Properties

Label 16.5.f.a.3.5
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 3.5
Root \(1.03712 + 2.63142i\) of defining polynomial
Character \(\chi\) \(=\) 16.3
Dual form 16.5.f.a.11.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.59430 + 3.66854i) q^{2} +(11.5209 - 11.5209i) q^{3} +(-10.9164 + 11.6975i) q^{4} +(-14.6016 + 14.6016i) q^{5} +(60.6325 + 23.8971i) q^{6} -24.0210 q^{7} +(-60.3169 - 21.3980i) q^{8} -184.461i q^{9} +O(q^{10})\) \(q+(1.59430 + 3.66854i) q^{2} +(11.5209 - 11.5209i) q^{3} +(-10.9164 + 11.6975i) q^{4} +(-14.6016 + 14.6016i) q^{5} +(60.6325 + 23.8971i) q^{6} -24.0210 q^{7} +(-60.3169 - 21.3980i) q^{8} -184.461i q^{9} +(-76.8459 - 30.2872i) q^{10} +(61.7287 + 61.7287i) q^{11} +(8.99896 + 260.532i) q^{12} +(-37.5611 - 37.5611i) q^{13} +(-38.2966 - 88.1219i) q^{14} +336.446i q^{15} +(-17.6638 - 255.390i) q^{16} +96.8718 q^{17} +(676.702 - 294.086i) q^{18} +(-156.751 + 156.751i) q^{19} +(-11.4053 - 330.199i) q^{20} +(-276.742 + 276.742i) q^{21} +(-128.040 + 324.868i) q^{22} +959.783 q^{23} +(-941.426 + 448.379i) q^{24} +198.587i q^{25} +(77.9109 - 197.678i) q^{26} +(-1191.96 - 1191.96i) q^{27} +(262.223 - 280.986i) q^{28} +(-350.180 - 350.180i) q^{29} +(-1234.27 + 536.396i) q^{30} +237.885i q^{31} +(908.747 - 471.968i) q^{32} +1422.34 q^{33} +(154.443 + 355.378i) q^{34} +(350.744 - 350.744i) q^{35} +(2157.73 + 2013.65i) q^{36} +(-560.815 + 560.815i) q^{37} +(-824.957 - 325.140i) q^{38} -865.473 q^{39} +(1193.17 - 568.278i) q^{40} -1802.95i q^{41} +(-1456.45 - 574.031i) q^{42} +(206.090 + 206.090i) q^{43} +(-1395.93 + 48.2163i) q^{44} +(2693.42 + 2693.42i) q^{45} +(1530.18 + 3521.01i) q^{46} -1599.92i q^{47} +(-3145.81 - 2738.81i) q^{48} -1823.99 q^{49} +(-728.526 + 316.608i) q^{50} +(1116.05 - 1116.05i) q^{51} +(849.405 - 29.3390i) q^{52} +(-2234.17 + 2234.17i) q^{53} +(2472.41 - 6273.08i) q^{54} -1802.67 q^{55} +(1448.87 + 514.000i) q^{56} +3611.82i q^{57} +(726.358 - 1842.94i) q^{58} +(2353.11 + 2353.11i) q^{59} +(-3935.58 - 3672.78i) q^{60} +(-4443.45 - 4443.45i) q^{61} +(-872.690 + 379.260i) q^{62} +4430.92i q^{63} +(3180.25 + 2581.32i) q^{64} +1096.90 q^{65} +(2267.63 + 5217.90i) q^{66} +(-3995.40 + 3995.40i) q^{67} +(-1057.49 + 1133.16i) q^{68} +(11057.5 - 11057.5i) q^{69} +(1845.91 + 727.529i) q^{70} +4929.25 q^{71} +(-3947.09 + 11126.1i) q^{72} -2651.57i q^{73} +(-2951.48 - 1163.27i) q^{74} +(2287.90 + 2287.90i) q^{75} +(-122.438 - 3544.76i) q^{76} +(-1482.78 - 1482.78i) q^{77} +(-1379.82 - 3175.03i) q^{78} -8792.34i q^{79} +(3987.02 + 3471.18i) q^{80} -12523.4 q^{81} +(6614.21 - 2874.45i) q^{82} +(-228.231 + 228.231i) q^{83} +(-216.164 - 6258.23i) q^{84} +(-1414.48 + 1414.48i) q^{85} +(-427.480 + 1084.62i) q^{86} -8068.75 q^{87} +(-2402.41 - 5044.15i) q^{88} +10596.7i q^{89} +(-5586.81 + 14175.0i) q^{90} +(902.254 + 902.254i) q^{91} +(-10477.4 + 11227.1i) q^{92} +(2740.64 + 2740.64i) q^{93} +(5869.38 - 2550.75i) q^{94} -4577.63i q^{95} +(5032.07 - 15907.0i) q^{96} +11048.3 q^{97} +(-2907.99 - 6691.40i) q^{98} +(11386.5 - 11386.5i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.59430 + 3.66854i 0.398575 + 0.917136i
\(3\) 11.5209 11.5209i 1.28010 1.28010i 0.339485 0.940612i \(-0.389747\pi\)
0.940612 0.339485i \(-0.110253\pi\)
\(4\) −10.9164 + 11.6975i −0.682276 + 0.731095i
\(5\) −14.6016 + 14.6016i −0.584063 + 0.584063i −0.936017 0.351954i \(-0.885517\pi\)
0.351954 + 0.936017i \(0.385517\pi\)
\(6\) 60.6325 + 23.8971i 1.68424 + 0.663808i
\(7\) −24.0210 −0.490224 −0.245112 0.969495i \(-0.578825\pi\)
−0.245112 + 0.969495i \(0.578825\pi\)
\(8\) −60.3169 21.3980i −0.942451 0.334344i
\(9\) 184.461i 2.27729i
\(10\) −76.8459 30.2872i −0.768459 0.302872i
\(11\) 61.7287 + 61.7287i 0.510154 + 0.510154i 0.914574 0.404419i \(-0.132526\pi\)
−0.404419 + 0.914574i \(0.632526\pi\)
\(12\) 8.99896 + 260.532i 0.0624928 + 1.80925i
\(13\) −37.5611 37.5611i −0.222255 0.222255i 0.587192 0.809447i \(-0.300233\pi\)
−0.809447 + 0.587192i \(0.800233\pi\)
\(14\) −38.2966 88.1219i −0.195391 0.449602i
\(15\) 336.446i 1.49531i
\(16\) −17.6638 255.390i −0.0689991 0.997617i
\(17\) 96.8718 0.335197 0.167598 0.985855i \(-0.446399\pi\)
0.167598 + 0.985855i \(0.446399\pi\)
\(18\) 676.702 294.086i 2.08859 0.907672i
\(19\) −156.751 + 156.751i −0.434214 + 0.434214i −0.890059 0.455845i \(-0.849337\pi\)
0.455845 + 0.890059i \(0.349337\pi\)
\(20\) −11.4053 330.199i −0.0285133 0.825498i
\(21\) −276.742 + 276.742i −0.627534 + 0.627534i
\(22\) −128.040 + 324.868i −0.264546 + 0.671216i
\(23\) 959.783 1.81433 0.907167 0.420770i \(-0.138240\pi\)
0.907167 + 0.420770i \(0.138240\pi\)
\(24\) −941.426 + 448.379i −1.63442 + 0.778436i
\(25\) 198.587i 0.317740i
\(26\) 77.9109 197.678i 0.115253 0.292424i
\(27\) −1191.96 1191.96i −1.63506 1.63506i
\(28\) 262.223 280.986i 0.334468 0.358400i
\(29\) −350.180 350.180i −0.416385 0.416385i 0.467571 0.883956i \(-0.345129\pi\)
−0.883956 + 0.467571i \(0.845129\pi\)
\(30\) −1234.27 + 536.396i −1.37141 + 0.595995i
\(31\) 237.885i 0.247539i 0.992311 + 0.123769i \(0.0394983\pi\)
−0.992311 + 0.123769i \(0.960502\pi\)
\(32\) 908.747 471.968i 0.887449 0.460907i
\(33\) 1422.34 1.30609
\(34\) 154.443 + 355.378i 0.133601 + 0.307421i
\(35\) 350.744 350.744i 0.286322 0.286322i
\(36\) 2157.73 + 2013.65i 1.66492 + 1.55374i
\(37\) −560.815 + 560.815i −0.409653 + 0.409653i −0.881617 0.471965i \(-0.843545\pi\)
0.471965 + 0.881617i \(0.343545\pi\)
\(38\) −824.957 325.140i −0.571300 0.225166i
\(39\) −865.473 −0.569016
\(40\) 1193.17 568.278i 0.745729 0.355173i
\(41\) 1802.95i 1.07255i −0.844044 0.536274i \(-0.819831\pi\)
0.844044 0.536274i \(-0.180169\pi\)
\(42\) −1456.45 574.031i −0.825653 0.325414i
