Properties

Label 10.3.c.a.3.1
Level $10$
Weight $3$
Character 10.3
Analytic conductor $0.272$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 10.c (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.272480264360\)
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 3.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 10.3
Dual form 10.3.c.a.7.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} +(-2.00000 - 2.00000i) q^{3} -2.00000i q^{4} +5.00000i q^{5} +4.00000 q^{6} +(2.00000 - 2.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.00000i) q^{2} +(-2.00000 - 2.00000i) q^{3} -2.00000i q^{4} +5.00000i q^{5} +4.00000 q^{6} +(2.00000 - 2.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} -1.00000i q^{9} +(-5.00000 - 5.00000i) q^{10} -8.00000 q^{11} +(-4.00000 + 4.00000i) q^{12} +(3.00000 + 3.00000i) q^{13} +4.00000i q^{14} +(10.0000 - 10.0000i) q^{15} -4.00000 q^{16} +(7.00000 - 7.00000i) q^{17} +(1.00000 + 1.00000i) q^{18} +20.0000i q^{19} +10.0000 q^{20} -8.00000 q^{21} +(8.00000 - 8.00000i) q^{22} +(-2.00000 - 2.00000i) q^{23} -8.00000i q^{24} -25.0000 q^{25} -6.00000 q^{26} +(-20.0000 + 20.0000i) q^{27} +(-4.00000 - 4.00000i) q^{28} -40.0000i q^{29} +20.0000i q^{30} +52.0000 q^{31} +(4.00000 - 4.00000i) q^{32} +(16.0000 + 16.0000i) q^{33} +14.0000i q^{34} +(10.0000 + 10.0000i) q^{35} -2.00000 q^{36} +(-3.00000 + 3.00000i) q^{37} +(-20.0000 - 20.0000i) q^{38} -12.0000i q^{39} +(-10.0000 + 10.0000i) q^{40} -8.00000 q^{41} +(8.00000 - 8.00000i) q^{42} +(-42.0000 - 42.0000i) q^{43} +16.0000i q^{44} +5.00000 q^{45} +4.00000 q^{46} +(-18.0000 + 18.0000i) q^{47} +(8.00000 + 8.00000i) q^{48} +41.0000i q^{49} +(25.0000 - 25.0000i) q^{50} -28.0000 q^{51} +(6.00000 - 6.00000i) q^{52} +(53.0000 + 53.0000i) q^{53} -40.0000i q^{54} -40.0000i q^{55} +8.00000 q^{56} +(40.0000 - 40.0000i) q^{57} +(40.0000 + 40.0000i) q^{58} +20.0000i q^{59} +(-20.0000 - 20.0000i) q^{60} -48.0000 q^{61} +(-52.0000 + 52.0000i) q^{62} +(-2.00000 - 2.00000i) q^{63} +8.00000i q^{64} +(-15.0000 + 15.0000i) q^{65} -32.0000 q^{66} +(62.0000 - 62.0000i) q^{67} +(-14.0000 - 14.0000i) q^{68} +8.00000i q^{69} -20.0000 q^{70} -28.0000 q^{71} +(2.00000 - 2.00000i) q^{72} +(-47.0000 - 47.0000i) q^{73} -6.00000i q^{74} +(50.0000 + 50.0000i) q^{75} +40.0000 q^{76} +(-16.0000 + 16.0000i) q^{77} +(12.0000 + 12.0000i) q^{78} -20.0000i q^{80} +71.0000 q^{81} +(8.00000 - 8.00000i) q^{82} +(18.0000 + 18.0000i) q^{83} +16.0000i q^{84} +(35.0000 + 35.0000i) q^{85} +84.0000 q^{86} +(-80.0000 + 80.0000i) q^{87} +(-16.0000 - 16.0000i) q^{88} -80.0000i q^{89} +(-5.00000 + 5.00000i) q^{90} +12.0000 q^{91} +(-4.00000 + 4.00000i) q^{92} +(-104.000 - 104.000i) q^{93} -36.0000i q^{94} -100.000 q^{95} -16.0000 q^{96} +(-63.0000 + 63.0000i) q^{97} +(-41.0000 - 41.0000i) q^{98} +8.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} - 4q^{3} + 8q^{6} + 4q^{7} + 4q^{8} + O(q^{10}) \) \( 2q - 2q^{2} - 4q^{3} + 8q^{6} + 4q^{7} + 4q^{8} - 10q^{10} - 16q^{11} - 8q^{12} + 6q^{13} + 20q^{15} - 8q^{16} + 14q^{17} + 2q^{18} + 20q^{20} - 16q^{21} + 16q^{22} - 4q^{23} - 50q^{25} - 12q^{26} - 40q^{27} - 8q^{28} + 104q^{31} + 8q^{32} + 32q^{33} + 20q^{35} - 4q^{36} - 6q^{37} - 40q^{38} - 20q^{40} - 16q^{41} + 16q^{42} - 84q^{43} + 10q^{45} + 8q^{46} - 36q^{47} + 16q^{48} + 50q^{50} - 56q^{51} + 12q^{52} + 106q^{53} + 16q^{56} + 80q^{57} + 80q^{58} - 40q^{60} - 96q^{61} - 104q^{62} - 4q^{63} - 30q^{65} - 64q^{66} + 124q^{67} - 28q^{68} - 40q^{70} - 56q^{71} + 4q^{72} - 94q^{73} + 100q^{75} + 80q^{76} - 32q^{77} + 24q^{78} + 142q^{81} + 16q^{82} + 36q^{83} + 70q^{85} + 168q^{86} - 160q^{87} - 32q^{88} - 10q^{90} + 24q^{91} - 8q^{92} - 208q^{93} - 200q^{95} - 32q^{96} - 126q^{97} - 82q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).

\(n\) \(7\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) −2.00000 2.00000i −0.666667 0.666667i 0.290276 0.956943i \(-0.406253\pi\)
−0.956943 + 0.290276i \(0.906253\pi\)
\(4\) 2.00000i 0.500000i
\(5\) 5.00000i 1.00000i
\(6\) 4.00000 0.666667
\(7\) 2.00000 2.00000i 0.285714 0.285714i −0.549669 0.835383i \(-0.685246\pi\)
0.835383 + 0.549669i \(0.185246\pi\)
\(8\) 2.00000 + 2.00000i 0.250000 + 0.250000i
\(9\) 1.00000i 0.111111i
\(10\) −5.00000 5.00000i −0.500000 0.500000i
\(11\) −8.00000 −0.727273 −0.363636 0.931541i \(-0.618465\pi\)
−0.363636 + 0.931541i \(0.618465\pi\)
\(12\) −4.00000 + 4.00000i −0.333333 + 0.333333i
\(13\) 3.00000 + 3.00000i 0.230769 + 0.230769i 0.813014 0.582245i \(-0.197825\pi\)
−0.582245 + 0.813014i \(0.697825\pi\)
\(14\) 4.00000i 0.285714i
\(15\) 10.0000 10.0000i 0.666667 0.666667i
\(16\) −4.00000 −0.250000
\(17\) 7.00000 7.00000i 0.411765 0.411765i −0.470588 0.882353i \(-0.655958\pi\)
0.882353 + 0.470588i \(0.155958\pi\)
\(18\) 1.00000 + 1.00000i 0.0555556 + 0.0555556i
\(19\) 20.0000i 1.05263i 0.850289 + 0.526316i \(0.176427\pi\)
−0.850289 + 0.526316i \(0.823573\pi\)
\(20\) 10.0000 0.500000
\(21\) −8.00000 −0.380952
\(22\) 8.00000 8.00000i 0.363636 0.363636i
\(23\) −2.00000 2.00000i −0.0869565 0.0869565i 0.662291 0.749247i \(-0.269584\pi\)
−0.749247 + 0.662291i \(0.769584\pi\)
\(24\) 8.00000i 0.333333i
\(25\) −25.0000 −1.00000
\(26\) −6.00000 −0.230769
\(27\) −20.0000 + 20.0000i −0.740741 + 0.740741i
\(28\) −4.00000 4.00000i −0.142857 0.142857i
\(29\) 40.0000i 1.37931i −0.724138 0.689655i \(-0.757762\pi\)
0.724138 0.689655i \(-0.242238\pi\)
