Properties

Label 114.2.h.c.107.1
Level $114$
Weight $2$
Character 114.107
Analytic conductor $0.910$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 114.h (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.910294583043\)
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: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 114.107
Dual form 114.2.h.c.65.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-3.00000 + 1.73205i) q^{5} +(-1.50000 - 0.866025i) q^{6} +1.00000 q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-3.00000 + 1.73205i) q^{5} +(-1.50000 - 0.866025i) q^{6} +1.00000 q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-3.00000 - 1.73205i) q^{10} +3.46410i q^{11} -1.73205i q^{12} +(4.50000 + 2.59808i) q^{13} +(0.500000 + 0.866025i) q^{14} +(3.00000 - 5.19615i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 1.73205i) q^{17} +3.00000 q^{18} +(-4.00000 + 1.73205i) q^{19} -3.46410i q^{20} +(-1.50000 + 0.866025i) q^{21} +(-3.00000 + 1.73205i) q^{22} +(1.50000 - 0.866025i) q^{24} +(3.50000 - 6.06218i) q^{25} +5.19615i q^{26} +5.19615i q^{27} +(-0.500000 + 0.866025i) q^{28} +(3.00000 - 5.19615i) q^{29} +6.00000 q^{30} +1.73205i q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} +(3.00000 + 1.73205i) q^{34} +(-3.00000 + 1.73205i) q^{35} +(1.50000 + 2.59808i) q^{36} -5.19615i q^{37} +(-3.50000 - 2.59808i) q^{38} -9.00000 q^{39} +(3.00000 - 1.73205i) q^{40} +(6.00000 + 10.3923i) q^{41} +(-1.50000 - 0.866025i) q^{42} +(0.500000 + 0.866025i) q^{43} +(-3.00000 - 1.73205i) q^{44} +10.3923i q^{45} +(-6.00000 - 3.46410i) q^{47} +(1.50000 + 0.866025i) q^{48} -6.00000 q^{49} +7.00000 q^{50} +(-3.00000 + 5.19615i) q^{51} +(-4.50000 + 2.59808i) q^{52} +(6.00000 - 10.3923i) q^{53} +(-4.50000 + 2.59808i) q^{54} +(-6.00000 - 10.3923i) q^{55} -1.00000 q^{56} +(4.50000 - 6.06218i) q^{57} +6.00000 q^{58} +(3.00000 + 5.19615i) q^{60} +(-3.50000 + 6.06218i) q^{61} +(-1.50000 + 0.866025i) q^{62} +(1.50000 - 2.59808i) q^{63} +1.00000 q^{64} -18.0000 q^{65} +(3.00000 - 5.19615i) q^{66} +(7.50000 + 4.33013i) q^{67} +3.46410i q^{68} +(-3.00000 - 1.73205i) q^{70} +(3.00000 + 5.19615i) q^{71} +(-1.50000 + 2.59808i) q^{72} +(3.50000 + 6.06218i) q^{73} +(4.50000 - 2.59808i) q^{74} +12.1244i q^{75} +(0.500000 - 4.33013i) q^{76} +3.46410i q^{77} +(-4.50000 - 7.79423i) q^{78} +(4.50000 - 2.59808i) q^{79} +(3.00000 + 1.73205i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-6.00000 + 10.3923i) q^{82} -10.3923i q^{83} -1.73205i q^{84} +(-6.00000 + 10.3923i) q^{85} +(-0.500000 + 0.866025i) q^{86} +10.3923i q^{87} -3.46410i q^{88} +(-9.00000 + 5.19615i) q^{90} +(4.50000 + 2.59808i) q^{91} +(-1.50000 - 2.59808i) q^{93} -6.92820i q^{94} +(9.00000 - 12.1244i) q^{95} +1.73205i q^{96} +(6.00000 - 3.46410i) q^{97} +(-3.00000 - 5.19615i) q^{98} +(9.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - 3q^{3} - q^{4} - 6q^{5} - 3q^{6} + 2q^{7} - 2q^{8} + 3q^{9} + O(q^{10}) \) \( 2q + q^{2} - 3q^{3} - q^{4} - 6q^{5} - 3q^{6} + 2q^{7} - 2q^{8} + 3q^{9} - 6q^{10} + 9q^{13} + q^{14} + 6q^{15} - q^{16} + 6q^{17} + 6q^{18} - 8q^{19} - 3q^{21} - 6q^{22} + 3q^{24} + 7q^{25} - q^{28} + 6q^{29} + 12q^{30} + q^{32} - 6q^{33} + 6q^{34} - 6q^{35} + 3q^{36} - 7q^{38} - 18q^{39} + 6q^{40} + 12q^{41} - 3q^{42} + q^{43} - 6q^{44} - 12q^{47} + 3q^{48} - 12q^{49} + 14q^{50} - 6q^{51} - 9q^{52} + 12q^{53} - 9q^{54} - 12q^{55} - 2q^{56} + 9q^{57} + 12q^{58} + 6q^{60} - 7q^{61} - 3q^{62} + 3q^{63} + 2q^{64} - 36q^{65} + 6q^{66} + 15q^{67} - 6q^{70} + 6q^{71} - 3q^{72} + 7q^{73} + 9q^{74} + q^{76} - 9q^{78} + 9q^{79} + 6q^{80} - 9q^{81} - 12q^{82} - 12q^{85} - q^{86} - 18q^{90} + 9q^{91} - 3q^{93} + 18q^{95} + 12q^{97} - 6q^{98} + 18q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/114\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(97\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −1.50000 + 0.866025i −0.866025 + 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −3.00000 + 1.73205i −1.34164 + 0.774597i −0.987048 0.160424i \(-0.948714\pi\)
−0.354593 + 0.935021i \(0.615380\pi\)
\(6\) −1.50000 0.866025i −0.612372 0.353553i
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) −3.00000 1.73205i −0.948683 0.547723i
\(11\) 3.46410i 1.04447i 0.852803 + 0.522233i \(0.174901\pi\)
−0.852803 + 0.522233i \(0.825099\pi\)
\(12\) 1.73205i 0.500000i
\(13\) 4.50000 + 2.59808i 1.24808 + 0.720577i 0.970725 0.240192i \(-0.0772105\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0.500000 + 0.866025i 0.133631 + 0.231455i
\(15\) 3.00000 5.19615i 0.774597 1.34164i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.00000 1.73205i 0.727607 0.420084i −0.0899392 0.995947i \(-0.528667\pi\)
0.817546 + 0.575863i \(0.195334\pi\)
\(18\) 3.00000 0.707107
\(19\) −4.00000 + 1.73205i −0.917663 + 0.397360i
\(20\) 3.46410i 0.774597i
\(21\) −1.50000 + 0.866025i −0.327327 + 0.188982i
\(22\) −3.00000 + 1.73205i −0.639602 + 0.369274i
\(23\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) 1.50000 0.866025i 0.306186 0.176777i
\(25\) 3.50000 6.06218i 0.700000 1.21244i
\(26\) 5.19615i 1.01905i
\(27\) 5.19615i 1.00000i
\(28\) −0.500000 + 0.866025i −0.0944911 + 0.163663i
\(29\) 3.00000 5.19615i 0.557086 0.964901i −0.440652 0.897678i \(-0.645253\pi\)
0.997738 0.0672232i \(-0.0214140\pi\)
\(30\) 6.00000 1.09545
