Properties

Label 138.5.h.a.7.8
Level $138$
Weight $5$
Character 138.7
Analytic conductor $14.265$
Analytic rank $0$
Dimension $160$
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] = [138,5,Mod(7,138)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(138, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 19]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("138.7");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 138.h (of order \(22\), degree \(10\), 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: \(14.2650549056\)
Analytic rank: \(0\)
Dimension: \(160\)
Relative dimension: \(16\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 7.8
Character \(\chi\) \(=\) 138.7
Dual form 138.5.h.a.79.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.85223 + 2.13758i) q^{2} +(4.37128 - 2.80925i) q^{3} +(-1.13852 - 7.91857i) q^{4} +(43.6718 - 19.9442i) q^{5} +(-2.09159 + 14.5473i) q^{6} +(-0.290384 - 0.988957i) q^{7} +(19.0354 + 12.2333i) q^{8} +(11.2162 - 24.5601i) q^{9} +O(q^{10})\) \(q+(-1.85223 + 2.13758i) q^{2} +(4.37128 - 2.80925i) q^{3} +(-1.13852 - 7.91857i) q^{4} +(43.6718 - 19.9442i) q^{5} +(-2.09159 + 14.5473i) q^{6} +(-0.290384 - 0.988957i) q^{7} +(19.0354 + 12.2333i) q^{8} +(11.2162 - 24.5601i) q^{9} +(-38.2575 + 130.293i) q^{10} +(97.5081 - 84.4913i) q^{11} +(-27.2220 - 31.4159i) q^{12} +(-28.6351 - 8.40802i) q^{13} +(2.65183 + 1.21105i) q^{14} +(134.873 - 209.867i) q^{15} +(-61.4076 + 18.0309i) q^{16} +(-479.269 - 68.9085i) q^{17} +(31.7242 + 69.4664i) q^{18} +(-258.631 + 37.1855i) q^{19} +(-207.651 - 323.111i) q^{20} +(-4.04758 - 3.50725i) q^{21} +364.929i q^{22} +(527.280 - 42.6289i) q^{23} +117.576 q^{24} +(1100.16 - 1269.66i) q^{25} +(71.0115 - 45.6363i) q^{26} +(-19.9662 - 138.868i) q^{27} +(-7.50052 + 3.42537i) q^{28} +(-35.5450 + 247.221i) q^{29} +(198.792 + 677.023i) q^{30} +(-117.324 - 75.3998i) q^{31} +(75.1981 - 164.661i) q^{32} +(188.878 - 643.260i) q^{33} +(1035.01 - 896.843i) q^{34} +(-32.4056 - 37.3980i) q^{35} +(-207.250 - 60.8542i) q^{36} +(2344.23 + 1070.57i) q^{37} +(399.556 - 621.721i) q^{38} +(-148.792 + 43.6893i) q^{39} +(1075.29 + 154.604i) q^{40} +(1039.67 + 2276.56i) q^{41} +(14.9941 - 2.15582i) q^{42} +(-1486.88 - 2313.64i) q^{43} +(-780.065 - 675.930i) q^{44} -1296.28i q^{45} +(-885.518 + 1206.06i) q^{46} +70.8451 q^{47} +(-217.776 + 251.327i) q^{48} +(2018.96 - 1297.50i) q^{49} +(676.243 + 4703.38i) q^{50} +(-2288.60 + 1045.17i) q^{51} +(-33.9779 + 236.322i) q^{52} +(86.3704 + 294.151i) q^{53} +(333.824 + 214.536i) q^{54} +(2573.24 - 5634.61i) q^{55} +(6.57064 - 22.3775i) q^{56} +(-1026.08 + 889.107i) q^{57} +(-462.618 - 533.889i) q^{58} +(-4320.25 - 1268.54i) q^{59} +(-1815.40 - 829.066i) q^{60} +(1403.22 - 2183.45i) q^{61} +(378.485 - 111.133i) q^{62} +(-27.5459 - 3.96050i) q^{63} +(212.692 + 465.732i) q^{64} +(-1418.24 + 203.911i) q^{65} +(1025.18 + 1595.21i) q^{66} +(2673.90 + 2316.95i) q^{67} +3873.58i q^{68} +(2185.13 - 1667.60i) q^{69} +139.964 q^{70} +(-4844.91 + 5591.33i) q^{71} +(513.956 - 330.299i) q^{72} +(-535.590 - 3725.11i) q^{73} +(-6630.48 + 3028.04i) q^{74} +(1242.34 - 8640.65i) q^{75} +(588.912 + 2005.65i) q^{76} +(-111.873 - 71.8964i) q^{77} +(182.207 - 398.978i) q^{78} +(-2923.47 + 9956.42i) q^{79} +(-2322.16 + 2012.17i) q^{80} +(-477.393 - 550.941i) q^{81} +(-6792.03 - 1994.32i) q^{82} +(2451.63 + 1119.62i) q^{83} +(-23.1642 + 36.0441i) q^{84} +(-22304.8 + 6549.29i) q^{85} +(7699.64 + 1107.04i) q^{86} +(539.128 + 1180.53i) q^{87} +(2889.71 - 415.478i) q^{88} +(-953.129 - 1483.10i) q^{89} +(2770.90 + 2401.00i) q^{90} +30.7604i q^{91} +(-937.878 - 4126.77i) q^{92} -724.675 q^{93} +(-131.221 + 151.437i) q^{94} +(-10553.2 + 6782.15i) q^{95} +(-133.862 - 931.030i) q^{96} +(-4395.61 + 2007.41i) q^{97} +(-966.040 + 6718.96i) q^{98} +(-981.440 - 3342.48i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 160 q - 128 q^{4} - 432 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 160 q - 128 q^{4} - 432 q^{9} + 208 q^{13} - 1024 q^{16} - 1980 q^{17} - 3828 q^{19} - 3168 q^{20} + 3120 q^{23} + 9768 q^{25} + 4416 q^{26} + 5280 q^{28} - 828 q^{29} - 7748 q^{31} + 16464 q^{35} - 3456 q^{36} - 3520 q^{37} - 9072 q^{39} - 5472 q^{41} - 7216 q^{43} - 1280 q^{46} + 6960 q^{47} + 13888 q^{49} - 7296 q^{50} + 17424 q^{51} + 1664 q^{52} + 14784 q^{53} + 37316 q^{55} - 15840 q^{57} - 9984 q^{58} - 29808 q^{59} - 44968 q^{61} - 8192 q^{64} - 5852 q^{67} - 10584 q^{69} + 4352 q^{70} + 30048 q^{71} + 17084 q^{73} + 4176 q^{75} - 14160 q^{77} - 6912 q^{78} + 28424 q^{79} - 11664 q^{81} - 128 q^{82} - 35904 q^{83} - 91892 q^{85} + 8064 q^{87} - 15312 q^{89} - 6720 q^{92} + 11952 q^{93} + 21248 q^{94} + 224268 q^{95} + 41712 q^{97} + 62976 q^{98} + 17820 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/138\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(97\)
\(\chi(n)\) \(1\) \(e\left(\frac{19}{22}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.85223 + 2.13758i −0.463056 + 0.534396i
\(3\) 4.37128 2.80925i 0.485698 0.312139i
\(4\) −1.13852 7.91857i −0.0711574 0.494911i
\(5\) 43.6718 19.9442i 1.74687 0.797769i 0.757415 0.652934i \(-0.226462\pi\)
0.989456 0.144835i \(-0.0462650\pi\)
\(6\) −2.09159 + 14.5473i −0.0580998 + 0.404093i
\(7\) −0.290384 0.988957i −0.00592620 0.0201828i 0.956477 0.291808i \(-0.0942570\pi\)
−0.962403 + 0.271626i \(0.912439\pi\)
\(8\) 19.0354 + 12.2333i 0.297428 + 0.191145i
\(9\) 11.2162 24.5601i 0.138472 0.303211i
\(10\) −38.2575 + 130.293i −0.382575 + 1.30293i
\(11\) 97.5081 84.4913i 0.805852 0.698275i −0.151101 0.988518i \(-0.548282\pi\)
0.956953 + 0.290243i \(0.0937363\pi\)
\(12\) −27.2220 31.4159i −0.189042 0.218166i
\(13\) −28.6351 8.40802i −0.169438 0.0497516i 0.195913 0.980621i \(-0.437233\pi\)
−0.365351 + 0.930870i \(0.619051\pi\)
\(14\) 2.65183 + 1.21105i 0.0135298 + 0.00617884i
\(15\) 134.873 209.867i 0.599436 0.932741i
\(16\) −61.4076 + 18.0309i −0.239873 + 0.0704331i
\(17\) −479.269 68.9085i −1.65837 0.238438i −0.751465 0.659773i \(-0.770653\pi\)
−0.906905 + 0.421335i \(0.861562\pi\)
\(18\) 31.7242 + 69.4664i 0.0979143 + 0.214402i
\(19\) −258.631 + 37.1855i −0.716429 + 0.103007i −0.490883 0.871226i \(-0.663326\pi\)
−0.225546 + 0.974233i \(0.572417\pi\)
\(20\) −207.651 323.111i −0.519127 0.807778i
\(21\) −4.04758 3.50725i −0.00917819 0.00795294i
\(22\) 364.929i 0.753985i
\(23\) 527.280 42.6289i 0.996748 0.0805840i
\(24\) 117.576 0.204124
\(25\) 1100.16 1269.66i 1.76026 2.03145i
\(26\) 71.0115 45.6363i 0.105047 0.0675093i
\(27\) −19.9662 138.868i −0.0273885 0.190491i
\(28\) −7.50052 + 3.42537i −0.00956699 + 0.00436910i
\(29\) −35.5450 + 247.221i −0.0422651 + 0.293961i 0.957715 + 0.287717i \(0.0928964\pi\)
−0.999981 + 0.00624317i \(0.998013\pi\)
\(30\) 198.792 + 677.023i 0.220880 + 0.752248i
\(31\) −117.324 75.3998i −0.122086 0.0784598i 0.478173 0.878266i \(-0.341299\pi\)
−0.600259 + 0.799806i \(0.704936\pi\)
\(32\) 75.1981 164.661i 0.0734357 0.160802i
\(33\) 188.878 643.260i 0.173442 0.590689i
\(34\) 1035.01 896.843i 0.895339 0.775816i
\(35\) −32.4056 37.3980i −0.0264535 0.0305290i
\(36\) −207.250 60.8542i −0.159915 0.0469554i
\(37\) 2344.23 + 1070.57i 1.71237 + 0.782012i 0.996483 + 0.0837917i \(0.0267031\pi\)
0.715883 + 0.698220i \(0.246024\pi\)
\(38\) 399.556 621.721i 0.276701 0.430555i
\(39\) −148.792 + 43.6893i −0.0978253 + 0.0287241i
\(40\) 1075.29 + 154.604i 0.672058 + 0.0966274i
\(41\) 1039.67 + 2276.56i 0.618482 + 1.35429i 0.916618 + 0.399764i \(0.130908\pi\)
−0.298136 + 0.954523i \(0.596365\pi\)
\(42\) 14.9941 2.15582i 0.00850004 0.00122212i
\(43\) −1486.88 2313.64i −0.804156 1.25129i −0.964461 0.264224i \(-0.914884\pi\)
0.160305 0.987068i \(-0.448752\pi\)
\(44\) −780.065 675.930i −0.402926 0.349138i
\(45\) 1296.28i 0.640138i
\(46\) −885.518 + 1206.06i −0.418487 + 0.569973i
\(47\) 70.8451 0.0320711 0.0160356 0.999871i \(-0.494896\pi\)
0.0160356 + 0.999871i \(0.494896\pi\)
\(48\) −217.776 + 251.327i −0.0945210 + 0.109083i
\(49\) 2018.96 1297.50i 0.840881 0.540402i
