Properties

Label 201.4.e.a.37.15
Level $201$
Weight $4$
Character 201.37
Analytic conductor $11.859$
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] = [201,4,Mod(37,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.37");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 201.e (of order \(3\), 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: \(11.8593839112\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.15
Character \(\chi\) \(=\) 201.37
Dual form 201.4.e.a.163.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.46601 + 4.27125i) q^{2} +3.00000 q^{3} +(-8.16236 + 14.1376i) q^{4} +11.8437 q^{5} +(7.39802 + 12.8137i) q^{6} +(-12.5285 + 21.6999i) q^{7} -41.0576 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+(2.46601 + 4.27125i) q^{2} +3.00000 q^{3} +(-8.16236 + 14.1376i) q^{4} +11.8437 q^{5} +(7.39802 + 12.8137i) q^{6} +(-12.5285 + 21.6999i) q^{7} -41.0576 q^{8} +9.00000 q^{9} +(29.2066 + 50.5874i) q^{10} +(12.1897 - 21.1131i) q^{11} +(-24.4871 + 42.4129i) q^{12} +(-1.08813 - 1.88470i) q^{13} -123.581 q^{14} +35.5311 q^{15} +(-35.9494 - 62.2662i) q^{16} +(-6.60849 - 11.4462i) q^{17} +(22.1940 + 38.4412i) q^{18} +(34.8110 + 60.2944i) q^{19} +(-96.6726 + 167.442i) q^{20} +(-37.5854 + 65.0998i) q^{21} +120.239 q^{22} +(-52.0095 - 90.0832i) q^{23} -123.173 q^{24} +15.2733 q^{25} +(5.36667 - 9.29534i) q^{26} +27.0000 q^{27} +(-204.524 - 354.245i) q^{28} +(-9.33678 + 16.1718i) q^{29} +(87.6199 + 151.762i) q^{30} +(32.5894 - 56.4465i) q^{31} +(13.0724 - 22.6421i) q^{32} +(36.5690 - 63.3393i) q^{33} +(32.5932 - 56.4530i) q^{34} +(-148.383 + 257.007i) q^{35} +(-73.4613 + 127.239i) q^{36} +(47.4397 + 82.1680i) q^{37} +(-171.688 + 297.373i) q^{38} +(-3.26439 - 5.65409i) q^{39} -486.274 q^{40} +(213.236 - 369.336i) q^{41} -370.743 q^{42} +73.4294 q^{43} +(198.993 + 344.666i) q^{44} +106.593 q^{45} +(256.512 - 444.291i) q^{46} +(234.747 - 406.593i) q^{47} +(-107.848 - 186.799i) q^{48} +(-142.425 - 246.687i) q^{49} +(37.6639 + 65.2359i) q^{50} +(-19.8255 - 34.3387i) q^{51} +35.5268 q^{52} +205.002 q^{53} +(66.5821 + 115.324i) q^{54} +(144.371 - 250.057i) q^{55} +(514.389 - 890.948i) q^{56} +(104.433 + 180.883i) q^{57} -92.0982 q^{58} +743.979 q^{59} +(-290.018 + 502.325i) q^{60} +(21.6336 + 37.4706i) q^{61} +321.463 q^{62} +(-112.756 + 195.299i) q^{63} -446.244 q^{64} +(-12.8875 - 22.3218i) q^{65} +360.717 q^{66} +(280.752 + 471.107i) q^{67} +215.764 q^{68} +(-156.029 - 270.250i) q^{69} -1463.66 q^{70} +(-509.735 + 882.887i) q^{71} -369.519 q^{72} +(-587.407 - 1017.42i) q^{73} +(-233.973 + 405.253i) q^{74} +45.8198 q^{75} -1136.56 q^{76} +(305.435 + 529.029i) q^{77} +(16.1000 - 27.8860i) q^{78} +(-199.347 + 345.278i) q^{79} +(-425.774 - 737.463i) q^{80} +81.0000 q^{81} +2103.37 q^{82} +(534.279 + 925.398i) q^{83} +(-613.571 - 1062.74i) q^{84} +(-78.2690 - 135.566i) q^{85} +(181.077 + 313.635i) q^{86} +(-28.0103 + 48.5153i) q^{87} +(-500.479 + 866.854i) q^{88} -653.789 q^{89} +(262.860 + 455.286i) q^{90} +54.5303 q^{91} +1698.08 q^{92} +(97.7682 - 169.340i) q^{93} +2315.55 q^{94} +(412.291 + 714.109i) q^{95} +(39.2173 - 67.9264i) q^{96} +(380.011 + 658.198i) q^{97} +(702.440 - 1216.66i) q^{98} +(109.707 - 190.018i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9} - 2 q^{10} + 16 q^{11} - 198 q^{12} + 88 q^{13} + 214 q^{14} + 12 q^{15} - 298 q^{16} + 52 q^{17} + 18 q^{18} - 2 q^{19} + 164 q^{20} - 42 q^{21} - 506 q^{22} + 160 q^{23} + 324 q^{24} + 572 q^{25} + 353 q^{26} + 864 q^{27} - 433 q^{28} + 48 q^{29} - 6 q^{30} + 292 q^{31} - 525 q^{32} + 48 q^{33} + 138 q^{34} - 328 q^{35} - 594 q^{36} - 616 q^{37} - 194 q^{38} + 264 q^{39} - 1794 q^{40} + 124 q^{41} + 642 q^{42} - 292 q^{43} - 179 q^{44} + 36 q^{45} + 1324 q^{46} + 402 q^{47} - 894 q^{48} + 172 q^{49} + 171 q^{50} + 156 q^{51} - 3344 q^{52} + 852 q^{53} + 54 q^{54} + 1238 q^{55} - 47 q^{56} - 6 q^{57} - 3320 q^{58} + 1200 q^{59} + 492 q^{60} - 454 q^{61} - 5810 q^{62} - 126 q^{63} + 2340 q^{64} - 24 q^{65} - 1518 q^{66} + 110 q^{67} + 906 q^{68} + 480 q^{69} - 10 q^{70} + 406 q^{71} + 972 q^{72} + 1274 q^{73} - 1945 q^{74} + 1716 q^{75} - 2698 q^{76} + 1436 q^{77} + 1059 q^{78} + 1236 q^{79} + 6697 q^{80} + 2592 q^{81} + 2950 q^{82} + 2190 q^{83} - 1299 q^{84} + 2032 q^{85} + 273 q^{86} + 144 q^{87} + 1938 q^{88} - 2160 q^{89} - 18 q^{90} - 3020 q^{91} - 3020 q^{92} + 876 q^{93} - 2886 q^{94} - 102 q^{95} - 1575 q^{96} + 1860 q^{97} + 2612 q^{98} + 144 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\) \(68\) \(136\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.46601 + 4.27125i 0.871864 + 1.51011i 0.860066 + 0.510183i \(0.170422\pi\)
0.0117987 + 0.999930i \(0.496244\pi\)
\(3\) 3.00000 0.577350
\(4\) −8.16236 + 14.1376i −1.02030 + 1.76720i
\(5\) 11.8437 1.05933 0.529666 0.848206i \(-0.322317\pi\)
0.529666 + 0.848206i \(0.322317\pi\)
\(6\) 7.39802 + 12.8137i 0.503371 + 0.871864i
\(7\) −12.5285 + 21.6999i −0.676473 + 1.17169i 0.299563 + 0.954077i \(0.403159\pi\)
−0.976036 + 0.217609i \(0.930174\pi\)
\(8\) −41.0576 −1.81451
\(9\) 9.00000 0.333333
\(10\) 29.2066 + 50.5874i 0.923595 + 1.59971i
\(11\) 12.1897 21.1131i 0.334120 0.578713i −0.649195 0.760622i \(-0.724894\pi\)
0.983315 + 0.181909i \(0.0582276\pi\)
\(12\) −24.4871 + 42.4129i −0.589068 + 1.02030i
\(13\) −1.08813 1.88470i −0.0232148 0.0402093i 0.854185 0.519970i \(-0.174057\pi\)
−0.877399 + 0.479761i \(0.840724\pi\)
\(14\) −123.581 −2.35917
\(15\) 35.5311 0.611606
\(16\) −35.9494 62.2662i −0.561710 0.972910i
\(17\) −6.60849 11.4462i −0.0942821 0.163301i 0.815027 0.579423i \(-0.196722\pi\)
−0.909309 + 0.416122i \(0.863389\pi\)
\(18\) 22.1940 + 38.4412i 0.290621 + 0.503371i
\(19\) 34.8110 + 60.2944i 0.420326 + 0.728026i 0.995971 0.0896736i \(-0.0285824\pi\)
−0.575645 + 0.817700i \(0.695249\pi\)
\(20\) −96.6726 + 167.442i −1.08083 + 1.87206i
\(21\) −37.5854 + 65.0998i −0.390562 + 0.676473i
\(22\) 120.239 1.16523
\(23\) −52.0095 90.0832i −0.471510 0.816680i 0.527958 0.849270i \(-0.322958\pi\)
−0.999469 + 0.0325902i \(0.989624\pi\)
\(24\) −123.173 −1.04761
\(25\) 15.2733 0.122186
\(26\) 5.36667 9.29534i 0.0404804 0.0701141i
\(27\) 27.0000 0.192450
\(28\) −204.524 354.245i −1.38040 2.39093i
\(29\) −9.33678 + 16.1718i −0.0597861 + 0.103553i −0.894369 0.447329i \(-0.852375\pi\)
0.834583 + 0.550882i \(0.185709\pi\)
\(30\) 87.6199 + 151.762i 0.533238 + 0.923595i
\(31\) 32.5894 56.4465i 0.188814 0.327035i −0.756041 0.654524i \(-0.772869\pi\)
0.944855 + 0.327489i \(0.106202\pi\)
\(32\) 13.0724 22.6421i 0.0722157 0.125081i
\(33\) 36.5690 63.3393i 0.192904 0.334120i
\(34\) 32.5932 56.4530i 0.164402 0.284753i
\(35\) −148.383 + 257.007i −0.716610 + 1.24121i
\(36\) −73.4613 + 127.239i −0.340098 + 0.589068i
\(37\) 47.4397 + 82.1680i 0.210785 + 0.365090i 0.951960 0.306221i \(-0.0990647\pi\)
−0.741176 + 0.671311i \(0.765731\pi\)
\(38\) −171.688 + 297.373i −0.732935 + 1.26948i
\(39\) −3.26439 5.65409i −0.0134031 0.0232148i
\(40\) −486.274 −1.92217
\(41\) 213.236 369.336i 0.812241 1.40684i −0.0990507 0.995082i \(-0.531581\pi\)
0.911292 0.411761i \(-0.135086\pi\)
\(42\) −370.743 −1.36207
\(43\) 73.4294 0.260416 0.130208 0.991487i \(-0.458436\pi\)
0.130208 + 0.991487i \(0.458436\pi\)
