Properties

Label 70.2.e.c.51.1
Level $70$
Weight $2$
Character 70.51
Analytic conductor $0.559$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 70.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.558952814149\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 51.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 70.51
Dual form 70.2.e.c.11.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(3.00000 + 5.19615i) q^{11} +(-0.500000 + 0.866025i) q^{12} -4.00000 q^{13} +(2.00000 + 1.73205i) q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{18} +(-1.00000 + 1.73205i) q^{19} -1.00000 q^{20} +(2.50000 - 0.866025i) q^{21} +6.00000 q^{22} +(1.50000 - 2.59808i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.00000 + 3.46410i) q^{26} -5.00000 q^{27} +(2.50000 - 0.866025i) q^{28} -3.00000 q^{29} +(-0.500000 + 0.866025i) q^{30} +(-4.00000 - 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.00000 - 5.19615i) q^{33} +(2.00000 + 1.73205i) q^{35} -2.00000 q^{36} +(2.00000 - 3.46410i) q^{37} +(1.00000 + 1.73205i) q^{38} +(2.00000 + 3.46410i) q^{39} +(-0.500000 + 0.866025i) q^{40} +9.00000 q^{41} +(0.500000 - 2.59808i) q^{42} -7.00000 q^{43} +(3.00000 - 5.19615i) q^{44} +(-1.00000 - 1.73205i) q^{45} +(-1.50000 - 2.59808i) q^{46} +1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} -1.00000 q^{50} +(2.00000 + 3.46410i) q^{52} +(3.00000 + 5.19615i) q^{53} +(-2.50000 + 4.33013i) q^{54} +6.00000 q^{55} +(0.500000 - 2.59808i) q^{56} +2.00000 q^{57} +(-1.50000 + 2.59808i) q^{58} +(3.00000 + 5.19615i) q^{59} +(0.500000 + 0.866025i) q^{60} +(-2.50000 + 4.33013i) q^{61} -8.00000 q^{62} +(4.00000 + 3.46410i) q^{63} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(-3.00000 - 5.19615i) q^{66} +(-2.50000 - 4.33013i) q^{67} -3.00000 q^{69} +(2.50000 - 0.866025i) q^{70} -6.00000 q^{71} +(-1.00000 + 1.73205i) q^{72} +(8.00000 + 13.8564i) q^{73} +(-2.00000 - 3.46410i) q^{74} +(-0.500000 + 0.866025i) q^{75} +2.00000 q^{76} +(-15.0000 + 5.19615i) q^{77} +4.00000 q^{78} +(-1.00000 + 1.73205i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.50000 - 7.79423i) q^{82} +3.00000 q^{83} +(-2.00000 - 1.73205i) q^{84} +(-3.50000 + 6.06218i) q^{86} +(1.50000 + 2.59808i) q^{87} +(-3.00000 - 5.19615i) q^{88} +(7.50000 - 12.9904i) q^{89} -2.00000 q^{90} +(2.00000 - 10.3923i) q^{91} -3.00000 q^{92} +(-4.00000 + 6.92820i) q^{93} +(1.00000 + 1.73205i) q^{95} +(0.500000 - 0.866025i) q^{96} +14.0000 q^{97} +(-5.50000 + 4.33013i) q^{98} +12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{3} - q^{4} + q^{5} - 2 q^{6} - q^{7} - 2 q^{8} + 2 q^{9} + O(q^{10}) \) \( 2 q + q^{2} - q^{3} - q^{4} + q^{5} - 2 q^{6} - q^{7} - 2 q^{8} + 2 q^{9} - q^{10} + 6 q^{11} - q^{12} - 8 q^{13} + 4 q^{14} - 2 q^{15} - q^{16} - 2 q^{18} - 2 q^{19} - 2 q^{20} + 5 q^{21} + 12 q^{22} + 3 q^{23} + q^{24} - q^{25} - 4 q^{26} - 10 q^{27} + 5 q^{28} - 6 q^{29} - q^{30} - 8 q^{31} + q^{32} + 6 q^{33} + 4 q^{35} - 4 q^{36} + 4 q^{37} + 2 q^{38} + 4 q^{39} - q^{40} + 18 q^{41} + q^{42} - 14 q^{43} + 6 q^{44} - 2 q^{45} - 3 q^{46} + 2 q^{48} - 13 q^{49} - 2 q^{50} + 4 q^{52} + 6 q^{53} - 5 q^{54} + 12 q^{55} + q^{56} + 4 q^{57} - 3 q^{58} + 6 q^{59} + q^{60} - 5 q^{61} - 16 q^{62} + 8 q^{63} + 2 q^{64} - 4 q^{65} - 6 q^{66} - 5 q^{67} - 6 q^{69} + 5 q^{70} - 12 q^{71} - 2 q^{72} + 16 q^{73} - 4 q^{74} - q^{75} + 4 q^{76} - 30 q^{77} + 8 q^{78} - 2 q^{79} + q^{80} - q^{81} + 9 q^{82} + 6 q^{83} - 4 q^{84} - 7 q^{86} + 3 q^{87} - 6 q^{88} + 15 q^{89} - 4 q^{90} + 4 q^{91} - 6 q^{92} - 8 q^{93} + 2 q^{95} + q^{96} + 28 q^{97} - 11 q^{98} + 24 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/70\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(57\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) −0.500000 0.866025i −0.288675 0.500000i 0.684819 0.728714i \(-0.259881\pi\)
−0.973494 + 0.228714i \(0.926548\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) −1.00000 −0.408248
\(7\) −0.500000 + 2.59808i −0.188982 + 0.981981i
\(8\) −1.00000 −0.353553
\(9\) 1.00000 1.73205i 0.333333 0.577350i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) 3.00000 + 5.19615i 0.904534 + 1.56670i 0.821541 + 0.570149i \(0.193114\pi\)
0.0829925 + 0.996550i \(0.473552\pi\)
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 2.00000 + 1.73205i 0.534522 + 0.462910i
\(15\) −1.00000 −0.258199
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) −1.00000 1.73205i −0.235702 0.408248i
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) −1.00000 −0.223607
\(21\) 2.50000 0.866025i 0.545545 0.188982i
\(22\) 6.00000 1.27920
\(23\) 1.50000 2.59808i 0.312772 0.541736i −0.666190 0.745782i \(-0.732076\pi\)
0.978961 + 0.204046i \(0.0654092\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −2.00000 + 3.46410i −0.392232 + 0.679366i
\(27\) −5.00000 −0.962250
\(28\) 2.50000 0.866025i 0.472456 0.163663i
\(29\) −3.00000 −0.557086 −0.278543 0.960424i \(-0.589851\pi\)
−0.278543 + 0.960424i \(0.589851\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) −4.00000 6.92820i −0.718421 1.24434i −0.961625 0.274367i \(-0.911532\pi\)
0.243204 0.969975i \(-0.421802\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 3.00000 5.19615i 0.522233 0.904534i
\(34\) 0 0
\(35\) 2.00000 + 1.73205i 0.338062 + 0.292770i
\(36\) −2.00000 −0.333333
