
\(254\) 19.5000 11.2583i 1.22354 0.706410i
\(255\) 9.00000 5.19615i 0.563602 0.325396i
\(256\) 19.0000 1.18750
\(257\) 30.0000 1.87135 0.935674 0.352865i \(-0.114792\pi\)
0.935674 + 0.352865i \(0.114792\pi\)
\(258\) −16.5000 + 9.52628i −1.02725 + 0.593080i
\(259\) 0 0
\(260\) −1.50000 + 6.06218i −0.0930261 + 0.375960i
\(261\) 3.00000 5.19615i 0.185695 0.321634i
\(262\) −22.5000 12.9904i −1.39005 0.802548i
\(263\) −1.50000 + 2.59808i −0.0924940 + 0.160204i −0.908560 0.417755i \(-0.862817\pi\)
0.816066 + 0.577959i \(0.196151\pi\)
\(264\) −4.50000 7.79423i −0.276956 0.479702i
\(265\) 15.5885i 0.957591i
\(266\) −1.50000 + 7.79423i −0.0919709 + 0.477895i
\(267\) 6.00000 + 3.46410i 0.367194 + 0.212000i
\(268\) −7.50000 4.33013i −0.458135 0.264505i
\(269\) −6.00000 −0.365826 −0.182913 0.983129i \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(270\) −7.50000 + 12.9904i −0.456435 + 0.790569i
\(271\) 17.3205i 1.05215i 0.850439 + 0.526073i \(0.176336\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) −30.0000 −1.81902
\(273\) 5.50000 + 7.79423i 0.332875 + 0.471728i
\(274\) 0 0
\(275\) 10.3923i 0.626680i
\(276\) 0 0
\(277\) −10.0000 −0.600842 −0.300421 0.953807i \(-0.597127\pi\)
−0.300421 + 0.953807i \(0.597127\pi\)
\(278\) 19.5000 + 11.2583i 1.16953 + 0.675230i
\(279\) −3.00000 1.73205i −0.179605 0.103695i
\(280\) 7.50000 2.59808i 0.448211 0.155265i
\(281\) 6.92820i 0.413302i −0.978415 0.206651i \(-0.933744\pi\)
0.978415 0.206651i \(-0.0662565\pi\)
\(282\) 7.50000 + 12.9904i 0.446619 + 0.773566i
\(283\) −9.50000 + 16.4545i −0.564716 + 0.978117i 0.432360 + 0.901701i \(0.357681\pi\)
−0.997076 + 0.0764162i \(0.975652\pi\)
\(284\) −1.50000 0.866025i −0.0890086 0.0513892i
\(285\) −1.50000 + 2.59808i −0.0888523 + 0.153897i
\(286\) −31.5000 7.79423i −1.86263 0.460882i
\(287\) 13.5000 + 2.59808i 0.796880 + 0.153360i
\(288\) 9.00000 5.19615i 0.530330 0.306186i
\(289\) 19.0000 1.11765
\(290\) 9.00000 0.528498
\(291\) −4.50000 + 2.59808i −0.263795 + 0.152302i
\(292\) −7.50000 + 4.33013i −0.438904 + 0.253402i
\(293\) −22.5000 12.9904i −1.31446 0.758906i −0.331632 0.943409i \(-0.607599\pi\)
−0.982832 + 0.184503i \(0.940933\pi\)
\(294\) −4.50000 + 11.2583i −0.262445 + 0.656599i
\(295\) 3.00000 5.19615i 0.174667 0.302532i
\(296\) 0 0
\(297\) −22.5000 12.9904i −1.30558 0.753778i
\(298\) −16.5000 28.5788i −0.955819 1.65553i
\(299\) 0 0
\(300\) 2.00000 0.115470
\(301\) 27.5000 9.52628i 1.58507 0.549086i
\(302\) 10.5000 + 18.1865i 0.604207 + 1.04652i
\(303\) −4.50000 7.79423i −0.258518 0.447767i
\(304\) 7.50000 4.33013i 0.430155 0.248350i
\(305\) 12.1244i 0.694239i
\(306\) −18.0000 + 10.3923i −1.02899 + 0.594089i
\(307\) 24.2487i 1.38395i 0.721923 + 0.691974i \(0.243259\pi\)
−0.721923 + 0.691974i \(0.756741\pi\)
\(308\) −4.50000 12.9904i −0.256411 0.740196i
\(309\) −6.50000 11.2583i −0.369772 0.640464i
\(310\) 5.19615i 0.295122i
\(311\) 7.50000 + 12.9904i 0.425286 + 0.736617i 0.996447 0.0842210i \(-0.0268402\pi\)
−0.571161 + 0.820838i \(0.693507\pi\)
\(312\) 1.50000 6.06218i 0.0849208 0.343203i
\(313\) −9.50000 + 16.4545i −0.536972 + 0.930062i 0.462093 + 0.886831i \(0.347098\pi\)
−0.999065 + 0.0432311i \(0.986235\pi\)
\(314\) 34.5000 19.9186i 1.94695 1.12407i
\(315\) 6.00000 6.92820i 0.338062 0.390360i
\(316\) −2.50000 + 4.33013i −0.140636 + 0.243589i
