Properties

Label 74.3.d.b.31.1
Level $74$
Weight $3$
Character 74.31
Analytic conductor $2.016$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 74.d (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.01635395627\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 31.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 74.31
Dual form 74.3.d.b.43.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +4.00000i q^{3} +2.00000i q^{4} +(3.00000 - 3.00000i) q^{5} +(-4.00000 + 4.00000i) q^{6} -4.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} -7.00000 q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +4.00000i q^{3} +2.00000i q^{4} +(3.00000 - 3.00000i) q^{5} +(-4.00000 + 4.00000i) q^{6} -4.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} -7.00000 q^{9} +6.00000 q^{10} +4.00000i q^{11} -8.00000 q^{12} +(3.00000 - 3.00000i) q^{13} +(-4.00000 - 4.00000i) q^{14} +(12.0000 + 12.0000i) q^{15} -4.00000 q^{16} +(23.0000 - 23.0000i) q^{17} +(-7.00000 - 7.00000i) q^{18} +(10.0000 - 10.0000i) q^{19} +(6.00000 + 6.00000i) q^{20} -16.0000i q^{21} +(-4.00000 + 4.00000i) q^{22} +(-10.0000 + 10.0000i) q^{23} +(-8.00000 - 8.00000i) q^{24} +7.00000i q^{25} +6.00000 q^{26} +8.00000i q^{27} -8.00000i q^{28} +(-19.0000 - 19.0000i) q^{29} +24.0000i q^{30} +(-18.0000 - 18.0000i) q^{31} +(-4.00000 - 4.00000i) q^{32} -16.0000 q^{33} +46.0000 q^{34} +(-12.0000 + 12.0000i) q^{35} -14.0000i q^{36} -37.0000i q^{37} +20.0000 q^{38} +(12.0000 + 12.0000i) q^{39} +12.0000i q^{40} +74.0000i q^{41} +(16.0000 - 16.0000i) q^{42} +(42.0000 - 42.0000i) q^{43} -8.00000 q^{44} +(-21.0000 + 21.0000i) q^{45} -20.0000 q^{46} -44.0000 q^{47} -16.0000i q^{48} -33.0000 q^{49} +(-7.00000 + 7.00000i) q^{50} +(92.0000 + 92.0000i) q^{51} +(6.00000 + 6.00000i) q^{52} -80.0000 q^{53} +(-8.00000 + 8.00000i) q^{54} +(12.0000 + 12.0000i) q^{55} +(8.00000 - 8.00000i) q^{56} +(40.0000 + 40.0000i) q^{57} -38.0000i q^{58} +(-54.0000 + 54.0000i) q^{59} +(-24.0000 + 24.0000i) q^{60} +(-3.00000 - 3.00000i) q^{61} -36.0000i q^{62} +28.0000 q^{63} -8.00000i q^{64} -18.0000i q^{65} +(-16.0000 - 16.0000i) q^{66} -12.0000i q^{67} +(46.0000 + 46.0000i) q^{68} +(-40.0000 - 40.0000i) q^{69} -24.0000 q^{70} +124.000 q^{71} +(14.0000 - 14.0000i) q^{72} -10.0000i q^{73} +(37.0000 - 37.0000i) q^{74} -28.0000 q^{75} +(20.0000 + 20.0000i) q^{76} -16.0000i q^{77} +24.0000i q^{78} +(14.0000 - 14.0000i) q^{79} +(-12.0000 + 12.0000i) q^{80} -95.0000 q^{81} +(-74.0000 + 74.0000i) q^{82} -64.0000 q^{83} +32.0000 q^{84} -138.000i q^{85} +84.0000 q^{86} +(76.0000 - 76.0000i) q^{87} +(-8.00000 - 8.00000i) q^{88} +(17.0000 + 17.0000i) q^{89} -42.0000 q^{90} +(-12.0000 + 12.0000i) q^{91} +(-20.0000 - 20.0000i) q^{92} +(72.0000 - 72.0000i) q^{93} +(-44.0000 - 44.0000i) q^{94} -60.0000i q^{95} +(16.0000 - 16.0000i) q^{96} +(129.000 - 129.000i) q^{97} +(-33.0000 - 33.0000i) q^{98} -28.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + 6 q^{5} - 8 q^{6} - 8 q^{7} - 4 q^{8} - 14 q^{9} + O(q^{10}) \) \( 2 q + 2 q^{2} + 6 q^{5} - 8 q^{6} - 8 q^{7} - 4 q^{8} - 14 q^{9} + 12 q^{10} - 16 q^{12} + 6 q^{13} - 8 q^{14} + 24 q^{15} - 8 q^{16} + 46 q^{17} - 14 q^{18} + 20 q^{19} + 12 q^{20} - 8 q^{22} - 20 q^{23} - 16 q^{24} + 12 q^{26} - 38 q^{29} - 36 q^{31} - 8 q^{32} - 32 q^{33} + 92 q^{34} - 24 q^{35} + 40 q^{38} + 24 q^{39} + 32 q^{42} + 84 q^{43} - 16 q^{44} - 42 q^{45} - 40 q^{46} - 88 q^{47} - 66 q^{49} - 14 q^{50} + 184 q^{51} + 12 q^{52} - 160 q^{53} - 16 q^{54} + 24 q^{55} + 16 q^{56} + 80 q^{57} - 108 q^{59} - 48 q^{60} - 6 q^{61} + 56 q^{63} - 32 q^{66} + 92 q^{68} - 80 q^{69} - 48 q^{70} + 248 q^{71} + 28 q^{72} + 74 q^{74} - 56 q^{75} + 40 q^{76} + 28 q^{79} - 24 q^{80} - 190 q^{81} - 148 q^{82} - 128 q^{83} + 64 q^{84} + 168 q^{86} + 152 q^{87} - 16 q^{88} + 34 q^{89} - 84 q^{90} - 24 q^{91} - 40 q^{92} + 144 q^{93} - 88 q^{94} + 32 q^{96} + 258 q^{97} - 66 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) 4.00000i 1.33333i 0.745356 + 0.666667i \(0.232280\pi\)
−0.745356 + 0.666667i \(0.767720\pi\)
\(4\) 2.00000i 0.500000i
\(5\) 3.00000 3.00000i 0.600000 0.600000i −0.340312 0.940312i \(-0.610533\pi\)
0.940312 + 0.340312i \(0.110533\pi\)
\(6\) −4.00000 + 4.00000i −0.666667 + 0.666667i
\(7\) −4.00000 −0.571429 −0.285714 0.958315i \(-0.592231\pi\)
−0.285714 + 0.958315i \(0.592231\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) −7.00000 −0.777778
\(10\) 6.00000 0.600000
\(11\) 4.00000i 0.363636i 0.983332 + 0.181818i \(0.0581982\pi\)
−0.983332 + 0.181818i \(0.941802\pi\)
\(12\) −8.00000 −0.666667
\(13\) 3.00000 3.00000i 0.230769 0.230769i −0.582245 0.813014i \(-0.697825\pi\)
0.813014 + 0.582245i \(0.197825\pi\)
\(14\) −4.00000 4.00000i −0.285714 0.285714i
\(15\) 12.0000 + 12.0000i 0.800000 + 0.800000i
\(16\) −4.00000 −0.250000
\(17\) 23.0000 23.0000i 1.35294 1.35294i 0.470588 0.882353i \(-0.344042\pi\)
0.882353 0.470588i \(-0.155958\pi\)
\(18\) −7.00000 7.00000i −0.388889 0.388889i
\(19\) 10.0000 10.0000i 0.526316 0.526316i −0.393156 0.919472i \(-0.628617\pi\)
0.919472 + 0.393156i \(0.128617\pi\)
\(20\) 6.00000 + 6.00000i 0.300000 + 0.300000i
\(21\) 16.0000i 0.761905i
\(22\) −4.00000 + 4.00000i −0.181818 + 0.181818i
\(23\) −10.0000 + 10.0000i −0.434783 + 0.434783i −0.890252 0.455469i \(-0.849472\pi\)
0.455469 + 0.890252i \(0.349472\pi\)