\(37\) 2.00000 3.46410i 0.328798 0.569495i −0.653476 0.756948i \(-0.726690\pi\)
0.982274 + 0.187453i \(0.0600231\pi\)
\(38\) 1.00000 + 1.73205i 0.162221 + 0.280976i
\(39\) 2.00000 + 3.46410i 0.320256 + 0.554700i
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) 9.00000 1.40556 0.702782 0.711405i \(-0.251941\pi\)
0.702782 + 0.711405i \(0.251941\pi\)
\(42\) 0.500000 2.59808i 0.0771517 0.400892i
\(43\) −7.00000 −1.06749 −0.533745 0.845645i \(-0.679216\pi\)
−0.533745 + 0.845645i \(0.679216\pi\)
\(44\) 3.00000 5.19615i 0.452267 0.783349i
\(45\) −1.00000 1.73205i −0.149071 0.258199i
\(46\) −1.50000 2.59808i −0.221163 0.383065i
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 1.00000 0.144338
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) 2.00000 + 3.46410i 0.277350 + 0.480384i
\(53\) 3.00000 + 5.19615i 0.412082 + 0.713746i 0.995117 0.0987002i \(-0.0314685\pi\)
−0.583036 + 0.812447i \(0.698135\pi\)
\(54\) −2.50000 + 4.33013i −0.340207 + 0.589256i
\(55\) 6.00000 0.809040
\(56\) 0.500000 2.59808i 0.0668153 0.347183i
\(57\) 2.00000 0.264906
\(58\) −1.50000 + 2.59808i −0.196960 + 0.341144i
\(59\) 3.00000 + 5.19615i 0.390567 + 0.676481i 0.992524 0.122047i \(-0.0389457\pi\)
−0.601958 + 0.798528i \(0.705612\pi\)
\(60\) 0.500000 + 0.866025i 0.0645497 + 0.111803i
\(61\) −2.50000 + 4.33013i −0.320092 + 0.554416i −0.980507 0.196485i \(-0.937047\pi\)
0.660415 + 0.750901i \(0.270381\pi\)
\(62\) −8.00000 −1.01600
\(63\) 4.00000 + 3.46410i 0.503953 + 0.436436i
\(64\) 1.00000 0.125000
\(65\) −2.00000 + 3.46410i −0.248069 + 0.429669i
\(66\) −3.00000 5.19615i −0.369274 0.639602i
\(67\) −2.50000 4.33013i −0.305424 0.529009i 0.671932 0.740613i \(-0.265465\pi\)
−0.977356 + 0.211604i \(0.932131\pi\)
\(68\) 0 0
\(69\) −3.00000 −0.361158
\(70\) 2.50000 0.866025i 0.298807 0.103510i
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) −1.00000 + 1.73205i −0.117851 + 0.204124i
\(73\) 8.00000 + 13.8564i 0.936329 + 1.62177i 0.772246 + 0.635323i \(0.219133\pi\)
0.164083 + 0.986447i \(0.447534\pi\)
\(74\) −2.00000 3.46410i −0.232495 0.402694i
\(75\) −0.500000 + 0.866025i −0.0577350 + 0.100000i
\(76\) 2.00000 0.229416
\(77\) −15.0000 + 5.19615i −1.70941 + 0.592157i
\(78\) 4.00000 0.452911
\(79\) −1.00000 + 1.73205i −0.112509 + 0.194871i −0.916781 0.399390i \(-0.869222\pi\)
0.804272 + 0.594261i \(0.202555\pi\)
\(80\) 0.500000 + 0.866025i 0.0559017 + 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 4.50000 7.79423i 0.496942 0.860729i
\(83\) 3.00000 0.329293 0.164646 0.986353i \(-0.447352\pi\)
0.164646 + 0.986353i \(0.447352\pi\)
\(84\) −2.00000 1.73205i −0.218218 0.188982i
\(85\) 0 0
\(86\) −3.50000 + 6.06218i −0.377415 + 0.653701i
\(87\) 1.50000 + 2.59808i 0.160817 + 0.278543i
\(88\) −3.00000 5.19615i −0.319801 0.553912i
\(89\) 7.50000 12.9904i 0.794998 1.37698i −0.127842 0.991795i \(-0.540805\pi\)
0.922840 0.385183i \(-0.125862\pi\)
\(90\) −2.00000 −0.210819
\(91\) 2.00000 10.3923i 0.209657 1.08941i
\(92\) −3.00000 −0.312772
\(93\) −4.00000 + 6.92820i −0.414781 + 0.718421i
\(94\) 0 0
\(95\) 1.00000 + 1.73205i 0.102598 + 0.177705i
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) 14.0000 1.42148 0.710742 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) −5.50000 + 4.33013i −0.555584 + 0.437409i
\(99\) 12.0000 1.20605
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) −7.50000 12.9904i −0.746278 1.29259i −0.949595 0.313478i \(-0.898506\pi\)
0.203317 0.979113i \(-0.434828\pi\)
\(102\) 0 0
\(103\) 0.500000 0.866025i 0.0492665 0.0853320i −0.840341 0.542059i \(-0.817645\pi\)
0.889607 + 0.456727i \(0.150978\pi\)
\(104\) 4.00000 0.392232
\(105\) 0.500000 2.59808i 0.0487950 0.253546i
\(106\) 6.00000 0.582772
\(107\) 7.50000 12.9904i 0.725052 1.25583i −0.233900 0.972261i \(-0.575149\pi\)
0.958952 0.283567i \(-0.0915178\pi\)
\(108\) 2.50000 + 4.33013i 0.240563 + 0.416667i
\(109\) −5.50000 9.52628i −0.526804 0.912452i −0.999512 0.0312328i \(-0.990057\pi\)
0.472708 0.881219i \(-0.343277\pi\)
\(110\) 3.00000 5.19615i 0.286039 0.495434i
\(111\) −4.00000 −0.379663
\(112\) −2.00000 1.73205i −0.188982 0.163663i
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 1.00000 1.73205i 0.0936586 0.162221i
\(115\) −1.50000 2.59808i −0.139876 0.242272i
\(116\) 1.50000 + 2.59808i 0.139272 + 0.241225i
\(117\) −4.00000 + 6.92820i −0.369800 + 0.640513i
\(118\) 6.00000 0.552345
\(119\) 0 0
\(120\) 1.00000 0.0912871
\(121\) −12.5000 + 21.6506i −1.13636 + 1.96824i
\(122\) 2.50000 + 4.33013i 0.226339 + 0.392031i
\(123\) −4.50000 7.79423i −0.405751 0.702782i
\(124\) −4.00000 + 6.92820i −0.359211 + 0.622171i
\(125\) −1.00000 −0.0894427
\(126\) 5.00000 1.73205i 0.445435 0.154303i
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 3.50000 + 6.06218i 0.308158 + 0.533745i
\(130\) 2.00000 + 3.46410i 0.175412 + 0.303822i
\(131\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(132\) −6.00000 −0.522233
\(133\) −4.00000 3.46410i −0.346844 0.300376i
\(134\) −5.00000 −0.431934
\(135\) −2.50000 + 4.33013i −0.215166 + 0.372678i
\(136\) 0 0
\(137\) −6.00000 10.3923i −0.512615 0.887875i −0.999893 0.0146279i \(-0.995344\pi\)
0.487278 0.873247i \(-0.337990\pi\)
\(138\) −1.50000 + 2.59808i −0.127688 + 0.221163i
\(139\) −10.0000 −0.848189 −0.424094 0.905618i \(-0.639408\pi\)
−0.424094 + 0.905618i \(0.639408\pi\)
