Properties

Label 882.2.h.l.67.2
Level $882$
Weight $2$
Character 882.67
Analytic conductor $7.043$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} - 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.2
Root \(1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 882.67
Dual form 882.2.h.l.79.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.72474 - 0.158919i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.44949 q^{5} +(-0.724745 + 1.57313i) q^{6} +1.00000 q^{8} +(2.94949 - 0.548188i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.72474 - 0.158919i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.44949 q^{5} +(-0.724745 + 1.57313i) q^{6} +1.00000 q^{8} +(2.94949 - 0.548188i) q^{9} +(1.72474 - 2.98735i) q^{10} +2.00000 q^{11} +(-1.00000 - 1.41421i) q^{12} +(-2.44949 + 4.24264i) q^{13} +(-5.94949 + 0.548188i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +(-1.00000 + 2.82843i) q^{18} +(3.72474 + 6.45145i) q^{19} +(1.72474 + 2.98735i) q^{20} +(-1.00000 + 1.73205i) q^{22} -1.00000 q^{23} +(1.72474 - 0.158919i) q^{24} +6.89898 q^{25} +(-2.44949 - 4.24264i) q^{26} +(5.00000 - 1.41421i) q^{27} +(-1.44949 - 2.51059i) q^{29} +(2.50000 - 5.42650i) q^{30} +(3.00000 + 5.19615i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.44949 - 0.317837i) q^{33} +(1.00000 + 1.73205i) q^{34} +(-1.94949 - 2.28024i) q^{36} +(3.89898 + 6.75323i) q^{37} -7.44949 q^{38} +(-3.55051 + 7.70674i) q^{39} -3.44949 q^{40} +(-4.89898 + 8.48528i) q^{41} +(1.44949 + 2.51059i) q^{43} +(-1.00000 - 1.73205i) q^{44} +(-10.1742 + 1.89097i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-4.89898 + 8.48528i) q^{47} +(-0.724745 + 1.57313i) q^{48} +(-3.44949 + 5.97469i) q^{50} +(1.44949 - 3.14626i) q^{51} +4.89898 q^{52} +(0.550510 - 0.953512i) q^{53} +(-1.27526 + 5.03723i) q^{54} -6.89898 q^{55} +(7.44949 + 10.5352i) q^{57} +2.89898 q^{58} +(-1.00000 - 1.73205i) q^{59} +(3.44949 + 4.87832i) q^{60} +(5.72474 - 9.91555i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(8.44949 - 14.6349i) q^{65} +(-1.44949 + 3.14626i) q^{66} +(1.55051 + 2.68556i) q^{67} -2.00000 q^{68} +(-1.72474 + 0.158919i) q^{69} +9.89898 q^{71} +(2.94949 - 0.548188i) q^{72} +(1.44949 - 2.51059i) q^{73} -7.79796 q^{74} +(11.8990 - 1.09638i) q^{75} +(3.72474 - 6.45145i) q^{76} +(-4.89898 - 6.92820i) q^{78} +(-3.94949 + 6.84072i) q^{79} +(1.72474 - 2.98735i) q^{80} +(8.39898 - 3.23375i) q^{81} +(-4.89898 - 8.48528i) q^{82} +(1.00000 + 1.73205i) q^{83} +(-3.44949 + 5.97469i) q^{85} -2.89898 q^{86} +(-2.89898 - 4.09978i) q^{87} +2.00000 q^{88} +(-3.55051 - 6.14966i) q^{89} +(3.44949 - 9.75663i) q^{90} +(0.500000 + 0.866025i) q^{92} +(6.00000 + 8.48528i) q^{93} +(-4.89898 - 8.48528i) q^{94} +(-12.8485 - 22.2542i) q^{95} +(-1.00000 - 1.41421i) q^{96} +(-3.44949 - 5.97469i) q^{97} +(5.89898 - 1.09638i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} + 2q^{3} - 2q^{4} - 4q^{5} + 2q^{6} + 4q^{8} + 2q^{9} + O(q^{10}) \) \( 4q - 2q^{2} + 2q^{3} - 2q^{4} - 4q^{5} + 2q^{6} + 4q^{8} + 2q^{9} + 2q^{10} + 8q^{11} - 4q^{12} - 14q^{15} - 2q^{16} + 4q^{17} - 4q^{18} + 10q^{19} + 2q^{20} - 4q^{22} - 4q^{23} + 2q^{24} + 8q^{25} + 20q^{27} + 4q^{29} + 10q^{30} + 12q^{31} - 2q^{32} + 4q^{33} + 4q^{34} + 2q^{36} - 4q^{37} - 20q^{38} - 24q^{39} - 4q^{40} - 4q^{43} - 4q^{44} - 26q^{45} + 2q^{46} + 2q^{48} - 4q^{50} - 4q^{51} + 12q^{53} - 10q^{54} - 8q^{55} + 20q^{57} - 8q^{58} - 4q^{59} + 4q^{60} + 18q^{61} - 24q^{62} + 4q^{64} + 24q^{65} + 4q^{66} + 16q^{67} - 8q^{68} - 2q^{69} + 20q^{71} + 2q^{72} - 4q^{73} + 8q^{74} + 28q^{75} + 10q^{76} - 6q^{79} + 2q^{80} + 14q^{81} + 4q^{83} - 4q^{85} + 8q^{86} + 8q^{87} + 8q^{88} - 24q^{89} + 4q^{90} + 2q^{92} + 24q^{93} - 22q^{95} - 4q^{96} - 4q^{97} + 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 1.72474 0.158919i 0.995782 0.0917517i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −3.44949 −1.54266 −0.771329 0.636436i \(-0.780408\pi\)
−0.771329 + 0.636436i \(0.780408\pi\)
\(6\) −0.724745 + 1.57313i −0.295876 + 0.642229i
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 2.94949 0.548188i 0.983163 0.182729i
\(10\) 1.72474 2.98735i 0.545412 0.944682i
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) −1.00000 1.41421i −0.288675 0.408248i
\(13\) −2.44949 + 4.24264i −0.679366 + 1.17670i 0.295806 + 0.955248i \(0.404412\pi\)
−0.975172 + 0.221449i \(0.928921\pi\)
\(14\) 0 0
\(15\) −5.94949 + 0.548188i −1.53615 + 0.141542i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.00000 1.73205i 0.242536 0.420084i −0.718900 0.695113i \(-0.755354\pi\)
0.961436 + 0.275029i \(0.0886875\pi\)
\(18\) −1.00000 + 2.82843i −0.235702 + 0.666667i
\(19\) 3.72474 + 6.45145i 0.854515 + 1.48006i 0.877094 + 0.480318i \(0.159479\pi\)
−0.0225791 + 0.999745i \(0.507188\pi\)
\(20\) 1.72474 + 2.98735i 0.385665 + 0.667991i
\(21\) 0 0
\(22\) −1.00000 + 1.73205i −0.213201 + 0.369274i
\(23\) −1.00000 −0.208514 −0.104257 0.994550i \(-0.533247\pi\)
−0.104257 + 0.994550i \(0.533247\pi\)
\(24\) 1.72474 0.158919i 0.352062 0.0324391i
\(25\) 6.89898 1.37980
\(26\) −2.44949 4.24264i −0.480384 0.832050i
\(27\) 5.00000 1.41421i 0.962250 0.272166i
\(28\) 0 0
\(29\) −1.44949 2.51059i −0.269163 0.466205i 0.699483 0.714650i \(-0.253414\pi\)
−0.968646 + 0.248445i \(0.920081\pi\)
\(30\) 2.50000 5.42650i 0.456435 0.990739i
\(31\) 3.00000 + 5.19615i 0.538816 + 0.933257i 0.998968 + 0.0454165i \(0.0144615\pi\)
