Properties

Label 16.5.f.a.3.2
Level $16$
Weight $5$
Character 16.3
Analytic conductor $1.654$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 16.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.65391940934\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + 11456 x^{6} - 19968 x^{5} + 31744 x^{4} - 139264 x^{3} + 491520 x^{2} - 1048576 x + 2097152\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{21} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 3.2
Root \(0.153862 - 2.82424i\) of defining polynomial
Character \(\chi\) \(=\) 16.3
Dual form 16.5.f.a.11.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.97810 - 2.67038i) q^{2} +(-9.42589 + 9.42589i) q^{3} +(1.73818 + 15.9053i) q^{4} +(-2.84710 + 2.84710i) q^{5} +(53.2419 - 2.90058i) q^{6} -76.7794 q^{7} +(37.2967 - 52.0092i) q^{8} -96.6949i q^{9} +O(q^{10})\) \(q+(-2.97810 - 2.67038i) q^{2} +(-9.42589 + 9.42589i) q^{3} +(1.73818 + 15.9053i) q^{4} +(-2.84710 + 2.84710i) q^{5} +(53.2419 - 2.90058i) q^{6} -76.7794 q^{7} +(37.2967 - 52.0092i) q^{8} -96.6949i q^{9} +(16.0818 - 0.876123i) q^{10} +(121.488 + 121.488i) q^{11} +(-166.306 - 133.538i) q^{12} +(27.1604 + 27.1604i) q^{13} +(228.657 + 205.030i) q^{14} -53.6729i q^{15} +(-249.957 + 55.2924i) q^{16} -88.0613 q^{17} +(-258.212 + 287.967i) q^{18} +(-261.112 + 261.112i) q^{19} +(-50.2328 - 40.3352i) q^{20} +(723.714 - 723.714i) q^{21} +(-37.3847 - 686.220i) q^{22} +93.4210 q^{23} +(138.678 + 841.788i) q^{24} +608.788i q^{25} +(-8.35791 - 153.415i) q^{26} +(147.938 + 147.938i) q^{27} +(-133.456 - 1221.20i) q^{28} +(272.522 + 272.522i) q^{29} +(-143.327 + 159.843i) q^{30} -1232.20i q^{31} +(892.050 + 502.814i) q^{32} -2290.26 q^{33} +(262.256 + 235.157i) q^{34} +(218.599 - 218.599i) q^{35} +(1537.96 - 168.073i) q^{36} +(-1046.16 + 1046.16i) q^{37} +(1474.89 - 80.3506i) q^{38} -512.021 q^{39} +(41.8880 + 254.263i) q^{40} +915.267i q^{41} +(-4087.88 + 222.705i) q^{42} +(1116.82 + 1116.82i) q^{43} +(-1721.13 + 2143.47i) q^{44} +(275.300 + 275.300i) q^{45} +(-278.217 - 249.469i) q^{46} -1720.70i q^{47} +(1834.89 - 2877.25i) q^{48} +3494.07 q^{49} +(1625.69 - 1813.03i) q^{50} +(830.056 - 830.056i) q^{51} +(-384.784 + 479.203i) q^{52} +(734.019 - 734.019i) q^{53} +(-45.5242 - 835.626i) q^{54} -691.775 q^{55} +(-2863.62 + 3993.23i) q^{56} -4922.43i q^{57} +(-83.8616 - 1539.33i) q^{58} +(-1202.73 - 1202.73i) q^{59} +(853.684 - 93.2930i) q^{60} +(580.221 + 580.221i) q^{61} +(-3290.44 + 3669.61i) q^{62} +7424.17i q^{63} +(-1313.91 - 3879.54i) q^{64} -154.657 q^{65} +(6820.62 + 6115.86i) q^{66} +(-1483.97 + 1483.97i) q^{67} +(-153.066 - 1400.64i) q^{68} +(-880.576 + 880.576i) q^{69} +(-1234.75 + 67.2681i) q^{70} +5571.73 q^{71} +(-5029.02 - 3606.40i) q^{72} +6615.21i q^{73} +(5909.20 - 321.929i) q^{74} +(-5738.37 - 5738.37i) q^{75} +(-4606.93 - 3699.21i) q^{76} +(-9327.75 - 9327.75i) q^{77} +(1524.85 + 1367.29i) q^{78} +5391.66i q^{79} +(554.231 - 869.077i) q^{80} +5043.39 q^{81} +(2444.11 - 2725.76i) q^{82} +(-2554.07 + 2554.07i) q^{83} +(12768.8 + 10252.9i) q^{84} +(250.719 - 250.719i) q^{85} +(-343.673 - 6308.34i) q^{86} -5137.52 q^{87} +(10849.6 - 1787.39i) q^{88} -10962.7i q^{89} +(-84.7166 - 1555.03i) q^{90} +(-2085.35 - 2085.35i) q^{91} +(162.382 + 1485.89i) q^{92} +(11614.6 + 11614.6i) q^{93} +(-4594.92 + 5124.42i) q^{94} -1486.83i q^{95} +(-13147.8 + 3668.90i) q^{96} +4713.20 q^{97} +(-10405.7 - 9330.48i) q^{98} +(11747.2 - 11747.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 2q^{2} - 2q^{3} - 8q^{4} - 2q^{5} + 64q^{6} - 4q^{7} - 92q^{8} + O(q^{10}) \) \( 14q - 2q^{2} - 2q^{3} - 8q^{4} - 2q^{5} + 64q^{6} - 4q^{7} - 92q^{8} - 100q^{10} + 94q^{11} - 332q^{12} - 2q^{13} + 44q^{14} - 168q^{16} - 4q^{17} + 1390q^{18} - 706q^{19} + 1900q^{20} - 164q^{21} + 900q^{22} + 1148q^{23} - 1872q^{24} - 3416q^{26} - 1664q^{27} - 3784q^{28} + 862q^{29} - 3740q^{30} + 3208q^{32} - 4q^{33} + 7508q^{34} + 1340q^{35} + 11468q^{36} - 1826q^{37} + 3568q^{38} + 2684q^{39} - 5144q^{40} - 17064q^{42} + 1694q^{43} - 14636q^{44} + 1410q^{45} - 5316q^{46} + 6888q^{48} + 682q^{49} + 20070q^{50} - 3012q^{51} + 20452q^{52} - 482q^{53} + 10784q^{54} - 11780q^{55} - 6952q^{56} - 20456q^{58} - 2786q^{59} - 29920q^{60} - 3778q^{61} - 11472q^{62} + 15808q^{64} - 2020q^{65} + 30148q^{66} + 7998q^{67} + 18032q^{68} + 9628q^{69} + 15296q^{70} + 19964q^{71} - 17708q^{72} - 23780q^{74} + 17570q^{75} - 23996q^{76} - 9508q^{77} - 8052q^{78} + 1384q^{80} + 1454q^{81} + 16016q^{82} - 17282q^{83} + 19624q^{84} + 9948q^{85} - 4796q^{86} - 49284q^{87} + 7288q^{88} - 5416q^{90} - 28036q^{91} - 14632q^{92} + 8896q^{93} + 432q^{94} + 6064q^{96} - 4q^{97} - 12246q^{98} + 49214q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.97810 2.67038i −0.744525 0.667594i
\(3\) −9.42589 + 9.42589i −1.04732 + 1.04732i −0.0484980 + 0.998823i \(0.515443\pi\)
−0.998823 + 0.0484980i \(0.984557\pi\)
\(4\) 1.73818 + 15.9053i 0.108636 + 0.994082i
\(5\) −2.84710 + 2.84710i −0.113884 + 0.113884i −0.761752 0.647868i \(-0.775661\pi\)
0.647868 + 0.761752i \(0.275661\pi\)
\(6\) 53.2419 2.90058i 1.47894 0.0805716i
\(7\) −76.7794 −1.56693 −0.783463 0.621439i \(-0.786549\pi\)
−0.783463 + 0.621439i \(0.786549\pi\)
\(8\) 37.2967 52.0092i 0.582761 0.812644i
\(9\) 96.6949i 1.19376i
\(10\) 16.0818 0.876123i 0.160818 0.00876123i
\(11\) 121.488 + 121.488i 1.00403 + 1.00403i 0.999992 + 0.00403849i \(0.00128549\pi\)
0.00403849 + 0.999992i \(0.498715\pi\)
\(12\) −166.306 133.538i −1.15490 0.927346i
\(13\) 27.1604 + 27.1604i 0.160712 + 0.160712i 0.782882 0.622170i \(-0.213749\pi\)
−0.622170 + 0.782882i \(0.713749\pi\)
\(14\) 228.657 + 205.030i 1.16662 + 1.04607i
\(15\) 53.6729i 0.238546i
\(16\) −249.957 + 55.2924i −0.976396 + 0.215986i
\(17\) −88.0613 −0.304710 −0.152355 0.988326i \(-0.548686\pi\)
−0.152355 + 0.988326i \(0.548686\pi\)
\(18\) −258.212 + 287.967i −0.796950 + 0.888787i
