Properties

Label 70.2.e.a.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.a.51.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.00000 q^{6} +(0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.00000 q^{6} +(0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +(0.500000 - 0.866025i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-1.50000 - 2.59808i) q^{12} +(2.00000 - 1.73205i) q^{14} -3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +(-3.00000 + 5.19615i) q^{18} +(3.00000 + 5.19615i) q^{19} -1.00000 q^{20} +(-7.50000 - 2.59808i) q^{21} -2.00000 q^{22} +(-1.50000 - 2.59808i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(-0.500000 + 0.866025i) q^{25} +9.00000 q^{27} +(-2.50000 - 0.866025i) q^{28} +9.00000 q^{29} +(1.50000 + 2.59808i) q^{30} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{33} -4.00000 q^{34} +(-2.00000 + 1.73205i) q^{35} +6.00000 q^{36} +(2.00000 + 3.46410i) q^{37} +(3.00000 - 5.19615i) q^{38} +(0.500000 + 0.866025i) q^{40} -7.00000 q^{41} +(1.50000 + 7.79423i) q^{42} -5.00000 q^{43} +(1.00000 + 1.73205i) q^{44} +(3.00000 - 5.19615i) q^{45} +(-1.50000 + 2.59808i) q^{46} +(-4.00000 - 6.92820i) q^{47} +3.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} +1.00000 q^{50} +(6.00000 + 10.3923i) q^{51} +(1.00000 - 1.73205i) q^{53} +(-4.50000 - 7.79423i) q^{54} +2.00000 q^{55} +(0.500000 + 2.59808i) q^{56} -18.0000 q^{57} +(-4.50000 - 7.79423i) q^{58} +(-5.00000 + 8.66025i) q^{59} +(1.50000 - 2.59808i) q^{60} +(-0.500000 - 0.866025i) q^{61} -4.00000 q^{62} +(12.0000 - 10.3923i) q^{63} +1.00000 q^{64} +(3.00000 - 5.19615i) q^{66} +(4.50000 - 7.79423i) q^{67} +(2.00000 + 3.46410i) q^{68} +9.00000 q^{69} +(2.50000 + 0.866025i) q^{70} +2.00000 q^{71} +(-3.00000 - 5.19615i) q^{72} +(2.00000 - 3.46410i) q^{73} +(2.00000 - 3.46410i) q^{74} +(-1.50000 - 2.59808i) q^{75} -6.00000 q^{76} +(5.00000 + 1.73205i) q^{77} +(-5.00000 - 8.66025i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(3.50000 + 6.06218i) q^{82} -7.00000 q^{83} +(6.00000 - 5.19615i) q^{84} +4.00000 q^{85} +(2.50000 + 4.33013i) q^{86} +(-13.5000 + 23.3827i) q^{87} +(1.00000 - 1.73205i) q^{88} +(-0.500000 - 0.866025i) q^{89} -6.00000 q^{90} +3.00000 q^{92} +(6.00000 + 10.3923i) q^{93} +(-4.00000 + 6.92820i) q^{94} +(-3.00000 + 5.19615i) q^{95} +(-1.50000 - 2.59808i) q^{96} +14.0000 q^{97} +(5.50000 + 4.33013i) q^{98} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - 3 q^{3} - q^{4} + q^{5} + 6 q^{6} + q^{7} + 2 q^{8} - 6 q^{9} + O(q^{10}) \) \( 2 q - q^{2} - 3 q^{3} - q^{4} + q^{5} + 6 q^{6} + q^{7} + 2 q^{8} - 6 q^{9} + q^{10} + 2 q^{11} - 3 q^{12} + 4 q^{14} - 6 q^{15} - q^{16} + 4 q^{17} - 6 q^{18} + 6 q^{19} - 2 q^{20} - 15 q^{21} - 4 q^{22} - 3 q^{23} - 3 q^{24} - q^{25} + 18 q^{27} - 5 q^{28} + 18 q^{29} + 3 q^{30} + 4 q^{31} - q^{32} + 6 q^{33} - 8 q^{34} - 4 q^{35} + 12 q^{36} + 4 q^{37} + 6 q^{38} + q^{40} - 14 q^{41} + 3 q^{42} - 10 q^{43} + 2 q^{44} + 6 q^{45} - 3 q^{46} - 8 q^{47} + 6 q^{48} - 13 q^{49} + 2 q^{50} + 12 q^{51} + 2 q^{53} - 9 q^{54} + 4 q^{55} + q^{56} - 36 q^{57} - 9 q^{58} - 10 q^{59} + 3 q^{60} - q^{61} - 8 q^{62} + 24 q^{63} + 2 q^{64} + 6 q^{66} + 9 q^{67} + 4 q^{68} + 18 q^{69} + 5 q^{70} + 4 q^{71} - 6 q^{72} + 4 q^{73} + 4 q^{74} - 3 q^{75} - 12 q^{76} + 10 q^{77} - 10 q^{79} + q^{80} - 9 q^{81} + 7 q^{82} - 14 q^{83} + 12 q^{84} + 8 q^{85} + 5 q^{86} - 27 q^{87} + 2 q^{88} - q^{89} - 12 q^{90} + 6 q^{92} + 12 q^{93} - 8 q^{94} - 6 q^{95} - 3 q^{96} + 28 q^{97} + 11 q^{98} - 24 q^{99} + O(q^{100}) \)

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
\(3\) −1.50000 + 2.59808i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 3.00000 1.22474
\(7\) 0.500000 + 2.59808i 0.188982 + 0.981981i
\(8\) 1.00000 0.353553
\(9\) −3.00000 5.19615i −1.00000 1.73205i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i \(-0.735842\pi\)
0.976478 + 0.215615i \(0.0691756\pi\)
\(12\) −1.50000 2.59808i −0.433013 0.750000i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 2.00000 1.73205i 0.534522 0.462910i
\(15\) −3.00000 −0.774597
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.00000 3.46410i 0.485071 0.840168i −0.514782 0.857321i \(-0.672127\pi\)
0.999853 + 0.0171533i \(0.00546033\pi\)
\(18\) −3.00000 + 5.19615i −0.707107 + 1.22474i
\(19\) 3.00000 + 5.19615i 0.688247 + 1.19208i 0.972404 + 0.233301i \(0.0749529\pi\)
−0.284157 + 0.958778i \(0.591714\pi\)
\(20\) −1.00000 −0.223607
\(21\) −7.50000 2.59808i −1.63663 0.566947i
\(22\) −2.00000 −0.426401
\(23\) −1.50000 2.59808i −0.312772 0.541736i 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) −1.50000 + 2.59808i −0.306186 + 0.530330i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 9.00000 1.73205
\(28\) −2.50000 0.866025i −0.472456 0.163663i
\(29\) 9.00000 1.67126 0.835629 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) 1.50000 + 2.59808i 0.273861 + 0.474342i
\(31\) 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i \(-0.716379\pi\)
0.987829 + 0.155543i \(0.0497126\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 3.00000 + 5.19615i 0.522233 + 0.904534i
\(34\) −4.00000 −0.685994
\(35\) −2.00000 + 1.73205i −0.338062 + 0.292770i
\(36\) 6.00000 1.00000
\(37\) 2.00000 + 3.46410i 0.328798 + 0.569495i 0.982274 0.187453i \(-0.0600231\pi\)
