Properties

Label 105.4.s.a.101.15
Level $105$
Weight $4$
Character 105.101
Analytic conductor $6.195$
Analytic rank $0$
Dimension $32$
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] = [105,4,Mod(26,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 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("105.26");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.s (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: \(6.19520055060\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 101.15
Character \(\chi\) \(=\) 105.101
Dual form 105.4.s.a.26.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.95258 - 2.28202i) q^{2} +(3.88244 - 3.45350i) q^{3} +(6.41528 - 11.1116i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(7.46472 - 22.5101i) q^{6} +(-15.3726 + 10.3287i) q^{7} -22.0469i q^{8} +(3.14674 - 26.8160i) q^{9} +O(q^{10})\) \(q+(3.95258 - 2.28202i) q^{2} +(3.88244 - 3.45350i) q^{3} +(6.41528 - 11.1116i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(7.46472 - 22.5101i) q^{6} +(-15.3726 + 10.3287i) q^{7} -22.0469i q^{8} +(3.14674 - 26.8160i) q^{9} +(-19.7629 - 11.4101i) q^{10} +(38.8392 + 22.4238i) q^{11} +(-13.4669 - 65.2952i) q^{12} +21.9561i q^{13} +(-37.1911 + 75.9059i) q^{14} +(-24.6602 - 8.17773i) q^{15} +(1.01069 + 1.75057i) q^{16} +(-18.3222 + 31.7351i) q^{17} +(-48.7571 - 113.173i) q^{18} +(91.7755 - 52.9866i) q^{19} -64.1528 q^{20} +(-24.0130 + 93.1900i) q^{21} +204.687 q^{22} +(-21.5307 + 12.4308i) q^{23} +(-76.1388 - 85.5957i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(50.1044 + 86.7834i) q^{26} +(-80.3919 - 114.979i) q^{27} +(16.1491 + 237.076i) q^{28} -31.6068i q^{29} +(-116.133 + 23.9520i) q^{30} +(-262.288 - 151.432i) q^{31} +(160.735 + 92.8003i) q^{32} +(228.232 - 47.0718i) q^{33} +167.247i q^{34} +(83.1563 + 40.7435i) q^{35} +(-277.781 - 206.997i) q^{36} +(130.913 + 226.748i) q^{37} +(241.834 - 418.868i) q^{38} +(75.8254 + 85.2434i) q^{39} +(-95.4658 + 55.1172i) q^{40} -294.707 q^{41} +(117.748 + 423.140i) q^{42} -302.029 q^{43} +(498.329 - 287.710i) q^{44} +(-123.984 + 53.4142i) q^{45} +(-56.7346 + 98.2673i) q^{46} +(59.6172 + 103.260i) q^{47} +(9.96952 + 3.30606i) q^{48} +(129.634 - 317.559i) q^{49} +114.101i q^{50} +(38.4618 + 186.485i) q^{51} +(243.967 + 140.855i) q^{52} +(560.586 + 323.654i) q^{53} +(-580.140 - 271.007i) q^{54} -224.238i q^{55} +(227.716 + 338.918i) q^{56} +(173.324 - 522.664i) q^{57} +(-72.1275 - 124.928i) q^{58} +(3.12046 - 5.40479i) q^{59} +(-249.069 + 221.551i) q^{60} +(-702.683 + 405.694i) q^{61} -1382.29 q^{62} +(228.602 + 444.734i) q^{63} +830.920 q^{64} +(95.0728 - 54.8903i) q^{65} +(794.686 - 706.886i) q^{66} +(13.4336 - 23.2677i) q^{67} +(235.085 + 407.178i) q^{68} +(-40.6622 + 122.618i) q^{69} +(421.660 - 28.7226i) q^{70} +639.735i q^{71} +(-591.209 - 69.3757i) q^{72} +(-619.765 - 357.821i) q^{73} +(1034.89 + 597.493i) q^{74} +(26.2398 + 127.226i) q^{75} -1359.69i q^{76} +(-828.671 + 56.4473i) q^{77} +(494.234 + 163.896i) q^{78} +(-312.723 - 541.652i) q^{79} +(5.05345 - 8.75283i) q^{80} +(-709.196 - 168.766i) q^{81} +(-1164.85 + 672.529i) q^{82} +630.475 q^{83} +(881.438 + 864.662i) q^{84} +183.222 q^{85} +(-1193.80 + 689.239i) q^{86} +(-109.154 - 122.712i) q^{87} +(494.376 - 856.284i) q^{88} +(-350.854 - 607.698i) q^{89} +(-368.163 + 494.058i) q^{90} +(-226.779 - 337.523i) q^{91} +318.987i q^{92} +(-1541.29 + 317.884i) q^{93} +(471.284 + 272.096i) q^{94} +(-458.878 - 264.933i) q^{95} +(944.530 - 194.805i) q^{96} -528.346i q^{97} +(-212.288 - 1551.01i) q^{98} +(723.535 - 970.951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9} + 36 q^{11} + 246 q^{12} + 18 q^{14} + 20 q^{15} - 376 q^{16} - 72 q^{17} - 442 q^{18} - 198 q^{19} - 640 q^{20} - 218 q^{21} + 204 q^{22} + 72 q^{23} - 50 q^{24} - 400 q^{25} - 312 q^{26} + 508 q^{27} + 350 q^{28} + 40 q^{30} + 510 q^{31} + 810 q^{32} + 290 q^{33} - 70 q^{35} - 612 q^{36} - 658 q^{37} - 192 q^{38} - 648 q^{39} - 1404 q^{41} + 1892 q^{42} + 332 q^{43} + 2034 q^{44} - 490 q^{45} - 468 q^{46} + 408 q^{47} + 2810 q^{48} + 980 q^{49} - 888 q^{51} + 3378 q^{52} + 1152 q^{53} + 2714 q^{54} - 3354 q^{56} - 816 q^{57} - 1080 q^{58} - 48 q^{59} - 420 q^{60} - 1662 q^{61} - 2076 q^{62} + 874 q^{63} - 1952 q^{64} + 870 q^{65} - 1892 q^{66} - 1298 q^{67} + 1182 q^{68} + 2450 q^{69} - 450 q^{70} - 2708 q^{72} + 378 q^{73} + 2898 q^{74} - 50 q^{75} - 3528 q^{77} - 1896 q^{78} - 326 q^{79} - 1880 q^{80} - 3308 q^{81} - 2916 q^{82} - 1536 q^{83} + 1380 q^{84} + 720 q^{85} + 5202 q^{86} - 1090 q^{87} + 1668 q^{88} - 1590 q^{89} + 910 q^{90} + 2082 q^{91} - 4950 q^{93} - 1152 q^{94} + 990 q^{95} + 7416 q^{96} - 7830 q^{98} + 3128 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.95258 2.28202i 1.39745 0.806818i 0.403324 0.915057i \(-0.367855\pi\)
0.994125 + 0.108239i \(0.0345213\pi\)
\(3\) 3.88244 3.45350i 0.747177 0.664626i
\(4\) 6.41528 11.1116i 0.801909 1.38895i
\(5\) −2.50000 4.33013i −0.223607 0.387298i
\(6\) 7.46472 22.5101i 0.507910 1.53162i
\(7\) −15.3726 + 10.3287i −0.830043 + 0.557699i
\(8\) 22.0469i 0.974343i
\(9\) 3.14674 26.8160i 0.116546 0.993185i
\(10\) −19.7629 11.4101i −0.624958 0.360820i
\(11\) 38.8392 + 22.4238i 1.06459 + 0.614640i 0.926698 0.375807i \(-0.122634\pi\)
0.137890 + 0.990447i \(0.455968\pi\)
\(12\) −13.4669 65.2952i −0.323962 1.57076i
\(13\) 21.9561i 0.468426i 0.972185 + 0.234213i \(0.0752513\pi\)
−0.972185 + 0.234213i \(0.924749\pi\)
\(14\) −37.1911 + 75.9059i −0.709981 + 1.44905i
\(15\) −24.6602 8.17773i −0.424482 0.140765i
\(16\) 1.01069 + 1.75057i 0.0157920 + 0.0273526i
\(17\) −18.3222 + 31.7351i −0.261400 + 0.452758i −0.966614 0.256236i \(-0.917517\pi\)
0.705214 + 0.708994i \(0.250851\pi\)
\(18\) −48.7571 113.173i −0.638453 1.48196i
\(19\) 91.7755 52.9866i 1.10814 0.639788i 0.169796 0.985479i \(-0.445689\pi\)
0.938348 + 0.345692i \(0.112356\pi\)
\(20\) −64.1528 −0.717250
\(21\) −24.0130 + 93.1900i −0.249527 + 0.968368i
\(22\) 204.687 1.98361
\(23\) −21.5307 + 12.4308i −0.195194 + 0.112695i −0.594412 0.804161i \(-0.702615\pi\)
0.399218 + 0.916856i \(0.369282\pi\)
\(24\) −76.1388 85.5957i −0.647573 0.728007i
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) 50.1044 + 86.7834i 0.377934 + 0.654601i
\(27\) −80.3919 114.979i −0.573016 0.819544i
\(28\) 16.1491 + 237.076i 0.108996 + 1.60011i
\(29\) 31.6068i 0.202387i −0.994867 0.101194i \(-0.967734\pi\)
0.994867 0.101194i \(-0.0322662\pi\)
\(30\) −116.133 + 23.9520i −0.706764 + 0.145767i
\(31\) −262.288 151.432i −1.51962 0.877356i −0.999733 0.0231240i \(-0.992639\pi\)
−0.519892 0.854232i \(-0.674028\pi\)
\(32\) 160.735 + 92.8003i 0.887943 + 0.512654i
\(33\) 228.232 47.0718i 1.20394 0.248308i
\(34\) 167.247i 0.843608i
\(35\) 83.1563 + 40.7435i 0.401599 + 0.196769i
\(36\) −277.781 206.997i −1.28602 0.958321i
\(37\) 130.913 + 226.748i 0.581674 + 1.00749i 0.995281 + 0.0970336i \(0.0309354\pi\)
−0.413607 + 0.910456i \(0.635731\pi\)
\(38\) 241.834 418.868i 1.03238 1.78814i
\(39\) 75.8254 + 85.2434i 0.311328 + 0.349997i
\(40\) −95.4658 + 55.1172i −0.377362 + 0.217870i
\(41\) −294.707 −1.12257 −0.561287 0.827621i \(-0.689693\pi\)
−0.561287 + 0.827621i \(0.689693\pi\)
\(42\) 117.748 + 423.140i 0.432594 + 1.55457i
\(43\) −302.029 −1.07114 −0.535570 0.844491i \(-0.679903\pi\)
−0.535570 + 0.844491i \(0.679903\pi\)
\(44\) 498.329 287.710i 1.70741 0.985772i
\(45\) −123.984 + 53.4142i −0.410719 + 0.176945i
\(46\) −56.7346 + 98.2673i −0.181849 + 0.314972i
\(47\) 59.6172 + 103.260i 0.185023 + 0.320468i 0.943584 0.331133i \(-0.107431\pi\)
−0.758562 + 0.651601i \(0.774098\pi\)
\(48\) 9.96952 + 3.30606i 0.0299787 + 0.00994143i
