Properties

Label 143.4.j.a.23.18
Level $143$
Weight $4$
Character 143.23
Analytic conductor $8.437$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [143,4,Mod(23,143)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(143, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("143.23");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 143.j (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.43727313082\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 23.18
Character \(\chi\) \(=\) 143.23
Dual form 143.4.j.a.56.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.575952 + 0.332526i) q^{2} +(1.60738 + 2.78407i) q^{3} +(-3.77885 + 6.54517i) q^{4} +10.5229i q^{5} +(-1.85155 - 1.06899i) q^{6} +(25.1101 + 14.4973i) q^{7} -10.3467i q^{8} +(8.33263 - 14.4325i) q^{9} +O(q^{10})\) \(q+(-0.575952 + 0.332526i) q^{2} +(1.60738 + 2.78407i) q^{3} +(-3.77885 + 6.54517i) q^{4} +10.5229i q^{5} +(-1.85155 - 1.06899i) q^{6} +(25.1101 + 14.4973i) q^{7} -10.3467i q^{8} +(8.33263 - 14.4325i) q^{9} +(-3.49915 - 6.06070i) q^{10} +(-9.52628 + 5.50000i) q^{11} -24.2963 q^{12} +(-42.0756 + 20.6553i) q^{13} -19.2829 q^{14} +(-29.2966 + 16.9144i) q^{15} +(-26.7903 - 46.4021i) q^{16} +(-19.0169 + 32.9382i) q^{17} +11.0833i q^{18} +(-61.1353 - 35.2965i) q^{19} +(-68.8744 - 39.7646i) q^{20} +93.2109i q^{21} +(3.65779 - 6.33547i) q^{22} +(96.2881 + 166.776i) q^{23} +(28.8059 - 16.6311i) q^{24} +14.2678 q^{25} +(17.3651 - 25.8877i) q^{26} +140.374 q^{27} +(-189.774 + 109.566i) q^{28} +(-85.5932 - 148.252i) q^{29} +(11.2490 - 19.4838i) q^{30} -168.441i q^{31} +(102.544 + 59.2037i) q^{32} +(-30.6248 - 17.6812i) q^{33} -25.2944i q^{34} +(-152.554 + 264.231i) q^{35} +(62.9756 + 109.077i) q^{36} +(-212.993 + 122.971i) q^{37} +46.9480 q^{38} +(-125.138 - 83.9406i) q^{39} +108.877 q^{40} +(54.9558 - 31.7287i) q^{41} +(-30.9950 - 53.6850i) q^{42} +(42.5257 - 73.6567i) q^{43} -83.1348i q^{44} +(151.873 + 87.6837i) q^{45} +(-110.915 - 64.0366i) q^{46} +61.8204i q^{47} +(86.1246 - 149.172i) q^{48} +(248.843 + 431.009i) q^{49} +(-8.21757 + 4.74442i) q^{50} -122.270 q^{51} +(23.8054 - 353.445i) q^{52} -216.218 q^{53} +(-80.8485 + 46.6779i) q^{54} +(-57.8761 - 100.244i) q^{55} +(149.999 - 259.806i) q^{56} -226.940i q^{57} +(98.5951 + 56.9239i) q^{58} +(563.238 + 325.185i) q^{59} -255.668i q^{60} +(190.028 - 329.139i) q^{61} +(56.0110 + 97.0139i) q^{62} +(418.466 - 241.601i) q^{63} +349.898 q^{64} +(-217.354 - 442.759i) q^{65} +23.5179 q^{66} +(409.382 - 236.357i) q^{67} +(-143.724 - 248.937i) q^{68} +(-309.544 + 536.146i) q^{69} -202.913i q^{70} +(298.613 + 172.404i) q^{71} +(-149.329 - 86.2151i) q^{72} +784.161i q^{73} +(81.7824 - 141.651i) q^{74} +(22.9339 + 39.7226i) q^{75} +(462.043 - 266.760i) q^{76} -318.940 q^{77} +(99.9856 + 6.73428i) q^{78} +408.156 q^{79} +(488.287 - 281.912i) q^{80} +(0.653583 + 1.13204i) q^{81} +(-21.1013 + 36.5484i) q^{82} +1091.09i q^{83} +(-610.081 - 352.230i) q^{84} +(-346.607 - 200.114i) q^{85} +56.5636i q^{86} +(275.162 - 476.595i) q^{87} +(56.9067 + 98.5654i) q^{88} +(573.719 - 331.237i) q^{89} -116.628 q^{90} +(-1355.97 - 91.3278i) q^{91} -1455.43 q^{92} +(468.952 - 270.750i) q^{93} +(-20.5569 - 35.6056i) q^{94} +(371.423 - 643.323i) q^{95} +380.652i q^{96} +(1520.76 + 878.012i) q^{97} +(-286.643 - 165.494i) q^{98} +183.318i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9} - 56 q^{10} - 132 q^{12} - 46 q^{13} + 328 q^{14} - 644 q^{16} + 138 q^{17} + 492 q^{19} + 540 q^{20} - 44 q^{22} + 46 q^{23} + 720 q^{24} - 1636 q^{25} - 902 q^{26} + 48 q^{27} - 714 q^{28} - 262 q^{29} + 104 q^{30} + 144 q^{32} - 68 q^{35} + 1960 q^{36} + 630 q^{37} - 448 q^{38} - 1612 q^{39} + 216 q^{40} + 126 q^{41} - 82 q^{42} + 436 q^{43} - 570 q^{45} - 1590 q^{46} + 1944 q^{48} + 1192 q^{49} + 1290 q^{50} - 1424 q^{51} + 590 q^{52} + 292 q^{53} - 528 q^{54} - 440 q^{55} - 102 q^{56} - 1128 q^{58} + 504 q^{59} + 590 q^{61} + 1776 q^{62} + 1884 q^{63} - 5028 q^{64} + 994 q^{65} + 2156 q^{66} + 3396 q^{67} + 1530 q^{68} + 12 q^{69} - 1014 q^{71} - 1062 q^{72} - 1568 q^{74} + 4688 q^{75} + 7872 q^{76} - 1232 q^{77} - 4964 q^{78} - 2928 q^{79} - 558 q^{80} - 3780 q^{81} - 4072 q^{82} + 696 q^{84} + 4662 q^{85} + 1832 q^{87} + 924 q^{88} + 1014 q^{89} + 6844 q^{90} + 2900 q^{91} - 1336 q^{92} - 4092 q^{93} + 4166 q^{94} - 256 q^{95} - 5070 q^{97} - 8550 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.575952 + 0.332526i −0.203630 + 0.117566i −0.598347 0.801237i \(-0.704176\pi\)
0.394718 + 0.918802i \(0.370842\pi\)
\(3\) 1.60738 + 2.78407i 0.309341 + 0.535795i 0.978218 0.207578i \(-0.0665581\pi\)
−0.668877 + 0.743373i \(0.733225\pi\)
\(4\) −3.77885 + 6.54517i −0.472357 + 0.818146i
\(5\) 10.5229i 0.941200i 0.882347 + 0.470600i \(0.155963\pi\)
−0.882347 + 0.470600i \(0.844037\pi\)
\(6\) −1.85155 1.06899i −0.125982 0.0727358i
\(7\) 25.1101 + 14.4973i 1.35582 + 0.782780i 0.989057 0.147536i \(-0.0471342\pi\)
0.366759 + 0.930316i \(0.380467\pi\)
\(8\) 10.3467i 0.457263i
\(9\) 8.33263 14.4325i 0.308616 0.534538i
\(10\) −3.49915 6.06070i −0.110653 0.191656i
\(11\) −9.52628 + 5.50000i −0.261116 + 0.150756i
\(12\) −24.2963 −0.584478
\(13\) −42.0756 + 20.6553i −0.897668 + 0.440673i
\(14\) −19.2829 −0.368112
\(15\) −29.2966 + 16.9144i −0.504290 + 0.291152i
\(16\) −26.7903 46.4021i −0.418598 0.725033i
\(17\) −19.0169 + 32.9382i −0.271310 + 0.469923i −0.969198 0.246284i \(-0.920790\pi\)
0.697887 + 0.716208i \(0.254124\pi\)
\(18\) 11.0833i 0.145131i
\(19\) −61.1353 35.2965i −0.738179 0.426188i 0.0832278 0.996531i \(-0.473477\pi\)
−0.821407 + 0.570343i \(0.806810\pi\)
\(20\) −68.8744 39.7646i −0.770039 0.444582i
\(21\) 93.2109i 0.968585i
\(22\) 3.65779 6.33547i 0.0354474 0.0613967i
\(23\) 96.2881 + 166.776i 0.872933 + 1.51196i 0.858948 + 0.512063i \(0.171118\pi\)
0.0139852 + 0.999902i \(0.495548\pi\)
\(24\) 28.8059 16.6311i 0.244999 0.141450i
\(25\) 14.2678 0.114142
\(26\) 17.3651 25.8877i 0.130984 0.195269i
\(27\) 140.374 1.00055
\(28\) −189.774 + 109.566i −1.28086 + 0.739503i
\(29\) −85.5932 148.252i −0.548078 0.949298i −0.998406 0.0564355i \(-0.982026\pi\)
0.450329 0.892863i \(-0.351307\pi\)
\(30\) 11.2490 19.4838i 0.0684590 0.118574i
\(31\) 168.441i 0.975900i −0.872872 0.487950i \(-0.837745\pi\)
0.872872 0.487950i \(-0.162255\pi\)
\(32\) 102.544 + 59.2037i 0.566479 + 0.327057i
\(33\) −30.6248 17.6812i −0.161548 0.0932699i
\(34\) 25.2944i 0.127587i
\(35\) −152.554 + 264.231i −0.736753 + 1.27609i
\(36\) 62.9756 + 109.077i 0.291554 + 0.504986i
\(37\) −212.993 + 122.971i −0.946373 + 0.546389i −0.891952 0.452129i \(-0.850664\pi\)
−0.0544206 + 0.998518i \(0.517331\pi\)
\(38\) 46.9480 0.200420
\(39\) −125.138 83.9406i −0.513796 0.344648i
\(40\) 108.877 0.430376
\(41\) 54.9558 31.7287i 0.209333 0.120858i −0.391668 0.920106i \(-0.628102\pi\)
0.601001 + 0.799248i \(0.294769\pi\)
\(42\) −30.9950 53.6850i −0.113872 0.197233i
\(43\) 42.5257 73.6567i 0.150817 0.261222i −0.780711 0.624892i \(-0.785143\pi\)
0.931528 + 0.363670i \(0.118476\pi\)
\(44\) 83.1348i 0.284842i
\(45\) 151.873 + 87.6837i 0.503108 + 0.290469i
\(46\) −110.915 64.0366i −0.355510 0.205254i
\(47\) 61.8204i 0.191860i 0.995388 + 0.0959301i \(0.0305825\pi\)
−0.995388 + 0.0959301i \(0.969417\pi\)
\(48\) 86.1246 149.172i 0.258979 0.448566i
\(49\) 248.843 + 431.009i 0.725490 + 1.25659i
