Properties

Label 546.2.p.c.281.10
Level $546$
Weight $2$
Character 546.281
Analytic conductor $4.360$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.p (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + 1065 x^{12} - 2080 x^{11} + 3712 x^{10} - 6240 x^{9} + 9585 x^{8} - 14364 x^{7} + 23328 x^{6} - 34020 x^{5} + 40824 x^{4} - 43740 x^{3} + 52488 x^{2} - 78732 x + 59049\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 281.10
Root \(-1.39758 - 1.02312i\) of defining polynomial
Character \(\chi\) \(=\) 546.281
Dual form 546.2.p.c.239.10

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(1.71169 - 0.264783i) q^{3} -1.00000i q^{4} +(0.790081 - 0.790081i) q^{5} +(1.02312 - 1.39758i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.85978 - 0.906454i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(1.71169 - 0.264783i) q^{3} -1.00000i q^{4} +(0.790081 - 0.790081i) q^{5} +(1.02312 - 1.39758i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.85978 - 0.906454i) q^{9} -1.11734i q^{10} +(-3.45508 - 3.45508i) q^{11} +(-0.264783 - 1.71169i) q^{12} +(-1.18766 - 3.40433i) q^{13} +1.00000i q^{14} +(1.14317 - 1.56157i) q^{15} -1.00000 q^{16} +0.401161 q^{17} +(1.38121 - 2.66313i) q^{18} +(4.88536 + 4.88536i) q^{19} +(-0.790081 - 0.790081i) q^{20} +(-1.02312 + 1.39758i) q^{21} -4.88622 q^{22} +6.12089 q^{23} +(-1.39758 - 1.02312i) q^{24} +3.75155i q^{25} +(-3.24703 - 1.56742i) q^{26} +(4.65505 - 2.30879i) q^{27} +(0.707107 + 0.707107i) q^{28} +1.16528i q^{29} +(-0.295853 - 1.91255i) q^{30} +(2.88418 + 2.88418i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-6.82887 - 4.99918i) q^{33} +(0.283664 - 0.283664i) q^{34} +1.11734i q^{35} +(-0.906454 - 2.85978i) q^{36} +(-4.48595 + 4.48595i) q^{37} +6.90894 q^{38} +(-2.93432 - 5.51269i) q^{39} -1.11734 q^{40} +(-6.76896 + 6.76896i) q^{41} +(0.264783 + 1.71169i) q^{42} -2.74375i q^{43} +(-3.45508 + 3.45508i) q^{44} +(1.54328 - 2.97563i) q^{45} +(4.32812 - 4.32812i) q^{46} +(-5.67285 - 5.67285i) q^{47} +(-1.71169 + 0.264783i) q^{48} -1.00000i q^{49} +(2.65274 + 2.65274i) q^{50} +(0.686665 - 0.106221i) q^{51} +(-3.40433 + 1.18766i) q^{52} +3.46244i q^{53} +(1.65905 - 4.92418i) q^{54} -5.45958 q^{55} +1.00000 q^{56} +(9.65578 + 7.06867i) q^{57} +(0.823979 + 0.823979i) q^{58} +(8.03324 + 8.03324i) q^{59} +(-1.56157 - 1.14317i) q^{60} -0.717748 q^{61} +4.07885 q^{62} +(-1.38121 + 2.66313i) q^{63} +1.00000i q^{64} +(-3.62804 - 1.75134i) q^{65} +(-8.36370 + 1.29379i) q^{66} +(-0.693547 - 0.693547i) q^{67} -0.401161i q^{68} +(10.4771 - 1.62071i) q^{69} +(0.790081 + 0.790081i) q^{70} +(-5.15463 + 5.15463i) q^{71} +(-2.66313 - 1.38121i) q^{72} +(-0.0455596 + 0.0455596i) q^{73} +6.34409i q^{74} +(0.993346 + 6.42149i) q^{75} +(4.88536 - 4.88536i) q^{76} +4.88622 q^{77} +(-5.97294 - 1.82318i) q^{78} -4.24647 q^{79} +(-0.790081 + 0.790081i) q^{80} +(7.35668 - 5.18452i) q^{81} +9.57276i q^{82} +(1.74175 - 1.74175i) q^{83} +(1.39758 + 1.02312i) q^{84} +(0.316950 - 0.316950i) q^{85} +(-1.94012 - 1.94012i) q^{86} +(0.308547 + 1.99461i) q^{87} +4.88622i q^{88} +(-8.55005 - 8.55005i) q^{89} +(-1.01282 - 3.19535i) q^{90} +(3.24703 + 1.56742i) q^{91} -6.12089i q^{92} +(5.70051 + 4.17315i) q^{93} -8.02263 q^{94} +7.71965 q^{95} +(-1.02312 + 1.39758i) q^{96} +(-7.03452 - 7.03452i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(-13.0126 - 6.74889i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 4q^{5} - 4q^{6} - 8q^{9} + O(q^{10}) \) \( 20q - 4q^{5} - 4q^{6} - 8q^{9} - 16q^{11} - 8q^{12} + 4q^{13} - 4q^{15} - 20q^{16} + 12q^{17} - 8q^{18} + 12q^{19} + 4q^{20} + 4q^{21} - 12q^{22} - 4q^{23} + 4q^{24} + 24q^{27} + 12q^{30} - 8q^{31} - 48q^{33} - 4q^{34} + 32q^{37} - 4q^{38} - 16q^{39} - 4q^{40} + 8q^{41} + 8q^{42} - 16q^{44} + 16q^{45} - 8q^{46} + 32q^{50} - 8q^{51} - 8q^{52} + 28q^{54} + 28q^{55} + 20q^{56} + 36q^{57} - 4q^{58} + 20q^{59} - 4q^{60} - 4q^{61} + 48q^{62} + 8q^{63} + 52q^{65} - 36q^{67} + 68q^{69} - 4q^{70} - 28q^{71} - 16q^{72} - 24q^{73} - 76q^{75} + 12q^{76} + 12q^{77} + 40q^{78} - 64q^{79} + 4q^{80} + 32q^{81} - 24q^{83} - 4q^{84} + 24q^{85} + 4q^{86} + 4q^{87} - 4q^{89} - 8q^{90} - 32q^{93} - 40q^{94} - 76q^{95} + 4q^{96} + 32q^{97} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) 1.71169 0.264783i 0.988246 0.152873i
\(4\) 1.00000i 0.500000i
\(5\) 0.790081 0.790081i 0.353335 0.353335i −0.508014 0.861349i \(-0.669620\pi\)
0.861349 + 0.508014i \(0.169620\pi\)
\(6\) 1.02312 1.39758i 0.417687 0.570559i
\(7\) −0.707107 + 0.707107i −0.267261 + 0.267261i
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 2.85978 0.906454i 0.953260 0.302151i
\(10\) 1.11734i 0.353335i
\(11\) −3.45508 3.45508i −1.04174 1.04174i −0.999090 0.0426547i \(-0.986418\pi\)
−0.0426547 0.999090i \(-0.513582\pi\)
\(12\) −0.264783 1.71169i −0.0764363 0.494123i
\(13\) −1.18766 3.40433i −0.329399 0.944191i
\(14\) 1.00000i 0.267261i
\(15\) 1.14317 1.56157i 0.295166 0.403197i
\(16\) −1.00000 −0.250000
\(17\) 0.401161 0.0972959 0.0486480 0.998816i \(-0.484509\pi\)
0.0486480 + 0.998816i \(0.484509\pi\)
\(18\) 1.38121 2.66313i 0.325554 0.627706i
\(19\) 4.88536 + 4.88536i 1.12078 + 1.12078i 0.991625 + 0.129153i \(0.0412258\pi\)
0.129153 + 0.991625i \(0.458774\pi\)
\(20\) −0.790081 0.790081i −0.176667 0.176667i
\(21\) −1.02312 + 1.39758i −0.223263 + 0.304977i
\(22\) −4.88622 −1.04174
\(23\) 6.12089 1.27629 0.638147 0.769915i \(-0.279701\pi\)
0.638147 + 0.769915i \(0.279701\pi\)
\(24\) −1.39758 1.02312i −0.285280 0.208843i
\(25\) 3.75155i 0.750309i
\(26\) −3.24703 1.56742i −0.636795 0.307396i
\(27\) 4.65505 2.30879i 0.895865 0.444327i
\(28\) 0.707107 + 0.707107i 0.133631 + 0.133631i
\(29\) 1.16528i 0.216388i 0.994130 + 0.108194i \(0.0345067\pi\)
−0.994130 + 0.108194i \(0.965493\pi\)