\(30\) 20.0000i 0.666667i
\(31\) 52.0000 1.67742 0.838710 0.544579i \(-0.183310\pi\)
0.838710 + 0.544579i \(0.183310\pi\)
\(32\) 4.00000 4.00000i 0.125000 0.125000i
\(33\) 16.0000 + 16.0000i 0.484848 + 0.484848i
\(34\) 14.0000i 0.411765i
\(35\) 10.0000 + 10.0000i 0.285714 + 0.285714i
\(36\) −2.00000 −0.0555556
\(37\) −3.00000 + 3.00000i −0.0810811 + 0.0810811i −0.746484 0.665403i \(-0.768260\pi\)
0.665403 + 0.746484i \(0.268260\pi\)
\(38\) −20.0000 20.0000i −0.526316 0.526316i
\(39\) 12.0000i 0.307692i
\(40\) −10.0000 + 10.0000i −0.250000 + 0.250000i
\(41\) −8.00000 −0.195122 −0.0975610 0.995230i \(-0.531104\pi\)
−0.0975610 + 0.995230i \(0.531104\pi\)
\(42\) 8.00000 8.00000i 0.190476 0.190476i
\(43\) −42.0000 42.0000i −0.976744 0.976744i 0.0229915 0.999736i \(-0.492681\pi\)
−0.999736 + 0.0229915i \(0.992681\pi\)
\(44\) 16.0000i 0.363636i
\(45\) 5.00000 0.111111
\(46\) 4.00000 0.0869565
\(47\) −18.0000 + 18.0000i −0.382979 + 0.382979i −0.872174 0.489195i \(-0.837290\pi\)
0.489195 + 0.872174i \(0.337290\pi\)
\(48\) 8.00000 + 8.00000i 0.166667 + 0.166667i
\(49\) 41.0000i 0.836735i
\(50\) 25.0000 25.0000i 0.500000 0.500000i
\(51\) −28.0000 −0.549020
\(52\) 6.00000 6.00000i 0.115385 0.115385i
\(53\) 53.0000 + 53.0000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(54\) 40.0000i 0.740741i
\(55\) 40.0000i 0.727273i
\(56\) 8.00000 0.142857
\(57\) 40.0000 40.0000i 0.701754 0.701754i
\(58\) 40.0000 + 40.0000i 0.689655 + 0.689655i
\(59\) 20.0000i 0.338983i 0.985532 + 0.169492i \(0.0542125\pi\)
−0.985532 + 0.169492i \(0.945787\pi\)
\(60\) −20.0000 20.0000i −0.333333 0.333333i
\(61\) −48.0000 −0.786885 −0.393443 0.919349i \(-0.628716\pi\)
−0.393443 + 0.919349i \(0.628716\pi\)
\(62\) −52.0000 + 52.0000i −0.838710 + 0.838710i
\(63\) −2.00000 2.00000i −0.0317460 0.0317460i
\(64\) 8.00000i 0.125000i
\(65\) −15.0000 + 15.0000i −0.230769 + 0.230769i
\(66\) −32.0000 −0.484848
\(67\) 62.0000 62.0000i 0.925373 0.925373i −0.0720294 0.997403i \(-0.522948\pi\)
0.997403 + 0.0720294i \(0.0229475\pi\)
\(68\) −14.0000 14.0000i −0.205882 0.205882i
\(69\) 8.00000i 0.115942i
\(70\) −20.0000 −0.285714
\(71\) −28.0000 −0.394366 −0.197183 0.980367i \(-0.563179\pi\)
−0.197183 + 0.980367i \(0.563179\pi\)
\(72\) 2.00000 2.00000i 0.0277778 0.0277778i
\(73\) −47.0000 47.0000i −0.643836 0.643836i 0.307661 0.951496i \(-0.400454\pi\)
−0.951496 + 0.307661i \(0.900454\pi\)
\(74\) 6.00000i 0.0810811i
\(75\) 50.0000 + 50.0000i 0.666667 + 0.666667i
\(76\) 40.0000 0.526316
\(77\) −16.0000 + 16.0000i −0.207792 + 0.207792i
\(78\) 12.0000 + 12.0000i 0.153846 + 0.153846i
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 20.0000i 0.250000i
\(81\) 71.0000 0.876543
\(82\) 8.00000 8.00000i 0.0975610 0.0975610i
\(83\) 18.0000 + 18.0000i 0.216867 + 0.216867i 0.807177 0.590310i \(-0.200994\pi\)
−0.590310 + 0.807177i \(0.700994\pi\)
\(84\) 16.0000i 0.190476i
\(85\) 35.0000 + 35.0000i 0.411765 + 0.411765i
\(86\) 84.0000 0.976744
\(87\) −80.0000 + 80.0000i −0.919540 + 0.919540i
\(88\) −16.0000 16.0000i −0.181818 0.181818i
\(89\) 80.0000i 0.898876i −0.893311 0.449438i \(-0.851624\pi\)
0.893311 0.449438i \(-0.148376\pi\)
\(90\) −5.00000 + 5.00000i −0.0555556 + 0.0555556i
\(91\) 12.0000 0.131868
\(92\) −4.00000 + 4.00000i −0.0434783 + 0.0434783i
\(93\) −104.000 104.000i −1.11828 1.11828i
\(94\) 36.0000i 0.382979i
\(95\) −100.000 −1.05263
\(96\) −16.0000 −0.166667
\(97\) −63.0000 + 63.0000i −0.649485 + 0.649485i −0.952868 0.303384i \(-0.901884\pi\)
0.303384 + 0.952868i \(0.401884\pi\)
\(98\) −41.0000 41.0000i −0.418367 0.418367i
\(99\) 8.00000i 0.0808081i
\(100\) 50.0000i 0.500000i
\(101\) 62.0000 0.613861 0.306931 0.951732i \(-0.400698\pi\)
0.306931 + 0.951732i \(0.400698\pi\)
\(102\) 28.0000 28.0000i 0.274510 0.274510i
\(103\) 118.000 + 118.000i 1.14563 + 1.14563i 0.987403 + 0.158229i \(0.0505783\pi\)
0.158229 + 0.987403i \(0.449422\pi\)
\(104\) 12.0000i 0.115385i
\(105\) 40.0000i 0.380952i
\(106\) −106.000 −1.00000
\(107\) 142.000 142.000i 1.32710 1.32710i 0.419217 0.907886i \(-0.362305\pi\)
0.907886 0.419217i \(-0.137695\pi\)
\(108\) 40.0000 + 40.0000i 0.370370 + 0.370370i
\(109\) 10.0000i 0.0917431i 0.998947 + 0.0458716i \(0.0146065\pi\)
−0.998947 + 0.0458716i \(0.985394\pi\)
\(110\) 40.0000 + 40.0000i 0.363636 + 0.363636i
\(111\) 12.0000 0.108108
\(112\) −8.00000 + 8.00000i −0.0714286 + 0.0714286i
\(113\) 23.0000 + 23.0000i 0.203540 + 0.203540i 0.801515 0.597975i \(-0.204028\pi\)
−0.597975 + 0.801515i \(0.704028\pi\)
\(114\) 80.0000i 0.701754i
\(115\) 10.0000 10.0000i 0.0869565 0.0869565i
\(116\) −80.0000 −0.689655
\(117\) 3.00000 3.00000i 0.0256410 0.0256410i
\(118\) −20.0000 20.0000i −0.169492 0.169492i
\(119\) 28.0000i 0.235294i
\(120\) 40.0000 0.333333
\(121\) −57.0000 −0.471074
\(122\) 48.0000 48.0000i 0.393443 0.393443i
\(123\) 16.0000 + 16.0000i 0.130081 + 0.130081i
\(124\) 104.000i 0.838710i
\(125\) 125.000i 1.00000i
\(126\) 4.00000 0.0317460
\(127\) −118.000 + 118.000i −0.929134 + 0.929134i −0.997650 0.0685161i \(-0.978174\pi\)
0.0685161 + 0.997650i \(0.478174\pi\)
\(128\) −8.00000 8.00000i −0.0625000 0.0625000i
\(129\) 168.000i 1.30233i
\(130\) 30.0000i 0.230769i
\(131\) −128.000 −0.977099 −0.488550 0.872536i \(-0.662474\pi\)
−0.488550 + 0.872536i \(0.662474\pi\)
\(132\) 32.0000 32.0000i 0.242424 0.242424i
\(133\) 40.0000 + 40.0000i 0.300752 + 0.300752i
\(134\) 124.000i 0.925373i
