Properties

Label 16.5.f.a.11.3
Level $16$
Weight $5$
Character 16.11
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 11.3
Root \(2.79265 - 0.448449i\) of defining polynomial
Character \(\chi\) \(=\) 16.11
Dual form 16.5.f.a.3.3

$q$-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 \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

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

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 0.401014 0.916072i \(-0.368658\pi\)
−0.916072 + 0.401014i \(0.868658\pi\)
\(4\) −5.00945 + 15.1956i −0.313090 + 0.949723i
\(5\) −29.2002 29.2002i −1.16801 1.16801i −0.982676 0.185330i \(-0.940665\pi\)
−0.185330 0.982676i \(-0.559335\pi\)
\(6\) −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 −0.777873 0.628421i \(-0.783701\pi\)
0.628421 + 0.777873i \(0.283701\pi\)
\(12\) 93.6607 47.2180i 0.650422 0.327903i
\(13\) 50.7721 50.7721i 0.300427 0.300427i −0.540754 0.841181i \(-0.681861\pi\)
0.841181 + 0.540754i \(0.181861\pi\)
\(14\) −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 0.727222 0.686402i \(-0.240811\pi\)
−0.686402 + 0.727222i \(0.740811\pi\)
\(20\) 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 0.124150 0.992263i \(-0.460380\pi\)
0.992263 0.124150i \(-0.0396204\pi\)
\(30\) 877.416 634.612i 0.974907 0.705124i
\(31\) 938.741i 0.976838i −0.872609 0.488419i \(-0.837574\pi\)
0.872609 0.488419i \(-0.162426\pi\)
\(32\) −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 0.796871 0.604149i \(-0.206487\pi\)
−0.604149 + 0.796871i \(0.706487\pi\)
\(38\) 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 \(0.0235815\pi\)
−0.997257 + 0.0740157i \(0.976418\pi\)
\(42\) −247.874 + 1543.60i −0.140518 + 0.875055i
\(43\) 1035.00 1035.00i 0.559765 0.559765i −0.369476 0.929240i \(-0.620463\pi\)
0.929240 + 0.369476i \(0.120463\pi\)
\(44\) −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 \(0.151031\pi\)
−0.889532 + 0.456873i \(0.848969\pi\)
\(48\) 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 0.839693 0.543061i \(-0.182735\pi\)
−0.543061 + 0.839693i \(0.682735\pi\)
\(54\) 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 −0.950225 0.311565i \(-0.899147\pi\)
0.311565 + 0.950225i \(0.399147\pi\)
\(60\) −4113.68 1356.14i −1.14269 0.376704i
\(61\) −341.374 + 341.374i −0.0917425 + 0.0917425i −0.751489 0.659746i \(-0.770664\pi\)
0.659746 + 0.751489i \(0.270664\pi\)
\(62\) −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 0.996563 + 0.0828379i \(0.0263984\pi\)
0.0828379 + 0.996563i \(0.473602\pi\)
\(68\) 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 \(-0.675917\pi\)
0.524953 0.851131i \(-0.324083\pi\)
\(74\) 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 \(0.0187682\pi\)
−0.998262 + 0.0589277i \(0.981232\pi\)
\(80\) 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 0.803972 0.594667i \(-0.202716\pi\)
−0.594667 + 0.803972i \(0.702716\pi\)
\(84\) 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 \(-0.896268\pi\)
0.947368 0.320147i \(-0.103732\pi\)
\(90\) 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 0.727678 0.685919i \(-0.240599\pi\)
−0.685919 + 0.727678i \(0.740599\pi\)
\(102\) 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 −0.998574 0.0533845i \(-0.982999\pi\)
0.0533845 + 0.998574i \(0.482999\pi\)
\(108\) −5620.07 11147.9i −0.481830 0.955750i
\(109\) −1428.57 + 1428.57i −0.120240 + 0.120240i −0.764666 0.644426i \(-0.777096\pi\)
0.644426 + 0.764666i \(0.277096\pi\)
\(110\) −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 \(0.0259861\pi\)
−0.996669 + 0.0815470i \(0.974014\pi\)