\(50\) −8.21757 + 4.74442i −0.0232428 + 0.0134192i
\(51\) −122.270 −0.335710
\(52\) 23.8054 353.445i 0.0634850 0.942578i
\(53\) −216.218 −0.560373 −0.280187 0.959946i \(-0.590396\pi\)
−0.280187 + 0.959946i \(0.590396\pi\)
\(54\) −80.8485 + 46.6779i −0.203742 + 0.117631i
\(55\) −57.8761 100.244i −0.141891 0.245763i
\(56\) 149.999 259.806i 0.357936 0.619964i
\(57\) 226.940i 0.527350i
\(58\) 98.5951 + 56.9239i 0.223210 + 0.128870i
\(59\) 563.238 + 325.185i 1.24284 + 0.717551i 0.969671 0.244416i \(-0.0785962\pi\)
0.273165 + 0.961967i \(0.411930\pi\)
\(60\) 255.668i 0.550110i
\(61\) 190.028 329.139i 0.398863 0.690851i −0.594723 0.803931i \(-0.702738\pi\)
0.993586 + 0.113080i \(0.0360716\pi\)
\(62\) 56.0110 + 97.0139i 0.114732 + 0.198722i
\(63\) 418.466 241.601i 0.836852 0.483157i
\(64\) 349.898 0.683394
\(65\) −217.354 442.759i −0.414761 0.844885i
\(66\) 23.5179 0.0438614
\(67\) 409.382 236.357i 0.746478 0.430979i −0.0779421 0.996958i \(-0.524835\pi\)
0.824420 + 0.565979i \(0.191502\pi\)
\(68\) −143.724 248.937i −0.256310 0.443943i
\(69\) −309.544 + 536.146i −0.540069 + 0.935426i
\(70\) 202.913i 0.346467i
\(71\) 298.613 + 172.404i 0.499138 + 0.288177i 0.728357 0.685197i \(-0.240284\pi\)
−0.229220 + 0.973375i \(0.573617\pi\)
\(72\) −149.329 86.2151i −0.244425 0.141119i
\(73\) 784.161i 1.25725i 0.777709 + 0.628624i \(0.216382\pi\)
−0.777709 + 0.628624i \(0.783618\pi\)
\(74\) 81.7824 141.651i 0.128473 0.222522i
\(75\) 22.9339 + 39.7226i 0.0353090 + 0.0611570i
\(76\) 462.043 266.760i 0.697368 0.402625i
\(77\) −318.940 −0.472034
\(78\) 99.9856 + 6.73428i 0.145143 + 0.00977574i
\(79\) 408.156 0.581280 0.290640 0.956832i \(-0.406132\pi\)
0.290640 + 0.956832i \(0.406132\pi\)
\(80\) 488.287 281.912i 0.682401 0.393985i
\(81\) 0.653583 + 1.13204i 0.000896548 + 0.00155287i
\(82\) −21.1013 + 36.5484i −0.0284176 + 0.0492207i
\(83\) 1091.09i 1.44292i 0.692456 + 0.721460i \(0.256529\pi\)
−0.692456 + 0.721460i \(0.743471\pi\)
\(84\) −610.081 352.230i −0.792444 0.457518i
\(85\) −346.607 200.114i −0.442292 0.255357i
\(86\) 56.5636i 0.0709234i
\(87\) 275.162 476.595i 0.339086 0.587314i
\(88\) 56.9067 + 98.5654i 0.0689350 + 0.119399i
\(89\) 573.719 331.237i 0.683305 0.394506i −0.117794 0.993038i \(-0.537582\pi\)
0.801099 + 0.598532i \(0.204249\pi\)
\(90\) −116.628 −0.136597
\(91\) −1355.97 91.3278i −1.56202 0.105206i
\(92\) −1455.43 −1.64934
\(93\) 468.952 270.750i 0.522882 0.301886i
\(94\) −20.5569 35.6056i −0.0225562 0.0390685i
\(95\) 371.423 643.323i 0.401128 0.694774i
\(96\) 380.652i 0.404689i
\(97\) 1520.76 + 878.012i 1.59186 + 0.919058i 0.992989 + 0.118209i \(0.0377154\pi\)
0.598867 + 0.800849i \(0.295618\pi\)
\(98\) −286.643 165.494i −0.295463 0.170585i
\(99\) 183.318i 0.186102i
\(100\) −53.9160 + 93.3852i −0.0539160 + 0.0933852i
\(101\) 24.9954 + 43.2933i 0.0246251 + 0.0426519i 0.878075 0.478522i \(-0.158827\pi\)
−0.853450 + 0.521174i \(0.825494\pi\)
\(102\) 70.4215 40.6579i 0.0683605 0.0394680i
\(103\) −1388.01 −1.32782 −0.663908 0.747814i \(-0.731103\pi\)
−0.663908 + 0.747814i \(0.731103\pi\)
\(104\) 213.714 + 435.343i 0.201503 + 0.410470i
\(105\) −980.853 −0.911632
\(106\) 124.531 71.8980i 0.114109 0.0658807i
\(107\) 649.042 + 1124.17i 0.586404 + 1.01568i 0.994699 + 0.102832i \(0.0327903\pi\)
−0.408294 + 0.912850i \(0.633876\pi\)
\(108\) −530.452 + 918.769i −0.472618 + 0.818598i
\(109\) 1113.79i 0.978731i −0.872079 0.489365i \(-0.837228\pi\)
0.872079 0.489365i \(-0.162772\pi\)
\(110\) 66.6677 + 38.4906i 0.0577865 + 0.0333631i
\(111\) −684.723 395.325i −0.585504 0.338041i
\(112\) 1553.55i 1.31068i
\(113\) −185.925 + 322.031i −0.154782 + 0.268090i −0.932980 0.359929i \(-0.882801\pi\)
0.778198 + 0.628019i \(0.216134\pi\)
\(114\) 75.4635 + 130.707i 0.0619983 + 0.107384i
\(115\) −1754.97 + 1013.23i −1.42306 + 0.821605i
\(116\) 1293.78 1.03555
\(117\) −52.4926 + 779.371i −0.0414782 + 0.615837i
\(118\) −432.530 −0.337438
\(119\) −955.030 + 551.387i −0.735693 + 0.424753i
\(120\) 175.008 + 303.123i 0.133133 + 0.230593i
\(121\) 60.5000 104.789i 0.0454545 0.0787296i
\(122\) 252.757i 0.187570i
\(123\) 176.670 + 102.001i 0.129511 + 0.0747730i
\(124\) 1102.47 + 636.514i 0.798429 + 0.460973i
\(125\) 1465.51i 1.04863i
\(126\) −160.677 + 278.301i −0.113605 + 0.196770i
\(127\) −7.95328 13.7755i −0.00555701 0.00962502i 0.863234 0.504805i \(-0.168436\pi\)
−0.868791 + 0.495180i \(0.835102\pi\)
\(128\) −1021.87 + 589.979i −0.705639 + 0.407401i
\(129\) 273.421 0.186615
\(130\) 272.414 + 182.732i 0.183787 + 0.123282i
\(131\) −1358.53 −0.906073 −0.453037 0.891492i \(-0.649659\pi\)
−0.453037 + 0.891492i \(0.649659\pi\)
\(132\) 231.453 133.630i 0.152617 0.0881133i
\(133\) −1023.41 1772.59i −0.667223 1.15566i
\(134\) −157.190 + 272.260i −0.101337 + 0.175520i
\(135\) 1477.14i 0.941721i
\(136\) 340.801 + 196.762i 0.214878 + 0.124060i
\(137\) 606.241 + 350.013i 0.378063 + 0.218275i 0.676975 0.736006i \(-0.263290\pi\)
−0.298912 + 0.954281i \(0.596624\pi\)
\(138\) 411.726i 0.253974i
\(139\) 1101.43 1907.74i 0.672103 1.16412i −0.305204 0.952287i \(-0.598725\pi\)
0.977307 0.211829i \(-0.0679420\pi\)
\(140\) −1152.96 1996.98i −0.696020 1.20554i
\(141\) −172.112 + 99.3692i −0.102798 + 0.0593503i
\(142\) −229.315 −0.135519
\(143\) 287.220 428.184i 0.167962 0.250395i
\(144\) −892.934 −0.516744
\(145\) 1560.04 900.692i 0.893480 0.515851i
\(146\) −260.754 451.639i −0.147809 0.256013i
\(147\) −799.973 + 1385.59i −0.448848 + 0.777428i
\(148\) 1858.76i 1.03236i
\(149\) 1465.06 + 845.851i 0.805518 + 0.465066i 0.845397 0.534138i \(-0.179364\pi\)
−0.0398790 + 0.999205i \(0.512697\pi\)
\(150\) −26.4176 15.2522i −0.0143799 0.00830225i
\(151\) 2987.30i 1.60996i −0.593305 0.804978i \(-0.702177\pi\)
0.593305 0.804978i \(-0.297823\pi\)
\(152\) −365.201 + 632.548i −0.194880 + 0.337542i
\(153\) 316.921 + 548.924i 0.167461 + 0.290051i
\(154\) 183.694 106.056i 0.0961202 0.0554950i
\(155\) 1772.49 0.918517
\(156\) 1022.28 501.846i 0.524667 0.257563i
\(157\) −2277.76 −1.15787 −0.578934 0.815374i \(-0.696531\pi\)
−0.578934 + 0.815374i \(0.696531\pi\)
\(158\) −235.078 + 135.722i −0.118366 + 0.0683386i
\(159\) −347.545 601.966i −0.173347 0.300245i
\(160\) −622.996 + 1079.06i −0.307826 + 0.533170i
\(161\) 5583.67i 2.73326i
\(162\) −0.752865 0.434667i −0.000365128 0.000210806i
\(163\) −591.552 341.533i −0.284257 0.164116i 0.351092 0.936341i \(-0.385810\pi\)
−0.635349 + 0.772225i \(0.719144\pi\)
\(164\) 479.593i 0.228353i
\(165\) 186.058 322.263i 0.0877856 0.152049i
\(166\) −362.815 628.414i −0.169638 0.293822i
\(167\) 141.856 81.9005i 0.0657313 0.0379500i −0.466774 0.884377i \(-0.654584\pi\)
0.532505 + 0.846427i \(0.321251\pi\)
\(168\) 964.424 0.442898
\(169\) 1343.72 1738.17i 0.611615 0.791155i
\(170\) 266.172 0.120085
\(171\) −1018.84 + 588.225i −0.455628 + 0.263057i
\(172\) 321.397 + 556.676i 0.142478 + 0.246780i
\(173\) 1050.79 1820.02i 0.461792 0.799847i −0.537258 0.843418i \(-0.680540\pi\)
0.999050 + 0.0435704i \(0.0138733\pi\)
\(174\) 365.994i 0.159460i
\(175\) 358.266 + 206.845i 0.154756 + 0.0893485i
\(176\) 510.423 + 294.693i 0.218606 + 0.126212i
\(177\) 2090.79i 0.887873i
\(178\) −220.290 + 381.553i −0.0927608 + 0.160666i
\(179\) −74.2953 128.683i −0.0310228 0.0537332i 0.850097 0.526626i \(-0.176543\pi\)
−0.881120 + 0.472893i \(0.843210\pi\)
\(180\) −1147.81 + 662.688i −0.475292 + 0.274410i
