Properties

Label 722.2.c.m.429.3
Level $722$
Weight $2$
Character 722.429
Analytic conductor $5.765$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 722 = 2 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 722.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.76519902594\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.324000000.2
Defining polynomial: \(x^{8} + 5 x^{6} + 20 x^{4} + 25 x^{2} + 25\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 429.3
Root \(0.951057 - 1.64728i\) of defining polynomial
Character \(\chi\) \(=\) 722.429
Dual form 722.2.c.m.653.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.221232 + 0.383185i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.445746 - 0.772054i) q^{5} +(-0.221232 - 0.383185i) q^{6} +2.52015 q^{7} +1.00000 q^{8} +(1.40211 + 2.42853i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.221232 + 0.383185i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.445746 - 0.772054i) q^{5} +(-0.221232 - 0.383185i) q^{6} +2.52015 q^{7} +1.00000 q^{8} +(1.40211 + 2.42853i) q^{9} +(0.445746 + 0.772054i) q^{10} +1.95199 q^{11} +0.442463 q^{12} +(-3.22982 - 5.59422i) q^{13} +(-1.26007 + 2.18251i) q^{14} +(0.197226 + 0.341606i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.71113 - 2.96376i) q^{17} -2.80423 q^{18} -0.891491 q^{20} +(-0.557537 + 0.965682i) q^{21} +(-0.975994 + 1.69047i) q^{22} +(-4.09252 - 7.08845i) q^{23} +(-0.221232 + 0.383185i) q^{24} +(2.10262 + 3.64185i) q^{25} +6.45965 q^{26} -2.56816 q^{27} +(-1.26007 - 2.18251i) q^{28} +(2.29032 + 3.96695i) q^{29} -0.394452 q^{30} +8.79360 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.431842 + 0.747972i) q^{33} +(1.71113 + 2.96376i) q^{34} +(1.12334 - 1.94569i) q^{35} +(1.40211 - 2.42853i) q^{36} +5.97980 q^{37} +2.85816 q^{39} +(0.445746 - 0.772054i) q^{40} +(-1.74466 + 3.02184i) q^{41} +(-0.557537 - 0.965682i) q^{42} +(3.12334 - 5.40979i) q^{43} +(-0.975994 - 1.69047i) q^{44} +2.49994 q^{45} +8.18504 q^{46} +(5.27491 + 9.13641i) q^{47} +(-0.221232 - 0.383185i) q^{48} -0.648859 q^{49} -4.20524 q^{50} +(0.757113 + 1.31136i) q^{51} +(-3.22982 + 5.59422i) q^{52} +(1.88139 + 3.25866i) q^{53} +(1.28408 - 2.22409i) q^{54} +(0.870091 - 1.50704i) q^{55} +2.52015 q^{56} -4.58064 q^{58} +(1.42081 - 2.46091i) q^{59} +(0.197226 - 0.341606i) q^{60} +(1.22747 + 2.12605i) q^{61} +(-4.39680 + 7.61548i) q^{62} +(3.53353 + 6.12026i) q^{63} +1.00000 q^{64} -5.75872 q^{65} +(-0.431842 - 0.747972i) q^{66} +(-1.33630 - 2.31455i) q^{67} -3.42226 q^{68} +3.62158 q^{69} +(1.12334 + 1.94569i) q^{70} +(0.0282202 - 0.0488788i) q^{71} +(1.40211 + 2.42853i) q^{72} +(3.48459 - 6.03548i) q^{73} +(-2.98990 + 5.17866i) q^{74} -1.86067 q^{75} +4.91930 q^{77} +(-1.42908 + 2.47524i) q^{78} +(-4.56581 + 7.90821i) q^{79} +(0.445746 + 0.772054i) q^{80} +(-3.63818 + 6.30151i) q^{81} +(-1.74466 - 3.02184i) q^{82} -14.1239 q^{83} +1.11507 q^{84} +(-1.52546 - 2.64217i) q^{85} +(3.12334 + 5.40979i) q^{86} -2.02677 q^{87} +1.95199 q^{88} +(0.933870 + 1.61751i) q^{89} +(-1.24997 + 2.16501i) q^{90} +(-8.13963 - 14.0983i) q^{91} +(-4.09252 + 7.08845i) q^{92} +(-1.94542 + 3.36957i) q^{93} -10.5498 q^{94} +0.442463 q^{96} +(3.91216 - 6.77606i) q^{97} +(0.324429 - 0.561928i) q^{98} +(2.73691 + 4.74047i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{2} - 2q^{3} - 4q^{4} + 2q^{5} - 2q^{6} - 4q^{7} + 8q^{8} - 4q^{9} + O(q^{10}) \) \( 8q - 4q^{2} - 2q^{3} - 4q^{4} + 2q^{5} - 2q^{6} - 4q^{7} + 8q^{8} - 4q^{9} + 2q^{10} + 4q^{11} + 4q^{12} - 18q^{13} + 2q^{14} - 4q^{15} - 4q^{16} - 6q^{17} + 8q^{18} - 4q^{20} - 4q^{21} - 2q^{22} + 10q^{23} - 2q^{24} - 6q^{25} + 36q^{26} - 8q^{27} + 2q^{28} + 2q^{29} + 8q^{30} + 52q^{31} - 4q^{32} - 16q^{33} - 6q^{34} - 6q^{35} - 4q^{36} + 8q^{37} - 12q^{39} + 2q^{40} + 12q^{41} - 4q^{42} + 10q^{43} - 2q^{44} - 44q^{45} - 20q^{46} + 12q^{47} - 2q^{48} - 24q^{49} + 12q^{50} + 2q^{51} - 18q^{52} - 8q^{53} + 4q^{54} + 26q^{55} - 4q^{56} - 4q^{58} + 8q^{59} - 4q^{60} - 26q^{62} + 22q^{63} + 8q^{64} - 8q^{65} - 16q^{66} - 10q^{67} + 12q^{68} - 40q^{69} - 6q^{70} - 4q^{72} + 14q^{73} - 4q^{74} + 16q^{75} + 8q^{77} + 6q^{78} - 22q^{79} + 2q^{80} + 4q^{81} + 12q^{82} - 24q^{83} + 8q^{84} + 18q^{85} + 10q^{86} - 52q^{87} + 4q^{88} + 16q^{89} + 22q^{90} + 4q^{91} + 10q^{92} - 8q^{93} - 24q^{94} + 4q^{96} - 28q^{97} + 12q^{98} - 22q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).