\(43\) 206.090 + 206.090i 0.111460 + 0.111460i 0.760637 0.649177i \(-0.224887\pi\)
−0.649177 + 0.760637i \(0.724887\pi\)
\(44\) −1395.93 + 48.2163i −0.721037 + 0.0249051i
\(45\) 2693.42 + 2693.42i 1.33008 + 1.33008i
\(46\) 1530.18 + 3521.01i 0.723149 + 1.66399i
\(47\) 1599.92i 0.724274i −0.932125 0.362137i \(-0.882047\pi\)
0.932125 0.362137i \(-0.117953\pi\)
\(48\) −3145.81 2738.81i −1.36537 1.18872i
\(49\) −1823.99 −0.759681
\(50\) −728.526 + 316.608i −0.291410 + 0.126643i
\(51\) 1116.05 1116.05i 0.429084 0.429084i
\(52\) 849.405 29.3390i 0.314129 0.0108502i
\(53\) −2234.17 + 2234.17i −0.795360 + 0.795360i −0.982360 0.187000i \(-0.940124\pi\)
0.187000 + 0.982360i \(0.440124\pi\)
\(54\) 2472.41 6273.08i 0.847877 2.15126i
\(55\) −1802.67 −0.595925
\(56\) 1448.87 + 514.000i 0.462012 + 0.163903i
\(57\) 3611.82i 1.11167i
\(58\) 726.358 1842.94i 0.215921 0.547842i
\(59\) 2353.11 + 2353.11i 0.675988 + 0.675988i 0.959090 0.283102i \(-0.0913636\pi\)
−0.283102 + 0.959090i \(0.591364\pi\)
\(60\) −3935.58 3672.78i −1.09322 1.02022i
\(61\) −4443.45 4443.45i −1.19415 1.19415i −0.975890 0.218264i \(-0.929961\pi\)
−0.218264 0.975890i \(-0.570039\pi\)
\(62\) −872.690 + 379.260i −0.227027 + 0.0986627i
\(63\) 4430.92i 1.11638i
\(64\) 3180.25 + 2581.32i 0.776429 + 0.630205i
\(65\) 1096.90 0.259622
\(66\) 2267.63 + 5217.90i 0.520576 + 1.19786i
\(67\) −3995.40 + 3995.40i −0.890042 + 0.890042i −0.994527 0.104485i \(-0.966681\pi\)
0.104485 + 0.994527i \(0.466681\pi\)
\(68\) −1057.49 + 1133.16i −0.228697 + 0.245060i
\(69\) 11057.5 11057.5i 2.32252 2.32252i
\(70\) 1845.91 + 727.529i 0.376717 + 0.148475i
\(71\) 4929.25 0.977832 0.488916 0.872331i \(-0.337392\pi\)
0.488916 + 0.872331i \(0.337392\pi\)
\(72\) −3947.09 + 11126.1i −0.761398 + 2.14624i
\(73\) 2651.57i 0.497574i −0.968558 0.248787i \(-0.919968\pi\)
0.968558 0.248787i \(-0.0800319\pi\)
\(74\) −2951.48 1163.27i −0.538984 0.212430i
\(75\) 2287.90 + 2287.90i 0.406737 + 0.406737i
\(76\) −122.438 3544.76i −0.0211978 0.613705i
\(77\) −1482.78 1482.78i −0.250090 0.250090i
\(78\) −1379.82 3175.03i −0.226796 0.521865i
\(79\) 8792.34i 1.40880i −0.709801 0.704402i \(-0.751215\pi\)
0.709801 0.704402i \(-0.248785\pi\)
\(80\) 3987.02 + 3471.18i 0.622971 + 0.542372i
\(81\) −12523.4 −1.90877
\(82\) 6614.21 2874.45i 0.983672 0.427491i
\(83\) −228.231 + 228.231i −0.0331298 + 0.0331298i −0.723478 0.690348i \(-0.757458\pi\)
0.690348 + 0.723478i \(0.257458\pi\)
\(84\) −216.164 6258.23i −0.0306354 0.886938i
\(85\) −1414.48 + 1414.48i −0.195776 + 0.195776i
\(86\) −427.480 + 1084.62i −0.0577988 + 0.146649i
\(87\) −8068.75 −1.06603
\(88\) −2402.41 5044.15i −0.310229 0.651362i
\(89\) 10596.7i 1.33780i 0.743353 + 0.668899i \(0.233234\pi\)
−0.743353 + 0.668899i \(0.766766\pi\)
\(90\) −5586.81 + 14175.0i −0.689729 + 1.75001i
\(91\) 902.254 + 902.254i 0.108955 + 0.108955i
\(92\) −10477.4 + 11227.1i −1.23788 + 1.32645i
\(93\) 2740.64 + 2740.64i 0.316873 + 0.316873i
\(94\) 5869.38 2550.75i 0.664258 0.288677i
\(95\) 4577.63i 0.507217i
\(96\) 5032.07 15907.0i 0.546015 1.72602i
\(97\) 11048.3 1.17422 0.587111 0.809506i \(-0.300265\pi\)
0.587111 + 0.809506i \(0.300265\pi\)
\(98\) −2907.99 6691.40i −0.302790 0.696730i
\(99\) 11386.5 11386.5i 1.16177 1.16177i
\(100\) −2322.98 2167.86i −0.232298 0.216786i
\(101\) −7543.12 + 7543.12i −0.739449 + 0.739449i −0.972471 0.233022i \(-0.925139\pi\)
0.233022 + 0.972471i \(0.425139\pi\)
\(102\) 5873.58 + 2314.95i 0.564550 + 0.222506i
\(103\) −6124.81 −0.577322 −0.288661 0.957431i \(-0.593210\pi\)
−0.288661 + 0.957431i \(0.593210\pi\)
\(104\) 1461.84 + 3069.30i 0.135155 + 0.283774i
\(105\) 8081.75i 0.733039i
\(106\) −11758.1 4634.20i −1.04646 0.412442i
\(107\) 4636.79 + 4636.79i 0.404995 + 0.404995i 0.879989 0.474994i \(-0.157550\pi\)
−0.474994 + 0.879989i \(0.657550\pi\)
\(108\) 26954.8 931.038i 2.31094 0.0798215i
\(109\) 15235.6 + 15235.6i 1.28235 + 1.28235i 0.939327 + 0.343022i \(0.111451\pi\)
0.343022 + 0.939327i \(0.388549\pi\)
\(110\) −2874.00 6613.18i −0.237521 0.546544i
\(111\) 12922.1i 1.04879i
\(112\) 424.301 + 6134.71i 0.0338250 + 0.489055i
\(113\) 2902.13 0.227279 0.113639 0.993522i \(-0.463749\pi\)
0.113639 + 0.993522i \(0.463749\pi\)
\(114\) −13250.1 + 5758.32i −1.01955 + 0.443084i
\(115\) −14014.4 + 14014.4i −1.05969 + 1.05969i
\(116\) 7918.94 273.526i 0.588506 0.0203274i
\(117\) −6928.55 + 6928.55i −0.506140 + 0.506140i
\(118\) −4880.93 + 12384.1i −0.350541 + 0.889404i
\(119\) −2326.95 −0.164321
\(120\) 7199.26 20293.4i 0.499949 1.40926i
\(121\) 7020.14i 0.479485i
\(122\) 9216.79 23385.2i 0.619241 1.57116i
\(123\) −20771.6 20771.6i −1.37296 1.37296i
\(124\) −2782.66 2596.85i −0.180974 0.168890i
\(125\) −12025.7 12025.7i −0.769644 0.769644i
\(126\) −16255.0 + 7064.22i −1.02387 + 0.444962i
\(127\) 3992.46i 0.247533i −0.992311 0.123766i \(-0.960503\pi\)
0.992311 0.123766i \(-0.0394974\pi\)
\(128\) −4399.41 + 15782.3i −0.268518 + 0.963275i
\(129\) 4748.66 0.285359
\(130\) 1748.79 + 4024.04i 0.103479 + 0.238109i
\(131\) 16640.1 16640.1i 0.969645 0.969645i −0.0299081 0.999553i \(-0.509521\pi\)
0.999553 + 0.0299081i \(0.00952147\pi\)
\(132\) −15526.8 + 16637.8i −0.891116 + 0.954878i
\(133\) 3765.31 3765.31i 0.212862 0.212862i
\(134\) −21027.2 8287.43i −1.17104 0.461541i
\(135\) 34808.9 1.90995
\(136\) −5843.01 2072.86i −0.315906 0.112071i
\(137\) 10746.6i 0.572573i 0.958144 + 0.286286i \(0.0924209\pi\)
−0.958144 + 0.286286i \(0.907579\pi\)
\(138\) 58194.1 + 22936.0i 3.05577 + 1.20437i
\(139\) −7583.76 7583.76i −0.392514 0.392514i 0.483069 0.875582i \(-0.339522\pi\)
−0.875582 + 0.483069i \(0.839522\pi\)
\(140\) 273.967 + 7931.70i 0.0139779 + 0.404679i
\(141\) −18432.5 18432.5i −0.927140 0.927140i