\(19\) −261.112 + 261.112i −0.723302 + 0.723302i −0.969276 0.245974i \(-0.920892\pi\)
0.245974 + 0.969276i \(0.420892\pi\)
\(20\) −50.2328 40.3352i −0.125582 0.100838i
\(21\) 723.714 723.714i 1.64107 1.64107i
\(22\) −37.3847 686.220i −0.0772412 1.41781i
\(23\) 93.4210 0.176599 0.0882996 0.996094i \(-0.471857\pi\)
0.0882996 + 0.996094i \(0.471857\pi\)
\(24\) 138.678 + 841.788i 0.240761 + 1.46144i
\(25\) 608.788i 0.974061i
\(26\) −8.35791 153.415i −0.0123638 0.226945i
\(27\) 147.938 + 147.938i 0.202933 + 0.202933i
\(28\) −133.456 1221.20i −0.170224 1.55765i
\(29\) 272.522 + 272.522i 0.324045 + 0.324045i 0.850316 0.526272i \(-0.176410\pi\)
−0.526272 + 0.850316i \(0.676410\pi\)
\(30\) −143.327 + 159.843i −0.159252 + 0.177604i
\(31\) 1232.20i 1.28220i −0.767455 0.641102i \(-0.778477\pi\)
0.767455 0.641102i \(-0.221523\pi\)
\(32\) 892.050 + 502.814i 0.871143 + 0.491030i
\(33\) −2290.26 −2.10308
\(34\) 262.256 + 235.157i 0.226865 + 0.203423i
\(35\) 218.599 218.599i 0.178448 0.178448i
\(36\) 1537.96 168.073i 1.18670 0.129686i
\(37\) −1046.16 + 1046.16i −0.764177 + 0.764177i −0.977075 0.212898i \(-0.931710\pi\)
0.212898 + 0.977075i \(0.431710\pi\)
\(38\) 1474.89 80.3506i 1.02139 0.0556445i
\(39\) −512.021 −0.336635
\(40\) 41.8880 + 254.263i 0.0261800 + 0.158914i
\(41\) 915.267i 0.544478i 0.962230 + 0.272239i \(0.0877641\pi\)
−0.962230 + 0.272239i \(0.912236\pi\)
\(42\) −4087.88 + 222.705i −2.31739 + 0.126250i
\(43\) 1116.82 + 1116.82i 0.604013 + 0.604013i 0.941375 0.337362i \(-0.109535\pi\)
−0.337362 + 0.941375i \(0.609535\pi\)
\(44\) −1721.13 + 2143.47i −0.889014 + 1.10716i
\(45\) 275.300 + 275.300i 0.135951 + 0.135951i
\(46\) −278.217 249.469i −0.131483 0.117897i
\(47\) 1720.70i 0.778949i −0.921037 0.389475i \(-0.872657\pi\)
0.921037 0.389475i \(-0.127343\pi\)
\(48\) 1834.89 2877.25i 0.796394 1.24881i
\(49\) 3494.07 1.45526
\(50\) 1625.69 1813.03i 0.650277 0.725213i
\(51\) 830.056 830.056i 0.319130 0.319130i
\(52\) −384.784 + 479.203i −0.142302 + 0.177220i
\(53\) 734.019 734.019i 0.261310 0.261310i −0.564276 0.825586i \(-0.690845\pi\)
0.825586 + 0.564276i \(0.190845\pi\)
\(54\) −45.5242 835.626i −0.0156119 0.286566i
\(55\) −691.775 −0.228686
\(56\) −2863.62 + 3993.23i −0.913143 + 1.27335i
\(57\) 4922.43i 1.51506i
\(58\) −83.8616 1539.33i −0.0249291 0.457590i
\(59\) −1202.73 1202.73i −0.345512 0.345512i 0.512923 0.858435i \(-0.328563\pi\)
−0.858435 + 0.512923i \(0.828563\pi\)
\(60\) 853.684 93.2930i 0.237135 0.0259147i
\(61\) 580.221 + 580.221i 0.155932 + 0.155932i 0.780761 0.624830i \(-0.214832\pi\)
−0.624830 + 0.780761i \(0.714832\pi\)
\(62\) −3290.44 + 3669.61i −0.855993 + 0.954634i
\(63\) 7424.17i 1.87054i
\(64\) −1313.91 3879.54i −0.320779 0.947154i
\(65\) −154.657 −0.0366051
\(66\) 6820.62 + 6115.86i 1.56580 + 1.40401i
\(67\) −1483.97 + 1483.97i −0.330580 + 0.330580i −0.852807 0.522227i \(-0.825101\pi\)
0.522227 + 0.852807i \(0.325101\pi\)
\(68\) −153.066 1400.64i −0.0331025 0.302907i
\(69\) −880.576 + 880.576i −0.184956 + 0.184956i
\(70\) −1234.75 + 67.2681i −0.251990 + 0.0137282i
\(71\) 5571.73 1.10528 0.552641 0.833419i \(-0.313620\pi\)
0.552641 + 0.833419i \(0.313620\pi\)
\(72\) −5029.02 3606.40i −0.970105 0.695679i
\(73\) 6615.21i 1.24136i 0.784064 + 0.620681i \(0.213144\pi\)
−0.784064 + 0.620681i \(0.786856\pi\)
\(74\) 5909.20 321.929i 1.07911 0.0587890i
\(75\) −5738.37 5738.37i −1.02015 1.02015i
\(76\) −4606.93 3699.21i −0.797598 0.640445i
\(77\) −9327.75 9327.75i −1.57324 1.57324i
\(78\) 1524.85 + 1367.29i 0.250633 + 0.224735i
\(79\) 5391.66i 0.863910i 0.901895 + 0.431955i \(0.142176\pi\)
−0.901895 + 0.431955i \(0.857824\pi\)
\(80\) 554.231 869.077i 0.0865986 0.135793i
\(81\) 5043.39 0.768692
\(82\) 2444.11 2725.76i 0.363490 0.405378i
\(83\) −2554.07 + 2554.07i −0.370747 + 0.370747i −0.867749 0.497002i \(-0.834434\pi\)
0.497002 + 0.867749i \(0.334434\pi\)
\(84\) 12768.8 + 10252.9i 1.80964 + 1.45308i
\(85\) 250.719 250.719i 0.0347017 0.0347017i
\(86\) −343.673 6308.34i −0.0464674 0.852939i
\(87\) −5137.52 −0.678758
\(88\) 10849.6 1787.39i 1.40103 0.230809i
\(89\) 10962.7i 1.38400i −0.721898 0.691999i \(-0.756730\pi\)
0.721898 0.691999i \(-0.243270\pi\)
\(90\) −84.7166 1555.03i −0.0104588 0.191979i
\(91\) −2085.35 2085.35i −0.251824 0.251824i
\(92\) 162.382 + 1485.89i 0.0191850 + 0.175554i
\(93\) 11614.6 + 11614.6i 1.34288 + 1.34288i
\(94\) −4594.92 + 5124.42i −0.520022 + 0.579948i
\(95\) 1486.83i 0.164745i
\(96\) −13147.8 + 3668.90i −1.42663 + 0.398101i
\(97\) 4713.20 0.500925 0.250462 0.968126i \(-0.419417\pi\)
0.250462 + 0.968126i \(0.419417\pi\)
\(98\) −10405.7 9330.48i −1.08347 0.971520i
\(99\) 11747.2 11747.2i 1.19858 1.19858i
\(100\) −9682.96 + 1058.18i −0.968296 + 0.105818i
\(101\) −11381.0 + 11381.0i −1.11568 + 1.11568i −0.123307 + 0.992369i \(0.539350\pi\)
−0.992369 + 0.123307i \(0.960650\pi\)
\(102\) −4688.56 + 255.429i −0.450649 + 0.0245510i
\(103\) 175.758 0.0165668 0.00828342 0.999966i \(-0.497363\pi\)
0.00828342 + 0.999966i \(0.497363\pi\)
\(104\) 2425.58 399.597i 0.224258 0.0369450i
\(105\) 4120.97i 0.373784i
\(106\) −4146.09 + 225.876i −0.369000 + 0.0201028i
\(107\) 15151.8 + 15151.8i 1.32342 + 1.32342i 0.910988 + 0.412432i \(0.135321\pi\)
0.412432 + 0.910988i \(0.364679\pi\)
\(108\) −2095.86 + 2610.14i −0.179686 + 0.223778i
\(109\) −2349.51 2349.51i −0.197754 0.197754i 0.601283 0.799036i \(-0.294657\pi\)
−0.799036 + 0.601283i \(0.794657\pi\)
\(110\) 2060.18 + 1847.30i 0.170263 + 0.152669i
\(111\) 19721.9i 1.60068i
\(112\) 19191.6 4245.32i 1.52994 0.338434i
\(113\) −8526.30 −0.667734 −0.333867 0.942620i \(-0.608354\pi\)
−0.333867 + 0.942620i \(0.608354\pi\)
\(114\) −13144.7 + 14659.5i −1.01145 + 1.12800i
\(115\) −265.979 + 265.979i −0.0201118 + 0.0201118i
\(116\) −3860.85 + 4808.23i −0.286924 + 0.357330i
\(117\) 2626.27 2626.27i 0.191852 0.191852i
\(118\) 370.108 + 6793.57i 0.0265806 + 0.487904i
\(119\) 6761.29 0.477459
\(120\) −2791.49 2001.82i −0.193853 0.139015i
