Properties

Label 56.3.k.a.11.1
Level 56
Weight 3
Character 56.11
Analytic conductor 1.526
Analytic rank 0
Dimension 2
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 56 = 2^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 56.k (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.52588948042\)
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 11.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 56.11
Dual form 56.3.k.a.51.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +4.00000 q^{4} +(-4.50000 + 2.59808i) q^{5} +(1.00000 - 1.73205i) q^{6} +(-1.00000 + 6.92820i) q^{7} -8.00000 q^{8} +(4.00000 + 6.92820i) q^{9} +O(q^{10})\) \(q-2.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +4.00000 q^{4} +(-4.50000 + 2.59808i) q^{5} +(1.00000 - 1.73205i) q^{6} +(-1.00000 + 6.92820i) q^{7} -8.00000 q^{8} +(4.00000 + 6.92820i) q^{9} +(9.00000 - 5.19615i) q^{10} +(-8.50000 + 14.7224i) q^{11} +(-2.00000 + 3.46410i) q^{12} -13.8564i q^{13} +(2.00000 - 13.8564i) q^{14} -5.19615i q^{15} +16.0000 q^{16} +(12.5000 - 21.6506i) q^{17} +(-8.00000 - 13.8564i) q^{18} +(3.50000 + 6.06218i) q^{19} +(-18.0000 + 10.3923i) q^{20} +(-5.50000 - 4.33013i) q^{21} +(17.0000 - 29.4449i) q^{22} +(4.50000 - 2.59808i) q^{23} +(4.00000 - 6.92820i) q^{24} +(1.00000 - 1.73205i) q^{25} +27.7128i q^{26} -17.0000 q^{27} +(-4.00000 + 27.7128i) q^{28} +13.8564i q^{29} +10.3923i q^{30} +(28.5000 + 16.4545i) q^{31} -32.0000 q^{32} +(-8.50000 - 14.7224i) q^{33} +(-25.0000 + 43.3013i) q^{34} +(-13.5000 - 33.7750i) q^{35} +(16.0000 + 27.7128i) q^{36} +(7.50000 - 4.33013i) q^{37} +(-7.00000 - 12.1244i) q^{38} +(12.0000 + 6.92820i) q^{39} +(36.0000 - 20.7846i) q^{40} +26.0000 q^{41} +(11.0000 + 8.66025i) q^{42} +14.0000 q^{43} +(-34.0000 + 58.8897i) q^{44} +(-36.0000 - 20.7846i) q^{45} +(-9.00000 + 5.19615i) q^{46} +(-43.5000 + 25.1147i) q^{47} +(-8.00000 + 13.8564i) q^{48} +(-47.0000 - 13.8564i) q^{49} +(-2.00000 + 3.46410i) q^{50} +(12.5000 + 21.6506i) q^{51} -55.4256i q^{52} +(79.5000 + 45.8993i) q^{53} +34.0000 q^{54} -88.3346i q^{55} +(8.00000 - 55.4256i) q^{56} -7.00000 q^{57} -27.7128i q^{58} +(27.5000 - 47.6314i) q^{59} -20.7846i q^{60} +(19.5000 - 11.2583i) q^{61} +(-57.0000 - 32.9090i) q^{62} +(-52.0000 + 20.7846i) q^{63} +64.0000 q^{64} +(36.0000 + 62.3538i) q^{65} +(17.0000 + 29.4449i) q^{66} +(-8.50000 + 14.7224i) q^{67} +(50.0000 - 86.6025i) q^{68} +5.19615i q^{69} +(27.0000 + 67.5500i) q^{70} +(-32.0000 - 55.4256i) q^{72} +(-59.5000 + 103.057i) q^{73} +(-15.0000 + 8.66025i) q^{74} +(1.00000 + 1.73205i) q^{75} +(14.0000 + 24.2487i) q^{76} +(-93.5000 - 73.6122i) q^{77} +(-24.0000 - 13.8564i) q^{78} +(64.5000 - 37.2391i) q^{79} +(-72.0000 + 41.5692i) q^{80} +(-27.5000 + 47.6314i) q^{81} -52.0000 q^{82} +110.000 q^{83} +(-22.0000 - 17.3205i) q^{84} +129.904i q^{85} -28.0000 q^{86} +(-12.0000 - 6.92820i) q^{87} +(68.0000 - 117.779i) q^{88} +(-35.5000 - 61.4878i) q^{89} +(72.0000 + 41.5692i) q^{90} +(96.0000 + 13.8564i) q^{91} +(18.0000 - 10.3923i) q^{92} +(-28.5000 + 16.4545i) q^{93} +(87.0000 - 50.2295i) q^{94} +(-31.5000 - 18.1865i) q^{95} +(16.0000 - 27.7128i) q^{96} -22.0000 q^{97} +(94.0000 + 27.7128i) q^{98} -136.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 4q^{2} - q^{3} + 8q^{4} - 9q^{5} + 2q^{6} - 2q^{7} - 16q^{8} + 8q^{9} + O(q^{10}) \) \( 2q - 4q^{2} - q^{3} + 8q^{4} - 9q^{5} + 2q^{6} - 2q^{7} - 16q^{8} + 8q^{9} + 18q^{10} - 17q^{11} - 4q^{12} + 4q^{14} + 32q^{16} + 25q^{17} - 16q^{18} + 7q^{19} - 36q^{20} - 11q^{21} + 34q^{22} + 9q^{23} + 8q^{24} + 2q^{25} - 34q^{27} - 8q^{28} + 57q^{31} - 64q^{32} - 17q^{33} - 50q^{34} - 27q^{35} + 32q^{36} + 15q^{37} - 14q^{38} + 24q^{39} + 72q^{40} + 52q^{41} + 22q^{42} + 28q^{43} - 68q^{44} - 72q^{45} - 18q^{46} - 87q^{47} - 16q^{48} - 94q^{49} - 4q^{50} + 25q^{51} + 159q^{53} + 68q^{54} + 16q^{56} - 14q^{57} + 55q^{59} + 39q^{61} - 114q^{62} - 104q^{63} + 128q^{64} + 72q^{65} + 34q^{66} - 17q^{67} + 100q^{68} + 54q^{70} - 64q^{72} - 119q^{73} - 30q^{74} + 2q^{75} + 28q^{76} - 187q^{77} - 48q^{78} + 129q^{79} - 144q^{80} - 55q^{81} - 104q^{82} + 220q^{83} - 44q^{84} - 56q^{86} - 24q^{87} + 136q^{88} - 71q^{89} + 144q^{90} + 192q^{91} + 36q^{92} - 57q^{93} + 174q^{94} - 63q^{95} + 32q^{96} - 44q^{97} + 188q^{98} - 272q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/56\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(17\) \(29\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −1.00000
\(3\) −0.500000 + 0.866025i −0.166667 + 0.288675i −0.937246 0.348669i \(-0.886634\pi\)
0.770579 + 0.637344i \(0.219967\pi\)
\(4\) 4.00000 1.00000
\(5\) −4.50000 + 2.59808i −0.900000 + 0.519615i −0.877200 0.480125i \(-0.840591\pi\)
−0.0227998 + 0.999740i \(0.507258\pi\)
\(6\) 1.00000 1.73205i 0.166667 0.288675i
\(7\) −1.00000 + 6.92820i −0.142857 + 0.989743i
\(8\) −8.00000 −1.00000
\(9\) 4.00000 + 6.92820i 0.444444 + 0.769800i
\(10\) 9.00000 5.19615i 0.900000 0.519615i
\(11\) −8.50000 + 14.7224i −0.772727 + 1.33840i 0.163336 + 0.986571i \(0.447775\pi\)
−0.936063 + 0.351832i \(0.885559\pi\)
\(12\) −2.00000 + 3.46410i −0.166667 + 0.288675i
\(13\) 13.8564i 1.06588i −0.846154 0.532939i \(-0.821088\pi\)
0.846154 0.532939i \(-0.178912\pi\)
\(14\) 2.00000 13.8564i 0.142857 0.989743i
\(15\) 5.19615i 0.346410i
\(16\) 16.0000 1.00000
\(17\) 12.5000 21.6506i 0.735294 1.27357i −0.219300 0.975657i \(-0.570377\pi\)
0.954594 0.297909i \(-0.0962893\pi\)
\(18\) −8.00000 13.8564i −0.444444 0.769800i
\(19\) 3.50000 + 6.06218i 0.184211 + 0.319062i 0.943310 0.331912i \(-0.107694\pi\)
−0.759100 + 0.650974i \(0.774361\pi\)
\(20\) −18.0000 + 10.3923i −0.900000 + 0.519615i
\(21\) −5.50000 4.33013i −0.261905 0.206197i
\(22\) 17.0000 29.4449i 0.772727 1.33840i
\(23\) 4.50000 2.59808i 0.195652 0.112960i −0.398974 0.916962i \(-0.630634\pi\)
0.594626 + 0.804003i \(0.297300\pi\)