\(142\) 7858.70 + 18083.2i 0.389739 + 0.896805i
\(143\) 4637.20i 0.226769i
\(144\) −47109.4 + 3258.27i −2.27187 + 0.157131i
\(145\) 10226.4 0.486390
\(146\) 9727.41 4227.40i 0.456343 0.198321i
\(147\) −21014.0 + 21014.0i −0.972464 + 0.972464i
\(148\) −438.053 12682.2i −0.0199988 0.578991i
\(149\) 3385.37 3385.37i 0.152487 0.152487i −0.626741 0.779228i \(-0.715611\pi\)
0.779228 + 0.626741i \(0.215611\pi\)
\(150\) −4745.66 + 12040.8i −0.210918 + 0.535149i
\(151\) 21697.8 0.951617 0.475809 0.879549i \(-0.342155\pi\)
0.475809 + 0.879549i \(0.342155\pi\)
\(152\) 12808.9 6100.58i 0.554402 0.264049i
\(153\) 17869.0i 0.763341i
\(154\) 3075.65 7803.65i 0.129687 0.329046i
\(155\) −3473.49 3473.49i −0.144578 0.144578i
\(156\) 9447.87 10123.9i 0.388226 0.416005i
\(157\) 14212.7 + 14212.7i 0.576603 + 0.576603i 0.933966 0.357363i \(-0.116324\pi\)
−0.357363 + 0.933966i \(0.616324\pi\)
\(158\) 32255.1 14017.6i 1.29206 0.561514i
\(159\) 51479.0i 2.03627i
\(160\) −6377.67 + 20160.6i −0.249128 + 0.787525i
\(161\) −23054.9 −0.889430
\(162\) −19966.1 45942.8i −0.760788 1.75060i
\(163\) −7450.28 + 7450.28i −0.280412 + 0.280412i −0.833273 0.552861i \(-0.813536\pi\)
0.552861 + 0.833273i \(0.313536\pi\)
\(164\) 21090.1 + 19681.8i 0.784134 + 0.731773i
\(165\) −20768.4 + 20768.4i −0.762841 + 0.762841i
\(166\) −1201.14 473.407i −0.0435892 0.0171798i
\(167\) −3997.25 −0.143327 −0.0716635 0.997429i \(-0.522831\pi\)
−0.0716635 + 0.997429i \(0.522831\pi\)
\(168\) 22614.0 10770.5i 0.801232 0.381608i
\(169\) 25739.3i 0.901205i
\(170\) −7444.20 2933.98i −0.257585 0.101522i
\(171\) 28914.4 + 28914.4i 0.988832 + 0.988832i
\(172\) −4660.50 + 160.977i −0.157534 + 0.00544134i
\(173\) −16996.8 16996.8i −0.567903 0.567903i 0.363638 0.931540i \(-0.381535\pi\)
−0.931540 + 0.363638i \(0.881535\pi\)
\(174\) −12864.0 29600.5i −0.424891 0.977690i
\(175\) 4770.26i 0.155764i
\(176\) 14674.5 16855.2i 0.473738 0.544139i
\(177\) 54219.8 1.73066
\(178\) −38874.4 + 16894.3i −1.22694 + 0.533213i
\(179\) 24121.3 24121.3i 0.752826 0.752826i −0.222180 0.975006i \(-0.571317\pi\)
0.975006 + 0.222180i \(0.0713173\pi\)
\(180\) −60908.8 + 2103.83i −1.87990 + 0.0649331i
\(181\) 13837.8 13837.8i 0.422386 0.422386i −0.463638 0.886025i \(-0.653456\pi\)
0.886025 + 0.463638i \(0.153456\pi\)
\(182\) −1871.50 + 4748.42i −0.0564997 + 0.143353i
\(183\) −102385. −3.05726
\(184\) −57891.1 20537.4i −1.70992 0.606611i
\(185\) 16377.6i 0.478526i
\(186\) −5684.75 + 14423.5i −0.164318 + 0.416914i
\(187\) 5979.77 + 5979.77i 0.171002 + 0.171002i
\(188\) 18715.1 + 17465.4i 0.529513 + 0.494155i
\(189\) 28632.0 + 28632.0i 0.801544 + 0.801544i
\(190\) 16793.2 7298.12i 0.465187 0.202164i
\(191\) 11717.4i 0.321193i 0.987020 + 0.160596i \(0.0513417\pi\)
−0.987020 + 0.160596i \(0.948658\pi\)
\(192\) 66378.3 6900.22i 1.80063 0.187180i
\(193\) −68633.2 −1.84255 −0.921276 0.388910i \(-0.872852\pi\)
−0.921276 + 0.388910i \(0.872852\pi\)
\(194\) 17614.2 + 40531.0i 0.468016 + 1.07692i
\(195\) 12637.3 12637.3i 0.332341 0.332341i
\(196\) 19911.5 21336.2i 0.518312 0.555399i
\(197\) −22885.3 + 22885.3i −0.589689 + 0.589689i −0.937547 0.347858i \(-0.886909\pi\)
0.347858 + 0.937547i \(0.386909\pi\)
\(198\) 59925.4 + 23618.4i 1.52855 + 0.602449i
\(199\) 59936.9 1.51352 0.756761 0.653692i \(-0.226781\pi\)
0.756761 + 0.653692i \(0.226781\pi\)
\(200\) 4249.37 11978.2i 0.106234 0.299454i
\(201\) 92060.9i 2.27868i
\(202\) −39698.3 15646.3i −0.972901 0.383449i
\(203\) 8411.65 + 8411.65i 0.204122 + 0.204122i
\(204\) 871.745 + 25238.2i 0.0209474 + 0.606455i
\(205\) 26326.0 + 26326.0i 0.626436 + 0.626436i
\(206\) −9764.78 22469.1i −0.230106 0.529483i
\(207\) 177042.i 4.13177i
\(208\) −8929.26 + 10256.2i −0.206390 + 0.237061i
\(209\) −19352.1 −0.443032
\(210\) 29648.3 12884.7i 0.672296 0.292171i
\(211\) −12558.8 + 12558.8i −0.282086 + 0.282086i −0.833941 0.551854i \(-0.813920\pi\)
0.551854 + 0.833941i \(0.313920\pi\)
\(212\) −1745.11 50523.3i −0.0388285 1.12414i
\(213\) 56789.2 56789.2i 1.25172 1.25172i
\(214\) −9617.83 + 24402.7i −0.210015 + 0.532856i
\(215\) −6018.47 −0.130199
\(216\) 46389.6 + 97400.6i 0.994291 + 2.08763i
\(217\) 5714.22i 0.121349i
\(218\) −31602.3 + 80182.5i −0.664976 + 1.68720i
\(219\) −30548.4 30548.4i −0.636943 0.636943i
\(220\) 19678.7 21086.8i 0.406585 0.435678i
\(221\) −3638.61 3638.61i −0.0744992 0.0744992i
\(222\) −47405.4 + 20601.8i −0.961883 + 0.418021i
\(223\) 22761.5i 0.457711i 0.973460 + 0.228856i \(0.0734983\pi\)
−0.973460 + 0.228856i \(0.926502\pi\)
\(224\) −21829.0 + 11337.1i −0.435048 + 0.225947i
\(225\) 36631.6 0.723586
\(226\) 4626.86 + 10646.6i 0.0905877 + 0.208446i
\(227\) 6480.30 6480.30i 0.125760 0.125760i −0.641425 0.767186i \(-0.721657\pi\)
0.767186 + 0.641425i \(0.221657\pi\)
\(228\) −42249.3 39428.1i −0.812737 0.758466i
\(229\) 36068.6 36068.6i 0.687795 0.687795i −0.273949 0.961744i \(-0.588330\pi\)
0.961744 + 0.273949i \(0.0883301\pi\)
\(230\) −73755.4 29069.2i −1.39424 0.549512i
\(231\) −34165.9 −0.640278
\(232\) 13628.6 + 28614.9i 0.253207 + 0.531638i
\(233\) 68226.4i 1.25673i 0.777920 + 0.628363i \(0.216275\pi\)
−0.777920 + 0.628363i \(0.783725\pi\)
\(234\) −36463.9 14371.5i −0.665934 0.262464i
\(235\) 23361.4 + 23361.4i 0.423022 + 0.423022i
\(236\) −53213.1 + 1838.02i −0.955421 + 0.0330009i
\(237\) −101295. 101295.i −1.80340 1.80340i
\(238\) −3709.86 8536.53i −0.0654944 0.150705i
\(239\) 100556.i 1.76040i 0.474599 + 0.880202i \(0.342593\pi\)
−0.474599 + 0.880202i \(0.657407\pi\)
\(240\) 85924.9 5942.90i 1.49175 0.103175i
\(241\) −35563.1 −0.612302 −0.306151 0.951983i \(-0.599041\pi\)
−0.306151 + 0.951983i \(0.599041\pi\)
\(242\) 25753.7 11192.2i 0.439753 0.191111i
\(243\) −47732.3 + 47732.3i −0.808351 + 0.808351i