\(30\) −0.295853 1.91255i −0.0540152 0.349182i
\(31\) 2.88418 + 2.88418i 0.518014 + 0.518014i 0.916970 0.398956i \(-0.130627\pi\)
−0.398956 + 0.916970i \(0.630627\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −6.82887 4.99918i −1.18875 0.870246i
\(34\) 0.283664 0.283664i 0.0486480 0.0486480i
\(35\) 1.11734i 0.188865i
\(36\) −0.906454 2.85978i −0.151076 0.476630i
\(37\) −4.48595 + 4.48595i −0.737486 + 0.737486i −0.972091 0.234605i \(-0.924620\pi\)
0.234605 + 0.972091i \(0.424620\pi\)
\(38\) 6.90894 1.12078
\(39\) −2.93432 5.51269i −0.469868 0.882737i
\(40\) −1.11734 −0.176667
\(41\) −6.76896 + 6.76896i −1.05713 + 1.05713i −0.0588688 + 0.998266i \(0.518749\pi\)
−0.998266 + 0.0588688i \(0.981251\pi\)
\(42\) 0.264783 + 1.71169i 0.0408569 + 0.264120i
\(43\) 2.74375i 0.418418i −0.977871 0.209209i \(-0.932911\pi\)
0.977871 0.209209i \(-0.0670889\pi\)
\(44\) −3.45508 + 3.45508i −0.520872 + 0.520872i
\(45\) 1.54328 2.97563i 0.230059 0.443580i
\(46\) 4.32812 4.32812i 0.638147 0.638147i
\(47\) −5.67285 5.67285i −0.827471 0.827471i 0.159696 0.987166i \(-0.448949\pi\)
−0.987166 + 0.159696i \(0.948949\pi\)
\(48\) −1.71169 + 0.264783i −0.247061 + 0.0382181i
\(49\) 1.00000i 0.142857i
\(50\) 2.65274 + 2.65274i 0.375155 + 0.375155i
\(51\) 0.686665 0.106221i 0.0961523 0.0148739i
\(52\) −3.40433 + 1.18766i −0.472095 + 0.164699i
\(53\) 3.46244i 0.475603i 0.971314 + 0.237801i \(0.0764267\pi\)
−0.971314 + 0.237801i \(0.923573\pi\)
\(54\) 1.65905 4.92418i 0.225769 0.670096i
\(55\) −5.45958 −0.736169
\(56\) 1.00000 0.133631
\(57\) 9.65578 + 7.06867i 1.27894 + 0.936268i
\(58\) 0.823979 + 0.823979i 0.108194 + 0.108194i
\(59\) 8.03324 + 8.03324i 1.04584 + 1.04584i 0.998898 + 0.0469418i \(0.0149475\pi\)
0.0469418 + 0.998898i \(0.485052\pi\)
\(60\) −1.56157 1.14317i −0.201598 0.147583i
\(61\) −0.717748 −0.0918983 −0.0459491 0.998944i \(-0.514631\pi\)
−0.0459491 + 0.998944i \(0.514631\pi\)
\(62\) 4.07885 0.518014
\(63\) −1.38121 + 2.66313i −0.174016 + 0.335523i
\(64\) 1.00000i 0.125000i
\(65\) −3.62804 1.75134i −0.450003 0.217228i
\(66\) −8.36370 + 1.29379i −1.02950 + 0.159254i
\(67\) −0.693547 0.693547i −0.0847303 0.0847303i 0.663471 0.748202i \(-0.269082\pi\)
−0.748202 + 0.663471i \(0.769082\pi\)
\(68\) 0.401161i 0.0486480i
\(69\) 10.4771 1.62071i 1.26129 0.195110i
\(70\) 0.790081 + 0.790081i 0.0944327 + 0.0944327i
\(71\) −5.15463 + 5.15463i −0.611742 + 0.611742i −0.943400 0.331658i \(-0.892392\pi\)
0.331658 + 0.943400i \(0.392392\pi\)
\(72\) −2.66313 1.38121i −0.313853 0.162777i
\(73\) −0.0455596 + 0.0455596i −0.00533235 + 0.00533235i −0.709768 0.704436i \(-0.751200\pi\)
0.704436 + 0.709768i \(0.251200\pi\)
\(74\) 6.34409i 0.737486i
\(75\) 0.993346 + 6.42149i 0.114702 + 0.741490i
\(76\) 4.88536 4.88536i 0.560389 0.560389i
\(77\) 4.88622 0.556836
\(78\) −5.97294 1.82318i −0.676302 0.206435i
\(79\) −4.24647 −0.477765 −0.238882 0.971048i \(-0.576781\pi\)
−0.238882 + 0.971048i \(0.576781\pi\)
\(80\) −0.790081 + 0.790081i −0.0883337 + 0.0883337i
\(81\) 7.35668 5.18452i 0.817409 0.576058i
\(82\) 9.57276i 1.05713i
\(83\) 1.74175 1.74175i 0.191182 0.191182i −0.605025 0.796207i \(-0.706837\pi\)
0.796207 + 0.605025i \(0.206837\pi\)
\(84\) 1.39758 + 1.02312i 0.152488 + 0.111631i
\(85\) 0.316950 0.316950i 0.0343780 0.0343780i
\(86\) −1.94012 1.94012i −0.209209 0.209209i
\(87\) 0.308547 + 1.99461i 0.0330797 + 0.213844i
\(88\) 4.88622i 0.520872i
\(89\) −8.55005 8.55005i −0.906304 0.906304i 0.0896678 0.995972i \(-0.471419\pi\)
−0.995972 + 0.0896678i \(0.971419\pi\)
\(90\) −1.01282 3.19535i −0.106761 0.336820i
\(91\) 3.24703 + 1.56742i 0.340381 + 0.164310i
\(92\) 6.12089i 0.638147i
\(93\) 5.70051 + 4.17315i 0.591115 + 0.432735i
\(94\) −8.02263 −0.827471
\(95\) 7.71965 0.792019
\(96\) −1.02312 + 1.39758i −0.104422 + 0.142640i
\(97\) −7.03452 7.03452i −0.714247 0.714247i 0.253174 0.967421i \(-0.418525\pi\)
−0.967421 + 0.253174i \(0.918525\pi\)
\(98\) −0.707107 0.707107i −0.0714286 0.0714286i
\(99\) −13.0126 6.74889i −1.30782 0.678289i
\(100\) 3.75155 0.375155
\(101\) 3.38548 0.336868 0.168434 0.985713i \(-0.446129\pi\)
0.168434 + 0.985713i \(0.446129\pi\)
\(102\) 0.410436 0.560655i 0.0406392 0.0555131i
\(103\) 13.1959i 1.30023i −0.759835 0.650116i \(-0.774720\pi\)
0.759835 0.650116i \(-0.225280\pi\)
\(104\) −1.56742 + 3.24703i −0.153698 + 0.318397i
\(105\) 0.295853 + 1.91255i 0.0288723 + 0.186645i
\(106\) 2.44831 + 2.44831i 0.237801 + 0.237801i
\(107\) 18.9481i 1.83178i 0.401432 + 0.915889i \(0.368513\pi\)
−0.401432 + 0.915889i \(0.631487\pi\)
\(108\) −2.30879 4.65505i −0.222164 0.447932i
\(109\) −5.81740 5.81740i −0.557206 0.557206i 0.371305 0.928511i \(-0.378910\pi\)
−0.928511 + 0.371305i \(0.878910\pi\)
\(110\) −3.86050 + 3.86050i −0.368085 + 0.368085i
\(111\) −6.49076 + 8.86637i −0.616076 + 0.841559i
\(112\) 0.707107 0.707107i 0.0668153 0.0668153i
\(113\) 14.8579i 1.39771i 0.715262 + 0.698856i \(0.246307\pi\)
−0.715262 + 0.698856i \(0.753693\pi\)
\(114\) 11.8260 1.82937i 1.10760 0.171336i
\(115\) 4.83599 4.83599i 0.450959 0.450959i
\(116\) 1.16528 0.108194
\(117\) −6.48232 8.65907i −0.599291 0.800531i
\(118\) 11.3607 1.04584
\(119\) −0.283664 + 0.283664i −0.0260034 + 0.0260034i
\(120\) −1.91255 + 0.295853i −0.174591 + 0.0270076i
\(121\) 12.8751i 1.17046i
\(122\) −0.507525 + 0.507525i −0.0459491 + 0.0459491i
\(123\) −9.79407 + 13.3787i −0.883102 + 1.20632i
\(124\) 2.88418 2.88418i 0.259007 0.259007i
\(125\) 6.91443 + 6.91443i 0.618445 + 0.618445i
\(126\) 0.906454 + 2.85978i 0.0807534 + 0.254769i
\(127\) 2.26219i 0.200737i −0.994950 0.100368i \(-0.967998\pi\)
0.994950 0.100368i \(-0.0320021\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) −0.726498 4.69645i −0.0639646 0.413500i
\(130\) −3.80380 + 1.32703i −0.333615 + 0.116388i
\(131\) 12.7200i 1.11135i −0.831400 0.555675i \(-0.812460\pi\)