\(317\) −4.50000 2.59808i −0.252745 0.145922i 0.368275 0.929717i \(-0.379948\pi\)
−0.621021 + 0.783794i \(0.713282\pi\)
\(318\) 15.5885i 0.874157i
\(319\) 15.5885i 0.872786i
\(320\) −1.50000 0.866025i −0.0838525 0.0484123i
\(321\) 0 0
\(322\) 0 0
\(323\) −9.00000 + 5.19615i −0.500773 + 0.289122i
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) −5.00000 + 5.19615i −0.277350 + 0.288231i
\(326\) 10.5000 + 18.1865i 0.581541 + 1.00726i
\(327\) 5.19615i 0.287348i
\(328\) −4.50000 7.79423i −0.248471 0.430364i
\(329\) −7.50000 21.6506i −0.413488 1.19364i
\(330\) 15.5885i 0.858116i
\(331\) 28.5000 16.4545i 1.56650 0.904420i 0.569929 0.821694i \(-0.306971\pi\)
0.996572 0.0827265i \(-0.0263628\pi\)
\(332\) 3.46410i 0.190117i
\(333\) 0 0
\(334\) −1.50000 2.59808i −0.0820763 0.142160i
\(335\) 7.50000 + 12.9904i 0.409769 + 0.709740i
\(336\) 12.5000 4.33013i 0.681931 0.236228i
\(337\) 22.0000 1.19842 0.599208 0.800593i \(-0.295482\pi\)
0.599208 + 0.800593i \(0.295482\pi\)
\(338\) −12.0000 19.0526i −0.652714 1.03632i
\(339\) 7.50000 + 12.9904i 0.407344 + 0.705541i
\(340\) −9.00000 5.19615i −0.488094 0.281801i
\(341\) 9.00000 0.487377
\(342\) 3.00000 5.19615i 0.162221 0.280976i
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) −16.5000 9.52628i −0.889620 0.513623i
\(345\) 0 0
\(346\) 22.5000 12.9904i 1.20961 0.698367i
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 3.00000 0.160817
\(349\) −4.50000 + 2.59808i −0.240879 + 0.139072i −0.615581 0.788074i \(-0.711079\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) −9.00000 1.73205i −0.481070 0.0925820i
\(351\) −5.00000 17.3205i −0.266880 0.924500i
\(352\) −13.5000 + 23.3827i −0.719552 + 1.24630i
\(353\) 1.50000 + 0.866025i 0.0798369 + 0.0460939i 0.539387 0.842058i \(-0.318656\pi\)
−0.459550 + 0.888152i \(0.651989\pi\)
\(354\) 3.00000 5.19615i 0.159448 0.276172i
\(355\) 1.50000 + 2.59808i 0.0796117 + 0.137892i
\(356\) 6.92820i 0.367194i
\(357\) −15.0000 + 5.19615i −0.793884 + 0.275010i
\(358\) −4.50000 2.59808i −0.237832 0.137313i
\(359\) −16.5000 9.52628i −0.870837 0.502778i −0.00321050 0.999995i \(-0.501022\pi\)
−0.867626 + 0.497217i \(0.834355\pi\)
\(360\) −6.00000 −0.316228
\(361\) −8.00000 + 13.8564i −0.421053 + 0.729285i
\(362\) 3.46410i 0.182069i
\(363\) 16.0000 0.839782
\(364\) 4.00000 8.66025i 0.209657 0.453921i
\(365\) 15.0000 0.785136
\(366\) 12.1244i 0.633750i
\(367\) −11.5000 + 19.9186i −0.600295 + 1.03974i 0.392481 + 0.919760i \(0.371617\pi\)
−0.992776 + 0.119982i \(0.961716\pi\)
\(368\) 0 0
\(369\) −9.00000 5.19615i −0.468521 0.270501i
\(370\) 0 0
\(371\) 4.50000 23.3827i 0.233628 1.21397i
\(372\) 1.73205i 0.0898027i
\(373\) −9.50000 16.4545i −0.491891 0.851981i 0.508065 0.861319i \(-0.330361\pi\)
−0.999956 + 0.00933789i \(0.997028\pi\)
\(374\) 27.0000 46.7654i 1.39614 2.41818i
\(375\) −10.5000 6.06218i −0.542218 0.313050i
\(376\) −7.50000 + 12.9904i −0.386783 + 0.669928i
\(377\) −7.50000 + 7.79423i −0.386270 + 0.401423i
\(378\) 15.0000 17.3205i 0.771517 0.890871i
\(379\) −1.50000 + 0.866025i −0.0770498 + 0.0444847i −0.538030 0.842926i \(-0.680831\pi\)
0.460980 + 0.887410i \(0.347498\pi\)
\(380\) 3.00000 0.153897
\(381\) −13.0000 −0.666010
\(382\) −22.5000 + 12.9904i −1.15120 + 0.664646i
\(383\) −13.5000 + 7.79423i −0.689818 + 0.398266i −0.803544 0.595246i \(-0.797055\pi\)