\(135\) −100.000 100.000i −0.740741 0.740741i
\(136\) 28.0000 0.205882
\(137\) −63.0000 + 63.0000i −0.459854 + 0.459854i −0.898607 0.438753i \(-0.855420\pi\)
0.438753 + 0.898607i \(0.355420\pi\)
\(138\) −8.00000 8.00000i −0.0579710 0.0579710i
\(139\) 140.000i 1.00719i −0.863939 0.503597i \(-0.832010\pi\)
0.863939 0.503597i \(-0.167990\pi\)
\(140\) 20.0000 20.0000i 0.142857 0.142857i
\(141\) 72.0000 0.510638
\(142\) 28.0000 28.0000i 0.197183 0.197183i
\(143\) −24.0000 24.0000i −0.167832 0.167832i
\(144\) 4.00000i 0.0277778i
\(145\) 200.000 1.37931
\(146\) 94.0000 0.643836
\(147\) 82.0000 82.0000i 0.557823 0.557823i
\(148\) 6.00000 + 6.00000i 0.0405405 + 0.0405405i
\(149\) 150.000i 1.00671i 0.864079 + 0.503356i \(0.167901\pi\)
−0.864079 + 0.503356i \(0.832099\pi\)
\(150\) −100.000 −0.666667
\(151\) 52.0000 0.344371 0.172185 0.985065i \(-0.444917\pi\)
0.172185 + 0.985065i \(0.444917\pi\)
\(152\) −40.0000 + 40.0000i −0.263158 + 0.263158i
\(153\) −7.00000 7.00000i −0.0457516 0.0457516i
\(154\) 32.0000i 0.207792i
\(155\) 260.000i 1.67742i
\(156\) −24.0000 −0.153846
\(157\) 27.0000 27.0000i 0.171975 0.171975i −0.615872 0.787846i \(-0.711196\pi\)
0.787846 + 0.615872i \(0.211196\pi\)
\(158\) 0 0
\(159\) 212.000i 1.33333i
\(160\) 20.0000 + 20.0000i 0.125000 + 0.125000i
\(161\) −8.00000 −0.0496894
\(162\) −71.0000 + 71.0000i −0.438272 + 0.438272i
\(163\) −82.0000 82.0000i −0.503067 0.503067i 0.409322 0.912390i \(-0.365765\pi\)
−0.912390 + 0.409322i \(0.865765\pi\)
\(164\) 16.0000i 0.0975610i
\(165\) −80.0000 + 80.0000i −0.484848 + 0.484848i
\(166\) −36.0000 −0.216867
\(167\) 62.0000 62.0000i 0.371257 0.371257i −0.496678 0.867935i \(-0.665447\pi\)
0.867935 + 0.496678i \(0.165447\pi\)
\(168\) −16.0000 16.0000i −0.0952381 0.0952381i
\(169\) 151.000i 0.893491i
\(170\) −70.0000 −0.411765
\(171\) 20.0000 0.116959
\(172\) −84.0000 + 84.0000i −0.488372 + 0.488372i
\(173\) −107.000 107.000i −0.618497 0.618497i 0.326649 0.945146i \(-0.394081\pi\)
−0.945146 + 0.326649i \(0.894081\pi\)
\(174\) 160.000i 0.919540i
\(175\) −50.0000 + 50.0000i −0.285714 + 0.285714i
\(176\) 32.0000 0.181818
\(177\) 40.0000 40.0000i 0.225989 0.225989i
\(178\) 80.0000 + 80.0000i 0.449438 + 0.449438i
\(179\) 220.000i 1.22905i 0.788897 + 0.614525i \(0.210652\pi\)
−0.788897 + 0.614525i \(0.789348\pi\)
\(180\) 10.0000i 0.0555556i
\(181\) 2.00000 0.0110497 0.00552486 0.999985i \(-0.498241\pi\)
0.00552486 + 0.999985i \(0.498241\pi\)
\(182\) −12.0000 + 12.0000i −0.0659341 + 0.0659341i
\(183\) 96.0000 + 96.0000i 0.524590 + 0.524590i
\(184\) 8.00000i 0.0434783i
\(185\) −15.0000 15.0000i −0.0810811 0.0810811i
\(186\) 208.000 1.11828
\(187\) −56.0000 + 56.0000i −0.299465 + 0.299465i
\(188\) 36.0000 + 36.0000i 0.191489 + 0.191489i
\(189\) 80.0000i 0.423280i
\(190\) 100.000 100.000i 0.526316 0.526316i
\(191\) 212.000 1.10995 0.554974 0.831868i \(-0.312728\pi\)
0.554974 + 0.831868i \(0.312728\pi\)
\(192\) 16.0000 16.0000i 0.0833333 0.0833333i
\(193\) −57.0000 57.0000i −0.295337 0.295337i 0.543847 0.839184i \(-0.316967\pi\)
−0.839184 + 0.543847i \(0.816967\pi\)
\(194\) 126.000i 0.649485i
\(195\) 60.0000 0.307692
\(196\) 82.0000 0.418367
\(197\) −3.00000 + 3.00000i −0.0152284 + 0.0152284i −0.714680 0.699452i \(-0.753428\pi\)
0.699452 + 0.714680i \(0.253428\pi\)
\(198\) −8.00000 8.00000i −0.0404040 0.0404040i
\(199\) 120.000i 0.603015i 0.953464 + 0.301508i \(0.0974898\pi\)
−0.953464 + 0.301508i \(0.902510\pi\)
\(200\) −50.0000 50.0000i −0.250000 0.250000i
\(201\) −248.000 −1.23383
\(202\) −62.0000 + 62.0000i −0.306931 + 0.306931i
\(203\) −80.0000 80.0000i −0.394089 0.394089i
\(204\) 56.0000i 0.274510i
\(205\) 40.0000i 0.195122i
\(206\) −236.000 −1.14563
\(207\) −2.00000 + 2.00000i −0.00966184 + 0.00966184i
\(208\) −12.0000 12.0000i −0.0576923 0.0576923i
\(209\) 160.000i 0.765550i
\(210\) 40.0000 + 40.0000i 0.190476 + 0.190476i
\(211\) −328.000 −1.55450 −0.777251 0.629190i \(-0.783387\pi\)
−0.777251 + 0.629190i \(0.783387\pi\)
\(212\) 106.000 106.000i 0.500000 0.500000i
\(213\) 56.0000 + 56.0000i 0.262911 + 0.262911i
\(214\) 284.000i 1.32710i
\(215\) 210.000 210.000i 0.976744 0.976744i
\(216\) −80.0000 −0.370370
\(217\) 104.000 104.000i 0.479263 0.479263i
\(218\) −10.0000 10.0000i −0.0458716 0.0458716i
\(219\) 188.000i 0.858447i
\(220\) −80.0000 −0.363636
\(221\) 42.0000 0.190045
\(222\) −12.0000 + 12.0000i −0.0540541 + 0.0540541i
\(223\) 138.000 + 138.000i 0.618834 + 0.618834i 0.945232 0.326398i \(-0.105835\pi\)
−0.326398 + 0.945232i \(0.605835\pi\)
\(224\) 16.0000i 0.0714286i
\(225\) 25.0000i 0.111111i
\(226\) −46.0000 −0.203540
\(227\) 2.00000 2.00000i 0.00881057 0.00881057i −0.702688 0.711498i \(-0.748017\pi\)
0.711498 + 0.702688i \(0.248017\pi\)
\(228\) −80.0000 80.0000i −0.350877 0.350877i
\(229\) 120.000i 0.524017i −0.965066 0.262009i \(-0.915615\pi\)
0.965066 0.262009i \(-0.0843849\pi\)
\(230\) 20.0000i 0.0869565i
\(231\) 64.0000 0.277056
\(232\) 80.0000 80.0000i 0.344828 0.344828i
\(233\) 183.000 + 183.000i 0.785408 + 0.785408i 0.980738 0.195330i \(-0.0625777\pi\)
−0.195330 + 0.980738i \(0.562578\pi\)
\(234\) 6.00000i 0.0256410i
\(235\) −90.0000 90.0000i −0.382979 0.382979i
\(236\) 40.0000 0.169492
\(237\) 0 0
\(238\) 28.0000 + 28.0000i 0.117647 + 0.117647i
\(239\) 120.000i 0.502092i −0.967975 0.251046i \(-0.919225\pi\)
0.967975 0.251046i \(-0.0807746\pi\)
\(240\) −40.0000 + 40.0000i −0.166667 + 0.166667i
