Properties

Label 462.2.c.a.197.8
Level $462$
Weight $2$
Character 462.197
Analytic conductor $3.689$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 16 x^{10} + 94 x^{8} + 246 x^{6} + 277 x^{4} + 114 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 197.8
Root \(-2.33939i\) of defining polynomial
Character \(\chi\) \(=\) 462.197
Dual form 462.2.c.a.197.7

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(0.806630 + 1.53276i) q^{3} +1.00000 q^{4} +3.86104i q^{5} +(-0.806630 - 1.53276i) q^{6} +1.00000i q^{7} -1.00000 q^{8} +(-1.69870 + 2.47274i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(0.806630 + 1.53276i) q^{3} +1.00000 q^{4} +3.86104i q^{5} +(-0.806630 - 1.53276i) q^{6} +1.00000i q^{7} -1.00000 q^{8} +(-1.69870 + 2.47274i) q^{9} -3.86104i q^{10} +(-1.72613 - 2.83205i) q^{11} +(0.806630 + 1.53276i) q^{12} +5.06552i q^{13} -1.00000i q^{14} +(-5.91804 + 3.11443i) q^{15} +1.00000 q^{16} +2.69769 q^{17} +(1.69870 - 2.47274i) q^{18} -7.70835i q^{19} +3.86104i q^{20} +(-1.53276 + 0.806630i) q^{21} +(1.72613 + 2.83205i) q^{22} -3.49322i q^{23} +(-0.806630 - 1.53276i) q^{24} -9.90764 q^{25} -5.06552i q^{26} +(-5.16033 - 0.609106i) q^{27} +1.00000i q^{28} +0.831472 q^{29} +(5.91804 - 3.11443i) q^{30} +9.19326 q^{31} -1.00000 q^{32} +(2.94849 - 4.93015i) q^{33} -2.69769 q^{34} -3.86104 q^{35} +(-1.69870 + 2.47274i) q^{36} +3.04331 q^{37} +7.70835i q^{38} +(-7.76421 + 4.08600i) q^{39} -3.86104i q^{40} -5.28064 q^{41} +(1.53276 - 0.806630i) q^{42} +12.5717i q^{43} +(-1.72613 - 2.83205i) q^{44} +(-9.54734 - 6.55874i) q^{45} +3.49322i q^{46} +4.96439i q^{47} +(0.806630 + 1.53276i) q^{48} -1.00000 q^{49} +9.90764 q^{50} +(2.17604 + 4.13491i) q^{51} +5.06552i q^{52} +0.602608i q^{53} +(5.16033 + 0.609106i) q^{54} +(10.9346 - 6.66465i) q^{55} -1.00000i q^{56} +(11.8150 - 6.21778i) q^{57} -0.831472 q^{58} -0.161004i q^{59} +(-5.91804 + 3.11443i) q^{60} +4.61360i q^{61} -9.19326 q^{62} +(-2.47274 - 1.69870i) q^{63} +1.00000 q^{64} -19.5582 q^{65} +(-2.94849 + 4.93015i) q^{66} -4.22686 q^{67} +2.69769 q^{68} +(5.35426 - 2.81774i) q^{69} +3.86104 q^{70} +12.0213i q^{71} +(1.69870 - 2.47274i) q^{72} +6.15308i q^{73} -3.04331 q^{74} +(-7.99180 - 15.1860i) q^{75} -7.70835i q^{76} +(2.83205 - 1.72613i) q^{77} +(7.76421 - 4.08600i) q^{78} -2.49556i q^{79} +3.86104i q^{80} +(-3.22886 - 8.40086i) q^{81} +5.28064 q^{82} +3.53635 q^{83} +(-1.53276 + 0.806630i) q^{84} +10.4159i q^{85} -12.5717i q^{86} +(0.670690 + 1.27445i) q^{87} +(1.72613 + 2.83205i) q^{88} -7.35755i q^{89} +(9.54734 + 6.55874i) q^{90} -5.06552 q^{91} -3.49322i q^{92} +(7.41556 + 14.0910i) q^{93} -4.96439i q^{94} +29.7622 q^{95} +(-0.806630 - 1.53276i) q^{96} +12.0650 q^{97} +1.00000 q^{98} +(9.93507 + 0.542522i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 12q^{2} + 4q^{3} + 12q^{4} - 4q^{6} - 12q^{8} + O(q^{10}) \) \( 12q - 12q^{2} + 4q^{3} + 12q^{4} - 4q^{6} - 12q^{8} - 8q^{11} + 4q^{12} + 4q^{15} + 12q^{16} - 4q^{17} + 8q^{22} - 4q^{24} - 28q^{25} - 8q^{27} + 8q^{29} - 4q^{30} + 12q^{31} - 12q^{32} + 16q^{33} + 4q^{34} - 4q^{35} - 36q^{39} + 20q^{41} - 8q^{44} - 12q^{45} + 4q^{48} - 12q^{49} + 28q^{50} + 8q^{51} + 8q^{54} + 4q^{55} + 28q^{57} - 8q^{58} + 4q^{60} - 12q^{62} + 4q^{63} + 12q^{64} - 16q^{66} + 24q^{67} - 4q^{68} - 20q^{69} + 4q^{70} - 40q^{75} + 4q^{77} + 36q^{78} + 4q^{81} - 20q^{82} + 44q^{83} + 8q^{87} + 8q^{88} + 12q^{90} - 24q^{91} - 24q^{93} - 4q^{96} - 48q^{97} + 12q^{98} + 36q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.806630 + 1.53276i 0.465708 + 0.884938i
\(4\) 1.00000 0.500000
\(5\) 3.86104i 1.72671i 0.504597 + 0.863355i \(0.331641\pi\)
−0.504597 + 0.863355i \(0.668359\pi\)
\(6\) −0.806630 1.53276i −0.329305 0.625746i
\(7\) 1.00000i 0.377964i
\(8\) −1.00000 −0.353553
\(9\) −1.69870 + 2.47274i −0.566232 + 0.824246i
\(10\) 3.86104i 1.22097i
\(11\) −1.72613 2.83205i −0.520447 0.853894i
\(12\) 0.806630 + 1.53276i 0.232854 + 0.442469i
\(13\) 5.06552i 1.40492i 0.711722 + 0.702461i \(0.247915\pi\)
−0.711722 + 0.702461i \(0.752085\pi\)
\(14\) 1.00000i 0.267261i
\(15\) −5.91804 + 3.11443i −1.52803 + 0.804143i
\(16\) 1.00000 0.250000
\(17\) 2.69769 0.654287 0.327143 0.944975i \(-0.393914\pi\)
0.327143 + 0.944975i \(0.393914\pi\)
\(18\) 1.69870 2.47274i 0.400386 0.582830i
\(19\) 7.70835i 1.76842i −0.467093 0.884208i \(-0.654699\pi\)
0.467093 0.884208i \(-0.345301\pi\)
\(20\) 3.86104i 0.863355i
\(21\) −1.53276 + 0.806630i −0.334475 + 0.176021i
\(22\) 1.72613 + 2.83205i 0.368012 + 0.603794i
\(23\) 3.49322i 0.728386i −0.931323 0.364193i \(-0.881345\pi\)
0.931323 0.364193i \(-0.118655\pi\)
\(24\) −0.806630 1.53276i −0.164653 0.312873i
\(25\) −9.90764 −1.98153
\(26\) 5.06552i 0.993430i
\(27\) −5.16033 0.609106i −0.993106 0.117222i
\(28\) 1.00000i 0.188982i
\(29\) 0.831472 0.154400 0.0772002 0.997016i \(-0.475402\pi\)
0.0772002 + 0.997016i \(0.475402\pi\)
\(30\) 5.91804 3.11443i 1.08048 0.568615i
\(31\) 9.19326 1.65116 0.825579 0.564287i \(-0.190849\pi\)
0.825579 + 0.564287i \(0.190849\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.94849 4.93015i 0.513267 0.858229i