0.113726 + 0.993512i \(0.463721\pi\)
\(384\) −10.5000 6.06218i −0.535826 0.309359i
\(385\) −4.50000 + 23.3827i −0.229341 + 1.19169i
\(386\) −1.50000 + 2.59808i −0.0763480 + 0.132239i
\(387\) −22.0000 −1.11832
\(388\) 4.50000 + 2.59808i 0.228453 + 0.131897i
\(389\) −1.50000 2.59808i −0.0760530 0.131728i 0.825491 0.564416i \(-0.190898\pi\)
−0.901544 + 0.432688i \(0.857565\pi\)
\(390\) 7.50000 7.79423i 0.379777 0.394676i
\(391\) 0 0
\(392\) −12.0000 + 1.73205i −0.606092 + 0.0874818i
\(393\) 7.50000 + 12.9904i 0.378325 + 0.655278i
\(394\) 19.5000 + 33.7750i 0.982396 + 1.70156i
\(395\) 7.50000 4.33013i 0.377366 0.217872i
\(396\) 10.3923i 0.522233i
\(397\) 31.5000 18.1865i 1.58094 0.912756i 0.586217 0.810154i \(-0.300617\pi\)
0.994722 0.102602i \(-0.0327168\pi\)
\(398\) 6.92820i 0.347279i
\(399\) 3.00000 3.46410i 0.150188 0.173422i
\(400\) 5.00000 + 8.66025i 0.250000 + 0.433013i
\(401\) 6.92820i 0.345978i 0.984924 + 0.172989i \(0.0553425\pi\)
−0.984924 + 0.172989i \(0.944657\pi\)
\(402\) 7.50000 + 12.9904i 0.374066 + 0.647901i
\(403\) 4.50000 + 4.33013i 0.224161 + 0.215699i
\(404\) −4.50000 + 7.79423i −0.223883 + 0.387777i
\(405\) −1.50000 + 0.866025i −0.0745356 + 0.0430331i
\(406\) −13.5000 2.59808i −0.669994 0.128940i
\(407\) 0 0
\(408\) 9.00000 + 5.19615i 0.445566 + 0.257248i
\(409\) 6.92820i 0.342578i 0.985221 + 0.171289i \(0.0547931\pi\)
−0.985221 + 0.171289i \(0.945207\pi\)
\(410\) 15.5885i 0.769859i
\(411\) 0 0
\(412\) −6.50000 + 11.2583i −0.320232 + 0.554658i
\(413\) −6.00000 + 6.92820i −0.295241 + 0.340915i
\(414\) 0 0
\(415\) −3.00000 + 5.19615i −0.147264 + 0.255069i
\(416\) −18.0000 + 5.19615i −0.882523 + 0.254762i
\(417\) −6.50000 11.2583i −0.318306 0.551323i
\(418\) 15.5885i 0.762456i
\(419\) −10.5000 18.1865i −0.512959 0.888470i −0.999887 0.0150285i \(-0.995216\pi\)
0.486928 0.873442i \(-0.338117\pi\)
\(420\) 4.50000 + 0.866025i 0.219578 + 0.0422577i
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 19.5000 11.2583i 0.949245 0.548047i
\(423\) 17.3205i 0.842152i
\(424\) −13.5000 + 7.79423i −0.655618 + 0.378521i
\(425\) −6.00000 10.3923i −0.291043 0.504101i
\(426\) 1.50000 + 2.59808i 0.0726752 + 0.125877i
\(427\) −3.50000 + 18.1865i −0.169377 + 0.880108i
\(428\) 0 0
\(429\) 13.5000 + 12.9904i 0.651786 + 0.627182i
\(430\) −16.5000 28.5788i −0.795701 1.37819i
\(431\) −28.5000 16.4545i −1.37280 0.792585i −0.381517 0.924362i \(-0.624598\pi\)
−0.991279 + 0.131777i \(0.957932\pi\)
\(432\) −25.0000 −1.20281
\(433\) −9.50000 + 16.4545i −0.456541 + 0.790752i −0.998775 0.0494752i \(-0.984245\pi\)
0.542234 + 0.840227i \(0.317578\pi\)
\(434\) −1.50000 + 7.79423i −0.0720023 + 0.374135i
\(435\) −4.50000 2.59808i −0.215758 0.124568i
\(436\) 4.50000 2.59808i 0.215511 0.124425i
\(437\) 0 0
\(438\) 15.0000 0.716728
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 13.5000 7.79423i 0.643587 0.371575i
\(441\) −11.0000 + 8.66025i −0.523810 + 0.412393i
\(442\) 36.0000 10.3923i 1.71235 0.494312i
\(443\) −7.50000 + 12.9904i −0.356336 + 0.617192i −0.987346 0.158583i \(-0.949307\pi\)
0.631010 + 0.775775i \(0.282641\pi\)
\(444\) 0 0
\(445\) −6.00000 + 10.3923i −0.284427 + 0.492642i
\(446\) 4.50000 + 7.79423i 0.213081 + 0.369067i
\(447\) 19.0526i 0.901155i
\(448\) 2.00000 + 1.73205i 0.0944911 + 0.0818317i
