Properties

Label 18.4.c.a.13.1
Level $18$
Weight $4$
Character 18.13
Analytic conductor $1.062$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 18.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.06203438010\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 13.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 18.13
Dual form 18.4.c.a.7.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} -5.19615i q^{3} +(-2.00000 + 3.46410i) q^{4} +(4.50000 - 7.79423i) q^{5} +(-9.00000 + 5.19615i) q^{6} +(15.5000 + 26.8468i) q^{7} +8.00000 q^{8} -27.0000 q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} -5.19615i q^{3} +(-2.00000 + 3.46410i) q^{4} +(4.50000 - 7.79423i) q^{5} +(-9.00000 + 5.19615i) q^{6} +(15.5000 + 26.8468i) q^{7} +8.00000 q^{8} -27.0000 q^{9} -18.0000 q^{10} +(7.50000 + 12.9904i) q^{11} +(18.0000 + 10.3923i) q^{12} +(18.5000 - 32.0429i) q^{13} +(31.0000 - 53.6936i) q^{14} +(-40.5000 - 23.3827i) q^{15} +(-8.00000 - 13.8564i) q^{16} -42.0000 q^{17} +(27.0000 + 46.7654i) q^{18} -28.0000 q^{19} +(18.0000 + 31.1769i) q^{20} +(139.500 - 80.5404i) q^{21} +(15.0000 - 25.9808i) q^{22} +(-97.5000 + 168.875i) q^{23} -41.5692i q^{24} +(22.0000 + 38.1051i) q^{25} -74.0000 q^{26} +140.296i q^{27} -124.000 q^{28} +(-55.5000 - 96.1288i) q^{29} +93.5307i q^{30} +(102.500 - 177.535i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(67.5000 - 38.9711i) q^{33} +(42.0000 + 72.7461i) q^{34} +279.000 q^{35} +(54.0000 - 93.5307i) q^{36} -166.000 q^{37} +(28.0000 + 48.4974i) q^{38} +(-166.500 - 96.1288i) q^{39} +(36.0000 - 62.3538i) q^{40} +(130.500 - 226.033i) q^{41} +(-279.000 - 161.081i) q^{42} +(21.5000 + 37.2391i) q^{43} -60.0000 q^{44} +(-121.500 + 210.444i) q^{45} +390.000 q^{46} +(-88.5000 - 153.286i) q^{47} +(-72.0000 + 41.5692i) q^{48} +(-309.000 + 535.204i) q^{49} +(44.0000 - 76.2102i) q^{50} +218.238i q^{51} +(74.0000 + 128.172i) q^{52} +114.000 q^{53} +(243.000 - 140.296i) q^{54} +135.000 q^{55} +(124.000 + 214.774i) q^{56} +145.492i q^{57} +(-111.000 + 192.258i) q^{58} +(-79.5000 + 137.698i) q^{59} +(162.000 - 93.5307i) q^{60} +(-95.5000 - 165.411i) q^{61} -410.000 q^{62} +(-418.500 - 724.863i) q^{63} +64.0000 q^{64} +(-166.500 - 288.386i) q^{65} +(-135.000 - 77.9423i) q^{66} +(210.500 - 364.597i) q^{67} +(84.0000 - 145.492i) q^{68} +(877.500 + 506.625i) q^{69} +(-279.000 - 483.242i) q^{70} +156.000 q^{71} -216.000 q^{72} +182.000 q^{73} +(166.000 + 287.520i) q^{74} +(198.000 - 114.315i) q^{75} +(56.0000 - 96.9948i) q^{76} +(-232.500 + 402.702i) q^{77} +384.515i q^{78} +(-566.500 - 981.207i) q^{79} -144.000 q^{80} +729.000 q^{81} -522.000 q^{82} +(541.500 + 937.906i) q^{83} +644.323i q^{84} +(-189.000 + 327.358i) q^{85} +(43.0000 - 74.4782i) q^{86} +(-499.500 + 288.386i) q^{87} +(60.0000 + 103.923i) q^{88} -1050.00 q^{89} +486.000 q^{90} +1147.00 q^{91} +(-390.000 - 675.500i) q^{92} +(-922.500 - 532.606i) q^{93} +(-177.000 + 306.573i) q^{94} +(-126.000 + 218.238i) q^{95} +(144.000 + 83.1384i) q^{96} +(450.500 + 780.289i) q^{97} +1236.00 q^{98} +(-202.500 - 350.740i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - 4 q^{4} + 9 q^{5} - 18 q^{6} + 31 q^{7} + 16 q^{8} - 54 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} - 4 q^{4} + 9 q^{5} - 18 q^{6} + 31 q^{7} + 16 q^{8} - 54 q^{9} - 36 q^{10} + 15 q^{11} + 36 q^{12} + 37 q^{13} + 62 q^{14} - 81 q^{15} - 16 q^{16} - 84 q^{17} + 54 q^{18} - 56 q^{19} + 36 q^{20} + 279 q^{21} + 30 q^{22} - 195 q^{23} + 44 q^{25} - 148 q^{26} - 248 q^{28} - 111 q^{29} + 205 q^{31} - 32 q^{32} + 135 q^{33} + 84 q^{34} + 558 q^{35} + 108 q^{36} - 332 q^{37} + 56 q^{38} - 333 q^{39} + 72 q^{40} + 261 q^{41} - 558 q^{42} + 43 q^{43} - 120 q^{44} - 243 q^{45} + 780 q^{46} - 177 q^{47} - 144 q^{48} - 618 q^{49} + 88 q^{50} + 148 q^{52} + 228 q^{53} + 486 q^{54} + 270 q^{55} + 248 q^{56} - 222 q^{58} - 159 q^{59} + 324 q^{60} - 191 q^{61} - 820 q^{62} - 837 q^{63} + 128 q^{64} - 333 q^{65} - 270 q^{66} + 421 q^{67} + 168 q^{68} + 1755 q^{69} - 558 q^{70} + 312 q^{71} - 432 q^{72} + 364 q^{73} + 332 q^{74} + 396 q^{75} + 112 q^{76} - 465 q^{77} - 1133 q^{79} - 288 q^{80} + 1458 q^{81} - 1044 q^{82} + 1083 q^{83} - 378 q^{85} + 86 q^{86} - 999 q^{87} + 120 q^{88} - 2100 q^{89} + 972 q^{90} + 2294 q^{91} - 780 q^{92} - 1845 q^{93} - 354 q^{94} - 252 q^{95} + 288 q^{96} + 901 q^{97} + 2472 q^{98} - 405 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/18\mathbb{Z}\right)^\times\).

