Properties

Label 78.2.i.b.43.2
Level $78$
Weight $2$
Character 78.43
Analytic conductor $0.623$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 78 = 2 \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 78.i (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.622833135766\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
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 43.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 78.43
Dual form 78.2.i.b.49.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.73205i q^{5} +(0.866025 - 0.500000i) q^{6} +(-4.09808 + 2.36603i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.73205i q^{5} +(0.866025 - 0.500000i) q^{6} +(-4.09808 + 2.36603i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.866025 - 1.50000i) q^{10} +(4.09808 + 2.36603i) q^{11} +1.00000 q^{12} +(-3.59808 + 0.232051i) q^{13} -4.73205 q^{14} +(-1.50000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.59808 - 4.50000i) q^{17} -1.00000i q^{18} +(1.09808 - 0.633975i) q^{19} +(1.50000 - 0.866025i) q^{20} +4.73205i q^{21} +(2.36603 + 4.09808i) q^{22} +(1.09808 - 1.90192i) q^{23} +(0.866025 + 0.500000i) q^{24} +2.00000 q^{25} +(-3.23205 - 1.59808i) q^{26} -1.00000 q^{27} +(-4.09808 - 2.36603i) q^{28} +(1.50000 - 2.59808i) q^{29} +(-0.866025 - 1.50000i) q^{30} +2.53590i q^{31} +(-0.866025 + 0.500000i) q^{32} +(4.09808 - 2.36603i) q^{33} -5.19615i q^{34} +(4.09808 + 7.09808i) q^{35} +(0.500000 - 0.866025i) q^{36} +(2.59808 + 1.50000i) q^{37} +1.26795 q^{38} +(-1.59808 + 3.23205i) q^{39} +1.73205 q^{40} +(0.401924 + 0.232051i) q^{41} +(-2.36603 + 4.09808i) q^{42} +(3.09808 + 5.36603i) q^{43} +4.73205i q^{44} +(-1.50000 + 0.866025i) q^{45} +(1.90192 - 1.09808i) q^{46} +1.26795i q^{47} +(0.500000 + 0.866025i) q^{48} +(7.69615 - 13.3301i) q^{49} +(1.73205 + 1.00000i) q^{50} -5.19615 q^{51} +(-2.00000 - 3.00000i) q^{52} +3.00000 q^{53} +(-0.866025 - 0.500000i) q^{54} +(4.09808 - 7.09808i) q^{55} +(-2.36603 - 4.09808i) q^{56} -1.26795i q^{57} +(2.59808 - 1.50000i) q^{58} +(-12.0000 + 6.92820i) q^{59} -1.73205i q^{60} +(-2.40192 - 4.16025i) q^{61} +(-1.26795 + 2.19615i) q^{62} +(4.09808 + 2.36603i) q^{63} -1.00000 q^{64} +(0.401924 + 6.23205i) q^{65} +4.73205 q^{66} +(-9.29423 - 5.36603i) q^{67} +(2.59808 - 4.50000i) q^{68} +(-1.09808 - 1.90192i) q^{69} +8.19615i q^{70} +(7.09808 - 4.09808i) q^{71} +(0.866025 - 0.500000i) q^{72} +12.1244i q^{73} +(1.50000 + 2.59808i) q^{74} +(1.00000 - 1.73205i) q^{75} +(1.09808 + 0.633975i) q^{76} -22.3923 q^{77} +(-3.00000 + 2.00000i) q^{78} -12.3923 q^{79} +(1.50000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.232051 + 0.401924i) q^{82} -11.6603i q^{83} +(-4.09808 + 2.36603i) q^{84} +(-7.79423 + 4.50000i) q^{85} +6.19615i q^{86} +(-1.50000 - 2.59808i) q^{87} +(-2.36603 + 4.09808i) q^{88} +(2.19615 + 1.26795i) q^{89} -1.73205 q^{90} +(14.1962 - 9.46410i) q^{91} +2.19615 q^{92} +(2.19615 + 1.26795i) q^{93} +(-0.633975 + 1.09808i) q^{94} +(-1.09808 - 1.90192i) q^{95} +1.00000i q^{96} +(5.19615 - 3.00000i) q^{97} +(13.3301 - 7.69615i) q^{98} -4.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} + 2 q^{4} - 6 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{3} + 2 q^{4} - 6 q^{7} - 2 q^{9} + 6 q^{11} + 4 q^{12} - 4 q^{13} - 12 q^{14} - 6 q^{15} - 2 q^{16} - 6 q^{19} + 6 q^{20} + 6 q^{22} - 6 q^{23} + 8 q^{25} - 6 q^{26} - 4 q^{27} - 6 q^{28} + 6 q^{29} + 6 q^{33} + 6 q^{35} + 2 q^{36} + 12 q^{38} + 4 q^{39} + 12 q^{41} - 6 q^{42} + 2 q^{43} - 6 q^{45} + 18 q^{46} + 2 q^{48} + 10 q^{49} - 8 q^{52} + 12 q^{53} + 6 q^{55} - 6 q^{56} - 48 q^{59} - 20 q^{61} - 12 q^{62} + 6 q^{63} - 4 q^{64} + 12 q^{65} + 12 q^{66} - 6 q^{67} + 6 q^{69} + 18 q^{71} + 6 q^{74} + 4 q^{75} - 6 q^{76} - 48 q^{77} - 12 q^{78} - 8 q^{79} + 6 q^{80} - 2 q^{81} - 6 q^{82} - 6 q^{84} - 6 q^{87} - 6 q^{88} - 12 q^{89} + 36 q^{91} - 12 q^{92} - 12 q^{93} - 6 q^{94} + 6 q^{95} + 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/78\mathbb{Z}\right)^\times\).

\(n\) \(53\) \(67\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.73205i 0.774597i −0.921954 0.387298i \(-0.873408\pi\)
0.921954 0.387298i \(-0.126592\pi\)
\(6\) 0.866025 0.500000i 0.353553 0.204124i
\(7\) −4.09808 + 2.36603i −1.54893 + 0.894274i −0.550703 + 0.834701i \(0.685640\pi\)
−0.998224 + 0.0595724i \(0.981026\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.866025 1.50000i 0.273861 0.474342i
\(11\) 4.09808 + 2.36603i 1.23562 + 0.713384i 0.968195 0.250196i \(-0.0804951\pi\)
0.267421 + 0.963580i \(0.413828\pi\)
\(12\) 1.00000 0.288675
\(13\) −3.59808 + 0.232051i −0.997927 + 0.0643593i
\(14\) −4.73205 −1.26469
\(15\) −1.50000 0.866025i −0.387298 0.223607i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.59808 4.50000i −0.630126 1.09141i −0.987526 0.157459i \(-0.949670\pi\)
0.357400 0.933952i \(-0.383663\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 1.09808 0.633975i 0.251916 0.145444i −0.368725 0.929538i \(-0.620206\pi\)
0.620641 + 0.784095i \(0.286872\pi\)
\(20\) 1.50000 0.866025i 0.335410 0.193649i
\(21\) 4.73205i 1.03262i
\(22\) 2.36603 + 4.09808i 0.504438 + 0.873713i
\(23\) 1.09808 1.90192i 0.228965 0.396579i −0.728537 0.685007i \(-0.759799\pi\)
0.957502 + 0.288428i \(0.0931326\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) 2.00000 0.400000
\(26\) −3.23205 1.59808i −0.633857 0.313409i
\(27\) −1.00000 −0.192450
\(28\) −4.09808 2.36603i −0.774464 0.447137i
\(29\) 1.50000 2.59808i 0.278543 0.482451i −0.692480 0.721437i \(-0.743482\pi\)
0.971023 + 0.238987i \(0.0768152\pi\)
\(30\) −0.866025 1.50000i −0.158114 0.273861i
\(31\) 2.53590i 0.455461i 0.973724 + 0.227730i \(0.0731305\pi\)