\(34\) −2.69769 −0.462651
\(35\) −3.86104 −0.652635
\(36\) −1.69870 + 2.47274i −0.283116 + 0.412123i
\(37\) 3.04331 0.500316 0.250158 0.968205i \(-0.419517\pi\)
0.250158 + 0.968205i \(0.419517\pi\)
\(38\) 7.70835i 1.25046i
\(39\) −7.76421 + 4.08600i −1.24327 + 0.654283i
\(40\) 3.86104i 0.610484i
\(41\) −5.28064 −0.824698 −0.412349 0.911026i \(-0.635292\pi\)
−0.412349 + 0.911026i \(0.635292\pi\)
\(42\) 1.53276 0.806630i 0.236510 0.124466i
\(43\) 12.5717i 1.91717i 0.284805 + 0.958586i \(0.408071\pi\)
−0.284805 + 0.958586i \(0.591929\pi\)
\(44\) −1.72613 2.83205i −0.260224 0.426947i
\(45\) −9.54734 6.55874i −1.42323 0.977719i
\(46\) 3.49322i 0.515047i
\(47\) 4.96439i 0.724131i 0.932153 + 0.362066i \(0.117928\pi\)
−0.932153 + 0.362066i \(0.882072\pi\)
\(48\) 0.806630 + 1.53276i 0.116427 + 0.221235i
\(49\) −1.00000 −0.142857
\(50\) 9.90764 1.40115
\(51\) 2.17604 + 4.13491i 0.304707 + 0.579004i
\(52\) 5.06552i 0.702461i
\(53\) 0.602608i 0.0827746i 0.999143 + 0.0413873i \(0.0131777\pi\)
−0.999143 + 0.0413873i \(0.986822\pi\)
\(54\) 5.16033 + 0.609106i 0.702232 + 0.0828888i
\(55\) 10.9346 6.66465i 1.47443 0.898662i
\(56\) 1.00000i 0.133631i
\(57\) 11.8150 6.21778i 1.56494 0.823566i
\(58\) −0.831472 −0.109178
\(59\) 0.161004i 0.0209609i −0.999945 0.0104804i \(-0.996664\pi\)
0.999945 0.0104804i \(-0.00333609\pi\)
\(60\) −5.91804 + 3.11443i −0.764016 + 0.402071i
\(61\) 4.61360i 0.590711i 0.955387 + 0.295355i \(0.0954381\pi\)
−0.955387 + 0.295355i \(0.904562\pi\)
\(62\) −9.19326 −1.16754
\(63\) −2.47274 1.69870i −0.311536 0.214016i
\(64\) 1.00000 0.125000
\(65\) −19.5582 −2.42589
\(66\) −2.94849 + 4.93015i −0.362935 + 0.606860i
\(67\) −4.22686 −0.516393 −0.258197 0.966092i \(-0.583128\pi\)
−0.258197 + 0.966092i \(0.583128\pi\)
\(68\) 2.69769 0.327143
\(69\) 5.35426 2.81774i 0.644577 0.339215i
\(70\) 3.86104 0.461483
\(71\) 12.0213i 1.42667i 0.700825 + 0.713333i \(0.252815\pi\)
−0.700825 + 0.713333i \(0.747185\pi\)
\(72\) 1.69870 2.47274i 0.200193 0.291415i
\(73\) 6.15308i 0.720163i 0.932921 + 0.360082i \(0.117251\pi\)
−0.932921 + 0.360082i \(0.882749\pi\)
\(74\) −3.04331 −0.353777
\(75\) −7.99180 15.1860i −0.922814 1.75353i
\(76\) 7.70835i 0.884208i
\(77\) 2.83205 1.72613i 0.322742 0.196711i
\(78\) 7.76421 4.08600i 0.879124 0.462648i
\(79\) 2.49556i 0.280773i −0.990097 0.140386i \(-0.955166\pi\)
0.990097 0.140386i \(-0.0448345\pi\)
\(80\) 3.86104i 0.431678i
\(81\) −3.22886 8.40086i −0.358763 0.933429i
\(82\) 5.28064 0.583150
\(83\) 3.53635 0.388165 0.194082 0.980985i \(-0.437827\pi\)
0.194082 + 0.980985i \(0.437827\pi\)
\(84\) −1.53276 + 0.806630i −0.167238 + 0.0880106i
\(85\) 10.4159i 1.12976i
\(86\) 12.5717i 1.35564i
\(87\) 0.670690 + 1.27445i 0.0719055 + 0.136635i
\(88\) 1.72613 + 2.83205i 0.184006 + 0.301897i
\(89\) 7.35755i 0.779899i −0.920836 0.389950i \(-0.872492\pi\)
0.920836 0.389950i \(-0.127508\pi\)
\(90\) 9.54734 + 6.55874i 1.00638 + 0.691351i
\(91\) −5.06552 −0.531010
\(92\) 3.49322i 0.364193i
\(93\) 7.41556 + 14.0910i 0.768957 + 1.46117i
\(94\) 4.96439i 0.512038i
\(95\) 29.7622 3.05354
\(96\) −0.806630 1.53276i −0.0823263 0.156436i
\(97\) 12.0650 1.22501 0.612505 0.790467i \(-0.290162\pi\)
0.612505 + 0.790467i \(0.290162\pi\)
\(98\) 1.00000 0.101015
\(99\) 9.93507 + 0.542522i 0.998512 + 0.0545255i
\(100\) −9.90764 −0.990764
\(101\) 10.4799 1.04279 0.521396 0.853315i \(-0.325411\pi\)
0.521396 + 0.853315i \(0.325411\pi\)
\(102\) −2.17604 4.13491i −0.215460 0.409417i
\(103\) −4.76959 −0.469961 −0.234981 0.972000i \(-0.575503\pi\)
−0.234981 + 0.972000i \(0.575503\pi\)
\(104\) 5.06552i 0.496715i
\(105\) −3.11443 5.91804i −0.303937 0.577542i
\(106\) 0.602608i 0.0585305i
\(107\) 5.70706 0.551722 0.275861 0.961198i \(-0.411037\pi\)
0.275861 + 0.961198i \(0.411037\pi\)
\(108\) −5.16033 0.609106i −0.496553 0.0586112i
\(109\) 0.152695i 0.0146255i −0.999973 0.00731277i \(-0.997672\pi\)
0.999973 0.00731277i \(-0.00232775\pi\)
\(110\) −10.9346 + 6.66465i −1.04258 + 0.635450i
\(111\) 2.45482 + 4.66465i 0.233001 + 0.442749i
\(112\) 1.00000i 0.0944911i
\(113\) 5.39852i 0.507850i −0.967224 0.253925i \(-0.918278\pi\)
0.967224 0.253925i \(-0.0817216\pi\)
\(114\) −11.8150 + 6.21778i −1.10658 + 0.582349i
\(115\) 13.4875 1.25771
\(116\) 0.831472 0.0772002
\(117\) −12.5257 8.60477i −1.15800 0.795512i
\(118\) 0.161004i 0.0148216i
\(119\) 2.69769i 0.247297i
\(120\) 5.91804 3.11443i 0.540241 0.284307i
\(121\) −5.04096 + 9.77695i −0.458269 + 0.888813i
\(122\) 4.61360i 0.417696i
\(123\) −4.25953 8.09395i −0.384069 0.729807i
\(124\) 9.19326 0.825579
\(125\) 18.9486i 1.69481i
\(126\) 2.47274 + 1.69870i 0.220289 + 0.151332i
\(127\) 14.2439i 1.26394i −0.774993 0.631970i \(-0.782246\pi\)
0.774993 0.631970i \(-0.217754\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −19.2694 + 10.1407i −1.69658 + 0.892842i
\(130\) 19.5582 1.71536
\(131\) 17.0775 1.49207 0.746034 0.665908i \(-0.231956\pi\)
0.746034 + 0.665908i \(0.231956\pi\)
\(132\) 2.94849 4.93015i 0.256633 0.429115i
\(133\) 7.70835 0.668398
\(134\) 4.22686 0.365145
\(135\) 2.35178 19.9242i 0.202409 1.71481i
\(136\) −2.69769 −0.231325