\(24\) 4.00000 6.92820i 0.166667 0.288675i
\(25\) 1.00000 1.73205i 0.0400000 0.0692820i
\(26\) 27.7128i 1.06588i
\(27\) −17.0000 −0.629630
\(28\) −4.00000 + 27.7128i −0.142857 + 0.989743i
\(29\) 13.8564i 0.477807i 0.971043 + 0.238904i \(0.0767880\pi\)
−0.971043 + 0.238904i \(0.923212\pi\)
\(30\) 10.3923i 0.346410i
\(31\) 28.5000 + 16.4545i 0.919355 + 0.530790i 0.883429 0.468565i \(-0.155229\pi\)
0.0359257 + 0.999354i \(0.488562\pi\)
\(32\) −32.0000 −1.00000
\(33\) −8.50000 14.7224i −0.257576 0.446134i
\(34\) −25.0000 + 43.3013i −0.735294 + 1.27357i
\(35\) −13.5000 33.7750i −0.385714 0.965000i
\(36\) 16.0000 + 27.7128i 0.444444 + 0.769800i
\(37\) 7.50000 4.33013i 0.202703 0.117030i −0.395213 0.918590i \(-0.629329\pi\)
0.597916 + 0.801559i \(0.295996\pi\)
\(38\) −7.00000 12.1244i −0.184211 0.319062i
\(39\) 12.0000 + 6.92820i 0.307692 + 0.177646i
\(40\) 36.0000 20.7846i 0.900000 0.519615i
\(41\) 26.0000 0.634146 0.317073 0.948401i \(-0.397300\pi\)
0.317073 + 0.948401i \(0.397300\pi\)
\(42\) 11.0000 + 8.66025i 0.261905 + 0.206197i
\(43\) 14.0000 0.325581 0.162791 0.986661i \(-0.447950\pi\)
0.162791 + 0.986661i \(0.447950\pi\)
\(44\) −34.0000 + 58.8897i −0.772727 + 1.33840i
\(45\) −36.0000 20.7846i −0.800000 0.461880i
\(46\) −9.00000 + 5.19615i −0.195652 + 0.112960i
\(47\) −43.5000 + 25.1147i −0.925532 + 0.534356i −0.885396 0.464838i \(-0.846113\pi\)
−0.0401362 + 0.999194i \(0.512779\pi\)
\(48\) −8.00000 + 13.8564i −0.166667 + 0.288675i
\(49\) −47.0000 13.8564i −0.959184 0.282784i
\(50\) −2.00000 + 3.46410i −0.0400000 + 0.0692820i
\(51\) 12.5000 + 21.6506i 0.245098 + 0.424522i
\(52\) 55.4256i 1.06588i
\(53\) 79.5000 + 45.8993i 1.50000 + 0.866025i 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) 34.0000 0.629630
\(55\) 88.3346i 1.60608i
\(56\) 8.00000 55.4256i 0.142857 0.989743i
\(57\) −7.00000 −0.122807
\(58\) 27.7128i 0.477807i
\(59\) 27.5000 47.6314i 0.466102 0.807312i −0.533149 0.846021i \(-0.678991\pi\)
0.999250 + 0.0387097i \(0.0123247\pi\)
\(60\) 20.7846i 0.346410i
\(61\) 19.5000 11.2583i 0.319672 0.184563i −0.331574 0.943429i \(-0.607580\pi\)
0.651246 + 0.758866i \(0.274246\pi\)
\(62\) −57.0000 32.9090i −0.919355 0.530790i
\(63\) −52.0000 + 20.7846i −0.825397 + 0.329914i
\(64\) 64.0000 1.00000
\(65\) 36.0000 + 62.3538i 0.553846 + 0.959290i
\(66\) 17.0000 + 29.4449i 0.257576 + 0.446134i
\(67\) −8.50000 + 14.7224i −0.126866 + 0.219738i −0.922461 0.386091i \(-0.873825\pi\)
0.795595 + 0.605829i \(0.207158\pi\)
\(68\) 50.0000 86.6025i 0.735294 1.27357i
\(69\) 5.19615i 0.0753066i
\(70\) 27.0000 + 67.5500i 0.385714 + 0.965000i
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −32.0000 55.4256i −0.444444 0.769800i
\(73\) −59.5000 + 103.057i −0.815068 + 1.41174i 0.0942102 + 0.995552i \(0.469967\pi\)
−0.909279 + 0.416188i \(0.863366\pi\)
\(74\) −15.0000 + 8.66025i −0.202703 + 0.117030i
\(75\) 1.00000 + 1.73205i 0.0133333 + 0.0230940i
\(76\) 14.0000 + 24.2487i 0.184211 + 0.319062i
\(77\) −93.5000 73.6122i −1.21429 0.956002i
\(78\) −24.0000 13.8564i −0.307692 0.177646i
\(79\) 64.5000 37.2391i 0.816456 0.471381i −0.0327370 0.999464i \(-0.510422\pi\)
0.849193 + 0.528083i \(0.177089\pi\)
\(80\) −72.0000 + 41.5692i −0.900000 + 0.519615i
\(81\) −27.5000 + 47.6314i −0.339506 + 0.588042i
\(82\) −52.0000 −0.634146
\(83\) 110.000 1.32530 0.662651 0.748929i \(-0.269431\pi\)
0.662651 + 0.748929i \(0.269431\pi\)
\(84\) −22.0000 17.3205i −0.261905 0.206197i
\(85\) 129.904i 1.52828i
\(86\) −28.0000 −0.325581
\(87\) −12.0000 6.92820i −0.137931 0.0796345i
\(88\) 68.0000 117.779i 0.772727 1.33840i
\(89\) −35.5000 61.4878i −0.398876 0.690874i 0.594711 0.803939i \(-0.297266\pi\)
−0.993588 + 0.113065i \(0.963933\pi\)
\(90\) 72.0000 + 41.5692i 0.800000 + 0.461880i
\(91\) 96.0000 + 13.8564i 1.05495 + 0.152268i
\(92\) 18.0000 10.3923i 0.195652 0.112960i
\(93\) −28.5000 + 16.4545i −0.306452 + 0.176930i
\(94\) 87.0000 50.2295i 0.925532 0.534356i
\(95\) −31.5000 18.1865i −0.331579 0.191437i
\(96\) 16.0000 27.7128i 0.166667 0.288675i
\(97\) −22.0000 −0.226804 −0.113402 0.993549i \(-0.536175\pi\)
−0.113402 + 0.993549i \(0.536175\pi\)
\(98\) 94.0000 + 27.7128i 0.959184 + 0.282784i
\(99\) −136.000 −1.37374
\(100\) 4.00000 6.92820i 0.0400000 0.0692820i
\(101\) 67.5000 + 38.9711i 0.668317 + 0.385853i 0.795439 0.606034i \(-0.207241\pi\)
−0.127122 + 0.991887i \(0.540574\pi\)
\(102\) −25.0000 43.3013i −0.245098 0.424522i
\(103\) −139.500 + 80.5404i −1.35437 + 0.781945i −0.988858 0.148862i \(-0.952439\pi\)
−0.365511 + 0.930807i \(0.619106\pi\)
\(104\) 110.851i 1.06588i
\(105\) 36.0000 + 5.19615i 0.342857 + 0.0494872i
\(106\) −159.000 91.7987i −1.50000 0.866025i
\(107\) −32.5000 56.2917i −0.303738 0.526090i 0.673241 0.739423i \(-0.264902\pi\)
−0.976980 + 0.213333i \(0.931568\pi\)
\(108\) −68.0000 −0.629630
\(109\) 7.50000 + 4.33013i 0.0688073 + 0.0397259i 0.534009 0.845479i \(-0.320685\pi\)
−0.465202 + 0.885205i \(0.654018\pi\)
\(110\) 176.669i 1.60608i
\(111\) 8.66025i 0.0780203i
\(112\) −16.0000 + 110.851i −0.142857 + 0.989743i
\(113\) 122.000 1.07965 0.539823 0.841779i \(-0.318491\pi\)
0.539823 + 0.841779i \(0.318491\pi\)
\(114\) 14.0000 0.122807
\(115\) −13.5000 + 23.3827i −0.117391 + 0.203328i
\(116\) 55.4256i 0.477807i
\(117\) 96.0000 55.4256i 0.820513 0.473723i
\(118\) −55.0000 + 95.2628i −0.466102 + 0.807312i
\(119\) 137.500 + 108.253i 1.15546 + 0.909691i
\(120\) 41.5692i 0.346410i
\(121\) −84.0000 145.492i −0.694215 1.20242i
\(122\) −39.0000 + 22.5167i −0.319672 + 0.184563i
\(123\) −13.0000 + 22.5167i −0.105691 + 0.183062i
\(124\) 114.000 + 65.8179i 0.919355 + 0.530790i
\(125\) 119.512i 0.956092i
\(126\) 104.000 41.5692i 0.825397 0.329914i
\(127\) 166.277i 1.30927i −0.755947 0.654633i \(-0.772823\pi\)
0.755947 0.654633i \(-0.227177\pi\)
\(128\) −128.000 −1.00000
\(129\) −7.00000 + 12.1244i −0.0542636 + 0.0939873i