−0.460152 + 0.887840i \(0.652205\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 3.44949 0.317837i 0.600479 0.0553284i
\(34\) 1.00000 + 1.73205i 0.171499 + 0.297044i
\(35\) 0 0
\(36\) −1.94949 2.28024i −0.324915 0.380040i
\(37\) 3.89898 + 6.75323i 0.640988 + 1.11022i 0.985213 + 0.171337i \(0.0548086\pi\)
−0.344224 + 0.938887i \(0.611858\pi\)
\(38\) −7.44949 −1.20847
\(39\) −3.55051 + 7.70674i −0.568537 + 1.23407i
\(40\) −3.44949 −0.545412
\(41\) −4.89898 + 8.48528i −0.765092 + 1.32518i 0.175106 + 0.984550i \(0.443973\pi\)
−0.940198 + 0.340629i \(0.889360\pi\)
\(42\) 0 0
\(43\) 1.44949 + 2.51059i 0.221045 + 0.382861i 0.955126 0.296201i \(-0.0957199\pi\)
−0.734080 + 0.679062i \(0.762387\pi\)
\(44\) −1.00000 1.73205i −0.150756 0.261116i
\(45\) −10.1742 + 1.89097i −1.51669 + 0.281889i
\(46\) 0.500000 0.866025i 0.0737210 0.127688i
\(47\) −4.89898 + 8.48528i −0.714590 + 1.23771i 0.248528 + 0.968625i \(0.420053\pi\)
−0.963118 + 0.269081i \(0.913280\pi\)
\(48\) −0.724745 + 1.57313i −0.104608 + 0.227062i
\(49\) 0 0
\(50\) −3.44949 + 5.97469i −0.487832 + 0.844949i
\(51\) 1.44949 3.14626i 0.202969 0.440565i
\(52\) 4.89898 0.679366
\(53\) 0.550510 0.953512i 0.0756184 0.130975i −0.825737 0.564056i \(-0.809240\pi\)
0.901355 + 0.433081i \(0.142574\pi\)
\(54\) −1.27526 + 5.03723i −0.173540 + 0.685481i
\(55\) −6.89898 −0.930258
\(56\) 0 0
\(57\) 7.44949 + 10.5352i 0.986709 + 1.39542i
\(58\) 2.89898 0.380655
\(59\) −1.00000 1.73205i −0.130189 0.225494i 0.793560 0.608492i \(-0.208225\pi\)
−0.923749 + 0.382998i \(0.874892\pi\)
\(60\) 3.44949 + 4.87832i 0.445327 + 0.629788i
\(61\) 5.72474 9.91555i 0.732978 1.26956i −0.222626 0.974904i \(-0.571463\pi\)
0.955605 0.294652i \(-0.0952037\pi\)
\(62\) −6.00000 −0.762001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 8.44949 14.6349i 1.04803 1.81524i
\(66\) −1.44949 + 3.14626i −0.178420 + 0.387278i
\(67\) 1.55051 + 2.68556i 0.189425 + 0.328094i 0.945059 0.326901i \(-0.106004\pi\)
−0.755634 + 0.654994i \(0.772671\pi\)
\(68\) −2.00000 −0.242536
\(69\) −1.72474 + 0.158919i −0.207635 + 0.0191316i
\(70\) 0 0
\(71\) 9.89898 1.17479 0.587396 0.809299i \(-0.300153\pi\)
0.587396 + 0.809299i \(0.300153\pi\)
\(72\) 2.94949 0.548188i 0.347601 0.0646046i
\(73\) 1.44949 2.51059i 0.169650 0.293842i −0.768647 0.639673i \(-0.779070\pi\)
0.938297 + 0.345831i \(0.112403\pi\)
\(74\) −7.79796 −0.906494
\(75\) 11.8990 1.09638i 1.37398 0.126599i
\(76\) 3.72474 6.45145i 0.427258 0.740032i
\(77\) 0 0
\(78\) −4.89898 6.92820i −0.554700 0.784465i
\(79\) −3.94949 + 6.84072i −0.444352 + 0.769641i −0.998007 0.0631057i \(-0.979899\pi\)
0.553655 + 0.832746i \(0.313233\pi\)
\(80\) 1.72474 2.98735i 0.192832 0.333995i
\(81\) 8.39898 3.23375i 0.933220 0.359306i
\(82\) −4.89898 8.48528i −0.541002 0.937043i
\(83\) 1.00000 + 1.73205i 0.109764 + 0.190117i 0.915675 0.401920i \(-0.131657\pi\)
−0.805910 + 0.592037i \(0.798324\pi\)
\(84\) 0 0
\(85\) −3.44949 + 5.97469i −0.374150 + 0.648046i
\(86\) −2.89898 −0.312605
\(87\) −2.89898 4.09978i −0.310803 0.439542i
\(88\) 2.00000 0.213201
\(89\) −3.55051 6.14966i −0.376353 0.651863i 0.614175 0.789170i \(-0.289489\pi\)
−0.990529 + 0.137307i \(0.956155\pi\)
\(90\) 3.44949 9.75663i 0.363608 1.02844i
\(91\) 0 0
\(92\) 0.500000 + 0.866025i 0.0521286 + 0.0902894i
\(93\) 6.00000 + 8.48528i 0.622171 + 0.879883i
\(94\) −4.89898 8.48528i −0.505291 0.875190i
\(95\) −12.8485 22.2542i −1.31823 2.28323i
\(96\) −1.00000 1.41421i −0.102062 0.144338i
\(97\) −3.44949 5.97469i −0.350243 0.606638i 0.636049 0.771649i \(-0.280568\pi\)
−0.986292 + 0.165011i \(0.947234\pi\)
\(98\) 0 0
\(99\) 5.89898 1.09638i 0.592870 0.110190i
\(100\) −3.44949 5.97469i −0.344949 0.597469i
\(101\) −7.24745 −0.721148 −0.360574 0.932731i \(-0.617419\pi\)
−0.360574 + 0.932731i \(0.617419\pi\)
\(102\) 2.00000 + 2.82843i 0.198030 + 0.280056i
\(103\) −14.0000 −1.37946 −0.689730 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) −2.44949 + 4.24264i −0.240192 + 0.416025i
\(105\) 0 0
\(106\) 0.550510 + 0.953512i 0.0534703 + 0.0926132i
\(107\) 6.00000 + 10.3923i 0.580042 + 1.00466i 0.995474 + 0.0950377i \(0.0302972\pi\)
−0.415432 + 0.909624i \(0.636370\pi\)
\(108\) −3.72474 3.62302i −0.358414 0.348625i
\(109\) 8.34847 14.4600i 0.799638 1.38501i −0.120213 0.992748i \(-0.538358\pi\)
0.919852 0.392266i \(-0.128309\pi\)
\(110\) 3.44949 5.97469i 0.328896 0.569664i
\(111\) 7.79796 + 11.0280i 0.740150 + 1.04673i
\(112\) 0 0
\(113\) 7.94949 13.7689i 0.747825 1.29527i −0.201038 0.979583i \(-0.564431\pi\)
0.948863 0.315688i \(-0.102235\pi\)
\(114\) −12.8485 + 1.18386i −1.20337 + 0.110879i
\(115\) 3.44949 0.321667
\(116\) −1.44949 + 2.51059i −0.134582 + 0.233102i
\(117\) −4.89898 + 13.8564i −0.452911 + 1.28103i
\(118\) 2.00000 0.184115
\(119\) 0 0
\(120\) −5.94949 + 0.548188i −0.543112 + 0.0500425i
\(121\) −7.00000 −0.636364
\(122\) 5.72474 + 9.91555i 0.518294 + 0.897712i
\(123\) −7.10102 + 15.4135i −0.640277 + 1.38979i
\(124\) 3.00000 5.19615i 0.269408 0.466628i
\(125\) −6.55051 −0.585895
\(126\) 0 0
\(127\) −3.00000 −0.266207 −0.133103 0.991102i \(-0.542494\pi\)
−0.133103 + 0.991102i \(0.542494\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 2.89898 + 4.09978i 0.255241 + 0.360965i
\(130\) 8.44949 + 14.6349i 0.741069 + 1.28357i
\(131\) 13.4495 1.17509 0.587544 0.809192i \(-0.300095\pi\)
0.587544 + 0.809192i \(0.300095\pi\)
\(132\) −2.00000 2.82843i −0.174078 0.246183i
\(133\) 0 0
\(134\) −3.10102 −0.267887
\(135\) −17.2474 + 4.87832i −1.48442 + 0.419859i