\(137\) 10.9911i 0.939035i −0.882923 0.469518i \(-0.844428\pi\)
0.882923 0.469518i \(-0.155572\pi\)
\(138\) −5.35426 + 2.81774i −0.455785 + 0.239862i
\(139\) 8.67348i 0.735675i 0.929890 + 0.367837i \(0.119902\pi\)
−0.929890 + 0.367837i \(0.880098\pi\)
\(140\) −3.86104 −0.326318
\(141\) −7.60921 + 4.00443i −0.640811 + 0.337234i
\(142\) 12.0213i 1.00881i
\(143\) 14.3458 8.74373i 1.19965 0.731188i
\(144\) −1.69870 + 2.47274i −0.141558 + 0.206061i
\(145\) 3.21035i 0.266605i
\(146\) 6.15308i 0.509232i
\(147\) −0.806630 1.53276i −0.0665297 0.126420i
\(148\) 3.04331 0.250158
\(149\) −3.59764 −0.294730 −0.147365 0.989082i \(-0.547079\pi\)
−0.147365 + 0.989082i \(0.547079\pi\)
\(150\) 7.99180 + 15.1860i 0.652528 + 1.23993i
\(151\) 17.5295i 1.42653i −0.700892 0.713267i \(-0.747215\pi\)
0.700892 0.713267i \(-0.252785\pi\)
\(152\) 7.70835i 0.625229i
\(153\) −4.58256 + 6.67069i −0.370478 + 0.539293i
\(154\) −2.83205 + 1.72613i −0.228213 + 0.139095i
\(155\) 35.4955i 2.85107i
\(156\) −7.76421 + 4.08600i −0.621635 + 0.327142i
\(157\) −7.25956 −0.579376 −0.289688 0.957121i \(-0.593551\pi\)
−0.289688 + 0.957121i \(0.593551\pi\)
\(158\) 2.49556i 0.198536i
\(159\) −0.923652 + 0.486082i −0.0732504 + 0.0385488i
\(160\) 3.86104i 0.305242i
\(161\) 3.49322 0.275304
\(162\) 3.22886 + 8.40086i 0.253683 + 0.660034i
\(163\) 15.4886 1.21316 0.606580 0.795023i \(-0.292541\pi\)
0.606580 + 0.795023i \(0.292541\pi\)
\(164\) −5.28064 −0.412349
\(165\) 19.0355 + 11.3843i 1.48191 + 0.886263i
\(166\) −3.53635 −0.274474
\(167\) −3.94198 −0.305040 −0.152520 0.988300i \(-0.548739\pi\)
−0.152520 + 0.988300i \(0.548739\pi\)
\(168\) 1.53276 0.806630i 0.118255 0.0622329i
\(169\) −12.6595 −0.973804
\(170\) 10.4159i 0.798864i
\(171\) 19.0607 + 13.0941i 1.45761 + 1.00133i
\(172\) 12.5717i 0.958586i
\(173\) −5.16603 −0.392766 −0.196383 0.980527i \(-0.562920\pi\)
−0.196383 + 0.980527i \(0.562920\pi\)
\(174\) −0.670690 1.27445i −0.0508449 0.0966155i
\(175\) 9.90764i 0.748947i
\(176\) −1.72613 2.83205i −0.130112 0.213473i
\(177\) 0.246779 0.129870i 0.0185491 0.00976165i
\(178\) 7.35755i 0.551472i
\(179\) 5.01937i 0.375166i 0.982249 + 0.187583i \(0.0600653\pi\)
−0.982249 + 0.187583i \(0.939935\pi\)
\(180\) −9.54734 6.55874i −0.711617 0.488859i
\(181\) −9.50810 −0.706732 −0.353366 0.935485i \(-0.614963\pi\)
−0.353366 + 0.935485i \(0.614963\pi\)
\(182\) 5.06552 0.375481
\(183\) −7.07153 + 3.72147i −0.522743 + 0.275099i
\(184\) 3.49322i 0.257524i
\(185\) 11.7503i 0.863901i
\(186\) −7.41556 14.0910i −0.543735 1.03321i
\(187\) −4.65657 7.63999i −0.340522 0.558692i
\(188\) 4.96439i 0.362066i
\(189\) 0.609106 5.16033i 0.0443059 0.375359i
\(190\) −29.7622 −2.15918
\(191\) 8.73096i 0.631750i −0.948801 0.315875i \(-0.897702\pi\)
0.948801 0.315875i \(-0.102298\pi\)
\(192\) 0.806630 + 1.53276i 0.0582135 + 0.110617i
\(193\) 11.2644i 0.810830i 0.914133 + 0.405415i \(0.132873\pi\)
−0.914133 + 0.405415i \(0.867127\pi\)
\(194\) −12.0650 −0.866213
\(195\) −15.7762 29.9779i −1.12976 2.14677i
\(196\) −1.00000 −0.0714286
\(197\) 26.1013 1.85964 0.929820 0.368016i \(-0.119963\pi\)
0.929820 + 0.368016i \(0.119963\pi\)
\(198\) −9.93507 0.542522i −0.706055 0.0385553i
\(199\) −20.1620 −1.42925 −0.714625 0.699508i \(-0.753402\pi\)
−0.714625 + 0.699508i \(0.753402\pi\)
\(200\) 9.90764 0.700576
\(201\) −3.40951 6.47875i −0.240488 0.456976i
\(202\) −10.4799 −0.737366
\(203\) 0.831472i 0.0583579i
\(204\) 2.17604 + 4.13491i 0.152353 + 0.289502i
\(205\) 20.3888i 1.42401i
\(206\) 4.76959 0.332313
\(207\) 8.63781 + 5.93392i 0.600370 + 0.412436i
\(208\) 5.06552i 0.351230i
\(209\) −21.8304 + 13.3056i −1.51004 + 0.920367i
\(210\) 3.11443 + 5.91804i 0.214916 + 0.408384i
\(211\) 20.1922i 1.39009i 0.718968 + 0.695043i \(0.244615\pi\)
−0.718968 + 0.695043i \(0.755385\pi\)
\(212\) 0.602608i 0.0413873i
\(213\) −18.4258 + 9.69674i −1.26251 + 0.664410i
\(214\) −5.70706 −0.390126
\(215\) −48.5400 −3.31040
\(216\) 5.16033 + 0.609106i 0.351116 + 0.0414444i
\(217\) 9.19326i 0.624079i
\(218\) 0.152695i 0.0103418i
\(219\) −9.43118 + 4.96326i −0.637300 + 0.335386i
\(220\) 10.9346 6.66465i 0.737214 0.449331i
\(221\) 13.6652i 0.919222i
\(222\) −2.45482 4.66465i −0.164757 0.313071i
\(223\) −0.163853 −0.0109724 −0.00548620 0.999985i \(-0.501746\pi\)
−0.00548620 + 0.999985i \(0.501746\pi\)
\(224\) 1.00000i 0.0668153i
\(225\) 16.8301 24.4990i 1.12200 1.63327i
\(226\) 5.39852i 0.359104i
\(227\) 9.14938 0.607266 0.303633 0.952789i \(-0.401800\pi\)
0.303633 + 0.952789i \(0.401800\pi\)
\(228\) 11.8150 6.21778i 0.782470 0.411783i
\(229\) 9.97390 0.659094 0.329547 0.944139i \(-0.393104\pi\)
0.329547 + 0.944139i \(0.393104\pi\)
\(230\) −13.4875 −0.889337
\(231\) 4.93015 + 2.94849i 0.324380 + 0.193997i
\(232\) −0.831472 −0.0545888
\(233\) −2.49984 −0.163770 −0.0818849 0.996642i \(-0.526094\pi\)
−0.0818849 + 0.996642i \(0.526094\pi\)
\(234\) 12.5257 + 8.60477i 0.818830 + 0.562512i
\(235\) −19.1677 −1.25036
\(236\) 0.161004i 0.0104804i
\(237\) 3.82509 2.01300i 0.248467 0.130758i
\(238\) 2.69769i 0.174866i
\(239\) 8.25748 0.534132 0.267066 0.963678i \(-0.413946\pi\)