\(241\) 232.000 0.962656 0.481328 0.876541i \(-0.340155\pi\)
0.481328 + 0.876541i \(0.340155\pi\)
\(242\) 57.0000 57.0000i 0.235537 0.235537i
\(243\) 38.0000 + 38.0000i 0.156379 + 0.156379i
\(244\) 96.0000i 0.393443i
\(245\) −205.000 −0.836735
\(246\) −32.0000 −0.130081
\(247\) −60.0000 + 60.0000i −0.242915 + 0.242915i
\(248\) 104.000 + 104.000i 0.419355 + 0.419355i
\(249\) 72.0000i 0.289157i
\(250\) 125.000 + 125.000i 0.500000 + 0.500000i
\(251\) −48.0000 −0.191235 −0.0956175 0.995418i \(-0.530483\pi\)
−0.0956175 + 0.995418i \(0.530483\pi\)
\(252\) −4.00000 + 4.00000i −0.0158730 + 0.0158730i
\(253\) 16.0000 + 16.0000i 0.0632411 + 0.0632411i
\(254\) 236.000i 0.929134i
\(255\) 140.000i 0.549020i
\(256\) 16.0000 0.0625000
\(257\) −313.000 + 313.000i −1.21790 + 1.21790i −0.249532 + 0.968366i \(0.580277\pi\)
−0.968366 + 0.249532i \(0.919723\pi\)
\(258\) −168.000 168.000i −0.651163 0.651163i
\(259\) 12.0000i 0.0463320i
\(260\) 30.0000 + 30.0000i 0.115385 + 0.115385i
\(261\) −40.0000 −0.153257
\(262\) 128.000 128.000i 0.488550 0.488550i
\(263\) −262.000 262.000i −0.996198 0.996198i 0.00379508 0.999993i \(-0.498792\pi\)
−0.999993 + 0.00379508i \(0.998792\pi\)
\(264\) 64.0000i 0.242424i
\(265\) −265.000 + 265.000i −1.00000 + 1.00000i
\(266\) −80.0000 −0.300752
\(267\) −160.000 + 160.000i −0.599251 + 0.599251i
\(268\) −124.000 124.000i −0.462687 0.462687i
\(269\) 10.0000i 0.0371747i −0.999827 0.0185874i \(-0.994083\pi\)
0.999827 0.0185874i \(-0.00591688\pi\)
\(270\) 200.000 0.740741
\(271\) 252.000 0.929889 0.464945 0.885340i \(-0.346074\pi\)
0.464945 + 0.885340i \(0.346074\pi\)
\(272\) −28.0000 + 28.0000i −0.102941 + 0.102941i
\(273\) −24.0000 24.0000i −0.0879121 0.0879121i
\(274\) 126.000i 0.459854i
\(275\) 200.000 0.727273
\(276\) 16.0000 0.0579710
\(277\) 267.000 267.000i 0.963899 0.963899i −0.0354718 0.999371i \(-0.511293\pi\)
0.999371 + 0.0354718i \(0.0112934\pi\)
\(278\) 140.000 + 140.000i 0.503597 + 0.503597i
\(279\) 52.0000i 0.186380i
\(280\) 40.0000i 0.142857i
\(281\) 312.000 1.11032 0.555160 0.831743i \(-0.312657\pi\)
0.555160 + 0.831743i \(0.312657\pi\)
\(282\) −72.0000 + 72.0000i −0.255319 + 0.255319i
\(283\) −262.000 262.000i −0.925795 0.925795i 0.0716358 0.997431i \(-0.477178\pi\)
−0.997431 + 0.0716358i \(0.977178\pi\)
\(284\) 56.0000i 0.197183i
\(285\) 200.000 + 200.000i 0.701754 + 0.701754i
\(286\) 48.0000 0.167832
\(287\) −16.0000 + 16.0000i −0.0557491 + 0.0557491i
\(288\) −4.00000 4.00000i −0.0138889 0.0138889i
\(289\) 191.000i 0.660900i
\(290\) −200.000 + 200.000i −0.689655 + 0.689655i
\(291\) 252.000 0.865979
\(292\) −94.0000 + 94.0000i −0.321918 + 0.321918i
\(293\) 243.000 + 243.000i 0.829352 + 0.829352i 0.987427 0.158075i \(-0.0505289\pi\)
−0.158075 + 0.987427i \(0.550529\pi\)
\(294\) 164.000i 0.557823i
\(295\) −100.000 −0.338983
\(296\) −12.0000 −0.0405405
\(297\) 160.000 160.000i 0.538721 0.538721i
\(298\) −150.000 150.000i −0.503356 0.503356i
\(299\) 12.0000i 0.0401338i
\(300\) 100.000 100.000i 0.333333 0.333333i
\(301\) −168.000 −0.558140
\(302\) −52.0000 + 52.0000i −0.172185 + 0.172185i
\(303\) −124.000 124.000i −0.409241 0.409241i
\(304\) 80.0000i 0.263158i
\(305\) 240.000i 0.786885i
\(306\) 14.0000 0.0457516
\(307\) −18.0000 + 18.0000i −0.0586319 + 0.0586319i −0.735815 0.677183i \(-0.763201\pi\)
0.677183 + 0.735815i \(0.263201\pi\)
\(308\) 32.0000 + 32.0000i 0.103896 + 0.103896i
\(309\) 472.000i 1.52751i
\(310\) −260.000 260.000i −0.838710 0.838710i
\(311\) −388.000 −1.24759 −0.623794 0.781589i \(-0.714410\pi\)
−0.623794 + 0.781589i \(0.714410\pi\)
\(312\) 24.0000 24.0000i 0.0769231 0.0769231i
\(313\) 183.000 + 183.000i 0.584665 + 0.584665i 0.936182 0.351517i \(-0.114334\pi\)
−0.351517 + 0.936182i \(0.614334\pi\)
\(314\) 54.0000i 0.171975i
\(315\) 10.0000 10.0000i 0.0317460 0.0317460i
\(316\) 0 0
\(317\) −213.000 + 213.000i −0.671924 + 0.671924i −0.958159 0.286235i \(-0.907596\pi\)
0.286235 + 0.958159i \(0.407596\pi\)
\(318\) 212.000 + 212.000i 0.666667 + 0.666667i
\(319\) 320.000i 1.00313i
\(320\) −40.0000 −0.125000
\(321\) −568.000 −1.76947
\(322\) 8.00000 8.00000i 0.0248447 0.0248447i
\(323\) 140.000 + 140.000i 0.433437 + 0.433437i
\(324\) 142.000i 0.438272i
\(325\) −75.0000 75.0000i −0.230769 0.230769i
\(326\) 164.000 0.503067
\(327\) 20.0000 20.0000i 0.0611621 0.0611621i
\(328\) −16.0000 16.0000i −0.0487805 0.0487805i
\(329\) 72.0000i 0.218845i
\(330\) 160.000i 0.484848i
\(331\) 232.000 0.700906 0.350453 0.936580i \(-0.386028\pi\)
0.350453 + 0.936580i \(0.386028\pi\)
\(332\) 36.0000 36.0000i 0.108434 0.108434i
\(333\) 3.00000 + 3.00000i 0.00900901 + 0.00900901i
\(334\) 124.000i 0.371257i
\(335\) 310.000 + 310.000i 0.925373 + 0.925373i
\(336\) 32.0000 0.0952381
\(337\) 417.000 417.000i 1.23739 1.23739i 0.276324 0.961064i \(-0.410884\pi\)
0.961064 0.276324i \(-0.0891164\pi\)
\(338\) 151.000 + 151.000i 0.446746 + 0.446746i
\(339\) 92.0000i 0.271386i
\(340\) 70.0000 70.0000i 0.205882 0.205882i
\(341\) −416.000 −1.21994
\(342\) −20.0000 + 20.0000i −0.0584795 + 0.0584795i
\(343\) 180.000 + 180.000i 0.524781 + 0.524781i
\(344\) 168.000i 0.488372i
\(345\) −40.0000 −0.115942
\(346\) 214.000 0.618497
\(347\) 202.000 202.000i 0.582133 0.582133i −0.353356 0.935489i \(-0.614960\pi\)
0.935489 + 0.353356i \(0.114960\pi\)
\(348\) 160.000 + 160.000i 0.459770 + 0.459770i
\(349\) 440.000i 1.26074i 0.776293 + 0.630372i \(0.217098\pi\)