\(44\) 198.993 + 344.666i 0.681802 + 1.18092i
\(45\) 106.593 0.353111
\(46\) 256.512 444.291i 0.822186 1.42407i
\(47\) 234.747 406.593i 0.728539 1.26187i −0.228962 0.973435i \(-0.573533\pi\)
0.957501 0.288431i \(-0.0931334\pi\)
\(48\) −107.848 186.799i −0.324303 0.561710i
\(49\) −142.425 246.687i −0.415232 0.719203i
\(50\) 37.6639 + 65.2359i 0.106530 + 0.184515i
\(51\) −19.8255 34.3387i −0.0544338 0.0942821i
\(52\) 35.5268 0.0947439
\(53\) 205.002 0.531305 0.265653 0.964069i \(-0.414413\pi\)
0.265653 + 0.964069i \(0.414413\pi\)
\(54\) 66.5821 + 115.324i 0.167790 + 0.290621i
\(55\) 144.371 250.057i 0.353944 0.613050i
\(56\) 514.389 890.948i 1.22747 2.12603i
\(57\) 104.433 + 180.883i 0.242675 + 0.420326i
\(58\) −92.0982 −0.208501
\(59\) 743.979 1.64166 0.820829 0.571175i \(-0.193512\pi\)
0.820829 + 0.571175i \(0.193512\pi\)
\(60\) −290.018 + 502.325i −0.624019 + 1.08083i
\(61\) 21.6336 + 37.4706i 0.0454083 + 0.0786494i 0.887836 0.460160i \(-0.152208\pi\)
−0.842428 + 0.538809i \(0.818874\pi\)
\(62\) 321.463 0.658480
\(63\) −112.756 + 195.299i −0.225491 + 0.390562i
\(64\) −446.244 −0.871571
\(65\) −12.8875 22.3218i −0.0245922 0.0425950i
\(66\) 360.717 0.672746
\(67\) 280.752 + 471.107i 0.511930 + 0.859027i
\(68\) 215.764 0.384782
\(69\) −156.029 270.250i −0.272227 0.471510i
\(70\) −1463.66 −2.49915
\(71\) −509.735 + 882.887i −0.852034 + 1.47577i 0.0273353 + 0.999626i \(0.491298\pi\)
−0.879369 + 0.476140i \(0.842036\pi\)
\(72\) −369.519 −0.604836
\(73\) −587.407 1017.42i −0.941792 1.63123i −0.762050 0.647518i \(-0.775807\pi\)
−0.179742 0.983714i \(-0.557526\pi\)
\(74\) −233.973 + 405.253i −0.367552 + 0.636618i
\(75\) 45.8198 0.0705442
\(76\) −1136.56 −1.71543
\(77\) 305.435 + 529.029i 0.452046 + 0.782967i
\(78\) 16.1000 27.8860i 0.0233714 0.0404804i
\(79\) −199.347 + 345.278i −0.283902 + 0.491732i −0.972342 0.233561i \(-0.924962\pi\)
0.688441 + 0.725293i \(0.258296\pi\)
\(80\) −425.774 737.463i −0.595038 1.03064i
\(81\) 81.0000 0.111111
\(82\) 2103.37 2.83266
\(83\) 534.279 + 925.398i 0.706563 + 1.22380i 0.966125 + 0.258076i \(0.0830885\pi\)
−0.259562 + 0.965726i \(0.583578\pi\)
\(84\) −613.571 1062.74i −0.796977 1.38040i
\(85\) −78.2690 135.566i −0.0998761 0.172990i
\(86\) 181.077 + 313.635i 0.227047 + 0.393257i
\(87\) −28.0103 + 48.5153i −0.0345175 + 0.0597861i
\(88\) −500.479 + 866.854i −0.606264 + 1.05008i
\(89\) −653.789 −0.778669 −0.389334 0.921097i \(-0.627295\pi\)
−0.389334 + 0.921097i \(0.627295\pi\)
\(90\) 262.860 + 455.286i 0.307865 + 0.533238i
\(91\) 54.5303 0.0628168
\(92\) 1698.08 1.92432
\(93\) 97.7682 169.340i 0.109012 0.188814i
\(94\) 2315.55 2.54075
\(95\) 412.291 + 714.109i 0.445265 + 0.771222i
\(96\) 39.2173 67.9264i 0.0416938 0.0722157i
\(97\) 380.011 + 658.198i 0.397776 + 0.688967i 0.993451 0.114258i \(-0.0364489\pi\)
−0.595676 + 0.803225i \(0.703116\pi\)
\(98\) 702.440 1216.66i 0.724052 1.25410i
\(99\) 109.707 190.018i 0.111373 0.192904i
\(100\) −124.666 + 215.928i −0.124666 + 0.215928i
\(101\) 818.248 1417.25i 0.806126 1.39625i −0.109403 0.993998i \(-0.534894\pi\)
0.915528 0.402253i \(-0.131773\pi\)
\(102\) 97.7795 169.359i 0.0949178 0.164402i
\(103\) 203.559 352.574i 0.194731 0.337283i −0.752082 0.659070i \(-0.770950\pi\)
0.946812 + 0.321787i \(0.104283\pi\)
\(104\) 44.6760 + 77.3811i 0.0421235 + 0.0729600i
\(105\) −445.150 + 771.022i −0.413735 + 0.716610i
\(106\) 505.536 + 875.614i 0.463226 + 0.802331i
\(107\) −208.689 −0.188549 −0.0942744 0.995546i \(-0.530053\pi\)
−0.0942744 + 0.995546i \(0.530053\pi\)
\(108\) −220.384 + 381.716i −0.196356 + 0.340098i
\(109\) −1400.57 −1.23074 −0.615369 0.788239i \(-0.710993\pi\)
−0.615369 + 0.788239i \(0.710993\pi\)
\(110\) 1424.08 1.23437
\(111\) 142.319 + 246.504i 0.121697 + 0.210785i
\(112\) 1801.56 1.51993
\(113\) 736.971 1276.47i 0.613525 1.06266i −0.377116 0.926166i \(-0.623084\pi\)
0.990641 0.136491i \(-0.0435825\pi\)
\(114\) −515.065 + 892.118i −0.423160 + 0.732935i
\(115\) −615.986 1066.92i −0.499487 0.865136i
\(116\) −152.420 264.000i −0.121999 0.211308i
\(117\) −9.79316 16.9623i −0.00773828 0.0134031i
\(118\) 1834.66 + 3177.72i 1.43130 + 2.47909i
\(119\) 331.177 0.255117
\(120\) −1458.82 −1.10976
\(121\) 368.324 + 637.957i 0.276728 + 0.479306i
\(122\) −106.697 + 184.805i −0.0791797 + 0.137143i
\(123\) 639.708 1108.01i 0.468948 0.812241i
\(124\) 532.013 + 921.474i 0.385292 + 0.667345i
\(125\) −1299.57 −0.929897
\(126\) −1112.23 −0.786391
\(127\) 903.773 1565.38i 0.631471 1.09374i −0.355780 0.934570i \(-0.615785\pi\)
0.987251 0.159171i \(-0.0508820\pi\)
\(128\) −1205.02 2087.16i −0.832107 1.44125i
\(129\) 220.288 0.150351
\(130\) 63.5612 110.091i 0.0428822 0.0742741i
\(131\) −1893.87 −1.26312 −0.631558 0.775329i \(-0.717584\pi\)
−0.631558 + 0.775329i \(0.717584\pi\)
\(132\) 596.978 + 1034.00i 0.393639 + 0.681802i
\(133\) −1744.51 −1.13736
\(134\) −1319.88 + 2360.91i −0.850896 + 1.52203i
\(135\) 319.780 0.203869
\(136\) 271.329 + 469.956i 0.171076 + 0.296312i
\(137\) 899.730 0.561089 0.280544 0.959841i \(-0.409485\pi\)
0.280544 + 0.959841i \(0.409485\pi\)
\(138\) 769.535 1332.87i 0.474690 0.822186i
\(139\) 835.115 0.509594 0.254797 0.966995i \(-0.417991\pi\)
0.254797 + 0.966995i \(0.417991\pi\)
\(140\) −2422.32 4195.58i −1.46231 2.53279i
\(141\) 704.240 1219.78i 0.420622 0.728539i
\(142\) −5028.04 −2.97143
\(143\) −53.0557 −0.0310262
\(144\) −323.545 560.396i −0.187237 0.324303i
\(145\) −110.582 + 191.534i −0.0633333 + 0.109697i
\(146\) 2897.10 5017.92i 1.64223 2.84443i
\(147\) −427.274 740.060i −0.239734 0.415232i
\(148\) −1548.88 −0.860251
\(149\) −1348.31 −0.741330 −0.370665 0.928767i \(-0.620870\pi\)
−0.370665 + 0.928767i \(0.620870\pi\)
\(150\) 112.992 + 195.708i 0.0615050 + 0.106530i
\(151\) −1271.16 2201.71i −0.685068 1.18657i −0.973415 0.229047i \(-0.926439\pi\)
0.288347 0.957526i \(-0.406894\pi\)
\(152\) −1429.26 2475.55i −0.762685 1.32101i
\(153\) −59.4764 103.016i −0.0314274 0.0544338i
\(154\) −1506.41 + 2609.18i −0.788247 + 1.36528i
\(155\) 385.979 668.536i 0.200017 0.346439i
\(156\) 106.580 0.0547004
\(157\) −66.9625 115.982i −0.0340394 0.0589580i 0.848504 0.529189i \(-0.177504\pi\)
−0.882543 + 0.470231i \(0.844171\pi\)
\(158\) −1966.36 −0.990095
\(159\) 615.006 0.306749
\(160\) 154.826 268.167i 0.0765005 0.132503i
\(161\) 2606.40 1.27586
\(162\) 199.746 + 345.971i 0.0968738 + 0.167790i
\(163\) −827.140 + 1432.65i −0.397464 + 0.688428i −0.993412 0.114595i \(-0.963443\pi\)
0.595948 + 0.803023i \(0.296776\pi\)
\(164\) 3481.02 + 6029.31i 1.65745 + 2.87079i
\(165\) 433.112 750.172i 0.204350 0.353944i
\(166\) −2635.07 + 4564.07i −1.23205 + 2.13398i
\(167\) −182.078 + 315.369i −0.0843690 + 0.146131i −0.905122 0.425152i \(-0.860221\pi\)
0.820753 + 0.571283i \(0.193554\pi\)
\(168\) 1543.17 2672.84i 0.708678 1.22747i
\(169\) 1096.13 1898.56i 0.498922 0.864159i
\(170\) 386.024 668.613i 0.174157 0.301648i
\(171\) 313.299 + 542.650i 0.140109 + 0.242675i
\(172\) −599.357 + 1038.12i −0.265701 + 0.460207i
\(173\) −2033.81 3522.67i −0.893803 1.54811i −0.835279 0.549826i \(-0.814694\pi\)
−0.0585236 0.998286i \(-0.518639\pi\)
\(174\) −276.294 −0.120378
\(175\) −191.350 + 331.429i −0.0826556 + 0.143164i
\(176\) −1752.85 −0.750714