\(449\) 1.50000 + 0.866025i 0.0707894 + 0.0408703i 0.534977 0.844867i \(-0.320320\pi\)
−0.464188 + 0.885737i \(0.653654\pi\)
\(450\) 6.00000 + 3.46410i 0.282843 + 0.163299i
\(451\) 27.0000 1.27138
\(452\) 7.50000 12.9904i 0.352770 0.611016i
\(453\) 12.1244i 0.569652i
\(454\) 30.0000 1.40797
\(455\) −13.5000 + 9.52628i −0.632890 + 0.446599i
\(456\) −3.00000 −0.140488
\(457\) 34.6410i 1.62044i 0.586127 + 0.810219i \(0.300652\pi\)
−0.586127 + 0.810219i \(0.699348\pi\)
\(458\) 10.5000 18.1865i 0.490633 0.849801i
\(459\) 30.0000 1.40028
\(460\) 0 0
\(461\) 25.5000 + 14.7224i 1.18765 + 0.685692i 0.957773 0.287527i \(-0.0928330\pi\)
0.229881 + 0.973219i \(0.426166\pi\)
\(462\) −4.50000 + 23.3827i −0.209359 + 1.08786i
\(463\) 24.2487i 1.12693i −0.826139 0.563467i \(-0.809467\pi\)
0.826139 0.563467i \(-0.190533\pi\)
\(464\) 7.50000 + 12.9904i 0.348179 + 0.603063i
\(465\) −1.50000 + 2.59808i −0.0695608 + 0.120483i
\(466\) −4.50000 2.59808i −0.208458 0.120354i
\(467\) 10.5000 18.1865i 0.485882 0.841572i −0.513986 0.857798i \(-0.671832\pi\)
0.999868 + 0.0162260i \(0.00516512\pi\)
\(468\) −5.00000 + 5.19615i −0.231125 + 0.240192i
\(469\) −7.50000 21.6506i −0.346318 0.999733i
\(470\) −22.5000 + 12.9904i −1.03785 + 0.599202i
\(471\) −23.0000 −1.05978
\(472\) 6.00000 0.276172
\(473\) 49.5000 28.5788i 2.27601 1.31406i
\(474\) 7.50000 4.33013i 0.344486 0.198889i
\(475\) 3.00000 + 1.73205i 0.137649 + 0.0794719i
\(476\) 12.0000 + 10.3923i 0.550019 + 0.476331i
\(477\) −9.00000 + 15.5885i −0.412082 + 0.713746i
\(478\) −18.0000 −0.823301
\(479\) 25.5000 + 14.7224i 1.16512 + 0.672685i 0.952527 0.304455i \(-0.0984742\pi\)
0.212598 + 0.977140i \(0.431808\pi\)
\(480\) −4.50000 7.79423i −0.205396 0.355756i
\(481\) 0 0
\(482\) 12.0000 0.546585
\(483\) 0 0
\(484\) −8.00000 13.8564i −0.363636 0.629837i
\(485\) −4.50000 7.79423i −0.204334 0.353918i
\(486\) −24.0000 + 13.8564i −1.08866 + 0.628539i
\(487\) 24.2487i 1.09881i −0.835555 0.549407i \(-0.814854\pi\)
0.835555 0.549407i \(-0.185146\pi\)
\(488\) 10.5000 6.06218i 0.475313 0.274422i
\(489\) 12.1244i 0.548282i
\(490\) −19.5000 7.79423i −0.880920 0.352107i
\(491\) 13.5000 + 23.3827i 0.609246 + 1.05525i 0.991365 + 0.131132i \(0.0418613\pi\)
−0.382118 + 0.924113i \(0.624805\pi\)
\(492\) 5.19615i 0.234261i
\(493\) −9.00000 15.5885i −0.405340 0.702069i
\(494\) −7.50000 + 7.79423i −0.337441 + 0.350679i
\(495\) 9.00000 15.5885i 0.404520 0.700649i
\(496\) 7.50000 4.33013i 0.336760 0.194428i
\(497\) −1.50000 4.33013i −0.0672842 0.194233i
\(498\) −3.00000 + 5.19615i −0.134433 + 0.232845i
\(499\) 1.50000 + 0.866025i 0.0671492 + 0.0387686i 0.533199 0.845990i \(-0.320990\pi\)
−0.466049 + 0.884759i \(0.654323\pi\)
\(500\) 12.1244i 0.542218i
\(501\) 1.73205i 0.0773823i
\(502\) −4.50000 2.59808i −0.200845 0.115958i
\(503\) 4.50000 7.79423i 0.200645 0.347527i −0.748091 0.663596i \(-0.769030\pi\)
0.948736 + 0.316068i \(0.102363\pi\)
\(504\) 9.00000 + 1.73205i 0.400892 + 0.0771517i
\(505\) 13.5000 7.79423i 0.600742 0.346839i
\(506\) 0 0
\(507\) 0.500000 + 12.9904i 0.0222058 + 0.576923i
\(508\) 6.50000 + 11.2583i 0.288391 + 0.499508i
\(509\) 6.92820i 0.307087i 0.988142 + 0.153544i \(0.0490686\pi\)
−0.988142 + 0.153544i \(0.950931\pi\)
\(510\) 9.00000 + 15.5885i 0.398527 + 0.690268i
\(511\) −22.5000 4.33013i −0.995341 0.191554i
\(512\) 8.66025i 0.382733i