\(49\) 129.634 317.559i 0.377943 0.925829i
\(50\) 114.101i 0.322727i
\(51\) 38.4618 + 186.485i 0.105603 + 0.512023i
\(52\) 243.967 + 140.855i 0.650619 + 0.375635i
\(53\) 560.586 + 323.654i 1.45287 + 0.838818i 0.998644 0.0520662i \(-0.0165807\pi\)
0.454231 + 0.890884i \(0.349914\pi\)
\(54\) −580.140 271.007i −1.46198 0.682952i
\(55\) 224.238i 0.549751i
\(56\) 227.716 + 338.918i 0.543391 + 0.808747i
\(57\) 173.324 522.664i 0.402761 1.21454i
\(58\) −72.1275 124.928i −0.163290 0.282826i
\(59\) 3.12046 5.40479i 0.00688557 0.0119262i −0.862562 0.505951i \(-0.831142\pi\)
0.869448 + 0.494025i \(0.164475\pi\)
\(60\) −249.069 + 221.551i −0.535912 + 0.476702i
\(61\) −702.683 + 405.694i −1.47491 + 0.851538i −0.999600 0.0282811i \(-0.990997\pi\)
−0.475308 + 0.879820i \(0.657663\pi\)
\(62\) −1382.29 −2.83146
\(63\) 228.602 + 444.734i 0.457161 + 0.889384i
\(64\) 830.920 1.62289
\(65\) 95.0728 54.8903i 0.181420 0.104743i
\(66\) 794.686 706.886i 1.48211 1.31836i
\(67\) 13.4336 23.2677i 0.0244952 0.0424269i −0.853518 0.521063i \(-0.825536\pi\)
0.878013 + 0.478637i \(0.158869\pi\)
\(68\) 235.085 + 407.178i 0.419238 + 0.726142i
\(69\) −40.6622 + 122.618i −0.0709443 + 0.213934i
\(70\) 421.660 28.7226i 0.719971 0.0490430i
\(71\) 639.735i 1.06933i 0.845064 + 0.534666i \(0.179563\pi\)
−0.845064 + 0.534666i \(0.820437\pi\)
\(72\) −591.209 69.3757i −0.967703 0.113556i
\(73\) −619.765 357.821i −0.993671 0.573696i −0.0873014 0.996182i \(-0.527824\pi\)
−0.906370 + 0.422486i \(0.861158\pi\)
\(74\) 1034.89 + 597.493i 1.62572 + 0.938610i
\(75\) 26.2398 + 127.226i 0.0403989 + 0.195877i
\(76\) 1359.69i 2.05221i
\(77\) −828.671 + 56.4473i −1.22644 + 0.0835425i
\(78\) 494.234 + 163.896i 0.717448 + 0.237918i
\(79\) −312.723 541.652i −0.445368 0.771401i 0.552709 0.833374i \(-0.313594\pi\)
−0.998078 + 0.0619733i \(0.980261\pi\)
\(80\) 5.05345 8.75283i 0.00706241 0.0122324i
\(81\) −709.196 168.766i −0.972834 0.231503i
\(82\) −1164.85 + 672.529i −1.56874 + 0.905712i
\(83\) 630.475 0.833778 0.416889 0.908957i \(-0.363120\pi\)
0.416889 + 0.908957i \(0.363120\pi\)
\(84\) 881.438 + 864.662i 1.14491 + 1.12312i
\(85\) 183.222 0.233803
\(86\) −1193.80 + 689.239i −1.49686 + 0.864215i
\(87\) −109.154 122.712i −0.134512 0.151219i
\(88\) 494.376 856.284i 0.598871 1.03727i
\(89\) −350.854 607.698i −0.417871 0.723773i 0.577854 0.816140i \(-0.303890\pi\)
−0.995725 + 0.0923667i \(0.970557\pi\)
\(90\) −368.163 + 494.058i −0.431197 + 0.578647i
\(91\) −226.779 337.523i −0.261241 0.388813i
\(92\) 318.987i 0.361486i
\(93\) −1541.29 + 317.884i −1.71854 + 0.354442i
\(94\) 471.284 + 272.096i 0.517119 + 0.298559i
\(95\) −458.878 264.933i −0.495577 0.286122i
\(96\) 944.530 194.805i 1.00417 0.207106i
\(97\) 528.346i 0.553046i −0.961007 0.276523i \(-0.910818\pi\)
0.961007 0.276523i \(-0.0891822\pi\)
\(98\) −212.288 1551.01i −0.218820 1.59873i
\(99\) 723.535 970.951i 0.734525 0.985700i
\(100\) 160.382 + 277.790i 0.160382 + 0.277790i
\(101\) 862.493 1493.88i 0.849716 1.47175i −0.0317464 0.999496i \(-0.510107\pi\)
0.881462 0.472255i \(-0.156560\pi\)
\(102\) 577.588 + 649.328i 0.560684 + 0.630324i
\(103\) −337.686 + 194.963i −0.323041 + 0.186508i −0.652747 0.757576i \(-0.726384\pi\)
0.329706 + 0.944083i \(0.393050\pi\)
\(104\) 484.064 0.456407
\(105\) 463.557 128.995i 0.430843 0.119892i
\(106\) 2954.35 2.70709
\(107\) 271.579 156.796i 0.245369 0.141664i −0.372273 0.928123i \(-0.621421\pi\)
0.617642 + 0.786459i \(0.288088\pi\)
\(108\) −1793.33 + 155.661i −1.59781 + 0.138689i
\(109\) 395.429 684.903i 0.347479 0.601852i −0.638322 0.769770i \(-0.720371\pi\)
0.985801 + 0.167918i \(0.0537044\pi\)
\(110\) −511.718 886.321i −0.443549 0.768249i
\(111\) 1291.33 + 428.228i 1.10422 + 0.366177i
\(112\) −33.6181 16.4716i −0.0283626 0.0138966i
\(113\) 2390.56i 1.99014i −0.0991983 0.995068i \(-0.531628\pi\)
0.0991983 0.995068i \(-0.468372\pi\)
\(114\) −507.654 2461.40i −0.417071 2.02221i
\(115\) 107.654 + 62.1538i 0.0872935 + 0.0503989i
\(116\) −351.201 202.766i −0.281105 0.162296i
\(117\) 588.776 + 69.0901i 0.465234 + 0.0545930i
\(118\) 28.4838i 0.0222216i
\(119\) −46.1224 677.097i −0.0355297 0.521591i
\(120\) −180.293 + 543.680i −0.137154 + 0.413591i
\(121\) 340.158 + 589.170i 0.255566 + 0.442652i
\(122\) −1851.61 + 3207.08i −1.37407 + 2.37996i
\(123\) −1144.18 + 1017.77i −0.838760 + 0.746091i
\(124\) −3365.30 + 1942.96i −2.43720 + 1.40712i
\(125\) 125.000 0.0894427
\(126\) 1918.46 + 1236.17i 1.35643 + 0.874023i
\(127\) −2416.95 −1.68874 −0.844369 0.535762i \(-0.820024\pi\)
−0.844369 + 0.535762i \(0.820024\pi\)
\(128\) 1998.40 1153.78i 1.37996 0.796722i
\(129\) −1172.61 + 1043.06i −0.800331 + 0.711907i
\(130\) 250.522 433.917i 0.169017 0.292747i
\(131\) 718.896 + 1245.16i 0.479467 + 0.830462i 0.999723 0.0235490i \(-0.00749658\pi\)
−0.520255 + 0.854011i \(0.674163\pi\)
\(132\) 941.127 2838.00i 0.620565 1.87133i
\(133\) −863.544 + 1762.47i −0.562998 + 1.14906i
\(134\) 122.623i 0.0790525i
\(135\) −296.893 + 635.554i −0.189278 + 0.405184i
\(136\) 699.659 + 403.948i 0.441142 + 0.254693i
\(137\) 1162.71 + 671.288i 0.725085 + 0.418628i 0.816621 0.577174i \(-0.195844\pi\)
−0.0915363 + 0.995802i \(0.529178\pi\)
\(138\) 119.097 + 577.450i 0.0734650 + 0.356201i
\(139\) 644.525i 0.393294i −0.980474 0.196647i \(-0.936995\pi\)
0.980474 0.196647i \(-0.0630053\pi\)
\(140\) 986.195 662.617i 0.595348 0.400010i
\(141\) 588.068 + 195.013i 0.351236 + 0.116476i
\(142\) 1459.89 + 2528.61i 0.862756 + 1.49434i
\(143\) −492.341 + 852.759i −0.287913 + 0.498681i
\(144\) 50.1235 21.5941i 0.0290067 0.0124966i
\(145\) −136.861 + 79.0170i −0.0783843 + 0.0452552i
\(146\) −3266.23 −1.85147
\(147\) −593.392 1680.60i −0.332940 0.942948i
\(148\) 3359.37 1.86580
\(149\) −1048.47 + 605.332i −0.576467 + 0.332823i −0.759728 0.650241i \(-0.774668\pi\)
0.183261 + 0.983064i \(0.441335\pi\)
\(150\) 394.048 + 442.992i 0.214493 + 0.241134i
\(151\) −276.105 + 478.227i −0.148802 + 0.257732i −0.930785 0.365567i \(-0.880875\pi\)
0.781983 + 0.623300i \(0.214208\pi\)
\(152\) −1168.19 2023.36i −0.623373 1.07971i
\(153\) 793.352 + 591.191i 0.419207 + 0.312386i
\(154\) −3146.57 + 2114.16i −1.64648 + 1.10626i
\(155\) 1514.32i 0.784731i
\(156\) 1433.63 295.680i 0.735784 0.151752i
\(157\) 1891.12 + 1091.84i 0.961326 + 0.555022i 0.896581 0.442880i \(-0.146043\pi\)
0.0647452 + 0.997902i \(0.479377\pi\)
\(158\) −2472.13 1427.28i −1.24476 0.718662i
\(159\) 3294.18 679.411i 1.64305 0.338873i
\(160\) 928.003i 0.458532i
\(161\) 202.589 413.479i 0.0991694 0.202402i
\(162\) −3188.28 + 951.343i −1.54627 + 0.461386i
\(163\) 1805.11 + 3126.55i 0.867407 + 1.50239i 0.864637 + 0.502397i \(0.167548\pi\)
0.00277017 + 0.999996i \(0.499118\pi\)
\(164\) −1890.63 + 3274.66i −0.900202 + 1.55920i
\(165\) −774.407 870.593i −0.365379 0.410761i
\(166\) 2492.00 1438.76i 1.16516 0.672707i
\(167\) 1747.33 0.809657 0.404829 0.914393i \(-0.367331\pi\)
0.404829 + 0.914393i \(0.367331\pi\)
\(168\) 2054.55 + 529.412i 0.943523 + 0.243125i
\(169\) 1714.93 0.780577
\(170\) 724.202 418.118i 0.326728 0.188637i
\(171\) −1132.10 2627.79i −0.506278 1.17516i
\(172\) −1937.60 + 3356.02i −0.858958 + 1.48776i
\(173\) 1752.80 + 3035.94i 0.770306 + 1.33421i 0.937395 + 0.348268i \(0.113230\pi\)
−0.167089 + 0.985942i \(0.553437\pi\)
\(174\) −711.471 235.936i −0.309980 0.102794i
\(175\) −31.4661 461.936i −0.0135921 0.199538i
\(176\) 90.6542i 0.0388257i
\(177\) −6.55042 31.7603i −0.00278169 0.0134873i
\(178\) −2773.56 1601.32i −1.16791 0.674291i
\(179\) −1735.08 1001.75i −0.724502 0.418291i 0.0919057 0.995768i \(-0.470704\pi\)
−0.816407 + 0.577477i \(0.804037\pi\)