\(140\) 0.500000 2.59808i 0.0422577 0.219578i
\(141\) 0 0
\(142\) −3.00000 + 5.19615i −0.251754 + 0.436051i
\(143\) −12.0000 20.7846i −1.00349 1.73810i
\(144\) 1.00000 + 1.73205i 0.0833333 + 0.144338i
\(145\) −1.50000 + 2.59808i −0.124568 + 0.215758i
\(146\) 16.0000 1.32417
\(147\) 1.00000 + 6.92820i 0.0824786 + 0.571429i
\(148\) −4.00000 −0.328798
\(149\) −7.50000 + 12.9904i −0.614424 + 1.06421i 0.376061 + 0.926595i \(0.377278\pi\)
−0.990485 + 0.137619i \(0.956055\pi\)
\(150\) 0.500000 + 0.866025i 0.0408248 + 0.0707107i
\(151\) 2.00000 + 3.46410i 0.162758 + 0.281905i 0.935857 0.352381i \(-0.114628\pi\)
−0.773099 + 0.634285i \(0.781294\pi\)
\(152\) 1.00000 1.73205i 0.0811107 0.140488i
\(153\) 0 0
\(154\) −3.00000 + 15.5885i −0.241747 + 1.25615i
\(155\) −8.00000 −0.642575
\(156\) 2.00000 3.46410i 0.160128 0.277350i
\(157\) 11.0000 + 19.0526i 0.877896 + 1.52056i 0.853646 + 0.520854i \(0.174386\pi\)
0.0242497 + 0.999706i \(0.492280\pi\)
\(158\) 1.00000 + 1.73205i 0.0795557 + 0.137795i
\(159\) 3.00000 5.19615i 0.237915 0.412082i
\(160\) 1.00000 0.0790569
\(161\) 6.00000 + 5.19615i 0.472866 + 0.409514i
\(162\) −1.00000 −0.0785674
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) −4.50000 7.79423i −0.351391 0.608627i
\(165\) −3.00000 5.19615i −0.233550 0.404520i
\(166\) 1.50000 2.59808i 0.116423 0.201650i
\(167\) −3.00000 −0.232147 −0.116073 0.993241i \(-0.537031\pi\)
−0.116073 + 0.993241i \(0.537031\pi\)
\(168\) −2.50000 + 0.866025i −0.192879 + 0.0668153i
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 2.00000 + 3.46410i 0.152944 + 0.264906i
\(172\) 3.50000 + 6.06218i 0.266872 + 0.462237i
\(173\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(174\) 3.00000 0.227429
\(175\) 2.50000 0.866025i 0.188982 0.0654654i
\(176\) −6.00000 −0.452267
\(177\) 3.00000 5.19615i 0.225494 0.390567i
\(178\) −7.50000 12.9904i −0.562149 0.973670i
\(179\) 12.0000 + 20.7846i 0.896922 + 1.55351i 0.831408 + 0.555663i \(0.187536\pi\)
0.0655145 + 0.997852i \(0.479131\pi\)
\(180\) −1.00000 + 1.73205i −0.0745356 + 0.129099i
\(181\) 11.0000 0.817624 0.408812 0.912619i \(-0.365943\pi\)
0.408812 + 0.912619i \(0.365943\pi\)
\(182\) −8.00000 6.92820i −0.592999 0.513553i
\(183\) 5.00000 0.369611
\(184\) −1.50000 + 2.59808i −0.110581 + 0.191533i
\(185\) −2.00000 3.46410i −0.147043 0.254686i
\(186\) 4.00000 + 6.92820i 0.293294 + 0.508001i
\(187\) 0 0
\(188\) 0 0
\(189\) 2.50000 12.9904i 0.181848 0.944911i
\(190\) 2.00000 0.145095
\(191\) 3.00000 5.19615i 0.217072 0.375980i −0.736839 0.676068i \(-0.763683\pi\)
0.953912 + 0.300088i \(0.0970159\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −1.00000 1.73205i −0.0719816 0.124676i 0.827788 0.561041i \(-0.189599\pi\)
−0.899770 + 0.436365i \(0.856266\pi\)
\(194\) 7.00000 12.1244i 0.502571 0.870478i
\(195\) 4.00000 0.286446
\(196\) 1.00000 + 6.92820i 0.0714286 + 0.494872i
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 6.00000 10.3923i 0.426401 0.738549i
\(199\) 2.00000 + 3.46410i 0.141776 + 0.245564i 0.928166 0.372168i \(-0.121385\pi\)
−0.786389 + 0.617731i \(0.788052\pi\)
\(200\) 0.500000 + 0.866025i 0.0353553 + 0.0612372i
\(201\) −2.50000 + 4.33013i −0.176336 + 0.305424i
\(202\) −15.0000 −1.05540
\(203\) 1.50000 7.79423i 0.105279 0.547048i
\(204\) 0 0
\(205\) 4.50000 7.79423i 0.314294 0.544373i
\(206\) −0.500000 0.866025i −0.0348367 0.0603388i
\(207\) −3.00000 5.19615i −0.208514 0.361158i
\(208\) 2.00000 3.46410i 0.138675 0.240192i
\(209\) −12.0000 −0.830057
\(210\) −2.00000 1.73205i −0.138013 0.119523i
\(211\) −10.0000 −0.688428 −0.344214 0.938891i \(-0.611855\pi\)
−0.344214 + 0.938891i \(0.611855\pi\)
\(212\) 3.00000 5.19615i 0.206041 0.356873i
\(213\) 3.00000 + 5.19615i 0.205557 + 0.356034i
\(214\) −7.50000 12.9904i −0.512689 0.888004i
\(215\) −3.50000 + 6.06218i −0.238698 + 0.413437i
\(216\) 5.00000 0.340207
\(217\) 20.0000 6.92820i 1.35769 0.470317i
\(218\) −11.0000 −0.745014
\(219\) 8.00000 13.8564i 0.540590 0.936329i
\(220\) −3.00000 5.19615i −0.202260 0.350325i
\(221\) 0 0
\(222\) −2.00000 + 3.46410i −0.134231 + 0.232495i
\(223\) −28.0000 −1.87502 −0.937509 0.347960i \(-0.886874\pi\)
−0.937509 + 0.347960i \(0.886874\pi\)
\(224\) −2.50000 + 0.866025i −0.167038 + 0.0578638i
\(225\) −2.00000 −0.133333
\(226\) 3.00000 5.19615i 0.199557 0.345643i
\(227\) 6.00000 + 10.3923i 0.398234 + 0.689761i 0.993508 0.113761i \(-0.0362899\pi\)
−0.595274 + 0.803523i \(0.702957\pi\)
\(228\) −1.00000 1.73205i −0.0662266 0.114708i
\(229\) −7.00000 + 12.1244i −0.462573 + 0.801200i −0.999088 0.0426906i \(-0.986407\pi\)
0.536515 + 0.843891i \(0.319740\pi\)
\(230\) −3.00000 −0.197814
\(231\) 12.0000 + 10.3923i 0.789542 + 0.683763i
\(232\) 3.00000 0.196960
\(233\) 6.00000 10.3923i 0.393073 0.680823i −0.599780 0.800165i \(-0.704745\pi\)
0.992853 + 0.119342i \(0.0380786\pi\)
\(234\) 4.00000 + 6.92820i 0.261488 + 0.452911i
\(235\) 0 0
\(236\) 3.00000 5.19615i 0.195283 0.338241i
\(237\) 2.00000 0.129914
\(238\) 0 0
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0.500000 0.866025i 0.0322749 0.0559017i
\(241\) −1.00000 1.73205i −0.0644157 0.111571i 0.832019 0.554747i \(-0.187185\pi\)
−0.896435 + 0.443176i \(0.853852\pi\)
\(242\) 12.5000 + 21.6506i 0.803530 + 1.39176i
\(243\) −8.00000 + 13.8564i −0.513200 + 0.888889i
\(244\) 5.00000 0.320092
