Properties

Label 16.5.f.a.3.1
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 3.1
Root \(2.24452 - 1.72109i\) of defining polynomial
Character \(\chi\) \(=\) 16.3
Dual form 16.5.f.a.11.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.96560 + 0.523430i) q^{2} +(5.54016 - 5.54016i) q^{3} +(15.4520 - 4.15143i) q^{4} +(21.7374 - 21.7374i) q^{5} +(-19.0702 + 24.8700i) q^{6} -6.62054 q^{7} +(-59.1037 + 24.5510i) q^{8} +19.6133i q^{9} +O(q^{10})\) \(q+(-3.96560 + 0.523430i) q^{2} +(5.54016 - 5.54016i) q^{3} +(15.4520 - 4.15143i) q^{4} +(21.7374 - 21.7374i) q^{5} +(-19.0702 + 24.8700i) q^{6} -6.62054 q^{7} +(-59.1037 + 24.5510i) q^{8} +19.6133i q^{9} +(-74.8239 + 97.5799i) q^{10} +(-90.9986 - 90.9986i) q^{11} +(62.6071 - 108.606i) q^{12} +(221.402 + 221.402i) q^{13} +(26.2544 - 3.46539i) q^{14} -240.857i q^{15} +(221.531 - 128.296i) q^{16} -132.575 q^{17} +(-10.2662 - 77.7787i) q^{18} +(-402.520 + 402.520i) q^{19} +(245.646 - 426.128i) q^{20} +(-36.6788 + 36.6788i) q^{21} +(408.496 + 313.233i) q^{22} +27.5037 q^{23} +(-191.427 + 463.460i) q^{24} -320.028i q^{25} +(-993.879 - 762.103i) q^{26} +(557.414 + 557.414i) q^{27} +(-102.301 + 27.4847i) q^{28} +(174.909 + 174.909i) q^{29} +(126.072 + 955.144i) q^{30} -1083.96i q^{31} +(-811.351 + 624.728i) q^{32} -1008.29 q^{33} +(525.742 - 69.3940i) q^{34} +(-143.913 + 143.913i) q^{35} +(81.4234 + 303.066i) q^{36} +(553.474 - 553.474i) q^{37} +(1385.54 - 1806.93i) q^{38} +2453.20 q^{39} +(-751.085 + 1818.43i) q^{40} -1803.47i q^{41} +(126.255 - 164.653i) q^{42} +(17.8633 + 17.8633i) q^{43} +(-1783.89 - 1028.34i) q^{44} +(426.342 + 426.342i) q^{45} +(-109.069 + 14.3963i) q^{46} +2268.26i q^{47} +(516.536 - 1938.10i) q^{48} -2357.17 q^{49} +(167.512 + 1269.10i) q^{50} +(-734.489 + 734.489i) q^{51} +(4340.24 + 2501.97i) q^{52} +(-822.415 + 822.415i) q^{53} +(-2502.25 - 1918.71i) q^{54} -3956.14 q^{55} +(391.298 - 162.541i) q^{56} +4460.05i q^{57} +(-785.174 - 602.068i) q^{58} +(-972.483 - 972.483i) q^{59} +(-999.902 - 3721.73i) q^{60} +(-2056.32 - 2056.32i) q^{61} +(567.378 + 4298.57i) q^{62} -129.851i q^{63} +(2890.50 - 2902.11i) q^{64} +9625.38 q^{65} +(3998.49 - 527.771i) q^{66} +(4611.22 - 4611.22i) q^{67} +(-2048.56 + 550.378i) q^{68} +(152.375 - 152.375i) q^{69} +(495.374 - 646.031i) q^{70} -3105.84 q^{71} +(-481.527 - 1159.22i) q^{72} +723.400i q^{73} +(-1905.15 + 2484.56i) q^{74} +(-1773.00 - 1773.00i) q^{75} +(-4548.72 + 7890.79i) q^{76} +(602.460 + 602.460i) q^{77} +(-9728.41 + 1284.08i) q^{78} -3418.44i q^{79} +(2026.68 - 7604.33i) q^{80} +4587.64 q^{81} +(943.989 + 7151.83i) q^{82} +(-161.591 + 161.591i) q^{83} +(-414.493 + 719.033i) q^{84} +(-2881.84 + 2881.84i) q^{85} +(-80.1892 - 61.4887i) q^{86} +1938.05 q^{87} +(7612.46 + 3144.25i) q^{88} -1464.04i q^{89} +(-1913.87 - 1467.55i) q^{90} +(-1465.80 - 1465.80i) q^{91} +(424.988 - 114.180i) q^{92} +(-6005.32 - 6005.32i) q^{93} +(-1187.28 - 8995.04i) q^{94} +17499.5i q^{95} +(-1033.92 + 7956.10i) q^{96} -8264.99 q^{97} +(9347.60 - 1233.81i) q^{98} +(1784.78 - 1784.78i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.96560 + 0.523430i −0.991401 + 0.130858i
\(3\) 5.54016 5.54016i 0.615573 0.615573i −0.328820 0.944393i \(-0.606651\pi\)
0.944393 + 0.328820i \(0.106651\pi\)
\(4\) 15.4520 4.15143i 0.965753 0.259465i
\(5\) 21.7374 21.7374i 0.869495 0.869495i −0.122921 0.992416i \(-0.539226\pi\)
0.992416 + 0.122921i \(0.0392262\pi\)
\(6\) −19.0702 + 24.8700i −0.529727 + 0.690832i
\(7\) −6.62054 −0.135113 −0.0675565 0.997715i \(-0.521520\pi\)
−0.0675565 + 0.997715i \(0.521520\pi\)
\(8\) −59.1037 + 24.5510i −0.923495 + 0.383610i
\(9\) 19.6133i 0.242140i
\(10\) −74.8239 + 97.5799i −0.748239 + 0.975799i
\(11\) −90.9986 90.9986i −0.752054 0.752054i 0.222808 0.974862i \(-0.428478\pi\)
−0.974862 + 0.222808i \(0.928478\pi\)
\(12\) 62.6071 108.606i 0.434772 0.754211i
\(13\) 221.402 + 221.402i 1.31007 + 1.31007i 0.921362 + 0.388707i \(0.127078\pi\)
0.388707 + 0.921362i \(0.372922\pi\)
\(14\) 26.2544 3.46539i 0.133951 0.0176806i
\(15\) 240.857i 1.07048i
\(16\) 221.531 128.296i 0.865356 0.501157i
\(17\) −132.575 −0.458738 −0.229369 0.973339i \(-0.573666\pi\)
−0.229369 + 0.973339i \(0.573666\pi\)
\(18\) −10.2662 77.7787i −0.0316858 0.240058i
\(19\) −402.520 + 402.520i −1.11501 + 1.11501i −0.122552 + 0.992462i \(0.539108\pi\)
−0.992462 + 0.122552i \(0.960892\pi\)
\(20\) 245.646 426.128i 0.614114 1.06532i
\(21\) −36.6788 + 36.6788i −0.0831720 + 0.0831720i
\(22\) 408.496 + 313.233i 0.843999 + 0.647175i
\(23\) 27.5037 0.0519918 0.0259959 0.999662i \(-0.491724\pi\)
0.0259959 + 0.999662i \(0.491724\pi\)
\(24\) −191.427 + 463.460i −0.332339 + 0.804618i
\(25\) 320.028i 0.512044i
\(26\) −993.879 762.103i −1.47024 1.12737i
\(27\) 557.414 + 557.414i 0.764628 + 0.764628i
\(28\) −102.301 + 27.4847i −0.130486 + 0.0350571i
\(29\) 174.909 + 174.909i 0.207978 + 0.207978i 0.803407 0.595430i \(-0.203018\pi\)
−0.595430 + 0.803407i \(0.703018\pi\)
\(30\) 126.072 + 955.144i 0.140080 + 1.06127i
\(31\) 1083.96i 1.12795i −0.825791 0.563976i \(-0.809271\pi\)
0.825791 0.563976i \(-0.190729\pi\)
\(32\) −811.351 + 624.728i −0.792335 + 0.610086i
\(33\) −1008.29 −0.925888
\(34\) 525.742 69.3940i 0.454794 0.0600294i
\(35\) −143.913 + 143.913i −0.117480 + 0.117480i
\(36\) 81.4234 + 303.066i 0.0628267 + 0.233847i
\(37\) 553.474 553.474i 0.404291 0.404291i −0.475451 0.879742i \(-0.657715\pi\)
0.879742 + 0.475451i \(0.157715\pi\)
\(38\) 1385.54 1806.93i 0.959518 1.25133i
\(39\) 2453.20 1.61289
\(40\) −751.085 + 1818.43i −0.469428 + 1.13652i
\(41\) 1803.47i 1.07285i −0.843947 0.536427i \(-0.819774\pi\)
0.843947 0.536427i \(-0.180226\pi\)
\(42\) 126.255 164.653i 0.0715731 0.0933404i
