Properties

Label 722.2.c.l.429.3
Level $722$
Weight $2$
Character 722.429
Analytic conductor $5.765$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \(x^{6} - x^{3} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 38)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 429.3
Root \(-0.173648 + 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 722.429
Dual form 722.2.c.l.653.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.766044 - 1.32683i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(-0.766044 - 1.32683i) q^{6} +2.69459 q^{7} -1.00000 q^{8} +(0.326352 + 0.565258i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.766044 - 1.32683i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(-0.766044 - 1.32683i) q^{6} +2.69459 q^{7} -1.00000 q^{8} +(0.326352 + 0.565258i) q^{9} +(1.00000 + 1.73205i) q^{10} +3.18479 q^{11} -1.53209 q^{12} +(-2.87939 - 4.98724i) q^{13} +(1.34730 - 2.33359i) q^{14} +(1.53209 + 2.65366i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.25877 - 5.64436i) q^{17} +0.652704 q^{18} +2.00000 q^{20} +(2.06418 - 3.57526i) q^{21} +(1.59240 - 2.75811i) q^{22} +(0.347296 + 0.601535i) q^{23} +(-0.766044 + 1.32683i) q^{24} +(0.500000 + 0.866025i) q^{25} -5.75877 q^{26} +5.59627 q^{27} +(-1.34730 - 2.33359i) q^{28} +(-1.41147 - 2.44474i) q^{29} +3.06418 q^{30} -2.45336 q^{31} +(0.500000 + 0.866025i) q^{32} +(2.43969 - 4.22567i) q^{33} +(-3.25877 - 5.64436i) q^{34} +(-2.69459 + 4.66717i) q^{35} +(0.326352 - 0.565258i) q^{36} +4.36959 q^{37} -8.82295 q^{39} +(1.00000 - 1.73205i) q^{40} +(-0.173648 + 0.300767i) q^{41} +(-2.06418 - 3.57526i) q^{42} +(-3.03209 + 5.25173i) q^{43} +(-1.59240 - 2.75811i) q^{44} -1.30541 q^{45} +0.694593 q^{46} +(-3.94356 - 6.83045i) q^{47} +(0.766044 + 1.32683i) q^{48} +0.260830 q^{49} +1.00000 q^{50} +(-4.99273 - 8.64766i) q^{51} +(-2.87939 + 4.98724i) q^{52} +(4.10607 + 7.11192i) q^{53} +(2.79813 - 4.84651i) q^{54} +(-3.18479 + 5.51622i) q^{55} -2.69459 q^{56} -2.82295 q^{58} +(0.286989 - 0.497079i) q^{59} +(1.53209 - 2.65366i) q^{60} +(-1.46791 - 2.54250i) q^{61} +(-1.22668 + 2.12467i) q^{62} +(0.879385 + 1.52314i) q^{63} +1.00000 q^{64} +11.5175 q^{65} +(-2.43969 - 4.22567i) q^{66} +(-2.47906 - 4.29385i) q^{67} -6.51754 q^{68} +1.06418 q^{69} +(2.69459 + 4.66717i) q^{70} +(-4.22668 + 7.32083i) q^{71} +(-0.326352 - 0.565258i) q^{72} +(-7.88326 + 13.6542i) q^{73} +(2.18479 - 3.78417i) q^{74} +1.53209 q^{75} +8.58172 q^{77} +(-4.41147 + 7.64090i) q^{78} +(-4.53209 + 7.84981i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(3.30793 - 5.72951i) q^{81} +(0.173648 + 0.300767i) q^{82} +8.47565 q^{83} -4.12836 q^{84} +(6.51754 + 11.2887i) q^{85} +(3.03209 + 5.25173i) q^{86} -4.32501 q^{87} -3.18479 q^{88} +(3.86959 + 6.70232i) q^{89} +(-0.652704 + 1.13052i) q^{90} +(-7.75877 - 13.4386i) q^{91} +(0.347296 - 0.601535i) q^{92} +(-1.87939 + 3.25519i) q^{93} -7.88713 q^{94} +1.53209 q^{96} +(-0.173648 + 0.300767i) q^{97} +(0.130415 - 0.225885i) q^{98} +(1.03936 + 1.80023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{7} - 6 q^{8} + 3 q^{9} + O(q^{10}) \) \( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{7} - 6 q^{8} + 3 q^{9} + 6 q^{10} + 12 q^{11} - 6 q^{13} + 6 q^{14} - 3 q^{16} - 3 q^{17} + 6 q^{18} + 12 q^{20} - 6 q^{21} + 6 q^{22} + 3 q^{25} - 12 q^{26} + 6 q^{27} - 6 q^{28} + 12 q^{29} + 12 q^{31} + 3 q^{32} + 9 q^{33} + 3 q^{34} - 12 q^{35} + 3 q^{36} + 12 q^{37} - 12 q^{39} + 6 q^{40} + 6 q^{42} - 9 q^{43} - 6 q^{44} - 12 q^{45} + 6 q^{47} + 30 q^{49} + 6 q^{50} - 12 q^{51} - 6 q^{52} + 3 q^{54} - 12 q^{55} - 12 q^{56} + 24 q^{58} - 6 q^{59} - 18 q^{61} + 6 q^{62} - 6 q^{63} + 6 q^{64} + 24 q^{65} - 9 q^{66} - 18 q^{67} + 6 q^{68} - 12 q^{69} + 12 q^{70} - 12 q^{71} - 3 q^{72} - 12 q^{73} + 6 q^{74} - 12 q^{77} - 6 q^{78} - 18 q^{79} - 6 q^{80} + 9 q^{81} + 12 q^{83} + 12 q^{84} - 6 q^{85} + 9 q^{86} - 36 q^{87} - 12 q^{88} + 9 q^{89} - 6 q^{90} - 24 q^{91} + 12 q^{94} + 15 q^{98} + 15 q^{99} + O(q^{100}) \)

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
\(3\) 0.766044 1.32683i 0.442276 0.766044i −0.555582 0.831462i \(-0.687505\pi\)
0.997858 + 0.0654173i \(0.0208378\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.00000 + 1.73205i −0.447214 + 0.774597i −0.998203 0.0599153i \(-0.980917\pi\)
0.550990 + 0.834512i \(0.314250\pi\)
\(6\) −0.766044 1.32683i −0.312736 0.541675i
\(7\) 2.69459 1.01846 0.509230 0.860630i \(-0.329930\pi\)
0.509230 + 0.860630i \(0.329930\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.326352 + 0.565258i 0.108784 + 0.188419i
\(10\) 1.00000 + 1.73205i 0.316228 + 0.547723i
\(11\) 3.18479 0.960251 0.480126 0.877200i \(-0.340591\pi\)
0.480126 + 0.877200i \(0.340591\pi\)
\(12\) −1.53209 −0.442276
\(13\) −2.87939 4.98724i −0.798598 1.38321i −0.920529 0.390673i \(-0.872242\pi\)
0.121932 0.992539i \(-0.461091\pi\)
\(14\) 1.34730 2.33359i 0.360080 0.623677i
\(15\) 1.53209 + 2.65366i 0.395584 + 0.685171i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.25877 5.64436i 0.790368 1.36896i −0.135371 0.990795i \(-0.543223\pi\)
0.925739 0.378162i \(-0.123444\pi\)
\(18\) 0.652704 0.153844
\(19\) 0 0
\(20\) 2.00000 0.447214
\(21\) 2.06418 3.57526i 0.450441 0.780186i
\(22\) 1.59240 2.75811i 0.339500 0.588031i
\(23\) 0.347296 + 0.601535i 0.0724163 + 0.125429i 0.899960 0.435973i \(-0.143596\pi\)
−0.827544 + 0.561402i \(0.810262\pi\)
\(24\) −0.766044 + 1.32683i −0.156368 + 0.270838i
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) −5.75877 −1.12939
\(27\) 5.59627 1.07700
\(28\) −1.34730 2.33359i −0.254615 0.441006i