\(n\) \(363\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −0.221232 + 0.383185i −0.127728 + 0.221232i −0.922796 0.385289i \(-0.874102\pi\)
0.795068 + 0.606520i \(0.207435\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.445746 0.772054i 0.199344 0.345273i −0.748972 0.662601i \(-0.769452\pi\)
0.948316 + 0.317328i \(0.102786\pi\)
\(6\) −0.221232 0.383185i −0.0903175 0.156434i
\(7\) 2.52015 0.952526 0.476263 0.879303i \(-0.341991\pi\)
0.476263 + 0.879303i \(0.341991\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.40211 + 2.42853i 0.467371 + 0.809510i
\(10\) 0.445746 + 0.772054i 0.140957 + 0.244145i
\(11\) 1.95199 0.588547 0.294273 0.955721i \(-0.404922\pi\)
0.294273 + 0.955721i \(0.404922\pi\)
\(12\) 0.442463 0.127728
\(13\) −3.22982 5.59422i −0.895792 1.55156i −0.832821 0.553542i \(-0.813276\pi\)
−0.0629711 0.998015i \(-0.520058\pi\)
\(14\) −1.26007 + 2.18251i −0.336769 + 0.583301i
\(15\) 0.197226 + 0.341606i 0.0509236 + 0.0882022i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.71113 2.96376i 0.415010 0.718818i −0.580420 0.814318i \(-0.697111\pi\)
0.995430 + 0.0954992i \(0.0304447\pi\)
\(18\) −2.80423 −0.660962
\(19\) 0 0
\(20\) −0.891491 −0.199344
\(21\) −0.557537 + 0.965682i −0.121664 + 0.210729i
\(22\) −0.975994 + 1.69047i −0.208083 + 0.360410i
\(23\) −4.09252 7.08845i −0.853349 1.47804i −0.878168 0.478352i \(-0.841234\pi\)
0.0248186 0.999692i \(-0.492099\pi\)
\(24\) −0.221232 + 0.383185i −0.0451587 + 0.0782172i
\(25\) 2.10262 + 3.64185i 0.420524 + 0.728369i
\(26\) 6.45965 1.26684
\(27\) −2.56816 −0.494242
\(28\) −1.26007 2.18251i −0.238132 0.412456i
\(29\) 2.29032 + 3.96695i 0.425302 + 0.736645i 0.996449 0.0842032i \(-0.0268345\pi\)
−0.571146 + 0.820848i \(0.693501\pi\)
\(30\) −0.394452 −0.0720168
\(31\) 8.79360 1.57938 0.789689 0.613507i \(-0.210242\pi\)
0.789689 + 0.613507i \(0.210242\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −0.431842 + 0.747972i −0.0751740 + 0.130205i
\(34\) 1.71113 + 2.96376i 0.293456 + 0.508281i
\(35\) 1.12334 1.94569i 0.189880 0.328882i
\(36\) 1.40211 2.42853i 0.233686 0.404755i
\(37\) 5.97980 0.983073 0.491536 0.870857i \(-0.336436\pi\)
0.491536 + 0.870857i \(0.336436\pi\)
\(38\) 0 0
\(39\) 2.85816 0.457672
\(40\) 0.445746 0.772054i 0.0704786 0.122072i
\(41\) −1.74466 + 3.02184i −0.272470 + 0.471932i −0.969494 0.245116i \(-0.921174\pi\)
0.697024 + 0.717048i \(0.254507\pi\)
\(42\) −0.557537 0.965682i −0.0860298 0.149008i
\(43\) 3.12334 5.40979i 0.476306 0.824986i −0.523326 0.852133i \(-0.675309\pi\)
0.999631 + 0.0271471i \(0.00864226\pi\)
\(44\) −0.975994 1.69047i −0.147137 0.254848i
\(45\) 2.49994 0.372670
\(46\) 8.18504 1.20682
\(47\) 5.27491 + 9.13641i 0.769425 + 1.33268i 0.937875 + 0.346973i \(0.112790\pi\)
−0.168451 + 0.985710i \(0.553876\pi\)
\(48\) −0.221232 0.383185i −0.0319321 0.0553079i
\(49\) −0.648859 −0.0926941
\(50\) −4.20524 −0.594711
\(51\) 0.757113 + 1.31136i 0.106017 + 0.183627i
\(52\) −3.22982 + 5.59422i −0.447896 + 0.775779i
\(53\) 1.88139 + 3.25866i 0.258429 + 0.447612i 0.965821 0.259209i \(-0.0834619\pi\)
−0.707392 + 0.706821i \(0.750129\pi\)
\(54\) 1.28408 2.22409i 0.174741 0.302660i
\(55\) 0.870091 1.50704i 0.117323 0.203209i
\(56\) 2.52015 0.336769
\(57\) 0 0
\(58\) −4.58064 −0.601468
\(59\) 1.42081 2.46091i 0.184973 0.320383i −0.758594 0.651563i \(-0.774113\pi\)
0.943568 + 0.331180i \(0.107447\pi\)
\(60\) 0.197226 0.341606i 0.0254618 0.0441011i
\(61\) 1.22747 + 2.12605i 0.157162 + 0.272213i 0.933844 0.357680i \(-0.116432\pi\)
−0.776682 + 0.629893i \(0.783099\pi\)
\(62\) −4.39680 + 7.61548i −0.558394 + 0.967168i
\(63\) 3.53353 + 6.12026i 0.445183 + 0.771080i
\(64\) 1.00000 0.125000
\(65\) −5.75872 −0.714282
\(66\) −0.431842 0.747972i −0.0531561 0.0920690i
\(67\) −1.33630 2.31455i −0.163256 0.282767i 0.772779 0.634675i \(-0.218866\pi\)
−0.936034 + 0.351908i \(0.885533\pi\)
\(68\) −3.42226 −0.415010
\(69\) 3.62158 0.435987
\(70\) 1.12334 + 1.94569i 0.134265 + 0.232554i
\(71\) 0.0282202 0.0488788i 0.00334912 0.00580085i −0.864346 0.502898i \(-0.832267\pi\)
0.867695 + 0.497097i \(0.165601\pi\)
\(72\) 1.40211 + 2.42853i 0.165241 + 0.286205i
\(73\) 3.48459 6.03548i 0.407840 0.706400i −0.586807 0.809727i \(-0.699615\pi\)
0.994647 + 0.103327i \(0.0329487\pi\)
\(74\) −2.98990 + 5.17866i −0.347569 + 0.602007i
\(75\) −1.86067 −0.214851
\(76\) 0 0
\(77\) 4.91930 0.560606
\(78\) −1.42908 + 2.47524i −0.161811 + 0.280266i
\(79\) −4.56581 + 7.90821i −0.513694 + 0.889743i 0.486180 + 0.873859i \(0.338390\pi\)
−0.999874 + 0.0158848i \(0.994943\pi\)
\(80\) 0.445746 + 0.772054i 0.0498359 + 0.0863183i
\(81\) −3.63818 + 6.30151i −0.404242 + 0.700168i
\(82\) −1.74466 3.02184i −0.192666 0.333707i
\(83\) −14.1239 −1.55030 −0.775150 0.631778i \(-0.782326\pi\)
−0.775150 + 0.631778i \(0.782326\pi\)
\(84\) 1.11507 0.121664
\(85\) −1.52546 2.64217i −0.165459 0.286584i
\(86\) 3.12334 + 5.40979i 0.336799 + 0.583353i
\(87\) −2.02677 −0.217292
\(88\) 1.95199 0.208083
\(89\) 0.933870 + 1.61751i 0.0989901 + 0.171456i 0.911267 0.411816i \(-0.135105\pi\)
−0.812277 + 0.583272i \(0.801772\pi\)
\(90\) −1.24997 + 2.16501i −0.131759 + 0.228213i
\(91\) −8.13963 14.0983i −0.853265 1.47790i
\(92\) −4.09252 + 7.08845i −0.426675 + 0.739022i
\(93\) −1.94542 + 3.36957i −0.201731 + 0.349409i
\(94\) −10.5498 −1.08813
\(95\) 0 0
\(96\) 0.442463 0.0451587
\(97\) 3.91216 6.77606i 0.397219 0.688004i −0.596162 0.802864i \(-0.703308\pi\)
0.993382 + 0.114860i \(0.0366418\pi\)
\(98\) 0.324429 0.561928i 0.0327723 0.0567633i
\(99\) 2.73691 + 4.74047i 0.275070 + 0.476435i
\(100\) 2.10262 3.64185i 0.210262 0.364185i
\(101\) 2.69244 + 4.66343i 0.267907 + 0.464029i 0.968321 0.249708i \(-0.0803346\pi\)
−0.700414 + 0.713737i \(0.747001\pi\)
\(102\) −1.51423 −0.149931
\(103\) 4.69468 0.462580 0.231290 0.972885i \(-0.425705\pi\)
0.231290 + 0.972885i \(0.425705\pi\)
