Properties

Label 74.4.f.b.53.5
Level $74$
Weight $4$
Character 74.53
Analytic conductor $4.366$
Analytic rank $0$
Dimension $30$
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] = [74,4,Mod(7,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.7");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 74.f (of order \(9\), degree \(6\), 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: \(4.36614134042\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(5\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 53.5
Character \(\chi\) \(=\) 74.53
Dual form 74.4.f.b.7.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.87939 - 0.684040i) q^{2} +(6.95420 - 2.53112i) q^{3} +(3.06418 + 2.57115i) q^{4} +(2.65487 - 15.0565i) q^{5} -14.8010 q^{6} +(-1.00418 + 5.69497i) q^{7} +(-4.00000 - 6.92820i) q^{8} +(21.2711 - 17.8486i) q^{9} +O(q^{10})\) \(q+(-1.87939 - 0.684040i) q^{2} +(6.95420 - 2.53112i) q^{3} +(3.06418 + 2.57115i) q^{4} +(2.65487 - 15.0565i) q^{5} -14.8010 q^{6} +(-1.00418 + 5.69497i) q^{7} +(-4.00000 - 6.92820i) q^{8} +(21.2711 - 17.8486i) q^{9} +(-15.2888 + 26.4809i) q^{10} +(19.0761 + 33.0407i) q^{11} +(27.8168 + 10.1245i) q^{12} +(-55.8829 - 46.8913i) q^{13} +(5.78283 - 10.0162i) q^{14} +(-19.6474 - 111.426i) q^{15} +(2.77837 + 15.7569i) q^{16} +(91.0273 - 76.3810i) q^{17} +(-52.1858 + 18.9941i) q^{18} +(24.7038 - 8.99144i) q^{19} +(46.8475 - 39.3097i) q^{20} +(7.43142 + 42.1457i) q^{21} +(-13.2501 - 75.1451i) q^{22} +(-62.8740 + 108.901i) q^{23} +(-45.3529 - 38.0556i) q^{24} +(-102.188 - 37.1935i) q^{25} +(72.9500 + 126.353i) q^{26} +(2.83987 - 4.91879i) q^{27} +(-17.7196 + 14.8685i) q^{28} +(93.1453 + 161.332i) q^{29} +(-39.2947 + 222.851i) q^{30} +76.2804 q^{31} +(5.55674 - 31.5138i) q^{32} +(216.289 + 181.488i) q^{33} +(-223.323 + 81.2830i) q^{34} +(83.0804 + 30.2388i) q^{35} +111.070 q^{36} +(-108.141 + 197.379i) q^{37} -52.5784 q^{38} +(-507.309 - 184.645i) q^{39} +(-114.934 + 41.8325i) q^{40} +(32.1784 + 27.0009i) q^{41} +(14.8628 - 84.2914i) q^{42} +83.1778 q^{43} +(-26.5002 + 150.290i) q^{44} +(-212.265 - 367.654i) q^{45} +(192.657 - 161.659i) q^{46} +(-286.373 + 496.013i) q^{47} +(59.2040 + 102.544i) q^{48} +(290.890 + 105.875i) q^{49} +(166.609 + 139.802i) q^{50} +(439.693 - 761.570i) q^{51} +(-50.6705 - 287.367i) q^{52} +(-50.3034 - 285.285i) q^{53} +(-8.70186 + 7.30172i) q^{54} +(548.122 - 199.500i) q^{55} +(43.4727 - 15.8228i) q^{56} +(149.037 - 125.057i) q^{57} +(-64.6981 - 366.921i) q^{58} +(49.2888 + 279.530i) q^{59} +(226.289 - 391.945i) q^{60} +(-312.454 - 262.180i) q^{61} +(-143.360 - 52.1789i) q^{62} +(80.2873 + 139.062i) q^{63} +(-32.0000 + 55.4256i) q^{64} +(-854.381 + 716.911i) q^{65} +(-282.345 - 489.036i) q^{66} +(48.3369 - 274.132i) q^{67} +475.311 q^{68} +(-161.597 + 916.461i) q^{69} +(-135.456 - 113.661i) q^{70} +(934.672 - 340.193i) q^{71} +(-208.743 - 75.9763i) q^{72} -970.763 q^{73} +(338.253 - 296.979i) q^{74} -804.780 q^{75} +(98.8152 + 35.9658i) q^{76} +(-207.322 + 75.4590i) q^{77} +(827.124 + 694.039i) q^{78} +(-80.9291 + 458.972i) q^{79} +244.620 q^{80} +(-122.889 + 696.938i) q^{81} +(-42.0060 - 72.7565i) q^{82} +(402.112 - 337.412i) q^{83} +(-85.5917 + 148.249i) q^{84} +(-908.365 - 1573.33i) q^{85} +(-156.323 - 56.8970i) q^{86} +(1056.10 + 886.176i) q^{87} +(152.609 - 264.326i) q^{88} +(118.588 + 672.548i) q^{89} +(147.438 + 836.162i) q^{90} +(323.161 - 271.165i) q^{91} +(-472.658 + 172.033i) q^{92} +(530.469 - 193.075i) q^{93} +(877.498 - 736.308i) q^{94} +(-69.7944 - 395.824i) q^{95} +(-41.1227 - 233.218i) q^{96} +(-259.897 + 450.155i) q^{97} +(-474.272 - 397.961i) q^{98} +(995.500 + 362.332i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q + 6 q^{3} - 6 q^{5} - 36 q^{6} - 75 q^{7} - 120 q^{8} - 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q + 6 q^{3} - 6 q^{5} - 36 q^{6} - 75 q^{7} - 120 q^{8} - 48 q^{9} + 54 q^{10} - 21 q^{11} + 24 q^{12} - 159 q^{13} + 6 q^{14} - 69 q^{15} - 171 q^{17} + 192 q^{18} - 45 q^{19} - 24 q^{20} + 579 q^{21} + 42 q^{22} + 459 q^{23} + 48 q^{24} - 204 q^{25} + 264 q^{26} + 435 q^{27} + 96 q^{28} + 273 q^{29} - 138 q^{30} - 258 q^{31} - 318 q^{33} - 558 q^{34} - 753 q^{35} + 1296 q^{36} - 891 q^{37} - 2556 q^{38} - 504 q^{39} + 96 q^{40} + 648 q^{41} + 1158 q^{42} - 216 q^{43} + 84 q^{44} + 1731 q^{45} - 6 q^{46} + 48 q^{47} + 144 q^{48} + 1731 q^{49} + 240 q^{50} + 972 q^{51} + 48 q^{52} - 135 q^{53} + 360 q^{54} + 765 q^{55} + 408 q^{56} - 405 q^{57} - 762 q^{58} + 1836 q^{59} + 108 q^{60} - 684 q^{61} - 204 q^{62} - 3264 q^{63} - 960 q^{64} - 1350 q^{65} + 252 q^{66} + 1095 q^{67} - 432 q^{68} - 5823 q^{69} - 1146 q^{70} + 4179 q^{71} + 768 q^{72} - 2658 q^{73} - 1692 q^{74} - 10416 q^{75} - 180 q^{76} + 267 q^{77} + 1530 q^{78} + 4866 q^{79} - 864 q^{80} - 2076 q^{81} + 1800 q^{82} - 186 q^{83} + 504 q^{84} + 753 q^{85} + 648 q^{86} - 525 q^{87} - 168 q^{88} + 687 q^{89} + 768 q^{90} + 3990 q^{91} + 132 q^{92} + 3753 q^{93} + 6210 q^{94} + 9000 q^{95} - 384 q^{96} + 7428 q^{97} - 1542 q^{98} + 6324 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.87939 0.684040i −0.664463 0.241845i
\(3\) 6.95420 2.53112i 1.33834 0.487115i 0.429048 0.903282i \(-0.358849\pi\)
0.909288 + 0.416167i \(0.136627\pi\)
\(4\) 3.06418 + 2.57115i 0.383022 + 0.321394i
\(5\) 2.65487 15.0565i 0.237459 1.34669i −0.599915 0.800064i \(-0.704799\pi\)
0.837374 0.546631i \(-0.184090\pi\)
\(6\) −14.8010 −1.00708
\(7\) −1.00418 + 5.69497i −0.0542205 + 0.307500i −0.999842 0.0177690i \(-0.994344\pi\)
0.945622 + 0.325269i \(0.105455\pi\)
\(8\) −4.00000 6.92820i −0.176777 0.306186i
\(9\) 21.2711 17.8486i 0.787819 0.661059i
\(10\) −15.2888 + 26.4809i −0.483473 + 0.837401i
\(11\) 19.0761 + 33.0407i 0.522878 + 0.905651i 0.999646 + 0.0266214i \(0.00847486\pi\)
−0.476768 + 0.879029i \(0.658192\pi\)
\(12\) 27.8168 + 10.1245i 0.669168 + 0.243557i
\(13\) −55.8829 46.8913i −1.19224 1.00041i −0.999818 0.0190968i \(-0.993921\pi\)
−0.192423 0.981312i \(-0.561635\pi\)
\(14\) 5.78283 10.0162i 0.110395 0.191209i
\(15\) −19.6474 111.426i −0.338195 1.91800i
\(16\) 2.77837 + 15.7569i 0.0434120 + 0.246202i
\(17\) 91.0273 76.3810i 1.29867 1.08971i 0.308295 0.951291i \(-0.400241\pi\)
0.990373 0.138422i \(-0.0442030\pi\)
\(18\) −52.1858 + 18.9941i −0.683350 + 0.248719i
\(19\) 24.7038 8.99144i 0.298286 0.108567i −0.188542 0.982065i \(-0.560376\pi\)
0.486828 + 0.873498i \(0.338154\pi\)
\(20\) 46.8475 39.3097i 0.523771 0.439496i
\(21\) 7.43142 + 42.1457i 0.0772223 + 0.437950i
\(22\) −13.2501 75.1451i −0.128406 0.728227i
\(23\) −62.8740 + 108.901i −0.570006 + 0.987280i 0.426558 + 0.904460i \(0.359726\pi\)
−0.996565 + 0.0828196i \(0.973607\pi\)
\(24\) −45.3529 38.0556i −0.385734 0.323670i
\(25\) −102.188 37.1935i −0.817507 0.297548i
\(26\) 72.9500 + 126.353i 0.550256 + 0.953072i
\(27\) 2.83987 4.91879i 0.0202419 0.0350601i
\(28\) −17.7196 + 14.8685i −0.119596 + 0.100353i
\(29\) 93.1453 + 161.332i 0.596436 + 1.03306i 0.993342 + 0.115199i \(0.0367505\pi\)
−0.396906 + 0.917859i \(0.629916\pi\)
\(30\) −39.2947 + 222.851i −0.239140 + 1.35623i
\(31\) 76.2804 0.441947 0.220974 0.975280i \(-0.429076\pi\)
0.220974 + 0.975280i \(0.429076\pi\)
\(32\) 5.55674 31.5138i 0.0306970 0.174091i
\(33\) 216.289 + 181.488i 1.14094 + 0.957364i
\(34\) −223.323 + 81.2830i −1.12646 + 0.409997i
\(35\) 83.0804 + 30.2388i 0.401233 + 0.146037i
\(36\) 111.070 0.514213
\(37\) −108.141 + 197.379i −0.480492 + 0.876999i
\(38\) −52.5784 −0.224457
\(39\) −507.309 184.645i −2.08293 0.758126i
\(40\) −114.934 + 41.8325i −0.454316 + 0.165358i
\(41\) 32.1784 + 27.0009i 0.122571 + 0.102850i 0.702013 0.712164i \(-0.252285\pi\)
−0.579442 + 0.815014i \(0.696729\pi\)
\(42\) 14.8628 84.2914i 0.0546044 0.309677i
\(43\) 83.1778 0.294988 0.147494 0.989063i \(-0.452879\pi\)
0.147494 + 0.989063i \(0.452879\pi\)
\(44\) −26.5002 + 150.290i −0.0907967 + 0.514934i
