Properties

Label 13.5.f.a.11.2
Level $13$
Weight $5$
Character 13.11
Analytic conductor $1.344$
Analytic rank $0$
Dimension $16$
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] = [13,5,Mod(2,13)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(13, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("13.2");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 13 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 13.f (of order \(12\), degree \(4\), 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: \(1.34380952009\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 152 x^{14} + 9190 x^{12} + 285720 x^{10} + 4862025 x^{8} + 43573680 x^{6} + 169417008 x^{4} + 100636992 x^{2} + 3779136 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{2}\cdot 13^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 11.2
Root \(7.09996i\) of defining polynomial
Character \(\chi\) \(=\) 13.11
Dual form 13.5.f.a.6.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.387376 + 1.44571i) q^{2} +(3.29308 + 5.70378i) q^{3} +(11.9164 + 6.87993i) q^{4} +(-10.5663 - 10.5663i) q^{5} +(-9.52166 + 2.55132i) q^{6} +(-14.3010 - 53.3722i) q^{7} +(-31.4958 + 31.4958i) q^{8} +(18.8113 - 32.5821i) q^{9} +O(q^{10})\) \(q+(-0.387376 + 1.44571i) q^{2} +(3.29308 + 5.70378i) q^{3} +(11.9164 + 6.87993i) q^{4} +(-10.5663 - 10.5663i) q^{5} +(-9.52166 + 2.55132i) q^{6} +(-14.3010 - 53.3722i) q^{7} +(-31.4958 + 31.4958i) q^{8} +(18.8113 - 32.5821i) q^{9} +(19.3688 - 11.1826i) q^{10} +(-52.6981 - 14.1204i) q^{11} +90.6246i q^{12} +(115.664 + 123.219i) q^{13} +82.7005 q^{14} +(25.4721 - 95.0631i) q^{15} +(76.7460 + 132.928i) q^{16} +(-171.531 - 99.0336i) q^{17} +(39.8171 + 39.8171i) q^{18} +(-106.721 + 28.5959i) q^{19} +(-53.2166 - 198.607i) q^{20} +(257.329 - 257.329i) q^{21} +(40.8279 - 70.7161i) q^{22} +(-761.646 + 439.737i) q^{23} +(-283.363 - 75.9269i) q^{24} -401.708i q^{25} +(-222.944 + 119.484i) q^{26} +781.267 q^{27} +(196.781 - 734.395i) q^{28} +(398.637 + 690.460i) q^{29} +(127.566 + 73.6504i) q^{30} +(1101.81 + 1101.81i) q^{31} +(-910.290 + 243.911i) q^{32} +(-92.9992 - 347.078i) q^{33} +(209.621 - 209.621i) q^{34} +(-412.836 + 715.053i) q^{35} +(448.325 - 258.841i) q^{36} +(-1201.99 - 322.072i) q^{37} -165.365i q^{38} +(-321.924 + 1065.49i) q^{39} +665.586 q^{40} +(802.734 - 2995.84i) q^{41} +(272.339 + 471.706i) q^{42} +(-798.822 - 461.200i) q^{43} +(-530.823 - 530.823i) q^{44} +(-543.036 + 145.506i) q^{45} +(-340.687 - 1271.46i) q^{46} +(-995.185 + 995.185i) q^{47} +(-505.461 + 875.484i) q^{48} +(-564.749 + 326.058i) q^{49} +(580.753 + 155.612i) q^{50} -1304.50i q^{51} +(530.557 + 2264.08i) q^{52} +3865.42 q^{53} +(-302.644 + 1129.48i) q^{54} +(407.622 + 706.021i) q^{55} +(2131.42 + 1230.58i) q^{56} +(-514.546 - 514.546i) q^{57} +(-1152.63 + 308.845i) q^{58} +(216.499 + 807.984i) q^{59} +(957.564 - 957.564i) q^{60} +(1383.34 - 2396.02i) q^{61} +(-2019.71 + 1166.08i) q^{62} +(-2008.00 - 538.042i) q^{63} +1045.37i q^{64} +(79.8300 - 2524.10i) q^{65} +537.798 q^{66} +(-783.745 + 2924.98i) q^{67} +(-1362.69 - 2360.25i) q^{68} +(-5016.32 - 2896.17i) q^{69} +(-873.835 - 873.835i) q^{70} +(4083.09 - 1094.06i) q^{71} +(433.723 + 1618.68i) q^{72} +(-918.987 + 918.987i) q^{73} +(931.243 - 1612.96i) q^{74} +(2291.26 - 1322.86i) q^{75} +(-1468.47 - 393.476i) q^{76} +3014.55i q^{77} +(-1415.68 - 878.153i) q^{78} -7901.53 q^{79} +(593.633 - 2215.47i) q^{80} +(1049.06 + 1817.02i) q^{81} +(4020.15 + 2321.04i) q^{82} +(2976.10 + 2976.10i) q^{83} +(4836.84 - 1296.03i) q^{84} +(766.029 + 2858.86i) q^{85} +(976.206 - 976.206i) q^{86} +(-2625.49 + 4547.48i) q^{87} +(2104.50 - 1215.03i) q^{88} +(12196.3 + 3267.99i) q^{89} -841.436i q^{90} +(4922.36 - 7935.39i) q^{91} -12101.4 q^{92} +(-2656.13 + 9912.80i) q^{93} +(-1053.24 - 1824.26i) q^{94} +(1429.80 + 825.493i) q^{95} +(-4388.87 - 4388.87i) q^{96} +(-7629.42 + 2044.30i) q^{97} +(-252.614 - 942.769i) q^{98} +(-1451.39 + 1451.39i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{2} - 2 q^{3} - 6 q^{4} + 8 q^{5} - 38 q^{6} + 56 q^{7} + 90 q^{8} - 164 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{2} - 2 q^{3} - 6 q^{4} + 8 q^{5} - 38 q^{6} + 56 q^{7} + 90 q^{8} - 164 q^{9} - 486 q^{10} - 100 q^{11} + 294 q^{13} + 808 q^{14} + 346 q^{15} + 230 q^{16} + 984 q^{17} + 2434 q^{18} - 1498 q^{19} - 3962 q^{20} - 1076 q^{21} - 1524 q^{22} - 1014 q^{23} - 2142 q^{24} + 614 q^{26} + 3352 q^{27} + 5764 q^{28} + 814 q^{29} + 9162 q^{30} + 4060 q^{31} - 4996 q^{32} - 5636 q^{33} - 2502 q^{34} - 4892 q^{35} - 15750 q^{36} - 1790 q^{37} + 6982 q^{39} + 18816 q^{40} + 4280 q^{41} - 1204 q^{42} - 1368 q^{43} + 10736 q^{44} - 6806 q^{45} - 15246 q^{46} + 1484 q^{47} - 3002 q^{48} - 11820 q^{49} - 13574 q^{50} + 1432 q^{52} + 7204 q^{53} + 13240 q^{54} + 6936 q^{55} + 8124 q^{56} + 12736 q^{57} + 3030 q^{58} - 2380 q^{59} - 6472 q^{60} - 162 q^{61} + 19614 q^{62} + 12004 q^{63} - 5248 q^{65} - 23872 q^{66} - 14854 q^{67} - 6444 q^{68} + 2412 q^{69} - 34524 q^{70} - 8050 q^{71} + 15420 q^{72} - 15448 q^{73} - 2882 q^{74} + 8280 q^{75} + 10622 q^{76} - 11672 q^{78} - 17064 q^{79} + 2564 q^{80} + 2128 q^{81} - 5346 q^{82} + 12788 q^{83} + 25948 q^{84} + 35382 q^{85} + 67260 q^{86} + 29342 q^{87} + 40836 q^{88} + 20492 q^{89} + 8996 q^{91} - 49884 q^{92} - 78920 q^{93} - 30606 q^{94} - 98574 q^{95} - 94664 q^{96} + 50944 q^{97} + 61484 q^{98} - 21632 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.387376 + 1.44571i −0.0968440 + 0.361427i −0.997293 0.0735357i \(-0.976572\pi\)
0.900449 + 0.434963i \(0.143238\pi\)
\(3\) 3.29308 + 5.70378i 0.365898 + 0.633753i 0.988920 0.148451i \(-0.0474287\pi\)
−0.623022 + 0.782204i \(0.714095\pi\)
\(4\) 11.9164 + 6.87993i 0.744775 + 0.429996i
\(5\) −10.5663 10.5663i −0.422650 0.422650i 0.463465 0.886115i \(-0.346606\pi\)
−0.886115 + 0.463465i \(0.846606\pi\)
\(6\) −9.52166 + 2.55132i −0.264490 + 0.0708700i
\(7\) −14.3010 53.3722i −0.291858 1.08923i −0.943681 0.330858i \(-0.892662\pi\)
0.651823 0.758372i \(-0.274005\pi\)
\(8\) −31.4958 + 31.4958i −0.492122 + 0.492122i
\(9\) 18.8113 32.5821i 0.232238 0.402248i
\(10\) 19.3688 11.1826i 0.193688 0.111826i
\(11\) −52.6981 14.1204i −0.435521 0.116698i 0.0343956 0.999408i \(-0.489049\pi\)
−0.469917 + 0.882711i \(0.655716\pi\)
\(12\) 90.6246i 0.629338i
\(13\) 115.664 + 123.219i 0.684401 + 0.729106i
\(14\) 82.7005 0.421941
\(15\) 25.4721 95.0631i 0.113209 0.422503i
\(16\) 76.7460 + 132.928i 0.299789 + 0.519250i
\(17\) −171.531 99.0336i −0.593534 0.342677i 0.172960 0.984929i \(-0.444667\pi\)
−0.766494 + 0.642252i \(0.778000\pi\)
\(18\) 39.8171 + 39.8171i 0.122892 + 0.122892i
\(19\) −106.721 + 28.5959i −0.295627 + 0.0792130i −0.403584 0.914943i \(-0.632236\pi\)
0.107957 + 0.994156i \(0.465569\pi\)
\(20\) −53.2166 198.607i −0.133041 0.496517i
\(21\) 257.329 257.329i 0.583512 0.583512i
\(22\) 40.8279 70.7161i 0.0843553 0.146108i
\(23\) −761.646 + 439.737i −1.43979 + 0.831260i −0.997834 0.0657787i \(-0.979047\pi\)
−0.441951 + 0.897039i \(0.645714\pi\)
\(24\) −283.363 75.9269i −0.491950 0.131818i
\(25\) 401.708i 0.642733i
\(26\) −222.944 + 119.484i −0.329799 + 0.176751i
\(27\) 781.267 1.07170
\(28\) 196.781 734.395i 0.250996 0.936728i
\(29\) 398.637 + 690.460i 0.474004 + 0.820999i 0.999557 0.0297621i \(-0.00947496\pi\)
−0.525553 + 0.850761i \(0.676142\pi\)