\(104\) −3.22982 5.59422i −0.316710 0.548558i
\(105\) 0.497039 + 0.860897i 0.0485060 + 0.0840149i
\(106\) −3.76278 −0.365473
\(107\) −16.0373 −1.55038 −0.775191 0.631727i \(-0.782346\pi\)
−0.775191 + 0.631727i \(0.782346\pi\)
\(108\) 1.28408 + 2.22409i 0.123561 + 0.214013i
\(109\) 7.05040 12.2116i 0.675305 1.16966i −0.301074 0.953601i \(-0.597345\pi\)
0.976380 0.216063i \(-0.0693215\pi\)
\(110\) 0.870091 + 1.50704i 0.0829599 + 0.143691i
\(111\) −1.32292 + 2.29137i −0.125566 + 0.217487i
\(112\) −1.26007 + 2.18251i −0.119066 + 0.206228i
\(113\) 12.7224 1.19682 0.598410 0.801190i \(-0.295799\pi\)
0.598410 + 0.801190i \(0.295799\pi\)
\(114\) 0 0
\(115\) −7.29689 −0.680439
\(116\) 2.29032 3.96695i 0.212651 0.368322i
\(117\) 9.05716 15.6875i 0.837335 1.45031i
\(118\) 1.42081 + 2.46091i 0.130796 + 0.226545i
\(119\) 4.31230 7.46912i 0.395308 0.684693i
\(120\) 0.197226 + 0.341606i 0.0180042 + 0.0311842i
\(121\) −7.18974 −0.653613
\(122\) −2.45495 −0.222261
\(123\) −0.771949 1.33705i −0.0696043 0.120558i
\(124\) −4.39680 7.61548i −0.394844 0.683891i
\(125\) 8.20640 0.734002
\(126\) −7.06706 −0.629584
\(127\) 3.58721 + 6.21323i 0.318313 + 0.551335i 0.980136 0.198325i \(-0.0635503\pi\)
−0.661823 + 0.749660i \(0.730217\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 1.38197 + 2.39364i 0.121675 + 0.210748i
\(130\) 2.87936 4.98720i 0.252537 0.437406i
\(131\) 1.76133 3.05071i 0.153888 0.266542i −0.778766 0.627315i \(-0.784154\pi\)
0.932654 + 0.360773i \(0.117487\pi\)
\(132\) 0.863684 0.0751740
\(133\) 0 0
\(134\) 2.67261 0.230878
\(135\) −1.14475 + 1.98276i −0.0985240 + 0.170649i
\(136\) 1.71113 2.96376i 0.146728 0.254141i
\(137\) 5.50177 + 9.52935i 0.470048 + 0.814147i 0.999413 0.0342466i \(-0.0109032\pi\)
−0.529365 + 0.848394i \(0.677570\pi\)
\(138\) −1.81079 + 3.13638i −0.154145 + 0.266987i
\(139\) −10.8793 18.8435i −0.922771 1.59829i −0.795108 0.606468i \(-0.792586\pi\)
−0.127663 0.991818i \(-0.540747\pi\)
\(140\) −2.24669 −0.189880
\(141\) −4.66791 −0.393109
\(142\) 0.0282202 + 0.0488788i 0.00236819 + 0.00410182i
\(143\) −6.30458 10.9199i −0.527216 0.913164i
\(144\) −2.80423 −0.233686
\(145\) 4.08361 0.339125
\(146\) 3.48459 + 6.03548i 0.288387 + 0.499500i
\(147\) 0.143548 0.248633i 0.0118397 0.0205069i
\(148\) −2.98990 5.17866i −0.245768 0.425683i
\(149\) −7.19479 + 12.4617i −0.589420 + 1.02090i 0.404889 + 0.914366i \(0.367310\pi\)
−0.994309 + 0.106539i \(0.966023\pi\)
\(150\) 0.930333 1.61138i 0.0759614 0.131569i
\(151\) −12.4068 −1.00965 −0.504824 0.863222i \(-0.668443\pi\)
−0.504824 + 0.863222i \(0.668443\pi\)
\(152\) 0 0
\(153\) 9.59679 0.775855
\(154\) −2.45965 + 4.26024i −0.198204 + 0.343300i
\(155\) 3.91971 6.78914i 0.314839 0.545317i
\(156\) −1.42908 2.47524i −0.114418 0.198178i
\(157\) 0.225610 0.390768i 0.0180056 0.0311867i −0.856882 0.515512i \(-0.827602\pi\)
0.874888 + 0.484326i \(0.160935\pi\)
\(158\) −4.56581 7.90821i −0.363236 0.629144i
\(159\) −1.66489 −0.132035
\(160\) −0.891491 −0.0704786
\(161\) −10.3138 17.8639i −0.812837 1.40788i
\(162\) −3.63818 6.30151i −0.285842 0.495094i
\(163\) −0.0692542 −0.00542441 −0.00271220 0.999996i \(-0.500863\pi\)
−0.00271220 + 0.999996i \(0.500863\pi\)
\(164\) 3.48932 0.272470
\(165\) 0.384983 + 0.666811i 0.0299709 + 0.0519111i
\(166\) 7.06195 12.2317i 0.548114 0.949361i
\(167\) 1.08685 + 1.88248i 0.0841032 + 0.145671i 0.905009 0.425393i \(-0.139864\pi\)
−0.820906 + 0.571064i \(0.806531\pi\)
\(168\) −0.557537 + 0.965682i −0.0430149 + 0.0745040i
\(169\) −14.3635 + 24.8784i −1.10489 + 1.91372i
\(170\) 3.05092 0.233995
\(171\) 0 0
\(172\) −6.24669 −0.476306
\(173\) −8.42464 + 14.5919i −0.640514 + 1.10940i 0.344804 + 0.938675i \(0.387945\pi\)
−0.985318 + 0.170728i \(0.945388\pi\)
\(174\) 1.01338 1.75523i 0.0768244 0.133064i
\(175\) 5.29892 + 9.17799i 0.400560 + 0.693791i
\(176\) −0.975994 + 1.69047i −0.0735684 + 0.127424i
\(177\) 0.628656 + 1.08886i 0.0472526 + 0.0818440i
\(178\) −1.86774 −0.139993
\(179\) −18.9655 −1.41755 −0.708775 0.705435i \(-0.750752\pi\)
−0.708775 + 0.705435i \(0.750752\pi\)
\(180\) −1.24997 2.16501i −0.0931674 0.161371i
\(181\) −0.993436 1.72068i −0.0738415 0.127897i 0.826740 0.562584i \(-0.190193\pi\)
−0.900582 + 0.434686i \(0.856859\pi\)
\(182\) 16.2793 1.20670
\(183\) −1.08623 −0.0802961
\(184\) −4.09252 7.08845i −0.301705 0.522568i
\(185\) 2.66547 4.61673i 0.195969 0.339429i
\(186\) −1.94542 3.36957i −0.142645 0.247069i
\(187\) 3.34011 5.78523i 0.244253 0.423058i
\(188\) 5.27491 9.13641i 0.384712 0.666341i
\(189\) −6.47214 −0.470779
\(190\) 0 0
\(191\) −20.9259 −1.51415 −0.757074 0.653329i \(-0.773372\pi\)
−0.757074 + 0.653329i \(0.773372\pi\)
\(192\) −0.221232 + 0.383185i −0.0159660 + 0.0276540i
\(193\) 3.89440 6.74529i 0.280325 0.485537i −0.691140 0.722721i \(-0.742891\pi\)
0.971465 + 0.237184i \(0.0762245\pi\)
\(194\) 3.91216 + 6.77606i 0.280877 + 0.486493i
\(195\) 1.27401 2.20665i 0.0912339 0.158022i
\(196\) 0.324429 + 0.561928i 0.0231735 + 0.0401377i
\(197\) 1.82514 0.130036 0.0650180 0.997884i \(-0.479290\pi\)
0.0650180 + 0.997884i \(0.479290\pi\)
\(198\) −5.47382 −0.389007
\(199\) −1.17963 2.04317i −0.0836216 0.144837i 0.821181 0.570667i \(-0.193315\pi\)
−0.904803 + 0.425830i \(0.859982\pi\)
\(200\) 2.10262 + 3.64185i 0.148678 + 0.257517i
\(201\) 1.18253 0.0834094
\(202\) −5.38487 −0.378878
\(203\) 5.77195 + 9.99731i 0.405111 + 0.701674i
\(204\) 0.757113 1.31136i 0.0530085 0.0918134i
\(205\) 1.55535 + 2.69395i 0.108630 + 0.188153i
\(206\) −2.34734 + 4.06571i −0.163547 + 0.283271i
\(207\) 11.4764 19.8776i 0.797662 1.38159i
\(208\) 6.45965 0.447896
\(209\) 0 0
\(210\) −0.994078 −0.0685979
\(211\) −0.180525 + 0.312679i −0.0124279 + 0.0215257i −0.872172 0.489199i \(-0.837289\pi\)
0.859745 + 0.510724i \(0.170623\pi\)
\(212\) 1.88139 3.25866i 0.129214 0.223806i