\(130\) −72.0000 124.708i −0.553846 0.959290i
\(131\) −8.50000 14.7224i −0.0648855 0.112385i 0.831758 0.555139i \(-0.187335\pi\)
−0.896643 + 0.442754i \(0.854002\pi\)
\(132\) −34.0000 58.8897i −0.257576 0.446134i
\(133\) −45.5000 + 18.1865i −0.342105 + 0.136741i
\(134\) 17.0000 29.4449i 0.126866 0.219738i
\(135\) 76.5000 44.1673i 0.566667 0.327165i
\(136\) −100.000 + 173.205i −0.735294 + 1.27357i
\(137\) 72.5000 125.574i 0.529197 0.916596i −0.470223 0.882548i \(-0.655827\pi\)
0.999420 0.0340486i \(-0.0108401\pi\)
\(138\) 10.3923i 0.0753066i
\(139\) −82.0000 −0.589928 −0.294964 0.955508i \(-0.595308\pi\)
−0.294964 + 0.955508i \(0.595308\pi\)
\(140\) −54.0000 135.100i −0.385714 0.965000i
\(141\) 50.2295i 0.356237i
\(142\) 0 0
\(143\) 204.000 + 117.779i 1.42657 + 0.823633i
\(144\) 64.0000 + 110.851i 0.444444 + 0.769800i
\(145\) −36.0000 62.3538i −0.248276 0.430026i
\(146\) 119.000 206.114i 0.815068 1.41174i
\(147\) 35.5000 33.7750i 0.241497 0.229762i
\(148\) 30.0000 17.3205i 0.202703 0.117030i
\(149\) −4.50000 + 2.59808i −0.0302013 + 0.0174368i −0.515025 0.857175i \(-0.672217\pi\)
0.484823 + 0.874612i \(0.338884\pi\)
\(150\) −2.00000 3.46410i −0.0133333 0.0230940i
\(151\) −31.5000 18.1865i −0.208609 0.120441i 0.392056 0.919942i \(-0.371764\pi\)
−0.600665 + 0.799501i \(0.705097\pi\)
\(152\) −28.0000 48.4974i −0.184211 0.319062i
\(153\) 200.000 1.30719
\(154\) 187.000 + 147.224i 1.21429 + 0.956002i
\(155\) −171.000 −1.10323
\(156\) 48.0000 + 27.7128i 0.307692 + 0.177646i
\(157\) −268.500 155.019i −1.71019 0.987379i −0.934282 0.356534i \(-0.883958\pi\)
−0.775909 0.630845i \(1.21729\pi\)
\(158\) −129.000 + 74.4782i −0.816456 + 0.471381i
\(159\) −79.5000 + 45.8993i −0.500000 + 0.288675i
\(160\) 144.000 83.1384i 0.900000 0.519615i
\(161\) 13.5000 + 33.7750i 0.0838509 + 0.209783i
\(162\) 55.0000 95.2628i 0.339506 0.588042i
\(163\) −8.50000 14.7224i −0.0521472 0.0903217i 0.838773 0.544481i \(-0.183273\pi\)
−0.890921 + 0.454159i \(0.849940\pi\)
\(164\) 104.000 0.634146
\(165\) 76.5000 + 44.1673i 0.463636 + 0.267681i
\(166\) −220.000 −1.32530
\(167\) 13.8564i 0.0829725i −0.999139 0.0414862i \(-0.986791\pi\)
0.999139 0.0414862i \(-0.0132093\pi\)
\(168\) 44.0000 + 34.6410i 0.261905 + 0.206197i
\(169\) −23.0000 −0.136095
\(170\) 259.808i 1.52828i
\(171\) −28.0000 + 48.4974i −0.163743 + 0.283611i
\(172\) 56.0000 0.325581
\(173\) 91.5000 52.8275i 0.528902 0.305362i −0.211667 0.977342i \(-0.567889\pi\)
0.740569 + 0.671980i \(0.234556\pi\)
\(174\) 24.0000 + 13.8564i 0.137931 + 0.0796345i
\(175\) 11.0000 + 8.66025i 0.0628571 + 0.0494872i
\(176\) −136.000 + 235.559i −0.772727 + 1.33840i
\(177\) 27.5000 + 47.6314i 0.155367 + 0.269104i
\(178\) 71.0000 + 122.976i 0.398876 + 0.690874i
\(179\) −44.5000 + 77.0763i −0.248603 + 0.430594i −0.963139 0.269006i \(-0.913305\pi\)
0.714535 + 0.699600i \(0.246638\pi\)
\(180\) −144.000 83.1384i −0.800000 0.461880i
\(181\) 249.415i 1.37799i 0.724768 + 0.688993i \(0.241947\pi\)
−0.724768 + 0.688993i \(0.758053\pi\)
\(182\) −192.000 27.7128i −1.05495 0.152268i
\(183\) 22.5167i 0.123042i
\(184\) −36.0000 + 20.7846i −0.195652 + 0.112960i
\(185\) −22.5000 + 38.9711i −0.121622 + 0.210655i
\(186\) 57.0000 32.9090i 0.306452 0.176930i
\(187\) 212.500 + 368.061i 1.13636 + 1.96824i
\(188\) −174.000 + 100.459i −0.925532 + 0.534356i
\(189\) 17.0000 117.779i 0.0899471 0.623172i
\(190\) 63.0000 + 36.3731i 0.331579 + 0.191437i
\(191\) −187.500 + 108.253i −0.981675 + 0.566771i −0.902776 0.430112i \(-0.858474\pi\)
−0.0788999 + 0.996883i \(0.525141\pi\)
\(192\) −32.0000 + 55.4256i −0.166667 + 0.288675i
\(193\) 36.5000 63.2199i 0.189119 0.327564i −0.755838 0.654759i \(-0.772770\pi\)
0.944957 + 0.327195i \(0.106103\pi\)
\(194\) 44.0000 0.226804
\(195\) −72.0000 −0.369231
\(196\) −188.000 55.4256i −0.959184 0.282784i
\(197\) 207.846i 1.05506i 0.849538 + 0.527528i \(0.176881\pi\)
−0.849538 + 0.527528i \(0.823119\pi\)
\(198\) 272.000 1.37374
\(199\) −55.5000 32.0429i −0.278894 0.161020i 0.354028 0.935235i \(-0.384812\pi\)
−0.632923 + 0.774215i \(0.718145\pi\)
\(200\) −8.00000 + 13.8564i −0.0400000 + 0.0692820i
\(201\) −8.50000 14.7224i −0.0422886 0.0732459i
\(202\) −135.000 77.9423i −0.668317 0.385853i
\(203\) −96.0000 13.8564i −0.472906 0.0682582i
\(204\) 50.0000 + 86.6025i 0.245098 + 0.424522i
\(205\) −117.000 + 67.5500i −0.570732 + 0.329512i
\(206\) 279.000 161.081i 1.35437 0.781945i
\(207\) 36.0000 + 20.7846i 0.173913 + 0.100409i
\(208\) 221.703i 1.06588i
\(209\) −119.000 −0.569378
\(210\) −72.0000 10.3923i −0.342857 0.0494872i
\(211\) 302.000 1.43128 0.715640 0.698470i \(-0.246135\pi\)
0.715640 + 0.698470i \(0.246135\pi\)
\(212\) 318.000 + 183.597i 1.50000 + 0.866025i
\(213\) 0 0
\(214\) 65.0000 + 112.583i 0.303738 + 0.526090i
\(215\) −63.0000 + 36.3731i −0.293023 + 0.169177i
\(216\) 136.000 0.629630
\(217\) −142.500 + 180.999i −0.656682 + 0.834098i
\(218\) −15.0000 8.66025i −0.0688073 0.0397259i
\(219\) −59.5000 103.057i −0.271689 0.470580i
\(220\) 353.338i 1.60608i
\(221\) −300.000 173.205i −1.35747 0.783733i
\(222\) 17.3205i 0.0780203i
\(223\) 138.564i 0.621364i 0.950514 + 0.310682i \(0.100557\pi\)
−0.950514 + 0.310682i \(0.899443\pi\)
\(224\) 32.0000 221.703i 0.142857 0.989743i
\(225\) 16.0000 0.0711111
\(226\) −244.000 −1.07965
\(227\) 27.5000 47.6314i 0.121145 0.209830i −0.799074 0.601232i \(-0.794677\pi\)
0.920220 + 0.391402i \(0.128010\pi\)
\(228\) −28.0000 −0.122807
\(229\) 283.500 163.679i 1.23799 0.714755i 0.269308 0.963054i \(-0.413205\pi\)
0.968683 + 0.248300i \(0.0798717\pi\)
\(230\) 27.0000 46.7654i 0.117391 0.203328i
\(231\) 110.500 44.1673i 0.478355 0.191200i
\(232\) 110.851i 0.477807i
\(233\) 192.500 + 333.420i 0.826180 + 1.43099i 0.901014 + 0.433790i \(0.142824\pi\)
−0.0748337 + 0.997196i \(0.523843\pi\)
\(234\) −192.000 + 110.851i −0.820513 + 0.473723i