\(244\) 100484. 3470.78i 1.68778 0.0582972i
\(245\) 26633.2 26633.2i 0.443702 0.443702i
\(246\) 43085.3 109318.i 0.711965 1.80642i
\(247\) 11775.5 0.193013
\(248\) 5090.25 14348.5i 0.0827630 0.233293i
\(249\) 5258.84i 0.0848186i
\(250\) 24944.2 63289.3i 0.399107 1.01263i
\(251\) −29206.3 29206.3i −0.463585 0.463585i 0.436244 0.899829i \(-0.356309\pi\)
−0.899829 + 0.436244i \(0.856309\pi\)
\(252\) −51830.8 48369.8i −0.816182 0.761681i
\(253\) 59246.1 + 59246.1i 0.925591 + 0.925591i
\(254\) 14646.5 6365.18i 0.227021 0.0986604i
\(255\) 32592.1i 0.501224i
\(256\) −64912.0 + 9022.29i −0.990478 + 0.137669i
\(257\) 2932.77 0.0444029 0.0222015 0.999754i \(-0.492932\pi\)
0.0222015 + 0.999754i \(0.492932\pi\)
\(258\) 7570.79 + 17420.7i 0.113737 + 0.261713i
\(259\) 13471.3 13471.3i 0.200821 0.200821i
\(260\) −11974.3 + 12831.1i −0.177134 + 0.189808i
\(261\) −64594.4 + 64594.4i −0.948230 + 0.948230i
\(262\) 87574.1 + 34515.5i 1.27577 + 0.502820i
\(263\) 23253.5 0.336184 0.168092 0.985771i \(-0.446239\pi\)
0.168092 + 0.985771i \(0.446239\pi\)
\(264\) −85790.8 30435.1i −1.23093 0.436684i
\(265\) 65244.7i 0.929081i
\(266\) 19816.3 + 7810.18i 0.280065 + 0.110382i
\(267\) 122083. + 122083.i 1.71251 + 1.71251i
\(268\) −3120.81 90351.7i −0.0434508 1.25796i
\(269\) 56836.3 + 56836.3i 0.785455 + 0.785455i 0.980745 0.195290i \(-0.0625649\pi\)
−0.195290 + 0.980745i \(0.562565\pi\)
\(270\) 55495.9 + 127698.i 0.761260 + 1.75169i
\(271\) 91679.6i 1.24834i −0.781287 0.624172i \(-0.785436\pi\)
0.781287 0.624172i \(-0.214564\pi\)
\(272\) −1711.12 24740.1i −0.0231283 0.334398i
\(273\) 20789.5 0.278945
\(274\) −39424.4 + 17133.3i −0.525127 + 0.228213i
\(275\) −12258.5 + 12258.5i −0.162096 + 0.162096i
\(276\) 8637.05 + 250054.i 0.113383 + 3.28259i
\(277\) −75831.0 + 75831.0i −0.988297 + 0.988297i −0.999932 0.0116353i \(-0.996296\pi\)
0.0116353 + 0.999932i \(0.496296\pi\)
\(278\) 15730.6 39912.1i 0.203542 0.516435i
\(279\) 43880.4 0.563718
\(280\) −28661.0 + 13650.6i −0.365574 + 0.174114i
\(281\) 77682.2i 0.983805i −0.870650 0.491903i \(-0.836302\pi\)
0.870650 0.491903i \(-0.163698\pi\)
\(282\) 38233.4 97007.2i 0.480779 1.21985i
\(283\) −43834.7 43834.7i −0.547325 0.547325i 0.378341 0.925666i \(-0.376495\pi\)
−0.925666 + 0.378341i \(0.876495\pi\)
\(284\) −53809.7 + 57660.0i −0.667151 + 0.714888i
\(285\) −52738.3 52738.3i −0.649286 0.649286i
\(286\) 17011.8 7393.08i 0.207978 0.0903844i
\(287\) 43308.7i 0.525788i
\(288\) −87059.6 167628.i −1.04962 2.02098i
\(289\) −74136.9 −0.887643
\(290\) 16303.9 + 37515.8i 0.193863 + 0.446086i
\(291\) 127286. 127286.i 1.50312 1.50312i
\(292\) 31016.8 + 28945.7i 0.363774 + 0.339483i
\(293\) 61916.9 61916.9i 0.721231 0.721231i −0.247625 0.968856i \(-0.579650\pi\)
0.968856 + 0.247625i \(0.0796501\pi\)
\(294\) −110593. 43588.1i −1.27948 0.504282i
\(295\) −68718.4 −0.789639
\(296\) 45826.9 21826.3i 0.523042 0.249113i
\(297\) 147156.i 1.66826i
\(298\) 17816.7 + 7022.09i 0.200629 + 0.0790740i
\(299\) −36050.5 36050.5i −0.403245 0.403245i
\(300\) −51738.4 + 1787.08i −0.574871 + 0.0198564i
\(301\) −4950.47 4950.47i −0.0546404 0.0546404i
\(302\) 34592.8 + 79599.4i 0.379291 + 0.872762i
\(303\) 173807.i 1.89313i
\(304\) 42801.5 + 37263.9i 0.463139 + 0.403219i
\(305\) 129763. 1.39492
\(306\) 65553.4 28488.6i 0.700087 0.304249i
\(307\) −99698.5 + 99698.5i −1.05782 + 1.05782i −0.0595972 + 0.998223i \(0.518982\pi\)
−0.998223 + 0.0595972i \(0.981018\pi\)
\(308\) 33531.5 1158.20i 0.353470 0.0122091i
\(309\) −70563.1 + 70563.1i −0.739028 + 0.739028i
\(310\) 7204.87 18280.5i 0.0749726 0.190223i
\(311\) −127678. −1.32006 −0.660031 0.751238i \(-0.729457\pi\)
−0.660031 + 0.751238i \(0.729457\pi\)
\(312\) 52202.7 + 18519.4i 0.536270 + 0.190247i
\(313\) 24132.5i 0.246328i −0.992386 0.123164i \(-0.960696\pi\)
0.992386 0.123164i \(-0.0393042\pi\)
\(314\) −29480.6 + 74799.2i −0.299004 + 0.758643i
\(315\) −64698.5 64698.5i −0.652039 0.652039i
\(316\) 102849. + 95980.9i 1.02997 + 0.961193i
\(317\) −63739.0 63739.0i −0.634289 0.634289i 0.314852 0.949141i \(-0.398045\pi\)
−0.949141 + 0.314852i \(0.898045\pi\)
\(318\) −188853. + 82073.0i −1.86754 + 0.811608i
\(319\) 43232.3i 0.424841i
\(320\) −84128.1 + 8745.36i −0.821563 + 0.0854039i
\(321\) 106840. 1.03687
\(322\) −36756.5 84578.0i −0.354505 0.815728i
\(323\) −15184.8 + 15184.8i −0.145547 + 0.145547i
\(324\) 136711. 146493.i 1.30231 1.39549i
\(325\) 7459.16 7459.16i 0.0706193 0.0706193i
\(326\) −39209.6 15453.7i −0.368942 0.145411i
\(327\) 351055. 3.28306
\(328\) −38579.6 + 108748.i −0.358599 + 1.01082i
\(329\) 38431.6i 0.355056i
\(330\) −109301. 43078.6i −1.00368 0.395580i
\(331\) −111266. 111266.i −1.01556 1.01556i −0.999877 0.0156868i \(-0.995007\pi\)
−0.0156868 0.999877i \(-0.504993\pi\)
\(332\) −178.271 5161.20i −0.00161736 0.0468247i
\(333\) 103448. + 103448.i 0.932899 + 0.932899i
\(334\) −6372.81 14664.1i −0.0571266 0.131450i
\(335\) 116678.i 1.03968i
\(336\) 75565.5 + 65788.9i 0.669337 + 0.582739i
\(337\) −89183.5 −0.785280 −0.392640 0.919692i \(-0.628438\pi\)
−0.392640 + 0.919692i \(0.628438\pi\)
\(338\) 94425.8 41036.2i 0.826528 0.359198i
\(339\) 33435.0 33435.0i 0.290939 0.290939i
\(340\) −1104.85 31987.0i −0.00955755 0.276704i
\(341\) −14684.3 + 14684.3i −0.126283 + 0.126283i
\(342\) −59975.6 + 152172.i −0.512769 + 1.30102i
\(343\) 101488. 0.862637
\(344\) −8020.78 16840.6i −0.0677797 0.142312i
\(345\) 322915.i 2.71300i
\(346\) 35255.4 89451.3i 0.294492 0.747196i
\(347\) −17075.7 17075.7i −0.141814 0.141814i 0.632635 0.774450i \(-0.281973\pi\)
−0.774450 + 0.632635i \(0.781973\pi\)
\(348\) 88081.8 94384.3i 0.727323 0.779366i
\(349\) −25961.7 25961.7i −0.213149 0.213149i 0.592455 0.805604i \(-0.298159\pi\)