\(29\) −1.41147 2.44474i −0.262104 0.453978i 0.704697 0.709509i \(-0.251083\pi\)
−0.966801 + 0.255531i \(0.917750\pi\)
\(30\) 3.06418 0.559440
\(31\) −2.45336 −0.440637 −0.220319 0.975428i \(-0.570710\pi\)
−0.220319 + 0.975428i \(0.570710\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 2.43969 4.22567i 0.424696 0.735595i
\(34\) −3.25877 5.64436i −0.558875 0.967999i
\(35\) −2.69459 + 4.66717i −0.455469 + 0.788896i
\(36\) 0.326352 0.565258i 0.0543920 0.0942097i
\(37\) 4.36959 0.718355 0.359178 0.933269i \(-0.383057\pi\)
0.359178 + 0.933269i \(0.383057\pi\)
\(38\) 0 0
\(39\) −8.82295 −1.41280
\(40\) 1.00000 1.73205i 0.158114 0.273861i
\(41\) −0.173648 + 0.300767i −0.0271193 + 0.0469720i −0.879267 0.476330i \(-0.841967\pi\)
0.852147 + 0.523302i \(0.175300\pi\)
\(42\) −2.06418 3.57526i −0.318510 0.551675i
\(43\) −3.03209 + 5.25173i −0.462389 + 0.800882i −0.999079 0.0428977i \(-0.986341\pi\)
0.536690 + 0.843779i \(0.319674\pi\)
\(44\) −1.59240 2.75811i −0.240063 0.415801i
\(45\) −1.30541 −0.194599
\(46\) 0.694593 0.102412
\(47\) −3.94356 6.83045i −0.575228 0.996324i −0.996017 0.0891652i \(-0.971580\pi\)
0.420789 0.907159i \(-0.361753\pi\)
\(48\) 0.766044 + 1.32683i 0.110569 + 0.191511i
\(49\) 0.260830 0.0372614
\(50\) 1.00000 0.141421
\(51\) −4.99273 8.64766i −0.699121 1.21091i
\(52\) −2.87939 + 4.98724i −0.399299 + 0.691606i
\(53\) 4.10607 + 7.11192i 0.564012 + 0.976897i 0.997141 + 0.0755650i \(0.0240760\pi\)
−0.433129 + 0.901332i \(0.642591\pi\)
\(54\) 2.79813 4.84651i 0.380778 0.659526i
\(55\) −3.18479 + 5.51622i −0.429437 + 0.743807i
\(56\) −2.69459 −0.360080
\(57\) 0 0
\(58\) −2.82295 −0.370671
\(59\) 0.286989 0.497079i 0.0373628 0.0647142i −0.846739 0.532008i \(-0.821438\pi\)
0.884102 + 0.467294i \(0.154771\pi\)
\(60\) 1.53209 2.65366i 0.197792 0.342585i
\(61\) −1.46791 2.54250i −0.187947 0.325533i 0.756619 0.653856i \(-0.226850\pi\)
−0.944566 + 0.328323i \(0.893517\pi\)
\(62\) −1.22668 + 2.12467i −0.155789 + 0.269834i
\(63\) 0.879385 + 1.52314i 0.110792 + 0.191898i
\(64\) 1.00000 0.125000
\(65\) 11.5175 1.42858
\(66\) −2.43969 4.22567i −0.300305 0.520144i
\(67\) −2.47906 4.29385i −0.302865 0.524577i 0.673919 0.738805i \(-0.264610\pi\)
−0.976784 + 0.214228i \(0.931276\pi\)
\(68\) −6.51754 −0.790368
\(69\) 1.06418 0.128112
\(70\) 2.69459 + 4.66717i 0.322065 + 0.557834i
\(71\) −4.22668 + 7.32083i −0.501615 + 0.868822i 0.498383 + 0.866957i \(0.333927\pi\)
−0.999998 + 0.00186564i \(0.999406\pi\)
\(72\) −0.326352 0.565258i −0.0384609 0.0666163i
\(73\) −7.88326 + 13.6542i −0.922665 + 1.59810i −0.127392 + 0.991852i \(0.540661\pi\)
−0.795274 + 0.606251i \(0.792673\pi\)
\(74\) 2.18479 3.78417i 0.253977 0.439901i
\(75\) 1.53209 0.176910
\(76\) 0 0
\(77\) 8.58172 0.977978
\(78\) −4.41147 + 7.64090i −0.499501 + 0.865161i
\(79\) −4.53209 + 7.84981i −0.509900 + 0.883172i 0.490034 + 0.871703i \(0.336984\pi\)
−0.999934 + 0.0114693i \(0.996349\pi\)
\(80\) −1.00000 1.73205i −0.111803 0.193649i
\(81\) 3.30793 5.72951i 0.367548 0.636612i
\(82\) 0.173648 + 0.300767i 0.0191762 + 0.0332142i
\(83\) 8.47565 0.930324 0.465162 0.885226i \(-0.345996\pi\)
0.465162 + 0.885226i \(0.345996\pi\)
\(84\) −4.12836 −0.450441
\(85\) 6.51754 + 11.2887i 0.706927 + 1.22443i
\(86\) 3.03209 + 5.25173i 0.326959 + 0.566309i
\(87\) −4.32501 −0.463689
\(88\) −3.18479 −0.339500
\(89\) 3.86959 + 6.70232i 0.410175 + 0.710444i 0.994909 0.100781i \(-0.0321342\pi\)
−0.584733 + 0.811226i \(0.698801\pi\)
\(90\) −0.652704 + 1.13052i −0.0688010 + 0.119167i
\(91\) −7.75877 13.4386i −0.813340 1.40875i
\(92\) 0.347296 0.601535i 0.0362081 0.0627144i
\(93\) −1.87939 + 3.25519i −0.194883 + 0.337548i
\(94\) −7.88713 −0.813495
\(95\) 0 0
\(96\) 1.53209 0.156368
\(97\) −0.173648 + 0.300767i −0.0176313 + 0.0305383i −0.874706 0.484653i \(-0.838946\pi\)
0.857075 + 0.515191i \(0.172279\pi\)
\(98\) 0.130415 0.225885i 0.0131739 0.0228179i
\(99\) 1.03936 + 1.80023i 0.104460 + 0.180930i
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) 0.184793 + 0.320070i 0.0183875 + 0.0318482i 0.875073 0.483991i \(-0.160813\pi\)
−0.856685 + 0.515840i \(0.827480\pi\)
\(102\) −9.98545 −0.988707
\(103\) −8.58172 −0.845582 −0.422791 0.906227i \(-0.638950\pi\)
−0.422791 + 0.906227i \(0.638950\pi\)
\(104\) 2.87939 + 4.98724i 0.282347 + 0.489039i
\(105\) 4.12836 + 7.15052i 0.402886 + 0.697819i
\(106\) 8.21213 0.797633
\(107\) 11.4534 1.10724 0.553619 0.832770i \(-0.313246\pi\)
0.553619 + 0.832770i \(0.313246\pi\)
\(108\) −2.79813 4.84651i −0.269251 0.466356i
\(109\) 4.34730 7.52974i 0.416395 0.721218i −0.579178 0.815201i \(-0.696627\pi\)
0.995574 + 0.0939827i \(0.0299599\pi\)
\(110\) 3.18479 + 5.51622i 0.303658 + 0.525951i
\(111\) 3.34730 5.79769i 0.317711 0.550292i
\(112\) −1.34730 + 2.33359i −0.127308 + 0.220503i
\(113\) −2.85978 −0.269026 −0.134513 0.990912i \(-0.542947\pi\)
−0.134513 + 0.990912i \(0.542947\pi\)
\(114\) 0 0
\(115\) −1.38919 −0.129542
\(116\) −1.41147 + 2.44474i −0.131052 + 0.226989i
\(117\) 1.87939 3.25519i 0.173749 0.300942i
\(118\) −0.286989 0.497079i −0.0264195 0.0457599i
\(119\) 8.78106 15.2092i 0.804958 1.39423i
\(120\) −1.53209 2.65366i −0.139860 0.242245i
\(121\) −0.857097 −0.0779179
\(122\) −2.93582 −0.265797
\(123\) 0.266044 + 0.460802i 0.0239884 + 0.0415492i
\(124\) 1.22668 + 2.12467i 0.110159 + 0.190801i
\(125\) −12.0000 −1.07331
\(126\) 1.75877 0.156684
\(127\) 4.86484 + 8.42615i 0.431685 + 0.747699i 0.997019 0.0771626i \(-0.0245861\pi\)
−0.565334 + 0.824862i \(0.691253\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 4.64543 + 8.04612i 0.409007 + 0.708421i
