Properties

Label 70.2.e.c.11.1
Level $70$
Weight $2$
Character 70.11
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 11.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 70.11
Dual form 70.2.e.c.51.1

$q$-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 \(\left(\mathbb{Z}/70\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(57\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i −0.973494 0.228714i \(-0.926548\pi\)
0.684819 + 0.728714i \(0.259881\pi\)
\(4\) −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 0.0829925 0.996550i \(-0.473552\pi\)
0.821541 0.570149i \(-0.193114\pi\)
\(12\) −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) −1.00000 + 1.73205i −0.235702 + 0.408248i
\(19\) −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287984i \(0.907015\pi\)
\(20\) −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 0.978961 0.204046i \(-0.0654092\pi\)
−0.666190 + 0.745782i \(0.732076\pi\)
\(24\) 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 0.243204 + 0.969975i \(0.421802\pi\)
−0.961625 + 0.274367i \(0.911532\pi\)
\(32\) 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 0.982274 0.187453i \(-0.0600231\pi\)
−0.653476 + 0.756948i \(0.726690\pi\)
\(38\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 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 −0.583036 0.812447i \(-0.698135\pi\)
0.995117 + 0.0987002i \(0.0314685\pi\)
\(54\) −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 −0.601958 0.798528i \(-0.705612\pi\)
0.992524 + 0.122047i \(0.0389457\pi\)
\(60\) 0.500000 0.866025i 0.0645497 0.111803i
\(61\) −2.50000 4.33013i −0.320092 0.554416i 0.660415 0.750901i \(-0.270381\pi\)
−0.980507 + 0.196485i \(0.937047\pi\)
\(62\) −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 −0.977356 0.211604i \(-0.932131\pi\)
0.671932 + 0.740613i \(0.265465\pi\)
\(68\) 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 0.164083 0.986447i \(-0.447534\pi\)
0.772246 0.635323i \(-0.219133\pi\)
\(74\) −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 0.804272 0.594261i \(-0.202555\pi\)
−0.916781 + 0.399390i \(0.869222\pi\)
\(80\) 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 0.922840 + 0.385183i \(0.125862\pi\)
−0.127842 + 0.991795i \(0.540805\pi\)
\(90\) −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 0.203317 + 0.979113i \(0.434828\pi\)
−0.949595 + 0.313478i \(0.898506\pi\)
\(102\) 0 0
\(103\) 0.500000 + 0.866025i 0.0492665 + 0.0853320i 0.889607 0.456727i \(-0.150978\pi\)
−0.840341 + 0.542059i \(0.817645\pi\)
\(104\) 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 0.958952 + 0.283567i \(0.0915178\pi\)
−0.233900 + 0.972261i \(0.575149\pi\)
\(108\) 2.50000 4.33013i 0.240563 0.416667i
\(109\) −5.50000 + 9.52628i −0.526804 + 0.912452i 0.472708 + 0.881219i \(0.343277\pi\)
−0.999512 + 0.0312328i \(0.990057\pi\)
\(110\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) −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 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) −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 −0.990485 0.137619i \(-0.956055\pi\)
0.376061 0.926595i \(-0.377278\pi\)
\(150\) 0.500000 0.866025i 0.0408248 0.0707107i
\(151\) 2.00000 3.46410i 0.162758 0.281905i −0.773099 0.634285i \(-0.781294\pi\)
0.935857 + 0.352381i \(0.114628\pi\)
\(152\) 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 0.0242497 0.999706i \(-0.492280\pi\)
0.853646 0.520854i \(-0.174386\pi\)
\(158\) 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 0.933659 0.358162i \(-0.116597\pi\)
−0.777007 + 0.629492i \(0.783263\pi\)
\(164\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(174\) 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 0.0655145 0.997852i \(-0.479131\pi\)
0.831408 0.555663i \(-0.187536\pi\)
\(180\) −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 0.953912 0.300088i \(-0.0970159\pi\)
−0.736839 + 0.676068i \(0.763683\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −1.00000 + 1.73205i −0.0719816 + 0.124676i −0.899770 0.436365i \(-0.856266\pi\)
0.827788 + 0.561041i \(0.189599\pi\)
\(194\) 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 −0.786389 0.617731i \(-0.788052\pi\)
0.928166 + 0.372168i \(0.121385\pi\)