−0.805604 + 0.592455i \(0.798159\pi\)
\(350\) 17499.9 7605.22i 0.142856 0.0620835i
\(351\) 89542.5i 0.726800i
\(352\) 85229.8 + 26961.8i 0.687869 + 0.217602i
\(353\) 221897. 1.78075 0.890374 0.455230i \(-0.150443\pi\)
0.890374 + 0.455230i \(0.150443\pi\)
\(354\) 86442.6 + 198908.i 0.689797 + 1.58725i
\(355\) −71974.9 + 71974.9i −0.571116 + 0.571116i
\(356\) −123955. 115678.i −0.978057 0.912747i
\(357\) −26808.5 + 26808.5i −0.210347 + 0.210347i
\(358\) 126947. + 50033.4i 0.990501 + 0.390386i
\(359\) −106831. −0.828908 −0.414454 0.910070i \(-0.636027\pi\)
−0.414454 + 0.910070i \(0.636027\pi\)
\(360\) −104825. 220092.i −0.808834 1.69824i
\(361\) 81179.1i 0.622917i
\(362\) 72826.1 + 28702.9i 0.555738 + 0.219033i
\(363\) −80878.1 80878.1i −0.613787 0.613787i
\(364\) −20403.5 + 704.752i −0.153993 + 0.00531904i
\(365\) 38717.2 + 38717.2i 0.290615 + 0.290615i
\(366\) −163232. 375603.i −1.21855 2.80393i
\(367\) 79074.9i 0.587093i −0.955945 0.293546i \(-0.905164\pi\)
0.955945 0.293546i \(-0.0948355\pi\)
\(368\) −16953.4 245119.i −0.125187 1.81001i
\(369\) −332574. −2.44250
\(370\) 60081.8 26110.7i 0.438874 0.190729i
\(371\) 53666.8 53666.8i 0.389904 0.389904i
\(372\) −61976.6 + 2140.71i −0.447859 + 0.0154694i
\(373\) −86341.4 + 86341.4i −0.620585 + 0.620585i −0.945681 0.325096i \(-0.894603\pi\)
0.325096 + 0.945681i \(0.394603\pi\)
\(374\) −12403.5 + 31470.6i −0.0886749 + 0.224989i
\(375\) −277093. −1.97044
\(376\) −34235.1 + 96502.3i −0.242156 + 0.682593i
\(377\) 26306.3i 0.185087i
\(378\) −59389.6 + 150685.i −0.415649 + 1.05460i
\(379\) 168223. + 168223.i 1.17114 + 1.17114i 0.981939 + 0.189199i \(0.0605890\pi\)
0.189199 + 0.981939i \(0.439411\pi\)
\(380\) 53546.9 + 49971.3i 0.370824 + 0.346062i
\(381\) −45996.6 45996.6i −0.316866 0.316866i
\(382\) −42985.9 + 18681.1i −0.294577 + 0.128019i
\(383\) 22177.8i 0.151189i −0.997139 0.0755946i \(-0.975915\pi\)
0.997139 0.0755946i \(-0.0240855\pi\)
\(384\) 131141. + 232511.i 0.889355 + 1.57681i
\(385\) 43301.9 0.292137
\(386\) −109422. 251784.i −0.734395 1.68987i
\(387\) 38015.4 38015.4i 0.253827 0.253827i
\(388\) −120607. + 129237.i −0.801144 + 0.858468i
\(389\) 163109. 163109.i 1.07790 1.07790i 0.0812004 0.996698i \(-0.474125\pi\)
0.996698 0.0812004i \(-0.0258754\pi\)
\(390\) 66508.0 + 26212.8i 0.437265 + 0.172339i
\(391\) 92975.9 0.608159
\(392\) 110018. + 39029.8i 0.715962 + 0.253994i
\(393\) 383416.i 2.48248i
\(394\) −120442. 47469.6i −0.775861 0.305790i
\(395\) 128382. + 128382.i 0.822831 + 0.822831i
\(396\) 8894.02 + 257494.i 0.0567163 + 1.64201i
\(397\) 110463. + 110463.i 0.700868 + 0.700868i 0.964597 0.263729i \(-0.0849525\pi\)
−0.263729 + 0.964597i \(0.584953\pi\)
\(398\) 95557.5 + 219881.i 0.603252 + 1.38810i
\(399\) 86759.4i 0.544968i
\(400\) 50717.2 3507.80i 0.316982 0.0219237i
\(401\) 43913.8 0.273094 0.136547 0.990634i \(-0.456399\pi\)
0.136547 + 0.990634i \(0.456399\pi\)
\(402\) −337729. + 146773.i −2.08986 + 0.908224i
\(403\) 8935.22 8935.22i 0.0550168 0.0550168i
\(404\) −5891.94 170580.i −0.0360990 1.04512i
\(405\) 182862. 182862.i 1.11484 1.11484i
\(406\) −17447.8 + 44269.2i −0.105850 + 0.268565i
\(407\) −69236.7 −0.417972
\(408\) −91197.7 + 43435.3i −0.547852 + 0.260929i
\(409\) 188666.i 1.12784i −0.825830 0.563919i \(-0.809293\pi\)
0.825830 0.563919i \(-0.190707\pi\)
\(410\) −54606.5 + 138549.i −0.324845 + 0.824208i
\(411\) 123810. + 123810.i 0.732948 + 0.732948i
\(412\) 66861.0 71645.0i 0.393893 0.422077i
\(413\) −56524.0 56524.0i −0.331385 0.331385i
\(414\) 649487. 282259.i 3.78940 1.64682i
\(415\) 6665.07i 0.0386998i
\(416\) −51861.2 16405.9i −0.299679 0.0948012i
\(417\) −174743. −1.00491
\(418\) −30853.0 70994.0i −0.176582 0.406321i
\(419\) −88556.3 + 88556.3i −0.504419 + 0.504419i −0.912808 0.408389i \(-0.866091\pi\)
0.408389 + 0.912808i \(0.366091\pi\)
\(420\) 94536.4 + 88223.8i 0.535921 + 0.500135i
\(421\) −42983.4 + 42983.4i −0.242514 + 0.242514i −0.817889 0.575375i \(-0.804856\pi\)
0.575375 + 0.817889i \(0.304856\pi\)
\(422\) −66094.8 26049.9i −0.371144 0.146279i
\(423\) −295123. −1.64938
\(424\) 182565. 86951.2i 1.01551 0.483664i
\(425\) 19237.5i 0.106505i
\(426\) 298873. + 117795.i 1.64690 + 0.649092i
\(427\) 106736. + 106736.i 0.585403 + 0.585403i
\(428\) −104856. + 3621.80i −0.572408 + 0.0197714i
\(429\) −53424.5 53424.5i −0.290286 0.290286i
\(430\) −9595.25 22079.0i −0.0518942 0.119411i
\(431\) 163696.i 0.881219i 0.897699 + 0.440609i \(0.145238\pi\)
−0.897699 + 0.440609i \(0.854762\pi\)
\(432\) −283359. + 325468.i −1.51834 + 1.74398i
\(433\) 49710.2 0.265137 0.132568 0.991174i \(-0.457678\pi\)
0.132568 + 0.991174i \(0.457678\pi\)
\(434\) 20962.9 9110.18i 0.111294 0.0483668i
\(435\) 117816. 117816.i 0.622626 0.622626i
\(436\) −344537. + 11900.5i −1.81244 + 0.0626028i
\(437\) −150447. + 150447.i −0.787809 + 0.787809i
\(438\) 63364.8 160772.i 0.330294 0.838032i
\(439\) 182166. 0.945233 0.472617 0.881268i \(-0.343310\pi\)
0.472617 + 0.881268i \(0.343310\pi\)
\(440\) 108732. + 38573.6i 0.561630 + 0.199244i
\(441\) 336455.i 1.73002i
\(442\) 7547.37 19149.5i 0.0386324 0.0980194i
\(443\) −3141.28 3141.28i −0.0160066 0.0160066i 0.699058 0.715065i \(-0.253603\pi\)
−0.715065 + 0.699058i \(0.753603\pi\)
\(444\) −151157. 141063.i −0.766765 0.715564i
\(445\) −154729. 154729.i −0.781359 0.781359i
\(446\) −83501.6 + 36288.7i −0.419783 + 0.182432i
\(447\) 78004.9i 0.390397i
\(448\) −76392.7 62005.8i −0.380624 0.308941i
\(449\) −108328. −0.537341 −0.268670 0.963232i \(-0.586584\pi\)
−0.268670 + 0.963232i \(0.586584\pi\)
\(450\) 58401.7 + 134384.i 0.288403 + 0.663627i
\(451\) 111294. 111294.i 0.547165 0.547165i
\(452\) −31680.8 + 33947.7i −0.155067 + 0.166162i