−0.653476 + 0.756948i \(0.726690\pi\)
\(38\) 3.00000 5.19615i 0.486664 0.842927i
\(39\) 0 0
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) −7.00000 −1.09322 −0.546608 0.837389i \(-0.684081\pi\)
−0.546608 + 0.837389i \(0.684081\pi\)
\(42\) 1.50000 + 7.79423i 0.231455 + 1.20268i
\(43\) −5.00000 −0.762493 −0.381246 0.924473i \(-0.624505\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) 1.00000 + 1.73205i 0.150756 + 0.261116i
\(45\) 3.00000 5.19615i 0.447214 0.774597i
\(46\) −1.50000 + 2.59808i −0.221163 + 0.383065i
\(47\) −4.00000 6.92820i −0.583460 1.01058i −0.995066 0.0992202i \(-0.968365\pi\)
0.411606 0.911362i \(-0.364968\pi\)
\(48\) 3.00000 0.433013
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) 1.00000 0.141421
\(51\) 6.00000 + 10.3923i 0.840168 + 1.45521i
\(52\) 0 0
\(53\) 1.00000 1.73205i 0.137361 0.237915i −0.789136 0.614218i \(-0.789471\pi\)
0.926497 + 0.376303i \(0.122805\pi\)
\(54\) −4.50000 7.79423i −0.612372 1.06066i
\(55\) 2.00000 0.269680
\(56\) 0.500000 + 2.59808i 0.0668153 + 0.347183i
\(57\) −18.0000 −2.38416
\(58\) −4.50000 7.79423i −0.590879 1.02343i
\(59\) −5.00000 + 8.66025i −0.650945 + 1.12747i 0.331949 + 0.943297i \(0.392294\pi\)
−0.982894 + 0.184172i \(0.941040\pi\)
\(60\) 1.50000 2.59808i 0.193649 0.335410i
\(61\) −0.500000 0.866025i −0.0640184 0.110883i 0.832240 0.554416i \(-0.187058\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) −4.00000 −0.508001
\(63\) 12.0000 10.3923i 1.51186 1.30931i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 3.00000 5.19615i 0.369274 0.639602i
\(67\) 4.50000 7.79423i 0.549762 0.952217i −0.448528 0.893769i \(-0.648052\pi\)
0.998290 0.0584478i \(-0.0186151\pi\)
\(68\) 2.00000 + 3.46410i 0.242536 + 0.420084i
\(69\) 9.00000 1.08347
\(70\) 2.50000 + 0.866025i 0.298807 + 0.103510i
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) −3.00000 5.19615i −0.353553 0.612372i
\(73\) 2.00000 3.46410i 0.234082 0.405442i −0.724923 0.688830i \(-0.758125\pi\)
0.959006 + 0.283387i \(0.0914581\pi\)
\(74\) 2.00000 3.46410i 0.232495 0.402694i
\(75\) −1.50000 2.59808i −0.173205 0.300000i
\(76\) −6.00000 −0.688247
\(77\) 5.00000 + 1.73205i 0.569803 + 0.197386i
\(78\) 0 0
\(79\) −5.00000 8.66025i −0.562544 0.974355i −0.997274 0.0737937i \(-0.976489\pi\)
0.434730 0.900561i \(-0.356844\pi\)
\(80\) 0.500000 0.866025i 0.0559017 0.0968246i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 3.50000 + 6.06218i 0.386510 + 0.669456i
\(83\) −7.00000 −0.768350 −0.384175 0.923260i \(-0.625514\pi\)
−0.384175 + 0.923260i \(0.625514\pi\)
\(84\) 6.00000 5.19615i 0.654654 0.566947i
\(85\) 4.00000 0.433861
\(86\) 2.50000 + 4.33013i 0.269582 + 0.466930i
\(87\) −13.5000 + 23.3827i −1.44735 + 2.50689i
\(88\) 1.00000 1.73205i 0.106600 0.184637i
\(89\) −0.500000 0.866025i −0.0529999 0.0917985i 0.838308 0.545197i \(-0.183545\pi\)
−0.891308 + 0.453398i \(0.850212\pi\)
\(90\) −6.00000 −0.632456
\(91\) 0 0
\(92\) 3.00000 0.312772
\(93\) 6.00000 + 10.3923i 0.622171 + 1.07763i
\(94\) −4.00000 + 6.92820i −0.412568 + 0.714590i
\(95\) −3.00000 + 5.19615i −0.307794 + 0.533114i
\(96\) −1.50000 2.59808i −0.153093 0.265165i
\(97\) 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
\(101\) −1.50000 + 2.59808i −0.149256 + 0.258518i −0.930953 0.365140i \(-0.881021\pi\)
0.781697 + 0.623658i \(0.214354\pi\)
\(102\) 6.00000 10.3923i 0.594089 1.02899i
\(103\) −0.500000 0.866025i −0.0492665 0.0853320i 0.840341 0.542059i \(-0.182355\pi\)
−0.889607 + 0.456727i \(0.849022\pi\)
\(104\) 0 0
\(105\) −1.50000 7.79423i −0.146385 0.760639i
\(106\) −2.00000 −0.194257
\(107\) −1.50000 2.59808i −0.145010 0.251166i 0.784366 0.620298i \(-0.212988\pi\)
−0.929377 + 0.369132i \(0.879655\pi\)
\(108\) −4.50000 + 7.79423i −0.433013 + 0.750000i
\(109\) 4.50000 7.79423i 0.431022 0.746552i −0.565940 0.824447i \(-0.691487\pi\)
0.996962 + 0.0778949i \(0.0248199\pi\)
\(110\) −1.00000 1.73205i −0.0953463 0.165145i
\(111\) −12.0000 −1.13899
\(112\) 2.00000 1.73205i 0.188982 0.163663i
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 9.00000 + 15.5885i 0.842927 + 1.45999i
\(115\) 1.50000 2.59808i 0.139876 0.242272i
\(116\) −4.50000 + 7.79423i −0.417815 + 0.723676i
\(117\) 0 0
\(118\) 10.0000 0.920575
\(119\) 10.0000 + 3.46410i 0.916698 + 0.317554i
\(120\) −3.00000 −0.273861
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) −0.500000 + 0.866025i −0.0452679 + 0.0784063i
\(123\) 10.5000 18.1865i 0.946753 1.63982i
\(124\) 2.00000 + 3.46410i 0.179605 + 0.311086i
\(125\) −1.00000 −0.0894427
\(126\) −15.0000 5.19615i −1.33631 0.462910i
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 7.50000 12.9904i 0.660338 1.14374i
\(130\) 0 0
\(131\) −4.00000 6.92820i −0.349482 0.605320i 0.636676 0.771132i \(-0.280309\pi\)
−0.986157 + 0.165812i \(0.946976\pi\)
\(132\) −6.00000 −0.522233
\(133\) −12.0000 + 10.3923i −1.04053 + 0.901127i
\(134\) −9.00000 −0.777482
\(135\) 4.50000 + 7.79423i 0.387298 + 0.670820i
\(136\) 2.00000 3.46410i 0.171499 0.297044i
\(137\) −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) −4.50000 7.79423i −0.383065 0.663489i
\(139\) −14.0000 −1.18746 −0.593732 0.804663i \(-0.702346\pi\)
−0.593732 + 0.804663i \(0.702346\pi\)
\(140\) −0.500000 2.59808i −0.0422577 0.219578i
\(141\) 24.0000 2.02116
\(142\) −1.00000 1.73205i −0.0839181 0.145350i
\(143\) 0 0
