Properties

Label 16.5.f.a.3.3
Level $16$
Weight $5$
Character 16.3
Analytic conductor $1.654$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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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 3.3
Root \(2.79265 + 0.448449i\) of defining polynomial
Character \(\chi\) \(=\) 16.3
Dual form 16.5.f.a.11.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.34420 + 3.24110i) q^{2} +(-4.63552 + 4.63552i) q^{3} +(-5.00945 - 15.1956i) q^{4} +(-29.2002 + 29.2002i) q^{5} +(-4.15759 - 25.8908i) q^{6} +59.6196 q^{7} +(60.9935 + 19.3854i) q^{8} +38.0239i q^{9} +O(q^{10})\) \(q+(-2.34420 + 3.24110i) q^{2} +(-4.63552 + 4.63552i) q^{3} +(-5.00945 - 15.1956i) q^{4} +(-29.2002 + 29.2002i) q^{5} +(-4.15759 - 25.8908i) q^{6} +59.6196 q^{7} +(60.9935 + 19.3854i) q^{8} +38.0239i q^{9} +(-26.1896 - 163.092i) q^{10} +(-18.0837 - 18.0837i) q^{11} +(93.6607 + 47.2180i) q^{12} +(50.7721 + 50.7721i) q^{13} +(-139.760 + 193.233i) q^{14} -270.716i q^{15} +(-205.811 + 152.243i) q^{16} -223.769 q^{17} +(-123.239 - 89.1358i) q^{18} +(14.7360 - 14.7360i) q^{19} +(589.990 + 297.436i) q^{20} +(-276.368 + 276.368i) q^{21} +(101.003 - 16.2192i) q^{22} +739.082 q^{23} +(-372.598 + 192.875i) q^{24} -1080.30i q^{25} +(-283.577 + 45.5374i) q^{26} +(-551.738 - 551.738i) q^{27} +(-298.661 - 905.954i) q^{28} +(938.904 + 938.904i) q^{29} +(877.416 + 634.612i) q^{30} +938.741i q^{31} +(-10.9723 - 1023.94i) q^{32} +167.655 q^{33} +(524.560 - 725.259i) q^{34} +(-1740.90 + 1740.90i) q^{35} +(577.796 - 190.479i) q^{36} +(263.837 - 263.837i) q^{37} +(13.2167 + 82.3049i) q^{38} -470.710 q^{39} +(-2347.08 + 1214.96i) q^{40} -248.841i q^{41} +(-247.874 - 1543.60i) q^{42} +(1035.00 + 1035.00i) q^{43} +(-184.203 + 365.381i) q^{44} +(-1110.31 - 1110.31i) q^{45} +(-1732.56 + 2395.44i) q^{46} -2018.46i q^{47} +(248.315 - 1659.76i) q^{48} +1153.50 q^{49} +(3501.35 + 2532.44i) q^{50} +(1037.29 - 1037.29i) q^{51} +(517.171 - 1025.85i) q^{52} +(833.240 - 833.240i) q^{53} +(3081.62 - 494.853i) q^{54} +1056.09 q^{55} +(3636.41 + 1155.75i) q^{56} +136.618i q^{57} +(-5244.06 + 842.101i) q^{58} +(-2223.17 - 2223.17i) q^{59} +(-4113.68 + 1356.14i) q^{60} +(-341.374 - 341.374i) q^{61} +(-3042.55 - 2200.60i) q^{62} +2266.97i q^{63} +(3344.42 + 2364.76i) q^{64} -2965.11 q^{65} +(-393.016 + 543.385i) q^{66} +(4845.43 - 4845.43i) q^{67} +(1120.96 + 3400.30i) q^{68} +(-3426.03 + 3426.03i) q^{69} +(-1561.41 - 9723.46i) q^{70} -4180.93 q^{71} +(-737.108 + 2319.21i) q^{72} +9071.36i q^{73} +(236.635 + 1473.61i) q^{74} +(5007.74 + 5007.74i) q^{75} +(-297.741 - 150.103i) q^{76} +(-1078.14 - 1078.14i) q^{77} +(1103.44 - 1525.62i) q^{78} -735.536i q^{79} +(1564.19 - 10455.2i) q^{80} +2035.24 q^{81} +(806.518 + 583.333i) q^{82} +(1441.90 - 1441.90i) q^{83} +(5584.02 + 2815.12i) q^{84} +(6534.10 - 6534.10i) q^{85} +(-5780.81 + 928.294i) q^{86} -8704.61 q^{87} +(-752.429 - 1453.55i) q^{88} +5071.77i q^{89} +(6201.39 - 995.831i) q^{90} +(3027.01 + 3027.01i) q^{91} +(-3702.39 - 11230.8i) q^{92} +(-4351.55 - 4351.55i) q^{93} +(6542.05 + 4731.69i) q^{94} +860.586i q^{95} +(4797.36 + 4695.64i) q^{96} -2523.85 q^{97} +(-2704.03 + 3738.60i) q^{98} +(687.613 - 687.613i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.34420 + 3.24110i −0.586050 + 0.810275i
\(3\) −4.63552 + 4.63552i −0.515058 + 0.515058i −0.916072 0.401014i \(-0.868658\pi\)
0.401014 + 0.916072i \(0.368658\pi\)
\(4\) −5.00945 15.1956i −0.313090 0.949723i
\(5\) −29.2002 + 29.2002i −1.16801 + 1.16801i −0.185330 + 0.982676i \(0.559335\pi\)
−0.982676 + 0.185330i \(0.940665\pi\)
\(6\) −4.15759 25.8908i −0.115489 0.719188i
\(7\) 59.6196 1.21673 0.608363 0.793659i \(-0.291826\pi\)
0.608363 + 0.793659i \(0.291826\pi\)
\(8\) 60.9935 + 19.3854i 0.953024 + 0.302896i
\(9\) 38.0239i 0.469431i
\(10\) −26.1896 163.092i −0.261896 1.63092i
\(11\) −18.0837 18.0837i −0.149452 0.149452i 0.628421 0.777873i \(-0.283701\pi\)
−0.777873 + 0.628421i \(0.783701\pi\)
\(12\) 93.6607 + 47.2180i 0.650422 + 0.327903i
\(13\) 50.7721 + 50.7721i 0.300427 + 0.300427i 0.841181 0.540754i \(-0.181861\pi\)
−0.540754 + 0.841181i \(0.681861\pi\)
\(14\) −139.760 + 193.233i −0.713063 + 0.985883i
\(15\) 270.716i 1.20318i
\(16\) −205.811 + 152.243i −0.803949 + 0.594699i
\(17\) −223.769 −0.774289 −0.387144 0.922019i \(-0.626538\pi\)
−0.387144 + 0.922019i \(0.626538\pi\)
\(18\) −123.239 89.1358i −0.380368 0.275110i
\(19\) 14.7360 14.7360i 0.0408199 0.0408199i −0.686402 0.727222i \(-0.740811\pi\)
0.727222 + 0.686402i \(0.240811\pi\)
\(20\) 589.990 + 297.436i 1.47497 + 0.743591i
\(21\) −276.368 + 276.368i −0.626684 + 0.626684i
\(22\) 101.003 16.2192i 0.208684 0.0335108i
\(23\) 739.082 1.39713 0.698565 0.715547i \(-0.253822\pi\)
0.698565 + 0.715547i \(0.253822\pi\)
\(24\) −372.598 + 192.875i −0.646871 + 0.334853i
\(25\) 1080.30i 1.72848i
\(26\) −283.577 + 45.5374i −0.419493 + 0.0673631i
\(27\) −551.738 551.738i −0.756842 0.756842i
\(28\) −298.661 905.954i −0.380946 1.15555i
\(29\) 938.904 + 938.904i 1.11641 + 1.11641i 0.992263 + 0.124150i \(0.0396204\pi\)
0.124150 + 0.992263i \(0.460380\pi\)
\(30\) 877.416 + 634.612i 0.974907 + 0.705124i
\(31\) 938.741i 0.976838i 0.872609 + 0.488419i \(0.162426\pi\)
−0.872609 + 0.488419i \(0.837574\pi\)
\(32\) −10.9723 1023.94i −0.0107151 0.999943i
\(33\) 167.655 0.153953
\(34\) 524.560 725.259i 0.453772 0.627387i
\(35\) −1740.90 + 1740.90i −1.42114 + 1.42114i
\(36\) 577.796 190.479i 0.445830 0.146975i
\(37\) 263.837 263.837i 0.192722 0.192722i −0.604149 0.796871i \(-0.706487\pi\)
0.796871 + 0.604149i \(0.206487\pi\)
\(38\) 13.2167 + 82.3049i 0.00915283 + 0.0569979i
\(39\) −470.710 −0.309474
\(40\) −2347.08 + 1214.96i −1.46692 + 0.759353i