\(45\) −212.265 367.654i −0.703170 1.21793i
\(46\) 192.657 161.659i 0.617516 0.518158i
\(47\) −286.373 + 496.013i −0.888762 + 1.53938i −0.0474213 + 0.998875i \(0.515100\pi\)
−0.841340 + 0.540506i \(0.818233\pi\)
\(48\) 59.2040 + 102.544i 0.178028 + 0.308354i
\(49\) 290.890 + 105.875i 0.848076 + 0.308675i
\(50\) 166.609 + 139.802i 0.471243 + 0.395419i
\(51\) 439.693 761.570i 1.20724 2.09100i
\(52\) −50.6705 287.367i −0.135130 0.766358i
\(53\) −50.3034 285.285i −0.130372 0.739375i −0.977971 0.208739i \(-0.933064\pi\)
0.847600 0.530636i \(-0.178047\pi\)
\(54\) −8.70186 + 7.30172i −0.0219291 + 0.0184007i
\(55\) 548.122 199.500i 1.34380 0.489102i
\(56\) 43.4727 15.8228i 0.103737 0.0377572i
\(57\) 149.037 125.057i 0.346323 0.290599i
\(58\) −64.6981 366.921i −0.146470 0.830674i
\(59\) 49.2888 + 279.530i 0.108760 + 0.616810i 0.989652 + 0.143491i \(0.0458329\pi\)
−0.880891 + 0.473318i \(0.843056\pi\)
\(60\) 226.289 391.945i 0.486897 0.843330i
\(61\) −312.454 262.180i −0.655829 0.550306i 0.253004 0.967465i \(-0.418581\pi\)
−0.908834 + 0.417159i \(0.863026\pi\)
\(62\) −143.360 52.1789i −0.293658 0.106883i
\(63\) 80.2873 + 139.062i 0.160559 + 0.278097i
\(64\) −32.0000 + 55.4256i −0.0625000 + 0.108253i
\(65\) −854.381 + 716.911i −1.63035 + 1.36803i
\(66\) −282.345 489.036i −0.526580 0.912064i
\(67\) 48.3369 274.132i 0.0881387 0.499859i −0.908496 0.417893i \(-0.862769\pi\)
0.996635 0.0819667i \(-0.0261201\pi\)
\(68\) 475.311 0.847646
\(69\) −161.597 + 916.461i −0.281942 + 1.59897i
\(70\) −135.456 113.661i −0.231286 0.194072i
\(71\) 934.672 340.193i 1.56233 0.568640i 0.591058 0.806629i \(-0.298710\pi\)
0.971268 + 0.237989i \(0.0764882\pi\)
\(72\) −208.743 75.9763i −0.341675 0.124360i
\(73\) −970.763 −1.55643 −0.778214 0.628000i \(-0.783874\pi\)
−0.778214 + 0.628000i \(0.783874\pi\)
\(74\) 338.253 296.979i 0.531367 0.466529i
\(75\) −804.780 −1.23904
\(76\) 98.8152 + 35.9658i 0.149143 + 0.0542836i
\(77\) −207.322 + 75.4590i −0.306838 + 0.111680i
\(78\) 827.124 + 694.039i 1.20068 + 1.00749i
\(79\) −80.9291 + 458.972i −0.115256 + 0.653650i 0.871367 + 0.490632i \(0.163234\pi\)
−0.986623 + 0.163018i \(0.947877\pi\)
\(80\) 244.620 0.341867
\(81\) −122.889 + 696.938i −0.168572 + 0.956019i
\(82\) −42.0060 72.7565i −0.0565705 0.0979830i
\(83\) 402.112 337.412i 0.531777 0.446214i −0.336937 0.941527i \(-0.609391\pi\)
0.868715 + 0.495313i \(0.164947\pi\)
\(84\) −85.5917 + 148.249i −0.111176 + 0.192563i
\(85\) −908.365 1573.33i −1.15913 2.00767i
\(86\) −156.323 56.8970i −0.196009 0.0713414i
\(87\) 1056.10 + 886.176i 1.30145 + 1.09205i
\(88\) 152.609 264.326i 0.184865 0.320196i
\(89\) 118.588 + 672.548i 0.141240 + 0.801011i 0.970310 + 0.241866i \(0.0777594\pi\)
−0.829070 + 0.559145i \(0.811129\pi\)
\(90\) 147.438 + 836.162i 0.172681 + 0.979325i
\(91\) 323.161 271.165i 0.372269 0.312371i
\(92\) −472.658 + 172.033i −0.535631 + 0.194954i
\(93\) 530.469 193.075i 0.591474 0.215279i
\(94\) 877.498 736.308i 0.962840 0.807919i
\(95\) −69.7944 395.824i −0.0753764 0.427481i
\(96\) −41.1227 233.218i −0.0437195 0.247945i
\(97\) −259.897 + 450.155i −0.272047 + 0.471199i −0.969386 0.245542i \(-0.921034\pi\)
0.697339 + 0.716742i \(0.254367\pi\)
\(98\) −474.272 397.961i −0.488864 0.410206i
\(99\) 995.500 + 362.332i 1.01062 + 0.367836i
\(100\) −217.493 376.709i −0.217493 0.376709i
\(101\) 668.906 1158.58i 0.658997 1.14142i −0.321879 0.946781i \(-0.604314\pi\)
0.980876 0.194635i \(-0.0623523\pi\)
\(102\) −1347.30 + 1130.52i −1.30786 + 1.09743i
\(103\) −208.341 360.856i −0.199305 0.345206i 0.748998 0.662572i \(-0.230535\pi\)
−0.948303 + 0.317366i \(0.897202\pi\)
\(104\) −101.341 + 574.733i −0.0955510 + 0.541897i
\(105\) 654.296 0.608122
\(106\) −100.607 + 570.569i −0.0921868 + 0.522817i
\(107\) −337.650 283.322i −0.305064 0.255979i 0.477384 0.878695i \(-0.341585\pi\)
−0.782448 + 0.622715i \(0.786029\pi\)
\(108\) 21.3488 7.77033i 0.0190212 0.00692315i
\(109\) −1626.54 592.012i −1.42931 0.520225i −0.492573 0.870271i \(-0.663944\pi\)
−0.936732 + 0.350047i \(0.886166\pi\)
\(110\) −1166.60 −1.01119
\(111\) −252.441 + 1646.33i −0.215861 + 1.40777i
\(112\) −92.5253 −0.0780609
\(113\) 93.4451 + 34.0112i 0.0777927 + 0.0283142i 0.380623 0.924730i \(-0.375709\pi\)
−0.302831 + 0.953044i \(0.597932\pi\)
\(114\) −365.641 + 133.082i −0.300398 + 0.109336i
\(115\) 1472.75 + 1235.78i 1.19421 + 1.00206i
\(116\) −129.396 + 733.842i −0.103570 + 0.587375i
\(117\) −2025.64 −1.60060
\(118\) 98.5775 559.061i 0.0769051 0.436150i
\(119\) 343.580 + 595.098i 0.264672 + 0.458425i
\(120\) −693.391 + 581.824i −0.527480 + 0.442608i
\(121\) −62.2934 + 107.895i −0.0468020 + 0.0810634i
\(122\) 407.879 + 706.468i 0.302686 + 0.524267i
\(123\) 292.118 + 106.322i 0.214141 + 0.0779411i
\(124\) 233.737 + 196.129i 0.169276 + 0.142039i
\(125\) 124.248 215.203i 0.0889043 0.153987i
\(126\) −55.7670 316.270i −0.0394295 0.223616i
\(127\) −331.622 1880.72i −0.231706 1.31407i −0.849440 0.527684i \(-0.823060\pi\)
0.617734 0.786387i \(-0.288051\pi\)
\(128\) 98.0537 82.2768i 0.0677094 0.0568149i
\(129\) 578.435 210.533i 0.394794 0.143693i
\(130\) 2096.11 762.921i 1.41416 0.514712i
\(131\) 1863.69 1563.82i 1.24299 1.04299i 0.245705 0.969345i \(-0.420981\pi\)
0.997284 0.0736468i \(-0.0234638\pi\)
\(132\) 196.115 + 1112.22i 0.129315 + 0.733383i
\(133\) 26.3991 + 149.716i 0.0172112 + 0.0976095i
\(134\) −278.361 + 482.136i −0.179453 + 0.310822i
\(135\) −66.5204 55.8172i −0.0424086 0.0355850i
\(136\) −893.292 325.132i −0.563229 0.204999i
\(137\) −89.3540 154.766i −0.0557228 0.0965147i 0.836818 0.547481i \(-0.184413\pi\)
−0.892541 + 0.450966i \(0.851080\pi\)
\(138\) 930.599 1611.84i 0.574042 0.994271i
\(139\) −1773.02 + 1487.74i −1.08191 + 0.907831i −0.996078 0.0884787i \(-0.971799\pi\)
−0.0858326 + 0.996310i \(0.527355\pi\)
\(140\) 176.825 + 306.269i 0.106746 + 0.184889i
\(141\) −736.027 + 4174.22i −0.439607 + 2.49314i
\(142\) −1989.31 −1.17563
\(143\) 483.297 2740.92i 0.282625 1.60284i
\(144\) 340.338 + 285.577i 0.196955 + 0.165265i
\(145\) 2676.39 974.126i 1.53284 0.557909i
\(146\) 1824.44 + 664.041i 1.03419 + 0.376414i
\(147\) 2290.89 1.28537
\(148\) −838.854 + 326.759i −0.465901 + 0.181483i
\(149\) −2859.71 −1.57233 −0.786164 0.618018i \(-0.787936\pi\)
−0.786164 + 0.618018i \(0.787936\pi\)
\(150\) 1512.49 + 550.502i 0.823296 + 0.299655i
\(151\) −2201.06 + 801.121i −1.18622 + 0.431750i −0.858396 0.512987i \(-0.828539\pi\)
−0.327828 + 0.944738i \(0.606317\pi\)
\(152\) −161.110 135.187i −0.0859719 0.0721390i
\(153\) 572.960 3249.42i 0.302752 1.71699i
\(154\) 441.255 0.230892
\(155\) 202.514 1148.52i 0.104944 0.595168i
\(156\) −1079.73 1870.15i −0.554153 0.959821i
\(157\) 317.291 266.239i 0.161290 0.135339i −0.558571 0.829457i \(-0.688650\pi\)
0.719861 + 0.694118i \(0.244206\pi\)
\(158\) 466.052 807.226i 0.234665 0.406452i
\(159\) −1071.91 1856.60i −0.534642 0.926026i
\(160\) −459.736 167.330i −0.227158 0.0826788i
\(161\) −557.052 467.422i −0.272682 0.228808i
\(162\) 707.689 1225.75i 0.343218 0.594471i
\(163\) −419.705 2380.27i −0.201680 1.14378i −0.902579 0.430524i \(-0.858329\pi\)
0.700899 0.713261i \(-0.252782\pi\)
\(164\) 29.1770 + 165.471i 0.0138923 + 0.0787874i
\(165\) 3306.79 2774.73i 1.56020 1.30917i
\(166\) −986.526 + 359.066i −0.461261 + 0.167885i
\(167\) −2601.64 + 946.918i −1.20551 + 0.438771i −0.865145 0.501522i \(-0.832774\pi\)
−0.340367 + 0.940293i \(0.610551\pi\)
\(168\) 262.268 220.069i 0.120443 0.101064i
\(169\) 542.598 + 3077.23i 0.246972 + 1.40065i
\(170\) 630.944 + 3578.26i 0.284654 + 1.61435i
\(171\) 364.993 632.186i 0.163226 0.282716i
\(172\) 254.872 + 213.863i 0.112987 + 0.0948074i
\(173\) 3270.91 + 1190.51i 1.43747 + 0.523197i 0.939063 0.343744i \(-0.111695\pi\)
0.498410 + 0.866942i \(0.333918\pi\)
\(174\) −1378.64 2387.88i −0.600660 1.04037i
\(175\) 314.431 544.611i 0.135822 0.235250i