\(144\) −3.00000 + 5.19615i −0.250000 + 0.433013i
\(145\) 4.50000 + 7.79423i 0.373705 + 0.647275i
\(146\) −4.00000 −0.331042
\(147\) 3.00000 20.7846i 0.247436 1.71429i
\(148\) −4.00000 −0.328798
\(149\) −1.50000 2.59808i −0.122885 0.212843i 0.798019 0.602632i \(-0.205881\pi\)
−0.920904 + 0.389789i \(0.872548\pi\)
\(150\) −1.50000 + 2.59808i −0.122474 + 0.212132i
\(151\) 8.00000 13.8564i 0.651031 1.12762i −0.331842 0.943335i \(-0.607670\pi\)
0.982873 0.184284i \(-0.0589965\pi\)
\(152\) 3.00000 + 5.19615i 0.243332 + 0.421464i
\(153\) −24.0000 −1.94029
\(154\) −1.00000 5.19615i −0.0805823 0.418718i
\(155\) 4.00000 0.321288
\(156\) 0 0
\(157\) −5.00000 + 8.66025i −0.399043 + 0.691164i −0.993608 0.112884i \(-0.963991\pi\)
0.594565 + 0.804048i \(0.297324\pi\)
\(158\) −5.00000 + 8.66025i −0.397779 + 0.688973i
\(159\) 3.00000 + 5.19615i 0.237915 + 0.412082i
\(160\) −1.00000 −0.0790569
\(161\) 6.00000 5.19615i 0.472866 0.409514i
\(162\) 9.00000 0.707107
\(163\) 2.00000 + 3.46410i 0.156652 + 0.271329i 0.933659 0.358162i \(-0.116597\pi\)
−0.777007 + 0.629492i \(0.783263\pi\)
\(164\) 3.50000 6.06218i 0.273304 0.473377i
\(165\) −3.00000 + 5.19615i −0.233550 + 0.404520i
\(166\) 3.50000 + 6.06218i 0.271653 + 0.470516i
\(167\) −21.0000 −1.62503 −0.812514 0.582941i \(-0.801902\pi\)
−0.812514 + 0.582941i \(0.801902\pi\)
\(168\) −7.50000 2.59808i −0.578638 0.200446i
\(169\) −13.0000 −1.00000
\(170\) −2.00000 3.46410i −0.153393 0.265684i
\(171\) 18.0000 31.1769i 1.37649 2.38416i
\(172\) 2.50000 4.33013i 0.190623 0.330169i
\(173\) −4.00000 6.92820i −0.304114 0.526742i 0.672949 0.739689i \(-0.265027\pi\)
−0.977064 + 0.212947i \(0.931694\pi\)
\(174\) 27.0000 2.04686
\(175\) −2.50000 0.866025i −0.188982 0.0654654i
\(176\) −2.00000 −0.150756
\(177\) −15.0000 25.9808i −1.12747 1.95283i
\(178\) −0.500000 + 0.866025i −0.0374766 + 0.0649113i
\(179\) −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i \(-0.981361\pi\)
0.549825 + 0.835280i \(0.314694\pi\)
\(180\) 3.00000 + 5.19615i 0.223607 + 0.387298i
\(181\) 7.00000 0.520306 0.260153 0.965567i \(-0.416227\pi\)
0.260153 + 0.965567i \(0.416227\pi\)
\(182\) 0 0
\(183\) 3.00000 0.221766
\(184\) −1.50000 2.59808i −0.110581 0.191533i
\(185\) −2.00000 + 3.46410i −0.147043 + 0.254686i
\(186\) 6.00000 10.3923i 0.439941 0.762001i
\(187\) −4.00000 6.92820i −0.292509 0.506640i
\(188\) 8.00000 0.583460
\(189\) 4.50000 + 23.3827i 0.327327 + 1.70084i
\(190\) 6.00000 0.435286
\(191\) 9.00000 + 15.5885i 0.651217 + 1.12794i 0.982828 + 0.184525i \(0.0590746\pi\)
−0.331611 + 0.943416i \(0.607592\pi\)
\(192\) −1.50000 + 2.59808i −0.108253 + 0.187500i
\(193\) −13.0000 + 22.5167i −0.935760 + 1.62078i −0.162488 + 0.986710i \(0.551952\pi\)
−0.773272 + 0.634074i \(0.781381\pi\)
\(194\) −7.00000 12.1244i −0.502571 0.870478i
\(195\) 0 0
\(196\) 1.00000 6.92820i 0.0714286 0.494872i
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 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
\(201\) 13.5000 + 23.3827i 0.952217 + 1.64929i
\(202\) 3.00000 0.211079
\(203\) 4.50000 + 23.3827i 0.315838 + 1.64114i
\(204\) −12.0000 −0.840168
\(205\) −3.50000 6.06218i −0.244451 0.423401i
\(206\) −0.500000 + 0.866025i −0.0348367 + 0.0603388i
\(207\) −9.00000 + 15.5885i −0.625543 + 1.08347i
\(208\) 0 0
\(209\) 12.0000 0.830057
\(210\) −6.00000 + 5.19615i −0.414039 + 0.358569i
\(211\) −26.0000 −1.78991 −0.894957 0.446153i \(-0.852794\pi\)
−0.894957 + 0.446153i \(0.852794\pi\)
\(212\) 1.00000 + 1.73205i 0.0686803 + 0.118958i
\(213\) −3.00000 + 5.19615i −0.205557 + 0.356034i
\(214\) −1.50000 + 2.59808i −0.102538 + 0.177601i
\(215\) −2.50000 4.33013i −0.170499 0.295312i
\(216\) 9.00000 0.612372
\(217\) 10.0000 + 3.46410i 0.678844 + 0.235159i
\(218\) −9.00000 −0.609557
\(219\) 6.00000 + 10.3923i 0.405442 + 0.702247i
\(220\) −1.00000 + 1.73205i −0.0674200 + 0.116775i
\(221\) 0 0
\(222\) 6.00000 + 10.3923i 0.402694 + 0.697486i
\(223\) 28.0000 1.87502 0.937509 0.347960i \(-0.113126\pi\)
0.937509 + 0.347960i \(0.113126\pi\)
\(224\) −2.50000 0.866025i −0.167038 0.0578638i
\(225\) 6.00000 0.400000
\(226\) −1.00000 1.73205i −0.0665190 0.115214i
\(227\) 2.00000 3.46410i 0.132745 0.229920i −0.791989 0.610535i \(-0.790954\pi\)
0.924734 + 0.380615i \(0.124288\pi\)
\(228\) 9.00000 15.5885i 0.596040 1.03237i
\(229\) −11.0000 19.0526i −0.726900 1.25903i −0.958187 0.286143i \(-0.907627\pi\)
0.231287 0.972886i \(-0.425707\pi\)
\(230\) −3.00000 −0.197814
\(231\) −12.0000 + 10.3923i −0.789542 + 0.683763i
\(232\) 9.00000 0.590879
\(233\) −12.0000 20.7846i −0.786146 1.36165i −0.928312 0.371802i \(-0.878740\pi\)
0.142166 0.989843i \(-0.454593\pi\)
\(234\) 0 0
\(235\) 4.00000 6.92820i 0.260931 0.451946i
\(236\) −5.00000 8.66025i −0.325472 0.563735i
\(237\) 30.0000 1.94871
\(238\) −2.00000 10.3923i −0.129641 0.673633i
\(239\) 16.0000 1.03495 0.517477 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) 1.50000 + 2.59808i 0.0968246 + 0.167705i
\(241\) −5.00000 + 8.66025i −0.322078 + 0.557856i −0.980917 0.194429i \(-0.937715\pi\)
0.658838 + 0.752285i \(0.271048\pi\)
\(242\) 3.50000 6.06218i 0.224989 0.389692i
\(243\) 0 0
\(244\) 1.00000 0.0640184
\(245\) −5.50000 4.33013i −0.351382 0.276642i
\(246\) −21.0000 −1.33891
\(247\) 0 0
\(248\) 2.00000 3.46410i 0.127000 0.219971i
\(249\) 10.5000 18.1865i 0.665410 1.15252i