\(213\) 0.0124864 + 0.0216271i 0.000855554 + 0.00148186i
\(214\) 8.01864 13.8887i 0.548143 0.949411i
\(215\) −2.78444 4.82278i −0.189897 0.328911i
\(216\) −2.56816 −0.174741
\(217\) 22.1612 1.50440
\(218\) 7.05040 + 12.2116i 0.477513 + 0.827077i
\(219\) 1.54180 + 2.67048i 0.104185 + 0.180454i
\(220\) −1.74018 −0.117323
\(221\) −22.1066 −1.48705
\(222\) −1.32292 2.29137i −0.0887886 0.153786i
\(223\) 9.02431 15.6306i 0.604312 1.04670i −0.387848 0.921724i \(-0.626781\pi\)
0.992160 0.124976i \(-0.0398854\pi\)
\(224\) −1.26007 2.18251i −0.0841922 0.145825i
\(225\) −5.89623 + 10.2126i −0.393082 + 0.680838i
\(226\) −6.36119 + 11.0179i −0.423140 + 0.732900i
\(227\) −12.2845 −0.815349 −0.407675 0.913127i \(-0.633660\pi\)
−0.407675 + 0.913127i \(0.633660\pi\)
\(228\) 0 0
\(229\) 6.79174 0.448811 0.224405 0.974496i \(-0.427956\pi\)
0.224405 + 0.974496i \(0.427956\pi\)
\(230\) 3.64845 6.31929i 0.240571 0.416682i
\(231\) −1.08831 + 1.88500i −0.0716052 + 0.124024i
\(232\) 2.29032 + 3.96695i 0.150367 + 0.260443i
\(233\) −10.7147 + 18.5584i −0.701942 + 1.21580i 0.265842 + 0.964017i \(0.414350\pi\)
−0.967784 + 0.251782i \(0.918983\pi\)
\(234\) 9.05716 + 15.6875i 0.592085 + 1.02552i
\(235\) 9.40507 0.613519
\(236\) −2.84162 −0.184973
\(237\) −2.02020 3.49909i −0.131226 0.227291i
\(238\) 4.31230 + 7.46912i 0.279525 + 0.484151i
\(239\) −11.8376 −0.765713 −0.382856 0.923808i \(-0.625060\pi\)
−0.382856 + 0.923808i \(0.625060\pi\)
\(240\) −0.394452 −0.0254618
\(241\) −10.8732 18.8329i −0.700401 1.21313i −0.968326 0.249691i \(-0.919671\pi\)
0.267924 0.963440i \(-0.413662\pi\)
\(242\) 3.59487 6.22650i 0.231087 0.400254i
\(243\) −5.46200 9.46046i −0.350387 0.606889i
\(244\) 1.22747 2.12605i 0.0785810 0.136106i
\(245\) −0.289226 + 0.500954i −0.0184780 + 0.0320048i
\(246\) 1.54390 0.0984353
\(247\) 0 0
\(248\) 8.79360 0.558394
\(249\) 3.12465 5.41206i 0.198017 0.342975i
\(250\) −4.10320 + 7.10695i −0.259509 + 0.449483i
\(251\) −11.8205 20.4737i −0.746104 1.29229i −0.949677 0.313231i \(-0.898589\pi\)
0.203573 0.979060i \(-0.434745\pi\)
\(252\) 3.53353 6.12026i 0.222592 0.385540i
\(253\) −7.98855 13.8366i −0.502236 0.869898i
\(254\) −7.17442 −0.450163
\(255\) 1.34992 0.0845352
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −0.461734 0.799748i −0.0288022 0.0498869i 0.851265 0.524736i \(-0.175836\pi\)
−0.880067 + 0.474849i \(0.842503\pi\)
\(258\) −2.76393 −0.172075
\(259\) 15.0700 0.936402
\(260\) 2.87936 + 4.98720i 0.178570 + 0.309293i
\(261\) −6.42258 + 11.1242i −0.397548 + 0.688573i
\(262\) 1.76133 + 3.05071i 0.108815 + 0.188473i
\(263\) −2.15984 + 3.74095i −0.133181 + 0.230677i −0.924901 0.380208i \(-0.875853\pi\)
0.791720 + 0.610884i \(0.209186\pi\)
\(264\) −0.431842 + 0.747972i −0.0265780 + 0.0460345i
\(265\) 3.35449 0.206064
\(266\) 0 0
\(267\) −0.826407 −0.0505753
\(268\) −1.33630 + 2.31455i −0.0816278 + 0.141384i
\(269\) −5.39768 + 9.34905i −0.329102 + 0.570022i −0.982334 0.187136i \(-0.940079\pi\)
0.653232 + 0.757158i \(0.273413\pi\)
\(270\) −1.14475 1.98276i −0.0696670 0.120667i
\(271\) −0.403622 + 0.699093i −0.0245183 + 0.0424669i −0.878024 0.478616i \(-0.841139\pi\)
0.853506 + 0.521083i \(0.174472\pi\)
\(272\) 1.71113 + 2.96376i 0.103752 + 0.179705i
\(273\) 7.20298 0.435944
\(274\) −11.0035 −0.664749
\(275\) 4.10429 + 7.10885i 0.247498 + 0.428680i
\(276\) −1.81079 3.13638i −0.108997 0.188788i
\(277\) −9.14869 −0.549691 −0.274846 0.961488i \(-0.588627\pi\)
−0.274846 + 0.961488i \(0.588627\pi\)
\(278\) 21.7586 1.30499
\(279\) 12.3296 + 21.3555i 0.738155 + 1.27852i
\(280\) 1.12334 1.94569i 0.0671327 0.116277i
\(281\) 10.6079 + 18.3734i 0.632813 + 1.09606i 0.986974 + 0.160880i \(0.0514331\pi\)
−0.354161 + 0.935184i \(0.615234\pi\)
\(282\) 2.33395 4.04253i 0.138985 0.240729i
\(283\) −2.59493 + 4.49454i −0.154252 + 0.267173i −0.932787 0.360429i \(-0.882630\pi\)
0.778534 + 0.627602i \(0.215964\pi\)
\(284\) −0.0564404 −0.00334912
\(285\) 0 0
\(286\) 12.6092 0.745596
\(287\) −4.39680 + 7.61548i −0.259535 + 0.449528i
\(288\) 1.40211 2.42853i 0.0826203 0.143103i
\(289\) 2.64407 + 4.57966i 0.155533 + 0.269392i
\(290\) −2.04180 + 3.53651i −0.119899 + 0.207671i
\(291\) 1.73099 + 2.99816i 0.101472 + 0.175755i
\(292\) −6.96917 −0.407840
\(293\) 17.5660 1.02621 0.513107 0.858324i \(-0.328494\pi\)
0.513107 + 0.858324i \(0.328494\pi\)
\(294\) 0.143548 + 0.248633i 0.00837190 + 0.0145006i
\(295\) −1.26664 2.19388i −0.0737465 0.127733i
\(296\) 5.97980 0.347569
\(297\) −5.01302 −0.290885
\(298\) −7.19479 12.4617i −0.416783 0.721889i
\(299\) −26.4362 + 45.7889i −1.52885 + 2.64804i
\(300\) 0.930333 + 1.61138i 0.0537128 + 0.0930333i
\(301\) 7.87129 13.6335i 0.453693 0.785820i
\(302\) 6.20338 10.7446i 0.356964 0.618280i
\(303\) −2.38261 −0.136877
\(304\) 0 0
\(305\) 2.18857 0.125317
\(306\) −4.79840 + 8.31106i −0.274306 + 0.475112i
\(307\) −10.7842 + 18.6787i −0.615486 + 1.06605i 0.374813 + 0.927100i \(0.377707\pi\)
−0.990299 + 0.138952i \(0.955627\pi\)
\(308\) −2.45965 4.26024i −0.140152 0.242750i
\(309\) −1.03861 + 1.79893i −0.0590846 + 0.102337i
\(310\) 3.91971 + 6.78914i 0.222625 + 0.385597i
\(311\) −2.57368 −0.145940 −0.0729701 0.997334i \(-0.523248\pi\)
−0.0729701 + 0.997334i \(0.523248\pi\)
\(312\) 2.85816 0.161811
\(313\) 2.59194 + 4.48938i 0.146505 + 0.253755i 0.929934 0.367728i \(-0.119864\pi\)
−0.783428 + 0.621482i \(0.786531\pi\)
\(314\) 0.225610 + 0.390768i 0.0127319 + 0.0220523i
\(315\) 6.30023 0.354977
\(316\) 9.13162 0.513694
\(317\) −10.1281 17.5423i −0.568850 0.985276i −0.996680 0.0814174i \(-0.974055\pi\)
0.427830 0.903859i \(-0.359278\pi\)
\(318\) 0.832446 1.44184i 0.0466813 0.0808543i
\(319\) 4.47068 + 7.74345i 0.250310 + 0.433550i
\(320\) 0.445746 0.772054i 0.0249179 0.0431591i
\(321\) 3.54795 6.14524i 0.198028 0.342994i
\(322\) 20.6275 1.14953
\(323\) 0 0
\(324\) 7.27636 0.404242