\(176\) −467.620 + 392.380i −0.200274 + 0.168050i
\(177\) 1050.29 + 1819.16i 0.446015 + 0.772520i
\(178\) 237.177 1345.10i 0.0998716 0.566400i
\(179\) −3103.34 −1.29584 −0.647919 0.761710i \(-0.724360\pi\)
−0.647919 + 0.761710i \(0.724360\pi\)
\(180\) 294.876 1672.32i 0.122104 0.692487i
\(181\) 130.827 + 109.777i 0.0537254 + 0.0450809i 0.669255 0.743033i \(-0.266613\pi\)
−0.615530 + 0.788114i \(0.711058\pi\)
\(182\) −792.832 + 288.567i −0.322905 + 0.117528i
\(183\) −2836.47 1032.39i −1.14578 0.417031i
\(184\) 1005.98 0.403055
\(185\) 2684.74 + 2152.24i 1.06695 + 0.855327i
\(186\) −1129.03 −0.445077
\(187\) 4260.13 + 1550.56i 1.66594 + 0.606354i
\(188\) −2152.82 + 783.563i −0.835163 + 0.303974i
\(189\) 25.1607 + 21.1123i 0.00968344 + 0.00812537i
\(190\) −139.589 + 791.647i −0.0532991 + 0.302274i
\(191\) −738.788 −0.279879 −0.139939 0.990160i \(-0.544691\pi\)
−0.139939 + 0.990160i \(0.544691\pi\)
\(192\) −82.2454 + 466.437i −0.0309143 + 0.175324i
\(193\) −471.737 817.072i −0.175940 0.304736i 0.764546 0.644569i \(-0.222963\pi\)
−0.940486 + 0.339832i \(0.889630\pi\)
\(194\) 796.371 668.235i 0.294722 0.247301i
\(195\) −4126.95 + 7148.08i −1.51557 + 2.62505i
\(196\) 619.118 + 1072.34i 0.225626 + 0.390796i
\(197\) −1753.11 638.080i −0.634030 0.230768i 0.00495424 0.999988i \(-0.498423\pi\)
−0.638985 + 0.769220i \(0.720645\pi\)
\(198\) −1623.08 1361.92i −0.582561 0.488827i
\(199\) 631.547 1093.87i 0.224971 0.389661i −0.731340 0.682013i \(-0.761105\pi\)
0.956311 + 0.292352i \(0.0944380\pi\)
\(200\) 151.069 + 856.756i 0.0534110 + 0.302909i
\(201\) −357.718 2028.72i −0.125530 0.711914i
\(202\) −2049.65 + 1719.86i −0.713924 + 0.599054i
\(203\) −1012.32 + 368.454i −0.350004 + 0.127391i
\(204\) 3305.41 1203.07i 1.13444 0.412901i
\(205\) 491.969 412.811i 0.167613 0.140644i
\(206\) 144.712 + 820.702i 0.0489444 + 0.277578i
\(207\) 606.328 + 3438.66i 0.203588 + 1.15461i
\(208\) 583.600 1010.82i 0.194545 0.336962i
\(209\) 768.335 + 644.710i 0.254291 + 0.213376i
\(210\) −1229.67 447.565i −0.404074 0.147071i
\(211\) 399.625 + 692.171i 0.130385 + 0.225834i 0.923825 0.382815i \(-0.125045\pi\)
−0.793440 + 0.608649i \(0.791712\pi\)
\(212\) 579.371 1003.50i 0.187695 0.325098i
\(213\) 5638.83 4731.54i 1.81392 1.52206i
\(214\) 440.771 + 763.437i 0.140797 + 0.243867i
\(215\) 220.826 1252.37i 0.0700475 0.397259i
\(216\) −45.4379 −0.0143132
\(217\) −76.5991 + 434.415i −0.0239626 + 0.135899i
\(218\) 2651.93 + 2225.24i 0.823907 + 0.691340i
\(219\) −6750.88 + 2457.12i −2.08302 + 0.758159i
\(220\) 2192.49 + 798.001i 0.671898 + 0.244551i
\(221\) −8668.48 −2.63848
\(222\) 1600.59 2921.41i 0.483895 0.883209i
\(223\) 848.582 0.254822 0.127411 0.991850i \(-0.459333\pi\)
0.127411 + 0.991850i \(0.459333\pi\)
\(224\) 173.891 + 63.2910i 0.0518685 + 0.0188786i
\(225\) −2837.51 + 1032.77i −0.840745 + 0.306006i
\(226\) −152.354 127.840i −0.0448427 0.0376275i
\(227\) 1076.00 6102.29i 0.314610 1.78424i −0.259786 0.965666i \(-0.583652\pi\)
0.574397 0.818577i \(-0.305237\pi\)
\(228\) 778.214 0.226046
\(229\) −1085.72 + 6157.44i −0.313304 + 1.77684i 0.268272 + 0.963343i \(0.413548\pi\)
−0.581576 + 0.813492i \(0.697564\pi\)
\(230\) −1922.53 3329.93i −0.551166 0.954647i
\(231\) −1250.76 + 1049.51i −0.356252 + 0.298931i
\(232\) 745.163 1290.66i 0.210872 0.365241i
\(233\) 3224.09 + 5584.28i 0.906510 + 1.57012i 0.818877 + 0.573969i \(0.194597\pi\)
0.0876328 + 0.996153i \(0.472070\pi\)
\(234\) 3806.95 + 1385.62i 1.06354 + 0.387097i
\(235\) 6707.93 + 5628.62i 1.86203 + 1.56243i
\(236\) −567.685 + 983.260i −0.156581 + 0.271207i
\(237\) 598.916 + 3396.62i 0.164151 + 0.930946i
\(238\) −238.648 1353.44i −0.0649969 0.368616i
\(239\) 1900.06 1594.34i 0.514244 0.431502i −0.348375 0.937355i \(-0.613267\pi\)
0.862620 + 0.505853i \(0.168822\pi\)
\(240\) 1701.14 619.164i 0.457534 0.166529i
\(241\) −2919.29 + 1062.53i −0.780281 + 0.283999i −0.701290 0.712876i \(-0.747392\pi\)
−0.0789913 + 0.996875i \(0.525170\pi\)
\(242\) 190.878 160.166i 0.0507029 0.0425448i
\(243\) 936.069 + 5308.71i 0.247115 + 1.40146i
\(244\) −283.310 1606.73i −0.0743322 0.421559i
\(245\) 2366.39 4098.70i 0.617073 1.06880i
\(246\) −476.273 399.641i −0.123439 0.103578i
\(247\) −1802.14 655.925i −0.464241 0.168970i
\(248\) −305.122 528.486i −0.0781260 0.135318i
\(249\) 1942.34 3364.22i 0.494339 0.856221i
\(250\) −380.717 + 319.459i −0.0963145 + 0.0808175i
\(251\) 2984.80 + 5169.83i 0.750594 + 1.30007i 0.947535 + 0.319652i \(0.103566\pi\)
−0.196941 + 0.980415i \(0.563101\pi\)
\(252\) −111.534 + 632.540i −0.0278809 + 0.158120i
\(253\) −4797.56 −1.19217
\(254\) −663.244 + 3761.44i −0.163841 + 0.929189i
\(255\) −10299.3 8642.10i −2.52927 2.12231i
\(256\) −240.561 + 87.5572i −0.0587308 + 0.0213763i
\(257\) −2314.83 842.529i −0.561849 0.204496i 0.0454545 0.998966i \(-0.485526\pi\)
−0.607303 + 0.794470i \(0.707749\pi\)
\(258\) −1231.12 −0.297077
\(259\) −1015.48 814.062i −0.243624 0.195303i
\(260\) −4461.26 −1.06414
\(261\) 4860.86 + 1769.21i 1.15280 + 0.419583i
\(262\) −4572.31 + 1664.19i −1.07816 + 0.392419i
\(263\) −2026.91 1700.78i −0.475226 0.398762i 0.373470 0.927642i \(-0.378168\pi\)
−0.848697 + 0.528880i \(0.822612\pi\)
\(264\) 392.230 2224.45i 0.0914397 0.518580i
\(265\) −4428.94 −1.02667
\(266\) 52.7981 299.433i 0.0121701 0.0690203i
\(267\) 2526.99 + 4376.87i 0.579211 + 1.00322i
\(268\) 852.948 715.708i 0.194411 0.163130i
\(269\) 2749.46 4762.21i 0.623188 1.07939i −0.365700 0.930733i \(-0.619170\pi\)
0.988888 0.148661i \(-0.0474963\pi\)
\(270\) 86.8362 + 150.405i 0.0195729 + 0.0339012i
\(271\) 3626.78 + 1320.04i 0.812957 + 0.295892i 0.714845 0.699283i \(-0.246497\pi\)
0.0981123 + 0.995175i \(0.468720\pi\)
\(272\) 1456.44 + 1222.10i 0.324667 + 0.272428i
\(273\) 1560.98 2703.69i 0.346061 0.599395i
\(274\) 62.0646 + 351.986i 0.0136842 + 0.0776067i
\(275\) −720.452 4085.88i −0.157981 0.895957i
\(276\) −2851.52 + 2392.71i −0.621889 + 0.521827i
\(277\) 7219.15 2627.56i 1.56591 0.569944i 0.593829 0.804591i \(-0.297616\pi\)
0.972081 + 0.234647i \(0.0753934\pi\)
\(278\) 4349.86 1583.22i 0.938444 0.341566i
\(279\) 1622.57 1361.50i 0.348175 0.292153i
\(280\) −122.821 696.553i −0.0262142 0.148668i
\(281\) −1142.21 6477.78i −0.242485 1.37520i −0.826261 0.563287i \(-0.809536\pi\)
0.583776 0.811915i \(-0.301575\pi\)
\(282\) 4238.61 7341.49i 0.895055 1.55028i
\(283\) −1492.76 1252.57i −0.313552 0.263101i 0.472407 0.881381i \(-0.343385\pi\)
−0.785958 + 0.618280i \(0.787830\pi\)
\(284\) 3738.69 + 1360.77i 0.781163 + 0.284320i
\(285\) −1487.24 2575.98i −0.309111 0.535396i
\(286\) −2783.20 + 4820.64i −0.575433 + 0.996680i
\(287\) −186.082 + 156.142i −0.0382721 + 0.0321141i
\(288\) −444.280 769.515i −0.0909008 0.157445i
\(289\) 1598.78 9067.16i 0.325419 1.84554i
\(290\) −5696.31 −1.15344
\(291\) −667.980 + 3788.30i −0.134562 + 0.763141i
\(292\) −2974.59 2495.98i −0.596146 0.500226i
\(293\) 5244.38 1908.80i 1.04567 0.380591i 0.238640 0.971108i \(-0.423298\pi\)
0.807025 + 0.590517i \(0.201076\pi\)
\(294\) −4305.47 1567.06i −0.854082 0.310860i
\(295\) 4339.61 0.856480
\(296\) 1800.05 40.2968i 0.353465 0.00791286i
\(297\) 216.694 0.0423362
\(298\) 5374.50 + 1956.16i 1.04475 + 0.380259i
\(299\) 8620.10 3137.46i 1.66727 0.606836i
\(300\) −2465.99 2069.21i −0.474580 0.398220i
\(301\) −83.5253 + 473.696i −0.0159944 + 0.0907089i
\(302\) 4684.64 0.892618
\(303\) 1719.20 9750.08i 0.325959 1.84861i
\(304\) 210.314 + 364.274i 0.0396787 + 0.0687255i
\(305\) −4777.03 + 4008.41i −0.896827 + 0.752527i
\(306\) −3299.55 + 5714.98i −0.616413 + 1.06766i
\(307\) 1584.42 + 2744.30i 0.294553 + 0.510181i 0.974881 0.222727i \(-0.0714958\pi\)
−0.680327 + 0.732908i \(0.738162\pi\)
\(308\) −829.288 301.836i −0.153419 0.0558399i
\(309\) −2362.21 1982.13i −0.434892 0.364918i
\(310\) −1166.23 + 2019.98i −0.213670 + 0.370087i
\(311\) 288.839 + 1638.09i 0.0526642 + 0.298673i 0.999751 0.0223034i \(-0.00709998\pi\)