\(128\) −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 0.969563 0.244841i \(-0.0787357\pi\)
−0.244841 + 0.969563i \(0.578736\pi\)
\(132\) −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 \(-0.865515\pi\)
0.912068 0.410039i \(-0.134485\pi\)
\(138\) −3072.80 + 19135.4i −0.161353 + 1.00480i
\(139\) 12151.3 12151.3i 0.628915 0.628915i −0.318880 0.947795i \(-0.603307\pi\)
0.947795 + 0.318880i \(0.103307\pi\)
\(140\) 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 0.0610710 0.998133i \(-0.480548\pi\)
−0.998133 + 0.0610710i \(0.980548\pi\)
\(150\) −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 −0.549727 0.835345i \(-0.685268\pi\)
0.835345 + 0.549727i \(0.185268\pi\)
\(158\) 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 0.830610 0.556854i \(-0.187992\pi\)
−0.556854 + 0.830610i \(0.687992\pi\)
\(164\) −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 −0.832436 0.554121i \(-0.813055\pi\)
0.554121 + 0.832436i \(0.313055\pi\)
\(174\) 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 0.579632 0.814879i \(-0.303197\pi\)
−0.814879 + 0.579632i \(0.803197\pi\)
\(180\) −11309.7 22433.7i −0.349065 0.692399i
\(181\) 3802.64 + 3802.64i 0.116072 + 0.116072i 0.762757 0.646685i \(-0.223845\pi\)
−0.646685 + 0.762757i \(0.723845\pi\)
\(182\) −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 \(-0.745925\pi\)
0.697997 0.716100i \(-0.254075\pi\)
\(192\) −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 0.985030 0.172386i \(-0.0551476\pi\)
−0.172386 + 0.985030i \(0.555148\pi\)
\(198\) 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 0.540507 0.841340i \(-0.318233\pi\)
−0.841340 + 0.540507i \(0.818233\pi\)
\(212\) −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 \(-0.816292\pi\)
0.838029 0.545626i \(-0.183708\pi\)
\(224\) −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 0.833889 0.551932i \(-0.186109\pi\)
−0.551932 + 0.833889i \(0.686109\pi\)
\(228\) 2075.99 + 684.380i 0.0399351 + 0.0131652i
\(229\) 21618.1 + 21618.1i 0.412237 + 0.412237i 0.882517 0.470280i \(-0.155847\pi\)
−0.470280 + 0.882517i \(0.655847\pi\)
\(230\) −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 \(0.322356\pi\)
−0.529562 + 0.848271i \(0.677644\pi\)
\(234\) −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 \(0.211382\pi\)
−0.787487 + 0.616332i \(0.788618\pi\)
\(240\) 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 −0.162621 + 0.986689i \(0.551995\pi\)
−0.986689 + 0.162621i \(0.948005\pi\)
\(252\) 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 −0.693652 0.720310i \(-0.744000\pi\)
0.720310 + 0.693652i \(0.244000\pi\)
\(270\) −75534.0 104434.i −1.03613 1.43256i
\(271\) 128685.i 1.75222i 0.482109 + 0.876111i \(0.339871\pi\)
−0.482109 + 0.876111i \(0.660129\pi\)
\(272\) 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 0.972313 0.233681i \(-0.0750772\pi\)
−0.233681 + 0.972313i \(0.575077\pi\)
\(278\) −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 \(-0.978619\pi\)
0.997745 0.0671200i \(-0.0213810\pi\)
\(282\) −52259.6 8391.95i −0.657155 0.105527i
\(283\) 63293.6 63293.6i 0.790291 0.790291i −0.191251 0.981541i \(-0.561254\pi\)
0.981541 + 0.191251i \(0.0612543\pi\)
\(284\) 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 −0.999267 0.0382867i \(-0.987810\pi\)
−0.0382867 0.999267i \(-0.512190\pi\)
\(294\) −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 −0.915302 0.402769i \(-0.868048\pi\)
−0.402769 0.915302i \(-0.631952\pi\)
\(308\) −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 \(0.179163\pi\)
−0.845733 + 0.533606i \(0.820837\pi\)