0.267066 + 0.963678i \(0.413946\pi\)
\(240\) −5.91804 + 3.11443i −0.382008 + 0.201036i
\(241\) 15.0943i 0.972309i −0.873873 0.486155i \(-0.838399\pi\)
0.873873 0.486155i \(-0.161601\pi\)
\(242\) 5.04096 9.77695i 0.324045 0.628486i
\(243\) 10.2720 11.7255i 0.658948 0.752188i
\(244\) 4.61360i 0.295355i
\(245\) 3.86104i 0.246673i
\(246\) 4.25953 + 8.09395i 0.271577 + 0.516051i
\(247\) 39.0468 2.48449
\(248\) −9.19326 −0.583772
\(249\) 2.85253 + 5.42037i 0.180772 + 0.343502i
\(250\) 18.9486i 1.19841i
\(251\) 13.7304i 0.866655i 0.901237 + 0.433327i \(0.142661\pi\)
−0.901237 + 0.433327i \(0.857339\pi\)
\(252\) −2.47274 1.69870i −0.155768 0.107008i
\(253\) −9.89295 + 6.02974i −0.621965 + 0.379087i
\(254\) 14.2439i 0.893741i
\(255\) −15.9651 + 8.40178i −0.999771 + 0.526140i
\(256\) 1.00000 0.0625000
\(257\) 5.93347i 0.370120i 0.982727 + 0.185060i \(0.0592479\pi\)
−0.982727 + 0.185060i \(0.940752\pi\)
\(258\) 19.2694 10.1407i 1.19966 0.631335i
\(259\) 3.04331i 0.189102i
\(260\) −19.5582 −1.21295
\(261\) −1.41242 + 2.05601i −0.0874265 + 0.127264i
\(262\) −17.0775 −1.05505
\(263\) −20.1194 −1.24062 −0.620308 0.784359i \(-0.712992\pi\)
−0.620308 + 0.784359i \(0.712992\pi\)
\(264\) −2.94849 + 4.93015i −0.181467 + 0.303430i
\(265\) −2.32669 −0.142928
\(266\) −7.70835 −0.472629
\(267\) 11.2774 5.93482i 0.690163 0.363205i
\(268\) −4.22686 −0.258197
\(269\) 23.5034i 1.43303i 0.697571 + 0.716515i \(0.254264\pi\)
−0.697571 + 0.716515i \(0.745736\pi\)
\(270\) −2.35178 + 19.9242i −0.143125 + 1.21255i
\(271\) 30.2007i 1.83456i −0.398243 0.917280i \(-0.630380\pi\)
0.398243 0.917280i \(-0.369620\pi\)
\(272\) 2.69769 0.163572
\(273\) −4.08600 7.76421i −0.247296 0.469912i
\(274\) 10.9911i 0.663998i
\(275\) 17.1019 + 28.0589i 1.03128 + 1.69201i
\(276\) 5.35426 2.81774i 0.322289 0.169608i
\(277\) 3.10788i 0.186735i −0.995632 0.0933673i \(-0.970237\pi\)
0.995632 0.0933673i \(-0.0297631\pi\)
\(278\) 8.67348i 0.520201i
\(279\) −15.6165 + 22.7325i −0.934938 + 1.36096i
\(280\) 3.86104 0.230741
\(281\) −1.17009 −0.0698016 −0.0349008 0.999391i \(-0.511112\pi\)
−0.0349008 + 0.999391i \(0.511112\pi\)
\(282\) 7.60921 4.00443i 0.453122 0.238460i
\(283\) 32.3497i 1.92299i −0.274826 0.961494i \(-0.588620\pi\)
0.274826 0.961494i \(-0.411380\pi\)
\(284\) 12.0213i 0.713333i
\(285\) 24.0071 + 45.6183i 1.42206 + 2.70220i
\(286\) −14.3458 + 8.74373i −0.848283 + 0.517028i
\(287\) 5.28064i 0.311707i
\(288\) 1.69870 2.47274i 0.100097 0.145707i
\(289\) −9.72245 −0.571909
\(290\) 3.21035i 0.188518i
\(291\) 9.73195 + 18.4927i 0.570497 + 1.08406i
\(292\) 6.15308i 0.360082i
\(293\) 10.6481 0.622070 0.311035 0.950398i \(-0.399324\pi\)
0.311035 + 0.950398i \(0.399324\pi\)
\(294\) 0.806630 + 1.53276i 0.0470436 + 0.0893923i
\(295\) 0.621641 0.0361934
\(296\) −3.04331 −0.176889
\(297\) 7.18237 + 15.6657i 0.416764 + 0.909015i
\(298\) 3.59764 0.208405
\(299\) 17.6950 1.02333
\(300\) −7.99180 15.1860i −0.461407 0.876765i
\(301\) −12.5717 −0.724623
\(302\) 17.5295i 1.00871i
\(303\) 8.45343 + 16.0632i 0.485637 + 0.922807i
\(304\) 7.70835i 0.442104i
\(305\) −17.8133 −1.01999
\(306\) 4.58256 6.67069i 0.261968 0.381338i
\(307\) 14.4447i 0.824401i −0.911093 0.412200i \(-0.864760\pi\)
0.911093 0.412200i \(-0.135240\pi\)
\(308\) 2.83205 1.72613i 0.161371 0.0983553i
\(309\) −3.84729 7.31063i −0.218865 0.415887i
\(310\) 35.4955i 2.01601i
\(311\) 27.8091i 1.57691i −0.615094 0.788454i \(-0.710882\pi\)
0.615094 0.788454i \(-0.289118\pi\)
\(312\) 7.76421 4.08600i 0.439562 0.231324i
\(313\) 14.5554 0.822719 0.411359 0.911473i \(-0.365054\pi\)
0.411359 + 0.911473i \(0.365054\pi\)
\(314\) 7.25956 0.409681
\(315\) 6.55874 9.54734i 0.369543 0.537932i
\(316\) 2.49556i 0.140386i
\(317\) 1.42646i 0.0801177i 0.999197 + 0.0400589i \(0.0127545\pi\)
−0.999197 + 0.0400589i \(0.987245\pi\)
\(318\) 0.923652 0.486082i 0.0517959 0.0272581i
\(319\) −1.43523 2.35477i −0.0803573 0.131842i
\(320\) 3.86104i 0.215839i
\(321\) 4.60348 + 8.74754i 0.256941 + 0.488240i
\(322\) −3.49322 −0.194669
\(323\) 20.7948i 1.15705i
\(324\) −3.22886 8.40086i −0.179381 0.466714i
\(325\) 50.1873i 2.78389i
\(326\) −15.4886 −0.857833
\(327\) 0.234045 0.123169i 0.0129427 0.00681123i
\(328\) 5.28064 0.291575
\(329\) −4.96439 −0.273696
\(330\) −19.0355 11.3843i −1.04787 0.626683i
\(331\) 7.00503 0.385031 0.192516 0.981294i \(-0.438335\pi\)
0.192516 + 0.981294i \(0.438335\pi\)
\(332\) 3.53635 0.194082
\(333\) −5.16965 + 7.52530i −0.283295 + 0.412384i
\(334\) 3.94198 0.215696
\(335\) 16.3201i 0.891661i
\(336\) −1.53276 + 0.806630i −0.0836188 + 0.0440053i
\(337\) 15.1925i 0.827589i 0.910370 + 0.413795i \(0.135797\pi\)
−0.910370 + 0.413795i \(0.864203\pi\)
\(338\) 12.6595 0.688584
\(339\) 8.27462 4.35460i 0.449416 0.236510i
\(340\) 10.4159i 0.564882i
\(341\) −15.8687 26.0357i −0.859340 1.40991i
\(342\) −19.0607 13.0941i −1.03069 0.708050i
\(343\) 1.00000i 0.0539949i
\(344\) 12.5717i 0.677822i
\(345\) 10.8794 + 20.6730i 0.585727 + 1.11300i
\(346\) 5.16603 0.277728
\(347\) 17.4151 0.934893 0.467446 0.884021i \(-0.345174\pi\)
0.467446 + 0.884021i \(0.345174\pi\)