\(50\) 676.243 + 4703.38i 0.270497 + 1.88135i
\(51\) −2288.60 + 1045.17i −0.879893 + 0.401834i
\(52\) −33.9779 + 236.322i −0.0125658 + 0.0873970i
\(53\) 86.3704 + 294.151i 0.0307477 + 0.104717i 0.973437 0.228954i \(-0.0735306\pi\)
−0.942689 + 0.333671i \(0.891712\pi\)
\(54\) 333.824 + 214.536i 0.114480 + 0.0735719i
\(55\) 2573.24 5634.61i 0.850657 1.86268i
\(56\) 6.57064 22.3775i 0.00209523 0.00713570i
\(57\) −1026.08 + 889.107i −0.315816 + 0.273656i
\(58\) −462.618 533.889i −0.137520 0.158707i
\(59\) −4320.25 1268.54i −1.24109 0.364418i −0.405667 0.914021i \(-0.632961\pi\)
−0.835426 + 0.549603i \(0.814779\pi\)
\(60\) −1815.40 829.066i −0.504278 0.230296i
\(61\) 1403.22 2183.45i 0.377107 0.586790i −0.599880 0.800090i \(-0.704785\pi\)
0.976987 + 0.213300i \(0.0684212\pi\)
\(62\) 378.485 111.133i 0.0984612 0.0289108i
\(63\) −27.5459 3.96050i −0.00694025 0.000997857i
\(64\) 212.692 + 465.732i 0.0519269 + 0.113704i
\(65\) −1418.24 + 203.911i −0.335677 + 0.0482631i
\(66\) 1025.18 + 1595.21i 0.235348 + 0.366209i
\(67\) 2673.90 + 2316.95i 0.595657 + 0.516140i 0.899694 0.436521i \(-0.143789\pi\)
−0.304038 + 0.952660i \(0.598335\pi\)
\(68\) 3873.58i 0.837712i
\(69\) 2185.13 1667.60i 0.458965 0.350263i
\(70\) 139.964 0.0285640
\(71\) −4844.91 + 5591.33i −0.961101 + 1.10917i 0.0328625 + 0.999460i \(0.489538\pi\)
−0.993964 + 0.109710i \(0.965008\pi\)
\(72\) 513.956 330.299i 0.0991427 0.0637151i
\(73\) −535.590 3725.11i −0.100505 0.699027i −0.976312 0.216366i \(-0.930580\pi\)
0.875807 0.482661i \(-0.160330\pi\)
\(74\) −6630.48 + 3028.04i −1.21083 + 0.552966i
\(75\) 1242.34 8640.65i 0.220860 1.53612i
\(76\) 588.912 + 2005.65i 0.101958 + 0.347239i
\(77\) −111.873 71.8964i −0.0188688 0.0121262i
\(78\) 182.207 398.978i 0.0299486 0.0655783i
\(79\) −2923.47 + 9956.42i −0.468430 + 1.59533i 0.299040 + 0.954240i \(0.403333\pi\)
−0.767470 + 0.641085i \(0.778485\pi\)
\(80\) −2322.16 + 2012.17i −0.362838 + 0.314401i
\(81\) −477.393 550.941i −0.0727623 0.0839722i
\(82\) −6792.03 1994.32i −1.01012 0.296597i
\(83\) 2451.63 + 1119.62i 0.355875 + 0.162523i 0.585327 0.810797i \(-0.300966\pi\)
−0.229452 + 0.973320i \(0.573693\pi\)
\(84\) −23.1642 + 36.0441i −0.00328290 + 0.00510829i
\(85\) −22304.8 + 6549.29i −3.08718 + 0.906477i
\(86\) 7699.64 + 1107.04i 1.04105 + 0.149681i
\(87\) 539.128 + 1180.53i 0.0712285 + 0.155969i
\(88\) 2889.71 415.478i 0.373155 0.0536516i
\(89\) −953.129 1483.10i −0.120329 0.187236i 0.775863 0.630901i \(-0.217315\pi\)
−0.896193 + 0.443665i \(0.853678\pi\)
\(90\) 2770.90 + 2401.00i 0.342087 + 0.296420i
\(91\) 30.7604i 0.00371458i
\(92\) −937.878 4126.77i −0.110808 0.487567i
\(93\) −724.675 −0.0837872
\(94\) −131.221 + 151.437i −0.0148507 + 0.0171387i
\(95\) −10553.2 + 6782.15i −1.16933 + 0.751484i
\(96\) −133.862 931.030i −0.0145249 0.101023i
\(97\) −4395.61 + 2007.41i −0.467170 + 0.213350i −0.635070 0.772455i \(-0.719029\pi\)
0.167900 + 0.985804i \(0.446302\pi\)
\(98\) −966.040 + 6718.96i −0.100587 + 0.699600i
\(99\) −981.440 3342.48i −0.100137 0.341034i
\(100\) −11306.4 7266.19i −1.13064 0.726619i
\(101\) 1689.99 3700.57i 0.165669 0.362765i −0.808530 0.588455i \(-0.799736\pi\)
0.974199 + 0.225690i \(0.0724636\pi\)
\(102\) 2004.87 6827.96i 0.192702 0.656282i
\(103\) −3703.17 + 3208.81i −0.349059 + 0.302462i −0.811689 0.584090i \(-0.801451\pi\)
0.462630 + 0.886552i \(0.346906\pi\)
\(104\) −442.222 510.352i −0.0408859 0.0471849i
\(105\) −246.714 72.4419i −0.0223777 0.00657069i
\(106\) −788.749 360.209i −0.0701983 0.0320585i
\(107\) 154.840 240.935i 0.0135243 0.0210442i −0.834426 0.551121i \(-0.814200\pi\)
0.847950 + 0.530076i \(0.177837\pi\)
\(108\) −1076.91 + 316.208i −0.0923273 + 0.0271097i
\(109\) 20740.8 + 2982.08i 1.74572 + 0.250996i 0.939968 0.341263i \(-0.110855\pi\)
0.805748 + 0.592259i \(0.201764\pi\)
\(110\) 7278.22 + 15937.1i 0.601506 + 1.31711i
\(111\) 13254.8 1905.75i 1.07579 0.154675i
\(112\) 35.6635 + 55.4936i 0.00284308 + 0.00442391i
\(113\) 9424.28 + 8166.19i 0.738060 + 0.639532i 0.940512 0.339760i \(-0.110346\pi\)
−0.202453 + 0.979292i \(0.564891\pi\)
\(114\) 3840.17i 0.295489i
\(115\) 22177.0 12377.9i 1.67690 0.935944i
\(116\) 1998.10 0.148492
\(117\) −527.678 + 608.973i −0.0385476 + 0.0444863i
\(118\) 10713.7 6885.26i 0.769440 0.494489i
\(119\) 71.0245 + 493.986i 0.00501550 + 0.0348836i
\(120\) 5134.73 2344.95i 0.356578 0.162844i
\(121\) 285.428 1985.20i 0.0194951 0.135592i
\(122\) 2068.22 + 7043.73i 0.138956 + 0.473241i
\(123\) 10940.1 + 7030.78i 0.723121 + 0.464722i
\(124\) −463.483 + 1014.89i −0.0301433 + 0.0660046i
\(125\) 14269.9 48599.0i 0.913276 3.11033i
\(126\) 59.4870 51.5458i 0.00374698 0.00324678i
\(127\) 9266.78 + 10694.4i 0.574542 + 0.663056i 0.966422 0.256960i \(-0.0827208\pi\)
−0.391880 + 0.920016i \(0.628175\pi\)
\(128\) −1389.49 407.992i −0.0848080 0.0249019i
\(129\) −12999.2 5936.53i −0.781154 0.356741i
\(130\) 2191.01 3409.29i 0.129646 0.201733i
\(131\) −15144.7 + 4446.89i −0.882508 + 0.259128i −0.691427 0.722446i \(-0.743018\pi\)
−0.191081 + 0.981574i \(0.561199\pi\)
\(132\) −5308.74 763.282i −0.304680 0.0438064i
\(133\) 111.877 + 244.977i 0.00632467 + 0.0138491i
\(134\) −9905.35 + 1424.17i −0.551645 + 0.0793146i
\(135\) −3641.58 5666.40i −0.199812 0.310914i
\(136\) −8280.10 7174.74i −0.447670 0.387908i
\(137\) 31843.0i 1.69657i 0.529536 + 0.848287i \(0.322366\pi\)
−0.529536 + 0.848287i \(0.677634\pi\)
\(138\) −482.717 + 7759.68i −0.0253474 + 0.407461i
\(139\) −4575.12 −0.236795 −0.118398 0.992966i \(-0.537776\pi\)
−0.118398 + 0.992966i \(0.537776\pi\)
\(140\) −259.245 + 299.184i −0.0132268 + 0.0152645i
\(141\) 309.684 199.022i 0.0155769 0.0100107i
\(142\) −2978.05 20712.8i −0.147691 1.02722i
\(143\) −3502.56 + 1599.56i −0.171283 + 0.0782221i
\(144\) −245.920 + 1710.41i −0.0118596 + 0.0824851i
\(145\) 3378.32 + 11505.5i 0.160681 + 0.547229i
\(146\) 8954.77 + 5754.88i 0.420096 + 0.269979i
\(147\) 5180.41 11343.5i 0.239734 0.524944i
\(148\) 5808.47 19781.8i 0.265178 0.903115i
\(149\) −8914.90 + 7724.81i −0.401554 + 0.347949i −0.832105 0.554618i \(-0.812865\pi\)
0.430551 + 0.902566i \(0.358319\pi\)
\(150\) 16169.0 + 18660.0i 0.718623 + 0.829335i
\(151\) −1756.33 515.704i −0.0770285 0.0226176i 0.242991 0.970028i \(-0.421871\pi\)
−0.320020 + 0.947411i \(0.603690\pi\)
\(152\) −5378.04 2456.07i −0.232775 0.106305i
\(153\) −7067.98 + 10998.0i −0.301934 + 0.469819i
\(154\) 360.899 105.969i 0.0152175 0.00446827i
\(155\) −6627.56 952.899i −0.275861 0.0396628i
\(156\) 515.360 + 1128.48i 0.0211769 + 0.0463708i
\(157\) 11103.9 1596.50i 0.450481 0.0647694i 0.0866595 0.996238i \(-0.472381\pi\)
0.363822 + 0.931469i \(0.381472\pi\)
\(158\) −15867.8 24690.7i −0.635625 0.989052i
\(159\) 1203.89 + 1043.18i 0.0476204 + 0.0412633i
\(160\) 8690.80i 0.339485i
\(161\) −195.272 509.078i −0.00753334 0.0196396i
\(162\) 2061.92 0.0785674
\(163\) 6269.33 7235.20i 0.235964 0.272317i −0.625401 0.780304i \(-0.715065\pi\)
0.861365 + 0.507986i \(0.169610\pi\)
\(164\) 16843.4 10824.6i 0.626242 0.402461i
\(165\) −4580.68 31859.3i −0.168253 1.17022i
\(166\) −6934.25 + 3166.76i −0.251642 + 0.114921i
\(167\) −6191.45 + 43062.5i −0.222003 + 1.54407i 0.508443 + 0.861096i \(0.330221\pi\)
−0.730446 + 0.682971i \(0.760688\pi\)
\(168\) −34.1420 116.277i −0.00120968 0.00411980i
\(169\) −23277.8 14959.7i −0.815019 0.523781i
\(170\) 27314.0 59809.2i 0.945120 2.06952i
\(171\) −1987.58 + 6769.07i −0.0679723 + 0.231492i
\(172\) −16627.9 + 14408.1i −0.562056 + 0.487024i
\(173\) 18146.2 + 20941.8i 0.606307 + 0.699715i 0.973047 0.230608i \(-0.0740716\pi\)
−0.366740 + 0.930323i \(0.619526\pi\)
\(174\) −3522.06 1034.17i −0.116332 0.0341581i
\(175\) −1575.10 719.326i −0.0514320 0.0234882i
\(176\) −4464.28 + 6946.56i −0.144121 + 0.224256i
\(177\) −22448.7 + 6591.52i −0.716545 + 0.210397i
\(178\) 4935.66 + 709.640i 0.155778 + 0.0223974i
\(179\) −15916.2 34851.6i −0.496745 1.08772i −0.977514 0.210872i \(-0.932370\pi\)
0.480768 0.876848i \(-0.340358\pi\)