\(41\) 248.841i 0.148031i −0.997257 0.0740157i \(-0.976418\pi\)
0.997257 0.0740157i \(-0.0235815\pi\)
\(42\) −247.874 1543.60i −0.140518 0.875055i
\(43\) 1035.00 + 1035.00i 0.559765 + 0.559765i 0.929240 0.369476i \(-0.120463\pi\)
−0.369476 + 0.929240i \(0.620463\pi\)
\(44\) −184.203 + 365.381i −0.0951461 + 0.188730i
\(45\) −1110.31 1110.31i −0.548299 0.548299i
\(46\) −1732.56 + 2395.44i −0.818788 + 1.13206i
\(47\) 2018.46i 0.913746i −0.889532 0.456873i \(-0.848969\pi\)
0.889532 0.456873i \(-0.151031\pi\)
\(48\) 248.315 1659.76i 0.107776 0.720384i
\(49\) 1153.50 0.480424
\(50\) 3501.35 + 2532.44i 1.40054 + 1.01297i
\(51\) 1037.29 1037.29i 0.398803 0.398803i
\(52\) 517.171 1025.85i 0.191261 0.379383i
\(53\) 833.240 833.240i 0.296632 0.296632i −0.543061 0.839693i \(-0.682735\pi\)
0.839693 + 0.543061i \(0.182735\pi\)
\(54\) 3081.62 494.853i 1.05680 0.169703i
\(55\) 1056.09 0.349122
\(56\) 3636.41 + 1155.75i 1.15957 + 0.368542i
\(57\) 136.618i 0.0420492i
\(58\) −5244.06 + 842.101i −1.55888 + 0.250327i
\(59\) −2223.17 2223.17i −0.638660 0.638660i 0.311565 0.950225i \(-0.399147\pi\)
−0.950225 + 0.311565i \(0.899147\pi\)
\(60\) −4113.68 + 1356.14i −1.14269 + 0.376704i
\(61\) −341.374 341.374i −0.0917425 0.0917425i 0.659746 0.751489i \(-0.270664\pi\)
−0.751489 + 0.659746i \(0.770664\pi\)
\(62\) −3042.55 2200.60i −0.791507 0.572476i
\(63\) 2266.97i 0.571170i
\(64\) 3344.42 + 2364.76i 0.816508 + 0.577334i
\(65\) −2965.11 −0.701800
\(66\) −393.016 + 543.385i −0.0902240 + 0.124744i
\(67\) 4845.43 4845.43i 1.07940 1.07940i 0.0828379 0.996563i \(-0.473602\pi\)
0.996563 0.0828379i \(-0.0263984\pi\)
\(68\) 1120.96 + 3400.30i 0.242422 + 0.735360i
\(69\) −3426.03 + 3426.03i −0.719602 + 0.719602i
\(70\) −1561.41 9723.46i −0.318656 1.98438i
\(71\) −4180.93 −0.829386 −0.414693 0.909961i \(-0.636111\pi\)
−0.414693 + 0.909961i \(0.636111\pi\)
\(72\) −737.108 + 2319.21i −0.142189 + 0.447379i
\(73\) 9071.36i 1.70226i 0.524953 + 0.851131i \(0.324083\pi\)
−0.524953 + 0.851131i \(0.675917\pi\)
\(74\) 236.635 + 1473.61i 0.0432131 + 0.269103i
\(75\) 5007.74 + 5007.74i 0.890265 + 0.890265i
\(76\) −297.741 150.103i −0.0515479 0.0259873i
\(77\) −1078.14 1078.14i −0.181842 0.181842i
\(78\) 1103.44 1525.62i 0.181367 0.250759i
\(79\) 735.536i 0.117855i −0.998262 0.0589277i \(-0.981232\pi\)
0.998262 0.0589277i \(-0.0187682\pi\)
\(80\) 1564.19 10455.2i 0.244405 1.63363i
\(81\) 2035.24 0.310203
\(82\) 806.518 + 583.333i 0.119946 + 0.0867539i
\(83\) 1441.90 1441.90i 0.209305 0.209305i −0.594667 0.803972i \(-0.702716\pi\)
0.803972 + 0.594667i \(0.202716\pi\)
\(84\) 5584.02 + 2815.12i 0.791385 + 0.398968i
\(85\) 6534.10 6534.10i 0.904374 0.904374i
\(86\) −5780.81 + 928.294i −0.781613 + 0.125513i
\(87\) −8704.61 −1.15003
\(88\) −752.429 1453.55i −0.0971628 0.187700i
\(89\) 5071.77i 0.640294i 0.947368 + 0.320147i \(0.103732\pi\)
−0.947368 + 0.320147i \(0.896268\pi\)
\(90\) 6201.39 995.831i 0.765603 0.122942i
\(91\) 3027.01 + 3027.01i 0.365537 + 0.365537i
\(92\) −3702.39 11230.8i −0.437428 1.32689i
\(93\) −4351.55 4351.55i −0.503128 0.503128i
\(94\) 6542.05 + 4731.69i 0.740385 + 0.535501i
\(95\) 860.586i 0.0953558i
\(96\) 4797.36 + 4695.64i 0.520547 + 0.509509i
\(97\) −2523.85 −0.268238 −0.134119 0.990965i \(-0.542820\pi\)
−0.134119 + 0.990965i \(0.542820\pi\)
\(98\) −2704.03 + 3738.60i −0.281552 + 0.389275i
\(99\) 687.613 687.613i 0.0701575 0.0701575i
\(100\) −16415.7 + 5411.70i −1.64157 + 0.541170i
\(101\) 425.990 425.990i 0.0417596 0.0417596i −0.685919 0.727678i \(-0.740599\pi\)
0.727678 + 0.685919i \(0.240599\pi\)
\(102\) 930.341 + 5793.56i 0.0894215 + 0.556859i
\(103\) 13178.6 1.24221 0.621103 0.783729i \(-0.286685\pi\)
0.621103 + 0.783729i \(0.286685\pi\)
\(104\) 2112.53 + 4081.00i 0.195316 + 0.377312i
\(105\) 16140.0i 1.46394i
\(106\) 747.332 + 4653.90i 0.0665123 + 0.414195i
\(107\) −10821.5 10821.5i −0.945190 0.945190i 0.0533845 0.998574i \(-0.482999\pi\)
−0.998574 + 0.0533845i \(0.982999\pi\)
\(108\) −5620.07 + 11147.9i −0.481830 + 0.955750i
\(109\) −1428.57 1428.57i −0.120240 0.120240i 0.644426 0.764666i \(-0.277096\pi\)
−0.764666 + 0.644426i \(0.777096\pi\)
\(110\) −2475.69 + 3422.90i −0.204603 + 0.282885i
\(111\) 2446.04i 0.198526i
\(112\) −12270.4 + 9076.66i −0.978186 + 0.723586i
\(113\) 20121.5 1.57581 0.787904 0.615798i \(-0.211166\pi\)
0.787904 + 0.615798i \(0.211166\pi\)
\(114\) −442.792 320.260i −0.0340714 0.0246429i
\(115\) −21581.3 + 21581.3i −1.63186 + 1.63186i
\(116\) 9563.79 18970.6i 0.710745 1.40982i
\(117\) −1930.56 + 1930.56i −0.141030 + 0.141030i
\(118\) 12417.1 1993.96i 0.891776 0.143203i
\(119\) −13341.0 −0.942098
\(120\) 5247.92 16511.9i 0.364439 1.14666i
\(121\) 13987.0i 0.955328i
\(122\) 1906.68 306.178i 0.128102 0.0205709i
\(123\) 1153.51 + 1153.51i 0.0762447 + 0.0762447i
\(124\) 14264.7 4702.57i 0.927725 0.305839i
\(125\) 13294.8 + 13294.8i 0.850865 + 0.850865i
\(126\) −7347.48 5314.24i −0.462804 0.334734i
\(127\) 2630.54i 0.163094i −0.996669 0.0815470i \(-0.974014\pi\)
0.996669 0.0815470i \(-0.0259861\pi\)
\(128\) −15504.4 + 5296.11i −0.946314 + 0.323249i
\(129\) −9595.57 −0.576622
\(130\) 6950.80 9610.20i 0.411290 0.568651i
\(131\) 12437.0 12437.0i 0.724722 0.724722i −0.244841 0.969563i \(-0.578736\pi\)
0.969563 + 0.244841i \(0.0787357\pi\)
\(132\) −839.857 2547.61i −0.0482011 0.146213i
\(133\) 878.554 878.554i 0.0496667 0.0496667i
\(134\) 4345.86 + 27063.2i 0.242028 + 1.50719i
\(135\) 32221.6 1.76799
\(136\) −13648.5 4337.85i −0.737915 0.234529i
\(137\) 15392.0i 0.820078i 0.912068 + 0.410039i \(0.134485\pi\)
−0.912068 + 0.410039i \(0.865515\pi\)
\(138\) −3072.80 19135.4i −0.161353 1.00480i
\(139\) 12151.3 + 12151.3i 0.628915 + 0.628915i 0.947795 0.318880i \(-0.103307\pi\)
−0.318880 + 0.947795i \(0.603307\pi\)