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 3.00000 + 15.5885i 0.188982 + 0.981981i
\(253\) −6.00000 −0.377217
\(254\) −8.00000 13.8564i −0.501965 0.869428i
\(255\) −6.00000 + 10.3923i −0.375735 + 0.650791i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −4.00000 6.92820i −0.249513 0.432169i 0.713878 0.700270i \(-0.246937\pi\)
−0.963391 + 0.268101i \(0.913604\pi\)
\(258\) −15.0000 −0.933859
\(259\) −8.00000 + 6.92820i −0.497096 + 0.430498i
\(260\) 0 0
\(261\) −27.0000 46.7654i −1.67126 2.89470i
\(262\) −4.00000 + 6.92820i −0.247121 + 0.428026i
\(263\) −2.50000 + 4.33013i −0.154157 + 0.267007i −0.932752 0.360520i \(-0.882599\pi\)
0.778595 + 0.627527i \(0.215933\pi\)
\(264\) 3.00000 + 5.19615i 0.184637 + 0.319801i
\(265\) 2.00000 0.122859
\(266\) 15.0000 + 5.19615i 0.919709 + 0.318597i
\(267\) 3.00000 0.183597
\(268\) 4.50000 + 7.79423i 0.274881 + 0.476108i
\(269\) −1.50000 + 2.59808i −0.0914566 + 0.158408i −0.908124 0.418701i \(-0.862486\pi\)
0.816668 + 0.577108i \(0.195819\pi\)
\(270\) 4.50000 7.79423i 0.273861 0.474342i
\(271\) 3.00000 + 5.19615i 0.182237 + 0.315644i 0.942642 0.333805i \(-0.108333\pi\)
−0.760405 + 0.649449i \(0.775000\pi\)
\(272\) −4.00000 −0.242536
\(273\) 0 0
\(274\) 12.0000 0.724947
\(275\) 1.00000 + 1.73205i 0.0603023 + 0.104447i
\(276\) −4.50000 + 7.79423i −0.270868 + 0.469157i
\(277\) −6.00000 + 10.3923i −0.360505 + 0.624413i −0.988044 0.154172i \(-0.950729\pi\)
0.627539 + 0.778585i \(0.284062\pi\)
\(278\) 7.00000 + 12.1244i 0.419832 + 0.727171i
\(279\) −24.0000 −1.43684
\(280\) −2.00000 + 1.73205i −0.119523 + 0.103510i
\(281\) 2.00000 0.119310 0.0596550 0.998219i \(-0.481000\pi\)
0.0596550 + 0.998219i \(0.481000\pi\)
\(282\) −12.0000 20.7846i −0.714590 1.23771i
\(283\) 2.00000 3.46410i 0.118888 0.205919i −0.800439 0.599414i \(-0.795400\pi\)
0.919327 + 0.393494i \(0.128734\pi\)
\(284\) −1.00000 + 1.73205i −0.0593391 + 0.102778i
\(285\) −9.00000 15.5885i −0.533114 0.923381i
\(286\) 0 0
\(287\) −3.50000 18.1865i −0.206598 1.07352i
\(288\) 6.00000 0.353553
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) 4.50000 7.79423i 0.264249 0.457693i
\(291\) −21.0000 + 36.3731i −1.23104 + 2.13223i
\(292\) 2.00000 + 3.46410i 0.117041 + 0.202721i
\(293\) 28.0000 1.63578 0.817889 0.575376i \(-0.195144\pi\)
0.817889 + 0.575376i \(0.195144\pi\)
\(294\) −19.5000 + 7.79423i −1.13726 + 0.454569i
\(295\) −10.0000 −0.582223
\(296\) 2.00000 + 3.46410i 0.116248 + 0.201347i
\(297\) 9.00000 15.5885i 0.522233 0.904534i
\(298\) −1.50000 + 2.59808i −0.0868927 + 0.150503i
\(299\) 0 0
\(300\) 3.00000 0.173205
\(301\) −2.50000 12.9904i −0.144098 0.748753i
\(302\) −16.0000 −0.920697
\(303\) −4.50000 7.79423i −0.258518 0.447767i
\(304\) 3.00000 5.19615i 0.172062 0.298020i
\(305\) 0.500000 0.866025i 0.0286299 0.0495885i
\(306\) 12.0000 + 20.7846i 0.685994 + 1.18818i
\(307\) 7.00000 0.399511 0.199756 0.979846i \(-0.435985\pi\)
0.199756 + 0.979846i \(0.435985\pi\)
\(308\) −4.00000 + 3.46410i −0.227921 + 0.197386i
\(309\) 3.00000 0.170664
\(310\) −2.00000 3.46410i −0.113592 0.196748i
\(311\) 9.00000 15.5885i 0.510343 0.883940i −0.489585 0.871956i \(-0.662852\pi\)
0.999928 0.0119847i \(-0.00381495\pi\)
\(312\) 0 0
\(313\) −4.00000 6.92820i −0.226093 0.391605i 0.730554 0.682855i \(-0.239262\pi\)
−0.956647 + 0.291250i \(0.905929\pi\)
\(314\) 10.0000 0.564333
\(315\) 15.0000 + 5.19615i 0.845154 + 0.292770i
\(316\) 10.0000 0.562544
\(317\) 16.0000 + 27.7128i 0.898650 + 1.55651i 0.829222 + 0.558920i \(0.188784\pi\)
0.0694277 + 0.997587i \(0.477883\pi\)
\(318\) 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
\(321\) 9.00000 0.502331
\(322\) −7.50000 2.59808i −0.417959 0.144785i
\(323\) 24.0000 1.33540
\(324\) −4.50000 7.79423i −0.250000 0.433013i
\(325\) 0 0
\(326\) 2.00000 3.46410i 0.110770 0.191859i
\(327\) 13.5000 + 23.3827i 0.746552 + 1.29307i
\(328\) −7.00000 −0.386510
\(329\) 16.0000 13.8564i 0.882109 0.763928i
\(330\) 6.00000 0.330289
\(331\) 16.0000 + 27.7128i 0.879440 + 1.52323i 0.851957 + 0.523612i \(0.175416\pi\)
0.0274825 + 0.999622i \(0.491251\pi\)
\(332\) 3.50000 6.06218i 0.192087 0.332705i
\(333\) 12.0000 20.7846i 0.657596 1.13899i
\(334\) 10.5000 + 18.1865i 0.574534 + 0.995123i
\(335\) 9.00000 0.491723
\(336\) 1.50000 + 7.79423i 0.0818317 + 0.425210i
\(337\) −26.0000 −1.41631 −0.708155 0.706057i \(-0.750472\pi\)
−0.708155 + 0.706057i \(0.750472\pi\)
\(338\) 6.50000 + 11.2583i 0.353553 + 0.612372i
\(339\) −3.00000 + 5.19615i −0.162938 + 0.282216i
\(340\) −2.00000 + 3.46410i −0.108465 + 0.187867i
\(341\) −4.00000 6.92820i −0.216612 0.375183i
\(342\) −36.0000 −1.94666
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) −5.00000 −0.269582
\(345\) 4.50000 + 7.79423i 0.242272 + 0.419627i
\(346\) −4.00000 + 6.92820i −0.215041 + 0.372463i
\(347\) −9.50000 + 16.4545i −0.509987 + 0.883323i 0.489946 + 0.871753i \(0.337016\pi\)
−0.999933 + 0.0115703i \(0.996317\pi\)
\(348\) −13.5000 23.3827i −0.723676 1.25344i
\(349\) −35.0000 −1.87351 −0.936754 0.349990i \(-0.886185\pi\)
−0.936754 + 0.349990i \(0.886185\pi\)
\(350\) 0.500000 + 2.59808i 0.0267261 + 0.138873i
\(351\) 0 0
\(352\) 1.00000 + 1.73205i 0.0533002 + 0.0923186i
\(353\) 9.00000 15.5885i 0.479022 0.829690i −0.520689 0.853746i \(-0.674325\pi\)
0.999711 + 0.0240566i \(0.00765819\pi\)