\(181\) −2458.73 −1.00970 −0.504851 0.863206i \(-0.668453\pi\)
−0.504851 + 0.863206i \(0.668453\pi\)
\(182\) 811.341 398.294i 0.330443 0.162217i
\(183\) 1221.79 0.493539
\(184\) 1725.58 996.263i 0.691366 0.399160i
\(185\) −1294.02 2241.31i −0.514261 0.890726i
\(186\) −180.062 + 311.877i −0.0709829 + 0.122946i
\(187\) 418.372i 0.163606i
\(188\) −404.625 233.610i −0.156970 0.0906265i
\(189\) 3524.79 + 2035.04i 1.35657 + 0.783213i
\(190\) 494.031i 0.188636i
\(191\) −2258.35 + 3911.57i −0.855541 + 1.48184i 0.0206014 + 0.999788i \(0.493442\pi\)
−0.876142 + 0.482053i \(0.839891\pi\)
\(192\) 562.420 + 974.140i 0.211402 + 0.366159i
\(193\) 1043.17 602.276i 0.389064 0.224626i −0.292691 0.956207i \(-0.594551\pi\)
0.681754 + 0.731581i \(0.261217\pi\)
\(194\) −1167.85 −0.432199
\(195\) 883.302 1316.81i 0.324382 0.483585i
\(196\) −3761.37 −1.37076
\(197\) −280.818 + 162.130i −0.101561 + 0.0586360i −0.549920 0.835217i \(-0.685342\pi\)
0.448359 + 0.893853i \(0.352008\pi\)
\(198\) −60.9579 105.582i −0.0218793 0.0378960i
\(199\) 2175.27 3767.68i 0.774880 1.34213i −0.159982 0.987120i \(-0.551144\pi\)
0.934862 0.355011i \(-0.115523\pi\)
\(200\) 147.625i 0.0521931i
\(201\) 1316.07 + 759.833i 0.461833 + 0.266639i
\(202\) −28.7923 16.6232i −0.0100288 0.00579013i
\(203\) 4963.48i 1.71610i
\(204\) 462.040 800.276i 0.158575 0.274660i
\(205\) 333.880 + 578.296i 0.113752 + 0.197024i
\(206\) 799.429 461.551i 0.270383 0.156106i
\(207\) 3209.33 1.07760
\(208\) 2085.67 + 1399.04i 0.695264 + 0.466374i
\(209\) 776.523 0.257001
\(210\) 564.924 326.159i 0.185635 0.107177i
\(211\) −1990.02 3446.81i −0.649281 1.12459i −0.983295 0.182020i \(-0.941736\pi\)
0.334013 0.942568i \(-0.391597\pi\)
\(212\) 817.055 1415.18i 0.264696 0.458467i
\(213\) 1108.48i 0.356581i
\(214\) −747.634 431.647i −0.238819 0.137882i
\(215\) 775.085 + 447.496i 0.245862 + 0.141949i
\(216\) 1452.40i 0.457516i
\(217\) 2441.94 4229.56i 0.763915 1.32314i
\(218\) 370.364 + 641.489i 0.115065 + 0.199299i
\(219\) −2183.16 + 1260.45i −0.673627 + 0.388919i
\(220\) 874.822 0.268093
\(221\) 119.800 1778.70i 0.0364643 0.541394i
\(222\) 525.823 0.158968
\(223\) 1586.39 915.903i 0.476379 0.275038i −0.242527 0.970145i \(-0.577976\pi\)
0.718906 + 0.695107i \(0.244643\pi\)
\(224\) 1716.59 + 2973.21i 0.512028 + 0.886858i
\(225\) 118.888 205.921i 0.0352262 0.0610136i
\(226\) 247.299i 0.0727881i
\(227\) −3077.89 1777.02i −0.899943 0.519582i −0.0227610 0.999741i \(-0.507246\pi\)
−0.877182 + 0.480159i \(0.840579\pi\)
\(228\) 1485.36 + 857.573i 0.431449 + 0.249097i
\(229\) 525.734i 0.151709i 0.997119 + 0.0758547i \(0.0241685\pi\)
−0.997119 + 0.0758547i \(0.975831\pi\)
\(230\) 673.853 1167.15i 0.193185 0.334606i
\(231\) −512.660 887.953i −0.146020 0.252914i
\(232\) −1533.91 + 885.605i −0.434079 + 0.250616i
\(233\) −45.3279 −0.0127448 −0.00637238 0.999980i \(-0.502028\pi\)
−0.00637238 + 0.999980i \(0.502028\pi\)
\(234\) −228.928 466.335i −0.0639550 0.130279i
\(235\) −650.532 −0.180579
\(236\) −4256.78 + 2457.66i −1.17412 + 0.677880i
\(237\) 656.064 + 1136.34i 0.179814 + 0.311447i
\(238\) 366.701 635.145i 0.0998727 0.172985i
\(239\) 2128.63i 0.576107i −0.957614 0.288053i \(-0.906992\pi\)
0.957614 0.288053i \(-0.0930081\pi\)
\(240\) 1569.73 + 906.284i 0.422190 + 0.243751i
\(241\) 4404.66 + 2543.03i 1.17730 + 0.679713i 0.955388 0.295354i \(-0.0954375\pi\)
0.221910 + 0.975067i \(0.428771\pi\)
\(242\) 80.4713i 0.0213756i
\(243\) 1892.94 3278.68i 0.499722 0.865544i
\(244\) 1436.18 + 2487.53i 0.376811 + 0.652656i
\(245\) −4535.48 + 2618.56i −1.18270 + 0.682831i
\(246\) −135.671 −0.0351630
\(247\) 3301.37 + 222.355i 0.850449 + 0.0572799i
\(248\) −1742.81 −0.446243
\(249\) −3037.67 + 1753.80i −0.773110 + 0.446355i
\(250\) −487.319 844.061i −0.123283 0.213532i
\(251\) −706.046 + 1222.91i −0.177551 + 0.307527i −0.941041 0.338292i \(-0.890151\pi\)
0.763490 + 0.645819i \(0.223484\pi\)
\(252\) 3651.90i 0.912890i
\(253\) −1834.54 1059.17i −0.455875 0.263199i
\(254\) 9.16141 + 5.28934i 0.00226314 + 0.00130663i
\(255\) 1286.64i 0.315970i
\(256\) −1007.22 + 1744.56i −0.245904 + 0.425919i
\(257\) 3517.46 + 6092.43i 0.853749 + 1.47874i 0.877801 + 0.479025i \(0.159010\pi\)
−0.0240525 + 0.999711i \(0.507657\pi\)
\(258\) −157.477 + 90.9195i −0.0380004 + 0.0219395i
\(259\) −7131.01 −1.71081
\(260\) 3719.28 + 250.503i 0.887154 + 0.0597521i
\(261\) −2852.86 −0.676582
\(262\) 782.450 451.747i 0.184503 0.106523i
\(263\) −3259.44 5645.51i −0.764204 1.32364i −0.940667 0.339332i \(-0.889799\pi\)
0.176463 0.984307i \(-0.443534\pi\)
\(264\) −182.942 + 316.865i −0.0426489 + 0.0738700i
\(265\) 2275.25i 0.527423i
\(266\) 1178.87 + 680.619i 0.271733 + 0.156885i
\(267\) 1844.38 + 1064.85i 0.422749 + 0.244074i
\(268\) 3572.63i 0.814303i
\(269\) 2933.22 5080.49i 0.664839 1.15153i −0.314490 0.949261i \(-0.601834\pi\)
0.979329 0.202274i \(-0.0648332\pi\)
\(270\) −491.189 850.764i −0.110714 0.191762i
\(271\) −6256.02 + 3611.92i −1.40231 + 0.809624i −0.994629 0.103500i \(-0.966996\pi\)
−0.407681 + 0.913124i \(0.633663\pi\)
\(272\) 2037.87 0.454280
\(273\) −1925.30 3921.91i −0.426829 0.869468i
\(274\) −465.554 −0.102647
\(275\) −135.919 + 78.4730i −0.0298045 + 0.0172076i
\(276\) −2339.44 4052.04i −0.510210 0.883710i
\(277\) 2787.06 4827.33i 0.604542 1.04710i −0.387582 0.921835i \(-0.626689\pi\)
0.992124 0.125262i \(-0.0399772\pi\)
\(278\) 1465.02i 0.316065i
\(279\) −2431.03 1403.56i −0.521656 0.301178i
\(280\) 2733.92 + 1578.43i 0.583510 + 0.336890i
\(281\) 83.0572i 0.0176326i −0.999961 0.00881632i \(-0.997194\pi\)
0.999961 0.00881632i \(-0.00280636\pi\)
\(282\) 66.0856 114.464i 0.0139551 0.0241710i
\(283\) 2225.48 + 3854.65i 0.467460 + 0.809664i 0.999309 0.0371751i \(-0.0118359\pi\)
−0.531849 + 0.846839i \(0.678503\pi\)
\(284\) −2256.83 + 1302.98i −0.471542 + 0.272245i
\(285\) 2388.08 0.496342
\(286\) −23.0428 + 342.122i −0.00476415 + 0.0707345i
\(287\) 1839.92 0.378422
\(288\) 1708.92 986.644i 0.349649 0.201870i
\(289\) 1733.22 + 3002.02i 0.352782 + 0.611035i
\(290\) −599.007 + 1037.51i −0.121293 + 0.210085i
\(291\) 5645.21i 1.13721i
\(292\) −5132.46 2963.23i −1.02861 0.593870i
\(293\) −648.797 374.583i −0.129362 0.0746872i 0.433922 0.900950i \(-0.357129\pi\)
−0.563285 + 0.826263i \(0.690463\pi\)
\(294\) 1064.05i 0.211077i
\(295\) −3421.91 + 5926.91i −0.675359 + 1.16976i
\(296\) 1272.35 + 2203.77i 0.249843 + 0.432741i
\(297\) −1337.24 + 772.056i −0.261261 + 0.150839i
\(298\) −1125.07 −0.218703
\(299\) −7496.19 5028.35i −1.44989 0.972565i
\(300\) −346.655 −0.0667137
\(301\) 2135.65 1233.02i 0.408959 0.236113i
\(302\) 993.356 + 1720.54i 0.189276 + 0.327835i
\(303\) −80.3545 + 139.178i −0.0152351 + 0.0263880i
\(304\) 3782.41i 0.713606i
\(305\) 3463.51 + 1999.66i 0.650229 + 0.375410i
\(306\) −365.063 210.769i −0.0682002 0.0393754i
\(307\) 6250.03i 1.16192i −0.813934 0.580958i \(-0.802678\pi\)
0.813934 0.580958i \(-0.197322\pi\)
\(308\) 1205.23 2087.52i 0.222969 0.386193i
\(309\) −2231.07 3864.33i −0.410748 0.711437i
\(310\) −1020.87 + 589.400i −0.187037 + 0.107986i
\(311\) −4650.16 −0.847866 −0.423933 0.905694i \(-0.639351\pi\)
−0.423933 + 0.905694i \(0.639351\pi\)
\(312\) −868.507 + 1294.76i −0.157595 + 0.234940i
\(313\) −2500.00 −0.451465 −0.225732 0.974189i \(-0.572477\pi\)
−0.225732 + 0.974189i \(0.572477\pi\)