\(136\) 1.00000 1.73205i 0.0857493 0.148522i
\(137\) −11.7980 −1.00797 −0.503984 0.863713i \(-0.668133\pi\)
−0.503984 + 0.863713i \(0.668133\pi\)
\(138\) 0.724745 1.57313i 0.0616944 0.133914i
\(139\) 4.72474 8.18350i 0.400748 0.694115i −0.593069 0.805152i \(-0.702084\pi\)
0.993816 + 0.111037i \(0.0354171\pi\)
\(140\) 0 0
\(141\) −7.10102 + 15.4135i −0.598014 + 1.29805i
\(142\) −4.94949 + 8.57277i −0.415352 + 0.719411i
\(143\) −4.89898 + 8.48528i −0.409673 + 0.709575i
\(144\) −1.00000 + 2.82843i −0.0833333 + 0.235702i
\(145\) 5.00000 + 8.66025i 0.415227 + 0.719195i
\(146\) 1.44949 + 2.51059i 0.119961 + 0.207778i
\(147\) 0 0
\(148\) 3.89898 6.75323i 0.320494 0.555112i
\(149\) −6.00000 −0.491539 −0.245770 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) −5.00000 + 10.8530i −0.408248 + 0.886144i
\(151\) −5.00000 −0.406894 −0.203447 0.979086i \(-0.565214\pi\)
−0.203447 + 0.979086i \(0.565214\pi\)
\(152\) 3.72474 + 6.45145i 0.302117 + 0.523281i
\(153\) 2.00000 5.65685i 0.161690 0.457330i
\(154\) 0 0
\(155\) −10.3485 17.9241i −0.831209 1.43970i
\(156\) 8.44949 0.778539i 0.676501 0.0623330i
\(157\) 3.17423 + 5.49794i 0.253332 + 0.438783i 0.964441 0.264298i \(-0.0851403\pi\)
−0.711109 + 0.703081i \(0.751807\pi\)
\(158\) −3.94949 6.84072i −0.314205 0.544218i
\(159\) 0.797959 1.73205i 0.0632823 0.137361i
\(160\) 1.72474 + 2.98735i 0.136353 + 0.236170i
\(161\) 0 0
\(162\) −1.39898 + 8.89060i −0.109914 + 0.698512i
\(163\) 0.101021 + 0.174973i 0.00791254 + 0.0137049i 0.869955 0.493132i \(-0.164148\pi\)
−0.862042 + 0.506837i \(0.830815\pi\)
\(164\) 9.79796 0.765092
\(165\) −11.8990 + 1.09638i −0.926334 + 0.0853528i
\(166\) −2.00000 −0.155230
\(167\) 9.34847 16.1920i 0.723406 1.25298i −0.236220 0.971700i \(-0.575909\pi\)
0.959627 0.281277i \(-0.0907579\pi\)
\(168\) 0 0
\(169\) −5.50000 9.52628i −0.423077 0.732791i
\(170\) −3.44949 5.97469i −0.264564 0.458238i
\(171\) 14.5227 + 16.9866i 1.11058 + 1.29900i
\(172\) 1.44949 2.51059i 0.110523 0.191431i
\(173\) −6.44949 + 11.1708i −0.490346 + 0.849304i −0.999938 0.0111123i \(-0.996463\pi\)
0.509593 + 0.860416i \(0.329796\pi\)
\(174\) 5.00000 0.460702i 0.379049 0.0349257i
\(175\) 0 0
\(176\) −1.00000 + 1.73205i −0.0753778 + 0.130558i
\(177\) −2.00000 2.82843i −0.150329 0.212598i
\(178\) 7.10102 0.532244
\(179\) 4.34847 7.53177i 0.325020 0.562951i −0.656497 0.754329i \(-0.727962\pi\)
0.981516 + 0.191378i \(0.0612957\pi\)
\(180\) 6.72474 + 7.86566i 0.501233 + 0.586272i
\(181\) −4.34847 −0.323219 −0.161610 0.986855i \(-0.551669\pi\)
−0.161610 + 0.986855i \(0.551669\pi\)
\(182\) 0 0
\(183\) 8.29796 18.0116i 0.613403 1.33145i
\(184\) −1.00000 −0.0737210
\(185\) −13.4495 23.2952i −0.988826 1.71270i
\(186\) −10.3485 + 0.953512i −0.758787 + 0.0699149i
\(187\) 2.00000 3.46410i 0.146254 0.253320i
\(188\) 9.79796 0.714590
\(189\) 0 0
\(190\) 25.6969 1.86425
\(191\) −6.94949 + 12.0369i −0.502847 + 0.870957i 0.497147 + 0.867666i \(0.334381\pi\)
−0.999995 + 0.00329106i \(0.998952\pi\)
\(192\) 1.72474 0.158919i 0.124473 0.0114690i
\(193\) 4.05051 + 7.01569i 0.291562 + 0.505000i 0.974179 0.225776i \(-0.0724917\pi\)
−0.682617 + 0.730776i \(0.739158\pi\)
\(194\) 6.89898 0.495318
\(195\) 12.2474 26.5843i 0.877058 1.90374i
\(196\) 0 0
\(197\) −12.6969 −0.904619 −0.452310 0.891861i \(-0.649400\pi\)
−0.452310 + 0.891861i \(0.649400\pi\)
\(198\) −2.00000 + 5.65685i −0.142134 + 0.402015i
\(199\) 3.44949 5.97469i 0.244528 0.423535i −0.717471 0.696588i \(-0.754700\pi\)
0.961999 + 0.273054i \(0.0880337\pi\)
\(200\) 6.89898 0.487832
\(201\) 3.10102 + 4.38551i 0.218729 + 0.309330i
\(202\) 3.62372 6.27647i 0.254964 0.441611i
\(203\) 0 0
\(204\) −3.44949 + 0.317837i −0.241513 + 0.0222531i
\(205\) 16.8990 29.2699i 1.18028 2.04430i
\(206\) 7.00000 12.1244i 0.487713 0.844744i
\(207\) −2.94949 + 0.548188i −0.205004 + 0.0381017i
\(208\) −2.44949 4.24264i −0.169842 0.294174i
\(209\) 7.44949 + 12.9029i 0.515292 + 0.892512i
\(210\) 0 0
\(211\) −1.55051 + 2.68556i −0.106742 + 0.184882i −0.914448 0.404703i \(-0.867375\pi\)
0.807707 + 0.589584i \(0.200708\pi\)
\(212\) −1.10102 −0.0756184
\(213\) 17.0732 1.57313i 1.16984 0.107789i
\(214\) −12.0000 −0.820303
\(215\) −5.00000 8.66025i −0.340997 0.590624i
\(216\) 5.00000 1.41421i 0.340207 0.0962250i
\(217\) 0 0
\(218\) 8.34847 + 14.4600i 0.565430 + 0.979353i
\(219\) 2.10102 4.56048i 0.141974 0.308169i
\(220\) 3.44949 + 5.97469i 0.232565 + 0.402814i
\(221\) 4.89898 + 8.48528i 0.329541 + 0.570782i
\(222\) −13.4495 + 1.23924i −0.902671 + 0.0831724i
\(223\) −10.4495 18.0990i −0.699750 1.21200i −0.968553 0.248807i \(-0.919962\pi\)
0.268804 0.963195i \(-0.413372\pi\)
\(224\) 0 0
\(225\) 20.3485 3.78194i 1.35656 0.252129i
\(226\) 7.94949 + 13.7689i 0.528792 + 0.915895i
\(227\) 0.550510 0.0365386 0.0182693 0.999833i \(-0.494184\pi\)
0.0182693 + 0.999833i \(0.494184\pi\)
\(228\) 5.39898 11.7190i 0.357556 0.776112i
\(229\) 23.2474 1.53623 0.768117 0.640309i \(-0.221194\pi\)
0.768117 + 0.640309i \(0.221194\pi\)
\(230\) −1.72474 + 2.98735i −0.113726 + 0.196980i
\(231\) 0 0
\(232\) −1.44949 2.51059i −0.0951637 0.164828i
\(233\) 3.50000 + 6.06218i 0.229293 + 0.397146i 0.957599 0.288106i \(-0.0930254\pi\)
−0.728306 + 0.685252i \(0.759692\pi\)
\(234\) −9.55051 11.1708i −0.624336 0.730261i
\(235\) 16.8990 29.2699i 1.10237 1.90936i
\(236\) −1.00000 + 1.73205i −0.0650945 + 0.112747i
\(237\) −5.72474 + 12.4261i −0.371862 + 0.807164i
\(238\) 0 0