\(325\) 13.5822 23.5251i 0.753405 1.30494i
\(326\) 0.0346271 0.0599759i 0.00191782 0.00332176i
\(327\) 3.11954 + 5.40321i 0.172511 + 0.298798i
\(328\) −1.74466 + 3.02184i −0.0963328 + 0.166853i
\(329\) 13.2935 + 23.0251i 0.732897 + 1.26941i
\(330\) −0.769967 −0.0423853
\(331\) 21.3280 1.17229 0.586146 0.810205i \(-0.300644\pi\)
0.586146 + 0.810205i \(0.300644\pi\)
\(332\) 7.06195 + 12.2317i 0.387575 + 0.671299i
\(333\) 8.38435 + 14.5221i 0.459460 + 0.795807i
\(334\) −2.17371 −0.118940
\(335\) −2.38261 −0.130176
\(336\) −0.557537 0.965682i −0.0304161 0.0526822i
\(337\) −11.3637 + 19.6826i −0.619022 + 1.07218i 0.370642 + 0.928776i \(0.379138\pi\)
−0.989665 + 0.143402i \(0.954196\pi\)
\(338\) −14.3635 24.8784i −0.781273 1.35321i
\(339\) −2.81459 + 4.87502i −0.152868 + 0.264775i
\(340\) −1.52546 + 2.64217i −0.0827296 + 0.143292i
\(341\) 17.1650 0.929538
\(342\) 0 0
\(343\) −19.2762 −1.04082
\(344\) 3.12334 5.40979i 0.168399 0.291676i
\(345\) 1.61430 2.79606i 0.0869112 0.150535i
\(346\) −8.42464 14.5919i −0.452912 0.784466i
\(347\) 2.46428 4.26825i 0.132289 0.229132i −0.792269 0.610171i \(-0.791101\pi\)
0.924559 + 0.381040i \(0.124434\pi\)
\(348\) 1.01338 + 1.75523i 0.0543231 + 0.0940903i
\(349\) 26.1615 1.40039 0.700197 0.713950i \(-0.253096\pi\)
0.700197 + 0.713950i \(0.253096\pi\)
\(350\) −10.5978 −0.566478
\(351\) 8.29470 + 14.3668i 0.442738 + 0.766845i
\(352\) −0.975994 1.69047i −0.0520207 0.0901025i
\(353\) 2.70813 0.144139 0.0720697 0.997400i \(-0.477040\pi\)
0.0720697 + 0.997400i \(0.477040\pi\)
\(354\) −1.25731 −0.0668253
\(355\) −0.0251581 0.0435750i −0.00133525 0.00231272i
\(356\) 0.933870 1.61751i 0.0494950 0.0857279i
\(357\) 1.90803 + 3.30481i 0.100984 + 0.174909i
\(358\) 9.48276 16.4246i 0.501179 0.868068i
\(359\) 4.65501 8.06272i 0.245682 0.425534i −0.716641 0.697442i \(-0.754321\pi\)
0.962323 + 0.271908i \(0.0876547\pi\)
\(360\) 2.49994 0.131759
\(361\) 0 0
\(362\) 1.98687 0.104428
\(363\) 1.59060 2.75500i 0.0834848 0.144600i
\(364\) −8.13963 + 14.0983i −0.426633 + 0.738950i
\(365\) −3.10648 5.38058i −0.162601 0.281632i
\(366\) 0.543113 0.940699i 0.0283890 0.0491711i
\(367\) −3.87721 6.71552i −0.202389 0.350548i 0.746909 0.664926i \(-0.231537\pi\)
−0.949298 + 0.314379i \(0.898204\pi\)
\(368\) 8.18504 0.426675
\(369\) −9.78485 −0.509379
\(370\) 2.66547 + 4.61673i 0.138571 + 0.240012i
\(371\) 4.74138 + 8.21231i 0.246160 + 0.426362i
\(372\) 3.89085 0.201731
\(373\) 25.0124 1.29509 0.647546 0.762027i \(-0.275795\pi\)
0.647546 + 0.762027i \(0.275795\pi\)
\(374\) 3.34011 + 5.78523i 0.172713 + 0.299147i
\(375\) −1.81552 + 3.14456i −0.0937528 + 0.162385i
\(376\) 5.27491 + 9.13641i 0.272033 + 0.471174i
\(377\) 14.7947 25.6251i 0.761965 1.31976i
\(378\) 3.23607 5.60503i 0.166445 0.288292i
\(379\) −19.1802 −0.985222 −0.492611 0.870250i \(-0.663957\pi\)
−0.492611 + 0.870250i \(0.663957\pi\)
\(380\) 0 0
\(381\) −3.17442 −0.162630
\(382\) 10.4630 18.1224i 0.535332 0.927222i
\(383\) −2.41659 + 4.18566i −0.123482 + 0.213877i −0.921139 0.389235i \(-0.872739\pi\)
0.797656 + 0.603112i \(0.206073\pi\)
\(384\) −0.221232 0.383185i −0.0112897 0.0195543i
\(385\) 2.19276 3.79797i 0.111753 0.193562i
\(386\) 3.89440 + 6.74529i 0.198220 + 0.343326i
\(387\) 17.5171 0.890446
\(388\) −7.82432 −0.397219
\(389\) −10.8646 18.8180i −0.550855 0.954109i −0.998213 0.0597540i \(-0.980968\pi\)
0.447358 0.894355i \(-0.352365\pi\)
\(390\) 1.27401 + 2.20665i 0.0645121 + 0.111738i
\(391\) −28.0113 −1.41659
\(392\) −0.648859 −0.0327723
\(393\) 0.779323 + 1.34983i 0.0393116 + 0.0680898i
\(394\) −0.912571 + 1.58062i −0.0459747 + 0.0796304i
\(395\) 4.07038 + 7.05010i 0.204803 + 0.354729i
\(396\) 2.73691 4.74047i 0.137535 0.238217i
\(397\) −5.85701 + 10.1446i −0.293955 + 0.509145i −0.974741 0.223337i \(-0.928305\pi\)
0.680786 + 0.732482i \(0.261638\pi\)
\(398\) 2.35926 0.118259
\(399\) 0 0
\(400\) −4.20524 −0.210262
\(401\) −5.90617 + 10.2298i −0.294940 + 0.510851i −0.974971 0.222332i \(-0.928633\pi\)
0.680031 + 0.733183i \(0.261966\pi\)
\(402\) −0.591266 + 1.02410i −0.0294897 + 0.0510776i
\(403\) −28.4018 49.1934i −1.41479 2.45050i
\(404\) 2.69244 4.66343i 0.133954 0.232015i
\(405\) 3.24341 + 5.61775i 0.161166 + 0.279148i
\(406\) −11.5439 −0.572914
\(407\) 11.6725 0.578584
\(408\) 0.757113 + 1.31136i 0.0374827 + 0.0649219i
\(409\) 12.6331 + 21.8812i 0.624668 + 1.08196i 0.988605 + 0.150534i \(0.0480992\pi\)
−0.363937 + 0.931424i \(0.618568\pi\)
\(410\) −3.11070 −0.153627
\(411\) −4.86867 −0.240154
\(412\) −2.34734 4.06571i −0.115645 0.200303i
\(413\) 3.58064 6.20186i 0.176192 0.305173i
\(414\) 11.4764 + 19.8776i 0.564032 + 0.976932i
\(415\) −6.29567 + 10.9044i −0.309042 + 0.535277i
\(416\) −3.22982 + 5.59422i −0.158355 + 0.274279i
\(417\) 9.62739 0.471455
\(418\) 0 0
\(419\) 31.6143 1.54446 0.772229 0.635344i \(-0.219142\pi\)
0.772229 + 0.635344i \(0.219142\pi\)
\(420\) 0.497039 0.860897i 0.0242530 0.0420075i
\(421\) −1.09486 + 1.89635i −0.0533602 + 0.0924226i −0.891472 0.453076i \(-0.850326\pi\)
0.838112 + 0.545499i \(0.183660\pi\)
\(422\) −0.180525 0.312679i −0.00878783 0.0152210i
\(423\) −14.7920 + 25.6206i −0.719214 + 1.24571i
\(424\) 1.88139 + 3.25866i 0.0913684 + 0.158255i
\(425\) 14.3914 0.698087
\(426\) −0.0249728 −0.00120994
\(427\) 3.09342 + 5.35796i 0.149701 + 0.259290i
\(428\) 8.01864 + 13.8887i 0.387596 + 0.671335i
\(429\) 5.57909 0.269361
\(430\) 5.56887 0.268555
\(431\) −0.901858 1.56206i −0.0434410 0.0752420i 0.843487 0.537149i \(-0.180499\pi\)
−0.886928 + 0.461907i \(0.847165\pi\)
\(432\) 1.28408 2.22409i 0.0617803 0.107007i
\(433\) −3.28616 5.69180i −0.157923 0.273531i 0.776197 0.630491i \(-0.217146\pi\)
−0.934120 + 0.356960i \(0.883813\pi\)
\(434\) −11.0806 + 19.1921i −0.531885 + 0.921252i
\(435\) −0.903423 + 1.56477i −0.0433158 + 0.0750252i
\(436\) −14.1008 −0.675305
\(437\) 0 0
\(438\) −3.08361 −0.147340