\(130\) 5.75877 9.97448i 0.505078 0.874820i
\(131\) 3.23396 5.60138i 0.282552 0.489394i −0.689461 0.724323i \(-0.742152\pi\)
0.972013 + 0.234929i \(0.0754857\pi\)
\(132\) −4.87939 −0.424696
\(133\) 0 0
\(134\) −4.95811 −0.428316
\(135\) −5.59627 + 9.69302i −0.481650 + 0.834242i
\(136\) −3.25877 + 5.64436i −0.279437 + 0.484000i
\(137\) 5.83022 + 10.0982i 0.498109 + 0.862751i 0.999998 0.00218159i \(-0.000694422\pi\)
−0.501888 + 0.864933i \(0.667361\pi\)
\(138\) 0.532089 0.921605i 0.0452944 0.0784522i
\(139\) 4.13176 + 7.15642i 0.350451 + 0.606999i 0.986329 0.164791i \(-0.0526949\pi\)
−0.635877 + 0.771790i \(0.719362\pi\)
\(140\) 5.38919 0.455469
\(141\) −12.0838 −1.01764
\(142\) 4.22668 + 7.32083i 0.354695 + 0.614350i
\(143\) −9.17024 15.8833i −0.766854 1.32823i
\(144\) −0.652704 −0.0543920
\(145\) 5.64590 0.468866
\(146\) 7.88326 + 13.6542i 0.652423 + 1.13003i
\(147\) 0.199807 0.346076i 0.0164798 0.0285439i
\(148\) −2.18479 3.78417i −0.179589 0.311057i
\(149\) 8.22668 14.2490i 0.673956 1.16733i −0.302817 0.953049i \(-0.597927\pi\)
0.976773 0.214277i \(-0.0687396\pi\)
\(150\) 0.766044 1.32683i 0.0625473 0.108335i
\(151\) −4.65539 −0.378850 −0.189425 0.981895i \(-0.560662\pi\)
−0.189425 + 0.981895i \(0.560662\pi\)
\(152\) 0 0
\(153\) 4.25402 0.343917
\(154\) 4.29086 7.43199i 0.345767 0.598887i
\(155\) 2.45336 4.24935i 0.197059 0.341316i
\(156\) 4.41147 + 7.64090i 0.353201 + 0.611761i
\(157\) −4.22668 + 7.32083i −0.337326 + 0.584266i −0.983929 0.178561i \(-0.942856\pi\)
0.646603 + 0.762827i \(0.276189\pi\)
\(158\) 4.53209 + 7.84981i 0.360554 + 0.624497i
\(159\) 12.5817 0.997795
\(160\) −2.00000 −0.158114
\(161\) 0.935822 + 1.62089i 0.0737531 + 0.127744i
\(162\) −3.30793 5.72951i −0.259896 0.450153i
\(163\) 17.0496 1.33543 0.667715 0.744417i \(-0.267272\pi\)
0.667715 + 0.744417i \(0.267272\pi\)
\(164\) 0.347296 0.0271193
\(165\) 4.87939 + 8.45134i 0.379860 + 0.657936i
\(166\) 4.23783 7.34013i 0.328919 0.569705i
\(167\) −1.59627 2.76481i −0.123523 0.213948i 0.797632 0.603145i \(-0.206086\pi\)
−0.921155 + 0.389197i \(0.872753\pi\)
\(168\) −2.06418 + 3.57526i −0.159255 + 0.275837i
\(169\) −10.0817 + 17.4620i −0.775517 + 1.34323i
\(170\) 13.0351 0.999745
\(171\) 0 0
\(172\) 6.06418 0.462389
\(173\) 4.81521 8.34018i 0.366093 0.634092i −0.622858 0.782335i \(-0.714028\pi\)
0.988951 + 0.148243i \(0.0473617\pi\)
\(174\) −2.16250 + 3.74557i −0.163939 + 0.283951i
\(175\) 1.34730 + 2.33359i 0.101846 + 0.176403i
\(176\) −1.59240 + 2.75811i −0.120031 + 0.207900i
\(177\) −0.439693 0.761570i −0.0330493 0.0572431i
\(178\) 7.73917 0.580075
\(179\) −18.8161 −1.40638 −0.703192 0.711000i \(-0.748243\pi\)
−0.703192 + 0.711000i \(0.748243\pi\)
\(180\) 0.652704 + 1.13052i 0.0486497 + 0.0842637i
\(181\) 1.38919 + 2.40614i 0.103257 + 0.178847i 0.913025 0.407904i \(-0.133740\pi\)
−0.809768 + 0.586751i \(0.800407\pi\)
\(182\) −15.5175 −1.15024
\(183\) −4.49794 −0.332497
\(184\) −0.347296 0.601535i −0.0256030 0.0443457i
\(185\) −4.36959 + 7.56834i −0.321258 + 0.556436i
\(186\) 1.87939 + 3.25519i 0.137803 + 0.238682i
\(187\) 10.3785 17.9761i 0.758952 1.31454i
\(188\) −3.94356 + 6.83045i −0.287614 + 0.498162i
\(189\) 15.0797 1.09688
\(190\) 0 0
\(191\) 9.56212 0.691891 0.345945 0.938255i \(-0.387558\pi\)
0.345945 + 0.938255i \(0.387558\pi\)
\(192\) 0.766044 1.32683i 0.0552845 0.0957556i
\(193\) −11.8405 + 20.5083i −0.852297 + 1.47622i 0.0268330 + 0.999640i \(0.491458\pi\)
−0.879130 + 0.476582i \(0.841876\pi\)
\(194\) 0.173648 + 0.300767i 0.0124672 + 0.0215938i
\(195\) 8.82295 15.2818i 0.631824 1.09435i
\(196\) −0.130415 0.225885i −0.00931535 0.0161347i
\(197\) −22.9222 −1.63314 −0.816570 0.577247i \(-0.804127\pi\)
−0.816570 + 0.577247i \(0.804127\pi\)
\(198\) 2.07873 0.147729
\(199\) −5.04189 8.73281i −0.357410 0.619052i 0.630117 0.776500i \(-0.283007\pi\)
−0.987527 + 0.157448i \(0.949673\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) −7.59627 −0.535799
\(202\) 0.369585 0.0260039
\(203\) −3.80335 6.58759i −0.266943 0.462358i
\(204\) −4.99273 + 8.64766i −0.349561 + 0.605457i
\(205\) −0.347296 0.601535i −0.0242562 0.0420130i
\(206\) −4.29086 + 7.43199i −0.298958 + 0.517811i
\(207\) −0.226682 + 0.392624i −0.0157555 + 0.0272893i
\(208\) 5.75877 0.399299
\(209\) 0 0
\(210\) 8.25671 0.569767
\(211\) −11.1800 + 19.3644i −0.769666 + 1.33310i 0.168078 + 0.985774i \(0.446244\pi\)
−0.937744 + 0.347327i \(0.887089\pi\)
\(212\) 4.10607 7.11192i 0.282006 0.488448i
\(213\) 6.47565 + 11.2162i 0.443704 + 0.768518i
\(214\) 5.72668 9.91890i 0.391468 0.678042i
\(215\) −6.06418 10.5035i −0.413573 0.716330i
\(216\) −5.59627 −0.380778
\(217\) −6.61081 −0.448771
\(218\) −4.34730 7.52974i −0.294436 0.509978i
\(219\) 12.0778 + 20.9194i 0.816145 + 1.41361i
\(220\) 6.36959 0.429437
\(221\) −37.5330 −2.52474
\(222\) −3.34730 5.79769i −0.224656 0.389115i
\(223\) −4.63816 + 8.03352i −0.310594 + 0.537964i −0.978491 0.206289i \(-0.933861\pi\)
0.667897 + 0.744254i \(0.267195\pi\)
\(224\) 1.34730 + 2.33359i 0.0900200 + 0.155919i
\(225\) −0.326352 + 0.565258i −0.0217568 + 0.0376839i
\(226\) −1.42989 + 2.47665i −0.0951150 + 0.164744i
\(227\) −7.73648 −0.513488 −0.256744 0.966479i \(-0.582650\pi\)
−0.256744 + 0.966479i \(0.582650\pi\)
\(228\) 0 0
\(229\) −23.0351 −1.52220 −0.761101 0.648634i \(-0.775341\pi\)
−0.761101 + 0.648634i \(0.775341\pi\)
\(230\) −0.694593 + 1.20307i −0.0458001 + 0.0793281i
\(231\) 6.57398 11.3865i 0.432536 0.749174i
\(232\) 1.41147 + 2.44474i 0.0926678 + 0.160505i
\(233\) −4.19981 + 7.27428i −0.275139 + 0.476554i −0.970170 0.242425i \(-0.922057\pi\)
0.695032 + 0.718979i \(0.255390\pi\)