\(513\) −7.50000 + 4.33013i −0.331133 + 0.191180i
\(514\) 51.9615i 2.29192i
\(515\) 19.5000 11.2583i 0.859273 0.496101i
\(516\) −5.50000 9.52628i −0.242124 0.419371i
\(517\) −22.5000 38.9711i −0.989549 1.71395i
\(518\) 0 0
\(519\) −15.0000 −0.658427
\(520\) 10.5000 + 2.59808i 0.460455 + 0.113933i
\(521\) −19.5000 33.7750i −0.854311 1.47971i −0.877283 0.479973i \(-0.840646\pi\)
0.0229727 0.999736i \(-0.492687\pi\)
\(522\) 9.00000 + 5.19615i 0.393919 + 0.227429i
\(523\) −4.00000 −0.174908 −0.0874539 0.996169i \(-0.527873\pi\)
−0.0874539 + 0.996169i \(0.527873\pi\)
\(524\) 7.50000 12.9904i 0.327639 0.567487i
\(525\) 4.00000 + 3.46410i 0.174574 + 0.151186i
\(526\) −4.50000 2.59808i −0.196209 0.113282i
\(527\) −9.00000 + 5.19615i −0.392046 + 0.226348i
\(528\) 22.5000 12.9904i 0.979187 0.565334i
\(529\) −23.0000 −1.00000
\(530\) −27.0000 −1.17281
\(531\) 6.00000 3.46410i 0.260378 0.150329i
\(532\) −4.50000 0.866025i −0.195100 0.0375470i
\(533\) 13.5000 + 12.9904i 0.584750 + 0.562676i
\(534\) −6.00000 + 10.3923i −0.259645 + 0.449719i
\(535\) 0 0
\(536\) −7.50000 + 12.9904i −0.323951 + 0.561099i
\(537\) 1.50000 + 2.59808i 0.0647298 + 0.112115i
\(538\) 10.3923i 0.448044i
\(539\) 13.5000 33.7750i 0.581486 1.45479i
\(540\) −7.50000 4.33013i −0.322749 0.186339i
\(541\) −10.5000 6.06218i −0.451430 0.260633i 0.257004 0.966410i \(-0.417265\pi\)
−0.708434 + 0.705777i \(0.750598\pi\)
\(542\) −30.0000 −1.28861
\(543\) 1.00000 1.73205i 0.0429141 0.0743294i
\(544\) 31.1769i 1.33670i
\(545\) −9.00000 −0.385518
\(546\) −13.5000 + 9.52628i −0.577747 + 0.407687i
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 0 0
\(549\) 7.00000 12.1244i 0.298753 0.517455i
\(550\) −18.0000 −0.767523
\(551\) 4.50000 + 2.59808i 0.191706 + 0.110682i
\(552\) 0 0
\(553\) −12.5000 + 4.33013i −0.531554 + 0.184136i
\(554\) 17.3205i 0.735878i
\(555\) 0 0
\(556\) −6.50000 + 11.2583i −0.275661 + 0.477460i
\(557\) 13.5000 + 7.79423i 0.572013 + 0.330252i 0.757953 0.652309i \(-0.226200\pi\)
−0.185940 + 0.982561i \(0.559533\pi\)
\(558\) 3.00000 5.19615i 0.127000 0.219971i
\(559\) 38.5000 + 9.52628i 1.62838 + 0.402919i
\(560\) 7.50000 + 21.6506i 0.316933 + 0.914906i
\(561\) −27.0000 + 15.5885i −1.13994 + 0.658145i
\(562\) 12.0000 0.506189
\(563\) −36.0000 −1.51722 −0.758610 0.651546i \(-0.774121\pi\)
−0.758610 + 0.651546i \(0.774121\pi\)
\(564\) −7.50000 + 4.33013i −0.315807 + 0.182331i
\(565\) −22.5000 + 12.9904i −0.946582 + 0.546509i
\(566\) −28.5000 16.4545i −1.19794 0.691633i
\(567\) 2.50000 0.866025i 0.104990 0.0363696i
\(568\) −1.50000 + 2.59808i −0.0629386 + 0.109013i
\(569\) −6.00000 −0.251533 −0.125767 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) −4.50000 2.59808i −0.188484 0.108821i
\(571\) 11.5000 + 19.9186i 0.481260 + 0.833567i 0.999769 0.0215055i \(-0.00684595\pi\)
−0.518509 + 0.855072i \(0.673513\pi\)
\(572\) 4.50000 18.1865i 0.188154 0.760417i
\(573\) 15.0000 0.626634
\(574\) −4.50000 + 23.3827i −0.187826 + 0.975974i
\(575\) 0 0
\(576\) −1.00000 1.73205i −0.0416667 0.0721688i
\(577\) 13.5000 7.79423i 0.562012 0.324478i −0.191940 0.981407i \(-0.561478\pi\)
0.753953 + 0.656929i \(0.228145\pi\)
\(578\) 32.9090i 1.36883i
\(579\) 1.50000 0.866025i 0.0623379 0.0359908i
\(580\) 5.19615i 0.215758i
\(581\) 6.00000 6.92820i 0.248922 0.287430i
\(582\) −4.50000 7.79423i −0.186531 0.323081i