0.831400 0.555675i \(-0.187540\pi\)
\(132\) −4.99918 + 6.82887i −0.435123 + 0.594377i
\(133\) −6.90894 −0.599081
\(134\) −0.980824 −0.0847303
\(135\) 1.85373 5.50200i 0.159544 0.473536i
\(136\) −0.283664 0.283664i −0.0243240 0.0243240i
\(137\) 15.4491 + 15.4491i 1.31991 + 1.31991i 0.913844 + 0.406065i \(0.133099\pi\)
0.406065 + 0.913844i \(0.366901\pi\)
\(138\) 6.26240 8.55442i 0.533091 0.728201i
\(139\) 2.96141 0.251184 0.125592 0.992082i \(-0.459917\pi\)
0.125592 + 0.992082i \(0.459917\pi\)
\(140\) 1.11734 0.0944327
\(141\) −11.2123 8.20810i −0.944242 0.691247i
\(142\) 7.28975i 0.611742i
\(143\) −7.65875 + 15.8657i −0.640457 + 1.32676i
\(144\) −2.85978 + 0.906454i −0.238315 + 0.0755379i
\(145\) 0.920667 + 0.920667i 0.0764572 + 0.0764572i
\(146\) 0.0644310i 0.00533235i
\(147\) −0.264783 1.71169i −0.0218389 0.141178i
\(148\) 4.48595 + 4.48595i 0.368743 + 0.368743i
\(149\) −3.74411 + 3.74411i −0.306730 + 0.306730i −0.843640 0.536910i \(-0.819591\pi\)
0.536910 + 0.843640i \(0.319591\pi\)
\(150\) 5.24308 + 3.83828i 0.428096 + 0.313394i
\(151\) 12.1505 12.1505i 0.988794 0.988794i −0.0111437 0.999938i \(-0.503547\pi\)
0.999938 + 0.0111437i \(0.00354723\pi\)
\(152\) 6.90894i 0.560389i
\(153\) 1.14723 0.363634i 0.0927483 0.0293981i
\(154\) 3.45508 3.45508i 0.278418 0.278418i
\(155\) 4.55747 0.366065
\(156\) −5.51269 + 2.93432i −0.441368 + 0.234934i
\(157\) 20.3675 1.62550 0.812750 0.582613i \(-0.197970\pi\)
0.812750 + 0.582613i \(0.197970\pi\)
\(158\) −3.00271 + 3.00271i −0.238882 + 0.238882i
\(159\) 0.916795 + 5.92663i 0.0727066 + 0.470012i
\(160\) 1.11734i 0.0883337i
\(161\) −4.32812 + 4.32812i −0.341104 + 0.341104i
\(162\) 1.53595 8.86797i 0.120676 0.696733i
\(163\) 8.52261 8.52261i 0.667542 0.667542i −0.289604 0.957147i \(-0.593524\pi\)
0.957147 + 0.289604i \(0.0935237\pi\)
\(164\) 6.76896 + 6.76896i 0.528567 + 0.528567i
\(165\) −9.34511 + 1.44560i −0.727516 + 0.112540i
\(166\) 2.46321i 0.191182i
\(167\) −12.4225 12.4225i −0.961284 0.961284i 0.0379938 0.999278i \(-0.487903\pi\)
−0.999278 + 0.0379938i \(0.987903\pi\)
\(168\) 1.71169 0.264783i 0.132060 0.0204285i
\(169\) −10.1789 + 8.08639i −0.782993 + 0.622030i
\(170\) 0.448235i 0.0343780i
\(171\) 18.3994 + 9.54269i 1.40704 + 0.729748i
\(172\) −2.74375 −0.209209
\(173\) −21.8487 −1.66112 −0.830562 0.556926i \(-0.811981\pi\)
−0.830562 + 0.556926i \(0.811981\pi\)
\(174\) 1.62857 + 1.19222i 0.123462 + 0.0903822i
\(175\) −2.65274 2.65274i −0.200529 0.200529i
\(176\) 3.45508 + 3.45508i 0.260436 + 0.260436i
\(177\) 15.8775 + 11.6234i 1.19343 + 0.873666i
\(178\) −12.0916 −0.906304
\(179\) 13.0946 0.978737 0.489369 0.872077i \(-0.337227\pi\)
0.489369 + 0.872077i \(0.337227\pi\)
\(180\) −2.97563 1.54328i −0.221790 0.115030i
\(181\) 18.6617i 1.38711i −0.720403 0.693556i \(-0.756043\pi\)
0.720403 0.693556i \(-0.243957\pi\)
\(182\) 3.40433 1.18766i 0.252346 0.0880355i
\(183\) −1.22856 + 0.190048i −0.0908181 + 0.0140487i
\(184\) −4.32812 4.32812i −0.319073 0.319073i
\(185\) 7.08853i 0.521159i
\(186\) 6.98173 1.08001i 0.511925 0.0791901i
\(187\) −1.38604 1.38604i −0.101358 0.101358i
\(188\) −5.67285 + 5.67285i −0.413735 + 0.413735i
\(189\) −1.65905 + 4.92418i −0.120678 + 0.358181i
\(190\) 5.45862 5.45862i 0.396010 0.396010i
\(191\) 7.22379i 0.522695i 0.965245 + 0.261347i \(0.0841668\pi\)
−0.965245 + 0.261347i \(0.915833\pi\)
\(192\) 0.264783 + 1.71169i 0.0191091 + 0.123531i
\(193\) −19.1571 + 19.1571i −1.37896 + 1.37896i −0.532568 + 0.846387i \(0.678773\pi\)
−0.846387 + 0.532568i \(0.821227\pi\)
\(194\) −9.94831 −0.714247
\(195\) −6.67382 2.03712i −0.477922 0.145881i
\(196\) −1.00000 −0.0714286
\(197\) 17.1364 17.1364i 1.22092 1.22092i 0.253610 0.967307i \(-0.418382\pi\)
0.967307 0.253610i \(-0.0816179\pi\)
\(198\) −13.9735 + 4.42913i −0.993053 + 0.314765i
\(199\) 9.75133i 0.691253i −0.938372 0.345627i \(-0.887666\pi\)
0.938372 0.345627i \(-0.112334\pi\)
\(200\) 2.65274 2.65274i 0.187577 0.187577i
\(201\) −1.37078 1.00350i −0.0966873 0.0707814i
\(202\) 2.39390 2.39390i 0.168434 0.168434i
\(203\) −0.823979 0.823979i −0.0578320 0.0578320i
\(204\) −0.106221 0.686665i −0.00743694 0.0480762i
\(205\) 10.6961i 0.747045i
\(206\) −9.33092 9.33092i −0.650116 0.650116i
\(207\) 17.5044 5.54830i 1.21664 0.385634i
\(208\) 1.18766 + 3.40433i 0.0823496 + 0.236048i
\(209\) 33.7586i 2.33513i
\(210\) 1.56157 + 1.14317i 0.107759 + 0.0788865i
\(211\) 7.32056 0.503968 0.251984 0.967731i \(-0.418917\pi\)
0.251984 + 0.967731i \(0.418917\pi\)
\(212\) 3.46244 0.237801
\(213\) −7.45828 + 10.1880i −0.511033 + 0.698070i
\(214\) 13.3983 + 13.3983i 0.915889 + 0.915889i
\(215\) −2.16778 2.16778i −0.147842 0.147842i
\(216\) −4.92418 1.65905i −0.335048 0.112884i
\(217\) −4.07885 −0.276890
\(218\) −8.22704 −0.557206
\(219\) −0.0659206 + 0.0900475i −0.00445450 + 0.00608484i
\(220\) 5.45958i 0.368085i
\(221\) −0.476445 1.36569i −0.0320491 0.0918659i
\(222\) 1.67981 + 10.8591i 0.112741 + 0.728818i
\(223\) −5.34679 5.34679i −0.358047 0.358047i 0.505045 0.863093i \(-0.331476\pi\)
−0.863093 + 0.505045i \(0.831476\pi\)
\(224\) 1.00000i 0.0668153i
\(225\) 3.40060 + 10.7286i 0.226707 + 0.715240i
\(226\) 10.5061 + 10.5061i 0.698856 + 0.698856i
\(227\) 3.12944 3.12944i 0.207708 0.207708i −0.595584 0.803293i \(-0.703079\pi\)
0.803293 + 0.595584i \(0.203079\pi\)
\(228\) 7.06867 9.65578i 0.468134 0.639470i
\(229\) −18.3485 + 18.3485i −1.21250 + 1.21250i −0.242300 + 0.970201i \(0.577902\pi\)
−0.970201 + 0.242300i \(0.922098\pi\)
\(230\) 6.83913i 0.450959i
\(231\) 8.36370 1.29379i 0.550291 0.0851249i
\(232\) 0.823979 0.823979i 0.0540969 0.0540969i
\(233\) −11.2420 −0.736486 −0.368243 0.929730i \(-0.620041\pi\)
−0.368243 + 0.929730i \(0.620041\pi\)
\(234\) −10.7066 1.53919i −0.699911 0.100620i
\(235\) −8.96402 −0.584748