\(31\) 1.73205i 0.311086i 0.987829 + 0.155543i \(0.0497126\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −3.00000 5.19615i −0.522233 0.904534i
\(34\) 3.00000 + 1.73205i 0.514496 + 0.297044i
\(35\) −3.00000 + 1.73205i −0.507093 + 0.292770i
\(36\) 1.50000 + 2.59808i 0.250000 + 0.433013i
\(37\) 5.19615i 0.854242i −0.904194 0.427121i \(-0.859528\pi\)
0.904194 0.427121i \(-0.140472\pi\)
\(38\) −3.50000 2.59808i −0.567775 0.421464i
\(39\) −9.00000 −1.44115
\(40\) 3.00000 1.73205i 0.474342 0.273861i
\(41\) 6.00000 + 10.3923i 0.937043 + 1.62301i 0.770950 + 0.636895i \(0.219782\pi\)
0.166092 + 0.986110i \(0.446885\pi\)
\(42\) −1.50000 0.866025i −0.231455 0.133631i
\(43\) 0.500000 + 0.866025i 0.0762493 + 0.132068i 0.901629 0.432511i \(-0.142372\pi\)
−0.825380 + 0.564578i \(0.809039\pi\)
\(44\) −3.00000 1.73205i −0.452267 0.261116i
\(45\) 10.3923i 1.54919i
\(46\) 0 0
\(47\) −6.00000 3.46410i −0.875190 0.505291i −0.00612051 0.999981i \(-0.501948\pi\)
−0.869069 + 0.494690i \(0.835282\pi\)
\(48\) 1.50000 + 0.866025i 0.216506 + 0.125000i
\(49\) −6.00000 −0.857143
\(50\) 7.00000 0.989949
\(51\) −3.00000 + 5.19615i −0.420084 + 0.727607i
\(52\) −4.50000 + 2.59808i −0.624038 + 0.360288i
\(53\) 6.00000 10.3923i 0.824163 1.42749i −0.0783936 0.996922i \(-0.524979\pi\)
0.902557 0.430570i \(-0.141688\pi\)
\(54\) −4.50000 + 2.59808i −0.612372 + 0.353553i
\(55\) −6.00000 10.3923i −0.809040 1.40130i
\(56\) −1.00000 −0.133631
\(57\) 4.50000 6.06218i 0.596040 0.802955i
\(58\) 6.00000 0.787839
\(59\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 3.00000 + 5.19615i 0.387298 + 0.670820i
\(61\) −3.50000 + 6.06218i −0.448129 + 0.776182i −0.998264 0.0588933i \(-0.981243\pi\)
0.550135 + 0.835076i \(0.314576\pi\)
\(62\) −1.50000 + 0.866025i −0.190500 + 0.109985i
\(63\) 1.50000 2.59808i 0.188982 0.327327i
\(64\) 1.00000 0.125000
\(65\) −18.0000 −2.23263
\(66\) 3.00000 5.19615i 0.369274 0.639602i
\(67\) 7.50000 + 4.33013i 0.916271 + 0.529009i 0.882443 0.470418i \(-0.155897\pi\)
0.0338274 + 0.999428i \(0.489230\pi\)
\(68\) 3.46410i 0.420084i
\(69\) 0 0
\(70\) −3.00000 1.73205i −0.358569 0.207020i
\(71\) 3.00000 + 5.19615i 0.356034 + 0.616670i 0.987294 0.158901i \(-0.0507952\pi\)
−0.631260 + 0.775571i \(0.717462\pi\)
\(72\) −1.50000 + 2.59808i −0.176777 + 0.306186i
\(73\) 3.50000 + 6.06218i 0.409644 + 0.709524i 0.994850 0.101361i \(-0.0323196\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 4.50000 2.59808i 0.523114 0.302020i
\(75\) 12.1244i 1.40000i
\(76\) 0.500000 4.33013i 0.0573539 0.496700i
\(77\) 3.46410i 0.394771i
\(78\) −4.50000 7.79423i −0.509525 0.882523i
\(79\) 4.50000 2.59808i 0.506290 0.292306i −0.225018 0.974355i \(-0.572244\pi\)
0.731307 + 0.682048i \(0.238911\pi\)
\(80\) 3.00000 + 1.73205i 0.335410 + 0.193649i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) −6.00000 + 10.3923i −0.662589 + 1.14764i
\(83\) 10.3923i 1.14070i −0.821401 0.570352i \(-0.806807\pi\)
0.821401 0.570352i \(-0.193193\pi\)
\(84\) 1.73205i 0.188982i
\(85\) −6.00000 + 10.3923i −0.650791 + 1.12720i
\(86\) −0.500000 + 0.866025i −0.0539164 + 0.0933859i
\(87\) 10.3923i 1.11417i
\(88\) 3.46410i 0.369274i
\(89\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(90\) −9.00000 + 5.19615i −0.948683 + 0.547723i
\(91\) 4.50000 + 2.59808i 0.471728 + 0.272352i
\(92\) 0 0
\(93\) −1.50000 2.59808i −0.155543 0.269408i
\(94\) 6.92820i 0.714590i
\(95\) 9.00000 12.1244i 0.923381 1.24393i
\(96\) 1.73205i 0.176777i
\(97\) 6.00000 3.46410i 0.609208 0.351726i −0.163448 0.986552i \(-0.552261\pi\)
0.772655 + 0.634826i \(0.218928\pi\)
\(98\) −3.00000 5.19615i −0.303046 0.524891i
\(99\) 9.00000 + 5.19615i 0.904534 + 0.522233i
\(100\) 3.50000 + 6.06218i 0.350000 + 0.606218i
\(101\) −9.00000 5.19615i −0.895533 0.517036i −0.0197851 0.999804i \(-0.506298\pi\)
−0.875748 + 0.482768i \(0.839632\pi\)
\(102\) −6.00000 −0.594089
\(103\) 8.66025i 0.853320i −0.904412 0.426660i \(-0.859690\pi\)
0.904412 0.426660i \(-0.140310\pi\)
\(104\) −4.50000 2.59808i −0.441261 0.254762i
\(105\) 3.00000 5.19615i 0.292770 0.507093i
\(106\) 12.0000 1.16554
\(107\) 18.0000 1.74013 0.870063 0.492941i \(-0.164078\pi\)
0.870063 + 0.492941i \(0.164078\pi\)
\(108\) −4.50000 2.59808i −0.433013 0.250000i
\(109\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(110\) 6.00000 10.3923i 0.572078 0.990867i
\(111\) 4.50000 + 7.79423i 0.427121 + 0.739795i
\(112\) −0.500000 0.866025i −0.0472456 0.0818317i
\(113\) 12.0000 1.12887 0.564433 0.825479i \(-0.309095\pi\)
0.564433 + 0.825479i \(0.309095\pi\)
\(114\) 7.50000 + 0.866025i 0.702439 + 0.0811107i
\(115\) 0 0
\(116\) 3.00000 + 5.19615i 0.278543 + 0.482451i
\(117\) 13.5000 7.79423i 1.24808 0.720577i
\(118\) 0 0
\(119\) 3.00000 1.73205i 0.275010 0.158777i
\(120\) −3.00000 + 5.19615i −0.273861 + 0.474342i
\(121\) −1.00000 −0.0909091
\(122\) −7.00000 −0.633750
\(123\) −18.0000 10.3923i −1.62301 0.937043i
\(124\) −1.50000 0.866025i −0.134704 0.0777714i
\(125\) 6.92820i 0.619677i
\(126\) 3.00000 0.267261
\(127\) −9.00000 5.19615i −0.798621 0.461084i 0.0443678 0.999015i \(-0.485873\pi\)
−0.842989 + 0.537931i \(0.819206\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −1.50000 0.866025i −0.132068 0.0762493i
\(130\) −9.00000 15.5885i −0.789352 1.36720i
\(131\) −3.00000 + 1.73205i −0.262111 + 0.151330i −0.625297 0.780387i \(-0.715022\pi\)