\(314\) 1311.88 757.415i 0.235776 0.136126i
\(315\) 2542.35 + 4403.49i 0.454747 + 0.787645i
\(316\) −1542.36 + 2671.45i −0.274572 + 0.475572i
\(317\) 9258.35i 1.64038i 0.572091 + 0.820190i \(0.306132\pi\)
−0.572091 + 0.820190i \(0.693868\pi\)
\(318\) 400.338 + 231.135i 0.0705970 + 0.0407592i
\(319\) 1630.77 + 941.525i 0.286224 + 0.165252i
\(320\) 3681.95i 0.643210i
\(321\) −2086.52 + 3613.96i −0.362798 + 0.628385i
\(322\) −1856.72 3215.92i −0.321338 0.556573i
\(323\) 2325.21 1342.46i 0.400551 0.231258i
\(324\) −9.87918 −0.00169396
\(325\) −600.327 + 294.706i −0.102462 + 0.0502995i
\(326\) 454.274 0.0771776
\(327\) 3100.87 1790.29i 0.524399 0.302762i
\(328\) −328.287 568.610i −0.0552641 0.0957202i
\(329\) −896.229 + 1552.31i −0.150184 + 0.260127i
\(330\) 247.477i 0.0412823i
\(331\) 4797.36 + 2769.76i 0.796636 + 0.459938i 0.842294 0.539019i \(-0.181205\pi\)
−0.0456573 + 0.998957i \(0.514538\pi\)
\(332\) −7141.35 4123.06i −1.18052 0.681573i
\(333\) 4098.70i 0.674497i
\(334\) −54.4681 + 94.3415i −0.00892323 + 0.0154555i
\(335\) 2487.17 + 4307.90i 0.405638 + 0.702585i
\(336\) 4325.19 2497.15i 0.702257 0.405448i
\(337\) −8246.13 −1.33292 −0.666462 0.745539i \(-0.732192\pi\)
−0.666462 + 0.745539i \(0.732192\pi\)
\(338\) −195.931 + 1447.92i −0.0315303 + 0.233008i
\(339\) −1195.41 −0.191522
\(340\) 2619.55 1512.40i 0.417839 0.241239i
\(341\) 926.426 + 1604.62i 0.147122 + 0.254824i
\(342\) 391.200 677.579i 0.0618529 0.107132i
\(343\) 4485.06i 0.706037i
\(344\) −762.103 440.000i −0.119447 0.0689629i
\(345\) −5641.83 3257.31i −0.880423 0.508313i
\(346\) 1397.66i 0.217164i
\(347\) 3347.54 5798.12i 0.517883 0.897000i −0.481901 0.876226i \(-0.660053\pi\)
0.999784 0.0207747i \(-0.00661326\pi\)
\(348\) 2079.60 + 3601.97i 0.320339 + 0.554844i
\(349\) 4222.44 2437.82i 0.647627 0.373908i −0.139919 0.990163i \(-0.544684\pi\)
0.787546 + 0.616255i \(0.211351\pi\)
\(350\) −275.125 −0.0420173
\(351\) −5906.31 + 2899.46i −0.898165 + 0.440916i
\(352\) −1302.48 −0.197223
\(353\) 10663.7 6156.67i 1.60784 0.928290i 0.617993 0.786183i \(-0.287946\pi\)
0.989851 0.142106i \(-0.0453875\pi\)
\(354\) −695.242 1204.20i −0.104383 0.180797i
\(355\) −1814.20 + 3142.28i −0.271233 + 0.469789i
\(356\) 5006.79i 0.745391i
\(357\) −3070.20 1772.58i −0.455161 0.262787i
\(358\) 85.5810 + 49.4102i 0.0126343 + 0.00729444i
\(359\) 12095.7i 1.77824i −0.457678 0.889118i \(-0.651319\pi\)
0.457678 0.889118i \(-0.348681\pi\)
\(360\) 907.236 1571.38i 0.132821 0.230052i
\(361\) −937.816 1624.34i −0.136728 0.236819i
\(362\) 1416.11 817.592i 0.205605 0.118706i
\(363\) 388.987 0.0562439
\(364\) 5721.76 8529.91i 0.823905 1.22827i
\(365\) −8251.68 −1.18332
\(366\) −703.695 + 406.278i −0.100499 + 0.0580233i
\(367\) −4318.51 7479.88i −0.614236 1.06389i −0.990518 0.137383i \(-0.956131\pi\)
0.376282 0.926505i \(-0.377202\pi\)
\(368\) 5159.17 8935.95i 0.730817 1.26581i
\(369\) 1057.54i 0.149195i
\(370\) 1490.59 + 860.591i 0.209438 + 0.120919i
\(371\) −5429.24 3134.57i −0.759763 0.438649i
\(372\) 4092.49i 0.570392i
\(373\) 6914.12 11975.6i 0.959784 1.66239i 0.236764 0.971567i \(-0.423913\pi\)
0.723020 0.690827i \(-0.242753\pi\)
\(374\) 139.119 + 240.962i 0.0192345 + 0.0333151i
\(375\) −4080.07 + 2355.63i −0.561851 + 0.324385i
\(376\) 639.636 0.0877306
\(377\) 6663.57 + 4469.84i 0.910322 + 0.610632i
\(378\) −2706.81 −0.368316
\(379\) −9623.53 + 5556.15i −1.30429 + 0.753035i −0.981138 0.193310i \(-0.938078\pi\)
−0.323157 + 0.946345i \(0.604744\pi\)
\(380\) 2807.10 + 4862.05i 0.378951 + 0.656362i
\(381\) 25.5680 44.2850i 0.00343802 0.00595483i
\(382\) 3003.84i 0.402329i
\(383\) 10575.7 + 6105.88i 1.41095 + 0.814611i 0.995478 0.0949964i \(-0.0302839\pi\)
0.415470 + 0.909607i \(0.363617\pi\)
\(384\) −3285.09 1896.65i −0.436566 0.252052i
\(385\) 3356.19i 0.444279i
\(386\) −400.545 + 693.764i −0.0528166 + 0.0914810i
\(387\) −708.702 1227.51i −0.0930888 0.161235i
\(388\) −11493.5 + 6635.76i −1.50385 + 0.868246i
\(389\) 6803.65 0.886783 0.443392 0.896328i \(-0.353775\pi\)
0.443392 + 0.896328i \(0.353775\pi\)
\(390\) −70.8644 + 1052.14i −0.00920092 + 0.136608i
\(391\) −7324.41 −0.947343
\(392\) 4459.51 2574.70i 0.574590 0.331740i
\(393\) −2183.69 3782.25i −0.280286 0.485469i
\(394\) 107.825 186.758i 0.0137872 0.0238801i
\(395\) 4295.00i 0.547101i
\(396\) −1199.85 692.731i −0.152259 0.0879067i
\(397\) 2446.94 + 1412.74i 0.309341 + 0.178598i 0.646631 0.762803i \(-0.276177\pi\)
−0.337291 + 0.941401i \(0.609511\pi\)
\(398\) 2893.34i 0.364397i
\(399\) 3290.02 5698.48i 0.412799 0.714989i
\(400\) −382.239 662.057i −0.0477798 0.0827571i
\(401\) 11999.5 6927.92i 1.49433 0.862752i 0.494352 0.869262i \(-0.335406\pi\)
0.999979 + 0.00650991i \(0.00207218\pi\)
\(402\) −1010.66 −0.125390
\(403\) 3479.20 + 7087.26i 0.430052 + 0.876034i
\(404\) −377.816 −0.0465273
\(405\) −11.9124 + 6.87762i −0.00146156 + 0.000843831i
\(406\) 1650.49 + 2858.72i 0.201754 + 0.349448i
\(407\) 1352.69 2342.92i 0.164742 0.285342i
\(408\) 1265.09i 0.153508i
\(409\) 7714.62 + 4454.04i 0.932673 + 0.538479i 0.887656 0.460507i \(-0.152332\pi\)
0.0450171 + 0.998986i \(0.485666\pi\)
\(410\) −384.597 222.047i −0.0463266 0.0267467i
\(411\) 2250.42i 0.270086i
\(412\) 5245.10 9084.78i 0.627203 1.08635i
\(413\) 9428.62 + 16330.8i 1.12337 + 1.94573i
\(414\) −1848.42 + 1067.19i −0.219432 + 0.126689i
\(415\) −11481.4 −1.35808
\(416\) −5537.46 372.962i −0.652635 0.0439567i
\(417\) 7081.70 0.831637
\(418\) −447.240 + 258.214i −0.0523330 + 0.0302145i
\(419\) −104.511 181.018i −0.0121854 0.0211058i 0.859868 0.510516i \(-0.170546\pi\)
−0.872054 + 0.489410i \(0.837212\pi\)
\(420\) 3706.50 6419.84i 0.430616 0.745848i
\(421\) 6752.89i 0.781747i −0.920444 0.390874i \(-0.872173\pi\)
0.920444 0.390874i \(-0.127827\pi\)
\(422\) 2292.31 + 1323.46i 0.264426 + 0.152666i
\(423\) 892.225 + 515.127i 0.102557 + 0.0592111i
\(424\) 2237.14i 0.256238i
\(425\) −271.329 + 469.956i −0.0309680 + 0.0536382i
\(426\) −368.598 638.430i −0.0419216 0.0726104i
\(427\) 9543.24 5509.79i 1.08157 0.624444i
\(428\) −9810.54 −1.10797
\(429\) 1653.77 + 111.385i 0.186118 + 0.0125355i
\(430\) −595.216 −0.0667531
\(431\) −589.167 + 340.156i −0.0658450 + 0.0380156i −0.532561 0.846392i \(-0.678770\pi\)
0.466716 + 0.884407i \(0.345437\pi\)
\(432\) −3760.65 6513.64i −0.418830 0.725434i
\(433\) −5641.40 + 9771.19i −0.626116 + 1.08447i 0.362208 + 0.932097i \(0.382023\pi\)
−0.988324 + 0.152368i \(0.951310\pi\)
\(434\) 3248.03i 0.359241i
\(435\) 5015.18 + 2895.52i 0.552780 + 0.319148i
\(436\) 7289.93 + 4208.85i 0.800744 + 0.462310i
\(437\) 13594.5i 1.48813i
\(438\) 838.264 1451.92i 0.0914470 0.158391i
\(439\) 2365.18 + 4096.61i 0.257139 + 0.445377i 0.965474 0.260499i \(-0.0838869\pi\)
−0.708335 + 0.705876i \(0.750554\pi\)
\(440\) −1037.20 + 598.826i −0.112378 + 0.0648816i
\(441\) 8294.07 0.895591
\(442\) 522.464 + 1064.28i 0.0562241 + 0.114531i
\(443\) −669.977 −0.0718546 −0.0359273 0.999354i \(-0.511438\pi\)
−0.0359273 + 0.999354i \(0.511438\pi\)
\(444\) 5174.93 2987.75i 0.553134 0.319352i
\(445\) 3485.59 + 6037.21i 0.371309 + 0.643127i
\(446\) −609.123 + 1055.03i −0.0646700 + 0.112012i
\(447\) 5438.43i 0.575457i
\(448\) 8785.95 + 5072.57i 0.926556 + 0.534947i
\(449\) 1411.20 + 814.754i 0.148326 + 0.0856361i 0.572326 0.820026i \(-0.306041\pi\)
−0.424000 + 0.905662i \(0.639374\pi\)