\(121\) 14877.5i 1.01615i
\(122\) −178.548 3277.37i −0.0119960 0.220194i
\(123\) −8627.21 8627.21i −0.570243 0.570243i
\(124\) 19598.5 2141.78i 1.27462 0.139294i
\(125\) −3512.72 3512.72i −0.224814 0.224814i
\(126\) 19825.3 22109.9i 1.24876 1.39266i
\(127\) 2844.31i 0.176347i −0.996105 0.0881737i \(-0.971897\pi\)
0.996105 0.0881737i \(-0.0281031\pi\)
\(128\) −6446.87 + 15062.3i −0.393486 + 0.919331i
\(129\) −21054.1 −1.26519
\(130\) 460.583 + 412.991i 0.0272534 + 0.0244373i
\(131\) −6989.87 + 6989.87i −0.407311 + 0.407311i −0.880800 0.473489i \(-0.842994\pi\)
0.473489 + 0.880800i \(0.342994\pi\)
\(132\) −3980.87 36427.3i −0.228471 2.09064i
\(133\) 20048.0 20048.0i 1.13336 1.13336i
\(134\) 8382.19 456.655i 0.466818 0.0254319i
\(135\) −842.390 −0.0462217
\(136\) −3284.40 + 4580.00i −0.177573 + 0.247621i
\(137\) 3669.69i 0.195519i −0.995210 0.0977594i \(-0.968832\pi\)
0.995210 0.0977594i \(-0.0311676\pi\)
\(138\) 4973.92 270.975i 0.261180 0.0142289i
\(139\) 4401.33 + 4401.33i 0.227800 + 0.227800i 0.811773 0.583973i \(-0.198503\pi\)
−0.583973 + 0.811773i \(0.698503\pi\)
\(140\) 3856.84 + 3096.91i 0.196778 + 0.158006i
\(141\) 16219.1 + 16219.1i 0.815810 + 0.815810i
\(142\) −16593.2 14878.6i −0.822911 0.737880i
\(143\) 6599.30i 0.322720i
\(144\) 5346.49 + 24169.6i 0.257836 + 1.16559i
\(145\) −1551.79 −0.0738071
\(146\) 17665.1 19700.8i 0.828725 0.924225i
\(147\) −32934.7 + 32934.7i −1.52412 + 1.52412i
\(148\) −18457.9 14821.1i −0.842671 0.676637i
\(149\) 15737.5 15737.5i 0.708863 0.708863i −0.257433 0.966296i \(-0.582877\pi\)
0.966296 + 0.257433i \(0.0828766\pi\)
\(150\) 1765.84 + 32413.1i 0.0784817 + 1.44058i
\(151\) −41972.2 −1.84080 −0.920402 0.390974i \(-0.872138\pi\)
−0.920402 + 0.390974i \(0.872138\pi\)
\(152\) 3841.61 + 23318.9i 0.166275 + 1.00930i
\(153\) 8515.08i 0.363752i
\(154\) 2870.38 + 52687.6i 0.121031 + 2.22160i
\(155\) 3508.19 + 3508.19i 0.146023 + 0.146023i
\(156\) −889.982 8143.85i −0.0365706 0.334642i
\(157\) −24735.4 24735.4i −1.00351 1.00351i −0.999994 0.00351271i \(-0.998882\pi\)
−0.00351271 0.999994i \(-0.501118\pi\)
\(158\) 14397.8 16056.9i 0.576741 0.643203i
\(159\) 13837.6i 0.547350i
\(160\) −3971.32 + 1108.19i −0.155130 + 0.0432888i
\(161\) −7172.80 −0.276718
\(162\) −15019.7 13467.7i −0.572310 0.513174i
\(163\) 24429.8 24429.8i 0.919483 0.919483i −0.0775084 0.996992i \(-0.524696\pi\)
0.996992 + 0.0775084i \(0.0246965\pi\)
\(164\) −14557.6 + 1590.90i −0.541255 + 0.0591499i
\(165\) 6520.60 6520.60i 0.239508 0.239508i
\(166\) 14426.6 785.951i 0.523539 0.0285220i
\(167\) 52178.2 1.87093 0.935463 0.353425i \(-0.114983\pi\)
0.935463 + 0.353425i \(0.114983\pi\)
\(168\) −10647.6 64631.9i −0.377255 2.28996i
\(169\) 27085.6i 0.948343i
\(170\) −1416.18 + 77.1525i −0.0490029 + 0.00266964i
\(171\) 25248.2 + 25248.2i 0.863452 + 0.863452i
\(172\) −15822.1 + 19704.6i −0.534821 + 0.666056i
\(173\) 26316.2 + 26316.2i 0.879289 + 0.879289i 0.993461 0.114172i \(-0.0364216\pi\)
−0.114172 + 0.993461i \(0.536422\pi\)
\(174\) 15300.1 + 13719.1i 0.505353 + 0.453135i
\(175\) 46742.4i 1.52628i
\(176\) −37084.1 23649.4i −1.19719 0.763475i
\(177\) 22673.5 0.723723
\(178\) −29274.4 + 32647.9i −0.923949 + 1.03042i
\(179\) 4815.78 4815.78i 0.150301 0.150301i −0.627952 0.778252i \(-0.716106\pi\)
0.778252 + 0.627952i \(0.216106\pi\)
\(180\) −3900.21 + 4857.25i −0.120377 + 0.149915i
\(181\) −23924.9 + 23924.9i −0.730286 + 0.730286i −0.970676 0.240391i \(-0.922724\pi\)
0.240391 + 0.970676i \(0.422724\pi\)
\(182\) 641.715 + 11779.1i 0.0193731 + 0.355606i
\(183\) −10938.2 −0.326621
\(184\) 3484.29 4858.75i 0.102915 0.143512i
\(185\) 5957.04i 0.174055i
\(186\) −3574.09 65604.7i −0.103309 1.89631i
\(187\) −10698.4 10698.4i −0.305939 0.305939i
\(188\) 27368.2 2990.88i 0.774339 0.0846219i
\(189\) −11358.6 11358.6i −0.317981 0.317981i
\(190\) −3970.38 + 4427.92i −0.109983 + 0.122657i
\(191\) 45079.4i 1.23569i 0.786298 + 0.617847i \(0.211995\pi\)
−0.786298 + 0.617847i \(0.788005\pi\)
\(192\) 48952.9 + 24183.3i 1.32793 + 0.656015i
\(193\) 50286.0 1.34999 0.674997 0.737820i \(-0.264145\pi\)
0.674997 + 0.737820i \(0.264145\pi\)
\(194\) −14036.4 12586.0i −0.372951 0.334415i
\(195\) 1457.78 1457.78i 0.0383373 0.0383373i
\(196\) 6073.31 + 55574.2i 0.158093 + 1.44664i
\(197\) −25662.2 + 25662.2i −0.661243 + 0.661243i −0.955673 0.294430i \(-0.904870\pi\)
0.294430 + 0.955673i \(0.404870\pi\)
\(198\) −66354.0 + 3614.91i −1.69253 + 0.0922077i
\(199\) −44599.1 −1.12621 −0.563106 0.826385i \(-0.690394\pi\)
−0.563106 + 0.826385i \(0.690394\pi\)
\(200\) 31662.6 + 22705.8i 0.791564 + 0.567645i
\(201\) 27975.5i 0.692447i
\(202\) 64285.4 3502.21i 1.57547 0.0858302i
\(203\) −20924.0 20924.0i −0.507754 0.507754i
\(204\) 14645.1 + 11759.5i 0.351910 + 0.282572i
\(205\) −2605.86 2605.86i −0.0620073 0.0620073i
\(206\) −523.424 469.339i −0.0123344 0.0110599i
\(207\) 9033.33i 0.210818i
\(208\) −8290.70 5287.17i −0.191630 0.122207i
\(209\) −63443.8 −1.45244
\(210\) 11004.6 12272.7i 0.249536 0.278292i
\(211\) 25828.5 25828.5i 0.580143 0.580143i −0.354800 0.934942i \(-0.615451\pi\)
0.934942 + 0.354800i \(0.115451\pi\)
\(212\) 12950.6 + 10398.9i 0.288151 + 0.231375i
\(213\) −52518.5 + 52518.5i −1.15759 + 1.15759i
\(214\) −4662.59 85584.8i −0.101812 1.86883i
\(215\) −6359.40 −0.137575
\(216\) 13211.8 2176.54i 0.283174 0.0466508i
\(217\) 94607.4i 2.00912i
\(218\) 723.003 + 13271.2i 0.0152134 + 0.279252i
\(219\) −62354.3 62354.3i −1.30010 1.30010i
\(220\) −1202.43 11002.9i −0.0248435 0.227333i
\(221\) −2391.78 2391.78i −0.0489707 0.0489707i
\(222\) −52665.0 + 58734.0i −1.06860 + 1.19175i
\(223\) 72650.0i 1.46092i 0.682957 + 0.730459i \(0.260694\pi\)
−0.682957 + 0.730459i \(0.739306\pi\)
\(224\) −68491.1 38605.8i −1.36502 0.769407i
\(225\) 58866.7 1.16280
\(226\) 25392.2 + 22768.4i 0.497145 + 0.445776i
\(227\) 18858.2 18858.2i 0.365972 0.365972i −0.500034 0.866006i \(-0.666679\pi\)