\(583\) 46.7654i 1.93682i
\(584\) 7.50000 + 12.9904i 0.310352 + 0.537546i
\(585\) 12.0000 3.46410i 0.496139 0.143223i
\(586\) 22.5000 38.9711i 0.929466 1.60988i
\(587\) −13.5000 + 7.79423i −0.557205 + 0.321702i −0.752023 0.659137i \(-0.770922\pi\)
0.194818 + 0.980839i \(0.437588\pi\)
\(588\) −6.50000 2.59808i −0.268055 0.107143i
\(589\) 1.50000 2.59808i 0.0618064 0.107052i
\(590\) 9.00000 + 5.19615i 0.370524 + 0.213922i
\(591\) 22.5167i 0.926212i
\(592\) 0 0
\(593\) −4.50000 2.59808i −0.184793 0.106690i 0.404750 0.914428i \(-0.367359\pi\)
−0.589543 + 0.807737i \(0.700692\pi\)
\(594\) 22.5000 38.9711i 0.923186 1.59901i
\(595\) −9.00000 25.9808i −0.368964 1.06511i
\(596\) 16.5000 9.52628i 0.675866 0.390212i
\(597\) 2.00000 3.46410i 0.0818546 0.141776i
\(598\) 0 0
\(599\) −4.50000 7.79423i −0.183865 0.318464i 0.759328 0.650708i \(-0.225528\pi\)
−0.943193 + 0.332244i \(0.892194\pi\)
\(600\) 3.46410i 0.141421i
\(601\) −9.50000 16.4545i −0.387513 0.671192i 0.604601 0.796528i \(-0.293332\pi\)
−0.992114 + 0.125336i \(0.959999\pi\)
\(602\) 16.5000 + 47.6314i 0.672490 + 1.94131i
\(603\) 17.3205i 0.705346i
\(604\) −10.5000 + 6.06218i −0.427239 + 0.246667i
\(605\) 27.7128i 1.12669i
\(606\) 13.5000 7.79423i 0.548400 0.316619i
\(607\) 21.5000 + 37.2391i 0.872658 + 1.51149i 0.859237 + 0.511578i \(0.170939\pi\)
0.0134214 + 0.999910i \(0.495728\pi\)
\(608\) 4.50000 + 7.79423i 0.182499 + 0.316098i
\(609\) 6.00000 + 5.19615i 0.243132 + 0.210559i
\(610\) 21.0000 0.850265
\(611\) 7.50000 30.3109i 0.303418 1.22625i
\(612\) −6.00000 10.3923i −0.242536 0.420084i
\(613\) 31.5000 + 18.1865i 1.27227 + 0.734547i 0.975415 0.220375i \(-0.0707280\pi\)
0.296858 + 0.954922i \(0.404061\pi\)
\(614\) −42.0000 −1.69498
\(615\) −4.50000 + 7.79423i −0.181458 + 0.314294i
\(616\) −22.5000 + 7.79423i −0.906551 + 0.314038i
\(617\) 37.5000 + 21.6506i 1.50969 + 0.871622i 0.999936 + 0.0113033i \(0.00359804\pi\)
0.509757 + 0.860318i \(0.329735\pi\)
\(618\) 19.5000 11.2583i 0.784405 0.452876i
\(619\) 16.5000 9.52628i 0.663191 0.382893i −0.130301 0.991475i \(-0.541594\pi\)
0.793492 + 0.608581i \(0.208261\pi\)
\(620\) 3.00000 0.120483
\(621\) 0 0
\(622\) −22.5000 + 12.9904i −0.902168 + 0.520867i
\(623\) 12.0000 13.8564i 0.480770 0.555145i
\(624\) 17.5000 + 4.33013i 0.700561 + 0.173344i
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) −28.5000 16.4545i −1.13909 0.657653i
\(627\) 4.50000 7.79423i 0.179713 0.311272i
\(628\) 11.5000 + 19.9186i 0.458900 + 0.794838i
\(629\) 0 0
\(630\) 12.0000 + 10.3923i 0.478091 + 0.414039i
\(631\) −40.5000 23.3827i −1.61228 0.930850i −0.988841 0.148978i \(-0.952402\pi\)
−0.623439 0.781872i \(-0.714265\pi\)
\(632\) 7.50000 + 4.33013i 0.298334 + 0.172243i
\(633\) −13.0000 −0.516704
\(634\) 4.50000 7.79423i 0.178718 0.309548i
\(635\) 22.5167i 0.893546i
\(636\) −9.00000 −0.356873
\(637\) 23.0000 10.3923i 0.911293 0.411758i
\(638\) −27.0000 −1.06894
\(639\) 3.46410i 0.137038i
\(640\) 10.5000 18.1865i 0.415049 0.718886i
\(641\) 30.0000 1.18493 0.592464 0.805597i \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) 0 0
\(643\) −4.50000 2.59808i −0.177463 0.102458i 0.408637 0.912697i \(-0.366004\pi\)
−0.586100 + 0.810239i \(0.699337\pi\)
\(644\) 0 0
\(645\) 19.0526i 0.750194i
\(646\) −9.00000 15.5885i −0.354100 0.613320i