\(200\) 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 −0.595274 0.803523i \(-0.702957\pi\)
0.993508 + 0.113761i \(0.0362899\pi\)
\(228\) −1.00000 + 1.73205i −0.0662266 + 0.114708i
\(229\) −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i \(-0.319740\pi\)
−0.999088 + 0.0426906i \(0.986407\pi\)
\(230\) −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 0.992853 0.119342i \(-0.0380786\pi\)
−0.599780 + 0.800165i \(0.704745\pi\)
\(234\) 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 −0.896435 0.443176i \(-0.853852\pi\)
0.832019 + 0.554747i \(0.187185\pi\)
\(242\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(258\) 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 −0.336270 0.941766i \(-0.609166\pi\)
0.983728 0.179664i \(-0.0575011\pi\)
\(264\) −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 −0.998816 0.0486418i \(-0.984511\pi\)
0.541533 + 0.840679i \(0.317844\pi\)
\(270\) 2.50000 4.33013i 0.152145 0.263523i
\(271\) −1.00000 1.73205i −0.0607457 0.105215i 0.834053 0.551684i \(-0.186015\pi\)
−0.894799 + 0.446469i \(0.852681\pi\)
\(272\) 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 −0.960810 0.277207i \(-0.910591\pi\)
0.720473 + 0.693482i \(0.243925\pi\)
\(278\) −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 −0.800439 0.599414i \(-0.795400\pi\)
0.919327 + 0.393494i \(0.128734\pi\)
\(284\) 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 −0.489585 0.871956i \(-0.662852\pi\)
0.999928 0.0119847i \(-0.00381495\pi\)
\(312\) −2.00000 + 3.46410i −0.113228 + 0.196116i
\(313\) −4.00000 6.92820i −0.226093 0.391605i 0.730554 0.682855i \(-0.239262\pi\)
−0.956647 + 0.291250i \(0.905929\pi\)
\(314\) 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 0.646872 0.762598i \(-0.276077\pi\)
−0.983866 + 0.178908i \(0.942743\pi\)
\(318\) −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 0.937829 + 0.347097i \(0.112833\pi\)
−0.168320 + 0.985732i \(0.553834\pi\)
\(332\) −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 −0.961162 0.275983i \(-0.910997\pi\)
0.719590 + 0.694399i \(0.244330\pi\)
\(348\) 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 −0.775077 0.631867i \(-0.782289\pi\)
0.934751 + 0.355303i \(0.115622\pi\)
\(354\) −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 −0.986865 0.161546i \(-0.948352\pi\)
0.353529 0.935423i \(-0.384981\pi\)
\(360\) 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 −0.104399 + 0.994535i \(0.533292\pi\)
−0.809093 + 0.587680i \(0.800041\pi\)
\(368\) 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 0.913147 0.407630i \(-0.133645\pi\)
−0.809591 + 0.586994i \(0.800311\pi\)
\(374\) 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 0.991522 0.129937i \(-0.0414776\pi\)
−0.608290 + 0.793715i \(0.708144\pi\)
\(384\) −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 −0.182047 0.983290i \(-0.558272\pi\)
0.942578 0.333987i \(-0.108394\pi\)
\(390\) 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 0.635161 0.772380i \(-0.280934\pi\)
−0.986481 + 0.163876i \(0.947600\pi\)
\(398\) 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 0.615725 0.787961i \(-0.288863\pi\)
−0.990257 + 0.139253i \(0.955530\pi\)
\(402\) 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 −0.659374 0.751815i \(-0.729178\pi\)
0.980778 + 0.195127i \(0.0625118\pi\)
\(410\) −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 0.237460 + 0.971397i \(0.423685\pi\)
−0.959985 + 0.280052i \(0.909648\pi\)
\(432\) 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 0.978412 + 0.206666i \(0.0662612\pi\)
−0.310228 + 0.950662i \(0.600405\pi\)
\(440\) −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 0.501129 0.865373i \(-0.332918\pi\)
−0.999999 + 0.00130426i \(0.999585\pi\)
\(444\) 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 −0.948566 0.316579i \(-0.897466\pi\)
0.200118 0.979772i \(-0.435868\pi\)
\(458\) 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 0.985726 0.168360i \(-0.0538472\pi\)
−0.638667 + 0.769483i \(0.720514\pi\)
\(468\) 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 −0.969920 0.243426i \(-0.921729\pi\)
0.695773 + 0.718262i \(0.255062\pi\)
\(480\) −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 −0.625859 0.779936i \(-0.715252\pi\)