\(180\) −10264.7 + 1475.84i −0.316811 + 0.0455506i
\(181\) 9434.60 + 14680.5i 0.287983 + 0.448110i 0.954859 0.297058i \(-0.0960056\pi\)
−0.666877 + 0.745168i \(0.732369\pi\)
\(182\) −65.7529 56.9752i −0.00198505 0.00172006i
\(183\) 13486.4i 0.402713i
\(184\) 10558.5 + 5638.91i 0.311864 + 0.166556i
\(185\) 123728. 3.61515
\(186\) 1342.26 1549.05i 0.0387982 0.0447755i
\(187\) −52554.8 + 33774.9i −1.50290 + 0.965853i
\(188\) −80.6585 560.992i −0.00228210 0.0158723i
\(189\) −131.537 + 60.0708i −0.00368234 + 0.00168167i
\(190\) 5049.56 35120.5i 0.139877 0.972866i
\(191\) 3376.03 + 11497.7i 0.0925422 + 0.315170i 0.992735 0.120322i \(-0.0383927\pi\)
−0.900193 + 0.435492i \(0.856575\pi\)
\(192\) 2238.10 + 1438.34i 0.0607122 + 0.0390174i
\(193\) 9685.18 21207.6i 0.260012 0.569347i −0.733934 0.679221i \(-0.762318\pi\)
0.993945 + 0.109875i \(0.0350449\pi\)
\(194\) 3850.66 13114.1i 0.102313 0.348447i
\(195\) −5626.67 + 4875.54i −0.147973 + 0.128219i
\(196\) −12573.0 14510.0i −0.327285 0.377708i
\(197\) −55886.2 16409.7i −1.44003 0.422831i −0.533799 0.845611i \(-0.679236\pi\)
−0.906232 + 0.422780i \(0.861054\pi\)
\(198\) 8962.67 + 4093.11i 0.228616 + 0.104406i
\(199\) −15250.4 + 23730.1i −0.385102 + 0.599230i −0.978641 0.205574i \(-0.934094\pi\)
0.593539 + 0.804805i \(0.297730\pi\)
\(200\) 36474.1 10709.8i 0.911853 0.267744i
\(201\) 18197.3 + 2616.37i 0.450417 + 0.0647601i
\(202\) 4780.02 + 10466.8i 0.117146 + 0.256514i
\(203\) 254.812 36.6365i 0.00618342 0.000889041i
\(204\) 10881.9 + 16932.5i 0.261483 + 0.406875i
\(205\) 90808.3 + 78685.8i 2.16082 + 1.87236i
\(206\) 13859.3i 0.326592i
\(207\) 4867.11 13428.2i 0.113587 0.313383i
\(208\) 1910.01 0.0441479
\(209\) −22076.8 + 25477.9i −0.505409 + 0.583273i
\(210\) 611.821 393.194i 0.0138735 0.00891595i
\(211\) 7866.25 + 54711.0i 0.176686 + 1.22888i 0.864365 + 0.502865i \(0.167721\pi\)
−0.687679 + 0.726015i \(0.741370\pi\)
\(212\) 2230.92 1018.83i 0.0496377 0.0226688i
\(213\) −5471.03 + 38051.8i −0.120590 + 0.838719i
\(214\) 228.221 + 777.249i 0.00498343 + 0.0169720i
\(215\) −111079. 71385.9i −2.40300 1.54431i
\(216\) 1318.75 2887.66i 0.0282654 0.0618926i
\(217\) −40.4981 + 137.924i −0.000860032 + 0.00292900i
\(218\) −44791.2 + 38811.8i −0.942496 + 0.816678i
\(219\) −12806.0 14778.9i −0.267009 0.308144i
\(220\) −47547.7 13961.3i −0.982391 0.288456i
\(221\) 13144.5 + 6002.90i 0.269129 + 0.122907i
\(222\) −20477.2 + 31863.1i −0.415494 + 0.646521i
\(223\) −19233.0 + 5647.31i −0.386755 + 0.113562i −0.469329 0.883023i \(-0.655504\pi\)
0.0825737 + 0.996585i \(0.473686\pi\)
\(224\) −184.679 26.5528i −0.00368062 0.000529194i
\(225\) −18843.2 41260.8i −0.372211 0.815028i
\(226\) −34911.8 + 5019.56i −0.683527 + 0.0982763i
\(227\) −35157.2 54705.6i −0.682279 1.06165i −0.993776 0.111400i \(-0.964467\pi\)
0.311497 0.950247i \(-0.399170\pi\)
\(228\) 8208.68 + 7112.86i 0.157908 + 0.136828i
\(229\) 9449.87i 0.180200i −0.995933 0.0901000i \(-0.971281\pi\)
0.995933 0.0901000i \(-0.0287187\pi\)
\(230\) −14618.2 + 70331.8i −0.276336 + 1.32952i
\(231\) −691.004 −0.0129496
\(232\) −3700.94 + 4271.11i −0.0687600 + 0.0793533i
\(233\) 67884.5 43626.7i 1.25043 0.803601i 0.263484 0.964664i \(-0.415128\pi\)
0.986944 + 0.161062i \(0.0514920\pi\)
\(234\) −324.351 2255.91i −0.00592357 0.0411994i
\(235\) 3093.93 1412.95i 0.0560241 0.0255853i
\(236\) −5126.33 + 35654.4i −0.0920413 + 0.640161i
\(237\) 15190.8 + 51735.1i 0.270448 + 0.921061i
\(238\) −1187.49 763.154i −0.0209641 0.0134728i
\(239\) −12335.1 + 27010.0i −0.215946 + 0.472856i −0.986342 0.164710i \(-0.947331\pi\)
0.770396 + 0.637566i \(0.220059\pi\)
\(240\) −4498.15 + 15319.3i −0.0780929 + 0.265960i
\(241\) −34955.0 + 30288.7i −0.601831 + 0.521490i −0.901627 0.432513i \(-0.857627\pi\)
0.299796 + 0.954003i \(0.403081\pi\)
\(242\) 3714.85 + 4287.16i 0.0634322 + 0.0732047i
\(243\) −3634.55 1067.20i −0.0615515 0.0180732i
\(244\) −18887.4 8625.57i −0.317243 0.144880i
\(245\) 62293.6 96930.8i 1.03780 1.61484i
\(246\) −35292.4 + 10362.8i −0.583191 + 0.171240i
\(247\) 7718.57 + 1109.76i 0.126515 + 0.0181901i
\(248\) −1310.93 2870.53i −0.0213145 0.0466723i
\(249\) 13862.0 1993.06i 0.223578 0.0321456i
\(250\) 77453.1 + 120519.i 1.23925 + 1.92831i
\(251\) −16003.2 13866.8i −0.254014 0.220105i 0.518540 0.855053i \(-0.326476\pi\)
−0.772554 + 0.634949i \(0.781021\pi\)
\(252\) 222.633i 0.00350581i
\(253\) 47812.3 48707.2i 0.746962 0.760943i
\(254\) −40024.4 −0.620380
\(255\) −79102.1 + 91288.7i −1.21649 + 1.40390i
\(256\) 3445.77 2214.46i 0.0525783 0.0337901i
\(257\) 4791.53 + 33325.9i 0.0725451 + 0.504563i 0.993404 + 0.114667i \(0.0365800\pi\)
−0.920859 + 0.389896i \(0.872511\pi\)
\(258\) 36767.2 16791.0i 0.552359 0.252254i
\(259\) 378.025 2629.22i 0.00563535 0.0391947i
\(260\) 3229.38 + 10998.2i 0.0477718 + 0.162696i
\(261\) 5673.08 + 3645.87i 0.0832794 + 0.0535204i
\(262\) 18545.8 40609.7i 0.270174 0.591599i
\(263\) −23422.9 + 79771.1i −0.338633 + 1.15328i 0.597569 + 0.801817i \(0.296133\pi\)
−0.936202 + 0.351461i \(0.885685\pi\)
\(264\) 11464.6 9934.10i 0.164494 0.142535i
\(265\) 9638.55 + 11123.5i 0.137252 + 0.158398i
\(266\) −730.880 214.606i −0.0103296 0.00303304i
\(267\) −8332.79 3805.46i −0.116888 0.0533807i
\(268\) 15302.6 23811.4i 0.213058 0.331524i
\(269\) 51956.3 15255.8i 0.718016 0.210828i 0.0977396 0.995212i \(-0.468839\pi\)
0.620276 + 0.784384i \(0.287021\pi\)
\(270\) 18857.4 + 2711.29i 0.258675 + 0.0371919i
\(271\) 21226.7 + 46480.1i 0.289031 + 0.632890i 0.997330 0.0730224i \(-0.0232645\pi\)
−0.708299 + 0.705912i \(0.750537\pi\)
\(272\) 30673.2 4410.14i 0.414593 0.0596094i
\(273\) 86.4138 + 134.462i 0.00115946 + 0.00180416i
\(274\) −68067.1 58980.4i −0.906642 0.785610i
\(275\) 216756.i 2.86619i
\(276\) −15692.9 15404.5i −0.206008 0.202223i
\(277\) 18672.2 0.243353 0.121676 0.992570i \(-0.461173\pi\)
0.121676 + 0.992570i \(0.461173\pi\)
\(278\) 8474.15 9779.69i 0.109650 0.126542i
\(279\) −3167.76 + 2035.80i −0.0406953 + 0.0261533i
\(280\) −159.351 1108.31i −0.00203254 0.0141366i
\(281\) −86945.0 + 39706.4i −1.10111 + 0.502861i −0.881241 0.472667i \(-0.843291\pi\)
−0.219872 + 0.975529i \(0.570564\pi\)
\(282\) −148.179 + 1030.61i −0.00186333 + 0.0129597i
\(283\) −43801.6 149174.i −0.546911 1.86261i −0.504322 0.863516i \(-0.668257\pi\)
−0.0425896 0.999093i \(-0.513561\pi\)
\(284\) 49791.3 + 31998.9i 0.617330 + 0.396734i
\(285\) −27078.4 + 59293.4i −0.333375 + 0.729989i
\(286\) 3068.33 10449.8i 0.0375119 0.127754i
\(287\) 1949.51 1689.26i 0.0236681 0.0205085i
\(288\) −3200.65 3693.74i −0.0385880 0.0445330i
\(289\) 144813. + 42520.8i 1.73385 + 0.509103i
\(290\) −30851.3 14089.3i −0.366841 0.167531i
\(291\) −13575.1 + 21123.3i −0.160309 + 0.249446i
\(292\) −28887.8 + 8482.22i −0.338804 + 0.0994819i
\(293\) −96973.2 13942.6i −1.12958 0.162409i −0.447916 0.894075i \(-0.647834\pi\)
−0.681663 + 0.731667i \(0.738743\pi\)
\(294\) 14652.4 + 32084.3i 0.169517 + 0.371191i
\(295\) −213973. + 30764.6i −2.45875 + 0.353515i
\(296\) 31526.7 + 49056.5i 0.359828 + 0.559903i
\(297\) −13680.0 11853.8i −0.155086 0.134383i
\(298\) 33364.4i 0.375709i
\(299\) −15457.1 3212.69i −0.172896 0.0359358i
\(300\) −69836.1 −0.775956
\(301\) −1856.32 + 2142.31i −0.0204890 + 0.0236455i
\(302\) 4355.47 2799.09i 0.0477553 0.0306905i
\(303\) −3008.39 20923.8i −0.0327680 0.227906i
\(304\) 15211.4 6946.81i 0.164597 0.0751689i
\(305\) 17733.8 123341.i 0.190634 1.32589i
\(306\) −10417.6 35479.1i −0.111257 0.378905i
\(307\) −14159.8 9099.94i −0.150238 0.0965521i 0.463362 0.886169i \(-0.346643\pi\)
−0.613600 + 0.789617i \(0.710279\pi\)
\(308\) −441.948 + 967.730i −0.00465875 + 0.0102012i
\(309\) −7173.23 + 24429.8i −0.0751273 + 0.255860i
\(310\) 14312.6 12402.0i 0.148935 0.129053i
\(311\) 18948.9 + 21868.2i 0.195913 + 0.226096i 0.845203 0.534445i \(-0.179479\pi\)
−0.649290 + 0.760541i \(0.724934\pi\)
\(312\) −3366.78 988.577i −0.0345864 0.0101555i
\(313\) 68612.0 + 31334.0i 0.700344 + 0.319836i 0.733572 0.679612i \(-0.237852\pi\)
−0.0332285 + 0.999448i \(0.510579\pi\)