\(234\) −1.87939 3.25519i −0.122859 0.212798i
\(235\) 15.7743 1.02900
\(236\) −0.573978 −0.0373628
\(237\) 6.94356 + 12.0266i 0.451033 + 0.781212i
\(238\) −8.78106 15.2092i −0.569192 0.985869i
\(239\) −15.7297 −1.01747 −0.508734 0.860924i \(-0.669886\pi\)
−0.508734 + 0.860924i \(0.669886\pi\)
\(240\) −3.06418 −0.197792
\(241\) 8.75150 + 15.1580i 0.563733 + 0.976415i 0.997166 + 0.0752291i \(0.0239688\pi\)
−0.433433 + 0.901186i \(0.642698\pi\)
\(242\) −0.428548 + 0.742267i −0.0275481 + 0.0477148i
\(243\) 3.32635 + 5.76141i 0.213386 + 0.369595i
\(244\) −1.46791 + 2.54250i −0.0939734 + 0.162767i
\(245\) −0.260830 + 0.451771i −0.0166638 + 0.0288626i
\(246\) 0.532089 0.0339247
\(247\) 0 0
\(248\) 2.45336 0.155789
\(249\) 6.49273 11.2457i 0.411460 0.712669i
\(250\) −6.00000 + 10.3923i −0.379473 + 0.657267i
\(251\) −4.28359 7.41939i −0.270378 0.468308i 0.698581 0.715531i \(-0.253815\pi\)
−0.968959 + 0.247223i \(0.920482\pi\)
\(252\) 0.879385 1.52314i 0.0553961 0.0959488i
\(253\) 1.10607 + 1.91576i 0.0695378 + 0.120443i
\(254\) 9.72967 0.610494
\(255\) 19.9709 1.25063
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −4.01233 6.94955i −0.250282 0.433501i 0.713321 0.700837i \(-0.247190\pi\)
−0.963603 + 0.267336i \(0.913857\pi\)
\(258\) 9.29086 0.578424
\(259\) 11.7743 0.731616
\(260\) −5.75877 9.97448i −0.357144 0.618591i
\(261\) 0.921274 1.59569i 0.0570254 0.0987710i
\(262\) −3.23396 5.60138i −0.199794 0.346054i
\(263\) 2.98040 5.16220i 0.183779 0.318315i −0.759385 0.650641i \(-0.774500\pi\)
0.943165 + 0.332326i \(0.107833\pi\)
\(264\) −2.43969 + 4.22567i −0.150153 + 0.260072i
\(265\) −16.4243 −1.00893
\(266\) 0 0
\(267\) 11.8571 0.725643
\(268\) −2.47906 + 4.29385i −0.151432 + 0.262289i
\(269\) −0.573978 + 0.994159i −0.0349961 + 0.0606149i −0.882993 0.469386i \(-0.844475\pi\)
0.847997 + 0.530001i \(0.177809\pi\)
\(270\) 5.59627 + 9.69302i 0.340578 + 0.589898i
\(271\) −10.0273 + 17.3679i −0.609118 + 1.05502i 0.382269 + 0.924051i \(0.375143\pi\)
−0.991386 + 0.130971i \(0.958190\pi\)
\(272\) 3.25877 + 5.64436i 0.197592 + 0.342239i
\(273\) −23.7743 −1.43888
\(274\) 11.6604 0.704433
\(275\) 1.59240 + 2.75811i 0.0960251 + 0.166320i
\(276\) −0.532089 0.921605i −0.0320280 0.0554741i
\(277\) 17.3601 1.04307 0.521533 0.853231i \(-0.325360\pi\)
0.521533 + 0.853231i \(0.325360\pi\)
\(278\) 8.26352 0.495613
\(279\) −0.800660 1.38678i −0.0479342 0.0830245i
\(280\) 2.69459 4.66717i 0.161033 0.278917i
\(281\) 1.46064 + 2.52990i 0.0871343 + 0.150921i 0.906299 0.422638i \(-0.138896\pi\)
−0.819164 + 0.573559i \(0.805562\pi\)
\(282\) −6.04189 + 10.4649i −0.359789 + 0.623173i
\(283\) 4.74035 8.21053i 0.281785 0.488065i −0.690040 0.723772i \(-0.742407\pi\)
0.971824 + 0.235706i \(0.0757403\pi\)
\(284\) 8.45336 0.501615
\(285\) 0 0
\(286\) −18.3405 −1.08450
\(287\) −0.467911 + 0.810446i −0.0276199 + 0.0478391i
\(288\) −0.326352 + 0.565258i −0.0192305 + 0.0333081i
\(289\) −12.7392 22.0649i −0.749363 1.29793i
\(290\) 2.82295 4.88949i 0.165769 0.287121i
\(291\) 0.266044 + 0.460802i 0.0155958 + 0.0270127i
\(292\) 15.7665 0.922665
\(293\) 27.2918 1.59440 0.797202 0.603713i \(-0.206313\pi\)
0.797202 + 0.603713i \(0.206313\pi\)
\(294\) −0.199807 0.346076i −0.0116530 0.0201836i
\(295\) 0.573978 + 0.994159i 0.0334183 + 0.0578822i
\(296\) −4.36959 −0.253977
\(297\) 17.8229 1.03419
\(298\) −8.22668 14.2490i −0.476559 0.825424i
\(299\) 2.00000 3.46410i 0.115663 0.200334i
\(300\) −0.766044 1.32683i −0.0442276 0.0766044i
\(301\) −8.17024 + 14.1513i −0.470925 + 0.815666i
\(302\) −2.32770 + 4.03169i −0.133944 + 0.231998i
\(303\) 0.566237 0.0325295
\(304\) 0 0
\(305\) 5.87164 0.336209
\(306\) 2.12701 3.68409i 0.121593 0.210606i
\(307\) 10.6643 18.4711i 0.608645 1.05420i −0.382819 0.923823i \(-0.625047\pi\)
0.991464 0.130380i \(-0.0416198\pi\)
\(308\) −4.29086 7.43199i −0.244494 0.423477i
\(309\) −6.57398 + 11.3865i −0.373981 + 0.647753i
\(310\) −2.45336 4.24935i −0.139342 0.241347i
\(311\) −29.2918 −1.66099 −0.830493 0.557030i \(-0.811941\pi\)
−0.830493 + 0.557030i \(0.811941\pi\)
\(312\) 8.82295 0.499501
\(313\) −2.78059 4.81613i −0.157168 0.272224i 0.776678 0.629898i \(-0.216903\pi\)
−0.933846 + 0.357674i \(0.883570\pi\)
\(314\) 4.22668 + 7.32083i 0.238525 + 0.413138i
\(315\) −3.51754 −0.198191
\(316\) 9.06418 0.509900
\(317\) 1.90167 + 3.29380i 0.106809 + 0.184998i 0.914476 0.404641i \(-0.132603\pi\)
−0.807667 + 0.589639i \(0.799270\pi\)
\(318\) 6.29086 10.8961i 0.352774 0.611022i
\(319\) −4.49525 7.78601i −0.251686 0.435933i
\(320\) −1.00000 + 1.73205i −0.0559017 + 0.0968246i
\(321\) 8.77379 15.1966i 0.489705 0.848194i
\(322\) 1.87164 0.104303
\(323\) 0 0
\(324\) −6.61587 −0.367548
\(325\) 2.87939 4.98724i 0.159720 0.276642i
\(326\) 8.52481 14.7654i 0.472146 0.817781i
\(327\) −6.66044 11.5362i −0.368323 0.637955i
\(328\) 0.173648 0.300767i 0.00958812 0.0166071i
\(329\) −10.6263 18.4053i −0.585847 1.01472i
\(330\) 9.75877 0.537203
\(331\) −20.4219 −1.12249 −0.561245 0.827650i \(-0.689677\pi\)
−0.561245 + 0.827650i \(0.689677\pi\)
\(332\) −4.23783 7.34013i −0.232581 0.402842i
\(333\) 1.42602 + 2.46994i 0.0781455 + 0.135352i
\(334\) −3.19253 −0.174688
\(335\) 9.91622 0.541781
\(336\) 2.06418 + 3.57526i 0.112610 + 0.195046i
\(337\) 10.1552 17.5894i 0.553191 0.958154i −0.444851 0.895604i \(-0.646743\pi\)
0.998042 0.0625498i \(-0.0199232\pi\)
\(338\) 10.0817 + 17.4620i 0.548373 + 0.949810i
\(339\) −2.19072 + 3.79444i −0.118984 + 0.206086i
\(340\) 6.51754 11.2887i 0.353463 0.612216i
\(341\) −7.81345 −0.423122
\(342\) 0 0
\(343\) −18.1593 −0.980511
\(344\) 3.03209 5.25173i 0.163479 0.283154i