\(24\) −8.00000 8.00000i −0.333333 0.333333i
\(25\) 7.00000i 0.280000i
\(26\) 6.00000 0.230769
\(27\) 8.00000i 0.296296i
\(28\) 8.00000i 0.285714i
\(29\) −19.0000 19.0000i −0.655172 0.655172i 0.299061 0.954234i \(-0.403326\pi\)
−0.954234 + 0.299061i \(0.903326\pi\)
\(30\) 24.0000i 0.800000i
\(31\) −18.0000 18.0000i −0.580645 0.580645i 0.354435 0.935081i \(-0.384673\pi\)
−0.935081 + 0.354435i \(0.884673\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) −16.0000 −0.484848
\(34\) 46.0000 1.35294
\(35\) −12.0000 + 12.0000i −0.342857 + 0.342857i
\(36\) 14.0000i 0.388889i
\(37\) 37.0000i 1.00000i
\(38\) 20.0000 0.526316
\(39\) 12.0000 + 12.0000i 0.307692 + 0.307692i
\(40\) 12.0000i 0.300000i
\(41\) 74.0000i 1.80488i 0.430818 + 0.902439i \(0.358225\pi\)
−0.430818 + 0.902439i \(0.641775\pi\)
\(42\) 16.0000 16.0000i 0.380952 0.380952i
\(43\) 42.0000 42.0000i 0.976744 0.976744i −0.0229915 0.999736i \(-0.507319\pi\)
0.999736 + 0.0229915i \(0.00731906\pi\)
\(44\) −8.00000 −0.181818
\(45\) −21.0000 + 21.0000i −0.466667 + 0.466667i
\(46\) −20.0000 −0.434783
\(47\) −44.0000 −0.936170 −0.468085 0.883683i \(-0.655056\pi\)
−0.468085 + 0.883683i \(0.655056\pi\)
\(48\) 16.0000i 0.333333i
\(49\) −33.0000 −0.673469
\(50\) −7.00000 + 7.00000i −0.140000 + 0.140000i
\(51\) 92.0000 + 92.0000i 1.80392 + 1.80392i
\(52\) 6.00000 + 6.00000i 0.115385 + 0.115385i
\(53\) −80.0000 −1.50943 −0.754717 0.656051i \(-0.772226\pi\)
−0.754717 + 0.656051i \(0.772226\pi\)
\(54\) −8.00000 + 8.00000i −0.148148 + 0.148148i
\(55\) 12.0000 + 12.0000i 0.218182 + 0.218182i
\(56\) 8.00000 8.00000i 0.142857 0.142857i
\(57\) 40.0000 + 40.0000i 0.701754 + 0.701754i
\(58\) 38.0000i 0.655172i
\(59\) −54.0000 + 54.0000i −0.915254 + 0.915254i −0.996679 0.0814252i \(-0.974053\pi\)
0.0814252 + 0.996679i \(0.474053\pi\)
\(60\) −24.0000 + 24.0000i −0.400000 + 0.400000i
\(61\) −3.00000 3.00000i −0.0491803 0.0491803i 0.682089 0.731269i \(-0.261072\pi\)
−0.731269 + 0.682089i \(0.761072\pi\)
\(62\) 36.0000i 0.580645i
\(63\) 28.0000 0.444444
\(64\) 8.00000i 0.125000i
\(65\) 18.0000i 0.276923i
\(66\) −16.0000 16.0000i −0.242424 0.242424i
\(67\) 12.0000i 0.179104i −0.995982 0.0895522i \(-0.971456\pi\)
0.995982 0.0895522i \(-0.0285436\pi\)
\(68\) 46.0000 + 46.0000i 0.676471 + 0.676471i
\(69\) −40.0000 40.0000i −0.579710 0.579710i
\(70\) −24.0000 −0.342857
\(71\) 124.000 1.74648 0.873239 0.487291i \(-0.162015\pi\)
0.873239 + 0.487291i \(0.162015\pi\)
\(72\) 14.0000 14.0000i 0.194444 0.194444i
\(73\) 10.0000i 0.136986i −0.997652 0.0684932i \(-0.978181\pi\)
0.997652 0.0684932i \(-0.0218191\pi\)
\(74\) 37.0000 37.0000i 0.500000 0.500000i
\(75\) −28.0000 −0.373333
\(76\) 20.0000 + 20.0000i 0.263158 + 0.263158i
\(77\) 16.0000i 0.207792i
\(78\) 24.0000i 0.307692i
\(79\) 14.0000 14.0000i 0.177215 0.177215i −0.612926 0.790141i \(-0.710007\pi\)
0.790141 + 0.612926i \(0.210007\pi\)
\(80\) −12.0000 + 12.0000i −0.150000 + 0.150000i
\(81\) −95.0000 −1.17284
\(82\) −74.0000 + 74.0000i −0.902439 + 0.902439i
\(83\) −64.0000 −0.771084 −0.385542 0.922690i \(-0.625986\pi\)
−0.385542 + 0.922690i \(0.625986\pi\)
\(84\) 32.0000 0.380952
\(85\) 138.000i 1.62353i
\(86\) 84.0000 0.976744
\(87\) 76.0000 76.0000i 0.873563 0.873563i
\(88\) −8.00000 8.00000i −0.0909091 0.0909091i
\(89\) 17.0000 + 17.0000i 0.191011 + 0.191011i 0.796133 0.605122i \(-0.206876\pi\)
−0.605122 + 0.796133i \(0.706876\pi\)
\(90\) −42.0000 −0.466667
\(91\) −12.0000 + 12.0000i −0.131868 + 0.131868i
\(92\) −20.0000 20.0000i −0.217391 0.217391i
\(93\) 72.0000 72.0000i 0.774194 0.774194i
\(94\) −44.0000 44.0000i −0.468085 0.468085i
\(95\) 60.0000i 0.631579i
\(96\) 16.0000 16.0000i 0.166667 0.166667i
\(97\) 129.000 129.000i 1.32990 1.32990i 0.424442 0.905455i \(-0.360470\pi\)
0.905455 0.424442i \(-0.139530\pi\)
\(98\) −33.0000 33.0000i −0.336735 0.336735i
\(99\) 28.0000i 0.282828i
\(100\) −14.0000 −0.140000
\(101\) 118.000i 1.16832i 0.811640 + 0.584158i \(0.198575\pi\)
−0.811640 + 0.584158i \(0.801425\pi\)
\(102\) 184.000i 1.80392i
\(103\) −42.0000 42.0000i −0.407767 0.407767i 0.473192 0.880959i \(-0.343102\pi\)
−0.880959 + 0.473192i \(0.843102\pi\)
\(104\) 12.0000i 0.115385i
\(105\) −48.0000 48.0000i −0.457143 0.457143i
\(106\) −80.0000 80.0000i −0.754717 0.754717i
\(107\) −24.0000 −0.224299 −0.112150 0.993691i \(-0.535774\pi\)
−0.112150 + 0.993691i \(0.535774\pi\)
\(108\) −16.0000 −0.148148
\(109\) −91.0000 + 91.0000i −0.834862 + 0.834862i −0.988177 0.153315i \(-0.951005\pi\)
0.153315 + 0.988177i \(0.451005\pi\)
\(110\) 24.0000i 0.218182i
\(111\) 148.000 1.33333
\(112\) 16.0000 0.142857
\(113\) 7.00000 + 7.00000i 0.0619469 + 0.0619469i 0.737402 0.675455i \(-0.236053\pi\)
−0.675455 + 0.737402i \(0.736053\pi\)
\(114\) 80.0000i 0.701754i
\(115\) 60.0000i 0.521739i
\(116\) 38.0000 38.0000i 0.327586 0.327586i
\(117\) −21.0000 + 21.0000i −0.179487 + 0.179487i
\(118\) −108.000 −0.915254
\(119\) −92.0000 + 92.0000i −0.773109 + 0.773109i
\(120\) −48.0000 −0.400000
\(121\) 105.000 0.867769
\(122\) 6.00000i 0.0491803i
\(123\) −296.000 −2.40650
\(124\) 36.0000 36.0000i 0.290323 0.290323i
\(125\) 96.0000 + 96.0000i 0.768000 + 0.768000i
\(126\) 28.0000 + 28.0000i 0.222222 + 0.222222i
\(127\) 76.0000 0.598425 0.299213 0.954186i \(-0.403276\pi\)
0.299213 + 0.954186i \(0.403276\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 168.000 + 168.000i 1.30233 + 1.30233i