\(235\) 130.500 226.033i 0.555319 0.961841i
\(236\) 110.000 190.526i 0.466102 0.807312i
\(237\) 74.4782i 0.314254i
\(238\) −275.000 216.506i −1.15546 0.909691i
\(239\) 429.549i 1.79727i −0.438693 0.898637i \(-0.644558\pi\)
0.438693 0.898637i \(-0.355442\pi\)
\(240\) 83.1384i 0.346410i
\(241\) 72.5000 125.574i 0.300830 0.521053i −0.675494 0.737365i \(-0.736070\pi\)
0.976324 + 0.216313i \(0.0694030\pi\)
\(242\) 168.000 + 290.985i 0.694215 + 1.20242i
\(243\) −104.000 180.133i −0.427984 0.741289i
\(244\) 78.0000 45.0333i 0.319672 0.184563i
\(245\) 247.500 59.7558i 1.01020 0.243901i
\(246\) 26.0000 45.0333i 0.105691 0.183062i
\(247\) 84.0000 48.4974i 0.340081 0.196346i
\(248\) −228.000 131.636i −0.919355 0.530790i
\(249\) −55.0000 + 95.2628i −0.220884 + 0.382582i
\(250\) 239.023i 0.956092i
\(251\) −58.0000 −0.231076 −0.115538 0.993303i \(-0.536859\pi\)
−0.115538 + 0.993303i \(0.536859\pi\)
\(252\) −208.000 + 83.1384i −0.825397 + 0.329914i
\(253\) 88.3346i 0.349149i
\(254\) 332.554i 1.30927i
\(255\) −112.500 64.9519i −0.441176 0.254713i
\(256\) 256.000 1.00000
\(257\) −59.5000 103.057i −0.231518 0.401000i 0.726737 0.686915i \(-0.241036\pi\)
−0.958255 + 0.285915i \(0.907702\pi\)
\(258\) 14.0000 24.2487i 0.0542636 0.0939873i
\(259\) 22.5000 + 56.2917i 0.0868726 + 0.217342i
\(260\) 144.000 + 249.415i 0.553846 + 0.959290i
\(261\) −96.0000 + 55.4256i −0.367816 + 0.212359i
\(262\) 17.0000 + 29.4449i 0.0648855 + 0.112385i
\(263\) −283.500 163.679i −1.07795 0.622353i −0.147605 0.989046i \(-0.547156\pi\)
−0.930342 + 0.366694i \(0.880490\pi\)
\(264\) 68.0000 + 117.779i 0.257576 + 0.446134i
\(265\) −477.000 −1.80000
\(266\) 91.0000 36.3731i 0.342105 0.136741i
\(267\) 71.0000 0.265918
\(268\) −34.0000 + 58.8897i −0.126866 + 0.219738i
\(269\) 115.500 + 66.6840i 0.429368 + 0.247896i 0.699077 0.715046i \(-0.253594\pi\)
−0.269709 + 0.962942i \(0.586928\pi\)
\(270\) −153.000 + 88.3346i −0.566667 + 0.327165i
\(271\) 376.500 217.372i 1.38930 0.802112i 0.396063 0.918223i \(-0.370376\pi\)
0.993236 + 0.116111i \(0.0370430\pi\)
\(272\) 200.000 346.410i 0.735294 1.27357i
\(273\) −60.0000 + 76.2102i −0.219780 + 0.279158i
\(274\) −145.000 + 251.147i −0.529197 + 0.916596i
\(275\) 17.0000 + 29.4449i 0.0618182 + 0.107072i
\(276\) 20.7846i 0.0753066i
\(277\) 175.500 + 101.325i 0.633574 + 0.365794i 0.782135 0.623109i \(-0.214131\pi\)
−0.148561 + 0.988903i \(0.547464\pi\)
\(278\) 164.000 0.589928
\(279\) 263.272i 0.943626i
\(280\) 108.000 + 270.200i 0.385714 + 0.965000i
\(281\) 74.0000 0.263345 0.131673 0.991293i \(-0.457965\pi\)
0.131673 + 0.991293i \(0.457965\pi\)
\(282\) 100.459i 0.356237i
\(283\) 231.500 400.970i 0.818021 1.41685i −0.0891169 0.996021i \(-0.528404\pi\)
0.907138 0.420833i \(-0.138262\pi\)
\(284\) 0 0
\(285\) 31.5000 18.1865i 0.110526 0.0638124i
\(286\) −408.000 235.559i −1.42657 0.823633i
\(287\) −26.0000 + 180.133i −0.0905923 + 0.627642i
\(288\) −128.000 221.703i −0.444444 0.769800i
\(289\) −168.000 290.985i −0.581315 1.00687i
\(290\) 72.0000 + 124.708i 0.248276 + 0.430026i
\(291\) 11.0000 19.0526i 0.0378007 0.0654727i
\(292\) −238.000 + 412.228i −0.815068 + 1.41174i
\(293\) 110.851i 0.378332i 0.981945 + 0.189166i \(0.0605784\pi\)
−0.981945 + 0.189166i \(0.939422\pi\)
\(294\) −71.0000 + 67.5500i −0.241497 + 0.229762i
\(295\) 285.788i 0.968774i
\(296\) −60.0000 + 34.6410i −0.202703 + 0.117030i
\(297\) 144.500 250.281i 0.486532 0.842698i
\(298\) 9.00000 5.19615i 0.0302013 0.0174368i
\(299\) −36.0000 62.3538i −0.120401 0.208541i
\(300\) 4.00000 + 6.92820i 0.0133333 + 0.0230940i
\(301\) −14.0000 + 96.9948i −0.0465116 + 0.322242i
\(302\) 63.0000 + 36.3731i 0.208609 + 0.120441i
\(303\) −67.5000 + 38.9711i −0.222772 + 0.128618i
\(304\) 56.0000 + 96.9948i 0.184211 + 0.319062i
\(305\) −58.5000 + 101.325i −0.191803 + 0.332213i
\(306\) −400.000 −1.30719
\(307\) −274.000 −0.892508 −0.446254 0.894906i \(-0.647242\pi\)
−0.446254 + 0.894906i \(0.647242\pi\)
\(308\) −374.000 294.449i −1.21429 0.956002i
\(309\) 161.081i 0.521297i
\(310\) 342.000 1.10323
\(311\) −43.5000 25.1147i −0.139871 0.0807548i 0.428431 0.903574i \(-0.359066\pi\)
−0.568303 + 0.822820i \(0.692400\pi\)
\(312\) −96.0000 55.4256i −0.307692 0.177646i
\(313\) 204.500 + 354.204i 0.653355 + 1.13164i 0.982304 + 0.187296i \(0.0599723\pi\)
−0.328949 + 0.944348i \(0.606694\pi\)
\(314\) 537.000 + 310.037i 1.71019 + 0.987379i
\(315\) 180.000 228.631i 0.571429 0.725812i
\(316\) 258.000 148.956i 0.816456 0.471381i
\(317\) 163.500 94.3968i 0.515773 0.297782i −0.219431 0.975628i \(-0.570420\pi\)
0.735203 + 0.677847i \(0.237087\pi\)
\(318\) 159.000 91.7987i 0.500000 0.288675i
\(319\) −204.000 117.779i −0.639498 0.369215i
\(320\) −288.000 + 166.277i −0.900000 + 0.519615i
\(321\) 65.0000 0.202492
\(322\) −27.0000 67.5500i −0.0838509 0.209783i
\(323\) 175.000 0.541796
\(324\) −110.000 + 190.526i −0.339506 + 0.588042i
\(325\) −24.0000 13.8564i −0.0738462 0.0426351i
\(326\) 17.0000 + 29.4449i 0.0521472 + 0.0903217i
\(327\) −7.50000 + 4.33013i −0.0229358 + 0.0132420i
\(328\) −208.000 −0.634146
\(329\) −130.500 326.492i −0.396657 0.992376i
\(330\) −153.000 88.3346i −0.463636 0.267681i
\(331\) 147.500 + 255.477i 0.445619 + 0.771835i 0.998095 0.0616936i \(-0.0196502\pi\)
−0.552476 + 0.833529i \(0.686317\pi\)
\(332\) 440.000 1.32530
\(333\) 60.0000 + 34.6410i 0.180180 + 0.104027i
\(334\) 27.7128i 0.0829725i
\(335\) 88.3346i 0.263685i
\(336\) −88.0000 69.2820i −0.261905 0.206197i
\(337\) 26.0000 0.0771513 0.0385757 0.999256i \(-0.487718\pi\)
0.0385757 + 0.999256i \(0.487718\pi\)
\(338\) 46.0000 0.136095
\(339\) −61.0000 + 105.655i −0.179941 + 0.311667i
\(340\) 519.615i 1.52828i
\(341\) −484.500 + 279.726i −1.42082 + 0.820311i
\(342\) 56.0000 96.9948i 0.163743 0.283611i
\(343\) 143.000 311.769i 0.416910 0.908948i
\(344\) −112.000 −0.325581