\(354\) −15.0000 + 25.9808i −0.797241 + 1.38086i
\(355\) 1.00000 + 1.73205i 0.0530745 + 0.0919277i
\(356\) 1.00000 0.0529999
\(357\) −24.0000 + 20.7846i −1.27021 + 1.10004i
\(358\) 12.0000 0.634220
\(359\) 2.00000 + 3.46410i 0.105556 + 0.182828i 0.913965 0.405793i \(-0.133004\pi\)
−0.808409 + 0.588621i \(0.799671\pi\)
\(360\) 3.00000 5.19615i 0.158114 0.273861i
\(361\) −8.50000 + 14.7224i −0.447368 + 0.774865i
\(362\) −3.50000 6.06218i −0.183956 0.318621i
\(363\) −21.0000 −1.10221
\(364\) 0 0
\(365\) 4.00000 0.209370
\(366\) −1.50000 2.59808i −0.0784063 0.135804i
\(367\) 5.50000 9.52628i 0.287098 0.497268i −0.686018 0.727585i \(-0.740643\pi\)
0.973116 + 0.230317i \(0.0739762\pi\)
\(368\) −1.50000 + 2.59808i −0.0781929 + 0.135434i
\(369\) 21.0000 + 36.3731i 1.09322 + 1.89351i
\(370\) 4.00000 0.207950
\(371\) 5.00000 + 1.73205i 0.259587 + 0.0899236i
\(372\) −12.0000 −0.622171
\(373\) 2.00000 + 3.46410i 0.103556 + 0.179364i 0.913147 0.407630i \(-0.133645\pi\)
−0.809591 + 0.586994i \(0.800311\pi\)
\(374\) −4.00000 + 6.92820i −0.206835 + 0.358249i
\(375\) 1.50000 2.59808i 0.0774597 0.134164i
\(376\) −4.00000 6.92820i −0.206284 0.357295i
\(377\) 0 0
\(378\) 18.0000 15.5885i 0.925820 0.801784i
\(379\) 30.0000 1.54100 0.770498 0.637442i \(-0.220007\pi\)
0.770498 + 0.637442i \(0.220007\pi\)
\(380\) −3.00000 5.19615i −0.153897 0.266557i
\(381\) −24.0000 + 41.5692i −1.22956 + 2.12966i
\(382\) 9.00000 15.5885i 0.460480 0.797575i
\(383\) −7.50000 12.9904i −0.383232 0.663777i 0.608290 0.793715i \(-0.291856\pi\)
−0.991522 + 0.129937i \(0.958522\pi\)
\(384\) 3.00000 0.153093
\(385\) 1.00000 + 5.19615i 0.0509647 + 0.264820i
\(386\) 26.0000 1.32337
\(387\) 15.0000 + 25.9808i 0.762493 + 1.32068i
\(388\) −7.00000 + 12.1244i −0.355371 + 0.615521i
\(389\) −13.0000 + 22.5167i −0.659126 + 1.14164i 0.321716 + 0.946836i \(0.395740\pi\)
−0.980842 + 0.194804i \(0.937593\pi\)
\(390\) 0 0
\(391\) −12.0000 −0.606866
\(392\) −6.50000 + 2.59808i −0.328300 + 0.131223i
\(393\) 24.0000 1.21064
\(394\) −1.00000 1.73205i −0.0503793 0.0872595i
\(395\) 5.00000 8.66025i 0.251577 0.435745i
\(396\) 6.00000 10.3923i 0.301511 0.522233i
\(397\) −11.0000 19.0526i −0.552074 0.956221i −0.998125 0.0612128i \(-0.980503\pi\)
0.446051 0.895008i \(-0.352830\pi\)
\(398\) −4.00000 −0.200502
\(399\) −9.00000 46.7654i −0.450564 2.34120i
\(400\) 1.00000 0.0500000
\(401\) −15.5000 26.8468i −0.774033 1.34066i −0.935336 0.353760i \(-0.884903\pi\)
0.161303 0.986905i \(-0.448430\pi\)
\(402\) 13.5000 23.3827i 0.673319 1.16622i
\(403\) 0 0
\(404\) −1.50000 2.59808i −0.0746278 0.129259i
\(405\) −9.00000 −0.447214
\(406\) 18.0000 15.5885i 0.893325 0.773642i
\(407\) 8.00000 0.396545
\(408\) 6.00000 + 10.3923i 0.297044 + 0.514496i
\(409\) −1.50000 + 2.59808i −0.0741702 + 0.128467i −0.900725 0.434389i \(-0.856964\pi\)
0.826555 + 0.562856i \(0.190297\pi\)
\(410\) −3.50000 + 6.06218i −0.172853 + 0.299390i
\(411\) −18.0000 31.1769i −0.887875 1.53784i
\(412\) 1.00000 0.0492665
\(413\) −25.0000 8.66025i −1.23017 0.426143i
\(414\) 18.0000 0.884652
\(415\) −3.50000 6.06218i −0.171808 0.297581i
\(416\) 0 0
\(417\) 21.0000 36.3731i 1.02837 1.78120i
\(418\) −6.00000 10.3923i −0.293470 0.508304i
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 7.50000 + 2.59808i 0.365963 + 0.126773i
\(421\) −19.0000 −0.926003 −0.463002 0.886357i \(-0.653228\pi\)
−0.463002 + 0.886357i \(0.653228\pi\)
\(422\) 13.0000 + 22.5167i 0.632830 + 1.09609i
\(423\) −24.0000 + 41.5692i −1.16692 + 2.02116i
\(424\) 1.00000 1.73205i 0.0485643 0.0841158i
\(425\) 2.00000 + 3.46410i 0.0970143 + 0.168034i
\(426\) 6.00000 0.290701
\(427\) 2.00000 1.73205i 0.0967868 0.0838198i
\(428\) 3.00000 0.145010
\(429\) 0 0
\(430\) −2.50000 + 4.33013i −0.120561 + 0.208817i
\(431\) 15.0000 25.9808i 0.722525 1.25145i −0.237460 0.971397i \(-0.576315\pi\)
0.959985 0.280052i \(-0.0903517\pi\)
\(432\) −4.50000 7.79423i −0.216506 0.375000i
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) −2.00000 10.3923i −0.0960031 0.498847i
\(435\) −27.0000 −1.29455
\(436\) 4.50000 + 7.79423i 0.215511 + 0.373276i
\(437\) 9.00000 15.5885i 0.430528 0.745697i
\(438\) 6.00000 10.3923i 0.286691 0.496564i
\(439\) 10.0000 + 17.3205i 0.477274 + 0.826663i 0.999661 0.0260459i \(-0.00829161\pi\)
−0.522387 + 0.852709i \(0.674958\pi\)
\(440\) 2.00000 0.0953463
\(441\) 33.0000 + 25.9808i 1.57143 + 1.23718i
\(442\) 0 0
\(443\) −15.5000 26.8468i −0.736427 1.27553i −0.954094 0.299506i \(-0.903178\pi\)
0.217667 0.976023i \(-0.430155\pi\)
\(444\) 6.00000 10.3923i 0.284747 0.493197i
\(445\) 0.500000 0.866025i 0.0237023 0.0410535i
\(446\) −14.0000 24.2487i −0.662919 1.14821i
\(447\) 9.00000 0.425685
\(448\) 0.500000 + 2.59808i 0.0236228 + 0.122748i
\(449\) −33.0000 −1.55737 −0.778683 0.627417i \(-0.784112\pi\)
−0.778683 + 0.627417i \(0.784112\pi\)
\(450\) −3.00000 5.19615i −0.141421 0.244949i
\(451\) −7.00000 + 12.1244i −0.329617 + 0.570914i
\(452\) −1.00000 + 1.73205i −0.0470360 + 0.0814688i
\(453\) 24.0000 + 41.5692i 1.12762 + 1.95309i
\(454\) −4.00000 −0.187729
\(455\) 0 0
\(456\) −18.0000 −0.842927
\(457\) 16.0000 + 27.7128i 0.748448 + 1.29635i 0.948566 + 0.316579i \(0.102534\pi\)
−0.200118 + 0.979772i \(0.564132\pi\)
\(458\) −11.0000 + 19.0526i −0.513996 + 0.890268i
\(459\) 18.0000 31.1769i 0.840168 1.45521i