\(314\) −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 −0.441174 0.897422i \(-0.645438\pi\)
0.897422 + 0.441174i \(0.145438\pi\)
\(318\) −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 −0.302159 + 0.953258i \(0.597707\pi\)
−0.953258 + 0.302159i \(0.902293\pi\)
\(332\) −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 −0.612819 0.790223i \(-0.709965\pi\)
0.790223 + 0.612819i \(0.209965\pi\)
\(348\) 43605.3 132272.i 0.360065 1.09221i
\(349\) 139275. 139275.i 1.14347 1.14347i 0.155654 0.987812i \(-0.450252\pi\)
0.987812 0.155654i \(-0.0497484\pi\)
\(350\) 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 \(0.250305\pi\)
−0.706429 + 0.707784i \(0.749695\pi\)
\(368\) −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 0.868247 0.496133i \(-0.165247\pi\)
−0.496133 + 0.868247i \(0.665247\pi\)
\(374\) −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 −0.145385 0.989375i \(-0.546442\pi\)
0.989375 + 0.145385i \(0.0464420\pi\)
\(380\) 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 \(-0.991034\pi\)
0.999603 0.0281623i \(-0.00896552\pi\)
\(384\) 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 0.837294 0.546753i \(-0.184136\pi\)
−0.546753 + 0.837294i \(0.684136\pi\)
\(390\) 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 −0.437101 0.899412i \(-0.643995\pi\)
0.899412 + 0.437101i \(0.143995\pi\)
\(398\) 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 \(-0.851968\pi\)
0.893797 0.448473i \(-0.148032\pi\)
\(410\) −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 0.881302 0.472554i \(-0.156668\pi\)
−0.472554 + 0.881302i \(0.656668\pi\)
\(420\) −245256. 80852.3i −1.39034 0.458346i
\(421\) −209821. 209821.i −1.18382 1.18382i −0.978747 0.205070i \(-0.934258\pi\)
−0.205070 0.978747i \(-0.565742\pi\)
\(422\) −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 \(-0.891816\pi\)
0.942798 0.333366i \(-0.108184\pi\)
\(432\) 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 −0.638817 0.769359i \(-0.720576\pi\)
0.769359 + 0.638817i \(0.220576\pi\)
\(444\) 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 \(0.216189\pi\)
−0.778090 + 0.628153i \(0.783811\pi\)
\(458\) 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 −0.307866 0.951430i \(-0.599615\pi\)
0.951430 + 0.307866i \(0.0996148\pi\)
\(462\) −23431.5 32396.4i −0.109778 0.151779i
\(463\) 22250.8i 0.103797i 0.998652 + 0.0518983i \(0.0165272\pi\)
−0.998652 + 0.0518983i \(0.983473\pi\)
\(464\) −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 0.983858 0.178952i \(-0.0572708\pi\)
−0.178952 + 0.983858i \(0.557271\pi\)
\(468\) 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 \(0.0827250\pi\)
−0.966419 + 0.256973i \(0.917275\pi\)
\(480\) −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 −0.913963 0.405797i \(-0.866994\pi\)
0.405797 + 0.913963i \(0.366994\pi\)
\(492\) 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 0.611205 0.791473i \(-0.290685\pi\)
−0.791473 + 0.611205i \(0.790685\pi\)
\(500\) 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 −0.114155 0.993463i \(-0.536416\pi\)
0.993463 + 0.114155i \(0.0364161\pi\)
\(510\) −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 \(0.465429\pi\)
−0.108395 + 0.994108i \(0.534571\pi\)
\(522\) −32020.0 + 199400.i −0.117512 + 0.731785i
\(523\) −175071. + 175071.i −0.640044 + 0.640044i −0.950566 0.310522i \(-0.899496\pi\)
0.310522 + 0.950566i \(0.399496\pi\)
\(524\) −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 −0.906998 0.421135i \(-0.861632\pi\)
0.421135 + 0.906998i \(0.361632\pi\)