\(140\) 35175.0 + 17733.0i 1.79464 + 0.904747i
\(141\) 9356.63 + 9356.63i 0.470632 + 0.470632i
\(142\) 9800.95 13550.8i 0.486062 0.672030i
\(143\) 1836.29i 0.0897987i
\(144\) −5788.87 7825.74i −0.279170 0.377399i
\(145\) −54832.3 −2.60796
\(146\) −29401.2 21265.1i −1.37930 0.997611i
\(147\) −5347.06 + 5347.06i −0.247446 + 0.247446i
\(148\) −5330.83 2687.48i −0.243373 0.122693i
\(149\) −20803.7 + 20803.7i −0.937062 + 0.937062i −0.998133 0.0610710i \(-0.980548\pi\)
0.0610710 + 0.998133i \(0.480548\pi\)
\(150\) −27969.7 + 4491.44i −1.24310 + 0.199619i
\(151\) −7756.67 −0.340190 −0.170095 0.985428i \(-0.554407\pi\)
−0.170095 + 0.985428i \(0.554407\pi\)
\(152\) 1184.46 613.137i 0.0512665 0.0265381i
\(153\) 8508.60i 0.363475i
\(154\) 6021.75 966.985i 0.253911 0.0407735i
\(155\) −27411.4 27411.4i −1.14095 1.14095i
\(156\) 2358.00 + 7152.71i 0.0968934 + 0.293915i
\(157\) 7040.20 + 7040.20i 0.285618 + 0.285618i 0.835345 0.549727i \(-0.185268\pi\)
−0.549727 + 0.835345i \(0.685268\pi\)
\(158\) 2383.95 + 1724.24i 0.0954953 + 0.0690692i
\(159\) 7725.00i 0.305565i
\(160\) 30219.6 + 29578.8i 1.18045 + 1.15542i
\(161\) 44063.8 1.69993
\(162\) −4771.01 + 6596.41i −0.181794 + 0.251349i
\(163\) 7273.43 7273.43i 0.273756 0.273756i −0.556854 0.830610i \(-0.687992\pi\)
0.830610 + 0.556854i \(0.187992\pi\)
\(164\) −3781.28 + 1246.56i −0.140589 + 0.0463472i
\(165\) −4895.54 + 4895.54i −0.179818 + 0.179818i
\(166\) 1293.24 + 8053.46i 0.0469313 + 0.292258i
\(167\) 30069.6 1.07819 0.539095 0.842245i \(-0.318766\pi\)
0.539095 + 0.842245i \(0.318766\pi\)
\(168\) −22214.1 + 11499.2i −0.787065 + 0.407425i
\(169\) 23405.4i 0.819488i
\(170\) 5860.43 + 36494.9i 0.202783 + 1.26280i
\(171\) 560.320 + 560.320i 0.0191621 + 0.0191621i
\(172\) 10542.7 20912.3i 0.356365 0.706878i
\(173\) −8329.72 8329.72i −0.278316 0.278316i 0.554121 0.832436i \(-0.313055\pi\)
−0.832436 + 0.554121i \(0.813055\pi\)
\(174\) 20405.3 28212.5i 0.673978 0.931844i
\(175\) 64406.9i 2.10308i
\(176\) 6474.93 + 968.707i 0.209031 + 0.0312728i
\(177\) 20611.1 0.657893
\(178\) −16438.1 11889.2i −0.518814 0.375244i
\(179\) −7537.56 + 7537.56i −0.235247 + 0.235247i −0.814879 0.579632i \(-0.803197\pi\)
0.579632 + 0.814879i \(0.303197\pi\)
\(180\) −11309.7 + 22433.7i −0.349065 + 0.692399i
\(181\) 3802.64 3802.64i 0.116072 0.116072i −0.646685 0.762757i \(-0.723845\pi\)
0.762757 + 0.646685i \(0.223845\pi\)
\(182\) −16906.8 + 2714.92i −0.510409 + 0.0819624i
\(183\) 3164.89 0.0945054
\(184\) 45079.2 + 14327.4i 1.33150 + 0.423185i
\(185\) 15408.2i 0.450202i
\(186\) 24304.7 3902.90i 0.702530 0.112814i
\(187\) 4046.58 + 4046.58i 0.115719 + 0.115719i
\(188\) −30671.7 + 10111.4i −0.867806 + 0.286085i
\(189\) −32894.4 32894.4i −0.920869 0.920869i
\(190\) −2789.25 2017.39i −0.0772644 0.0558833i
\(191\) 52248.1i 1.43220i 0.697997 + 0.716100i \(0.254075\pi\)
−0.697997 + 0.716100i \(0.745925\pi\)
\(192\) −26465.0 + 4541.21i −0.717909 + 0.123188i
\(193\) −24380.0 −0.654514 −0.327257 0.944935i \(-0.606124\pi\)
−0.327257 + 0.944935i \(0.606124\pi\)
\(194\) 5916.41 8180.04i 0.157201 0.217346i
\(195\) 13744.8 13744.8i 0.361468 0.361468i
\(196\) −5778.38 17528.0i −0.150416 0.456269i
\(197\) 31537.9 31537.9i 0.812644 0.812644i −0.172386 0.985030i \(-0.555148\pi\)
0.985030 + 0.172386i \(0.0551476\pi\)
\(198\) 616.720 + 3840.53i 0.0157310 + 0.0979626i
\(199\) −71129.4 −1.79615 −0.898076 0.439841i \(-0.855035\pi\)
−0.898076 + 0.439841i \(0.855035\pi\)
\(200\) 20942.0 65891.2i 0.523549 1.64728i
\(201\) 44922.2i 1.11191i
\(202\) 382.069 + 2379.28i 0.00936353 + 0.0583099i
\(203\) 55977.1 + 55977.1i 1.35837 + 1.35837i
\(204\) −20958.4 10565.9i −0.503614 0.253891i
\(205\) 7266.19 + 7266.19i 0.172902 + 0.172902i
\(206\) −30893.2 + 42713.0i −0.727995 + 1.00653i
\(207\) 28102.8i 0.655857i
\(208\) −18179.1 2719.76i −0.420191 0.0628643i
\(209\) −532.962 −0.0122012
\(210\) 52311.2 + 37835.3i 1.18620 + 0.857943i
\(211\) −13393.4 + 13393.4i −0.300833 + 0.300833i −0.841340 0.540507i \(-0.818233\pi\)
0.540507 + 0.841340i \(0.318233\pi\)
\(212\) −16835.6 8487.49i −0.374591 0.188846i
\(213\) 19380.8 19380.8i 0.427181 0.427181i
\(214\) 60441.2 9705.77i 1.31979 0.211935i
\(215\) −60444.6 −1.30762
\(216\) −22956.8 44348.0i −0.492044 0.950532i
\(217\) 55967.4i 1.18854i
\(218\) 7978.99 1281.28i 0.167894 0.0269607i
\(219\) −42050.4 42050.4i −0.876763 0.876763i
\(220\) −5290.44 16047.9i −0.109307 0.331569i
\(221\) −11361.2 11361.2i −0.232617 0.232617i
\(222\) −7927.86 5734.01i −0.160861 0.116346i
\(223\) 54266.9i 1.09125i 0.838029 + 0.545626i \(0.183708\pi\)
−0.838029 + 0.545626i \(0.816292\pi\)
\(224\) −654.161 61047.0i −0.0130373 1.21666i
\(225\) 41077.2 0.811401
\(226\) −47168.8 + 65215.7i −0.923502 + 1.27684i
\(227\) 14529.0 14529.0i 0.281957 0.281957i −0.551932 0.833889i \(-0.686109\pi\)
0.833889 + 0.551932i \(0.186109\pi\)
\(228\) 2075.99 684.380i 0.0399351 0.0131652i
\(229\) 21618.1 21618.1i 0.412237 0.412237i −0.470280 0.882517i \(-0.655847\pi\)
0.882517 + 0.470280i \(0.155847\pi\)
\(230\) −19356.2 120538.i −0.365902 2.27860i
\(231\) 9995.50 0.187318
\(232\) 39066.0 + 75468.0i 0.725811 + 1.40213i
\(233\) 92103.6i 1.69654i −0.529562 0.848271i \(-0.677644\pi\)
0.529562 0.848271i \(-0.322356\pi\)
\(234\) −1731.51 10782.7i −0.0316223 0.196923i
\(235\) 58939.5 + 58939.5i 1.06726 + 1.06726i
\(236\) −22645.5 + 44919.3i −0.406592 + 0.806508i
\(237\) 3409.59 + 3409.59i 0.0607024 + 0.0607024i
\(238\) 31274.1 43239.6i 0.552116 0.763358i
\(239\) 70411.0i 1.23266i −0.787487 0.616332i \(-0.788618\pi\)
0.787487 0.616332i \(-0.211382\pi\)
\(240\) 41214.5 + 55716.2i 0.715530 + 0.967296i
\(241\) 22402.6 0.385714 0.192857 0.981227i \(-0.438225\pi\)
0.192857 + 0.981227i \(0.438225\pi\)