0.363186 + 0.931717i \(0.381689\pi\)
\(132\) 6.00000 0.522233
\(133\) −4.00000 + 1.73205i −0.346844 + 0.150188i
\(134\) 8.66025i 0.748132i
\(135\) −9.00000 15.5885i −0.774597 1.34164i
\(136\) −3.00000 + 1.73205i −0.257248 + 0.148522i
\(137\) 3.00000 + 1.73205i 0.256307 + 0.147979i 0.622649 0.782501i \(-0.286057\pi\)
−0.366342 + 0.930480i \(0.619390\pi\)
\(138\) 0 0
\(139\) 2.50000 4.33013i 0.212047 0.367277i −0.740308 0.672268i \(-0.765320\pi\)
0.952355 + 0.304991i \(0.0986536\pi\)
\(140\) 3.46410i 0.292770i
\(141\) 12.0000 1.01058
\(142\) −3.00000 + 5.19615i −0.251754 + 0.436051i
\(143\) −9.00000 + 15.5885i −0.752618 + 1.30357i
\(144\) −3.00000 −0.250000
\(145\) 20.7846i 1.72607i
\(146\) −3.50000 + 6.06218i −0.289662 + 0.501709i
\(147\) 9.00000 5.19615i 0.742307 0.428571i
\(148\) 4.50000 + 2.59808i 0.369898 + 0.213561i
\(149\) −15.0000 + 8.66025i −1.22885 + 0.709476i −0.966789 0.255576i \(-0.917735\pi\)
−0.262059 + 0.965052i \(0.584401\pi\)
\(150\) −10.5000 + 6.06218i −0.857321 + 0.494975i
\(151\) 3.46410i 0.281905i −0.990016 0.140952i \(-0.954984\pi\)
0.990016 0.140952i \(-0.0450164\pi\)
\(152\) 4.00000 1.73205i 0.324443 0.140488i
\(153\) 10.3923i 0.840168i
\(154\) −3.00000 + 1.73205i −0.241747 + 0.139573i
\(155\) −3.00000 5.19615i −0.240966 0.417365i
\(156\) 4.50000 7.79423i 0.360288 0.624038i
\(157\) −3.50000 6.06218i −0.279330 0.483814i 0.691888 0.722005i \(-0.256779\pi\)
−0.971219 + 0.238190i \(0.923446\pi\)
\(158\) 4.50000 + 2.59808i 0.358001 + 0.206692i
\(159\) 20.7846i 1.64833i
\(160\) 3.46410i 0.273861i
\(161\) 0 0
\(162\) 4.50000 7.79423i 0.353553 0.612372i
\(163\) −11.0000 −0.861586 −0.430793 0.902451i \(-0.641766\pi\)
−0.430793 + 0.902451i \(0.641766\pi\)
\(164\) −12.0000 −0.937043
\(165\) 18.0000 + 10.3923i 1.40130 + 0.809040i
\(166\) 9.00000 5.19615i 0.698535 0.403300i
\(167\) −6.00000 + 10.3923i −0.464294 + 0.804181i −0.999169 0.0407502i \(-0.987025\pi\)
0.534875 + 0.844931i \(0.320359\pi\)
\(168\) 1.50000 0.866025i 0.115728 0.0668153i
\(169\) 7.00000 + 12.1244i 0.538462 + 0.932643i
\(170\) −12.0000 −0.920358
\(171\) −1.50000 + 12.9904i −0.114708 + 0.993399i
\(172\) −1.00000 −0.0762493
\(173\) −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) −9.00000 + 5.19615i −0.682288 + 0.393919i
\(175\) 3.50000 6.06218i 0.264575 0.458258i
\(176\) 3.00000 1.73205i 0.226134 0.130558i
\(177\) 0 0
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) −9.00000 5.19615i −0.670820 0.387298i
\(181\) −6.00000 3.46410i −0.445976 0.257485i 0.260153 0.965567i \(-0.416227\pi\)
−0.706129 + 0.708083i \(0.749560\pi\)
\(182\) 5.19615i 0.385164i
\(183\) 12.1244i 0.896258i
\(184\) 0 0
\(185\) 9.00000 + 15.5885i 0.661693 + 1.14609i
\(186\) 1.50000 2.59808i 0.109985 0.190500i
\(187\) 6.00000 + 10.3923i 0.438763 + 0.759961i
\(188\) 6.00000 3.46410i 0.437595 0.252646i
\(189\) 5.19615i 0.377964i
\(190\) 15.0000 + 1.73205i 1.08821 + 0.125656i
\(191\) 17.3205i 1.25327i 0.779314 + 0.626634i \(0.215568\pi\)
−0.779314 + 0.626634i \(0.784432\pi\)
\(192\) −1.50000 + 0.866025i −0.108253 + 0.0625000i
\(193\) −10.5000 + 6.06218i −0.755807 + 0.436365i −0.827788 0.561041i \(-0.810401\pi\)
0.0719816 + 0.997406i \(0.477068\pi\)
\(194\) 6.00000 + 3.46410i 0.430775 + 0.248708i
\(195\) 27.0000 15.5885i 1.93351 1.11631i
\(196\) 3.00000 5.19615i 0.214286 0.371154i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 10.3923i 0.738549i
\(199\) 12.5000 21.6506i 0.886102 1.53477i 0.0416556 0.999132i \(-0.486737\pi\)
0.844446 0.535641i \(-0.179930\pi\)
\(200\) −3.50000 + 6.06218i −0.247487 + 0.428661i
\(201\) −15.0000 −1.05802
\(202\) 10.3923i 0.731200i
\(203\) 3.00000 5.19615i 0.210559 0.364698i
\(204\) −3.00000 5.19615i −0.210042 0.363803i
\(205\) −36.0000 20.7846i −2.51435 1.45166i
\(206\) 7.50000 4.33013i 0.522550 0.301694i
\(207\) 0 0
\(208\) 5.19615i 0.360288i
\(209\) −6.00000 13.8564i −0.415029 0.958468i
\(210\) 6.00000 0.414039
\(211\) −19.5000 + 11.2583i −1.34244 + 0.775055i −0.987164 0.159708i \(-0.948945\pi\)
−0.355271 + 0.934763i \(0.615611\pi\)
\(212\) 6.00000 + 10.3923i 0.412082 + 0.713746i
\(213\) −9.00000 5.19615i −0.616670 0.356034i
\(214\) 9.00000 + 15.5885i 0.615227 + 1.06561i
\(215\) −3.00000 1.73205i −0.204598 0.118125i
\(216\) 5.19615i 0.353553i
\(217\) 1.73205i 0.117579i
\(218\) 0 0
\(219\) −10.5000 6.06218i −0.709524 0.409644i
\(220\) 12.0000 0.809040
\(221\) 18.0000 1.21081
\(222\) −4.50000 + 7.79423i −0.302020 + 0.523114i
\(223\) 16.5000 9.52628i 1.10492 0.637927i 0.167412 0.985887i \(-0.446459\pi\)
0.937509 + 0.347960i \(0.113126\pi\)
\(224\) 0.500000 0.866025i 0.0334077 0.0578638i
\(225\) −10.5000 18.1865i −0.700000 1.21244i
\(226\) 6.00000 + 10.3923i 0.399114 + 0.691286i
\(227\) −18.0000 −1.19470 −0.597351 0.801980i \(-0.703780\pi\)
−0.597351 + 0.801980i \(0.703780\pi\)
\(228\) 3.00000 + 6.92820i 0.198680 + 0.458831i
\(229\) 13.0000 0.859064 0.429532 0.903052i \(-0.358679\pi\)
0.429532 + 0.903052i \(0.358679\pi\)
\(230\) 0 0
\(231\) −3.00000 5.19615i −0.197386 0.341882i
\(232\) −3.00000 + 5.19615i −0.196960 + 0.341144i
\(233\) −15.0000 + 8.66025i −0.982683 + 0.567352i −0.903079 0.429474i \(-0.858699\pi\)
−0.0796037 + 0.996827i \(0.525365\pi\)
\(234\) 13.5000 + 7.79423i 0.882523 + 0.509525i
\(235\) 24.0000 1.56559
\(236\) 0 0
\(237\) −4.50000 + 7.79423i −0.292306 + 0.506290i