−0.973724 + 0.227730i \(0.926870\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 4.09808 2.36603i 0.713384 0.411872i
\(34\) 5.19615i 0.891133i
\(35\) 4.09808 + 7.09808i 0.692701 + 1.19979i
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) 2.59808 + 1.50000i 0.427121 + 0.246598i 0.698119 0.715981i \(-0.254020\pi\)
−0.270998 + 0.962580i \(0.587354\pi\)
\(38\) 1.26795 0.205689
\(39\) −1.59808 + 3.23205i −0.255897 + 0.517542i
\(40\) 1.73205 0.273861
\(41\) 0.401924 + 0.232051i 0.0627700 + 0.0362402i 0.531057 0.847336i \(-0.321795\pi\)
−0.468287 + 0.883577i \(0.655129\pi\)
\(42\) −2.36603 + 4.09808i −0.365086 + 0.632347i
\(43\) 3.09808 + 5.36603i 0.472452 + 0.818311i 0.999503 0.0315225i \(-0.0100356\pi\)
−0.527051 + 0.849834i \(0.676702\pi\)
\(44\) 4.73205i 0.713384i
\(45\) −1.50000 + 0.866025i −0.223607 + 0.129099i
\(46\) 1.90192 1.09808i 0.280423 0.161903i
\(47\) 1.26795i 0.184949i 0.995715 + 0.0924747i \(0.0294777\pi\)
−0.995715 + 0.0924747i \(0.970522\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) 7.69615 13.3301i 1.09945 1.90430i
\(50\) 1.73205 + 1.00000i 0.244949 + 0.141421i
\(51\) −5.19615 −0.727607
\(52\) −2.00000 3.00000i −0.277350 0.416025i
\(53\) 3.00000 0.412082 0.206041 0.978543i \(-0.433942\pi\)
0.206041 + 0.978543i \(0.433942\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) 4.09808 7.09808i 0.552584 0.957104i
\(56\) −2.36603 4.09808i −0.316173 0.547628i
\(57\) 1.26795i 0.167944i
\(58\) 2.59808 1.50000i 0.341144 0.196960i
\(59\) −12.0000 + 6.92820i −1.56227 + 0.901975i −0.565240 + 0.824927i \(0.691216\pi\)
−0.997027 + 0.0770484i \(0.975450\pi\)
\(60\) 1.73205i 0.223607i
\(61\) −2.40192 4.16025i −0.307535 0.532666i 0.670288 0.742101i \(-0.266171\pi\)
−0.977822 + 0.209435i \(0.932837\pi\)
\(62\) −1.26795 + 2.19615i −0.161030 + 0.278912i
\(63\) 4.09808 + 2.36603i 0.516309 + 0.298091i
\(64\) −1.00000 −0.125000
\(65\) 0.401924 + 6.23205i 0.0498525 + 0.772991i
\(66\) 4.73205 0.582475
\(67\) −9.29423 5.36603i −1.13547 0.655564i −0.190166 0.981752i \(-0.560903\pi\)
−0.945305 + 0.326188i \(0.894236\pi\)
\(68\) 2.59808 4.50000i 0.315063 0.545705i
\(69\) −1.09808 1.90192i −0.132193 0.228965i
\(70\) 8.19615i 0.979628i
\(71\) 7.09808 4.09808i 0.842387 0.486352i −0.0156881 0.999877i \(-0.504994\pi\)
0.858075 + 0.513525i \(0.171661\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) 12.1244i 1.41905i 0.704681 + 0.709524i \(0.251090\pi\)
−0.704681 + 0.709524i \(0.748910\pi\)
\(74\) 1.50000 + 2.59808i 0.174371 + 0.302020i
\(75\) 1.00000 1.73205i 0.115470 0.200000i
\(76\) 1.09808 + 0.633975i 0.125958 + 0.0727219i
\(77\) −22.3923 −2.55184
\(78\) −3.00000 + 2.00000i −0.339683 + 0.226455i
\(79\) −12.3923 −1.39424 −0.697122 0.716953i \(-0.745536\pi\)
−0.697122 + 0.716953i \(0.745536\pi\)
\(80\) 1.50000 + 0.866025i 0.167705 + 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0.232051 + 0.401924i 0.0256257 + 0.0443851i
\(83\) 11.6603i 1.27988i −0.768425 0.639940i \(-0.778959\pi\)
0.768425 0.639940i \(-0.221041\pi\)
\(84\) −4.09808 + 2.36603i −0.447137 + 0.258155i
\(85\) −7.79423 + 4.50000i −0.845403 + 0.488094i
\(86\) 6.19615i 0.668148i
\(87\) −1.50000 2.59808i −0.160817 0.278543i
\(88\) −2.36603 + 4.09808i −0.252219 + 0.436856i
\(89\) 2.19615 + 1.26795i 0.232792 + 0.134402i 0.611859 0.790967i \(-0.290422\pi\)
−0.379068 + 0.925369i \(0.623755\pi\)
\(90\) −1.73205 −0.182574
\(91\) 14.1962 9.46410i 1.48816 0.992107i
\(92\) 2.19615 0.228965
\(93\) 2.19615 + 1.26795i 0.227730 + 0.131480i
\(94\) −0.633975 + 1.09808i −0.0653895 + 0.113258i
\(95\) −1.09808 1.90192i −0.112660 0.195133i
\(96\) 1.00000i 0.102062i
\(97\) 5.19615 3.00000i 0.527589 0.304604i −0.212445 0.977173i \(-0.568143\pi\)
0.740034 + 0.672569i \(0.234809\pi\)
\(98\) 13.3301 7.69615i 1.34655 0.777429i
\(99\) 4.73205i 0.475589i
\(100\) 1.00000 + 1.73205i 0.100000 + 0.173205i
\(101\) −0.696152 + 1.20577i −0.0692698 + 0.119979i −0.898580 0.438810i \(-0.855400\pi\)
0.829310 + 0.558788i \(0.188734\pi\)
\(102\) −4.50000 2.59808i −0.445566 0.257248i
\(103\) 4.19615 0.413459 0.206730 0.978398i \(-0.433718\pi\)
0.206730 + 0.978398i \(0.433718\pi\)
\(104\) −0.232051 3.59808i −0.0227545 0.352820i
\(105\) 8.19615 0.799863
\(106\) 2.59808 + 1.50000i 0.252347 + 0.145693i
\(107\) −4.09808 + 7.09808i −0.396176 + 0.686197i −0.993251 0.115989i \(-0.962996\pi\)
0.597075 + 0.802186i \(0.296330\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 16.3923i 1.57010i 0.619434 + 0.785049i \(0.287362\pi\)
−0.619434 + 0.785049i \(0.712638\pi\)
\(110\) 7.09808 4.09808i 0.676775 0.390736i
\(111\) 2.59808 1.50000i 0.246598 0.142374i
\(112\) 4.73205i 0.447137i
\(113\) −5.59808 9.69615i −0.526623 0.912137i −0.999519 0.0310191i \(-0.990125\pi\)
0.472896 0.881118i \(-0.343209\pi\)
\(114\) 0.633975 1.09808i 0.0593772 0.102844i
\(115\) −3.29423 1.90192i −0.307188 0.177355i
\(116\) 3.00000 0.278543
\(117\) 2.00000 + 3.00000i 0.184900 + 0.277350i
\(118\) −13.8564 −1.27559
\(119\) 21.2942 + 12.2942i 1.95204 + 1.12701i
\(120\) 0.866025 1.50000i 0.0790569 0.136931i
\(121\) 5.69615 + 9.86603i 0.517832 + 0.896911i
\(122\) 4.80385i 0.434920i
\(123\) 0.401924 0.232051i 0.0362402 0.0209233i
\(124\) −2.19615 + 1.26795i −0.197220 + 0.113865i
\(125\) 12.1244i 1.08444i
\(126\) 2.36603 + 4.09808i 0.210782 + 0.365086i
\(127\) −2.00000 + 3.46410i −0.177471 + 0.307389i −0.941014 0.338368i \(-0.890125\pi\)
0.763542 + 0.645758i \(0.223458\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 6.19615 0.545541
\(130\) −2.76795 + 5.59808i −0.242765 + 0.490984i
\(131\) 16.3923 1.43220 0.716101 0.697997i \(-0.245925\pi\)
0.716101 + 0.697997i \(0.245925\pi\)
\(132\) 4.09808 + 2.36603i 0.356692 + 0.205936i
\(133\) −3.00000 + 5.19615i −0.260133 + 0.450564i