\(n\) \(11\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.73205i −0.353553 0.612372i
\(3\) 5.19615i 1.00000i
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) 4.50000 7.79423i 0.402492 0.697137i −0.591534 0.806280i \(-0.701477\pi\)
0.994026 + 0.109143i \(0.0348107\pi\)
\(6\) −9.00000 + 5.19615i −0.612372 + 0.353553i
\(7\) 15.5000 + 26.8468i 0.836921 + 1.44959i 0.892456 + 0.451134i \(0.148980\pi\)
−0.0555351 + 0.998457i \(0.517686\pi\)
\(8\) 8.00000 0.353553
\(9\) −27.0000 −1.00000
\(10\) −18.0000 −0.569210
\(11\) 7.50000 + 12.9904i 0.205576 + 0.356068i 0.950316 0.311287i \(-0.100760\pi\)
−0.744740 + 0.667355i \(0.767427\pi\)
\(12\) 18.0000 + 10.3923i 0.433013 + 0.250000i
\(13\) 18.5000 32.0429i 0.394691 0.683624i −0.598371 0.801219i \(-0.704185\pi\)
0.993062 + 0.117595i \(0.0375185\pi\)
\(14\) 31.0000 53.6936i 0.591793 1.02502i
\(15\) −40.5000 23.3827i −0.697137 0.402492i
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −42.0000 −0.599206 −0.299603 0.954064i \(-0.596854\pi\)
−0.299603 + 0.954064i \(0.596854\pi\)
\(18\) 27.0000 + 46.7654i 0.353553 + 0.612372i
\(19\) −28.0000 −0.338086 −0.169043 0.985609i \(-0.554068\pi\)
−0.169043 + 0.985609i \(0.554068\pi\)
\(20\) 18.0000 + 31.1769i 0.201246 + 0.348569i
\(21\) 139.500 80.5404i 1.44959 0.836921i
\(22\) 15.0000 25.9808i 0.145364 0.251778i
\(23\) −97.5000 + 168.875i −0.883920 + 1.53099i −0.0369731 + 0.999316i \(0.511772\pi\)
−0.846947 + 0.531678i \(0.821562\pi\)
\(24\) 41.5692i 0.353553i
\(25\) 22.0000 + 38.1051i 0.176000 + 0.304841i
\(26\) −74.0000 −0.558177
\(27\) 140.296i 1.00000i
\(28\) −124.000 −0.836921
\(29\) −55.5000 96.1288i −0.355382 0.615540i 0.631801 0.775131i \(-0.282316\pi\)
−0.987183 + 0.159590i \(0.948983\pi\)
\(30\) 93.5307i 0.569210i
\(31\) 102.500 177.535i 0.593856 1.02859i −0.399851 0.916580i \(-0.630938\pi\)
0.993707 0.112009i \(-0.0357285\pi\)
\(32\) −16.0000 + 27.7128i −0.0883883 + 0.153093i
\(33\) 67.5000 38.9711i 0.356068 0.205576i
\(34\) 42.0000 + 72.7461i 0.211851 + 0.366937i
\(35\) 279.000 1.34742
\(36\) 54.0000 93.5307i 0.250000 0.433013i
\(37\) −166.000 −0.737574 −0.368787 0.929514i \(-0.620227\pi\)
−0.368787 + 0.929514i \(0.620227\pi\)
\(38\) 28.0000 + 48.4974i 0.119532 + 0.207035i
\(39\) −166.500 96.1288i −0.683624 0.394691i
\(40\) 36.0000 62.3538i 0.142302 0.246475i
\(41\) 130.500 226.033i 0.497090 0.860985i −0.502905 0.864342i \(-0.667735\pi\)
0.999994 + 0.00335732i \(0.00106867\pi\)
\(42\) −279.000 161.081i −1.02502 0.591793i
\(43\) 21.5000 + 37.2391i 0.0762493 + 0.132068i 0.901629 0.432511i \(-0.142372\pi\)
−0.825380 + 0.564578i \(0.809039\pi\)
\(44\) −60.0000 −0.205576
\(45\) −121.500 + 210.444i −0.402492 + 0.697137i
\(46\) 390.000 1.25005
\(47\) −88.5000 153.286i −0.274661 0.475726i 0.695389 0.718634i \(-0.255232\pi\)
−0.970049 + 0.242907i \(0.921899\pi\)
\(48\) −72.0000 + 41.5692i −0.216506 + 0.125000i
\(49\) −309.000 + 535.204i −0.900875 + 1.56036i
\(50\) 44.0000 76.2102i 0.124451 0.215555i
\(51\) 218.238i 0.599206i
\(52\) 74.0000 + 128.172i 0.197345 + 0.341812i
\(53\) 114.000 0.295455 0.147727 0.989028i \(-0.452804\pi\)
0.147727 + 0.989028i \(0.452804\pi\)
\(54\) 243.000 140.296i 0.612372 0.353553i
\(55\) 135.000 0.330971
\(56\) 124.000 + 214.774i 0.295896 + 0.512508i
\(57\) 145.492i 0.338086i
\(58\) −111.000 + 192.258i −0.251293 + 0.435253i
\(59\) −79.5000 + 137.698i −0.175424 + 0.303843i −0.940308 0.340325i \(-0.889463\pi\)
0.764884 + 0.644168i \(0.222796\pi\)
\(60\) 162.000 93.5307i 0.348569 0.201246i
\(61\) −95.5000 165.411i −0.200451 0.347192i 0.748223 0.663448i \(-0.230907\pi\)
−0.948674 + 0.316256i \(0.897574\pi\)
\(62\) −410.000 −0.839840
\(63\) −418.500 724.863i −0.836921 1.44959i
\(64\) 64.0000 0.125000
\(65\) −166.500 288.386i −0.317720 0.550307i
\(66\) −135.000 77.9423i −0.251778 0.145364i
\(67\) 210.500 364.597i 0.383831 0.664815i −0.607775 0.794109i \(-0.707938\pi\)
0.991606 + 0.129294i \(0.0412712\pi\)
\(68\) 84.0000 145.492i 0.149801 0.259464i
\(69\) 877.500 + 506.625i 1.53099 + 0.883920i
\(70\) −279.000 483.242i −0.476384 0.825121i
\(71\) 156.000 0.260758 0.130379 0.991464i \(-0.458381\pi\)
0.130379 + 0.991464i \(0.458381\pi\)
\(72\) −216.000 −0.353553
\(73\) 182.000 0.291801 0.145901 0.989299i \(-0.453392\pi\)
0.145901 + 0.989299i \(0.453392\pi\)
\(74\) 166.000 + 287.520i 0.260772 + 0.451670i
\(75\) 198.000 114.315i 0.304841 0.176000i
\(76\) 56.0000 96.9948i 0.0845216 0.146396i
\(77\) −232.500 + 402.702i −0.344102 + 0.596002i
\(78\) 384.515i 0.558177i
\(79\) −566.500 981.207i −0.806788 1.39740i −0.915078 0.403278i \(-0.867871\pi\)
0.108290 0.994119i \(-0.465463\pi\)
\(80\) −144.000 −0.201246
\(81\) 729.000 1.00000
\(82\) −522.000 −0.702991
\(83\) 541.500 + 937.906i 0.716113 + 1.24034i 0.962529 + 0.271179i \(0.0874136\pi\)
−0.246416 + 0.969164i \(0.579253\pi\)
\(84\) 644.323i 0.836921i
\(85\) −189.000 + 327.358i −0.241176 + 0.417728i
\(86\) 43.0000 74.4782i 0.0539164 0.0933859i
\(87\) −499.500 + 288.386i −0.615540 + 0.355382i
\(88\) 60.0000 + 103.923i 0.0726821 + 0.125889i
\(89\) −1050.00 −1.25056 −0.625280 0.780401i \(-0.715015\pi\)
−0.625280 + 0.780401i \(0.715015\pi\)
\(90\) 486.000 0.569210
\(91\) 1147.00 1.32130
\(92\) −390.000 675.500i −0.441960 0.765497i
\(93\) −922.500 532.606i −1.02859 0.593856i
\(94\) −177.000 + 306.573i −0.194214 + 0.336389i
\(95\) −126.000 + 218.238i −0.136077 + 0.235693i
\(96\) 144.000 + 83.1384i 0.153093 + 0.0883883i
\(97\) 450.500 + 780.289i 0.471560 + 0.816766i 0.999471 0.0325338i \(-0.0103576\pi\)
−0.527910 + 0.849300i \(0.677024\pi\)
\(98\) 1236.00 1.27403
\(99\) −202.500 350.740i −0.205576 0.356068i
\(100\) −176.000 −0.176000
\(101\) −193.500 335.152i −0.190633 0.330187i 0.754827 0.655924i \(-0.227721\pi\)
−0.945460 + 0.325737i \(0.894387\pi\)
\(102\) 378.000 218.238i 0.366937 0.211851i
\(103\) −275.500 + 477.180i −0.263552 + 0.456485i −0.967183 0.254080i \(-0.918227\pi\)