\(130\) 18.0000 18.0000i 0.138462 0.138462i
\(131\) 70.0000 + 70.0000i 0.534351 + 0.534351i 0.921864 0.387513i \(-0.126666\pi\)
−0.387513 + 0.921864i \(0.626666\pi\)
\(132\) 32.0000i 0.242424i
\(133\) −40.0000 + 40.0000i −0.300752 + 0.300752i
\(134\) 12.0000 12.0000i 0.0895522 0.0895522i
\(135\) 24.0000 + 24.0000i 0.177778 + 0.177778i
\(136\) 92.0000i 0.676471i
\(137\) 216.000 1.57664 0.788321 0.615264i \(-0.210951\pi\)
0.788321 + 0.615264i \(0.210951\pi\)
\(138\) 80.0000i 0.579710i
\(139\) 180.000i 1.29496i 0.762081 + 0.647482i \(0.224178\pi\)
−0.762081 + 0.647482i \(0.775822\pi\)
\(140\) −24.0000 24.0000i −0.171429 0.171429i
\(141\) 176.000i 1.24823i
\(142\) 124.000 + 124.000i 0.873239 + 0.873239i
\(143\) 12.0000 + 12.0000i 0.0839161 + 0.0839161i
\(144\) 28.0000 0.194444
\(145\) −114.000 −0.786207
\(146\) 10.0000 10.0000i 0.0684932 0.0684932i
\(147\) 132.000i 0.897959i
\(148\) 74.0000 0.500000
\(149\) −34.0000 −0.228188 −0.114094 0.993470i \(-0.536396\pi\)
−0.114094 + 0.993470i \(0.536396\pi\)
\(150\) −28.0000 28.0000i −0.186667 0.186667i
\(151\) 72.0000i 0.476821i −0.971164 0.238411i \(-0.923374\pi\)
0.971164 0.238411i \(-0.0766264\pi\)
\(152\) 40.0000i 0.263158i
\(153\) −161.000 + 161.000i −1.05229 + 1.05229i
\(154\) 16.0000 16.0000i 0.103896 0.103896i
\(155\) −108.000 −0.696774
\(156\) −24.0000 + 24.0000i −0.153846 + 0.153846i
\(157\) −14.0000 −0.0891720 −0.0445860 0.999006i \(-0.514197\pi\)
−0.0445860 + 0.999006i \(0.514197\pi\)
\(158\) 28.0000 0.177215
\(159\) 320.000i 2.01258i
\(160\) −24.0000 −0.150000
\(161\) 40.0000 40.0000i 0.248447 0.248447i
\(162\) −95.0000 95.0000i −0.586420 0.586420i
\(163\) −66.0000 66.0000i −0.404908 0.404908i 0.475051 0.879959i \(-0.342430\pi\)
−0.879959 + 0.475051i \(0.842430\pi\)
\(164\) −148.000 −0.902439
\(165\) −48.0000 + 48.0000i −0.290909 + 0.290909i
\(166\) −64.0000 64.0000i −0.385542 0.385542i
\(167\) −230.000 + 230.000i −1.37725 + 1.37725i −0.528003 + 0.849242i \(0.677059\pi\)
−0.849242 + 0.528003i \(0.822941\pi\)
\(168\) 32.0000 + 32.0000i 0.190476 + 0.190476i
\(169\) 151.000i 0.893491i
\(170\) 138.000 138.000i 0.811765 0.811765i
\(171\) −70.0000 + 70.0000i −0.409357 + 0.409357i
\(172\) 84.0000 + 84.0000i 0.488372 + 0.488372i
\(173\) 88.0000i 0.508671i −0.967116 0.254335i \(-0.918143\pi\)
0.967116 0.254335i \(-0.0818567\pi\)
\(174\) 152.000 0.873563
\(175\) 28.0000i 0.160000i
\(176\) 16.0000i 0.0909091i
\(177\) −216.000 216.000i −1.22034 1.22034i
\(178\) 34.0000i 0.191011i
\(179\) −166.000 166.000i −0.927374 0.927374i 0.0701614 0.997536i \(-0.477649\pi\)
−0.997536 + 0.0701614i \(0.977649\pi\)
\(180\) −42.0000 42.0000i −0.233333 0.233333i
\(181\) 304.000 1.67956 0.839779 0.542928i \(-0.182684\pi\)
0.839779 + 0.542928i \(0.182684\pi\)
\(182\) −24.0000 −0.131868
\(183\) 12.0000 12.0000i 0.0655738 0.0655738i
\(184\) 40.0000i 0.217391i
\(185\) −111.000 111.000i −0.600000 0.600000i
\(186\) 144.000 0.774194
\(187\) 92.0000 + 92.0000i 0.491979 + 0.491979i
\(188\) 88.0000i 0.468085i
\(189\) 32.0000i 0.169312i
\(190\) 60.0000 60.0000i 0.315789 0.315789i
\(191\) 186.000 186.000i 0.973822 0.973822i −0.0258440 0.999666i \(-0.508227\pi\)
0.999666 + 0.0258440i \(0.00822732\pi\)
\(192\) 32.0000 0.166667
\(193\) −9.00000 + 9.00000i −0.0466321 + 0.0466321i −0.730038 0.683406i \(-0.760498\pi\)
0.683406 + 0.730038i \(0.260498\pi\)
\(194\) 258.000 1.32990
\(195\) 72.0000 0.369231
\(196\) 66.0000i 0.336735i
\(197\) 34.0000 0.172589 0.0862944 0.996270i \(-0.472497\pi\)
0.0862944 + 0.996270i \(0.472497\pi\)
\(198\) 28.0000 28.0000i 0.141414 0.141414i
\(199\) 46.0000 + 46.0000i 0.231156 + 0.231156i 0.813175 0.582019i \(-0.197737\pi\)
−0.582019 + 0.813175i \(0.697737\pi\)
\(200\) −14.0000 14.0000i −0.0700000 0.0700000i
\(201\) 48.0000 0.238806
\(202\) −118.000 + 118.000i −0.584158 + 0.584158i
\(203\) 76.0000 + 76.0000i 0.374384 + 0.374384i
\(204\) −184.000 + 184.000i −0.901961 + 0.901961i
\(205\) 222.000 + 222.000i 1.08293 + 1.08293i
\(206\) 84.0000i 0.407767i
\(207\) 70.0000 70.0000i 0.338164 0.338164i
\(208\) −12.0000 + 12.0000i −0.0576923 + 0.0576923i
\(209\) 40.0000 + 40.0000i 0.191388 + 0.191388i
\(210\) 96.0000i 0.457143i
\(211\) −208.000 −0.985782 −0.492891 0.870091i \(-0.664060\pi\)
−0.492891 + 0.870091i \(0.664060\pi\)
\(212\) 160.000i 0.754717i
\(213\) 496.000i 2.32864i
\(214\) −24.0000 24.0000i −0.112150 0.112150i
\(215\) 252.000i 1.17209i
\(216\) −16.0000 16.0000i −0.0740741 0.0740741i
\(217\) 72.0000 + 72.0000i 0.331797 + 0.331797i
\(218\) −182.000 −0.834862
\(219\) 40.0000 0.182648
\(220\) −24.0000 + 24.0000i −0.109091 + 0.109091i
\(221\) 138.000i 0.624434i
\(222\) 148.000 + 148.000i 0.666667 + 0.666667i
\(223\) −124.000 −0.556054 −0.278027 0.960573i \(-0.589680\pi\)
−0.278027 + 0.960573i \(0.589680\pi\)
\(224\) 16.0000 + 16.0000i 0.0714286 + 0.0714286i
\(225\) 49.0000i 0.217778i
\(226\) 14.0000i 0.0619469i
\(227\) −90.0000 + 90.0000i −0.396476 + 0.396476i −0.876988 0.480512i \(-0.840451\pi\)
0.480512 + 0.876988i \(0.340451\pi\)
\(228\) −80.0000 + 80.0000i −0.350877 + 0.350877i
\(229\) −2.00000 −0.00873362 −0.00436681 0.999990i \(-0.501390\pi\)
−0.00436681 + 0.999990i \(0.501390\pi\)
\(230\) −60.0000 + 60.0000i −0.260870 + 0.260870i
\(231\) 64.0000 0.277056
\(232\) 76.0000 0.327586