\(453\) 249978. 249978.i 1.21816 1.21816i
\(454\) 34104.8 + 13441.7i 0.165464 + 0.0652143i
\(455\) −26348.7 −0.127273
\(456\) 77285.7 217854.i 0.371680 1.04770i
\(457\) 220908.i 1.05774i 0.848703 + 0.528870i \(0.177384\pi\)
−0.848703 + 0.528870i \(0.822616\pi\)
\(458\) 189824. + 74815.1i 0.904939 + 0.356663i
\(459\) −115467. 115467.i −0.548066 0.548066i
\(460\) −10946.6 316920.i −0.0517326 1.49773i
\(461\) −137539. 137539.i −0.647176 0.647176i 0.305133 0.952310i \(-0.401299\pi\)
−0.952310 + 0.305133i \(0.901299\pi\)
\(462\) −54470.6 125339.i −0.255199 0.587222i
\(463\) 53332.6i 0.248789i −0.992233 0.124394i \(-0.960301\pi\)
0.992233 0.124394i \(-0.0396988\pi\)
\(464\) −83246.8 + 95617.8i −0.386662 + 0.444123i
\(465\) −80035.3 −0.370148
\(466\) −250291. + 108773.i −1.15259 + 0.500899i
\(467\) −207164. + 207164.i −0.949908 + 0.949908i −0.998804 0.0488961i \(-0.984430\pi\)
0.0488961 + 0.998804i \(0.484430\pi\)
\(468\) −5411.90 156682.i −0.0247092 0.715364i
\(469\) 95973.3 95973.3i 0.436320 0.436320i
\(470\) −48457.2 + 122947.i −0.219363 + 0.556575i
\(471\) 327485. 1.47622
\(472\) −91580.5 192284.i −0.411073 0.863097i
\(473\) 25443.3i 0.113724i
\(474\) 210111. 533102.i 0.935175 2.37276i
\(475\) −31128.8 31128.8i −0.137967 0.137967i
\(476\) 25402.0 27219.6i 0.112113 0.120134i
\(477\) 412116. + 412116.i 1.81127 + 1.81127i
\(478\) −368894. + 160316.i −1.61453 + 0.701653i
\(479\) 269434.i 1.17430i −0.809477 0.587152i \(-0.800249\pi\)
0.809477 0.587152i \(-0.199751\pi\)
\(480\) 158792. + 305744.i 0.689200 + 1.32702i
\(481\) 42129.6 0.182095
\(482\) −56698.2 130465.i −0.244048 0.561564i
\(483\) −265613. + 265613.i −1.13856 + 1.13856i
\(484\) 82118.2 + 76634.8i 0.350549 + 0.327141i
\(485\) −161322. + 161322.i −0.685821 + 0.685821i
\(486\) −251208. 99008.4i −1.06356 0.419179i
\(487\) −114893. −0.484436 −0.242218 0.970222i \(-0.577875\pi\)
−0.242218 + 0.970222i \(0.577875\pi\)
\(488\) 172934. + 363096.i 0.726174 + 1.52469i
\(489\) 171667.i 0.717910i
\(490\) 140166. + 55243.7i 0.583783 + 0.230086i
\(491\) 83485.8 + 83485.8i 0.346298 + 0.346298i 0.858728 0.512431i \(-0.171255\pi\)
−0.512431 + 0.858728i \(0.671255\pi\)
\(492\) 469727. 16224.7i 1.94051 0.0670265i
\(493\) −33922.5 33922.5i −0.139571 0.139571i
\(494\) 18773.7 + 43198.9i 0.0769300 + 0.177019i
\(495\) 332522.i 1.35710i
\(496\) 60753.3 4201.94i 0.246949 0.0170799i
\(497\) −118405. −0.479356
\(498\) −19292.3 + 8384.17i −0.0777902 + 0.0338066i
\(499\) −8291.04 + 8291.04i −0.0332972 + 0.0332972i −0.723559 0.690262i \(-0.757495\pi\)
0.690262 + 0.723559i \(0.257495\pi\)
\(500\) 271948. 9393.27i 1.08779 0.0375731i
\(501\) −46051.8 + 46051.8i −0.183472 + 0.183472i
\(502\) 60581.0 153708.i 0.240397 0.609944i
\(503\) 302384. 1.19515 0.597575 0.801813i \(-0.296131\pi\)
0.597575 + 0.801813i \(0.296131\pi\)
\(504\) 94812.9 267260.i 0.373255 1.05214i
\(505\) 220283.i 0.863770i
\(506\) −122891. + 311803.i −0.479975 + 1.21781i
\(507\) −296539. 296539.i −1.15363 1.15363i
\(508\) 46701.8 + 43583.3i 0.180970 + 0.168886i
\(509\) −41954.6 41954.6i −0.161936 0.161936i 0.621488 0.783424i \(-0.286529\pi\)
−0.783424 + 0.621488i \(0.786529\pi\)
\(510\) −119566. + 51961.6i −0.459691 + 0.199776i
\(511\) 63693.3i 0.243923i
\(512\) −136588. 223748.i −0.521041 0.853532i
\(513\) 373681. 1.41993
\(514\) 4675.71 + 10759.0i 0.0176979 + 0.0407235i
\(515\) 89431.9 89431.9i 0.337193 0.337193i
\(516\) −51838.4 + 55547.5i −0.194694 + 0.208625i
\(517\) 98761.0 98761.0i 0.369492 0.369492i
\(518\) 70897.4 + 27942.8i 0.264223 + 0.104138i
\(519\) −391635. −1.45394
\(520\) −66161.8 23471.5i −0.244681 0.0868030i
\(521\) 16852.7i 0.0620860i 0.999518 + 0.0310430i \(0.00988289\pi\)
−0.999518 + 0.0310430i \(0.990117\pi\)
\(522\) −339950. 133984.i −1.24760 0.491715i
\(523\) −92911.9 92911.9i −0.339678 0.339678i 0.516568 0.856246i \(-0.327209\pi\)
−0.856246 + 0.516568i \(0.827209\pi\)
\(524\) 12997.6 + 376297.i 0.0473369 + 1.37047i
\(525\) −54957.5 54957.5i −0.199392 0.199392i
\(526\) 37073.1 + 85306.6i 0.133995 + 0.308327i
\(527\) 23044.3i 0.0829741i
\(528\) −25123.8 363250.i −0.0901192 1.30298i
\(529\) 641343. 2.29181
\(530\) 239353. 104020.i 0.852094 0.370309i
\(531\) 434057. 434057.i 1.53942 1.53942i
\(532\) 2941.09 + 85148.6i 0.0103917 + 0.300853i
\(533\) −67720.9 + 67720.9i −0.238379 + 0.238379i
\(534\) −253230. + 642504.i −0.888041 + 2.25317i
\(535\) −135409. −0.473086
\(536\) 326483. 155496.i 1.13640 0.541241i
\(537\) 555796.i 1.92738i
\(538\) −117892. + 299121.i −0.407306 + 1.03343i
\(539\) −112593. 112593.i −0.387554 0.387554i
\(540\) −379989. + 407178.i −1.30312 + 1.39636i
\(541\) −40690.8 40690.8i −0.139028 0.139028i 0.634168 0.773196i \(-0.281343\pi\)
−0.773196 + 0.634168i \(0.781343\pi\)
\(542\) 336331. 146165.i 1.14490 0.497559i
\(543\) 318847.i 1.08139i
\(544\) 88032.0 45720.4i 0.297470 0.154494i
\(545\) −444928. −1.49795
\(546\) 33144.7 + 76267.2i 0.111181 + 0.255831i
\(547\) 222264. 222264.i 0.742839 0.742839i −0.230284 0.973123i \(-0.573966\pi\)
0.973123 + 0.230284i \(0.0739656\pi\)
\(548\) −125709. 117315.i −0.418605 0.390653i
\(549\) −819641. + 819641.i −2.71944 + 2.71944i
\(550\) −64514.7 25427.2i −0.213272 0.0840568i
\(551\) 109782. 0.361600
\(552\) −903565. + 430347.i −2.96539 + 1.41234i
\(553\) 211201.i 0.690629i
\(554\) −399087. 157292.i −1.30031 0.512492i
\(555\) −188684. 188684.i −0.612560 0.612560i
\(556\) 171499. 5923.68i 0.554768 0.0191621i
\(557\) 223795. + 223795.i 0.721341 + 0.721341i 0.968878 0.247537i \(-0.0796213\pi\)
−0.247537 + 0.968878i \(0.579621\pi\)
\(558\) 69958.5 + 160977.i 0.224684 + 0.517006i
\(559\) 15481.9i 0.0495451i
\(560\) −95772.0 83381.1i −0.305395 0.265883i
\(561\) 137784. 0.437798