−0.776293 + 0.630372i \(0.782902\pi\)
\(350\) 100.000i 0.285714i
\(351\) −120.000 −0.341880
\(352\) −32.0000 + 32.0000i −0.0909091 + 0.0909091i
\(353\) −447.000 447.000i −1.26629 1.26629i −0.947991 0.318298i \(-0.896889\pi\)
−0.318298 0.947991i \(-0.603111\pi\)
\(354\) 80.0000i 0.225989i
\(355\) 140.000i 0.394366i
\(356\) −160.000 −0.449438
\(357\) −56.0000 + 56.0000i −0.156863 + 0.156863i
\(358\) −220.000 220.000i −0.614525 0.614525i
\(359\) 400.000i 1.11421i 0.830443 + 0.557103i \(0.188087\pi\)
−0.830443 + 0.557103i \(0.811913\pi\)
\(360\) 10.0000 + 10.0000i 0.0277778 + 0.0277778i
\(361\) −39.0000 −0.108033
\(362\) −2.00000 + 2.00000i −0.00552486 + 0.00552486i
\(363\) 114.000 + 114.000i 0.314050 + 0.314050i
\(364\) 24.0000i 0.0659341i
\(365\) 235.000 235.000i 0.643836 0.643836i
\(366\) −192.000 −0.524590
\(367\) −118.000 + 118.000i −0.321526 + 0.321526i −0.849352 0.527826i \(-0.823007\pi\)
0.527826 + 0.849352i \(0.323007\pi\)
\(368\) 8.00000 + 8.00000i 0.0217391 + 0.0217391i
\(369\) 8.00000i 0.0216802i
\(370\) 30.0000 0.0810811
\(371\) 212.000 0.571429
\(372\) −208.000 + 208.000i −0.559140 + 0.559140i
\(373\) −107.000 107.000i −0.286863 0.286863i 0.548975 0.835839i \(-0.315018\pi\)
−0.835839 + 0.548975i \(0.815018\pi\)
\(374\) 112.000i 0.299465i
\(375\) −250.000 + 250.000i −0.666667 + 0.666667i
\(376\) −72.0000 −0.191489
\(377\) 120.000 120.000i 0.318302 0.318302i
\(378\) −80.0000 80.0000i −0.211640 0.211640i
\(379\) 340.000i 0.897098i −0.893758 0.448549i \(-0.851941\pi\)
0.893758 0.448549i \(-0.148059\pi\)
\(380\) 200.000i 0.526316i
\(381\) 472.000 1.23885
\(382\) −212.000 + 212.000i −0.554974 + 0.554974i
\(383\) −342.000 342.000i −0.892950 0.892950i 0.101849 0.994800i \(-0.467524\pi\)
−0.994800 + 0.101849i \(0.967524\pi\)
\(384\) 32.0000i 0.0833333i
\(385\) −80.0000 80.0000i −0.207792 0.207792i
\(386\) 114.000 0.295337
\(387\) −42.0000 + 42.0000i −0.108527 + 0.108527i
\(388\) 126.000 + 126.000i 0.324742 + 0.324742i
\(389\) 390.000i 1.00257i −0.865282 0.501285i \(-0.832861\pi\)
0.865282 0.501285i \(-0.167139\pi\)
\(390\) −60.0000 + 60.0000i −0.153846 + 0.153846i
\(391\) −28.0000 −0.0716113
\(392\) −82.0000 + 82.0000i −0.209184 + 0.209184i
\(393\) 256.000 + 256.000i 0.651399 + 0.651399i
\(394\) 6.00000i 0.0152284i
\(395\) 0 0
\(396\) 16.0000 0.0404040
\(397\) −323.000 + 323.000i −0.813602 + 0.813602i −0.985172 0.171570i \(-0.945116\pi\)
0.171570 + 0.985172i \(0.445116\pi\)
\(398\) −120.000 120.000i −0.301508 0.301508i
\(399\) 160.000i 0.401003i
\(400\) 100.000 0.250000
\(401\) 642.000 1.60100 0.800499 0.599334i \(-0.204568\pi\)
0.800499 + 0.599334i \(0.204568\pi\)
\(402\) 248.000 248.000i 0.616915 0.616915i
\(403\) 156.000 + 156.000i 0.387097 + 0.387097i
\(404\) 124.000i 0.306931i
\(405\) 355.000i 0.876543i
\(406\) 160.000 0.394089
\(407\) 24.0000 24.0000i 0.0589681 0.0589681i
\(408\) −56.0000 56.0000i −0.137255 0.137255i
\(409\) 150.000i 0.366748i 0.983043 + 0.183374i \(0.0587020\pi\)
−0.983043 + 0.183374i \(0.941298\pi\)
\(410\) 40.0000 + 40.0000i 0.0975610 + 0.0975610i
\(411\) 252.000 0.613139
\(412\) 236.000 236.000i 0.572816 0.572816i
\(413\) 40.0000 + 40.0000i 0.0968523 + 0.0968523i
\(414\) 4.00000i 0.00966184i
\(415\) −90.0000 + 90.0000i −0.216867 + 0.216867i
\(416\) 24.0000 0.0576923
\(417\) −280.000 + 280.000i −0.671463 + 0.671463i
\(418\) 160.000 + 160.000i 0.382775 + 0.382775i
\(419\) 300.000i 0.715990i −0.933723 0.357995i \(-0.883460\pi\)
0.933723 0.357995i \(-0.116540\pi\)
\(420\) −80.0000 −0.190476
\(421\) −208.000 −0.494062 −0.247031 0.969008i \(-0.579455\pi\)
−0.247031 + 0.969008i \(0.579455\pi\)
\(422\) 328.000 328.000i 0.777251 0.777251i
\(423\) 18.0000 + 18.0000i 0.0425532 + 0.0425532i
\(424\) 212.000i 0.500000i
\(425\) −175.000 + 175.000i −0.411765 + 0.411765i
\(426\) −112.000 −0.262911
\(427\) −96.0000 + 96.0000i −0.224824 + 0.224824i
\(428\) −284.000 284.000i −0.663551 0.663551i
\(429\) 96.0000i 0.223776i
\(430\) 420.000i 0.976744i
\(431\) −788.000 −1.82831 −0.914153 0.405369i \(-0.867143\pi\)
−0.914153 + 0.405369i \(0.867143\pi\)
\(432\) 80.0000 80.0000i 0.185185 0.185185i
\(433\) −367.000 367.000i −0.847575 0.847575i 0.142255 0.989830i \(-0.454565\pi\)
−0.989830 + 0.142255i \(0.954565\pi\)
\(434\) 208.000i 0.479263i
\(435\) −400.000 400.000i −0.919540 0.919540i
\(436\) 20.0000 0.0458716
\(437\) 40.0000 40.0000i 0.0915332 0.0915332i
\(438\) −188.000 188.000i −0.429224 0.429224i
\(439\) 560.000i 1.27563i −0.770191 0.637813i \(-0.779839\pi\)
0.770191 0.637813i \(-0.220161\pi\)
\(440\) 80.0000 80.0000i 0.181818 0.181818i
\(441\) 41.0000 0.0929705
\(442\) −42.0000 + 42.0000i −0.0950226 + 0.0950226i
\(443\) 378.000 + 378.000i 0.853273 + 0.853273i 0.990535 0.137262i \(-0.0438301\pi\)
−0.137262 + 0.990535i \(0.543830\pi\)
\(444\) 24.0000i 0.0540541i
\(445\) 400.000 0.898876
\(446\) −276.000 −0.618834
\(447\) 300.000 300.000i 0.671141 0.671141i
\(448\) 16.0000 + 16.0000i 0.0357143 + 0.0357143i
\(449\) 410.000i 0.913140i 0.889687 + 0.456570i \(0.150922\pi\)
−0.889687 + 0.456570i \(0.849078\pi\)
\(450\) −25.0000 25.0000i −0.0555556 0.0555556i
\(451\) 64.0000 0.141907
\(452\) 46.0000 46.0000i 0.101770 0.101770i
\(453\) −104.000 104.000i −0.229581 0.229581i
\(454\) 4.00000i 0.00881057i
\(455\) 60.0000i 0.131868i
\(456\) 160.000 0.350877
\(457\) −393.000 + 393.000i −0.859956 + 0.859956i −0.991333 0.131376i \(-0.958060\pi\)