0.703631 + 0.710565i \(0.251561\pi\)
\(104\) 148.000 256.344i 0.139544 0.241698i
\(105\) 1449.73i 1.34742i
\(106\) −114.000 197.454i −0.104459 0.180928i
\(107\) −12.0000 −0.0108419 −0.00542095 0.999985i \(-0.501726\pi\)
−0.00542095 + 0.999985i \(0.501726\pi\)
\(108\) −486.000 280.592i −0.433013 0.250000i
\(109\) −502.000 −0.441127 −0.220564 0.975373i \(-0.570790\pi\)
−0.220564 + 0.975373i \(0.570790\pi\)
\(110\) −135.000 233.827i −0.117016 0.202677i
\(111\) 862.561i 0.737574i
\(112\) 248.000 429.549i 0.209230 0.362398i
\(113\) 700.500 1213.30i 0.583164 1.01007i −0.411938 0.911212i \(-0.635148\pi\)
0.995102 0.0988572i \(-0.0315187\pi\)
\(114\) 252.000 145.492i 0.207035 0.119532i
\(115\) 877.500 + 1519.87i 0.711542 + 1.23243i
\(116\) 444.000 0.355382
\(117\) −499.500 + 865.159i −0.394691 + 0.683624i
\(118\) 318.000 0.248087
\(119\) −651.000 1127.57i −0.501488 0.868603i
\(120\) −324.000 187.061i −0.246475 0.142302i
\(121\) 553.000 957.824i 0.415477 0.719627i
\(122\) −191.000 + 330.822i −0.141740 + 0.245502i
\(123\) −1174.50 678.098i −0.860985 0.497090i
\(124\) 410.000 + 710.141i 0.296928 + 0.514295i
\(125\) 1521.00 1.08834
\(126\) −837.000 + 1449.73i −0.591793 + 1.02502i
\(127\) −880.000 −0.614861 −0.307431 0.951571i \(-0.599469\pi\)
−0.307431 + 0.951571i \(0.599469\pi\)
\(128\) −64.0000 110.851i −0.0441942 0.0765466i
\(129\) 193.500 111.717i 0.132068 0.0762493i
\(130\) −333.000 + 576.773i −0.224662 + 0.389126i
\(131\) −751.500 + 1301.64i −0.501213 + 0.868126i 0.498786 + 0.866725i \(0.333779\pi\)
−0.999999 + 0.00140084i \(0.999554\pi\)
\(132\) 311.769i 0.205576i
\(133\) −434.000 751.710i −0.282952 0.490087i
\(134\) −842.000 −0.542819
\(135\) 1093.50 + 631.333i 0.697137 + 0.402492i
\(136\) −336.000 −0.211851
\(137\) 1330.50 + 2304.49i 0.829725 + 1.43713i 0.898254 + 0.439476i \(0.144836\pi\)
−0.0685295 + 0.997649i \(0.521831\pi\)
\(138\) 2026.50i 1.25005i
\(139\) 60.5000 104.789i 0.0369176 0.0639431i −0.846976 0.531631i \(-0.821579\pi\)
0.883894 + 0.467688i \(0.154913\pi\)
\(140\) −558.000 + 966.484i −0.336854 + 0.583449i
\(141\) −796.500 + 459.859i −0.475726 + 0.274661i
\(142\) −156.000 270.200i −0.0921918 0.159681i
\(143\) 555.000 0.324555
\(144\) 216.000 + 374.123i 0.125000 + 0.216506i
\(145\) −999.000 −0.572155
\(146\) −182.000 315.233i −0.103167 0.178691i
\(147\) 2781.00 + 1605.61i 1.56036 + 0.900875i
\(148\) 332.000 575.041i 0.184393 0.319379i
\(149\) 1414.50 2449.99i 0.777721 1.34705i −0.155532 0.987831i \(-0.549709\pi\)
0.933253 0.359221i \(-0.116957\pi\)
\(150\) −396.000 228.631i −0.215555 0.124451i
\(151\) −230.500 399.238i −0.124224 0.215162i 0.797205 0.603708i \(-0.206311\pi\)
−0.921429 + 0.388546i \(0.872977\pi\)
\(152\) −224.000 −0.119532
\(153\) 1134.00 0.599206
\(154\) 930.000 0.486633
\(155\) −922.500 1597.82i −0.478045 0.827998i
\(156\) 666.000 384.515i 0.341812 0.197345i
\(157\) 1488.50 2578.16i 0.756658 1.31057i −0.187889 0.982190i \(-0.560164\pi\)
0.944546 0.328379i \(-0.106502\pi\)
\(158\) −1133.00 + 1962.41i −0.570485 + 0.988109i
\(159\) 592.361i 0.295455i
\(160\) 144.000 + 249.415i 0.0711512 + 0.123238i
\(161\) −6045.00 −2.95909
\(162\) −729.000 1262.67i −0.353553 0.612372i
\(163\) −3316.00 −1.59343 −0.796715 0.604355i \(-0.793431\pi\)
−0.796715 + 0.604355i \(0.793431\pi\)
\(164\) 522.000 + 904.131i 0.248545 + 0.430492i
\(165\) 701.481i 0.330971i
\(166\) 1083.00 1875.81i 0.506368 0.877055i
\(167\) 340.500 589.763i 0.157777 0.273277i −0.776290 0.630376i \(-0.782901\pi\)
0.934067 + 0.357099i \(0.116234\pi\)
\(168\) 1116.00 644.323i 0.512508 0.295896i
\(169\) 414.000 + 717.069i 0.188439 + 0.326386i
\(170\) 756.000 0.341074
\(171\) 756.000 0.338086
\(172\) −172.000 −0.0762493
\(173\) 1990.50 + 3447.65i 0.874768 + 1.51514i 0.857009 + 0.515301i \(0.172320\pi\)
0.0177589 + 0.999842i \(0.494347\pi\)
\(174\) 999.000 + 576.773i 0.435253 + 0.251293i
\(175\) −682.000 + 1181.26i −0.294596 + 0.510256i
\(176\) 120.000 207.846i 0.0513940 0.0890170i
\(177\) 715.500 + 413.094i 0.303843 + 0.175424i
\(178\) 1050.00 + 1818.65i 0.442139 + 0.765808i
\(179\) 2004.00 0.836793 0.418397 0.908264i \(-0.362592\pi\)
0.418397 + 0.908264i \(0.362592\pi\)
\(180\) −486.000 841.777i −0.201246 0.348569i
\(181\) 1274.00 0.523181 0.261590 0.965179i \(-0.415753\pi\)
0.261590 + 0.965179i \(0.415753\pi\)
\(182\) −1147.00 1986.66i −0.467150 0.809128i
\(183\) −859.500 + 496.233i −0.347192 + 0.200451i
\(184\) −780.000 + 1351.00i −0.312513 + 0.541288i
\(185\) −747.000 + 1293.84i −0.296868 + 0.514190i
\(186\) 2130.42i 0.839840i
\(187\) −315.000 545.596i −0.123182 0.213358i
\(188\) 708.000 0.274661
\(189\) −3766.50 + 2174.59i −1.44959 + 0.836921i
\(190\) 504.000 0.192442
\(191\) −580.500 1005.46i −0.219914 0.380902i 0.734868 0.678210i \(-0.237244\pi\)
−0.954781 + 0.297309i \(0.903911\pi\)
\(192\) 332.554i 0.125000i
\(193\) −1805.50 + 3127.22i −0.673382 + 1.16633i 0.303557 + 0.952813i \(0.401826\pi\)
−0.976939 + 0.213519i \(0.931508\pi\)
\(194\) 901.000 1560.58i 0.333443 0.577541i
\(195\) −1498.50 + 865.159i −0.550307 + 0.317720i
\(196\) −1236.00 2140.81i −0.450437 0.780180i
\(197\) 2046.00 0.739957 0.369978 0.929040i \(-0.379365\pi\)
0.369978 + 0.929040i \(0.379365\pi\)
\(198\) −405.000 + 701.481i −0.145364 + 0.251778i
\(199\) 2996.00 1.06724 0.533620 0.845724i \(-0.320831\pi\)
0.533620 + 0.845724i \(0.320831\pi\)
\(200\) 176.000 + 304.841i 0.0622254 + 0.107778i
\(201\) −1894.50 1093.79i −0.664815 0.383831i
\(202\) −387.000 + 670.304i −0.134798 + 0.233477i
\(203\) 1720.50 2979.99i 0.594854 1.03032i
\(204\) −756.000 436.477i −0.259464 0.149801i
\(205\) −1174.50 2034.29i −0.400149 0.693079i
\(206\) 1102.00 0.372718
\(207\) 2632.50 4559.62i 0.883920 1.53099i
\(208\) −592.000 −0.197345
\(209\) −210.000 363.731i −0.0695024 0.120382i
\(210\) −2511.00 + 1449.73i −0.825121 + 0.476384i
\(211\) −377.500 + 653.849i −0.123167 + 0.213331i −0.921015 0.389528i \(-0.872638\pi\)