\(177\) 2231.94 0.947811
\(178\) −1612.25 2792.49i −0.678893 1.17588i
\(179\) −1250.67 −0.522232 −0.261116 0.965307i \(-0.584090\pi\)
−0.261116 + 0.965307i \(0.584090\pi\)
\(180\) −870.053 + 1506.98i −0.360277 + 0.624019i
\(181\) 97.2319 168.411i 0.0399292 0.0691594i −0.845370 0.534181i \(-0.820620\pi\)
0.885299 + 0.465022i \(0.153953\pi\)
\(182\) 134.472 + 232.913i 0.0547678 + 0.0948606i
\(183\) 64.9009 + 112.412i 0.0262165 + 0.0454083i
\(184\) 2135.39 + 3698.60i 0.855560 + 1.48187i
\(185\) 561.862 + 973.173i 0.223291 + 0.386752i
\(186\) 964.388 0.380174
\(187\) −322.221 −0.126006
\(188\) 3832.17 + 6637.52i 1.48665 + 2.57495i
\(189\) −338.268 + 585.898i −0.130187 + 0.225491i
\(190\) −2033.42 + 3521.99i −0.776422 + 1.34480i
\(191\) 759.632 + 1315.72i 0.287775 + 0.498441i 0.973278 0.229628i \(-0.0737511\pi\)
−0.685503 + 0.728070i \(0.740418\pi\)
\(192\) −1338.73 −0.503201
\(193\) −3681.66 −1.37312 −0.686558 0.727075i \(-0.740879\pi\)
−0.686558 + 0.727075i \(0.740879\pi\)
\(194\) −1874.22 + 3246.24i −0.693613 + 1.20137i
\(195\) −38.6624 66.9653i −0.0141983 0.0245922i
\(196\) 4650.08 1.69464
\(197\) −2656.11 + 4600.52i −0.960609 + 1.66382i −0.239635 + 0.970863i \(0.577028\pi\)
−0.720975 + 0.692961i \(0.756306\pi\)
\(198\) 1082.15 0.388410
\(199\) −1010.10 1749.54i −0.359819 0.623225i 0.628111 0.778124i \(-0.283828\pi\)
−0.987930 + 0.154898i \(0.950495\pi\)
\(200\) −627.084 −0.221708
\(201\) 842.255 + 1413.32i 0.295563 + 0.495960i
\(202\) 8071.21 2.81133
\(203\) −233.951 405.215i −0.0808873 0.140101i
\(204\) 647.291 0.222154
\(205\) 2525.51 4374.30i 0.860434 1.49032i
\(206\) 2007.91 0.679115
\(207\) −468.086 810.749i −0.157170 0.272227i
\(208\) −78.2353 + 135.507i −0.0260800 + 0.0451719i
\(209\) 1697.34 0.561757
\(210\) −4390.97 −1.44288
\(211\) −1348.08 2334.94i −0.439837 0.761820i 0.557840 0.829949i \(-0.311630\pi\)
−0.997677 + 0.0681288i \(0.978297\pi\)
\(212\) −1673.30 + 2898.24i −0.542088 + 0.938925i
\(213\) −1529.21 + 2648.66i −0.491922 + 0.852034i
\(214\) −514.628 891.362i −0.164389 0.284730i
\(215\) 869.676 0.275867
\(216\) −1108.56 −0.349202
\(217\) 816.590 + 1414.38i 0.255455 + 0.442461i
\(218\) −3453.82 5982.18i −1.07304 1.85855i
\(219\) −1762.22 3052.26i −0.543744 0.941792i
\(220\) 2356.81 + 4082.12i 0.722255 + 1.25098i
\(221\) −14.3818 + 24.9100i −0.00437748 + 0.00758203i
\(222\) −701.919 + 1215.76i −0.212206 + 0.367552i
\(223\) −3105.53 −0.932563 −0.466281 0.884636i \(-0.654407\pi\)
−0.466281 + 0.884636i \(0.654407\pi\)
\(224\) 327.555 + 567.342i 0.0977040 + 0.169228i
\(225\) 137.459 0.0407287
\(226\) 7269.49 2.13964
\(227\) −1609.37 + 2787.52i −0.470564 + 0.815040i −0.999433 0.0336629i \(-0.989283\pi\)
0.528870 + 0.848703i \(0.322616\pi\)
\(228\) −3409.68 −0.990402
\(229\) −1853.54 3210.42i −0.534870 0.926422i −0.999170 0.0407441i \(-0.987027\pi\)
0.464299 0.885678i \(-0.346306\pi\)
\(230\) 3038.05 5262.05i 0.870969 1.50856i
\(231\) 916.306 + 1587.09i 0.260989 + 0.452046i
\(232\) 383.346 663.975i 0.108482 0.187897i
\(233\) −2134.98 + 3697.89i −0.600288 + 1.03973i 0.392490 + 0.919756i \(0.371614\pi\)
−0.992777 + 0.119972i \(0.961719\pi\)
\(234\) 48.3000 83.6580i 0.0134935 0.0233714i
\(235\) 2780.27 4815.57i 0.771765 1.33674i
\(236\) −6072.62 + 10518.1i −1.67498 + 2.90114i
\(237\) −598.040 + 1035.83i −0.163911 + 0.283902i
\(238\) 816.684 + 1414.54i 0.222428 + 0.385256i
\(239\) 2848.18 4933.18i 0.770850 1.33515i −0.166248 0.986084i \(-0.553165\pi\)
0.937098 0.349067i \(-0.113502\pi\)
\(240\) −1277.32 2212.39i −0.343545 0.595038i
\(241\) −4830.04 −1.29100 −0.645499 0.763761i \(-0.723350\pi\)
−0.645499 + 0.763761i \(0.723350\pi\)
\(242\) −1816.58 + 3146.41i −0.482538 + 0.835780i
\(243\) 243.000 0.0641500
\(244\) −706.327 −0.185319
\(245\) −1686.83 2921.68i −0.439869 0.761875i
\(246\) 6310.10 1.63544
\(247\) 75.7578 131.216i 0.0195156 0.0338020i
\(248\) −1338.04 + 2317.56i −0.342604 + 0.593408i
\(249\) 1602.84 + 2776.19i 0.407934 + 0.706563i
\(250\) −3204.75 5550.79i −0.810744 1.40425i
\(251\) 2129.94 + 3689.17i 0.535621 + 0.927722i 0.999133 + 0.0416319i \(0.0132557\pi\)
−0.463512 + 0.886091i \(0.653411\pi\)
\(252\) −1840.71 3188.21i −0.460135 0.796977i
\(253\) −2535.91 −0.630164
\(254\) 8914.83 2.20223
\(255\) −234.807 406.698i −0.0576635 0.0998761i
\(256\) 4158.19 7202.20i 1.01518 1.75835i
\(257\) −3647.43 + 6317.54i −0.885294 + 1.53337i −0.0399173 + 0.999203i \(0.512709\pi\)
−0.845377 + 0.534171i \(0.820624\pi\)
\(258\) 543.232 + 940.905i 0.131086 + 0.227047i
\(259\) −2377.39 −0.570361
\(260\) 420.769 0.100365
\(261\) −84.0310 + 145.546i −0.0199287 + 0.0345175i
\(262\) −4670.29 8089.18i −1.10127 1.90745i
\(263\) −4557.48 −1.06854 −0.534270 0.845314i \(-0.679414\pi\)
−0.534270 + 0.845314i \(0.679414\pi\)
\(264\) −1501.44 + 2600.56i −0.350026 + 0.606264i
\(265\) 2427.98 0.562829
\(266\) −4301.98 7451.25i −0.991621 1.71754i
\(267\) −1961.37 −0.449565
\(268\) −8951.93 + 123.820i −2.04040 + 0.0282221i
\(269\) 8015.80 1.81685 0.908424 0.418051i \(-0.137287\pi\)
0.908424 + 0.418051i \(0.137287\pi\)
\(270\) 788.579 + 1365.86i 0.177746 + 0.307865i
\(271\) 1134.10 0.254212 0.127106 0.991889i \(-0.459431\pi\)
0.127106 + 0.991889i \(0.459431\pi\)
\(272\) −475.143 + 822.972i −0.105918 + 0.183456i
\(273\) 163.591 0.0362673
\(274\) 2218.74 + 3842.97i 0.489193 + 0.847307i
\(275\) 186.176 322.466i 0.0408248 0.0707107i
\(276\) 5094.25 1.11101
\(277\) −4483.83 −0.972590 −0.486295 0.873795i \(-0.661652\pi\)
−0.486295 + 0.873795i \(0.661652\pi\)
\(278\) 2059.40 + 3566.98i 0.444297 + 0.769545i
\(279\) 293.305 508.019i 0.0629380 0.109012i
\(280\) 6092.27 10552.1i 1.30030 2.25218i
\(281\) −776.601 1345.11i −0.164869 0.285561i 0.771740 0.635938i \(-0.219387\pi\)
−0.936609 + 0.350377i \(0.886053\pi\)
\(282\) 6946.64 1.46690
\(283\) 1141.41 0.239751 0.119876 0.992789i \(-0.461750\pi\)
0.119876 + 0.992789i \(0.461750\pi\)
\(284\) −8321.29 14412.9i −1.73865 3.01144i
\(285\) 1236.87 + 2142.33i 0.257074 + 0.445265i
\(286\) −130.836 226.614i −0.0270506 0.0468530i
\(287\) 5343.04 + 9254.42i 1.09892 + 1.90338i
\(288\) 117.652 203.779i 0.0240719 0.0416938i
\(289\) 2369.16 4103.50i 0.482222 0.835233i
\(290\) −1090.78 −0.220872
\(291\) 1140.03 + 1974.59i 0.229656 + 0.397776i
\(292\) 19178.5 3.84362
\(293\) 1297.80 0.258765 0.129383 0.991595i \(-0.458700\pi\)
0.129383 + 0.991595i \(0.458700\pi\)
\(294\) 2107.32 3649.98i 0.418032 0.724052i
\(295\) 8811.46 1.73906
\(296\) −1947.76 3373.62i −0.382471 0.662459i
\(297\) 329.121 570.054i 0.0643014 0.111373i
\(298\) −3324.95 5758.98i −0.646339 1.11949i
\(299\) −113.186 + 196.044i −0.0218921 + 0.0379182i
\(300\) −373.998 + 647.783i −0.0719759 + 0.124666i
\(301\) −919.957 + 1593.41i −0.176164 + 0.305125i
\(302\) 6269.36 10858.8i 1.19457 2.06906i
\(303\) 2454.74 4251.74i 0.465417 0.806126i
\(304\) 2502.87 4335.10i 0.472203 0.817879i
\(305\) 256.222 + 443.790i 0.0481025 + 0.0833159i
\(306\) 293.338 508.077i 0.0548008 0.0949178i
\(307\) 4925.87 + 8531.86i 0.915747 + 1.58612i 0.805804 + 0.592183i \(0.201734\pi\)
0.109943 + 0.993938i \(0.464933\pi\)
\(308\) −9972.29 −1.84488
\(309\) 610.677 1057.72i 0.112428 0.194731i
\(310\) 3807.31 0.697550
\(311\) 3352.19 0.611207 0.305604 0.952159i \(-0.401142\pi\)