\(245\) −5.50000 + 4.33013i −0.351382 + 0.276642i
\(246\) −9.00000 −0.573819
\(247\) 4.00000 6.92820i 0.254514 0.440831i
\(248\) 4.00000 + 6.92820i 0.254000 + 0.439941i
\(249\) −1.50000 2.59808i −0.0950586 0.164646i
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 1.00000 5.19615i 0.0629941 0.327327i
\(253\) 18.0000 1.13165
\(254\) 4.00000 6.92820i 0.250982 0.434714i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(258\) 7.00000 0.435801
\(259\) 8.00000 + 6.92820i 0.497096 + 0.430498i
\(260\) 4.00000 0.248069
\(261\) −3.00000 + 5.19615i −0.185695 + 0.321634i
\(262\) 0 0
\(263\) 10.5000 + 18.1865i 0.647458 + 1.12143i 0.983728 + 0.179664i \(0.0575011\pi\)
−0.336270 + 0.941766i \(0.609166\pi\)
\(264\) −3.00000 + 5.19615i −0.184637 + 0.319801i
\(265\) 6.00000 0.368577
\(266\) −5.00000 + 1.73205i −0.306570 + 0.106199i
\(267\) −15.0000 −0.917985
\(268\) −2.50000 + 4.33013i −0.152712 + 0.264505i
\(269\) −7.50000 12.9904i −0.457283 0.792038i 0.541533 0.840679i \(-0.317844\pi\)
−0.998816 + 0.0486418i \(0.984511\pi\)
\(270\) 2.50000 + 4.33013i 0.152145 + 0.263523i
\(271\) −1.00000 + 1.73205i −0.0607457 + 0.105215i −0.894799 0.446469i \(-0.852681\pi\)
0.834053 + 0.551684i \(0.186015\pi\)
\(272\) 0 0
\(273\) −10.0000 + 3.46410i −0.605228 + 0.209657i
\(274\) −12.0000 −0.724947
\(275\) 3.00000 5.19615i 0.180907 0.313340i
\(276\) 1.50000 + 2.59808i 0.0902894 + 0.156386i
\(277\) −4.00000 6.92820i −0.240337 0.416275i 0.720473 0.693482i \(-0.243925\pi\)
−0.960810 + 0.277207i \(0.910591\pi\)
\(278\) −5.00000 + 8.66025i −0.299880 + 0.519408i
\(279\) −16.0000 −0.957895
\(280\) −2.00000 1.73205i −0.119523 0.103510i
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 0 0
\(283\) 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) 3.00000 + 5.19615i 0.178017 + 0.308335i
\(285\) 1.00000 1.73205i 0.0592349 0.102598i
\(286\) −24.0000 −1.41915
\(287\) −4.50000 + 23.3827i −0.265627 + 1.38024i
\(288\) 2.00000 0.117851
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) 1.50000 + 2.59808i 0.0880830 + 0.152564i
\(291\) −7.00000 12.1244i −0.410347 0.710742i
\(292\) 8.00000 13.8564i 0.468165 0.810885i
\(293\) 12.0000 0.701047 0.350524 0.936554i \(-0.386004\pi\)
0.350524 + 0.936554i \(0.386004\pi\)
\(294\) 6.50000 + 2.59808i 0.379088 + 0.151523i
\(295\) 6.00000 0.349334
\(296\) −2.00000 + 3.46410i −0.116248 + 0.201347i
\(297\) −15.0000 25.9808i −0.870388 1.50756i
\(298\) 7.50000 + 12.9904i 0.434463 + 0.752513i
\(299\) −6.00000 + 10.3923i −0.346989 + 0.601003i
\(300\) 1.00000 0.0577350
\(301\) 3.50000 18.1865i 0.201737 1.04825i
\(302\) 4.00000 0.230174
\(303\) −7.50000 + 12.9904i −0.430864 + 0.746278i
\(304\) −1.00000 1.73205i −0.0573539 0.0993399i
\(305\) 2.50000 + 4.33013i 0.143150 + 0.247942i
\(306\) 0 0
\(307\) 5.00000 0.285365 0.142683 0.989769i \(-0.454427\pi\)
0.142683 + 0.989769i \(0.454427\pi\)
\(308\) 12.0000 + 10.3923i 0.683763 + 0.592157i
\(309\) −1.00000 −0.0568880
\(310\) −4.00000 + 6.92820i −0.227185 + 0.393496i
\(311\) 9.00000 + 15.5885i 0.510343 + 0.883940i 0.999928 + 0.0119847i \(0.00381495\pi\)
−0.489585 + 0.871956i \(0.662852\pi\)
\(312\) −2.00000 3.46410i −0.113228 0.196116i
\(313\) −4.00000 + 6.92820i −0.226093 + 0.391605i −0.956647 0.291250i \(-0.905929\pi\)
0.730554 + 0.682855i \(0.239262\pi\)
\(314\) 22.0000 1.24153
\(315\) 5.00000 1.73205i 0.281718 0.0975900i
\(316\) 2.00000 0.112509
\(317\) −6.00000 + 10.3923i −0.336994 + 0.583690i −0.983866 0.178908i \(-0.942743\pi\)
0.646872 + 0.762598i \(0.276077\pi\)
\(318\) −3.00000 5.19615i −0.168232 0.291386i
\(319\) −9.00000 15.5885i −0.503903 0.872786i
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) −15.0000 −0.837218
\(322\) 7.50000 2.59808i 0.417959 0.144785i
\(323\) 0 0
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 2.00000 + 3.46410i 0.110940 + 0.192154i
\(326\) −2.00000 3.46410i −0.110770 0.191859i
\(327\) −5.50000 + 9.52628i −0.304151 + 0.526804i
\(328\) −9.00000 −0.496942
\(329\) 0 0
\(330\) −6.00000 −0.330289
\(331\) 14.0000 24.2487i 0.769510 1.33283i −0.168320 0.985732i \(-0.553834\pi\)
0.937829 0.347097i \(-0.112833\pi\)
\(332\) −1.50000 2.59808i −0.0823232 0.142588i
\(333\) −4.00000 6.92820i −0.219199 0.379663i
\(334\) −1.50000 + 2.59808i −0.0820763 + 0.142160i
\(335\) −5.00000 −0.273179
\(336\) −0.500000 + 2.59808i −0.0272772 + 0.141737i
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) 1.50000 2.59808i 0.0815892 0.141317i
\(339\) −3.00000 5.19615i −0.162938 0.282216i
\(340\) 0 0
\(341\) 24.0000 41.5692i 1.29967 2.25110i
\(342\) 4.00000 0.216295
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 7.00000 0.377415
\(345\) −1.50000 + 2.59808i −0.0807573 + 0.139876i
\(346\) 0 0
\(347\) −4.50000 7.79423i −0.241573 0.418416i 0.719590 0.694399i \(-0.244330\pi\)
−0.961162 + 0.275983i \(0.910997\pi\)
\(348\) 1.50000 2.59808i 0.0804084 0.139272i
\(349\) 17.0000 0.909989 0.454995 0.890494i \(-0.349641\pi\)
0.454995 + 0.890494i \(0.349641\pi\)
\(350\) 0.500000 2.59808i 0.0267261 0.138873i
\(351\) 20.0000 1.06752
\(352\) −3.00000 + 5.19615i −0.159901 + 0.276956i
\(353\) 3.00000 + 5.19615i 0.159674 + 0.276563i 0.934751 0.355303i \(-0.115622\pi\)
−0.775077 + 0.631867i \(0.782289\pi\)
\(354\) −3.00000 5.19615i −0.159448 0.276172i
\(355\) −3.00000 + 5.19615i −0.159223 + 0.275783i
\(356\) −15.0000 −0.794998
\(357\) 0 0