\(345\) −1.06418 + 1.84321i −0.0572934 + 0.0992351i
\(346\) −4.81521 8.34018i −0.258867 0.448371i
\(347\) −2.60741 + 4.51617i −0.139973 + 0.242441i −0.927486 0.373857i \(-0.878035\pi\)
0.787513 + 0.616298i \(0.211368\pi\)
\(348\) 2.16250 + 3.74557i 0.115922 + 0.200783i
\(349\) 14.3405 0.767629 0.383814 0.923410i \(-0.374610\pi\)
0.383814 + 0.923410i \(0.374610\pi\)
\(350\) 2.69459 0.144032
\(351\) −16.1138 27.9099i −0.860091 1.48972i
\(352\) 1.59240 + 2.75811i 0.0848750 + 0.147008i
\(353\) 26.2499 1.39714 0.698571 0.715541i \(-0.253820\pi\)
0.698571 + 0.715541i \(0.253820\pi\)
\(354\) −0.879385 −0.0467388
\(355\) −8.45336 14.6417i −0.448658 0.777098i
\(356\) 3.86959 6.70232i 0.205088 0.355222i
\(357\) −13.4534 23.3019i −0.712027 1.23327i
\(358\) −9.40807 + 16.2953i −0.497232 + 0.861231i
\(359\) 16.8452 29.1768i 0.889058 1.53989i 0.0480664 0.998844i \(-0.484694\pi\)
0.840991 0.541049i \(-0.181973\pi\)
\(360\) 1.30541 0.0688010
\(361\) 0 0
\(362\) 2.77837 0.146028
\(363\) −0.656574 + 1.13722i −0.0344612 + 0.0596885i
\(364\) −7.75877 + 13.4386i −0.406670 + 0.704373i
\(365\) −15.7665 27.3084i −0.825257 1.42939i
\(366\) −2.24897 + 3.89533i −0.117556 + 0.203612i
\(367\) 5.23442 + 9.06629i 0.273235 + 0.473256i 0.969688 0.244346i \(-0.0785731\pi\)
−0.696454 + 0.717602i \(0.745240\pi\)
\(368\) −0.694593 −0.0362081
\(369\) −0.226682 −0.0118006
\(370\) 4.36959 + 7.56834i 0.227164 + 0.393459i
\(371\) 11.0642 + 19.1637i 0.574423 + 0.994931i
\(372\) 3.75877 0.194883
\(373\) −23.9026 −1.23763 −0.618815 0.785537i \(-0.712387\pi\)
−0.618815 + 0.785537i \(0.712387\pi\)
\(374\) −10.3785 17.9761i −0.536660 0.929522i
\(375\) −9.19253 + 15.9219i −0.474700 + 0.822205i
\(376\) 3.94356 + 6.83045i 0.203374 + 0.352254i
\(377\) −8.12836 + 14.0787i −0.418632 + 0.725091i
\(378\) 7.53983 13.0594i 0.387807 0.671701i
\(379\) −17.8135 −0.915016 −0.457508 0.889206i \(-0.651258\pi\)
−0.457508 + 0.889206i \(0.651258\pi\)
\(380\) 0 0
\(381\) 14.9067 0.763695
\(382\) 4.78106 8.28104i 0.244620 0.423695i
\(383\) 12.5398 21.7196i 0.640755 1.10982i −0.344509 0.938783i \(-0.611955\pi\)
0.985264 0.171038i \(-0.0547120\pi\)
\(384\) −0.766044 1.32683i −0.0390920 0.0677094i
\(385\) −8.58172 + 14.8640i −0.437365 + 0.757538i
\(386\) 11.8405 + 20.5083i 0.602665 + 1.04385i
\(387\) −3.95811 −0.201202
\(388\) 0.347296 0.0176313
\(389\) 4.70914 + 8.15647i 0.238763 + 0.413549i 0.960360 0.278764i \(-0.0899248\pi\)
−0.721597 + 0.692314i \(0.756591\pi\)
\(390\) −8.82295 15.2818i −0.446767 0.773824i
\(391\) 4.52704 0.228942
\(392\) −0.260830 −0.0131739
\(393\) −4.95471 8.58180i −0.249932 0.432895i
\(394\) −11.4611 + 19.8512i −0.577402 + 1.00009i
\(395\) −9.06418 15.6996i −0.456068 0.789933i
\(396\) 1.03936 1.80023i 0.0522299 0.0904649i
\(397\) −3.42602 + 5.93404i −0.171947 + 0.297821i −0.939101 0.343643i \(-0.888339\pi\)
0.767153 + 0.641464i \(0.221672\pi\)
\(398\) −10.0838 −0.505454
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) 2.37346 4.11095i 0.118525 0.205291i −0.800659 0.599121i \(-0.795517\pi\)
0.919183 + 0.393830i \(0.128850\pi\)
\(402\) −3.79813 + 6.57856i −0.189434 + 0.328109i
\(403\) 7.06418 + 12.2355i 0.351892 + 0.609494i
\(404\) 0.184793 0.320070i 0.00919377 0.0159241i
\(405\) 6.61587 + 11.4590i 0.328745 + 0.569403i
\(406\) −7.60670 −0.377514
\(407\) 13.9162 0.689802
\(408\) 4.99273 + 8.64766i 0.247177 + 0.428123i
\(409\) 15.8464 + 27.4468i 0.783555 + 1.35716i 0.929859 + 0.367917i \(0.119929\pi\)
−0.146304 + 0.989240i \(0.546738\pi\)
\(410\) −0.694593 −0.0343035
\(411\) 17.8648 0.881207
\(412\) 4.29086 + 7.43199i 0.211395 + 0.366148i
\(413\) 0.773318 1.33943i 0.0380525 0.0659089i
\(414\) 0.226682 + 0.392624i 0.0111408 + 0.0192964i
\(415\) −8.47565 + 14.6803i −0.416053 + 0.720626i
\(416\) 2.87939 4.98724i 0.141173 0.244520i
\(417\) 12.6604 0.619985
\(418\) 0 0
\(419\) −11.0101 −0.537879 −0.268939 0.963157i \(-0.586673\pi\)
−0.268939 + 0.963157i \(0.586673\pi\)
\(420\) 4.12836 7.15052i 0.201443 0.348910i
\(421\) −4.33275 + 7.50454i −0.211165 + 0.365749i −0.952079 0.305851i \(-0.901059\pi\)
0.740914 + 0.671600i \(0.234392\pi\)
\(422\) 11.1800 + 19.3644i 0.544236 + 0.942645i
\(423\) 2.57398 4.45826i 0.125151 0.216768i
\(424\) −4.10607 7.11192i −0.199408 0.345385i
\(425\) 6.51754 0.316147
\(426\) 12.9513 0.627493
\(427\) −3.95542 6.85099i −0.191416 0.331543i
\(428\) −5.72668 9.91890i −0.276810 0.479448i
\(429\) −28.0993 −1.35665
\(430\) −12.1284 −0.584881
\(431\) −14.9436 25.8830i −0.719806 1.24674i −0.961076 0.276283i \(-0.910897\pi\)
0.241270 0.970458i \(-0.422436\pi\)
\(432\) −2.79813 + 4.84651i −0.134625 + 0.233178i
\(433\) 4.63041 + 8.02011i 0.222524 + 0.385422i 0.955574 0.294753i \(-0.0952372\pi\)
−0.733050 + 0.680175i \(0.761904\pi\)
\(434\) −3.30541 + 5.72513i −0.158665 + 0.274815i
\(435\) 4.32501 7.49113i 0.207368 0.359172i
\(436\) −8.69459 −0.416395
\(437\) 0 0
\(438\) 24.1557 1.15420
\(439\) 10.4311 18.0672i 0.497848 0.862298i −0.502149 0.864781i \(-0.667457\pi\)
0.999997 + 0.00248311i \(0.000790399\pi\)
\(440\) 3.18479 5.51622i 0.151829 0.262976i
\(441\) 0.0851223 + 0.147436i 0.00405344 + 0.00702077i
\(442\) −18.7665 + 32.5046i −0.892632 + 1.54608i
\(443\) −11.9140 20.6357i −0.566051 0.980430i −0.996951 0.0780297i \(-0.975137\pi\)
0.430900 0.902400i \(-0.358196\pi\)
\(444\) −6.69459 −0.317711
\(445\) −15.4783 −0.733744
\(446\) 4.63816 + 8.03352i 0.219623 + 0.380398i
\(447\) −12.6040 21.8308i −0.596149 1.03256i
\(448\) 2.69459 0.127308
\(449\) 2.18210 0.102980 0.0514899 0.998674i \(-0.483603\pi\)
0.0514899 + 0.998674i \(0.483603\pi\)