−0.947087 + 0.320977i \(0.895989\pi\)
\(312\) 749.975 + 4253.32i 0.136086 + 0.771784i
\(313\) 1246.69 1046.10i 0.225135 0.188911i −0.523242 0.852184i \(-0.675278\pi\)
0.748377 + 0.663273i \(0.230833\pi\)
\(314\) −778.430 + 283.325i −0.139902 + 0.0509203i
\(315\) 2306.93 839.655i 0.412638 0.150188i
\(316\) −1428.07 + 1198.29i −0.254225 + 0.213320i
\(317\) −15.2333 86.3925i −0.00269902 0.0153069i 0.983429 0.181296i \(-0.0580293\pi\)
−0.986128 + 0.165989i \(0.946918\pi\)
\(318\) 744.541 + 4222.50i 0.131295 + 0.744611i
\(319\) −3553.69 + 6155.18i −0.623726 + 1.08033i
\(320\) 749.560 + 628.956i 0.130943 + 0.109874i
\(321\) −3065.21 1115.64i −0.532970 0.193985i
\(322\) 727.179 + 1259.51i 0.125851 + 0.217981i
\(323\) 1561.94 2705.37i 0.269068 0.466039i
\(324\) −2168.49 + 1819.57i −0.371825 + 0.311998i
\(325\) 3966.53 + 6870.23i 0.676995 + 1.17259i
\(326\) −839.411 + 4760.54i −0.142609 + 0.808778i
\(327\) −12809.7 −2.16630
\(328\) 58.3541 330.942i 0.00982337 0.0557111i
\(329\) −2537.21 2128.97i −0.425170 0.356760i
\(330\) −8112.76 + 2952.80i −1.35331 + 0.492565i
\(331\) −2220.82 808.312i −0.368783 0.134226i 0.150979 0.988537i \(-0.451757\pi\)
−0.519763 + 0.854311i \(0.673980\pi\)
\(332\) 2099.68 0.347093
\(333\) 1222.67 + 6128.64i 0.201207 + 1.00855i
\(334\) 5537.20 0.907133
\(335\) −3999.14 1455.57i −0.652229 0.237392i
\(336\) −643.439 + 234.193i −0.104472 + 0.0380246i
\(337\) 571.075 + 479.189i 0.0923099 + 0.0774572i 0.687775 0.725924i \(-0.258588\pi\)
−0.595465 + 0.803381i \(0.703032\pi\)
\(338\) 1085.20 6154.45i 0.174636 0.990408i
\(339\) 735.923 0.117905
\(340\) 1261.89 7156.52i 0.201281 1.14152i
\(341\) 1455.13 + 2520.36i 0.231084 + 0.400250i
\(342\) −1118.40 + 938.451i −0.176831 + 0.148379i
\(343\) −1886.82 + 3268.06i −0.297022 + 0.514457i
\(344\) −332.711 576.273i −0.0521471 0.0903214i
\(345\) 13369.7 + 4866.17i 2.08638 + 0.759379i
\(346\) −5332.94 4474.87i −0.828615 0.695291i
\(347\) −1138.81 + 1972.48i −0.176180 + 0.305153i −0.940569 0.339602i \(-0.889708\pi\)
0.764389 + 0.644756i \(0.223041\pi\)
\(348\) 957.597 + 5430.80i 0.147507 + 0.836556i
\(349\) 1567.91 + 8892.09i 0.240483 + 1.36385i 0.830753 + 0.556641i \(0.187910\pi\)
−0.590270 + 0.807206i \(0.700979\pi\)
\(350\) −963.474 + 808.450i −0.147142 + 0.123467i
\(351\) −389.349 + 141.711i −0.0592077 + 0.0215498i
\(352\) 1147.24 417.562i 0.173716 0.0632276i
\(353\) −4482.64 + 3761.38i −0.675884 + 0.567134i −0.914800 0.403906i \(-0.867652\pi\)
0.238916 + 0.971040i \(0.423208\pi\)
\(354\) −729.524 4137.33i −0.109530 0.621177i
\(355\) −2640.68 14976.1i −0.394797 2.23900i
\(356\) −1365.85 + 2365.72i −0.203342 + 0.352199i
\(357\) 3895.59 + 3268.79i 0.577526 + 0.484601i
\(358\) 5832.38 + 2122.81i 0.861036 + 0.313391i
\(359\) 4354.29 + 7541.86i 0.640141 + 1.10876i 0.985401 + 0.170250i \(0.0544576\pi\)
−0.345259 + 0.938507i \(0.612209\pi\)
\(360\) −1698.12 + 2941.23i −0.248608 + 0.430602i
\(361\) −4724.87 + 3964.63i −0.688857 + 0.578019i
\(362\) −170.783 295.804i −0.0247959 0.0429478i
\(363\) −160.105 + 907.999i −0.0231496 + 0.131288i
\(364\) 1687.43 0.242982
\(365\) −2577.25 + 14616.3i −0.369587 + 2.09603i
\(366\) 4624.63 + 3880.53i 0.660474 + 0.554203i
\(367\) −3546.32 + 1290.76i −0.504405 + 0.183588i −0.581674 0.813422i \(-0.697602\pi\)
0.0772694 + 0.997010i \(0.475380\pi\)
\(368\) −1890.63 688.134i −0.267815 0.0974768i
\(369\) 1166.40 0.164554
\(370\) −3573.45 5881.35i −0.502094 0.826370i
\(371\) 1675.20 0.234426
\(372\) 2121.88 + 772.300i 0.295737 + 0.107640i
\(373\) −1939.63 + 705.966i −0.269249 + 0.0979987i −0.473117 0.881000i \(-0.656871\pi\)
0.203867 + 0.978999i \(0.434649\pi\)
\(374\) −6945.78 5828.20i −0.960314 0.805799i
\(375\) 319.337 1811.05i 0.0439747 0.249393i
\(376\) 4581.97 0.628449
\(377\) 2359.86 13383.4i 0.322385 1.82833i
\(378\) −32.8449 56.8891i −0.00446921 0.00774090i
\(379\) −4119.94 + 3457.04i −0.558383 + 0.468539i −0.877768 0.479086i \(-0.840968\pi\)
0.319385 + 0.947625i \(0.396524\pi\)
\(380\) 803.860 1392.33i 0.108519 0.187960i
\(381\) −7066.50 12239.5i −0.950204 1.64580i
\(382\) 1388.47 + 505.361i 0.185969 + 0.0676872i
\(383\) −9614.39 8067.43i −1.28270 1.07631i −0.992867 0.119231i \(-0.961957\pi\)
−0.289829 0.957079i \(-0.593598\pi\)
\(384\) 473.632 820.355i 0.0629426 0.109020i
\(385\) 585.736 + 3321.88i 0.0775374 + 0.439736i
\(386\) 327.665 + 1858.28i 0.0432065 + 0.245036i
\(387\) 1769.29 1484.61i 0.232398 0.195005i
\(388\) −1953.79 + 711.121i −0.255641 + 0.0930456i
\(389\) 2199.10 800.408i 0.286630 0.104325i −0.194704 0.980862i \(-0.562375\pi\)
0.481334 + 0.876537i \(0.340152\pi\)
\(390\) 12645.7 10611.0i 1.64190 1.37772i
\(391\) 2594.71 + 14715.3i 0.335602 + 1.90329i
\(392\) −430.035 2438.85i −0.0554082 0.314236i
\(393\) 9002.26 15592.4i 1.15548 2.00135i
\(394\) 2858.30 + 2398.40i 0.365480 + 0.306674i
\(395\) 6695.65 + 2437.02i 0.852898 + 0.310429i
\(396\) 2118.78 + 3669.83i 0.268870 + 0.465697i
\(397\) 2946.46 5103.42i 0.372490 0.645172i −0.617458 0.786604i \(-0.711837\pi\)
0.989948 + 0.141432i \(0.0451706\pi\)
\(398\) −1935.17 + 1623.80i −0.243722 + 0.204507i
\(399\) 562.535 + 974.339i 0.0705814 + 0.122251i
\(400\) 302.138 1713.51i 0.0377673 0.214189i
\(401\) −7291.93 −0.908084 −0.454042 0.890980i \(-0.650018\pi\)
−0.454042 + 0.890980i \(0.650018\pi\)
\(402\) −715.435 + 4057.43i −0.0887628 + 0.503399i
\(403\) −4262.77 3576.89i −0.526908 0.442128i
\(404\) 5028.53 1830.24i 0.619254 0.225390i
\(405\) 10167.2 + 3700.55i 1.24744 + 0.454030i
\(406\) 2154.57 0.263374
\(407\) −8584.46 + 192.176i −1.04549 + 0.0234050i
\(408\) −7035.08 −0.853648
\(409\) −1956.72 712.189i −0.236562 0.0861014i 0.221019 0.975269i \(-0.429062\pi\)
−0.457581 + 0.889168i \(0.651284\pi\)
\(410\) −1206.98 + 439.304i −0.145386 + 0.0529163i
\(411\) −1013.12 850.105i −0.121590 0.102026i
\(412\) 289.424 1641.40i 0.0346089 0.196277i
\(413\) −1641.41 −0.195566
\(414\) 1212.66 6877.32i 0.143959 0.816429i
\(415\) −4012.69 6950.18i −0.474639 0.822099i
\(416\) −1788.25 + 1500.52i −0.210760 + 0.176849i
\(417\) −8564.28 + 14833.8i −1.00574 + 1.74200i
\(418\) −1002.99 1737.23i −0.117363 0.203279i
\(419\) 6237.21 + 2270.16i 0.727225 + 0.264688i 0.678990 0.734148i \(-0.262418\pi\)
0.0482355 + 0.998836i \(0.484640\pi\)
\(420\) 2004.88 + 1682.29i 0.232924 + 0.195446i
\(421\) −440.919 + 763.695i −0.0510430 + 0.0884090i −0.890418 0.455144i \(-0.849588\pi\)
0.839375 + 0.543553i \(0.182921\pi\)
\(422\) −277.577 1574.22i −0.0320195 0.181591i
\(423\) 2761.65 + 15662.1i 0.317438 + 1.80028i
\(424\) −1775.30 + 1489.65i −0.203340 + 0.170622i
\(425\) −12142.8 + 4419.62i −1.38591 + 0.504431i
\(426\) −13834.1 + 5035.20i −1.57339 + 0.572667i
\(427\) 1806.87 1516.14i 0.204778 0.171830i
\(428\) −306.156 1736.30i −0.0345762 0.196091i
\(429\) −3576.64 20284.2i −0.402522 2.28282i
\(430\) −1271.69 + 2202.63i −0.142619 + 0.247023i
\(431\) 5768.12 + 4840.02i 0.644641 + 0.540918i 0.905440 0.424475i \(-0.139541\pi\)
−0.260798 + 0.965393i \(0.583986\pi\)
\(432\) 85.3953 + 31.0813i 0.00951061 + 0.00346158i
\(433\) −1367.08 2367.85i −0.151727 0.262798i 0.780136 0.625610i \(-0.215150\pi\)
−0.931862 + 0.362812i \(0.881817\pi\)
\(434\) 441.117 764.037i 0.0487887 0.0845045i
\(435\) 16146.5 13548.5i 1.77969 1.49334i
\(436\) −3461.86 5996.11i −0.380259 0.658627i
\(437\) −574.049 + 3255.60i −0.0628387 + 0.356376i
\(438\) 14368.3 1.56745
\(439\) −420.400 + 2384.21i −0.0457052 + 0.259207i −0.999095 0.0425343i \(-0.986457\pi\)
0.953390 + 0.301741i \(0.0975679\pi\)
\(440\) −3574.67 2999.50i −0.387308 0.324990i
\(441\) 8077.29 2939.89i 0.872183 0.317449i
\(442\) 16291.4 + 5929.59i 1.75318 + 0.638104i
\(443\) 11706.2 1.25548 0.627739 0.778424i \(-0.283981\pi\)
0.627739 + 0.778424i \(0.283981\pi\)
\(444\) −5006.49 + 4395.59i −0.535130 + 0.469832i
\(445\) 10441.1 1.11226
\(446\) −1594.81 580.464i −0.169320 0.0616273i