\(314\) −17154.3 + 26692.6i −0.173986 + 0.270727i
\(315\) −1281.97 + 376.419i −0.0129198 + 0.00379359i
\(316\) 82169.1 + 11814.1i 0.822876 + 0.118312i
\(317\) −11537.5 25263.7i −0.114814 0.251407i 0.843498 0.537133i \(-0.180493\pi\)
−0.958311 + 0.285726i \(0.907765\pi\)
\(318\) −4459.76 + 641.217i −0.0441019 + 0.00634090i
\(319\) 17422.1 + 27109.3i 0.171206 + 0.266401i
\(320\) 18577.3 + 16097.3i 0.181419 + 0.157200i
\(321\) 1488.18i 0.0144426i
\(322\) 1449.88 + 525.518i 0.0139837 + 0.00506846i
\(323\) 126516. 1.21267
\(324\) −3819.15 + 4407.53i −0.0363812 + 0.0419861i
\(325\) −42178.5 + 27106.5i −0.399323 + 0.256629i
\(326\) 3853.61 + 26802.4i 0.0362604 + 0.252197i
\(327\) 99041.5 45230.7i 0.926236 0.422998i
\(328\) −8059.31 + 56053.7i −0.0749118 + 0.521023i
\(329\) −20.5723 70.0628i −0.000190060 0.000647285i
\(330\) 76586.4 + 49219.1i 0.703273 + 0.451966i
\(331\) 15792.8 34581.3i 0.144146 0.315636i −0.823764 0.566933i \(-0.808130\pi\)
0.967910 + 0.251297i \(0.0808572\pi\)
\(332\) 6074.57 20688.1i 0.0551111 0.187691i
\(333\) 52586.7 45566.7i 0.474229 0.410921i
\(334\) −80581.6 92996.2i −0.722342 0.833628i
\(335\) 162984. + 47856.4i 1.45230 + 0.426432i
\(336\) 311.791 + 142.390i 0.00276175 + 0.00126125i
\(337\) 30234.0 47045.0i 0.266217 0.414241i −0.682250 0.731119i \(-0.738998\pi\)
0.948466 + 0.316878i \(0.102635\pi\)
\(338\) 75093.3 22049.4i 0.657306 0.193003i
\(339\) 64137.1 + 9221.52i 0.558097 + 0.0802423i
\(340\) 77255.5 + 169166.i 0.668300 + 1.46337i
\(341\) −17810.7 + 2560.79i −0.153170 + 0.0220225i
\(342\) −10788.0 16786.5i −0.0922335 0.143518i
\(343\) −3739.72 3240.49i −0.0317871 0.0275437i
\(344\) 62230.5i 0.525880i
\(345\) 62169.5 116408.i 0.522323 0.978013i
\(346\) −78375.5 −0.654679
\(347\) 57267.0 66089.6i 0.475604 0.548876i −0.466358 0.884596i \(-0.654434\pi\)
0.941962 + 0.335720i \(0.108980\pi\)
\(348\) 8734.28 5613.18i 0.0721221 0.0463501i
\(349\) −28926.5 201188.i −0.237489 1.65178i −0.664323 0.747445i \(-0.731280\pi\)
0.426834 0.904330i \(-0.359629\pi\)
\(350\) 4455.07 2034.56i 0.0363679 0.0166087i
\(351\) −595.871 + 4144.37i −0.00483658 + 0.0336391i
\(352\) −6579.99 22409.4i −0.0531055 0.180861i
\(353\) 47380.6 + 30449.6i 0.380234 + 0.244362i 0.716771 0.697309i \(-0.245619\pi\)
−0.336537 + 0.941670i \(0.609256\pi\)
\(354\) 27490.1 60194.8i 0.219366 0.480344i
\(355\) −100071. + 340811.i −0.794058 + 2.70431i
\(356\) −10658.9 + 9235.96i −0.0841029 + 0.0728756i
\(357\) 1698.20 + 1959.83i 0.0133246 + 0.0153774i
\(358\) 103979. + 30530.9i 0.811294 + 0.238217i
\(359\) 104812. + 47865.8i 0.813243 + 0.371395i 0.778221 0.627991i \(-0.216123\pi\)
0.0350221 + 0.999387i \(0.488850\pi\)
\(360\) 15857.8 24675.2i 0.122359 0.190395i
\(361\) −59534.9 + 17481.0i −0.456833 + 0.134138i
\(362\) −48855.9 7024.41i −0.372820 0.0536035i
\(363\) −4329.23 9479.70i −0.0328547 0.0719418i
\(364\) 243.579 35.0213i 0.00183838 0.000264320i
\(365\) −97684.7 152000.i −0.733231 1.14093i
\(366\) 28828.4 + 24979.9i 0.215208 + 0.186479i
\(367\) 201284.i 1.49443i −0.664581 0.747217i \(-0.731390\pi\)
0.664581 0.747217i \(-0.268610\pi\)
\(368\) −31610.3 + 12125.1i −0.233417 + 0.0895340i
\(369\) 67573.5 0.496277
\(370\) −229173. + 264480.i −1.67402 + 1.93192i
\(371\) 265.822 170.833i 0.00193127 0.00124115i
\(372\) 825.056 + 5738.39i 0.00596208 + 0.0414672i
\(373\) 164888. 75301.6i 1.18514 0.541236i 0.277395 0.960756i \(-0.410529\pi\)
0.907746 + 0.419520i \(0.137802\pi\)
\(374\) 25146.7 174899.i 0.179778 1.25039i
\(375\) −74148.8 252528.i −0.527280 1.79575i
\(376\) 1348.56 + 866.670i 0.00953885 + 0.00613025i
\(377\) 3096.47 6780.32i 0.0217863 0.0477054i
\(378\) 115.229 392.435i 0.000806454 0.00274653i
\(379\) 38940.6 33742.3i 0.271097 0.234907i −0.508693 0.860948i \(-0.669871\pi\)
0.779790 + 0.626041i \(0.215326\pi\)
\(380\) 65720.0 + 75844.9i 0.455124 + 0.525242i
\(381\) 70551.1 + 20715.7i 0.486020 + 0.142708i
\(382\) −30830.5 14079.8i −0.211278 0.0964872i
\(383\) 121497. 189053.i 0.828261 1.28880i −0.126662 0.991946i \(-0.540426\pi\)
0.954923 0.296854i \(-0.0959373\pi\)
\(384\) −7220.02 + 2119.99i −0.0489639 + 0.0143771i
\(385\) −6319.61 908.623i −0.0426353 0.00613003i
\(386\) 27393.8 + 59984.1i 0.183856 + 0.402589i
\(387\) −73500.3 + 10567.7i −0.490758 + 0.0705603i
\(388\) 20900.3 + 32521.5i 0.138832 + 0.216026i
\(389\) 54322.6 + 47070.8i 0.358989 + 0.311066i 0.815617 0.578592i \(-0.196398\pi\)
−0.456628 + 0.889658i \(0.650943\pi\)
\(390\) 21058.1i 0.138449i
\(391\) −255646. 15903.3i −1.67219 0.104024i
\(392\) 54304.4 0.353397
\(393\) −53709.4 + 61984.0i −0.347748 + 0.401323i
\(394\) 138591. 89066.9i 0.892775 0.573752i
\(395\) 70900.1 + 493121.i 0.454415 + 3.16052i
\(396\) −25350.3 + 11577.1i −0.161656 + 0.0738259i
\(397\) −4531.10 + 31514.5i −0.0287490 + 0.199954i −0.999134 0.0416102i \(-0.986751\pi\)
0.970385 + 0.241564i \(0.0776603\pi\)
\(398\) −22477.9 76552.6i −0.141902 0.483274i
\(399\) 1177.25 + 756.571i 0.00739473 + 0.00475230i
\(400\) −44665.3 + 97803.3i −0.279158 + 0.611271i
\(401\) −79658.5 + 271292.i −0.495386 + 1.68713i 0.209501 + 0.977808i \(0.432816\pi\)
−0.704887 + 0.709320i \(0.749002\pi\)
\(402\) −39298.2 + 34052.1i −0.243176 + 0.210713i
\(403\) 2725.63 + 3145.55i 0.0167825 + 0.0193681i
\(404\) −31227.3 9169.16i −0.191325 0.0561781i
\(405\) −31836.7 14539.3i −0.194097 0.0886410i
\(406\) −393.657 + 612.542i −0.00238817 + 0.00371607i
\(407\) 319036. 93677.3i 1.92597 0.565517i
\(408\) −56350.3 8101.95i −0.338513 0.0486709i
\(409\) −132229. 289541.i −0.790461 1.73087i −0.675327 0.737518i \(-0.735998\pi\)
−0.115134 0.993350i \(-0.536730\pi\)
\(410\) −336395. + 48366.3i −2.00116 + 0.287723i
\(411\) 89455.0 + 139195.i 0.529567 + 0.824023i
\(412\) 29625.4 + 25670.5i 0.174530 + 0.151231i
\(413\) 4640.90i 0.0272083i
\(414\) 19688.8 + 35275.8i 0.114873 + 0.205815i
\(415\) 129397. 0.751324
\(416\) −3537.78 + 4082.81i −0.0204430 + 0.0235924i
\(417\) −19999.1 + 12852.7i −0.115011 + 0.0739130i
\(418\) −13570.1 94381.8i −0.0776656 0.540176i
\(419\) −123997. + 56627.4i −0.706288 + 0.322551i −0.735976 0.677008i \(-0.763276\pi\)
0.0296871 + 0.999559i \(0.490549\pi\)
\(420\) −292.747 + 2036.10i −0.00165956 + 0.0115425i
\(421\) −39709.6 135239.i −0.224043 0.763021i −0.992406 0.123006i \(-0.960747\pi\)
0.768363 0.640014i \(-0.221072\pi\)
\(422\) −131519. 84522.3i −0.738524 0.474620i
\(423\) 794.613 1739.96i 0.00444094 0.00972431i
\(424\) −1954.34 + 6655.87i −0.0108710 + 0.0370231i
\(425\) −614764. + 532696.i −3.40354 + 2.94918i
\(426\) −71205.4 82175.4i −0.392368 0.452817i
\(427\) −2566.81 753.682i −0.0140779 0.00413364i
\(428\) −2084.15 951.800i −0.0113774 0.00519587i
\(429\) −10817.1 + 16831.7i −0.0587754 + 0.0914563i
\(430\) 358336. 105217.i 1.93800 0.569048i
\(431\) −323819. 46558.2i −1.74320 0.250635i −0.804156 0.594419i \(-0.797382\pi\)
−0.939049 + 0.343784i \(0.888291\pi\)
\(432\) 3729.99 + 8167.54i 0.0199867 + 0.0437647i
\(433\) 79464.5 11425.3i 0.423836 0.0609384i 0.0729029 0.997339i \(-0.476774\pi\)
0.350933 + 0.936401i \(0.385865\pi\)
\(434\) −219.812 342.034i −0.00116700 0.00181589i
\(435\) 47089.4 + 40803.2i 0.248854 + 0.215633i
\(436\) 167633.i 0.881834i
\(437\) −134786. + 30632.3i −0.705798 + 0.160405i
\(438\) 55310.8 0.288311
\(439\) −86954.8 + 100351.i −0.451195 + 0.520707i −0.935086 0.354422i \(-0.884678\pi\)
0.483891 + 0.875128i \(0.339223\pi\)
\(440\) 117912. 75777.7i 0.609052 0.391414i
\(441\) −9221.76 64138.8i −0.0474173 0.329794i
\(442\) −37178.3 + 16978.8i −0.190303 + 0.0869084i
\(443\) −388.661 + 2703.20i −0.00198045 + 0.0137743i −0.990788 0.135424i \(-0.956760\pi\)
0.988807 + 0.149199i \(0.0476694\pi\)
\(444\) −30181.7 102789.i −0.153101 0.521413i
\(445\) −71204.1 45760.1i −0.359571 0.231082i
\(446\) 23552.2 51572.1i 0.118403 0.259266i
\(447\) −17268.6 + 58811.5i −0.0864256 + 0.294339i
\(448\) 398.826 345.585i 0.00198714 0.00172186i
\(449\) 149434. + 172456.i 0.741235 + 0.855430i 0.993688 0.112179i \(-0.0357829\pi\)
−0.252454 + 0.967609i \(0.581237\pi\)