\(238\) 3.00000 + 1.73205i 0.194461 + 0.112272i
\(239\) 24.2487i 1.56852i −0.620433 0.784259i \(-0.713043\pi\)
0.620433 0.784259i \(-0.286957\pi\)
\(240\) −6.00000 −0.387298
\(241\) −1.50000 0.866025i −0.0966235 0.0557856i 0.450910 0.892570i \(-0.351100\pi\)
−0.547533 + 0.836784i \(0.684433\pi\)
\(242\) −0.500000 0.866025i −0.0321412 0.0556702i
\(243\) 13.5000 + 7.79423i 0.866025 + 0.500000i
\(244\) −3.50000 6.06218i −0.224065 0.388091i
\(245\) 18.0000 10.3923i 1.14998 0.663940i
\(246\) 20.7846i 1.32518i
\(247\) −22.5000 2.59808i −1.43164 0.165312i
\(248\) 1.73205i 0.109985i
\(249\) 9.00000 + 15.5885i 0.570352 + 0.987878i
\(250\) −6.00000 + 3.46410i −0.379473 + 0.219089i
\(251\) 6.00000 + 3.46410i 0.378717 + 0.218652i 0.677260 0.735744i \(-0.263167\pi\)
−0.298543 + 0.954396i \(0.596501\pi\)
\(252\) 1.50000 + 2.59808i 0.0944911 + 0.163663i
\(253\) 0 0
\(254\) 10.3923i 0.652071i
\(255\) 20.7846i 1.30158i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(258\) 1.73205i 0.107833i
\(259\) 5.19615i 0.322873i
\(260\) 9.00000 15.5885i 0.558156 0.966755i
\(261\) −9.00000 15.5885i −0.557086 0.964901i
\(262\) −3.00000 1.73205i −0.185341 0.107006i
\(263\) 21.0000 12.1244i 1.29492 0.747620i 0.315394 0.948961i \(-0.397863\pi\)
0.979521 + 0.201341i \(0.0645299\pi\)
\(264\) 3.00000 + 5.19615i 0.184637 + 0.319801i
\(265\) 41.5692i 2.55358i
\(266\) −3.50000 2.59808i −0.214599 0.159298i
\(267\) 0 0
\(268\) −7.50000 + 4.33013i −0.458135 + 0.264505i
\(269\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(270\) 9.00000 15.5885i 0.547723 0.948683i
\(271\) −4.00000 6.92820i −0.242983 0.420858i 0.718580 0.695444i \(-0.244792\pi\)
−0.961563 + 0.274586i \(0.911459\pi\)
\(272\) −3.00000 1.73205i −0.181902 0.105021i
\(273\) −9.00000 −0.544705
\(274\) 3.46410i 0.209274i
\(275\) 21.0000 + 12.1244i 1.26635 + 0.731126i
\(276\) 0 0
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) 5.00000 0.299880
\(279\) 4.50000 + 2.59808i 0.269408 + 0.155543i
\(280\) 3.00000 1.73205i 0.179284 0.103510i
\(281\) 3.00000 5.19615i 0.178965 0.309976i −0.762561 0.646916i \(-0.776058\pi\)
0.941526 + 0.336939i \(0.109392\pi\)
\(282\) 6.00000 + 10.3923i 0.357295 + 0.618853i
\(283\) 14.0000 + 24.2487i 0.832214 + 1.44144i 0.896279 + 0.443491i \(0.146260\pi\)
−0.0640654 + 0.997946i \(0.520407\pi\)
\(284\) −6.00000 −0.356034
\(285\) −3.00000 + 25.9808i −0.177705 + 1.53897i
\(286\) −18.0000 −1.06436
\(287\) 6.00000 + 10.3923i 0.354169 + 0.613438i
\(288\) −1.50000 2.59808i −0.0883883 0.153093i
\(289\) −2.50000 + 4.33013i −0.147059 + 0.254713i
\(290\) −18.0000 + 10.3923i −1.05700 + 0.610257i
\(291\) −6.00000 + 10.3923i −0.351726 + 0.609208i
\(292\) −7.00000 −0.409644
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 9.00000 + 5.19615i 0.524891 + 0.303046i
\(295\) 0 0
\(296\) 5.19615i 0.302020i
\(297\) −18.0000 −1.04447
\(298\) −15.0000 8.66025i −0.868927 0.501675i
\(299\) 0 0
\(300\) −10.5000 6.06218i −0.606218 0.350000i
\(301\) 0.500000 + 0.866025i 0.0288195 + 0.0499169i
\(302\) 3.00000 1.73205i 0.172631 0.0996683i
\(303\) 18.0000 1.03407
\(304\) 3.50000 + 2.59808i 0.200739 + 0.149010i
\(305\) 24.2487i 1.38848i
\(306\) 9.00000 5.19615i 0.514496 0.297044i
\(307\) 27.0000 15.5885i 1.54097 0.889680i 0.542194 0.840254i \(-0.317594\pi\)
0.998778 0.0494267i \(-0.0157394\pi\)
\(308\) −3.00000 1.73205i −0.170941 0.0986928i
\(309\) 7.50000 + 12.9904i 0.426660 + 0.738997i
\(310\) 3.00000 5.19615i 0.170389 0.295122i
\(311\) 13.8564i 0.785725i −0.919597 0.392862i \(-0.871485\pi\)
0.919597 0.392862i \(-0.128515\pi\)
\(312\) 9.00000 0.509525
\(313\) 7.00000 12.1244i 0.395663 0.685309i −0.597522 0.801852i \(-0.703848\pi\)
0.993186 + 0.116543i \(0.0371814\pi\)
\(314\) 3.50000 6.06218i 0.197516 0.342108i
\(315\) 10.3923i 0.585540i
\(316\) 5.19615i 0.292306i
\(317\) −3.00000 + 5.19615i −0.168497 + 0.291845i −0.937892 0.346929i \(-0.887225\pi\)
0.769395 + 0.638774i \(0.220558\pi\)
\(318\) −18.0000 + 10.3923i −1.00939 + 0.582772i
\(319\) 18.0000 + 10.3923i 1.00781 + 0.581857i
\(320\) −3.00000 + 1.73205i −0.167705 + 0.0968246i
\(321\) −27.0000 + 15.5885i −1.50699 + 0.870063i
\(322\) 0 0
\(323\) −9.00000 + 12.1244i −0.500773 + 0.674617i
\(324\) 9.00000 0.500000
\(325\) 31.5000 18.1865i 1.74731 1.00881i
\(326\) −5.50000 9.52628i −0.304617 0.527612i
\(327\) 0 0
\(328\) −6.00000 10.3923i −0.331295 0.573819i
\(329\) −6.00000 3.46410i −0.330791 0.190982i
\(330\) 20.7846i 1.14416i
\(331\) 5.19615i 0.285606i −0.989751 0.142803i \(-0.954388\pi\)
0.989751 0.142803i \(-0.0456116\pi\)
\(332\) 9.00000 + 5.19615i 0.493939 + 0.285176i
\(333\) −13.5000 7.79423i −0.739795 0.427121i
\(334\) −12.0000 −0.656611
\(335\) −30.0000 −1.63908
\(336\) 1.50000 + 0.866025i 0.0818317 + 0.0472456i
\(337\) 1.50000 0.866025i 0.0817102 0.0471754i −0.458588 0.888649i \(-0.651645\pi\)
0.540298 + 0.841473i \(0.318311\pi\)
\(338\) −7.00000 + 12.1244i −0.380750 + 0.659478i
\(339\) −18.0000 + 10.3923i −0.977626 + 0.564433i
\(340\) −6.00000 10.3923i −0.325396 0.563602i
\(341\) −6.00000 −0.324918
\(342\) −12.0000 + 5.19615i −0.648886 + 0.280976i
\(343\) −13.0000 −0.701934
\(344\) −0.500000 0.866025i −0.0269582 0.0466930i
\(345\) 0 0
\(346\) 3.00000 5.19615i 0.161281 0.279347i
\(347\) −21.0000 + 12.1244i −1.12734 + 0.650870i −0.943264 0.332043i \(-0.892262\pi\)
−0.184075 + 0.982912i \(0.558929\pi\)