\(447\) −19887.0 + 7238.28i −2.10430 + 0.765904i
\(448\) −283.514 237.896i −0.0298990 0.0250883i
\(449\) −2220.62 + 12593.8i −0.233402 + 1.32369i 0.612550 + 0.790432i \(0.290144\pi\)
−0.845952 + 0.533259i \(0.820967\pi\)
\(450\) 6039.24 0.632650
\(451\) −278.292 + 1578.27i −0.0290560 + 0.164785i
\(452\) 198.884 + 344.478i 0.0206963 + 0.0358471i
\(453\) −13278.9 + 11142.3i −1.37725 + 1.15565i
\(454\) −6196.43 + 10732.5i −0.640557 + 1.10948i
\(455\) −3224.84 5585.58i −0.332270 0.575508i
\(456\) −1462.56 532.330i −0.150199 0.0546680i
\(457\) 1696.77 + 1423.76i 0.173680 + 0.145734i 0.725484 0.688239i \(-0.241616\pi\)
−0.551804 + 0.833974i \(0.686060\pi\)
\(458\) 6252.43 10829.5i 0.637897 1.10487i
\(459\) −117.197 664.656i −0.0119178 0.0675893i
\(460\) 1335.38 + 7573.30i 0.135353 + 0.767624i
\(461\) 4674.34 3922.24i 0.472247 0.396262i −0.375367 0.926876i \(-0.622483\pi\)
0.847613 + 0.530614i \(0.178039\pi\)
\(462\) 3068.57 1116.87i 0.309011 0.112471i
\(463\) 7043.58 2563.65i 0.707004 0.257329i 0.0366058 0.999330i \(-0.488345\pi\)
0.670398 + 0.742001i \(0.266123\pi\)
\(464\) −2283.31 + 1915.92i −0.228448 + 0.191691i
\(465\) −1498.71 8499.60i −0.149464 0.847655i
\(466\) −2239.43 12700.4i −0.222617 1.26252i
\(467\) 1968.36 3409.29i 0.195042 0.337823i −0.751872 0.659309i \(-0.770849\pi\)
0.946914 + 0.321486i \(0.104182\pi\)
\(468\) −6206.91 5208.22i −0.613065 0.514423i
\(469\) 1512.64 + 550.555i 0.148928 + 0.0542053i
\(470\) −8756.58 15166.8i −0.859385 1.48850i
\(471\) 1532.62 2654.58i 0.149935 0.259695i
\(472\) 1739.49 1459.60i 0.169632 0.142338i
\(473\) 1586.71 + 2748.26i 0.154243 + 0.267156i
\(474\) 1197.83 6793.24i 0.116072 0.658278i
\(475\) −2858.86 −0.276155
\(476\) −477.297 + 2706.88i −0.0459598 + 0.260651i
\(477\) −6161.94 5170.48i −0.591480 0.496311i
\(478\) −4661.53 + 1696.66i −0.446053 + 0.162350i
\(479\) −4643.37 1690.05i −0.442925 0.161211i 0.110924 0.993829i \(-0.464619\pi\)
−0.553849 + 0.832617i \(0.686841\pi\)
\(480\) −3620.63 −0.344288
\(481\) 15298.6 5959.27i 1.45022 0.564905i
\(482\) 6213.28 0.587152
\(483\) −5056.95 1840.58i −0.476396 0.173394i
\(484\) −468.293 + 170.445i −0.0439795 + 0.0160072i
\(485\) 6087.77 + 5108.24i 0.569962 + 0.478255i
\(486\) 1872.14 10617.4i 0.174737 0.990980i
\(487\) −1175.39 −0.109367 −0.0546837 0.998504i \(-0.517415\pi\)
−0.0546837 + 0.998504i \(0.517415\pi\)
\(488\) −566.620 + 3213.46i −0.0525608 + 0.298087i
\(489\) −8943.46 15490.5i −0.827070 1.43253i
\(490\) −7251.03 + 6084.34i −0.668507 + 0.560944i
\(491\) 1787.98 3096.88i 0.164339 0.284644i −0.772081 0.635524i \(-0.780784\pi\)
0.936420 + 0.350880i \(0.114117\pi\)
\(492\) 621.731 + 1076.87i 0.0569711 + 0.0986769i
\(493\) 20801.5 + 7571.13i 1.90031 + 0.691656i
\(494\) 2938.24 + 2465.47i 0.267606 + 0.224548i
\(495\) 8098.38 14026.8i 0.735344 1.27365i
\(496\) 211.935 + 1201.95i 0.0191858 + 0.108808i
\(497\) 998.812 + 5664.55i 0.0901466 + 0.511247i
\(498\) −5951.66 + 4994.04i −0.535543 + 0.449374i
\(499\) −8619.96 + 3137.41i −0.773311 + 0.281462i −0.698381 0.715726i \(-0.746096\pi\)
−0.0749306 + 0.997189i \(0.523874\pi\)
\(500\) 934.036 339.961i 0.0835427 0.0304071i
\(501\) −15695.5 + 13170.1i −1.39965 + 1.17445i
\(502\) −2073.22 11757.8i −0.184328 1.04537i
\(503\) −2011.94 11410.3i −0.178345 1.01145i −0.934211 0.356721i \(-0.883895\pi\)
0.755866 0.654727i \(-0.227216\pi\)
\(504\) 642.298 1112.49i 0.0567664 0.0983222i
\(505\) −15668.3 13147.3i −1.38065 1.15851i
\(506\) 9016.46 + 3281.72i 0.792155 + 0.288321i
\(507\) 11562.2 + 20026.3i 1.01281 + 1.75424i
\(508\) 3819.47 6615.52i 0.333586 0.577788i
\(509\) −8634.81 + 7245.47i −0.751928 + 0.630942i −0.936012 0.351968i \(-0.885513\pi\)
0.184084 + 0.982910i \(0.441068\pi\)
\(510\) 13444.7 + 23286.9i 1.16734 + 2.02189i
\(511\) 974.818 5528.47i 0.0843903 0.478601i
\(512\) 512.000 0.0441942
\(513\) 25.9284 147.047i 0.00223152 0.0126556i
\(514\) 3774.13 + 3166.87i 0.323871 + 0.271760i
\(515\) −5986.35 + 2178.85i −0.512214 + 0.186431i
\(516\) 2313.74 + 842.133i 0.197397 + 0.0718466i
\(517\) −21851.5 −1.85885
\(518\) 1351.62 + 2224.56i 0.114647 + 0.188691i
\(519\) 25759.9 2.17868
\(520\) 8384.43 + 3051.68i 0.707080 + 0.257356i
\(521\) 3800.56 1383.29i 0.319589 0.116321i −0.177244 0.984167i \(-0.556718\pi\)
0.496833 + 0.867846i \(0.334496\pi\)
\(522\) −7925.22 6650.05i −0.664516 0.557595i
\(523\) −2591.09 + 14694.8i −0.216636 + 1.22860i 0.661409 + 0.750025i \(0.269959\pi\)
−0.878045 + 0.478578i \(0.841152\pi\)
\(524\) 9731.51 0.811303
\(525\) 808.142 4583.20i 0.0671813 0.381004i
\(526\) 2645.94 + 4582.91i 0.219332 + 0.379894i
\(527\) 6943.61 5826.38i 0.573943 0.481596i
\(528\) −2258.76 + 3912.29i −0.186174 + 0.322463i
\(529\) −1822.79 3157.16i −0.149814 0.259485i
\(530\) 8323.68 + 3029.57i 0.682184 + 0.248295i
\(531\) 6037.65 + 5066.19i 0.493431 + 0.414038i
\(532\) −304.052 + 526.634i −0.0247788 + 0.0429182i
\(533\) −532.116 3017.78i −0.0432430 0.245243i
\(534\) −1755.23 9954.39i −0.142240 0.806683i
\(535\) −5162.25 + 4331.64i −0.417166 + 0.350044i
\(536\) −2092.59 + 761.641i −0.168631 + 0.0613766i
\(537\) −21581.3 + 7854.94i −1.73427 + 0.631221i
\(538\) −8424.84 + 7069.28i −0.675131 + 0.566502i
\(539\) 2050.84 + 11630.9i 0.163889 + 0.929460i
\(540\) −60.3158 342.068i −0.00480662 0.0272597i
\(541\) 3828.87 6631.80i 0.304281 0.527031i −0.672820 0.739806i \(-0.734917\pi\)
0.977101 + 0.212776i \(0.0682504\pi\)
\(542\) −5913.16 4961.73i −0.468620 0.393219i
\(543\) 1187.66 + 432.271i 0.0938622 + 0.0341631i
\(544\) −1901.24 3293.05i −0.149844 0.259537i
\(545\) −13231.9 + 22918.3i −1.03998 + 1.80131i
\(546\) −4783.11 + 4013.51i −0.374905 + 0.314583i
\(547\) −5585.69 9674.70i −0.436612 0.756235i 0.560813 0.827942i \(-0.310489\pi\)
−0.997426 + 0.0717076i \(0.977155\pi\)
\(548\) 124.129 703.972i 0.00967616 0.0548763i
\(549\) −11325.8 −0.880460
\(550\) −1440.90 + 8171.77i −0.111710 + 0.633537i
\(551\) 3751.65 + 3148.01i 0.290065 + 0.243393i
\(552\) 6995.82 2546.27i 0.539423 0.196334i
\(553\) −2532.56 921.778i −0.194748 0.0708824i
\(554\) −15364.9 −1.17833
\(555\) 24117.8 + 8171.67i 1.84458 + 0.624987i
\(556\) −9258.05 −0.706167
\(557\) −18990.0 6911.79i −1.44458 0.525784i −0.503508 0.863991i \(-0.667958\pi\)
−0.941072 + 0.338206i \(0.890180\pi\)
\(558\) −3980.76 + 1448.88i −0.302005 + 0.109921i
\(559\) −4648.22 3900.32i −0.351697 0.295109i
\(560\) −245.642 + 1393.11i −0.0185362 + 0.105124i
\(561\) 33550.4 2.52496
\(562\) −2284.41 + 12955.6i −0.171463 + 0.972415i
\(563\) 6157.09 + 10664.4i 0.460906 + 0.798313i 0.999006 0.0445677i \(-0.0141910\pi\)
−0.538100 + 0.842881i \(0.680858\pi\)
\(564\) −12987.9 + 10898.1i −0.969659 + 0.813640i
\(565\) 760.175 1316.66i 0.0566032 0.0980396i
\(566\) 1948.65 + 3375.17i 0.144714 + 0.250652i
\(567\) −3845.64 1399.70i −0.284835 0.103672i
\(568\) −6095.61 5114.83i −0.450293 0.377840i
\(569\) 2372.55 4109.37i 0.174802 0.302766i −0.765291 0.643685i \(-0.777405\pi\)
0.940093 + 0.340919i \(0.110738\pi\)
\(570\) 1033.03 + 5858.59i 0.0759101 + 0.430508i
\(571\) −3100.31 17582.7i −0.227222 1.28864i −0.858391 0.512996i \(-0.828536\pi\)
0.631169 0.775645i \(-0.282575\pi\)
\(572\) 8528.21 7156.02i 0.623396 0.523091i
\(573\) −5137.68 + 1869.96i −0.374572 + 0.136333i
\(574\) 456.528 166.162i 0.0331970 0.0120827i
\(575\) 10475.4 8789.91i 0.759747 0.637503i
\(576\) 308.593 + 1750.12i 0.0223230 + 0.126600i
\(577\) 1031.54 + 5850.17i 0.0744258 + 0.422090i 0.999141 + 0.0414309i \(0.0131916\pi\)
−0.924716 + 0.380659i \(0.875697\pi\)
\(578\) −9207.03 + 15947.0i −0.662564 + 1.14759i
\(579\) −5348.66 4488.06i −0.383908 0.322137i
\(580\) 10705.6 + 3896.51i 0.766421 + 0.278954i
\(581\) 1517.76 + 2628.84i 0.108377 + 0.187715i
\(582\) 3846.74 6662.75i 0.273973 0.474536i
\(583\) 8466.43 7104.18i 0.601447 0.504674i
\(584\) 3883.05 + 6725.64i 0.275140 + 0.476557i
\(585\) −5377.80 + 30499.0i −0.380076 + 2.15552i
\(586\) −11161.9 −0.786850