0.797848 + 0.602858i \(0.205972\pi\)
\(212\) −228.000 + 394.908i −0.0738637 + 0.127936i
\(213\) 810.600i 0.260758i
\(214\) 12.0000 + 20.7846i 0.00383319 + 0.00663928i
\(215\) 387.000 0.122759
\(216\) 1122.37i 0.353553i
\(217\) 6355.00 1.98804
\(218\) 502.000 + 869.490i 0.155962 + 0.270134i
\(219\) 945.700i 0.291801i
\(220\) −270.000 + 467.654i −0.0827427 + 0.143315i
\(221\) −777.000 + 1345.80i −0.236501 + 0.409631i
\(222\) 1494.00 862.561i 0.451670 0.260772i
\(223\) 1731.50 + 2999.05i 0.519954 + 0.900587i 0.999731 + 0.0231966i \(0.00738438\pi\)
−0.479777 + 0.877391i \(0.659282\pi\)
\(224\) −992.000 −0.295896
\(225\) −594.000 1028.84i −0.176000 0.304841i
\(226\) −2802.00 −0.824718
\(227\) −3112.50 5391.01i −0.910061 1.57627i −0.813976 0.580899i \(-0.802701\pi\)
−0.0960856 0.995373i \(-0.530632\pi\)
\(228\) −504.000 290.985i −0.146396 0.0845216i
\(229\) 732.500 1268.73i 0.211375 0.366113i −0.740770 0.671759i \(-0.765539\pi\)
0.952145 + 0.305646i \(0.0988724\pi\)
\(230\) 1755.00 3039.75i 0.503136 0.871457i
\(231\) 2092.50 + 1208.11i 0.596002 + 0.344102i
\(232\) −444.000 769.031i −0.125647 0.217626i
\(233\) 2634.00 0.740597 0.370298 0.928913i \(-0.379255\pi\)
0.370298 + 0.928913i \(0.379255\pi\)
\(234\) 1998.00 0.558177
\(235\) −1593.00 −0.442195
\(236\) −318.000 550.792i −0.0877120 0.151922i
\(237\) −5098.50 + 2943.62i −1.39740 + 0.806788i
\(238\) −1302.00 + 2255.13i −0.354606 + 0.614195i
\(239\) −3457.50 + 5988.57i −0.935762 + 1.62079i −0.162492 + 0.986710i \(0.551953\pi\)
−0.773270 + 0.634077i \(0.781380\pi\)
\(240\) 748.246i 0.201246i
\(241\) 744.500 + 1289.51i 0.198994 + 0.344667i 0.948202 0.317667i \(-0.102899\pi\)
−0.749209 + 0.662334i \(0.769566\pi\)
\(242\) −2212.00 −0.587573
\(243\) 3788.00i 1.00000i
\(244\) 764.000 0.200451
\(245\) 2781.00 + 4816.83i 0.725190 + 1.25607i
\(246\) 2712.39i 0.702991i
\(247\) −518.000 + 897.202i −0.133439 + 0.231124i
\(248\) 820.000 1420.28i 0.209960 0.363661i
\(249\) 4873.50 2813.72i 1.24034 0.716113i
\(250\) −1521.00 2634.45i −0.384786 0.666469i
\(251\) −4620.00 −1.16180 −0.580900 0.813975i \(-0.697299\pi\)
−0.580900 + 0.813975i \(0.697299\pi\)
\(252\) 3348.00 0.836921
\(253\) −2925.00 −0.726850
\(254\) 880.000 + 1524.20i 0.217386 + 0.376524i
\(255\) 1701.00 + 982.073i 0.417728 + 0.241176i
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −1675.50 + 2902.05i −0.406672 + 0.704377i −0.994515 0.104598i \(-0.966644\pi\)
0.587842 + 0.808976i \(0.299978\pi\)
\(258\) −387.000 223.435i −0.0933859 0.0539164i
\(259\) −2573.00 4456.57i −0.617291 1.06918i
\(260\) 1332.00 0.317720
\(261\) 1498.50 + 2595.48i 0.355382 + 0.615540i
\(262\) 3006.00 0.708822
\(263\) 301.500 + 522.213i 0.0706893 + 0.122437i 0.899204 0.437530i \(-0.144147\pi\)
−0.828514 + 0.559968i \(0.810813\pi\)
\(264\) 540.000 311.769i 0.125889 0.0726821i
\(265\) 513.000 888.542i 0.118918 0.205972i
\(266\) −868.000 + 1503.42i −0.200077 + 0.346544i
\(267\) 5455.96i 1.25056i
\(268\) 842.000 + 1458.39i 0.191915 + 0.332407i
\(269\) −1470.00 −0.333188 −0.166594 0.986026i \(-0.553277\pi\)
−0.166594 + 0.986026i \(0.553277\pi\)
\(270\) 2525.33i 0.569210i
\(271\) 2072.00 0.464447 0.232223 0.972662i \(-0.425400\pi\)
0.232223 + 0.972662i \(0.425400\pi\)
\(272\) 336.000 + 581.969i 0.0749007 + 0.129732i
\(273\) 5959.99i 1.32130i
\(274\) 2661.00 4608.99i 0.586704 1.01620i
\(275\) −330.000 + 571.577i −0.0723627 + 0.125336i
\(276\) −3510.00 + 2026.50i −0.765497 + 0.441960i
\(277\) −3569.50 6182.56i −0.774262 1.34106i −0.935209 0.354097i \(-0.884788\pi\)
0.160947 0.986963i \(-0.448545\pi\)
\(278\) −242.000 −0.0522093
\(279\) −2767.50 + 4793.45i −0.593856 + 1.02859i
\(280\) 2232.00 0.476384
\(281\) −4213.50 7298.00i −0.894507 1.54933i −0.834414 0.551138i \(-0.814194\pi\)
−0.0600924 0.998193i \(-0.519140\pi\)
\(282\) 1593.00 + 919.719i 0.336389 + 0.194214i
\(283\) 228.500 395.774i 0.0479962 0.0831318i −0.841029 0.540990i \(-0.818050\pi\)
0.889025 + 0.457858i \(0.151383\pi\)
\(284\) −312.000 + 540.400i −0.0651894 + 0.112911i
\(285\) 1134.00 + 654.715i 0.235693 + 0.136077i
\(286\) −555.000 961.288i −0.114748 0.198749i
\(287\) 8091.00 1.66410
\(288\) 432.000 748.246i 0.0883883 0.153093i
\(289\) −3149.00 −0.640953
\(290\) 999.000 + 1730.32i 0.202287 + 0.350372i
\(291\) 4054.50 2340.87i 0.816766 0.471560i
\(292\) −364.000 + 630.466i −0.0729503 + 0.126354i
\(293\) 2944.50 5100.02i 0.587097 1.01688i −0.407513 0.913199i \(-0.633604\pi\)
0.994610 0.103683i \(-0.0330628\pi\)
\(294\) 6422.44i 1.27403i
\(295\) 715.500 + 1239.28i 0.141214 + 0.244589i
\(296\) −1328.00 −0.260772
\(297\) −1822.50 + 1052.22i −0.356068 + 0.205576i
\(298\) −5658.00 −1.09986
\(299\) 3607.50 + 6248.37i 0.697750 + 1.20854i
\(300\) 914.523i 0.176000i
\(301\) −666.500 + 1154.41i −0.127629 + 0.221060i
\(302\) −461.000 + 798.475i −0.0878396 + 0.152143i
\(303\) −1741.50 + 1005.46i −0.330187 + 0.190633i
\(304\) 224.000 + 387.979i 0.0422608 + 0.0731978i
\(305\) −1719.00 −0.322720
\(306\) −1134.00 1964.15i −0.211851 0.366937i
\(307\) −1204.00 −0.223830 −0.111915 0.993718i \(-0.535698\pi\)
−0.111915 + 0.993718i \(0.535698\pi\)
\(308\) −930.000 1610.81i −0.172051 0.298001i
\(309\) 2479.50 + 1431.54i 0.456485 + 0.263552i
\(310\) −1845.00 + 3195.63i −0.338029 + 0.585483i
\(311\) 1642.50 2844.89i 0.299478 0.518711i −0.676539 0.736407i \(-0.736521\pi\)
0.976017 + 0.217696i \(0.0698542\pi\)
\(312\) −1332.00 769.031i −0.241698 0.139544i
\(313\) 5028.50 + 8709.62i 0.908075 + 1.57283i 0.816735 + 0.577013i \(0.195782\pi\)
0.0913406 + 0.995820i \(0.470885\pi\)
\(314\) −5954.00 −1.07008
\(315\) −7533.00 −1.34742
\(316\) 4532.00 0.806788
\(317\) −1147.50 1987.53i −0.203312 0.352147i 0.746281 0.665631i \(-0.231837\pi\)
−0.949594 + 0.313483i \(0.898504\pi\)
\(318\) −1026.00 + 592.361i −0.180928 + 0.104459i
\(319\) 832.500 1441.93i 0.146116 0.253081i
\(320\) 288.000 498.831i 0.0503115 0.0871421i