\(450\) 158.134i 0.0165656i
\(451\) −349.016 + 604.514i −0.0364402 + 0.0631163i
\(452\) −1405.17 2433.82i −0.146224 0.253268i
\(453\) 8316.87 4801.75i 0.862606 0.498026i
\(454\) 2363.62 0.244340
\(455\) 961.037 14268.8i 0.0990200 1.47017i
\(456\) −2348.08 −0.241138
\(457\) 9977.27 5760.38i 1.02126 0.589626i 0.106793 0.994281i \(-0.465942\pi\)
0.914469 + 0.404655i \(0.132608\pi\)
\(458\) −174.820 302.797i −0.0178358 0.0308925i
\(459\) −2669.47 + 4623.66i −0.271460 + 0.470183i
\(460\) 15315.4i 1.55236i
\(461\) −7157.57 4132.42i −0.723126 0.417497i 0.0927762 0.995687i \(-0.470426\pi\)
−0.815902 + 0.578190i \(0.803759\pi\)
\(462\) 590.535 + 340.945i 0.0594679 + 0.0343338i
\(463\) 8472.07i 0.850390i 0.905102 + 0.425195i \(0.139794\pi\)
−0.905102 + 0.425195i \(0.860206\pi\)
\(464\) −4586.13 + 7943.41i −0.458849 + 0.794749i
\(465\) 2849.08 + 4934.75i 0.284135 + 0.492137i
\(466\) 26.1067 15.0727i 0.00259521 0.00149835i
\(467\) −6897.41 −0.683456 −0.341728 0.939799i \(-0.611012\pi\)
−0.341728 + 0.939799i \(0.611012\pi\)
\(468\) −4902.75 3288.70i −0.484252 0.324830i
\(469\) 13706.1 1.34945
\(470\) 374.675 216.319i 0.0367712 0.0212299i
\(471\) −3661.24 6341.46i −0.358176 0.620380i
\(472\) 3364.59 5827.64i 0.328110 0.568303i
\(473\) 935.566i 0.0909458i
\(474\) −755.722 436.316i −0.0732309 0.0422799i
\(475\) −872.267 503.604i −0.0842576 0.0486461i
\(476\) 8334.44i 0.802539i
\(477\) −1801.66 + 3120.57i −0.172940 + 0.299541i
\(478\) 707.824 + 1225.99i 0.0677304 + 0.117312i
\(479\) −8393.77 + 4846.14i −0.800670 + 0.462267i −0.843705 0.536806i \(-0.819631\pi\)
0.0430354 + 0.999074i \(0.486297\pi\)
\(480\) −4005.58 −0.380893
\(481\) 6421.80 9573.53i 0.608750 0.907516i
\(482\) −3382.49 −0.319644
\(483\) −15545.3 + 8975.11i −1.46447 + 0.845510i
\(484\) 457.241 + 791.965i 0.0429415 + 0.0743769i
\(485\) −9239.27 + 16002.9i −0.865018 + 1.49825i
\(486\) 2517.81i 0.235001i
\(487\) 3531.16 + 2038.72i 0.328567 + 0.189698i 0.655205 0.755451i \(-0.272582\pi\)
−0.326638 + 0.945150i \(0.605916\pi\)
\(488\) −3405.49 1966.16i −0.315901 0.182385i
\(489\) 2195.90i 0.203071i
\(490\) 1741.48 3016.33i 0.160555 0.278089i
\(491\) −10238.5 17733.6i −0.941054 1.62995i −0.763466 0.645848i \(-0.776504\pi\)
−0.177588 0.984105i \(-0.556830\pi\)
\(492\) −1335.22 + 770.890i −0.122350 + 0.0706391i
\(493\) 6510.87 0.594796
\(494\) −1975.37 + 969.724i −0.179911 + 0.0883197i
\(495\) −1929.04 −0.175160
\(496\) −7816.02 + 4512.58i −0.707560 + 0.408510i
\(497\) 4998.78 + 8658.15i 0.451159 + 0.781431i
\(498\) 1166.37 2020.21i 0.104952 0.181782i
\(499\) 11763.9i 1.05536i −0.849444 0.527679i \(-0.823062\pi\)
0.849444 0.527679i \(-0.176938\pi\)
\(500\) −9591.98 5537.93i −0.857933 0.495328i
\(501\) 456.034 + 263.291i 0.0406668 + 0.0234790i
\(502\) 939.115i 0.0834955i
\(503\) −11241.8 + 19471.4i −0.996515 + 1.72601i −0.426021 + 0.904713i \(0.640085\pi\)
−0.570494 + 0.821301i \(0.693248\pi\)
\(504\) −2499.77 4329.73i −0.220930 0.382662i
\(505\) −455.573 + 263.025i −0.0401440 + 0.0231772i
\(506\) 1408.81 0.123773
\(507\) 6999.06 + 947.105i 0.613095 + 0.0829633i
\(508\) 120.217 0.0104996
\(509\) −4041.33 + 2333.26i −0.351923 + 0.203183i −0.665532 0.746370i \(-0.731795\pi\)
0.313609 + 0.949552i \(0.398462\pi\)
\(510\) 427.840 + 741.041i 0.0371472 + 0.0643409i
\(511\) −11368.2 + 19690.3i −0.984149 + 1.70460i
\(512\) 10779.4i 0.930441i
\(513\) −8581.79 4954.70i −0.738587 0.426424i
\(514\) −4051.78 2339.30i −0.347697 0.200743i
\(515\) 14606.0i 1.24974i
\(516\) −1033.22 + 1789.58i −0.0881489 + 0.152678i
\(517\) −340.012 588.918i −0.0289240 0.0500979i
\(518\) 4107.12 2371.25i 0.348372 0.201132i
\(519\) 6756.09 0.571405
\(520\) −4581.09 + 2248.89i −0.386335 + 0.189655i
\(521\) −18591.4 −1.56335 −0.781674 0.623687i \(-0.785634\pi\)
−0.781674 + 0.623687i \(0.785634\pi\)
\(522\) 1643.11 948.651i 0.137772 0.0795428i
\(523\) 2981.38 + 5163.90i 0.249267 + 0.431743i 0.963323 0.268346i \(-0.0864771\pi\)
−0.714056 + 0.700089i \(0.753144\pi\)
\(524\) 5133.70 8891.82i 0.427990 0.741300i
\(525\) 1329.92i 0.110557i
\(526\) 3754.56 + 2167.69i 0.311229 + 0.179688i
\(527\) 5548.15 + 3203.23i 0.458598 + 0.264772i
\(528\) 1894.74i 0.156170i
\(529\) −12459.3 + 21580.2i −1.02403 + 1.77366i
\(530\) 756.578 + 1310.43i 0.0620069 + 0.107399i
\(531\) 9386.50 5419.30i 0.767118 0.442896i
\(532\) 15469.2 1.26067
\(533\) −1656.93 + 2470.13i −0.134652 + 0.200738i
\(534\) −1416.36 −0.114779
\(535\) −11829.6 + 6829.83i −0.955960 + 0.551924i
\(536\) −2445.51 4235.75i −0.197071 0.341337i
\(537\) 238.842 413.687i 0.0191933 0.0332438i
\(538\) 3901.49i 0.312649i
\(539\) −4741.10 2737.27i −0.378875 0.218744i
\(540\) −9668.15 5581.91i −0.770465 0.444828i
\(541\) 10281.4i 0.817068i 0.912743 + 0.408534i \(0.133960\pi\)
−0.912743 + 0.408534i \(0.866040\pi\)
\(542\) 2402.11 4160.58i 0.190368 0.329727i
\(543\) −3952.13 6845.29i −0.312343 0.540993i
\(544\) −3900.13 + 2251.74i −0.307383 + 0.177468i
\(545\) 11720.3 0.921181
\(546\) 2413.01 + 1618.62i 0.189135 + 0.126869i
\(547\) −2031.38 −0.158785 −0.0793926 0.996843i \(-0.525298\pi\)
−0.0793926 + 0.996843i \(0.525298\pi\)
\(548\) −4581.79 + 2645.30i −0.357161 + 0.206207i
\(549\) −3166.87 5485.18i −0.246191 0.426415i
\(550\) 52.1886 90.3933i 0.00404605 0.00700797i
\(551\) 12084.6i 0.934336i
\(552\) 5547.33 + 3202.75i 0.427736 + 0.246953i
\(553\) 10248.8 + 5917.16i 0.788109 + 0.455015i
\(554\) 3707.08i 0.284294i
\(555\) 4159.98 7205.29i 0.318164 0.551077i
\(556\) 8324.30 + 14418.1i 0.634944 + 1.09976i
\(557\) −8868.27 + 5120.10i −0.674615 + 0.389489i −0.797823 0.602892i \(-0.794015\pi\)
0.123208 + 0.992381i \(0.460682\pi\)
\(558\) 1866.88 0.141633
\(559\) −267.897 + 3977.54i −0.0202698 + 0.300951i
\(560\) 16347.9 1.23361
\(561\) 1164.78 672.484i 0.0876594 0.0506102i
\(562\) 27.6187 + 47.8369i 0.00207299 + 0.00359053i
\(563\) 9525.14 16498.0i 0.713031 1.23501i −0.250683 0.968069i \(-0.580655\pi\)
0.963714 0.266937i \(-0.0860116\pi\)
\(564\) 1502.01i 0.112138i
\(565\) −3388.72 1956.48i −0.252326 0.145681i
\(566\) −2563.54 1480.06i −0.190377 0.109914i
\(567\) 37.9008i 0.00280720i
\(568\) 1783.81 3089.65i 0.131773 0.228237i
\(569\) 3442.50 + 5962.59i 0.253633 + 0.439305i 0.964523 0.263998i \(-0.0850411\pi\)
−0.710890 + 0.703303i \(0.751708\pi\)
\(570\) −1375.42 + 794.097i −0.101070 + 0.0583528i
\(571\) −26902.4 −1.97168 −0.985839 0.167692i \(-0.946369\pi\)
−0.985839 + 0.167692i \(0.946369\pi\)
\(572\) 1717.17 + 3497.95i 0.125522 + 0.255693i
\(573\) −14520.1 −1.05862
\(574\) −1059.71 + 611.822i −0.0770581 + 0.0444895i
\(575\) 1373.82 + 2379.53i 0.0996388 + 0.172579i
\(576\) 2915.57 5049.91i 0.210906 0.365300i
\(577\) 2399.20i 0.173102i 0.996247 + 0.0865512i \(0.0275846\pi\)
−0.996247 + 0.0865512i \(0.972415\pi\)
\(578\) −1996.50 1152.68i −0.143674 0.0829500i
\(579\) 3353.56 + 1936.18i 0.240707 + 0.138972i
\(580\) 13614.3i 0.974662i
\(581\) −15817.8 + 27397.3i −1.12949 + 1.95633i
\(582\) −1877.18 3251.37i −0.133697 0.231570i
\(583\) 2059.75 1189.20i 0.146323 0.0844795i
\(584\) 8113.47 0.574893
\(585\) −8201.27 552.376i −0.579625 0.0390392i
\(586\) 498.234 0.0351226
\(587\) 13742.7 7934.34i 0.966305 0.557897i 0.0681974 0.997672i \(-0.478275\pi\)
0.898108 + 0.439775i \(0.144942\pi\)
\(588\) −6045.96 10471.9i −0.424033 0.734446i
\(589\) −5945.38 + 10297.7i −0.415917 + 0.720389i
\(590\) 4551.49i 0.317596i