\(134\) −5.36603 9.29423i −0.463554 0.802899i
\(135\) 1.73205i 0.149071i
\(136\) 4.50000 2.59808i 0.385872 0.222783i
\(137\) 7.79423 4.50000i 0.665906 0.384461i −0.128618 0.991694i \(-0.541054\pi\)
0.794524 + 0.607233i \(0.207721\pi\)
\(138\) 2.19615i 0.186949i
\(139\) 2.00000 + 3.46410i 0.169638 + 0.293821i 0.938293 0.345843i \(-0.112407\pi\)
−0.768655 + 0.639664i \(0.779074\pi\)
\(140\) −4.09808 + 7.09808i −0.346351 + 0.599897i
\(141\) 1.09808 + 0.633975i 0.0924747 + 0.0533903i
\(142\) 8.19615 0.687806
\(143\) −15.2942 7.56218i −1.27897 0.632381i
\(144\) 1.00000 0.0833333
\(145\) −4.50000 2.59808i −0.373705 0.215758i
\(146\) −6.06218 + 10.5000i −0.501709 + 0.868986i
\(147\) −7.69615 13.3301i −0.634768 1.09945i
\(148\) 3.00000i 0.246598i
\(149\) −15.6962 + 9.06218i −1.28588 + 0.742403i −0.977916 0.208996i \(-0.932980\pi\)
−0.307962 + 0.951399i \(0.599647\pi\)
\(150\) 1.73205 1.00000i 0.141421 0.0816497i
\(151\) 7.26795i 0.591457i −0.955272 0.295729i \(-0.904438\pi\)
0.955272 0.295729i \(-0.0955624\pi\)
\(152\) 0.633975 + 1.09808i 0.0514221 + 0.0890657i
\(153\) −2.59808 + 4.50000i −0.210042 + 0.363803i
\(154\) −19.3923 11.1962i −1.56268 0.902212i
\(155\) 4.39230 0.352798
\(156\) −3.59808 + 0.232051i −0.288077 + 0.0185789i
\(157\) −3.19615 −0.255081 −0.127540 0.991833i \(-0.540708\pi\)
−0.127540 + 0.991833i \(0.540708\pi\)
\(158\) −10.7321 6.19615i −0.853796 0.492939i
\(159\) 1.50000 2.59808i 0.118958 0.206041i
\(160\) 0.866025 + 1.50000i 0.0684653 + 0.118585i
\(161\) 10.3923i 0.819028i
\(162\) −0.866025 + 0.500000i −0.0680414 + 0.0392837i
\(163\) −8.19615 + 4.73205i −0.641972 + 0.370643i −0.785374 0.619022i \(-0.787529\pi\)
0.143402 + 0.989665i \(0.454196\pi\)
\(164\) 0.464102i 0.0362402i
\(165\) −4.09808 7.09808i −0.319035 0.552584i
\(166\) 5.83013 10.0981i 0.452506 0.783763i
\(167\) −2.19615 1.26795i −0.169943 0.0981169i 0.412616 0.910905i \(-0.364615\pi\)
−0.582559 + 0.812788i \(0.697949\pi\)
\(168\) −4.73205 −0.365086
\(169\) 12.8923 1.66987i 0.991716 0.128452i
\(170\) −9.00000 −0.690268
\(171\) −1.09808 0.633975i −0.0839720 0.0484812i
\(172\) −3.09808 + 5.36603i −0.236226 + 0.409156i
\(173\) 8.19615 + 14.1962i 0.623142 + 1.07931i 0.988897 + 0.148602i \(0.0474774\pi\)
−0.365755 + 0.930711i \(0.619189\pi\)
\(174\) 3.00000i 0.227429i
\(175\) −8.19615 + 4.73205i −0.619571 + 0.357709i
\(176\) −4.09808 + 2.36603i −0.308904 + 0.178346i
\(177\) 13.8564i 1.04151i
\(178\) 1.26795 + 2.19615i 0.0950368 + 0.164609i
\(179\) −4.09808 + 7.09808i −0.306305 + 0.530535i −0.977551 0.210699i \(-0.932426\pi\)
0.671246 + 0.741234i \(0.265759\pi\)
\(180\) −1.50000 0.866025i −0.111803 0.0645497i
\(181\) 11.5885 0.861363 0.430682 0.902504i \(-0.358273\pi\)
0.430682 + 0.902504i \(0.358273\pi\)
\(182\) 17.0263 1.09808i 1.26207 0.0813948i
\(183\) −4.80385 −0.355111
\(184\) 1.90192 + 1.09808i 0.140212 + 0.0809513i
\(185\) 2.59808 4.50000i 0.191014 0.330847i
\(186\) 1.26795 + 2.19615i 0.0929705 + 0.161030i
\(187\) 24.5885i 1.79809i
\(188\) −1.09808 + 0.633975i −0.0800854 + 0.0462373i
\(189\) 4.09808 2.36603i 0.298091 0.172103i
\(190\) 2.19615i 0.159326i
\(191\) −10.3923 18.0000i −0.751961 1.30243i −0.946871 0.321613i \(-0.895775\pi\)
0.194910 0.980821i \(-0.437558\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −11.0885 6.40192i −0.798165 0.460821i 0.0446644 0.999002i \(-0.485778\pi\)
−0.842829 + 0.538181i \(0.819111\pi\)
\(194\) 6.00000 0.430775
\(195\) 5.59808 + 2.76795i 0.400887 + 0.198217i
\(196\) 15.3923 1.09945
\(197\) −6.00000 3.46410i −0.427482 0.246807i 0.270791 0.962638i \(-0.412715\pi\)
−0.698273 + 0.715831i \(0.746048\pi\)
\(198\) 2.36603 4.09808i 0.168146 0.291238i
\(199\) 4.29423 + 7.43782i 0.304410 + 0.527253i 0.977130 0.212644i \(-0.0682074\pi\)
−0.672720 + 0.739897i \(0.734874\pi\)
\(200\) 2.00000i 0.141421i
\(201\) −9.29423 + 5.36603i −0.655564 + 0.378490i
\(202\) −1.20577 + 0.696152i −0.0848378 + 0.0489811i
\(203\) 14.1962i 0.996375i
\(204\) −2.59808 4.50000i −0.181902 0.315063i
\(205\) 0.401924 0.696152i 0.0280716 0.0486214i
\(206\) 3.63397 + 2.09808i 0.253191 + 0.146180i
\(207\) −2.19615 −0.152643
\(208\) 1.59808 3.23205i 0.110807 0.224102i
\(209\) 6.00000 0.415029
\(210\) 7.09808 + 4.09808i 0.489814 + 0.282794i
\(211\) 1.80385 3.12436i 0.124182 0.215090i −0.797231 0.603674i \(-0.793703\pi\)
0.921413 + 0.388585i \(0.127036\pi\)
\(212\) 1.50000 + 2.59808i 0.103020 + 0.178437i
\(213\) 8.19615i 0.561591i
\(214\) −7.09808 + 4.09808i −0.485215 + 0.280139i
\(215\) 9.29423 5.36603i 0.633861 0.365960i
\(216\) 1.00000i 0.0680414i
\(217\) −6.00000 10.3923i −0.407307 0.705476i
\(218\) −8.19615 + 14.1962i −0.555113 + 0.961485i
\(219\) 10.5000 + 6.06218i 0.709524 + 0.409644i
\(220\) 8.19615 0.552584
\(221\) 10.3923 + 15.5885i 0.699062 + 1.04859i
\(222\) 3.00000 0.201347
\(223\) 16.3923 + 9.46410i 1.09771 + 0.633763i 0.935619 0.353013i \(-0.114843\pi\)
0.162091 + 0.986776i \(0.448176\pi\)
\(224\) 2.36603 4.09808i 0.158087 0.273814i
\(225\) −1.00000 1.73205i −0.0666667 0.115470i
\(226\) 11.1962i 0.744757i
\(227\) −8.49038 + 4.90192i −0.563526 + 0.325352i −0.754560 0.656231i \(-0.772149\pi\)
0.191033 + 0.981584i \(0.438816\pi\)
\(228\) 1.09808 0.633975i 0.0727219 0.0419860i
\(229\) 19.8564i 1.31215i −0.754696 0.656074i \(-0.772216\pi\)
0.754696 0.656074i \(-0.227784\pi\)
\(230\) −1.90192 3.29423i −0.125409 0.217215i
\(231\) −11.1962 + 19.3923i −0.736653 + 1.27592i
\(232\) 2.59808 + 1.50000i 0.170572 + 0.0984798i
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 0.232051 + 3.59808i 0.0151696 + 0.235214i
\(235\) 2.19615 0.143261
\(236\) −12.0000 6.92820i −0.781133 0.450988i
\(237\) −6.19615 + 10.7321i −0.402483 + 0.697122i