\(30\) 127.566 + 73.6504i 0.141740 + 0.0818337i
\(31\) 1101.81 + 1101.81i 1.14652 + 1.14652i 0.987232 + 0.159290i \(0.0509205\pi\)
0.159290 + 0.987232i \(0.449079\pi\)
\(32\) −910.290 + 243.911i −0.888955 + 0.238195i
\(33\) −92.9992 347.078i −0.0853987 0.318712i
\(34\) 209.621 209.621i 0.181333 0.181333i
\(35\) −412.836 + 715.053i −0.337009 + 0.583717i
\(36\) 448.325 258.841i 0.345930 0.199723i
\(37\) −1201.99 322.072i −0.878005 0.235261i −0.208459 0.978031i \(-0.566845\pi\)
−0.669546 + 0.742771i \(0.733511\pi\)
\(38\) 165.365i 0.114519i
\(39\) −321.924 + 1065.49i −0.211653 + 0.700519i
\(40\) 665.586 0.415991
\(41\) 802.734 2995.84i 0.477534 1.78218i −0.134022 0.990978i \(-0.542789\pi\)
0.611556 0.791201i \(-0.290544\pi\)
\(42\) 272.339 + 471.706i 0.154387 + 0.267407i
\(43\) −798.822 461.200i −0.432029 0.249432i 0.268181 0.963368i \(-0.413577\pi\)
−0.700211 + 0.713936i \(0.746911\pi\)
\(44\) −530.823 530.823i −0.274186 0.274186i
\(45\) −543.036 + 145.506i −0.268166 + 0.0718548i
\(46\) −340.687 1271.46i −0.161005 0.600880i
\(47\) −995.185 + 995.185i −0.450514 + 0.450514i −0.895525 0.445011i \(-0.853200\pi\)
0.445011 + 0.895525i \(0.353200\pi\)
\(48\) −505.461 + 875.484i −0.219384 + 0.379984i
\(49\) −564.749 + 326.058i −0.235214 + 0.135801i
\(50\) 580.753 + 155.612i 0.232301 + 0.0622449i
\(51\) 1304.50i 0.501538i
\(52\) 530.557 + 2264.08i 0.196212 + 0.837309i
\(53\) 3865.42 1.37608 0.688042 0.725671i \(-0.258471\pi\)
0.688042 + 0.725671i \(0.258471\pi\)
\(54\) −302.644 + 1129.48i −0.103787 + 0.387340i
\(55\) 407.622 + 706.021i 0.134751 + 0.233395i
\(56\) 2131.42 + 1230.58i 0.679663 + 0.392404i
\(57\) −514.546 514.546i −0.158371 0.158371i
\(58\) −1152.63 + 308.845i −0.342635 + 0.0918089i
\(59\) 216.499 + 807.984i 0.0621944 + 0.232113i 0.990026 0.140888i \(-0.0449957\pi\)
−0.927831 + 0.373000i \(0.878329\pi\)
\(60\) 957.564 957.564i 0.265990 0.265990i
\(61\) 1383.34 2396.02i 0.371766 0.643917i −0.618072 0.786122i \(-0.712086\pi\)
0.989837 + 0.142205i \(0.0454191\pi\)
\(62\) −2019.71 + 1166.08i −0.525418 + 0.303350i
\(63\) −2008.00 538.042i −0.505921 0.135561i
\(64\) 1045.37i 0.255218i
\(65\) 79.8300 2524.10i 0.0188947 0.597419i
\(66\) 537.798 0.123462
\(67\) −783.745 + 2924.98i −0.174592 + 0.651588i 0.822028 + 0.569447i \(0.192842\pi\)
−0.996621 + 0.0821411i \(0.973824\pi\)
\(68\) −1362.69 2360.25i −0.294699 0.510434i
\(69\) −5016.32 2896.17i −1.05363 0.608312i
\(70\) −873.835 873.835i −0.178334 0.178334i
\(71\) 4083.09 1094.06i 0.809977 0.217033i 0.170017 0.985441i \(-0.445618\pi\)
0.639960 + 0.768409i \(0.278951\pi\)
\(72\) 433.723 + 1618.68i 0.0836656 + 0.312244i
\(73\) −918.987 + 918.987i −0.172450 + 0.172450i −0.788055 0.615605i \(-0.788912\pi\)
0.615605 + 0.788055i \(0.288912\pi\)
\(74\) 931.243 1612.96i 0.170059 0.294551i
\(75\) 2291.26 1322.86i 0.407334 0.235175i
\(76\) −1468.47 393.476i −0.254237 0.0681225i
\(77\) 3014.55i 0.508442i
\(78\) −1415.68 878.153i −0.232689 0.144338i
\(79\) −7901.53 −1.26607 −0.633034 0.774124i \(-0.718191\pi\)
−0.633034 + 0.774124i \(0.718191\pi\)
\(80\) 593.633 2215.47i 0.0927551 0.346167i
\(81\) 1049.06 + 1817.02i 0.159893 + 0.276943i
\(82\) 4020.15 + 2321.04i 0.597881 + 0.345187i
\(83\) 2976.10 + 2976.10i 0.432007 + 0.432007i 0.889311 0.457304i \(-0.151185\pi\)
−0.457304 + 0.889311i \(0.651185\pi\)
\(84\) 4836.84 1296.03i 0.685493 0.183677i
\(85\) 766.029 + 2858.86i 0.106025 + 0.395690i
\(86\) 976.206 976.206i 0.131991 0.131991i
\(87\) −2625.49 + 4547.48i −0.346874 + 0.600803i
\(88\) 2104.50 1215.03i 0.271759 0.156900i
\(89\) 12196.3 + 3267.99i 1.53974 + 0.412573i 0.926183 0.377074i \(-0.123070\pi\)
0.613561 + 0.789647i \(0.289736\pi\)
\(90\) 841.436i 0.103881i
\(91\) 4922.36 7935.39i 0.594416 0.958265i
\(92\) −12101.4 −1.42975
\(93\) −2656.13 + 9912.80i −0.307102 + 1.14612i
\(94\) −1053.24 1824.26i −0.119198 0.206457i
\(95\) 1429.80 + 825.493i 0.158426 + 0.0914674i
\(96\) −4388.87 4388.87i −0.476223 0.476223i
\(97\) −7629.42 + 2044.30i −0.810864 + 0.217270i −0.640348 0.768085i \(-0.721210\pi\)
−0.170516 + 0.985355i \(0.554543\pi\)
\(98\) −252.614 942.769i −0.0263030 0.0981642i
\(99\) −1451.39 + 1451.39i −0.148086 + 0.148086i
\(100\) 2763.73 4786.92i 0.276373 0.478692i
\(101\) 6889.37 3977.58i 0.675362 0.389921i −0.122743 0.992438i \(-0.539169\pi\)
0.798105 + 0.602518i \(0.205836\pi\)
\(102\) 1885.93 + 505.333i 0.181269 + 0.0485710i
\(103\) 2165.17i 0.204088i −0.994780 0.102044i \(-0.967462\pi\)
0.994780 0.102044i \(-0.0325383\pi\)
\(104\) −7523.80 237.957i −0.695618 0.0220004i
\(105\) −5438.01 −0.493243
\(106\) −1497.37 + 5588.26i −0.133265 + 0.497354i
\(107\) −9354.92 16203.2i −0.817095 1.41525i −0.907814 0.419373i \(-0.862250\pi\)
0.0907190 0.995877i \(-0.471083\pi\)
\(108\) 9309.88 + 5375.06i 0.798172 + 0.460825i
\(109\) −2940.23 2940.23i −0.247474 0.247474i 0.572459 0.819933i \(-0.305989\pi\)
−0.819933 + 0.572459i \(0.805989\pi\)
\(110\) −1178.60 + 315.806i −0.0974052 + 0.0260996i
\(111\) −2121.22 7916.48i −0.172163 0.642520i
\(112\) 5997.11 5997.11i 0.478086 0.478086i
\(113\) −3629.31 + 6286.15i −0.284228 + 0.492298i −0.972422 0.233230i \(-0.925071\pi\)
0.688194 + 0.725527i \(0.258404\pi\)
\(114\) 943.206 544.560i 0.0725767 0.0419022i
\(115\) 12694.1 + 3401.38i 0.959858 + 0.257193i
\(116\) 10970.4i 0.815279i
\(117\) 6190.51 1450.66i 0.452225 0.105973i
\(118\) −1251.97 −0.0899149
\(119\) −2832.57 + 10571.3i −0.200026 + 0.746507i
\(120\) 2191.83 + 3796.35i 0.152210 + 0.263636i
\(121\) −10101.8 5832.26i −0.689965 0.398352i
\(122\) 2928.06 + 2928.06i 0.196726 + 0.196726i
\(123\) 19731.1 5286.93i 1.30419 0.349457i
\(124\) 5549.21 + 20709.9i 0.360901 + 1.34690i
\(125\) −10848.5 + 10848.5i −0.694302 + 0.694302i
\(126\) 1555.70 2694.56i 0.0979908 0.169725i
\(127\) 3292.61 1900.99i 0.204142 0.117862i −0.394444 0.918920i \(-0.629063\pi\)
0.598586 + 0.801058i \(0.295729\pi\)
\(128\) −16075.9 4307.53i −0.981197 0.262911i
\(129\) 6075.07i 0.365067i
\(130\) 3618.18 + 1093.19i 0.214094 + 0.0646855i
\(131\) 5278.85 0.307607 0.153804 0.988101i \(-0.450848\pi\)
0.153804 + 0.988101i \(0.450848\pi\)
\(132\) 1279.66 4775.74i 0.0734422 0.274090i
\(133\) 3052.45 + 5287.00i 0.172562 + 0.298887i
\(134\) −3925.06 2266.13i −0.218593 0.126205i
\(135\) −8255.07 8255.07i −0.452953 0.452953i
\(136\) 8521.66 2283.37i 0.460730 0.123452i
\(137\) 303.931 + 1134.29i 0.0161933 + 0.0604341i 0.973550 0.228475i \(-0.0733740\pi\)
−0.957356 + 0.288909i \(0.906707\pi\)
\(138\) 6130.23 6130.23i 0.321898 0.321898i
\(139\) 6086.83 10542.7i 0.315037 0.545660i −0.664408 0.747370i \(-0.731316\pi\)
0.979445 + 0.201710i \(0.0646497\pi\)
\(140\) −9839.04 + 5680.57i −0.501992 + 0.289825i
\(141\) −8953.54 2399.09i −0.450356 0.120673i
\(142\) 6326.77i 0.313766i
\(143\) −4355.35 8126.62i −0.212986 0.397409i
\(144\) 5774.76 0.278489
\(145\) 3083.47 11507.7i 0.146658 0.547333i
\(146\) −972.593 1684.58i −0.0456274 0.0790289i
\(147\) −3719.52 2147.47i −0.172128 0.0993784i
\(148\) −12107.5 12107.5i −0.552755 0.552755i
\(149\) −20323.5 + 5445.66i −0.915431 + 0.245289i −0.685631 0.727949i \(-0.740474\pi\)
−0.229800 + 0.973238i \(0.573807\pi\)
\(150\) 1024.89 + 3824.93i 0.0455505 + 0.169997i
\(151\) −22690.8 + 22690.8i −0.995167 + 0.995167i −0.999988 0.00482166i \(-0.998465\pi\)
0.00482166 + 0.999988i \(0.498465\pi\)