\(233\) 42.0000i 0.180258i 0.995930 + 0.0901288i \(0.0287279\pi\)
−0.995930 + 0.0901288i \(0.971272\pi\)
\(234\) −42.0000 −0.179487
\(235\) −132.000 + 132.000i −0.561702 + 0.561702i
\(236\) −108.000 108.000i −0.457627 0.457627i
\(237\) 56.0000 + 56.0000i 0.236287 + 0.236287i
\(238\) −184.000 −0.773109
\(239\) 22.0000 22.0000i 0.0920502 0.0920502i −0.659582 0.751632i \(-0.729267\pi\)
0.751632 + 0.659582i \(0.229267\pi\)
\(240\) −48.0000 48.0000i −0.200000 0.200000i
\(241\) −175.000 + 175.000i −0.726141 + 0.726141i −0.969849 0.243708i \(-0.921636\pi\)
0.243708 + 0.969849i \(0.421636\pi\)
\(242\) 105.000 + 105.000i 0.433884 + 0.433884i
\(243\) 308.000i 1.26749i
\(244\) 6.00000 6.00000i 0.0245902 0.0245902i
\(245\) −99.0000 + 99.0000i −0.404082 + 0.404082i
\(246\) −296.000 296.000i −1.20325 1.20325i
\(247\) 60.0000i 0.242915i
\(248\) 72.0000 0.290323
\(249\) 256.000i 1.02811i
\(250\) 192.000i 0.768000i
\(251\) −198.000 198.000i −0.788845 0.788845i 0.192460 0.981305i \(-0.438353\pi\)
−0.981305 + 0.192460i \(0.938353\pi\)
\(252\) 56.0000i 0.222222i
\(253\) −40.0000 40.0000i −0.158103 0.158103i
\(254\) 76.0000 + 76.0000i 0.299213 + 0.299213i
\(255\) 552.000 2.16471
\(256\) 16.0000 0.0625000
\(257\) −159.000 + 159.000i −0.618677 + 0.618677i −0.945192 0.326515i \(-0.894126\pi\)
0.326515 + 0.945192i \(0.394126\pi\)
\(258\) 336.000i 1.30233i
\(259\) 148.000i 0.571429i
\(260\) 36.0000 0.138462
\(261\) 133.000 + 133.000i 0.509579 + 0.509579i
\(262\) 140.000i 0.534351i
\(263\) 88.0000i 0.334601i −0.985906 0.167300i \(-0.946495\pi\)
0.985906 0.167300i \(-0.0535050\pi\)
\(264\) 32.0000 32.0000i 0.121212 0.121212i
\(265\) −240.000 + 240.000i −0.905660 + 0.905660i
\(266\) −80.0000 −0.300752
\(267\) −68.0000 + 68.0000i −0.254682 + 0.254682i
\(268\) 24.0000 0.0895522
\(269\) 178.000 0.661710 0.330855 0.943682i \(-0.392663\pi\)
0.330855 + 0.943682i \(0.392663\pi\)
\(270\) 48.0000i 0.177778i
\(271\) 404.000 1.49077 0.745387 0.666631i \(-0.232265\pi\)
0.745387 + 0.666631i \(0.232265\pi\)
\(272\) −92.0000 + 92.0000i −0.338235 + 0.338235i
\(273\) −48.0000 48.0000i −0.175824 0.175824i
\(274\) 216.000 + 216.000i 0.788321 + 0.788321i
\(275\) −28.0000 −0.101818
\(276\) 80.0000 80.0000i 0.289855 0.289855i
\(277\) −147.000 147.000i −0.530686 0.530686i 0.390091 0.920776i \(-0.372444\pi\)
−0.920776 + 0.390091i \(0.872444\pi\)
\(278\) −180.000 + 180.000i −0.647482 + 0.647482i
\(279\) 126.000 + 126.000i 0.451613 + 0.451613i
\(280\) 48.0000i 0.171429i
\(281\) 135.000 135.000i 0.480427 0.480427i −0.424841 0.905268i \(-0.639670\pi\)
0.905268 + 0.424841i \(0.139670\pi\)
\(282\) 176.000 176.000i 0.624113 0.624113i
\(283\) −258.000 258.000i −0.911661 0.911661i 0.0847421 0.996403i \(-0.472993\pi\)
−0.996403 + 0.0847421i \(0.972993\pi\)
\(284\) 248.000i 0.873239i
\(285\) 240.000 0.842105
\(286\) 24.0000i 0.0839161i
\(287\) 296.000i 1.03136i
\(288\) 28.0000 + 28.0000i 0.0972222 + 0.0972222i
\(289\) 769.000i 2.66090i
\(290\) −114.000 114.000i −0.393103 0.393103i
\(291\) 516.000 + 516.000i 1.77320 + 1.77320i
\(292\) 20.0000 0.0684932
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 132.000 132.000i 0.448980 0.448980i
\(295\) 324.000i 1.09831i
\(296\) 74.0000 + 74.0000i 0.250000 + 0.250000i
\(297\) −32.0000 −0.107744
\(298\) −34.0000 34.0000i −0.114094 0.114094i
\(299\) 60.0000i 0.200669i
\(300\) 56.0000i 0.186667i
\(301\) −168.000 + 168.000i −0.558140 + 0.558140i
\(302\) 72.0000 72.0000i 0.238411 0.238411i
\(303\) −472.000 −1.55776
\(304\) −40.0000 + 40.0000i −0.131579 + 0.131579i
\(305\) −18.0000 −0.0590164
\(306\) −322.000 −1.05229
\(307\) 364.000i 1.18567i 0.805325 + 0.592834i \(0.201991\pi\)
−0.805325 + 0.592834i \(0.798009\pi\)
\(308\) 32.0000 0.103896
\(309\) 168.000 168.000i 0.543689 0.543689i
\(310\) −108.000 108.000i −0.348387 0.348387i
\(311\) −238.000 238.000i −0.765273 0.765273i 0.211997 0.977270i \(-0.432003\pi\)
−0.977270 + 0.211997i \(0.932003\pi\)
\(312\) −48.0000 −0.153846
\(313\) 87.0000 87.0000i 0.277955 0.277955i −0.554337 0.832292i \(-0.687028\pi\)
0.832292 + 0.554337i \(0.187028\pi\)
\(314\) −14.0000 14.0000i −0.0445860 0.0445860i
\(315\) 84.0000 84.0000i 0.266667 0.266667i
\(316\) 28.0000 + 28.0000i 0.0886076 + 0.0886076i
\(317\) 264.000i 0.832808i 0.909180 + 0.416404i \(0.136710\pi\)
−0.909180 + 0.416404i \(0.863290\pi\)
\(318\) 320.000 320.000i 1.00629 1.00629i
\(319\) 76.0000 76.0000i 0.238245 0.238245i
\(320\) −24.0000 24.0000i −0.0750000 0.0750000i
\(321\) 96.0000i 0.299065i
\(322\) 80.0000 0.248447
\(323\) 460.000i 1.42415i
\(324\) 190.000i 0.586420i
\(325\) 21.0000 + 21.0000i 0.0646154 + 0.0646154i
\(326\) 132.000i 0.404908i
\(327\) −364.000 364.000i −1.11315 1.11315i
\(328\) −148.000 148.000i −0.451220 0.451220i
\(329\) 176.000 0.534954
\(330\) −96.0000 −0.290909
\(331\) −326.000 + 326.000i −0.984894 + 0.984894i −0.999888 0.0149933i \(-0.995227\pi\)
0.0149933 + 0.999888i \(0.495227\pi\)
\(332\) 128.000i 0.385542i
\(333\) 259.000i 0.777778i
\(334\) −460.000 −1.37725
\(335\) −36.0000 36.0000i −0.107463 0.107463i
\(336\) 64.0000i 0.190476i
\(337\) 230.000i 0.682493i −0.939974 0.341246i \(-0.889151\pi\)
0.939974 0.341246i \(-0.110849\pi\)
\(338\) −151.000 + 151.000i −0.446746 + 0.446746i
\(339\) −28.0000 + 28.0000i −0.0825959 + 0.0825959i
\(340\) 276.000 0.811765
\(341\) 72.0000 72.0000i 0.211144 0.211144i