\(180\) −201.872 + 1720.32i −0.0835924 + 0.712362i
\(181\) 1090.28i 0.447734i −0.974620 0.223867i \(-0.928132\pi\)
0.974620 0.223867i \(-0.0718682\pi\)
\(182\) −1666.60 816.572i −0.678772 0.332573i
\(183\) −1327.06 + 4001.80i −0.536062 + 1.61651i
\(184\) 274.060 + 474.685i 0.109804 + 0.190186i
\(185\) 654.564 1133.74i 0.260133 0.450563i
\(186\) −5366.66 + 4773.73i −2.11560 + 1.88186i
\(187\) −1423.24 + 821.711i −0.556567 + 0.321334i
\(188\) 1529.84 0.593485
\(189\) 2423.42 + 937.178i 0.932687 + 0.360686i
\(190\) −2418.34 −0.923392
\(191\) −943.845 + 544.929i −0.357561 + 0.206438i −0.668011 0.744152i \(-0.732854\pi\)
0.310449 + 0.950590i \(0.399521\pi\)
\(192\) 3226.00 2869.58i 1.21259 1.07861i
\(193\) 2473.45 4284.14i 0.922502 1.59782i 0.126973 0.991906i \(-0.459474\pi\)
0.795530 0.605915i \(-0.207193\pi\)
\(194\) −1205.70 2088.33i −0.446207 0.772854i
\(195\) 179.551 541.442i 0.0659382 0.198838i
\(196\) −2696.95 3477.67i −0.982853 1.26737i
\(197\) 3296.31i 1.19215i −0.802930 0.596073i \(-0.796727\pi\)
0.802930 0.596073i \(-0.203273\pi\)
\(198\) 644.096 5488.89i 0.231181 1.97009i
\(199\) −680.689 392.996i −0.242476 0.139994i 0.373838 0.927494i \(-0.378042\pi\)
−0.616314 + 0.787500i \(0.711375\pi\)
\(200\) 477.329 + 275.586i 0.168761 + 0.0974343i
\(201\) −28.1996 136.728i −0.00989577 0.0479805i
\(202\) 7872.92i 2.74226i
\(203\) 326.458 + 485.879i 0.112871 + 0.167990i
\(204\) 2318.89 + 768.984i 0.795857 + 0.263920i
\(205\) 736.768 + 1276.12i 0.251015 + 0.434771i
\(206\) −889.821 + 1541.22i −0.300955 + 0.521270i
\(207\) 265.592 + 616.484i 0.0891784 + 0.206998i
\(208\) −38.4356 + 22.1908i −0.0128127 + 0.00739739i
\(209\) 4752.65 1.57296
\(210\) 1537.88 1567.71i 0.505350 0.515155i
\(211\) −117.042 −0.0381872 −0.0190936 0.999818i \(-0.506078\pi\)
−0.0190936 + 0.999818i \(0.506078\pi\)
\(212\) 7192.62 4152.66i 2.33015 1.34531i
\(213\) 2209.32 + 2483.73i 0.710705 + 0.798980i
\(214\) 715.625 1239.50i 0.228594 0.395936i
\(215\) 755.073 + 1307.83i 0.239514 + 0.414851i
\(216\) −2534.92 + 1772.39i −0.798517 + 0.558314i
\(217\) 5596.16 381.199i 1.75065 0.119251i
\(218\) 3609.52i 1.12141i
\(219\) −3641.94 + 751.134i −1.12374 + 0.231767i
\(220\) −2491.64 1438.55i −0.763576 0.440851i
\(221\) −696.779 402.286i −0.212083 0.122446i
\(222\) 6081.33 1254.25i 1.83852 0.379188i
\(223\) 3582.58i 1.07582i 0.843003 + 0.537908i \(0.180785\pi\)
−0.843003 + 0.537908i \(0.819215\pi\)
\(224\) −3429.43 + 233.605i −1.02294 + 0.0696804i
\(225\) 541.249 + 403.329i 0.160370 + 0.119505i
\(226\) −5455.33 9448.90i −1.60568 2.78111i
\(227\) −635.352 + 1100.46i −0.185770 + 0.321763i −0.943836 0.330415i \(-0.892811\pi\)
0.758066 + 0.652178i \(0.226145\pi\)
\(228\) −4695.70 5278.94i −1.36395 1.53336i
\(229\) 2500.75 1443.81i 0.721633 0.416635i −0.0937206 0.995599i \(-0.529876\pi\)
0.815353 + 0.578964i \(0.196543\pi\)
\(230\) 567.346 0.162651
\(231\) −3022.33 + 3080.96i −0.860842 + 0.877543i
\(232\) −696.831 −0.197195
\(233\) −1421.01 + 820.421i −0.399543 + 0.230676i −0.686287 0.727331i \(-0.740760\pi\)
0.286744 + 0.958007i \(0.407427\pi\)
\(234\) 2484.85 1070.52i 0.694187 0.299068i
\(235\) 298.086 516.300i 0.0827446 0.143318i
\(236\) −40.0372 69.3464i −0.0110432 0.0191274i
\(237\) −3084.72 1022.95i −0.845462 0.280369i
\(238\) −1727.45 2571.03i −0.470480 0.700231i
\(239\) 3084.64i 0.834849i −0.908712 0.417424i \(-0.862933\pi\)
0.908712 0.417424i \(-0.137067\pi\)
\(240\) −10.6081 51.4344i −0.00285313 0.0138337i
\(241\) 493.799 + 285.095i 0.131985 + 0.0762015i 0.564539 0.825407i \(-0.309054\pi\)
−0.432554 + 0.901608i \(0.642387\pi\)
\(242\) 2689.00 + 1552.50i 0.714280 + 0.412390i
\(243\) −3336.25 + 1793.98i −0.880742 + 0.473597i
\(244\) 10410.6i 2.73143i
\(245\) −1699.16 + 232.565i −0.443083 + 0.0606452i
\(246\) −2199.90 + 6633.87i −0.570166 + 1.71935i
\(247\) 1163.38 + 2015.03i 0.299693 + 0.519083i
\(248\) −3338.61 + 5782.64i −0.854846 + 1.48064i
\(249\) 2447.78 2177.34i 0.622980 0.554150i
\(250\) 494.073 285.253i 0.124992 0.0721640i
\(251\) 3678.99 0.925162 0.462581 0.886577i \(-0.346923\pi\)
0.462581 + 0.886577i \(0.346923\pi\)
\(252\) 6408.24 + 312.960i 1.60191 + 0.0782326i
\(253\) −1114.98 −0.277069
\(254\) −9553.20 + 5515.54i −2.35993 + 1.36250i
\(255\) 711.351 632.758i 0.174692 0.155392i
\(256\) 1942.22 3364.02i 0.474174 0.821293i
\(257\) 2372.26 + 4108.88i 0.575789 + 0.997295i 0.995955 + 0.0898484i \(0.0286382\pi\)
−0.420167 + 0.907447i \(0.638028\pi\)
\(258\) −2254.56 + 6798.70i −0.544043 + 1.64058i
\(259\) −4354.49 2133.54i −1.04469 0.511860i
\(260\) 1408.55i 0.335978i
\(261\) −847.568 99.4582i −0.201008 0.0235874i
\(262\) 5682.99 + 3281.08i 1.34006 + 0.773685i
\(263\) −714.976 412.792i −0.167632 0.0967826i 0.413837 0.910351i \(-0.364188\pi\)
−0.581469 + 0.813569i \(0.697522\pi\)
\(264\) −1037.79 5031.80i −0.241937 1.17305i
\(265\) 3236.54i 0.750261i
\(266\) 608.765 + 8936.93i 0.140323 + 2.05999i
\(267\) −3460.85 1147.68i −0.793261 0.263059i
\(268\) −172.361 298.537i −0.0392858 0.0680450i
\(269\) 2053.16 3556.17i 0.465365 0.806036i −0.533853 0.845577i \(-0.679256\pi\)
0.999218 + 0.0395417i \(0.0125898\pi\)
\(270\) 276.856 + 3189.60i 0.0624034 + 0.718936i
\(271\) −4293.33 + 2478.76i −0.962367 + 0.555623i −0.896901 0.442232i \(-0.854187\pi\)
−0.0654661 + 0.997855i \(0.520853\pi\)
\(272\) −74.0724 −0.0165121
\(273\) −2046.09 527.233i −0.453608 0.116885i
\(274\) 6127.59 1.35103
\(275\) −970.981 + 560.596i −0.212918 + 0.122928i
\(276\) 1101.62 + 1238.45i 0.240253 + 0.270094i
\(277\) −1146.40 + 1985.63i −0.248667 + 0.430704i −0.963156 0.268943i \(-0.913326\pi\)
0.714489 + 0.699646i \(0.246659\pi\)
\(278\) −1470.82 2547.54i −0.317316 0.549608i
\(279\) −4886.16 + 6557.01i −1.04848 + 1.40702i
\(280\) 898.267 1833.34i 0.191720 0.391296i
\(281\) 4298.26i 0.912501i −0.889851 0.456250i \(-0.849192\pi\)
0.889851 0.456250i \(-0.150808\pi\)
\(282\) 2769.41 571.180i 0.584809 0.120614i
\(283\) −1454.18 839.571i −0.305449 0.176351i 0.339439 0.940628i \(-0.389763\pi\)
−0.644888 + 0.764277i \(0.723096\pi\)
\(284\) 7108.47 + 4104.07i 1.48525 + 0.857507i
\(285\) −2696.51 + 556.144i −0.560448 + 0.115590i
\(286\) 4494.14i 0.929174i
\(287\) 4530.42 3043.95i 0.931784 0.626059i
\(288\) 2994.32 4018.25i 0.612647 0.822144i
\(289\) 1785.09 + 3091.87i 0.363340 + 0.629324i
\(290\) −360.637 + 624.642i −0.0730254 + 0.126484i
\(291\) −1824.64 2051.28i −0.367568 0.413223i
\(292\) −7951.92 + 4591.04i −1.59367 + 0.920105i
\(293\) −3429.39 −0.683779 −0.341889 0.939740i \(-0.611067\pi\)
−0.341889 + 0.939740i \(0.611067\pi\)
\(294\) −6180.60 5288.57i −1.22605 1.04910i
\(295\) −31.2046 −0.00615864
\(296\) 4999.08 2886.22i 0.981640 0.566750i
\(297\) −544.093 6268.39i −0.106301 1.22468i
\(298\) −2762.76 + 4785.25i −0.537056 + 0.930208i
\(299\) −272.932 472.731i −0.0527894 0.0914340i
\(300\) 1582.02 + 524.624i 0.304460 + 0.100964i
\(301\) 4642.98 3119.58i 0.889093 0.597375i
\(302\) 2520.31i 0.480224i
\(303\) −1810.53 8778.53i −0.343275 1.66440i
\(304\) 185.513 + 107.106i 0.0349997 + 0.0202071i
\(305\) 3513.42 + 2028.47i 0.659599 + 0.380820i
\(306\) 4484.90 + 526.283i 0.837859 + 0.0983189i
\(307\) 726.092i 0.134985i 0.997720 + 0.0674923i \(0.0214998\pi\)
−0.997720 + 0.0674923i \(0.978500\pi\)
\(308\) −4688.93 + 9569.97i −0.867456 + 1.77045i
\(309\) −637.742 + 1923.13i −0.117411 + 0.354055i
\(310\) 3455.72 + 5985.48i 0.633135 + 1.09662i
\(311\) 3360.18 5820.01i 0.612664 1.06116i −0.378126 0.925754i \(-0.623431\pi\)
0.990790 0.135411i \(-0.0432353\pi\)
\(312\) 1879.35 1671.71i 0.341017 0.303340i
\(313\) 5210.38 3008.21i 0.940920 0.543241i 0.0506716 0.998715i \(-0.483864\pi\)