\(321\) 62.3538i 0.0108419i
\(322\) 6045.00 + 10470.2i 1.04619 + 1.81206i
\(323\) 1176.00 0.202583
\(324\) −1458.00 + 2525.33i −0.250000 + 0.433013i
\(325\) 1628.00 0.277862
\(326\) 3316.00 + 5743.48i 0.563363 + 0.975773i
\(327\) 2608.47i 0.441127i
\(328\) 1044.00 1808.26i 0.175748 0.304404i
\(329\) 2743.50 4751.88i 0.459739 0.796291i
\(330\) −1215.00 + 701.481i −0.202677 + 0.117016i
\(331\) 3339.50 + 5784.18i 0.554548 + 0.960506i 0.997939 + 0.0641773i \(0.0204423\pi\)
−0.443390 + 0.896329i \(0.646224\pi\)
\(332\) −4332.00 −0.716113
\(333\) 4482.00 0.737574
\(334\) −1362.00 −0.223130
\(335\) −1894.50 3281.37i −0.308978 0.535165i
\(336\) −2232.00 1288.65i −0.362398 0.209230i
\(337\) −1091.50 + 1890.53i −0.176433 + 0.305590i −0.940656 0.339361i \(-0.889789\pi\)
0.764224 + 0.644951i \(0.223122\pi\)
\(338\) 828.000 1434.14i 0.133246 0.230789i
\(339\) −6304.50 3639.90i −1.01007 0.583164i
\(340\) −756.000 1309.43i −0.120588 0.208864i
\(341\) 3075.00 0.488330
\(342\) −756.000 1309.43i −0.119532 0.207035i
\(343\) −8525.00 −1.34200
\(344\) 172.000 + 297.913i 0.0269582 + 0.0466930i
\(345\) 7897.50 4559.62i 1.23243 0.711542i
\(346\) 3981.00 6895.29i 0.618555 1.07137i
\(347\) −1945.50 + 3369.70i −0.300980 + 0.521312i −0.976358 0.216159i \(-0.930647\pi\)
0.675379 + 0.737471i \(0.263980\pi\)
\(348\) 2307.09i 0.355382i
\(349\) −1397.50 2420.54i −0.214345 0.371257i 0.738725 0.674007i \(-0.235428\pi\)
−0.953070 + 0.302751i \(0.902095\pi\)
\(350\) 2728.00 0.416622
\(351\) 4495.50 + 2595.48i 0.683624 + 0.394691i
\(352\) −480.000 −0.0726821
\(353\) −2377.50 4117.95i −0.358475 0.620896i 0.629232 0.777218i \(-0.283370\pi\)
−0.987706 + 0.156322i \(0.950036\pi\)
\(354\) 1652.38i 0.248087i
\(355\) 702.000 1215.90i 0.104953 0.181784i
\(356\) 2100.00 3637.31i 0.312640 0.541508i
\(357\) −5859.00 + 3382.70i −0.868603 + 0.501488i
\(358\) −2004.00 3471.03i −0.295851 0.512429i
\(359\) 4608.00 0.677440 0.338720 0.940887i \(-0.390006\pi\)
0.338720 + 0.940887i \(0.390006\pi\)
\(360\) −972.000 + 1683.55i −0.142302 + 0.246475i
\(361\) −6075.00 −0.885698
\(362\) −1274.00 2206.63i −0.184972 0.320381i
\(363\) −4977.00 2873.47i −0.719627 0.415477i
\(364\) −2294.00 + 3973.32i −0.330325 + 0.572140i
\(365\) 819.000 1418.55i 0.117448 0.203425i
\(366\) 1719.00 + 992.465i 0.245502 + 0.141740i
\(367\) −1922.50 3329.87i −0.273443 0.473618i 0.696298 0.717753i \(-0.254829\pi\)
−0.969741 + 0.244135i \(0.921496\pi\)
\(368\) 3120.00 0.441960
\(369\) −3523.50 + 6102.88i −0.497090 + 0.860985i
\(370\) 2988.00 0.419834
\(371\) 1767.00 + 3060.53i 0.247272 + 0.428288i
\(372\) 3690.00 2130.42i 0.514295 0.296928i
\(373\) 4158.50 7202.73i 0.577263 0.999848i −0.418529 0.908203i \(-0.637454\pi\)
0.995792 0.0916449i \(-0.0292125\pi\)
\(374\) −630.000 + 1091.19i −0.0871030 + 0.150867i
\(375\) 7903.35i 1.08834i
\(376\) −708.000 1226.29i −0.0971072 0.168195i
\(377\) −4107.00 −0.561064
\(378\) 7533.00 + 4349.18i 1.02502 + 0.591793i
\(379\) 12560.0 1.70228 0.851140 0.524939i \(-0.175912\pi\)
0.851140 + 0.524939i \(0.175912\pi\)
\(380\) −504.000 872.954i −0.0680386 0.117846i
\(381\) 4572.61i 0.614861i
\(382\) −1161.00 + 2010.91i −0.155502 + 0.269338i
\(383\) −6043.50 + 10467.6i −0.806288 + 1.39653i 0.109130 + 0.994028i \(0.465194\pi\)
−0.915418 + 0.402505i \(0.868140\pi\)
\(384\) −576.000 + 332.554i −0.0765466 + 0.0441942i
\(385\) 2092.50 + 3624.32i 0.276997 + 0.479772i
\(386\) 7222.00 0.952306
\(387\) −580.500 1005.46i −0.0762493 0.132068i
\(388\) −3604.00 −0.471560
\(389\) 4270.50 + 7396.72i 0.556614 + 0.964084i 0.997776 + 0.0666565i \(0.0212332\pi\)
−0.441162 + 0.897428i \(0.645433\pi\)
\(390\) 2997.00 + 1730.32i 0.389126 + 0.224662i
\(391\) 4095.00 7092.75i 0.529650 0.917380i
\(392\) −2472.00 + 4281.63i −0.318507 + 0.551671i
\(393\) 6763.50 + 3904.91i 0.868126 + 0.501213i
\(394\) −2046.00 3543.78i −0.261614 0.453129i
\(395\) −10197.0 −1.29890
\(396\) 1620.00 0.205576
\(397\) −13174.0 −1.66545 −0.832726 0.553686i \(-0.813221\pi\)
−0.832726 + 0.553686i \(0.813221\pi\)
\(398\) −2996.00 5189.22i −0.377326 0.653549i
\(399\) −3906.00 + 2255.13i −0.490087 + 0.282952i
\(400\) 352.000 609.682i 0.0440000 0.0762102i
\(401\) −4801.50 + 8316.44i −0.597944 + 1.03567i 0.395180 + 0.918604i \(0.370682\pi\)
−0.993124 + 0.117066i \(0.962651\pi\)
\(402\) 4375.16i 0.542819i
\(403\) −3792.50 6568.80i −0.468779 0.811949i
\(404\) 1548.00 0.190633
\(405\) 3280.50 5681.99i 0.402492 0.697137i
\(406\) −6882.00 −0.841251
\(407\) −1245.00 2156.40i −0.151627 0.262626i
\(408\) 1745.91i 0.211851i
\(409\) −5735.50 + 9934.18i −0.693404 + 1.20101i 0.277312 + 0.960780i \(0.410557\pi\)
−0.970716 + 0.240231i \(0.922777\pi\)
\(410\) −2349.00 + 4068.59i −0.282948 + 0.490081i
\(411\) 11974.5 6913.48i 1.43713 0.829725i
\(412\) −1102.00 1908.72i −0.131776 0.228242i
\(413\) −4929.00 −0.587264
\(414\) −10530.0 −1.25005
\(415\) 9747.00 1.15292
\(416\) 592.000 + 1025.37i 0.0697721 + 0.120849i
\(417\) −544.500 314.367i −0.0639431 0.0369176i
\(418\) −420.000 + 727.461i −0.0491456 + 0.0851227i
\(419\) 2986.50 5172.77i 0.348210 0.603118i −0.637721 0.770267i \(-0.720123\pi\)
0.985932 + 0.167149i \(0.0534562\pi\)
\(420\) 5022.00 + 2899.45i 0.583449 + 0.336854i
\(421\) 4452.50 + 7711.96i 0.515443 + 0.892774i 0.999839 + 0.0179250i \(0.00570601\pi\)
−0.484396 + 0.874849i \(0.660961\pi\)
\(422\) 1510.00 0.174184
\(423\) 2389.50 + 4138.74i 0.274661 + 0.475726i
\(424\) 912.000 0.104459
\(425\) −924.000 1600.41i −0.105460 0.182662i
\(426\) −1404.00 + 810.600i −0.159681 + 0.0921918i
\(427\) 2960.50 5127.74i 0.335524 0.581144i
\(428\) 24.0000 41.5692i 0.00271048 0.00469468i
\(429\) 2883.86i 0.324555i
\(430\) −387.000 670.304i −0.0434019 0.0751742i
\(431\) 1416.00 0.158251 0.0791257 0.996865i \(-0.474787\pi\)
0.0791257 + 0.996865i \(0.474787\pi\)
\(432\) 1944.00 1122.37i 0.216506 0.125000i
\(433\) 10766.0 1.19488 0.597438 0.801915i \(-0.296186\pi\)