\(348\) 0.670690 + 1.27445i 0.0359528 + 0.0683174i
\(349\) 12.0560i 0.645341i 0.946511 + 0.322670i \(0.104581\pi\)
−0.946511 + 0.322670i \(0.895419\pi\)
\(350\) 9.90764i 0.529586i
\(351\) 3.08544 26.1397i 0.164688 1.39524i
\(352\) 1.72613 + 2.83205i 0.0920029 + 0.150949i
\(353\) 23.4434i 1.24776i −0.781518 0.623882i \(-0.785555\pi\)
0.781518 0.623882i \(-0.214445\pi\)
\(354\) −0.246779 + 0.129870i −0.0131162 + 0.00690253i
\(355\) −46.4148 −2.46344
\(356\) 7.35755i 0.389950i
\(357\) −4.13491 + 2.17604i −0.218843 + 0.115168i
\(358\) 5.01937i 0.265282i
\(359\) 5.26816 0.278043 0.139021 0.990289i \(-0.455604\pi\)
0.139021 + 0.990289i \(0.455604\pi\)
\(360\) 9.54734 + 6.55874i 0.503189 + 0.345676i
\(361\) −40.4186 −2.12729
\(362\) 9.50810 0.499735
\(363\) −19.0519 + 0.159802i −0.999965 + 0.00838745i
\(364\) −5.06552 −0.265505
\(365\) −23.7573 −1.24351
\(366\) 7.07153 3.72147i 0.369635 0.194524i
\(367\) 19.4642 1.01602 0.508012 0.861350i \(-0.330380\pi\)
0.508012 + 0.861350i \(0.330380\pi\)
\(368\) 3.49322i 0.182097i
\(369\) 8.97021 13.0576i 0.466970 0.679754i
\(370\) 11.7503i 0.610871i
\(371\) −0.602608 −0.0312858
\(372\) 7.41556 + 14.0910i 0.384479 + 0.730586i
\(373\) 5.38807i 0.278984i 0.990223 + 0.139492i \(0.0445469\pi\)
−0.990223 + 0.139492i \(0.955453\pi\)
\(374\) 4.65657 + 7.63999i 0.240785 + 0.395055i
\(375\) 29.0436 15.2845i 1.49981 0.789289i
\(376\) 4.96439i 0.256019i
\(377\) 4.21183i 0.216921i
\(378\) −0.609106 + 5.16033i −0.0313290 + 0.265419i
\(379\) −8.29732 −0.426205 −0.213102 0.977030i \(-0.568357\pi\)
−0.213102 + 0.977030i \(0.568357\pi\)
\(380\) 29.7622 1.52677
\(381\) 21.8324 11.4895i 1.11851 0.588627i
\(382\) 8.73096i 0.446715i
\(383\) 27.2636i 1.39311i 0.717506 + 0.696553i \(0.245284\pi\)
−0.717506 + 0.696553i \(0.754716\pi\)
\(384\) −0.806630 1.53276i −0.0411632 0.0782182i
\(385\) 6.66465 + 10.9346i 0.339662 + 0.557281i
\(386\) 11.2644i 0.573343i
\(387\) −31.0866 21.3555i −1.58022 1.08556i
\(388\) 12.0650 0.612505
\(389\) 26.4139i 1.33924i −0.742705 0.669619i \(-0.766457\pi\)
0.742705 0.669619i \(-0.233543\pi\)
\(390\) 15.7762 + 29.9779i 0.798859 + 1.51799i
\(391\) 9.42364i 0.476574i
\(392\) 1.00000 0.0505076
\(393\) 13.7752 + 26.1757i 0.694868 + 1.32039i
\(394\) −26.1013 −1.31496
\(395\) 9.63547 0.484813
\(396\) 9.93507 + 0.542522i 0.499256 + 0.0272627i
\(397\) 2.10425 0.105609 0.0528047 0.998605i \(-0.483184\pi\)
0.0528047 + 0.998605i \(0.483184\pi\)
\(398\) 20.1620 1.01063
\(399\) 6.21778 + 11.8150i 0.311279 + 0.591491i
\(400\) −9.90764 −0.495382
\(401\) 18.9795i 0.947793i −0.880581 0.473896i \(-0.842847\pi\)
0.880581 0.473896i \(-0.157153\pi\)
\(402\) 3.40951 + 6.47875i 0.170051 + 0.323131i
\(403\) 46.5686i 2.31975i
\(404\) 10.4799 0.521396
\(405\) 32.4361 12.4668i 1.61176 0.619479i
\(406\) 0.831472i 0.0412653i
\(407\) −5.25314 8.61878i −0.260388 0.427217i
\(408\) −2.17604 4.13491i −0.107730 0.204709i
\(409\) 5.10349i 0.252352i 0.992008 + 0.126176i \(0.0402703\pi\)
−0.992008 + 0.126176i \(0.959730\pi\)
\(410\) 20.3888i 1.00693i
\(411\) 16.8467 8.86577i 0.830988 0.437316i
\(412\) −4.76959 −0.234981
\(413\) 0.161004 0.00792246
\(414\) −8.63781 5.93392i −0.424525 0.291636i
\(415\) 13.6540i 0.670248i
\(416\) 5.06552i 0.248357i
\(417\) −13.2943 + 6.99629i −0.651027 + 0.342610i
\(418\) 21.8304 13.3056i 1.06776 0.650798i
\(419\) 6.15406i 0.300645i −0.988637 0.150323i \(-0.951969\pi\)
0.988637 0.150323i \(-0.0480313\pi\)
\(420\) −3.11443 5.91804i −0.151969 0.288771i
\(421\) 18.8837 0.920334 0.460167 0.887832i \(-0.347790\pi\)
0.460167 + 0.887832i \(0.347790\pi\)
\(422\) 20.1922i 0.982940i
\(423\) −12.2756 8.43299i −0.596862 0.410026i
\(424\) 0.602608i 0.0292652i
\(425\) −26.7278 −1.29649
\(426\) 18.4258 9.69674i 0.892731 0.469809i
\(427\) −4.61360 −0.223268
\(428\) 5.70706 0.275861
\(429\) 24.9738 + 14.9356i 1.20574 + 0.721100i
\(430\) 48.5400 2.34081
\(431\) −4.81981 −0.232162 −0.116081 0.993240i \(-0.537033\pi\)
−0.116081 + 0.993240i \(0.537033\pi\)
\(432\) −5.16033 0.609106i −0.248276 0.0293056i
\(433\) −18.0162 −0.865802 −0.432901 0.901441i \(-0.642510\pi\)
−0.432901 + 0.901441i \(0.642510\pi\)
\(434\) 9.19326i 0.441290i
\(435\) −4.92069 + 2.58956i −0.235929 + 0.124160i
\(436\) 0.152695i 0.00731277i
\(437\) −26.9269 −1.28809
\(438\) 9.43118 4.96326i 0.450639 0.237154i
\(439\) 10.9524i 0.522729i −0.965240 0.261364i \(-0.915828\pi\)
0.965240 0.261364i \(-0.0841724\pi\)
\(440\) −10.9346 + 6.66465i −0.521289 + 0.317725i
\(441\) 1.69870 2.47274i 0.0808903 0.117749i
\(442\) 13.6652i 0.649988i
\(443\) 3.51803i 0.167147i 0.996502 + 0.0835734i \(0.0266333\pi\)
−0.996502 + 0.0835734i \(0.973367\pi\)
\(444\) 2.45482 + 4.66465i 0.116501 + 0.221375i
\(445\) 28.4078 1.34666
\(446\) 0.163853 0.00775866
\(447\) −2.90196 5.51431i −0.137258 0.260818i
\(448\) 1.00000i 0.0472456i
\(449\) 10.5334i 0.497102i 0.968619 + 0.248551i \(0.0799543\pi\)
−0.968619 + 0.248551i \(0.920046\pi\)
\(450\) −16.8301 + 24.4990i −0.793377 + 1.15489i
\(451\) 9.11507 + 14.9550i 0.429212 + 0.704205i
\(452\) 5.39852i 0.253925i
\(453\) 26.8686 14.1399i 1.26240 0.664349i
\(454\) −9.14938 −0.429402