\(43\) 17.8633 + 17.8633i 0.00966108 + 0.00966108i 0.711921 0.702260i \(-0.247825\pi\)
−0.702260 + 0.711921i \(0.747825\pi\)
\(44\) −1783.89 1028.34i −0.921430 0.531167i
\(45\) 426.342 + 426.342i 0.210539 + 0.210539i
\(46\) −109.069 + 14.3963i −0.0515448 + 0.00680352i
\(47\) 2268.26i 1.02683i 0.858141 + 0.513414i \(0.171620\pi\)
−0.858141 + 0.513414i \(0.828380\pi\)
\(48\) 516.536 1938.10i 0.224191 0.841189i
\(49\) −2357.17 −0.981744
\(50\) 167.512 + 1269.10i 0.0670048 + 0.507641i
\(51\) −734.489 + 734.489i −0.282387 + 0.282387i
\(52\) 4340.24 + 2501.97i 1.60512 + 0.925285i
\(53\) −822.415 + 822.415i −0.292779 + 0.292779i −0.838177 0.545398i \(-0.816378\pi\)
0.545398 + 0.838177i \(0.316378\pi\)
\(54\) −2502.25 1918.71i −0.858110 0.657996i
\(55\) −3956.14 −1.30782
\(56\) 391.298 162.541i 0.124776 0.0518307i
\(57\) 4460.05i 1.37275i
\(58\) −785.174 602.068i −0.233405 0.178974i
\(59\) −972.483 972.483i −0.279369 0.279369i 0.553488 0.832857i \(-0.313296\pi\)
−0.832857 + 0.553488i \(0.813296\pi\)
\(60\) −999.902 3721.73i −0.277751 1.03381i
\(61\) −2056.32 2056.32i −0.552626 0.552626i 0.374572 0.927198i \(-0.377790\pi\)
−0.927198 + 0.374572i \(0.877790\pi\)
\(62\) 567.378 + 4298.57i 0.147601 + 1.11825i
\(63\) 129.851i 0.0327163i
\(64\) 2890.50 2902.11i 0.705687 0.708523i
\(65\) 9625.38 2.27820
\(66\) 3998.49 527.771i 0.917927 0.121159i
\(67\) 4611.22 4611.22i 1.02723 1.02723i 0.0276077 0.999619i \(-0.491211\pi\)
0.999619 0.0276077i \(-0.00878893\pi\)
\(68\) −2048.56 + 550.378i −0.443028 + 0.119026i
\(69\) 152.375 152.375i 0.0320048 0.0320048i
\(70\) 495.374 646.031i 0.101097 0.131843i
\(71\) −3105.84 −0.616115 −0.308058 0.951368i \(-0.599679\pi\)
−0.308058 + 0.951368i \(0.599679\pi\)
\(72\) −481.527 1159.22i −0.0928872 0.223615i
\(73\) 723.400i 0.135748i 0.997694 + 0.0678739i \(0.0216216\pi\)
−0.997694 + 0.0678739i \(0.978378\pi\)
\(74\) −1905.15 + 2484.56i −0.347910 + 0.453719i
\(75\) −1773.00 1773.00i −0.315200 0.315200i
\(76\) −4548.72 + 7890.79i −0.787521 + 1.36613i
\(77\) 602.460 + 602.460i 0.101612 + 0.101612i
\(78\) −9728.41 + 1284.08i −1.59902 + 0.211058i
\(79\) 3418.44i 0.547739i −0.961767 0.273869i \(-0.911696\pi\)
0.961767 0.273869i \(-0.0883036\pi\)
\(80\) 2026.68 7604.33i 0.316669 1.18818i
\(81\) 4587.64 0.699228
\(82\) 943.989 + 7151.83i 0.140391 + 1.06363i
\(83\) −161.591 + 161.591i −0.0234563 + 0.0234563i −0.718738 0.695281i \(-0.755280\pi\)
0.695281 + 0.718738i \(0.255280\pi\)
\(84\) −414.493 + 719.033i −0.0587434 + 0.101904i
\(85\) −2881.84 + 2881.84i −0.398871 + 0.398871i
\(86\) −80.1892 61.4887i −0.0108422 0.00831378i
\(87\) 1938.05 0.256051
\(88\) 7612.46 + 3144.25i 0.983014 + 0.406023i
\(89\) 1464.04i 0.184830i −0.995721 0.0924150i \(-0.970541\pi\)
0.995721 0.0924150i \(-0.0294586\pi\)
\(90\) −1913.87 1467.55i −0.236280 0.181178i
\(91\) −1465.80 1465.80i −0.177007 0.177007i
\(92\) 424.988 114.180i 0.0502113 0.0134900i
\(93\) −6005.32 6005.32i −0.694337 0.694337i
\(94\) −1187.28 8995.04i −0.134368 1.01800i
\(95\) 17499.5i 1.93900i
\(96\) −1033.92 + 7956.10i −0.112187 + 0.863293i
\(97\) −8264.99 −0.878413 −0.439207 0.898386i \(-0.644740\pi\)
−0.439207 + 0.898386i \(0.644740\pi\)
\(98\) 9347.60 1233.81i 0.973303 0.128469i
\(99\) 1784.78 1784.78i 0.182102 0.182102i
\(100\) −1328.57 4945.08i −0.132857 0.494508i
\(101\) 5035.04 5035.04i 0.493583 0.493583i −0.415850 0.909433i \(-0.636516\pi\)
0.909433 + 0.415850i \(0.136516\pi\)
\(102\) 2528.24 3297.14i 0.243006 0.316911i
\(103\) 1427.24 0.134531 0.0672653 0.997735i \(-0.478573\pi\)
0.0672653 + 0.997735i \(0.478573\pi\)
\(104\) −18521.3 7650.02i −1.71240 0.707287i
\(105\) 1594.60i 0.144635i
\(106\) 2830.90 3691.85i 0.251949 0.328573i
\(107\) 9978.53 + 9978.53i 0.871564 + 0.871564i 0.992643 0.121079i \(-0.0386355\pi\)
−0.121079 + 0.992643i \(0.538635\pi\)
\(108\) 10927.2 + 6299.11i 0.936835 + 0.540047i
\(109\) 9.47842 + 9.47842i 0.000797780 + 0.000797780i 0.707506 0.706708i \(-0.249820\pi\)
−0.706708 + 0.707506i \(0.749820\pi\)
\(110\) 15688.5 2070.76i 1.29657 0.171137i
\(111\) 6132.67i 0.497741i
\(112\) −1466.66 + 849.391i −0.116921 + 0.0677129i
\(113\) −13634.7 −1.06780 −0.533900 0.845548i \(-0.679274\pi\)
−0.533900 + 0.845548i \(0.679274\pi\)
\(114\) −2334.52 17686.8i −0.179634 1.36094i
\(115\) 597.858 597.858i 0.0452067 0.0452067i
\(116\) 3428.83 + 1976.58i 0.254818 + 0.146892i
\(117\) −4342.42 + 4342.42i −0.317220 + 0.317220i
\(118\) 4365.51 + 3347.46i 0.313524 + 0.240409i
\(119\) 877.721 0.0619816
\(120\) 5913.28 + 14235.5i 0.410645 + 0.988579i
\(121\) 1920.47i 0.131171i
\(122\) 9230.89 + 7078.21i 0.620189 + 0.475559i
\(123\) −9991.49 9991.49i −0.660419 0.660419i
\(124\) −4500.00 16749.4i −0.292664 1.08932i
\(125\) 6629.30 + 6629.30i 0.424275 + 0.424275i
\(126\) 67.9678 + 514.937i 0.00428117 + 0.0324349i
\(127\) 8047.14i 0.498923i −0.968385 0.249462i \(-0.919746\pi\)
0.968385 0.249462i \(-0.0802537\pi\)
\(128\) −9943.51 + 13021.6i −0.606904 + 0.794775i
\(129\) 197.931 0.0118942
\(130\) −38170.5 + 5038.21i −2.25861 + 0.298119i
\(131\) −15904.8 + 15904.8i −0.926799 + 0.926799i −0.997498 0.0706991i \(-0.977477\pi\)
0.0706991 + 0.997498i \(0.477477\pi\)
\(132\) −15580.2 + 4185.86i −0.894179 + 0.240235i
\(133\) 2664.90 2664.90i 0.150653 0.150653i
\(134\) −15872.6 + 20699.9i −0.883973 + 1.15281i
\(135\) 24233.4 1.32968
\(136\) 7835.70 3254.86i 0.423643 0.175976i
\(137\) 31169.3i 1.66068i −0.557257 0.830340i \(-0.688146\pi\)
0.557257 0.830340i \(-0.311854\pi\)
\(138\) −524.500 + 684.015i −0.0275415 + 0.0359176i
\(139\) 21432.1 + 21432.1i 1.10926 + 1.10926i 0.993247 + 0.116017i \(0.0370126\pi\)
0.116017 + 0.993247i \(0.462987\pi\)
\(140\) −1626.31 + 2821.20i −0.0829748 + 0.143939i
\(141\) 12566.5 + 12566.5i 0.632088 + 0.632088i
\(142\) 12316.5 1625.69i 0.610818 0.0806233i