\(450\) 123100. + 36145.5i 0.607902 + 0.178496i
\(451\) 293725. + 134140.i 1.44407 + 0.659485i
\(452\) 53934.8 83924.2i 0.263993 0.410781i
\(453\) −9126.14 + 2679.68i −0.0444724 + 0.0130583i
\(454\) 182057. + 26175.8i 0.883273 + 0.126996i
\(455\) 613.493 + 1343.36i 0.00296337 + 0.00648889i
\(456\) −30408.7 + 4372.10i −0.146240 + 0.0210262i
\(457\) 82351.8 + 128142.i 0.394313 + 0.613563i 0.980478 0.196629i \(-0.0629994\pi\)
−0.586165 + 0.810192i \(0.699363\pi\)
\(458\) 20199.9 + 17503.3i 0.0962981 + 0.0834428i
\(459\) 67931.0i 0.322435i
\(460\) −123264. 161518.i −0.582533 0.763317i
\(461\) 90582.3 0.426228 0.213114 0.977027i \(-0.431639\pi\)
0.213114 + 0.977027i \(0.431639\pi\)
\(462\) 1279.90 1477.08i 0.00599640 0.00692021i
\(463\) 253175. 162706.i 1.18102 0.758999i 0.205450 0.978668i \(-0.434134\pi\)
0.975574 + 0.219669i \(0.0704977\pi\)
\(464\) −2274.88 15822.1i −0.0105663 0.0734901i
\(465\) −31647.8 + 14453.1i −0.146365 + 0.0668428i
\(466\) −32481.7 + 225915.i −0.149578 + 1.04034i
\(467\) 115223. + 392414.i 0.528331 + 1.79933i 0.597676 + 0.801738i \(0.296091\pi\)
−0.0693449 + 0.997593i \(0.522091\pi\)
\(468\) 5422.97 + 3485.13i 0.0247597 + 0.0159121i
\(469\) 1514.91 3317.18i 0.00688716 0.0150808i
\(470\) −2710.36 + 9230.64i −0.0122696 + 0.0417865i
\(471\) 44053.4 38172.5i 0.198581 0.172071i
\(472\) −66719.2 76998.0i −0.299479 0.345617i
\(473\) −340466. 99969.7i −1.52178 0.446834i
\(474\) −138725. 63353.5i −0.617444 0.281977i
\(475\) −237323. + 369282.i −1.05185 + 1.63671i
\(476\) 3830.80 1124.83i 0.0169074 0.00496445i
\(477\) 8193.10 + 1177.99i 0.0360091 + 0.00517732i
\(478\) −34888.8 76395.8i −0.152697 0.334360i
\(479\) −188640. + 27122.3i −0.822170 + 0.118210i −0.540546 0.841315i \(-0.681782\pi\)
−0.281624 + 0.959525i \(0.590873\pi\)
\(480\) −24414.7 37989.9i −0.105966 0.164887i
\(481\) −58125.8 50366.3i −0.251234 0.217696i
\(482\) 130821.i 0.563095i
\(483\) −2283.72 1676.76i −0.00978922 0.00718746i
\(484\) −16044.9 −0.0684930
\(485\) −151928. + 175334.i −0.645883 + 0.745388i
\(486\) 9013.25 5792.46i 0.0381600 0.0245240i
\(487\) −52435.1 364694.i −0.221088 1.53770i −0.733936 0.679219i \(-0.762319\pi\)
0.512849 0.858479i \(-0.328590\pi\)
\(488\) 53421.5 24396.8i 0.224324 0.102446i
\(489\) 7079.53 49239.2i 0.0296065 0.205918i
\(490\) 91815.7 + 312696.i 0.382406 + 1.30236i
\(491\) 197844. + 127146.i 0.820652 + 0.527401i 0.882295 0.470697i \(-0.155998\pi\)
−0.0616427 + 0.998098i \(0.519634\pi\)
\(492\) 43218.2 94634.7i 0.178540 0.390949i
\(493\) 34071.2 116036.i 0.140183 0.477418i
\(494\) −16668.7 + 14443.5i −0.0683044 + 0.0591861i
\(495\) −109524. 126398.i −0.446992 0.515857i
\(496\) 8564.13 + 2514.66i 0.0348113 + 0.0102215i
\(497\) 6936.47 + 3167.78i 0.0280818 + 0.0128245i
\(498\) −21415.3 + 33322.9i −0.0863506 + 0.134364i
\(499\) −259585. + 76220.9i −1.04250 + 0.306107i −0.757785 0.652504i \(-0.773718\pi\)
−0.284719 + 0.958611i \(0.591900\pi\)
\(500\) −401081. 57666.7i −1.60432 0.230667i
\(501\) 93908.8 + 205632.i 0.374137 + 0.819246i
\(502\) 59283.0 8523.60i 0.235246 0.0338233i
\(503\) −181205. 281960.i −0.716199 1.11443i −0.988354 0.152174i \(-0.951373\pi\)
0.272155 0.962253i \(-0.412264\pi\)
\(504\) −475.896 412.366i −0.00187349 0.00162339i
\(505\) 195316.i 0.765870i
\(506\) 15556.5 + 192419.i 0.0607591 + 0.751533i
\(507\) −143779. −0.559346
\(508\) 74134.3 85555.5i 0.287271 0.331528i
\(509\) 535.016 343.834i 0.00206505 0.00132713i −0.539608 0.841916i \(-0.681427\pi\)
0.541673 + 0.840589i \(0.317791\pi\)
\(510\) −48622.2 338175.i −0.186937 1.30017i
\(511\) −3528.45 + 1611.39i −0.0135127 + 0.00617105i
\(512\) −1648.75 + 11467.3i −0.00628949 + 0.0437443i
\(513\) 10327.8 + 35173.1i 0.0392438 + 0.133652i
\(514\) −80111.8 51484.7i −0.303229 0.194873i
\(515\) −97726.6 + 213991.i −0.368467 + 0.806830i
\(516\) −32209.0 + 109694.i −0.120970 + 0.411986i
\(517\) 6907.97 5985.79i 0.0258446 0.0223945i
\(518\) 4919.99 + 5677.97i 0.0183360 + 0.0211609i
\(519\) 138153. + 40565.3i 0.512890 + 0.150598i
\(520\) −29491.2 13468.2i −0.109065 0.0498083i
\(521\) −200890. + 312591.i −0.740086 + 1.15160i 0.243279 + 0.969956i \(0.421777\pi\)
−0.983365 + 0.181640i \(0.941859\pi\)
\(522\) −18301.2 + 5373.71i −0.0671642 + 0.0197212i
\(523\) −444281. 63878.0i −1.62426 0.233533i −0.730770 0.682624i \(-0.760839\pi\)
−0.893486 + 0.449091i \(0.851748\pi\)
\(524\) 52455.6 + 114862.i 0.191042 + 0.418324i
\(525\) −8905.99 + 1280.49i −0.0323120 + 0.00464576i
\(526\) −127133. 197823.i −0.459501 0.714997i
\(527\) 51034.3 + 44221.5i 0.183756 + 0.159225i
\(528\) 42906.7i 0.153906i
\(529\) 276207. 44954.7i 0.987012 0.160644i
\(530\) −41630.1 −0.148203
\(531\) −79612.1 + 91877.3i −0.282352 + 0.325851i
\(532\) 1812.49 1164.82i 0.00640402 0.00411561i
\(533\) −10629.7 73930.9i −0.0374167 0.260239i
\(534\) 23568.7 10763.5i 0.0826520 0.0377459i
\(535\) 1956.86 13610.2i 0.00683677 0.0475508i
\(536\) 22554.8 + 76814.7i 0.0785073 + 0.267371i
\(537\) −167481. 107634.i −0.580788 0.373250i
\(538\) −63624.4 + 139318.i −0.219816 + 0.481330i
\(539\) 87236.8 297101.i 0.300277 1.02265i
\(540\) −40723.8 + 35287.4i −0.139656 + 0.121013i
\(541\) 204689. + 236224.i 0.699360 + 0.807104i 0.988666 0.150132i \(-0.0479700\pi\)
−0.289306 + 0.957237i \(0.593425\pi\)
\(542\) −138672. 40717.7i −0.472051 0.138607i
\(543\) 82482.6 + 37668.5i 0.279745 + 0.127755i
\(544\) −47386.7 + 73735.1i −0.160125 + 0.249159i
\(545\) 965265. 283427.i 3.24978 0.954220i
\(546\) −447.482 64.3382i −0.00150103 0.000215816i
\(547\) −76186.2 166824.i −0.254625 0.557552i 0.738548 0.674201i \(-0.235512\pi\)
−0.993173 + 0.116649i \(0.962785\pi\)
\(548\) 252151. 36253.9i 0.839653 0.120724i
\(549\) −37886.8 58953.1i −0.125702 0.195597i
\(550\) 463334. + 401481.i 1.53168 + 1.32721i
\(551\) 65260.7i 0.214955i
\(552\) 61995.2 5012.12i 0.203460 0.0164491i
\(553\) 10695.4 0.0349741
\(554\) −34585.2 + 39913.4i −0.112686 + 0.130047i
\(555\) 540852. 347584.i 1.75587 1.12843i
\(556\) 5208.86 + 36228.4i 0.0168497 + 0.117192i
\(557\) 182237. 83224.8i 0.587389 0.268252i −0.0994720 0.995040i \(-0.531715\pi\)
0.686861 + 0.726789i \(0.258988\pi\)
\(558\) 1515.73 10542.1i 0.00486802 0.0338578i
\(559\) 23124.0 + 78752.9i 0.0740011 + 0.252025i
\(560\) 2664.27 + 1712.22i 0.00849574 + 0.00545988i
\(561\) −134850. + 295279.i −0.428473 + 0.938226i
\(562\) 76165.9 259397.i 0.241150 0.821283i
\(563\) 45108.0 39086.3i 0.142311 0.123313i −0.580796 0.814049i \(-0.697259\pi\)
0.723107 + 0.690736i \(0.242713\pi\)
\(564\) −1928.55 2225.66i −0.00606279 0.00699683i
\(565\) 574443. + 168672.i 1.79949 + 0.528379i
\(566\) 400003. + 182675.i 1.24862 + 0.570226i
\(567\) −406.230 + 632.106i −0.00126359 + 0.00196618i
\(568\) −160625. + 47163.8i −0.497871 + 0.146188i
\(569\) 467793. + 67258.4i 1.44487 + 0.207741i 0.819720 0.572764i \(-0.194129\pi\)
0.625150 + 0.780505i \(0.285038\pi\)
\(570\) −76589.2 167707.i −0.235732 0.516180i
\(571\) −242585. + 34878.5i −0.744032 + 0.106976i −0.503897 0.863764i \(-0.668101\pi\)
−0.240135 + 0.970739i \(0.577192\pi\)
\(572\) 16654.0 + 25914.1i 0.0509010 + 0.0792035i
\(573\) 47057.5 + 40775.6i 0.143324 + 0.124191i
\(574\) 7296.14i 0.0221447i
\(575\) 525969. 716362.i 1.59083 2.16669i
\(576\) 13824.0 0.0416667
\(577\) −144046. + 166238.i −0.432663 + 0.499320i −0.929653 0.368436i \(-0.879893\pi\)
0.496990 + 0.867756i \(0.334439\pi\)
\(578\) −359117. + 230791.i −1.07493 + 0.690816i
\(579\) −17240.8 119912.i −0.0514281 0.357690i
\(580\) 87260.7 39850.6i 0.259396 0.118462i
\(581\) 395.343 2749.67i 0.00117118 0.00814571i
\(582\) −20008.6 68143.1i −0.0590706 0.201176i
\(583\) 33275.0 + 21384.5i 0.0978995 + 0.0629162i
\(584\) 35375.3 77461.1i 0.103723 0.227121i
\(585\) −10899.1 + 37119.1i −0.0318479 + 0.108464i
\(586\) 209420. 181463.i 0.609850 0.528438i
\(587\) −94656.4 109239.i −0.274710 0.317032i 0.601584 0.798810i \(-0.294537\pi\)
−0.876293 + 0.481778i \(0.839991\pi\)
\(588\) −95722.4 28106.6i −0.276859 0.0812932i
\(589\) 33147.5 + 15138.0i 0.0955477 + 0.0436352i