\(439\) −4.56530 + 7.90733i −0.217890 + 0.377396i −0.954163 0.299289i \(-0.903251\pi\)
0.736273 + 0.676685i \(0.236584\pi\)
\(440\) 0.870091 1.50704i 0.0414799 0.0718454i
\(441\) −0.909774 1.57577i −0.0433226 0.0750369i
\(442\) 11.0533 19.1449i 0.525752 0.910629i
\(443\) 13.7343 + 23.7885i 0.652536 + 1.13023i 0.982505 + 0.186235i \(0.0596284\pi\)
−0.329969 + 0.943992i \(0.607038\pi\)
\(444\) 2.64584 0.125566
\(445\) 1.66508 0.0789321
\(446\) 9.02431 + 15.6306i 0.427313 + 0.740128i
\(447\) −3.18343 5.51386i −0.150571 0.260797i
\(448\) 2.52015 0.119066
\(449\) 7.57293 0.357389 0.178694 0.983905i \(-0.442813\pi\)
0.178694 + 0.983905i \(0.442813\pi\)
\(450\) −5.89623 10.2126i −0.277951 0.481425i
\(451\) −3.40556 + 5.89860i −0.160362 + 0.277754i
\(452\) −6.36119 11.0179i −0.299205 0.518238i
\(453\) 2.74477 4.75408i 0.128960 0.223366i
\(454\) 6.14224 10.6387i 0.288270 0.499297i
\(455\) −14.5128 −0.680372
\(456\) 0 0
\(457\) −21.7675 −1.01824 −0.509120 0.860696i \(-0.670029\pi\)
−0.509120 + 0.860696i \(0.670029\pi\)
\(458\) −3.39587 + 5.88182i −0.158679 + 0.274839i
\(459\) −4.39445 + 7.61141i −0.205115 + 0.355270i
\(460\) 3.64845 + 6.31929i 0.170110 + 0.294639i
\(461\) −5.97219 + 10.3441i −0.278153 + 0.481775i −0.970926 0.239381i \(-0.923055\pi\)
0.692773 + 0.721156i \(0.256389\pi\)
\(462\) −1.08831 1.88500i −0.0506325 0.0876981i
\(463\) −8.75371 −0.406819 −0.203410 0.979094i \(-0.565202\pi\)
−0.203410 + 0.979094i \(0.565202\pi\)
\(464\) −4.58064 −0.212651
\(465\) 1.73433 + 3.00395i 0.0804276 + 0.139305i
\(466\) −10.7147 18.5584i −0.496348 0.859700i
\(467\) 29.3568 1.35847 0.679236 0.733920i \(-0.262311\pi\)
0.679236 + 0.733920i \(0.262311\pi\)
\(468\) −18.1143 −0.837335
\(469\) −3.36768 5.83300i −0.155505 0.269343i
\(470\) −4.70254 + 8.14503i −0.216912 + 0.375702i
\(471\) 0.0998242 + 0.172901i 0.00459966 + 0.00796684i
\(472\) 1.42081 2.46091i 0.0653980 0.113273i
\(473\) 6.09673 10.5599i 0.280328 0.485543i
\(474\) 4.04041 0.185582
\(475\) 0 0
\(476\) −8.62460 −0.395308
\(477\) −5.27584 + 9.13803i −0.241564 + 0.418401i
\(478\) 5.91881 10.2517i 0.270720 0.468901i
\(479\) 12.4352 + 21.5385i 0.568180 + 0.984117i 0.996746 + 0.0806064i \(0.0256857\pi\)
−0.428566 + 0.903511i \(0.640981\pi\)
\(480\) 0.197226 0.341606i 0.00900210 0.0155921i
\(481\) −19.3137 33.4523i −0.880629 1.52529i
\(482\) 21.7463 0.990517
\(483\) 9.12692 0.415289
\(484\) 3.59487 + 6.22650i 0.163403 + 0.283023i
\(485\) −3.48766 6.04080i −0.158366 0.274298i
\(486\) 10.9240 0.495523
\(487\) 8.53766 0.386878 0.193439 0.981112i \(-0.438036\pi\)
0.193439 + 0.981112i \(0.438036\pi\)
\(488\) 1.22747 + 2.12605i 0.0555652 + 0.0962417i
\(489\) 0.0153212 0.0265371i 0.000692850 0.00120005i
\(490\) −0.289226 0.500954i −0.0130659 0.0226308i
\(491\) 5.76985 9.99368i 0.260390 0.451008i −0.705956 0.708256i \(-0.749482\pi\)
0.966346 + 0.257248i \(0.0828156\pi\)
\(492\) −0.771949 + 1.33705i −0.0348021 + 0.0602791i
\(493\) 15.6762 0.706019
\(494\) 0 0
\(495\) 4.87986 0.219333
\(496\) −4.39680 + 7.61548i −0.197422 + 0.341945i
\(497\) 0.0711190 0.123182i 0.00319013 0.00552546i
\(498\) 3.12465 + 5.41206i 0.140019 + 0.242520i
\(499\) 14.8045 25.6422i 0.662742 1.14790i −0.317151 0.948375i \(-0.602726\pi\)
0.979892 0.199527i \(-0.0639406\pi\)
\(500\) −4.10320 7.10695i −0.183501 0.317832i
\(501\) −0.961785 −0.0429694
\(502\) 23.6410 1.05515
\(503\) −2.93414 5.08207i −0.130827 0.226598i 0.793169 0.609002i \(-0.208430\pi\)
−0.923995 + 0.382403i \(0.875096\pi\)
\(504\) 3.53353 + 6.12026i 0.157396 + 0.272618i
\(505\) 4.80057 0.213622
\(506\) 15.9771 0.710269
\(507\) −6.35534 11.0078i −0.282251 0.488872i
\(508\) 3.58721 6.21323i 0.159157 0.275667i
\(509\) 12.7843 + 22.1431i 0.566656 + 0.981477i 0.996893 + 0.0787614i \(0.0250965\pi\)
−0.430237 + 0.902716i \(0.641570\pi\)
\(510\) −0.674959 + 1.16906i −0.0298877 + 0.0517670i
\(511\) 8.78167 15.2103i 0.388478 0.672864i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 0.923469 0.0407325
\(515\) 2.09263 3.62455i 0.0922124 0.159717i
\(516\) 1.38197 2.39364i 0.0608377 0.105374i
\(517\) 10.2966 + 17.8342i 0.452842 + 0.784346i
\(518\) −7.53498 + 13.0510i −0.331068 + 0.573427i
\(519\) −3.72760 6.45639i −0.163623 0.283404i
\(520\) −5.75872 −0.252537
\(521\) −14.0332 −0.614807 −0.307403 0.951579i \(-0.599460\pi\)
−0.307403 + 0.951579i \(0.599460\pi\)
\(522\) −6.42258 11.1242i −0.281109 0.486895i
\(523\) −15.5392 26.9147i −0.679482 1.17690i −0.975137 0.221602i \(-0.928871\pi\)
0.295655 0.955295i \(-0.404462\pi\)
\(524\) −3.52265 −0.153888
\(525\) −4.68915 −0.204651
\(526\) −2.15984 3.74095i −0.0941734 0.163113i
\(527\) 15.0470 26.0622i 0.655458 1.13529i
\(528\) −0.431842 0.747972i −0.0187935 0.0325513i
\(529\) −21.9974 + 38.1007i −0.956410 + 1.65655i
\(530\) −1.67724 + 2.90507i −0.0728548 + 0.126188i
\(531\) 7.96853 0.345805
\(532\) 0 0
\(533\) 22.5398 0.976307
\(534\) 0.413204 0.715690i 0.0178811 0.0309709i
\(535\) −7.14855 + 12.3816i −0.309059 + 0.535305i
\(536\) −1.33630 2.31455i −0.0577196 0.0999732i
\(537\) 4.19577 7.26729i 0.181061 0.313607i
\(538\) −5.39768 9.34905i −0.232710 0.403066i
\(539\) −1.26657 −0.0545548
\(540\) 2.28949 0.0985240
\(541\) −1.44804 2.50808i −0.0622561 0.107831i 0.833217 0.552945i \(-0.186496\pi\)
−0.895474 + 0.445115i \(0.853163\pi\)
\(542\) −0.403622 0.699093i −0.0173370 0.0300286i
\(543\) 0.879118 0.0377266
\(544\) −3.42226 −0.146728
\(545\) −6.28537 10.8866i −0.269236 0.466330i
\(546\) −3.60149 + 6.23796i −0.154130 + 0.266960i
\(547\) −15.1931 26.3151i −0.649608 1.12515i −0.983217 0.182443i \(-0.941600\pi\)
0.333608 0.942712i \(-0.391734\pi\)
\(548\) 5.50177 9.52935i 0.235024 0.407074i
\(549\) −3.44212 + 5.96192i −0.146906 + 0.254449i
\(550\) −8.20859 −0.350015
\(551\) 0 0
\(552\) 3.62158 0.154145
\(553\) −11.5065 + 19.9299i −0.489306 + 0.847504i