\(239\) 6.39898 11.0834i 0.413916 0.716923i −0.581398 0.813619i \(-0.697494\pi\)
0.995314 + 0.0966962i \(0.0308275\pi\)
\(240\) 2.50000 5.42650i 0.161374 0.350279i
\(241\) 8.89898 0.573234 0.286617 0.958045i \(-0.407469\pi\)
0.286617 + 0.958045i \(0.407469\pi\)
\(242\) 3.50000 6.06218i 0.224989 0.389692i
\(243\) 13.9722 6.91215i 0.896317 0.443415i
\(244\) −11.4495 −0.732978
\(245\) 0 0
\(246\) −9.79796 13.8564i −0.624695 0.883452i
\(247\) −36.4949 −2.32211
\(248\) 3.00000 + 5.19615i 0.190500 + 0.329956i
\(249\) 2.00000 + 2.82843i 0.126745 + 0.179244i
\(250\) 3.27526 5.67291i 0.207145 0.358786i
\(251\) −12.5505 −0.792181 −0.396091 0.918211i \(-0.629633\pi\)
−0.396091 + 0.918211i \(0.629633\pi\)
\(252\) 0 0
\(253\) −2.00000 −0.125739
\(254\) 1.50000 2.59808i 0.0941184 0.163018i
\(255\) −5.00000 + 10.8530i −0.313112 + 0.679642i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −27.7980 −1.73399 −0.866995 0.498318i \(-0.833951\pi\)
−0.866995 + 0.498318i \(0.833951\pi\)
\(258\) −5.00000 + 0.460702i −0.311286 + 0.0286820i
\(259\) 0 0
\(260\) −16.8990 −1.04803
\(261\) −5.65153 6.61037i −0.349821 0.409171i
\(262\) −6.72474 + 11.6476i −0.415456 + 0.719591i
\(263\) 16.1010 0.992831 0.496416 0.868085i \(-0.334649\pi\)
0.496416 + 0.868085i \(0.334649\pi\)
\(264\) 3.44949 0.317837i 0.212301 0.0195615i
\(265\) −1.89898 + 3.28913i −0.116653 + 0.202050i
\(266\) 0 0
\(267\) −7.10102 10.0424i −0.434575 0.614582i
\(268\) 1.55051 2.68556i 0.0947125 0.164047i
\(269\) −1.82577 + 3.16232i −0.111319 + 0.192810i −0.916302 0.400487i \(-0.868841\pi\)
0.804983 + 0.593297i \(0.202174\pi\)
\(270\) 4.39898 17.3759i 0.267713 1.05746i
\(271\) 8.44949 + 14.6349i 0.513270 + 0.889010i 0.999882 + 0.0153912i \(0.00489937\pi\)
−0.486612 + 0.873618i \(0.661767\pi\)
\(272\) 1.00000 + 1.73205i 0.0606339 + 0.105021i
\(273\) 0 0
\(274\) 5.89898 10.2173i 0.356370 0.617252i
\(275\) 13.7980 0.832048
\(276\) 1.00000 + 1.41421i 0.0601929 + 0.0851257i
\(277\) 10.6969 0.642717 0.321358 0.946958i \(-0.395861\pi\)
0.321358 + 0.946958i \(0.395861\pi\)
\(278\) 4.72474 + 8.18350i 0.283371 + 0.490814i
\(279\) 11.6969 + 13.6814i 0.700277 + 0.819086i
\(280\) 0 0
\(281\) 9.50000 + 16.4545i 0.566722 + 0.981592i 0.996887 + 0.0788417i \(0.0251222\pi\)
−0.430165 + 0.902750i \(0.641545\pi\)
\(282\) −9.79796 13.8564i −0.583460 0.825137i
\(283\) −10.2753 17.7973i −0.610801 1.05794i −0.991106 0.133077i \(-0.957514\pi\)
0.380305 0.924861i \(-0.375819\pi\)
\(284\) −4.94949 8.57277i −0.293698 0.508700i
\(285\) −25.6969 36.3410i −1.52216 2.15265i
\(286\) −4.89898 8.48528i −0.289683 0.501745i
\(287\) 0 0
\(288\) −1.94949 2.28024i −0.114875 0.134364i
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) −10.0000 −0.587220
\(291\) −6.89898 9.75663i −0.404425 0.571944i
\(292\) −2.89898 −0.169650
\(293\) 13.6237 23.5970i 0.795906 1.37855i −0.126356 0.991985i \(-0.540328\pi\)
0.922262 0.386565i \(-0.126339\pi\)
\(294\) 0 0
\(295\) 3.44949 + 5.97469i 0.200837 + 0.347860i
\(296\) 3.89898 + 6.75323i 0.226624 + 0.392524i
\(297\) 10.0000 2.82843i 0.580259 0.164122i
\(298\) 3.00000 5.19615i 0.173785 0.301005i
\(299\) 2.44949 4.24264i 0.141658 0.245358i
\(300\) −6.89898 9.75663i −0.398313 0.563299i
\(301\) 0 0
\(302\) 2.50000 4.33013i 0.143859 0.249171i
\(303\) −12.5000 + 1.15175i −0.718106 + 0.0661666i
\(304\) −7.44949 −0.427258
\(305\) −19.7474 + 34.2036i −1.13074 + 1.95849i
\(306\) 3.89898 + 4.56048i 0.222890 + 0.260705i
\(307\) −0.752551 −0.0429504 −0.0214752 0.999769i \(-0.506836\pi\)
−0.0214752 + 0.999769i \(0.506836\pi\)
\(308\) 0 0
\(309\) −24.1464 + 2.22486i −1.37364 + 0.126568i
\(310\) 20.6969 1.17551
\(311\) 0.651531 + 1.12848i 0.0369449 + 0.0639905i 0.883907 0.467663i \(-0.154904\pi\)
−0.846962 + 0.531654i \(0.821571\pi\)
\(312\) −3.55051 + 7.70674i −0.201008 + 0.436308i
\(313\) 12.3485 21.3882i 0.697977 1.20893i −0.271190 0.962526i \(-0.587417\pi\)
0.969167 0.246405i \(-0.0792495\pi\)
\(314\) −6.34847 −0.358265
\(315\) 0 0
\(316\) 7.89898 0.444352
\(317\) 4.34847 7.53177i 0.244234 0.423026i −0.717682 0.696371i \(-0.754797\pi\)
0.961916 + 0.273345i \(0.0881300\pi\)
\(318\) 1.10102 + 1.55708i 0.0617422 + 0.0873166i
\(319\) −2.89898 5.02118i −0.162312 0.281132i
\(320\) −3.44949 −0.192832
\(321\) 12.0000 + 16.9706i 0.669775 + 0.947204i
\(322\) 0 0
\(323\) 14.8990 0.829001
\(324\) −7.00000 5.65685i −0.388889 0.314270i
\(325\) −16.8990 + 29.2699i −0.937387 + 1.62360i
\(326\) −0.202041 −0.0111900
\(327\) 12.1010 26.2665i 0.669188 1.45254i
\(328\) −4.89898 + 8.48528i −0.270501 + 0.468521i
\(329\) 0 0
\(330\) 5.00000 10.8530i 0.275241 0.597438i
\(331\) 12.3485 21.3882i 0.678733 1.17560i −0.296629 0.954993i \(-0.595863\pi\)
0.975363 0.220608i \(-0.0708041\pi\)
\(332\) 1.00000 1.73205i 0.0548821 0.0950586i
\(333\) 15.2020 + 17.7812i 0.833067 + 0.974404i
\(334\) 9.34847 + 16.1920i 0.511525 + 0.885988i
\(335\) −5.34847 9.26382i −0.292218 0.506137i
\(336\) 0 0
\(337\) −17.6969 + 30.6520i −0.964014 + 1.66972i −0.251772 + 0.967787i \(0.581013\pi\)
−0.712242 + 0.701934i \(0.752320\pi\)
\(338\) 11.0000 0.598321
\(339\) 11.5227 25.0112i 0.625827 1.35842i
\(340\) 6.89898 0.374150
\(341\) 6.00000 + 10.3923i 0.324918 + 0.562775i
\(342\) −21.9722 + 4.08372i −1.18812 + 0.220822i
\(343\) 0 0
\(344\) 1.44949 + 2.51059i 0.0781512 + 0.135362i
\(345\) 5.94949 0.548188i 0.320310 0.0295135i
\(346\) −6.44949 11.1708i −0.346727 0.600548i
\(347\) 9.79796 + 16.9706i 0.525982 + 0.911028i 0.999542 + 0.0302659i \(0.00963541\pi\)