\(590\) 330564. 514367.i 0.949623 1.47764i
\(591\) −290393. + 85267.1i −0.831402 + 0.244122i
\(592\) −163257. 23472.8i −0.465830 0.0669763i
\(593\) 124282. + 272140.i 0.353426 + 0.773896i 0.999940 + 0.0109928i \(0.00349920\pi\)
−0.646513 + 0.762903i \(0.723774\pi\)
\(594\) 50676.9 7286.24i 0.143627 0.0206505i
\(595\) 12953.9 + 20156.7i 0.0365905 + 0.0569359i
\(596\) 71319.2 + 61798.4i 0.200777 + 0.173974i
\(597\) 146573.i 0.411250i
\(598\) 35497.5 27090.2i 0.0992647 0.0757548i
\(599\) −478840. −1.33456 −0.667278 0.744809i \(-0.732541\pi\)
−0.667278 + 0.744809i \(0.732541\pi\)
\(600\) 129352. 149280.i 0.359312 0.414668i
\(601\) −8590.41 + 5520.72i −0.0237829 + 0.0152843i −0.552478 0.833527i \(-0.686318\pi\)
0.528695 + 0.848812i \(0.322681\pi\)
\(602\) −1141.04 7936.08i −0.00314852 0.0218984i
\(603\) 86895.5 39683.8i 0.238981 0.109139i
\(604\) −2084.03 + 14494.7i −0.00571255 + 0.0397316i
\(605\) −27128.1 92389.7i −0.0741153 0.252414i
\(606\) 50298.7 + 32325.0i 0.136966 + 0.0880224i
\(607\) 219927. 481572.i 0.596898 1.30702i −0.334285 0.942472i \(-0.608495\pi\)
0.931183 0.364553i \(-0.118778\pi\)
\(608\) −13325.6 + 45382.7i −0.0360478 + 0.122767i
\(609\) 1010.94 875.981i 0.00272577 0.00236189i
\(610\) 230805. + 266363.i 0.620276 + 0.715836i
\(611\) −2028.65 595.667i −0.00543408 0.00159559i
\(612\) 95135.4 + 43446.9i 0.254003 + 0.115999i
\(613\) −155923. + 242621.i −0.414943 + 0.645664i −0.984316 0.176415i \(-0.943550\pi\)
0.569373 + 0.822080i \(0.307186\pi\)
\(614\) 45679.0 13412.6i 0.121166 0.0355775i
\(615\) 617997. + 88854.6i 1.63394 + 0.234925i
\(616\) −1250.02 2737.15i −0.00329423 0.00721336i
\(617\) −520305. + 74808.6i −1.36675 + 0.196508i −0.786327 0.617810i \(-0.788020\pi\)
−0.580418 + 0.814319i \(0.697111\pi\)
\(618\) −38934.2 60582.8i −0.101942 0.158625i
\(619\) 560712. + 485859.i 1.46338 + 1.26803i 0.895607 + 0.444847i \(0.146742\pi\)
0.567777 + 0.823182i \(0.307804\pi\)
\(620\) 53565.7i 0.139349i
\(621\) −16447.6 72371.2i −0.0426500 0.187665i
\(622\) −81842.9 −0.211544
\(623\) −1189.95 + 1373.27i −0.00306585 + 0.00353818i
\(624\) 8349.21 5365.71i 0.0214425 0.0137803i
\(625\) −196645. 1.36770e6i −0.503411 3.50130i
\(626\) −194064. + 88626.0i −0.495218 + 0.226158i
\(627\) −24929.8 + 173390.i −0.0634137 + 0.441052i
\(628\) −25284.0 86109.5i −0.0641102 0.218339i
\(629\) −1.04975e6 674630.i −2.65328 1.70516i
\(630\) 1569.86 3437.52i 0.00395531 0.00866092i
\(631\) 176841. 602264.i 0.444144 1.51261i −0.368374 0.929678i \(-0.620085\pi\)
0.812518 0.582937i \(-0.198096\pi\)
\(632\) −177449. + 153761.i −0.444263 + 0.384956i
\(633\) 188082. + 217059.i 0.469398 + 0.541714i
\(634\) 75373.2 + 22131.6i 0.187516 + 0.0550597i
\(635\) 617989. + 282226.i 1.53262 + 0.699922i
\(636\) 6889.83 10720.8i 0.0170331 0.0265041i
\(637\) −68722.4 + 20178.7i −0.169363 + 0.0497296i
\(638\) −90217.9 12971.4i −0.221642 0.0318673i
\(639\) 82981.8 + 181705.i 0.203227 + 0.445005i
\(640\) −68818.7 + 9894.64i −0.168015 + 0.0241568i
\(641\) 130115. + 202462.i 0.316672 + 0.492751i 0.962703 0.270560i \(-0.0872087\pi\)
−0.646031 + 0.763311i \(0.723572\pi\)
\(642\) 3181.11 + 2756.45i 0.00771806 + 0.00668774i
\(643\) 113232.i 0.273871i 0.990580 + 0.136935i \(0.0437253\pi\)
−0.990580 + 0.136935i \(0.956275\pi\)
\(644\) −3808.85 + 2125.87i −0.00918380 + 0.00512583i
\(645\) −686097. −1.64917
\(646\) −234336. + 270439.i −0.561532 + 0.648043i
\(647\) 497928. 319999.i 1.18948 0.764434i 0.212376 0.977188i \(-0.431880\pi\)
0.977106 + 0.212754i \(0.0682434\pi\)
\(648\) −2347.54 16327.5i −0.00559065 0.0388839i
\(649\) −528439. + 241330.i −1.25460 + 0.572957i
\(650\) 20181.8 140367.i 0.0477675 0.332231i
\(651\) 210.434 + 716.673i 0.000496540 + 0.00169106i
\(652\) −64430.2 41406.8i −0.151563 0.0974039i
\(653\) 166471. 364520.i 0.390401 0.854860i −0.607753 0.794126i \(-0.707929\pi\)
0.998154 0.0607333i \(-0.0193439\pi\)
\(654\) −86762.8 + 295487.i −0.202851 + 0.690848i
\(655\) −572707. + 496253.i −1.33490 + 1.15670i
\(656\) −104892. 121052.i −0.243744 0.281296i
\(657\) −97496.3 28627.5i −0.225869 0.0663213i
\(658\) 187.869 + 85.7971i 0.000433915 + 0.000198162i
\(659\) −100757. + 156782.i −0.232010 + 0.361014i −0.937665 0.347541i \(-0.887017\pi\)
0.705655 + 0.708556i \(0.250653\pi\)
\(660\) −247065. + 72544.9i −0.567184 + 0.166540i
\(661\) −560482. 80585.2i −1.28280 0.184439i −0.533007 0.846111i \(-0.678938\pi\)
−0.749793 + 0.661672i \(0.769847\pi\)
\(662\) 44668.7 + 97810.8i 0.101927 + 0.223188i
\(663\) 74322.1 10685.9i 0.169079 0.0243099i
\(664\) 32971.0 + 51303.9i 0.0747818 + 0.116363i
\(665\) 9771.74 + 8467.26i 0.0220968 + 0.0191470i
\(666\) 196808.i 0.443705i
\(667\) −8203.39 + 131870.i −0.0184392 + 0.296410i
\(668\) 348042. 0.779972
\(669\) −68208.0 + 78716.2i −0.152399 + 0.175878i
\(670\) −404180. + 259751.i −0.900378 + 0.578638i
\(671\) −47657.2 331463.i −0.105848 0.736191i
\(672\) −881.877 + 402.740i −0.00195285 + 0.000891838i
\(673\) 66638.8 463483.i 0.147129 1.02330i −0.773761 0.633478i \(-0.781627\pi\)
0.920889 0.389824i \(-0.127464\pi\)
\(674\) 44562.4 + 151765.i 0.0980954 + 0.334082i
\(675\) −198281. 127427.i −0.435184 0.279676i
\(676\) −91957.4 + 201359.i −0.201230 + 0.440633i
\(677\) 228261. 777385.i 0.498028 1.69613i −0.199778 0.979841i \(-0.564022\pi\)
0.697806 0.716287i \(-0.254160\pi\)
\(678\) −138508. + 120018.i −0.301312 + 0.261088i
\(679\) 3261.65 + 3764.15i 0.00707454 + 0.00816445i
\(680\) −504701. 148194.i −1.09148 0.320488i
\(681\) −307364. 140368.i −0.662763 0.302674i
\(682\) 27515.6 42815.0i 0.0591575 0.0920508i
\(683\) −332660. + 97677.7i −0.713113 + 0.209389i −0.618114 0.786088i \(-0.712103\pi\)
−0.0949992 + 0.995477i \(0.530285\pi\)
\(684\) 55864.3 + 8032.07i 0.119405 + 0.0171678i
\(685\) 635084. + 1.39064e6i 1.35347 + 2.96370i
\(686\) 13853.6 1991.85i 0.0294385 0.00423261i
\(687\) −26547.1 41308.1i −0.0562475 0.0875228i
\(688\) 133023. + 115265.i 0.281028 + 0.243512i
\(689\) 9149.23i 0.0192729i
\(690\) 133680. + 348506.i 0.280781 + 0.732002i
\(691\) 784967. 1.64398 0.821988 0.569505i \(-0.192865\pi\)
0.821988 + 0.569505i \(0.192865\pi\)
\(692\) 145169. 167534.i 0.303153 0.349858i
\(693\) −3020.57 + 1941.20i −0.00628960 + 0.00404208i
\(694\) 35200.6 + 244826.i 0.0730855 + 0.508321i
\(695\) −199803. + 91247.2i −0.413650 + 0.188908i
\(696\) −4179.22 + 29067.1i −0.00862734 + 0.0600044i
\(697\) −341407. 1.16272e6i −0.702759 2.39338i
\(698\) 483634. + 310813.i 0.992673 + 0.637952i
\(699\) 174184. 381409.i 0.356495 0.780615i
\(700\) −3902.75 + 13291.5i −0.00796479 + 0.0271256i
\(701\) −345358. + 299255.i −0.702804 + 0.608983i −0.931167 0.364593i \(-0.881208\pi\)
0.228363 + 0.973576i \(0.426663\pi\)
\(702\) −7755.26 8950.04i −0.0157370 0.0181615i
\(703\) −646100. 189712.i −1.30734 0.383870i
\(704\) 60089.5 + 27442.0i 0.121242 + 0.0553694i
\(705\) 9555.11 14868.0i 0.0192246 0.0299141i
\(706\) −152848. + 44880.3i −0.306656 + 0.0900422i
\(707\) −4150.45 596.745i −0.00830341 0.00119385i
\(708\) 77753.6 + 170257.i 0.155115 + 0.339655i
\(709\) −244043. + 35088.1i −0.485483 + 0.0698019i −0.380711 0.924694i \(-0.624321\pi\)
−0.104773 + 0.994496i \(0.533411\pi\)
\(710\) −543157. 845169.i −1.07748 1.67659i
\(711\) 211740. + 183474.i 0.418855 + 0.362940i
\(712\) 39891.3i 0.0786897i
\(713\) −65077.0 34755.4i −0.128011 0.0683665i
\(714\) −7334.75 −0.0143876
\(715\) −121061. + 139712.i −0.236805 + 0.273288i
\(716\) −257854. + 165713.i −0.502977 + 0.323244i
\(717\) 21957.9 + 152721.i 0.0427123 + 0.297070i
\(718\) −296452. + 135385.i −0.575049 + 0.262616i
\(719\) 115955. 806484.i 0.224301 1.56005i −0.497201 0.867635i \(-0.665639\pi\)
0.721502 0.692412i \(-0.243452\pi\)
\(720\) 23373.1 + 79601.4i 0.0450869 + 0.153552i
\(721\) 4248.72 + 2730.49i 0.00817312 + 0.00525254i
\(722\) 72905.0 159640.i 0.139857 0.306243i
\(723\) −67709.5 + 230598.i −0.129531 + 0.441142i
\(724\) 105507. 91422.6i 0.201282 0.174412i
\(725\) 274780. + 317113.i 0.522768 + 0.603306i
\(726\) 28282.3 + 8304.45i 0.0536590 + 0.0157557i