0.866006 + 0.500034i \(0.166679\pi\)
\(228\) 78292.8 8556.05i 1.50609 0.164590i
\(229\) 41675.9 41675.9i 0.794721 0.794721i −0.187537 0.982258i \(-0.560050\pi\)
0.982258 + 0.187537i \(0.0600504\pi\)
\(230\) 1502.38 81.8483i 0.0284003 0.00154723i
\(231\) 175845. 3.29538
\(232\) 24337.8 4009.48i 0.452174 0.0744923i
\(233\) 2767.61i 0.0509792i −0.999675 0.0254896i \(-0.991886\pi\)
0.999675 0.0254896i \(-0.00811447\pi\)
\(234\) −14834.4 + 808.167i −0.270918 + 0.0147594i
\(235\) 4899.00 + 4899.00i 0.0887099 + 0.0887099i
\(236\) 17039.2 21220.3i 0.305932 0.381002i
\(237\) −50821.2 50821.2i −0.904791 0.904791i
\(238\) −20135.8 18055.2i −0.355480 0.318749i
\(239\) 49981.8i 0.875016i −0.899215 0.437508i \(-0.855861\pi\)
0.899215 0.437508i \(-0.144139\pi\)
\(240\) 2967.71 + 13416.0i 0.0515227 + 0.232916i
\(241\) −44076.0 −0.758872 −0.379436 0.925218i \(-0.623882\pi\)
−0.379436 + 0.925218i \(0.623882\pi\)
\(242\) 39728.6 44306.7i 0.678378 0.756552i
\(243\) −59521.4 + 59521.4i −1.00800 + 1.00800i
\(244\) −8220.07 + 10237.1i −0.138069 + 0.171948i
\(245\) −9947.97 + 9947.97i −0.165730 + 0.165730i
\(246\) 2654.80 + 48730.6i 0.0438695 + 0.805252i
\(247\) −14183.8 −0.232487
\(248\) −64085.7 45957.0i −1.04198 0.747219i
\(249\) 48148.8i 0.776582i
\(250\) 1080.95 + 19841.5i 0.0172952 + 0.317464i
\(251\) −31786.2 31786.2i −0.504534 0.504534i 0.408309 0.912844i \(-0.366119\pi\)
−0.912844 + 0.408309i \(0.866119\pi\)
\(252\) −118084. + 12904.5i −1.85947 + 0.203208i
\(253\) 11349.5 + 11349.5i 0.177311 + 0.177311i
\(254\) −7595.38 + 8470.64i −0.117729 + 0.131295i
\(255\) 4726.51i 0.0726876i
\(256\) 59421.5 27641.5i 0.906700 0.421776i
\(257\) 70865.6 1.07292 0.536462 0.843924i \(-0.319760\pi\)
0.536462 + 0.843924i \(0.319760\pi\)
\(258\) 62701.1 + 56222.3i 0.941968 + 0.844635i
\(259\) 80323.4 80323.4i 1.19741 1.19741i
\(260\) −268.820 2459.86i −0.00397663 0.0363885i
\(261\) 26351.5 26351.5i 0.386833 0.386833i
\(262\) 39482.1 2150.95i 0.575172 0.0313349i
\(263\) −113289. −1.63786 −0.818929 0.573894i \(-0.805432\pi\)
−0.818929 + 0.573894i \(0.805432\pi\)
\(264\) −85419.1 + 119115.i −1.22560 + 1.70906i
\(265\) 4179.65i 0.0595180i
\(266\) −113241. + 6169.27i −1.60044 + 0.0871908i
\(267\) 103333. + 103333.i 1.44949 + 1.44949i
\(268\) −26182.5 21023.6i −0.364536 0.292711i
\(269\) 70652.7 + 70652.7i 0.976393 + 0.976393i 0.999728 0.0233352i \(-0.00742850\pi\)
−0.0233352 + 0.999728i \(0.507428\pi\)
\(270\) 2508.72 + 2249.50i 0.0344132 + 0.0308573i
\(271\) 110180.i 1.50025i 0.661294 + 0.750126i \(0.270007\pi\)
−0.661294 + 0.750126i \(0.729993\pi\)
\(272\) 22011.6 4869.12i 0.297518 0.0658132i
\(273\) 39312.7 0.527481
\(274\) −9799.47 + 10928.7i −0.130527 + 0.145569i
\(275\) −73960.2 + 73960.2i −0.977987 + 0.977987i
\(276\) −15536.4 12475.2i −0.203954 0.163769i
\(277\) 34611.0 34611.0i 0.451081 0.451081i −0.444632 0.895713i \(-0.646666\pi\)
0.895713 + 0.444632i \(0.146666\pi\)
\(278\) −1354.40 24860.8i −0.0175249 0.321681i
\(279\) −119147. −1.53065
\(280\) −3216.13 19522.1i −0.0410221 0.249007i
\(281\) 147980.i 1.87408i −0.349216 0.937042i \(-0.613552\pi\)
0.349216 0.937042i \(-0.386448\pi\)
\(282\) −4991.02 91613.4i −0.0627612 1.15202i
\(283\) 39761.2 + 39761.2i 0.496463 + 0.496463i 0.910335 0.413872i \(-0.135824\pi\)
−0.413872 + 0.910335i \(0.635824\pi\)
\(284\) 9684.65 + 88620.1i 0.120073 + 1.09874i
\(285\) 14014.7 + 14014.7i 0.172541 + 0.172541i
\(286\) 17622.6 19653.4i 0.215446 0.240273i
\(287\) 70273.6i 0.853156i
\(288\) 48619.6 86256.7i 0.586173 1.03994i
\(289\) −75766.2 −0.907152
\(290\) 4621.40 + 4143.87i 0.0549512 + 0.0492732i
\(291\) −44426.1 + 44426.1i −0.524629 + 0.524629i
\(292\) −105217. + 11498.4i −1.23401 + 0.134856i
\(293\) −708.909 + 708.909i −0.00825763 + 0.00825763i −0.711224 0.702966i \(-0.751859\pi\)
0.702966 + 0.711224i \(0.251859\pi\)
\(294\) 186031. 10134.8i 2.15224 0.117252i
\(295\) 6848.56 0.0786965
\(296\) 15391.6 + 93428.1i 0.175671 + 1.06634i
\(297\) 35945.3i 0.407502i
\(298\) −88892.8 + 4842.81i −1.00100 + 0.0545337i
\(299\) 2537.35 + 2537.35i 0.0283816 + 0.0283816i
\(300\) 81296.2 101245.i 0.903292 1.12494i
\(301\) −85748.8 85748.8i −0.946444 0.946444i
\(302\) 124997. + 112081.i 1.37052 + 1.22891i
\(303\) 214552.i 2.33694i
\(304\) 50829.4 79704.5i 0.550007 0.862453i
\(305\) −3303.90 −0.0355162
\(306\) 22738.5 25358.8i 0.242839 0.270823i
\(307\) −20597.1 + 20597.1i −0.218539 + 0.218539i −0.807883 0.589344i \(-0.799386\pi\)
0.589344 + 0.807883i \(0.299386\pi\)
\(308\) 132147. 164574.i 1.39302 1.73484i
\(309\) −1656.67 + 1656.67i −0.0173508 + 0.0173508i
\(310\) −1079.56 19816.0i −0.0112337 0.206201i
\(311\) 82310.6 0.851011 0.425505 0.904956i \(-0.360096\pi\)
0.425505 + 0.904956i \(0.360096\pi\)
\(312\) −19096.7 + 26629.8i −0.196177 + 0.273564i
\(313\) 120415.i 1.22911i 0.788872 + 0.614557i \(0.210665\pi\)
−0.788872 + 0.614557i \(0.789335\pi\)
\(314\) 7611.70 + 139718.i 0.0772009 + 1.41707i
\(315\) −21137.4 21137.4i −0.213025 0.213025i
\(316\) −85756.0 + 9371.65i −0.858797 + 0.0938517i
\(317\) 14795.3 + 14795.3i 0.147233 + 0.147233i 0.776881 0.629648i \(-0.216801\pi\)
−0.629648 + 0.776881i \(0.716801\pi\)
\(318\) 36951.5 41209.7i 0.365408 0.407516i
\(319\) 66216.1i 0.650702i
\(320\) 14786.3 + 7304.61i 0.144397 + 0.0713340i
\(321\) −285639. −2.77209
\(322\) 21361.3 + 19154.1i 0.206023 + 0.184735i
\(323\) 22993.9 22993.9i 0.220398 0.220398i
\(324\) 8766.29 + 80216.6i 0.0835076 + 0.764142i
\(325\) −16534.9 + 16534.9i −0.156543 + 0.156543i
\(326\) −137991. + 7517.63i −1.29842 + 0.0707369i
\(327\) 44292.5 0.414224
\(328\) 47602.3 + 34136.4i 0.442467 + 0.317300i
\(329\) 132114.i 1.22056i
\(330\) −36831.5 + 2006.55i −0.338214 + 0.0184256i
\(331\) 82868.2 + 82868.2i 0.756366 + 0.756366i 0.975659 0.219293i \(-0.0703752\pi\)
−0.219293 + 0.975659i \(0.570375\pi\)
\(332\) −45062.8 36183.9i −0.408829 0.328276i
\(333\) 101158. + 101158.i 0.912247 + 0.912247i
\(334\) −155392. 139336.i −1.39295 1.24902i