\(143\) 40294.4i 1.97048i
\(144\) 2516.32 + 4344.96i 0.121350 + 0.209537i
\(145\) 7604.14 0.361671
\(146\) −378.649 2868.72i −0.0177636 0.134581i
\(147\) −13059.1 + 13059.1i −0.604335 + 0.604335i
\(148\) 6254.59 10850.0i 0.285546 0.495344i
\(149\) 11772.7 11772.7i 0.530276 0.530276i −0.390378 0.920654i \(-0.627656\pi\)
0.920654 + 0.390378i \(0.127656\pi\)
\(150\) 7959.07 + 6102.99i 0.353736 + 0.271244i
\(151\) −19454.9 −0.853246 −0.426623 0.904429i \(-0.640297\pi\)
−0.426623 + 0.904429i \(0.640297\pi\)
\(152\) 13908.2 33672.7i 0.601980 1.45744i
\(153\) 2600.25i 0.111079i
\(154\) −2704.46 2073.77i −0.114035 0.0874419i
\(155\) −23562.5 23562.5i −0.980749 0.980749i
\(156\) 37906.9 10184.3i 1.55765 0.418487i
\(157\) 18097.5 + 18097.5i 0.734208 + 0.734208i 0.971450 0.237242i \(-0.0762436\pi\)
−0.237242 + 0.971450i \(0.576244\pi\)
\(158\) 1789.31 + 13556.2i 0.0716757 + 0.543029i
\(159\) 9112.62i 0.360453i
\(160\) −4056.69 + 31216.6i −0.158464 + 1.21940i
\(161\) −182.089 −0.00702478
\(162\) −18192.8 + 2401.31i −0.693216 + 0.0914993i
\(163\) 17673.1 17673.1i 0.665178 0.665178i −0.291418 0.956596i \(-0.594127\pi\)
0.956596 + 0.291418i \(0.0941270\pi\)
\(164\) −7486.97 27867.2i −0.278367 1.03611i
\(165\) −21917.6 + 21917.6i −0.805056 + 0.805056i
\(166\) 556.223 725.386i 0.0201852 0.0263241i
\(167\) −11374.1 −0.407834 −0.203917 0.978988i \(-0.565367\pi\)
−0.203917 + 0.978988i \(0.565367\pi\)
\(168\) 1267.35 3068.36i 0.0449034 0.108714i
\(169\) 69476.3i 2.43256i
\(170\) 9919.80 12936.7i 0.343246 0.447636i
\(171\) −7894.76 7894.76i −0.269989 0.269989i
\(172\) 350.184 + 201.867i 0.0118369 + 0.00682351i
\(173\) −11289.3 11289.3i −0.377204 0.377204i 0.492888 0.870092i \(-0.335941\pi\)
−0.870092 + 0.492888i \(0.835941\pi\)
\(174\) −7685.54 + 1014.43i −0.253849 + 0.0335062i
\(175\) 2118.76i 0.0691838i
\(176\) −31833.8 8484.24i −1.02769 0.273897i
\(177\) −10775.4 −0.343944
\(178\) 766.322 + 5805.80i 0.0241864 + 0.183241i
\(179\) −25338.8 + 25338.8i −0.790825 + 0.790825i −0.981628 0.190803i \(-0.938891\pi\)
0.190803 + 0.981628i \(0.438891\pi\)
\(180\) 8357.79 + 4817.93i 0.257957 + 0.148702i
\(181\) 22579.8 22579.8i 0.689228 0.689228i −0.272833 0.962061i \(-0.587961\pi\)
0.962061 + 0.272833i \(0.0879608\pi\)
\(182\) 6580.02 + 5045.53i 0.198648 + 0.152323i
\(183\) −22784.7 −0.680363
\(184\) −1625.57 + 675.243i −0.0480142 + 0.0199446i
\(185\) 24062.2i 0.703058i
\(186\) 26958.1 + 20671.4i 0.779226 + 0.597507i
\(187\) 12064.2 + 12064.2i 0.344996 + 0.344996i
\(188\) 9416.55 + 35049.3i 0.266426 + 0.991663i
\(189\) −3690.38 3690.38i −0.103311 0.103311i
\(190\) −9159.75 69396.0i −0.253733 1.92233i
\(191\) 62994.4i 1.72677i 0.504543 + 0.863386i \(0.331661\pi\)
−0.504543 + 0.863386i \(0.668339\pi\)
\(192\) −64.3511 32092.0i −0.00174564 0.870550i
\(193\) −25039.7 −0.672225 −0.336112 0.941822i \(-0.609112\pi\)
−0.336112 + 0.941822i \(0.609112\pi\)
\(194\) 32775.7 4326.14i 0.870860 0.114947i
\(195\) 53326.1 53326.1i 1.40240 1.40240i
\(196\) −36423.1 + 9785.63i −0.948122 + 0.254728i
\(197\) −6468.96 + 6468.96i −0.166687 + 0.166687i −0.785521 0.618834i \(-0.787605\pi\)
0.618834 + 0.785521i \(0.287605\pi\)
\(198\) −6143.54 + 8011.96i −0.156707 + 0.204366i
\(199\) 55793.6 1.40889 0.704446 0.709757i \(-0.251195\pi\)
0.704446 + 0.709757i \(0.251195\pi\)
\(200\) 7857.00 + 18914.8i 0.196425 + 0.472870i
\(201\) 51093.8i 1.26467i
\(202\) −17331.5 + 22602.5i −0.424750 + 0.553928i
\(203\) −1157.99 1157.99i −0.0281005 0.0281005i
\(204\) −8300.17 + 14398.5i −0.199447 + 0.345985i
\(205\) −39202.6 39202.6i −0.932841 0.932841i
\(206\) −5659.85 + 747.058i −0.133374 + 0.0176044i
\(207\) 539.439i 0.0125893i
\(208\) 77452.3 + 20642.4i 1.79023 + 0.477126i
\(209\) 73257.5 1.67710
\(210\) −834.663 6323.57i −0.0189266 0.143392i
\(211\) −11403.6 + 11403.6i −0.256139 + 0.256139i −0.823482 0.567343i \(-0.807971\pi\)
0.567343 + 0.823482i \(0.307971\pi\)
\(212\) −9293.79 + 16122.2i −0.206786 + 0.358717i
\(213\) −17206.8 + 17206.8i −0.379264 + 0.379264i
\(214\) −44794.0 34347.9i −0.978120 0.750019i
\(215\) 776.604 0.0168005
\(216\) −46630.3 19260.1i −0.999449 0.412812i
\(217\) 7176.41i 0.152401i
\(218\) −42.5490 32.6264i −0.000895315 0.000686524i
\(219\) 4007.75 + 4007.75i 0.0835627 + 0.0835627i
\(220\) −61130.5 + 16423.7i −1.26303 + 0.339332i
\(221\) −29352.4 29352.4i −0.600979 0.600979i
\(222\) 3210.02 + 24319.7i 0.0651331 + 0.493461i
\(223\) 15194.4i 0.305545i −0.988261 0.152772i \(-0.951180\pi\)
0.988261 0.152772i \(-0.0488201\pi\)
\(224\) 5371.58 4136.04i 0.107055 0.0824306i
\(225\) 6276.81 0.123986
\(226\) 54070.0 7136.83i 1.05862 0.139730i
\(227\) 47509.0 47509.0i 0.921986 0.921986i −0.0751841 0.997170i \(-0.523954\pi\)
0.997170 + 0.0751841i \(0.0239544\pi\)
\(228\) 18515.6 + 68916.9i 0.356179 + 1.32573i
\(229\) 15628.9 15628.9i 0.298028 0.298028i −0.542213 0.840241i \(-0.682413\pi\)
0.840241 + 0.542213i \(0.182413\pi\)
\(230\) −2057.93 + 2683.81i −0.0389023 + 0.0507336i
\(231\) 6675.44 0.125100
\(232\) −14632.0 6043.59i −0.271849 0.112284i
\(233\) 63151.2i 1.16324i 0.813460 + 0.581621i \(0.197581\pi\)
−0.813460 + 0.581621i \(0.802419\pi\)
\(234\) 14947.4 19493.3i 0.272981 0.356003i
\(235\) 49306.1 + 49306.1i 0.892823 + 0.892823i
\(236\) −19064.1 10989.7i −0.342288 0.197315i
\(237\) −18938.7 18938.7i −0.337173 0.337173i
\(238\) −3480.69 + 459.426i −0.0614486 + 0.00811075i
\(239\) 33331.4i 0.583522i 0.956491 + 0.291761i \(0.0942412\pi\)
−0.956491 + 0.291761i \(0.905759\pi\)
\(240\) −30901.1 53357.3i −0.536477 0.926343i
\(241\) 5625.72 0.0968599 0.0484299 0.998827i \(-0.484578\pi\)
0.0484299 + 0.998827i \(0.484578\pi\)
\(242\) −1005.23 7615.84i −0.0171647 0.130043i
\(243\) −19734.3 + 19734.3i −0.334202 + 0.334202i