\(348\) −9.00000 5.19615i −0.482451 0.278543i
\(349\) −7.00000 −0.374701 −0.187351 0.982293i \(-0.559990\pi\)
−0.187351 + 0.982293i \(0.559990\pi\)
\(350\) 7.00000 0.374166
\(351\) −13.5000 + 23.3827i −0.720577 + 1.24808i
\(352\) 3.00000 + 1.73205i 0.159901 + 0.0923186i
\(353\) 10.3923i 0.553127i 0.960996 + 0.276563i \(0.0891955\pi\)
−0.960996 + 0.276563i \(0.910804\pi\)
\(354\) 0 0
\(355\) −18.0000 10.3923i −0.955341 0.551566i
\(356\) 0 0
\(357\) −3.00000 + 5.19615i −0.158777 + 0.275010i
\(358\) −6.00000 10.3923i −0.317110 0.549250i
\(359\) 6.00000 3.46410i 0.316668 0.182828i −0.333238 0.942843i \(-0.608141\pi\)
0.649906 + 0.760014i \(0.274808\pi\)
\(360\) 10.3923i 0.547723i
\(361\) 13.0000 13.8564i 0.684211 0.729285i
\(362\) 6.92820i 0.364138i
\(363\) 1.50000 0.866025i 0.0787296 0.0454545i
\(364\) −4.50000 + 2.59808i −0.235864 + 0.136176i
\(365\) −21.0000 12.1244i −1.09919 0.634618i
\(366\) 10.5000 6.06218i 0.548844 0.316875i
\(367\) −8.50000 + 14.7224i −0.443696 + 0.768505i −0.997960 0.0638362i \(-0.979666\pi\)
0.554264 + 0.832341i \(0.313000\pi\)
\(368\) 0 0
\(369\) 36.0000 1.87409
\(370\) −9.00000 + 15.5885i −0.467888 + 0.810405i
\(371\) 6.00000 10.3923i 0.311504 0.539542i
\(372\) 3.00000 0.155543
\(373\) 6.92820i 0.358729i 0.983783 + 0.179364i \(0.0574041\pi\)
−0.983783 + 0.179364i \(0.942596\pi\)
\(374\) −6.00000 + 10.3923i −0.310253 + 0.537373i
\(375\) −6.00000 10.3923i −0.309839 0.536656i
\(376\) 6.00000 + 3.46410i 0.309426 + 0.178647i
\(377\) 27.0000 15.5885i 1.39057 0.802846i
\(378\) −4.50000 + 2.59808i −0.231455 + 0.133631i
\(379\) 12.1244i 0.622786i −0.950281 0.311393i \(-0.899204\pi\)
0.950281 0.311393i \(-0.100796\pi\)
\(380\) 6.00000 + 13.8564i 0.307794 + 0.710819i
\(381\) 18.0000 0.922168
\(382\) −15.0000 + 8.66025i −0.767467 + 0.443097i
\(383\) −3.00000 5.19615i −0.153293 0.265511i 0.779143 0.626846i \(-0.215654\pi\)
−0.932436 + 0.361335i \(0.882321\pi\)
\(384\) −1.50000 0.866025i −0.0765466 0.0441942i
\(385\) −6.00000 10.3923i −0.305788 0.529641i
\(386\) −10.5000 6.06218i −0.534436 0.308557i
\(387\) 3.00000 0.152499
\(388\) 6.92820i 0.351726i
\(389\) 24.0000 + 13.8564i 1.21685 + 0.702548i 0.964242 0.265022i \(-0.0853791\pi\)
0.252606 + 0.967569i \(0.418712\pi\)
\(390\) 27.0000 + 15.5885i 1.36720 + 0.789352i
\(391\) 0 0
\(392\) 6.00000 0.303046
\(393\) 3.00000 5.19615i 0.151330 0.262111i
\(394\) 0 0
\(395\) −9.00000 + 15.5885i −0.452839 + 0.784340i
\(396\) −9.00000 + 5.19615i −0.452267 + 0.261116i
\(397\) −14.5000 25.1147i −0.727734 1.26047i −0.957839 0.287307i \(-0.907240\pi\)
0.230105 0.973166i \(-0.426093\pi\)
\(398\) 25.0000 1.25314
\(399\) 4.50000 6.06218i 0.225282 0.303488i
\(400\) −7.00000 −0.350000
\(401\) 12.0000 + 20.7846i 0.599251 + 1.03793i 0.992932 + 0.118686i \(0.0378683\pi\)
−0.393680 + 0.919247i \(0.628798\pi\)
\(402\) −7.50000 12.9904i −0.374066 0.647901i
\(403\) −4.50000 + 7.79423i −0.224161 + 0.388258i
\(404\) 9.00000 5.19615i 0.447767 0.258518i
\(405\) 27.0000 + 15.5885i 1.34164 + 0.774597i
\(406\) 6.00000 0.297775
\(407\) 18.0000 0.892227
\(408\) 3.00000 5.19615i 0.148522 0.257248i
\(409\) 30.0000 + 17.3205i 1.48340 + 0.856444i 0.999822 0.0188549i \(-0.00600205\pi\)
0.483582 + 0.875299i \(0.339335\pi\)
\(410\) 41.5692i 2.05296i
\(411\) −6.00000 −0.295958
\(412\) 7.50000 + 4.33013i 0.369498 + 0.213330i
\(413\) 0 0
\(414\) 0 0
\(415\) 18.0000 + 31.1769i 0.883585 + 1.53041i
\(416\) 4.50000 2.59808i 0.220631 0.127381i
\(417\) 8.66025i 0.424094i
\(418\) 9.00000 12.1244i 0.440204 0.593022i
\(419\) 10.3923i 0.507697i −0.967244 0.253849i \(-0.918303\pi\)
0.967244 0.253849i \(-0.0816965\pi\)
\(420\) 3.00000 + 5.19615i 0.146385 + 0.253546i
\(421\) 12.0000 6.92820i 0.584844 0.337660i −0.178212 0.983992i \(-0.557031\pi\)
0.763056 + 0.646332i \(0.223698\pi\)
\(422\) −19.5000 11.2583i −0.949245 0.548047i
\(423\) −18.0000 + 10.3923i −0.875190 + 0.505291i
\(424\) −6.00000 + 10.3923i −0.291386 + 0.504695i
\(425\) 24.2487i 1.17624i
\(426\) 10.3923i 0.503509i
\(427\) −3.50000 + 6.06218i −0.169377 + 0.293369i
\(428\) −9.00000 + 15.5885i −0.435031 + 0.753497i
\(429\) 31.1769i 1.50524i
\(430\) 3.46410i 0.167054i
\(431\) 6.00000 10.3923i 0.289010 0.500580i −0.684564 0.728953i \(-0.740007\pi\)
0.973574 + 0.228373i \(0.0733406\pi\)
\(432\) 4.50000 2.59808i 0.216506 0.125000i
\(433\) −16.5000 9.52628i −0.792939 0.457804i 0.0480569 0.998845i \(-0.484697\pi\)
−0.840996 + 0.541041i \(0.818030\pi\)
\(434\) −1.50000 + 0.866025i −0.0720023 + 0.0415705i
\(435\) −18.0000 31.1769i −0.863034 1.49482i
\(436\) 0 0
\(437\) 0 0
\(438\) 12.1244i 0.579324i
\(439\) −7.50000 + 4.33013i −0.357955 + 0.206666i −0.668184 0.743996i \(-0.732928\pi\)
0.310228 + 0.950662i \(0.399595\pi\)
\(440\) 6.00000 + 10.3923i 0.286039 + 0.495434i
\(441\) −9.00000 + 15.5885i −0.428571 + 0.742307i
\(442\) 9.00000 + 15.5885i 0.428086 + 0.741467i
\(443\) 21.0000 + 12.1244i 0.997740 + 0.576046i 0.907579 0.419882i \(-0.137928\pi\)
0.0901612 + 0.995927i \(0.471262\pi\)
\(444\) −9.00000 −0.427121
\(445\) 0 0
\(446\) 16.5000 + 9.52628i 0.781298 + 0.451082i
\(447\) 15.0000 25.9808i 0.709476 1.22885i
\(448\) 1.00000 0.0472456
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 10.5000 18.1865i 0.494975 0.857321i
\(451\) −36.0000 + 20.7846i −1.69517 + 0.978709i
\(452\) −6.00000 + 10.3923i −0.282216 + 0.488813i