0.988374 + 0.152042i \(0.0485850\pi\)
\(488\) 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 0.999962 0.00872186i \(-0.00277629\pi\)
−0.507534 + 0.861632i \(0.669443\pi\)
\(500\) 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 0.533815 0.845601i \(-0.320758\pi\)
−0.999220 + 0.0394971i \(0.987424\pi\)
\(510\) 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 −0.598714 0.800963i \(-0.704321\pi\)
0.993011 + 0.118020i \(0.0376547\pi\)
\(522\) 3.00000 5.19615i 0.131306 0.227429i
\(523\) 14.0000 + 24.2487i 0.612177 + 1.06032i 0.990873 + 0.134801i \(0.0430394\pi\)
−0.378695 + 0.925521i \(0.623627\pi\)
\(524\) 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 0.999042 + 0.0437584i \(0.0139332\pi\)
−0.461625 + 0.887075i \(0.652733\pi\)
\(542\) 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 −0.609912 0.792469i \(-0.708795\pi\)
0.991254 + 0.131965i \(0.0421286\pi\)
\(558\) −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 0.427712 + 0.903915i \(0.359320\pi\)
−0.996669 + 0.0815478i \(0.974014\pi\)
\(564\) 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 0.796266 0.604947i \(-0.206806\pi\)
−0.922032 + 0.387113i \(0.873472\pi\)
\(570\) −1.00000 + 1.73205i −0.0418854 + 0.0725476i
\(571\) 11.0000 19.0526i 0.460336 0.797325i −0.538642 0.842535i \(-0.681062\pi\)
0.998978 + 0.0452101i \(0.0143957\pi\)
\(572\) −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 0.457639 + 0.889138i \(0.348695\pi\)
−0.998836 + 0.0482425i \(0.984638\pi\)
\(578\) −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 0.797831 0.602881i \(-0.205981\pi\)
−0.921026 + 0.389501i \(0.872647\pi\)
\(594\) −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 −0.962175 0.272433i \(-0.912172\pi\)
0.717021 + 0.697051i \(0.245505\pi\)
\(600\) 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 0.532509 0.846424i \(-0.321249\pi\)
−0.999279 + 0.0379540i \(0.987916\pi\)
\(608\) −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 −0.658012 0.753007i \(-0.728603\pi\)
0.981129 + 0.193352i \(0.0619359\pi\)
\(614\) 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 −0.971718 0.236143i \(-0.924117\pi\)
0.690365 + 0.723462i \(0.257450\pi\)
\(620\) 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 −0.834881 0.550431i \(-0.814464\pi\)
0.894127 + 0.447813i \(0.147797\pi\)
\(642\) −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 −0.894004 0.448059i \(-0.852115\pi\)
0.835033 + 0.550200i \(0.185449\pi\)
\(648\) 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 0.766982 + 0.641669i \(0.221758\pi\)
0.172211 + 0.985060i \(0.444909\pi\)
\(654\) 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 0.123974 + 0.992286i \(0.460436\pi\)
−0.921331 + 0.388778i \(0.872897\pi\)
\(662\) −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 0.727386 0.686229i \(-0.240735\pi\)
−0.957984 + 0.286820i \(0.907402\pi\)
\(678\) −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 −0.939184 0.343413i \(-0.888417\pi\)
0.766997 + 0.641651i \(0.221750\pi\)
\(684\) 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 0.995785 0.0917209i \(-0.0292368\pi\)
−0.577325 + 0.816514i \(0.695903\pi\)
\(692\) 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 0.995228 + 0.0975728i \(0.0311079\pi\)
−0.413114 + 0.910679i \(0.635559\pi\)
\(710\) 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 0.983608 0.180319i \(-0.0577130\pi\)
−0.647965 + 0.761670i \(0.724380\pi\)
\(720\) 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 0.987971 + 0.154642i \(0.0494225\pi\)
−0.360061 + 0.932929i \(0.617244\pi\)
\(734\) −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 −0.999688 0.0249776i \(-0.992049\pi\)
0.521475 + 0.853266i \(0.325382\pi\)
\(740\) −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 0.900207 0.435463i \(-0.143415\pi\)
−0.827225 + 0.561870i \(0.810082\pi\)
\(752\) 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 −0.942207 0.335032i \(-0.891253\pi\)
0.180957 0.983491i \(-0.442080\pi\)
\(762\) −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 −0.737716 0.675111i \(-0.764096\pi\)
0.953521 + 0.301326i \(0.0974291\pi\)
\(774\) 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