\(587\) −3198.29 + 18138.4i −0.224885 + 1.27539i 0.638019 + 0.770021i \(0.279754\pi\)
−0.862904 + 0.505367i \(0.831357\pi\)
\(588\) 7019.70 + 5890.23i 0.492326 + 0.413110i
\(589\) 1884.42 685.871i 0.131827 0.0479810i
\(590\) −8155.79 2968.47i −0.569099 0.207135i
\(591\) −13806.5 −0.960956
\(592\) −3410.55 1155.57i −0.236778 0.0802258i
\(593\) 10551.1 0.730659 0.365330 0.930878i \(-0.380956\pi\)
0.365330 + 0.930878i \(0.380956\pi\)
\(594\) −407.252 148.227i −0.0281309 0.0102388i
\(595\) 9872.26 3593.21i 0.680207 0.247575i
\(596\) −8762.67 7352.75i −0.602237 0.505337i
\(597\) 1623.18 9205.52i 0.111277 0.631083i
\(598\) −18346.6 −1.25460
\(599\) 4570.25 25919.2i 0.311745 1.76800i −0.278171 0.960531i \(-0.589728\pi\)
0.589917 0.807464i \(-0.299161\pi\)
\(600\) 3219.12 + 5575.68i 0.219033 + 0.379377i
\(601\) 19667.2 16502.7i 1.33484 1.12007i 0.351923 0.936029i \(-0.385528\pi\)
0.982919 0.184037i \(-0.0589166\pi\)
\(602\) 481.003 833.122i 0.0325652 0.0564045i
\(603\) −3864.69 6693.85i −0.260999 0.452064i
\(604\) −8804.24 3204.48i −0.593112 0.215875i
\(605\) 1459.15 + 1224.37i 0.0980541 + 0.0822772i
\(606\) −9900.49 + 17148.2i −0.663663 + 1.14950i
\(607\) 3112.31 + 17650.8i 0.208113 + 1.18027i 0.892465 + 0.451116i \(0.148974\pi\)
−0.684352 + 0.729152i \(0.739915\pi\)
\(608\) −146.082 828.475i −0.00974412 0.0552616i
\(609\) −6107.26 + 5124.60i −0.406369 + 0.340984i
\(610\) 11719.8 4265.66i 0.777903 0.283134i
\(611\) 39262.1 14290.2i 2.59963 0.946187i
\(612\) 10110.4 8483.63i 0.667792 0.560344i
\(613\) −1223.38 6938.12i −0.0806065 0.457142i −0.998218 0.0596648i \(-0.980997\pi\)
0.917612 0.397477i \(-0.130114\pi\)
\(614\) −1100.53 6241.42i −0.0723351 0.410233i
\(615\) 2376.38 4116.00i 0.155813 0.269875i
\(616\) 1352.08 + 1134.53i 0.0884367 + 0.0742072i
\(617\) 1218.75 + 443.590i 0.0795221 + 0.0289437i 0.381475 0.924379i \(-0.375416\pi\)
−0.301953 + 0.953323i \(0.597638\pi\)
\(618\) 3083.65 + 5341.04i 0.200716 + 0.347651i
\(619\) 10844.0 18782.3i 0.704129 1.21959i −0.262876 0.964830i \(-0.584671\pi\)
0.967005 0.254758i \(-0.0819957\pi\)
\(620\) 3573.55 2998.56i 0.231479 0.194234i
\(621\) 357.108 + 618.529i 0.0230761 + 0.0399689i
\(622\) 577.678 3276.17i 0.0372392 0.211194i
\(623\) −3949.23 −0.253969
\(624\) 1499.95 8506.64i 0.0962276 0.545734i
\(625\) −13323.4 11179.7i −0.852700 0.715500i
\(626\) −3058.59 + 1113.24i −0.195281 + 0.0710765i
\(627\) 6975.00 + 2538.69i 0.444266 + 0.161699i
\(628\) 1656.78 0.105275
\(629\) 5232.27 + 26226.8i 0.331676 + 1.66253i
\(630\) −4909.98 −0.310505
\(631\) 20948.7 + 7624.69i 1.32164 + 0.481037i 0.903983 0.427569i \(-0.140630\pi\)
0.417655 + 0.908606i \(0.362852\pi\)
\(632\) 3503.56 1275.19i 0.220513 0.0802602i
\(633\) 4531.04 + 3801.99i 0.284507 + 0.238729i
\(634\) −30.4667 + 172.785i −0.00190850 + 0.0108236i
\(635\) −29197.5 −1.82467
\(636\) 1489.08 8445.01i 0.0928395 0.526519i
\(637\) −11291.2 19556.9i −0.702311 1.21644i
\(638\) 10889.2 9137.08i 0.675714 0.566991i
\(639\) 13809.6 23918.9i 0.854926 1.48078i
\(640\) −978.481 1694.78i −0.0604342 0.104675i
\(641\) 63.9273 + 23.2676i 0.00393912 + 0.00143372i 0.343989 0.938974i \(-0.388222\pi\)
−0.340050 + 0.940407i \(0.610444\pi\)
\(642\) 4997.56 + 4193.45i 0.307224 + 0.257792i
\(643\) 1144.04 1981.54i 0.0701657 0.121531i −0.828808 0.559533i \(-0.810981\pi\)
0.898974 + 0.438002i \(0.144314\pi\)
\(644\) −505.094 2864.53i −0.0309060 0.175277i
\(645\) −1634.23 9268.15i −0.0997636 0.565788i
\(646\) −4786.08 + 4015.99i −0.291495 + 0.244593i
\(647\) −1132.87 + 412.332i −0.0688375 + 0.0250548i −0.376209 0.926535i \(-0.622773\pi\)
0.307372 + 0.951589i \(0.400550\pi\)
\(648\) 5320.08 1936.35i 0.322519 0.117387i
\(649\) −8295.66 + 6960.88i −0.501746 + 0.421015i
\(650\) −2755.12 15625.1i −0.166253 0.942870i
\(651\) 566.872 + 3214.89i 0.0341282 + 0.193551i
\(652\) 4833.97 8372.69i 0.290357 0.502914i
\(653\) 1248.39 + 1047.52i 0.0748135 + 0.0627760i 0.679428 0.733743i \(-0.262228\pi\)
−0.604614 + 0.796519i \(0.706673\pi\)
\(654\) 24074.4 + 8762.38i 1.43943 + 0.523908i
\(655\) −18597.9 32212.4i −1.10943 1.92159i
\(656\) −336.048 + 582.052i −0.0200007 + 0.0346422i
\(657\) −20649.2 + 17326.7i −1.22618 + 1.02889i
\(658\) 3312.09 + 5736.71i 0.196229 + 0.339879i
\(659\) 156.988 890.320i 0.00927977 0.0526282i −0.979816 0.199900i \(-0.935938\pi\)
0.989096 + 0.147272i \(0.0470493\pi\)
\(660\) 17266.8 1.01835
\(661\) 3367.76 19099.5i 0.198170 1.12388i −0.709661 0.704543i \(-0.751152\pi\)
0.907831 0.419336i \(-0.137737\pi\)
\(662\) 3620.86 + 3038.26i 0.212581 + 0.178377i
\(663\) −60282.3 + 21941.0i −3.53118 + 1.28524i
\(664\) −3946.11 1436.26i −0.230630 0.0839426i
\(665\) 2324.29 0.135537
\(666\) 1894.37 12354.4i 0.110218 0.718805i
\(667\) −23425.7 −1.35989
\(668\) −10406.5 3787.67i −0.602756 0.219385i
\(669\) 5901.21 2147.86i 0.341037 0.124127i
\(670\) 6520.26 + 5471.15i 0.375970 + 0.315476i
\(671\) 2702.22 15325.1i 0.155467 0.881695i
\(672\) 1369.47 0.0786136
\(673\) 3895.85 22094.5i 0.223141 1.26550i −0.643065 0.765811i \(-0.722338\pi\)
0.866207 0.499686i \(-0.166551\pi\)
\(674\) −745.486 1291.22i −0.0426039 0.0737921i
\(675\) −473.149 + 397.019i −0.0269800 + 0.0226389i
\(676\) −6249.39 + 10824.3i −0.355564 + 0.615855i
\(677\) 6276.31 + 10870.9i 0.356305 + 0.617138i 0.987340 0.158616i \(-0.0507032\pi\)
−0.631036 + 0.775754i \(0.717370\pi\)
\(678\) −1383.08 503.401i −0.0783436 0.0285147i
\(679\) −2302.64 1932.14i −0.130143 0.109203i
\(680\) −7266.92 + 12586.7i −0.409814 + 0.709819i
\(681\) −7962.93 45160.0i −0.448077 2.54117i
\(682\) −1010.72 5732.10i −0.0567487 0.321838i
\(683\) −19183.6 + 16096.9i −1.07473 + 0.901803i −0.995472 0.0950514i \(-0.969698\pi\)
−0.0792546 + 0.996854i \(0.525254\pi\)
\(684\) 2743.85 998.679i 0.153383 0.0558267i
\(685\) −2567.45 + 934.476i −0.143208 + 0.0521233i
\(686\) 5781.55 4851.29i 0.321779 0.270005i
\(687\) 8034.90 + 45568.2i 0.446216 + 2.53062i
\(688\) 231.099 + 1310.63i 0.0128061 + 0.0726267i
\(689\) −10566.3 + 18301.3i −0.584243 + 1.01194i
\(690\) −21798.1 18290.8i −1.20267 1.00916i
\(691\) −9158.70 3333.49i −0.504216 0.183520i 0.0773733 0.997002i \(-0.475347\pi\)
−0.581589 + 0.813483i \(0.697569\pi\)
\(692\) 6961.66 + 12058.0i 0.382432 + 0.662391i
\(693\) −3063.13 + 5305.50i −0.167906 + 0.290822i
\(694\) 3489.52 2928.05i 0.190865 0.160155i
\(695\) 17693.0 + 30645.2i 0.965662 + 1.67258i
\(696\) 1915.19 10861.6i 0.104303 0.591534i
\(697\) 4991.47 0.271256
\(698\) 3135.83 17784.2i 0.170047 0.964385i
\(699\) 36555.4 + 30673.6i 1.97804 + 1.65978i
\(700\) 2363.75 860.335i 0.127631 0.0464537i
\(701\) −23296.2 8479.13i −1.25519 0.456851i −0.373036 0.927817i \(-0.621683\pi\)
−0.882151 + 0.470966i \(0.843905\pi\)
\(702\) 828.673 0.0445530
\(703\) −896.759 + 5848.36i −0.0481108 + 0.313762i
\(704\) −2441.74 −0.130719
\(705\) 60895.0 + 22164.0i 3.25311 + 1.18403i
\(706\) 10997.6 4002.78i 0.586258 0.213381i
\(707\) 5926.38 + 4972.83i 0.315254 + 0.264529i
\(708\) −1459.05 + 8274.67i −0.0774496 + 0.439239i
\(709\) 14567.1 0.771621 0.385811 0.922578i \(-0.373922\pi\)
0.385811 + 0.922578i \(0.373922\pi\)
\(710\) −5281.36 + 29952.1i −0.279164 + 1.58321i
\(711\) 6470.54 + 11207.3i 0.341300 + 0.591149i
\(712\) 4185.20 3511.80i 0.220291 0.184846i
\(713\) −4796.06 + 8307.02i −0.251913 + 0.436326i
\(714\) −5085.33 8808.06i −0.266546 0.461671i
\(715\) −39985.5 14553.5i −2.09143 0.761219i
\(716\) −9509.20 7979.17i −0.496334 0.416474i
\(717\) 9177.91 15896.6i 0.478041 0.827991i
\(718\) −3024.46 17152.6i −0.157203 0.891543i
\(719\) 866.250 + 4912.75i 0.0449314 + 0.254819i 0.998997 0.0447795i \(-0.0142585\pi\)
−0.954065 + 0.299598i \(0.903147\pi\)
\(720\) 5203.35 4366.13i 0.269330 0.225994i
\(721\) 2264.28 824.130i 0.116957 0.0425690i
\(722\) 11591.8 4219.08i 0.597511 0.217476i
\(723\) −17611.9 + 14778.1i −0.905939 + 0.760173i
\(724\) 118.624 + 672.752i 0.00608928 + 0.0345340i