\(152\) 2460.62 4261.92i 0.106502 0.184467i
\(153\) −6453.44 + 3725.90i −0.275682 + 0.159165i
\(154\) −4358.16 1167.76i −0.183764 0.0492395i
\(155\) 23284.0i 0.969156i
\(156\) −11166.7 + 10482.0i −0.458854 + 0.430719i
\(157\) 35324.6 1.43310 0.716552 0.697534i \(-0.245719\pi\)
0.716552 + 0.697534i \(0.245719\pi\)
\(158\) 3060.86 11423.3i 0.122611 0.457591i
\(159\) 12729.1 + 22047.5i 0.503506 + 0.872097i
\(160\) 12195.6 + 7041.12i 0.476390 + 0.275044i
\(161\) 34362.1 + 34362.1i 1.32565 + 1.32565i
\(162\) −3033.26 + 812.761i −0.115579 + 0.0309694i
\(163\) −5807.75 21674.8i −0.218591 0.815793i −0.984871 0.173287i \(-0.944561\pi\)
0.766280 0.642506i \(-0.222105\pi\)
\(164\) 30176.9 30176.9i 1.12199 1.12199i
\(165\) −2684.66 + 4649.97i −0.0986101 + 0.170798i
\(166\) −5455.43 + 3149.70i −0.197976 + 0.114302i
\(167\) 1455.11 + 389.896i 0.0521751 + 0.0139803i 0.284812 0.958583i \(-0.408069\pi\)
−0.232637 + 0.972564i \(0.574735\pi\)
\(168\) 16209.6i 0.574318i
\(169\) −1804.80 + 28503.9i −0.0631911 + 0.998001i
\(170\) −4429.81 −0.153281
\(171\) −1075.85 + 4015.13i −0.0367925 + 0.137312i
\(172\) −6346.06 10991.7i −0.214510 0.371542i
\(173\) 3791.94 + 2189.28i 0.126698 + 0.0731491i 0.562010 0.827131i \(-0.310028\pi\)
−0.435312 + 0.900280i \(0.643362\pi\)
\(174\) −5557.27 5557.27i −0.183554 0.183554i
\(175\) −21440.1 + 5744.85i −0.700084 + 0.187587i
\(176\) −2167.37 8088.73i −0.0699693 0.261129i
\(177\) −3895.61 + 3895.61i −0.124345 + 0.124345i
\(178\) −9449.12 + 16366.4i −0.298230 + 0.516550i
\(179\) 10787.3 6228.06i 0.336672 0.194378i −0.322127 0.946696i \(-0.604398\pi\)
0.658800 + 0.752319i \(0.271065\pi\)
\(180\) −7472.10 2002.14i −0.230620 0.0617945i
\(181\) 23085.8i 0.704673i −0.935873 0.352336i \(-0.885387\pi\)
0.935873 0.352336i \(-0.114613\pi\)
\(182\) 9565.45 + 10190.3i 0.288777 + 0.307640i
\(183\) 18221.8 0.544113
\(184\) 10138.8 37838.5i 0.299468 1.11763i
\(185\) 9297.43 + 16103.6i 0.271656 + 0.470522i
\(186\) −13302.1 7679.97i −0.384498 0.221990i
\(187\) 7640.97 + 7640.97i 0.218507 + 0.218507i
\(188\) −18705.8 + 5012.21i −0.529250 + 0.141812i
\(189\) −11172.9 41697.9i −0.312783 1.16732i
\(190\) −1747.29 + 1747.29i −0.0484014 + 0.0484014i
\(191\) −30414.3 + 52679.1i −0.833703 + 1.44402i 0.0613793 + 0.998115i \(0.480450\pi\)
−0.895082 + 0.445901i \(0.852883\pi\)
\(192\) −5962.57 + 3442.49i −0.161745 + 0.0933836i
\(193\) −9841.71 2637.08i −0.264214 0.0707959i 0.124280 0.992247i \(-0.460338\pi\)
−0.388494 + 0.921451i \(0.627005\pi\)
\(194\) 11821.8i 0.314109i
\(195\) 14659.8 7856.71i 0.385530 0.206620i
\(196\) −8973.03 −0.233575
\(197\) 14724.5 54952.4i 0.379408 1.41597i −0.467387 0.884053i \(-0.654804\pi\)
0.846795 0.531919i \(-0.178529\pi\)
\(198\) −1536.05 2660.52i −0.0391810 0.0678635i
\(199\) −31073.9 17940.5i −0.784673 0.453031i 0.0534105 0.998573i \(-0.482991\pi\)
−0.838084 + 0.545541i \(0.816324\pi\)
\(200\) 12652.1 + 12652.1i 0.316303 + 0.316303i
\(201\) −19264.4 + 5161.87i −0.476829 + 0.127766i
\(202\) 3081.64 + 11500.8i 0.0755230 + 0.281856i
\(203\) 31150.5 31150.5i 0.755914 0.755914i
\(204\) 8974.89 15545.0i 0.215659 0.373533i
\(205\) −40136.8 + 23173.0i −0.955069 + 0.551409i
\(206\) 3130.20 + 838.735i 0.0737629 + 0.0197647i
\(207\) 33088.0i 0.772201i
\(208\) −7502.51 + 24831.5i −0.173412 + 0.573953i
\(209\) 6027.79 0.137996
\(210\) 2106.56 7861.77i 0.0477677 0.178271i
\(211\) 14344.6 + 24845.6i 0.322199 + 0.558066i 0.980942 0.194303i \(-0.0622446\pi\)
−0.658742 + 0.752369i \(0.728911\pi\)
\(212\) 46061.9 + 26593.8i 1.02487 + 0.591710i
\(213\) 19686.2 + 19686.2i 0.433913 + 0.433913i
\(214\) 27049.0 7247.75i 0.590640 0.158262i
\(215\) 3567.40 + 13313.7i 0.0771747 + 0.288020i
\(216\) −24606.6 + 24606.6i −0.527405 + 0.527405i
\(217\) 43048.9 74562.9i 0.914204 1.58345i
\(218\) 5389.69 3111.74i 0.113410 0.0654773i
\(219\) −8267.99 2215.40i −0.172390 0.0461917i
\(220\) 11217.6i 0.231769i
\(221\) −7637.13 32590.5i −0.156367 0.667277i
\(222\) 12266.6 0.248897
\(223\) −18745.8 + 69960.4i −0.376960 + 1.40683i 0.473501 + 0.880794i \(0.342990\pi\)
−0.850460 + 0.526039i \(0.823676\pi\)
\(224\) 26036.2 + 45096.0i 0.518897 + 0.898756i
\(225\) −13088.5 7556.65i −0.258538 0.149267i
\(226\) −7682.02 7682.02i −0.150404 0.150404i
\(227\) −3711.35 + 994.452i −0.0720244 + 0.0192989i −0.294651 0.955605i \(-0.595203\pi\)
0.222627 + 0.974904i \(0.428537\pi\)
\(228\) −2591.49 9671.58i −0.0498517 0.186049i
\(229\) −4649.95 + 4649.95i −0.0886701 + 0.0886701i −0.750051 0.661380i \(-0.769971\pi\)
0.661380 + 0.750051i \(0.269971\pi\)
\(230\) −9834.80 + 17034.4i −0.185913 + 0.322011i
\(231\) −17194.3 + 9927.15i −0.322226 + 0.186038i
\(232\) −34302.0 9191.19i −0.637299 0.170764i
\(233\) 56025.7i 1.03199i −0.856592 0.515995i \(-0.827422\pi\)
0.856592 0.515995i \(-0.172578\pi\)
\(234\) −300.826 + 9511.62i −0.00549393 + 0.173709i
\(235\) 21030.8 0.380820
\(236\) −2978.99 + 11117.8i −0.0534866 + 0.199615i
\(237\) −26020.3 45068.6i −0.463251 0.802374i
\(238\) −14185.7 8190.13i −0.250437 0.144590i
\(239\) −23621.5 23621.5i −0.413534 0.413534i 0.469434 0.882968i \(-0.344458\pi\)
−0.882968 + 0.469434i \(0.844458\pi\)
\(240\) 14591.4 3909.76i 0.253323 0.0678778i
\(241\) 2176.28 + 8122.00i 0.0374698 + 0.139839i 0.982127 0.188221i \(-0.0602720\pi\)
−0.944657 + 0.328060i \(0.893605\pi\)
\(242\) 12344.9 12344.9i 0.210794 0.210794i
\(243\) 24732.0 42837.1i 0.418839 0.725451i
\(244\) 32968.9 19034.6i 0.553763 0.319715i
\(245\) 9412.49 + 2522.07i 0.156810 + 0.0420170i
\(246\) 30573.4i 0.505212i
\(247\) −15867.3 9842.58i −0.260082 0.161330i
\(248\) −69404.6 −1.12846
\(249\) −7174.47 + 26775.5i −0.115715 + 0.431856i
\(250\) −11481.3 19886.1i −0.183700 0.318178i
\(251\) −25257.5 14582.4i −0.400906 0.231463i 0.285969 0.958239i \(-0.407685\pi\)
−0.686875 + 0.726776i \(0.741018\pi\)
\(252\) −20226.4 20226.4i −0.318506 0.318506i
\(253\) 46346.5 12418.5i 0.724063 0.194012i
\(254\) 1472.80 + 5496.55i 0.0228284 + 0.0851967i
\(255\) −13783.7 + 13783.7i −0.211975 + 0.211975i
\(256\) 4091.89 7087.36i 0.0624372 0.108144i
\(257\) 5674.86 3276.38i 0.0859189 0.0496053i −0.456425 0.889762i \(-0.650870\pi\)
0.542344 + 0.840157i \(0.317537\pi\)
\(258\) 8782.78 + 2353.34i 0.131945 + 0.0353545i
\(259\) 68758.8i 1.02501i
\(260\) 18316.9 29528.9i 0.270960 0.436818i
\(261\) 29995.5 0.440327
\(262\) −2044.90 + 7631.67i −0.0297899 + 0.111178i
\(263\) −10037.2 17384.9i −0.145111 0.251340i 0.784303 0.620378i \(-0.213021\pi\)
−0.929414 + 0.369038i \(0.879687\pi\)
\(264\) 13860.6 + 8002.41i 0.198872 + 0.114819i
\(265\) −40843.0 40843.0i −0.581602 0.581602i
\(266\) −8825.91 + 2364.90i −0.124737 + 0.0334232i
\(267\) 21523.5 + 80326.8i 0.301919 + 1.12678i
\(268\) −29463.1 + 29463.1i −0.410212 + 0.410212i
\(269\) −63876.4 + 110637.i −0.882747 + 1.52896i −0.0344720 + 0.999406i \(0.510975\pi\)
−0.848275 + 0.529556i \(0.822358\pi\)
\(270\) 15132.2 8736.60i 0.207575 0.119844i
\(271\) 96583.1 + 25879.4i 1.31511 + 0.352383i 0.847145 0.531362i \(-0.178320\pi\)
0.467967 + 0.883746i \(0.344986\pi\)
\(272\) 30401.7i 0.410923i
\(273\) 61471.4 + 1944.17i 0.824799 + 0.0260861i
\(274\) −1757.58 −0.0234107
\(275\) −5672.28 + 21169.2i −0.0750054 + 0.279924i
\(276\) −39851.0 69023.9i −0.523144 0.906111i
\(277\) 58305.7 + 33662.8i 0.759892 + 0.438724i 0.829257 0.558868i \(-0.188764\pi\)
−0.0693651 + 0.997591i \(0.522097\pi\)