0.597438 + 0.801915i \(0.296186\pi\)
\(434\) −6355.00 11007.2i −0.702880 1.21742i
\(435\) 5190.96i 0.572155i
\(436\) 1004.00 1738.98i 0.110282 0.191014i
\(437\) 2730.00 4728.50i 0.298841 0.517608i
\(438\) −1638.00 + 945.700i −0.178691 + 0.103167i
\(439\) −2174.50 3766.34i −0.236408 0.409471i 0.723273 0.690562i \(-0.242637\pi\)
−0.959681 + 0.281091i \(0.909304\pi\)
\(440\) 1080.00 0.117016
\(441\) 8343.00 14450.5i 0.900875 1.56036i
\(442\) 3108.00 0.334463
\(443\) 7273.50 + 12598.1i 0.780078 + 1.35113i 0.931896 + 0.362726i \(0.118154\pi\)
−0.151818 + 0.988408i \(0.548513\pi\)
\(444\) −2988.00 1725.12i −0.319379 0.184393i
\(445\) −4725.00 + 8183.94i −0.503340 + 0.871811i
\(446\) 3463.00 5998.09i 0.367663 0.636811i
\(447\) −12730.5 7349.96i −1.34705 0.777721i
\(448\) 992.000 + 1718.19i 0.104615 + 0.181199i
\(449\) −3330.00 −0.350005 −0.175003 0.984568i \(-0.555993\pi\)
−0.175003 + 0.984568i \(0.555993\pi\)
\(450\) −1188.00 + 2057.68i −0.124451 + 0.215555i
\(451\) 3915.00 0.408759
\(452\) 2802.00 + 4853.21i 0.291582 + 0.505035i
\(453\) −2074.50 + 1197.71i −0.215162 + 0.124224i
\(454\) −6225.00 + 10782.0i −0.643510 + 1.11459i
\(455\) 5161.50 8939.98i 0.531813 0.921127i
\(456\) 1163.94i 0.119532i
\(457\) −4073.50 7055.51i −0.416959 0.722194i 0.578673 0.815560i \(-0.303571\pi\)
−0.995632 + 0.0933655i \(0.970237\pi\)
\(458\) −2930.00 −0.298930
\(459\) 5892.44i 0.599206i
\(460\) −7020.00 −0.711542
\(461\) −4015.50 6955.05i −0.405684 0.702666i 0.588717 0.808340i \(-0.299633\pi\)
−0.994401 + 0.105674i \(0.966300\pi\)
\(462\) 4832.42i 0.486633i
\(463\) −2141.50 + 3709.19i −0.214955 + 0.372312i −0.953259 0.302156i \(-0.902294\pi\)
0.738304 + 0.674468i \(0.235627\pi\)
\(464\) −888.000 + 1538.06i −0.0888456 + 0.153885i
\(465\) −8302.50 + 4793.45i −0.827998 + 0.478045i
\(466\) −2634.00 4562.22i −0.261841 0.453521i
\(467\) 5460.00 0.541025 0.270512 0.962716i \(-0.412807\pi\)
0.270512 + 0.962716i \(0.412807\pi\)
\(468\) −1998.00 3460.64i −0.197345 0.341812i
\(469\) 13051.0 1.28494
\(470\) 1593.00 + 2759.16i 0.156340 + 0.270788i
\(471\) −13396.5 7734.47i −1.31057 0.756658i
\(472\) −636.000 + 1101.58i −0.0620218 + 0.107425i
\(473\) −322.500 + 558.586i −0.0313500 + 0.0542999i
\(474\) 10197.0 + 5887.24i 0.988109 + 0.570485i
\(475\) −616.000 1066.94i −0.0595032 0.103063i
\(476\) 5208.00 0.501488
\(477\) −3078.00 −0.295455
\(478\) 13830.0 1.32337
\(479\) −214.500 371.525i −0.0204609 0.0354393i 0.855614 0.517615i \(-0.173180\pi\)
−0.876075 + 0.482176i \(0.839847\pi\)
\(480\) 1296.00 748.246i 0.123238 0.0711512i
\(481\) −3071.00 + 5319.13i −0.291113 + 0.504223i
\(482\) 1489.00 2579.02i 0.140710 0.243716i
\(483\) 31410.7i 2.95909i
\(484\) 2212.00 + 3831.30i 0.207739 + 0.359814i
\(485\) 8109.00 0.759197
\(486\) −6561.00 + 3788.00i −0.612372 + 0.353553i
\(487\) −11296.0 −1.05107 −0.525535 0.850772i \(-0.676135\pi\)
−0.525535 + 0.850772i \(0.676135\pi\)
\(488\) −764.000 1323.29i −0.0708702 0.122751i
\(489\) 17230.4i 1.59343i
\(490\) 5562.00 9633.67i 0.512787 0.888173i
\(491\) 7336.50 12707.2i 0.674321 1.16796i −0.302346 0.953198i \(-0.597770\pi\)
0.976667 0.214760i \(-0.0688969\pi\)
\(492\) 4698.00 2712.39i 0.430492 0.248545i
\(493\) 2331.00 + 4037.41i 0.212947 + 0.368835i
\(494\) 2072.00 0.188712
\(495\) −3645.00 −0.330971
\(496\) −3280.00 −0.296928
\(497\) 2418.00 + 4188.10i 0.218234 + 0.377992i
\(498\) −9747.00 5627.43i −0.877055 0.506368i
\(499\) −6719.50 + 11638.5i −0.602818 + 1.04411i 0.389574 + 0.920995i \(0.372622\pi\)
−0.992392 + 0.123116i \(0.960711\pi\)
\(500\) −3042.00 + 5268.90i −0.272085 + 0.471265i
\(501\) −3064.50 1769.29i −0.273277 0.157777i
\(502\) 4620.00 + 8002.07i 0.410758 + 0.711454i
\(503\) −17388.0 −1.54134 −0.770669 0.637236i \(-0.780078\pi\)
−0.770669 + 0.637236i \(0.780078\pi\)
\(504\) −3348.00 5798.91i −0.295896 0.512508i
\(505\) −3483.00 −0.306914
\(506\) 2925.00 + 5066.25i 0.256980 + 0.445103i
\(507\) 3726.00 2151.21i 0.326386 0.188439i
\(508\) 1760.00 3048.41i 0.153715 0.266243i
\(509\) 1894.50 3281.37i 0.164975 0.285745i −0.771671 0.636021i \(-0.780579\pi\)
0.936646 + 0.350276i \(0.113912\pi\)
\(510\) 3928.29i 0.341074i
\(511\) 2821.00 + 4886.12i 0.244215 + 0.422992i
\(512\) 512.000 0.0441942
\(513\) 3928.29i 0.338086i
\(514\) 6702.00 0.575122
\(515\) 2479.50 + 4294.62i 0.212155 + 0.367463i
\(516\) 893.738i 0.0762493i
\(517\) 1327.50 2299.30i 0.112927 0.195596i
\(518\) −5146.00 + 8913.13i −0.436491 + 0.756024i
\(519\) 17914.5 10342.9i 1.51514 0.874768i
\(520\) −1332.00 2307.09i −0.112331 0.194563i
\(521\) 9786.00 0.822903 0.411451 0.911432i \(-0.365022\pi\)
0.411451 + 0.911432i \(0.365022\pi\)
\(522\) 2997.00 5190.96i 0.251293 0.435253i
\(523\) −8008.00 −0.669532 −0.334766 0.942301i \(-0.608657\pi\)
−0.334766 + 0.942301i \(0.608657\pi\)
\(524\) −3006.00 5206.54i −0.250606 0.434063i
\(525\) 6138.00 + 3543.78i 0.510256 + 0.294596i
\(526\) 603.000 1044.43i 0.0499849 0.0865764i
\(527\) −4305.00 + 7456.48i −0.355842 + 0.616336i
\(528\) −1080.00 623.538i −0.0890170 0.0513940i
\(529\) −12929.0 22393.7i −1.06263 1.84053i
\(530\) −2052.00 −0.168176
\(531\) 2146.50 3717.85i 0.175424 0.303843i
\(532\) 3472.00 0.282952
\(533\) −4828.50 8363.21i −0.392393 0.679645i
\(534\) 9450.00 5455.96i 0.765808 0.442139i
\(535\) −54.0000 + 93.5307i −0.00436378 + 0.00755829i
\(536\) 1684.00 2916.77i 0.135705 0.235047i
\(537\) 10413.1i 0.836793i
\(538\) 1470.00 + 2546.11i 0.117800 + 0.204035i
\(539\) −9270.00 −0.740793
\(540\) −4374.00 + 2525.33i −0.348569 + 0.201246i
\(541\) −2938.00 −0.233483 −0.116742 0.993162i \(-0.537245\pi\)
−0.116742 + 0.993162i \(0.537245\pi\)
\(542\) −2072.00 3588.81i −0.164207 0.284414i
\(543\) 6619.90i 0.523181i
\(544\) 672.000 1163.94i 0.0529628 0.0917343i
\(545\) −2259.00 + 3912.70i −0.177550 + 0.307526i
\(546\) −10323.0 + 5959.99i −0.809128 + 0.467150i