\(453\) 3.00000 + 5.19615i 0.140952 + 0.244137i
\(454\) −9.00000 15.5885i −0.422391 0.731603i
\(455\) −18.0000 −0.843853
\(456\) −4.50000 + 6.06218i −0.210732 + 0.283887i
\(457\) 17.0000 0.795226 0.397613 0.917553i \(-0.369839\pi\)
0.397613 + 0.917553i \(0.369839\pi\)
\(458\) 6.50000 + 11.2583i 0.303725 + 0.526067i
\(459\) 9.00000 + 15.5885i 0.420084 + 0.727607i
\(460\) 0 0
\(461\) −6.00000 + 3.46410i −0.279448 + 0.161339i −0.633173 0.774010i \(-0.718248\pi\)
0.353726 + 0.935349i \(0.384915\pi\)
\(462\) 3.00000 5.19615i 0.139573 0.241747i
\(463\) −19.0000 −0.883005 −0.441502 0.897260i \(-0.645554\pi\)
−0.441502 + 0.897260i \(0.645554\pi\)
\(464\) −6.00000 −0.278543
\(465\) 9.00000 + 5.19615i 0.417365 + 0.240966i
\(466\) −15.0000 8.66025i −0.694862 0.401179i
\(467\) 27.7128i 1.28240i −0.767375 0.641198i \(-0.778438\pi\)
0.767375 0.641198i \(-0.221562\pi\)
\(468\) 15.5885i 0.720577i
\(469\) 7.50000 + 4.33013i 0.346318 + 0.199947i
\(470\) 12.0000 + 20.7846i 0.553519 + 0.958723i
\(471\) 10.5000 + 6.06218i 0.483814 + 0.279330i
\(472\) 0 0
\(473\) −3.00000 + 1.73205i −0.137940 + 0.0796398i
\(474\) −9.00000 −0.413384
\(475\) −3.50000 + 30.3109i −0.160591 + 1.39076i
\(476\) 3.46410i 0.158777i
\(477\) −18.0000 31.1769i −0.824163 1.42749i
\(478\) 21.0000 12.1244i 0.960518 0.554555i
\(479\) −9.00000 5.19615i −0.411220 0.237418i 0.280094 0.959973i \(-0.409635\pi\)
−0.691314 + 0.722554i \(0.742968\pi\)
\(480\) −3.00000 5.19615i −0.136931 0.237171i
\(481\) 13.5000 23.3827i 0.615547 1.06616i
\(482\) 1.73205i 0.0788928i
\(483\) 0 0
\(484\) 0.500000 0.866025i 0.0227273 0.0393648i
\(485\) −12.0000 + 20.7846i −0.544892 + 0.943781i
\(486\) 15.5885i 0.707107i
\(487\) 3.46410i 0.156973i −0.996915 0.0784867i \(-0.974991\pi\)
0.996915 0.0784867i \(-0.0250088\pi\)
\(488\) 3.50000 6.06218i 0.158438 0.274422i
\(489\) 16.5000 9.52628i 0.746156 0.430793i
\(490\) 18.0000 + 10.3923i 0.813157 + 0.469476i
\(491\) 9.00000 5.19615i 0.406164 0.234499i −0.282976 0.959127i \(-0.591322\pi\)
0.689140 + 0.724628i \(0.257988\pi\)
\(492\) 18.0000 10.3923i 0.811503 0.468521i
\(493\) 20.7846i 0.936092i
\(494\) −9.00000 20.7846i −0.404929 0.935144i
\(495\) −36.0000 −1.61808
\(496\) 1.50000 0.866025i 0.0673520 0.0388857i
\(497\) 3.00000 + 5.19615i 0.134568 + 0.233079i
\(498\) −9.00000 + 15.5885i −0.403300 + 0.698535i
\(499\) −15.5000 26.8468i −0.693875 1.20183i −0.970558 0.240866i \(-0.922569\pi\)
0.276683 0.960961i \(-0.410765\pi\)
\(500\) −6.00000 3.46410i −0.268328 0.154919i
\(501\) 20.7846i 0.928588i
\(502\) 6.92820i 0.309221i
\(503\) 27.0000 + 15.5885i 1.20387 + 0.695055i 0.961414 0.275107i \(-0.0887134\pi\)
0.242457 + 0.970162i \(0.422047\pi\)
\(504\) −1.50000 + 2.59808i −0.0668153 + 0.115728i
\(505\) 36.0000 1.60198
\(506\) 0 0
\(507\) −21.0000 12.1244i −0.932643 0.538462i
\(508\) 9.00000 5.19615i 0.399310 0.230542i
\(509\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(510\) 18.0000 10.3923i 0.797053 0.460179i
\(511\) 3.50000 + 6.06218i 0.154831 + 0.268175i
\(512\) −1.00000 −0.0441942
\(513\) −9.00000 20.7846i −0.397360 0.917663i
\(514\) 0 0
\(515\) 15.0000 + 25.9808i 0.660979 + 1.14485i
\(516\) 1.50000 0.866025i 0.0660338 0.0381246i
\(517\) 12.0000 20.7846i 0.527759 0.914106i
\(518\) 4.50000 2.59808i 0.197719 0.114153i
\(519\) 9.00000 + 5.19615i 0.395056 + 0.228086i
\(520\) 18.0000 0.789352
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) 9.00000 15.5885i 0.393919 0.682288i
\(523\) −4.50000 2.59808i −0.196771 0.113606i 0.398377 0.917222i \(-0.369573\pi\)
−0.595149 + 0.803616i \(0.702907\pi\)
\(524\) 3.46410i 0.151330i
\(525\) 12.1244i 0.529150i
\(526\) 21.0000 + 12.1244i 0.915644 + 0.528647i
\(527\) 3.00000 + 5.19615i 0.130682 + 0.226348i
\(528\) −3.00000 + 5.19615i −0.130558 + 0.226134i
\(529\) −11.5000 19.9186i −0.500000 0.866025i
\(530\) −36.0000 + 20.7846i −1.56374 + 0.902826i
\(531\) 0 0
\(532\) 0.500000 4.33013i 0.0216777 0.187735i
\(533\) 62.3538i 2.70084i
\(534\) 0 0
\(535\) −54.0000 + 31.1769i −2.33462 + 1.34790i
\(536\) −7.50000 4.33013i −0.323951 0.187033i
\(537\) 18.0000 10.3923i 0.776757 0.448461i
\(538\) 0 0
\(539\) 20.7846i 0.895257i
\(540\) 18.0000 0.774597
\(541\) 6.50000 11.2583i 0.279457 0.484033i −0.691793 0.722096i \(-0.743179\pi\)
0.971250 + 0.238062i \(0.0765123\pi\)
\(542\) 4.00000 6.92820i 0.171815 0.297592i
\(543\) 12.0000 0.514969
\(544\) 3.46410i 0.148522i
\(545\) 0 0
\(546\) −4.50000 7.79423i −0.192582 0.333562i
\(547\) 22.5000 + 12.9904i 0.962031 + 0.555429i 0.896797 0.442441i \(-0.145888\pi\)
0.0652331 + 0.997870i \(0.479221\pi\)
\(548\) −3.00000 + 1.73205i −0.128154 + 0.0739895i
\(549\) 10.5000 + 18.1865i 0.448129 + 0.776182i
\(550\) 24.2487i 1.03397i
\(551\) −3.00000 + 25.9808i −0.127804 + 1.10682i
\(552\) 0 0
\(553\) 4.50000 2.59808i 0.191359 0.110481i
\(554\) −1.00000 1.73205i −0.0424859 0.0735878i
\(555\) −27.0000 15.5885i −1.14609 0.661693i
\(556\) 2.50000 + 4.33013i 0.106024 + 0.183638i
\(557\) 3.00000 + 1.73205i 0.127114 + 0.0733893i 0.562209 0.826995i \(-0.309952\pi\)
−0.435095 + 0.900385i \(0.643285\pi\)
\(558\) 5.19615i 0.219971i
\(559\) 5.19615i 0.219774i
\(560\) 3.00000 + 1.73205i 0.126773 + 0.0731925i
\(561\) −18.0000 10.3923i −0.759961 0.438763i
\(562\) 6.00000 0.253095
\(563\) −18.0000 −0.758610 −0.379305 0.925272i \(-0.623837\pi\)
−0.379305 + 0.925272i \(0.623837\pi\)