\(236\) 8.03324 8.03324i 0.522920 0.522920i
\(237\) −7.26864 + 1.12439i −0.472149 + 0.0730372i
\(238\) 0.401161i 0.0260034i
\(239\) −5.38574 + 5.38574i −0.348375 + 0.348375i −0.859504 0.511129i \(-0.829227\pi\)
0.511129 + 0.859504i \(0.329227\pi\)
\(240\) −1.14317 + 1.56157i −0.0737916 + 0.100799i
\(241\) −6.88932 + 6.88932i −0.443780 + 0.443780i −0.893280 0.449500i \(-0.851602\pi\)
0.449500 + 0.893280i \(0.351602\pi\)
\(242\) 9.10407 + 9.10407i 0.585232 + 0.585232i
\(243\) 11.2196 10.8222i 0.719738 0.694246i
\(244\) 0.717748i 0.0459491i
\(245\) −0.790081 0.790081i −0.0504764 0.0504764i
\(246\) 2.53471 + 16.3856i 0.161607 + 1.04471i
\(247\) 10.8292 22.4335i 0.689045 1.42741i
\(248\) 4.07885i 0.259007i
\(249\) 2.52015 3.44253i 0.159708 0.218161i
\(250\) 9.77847 0.618445
\(251\) −7.66247 −0.483651 −0.241825 0.970320i \(-0.577746\pi\)
−0.241825 + 0.970320i \(0.577746\pi\)
\(252\) 2.66313 + 1.38121i 0.167761 + 0.0870080i
\(253\) −21.1481 21.1481i −1.32957 1.32957i
\(254\) −1.59961 1.59961i −0.100368 0.100368i
\(255\) 0.458598 0.626443i 0.0287185 0.0392294i
\(256\) 1.00000 0.0625000
\(257\) 16.8782 1.05283 0.526417 0.850227i \(-0.323535\pi\)
0.526417 + 0.850227i \(0.323535\pi\)
\(258\) −3.83461 2.80718i −0.238732 0.174768i
\(259\) 6.34409i 0.394203i
\(260\) −1.75134 + 3.62804i −0.108614 + 0.225002i
\(261\) 1.05628 + 3.33245i 0.0653818 + 0.206274i
\(262\) −8.99439 8.99439i −0.555675 0.555675i
\(263\) 8.93905i 0.551206i −0.961272 0.275603i \(-0.911123\pi\)
0.961272 0.275603i \(-0.0888774\pi\)
\(264\) 1.29379 + 8.36370i 0.0796271 + 0.514750i
\(265\) 2.73561 + 2.73561i 0.168047 + 0.168047i
\(266\) −4.88536 + 4.88536i −0.299540 + 0.299540i
\(267\) −16.8990 12.3712i −1.03420 0.757102i
\(268\) −0.693547 + 0.693547i −0.0423651 + 0.0423651i
\(269\) 12.7919i 0.779934i −0.920829 0.389967i \(-0.872486\pi\)
0.920829 0.389967i \(-0.127514\pi\)
\(270\) −2.57971 5.20128i −0.156996 0.316540i
\(271\) 8.84670 8.84670i 0.537399 0.537399i −0.385365 0.922764i \(-0.625925\pi\)
0.922764 + 0.385365i \(0.125925\pi\)
\(272\) −0.401161 −0.0243240
\(273\) 5.97294 + 1.82318i 0.361499 + 0.110344i
\(274\) 21.8484 1.31991
\(275\) 12.9619 12.9619i 0.781630 0.781630i
\(276\) −1.62071 10.4771i −0.0975551 0.630646i
\(277\) 20.8417i 1.25226i 0.779720 + 0.626128i \(0.215361\pi\)
−0.779720 + 0.626128i \(0.784639\pi\)
\(278\) 2.09403 2.09403i 0.125592 0.125592i
\(279\) 10.8625 + 5.63374i 0.650321 + 0.337283i
\(280\) 0.790081 0.790081i 0.0472163 0.0472163i
\(281\) −16.1377 16.1377i −0.962693 0.962693i 0.0366360 0.999329i \(-0.488336\pi\)
−0.999329 + 0.0366360i \(0.988336\pi\)
\(282\) −13.7323 + 2.12426i −0.817745 + 0.126498i
\(283\) 10.2026i 0.606483i −0.952914 0.303242i \(-0.901931\pi\)
0.952914 0.303242i \(-0.0980690\pi\)
\(284\) 5.15463 + 5.15463i 0.305871 + 0.305871i
\(285\) 13.2137 2.04403i 0.782710 0.121078i
\(286\) 5.80318 + 16.6343i 0.343149 + 0.983606i
\(287\) 9.57276i 0.565062i
\(288\) −1.38121 + 2.66313i −0.0813886 + 0.156926i
\(289\) −16.8391 −0.990534
\(290\) 1.30202 0.0764572
\(291\) −13.9035 10.1783i −0.815040 0.596663i
\(292\) 0.0455596 + 0.0455596i 0.00266618 + 0.00266618i
\(293\) −21.5130 21.5130i −1.25680 1.25680i −0.952612 0.304189i \(-0.901614\pi\)
−0.304189 0.952612i \(-0.598386\pi\)
\(294\) −1.39758 1.02312i −0.0815085 0.0596695i
\(295\) 12.6938 0.739063
\(296\) 6.34409 0.368743
\(297\) −24.0606 8.10650i −1.39614 0.470387i
\(298\) 5.29497i 0.306730i
\(299\) −7.26955 20.8375i −0.420409 1.20506i
\(300\) 6.42149 0.993346i 0.370745 0.0573508i
\(301\) 1.94012 + 1.94012i 0.111827 + 0.111827i
\(302\) 17.1834i 0.988794i
\(303\) 5.79490 0.896418i 0.332908 0.0514979i
\(304\) −4.88536 4.88536i −0.280194 0.280194i
\(305\) −0.567079 + 0.567079i −0.0324709 + 0.0324709i
\(306\) 0.554088 1.06834i 0.0316751 0.0610732i
\(307\) 6.55827 6.55827i 0.374300 0.374300i −0.494741 0.869041i \(-0.664737\pi\)
0.869041 + 0.494741i \(0.164737\pi\)
\(308\) 4.88622i 0.278418i
\(309\) −3.49405 22.5873i −0.198770 1.28495i
\(310\) 3.22262 3.22262i 0.183032 0.183032i
\(311\) 13.0914 0.742343 0.371171 0.928564i \(-0.378956\pi\)
0.371171 + 0.928564i \(0.378956\pi\)
\(312\) −1.82318 + 5.97294i −0.103217 + 0.338151i
\(313\) 4.62512 0.261427 0.130714 0.991420i \(-0.458273\pi\)
0.130714 + 0.991420i \(0.458273\pi\)
\(314\) 14.4020 14.4020i 0.812750 0.812750i
\(315\) 1.01282 + 3.19535i 0.0570659 + 0.180038i
\(316\) 4.24647i 0.238882i
\(317\) 10.8188 10.8188i 0.607643 0.607643i −0.334686 0.942330i \(-0.608630\pi\)
0.942330 + 0.334686i \(0.108630\pi\)
\(318\) 4.83903 + 3.54249i 0.271359 + 0.198653i
\(319\) 4.02614 4.02614i 0.225421 0.225421i
\(320\) 0.790081 + 0.790081i 0.0441668 + 0.0441668i
\(321\) 5.01712 + 32.4332i 0.280029 + 1.81025i
\(322\) 6.12089i 0.341104i
\(323\) 1.95982 + 1.95982i 0.109047 + 0.109047i
\(324\) −5.18452 7.35668i −0.288029 0.408705i
\(325\) 12.7715 4.45557i 0.708435 0.247151i
\(326\) 12.0528i 0.667542i
\(327\) −11.4979 8.41725i −0.635838 0.465475i
\(328\) 9.57276 0.528567
\(329\) 8.02263 0.442302
\(330\) −5.58580 + 7.63019i −0.307488 + 0.420028i
\(331\) −4.19602 4.19602i −0.230634 0.230634i 0.582323 0.812957i \(-0.302144\pi\)
−0.812957 + 0.582323i \(0.802144\pi\)
\(332\) −1.74175 1.74175i −0.0955910 0.0955910i
\(333\) −8.76253 + 16.8951i −0.480183 + 0.925848i
\(334\) −17.5681 −0.961284
\(335\) −1.09592 −0.0598763
\(336\) 1.02312 1.39758i 0.0558157 0.0762442i
\(337\) 13.8715i 0.755631i −0.925881 0.377815i \(-0.876675\pi\)
0.925881 0.377815i \(-0.123325\pi\)
\(338\) −1.47963 + 12.9155i −0.0804815 + 0.702512i
\(339\) 3.93412 + 25.4321i 0.213672 + 1.38128i
\(340\) −0.316950 0.316950i −0.0171890 0.0171890i
\(341\) 19.9301i 1.07928i
\(342\) 19.7580 6.26263i 1.06839 0.338644i
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) −1.94012 + 1.94012i −0.104604 + 0.104604i