\(244\) −40311.0 23237.7i −0.677087 0.390313i
\(245\) −51238.7 + 51238.7i −0.853622 + 0.853622i
\(246\) 44852.1 + 34392.4i 0.741162 + 0.568320i
\(247\) −178237. −2.92149
\(248\) 26612.4 + 64066.2i 0.432693 + 1.04166i
\(249\) 1790.47i 0.0288782i
\(250\) −29759.2 22819.2i −0.476147 0.365107i
\(251\) −62195.0 62195.0i −0.987206 0.987206i 0.0127130 0.999919i \(-0.495953\pi\)
−0.999919 + 0.0127130i \(0.995953\pi\)
\(252\) −539.067 2006.46i −0.00848871 0.0315958i
\(253\) −2502.80 2502.80i −0.0391007 0.0391007i
\(254\) 4212.11 + 31911.8i 0.0652879 + 0.494633i
\(255\) 31931.7i 0.491068i
\(256\) 32616.1 56843.2i 0.497683 0.867359i
\(257\) 22791.9 0.345075 0.172538 0.985003i \(-0.444803\pi\)
0.172538 + 0.985003i \(0.444803\pi\)
\(258\) −784.918 + 103.603i −0.0117919 + 0.00155645i
\(259\) −3664.30 + 3664.30i −0.0546250 + 0.0546250i
\(260\) 148732. 39959.1i 2.20017 0.591111i
\(261\) −3430.55 + 3430.55i −0.0503597 + 0.0503597i
\(262\) 54747.1 71397.2i 0.797551 1.04011i
\(263\) 126611. 1.83047 0.915233 0.402926i \(-0.132007\pi\)
0.915233 + 0.402926i \(0.132007\pi\)
\(264\) 59593.8 24754.6i 0.855054 0.355180i
\(265\) 35754.3i 0.509139i
\(266\) −9173.05 + 11962.8i −0.129643 + 0.169072i
\(267\) −8111.00 8111.00i −0.113776 0.113776i
\(268\) 52109.6 90395.9i 0.725518 1.25858i
\(269\) 65428.7 + 65428.7i 0.904198 + 0.904198i 0.995796 0.0915982i \(-0.0291975\pi\)
−0.0915982 + 0.995796i \(0.529198\pi\)
\(270\) −96100.2 + 12684.5i −1.31825 + 0.173999i
\(271\) 93429.2i 1.27217i −0.771621 0.636083i \(-0.780554\pi\)
0.771621 0.636083i \(-0.219446\pi\)
\(272\) −29369.6 + 17008.9i −0.396972 + 0.229900i
\(273\) −16241.5 −0.217922
\(274\) 16314.9 + 123605.i 0.217312 + 1.64640i
\(275\) −29122.0 + 29122.0i −0.385085 + 0.385085i
\(276\) 1721.93 2987.07i 0.0226046 0.0392128i
\(277\) 105271. 105271.i 1.37198 1.37198i 0.514477 0.857504i \(-0.327986\pi\)
0.857504 0.514477i \(-0.172014\pi\)
\(278\) −96209.4 73773.0i −1.24488 0.954570i
\(279\) 21260.1 0.273122
\(280\) 4972.59 12039.0i 0.0634259 0.153559i
\(281\) 42955.1i 0.544004i −0.962297 0.272002i \(-0.912314\pi\)
0.962297 0.272002i \(-0.0876857\pi\)
\(282\) −56411.6 43256.2i −0.709366 0.543939i
\(283\) −36538.7 36538.7i −0.456226 0.456226i 0.441189 0.897414i \(-0.354557\pi\)
−0.897414 + 0.441189i \(0.854557\pi\)
\(284\) −47991.5 + 12893.7i −0.595015 + 0.159860i
\(285\) 96949.8 + 96949.8i 1.19360 + 1.19360i
\(286\) 21091.3 + 159792.i 0.257853 + 1.95354i
\(287\) 11939.9i 0.144957i
\(288\) −12253.0 15913.3i −0.147726 0.191856i
\(289\) −65944.8 −0.789559
\(290\) −30155.0 + 3980.24i −0.358561 + 0.0473274i
\(291\) −45789.3 + 45789.3i −0.540727 + 0.540727i
\(292\) 3003.15 + 11178.0i 0.0352217 + 0.131099i
\(293\) −45359.7 + 45359.7i −0.528367 + 0.528367i −0.920085 0.391719i \(-0.871881\pi\)
0.391719 + 0.920085i \(0.371881\pi\)
\(294\) 44951.6 58622.7i 0.520057 0.678221i
\(295\) −42278.5 −0.485820
\(296\) −19124.0 + 46300.7i −0.218271 + 0.528450i
\(297\) 101448.i 1.15008i
\(298\) −40523.5 + 52847.9i −0.456326 + 0.595107i
\(299\) 6089.36 + 6089.36i 0.0681129 + 0.0681129i
\(300\) −34757.0 20036.0i −0.386189 0.222622i
\(301\) −118.265 118.265i −0.00130534 0.00130534i
\(302\) 77150.3 10183.3i 0.845909 0.111654i
\(303\) 55789.9i 0.607673i
\(304\) −37528.9 + 140813.i −0.406087 + 1.52368i
\(305\) −89398.0 −0.961011
\(306\) 1361.05 + 10311.5i 0.0145355 + 0.110124i
\(307\) −10035.4 + 10035.4i −0.106478 + 0.106478i −0.758339 0.651861i \(-0.773989\pi\)
0.651861 + 0.758339i \(0.273989\pi\)
\(308\) 11810.3 + 6808.16i 0.124497 + 0.0717676i
\(309\) 7907.11 7907.11i 0.0828134 0.0828134i
\(310\) 105773. + 81106.2i 1.10065 + 0.843977i
\(311\) 102401. 1.05873 0.529365 0.848394i \(-0.322430\pi\)
0.529365 + 0.848394i \(0.322430\pi\)
\(312\) −144993. + 60228.5i −1.48949 + 0.618718i
\(313\) 60933.1i 0.621963i 0.950416 + 0.310981i \(0.100658\pi\)
−0.950416 + 0.310981i \(0.899342\pi\)
\(314\) −81240.3 62294.7i −0.823971 0.631818i
\(315\) −2822.62 2822.62i −0.0284466 0.0284466i
\(316\) −14191.4 52821.8i −0.142119 0.528980i
\(317\) −10217.2 10217.2i −0.101675 0.101675i 0.654439 0.756115i \(-0.272905\pi\)
−0.756115 + 0.654439i \(0.772905\pi\)
\(318\) −4769.82 36137.0i −0.0471680 0.357354i
\(319\) 31833.0i 0.312821i
\(320\) −252.488 125916.i −0.00246571 1.22965i
\(321\) 110565. 1.07302
\(322\) 722.094 95.3110i 0.00696437 0.000919245i
\(323\) 53364.3 53364.3i 0.511500 0.511500i
\(324\) 70888.4 19045.3i 0.675282 0.181425i
\(325\) 70854.6 70854.6i 0.670813 0.670813i
\(326\) −60834.0 + 79335.2i −0.572415 + 0.746502i
\(327\) 105.024 0.000982183
\(328\) 44276.9 + 106592.i 0.411557 + 0.990775i
\(329\) 15017.1i 0.138738i
\(330\) 75444.3 98389.0i 0.692785 0.903481i
\(331\) 123603. + 123603.i 1.12817 + 1.12817i 0.990475 + 0.137692i \(0.0439684\pi\)
0.137692 + 0.990475i \(0.456032\pi\)
\(332\) −1826.07 + 3167.74i −0.0165669 + 0.0287391i
\(333\) 10855.5 + 10855.5i 0.0978949 + 0.0978949i
\(334\) 45105.1 5953.53i 0.404327 0.0533681i
\(335\) 200472.i 1.78634i
\(336\) −3419.75 + 12831.3i −0.0302911 + 0.113656i
\(337\) −102441. −0.902018 −0.451009 0.892519i \(-0.648936\pi\)
−0.451009 + 0.892519i \(0.648936\pi\)
\(338\) −36366.0 275515.i −0.318318 2.41164i
\(339\) −75538.6 + 75538.6i −0.657309 + 0.657309i
\(340\) −32566.6 + 56494.1i −0.281718 + 0.488704i
\(341\) −98639.0 + 98639.0i −0.848281 + 0.848281i
\(342\) 35439.9 + 27175.1i 0.302998 + 0.232338i
\(343\) 31501.6 0.267760
\(344\) −1494.35 617.227i −0.0126280 0.00521588i
\(345\) 6624.45i 0.0556560i
\(346\) 50678.2 + 38859.9i 0.423320 + 0.324601i
\(347\) 63342.4 + 63342.4i 0.526061 + 0.526061i 0.919395 0.393335i \(-0.128679\pi\)
−0.393335 + 0.919395i \(0.628679\pi\)
\(348\) 29946.8 8045.68i 0.247282 0.0664362i
\(349\) −114645. 114645.i −0.941247 0.941247i 0.0571205 0.998367i \(-0.481808\pi\)