0.305604 + 0.952159i \(0.401142\pi\)
\(312\) 134.028 + 232.143i 0.0243200 + 0.0421235i
\(313\) 6712.49 1.21218 0.606090 0.795396i \(-0.292737\pi\)
0.606090 + 0.795396i \(0.292737\pi\)
\(314\) 330.260 572.027i 0.0593555 0.102807i
\(315\) −1335.45 + 2313.07i −0.238870 + 0.413735i
\(316\) −3254.28 5636.57i −0.579327 1.00342i
\(317\) 286.957 + 497.024i 0.0508426 + 0.0880620i 0.890327 0.455322i \(-0.150476\pi\)
−0.839484 + 0.543384i \(0.817143\pi\)
\(318\) 1516.61 + 2626.84i 0.267444 + 0.463226i
\(319\) 227.624 + 394.257i 0.0399514 + 0.0691979i
\(320\) −5285.18 −0.923283
\(321\) −626.067 −0.108859
\(322\) 6427.39 + 11132.6i 1.11237 + 1.92669i
\(323\) 460.097 796.911i 0.0792584 0.137280i
\(324\) −661.151 + 1145.15i −0.113366 + 0.196356i
\(325\) −16.6193 28.7854i −0.00283653 0.00491301i
\(326\) −8158.93 −1.38614
\(327\) −4201.71 −0.710567
\(328\) −8754.97 + 15164.1i −1.47382 + 2.55273i
\(329\) 5882.03 + 10188.0i 0.985674 + 1.70724i
\(330\) 4272.23 0.712661
\(331\) 3229.87 5594.31i 0.536344 0.928975i −0.462753 0.886487i \(-0.653138\pi\)
0.999097 0.0424881i \(-0.0135284\pi\)
\(332\) −17443.9 −2.88361
\(333\) 426.957 + 739.512i 0.0702616 + 0.121697i
\(334\) −1796.02 −0.294233
\(335\) 3325.14 + 5579.65i 0.542304 + 0.909996i
\(336\) 5404.69 0.877530
\(337\) −270.868 469.158i −0.0437838 0.0758358i 0.843303 0.537438i \(-0.180608\pi\)
−0.887087 + 0.461603i \(0.847275\pi\)
\(338\) 10812.3 1.73997
\(339\) 2210.91 3829.41i 0.354219 0.613525i
\(340\) 2555.44 0.407612
\(341\) −794.507 1376.13i −0.126173 0.218538i
\(342\) −1545.19 + 2676.36i −0.244312 + 0.423160i
\(343\) −1457.08 −0.229373
\(344\) −3014.84 −0.472526
\(345\) −1847.96 3200.75i −0.288379 0.499487i
\(346\) 10030.8 17373.8i 1.55855 2.69949i
\(347\) −143.702 + 248.899i −0.0222315 + 0.0385061i −0.876927 0.480623i \(-0.840410\pi\)
0.854696 + 0.519129i \(0.173744\pi\)
\(348\) −457.261 791.999i −0.0704361 0.121999i
\(349\) −11228.2 −1.72215 −0.861074 0.508479i \(-0.830208\pi\)
−0.861074 + 0.508479i \(0.830208\pi\)
\(350\) −1887.48 −0.288258
\(351\) −29.3795 50.8868i −0.00446770 0.00773828i
\(352\) −318.697 552.000i −0.0482574 0.0835843i
\(353\) −5167.60 8950.54i −0.779160 1.34955i −0.932426 0.361360i \(-0.882313\pi\)
0.153266 0.988185i \(-0.451021\pi\)
\(354\) 5503.97 + 9533.15i 0.826363 + 1.43130i
\(355\) −6037.15 + 10456.7i −0.902588 + 1.56333i
\(356\) 5336.46 9243.03i 0.794472 1.37607i
\(357\) 993.531 0.147292
\(358\) −3084.16 5341.92i −0.455315 0.788629i
\(359\) 477.406 0.0701853 0.0350927 0.999384i \(-0.488827\pi\)
0.0350927 + 0.999384i \(0.488827\pi\)
\(360\) −4376.47 −0.640723
\(361\) 1005.89 1742.25i 0.146652 0.254009i
\(362\) 959.097 0.139251
\(363\) 1104.97 + 1913.87i 0.159769 + 0.276728i
\(364\) −445.096 + 770.930i −0.0640917 + 0.111010i
\(365\) −6957.08 12050.0i −0.997671 1.72802i
\(366\) −320.092 + 554.416i −0.0457144 + 0.0791797i
\(367\) 534.369 925.554i 0.0760050 0.131645i −0.825518 0.564376i \(-0.809117\pi\)
0.901523 + 0.432731i \(0.142450\pi\)
\(368\) −3739.43 + 6476.88i −0.529704 + 0.917475i
\(369\) 1919.13 3324.02i 0.270747 0.468948i
\(370\) −2771.11 + 4799.70i −0.389359 + 0.674390i
\(371\) −2568.36 + 4448.53i −0.359414 + 0.622523i
\(372\) 1596.04 + 2764.42i 0.222448 + 0.385292i
\(373\) −1986.99 + 3441.56i −0.275824 + 0.477741i −0.970343 0.241734i \(-0.922284\pi\)
0.694519 + 0.719474i \(0.255617\pi\)
\(374\) −794.599 1376.29i −0.109860 0.190284i
\(375\) −3898.71 −0.536876
\(376\) −9638.14 + 16693.7i −1.32194 + 2.28967i
\(377\) 40.6385 0.00555169
\(378\) −3336.69 −0.454023
\(379\) 4873.06 + 8440.39i 0.660454 + 1.14394i 0.980496 + 0.196537i \(0.0629697\pi\)
−0.320042 + 0.947403i \(0.603697\pi\)
\(380\) −13461.1 −1.81721
\(381\) 2711.32 4696.14i 0.364580 0.631471i
\(382\) −3746.51 + 6489.15i −0.501802 + 0.869146i
\(383\) 1192.88 + 2066.14i 0.159148 + 0.275652i 0.934562 0.355802i \(-0.115792\pi\)
−0.775414 + 0.631453i \(0.782459\pi\)
\(384\) −3615.06 6261.47i −0.480417 0.832107i
\(385\) 3617.48 + 6265.67i 0.478868 + 0.829423i
\(386\) −9078.99 15725.3i −1.19717 2.07356i
\(387\) 660.864 0.0868052
\(388\) −12407.1 −1.62339
\(389\) −1061.36 1838.33i −0.138337 0.239607i 0.788530 0.614996i \(-0.210842\pi\)
−0.926867 + 0.375389i \(0.877509\pi\)
\(390\) 190.684 330.274i 0.0247580 0.0428822i
\(391\) −687.410 + 1190.63i −0.0889100 + 0.153997i
\(392\) 5847.62 + 10128.4i 0.753442 + 1.30500i
\(393\) −5681.61 −0.729260
\(394\) −26199.9 −3.35008
\(395\) −2361.00 + 4089.37i −0.300746 + 0.520908i
\(396\) 1790.94 + 3101.99i 0.227267 + 0.393639i
\(397\) 3305.75 0.417912 0.208956 0.977925i \(-0.432993\pi\)
0.208956 + 0.977925i \(0.432993\pi\)
\(398\) 4981.82 8628.77i 0.627427 1.08674i
\(399\) −5233.54 −0.656653
\(400\) −549.065 951.009i −0.0686331 0.118876i
\(401\) 10699.5 1.33243 0.666217 0.745758i \(-0.267913\pi\)
0.666217 + 0.745758i \(0.267913\pi\)
\(402\) −3959.63 + 7082.73i −0.491265 + 0.878743i
\(403\) −141.846 −0.0175331
\(404\) 13357.7 + 23136.2i 1.64497 + 2.84918i
\(405\) 959.340 0.117704
\(406\) 1153.85 1998.52i 0.141046 0.244298i
\(407\) 2313.09 0.281710
\(408\) 813.987 + 1409.87i 0.0987705 + 0.171076i
\(409\) 746.830 1293.55i 0.0902894 0.156386i −0.817343 0.576151i \(-0.804554\pi\)
0.907633 + 0.419765i \(0.137887\pi\)
\(410\) 24911.6 3.00073
\(411\) 2699.19 0.323945
\(412\) 3323.04 + 5755.68i 0.397365 + 0.688257i
\(413\) −9320.91 + 16144.3i −1.11054 + 1.92351i
\(414\) 2308.60 3998.62i 0.274062 0.474690i
\(415\) 6327.84 + 10960.1i 0.748485 + 1.29641i
\(416\) −56.8980 −0.00670590
\(417\) 2505.35 0.294214
\(418\) 4185.64 + 7249.75i 0.489776 + 0.848317i
\(419\) 7177.13 + 12431.2i 0.836816 + 1.44941i 0.892544 + 0.450961i \(0.148919\pi\)
−0.0557280 + 0.998446i \(0.517748\pi\)
\(420\) −7266.95 12586.7i −0.844264 1.46231i
\(421\) 904.385 + 1566.44i 0.104696 + 0.181339i 0.913614 0.406583i \(-0.133280\pi\)
−0.808918 + 0.587922i \(0.799946\pi\)
\(422\) 6648.74 11516.0i 0.766957 1.32841i
\(423\) 2112.72 3659.34i 0.242846 0.420622i
\(424\) −8416.89 −0.964058
\(425\) −100.933 174.821i −0.0115200 0.0199531i
\(426\) −15084.1 −1.71556
\(427\) −1084.14 −0.122870
\(428\) 1703.40 2950.37i 0.192376 0.333204i
\(429\) −159.167 −0.0179130
\(430\) 2144.62 + 3714.60i 0.240519 + 0.416590i
\(431\) −5613.63 + 9723.09i −0.627376 + 1.08665i 0.360700 + 0.932682i \(0.382538\pi\)
−0.988076 + 0.153965i \(0.950796\pi\)
\(432\) −970.635 1681.19i −0.108101 0.187237i
\(433\) −4180.33 + 7240.54i −0.463958 + 0.803598i −0.999154 0.0411296i \(-0.986904\pi\)
0.535196 + 0.844728i \(0.320238\pi\)
\(434\) −4027.43 + 6975.71i −0.445444 + 0.771532i
\(435\) −331.746 + 574.601i −0.0365655 + 0.0633333i
\(436\) 11432.0 19800.7i 1.25572 2.17496i
\(437\) 3621.01 6271.77i 0.396376 0.686544i
\(438\) 8691.30 15053.8i 0.948142 1.64223i
\(439\) 6488.24 + 11238.0i 0.705391 + 1.22177i 0.966550 + 0.256478i \(0.0825620\pi\)
−0.261159 + 0.965296i \(0.584105\pi\)
\(440\) −5927.52 + 10266.8i −0.642235 + 1.11238i
\(441\) −1281.82 2220.18i −0.138411 0.239734i
\(442\) −141.862 −0.0152663
\(443\) −2642.75 + 4577.38i −0.283433 + 0.490920i −0.972228 0.234036i \(-0.924807\pi\)
0.688795 + 0.724956i \(0.258140\pi\)
\(444\) −4646.64 −0.496666
\(445\) −7743.28 −0.824869
\(446\) −7658.25 13264.5i −0.813069 1.40828i