\(554\) 4.57434 7.92300i 0.194345 0.336616i
\(555\) 1.17937 + 2.04273i 0.0500616 + 0.0867092i
\(556\) −10.8793 + 18.8435i −0.461385 + 0.799143i
\(557\) 3.06706 + 5.31231i 0.129956 + 0.225090i 0.923659 0.383215i \(-0.125183\pi\)
−0.793704 + 0.608305i \(0.791850\pi\)
\(558\) −24.6593 −1.04391
\(559\) −40.3514 −1.70668
\(560\) 1.12334 + 1.94569i 0.0474700 + 0.0822204i
\(561\) 1.47788 + 2.55976i 0.0623959 + 0.108073i
\(562\) −21.2158 −0.894932
\(563\) −28.1917 −1.18814 −0.594069 0.804414i \(-0.702479\pi\)
−0.594069 + 0.804414i \(0.702479\pi\)
\(564\) 2.33395 + 4.04253i 0.0982772 + 0.170221i
\(565\) 5.67094 9.82236i 0.238578 0.413230i
\(566\) −2.59493 4.49454i −0.109073 0.188920i
\(567\) −9.16875 + 15.8807i −0.385051 + 0.666929i
\(568\) 0.0282202 0.0488788i 0.00118409 0.00205091i
\(569\) −42.1145 −1.76553 −0.882766 0.469812i \(-0.844322\pi\)
−0.882766 + 0.469812i \(0.844322\pi\)
\(570\) 0 0
\(571\) 0.166927 0.00698566 0.00349283 0.999994i \(-0.498888\pi\)
0.00349283 + 0.999994i \(0.498888\pi\)
\(572\) −6.30458 + 10.9199i −0.263608 + 0.456582i
\(573\) 4.62948 8.01850i 0.193399 0.334977i
\(574\) −4.39680 7.61548i −0.183519 0.317864i
\(575\) 17.2100 29.8087i 0.717708 1.24311i
\(576\) 1.40211 + 2.42853i 0.0584214 + 0.101189i
\(577\) −19.9631 −0.831076 −0.415538 0.909576i \(-0.636407\pi\)
−0.415538 + 0.909576i \(0.636407\pi\)
\(578\) −5.28814 −0.219957
\(579\) 1.72313 + 2.98455i 0.0716108 + 0.124033i
\(580\) −2.04180 3.53651i −0.0847812 0.146845i
\(581\) −35.5943 −1.47670
\(582\) −3.46197 −0.143503
\(583\) 3.67245 + 6.36087i 0.152097 + 0.263440i
\(584\) 3.48459 6.03548i 0.144193 0.249750i
\(585\) −8.07438 13.9852i −0.333835 0.578218i
\(586\) −8.78298 + 15.2126i −0.362822 + 0.628426i
\(587\) −5.07202 + 8.78499i −0.209345 + 0.362595i −0.951508 0.307623i \(-0.900466\pi\)
0.742164 + 0.670219i \(0.233800\pi\)
\(588\) −0.287096 −0.0118397
\(589\) 0 0
\(590\) 2.53328 0.104293
\(591\) −0.403779 + 0.699366i −0.0166093 + 0.0287681i
\(592\) −2.98990 + 5.17866i −0.122884 + 0.212841i
\(593\) −3.72658 6.45462i −0.153032 0.265060i 0.779309 0.626640i \(-0.215570\pi\)
−0.932341 + 0.361581i \(0.882237\pi\)
\(594\) 2.50651 4.34140i 0.102843 0.178130i
\(595\) −3.84438 6.65866i −0.157604 0.272978i
\(596\) 14.3896 0.589420
\(597\) 1.04388 0.0427233
\(598\) −26.4362 45.7889i −1.08106 1.87245i
\(599\) 3.18571 + 5.51781i 0.130164 + 0.225451i 0.923740 0.383020i \(-0.125116\pi\)
−0.793575 + 0.608472i \(0.791783\pi\)
\(600\) −1.86067 −0.0759614
\(601\) 1.74631 0.0712333 0.0356166 0.999366i \(-0.488660\pi\)
0.0356166 + 0.999366i \(0.488660\pi\)
\(602\) 7.87129 + 13.6335i 0.320810 + 0.555659i
\(603\) 3.74730 6.49052i 0.152602 0.264314i
\(604\) 6.20338 + 10.7446i 0.252412 + 0.437190i
\(605\) −3.20480 + 5.55087i −0.130293 + 0.225675i
\(606\) 1.19130 2.06340i 0.0483934 0.0838199i
\(607\) 32.1612 1.30538 0.652691 0.757624i \(-0.273640\pi\)
0.652691 + 0.757624i \(0.273640\pi\)
\(608\) 0 0
\(609\) −5.10775 −0.206977
\(610\) −1.09428 + 1.89535i −0.0443062 + 0.0767407i
\(611\) 34.0741 59.0180i 1.37849 2.38761i
\(612\) −4.79840 8.31106i −0.193964 0.335955i
\(613\) −6.38223 + 11.0543i −0.257776 + 0.446481i −0.965646 0.259862i \(-0.916323\pi\)
0.707870 + 0.706343i \(0.249656\pi\)
\(614\) −10.7842 18.6787i −0.435214 0.753813i
\(615\) −1.37637 −0.0555007
\(616\) 4.91930 0.198204
\(617\) 0.841616 + 1.45772i 0.0338822 + 0.0586856i 0.882469 0.470370i \(-0.155880\pi\)
−0.848587 + 0.529056i \(0.822546\pi\)
\(618\) −1.03861 1.79893i −0.0417791 0.0723635i
\(619\) 31.5285 1.26724 0.633618 0.773646i \(-0.281569\pi\)
0.633618 + 0.773646i \(0.281569\pi\)
\(620\) −7.83942 −0.314839
\(621\) 10.5102 + 18.2043i 0.421761 + 0.730512i
\(622\) 1.28684 2.22887i 0.0515976 0.0893697i
\(623\) 2.35349 + 4.07637i 0.0942906 + 0.163316i
\(624\) −1.42908 + 2.47524i −0.0572090 + 0.0990888i
\(625\) −6.85514 + 11.8735i −0.274206 + 0.474938i
\(626\) −5.18389 −0.207190
\(627\) 0 0
\(628\) −0.451220 −0.0180056
\(629\) 10.2322 17.7227i 0.407985 0.706651i
\(630\) −3.15011 + 5.45616i −0.125503 + 0.217378i
\(631\) 15.8831 + 27.5103i 0.632297 + 1.09517i 0.987081 + 0.160222i \(0.0512209\pi\)
−0.354785 + 0.934948i \(0.615446\pi\)
\(632\) −4.56581 + 7.90821i −0.181618 + 0.314572i
\(633\) −0.0798758 0.138349i −0.00317478 0.00549888i
\(634\) 20.2562 0.804475
\(635\) 6.39593 0.253815
\(636\) 0.832446 + 1.44184i 0.0330086 + 0.0571726i
\(637\) 2.09570 + 3.62986i 0.0830347 + 0.143820i
\(638\) −8.94137 −0.353992
\(639\) 0.158272 0.00626113
\(640\) 0.445746 + 0.772054i 0.0176196 + 0.0305181i
\(641\) 20.2219 35.0253i 0.798715 1.38342i −0.121738 0.992562i \(-0.538847\pi\)
0.920453 0.390853i \(-0.127820\pi\)
\(642\) 3.54795 + 6.14524i 0.140027 + 0.242533i
\(643\) 13.0516 22.6061i 0.514706 0.891497i −0.485148 0.874432i \(-0.661234\pi\)
0.999854 0.0170651i \(-0.00543224\pi\)
\(644\) −10.3138 + 17.8639i −0.406419 + 0.703938i
\(645\) 2.46402 0.0970208
\(646\) 0 0
\(647\) −48.7713 −1.91740 −0.958699 0.284423i \(-0.908198\pi\)
−0.958699 + 0.284423i \(0.908198\pi\)
\(648\) −3.63818 + 6.30151i −0.142921 + 0.247547i
\(649\) 2.77340 4.80367i 0.108866 0.188561i
\(650\) 13.5822 + 23.5251i 0.532738 + 0.922729i
\(651\) −4.90276 + 8.49182i −0.192154 + 0.332821i
\(652\) 0.0346271 + 0.0599759i 0.00135610 + 0.00234884i
\(653\) −43.1831 −1.68988 −0.844942 0.534858i \(-0.820365\pi\)
−0.844942 + 0.534858i \(0.820365\pi\)
\(654\) −6.23909 −0.243968
\(655\) −1.57021 2.71968i −0.0613531 0.106267i
\(656\) −1.74466 3.02184i −0.0681176 0.117983i
\(657\) 19.5431 0.762451
\(658\) −26.5871 −1.03647
\(659\) 7.13844 + 12.3641i 0.278074 + 0.481638i 0.970906 0.239461i \(-0.0769706\pi\)
−0.692832 + 0.721099i \(0.743637\pi\)
\(660\) 0.384983 0.666811i 0.0149855 0.0259556i
\(661\) −17.8748 30.9601i −0.695251 1.20421i −0.970096 0.242721i \(-0.921960\pi\)
0.274846 0.961488i \(-0.411373\pi\)
\(662\) −10.6640 + 18.4706i −0.414468 + 0.717880i