−0.998367 + 0.0571205i \(0.981808\pi\)
\(350\) −1109.02 8402.15i −0.00905323 0.0685889i
\(351\) 246824.i 2.00343i
\(352\) 130681. + 16982.4i 1.05470 + 0.137061i
\(353\) −94430.7 −0.757816 −0.378908 0.925434i \(-0.623700\pi\)
−0.378908 + 0.925434i \(0.623700\pi\)
\(354\) 42731.1 5640.18i 0.340986 0.0450076i
\(355\) −67512.8 + 67512.8i −0.535709 + 0.535709i
\(356\) −6077.86 22622.4i −0.0479568 0.178500i
\(357\) 4862.71 4862.71i 0.0381542 0.0381542i
\(358\) 87220.7 113747.i 0.680540 0.887511i
\(359\) −59001.0 −0.457794 −0.228897 0.973451i \(-0.573512\pi\)
−0.228897 + 0.973451i \(0.573512\pi\)
\(360\) −35665.6 14731.3i −0.275197 0.113667i
\(361\) 193724.i 1.48651i
\(362\) −77723.6 + 101361.i −0.593111 + 0.773492i
\(363\) 10639.7 + 10639.7i 0.0807453 + 0.0807453i
\(364\) −28734.7 16564.4i −0.216872 0.125018i
\(365\) 15724.8 + 15724.8i 0.118032 + 0.118032i
\(366\) 90355.0 11926.2i 0.674513 0.0890306i
\(367\) 120112.i 0.891775i 0.895089 + 0.445888i \(0.147112\pi\)
−0.895089 + 0.445888i \(0.852888\pi\)
\(368\) 6092.92 3528.62i 0.0449915 0.0260561i
\(369\) 35372.0 0.259781
\(370\) 12594.9 + 95421.0i 0.0920004 + 0.697012i
\(371\) 5444.83 5444.83i 0.0395582 0.0395582i
\(372\) −117725. 67863.8i −0.850713 0.490402i
\(373\) −113849. + 113849.i −0.818300 + 0.818300i −0.985862 0.167562i \(-0.946411\pi\)
0.167562 + 0.985862i \(0.446411\pi\)
\(374\) −54156.5 41527.0i −0.387175 0.296884i
\(375\) 73454.7 0.522345
\(376\) −55688.2 134063.i −0.393901 0.948272i
\(377\) 77450.4i 0.544930i
\(378\) 16566.2 + 12702.9i 0.115942 + 0.0889038i
\(379\) −75841.4 75841.4i −0.527993 0.527993i 0.391981 0.919973i \(-0.371790\pi\)
−0.919973 + 0.391981i \(0.871790\pi\)
\(380\) 72647.9 + 270403.i 0.503102 + 1.87259i
\(381\) −44582.4 44582.4i −0.307124 0.307124i
\(382\) −32973.2 249811.i −0.225961 1.71192i
\(383\) 80282.4i 0.547297i −0.961830 0.273648i \(-0.911770\pi\)
0.961830 0.273648i \(-0.0882304\pi\)
\(384\) 17053.1 + 127230.i 0.115649 + 0.862836i
\(385\) 26191.8 0.176703
\(386\) 99297.6 13106.5i 0.666445 0.0879657i
\(387\) −350.360 + 350.360i −0.00233933 + 0.00233933i
\(388\) −127711. + 34311.6i −0.848330 + 0.227917i
\(389\) 89476.2 89476.2i 0.591301 0.591301i −0.346682 0.937983i \(-0.612692\pi\)
0.937983 + 0.346682i \(0.112692\pi\)
\(390\) −183558. + 239383.i −1.20682 + 1.57385i
\(391\) −3646.31 −0.0238507
\(392\) 139317. 57870.9i 0.906636 0.376607i
\(393\) 176230.i 1.14102i
\(394\) 22267.3 29039.4i 0.143441 0.187066i
\(395\) −74307.8 74307.8i −0.476256 0.476256i
\(396\) 20169.2 34988.0i 0.128617 0.223115i
\(397\) 128824. + 128824.i 0.817363 + 0.817363i 0.985725 0.168362i \(-0.0538479\pi\)
−0.168362 + 0.985725i \(0.553848\pi\)
\(398\) −221255. + 29204.0i −1.39678 + 0.184364i
\(399\) 29527.9i 0.185476i
\(400\) −41058.3 70896.1i −0.256615 0.443101i
\(401\) 71110.1 0.442224 0.221112 0.975248i \(-0.429031\pi\)
0.221112 + 0.975248i \(0.429031\pi\)
\(402\) 26744.0 + 202618.i 0.165491 + 1.25379i
\(403\) 239991. 239991.i 1.47769 1.47769i
\(404\) 56899.1 98704.4i 0.348612 0.604747i
\(405\) 99723.2 99723.2i 0.607976 0.607976i
\(406\) 5198.27 + 3986.02i 0.0315360 + 0.0241817i
\(407\) −100731. −0.608097
\(408\) 25378.6 61443.4i 0.152457 0.369109i
\(409\) 87416.4i 0.522572i 0.965261 + 0.261286i \(0.0841466\pi\)
−0.965261 + 0.261286i \(0.915853\pi\)
\(410\) 175982. + 134942.i 1.04689 + 0.802750i
\(411\) −172683. 172683.i −1.02227 1.02227i
\(412\) 22053.7 5925.08i 0.129923 0.0349059i
\(413\) 6438.36 + 6438.36i 0.0377464 + 0.0377464i
\(414\) −282.358 2139.20i −0.00164740 0.0124810i
\(415\) 7025.11i 0.0407903i
\(416\) −317950. 41318.5i −1.83727 0.238758i
\(417\) 237474. 1.36567
\(418\) −290510. + 38345.2i −1.66268 + 0.219461i
\(419\) 156666. 156666.i 0.892373 0.892373i −0.102373 0.994746i \(-0.532644\pi\)
0.994746 + 0.102373i \(0.0326436\pi\)
\(420\) 6619.89 + 24639.9i 0.0375277 + 0.139682i
\(421\) 20636.7 20636.7i 0.116433 0.116433i −0.646490 0.762923i \(-0.723764\pi\)
0.762923 + 0.646490i \(0.223764\pi\)
\(422\) 39253.1 51191.0i 0.220419 0.287454i
\(423\) −44488.2 −0.248636
\(424\) 28416.7 68798.9i 0.158067 0.382692i
\(425\) 42427.8i 0.234894i
\(426\) 59228.9 77242.0i 0.326373 0.425632i
\(427\) 13614.0 + 13614.0i 0.0746670 + 0.0746670i
\(428\) 195614. + 112763.i 1.06785 + 0.615575i
\(429\) −223238. 223238.i −1.21298 1.21298i
\(430\) −3079.71 + 406.498i −0.0166561 + 0.00219848i
\(431\) 294349.i 1.58456i 0.610160 + 0.792279i \(0.291105\pi\)
−0.610160 + 0.792279i \(0.708895\pi\)
\(432\) 194999. + 51970.4i 1.04487 + 0.278477i
\(433\) 240460. 1.28253 0.641264 0.767321i \(-0.278411\pi\)
0.641264 + 0.767321i \(0.278411\pi\)
\(434\) −3756.35 28458.8i −0.0199428 0.151091i
\(435\) 42128.1 42128.1i 0.222635 0.222635i
\(436\) 185.810 + 107.112i 0.000977454 + 0.000563462i
\(437\) −11070.8 + 11070.8i −0.0579716 + 0.0579716i
\(438\) −17990.9 13795.4i −0.0937789 0.0719093i
\(439\) −294699. −1.52915 −0.764574 0.644536i \(-0.777051\pi\)
−0.764574 + 0.644536i \(0.777051\pi\)
\(440\) 233823. 97127.2i 1.20776 0.501690i
\(441\) 46231.9i 0.237719i
\(442\) 131764. + 101036.i 0.674454 + 0.517168i
\(443\) 118964. + 118964.i 0.606187 + 0.606187i 0.941948 0.335760i \(-0.108993\pi\)
−0.335760 + 0.941948i \(0.608993\pi\)
\(444\) −25459.4 94762.2i −0.129146 0.480695i
\(445\) −31824.4 31824.4i −0.160709 0.160709i
\(446\) 7953.22 + 60255.1i 0.0399828 + 0.302917i
\(447\) 130445.i 0.652847i
\(448\) −19136.6 + 19213.5i −0.0953476 + 0.0957308i
\(449\) −82129.5 −0.407386 −0.203693 0.979035i \(-0.565294\pi\)
−0.203693 + 0.979035i \(0.565294\pi\)
\(450\) −24891.3 + 3285.47i −0.122920 + 0.0162245i
\(451\) −164113. + 164113.i −0.806844 + 0.806844i
\(452\) −210684. + 56603.7i −1.03123 + 0.277056i
\(453\) −107783. + 107783.i −0.525235 + 0.525235i