\(450\) 0.326352 + 0.565258i 0.0153844 + 0.0266465i
\(451\) −0.553033 + 0.957882i −0.0260413 + 0.0451049i
\(452\) 1.42989 + 2.47665i 0.0672565 + 0.116492i
\(453\) −3.56624 + 6.17690i −0.167556 + 0.290216i
\(454\) −3.86824 + 6.69999i −0.181546 + 0.314446i
\(455\) 31.0351 1.45495
\(456\) 0 0
\(457\) 1.78106 0.0833144 0.0416572 0.999132i \(-0.486736\pi\)
0.0416572 + 0.999132i \(0.486736\pi\)
\(458\) −11.5175 + 19.9490i −0.538179 + 0.932154i
\(459\) 18.2369 31.5873i 0.851228 1.47437i
\(460\) 0.694593 + 1.20307i 0.0323856 + 0.0560934i
\(461\) 7.74422 13.4134i 0.360684 0.624724i −0.627389 0.778706i \(-0.715876\pi\)
0.988074 + 0.153982i \(0.0492098\pi\)
\(462\) −6.57398 11.3865i −0.305849 0.529746i
\(463\) −2.71007 −0.125948 −0.0629739 0.998015i \(-0.520058\pi\)
−0.0629739 + 0.998015i \(0.520058\pi\)
\(464\) 2.82295 0.131052
\(465\) −3.75877 6.51038i −0.174309 0.301912i
\(466\) 4.19981 + 7.27428i 0.194552 + 0.336974i
\(467\) 12.9135 0.597567 0.298784 0.954321i \(-0.403419\pi\)
0.298784 + 0.954321i \(0.403419\pi\)
\(468\) −3.75877 −0.173749
\(469\) −6.68004 11.5702i −0.308456 0.534261i
\(470\) 7.88713 13.6609i 0.363806 0.630130i
\(471\) 6.47565 + 11.2162i 0.298382 + 0.516813i
\(472\) −0.286989 + 0.497079i −0.0132097 + 0.0228799i
\(473\) −9.65657 + 16.7257i −0.444010 + 0.769047i
\(474\) 13.8871 0.637857
\(475\) 0 0
\(476\) −17.5621 −0.804958
\(477\) −2.68004 + 4.64197i −0.122711 + 0.212541i
\(478\) −7.86484 + 13.6223i −0.359729 + 0.623069i
\(479\) 9.27631 + 16.0670i 0.423845 + 0.734122i 0.996312 0.0858063i \(-0.0273466\pi\)
−0.572466 + 0.819928i \(0.694013\pi\)
\(480\) −1.53209 + 2.65366i −0.0699300 + 0.121122i
\(481\) −12.5817 21.7922i −0.573677 0.993638i
\(482\) 17.5030 0.797239
\(483\) 2.86753 0.130477
\(484\) 0.428548 + 0.742267i 0.0194795 + 0.0337394i
\(485\) −0.347296 0.601535i −0.0157699 0.0273143i
\(486\) 6.65270 0.301773
\(487\) −41.1735 −1.86575 −0.932876 0.360199i \(-0.882709\pi\)
−0.932876 + 0.360199i \(0.882709\pi\)
\(488\) 1.46791 + 2.54250i 0.0664492 + 0.115093i
\(489\) 13.0608 22.6219i 0.590629 1.02300i
\(490\) 0.260830 + 0.451771i 0.0117831 + 0.0204089i
\(491\) 11.2888 19.5528i 0.509456 0.882404i −0.490484 0.871450i \(-0.663180\pi\)
0.999940 0.0109540i \(-0.00348682\pi\)
\(492\) 0.266044 0.460802i 0.0119942 0.0207746i
\(493\) −18.3987 −0.828635
\(494\) 0 0
\(495\) −4.15745 −0.186864
\(496\) 1.22668 2.12467i 0.0550796 0.0954007i
\(497\) −11.3892 + 19.7266i −0.510875 + 0.884861i
\(498\) −6.49273 11.2457i −0.290946 0.503933i
\(499\) 14.6643 25.3993i 0.656465 1.13703i −0.325060 0.945694i \(-0.605384\pi\)
0.981524 0.191337i \(-0.0612823\pi\)
\(500\) 6.00000 + 10.3923i 0.268328 + 0.464758i
\(501\) −4.89124 −0.218525
\(502\) −8.56717 −0.382372
\(503\) −16.8084 29.1130i −0.749450 1.29808i −0.948087 0.318012i \(-0.896985\pi\)
0.198637 0.980073i \(-0.436348\pi\)
\(504\) −0.879385 1.52314i −0.0391709 0.0678460i
\(505\) −0.739170 −0.0328926
\(506\) 2.21213 0.0983413
\(507\) 15.4461 + 26.7534i 0.685985 + 1.18816i
\(508\) 4.86484 8.42615i 0.215842 0.373850i
\(509\) 2.01455 + 3.48930i 0.0892933 + 0.154660i 0.907213 0.420672i \(-0.138206\pi\)
−0.817919 + 0.575333i \(0.804872\pi\)
\(510\) 9.98545 17.2953i 0.442163 0.765849i
\(511\) −21.2422 + 36.7925i −0.939698 + 1.62760i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −8.02465 −0.353952
\(515\) 8.58172 14.8640i 0.378156 0.654985i
\(516\) 4.64543 8.04612i 0.204504 0.354211i
\(517\) −12.5594 21.7536i −0.552363 0.956721i
\(518\) 5.88713 10.1968i 0.258665 0.448022i
\(519\) −7.37733 12.7779i −0.323829 0.560888i
\(520\) −11.5175 −0.505078
\(521\) −4.98957 −0.218597 −0.109299 0.994009i \(-0.534860\pi\)
−0.109299 + 0.994009i \(0.534860\pi\)
\(522\) −0.921274 1.59569i −0.0403231 0.0698416i
\(523\) −13.2763 22.9952i −0.580533 1.00551i −0.995416 0.0956374i \(-0.969511\pi\)
0.414884 0.909874i \(-0.363822\pi\)
\(524\) −6.46791 −0.282552
\(525\) 4.12836 0.180176
\(526\) −2.98040 5.16220i −0.129952 0.225083i
\(527\) −7.99495 + 13.8477i −0.348265 + 0.603213i
\(528\) 2.43969 + 4.22567i 0.106174 + 0.183899i
\(529\) 11.2588 19.5008i 0.489512 0.847859i
\(530\) −8.21213 + 14.2238i −0.356712 + 0.617844i
\(531\) 0.374638 0.0162579
\(532\) 0 0
\(533\) 2.00000 0.0866296
\(534\) 5.92855 10.2685i 0.256553 0.444363i
\(535\) −11.4534 + 19.8378i −0.495172 + 0.857663i
\(536\) 2.47906 + 4.29385i 0.107079 + 0.185466i
\(537\) −14.4140 + 24.9658i −0.622010 + 1.07735i
\(538\) 0.573978 + 0.994159i 0.0247459 + 0.0428612i
\(539\) 0.830689 0.0357803
\(540\) 11.1925 0.481650
\(541\) 5.98545 + 10.3671i 0.257335 + 0.445717i 0.965527 0.260303i \(-0.0838224\pi\)
−0.708192 + 0.706020i \(0.750489\pi\)
\(542\) 10.0273 + 17.3679i 0.430711 + 0.746014i
\(543\) 4.25671 0.182673
\(544\) 6.51754 0.279437
\(545\) 8.69459 + 15.0595i 0.372435 + 0.645077i
\(546\) −11.8871 + 20.5891i −0.508722 + 0.881132i
\(547\) 1.59833 + 2.76838i 0.0683395 + 0.118367i 0.898170 0.439647i \(-0.144897\pi\)
−0.829831 + 0.558015i \(0.811563\pi\)
\(548\) 5.83022 10.0982i 0.249055 0.431375i
\(549\) 0.958111 1.65950i 0.0408912 0.0708256i
\(550\) 3.18479 0.135800
\(551\) 0 0
\(552\) −1.06418 −0.0452944
\(553\) −12.2121 + 21.1520i −0.519313 + 0.899476i
\(554\) 8.68004 15.0343i 0.368780 0.638745i
\(555\) 6.69459 + 11.5954i 0.284170 + 0.492196i
\(556\) 4.13176 7.15642i 0.175226 0.303500i
\(557\) 11.9881 + 20.7641i 0.507954 + 0.879802i 0.999958 + 0.00920875i \(0.00293128\pi\)
−0.492004 + 0.870593i \(0.663735\pi\)
\(558\) −1.60132 −0.0677892
\(559\) 34.9222 1.47705
\(560\) −2.69459 4.66717i −0.113867 0.197224i
\(561\) −15.9008 27.5410i −0.671332 1.16278i