\(547\) 5187.50 + 8985.01i 0.405487 + 0.702324i 0.994378 0.105888i \(-0.0337686\pi\)
−0.588891 + 0.808213i \(0.700435\pi\)
\(548\) −10644.0 −0.829725
\(549\) 2578.50 + 4466.09i 0.200451 + 0.347192i
\(550\) 1320.00 0.102336
\(551\) 1554.00 + 2691.61i 0.120150 + 0.208106i
\(552\) 7020.00 + 4053.00i 0.541288 + 0.312513i
\(553\) 17561.5 30417.4i 1.35044 2.33902i
\(554\) −7139.00 + 12365.1i −0.547486 + 0.948273i
\(555\) 6723.00 + 3881.53i 0.514190 + 0.296868i
\(556\) 242.000 + 419.156i 0.0184588 + 0.0319716i
\(557\) 3306.00 0.251490 0.125745 0.992063i \(-0.459868\pi\)
0.125745 + 0.992063i \(0.459868\pi\)
\(558\) 11070.0 0.839840
\(559\) 1591.00 0.120379
\(560\) −2232.00 3865.94i −0.168427 0.291724i
\(561\) −2835.00 + 1636.79i −0.213358 + 0.123182i
\(562\) −8427.00 + 14596.0i −0.632512 + 1.09554i
\(563\) 10546.5 18267.1i 0.789488 1.36743i −0.136792 0.990600i \(-0.543679\pi\)
0.926281 0.376834i \(-0.122987\pi\)
\(564\) 3678.88i 0.274661i
\(565\) −6304.50 10919.7i −0.469438 0.813090i
\(566\) −914.000 −0.0678768
\(567\) 11299.5 + 19571.3i 0.836921 + 1.44959i
\(568\) 1248.00 0.0921918
\(569\) −643.500 1114.57i −0.0474111 0.0821185i 0.841346 0.540497i \(-0.181764\pi\)
−0.888757 + 0.458379i \(0.848430\pi\)
\(570\) 2618.86i 0.192442i
\(571\) −7517.50 + 13020.7i −0.550959 + 0.954289i 0.447247 + 0.894411i \(0.352405\pi\)
−0.998206 + 0.0598783i \(0.980929\pi\)
\(572\) −1110.00 + 1922.58i −0.0811389 + 0.140537i
\(573\) −5224.50 + 3016.37i −0.380902 + 0.219914i
\(574\) −8091.00 14014.0i −0.588348 1.01905i
\(575\) −8580.00 −0.622280
\(576\) −1728.00 −0.125000
\(577\) 1190.00 0.0858585 0.0429292 0.999078i \(-0.486331\pi\)
0.0429292 + 0.999078i \(0.486331\pi\)
\(578\) 3149.00 + 5454.23i 0.226611 + 0.392502i
\(579\) 16249.5 + 9381.65i 1.16633 + 0.673382i
\(580\) 1998.00 3460.64i 0.143039 0.247750i
\(581\) −16786.5 + 29075.1i −1.19866 + 2.07614i
\(582\) −8109.00 4681.73i −0.577541 0.333443i
\(583\) 855.000 + 1480.90i 0.0607384 + 0.105202i
\(584\) 1456.00 0.103167
\(585\) 4495.50 + 7786.43i 0.317720 + 0.550307i
\(586\) −11778.0 −0.830281
\(587\) 8941.50 + 15487.1i 0.628714 + 1.08896i 0.987810 + 0.155664i \(0.0497518\pi\)
−0.359096 + 0.933301i \(0.616915\pi\)
\(588\) −11124.0 + 6422.44i −0.780180 + 0.450437i
\(589\) −2870.00 + 4970.99i −0.200775 + 0.347752i
\(590\) 1431.00 2478.56i 0.0998531 0.172951i
\(591\) 10631.3i 0.739957i
\(592\) 1328.00 + 2300.16i 0.0921967 + 0.159689i
\(593\) 20118.0 1.39317 0.696583 0.717476i \(-0.254703\pi\)
0.696583 + 0.717476i \(0.254703\pi\)
\(594\) 3645.00 + 2104.44i 0.251778 + 0.145364i
\(595\) −11718.0 −0.807380
\(596\) 5658.00 + 9799.94i 0.388860 + 0.673526i
\(597\) 15567.7i 1.06724i
\(598\) 7215.00 12496.7i 0.493383 0.854565i
\(599\) 532.500 922.317i 0.0363228 0.0629129i −0.847293 0.531127i \(-0.821769\pi\)
0.883615 + 0.468214i \(0.155102\pi\)
\(600\) 1584.00 914.523i 0.107778 0.0622254i
\(601\) 10362.5 + 17948.4i 0.703320 + 1.21819i 0.967294 + 0.253656i \(0.0816331\pi\)
−0.263975 + 0.964530i \(0.585034\pi\)
\(602\) 2666.00 0.180495
\(603\) −5683.50 + 9844.11i −0.383831 + 0.664815i
\(604\) 1844.00 0.124224
\(605\) −4977.00 8620.42i −0.334453 0.579289i
\(606\) 3483.00 + 2010.91i 0.233477 + 0.134798i
\(607\) 7872.50 13635.6i 0.526417 0.911780i −0.473110 0.881004i \(-0.656869\pi\)
0.999526 0.0307768i \(-0.00979812\pi\)
\(608\) 448.000 775.959i 0.0298829 0.0517587i
\(609\) −15484.5 8939.98i −1.03032 0.594854i
\(610\) 1719.00 + 2977.40i 0.114099 + 0.197625i
\(611\) −6549.00 −0.433624
\(612\) −2268.00 + 3928.29i −0.149801 + 0.259464i
\(613\) 5042.00 0.332210 0.166105 0.986108i \(-0.446881\pi\)
0.166105 + 0.986108i \(0.446881\pi\)
\(614\) 1204.00 + 2085.39i 0.0791360 + 0.137068i
\(615\) −10570.5 + 6102.88i −0.693079 + 0.400149i
\(616\) −1860.00 + 3221.61i −0.121658 + 0.210718i
\(617\) 5026.50 8706.15i 0.327973 0.568066i −0.654137 0.756376i \(-0.726968\pi\)
0.982110 + 0.188311i \(0.0603012\pi\)
\(618\) 5726.16i 0.372718i
\(619\) 2991.50 + 5181.43i 0.194246 + 0.336445i 0.946653 0.322254i \(-0.104441\pi\)
−0.752407 + 0.658699i \(0.771107\pi\)
\(620\) 7380.00 0.478045
\(621\) −23692.5 13678.9i −1.53099 0.883920i
\(622\) −6570.00 −0.423526
\(623\) −16275.0 28189.1i −1.04662 1.81280i
\(624\) 3076.12i 0.197345i
\(625\) 4094.50 7091.88i 0.262048 0.453880i
\(626\) 10057.0 17419.2i 0.642106 1.11216i
\(627\) −1890.00 + 1091.19i −0.120382 + 0.0695024i
\(628\) 5954.00 + 10312.6i 0.378329 + 0.655285i
\(629\) 6972.00 0.441958
\(630\) 7533.00 + 13047.5i 0.476384 + 0.825121i
\(631\) −19696.0 −1.24261 −0.621304 0.783570i \(-0.713397\pi\)
−0.621304 + 0.783570i \(0.713397\pi\)
\(632\) −4532.00 7849.65i −0.285243 0.494055i
\(633\) 3397.50 + 1961.55i 0.213331 + 0.123167i
\(634\) −2295.00 + 3975.06i −0.143764 + 0.249006i
\(635\) −3960.00 + 6858.92i −0.247477 + 0.428642i
\(636\) 2052.00 + 1184.72i 0.127936 + 0.0738637i
\(637\) 11433.0 + 19802.5i 0.711133 + 1.23172i
\(638\) −3330.00 −0.206639
\(639\) −4212.00 −0.260758
\(640\) −1152.00 −0.0711512
\(641\) 5488.50 + 9506.36i 0.338195 + 0.585770i 0.984093 0.177653i \(-0.0568505\pi\)
−0.645899 + 0.763423i \(0.723517\pi\)
\(642\) 108.000 62.3538i 0.00663928 0.00383319i
\(643\) 7914.50 13708.3i 0.485408 0.840752i −0.514451 0.857520i \(-0.672004\pi\)
0.999859 + 0.0167681i \(0.00533770\pi\)
\(644\) 12090.0 20940.5i 0.739771 1.28132i
\(645\) 2010.91i 0.122759i
\(646\) −1176.00 2036.89i −0.0716240 0.124056i
\(647\) 28224.0 1.71499 0.857496 0.514490i \(-0.172019\pi\)
0.857496 + 0.514490i \(0.172019\pi\)
\(648\) 5832.00 0.353553
\(649\) −2385.00 −0.144252
\(650\) −1628.00 2819.78i −0.0982391 0.170155i
\(651\) 33021.5i 1.98804i
\(652\) 6632.00 11487.0i 0.398358 0.689976i
\(653\) −14083.5 + 24393.3i −0.843997 + 1.46185i 0.0424927 + 0.999097i \(0.486470\pi\)
−0.886490 + 0.462749i \(0.846863\pi\)
\(654\) 4518.00 2608.47i 0.270134 0.155962i
\(655\) 6763.50 + 11714.7i 0.403468 + 0.698828i
\(656\) −4176.00 −0.248545
\(657\) −4914.00 −0.291801