\(460\) 1.50000 + 2.59808i 0.0699379 + 0.121136i
\(461\) −14.0000 −0.652045 −0.326023 0.945362i \(-0.605709\pi\)
−0.326023 + 0.945362i \(0.605709\pi\)
\(462\) 15.0000 + 5.19615i 0.697863 + 0.241747i
\(463\) −19.0000 −0.883005 −0.441502 0.897260i \(-0.645554\pi\)
−0.441502 + 0.897260i \(0.645554\pi\)
\(464\) −4.50000 7.79423i −0.208907 0.361838i
\(465\) −6.00000 + 10.3923i −0.278243 + 0.481932i
\(466\) −12.0000 + 20.7846i −0.555889 + 0.962828i
\(467\) 6.50000 + 11.2583i 0.300784 + 0.520973i 0.976314 0.216359i \(-0.0694183\pi\)
−0.675530 + 0.737333i \(0.736085\pi\)
\(468\) 0 0
\(469\) 22.5000 + 7.79423i 1.03895 + 0.359904i
\(470\) −8.00000 −0.369012
\(471\) −15.0000 25.9808i −0.691164 1.19713i
\(472\) −5.00000 + 8.66025i −0.230144 + 0.398621i
\(473\) −5.00000 + 8.66025i −0.229900 + 0.398199i
\(474\) −15.0000 25.9808i −0.688973 1.19334i
\(475\) −6.00000 −0.275299
\(476\) −8.00000 + 6.92820i −0.366679 + 0.317554i
\(477\) −12.0000 −0.549442
\(478\) −8.00000 13.8564i −0.365911 0.633777i
\(479\) −12.0000 + 20.7846i −0.548294 + 0.949673i 0.450098 + 0.892979i \(0.351389\pi\)
−0.998392 + 0.0566937i \(0.981944\pi\)
\(480\) 1.50000 2.59808i 0.0684653 0.118585i
\(481\) 0 0
\(482\) 10.0000 0.455488
\(483\) 4.50000 + 23.3827i 0.204757 + 1.06395i
\(484\) −7.00000 −0.318182
\(485\) 7.00000 + 12.1244i 0.317854 + 0.550539i
\(486\) 0 0
\(487\) 8.00000 13.8564i 0.362515 0.627894i −0.625859 0.779936i \(-0.715252\pi\)
0.988374 + 0.152042i \(0.0485850\pi\)
\(488\) −0.500000 0.866025i −0.0226339 0.0392031i
\(489\) −12.0000 −0.542659
\(490\) −1.00000 + 6.92820i −0.0451754 + 0.312984i
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 10.5000 + 18.1865i 0.473377 + 0.819912i
\(493\) 18.0000 31.1769i 0.810679 1.40414i
\(494\) 0 0
\(495\) −6.00000 10.3923i −0.269680 0.467099i
\(496\) −4.00000 −0.179605
\(497\) 1.00000 + 5.19615i 0.0448561 + 0.233079i
\(498\) −21.0000 −0.941033
\(499\) 9.00000 + 15.5885i 0.402895 + 0.697835i 0.994074 0.108705i \(-0.0346705\pi\)
−0.591179 + 0.806541i \(0.701337\pi\)
\(500\) 0.500000 0.866025i 0.0223607 0.0387298i
\(501\) 31.5000 54.5596i 1.40732 2.43754i
\(502\) 0 0
\(503\) −21.0000 −0.936344 −0.468172 0.883637i \(-0.655087\pi\)
−0.468172 + 0.883637i \(0.655087\pi\)
\(504\) 12.0000 10.3923i 0.534522 0.462910i
\(505\) −3.00000 −0.133498
\(506\) 3.00000 + 5.19615i 0.133366 + 0.230997i
\(507\) 19.5000 33.7750i 0.866025 1.50000i
\(508\) −8.00000 + 13.8564i −0.354943 + 0.614779i
\(509\) −0.500000 0.866025i −0.0221621 0.0383859i 0.854732 0.519070i \(-0.173722\pi\)
−0.876894 + 0.480684i \(0.840388\pi\)
\(510\) 12.0000 0.531369
\(511\) 10.0000 + 3.46410i 0.442374 + 0.153243i
\(512\) 1.00000 0.0441942
\(513\) 27.0000 + 46.7654i 1.19208 + 2.06474i
\(514\) −4.00000 + 6.92820i −0.176432 + 0.305590i
\(515\) 0.500000 0.866025i 0.0220326 0.0381616i
\(516\) 7.50000 + 12.9904i 0.330169 + 0.571870i
\(517\) −16.0000 −0.703679
\(518\) 10.0000 + 3.46410i 0.439375 + 0.152204i
\(519\) 24.0000 1.05348
\(520\) 0 0
\(521\) −19.0000 + 32.9090i −0.832405 + 1.44177i 0.0637207 + 0.997968i \(0.479703\pi\)
−0.896126 + 0.443800i \(0.853630\pi\)
\(522\) −27.0000 + 46.7654i −1.18176 + 2.04686i
\(523\) 10.0000 + 17.3205i 0.437269 + 0.757373i 0.997478 0.0709788i \(-0.0226123\pi\)
−0.560208 + 0.828352i \(0.689279\pi\)
\(524\) 8.00000 0.349482
\(525\) 6.00000 5.19615i 0.261861 0.226779i
\(526\) 5.00000 0.218010
\(527\) −8.00000 13.8564i −0.348485 0.603595i
\(528\) 3.00000 5.19615i 0.130558 0.226134i
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) −1.00000 1.73205i −0.0434372 0.0752355i
\(531\) 60.0000 2.60378
\(532\) −3.00000 15.5885i −0.130066 0.675845i
\(533\) 0 0
\(534\) −1.50000 2.59808i −0.0649113 0.112430i
\(535\) 1.50000 2.59808i 0.0648507 0.112325i
\(536\) 4.50000 7.79423i 0.194370 0.336659i
\(537\) −18.0000 31.1769i −0.776757 1.34538i
\(538\) 3.00000 0.129339
\(539\) −2.00000 + 13.8564i −0.0861461 + 0.596838i
\(540\) −9.00000 −0.387298
\(541\) −1.50000 2.59808i −0.0644900 0.111700i 0.831978 0.554809i \(-0.187209\pi\)
−0.896468 + 0.443109i \(0.853875\pi\)
\(542\) 3.00000 5.19615i 0.128861 0.223194i
\(543\) −10.5000 + 18.1865i −0.450598 + 0.780459i
\(544\) 2.00000 + 3.46410i 0.0857493 + 0.148522i
\(545\) 9.00000 0.385518
\(546\) 0 0
\(547\) −33.0000 −1.41098 −0.705489 0.708721i \(-0.749273\pi\)
−0.705489 + 0.708721i \(0.749273\pi\)
\(548\) −6.00000 10.3923i −0.256307 0.443937i
\(549\) −3.00000 + 5.19615i −0.128037 + 0.221766i
\(550\) 1.00000 1.73205i 0.0426401 0.0738549i
\(551\) 27.0000 + 46.7654i 1.15024 + 1.99227i
\(552\) 9.00000 0.383065
\(553\) 20.0000 17.3205i 0.850487 0.736543i
\(554\) 12.0000 0.509831
\(555\) −6.00000 10.3923i −0.254686 0.441129i
\(556\) 7.00000 12.1244i 0.296866 0.514187i
\(557\) 1.00000 1.73205i 0.0423714 0.0733893i −0.844062 0.536246i \(-0.819842\pi\)
0.886433 + 0.462856i \(0.153175\pi\)
\(558\) 12.0000 + 20.7846i 0.508001 + 0.879883i
\(559\) 0 0
\(560\) 2.50000 + 0.866025i 0.105644 + 0.0365963i
\(561\) 24.0000 1.01328
\(562\) −1.00000 1.73205i −0.0421825 0.0730622i
\(563\) −8.50000 + 14.7224i −0.358232 + 0.620477i −0.987666 0.156578i \(-0.949954\pi\)
0.629433 + 0.777055i \(0.283287\pi\)
\(564\) −12.0000 + 20.7846i −0.505291 + 0.875190i
\(565\) 1.00000 + 1.73205i 0.0420703 + 0.0728679i
\(566\) −4.00000 −0.168133
\(567\) −22.5000 7.79423i −0.944911 0.327327i