\(238\) 12.2942 + 21.2942i 0.796916 + 1.38030i
\(239\) 24.5885i 1.59050i −0.606285 0.795248i \(-0.707341\pi\)
0.606285 0.795248i \(-0.292659\pi\)
\(240\) 1.50000 0.866025i 0.0968246 0.0559017i
\(241\) −0.696152 + 0.401924i −0.0448431 + 0.0258902i −0.522254 0.852790i \(-0.674909\pi\)
0.477411 + 0.878680i \(0.341575\pi\)
\(242\) 11.3923i 0.732325i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 2.40192 4.16025i 0.153767 0.266333i
\(245\) −23.0885 13.3301i −1.47507 0.851631i
\(246\) 0.464102 0.0295900
\(247\) −3.80385 + 2.53590i −0.242033 + 0.161355i
\(248\) −2.53590 −0.161030
\(249\) −10.0981 5.83013i −0.639940 0.369469i
\(250\) 6.06218 10.5000i 0.383406 0.664078i
\(251\) −2.19615 3.80385i −0.138620 0.240097i 0.788355 0.615221i \(-0.210933\pi\)
−0.926974 + 0.375124i \(0.877600\pi\)
\(252\) 4.73205i 0.298091i
\(253\) 9.00000 5.19615i 0.565825 0.326679i
\(254\) −3.46410 + 2.00000i −0.217357 + 0.125491i
\(255\) 9.00000i 0.563602i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.40192 11.0885i 0.399341 0.691679i −0.594304 0.804241i \(-0.702572\pi\)
0.993645 + 0.112562i \(0.0359056\pi\)
\(258\) 5.36603 + 3.09808i 0.334074 + 0.192878i
\(259\) −14.1962 −0.882106
\(260\) −5.19615 + 3.46410i −0.322252 + 0.214834i
\(261\) −3.00000 −0.185695
\(262\) 14.1962 + 8.19615i 0.877041 + 0.506360i
\(263\) 1.09808 1.90192i 0.0677103 0.117278i −0.830183 0.557491i \(-0.811764\pi\)
0.897893 + 0.440214i \(0.145097\pi\)
\(264\) 2.36603 + 4.09808i 0.145619 + 0.252219i
\(265\) 5.19615i 0.319197i
\(266\) −5.19615 + 3.00000i −0.318597 + 0.183942i
\(267\) 2.19615 1.26795i 0.134402 0.0775972i
\(268\) 10.7321i 0.655564i
\(269\) 14.1962 + 24.5885i 0.865555 + 1.49918i 0.866495 + 0.499185i \(0.166367\pi\)
−0.000940662 1.00000i \(0.500299\pi\)
\(270\) −0.866025 + 1.50000i −0.0527046 + 0.0912871i
\(271\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(272\) 5.19615 0.315063
\(273\) −1.09808 17.0263i −0.0664586 1.03048i
\(274\) 9.00000 0.543710
\(275\) 8.19615 + 4.73205i 0.494247 + 0.285353i
\(276\) 1.09808 1.90192i 0.0660964 0.114482i
\(277\) 7.59808 + 13.1603i 0.456524 + 0.790723i 0.998774 0.0494940i \(-0.0157609\pi\)
−0.542250 + 0.840217i \(0.682428\pi\)
\(278\) 4.00000i 0.239904i
\(279\) 2.19615 1.26795i 0.131480 0.0759101i
\(280\) −7.09808 + 4.09808i −0.424191 + 0.244907i
\(281\) 24.4641i 1.45941i −0.683764 0.729703i \(-0.739658\pi\)
0.683764 0.729703i \(-0.260342\pi\)
\(282\) 0.633975 + 1.09808i 0.0377526 + 0.0653895i
\(283\) −15.0981 + 26.1506i −0.897487 + 1.55449i −0.0667919 + 0.997767i \(0.521276\pi\)
−0.830696 + 0.556727i \(0.812057\pi\)
\(284\) 7.09808 + 4.09808i 0.421193 + 0.243176i
\(285\) −2.19615 −0.130089
\(286\) −9.46410 14.1962i −0.559624 0.839436i
\(287\) −2.19615 −0.129635
\(288\) 0.866025 + 0.500000i 0.0510310 + 0.0294628i
\(289\) −5.00000 + 8.66025i −0.294118 + 0.509427i
\(290\) −2.59808 4.50000i −0.152564 0.264249i
\(291\) 6.00000i 0.351726i
\(292\) −10.5000 + 6.06218i −0.614466 + 0.354762i
\(293\) 12.6962 7.33013i 0.741717 0.428231i −0.0809762 0.996716i \(-0.525804\pi\)
0.822693 + 0.568485i \(0.192470\pi\)
\(294\) 15.3923i 0.897697i
\(295\) 12.0000 + 20.7846i 0.698667 + 1.21013i
\(296\) −1.50000 + 2.59808i −0.0871857 + 0.151010i
\(297\) −4.09808 2.36603i −0.237795 0.137291i
\(298\) −18.1244 −1.04992
\(299\) −3.50962 + 7.09808i −0.202967 + 0.410492i
\(300\) 2.00000 0.115470
\(301\) −25.3923 14.6603i −1.46359 0.845003i
\(302\) 3.63397 6.29423i 0.209112 0.362192i
\(303\) 0.696152 + 1.20577i 0.0399929 + 0.0692698i
\(304\) 1.26795i 0.0727219i
\(305\) −7.20577 + 4.16025i −0.412601 + 0.238215i
\(306\) −4.50000 + 2.59808i −0.257248 + 0.148522i
\(307\) 10.7321i 0.612510i −0.951949 0.306255i \(-0.900924\pi\)
0.951949 0.306255i \(-0.0990761\pi\)
\(308\) −11.1962 19.3923i −0.637960 1.10498i
\(309\) 2.09808 3.63397i 0.119355 0.206730i
\(310\) 3.80385 + 2.19615i 0.216044 + 0.124733i
\(311\) −2.19615 −0.124532 −0.0622662 0.998060i \(-0.519833\pi\)
−0.0622662 + 0.998060i \(0.519833\pi\)
\(312\) −3.23205 1.59808i −0.182979 0.0904732i
\(313\) −24.3923 −1.37873 −0.689367 0.724412i \(-0.742111\pi\)
−0.689367 + 0.724412i \(0.742111\pi\)
\(314\) −2.76795 1.59808i −0.156204 0.0901847i
\(315\) 4.09808 7.09808i 0.230900 0.399931i
\(316\) −6.19615 10.7321i −0.348561 0.603725i
\(317\) 6.12436i 0.343978i 0.985099 + 0.171989i \(0.0550194\pi\)
−0.985099 + 0.171989i \(0.944981\pi\)
\(318\) 2.59808 1.50000i 0.145693 0.0841158i
\(319\) 12.2942 7.09808i 0.688345 0.397416i
\(320\) 1.73205i 0.0968246i
\(321\) 4.09808 + 7.09808i 0.228732 + 0.396176i
\(322\) −5.19615 + 9.00000i −0.289570 + 0.501550i
\(323\) −5.70577 3.29423i −0.317478 0.183296i
\(324\) −1.00000 −0.0555556
\(325\) −7.19615 + 0.464102i −0.399171 + 0.0257437i
\(326\) −9.46410 −0.524168
\(327\) 14.1962 + 8.19615i 0.785049 + 0.453248i
\(328\) −0.232051 + 0.401924i −0.0128129 + 0.0221925i
\(329\) −3.00000 5.19615i −0.165395 0.286473i
\(330\) 8.19615i 0.451183i
\(331\) 10.3923 6.00000i 0.571213 0.329790i −0.186421 0.982470i \(-0.559689\pi\)
0.757634 + 0.652680i \(0.226355\pi\)
\(332\) 10.0981 5.83013i 0.554204 0.319970i
\(333\) 3.00000i 0.164399i
\(334\) −1.26795 2.19615i −0.0693791 0.120168i
\(335\) −9.29423 + 16.0981i −0.507798 + 0.879532i
\(336\) −4.09808 2.36603i −0.223568 0.129077i
\(337\) 31.0000 1.68868 0.844339 0.535810i \(-0.179994\pi\)
0.844339 + 0.535810i \(0.179994\pi\)
\(338\) 12.0000 + 5.00000i 0.652714 + 0.271964i
\(339\) −11.1962 −0.608092
\(340\) −7.79423 4.50000i −0.422701 0.244047i
\(341\) −6.00000 + 10.3923i −0.324918 + 0.562775i
\(342\) −0.633975 1.09808i −0.0342814 0.0593772i
\(343\) 39.7128i 2.14429i
\(344\) −5.36603 + 3.09808i −0.289317 + 0.167037i
\(345\) −3.29423 + 1.90192i −0.177355 + 0.102396i