0.890249 + 0.455475i \(0.150531\pi\)
\(314\) 9966.44 1.79121
\(315\) 1354.25 2101.71i 0.242233 0.375930i
\(316\) −8024.82 −1.42858
\(317\) −4471.73 + 2581.75i −0.792295 + 0.457431i −0.840770 0.541393i \(-0.817897\pi\)
0.0484752 + 0.998824i \(0.484564\pi\)
\(318\) 11470.1 10202.8i 2.02268 1.79920i
\(319\) 708.746 1227.58i 0.124395 0.215459i
\(320\) −2077.30 3597.99i −0.362889 0.628543i
\(321\) 512.894 1546.65i 0.0891806 0.268927i
\(322\) −142.818 2096.62i −0.0247171 0.362858i
\(323\) 3883.34i 0.668962i
\(324\) −6424.94 + 6797.61i −1.10167 + 1.16557i
\(325\) −475.364 274.452i −0.0811337 0.0468426i
\(326\) 14269.7 + 8238.63i 2.42431 + 1.39968i
\(327\) −830.079 4024.71i −0.140378 0.680633i
\(328\) 6497.37i 1.09377i
\(329\) −1983.02 971.605i −0.332302 0.162816i
\(330\) −5047.62 1673.88i −0.842007 0.279224i
\(331\) 1601.38 + 2773.68i 0.265921 + 0.460589i 0.967805 0.251703i \(-0.0809905\pi\)
−0.701883 + 0.712292i \(0.747657\pi\)
\(332\) 4044.67 7005.57i 0.668615 1.15807i
\(333\) 6492.42 2797.04i 1.06842 0.460292i
\(334\) 6906.48 3987.46i 1.13145 0.653246i
\(335\) −134.336 −0.0219091
\(336\) −187.405 + 52.1498i −0.0304279 + 0.00846727i
\(337\) −11770.7 −1.90264 −0.951320 0.308204i \(-0.900272\pi\)
−0.951320 + 0.308204i \(0.900272\pi\)
\(338\) 6778.40 3913.51i 1.09082 0.629784i
\(339\) −8255.80 9281.23i −1.32269 1.48698i
\(340\) 1175.42 2035.89i 0.187489 0.324740i
\(341\) −6791.39 11763.0i −1.07852 1.86805i
\(342\) −10471.4 7803.08i −1.65564 1.23375i
\(343\) 1287.17 + 6220.68i 0.202626 + 0.979256i
\(344\) 6658.80i 1.04366i
\(345\) 632.607 130.472i 0.0987200 0.0203606i
\(346\) 13856.2 + 7999.87i 2.15293 + 1.24299i
\(347\) 810.218 + 467.780i 0.125345 + 0.0723681i 0.561362 0.827571i \(-0.310278\pi\)
−0.436016 + 0.899939i \(0.643611\pi\)
\(348\) −2063.77 + 425.644i −0.317902 + 0.0655659i
\(349\) 6000.40i 0.920326i 0.887834 + 0.460163i \(0.152209\pi\)
−0.887834 + 0.460163i \(0.847791\pi\)
\(350\) −1178.52 1754.03i −0.179985 0.267877i
\(351\) 2524.49 1765.10i 0.383896 0.268415i
\(352\) 4161.88 + 7208.59i 0.630196 + 1.09153i
\(353\) −3391.26 + 5873.83i −0.511327 + 0.885644i 0.488587 + 0.872515i \(0.337513\pi\)
−0.999914 + 0.0131291i \(0.995821\pi\)
\(354\) −98.3688 110.587i −0.0147690 0.0166035i
\(355\) 2770.13 1599.34i 0.414150 0.239110i
\(356\) −9003.31 −1.34038
\(357\) −2517.42 2469.51i −0.373210 0.366107i
\(358\) −9144.05 −1.34994
\(359\) −394.879 + 227.984i −0.0580528 + 0.0335168i −0.528745 0.848780i \(-0.677337\pi\)
0.470693 + 0.882297i \(0.344004\pi\)
\(360\) 1177.62 + 2733.45i 0.172405 + 0.400182i
\(361\) 2185.66 3785.68i 0.318656 0.551929i
\(362\) −2488.05 4309.42i −0.361240 0.625686i
\(363\) 3355.34 + 1112.69i 0.485151 + 0.160884i
\(364\) −5205.27 + 354.572i −0.749533 + 0.0510567i
\(365\) 3578.21i 0.513129i
\(366\) 3886.87 + 18845.8i 0.555110 + 2.69150i
\(367\) −4548.06 2625.82i −0.646884 0.373479i 0.140377 0.990098i \(-0.455169\pi\)
−0.787262 + 0.616619i \(0.788502\pi\)
\(368\) −43.5217 25.1273i −0.00616502 0.00355938i
\(369\) −927.365 + 7902.86i −0.130831 + 1.11492i
\(370\) 5974.93i 0.839518i
\(371\) −11960.6 + 814.732i −1.67376 + 0.114013i
\(372\) −6355.60 + 19165.5i −0.885813 + 2.67119i
\(373\) 277.993 + 481.498i 0.0385896 + 0.0668391i 0.884675 0.466208i \(-0.154380\pi\)
−0.846086 + 0.533047i \(0.821047\pi\)
\(374\) −3750.33 + 6495.76i −0.518516 + 0.898095i
\(375\) 485.305 431.687i 0.0668295 0.0594459i
\(376\) 2276.56 1314.37i 0.312246 0.180276i
\(377\) 693.963 0.0948034
\(378\) 11717.4 1826.03i 1.59439 0.248468i
\(379\) −775.818 −0.105148 −0.0525740 0.998617i \(-0.516743\pi\)
−0.0525740 + 0.998617i \(0.516743\pi\)
\(380\) −5887.65 + 3399.24i −0.794816 + 0.458887i
\(381\) −9383.67 + 8346.93i −1.26179 + 1.12238i
\(382\) −2487.08 + 4307.76i −0.333116 + 0.576974i
\(383\) 2985.84 + 5171.63i 0.398354 + 0.689969i 0.993523 0.113631i \(-0.0362483\pi\)
−0.595169 + 0.803600i \(0.702915\pi\)
\(384\) 3774.11 11380.9i 0.501554 1.51245i
\(385\) 2316.10 + 3447.13i 0.306596 + 0.456317i
\(386\) 22577.9i 2.97716i
\(387\) −950.406 + 8099.22i −0.124837 + 1.06384i
\(388\) −5870.77 3389.49i −0.768152 0.443493i
\(389\) 677.294 + 391.036i 0.0882781 + 0.0509674i 0.543489 0.839416i \(-0.317103\pi\)
−0.455211 + 0.890384i \(0.650436\pi\)
\(390\) −525.893 2549.84i −0.0682811 0.331067i
\(391\) 911.038i 0.117834i
\(392\) −7001.19 2858.03i −0.902075 0.368246i
\(393\) 7091.24 + 2351.58i 0.910193 + 0.301835i
\(394\) −7522.27 13029.0i −0.961844 1.66596i
\(395\) −1563.62 + 2708.26i −0.199175 + 0.344981i
\(396\) −6147.13 14268.5i −0.780063 1.81066i
\(397\) 2311.52 1334.56i 0.292221 0.168714i −0.346722 0.937968i \(-0.612705\pi\)
0.638943 + 0.769254i \(0.279372\pi\)
\(398\) −3587.31 −0.451798
\(399\) 2734.01 + 9824.93i 0.343037 + 1.23274i
\(400\) −50.5345 −0.00631681
\(401\) 12909.6 7453.36i 1.60767 0.928187i 0.617777 0.786353i \(-0.288033\pi\)
0.989890 0.141834i \(-0.0452999\pi\)
\(402\) −423.479 476.078i −0.0525403 0.0590662i
\(403\) 3324.87 5758.84i 0.410976 0.711831i
\(404\) −11066.3 19167.3i −1.36279 2.36042i
\(405\) 1042.21 + 3492.82i 0.127872 + 0.428543i
\(406\) 2399.14 + 1175.49i 0.293269 + 0.143691i
\(407\) 11742.3i 1.43008i
\(408\) 4111.42 847.963i 0.498886 0.102893i
\(409\) −6740.03 3891.36i −0.814849 0.470453i 0.0337880 0.999429i \(-0.489243\pi\)
−0.848637 + 0.528976i \(0.822576\pi\)
\(410\) 5824.27 + 3362.64i 0.701561 + 0.405047i
\(411\) 6832.43 1409.16i 0.819998 0.169121i
\(412\) 5002.97i 0.598249i
\(413\) 7.85510 + 115.316i 0.000935894 + 0.0137393i
\(414\) 2456.61 + 1830.62i 0.291632 + 0.217319i
\(415\) −1576.19 2730.04i −0.186438 0.322921i
\(416\) −2037.54 + 3529.12i −0.240140 + 0.415935i
\(417\) −2225.86 2502.33i −0.261393 0.293860i
\(418\) 18785.3 10845.7i 2.19813 1.26909i
\(419\) −10191.7 −1.18830 −0.594149 0.804355i \(-0.702511\pi\)
−0.594149 + 0.804355i \(0.702511\pi\)
\(420\) 1540.50 5978.39i 0.178973 0.694561i
\(421\) 11747.0 1.35989 0.679946 0.733262i \(-0.262003\pi\)
0.679946 + 0.733262i \(0.262003\pi\)
\(422\) −462.618 + 267.093i −0.0533647 + 0.0308101i
\(423\) 2956.62 1273.76i 0.339848 0.146412i
\(424\) 7135.57 12359.2i 0.817296 1.41560i
\(425\) −458.056 793.377i −0.0522800 0.0905516i
\(426\) 14400.5 + 4775.44i 1.63781 + 0.543124i
\(427\) 6611.76 13494.4i 0.749334 1.52937i
\(428\) 4023.56i 0.454407i
\(429\) 1033.52 + 5011.09i 0.116314 + 0.563957i
\(430\) 5968.98 + 3446.19i 0.669418 + 0.386489i
\(431\) 4728.20 + 2729.83i 0.528421 + 0.305084i 0.740373 0.672196i \(-0.234649\pi\)
−0.211952 + 0.977280i \(0.567982\pi\)
\(432\) 120.027 256.939i 0.0133676 0.0286157i
\(433\) 1450.51i 0.160987i −0.996755 0.0804934i \(-0.974350\pi\)
0.996755 0.0804934i \(-0.0256496\pi\)
\(434\) 21249.4 14277.3i 2.35024 1.57911i
\(435\) −258.472 + 779.429i −0.0284891 + 0.0859098i
\(436\) −5073.57 8787.69i −0.557294 0.965261i
\(437\) −1317.33 + 2281.68i −0.144202 + 0.249766i
\(438\) −12680.9 + 11279.9i −1.38338 + 1.23054i
\(439\) −7329.40 + 4231.63i −0.796841 + 0.460056i −0.842365 0.538907i \(-0.818837\pi\)
0.0455245 + 0.998963i \(0.485504\pi\)
\(440\) −4943.76 −0.535646
\(441\) −8107.75 4475.55i −0.875472 0.483268i
\(442\) −3672.10 −0.395168
\(443\) −36.6425 + 21.1556i −0.00392988 + 0.00226892i −0.501964 0.864889i \(-0.667389\pi\)
0.498034 + 0.867158i \(0.334056\pi\)
\(444\) 13042.6 11601.6i 1.39408 1.24006i
\(445\) −1754.27 + 3038.49i −0.186877 + 0.323681i
\(446\) 8175.53 + 14160.4i 0.867987 + 1.50340i
\(447\) −1980.10 + 5971.04i −0.209520 + 0.631813i
\(448\) −12773.4 + 8582.35i −1.34707 + 0.905085i
\(449\) 944.250i 0.0992470i −0.998768 0.0496235i \(-0.984198\pi\)
0.998768 0.0496235i \(-0.0158021\pi\)
\(450\) 3059.74 + 359.046i 0.320528 + 0.0376125i