\(562\) 284981. 123849.i 0.902283 0.392120i
\(563\) 201474. 201474.i 0.635626 0.635626i −0.313847 0.949474i \(-0.601618\pi\)
0.949474 + 0.313847i \(0.101618\pi\)
\(564\) 416831. 14397.6i 1.31039 0.0452619i
\(565\) −42375.6 + 42375.6i −0.132745 + 0.132745i
\(566\) 90923.9 230695.i 0.283821 0.720121i
\(567\) 300825. 0.935724
\(568\) −297317. 105476.i −0.921559 0.326932i
\(569\) 473995.i 1.46403i −0.681289 0.732014i \(-0.738580\pi\)
0.681289 0.732014i \(-0.261420\pi\)
\(570\) 109392. 277553.i 0.336694 0.854273i
\(571\) 303262. + 303262.i 0.930133 + 0.930133i 0.997714 0.0675806i \(-0.0215280\pi\)
−0.0675806 + 0.997714i \(0.521528\pi\)
\(572\) 54243.7 + 50621.6i 0.165790 + 0.154719i
\(573\) 134995. + 134995.i 0.411158 + 0.411158i
\(574\) −158880. + 69047.0i −0.482219 + 0.209566i
\(575\) 190601.i 0.576486i
\(576\) 476152. 586632.i 1.43516 1.76816i
\(577\) −340809. −1.02367 −0.511834 0.859084i \(-0.671034\pi\)
−0.511834 + 0.859084i \(0.671034\pi\)
\(578\) −118196. 271974.i −0.353792 0.814089i
\(579\) −790714. + 790714.i −2.35864 + 2.35864i
\(580\) −111635. + 119623.i −0.331852 + 0.355597i
\(581\) 5482.33 5482.33i 0.0162410 0.0162410i
\(582\) 669884. + 264021.i 1.97767 + 0.779458i
\(583\) −275824. −0.811512
\(584\) −56738.3 + 159935.i −0.166361 + 0.468939i
\(585\) 202336.i 0.591236i
\(586\) 325859. + 128431.i 0.948931 + 0.374002i
\(587\) −253433. 253433.i −0.735507 0.735507i 0.236198 0.971705i \(-0.424099\pi\)
−0.971705 + 0.236198i \(0.924099\pi\)
\(588\) −16414.0 475209.i −0.0474745 1.37445i
\(589\) −37288.7 37288.7i −0.107485 0.107485i
\(590\) −109558. 252096.i −0.314730 0.724206i
\(591\) 527316.i 1.50972i
\(592\) 153132. + 133320.i 0.436942 + 0.380411i
\(593\) 117236. 0.333390 0.166695 0.986009i \(-0.446691\pi\)
0.166695 + 0.986009i \(0.446691\pi\)
\(594\) 539848. 234611.i 1.53002 0.664928i
\(595\) 33977.2 33977.2i 0.0959741 0.0959741i
\(596\) 2644.32 + 76556.6i 0.00744425 + 0.215521i
\(597\) 690526. 690526.i 1.93745 1.93745i
\(598\) 74777.6 189728.i 0.209107 0.530554i
\(599\) 277087. 0.772257 0.386129 0.922445i \(-0.373812\pi\)
0.386129 + 0.922445i \(0.373812\pi\)
\(600\) −89042.5 186955.i −0.247340 0.519320i
\(601\) 323876.i 0.896665i 0.893867 + 0.448333i \(0.147982\pi\)
−0.893867 + 0.448333i \(0.852018\pi\)
\(602\) 10268.5 26053.5i 0.0283343 0.0718909i
\(603\) 736994. + 736994.i 2.02689 + 2.02689i
\(604\) −236863. + 253811.i −0.649266 + 0.695723i
\(605\) 102505. + 102505.i 0.280050 + 0.280050i
\(606\) −637617. + 277100.i −1.73626 + 0.754555i
\(607\) 715467.i 1.94184i 0.239414 + 0.970918i \(0.423045\pi\)
−0.239414 + 0.970918i \(0.576955\pi\)
\(608\) −68465.6 + 216429.i −0.185210 + 0.585475i
\(609\) 193819. 0.522591
\(610\) 206881. + 476040.i 0.555982 + 1.27933i
\(611\) −60094.8 + 60094.8i −0.160974 + 0.160974i
\(612\) 209023. + 195066.i 0.558074 + 0.520809i
\(613\) 137200. 137200.i 0.365117 0.365117i −0.500576 0.865693i \(-0.666878\pi\)
0.865693 + 0.500576i \(0.166878\pi\)
\(614\) −524697. 206799.i −1.39178 0.548544i
\(615\) 606596. 1.60380
\(616\) 57708.2 + 121165.i 0.152082 + 0.319313i
\(617\) 106650.i 0.280149i 0.990141 + 0.140074i \(0.0447342\pi\)
−0.990141 + 0.140074i \(0.955266\pi\)
\(618\) −371362. 146365.i −0.972347 0.383231i
\(619\) −373667. 373667.i −0.975221 0.975221i 0.0244790 0.999700i \(-0.492207\pi\)
−0.999700 + 0.0244790i \(0.992207\pi\)
\(620\) 78549.3 2713.15i 0.204343 0.00705814i
\(621\) −1.14402e6 1.14402e6i −2.96654 2.96654i
\(622\) −203557. 468392.i −0.526144 1.21068i
\(623\) 254543.i 0.655820i
\(624\) 15287.5 + 221033.i 0.0392616 + 0.567660i
\(625\) 227071. 0.581302
\(626\) 88531.2 38474.5i 0.225916 0.0981803i
\(627\) −222953. + 222953.i −0.567124 + 0.567124i
\(628\) −321405. + 11101.5i −0.814954 + 0.0281491i
\(629\) −54327.1 + 54327.1i −0.137314 + 0.137314i
\(630\) 134200. 340498.i 0.338122 0.857894i
\(631\) −445762. −1.11955 −0.559777 0.828644i \(-0.689113\pi\)
−0.559777 + 0.828644i \(0.689113\pi\)
\(632\) −188138. + 530327.i −0.471024 + 1.32773i
\(633\) 289376.i 0.722195i
\(634\) 132210. 335449.i 0.328917 0.834540i
\(635\) 58296.2 + 58296.2i 0.144575 + 0.144575i
\(636\) −602177. 561967.i −1.48871 1.38930i
\(637\) 68511.2 + 68511.2i 0.168843 + 0.168843i
\(638\) 158599. 68925.2i 0.389637 0.169331i
\(639\) 909253.i 2.22681i
\(640\) −166208. 294685.i −0.405782 0.719445i
\(641\) −412550. −1.00406 −0.502031 0.864850i \(-0.667414\pi\)
−0.502031 + 0.864850i \(0.667414\pi\)
\(642\) 170334. + 391946.i 0.413269 + 0.950946i
\(643\) −71290.0 + 71290.0i −0.172428 + 0.172428i −0.788045 0.615617i \(-0.788907\pi\)
0.615617 + 0.788045i \(0.288907\pi\)
\(644\) 251677. 269685.i 0.606837 0.650258i
\(645\) −69338.0 + 69338.0i −0.166668 + 0.166668i
\(646\) −79915.1 31496.9i −0.191498 0.0754750i
\(647\) 138722. 0.331388 0.165694 0.986177i \(-0.447014\pi\)
0.165694 + 0.986177i \(0.447014\pi\)
\(648\) 755375. + 267976.i 1.79892 + 0.638185i
\(649\) 290509.i 0.689716i
\(650\) 39256.4 + 15472.1i 0.0929146 + 0.0366204i
\(651\) −65832.7 65832.7i −0.155339 0.155339i
\(652\) −5819.42 168480.i −0.0136894 0.396327i
\(653\) 467444. + 467444.i 1.09623 + 1.09623i 0.994847 + 0.101387i \(0.0323281\pi\)
0.101387 + 0.994847i \(0.467672\pi\)
\(654\) 559686. + 1.28786e6i 1.30855 + 3.01101i
\(655\) 485943.i 1.13267i
\(656\) −460456. + 31846.9i −1.06999 + 0.0740048i
\(657\) −489111. −1.13312
\(658\) −140988. + 61271.6i −0.325635 + 0.141517i
\(659\) 180573. 180573.i 0.415797 0.415797i −0.467955 0.883752i \(-0.655009\pi\)
0.883752 + 0.467955i \(0.155009\pi\)
\(660\) −16222.2 469654.i −0.0372410 1.07818i
\(661\) 142726. 142726.i 0.326664 0.326664i −0.524652 0.851317i \(-0.675805\pi\)
0.851317 + 0.524652i \(0.175805\pi\)
\(662\) 230793. 585576.i 0.526631 1.33619i