\(358\) 24.0000 1.26844
\(359\) −12.0000 + 20.7846i −0.633336 + 1.09697i 0.353529 + 0.935423i \(0.384981\pi\)
−0.986865 + 0.161546i \(0.948352\pi\)
\(360\) 1.00000 + 1.73205i 0.0527046 + 0.0912871i
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 5.50000 9.52628i 0.289074 0.500690i
\(363\) 25.0000 1.31216
\(364\) −10.0000 + 3.46410i −0.524142 + 0.181568i
\(365\) 16.0000 0.837478
\(366\) 2.50000 4.33013i 0.130677 0.226339i
\(367\) −17.5000 30.3109i −0.913493 1.58222i −0.809093 0.587680i \(-0.800041\pi\)
−0.104399 0.994535i \(-0.533292\pi\)
\(368\) 1.50000 + 2.59808i 0.0781929 + 0.135434i
\(369\) 9.00000 15.5885i 0.468521 0.811503i
\(370\) −4.00000 −0.207950
\(371\) −15.0000 + 5.19615i −0.778761 + 0.269771i
\(372\) 8.00000 0.414781
\(373\) 2.00000 3.46410i 0.103556 0.179364i −0.809591 0.586994i \(-0.800311\pi\)
0.913147 + 0.407630i \(0.133645\pi\)
\(374\) 0 0
\(375\) 0.500000 + 0.866025i 0.0258199 + 0.0447214i
\(376\) 0 0
\(377\) 12.0000 0.618031
\(378\) −10.0000 8.66025i −0.514344 0.445435i
\(379\) −34.0000 −1.74646 −0.873231 0.487306i \(-0.837980\pi\)
−0.873231 + 0.487306i \(0.837980\pi\)
\(380\) 1.00000 1.73205i 0.0512989 0.0888523i
\(381\) −4.00000 6.92820i −0.204926 0.354943i
\(382\) −3.00000 5.19615i −0.153493 0.265858i
\(383\) 7.50000 12.9904i 0.383232 0.663777i −0.608290 0.793715i \(-0.708144\pi\)
0.991522 + 0.129937i \(0.0414776\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −3.00000 + 15.5885i −0.152894 + 0.794461i
\(386\) −2.00000 −0.101797
\(387\) −7.00000 + 12.1244i −0.355830 + 0.616316i
\(388\) −7.00000 12.1244i −0.355371 0.615521i
\(389\) 15.0000 + 25.9808i 0.760530 + 1.31728i 0.942578 + 0.333987i \(0.108394\pi\)
−0.182047 + 0.983290i \(0.558272\pi\)
\(390\) 2.00000 3.46410i 0.101274 0.175412i
\(391\) 0 0
\(392\) 6.50000 + 2.59808i 0.328300 + 0.131223i
\(393\) 0 0
\(394\) −3.00000 + 5.19615i −0.151138 + 0.261778i
\(395\) 1.00000 + 1.73205i 0.0503155 + 0.0871489i
\(396\) −6.00000 10.3923i −0.301511 0.522233i
\(397\) −7.00000 + 12.1244i −0.351320 + 0.608504i −0.986481 0.163876i \(-0.947600\pi\)
0.635161 + 0.772380i \(0.280934\pi\)
\(398\) 4.00000 0.200502
\(399\) −1.00000 + 5.19615i −0.0500626 + 0.260133i
\(400\) 1.00000 0.0500000
\(401\) −7.50000 + 12.9904i −0.374532 + 0.648709i −0.990257 0.139253i \(-0.955530\pi\)
0.615725 + 0.787961i \(0.288863\pi\)
\(402\) 2.50000 + 4.33013i 0.124689 + 0.215967i
\(403\) 16.0000 + 27.7128i 0.797017 + 1.38047i
\(404\) −7.50000 + 12.9904i −0.373139 + 0.646296i
\(405\) −1.00000 −0.0496904
\(406\) −6.00000 5.19615i −0.297775 0.257881i
\(407\) 24.0000 1.18964
\(408\) 0 0
\(409\) 6.50000 + 11.2583i 0.321404 + 0.556689i 0.980778 0.195127i \(-0.0625118\pi\)
−0.659374 + 0.751815i \(0.729178\pi\)
\(410\) −4.50000 7.79423i −0.222239 0.384930i
\(411\) −6.00000 + 10.3923i −0.295958 + 0.512615i
\(412\) −1.00000 −0.0492665
\(413\) −15.0000 + 5.19615i −0.738102 + 0.255686i
\(414\) −6.00000 −0.294884
\(415\) 1.50000 2.59808i 0.0736321 0.127535i
\(416\) −2.00000 3.46410i −0.0980581 0.169842i
\(417\) 5.00000 + 8.66025i 0.244851 + 0.424094i
\(418\) −6.00000 + 10.3923i −0.293470 + 0.508304i
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) −2.50000 + 0.866025i −0.121988 + 0.0422577i
\(421\) 17.0000 0.828529 0.414265 0.910156i \(-0.364039\pi\)
0.414265 + 0.910156i \(0.364039\pi\)
\(422\) −5.00000 + 8.66025i −0.243396 + 0.421575i
\(423\) 0 0
\(424\) −3.00000 5.19615i −0.145693 0.252347i
\(425\) 0 0
\(426\) 6.00000 0.290701
\(427\) −10.0000 8.66025i −0.483934 0.419099i
\(428\) −15.0000 −0.725052
\(429\) −12.0000 + 20.7846i −0.579365 + 1.00349i
\(430\) 3.50000 + 6.06218i 0.168785 + 0.292344i
\(431\) −15.0000 25.9808i −0.722525 1.25145i −0.959985 0.280052i \(-0.909648\pi\)
0.237460 0.971397i \(-0.423685\pi\)
\(432\) 2.50000 4.33013i 0.120281 0.208333i
\(433\) −22.0000 −1.05725 −0.528626 0.848855i \(-0.677293\pi\)
−0.528626 + 0.848855i \(0.677293\pi\)
\(434\) 4.00000 20.7846i 0.192006 0.997693i
\(435\) 3.00000 0.143839
\(436\) −5.50000 + 9.52628i −0.263402 + 0.456226i
\(437\) 3.00000 + 5.19615i 0.143509 + 0.248566i
\(438\) −8.00000 13.8564i −0.382255 0.662085i
\(439\) 14.0000 24.2487i 0.668184 1.15733i −0.310228 0.950662i \(-0.600405\pi\)
0.978412 0.206666i \(-0.0662612\pi\)
\(440\) −6.00000 −0.286039
\(441\) −11.0000 + 8.66025i −0.523810 + 0.412393i
\(442\) 0 0
\(443\) −10.5000 + 18.1865i −0.498870 + 0.864068i −0.999999 0.00130426i \(-0.999585\pi\)
0.501129 + 0.865373i \(0.332918\pi\)
\(444\) 2.00000 + 3.46410i 0.0949158 + 0.164399i
\(445\) −7.50000 12.9904i −0.355534 0.615803i
\(446\) −14.0000 + 24.2487i −0.662919 + 1.14821i
\(447\) 15.0000 0.709476
\(448\) −0.500000 + 2.59808i −0.0236228 + 0.122748i
\(449\) −9.00000 −0.424736 −0.212368 0.977190i \(-0.568118\pi\)
−0.212368 + 0.977190i \(0.568118\pi\)
\(450\) −1.00000 + 1.73205i −0.0471405 + 0.0816497i
\(451\) 27.0000 + 46.7654i 1.27138 + 2.20210i
\(452\) −3.00000 5.19615i −0.141108 0.244406i
\(453\) 2.00000 3.46410i 0.0939682 0.162758i
\(454\) 12.0000 0.563188
\(455\) −8.00000 6.92820i −0.375046 0.324799i
\(456\) −2.00000 −0.0936586
\(457\) −16.0000 + 27.7128i −0.748448 + 1.29635i 0.200118 + 0.979772i \(0.435868\pi\)
−0.948566 + 0.316579i \(0.897466\pi\)
\(458\) 7.00000 + 12.1244i 0.327089 + 0.566534i
\(459\) 0 0
\(460\) −1.50000 + 2.59808i −0.0699379 + 0.121136i