\(451\) −11446.2 6608.46i −1.19508 0.689979i
\(452\) −26562.9 15336.1i −2.76419 1.59591i
\(453\) 579.595 + 2810.22i 0.0601143 + 0.291469i
\(454\) 5799.55i 0.599530i
\(455\) −894.570 + 1825.79i −0.0921716 + 0.188119i
\(456\) −11523.1 3821.26i −1.18337 0.392427i
\(457\) −4436.67 7684.53i −0.454133 0.786581i 0.544505 0.838757i \(-0.316717\pi\)
−0.998638 + 0.0521768i \(0.983384\pi\)
\(458\) 6589.60 11413.5i 0.672297 1.16445i
\(459\) 5121.82 444.572i 0.520841 0.0452088i
\(460\) 1381.25 797.468i 0.140003 0.0808307i
\(461\) 8958.04 0.905027 0.452514 0.891757i \(-0.350527\pi\)
0.452514 + 0.891757i \(0.350527\pi\)
\(462\) −4915.16 + 19074.8i −0.494965 + 1.92086i
\(463\) −5709.17 −0.573062 −0.286531 0.958071i \(-0.592502\pi\)
−0.286531 + 0.958071i \(0.592502\pi\)
\(464\) 55.3297 31.9446i 0.00553582 0.00319611i
\(465\) 5229.71 + 5879.27i 0.521552 + 0.586333i
\(466\) −3744.44 + 6485.56i −0.372227 + 0.644716i
\(467\) 9120.65 + 15797.4i 0.903754 + 1.56535i 0.822581 + 0.568648i \(0.192533\pi\)
0.0811730 + 0.996700i \(0.474133\pi\)
\(468\) 4544.86 6099.00i 0.448902 0.602406i
\(469\) 33.8163 + 496.437i 0.00332940 + 0.0488771i
\(470\) 2720.96i 0.267039i
\(471\) 11112.9 2291.98i 1.08716 0.224223i
\(472\) −119.159 68.7963i −0.0116202 0.00670891i
\(473\) −11730.6 6772.66i −1.14032 0.658366i
\(474\) −14527.0 + 2996.14i −1.40770 + 0.290331i
\(475\) 2649.33i 0.255915i
\(476\) −7819.50 3831.27i −0.752954 0.368920i
\(477\) 10443.1 14014.2i 1.00243 1.34521i
\(478\) −7039.23 12192.3i −0.673571 1.16666i
\(479\) −4771.66 + 8264.76i −0.455162 + 0.788364i −0.998698 0.0510220i \(-0.983752\pi\)
0.543535 + 0.839386i \(0.317085\pi\)
\(480\) −3204.86 3602.92i −0.304752 0.342604i
\(481\) −4978.50 + 2874.34i −0.471934 + 0.272471i
\(482\) 2602.37 0.245923
\(483\) −641.405 2304.95i −0.0604243 0.217140i
\(484\) 8728.82 0.819762
\(485\) −2287.81 + 1320.87i −0.214194 + 0.123665i
\(486\) −9092.88 + 14704.3i −0.848686 + 1.37243i
\(487\) −3629.41 + 6286.32i −0.337709 + 0.584929i −0.984001 0.178161i \(-0.942985\pi\)
0.646293 + 0.763090i \(0.276319\pi\)
\(488\) 8944.29 + 15492.0i 0.829691 + 1.43707i
\(489\) 17805.8 + 5904.69i 1.64664 + 0.546052i
\(490\) −6185.34 + 4796.76i −0.570256 + 0.442235i
\(491\) 4273.37i 0.392779i 0.980526 + 0.196390i \(0.0629218\pi\)
−0.980526 + 0.196390i \(0.937078\pi\)
\(492\) 3968.78 + 19243.0i 0.363671 + 1.76329i
\(493\) 1003.04 + 579.107i 0.0916325 + 0.0529040i
\(494\) 9196.72 + 5309.73i 0.837611 + 0.483595i
\(495\) −6013.18 705.619i −0.546005 0.0640711i
\(496\) 612.204i 0.0554209i
\(497\) −6607.65 9834.39i −0.596366 0.887591i
\(498\) 4706.32 14192.0i 0.423484 1.27703i
\(499\) 570.563 + 988.245i 0.0511862 + 0.0886571i 0.890483 0.455016i \(-0.150366\pi\)
−0.839297 + 0.543673i \(0.817033\pi\)
\(500\) 801.909 1388.95i 0.0717250 0.124231i
\(501\) 6783.93 6034.41i 0.604957 0.538119i
\(502\) 14541.5 8395.54i 1.29287 0.746437i
\(503\) −8487.44 −0.752358 −0.376179 0.926547i \(-0.622762\pi\)
−0.376179 + 0.926547i \(0.622762\pi\)
\(504\) 9804.99 5039.96i 0.866565 0.445432i
\(505\) −8624.93 −0.760009
\(506\) −4407.06 + 2544.42i −0.387189 + 0.223544i
\(507\) 6658.11 5922.50i 0.583229 0.518792i
\(508\) −15505.4 + 26856.1i −1.35421 + 2.34557i
\(509\) −332.930 576.652i −0.0289919 0.0502154i 0.851165 0.524898i \(-0.175896\pi\)
−0.880157 + 0.474682i \(0.842563\pi\)
\(510\) 1367.70 4124.35i 0.118751 0.358097i
\(511\) 13223.2 900.740i 1.14474 0.0779773i
\(512\) 731.690i 0.0631571i
\(513\) −13470.4 6292.55i −1.15932 0.541565i
\(514\) 18753.1 + 10827.1i 1.60927 + 0.929113i
\(515\) 1688.43 + 974.815i 0.144468 + 0.0834087i
\(516\) 4067.39 + 19721.1i 0.347009 + 1.68250i
\(517\) 5347.39i 0.454889i
\(518\) −22080.3 + 1504.06i −1.87288 + 0.127577i
\(519\) 17289.8 + 5733.58i 1.46230 + 0.484925i
\(520\) −1210.16 2096.06i −0.102056 0.176766i
\(521\) −4394.33 + 7611.20i −0.369518 + 0.640024i −0.989490 0.144600i \(-0.953811\pi\)
0.619972 + 0.784624i \(0.287144\pi\)
\(522\) −3577.05 + 1541.05i −0.299929 + 0.129215i
\(523\) 9827.76 5674.06i 0.821679 0.474396i −0.0293162 0.999570i \(-0.509333\pi\)
0.850995 + 0.525174i \(0.176000\pi\)
\(524\) 18447.7 1.53796
\(525\) −1717.46 1684.77i −0.142773 0.140056i
\(526\) −3768.00 −0.312344
\(527\) 9611.42 5549.16i 0.794460 0.458681i
\(528\) 313.074 + 351.960i 0.0258045 + 0.0290096i
\(529\) −5774.45 + 10001.6i −0.474599 + 0.822030i
\(530\) −7385.87 12792.7i −0.605324 1.04845i
\(531\) −135.116 100.686i −0.0110424 0.00822859i
\(532\) 14043.9 + 20902.1i 1.14451 + 1.70342i
\(533\) 6470.62i 0.525842i
\(534\) −16298.3 + 3361.46i −1.32078 + 0.272406i
\(535\) −1357.89 783.980i −0.109732 0.0633540i
\(536\) −512.980 296.169i −0.0413383 0.0238667i
\(537\) −10195.9 + 2102.85i −0.819338 + 0.168985i
\(538\) 18741.4i 1.50186i
\(539\) 12155.8 9426.86i 0.971405 0.753328i
\(540\) 5157.36 + 7376.21i 0.410996 + 0.587818i
\(541\) −9438.27 16347.6i −0.750061 1.29914i −0.947793 0.318887i \(-0.896691\pi\)
0.197732 0.980256i \(-0.436643\pi\)
\(542\) −11313.2 + 19595.0i −0.896572 + 1.55291i
\(543\) −3765.28 4232.95i −0.297576 0.334537i
\(544\) −5890.05 + 3400.62i −0.464216 + 0.268016i
\(545\) −3954.29 −0.310795
\(546\) −9290.51 + 2585.30i −0.728199 + 0.202638i
\(547\) 15999.4 1.25061 0.625307 0.780379i \(-0.284974\pi\)
0.625307 + 0.780379i \(0.284974\pi\)
\(548\) 14918.2 8613.00i 1.16291 0.671404i
\(549\) 8667.94 + 20119.8i 0.673841 + 1.56410i
\(550\) −2558.59 + 4431.61i −0.198361 + 0.343571i
\(551\) −1674.74 2900.73i −0.129485 0.224274i
\(552\) 2703.34 + 896.474i 0.208446 + 0.0691241i
\(553\) 10402.0 + 5096.58i 0.799885 + 0.391914i
\(554\) 10464.5i 0.802515i
\(555\) −1374.05 6662.21i −0.105091 0.509541i
\(556\) −7161.69 4134.80i −0.546265 0.315386i
\(557\) −11300.4 6524.27i −0.859627 0.496306i 0.00426065 0.999991i \(-0.498644\pi\)
−0.863887 + 0.503685i \(0.831977\pi\)
\(558\) −4349.70 + 37067.5i −0.329995 + 2.81217i
\(559\) 6631.40i 0.501750i
\(560\) 12.7210 + 186.750i 0.000959929 + 0.0140922i
\(561\) −2687.89 + 8105.41i −0.202287 + 0.610001i
\(562\) −9808.74 16989.2i −0.736222 1.27517i
\(563\) 1062.90 1840.99i 0.0795661 0.137813i −0.823497 0.567321i \(-0.807980\pi\)
0.903063 + 0.429508i \(0.141313\pi\)
\(564\) 5939.53 5283.31i 0.443438 0.394446i
\(565\) −10351.4 + 5976.41i −0.770776 + 0.445008i
\(566\) −7663.68 −0.569132
\(567\) 12645.3 4730.73i 0.936603 0.350392i
\(568\) 14104.2 1.04190
\(569\) 22953.8 13252.4i 1.69116 0.976394i 0.737583 0.675257i \(-0.235967\pi\)
0.953581 0.301137i \(-0.0973661\pi\)
\(570\) −9389.05 + 8351.71i −0.689937 + 0.613710i
\(571\) −10310.6 + 17858.5i −0.755667 + 1.30885i 0.189375 + 0.981905i \(0.439354\pi\)
−0.945042 + 0.326949i \(0.893979\pi\)
\(572\) 6317.00 + 10941.4i 0.461761 + 0.799793i
\(573\) −1782.51 + 5375.22i −0.129957 + 0.391890i
\(574\) 10960.5 22370.0i 0.797006 1.62666i
\(575\) 621.538i 0.0450782i
\(576\) 2614.68 22281.9i 0.189141 1.61183i
\(577\) 12030.2 + 6945.61i 0.867976 + 0.501126i 0.866675 0.498873i \(-0.166253\pi\)
0.00130062 + 0.999999i \(0.499586\pi\)
\(578\) 14111.4 + 8147.24i 1.01550 + 0.586299i
\(579\) −5192.24 25175.0i −0.372680 1.80697i
\(580\) 2027.66i 0.145162i
\(581\) −9692.04 + 6512.01i −0.692072 + 0.464998i
\(582\) −11893.1 3943.96i −0.847054 0.280897i
\(583\) 14515.1 + 25141.0i 1.03114 + 1.78599i
\(584\) −7888.84 + 13663.9i −0.558977 + 0.968177i
\(585\) −1172.77 2722.20i −0.0828856 0.192392i
\(586\) −13555.0 + 7825.96i −0.955546 + 0.551685i
\(587\) −1785.23 −0.125527 −0.0627634 0.998028i \(-0.519991\pi\)
−0.0627634 + 0.998028i \(0.519991\pi\)
\(588\) −22480.9 4187.97i −1.57669 0.293723i
\(589\) −32095.5 −2.24529
\(590\) −123.339 + 71.2096i −0.00860639 + 0.00496890i