\(335\) 8450.04i 0.0752955i
\(336\) −140882. + 220914.i −1.24789 + 1.95679i
\(337\) 78854.4 0.694331 0.347165 0.937804i \(-0.387144\pi\)
0.347165 + 0.937804i \(0.387144\pi\)
\(338\) −72328.8 + 80663.8i −0.633108 + 0.706066i
\(339\) 80368.0 80368.0i 0.699332 0.699332i
\(340\) 4423.56 + 3551.98i 0.0382661 + 0.0307264i
\(341\) 149697. 149697.i 1.28737 1.28737i
\(342\) −7769.49 142614.i −0.0664264 1.21930i
\(343\) −83925.2 −0.713352
\(344\) 99738.7 16431.2i 0.842843 0.138852i
\(345\) 5014.18i 0.0421271i
\(346\) −8098.15 148647.i −0.0676447 1.24166i
\(347\) −59543.0 59543.0i −0.494506 0.494506i 0.415216 0.909723i \(-0.363706\pi\)
−0.909723 + 0.415216i \(0.863706\pi\)
\(348\) −8929.91 81713.8i −0.0737375 0.674741i
\(349\) −756.172 756.172i −0.00620826 0.00620826i 0.703996 0.710204i \(-0.251397\pi\)
−0.710204 + 0.703996i \(0.751397\pi\)
\(350\) −124820. + 139203.i −1.01894 + 1.13635i
\(351\) 8036.11i 0.0652276i
\(352\) 47287.4 + 169459.i 0.381645 + 1.36766i
\(353\) 23723.5 0.190384 0.0951918 0.995459i \(-0.469654\pi\)
0.0951918 + 0.995459i \(0.469654\pi\)
\(354\) −67524.1 60546.9i −0.538830 0.483154i
\(355\) −15863.3 + 15863.3i −0.125874 + 0.125874i
\(356\) 174364. 19055.0i 1.37581 0.150352i
\(357\) −63731.2 + 63731.2i −0.500053 + 0.500053i
\(358\) −27201.8 + 1481.93i −0.212242 + 0.0115628i
\(359\) 146064. 1.13333 0.566663 0.823950i \(-0.308234\pi\)
0.566663 + 0.823950i \(0.308234\pi\)
\(360\) 24585.9 4050.35i 0.189706 0.0312527i
\(361\) 6038.12i 0.0463327i
\(362\) 135139. 7362.28i 1.03125 0.0561817i
\(363\) −140234. 140234.i −1.06424 1.06424i
\(364\) 29543.5 36792.9i 0.222976 0.277691i
\(365\) −18834.2 18834.2i −0.141371 0.141371i
\(366\) 32575.1 + 29209.1i 0.243177 + 0.218050i
\(367\) 151129.i 1.12206i −0.827797 0.561028i \(-0.810406\pi\)
0.827797 0.561028i \(-0.189594\pi\)
\(368\) −23351.3 + 5165.47i −0.172431 + 0.0381430i
\(369\) 88501.7 0.649978
\(370\) −15907.5 + 17740.7i −0.116198 + 0.129588i
\(371\) −56357.5 + 56357.5i −0.409453 + 0.409453i
\(372\) −164545. + 204922.i −1.18905 + 1.48082i
\(373\) 26207.7 26207.7i 0.188370 0.188370i −0.606621 0.794991i \(-0.707476\pi\)
0.794991 + 0.606621i \(0.207476\pi\)
\(374\) 3292.15 + 60429.5i 0.0235362 + 0.432022i
\(375\) 66221.0 0.470905
\(376\) −89492.2 64176.4i −0.633008 0.453941i
\(377\) 14803.6i 0.104156i
\(378\) 3495.32 + 64158.8i 0.0244626 + 0.449027i
\(379\) 110424. + 110424.i 0.768752 + 0.768752i 0.977887 0.209135i \(-0.0670647\pi\)
−0.209135 + 0.977887i \(0.567065\pi\)
\(380\) 23648.4 2584.36i 0.163770 0.0178973i
\(381\) 26810.1 + 26810.1i 0.184692 + 0.184692i
\(382\) 120379. 134251.i 0.824942 0.920006i
\(383\) 10514.9i 0.0716819i 0.999358 + 0.0358409i \(0.0114110\pi\)
−0.999358 + 0.0358409i \(0.988589\pi\)
\(384\) −81208.2 202743.i −0.550728 1.37494i
\(385\) 53114.1 0.358334
\(386\) −149757. 134282.i −1.00511 0.901249i
\(387\) 107991. 107991.i 0.721049 0.721049i
\(388\) 8192.37 + 74964.9i 0.0544185 + 0.497960i
\(389\) −166762. + 166762.i −1.10204 + 1.10204i −0.107877 + 0.994164i \(0.534405\pi\)
−0.994164 + 0.107877i \(0.965595\pi\)
\(390\) −8234.21 + 448.593i −0.0541368 + 0.00294933i
\(391\) −8226.78 −0.0538116
\(392\) 130317. 181724.i 0.848066 1.18260i
\(393\) 131772.i 0.853172i
\(394\) 144952. 7896.89i 0.933755 0.0508702i
\(395\) −15350.6 15350.6i −0.0983855 0.0983855i
\(396\) 207262. + 166425.i 1.32169 + 1.06127i
\(397\) −192542. 192542.i −1.22164 1.22164i −0.967048 0.254594i \(-0.918058\pi\)
−0.254594 0.967048i \(-0.581942\pi\)
\(398\) 132821. + 119096.i 0.838494 + 0.751853i
\(399\) 377941.i 2.37399i
\(400\) −33661.4 152171.i −0.210384 0.951070i
\(401\) 91157.6 0.566897 0.283448 0.958987i \(-0.408522\pi\)
0.283448 + 0.958987i \(0.408522\pi\)
\(402\) −74705.2 + 83314.0i −0.462273 + 0.515544i
\(403\) 33467.0 33467.0i 0.206066 0.206066i
\(404\) −200801. 161236.i −1.23027 0.987870i
\(405\) −14359.0 + 14359.0i −0.0875417 + 0.0875417i
\(406\) 6438.84 + 118189.i 0.0390621 + 0.717010i
\(407\) −254191. −1.53451
\(408\) −12212.2 74128.9i −0.0733624 0.445315i
\(409\) 107774.i 0.644272i −0.946693 0.322136i \(-0.895599\pi\)
0.946693 0.322136i \(-0.104401\pi\)
\(410\) 801.887 + 14719.1i 0.00477029 + 0.0875618i
\(411\) 34590.1 + 34590.1i 0.204771 + 0.204771i
\(412\) 305.497 + 2795.48i 0.00179975 + 0.0164688i
\(413\) 92344.5 + 92344.5i 0.541391 + 0.541391i
\(414\) −24122.4 + 26902.2i −0.140741 + 0.156959i
\(415\) 14543.4i 0.0844442i
\(416\) 10571.8 + 37885.0i 0.0610888 + 0.218918i
\(417\) −82972.9 −0.477160
\(418\) 188942. + 169419.i 1.08137 + 0.969637i
\(419\) −118524. + 118524.i −0.675115 + 0.675115i −0.958891 0.283776i \(-0.908413\pi\)
0.283776 + 0.958891i \(0.408413\pi\)
\(420\) −65545.3 + 7162.97i −0.371572 + 0.0406064i
\(421\) −226616. + 226616.i −1.27858 + 1.27858i −0.337113 + 0.941464i \(0.609451\pi\)
−0.941464 + 0.337113i \(0.890549\pi\)
\(422\) −145892. + 7948.08i −0.819231 + 0.0446310i
\(423\) −166383. −0.929882
\(424\) −10799.2 65552.2i −0.0600706 0.364633i
\(425\) 53610.7i 0.296807i
\(426\) 296650. 16161.2i 1.63465 0.0890544i
\(427\) −44549.0 44549.0i −0.244333 0.244333i
\(428\) −214658. + 267331.i −1.17182 + 1.45936i
\(429\) −62204.3 62204.3i −0.337991 0.337991i
\(430\) 18938.9 + 16982.0i 0.102428 + 0.0918442i
\(431\) 5397.51i 0.0290562i −0.999894 0.0145281i \(-0.995375\pi\)
0.999894 0.0145281i \(-0.00462460\pi\)
\(432\) −45158.1 28798.4i −0.241974 0.154312i
\(433\) 163835. 0.873840 0.436920 0.899500i \(-0.356069\pi\)
0.436920 + 0.899500i \(0.356069\pi\)
\(434\) 252638. 281751.i 1.34128 1.49584i
\(435\) 14627.0 14627.0i 0.0772997 0.0772997i
\(436\) 33285.9 41453.6i 0.175100 0.218067i
\(437\) −24393.4 + 24393.4i −0.127735 + 0.127735i
\(438\) 19187.9 + 352207.i 0.100018 + 1.83590i
\(439\) 158472. 0.822289 0.411144 0.911570i \(-0.365129\pi\)
0.411144 + 0.911570i \(0.365129\pi\)
\(440\) −25800.9 + 35978.7i −0.133269 + 0.185840i
\(441\) 337859.i 1.73723i
\(442\) 736.008 + 13509.9i 0.00376737 + 0.0691524i