\(647\) 4.50000 7.79423i 0.176913 0.306423i −0.763908 0.645325i \(-0.776722\pi\)
0.940822 + 0.338902i \(0.110055\pi\)
\(648\) −1.50000 0.866025i −0.0589256 0.0340207i
\(649\) −9.00000 + 15.5885i −0.353281 + 0.611900i
\(650\) −9.00000 8.66025i −0.353009 0.339683i
\(651\) 3.00000 3.46410i 0.117579 0.135769i
\(652\) −10.5000 + 6.06218i −0.411212 + 0.237413i
\(653\) −30.0000 −1.17399 −0.586995 0.809590i \(-0.699689\pi\)
−0.586995 + 0.809590i \(0.699689\pi\)
\(654\) −9.00000 −0.351928
\(655\) −22.5000 + 12.9904i −0.879148 + 0.507576i
\(656\) 22.5000 12.9904i 0.878477 0.507189i
\(657\) 15.0000 + 8.66025i 0.585206 + 0.337869i
\(658\) 37.5000 12.9904i 1.46190 0.506418i
\(659\) −7.50000 + 12.9904i −0.292159 + 0.506033i −0.974320 0.225168i \(-0.927707\pi\)
0.682161 + 0.731202i \(0.261040\pi\)
\(660\) 9.00000 0.350325
\(661\) 31.5000 + 18.1865i 1.22521 + 0.707374i 0.966024 0.258454i \(-0.0832129\pi\)
0.259184 + 0.965828i \(0.416546\pi\)
\(662\) 28.5000 + 49.3634i 1.10768 + 1.91856i
\(663\) −21.0000 5.19615i −0.815572 0.201802i
\(664\) −6.00000 −0.232845
\(665\) 6.00000 + 5.19615i 0.232670 + 0.201498i
\(666\) 0 0
\(667\) 0 0
\(668\) 1.50000 0.866025i 0.0580367 0.0335075i
\(669\) 5.19615i 0.200895i
\(670\) −22.5000 + 12.9904i −0.869251 + 0.501862i
\(671\) 36.3731i 1.40417i
\(672\) 4.50000 + 12.9904i 0.173591 + 0.501115i
\(673\) 0.500000 + 0.866025i 0.0192736 + 0.0333828i 0.875501 0.483216i \(-0.160531\pi\)
−0.856228 + 0.516599i \(0.827198\pi\)
\(674\) 38.1051i 1.46775i
\(675\) −5.00000 8.66025i −0.192450 0.333333i
\(676\) 11.0000 6.92820i 0.423077 0.266469i
\(677\) −13.5000 + 23.3827i −0.518847 + 0.898670i 0.480913 + 0.876768i \(0.340305\pi\)
−0.999760 + 0.0219013i \(0.993028\pi\)
\(678\) −22.5000 + 12.9904i −0.864107 + 0.498893i
\(679\) 4.50000 + 12.9904i 0.172694 + 0.498525i
\(680\) −9.00000 + 15.5885i −0.345134 + 0.597790i
\(681\) −15.0000 8.66025i −0.574801 0.331862i
\(682\) 15.5885i 0.596913i
\(683\) 24.2487i 0.927851i 0.885874 + 0.463926i \(0.153559\pi\)
−0.885874 + 0.463926i \(0.846441\pi\)
\(684\) 3.00000 + 1.73205i 0.114708 + 0.0662266i
\(685\) 0 0
\(686\) 27.0000 + 17.3205i 1.03086 + 0.661300i
\(687\) −10.5000 + 6.06218i −0.400600 + 0.231287i
\(688\) 27.5000 47.6314i 1.04843 1.81593i
\(689\) 22.5000 23.3827i 0.857182 0.890809i
\(690\) 0 0
\(691\) 31.1769i 1.18603i −0.805193 0.593013i \(-0.797938\pi\)
0.805193 0.593013i \(-0.202062\pi\)
\(692\) 7.50000 + 12.9904i 0.285107 + 0.493820i
\(693\) −18.0000 + 20.7846i −0.683763 + 0.789542i
\(694\) 0 0
\(695\) 19.5000 11.2583i 0.739677 0.427053i
\(696\) 5.19615i 0.196960i
\(697\) −27.0000 + 15.5885i −1.02270 + 0.590455i
\(698\) −4.50000 7.79423i −0.170328 0.295016i
\(699\) 1.50000 + 2.59808i 0.0567352 + 0.0982683i
\(700\) 1.00000 5.19615i 0.0377964 0.196396i
\(701\) −6.00000 −0.226617 −0.113308 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) 30.0000 8.66025i 1.13228 0.326860i
\(703\) 0 0
\(704\) 4.50000 + 2.59808i 0.169600 + 0.0979187i
\(705\) 15.0000 0.564933
\(706\) −1.50000 + 2.59808i −0.0564532 + 0.0977799i
\(707\) −22.5000 + 7.79423i −0.846200 + 0.293132i
\(708\) 3.00000 + 1.73205i 0.112747 + 0.0650945i
\(709\) −10.5000 + 6.06218i −0.394336 + 0.227670i −0.684037 0.729447i \(-0.739777\pi\)
0.289701 + 0.957117i \(0.406444\pi\)
\(710\) −4.50000 + 2.59808i −0.168882 + 0.0975041i
\(711\) 10.0000 0.375029