\(346\) 16.3923i 0.881256i
\(347\) 6.29423 + 10.9019i 0.337892 + 0.585246i 0.984036 0.177969i \(-0.0569528\pi\)
−0.646144 + 0.763215i \(0.723620\pi\)
\(348\) 1.50000 2.59808i 0.0804084 0.139272i
\(349\) 2.19615 + 1.26795i 0.117557 + 0.0678718i 0.557626 0.830093i \(-0.311712\pi\)
−0.440068 + 0.897964i \(0.645046\pi\)
\(350\) −9.46410 −0.505878
\(351\) 3.59808 0.232051i 0.192051 0.0123860i
\(352\) −4.73205 −0.252219
\(353\) −5.00962 2.89230i −0.266635 0.153942i 0.360722 0.932673i \(-0.382530\pi\)
−0.627358 + 0.778731i \(0.715864\pi\)
\(354\) −6.92820 + 12.0000i −0.368230 + 0.637793i
\(355\) −7.09808 12.2942i −0.376727 0.652510i
\(356\) 2.53590i 0.134402i
\(357\) 21.2942 12.2942i 1.12701 0.650680i
\(358\) −7.09808 + 4.09808i −0.375145 + 0.216590i
\(359\) 22.0526i 1.16389i −0.813228 0.581945i \(-0.802292\pi\)
0.813228 0.581945i \(-0.197708\pi\)
\(360\) −0.866025 1.50000i −0.0456435 0.0790569i
\(361\) −8.69615 + 15.0622i −0.457692 + 0.792746i
\(362\) 10.0359 + 5.79423i 0.527475 + 0.304538i
\(363\) 11.3923 0.597941
\(364\) 15.2942 + 7.56218i 0.801635 + 0.396366i
\(365\) 21.0000 1.09919
\(366\) −4.16025 2.40192i −0.217460 0.125551i
\(367\) 12.0981 20.9545i 0.631514 1.09382i −0.355728 0.934590i \(-0.615767\pi\)
0.987242 0.159225i \(-0.0508997\pi\)
\(368\) 1.09808 + 1.90192i 0.0572412 + 0.0991446i
\(369\) 0.464102i 0.0241602i
\(370\) 4.50000 2.59808i 0.233944 0.135068i
\(371\) −12.2942 + 7.09808i −0.638285 + 0.368514i
\(372\) 2.53590i 0.131480i
\(373\) −11.9904 20.7679i −0.620838 1.07532i −0.989330 0.145693i \(-0.953459\pi\)
0.368492 0.929631i \(-0.379874\pi\)
\(374\) 12.2942 21.2942i 0.635719 1.10110i
\(375\) −10.5000 6.06218i −0.542218 0.313050i
\(376\) −1.26795 −0.0653895
\(377\) −4.79423 + 9.69615i −0.246915 + 0.499377i
\(378\) 4.73205 0.243390
\(379\) 15.8038 + 9.12436i 0.811789 + 0.468687i 0.847577 0.530673i \(-0.178061\pi\)
−0.0357877 + 0.999359i \(0.511394\pi\)
\(380\) 1.09808 1.90192i 0.0563301 0.0975666i
\(381\) 2.00000 + 3.46410i 0.102463 + 0.177471i
\(382\) 20.7846i 1.06343i
\(383\) 9.80385 5.66025i 0.500953 0.289225i −0.228154 0.973625i \(-0.573269\pi\)
0.729107 + 0.684400i \(0.239936\pi\)
\(384\) −0.866025 + 0.500000i −0.0441942 + 0.0255155i
\(385\) 38.7846i 1.97665i
\(386\) −6.40192 11.0885i −0.325849 0.564388i
\(387\) 3.09808 5.36603i 0.157484 0.272770i
\(388\) 5.19615 + 3.00000i 0.263795 + 0.152302i
\(389\) 13.3923 0.679017 0.339508 0.940603i \(-0.389739\pi\)
0.339508 + 0.940603i \(0.389739\pi\)
\(390\) 3.46410 + 5.19615i 0.175412 + 0.263117i
\(391\) −11.4115 −0.577107
\(392\) 13.3301 + 7.69615i 0.673273 + 0.388714i
\(393\) 8.19615 14.1962i 0.413441 0.716101i
\(394\) −3.46410 6.00000i −0.174519 0.302276i
\(395\) 21.4641i 1.07998i
\(396\) 4.09808 2.36603i 0.205936 0.118897i
\(397\) 14.1962 8.19615i 0.712484 0.411353i −0.0994958 0.995038i \(-0.531723\pi\)
0.811980 + 0.583685i \(0.198390\pi\)
\(398\) 8.58846i 0.430500i
\(399\) 3.00000 + 5.19615i 0.150188 + 0.260133i
\(400\) −1.00000 + 1.73205i −0.0500000 + 0.0866025i
\(401\) 18.1865 + 10.5000i 0.908192 + 0.524345i 0.879849 0.475253i \(-0.157644\pi\)
0.0283431 + 0.999598i \(0.490977\pi\)
\(402\) −10.7321 −0.535266
\(403\) −0.588457 9.12436i −0.0293131 0.454517i
\(404\) −1.39230 −0.0692698
\(405\) 1.50000 + 0.866025i 0.0745356 + 0.0430331i
\(406\) −7.09808 + 12.2942i −0.352272 + 0.610152i
\(407\) 7.09808 + 12.2942i 0.351839 + 0.609402i
\(408\) 5.19615i 0.257248i
\(409\) −2.89230 + 1.66987i −0.143015 + 0.0825699i −0.569800 0.821783i \(-0.692979\pi\)
0.426785 + 0.904353i \(0.359646\pi\)
\(410\) 0.696152 0.401924i 0.0343805 0.0198496i
\(411\) 9.00000i 0.443937i
\(412\) 2.09808 + 3.63397i 0.103365 + 0.179033i
\(413\) 32.7846 56.7846i 1.61323 2.79419i
\(414\) −1.90192 1.09808i −0.0934745 0.0539675i
\(415\) −20.1962 −0.991390
\(416\) 3.00000 2.00000i 0.147087 0.0980581i
\(417\) 4.00000 0.195881
\(418\) 5.19615 + 3.00000i 0.254152 + 0.146735i
\(419\) −8.19615 + 14.1962i −0.400408 + 0.693527i −0.993775 0.111405i \(-0.964465\pi\)
0.593367 + 0.804932i \(0.297798\pi\)
\(420\) 4.09808 + 7.09808i 0.199966 + 0.346351i
\(421\) 0.464102i 0.0226189i 0.999936 + 0.0113095i \(0.00359999\pi\)
−0.999936 + 0.0113095i \(0.996400\pi\)
\(422\) 3.12436 1.80385i 0.152091 0.0878099i
\(423\) 1.09808 0.633975i 0.0533903 0.0308249i
\(424\) 3.00000i 0.145693i
\(425\) −5.19615 9.00000i −0.252050 0.436564i
\(426\) 4.09808 7.09808i 0.198552 0.343903i
\(427\) 19.6865 + 11.3660i 0.952698 + 0.550041i
\(428\) −8.19615 −0.396176
\(429\) −14.1962 + 9.46410i −0.685397 + 0.456931i
\(430\) 10.7321 0.517545
\(431\) −24.0788 13.9019i −1.15984 0.669632i −0.208572 0.978007i \(-0.566882\pi\)
−0.951265 + 0.308375i \(0.900215\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −16.8923 29.2583i −0.811792 1.40607i −0.911608 0.411060i \(-0.865159\pi\)
0.0998161 0.995006i \(-0.468175\pi\)
\(434\) 12.0000i 0.576018i
\(435\) −4.50000 + 2.59808i −0.215758 + 0.124568i
\(436\) −14.1962 + 8.19615i −0.679872 + 0.392525i
\(437\) 2.78461i 0.133206i
\(438\) 6.06218 + 10.5000i 0.289662 + 0.501709i
\(439\) 8.29423 14.3660i 0.395862 0.685653i −0.597349 0.801982i \(-0.703779\pi\)
0.993211 + 0.116329i \(0.0371125\pi\)
\(440\) 7.09808 + 4.09808i 0.338388 + 0.195368i
\(441\) −15.3923 −0.732967
\(442\) 1.20577 + 18.6962i 0.0573527 + 0.889285i
\(443\) −4.39230 −0.208685 −0.104342 0.994541i \(-0.533274\pi\)
−0.104342 + 0.994541i \(0.533274\pi\)
\(444\) 2.59808 + 1.50000i 0.123299 + 0.0711868i
\(445\) 2.19615 3.80385i 0.104108 0.180320i
\(446\) 9.46410 + 16.3923i 0.448138 + 0.776198i
\(447\) 18.1244i 0.857253i
\(448\) 4.09808 2.36603i 0.193616 0.111784i
\(449\) −28.9808 + 16.7321i −1.36769 + 0.789634i −0.990632 0.136557i \(-0.956396\pi\)