\(461\) 18.0000 0.838344 0.419172 0.907907i \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(462\) 15.0000 5.19615i 0.697863 0.241747i
\(463\) −13.0000 −0.604161 −0.302081 0.953282i \(-0.597681\pi\)
−0.302081 + 0.953282i \(0.597681\pi\)
\(464\) 1.50000 2.59808i 0.0696358 0.120613i
\(465\) 4.00000 + 6.92820i 0.185496 + 0.321288i
\(466\) −6.00000 10.3923i −0.277945 0.481414i
\(467\) 7.50000 12.9904i 0.347059 0.601123i −0.638667 0.769483i \(-0.720514\pi\)
0.985726 + 0.168360i \(0.0538472\pi\)
\(468\) 8.00000 0.369800
\(469\) 12.5000 4.33013i 0.577196 0.199947i
\(470\) 0 0
\(471\) 11.0000 19.0526i 0.506853 0.877896i
\(472\) −3.00000 5.19615i −0.138086 0.239172i
\(473\) −21.0000 36.3731i −0.965581 1.67244i
\(474\) 1.00000 1.73205i 0.0459315 0.0795557i
\(475\) 2.00000 0.0917663
\(476\) 0 0
\(477\) 12.0000 0.549442
\(478\) 6.00000 10.3923i 0.274434 0.475333i
\(479\) −6.00000 10.3923i −0.274147 0.474837i 0.695773 0.718262i \(-0.255062\pi\)
−0.969920 + 0.243426i \(0.921729\pi\)
\(480\) −0.500000 0.866025i −0.0228218 0.0395285i
\(481\) −8.00000 + 13.8564i −0.364769 + 0.631798i
\(482\) −2.00000 −0.0910975
\(483\) 1.50000 7.79423i 0.0682524 0.354650i
\(484\) 25.0000 1.13636
\(485\) 7.00000 12.1244i 0.317854 0.550539i
\(486\) 8.00000 + 13.8564i 0.362887 + 0.628539i
\(487\) 8.00000 + 13.8564i 0.362515 + 0.627894i 0.988374 0.152042i \(-0.0485850\pi\)
−0.625859 + 0.779936i \(0.715252\pi\)
\(488\) 2.50000 4.33013i 0.113170 0.196016i
\(489\) −4.00000 −0.180886
\(490\) 1.00000 + 6.92820i 0.0451754 + 0.312984i
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) −4.50000 + 7.79423i −0.202876 + 0.351391i
\(493\) 0 0
\(494\) −4.00000 6.92820i −0.179969 0.311715i
\(495\) 6.00000 10.3923i 0.269680 0.467099i
\(496\) 8.00000 0.359211
\(497\) 3.00000 15.5885i 0.134568 0.699238i
\(498\) −3.00000 −0.134433
\(499\) 11.0000 19.0526i 0.492428 0.852910i −0.507534 0.861632i \(-0.669443\pi\)
0.999962 + 0.00872186i \(0.00277629\pi\)
\(500\) 0.500000 + 0.866025i 0.0223607 + 0.0387298i
\(501\) 1.50000 + 2.59808i 0.0670151 + 0.116073i
\(502\) −6.00000 + 10.3923i −0.267793 + 0.463831i
\(503\) 21.0000 0.936344 0.468172 0.883637i \(-0.344913\pi\)
0.468172 + 0.883637i \(0.344913\pi\)
\(504\) −4.00000 3.46410i −0.178174 0.154303i
\(505\) −15.0000 −0.667491
\(506\) 9.00000 15.5885i 0.400099 0.692991i
\(507\) −1.50000 2.59808i −0.0666173 0.115385i
\(508\) −4.00000 6.92820i −0.177471 0.307389i
\(509\) −10.5000 + 18.1865i −0.465404 + 0.806104i −0.999220 0.0394971i \(-0.987424\pi\)
0.533815 + 0.845601i \(0.320758\pi\)
\(510\) 0 0
\(511\) −40.0000 + 13.8564i −1.76950 + 0.612971i
\(512\) −1.00000 −0.0441942
\(513\) 5.00000 8.66025i 0.220755 0.382360i
\(514\) 0 0
\(515\) −0.500000 0.866025i −0.0220326 0.0381616i
\(516\) 3.50000 6.06218i 0.154079 0.266872i
\(517\) 0 0
\(518\) 10.0000 3.46410i 0.439375 0.152204i
\(519\) 0 0
\(520\) 2.00000 3.46410i 0.0877058 0.151911i
\(521\) 9.00000 + 15.5885i 0.394297 + 0.682943i 0.993011 0.118020i \(-0.0376547\pi\)
−0.598714 + 0.800963i \(0.704321\pi\)
\(522\) 3.00000 + 5.19615i 0.131306 + 0.227429i
\(523\) 14.0000 24.2487i 0.612177 1.06032i −0.378695 0.925521i \(-0.623627\pi\)
0.990873 0.134801i \(-0.0430394\pi\)
\(524\) 0 0
\(525\) −2.00000 1.73205i −0.0872872 0.0755929i
\(526\) 21.0000 0.915644
\(527\) 0 0
\(528\) 3.00000 + 5.19615i 0.130558 + 0.226134i
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) 3.00000 5.19615i 0.130312 0.225706i
\(531\) 12.0000 0.520756
\(532\) −1.00000 + 5.19615i −0.0433555 + 0.225282i
\(533\) −36.0000 −1.55933
\(534\) −7.50000 + 12.9904i −0.324557 + 0.562149i
\(535\) −7.50000 12.9904i −0.324253 0.561623i
\(536\) 2.50000 + 4.33013i 0.107984 + 0.187033i
\(537\) 12.0000 20.7846i 0.517838 0.896922i
\(538\) −15.0000 −0.646696
\(539\) −6.00000 41.5692i −0.258438 1.79051i
\(540\) 5.00000 0.215166
\(541\) 12.5000 21.6506i 0.537417 0.930834i −0.461625 0.887075i \(-0.652733\pi\)
0.999042 0.0437584i \(-0.0139332\pi\)
\(542\) 1.00000 + 1.73205i 0.0429537 + 0.0743980i
\(543\) −5.50000 9.52628i −0.236028 0.408812i
\(544\) 0 0
\(545\) −11.0000 −0.471188
\(546\) −2.00000 + 10.3923i −0.0855921 + 0.444750i
\(547\) −19.0000 −0.812381 −0.406191 0.913788i \(-0.633143\pi\)
−0.406191 + 0.913788i \(0.633143\pi\)
\(548\) −6.00000 + 10.3923i −0.256307 + 0.443937i
\(549\) 5.00000 + 8.66025i 0.213395 + 0.369611i
\(550\) −3.00000 5.19615i −0.127920 0.221565i
\(551\) 3.00000 5.19615i 0.127804 0.221364i
\(552\) 3.00000 0.127688
\(553\) −4.00000 3.46410i −0.170097 0.147309i
\(554\) −8.00000 −0.339887
\(555\) −2.00000 + 3.46410i −0.0848953 + 0.147043i
\(556\) 5.00000 + 8.66025i 0.212047 + 0.367277i
\(557\) 9.00000 + 15.5885i 0.381342 + 0.660504i 0.991254 0.131965i \(-0.0421286\pi\)
−0.609912 + 0.792469i \(0.708795\pi\)
\(558\) −8.00000 + 13.8564i −0.338667 + 0.586588i
\(559\) 28.0000 1.18427
\(560\) −2.50000 + 0.866025i −0.105644 + 0.0365963i
\(561\) 0 0
\(562\) −3.00000 + 5.19615i −0.126547 + 0.219186i
\(563\) −13.5000 23.3827i −0.568957 0.985463i −0.996669 0.0815478i \(-0.974014\pi\)
0.427712 0.903915i \(-0.359320\pi\)
\(564\) 0 0
\(565\) 3.00000 5.19615i 0.126211 0.218604i
\(566\) 4.00000 0.168133
\(567\) 2.50000 0.866025i 0.104990 0.0363696i
\(568\) 6.00000 0.251754
\(569\) −3.00000 + 5.19615i −0.125767 + 0.217834i −0.922032 0.387113i \(-0.873472\pi\)
0.796266 + 0.604947i \(0.206806\pi\)