\(658\) −10974.0 −0.650169
\(659\) −5368.50 9298.51i −0.317340 0.549649i 0.662592 0.748980i \(-0.269456\pi\)
−0.979932 + 0.199331i \(0.936123\pi\)
\(660\) 2430.00 + 1402.96i 0.143315 + 0.0827427i
\(661\) −5063.50 + 8770.24i −0.297954 + 0.516071i −0.975668 0.219255i \(-0.929637\pi\)
0.677714 + 0.735326i \(0.262971\pi\)
\(662\) 6679.00 11568.4i 0.392125 0.679180i
\(663\) 6993.00 + 4037.41i 0.409631 + 0.236501i
\(664\) 4332.00 + 7503.24i 0.253184 + 0.438528i
\(665\) −7812.00 −0.455543
\(666\) −4482.00 7763.05i −0.260772 0.451670i
\(667\) 21645.0 1.25652
\(668\) 1362.00 + 2359.05i 0.0788883 + 0.136638i
\(669\) 15583.5 8997.14i 0.900587 0.519954i
\(670\) −3789.00 + 6562.74i −0.218480 + 0.378419i
\(671\) 1432.50 2481.16i 0.0824159 0.142748i
\(672\) 5154.58i 0.295896i
\(673\) −125.500 217.372i −0.00718822 0.0124504i 0.862409 0.506212i \(-0.168955\pi\)
−0.869597 + 0.493762i \(0.835621\pi\)
\(674\) 4366.00 0.249513
\(675\) −5346.00 + 3086.51i −0.304841 + 0.176000i
\(676\) −3312.00 −0.188439
\(677\) −4225.50 7318.78i −0.239881 0.415485i 0.720799 0.693144i \(-0.243775\pi\)
−0.960680 + 0.277659i \(0.910442\pi\)
\(678\) 14559.6i 0.824718i
\(679\) −13965.5 + 24189.0i −0.789318 + 1.36714i
\(680\) −1512.00 + 2618.86i −0.0852685 + 0.147689i
\(681\) −28012.5 + 16173.0i −1.57627 + 0.910061i
\(682\) −3075.00 5326.06i −0.172651 0.299040i
\(683\) −25884.0 −1.45011 −0.725054 0.688692i \(-0.758185\pi\)
−0.725054 + 0.688692i \(0.758185\pi\)
\(684\) −1512.00 + 2618.86i −0.0845216 + 0.146396i
\(685\) 23949.0 1.33583
\(686\) 8525.00 + 14765.7i 0.474469 + 0.821805i
\(687\) −6592.50 3806.18i −0.366113 0.211375i
\(688\) 344.000 595.825i 0.0190623 0.0330169i
\(689\) 2109.00 3652.90i 0.116613 0.201980i
\(690\) −15795.0 9119.25i −0.871457 0.503136i
\(691\) −3182.50 5512.25i −0.175207 0.303467i 0.765026 0.643999i \(-0.222726\pi\)
−0.940233 + 0.340532i \(0.889393\pi\)
\(692\) −15924.0 −0.874768
\(693\) 6277.50 10872.9i 0.344102 0.596002i
\(694\) 7782.00 0.425649
\(695\) −544.500 943.102i −0.0297181 0.0514732i
\(696\) −3996.00 + 2307.09i −0.217626 + 0.125647i
\(697\) −5481.00 + 9493.37i −0.297859 + 0.515907i
\(698\) −2795.00 + 4841.08i −0.151565 + 0.262518i
\(699\) 13686.7i 0.740597i
\(700\) −2728.00 4725.03i −0.147298 0.255128i
\(701\) 1122.00 0.0604527 0.0302264 0.999543i \(-0.490377\pi\)
0.0302264 + 0.999543i \(0.490377\pi\)
\(702\) 10381.9i 0.558177i
\(703\) 4648.00 0.249364
\(704\) 480.000 + 831.384i 0.0256970 + 0.0445085i
\(705\) 8277.47i 0.442195i
\(706\) −4755.00 + 8235.90i −0.253480 + 0.439040i
\(707\) 5998.50 10389.7i 0.319090 0.552681i
\(708\) −2862.00 + 1652.38i −0.151922 + 0.0877120i
\(709\) −2141.50 3709.19i −0.113435 0.196476i 0.803718 0.595011i \(-0.202852\pi\)
−0.917153 + 0.398535i \(0.869519\pi\)
\(710\) −2808.00 −0.148426
\(711\) 15295.5 + 26492.6i 0.806788 + 1.39740i
\(712\) −8400.00 −0.442139
\(713\) 19987.5 + 34619.4i 1.04984 + 1.81838i
\(714\) 11718.0 + 6765.39i 0.614195 + 0.354606i
\(715\) 2497.50 4325.80i 0.130631 0.226260i
\(716\) −4008.00 + 6942.06i −0.209198 + 0.362342i
\(717\) 31117.5 + 17965.7i 1.62079 + 0.935762i
\(718\) −4608.00 7981.29i −0.239511 0.414846i
\(719\) 4032.00 0.209135 0.104568 0.994518i \(-0.466654\pi\)
0.104568 + 0.994518i \(0.466654\pi\)
\(720\) 3888.00 0.201246
\(721\) −17081.0 −0.882288
\(722\) 6075.00 + 10522.2i 0.313141 + 0.542377i
\(723\) 6700.50 3868.54i 0.344667 0.198994i
\(724\) −2548.00 + 4413.27i −0.130795 + 0.226544i
\(725\) 2442.00 4229.67i 0.125095 0.216670i
\(726\) 11493.9i 0.587573i
\(727\) −12002.5 20788.9i −0.612308 1.06055i −0.990850 0.134965i \(-0.956908\pi\)
0.378542 0.925584i \(-0.376426\pi\)
\(728\) 9176.00 0.467150
\(729\) −19683.0 −1.00000
\(730\) −3276.00 −0.166096
\(731\) −903.000 1564.04i −0.0456890 0.0791357i
\(732\) 3969.86i 0.200451i
\(733\) 18750.5 32476.8i 0.944837 1.63651i 0.188760 0.982023i \(-0.439553\pi\)
0.756077 0.654482i \(-0.227113\pi\)
\(734\) −3845.00 + 6659.74i −0.193354 + 0.334898i
\(735\) 25029.0 14450.5i 1.25607 0.725190i
\(736\) −3120.00 5404.00i −0.156256 0.270644i
\(737\) 6315.00 0.315626
\(738\) 14094.0 0.702991
\(739\) −880.000 −0.0438042 −0.0219021 0.999760i \(-0.506972\pi\)
−0.0219021 + 0.999760i \(0.506972\pi\)
\(740\) −2988.00 5175.37i −0.148434 0.257095i
\(741\) 4662.00 + 2691.61i 0.231124 + 0.133439i
\(742\) 3534.00 6121.07i 0.174848 0.302846i
\(743\) −811.500 + 1405.56i −0.0400687 + 0.0694010i −0.885364 0.464898i \(-0.846091\pi\)
0.845296 + 0.534299i \(0.179424\pi\)
\(744\) −7380.00 4260.84i −0.363661 0.209960i
\(745\) −12730.5 22049.9i −0.626053 1.08436i
\(746\) −16634.0 −0.816373
\(747\) −14620.5 25323.4i −0.716113 1.24034i
\(748\) 2520.00 0.123182
\(749\) −186.000 322.161i −0.00907382 0.0157163i
\(750\) −13689.0 + 7903.35i −0.666469 + 0.384786i
\(751\) 3444.50 5966.05i 0.167366 0.289886i −0.770127 0.637890i \(-0.779807\pi\)
0.937493 + 0.348005i \(0.113141\pi\)
\(752\) −1416.00 + 2452.58i −0.0686652 + 0.118932i
\(753\) 24006.2i 1.16180i
\(754\) 4107.00 + 7113.53i 0.198366 + 0.343580i
\(755\) −4149.00 −0.199997
\(756\) 17396.7i 0.836921i
\(757\) −12850.0 −0.616963 −0.308482 0.951230i \(-0.599821\pi\)
−0.308482 + 0.951230i \(0.599821\pi\)
\(758\) −12560.0 21754.6i −0.601847 1.04243i
\(759\) 15198.7i 0.726850i
\(760\) −1008.00 + 1745.91i −0.0481105 + 0.0833299i
\(761\) −2305.50 + 3993.24i −0.109822 + 0.190217i −0.915698 0.401867i \(-0.868361\pi\)
0.805876 + 0.592084i \(0.201695\pi\)
\(762\) 7920.00 4572.61i 0.376524 0.217386i
\(763\) −7781.00 13477.1i −0.369189 0.639454i
\(764\) 4644.00 0.219914
\(765\) 5103.00 8838.66i 0.241176 0.417728i
\(766\) 24174.0 1.14026
\(767\) 2941.50 + 5094.83i 0.138476 + 0.239848i
\(768\) 1152.00 + 665.108i 0.0541266 + 0.0312500i
\(769\) 1152.50 1996.19i 0.0540445 0.0936078i −0.837737 0.546073i \(-0.816122\pi\)
0.891782 + 0.452465i \(0.149455\pi\)
\(770\) 4185.00 7248.63i 0.195866 0.339250i
\(771\) 15079.5 + 8706.15i 0.704377