−0.473560 + 0.880762i \(0.657031\pi\)
\(348\) −2.10102 + 4.56048i −0.112627 + 0.244467i
\(349\) 10.4495 + 18.0990i 0.559348 + 0.968820i 0.997551 + 0.0699435i \(0.0222819\pi\)
−0.438203 + 0.898876i \(0.644385\pi\)
\(350\) 0 0
\(351\) −6.24745 + 24.6773i −0.333464 + 1.31718i
\(352\) −1.00000 1.73205i −0.0533002 0.0923186i
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 3.44949 0.317837i 0.183338 0.0168929i
\(355\) −34.1464 −1.81230
\(356\) −3.55051 + 6.14966i −0.188177 + 0.325932i
\(357\) 0 0
\(358\) 4.34847 + 7.53177i 0.229824 + 0.398066i
\(359\) −5.39898 9.35131i −0.284947 0.493543i 0.687649 0.726043i \(-0.258643\pi\)
−0.972596 + 0.232500i \(0.925309\pi\)
\(360\) −10.1742 + 1.89097i −0.536229 + 0.0996628i
\(361\) −18.2474 + 31.6055i −0.960392 + 1.66345i
\(362\) 2.17423 3.76588i 0.114275 0.197931i
\(363\) −12.0732 + 1.11243i −0.633679 + 0.0583875i
\(364\) 0 0
\(365\) −5.00000 + 8.66025i −0.261712 + 0.453298i
\(366\) 11.4495 + 16.1920i 0.598474 + 0.846371i
\(367\) −5.79796 −0.302651 −0.151325 0.988484i \(-0.548354\pi\)
−0.151325 + 0.988484i \(0.548354\pi\)
\(368\) 0.500000 0.866025i 0.0260643 0.0451447i
\(369\) −9.79796 + 27.7128i −0.510061 + 1.44267i
\(370\) 26.8990 1.39841
\(371\) 0 0
\(372\) 4.34847 9.43879i 0.225458 0.489379i
\(373\) 2.89898 0.150103 0.0750517 0.997180i \(-0.476088\pi\)
0.0750517 + 0.997180i \(0.476088\pi\)
\(374\) 2.00000 + 3.46410i 0.103418 + 0.179124i
\(375\) −11.2980 + 1.04100i −0.583424 + 0.0537569i
\(376\) −4.89898 + 8.48528i −0.252646 + 0.437595i
\(377\) 14.2020 0.731442
\(378\) 0 0
\(379\) −26.4949 −1.36095 −0.680476 0.732771i \(-0.738227\pi\)
−0.680476 + 0.732771i \(0.738227\pi\)
\(380\) −12.8485 + 22.2542i −0.659113 + 1.14162i
\(381\) −5.17423 + 0.476756i −0.265084 + 0.0244249i
\(382\) −6.94949 12.0369i −0.355567 0.615860i
\(383\) −6.89898 −0.352521 −0.176261 0.984344i \(-0.556400\pi\)
−0.176261 + 0.984344i \(0.556400\pi\)
\(384\) −0.724745 + 1.57313i −0.0369845 + 0.0802786i
\(385\) 0 0
\(386\) −8.10102 −0.412331
\(387\) 5.65153 + 6.61037i 0.287283 + 0.336024i
\(388\) −3.44949 + 5.97469i −0.175121 + 0.303319i
\(389\) −15.1010 −0.765652 −0.382826 0.923820i \(-0.625049\pi\)
−0.382826 + 0.923820i \(0.625049\pi\)
\(390\) 16.8990 + 23.8988i 0.855713 + 1.21016i
\(391\) −1.00000 + 1.73205i −0.0505722 + 0.0875936i
\(392\) 0 0
\(393\) 23.1969 2.13737i 1.17013 0.107816i
\(394\) 6.34847 10.9959i 0.319831 0.553964i
\(395\) 13.6237 23.5970i 0.685484 1.18729i
\(396\) −3.89898 4.56048i −0.195931 0.229173i
\(397\) 4.65153 + 8.05669i 0.233454 + 0.404354i 0.958822 0.284007i \(-0.0916640\pi\)
−0.725369 + 0.688361i \(0.758331\pi\)
\(398\) 3.44949 + 5.97469i 0.172907 + 0.299484i
\(399\) 0 0
\(400\) −3.44949 + 5.97469i −0.172474 + 0.298735i
\(401\) −10.1010 −0.504421 −0.252210 0.967672i \(-0.581158\pi\)
−0.252210 + 0.967672i \(0.581158\pi\)
\(402\) −5.34847 + 0.492810i −0.266757 + 0.0245791i
\(403\) −29.3939 −1.46421
\(404\) 3.62372 + 6.27647i 0.180287 + 0.312266i
\(405\) −28.9722 + 11.1548i −1.43964 + 0.554286i
\(406\) 0 0
\(407\) 7.79796 + 13.5065i 0.386530 + 0.669490i
\(408\) 1.44949 3.14626i 0.0717604 0.155763i
\(409\) 2.89898 + 5.02118i 0.143345 + 0.248281i 0.928754 0.370696i \(-0.120881\pi\)
−0.785409 + 0.618977i \(0.787547\pi\)
\(410\) 16.8990 + 29.2699i 0.834581 + 1.44554i
\(411\) −20.3485 + 1.87492i −1.00372 + 0.0924828i
\(412\) 7.00000 + 12.1244i 0.344865 + 0.597324i
\(413\) 0 0
\(414\) 1.00000 2.82843i 0.0491473 0.139010i
\(415\) −3.44949 5.97469i −0.169329 0.293286i
\(416\) 4.89898 0.240192
\(417\) 6.84847 14.8653i 0.335371 0.727957i
\(418\) −14.8990 −0.728733
\(419\) 12.2753 21.2614i 0.599685 1.03869i −0.393182 0.919461i \(-0.628626\pi\)
0.992867 0.119225i \(-0.0380410\pi\)
\(420\) 0 0
\(421\) −6.55051 11.3458i −0.319252 0.552961i 0.661080 0.750316i \(-0.270098\pi\)
−0.980332 + 0.197354i \(0.936765\pi\)
\(422\) −1.55051 2.68556i −0.0754777 0.130731i
\(423\) −9.79796 + 27.7128i −0.476393 + 1.34744i
\(424\) 0.550510 0.953512i 0.0267351 0.0463066i
\(425\) 6.89898 11.9494i 0.334650 0.579630i
\(426\) −7.17423 + 15.5724i −0.347593 + 0.754485i
\(427\) 0 0
\(428\) 6.00000 10.3923i 0.290021 0.502331i
\(429\) −7.10102 + 15.4135i −0.342841 + 0.744170i
\(430\) 10.0000 0.482243
\(431\) 3.79796 6.57826i 0.182941 0.316864i −0.759940 0.649994i \(-0.774772\pi\)
0.942881 + 0.333130i \(0.108105\pi\)
\(432\) −1.27526 + 5.03723i −0.0613557 + 0.242354i
\(433\) −11.7980 −0.566974 −0.283487 0.958976i \(-0.591491\pi\)
−0.283487 + 0.958976i \(0.591491\pi\)
\(434\) 0 0
\(435\) 10.0000 + 14.1421i 0.479463 + 0.678064i
\(436\) −16.6969 −0.799638
\(437\) −3.72474 6.45145i −0.178179 0.308615i
\(438\) 2.89898 + 4.09978i 0.138519 + 0.195895i
\(439\) 10.8990 18.8776i 0.520180 0.900978i −0.479545 0.877517i \(-0.659198\pi\)
0.999725 0.0234607i \(-0.00746845\pi\)
\(440\) −6.89898 −0.328896
\(441\) 0 0
\(442\) −9.79796 −0.466041
\(443\) 2.55051 4.41761i 0.121178 0.209887i −0.799054 0.601259i \(-0.794666\pi\)
0.920233 + 0.391372i \(0.127999\pi\)
\(444\) 5.65153 12.2672i 0.268210 0.582177i
\(445\) 12.2474 + 21.2132i 0.580585 + 1.00560i
\(446\) 20.8990 0.989595
\(447\) −10.3485 + 0.953512i −0.489466 + 0.0450996i
\(448\) 0 0
\(449\) −18.5959 −0.877596 −0.438798 0.898586i \(-0.644596\pi\)
−0.438798 + 0.898586i \(0.644596\pi\)
\(450\) −6.89898 + 19.5133i −0.325221 + 0.919864i
\(451\) −9.79796 + 16.9706i −0.461368 + 0.799113i
\(452\) −15.8990 −0.747825
\(453\) −8.62372 + 0.794593i −0.405178 + 0.0373332i