\(727\) 837399. + 382427.i 1.58440 + 0.723569i 0.996358 0.0852648i \(-0.0271736\pi\)
0.588037 + 0.808834i \(0.299901\pi\)
\(728\) −376.302 + 585.537i −0.000710024 + 0.00110482i
\(729\) −18885.7 + 5545.34i −0.0355368 + 0.0104345i
\(730\) 505847. + 72729.9i 0.949235 + 0.136479i
\(731\) 553189. + 1.21131e6i 1.03523 + 2.26685i
\(732\) −106793. + 15354.6i −0.199307 + 0.0286560i
\(733\) −7351.92 11439.8i −0.0136834 0.0212917i 0.834344 0.551243i \(-0.185846\pi\)
−0.848028 + 0.529952i \(0.822210\pi\)
\(734\) 430261. + 372823.i 0.798619 + 0.692007i
\(735\) 598710.i 1.10826i
\(736\) 32631.1 90028.0i 0.0602388 0.166197i
\(737\) 456489. 0.840419
\(738\) −125161. + 144444.i −0.229804 + 0.265208i
\(739\) 351337. 225791.i 0.643333 0.413445i −0.177892 0.984050i \(-0.556928\pi\)
0.821224 + 0.570605i \(0.193291\pi\)
\(740\) −140867. 979752.i −0.257245 1.78918i
\(741\) 36857.6 16832.3i 0.0671261 0.0306554i
\(742\) −127.192 + 884.638i −0.000231021 + 0.00160678i
\(743\) 69401.2 + 236359.i 0.125716 + 0.428148i 0.998165 0.0605569i \(-0.0192877\pi\)
−0.872449 + 0.488705i \(0.837469\pi\)
\(744\) −13794.5 8865.17i −0.0249207 0.0160155i
\(745\) −235264. + 515157.i −0.423880 + 0.928168i
\(746\) −144446. + 491936.i −0.259553 + 0.883957i
\(747\) 54995.9 47654.2i 0.0985573 0.0854004i
\(748\) 327284. + 377705.i 0.584953 + 0.675072i
\(749\) −283.238 83.1661i −0.000504879 0.000148246i
\(750\) 677139. + 309239.i 1.20380 + 0.549758i
\(751\) −436582. + 679335.i −0.774081 + 1.20449i 0.200332 + 0.979728i \(0.435798\pi\)
−0.974413 + 0.224765i \(0.927839\pi\)
\(752\) −4350.42 + 1277.40i −0.00769300 + 0.00225887i
\(753\) −108910. 15658.9i −0.192078 0.0276166i
\(754\) 8758.14 + 19177.6i 0.0154053 + 0.0337328i
\(755\) −86987.2 + 12506.9i −0.152602 + 0.0219409i
\(756\) 625.432 + 973.191i 0.00109430 + 0.00170276i
\(757\) −813249. 704685.i −1.41916 1.22971i −0.934959 0.354755i \(-0.884564\pi\)
−0.484203 0.874956i \(-0.660890\pi\)
\(758\) 145737.i 0.253648i
\(759\) 72170.1 347230.i 0.125278 0.602744i
\(760\) −283853. −0.491435
\(761\) −154258. + 178023.i −0.266366 + 0.307403i −0.873138 0.487473i \(-0.837919\pi\)
0.606772 + 0.794876i \(0.292464\pi\)
\(762\) −174958. + 112439.i −0.301317 + 0.193645i
\(763\) −3073.66 21377.8i −0.00527967 0.0367209i
\(764\) 87201.7 39823.7i 0.149396 0.0682268i
\(765\) −89324.7 + 621267.i −0.152633 + 1.06159i
\(766\) 179076. + 609878.i 0.305197 + 1.03941i
\(767\) 113045. + 72649.4i 0.192158 + 0.123493i
\(768\) 8841.46 19360.1i 0.0149900 0.0328235i
\(769\) 2150.79 7324.92i 0.00363702 0.0123865i −0.957654 0.287920i \(-0.907036\pi\)
0.961291 + 0.275533i \(0.0888545\pi\)
\(770\) 13647.6 11825.7i 0.0230184 0.0199456i
\(771\) 114566. + 132216.i 0.192729 + 0.222421i
\(772\) −178961. 52547.6i −0.300278 0.0881694i
\(773\) −695983. 317845.i −1.16477 0.531932i −0.263274 0.964721i \(-0.584802\pi\)
−0.901495 + 0.432789i \(0.857530\pi\)
\(774\) 113550. 176687.i 0.189541 0.294932i
\(775\) −224808. + 66009.5i −0.374290 + 0.109901i
\(776\) −108229. 15561.0i −0.179730 0.0258413i
\(777\) −5733.69 12555.0i −0.00949713 0.0207958i
\(778\) −201235. + 28933.3i −0.332464 + 0.0478011i
\(779\) −353545. 550127.i −0.582599 0.906542i
\(780\) 45013.3 + 39004.3i 0.0739864 + 0.0641096i
\(781\) 954552.i 1.56494i
\(782\) 507509. 517008.i 0.829909 0.845443i
\(783\) 35040.8 0.0571545
\(784\) −100584. + 116080.i −0.163643 + 0.188854i
\(785\) 453087. 291181.i 0.735261 0.472524i
\(786\) −33013.9 229617.i −0.0534382 0.371671i
\(787\) −492019. + 224697.i −0.794387 + 0.362784i −0.770913 0.636940i \(-0.780200\pi\)
−0.0234735 + 0.999724i \(0.507473\pi\)
\(788\) −66313.6 + 461221.i −0.106795 + 0.742774i
\(789\) 121709. + 414503.i 0.195510 + 0.665846i
\(790\) −1.18541e6 761816.i −1.89939 1.22066i
\(791\) 5339.35 11691.5i 0.00853366 0.0186861i
\(792\) 22207.5 75631.6i 0.0354037 0.120574i
\(793\) −58539.6 + 50724.9i −0.0930901 + 0.0806631i
\(794\) −58972.2 68057.6i −0.0935419 0.107953i
\(795\) 73381.5 + 21546.8i 0.116105 + 0.0340916i
\(796\) 205272. + 93744.4i 0.323968 + 0.147951i
\(797\) 235885. 367044.i 0.371350 0.577832i −0.604410 0.796673i \(-0.706591\pi\)
0.975761 + 0.218841i \(0.0702275\pi\)
\(798\) −3797.76 + 1115.12i −0.00596379 + 0.00175113i
\(799\) −33953.9 4881.83i −0.0531858 0.00764696i
\(800\) −126332. 276630.i −0.197395 0.432234i
\(801\) −47115.5 + 6774.18i −0.0734342 + 0.0105583i
\(802\) −432363. 672771.i −0.672203 1.04597i
\(803\) −366964. 317976.i −0.569105 0.493132i
\(804\) 147075.i 0.227524i
\(805\) −18681.0 18337.8i −0.0288276 0.0282980i
\(806\) −11772.3 −0.0181215
\(807\) 184258. 212646.i 0.282931 0.326520i
\(808\) 77439.9 49767.6i 0.118616 0.0762296i
\(809\) 94570.4 + 657752.i 0.144497 + 1.00500i 0.925033 + 0.379887i \(0.124037\pi\)
−0.780536 + 0.625111i \(0.785054\pi\)
\(810\) 90047.8 41123.5i 0.137247 0.0626787i
\(811\) −49086.1 + 341401.i −0.0746306 + 0.519067i 0.917875 + 0.396869i \(0.129903\pi\)
−0.992506 + 0.122198i \(0.961006\pi\)
\(812\) −580.218 1976.04i −0.000879992 0.00299698i
\(813\) 223362. + 143546.i 0.337932 + 0.217175i
\(814\) −390683. + 855477.i −0.589625 + 1.29110i
\(815\) 129492. 441011.i 0.194953 0.663948i
\(816\) 121692. 105447.i 0.182760 0.158363i
\(817\) 470588. + 543088.i 0.705012 + 0.813628i
\(818\) 863837. + 253645.i 1.29100 + 0.379071i
\(819\) 755.478 + 345.015i 0.00112630 + 0.000514364i
\(820\) 519693. 808657.i 0.772892 1.20264i
\(821\) −295983. + 86908.6i −0.439118 + 0.128937i −0.493816 0.869566i \(-0.664398\pi\)
0.0546984 + 0.998503i \(0.482580\pi\)
\(822\) −463231. 66602.6i −0.685574 0.0985706i
\(823\) 219430. + 480484.i 0.323963 + 0.709380i 0.999612 0.0278432i \(-0.00886390\pi\)
−0.675649 + 0.737223i \(0.736137\pi\)
\(824\) −109746. + 15779.0i −0.161634 + 0.0232395i
\(825\) −608922. 947501.i −0.894651 1.39210i
\(826\) −9920.31 8596.00i −0.0145400 0.0125990i
\(827\) 191705.i 0.280299i −0.990130 0.140149i \(-0.955242\pi\)
0.990130 0.140149i \(-0.0447583\pi\)
\(828\) −111873. 23252.3i −0.163179 0.0339161i
\(829\) −800291. −1.16450 −0.582249 0.813010i \(-0.697827\pi\)
−0.582249 + 0.813010i \(0.697827\pi\)
\(830\) −239672. + 276596.i −0.347905 + 0.401504i
\(831\) 81621.5 52455.0i 0.118196 0.0759599i
\(832\) −2174.59 15124.6i −0.00314145 0.0218493i
\(833\) −1.05703e6 + 482730.i −1.52334 + 0.695688i
\(834\) 9569.28 66555.8i 0.0137577 0.0956872i
\(835\) 588456. + 2.00410e6i 0.843997 + 2.87439i
\(836\) 226884. + 145809.i 0.324632 + 0.208628i
\(837\) −8128.11 + 17798.1i −0.0116022 + 0.0254052i
\(838\) 108624. 369940.i 0.154682 0.526797i
\(839\) 1.02581e6 888868.i 1.45728 1.26274i 0.554813 0.831975i \(-0.312790\pi\)
0.902465 0.430763i \(-0.141756\pi\)
\(840\) −3810.10 4397.09i −0.00539980 0.00623170i
\(841\) 618776. + 181689.i 0.874867 + 0.256884i
\(842\) 362635. + 165610.i 0.511499 + 0.233594i
\(843\) −268516. + 417818.i −0.377846 + 0.587939i
\(844\) 424277. 124579.i 0.595613 0.174888i
\(845\) −1.31494e6 189060.i −1.84159 0.264781i
\(846\) 2247.51 + 4921.35i 0.00314022 + 0.00687612i
\(847\) −2046.16 + 294.193i −0.00285215 + 0.000410077i
\(848\) −10607.6 16505.7i −0.0147511 0.0229532i
\(849\) −610538. 529034.i −0.847027 0.733953i
\(850\) 2.30078e6i 3.18447i
\(851\) 1.28170e6 + 464560.i 1.76982 + 0.641479i
\(852\) 307545. 0.423672
\(853\) 613930. 708512.i 0.843763 0.973754i −0.156139 0.987735i \(-0.549905\pi\)
0.999902 + 0.0139807i \(0.00445033\pi\)
\(854\) 6365.36 4090.77i 0.00872785 0.00560905i
\(855\) 48202.8 + 335258.i 0.0659387 + 0.458613i
\(856\) 5894.87 2692.10i 0.00804501 0.00367403i
\(857\) 109284. 760090.i 0.148798 1.03491i −0.769394 0.638775i \(-0.779441\pi\)
0.918191 0.396137i \(-0.129649\pi\)
\(858\) −15943.5 54298.5i −0.0216575 0.0737587i
\(859\) −581288. 373571.i −0.787781 0.506276i 0.0838269 0.996480i \(-0.473286\pi\)
−0.871607 + 0.490204i \(0.836922\pi\)
\(860\) −438809. + 960858.i −0.593306 + 1.29916i
\(861\) 3776.31 12860.9i 0.00509402 0.0173487i
\(862\) 699309. 605955.i 0.941140 0.815503i
\(863\) −328729. 379374.i −0.441384 0.509384i 0.490848 0.871245i \(-0.336687\pi\)