\(342\) −140.000 −0.409357
\(343\) 328.000 0.956268
\(344\) 168.000i 0.488372i
\(345\) −240.000 −0.695652
\(346\) 88.0000 88.0000i 0.254335 0.254335i
\(347\) 362.000 + 362.000i 1.04323 + 1.04323i 0.999022 + 0.0442052i \(0.0140755\pi\)
0.0442052 + 0.999022i \(0.485924\pi\)
\(348\) 152.000 + 152.000i 0.436782 + 0.436782i
\(349\) −48.0000 −0.137536 −0.0687679 0.997633i \(-0.521907\pi\)
−0.0687679 + 0.997633i \(0.521907\pi\)
\(350\) 28.0000 28.0000i 0.0800000 0.0800000i
\(351\) 24.0000 + 24.0000i 0.0683761 + 0.0683761i
\(352\) 16.0000 16.0000i 0.0454545 0.0454545i
\(353\) 343.000 + 343.000i 0.971671 + 0.971671i 0.999610 0.0279383i \(-0.00889418\pi\)
−0.0279383 + 0.999610i \(0.508894\pi\)
\(354\) 432.000i 1.22034i
\(355\) 372.000 372.000i 1.04789 1.04789i
\(356\) −34.0000 + 34.0000i −0.0955056 + 0.0955056i
\(357\) −368.000 368.000i −1.03081 1.03081i
\(358\) 332.000i 0.927374i
\(359\) −404.000 −1.12535 −0.562674 0.826679i \(-0.690227\pi\)
−0.562674 + 0.826679i \(0.690227\pi\)
\(360\) 84.0000i 0.233333i
\(361\) 161.000i 0.445983i
\(362\) 304.000 + 304.000i 0.839779 + 0.839779i
\(363\) 420.000i 1.15702i
\(364\) −24.0000 24.0000i −0.0659341 0.0659341i
\(365\) −30.0000 30.0000i −0.0821918 0.0821918i
\(366\) 24.0000 0.0655738
\(367\) 492.000 1.34060 0.670300 0.742090i \(-0.266166\pi\)
0.670300 + 0.742090i \(0.266166\pi\)
\(368\) 40.0000 40.0000i 0.108696 0.108696i
\(369\) 518.000i 1.40379i
\(370\) 222.000i 0.600000i
\(371\) 320.000 0.862534
\(372\) 144.000 + 144.000i 0.387097 + 0.387097i
\(373\) 488.000i 1.30831i −0.756360 0.654155i \(-0.773024\pi\)
0.756360 0.654155i \(-0.226976\pi\)
\(374\) 184.000i 0.491979i
\(375\) −384.000 + 384.000i −1.02400 + 1.02400i
\(376\) 88.0000 88.0000i 0.234043 0.234043i
\(377\) −114.000 −0.302387
\(378\) 32.0000 32.0000i 0.0846561 0.0846561i
\(379\) −440.000 −1.16095 −0.580475 0.814278i \(-0.697133\pi\)
−0.580475 + 0.814278i \(0.697133\pi\)
\(380\) 120.000 0.315789
\(381\) 304.000i 0.797900i
\(382\) 372.000 0.973822
\(383\) −450.000 + 450.000i −1.17493 + 1.17493i −0.193917 + 0.981018i \(0.562119\pi\)
−0.981018 + 0.193917i \(0.937881\pi\)
\(384\) 32.0000 + 32.0000i 0.0833333 + 0.0833333i
\(385\) −48.0000 48.0000i −0.124675 0.124675i
\(386\) −18.0000 −0.0466321
\(387\) −294.000 + 294.000i −0.759690 + 0.759690i
\(388\) 258.000 + 258.000i 0.664948 + 0.664948i
\(389\) 21.0000 21.0000i 0.0539846 0.0539846i −0.679599 0.733584i \(-0.737846\pi\)
0.733584 + 0.679599i \(0.237846\pi\)
\(390\) 72.0000 + 72.0000i 0.184615 + 0.184615i
\(391\) 460.000i 1.17647i
\(392\) 66.0000 66.0000i 0.168367 0.168367i
\(393\) −280.000 + 280.000i −0.712468 + 0.712468i
\(394\) 34.0000 + 34.0000i 0.0862944 + 0.0862944i
\(395\) 84.0000i 0.212658i
\(396\) 56.0000 0.141414
\(397\) 646.000i 1.62720i −0.581422 0.813602i \(-0.697504\pi\)
0.581422 0.813602i \(-0.302496\pi\)
\(398\) 92.0000i 0.231156i
\(399\) −160.000 160.000i −0.401003 0.401003i
\(400\) 28.0000i 0.0700000i
\(401\) 273.000 + 273.000i 0.680798 + 0.680798i 0.960180 0.279382i \(-0.0901296\pi\)
−0.279382 + 0.960180i \(0.590130\pi\)
\(402\) 48.0000 + 48.0000i 0.119403 + 0.119403i
\(403\) −108.000 −0.267990
\(404\) −236.000 −0.584158
\(405\) −285.000 + 285.000i −0.703704 + 0.703704i
\(406\) 152.000i 0.374384i
\(407\) 148.000 0.363636
\(408\) −368.000 −0.901961
\(409\) 39.0000 + 39.0000i 0.0953545 + 0.0953545i 0.753175 0.657820i \(-0.228521\pi\)
−0.657820 + 0.753175i \(0.728521\pi\)
\(410\) 444.000i 1.08293i
\(411\) 864.000i 2.10219i
\(412\) 84.0000 84.0000i 0.203883 0.203883i
\(413\) 216.000 216.000i 0.523002 0.523002i
\(414\) 140.000 0.338164
\(415\) −192.000 + 192.000i −0.462651 + 0.462651i
\(416\) −24.0000 −0.0576923
\(417\) −720.000 −1.72662
\(418\) 80.0000i 0.191388i
\(419\) 464.000 1.10740 0.553699 0.832717i \(-0.313216\pi\)
0.553699 + 0.832717i \(0.313216\pi\)
\(420\) 96.0000 96.0000i 0.228571 0.228571i
\(421\) −469.000 469.000i −1.11401 1.11401i −0.992602 0.121412i \(-0.961258\pi\)
−0.121412 0.992602i \(-0.538742\pi\)
\(422\) −208.000 208.000i −0.492891 0.492891i
\(423\) 308.000 0.728132
\(424\) 160.000 160.000i 0.377358 0.377358i
\(425\) 161.000 + 161.000i 0.378824 + 0.378824i
\(426\) −496.000 + 496.000i −1.16432 + 1.16432i
\(427\) 12.0000 + 12.0000i 0.0281030 + 0.0281030i
\(428\) 48.0000i 0.112150i
\(429\) −48.0000 + 48.0000i −0.111888 + 0.111888i
\(430\) 252.000 252.000i 0.586047 0.586047i
\(431\) 450.000 + 450.000i 1.04408 + 1.04408i 0.998982 + 0.0451011i \(0.0143610\pi\)
0.0451011 + 0.998982i \(0.485639\pi\)
\(432\) 32.0000i 0.0740741i
\(433\) 200.000 0.461894 0.230947 0.972966i \(-0.425818\pi\)
0.230947 + 0.972966i \(0.425818\pi\)
\(434\) 144.000i 0.331797i
\(435\) 456.000i 1.04828i
\(436\) −182.000 182.000i −0.417431 0.417431i
\(437\) 200.000i 0.457666i
\(438\) 40.0000 + 40.0000i 0.0913242 + 0.0913242i
\(439\) 246.000 + 246.000i 0.560364 + 0.560364i 0.929411 0.369046i \(-0.120316\pi\)
−0.369046 + 0.929411i \(0.620316\pi\)
\(440\) −48.0000 −0.109091
\(441\) 231.000 0.523810
\(442\) 138.000 138.000i 0.312217 0.312217i
\(443\) 668.000i 1.50790i −0.656931 0.753950i \(-0.728146\pi\)
0.656931 0.753950i \(-0.271854\pi\)
\(444\) 296.000i 0.666667i
\(445\) 102.000 0.229213
\(446\) −124.000 124.000i −0.278027 0.278027i
\(447\) 136.000i 0.304251i
\(448\) 32.0000i 0.0714286i
\(449\) 199.000 199.000i 0.443207 0.443207i −0.449881 0.893088i \(-0.648534\pi\)