\(278\) 12883.8 + 12883.8i 0.166707 + 0.166707i
\(279\) 56625.6 15172.8i 0.727452 0.194920i
\(280\) −9518.57 35523.8i −0.121410 0.453110i
\(281\) −9761.98 + 9761.98i −0.123630 + 0.123630i −0.766215 0.642584i \(-0.777862\pi\)
0.642584 + 0.766215i \(0.277862\pi\)
\(282\) 6936.77 12014.8i 0.0872287 0.151084i
\(283\) 75924.7 43835.2i 0.948004 0.547331i 0.0555440 0.998456i \(-0.482311\pi\)
0.892460 + 0.451126i \(0.148977\pi\)
\(284\) 56182.8 + 15054.1i 0.696573 + 0.186646i
\(285\) 10873.7i 0.133871i
\(286\) 13435.9 3148.51i 0.164261 0.0384922i
\(287\) −171375. −2.08057
\(288\) −9176.57 + 34247.4i −0.110636 + 0.412898i
\(289\) −22145.2 38356.6i −0.265145 0.459245i
\(290\) 15442.3 + 8915.60i 0.183618 + 0.106012i
\(291\) −36784.5 36784.5i −0.434389 0.434389i
\(292\) −17273.6 + 4628.44i −0.202589 + 0.0542837i
\(293\) 17014.8 + 63500.0i 0.198194 + 0.739671i 0.991417 + 0.130739i \(0.0417351\pi\)
−0.793223 + 0.608932i \(0.791598\pi\)
\(294\) 4545.47 4545.47i 0.0525876 0.0525876i
\(295\) 6249.79 10824.9i 0.0718160 0.124389i
\(296\) 48001.5 27713.7i 0.547862 0.316308i
\(297\) −41171.2 11031.8i −0.466746 0.125064i
\(298\) 31491.3i 0.354616i
\(299\) −142279. 42987.7i −1.59147 0.480841i
\(300\) 36404.7 0.404496
\(301\) −13191.3 + 49230.6i −0.145598 + 0.543378i
\(302\) −24014.4 41594.1i −0.263304 0.456056i
\(303\) 45374.5 + 26197.0i 0.494227 + 0.285342i
\(304\) −11991.6 11991.6i −0.129757 0.129757i
\(305\) −39933.7 + 10700.2i −0.429279 + 0.115025i
\(306\) −2886.65 10773.1i −0.0308284 0.115053i
\(307\) 24442.3 24442.3i 0.259337 0.259337i −0.565447 0.824785i \(-0.691296\pi\)
0.824785 + 0.565447i \(0.191296\pi\)
\(308\) −20739.9 + 35922.6i −0.218628 + 0.378674i
\(309\) 12349.7 7130.07i 0.129341 0.0746753i
\(310\) 33661.8 + 9019.66i 0.350279 + 0.0938570i
\(311\) 82049.3i 0.848309i −0.905590 0.424155i \(-0.860571\pi\)
0.905590 0.424155i \(-0.139429\pi\)
\(312\) −23419.2 43697.7i −0.240582 0.448900i
\(313\) −73633.7 −0.751602 −0.375801 0.926700i \(-0.622632\pi\)
−0.375801 + 0.926700i \(0.622632\pi\)
\(314\) −13683.9 + 51069.0i −0.138788 + 0.517962i
\(315\) 15532.0 + 26902.1i 0.156533 + 0.271123i
\(316\) −94157.7 54362.0i −0.942935 0.544404i
\(317\) 88575.1 + 88575.1i 0.881440 + 0.881440i 0.993681 0.112241i \(-0.0358028\pi\)
−0.112241 + 0.993681i \(0.535803\pi\)
\(318\) −36805.2 + 9861.92i −0.363961 + 0.0975230i
\(319\) −11257.8 42014.8i −0.110630 0.412877i
\(320\) 11045.7 11045.7i 0.107868 0.107868i
\(321\) 61613.0 106717.i 0.597946 1.03567i
\(322\) −62988.6 + 36366.5i −0.607505 + 0.350743i
\(323\) 21138.0 + 5663.91i 0.202609 + 0.0542889i
\(324\) 28869.8i 0.275013i
\(325\) 49498.1 46463.1i 0.468621 0.439887i
\(326\) 33585.2 0.316019
\(327\) 7088.02 26452.9i 0.0662872 0.247387i
\(328\) 69073.8 + 119639.i 0.642045 + 1.11205i
\(329\) 67347.4 + 38883.1i 0.622199 + 0.359227i
\(330\) −5682.52 5682.52i −0.0521811 0.0521811i
\(331\) 138582. 37132.9i 1.26488 0.338924i 0.436814 0.899552i \(-0.356107\pi\)
0.828068 + 0.560628i \(0.189440\pi\)
\(332\) 14989.0 + 55939.7i 0.135987 + 0.507509i
\(333\) −33104.7 + 33104.7i −0.298539 + 0.298539i
\(334\) −1127.35 + 1952.63i −0.0101057 + 0.0175036i
\(335\) 39187.3 22624.8i 0.349185 0.201602i
\(336\) 53955.2 + 14457.2i 0.477919 + 0.128058i
\(337\) 165153.i 1.45421i 0.686527 + 0.727104i \(0.259134\pi\)
−0.686527 + 0.727104i \(0.740866\pi\)
\(338\) −40509.2 13651.0i −0.354585 0.119489i
\(339\) −47806.4 −0.415994
\(340\) −10540.5 + 39337.5i −0.0911804 + 0.340290i
\(341\) −42505.2 73621.1i −0.365538 0.633131i
\(342\) −5387.94 3110.73i −0.0460650 0.0265956i
\(343\) −68331.0 68331.0i −0.580804 0.580804i
\(344\) 39685.4 10633.7i 0.335362 0.0898600i
\(345\) 22402.0 + 83605.5i 0.188213 + 0.702420i
\(346\) −4633.97 + 4633.97i −0.0387080 + 0.0387080i
\(347\) −27797.5 + 48146.6i −0.230859 + 0.399859i −0.958061 0.286564i \(-0.907487\pi\)
0.727202 + 0.686423i \(0.240820\pi\)
\(348\) −62572.7 + 36126.4i −0.516686 + 0.298309i
\(349\) −168206. 45070.6i −1.38099 0.370035i −0.509509 0.860465i \(-0.670173\pi\)
−0.871480 + 0.490431i \(0.836840\pi\)
\(350\) 33221.5i 0.271196i
\(351\) 90364.2 + 96266.8i 0.733470 + 0.781380i
\(352\) 51414.6 0.414955
\(353\) 43391.2 161938.i 0.348219 1.29957i −0.540587 0.841288i \(-0.681798\pi\)
0.888806 0.458283i \(-0.151536\pi\)
\(354\) −4122.85 7140.99i −0.0328996 0.0569838i
\(355\) −54703.1 31582.9i −0.434066 0.250608i
\(356\) 122853. + 122853.i 0.969358 + 0.969358i
\(357\) −69624.2 + 18655.7i −0.546290 + 0.146378i
\(358\) 4825.20 + 18007.9i 0.0376487 + 0.140507i
\(359\) 112373. 112373.i 0.871912 0.871912i −0.120769 0.992681i \(-0.538536\pi\)
0.992681 + 0.120769i \(0.0385360\pi\)
\(360\) 12520.5 21686.2i 0.0966089 0.167332i
\(361\) −102290. + 59056.9i −0.784905 + 0.453165i
\(362\) 33375.3 + 8942.89i 0.254688 + 0.0682434i
\(363\) 76824.4i 0.583023i
\(364\) 113252. 60695.8i 0.854756 0.458095i
\(365\) 19420.5 0.145772
\(366\) −7058.69 + 26343.4i −0.0526941 + 0.196657i
\(367\) 36242.1 + 62773.1i 0.269080 + 0.466060i 0.968624 0.248529i \(-0.0799472\pi\)
−0.699545 + 0.714589i \(0.746614\pi\)
\(368\) −116907. 67496.0i −0.863263 0.498405i
\(369\) −82510.4 82510.4i −0.605977 0.605977i
\(370\) −26882.7 + 7203.20i −0.196368 + 0.0526165i
\(371\) −55279.5 206306.i −0.401621 1.49887i
\(372\) −99850.9 + 99850.9i −0.721550 + 0.721550i
\(373\) 19788.5 34274.7i 0.142231 0.246352i −0.786105 0.618093i \(-0.787906\pi\)
0.928337 + 0.371741i \(0.121239\pi\)
\(374\) −14006.5 + 8086.68i −0.100135 + 0.0578132i
\(375\) −97602.1 26152.4i −0.694059 0.185973i
\(376\) 62688.3i 0.443415i
\(377\) −38969.9 + 128981.i −0.274186 + 0.907491i
\(378\) 64611.2 0.452193
\(379\) 3636.15 13570.3i 0.0253141 0.0944737i −0.952113 0.305746i \(-0.901094\pi\)
0.977427 + 0.211273i \(0.0677608\pi\)
\(380\) 11358.7 + 19673.8i 0.0786612 + 0.136245i
\(381\) 21685.7 + 12520.2i 0.149390 + 0.0862506i
\(382\) −64376.8 64376.8i −0.441167 0.441167i
\(383\) −41441.5 + 11104.2i −0.282513 + 0.0756991i −0.397293 0.917692i \(-0.630050\pi\)
0.114780 + 0.993391i \(0.463384\pi\)
\(384\) −28370.1 105879.i −0.192397 0.718035i
\(385\) 31852.5 31852.5i 0.214893 0.214893i
\(386\) 7624.88 13206.7i 0.0511751 0.0886379i
\(387\) −30053.7 + 17351.5i −0.200667 + 0.115855i
\(388\) −104980. 28129.3i −0.697336 0.186851i
\(389\) 204736.i 1.35299i 0.736446 + 0.676497i \(0.236503\pi\)
−0.736446 + 0.676497i \(0.763497\pi\)
\(390\) 5679.66 + 24237.2i 0.0373416 + 0.159351i
\(391\) 174195. 1.13941
\(392\) 7517.76 28056.7i 0.0489234 0.182585i
\(393\) 17383.7 + 30109.4i 0.112553 + 0.194947i
\(394\) 73741.3 + 42574.5i 0.475027 + 0.274257i
\(395\) 83489.6 + 83489.6i 0.535104 + 0.535104i
\(396\) −27280.8 + 7309.87i −0.173967 + 0.0466143i
\(397\) −19570.6 73038.4i −0.124172 0.463415i 0.875637 0.482970i \(-0.160442\pi\)
−0.999809 + 0.0195546i \(0.993775\pi\)
\(398\) 37974.0 37974.0i 0.239729 0.239729i
\(399\) −20103.9 + 34821.0i −0.126280 + 0.218724i
\(400\) 53398.2 30829.5i 0.333739 0.192684i
\(401\) 210254. + 56337.5i 1.30754 + 0.350355i 0.844298 0.535874i \(-0.180018\pi\)
0.463246 + 0.886229i \(0.346684\pi\)
\(402\) 29850.2i 0.184712i
\(403\) −8324.36 + 263203.i −0.0512555 + 1.62062i
\(404\) 109462. 0.670657
\(405\) 8114.51 30283.8i 0.0494712 0.184629i
\(406\) 32967.5 + 57101.4i 0.200002 + 0.346413i
\(407\) 58794.7 + 33945.1i 0.354935 + 0.204922i
\(408\) 41086.3 + 41086.3i 0.246818 + 0.246818i