\(447\) −4044.94 −0.428007
\(448\) 5590.75 9683.47i 0.589594 1.02121i
\(449\) 315.985 547.302i 0.0332121 0.0575251i −0.848942 0.528487i \(-0.822760\pi\)
0.882154 + 0.470962i \(0.156093\pi\)
\(450\) 338.975 + 587.123i 0.0355099 + 0.0615050i
\(451\) −5198.55 9004.16i −0.542772 0.940109i
\(452\) 12030.8 + 20838.0i 1.25195 + 2.16845i
\(453\) −3813.47 6605.12i −0.395524 0.685068i
\(454\) −15874.9 −1.64107
\(455\) 645.841 0.0665439
\(456\) −4287.77 7426.64i −0.440336 0.762685i
\(457\) 4438.33 7687.42i 0.454303 0.786876i −0.544345 0.838862i \(-0.683222\pi\)
0.998648 + 0.0519857i \(0.0165550\pi\)
\(458\) 9141.67 15833.8i 0.932669 1.61543i
\(459\) −178.429 309.049i −0.0181446 0.0314274i
\(460\) 20111.6 2.03850
\(461\) −4742.65 −0.479148 −0.239574 0.970878i \(-0.577008\pi\)
−0.239574 + 0.970878i \(0.577008\pi\)
\(462\) −4519.23 + 7827.54i −0.455094 + 0.788247i
\(463\) 5020.82 + 8696.31i 0.503968 + 0.872898i 0.999989 + 0.00458796i \(0.00146040\pi\)
−0.496021 + 0.868310i \(0.665206\pi\)
\(464\) 1342.61 0.134330
\(465\) 1157.94 2005.61i 0.115480 0.200017i
\(466\) −21059.5 −2.09348
\(467\) −4073.04 7054.72i −0.403593 0.699044i 0.590564 0.806991i \(-0.298905\pi\)
−0.994157 + 0.107947i \(0.965572\pi\)
\(468\) 319.741 0.0315813
\(469\) −13740.4 + 190.052i −1.35282 + 0.0187117i
\(470\) 27424.6 2.69150
\(471\) −200.887 347.947i −0.0196527 0.0340394i
\(472\) −30546.0 −2.97880
\(473\) 895.079 1550.32i 0.0870101 0.150706i
\(474\) −5899.07 −0.571632
\(475\) 531.678 + 920.893i 0.0513580 + 0.0889546i
\(476\) −2703.19 + 4682.06i −0.260295 + 0.450844i
\(477\) 1845.02 0.177102
\(478\) 28094.5 2.68831
\(479\) 1988.35 + 3443.92i 0.189666 + 0.328511i 0.945139 0.326669i \(-0.105926\pi\)
−0.755473 + 0.655180i \(0.772593\pi\)
\(480\) 464.478 804.500i 0.0441676 0.0765005i
\(481\) 103.241 178.819i 0.00978667 0.0169510i
\(482\) −11910.9 20630.3i −1.12557 1.94955i
\(483\) 7819.19 0.736616
\(484\) −12025.6 −1.12938
\(485\) 4500.73 + 7795.50i 0.421377 + 0.729846i
\(486\) 599.239 + 1037.91i 0.0559301 + 0.0968738i
\(487\) 5097.32 + 8828.81i 0.474295 + 0.821502i 0.999567 0.0294320i \(-0.00936985\pi\)
−0.525272 + 0.850934i \(0.676037\pi\)
\(488\) −888.226 1538.45i −0.0823937 0.142710i
\(489\) −2481.42 + 4297.95i −0.229476 + 0.397464i
\(490\) 8319.48 14409.8i 0.767012 1.32850i
\(491\) 4877.69 0.448324 0.224162 0.974552i \(-0.428036\pi\)
0.224162 + 0.974552i \(0.428036\pi\)
\(492\) 10443.1 + 18087.9i 0.956930 + 1.65745i
\(493\) 246.808 0.0225470
\(494\) 747.276 0.0680598
\(495\) 1299.34 2250.52i 0.117981 0.204350i
\(496\) −4686.28 −0.424234
\(497\) −12772.4 22122.4i −1.15276 1.99663i
\(498\) −7905.20 + 13692.2i −0.711327 + 1.23205i
\(499\) −5833.54 10104.0i −0.523337 0.906447i −0.999631 0.0271605i \(-0.991353\pi\)
0.476294 0.879286i \(-0.341980\pi\)
\(500\) 10607.6 18372.8i 0.948770 1.64332i
\(501\) −546.234 + 946.106i −0.0487105 + 0.0843690i
\(502\) −10504.9 + 18195.0i −0.933978 + 1.61770i
\(503\) 5531.99 9581.69i 0.490376 0.849357i −0.509562 0.860434i \(-0.670193\pi\)
0.999939 + 0.0110771i \(0.00352603\pi\)
\(504\) 4629.50 8018.53i 0.409155 0.708678i
\(505\) 9691.08 16785.4i 0.853955 1.47909i
\(506\) −6253.58 10831.5i −0.549418 0.951620i
\(507\) 3288.40 5695.67i 0.288053 0.498922i
\(508\) 14753.8 + 25554.4i 1.28857 + 2.23188i
\(509\) −6428.09 −0.559764 −0.279882 0.960034i \(-0.590295\pi\)
−0.279882 + 0.960034i \(0.590295\pi\)
\(510\) 1158.07 2005.84i 0.100549 0.174157i
\(511\) 29437.2 2.54839
\(512\) 21736.2 1.87620
\(513\) 939.897 + 1627.95i 0.0808918 + 0.140109i
\(514\) −35978.3 −3.08742
\(515\) 2410.89 4175.78i 0.206285 0.357295i
\(516\) −1798.07 + 3114.35i −0.153402 + 0.265701i
\(517\) −5722.96 9912.46i −0.486839 0.843229i
\(518\) −5862.64 10154.4i −0.497278 0.861310i
\(519\) −6101.44 10568.0i −0.516037 0.893803i
\(520\) 529.129 + 916.479i 0.0446228 + 0.0772890i
\(521\) −16960.5 −1.42621 −0.713103 0.701060i \(-0.752711\pi\)
−0.713103 + 0.701060i \(0.752711\pi\)
\(522\) −828.883 −0.0695005
\(523\) 6992.10 + 12110.7i 0.584595 + 1.01255i 0.994926 + 0.100612i \(0.0320800\pi\)
−0.410331 + 0.911937i \(0.634587\pi\)
\(524\) 15458.5 26774.8i 1.28875 2.23218i
\(525\) −574.051 + 994.286i −0.0477212 + 0.0826556i
\(526\) −11238.8 19466.1i −0.931622 1.61362i
\(527\) −861.467 −0.0712070
\(528\) −5258.54 −0.433425
\(529\) 673.514 1166.56i 0.0553558 0.0958790i
\(530\) 5987.42 + 10370.5i 0.490711 + 0.849936i
\(531\) 6695.81 0.547219
\(532\) 14239.4 24663.3i 1.16044 2.00994i
\(533\) −928.114 −0.0754242
\(534\) −4836.74 8377.48i −0.391959 0.678893i
\(535\) −2471.65 −0.199736
\(536\) −11527.0 19342.5i −0.928900 1.55871i
\(537\) −3752.01 −0.301511
\(538\) 19767.0 + 34237.5i 1.58404 + 2.74365i
\(539\) −6944.43 −0.554949
\(540\) −2610.16 + 4520.93i −0.208006 + 0.360277i
\(541\) 478.667 0.0380397 0.0190199 0.999819i \(-0.493945\pi\)
0.0190199 + 0.999819i \(0.493945\pi\)
\(542\) 2796.69 + 4844.00i 0.221638 + 0.383889i
\(543\) 291.696 505.232i 0.0230531 0.0399292i
\(544\) −345.556 −0.0272346
\(545\) −16587.9 −1.30376
\(546\) 403.416 + 698.738i 0.0316202 + 0.0547678i
\(547\) −8860.85 + 15347.4i −0.692619 + 1.19965i 0.278358 + 0.960477i \(0.410210\pi\)
−0.970977 + 0.239174i \(0.923123\pi\)
\(548\) −7343.92 + 12720.0i −0.572476 + 0.991558i
\(549\) 194.703 + 337.235i 0.0151361 + 0.0262165i
\(550\) 1836.44 0.142375
\(551\) −1300.09 −0.100519
\(552\) 6406.17 + 11095.8i 0.493958 + 0.855560i
\(553\) −4995.01 8651.61i −0.384104 0.665287i
\(554\) −11057.2 19151.6i −0.847967 1.46872i
\(555\) 1685.58 + 2919.52i 0.128917 + 0.223291i
\(556\) −6816.51 + 11806.5i −0.519936 + 0.900556i
\(557\) −5599.84 + 9699.21i −0.425984 + 0.737825i −0.996512 0.0834529i \(-0.973405\pi\)
0.570528 + 0.821278i \(0.306739\pi\)
\(558\) 2893.16 0.219493
\(559\) −79.9007 138.392i −0.00604551 0.0104711i
\(560\) 21337.2 1.61011
\(561\) −966.663 −0.0727497
\(562\) 3830.20 6634.11i 0.287486 0.497941i
\(563\) 2736.43 0.204843 0.102422 0.994741i \(-0.467341\pi\)
0.102422 + 0.994741i \(0.467341\pi\)
\(564\) 11496.5 + 19912.6i 0.858317 + 1.48665i
\(565\) 8728.46 15118.1i 0.649928 1.12571i
\(566\) 2814.72 + 4875.23i 0.209031 + 0.362052i
\(567\) −1014.81 + 1757.69i −0.0751637 + 0.130187i
\(568\) 20928.5 36249.3i 1.54602 2.67779i
\(569\) 2592.25 4489.91i 0.190989 0.330803i −0.754589 0.656197i \(-0.772164\pi\)
0.945578 + 0.325395i \(0.105497\pi\)
\(570\) −6100.27 + 10566.0i −0.448267 + 0.776422i
\(571\) 6515.50 11285.2i 0.477522 0.827093i −0.522146 0.852856i \(-0.674868\pi\)
0.999668 + 0.0257633i \(0.00820162\pi\)
\(572\) 433.060 750.082i 0.0316558 0.0548295i
\(573\) 2278.90 + 3947.16i 0.166147 + 0.287775i
\(574\) −26351.9 + 45642.9i −1.91622 + 3.31898i
\(575\) −794.355 1375.86i −0.0576120 0.0997869i
\(576\) −4016.20 −0.290524
\(577\) 5360.72 9285.05i 0.386776 0.669916i −0.605238 0.796045i \(-0.706922\pi\)
0.992014 + 0.126129i \(0.0402553\pi\)
\(578\) 23369.4 1.68173
\(579\) −11045.0 −0.792769
\(580\) −1805.22 3126.73i −0.129237 0.223846i
\(581\) −26774.8 −1.91188
\(582\) −5622.65 + 9738.71i −0.400458 + 0.693613i
\(583\) 2498.90 4328.23i 0.177520 0.307473i
\(584\) 24117.6 + 41772.8i 1.70889 + 2.95988i
\(585\) −115.987 200.896i −0.00819741 0.0141983i
\(586\) 3200.38 + 5543.21i 0.225608 + 0.390765i