−0.932232 + 0.361861i \(0.882142\pi\)
\(864\) −24367.6 7154.97i −0.0326426 0.00958474i
\(865\) 1.21014e6 + 552653.i 1.61735 + 0.738619i
\(866\) −122764. + 191024.i −0.163695 + 0.254714i
\(867\) 752468. 220945.i 1.00104 0.293931i
\(868\) 1138.27 + 163.658i 0.00151079 + 0.000217219i
\(869\) 556169. + 1.21784e6i 0.736490 + 1.61269i
\(870\) −174440. + 25080.7i −0.230467 + 0.0331361i
\(871\) −57086.5 88828.3i −0.0752483 0.117089i
\(872\) 358329. + 310494.i 0.471248 + 0.408339i
\(873\) 130472.i 0.171194i
\(874\) 184174. 344853.i 0.241105 0.451452i
\(875\) −52206.1 −0.0681875
\(876\) −102448. + 118231.i −0.133504 + 0.154072i
\(877\) 290349. 186596.i 0.377503 0.242607i −0.338105 0.941108i \(-0.609786\pi\)
0.715608 + 0.698502i \(0.246150\pi\)
\(878\) −53449.0 371746.i −0.0693347 0.482233i
\(879\) −463066. + 211475.i −0.599328 + 0.273704i
\(880\) −56419.3 + 392405.i −0.0728556 + 0.506722i
\(881\) −303167. 1.03249e6i −0.390598 1.33025i −0.886843 0.462071i \(-0.847106\pi\)
0.496245 0.868183i \(-0.334712\pi\)
\(882\) 154183. + 99087.2i 0.198198 + 0.127374i
\(883\) 578880. 1.26757e6i 0.742449 1.62574i −0.0370335 0.999314i \(-0.511791\pi\)
0.779483 0.626423i \(-0.215482\pi\)
\(884\) 32569.1 110920.i 0.0416775 0.141940i
\(885\) −848909. + 735584.i −1.08386 + 0.939174i
\(886\) −5058.42 5837.73i −0.00644388 0.00743663i
\(887\) 516399. + 151629.i 0.656355 + 0.192723i 0.592918 0.805263i \(-0.297976\pi\)
0.0634365 + 0.997986i \(0.479794\pi\)
\(888\) 275624. + 125873.i 0.349535 + 0.159627i
\(889\) 7885.41 12269.9i 0.00997748 0.0155253i
\(890\) 229702. 67446.6i 0.289991 0.0851491i
\(891\) −93099.5 13385.7i −0.117271 0.0168611i
\(892\) 66615.7 + 145868.i 0.0837234 + 0.183329i
\(893\) −18322.7 + 2634.41i −0.0229767 + 0.00330355i
\(894\) −93729.1 145845.i −0.117273 0.182481i
\(895\) −1.39018e6 1.20460e6i −1.73550 1.50382i
\(896\) 1492.62i 0.00185924i
\(897\) −76592.7 + 29379.3i −0.0951924 + 0.0365138i
\(898\) −645423. −0.800372
\(899\) 22810.7 26325.0i 0.0282240 0.0325723i
\(900\) −305273. + 196187.i −0.376880 + 0.242206i
\(901\) −21125.2 146929.i −0.0260226 0.180991i
\(902\) −830781. + 379405.i −1.02111 + 0.466326i
\(903\) −2096.22 + 14579.5i −0.00257076 + 0.0178800i
\(904\) 79495.5 + 270737.i 0.0972760 + 0.331292i
\(905\) 704818. + 452959.i 0.860557 + 0.553046i
\(906\) 11175.6 24471.2i 0.0136149 0.0298126i
\(907\) −49647.3 + 169083.i −0.0603505 + 0.205535i −0.984149 0.177345i \(-0.943249\pi\)
0.923798 + 0.382879i \(0.125067\pi\)
\(908\) −393163. + 340678.i −0.476871 + 0.413211i
\(909\) −71930.9 83012.7i −0.0870538 0.100465i
\(910\) −4007.87 1176.82i −0.00483984 0.00142111i
\(911\) −1.14254e6 521780.i −1.37668 0.628710i −0.416771 0.909011i \(-0.636838\pi\)
−0.959912 + 0.280301i \(0.909566\pi\)
\(912\) 46978.0 73099.1i 0.0564813 0.0878866i
\(913\) 333652. 97968.9i 0.400269 0.117529i
\(914\) −426448. 61314.0i −0.510474 0.0733951i
\(915\) −268977. 588977.i −0.321272 0.703487i
\(916\) −74829.5 + 10758.9i −0.0891830 + 0.0128226i
\(917\) 8795.57 + 13686.2i 0.0104598 + 0.0162758i
\(918\) −145208. 125824.i −0.172308 0.149306i
\(919\) 804105.i 0.952099i −0.879419 0.476049i \(-0.842068\pi\)
0.879419 0.476049i \(-0.157932\pi\)
\(920\) 573571. + 35680.9i 0.677659 + 0.0421560i
\(921\) −87460.4 −0.103108
\(922\) −167779. + 193627.i −0.197368 + 0.227774i
\(923\) 185746. 119372.i 0.218030 0.140120i
\(924\) 786.721 + 5471.76i 0.000921460 + 0.00640890i
\(925\) 3.93829e6 1.79856e6i 4.60283 2.10204i
\(926\) −121140. + 842551.i −0.141276 + 0.982594i
\(927\) 37273.2 + 126941.i 0.0433748 + 0.147721i
\(928\) 38034.7 + 24443.4i 0.0441656 + 0.0283835i
\(929\) −377047. + 825619.i −0.436882 + 0.956639i 0.555278 + 0.831665i \(0.312612\pi\)
−0.992160 + 0.124974i \(0.960115\pi\)
\(930\) 27724.3 94420.3i 0.0320549 0.109169i
\(931\) −473916. + 410650.i −0.546767 + 0.473776i
\(932\) −422749. 487878.i −0.486688 0.561668i
\(933\) 144265. + 42359.9i 0.165728 + 0.0486622i
\(934\) −1.05224e6 480541.i −1.20620 0.550854i
\(935\) −1.62155e6 + 2.52317e6i −1.85484 + 2.88618i
\(936\) −17494.3 + 5136.80i −0.0199685 + 0.00586328i
\(937\) 989584. + 142281.i 1.12713 + 0.162057i 0.680560 0.732693i \(-0.261737\pi\)
0.446569 + 0.894749i \(0.352646\pi\)
\(938\) 4284.80 + 9382.41i 0.00486996 + 0.0106637i
\(939\) 387947. 55778.4i 0.439989 0.0632608i
\(940\) −14711.0 22890.8i −0.0166490 0.0259063i
\(941\) 1.01813e6 + 882217.i 1.14981 + 0.996314i 0.999971 + 0.00760275i \(0.00242005\pi\)
0.149836 + 0.988711i \(0.452125\pi\)
\(942\) 164872.i 0.185799i
\(943\) 645243. + 1.15606e6i 0.725605 + 1.30004i
\(944\) 288169. 0.323372
\(945\) −4546.37 + 5246.80i −0.00509098 + 0.00587531i
\(946\) 844313. 542607.i 0.943455 0.606322i
\(947\) −136293. 947940.i −0.151976 1.05701i −0.912903 0.408177i \(-0.866165\pi\)
0.760927 0.648837i \(-0.224744\pi\)
\(948\) 392373. 179191.i 0.436599 0.199388i
\(949\) −15984.1 + 111172.i −0.0177483 + 0.123442i
\(950\) −349795. 1.19129e6i −0.387584 1.31999i
\(951\) −121406. 78022.7i −0.134239 0.0862701i
\(952\) −4691.11 + 10272.1i −0.00517609 + 0.0113340i
\(953\) −70744.0 + 240932.i −0.0778940 + 0.265283i −0.989228 0.146386i \(-0.953236\pi\)
0.911334 + 0.411669i \(0.135054\pi\)
\(954\) −17693.5 + 15331.5i −0.0194410 + 0.0168457i
\(955\) 376750. + 434793.i 0.413092 + 0.476733i
\(956\) 227924. + 66924.6i 0.249388 + 0.0732268i
\(957\) 152314. + 69559.3i 0.166309 + 0.0759506i
\(958\) 291427. 453469.i 0.317540 0.494102i
\(959\) 31491.4 9246.70i 0.0342416 0.0100542i
\(960\) 126428. + 18177.6i 0.137183 + 0.0197240i
\(961\) −375565. 822372.i −0.406666 0.890474i
\(962\) 215324. 30958.9i 0.232671 0.0334531i
\(963\) −4180.67 6505.25i −0.00450810 0.00701474i
\(964\) 279640. + 242309.i 0.300916 + 0.260745i
\(965\) 1.11934e6i 1.20200i
\(966\) 7814.16 1775.90i 0.00837391 0.00190311i
\(967\) 234469. 0.250745 0.125372 0.992110i \(-0.459987\pi\)
0.125372 + 0.992110i \(0.459987\pi\)
\(968\) 29718.8 34297.3i 0.0317161 0.0366023i
\(969\) 553038. 355416.i 0.588989 0.378520i
\(970\) −93386.3 649516.i −0.0992521 0.690314i
\(971\) 681861. 311395.i 0.723198 0.330274i −0.0195826 0.999808i \(-0.506234\pi\)
0.742781 + 0.669535i \(0.233506\pi\)
\(972\) −4312.70 + 29995.5i −0.00456475 + 0.0317485i
\(973\) 1328.54 + 4524.60i 0.00140330 + 0.00477919i
\(974\) 876686. + 563412.i 0.924115 + 0.593893i
\(975\) −108225. + 236980.i −0.113846 + 0.249289i
\(976\) −46798.6 + 159381.i −0.0491284 + 0.167316i
\(977\) −608331. + 527121.i −0.637310 + 0.552232i −0.912458 0.409170i \(-0.865818\pi\)
0.275149 + 0.961402i \(0.411273\pi\)
\(978\) 92140.0 + 106335.i 0.0963320 + 0.111173i
\(979\) −218247. 64083.0i −0.227710 0.0668617i
\(980\) −838476. 382919.i −0.873049 0.398708i
\(981\) 305874. 475949.i 0.317837 0.494564i
\(982\) −638237. + 187403.i −0.661849 + 0.194336i
\(983\) −1.76688e6 254040.i −1.82853 0.262902i −0.859728 0.510753i \(-0.829367\pi\)
−0.968798 + 0.247850i \(0.920276\pi\)
\(984\) 122240. + 267667.i 0.126247 + 0.276443i
\(985\) −2.76793e6 + 397968.i −2.85287 + 0.410181i
\(986\) 184929. + 287755.i 0.190218 + 0.295984i
\(987\) −286.751 248.471i −0.000294355 0.000255060i
\(988\) 62383.5i 0.0639081i
\(989\) −882632. 1.15655e6i −0.902375 1.18242i
\(990\) 473050. 0.482654
\(991\) −359256. + 414603.i −0.365811 + 0.422168i −0.908578 0.417715i \(-0.862831\pi\)
0.542767 + 0.839883i \(0.317377\pi\)
\(992\) −21238.0 + 13648.8i −0.0215819 + 0.0138699i
\(993\) −28113.1 195531.i −0.0285108 0.198297i
\(994\) −19619.3 + 8959.83i −0.0198569 + 0.00906832i
\(995\) −192734. + 1.34049e6i −0.194676 + 1.35400i
\(996\) −31564.4 107498.i −0.0318184 0.108364i
\(997\) 550110. + 353534.i 0.553426 + 0.355665i 0.787270 0.616609i \(-0.211494\pi\)
−0.233844 + 0.972274i \(0.575130\pi\)
\(998\) 317881. 696062.i 0.319156 0.698854i
\(999\) 101863. 346914.i 0.102067 0.347609i
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 138.5.h.a.7.8 160
23.10 odd 22 inner 138.5.h.a.79.8 yes 160
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
138.5.h.a.7.8 160 1.1 even 1 trivial
138.5.h.a.79.8 yes 160 23.10 odd 22 inner