−0.377054 + 0.926191i \(0.623063\pi\)
\(450\) 2.00000i 0.0942809i
\(451\) 1.09808 + 1.90192i 0.0517064 + 0.0895581i
\(452\) 5.59808 9.69615i 0.263311 0.456069i
\(453\) −6.29423 3.63397i −0.295729 0.170739i
\(454\) −9.80385 −0.460117
\(455\) −16.3923 24.5885i −0.768483 1.15272i
\(456\) 1.26795 0.0593772
\(457\) −17.3038 9.99038i −0.809440 0.467330i 0.0373215 0.999303i \(-0.488117\pi\)
−0.846761 + 0.531973i \(0.821451\pi\)
\(458\) 9.92820 17.1962i 0.463914 0.803523i
\(459\) 2.59808 + 4.50000i 0.121268 + 0.210042i
\(460\) 3.80385i 0.177355i
\(461\) −17.3038 + 9.99038i −0.805921 + 0.465298i −0.845537 0.533917i \(-0.820720\pi\)
0.0396167 + 0.999215i \(0.487386\pi\)
\(462\) −19.3923 + 11.1962i −0.902212 + 0.520892i
\(463\) 26.1962i 1.21744i 0.793386 + 0.608719i \(0.208316\pi\)
−0.793386 + 0.608719i \(0.791684\pi\)
\(464\) 1.50000 + 2.59808i 0.0696358 + 0.120613i
\(465\) 2.19615 3.80385i 0.101844 0.176399i
\(466\) 15.5885 + 9.00000i 0.722121 + 0.416917i
\(467\) −36.5885 −1.69311 −0.846556 0.532300i \(-0.821328\pi\)
−0.846556 + 0.532300i \(0.821328\pi\)
\(468\) −1.59808 + 3.23205i −0.0738711 + 0.149402i
\(469\) 50.7846 2.34502
\(470\) 1.90192 + 1.09808i 0.0877292 + 0.0506505i
\(471\) −1.59808 + 2.76795i −0.0736355 + 0.127540i
\(472\) −6.92820 12.0000i −0.318896 0.552345i
\(473\) 29.3205i 1.34816i
\(474\) −10.7321 + 6.19615i −0.492939 + 0.284599i
\(475\) 2.19615 1.26795i 0.100766 0.0581775i
\(476\) 24.5885i 1.12701i
\(477\) −1.50000 2.59808i −0.0686803 0.118958i
\(478\) 12.2942 21.2942i 0.562325 0.973975i
\(479\) −30.5885 17.6603i −1.39762 0.806918i −0.403479 0.914989i \(-0.632199\pi\)
−0.994143 + 0.108071i \(0.965533\pi\)
\(480\) 1.73205 0.0790569
\(481\) −9.69615 4.79423i −0.442106 0.218598i
\(482\) −0.803848 −0.0366143
\(483\) 9.00000 + 5.19615i 0.409514 + 0.236433i
\(484\) −5.69615 + 9.86603i −0.258916 + 0.448456i
\(485\) −5.19615 9.00000i −0.235945 0.408669i
\(486\) 1.00000i 0.0453609i
\(487\) 7.90192 4.56218i 0.358070 0.206732i −0.310164 0.950683i \(-0.600384\pi\)
0.668234 + 0.743951i \(0.267051\pi\)
\(488\) 4.16025 2.40192i 0.188326 0.108730i
\(489\) 9.46410i 0.427981i
\(490\) −13.3301 23.0885i −0.602194 1.04303i
\(491\) 0.294229 0.509619i 0.0132784 0.0229988i −0.859310 0.511455i \(-0.829107\pi\)
0.872588 + 0.488457i \(0.162440\pi\)
\(492\) 0.401924 + 0.232051i 0.0181201 + 0.0104617i
\(493\) −15.5885 −0.702069
\(494\) −4.56218 + 0.294229i −0.205262 + 0.0132380i
\(495\) −8.19615 −0.368390
\(496\) −2.19615 1.26795i −0.0986102 0.0569326i
\(497\) −19.3923 + 33.5885i −0.869864 + 1.50665i
\(498\) −5.83013 10.0981i −0.261254 0.452506i
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 10.5000 6.06218i 0.469574 0.271109i
\(501\) −2.19615 + 1.26795i −0.0981169 + 0.0566478i
\(502\) 4.39230i 0.196038i
\(503\) 9.29423 + 16.0981i 0.414409 + 0.717778i 0.995366 0.0961565i \(-0.0306549\pi\)
−0.580957 + 0.813934i \(0.697322\pi\)
\(504\) −2.36603 + 4.09808i −0.105391 + 0.182543i
\(505\) 2.08846 + 1.20577i 0.0929351 + 0.0536561i
\(506\) 10.3923 0.461994
\(507\) 5.00000 12.0000i 0.222058 0.532939i
\(508\) −4.00000 −0.177471
\(509\) −8.08846 4.66987i −0.358515 0.206988i 0.309914 0.950764i \(-0.399700\pi\)
−0.668429 + 0.743776i \(0.733033\pi\)
\(510\) −4.50000 + 7.79423i −0.199263 + 0.345134i
\(511\) −28.6865 49.6865i −1.26902 2.19800i
\(512\) 1.00000i 0.0441942i
\(513\) −1.09808 + 0.633975i −0.0484812 + 0.0279907i
\(514\) 11.0885 6.40192i 0.489091 0.282377i
\(515\) 7.26795i 0.320264i
\(516\) 3.09808 + 5.36603i 0.136385 + 0.236226i
\(517\) −3.00000 + 5.19615i −0.131940 + 0.228527i
\(518\) −12.2942 7.09808i −0.540177 0.311872i
\(519\) 16.3923 0.719542
\(520\) −6.23205 + 0.401924i −0.273294 + 0.0176255i
\(521\) −18.8038 −0.823812 −0.411906 0.911226i \(-0.635137\pi\)
−0.411906 + 0.911226i \(0.635137\pi\)
\(522\) −2.59808 1.50000i −0.113715 0.0656532i
\(523\) −0.705771 + 1.22243i −0.0308612 + 0.0534532i −0.881044 0.473035i \(-0.843158\pi\)
0.850182 + 0.526488i \(0.176492\pi\)
\(524\) 8.19615 + 14.1962i 0.358051 + 0.620162i
\(525\) 9.46410i 0.413047i
\(526\) 1.90192 1.09808i 0.0829278 0.0478784i
\(527\) 11.4115 6.58846i 0.497095 0.286998i
\(528\) 4.73205i 0.205936i
\(529\) 9.08846 + 15.7417i 0.395150 + 0.684420i
\(530\) 2.59808 4.50000i 0.112853 0.195468i
\(531\) 12.0000 + 6.92820i 0.520756 + 0.300658i
\(532\) −6.00000 −0.260133
\(533\) −1.50000 0.741670i −0.0649722 0.0321253i
\(534\) 2.53590 0.109739
\(535\) 12.2942 + 7.09808i 0.531526 + 0.306877i
\(536\) 5.36603 9.29423i 0.231777 0.401450i
\(537\) 4.09808 + 7.09808i 0.176845 + 0.306305i
\(538\) 28.3923i 1.22408i
\(539\) 63.0788 36.4186i 2.71700 1.56866i
\(540\) −1.50000 + 0.866025i −0.0645497 + 0.0372678i
\(541\) 16.8564i 0.724714i −0.932039 0.362357i \(-0.881972\pi\)
0.932039 0.362357i \(-0.118028\pi\)
\(542\) 0 0
\(543\) 5.79423 10.0359i 0.248654 0.430682i
\(544\) 4.50000 + 2.59808i 0.192936 + 0.111392i
\(545\) 28.3923 1.21619
\(546\) 7.56218 15.2942i 0.323631 0.654533i
\(547\) −6.19615 −0.264928 −0.132464 0.991188i \(-0.542289\pi\)
−0.132464 + 0.991188i \(0.542289\pi\)
\(548\) 7.79423 + 4.50000i 0.332953 + 0.192230i
\(549\) −2.40192 + 4.16025i −0.102512 + 0.177555i
\(550\) 4.73205 + 8.19615i 0.201775 + 0.349485i
\(551\) 3.80385i 0.162049i
\(552\) 1.90192 1.09808i 0.0809513 0.0467372i
\(553\) 50.7846 29.3205i 2.15958 1.24683i
\(554\) 15.1962i 0.645623i
\(555\) −2.59808 4.50000i −0.110282 0.191014i
\(556\) −2.00000 + 3.46410i −0.0848189 + 0.146911i
\(557\) 19.2846 + 11.1340i 0.817115 + 0.471762i 0.849421 0.527716i \(-0.176952\pi\)
−0.0323055 + 0.999478i \(0.510285\pi\)
\(558\) 2.53590 0.107353
\(559\) −12.3923 18.5885i −0.524139 0.786208i
\(560\) −8.19615 −0.346351
\(561\) −21.2942 12.2942i −0.899043 0.519063i