\(443\) −137929. 137929.i −0.702826 0.702826i 0.262190 0.965016i \(-0.415555\pi\)
−0.965016 + 0.262190i \(0.915555\pi\)
\(444\) 313684. 34280.2i 1.59120 0.173891i
\(445\) 31211.8 + 31211.8i 0.157615 + 0.157615i
\(446\) 194003. 216359.i 0.975300 1.08769i
\(447\) 296680.i 1.48482i
\(448\) 100881. + 297869.i 0.502638 + 1.48412i
\(449\) 327336. 1.62368 0.811841 0.583879i \(-0.198466\pi\)
0.811841 + 0.583879i \(0.198466\pi\)
\(450\) −175311. 157196.i −0.865733 0.776278i
\(451\) −111194. + 111194.i −0.546672 + 0.546672i
\(452\) −14820.2 135613.i −0.0725400 0.663782i
\(453\) 395625. 395625.i 1.92791 1.92791i
\(454\) −106520. + 5803.13i −0.516797 + 0.0281547i
\(455\) 11874.4 0.0573575
\(456\) −256012. 183590.i −1.23120 0.882918i
\(457\) 154510.i 0.739817i 0.929068 + 0.369909i \(0.120611\pi\)
−0.929068 + 0.369909i \(0.879389\pi\)
\(458\) −235406. + 12824.7i −1.12224 + 0.0611388i
\(459\) −13027.6 13027.6i −0.0618358 0.0618358i
\(460\) −4692.80 3768.16i −0.0221777 0.0178079i
\(461\) 19296.3 + 19296.3i 0.0907971 + 0.0907971i 0.751046 0.660249i \(-0.229549\pi\)
−0.660249 + 0.751046i \(0.729549\pi\)
\(462\) −523683. 469571.i −2.45349 2.19997i
\(463\) 26503.6i 0.123635i 0.998087 + 0.0618176i \(0.0196897\pi\)
−0.998087 + 0.0618176i \(0.980310\pi\)
\(464\) −83187.2 53050.5i −0.386385 0.246407i
\(465\) −66135.7 −0.305865
\(466\) −7390.56 + 8242.22i −0.0340334 + 0.0379553i
\(467\) 111797. 111797.i 0.512622 0.512622i −0.402707 0.915329i \(-0.631931\pi\)
0.915329 + 0.402707i \(0.131931\pi\)
\(468\) 46336.5 + 37206.7i 0.211559 + 0.169875i
\(469\) 113939. 113939.i 0.517994 0.517994i
\(470\) −1507.54 27671.9i −0.00682455 0.125269i
\(471\) 466307. 2.10199
\(472\) −107411. + 17695.1i −0.482129 + 0.0794272i
\(473\) 271360.i 1.21290i
\(474\) 15638.9 + 287063.i 0.0696066 + 1.27767i
\(475\) −158962. 158962.i −0.704541 0.704541i
\(476\) 11752.3 + 107540.i 0.0518692 + 0.474633i
\(477\) −70975.8 70975.8i −0.311942 0.311942i
\(478\) −133470. + 148851.i −0.584155 + 0.651471i
\(479\) 225380.i 0.982301i −0.871075 0.491150i \(-0.836577\pi\)
0.871075 0.491150i \(-0.163423\pi\)
\(480\) 26987.5 47879.0i 0.117133 0.207808i
\(481\) −56828.1 −0.245625
\(482\) 131263. + 117700.i 0.564999 + 0.506618i
\(483\) 67610.1 67610.1i 0.289813 0.289813i
\(484\) −236631. + 25859.7i −1.01014 + 0.110391i
\(485\) −13419.0 + 13419.0i −0.0570473 + 0.0570473i
\(486\) 336205. 18316.2i 1.42342 0.0775466i
\(487\) 8483.58 0.0357702 0.0178851 0.999840i \(-0.494307\pi\)
0.0178851 + 0.999840i \(0.494307\pi\)
\(488\) 51817.2 8536.50i 0.217588 0.0358460i
\(489\) 460544.i 1.92599i
\(490\) 56190.9 3061.23i 0.234031 0.0127498i
\(491\) 69265.0 + 69265.0i 0.287310 + 0.287310i 0.836016 0.548706i \(-0.184879\pi\)
−0.548706 + 0.836016i \(0.684879\pi\)
\(492\) 122223. 152214.i 0.504919 0.628817i
\(493\) −23998.6 23998.6i −0.0987399 0.0987399i
\(494\) 42240.8 + 37876.1i 0.173092 + 0.155207i
\(495\) 66891.1i 0.272997i
\(496\) 68131.3 + 307997.i 0.276938 + 1.25194i
\(497\) −427794. −1.73190
\(498\) −128576. + 143392.i −0.518441 + 0.578185i
\(499\) 86869.4 86869.4i 0.348872 0.348872i −0.510817 0.859689i \(-0.670657\pi\)
0.859689 + 0.510817i \(0.170657\pi\)
\(500\) 49765.1 61976.6i 0.199061 0.247906i
\(501\) −491827. + 491827.i −1.95946 + 1.95946i
\(502\) 9781.39 + 179544.i 0.0388144 + 0.712463i
\(503\) 112271. 0.443745 0.221872 0.975076i \(-0.428783\pi\)
0.221872 + 0.975076i \(0.428783\pi\)
\(504\) 386125. + 276897.i 1.52008 + 1.09008i
\(505\) 64805.7i 0.254115i
\(506\) −3492.52 64107.4i −0.0136407 0.250384i
\(507\) 255306. + 255306.i 0.993220 + 0.993220i
\(508\) 45239.6 4943.91i 0.175304 0.0191577i
\(509\) −167589. 167589.i −0.646861 0.646861i 0.305372 0.952233i \(-0.401219\pi\)
−0.952233 + 0.305372i \(0.901219\pi\)
\(510\) 12621.6 14076.0i 0.0485258 0.0541177i
\(511\) 507912.i 1.94512i
\(512\) −250776. 76358.6i −0.956636 0.291285i
\(513\) −77256.9 −0.293564
\(514\) −211045. 189238.i −0.798820 0.716278i
\(515\) −500.399 + 500.399i −0.00188670 + 0.00188670i
\(516\) −36595.7 334871.i −0.137445 1.25770i
\(517\) 209044. 209044.i 0.782089 0.782089i
\(518\) −453705. + 24717.5i −1.69088 + 0.0921180i
\(519\) −496108. −1.84180
\(520\) −5768.18 + 8043.56i −0.0213320 + 0.0297469i
\(521\) 287463.i 1.05903i −0.848302 0.529513i \(-0.822375\pi\)
0.848302 0.529513i \(-0.177625\pi\)
\(522\) −148846. + 8108.99i −0.546254 + 0.0297595i
\(523\) −203069. 203069.i −0.742404 0.742404i 0.230636 0.973040i \(-0.425919\pi\)
−0.973040 + 0.230636i \(0.925919\pi\)
\(524\) −123326. 99026.4i −0.449149 0.360652i
\(525\) 440588. + 440588.i 1.59851 + 1.59851i
\(526\) 337386. + 302524.i 1.21943 + 1.09343i
\(527\) 108509.i 0.390701i
\(528\) 572467. 126634.i 2.05344 0.454237i
\(529\) −271114. −0.968813
\(530\) 11161.2 12447.4i 0.0397339 0.0443126i
\(531\) −116297. + 116297.i −0.412459 + 0.412459i
\(532\) 353717. + 284023.i 1.24978 + 1.00353i
\(533\) −24859.0 + 24859.0i −0.0875042 + 0.0875042i
\(534\) −31798.0 583673.i −0.111511 2.04685i
\(535\) −86277.6 −0.301433
\(536\) 21833.0 + 132528.i 0.0759946 + 0.461293i
\(537\) 90786.1i 0.314826i
\(538\) −21741.6 399080.i −0.0751150 1.37878i
\(539\) 424486. + 424486.i 1.46112 + 1.46112i
\(540\) −1464.22 13398.5i −0.00502134 0.0459481i
\(541\) 308972. + 308972.i 1.05566 + 1.05566i 0.998357 + 0.0573036i \(0.0182503\pi\)
0.0573036 + 0.998357i \(0.481750\pi\)
\(542\) 294222. 328127.i 1.00156 1.11698i
\(543\) 451027.i 1.52969i
\(544\) −78555.1 44278.5i −0.265446 0.149622i
\(545\) 13378.6 0.0450420
\(546\) −117077. 104980.i −0.392723 0.352143i
\(547\) −8623.13 + 8623.13i −0.0288198 + 0.0288198i −0.721370 0.692550i \(-0.756487\pi\)
0.692550 + 0.721370i \(0.256487\pi\)
\(548\) 58367.6 6378.57i 0.194362 0.0212404i
\(549\) 56104.4 56104.4i 0.186145 0.186145i
\(550\) 417763. 22759.4i 1.38103 0.0752376i
\(551\) −142317. −0.468765
\(552\) 12955.5 + 78640.6i 0.0425182 + 0.258089i
\(553\) 413968.i 1.35368i