\(587\) 2286.50 + 3960.33i 0.160773 + 0.278467i 0.935146 0.354262i \(-0.115268\pi\)
−0.774373 + 0.632729i \(0.781935\pi\)
\(588\) 13950.3 0.978399
\(589\) 4537.88 0.317454
\(590\) 21729.1 + 37635.9i 1.51623 + 2.62618i
\(591\) −7968.33 + 13801.6i −0.554608 + 0.960609i
\(592\) 3410.86 5907.78i 0.236800 0.410149i
\(593\) −1041.60 1804.11i −0.0721306 0.124934i 0.827704 0.561165i \(-0.189647\pi\)
−0.899835 + 0.436231i \(0.856313\pi\)
\(594\) 3246.45 0.224249
\(595\) 3922.36 0.270254
\(596\) 11005.4 19062.0i 0.756376 1.31008i
\(597\) −3030.30 5248.63i −0.207742 0.359819i
\(598\) −1116.47 −0.0763477
\(599\) 8840.23 15311.7i 0.603008 1.04444i −0.389355 0.921088i \(-0.627302\pi\)
0.992363 0.123353i \(-0.0393648\pi\)
\(600\) −1881.25 −0.128003
\(601\) 2813.06 + 4872.37i 0.190927 + 0.330696i 0.945558 0.325454i \(-0.105517\pi\)
−0.754631 + 0.656150i \(0.772184\pi\)
\(602\) −9074.47 −0.614365
\(603\) 2526.77 + 4239.96i 0.170643 + 0.286342i
\(604\) 41502.6 2.79589
\(605\) 4362.32 + 7555.77i 0.293147 + 0.507745i
\(606\) 24213.6 1.62312
\(607\) 3081.75 5337.75i 0.206070 0.356923i −0.744403 0.667730i \(-0.767266\pi\)
0.950473 + 0.310807i \(0.100599\pi\)
\(608\) 1820.26 0.121417
\(609\) −701.853 1215.64i −0.0467003 0.0808873i
\(610\) −1263.69 + 2188.78i −0.0838777 + 0.145280i
\(611\) −1021.74 −0.0676516
\(612\) 1941.87 0.128261
\(613\) 12439.1 + 21545.2i 0.819593 + 1.41958i 0.905982 + 0.423315i \(0.139134\pi\)
−0.0863895 + 0.996261i \(0.527533\pi\)
\(614\) −24294.5 + 42079.2i −1.59681 + 2.76576i
\(615\) 7576.52 13122.9i 0.496772 0.860434i
\(616\) −12540.4 21720.7i −0.820242 1.42070i
\(617\) −9595.44 −0.626091 −0.313045 0.949738i \(-0.601349\pi\)
−0.313045 + 0.949738i \(0.601349\pi\)
\(618\) 6023.73 0.392087
\(619\) 3977.11 + 6888.56i 0.258245 + 0.447294i 0.965772 0.259393i \(-0.0835225\pi\)
−0.707527 + 0.706686i \(0.750189\pi\)
\(620\) 6301.00 + 10913.7i 0.408152 + 0.706941i
\(621\) −1404.26 2432.25i −0.0907422 0.157170i
\(622\) 8266.52 + 14318.0i 0.532890 + 0.922992i
\(623\) 8190.97 14187.2i 0.526748 0.912355i
\(624\) −234.706 + 406.522i −0.0150573 + 0.0260800i
\(625\) −17300.9 −1.10726
\(626\) 16553.0 + 28670.7i 1.05686 + 1.83053i
\(627\) 5092.01 0.324331
\(628\) 2186.29 0.138921
\(629\) 627.010 1086.01i 0.0397465 0.0688429i
\(630\) −13172.9 −0.833049
\(631\) −15502.1 26850.5i −0.978020 1.69398i −0.669586 0.742734i \(-0.733529\pi\)
−0.308433 0.951246i \(-0.599805\pi\)
\(632\) 8184.70 14176.3i 0.515142 0.892252i
\(633\) −4044.24 7004.83i −0.253940 0.439837i
\(634\) −1415.28 + 2451.33i −0.0886558 + 0.153556i
\(635\) 10704.0 18539.9i 0.668938 1.15864i
\(636\) −5019.90 + 8694.72i −0.312975 + 0.542088i
\(637\) −309.953 + 536.854i −0.0192791 + 0.0333924i
\(638\) −1122.65 + 1944.48i −0.0696645 + 0.120662i
\(639\) −4587.62 + 7945.98i −0.284011 + 0.491922i
\(640\) −14271.9 24719.6i −0.881478 1.52677i
\(641\) −4248.49 + 7358.60i −0.261787 + 0.453428i −0.966717 0.255849i \(-0.917645\pi\)
0.704930 + 0.709277i \(0.250978\pi\)
\(642\) −1543.88 2674.09i −0.0949101 0.164389i
\(643\) 129.803 0.00796098 0.00398049 0.999992i \(-0.498733\pi\)
0.00398049 + 0.999992i \(0.498733\pi\)
\(644\) −21274.4 + 36848.3i −1.30175 + 2.25470i
\(645\) 2609.03 0.159272
\(646\) 4538.40 0.276410
\(647\) 2559.96 + 4433.98i 0.155552 + 0.269425i 0.933260 0.359202i \(-0.116951\pi\)
−0.777708 + 0.628626i \(0.783618\pi\)
\(648\) −3325.67 −0.201612
\(649\) 9068.85 15707.7i 0.548511 0.950048i
\(650\) 81.9665 141.970i 0.00494614 0.00856696i
\(651\) 2449.77 + 4243.13i 0.147487 + 0.255455i
\(652\) −13502.8 23387.6i −0.811061 1.40480i
\(653\) −5323.03 9219.75i −0.318999 0.552522i 0.661281 0.750139i \(-0.270013\pi\)
−0.980279 + 0.197617i \(0.936680\pi\)
\(654\) −10361.4 17946.5i −0.619518 1.07304i
\(655\) −22430.4 −1.33806
\(656\) −30662.9 −1.82498
\(657\) −5286.67 9156.77i −0.313931 0.543744i
\(658\) −29010.2 + 50247.2i −1.71875 + 2.97696i
\(659\) 7038.61 12191.2i 0.416062 0.720641i −0.579477 0.814989i \(-0.696743\pi\)
0.995539 + 0.0943473i \(0.0300764\pi\)
\(660\) 7070.43 + 12246.4i 0.416994 + 0.722255i
\(661\) −17432.5 −1.02579 −0.512895 0.858451i \(-0.671427\pi\)
−0.512895 + 0.858451i \(0.671427\pi\)
\(662\) 31859.5 1.87048
\(663\) −43.1454 + 74.7300i −0.00252734 + 0.00437748i
\(664\) −21936.2 37994.6i −1.28206 2.22060i
\(665\) −20661.5 −1.20484
\(666\) −2105.76 + 3647.28i −0.122517 + 0.212206i
\(667\) 1942.41 0.112759
\(668\) −2972.38 5148.31i −0.172163 0.298194i
\(669\) −9316.58 −0.538415
\(670\) −15632.2 + 27961.9i −0.901382 + 1.61233i
\(671\) 1054.83 0.0606872
\(672\) 982.665 + 1702.03i 0.0564094 + 0.0977040i
\(673\) 15891.1 0.910186 0.455093 0.890444i \(-0.349606\pi\)
0.455093 + 0.890444i \(0.349606\pi\)
\(674\) 1335.93 2313.89i 0.0763471 0.132237i
\(675\) 412.378 0.0235147
\(676\) 17894.1 + 30993.4i 1.01810 + 1.76339i
\(677\) 4106.34 7112.38i 0.233116 0.403768i −0.725608 0.688109i \(-0.758441\pi\)
0.958723 + 0.284340i \(0.0917746\pi\)
\(678\) 21808.5 1.23532
\(679\) −19043.8 −1.07634
\(680\) 3213.54 + 5566.02i 0.181226 + 0.313893i
\(681\) −4828.12 + 8362.56i −0.271680 + 0.470564i
\(682\) 3918.52 6787.07i 0.220011 0.381071i
\(683\) −604.443 1046.93i −0.0338629 0.0586523i 0.848597 0.529039i \(-0.177448\pi\)
−0.882460 + 0.470387i \(0.844114\pi\)
\(684\) −10229.0 −0.571809
\(685\) 10656.1 0.594380
\(686\) −3593.17 6223.55i −0.199982 0.346379i
\(687\) −5560.62 9631.27i −0.308807 0.534870i
\(688\) −2639.74 4572.17i −0.146278 0.253361i
\(689\) −223.069 386.366i −0.0123342 0.0213634i
\(690\) 9114.14 15786.2i 0.502854 0.870969i
\(691\) 8014.30 13881.2i 0.441213 0.764204i −0.556566 0.830803i \(-0.687881\pi\)
0.997780 + 0.0665990i \(0.0212148\pi\)
\(692\) 66402.9 3.64777
\(693\) 2748.92 + 4761.26i 0.150682 + 0.260989i
\(694\) −1417.48 −0.0775314
\(695\) 9890.86 0.539830
\(696\) 1150.04 1991.92i 0.0626323 0.108482i
\(697\) −5636.68 −0.306319
\(698\) −27688.7 47958.3i −1.50148 2.60064i
\(699\) −6404.93 + 11093.7i −0.346576 + 0.600288i
\(700\) −3123.74 5410.48i −0.168666 0.292139i
\(701\) 11677.2 20225.4i 0.629158 1.08973i −0.358563 0.933506i \(-0.616733\pi\)
0.987721 0.156228i \(-0.0499336\pi\)
\(702\) 144.900 250.974i 0.00779045 0.0134935i
\(703\) −3302.85 + 5720.70i −0.177197 + 0.306914i
\(704\) −5439.56 + 9421.60i −0.291209 + 0.504389i
\(705\) 8340.81 14446.7i 0.445579 0.771765i
\(706\) 25486.7 44144.2i 1.35864 2.35324i
\(707\) 20502.8 + 35511.8i 1.09064 + 1.88905i
\(708\) −18217.9 + 31554.3i −0.967047 + 1.67498i
\(709\) 1684.39 + 2917.45i 0.0892223 + 0.154537i 0.907183 0.420737i \(-0.138229\pi\)
−0.817960 + 0.575275i \(0.804895\pi\)
\(710\) −59550.6 −3.14774
\(711\) −1794.12 + 3107.50i −0.0946339 + 0.163911i
\(712\) 26843.0 1.41290
\(713\) −6779.84 −0.356111
\(714\) 2450.05 + 4243.62i 0.128419 + 0.222428i
\(715\) −628.376 −0.0328670
\(716\) 10208.4 17681.5i 0.532831 0.922890i
\(717\) 8544.53 14799.6i 0.445050 0.770850i
\(718\) 1177.29 + 2039.12i 0.0611921 + 0.105988i
\(719\) 3997.36 + 6923.64i 0.207339 + 0.359121i 0.950875 0.309574i \(-0.100186\pi\)
−0.743537 + 0.668695i \(0.766853\pi\)
\(720\) −3831.97 6637.17i −0.198346 0.343545i
\(721\) 5100.56 + 8834.43i 0.263460 + 0.456326i
\(722\) 9922.09 0.511443
\(723\) −14490.1 −0.745358
\(724\) 1587.28 + 2749.26i 0.0814792 + 0.141126i