\(562\) 2.92127 0.123227
\(563\) 8.75702 0.369064 0.184532 0.982826i \(-0.440923\pi\)
0.184532 + 0.982826i \(0.440923\pi\)
\(564\) 6.04189 + 10.4649i 0.254409 + 0.440650i
\(565\) 2.85978 4.95329i 0.120312 0.208387i
\(566\) −4.74035 8.21053i −0.199252 0.345114i
\(567\) 8.91353 15.4387i 0.374333 0.648364i
\(568\) 4.22668 7.32083i 0.177348 0.307175i
\(569\) 36.4201 1.52681 0.763406 0.645919i \(-0.223526\pi\)
0.763406 + 0.645919i \(0.223526\pi\)
\(570\) 0 0
\(571\) 34.2131 1.43177 0.715886 0.698217i \(-0.246023\pi\)
0.715886 + 0.698217i \(0.246023\pi\)
\(572\) −9.17024 + 15.8833i −0.383427 + 0.664115i
\(573\) 7.32501 12.6873i 0.306007 0.530019i
\(574\) 0.467911 + 0.810446i 0.0195302 + 0.0338274i
\(575\) −0.347296 + 0.601535i −0.0144833 + 0.0250857i
\(576\) 0.326352 + 0.565258i 0.0135980 + 0.0235524i
\(577\) 15.5098 0.645681 0.322841 0.946453i \(-0.395362\pi\)
0.322841 + 0.946453i \(0.395362\pi\)
\(578\) −25.4783 −1.05976
\(579\) 18.1407 + 31.4206i 0.753901 + 1.30579i
\(580\) −2.82295 4.88949i −0.117217 0.203025i
\(581\) 22.8384 0.947498
\(582\) 0.532089 0.0220558
\(583\) 13.0770 + 22.6500i 0.541593 + 0.938066i
\(584\) 7.88326 13.6542i 0.326211 0.565015i
\(585\) 3.75877 + 6.51038i 0.155406 + 0.269171i
\(586\) 13.6459 23.6354i 0.563707 0.976369i
\(587\) 5.79086 10.0301i 0.239014 0.413985i −0.721417 0.692501i \(-0.756509\pi\)
0.960432 + 0.278516i \(0.0898424\pi\)
\(588\) −0.399615 −0.0164798
\(589\) 0 0
\(590\) 1.14796 0.0472606
\(591\) −17.5594 + 30.4138i −0.722298 + 1.25106i
\(592\) −2.18479 + 3.78417i −0.0897944 + 0.155528i
\(593\) 23.1964 + 40.1773i 0.952562 + 1.64989i 0.739851 + 0.672771i \(0.234896\pi\)
0.212711 + 0.977115i \(0.431771\pi\)
\(594\) 8.91147 15.4351i 0.365642 0.633311i
\(595\) 17.5621 + 30.4185i 0.719977 + 1.24704i
\(596\) −16.4534 −0.673956
\(597\) −15.4492 −0.632295
\(598\) −2.00000 3.46410i −0.0817861 0.141658i
\(599\) 12.8161 + 22.1982i 0.523653 + 0.906994i 0.999621 + 0.0275314i \(0.00876461\pi\)
−0.475968 + 0.879463i \(0.657902\pi\)
\(600\) −1.53209 −0.0625473
\(601\) −7.99226 −0.326011 −0.163006 0.986625i \(-0.552119\pi\)
−0.163006 + 0.986625i \(0.552119\pi\)
\(602\) 8.17024 + 14.1513i 0.332994 + 0.576763i
\(603\) 1.61809 2.80261i 0.0658937 0.114131i
\(604\) 2.32770 + 4.03169i 0.0947126 + 0.164047i
\(605\) 0.857097 1.48453i 0.0348459 0.0603549i
\(606\) 0.283119 0.490376i 0.0115009 0.0199202i
\(607\) 26.9905 1.09551 0.547755 0.836639i \(-0.315482\pi\)
0.547755 + 0.836639i \(0.315482\pi\)
\(608\) 0 0
\(609\) −11.6541 −0.472249
\(610\) 2.93582 5.08499i 0.118868 0.205885i
\(611\) −22.7101 + 39.3350i −0.918751 + 1.59132i
\(612\) −2.12701 3.68409i −0.0859793 0.148921i
\(613\) 7.12567 12.3420i 0.287803 0.498489i −0.685482 0.728090i \(-0.740409\pi\)
0.973285 + 0.229600i \(0.0737418\pi\)
\(614\) −10.6643 18.4711i −0.430377 0.745434i
\(615\) −1.06418 −0.0429118
\(616\) −8.58172 −0.345767
\(617\) 15.2802 + 26.4661i 0.615157 + 1.06548i 0.990357 + 0.138539i \(0.0442407\pi\)
−0.375200 + 0.926944i \(0.622426\pi\)
\(618\) 6.57398 + 11.3865i 0.264444 + 0.458031i
\(619\) −28.6750 −1.15255 −0.576273 0.817258i \(-0.695493\pi\)
−0.576273 + 0.817258i \(0.695493\pi\)
\(620\) −4.90673 −0.197059
\(621\) 1.94356 + 3.36635i 0.0779925 + 0.135087i
\(622\) −14.6459 + 25.3674i −0.587247 + 1.01714i
\(623\) 10.4270 + 18.0600i 0.417747 + 0.723559i
\(624\) 4.41147 7.64090i 0.176600 0.305881i
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) −5.56118 −0.222270
\(627\) 0 0
\(628\) 8.45336 0.337326
\(629\) 14.2395 24.6635i 0.567765 0.983398i
\(630\) −1.75877 + 3.04628i −0.0700711 + 0.121367i
\(631\) 2.24897 + 3.89533i 0.0895301 + 0.155071i 0.907313 0.420457i \(-0.138130\pi\)
−0.817783 + 0.575527i \(0.804797\pi\)
\(632\) 4.53209 7.84981i 0.180277 0.312249i
\(633\) 17.1288 + 29.6680i 0.680810 + 1.17920i
\(634\) 3.80335 0.151050
\(635\) −19.4593 −0.772221
\(636\) −6.29086 10.8961i −0.249449 0.432058i
\(637\) −0.751030 1.30082i −0.0297569 0.0515404i
\(638\) −8.99050 −0.355937
\(639\) −5.51754 −0.218271
\(640\) 1.00000 + 1.73205i 0.0395285 + 0.0684653i
\(641\) −5.80406 + 10.0529i −0.229247 + 0.397067i −0.957585 0.288151i \(-0.906960\pi\)
0.728338 + 0.685218i \(0.240293\pi\)
\(642\) −8.77379 15.1966i −0.346274 0.599764i
\(643\) −13.0228 + 22.5561i −0.513567 + 0.889525i 0.486309 + 0.873787i \(0.338343\pi\)
−0.999876 + 0.0157377i \(0.994990\pi\)
\(644\) 0.935822 1.62089i 0.0368766 0.0638721i
\(645\) −18.5817 −0.731654
\(646\) 0 0
\(647\) −2.31490 −0.0910082 −0.0455041 0.998964i \(-0.514489\pi\)
−0.0455041 + 0.998964i \(0.514489\pi\)
\(648\) −3.30793 + 5.72951i −0.129948 + 0.225076i
\(649\) 0.914000 1.58310i 0.0358777 0.0621419i
\(650\) −2.87939 4.98724i −0.112939 0.195616i
\(651\) −5.06418 + 8.77141i −0.198481 + 0.343779i
\(652\) −8.52481 14.7654i −0.333858 0.578258i
\(653\) 3.30541 0.129351 0.0646753 0.997906i \(-0.479399\pi\)
0.0646753 + 0.997906i \(0.479399\pi\)
\(654\) −13.3209 −0.520888
\(655\) 6.46791 + 11.2028i 0.252722 + 0.437728i
\(656\) −0.173648 0.300767i −0.00677982 0.0117430i
\(657\) −10.2909 −0.401485
\(658\) −21.2526 −0.828512
\(659\) −6.87464 11.9072i −0.267798 0.463839i 0.700495 0.713657i \(-0.252963\pi\)
−0.968293 + 0.249818i \(0.919629\pi\)
\(660\) 4.87939 8.45134i 0.189930 0.328968i
\(661\) −1.66725 2.88776i −0.0648486 0.112321i 0.831778 0.555108i \(-0.187323\pi\)
−0.896627 + 0.442787i \(0.853990\pi\)
\(662\) −10.2110 + 17.6859i −0.396860 + 0.687382i
\(663\) −28.7520 + 49.7999i −1.11663 + 1.93407i
\(664\) −8.47565 −0.328919
\(665\) 0 0
\(666\) 2.85204 0.110514
\(667\) 0.980400 1.69810i 0.0379612 0.0657508i
\(668\) −1.59627 + 2.76481i −0.0617614 + 0.106974i