\(591\) −11383.8 12797.8i −0.792330 0.890743i
\(592\) −264.625 + 458.343i −0.0183716 + 0.0318206i
\(593\) −3382.75 5859.10i −0.234255 0.405741i 0.724801 0.688958i \(-0.241932\pi\)
−0.959056 + 0.283217i \(0.908598\pi\)
\(594\) −16455.2 23534.7i −1.13664 1.62566i
\(595\) −2816.61 + 1892.46i −0.194067 + 0.130392i
\(596\) 15533.5i 1.06758i
\(597\) −3999.95 + 824.972i −0.274216 + 0.0565559i
\(598\) −2157.57 1245.67i −0.147541 0.0851829i
\(599\) −22410.2 12938.5i −1.52864 0.882561i −0.999419 0.0340772i \(-0.989151\pi\)
−0.529221 0.848484i \(-0.677516\pi\)
\(600\) 2804.94 578.506i 0.190852 0.0393624i
\(601\) 21917.8i 1.48760i 0.668403 + 0.743799i \(0.266978\pi\)
−0.668403 + 0.743799i \(0.733022\pi\)
\(602\) 11232.8 22925.8i 0.760490 1.55214i
\(603\) −581.674 433.453i −0.0392829 0.0292729i
\(604\) 3542.58 + 6135.92i 0.238651 + 0.413356i
\(605\) 1700.79 2945.85i 0.114292 0.197960i
\(606\) −27189.1 30566.2i −1.82258 2.04895i
\(607\) −10602.4 + 6121.27i −0.708956 + 0.409316i −0.810674 0.585497i \(-0.800899\pi\)
0.101718 + 0.994813i \(0.467566\pi\)
\(608\) 19668.7 1.31196
\(609\) 2945.44 + 758.975i 0.195985 + 0.0505012i
\(610\) 18516.1 1.22901
\(611\) −2267.19 + 1308.96i −0.150116 + 0.0866693i
\(612\) 11658.6 5022.75i 0.770054 0.331752i
\(613\) 9316.91 16137.4i 0.613877 1.06327i −0.376704 0.926334i \(-0.622943\pi\)
0.990580 0.136932i \(-0.0437242\pi\)
\(614\) 1656.96 + 2869.94i 0.108908 + 0.188634i
\(615\) 7267.53 + 2410.04i 0.476512 + 0.158020i
\(616\) 1244.49 + 18269.6i 0.0813991 + 1.19497i
\(617\) 11465.5i 0.748112i −0.927406 0.374056i \(-0.877967\pi\)
0.927406 0.374056i \(-0.122033\pi\)
\(618\) 1867.90 + 9056.68i 0.121582 + 0.589503i
\(619\) −5119.14 2955.53i −0.332400 0.191911i 0.324506 0.945884i \(-0.394802\pi\)
−0.656906 + 0.753972i \(0.728135\pi\)
\(620\) 16826.5 + 9714.79i 1.08995 + 0.629283i
\(621\) 3160.17 + 1476.24i 0.204208 + 0.0953939i
\(622\) 30672.1i 1.97723i
\(623\) 11670.3 + 5718.01i 0.750499 + 0.367717i
\(624\) −72.5883 + 218.892i −0.00465682 + 0.0140428i
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) 13729.6 23780.4i 0.876592 1.51830i
\(627\) 18451.9 16413.3i 1.17528 1.04543i
\(628\) 24264.2 14008.9i 1.54179 0.890155i
\(629\) −9594.47 −0.608198
\(630\) 556.626 11397.6i 0.0352008 0.720781i
\(631\) −6488.94 −0.409383 −0.204691 0.978827i \(-0.565619\pi\)
−0.204691 + 0.978827i \(0.565619\pi\)
\(632\) −11941.7 + 6894.57i −0.751609 + 0.433942i
\(633\) −454.409 + 404.204i −0.0285326 + 0.0253802i
\(634\) −11783.3 + 20409.2i −0.738128 + 1.27847i
\(635\) 6042.38 + 10465.7i 0.377613 + 0.654045i
\(636\) 13583.7 40962.2i 0.846904 2.55386i
\(637\) 6972.37 + 2846.27i 0.433682 + 0.177038i
\(638\) 6469.50i 0.401458i
\(639\) 17155.1 + 2013.08i 1.06204 + 0.124626i
\(640\) −9992.00 5768.88i −0.617138 0.356305i
\(641\) 5980.20 + 3452.67i 0.368493 + 0.212749i 0.672800 0.739825i \(-0.265092\pi\)
−0.304307 + 0.952574i \(0.598425\pi\)
\(642\) −1502.23 7283.69i −0.0923493 0.447764i
\(643\) 25890.4i 1.58790i −0.607983 0.793950i \(-0.708021\pi\)
0.607983 0.793950i \(-0.291979\pi\)
\(644\) −3294.74 4903.67i −0.201601 0.300049i
\(645\) 7448.10 + 2469.92i 0.454680 + 0.150780i
\(646\) 8861.87 + 15349.2i 0.539730 + 0.934840i
\(647\) −10178.6 + 17629.8i −0.618487 + 1.07125i 0.371275 + 0.928523i \(0.378921\pi\)
−0.989762 + 0.142728i \(0.954413\pi\)
\(648\) −3720.76 + 15635.6i −0.225563 + 0.947874i
\(649\) 242.392 139.945i 0.0146606 0.00846430i
\(650\) −2505.22 −0.151174
\(651\) 20410.3 20806.3i 1.22879 1.25263i
\(652\) 46321.2 2.78233
\(653\) 15369.4 8873.52i 0.921058 0.531773i 0.0370853 0.999312i \(-0.488193\pi\)
0.883972 + 0.467539i \(0.154859\pi\)
\(654\) −12465.4 14013.7i −0.745317 0.837891i
\(655\) 3594.48 6225.82i 0.214424 0.371394i
\(656\) −297.857 515.904i −0.0177277 0.0307053i
\(657\) −11545.6 + 15493.6i −0.685595 + 0.920038i
\(658\) −10055.3 + 684.944i −0.595737 + 0.0405804i
\(659\) 346.589i 0.0204874i 0.999948 + 0.0102437i \(0.00326073\pi\)
−0.999948 + 0.0102437i \(0.996739\pi\)
\(660\) −14641.7 + 3019.79i −0.863526 + 0.178099i
\(661\) −2606.71 1504.98i −0.153388 0.0885584i 0.421342 0.906902i \(-0.361559\pi\)
−0.574729 + 0.818344i \(0.694893\pi\)
\(662\) 12659.2 + 7308.79i 0.743223 + 0.429100i
\(663\) −4094.50 + 844.473i −0.239845 + 0.0494670i
\(664\) 13900.0i 0.812386i
\(665\) 9790.57 666.914i 0.570920 0.0388899i
\(666\) 19278.9 25871.4i 1.12168 1.50525i
\(667\) 392.897 + 680.517i 0.0228081 + 0.0395048i
\(668\) 11209.6 19415.6i 0.649272 1.12457i
\(669\) 12372.4 + 13909.1i 0.715015 + 0.803825i
\(670\) −530.974 + 306.558i −0.0306169 + 0.0176767i
\(671\) −36388.9 −2.09356
\(672\) −12507.8 + 12750.5i −0.718004 + 0.731934i
\(673\) −21537.4 −1.23359 −0.616795 0.787124i \(-0.711569\pi\)
−0.616795 + 0.787124i \(0.711569\pi\)
\(674\) −46524.6 + 26861.0i −2.65884 + 1.53508i
\(675\) 3494.26 303.301i 0.199251 0.0172949i
\(676\) 11001.7 19055.6i 0.625952 1.08418i
\(677\) −3113.61 5392.93i −0.176759 0.306155i 0.764010 0.645205i \(-0.223228\pi\)
−0.940769 + 0.339050i \(0.889895\pi\)
\(678\) −53811.7 17844.9i −3.04812 1.01081i
\(679\) 5457.15 + 8122.06i 0.308433 + 0.459052i
\(680\) 4039.48i 0.227805i
\(681\) 1333.72 + 6466.66i 0.0750490 + 0.363881i
\(682\) −53687.0 30996.2i −3.01434 1.74033i
\(683\) −10377.9 5991.66i −0.581402 0.335673i 0.180288 0.983614i \(-0.442297\pi\)
−0.761690 + 0.647941i \(0.775630\pi\)
\(684\) −36461.6 4278.60i −2.03822 0.239176i
\(685\) 6712.88i 0.374432i
\(686\) 19283.4 + 21650.4i 1.07324 + 1.20498i
\(687\) 4722.82 14241.8i 0.262281 0.790915i
\(688\) −305.258 528.722i −0.0169155 0.0292985i
\(689\) −7106.20 + 12308.3i −0.392924 + 0.680564i
\(690\) 2202.69 1959.33i 0.121529 0.108102i
\(691\) 21090.2 12176.5i 1.16109 0.670354i 0.209522 0.977804i \(-0.432809\pi\)
0.951564 + 0.307450i \(0.0994758\pi\)
\(692\) 44978.8 2.47086
\(693\) −1093.91 + 22399.3i −0.0599630 + 1.22782i
\(694\) 4269.94 0.233551
\(695\) −2790.87 + 1611.31i −0.152322 + 0.0879432i
\(696\) −2705.41 + 2406.50i −0.147339 + 0.131061i
\(697\) 5399.70 9352.55i 0.293441 0.508254i
\(698\) 13693.1 + 23717.1i 0.742536 + 1.28611i
\(699\) −2683.67 + 8092.69i −0.145216 + 0.437902i
\(700\) −5334.70 2613.81i −0.288047 0.141132i
\(701\) 23347.4i 1.25794i 0.777428 + 0.628972i \(0.216524\pi\)
−0.777428 + 0.628972i \(0.783476\pi\)
\(702\) 5950.27 12737.6i 0.319912 0.684831i
\(703\) 24029.2 + 13873.3i 1.28916 + 0.744296i
\(704\) 32272.3 + 18632.4i 1.72771 + 0.997494i
\(705\) −625.738 3033.94i −0.0334279 0.162078i
\(706\) 30955.7i 1.65019i
\(707\) 2171.15 + 31873.3i 0.115494 + 1.69550i
\(708\) −394.930 130.965i −0.0209638 0.00695195i
\(709\) 3202.09 + 5546.19i 0.169615 + 0.293782i 0.938285 0.345864i \(-0.112414\pi\)
−0.768669 + 0.639646i \(0.779081\pi\)
\(710\) 7299.45 12643.0i 0.385836 0.668288i
\(711\) −15509.0 + 6681.55i −0.818050 + 0.352430i
\(712\) −13397.8 + 7735.24i −0.705204 + 0.407149i
\(713\) 7529.67 0.395496
\(714\) −15585.8 4016.12i −0.816923 0.210503i
\(715\) 4923.41 0.257518
\(716\) −22262.0 + 12853.0i −1.16197 + 0.670863i
\(717\) −10652.8 11975.9i −0.554862 0.623779i
\(718\) −1040.53 + 1802.25i −0.0540839 + 0.0936760i
\(719\) −11057.5 19152.2i −0.573541 0.993403i −0.996198 0.0871132i \(-0.972236\pi\)
0.422657 0.906290i \(-0.361098\pi\)
\(720\) −218.814 163.056i −0.0113260 0.00843992i
\(721\) 3177.39 6484.96i 0.164122 0.334969i
\(722\) 19951.0i 1.02839i
\(723\) 2901.72 598.467i 0.149262 0.0307845i
\(724\) −12114.7 6994.45i −0.621879 0.359042i
\(725\) 684.307 + 395.085i 0.0350545 + 0.0202387i
\(726\) 15801.4 3258.98i 0.807778 0.166601i
\(727\) 2412.41i 0.123069i −0.998105 0.0615346i \(-0.980401\pi\)