\(345\) −13.5000 23.3827i −0.0391304 0.0677759i
\(346\) −183.000 + 105.655i −0.528902 + 0.305362i
\(347\) −188.500 + 326.492i −0.543228 + 0.940898i 0.455488 + 0.890242i \(0.349465\pi\)
−0.998716 + 0.0506562i \(0.983869\pi\)
\(348\) −48.0000 27.7128i −0.137931 0.0796345i
\(349\) 96.9948i 0.277922i 0.990298 + 0.138961i \(0.0443763\pi\)
−0.990298 + 0.138961i \(0.955624\pi\)
\(350\) −22.0000 17.3205i −0.0628571 0.0494872i
\(351\) 235.559i 0.671108i
\(352\) 272.000 471.118i 0.772727 1.33840i
\(353\) −251.500 + 435.611i −0.712465 + 1.23402i 0.251465 + 0.967866i \(0.419088\pi\)
−0.963929 + 0.266158i \(0.914246\pi\)
\(354\) −55.0000 95.2628i −0.155367 0.269104i
\(355\) 0 0
\(356\) −142.000 245.951i −0.398876 0.690874i
\(357\) −162.500 + 64.9519i −0.455182 + 0.181938i
\(358\) 89.0000 154.153i 0.248603 0.430594i
\(359\) 160.500 92.6647i 0.447075 0.258119i −0.259519 0.965738i \(-0.583564\pi\)
0.706594 + 0.707619i \(0.250231\pi\)
\(360\) 288.000 + 166.277i 0.800000 + 0.461880i
\(361\) 156.000 270.200i 0.432133 0.748476i
\(362\) 498.831i 1.37799i
\(363\) 168.000 0.462810
\(364\) 384.000 + 55.4256i 1.05495 + 0.152268i
\(365\) 618.342i 1.69409i
\(366\) 45.0333i 0.123042i
\(367\) 256.500 + 148.090i 0.698910 + 0.403516i 0.806941 0.590632i \(-0.201121\pi\)
−0.108031 + 0.994147i \(0.534455\pi\)
\(368\) 72.0000 41.5692i 0.195652 0.112960i
\(369\) 104.000 + 180.133i 0.281843 + 0.488166i
\(370\) 45.0000 77.9423i 0.121622 0.210655i
\(371\) −397.500 + 504.893i −1.07143 + 1.36090i
\(372\) −114.000 + 65.8179i −0.306452 + 0.176930i
\(373\) 103.500 59.7558i 0.277480 0.160203i −0.354802 0.934941i \(-0.615452\pi\)
0.632282 + 0.774738i \(0.282118\pi\)
\(374\) −425.000 736.122i −1.13636 1.96824i
\(375\) 103.500 + 59.7558i 0.276000 + 0.159349i
\(376\) 348.000 200.918i 0.925532 0.534356i
\(377\) 192.000 0.509284
\(378\) −34.0000 + 235.559i −0.0899471 + 0.623172i
\(379\) −634.000 −1.67282 −0.836412 0.548102i \(-0.815351\pi\)
−0.836412 + 0.548102i \(0.815351\pi\)
\(380\) −126.000 72.7461i −0.331579 0.191437i
\(381\) 144.000 + 83.1384i 0.377953 + 0.218211i
\(382\) 375.000 216.506i 0.981675 0.566771i
\(383\) −211.500 + 122.110i −0.552219 + 0.318824i −0.750017 0.661419i \(-0.769955\pi\)
0.197797 + 0.980243i \(0.436621\pi\)
\(384\) 64.0000 110.851i 0.166667 0.288675i
\(385\) 612.000 + 88.3346i 1.58961 + 0.229440i
\(386\) −73.0000 + 126.440i −0.189119 + 0.327564i
\(387\) 56.0000 + 96.9948i 0.144703 + 0.250633i
\(388\) −88.0000 −0.226804
\(389\) −508.500 293.583i −1.30720 0.754711i −0.325570 0.945518i \(-0.605556\pi\)
−0.981628 + 0.190807i \(0.938890\pi\)
\(390\) 144.000 0.369231
\(391\) 129.904i 0.332235i
\(392\) 376.000 + 110.851i 0.959184 + 0.282784i
\(393\) 17.0000 0.0432570
\(394\) 415.692i 1.05506i
\(395\) −193.500 + 335.152i −0.489873 + 0.848486i
\(396\) −544.000 −1.37374
\(397\) −208.500 + 120.378i −0.525189 + 0.303218i −0.739055 0.673645i \(-0.764728\pi\)
0.213866 + 0.976863i \(0.431394\pi\)
\(398\) 111.000 + 64.0859i 0.278894 + 0.161020i
\(399\) 7.00000 48.4974i 0.0175439 0.121547i
\(400\) 16.0000 27.7128i 0.0400000 0.0692820i
\(401\) −59.5000 103.057i −0.148379 0.257000i 0.782249 0.622965i \(-0.214072\pi\)
−0.930629 + 0.365965i \(0.880739\pi\)
\(402\) 17.0000 + 29.4449i 0.0422886 + 0.0732459i
\(403\) 228.000 394.908i 0.565757 0.979920i
\(404\) 270.000 + 155.885i 0.668317 + 0.385853i
\(405\) 285.788i 0.705650i
\(406\) 192.000 + 27.7128i 0.472906 + 0.0682582i
\(407\) 147.224i 0.361731i
\(408\) −100.000 173.205i −0.245098 0.424522i
\(409\) 72.5000 125.574i 0.177262 0.307026i −0.763680 0.645595i \(-0.776609\pi\)
0.940942 + 0.338569i \(0.109943\pi\)
\(410\) 234.000 135.100i 0.570732 0.329512i
\(411\) 72.5000 + 125.574i 0.176399 + 0.305532i
\(412\) −558.000 + 322.161i −1.35437 + 0.781945i
\(413\) 302.500 + 238.157i 0.732446 + 0.576651i
\(414\) −72.0000 41.5692i −0.173913 0.100409i
\(415\) −495.000 + 285.788i −1.19277 + 0.688647i
\(416\) 443.405i 1.06588i
\(417\) 41.0000 71.0141i 0.0983213 0.170298i
\(418\) 238.000 0.569378
\(419\) 302.000 0.720764 0.360382 0.932805i \(-0.382646\pi\)
0.360382 + 0.932805i \(0.382646\pi\)
\(420\) 144.000 + 20.7846i 0.342857 + 0.0494872i
\(421\) 401.836i 0.954479i −0.878773 0.477240i \(-0.841637\pi\)
0.878773 0.477240i \(-0.158363\pi\)
\(422\) −604.000 −1.43128
\(423\) −348.000 200.918i −0.822695 0.474983i
\(424\) −636.000 367.195i −1.50000 0.866025i
\(425\) −25.0000 43.3013i −0.0588235 0.101885i
\(426\) 0 0
\(427\) 58.5000 + 146.358i 0.137002 + 0.342759i
\(428\) −130.000 225.167i −0.303738 0.526090i
\(429\) −204.000 + 117.779i −0.475524 + 0.274544i
\(430\) 126.000 72.7461i 0.293023 0.169177i
\(431\) 700.500 + 404.434i 1.62529 + 0.938362i 0.985473 + 0.169835i \(0.0543234\pi\)
0.639817 + 0.768527i \(0.279010\pi\)
\(432\) −272.000 −0.629630
\(433\) 410.000 0.946882 0.473441 0.880825i \(-0.343012\pi\)
0.473441 + 0.880825i \(0.343012\pi\)
\(434\) 285.000 361.999i 0.656682 0.834098i
\(435\) 72.0000 0.165517
\(436\) 30.0000 + 17.3205i 0.0688073 + 0.0397259i
\(437\) 31.5000 + 18.1865i 0.0720824 + 0.0416168i
\(438\) 119.000 + 206.114i 0.271689 + 0.470580i
\(439\) 424.500 245.085i 0.966970 0.558281i 0.0686591 0.997640i \(-0.478128\pi\)
0.898311 + 0.439360i \(0.144795\pi\)
\(440\) 706.677i 1.60608i
\(441\) −92.0000 381.051i −0.208617 0.864062i
\(442\) 600.000 + 346.410i 1.35747 + 0.783733i
\(443\) −200.500 347.276i −0.452596 0.783919i 0.545950 0.837817i \(-0.316169\pi\)
−0.998546 + 0.0538983i \(0.982835\pi\)
\(444\) 34.6410i 0.0780203i
\(445\) 319.500 + 184.463i 0.717978 + 0.414525i
\(446\) 277.128i 0.621364i
\(447\) 5.19615i 0.0116245i
\(448\) −64.0000 + 443.405i −0.142857 + 0.989743i
\(449\) −310.000 −0.690423 −0.345212 0.938525i \(-0.612193\pi\)
−0.345212 + 0.938525i \(0.612193\pi\)
\(450\) −32.0000 −0.0711111
\(451\) −221.000 + 382.783i −0.490022 + 0.848743i
\(452\) 488.000 1.07965