\(242\) 45333.1 + 32788.2i 0.774078 + 0.559870i
\(243\) 35256.4 35256.4i 0.597070 0.597070i
\(244\) −3477.28 + 6897.47i −0.0584063 + 0.115854i
\(245\) −33682.3 + 33682.3i −0.561138 + 0.561138i
\(246\) −6442.68 + 1034.58i −0.106462 + 0.0170959i
\(247\) 1496.35 0.0245268
\(248\) −18197.8 + 57257.1i −0.295880 + 0.930949i
\(249\) 13367.9i 0.215608i
\(250\) −74255.3 + 11924.1i −1.18808 + 0.190785i
\(251\) −72407.6 72407.6i −1.14931 1.14931i −0.986689 0.162621i \(-0.948005\pi\)
−0.162621 0.986689i \(-0.551995\pi\)
\(252\) 34447.9 11356.3i 0.542453 0.178828i
\(253\) −13365.3 13365.3i −0.208804 0.208804i
\(254\) 8525.85 + 6166.52i 0.132151 + 0.0955813i
\(255\) 60577.9i 0.931609i
\(256\) 19180.2 62666.5i 0.292667 0.956214i
\(257\) −56466.3 −0.854916 −0.427458 0.904035i \(-0.640591\pi\)
−0.427458 + 0.904035i \(0.640591\pi\)
\(258\) 22493.9 31100.2i 0.337929 0.467222i
\(259\) 15729.9 15729.9i 0.234490 0.234490i
\(260\) 14853.5 + 45056.5i 0.219727 + 0.666516i
\(261\) −35700.8 + 35700.8i −0.524080 + 0.524080i
\(262\) 11154.7 + 69464.1i 0.162501 + 1.01195i
\(263\) 76515.5 1.10621 0.553105 0.833111i \(-0.313443\pi\)
0.553105 + 0.833111i \(0.313443\pi\)
\(264\) 10225.8 + 3250.04i 0.146721 + 0.0466317i
\(265\) 48661.5i 0.692937i
\(266\) 787.974 + 4906.99i 0.0111365 + 0.0693508i
\(267\) −23510.3 23510.3i −0.329788 0.329788i
\(268\) −97902.0 49356.2i −1.36308 0.687182i
\(269\) 1928.97 + 1928.97i 0.0266576 + 0.0266576i 0.720310 0.693652i \(-0.244000\pi\)
−0.693652 + 0.720310i \(0.744000\pi\)
\(270\) −75534.0 + 104434.i −1.03613 + 1.43256i
\(271\) 128685.i 1.75222i −0.482109 0.876111i \(-0.660129\pi\)
0.482109 0.876111i \(-0.339871\pi\)
\(272\) 46054.2 34067.3i 0.622488 0.460468i
\(273\) −28063.5 −0.376545
\(274\) −49887.1 36082.0i −0.664488 0.480607i
\(275\) −19535.8 + 19535.8i −0.258324 + 0.258324i
\(276\) 69222.9 + 34897.9i 0.908724 + 0.458122i
\(277\) 56674.5 56674.5i 0.738632 0.738632i −0.233681 0.972313i \(-0.575077\pi\)
0.972313 + 0.233681i \(0.0750772\pi\)
\(278\) −67868.5 + 10898.5i −0.878170 + 0.141018i
\(279\) −35694.6 −0.458558
\(280\) −139932. + 72435.7i −1.78484 + 0.923925i
\(281\) 10599.7i 0.134240i 0.997745 + 0.0671200i \(0.0213810\pi\)
−0.997745 + 0.0671200i \(0.978619\pi\)
\(282\) −52259.6 + 8391.95i −0.657155 + 0.105527i
\(283\) 63293.6 + 63293.6i 0.790291 + 0.790291i 0.981541 0.191251i \(-0.0612543\pi\)
−0.191251 + 0.981541i \(0.561254\pi\)
\(284\) 20944.2 + 63531.7i 0.259673 + 0.787687i
\(285\) −3989.26 3989.26i −0.0491137 0.0491137i
\(286\) 5951.61 + 4304.64i 0.0727617 + 0.0526266i
\(287\) 14835.8i 0.180114i
\(288\) 38934.3 417.208i 0.469405 0.00503000i
\(289\) −33448.2 −0.400477
\(290\) 128538. 177717.i 1.52839 2.11316i
\(291\) 11699.3 11699.3i 0.138158 0.138158i
\(292\) 137844. 45442.5i 1.61668 0.532962i
\(293\) −89072.9 + 89072.9i −1.03755 + 1.03755i −0.0382867 + 0.999267i \(0.512190\pi\)
−0.999267 + 0.0382867i \(0.987810\pi\)
\(294\) −4795.77 29864.9i −0.0554835 0.345515i
\(295\) 129834. 1.49192
\(296\) 21206.9 10977.8i 0.242044 0.125294i
\(297\) 19954.9i 0.226223i
\(298\) −18658.8 116195.i −0.210113 1.30844i
\(299\) 37524.7 + 37524.7i 0.419735 + 0.419735i
\(300\) 51009.5 101182.i 0.566772 1.12424i
\(301\) 61706.6 + 61706.6i 0.681080 + 0.681080i
\(302\) 18183.2 25140.1i 0.199368 0.275647i
\(303\) 3949.36i 0.0430172i
\(304\) −789.377 + 5276.27i −0.00854157 + 0.0570927i
\(305\) 19936.3 0.214312
\(306\) 27577.2 + 19945.9i 0.294515 + 0.213015i
\(307\) −124227. + 124227.i −1.31807 + 1.31807i −0.402769 + 0.915302i \(0.631952\pi\)
−0.915302 + 0.402769i \(0.868048\pi\)
\(308\) −10982.1 + 21783.9i −0.115767 + 0.229633i
\(309\) −61089.5 + 61089.5i −0.639808 + 0.639808i
\(310\) 153101. 24585.2i 1.59314 0.255830i
\(311\) 15733.9 0.162673 0.0813364 0.996687i \(-0.474081\pi\)
0.0813364 + 0.996687i \(0.474081\pi\)
\(312\) −28710.3 9124.88i −0.294936 0.0937385i
\(313\) 104554.i 1.06721i −0.845733 0.533606i \(-0.820837\pi\)
0.845733 0.533606i \(-0.179163\pi\)
\(314\) −39321.6 + 6314.34i −0.398816 + 0.0640426i
\(315\) −66196.0 66196.0i −0.667130 0.667130i
\(316\) −11176.9 + 3684.63i −0.111930 + 0.0368994i
\(317\) 45847.9 + 45847.9i 0.456248 + 0.456248i 0.897422 0.441174i \(-0.145438\pi\)
−0.441174 + 0.897422i \(0.645438\pi\)
\(318\) −25037.5 18108.9i −0.247592 0.179077i
\(319\) 33957.7i 0.333700i
\(320\) −166709. + 28606.1i −1.62802 + 0.279356i
\(321\) 100326. 0.973654
\(322\) −103294. + 142815.i −0.996241 + 1.37741i
\(323\) −3297.46 + 3297.46i −0.0316064 + 0.0316064i
\(324\) −10195.4 30926.6i −0.0971215 0.294607i
\(325\) 54849.0 54849.0i 0.519281 0.519281i
\(326\) 6523.53 + 40624.3i 0.0613829 + 0.382253i
\(327\) 13244.3 0.123861
\(328\) 4823.87 15177.7i 0.0448382 0.141077i
\(329\) 120340.i 1.11178i
\(330\) −4390.80 27343.1i −0.0403196 0.251084i
\(331\) −137545. 137545.i −1.25542 1.25542i −0.953258 0.302159i \(-0.902293\pi\)
−0.302159 0.953258i \(-0.597707\pi\)
\(332\) −29133.7 14687.4i −0.264313 0.133250i
\(333\) 10032.1 + 10032.1i 0.0904700 + 0.0904700i
\(334\) −70489.2 + 97458.6i −0.631873 + 0.873630i
\(335\) 282975.i 2.52149i
\(336\) 14804.5 98954.5i 0.131134 0.876510i
\(337\) −40849.6 −0.359690 −0.179845 0.983695i \(-0.557560\pi\)
−0.179845 + 0.983695i \(0.557560\pi\)
\(338\) 75859.2 + 54866.9i 0.664010 + 0.480261i
\(339\) −93273.5 + 93273.5i −0.811632 + 0.811632i
\(340\) −132022. 66557.2i −1.14206 0.575754i
\(341\) 16975.9 16975.9i 0.145990 0.145990i
\(342\) −3129.56 + 502.551i −0.0267566 + 0.00429663i
\(343\) −74375.6 −0.632182
\(344\) 43064.6 + 83192.5i 0.363918 + 0.703019i
\(345\) 200081.i 1.68100i
\(346\) 46524.0 7470.91i 0.388619 0.0624053i
\(347\) 21361.1 + 21361.1i 0.177404 + 0.177404i 0.790223 0.612819i \(-0.209965\pi\)
−0.612819 + 0.790223i \(0.709965\pi\)
\(348\) 43605.3 + 132272.i 0.360065 + 1.09221i