0.998105 0.0615346i \(-0.0195994\pi\)
\(728\) −7441.33 + 4999.77i −0.378838 + 0.254538i
\(729\) −6757.27 + 18486.7i −0.343305 + 0.939224i
\(730\) 8165.57 + 14143.2i 0.414002 + 0.717072i
\(731\) 5533.86 9584.92i 0.279996 0.484967i
\(732\) 35952.8 + 40418.4i 1.81538 + 2.04086i
\(733\) −25158.3 + 14525.2i −1.26773 + 0.731923i −0.974557 0.224138i \(-0.928043\pi\)
−0.293170 + 0.956060i \(0.594710\pi\)
\(734\) −23968.8 −1.20532
\(735\) −5793.72 + 6770.96i −0.290755 + 0.339797i
\(736\) −4614.32 −0.231095
\(737\) 1043.50 602.466i 0.0521545 0.0301114i
\(738\) 14369.0 + 33353.0i 0.716710 + 1.66361i
\(739\) 17961.7 31110.6i 0.894089 1.54861i 0.0591619 0.998248i \(-0.481157\pi\)
0.834928 0.550360i \(-0.185510\pi\)
\(740\) −8398.42 14546.5i −0.417206 0.722621i
\(741\) 11475.7 + 3805.53i 0.568920 + 0.188663i
\(742\) −45416.1 + 30514.7i −2.24700 + 1.50974i
\(743\) 707.501i 0.0349337i 0.999847 + 0.0174668i \(0.00556015\pi\)
−0.999847 + 0.0174668i \(0.994440\pi\)
\(744\) 7008.36 + 33980.6i 0.345348 + 1.67445i
\(745\) 5242.33 + 3026.66i 0.257804 + 0.148843i
\(746\) 2197.58 + 1268.77i 0.107854 + 0.0622695i
\(747\) 1983.94 16906.8i 0.0971733 0.828096i
\(748\) 21086.0i 1.03072i
\(749\) −2555.37 + 5215.43i −0.124661 + 0.254429i
\(750\) 933.090 2813.76i 0.0454288 0.136992i
\(751\) 9718.47 + 16832.9i 0.472213 + 0.817897i 0.999494 0.0317938i \(-0.0101220\pi\)
−0.527281 + 0.849691i \(0.676789\pi\)
\(752\) −120.509 + 208.728i −0.00584376 + 0.0101217i
\(753\) 14283.5 12705.4i 0.691259 0.614886i
\(754\) 2742.94 1583.64i 0.132483 0.0764891i
\(755\) 2761.05 0.133092
\(756\) 25960.4 20915.8i 1.24890 1.00622i
\(757\) 10730.3 0.515190 0.257595 0.966253i \(-0.417070\pi\)
0.257595 + 0.966253i \(0.417070\pi\)
\(758\) −3066.48 + 1770.44i −0.146939 + 0.0848352i
\(759\) −4328.86 + 3850.59i −0.207019 + 0.184147i
\(760\) −5840.95 + 10116.8i −0.278781 + 0.482862i
\(761\) −608.496 1053.95i −0.0289855 0.0502043i 0.851169 0.524892i \(-0.175894\pi\)
−0.880154 + 0.474688i \(0.842561\pi\)
\(762\) −18041.9 + 54405.7i −0.857726 + 2.58650i
\(763\) 995.410 + 14613.0i 0.0472297 + 0.693352i
\(764\) 13983.5i 0.662179i
\(765\) 576.553 4913.30i 0.0272488 0.232210i
\(766\) 23603.6 + 13627.5i 1.11336 + 0.642798i
\(767\) 118.668 + 68.5131i 0.00558652 + 0.00322538i
\(768\) −4077.07 19768.0i −0.191561 0.928799i
\(769\) 40387.9i 1.89392i −0.321349 0.946961i \(-0.604136\pi\)
0.321349 0.946961i \(-0.395864\pi\)
\(770\) 17021.0 + 8339.67i 0.796617 + 0.390313i
\(771\) 23400.2 + 7759.89i 1.09304 + 0.362472i
\(772\) −31735.7 54967.9i −1.47953 2.56262i
\(773\) 11554.8 20013.6i 0.537644 0.931226i −0.461387 0.887199i \(-0.652648\pi\)
0.999030 0.0440271i \(-0.0140188\pi\)
\(774\) 14726.1 + 34181.7i 0.683873 + 1.58738i
\(775\) 6557.21 3785.81i 0.303925 0.175471i
\(776\) −11648.4 −0.538857
\(777\) −24274.2 + 6754.87i −1.12076 + 0.311878i
\(778\) 3569.42 0.164486
\(779\) −27046.9 + 15615.5i −1.24397 + 0.718208i
\(780\) −4864.41 5468.60i −0.223300 0.251035i
\(781\) −14345.3 + 24846.8i −0.657254 + 1.13840i
\(782\) −2079.01 3600.96i −0.0950708 0.164667i
\(783\) −3634.11 + 2540.93i −0.165865 + 0.115971i
\(784\) 686.929 94.0206i 0.0312923 0.00428301i
\(785\) 10918.4i 0.496427i
\(786\) 33395.1 6887.59i 1.51547 0.312560i
\(787\) −6494.51 3749.61i −0.294161 0.169834i 0.345656 0.938361i \(-0.387656\pi\)
−0.639817 + 0.768528i \(0.720990\pi\)
\(788\) −36627.3 21146.8i −1.65583 0.955993i
\(789\) −4201.43 + 866.527i −0.189575 + 0.0390991i
\(790\) 14272.8i 0.642791i
\(791\) 24691.5 + 36749.2i 1.10990 + 1.65190i
\(792\) −21406.4 15951.7i −0.960410 0.715680i
\(793\) −8907.48 15428.2i −0.398882 0.690885i
\(794\) 6090.98 10549.9i 0.272243 0.471538i
\(795\) −11177.4 12565.7i −0.498643 0.560578i
\(796\) −8733.62 + 5042.36i −0.388888 + 0.224525i
\(797\) 38280.7 1.70134 0.850672 0.525697i \(-0.176195\pi\)
0.850672 + 0.525697i \(0.176195\pi\)
\(798\) 33227.1 + 32594.8i 1.47397 + 1.44592i
\(799\) −4369.28 −0.193460
\(800\) −4018.37 + 2320.01i −0.177589 + 0.102531i
\(801\) −17400.1 + 7496.25i −0.767542 + 0.330670i
\(802\) 34017.5 58920.1i 1.49776 2.59419i
\(803\) −16047.5 27795.0i −0.705234 1.22150i
\(804\) −1700.18 563.807i −0.0745779 0.0247313i
\(805\) −2296.89 + 156.459i −0.100565 + 0.00685027i
\(806\) 30349.7i 1.32633i
\(807\) −4309.96 20897.2i −0.188002 0.911544i
\(808\) −32935.4 19015.3i −1.43399 0.827915i
\(809\) 24427.1 + 14103.0i 1.06157 + 0.612899i 0.925867 0.377850i \(-0.123337\pi\)
0.135706 + 0.990749i \(0.456670\pi\)
\(810\) 12090.1 + 11427.3i 0.524450 + 0.495698i
\(811\) 14044.9i 0.608116i −0.952654 0.304058i \(-0.901658\pi\)
0.952654 0.304058i \(-0.0983417\pi\)
\(812\) 7493.20 510.422i 0.323842 0.0220595i
\(813\) −8108.25 + 24450.6i −0.349777 + 1.05476i
\(814\) 26796.2 + 46412.3i 1.15382 + 1.99847i
\(815\) 9025.57 15632.7i 0.387916 0.671891i
\(816\) −287.582 + 255.809i −0.0123375 + 0.0109744i
\(817\) −27718.9 + 16003.5i −1.18698 + 0.685302i
\(818\) −35520.7 −1.51828
\(819\) −9764.63 + 5019.21i −0.416610 + 0.214146i
\(820\) 18906.3 0.805165
\(821\) −12092.4 + 6981.54i −0.514041 + 0.296781i −0.734493 0.678616i \(-0.762580\pi\)
0.220452 + 0.975398i \(0.429247\pi\)
\(822\) 23790.0 21161.6i 1.00946 0.897926i
\(823\) −7562.23 + 13098.2i −0.320295 + 0.554767i −0.980549 0.196275i \(-0.937115\pi\)
0.660254 + 0.751043i \(0.270449\pi\)
\(824\) 4298.33 + 7444.92i 0.181722 + 0.314752i
\(825\) −1833.76 + 5529.76i −0.0773860 + 0.233359i
\(826\) 294.202 + 437.871i 0.0123930 + 0.0184449i
\(827\) 1559.49i 0.0655728i −0.999462 0.0327864i \(-0.989562\pi\)
0.999462 0.0327864i \(-0.0104381\pi\)
\(828\) 8553.96 + 1003.77i 0.359023 + 0.0421297i
\(829\) 5790.85 + 3343.35i 0.242611 + 0.140072i 0.616376 0.787452i \(-0.288600\pi\)
−0.373765 + 0.927523i \(0.621933\pi\)
\(830\) −12460.0 7193.80i −0.521077 0.300844i
\(831\) 2406.51 + 11668.2i 0.100459 + 0.487082i
\(832\) 18243.8i 0.760203i
\(833\) 7702.58 + 9932.35i 0.320382 + 0.413128i
\(834\) −14508.3 4811.19i −0.602375 0.199758i
\(835\) −4368.34 7566.18i −0.181045 0.313579i
\(836\) 30489.6 52809.5i 1.26137 2.18476i
\(837\) 3674.36 + 42331.5i 0.151738 + 1.74814i
\(838\) −40283.5 + 23257.7i −1.66059 + 0.958739i
\(839\) 28415.9 1.16928 0.584640 0.811293i \(-0.301236\pi\)
0.584640 + 0.811293i \(0.301236\pi\)
\(840\) −2843.95 10220.0i −0.116816 0.419789i
\(841\) 23390.0 0.959039
\(842\) 46431.1 26807.0i 1.90038 1.09718i
\(843\) −14844.0 16687.8i −0.606471 0.681799i
\(844\) −750.856 + 1300.52i −0.0306227 + 0.0530400i
\(845\) −4287.32 7425.86i −0.174542 0.302316i
\(846\) 8779.53 11781.7i 0.356792 0.478799i
\(847\) −11314.5 5543.69i −0.458997 0.224892i
\(848\) 1308.46i 0.0529865i
\(849\) −8545.22 + 1762.42i −0.345431 + 0.0712437i
\(850\) −3621.01 2090.59i −0.146117 0.0843608i
\(851\) −5637.30 3254.69i −0.227079 0.131104i
\(852\) 41771.6 8615.22i 1.67966 0.346423i
\(853\) 2437.87i 0.0978558i 0.998802 + 0.0489279i \(0.0155805\pi\)
−0.998802 + 0.0489279i \(0.984420\pi\)
\(854\) −4661.04 68426.0i −0.186765 2.74179i
\(855\) −8548.41 + 11471.6i −0.341929 + 0.458854i
\(856\) −3456.86 5987.46i −0.138029 0.239074i
\(857\) −15603.4 + 27025.9i −0.621940 + 1.07723i 0.367185 + 0.930148i \(0.380322\pi\)
−0.989124 + 0.147083i \(0.953012\pi\)
\(858\) 15520.5 + 17448.2i 0.617553 + 0.694257i
\(859\) 2757.08 1591.80i 0.109512 0.0632265i −0.444244 0.895906i \(-0.646528\pi\)
0.553755 + 0.832679i \(0.313194\pi\)
\(860\) 19376.0 0.768275
\(861\) 7076.81 27463.7i 0.280113 1.08706i
\(862\) 24918.1 0.984589
\(863\) 13566.8 7832.80i 0.535133 0.308959i −0.207971 0.978135i \(-0.566686\pi\)
0.743104 + 0.669176i \(0.233353\pi\)
\(864\) −2251.71 25941.5i −0.0886630 1.02147i
\(865\) 8764.01 15179.7i 0.344492 0.596677i