\(542\) 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 0.107193 0.994238i \(-0.465814\pi\)
−0.994238 + 0.107193i \(0.965814\pi\)
\(548\) 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 −0.382230 0.924067i \(-0.624844\pi\)
0.924067 + 0.382230i \(0.124844\pi\)
\(558\) 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 0.361127 0.932517i \(-0.382392\pi\)
−0.932517 + 0.361127i \(0.882392\pi\)
\(564\) 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 \(-0.938624\pi\)
0.981468 0.191627i \(-0.0613765\pi\)
\(570\) 22281.2 + 3577.96i 0.0685787 + 0.0110125i
\(571\) −92801.0 + 92801.0i −0.284630 + 0.284630i −0.834952 0.550322i \(-0.814505\pi\)
0.550322 + 0.834952i \(0.314505\pi\)
\(572\) −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 −0.360851 0.932623i \(-0.617514\pi\)
0.932623 + 0.360851i \(0.117514\pi\)
\(588\) 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 \(0.0224081\pi\)
−0.997523 + 0.0703391i \(0.977592\pi\)
\(602\) −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 \(0.208022\pi\)
−0.793948 + 0.607985i \(0.791978\pi\)
\(608\) −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 0.718643 0.695379i \(-0.244763\pi\)
−0.695379 + 0.718643i \(0.744763\pi\)
\(614\) −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 \(-0.778361\pi\)
0.767220 0.641384i \(-0.221639\pi\)
\(618\) −54791.1 + 341203.i −0.143461 + 0.893380i
\(619\) −416206. + 416206.i −1.08624 + 1.08624i −0.0903309 + 0.995912i \(0.528792\pi\)
−0.995912 + 0.0903309i \(0.971208\pi\)
\(620\) −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 0.956714 + 0.291031i \(0.0939984\pi\)
0.291031 + 0.956714i \(0.406002\pi\)
\(644\) −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 −0.138015 0.990430i \(-0.544072\pi\)
0.990430 + 0.138015i \(0.0440722\pi\)
\(654\) −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 0.635401 0.772182i \(-0.280835\pi\)
−0.772182 + 0.635401i \(0.780835\pi\)
\(660\) 98914.5 49866.6i 0.227076 0.114478i
\(661\) −352242. 352242.i −0.806191 0.806191i 0.177864 0.984055i \(-0.443081\pi\)
−0.984055 + 0.177864i \(0.943081\pi\)
\(662\) 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 0.216369 0.976312i \(-0.430579\pi\)
−0.976312 + 0.216369i \(0.930579\pi\)
\(678\) −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 −0.901721 0.432319i \(-0.857695\pi\)
0.432319 + 0.901721i \(0.357695\pi\)
\(684\) 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 0.859581 0.511000i \(-0.170725\pi\)
−0.511000 + 0.859581i \(0.670725\pi\)
\(692\) −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 −0.272188 + 0.962244i \(0.587747\pi\)
−0.962244 + 0.272188i \(0.912253\pi\)
\(702\) 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 0.981236 + 0.192811i \(0.0617603\pi\)
0.192811 + 0.981236i \(0.438240\pi\)
\(710\) 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 \(0.0999336\pi\)
−0.951121 + 0.308819i \(0.900066\pi\)
\(720\) 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 −0.296752 0.954955i \(-0.595903\pi\)
0.954955 + 0.296752i \(0.0959033\pi\)
\(734\) 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 0.684997 0.728546i \(-0.259803\pi\)
−0.728546 + 0.684997i \(0.759803\pi\)
\(740\) 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 \(-0.749446\pi\)
0.705875 0.708336i \(-0.250554\pi\)
\(752\) 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 0.685746 0.727841i \(-0.259476\pi\)
−0.727841 + 0.685746i \(0.759476\pi\)
\(758\) −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 \(0.0268116\pi\)
−0.996455 + 0.0841315i \(0.973188\pi\)
\(762\) −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
\(771\)