\(349\) 139275. + 139275.i 1.14347 + 1.14347i 0.987812 + 0.155654i \(0.0497484\pi\)
0.155654 + 0.987812i \(0.450252\pi\)
\(350\) 208749. + 150983.i 1.70408 + 1.23251i
\(351\) 56025.8i 0.454751i
\(352\) −18318.2 + 18715.1i −0.147842 + 0.151045i
\(353\) −100461. −0.806209 −0.403105 0.915154i \(-0.632069\pi\)
−0.403105 + 0.915154i \(0.632069\pi\)
\(354\) −48316.6 + 66802.7i −0.385558 + 0.533074i
\(355\) 122084. 122084.i 0.968728 0.968728i
\(356\) 77068.4 25406.7i 0.608102 0.200470i
\(357\) 61842.6 61842.6i 0.485234 0.485234i
\(358\) −6760.42 42099.5i −0.0527482 0.328482i
\(359\) 96352.7 0.747609 0.373805 0.927507i \(-0.378053\pi\)
0.373805 + 0.927507i \(0.378053\pi\)
\(360\) −46197.7 89245.1i −0.356464 0.688619i
\(361\) 129887.i 0.996667i
\(362\) 3410.58 + 21238.9i 0.0260262 + 0.162074i
\(363\) 64836.8 + 64836.8i 0.492049 + 0.492049i
\(364\) 30833.5 61160.9i 0.232713 0.461605i
\(365\) −264885. 264885.i −1.98825 1.98825i
\(366\) −7419.14 + 10257.7i −0.0553849 + 0.0765753i
\(367\) 190661.i 1.41557i −0.706429 0.707784i \(-0.749695\pi\)
0.706429 0.707784i \(-0.250305\pi\)
\(368\) −152111. + 112520.i −1.12322 + 0.830871i
\(369\) 9461.91 0.0694906
\(370\) −49939.4 36119.8i −0.364787 0.263841i
\(371\) 49677.5 49677.5i 0.360920 0.360920i
\(372\) −44325.4 + 87923.2i −0.320308 + 0.635356i
\(373\) 51771.9 51771.9i 0.372114 0.372114i −0.496133 0.868247i \(-0.665247\pi\)
0.868247 + 0.496133i \(0.165247\pi\)
\(374\) −22601.3 + 3629.37i −0.161581 + 0.0259471i
\(375\) −123256. −0.876489
\(376\) 39128.7 123113.i 0.276770 0.870821i
\(377\) 95340.2i 0.670801i
\(378\) 183725. 29502.9i 1.28583 0.206482i
\(379\) 121232. + 121232.i 0.843990 + 0.843990i 0.989375 0.145385i \(-0.0464420\pi\)
−0.145385 + 0.989375i \(0.546442\pi\)
\(380\) 13077.1 4311.06i 0.0905616 0.0298550i
\(381\) 12193.9 + 12193.9i 0.0840028 + 0.0840028i
\(382\) −169341. 122480.i −1.16048 0.839341i
\(383\) 8262.20i 0.0563246i 0.999603 + 0.0281623i \(0.00896552\pi\)
−0.999603 + 0.0281623i \(0.991034\pi\)
\(384\) 47320.8 96421.2i 0.320914 0.653898i
\(385\) 62963.9 0.424786
\(386\) 57151.6 79018.0i 0.383578 0.530336i
\(387\) −39355.0 + 39355.0i −0.262771 + 0.262771i
\(388\) 12643.1 + 38351.3i 0.0839826 + 0.254752i
\(389\) 43964.9 43964.9i 0.290541 0.290541i −0.546753 0.837294i \(-0.684136\pi\)
0.837294 + 0.546753i \(0.184136\pi\)
\(390\) 12327.7 + 76768.9i 0.0810499 + 0.504726i
\(391\) −165384. −1.08178
\(392\) 70355.8 + 22360.9i 0.457855 + 0.145518i
\(393\) 115303.i 0.746547i
\(394\) 28286.3 + 176149.i 0.182215 + 1.13471i
\(395\) 21477.8 + 21477.8i 0.137656 + 0.137656i
\(396\) −13893.2 7004.12i −0.0885958 0.0446645i
\(397\) 72864.3 + 72864.3i 0.462311 + 0.462311i 0.899412 0.437101i \(-0.143995\pi\)
−0.437101 + 0.899412i \(0.643995\pi\)
\(398\) 166742. 230537.i 1.05263 1.45538i
\(399\) 8145.10i 0.0511624i
\(400\) 164468. + 222337.i 1.02792 + 1.38961i
\(401\) 237249. 1.47542 0.737711 0.675116i \(-0.235907\pi\)
0.737711 + 0.675116i \(0.235907\pi\)
\(402\) −145597. 105307.i −0.900950 0.651633i
\(403\) −47661.9 + 47661.9i −0.293468 + 0.293468i
\(404\) −8607.13 4339.18i −0.0527346 0.0265855i
\(405\) −59429.3 + 59429.3i −0.362319 + 0.362319i
\(406\) −312649. + 50205.8i −1.89673 + 0.304580i
\(407\) −9542.29 −0.0576055
\(408\) 83376.0 43159.6i 0.500865 0.259273i
\(409\) 150042.i 0.896945i 0.893797 + 0.448473i \(0.148032\pi\)
−0.893797 + 0.448473i \(0.851968\pi\)
\(410\) −40583.9 + 6517.04i −0.241427 + 0.0387688i
\(411\) −71350.1 71350.1i −0.422387 0.422387i
\(412\) −66017.3 200256.i −0.388923 1.17975i
\(413\) −132545. 132545.i −0.777074 0.777074i
\(414\) −91084.0 65878.6i −0.531424 0.384365i
\(415\) 84207.5i 0.488939i
\(416\) 51430.6 52544.7i 0.297190 0.303629i
\(417\) −112655. −0.647855
\(418\) 1249.37 1727.38i 0.00715053 0.00988635i
\(419\) 71760.1 71760.1i 0.408747 0.408747i −0.472554 0.881302i \(-0.656668\pi\)
0.881302 + 0.472554i \(0.156668\pi\)
\(420\) −245256. + 80852.3i −1.39034 + 0.458346i
\(421\) −209821. + 209821.i −1.18382 + 1.18382i −0.205070 + 0.978747i \(0.565742\pi\)
−0.978747 + 0.205070i \(0.934258\pi\)
\(422\) −12012.5 74806.1i −0.0674542 0.420061i
\(423\) 76750.0 0.428941
\(424\) 66974.9 34669.6i 0.372546 0.192849i
\(425\) 241738.i 1.33834i
\(426\) 17382.6 + 108248.i 0.0957846 + 0.596484i
\(427\) −20352.6 20352.6i −0.111626 0.111626i
\(428\) −110229. + 218648.i −0.601739 + 1.19360i
\(429\) 8512.18 + 8512.18i 0.0462515 + 0.0462515i
\(430\) 141694. 195907.i 0.766329 1.05953i
\(431\) 123853.i 0.666731i 0.942798 + 0.333366i \(0.108184\pi\)
−0.942798 + 0.333366i \(0.891816\pi\)
\(432\) 197552. + 29555.5i 1.05855 + 0.158369i
\(433\) −265114. −1.41402 −0.707012 0.707202i \(-0.749957\pi\)
−0.707012 + 0.707202i \(0.749957\pi\)
\(434\) −181396. 131199.i −0.963047 0.696547i
\(435\) 254176. 254176.i 1.34325 1.34325i
\(436\) −14551.6 + 28864.3i −0.0765486 + 0.151841i
\(437\) 10891.1 10891.1i 0.0570307 0.0570307i
\(438\) 234864. 37715.0i 1.22425 0.196592i
\(439\) 186089. 0.965590 0.482795 0.875734i \(-0.339622\pi\)
0.482795 + 0.875734i \(0.339622\pi\)
\(440\) 64414.8 + 20472.7i 0.332721 + 0.105748i
\(441\) 43860.5i 0.225526i
\(442\) 63456.0 10189.9i 0.324809 0.0521585i
\(443\) 25618.8 + 25618.8i 0.130542 + 0.130542i 0.769359 0.638817i \(-0.220576\pi\)
−0.638817 + 0.769359i \(0.720576\pi\)
\(444\) 37169.0 12253.3i 0.188545 0.0621567i
\(445\) −148096. 148096.i −0.747867 0.747867i
\(446\) −175884. 127212.i −0.884214 0.639529i
\(447\) 192872.i 0.965282i
\(448\) 199393. + 140986.i 0.993467 + 0.702458i
\(449\) −2307.59 −0.0114463 −0.00572316 0.999984i \(-0.501822\pi\)
−0.00572316 + 0.999984i \(0.501822\pi\)
\(450\) −96293.2 + 133135.i −0.475522 + 0.657458i
\(451\) −4499.96 + 4499.96i −0.0221236 + 0.0221236i