\(554\) −195499. + 10650.6i −0.636980 + 0.0347022i
\(555\) 56150.4 + 56150.4i 0.182292 + 0.182292i
\(556\) −62354.2 + 77654.8i −0.201705 + 0.251199i
\(557\) −208785. 208785.i −0.672961 0.672961i 0.285437 0.958398i \(-0.407861\pi\)
−0.958398 + 0.285437i \(0.907861\pi\)
\(558\) 354833. + 318168.i 1.13961 + 1.02185i
\(559\) 60666.5i 0.194145i
\(560\) −42553.5 + 66727.2i −0.135694 + 0.212778i
\(561\) 201683. 0.640832
\(562\) −395161. + 440698.i −1.25113 + 1.39530i
\(563\) 127891. 127891.i 0.403480 0.403480i −0.475977 0.879458i \(-0.657906\pi\)
0.879458 + 0.475977i \(0.157906\pi\)
\(564\) −229778. + 286162.i −0.722356 + 0.899608i
\(565\) 24275.2 24275.2i 0.0760443 0.0760443i
\(566\) −12235.5 224590.i −0.0381935 0.701065i
\(567\) −387228. −1.20448
\(568\) 207807. 289781.i 0.644116 0.898201i
\(569\) 488561.i 1.50902i 0.656290 + 0.754509i \(0.272125\pi\)
−0.656290 + 0.754509i \(0.727875\pi\)
\(570\) −4312.65 79161.5i −0.0132738 0.243649i
\(571\) −17324.2 17324.2i −0.0531352 0.0531352i 0.680040 0.733175i \(-0.261962\pi\)
−0.733175 + 0.680040i \(0.761962\pi\)
\(572\) −104964. + 11470.7i −0.320810 + 0.0350590i
\(573\) −424913. 424913.i −1.29417 1.29417i
\(574\) −187657. + 209282.i −0.569562 + 0.635197i
\(575\) 56873.6i 0.172018i
\(576\) −375132. + 127049.i −1.13068 + 0.382935i
\(577\) −9362.93 −0.0281229 −0.0140615 0.999901i \(-0.504476\pi\)
−0.0140615 + 0.999901i \(0.504476\pi\)
\(578\) 225639. + 202324.i 0.675397 + 0.605609i
\(579\) −473990. + 473990.i −1.41388 + 1.41388i
\(580\) −2697.29 24681.8i −0.00801810 0.0733702i
\(581\) 196100. 196100.i 0.580932 0.580932i
\(582\) 250940. 13671.0i 0.740839 0.0403603i
\(583\) 178348. 0.524725
\(584\) 344052. + 246726.i 1.00878 + 0.723417i
\(585\) 14954.5i 0.0436978i
\(586\) 4004.26 218.149i 0.0116608 0.000635268i
\(587\) 46301.5 + 46301.5i 0.134375 + 0.134375i 0.771095 0.636720i \(-0.219709\pi\)
−0.636720 + 0.771095i \(0.719709\pi\)
\(588\) −581083. 466590.i −1.68067 1.34953i
\(589\) 321742. + 321742.i 0.927422 + 0.927422i
\(590\) −20395.7 18288.2i −0.0585916 0.0525373i
\(591\) 483778.i 1.38507i
\(592\) 203650. 319340.i 0.581088 0.911191i
\(593\) −194145. −0.552099 −0.276049 0.961143i \(-0.589025\pi\)
−0.276049 + 0.961143i \(0.589025\pi\)
\(594\) 95987.6 107049.i 0.272046 0.303395i
\(595\) −19250.1 + 19250.1i −0.0543749 + 0.0543749i
\(596\) 277664. + 222955.i 0.781676 + 0.627660i
\(597\) 420387. 420387.i 1.17951 1.17951i
\(598\) −780.804 14332.2i −0.00218343 0.0400783i
\(599\) 474516. 1.32250 0.661252 0.750164i \(-0.270025\pi\)
0.661252 + 0.750164i \(0.270025\pi\)
\(600\) −512470. + 84425.8i −1.42353 + 0.234516i
\(601\) 87515.3i 0.242290i −0.992635 0.121145i \(-0.961343\pi\)
0.992635 0.121145i \(-0.0386566\pi\)
\(602\) 26387.0 + 484350.i 0.0728110 + 1.33649i
\(603\) 143493. + 143493.i 0.394634 + 0.394634i
\(604\) −72955.0 667580.i −0.199977 1.82991i
\(605\) −42357.8 42357.8i −0.115724 0.115724i
\(606\) −572935. + 638958.i −1.56013 + 1.73991i
\(607\) 687260.i 1.86528i 0.360808 + 0.932640i \(0.382501\pi\)
−0.360808 + 0.932640i \(0.617499\pi\)
\(608\) −364216. + 101634.i −0.985263 + 0.274937i
\(609\) 394456. 1.06356
\(610\) 9839.34 + 8822.65i 0.0264427 + 0.0237104i
\(611\) 46734.8 46734.8i 0.125187 0.125187i
\(612\) −135435. + 14800.7i −0.361600 + 0.0395166i
\(613\) −220862. + 220862.i −0.587761 + 0.587761i −0.937025 0.349263i \(-0.886432\pi\)
0.349263 + 0.937025i \(0.386432\pi\)
\(614\) 116342. 6338.23i 0.308603 0.0168124i
\(615\) 49125.1 0.129883
\(616\) −833023. + 137234.i −2.19531 + 0.361661i
\(617\) 518967.i 1.36323i −0.731711 0.681615i \(-0.761278\pi\)
0.731711 0.681615i \(-0.238722\pi\)
\(618\) 9357.67 509.798i 0.0245014 0.00133482i
\(619\) −77555.3 77555.3i −0.202409 0.202409i 0.598622 0.801031i \(-0.295715\pi\)
−0.801031 + 0.598622i \(0.795715\pi\)
\(620\) −49701.1 + 61896.8i −0.129295 + 0.161022i
\(621\) 13820.5 + 13820.5i 0.0358378 + 0.0358378i
\(622\) −245129. 219800.i −0.633599 0.568130i
\(623\) 841705.i 2.16862i
\(624\) 127984. 28310.9i 0.328689 0.0727084i
\(625\) −360490. −0.922855
\(626\) 321554. 358609.i 0.820550 0.915107i
\(627\) 598015. 598015.i 1.52117 1.52117i
\(628\) 350430. 436419.i 0.888550 1.10658i
\(629\) 92126.1 92126.1i 0.232853 0.232853i
\(630\) 6504.48 + 119394.i 0.0163882 + 0.300816i
\(631\) 344653. 0.865612 0.432806 0.901487i \(-0.357523\pi\)
0.432806 + 0.901487i \(0.357523\pi\)
\(632\) 280416. + 201091.i 0.702051 + 0.503453i
\(633\) 486914.i 1.21519i
\(634\) −4552.88 83571.0i −0.0113268 0.207911i
\(635\) 8098.03 + 8098.03i 0.0200832 + 0.0200832i
\(636\) −220091. + 24052.1i −0.544111 + 0.0594619i
\(637\) 94900.2 + 94900.2i 0.233877 + 0.233877i
\(638\) 176822. 197198.i 0.434405 0.484464i
\(639\) 538758.i 1.31945i
\(640\) −24529.0 61238.8i −0.0598853 0.149509i
\(641\) −183353. −0.446243 −0.223122 0.974791i \(-0.571625\pi\)
−0.223122 + 0.974791i \(0.571625\pi\)
\(642\) 850662. + 762764.i 2.06389 + 1.85063i
\(643\) −541900. + 541900.i −1.31068 + 1.31068i −0.389768 + 0.920913i \(0.627445\pi\)
−0.920913 + 0.389768i \(0.872555\pi\)
\(644\) −12467.6 114086.i −0.0300615 0.275080i
\(645\) 59943.0 59943.0i 0.144085 0.144085i
\(646\) −129880. + 7075.78i −0.311228 + 0.0169555i
\(647\) −358562. −0.856555 −0.428278 0.903647i \(-0.640879\pi\)
−0.428278 + 0.903647i \(0.640879\pi\)
\(648\) 188102. 262302.i 0.447963 0.624672i
\(649\) 292233.i 0.693808i
\(650\) 93397.0 5088.19i 0.221058 0.0120431i
\(651\) −891760. 891760.i −2.10419 2.10419i
\(652\) 431026. + 346099.i 1.01393 + 0.814152i
\(653\) −73642.4 73642.4i −0.172704 0.172704i 0.615463 0.788166i \(-0.288969\pi\)
−0.788166 + 0.615463i \(0.788969\pi\)
\(654\) −131908. 118278.i −0.308400 0.276533i
\(655\) 39801.7i 0.0927725i
\(656\) −50607.3 228778.i −0.117600 0.531626i
\(657\) 639657. 1.48189
\(658\) 352795. 393449.i 0.814836 0.908735i
\(659\) 22081.7 22081.7i 0.0508467 0.0508467i −0.681226 0.732073i \(-0.738553\pi\)
0.732073 + 0.681226i \(0.238553\pi\)