\(345\) 6.99724 9.55822i 0.376719 0.514597i
\(346\) −15.4494 + 15.4494i −0.830562 + 0.830562i
\(347\) 31.5445i 1.69340i 0.532072 + 0.846699i \(0.321414\pi\)
−0.532072 + 0.846699i \(0.678586\pi\)
\(348\) 1.99461 0.308547i 0.106922 0.0165399i
\(349\) −17.5248 + 17.5248i −0.938083 + 0.938083i −0.998192 0.0601086i \(-0.980855\pi\)
0.0601086 + 0.998192i \(0.480855\pi\)
\(350\) −3.75155 −0.200529
\(351\) −13.3885 13.1053i −0.714626 0.699507i
\(352\) 4.88622 0.260436
\(353\) 13.8691 13.8691i 0.738177 0.738177i −0.234048 0.972225i \(-0.575197\pi\)
0.972225 + 0.234048i \(0.0751972\pi\)
\(354\) 19.4461 3.00813i 1.03355 0.159880i
\(355\) 8.14514i 0.432299i
\(356\) −8.55005 + 8.55005i −0.453152 + 0.453152i
\(357\) −0.410436 + 0.560655i −0.0217226 + 0.0296730i
\(358\) 9.25929 9.25929i 0.489369 0.489369i
\(359\) 3.97606 + 3.97606i 0.209848 + 0.209848i 0.804203 0.594355i \(-0.202592\pi\)
−0.594355 + 0.804203i \(0.702592\pi\)
\(360\) −3.19535 + 1.01282i −0.168410 + 0.0533803i
\(361\) 28.7334i 1.51228i
\(362\) −13.1958 13.1958i −0.693556 0.693556i
\(363\) 3.40911 + 22.0382i 0.178932 + 1.15671i
\(364\) 1.56742 3.24703i 0.0821551 0.170191i
\(365\) 0.0719915i 0.00376821i
\(366\) −0.734342 + 1.00311i −0.0383847 + 0.0524334i
\(367\) −0.717511 −0.0374538 −0.0187269 0.999825i \(-0.505961\pi\)
−0.0187269 + 0.999825i \(0.505961\pi\)
\(368\) −6.12089 −0.319073
\(369\) −13.2220 + 25.4935i −0.688309 + 1.32714i
\(370\) 5.01235 + 5.01235i 0.260579 + 0.260579i
\(371\) −2.44831 2.44831i −0.127110 0.127110i
\(372\) 4.17315 5.70051i 0.216368 0.295558i
\(373\) −9.28116 −0.480560 −0.240280 0.970704i \(-0.577239\pi\)
−0.240280 + 0.970704i \(0.577239\pi\)
\(374\) −1.96016 −0.101358
\(375\) 13.6662 + 10.0045i 0.705719 + 0.516632i
\(376\) 8.02263i 0.413735i
\(377\) 3.96701 1.38396i 0.204311 0.0712777i
\(378\) 2.30879 + 4.65505i 0.118751 + 0.239430i
\(379\) 12.4251 + 12.4251i 0.638236 + 0.638236i 0.950120 0.311884i \(-0.100960\pi\)
−0.311884 + 0.950120i \(0.600960\pi\)
\(380\) 7.71965i 0.396010i
\(381\) −0.598989 3.87217i −0.0306871 0.198377i
\(382\) 5.10799 + 5.10799i 0.261347 + 0.261347i
\(383\) −13.7627 + 13.7627i −0.703243 + 0.703243i −0.965105 0.261863i \(-0.915663\pi\)
0.261863 + 0.965105i \(0.415663\pi\)
\(384\) 1.39758 + 1.02312i 0.0713199 + 0.0522108i
\(385\) 3.86050 3.86050i 0.196749 0.196749i
\(386\) 27.0922i 1.37896i
\(387\) −2.48708 7.84652i −0.126426 0.398861i
\(388\) −7.03452 + 7.03452i −0.357123 + 0.357123i
\(389\) −4.94989 −0.250970 −0.125485 0.992096i \(-0.540049\pi\)
−0.125485 + 0.992096i \(0.540049\pi\)
\(390\) −6.15956 + 3.27864i −0.311902 + 0.166021i
\(391\) 2.45546 0.124178
\(392\) −0.707107 + 0.707107i −0.0357143 + 0.0357143i
\(393\) −3.36804 21.7727i −0.169895 1.09829i
\(394\) 24.2345i 1.22092i
\(395\) −3.35505 + 3.35505i −0.168811 + 0.168811i
\(396\) −6.74889 + 13.0126i −0.339144 + 0.653909i
\(397\) 9.83277 9.83277i 0.493493 0.493493i −0.415912 0.909405i \(-0.636538\pi\)
0.909405 + 0.415912i \(0.136538\pi\)
\(398\) −6.89523 6.89523i −0.345627 0.345627i
\(399\) −11.8260 + 1.82937i −0.592039 + 0.0915830i
\(400\) 3.75155i 0.187577i
\(401\) −1.18747 1.18747i −0.0592992 0.0592992i 0.676835 0.736134i \(-0.263351\pi\)
−0.736134 + 0.676835i \(0.763351\pi\)
\(402\) −1.67887 + 0.259706i −0.0837343 + 0.0129529i
\(403\) 6.39326 13.2441i 0.318471 0.659737i
\(404\) 3.38548i 0.168434i
\(405\) 1.71618 9.90856i 0.0852778 0.492360i
\(406\) −1.16528 −0.0578320
\(407\) 30.9986 1.53654
\(408\) −0.560655 0.410436i −0.0277565 0.0203196i
\(409\) −1.16592 1.16592i −0.0576512 0.0576512i 0.677693 0.735345i \(-0.262980\pi\)
−0.735345 + 0.677693i \(0.762980\pi\)
\(410\) 7.56325 + 7.56325i 0.373522 + 0.373522i
\(411\) 30.5348 + 22.3535i 1.50617 + 1.10262i
\(412\) −13.1959 −0.650116
\(413\) −11.3607 −0.559025
\(414\) 8.45423 16.3007i 0.415503 0.801137i
\(415\) 2.75225i 0.135102i
\(416\) 3.24703 + 1.56742i 0.159199 + 0.0768491i
\(417\) 5.06902 0.784131i 0.248231 0.0383991i
\(418\) −23.8709 23.8709i −1.16756 1.16756i
\(419\) 13.3819i 0.653748i 0.945068 + 0.326874i \(0.105995\pi\)
−0.945068 + 0.326874i \(0.894005\pi\)
\(420\) 1.91255 0.295853i 0.0933227 0.0144362i
\(421\) −25.6047 25.6047i −1.24790 1.24790i −0.956646 0.291253i \(-0.905928\pi\)
−0.291253 0.956646i \(-0.594072\pi\)
\(422\) 5.17642 5.17642i 0.251984 0.251984i
\(423\) −21.3653 11.0809i −1.03882 0.538773i
\(424\) 2.44831 2.44831i 0.118901 0.118901i
\(425\) 1.50498i 0.0730020i
\(426\) 1.93020 + 12.4778i 0.0935186 + 0.604551i
\(427\) 0.507525 0.507525i 0.0245608 0.0245608i
\(428\) 18.9481 0.915889
\(429\) −8.90845 + 29.1851i −0.430104 + 1.40907i
\(430\) −3.06571 −0.147842
\(431\) 1.57749 1.57749i 0.0759852 0.0759852i −0.668093 0.744078i \(-0.732889\pi\)
0.744078 + 0.668093i \(0.232889\pi\)
\(432\) −4.65505 + 2.30879i −0.223966 + 0.111082i
\(433\) 4.98342i 0.239488i −0.992805 0.119744i \(-0.961793\pi\)
0.992805 0.119744i \(-0.0382074\pi\)
\(434\) −2.88418 + 2.88418i −0.138445 + 0.138445i
\(435\) 1.81968 + 1.33212i 0.0872468 + 0.0638703i
\(436\) −5.81740 + 5.81740i −0.278603 + 0.278603i
\(437\) 29.9027 + 29.9027i 1.43044 + 1.43044i
\(438\) 0.0170602 + 0.110286i 0.000815170 + 0.00526967i
\(439\) 16.2436i 0.775265i 0.921814 + 0.387633i \(0.126707\pi\)
−0.921814 + 0.387633i \(0.873293\pi\)
\(440\) 3.86050 + 3.86050i 0.184042 + 0.184042i
\(441\) −0.906454 2.85978i −0.0431645 0.136180i
\(442\) −1.30258 0.628788i −0.0619575 0.0299084i
\(443\) 36.6212i 1.73993i −0.493115 0.869964i \(-0.664142\pi\)
0.493115 0.869964i \(-0.335858\pi\)
\(444\) 8.86637 + 6.49076i 0.420779 + 0.308038i
\(445\) −13.5105 −0.640457
\(446\) −7.56150 −0.358047
\(447\) −5.41739 + 7.40014i −0.256234 + 0.350015i
\(448\) −0.707107 0.707107i −0.0334077 0.0334077i
\(449\) 15.8676 + 15.8676i 0.748839 + 0.748839i 0.974261 0.225422i \(-0.0723762\pi\)