\(452\) −100798. 305758.i −0.493370 1.49658i
\(453\) 35956.2 35956.2i 0.175217 0.175217i
\(454\) 13031.0 + 81148.6i 0.0632217 + 0.393704i
\(455\) −176778. −0.853899
\(456\) −2648.39 + 8332.80i −0.0127365 + 0.0400739i
\(457\) 262378.i 1.25631i −0.778090 0.628153i \(-0.783811\pi\)
0.778090 0.628153i \(-0.216189\pi\)
\(458\) 19389.3 + 120744.i 0.0924338 + 0.575617i
\(459\) 123462. + 123462.i 0.586014 + 0.586014i
\(460\) 436051. + 219830.i 2.06073 + 1.03889i
\(461\) 136771. + 136771.i 0.643564 + 0.643564i 0.951430 0.307866i \(-0.0996148\pi\)
−0.307866 + 0.951430i \(0.599615\pi\)
\(462\) −23431.5 + 32396.4i −0.109778 + 0.151779i
\(463\) 22250.8i 0.103797i −0.998652 0.0518983i \(-0.983473\pi\)
0.998652 0.0518983i \(-0.0165272\pi\)
\(464\) −336178. 50295.2i −1.56147 0.233610i
\(465\) 254132. 1.17531
\(466\) 298517. + 215909.i 1.37467 + 0.994259i
\(467\) 175541. 175541.i 0.804906 0.804906i −0.178952 0.983858i \(-0.557271\pi\)
0.983858 + 0.178952i \(0.0572708\pi\)
\(468\) 39006.9 + 19664.9i 0.178094 + 0.0897842i
\(469\) 288883. 288883.i 1.31334 1.31334i
\(470\) −329195. + 52862.7i −1.49024 + 0.239306i
\(471\) −65269.9 −0.294219
\(472\) −92502.2 178696.i −0.415210 0.802105i
\(473\) 37433.4i 0.167316i
\(474\) −19043.6 + 3058.06i −0.0847602 + 0.0136110i
\(475\) −15919.3 15919.3i −0.0705563 0.0705563i
\(476\) 66831.3 + 202725.i 0.294962 + 0.894732i
\(477\) 31683.1 + 31683.1i 0.139249 + 0.139249i
\(478\) 228209. + 165057.i 0.998796 + 0.722403i
\(479\) 117920.i 0.513945i −0.966419 0.256973i \(-0.917275\pi\)
0.966419 0.256973i \(-0.0827250\pi\)
\(480\) −277197. + 2970.36i −1.20311 + 0.0128922i
\(481\) 26791.1 0.115798
\(482\) −52516.3 + 72609.2i −0.226048 + 0.312534i
\(483\) −204258. + 204258.i −0.875559 + 0.875559i
\(484\) −212540. + 70066.9i −0.907297 + 0.299104i
\(485\) 73696.7 73696.7i 0.313303 0.313303i
\(486\) 31621.4 + 196917.i 0.133878 + 0.833703i
\(487\) −449942. −1.89714 −0.948568 0.316574i \(-0.897467\pi\)
−0.948568 + 0.316574i \(0.897467\pi\)
\(488\) −14203.9 27439.2i −0.0596443 0.115221i
\(489\) 67432.3i 0.282001i
\(490\) −30209.6 188126.i −0.125821 0.783531i
\(491\) −122509. 122509.i −0.508166 0.508166i 0.405797 0.913963i \(-0.366994\pi\)
−0.913963 + 0.405797i \(0.866994\pi\)
\(492\) 11749.8 23306.6i 0.0485399 0.0962829i
\(493\) −210098. 210098.i −0.864426 0.864426i
\(494\) −3507.75 + 4849.83i −0.0143739 + 0.0198734i
\(495\) 40156.8i 0.163889i
\(496\) −142917. 193203.i −0.580924 0.785327i
\(497\) −249266. −1.00914
\(498\) −43326.8 31337.1i −0.174702 0.126357i
\(499\) −44886.9 + 44886.9i −0.180268 + 0.180268i −0.791473 0.611205i \(-0.790685\pi\)
0.611205 + 0.791473i \(0.290685\pi\)
\(500\) 135422. 268621.i 0.541689 1.07448i
\(501\) −139388. + 139388.i −0.555330 + 0.555330i
\(502\) 404418. 64942.3i 1.60481 0.257704i
\(503\) 235778. 0.931896 0.465948 0.884812i \(-0.345713\pi\)
0.465948 + 0.884812i \(0.345713\pi\)
\(504\) −43946.1 + 138271.i −0.173005 + 0.544338i
\(505\) 24877.9i 0.0975509i
\(506\) 74649.4 11987.3i 0.291558 0.0468190i
\(507\) 108496. + 108496.i 0.422083 + 0.422083i
\(508\) −39972.6 + 13177.6i −0.154894 + 0.0510632i
\(509\) 227812. + 227812.i 0.879308 + 0.879308i 0.993463 0.114155i \(-0.0364161\pi\)
−0.114155 + 0.993463i \(0.536416\pi\)
\(510\) −196339. 142007.i −0.754859 0.545970i
\(511\) 540831.i 2.07119i
\(512\) 158146. + 209068.i 0.603279 + 0.797530i
\(513\) −16260.8 −0.0617884
\(514\) 132368. 183013.i 0.501024 0.692717i
\(515\) −384816. + 384816.i −1.45090 + 1.45090i
\(516\) 48068.5 + 145810.i 0.180535 + 0.547631i
\(517\) −36501.3 + 36501.3i −0.136561 + 0.136561i
\(518\) 14108.1 + 87856.0i 0.0525785 + 0.327425i
\(519\) 77225.1 0.286697
\(520\) −180852. 57479.6i −0.668832 0.212573i
\(521\) 539683.i 1.98822i −0.108395 0.994108i \(-0.534571\pi\)
0.108395 0.994108i \(-0.465429\pi\)
\(522\) −32020.0 199400.i −0.117512 0.731785i
\(523\) −175071. 175071.i −0.640044 0.640044i 0.310522 0.950566i \(-0.399496\pi\)
−0.950566 + 0.310522i \(0.899496\pi\)
\(524\) −251289. 126684.i −0.915189 0.461382i
\(525\) 298560. + 298560.i 1.08321 + 1.08321i
\(526\) −179368. + 247994.i −0.648295 + 0.896334i
\(527\) 210062.i 0.756354i
\(528\) −34505.1 + 25524.2i −0.123770 + 0.0915555i
\(529\) 266401. 0.951972
\(530\) −157717. 114072.i −0.561469 0.406096i
\(531\) 84533.9 84533.9i 0.299807 0.299807i
\(532\) −17751.2 8949.06i −0.0627198 0.0316194i
\(533\) 12634.2 12634.2i 0.0444726 0.0444726i
\(534\) 131312. 21086.3i 0.460491 0.0739466i
\(535\) 631977. 2.20797
\(536\) 389470. 201609.i 1.35564 0.701748i
\(537\) 69880.9i 0.242332i
\(538\) −10773.9 + 1730.09i −0.0372227 + 0.00597729i
\(539\) −20859.5 20859.5i −0.0718003 0.0718003i
\(540\) −161413. 489626.i −0.553541 1.67910i
\(541\) −142203. 142203.i −0.485863 0.485863i 0.421135 0.906998i \(-0.361632\pi\)
−0.906998 + 0.421135i \(0.861632\pi\)
\(542\) 417081. + 301663.i 1.41978 + 1.02689i
\(543\) 35254.4i 0.119568i
\(544\) 2455.25 + 229127.i 0.00829657 + 0.774244i
\(545\) 83428.9 0.280882
\(546\) 65786.6 90956.7i 0.220674 0.305105i
\(547\) −265412. + 265412.i −0.887045 + 0.887045i −0.994238 0.107193i \(-0.965814\pi\)
0.107193 + 0.994238i \(0.465814\pi\)
\(548\) 233891. 77105.6i 0.778847 0.256758i
\(549\) 12980.4 12980.4i 0.0430668 0.0430668i
\(550\) −17521.6 109113.i −0.0579227 0.360705i
\(551\) 27671.3 0.0911438
\(552\) −275380. + 142551.i −0.903763 + 0.467833i
\(553\) 43852.4i 0.143398i
\(554\) 50831.3 + 316544.i 0.165620 + 1.03137i
\(555\) −71424.8 71424.8i −0.231880 0.231880i
\(556\) 123774. 245517.i 0.400388 0.794203i
\(557\) 168105. + 168105.i 0.541837 + 0.541837i 0.924067 0.382230i \(-0.124844\pi\)
−0.382230 + 0.924067i \(0.624844\pi\)
\(558\) 83675.4 115690.i 0.268738 0.371558i
\(559\) 105099.i 0.336336i
\(560\) 93256.6 623336.i 0.297374 1.98768i