0.893088 + 0.449881i \(0.148534\pi\)
\(450\) 49.0000 49.0000i 0.108889 0.108889i
\(451\) −296.000 −0.656319
\(452\) −14.0000 + 14.0000i −0.0309735 + 0.0309735i
\(453\) 288.000 0.635762
\(454\) −180.000 −0.396476
\(455\) 72.0000i 0.158242i
\(456\) −160.000 −0.350877
\(457\) −255.000 + 255.000i −0.557987 + 0.557987i −0.928734 0.370747i \(-0.879102\pi\)
0.370747 + 0.928734i \(0.379102\pi\)
\(458\) −2.00000 2.00000i −0.00436681 0.00436681i
\(459\) 184.000 + 184.000i 0.400871 + 0.400871i
\(460\) −120.000 −0.260870
\(461\) −555.000 + 555.000i −1.20390 + 1.20390i −0.230935 + 0.972969i \(0.574179\pi\)
−0.972969 + 0.230935i \(0.925821\pi\)
\(462\) 64.0000 + 64.0000i 0.138528 + 0.138528i
\(463\) 554.000 554.000i 1.19654 1.19654i 0.221350 0.975194i \(-0.428954\pi\)
0.975194 0.221350i \(-0.0710463\pi\)
\(464\) 76.0000 + 76.0000i 0.163793 + 0.163793i
\(465\) 432.000i 0.929032i
\(466\) −42.0000 + 42.0000i −0.0901288 + 0.0901288i
\(467\) 158.000 158.000i 0.338330 0.338330i −0.517409 0.855738i \(-0.673103\pi\)
0.855738 + 0.517409i \(0.173103\pi\)
\(468\) −42.0000 42.0000i −0.0897436 0.0897436i
\(469\) 48.0000i 0.102345i
\(470\) −264.000 −0.561702
\(471\) 56.0000i 0.118896i
\(472\) 216.000i 0.457627i
\(473\) 168.000 + 168.000i 0.355180 + 0.355180i
\(474\) 112.000i 0.236287i
\(475\) 70.0000 + 70.0000i 0.147368 + 0.147368i
\(476\) −184.000 184.000i −0.386555 0.386555i
\(477\) 560.000 1.17400
\(478\) 44.0000 0.0920502
\(479\) 290.000 290.000i 0.605428 0.605428i −0.336320 0.941748i \(-0.609182\pi\)
0.941748 + 0.336320i \(0.109182\pi\)
\(480\) 96.0000i 0.200000i
\(481\) −111.000 111.000i −0.230769 0.230769i
\(482\) −350.000 −0.726141
\(483\) 160.000 + 160.000i 0.331263 + 0.331263i
\(484\) 210.000i 0.433884i
\(485\) 774.000i 1.59588i
\(486\) 308.000 308.000i 0.633745 0.633745i
\(487\) 266.000 266.000i 0.546201 0.546201i −0.379139 0.925340i \(-0.623780\pi\)
0.925340 + 0.379139i \(0.123780\pi\)
\(488\) 12.0000 0.0245902
\(489\) 264.000 264.000i 0.539877 0.539877i
\(490\) −198.000 −0.404082
\(491\) 312.000 0.635438 0.317719 0.948185i \(-0.397083\pi\)
0.317719 + 0.948185i \(0.397083\pi\)
\(492\) 592.000i 1.20325i
\(493\) −874.000 −1.77282
\(494\) 60.0000 60.0000i 0.121457 0.121457i
\(495\) −84.0000 84.0000i −0.169697 0.169697i
\(496\) 72.0000 + 72.0000i 0.145161 + 0.145161i
\(497\) −496.000 −0.997988
\(498\) 256.000 256.000i 0.514056 0.514056i
\(499\) −210.000 210.000i −0.420842 0.420842i 0.464652 0.885493i \(-0.346180\pi\)
−0.885493 + 0.464652i \(0.846180\pi\)
\(500\) −192.000 + 192.000i −0.384000 + 0.384000i
\(501\) −920.000 920.000i −1.83633 1.83633i
\(502\) 396.000i 0.788845i
\(503\) 298.000 298.000i 0.592445 0.592445i −0.345846 0.938291i \(-0.612408\pi\)
0.938291 + 0.345846i \(0.112408\pi\)
\(504\) −56.0000 + 56.0000i −0.111111 + 0.111111i
\(505\) 354.000 + 354.000i 0.700990 + 0.700990i
\(506\) 80.0000i 0.158103i
\(507\) −604.000 −1.19132
\(508\) 152.000i 0.299213i
\(509\) 808.000i 1.58743i 0.608292 + 0.793713i \(0.291855\pi\)
−0.608292 + 0.793713i \(0.708145\pi\)
\(510\) 552.000 + 552.000i 1.08235 + 1.08235i
\(511\) 40.0000i 0.0782779i
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) 80.0000 + 80.0000i 0.155945 + 0.155945i
\(514\) −318.000 −0.618677
\(515\) −252.000 −0.489320
\(516\) −336.000 + 336.000i −0.651163 + 0.651163i
\(517\) 176.000i 0.340426i
\(518\) −148.000 + 148.000i −0.285714 + 0.285714i
\(519\) 352.000 0.678227
\(520\) 36.0000 + 36.0000i 0.0692308 + 0.0692308i
\(521\) 170.000i 0.326296i −0.986602 0.163148i \(-0.947835\pi\)
0.986602 0.163148i \(-0.0521647\pi\)
\(522\) 266.000i 0.509579i
\(523\) 654.000 654.000i 1.25048 1.25048i 0.294972 0.955506i \(-0.404690\pi\)
0.955506 0.294972i \(-0.0953104\pi\)
\(524\) −140.000 + 140.000i −0.267176 + 0.267176i
\(525\) 112.000 0.213333
\(526\) 88.0000 88.0000i 0.167300 0.167300i
\(527\) −828.000 −1.57116
\(528\) 64.0000 0.121212
\(529\) 329.000i 0.621928i
\(530\) −480.000 −0.905660
\(531\) 378.000 378.000i 0.711864 0.711864i
\(532\) −80.0000 80.0000i −0.150376 0.150376i
\(533\) 222.000 + 222.000i 0.416510 + 0.416510i
\(534\) −136.000 −0.254682
\(535\) −72.0000 + 72.0000i −0.134579 + 0.134579i
\(536\) 24.0000 + 24.0000i 0.0447761 + 0.0447761i
\(537\) 664.000 664.000i 1.23650 1.23650i
\(538\) 178.000 + 178.000i 0.330855 + 0.330855i
\(539\) 132.000i 0.244898i
\(540\) −48.0000 + 48.0000i −0.0888889 + 0.0888889i
\(541\) 147.000 147.000i 0.271719 0.271719i −0.558073 0.829792i \(-0.688459\pi\)
0.829792 + 0.558073i \(0.188459\pi\)
\(542\) 404.000 + 404.000i 0.745387 + 0.745387i
\(543\) 1216.00i 2.23941i
\(544\) −184.000 −0.338235
\(545\) 546.000i 1.00183i
\(546\) 96.0000i 0.175824i
\(547\) −294.000 294.000i −0.537477 0.537477i 0.385310 0.922787i \(-0.374095\pi\)
−0.922787 + 0.385310i \(0.874095\pi\)
\(548\) 432.000i 0.788321i
\(549\) 21.0000 + 21.0000i 0.0382514 + 0.0382514i
\(550\) −28.0000 28.0000i −0.0509091 0.0509091i
\(551\) −380.000 −0.689655
\(552\) 160.000 0.289855
\(553\) −56.0000 + 56.0000i −0.101266 + 0.101266i
\(554\) 294.000i 0.530686i
\(555\) 444.000 444.000i 0.800000 0.800000i
\(556\) −360.000 −0.647482
\(557\) −179.000 179.000i −0.321364 0.321364i 0.527926 0.849290i \(-0.322970\pi\)
−0.849290 + 0.527926i \(0.822970\pi\)
\(558\) 252.000i 0.451613i
\(559\) 252.000i 0.450805i
\(560\) 48.0000 48.0000i 0.0857143 0.0857143i