\(564\) −6.00000 + 10.3923i −0.252646 + 0.437595i
\(565\) −36.0000 + 20.7846i −1.51453 + 0.874415i
\(566\) −14.0000 + 24.2487i −0.588464 + 1.01925i
\(567\) −4.50000 7.79423i −0.188982 0.327327i
\(568\) −3.00000 5.19615i −0.125877 0.218026i
\(569\) −24.0000 −1.00613 −0.503066 0.864248i \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) −24.0000 + 10.3923i −1.00525 + 0.435286i
\(571\) 5.00000 0.209243 0.104622 0.994512i \(-0.466637\pi\)
0.104622 + 0.994512i \(0.466637\pi\)
\(572\) −9.00000 15.5885i −0.376309 0.651786i
\(573\) −15.0000 25.9808i −0.626634 1.08536i
\(574\) −6.00000 + 10.3923i −0.250435 + 0.433766i
\(575\) 0 0
\(576\) 1.50000 2.59808i 0.0625000 0.108253i
\(577\) −38.0000 −1.58196 −0.790980 0.611842i \(-0.790429\pi\)
−0.790980 + 0.611842i \(0.790429\pi\)
\(578\) −5.00000 −0.207973
\(579\) 10.5000 18.1865i 0.436365 0.755807i
\(580\) −18.0000 10.3923i −0.747409 0.431517i
\(581\) 10.3923i 0.431145i
\(582\) −12.0000 −0.497416
\(583\) 36.0000 + 20.7846i 1.49097 + 0.860811i
\(584\) −3.50000 6.06218i −0.144831 0.250855i
\(585\) −27.0000 + 46.7654i −1.11631 + 1.93351i
\(586\) 0 0
\(587\) −6.00000 + 3.46410i −0.247647 + 0.142979i −0.618686 0.785638i \(-0.712335\pi\)
0.371040 + 0.928617i \(0.379001\pi\)
\(588\) 10.3923i 0.428571i
\(589\) −3.00000 6.92820i −0.123613 0.285472i
\(590\) 0 0
\(591\) 0 0
\(592\) −4.50000 + 2.59808i −0.184949 + 0.106780i
\(593\) 36.0000 + 20.7846i 1.47834 + 0.853522i 0.999700 0.0244882i \(-0.00779560\pi\)
0.478643 + 0.878010i \(0.341129\pi\)
\(594\) −9.00000 15.5885i −0.369274 0.639602i
\(595\) −6.00000 + 10.3923i −0.245976 + 0.426043i
\(596\) 17.3205i 0.709476i
\(597\) 43.3013i 1.77220i
\(598\) 0 0
\(599\) −15.0000 + 25.9808i −0.612883 + 1.06155i 0.377869 + 0.925859i \(0.376657\pi\)
−0.990752 + 0.135686i \(0.956676\pi\)
\(600\) 12.1244i 0.494975i
\(601\) 1.73205i 0.0706518i −0.999376 0.0353259i \(-0.988753\pi\)
0.999376 0.0353259i \(-0.0112469\pi\)
\(602\) −0.500000 + 0.866025i −0.0203785 + 0.0352966i
\(603\) 22.5000 12.9904i 0.916271 0.529009i
\(604\) 3.00000 + 1.73205i 0.122068 + 0.0704761i
\(605\) 3.00000 1.73205i 0.121967 0.0704179i
\(606\) 9.00000 + 15.5885i 0.365600 + 0.633238i
\(607\) 32.9090i 1.33573i −0.744281 0.667867i \(-0.767208\pi\)
0.744281 0.667867i \(-0.232792\pi\)
\(608\) −0.500000 + 4.33013i −0.0202777 + 0.175610i
\(609\) 10.3923i 0.421117i
\(610\) 21.0000 12.1244i 0.850265 0.490901i
\(611\) −18.0000 31.1769i −0.728202 1.26128i
\(612\) 9.00000 + 5.19615i 0.363803 + 0.210042i
\(613\) 19.0000 + 32.9090i 0.767403 + 1.32918i 0.938967 + 0.344008i \(0.111785\pi\)
−0.171564 + 0.985173i \(0.554882\pi\)
\(614\) 27.0000 + 15.5885i 1.08963 + 0.629099i
\(615\) 72.0000 2.90332
\(616\) 3.46410i 0.139573i
\(617\) −33.0000 19.0526i −1.32853 0.767027i −0.343458 0.939168i \(-0.611598\pi\)
−0.985072 + 0.172141i \(0.944932\pi\)
\(618\) −7.50000 + 12.9904i −0.301694 + 0.522550i
\(619\) −17.0000 −0.683288 −0.341644 0.939829i \(-0.610984\pi\)
−0.341644 + 0.939829i \(0.610984\pi\)
\(620\) 6.00000 0.240966
\(621\) 0 0
\(622\) 12.0000 6.92820i 0.481156 0.277796i
\(623\) 0 0
\(624\) 4.50000 + 7.79423i 0.180144 + 0.312019i
\(625\) 5.50000 + 9.52628i 0.220000 + 0.381051i
\(626\) 14.0000 0.559553
\(627\) 21.0000 + 15.5885i 0.838659 + 0.622543i
\(628\) 7.00000 0.279330
\(629\) −9.00000 15.5885i −0.358854 0.621552i
\(630\) −9.00000 + 5.19615i −0.358569 + 0.207020i
\(631\) −6.50000 + 11.2583i −0.258761 + 0.448187i −0.965910 0.258877i \(-0.916648\pi\)
0.707149 + 0.707064i \(0.249981\pi\)
\(632\) −4.50000 + 2.59808i −0.179000 + 0.103346i
\(633\) 19.5000 33.7750i 0.775055 1.34244i
\(634\) −6.00000 −0.238290
\(635\) 36.0000 1.42862
\(636\) −18.0000 10.3923i −0.713746 0.412082i
\(637\) −27.0000 15.5885i −1.06978 0.617637i
\(638\) 20.7846i 0.822871i
\(639\) 18.0000 0.712069
\(640\) −3.00000 1.73205i −0.118585 0.0684653i
\(641\) −12.0000 20.7846i −0.473972 0.820943i 0.525584 0.850741i \(-0.323847\pi\)
−0.999556 + 0.0297987i \(0.990513\pi\)
\(642\) −27.0000 15.5885i −1.06561 0.615227i
\(643\) −2.50000 4.33013i −0.0985904 0.170764i 0.812511 0.582946i \(-0.198100\pi\)
−0.911101 + 0.412182i \(0.864767\pi\)
\(644\) 0 0
\(645\) 6.00000 0.236250
\(646\) −15.0000 1.73205i −0.590167 0.0681466i
\(647\) 38.1051i 1.49807i −0.662532 0.749033i \(-0.730518\pi\)
0.662532 0.749033i \(-0.269482\pi\)
\(648\) 4.50000 + 7.79423i 0.176777 + 0.306186i
\(649\) 0 0
\(650\) 31.5000 + 18.1865i 1.23553 + 0.713335i
\(651\) −1.50000 2.59808i −0.0587896 0.101827i
\(652\) 5.50000 9.52628i 0.215397 0.373078i
\(653\) 17.3205i 0.677804i 0.940822 + 0.338902i \(0.110055\pi\)
−0.940822 + 0.338902i \(0.889945\pi\)
\(654\) 0 0
\(655\) 6.00000 10.3923i 0.234439 0.406061i
\(656\) 6.00000 10.3923i 0.234261 0.405751i
\(657\) 21.0000 0.819288
\(658\) 6.92820i 0.270089i
\(659\) 3.00000 5.19615i 0.116863 0.202413i −0.801660 0.597781i \(-0.796049\pi\)
0.918523 + 0.395367i \(0.129383\pi\)
\(660\) −18.0000 + 10.3923i −0.700649 + 0.404520i
\(661\) −12.0000 6.92820i −0.466746 0.269476i 0.248131 0.968727i \(-0.420184\pi\)
−0.714877 + 0.699251i \(0.753517\pi\)
\(662\) 4.50000 2.59808i 0.174897 0.100977i
\(663\) −27.0000 + 15.5885i −1.04859 + 0.605406i
\(664\) 10.3923i 0.403300i
\(665\) 9.00000 12.1244i 0.349005 0.470162i
\(666\) 15.5885i 0.604040i
\(667\) 0 0
\(668\) −6.00000 10.3923i −0.232147 0.402090i