\(561\) −37516.0 −0.119204
\(562\) −34354.8 24847.9i −0.108771 0.0786714i
\(563\) −181113. + 181113.i −0.571389 + 0.571389i −0.932517 0.361127i \(-0.882392\pi\)
0.361127 + 0.932517i \(0.382392\pi\)
\(564\) 95307.8 189051.i 0.299620 0.594320i
\(565\) −587551. + 587551.i −1.84055 + 1.84055i
\(566\) −353514. + 56767.9i −1.10350 + 0.177203i
\(567\) 121340. 0.377432
\(568\) −255010. 81048.9i −0.790424 0.251218i
\(569\) 124083.i 0.383254i 0.981468 + 0.191627i \(0.0613765\pi\)
−0.981468 + 0.191627i \(0.938624\pi\)
\(570\) 22281.2 3577.96i 0.0685787 0.0110125i
\(571\) −92801.0 92801.0i −0.284630 0.284630i 0.550322 0.834952i \(-0.314505\pi\)
−0.834952 + 0.550322i \(0.814505\pi\)
\(572\) −27903.5 + 9198.82i −0.0852840 + 0.0281151i
\(573\) −242197. 242197.i −0.737666 0.737666i
\(574\) 48084.3 + 34778.1i 0.145942 + 0.105556i
\(575\) 798429.i 2.41491i
\(576\) −89917.6 + 127168.i −0.271019 + 0.383294i
\(577\) 182478. 0.548098 0.274049 0.961716i \(-0.411637\pi\)
0.274049 + 0.961716i \(0.411637\pi\)
\(578\) 78409.4 108409.i 0.234700 0.324496i
\(579\) 113014. 113014.i 0.337112 0.337112i
\(580\) 274679. + 833208.i 0.816526 + 2.47684i
\(581\) 85965.6 85965.6i 0.254667 0.254667i
\(582\) 10493.1 + 65344.3i 0.0309784 + 0.192913i
\(583\) −30136.1 −0.0886646
\(584\) −175851. + 553294.i −0.515609 + 1.62230i
\(585\) 112745.i 0.329447i
\(586\) −79889.4 497499.i −0.232645 1.44876i
\(587\) 197015. + 197015.i 0.571772 + 0.571772i 0.932623 0.360851i \(-0.117514\pi\)
−0.360851 + 0.932623i \(0.617514\pi\)
\(588\) 108037. + 54465.8i 0.312478 + 0.157532i
\(589\) 13833.3 + 13833.3i 0.0398744 + 0.0398744i
\(590\) −304357. + 420805.i −0.874338 + 1.20886i
\(591\) 292389.i 0.837116i
\(592\) −14133.2 + 94467.8i −0.0403272 + 0.269551i
\(593\) −478257. −1.36004 −0.680020 0.733194i \(-0.738029\pi\)
−0.680020 + 0.733194i \(0.738029\pi\)
\(594\) −64675.8 46778.3i −0.183303 0.132578i
\(595\) 389561. 389561.i 1.10038 1.10038i
\(596\) 420340. + 211909.i 1.18334 + 0.596565i
\(597\) 329722. 329722.i 0.925121 0.925121i
\(598\) −209587. + 33655.9i −0.586087 + 0.0941150i
\(599\) −141800. −0.395206 −0.197603 0.980282i \(-0.563316\pi\)
−0.197603 + 0.980282i \(0.563316\pi\)
\(600\) 208363. + 402516.i 0.578786 + 1.11810i
\(601\) 50813.1i 0.140678i −0.997523 0.0703391i \(-0.977592\pi\)
0.997523 0.0703391i \(-0.0224081\pi\)
\(602\) −344650. + 55344.5i −0.951010 + 0.152715i
\(603\) 184242. + 184242.i 0.506705 + 0.506705i
\(604\) 38856.6 + 117867.i 0.106510 + 0.323086i
\(605\) 408421. + 408421.i 1.11583 + 1.11583i
\(606\) −12800.3 9258.10i −0.0348557 0.0252102i
\(607\) 448023.i 1.21597i −0.793948 0.607985i \(-0.791978\pi\)
0.793948 0.607985i \(-0.208022\pi\)
\(608\) −15250.5 14927.1i −0.0412550 0.0403802i
\(609\) −518965. −1.39928
\(610\) −46734.8 + 64615.7i −0.125597 + 0.173651i
\(611\) 102482. 102482.i 0.274514 0.274514i
\(612\) −129293. + 42623.4i −0.345201 + 0.113801i
\(613\) 8742.04 8742.04i 0.0232644 0.0232644i −0.695379 0.718643i \(-0.744763\pi\)
0.718643 + 0.695379i \(0.244763\pi\)
\(614\) −111419. 693844.i −0.295544 1.84045i
\(615\) −67365.1 −0.178109
\(616\) −44859.5 86659.9i −0.118221 0.228379i
\(617\) 488336.i 1.28277i 0.767220 + 0.641384i \(0.221639\pi\)
−0.767220 + 0.641384i \(0.778361\pi\)
\(618\) −54791.1 341203.i −0.143461 0.893380i
\(619\) −416206. 416206.i −1.08624 1.08624i −0.995912 0.0903309i \(-0.971208\pi\)
−0.0903309 0.995912i \(-0.528792\pi\)
\(620\) −279216. + 553847.i −0.726368 + 1.44081i
\(621\) −407779. 407779.i −1.05741 1.05741i
\(622\) −36883.4 + 50995.1i −0.0953344 + 0.131810i
\(623\) 302377.i 0.779062i
\(624\) 96877.2 71662.2i 0.248801 0.184044i
\(625\) −101233. −0.259155
\(626\) 338869. + 245095.i 0.864734 + 0.625439i
\(627\) 2470.56 2470.56i 0.00628434 0.00628434i
\(628\) 71712.3 142247.i 0.181834 0.360682i
\(629\) −59038.6 + 59038.6i −0.149223 + 0.149223i
\(630\) 369724. 59371.1i 0.931530 0.149587i
\(631\) 77166.0 0.193806 0.0969030 0.995294i \(-0.469106\pi\)
0.0969030 + 0.995294i \(0.469106\pi\)
\(632\) 14258.6 44862.9i 0.0356980 0.112319i
\(633\) 124171.i 0.309893i
\(634\) −256074. + 41120.9i −0.637070 + 0.102302i
\(635\) 76812.3 + 76812.3i 0.190495 + 0.190495i
\(636\) 117386. 38698.0i 0.290203 0.0956696i
\(637\) 58565.5 + 58565.5i 0.144332 + 0.144332i
\(638\) 110060. + 79603.6i 0.270389 + 0.195565i
\(639\) 158976.i 0.389340i
\(640\) 298084. 607378.i 0.727744 1.48286i
\(641\) 692532. 1.68548 0.842740 0.538321i \(-0.180941\pi\)
0.842740 + 0.538321i \(0.180941\pi\)
\(642\) −235185. + 325167.i −0.570610 + 0.788927i
\(643\) 515879. 515879.i 1.24774 1.24774i 0.291031 0.956714i \(-0.406002\pi\)
0.956714 0.291031i \(-0.0939984\pi\)
\(644\) −220735. 669574.i −0.532230 1.61446i
\(645\) 280192. 280192.i 0.673498 0.673498i
\(646\) −2957.49 18417.3i −0.00708693 0.0441328i
\(647\) −187947. −0.448980 −0.224490 0.974476i \(-0.572072\pi\)
−0.224490 + 0.974476i \(0.572072\pi\)
\(648\) 124136. + 39453.8i 0.295630 + 0.0939592i
\(649\) 80406.4i 0.190898i
\(650\) 49194.0 + 306348.i 0.116435 + 0.725084i
\(651\) −259438. 259438.i −0.612169 0.612169i
\(652\) −146960. 74088.1i −0.345703 0.174282i
\(653\) 363478. + 363478.i 0.852415 + 0.852415i 0.990430 0.138015i \(-0.0440722\pi\)
−0.138015 + 0.990430i \(0.544072\pi\)
\(654\) −31047.3 + 42926.2i −0.0725887 + 0.100361i
\(655\) 726322.i 1.69296i
\(656\) 37884.2 + 51214.2i 0.0880341 + 0.119010i
\(657\) −344929. −0.799096
\(658\) 390034. + 282101.i 0.900847 + 0.651558i
\(659\) −59401.3 + 59401.3i −0.136781 + 0.136781i −0.772182 0.635401i \(-0.780835\pi\)
0.635401 + 0.772182i \(0.280835\pi\)
\(660\) 98914.5 + 49866.6i 0.227076 + 0.114478i
\(661\) −352242. + 352242.i −0.806191 + 0.806191i −0.984055 0.177864i \(-0.943081\pi\)
0.177864 + 0.984055i \(0.443081\pi\)