\(725\) −3517.85 19950.7i −0.180206 1.02200i
\(726\) 922.006 1596.96i 0.0471334 0.0816374i
\(727\) 20287.2 + 17023.0i 1.03495 + 0.868428i 0.991432 0.130625i \(-0.0416983\pi\)
0.0435200 + 0.999053i \(0.486143\pi\)
\(728\) −3171.33 1154.27i −0.161452 0.0587638i
\(729\) 10392.8 + 18000.9i 0.528010 + 0.914540i
\(730\) 14841.8 25706.7i 0.752491 1.30335i
\(731\) 7571.46 6353.21i 0.383092 0.321453i
\(732\) −6037.03 10456.4i −0.304829 0.527980i
\(733\) 1908.19 10821.9i 0.0961537 0.545315i −0.898234 0.439517i \(-0.855149\pi\)
0.994388 0.105797i \(-0.0337394\pi\)
\(734\) 7547.83 0.379558
\(735\) 6082.02 34492.8i 0.305222 1.73100i
\(736\) 3082.52 + 2586.54i 0.154379 + 0.129539i
\(737\) 9979.61 3632.28i 0.498784 0.181542i
\(738\) −2192.11 797.864i −0.109340 0.0397965i
\(739\) −28513.4 −1.41932 −0.709662 0.704542i \(-0.751153\pi\)
−0.709662 + 0.704542i \(0.751153\pi\)
\(740\) 2692.81 + 13497.7i 0.133770 + 0.670521i
\(741\) −14192.7 −0.703618
\(742\) −3148.35 1145.91i −0.155768 0.0566948i
\(743\) −2424.95 + 882.609i −0.119734 + 0.0435798i −0.401193 0.915994i \(-0.631404\pi\)
0.281458 + 0.959574i \(0.409182\pi\)
\(744\) −3459.54 2902.90i −0.170474 0.143045i
\(745\) −7592.16 + 43057.3i −0.373363 + 2.11745i
\(746\) 4128.21 0.202607
\(747\) 2531.04 14354.3i 0.123971 0.703072i
\(748\) 9067.07 + 15704.6i 0.443215 + 0.767671i
\(749\) 1952.57 1638.40i 0.0952542 0.0799278i
\(750\) −1838.99 + 3185.22i −0.0895339 + 0.155077i
\(751\) −3723.78 6449.78i −0.180936 0.313390i 0.761264 0.648442i \(-0.224579\pi\)
−0.942199 + 0.335053i \(0.891246\pi\)
\(752\) −8611.28 3134.25i −0.417581 0.151987i
\(753\) 33842.4 + 28397.2i 1.63783 + 1.37430i
\(754\) −13589.9 + 23538.4i −0.656386 + 1.13689i
\(755\) 6218.55 + 35267.1i 0.299757 + 1.70000i
\(756\) 22.8138 + 129.384i 0.00109753 + 0.00622439i
\(757\) 9980.77 8374.86i 0.479204 0.402100i −0.370935 0.928659i \(-0.620963\pi\)
0.850138 + 0.526559i \(0.176518\pi\)
\(758\) 10107.7 3678.91i 0.484339 0.176285i
\(759\) −33363.2 + 12143.2i −1.59553 + 0.580725i
\(760\) −2463.17 + 2066.84i −0.117564 + 0.0986478i
\(761\) −2182.22 12376.0i −0.103949 0.589526i −0.991635 0.129076i \(-0.958799\pi\)
0.887685 0.460451i \(-0.152312\pi\)
\(762\) 4908.34 + 27836.6i 0.233347 + 1.32338i
\(763\) 5004.83 8668.62i 0.237467 0.411304i
\(764\) −2263.78 1899.53i −0.107200 0.0899512i
\(765\) −47403.8 17253.6i −2.24037 0.815430i
\(766\) 12550.7 + 21738.4i 0.592004 + 1.02538i
\(767\) 10353.2 17932.2i 0.487393 0.844190i
\(768\) −1451.29 + 1217.78i −0.0681889 + 0.0572173i
\(769\) −5495.94 9519.25i −0.257723 0.446389i 0.707909 0.706304i \(-0.249639\pi\)
−0.965631 + 0.259915i \(0.916305\pi\)
\(770\) 1171.47 6643.75i 0.0548272 0.310941i
\(771\) −18230.3 −0.851556
\(772\) 655.330 3716.56i 0.0305516 0.173267i
\(773\) 25283.6 + 21215.5i 1.17644 + 0.987150i 0.999996 + 0.00283934i \(0.000903791\pi\)
0.176444 + 0.984311i \(0.443541\pi\)
\(774\) −4340.70 + 1579.89i −0.201580 + 0.0733693i
\(775\) −7794.97 2837.14i −0.361295 0.131501i
\(776\) 4158.35 0.192366
\(777\) −9122.33 3090.85i −0.421186 0.142708i
\(778\) −4680.47 −0.215685
\(779\) 1037.71 + 377.694i 0.0477275 + 0.0173714i
\(780\) −31024.5 + 11292.0i −1.42417 + 0.518357i
\(781\) 29070.1 + 24392.7i 1.33189 + 1.11759i
\(782\) 5189.43 29430.7i 0.237306 1.34583i
\(783\) 1058.08 0.0482921
\(784\) −860.069 + 4877.70i −0.0391795 + 0.222198i
\(785\) −3166.26 5484.12i −0.143960 0.249346i
\(786\) −27584.5 + 23146.2i −1.25179 + 1.05038i
\(787\) −685.955 + 1188.11i −0.0310695 + 0.0538139i −0.881142 0.472852i \(-0.843225\pi\)
0.850073 + 0.526666i \(0.176558\pi\)
\(788\) −3731.24 6462.70i −0.168680 0.292163i
\(789\) −18400.4 6697.20i −0.830256 0.302188i
\(790\) −10916.7 9160.19i −0.491643 0.412538i
\(791\) −287.529 + 498.014i −0.0129246 + 0.0223860i
\(792\) −1471.69 8346.36i −0.0660280 0.374463i
\(793\) 5166.86 + 29302.7i 0.231375 + 1.31220i
\(794\) −9028.48 + 7575.80i −0.403538 + 0.338608i
\(795\) −30799.7 + 11210.2i −1.37403 + 0.500106i
\(796\) 4747.68 1728.01i 0.211403 0.0769445i
\(797\) 10920.6 9163.50i 0.485356 0.407262i −0.367002 0.930220i \(-0.619616\pi\)
0.852359 + 0.522958i \(0.175171\pi\)
\(798\) −390.733 2215.95i −0.0173331 0.0983007i
\(799\) 11818.2 + 67024.2i 0.523275 + 2.96764i
\(800\) −1739.95 + 3013.67i −0.0768954 + 0.133187i
\(801\) 14526.5 + 12189.2i 0.640787 + 0.537684i
\(802\) 13704.3 + 4987.97i 0.603388 + 0.219615i
\(803\) −18518.3 32074.7i −0.813821 1.40958i
\(804\) 4120.03 7136.10i 0.180724 0.313023i
\(805\) −8516.64 + 7146.31i −0.372885 + 0.312887i
\(806\) 5564.66 + 9638.27i 0.243184 + 0.421208i
\(807\) 7066.58 40076.6i 0.308247 1.74816i
\(808\) −10702.5 −0.465981
\(809\) 4106.67 23290.1i 0.178471 1.01216i −0.755591 0.655044i \(-0.772650\pi\)
0.934061 0.357113i \(-0.116239\pi\)
\(810\) −16576.7 13909.5i −0.719071 0.603372i
\(811\) −158.800 + 57.7986i −0.00687575 + 0.00250257i −0.345456 0.938435i \(-0.612276\pi\)
0.338580 + 0.940938i \(0.390053\pi\)
\(812\) −4049.27 1473.82i −0.175002 0.0636955i
\(813\) 28562.6 1.23214
\(814\) 16265.0 + 5510.94i 0.700352 + 0.237295i
\(815\) −36952.8 −1.58822
\(816\) 13221.6 + 4812.28i 0.567218 + 0.206450i
\(817\) 2054.81 747.889i 0.0879910 0.0320261i
\(818\) 3190.27 + 2676.95i 0.136363 + 0.114422i
\(819\) 2034.10 11535.9i 0.0867853 0.492184i
\(820\) 2568.88 0.109401
\(821\) −954.314 + 5412.19i −0.0405674 + 0.230069i −0.998350 0.0574250i \(-0.981711\pi\)
0.957782 + 0.287494i \(0.0928221\pi\)
\(822\) 1322.53 + 2290.69i 0.0561174 + 0.0971982i
\(823\) −14763.5 + 12388.0i −0.625301 + 0.524690i −0.899465 0.436993i \(-0.856043\pi\)
0.274164 + 0.961683i \(0.411599\pi\)
\(824\) −1666.72 + 2886.85i −0.0704649 + 0.122049i
\(825\) −15352.0 26590.5i −0.647866 1.12214i
\(826\) 3084.85 + 1122.79i 0.129946 + 0.0472966i
\(827\) 28441.9 + 23865.6i 1.19591 + 1.00349i 0.999737 + 0.0229226i \(0.00729714\pi\)
0.196177 + 0.980569i \(0.437147\pi\)
\(828\) −6983.41 + 12095.6i −0.293104 + 0.507672i
\(829\) 2213.59 + 12553.9i 0.0927397 + 0.525953i 0.995417 + 0.0956339i \(0.0304878\pi\)
−0.902677 + 0.430319i \(0.858401\pi\)
\(830\) 2787.18 + 15806.9i 0.116560 + 0.661043i
\(831\) 43552.8 36545.1i 1.81809 1.52555i
\(832\) 4387.23 1596.82i 0.182812 0.0665383i
\(833\) 34565.8 12580.9i 1.43774 0.523293i
\(834\) 26242.5 22020.1i 1.08957 0.914259i
\(835\) 7350.27 + 41685.5i 0.304631 + 1.72765i
\(836\) 696.670 + 3951.01i 0.0288216 + 0.163455i
\(837\) 216.626 375.208i 0.00894588 0.0154947i
\(838\) −10169.2 8533.00i −0.419201 0.351751i
\(839\) −19687.6 7165.69i −0.810120 0.294860i −0.0964467 0.995338i \(-0.530748\pi\)
−0.713673 + 0.700479i \(0.752970\pi\)
\(840\) −2617.18 4533.10i −0.107502 0.186198i
\(841\) −5157.60 + 8933.22i −0.211472 + 0.366281i
\(842\) 1351.06 1133.67i 0.0552974 0.0464001i
\(843\) −24339.2 42156.7i −0.994408 1.72237i
\(844\) −555.153 + 3148.43i −0.0226412 + 0.128405i
\(845\) 47772.8 1.94489
\(846\) 5523.30 31324.2i 0.224462 1.27299i
\(847\) −551.908 463.106i −0.0223894 0.0187869i
\(848\) 4355.45 1585.25i 0.176376 0.0641956i
\(849\) −13551.3 4932.28i −0.547798 0.199382i
\(850\) 25844.2 1.04288
\(851\) −14695.6 24186.7i −0.591960 0.974275i
\(852\) 29443.9 1.18396
\(853\) −27297.9 9935.61i −1.09573 0.398815i −0.269992 0.962863i \(-0.587021\pi\)
−0.825742 + 0.564048i \(0.809243\pi\)
\(854\) −4432.90 + 1613.44i −0.177624 + 0.0646498i
\(855\) −8549.50 7173.88i −0.341973 0.286949i
\(856\) −612.312 + 3472.60i −0.0244491 + 0.138658i
\(857\) −31631.2 −1.26080 −0.630398 0.776272i \(-0.717108\pi\)
−0.630398 + 0.776272i \(0.717108\pi\)
\(858\) −7153.29 + 40568.3i −0.284626 + 1.61420i
\(859\) 3850.19 + 6668.72i 0.152930 + 0.264882i 0.932303 0.361677i \(-0.117796\pi\)
−0.779373 + 0.626560i \(0.784462\pi\)
\(860\) 3896.68 3269.70i 0.154506 0.129646i
\(861\) −898.841 + 1556.84i −0.0355777 + 0.0616224i
\(862\) −7529.74 13041.9i −0.297522 0.515323i
\(863\) 26844.2 + 9770.50i 1.05885 + 0.385390i 0.811997 0.583662i \(-0.198381\pi\)