\(568\) 2.00000 0.0839181
\(569\) 9.00000 + 15.5885i 0.377300 + 0.653502i 0.990668 0.136295i \(-0.0435194\pi\)
−0.613369 + 0.789797i \(0.710186\pi\)
\(570\) −9.00000 + 15.5885i −0.376969 + 0.652929i
\(571\) 15.0000 25.9808i 0.627730 1.08726i −0.360276 0.932846i \(-0.617317\pi\)
0.988006 0.154415i \(-0.0493493\pi\)
\(572\) 0 0
\(573\) −54.0000 −2.25588
\(574\) −14.0000 + 12.1244i −0.584349 + 0.506061i
\(575\) 3.00000 0.125109
\(576\) −3.00000 5.19615i −0.125000 0.216506i
\(577\) −5.00000 + 8.66025i −0.208153 + 0.360531i −0.951133 0.308783i \(-0.900078\pi\)
0.742980 + 0.669314i \(0.233412\pi\)
\(578\) 0.500000 0.866025i 0.0207973 0.0360219i
\(579\) −39.0000 67.5500i −1.62078 2.80728i
\(580\) −9.00000 −0.373705
\(581\) −3.50000 18.1865i −0.145204 0.754505i
\(582\) 42.0000 1.74096
\(583\) −2.00000 3.46410i −0.0828315 0.143468i
\(584\) 2.00000 3.46410i 0.0827606 0.143346i
\(585\) 0 0
\(586\) −14.0000 24.2487i −0.578335 1.00171i
\(587\) −28.0000 −1.15568 −0.577842 0.816149i \(-0.696105\pi\)
−0.577842 + 0.816149i \(0.696105\pi\)
\(588\) 16.5000 + 12.9904i 0.680449 + 0.535714i
\(589\) 24.0000 0.988903
\(590\) 5.00000 + 8.66025i 0.205847 + 0.356537i
\(591\) −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 \(-0.127353\pi\)
−0.797831 + 0.602881i \(0.794019\pi\)
\(594\) −18.0000 −0.738549
\(595\) 2.00000 + 10.3923i 0.0819920 + 0.426043i
\(596\) 3.00000 0.122885
\(597\) 6.00000 + 10.3923i 0.245564 + 0.425329i
\(598\) 0 0
\(599\) −6.00000 + 10.3923i −0.245153 + 0.424618i −0.962175 0.272433i \(-0.912172\pi\)
0.717021 + 0.697051i \(0.245505\pi\)
\(600\) −1.50000 2.59808i −0.0612372 0.106066i
\(601\) 42.0000 1.71322 0.856608 0.515968i \(-0.172568\pi\)
0.856608 + 0.515968i \(0.172568\pi\)
\(602\) −10.0000 + 8.66025i −0.407570 + 0.352966i
\(603\) −54.0000 −2.19905
\(604\) 8.00000 + 13.8564i 0.325515 + 0.563809i
\(605\) −3.50000 + 6.06218i −0.142295 + 0.246463i
\(606\) −4.50000 + 7.79423i −0.182800 + 0.316619i
\(607\) −0.500000 0.866025i −0.0202944 0.0351509i 0.855700 0.517472i \(-0.173127\pi\)
−0.875994 + 0.482322i \(0.839794\pi\)
\(608\) −6.00000 −0.243332
\(609\) −67.5000 23.3827i −2.73524 0.947514i
\(610\) −1.00000 −0.0404888
\(611\) 0 0
\(612\) 12.0000 20.7846i 0.485071 0.840168i
\(613\) −6.00000 + 10.3923i −0.242338 + 0.419741i −0.961380 0.275225i \(-0.911248\pi\)
0.719042 + 0.694967i \(0.244581\pi\)
\(614\) −3.50000 6.06218i −0.141249 0.244650i
\(615\) 21.0000 0.846802
\(616\) 5.00000 + 1.73205i 0.201456 + 0.0697863i
\(617\) 44.0000 1.77137 0.885687 0.464283i \(-0.153688\pi\)
0.885687 + 0.464283i \(0.153688\pi\)
\(618\) −1.50000 2.59808i −0.0603388 0.104510i
\(619\) 23.0000 39.8372i 0.924448 1.60119i 0.132002 0.991250i \(-0.457860\pi\)
0.792446 0.609941i \(-0.208807\pi\)
\(620\) −2.00000 + 3.46410i −0.0803219 + 0.139122i
\(621\) −13.5000 23.3827i −0.541736 0.938315i
\(622\) −18.0000 −0.721734
\(623\) 2.00000 1.73205i 0.0801283 0.0693932i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −4.00000 + 6.92820i −0.159872 + 0.276907i
\(627\) −18.0000 + 31.1769i −0.718851 + 1.24509i
\(628\) −5.00000 8.66025i −0.199522 0.345582i
\(629\) 16.0000 0.637962
\(630\) −3.00000 15.5885i −0.119523 0.621059i
\(631\) 2.00000 0.0796187 0.0398094 0.999207i \(-0.487325\pi\)
0.0398094 + 0.999207i \(0.487325\pi\)
\(632\) −5.00000 8.66025i −0.198889 0.344486i
\(633\) 39.0000 67.5500i 1.55011 2.68487i
\(634\) 16.0000 27.7128i 0.635441 1.10062i
\(635\) 8.00000 + 13.8564i 0.317470 + 0.549875i
\(636\) −6.00000 −0.237915
\(637\) 0 0
\(638\) −18.0000 −0.712627
\(639\) −6.00000 10.3923i −0.237356 0.411113i
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) −2.50000 + 4.33013i −0.0987441 + 0.171030i −0.911165 0.412042i \(-0.864816\pi\)
0.812421 + 0.583071i \(0.198149\pi\)
\(642\) −4.50000 7.79423i −0.177601 0.307614i
\(643\) 28.0000 1.10421 0.552106 0.833774i \(-0.313824\pi\)
0.552106 + 0.833774i \(0.313824\pi\)
\(644\) 1.50000 + 7.79423i 0.0591083 + 0.307136i
\(645\) 15.0000 0.590624
\(646\) −12.0000 20.7846i −0.472134 0.817760i
\(647\) 5.50000 9.52628i 0.216227 0.374517i −0.737424 0.675430i \(-0.763958\pi\)
0.953652 + 0.300913i \(0.0972914\pi\)
\(648\) −4.50000 + 7.79423i −0.176777 + 0.306186i
\(649\) 10.0000 + 17.3205i 0.392534 + 0.679889i
\(650\) 0 0
\(651\) −24.0000 + 20.7846i −0.940634 + 0.814613i
\(652\) −4.00000 −0.156652
\(653\) 2.00000 + 3.46410i 0.0782660 + 0.135561i 0.902502 0.430686i \(-0.141728\pi\)
−0.824236 + 0.566247i \(0.808395\pi\)
\(654\) 13.5000 23.3827i 0.527892 0.914335i
\(655\) 4.00000 6.92820i 0.156293 0.270707i
\(656\) 3.50000 + 6.06218i 0.136652 + 0.236688i
\(657\) −24.0000 −0.936329
\(658\) −20.0000 6.92820i −0.779681 0.270089i
\(659\) −26.0000 −1.01282 −0.506408 0.862294i \(-0.669027\pi\)
−0.506408 + 0.862294i \(0.669027\pi\)
\(660\) −3.00000 5.19615i −0.116775 0.202260i
\(661\) 5.50000 9.52628i 0.213925 0.370529i −0.739014 0.673690i \(-0.764708\pi\)
0.952940 + 0.303160i \(0.0980418\pi\)
\(662\) 16.0000 27.7128i 0.621858 1.07709i
\(663\) 0 0
\(664\) −7.00000 −0.271653
\(665\) −15.0000 5.19615i −0.581675 0.201498i
\(666\) −24.0000 −0.929981
\(667\) −13.5000 23.3827i −0.522722 0.905381i
\(668\) 10.5000 18.1865i 0.406257 0.703658i
\(669\) −42.0000 + 72.7461i −1.62381 + 2.81253i
\(670\) −4.50000 7.79423i −0.173850 0.301117i
\(671\) −2.00000 −0.0772091