\(562\) 12.2321 21.1865i 0.515978 0.893700i
\(563\) 4.39230 + 7.60770i 0.185114 + 0.320626i 0.943615 0.331046i \(-0.107401\pi\)
−0.758501 + 0.651672i \(0.774068\pi\)
\(564\) 1.26795i 0.0533903i
\(565\) −16.7942 + 9.69615i −0.706539 + 0.407920i
\(566\) −26.1506 + 15.0981i −1.09919 + 0.634619i
\(567\) 4.73205i 0.198727i
\(568\) 4.09808 + 7.09808i 0.171951 + 0.297829i
\(569\) −16.3923 + 28.3923i −0.687201 + 1.19027i 0.285538 + 0.958367i \(0.407828\pi\)
−0.972740 + 0.231900i \(0.925506\pi\)
\(570\) −1.90192 1.09808i −0.0796628 0.0459934i
\(571\) 13.8038 0.577673 0.288837 0.957378i \(-0.406732\pi\)
0.288837 + 0.957378i \(0.406732\pi\)
\(572\) −1.09808 17.0263i −0.0459129 0.711905i
\(573\) −20.7846 −0.868290
\(574\) −1.90192 1.09808i −0.0793848 0.0458328i
\(575\) 2.19615 3.80385i 0.0915859 0.158631i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 16.2679i 0.677244i −0.940923 0.338622i \(-0.890039\pi\)
0.940923 0.338622i \(-0.109961\pi\)
\(578\) −8.66025 + 5.00000i −0.360219 + 0.207973i
\(579\) −11.0885 + 6.40192i −0.460821 + 0.266055i
\(580\) 5.19615i 0.215758i
\(581\) 27.5885 + 47.7846i 1.14456 + 1.98244i
\(582\) 3.00000 5.19615i 0.124354 0.215387i
\(583\) 12.2942 + 7.09808i 0.509175 + 0.293972i
\(584\) −12.1244 −0.501709
\(585\) 5.19615 3.46410i 0.214834 0.143223i
\(586\) 14.6603 0.605610
\(587\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(588\) 7.69615 13.3301i 0.317384 0.549725i
\(589\) 1.60770 + 2.78461i 0.0662439 + 0.114738i
\(590\) 24.0000i 0.988064i
\(591\) −6.00000 + 3.46410i −0.246807 + 0.142494i
\(592\) −2.59808 + 1.50000i −0.106780 + 0.0616496i
\(593\) 46.8564i 1.92416i 0.272764 + 0.962081i \(0.412062\pi\)
−0.272764 + 0.962081i \(0.587938\pi\)
\(594\) −2.36603 4.09808i −0.0970792 0.168146i
\(595\) 21.2942 36.8827i 0.872978 1.51204i
\(596\) −15.6962 9.06218i −0.642939 0.371201i
\(597\) 8.58846 0.351502
\(598\) −6.58846 + 4.39230i −0.269422 + 0.179615i
\(599\) −4.39230 −0.179465 −0.0897324 0.995966i \(-0.528601\pi\)
−0.0897324 + 0.995966i \(0.528601\pi\)
\(600\) 1.73205 + 1.00000i 0.0707107 + 0.0408248i
\(601\) −10.8923 + 18.8660i −0.444306 + 0.769561i −0.998004 0.0631568i \(-0.979883\pi\)
0.553697 + 0.832718i \(0.313216\pi\)
\(602\) −14.6603 25.3923i −0.597507 1.03491i
\(603\) 10.7321i 0.437043i
\(604\) 6.29423 3.63397i 0.256109 0.147864i
\(605\) 17.0885 9.86603i 0.694745 0.401111i
\(606\) 1.39230i 0.0565585i
\(607\) 24.3923 + 42.2487i 0.990053 + 1.71482i 0.616871 + 0.787064i \(0.288400\pi\)
0.373182 + 0.927758i \(0.378267\pi\)
\(608\) −0.633975 + 1.09808i −0.0257111 + 0.0445329i
\(609\) 12.2942 + 7.09808i 0.498187 + 0.287629i
\(610\) −8.32051 −0.336888
\(611\) −0.294229 4.56218i −0.0119032 0.184566i
\(612\) −5.19615 −0.210042
\(613\) 35.3827 + 20.4282i 1.42909 + 0.825087i 0.997049 0.0767652i \(-0.0244592\pi\)
0.432044 + 0.901853i \(0.357793\pi\)
\(614\) 5.36603 9.29423i 0.216555 0.375085i
\(615\) −0.401924 0.696152i −0.0162071 0.0280716i
\(616\) 22.3923i 0.902212i
\(617\) 9.18653 5.30385i 0.369836 0.213525i −0.303551 0.952815i \(-0.598172\pi\)
0.673387 + 0.739290i \(0.264839\pi\)
\(618\) 3.63397 2.09808i 0.146180 0.0843970i
\(619\) 7.60770i 0.305779i 0.988243 + 0.152890i \(0.0488579\pi\)
−0.988243 + 0.152890i \(0.951142\pi\)
\(620\) 2.19615 + 3.80385i 0.0881996 + 0.152766i
\(621\) −1.09808 + 1.90192i −0.0440643 + 0.0763216i
\(622\) −1.90192 1.09808i −0.0762602 0.0440288i
\(623\) −12.0000 −0.480770
\(624\) −2.00000 3.00000i −0.0800641 0.120096i
\(625\) −11.0000 −0.440000
\(626\) −21.1244 12.1962i −0.844299 0.487456i
\(627\) 3.00000 5.19615i 0.119808 0.207514i
\(628\) −1.59808 2.76795i −0.0637702 0.110453i
\(629\) 15.5885i 0.621552i
\(630\) 7.09808 4.09808i 0.282794 0.163271i
\(631\) −22.3923 + 12.9282i −0.891424 + 0.514664i −0.874408 0.485192i \(-0.838750\pi\)
−0.0170157 + 0.999855i \(0.505417\pi\)
\(632\) 12.3923i 0.492939i
\(633\) −1.80385 3.12436i −0.0716965 0.124182i
\(634\) −3.06218 + 5.30385i −0.121615 + 0.210643i
\(635\) 6.00000 + 3.46410i 0.238103 + 0.137469i
\(636\) 3.00000 0.118958
\(637\) −24.5981 + 49.7487i −0.974611 + 1.97112i
\(638\) 14.1962 0.562031
\(639\) −7.09808 4.09808i −0.280796 0.162117i
\(640\) −0.866025 + 1.50000i −0.0342327 + 0.0592927i
\(641\) −15.4019 26.6769i −0.608339 1.05367i −0.991514 0.129999i \(-0.958503\pi\)
0.383175 0.923676i \(-0.374831\pi\)
\(642\) 8.19615i 0.323476i
\(643\) −24.0000 + 13.8564i −0.946468 + 0.546443i −0.891982 0.452071i \(-0.850685\pi\)
−0.0544858 + 0.998515i \(0.517352\pi\)
\(644\) −9.00000 + 5.19615i −0.354650 + 0.204757i
\(645\) 10.7321i 0.422574i
\(646\) −3.29423 5.70577i −0.129610 0.224491i
\(647\) 6.58846 11.4115i 0.259019 0.448634i −0.706960 0.707253i \(-0.749934\pi\)
0.965979 + 0.258619i \(0.0832674\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) −65.5692 −2.57382
\(650\) −6.46410 3.19615i −0.253543 0.125363i
\(651\) −12.0000 −0.470317
\(652\) −8.19615 4.73205i −0.320986 0.185321i
\(653\) 24.5885 42.5885i 0.962221 1.66662i 0.245317 0.969443i \(-0.421108\pi\)
0.716904 0.697172i \(-0.245559\pi\)
\(654\) 8.19615 + 14.1962i 0.320495 + 0.555113i
\(655\) 28.3923i 1.10938i
\(656\) −0.401924 + 0.232051i −0.0156925 + 0.00906006i
\(657\) 10.5000 6.06218i 0.409644 0.236508i
\(658\) 6.00000i 0.233904i
\(659\) −12.5885 21.8038i −0.490377 0.849357i 0.509562 0.860434i \(-0.329807\pi\)
−0.999939 + 0.0110766i \(0.996474\pi\)
\(660\) 4.09808 7.09808i 0.159517 0.276292i
\(661\) 7.79423 + 4.50000i 0.303160 + 0.175030i 0.643862 0.765142i \(-0.277331\pi\)
−0.340701 + 0.940172i \(0.610665\pi\)
\(662\) 12.0000 0.466393
\(663\) 18.6962 1.20577i 0.726098 0.0468283i
\(664\) 11.6603 0.452506
\(665\) 9.00000 + 5.19615i 0.349005 + 0.201498i