\(453\) 31.5000 18.1865i 0.0695364 0.0401469i
\(454\) −55.0000 + 95.2628i −0.121145 + 0.209830i
\(455\) −468.000 + 187.061i −1.02857 + 0.411124i
\(456\) 56.0000 0.122807
\(457\) −83.5000 144.626i −0.182713 0.316469i 0.760090 0.649818i \(-0.225155\pi\)
−0.942804 + 0.333349i \(0.891821\pi\)
\(458\) −567.000 + 327.358i −1.23799 + 0.714755i
\(459\) −212.500 + 368.061i −0.462963 + 0.801875i
\(460\) −54.0000 + 93.5307i −0.117391 + 0.203328i
\(461\) 13.8564i 0.0300573i 0.999887 + 0.0150286i \(0.00478394\pi\)
−0.999887 + 0.0150286i \(0.995216\pi\)
\(462\) −221.000 + 88.3346i −0.478355 + 0.191200i
\(463\) 609.682i 1.31681i 0.752665 + 0.658404i \(0.228768\pi\)
−0.752665 + 0.658404i \(0.771232\pi\)
\(464\) 221.703i 0.477807i
\(465\) 85.5000 148.090i 0.183871 0.318474i
\(466\) −385.000 666.840i −0.826180 1.43099i
\(467\) −392.500 679.830i −0.840471 1.45574i −0.889497 0.456941i \(-0.848945\pi\)
0.0490258 0.998798i \(-0.484388\pi\)
\(468\) 384.000 221.703i 0.820513 0.473723i
\(469\) −93.5000 73.6122i −0.199360 0.156956i
\(470\) −261.000 + 452.065i −0.555319 + 0.961841i
\(471\) 268.500 155.019i 0.570064 0.329126i
\(472\) −220.000 + 381.051i −0.466102 + 0.807312i
\(473\) −119.000 + 206.114i −0.251586 + 0.435759i
\(474\) 148.956i 0.314254i
\(475\) 14.0000 0.0294737
\(476\) 550.000 + 433.013i 1.15546 + 0.909691i
\(477\) 734.390i 1.53960i
\(478\) 859.097i 1.79727i
\(479\) −535.500 309.171i −1.11795 0.645451i −0.177076 0.984197i \(-0.556664\pi\)
−0.940878 + 0.338746i \(0.889997\pi\)
\(480\) 166.277i 0.346410i
\(481\) −60.0000 103.923i −0.124740 0.216056i
\(482\) −145.000 + 251.147i −0.300830 + 0.521053i
\(483\) −36.0000 5.19615i −0.0745342 0.0107581i
\(484\) −336.000 581.969i −0.694215 1.20242i
\(485\) 99.0000 57.1577i 0.204124 0.117851i
\(486\) 208.000 + 360.267i 0.427984 + 0.741289i
\(487\) 340.500 + 196.588i 0.699179 + 0.403671i 0.807041 0.590495i \(-0.201067\pi\)
−0.107863 + 0.994166i \(0.534401\pi\)
\(488\) −156.000 + 90.0666i −0.319672 + 0.184563i
\(489\) 17.0000 0.0347648
\(490\) −495.000 + 119.512i −1.01020 + 0.243901i
\(491\) 422.000 0.859470 0.429735 0.902955i \(-0.358607\pi\)
0.429735 + 0.902955i \(0.358607\pi\)
\(492\) −52.0000 + 90.0666i −0.105691 + 0.183062i
\(493\) 300.000 + 173.205i 0.608519 + 0.351329i
\(494\) −168.000 + 96.9948i −0.340081 + 0.196346i
\(495\) 612.000 353.338i 1.23636 0.713815i
\(496\) 456.000 + 263.272i 0.919355 + 0.530790i
\(497\) 0 0
\(498\) 110.000 190.526i 0.220884 0.382582i
\(499\) −32.5000 56.2917i −0.0651303 0.112809i 0.831622 0.555343i \(-0.187413\pi\)
−0.896752 + 0.442534i \(0.854080\pi\)
\(500\) 478.046i 0.956092i
\(501\) 12.0000 + 6.92820i 0.0239521 + 0.0138287i
\(502\) 116.000 0.231076
\(503\) 249.415i 0.495855i −0.968779 0.247928i \(-0.920250\pi\)
0.968779 0.247928i \(-0.0797496\pi\)
\(504\) 416.000 166.277i 0.825397 0.329914i
\(505\) −405.000 −0.801980
\(506\) 176.669i 0.349149i
\(507\) 11.5000 19.9186i 0.0226824 0.0392871i
\(508\) 665.108i 1.30927i
\(509\) −472.500 + 272.798i −0.928291 + 0.535949i −0.886271 0.463168i \(-0.846713\pi\)
−0.0420202 + 0.999117i \(0.513379\pi\)
\(510\) 225.000 + 129.904i 0.441176 + 0.254713i
\(511\) −654.500 515.285i −1.28082 1.00839i
\(512\) −512.000 −1.00000
\(513\) −59.5000 103.057i −0.115984 0.200891i
\(514\) 119.000 + 206.114i 0.231518 + 0.401000i
\(515\) 418.500 724.863i 0.812621 1.40750i
\(516\) −28.0000 + 48.4974i −0.0542636 + 0.0939873i
\(517\) 853.901i 1.65165i
\(518\) −45.0000 112.583i −0.0868726 0.217342i
\(519\) 105.655i 0.203574i
\(520\) −288.000 498.831i −0.553846 0.959290i
\(521\) 12.5000 21.6506i 0.0239923 0.0415559i −0.853780 0.520634i \(-0.825696\pi\)
0.877772 + 0.479078i \(0.159029\pi\)
\(522\) 192.000 110.851i 0.367816 0.212359i
\(523\) −296.500 513.553i −0.566922 0.981937i −0.996868 0.0790826i \(-0.974801\pi\)
0.429946 0.902854i \(-0.358532\pi\)
\(524\) −34.0000 58.8897i −0.0648855 0.112385i
\(525\) −13.0000 + 5.19615i −0.0247619 + 0.00989743i
\(526\) 567.000 + 327.358i 1.07795 + 0.622353i
\(527\) 712.500 411.362i 1.35199 0.780573i
\(528\) −136.000 235.559i −0.257576 0.446134i
\(529\) −251.000 + 434.745i −0.474480 + 0.821824i
\(530\) 954.000 1.80000
\(531\) 440.000 0.828625
\(532\) −182.000 + 72.7461i −0.342105 + 0.136741i
\(533\) 360.267i 0.675922i
\(534\) −142.000 −0.265918
\(535\) 292.500 + 168.875i 0.546729 + 0.315654i
\(536\) 68.0000 117.779i 0.126866 0.219738i
\(537\) −44.5000 77.0763i −0.0828678 0.143531i
\(538\) −231.000 133.368i −0.429368 0.247896i
\(539\) 603.500 574.175i 1.11967 1.06526i
\(540\) 306.000 176.669i 0.566667 0.327165i
\(541\) 655.500 378.453i 1.21165 0.699544i 0.248528 0.968625i \(-0.420053\pi\)
0.963117 + 0.269081i \(0.0867200\pi\)
\(542\) −753.000 + 434.745i −1.38930 + 0.802112i
\(543\) −216.000 124.708i −0.397790 0.229664i
\(544\) −400.000 + 692.820i −0.735294 + 1.27357i
\(545\) −45.0000 −0.0825688
\(546\) 120.000 152.420i 0.219780 0.279158i
\(547\) 662.000 1.21024 0.605119 0.796135i \(-0.293126\pi\)
0.605119 + 0.796135i \(0.293126\pi\)
\(548\) 290.000 502.295i 0.529197 0.916596i
\(549\) 156.000 + 90.0666i 0.284153 + 0.164056i
\(550\) −34.0000 58.8897i −0.0618182 0.107072i
\(551\) −84.0000 + 48.4974i −0.152450 + 0.0880171i
\(552\) 41.5692i 0.0753066i
\(553\) 193.500 + 484.108i 0.349910 + 0.875422i
\(554\) −351.000 202.650i −0.633574 0.365794i
\(555\) −22.5000 38.9711i −0.0405405 0.0702183i
\(556\) −328.000 −0.589928
\(557\) 511.500 + 295.315i 0.918312 + 0.530188i 0.883096 0.469192i \(-0.155455\pi\)
0.0352161 + 0.999380i \(0.488788\pi\)
\(558\) 526.543i 0.943626i
\(559\) 193.990i 0.347030i
\(560\) −216.000 540.400i −0.385714 0.965000i
\(561\) −425.000 −0.757576
\(562\) −148.000 −0.263345
\(563\) −368.500 + 638.261i −0.654529 + 1.13368i 0.327482 + 0.944857i \(0.393800\pi\)
−0.982012 + 0.188821i \(0.939534\pi\)
\(564\) 200.918i 0.356237i
\(565\) −549.000 + 316.965i −0.971681 + 0.561001i