0.131376 + 0.991333i \(0.458060\pi\)
\(458\) 120.000 + 120.000i 0.262009 + 0.262009i
\(459\) 280.000i 0.610022i
\(460\) −20.0000 20.0000i −0.0434783 0.0434783i
\(461\) 622.000 1.34924 0.674620 0.738165i \(-0.264307\pi\)
0.674620 + 0.738165i \(0.264307\pi\)
\(462\) −64.0000 + 64.0000i −0.138528 + 0.138528i
\(463\) 278.000 + 278.000i 0.600432 + 0.600432i 0.940427 0.339995i \(-0.110425\pi\)
−0.339995 + 0.940427i \(0.610425\pi\)
\(464\) 160.000i 0.344828i
\(465\) 520.000 520.000i 1.11828 1.11828i
\(466\) −366.000 −0.785408
\(467\) −38.0000 + 38.0000i −0.0813704 + 0.0813704i −0.746621 0.665250i \(-0.768325\pi\)
0.665250 + 0.746621i \(0.268325\pi\)
\(468\) −6.00000 6.00000i −0.0128205 0.0128205i
\(469\) 248.000i 0.528785i
\(470\) 180.000 0.382979
\(471\) −108.000 −0.229299
\(472\) −40.0000 + 40.0000i −0.0847458 + 0.0847458i
\(473\) 336.000 + 336.000i 0.710359 + 0.710359i
\(474\) 0 0
\(475\) 500.000i 1.05263i
\(476\) −56.0000 −0.117647
\(477\) 53.0000 53.0000i 0.111111 0.111111i
\(478\) 120.000 + 120.000i 0.251046 + 0.251046i
\(479\) 440.000i 0.918580i 0.888286 + 0.459290i \(0.151896\pi\)
−0.888286 + 0.459290i \(0.848104\pi\)
\(480\) 80.0000i 0.166667i
\(481\) −18.0000 −0.0374220
\(482\) −232.000 + 232.000i −0.481328 + 0.481328i
\(483\) 16.0000 + 16.0000i 0.0331263 + 0.0331263i
\(484\) 114.000i 0.235537i
\(485\) −315.000 315.000i −0.649485 0.649485i
\(486\) −76.0000 −0.156379
\(487\) 522.000 522.000i 1.07187 1.07187i 0.0746595 0.997209i \(-0.476213\pi\)
0.997209 0.0746595i \(-0.0237870\pi\)
\(488\) −96.0000 96.0000i −0.196721 0.196721i
\(489\) 328.000i 0.670757i
\(490\) 205.000 205.000i 0.418367 0.418367i
\(491\) −328.000 −0.668024 −0.334012 0.942569i \(-0.608403\pi\)
−0.334012 + 0.942569i \(0.608403\pi\)
\(492\) 32.0000 32.0000i 0.0650407 0.0650407i
\(493\) −280.000 280.000i −0.567951 0.567951i
\(494\) 120.000i 0.242915i
\(495\) −40.0000 −0.0808081
\(496\) −208.000 −0.419355
\(497\) −56.0000 + 56.0000i −0.112676 + 0.112676i
\(498\) 72.0000 + 72.0000i 0.144578 + 0.144578i
\(499\) 380.000i 0.761523i −0.924673 0.380762i \(-0.875662\pi\)
0.924673 0.380762i \(-0.124338\pi\)
\(500\) −250.000 −0.500000
\(501\) −248.000 −0.495010
\(502\) 48.0000 48.0000i 0.0956175 0.0956175i
\(503\) −42.0000 42.0000i −0.0834990 0.0834990i 0.664124 0.747623i \(-0.268805\pi\)
−0.747623 + 0.664124i \(0.768805\pi\)
\(504\) 8.00000i 0.0158730i
\(505\) 310.000i 0.613861i
\(506\) −32.0000 −0.0632411
\(507\) −302.000 + 302.000i −0.595661 + 0.595661i
\(508\) 236.000 + 236.000i 0.464567 + 0.464567i
\(509\) 440.000i 0.864440i 0.901768 + 0.432220i \(0.142270\pi\)
−0.901768 + 0.432220i \(0.857730\pi\)
\(510\) 140.000 + 140.000i 0.274510 + 0.274510i
\(511\) −188.000 −0.367906
\(512\) −16.0000 + 16.0000i −0.0312500 + 0.0312500i
\(513\) −400.000 400.000i −0.779727 0.779727i
\(514\) 626.000i 1.21790i
\(515\) −590.000 + 590.000i −1.14563 + 1.14563i
\(516\) 336.000 0.651163
\(517\) 144.000 144.000i 0.278530 0.278530i
\(518\) −12.0000 12.0000i −0.0231660 0.0231660i
\(519\) 428.000i 0.824663i
\(520\) −60.0000 −0.115385
\(521\) −258.000 −0.495202 −0.247601 0.968862i \(-0.579642\pi\)
−0.247601 + 0.968862i \(0.579642\pi\)
\(522\) 40.0000 40.0000i 0.0766284 0.0766284i
\(523\) 258.000 + 258.000i 0.493308 + 0.493308i 0.909347 0.416039i \(-0.136582\pi\)
−0.416039 + 0.909347i \(0.636582\pi\)
\(524\) 256.000i 0.488550i
\(525\) 200.000 0.380952
\(526\) 524.000 0.996198
\(527\) 364.000 364.000i 0.690702 0.690702i
\(528\) −64.0000 64.0000i −0.121212 0.121212i
\(529\) 521.000i 0.984877i
\(530\) 530.000i 1.00000i
\(531\) 20.0000 0.0376648
\(532\) 80.0000 80.0000i 0.150376 0.150376i
\(533\) −24.0000 24.0000i −0.0450281 0.0450281i
\(534\) 320.000i 0.599251i
\(535\) 710.000 + 710.000i 1.32710 + 1.32710i
\(536\) 248.000 0.462687
\(537\) 440.000 440.000i 0.819367 0.819367i
\(538\) 10.0000 + 10.0000i 0.0185874 + 0.0185874i
\(539\) 328.000i 0.608534i
\(540\) −200.000 + 200.000i −0.370370 + 0.370370i
\(541\) −338.000 −0.624769 −0.312384 0.949956i \(-0.601128\pi\)
−0.312384 + 0.949956i \(0.601128\pi\)
\(542\) −252.000 + 252.000i −0.464945 + 0.464945i
\(543\) −4.00000 4.00000i −0.00736648 0.00736648i
\(544\) 56.0000i 0.102941i
\(545\) −50.0000 −0.0917431
\(546\) 48.0000 0.0879121
\(547\) −558.000 + 558.000i −1.02011 + 1.02011i −0.0203161 + 0.999794i \(0.506467\pi\)
−0.999794 + 0.0203161i \(0.993533\pi\)
\(548\) 126.000 + 126.000i 0.229927 + 0.229927i
\(549\) 48.0000i 0.0874317i
\(550\) −200.000 + 200.000i −0.363636 + 0.363636i
\(551\) 800.000 1.45191
\(552\) −16.0000 + 16.0000i −0.0289855 + 0.0289855i
\(553\) 0 0
\(554\) 534.000i 0.963899i
\(555\) 60.0000i 0.108108i
\(556\) −280.000 −0.503597
\(557\) −3.00000 + 3.00000i −0.00538600 + 0.00538600i −0.709795 0.704409i \(-0.751212\pi\)
0.704409 + 0.709795i \(0.251212\pi\)
\(558\) 52.0000 + 52.0000i 0.0931900 + 0.0931900i
\(559\) 252.000i 0.450805i
\(560\) −40.0000 40.0000i −0.0714286 0.0714286i
\(561\) 224.000 0.399287
\(562\) −312.000 + 312.000i −0.555160 + 0.555160i
\(563\) −42.0000 42.0000i −0.0746004 0.0746004i 0.668822 0.743422i \(-0.266799\pi\)
−0.743422 + 0.668822i \(0.766799\pi\)
\(564\) 144.000i 0.255319i
\(565\) −115.000 + 115.000i −0.203540 + 0.203540i
\(566\) 524.000 0.925795
\(567\) 142.000 142.000i 0.250441 0.250441i
\(568\) −56.0000 56.0000i −0.0985915 0.0985915i
\(569\) 950.000i 1.66960i −0.550557 0.834798i \(-0.685584\pi\)