\(725\) −142.603 + 246.996i −0.00730502 + 0.0126527i
\(726\) −5449.74 + 9439.23i −0.278593 + 0.482538i
\(727\) −10212.6 17688.7i −0.520996 0.902392i −0.999702 0.0244167i \(-0.992227\pi\)
0.478705 0.877976i \(-0.341106\pi\)
\(728\) −2238.89 −0.113982
\(729\) 729.000 0.0370370
\(730\) 34312.4 59430.8i 1.73967 3.01319i
\(731\) −485.258 840.491i −0.0245525 0.0425262i
\(732\) −2118.98 −0.106994
\(733\) −15003.5 + 25986.8i −0.756024 + 1.30947i 0.188840 + 0.982008i \(0.439527\pi\)
−0.944864 + 0.327464i \(0.893806\pi\)
\(734\) 5271.03 0.265064
\(735\) −5060.50 8765.05i −0.253958 0.439869i
\(736\) −2719.57 −0.136202
\(737\) 13368.8 184.913i 0.668176 0.00924199i
\(738\) 18930.3 0.944219
\(739\) 2988.50 + 5176.23i 0.148760 + 0.257660i 0.930769 0.365607i \(-0.119138\pi\)
−0.782009 + 0.623267i \(0.785805\pi\)
\(740\) −18344.5 −0.911292
\(741\) 227.273 393.649i 0.0112673 0.0195156i
\(742\) −25334.3 −1.25344
\(743\) 17393.2 + 30125.9i 0.858808 + 1.48750i 0.873067 + 0.487600i \(0.162128\pi\)
−0.0142596 + 0.999898i \(0.504539\pi\)
\(744\) −4014.13 + 6952.68i −0.197803 + 0.342604i
\(745\) −15969.0 −0.785315
\(746\) −19599.7 −0.961923
\(747\) 4808.51 + 8328.58i 0.235521 + 0.407934i
\(748\) 2630.09 4555.44i 0.128563 0.222678i
\(749\) 2614.55 4528.54i 0.127548 0.220920i
\(750\) −9614.24 16652.4i −0.468083 0.810744i
\(751\) 8619.86 0.418832 0.209416 0.977827i \(-0.432844\pi\)
0.209416 + 0.977827i \(0.432844\pi\)
\(752\) −33756.0 −1.63691
\(753\) 6389.83 + 11067.5i 0.309241 + 0.535621i
\(754\) 100.215 + 173.577i 0.00484032 + 0.00838369i
\(755\) −15055.2 26076.4i −0.725715 1.25698i
\(756\) −5522.14 9564.63i −0.265659 0.460135i
\(757\) 6641.36 11503.2i 0.318869 0.552298i −0.661383 0.750048i \(-0.730030\pi\)
0.980252 + 0.197750i \(0.0633635\pi\)
\(758\) −24034.0 + 41628.1i −1.15165 + 1.99472i
\(759\) −7607.74 −0.363826
\(760\) −16927.7 29319.6i −0.807937 1.39939i
\(761\) 22374.1 1.06578 0.532890 0.846184i \(-0.321106\pi\)
0.532890 + 0.846184i \(0.321106\pi\)
\(762\) 26744.5 1.27146
\(763\) 17547.0 30392.3i 0.832561 1.44204i
\(764\) −24801.6 −1.17446
\(765\) −704.421 1220.09i −0.0332920 0.0576635i
\(766\) −5883.32 + 10190.2i −0.277510 + 0.480662i
\(767\) −809.545 1402.17i −0.0381108 0.0660098i
\(768\) 12474.6 21606.6i 0.586117 1.01518i
\(769\) 2816.97 4879.14i 0.132097 0.228799i −0.792388 0.610018i \(-0.791162\pi\)
0.924485 + 0.381219i \(0.124496\pi\)
\(770\) −17841.5 + 30902.3i −0.835015 + 1.44629i
\(771\) −10942.3 + 18952.6i −0.511125 + 0.885294i
\(772\) 30051.0 52049.9i 1.40098 2.42658i
\(773\) −3954.02 + 6848.56i −0.183980 + 0.318662i −0.943232 0.332134i \(-0.892231\pi\)
0.759253 + 0.650796i \(0.225565\pi\)
\(774\) 1629.69 + 2822.71i 0.0756824 + 0.131086i
\(775\) 497.746 862.122i 0.0230704 0.0399592i
\(776\) −15602.3 27024.0i −0.721767 1.25014i
\(777\) −7132.16 −0.329298
\(778\) 5234.64 9066.67i 0.241222 0.417810i
\(779\) 29691.9 1.36562
\(780\) 1262.31 0.0579460
\(781\) 12427.0 + 21524.2i 0.569363 + 0.986166i
\(782\) −6780.62 −0.310070
\(783\) −252.093 + 436.638i −0.0115058 + 0.0199287i
\(784\) −10240.2 + 17736.5i −0.466480 + 0.807967i
\(785\) −793.084 1373.66i −0.0360591 0.0624561i
\(786\) −14010.9 24267.6i −0.635816 1.10127i
\(787\) 3512.87 + 6084.47i 0.159111 + 0.275588i 0.934548 0.355836i \(-0.115804\pi\)
−0.775437 + 0.631424i \(0.782471\pi\)
\(788\) −43360.3 75102.2i −1.96021 3.39518i
\(789\) −13672.4 −0.616922
\(790\) −23289.0 −1.04884
\(791\) 18466.2 + 31984.4i 0.830067 + 1.43772i
\(792\) −4504.31 + 7801.69i −0.202088 + 0.350026i
\(793\) 47.0804 81.5457i 0.00210829 0.00365167i
\(794\) 8152.00 + 14119.7i 0.364362 + 0.631094i
\(795\) 7283.95 0.324950
\(796\) 32979.2 1.46849
\(797\) 314.397 544.551i 0.0139730 0.0242020i −0.858954 0.512052i \(-0.828885\pi\)
0.872927 + 0.487850i \(0.162219\pi\)
\(798\) −12905.9 22353.7i −0.572513 0.991621i
\(799\) −6205.29 −0.274752
\(800\) 199.659 345.819i 0.00882375 0.0152832i
\(801\) −5884.10 −0.259556
\(802\) 26384.9 + 45700.1i 1.16170 + 2.01213i
\(803\) −28641.2 −1.25869
\(804\) −26855.8 + 371.460i −1.17802 + 0.0162940i
\(805\) 30869.4 1.35156
\(806\) −349.793 605.859i −0.0152865 0.0264770i
\(807\) 24047.4 1.04896
\(808\) −33595.3 + 58188.8i −1.46272 + 2.53351i
\(809\) 13716.3 0.596092 0.298046 0.954551i \(-0.403665\pi\)
0.298046 + 0.954551i \(0.403665\pi\)
\(810\) 2365.74 + 4097.58i 0.102622 + 0.177746i
\(811\) 6663.65 11541.8i 0.288523 0.499737i −0.684934 0.728605i \(-0.740169\pi\)
0.973457 + 0.228868i \(0.0735024\pi\)
\(812\) 7638.37 0.330116
\(813\) 3402.29 0.146769
\(814\) 5704.10 + 9879.80i 0.245613 + 0.425414i
\(815\) −9796.40 + 16967.9i −0.421046 + 0.729274i
\(816\) −1425.43 + 2468.92i −0.0611520 + 0.105918i
\(817\) 2556.15 + 4427.38i 0.109459 + 0.189589i
\(818\) 7366.75 0.314881
\(819\) 490.773 0.0209389
\(820\) 41228.2 + 71409.3i 1.75579 + 3.04112i
\(821\) 12155.9 + 21054.7i 0.516742 + 0.895023i 0.999811 + 0.0194409i \(0.00618861\pi\)
−0.483069 + 0.875582i \(0.660478\pi\)
\(822\) 6656.22 + 11528.9i 0.282436 + 0.489193i
\(823\) 18352.7 + 31787.9i 0.777323 + 1.34636i 0.933480 + 0.358630i \(0.116756\pi\)
−0.156157 + 0.987732i \(0.549911\pi\)
\(824\) −8357.65 + 14475.9i −0.353340 + 0.612003i
\(825\) 558.527 967.398i 0.0235702 0.0408248i
\(826\) −91941.6 −3.87295
\(827\) −8879.65 15380.0i −0.373369 0.646693i 0.616713 0.787188i \(-0.288464\pi\)
−0.990081 + 0.140495i \(0.955131\pi\)
\(828\) 15282.7 0.641440
\(829\) −41668.9 −1.74574 −0.872871 0.487950i \(-0.837745\pi\)
−0.872871 + 0.487950i \(0.837745\pi\)
\(830\) −31209.0 + 54055.5i −1.30515 + 2.26059i
\(831\) −13451.5 −0.561525
\(832\) 485.571 + 841.034i 0.0202334 + 0.0350452i
\(833\) −1882.42 + 3260.45i −0.0782979 + 0.135616i
\(834\) 6178.20 + 10700.9i 0.256515 + 0.444297i
\(835\) −2156.48 + 3735.13i −0.0893749 + 0.154802i
\(836\) −13854.3 + 23996.3i −0.573158 + 0.992739i
\(837\) 879.914 1524.06i 0.0363372 0.0629380i
\(838\) −35397.7 + 61310.6i −1.45918 + 2.52737i
\(839\) −930.363 + 1611.44i −0.0382833 + 0.0663086i −0.884532 0.466479i \(-0.845522\pi\)
0.846249 + 0.532788i \(0.178856\pi\)
\(840\) 18276.8 31656.4i 0.750726 1.30030i
\(841\) 12020.1 + 20819.5i 0.492851 + 0.853643i
\(842\) −4460.44 + 7725.71i −0.182562 + 0.316206i
\(843\) −2329.80 4035.34i −0.0951870 0.164869i
\(844\) 44014.1 1.79505
\(845\) 12982.3 22485.9i 0.528525 0.915431i
\(846\) 20839.9 0.846916
\(847\) −18458.2 −0.748795
\(848\) −7369.70 12764.7i −0.298439 0.516912i
\(849\) 3424.22 0.138421
\(850\) 497.804 862.221i 0.0200877 0.0347929i
\(851\) 4934.63 8547.04i 0.198775 0.344288i
\(852\) −24963.9 43238.7i −1.00381 1.73865i
\(853\) 11360.1 + 19676.3i 0.455993 + 0.789803i 0.998745 0.0500901i \(-0.0159508\pi\)
−0.542752 + 0.839893i \(0.682618\pi\)
\(854\) −2673.51 4630.65i −0.107126 0.185548i
\(855\) 3710.62 + 6426.98i 0.148422 + 0.257074i
\(856\) 8568.28 0.342123
\(857\) −32567.5 −1.29812 −0.649058 0.760739i \(-0.724837\pi\)
−0.649058 + 0.760739i \(0.724837\pi\)
\(858\) −392.507 679.842i −0.0156177 0.0270506i
\(859\) 15104.2 26161.2i 0.599939 1.03913i −0.392890 0.919585i \(-0.628525\pi\)
0.992829 0.119540i \(-0.0381420\pi\)
\(860\) −7098.61 + 12295.1i −0.281466 + 0.487513i
\(861\) 16029.1 + 27763.3i 0.634461 + 1.09892i
\(862\) −55373.0 −2.18795