\(455\) 19.5582i 0.916901i
\(456\) −11.8150 + 6.21778i −0.553290 + 0.291174i
\(457\) 3.05021i 0.142683i −0.997452 0.0713414i \(-0.977272\pi\)
0.997452 0.0713414i \(-0.0227280\pi\)
\(458\) −9.97390 −0.466050
\(459\) −13.9210 1.64318i −0.649776 0.0766971i
\(460\) 13.4875 0.628856
\(461\) 41.6488 1.93978 0.969888 0.243551i \(-0.0783122\pi\)
0.969888 + 0.243551i \(0.0783122\pi\)
\(462\) −4.93015 2.94849i −0.229371 0.137176i
\(463\) −1.06374 −0.0494362 −0.0247181 0.999694i \(-0.507869\pi\)
−0.0247181 + 0.999694i \(0.507869\pi\)
\(464\) 0.831472 0.0386001
\(465\) −54.4061 + 28.6318i −2.52302 + 1.32777i
\(466\) 2.49984 0.115803
\(467\) 19.4950i 0.902121i −0.892493 0.451060i \(-0.851046\pi\)
0.892493 0.451060i \(-0.148954\pi\)
\(468\) −12.5257 8.60477i −0.579000 0.397756i
\(469\) 4.22686i 0.195178i
\(470\) 19.1677 0.884141
\(471\) −5.85578 11.1271i −0.269820 0.512712i
\(472\) 0.161004i 0.00741079i
\(473\) 35.6037 21.7004i 1.63706 0.997786i
\(474\) −3.82509 + 2.01300i −0.175692 + 0.0924600i
\(475\) 76.3715i 3.50417i
\(476\) 2.69769i 0.123649i
\(477\) −1.49009 1.02365i −0.0682266 0.0468696i
\(478\) −8.25748 −0.377689
\(479\) −7.07807 −0.323405 −0.161703 0.986840i \(-0.551699\pi\)
−0.161703 + 0.986840i \(0.551699\pi\)
\(480\) 5.91804 3.11443i 0.270120 0.142154i
\(481\) 15.4159i 0.702905i
\(482\) 15.0943i 0.687527i
\(483\) 2.81774 + 5.35426i 0.128211 + 0.243627i
\(484\) −5.04096 + 9.77695i −0.229135 + 0.444407i
\(485\) 46.5833i 2.11524i
\(486\) −10.2720 + 11.7255i −0.465947 + 0.531877i
\(487\) 30.7305 1.39253 0.696266 0.717784i \(-0.254843\pi\)
0.696266 + 0.717784i \(0.254843\pi\)
\(488\) 4.61360i 0.208848i
\(489\) 12.4936 + 23.7403i 0.564978 + 1.07357i
\(490\) 3.86104i 0.174424i
\(491\) −12.6920 −0.572781 −0.286391 0.958113i \(-0.592456\pi\)
−0.286391 + 0.958113i \(0.592456\pi\)
\(492\) −4.25953 8.09395i −0.192034 0.364903i
\(493\) 2.24306 0.101022
\(494\) −39.0468 −1.75680
\(495\) −2.09470 + 38.3597i −0.0941497 + 1.72414i
\(496\) 9.19326 0.412789
\(497\) −12.0213 −0.539229
\(498\) −2.85253 5.42037i −0.127825 0.242893i
\(499\) −25.1145 −1.12428 −0.562140 0.827042i \(-0.690022\pi\)
−0.562140 + 0.827042i \(0.690022\pi\)
\(500\) 18.9486i 0.847407i
\(501\) −3.17972 6.04211i −0.142060 0.269942i
\(502\) 13.7304i 0.612817i
\(503\) 2.25842 0.100698 0.0503489 0.998732i \(-0.483967\pi\)
0.0503489 + 0.998732i \(0.483967\pi\)
\(504\) 2.47274 + 1.69870i 0.110144 + 0.0756659i
\(505\) 40.4635i 1.80060i
\(506\) 9.89295 6.02974i 0.439795 0.268055i
\(507\) −10.2115 19.4039i −0.453509 0.861757i
\(508\) 14.2439i 0.631970i
\(509\) 38.1220i 1.68973i 0.534982 + 0.844863i \(0.320318\pi\)
−0.534982 + 0.844863i \(0.679682\pi\)
\(510\) 15.9651 8.40178i 0.706945 0.372037i
\(511\) −6.15308 −0.272196
\(512\) −1.00000 −0.0441942
\(513\) −4.69520 + 39.7776i −0.207298 + 1.75622i
\(514\) 5.93347i 0.261714i
\(515\) 18.4156i 0.811487i
\(516\) −19.2694 + 10.1407i −0.848289 + 0.446421i
\(517\) 14.0594 8.56918i 0.618331 0.376872i
\(518\) 3.04331i 0.133715i
\(519\) −4.16708 7.91828i −0.182914 0.347574i
\(520\) 19.5582 0.857682
\(521\) 28.2110i 1.23595i −0.786199 0.617974i \(-0.787954\pi\)
0.786199 0.617974i \(-0.212046\pi\)
\(522\) 1.41242 2.05601i 0.0618198 0.0899892i
\(523\) 0.946140i 0.0413718i 0.999786 + 0.0206859i \(0.00658500\pi\)
−0.999786 + 0.0206859i \(0.993415\pi\)
\(524\) 17.0775 0.746034
\(525\) 15.1860 7.99180i 0.662772 0.348791i
\(526\) 20.1194 0.877248
\(527\) 24.8006 1.08033
\(528\) 2.94849 4.93015i 0.128317 0.214557i
\(529\) 10.7974 0.469453
\(530\) 2.32669 0.101065
\(531\) 0.398119 + 0.273496i 0.0172769 + 0.0118687i
\(532\) 7.70835 0.334199
\(533\) 26.7492i 1.15864i
\(534\) −11.2774 + 5.93482i −0.488019 + 0.256825i
\(535\) 22.0352i 0.952664i
\(536\) 4.22686 0.182573
\(537\) −7.69349 + 4.04878i −0.331998 + 0.174718i
\(538\) 23.5034i 1.01331i
\(539\) 1.72613 + 2.83205i 0.0743496 + 0.121985i
\(540\) 2.35178 19.9242i 0.101205 0.857403i
\(541\) 13.1089i 0.563597i −0.959474 0.281799i \(-0.909069\pi\)
0.959474 0.281799i \(-0.0909310\pi\)
\(542\) 30.2007i 1.29723i
\(543\) −7.66952 14.5736i −0.329131 0.625414i
\(544\) −2.69769 −0.115663
\(545\) 0.589562 0.0252541
\(546\) 4.08600 + 7.76421i 0.174865 + 0.332278i
\(547\) 18.6449i 0.797198i −0.917125 0.398599i \(-0.869497\pi\)
0.917125 0.398599i \(-0.130503\pi\)
\(548\) 10.9911i 0.469518i
\(549\) −11.4082 7.83710i −0.486891 0.334479i
\(550\) −17.1019 28.0589i −0.729226 1.19643i
\(551\) 6.40927i 0.273044i
\(552\) −5.35426 + 2.81774i −0.227892 + 0.119931i
\(553\) 2.49556 0.106122
\(554\) 3.10788i 0.132041i
\(555\) −18.0104 + 9.47817i −0.764500 + 0.402326i
\(556\) 8.67348i 0.367837i
\(557\) −32.6578 −1.38376 −0.691878 0.722015i \(-0.743216\pi\)
−0.691878 + 0.722015i \(0.743216\pi\)
\(558\) 15.6165 22.7325i 0.661101 0.962344i
\(559\) −63.6823 −2.69347
\(560\) −3.86104 −0.163159
\(561\) 7.95414 13.3000i 0.335824 0.561528i
\(562\) 1.17009 0.0493572
\(563\) −42.8575 −1.80623 −0.903114 0.429400i \(-0.858725\pi\)
−0.903114 + 0.429400i \(0.858725\pi\)
\(564\) −7.60921 + 4.00443i −0.320406 + 0.168617i
\(565\) 20.8439 0.876909
\(566\) 32.3497i 1.35976i
\(567\) 8.40086 3.22886i 0.352803 0.135600i