−0.225422 + 0.974261i \(0.572376\pi\)
\(450\) 9.99085 + 5.18167i 0.470973 + 0.244266i
\(451\) 46.7746 2.20253
\(452\) 14.8579 0.698856
\(453\) 17.5807 24.0152i 0.826012 1.12833i
\(454\) 4.42570i 0.207708i
\(455\) 3.80380 1.32703i 0.178325 0.0622120i
\(456\) −1.82937 11.8260i −0.0856681 0.553802i
\(457\) 4.36244 + 4.36244i 0.204066 + 0.204066i 0.801740 0.597673i \(-0.203908\pi\)
−0.597673 + 0.801740i \(0.703908\pi\)
\(458\) 25.9487i 1.21250i
\(459\) 1.86743 0.926198i 0.0871640 0.0432312i
\(460\) −4.83599 4.83599i −0.225479 0.225479i
\(461\) −10.1936 + 10.1936i −0.474762 + 0.474762i −0.903452 0.428690i \(-0.858975\pi\)
0.428690 + 0.903452i \(0.358975\pi\)
\(462\) 4.99918 6.82887i 0.232583 0.317708i
\(463\) −26.1202 + 26.1202i −1.21391 + 1.21391i −0.244181 + 0.969730i \(0.578519\pi\)
−0.969730 + 0.244181i \(0.921481\pi\)
\(464\) 1.16528i 0.0540969i
\(465\) 7.80098 1.20674i 0.361762 0.0559613i
\(466\) −7.94927 + 7.94927i −0.368243 + 0.368243i
\(467\) 12.0016 0.555368 0.277684 0.960673i \(-0.410433\pi\)
0.277684 + 0.960673i \(0.410433\pi\)
\(468\) −8.65907 + 6.48232i −0.400266 + 0.299646i
\(469\) 0.980824 0.0452902
\(470\) −6.33852 + 6.33852i −0.292374 + 0.292374i
\(471\) 34.8628 5.39296i 1.60639 0.248494i
\(472\) 11.3607i 0.522920i
\(473\) −9.47986 + 9.47986i −0.435885 + 0.435885i
\(474\) −4.34464 + 5.93477i −0.199556 + 0.272593i
\(475\) −18.3276 + 18.3276i −0.840930 + 0.840930i
\(476\) 0.283664 + 0.283664i 0.0130017 + 0.0130017i
\(477\) 3.13854 + 9.90181i 0.143704 + 0.453373i
\(478\) 7.61659i 0.348375i
\(479\) −27.0032 27.0032i −1.23381 1.23381i −0.962490 0.271317i \(-0.912541\pi\)
−0.271317 0.962490i \(-0.587459\pi\)
\(480\) 0.295853 + 1.91255i 0.0135038 + 0.0872954i
\(481\) 20.5995 + 9.94386i 0.939254 + 0.453401i
\(482\) 9.74296i 0.443780i
\(483\) −6.26240 + 8.55442i −0.284949 + 0.389240i
\(484\) 12.8751 0.585232
\(485\) −11.1157 −0.504736
\(486\) 0.280987 15.5859i 0.0127458 0.706992i
\(487\) −25.0734 25.0734i −1.13618 1.13618i −0.989128 0.147055i \(-0.953020\pi\)
−0.147055 0.989128i \(-0.546980\pi\)
\(488\) 0.507525 + 0.507525i 0.0229746 + 0.0229746i
\(489\) 12.3314 16.8447i 0.557647 0.761745i
\(490\) −1.11734 −0.0504764
\(491\) 5.26963 0.237815 0.118907 0.992905i \(-0.462061\pi\)
0.118907 + 0.992905i \(0.462061\pi\)
\(492\) 13.3787 + 9.79407i 0.603158 + 0.441551i
\(493\) 0.467466i 0.0210536i
\(494\) −8.20549 23.5203i −0.369182 1.05823i
\(495\) −15.6132 + 4.94886i −0.701761 + 0.222435i
\(496\) −2.88418 2.88418i −0.129503 0.129503i
\(497\) 7.28975i 0.326990i
\(498\) −0.652216 4.21625i −0.0292265 0.188935i
\(499\) 2.56674 + 2.56674i 0.114903 + 0.114903i 0.762221 0.647317i \(-0.224109\pi\)
−0.647317 + 0.762221i \(0.724109\pi\)
\(500\) 6.91443 6.91443i 0.309223 0.309223i
\(501\) −24.5528 17.9743i −1.09694 0.803031i
\(502\) −5.41818 + 5.41818i −0.241825 + 0.241825i
\(503\) 9.03215i 0.402724i 0.979517 + 0.201362i \(0.0645367\pi\)
−0.979517 + 0.201362i \(0.935463\pi\)
\(504\) 2.85978 0.906454i 0.127385 0.0403767i
\(505\) 2.67480 2.67480i 0.119027 0.119027i
\(506\) −29.9080 −1.32957
\(507\) −15.2820 + 16.5366i −0.678698 + 0.734417i
\(508\) −2.26219 −0.100368
\(509\) −13.7882 + 13.7882i −0.611152 + 0.611152i −0.943246 0.332094i \(-0.892245\pi\)
0.332094 + 0.943246i \(0.392245\pi\)
\(510\) −0.118685 0.767240i −0.00525546 0.0339740i
\(511\) 0.0644310i 0.00285026i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 34.0208 + 11.4623i 1.50206 + 0.506073i
\(514\) 11.9347 11.9347i 0.526417 0.526417i
\(515\) −10.4258 10.4258i −0.459417 0.459417i
\(516\) −4.69645 + 0.726498i −0.206750 + 0.0319823i
\(517\) 39.2003i 1.72403i
\(518\) −4.48595 4.48595i −0.197101 0.197101i
\(519\) −37.3982 + 5.78516i −1.64160 + 0.253940i
\(520\) 1.32703 + 3.80380i 0.0581940 + 0.166808i
\(521\) 23.1627i 1.01477i 0.861718 + 0.507387i \(0.169389\pi\)
−0.861718 + 0.507387i \(0.830611\pi\)
\(522\) 3.10330 + 1.60950i 0.135828 + 0.0704459i
\(523\) 32.4378 1.41840 0.709202 0.705005i \(-0.249055\pi\)
0.709202 + 0.705005i \(0.249055\pi\)
\(524\) −12.7200 −0.555675
\(525\) −5.24308 3.83828i −0.228827 0.167516i
\(526\) −6.32086 6.32086i −0.275603 0.275603i
\(527\) 1.15702 + 1.15702i 0.0504007 + 0.0504007i
\(528\) 6.82887 + 4.99918i 0.297189 + 0.217561i
\(529\) 14.4653 0.628925
\(530\) 3.86873 0.168047
\(531\) 30.2551 + 15.6915i 1.31296 + 0.680955i
\(532\) 6.90894i 0.299540i
\(533\) 31.0830 + 15.0045i 1.34636 + 0.649918i
\(534\) −20.6971 + 3.20165i −0.895651 + 0.138549i
\(535\) 14.9705 + 14.9705i 0.647231 + 0.647231i
\(536\) 0.980824i 0.0423651i
\(537\) 22.4139 3.46723i 0.967233 0.149622i
\(538\) −9.04522 9.04522i −0.389967 0.389967i
\(539\) −3.45508 + 3.45508i −0.148821 + 0.148821i
\(540\) −5.50200 1.85373i −0.236768 0.0797719i
\(541\) −4.03020 + 4.03020i −0.173272 + 0.173272i −0.788415 0.615143i \(-0.789098\pi\)
0.615143 + 0.788415i \(0.289098\pi\)
\(542\) 12.5111i 0.537399i
\(543\) −4.94130 31.9431i −0.212051 1.37081i
\(544\) −0.283664 + 0.283664i −0.0121620 + 0.0121620i
\(545\) −9.19243 −0.393760
\(546\) 5.51269 2.93432i 0.235921 0.125577i
\(547\) −26.2318 −1.12159 −0.560795 0.827955i \(-0.689505\pi\)
−0.560795 + 0.827955i \(0.689505\pi\)
\(548\) 15.4491 15.4491i 0.659955 0.659955i
\(549\) −2.05260 + 0.650606i −0.0876029 + 0.0277672i
\(550\) 18.3309i 0.781630i
\(551\) −5.69282 + 5.69282i −0.242522 + 0.242522i
\(552\) −8.55442 6.26240i −0.364100 0.266545i
\(553\) 3.00271 3.00271i 0.127688 0.127688i
\(554\) 14.7373 + 14.7373i 0.626128 + 0.626128i
\(555\) 1.87692 + 12.1334i 0.0796709 + 0.515033i
\(556\) 2.96141i 0.125592i
\(557\) −16.9451 16.9451i −0.717988 0.717988i 0.250205 0.968193i \(-0.419502\pi\)
−0.968193 + 0.250205i \(0.919502\pi\)
\(558\) 11.6646 3.69729i 0.493802 0.156519i
\(559\) −9.34063 + 3.25865i −0.395066 + 0.137826i
\(560\) 1.11734i 0.0472163i