\(712\) −12.0000 −0.449719
\(713\) 0 0
\(714\) −9.00000 25.9808i −0.336817 0.972306i
\(715\) −22.5000 + 23.3827i −0.841452 + 0.874463i
\(716\) 1.50000 2.59808i 0.0560576 0.0970947i
\(717\) 9.00000 + 5.19615i 0.336111 + 0.194054i
\(718\) 16.5000 28.5788i 0.615775 1.06655i
\(719\) 7.50000 + 12.9904i 0.279703 + 0.484459i 0.971311 0.237814i \(-0.0764307\pi\)
−0.691608 + 0.722273i \(0.743097\pi\)
\(720\) 17.3205i 0.645497i
\(721\) −32.5000 + 11.2583i −1.21036 + 0.419282i
\(722\) −24.0000 13.8564i −0.893188 0.515682i
\(723\) −6.00000 3.46410i −0.223142 0.128831i
\(724\) −2.00000 −0.0743294
\(725\) −3.00000 + 5.19615i −0.111417 + 0.192980i
\(726\) 27.7128i 1.02852i
\(727\) −32.0000 −1.18681 −0.593407 0.804902i \(-0.702218\pi\)
−0.593407 + 0.804902i \(0.702218\pi\)
\(728\) −15.0000 6.92820i −0.555937 0.256776i
\(729\) 13.0000 0.481481
\(730\) 25.9808i 0.961591i
\(731\) −33.0000 + 57.1577i −1.22055 + 2.11405i
\(732\) 7.00000 0.258727
\(733\) 43.5000 + 25.1147i 1.60671 + 0.927634i 0.990100 + 0.140365i \(0.0448275\pi\)
0.616609 + 0.787269i \(0.288506\pi\)
\(734\) −34.5000 19.9186i −1.27342 0.735208i
\(735\) 7.50000 + 9.52628i 0.276642 + 0.351382i
\(736\) 0 0
\(737\) −22.5000 38.9711i −0.828798 1.43552i
\(738\) 9.00000 15.5885i 0.331295 0.573819i
\(739\) −34.5000 19.9186i −1.26910 0.732717i −0.294285 0.955718i \(-0.595081\pi\)
−0.974818 + 0.223001i \(0.928415\pi\)
\(740\) 0 0
\(741\) 6.00000 1.73205i 0.220416 0.0636285i
\(742\) 40.5000 + 7.79423i 1.48680 + 0.286135i
\(743\) −1.50000 + 0.866025i −0.0550297 + 0.0317714i −0.527262 0.849703i \(-0.676782\pi\)
0.472233 + 0.881474i \(0.343448\pi\)
\(744\) −3.00000 −0.109985
\(745\) −33.0000 −1.20903
\(746\) 28.5000 16.4545i 1.04346 0.602441i
\(747\) −6.00000 + 3.46410i −0.219529 + 0.126745i
\(748\) 27.0000 + 15.5885i 0.987218 + 0.569970i
\(749\) 0 0
\(750\) 10.5000 18.1865i 0.383406 0.664078i
\(751\) 20.0000 0.729810 0.364905 0.931045i \(-0.381101\pi\)
0.364905 + 0.931045i \(0.381101\pi\)
\(752\) −37.5000 21.6506i −1.36748 0.789517i
\(753\) 1.50000 + 2.59808i 0.0546630 + 0.0946792i
\(754\) −13.5000 12.9904i −0.491641 0.473082i
\(755\) 21.0000 0.764268
\(756\) 10.0000 + 8.66025i 0.363696 + 0.314970i
\(757\) 8.50000 + 14.7224i 0.308938 + 0.535096i 0.978130 0.207993i \(-0.0666932\pi\)
−0.669193 + 0.743089i \(0.733360\pi\)
\(758\) −1.50000 2.59808i −0.0544825 0.0943664i
\(759\) 0 0
\(760\) 5.19615i 0.188484i
\(761\) 25.5000 14.7224i 0.924374 0.533688i 0.0393463 0.999226i \(-0.487472\pi\)
0.885028 + 0.465538i \(0.154139\pi\)
\(762\) 22.5167i 0.815693i
\(763\) 13.5000 + 2.59808i 0.488733 + 0.0940567i
\(764\) −7.50000 12.9904i −0.271340 0.469975i
\(765\) 20.7846i 0.751469i
\(766\) −13.5000 23.3827i −0.487775 0.844851i
\(767\) −12.0000 + 3.46410i −0.433295 + 0.125081i
\(768\) 9.50000 16.4545i 0.342802 0.593750i
\(769\) −16.5000 + 9.52628i −0.595005 + 0.343526i −0.767074 0.641558i \(-0.778288\pi\)
0.172069 + 0.985085i \(0.444955\pi\)
\(770\) −40.5000 7.79423i −1.45952 0.280885i
\(771\) 15.0000 25.9808i 0.540212 0.935674i
\(772\) −1.50000 0.866025i −0.0539862 0.0311689i
\(773\) 13.8564i 0.498380i −0.968455 0.249190i \(-0.919836\pi\)
0.968455 0.249190i \(-0.0801644\pi\)
\(774\) 38.1051i 1.36966i
\(775\) 3.00000 + 1.73205i 0.107763 + 0.0622171i
\(776\) 4.50000 7.79423i 0.161541 0.279797i
\(777\) 0 0