0.550557 0.834798i \(-0.314416\pi\)
\(570\) −400.000 −0.701754
\(571\) 392.000 0.686515 0.343257 0.939241i \(-0.388470\pi\)
0.343257 + 0.939241i \(0.388470\pi\)
\(572\) −48.0000 + 48.0000i −0.0839161 + 0.0839161i
\(573\) −424.000 424.000i −0.739965 0.739965i
\(574\) 32.0000i 0.0557491i
\(575\) 50.0000 + 50.0000i 0.0869565 + 0.0869565i
\(576\) 8.00000 0.0138889
\(577\) −473.000 + 473.000i −0.819757 + 0.819757i −0.986073 0.166315i \(-0.946813\pi\)
0.166315 + 0.986073i \(0.446813\pi\)
\(578\) −191.000 191.000i −0.330450 0.330450i
\(579\) 228.000i 0.393782i
\(580\) 400.000i 0.689655i
\(581\) 72.0000 0.123924
\(582\) −252.000 + 252.000i −0.432990 + 0.432990i
\(583\) −424.000 424.000i −0.727273 0.727273i
\(584\) 188.000i 0.321918i
\(585\) 15.0000 + 15.0000i 0.0256410 + 0.0256410i
\(586\) −486.000 −0.829352
\(587\) −198.000 + 198.000i −0.337308 + 0.337308i −0.855353 0.518045i \(-0.826660\pi\)
0.518045 + 0.855353i \(0.326660\pi\)
\(588\) −164.000 164.000i −0.278912 0.278912i
\(589\) 1040.00i 1.76570i
\(590\) 100.000 100.000i 0.169492 0.169492i
\(591\) 12.0000 0.0203046
\(592\) 12.0000 12.0000i 0.0202703 0.0202703i
\(593\) −47.0000 47.0000i −0.0792580 0.0792580i 0.666366 0.745624i \(-0.267849\pi\)
−0.745624 + 0.666366i \(0.767849\pi\)
\(594\) 320.000i 0.538721i
\(595\) 140.000 0.235294
\(596\) 300.000 0.503356
\(597\) 240.000 240.000i 0.402010 0.402010i
\(598\) 12.0000 + 12.0000i 0.0200669 + 0.0200669i
\(599\) 520.000i 0.868114i −0.900886 0.434057i \(-0.857082\pi\)
0.900886 0.434057i \(-0.142918\pi\)
\(600\) 200.000i 0.333333i
\(601\) −328.000 −0.545757 −0.272879 0.962048i \(-0.587976\pi\)
−0.272879 + 0.962048i \(0.587976\pi\)
\(602\) 168.000 168.000i 0.279070 0.279070i
\(603\) −62.0000 62.0000i −0.102819 0.102819i
\(604\) 104.000i 0.172185i
\(605\) 285.000i 0.471074i
\(606\) 248.000 0.409241
\(607\) 462.000 462.000i 0.761120 0.761120i −0.215405 0.976525i \(-0.569107\pi\)
0.976525 + 0.215405i \(0.0691070\pi\)
\(608\) 80.0000 + 80.0000i 0.131579 + 0.131579i
\(609\) 320.000i 0.525452i
\(610\) 240.000 + 240.000i 0.393443 + 0.393443i
\(611\) −108.000 −0.176759
\(612\) −14.0000 + 14.0000i −0.0228758 + 0.0228758i
\(613\) 723.000 + 723.000i 1.17945 + 1.17945i 0.979886 + 0.199560i \(0.0639512\pi\)
0.199560 + 0.979886i \(0.436049\pi\)
\(614\) 36.0000i 0.0586319i
\(615\) −80.0000 + 80.0000i −0.130081 + 0.130081i
\(616\) −64.0000 −0.103896
\(617\) 327.000 327.000i 0.529984 0.529984i −0.390584 0.920567i \(-0.627727\pi\)
0.920567 + 0.390584i \(0.127727\pi\)
\(618\) 472.000 + 472.000i 0.763754 + 0.763754i
\(619\) 660.000i 1.06624i 0.846041 + 0.533118i \(0.178980\pi\)
−0.846041 + 0.533118i \(0.821020\pi\)
\(620\) 520.000 0.838710
\(621\) 80.0000 0.128824
\(622\) 388.000 388.000i 0.623794 0.623794i
\(623\) −160.000 160.000i −0.256822 0.256822i
\(624\) 48.0000i 0.0769231i
\(625\) 625.000 1.00000
\(626\) −366.000 −0.584665
\(627\) −320.000 + 320.000i −0.510367 + 0.510367i
\(628\) −54.0000 54.0000i −0.0859873 0.0859873i
\(629\) 42.0000i 0.0667727i
\(630\) 20.0000i 0.0317460i
\(631\) −548.000 −0.868463 −0.434231 0.900801i \(-0.642980\pi\)
−0.434231 + 0.900801i \(0.642980\pi\)
\(632\) 0 0
\(633\) 656.000 + 656.000i 1.03633 + 1.03633i
\(634\) 426.000i 0.671924i
\(635\) −590.000 590.000i −0.929134 0.929134i
\(636\) −424.000 −0.666667
\(637\) −123.000 + 123.000i −0.193093 + 0.193093i
\(638\) −320.000 320.000i −0.501567 0.501567i
\(639\) 28.0000i 0.0438185i
\(640\) 40.0000 40.0000i 0.0625000 0.0625000i
\(641\) −568.000 −0.886115 −0.443058 0.896493i \(-0.646106\pi\)
−0.443058 + 0.896493i \(0.646106\pi\)
\(642\) 568.000 568.000i 0.884735 0.884735i
\(643\) −342.000 342.000i −0.531882 0.531882i 0.389250 0.921132i \(-0.372734\pi\)
−0.921132 + 0.389250i \(0.872734\pi\)
\(644\) 16.0000i 0.0248447i
\(645\) −840.000 −1.30233
\(646\) −280.000 −0.433437
\(647\) −118.000 + 118.000i −0.182380 + 0.182380i −0.792392 0.610012i \(-0.791165\pi\)
0.610012 + 0.792392i \(0.291165\pi\)
\(648\) 142.000 + 142.000i 0.219136 + 0.219136i
\(649\) 160.000i 0.246533i
\(650\) 150.000 0.230769
\(651\) −416.000 −0.639017
\(652\) −164.000 + 164.000i −0.251534 + 0.251534i
\(653\) 453.000 + 453.000i 0.693721 + 0.693721i 0.963049 0.269327i \(-0.0868014\pi\)
−0.269327 + 0.963049i \(0.586801\pi\)
\(654\) 40.0000i 0.0611621i
\(655\) 640.000i 0.977099i
\(656\) 32.0000 0.0487805
\(657\) −47.0000 + 47.0000i −0.0715373 + 0.0715373i
\(658\) −72.0000 72.0000i −0.109422 0.109422i
\(659\) 140.000i 0.212443i −0.994342 0.106222i \(-0.966125\pi\)
0.994342 0.106222i \(-0.0338753\pi\)
\(660\) 160.000 + 160.000i 0.242424 + 0.242424i
\(661\) 512.000 0.774584 0.387292 0.921957i \(-0.373411\pi\)
0.387292 + 0.921957i \(0.373411\pi\)
\(662\) −232.000 + 232.000i −0.350453 + 0.350453i
\(663\) −84.0000 84.0000i −0.126697 0.126697i
\(664\) 72.0000i 0.108434i
\(665\) −200.000 + 200.000i −0.300752 + 0.300752i
\(666\) −6.00000 −0.00900901
\(667\) −80.0000 + 80.0000i −0.119940 + 0.119940i
\(668\) −124.000 124.000i −0.185629 0.185629i
\(669\) 552.000i 0.825112i
\(670\) −620.000 −0.925373
\(671\) 384.000 0.572280
\(672\) −32.0000 + 32.0000i −0.0476190 + 0.0476190i
\(673\) 193.000 + 193.000i 0.286776 + 0.286776i 0.835804 0.549028i \(-0.185002\pi\)
−0.549028 + 0.835804i \(0.685002\pi\)
\(674\) 834.000i 1.23739i
\(675\) 500.000 500.000i 0.740741 0.740741i
\(676\) −302.000 −0.446746
\(677\) 157.000 157.000i 0.231905 0.231905i −0.581582 0.813488i \(-0.697566\pi\)