\(570\) −1.00000 1.73205i −0.0418854 0.0725476i
\(571\) 11.0000 + 19.0526i 0.460336 + 0.797325i 0.998978 0.0452101i \(-0.0143957\pi\)
−0.538642 + 0.842535i \(0.681062\pi\)
\(572\) −12.0000 + 20.7846i −0.501745 + 0.869048i
\(573\) −6.00000 −0.250654
\(574\) 18.0000 + 15.5885i 0.751305 + 0.650650i
\(575\) −3.00000 −0.125109
\(576\) 1.00000 1.73205i 0.0416667 0.0721688i
\(577\) −13.0000 22.5167i −0.541197 0.937381i −0.998836 0.0482425i \(-0.984638\pi\)
0.457639 0.889138i \(-0.348695\pi\)
\(578\) −8.50000 14.7224i −0.353553 0.612372i
\(579\) −1.00000 + 1.73205i −0.0415586 + 0.0719816i
\(580\) 3.00000 0.124568
\(581\) −1.50000 + 7.79423i −0.0622305 + 0.323359i
\(582\) −14.0000 −0.580319
\(583\) −18.0000 + 31.1769i −0.745484 + 1.29122i
\(584\) −8.00000 13.8564i −0.331042 0.573382i
\(585\) 4.00000 + 6.92820i 0.165380 + 0.286446i
\(586\) 6.00000 10.3923i 0.247858 0.429302i
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 5.50000 4.33013i 0.226816 0.178571i
\(589\) 16.0000 0.659269
\(590\) 3.00000 5.19615i 0.123508 0.213922i
\(591\) 3.00000 + 5.19615i 0.123404 + 0.213741i
\(592\) 2.00000 + 3.46410i 0.0821995 + 0.142374i
\(593\) −3.00000 + 5.19615i −0.123195 + 0.213380i −0.921026 0.389501i \(-0.872647\pi\)
0.797831 + 0.602881i \(0.205981\pi\)
\(594\) −30.0000 −1.23091
\(595\) 0 0
\(596\) 15.0000 0.614424
\(597\) 2.00000 3.46410i 0.0818546 0.141776i
\(598\) 6.00000 + 10.3923i 0.245358 + 0.424973i
\(599\) −6.00000 10.3923i −0.245153 0.424618i 0.717021 0.697051i \(-0.245505\pi\)
−0.962175 + 0.272433i \(0.912172\pi\)
\(600\) 0.500000 0.866025i 0.0204124 0.0353553i
\(601\) −46.0000 −1.87638 −0.938190 0.346122i \(-0.887498\pi\)
−0.938190 + 0.346122i \(0.887498\pi\)
\(602\) −14.0000 12.1244i −0.570597 0.494152i
\(603\) −10.0000 −0.407231
\(604\) 2.00000 3.46410i 0.0813788 0.140952i
\(605\) 12.5000 + 21.6506i 0.508197 + 0.880223i
\(606\) 7.50000 + 12.9904i 0.304667 + 0.527698i
\(607\) −11.5000 + 19.9186i −0.466771 + 0.808470i −0.999279 0.0379540i \(-0.987916\pi\)
0.532509 + 0.846424i \(0.321249\pi\)
\(608\) −2.00000 −0.0811107
\(609\) −7.50000 + 2.59808i −0.303915 + 0.105279i
\(610\) 5.00000 0.202444
\(611\) 0 0
\(612\) 0 0
\(613\) 8.00000 + 13.8564i 0.323117 + 0.559655i 0.981129 0.193352i \(-0.0619359\pi\)
−0.658012 + 0.753007i \(0.728603\pi\)
\(614\) 2.50000 4.33013i 0.100892 0.174750i
\(615\) −9.00000 −0.362915
\(616\) 15.0000 5.19615i 0.604367 0.209359i
\(617\) −12.0000 −0.483102 −0.241551 0.970388i \(-0.577656\pi\)
−0.241551 + 0.970388i \(0.577656\pi\)
\(618\) −0.500000 + 0.866025i −0.0201129 + 0.0348367i
\(619\) −7.00000 12.1244i −0.281354 0.487319i 0.690365 0.723462i \(-0.257450\pi\)
−0.971718 + 0.236143i \(0.924117\pi\)
\(620\) 4.00000 + 6.92820i 0.160644 + 0.278243i
\(621\) −7.50000 + 12.9904i −0.300965 + 0.521286i
\(622\) 18.0000 0.721734
\(623\) 30.0000 + 25.9808i 1.20192 + 1.04090i
\(624\) −4.00000 −0.160128
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 4.00000 + 6.92820i 0.159872 + 0.276907i
\(627\) 6.00000 + 10.3923i 0.239617 + 0.415029i
\(628\) 11.0000 19.0526i 0.438948 0.760280i
\(629\) 0 0
\(630\) 1.00000 5.19615i 0.0398410 0.207020i
\(631\) 14.0000 0.557331 0.278666 0.960388i \(-0.410108\pi\)
0.278666 + 0.960388i \(0.410108\pi\)
\(632\) 1.00000 1.73205i 0.0397779 0.0688973i
\(633\) 5.00000 + 8.66025i 0.198732 + 0.344214i
\(634\) 6.00000 + 10.3923i 0.238290 + 0.412731i
\(635\) 4.00000 6.92820i 0.158735 0.274937i
\(636\) −6.00000 −0.237915
\(637\) 26.0000 + 10.3923i 1.03016 + 0.411758i
\(638\) −18.0000 −0.712627
\(639\) −6.00000 + 10.3923i −0.237356 + 0.411113i
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) 1.50000 + 2.59808i 0.0592464 + 0.102618i 0.894127 0.447813i \(-0.147797\pi\)
−0.834881 + 0.550431i \(0.814464\pi\)
\(642\) −7.50000 + 12.9904i −0.296001 + 0.512689i
\(643\) 20.0000 0.788723 0.394362 0.918955i \(-0.370966\pi\)
0.394362 + 0.918955i \(0.370966\pi\)
\(644\) 1.50000 7.79423i 0.0591083 0.307136i
\(645\) 7.00000 0.275625
\(646\) 0 0
\(647\) −1.50000 2.59808i −0.0589711 0.102141i 0.835033 0.550200i \(-0.185449\pi\)
−0.894004 + 0.448059i \(0.852115\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −18.0000 + 31.1769i −0.706562 + 1.22380i
\(650\) 4.00000 0.156893
\(651\) −16.0000 13.8564i −0.627089 0.543075i
\(652\) −4.00000 −0.156652
\(653\) 24.0000 41.5692i 0.939193 1.62673i 0.172211 0.985060i \(-0.444909\pi\)
0.766982 0.641669i \(-0.221758\pi\)
\(654\) 5.50000 + 9.52628i 0.215067 + 0.372507i
\(655\) 0 0
\(656\) −4.50000 + 7.79423i −0.175695 + 0.304314i
\(657\) 32.0000 1.24844
\(658\) 0 0
\(659\) 6.00000 0.233727 0.116863 0.993148i \(-0.462716\pi\)
0.116863 + 0.993148i \(0.462716\pi\)
\(660\) −3.00000 + 5.19615i −0.116775 + 0.202260i
\(661\) −20.5000 35.5070i −0.797358 1.38106i −0.921331 0.388778i \(-0.872897\pi\)
0.123974 0.992286i \(-0.460436\pi\)
\(662\) −14.0000 24.2487i −0.544125 0.942453i
\(663\) 0 0
\(664\) −3.00000 −0.116423
\(665\) −5.00000 + 1.73205i −0.193892 + 0.0671660i
\(666\) −8.00000 −0.309994
\(667\) −4.50000 + 7.79423i −0.174241 + 0.301794i
\(668\) 1.50000 + 2.59808i 0.0580367 + 0.100523i
\(669\) 14.0000 + 24.2487i 0.541271 + 0.937509i
\(670\) −2.50000 + 4.33013i −0.0965834 + 0.167287i
\(671\) −30.0000 −1.15814
\(672\) 2.00000 + 1.73205i 0.0771517 + 0.0668153i
\(673\) 8.00000 0.308377 0.154189 0.988041i \(-0.450724\pi\)