\(669\) −16.5000 + 28.5788i −0.637927 + 1.10492i
\(670\) −15.0000 25.9808i −0.579501 1.00372i
\(671\) −21.0000 12.1244i −0.810696 0.468056i
\(672\) 1.73205i 0.0668153i
\(673\) 12.1244i 0.467360i 0.972314 + 0.233680i \(0.0750767\pi\)
−0.972314 + 0.233680i \(0.924923\pi\)
\(674\) 1.50000 + 0.866025i 0.0577778 + 0.0333581i
\(675\) 31.5000 + 18.1865i 1.21244 + 0.700000i
\(676\) −14.0000 −0.538462
\(677\) 36.0000 1.38359 0.691796 0.722093i \(-0.256820\pi\)
0.691796 + 0.722093i \(0.256820\pi\)
\(678\) −18.0000 10.3923i −0.691286 0.399114i
\(679\) 6.00000 3.46410i 0.230259 0.132940i
\(680\) 6.00000 10.3923i 0.230089 0.398527i
\(681\) 27.0000 15.5885i 1.03464 0.597351i
\(682\) −3.00000 5.19615i −0.114876 0.198971i
\(683\) 30.0000 1.14792 0.573959 0.818884i \(-0.305407\pi\)
0.573959 + 0.818884i \(0.305407\pi\)
\(684\) −10.5000 7.79423i −0.401478 0.298020i
\(685\) −12.0000 −0.458496
\(686\) −6.50000 11.2583i −0.248171 0.429845i
\(687\) −19.5000 + 11.2583i −0.743971 + 0.429532i
\(688\) 0.500000 0.866025i 0.0190623 0.0330169i
\(689\) 54.0000 31.1769i 2.05724 1.18775i
\(690\) 0 0
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) 6.00000 0.228086
\(693\) 9.00000 + 5.19615i 0.341882 + 0.197386i
\(694\) −21.0000 12.1244i −0.797149 0.460234i
\(695\) 17.3205i 0.657004i
\(696\) 10.3923i 0.393919i
\(697\) 36.0000 + 20.7846i 1.36360 + 0.787273i
\(698\) −3.50000 6.06218i −0.132477 0.229457i
\(699\) 15.0000 25.9808i 0.567352 0.982683i
\(700\) 3.50000 + 6.06218i 0.132288 + 0.229129i
\(701\) 9.00000 5.19615i 0.339925 0.196256i −0.320314 0.947312i \(-0.603788\pi\)
0.660239 + 0.751056i \(0.270455\pi\)
\(702\) −27.0000 −1.01905
\(703\) 9.00000 + 20.7846i 0.339441 + 0.783906i
\(704\) 3.46410i 0.130558i
\(705\) −36.0000 + 20.7846i −1.35584 + 0.782794i
\(706\) −9.00000 + 5.19615i −0.338719 + 0.195560i
\(707\) −9.00000 5.19615i −0.338480 0.195421i
\(708\) 0 0
\(709\) 6.50000 11.2583i 0.244113 0.422815i −0.717769 0.696281i \(-0.754837\pi\)
0.961882 + 0.273466i \(0.0881700\pi\)
\(710\) 20.7846i 0.780033i
\(711\) 15.5885i 0.584613i
\(712\) 0 0
\(713\) 0 0
\(714\) −6.00000 −0.224544
\(715\) 62.3538i 2.33190i
\(716\) 6.00000 10.3923i 0.224231 0.388379i
\(717\) 21.0000 + 36.3731i 0.784259 + 1.35838i
\(718\) 6.00000 + 3.46410i 0.223918 + 0.129279i
\(719\) −24.0000 + 13.8564i −0.895049 + 0.516757i −0.875591 0.483054i \(-0.839528\pi\)
−0.0194584 + 0.999811i \(0.506194\pi\)
\(720\) 9.00000 5.19615i 0.335410 0.193649i
\(721\) 8.66025i 0.322525i
\(722\) 18.5000 + 4.33013i 0.688499 + 0.161151i
\(723\) 3.00000 0.111571
\(724\) 6.00000 3.46410i 0.222988 0.128742i
\(725\) −21.0000 36.3731i −0.779920 1.35086i
\(726\) 1.50000 + 0.866025i 0.0556702 + 0.0321412i
\(727\) 18.5000 + 32.0429i 0.686127 + 1.18841i 0.973081 + 0.230463i \(0.0740239\pi\)
−0.286954 + 0.957944i \(0.592643\pi\)
\(728\) −4.50000 2.59808i −0.166781 0.0962911i
\(729\) −27.0000 −1.00000
\(730\) 24.2487i 0.897485i
\(731\) 3.00000 + 1.73205i 0.110959 + 0.0640622i
\(732\) 10.5000 + 6.06218i 0.388091 + 0.224065i
\(733\) −22.0000 −0.812589 −0.406294 0.913742i \(-0.633179\pi\)
−0.406294 + 0.913742i \(0.633179\pi\)
\(734\) −17.0000 −0.627481
\(735\) −18.0000 + 31.1769i −0.663940 + 1.14998i
\(736\) 0 0
\(737\) −15.0000 + 25.9808i −0.552532 + 0.957014i
\(738\) 18.0000 + 31.1769i 0.662589 + 1.14764i
\(739\) −12.5000 21.6506i −0.459820 0.796431i 0.539131 0.842222i \(-0.318753\pi\)
−0.998951 + 0.0457903i \(0.985419\pi\)
\(740\) −18.0000 −0.661693
\(741\) 36.0000 15.5885i 1.32249 0.572656i
\(742\) 12.0000 0.440534
\(743\) 3.00000 + 5.19615i 0.110059 + 0.190628i 0.915794 0.401648i \(-0.131563\pi\)
−0.805735 + 0.592277i \(0.798229\pi\)
\(744\) 1.50000 + 2.59808i 0.0549927 + 0.0952501i
\(745\) 30.0000 51.9615i 1.09911 1.90372i
\(746\) −6.00000 + 3.46410i −0.219676 + 0.126830i
\(747\) −27.0000 15.5885i −0.987878 0.570352i
\(748\) −12.0000 −0.438763
\(749\) 18.0000 0.657706
\(750\) 6.00000 10.3923i 0.219089 0.379473i
\(751\) 31.5000 + 18.1865i 1.14945 + 0.663636i 0.948753 0.316017i \(-0.102346\pi\)
0.200698 + 0.979653i \(0.435679\pi\)
\(752\) 6.92820i 0.252646i
\(753\) −12.0000 −0.437304
\(754\) 27.0000 + 15.5885i 0.983282 + 0.567698i
\(755\) 6.00000 + 10.3923i 0.218362 + 0.378215i
\(756\) −4.50000 2.59808i −0.163663 0.0944911i
\(757\) −6.50000 11.2583i −0.236247 0.409191i 0.723388 0.690442i \(-0.242584\pi\)
−0.959634 + 0.281251i \(0.909251\pi\)
\(758\) 10.5000 6.06218i 0.381377 0.220188i
\(759\) 0 0
\(760\) −9.00000 + 12.1244i −0.326464 + 0.439797i
\(761\) 27.7128i 1.00459i −0.864697 0.502294i \(-0.832489\pi\)
0.864697 0.502294i \(-0.167511\pi\)
\(762\) 9.00000 + 15.5885i 0.326036 + 0.564710i
\(763\) 0 0
\(764\) −15.0000 8.66025i −0.542681 0.313317i
\(765\) 18.0000 + 31.1769i 0.650791 + 1.12720i
\(766\) 3.00000 5.19615i 0.108394 0.187745i
\(767\) 0 0
\(768\) 1.73205i 0.0625000i
\(769\) −18.5000 + 32.0429i −0.667127 + 1.15550i 0.311577 + 0.950221i \(0.399143\pi\)
−0.978704 + 0.205277i \(0.934190\pi\)
\(770\) 6.00000 10.3923i 0.216225 0.374513i
\(771\) 0 0
\(772\) 12.1244i 0.436365i
\(773\) 12.0000 20.7846i 0.431610 0.747570i −0.565402 0.824815i \(-0.691279\pi\)
0.997012 + 0.0772449i \(0.0246123\pi\)
\(774\) 1.50000 + 2.59808i 0.0539164 + 0.0933859i
\(775\) 10.5000 + 6.06218i 0.377171 + 0.217760i
\(776\) −6.00000 + 3.46410i −0.215387 + 0.124354i
\(777\) 4.50000 + 7.79423i