\(454\) −163534. + 213270.i −0.793409 + 1.03471i
\(455\) −63725.2 −0.307814
\(456\) −109499. 263605.i −0.526598 1.26772i
\(457\) 172358.i 0.825277i 0.910895 + 0.412638i \(0.135393\pi\)
−0.910895 + 0.412638i \(0.864607\pi\)
\(458\) −53797.4 + 70158.6i −0.256466 + 0.334465i
\(459\) −73899.3 73899.3i −0.350764 0.350764i
\(460\) 6756.16 11720.1i 0.0319289 0.0553880i
\(461\) 96898.8 + 96898.8i 0.455950 + 0.455950i 0.897323 0.441374i \(-0.145509\pi\)
−0.441374 + 0.897323i \(0.645509\pi\)
\(462\) −26472.2 + 3494.13i −0.124024 + 0.0163702i
\(463\) 142244.i 0.663549i 0.943359 + 0.331775i \(0.107647\pi\)
−0.943359 + 0.331775i \(0.892353\pi\)
\(464\) 61188.1 + 16307.7i 0.284204 + 0.0757453i
\(465\) −261080. −1.20745
\(466\) −33055.2 250433.i −0.152219 1.15324i
\(467\) −139194. + 139194.i −0.638246 + 0.638246i −0.950123 0.311877i \(-0.899042\pi\)
0.311877 + 0.950123i \(0.399042\pi\)
\(468\) −49072.0 + 85126.5i −0.224049 + 0.388663i
\(469\) −30528.8 + 30528.8i −0.138792 + 0.138792i
\(470\) −221337. 169720.i −1.00198 0.768313i
\(471\) 200526. 0.903917
\(472\) 81352.8 + 33601.9i 0.365164 + 0.150827i
\(473\) 3251.08i 0.0145313i
\(474\) 85016.4 + 65190.2i 0.378395 + 0.290152i
\(475\) 128818. + 128818.i 0.570936 + 0.570936i
\(476\) 13562.6 3643.80i 0.0598589 0.0160820i
\(477\) −16130.3 16130.3i −0.0708934 0.0708934i
\(478\) −17446.6 132179.i −0.0763582 0.578504i
\(479\) 216764.i 0.944749i −0.881398 0.472374i \(-0.843397\pi\)
0.881398 0.472374i \(-0.156603\pi\)
\(480\) 150470. + 195420.i 0.653082 + 0.848175i
\(481\) 245080. 1.05930
\(482\) −22309.4 + 2944.67i −0.0960270 + 0.0126748i
\(483\) −1008.80 + 1008.80i −0.00432426 + 0.00432426i
\(484\) 7972.72 + 29675.2i 0.0340342 + 0.126679i
\(485\) −179659. + 179659.i −0.763776 + 0.763776i
\(486\) 67928.8 88587.8i 0.287595 0.375061i
\(487\) 146986. 0.619752 0.309876 0.950777i \(-0.399713\pi\)
0.309876 + 0.950777i \(0.399713\pi\)
\(488\) 172021. + 71051.4i 0.722340 + 0.298355i
\(489\) 195824.i 0.818931i
\(490\) 176372. 230012.i 0.734579 0.957985i
\(491\) −207292. 207292.i −0.859843 0.859843i 0.131476 0.991319i \(-0.458028\pi\)
−0.991319 + 0.131476i \(0.958028\pi\)
\(492\) −195868. 112910.i −0.809157 0.466446i
\(493\) −23188.7 23188.7i −0.0954074 0.0954074i
\(494\) 706818. 93294.7i 2.89637 0.382299i
\(495\) 77593.1i 0.316674i
\(496\) −139068. 240131.i −0.565281 0.976080i
\(497\) 20562.3 0.0832452
\(498\) −937.188 7100.31i −0.00377892 0.0286298i
\(499\) 5591.76 5591.76i 0.0224568 0.0224568i −0.695789 0.718246i \(-0.744945\pi\)
0.718246 + 0.695789i \(0.244945\pi\)
\(500\) 129957. + 74915.2i 0.519829 + 0.299661i
\(501\) −63014.2 + 63014.2i −0.251051 + 0.251051i
\(502\) 279195. + 214086.i 1.10790 + 0.849534i
\(503\) 154345. 0.610037 0.305018 0.952346i \(-0.401337\pi\)
0.305018 + 0.952346i \(0.401337\pi\)
\(504\) 3187.97 + 7674.67i 0.0125503 + 0.0302133i
\(505\) 218897.i 0.858337i
\(506\) 11235.1 + 8615.06i 0.0438811 + 0.0336478i
\(507\) 384909. + 384909.i 1.49742 + 1.49742i
\(508\) −33407.2 124345.i −0.129453 0.481837i
\(509\) −7996.84 7996.84i −0.0308662 0.0308662i 0.691505 0.722371i \(-0.256948\pi\)
−0.722371 + 0.691505i \(0.756948\pi\)
\(510\) −16714.0 126629.i −0.0642600 0.486846i
\(511\) 4789.30i 0.0183413i
\(512\) −99589.3 + 242490.i −0.379903 + 0.925026i
\(513\) −448740. −1.70514
\(514\) −90383.6 + 11930.0i −0.342108 + 0.0451557i
\(515\) 31024.4 31024.4i 0.116974 0.116974i
\(516\) 3058.44 821.699i 0.0114869 0.00308612i
\(517\) 206409. 206409.i 0.772231 0.772231i
\(518\) 12613.2 16449.2i 0.0470072 0.0613033i
\(519\) −125089. −0.464393
\(520\) −568896. + 236313.i −2.10390 + 0.873938i
\(521\) 215831.i 0.795130i −0.917574 0.397565i \(-0.869855\pi\)
0.917574 0.397565i \(-0.130145\pi\)
\(522\) 11808.6 15399.9i 0.0433367 0.0565166i
\(523\) −73690.2 73690.2i −0.269405 0.269405i 0.559455 0.828861i \(-0.311010\pi\)
−0.828861 + 0.559455i \(0.811010\pi\)
\(524\) −179734. + 311789.i −0.654587 + 1.13553i
\(525\) 11738.2 + 11738.2i 0.0425877 + 0.0425877i
\(526\) −502091. + 66272.3i −1.81473 + 0.239530i
\(527\) 143707.i 0.517435i
\(528\) −223368. + 129360.i −0.801223 + 0.464016i
\(529\) −279085. −0.997297
\(530\) −18714.9 141787.i −0.0666247 0.504761i
\(531\) 19073.6 19073.6i 0.0676464 0.0676464i
\(532\) 30115.0 52241.3i 0.106404 0.184583i
\(533\) 399290. 399290.i 1.40551 1.40551i
\(534\) 36410.6 + 27919.5i 0.127686 + 0.0979095i
\(535\) 433814. 1.51564
\(536\) −159330. + 385750.i −0.554585 + 1.34269i
\(537\) 280762.i 0.973622i
\(538\) −293712. 225217.i −1.01474 0.778102i
\(539\) 214499. + 214499.i 0.738325 + 0.738325i
\(540\) 374456. 100603.i 1.28414 0.345005i
\(541\) 260589. + 260589.i 0.890352 + 0.890352i 0.994556 0.104204i \(-0.0332294\pi\)
−0.104204 + 0.994556i \(0.533229\pi\)
\(542\) 48903.6 + 370503.i 0.166473 + 1.26123i
\(543\) 250191.i 0.848540i
\(544\) 107565. 82823.6i 0.363475 0.279870i
\(545\) 412.072 0.00138733
\(546\) 64407.4 8501.29i 0.216048 0.0285167i
\(547\) −87290.1 + 87290.1i −0.291736 + 0.291736i −0.837766 0.546030i \(-0.816139\pi\)
0.546030 + 0.837766i \(0.316139\pi\)
\(548\) −129397. 481629.i −0.430888 1.60381i
\(549\) 40331.3 40331.3i 0.133813 0.133813i
\(550\) 100243. 130730.i 0.331382 0.432165i
\(551\) −140809. −0.463796
\(552\) −5264.96 + 12746.9i −0.0172789 + 0.0418336i
\(553\) 22631.9i 0.0740066i
\(554\) −362360. + 472564.i −1.18065 + 1.53972i
\(555\) −133308. 133308.i −0.432783 0.432783i
\(556\) 420143. + 242196.i 1.35909 + 0.783460i
\(557\) −342322. 342322.i −1.10338 1.10338i −0.994000 0.109377i \(-0.965114\pi\)
−0.109377 0.994000i \(-0.534886\pi\)
\(558\) −84309.2 + 11128.2i −0.270774 + 0.0357401i
\(559\) 7909.94i 0.0253134i
\(560\) −13417.7 + 50344.8i −0.0427862 + 0.160538i
\(561\) 133675. 0.424741