\(454\) −0.275255 + 0.476756i −0.0129184 + 0.0223753i
\(455\) 0 0
\(456\) 7.44949 + 10.5352i 0.348854 + 0.493355i
\(457\) −15.7474 + 27.2754i −0.736635 + 1.27589i 0.217368 + 0.976090i \(0.430253\pi\)
−0.954002 + 0.299799i \(0.903080\pi\)
\(458\) −11.6237 + 20.1329i −0.543141 + 0.940748i
\(459\) 2.55051 10.0745i 0.119048 0.470236i
\(460\) −1.72474 2.98735i −0.0804166 0.139286i
\(461\) 10.1742 + 17.6223i 0.473861 + 0.820752i 0.999552 0.0299238i \(-0.00952645\pi\)
−0.525691 + 0.850676i \(0.676193\pi\)
\(462\) 0 0
\(463\) 12.8485 22.2542i 0.597119 1.03424i −0.396125 0.918197i \(-0.629645\pi\)
0.993244 0.116044i \(-0.0370213\pi\)
\(464\) 2.89898 0.134582
\(465\) −20.6969 29.2699i −0.959798 1.35736i
\(466\) −7.00000 −0.324269
\(467\) 5.00000 + 8.66025i 0.231372 + 0.400749i 0.958212 0.286058i \(-0.0923451\pi\)
−0.726840 + 0.686807i \(0.759012\pi\)
\(468\) 14.4495 2.68556i 0.667928 0.124140i
\(469\) 0 0
\(470\) 16.8990 + 29.2699i 0.779492 + 1.35012i
\(471\) 6.34847 + 8.97809i 0.292522 + 0.413689i
\(472\) −1.00000 1.73205i −0.0460287 0.0797241i
\(473\) 2.89898 + 5.02118i 0.133295 + 0.230874i
\(474\) −7.89898 11.1708i −0.362812 0.513094i
\(475\) 25.6969 + 44.5084i 1.17906 + 2.04219i
\(476\) 0 0
\(477\) 1.10102 3.11416i 0.0504123 0.142587i
\(478\) 6.39898 + 11.0834i 0.292683 + 0.506941i
\(479\) 29.5959 1.35227 0.676136 0.736777i \(-0.263653\pi\)
0.676136 + 0.736777i \(0.263653\pi\)
\(480\) 3.44949 + 4.87832i 0.157447 + 0.222664i
\(481\) −38.2020 −1.74186
\(482\) −4.44949 + 7.70674i −0.202669 + 0.351032i
\(483\) 0 0
\(484\) 3.50000 + 6.06218i 0.159091 + 0.275554i
\(485\) 11.8990 + 20.6096i 0.540305 + 0.935835i
\(486\) −1.00000 + 15.5563i −0.0453609 + 0.705650i
\(487\) −11.1969 + 19.3937i −0.507382 + 0.878811i 0.492582 + 0.870266i \(0.336053\pi\)
−0.999963 + 0.00854475i \(0.997280\pi\)
\(488\) 5.72474 9.91555i 0.259147 0.448856i
\(489\) 0.202041 + 0.285729i 0.00913661 + 0.0129211i
\(490\) 0 0
\(491\) 1.89898 3.28913i 0.0856997 0.148436i −0.819989 0.572379i \(-0.806021\pi\)
0.905689 + 0.423942i \(0.139354\pi\)
\(492\) 16.8990 1.55708i 0.761865 0.0701985i
\(493\) −5.79796 −0.261127
\(494\) 18.2474 31.6055i 0.820992 1.42200i
\(495\) −20.3485 + 3.78194i −0.914596 + 0.169986i
\(496\) −6.00000 −0.269408
\(497\) 0 0
\(498\) −3.44949 + 0.317837i −0.154575 + 0.0142426i
\(499\) 33.3939 1.49492 0.747458 0.664309i \(-0.231274\pi\)
0.747458 + 0.664309i \(0.231274\pi\)
\(500\) 3.27526 + 5.67291i 0.146474 + 0.253700i
\(501\) 13.5505 29.4128i 0.605392 1.31407i
\(502\) 6.27526 10.8691i 0.280078 0.485110i
\(503\) −24.4949 −1.09217 −0.546087 0.837729i \(-0.683883\pi\)
−0.546087 + 0.837729i \(0.683883\pi\)
\(504\) 0 0
\(505\) 25.0000 1.11249
\(506\) 1.00000 1.73205i 0.0444554 0.0769991i
\(507\) −11.0000 15.5563i −0.488527 0.690882i
\(508\) 1.50000 + 2.59808i 0.0665517 + 0.115271i
\(509\) 16.8990 0.749034 0.374517 0.927220i \(-0.377809\pi\)
0.374517 + 0.927220i \(0.377809\pi\)
\(510\) −6.89898 9.75663i −0.305492 0.432031i
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 27.7474 + 26.9897i 1.22508 + 1.19162i
\(514\) 13.8990 24.0737i 0.613058 1.06185i
\(515\) 48.2929 2.12804
\(516\) 2.10102 4.56048i 0.0924923 0.200764i
\(517\) −9.79796 + 16.9706i −0.430914 + 0.746364i
\(518\) 0 0
\(519\) −9.34847 + 20.2918i −0.410352 + 0.890711i
\(520\) 8.44949 14.6349i 0.370535 0.641785i
\(521\) −19.3485 + 33.5125i −0.847672 + 1.46821i 0.0356087 + 0.999366i \(0.488663\pi\)
−0.883281 + 0.468845i \(0.844670\pi\)
\(522\) 8.55051 1.58919i 0.374246 0.0695568i
\(523\) 0.174235 + 0.301783i 0.00761875 + 0.0131961i 0.869810 0.493387i \(-0.164242\pi\)
−0.862191 + 0.506584i \(0.830908\pi\)
\(524\) −6.72474 11.6476i −0.293772 0.508828i
\(525\) 0 0
\(526\) −8.05051 + 13.9439i −0.351019 + 0.607983i
\(527\) 12.0000 0.522728
\(528\) −1.44949 + 3.14626i −0.0630809 + 0.136924i
\(529\) −22.0000 −0.956522
\(530\) −1.89898 3.28913i −0.0824864 0.142871i
\(531\) −3.89898 4.56048i −0.169201 0.197908i
\(532\) 0 0
\(533\) −24.0000 41.5692i −1.03956 1.80056i
\(534\) 12.2474 1.12848i 0.529999 0.0488343i
\(535\) −20.6969 35.8481i −0.894807 1.54985i
\(536\) 1.55051 + 2.68556i 0.0669718 + 0.115999i
\(537\) 6.30306 13.6814i 0.271997 0.590397i
\(538\) −1.82577 3.16232i −0.0787143 0.136337i
\(539\) 0 0
\(540\) 12.8485 + 12.4976i 0.552910 + 0.537810i
\(541\) −15.2474 26.4094i −0.655539 1.13543i −0.981758 0.190133i \(-0.939108\pi\)
0.326219 0.945294i \(-0.394225\pi\)
\(542\) −16.8990 −0.725873
\(543\) −7.50000 + 0.691053i −0.321856 + 0.0296559i
\(544\) −2.00000 −0.0857493
\(545\) −28.7980 + 49.8795i −1.23357 + 2.13660i
\(546\) 0 0
\(547\) −15.7980 27.3629i −0.675472 1.16995i −0.976331 0.216283i \(-0.930607\pi\)
0.300859 0.953669i \(-0.402727\pi\)
\(548\) 5.89898 + 10.2173i 0.251992 + 0.436463i
\(549\) 11.4495 32.3840i 0.488652 1.38212i
\(550\) −6.89898 + 11.9494i −0.294173 + 0.509523i
\(551\) 10.7980 18.7026i 0.460009 0.796758i
\(552\) −1.72474 + 0.158919i −0.0734100 + 0.00676403i
\(553\) 0 0
\(554\) −5.34847 + 9.26382i −0.227235 + 0.393582i
\(555\) −26.8990 38.0409i −1.14180 1.61475i
\(556\) −9.44949 −0.400748
\(557\) 1.55051 2.68556i 0.0656972 0.113791i −0.831306 0.555815i \(-0.812406\pi\)
0.897003 + 0.442024i \(0.145740\pi\)
\(558\) −17.6969 + 3.28913i −0.749171 + 0.139240i
\(559\) −14.2020 −0.600682
\(560\) 0 0
\(561\) 2.89898 6.29253i 0.122395 0.265671i
\(562\) −19.0000 −0.801467
\(563\) 6.97219 + 12.0762i 0.293843 + 0.508951i 0.974715 0.223451i \(-0.0717324\pi\)
−0.680872 + 0.732402i \(0.738399\pi\)