\(666\) 1.50000 2.59808i 0.0581238 0.100673i
\(667\) −3.29423 5.70577i −0.127553 0.220928i
\(668\) 2.53590i 0.0981169i
\(669\) 16.3923 9.46410i 0.633763 0.365903i
\(670\) −16.0981 + 9.29423i −0.621923 + 0.359067i
\(671\) 22.7321i 0.877561i
\(672\) −2.36603 4.09808i −0.0912714 0.158087i
\(673\) 0.500000 0.866025i 0.0192736 0.0333828i −0.856228 0.516599i \(-0.827198\pi\)
0.875501 + 0.483216i \(0.160531\pi\)
\(674\) 26.8468 + 15.5000i 1.03410 + 0.597038i
\(675\) −2.00000 −0.0769800
\(676\) 7.89230 + 10.3301i 0.303550 + 0.397313i
\(677\) 4.39230 0.168810 0.0844050 0.996432i \(-0.473101\pi\)
0.0844050 + 0.996432i \(0.473101\pi\)
\(678\) −9.69615 5.59808i −0.372378 0.214993i
\(679\) −14.1962 + 24.5885i −0.544798 + 0.943618i
\(680\) −4.50000 7.79423i −0.172567 0.298895i
\(681\) 9.80385i 0.375684i
\(682\) −10.3923 + 6.00000i −0.397942 + 0.229752i
\(683\) −24.0000 + 13.8564i −0.918334 + 0.530201i −0.883103 0.469179i \(-0.844550\pi\)
−0.0352311 + 0.999379i \(0.511217\pi\)
\(684\) 1.26795i 0.0484812i
\(685\) −7.79423 13.5000i −0.297802 0.515808i
\(686\) −19.8564 + 34.3923i −0.758121 + 1.31310i
\(687\) −17.1962 9.92820i −0.656074 0.378785i
\(688\) −6.19615 −0.236226
\(689\) −10.7942 + 0.696152i −0.411227 + 0.0265213i
\(690\) −3.80385 −0.144810
\(691\) 16.9019 + 9.75833i 0.642979 + 0.371224i 0.785761 0.618530i \(-0.212271\pi\)
−0.142782 + 0.989754i \(0.545605\pi\)
\(692\) −8.19615 + 14.1962i −0.311571 + 0.539657i
\(693\) 11.1962 + 19.3923i 0.425307 + 0.736653i
\(694\) 12.5885i 0.477851i
\(695\) 6.00000 3.46410i 0.227593 0.131401i
\(696\) 2.59808 1.50000i 0.0984798 0.0568574i
\(697\) 2.41154i 0.0913437i
\(698\) 1.26795 + 2.19615i 0.0479926 + 0.0831256i
\(699\) 9.00000 15.5885i 0.340411 0.589610i
\(700\) −8.19615 4.73205i −0.309785 0.178855i
\(701\) −4.39230 −0.165895 −0.0829475 0.996554i \(-0.526433\pi\)
−0.0829475 + 0.996554i \(0.526433\pi\)
\(702\) 3.23205 + 1.59808i 0.121986 + 0.0603155i
\(703\) 3.80385 0.143465
\(704\) −4.09808 2.36603i −0.154452 0.0891729i
\(705\) 1.09808 1.90192i 0.0413559 0.0716306i
\(706\) −2.89230 5.00962i −0.108853 0.188539i
\(707\) 6.58846i 0.247784i
\(708\) −12.0000 + 6.92820i −0.450988 + 0.260378i
\(709\) −2.81347 + 1.62436i −0.105662 + 0.0610040i −0.551900 0.833910i \(-0.686097\pi\)
0.446238 + 0.894914i \(0.352764\pi\)
\(710\) 14.1962i 0.532772i
\(711\) 6.19615 + 10.7321i 0.232374 + 0.402483i
\(712\) −1.26795 + 2.19615i −0.0475184 + 0.0823043i
\(713\) 4.82309 + 2.78461i 0.180626 + 0.104284i
\(714\) 24.5885 0.920200
\(715\) −13.0981 + 26.4904i −0.489840 + 0.990684i
\(716\) −8.19615 −0.306305
\(717\) −21.2942 12.2942i −0.795248 0.459136i
\(718\) 11.0263 19.0981i 0.411497 0.712734i
\(719\) 26.1962 + 45.3731i 0.976952 + 1.69213i 0.673338 + 0.739335i \(0.264860\pi\)
0.303613 + 0.952795i \(0.401807\pi\)
\(720\) 1.73205i 0.0645497i
\(721\) −17.1962 + 9.92820i −0.640418 + 0.369746i
\(722\) −15.0622 + 8.69615i −0.560556 + 0.323637i
\(723\) 0.803848i 0.0298954i
\(724\) 5.79423 + 10.0359i 0.215341 + 0.372981i
\(725\) 3.00000 5.19615i 0.111417 0.192980i
\(726\) 9.86603 + 5.69615i 0.366163 + 0.211404i
\(727\) 24.1962 0.897386 0.448693 0.893686i \(-0.351890\pi\)
0.448693 + 0.893686i \(0.351890\pi\)
\(728\) 9.46410 + 14.1962i 0.350763 + 0.526144i
\(729\) 1.00000 0.0370370
\(730\) 18.1865 + 10.5000i 0.673114 + 0.388622i
\(731\) 16.0981 27.8827i 0.595409 1.03128i
\(732\) −2.40192 4.16025i −0.0887777 0.153767i
\(733\) 14.3205i 0.528940i −0.964394 0.264470i \(-0.914803\pi\)
0.964394 0.264470i \(-0.0851970\pi\)
\(734\) 20.9545 12.0981i 0.773444 0.446548i
\(735\) −23.0885 + 13.3301i −0.851631 + 0.491689i
\(736\) 2.19615i 0.0809513i
\(737\) −25.3923 43.9808i −0.935338 1.62005i
\(738\) 0.232051 0.401924i 0.00854191 0.0147950i
\(739\) −16.3923 9.46410i −0.603001 0.348143i 0.167220 0.985920i \(-0.446521\pi\)
−0.770221 + 0.637777i \(0.779854\pi\)
\(740\) 5.19615 0.191014
\(741\) 0.294229 + 4.56218i 0.0108088 + 0.167596i
\(742\) −14.1962 −0.521157
\(743\) −3.80385 2.19615i −0.139550 0.0805690i 0.428600 0.903494i \(-0.359007\pi\)
−0.568149 + 0.822925i \(0.692340\pi\)
\(744\) −1.26795 + 2.19615i −0.0464853 + 0.0805149i
\(745\) 15.6962 + 27.1865i 0.575063 + 0.996038i
\(746\) 23.9808i 0.877998i
\(747\) −10.0981 + 5.83013i −0.369469 + 0.213313i
\(748\) 21.2942 12.2942i 0.778594 0.449522i
\(749\) 38.7846i 1.41716i
\(750\) −6.06218 10.5000i −0.221359 0.383406i
\(751\) −12.4904 + 21.6340i −0.455780 + 0.789435i −0.998733 0.0503286i \(-0.983973\pi\)
0.542952 + 0.839764i \(0.317306\pi\)
\(752\) −1.09808 0.633975i −0.0400427 0.0231187i
\(753\) −4.39230 −0.160064
\(754\) −9.00000 + 6.00000i −0.327761 + 0.218507i
\(755\) −12.5885 −0.458141
\(756\) 4.09808 + 2.36603i 0.149046 + 0.0860515i
\(757\) −9.39230 + 16.2679i −0.341369 + 0.591269i −0.984687 0.174330i \(-0.944224\pi\)
0.643318 + 0.765599i \(0.277557\pi\)
\(758\) 9.12436 + 15.8038i 0.331412 + 0.574022i
\(759\) 10.3923i 0.377217i
\(760\) 1.90192 1.09808i 0.0689900 0.0398314i
\(761\) 3.80385 2.19615i 0.137889 0.0796105i −0.429468 0.903082i \(-0.641299\pi\)
0.567358 + 0.823471i \(0.307966\pi\)
\(762\) 4.00000i 0.144905i
\(763\) −38.7846 67.1769i −1.40410 2.43197i
\(764\) 10.3923 18.0000i 0.375980 0.651217i
\(765\) 7.79423 + 4.50000i 0.281801 + 0.162698i
\(766\) 11.3205 0.409027
\(767\) 41.5692 27.7128i 1.50098 1.00065i
\(768\) −1.00000 −0.0360844
\(769\) −29.1962 16.8564i −1.05284 0.607858i −0.129397 0.991593i \(-0.541304\pi\)
−0.923443 + 0.383735i \(0.874638\pi\)
\(770\) −19.3923 + 33.5885i −0.698850 + 1.21044i
\(771\) −6.40192 11.0885i −0.230560 0.399341i
\(772\) 12.8038i 0.460821i
\(773\) −43.9808 + 25.3923i −1.58188 + 0.913298i −0.587293 + 0.809375i \(0.699806\pi\)
−0.994585 + 0.103923i \(0.966860\pi\)
\(774\) 5.36603