\(662\) 768228. 123364.i 1.75297 0.281495i
\(663\) 105331. 0.239622
\(664\) 115898. 59994.9i 0.262870 0.136075i
\(665\) 51307.8i 0.116022i
\(666\) −56032.4 + 8997.80i −0.126325 + 0.0202856i
\(667\) 693927. + 693927.i 1.55977 + 1.55977i
\(668\) −150632. 456925.i −0.337571 1.02398i
\(669\) −251555. 251555.i −0.562058 0.562058i
\(670\) −917149. 663349.i −2.04310 1.47772i
\(671\) 12346.6i 0.0274222i
\(672\) 286017. + 279952.i 0.633363 + 0.619933i
\(673\) 678354. 1.49771 0.748853 0.662736i \(-0.230605\pi\)
0.748853 + 0.662736i \(0.230605\pi\)
\(674\) 95759.7 132398.i 0.210796 0.291448i
\(675\) −596041. + 596041.i −1.30818 + 1.30818i
\(676\) −355658. + 117248.i −0.778287 + 0.256574i
\(677\) −348304. + 348304.i −0.759943 + 0.759943i −0.976312 0.216369i \(-0.930579\pi\)
0.216369 + 0.976312i \(0.430579\pi\)
\(678\) −83656.9 520961.i −0.181988 1.13330i
\(679\) −150471. −0.326372
\(680\) 525204. 271872.i 1.13582 0.587958i
\(681\) 134699.i 0.290448i
\(682\) 15225.7 + 94815.5i 0.0327346 + 0.203850i
\(683\) −218970. 218970.i −0.469401 0.469401i 0.432319 0.901721i \(-0.357695\pi\)
−0.901721 + 0.432319i \(0.857695\pi\)
\(684\) 5707.49 11321.3i 0.0121993 0.0241982i
\(685\) −449450. 449450.i −0.957856 0.957856i
\(686\) 174351. 241059.i 0.370491 0.512241i
\(687\) 200422.i 0.424652i
\(688\) −370587. 55443.1i −0.782913 0.117131i
\(689\) 84610.7 0.178233
\(690\) 648482. + 469030.i 1.36207 + 0.985150i
\(691\) 166441. 166441.i 0.348581 0.348581i −0.511000 0.859581i \(-0.670725\pi\)
0.859581 + 0.511000i \(0.170725\pi\)
\(692\) −84847.5 + 168302.i −0.177185 + 0.351461i
\(693\) 40995.2 40995.2i 0.0853625 0.0853625i
\(694\) −119308. + 19158.7i −0.247714 + 0.0397784i
\(695\) −709638. −1.46915
\(696\) −530925. 168742.i −1.09601 0.348341i
\(697\) 55683.0i 0.114619i
\(698\) −777894. + 124916.i −1.59665 + 0.256393i
\(699\) 426948. + 426948.i 0.873817 + 0.873817i
\(700\) −978700. + 322643.i −1.99735 + 0.658455i
\(701\) −606601. 606601.i −1.23443 1.23443i −0.962244 0.272188i \(-0.912253\pi\)
−0.272188 0.962244i \(-0.587747\pi\)
\(702\) 181585. + 131336.i 0.368473 + 0.266507i
\(703\) 7775.80i 0.0157338i
\(704\) −17715.8 103243.i −0.0357450 0.208313i
\(705\) −546430. −1.09940
\(706\) 235501. 325604.i 0.472479 0.653251i
\(707\) 25397.3 25397.3i 0.0508100 0.0508100i
\(708\) −103250. 313198.i −0.205980 0.624816i
\(709\) 590171. 590171.i 1.17405 1.17405i 0.192811 0.981236i \(-0.438240\pi\)
0.981236 0.192811i \(-0.0617603\pi\)
\(710\) 109497. + 681875.i 0.217213 + 1.35266i
\(711\) 27968.0 0.0553251
\(712\) −98318.0 + 309345.i −0.193942 + 0.610215i
\(713\) 693806.i 1.36477i
\(714\) 55466.6 + 345410.i 0.108802 + 0.677545i
\(715\) 53620.1 + 53620.1i 0.104885 + 0.104885i
\(716\) 152296. + 76778.5i 0.297073 + 0.149766i
\(717\) 326391. + 326391.i 0.634893 + 0.634893i
\(718\) −225870. + 312289.i −0.438137 + 0.605769i
\(719\) 319294.i 0.617637i −0.951121 0.308819i \(-0.900066\pi\)
0.951121 0.308819i \(-0.0999336\pi\)
\(720\) 397549. + 59476.8i 0.766877 + 0.114732i
\(721\) 785701. 1.51143
\(722\) −420976. 304480.i −0.807575 0.584097i
\(723\) −103848. + 103848.i −0.198665 + 0.198665i
\(724\) −76832.4 38734.2i −0.146578 0.0738954i
\(725\) 1.01430e6 1.01430e6i 1.92969 1.92969i
\(726\) −362133. + 58152.0i −0.687060 + 0.110330i
\(727\) −295780. −0.559628 −0.279814 0.960054i \(-0.590273\pi\)
−0.279814 + 0.960054i \(0.590273\pi\)
\(728\) 125948. + 243308.i 0.237646 + 0.459085i
\(729\) 491717.i 0.925253i
\(730\) 1.47946e6 237575.i 2.77625 0.445815i
\(731\) −231602. 231602.i −0.433419 0.433419i
\(732\) −15854.4 48092.3i −0.0295887 0.0897539i
\(733\) 353645. + 353645.i 0.658203 + 0.658203i 0.954955 0.296752i \(-0.0959033\pi\)
−0.296752 + 0.954955i \(0.595903\pi\)
\(734\) 617953. + 446949.i 1.14700 + 0.829594i
\(735\) 312270.i 0.578036i
\(736\) −8109.39 756776.i −0.0149704 1.39705i
\(737\) −175247. −0.322637
\(738\) −22180.6 + 30667.0i −0.0407250 + 0.0563065i
\(739\) −23782.9 + 23782.9i −0.0435488 + 0.0435488i −0.728546 0.684997i \(-0.759803\pi\)
0.684997 + 0.728546i \(0.259803\pi\)
\(740\) 234136. 77186.4i 0.427567 0.140954i
\(741\) −6936.38 + 6936.38i −0.0126327 + 0.0126327i
\(742\) 44555.6 + 277463.i 0.0809273 + 0.503962i
\(743\) −912931. −1.65371 −0.826857 0.562412i \(-0.809873\pi\)
−0.826857 + 0.562412i \(0.809873\pi\)
\(744\) −181060. 349773.i −0.327097 0.631888i
\(745\) 1.21494e6i 2.18899i
\(746\) 46434.1 + 289161.i 0.0834372 + 0.519592i
\(747\) 54826.8 + 54826.8i 0.0982543 + 0.0982543i
\(748\) 41218.9 81761.2i 0.0736705 0.146132i
\(749\) −645172. 645172.i −1.15004 1.15004i
\(750\) 288937. 399486.i 0.513667 0.710197i
\(751\) 799005.i 1.41667i 0.705875 + 0.708336i \(0.250554\pi\)
−0.705875 + 0.708336i \(0.749446\pi\)
\(752\) 307297. + 415422.i 0.543404 + 0.734605i
\(753\) 671294. 1.18392
\(754\) −309007. 223497.i −0.543533 0.393123i
\(755\) 226496. 226496.i 0.397344 0.397344i
\(756\) −335066. + 664632.i −0.586256 + 1.16289i
\(757\) −24122.0 + 24122.0i −0.0420940 + 0.0420940i −0.727841 0.685746i \(-0.759476\pi\)
0.685746 + 0.727841i \(0.259476\pi\)
\(758\) −677115. + 108732.i −1.17848 + 0.189243i
\(759\) 123910. 0.215092
\(760\) −16682.8 + 52490.2i −0.0288829 + 0.0908763i
\(761\) 97444.6i 0.168263i −0.996455 0.0841315i \(-0.973188\pi\)
0.996455 0.0841315i \(-0.0268116\pi\)
\(762\) −68106.8 + 10936.7i −0.117295 + 0.0188355i
\(763\) −85170.8 85170.8i −0.146299 0.146299i
\(764\) 793940. 261734.i 1.36019 0.448408i
\(765\) 248452. + 248452.i 0.424542 + 0.424542i
\(766\) −26778.6 19368.3i −0.0456384 0.0330090i
\(767\) 225750.i 0.383741i
\(768\) 201581. + 379402.i 0.341765 + 0.643246i
\(769\) −747937. −1.26477 −0.632386 0.774653i \(-0.717924\pi\)
−0.632386 + 0.774653i \(0.717924\pi\)
\(770\) −147600. + 204072.i −0.248946 + 0.344193i
\(771\) 261751. 261751.i