\(564\) 16.8990 1.55708i 0.711575 0.0655648i
\(565\) −27.4217 + 47.4957i −1.15364 + 1.99816i
\(566\) 20.5505 0.863802
\(567\) 0 0
\(568\) 9.89898 0.415352
\(569\) 15.0000 25.9808i 0.628833 1.08917i −0.358954 0.933355i \(-0.616866\pi\)
0.987786 0.155815i \(-0.0498003\pi\)
\(570\) 44.3207 4.08372i 1.85639 0.171048i
\(571\) −7.10102 12.2993i −0.297168 0.514711i 0.678319 0.734768i \(-0.262709\pi\)
−0.975487 + 0.220057i \(0.929376\pi\)
\(572\) 9.79796 0.409673
\(573\) −10.0732 + 21.8649i −0.420815 + 0.913421i
\(574\) 0 0
\(575\) −6.89898 −0.287707
\(576\) 2.94949 0.548188i 0.122895 0.0228412i
\(577\) 11.7980 20.4347i 0.491155 0.850706i −0.508793 0.860889i \(-0.669908\pi\)
0.999948 + 0.0101829i \(0.00324136\pi\)
\(578\) −13.0000 −0.540729
\(579\) 8.10102 + 11.4566i 0.336667 + 0.476119i
\(580\) 5.00000 8.66025i 0.207614 0.359597i
\(581\) 0 0
\(582\) 11.8990 1.09638i 0.493229 0.0454463i
\(583\) 1.10102 1.90702i 0.0455996 0.0789808i
\(584\) 1.44949 2.51059i 0.0599803 0.103889i
\(585\) 16.8990 47.7975i 0.698687 1.97618i
\(586\) 13.6237 + 23.5970i 0.562791 + 0.974782i
\(587\) −9.07321 15.7153i −0.374492 0.648639i 0.615759 0.787934i \(-0.288849\pi\)
−0.990251 + 0.139296i \(0.955516\pi\)
\(588\) 0 0
\(589\) −22.3485 + 38.7087i −0.920853 + 1.59496i
\(590\) −6.89898 −0.284026
\(591\) −21.8990 + 2.01778i −0.900804 + 0.0830004i
\(592\) −7.79796 −0.320494
\(593\) −7.34847 12.7279i −0.301765 0.522673i 0.674770 0.738028i \(-0.264243\pi\)
−0.976536 + 0.215355i \(0.930909\pi\)
\(594\) −2.55051 + 10.0745i −0.104649 + 0.413360i
\(595\) 0 0
\(596\) 3.00000 + 5.19615i 0.122885 + 0.212843i
\(597\) 5.00000 10.8530i 0.204636 0.444184i
\(598\) 2.44949 + 4.24264i 0.100167 + 0.173494i
\(599\) 7.10102 + 12.2993i 0.290140 + 0.502537i 0.973843 0.227224i \(-0.0729648\pi\)
−0.683703 + 0.729761i \(0.739632\pi\)
\(600\) 11.8990 1.09638i 0.485774 0.0447594i
\(601\) −6.34847 10.9959i −0.258959 0.448531i 0.707004 0.707210i \(-0.250046\pi\)
−0.965963 + 0.258679i \(0.916713\pi\)
\(602\) 0 0
\(603\) 6.04541 + 7.07107i 0.246188 + 0.287956i
\(604\) 2.50000 + 4.33013i 0.101724 + 0.176190i
\(605\) 24.1464 0.981692
\(606\) 5.25255 11.4012i 0.213370 0.463142i
\(607\) 8.69694 0.352998 0.176499 0.984301i \(-0.443523\pi\)
0.176499 + 0.984301i \(0.443523\pi\)
\(608\) 3.72474 6.45145i 0.151058 0.261641i
\(609\) 0 0
\(610\) −19.7474 34.2036i −0.799551 1.38486i
\(611\) −24.0000 41.5692i −0.970936 1.68171i
\(612\) −5.89898 + 1.09638i −0.238452 + 0.0443184i
\(613\) −7.34847 + 12.7279i −0.296802 + 0.514076i −0.975402 0.220432i \(-0.929253\pi\)
0.678601 + 0.734508i \(0.262587\pi\)
\(614\) 0.376276 0.651729i 0.0151852 0.0263016i
\(615\) 24.4949 53.1687i 0.987730 2.14397i
\(616\) 0 0
\(617\) −21.6969 + 37.5802i −0.873486 + 1.51292i −0.0151189 + 0.999886i \(0.504813\pi\)
−0.858367 + 0.513036i \(0.828521\pi\)
\(618\) 10.1464 22.0239i 0.408149 0.885929i
\(619\) 4.14643 0.166659 0.0833295 0.996522i \(-0.473445\pi\)
0.0833295 + 0.996522i \(0.473445\pi\)
\(620\) −10.3485 + 17.9241i −0.415605 + 0.719848i
\(621\) −5.00000 + 1.41421i −0.200643 + 0.0567504i
\(622\) −1.30306 −0.0522480
\(623\) 0 0
\(624\) −4.89898 6.92820i −0.196116 0.277350i
\(625\) −11.8990 −0.475959
\(626\) 12.3485 + 21.3882i 0.493544 + 0.854843i
\(627\) 14.8990 + 21.0703i 0.595008 + 0.841468i
\(628\) 3.17423 5.49794i 0.126666 0.219392i
\(629\) 15.5959 0.621850
\(630\) 0 0
\(631\) 18.1010 0.720590 0.360295 0.932838i \(-0.382676\pi\)
0.360295 + 0.932838i \(0.382676\pi\)
\(632\) −3.94949 + 6.84072i −0.157102 + 0.272109i
\(633\) −2.24745 + 4.87832i −0.0893281 + 0.193896i
\(634\) 4.34847 + 7.53177i 0.172700 + 0.299125i
\(635\) 10.3485 0.410666
\(636\) −1.89898 + 0.174973i −0.0752994 + 0.00693812i
\(637\) 0 0
\(638\) 5.79796 0.229543
\(639\) 29.1969 5.42650i 1.15501 0.214669i
\(640\) 1.72474 2.98735i 0.0681765 0.118085i
\(641\) 41.4949 1.63895 0.819475 0.573115i \(-0.194265\pi\)
0.819475 + 0.573115i \(0.194265\pi\)
\(642\) −20.6969 + 1.90702i −0.816843 + 0.0752642i
\(643\) 9.69694 16.7956i 0.382410 0.662353i −0.608996 0.793173i \(-0.708428\pi\)
0.991406 + 0.130820i \(0.0417609\pi\)
\(644\) 0 0
\(645\) −10.0000 14.1421i −0.393750 0.556846i
\(646\) −7.44949 + 12.9029i −0.293096 + 0.507658i
\(647\) −10.6515 + 18.4490i −0.418755 + 0.725305i −0.995815 0.0913973i \(-0.970867\pi\)
0.577060 + 0.816702i \(0.304200\pi\)
\(648\) 8.39898 3.23375i 0.329943 0.127034i
\(649\) −2.00000 3.46410i −0.0785069 0.135978i
\(650\) −16.8990 29.2699i −0.662833 1.14806i
\(651\) 0 0
\(652\) 0.101021 0.174973i 0.00395627 0.00685246i
\(653\) −9.79796 −0.383424 −0.191712 0.981451i \(-0.561404\pi\)
−0.191712 + 0.981451i \(0.561404\pi\)
\(654\) 16.6969 + 23.6130i 0.652902 + 0.923343i
\(655\) −46.3939 −1.81276
\(656\) −4.89898 8.48528i −0.191273 0.331295i
\(657\) 2.89898 8.19955i 0.113100 0.319895i
\(658\) 0 0
\(659\) −2.34847 4.06767i −0.0914834 0.158454i 0.816652 0.577130i \(-0.195828\pi\)
−0.908136 + 0.418676i \(0.862494\pi\)
\(660\) 6.89898 + 9.75663i 0.268542 + 0.379776i
\(661\) 4.72474 + 8.18350i 0.183771 + 0.318301i 0.943162 0.332334i \(-0.107836\pi\)
−0.759391 + 0.650635i \(0.774503\pi\)
\(662\) 12.3485 + 21.3882i 0.479937 + 0.831275i
\(663\) 9.79796 + 13.8564i 0.380521 + 0.538138i
\(664\) 1.00000 + 1.73205i 0.0388075 + 0.0672166i
\(665\) 0 0
\(666\) −23.0000 + 4.27475i −0.891232 + 0.165643i
\(667\) 1.44949 + 2.51059i 0.0561245 + 0.0972104i
\(668\) −18.6969 −0.723406
\(669\) −20.8990 29.5556i −0.808001 1.14269i