\(409\) −220545. + 59094.7i −1.31841 + 0.353266i −0.848381 0.529386i \(-0.822422\pi\)
−0.470026 + 0.882652i \(0.655756\pi\)
\(410\) −17953.3 67002.7i −0.106801 0.398588i
\(411\) −5468.86 + 5468.86i −0.0323752 + 0.0323752i
\(412\) 14896.2 25801.0i 0.0877570 0.152000i
\(413\) 40027.7 23110.0i 0.234672 0.135488i
\(414\) −47835.6 12817.5i −0.279094 0.0747831i
\(415\) 62892.4i 0.365176i
\(416\) −135342. 83953.2i −0.782070 0.485122i
\(417\) 80177.6 0.461085
\(418\) −2335.02 + 8714.42i −0.0133641 + 0.0498754i
\(419\) 55459.9 + 96059.4i 0.315901 + 0.547157i 0.979629 0.200818i \(-0.0643598\pi\)
−0.663727 + 0.747975i \(0.731026\pi\)
\(420\) −64801.5 37413.1i −0.367355 0.212093i
\(421\) 24030.5 + 24030.5i 0.135581 + 0.135581i 0.771640 0.636059i \(-0.219437\pi\)
−0.636059 + 0.771640i \(0.719437\pi\)
\(422\) −41476.3 + 11113.5i −0.232903 + 0.0624062i
\(423\) 13704.5 + 51145.9i 0.0765918 + 0.285845i
\(424\) −121744. + 121744.i −0.677201 + 0.677201i
\(425\) −39782.6 + 68905.5i −0.220250 + 0.381484i
\(426\) −36086.5 + 20834.5i −0.198850 + 0.114806i
\(427\) −147664. 39566.4i −0.809876 0.217006i
\(428\) 257445.i 1.40539i
\(429\) 32009.9 51603.5i 0.173928 0.280392i
\(430\) −20629.7 −0.111572
\(431\) 92790.6 346299.i 0.499516 1.86422i −0.00358674 0.999994i \(-0.501142\pi\)
0.503103 0.864226i \(-0.332192\pi\)
\(432\) 59959.1 + 103852.i 0.321283 + 0.556478i
\(433\) 117899. + 68068.7i 0.628829 + 0.363055i 0.780298 0.625407i \(-0.215067\pi\)
−0.151469 + 0.988462i \(0.548401\pi\)
\(434\) 91120.1 + 91120.1i 0.483765 + 0.483765i
\(435\) 75791.4 20308.2i 0.400536 0.107323i
\(436\) −14808.4 55265.6i −0.0778994 0.290725i
\(437\) 68709.2 68709.2i 0.359793 0.359793i
\(438\) 6405.65 11094.9i 0.0333899 0.0578330i
\(439\) −102882. + 59398.8i −0.533837 + 0.308211i −0.742578 0.669760i \(-0.766397\pi\)
0.208740 + 0.977971i \(0.433064\pi\)
\(440\) −35075.1 9398.34i −0.181173 0.0485451i
\(441\) 24534.3i 0.126152i
\(442\) 50074.8 + 1583.72i 0.256315 + 0.00810653i
\(443\) −112001. −0.570710 −0.285355 0.958422i \(-0.592112\pi\)
−0.285355 + 0.958422i \(0.592112\pi\)
\(444\) 29187.6 108930.i 0.148058 0.552562i
\(445\) −94339.0 163400.i −0.476399 0.825148i
\(446\) −93880.6 54202.0i −0.471961 0.272487i
\(447\) −97987.6 97987.6i −0.490407 0.490407i
\(448\) 55793.9 14949.9i 0.277991 0.0744874i
\(449\) 67319.2 + 251239.i 0.333923 + 1.24622i 0.905032 + 0.425343i \(0.139847\pi\)
−0.571109 + 0.820874i \(0.693487\pi\)
\(450\) 15994.9 15994.9i 0.0789870 0.0789870i
\(451\) −84605.1 + 146540.i −0.415952 + 0.720450i
\(452\) −86496.6 + 49938.8i −0.423372 + 0.244434i
\(453\) −204146. 54700.7i −0.994819 0.266561i
\(454\) 5750.75i 0.0279005i
\(455\) −135858. + 31836.5i −0.656241 + 0.153781i
\(456\) 32412.1 0.155875
\(457\) 42203.5 157506.i 0.202077 0.754161i −0.788244 0.615363i \(-0.789009\pi\)
0.990321 0.138798i \(-0.0443238\pi\)
\(458\) −4921.19 8523.74i −0.0234606 0.0406349i
\(459\) −134012. 77371.7i −0.636088 0.367246i
\(460\) 127867. + 127867.i 0.604286 + 0.604286i
\(461\) −118521. + 31757.7i −0.557693 + 0.149433i −0.526646 0.850085i \(-0.676551\pi\)
−0.0310467 + 0.999518i \(0.509884\pi\)
\(462\) −7691.08 28703.5i −0.0360332 0.134478i
\(463\) 93433.1 93433.1i 0.435852 0.435852i −0.454762 0.890613i \(-0.650276\pi\)
0.890613 + 0.454762i \(0.150276\pi\)
\(464\) −61187.6 + 105980.i −0.284202 + 0.492253i
\(465\) 132807. 76675.9i 0.614206 0.354612i
\(466\) 80996.8 + 21703.0i 0.372989 + 0.0999421i
\(467\) 40338.7i 0.184964i 0.995714 + 0.0924821i \(0.0294801\pi\)
−0.995714 + 0.0924821i \(0.970520\pi\)
\(468\) 83749.0 + 25303.7i 0.382374 + 0.115529i
\(469\) 167321. 0.760685
\(470\) −8146.82 + 30404.3i −0.0368801 + 0.137638i
\(471\) 116327. + 201483.i 0.524369 + 0.908234i
\(472\) −32266.9 18629.3i −0.144835 0.0836205i
\(473\) 35584.1 + 35584.1i 0.159050 + 0.159050i
\(474\) 75235.6 20159.3i 0.334863 0.0897262i
\(475\) 11487.2 + 42870.8i 0.0509128 + 0.190009i
\(476\) −106484. + 106484.i −0.469969 + 0.469969i
\(477\) 72713.5 125943.i 0.319579 0.553527i
\(478\) 43300.1 24999.3i 0.189511 0.109414i
\(479\) 100333. + 26884.1i 0.437292 + 0.117172i 0.470747 0.882268i \(-0.343984\pi\)
−0.0334553 + 0.999440i \(0.510651\pi\)
\(480\) 92747.9i 0.402552i
\(481\) −99341.1 185360.i −0.429377 0.801171i
\(482\) −12585.1 −0.0541703
\(483\) −82836.7 + 309151.i −0.355082 + 1.32518i
\(484\) −80251.2 138999.i −0.342579 0.593364i
\(485\) 102215. + 59013.9i 0.434541 + 0.250883i
\(486\) 52349.4 + 52349.4i 0.221635 + 0.221635i
\(487\) 335714. 89954.3i 1.41550 0.379283i 0.531618 0.846984i \(-0.321584\pi\)
0.883887 + 0.467701i \(0.154918\pi\)
\(488\) 31895.0 + 119034.i 0.133932 + 0.499840i
\(489\) 104503. 104503.i 0.437030 0.437030i
\(490\) −7292.35 + 12630.7i −0.0303721 + 0.0526061i
\(491\) −177842. + 102677.i −0.737685 + 0.425902i −0.821227 0.570602i \(-0.806710\pi\)
0.0835422 + 0.996504i \(0.473377\pi\)
\(492\) 271497. + 72747.5i 1.12159 + 0.300530i
\(493\) 157914.i 0.649721i
\(494\) 20376.1 19126.8i 0.0834964 0.0783768i
\(495\) 30671.5 0.125177
\(496\) −61901.7 + 231020.i −0.251617 + 0.939046i
\(497\) −116785. 202278.i −0.472796 0.818907i
\(498\) −35930.3 20744.4i −0.144878 0.0836454i
\(499\) −84685.9 84685.9i −0.340102 0.340102i 0.516303 0.856406i \(-0.327308\pi\)
−0.856406 + 0.516303i \(0.827308\pi\)
\(500\) −203911. + 54637.9i −0.815645 + 0.218552i
\(501\) 2567.92 + 9583.59i 0.0102307 + 0.0381815i
\(502\) 30866.1 30866.1i 0.122482 0.122482i
\(503\) −2971.77 + 5147.25i −0.0117457 + 0.0203441i −0.871839 0.489793i \(-0.837072\pi\)
0.860093 + 0.510138i \(0.170406\pi\)
\(504\) 80189.6 46297.5i 0.315687 0.182262i
\(505\) −114823. 30766.7i −0.450242 0.120642i
\(506\) 71814.2i 0.280485i
\(507\) −168523. + 83571.4i −0.655608 + 0.325119i
\(508\) 52314.8 0.202720
\(509\) −18497.0 + 69031.7i −0.0713946 + 0.266448i −0.992392 0.123121i \(-0.960710\pi\)
0.920997 + 0.389570i \(0.127376\pi\)
\(510\) −14587.7 25266.7i −0.0560851 0.0971422i
\(511\) 62190.9 + 35905.9i 0.238169 + 0.137507i
\(512\) −179633. 179633.i −0.685247 0.685247i
\(513\) −83377.8 + 22341.0i −0.316822 + 0.0848923i
\(514\) 2538.38 + 9473.38i 0.00960796 + 0.0358574i
\(515\) −22877.8 + 22877.8i −0.0862579 + 0.0862579i
\(516\) 41796.1 72393.0i 0.156977 0.271892i
\(517\) 66496.7 38391.9i 0.248782 0.143634i
\(518\) −99405.1 26635.5i −0.370467 0.0992662i
\(519\) 28837.9i 0.107060i
\(520\) 76984.1 + 82012.7i 0.284705 + 0.303302i
\(521\) −445916. −1.64277 −0.821386 0.570373i \(-0.806799\pi\)
−0.821386 + 0.570373i \(0.806799\pi\)
\(522\) −11619.5 + 43364.7i −0.0426430 + 0.159146i
\(523\) 14899.9 + 25807.4i 0.0544729 + 0.0943499i 0.891976 0.452083i \(-0.149319\pi\)
−0.837503 + 0.546433i \(0.815985\pi\)
\(524\) 62904.9 + 36318.1i 0.229098 + 0.132270i
\(525\) −103371. 103371.i −0.375043 0.375043i
\(526\) 29021.7 7776.35i 0.104894 0.0281063i
\(527\) −79878.4 298110.i −0.287613 1.07339i
\(528\) 38999.0 38999.0i 0.139890 0.139890i
\(529\) 246816. 427499.i 0.881988 1.52765i
\(530\) 74868.7 43225.4i 0.266531 0.153882i
\(531\) 30398.4 + 8145.23i 0.107811 + 0.0288878i
\(532\) 84002.7i 0.296804i
\(533\) 461992. 247599.i 1.62622 0.871553i
\(534\) −124467. −0.436487
\(535\) −72360.7 + 270054.i −0.252810 + 0.943501i
\(536\) −67439.8 116809.i −0.234740 0.406581i
\(537\) 71047.0 + 41019.0i 0.246375 + 0.142245i
\(538\) −135205. 135205.i −0.467119 0.467119i
\(539\) 34365.2 9208.14i 0.118288 0.0316952i