0.154189 + 0.988041i \(0.450724\pi\)
\(674\) −11.0000 + 19.0526i −0.423704 + 0.733877i
\(675\) 2.50000 + 4.33013i 0.0962250 + 0.166667i
\(676\) −1.50000 2.59808i −0.0576923 0.0999260i
\(677\) −6.00000 + 10.3923i −0.230599 + 0.399409i −0.957984 0.286820i \(-0.907402\pi\)
0.727386 + 0.686229i \(0.240735\pi\)
\(678\) −6.00000 −0.230429
\(679\) −7.00000 + 36.3731i −0.268635 + 1.39587i
\(680\) 0 0
\(681\) 6.00000 10.3923i 0.229920 0.398234i
\(682\) −24.0000 41.5692i −0.919007 1.59177i
\(683\) −4.50000 7.79423i −0.172188 0.298238i 0.766997 0.641651i \(-0.221750\pi\)
−0.939184 + 0.343413i \(0.888417\pi\)
\(684\) 2.00000 3.46410i 0.0764719 0.132453i
\(685\) −12.0000 −0.458496
\(686\) −8.50000 16.4545i −0.324532 0.628235i
\(687\) 14.0000 0.534133
\(688\) 3.50000 6.06218i 0.133436 0.231118i
\(689\) −12.0000 20.7846i −0.457164 0.791831i
\(690\) 1.50000 + 2.59808i 0.0571040 + 0.0989071i
\(691\) 11.0000 19.0526i 0.418460 0.724793i −0.577325 0.816514i \(-0.695903\pi\)
0.995785 + 0.0917209i \(0.0292368\pi\)
\(692\) 0 0
\(693\) −6.00000 + 31.1769i −0.227921 + 1.18431i
\(694\) −9.00000 −0.341635
\(695\) −5.00000 + 8.66025i −0.189661 + 0.328502i
\(696\) −1.50000 2.59808i −0.0568574 0.0984798i
\(697\) 0 0
\(698\) 8.50000 14.7224i 0.321730 0.557252i
\(699\) −12.0000 −0.453882
\(700\) −2.00000 1.73205i −0.0755929 0.0654654i
\(701\) −3.00000 −0.113308 −0.0566542 0.998394i \(-0.518043\pi\)
−0.0566542 + 0.998394i \(0.518043\pi\)
\(702\) 10.0000 17.3205i 0.377426 0.653720i
\(703\) 4.00000 + 6.92820i 0.150863 + 0.261302i
\(704\) 3.00000 + 5.19615i 0.113067 + 0.195837i
\(705\) 0 0
\(706\) 6.00000 0.225813
\(707\) 37.5000 12.9904i 1.41033 0.488554i
\(708\) −6.00000 −0.225494
\(709\) 15.5000 26.8468i 0.582115 1.00825i −0.413114 0.910679i \(-0.635559\pi\)
0.995228 0.0975728i \(-0.0311079\pi\)
\(710\) 3.00000 + 5.19615i 0.112588 + 0.195008i
\(711\) 2.00000 + 3.46410i 0.0750059 + 0.129914i
\(712\) −7.50000 + 12.9904i −0.281074 + 0.486835i
\(713\) −24.0000 −0.898807
\(714\) 0 0
\(715\) −24.0000 −0.897549
\(716\) 12.0000 20.7846i 0.448461 0.776757i
\(717\) −6.00000 10.3923i −0.224074 0.388108i
\(718\) 12.0000 + 20.7846i 0.447836 + 0.775675i
\(719\) 9.00000 15.5885i 0.335643 0.581351i −0.647965 0.761670i \(-0.724380\pi\)
0.983608 + 0.180319i \(0.0577130\pi\)
\(720\) 2.00000 0.0745356
\(721\) 2.00000 + 1.73205i 0.0744839 + 0.0645049i
\(722\) 15.0000 0.558242
\(723\) −1.00000 + 1.73205i −0.0371904 + 0.0644157i
\(724\) −5.50000 9.52628i −0.204406 0.354041i
\(725\) 1.50000 + 2.59808i 0.0557086 + 0.0964901i
\(726\) 12.5000 21.6506i 0.463919 0.803530i
\(727\) −19.0000 −0.704671 −0.352335 0.935874i \(-0.614612\pi\)
−0.352335 + 0.935874i \(0.614612\pi\)
\(728\) −2.00000 + 10.3923i −0.0741249 + 0.385164i
\(729\) 13.0000 0.481481
\(730\) 8.00000 13.8564i 0.296093 0.512849i
\(731\) 0 0
\(732\) −2.50000 4.33013i −0.0924027 0.160046i
\(733\) 17.0000 29.4449i 0.627909 1.08757i −0.360061 0.932929i \(-0.617244\pi\)
0.987971 0.154642i \(-0.0494225\pi\)
\(734\) −35.0000 −1.29187
\(735\) 6.50000 + 2.59808i 0.239756 + 0.0958315i
\(736\) 3.00000 0.110581
\(737\) 15.0000 25.9808i 0.552532 0.957014i
\(738\) −9.00000 15.5885i −0.331295 0.573819i
\(739\) −13.0000 22.5167i −0.478213 0.828289i 0.521475 0.853266i \(-0.325382\pi\)
−0.999688 + 0.0249776i \(0.992049\pi\)
\(740\) −2.00000 + 3.46410i −0.0735215 + 0.127343i
\(741\) −8.00000 −0.293887
\(742\) −3.00000 + 15.5885i −0.110133 + 0.572270i
\(743\) 39.0000 1.43077 0.715386 0.698730i \(-0.246251\pi\)
0.715386 + 0.698730i \(0.246251\pi\)
\(744\) 4.00000 6.92820i 0.146647 0.254000i
\(745\) 7.50000 + 12.9904i 0.274779 + 0.475931i
\(746\) −2.00000 3.46410i −0.0732252 0.126830i
\(747\) 3.00000 5.19615i 0.109764 0.190117i
\(748\) 0 0
\(749\) 30.0000 + 25.9808i 1.09618 + 0.949316i
\(750\) 1.00000 0.0365148
\(751\) 2.00000 3.46410i 0.0729810 0.126407i −0.827225 0.561870i \(-0.810082\pi\)
0.900207 + 0.435463i \(0.143415\pi\)
\(752\) 0 0
\(753\) 6.00000 + 10.3923i 0.218652 + 0.378717i
\(754\) 6.00000 10.3923i 0.218507 0.378465i
\(755\) 4.00000 0.145575
\(756\) −12.5000 + 4.33013i −0.454621 + 0.157485i
\(757\) −28.0000 −1.01768 −0.508839 0.860862i \(-0.669925\pi\)
−0.508839 + 0.860862i \(0.669925\pi\)
\(758\) −17.0000 + 29.4449i −0.617468 + 1.06949i
\(759\) −9.00000 15.5885i −0.326679 0.565825i
\(760\) −1.00000 1.73205i −0.0362738 0.0628281i
\(761\) −21.0000 + 36.3731i −0.761249 + 1.31852i 0.180957 + 0.983491i \(0.442080\pi\)
−0.942207 + 0.335032i \(0.891253\pi\)
\(762\) −8.00000 −0.289809
\(763\) 27.5000 9.52628i 0.995567 0.344874i
\(764\) −6.00000 −0.217072
\(765\) 0 0
\(766\) −7.50000 12.9904i −0.270986 0.469362i
\(767\) −12.0000 20.7846i −0.433295 0.750489i
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) 50.0000 1.80305 0.901523 0.432731i \(-0.142450\pi\)
0.901523 + 0.432731i \(0.142450\pi\)
\(770\) 12.0000 + 10.3923i 0.432450 + 0.374513i
\(771\) 0 0
\(772\) −1.00000 + 1.73205i −0.0359908 + 0.0623379i
\(773\) 6.00000 + 10.3923i 0.215805 + 0.373785i 0.953521 0.301326i \(-0.0974291\pi\)
−0.737716 + 0.675111i \(0.764096\pi\)
\(774\) 7.00000 + 12.1244i 0.251610 + 0.435801i
\(775\) −4.00000 + 6.92820i −0.143684 + 0.248868i
\(776\) −14.0000 −0.502571
\(777\) 2.00000 10.3923i 0.0717496 0.372822i
\(778\) 30.0000 1.07555
\(779\) −9.00000 + 15.5885i −0.322458 + 0.558514i