\(663\) 4.89068 8.47091i 0.189938 0.328983i
\(664\) −14.1239 −0.548114
\(665\) 0 0
\(666\) −16.7687 −0.649774
\(667\) 18.7464 32.4697i 0.725863 1.25723i
\(668\) 1.08685 1.88248i 0.0420516 0.0728355i
\(669\) 3.99293 + 6.91595i 0.154375 + 0.267386i
\(670\) 1.19130 2.06340i 0.0460241 0.0797161i
\(671\) 2.39602 + 4.15002i 0.0924972 + 0.160210i
\(672\) 1.11507 0.0430149
\(673\) 10.3574 0.399248 0.199624 0.979873i \(-0.436028\pi\)
0.199624 + 0.979873i \(0.436028\pi\)
\(674\) −11.3637 19.6826i −0.437715 0.758144i
\(675\) −5.39986 9.35284i −0.207841 0.359991i
\(676\) 28.7271 1.10489
\(677\) −10.7171 −0.411891 −0.205945 0.978564i \(-0.566027\pi\)
−0.205945 + 0.978564i \(0.566027\pi\)
\(678\) −2.81459 4.87502i −0.108094 0.187224i
\(679\) 9.85921 17.0767i 0.378362 0.655342i
\(680\) −1.52546 2.64217i −0.0584986 0.101323i
\(681\) 2.71772 4.70722i 0.104143 0.180381i
\(682\) −8.58251 + 14.8653i −0.328641 + 0.569223i
\(683\) 0.122930 0.00470377 0.00235188 0.999997i \(-0.499251\pi\)
0.00235188 + 0.999997i \(0.499251\pi\)
\(684\) 0 0
\(685\) 9.80957 0.374804
\(686\) 9.63812 16.6937i 0.367985 0.637369i
\(687\) −1.50255 + 2.60249i −0.0573258 + 0.0992912i
\(688\) 3.12334 + 5.40979i 0.119076 + 0.206246i
\(689\) 12.1531 21.0498i 0.462997 0.801934i
\(690\) 1.61430 + 2.79606i 0.0614555 + 0.106444i
\(691\) −25.2815 −0.961752 −0.480876 0.876789i \(-0.659681\pi\)
−0.480876 + 0.876789i \(0.659681\pi\)
\(692\) 16.8493 0.640514
\(693\) 6.89741 + 11.9467i 0.262011 + 0.453816i
\(694\) 2.46428 + 4.26825i 0.0935427 + 0.162021i
\(695\) −19.3976 −0.735793
\(696\) −2.02677 −0.0768244
\(697\) 5.97068 + 10.3415i 0.226156 + 0.391713i
\(698\) −13.0808 + 22.6565i −0.495114 + 0.857562i
\(699\) −4.74085 8.21140i −0.179316 0.310584i
\(700\) 5.29892 9.17799i 0.200280 0.346895i
\(701\) 2.58643 4.47984i 0.0976883 0.169201i −0.813039 0.582209i \(-0.802189\pi\)
0.910727 + 0.413008i \(0.135522\pi\)
\(702\) −16.5894 −0.626127
\(703\) 0 0
\(704\) 1.95199 0.0735684
\(705\) −2.08070 + 3.60388i −0.0783637 + 0.135730i
\(706\) −1.35407 + 2.34531i −0.0509610 + 0.0882670i
\(707\) 6.78533 + 11.7525i 0.255189 + 0.442000i
\(708\) 0.628656 1.08886i 0.0236263 0.0409220i
\(709\) 14.9954 + 25.9727i 0.563162 + 0.975426i 0.997218 + 0.0745396i \(0.0237487\pi\)
−0.434056 + 0.900886i \(0.642918\pi\)
\(710\) 0.0503161 0.00188833
\(711\) −25.6071 −0.960342
\(712\) 0.933870 + 1.61751i 0.0349983 + 0.0606188i
\(713\) −35.9880 62.3330i −1.34776 2.33439i
\(714\) −3.81607 −0.142813
\(715\) −11.2410 −0.420388
\(716\) 9.48276 + 16.4246i 0.354387 + 0.613817i
\(717\) 2.61886 4.53600i 0.0978031 0.169400i
\(718\) 4.65501 + 8.06272i 0.173723 + 0.300898i
\(719\) 11.3516 19.6616i 0.423344 0.733254i −0.572920 0.819611i \(-0.694189\pi\)
0.996264 + 0.0863576i \(0.0275228\pi\)
\(720\) −1.24997 + 2.16501i −0.0465837 + 0.0806853i
\(721\) 11.8313 0.440620
\(722\) 0 0
\(723\) 9.62195 0.357844
\(724\) −0.993436 + 1.72068i −0.0369207 + 0.0639486i
\(725\) −9.63136 + 16.6820i −0.357700 + 0.619554i
\(726\) 1.59060 + 2.75500i 0.0590326 + 0.102248i
\(727\) −18.2969 + 31.6911i −0.678593 + 1.17536i 0.296811 + 0.954936i \(0.404077\pi\)
−0.975405 + 0.220422i \(0.929257\pi\)
\(728\) −8.13963 14.0983i −0.301675 0.522516i
\(729\) −16.9956 −0.629467
\(730\) 6.21296 0.229952
\(731\) −10.6889 18.5137i −0.395343 0.684754i
\(732\) 0.543113 + 0.940699i 0.0200740 + 0.0347692i
\(733\) 21.1522 0.781275 0.390637 0.920545i \(-0.372255\pi\)
0.390637 + 0.920545i \(0.372255\pi\)
\(734\) 7.75442 0.286221
\(735\) −0.127972 0.221654i −0.00472032 0.00817583i
\(736\) −4.09252 + 7.08845i −0.150852 + 0.261284i
\(737\) −2.60845 4.51797i −0.0960836 0.166422i
\(738\) 4.89242 8.47393i 0.180093 0.311930i
\(739\) −24.1533 + 41.8348i −0.888494 + 1.53892i −0.0468384 + 0.998902i \(0.514915\pi\)
−0.841656 + 0.540014i \(0.818419\pi\)
\(740\) −5.33094 −0.195969
\(741\) 0 0
\(742\) −9.48276 −0.348123
\(743\) −15.9299 + 27.5914i −0.584412 + 1.01223i 0.410536 + 0.911844i \(0.365341\pi\)
−0.994948 + 0.100387i \(0.967992\pi\)
\(744\) −1.94542 + 3.36957i −0.0713227 + 0.123535i
\(745\) 6.41409 + 11.1095i 0.234994 + 0.407022i
\(746\) −12.5062 + 21.6614i −0.457884 + 0.793078i
\(747\) −19.8033 34.3003i −0.724565 1.25498i
\(748\) −6.68021 −0.244253
\(749\) −40.4163 −1.47678
\(750\) −1.81552 3.14456i −0.0662932 0.114823i
\(751\) 20.4981 + 35.5038i 0.747987 + 1.29555i 0.948786 + 0.315919i \(0.102313\pi\)
−0.200799 + 0.979632i \(0.564354\pi\)
\(752\) −10.5498 −0.384712
\(753\) 10.4603 0.381194
\(754\) 14.7947 + 25.6251i 0.538790 + 0.933212i
\(755\) −5.53026 + 9.57869i −0.201267 + 0.348604i
\(756\) 3.23607 + 5.60503i 0.117695 + 0.203853i
\(757\) 6.41076 11.1038i 0.233003 0.403573i −0.725687 0.688025i \(-0.758478\pi\)
0.958690 + 0.284451i \(0.0918114\pi\)
\(758\) 9.59011 16.6106i 0.348329 0.603323i
\(759\) 7.06929 0.256599
\(760\) 0 0
\(761\) 35.6382 1.29188 0.645942 0.763386i \(-0.276465\pi\)
0.645942 + 0.763386i \(0.276465\pi\)
\(762\) 1.58721 2.74913i 0.0574985 0.0995903i
\(763\) 17.7680 30.7751i 0.643246 1.11413i
\(764\) 10.4630 + 18.1224i 0.378537 + 0.655645i
\(765\) 4.27773 7.40924i 0.154662 0.267882i
\(766\) −2.41659 4.18566i −0.0873151 0.151234i
\(767\) −18.3558 −0.662791
\(768\) 0.442463 0.0159660
\(769\) 2.78701 + 4.82723i 0.100502 + 0.174075i 0.911892 0.410431i \(-0.134622\pi\)
−0.811390 + 0.584506i \(0.801288\pi\)
\(770\) 2.19276 + 3.79797i 0.0790215 + 0.136869i
\(771\) 0.408601 0.0147154
\(772\) −7.78879 −0.280325
\(773\) 18.2060 + 31.5337i 0.654823 + 1.13419i 0.981938 + 0.189202i \(0.0605901\pi\)
−0.327115 + 0.944984i \(0.606077\pi\)
\(774\) −8.75856 + 15.1703i −0.314820 + 0.545284i
\(775\) 18.4896 + 32.0250i 0.664167 + 1.15037i
\(776\) 3.91216 6.77606i 0.140438 0.243246i
\(777\) −3.33395 + 5.77458i −0.119605 + 0.207162i
\(778\) 21.7291 0.779027
\(779\) 0 0
\(780\) −2.54802 −0.0912339