\(660\) 115046. + 92378.2i 0.264109 + 0.212071i
\(661\) 20869.3 20869.3i 0.0477644 0.0477644i −0.682821 0.730586i \(-0.739247\pi\)
0.730586 + 0.682821i \(0.239247\pi\)
\(662\) −25500.6 468079.i −0.0581881 1.06808i
\(663\) 45089.3 0.102576
\(664\) 37576.8 + 228094.i 0.0852283 + 0.517342i
\(665\) 114157.i 0.258143i
\(666\) −31128.8 571390.i −0.0701802 1.28820i
\(667\) 25459.3 + 25459.3i 0.0572261 + 0.0572261i
\(668\) 90694.9 + 829911.i 0.203250 + 1.85985i
\(669\) −684791. 684791.i −1.53005 1.53005i
\(670\) −22564.8 + 25165.1i −0.0502669 + 0.0560594i
\(671\) 140979.i 0.313120i
\(672\) 1.00948e6 281696.i 2.23543 0.623794i
\(673\) 379771. 0.838479 0.419239 0.907876i \(-0.362297\pi\)
0.419239 + 0.907876i \(0.362297\pi\)
\(674\) −234837. 210571.i −0.516947 0.463531i
\(675\) −90063.0 + 90063.0i −0.197669 + 0.197669i
\(676\) 430805. 47079.6i 0.942731 0.103024i
\(677\) −156167. + 156167.i −0.340731 + 0.340731i −0.856642 0.515911i \(-0.827454\pi\)
0.515911 + 0.856642i \(0.327454\pi\)
\(678\) −453957. + 24731.2i −0.987541 + 0.0538004i
\(679\) −361877. −0.784912
\(680\) −3688.71 22390.7i −0.00797731 0.0484228i
\(681\) 355511.i 0.766581i
\(682\) −845560. + 46065.4i −1.81792 + 0.0990390i
\(683\) 164044. + 164044.i 0.351656 + 0.351656i 0.860725 0.509070i \(-0.170010\pi\)
−0.509070 + 0.860725i \(0.670010\pi\)
\(684\) −357695. + 445466.i −0.764540 + 0.952144i
\(685\) 10448.0 + 10448.0i 0.0222665 + 0.0222665i
\(686\) 249938. + 224112.i 0.531109 + 0.476230i
\(687\) 785666.i 1.66466i
\(688\) −340909. 217406.i −0.720215 0.459298i
\(689\) 39872.4 0.0839912
\(690\) −13389.7 + 14932.7i −0.0281238 + 0.0313647i
\(691\) −288207. + 288207.i −0.603599 + 0.603599i −0.941266 0.337667i \(-0.890362\pi\)
0.337667 + 0.941266i \(0.390362\pi\)
\(692\) −372825. + 464310.i −0.778562 + 0.969607i
\(693\) −901945. + 901945.i −1.87808 + 1.87808i
\(694\) 18322.8 + 336327.i 0.0380429 + 0.698302i
\(695\) −25062.1 −0.0518856
\(696\) −191613. + 267198.i −0.395554 + 0.551589i
\(697\) 80599.7i 0.165908i
\(698\) 232.693 + 4271.22i 0.000477608 + 0.00876681i
\(699\) 26087.2 + 26087.2i 0.0533916 + 0.0533916i
\(700\) 743451. 81246.4i 1.51725 0.165809i
\(701\) 323248. + 323248.i 0.657808 + 0.657808i 0.954861 0.297053i \(-0.0960038\pi\)
−0.297053 + 0.954861i \(0.596004\pi\)
\(702\) 21459.4 23932.3i 0.0435456 0.0485636i
\(703\) 546329.i 1.10546i
\(704\) 311692. 630941.i 0.628899 1.27304i
\(705\) −92355.0 −0.185816
\(706\) −70651.0 63350.7i −0.141745 0.127099i
\(707\) 873826. 873826.i 1.74818 1.74818i
\(708\) 39410.6 + 360629.i 0.0786224 + 0.719440i
\(709\) −580085. + 580085.i −1.15398 + 1.15398i −0.168235 + 0.985747i \(0.553807\pi\)
−0.985747 + 0.168235i \(0.946193\pi\)
\(710\) 89603.4 4881.52i 0.177749 0.00968364i
\(711\) 521346. 1.03130
\(712\) −570159. 408871.i −1.12470 0.806540i
\(713\) 115113.i 0.226436i
\(714\) 359984. 19611.7i 0.706134 0.0384696i
\(715\) −18788.9 18788.9i −0.0367526 0.0367526i
\(716\) 84967.2 + 68225.8i 0.165739 + 0.133083i
\(717\) 471123. + 471123.i 0.916423 + 0.916423i
\(718\) −434994. 390046.i −0.843789 0.756601i
\(719\) 332243.i 0.642684i −0.946963 0.321342i \(-0.895866\pi\)
0.946963 0.321342i \(-0.104134\pi\)
\(720\) −84035.3 53591.3i −0.162105 0.103378i
\(721\) −13494.5 −0.0259590
\(722\) −16124.1 + 17982.1i −0.0309314 + 0.0344959i
\(723\) 415456. 415456.i 0.794783 0.794783i
\(724\) −422118. 338947.i −0.805299 0.646628i
\(725\) −165908. + 165908.i −0.315639 + 0.315639i
\(726\) 43153.4 + 792107.i 0.0818732 + 1.50283i
\(727\) 362311. 0.685508 0.342754 0.939425i \(-0.388640\pi\)
0.342754 + 0.939425i \(0.388640\pi\)
\(728\) −186234. + 30680.8i −0.351396 + 0.0578900i
\(729\) 713570.i 1.34271i
\(730\) 5795.74 + 106384.i 0.0108758 + 0.199633i
\(731\) −98348.7 98348.7i −0.184049 0.184049i
\(732\) −19012.5 173975.i −0.0354828 0.324688i
\(733\) 377844. + 377844.i 0.703242 + 0.703242i 0.965105 0.261863i \(-0.0843369\pi\)
−0.261863 + 0.965105i \(0.584337\pi\)
\(734\) −403570. + 450076.i −0.749078 + 0.835399i
\(735\) 187537.i 0.347146i
\(736\) 83336.2 + 46973.4i 0.153843 + 0.0867155i
\(737\) −360569. −0.663825
\(738\) −263567. 236333.i −0.483925 0.433922i
\(739\) 467502. 467502.i 0.856042 0.856042i −0.134828 0.990869i \(-0.543048\pi\)
0.990869 + 0.134828i \(0.0430480\pi\)
\(740\) 94748.5 10354.4i 0.173025 0.0189086i
\(741\) 133695. 133695.i 0.243489 0.243489i
\(742\) 318334. 17342.6i 0.578196 0.0314997i
\(743\) −555820. −1.00683 −0.503415 0.864045i \(-0.667923\pi\)
−0.503415 + 0.864045i \(0.667923\pi\)
\(744\) 1.03725e6 170879.i 1.87386 0.308705i
\(745\) 89612.4i 0.161456i
\(746\) −148034. + 8064.75i −0.266001 + 0.0144915i
\(747\) 246966. + 246966.i 0.442584 + 0.442584i
\(748\) 151565. 188756.i 0.270892 0.337364i
\(749\) −1.16335e6 1.16335e6i −2.07370 2.07370i
\(750\) −197213. 176835.i −0.350601 0.314373i
\(751\) 308308.i 0.546644i 0.961923 + 0.273322i \(0.0881224\pi\)
−0.961923 + 0.273322i \(0.911878\pi\)
\(752\) 95141.6 + 430102.i 0.168242 + 0.760563i
\(753\) 599226. 1.05682
\(754\) 39531.1 44086.5i 0.0695339 0.0775467i
\(755\) 119499. 119499.i 0.209638 0.209638i
\(756\) 160919. 200405.i 0.281555 0.350643i
\(757\) 34980.2 34980.2i 0.0610423 0.0610423i −0.675927 0.736969i \(-0.736256\pi\)
0.736969 + 0.675927i \(0.236256\pi\)
\(758\) −33980.3 623729.i −0.0591410 1.08557i
\(759\) −213958. −0.371403
\(760\) −77328.6 55453.7i −0.133879 0.0960070i
\(761\) 545745.i 0.942368i −0.882035 0.471184i \(-0.843827\pi\)
0.882035 0.471184i \(-0.156173\pi\)
\(762\) −8250.14 151437.i −0.0142086 0.260808i
\(763\) 180394. + 180394.i 0.309866 + 0.309866i
\(764\) −717001. + 78355.8i −1.22838 + 0.134241i
\(765\) −24243.3 24243.3i −0.0414256 0.0414256i
\(766\) 28078.9 31314.6i 0.0478544 0.0533690i
\(767\) 65332.9i 0.111056i
\(768\) −299555. + 820646.i −0.507871 + 1.39134i
\(769\) 510362. 0.863030 0.431515 0.902106i \(-0.357979\pi\)
0.431515 + 0.902106i \(0.357979\pi\)
\(770\) −158179. 141835.i −0.266789 0.239222i
\(771\) −667972.