\(591\) −902.764 521.211i −0.0628338 0.0362771i
\(592\) 11412.3 + 6588.88i 0.792300 + 0.457435i
\(593\) 795.575i 0.0550933i 0.999621 + 0.0275467i \(0.00876949\pi\)
−0.999621 + 0.0275467i \(0.991231\pi\)
\(594\) 513.457 889.333i 0.0354670 0.0614306i
\(595\) −5802.21 10049.7i −0.399777 0.692434i
\(596\) −11072.5 + 6392.70i −0.760984 + 0.439354i
\(597\) 13986.0 0.958809
\(598\) 5989.50 + 403.408i 0.409580 + 0.0275863i
\(599\) 11565.7 0.788917 0.394458 0.918914i \(-0.370932\pi\)
0.394458 + 0.918914i \(0.370932\pi\)
\(600\) 410.997 237.289i 0.0279648 0.0161455i
\(601\) −560.946 971.587i −0.0380723 0.0659432i 0.846361 0.532609i \(-0.178788\pi\)
−0.884434 + 0.466666i \(0.845455\pi\)
\(602\) −820.020 + 1420.32i −0.0555175 + 0.0961591i
\(603\) 7877.90i 0.532028i
\(604\) 19552.4 + 11288.6i 1.31718 + 0.760473i
\(605\) 1102.69 + 636.638i 0.0741003 + 0.0427818i
\(606\) 106.880i 0.00716451i
\(607\) −9491.63 + 16440.0i −0.634684 + 1.09931i 0.351898 + 0.936039i \(0.385537\pi\)
−0.986582 + 0.163267i \(0.947797\pi\)
\(608\) −4179.36 7238.87i −0.278776 0.482853i
\(609\) 13818.7 7978.22i 0.919476 0.530860i
\(610\) −2659.75 −0.176541
\(611\) −1276.92 2601.13i −0.0845476 0.172227i
\(612\) −4790.40 −0.316406
\(613\) −16635.1 + 9604.29i −1.09606 + 0.632812i −0.935184 0.354162i \(-0.884766\pi\)
−0.160878 + 0.986974i \(0.551433\pi\)
\(614\) 2078.30 + 3599.72i 0.136601 + 0.236601i
\(615\) −1073.35 + 1859.09i −0.0703764 + 0.121895i
\(616\) 3299.98i 0.215844i
\(617\) −23127.9 13352.9i −1.50907 0.871261i −0.999944 0.0105688i \(-0.996636\pi\)
−0.509125 0.860693i \(-0.670031\pi\)
\(618\) 2569.98 + 1483.78i 0.167281 + 0.0965798i
\(619\) 4297.92i 0.279076i −0.990217 0.139538i \(-0.955438\pi\)
0.990217 0.139538i \(-0.0445618\pi\)
\(620\) −6698.00 + 11601.3i −0.433868 + 0.751481i
\(621\) 13516.3 + 23411.0i 0.873416 + 1.51280i
\(622\) 2678.27 1546.30i 0.172651 0.0996799i
\(623\) 19208.2 1.23525
\(624\) −542.554 + 8055.44i −0.0348070 + 0.516788i
\(625\) −13638.0 −0.872829
\(626\) 1439.88 831.315i 0.0919316 0.0530767i
\(627\) 1248.17 + 2161.90i 0.0795010 + 0.137700i
\(628\) 8607.33 14908.3i 0.546927 0.947305i
\(629\) 9354.14i 0.592963i
\(630\) −2928.55 1690.80i −0.185200 0.106925i
\(631\) 6979.35 + 4029.53i 0.440322 + 0.254220i 0.703734 0.710463i \(-0.251515\pi\)
−0.263412 + 0.964683i \(0.584848\pi\)
\(632\) 4223.06i 0.265798i
\(633\) 6397.44 11080.7i 0.401699 0.695763i
\(634\) −3078.64 5332.36i −0.192852 0.334030i
\(635\) 144.959 83.6919i 0.00905906 0.00523025i
\(636\) 5253.29 0.327526
\(637\) −19372.8 12995.1i −1.20499 0.808293i
\(638\) −1252.33 −0.0777117
\(639\) 4976.46 2873.16i 0.308084 0.177872i
\(640\) −6208.31 10753.1i −0.383446 0.664147i
\(641\) 2919.34 5056.44i 0.179886 0.311571i −0.761955 0.647629i \(-0.775760\pi\)
0.941841 + 0.336058i \(0.109094\pi\)
\(642\) 2775.29i 0.170610i
\(643\) −5961.21 3441.70i −0.365610 0.211085i 0.305929 0.952054i \(-0.401033\pi\)
−0.671539 + 0.740969i \(0.734366\pi\)
\(644\) −36546.0 21099.9i −2.23620 1.29107i
\(645\) 2877.19i 0.175642i
\(646\) −892.805 + 1546.38i −0.0543761 + 0.0941821i
\(647\) −8582.42 14865.2i −0.521499 0.903262i −0.999687 0.0250052i \(-0.992040\pi\)
0.478189 0.878257i \(-0.341294\pi\)
\(648\) 11.7129 6.76242i 0.000710068 0.000409958i
\(649\) −7154.08 −0.432700
\(650\) 247.762 369.361i 0.0149508 0.0222885i
\(651\) 15700.5 0.945242
\(652\) 4470.78 2581.20i 0.268542 0.155043i
\(653\) −8188.61 14183.1i −0.490727 0.849965i 0.509216 0.860639i \(-0.329936\pi\)
−0.999943 + 0.0106743i \(0.996602\pi\)
\(654\) −1190.63 + 2062.24i −0.0711888 + 0.123303i
\(655\) 14295.8i 0.852796i
\(656\) −2944.56 1700.04i −0.175253 0.101182i
\(657\) 11317.4 + 6534.12i 0.672048 + 0.388007i
\(658\) 1192.08i 0.0706261i
\(659\) 10249.1 17752.0i 0.605839 1.04934i −0.386079 0.922466i \(-0.626171\pi\)
0.991918 0.126878i \(-0.0404958\pi\)
\(660\) 1406.18 + 2435.57i 0.0829323 + 0.143643i
\(661\) −12701.5 + 7333.19i −0.747397 + 0.431510i −0.824753 0.565494i \(-0.808686\pi\)
0.0773555 + 0.997004i \(0.475352\pi\)
\(662\) −3684.06 −0.216292
\(663\) 5144.58 2525.52i 0.301356 0.147938i
\(664\) 11289.1 0.659794
\(665\) 18652.9 10769.2i 1.08771 0.627990i
\(666\) −1362.92 2360.65i −0.0792977 0.137348i
\(667\) 16483.2 28549.8i 0.956871 1.65735i
\(668\) 1237.96i 0.0717037i
\(669\) 5099.88 + 2944.42i 0.294728 + 0.170161i
\(670\) −2864.98 1654.10i −0.165200 0.0953781i
\(671\) 4180.62i 0.240523i
\(672\) −5518.43 + 9558.20i −0.316783 + 0.548684i
\(673\) −12614.6 21849.1i −0.722520 1.25144i −0.959987 0.280045i \(-0.909651\pi\)
0.237467 0.971396i \(-0.423683\pi\)
\(674\) 4749.37 2742.05i 0.271423 0.156706i
\(675\) 2002.83 0.114206
\(676\) 6298.88 + 15363.1i 0.358380 + 0.874098i
\(677\) 25265.0 1.43429 0.717143 0.696926i \(-0.245449\pi\)
0.717143 + 0.696926i \(0.245449\pi\)
\(678\) 688.499 397.505i 0.0389995 0.0225164i
\(679\) 25457.6 + 44093.9i 1.43884 + 2.49215i
\(680\) −2070.51 + 3586.23i −0.116765 + 0.202244i
\(681\) 11425.4i 0.642913i
\(682\) −1067.15 616.121i −0.0599170 0.0345931i
\(683\) 13195.9 + 7618.66i 0.739279 + 0.426823i 0.821807 0.569766i \(-0.192966\pi\)
−0.0825281 + 0.996589i \(0.526299\pi\)
\(684\) 8891.26i 0.497026i
\(685\) −3683.17 + 6379.43i −0.205440 + 0.355833i
\(686\) −1491.40 2583.18i −0.0830057 0.143770i
\(687\) −1463.68 + 845.056i −0.0812851 + 0.0469300i
\(688\) −4557.11 −0.252526
\(689\) 9097.50 4466.04i 0.503029 0.246941i
\(690\) 4332.56 0.239040
\(691\) 2853.52 1647.48i 0.157096 0.0906992i −0.419391 0.907806i \(-0.637756\pi\)
0.576487 + 0.817106i \(0.304423\pi\)
\(692\) 7941.56 + 13755.2i 0.436261 + 0.755626i
\(693\) −2657.61 + 4603.12i −0.145677 + 0.252320i
\(694\) 4452.58i 0.243541i
\(695\) 20075.0 + 11590.3i 1.09567 + 0.632583i
\(696\) −4931.18 2847.02i −0.268557 0.155052i
\(697\) 2413.53i 0.131161i
\(698\) −1621.28 + 2808.14i −0.0879174 + 0.152277i
\(699\) −72.8593 126.196i −0.00394248 0.00682857i
\(700\) −2707.67 + 1563.27i −0.146200 + 0.0844087i
\(701\) −747.881 −0.0402954 −0.0201477 0.999797i \(-0.506414\pi\)
−0.0201477 + 0.999797i \(0.506414\pi\)
\(702\) 2437.61 3633.95i 0.131056 0.195377i
\(703\) 17361.8 0.931457
\(704\) −3333.22 + 1924.44i −0.178445 + 0.103025i
\(705\) −1045.66 1811.13i −0.0558605 0.0967532i
\(706\) −4094.50 + 7091.88i −0.218270 + 0.378055i
\(707\) 1449.46i 0.0771042i
\(708\) −13684.6 7900.80i −0.726410 0.419393i
\(709\) −5166.07 2982.63i −0.273647 0.157990i 0.356897 0.934144i \(-0.383835\pi\)
−0.630544 + 0.776154i \(0.717168\pi\)
\(710\) 2413.07i 0.127551i
\(711\) 3401.01 5890.73i 0.179392 0.310717i
\(712\) −3427.20 5936.09i −0.180393 0.312450i
\(713\) 28091.9 16218.9i 1.47553 0.851896i
\(714\) 2357.72 0.123579
\(715\) 4505.75 + 3022.40i 0.235672 + 0.158086i
\(716\) 1123.00 0.0586154
\(717\) 5926.25 3421.52i 0.308675 0.178214i
\(718\) 4022.13 + 6966.54i 0.209059 + 0.362102i
\(719\) −6847.41 + 11860.1i −0.355167 + 0.615167i −0.987147 0.159818i \(-0.948909\pi\)
0.631979 + 0.774985i \(0.282243\pi\)
\(720\) 9396.29i 0.486360i
\(721\) −34853.1 20122.4i −1.80027 1.03939i
\(722\) 1080.27 + 623.696i 0.0556837 + 0.0321490i
\(723\) 16350.5i 0.841054i
\(724\) 9291.19 16092.8i 0.476940 0.826084i
\(725\) −1221.23 2115.23i −0.0625590 0.108355i
\(726\) −224.038 + 129.348i −0.0114529 + 0.00661235i
\(727\) 11312.0 0.577081 0.288541 0.957468i \(-0.406830\pi\)
0.288541 + 0.957468i \(0.406830\pi\)