\(562\) 22484.0 + 170343.i 0.0711870 + 0.539326i
\(563\) −77521.3 + 77521.3i −0.244571 + 0.244571i −0.818738 0.574167i \(-0.805326\pi\)
0.574167 + 0.818738i \(0.305326\pi\)
\(564\) 246348. + 142010.i 0.774445 + 0.446436i
\(565\) −296383. + 296383.i −0.928447 + 0.928447i
\(566\) 164023. + 125772.i 0.512003 + 0.392602i
\(567\) −30372.6 −0.0944749
\(568\) 183567. 76251.5i 0.568980 0.236348i
\(569\) 304409.i 0.940229i −0.882605 0.470115i \(-0.844213\pi\)
0.882605 0.470115i \(-0.155787\pi\)
\(570\) −435211. 333718.i −1.33952 1.02714i
\(571\) −254051. 254051.i −0.779201 0.779201i 0.200494 0.979695i \(-0.435745\pi\)
−0.979695 + 0.200494i \(0.935745\pi\)
\(572\) −167280. 622631.i −0.511271 1.90300i
\(573\) 348999. + 348999.i 1.06295 + 1.06295i
\(574\) −6249.71 47349.0i −0.0189686 0.143710i
\(575\) 8801.94i 0.0266221i
\(576\) 56920.1 + 56692.2i 0.171562 + 0.170875i
\(577\) −486229. −1.46046 −0.730229 0.683202i \(-0.760587\pi\)
−0.730229 + 0.683202i \(0.760587\pi\)
\(578\) 261511. 34517.5i 0.782770 0.103320i
\(579\) −138724. + 138724.i −0.413803 + 0.413803i
\(580\) 117499. 31568.1i 0.349285 0.0938409i
\(581\) 1069.82 1069.82i 0.00316926 0.00316926i
\(582\) 157615. 205550.i 0.465320 0.606836i
\(583\) 149677. 0.440371
\(584\) −17760.2 42755.6i −0.0520741 0.125362i
\(585\) 188786.i 0.551642i
\(586\) 156136. 203621.i 0.454682 0.592964i
\(587\) −26612.4 26612.4i −0.0772339 0.0772339i 0.667435 0.744668i \(-0.267392\pi\)
−0.744668 + 0.667435i \(0.767392\pi\)
\(588\) −147576. + 256003.i −0.426835 + 0.740442i
\(589\) 436317. + 436317.i 1.25768 + 1.25768i
\(590\) 167660. 22129.8i 0.481642 0.0635732i
\(591\) 71678.1i 0.205216i
\(592\) 51603.1 193620.i 0.147242 0.552469i
\(593\) 301795. 0.858228 0.429114 0.903250i \(-0.358826\pi\)
0.429114 + 0.903250i \(0.358826\pi\)
\(594\) 53100.8 + 402301.i 0.150497 + 1.14019i
\(595\) 19079.4 19079.4i 0.0538927 0.0538927i
\(596\) 133038. 230785.i 0.374528 0.649703i
\(597\) 309105. 309105.i 0.867276 0.867276i
\(598\) −27335.3 20960.6i −0.0764402 0.0586141i
\(599\) −208748. −0.581795 −0.290897 0.956754i \(-0.593954\pi\)
−0.290897 + 0.956754i \(0.593954\pi\)
\(600\) 148320. + 61262.0i 0.412000 + 0.170172i
\(601\) 355946.i 0.985451i −0.870185 0.492725i \(-0.836001\pi\)
0.870185 0.492725i \(-0.163999\pi\)
\(602\) 530.896 + 407.089i 0.00146493 + 0.00112330i
\(603\) 90441.4 + 90441.4i 0.248733 + 0.248733i
\(604\) −300617. + 80765.6i −0.824025 + 0.221387i
\(605\) 41746.1 + 41746.1i 0.114053 + 0.114053i
\(606\) 29202.1 + 221241.i 0.0795186 + 0.602448i
\(607\) 680696.i 1.84746i −0.383040 0.923732i \(-0.625123\pi\)
0.383040 0.923732i \(-0.374877\pi\)
\(608\) 75119.4 578051.i 0.203210 1.56372i
\(609\) −12830.9 −0.0345958
\(610\) 354517. 46793.6i 0.952747 0.125756i
\(611\) −502197. + 502197.i −1.34522 + 1.34522i
\(612\) −10794.7 40179.1i −0.0288210 0.107275i
\(613\) −504818. + 504818.i −1.34343 + 1.34343i −0.450800 + 0.892625i \(0.648861\pi\)
−0.892625 + 0.450800i \(0.851139\pi\)
\(614\) 34543.7 45049.4i 0.0916289 0.119496i
\(615\) −434378. −1.14846
\(616\) −50398.6 20816.6i −0.132818 0.0548591i
\(617\) 601668.i 1.58047i 0.612803 + 0.790236i \(0.290042\pi\)
−0.612803 + 0.790236i \(0.709958\pi\)
\(618\) −27217.7 + 35495.3i −0.0712646 + 0.0929381i
\(619\) −34687.6 34687.6i −0.0905300 0.0905300i 0.660391 0.750922i \(-0.270390\pi\)
−0.750922 + 0.660391i \(0.770390\pi\)
\(620\) −461907. 266271.i −1.20163 0.692691i
\(621\) 15330.9 + 15330.9i 0.0397544 + 0.0397544i
\(622\) −406084. + 53600.0i −1.04963 + 0.138543i
\(623\) 9692.72i 0.0249729i
\(624\) 543460. 314736.i 1.39572 0.808309i
\(625\) 488225. 1.24985
\(626\) −31894.2 241636.i −0.0813885 0.616615i
\(627\) 405858. 405858.i 1.03238 1.03238i
\(628\) 354774. + 204513.i 0.899564 + 0.518562i
\(629\) −73377.0 + 73377.0i −0.185464 + 0.185464i
\(630\) 12670.8 + 9715.94i 0.0319245 + 0.0244796i
\(631\) 557209. 1.39946 0.699728 0.714409i \(-0.253304\pi\)
0.699728 + 0.714409i \(0.253304\pi\)
\(632\) 83926.1 + 202042.i 0.210118 + 0.505834i
\(633\) 126355.i 0.315345i
\(634\) 45865.6 + 35169.5i 0.114106 + 0.0874960i
\(635\) −174924. 174924.i −0.433812 0.433812i
\(636\) 37830.4 + 140809.i 0.0935248 + 0.348109i
\(637\) −521881. 521881.i −1.28615 1.28615i
\(638\) 16662.3 + 126237.i 0.0409350 + 0.310131i
\(639\) 60915.8i 0.149186i
\(640\) 66909.6 + 499201.i 0.163353 + 1.21875i
\(641\) 354670. 0.863193 0.431597 0.902067i \(-0.357950\pi\)
0.431597 + 0.902067i \(0.357950\pi\)
\(642\) −438458. + 57873.2i −1.06380 + 0.140413i
\(643\) −89105.3 + 89105.3i −0.215517 + 0.215517i −0.806606 0.591089i \(-0.798698\pi\)
0.591089 + 0.806606i \(0.298698\pi\)
\(644\) −2813.65 + 755.931i −0.00678420 + 0.00182268i
\(645\) 4302.51 4302.51i 0.0103420 0.0103420i
\(646\) −183689. + 239554.i −0.440168 + 0.574035i
\(647\) −669197. −1.59862 −0.799311 0.600918i \(-0.794802\pi\)
−0.799311 + 0.600918i \(0.794802\pi\)
\(648\) −271146. + 112631.i −0.645734 + 0.268231i
\(649\) 176989.i 0.420201i
\(650\) −243894. + 318069.i −0.577264 + 0.752825i
\(651\) 39758.5 + 39758.5i 0.0938140 + 0.0938140i
\(652\) 199717. 346455.i 0.469807 0.814988i
\(653\) 6136.50 + 6136.50i 0.0143911 + 0.0143911i 0.714266 0.699875i \(-0.246761\pi\)
−0.699875 + 0.714266i \(0.746761\pi\)
\(654\) −416.483 + 54.9727i −0.000973738 + 0.000128526i
\(655\) 691457.i 1.61169i
\(656\) −231378. 399524.i −0.537668 0.928400i
\(657\) −14188.3 −0.0328700
\(658\) 7860.42 + 59552.0i 0.0181549 + 0.137545i
\(659\) 484888. 484888.i 1.11653 1.11653i 0.124283 0.992247i \(-0.460337\pi\)
0.992247 0.124283i \(-0.0396632\pi\)
\(660\) −247683. + 429662.i −0.568601 + 0.986368i
\(661\) −71185.1 + 71185.1i −0.162924 + 0.162924i −0.783861 0.620937i \(-0.786752\pi\)
0.620937 + 0.783861i \(0.286752\pi\)
\(662\) −554859. 425463.i −1.26610 0.970837i