\(568\) 12.0213i 0.504403i
\(569\) −9.63357 −0.403860 −0.201930 0.979400i \(-0.564721\pi\)
−0.201930 + 0.979400i \(0.564721\pi\)
\(570\) −24.0071 45.6183i −1.00555 1.91074i
\(571\) 10.6965i 0.447634i 0.974631 + 0.223817i \(0.0718518\pi\)
−0.974631 + 0.223817i \(0.928148\pi\)
\(572\) 14.3458 8.74373i 0.599827 0.365594i
\(573\) 13.3824 7.04265i 0.559060 0.294211i
\(574\) 5.28064i 0.220410i
\(575\) 34.6096i 1.44332i
\(576\) −1.69870 + 2.47274i −0.0707790 + 0.103031i
\(577\) −30.7639 −1.28072 −0.640359 0.768076i \(-0.721214\pi\)
−0.640359 + 0.768076i \(0.721214\pi\)
\(578\) 9.72245 0.404400
\(579\) −17.2656 + 9.08621i −0.717535 + 0.377610i
\(580\) 3.21035i 0.133302i
\(581\) 3.53635i 0.146713i
\(582\) −9.73195 18.4927i −0.403402 0.766545i
\(583\) 1.70661 1.04018i 0.0706807 0.0430798i
\(584\) 6.15308i 0.254616i
\(585\) 33.2234 48.3622i 1.37362 1.99953i
\(586\) −10.6481 −0.439870
\(587\) 4.00060i 0.165122i −0.996586 0.0825612i \(-0.973690\pi\)
0.996586 0.0825612i \(-0.0263100\pi\)
\(588\) −0.806630 1.53276i −0.0332649 0.0632099i
\(589\) 70.8648i 2.91993i
\(590\) −0.621641 −0.0255926
\(591\) 21.0541 + 40.0070i 0.866049 + 1.64567i
\(592\) 3.04331 0.125079
\(593\) 35.7449 1.46787 0.733933 0.679222i \(-0.237683\pi\)
0.733933 + 0.679222i \(0.237683\pi\)
\(594\) −7.18237 15.6657i −0.294696 0.642771i
\(595\) −10.4159 −0.427011
\(596\) −3.59764 −0.147365
\(597\) −16.2633 30.9035i −0.665613 1.26480i
\(598\) −17.6950 −0.723601
\(599\) 18.2841i 0.747066i 0.927617 + 0.373533i \(0.121854\pi\)
−0.927617 + 0.373533i \(0.878146\pi\)
\(600\) 7.99180 + 15.1860i 0.326264 + 0.619967i
\(601\) 3.92580i 0.160137i 0.996789 + 0.0800683i \(0.0255138\pi\)
−0.996789 + 0.0800683i \(0.974486\pi\)
\(602\) 12.5717 0.512386
\(603\) 7.18015 10.4519i 0.292398 0.425635i
\(604\) 17.5295i 0.713267i
\(605\) −37.7492 19.4634i −1.53472 0.791298i
\(606\) −8.45343 16.0632i −0.343397 0.652523i
\(607\) 0.684969i 0.0278020i 0.999903 + 0.0139010i \(0.00442497\pi\)
−0.999903 + 0.0139010i \(0.995575\pi\)
\(608\) 7.70835i 0.312615i
\(609\) −1.27445 + 0.670690i −0.0516431 + 0.0271777i
\(610\) 17.8133 0.721239
\(611\) −25.1472 −1.01735
\(612\) −4.58256 + 6.67069i −0.185239 + 0.269647i
\(613\) 13.9389i 0.562987i −0.959563 0.281494i \(-0.909170\pi\)
0.959563 0.281494i \(-0.0908298\pi\)
\(614\) 14.4447i 0.582939i
\(615\) 31.2511 16.4462i 1.26017 0.663175i
\(616\) −2.83205 + 1.72613i −0.114106 + 0.0695477i
\(617\) 2.06877i 0.0832854i 0.999133 + 0.0416427i \(0.0132591\pi\)
−0.999133 + 0.0416427i \(0.986741\pi\)
\(618\) 3.84729 + 7.31063i 0.154761 + 0.294077i
\(619\) −32.1629 −1.29274 −0.646368 0.763026i \(-0.723713\pi\)
−0.646368 + 0.763026i \(0.723713\pi\)
\(620\) 35.4955i 1.42554i
\(621\) −2.12774 + 18.0262i −0.0853833 + 0.723365i
\(622\) 27.8091i 1.11504i
\(623\) 7.35755 0.294774
\(624\) −7.76421 + 4.08600i −0.310817 + 0.163571i
\(625\) 23.6231 0.944925
\(626\) −14.5554 −0.581750
\(627\) −38.0033 22.7280i −1.51771 0.907669i
\(628\) −7.25956 −0.289688
\(629\) 8.20991 0.327351
\(630\) −6.55874 + 9.54734i −0.261306 + 0.380375i
\(631\) 30.5134 1.21472 0.607359 0.794428i \(-0.292229\pi\)
0.607359 + 0.794428i \(0.292229\pi\)
\(632\) 2.49556i 0.0992682i
\(633\) −30.9497 + 16.2876i −1.23014 + 0.647375i
\(634\) 1.42646i 0.0566518i
\(635\) 54.9962 2.18246
\(636\) −0.923652 + 0.486082i −0.0366252 + 0.0192744i
\(637\) 5.06552i 0.200703i
\(638\) 1.43523 + 2.35477i 0.0568212 + 0.0932261i
\(639\) −29.7255 20.4205i −1.17592 0.807824i
\(640\) 3.86104i 0.152621i
\(641\) 5.28722i 0.208833i −0.994534 0.104416i \(-0.966703\pi\)
0.994534 0.104416i \(-0.0332974\pi\)
\(642\) −4.60348 8.74754i −0.181685 0.345238i
\(643\) 33.0075 1.30169 0.650845 0.759211i \(-0.274415\pi\)
0.650845 + 0.759211i \(0.274415\pi\)
\(644\) 3.49322 0.137652
\(645\) −39.1538 74.4000i −1.54168 2.92950i
\(646\) 20.7948i 0.818159i
\(647\) 19.8311i 0.779640i 0.920891 + 0.389820i \(0.127463\pi\)
−0.920891 + 0.389820i \(0.872537\pi\)
\(648\) 3.22886 + 8.40086i 0.126842 + 0.330017i
\(649\) −0.455969 + 0.277913i −0.0178984 + 0.0109090i
\(650\) 50.1873i 1.96851i
\(651\) −14.0910 + 7.41556i −0.552271 + 0.290639i
\(652\) 15.4886 0.606580
\(653\) 25.9231i 1.01445i 0.861814 + 0.507225i \(0.169329\pi\)
−0.861814 + 0.507225i \(0.830671\pi\)
\(654\) −0.234045 + 0.123169i −0.00915188 + 0.00481627i
\(655\) 65.9369i 2.57637i
\(656\) −5.28064 −0.206175
\(657\) −15.2149 10.4522i −0.593592 0.407780i
\(658\) 4.96439 0.193532
\(659\) −20.2139 −0.787421 −0.393710 0.919235i \(-0.628809\pi\)
−0.393710 + 0.919235i \(0.628809\pi\)
\(660\) 19.0355 + 11.3843i 0.740956 + 0.443132i
\(661\) 26.7459 1.04029 0.520147 0.854077i \(-0.325877\pi\)
0.520147 + 0.854077i \(0.325877\pi\)
\(662\) −7.00503 −0.272258
\(663\) −20.9455 + 11.0228i −0.813455 + 0.428089i
\(664\) −3.53635 −0.137237
\(665\) 29.7622i 1.15413i
\(666\) 5.16965 7.52530i 0.200320 0.291599i
\(667\) 2.90451i 0.112463i
\(668\) −3.94198 −0.152520
\(669\) −0.132169 0.251147i −0.00510993 0.00970990i
\(670\) 16.3201i 0.630500i
\(671\) 13.0659 7.96367i 0.504404 0.307434i
\(672\) 1.53276 0.806630i 0.0591274 0.0311164i