\(540\) −41576.3 155165.i −0.142580 0.532116i
\(541\) −382857. + 382857.i −1.30810 + 1.30810i −0.385322 + 0.922782i \(0.625910\pi\)
−0.922782 + 0.385322i \(0.874090\pi\)
\(542\) −74828.0 + 129606.i −0.254722 + 0.441191i
\(543\) 131676. 76023.3i 0.446589 0.257838i
\(544\) 180299. + 48310.8i 0.609248 + 0.163248i
\(545\) 62134.5i 0.209190i
\(546\) −26623.3 + 88116.6i −0.0893050 + 0.295578i
\(547\) −83576.4 −0.279325 −0.139662 0.990199i \(-0.544602\pi\)
−0.139662 + 0.990199i \(0.544602\pi\)
\(548\) −4182.06 + 15607.7i −0.0139261 + 0.0519728i
\(549\) −52044.8 90144.2i −0.172676 0.299084i
\(550\) −28407.2 16400.9i −0.0939082 0.0542179i
\(551\) −62287.4 62287.4i −0.205162 0.205162i
\(552\) 249210. 66775.7i 0.817877 0.219150i
\(553\) 113000. + 421722.i 0.369512 + 1.37904i
\(554\) −71252.9 + 71252.9i −0.232158 + 0.232158i
\(555\) −61234.3 + 106061.i −0.198797 + 0.344326i
\(556\) 145066. 83754.0i 0.469263 0.270929i
\(557\) 461816. + 123743.i 1.48853 + 0.398851i 0.909241 0.416270i \(-0.136663\pi\)
0.579291 + 0.815121i \(0.303329\pi\)
\(558\) 87741.6i 0.281798i
\(559\) −35566.2 151774.i −0.113819 0.485707i
\(560\) −126734. −0.404127
\(561\) −18420.1 + 68744.7i −0.0585283 + 0.218431i
\(562\) −10331.4 17894.5i −0.0327105 0.0566562i
\(563\) 102499. + 59178.1i 0.323374 + 0.186700i 0.652895 0.757448i \(-0.273554\pi\)
−0.329522 + 0.944148i \(0.606887\pi\)
\(564\) −90188.3 90188.3i −0.283525 0.283525i
\(565\) 104769. 28072.9i 0.328199 0.0879406i
\(566\) 33961.4 + 126746.i 0.106011 + 0.395640i
\(567\) 81975.9 81975.9i 0.254988 0.254988i
\(568\) −94141.9 + 163059.i −0.291801 + 0.505414i
\(569\) 28871.9 16669.2i 0.0891766 0.0514861i −0.454749 0.890620i \(-0.650271\pi\)
0.543925 + 0.839134i \(0.316938\pi\)
\(570\) −15720.1 4212.20i −0.0483845 0.0129646i
\(571\) 534672.i 1.63989i 0.572440 + 0.819947i \(0.305997\pi\)
−0.572440 + 0.819947i \(0.694003\pi\)
\(572\) 4010.47 126805.i 0.0122575 0.387563i
\(573\) −400627. −1.22020
\(574\) 66386.5 247758.i 0.201491 0.751976i
\(575\) 176646. + 305960.i 0.534279 + 0.925398i
\(576\) 34060.4 + 19664.8i 0.102661 + 0.0592713i
\(577\) 201296. + 201296.i 0.604622 + 0.604622i 0.941535 0.336914i \(-0.109383\pi\)
−0.336914 + 0.941535i \(0.609383\pi\)
\(578\) 64030.9 17157.0i 0.191661 0.0513555i
\(579\) −17368.2 64819.0i −0.0518081 0.193350i
\(580\) 115916. 115916.i 0.344578 0.344578i
\(581\) 116280. 201402.i 0.344470 0.596639i
\(582\) 67429.0 38930.2i 0.199068 0.114932i
\(583\) −203700. 54581.3i −0.599313 0.160586i
\(584\) 57888.5i 0.169733i
\(585\) −80738.6 50082.5i −0.235923 0.146344i
\(586\) −98393.6 −0.286531
\(587\) −100815. + 376246.i −0.292582 + 1.09193i 0.650536 + 0.759475i \(0.274544\pi\)
−0.943119 + 0.332457i \(0.892122\pi\)
\(588\) −29548.9 51180.2i −0.0854646 0.148029i
\(589\) −149094. 86079.2i −0.429762 0.248123i
\(590\) 13228.7 + 13228.7i 0.0380026 + 0.0380026i
\(591\) 361925. 96977.6i 1.03620 0.277649i
\(592\) −49435.4 184495.i −0.141057 0.526432i
\(593\) 29431.4 29431.4i 0.0836955 0.0836955i −0.664020 0.747715i \(-0.731151\pi\)
0.747715 + 0.664020i \(0.231151\pi\)
\(594\) 31897.5 55248.1i 0.0904032 0.156583i
\(595\) 141629. 81769.3i 0.400053 0.230971i
\(596\) −279648. 74931.6i −0.787263 0.210947i
\(597\) 236318.i 0.663052i
\(598\) 117263. 189041.i 0.327913 0.528632i
\(599\) 109234. 0.304442 0.152221 0.988346i \(-0.451357\pi\)
0.152221 + 0.988346i \(0.451357\pi\)
\(600\) −30500.5 + 113829.i −0.0847236 + 0.316193i
\(601\) −311032. 538723.i −0.861104 1.49148i −0.870864 0.491524i \(-0.836440\pi\)
0.00975940 0.999952i \(-0.496893\pi\)
\(602\) −66063.0 38141.5i −0.182291 0.105246i
\(603\) 80558.6 + 80558.6i 0.221553 + 0.221553i
\(604\) −426504. + 114281.i −1.16909 + 0.313257i
\(605\) 45112.8 + 168363.i 0.123251 + 0.459977i
\(606\) −55450.1 + 55450.1i −0.150993 + 0.150993i
\(607\) −125630. + 217598.i −0.340971 + 0.590579i −0.984613 0.174747i \(-0.944089\pi\)
0.643642 + 0.765327i \(0.277423\pi\)
\(608\) 90172.4 52061.1i 0.243931 0.140834i
\(609\) 280256. + 75094.4i 0.755650 + 0.202476i
\(610\) 61877.4i 0.166292i
\(611\) −237732. 7518.80i −0.636804 0.0201403i
\(612\) −102536. −0.273761
\(613\) −74439.2 + 277811.i −0.198098 + 0.739313i 0.793345 + 0.608773i \(0.208338\pi\)
−0.991443 + 0.130540i \(0.958329\pi\)
\(614\) 25868.0 + 44804.8i 0.0686162 + 0.118847i
\(615\) −264347. 152621.i −0.698915 0.403519i
\(616\) −94945.7 94945.7i −0.250215 0.250215i
\(617\) −24959.6 + 6687.91i −0.0655643 + 0.0175679i −0.291452 0.956585i \(-0.594138\pi\)
0.225888 + 0.974153i \(0.427472\pi\)
\(618\) 5524.04 + 20616.0i 0.0144637 + 0.0539793i
\(619\) 236220. 236220.i 0.616502 0.616502i −0.328130 0.944632i \(-0.606419\pi\)
0.944632 + 0.328130i \(0.106419\pi\)
\(620\) 160192. 277461.i 0.416733 0.721803i
\(621\) −595049. + 343552.i −1.54301 + 0.890859i
\(622\) 118619. + 31783.9i 0.306602 + 0.0821537i
\(623\) 697680.i 1.79755i
\(624\) −166340. + 38979.4i −0.427195 + 0.100107i
\(625\) −21812.3 −0.0558394
\(626\) 28523.9 106453.i 0.0727882 0.271649i
\(627\) 19850.0 + 34381.2i 0.0504923 + 0.0874552i
\(628\) 420941. + 243031.i 1.06734 + 0.616229i
\(629\) 174283. + 174283.i 0.440507 + 0.440507i
\(630\) −44909.3 + 12033.4i −0.113150 + 0.0303185i
\(631\) −34896.2 130234.i −0.0876434 0.327090i 0.908158 0.418627i \(-0.137489\pi\)
−0.995802 + 0.0915374i \(0.970822\pi\)
\(632\) 248865. 248865.i 0.623060 0.623060i
\(633\) −94476.0 + 163637.i −0.235784 + 0.408390i
\(634\) −162366. + 93741.8i −0.403939 + 0.233214i
\(635\) −54877.0 14704.2i −0.136095 0.0364666i
\(636\) 350302.i 0.866021i
\(637\) −105497. 31874.7i −0.259994 0.0785537i
\(638\) 65102.2 0.159939
\(639\) 41161.4 153616.i 0.100806 0.376215i
\(640\) 124348. + 215377.i 0.303584 + 0.525823i
\(641\) 273381. + 157836.i 0.665352 + 0.384141i 0.794313 0.607508i \(-0.207831\pi\)
−0.128961 + 0.991650i \(0.541164\pi\)
\(642\) 130414. + 130414.i 0.316413 + 0.316413i
\(643\) −234488. + 62830.7i −0.567150 + 0.151967i −0.530989 0.847379i \(-0.678180\pi\)
−0.0361607 + 0.999346i \(0.511513\pi\)
\(644\) 173063. + 645881.i 0.417285 + 1.55733i
\(645\) −64190.8 + 64190.8i −0.154296 + 0.154296i
\(646\) −16376.7 + 28365.3i −0.0392429 + 0.0679708i
\(647\) 170861. 98646.7i 0.408164 0.235653i −0.281837 0.959462i \(-0.590944\pi\)
0.690000 + 0.723809i \(0.257610\pi\)
\(648\) −90269.5 24187.6i −0.214977 0.0576028i
\(649\) 45636.2i 0.108348i
\(650\) 47997.7 + 89558.4i 0.113604 + 0.211973i
\(651\) 567054. 1.33802
\(652\) 79913.9 298243.i 0.187987 0.701576i
\(653\) −69052.8 119603.i −0.161940 0.280489i 0.773624 0.633645i \(-0.218442\pi\)
−0.935565 + 0.353156i \(0.885109\pi\)
\(654\) 35497.4 + 20494.4i 0.0829928 + 0.0479159i
\(655\) −55777.7 55777.7i −0.130010 0.130010i
\(656\) 459838. 123213.i 1.06856 0.286319i
\(657\) 12655.2 + 47229.8i 0.0293182 + 0.109417i
\(658\) −82302.3 + 82302.3i −0.190090 + 0.190090i
\(659\) −75236.5 + 130313.i −0.173244 + 0.300067i −0.939552 0.342406i \(-0.888758\pi\)
0.766308 + 0.642473i \(0.222092\pi\)
\(660\) −63982.9 + 36940.6i −0.146885 + 0.0848038i
\(661\) 401796. + 107661.i 0.919608 + 0.246408i 0.687418 0.726262i \(-0.258744\pi\)
0.232190 + 0.972670i \(0.425411\pi\)
\(662\) 214733.i 0.489985i
\(663\) 160739. 150884.i 0.365675 0.343253i
\(664\) −187469. −0.425200
\(665\) 23610.8 88116.9i 0.0533910 0.199258i
\(666\) −35035.8 60683.7i −0.0789883 0.136812i
\(667\) −607241. 350591.i −1.36493 0.788041i