\(561\) −368.000 + 368.000i −0.655971 + 0.655971i
\(562\) 270.000 0.480427
\(563\) 282.000 282.000i 0.500888 0.500888i −0.410826 0.911714i \(-0.634760\pi\)
0.911714 + 0.410826i \(0.134760\pi\)
\(564\) 352.000 0.624113
\(565\) 42.0000 0.0743363
\(566\) 516.000i 0.911661i
\(567\) 380.000 0.670194
\(568\) −248.000 + 248.000i −0.436620 + 0.436620i
\(569\) 375.000 + 375.000i 0.659051 + 0.659051i 0.955156 0.296105i \(-0.0956877\pi\)
−0.296105 + 0.955156i \(0.595688\pi\)
\(570\) 240.000 + 240.000i 0.421053 + 0.421053i
\(571\) −184.000 −0.322242 −0.161121 0.986935i \(-0.551511\pi\)
−0.161121 + 0.986935i \(0.551511\pi\)
\(572\) −24.0000 + 24.0000i −0.0419580 + 0.0419580i
\(573\) 744.000 + 744.000i 1.29843 + 1.29843i
\(574\) 296.000 296.000i 0.515679 0.515679i
\(575\) −70.0000 70.0000i −0.121739 0.121739i
\(576\) 56.0000i 0.0972222i
\(577\) −623.000 + 623.000i −1.07972 + 1.07972i −0.0831889 + 0.996534i \(0.526510\pi\)
−0.996534 + 0.0831889i \(0.973490\pi\)
\(578\) 769.000 769.000i 1.33045 1.33045i
\(579\) −36.0000 36.0000i −0.0621762 0.0621762i
\(580\) 228.000i 0.393103i
\(581\) 256.000 0.440620
\(582\) 1032.00i 1.77320i
\(583\) 320.000i 0.548885i
\(584\) 20.0000 + 20.0000i 0.0342466 + 0.0342466i
\(585\) 126.000i 0.215385i
\(586\) 0 0
\(587\) −382.000 382.000i −0.650767 0.650767i 0.302411 0.953178i \(-0.402208\pi\)
−0.953178 + 0.302411i \(0.902208\pi\)
\(588\) 264.000 0.448980
\(589\) −360.000 −0.611205
\(590\) −324.000 + 324.000i −0.549153 + 0.549153i
\(591\) 136.000i 0.230118i
\(592\) 148.000i 0.250000i
\(593\) 734.000 1.23777 0.618887 0.785480i \(-0.287584\pi\)
0.618887 + 0.785480i \(0.287584\pi\)
\(594\) −32.0000 32.0000i −0.0538721 0.0538721i
\(595\) 552.000i 0.927731i
\(596\) 68.0000i 0.114094i
\(597\) −184.000 + 184.000i −0.308208 + 0.308208i
\(598\) −60.0000 + 60.0000i −0.100334 + 0.100334i
\(599\) −1004.00 −1.67613 −0.838063 0.545573i \(-0.816312\pi\)
−0.838063 + 0.545573i \(0.816312\pi\)
\(600\) 56.0000 56.0000i 0.0933333 0.0933333i
\(601\) 306.000 0.509151 0.254576 0.967053i \(-0.418064\pi\)
0.254576 + 0.967053i \(0.418064\pi\)
\(602\) −336.000 −0.558140
\(603\) 84.0000i 0.139303i
\(604\) 144.000 0.238411
\(605\) 315.000 315.000i 0.520661 0.520661i
\(606\) −472.000 472.000i −0.778878 0.778878i
\(607\) 298.000 + 298.000i 0.490939 + 0.490939i 0.908602 0.417663i \(-0.137151\pi\)
−0.417663 + 0.908602i \(0.637151\pi\)
\(608\) −80.0000 −0.131579
\(609\) −304.000 + 304.000i −0.499179 + 0.499179i
\(610\) −18.0000 18.0000i −0.0295082 0.0295082i
\(611\) −132.000 + 132.000i −0.216039 + 0.216039i
\(612\) −322.000 322.000i −0.526144 0.526144i
\(613\) 470.000i 0.766721i 0.923599 + 0.383361i \(0.125233\pi\)
−0.923599 + 0.383361i \(0.874767\pi\)
\(614\) −364.000 + 364.000i −0.592834 + 0.592834i
\(615\) −888.000 + 888.000i −1.44390 + 1.44390i
\(616\) 32.0000 + 32.0000i 0.0519481 + 0.0519481i
\(617\) 304.000i 0.492707i 0.969180 + 0.246353i \(0.0792324\pi\)
−0.969180 + 0.246353i \(0.920768\pi\)
\(618\) 336.000 0.543689
\(619\) 956.000i 1.54443i 0.635363 + 0.772213i \(0.280850\pi\)
−0.635363 + 0.772213i \(0.719150\pi\)
\(620\) 216.000i 0.348387i
\(621\) −80.0000 80.0000i −0.128824 0.128824i
\(622\) 476.000i 0.765273i
\(623\) −68.0000 68.0000i −0.109149 0.109149i
\(624\) −48.0000 48.0000i −0.0769231 0.0769231i
\(625\) 401.000 0.641600
\(626\) 174.000 0.277955
\(627\) −160.000 + 160.000i −0.255183 + 0.255183i
\(628\) 28.0000i 0.0445860i
\(629\) −851.000 851.000i −1.35294 1.35294i
\(630\) 168.000 0.266667
\(631\) −362.000 362.000i −0.573693 0.573693i 0.359466 0.933158i \(-0.382959\pi\)
−0.933158 + 0.359466i \(0.882959\pi\)
\(632\) 56.0000i 0.0886076i
\(633\) 832.000i 1.31438i
\(634\) −264.000 + 264.000i −0.416404 + 0.416404i
\(635\) 228.000 228.000i 0.359055 0.359055i
\(636\) 640.000 1.00629
\(637\) −99.0000 + 99.0000i −0.155416 + 0.155416i
\(638\) 152.000 0.238245
\(639\) −868.000 −1.35837
\(640\) 48.0000i 0.0750000i
\(641\) −398.000 −0.620905 −0.310452 0.950589i \(-0.600481\pi\)
−0.310452 + 0.950589i \(0.600481\pi\)
\(642\) 96.0000 96.0000i 0.149533 0.149533i
\(643\) 218.000 + 218.000i 0.339036 + 0.339036i 0.856004 0.516969i \(-0.172940\pi\)
−0.516969 + 0.856004i \(0.672940\pi\)
\(644\) 80.0000 + 80.0000i 0.124224 + 0.124224i
\(645\) 1008.00 1.56279
\(646\) 460.000 460.000i 0.712074 0.712074i
\(647\) −358.000 358.000i −0.553323 0.553323i 0.374075 0.927398i \(-0.377960\pi\)
−0.927398 + 0.374075i \(0.877960\pi\)
\(648\) 190.000 190.000i 0.293210 0.293210i
\(649\) −216.000 216.000i −0.332820 0.332820i
\(650\) 42.0000i 0.0646154i
\(651\) −288.000 + 288.000i −0.442396 + 0.442396i
\(652\) 132.000 132.000i 0.202454 0.202454i
\(653\) 555.000 + 555.000i 0.849923 + 0.849923i 0.990123 0.140200i \(-0.0447745\pi\)
−0.140200 + 0.990123i \(0.544774\pi\)
\(654\) 728.000i 1.11315i
\(655\) 420.000 0.641221
\(656\) 296.000i 0.451220i
\(657\) 70.0000i 0.106545i
\(658\) 176.000 + 176.000i 0.267477 + 0.267477i
\(659\) 788.000i 1.19575i 0.801589 + 0.597876i \(0.203988\pi\)
−0.801589 + 0.597876i \(0.796012\pi\)
\(660\) −96.0000 96.0000i −0.145455 0.145455i
\(661\) −661.000 661.000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(662\) −652.000 −0.984894
\(663\) 552.000 0.832579
\(664\) 128.000 128.000i 0.192771 0.192771i
\(665\) 240.000i 0.360902i
\(666\) −259.000 + 259.000i −0.388889 + 0.388889i