\(663\) −325234. −0.739892
\(664\) 5583.39 13517.8i 0.0126637 0.0306599i
\(665\) 115856.i 0.261984i
\(666\) −48730.6 37366.4i −0.109863 0.0842428i
\(667\) 4810.65 + 4810.65i 0.0108131 + 0.0108131i
\(668\) −175753. + 47218.7i −0.393867 + 0.105818i
\(669\) −84179.5 84179.5i −0.188085 0.188085i
\(670\) 104933. + 794992.i 0.233756 + 1.77098i
\(671\) 374244.i 0.831209i
\(672\) 6845.10 52673.7i 0.0151580 0.116642i
\(673\) 116807. 0.257893 0.128947 0.991652i \(-0.458840\pi\)
0.128947 + 0.991652i \(0.458840\pi\)
\(674\) 406242. 53620.9i 0.894262 0.118036i
\(675\) 178388. 178388.i 0.391523 0.391523i
\(676\) 288426. + 1.07355e6i 0.631163 + 2.34925i
\(677\) 562443. 562443.i 1.22716 1.22716i 0.262127 0.965033i \(-0.415576\pi\)
0.965033 0.262127i \(-0.0844240\pi\)
\(678\) 260017. 339095.i 0.565643 0.737670i
\(679\) 54718.7 0.118685
\(680\) 99575.4 241080.i 0.215345 0.521366i
\(681\) 526415.i 1.13510i
\(682\) 339533. 442794.i 0.729983 0.951991i
\(683\) 392290. + 392290.i 0.840941 + 0.840941i 0.988981 0.148040i \(-0.0472965\pi\)
−0.148040 + 0.988981i \(0.547297\pi\)
\(684\) −154765. 89215.6i −0.330796 0.190690i
\(685\) −677539. 677539.i −1.44395 1.44395i
\(686\) −124923. + 16488.9i −0.265457 + 0.0350384i
\(687\) 173173.i 0.366916i
\(688\) 6249.09 + 1665.49i 0.0132020 + 0.00351856i
\(689\) −364168. −0.767120
\(690\) 3467.44 + 26270.0i 0.00728301 + 0.0551774i
\(691\) 424716. 424716.i 0.889493 0.889493i −0.104981 0.994474i \(-0.533478\pi\)
0.994474 + 0.104981i \(0.0334781\pi\)
\(692\) −221310. 127576.i −0.462157 0.266415i
\(693\) −11816.2 + 11816.2i −0.0246044 + 0.0246044i
\(694\) −284346. 218036.i −0.590376 0.452698i
\(695\) 931755. 1.92900
\(696\) −114546. + 47581.1i −0.236462 + 0.0982236i
\(697\) 239095.i 0.492159i
\(698\) 514645. + 394627.i 1.05632 + 0.809984i
\(699\) 349868. + 349868.i 0.716060 + 0.716060i
\(700\) 8795.87 + 32739.1i 0.0179508 + 0.0668145i
\(701\) −92393.5 92393.5i −0.188021 0.188021i 0.606819 0.794840i \(-0.292445\pi\)
−0.794840 + 0.606819i \(0.792445\pi\)
\(702\) −129195. 978808.i −0.262164 1.98620i
\(703\) 445569.i 0.901580i
\(704\) −527119. + 1056.98i −1.06356 + 0.00213267i
\(705\) 546327. 1.09920
\(706\) 374475. 49427.9i 0.751300 0.0991659i
\(707\) −33334.7 + 33334.7i −0.0666896 + 0.0666896i
\(708\) −166502. + 44733.4i −0.332165 + 0.0892413i
\(709\) 29997.3 29997.3i 0.0596746 0.0596746i −0.676640 0.736314i \(-0.736565\pi\)
0.736314 + 0.676640i \(0.236565\pi\)
\(710\) 232391. 303067.i 0.461001 0.601205i
\(711\) 67046.9 0.132629
\(712\) 35943.6 + 86530.1i 0.0709025 + 0.170690i
\(713\) 29812.9i 0.0586443i
\(714\) −16738.3 + 21828.9i −0.0328333 + 0.0428189i
\(715\) −875896. 875896.i −1.71333 1.71333i
\(716\) −286344. + 496729.i −0.558551 + 0.968933i
\(717\) 184661. + 184661.i 0.359200 + 0.359200i
\(718\) 233974. 30882.9i 0.453858 0.0599058i
\(719\) 284133.i 0.549622i 0.961498 + 0.274811i \(0.0886152\pi\)
−0.961498 + 0.274811i \(0.911385\pi\)
\(720\) 149146. + 39750.0i 0.287705 + 0.0766783i
\(721\) −9449.07 −0.0181769
\(722\) 101401. + 768232.i 0.194521 + 1.47373i
\(723\) 31167.4 31167.4i 0.0596243 0.0596243i
\(724\) 255165. 442642.i 0.486793 0.844454i
\(725\) 55975.8 55975.8i 0.106494 0.106494i
\(726\) −47762.1 36623.8i −0.0906171 0.0694848i
\(727\) 39096.3 0.0739719 0.0369860 0.999316i \(-0.488224\pi\)
0.0369860 + 0.999316i \(0.488224\pi\)
\(728\) 122621. + 50647.3i 0.231367 + 0.0955638i
\(729\) 590261.i 1.11068i
\(730\) −70589.3 54127.6i −0.132463 0.101572i
\(731\) −2368.24 2368.24i −0.00443191 0.00443191i
\(732\) −352070. + 94589.1i −0.657062 + 0.176530i
\(733\) 82927.3 + 82927.3i 0.154344 + 0.154344i 0.780055 0.625711i \(-0.215191\pi\)
−0.625711 + 0.780055i \(0.715191\pi\)
\(734\) −62870.4 476318.i −0.116695 0.884107i
\(735\) 567741.i 1.05093i
\(736\) −22315.1 + 17182.3i −0.0411950 + 0.0317195i
\(737\) −839229. −1.54506
\(738\) −140271. + 18514.8i −0.257547 + 0.0339942i
\(739\) −97643.8 + 97643.8i −0.178795 + 0.178795i −0.790830 0.612035i \(-0.790351\pi\)
0.612035 + 0.790830i \(0.290351\pi\)
\(740\) −99892.4 371809.i −0.182419 0.678980i
\(741\) −987462. + 987462.i −1.79839 + 1.79839i
\(742\) −18742.1 + 24442.0i −0.0340416 + 0.0443945i
\(743\) −552181. −1.00024 −0.500120 0.865956i \(-0.666711\pi\)
−0.500120 + 0.865956i \(0.666711\pi\)
\(744\) 502373. + 207500.i 0.907571 + 0.374863i
\(745\) 511813.i 0.922145i
\(746\) 391889. 511073.i 0.704182 0.918344i
\(747\) −3169.33 3169.33i −0.00567971 0.00567971i
\(748\) 236500. + 136332.i 0.422695 + 0.243667i
\(749\) −66063.3 66063.3i −0.117760 0.117760i
\(750\) −291293. + 38448.4i −0.517853 + 0.0683528i
\(751\) 318447.i 0.564621i −0.959323 0.282310i \(-0.908899\pi\)
0.959323 0.282310i \(-0.0911008\pi\)
\(752\) 291010. + 502491.i 0.514603 + 0.888573i
\(753\) −689140. −1.21539
\(754\) −40539.9 307138.i −0.0713082 0.540244i
\(755\) −422898. + 422898.i −0.741894 + 0.741894i
\(756\) −72344.3 41703.5i −0.126579 0.0729675i
\(757\) −478701. + 478701.i −0.835357 + 0.835357i −0.988244 0.152886i \(-0.951143\pi\)
0.152886 + 0.988244i \(0.451143\pi\)
\(758\) 340455. + 261059.i 0.592544 + 0.454361i
\(759\) −27731.8 −0.0481386
\(760\) −429630. 1.03428e6i −0.743819 1.79066i
\(761\) 398315.i 0.687793i 0.939008 + 0.343896i \(0.111747\pi\)
−0.939008 + 0.343896i \(0.888253\pi\)
\(762\) 200132. + 153460.i 0.344672 + 0.264293i
\(763\) −62.7523 62.7523i −0.000107790 0.000107790i
\(764\) 261517. + 973392.i 0.448036 + 1.66764i
\(765\) −56522.5 56522.5i −0.0965826 0.0965826i
\(766\) 42022.2 + 318368.i 0.0716179 + 0.542591i
\(767\) 430619.i 0.731985i
\(768\) −134222. 495619.i −0.227563 0.840283i
\(769\) 658868. 1.11416 0.557078 0.830460i \(-0.311922\pi\)
0.557078 + 0.830460i \(0.311922\pi\)
\(770\) −103866. + 13709.6i −0.175183 + 0.0231229i
\(771\) 126271.