\(672\) 6.00000 5.19615i 0.231455 0.200446i
\(673\) 16.0000 0.616755 0.308377 0.951264i \(-0.400214\pi\)
0.308377 + 0.951264i \(0.400214\pi\)
\(674\) 13.0000 + 22.5167i 0.500741 + 0.867309i
\(675\) −4.50000 + 7.79423i −0.173205 + 0.300000i
\(676\) 6.50000 11.2583i 0.250000 0.433013i
\(677\) 24.0000 + 41.5692i 0.922395 + 1.59763i 0.795698 + 0.605693i \(0.207104\pi\)
0.126697 + 0.991941i \(0.459562\pi\)
\(678\) 6.00000 0.230429
\(679\) 7.00000 + 36.3731i 0.268635 + 1.39587i
\(680\) 4.00000 0.153393
\(681\) 6.00000 + 10.3923i 0.229920 + 0.398234i
\(682\) −4.00000 + 6.92820i −0.153168 + 0.265295i
\(683\) 18.5000 32.0429i 0.707883 1.22609i −0.257758 0.966209i \(-0.582984\pi\)
0.965641 0.259880i \(-0.0836829\pi\)
\(684\) 18.0000 + 31.1769i 0.688247 + 1.19208i
\(685\) −12.0000 −0.458496
\(686\) −8.50000 + 16.4545i −0.324532 + 0.628235i
\(687\) 66.0000 2.51806
\(688\) 2.50000 + 4.33013i 0.0953116 + 0.165085i
\(689\) 0 0
\(690\) 4.50000 7.79423i 0.171312 0.296721i
\(691\) −11.0000 19.0526i −0.418460 0.724793i 0.577325 0.816514i \(-0.304097\pi\)
−0.995785 + 0.0917209i \(0.970763\pi\)
\(692\) 8.00000 0.304114
\(693\) −6.00000 31.1769i −0.227921 1.18431i
\(694\) 19.0000 0.721230
\(695\) −7.00000 12.1244i −0.265525 0.459903i
\(696\) −13.5000 + 23.3827i −0.511716 + 0.886318i
\(697\) −14.0000 + 24.2487i −0.530288 + 0.918485i
\(698\) 17.5000 + 30.3109i 0.662385 + 1.14728i
\(699\) 72.0000 2.72329
\(700\) 2.00000 1.73205i 0.0755929 0.0654654i
\(701\) −47.0000 −1.77517 −0.887583 0.460648i \(-0.847617\pi\)
−0.887583 + 0.460648i \(0.847617\pi\)
\(702\) 0 0
\(703\) −12.0000 + 20.7846i −0.452589 + 0.783906i
\(704\) 1.00000 1.73205i 0.0376889 0.0652791i
\(705\) 12.0000 + 20.7846i 0.451946 + 0.782794i
\(706\) −18.0000 −0.677439
\(707\) −7.50000 2.59808i −0.282067 0.0977107i
\(708\) 30.0000 1.12747
\(709\) 5.50000 + 9.52628i 0.206557 + 0.357767i 0.950628 0.310334i \(-0.100441\pi\)
−0.744071 + 0.668101i \(0.767108\pi\)
\(710\) 1.00000 1.73205i 0.0375293 0.0650027i
\(711\) −30.0000 + 51.9615i −1.12509 + 1.94871i
\(712\) −0.500000 0.866025i −0.0187383 0.0324557i
\(713\) −12.0000 −0.449404
\(714\) 30.0000 + 10.3923i 1.12272 + 0.388922i
\(715\) 0 0
\(716\) −6.00000 10.3923i −0.224231 0.388379i
\(717\) −24.0000 + 41.5692i −0.896296 + 1.55243i
\(718\) 2.00000 3.46410i 0.0746393 0.129279i
\(719\) 3.00000 + 5.19615i 0.111881 + 0.193784i 0.916529 0.399969i \(-0.130979\pi\)
−0.804648 + 0.593753i \(0.797646\pi\)
\(720\) −6.00000 −0.223607
\(721\) 2.00000 1.73205i 0.0744839 0.0645049i
\(722\) 17.0000 0.632674
\(723\) −15.0000 25.9808i −0.557856 0.966235i
\(724\) −3.50000 + 6.06218i −0.130076 + 0.225299i
\(725\) −4.50000 + 7.79423i −0.167126 + 0.289470i
\(726\) 10.5000 + 18.1865i 0.389692 + 0.674966i
\(727\) −21.0000 −0.778847 −0.389423 0.921059i \(-0.627326\pi\)
−0.389423 + 0.921059i \(0.627326\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) −2.00000 3.46410i −0.0740233 0.128212i
\(731\) −10.0000 + 17.3205i −0.369863 + 0.640622i
\(732\) −1.50000 + 2.59808i −0.0554416 + 0.0960277i
\(733\) −11.0000 19.0526i −0.406294 0.703722i 0.588177 0.808732i \(-0.299846\pi\)
−0.994471 + 0.105010i \(0.966513\pi\)
\(734\) −11.0000 −0.406017
\(735\) 19.5000 7.79423i 0.719268 0.287494i
\(736\) 3.00000 0.110581
\(737\) −9.00000 15.5885i −0.331519 0.574208i
\(738\) 21.0000 36.3731i 0.773021 1.33891i
\(739\) 1.00000 1.73205i 0.0367856 0.0637145i −0.847046 0.531519i \(-0.821621\pi\)
0.883832 + 0.467804i \(0.154955\pi\)
\(740\) −2.00000 3.46410i −0.0735215 0.127343i
\(741\) 0 0
\(742\) −1.00000 5.19615i −0.0367112 0.190757i
\(743\) 9.00000 0.330178 0.165089 0.986279i \(-0.447209\pi\)
0.165089 + 0.986279i \(0.447209\pi\)
\(744\) 6.00000 + 10.3923i 0.219971 + 0.381000i
\(745\) 1.50000 2.59808i 0.0549557 0.0951861i
\(746\) 2.00000 3.46410i 0.0732252 0.126830i
\(747\) 21.0000 + 36.3731i 0.768350 + 1.33082i
\(748\) 8.00000 0.292509
\(749\) 6.00000 5.19615i 0.219235 0.189863i
\(750\) −3.00000 −0.109545
\(751\) 2.00000 + 3.46410i 0.0729810 + 0.126407i 0.900207 0.435463i \(-0.143415\pi\)
−0.827225 + 0.561870i \(0.810082\pi\)
\(752\) −4.00000 + 6.92820i −0.145865 + 0.252646i
\(753\) 0 0
\(754\) 0 0
\(755\) 16.0000 0.582300
\(756\) −22.5000 7.79423i −0.818317 0.283473i
\(757\) 16.0000 0.581530 0.290765 0.956795i \(-0.406090\pi\)
0.290765 + 0.956795i \(0.406090\pi\)
\(758\) −15.0000 25.9808i −0.544825 0.943664i
\(759\) 9.00000 15.5885i 0.326679 0.565825i
\(760\) −3.00000 + 5.19615i −0.108821 + 0.188484i
\(761\) 3.00000 + 5.19615i 0.108750 + 0.188360i 0.915264 0.402854i \(-0.131982\pi\)
−0.806514 + 0.591215i \(0.798649\pi\)
\(762\) 48.0000 1.73886
\(763\) 22.5000 + 7.79423i 0.814555 + 0.282170i
\(764\) −18.0000 −0.651217
\(765\) −12.0000 20.7846i −0.433861 0.751469i
\(766\) −7.50000 + 12.9904i −0.270986 + 0.469362i
\(767\) 0 0
\(768\) −1.50000 2.59808i −0.0541266 0.0937500i
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 4.00000 3.46410i 0.144150 0.124838i
\(771\) 24.0000 0.864339
\(772\) −13.0000 22.5167i −0.467880 0.810392i
\(773\) −12.0000 + 20.7846i −0.431610 + 0.747570i −0.997012 0.0772449i \(-0.975388\pi\)
0.565402 + 0.824815i \(0.308721\pi\)
\(774\) 15.0000 25.9808i 0.539164 0.933859i
\(775\) 2.00000 + 3.46410i 0.0718421 + 0.124434i
\(776\) 14.0000 0.502571
\(777\) −6.00000 31.1769i −0.215249 1.11847i
\(778\) 26.0000 0.932145