\(566\) −463.000 + 801.940i −0.818021 + 1.41685i
\(567\) −302.500 238.157i −0.533510 0.420030i
\(568\) 0 0
\(569\) 60.5000 + 104.789i 0.106327 + 0.184164i 0.914280 0.405084i \(-0.132758\pi\)
−0.807953 + 0.589247i \(0.799424\pi\)
\(570\) −63.0000 + 36.3731i −0.110526 + 0.0638124i
\(571\) −368.500 + 638.261i −0.645359 + 1.11779i 0.338859 + 0.940837i \(0.389959\pi\)
−0.984218 + 0.176958i \(0.943374\pi\)
\(572\) 816.000 + 471.118i 1.42657 + 0.823633i
\(573\) 216.506i 0.377847i
\(574\) 52.0000 360.267i 0.0905923 0.627642i
\(575\) 10.3923i 0.0180736i
\(576\) 256.000 + 443.405i 0.444444 + 0.769800i
\(577\) −23.5000 + 40.7032i −0.0407279 + 0.0705428i −0.885671 0.464314i \(-0.846301\pi\)
0.844943 + 0.534857i \(0.179634\pi\)
\(578\) 336.000 + 581.969i 0.581315 + 1.00687i
\(579\) 36.5000 + 63.2199i 0.0630397 + 0.109188i
\(580\) −144.000 249.415i −0.248276 0.430026i
\(581\) −110.000 + 762.102i −0.189329 + 1.31171i
\(582\) −22.0000 + 38.1051i −0.0378007 + 0.0654727i
\(583\) −1351.50 + 780.289i −2.31818 + 1.33840i
\(584\) 476.000 824.456i 0.815068 1.41174i
\(585\) −288.000 + 498.831i −0.492308 + 0.852702i
\(586\) 221.703i 0.378332i
\(587\) 446.000 0.759796 0.379898 0.925028i \(-0.375959\pi\)
0.379898 + 0.925028i \(0.375959\pi\)
\(588\) 142.000 135.100i 0.241497 0.229762i
\(589\) 230.363i 0.391108i
\(590\) 571.577i 0.968774i
\(591\) −180.000 103.923i −0.304569 0.175843i
\(592\) 120.000 69.2820i 0.202703 0.117030i
\(593\) −107.500 186.195i −0.181282 0.313989i 0.761036 0.648710i \(-0.224691\pi\)
−0.942317 + 0.334721i \(0.891358\pi\)
\(594\) −289.000 + 500.563i −0.486532 + 0.842698i
\(595\) −900.000 129.904i −1.51261 0.218326i
\(596\) −18.0000 + 10.3923i −0.0302013 + 0.0174368i
\(597\) 55.5000 32.0429i 0.0929648 0.0536733i
\(598\) 72.0000 + 124.708i 0.120401 + 0.208541i
\(599\) 244.500 + 141.162i 0.408180 + 0.235663i 0.690008 0.723802i \(-0.257607\pi\)
−0.281827 + 0.959465i \(0.590941\pi\)
\(600\) −8.00000 13.8564i −0.0133333 0.0230940i
\(601\) 266.000 0.442596 0.221298 0.975206i \(-0.428971\pi\)
0.221298 + 0.975206i \(0.428971\pi\)
\(602\) 28.0000 193.990i 0.0465116 0.322242i
\(603\) −136.000 −0.225539
\(604\) −126.000 72.7461i −0.208609 0.120441i
\(605\) 756.000 + 436.477i 1.24959 + 0.721449i
\(606\) 135.000 77.9423i 0.222772 0.128618i
\(607\) −571.500 + 329.956i −0.941516 + 0.543584i −0.890435 0.455110i \(-0.849600\pi\)
−0.0510805 + 0.998695i \(0.516267\pi\)
\(608\) −112.000 193.990i −0.184211 0.319062i
\(609\) 60.0000 76.2102i 0.0985222 0.125140i
\(610\) 117.000 202.650i 0.191803 0.332213i
\(611\) 348.000 + 602.754i 0.569558 + 0.986504i
\(612\) 800.000 1.30719
\(613\) −604.500 349.008i −0.986134 0.569345i −0.0820174 0.996631i \(-0.526136\pi\)
−0.904116 + 0.427286i \(0.859470\pi\)
\(614\) 548.000 0.892508
\(615\) 135.100i 0.219675i
\(616\) 748.000 + 588.897i 1.21429 + 0.956002i
\(617\) −118.000 −0.191248 −0.0956240 0.995418i \(-0.530485\pi\)
−0.0956240 + 0.995418i \(0.530485\pi\)
\(618\) 322.161i 0.521297i
\(619\) 459.500 795.877i 0.742326 1.28575i −0.209107 0.977893i \(-0.567056\pi\)
0.951434 0.307854i \(-0.0996109\pi\)
\(620\) −684.000 −1.10323
\(621\) −76.5000 + 44.1673i −0.123188 + 0.0711229i
\(622\) 87.0000 + 50.2295i 0.139871 + 0.0807548i
\(623\) 461.500 184.463i 0.740770 0.296089i
\(624\) 192.000 + 110.851i 0.307692 + 0.177646i
\(625\) 335.500 + 581.103i 0.536800 + 0.929765i
\(626\) −409.000 708.409i −0.653355 1.13164i
\(627\) 59.5000 103.057i 0.0948963 0.164365i
\(628\) −1074.00 620.074i −1.71019 0.987379i
\(629\) 216.506i 0.344207i
\(630\) −360.000 + 457.261i −0.571429 + 0.725812i
\(631\) 166.277i 0.263513i −0.991282 0.131757i \(-0.957938\pi\)
0.991282 0.131757i \(-0.0420617\pi\)
\(632\) −516.000 + 297.913i −0.816456 + 0.471381i
\(633\) −151.000 + 261.540i −0.238547 + 0.413175i
\(634\) −327.000 + 188.794i −0.515773 + 0.297782i
\(635\) 432.000 + 748.246i 0.680315 + 1.17834i
\(636\) −318.000 + 183.597i −0.500000 + 0.288675i
\(637\) −192.000 + 651.251i −0.301413 + 1.02237i
\(638\) 408.000 + 235.559i 0.639498 + 0.369215i
\(639\) 0 0
\(640\) 576.000 332.554i 0.900000 0.519615i
\(641\) 0.500000 0.866025i 0.000780031 0.00135105i −0.865635 0.500675i \(-0.833085\pi\)
0.866415 + 0.499324i \(0.166418\pi\)
\(642\) −130.000 −0.202492
\(643\) −514.000 −0.799378 −0.399689 0.916651i \(-0.630882\pi\)
−0.399689 + 0.916651i \(0.630882\pi\)
\(644\) 54.0000 + 135.100i 0.0838509 + 0.209783i
\(645\) 72.7461i 0.112785i
\(646\) −350.000 −0.541796
\(647\) 52.5000 + 30.3109i 0.0811437 + 0.0468484i 0.540023 0.841650i \(-0.318416\pi\)
−0.458879 + 0.888499i \(0.651749\pi\)
\(648\) 220.000 381.051i 0.339506 0.588042i
\(649\) 467.500 + 809.734i 0.720339 + 1.24766i
\(650\) 48.0000 + 27.7128i 0.0738462 + 0.0426351i
\(651\) −85.5000 213.908i −0.131336 0.328584i
\(652\) −34.0000 58.8897i −0.0521472 0.0903217i
\(653\) 283.500 163.679i 0.434150 0.250657i −0.266963 0.963707i \(-0.586020\pi\)
0.701113 + 0.713050i \(0.252687\pi\)
\(654\) 15.0000 8.66025i 0.0229358 0.0132420i
\(655\) 76.5000 + 44.1673i 0.116794 + 0.0674310i
\(656\) 416.000 0.634146
\(657\) −952.000 −1.44901
\(658\) 261.000 + 652.983i 0.396657 + 0.992376i
\(659\) 542.000 0.822458 0.411229 0.911532i \(-0.365100\pi\)
0.411229 + 0.911532i \(0.365100\pi\)
\(660\) 306.000 + 176.669i 0.463636 + 0.267681i
\(661\) −1024.50 591.495i −1.54992 0.894849i −0.998146 0.0608582i \(-0.980616\pi\)
−0.551778 0.833991i \(1.31395\pi\)
\(662\) −295.000 510.955i −0.445619 0.771835i
\(663\) 300.000 173.205i 0.452489 0.261244i
\(664\) −880.000 −1.32530
\(665\) 157.500 200.052i 0.236842 0.300830i
\(666\) −120.000 69.2820i −0.180180 0.104027i
\(667\) 36.0000 + 62.3538i 0.0539730 + 0.0934840i
\(668\) 55.4256i 0.0829725i
\(669\) −120.000 69.2820i −0.179372 0.103561i
\(670\) 176.669i 0.263685i
\(671\) 382.783i 0.570467i
\(672\) 176.000 + 138.564i 0.261905 + 0.206197i