\(670\) 10.6969 0.413259
\(671\) 11.4495 19.8311i 0.442003 0.765571i
\(672\) 0 0
\(673\) −15.2980 26.4968i −0.589693 1.02138i −0.994272 0.106875i \(-0.965915\pi\)
0.404579 0.914503i \(-0.367418\pi\)
\(674\) −17.6969 30.6520i −0.681661 1.18067i
\(675\) 34.4949 9.75663i 1.32771 0.375533i
\(676\) −5.50000 + 9.52628i −0.211538 + 0.366395i
\(677\) −7.34847 + 12.7279i −0.282425 + 0.489174i −0.971981 0.235058i \(-0.924472\pi\)
0.689557 + 0.724232i \(0.257805\pi\)
\(678\) 15.8990 + 22.4846i 0.610597 + 0.863514i
\(679\) 0 0
\(680\) −3.44949 + 5.97469i −0.132282 + 0.229119i
\(681\) 0.949490 0.0874863i 0.0363845 0.00335248i
\(682\) −12.0000 −0.459504
\(683\) −16.1010 + 27.8878i −0.616088 + 1.06710i 0.374104 + 0.927387i \(0.377950\pi\)
−0.990193 + 0.139710i \(0.955383\pi\)
\(684\) 7.44949 21.0703i 0.284838 0.805645i
\(685\) 40.6969 1.55495
\(686\) 0 0
\(687\) 40.0959 3.69445i 1.52975 0.140952i
\(688\) −2.89898 −0.110523
\(689\) 2.69694 + 4.67123i 0.102745 + 0.177960i
\(690\) −2.50000 + 5.42650i −0.0951734 + 0.206583i
\(691\) 3.47730 6.02285i 0.132283 0.229120i −0.792274 0.610166i \(-0.791103\pi\)
0.924556 + 0.381046i \(0.124436\pi\)
\(692\) 12.8990 0.490346
\(693\) 0 0
\(694\) −19.5959 −0.743851
\(695\) −16.2980 + 28.2289i −0.618217 + 1.07078i
\(696\) −2.89898 4.09978i −0.109886 0.155402i
\(697\) 9.79796 + 16.9706i 0.371124 + 0.642806i
\(698\) −20.8990 −0.791038
\(699\) 7.00000 + 9.89949i 0.264764 + 0.374433i
\(700\) 0 0
\(701\) 51.3939 1.94112 0.970560 0.240860i \(-0.0774293\pi\)
0.970560 + 0.240860i \(0.0774293\pi\)
\(702\) −18.2474 17.7491i −0.688706 0.669897i
\(703\) −29.0454 + 50.3081i −1.09547 + 1.89741i
\(704\) 2.00000 0.0753778
\(705\) 24.4949 53.1687i 0.922531 2.00245i
\(706\) −3.00000 + 5.19615i −0.112906 + 0.195560i
\(707\) 0 0
\(708\) −1.44949 + 3.14626i −0.0544752 + 0.118244i
\(709\) 5.79796 10.0424i 0.217747 0.377149i −0.736372 0.676577i \(-0.763463\pi\)
0.954119 + 0.299428i \(0.0967959\pi\)
\(710\) 17.0732 29.5717i 0.640746 1.10981i
\(711\) −7.89898 + 22.3417i −0.296235 + 0.837879i
\(712\) −3.55051 6.14966i −0.133061 0.230468i
\(713\) −3.00000 5.19615i −0.112351 0.194597i
\(714\) 0 0
\(715\) 16.8990 29.2699i 0.631986 1.09463i
\(716\) −8.69694 −0.325020
\(717\) 9.27526 20.1329i 0.346391 0.751876i
\(718\) 10.7980 0.402976
\(719\) −4.89898 8.48528i −0.182701 0.316448i 0.760098 0.649808i \(-0.225151\pi\)
−0.942799 + 0.333360i \(0.891817\pi\)
\(720\) 3.44949 9.75663i 0.128555 0.363608i
\(721\) 0 0
\(722\) −18.2474 31.6055i −0.679100 1.17624i
\(723\) 15.3485 1.41421i 0.570816 0.0525952i
\(724\) 2.17423 + 3.76588i 0.0808048 + 0.139958i
\(725\) −10.0000 17.3205i −0.371391 0.643268i
\(726\) 5.07321 11.0119i 0.188285 0.408691i
\(727\) 20.2474 + 35.0696i 0.750936 + 1.30066i 0.947369 + 0.320143i \(0.103731\pi\)
−0.196433 + 0.980517i \(0.562936\pi\)
\(728\) 0 0
\(729\) 23.0000 14.1421i 0.851852 0.523783i
\(730\) −5.00000 8.66025i −0.185058 0.320530i
\(731\) 5.79796 0.214445
\(732\) −19.7474 + 1.81954i −0.729887 + 0.0672520i
\(733\) 12.5505 0.463564 0.231782 0.972768i \(-0.425544\pi\)
0.231782 + 0.972768i \(0.425544\pi\)
\(734\) 2.89898 5.02118i 0.107003 0.185335i
\(735\) 0 0
\(736\) 0.500000 + 0.866025i 0.0184302 + 0.0319221i
\(737\) 3.10102 + 5.37113i 0.114228 + 0.197848i
\(738\) −19.1010 22.3417i −0.703118 0.822409i
\(739\) 12.7980 22.1667i 0.470781 0.815416i −0.528661 0.848833i \(-0.677306\pi\)
0.999441 + 0.0334173i \(0.0106390\pi\)
\(740\) −13.4495 + 23.2952i −0.494413 + 0.856349i
\(741\) −62.9444 + 5.79972i −2.31232 + 0.213058i
\(742\) 0 0
\(743\) −18.0000 + 31.1769i −0.660356 + 1.14377i 0.320166 + 0.947361i \(0.396261\pi\)
−0.980522 + 0.196409i \(0.937072\pi\)
\(744\) 6.00000 + 8.48528i 0.219971 + 0.311086i
\(745\) 20.6969 0.758277
\(746\) −1.44949 + 2.51059i −0.0530696 + 0.0919192i
\(747\) 3.89898 + 4.56048i 0.142656 + 0.166859i
\(748\) −4.00000 −0.146254
\(749\) 0 0
\(750\) 4.74745 10.3048i 0.173352 0.376279i
\(751\) 40.5959 1.48137 0.740683 0.671855i \(-0.234502\pi\)
0.740683 + 0.671855i \(0.234502\pi\)
\(752\) −4.89898 8.48528i −0.178647 0.309426i
\(753\) −21.6464 + 1.99451i −0.788840 + 0.0726840i
\(754\) −7.10102 + 12.2993i −0.258604 + 0.447915i
\(755\) 17.2474 0.627699
\(756\) 0 0
\(757\) 23.3939 0.850265 0.425132 0.905131i \(-0.360228\pi\)
0.425132 + 0.905131i \(0.360228\pi\)
\(758\) 13.2474 22.9453i 0.481169 0.833409i
\(759\) −3.44949 + 0.317837i −0.125209 + 0.0115368i
\(760\) −12.8485 22.2542i −0.466063 0.807245i
\(761\) −2.00000 −0.0724999 −0.0362500 0.999343i \(-0.511541\pi\)
−0.0362500 + 0.999343i \(0.511541\pi\)
\(762\) 2.17423 4.71940i 0.0787642 0.170966i
\(763\) 0 0
\(764\) 13.8990 0.502847
\(765\) −6.89898 + 19.5133i −0.249433 + 0.705503i
\(766\) 3.44949 5.97469i 0.124635 0.215874i
\(767\) 9.79796 0.353784
\(768\) −1.00000 1.41421i −0.0360844 0.0510310i
\(769\) 27.0454 46.8440i 0.975282 1.68924i 0.296282 0.955100i \(-0.404253\pi\)
0.679000 0.734138i \(-0.262414\pi\)
\(770\) 0 0
\(771\) −47.9444 + 4.41761i −1.72667 + 0.159096i
\(772\) 4.05051 7.01569i 0.145781 0.252500i
\(773\) −9.97219 + 17.2723i −0.358675 + 0.621243i −0.987740 0.156110i \(-0.950105\pi\)
0.629065 + 0.777353i \(0.283438\pi\)
\(774\) −8.55051 + 1.58919i −0.307342 + 0.0571221i
\(775\) 20.6969 + 35.8481i 0.743456 + 1.28770i
\(776\) −3.44949 5.97469i −0.123829 0.214479i
\(777\) 0 0
\(778\) 7.55051 13.0779i 0.270699 0.468864i
\(779\) −72.9898 −2.61513
\(780\) −29.1464 + 2.68556i −1.04361 + 0.0961586i
\(781\) 19.7980 0.708427