\(866\) −3310.11 5733.28i −0.129887 0.224971i
\(867\) 17608.3 + 5839.20i 0.689744 + 0.228731i
\(868\) 31665.2 64627.7i 1.23823 2.52720i
\(869\) 28049.8i 1.09497i
\(870\) 757.045 + 3670.60i 0.0295014 + 0.143040i
\(871\) 510.868 + 294.950i 0.0198738 + 0.0114742i
\(872\) −15100.0 8717.97i −0.586410 0.338564i
\(873\) −14168.1 1662.57i −0.549277 0.0644552i
\(874\) 12024.7i 0.465380i
\(875\) −1921.58 + 1291.09i −0.0742413 + 0.0498822i
\(876\) −15017.7 + 45286.4i −0.579226 + 1.74667i
\(877\) −5140.43 8903.49i −0.197925 0.342816i 0.749931 0.661517i \(-0.230087\pi\)
−0.947855 + 0.318701i \(0.896754\pi\)
\(878\) −19313.4 + 33451.7i −0.742363 + 1.28581i
\(879\) −13314.4 + 11843.4i −0.510904 + 0.454457i
\(880\) 392.544 226.635i 0.0150371 0.00868168i
\(881\) −27228.8 −1.04127 −0.520636 0.853779i \(-0.674305\pi\)
−0.520636 + 0.853779i \(0.674305\pi\)
\(882\) −42259.9 + 812.105i −1.61334 + 0.0310034i
\(883\) −39997.5 −1.52437 −0.762187 0.647357i \(-0.775874\pi\)
−0.762187 + 0.647357i \(0.775874\pi\)
\(884\) −8940.06 + 5161.55i −0.340143 + 0.196382i
\(885\) −121.150 + 107.765i −0.00460159 + 0.00409319i
\(886\) −96.5550 + 167.238i −0.00366121 + 0.00634140i
\(887\) 8117.83 + 14060.5i 0.307294 + 0.532250i 0.977770 0.209682i \(-0.0672430\pi\)
−0.670475 + 0.741932i \(0.733910\pi\)
\(888\) 9441.09 28469.9i 0.356782 1.07589i
\(889\) 37154.8 24964.1i 1.40172 0.941808i
\(890\) 16013.2i 0.603104i
\(891\) −23760.3 22457.6i −0.893377 0.844399i
\(892\) 39808.1 + 22983.2i 1.49425 + 0.862707i
\(893\) 10942.8 + 6317.83i 0.410064 + 0.236750i
\(894\) 5799.56 + 28119.6i 0.216964 + 1.05197i
\(895\) 10017.5i 0.374131i
\(896\) −18803.6 + 38377.5i −0.701097 + 1.43092i
\(897\) −2692.22 892.785i −0.100212 0.0332321i
\(898\) −2154.80 3732.23i −0.0800743 0.138693i
\(899\) −4786.29 + 8290.09i −0.177566 + 0.307553i
\(900\) 7953.89 3426.67i 0.294588 0.126914i
\(901\) −20542.4 + 11860.1i −0.759563 + 0.438534i
\(902\) −60322.7 −2.22675
\(903\) 7252.64 28146.1i 0.267279 1.03726i
\(904\) −52704.4 −1.93908
\(905\) −4721.05 + 2725.70i −0.173407 + 0.100116i
\(906\) 8703.88 + 9784.97i 0.319169 + 0.358812i
\(907\) −113.354 + 196.335i −0.00414978 + 0.00718763i −0.868093 0.496402i \(-0.834654\pi\)
0.863943 + 0.503590i \(0.167988\pi\)
\(908\) 8151.91 + 14119.5i 0.297941 + 0.516050i
\(909\) −37345.9 27829.5i −1.36269 1.01545i
\(910\) 630.637 + 9258.02i 0.0229730 + 0.337253i
\(911\) 7251.95i 0.263741i −0.991267 0.131870i \(-0.957902\pi\)
0.991267 0.131870i \(-0.0420983\pi\)
\(912\) 1090.13 224.836i 0.0395811 0.00816343i
\(913\) 24487.2 + 14137.7i 0.887631 + 0.512474i
\(914\) −35072.6 20249.2i −1.26925 0.732804i
\(915\) 20646.0 4258.14i 0.745939 0.153847i
\(916\) 37049.7i 1.33641i
\(917\) −23912.3 11716.1i −0.861126 0.421920i
\(918\) 19229.9 13445.3i 0.691374 0.483401i
\(919\) 8177.68 + 14164.2i 0.293533 + 0.508414i 0.974643 0.223768i \(-0.0718356\pi\)
−0.681110 + 0.732181i \(0.738502\pi\)
\(920\) 1370.30 2373.43i 0.0491058 0.0850538i
\(921\) 2507.56 + 2819.01i 0.0897142 + 0.100857i
\(922\) 35407.4 20442.5i 1.26473 0.730192i
\(923\) −14046.1 −0.500902
\(924\) 14845.3 + 53348.1i 0.528545 + 1.89937i
\(925\) −6545.64 −0.232670
\(926\) −22566.0 + 13028.5i −0.800825 + 0.462357i
\(927\) 4165.52 + 9668.88i 0.147588 + 0.342576i
\(928\) 2933.12 5080.31i 0.103755 0.179708i
\(929\) 17239.9 + 29860.3i 0.608850 + 1.05456i 0.991430 + 0.130637i \(0.0417022\pi\)
−0.382580 + 0.923922i \(0.624964\pi\)
\(930\) 34087.5 + 11304.0i 1.20191 + 0.398572i
\(931\) −4929.14 36013.1i −0.173519 1.26776i
\(932\) 21052.9i 0.739925i
\(933\) −7053.65 34200.2i −0.247509 1.20007i
\(934\) 72100.2 + 41627.1i 2.52590 + 1.45833i
\(935\) 7116.22 + 4108.55i 0.248904 + 0.143705i
\(936\) 1523.22 12980.7i 0.0531923 0.453297i
\(937\) 23700.4i 0.826315i 0.910660 + 0.413158i \(0.135574\pi\)
−0.910660 + 0.413158i \(0.864426\pi\)
\(938\) 1266.54 + 1885.04i 0.0440875 + 0.0656170i
\(939\) 9840.15 29673.2i 0.341982 1.03126i
\(940\) −3824.61 6624.41i −0.132707 0.229856i
\(941\) 17640.5 30554.2i 0.611120 1.05849i −0.379932 0.925014i \(-0.624053\pi\)
0.991052 0.133476i \(-0.0426140\pi\)
\(942\) 38694.1 34419.0i 1.33835 1.19048i
\(943\) 6345.25 3663.43i 0.219120 0.126509i
\(944\) 12.6153 0.000434949
\(945\) −2000.45 12836.7i −0.0688621 0.441880i
\(946\) −61821.5 −2.12473
\(947\) −25823.1 + 14909.0i −0.886100 + 0.511590i −0.872665 0.488320i \(-0.837610\pi\)
−0.0134353 + 0.999910i \(0.504277\pi\)
\(948\) −31155.9 + 27713.7i −1.06740 + 0.949471i
\(949\) 7856.37 13607.6i 0.268734 0.465461i
\(950\) 6045.84 + 10471.7i 0.206477 + 0.357628i
\(951\) −8445.16 + 25466.6i −0.287963 + 0.868361i
\(952\) −14927.9 + 1016.86i −0.508209 + 0.0346181i
\(953\) 8553.43i 0.290737i −0.989378 0.145369i \(-0.953563\pi\)
0.989378 0.145369i \(-0.0464368\pi\)
\(954\) 9296.55 79223.8i 0.315500 2.68864i
\(955\) 4719.23 + 2724.65i 0.159906 + 0.0923220i
\(956\) −34275.2 19788.8i −1.15956 0.669473i
\(957\) −1487.79 7213.67i −0.0502543 0.243662i
\(958\) 43556.2i 1.46893i
\(959\) −24807.4 + 1689.83i −0.835320 + 0.0569003i
\(960\) −20490.6 6795.04i −0.688888 0.228447i
\(961\) 30967.9 + 53638.0i 1.03951 + 1.80048i
\(962\) −13118.6 + 22722.1i −0.439669 + 0.761529i
\(963\) −3350.06 7776.05i −0.112102 0.260207i
\(964\) 6335.71 3657.92i 0.211680 0.122213i
\(965\) −24734.5 −0.825111
\(966\) −7795.16 7646.80i −0.259633 0.254691i
\(967\) 37158.5 1.23572 0.617858 0.786290i \(-0.288001\pi\)
0.617858 + 0.786290i \(0.288001\pi\)
\(968\) 12989.4 7499.41i 0.431295 0.249009i
\(969\) 13411.1 + 15076.8i 0.444609 + 0.499832i
\(970\) −6028.50 + 10441.7i −0.199550 + 0.345631i
\(971\) 10770.2 + 18654.5i 0.355955 + 0.616532i 0.987281 0.158986i \(-0.0508223\pi\)
−0.631326 + 0.775518i \(0.717489\pi\)
\(972\) −1468.95 + 48579.9i −0.0484739 + 1.60309i
\(973\) 6657.13 + 9908.02i 0.219340 + 0.326451i
\(974\) 33129.6i 1.08988i
\(975\) −2793.39 + 576.125i −0.0917540 + 0.0189239i
\(976\) −1420.39 820.062i −0.0465836 0.0268950i
\(977\) −43080.4 24872.5i −1.41071 0.814475i −0.415256 0.909704i \(-0.636308\pi\)
−0.995455 + 0.0952296i \(0.969641\pi\)
\(978\) 83853.4 17294.4i 2.74165 0.565454i
\(979\) 31470.0i 1.02736i
\(980\) −8316.40 + 20372.3i −0.271079 + 0.664050i
\(981\) −17122.1 12759.0i −0.557253 0.415255i
\(982\) 9751.95 + 16890.9i 0.316901 + 0.548889i
\(983\) −8320.88 + 14412.2i −0.269985 + 0.467627i −0.968858 0.247619i \(-0.920352\pi\)
0.698873 + 0.715246i \(0.253685\pi\)
\(984\) 22438.6 + 25225.7i 0.726949 + 0.817241i
\(985\) −14273.5 + 8240.79i −0.461716 + 0.266572i
\(986\) 5286.15 0.170736
\(987\) −11054.4 + 3076.14i −0.356500 + 0.0992042i
\(988\) 29853.6 0.961306
\(989\) 6502.91 3754.46i 0.209080 0.120713i
\(990\) −25377.8 + 10933.2i −0.814707 + 0.350990i
\(991\) −9989.26 + 17301.9i −0.320201 + 0.554605i −0.980529 0.196372i \(-0.937084\pi\)
0.660328 + 0.750977i \(0.270417\pi\)
\(992\) −28105.9 48680.9i −0.899560 1.55808i
\(993\) 15796.2 + 5238.28i 0.504810 + 0.167403i
\(994\) −48559.6 23792.4i −1.54952 0.759205i
\(995\) 3929.96i 0.125214i
\(996\) −8490.51 41167.0i −0.270113 1.30966i
\(997\) −999.878 577.280i −0.0317617 0.0183377i 0.484035 0.875049i \(-0.339171\pi\)
−0.515797 + 0.856711i \(0.672504\pi\)
\(998\) 4510.40 + 2604.08i 0.143060 + 0.0825959i
\(999\) 15546.9 33280.9i 0.492373 1.05402i
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 105.4.s.a.101.15 yes 32
3.2 odd 2 105.4.s.b.101.2 yes 32
7.5 odd 6 105.4.s.b.26.2 yes 32
21.5 even 6 inner 105.4.s.a.26.15 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.s.a.26.15 32 21.5 even 6 inner
105.4.s.a.101.15 yes 32 1.1 even 1 trivial
105.4.s.b.26.2 yes 32 7.5 odd 6
105.4.s.b.101.2 yes 32 3.2 odd 2