0.813488 + 0.581582i \(0.197566\pi\)
\(678\) 92.0000 + 92.0000i 0.135693 + 0.135693i
\(679\) 252.000i 0.371134i
\(680\) 140.000i 0.205882i
\(681\) −8.00000 −0.0117474
\(682\) 416.000 416.000i 0.609971 0.609971i
\(683\) 438.000 + 438.000i 0.641288 + 0.641288i 0.950872 0.309584i \(-0.100190\pi\)
−0.309584 + 0.950872i \(0.600190\pi\)
\(684\) 40.0000i 0.0584795i
\(685\) −315.000 315.000i −0.459854 0.459854i
\(686\) −360.000 −0.524781
\(687\) −240.000 + 240.000i −0.349345 + 0.349345i
\(688\) 168.000 + 168.000i 0.244186 + 0.244186i
\(689\) 318.000i 0.461538i
\(690\) 40.0000 40.0000i 0.0579710 0.0579710i
\(691\) 1032.00 1.49349 0.746744 0.665112i \(-0.231616\pi\)
0.746744 + 0.665112i \(0.231616\pi\)
\(692\) −214.000 + 214.000i −0.309249 + 0.309249i
\(693\) 16.0000 + 16.0000i 0.0230880 + 0.0230880i
\(694\) 404.000i 0.582133i
\(695\) 700.000 1.00719
\(696\) −320.000 −0.459770
\(697\) −56.0000 + 56.0000i −0.0803443 + 0.0803443i
\(698\) −440.000 440.000i −0.630372 0.630372i
\(699\) 732.000i 1.04721i
\(700\) 100.000 + 100.000i 0.142857 + 0.142857i
\(701\) −128.000 −0.182596 −0.0912981 0.995824i \(-0.529102\pi\)
−0.0912981 + 0.995824i \(0.529102\pi\)
\(702\) 120.000 120.000i 0.170940 0.170940i
\(703\) −60.0000 60.0000i −0.0853485 0.0853485i
\(704\) 64.0000i 0.0909091i
\(705\) 360.000i 0.510638i
\(706\) 894.000 1.26629
\(707\) 124.000 124.000i 0.175389 0.175389i
\(708\) −80.0000 80.0000i −0.112994 0.112994i
\(709\) 760.000i 1.07193i −0.844239 0.535966i \(-0.819947\pi\)
0.844239 0.535966i \(-0.180053\pi\)
\(710\) 140.000 + 140.000i 0.197183 + 0.197183i
\(711\) 0 0
\(712\) 160.000 160.000i 0.224719 0.224719i
\(713\) −104.000 104.000i −0.145863 0.145863i
\(714\) 112.000i 0.156863i
\(715\) 120.000 120.000i 0.167832 0.167832i
\(716\) 440.000 0.614525
\(717\) −240.000 + 240.000i −0.334728 + 0.334728i
\(718\) −400.000 400.000i −0.557103 0.557103i
\(719\) 1160.00i 1.61335i 0.590994 + 0.806676i \(0.298736\pi\)
−0.590994 + 0.806676i \(0.701264\pi\)
\(720\) −20.0000 −0.0277778
\(721\) 472.000 0.654646
\(722\) 39.0000 39.0000i 0.0540166 0.0540166i
\(723\) −464.000 464.000i −0.641770 0.641770i
\(724\) 4.00000i 0.00552486i
\(725\) 1000.00i 1.37931i
\(726\) −228.000 −0.314050
\(727\) −558.000 + 558.000i −0.767538 + 0.767538i −0.977672 0.210135i \(-0.932610\pi\)
0.210135 + 0.977672i \(0.432610\pi\)
\(728\) 24.0000 + 24.0000i 0.0329670 + 0.0329670i
\(729\) 791.000i 1.08505i
\(730\) 470.000i 0.643836i
\(731\) −588.000 −0.804378
\(732\) 192.000 192.000i 0.262295 0.262295i
\(733\) −827.000 827.000i −1.12824 1.12824i −0.990463 0.137777i \(-0.956004\pi\)
−0.137777 0.990463i \(-0.543996\pi\)
\(734\) 236.000i 0.321526i
\(735\) 410.000 + 410.000i 0.557823 + 0.557823i
\(736\) −16.0000 −0.0217391
\(737\) −496.000 + 496.000i −0.672999 + 0.672999i
\(738\) −8.00000 8.00000i −0.0108401 0.0108401i
\(739\) 700.000i 0.947226i 0.880733 + 0.473613i \(0.157050\pi\)
−0.880733 + 0.473613i \(0.842950\pi\)
\(740\) −30.0000 + 30.0000i −0.0405405 + 0.0405405i
\(741\) 240.000 0.323887
\(742\) −212.000 + 212.000i −0.285714 + 0.285714i
\(743\) −382.000 382.000i −0.514132 0.514132i 0.401658 0.915790i \(-0.368434\pi\)
−0.915790 + 0.401658i \(0.868434\pi\)
\(744\) 416.000i 0.559140i
\(745\) −750.000 −1.00671
\(746\) 214.000 0.286863
\(747\) 18.0000 18.0000i 0.0240964 0.0240964i
\(748\) 112.000 + 112.000i 0.149733 + 0.149733i
\(749\) 568.000i 0.758344i
\(750\) 500.000i 0.666667i
\(751\) −588.000 −0.782956 −0.391478 0.920187i \(-0.628036\pi\)
−0.391478 + 0.920187i \(0.628036\pi\)
\(752\) 72.0000 72.0000i 0.0957447 0.0957447i
\(753\) 96.0000 + 96.0000i 0.127490 + 0.127490i
\(754\) 240.000i 0.318302i
\(755\) 260.000i 0.344371i
\(756\) 160.000 0.211640
\(757\) 987.000 987.000i 1.30383 1.30383i 0.378043 0.925788i \(-0.376597\pi\)
0.925788 0.378043i \(-0.123403\pi\)
\(758\) 340.000 + 340.000i 0.448549 + 0.448549i
\(759\) 64.0000i 0.0843215i
\(760\) −200.000 200.000i −0.263158 0.263158i
\(761\) −158.000 −0.207622 −0.103811 0.994597i \(-0.533104\pi\)
−0.103811 + 0.994597i \(0.533104\pi\)
\(762\) −472.000 + 472.000i −0.619423 + 0.619423i
\(763\) 20.0000 + 20.0000i 0.0262123 + 0.0262123i
\(764\) 424.000i 0.554974i
\(765\) 35.0000 35.0000i 0.0457516 0.0457516i
\(766\) 684.000 0.892950
\(767\) −60.0000 + 60.0000i −0.0782269 + 0.0782269i
\(768\) −32.0000 32.0000i −0.0416667 0.0416667i
\(769\) 80.0000i 0.104031i −0.998646 0.0520156i \(-0.983435\pi\)
0.998646 0.0520156i \(-0.0165646\pi\)
\(770\) 160.000 0.207792
\(771\) 1252.00 1.62387
\(772\) −114.000 + 114.000i −0.147668 + 0.147668i
\(773\) 243.000 + 243.000i 0.314360 + 0.314360i 0.846596 0.532236i \(-0.178648\pi\)
−0.532236 + 0.846596i \(0.678648\pi\)
\(774\) 84.0000i 0.108527i
\(775\) −1300.00 −1.67742
\(776\) −252.000 −0.324742
\(777\) 24.0000 24.0000i 0.0308880 0.0308880i
\(778\) 390.000 + 390.000i 0.501285 + 0.501285i
\(779\) 160.000i 0.205392i
\(780\) 120.000i 0.153846i
\(781\) 224.000 0.286812
\(782\) 28.0000 28.0000i 0.0358056 0.0358056i
\(783\) 800.000 + 800.000i 1.02171 + 1.02171i
\(784\) 164.000i 0.209184i
\(785\) 135.000 + 135.000i 0.171975 + 0.171975i
\(786\) −512.000 −0.651399
\(787\) 262.000 262.000i 0.332910 0.332910i −0.520781 0.853690i \(-0.674359\pi\)
0.853690 + 0.520781i \(0.174359\pi\)
\(788\) 6.00000 + 6.00000i 0.00761421 + 0.00761421i
\(789\) 1048.00i 1.32826i
\(790\) 0 0
\(791\) 92.0000 0.116308
\(792\) −16.0000 + 16.0000i