\(673\) 38.6571i 1.49012i −0.666996 0.745061i \(-0.732420\pi\)
0.666996 0.745061i \(-0.267580\pi\)
\(674\) 15.1925i 0.585194i
\(675\) 51.1267 + 6.03480i 1.96787 + 0.232280i
\(676\) −12.6595 −0.486902
\(677\) 7.55254 0.290268 0.145134 0.989412i \(-0.453639\pi\)
0.145134 + 0.989412i \(0.453639\pi\)
\(678\) −8.27462 + 4.35460i −0.317785 + 0.167238i
\(679\) 12.0650i 0.463010i
\(680\) 10.4159i 0.399432i
\(681\) 7.38017 + 14.0238i 0.282809 + 0.537393i
\(682\) 15.8687 + 26.0357i 0.607645 + 0.996959i
\(683\) 9.59137i 0.367004i −0.983019 0.183502i \(-0.941257\pi\)
0.983019 0.183502i \(-0.0587433\pi\)
\(684\) 19.0607 + 13.0941i 0.728805 + 0.500667i
\(685\) 42.4372 1.62144
\(686\) 1.00000i 0.0381802i
\(687\) 8.04525 + 15.2876i 0.306945 + 0.583257i
\(688\) 12.5717i 0.479293i
\(689\) −3.05252 −0.116292
\(690\) −10.8794 20.6730i −0.414171 0.787008i
\(691\) 11.3824 0.433008 0.216504 0.976282i \(-0.430535\pi\)
0.216504 + 0.976282i \(0.430535\pi\)
\(692\) −5.16603 −0.196383
\(693\) −0.542522 + 9.93507i −0.0206087 + 0.377402i
\(694\) −17.4151 −0.661069
\(695\) −33.4887 −1.27030
\(696\) −0.670690 1.27445i −0.0254224 0.0483077i
\(697\) −14.2456 −0.539589
\(698\) 12.0560i 0.456325i
\(699\) −2.01644 3.83165i −0.0762689 0.144926i
\(700\) 9.90764i 0.374474i
\(701\) −36.0942 −1.36326 −0.681630 0.731697i \(-0.738729\pi\)
−0.681630 + 0.731697i \(0.738729\pi\)
\(702\) −3.08544 + 26.1397i −0.116452 + 0.986581i
\(703\) 23.4589i 0.884768i
\(704\) −1.72613 2.83205i −0.0650559 0.106737i
\(705\) −15.4613 29.3795i −0.582305 1.10650i
\(706\) 23.4434i 0.882303i
\(707\) 10.4799i 0.394139i
\(708\) 0.246779 0.129870i 0.00927454 0.00488082i
\(709\) −10.7092 −0.402192 −0.201096 0.979571i \(-0.564450\pi\)
−0.201096 + 0.979571i \(0.564450\pi\)
\(710\) 46.4148 1.74191
\(711\) 6.17087 + 4.23920i 0.231426 + 0.158983i
\(712\) 7.35755i 0.275736i
\(713\) 32.1141i 1.20268i
\(714\) 4.13491 2.17604i 0.154745 0.0814363i
\(715\) 33.7599 + 55.3896i 1.26255 + 2.07145i
\(716\) 5.01937i 0.187583i
\(717\) 6.66073 + 12.6567i 0.248750 + 0.472674i
\(718\) −5.26816 −0.196606
\(719\) 48.6552i 1.81453i 0.420556 + 0.907267i \(0.361835\pi\)
−0.420556 + 0.907267i \(0.638165\pi\)
\(720\) −9.54734 6.55874i −0.355808 0.244430i
\(721\) 4.76959i 0.177629i
\(722\) 40.4186 1.50422
\(723\) 23.1359 12.1755i 0.860434 0.452812i
\(724\) −9.50810 −0.353366
\(725\) −8.23792 −0.305949
\(726\) 19.0519 0.159802i 0.707082 0.00593082i
\(727\) 3.44225 0.127666 0.0638329 0.997961i \(-0.479668\pi\)
0.0638329 + 0.997961i \(0.479668\pi\)
\(728\) 5.06552 0.187741
\(729\) 26.2580 + 6.28637i 0.972518 + 0.232829i
\(730\) 23.7573 0.879297
\(731\) 33.9147i 1.25438i
\(732\) −7.07153 + 3.72147i −0.261371 + 0.137549i
\(733\) 1.65107i 0.0609837i −0.999535 0.0304919i \(-0.990293\pi\)
0.999535 0.0304919i \(-0.00970737\pi\)
\(734\) −19.4642 −0.718438
\(735\) 5.91804 3.11443i 0.218290 0.114878i
\(736\) 3.49322i 0.128762i
\(737\) 7.29610 + 11.9707i 0.268755 + 0.440945i
\(738\) −8.97021 + 13.0576i −0.330198 + 0.480659i
\(739\) 21.9281i 0.806639i −0.915059 0.403319i \(-0.867856\pi\)
0.915059 0.403319i \(-0.132144\pi\)
\(740\) 11.7503i 0.431951i
\(741\) 31.4963 + 59.8492i 1.15704 + 2.19862i
\(742\) 0.602608 0.0221224
\(743\) −34.8682 −1.27919 −0.639596 0.768712i \(-0.720898\pi\)
−0.639596 + 0.768712i \(0.720898\pi\)
\(744\) −7.41556 14.0910i −0.271868 0.516603i
\(745\) 13.8906i 0.508913i
\(746\) 5.38807i 0.197271i
\(747\) −6.00718 + 8.74447i −0.219791 + 0.319943i
\(748\) −4.65657 7.63999i −0.170261 0.279346i
\(749\) 5.70706i 0.208531i
\(750\) −29.0436 + 15.2845i −1.06052 + 0.558111i
\(751\) 25.6297 0.935239 0.467620 0.883930i \(-0.345112\pi\)
0.467620 + 0.883930i \(0.345112\pi\)
\(752\) 4.96439i 0.181033i
\(753\) −21.0454 + 11.0753i −0.766936 + 0.403608i
\(754\) 4.21183i 0.153386i
\(755\) 67.6823 2.46321
\(756\) 0.609106 5.16033i 0.0221530 0.187679i
\(757\) −28.8949 −1.05020 −0.525102 0.851039i \(-0.675973\pi\)
−0.525102 + 0.851039i \(0.675973\pi\)
\(758\) 8.29732 0.301372
\(759\) −17.2221 10.2997i −0.625122 0.373857i
\(760\) −29.7622 −1.07959
\(761\) −11.0225 −0.399565 −0.199782 0.979840i \(-0.564024\pi\)
−0.199782 + 0.979840i \(0.564024\pi\)
\(762\) −21.8324 + 11.4895i −0.790906 + 0.416222i
\(763\) 0.152695 0.00552794
\(764\) 8.73096i 0.315875i
\(765\) −25.7558 17.6935i −0.931203 0.639708i
\(766\) 27.2636i 0.985074i
\(767\) 0.815566 0.0294484
\(768\) 0.806630 + 1.53276i 0.0291068 + 0.0553087i
\(769\) 31.5094i 1.13626i −0.822939 0.568129i \(-0.807667\pi\)
0.822939 0.568129i \(-0.192333\pi\)
\(770\) −6.66465 10.9346i −0.240177 0.394057i
\(771\) −9.09458 + 4.78612i −0.327533 + 0.172368i
\(772\) 11.2644i 0.405415i
\(773\) 46.5070i 1.67274i −0.548164 0.836371i \(-0.684673\pi\)
0.548164 0.836371i \(-0.315327\pi\)
\(774\) 31.0866 + 21.3555i 1.11738 + 0.767609i
\(775\) −91.0835 −3.27182
\(776\) −12.0650 −0.433106
\(777\) −4.66465 + 2.45482i −0.167343 + 0.0880663i
\(778\) 26.4139i 0.946984i
\(779\) 40.7050i 1.45841i
\(780\) −15.7762 29.9779i −0.564879 1.07338i
\(781\) 34.0449 20.7503i 1.21822 0.742505i
\(782\) 9.42364i 0.336989i
\(783\) −4.29067 0.506454i −0.153336 0.0180992i
\(784\)