\(561\) −2.73948 2.00548i −0.115661 0.0846714i
\(562\) −22.8221 −0.962693
\(563\) −43.2433 −1.82249 −0.911243 0.411869i \(-0.864876\pi\)
−0.911243 + 0.411869i \(0.864876\pi\)
\(564\) −8.20810 + 11.2123i −0.345623 + 0.472121i
\(565\) 11.7389 + 11.7389i 0.493860 + 0.493860i
\(566\) −7.21435 7.21435i −0.303242 0.303242i
\(567\) −1.53595 + 8.86797i −0.0645039 + 0.372420i
\(568\) 7.28975 0.305871
\(569\) −12.0354 −0.504549 −0.252274 0.967656i \(-0.581179\pi\)
−0.252274 + 0.967656i \(0.581179\pi\)
\(570\) 7.89812 10.7888i 0.330816 0.451894i
\(571\) 35.0986i 1.46883i 0.678699 + 0.734416i \(0.262544\pi\)
−0.678699 + 0.734416i \(0.737456\pi\)
\(572\) 15.8657 + 7.65875i 0.663378 + 0.320228i
\(573\) 1.91274 + 12.3649i 0.0799057 + 0.516551i
\(574\) −6.76896 6.76896i −0.282531 0.282531i
\(575\) 22.9628i 0.957615i
\(576\) 0.906454 + 2.85978i 0.0377689 + 0.119157i
\(577\) 8.36869 + 8.36869i 0.348393 + 0.348393i 0.859511 0.511118i \(-0.170768\pi\)
−0.511118 + 0.859511i \(0.670768\pi\)
\(578\) −11.9070 + 11.9070i −0.495267 + 0.495267i
\(579\) −27.7185 + 37.8635i −1.15194 + 1.57355i
\(580\) 0.920667 0.920667i 0.0382286 0.0382286i
\(581\) 2.46321i 0.102191i
\(582\) −17.0284 + 2.63414i −0.705851 + 0.109189i
\(583\) 11.9630 11.9630i 0.495456 0.495456i
\(584\) 0.0644310 0.00266618
\(585\) −11.9629 1.71980i −0.494606 0.0711051i
\(586\) −30.4239 −1.25680
\(587\) 23.2366 23.2366i 0.959076 0.959076i −0.0401193 0.999195i \(-0.512774\pi\)
0.999195 + 0.0401193i \(0.0127738\pi\)
\(588\) −1.71169 + 0.264783i −0.0705890 + 0.0109195i
\(589\) 28.1805i 1.16116i
\(590\) 8.97589 8.97589i 0.369531 0.369531i
\(591\) 24.7948 33.8696i 1.01992 1.39321i
\(592\) 4.48595 4.48595i 0.184371 0.184371i
\(593\) 14.2518 + 14.2518i 0.585250 + 0.585250i 0.936341 0.351091i \(-0.114189\pi\)
−0.351091 + 0.936341i \(0.614189\pi\)
\(594\) −22.7456 + 11.2813i −0.933262 + 0.462875i
\(595\) 0.448235i 0.0183758i
\(596\) 3.74411 + 3.74411i 0.153365 + 0.153365i
\(597\) −2.58199 16.6913i −0.105674 0.683128i
\(598\) −19.8747 9.59400i −0.812737 0.392328i
\(599\) 13.6271i 0.556787i −0.960467 0.278394i \(-0.910198\pi\)
0.960467 0.278394i \(-0.0898020\pi\)
\(600\) 3.83828 5.24308i 0.156697 0.214048i
\(601\) −8.52974 −0.347936 −0.173968 0.984751i \(-0.555659\pi\)
−0.173968 + 0.984751i \(0.555659\pi\)
\(602\) 2.74375 0.111827
\(603\) −2.61206 1.35472i −0.106371 0.0551686i
\(604\) −12.1505 12.1505i −0.494397 0.494397i
\(605\) 10.1724 + 10.1724i 0.413566 + 0.413566i
\(606\) 3.46375 4.73148i 0.140705 0.192203i
\(607\) −7.46360 −0.302938 −0.151469 0.988462i \(-0.548400\pi\)
−0.151469 + 0.988462i \(0.548400\pi\)
\(608\) −6.90894 −0.280194
\(609\) −1.62857 1.19222i −0.0659932 0.0483113i
\(610\) 0.801971i 0.0324709i
\(611\) −12.5748 + 26.0497i −0.508723 + 1.05386i
\(612\) −0.363634 1.14723i −0.0146991 0.0463742i
\(613\) 30.4690 + 30.4690i 1.23063 + 1.23063i 0.963721 + 0.266910i \(0.0860026\pi\)
0.266910 + 0.963721i \(0.413997\pi\)
\(614\) 9.27479i 0.374300i
\(615\) 2.83213 + 18.3083i 0.114203 + 0.738264i
\(616\) −3.45508 3.45508i −0.139209 0.139209i
\(617\) −21.2814 + 21.2814i −0.856755 + 0.856755i −0.990954 0.134199i \(-0.957154\pi\)
0.134199 + 0.990954i \(0.457154\pi\)
\(618\) −18.4423 13.5010i −0.741859 0.543089i
\(619\) 1.08316 1.08316i 0.0435359 0.0435359i −0.685004 0.728540i \(-0.740199\pi\)
0.728540 + 0.685004i \(0.240199\pi\)
\(620\) 4.55747i 0.183032i
\(621\) 28.4930 14.1319i 1.14339 0.567092i
\(622\) 9.25699 9.25699i 0.371171 0.371171i
\(623\) 12.0916 0.484440
\(624\) 2.93432 + 5.51269i 0.117467 + 0.220684i
\(625\) −7.83182 −0.313273
\(626\) 3.27045 3.27045i 0.130714 0.130714i
\(627\) −8.93869 57.7842i −0.356977 2.30768i
\(628\) 20.3675i 0.812750i
\(629\) −1.79959 + 1.79959i −0.0717544 + 0.0717544i
\(630\) 2.97563 + 1.54328i 0.118552 + 0.0614859i
\(631\) −7.38311 + 7.38311i −0.293917 + 0.293917i −0.838625 0.544709i \(-0.816640\pi\)
0.544709 + 0.838625i \(0.316640\pi\)
\(632\) 3.00271 + 3.00271i 0.119441 + 0.119441i
\(633\) 12.5305 1.93836i 0.498044 0.0770429i
\(634\) 15.3001i 0.607643i
\(635\) −1.78731 1.78731i −0.0709272 0.0709272i
\(636\) 5.92663 0.916795i 0.235006 0.0363533i
\(637\) −3.40433 + 1.18766i −0.134884 + 0.0470569i
\(638\) 5.69382i 0.225421i
\(639\) −10.0687 + 19.4135i −0.398310 + 0.767988i
\(640\) 1.11734 0.0441668
\(641\) −18.4812 −0.729964 −0.364982 0.931015i \(-0.618925\pi\)
−0.364982 + 0.931015i \(0.618925\pi\)
\(642\) 26.4814 + 19.3861i 1.04514 + 0.765109i
\(643\) 29.6076 + 29.6076i 1.16761 + 1.16761i 0.982768 + 0.184844i \(0.0591779\pi\)
0.184844 + 0.982768i \(0.440822\pi\)
\(644\) 4.32812 + 4.32812i 0.170552 + 0.170552i
\(645\) −4.28457 3.13659i −0.168705 0.123503i
\(646\) 2.77160 0.109047
\(647\) 22.8592 0.898690 0.449345 0.893358i \(-0.351657\pi\)
0.449345 + 0.893358i \(0.351657\pi\)
\(648\) −8.86797 1.53595i −0.348367 0.0603378i
\(649\) 55.5109i 2.17900i
\(650\) 5.88024 12.1814i 0.230642 0.477793i
\(651\) −6.98173 + 1.08001i −0.273636 + 0.0423289i
\(652\) −8.52261 8.52261i −0.333771 0.333771i
\(653\) 20.8455i 0.815748i −0.913038 0.407874i \(-0.866270\pi\)
0.913038 0.407874i \(-0.133730\pi\)
\(654\) −14.0822 + 2.17838i −0.550656 + 0.0851815i
\(655\) −10.0498 10.0498i −0.392679 0.392679i
\(656\) 6.76896 6.76896i 0.264284 0.264284i
\(657\) −0.0889928 + 0.171588i −0.00347194 + 0.00669429i
\(658\) 5.67285 5.67285i 0.221151 0.221151i
\(659\) 20.6669i 0.805067i 0.915405 + 0.402534i \(0.131870\pi\)
−0.915405 + 0.402534i \(0.868130\pi\)
\(660\) 1.44560 + 9.34511i 0.0562700 + 0.363758i
\(661\) 8.65092 8.65092i 0.336482 0.336482i −0.518560 0.855041i \(-0.673532\pi\)
0.855041 + 0.518560i \(0.173532\pi\)
\(662\) −5.93406 −0.230634
\(663\) −1.17714 2.21148i −0.0457162 0.0858867i
\(664\) −2.46321 −0.0955910
\(665\) −5.45862 + 5.45862i −0.211676 + 0.211676i
\(666\) 5.75063 + 18.1427i 0.222832 + 0.703016i