\(863\) 1493.14 0.0588958 0.0294479 0.999566i \(-0.490625\pi\)
0.0294479 + 0.999566i \(0.490625\pi\)
\(864\) 352.956 611.337i 0.0138979 0.0240719i
\(865\) −24087.9 41721.4i −0.946835 1.63997i
\(866\) −41234.8 −1.61803
\(867\) 7107.47 12310.5i 0.278411 0.482222i
\(868\) −26661.2 −1.04256
\(869\) 4859.93 + 8417.65i 0.189714 + 0.328595i
\(870\) −3272.35 −0.127521
\(871\) 582.398 1041.76i 0.0226565 0.0405265i
\(872\) 57504.1 2.23318
\(873\) 3420.10 + 5923.78i 0.132592 + 0.229656i
\(874\) 35717.7 1.38235
\(875\) 16281.6 28200.6i 0.629050 1.08955i
\(876\) 57535.6 2.21912
\(877\) −848.168 1469.07i −0.0326574 0.0565644i 0.849235 0.528015i \(-0.177064\pi\)
−0.881892 + 0.471451i \(0.843730\pi\)
\(878\) −32000.1 + 55425.7i −1.23001 + 2.13044i
\(879\) 3893.39 0.149398
\(880\) −20760.2 −0.795256
\(881\) −15236.5 26390.3i −0.582667 1.00921i −0.995162 0.0982490i \(-0.968676\pi\)
0.412495 0.910960i \(-0.364657\pi\)
\(882\) 6321.96 10949.9i 0.241351 0.418032i
\(883\) −11408.6 + 19760.2i −0.434800 + 0.753096i −0.997279 0.0737157i \(-0.976514\pi\)
0.562479 + 0.826811i \(0.309848\pi\)
\(884\) −234.779 406.649i −0.00893265 0.0154718i
\(885\) 26434.4 1.00405
\(886\) −26068.1 −0.988460
\(887\) 2861.62 + 4956.47i 0.108324 + 0.187623i 0.915092 0.403246i \(-0.132118\pi\)
−0.806767 + 0.590869i \(0.798785\pi\)
\(888\) −5843.29 10120.9i −0.220820 0.382471i
\(889\) 22645.8 + 39223.6i 0.854347 + 1.47977i
\(890\) −19095.0 33073.5i −0.719174 1.24565i
\(891\) 987.362 1710.16i 0.0371244 0.0643014i
\(892\) 25348.4 43904.8i 0.951490 1.64803i
\(893\) 32687.1 1.22489
\(894\) −9974.85 17276.9i −0.373164 0.646339i
\(895\) −14812.6 −0.553217
\(896\) 60388.2 2.25159
\(897\) −339.559 + 588.133i −0.0126394 + 0.0218921i
\(898\) 3116.88 0.115826
\(899\) 608.560 + 1054.06i 0.0225769 + 0.0391043i
\(900\) −1121.99 + 1943.35i −0.0415553 + 0.0719759i
\(901\) −1354.75 2346.50i −0.0500926 0.0867629i
\(902\) 25639.3 44408.6i 0.946448 1.63930i
\(903\) −2759.87 + 4780.24i −0.101708 + 0.176164i
\(904\) −30258.3 + 52408.9i −1.11325 + 1.92820i
\(905\) 1151.59 1994.60i 0.0422983 0.0732628i
\(906\) 18808.1 32576.5i 0.689687 1.19457i
\(907\) −10469.4 + 18133.5i −0.383275 + 0.663852i −0.991528 0.129891i \(-0.958537\pi\)
0.608253 + 0.793743i \(0.291871\pi\)
\(908\) −26272.6 45505.5i −0.960228 1.66316i
\(909\) 7364.23 12755.2i 0.268709 0.465417i
\(910\) 1592.65 + 2758.55i 0.0580173 + 0.100489i
\(911\) −8566.35 −0.311543 −0.155772 0.987793i \(-0.549786\pi\)
−0.155772 + 0.987793i \(0.549786\pi\)
\(912\) 7508.62 13005.3i 0.272626 0.472203i
\(913\) 26050.7 0.944307
\(914\) 43779.8 1.58436
\(915\) 768.667 + 1331.37i 0.0277720 + 0.0481025i
\(916\) 60517.0 2.18290
\(917\) 23727.3 41096.8i 0.854464 1.47998i
\(918\) 880.015 1524.23i 0.0316393 0.0548008i
\(919\) −24192.3 41902.3i −0.868369 1.50406i −0.863662 0.504071i \(-0.831835\pi\)
−0.00470687 0.999989i \(-0.501498\pi\)
\(920\) 25290.9 + 43805.1i 0.906322 + 1.56980i
\(921\) 14777.6 + 25595.6i 0.528707 + 0.915747i
\(922\) −11695.4 20257.0i −0.417752 0.723568i
\(923\) 2218.63 0.0791193
\(924\) −29916.9 −1.06514
\(925\) 724.559 + 1254.97i 0.0257550 + 0.0446089i
\(926\) −24762.7 + 42890.3i −0.878784 + 1.52210i
\(927\) 1832.03 3173.17i 0.0649102 0.112428i
\(928\) 244.109 + 422.809i 0.00863498 + 0.0149562i
\(929\) −43880.5 −1.54970 −0.774850 0.632145i \(-0.782175\pi\)
−0.774850 + 0.632145i \(0.782175\pi\)
\(930\) 11421.9 0.402731
\(931\) 9915.89 17174.8i 0.349066 0.604599i
\(932\) −34852.9 60367.0i −1.22494 2.12166i
\(933\) 10056.6 0.352881
\(934\) 20088.3 34793.9i 0.703757 1.21894i
\(935\) −3816.29 −0.133482
\(936\) 402.084 + 696.430i 0.0140412 + 0.0243200i
\(937\) 50209.4 1.75056 0.875278 0.483621i \(-0.160679\pi\)
0.875278 + 0.483621i \(0.160679\pi\)
\(938\) −34695.6 58219.8i −1.20773 2.02659i
\(939\) 20137.5 0.699853
\(940\) 45387.1 + 78612.8i 1.57486 + 2.72773i
\(941\) −28729.9 −0.995291 −0.497646 0.867380i \(-0.665802\pi\)
−0.497646 + 0.867380i \(0.665802\pi\)
\(942\) 990.779 1716.08i 0.0342689 0.0593555i
\(943\) −44361.3 −1.53192
\(944\) −26745.6 46324.8i −0.922135 1.59718i
\(945\) −4006.35 + 6939.20i −0.137912 + 0.238870i
\(946\) 8829.08 0.303444
\(947\) 2641.58 0.0906440 0.0453220 0.998972i \(-0.485569\pi\)
0.0453220 + 0.998972i \(0.485569\pi\)
\(948\) −9762.83 16909.7i −0.334475 0.579327i
\(949\) −1278.35 + 2214.17i −0.0437271 + 0.0757375i
\(950\) −2622.24 + 4541.85i −0.0895544 + 0.155113i
\(951\) 860.871 + 1491.07i 0.0293540 + 0.0508426i
\(952\) −13597.3 −0.462912
\(953\) 30354.2 1.03176 0.515881 0.856660i \(-0.327465\pi\)
0.515881 + 0.856660i \(0.327465\pi\)
\(954\) 4549.82 + 7880.52i 0.154409 + 0.267444i
\(955\) 8996.86 + 15583.0i 0.304850 + 0.528015i
\(956\) 46495.7 + 80532.9i 1.57299 + 2.72450i
\(957\) 682.873 + 1182.77i 0.0230660 + 0.0399514i
\(958\) −9806.55 + 16985.4i −0.330726 + 0.572834i
\(959\) −11272.2 + 19524.1i −0.379561 + 0.657420i
\(960\) −15855.5 −0.533058
\(961\) 12771.4 + 22120.6i 0.428699 + 0.742528i
\(962\) 1018.37 0.0341306
\(963\) −1878.20 −0.0628496
\(964\) 39424.6 68285.3i 1.31720 2.28145i
\(965\) −43604.4 −1.45459
\(966\) 19282.2 + 33397.7i 0.642230 + 1.11237i
\(967\) −24001.0 + 41571.0i −0.798160 + 1.38245i 0.122653 + 0.992450i \(0.460860\pi\)
−0.920813 + 0.390004i \(0.872474\pi\)
\(968\) −15122.5 26193.0i −0.502125 0.869705i
\(969\) 1380.29 2390.73i 0.0457599 0.0792584i
\(970\) −22197.7 + 38447.5i −0.734767 + 1.27265i
\(971\) −3427.23 + 5936.14i −0.113270 + 0.196189i −0.917087 0.398687i \(-0.869466\pi\)
0.803817 + 0.594877i \(0.202799\pi\)
\(972\) −1983.45 + 3435.44i −0.0654520 + 0.113366i
\(973\) −10462.7 + 18121.9i −0.344727 + 0.597084i
\(974\) −25140.0 + 43543.8i −0.827041 + 1.43248i
\(975\) −49.8579 86.3563i −0.00163767 0.00283653i
\(976\) 1555.43 2694.09i 0.0510125 0.0883563i
\(977\) −28848.7 49967.4i −0.944680 1.63623i −0.756391 0.654120i \(-0.773039\pi\)
−0.188289 0.982114i \(-0.560294\pi\)
\(978\) −24476.8 −0.800287
\(979\) −7969.47 + 13803.5i −0.260169 + 0.450626i
\(980\) 55074.2 1.79518
\(981\) −12605.1 −0.410246
\(982\) 12028.4 + 20833.8i 0.390878 + 0.677020i
\(983\) 42444.3 1.37717 0.688587 0.725153i \(-0.258231\pi\)
0.688587 + 0.725153i \(0.258231\pi\)
\(984\) −26264.9 + 45492.2i −0.850909 + 1.47382i
\(985\) −31458.2 + 54487.2i −1.01761 + 1.76254i
\(986\) 608.630 + 1054.18i 0.0196579 + 0.0340486i
\(987\) 17646.1 + 30563.9i 0.569079 + 0.985674i
\(988\) 1236.72 + 2142.07i 0.0398233 + 0.0689760i
\(989\) −3819.03 6614.75i −0.122789 0.212676i
\(990\) 12816.7 0.411455
\(991\) −48278.3 −1.54754 −0.773769 0.633467i \(-0.781631\pi\)
−0.773769 + 0.633467i \(0.781631\pi\)
\(992\) −852.046 1475.79i −0.0272706 0.0472342i
\(993\) 9689.62 16782.9i 0.309658 0.536344i
\(994\) 62993.6 109108.i 2.01009 3.48159i
\(995\) −11963.3 20721.1i −0.381168 0.660203i
\(996\) −52331.7 −1.66485
\(997\) 26719.8 0.848770 0.424385 0.905482i \(-0.360490\pi\)
0.424385 + 0.905482i \(0.360490\pi\)
\(998\) 28771.1 49833.0i 0.912558 1.58060i
\(999\) 1280.87 + 2218.54i 0.0405656 + 0.0702616i
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 201.4.e.a.37.15 32
67.29 even 3 inner 201.4.e.a.163.15 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.4.e.a.37.15 32 1.1 even 1 trivial
201.4.e.a.163.15 yes 32 67.29 even 3 inner