\(669\) 7.10607 + 12.3081i 0.274736 + 0.475857i
\(670\) 4.95811 8.58770i 0.191549 0.331772i
\(671\) −4.67499 8.09732i −0.180476 0.312594i
\(672\) 4.12836 0.159255
\(673\) −38.9810 −1.50261 −0.751304 0.659957i \(-0.770575\pi\)
−0.751304 + 0.659957i \(0.770575\pi\)
\(674\) −10.1552 17.5894i −0.391165 0.677517i
\(675\) 2.79813 + 4.84651i 0.107700 + 0.186542i
\(676\) 20.1634 0.775517
\(677\) 43.5877 1.67521 0.837606 0.546275i \(-0.183955\pi\)
0.837606 + 0.546275i \(0.183955\pi\)
\(678\) 2.19072 + 3.79444i 0.0841342 + 0.145725i
\(679\) −0.467911 + 0.810446i −0.0179568 + 0.0311021i
\(680\) −6.51754 11.2887i −0.249936 0.432902i
\(681\) −5.92649 + 10.2650i −0.227104 + 0.393355i
\(682\) −3.90673 + 6.76665i −0.149596 + 0.259108i
\(683\) −32.9317 −1.26010 −0.630048 0.776556i \(-0.716965\pi\)
−0.630048 + 0.776556i \(0.716965\pi\)
\(684\) 0 0
\(685\) −23.3209 −0.891045
\(686\) −9.07966 + 15.7264i −0.346663 + 0.600438i
\(687\) −17.6459 + 30.5636i −0.673233 + 1.16607i
\(688\) −3.03209 5.25173i −0.115597 0.200220i
\(689\) 23.6459 40.9559i 0.900837 1.56030i
\(690\) 1.06418 + 1.84321i 0.0405126 + 0.0701698i
\(691\) 34.3209 1.30563 0.652814 0.757518i \(-0.273588\pi\)
0.652814 + 0.757518i \(0.273588\pi\)
\(692\) −9.63041 −0.366093
\(693\) 2.80066 + 4.85088i 0.106388 + 0.184270i
\(694\) 2.60741 + 4.51617i 0.0989760 + 0.171431i
\(695\) −16.5270 −0.626906
\(696\) 4.32501 0.163939
\(697\) 1.13176 + 1.96026i 0.0428684 + 0.0742503i
\(698\) 7.17024 12.4192i 0.271398 0.470075i
\(699\) 6.43448 + 11.1448i 0.243374 + 0.421537i
\(700\) 1.34730 2.33359i 0.0509230 0.0882013i
\(701\) −3.22668 + 5.58878i −0.121870 + 0.211085i −0.920505 0.390730i \(-0.872222\pi\)
0.798635 + 0.601816i \(0.205556\pi\)
\(702\) −32.2276 −1.21635
\(703\) 0 0
\(704\) 3.18479 0.120031
\(705\) 12.0838 20.9297i 0.455101 0.788259i
\(706\) 13.1250 22.7331i 0.493964 0.855571i
\(707\) 0.497941 + 0.862458i 0.0187270 + 0.0324361i
\(708\) −0.439693 + 0.761570i −0.0165247 + 0.0286216i
\(709\) 1.68954 + 2.92637i 0.0634520 + 0.109902i 0.896006 0.444041i \(-0.146456\pi\)
−0.832554 + 0.553944i \(0.813122\pi\)
\(710\) −16.9067 −0.634498
\(711\) −5.91622 −0.221876
\(712\) −3.86959 6.70232i −0.145019 0.251180i
\(713\) −0.852044 1.47578i −0.0319093 0.0552685i
\(714\) −26.9067 −1.00696
\(715\) 36.6810 1.37179
\(716\) 9.40807 + 16.2953i 0.351596 + 0.608982i
\(717\) −12.0496 + 20.8706i −0.450002 + 0.779426i
\(718\) −16.8452 29.1768i −0.628659 1.08887i
\(719\) 15.6013 27.0223i 0.581831 1.00776i −0.413431 0.910535i \(-0.635670\pi\)
0.995262 0.0972256i \(-0.0309968\pi\)
\(720\) 0.652704 1.13052i 0.0243248 0.0421318i
\(721\) −23.1242 −0.861192
\(722\) 0 0
\(723\) 26.8161 0.997303
\(724\) 1.38919 2.40614i 0.0516287 0.0894235i
\(725\) 1.41147 2.44474i 0.0524208 0.0907955i
\(726\) 0.656574 + 1.13722i 0.0243677 + 0.0422062i
\(727\) 12.8307 22.2234i 0.475864 0.824220i −0.523754 0.851870i \(-0.675469\pi\)
0.999618 + 0.0276492i \(0.00880214\pi\)
\(728\) 7.75877 + 13.4386i 0.287559 + 0.498067i
\(729\) 30.0401 1.11260
\(730\) −31.5330 −1.16709
\(731\) 19.7618 + 34.2284i 0.730915 + 1.26598i
\(732\) 2.24897 + 3.89533i 0.0831243 + 0.143976i
\(733\) −23.8735 −0.881788 −0.440894 0.897559i \(-0.645339\pi\)
−0.440894 + 0.897559i \(0.645339\pi\)
\(734\) 10.4688 0.386412
\(735\) 0.399615 + 0.692153i 0.0147400 + 0.0255304i
\(736\) −0.347296 + 0.601535i −0.0128015 + 0.0221729i
\(737\) −7.89528 13.6750i −0.290826 0.503726i
\(738\) −0.113341 + 0.196312i −0.00417213 + 0.00722635i
\(739\) 22.9702 39.7855i 0.844972 1.46353i −0.0406734 0.999172i \(-0.512950\pi\)
0.885645 0.464362i \(-0.153716\pi\)
\(740\) 8.73917 0.321258
\(741\) 0 0
\(742\) 22.1284 0.812357
\(743\) −25.5057 + 44.1771i −0.935713 + 1.62070i −0.162355 + 0.986732i \(0.551909\pi\)
−0.773358 + 0.633969i \(0.781424\pi\)
\(744\) 1.87939 3.25519i 0.0689016 0.119341i
\(745\) 16.4534 + 28.4981i 0.602805 + 1.04409i
\(746\) −11.9513 + 20.7003i −0.437568 + 0.757891i
\(747\) 2.76604 + 4.79093i 0.101204 + 0.175291i
\(748\) −20.7570 −0.758952
\(749\) 30.8621 1.12768
\(750\) 9.19253 + 15.9219i 0.335664 + 0.581387i
\(751\) −18.1848 31.4970i −0.663573 1.14934i −0.979670 0.200615i \(-0.935706\pi\)
0.316098 0.948727i \(-0.397627\pi\)
\(752\) 7.88713 0.287614
\(753\) −13.1257 −0.478326
\(754\) 8.12836 + 14.0787i 0.296017 + 0.512717i
\(755\) 4.65539 8.06338i 0.169427 0.293456i
\(756\) −7.53983 13.0594i −0.274221 0.474965i
\(757\) 2.90167 5.02585i 0.105463 0.182668i −0.808464 0.588545i \(-0.799701\pi\)
0.913927 + 0.405878i \(0.133034\pi\)
\(758\) −8.90673 + 15.4269i −0.323507 + 0.560330i
\(759\) 3.38919 0.123020
\(760\) 0 0
\(761\) 22.6355 0.820535 0.410268 0.911965i \(-0.365435\pi\)
0.410268 + 0.911965i \(0.365435\pi\)
\(762\) 7.45336 12.9096i 0.270007 0.467666i
\(763\) 11.7142 20.2896i 0.424082 0.734532i
\(764\) −4.78106 8.28104i −0.172973 0.299597i
\(765\) −4.25402 + 7.36818i −0.153805 + 0.266397i
\(766\) −12.5398 21.7196i −0.453082 0.784762i
\(767\) −3.30541 −0.119351
\(768\) −1.53209 −0.0552845
\(769\) −5.45130 9.44194i −0.196579 0.340485i 0.750838 0.660486i \(-0.229650\pi\)
−0.947417 + 0.320002i \(0.896317\pi\)
\(770\) 8.58172 + 14.8640i 0.309264 + 0.535660i
\(771\) −12.2945 −0.442775
\(772\) 23.6810 0.852297
\(773\) −2.62536 4.54726i −0.0944277 0.163554i 0.814942 0.579543i \(-0.196769\pi\)
−0.909370 + 0.415989i \(0.863435\pi\)
\(774\) −1.97906 + 3.42782i −0.0711357 + 0.123211i
\(775\) −1.22668 2.12467i −0.0440637 0.0763206i
\(776\) 0.173648 0.300767i 0.00623361 0.0107969i
\(777\) 9.01960 15.6224i 0.323576 0.560451i
\(778\) 9.41828 0.337662
\(779\) 0 0
\(780\) −17.6