\(667\) 7.13256i 0.276174i
\(668\) −12.4225 + 12.4225i −0.480642 + 0.480642i
\(669\) −10.5678 7.73631i −0.408574 0.299103i
\(670\) −0.774930 + 0.774930i −0.0299381 + 0.0299381i
\(671\) 2.47988 + 2.47988i 0.0957345 + 0.0957345i
\(672\) −0.264783 1.71169i −0.0102142 0.0660300i
\(673\) 31.6297i 1.21924i −0.792696 0.609618i \(-0.791323\pi\)
0.792696 0.609618i \(-0.208677\pi\)
\(674\) −9.80866 9.80866i −0.377815 0.377815i
\(675\) 8.66154 + 17.4636i 0.333383 + 0.672175i
\(676\) 8.08639 + 10.1789i 0.311015 + 0.391497i
\(677\) 13.4729i 0.517805i 0.965903 + 0.258903i \(0.0833609\pi\)
−0.965903 + 0.258903i \(0.916639\pi\)
\(678\) 20.7651 + 15.2014i 0.797478 + 0.583806i
\(679\) 9.94831 0.381781
\(680\) −0.448235 −0.0171890
\(681\) 4.52802 6.18526i 0.173514 0.237020i
\(682\) −14.0927 14.0927i −0.539638 0.539638i
\(683\) 4.78530 + 4.78530i 0.183104 + 0.183104i 0.792707 0.609603i \(-0.208671\pi\)
−0.609603 + 0.792707i \(0.708671\pi\)
\(684\) 9.54269 18.3994i 0.364874 0.703518i
\(685\) 24.4121 0.932739
\(686\) 1.00000 0.0381802
\(687\) −26.5486 + 36.2653i −1.01289 + 1.38361i
\(688\) 2.74375i 0.104604i
\(689\) 11.7873 4.11221i 0.449060 0.156663i
\(690\) −1.81089 11.7065i −0.0689392 0.445658i
\(691\) 23.2258 + 23.2258i 0.883552 + 0.883552i 0.993894 0.110342i \(-0.0351946\pi\)
−0.110342 + 0.993894i \(0.535195\pi\)
\(692\) 21.8487i 0.830562i
\(693\) 13.9735 4.42913i 0.530809 0.168249i
\(694\) 22.3053 + 22.3053i 0.846699 + 0.846699i
\(695\) 2.33975 2.33975i 0.0887519 0.0887519i
\(696\) 1.19222 1.62857i 0.0451911 0.0617310i
\(697\) −2.71545 + 2.71545i −0.102855 + 0.102855i
\(698\) 24.7839i 0.938083i
\(699\) −19.2428 + 2.97668i −0.727829 + 0.112589i
\(700\) −2.65274 + 2.65274i −0.100264 + 0.100264i
\(701\) 4.56217 0.172311 0.0861554 0.996282i \(-0.472542\pi\)
0.0861554 + 0.996282i \(0.472542\pi\)
\(702\) −18.7339 + 0.200301i −0.707066 + 0.00755986i
\(703\) −43.8309 −1.65312
\(704\) 3.45508 3.45508i 0.130218 0.130218i
\(705\) −15.3436 + 2.37352i −0.577875 + 0.0893920i
\(706\) 19.6139i 0.738177i
\(707\) −2.39390 + 2.39390i −0.0900318 + 0.0900318i
\(708\) 11.6234 15.8775i 0.436833 0.596713i
\(709\) −6.99329 + 6.99329i −0.262638 + 0.262638i −0.826125 0.563487i \(-0.809460\pi\)
0.563487 + 0.826125i \(0.309460\pi\)
\(710\) 5.75949 + 5.75949i 0.216150 + 0.216150i
\(711\) −12.1440 + 3.84923i −0.455434 + 0.144357i
\(712\) 12.0916i 0.453152i
\(713\) 17.6537 + 17.6537i 0.661138 + 0.661138i
\(714\) 0.106221 + 0.686665i 0.00397521 + 0.0256978i
\(715\) 6.48414 + 18.5862i 0.242493 + 0.695084i
\(716\) 13.0946i 0.489369i
\(717\) −7.79268 + 10.6448i −0.291023 + 0.397537i
\(718\) 5.62299 0.209848
\(719\) −16.1959 −0.604005 −0.302002 0.953307i \(-0.597655\pi\)
−0.302002 + 0.953307i \(0.597655\pi\)
\(720\) −1.54328 + 2.97563i −0.0575148 + 0.110895i
\(721\) 9.33092 + 9.33092i 0.347502 + 0.347502i
\(722\) 20.3176 + 20.3176i 0.756142 + 0.756142i
\(723\) −9.96821 + 13.6166i −0.370722 + 0.506405i
\(724\) −18.6617 −0.693556
\(725\) −4.37161 −0.162358
\(726\) 17.9940 + 13.1728i 0.667819 + 0.488887i
\(727\) 11.3030i 0.419205i −0.977787 0.209602i \(-0.932783\pi\)
0.977787 0.209602i \(-0.0672169\pi\)
\(728\) −1.18766 3.40433i −0.0440177 0.126173i
\(729\) 16.3390 21.4951i 0.605147 0.796114i
\(730\) 0.0509057 + 0.0509057i 0.00188410 + 0.00188410i
\(731\) 1.10069i 0.0407104i
\(732\) 0.190048 + 1.22856i 0.00702436 + 0.0454090i
\(733\) −9.73470 9.73470i −0.359559 0.359559i 0.504091 0.863650i \(-0.331828\pi\)
−0.863650 + 0.504091i \(0.831828\pi\)
\(734\) −0.507357 + 0.507357i −0.0187269 + 0.0187269i
\(735\) −1.56157 1.14317i −0.0575995 0.0421666i
\(736\) −4.32812 + 4.32812i −0.159537 + 0.159537i
\(737\) 4.79252i 0.176535i
\(738\) 8.67727 + 27.3760i 0.319415 + 1.00772i
\(739\) 36.2462 36.2462i 1.33334 1.33334i 0.430971 0.902366i \(-0.358171\pi\)
0.902366 0.430971i \(-0.141829\pi\)
\(740\) 7.08853 0.260579
\(741\) 12.5962 41.2667i 0.462734 1.51597i
\(742\) −3.46244 −0.127110
\(743\) −2.02620 + 2.02620i −0.0743340 + 0.0743340i −0.743296 0.668962i \(-0.766739\pi\)
0.668962 + 0.743296i \(0.266739\pi\)
\(744\) −1.08001 6.98173i −0.0395951 0.255963i
\(745\) 5.91630i 0.216756i
\(746\) −6.56277 + 6.56277i −0.240280 + 0.240280i
\(747\) 3.40221 6.55984i 0.124480 0.240012i
\(748\) −1.38604 + 1.38604i −0.0506788 + 0.0506788i
\(749\) −13.3983 13.3983i −0.489563 0.489563i
\(750\) 16.7377 2.58917i 0.611176 0.0945433i
\(751\) 21.0845i 0.769385i −0.923045 0.384692i \(-0.874308\pi\)
0.923045 0.384692i \(-0.125692\pi\)
\(752\) 5.67285 + 5.67285i 0.206868 + 0.206868i
\(753\) −13.1158 + 2.02889i −0.477966 + 0.0739369i
\(754\) 1.82649 3.78371i 0.0665167 0.137794i
\(755\) 19.1998i 0.698751i
\(756\) 4.92418 + 1.65905i 0.179091 + 0.0603392i
\(757\) 6.62915 0.240941 0.120470 0.992717i \(-0.461560\pi\)
0.120470 + 0.992717i \(0.461560\pi\)
\(758\) 17.5718 0.638236
\(759\) −41.7988 30.5994i −1.51720 1.11069i
\(760\) −5.45862 5.45862i −0.198005 0.198005i
\(761\) 13.3011 + 13.3011i 0.482165 + 0.482165i 0.905822 0.423658i \(-0.139254\pi\)
−0.423658 + 0.905822i \(0.639254\pi\)
\(762\) −3.16158 2.31449i −0.114532 0.0838450i
\(763\) 8.22704 0.297839
\(764\) 7.22379 0.261347
\(765\) 0.619106 1.19371i 0.0223838 0.0431586i
\(766\) 19.4634i 0.703243i
\(767\) 17.8070 36.8886i 0.642974 1.33197i
\(768\) 1.71169 0.264783i 0.0617654 0.00955454i
\(769\) −30.0658 30.0658i −1.08420 1.08420i −0.996113 0.0880872i \(-0.971925\pi\)
−0.0880872 0.996113i \(-0.528075\pi\)
\(770\) 5.45958i 0.196749i
\(771\) 28.8903 4.46906i 1.04046 0.160949i
\(772\) 19.1571 + 19.1571i 0.689478 + 0.689478i
\(773\) −9.37726 + 9.37726i −0.337276 + 0.337276i −0.855341 0.518065i \(-0.826653\pi\)
0.518065 + 0.855341i \(0.326653\pi\)
\(774\) −7.30696 3.78969i −0.262643 0.136218i
\(775\) −10.8201 + 10.8201i −0.388671 + 0.388671i
\(776\) 9.94831i