\(668\) 14657.2 + 14657.2i 0.0328472 + 0.0328472i
\(669\) −460770. + 123463.i −1.02951 + 0.275857i
\(670\) 17528.6 + 65417.7i 0.0390480 + 0.145729i
\(671\) −106732. + 106732.i −0.237055 + 0.237055i
\(672\) −171478. + 297009.i −0.379726 + 0.657706i
\(673\) 16660.0 9618.68i 0.0367829 0.0212366i −0.481496 0.876448i \(-0.659906\pi\)
0.518279 + 0.855212i \(0.326573\pi\)
\(674\) −238763. 63976.4i −0.525590 0.140831i
\(675\) 313841.i 0.688815i
\(676\) −217612. + 327247.i −0.476200 + 0.716114i
\(677\) 600314. 1.30979 0.654895 0.755720i \(-0.272713\pi\)
0.654895 + 0.755720i \(0.272713\pi\)
\(678\) 18519.1 69114.1i 0.0402865 0.150351i
\(679\) 218217. + 377964.i 0.473315 + 0.819805i
\(680\) −114169. 65915.4i −0.246905 0.142551i
\(681\) −17893.9 17893.9i −0.0385843 0.0385843i
\(682\) 122900. 32931.0i 0.264231 0.0708004i
\(683\) −179215. 668838.i −0.384178 1.43377i −0.839459 0.543423i \(-0.817128\pi\)
0.455282 0.890348i \(-0.349539\pi\)
\(684\) −40444.1 + 40444.1i −0.0864456 + 0.0864456i
\(685\) 8773.76 15196.6i 0.0186984 0.0323866i
\(686\) 125256. 72316.8i 0.266166 0.153671i
\(687\) −41834.9 11209.6i −0.0886391 0.0237508i
\(688\) 141581.i 0.299108i
\(689\) 447089. + 476293.i 0.941793 + 1.00331i
\(690\) −129547. −0.272101
\(691\) 219977. 820967.i 0.460704 1.71937i −0.210049 0.977691i \(-0.567362\pi\)
0.670753 0.741681i \(-0.265971\pi\)
\(692\) 30124.2 + 52176.7i 0.0629077 + 0.108959i
\(693\) 98220.3 + 56707.5i 0.204520 + 0.118079i
\(694\) −58837.9 58837.9i −0.122163 0.122163i
\(695\) −175712. + 47081.9i −0.363774 + 0.0974730i
\(696\) −60534.6 225918.i −0.124964 0.466372i
\(697\) −434383. + 434383.i −0.894144 + 0.894144i
\(698\) 130318. 225717.i 0.267481 0.463291i
\(699\) 319558. 184497.i 0.654027 0.377603i
\(700\) −295013. 79048.4i −0.602066 0.161323i
\(701\) 318525.i 0.648198i 0.946023 + 0.324099i \(0.105061\pi\)
−0.946023 + 0.324099i \(0.894939\pi\)
\(702\) −174179. + 93348.8i −0.353444 + 0.189424i
\(703\) 137488. 0.278198
\(704\) 14761.1 55089.1i 0.0297833 0.111153i
\(705\) 69255.9 + 119955.i 0.139341 + 0.241346i
\(706\) 217307. + 125462.i 0.435977 + 0.251712i
\(707\) −310818. 310818.i −0.621823 0.621823i
\(708\) −73223.2 + 19620.1i −0.146077 + 0.0391413i
\(709\) −81416.6 303851.i −0.161965 0.604461i −0.998408 0.0564071i \(-0.982036\pi\)
0.836443 0.548054i \(-0.184631\pi\)
\(710\) 66850.3 66850.3i 0.132613 0.132613i
\(711\) −148638. + 257448.i −0.294029 + 0.509273i
\(712\) −487061. + 281205.i −0.960778 + 0.554706i
\(713\) −1.32369e6 354683.i −2.60380 0.697687i
\(714\) 107883.i 0.211620i
\(715\) −39848.1 + 131888.i −0.0779464 + 0.257984i
\(716\) 171395. 0.334327
\(717\) 56944.3 212519.i 0.110767 0.413389i
\(718\) 118928. + 205989.i 0.230693 + 0.399572i
\(719\) −341956. 197428.i −0.661473 0.381902i 0.131365 0.991334i \(-0.458064\pi\)
−0.792838 + 0.609433i \(0.791397\pi\)
\(720\) −61017.6 61017.6i −0.117704 0.117704i
\(721\) −115560. + 30964.2i −0.222299 + 0.0595648i
\(722\) −45754.5 170758.i −0.0877727 0.327572i
\(723\) −39159.4 + 39159.4i −0.0749134 + 0.0749134i
\(724\) 158829. 275099.i 0.303007 0.524823i
\(725\) 277363. 160136.i 0.527683 0.304658i
\(726\) 111066. + 29759.9i 0.210720 + 0.0564623i
\(727\) 77095.4i 0.145868i −0.997337 0.0729339i \(-0.976764\pi\)
0.997337 0.0729339i \(-0.0232362\pi\)
\(728\) 94898.0 + 404965.i 0.179058 + 0.764108i
\(729\) 495726. 0.932795
\(730\) −7523.04 + 28076.4i −0.0141172 + 0.0526860i
\(731\) 91348.7 + 158221.i 0.170949 + 0.296093i
\(732\) 217138. + 125365.i 0.405241 + 0.233966i
\(733\) 549893. + 549893.i 1.02346 + 1.02346i 0.999718 + 0.0237405i \(0.00755755\pi\)
0.0237405 + 0.999718i \(0.492442\pi\)
\(734\) −104791. + 28078.6i −0.194505 + 0.0521175i
\(735\) 16610.7 + 61992.1i 0.0307478 + 0.114752i
\(736\) 586062. 586062.i 1.08190 1.08190i
\(737\) 82603.7 143074.i 0.152077 0.263406i
\(738\) 151248. 87323.4i 0.277702 0.160331i
\(739\) 638068. + 170970.i 1.16836 + 0.313062i 0.790301 0.612718i \(-0.209924\pi\)
0.378062 + 0.925780i \(0.376591\pi\)
\(740\) 255863.i 0.467244i
\(741\) 3887.49 122916.i 0.00708000 0.223858i
\(742\) 319672. 0.580627
\(743\) −182602. + 681479.i −0.330771 + 1.23445i 0.577611 + 0.816312i \(0.303985\pi\)
−0.908382 + 0.418142i \(0.862681\pi\)
\(744\) −228555. 395869.i −0.412900 0.715163i
\(745\) 272283. + 157203.i 0.490579 + 0.283236i
\(746\) 41885.5 + 41885.5i 0.0752639 + 0.0752639i
\(747\) 152952. 40983.2i 0.274102 0.0734455i
\(748\) 38483.4 + 143622.i 0.0687814 + 0.256696i
\(749\) −731016. + 731016.i −1.30306 + 1.30306i
\(750\) 75617.5 130973.i 0.134431 0.232841i
\(751\) −343285. + 198196.i −0.608660 + 0.351410i −0.772441 0.635087i \(-0.780964\pi\)
0.163781 + 0.986497i \(0.447631\pi\)
\(752\) −208664. 55911.4i −0.368988 0.0988701i
\(753\) 192084.i 0.338767i
\(754\) −171373. 106303.i −0.301438 0.186983i
\(755\) 479514. 0.841215
\(756\) 153738. 573758.i 0.268991 1.00389i
\(757\) 310425. + 537672.i 0.541708 + 0.938266i 0.998806 + 0.0488493i \(0.0155554\pi\)
−0.457098 + 0.889416i \(0.651111\pi\)
\(758\) 18210.1 + 10513.6i 0.0316938 + 0.0182984i
\(759\) 223455. + 223455.i 0.387889 + 0.387889i
\(760\) −71032.2 + 19033.0i −0.122978 + 0.0329519i
\(761\) −87290.5 325773.i −0.150729 0.562529i −0.999433 0.0336612i \(-0.989283\pi\)
0.848704 0.528868i \(-0.177383\pi\)
\(762\) −26501.1 + 26501.1i −0.0456408 + 0.0456408i
\(763\) −114878. + 198975.i −0.197328 + 0.341783i
\(764\) −724858. + 418497.i −1.24184 + 0.716978i
\(765\) 107558. + 28820.0i 0.183788 + 0.0492459i
\(766\) 64213.8i 0.109439i
\(767\) −74517.8 + 120131.i −0.126669 + 0.204204i
\(768\) 53899.6 0.0913825
\(769\) 70356.3 262573.i 0.118973 0.444015i −0.880580 0.473898i \(-0.842847\pi\)
0.999553 + 0.0298827i \(0.00951336\pi\)
\(770\) 33710.5 + 58388.3i 0.0568570 + 0.0984792i
\(771\) 37375.5 + 21578.8i 0.0628750 + 0.0363009i
\(772\) −99134.7 99134.7i −0.166338 0.166338i
\(773\) −711148. + 190552.i −1.19015 + 0.318899i −0.798944 0.601405i \(-0.794608\pi\)
−0.391204 + 0.920304i \(0.627941\pi\)
\(774\) −13443.1 50170.5i −0.0224398 0.0837464i
\(775\) 442605. 442605.i 0.736908 0.736908i
\(776\) 175908. 304681.i 0.292120 0.505967i
\(777\) −392185. + 226428.i −0.649604 + 0.375049i
\(778\) −295989. 79310.0i −0.489008 0.131029i
\(779\) 342675.i 0.564687i
\(780\) 228745. + 7234.57i 0.375978 + 0.0118911i
\(781\) −230620. −0.378089
\(782\) −67478.9 + 251835.i −0.110346 + 0.411815i
\(783\) 311442. + 539433.i 0.507988 + 0.879861i
\(784\) −86684.4 50047.2i −0.141029 0.0814232i
\(785\) −373248. 373248.i −0.605702 0.605702i
\(786\) −50263.4 + 13468.0i −0.0813592 + 0.0218001i
\(787\) −75848.9 283072.i −0.122462 0.457033i 0.877275 0.479988i \(-0.159359\pi\)
−0.999736 + 0.0229554i \(0.992692\pi\)
\(788\) 553532. 553532.i 0.891436 0.891436i
\(789\) 66106.6 114500.i 0.106192 0.183929i
\(790\) −153043. + 88359.6i −0.245223 + 0.141579i
\(791\) 387409. + 103806.i 0.619179 + 0.165909i
\(792\) 91425.4i 0.145753i
\(793\) 455237. 106678.i 0.723921 0.169641i
\(794\) 113173. 0.179516
\(795\) 98460.3 367459.i 0.155785 0.581399i
\(796\) −246859. 427572.i −0.389603 0.674813i
\(797\) −882413. 509462.i −1.38917 0.802038i −0.395948 0.918273i \(-0.629584\pi\)
−0.993222 + 0.116235i \(0.962917\pi\)
\(798\) −42553.2 42553.2i −0.0668231 0.0668231i
\(799\) 269262. 72148.6i 0.421776 0.113014i
\(800\) 97981.2 + 365671.i 0.153096 + 0.571361i
\(801\) 335906. 335906.i 0.523544 0.523544i