\(728\) −944.940 + 14029.8i −0.0481069 + 0.714255i
\(729\) 12206.1 0.620132
\(730\) 4752.57 2743.90i 0.240960 0.139118i
\(731\) 1617.41 + 2801.44i 0.0818362 + 0.141744i
\(732\) −4616.98 + 7996.85i −0.233126 + 0.403787i
\(733\) 19038.0i 0.959326i 0.877453 + 0.479663i \(0.159241\pi\)
−0.877453 + 0.479663i \(0.840759\pi\)
\(734\) 4974.51 + 2872.04i 0.250153 + 0.144426i
\(735\) −14580.5 8418.07i −0.731715 0.422456i
\(736\) 22802.4i 1.14200i
\(737\) −2599.93 + 4503.20i −0.129945 + 0.225071i
\(738\) 351.658 + 609.089i 0.0175403 + 0.0303806i
\(739\) 5694.85 3287.92i 0.283476 0.163665i −0.351520 0.936180i \(-0.614335\pi\)
0.634996 + 0.772516i \(0.281002\pi\)
\(740\) 19559.7 0.971658
\(741\) 4687.51 + 9548.65i 0.232389 + 0.473385i
\(742\) 4169.31 0.206280
\(743\) −11618.4 + 6707.90i −0.573672 + 0.331210i −0.758615 0.651540i \(-0.774123\pi\)
0.184942 + 0.982749i \(0.440790\pi\)
\(744\) −2801.36 4852.10i −0.138041 0.239095i
\(745\) −8900.84 + 15416.7i −0.437720 + 0.758154i
\(746\) 9196.49i 0.451350i
\(747\) 15747.2 + 9091.63i 0.771297 + 0.445308i
\(748\) 2738.31 + 1580.96i 0.133854 + 0.0772805i
\(749\) 37637.4i 1.83610i
\(750\) 1566.62 2713.46i 0.0762730 0.132109i
\(751\) −10868.7 18825.2i −0.528104 0.914703i −0.999463 0.0327615i \(-0.989570\pi\)
0.471359 0.881941i \(-0.343763\pi\)
\(752\) 2868.60 1656.19i 0.139105 0.0803124i
\(753\) −4539.55 −0.219695
\(754\) −5324.23 358.600i −0.257158 0.0173202i
\(755\) 31435.2 1.51529
\(756\) −26639.3 + 15380.2i −1.28157 + 0.739912i
\(757\) −11241.0 19470.0i −0.539712 0.934808i −0.998919 0.0464789i \(-0.985200\pi\)
0.459208 0.888329i \(-0.348133\pi\)
\(758\) 3695.13 6400.15i 0.177062 0.306681i
\(759\) 6809.97i 0.325674i
\(760\) −6656.26 3842.99i −0.317695 0.183421i
\(761\) 7691.00 + 4440.40i 0.366358 + 0.211517i 0.671866 0.740673i \(-0.265493\pi\)
−0.305508 + 0.952189i \(0.598826\pi\)
\(762\) 34.0080i 0.00161677i
\(763\) 16146.9 27967.3i 0.766131 1.32698i
\(764\) −17067.9 29562.5i −0.808241 1.39991i
\(765\) −5776.29 + 3334.94i −0.272996 + 0.157615i
\(766\) −8121.45 −0.383081
\(767\) −30415.4 2048.55i −1.43186 0.0964393i
\(768\) −6475.98 −0.304273
\(769\) 8104.38 4679.06i 0.380041 0.219417i −0.297795 0.954630i \(-0.596251\pi\)
0.677836 + 0.735213i \(0.262918\pi\)
\(770\) 1116.02 + 1933.00i 0.0522319 + 0.0904683i
\(771\) −11307.8 + 19585.7i −0.528199 + 0.914868i
\(772\) 9103.66i 0.424414i
\(773\) −17249.5 9959.00i −0.802615 0.463390i 0.0417698 0.999127i \(-0.486700\pi\)
−0.844385 + 0.535737i \(0.820034\pi\)
\(774\) 816.357 + 471.324i 0.0379113 + 0.0218881i
\(775\) 2403.29i 0.111392i
\(776\) 9084.51 15734.8i 0.420251 0.727897i
\(777\) −11462.3 19853.3i −0.529224 0.916643i
\(778\) −3918.57 + 2262.39i −0.180575 + 0.104255i
\(779\) −4479.65 −0.206034
\(780\) 5280.90 + 10757.4i 0.242419 + 0.493816i
\(781\) −3792.89 −0.173778
\(782\) 4218.50 2435.55i 0.192907 0.111375i
\(783\) −12015.0 20810.6i −0.548381 0.949824i
\(784\) 13333.2 23093.7i 0.607378 1.05201i
\(785\) 23968.8i 1.08979i
\(786\) 2515.39 + 1452.26i 0.114149 + 0.0659040i
\(787\) 2175.43 + 1255.99i 0.0985334 + 0.0568883i 0.548457 0.836179i \(-0.315215\pi\)
−0.449924 + 0.893067i \(0.648549\pi\)
\(788\) 2450.66i 0.110788i
\(789\) 10478.3 18149.0i 0.472799 0.818913i
\(790\) −1428.20 2473.71i −0.0643203 0.111406i
\(791\) −9337.17 + 5390.82i −0.419711 + 0.242320i
\(792\) 1896.73 0.0850977
\(793\) −1197.11 + 17773.8i −0.0536074 + 0.795923i
\(794\) −1879.09 −0.0839880
\(795\) 6334.45 3657.19i 0.282591 0.163154i
\(796\) 16440.1 + 28475.1i 0.732039 + 1.26793i
\(797\) 6322.89 10951.6i 0.281014 0.486731i −0.690621 0.723217i \(-0.742663\pi\)
0.971635 + 0.236486i \(0.0759958\pi\)
\(798\) 4376.06i 0.194124i
\(799\) −2036.25 1175.63i −0.0901596 0.0520537i
\(800\) 1463.07 + 844.707i 0.0646594 + 0.0373311i
\(801\) 11040.3i 0.487004i
\(802\) −4607.42 + 7980.29i −0.202860 + 0.351364i
\(803\) −4312.89 7470.14i −0.189537 0.328288i
\(804\) −9946.47 + 5742.59i −0.436300 + 0.251898i
\(805\) −58756.6 −2.57254
\(806\) −4360.55 2925.00i −0.190563 0.127827i
\(807\) 18859.3 0.822649
\(808\) 447.942 258.619i 0.0195032 0.0112602i
\(809\) 7067.04 + 12240.5i 0.307125 + 0.531956i 0.977732 0.209857i \(-0.0672997\pi\)
−0.670607 + 0.741813i \(0.733966\pi\)
\(810\) 4.57397 7.92235i 0.000198411 0.000343658i
\(811\) 250.820i 0.0108600i 0.999985 + 0.00543002i \(0.00172844\pi\)
−0.999985 + 0.00543002i \(0.998272\pi\)
\(812\) 32486.8 + 18756.3i 1.40402 + 0.810610i
\(813\) −20111.7 11611.5i −0.867585 0.500901i
\(814\) 1799.21i 0.0774722i
\(815\) 3593.93 6224.87i 0.154466 0.267543i
\(816\) 3275.64 + 5673.58i 0.140528 + 0.243401i
\(817\) −5199.65 + 3002.02i −0.222659 + 0.128552i
\(818\) −5924.33 −0.253227
\(819\) −12616.9 + 18809.0i −0.538301 + 0.802492i
\(820\) −5046.73 −0.214926
\(821\) 11469.5 6621.90i 0.487560 0.281493i −0.236002 0.971753i \(-0.575837\pi\)
0.723562 + 0.690260i \(0.242504\pi\)
\(822\) −748.324 1296.14i −0.0317528 0.0549975i
\(823\) 12138.6 21024.7i 0.514127 0.890494i −0.485739 0.874104i \(-0.661449\pi\)
0.999866 0.0163900i \(-0.00521734\pi\)
\(824\) 14361.3i 0.607161i
\(825\) −436.949 252.272i −0.0184395 0.0106461i
\(826\) −10860.9 6270.52i −0.457503 0.264140i
\(827\) 34821.6i 1.46417i 0.681215 + 0.732083i \(0.261452\pi\)
−0.681215 + 0.732083i \(0.738548\pi\)
\(828\) −12127.6 + 21005.6i −0.509014 + 0.881637i
\(829\) 3350.63 + 5803.46i 0.140377 + 0.243139i 0.927638 0.373479i \(-0.121835\pi\)
−0.787262 + 0.616619i \(0.788502\pi\)
\(830\) 6612.76 3817.88i 0.276545 0.159663i
\(831\) 17919.5 0.748039
\(832\) −14722.2 + 7227.23i −0.613461 + 0.301153i
\(833\) −18928.9 −0.787332
\(834\) −4078.72 + 2354.85i −0.169346 + 0.0977719i
\(835\) 861.834 + 1492.74i 0.0357185 + 0.0618663i
\(836\) −2934.37 + 5082.47i −0.121396 + 0.210264i
\(837\) 23644.7i 0.976440i
\(838\) 120.386 + 69.5051i 0.00496263 + 0.00286517i
\(839\) −32308.5 18653.3i −1.32946 0.767562i −0.344240 0.938882i \(-0.611863\pi\)
−0.985215 + 0.171320i \(0.945197\pi\)
\(840\) 10148.6i 0.416856i
\(841\) −2457.88 + 4257.18i −0.100778 + 0.174553i
\(842\) 2245.51 + 3889.34i 0.0919066 + 0.159187i
\(843\) 231.237 133.505i 0.00944748 0.00545451i
\(844\) 30079.9 1.22677
\(845\) 18290.6 + 14139.9i 0.744635 + 0.575652i
\(846\) −685.172 −0.0278448
\(847\) 3038.32 1754.17i 0.123256 0.0711618i
\(848\) 5792.53 + 10033.0i 0.234571 + 0.406289i
\(849\) −7154.41 + 12391.8i −0.289209 + 0.500925i
\(850\) 360.896i 0.0145631i
\(851\) −41017.4 23681.4i −1.65224 0.953922i
\(852\) −7255.17 4188.78i −0.291735 0.168433i
\(853\) 36525.1i 1.46611i 0.680167 + 0.733057i \(0.261907\pi\)
−0.680167 + 0.733057i \(0.738093\pi\)
\(854\) −3664.30 + 6346.75i −0.146826 + 0.254311i
\(855\) −6189.86 10721.1i −0.247589 0.428837i
\(856\) 11631.5 6715.43i 0.464434 0.268141i
\(857\) 5408.05 0.215561 0.107780 0.994175i \(-0.465626\pi\)
0.107780 + 0.994175i \(0.465626\pi\)
\(858\) −989.529 + 485.768i −0.0393729 + 0.0193285i
\(859\) 38851.4 1.54318 0.771591 0.636119i \(-0.219461\pi\)
0.771591 + 0.636119i \(0.219461\pi\)
\(860\) −5857.87 + 3382.04i −0.232269 + 0.134101i
\(861\) 2957.46 + 5122.48i 0.117062 + 0.202757i
\(862\) 226.221 391.827i 0.00893866 0.0154822i
\(863\) 35630.7i 1.40543i −0.711474 0.702713i \(-0.751972\pi\)
0.711474 0.702713i \(-0.248028\pi\)
\(864\) 14394.4 + 8310.64i 0.566793 + 0.327238i
\(865\) 19152.0 + 11057.4i 0.752816 + 0.434639i