0.246855 + 0.969053i \(0.420603\pi\)
\(864\) −139.230 116.828i −0.00548228 0.00460018i
\(865\) 26608.8 46087.8i 1.04593 1.81160i
\(866\) 949.563 + 5385.24i 0.0372604 + 0.211314i
\(867\) −11831.8 67101.5i −0.463471 2.62847i
\(868\) −1351.66 + 1134.18i −0.0528552 + 0.0443508i
\(869\) −16708.6 + 6081.42i −0.652243 + 0.237397i
\(870\) −39613.3 + 14418.1i −1.54370 + 0.561860i
\(871\) −15555.6 + 13052.7i −0.605146 + 0.507778i
\(872\) 2404.58 + 13637.0i 0.0933823 + 0.529597i
\(873\) 2506.33 + 14214.1i 0.0971666 + 0.551059i
\(874\) 3305.82 5725.85i 0.127942 0.221601i
\(875\) 1100.81 + 923.689i 0.0425305 + 0.0356873i
\(876\) −27003.5 9828.48i −1.04151 0.379079i
\(877\) −6978.05 12086.3i −0.268680 0.465367i 0.699841 0.714298i \(-0.253254\pi\)
−0.968521 + 0.248931i \(0.919921\pi\)
\(878\) 2420.99 4193.27i 0.0930573 0.161180i
\(879\) 31639.1 26548.3i 1.21406 1.01872i
\(880\) 4666.40 + 8082.44i 0.178755 + 0.309612i
\(881\) −4704.22 + 26679.0i −0.179897 + 1.02025i 0.752441 + 0.658659i \(0.228876\pi\)
−0.932338 + 0.361587i \(0.882235\pi\)
\(882\) −17191.3 −0.656307
\(883\) 1415.74 8029.07i 0.0539564 0.306002i −0.945872 0.324541i \(-0.894790\pi\)
0.999828 + 0.0185387i \(0.00590138\pi\)
\(884\) −26561.8 22288.0i −1.01060 0.847992i
\(885\) 30178.5 10984.1i 1.14626 0.417204i
\(886\) −22000.4 8007.49i −0.834219 0.303631i
\(887\) 5769.35 0.218394 0.109197 0.994020i \(-0.465172\pi\)
0.109197 + 0.994020i \(0.465172\pi\)
\(888\) 12415.9 4836.37i 0.469200 0.182768i
\(889\) 11043.7 0.416640
\(890\) −19622.8 7142.11i −0.739053 0.268993i
\(891\) −25371.6 + 9234.50i −0.953961 + 0.347214i
\(892\) 2600.21 + 2181.83i 0.0976024 + 0.0818981i
\(893\) −2614.63 + 14828.3i −0.0979790 + 0.555666i
\(894\) 42326.7 1.58346
\(895\) −8238.97 + 46725.5i −0.307708 + 1.74510i
\(896\) 370.101 + 641.034i 0.0137993 + 0.0239012i
\(897\) 52004.6 43637.0i 1.93577 1.62430i
\(898\) 12788.1 22149.6i 0.475215 0.823096i
\(899\) 7105.17 + 12306.5i 0.263593 + 0.456557i
\(900\) −11350.1 4131.08i −0.420372 0.153003i
\(901\) −26369.3 22126.5i −0.975016 0.818135i
\(902\) 1602.62 2775.82i 0.0591589 0.102466i
\(903\) 618.130 + 3505.59i 0.0227797 + 0.129190i
\(904\) −138.144 783.452i −0.00508251 0.0288244i
\(905\) 2000.18 1678.35i 0.0734678 0.0616468i
\(906\) 32577.9 11857.4i 1.19462 0.434808i
\(907\) 43337.4 15773.5i 1.58654 0.577454i 0.609928 0.792457i \(-0.291198\pi\)
0.976613 + 0.215003i \(0.0689760\pi\)
\(908\) 18987.0 15931.9i 0.693947 0.582291i
\(909\) −6450.63 36583.3i −0.235373 1.33487i
\(910\) 2239.95 + 12703.4i 0.0815974 + 0.462762i
\(911\) −25826.7 + 44733.2i −0.939273 + 1.62687i −0.172442 + 0.985020i \(0.555166\pi\)
−0.766831 + 0.641849i \(0.778168\pi\)
\(912\) 2384.59 + 2000.91i 0.0865806 + 0.0726498i
\(913\) 18819.1 + 6849.58i 0.682168 + 0.248289i
\(914\) −2214.98 3836.45i −0.0801585 0.138839i
\(915\) −23074.7 + 39966.5i −0.833689 + 1.44399i
\(916\) −19158.6 + 16075.9i −0.691066 + 0.579874i
\(917\) 7034.46 + 12184.0i 0.253324 + 0.438770i
\(918\) −234.394 + 1329.31i −0.00842717 + 0.0477929i
\(919\) 41338.7 1.48383 0.741914 0.670495i \(-0.233918\pi\)
0.741914 + 0.670495i \(0.233918\pi\)
\(920\) 2670.76 15146.6i 0.0957089 0.542792i
\(921\) 17964.6 + 15074.1i 0.642728 + 0.539313i
\(922\) −11467.9 + 4173.96i −0.409624 + 0.149091i
\(923\) −68184.3 24817.0i −2.43154 0.885009i
\(924\) −6531.02 −0.232527
\(925\) 18391.9 16147.7i 0.653755 0.573983i
\(926\) −14991.2 −0.532012
\(927\) −10872.4 3957.24i −0.385218 0.140208i
\(928\) 5601.79 2038.88i 0.198155 0.0721225i
\(929\) −30439.8 25542.0i −1.07502 0.902052i −0.0795259 0.996833i \(-0.525341\pi\)
−0.995498 + 0.0947805i \(0.969785\pi\)
\(930\) −2997.42 + 16999.2i −0.105687 + 0.599383i
\(931\) 8138.06 0.286481
\(932\) −4478.85 + 25400.8i −0.157414 + 0.892738i
\(933\) 6154.84 + 10660.5i 0.215971 + 0.374072i
\(934\) −6031.39 + 5060.94i −0.211299 + 0.177301i
\(935\) 34656.1 60026.1i 1.21217 2.09953i
\(936\) 8102.55 + 14034.0i 0.282949 + 0.490082i
\(937\) 3858.14 + 1404.25i 0.134514 + 0.0489592i 0.408400 0.912803i \(-0.366087\pi\)
−0.273886 + 0.961762i \(0.588309\pi\)
\(938\) −2466.23 2069.41i −0.0858477 0.0720348i
\(939\) 6021.95 10430.3i 0.209285 0.362493i
\(940\) 6082.26 + 34494.2i 0.211044 + 1.19689i
\(941\) 313.614 + 1778.59i 0.0108645 + 0.0616158i 0.989758 0.142755i \(-0.0455962\pi\)
−0.978893 + 0.204371i \(0.934485\pi\)
\(942\) −4696.23 + 3940.60i −0.162432 + 0.136297i
\(943\) −4963.61 + 1806.61i −0.171408 + 0.0623873i
\(944\) −4267.60 + 1553.28i −0.147138 + 0.0535539i
\(945\) 384.676 322.781i 0.0132418 0.0111112i
\(946\) −1102.12 6250.41i −0.0378783 0.214818i
\(947\) −2822.18 16005.4i −0.0968411 0.549213i −0.994168 0.107846i \(-0.965605\pi\)
0.897327 0.441367i \(-0.145506\pi\)
\(948\) −6898.04 + 11947.8i −0.236327 + 0.409330i
\(949\) 54249.0 + 45520.4i 1.85564 + 1.55706i
\(950\) 5372.90 + 1955.58i 0.183495 + 0.0667866i
\(951\) −324.606 562.234i −0.0110684 0.0191711i
\(952\) 2748.64 4760.79i 0.0935756 0.162078i
\(953\) −28745.9 + 24120.7i −0.977096 + 0.819881i −0.983649 0.180098i \(-0.942359\pi\)
0.00655297 + 0.999979i \(0.497914\pi\)
\(954\) 8043.84 + 13932.3i 0.272986 + 0.472826i
\(955\) −1961.38 + 11123.6i −0.0664596 + 0.376911i
\(956\) 9921.39 0.335649
\(957\) −9133.59 + 51799.2i −0.308513 + 1.74967i
\(958\) 7570.62 + 6352.51i 0.255319 + 0.214238i
\(959\) 971.114 353.456i 0.0326996 0.0119017i
\(960\) 6804.56 + 2476.66i 0.228767 + 0.0832643i
\(961\) −23972.3 −0.804682
\(962\) −32828.3 + 734.913i −1.10024 + 0.0246305i
\(963\) −12239.1 −0.409553
\(964\) −11677.1 4250.13i −0.390141 0.142000i
\(965\) −13554.6 + 4933.49i −0.452165 + 0.164575i
\(966\) 8244.93 + 6918.32i 0.274613 + 0.230428i
\(967\) 1021.23 5791.65i 0.0339611 0.192603i −0.963107 0.269117i \(-0.913268\pi\)
0.997068 + 0.0765145i \(0.0243791\pi\)
\(968\) 996.695 0.0330940
\(969\) 4014.46 22767.1i 0.133089 0.754784i
\(970\) −7947.02 13764.6i −0.263055 0.455625i
\(971\) 34094.1 28608.3i 1.12681 0.945505i 0.127881 0.991790i \(-0.459182\pi\)
0.998928 + 0.0462843i \(0.0147380\pi\)
\(972\) −10781.2 + 18673.6i −0.355769 + 0.616210i
\(973\) −6692.22 11591.3i −0.220496 0.381910i
\(974\) 2209.01 + 804.013i 0.0726706 + 0.0264499i
\(975\) 44973.4 + 37737.2i 1.47723 + 1.23955i
\(976\) 3263.03 5651.74i 0.107016 0.185356i
\(977\) −7798.63 44228.3i −0.255374 1.44830i −0.795111 0.606464i \(-0.792587\pi\)
0.539737 0.841834i \(-0.318524\pi\)
\(978\) 6212.06 + 35230.4i 0.203108 + 1.15188i
\(979\) −19959.3 + 16747.8i −0.651585 + 0.546745i
\(980\) 17789.4 6474.82i 0.579859 0.211052i
\(981\) −45164.9 + 16438.7i −1.46993 + 0.535012i
\(982\) −5478.70 + 4597.17i −0.178037 + 0.149391i
\(983\) −3821.18 21671.0i −0.123984 0.703150i −0.981906 0.189369i \(-0.939356\pi\)
0.857922 0.513781i \(-0.171756\pi\)
\(984\) −431.850 2449.14i −0.0139907 0.0793453i
\(985\) −14261.5 + 24701.7i −0.461330 + 0.799047i
\(986\) −33915.1 28458.1i −1.09541 0.919160i
\(987\) −23033.0 8383.31i −0.742804 0.270358i
\(988\) −3835.60 6643.45i −0.123509 0.213923i
\(989\) −5229.73 + 9058.15i −0.168145 + 0.291236i
\(990\) −24814.9 + 20822.2i −0.796635 + 0.668456i
\(991\) 5050.20 + 8747.20i 0.161882 + 0.280387i 0.935544 0.353211i \(-0.114910\pi\)
−0.773662 + 0.633599i \(0.781577\pi\)
\(992\) 423.871 2403.89i 0.0135664 0.0769391i
\(993\) −17490.0 −0.558940
\(994\) 1997.62 11329.1i 0.0637433 0.361506i
\(995\) −14793.2 12413.0i −0.471333 0.395495i
\(996\) 14601.6 5314.54i 0.464527 0.169074i
\(997\) 12408.2 + 4516.22i 0.394154 + 0.143460i 0.531491 0.847064i \(-0.321632\pi\)
−0.137337 + 0.990524i \(0.543854\pi\)
\(998\) 18346.3 0.581907
\(999\) 663.763 + 1092.45i 0.0210216 + 0.0345983i
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 74.4.f.b.53.5 yes 30
37.7 even 9 inner 74.4.f.b.7.5 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.4.f.b.7.5 30 37.7 even 9 inner
74.4.f.b.53.5 yes 30 1.1 even 1 trivial