\(667\) 380.000 0.569715
\(668\) −460.000 460.000i −0.688623 0.688623i
\(669\) 496.000i 0.741405i
\(670\) 72.0000i 0.107463i
\(671\) 12.0000 12.0000i 0.0178838 0.0178838i
\(672\) −64.0000 + 64.0000i −0.0952381 + 0.0952381i
\(673\) 50.0000 0.0742942 0.0371471 0.999310i \(-0.488173\pi\)
0.0371471 + 0.999310i \(0.488173\pi\)
\(674\) 230.000 230.000i 0.341246 0.341246i
\(675\) −56.0000 −0.0829630
\(676\) −302.000 −0.446746
\(677\) 296.000i 0.437223i −0.975812 0.218612i \(-0.929847\pi\)
0.975812 0.218612i \(-0.0701527\pi\)
\(678\) −56.0000 −0.0825959
\(679\) −516.000 + 516.000i −0.759941 + 0.759941i
\(680\) 276.000 + 276.000i 0.405882 + 0.405882i
\(681\) −360.000 360.000i −0.528634 0.528634i
\(682\) 144.000 0.211144
\(683\) 6.00000 6.00000i 0.00878477 0.00878477i −0.702701 0.711486i \(-0.748023\pi\)
0.711486 + 0.702701i \(0.248023\pi\)
\(684\) −140.000 140.000i −0.204678 0.204678i
\(685\) 648.000 648.000i 0.945985 0.945985i
\(686\) 328.000 + 328.000i 0.478134 + 0.478134i
\(687\) 8.00000i 0.0116448i
\(688\) −168.000 + 168.000i −0.244186 + 0.244186i
\(689\) −240.000 + 240.000i −0.348331 + 0.348331i
\(690\) −240.000 240.000i −0.347826 0.347826i
\(691\) 708.000i 1.02460i −0.858806 0.512301i \(-0.828793\pi\)
0.858806 0.512301i \(-0.171207\pi\)
\(692\) 176.000 0.254335
\(693\) 112.000i 0.161616i
\(694\) 724.000i 1.04323i
\(695\) 540.000 + 540.000i 0.776978 + 0.776978i
\(696\) 304.000i 0.436782i
\(697\) 1702.00 + 1702.00i 2.44189 + 2.44189i
\(698\) −48.0000 48.0000i −0.0687679 0.0687679i
\(699\) −168.000 −0.240343
\(700\) 56.0000 0.0800000
\(701\) 291.000 291.000i 0.415121 0.415121i −0.468397 0.883518i \(-0.655168\pi\)
0.883518 + 0.468397i \(0.155168\pi\)
\(702\) 48.0000i 0.0683761i
\(703\) −370.000 370.000i −0.526316 0.526316i
\(704\) 32.0000 0.0454545
\(705\) −528.000 528.000i −0.748936 0.748936i
\(706\) 686.000i 0.971671i
\(707\) 472.000i 0.667610i
\(708\) 432.000 432.000i 0.610169 0.610169i
\(709\) −77.0000 + 77.0000i −0.108604 + 0.108604i −0.759320 0.650717i \(-0.774469\pi\)
0.650717 + 0.759320i \(0.274469\pi\)
\(710\) 744.000 1.04789
\(711\) −98.0000 + 98.0000i −0.137834 + 0.137834i
\(712\) −68.0000 −0.0955056
\(713\) 360.000 0.504909
\(714\) 736.000i 1.03081i
\(715\) 72.0000 0.100699
\(716\) 332.000 332.000i 0.463687 0.463687i
\(717\) 88.0000 + 88.0000i 0.122734 + 0.122734i
\(718\) −404.000 404.000i −0.562674 0.562674i
\(719\) −412.000 −0.573018 −0.286509 0.958078i \(-0.592495\pi\)
−0.286509 + 0.958078i \(0.592495\pi\)
\(720\) 84.0000 84.0000i 0.116667 0.116667i
\(721\) 168.000 + 168.000i 0.233010 + 0.233010i
\(722\) −161.000 + 161.000i −0.222992 + 0.222992i
\(723\) −700.000 700.000i −0.968188 0.968188i
\(724\) 608.000i 0.839779i
\(725\) 133.000 133.000i 0.183448 0.183448i
\(726\) −420.000 + 420.000i −0.578512 + 0.578512i
\(727\) −262.000 262.000i −0.360385 0.360385i 0.503570 0.863955i \(-0.332020\pi\)
−0.863955 + 0.503570i \(0.832020\pi\)
\(728\) 48.0000i 0.0659341i
\(729\) 377.000 0.517147
\(730\) 60.0000i 0.0821918i
\(731\) 1932.00i 2.64295i
\(732\) 24.0000 + 24.0000i 0.0327869 + 0.0327869i
\(733\) 682.000i 0.930423i 0.885200 + 0.465211i \(0.154022\pi\)
−0.885200 + 0.465211i \(0.845978\pi\)
\(734\) 492.000 + 492.000i 0.670300 + 0.670300i
\(735\) −396.000 396.000i −0.538776 0.538776i
\(736\) 80.0000 0.108696
\(737\) 48.0000 0.0651289
\(738\) 518.000 518.000i 0.701897 0.701897i
\(739\) 100.000i 0.135318i 0.997709 + 0.0676590i \(0.0215530\pi\)
−0.997709 + 0.0676590i \(0.978447\pi\)
\(740\) 222.000 222.000i 0.300000 0.300000i
\(741\) 240.000 0.323887
\(742\) 320.000 + 320.000i 0.431267 + 0.431267i
\(743\) 800.000i 1.07672i −0.842716 0.538358i \(-0.819045\pi\)
0.842716 0.538358i \(-0.180955\pi\)
\(744\) 288.000i 0.387097i
\(745\) −102.000 + 102.000i −0.136913 + 0.136913i
\(746\) 488.000 488.000i 0.654155 0.654155i
\(747\) 448.000 0.599732
\(748\) −184.000 + 184.000i −0.245989 + 0.245989i
\(749\) 96.0000 0.128171
\(750\) −768.000 −1.02400
\(751\) 536.000i 0.713715i 0.934159 + 0.356858i \(0.116152\pi\)
−0.934159 + 0.356858i \(0.883848\pi\)
\(752\) 176.000 0.234043
\(753\) 792.000 792.000i 1.05179 1.05179i
\(754\) −114.000 114.000i −0.151194 0.151194i
\(755\) −216.000 216.000i −0.286093 0.286093i
\(756\) 64.0000 0.0846561
\(757\) −157.000 + 157.000i −0.207398 + 0.207398i −0.803160 0.595763i \(-0.796850\pi\)
0.595763 + 0.803160i \(0.296850\pi\)
\(758\) −440.000 440.000i −0.580475 0.580475i
\(759\) 160.000 160.000i 0.210804 0.210804i
\(760\) 120.000 + 120.000i 0.157895 + 0.157895i
\(761\) 272.000i 0.357424i 0.983901 + 0.178712i \(0.0571931\pi\)
−0.983901 + 0.178712i \(0.942807\pi\)
\(762\) −304.000 + 304.000i −0.398950 + 0.398950i
\(763\) 364.000 364.000i 0.477064 0.477064i
\(764\) 372.000 + 372.000i 0.486911 + 0.486911i
\(765\) 966.000i 1.26275i
\(766\) −900.000 −1.17493
\(767\) 324.000i 0.422425i
\(768\) 64.0000i 0.0833333i
\(769\) −761.000 761.000i −0.989597 0.989597i 0.0103496 0.999946i \(-0.496706\pi\)
−0.999946 + 0.0103496i \(0.996706\pi\)
\(770\) 96.0000i 0.124675i
\(771\) −636.000 636.000i −0.824903 0.824903i
\(772\) −18.0000 18.0000i −0.0233161 0.0233161i
\(773\) −1282.00 −1.65847 −0.829237 0.558898i \(-0.811225\pi\)
−0.829237 + 0.558898i \(0.811225\pi\)
\(774\) −588.000 −0.759690
\(775\) 126.000 126.000i 0.162581 0.162581i
\(776\) 516.000i 0.664948i
\(777\) −592.000 −0.761905
\(778\)