\(663\) −83840.0 −0.190732
\(664\) 18649.9 8882.50i 0.0422999 0.0201465i
\(665\) 109959.i 0.248650i
\(666\) −214577. + 544432.i −0.483765 + 1.22743i
\(667\) −336097. 336097.i −0.755462 0.755462i
\(668\) 43635.6 46757.9i 0.0977886 0.104786i
\(669\) 262232. + 262232.i 0.585914 + 0.585914i
\(670\) 428039. 186020.i 0.953529 0.414391i
\(671\) 548576.i 1.21841i
\(672\) −120875. + 382102.i −0.267669 + 0.846138i
\(673\) −272445. −0.601517 −0.300759 0.953700i \(-0.597240\pi\)
−0.300759 + 0.953700i \(0.597240\pi\)
\(674\) −142185. 327173.i −0.312993 0.720208i
\(675\) 236708. 236708.i 0.519523 0.519523i
\(676\) 301086. + 280981.i 0.658866 + 0.614871i
\(677\) 285404. 285404.i 0.622706 0.622706i −0.323517 0.946222i \(-0.604865\pi\)
0.946222 + 0.323517i \(0.104865\pi\)
\(678\) 175963. + 69352.3i 0.382792 + 0.150870i
\(679\) −265390. −0.575632
\(680\) 115584. 55050.1i 0.249966 0.119053i
\(681\) 149317.i 0.321970i
\(682\) −77281.2 30458.8i −0.166152 0.0654854i
\(683\) 186551. + 186551.i 0.399904 + 0.399904i 0.878199 0.478295i \(-0.158745\pi\)
−0.478295 + 0.878199i \(0.658745\pi\)
\(684\) −653869. + 22585.1i −1.39759 + 0.0482736i
\(685\) −156918. 156918.i −0.334419 0.334419i
\(686\) 161803. + 372315.i 0.343826 + 0.791155i
\(687\) 831084.i 1.76089i
\(688\) 48992.9 56273.5i 0.103504 0.118885i
\(689\) 167836. 0.353546
\(690\) −1.18463e6 + 514823.i −2.48819 + 1.08133i
\(691\) 544261. 544261.i 1.13986 1.13986i 0.151383 0.988475i \(-0.451627\pi\)
0.988475 0.151383i \(-0.0483727\pi\)
\(692\) 384364. 13276.2i 0.802657 0.0277243i
\(693\) −273515. + 273515.i −0.569528 + 0.569528i
\(694\) 35419.2 89866.9i 0.0735394 0.186587i
\(695\) 221470. 0.458506
\(696\) 486682. + 172655.i 1.00468 + 0.356419i
\(697\) 174655.i 0.359514i
\(698\) 53850.9 136632.i 0.110531 0.280442i
\(699\) 786027. + 786027.i 1.60873 + 1.60873i
\(700\) 55800.2 + 52074.1i 0.113878 + 0.106274i
\(701\) −69213.2 69213.2i −0.140849 0.140849i 0.633167 0.774015i \(-0.281755\pi\)
−0.774015 + 0.633167i \(0.781755\pi\)
\(702\) −328490. + 142758.i −0.666574 + 0.289684i
\(703\) 175817.i 0.355754i
\(704\) 36971.3 + 355654.i 0.0745967 + 0.717600i
\(705\) 538287. 1.08302
\(706\) 353771. + 814040.i 0.709762 + 1.63319i
\(707\) 181193. 181193.i 0.362496 0.362496i
\(708\) −591886. + 634237.i −1.18079 + 1.26528i
\(709\) 133745. 133745.i 0.266063 0.266063i −0.561448 0.827512i \(-0.689756\pi\)
0.827512 + 0.561448i \(0.189756\pi\)
\(710\) −378792. 149293.i −0.751423 0.296158i
\(711\) −1.62184e6 −3.20826
\(712\) 226748. 639160.i 0.447284 1.26081i
\(713\) 228318.i 0.449118i
\(714\) −141089. 55607.4i −0.276756 0.109078i
\(715\) 67710.4 + 67710.4i 0.132447 + 0.132447i
\(716\) 18841.2 + 545477.i 0.0367520 + 1.06402i
\(717\) 1.15849e6 + 1.15849e6i 2.25349 + 2.25349i
\(718\) −170320. 391912.i −0.330382 0.760221i
\(719\) 762270.i 1.47452i 0.675609 + 0.737261i \(0.263881\pi\)
−0.675609 + 0.737261i \(0.736119\pi\)
\(720\) 640296. 735448.i 1.23514 1.41869i
\(721\) 147124. 0.283017
\(722\) −297809. + 129424.i −0.571299 + 0.248279i
\(723\) −409718. + 409718.i −0.783805 + 0.783805i
\(724\) 10808.7 + 312927.i 0.0206204 + 0.596988i
\(725\) 69541.2 69541.2i 0.132302 0.132302i
\(726\) 167761. 425649.i 0.318286 0.807566i
\(727\) −664888. −1.25800 −0.628999 0.777406i \(-0.716535\pi\)
−0.628999 + 0.777406i \(0.716535\pi\)
\(728\) −35114.7 73727.6i −0.0662562 0.139113i
\(729\) 85436.8i 0.160764i
\(730\) −80308.8 + 203762.i −0.150701 + 0.382365i
\(731\) 19964.3 + 19964.3i 0.0373610 + 0.0373610i
\(732\) 1.11767e6 1.19765e6i 2.08590 2.23515i
\(733\) −616942. 616942.i −1.14825 1.14825i −0.986897 0.161352i \(-0.948414\pi\)
−0.161352 0.986897i \(-0.551586\pi\)
\(734\) 290090. 126069.i 0.538444 0.234001i
\(735\) 613675.i 1.13596i
\(736\) 872201. 452987.i 1.61013 0.836239i
\(737\) −493261. −0.908117
\(738\) −530223. 1.22006e6i −0.973521 2.24011i
\(739\) −204895. + 204895.i −0.375182 + 0.375182i −0.869360 0.494179i \(-0.835469\pi\)
0.494179 + 0.869360i \(0.335469\pi\)
\(740\) 191577. + 178784.i 0.349848 + 0.326487i
\(741\) 135664. 135664.i 0.247075 0.247075i
\(742\) 282440. + 111318.i 0.513001 + 0.202189i
\(743\) 183598. 0.332576 0.166288 0.986077i \(-0.446822\pi\)
0.166288 + 0.986077i \(0.446822\pi\)
\(744\) −106663. 223951.i −0.192693 0.404582i
\(745\) 98863.7i 0.178125i
\(746\) −454401. 179093.i −0.816511 0.321811i
\(747\) 42099.7 + 42099.7i 0.0754462 + 0.0754462i
\(748\) −135226. + 4670.80i −0.241689 + 0.00834811i
\(749\) −111380. 111380.i −0.198538 0.198538i
\(750\) −441769. 1.01653e6i −0.785366 1.80716i
\(751\) 167996.i 0.297864i 0.988847 + 0.148932i \(0.0475836\pi\)
−0.988847 + 0.148932i \(0.952416\pi\)
\(752\) −408604. + 28260.6i −0.722548 + 0.0499742i
\(753\) −672964. −1.18687
\(754\) −96505.7 + 41940.1i −0.169750 + 0.0737712i
\(755\) −316823. + 316823.i −0.555805 + 0.555805i
\(756\) −647481. + 22364.4i −1.13288 + 0.0391304i
\(757\) −414105. + 414105.i −0.722634 + 0.722634i −0.969141 0.246507i \(-0.920717\pi\)
0.246507 + 0.969141i \(0.420717\pi\)
\(758\) −348936. + 885333.i −0.607306 + 1.54088i
\(759\) 1.36513e6 2.36969
\(760\) −97952.1 + 276109.i −0.169585 + 0.478027i
\(761\) 315375.i 0.544575i 0.962216 + 0.272287i \(0.0877801\pi\)
−0.962216 + 0.272287i \(0.912220\pi\)
\(762\) 95408.1 242073.i 0.164314 0.416904i
\(763\) −365974. 365974.i −0.628638 0.628638i
\(764\) −137065. 127912.i −0.234822 0.219142i
\(765\) 260916. + 260916.i 0.445839 + 0.445839i
\(766\) 81360.2 35358.1i 0.138661 0.0602603i
\(767\) 176771.i 0.300483i
\(768\) −643898. + 851787.i −1.09168 + 1.44414i
\(769\) 156016. 0.263825 0.131913 0.991261i \(-0.457888\pi\)
0.131913 + 0.991261i \(0.457888\pi\)
\(770\) 69036.3 + 158855.i 0.116438 + 0.267929i
\(771\) 33788.0 33788.0i