\(673\) 218.000 0.323923 0.161961 0.986797i \(-0.448218\pi\)
0.161961 + 0.986797i \(0.448218\pi\)
\(674\) −52.0000 −0.0771513
\(675\) −17.0000 + 29.4449i −0.0251852 + 0.0436220i
\(676\) −92.0000 −0.136095
\(677\) −556.500 + 321.295i −0.822009 + 0.474587i −0.851109 0.524989i \(-0.824069\pi\)
0.0290999 + 0.999577i \(0.490736\pi\)
\(678\) 122.000 211.310i 0.179941 0.311667i
\(679\) 22.0000 152.420i 0.0324006 0.224478i
\(680\) 1039.23i 1.52828i
\(681\) 27.5000 + 47.6314i 0.0403818 + 0.0699433i
\(682\) 969.000 559.452i 1.42082 0.820311i
\(683\) 183.500 317.831i 0.268668 0.465346i −0.699850 0.714289i \(-0.746750\pi\)
0.968518 + 0.248943i \(0.0800833\pi\)
\(684\) −112.000 + 193.990i −0.163743 + 0.283611i
\(685\) 753.442i 1.09992i
\(686\) −286.000 + 623.538i −0.416910 + 0.908948i
\(687\) 327.358i 0.476503i
\(688\) 224.000 0.325581
\(689\) 636.000 1101.58i 0.923077 1.59882i
\(690\) 27.0000 + 46.7654i 0.0391304 + 0.0677759i
\(691\) −248.500 430.415i −0.359624 0.622887i 0.628274 0.777992i \(-0.283762\pi\)
−0.987898 + 0.155105i \(0.950428\pi\)
\(692\) 366.000 211.310i 0.528902 0.305362i
\(693\) 136.000 942.236i 0.196248 1.35965i
\(694\) 377.000 652.983i 0.543228 0.940898i
\(695\) 369.000 213.042i 0.530935 0.306536i
\(696\) 96.0000 + 55.4256i 0.137931 + 0.0796345i
\(697\) 325.000 562.917i 0.466284 0.807628i
\(698\) 193.990i 0.277922i
\(699\) −385.000 −0.550787
\(700\) 44.0000 + 34.6410i 0.0628571 + 0.0494872i
\(701\) 332.554i 0.474399i −0.971461 0.237200i \(-0.923770\pi\)
0.971461 0.237200i \(-0.0762295\pi\)
\(702\) 471.118i 0.671108i
\(703\) 52.5000 + 30.3109i 0.0746799 + 0.0431165i
\(704\) −544.000 + 942.236i −0.772727 + 1.33840i
\(705\) 130.500 + 226.033i 0.185106 + 0.320614i
\(706\) 503.000 871.222i 0.712465 1.23402i
\(707\) −337.500 + 428.683i −0.477369 + 0.606340i
\(708\) 110.000 + 190.526i 0.155367 + 0.269104i
\(709\) 343.500 198.320i 0.484485 0.279718i −0.237799 0.971314i \(-0.576426\pi\)
0.722284 + 0.691597i \(0.243092\pi\)
\(710\) 0 0
\(711\) 516.000 + 297.913i 0.725738 + 0.419005i
\(712\) 284.000 + 491.902i 0.398876 + 0.690874i
\(713\) 171.000 0.239832
\(714\) 325.000 129.904i 0.455182 0.181938i
\(715\) −1224.00 −1.71189
\(716\) −178.000 + 308.305i −0.248603 + 0.430594i
\(717\) 372.000 + 214.774i 0.518828 + 0.299546i
\(718\) −321.000 + 185.329i −0.447075 + 0.258119i
\(719\) −55.5000 + 32.0429i −0.0771905 + 0.0445660i −0.538098 0.842882i \(-0.680857\pi\)
0.460908 + 0.887448i \(0.347524\pi\)
\(720\) −576.000 332.554i −0.800000 0.461880i
\(721\) −418.500 1047.02i −0.580444 1.45218i
\(722\) −312.000 + 540.400i −0.432133 + 0.748476i
\(723\) 72.5000 + 125.574i 0.100277 + 0.173684i
\(724\) 997.661i 1.37799i
\(725\) 24.0000 + 13.8564i 0.0331034 + 0.0191123i
\(726\) −336.000 −0.462810
\(727\) 55.4256i 0.0762388i 0.999273 + 0.0381194i \(0.0121367\pi\)
−0.999273 + 0.0381194i \(0.987863\pi\)
\(728\) −768.000 110.851i −1.05495 0.152268i
\(729\) −287.000 −0.393690
\(730\) 1236.68i 1.69409i
\(731\) 175.000 303.109i 0.239398 0.414650i
\(732\) 90.0666i 0.123042i
\(733\) 715.500 413.094i 0.976126 0.563566i 0.0750273 0.997181i \(-0.476096\pi\)
0.901098 + 0.433615i \(0.142762\pi\)
\(734\) −513.000 296.181i −0.698910 0.403516i
\(735\) −72.0000 + 244.219i −0.0979592 + 0.332271i
\(736\) −144.000 + 83.1384i −0.195652 + 0.112960i
\(737\) −144.500 250.281i −0.196065 0.339595i
\(738\) −208.000 360.267i −0.281843 0.488166i
\(739\) −356.500 + 617.476i −0.482409 + 0.835556i −0.999796 0.0201950i \(-0.993571\pi\)
0.517387 + 0.855751i \(0.326905\pi\)
\(740\) −90.0000 + 155.885i −0.121622 + 0.210655i
\(741\) 96.9948i 0.130897i
\(742\) 795.000 1009.79i 1.07143 1.36090i
\(743\) 637.395i 0.857866i −0.903336 0.428933i \(-0.858890\pi\)
0.903336 0.428933i \(-0.141110\pi\)
\(744\) 228.000 131.636i 0.306452 0.176930i
\(745\) 13.5000 23.3827i 0.0181208 0.0313862i
\(746\) −207.000 + 119.512i −0.277480 + 0.160203i
\(747\) 440.000 + 762.102i 0.589023 + 1.02022i
\(748\) 850.000 + 1472.24i 1.13636 + 1.96824i
\(749\) 422.500 168.875i 0.564085 0.225467i
\(750\) −207.000 119.512i −0.276000 0.159349i
\(751\) 1012.50 584.567i 1.34820 0.778385i 0.360208 0.932872i \(-0.382706\pi\)
0.987995 + 0.154487i \(0.0493725\pi\)
\(752\) −696.000 + 401.836i −0.925532 + 0.534356i
\(753\) 29.0000 50.2295i 0.0385126 0.0667058i
\(754\) −384.000 −0.509284
\(755\) 189.000 0.250331
\(756\) 68.0000 471.118i 0.0899471 0.623172i
\(757\) 1039.23i 1.37283i −0.727211 0.686414i \(-0.759184\pi\)
0.727211 0.686414i \(-0.240816\pi\)
\(758\) 1268.00 1.67282
\(759\) −76.5000 44.1673i −0.100791 0.0581914i
\(760\) 252.000 + 145.492i 0.331579 + 0.191437i
\(761\) −431.500 747.380i −0.567017 0.982102i −0.996859 0.0791982i \(-0.974764\pi\)
0.429842 0.902904i \(-0.358569\pi\)
\(762\) −288.000 166.277i −0.377953 0.218211i
\(763\) −37.5000 + 47.6314i −0.0491481 + 0.0624265i
\(764\) −750.000 + 433.013i −0.981675 + 0.566771i
\(765\) −900.000 + 519.615i −1.17647 + 0.679236i
\(766\) 423.000 244.219i 0.552219 0.318824i
\(767\) −660.000 381.051i −0.860495 0.496807i
\(768\) −128.000 + 221.703i −0.166667 + 0.288675i
\(769\) 410.000 0.533160 0.266580 0.963813i \(-0.414106\pi\)
0.266580 + 0.963813i \(0.414106\pi\)
\(770\) −1224.00 176.669i −1.58961 0.229440i
\(771\) 119.000 0.154345
\(772\) 146.000 252.879i 0.189119 0.327564i
\(773\) 691.500 + 399.238i 0.894567 + 0.516478i 0.875433 0.483339i \(-0.160576\pi\)
0.0191332 + 0.999817i \(0.493909\pi\)
\(774\) −112.000 193.990i −0.144703 0.250633i
\(775\) 57.0000 32.9090i 0.0735484 0.0424632i
\(776\) 176.000 0.226804
\(777\) −60.0000 8.66025i −0.0772201 0.0111458i
\(778\) 1017.00 + 587.165i 1.30720 + 0.754711i
\(779\) 91.0000 + 157.617i 0.116816 + 0.202332i
\(780\) −288.000 −0.369231
\(781\) 0 0
\(782\) 259.808i 0.332235i
\(783\) 235.559i 0.300842i
\(784\) −752.000 221.703i −0.959184 0.282784i
\(785\) 1611.00 2.05223
\(786\) −34.0000 −0.0432570