\(866\) 7503.65i 0.294439i
\(867\) −5571.89 + 9650.79i −0.218260 + 0.378037i
\(868\) 18455.5 + 31965.8i 0.721681 + 1.24999i
\(869\) −3888.21 + 2244.86i −0.151782 + 0.0876313i
\(870\) −3851.34 −0.150083
\(871\) −12343.0 + 18400.8i −0.480168 + 0.715828i
\(872\) −11524.0 −0.447537
\(873\) 25343.9 14632.3i 0.982544 0.567272i
\(874\) 4520.53 + 7829.80i 0.174954 + 0.303028i
\(875\) −21245.9 + 36798.9i −0.820848 + 1.42175i
\(876\) 19052.2i 0.734834i
\(877\) −20414.1 11786.1i −0.786015 0.453806i 0.0525425 0.998619i \(-0.483268\pi\)
−0.838558 + 0.544812i \(0.816601\pi\)
\(878\) −2724.46 1572.97i −0.104722 0.0604614i
\(879\) 2408.39i 0.0924154i
\(880\) −3101.04 + 5371.15i −0.118791 + 0.205752i
\(881\) 753.555 + 1305.19i 0.0288171 + 0.0499127i 0.880074 0.474836i \(-0.157493\pi\)
−0.851257 + 0.524749i \(0.824159\pi\)
\(882\) −4776.98 + 2757.99i −0.182369 + 0.105291i
\(883\) −12632.0 −0.481428 −0.240714 0.970596i \(-0.577382\pi\)
−0.240714 + 0.970596i \(0.577382\pi\)
\(884\) 11189.2 + 7505.54i 0.425715 + 0.285564i
\(885\) −22001.3 −0.835666
\(886\) 385.875 222.785i 0.0146317 0.00844763i
\(887\) −1660.05 2875.29i −0.0628399 0.108842i 0.832894 0.553433i \(-0.186682\pi\)
−0.895734 + 0.444591i \(0.853349\pi\)
\(888\) −4090.30 + 7084.61i −0.154574 + 0.267730i
\(889\) 461.204i 0.0173997i
\(890\) −4015.06 2318.10i −0.151219 0.0873065i
\(891\) −12.4524 7.18942i −0.000468207 0.000270319i
\(892\) 13844.3i 0.519664i
\(893\) 2182.04 3779.41i 0.0817685 0.141627i
\(894\) −1808.42 3132.28i −0.0676539 0.117180i
\(895\) 1354.13 781.805i 0.0505736 0.0291987i
\(896\) −34212.4 −1.27562
\(897\) 1950.02 28952.4i 0.0725855 1.07770i
\(898\) −1083.71 −0.0402715
\(899\) −24971.7 + 14417.4i −0.926421 + 0.534869i
\(900\) 898.524 + 1556.29i 0.0332786 + 0.0576403i
\(901\) 4111.79 7121.83i 0.152035 0.263332i
\(902\) 464.228i 0.0171365i
\(903\) 6865.61 + 3963.86i 0.253016 + 0.146079i
\(904\) 3331.96 + 1923.71i 0.122588 + 0.0707760i
\(905\) 25873.1i 0.950332i
\(906\) −3193.41 + 5531.15i −0.117102 + 0.202826i
\(907\) 10285.1 + 17814.3i 0.376527 + 0.652164i 0.990554 0.137121i \(-0.0437849\pi\)
−0.614027 + 0.789285i \(0.710452\pi\)
\(908\) 23261.8 13430.2i 0.850188 0.490856i
\(909\) 833.110 0.0303988
\(910\) 4191.22 + 8537.68i 0.152679 + 0.311013i
\(911\) 51427.6 1.87033 0.935165 0.354211i \(-0.115251\pi\)
0.935165 + 0.354211i \(0.115251\pi\)
\(912\) −10530.5 + 6079.79i −0.382346 + 0.220748i
\(913\) −6000.98 10394.0i −0.217529 0.376770i
\(914\) −3830.95 + 6635.40i −0.138640 + 0.240131i
\(915\) 12856.9i 0.464519i
\(916\) −3441.01 1986.67i −0.124120 0.0716609i
\(917\) −34112.8 19695.1i −1.22847 0.709256i
\(918\) 3550.67i 0.127658i
\(919\) 4715.43 8167.37i 0.169258 0.293163i −0.768901 0.639367i \(-0.779196\pi\)
0.938159 + 0.346204i \(0.112530\pi\)
\(920\) 10483.6 + 18158.1i 0.375690 + 0.650713i
\(921\) 17400.5 10046.2i 0.622549 0.359429i
\(922\) 5496.55 0.196333
\(923\) −16125.4 1086.08i −0.575052 0.0387312i
\(924\) 7749.07 0.275894
\(925\) −3038.94 + 1754.53i −0.108021 + 0.0623662i
\(926\) −2817.18 4879.50i −0.0999766 0.173165i
\(927\) −11565.8 + 20032.6i −0.409785 + 0.709769i
\(928\) 20269.7i 0.717011i
\(929\) 19629.5 + 11333.1i 0.693242 + 0.400244i 0.804826 0.593511i \(-0.202259\pi\)
−0.111583 + 0.993755i \(0.535592\pi\)
\(930\) −3281.87 1894.79i −0.115717 0.0668091i
\(931\) 35133.2i 1.23678i
\(932\) 171.287 296.678i 0.00602007 0.0104271i
\(933\) −7474.59 12946.4i −0.262280 0.454282i
\(934\) 3972.57 2293.57i 0.139172 0.0803510i
\(935\) 4402.50 0.153986
\(936\) 8063.90 + 543.124i 0.281599 + 0.0189664i
\(937\) 39917.7 1.39173 0.695867 0.718171i \(-0.255020\pi\)
0.695867 + 0.718171i \(0.255020\pi\)
\(938\) −7894.08 + 4557.65i −0.274788 + 0.158649i
\(939\) −4018.46 6960.18i −0.139657 0.241892i
\(940\) 2458.27 4257.84i 0.0852976 0.147740i
\(941\) 3426.69i 0.118711i 0.998237 + 0.0593554i \(0.0189045\pi\)
−0.998237 + 0.0593554i \(0.981095\pi\)
\(942\) 4217.40 + 2434.92i 0.145871 + 0.0842185i
\(943\) 10583.2 + 6110.20i 0.365467 + 0.211003i
\(944\) 34847.2i 1.20146i
\(945\) −21414.6 + 37091.2i −0.737160 + 1.27680i
\(946\) −311.100 538.841i −0.0106921 0.0185193i
\(947\) −23636.7 + 13646.6i −0.811075 + 0.468275i −0.847329 0.531068i \(-0.821791\pi\)
0.0362538 + 0.999343i \(0.488458\pi\)
\(948\) −9916.67 −0.339745
\(949\) −16197.1 32994.1i −0.554035 1.12859i
\(950\) 669.845 0.0228765
\(951\) −25775.9 + 14881.7i −0.878907 + 0.507437i
\(952\) 5705.03 + 9881.39i 0.194224 + 0.336405i
\(953\) −16703.7 + 28931.6i −0.567770 + 0.983406i 0.429016 + 0.903297i \(0.358860\pi\)
−0.996786 + 0.0801094i \(0.974473\pi\)
\(954\) 2396.40i 0.0813273i
\(955\) −41161.2 23764.4i −1.39471 0.805235i
\(956\) 13932.2 + 8043.77i 0.471339 + 0.272128i
\(957\) 6053.57i 0.204477i
\(958\) 3222.94 5582.29i 0.108693 0.188263i
\(959\) 10148.5 + 17577.7i 0.341723 + 0.591881i
\(960\) −10250.8 + 5918.31i −0.344629 + 0.198971i
\(961\) 1418.61 0.0476189
\(962\) −515.200 + 7649.30i −0.0172669 + 0.256365i
\(963\) 21632.9 0.723895
\(964\) −33289.1 + 19219.5i −1.11221 + 0.642134i
\(965\) 6337.72 + 10977.2i 0.211418 + 0.366187i
\(966\) 5968.91 10338.5i 0.198806 0.344342i
\(967\) 17254.6i 0.573807i −0.957959 0.286904i \(-0.907374\pi\)
0.957959 0.286904i \(-0.0926259\pi\)
\(968\) −1084.22 625.974i −0.0360001 0.0207847i
\(969\) 7475.00 + 4315.70i 0.247814 + 0.143075i
\(970\) 12289.2i 0.406785i
\(971\) −5488.49 + 9506.34i −0.181394 + 0.314184i −0.942356 0.334613i \(-0.891394\pi\)
0.760961 + 0.648797i \(0.224728\pi\)
\(972\) 14306.3 + 24779.3i 0.472094 + 0.817691i
\(973\) 55314.0 31935.6i 1.82249 1.05222i
\(974\) −2711.70 −0.0892080
\(975\) −1785.44 1197.65i −0.0586459 0.0393389i
\(976\) −20363.7 −0.667853
\(977\) −21386.1 + 12347.3i −0.700310 + 0.404324i −0.807463 0.589918i \(-0.799160\pi\)
0.107153 + 0.994243i \(0.465827\pi\)
\(978\) 730.193 + 1264.73i 0.0238742 + 0.0413514i
\(979\) −3643.61 + 6310.91i −0.118948 + 0.206024i
\(980\) 39580.6i 1.29016i
\(981\) −16074.8 9280.79i −0.523169 0.302052i
\(982\) 11793.8 + 6809.14i 0.383253 + 0.221271i
\(983\) 4763.40i 0.154556i −0.997010 0.0772782i \(-0.975377\pi\)
0.997010 0.0772782i \(-0.0246230\pi\)
\(984\) 1055.37 1827.95i 0.0341909 0.0592204i
\(985\) −1706.09 2955.03i −0.0551882 0.0955888i
\(986\) −3749.94 + 2165.03i −0.121118 + 0.0699276i
\(987\) −5762.34 −0.185833
\(988\) −13930.7 + 20767.7i −0.448579 + 0.668735i
\(989\) 16378.9 0.526611
\(990\) 1111.04 641.456i 0.0356677 0.0205928i
\(991\) 13846.1 + 23982.1i 0.443830 + 0.768736i 0.997970 0.0636877i \(-0.0202862\pi\)
−0.554140 + 0.832423i \(0.686953\pi\)
\(992\) 9972.32 17272.6i 0.319175 0.552827i
\(993\) 17808.3i 0.569112i
\(994\) −5758.12 3324.45i −0.183739 0.106082i
\(995\) 39647.1 + 22890.3i 1.26321 + 0.729317i
\(996\) 26509.4i 0.843355i
\(997\) 1668.22 2889.44i 0.0529920 0.0917848i −0.838313 0.545190i \(-0.816458\pi\)
0.891305 + 0.453405i \(0.149791\pi\)
\(998\) 3911.79 + 6775.43i 0.124074 + 0.214902i
\(999\) −29898.6 + 17262.0i −0.946896 + 0.546691i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 143.4.j.a.23.18 72
13.2 odd 12 1859.4.a.m.1.18 36
13.4 even 6 inner 143.4.j.a.56.18 yes 72
13.11 odd 12 1859.4.a.l.1.19 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.4.j.a.23.18 72 1.1 even 1 trivial
143.4.j.a.56.18 yes 72 13.4 even 6 inner
1859.4.a.l.1.19 36 13.11 odd 12
1859.4.a.m.1.18 36 13.2 odd 12