\(802\) −162895. + 282143.i −0.253256 + 0.438652i
\(803\) 61405.3 35452.4i 0.0952302 0.0549812i
\(804\) −265075. 71026.6i −0.410069 0.109878i
\(805\) 726157.i 1.12057i
\(806\) −377289. 113993.i −0.580771 0.175472i
\(807\) −841400. −1.29198
\(808\) −91709.2 + 342263.i −0.140472 + 0.524249i
\(809\) −201736. 349418.i −0.308239 0.533885i 0.669738 0.742597i \(-0.266406\pi\)
−0.977977 + 0.208712i \(0.933073\pi\)
\(810\) 40638.1 + 23462.4i 0.0619389 + 0.0357604i
\(811\) 514105. + 514105.i 0.781646 + 0.781646i 0.980108 0.198463i \(-0.0635949\pi\)
−0.198463 + 0.980108i \(0.563595\pi\)
\(812\) 585514. 156888.i 0.888026 0.237946i
\(813\) 170446. + 636112.i 0.257872 + 0.962393i
\(814\) −71850.4 + 71850.4i −0.108438 + 0.108438i
\(815\) −167656. + 290388.i −0.252408 + 0.437183i
\(816\) 173405. 100115.i 0.260424 0.150356i
\(817\) 98439.8 + 26376.9i 0.147478 + 0.0395166i
\(818\) 341735.i 0.510720i
\(819\) −165956. 309655.i −0.247414 0.461648i
\(820\) −637714. −0.948415
\(821\) 141194. 526943.i 0.209474 0.781767i −0.778565 0.627563i \(-0.784052\pi\)
0.988039 0.154203i \(-0.0492810\pi\)
\(822\) −5787.86 10024.9i −0.00856593 0.0148366i
\(823\) −364137. 210235.i −0.537608 0.310388i 0.206501 0.978446i \(-0.433792\pi\)
−0.744109 + 0.668058i \(0.767126\pi\)
\(824\) 68193.8 + 68193.8i 0.100436 + 0.100436i
\(825\) −139424. + 37358.5i −0.204847 + 0.0548886i
\(826\) 17904.5 + 66820.7i 0.0262424 + 0.0979379i
\(827\) −558727. + 558727.i −0.816937 + 0.816937i −0.985663 0.168726i \(-0.946035\pi\)
0.168726 + 0.985663i \(0.446035\pi\)
\(828\) −227644. + 394290.i −0.332043 + 0.575116i
\(829\) 550395. 317771.i 0.800877 0.462386i −0.0429010 0.999079i \(-0.513660\pi\)
0.843778 + 0.536693i \(0.180327\pi\)
\(830\) 90924.0 + 24363.0i 0.131984 + 0.0353651i
\(831\) 443417.i 0.642112i
\(832\) −128810. + 120912.i −0.186081 + 0.174671i
\(833\) 129163. 0.186143
\(834\) −31058.9 + 115913.i −0.0446534 + 0.166649i
\(835\) −11255.3 19494.8i −0.0161431 0.0279606i
\(836\) 71829.6 + 41470.8i 0.102776 + 0.0593376i
\(837\) 860805. + 860805.i 1.22872 + 1.22872i
\(838\) −160358. + 42967.7i −0.228350 + 0.0611863i
\(839\) −85900.8 320586.i −0.122032 0.455429i 0.877685 0.479239i \(-0.159087\pi\)
−0.999717 + 0.0238094i \(0.992421\pi\)
\(840\) 171274. 171274.i 0.242736 0.242736i
\(841\) 35817.3 62037.3i 0.0506408 0.0877124i
\(842\) −44049.9 + 25432.2i −0.0621327 + 0.0358723i
\(843\) −87827.2 23533.2i −0.123587 0.0331151i
\(844\) 394761.i 0.554177i
\(845\) 320250. 282110.i 0.448513 0.395098i
\(846\) −79250.8 −0.110729
\(847\) −166815. + 622562.i −0.232524 + 0.867792i
\(848\) 296655. + 513822.i 0.412535 + 0.714531i
\(849\) 500052. + 288705.i 0.693745 + 0.400534i
\(850\) −84206.4 84206.4i −0.116549 0.116549i
\(851\) 1.05712e6 283254.i 1.45970 0.391126i
\(852\) 99148.9 + 370029.i 0.136587 + 0.509749i
\(853\) 359793. 359793.i 0.494487 0.494487i −0.415229 0.909717i \(-0.636299\pi\)
0.909717 + 0.415229i \(0.136299\pi\)
\(854\) 114403. 198152.i 0.156863 0.271695i
\(855\) 53792.6 31057.2i 0.0735852 0.0424844i
\(856\) 804973. + 215692.i 1.09859 + 0.294365i
\(857\) 870729.i 1.18555i 0.805367 + 0.592777i \(0.201968\pi\)
−0.805367 + 0.592777i \(0.798032\pi\)
\(858\) 62203.8 + 66266.9i 0.0844972 + 0.0900165i
\(859\) −955429. −1.29483 −0.647414 0.762139i \(-0.724149\pi\)
−0.647414 + 0.762139i \(0.724149\pi\)
\(860\) −49087.0 + 183195.i −0.0663696 + 0.247695i
\(861\) −564351. 977484.i −0.761277 1.31857i
\(862\) 464703. + 268296.i 0.625404 + 0.361077i
\(863\) −997697. 997697.i −1.33961 1.33961i −0.896439 0.443166i \(-0.853855\pi\)
−0.443166 0.896439i \(-0.646145\pi\)
\(864\) −711179. + 190560.i −0.952689 + 0.255272i
\(865\) −16934.2 63199.2i −0.0226325 0.0844655i
\(866\) −144079. + 144079.i −0.192116 + 0.192116i
\(867\) 145852. 252622.i 0.194032 0.336073i
\(868\) 1.02598e6 592348.i 1.36175 0.786208i
\(869\) 416395. + 111573.i 0.551399 + 0.147747i
\(870\) 117439.i 0.155158i
\(871\) −451063. + 241742.i −0.594568 + 0.318651i
\(872\) 185210. 0.243574
\(873\) −76911.7 + 287038.i −0.100917 + 0.376627i
\(874\) 72717.2 + 125950.i 0.0951950 + 0.164883i
\(875\) 734151. + 423862.i 0.958892 + 0.553616i
\(876\) −83282.9 83282.9i −0.108529 0.108529i
\(877\) −294738. + 78974.8i −0.383210 + 0.102681i −0.445281 0.895391i \(-0.646896\pi\)
0.0620710 + 0.998072i \(0.480229\pi\)
\(878\) −46019.3 171746.i −0.0596968 0.222792i
\(879\) −306159. + 306159.i −0.396250 + 0.396250i
\(880\) −62566.6 + 108369.i −0.0807937 + 0.139939i
\(881\) −68696.3 + 39661.8i −0.0885078 + 0.0511000i −0.543601 0.839344i \(-0.682939\pi\)
0.455093 + 0.890444i \(0.349606\pi\)
\(882\) −35469.4 9503.99i −0.0455949 0.0122171i
\(883\) 1.21909e6i 1.56356i −0.623554 0.781781i \(-0.714312\pi\)
0.623554 0.781781i \(-0.285688\pi\)
\(884\) 133213. 440904.i 0.170468 0.564209i
\(885\) 82324.1 0.105109
\(886\) 43386.6 161921.i 0.0552699 0.206270i
\(887\) −226185. 391763.i −0.287485 0.497939i 0.685724 0.727862i \(-0.259486\pi\)
−0.973209 + 0.229923i \(0.926153\pi\)
\(888\) 316145. + 182527.i 0.400923 + 0.231473i
\(889\) −148548. 148548.i −0.187959 0.187959i
\(890\) 272773. 73089.3i 0.344367 0.0922729i
\(891\) −29626.3 110567.i −0.0373183 0.139274i
\(892\) −704706. + 704706.i −0.885682 + 0.885682i
\(893\) 77749.2 134666.i 0.0974974 0.168871i
\(894\) 179620. 103703.i 0.224739 0.129753i
\(895\) −179789. 48174.3i −0.224449 0.0601408i
\(896\) 919611.i 1.14548i
\(897\) −223343. 953088.i −0.277580 1.18454i
\(898\) −389296. −0.482755
\(899\) −321532. + 1.19998e6i −0.397837 + 1.48475i
\(900\) −103978. 180096.i −0.128368 0.222341i
\(901\) −663040. 382806.i −0.816752 0.471552i
\(902\) −179080. 179080.i −0.220108 0.220108i
\(903\) −324240. + 86879.9i −0.397641 + 0.106548i
\(904\) −83679.3 312295.i −0.102396 0.382145i
\(905\) −243930. + 243930.i −0.297830 + 0.297830i
\(906\) 158162. 273945.i 0.192685 0.333740i
\(907\) 322283. 186070.i 0.391763 0.226184i −0.291161 0.956674i \(-0.594041\pi\)
0.682924 + 0.730490i \(0.260708\pi\)
\(908\) −51067.6 13683.5i −0.0619404 0.0165969i
\(909\) 299293.i 0.362217i
\(910\) 6601.99 208744.i 0.00797245 0.252076i
\(911\) −106064. −0.127800 −0.0639001 0.997956i \(-0.520354\pi\)
−0.0639001 + 0.997956i \(0.520354\pi\)
\(912\) 28908.2 107887.i 0.0347561 0.129712i
\(913\) −114811. 198858.i −0.137734 0.238562i
\(914\) 211359. + 122028.i 0.253004 + 0.146072i
\(915\) −192536. 192536.i −0.229969 0.229969i
\(916\) −87402.0 + 23419.3i −0.104167 + 0.0279115i
\(917\) −75493.1 281744.i −0.0897777 0.335055i
\(918\) 163770. 163770.i 0.194334 0.194334i
\(919\) −232722. + 403086.i −0.275554 + 0.477273i −0.970275 0.242006i \(-0.922194\pi\)
0.694721 + 0.719279i \(0.255528\pi\)
\(920\) −506941. + 292683.i −0.598938 + 0.345797i
\(921\) 219904. + 58923.0i 0.259247 + 0.0694650i
\(922\) 183650.i 0.216037i
\(923\) 607075. + 376571.i 0.712588 + 0.442021i
\(924\) −273192. −0.319981
\(925\) −129379. + 482849.i −0.151210 + 0.564323i
\(926\) 98883.2 + 171271.i 0.115319 + 0.199738i
\(927\) −70545.8 40729.6i −0.0820940 0.0473970i
\(928\) −531286. 531286.i −0.616925 0.616925i
\(929\) 1.58177e6 423834.i 1.83279 0.491094i 0.834576 0.550892i \(-0.185712\pi\)
0.998210 + 0.0597983i \(0.0190457\pi\)
\(930\) 59404.9 + 221702.i 0.0686841 + 0.256332i
\(931\) 50946.8 50946.8i 0.0587784 0.0587784i
\(932\) 385453. 667625.i 0.443752 0.768600i
\(933\) 467991. 270195.i 0.537619 0.310394i
\(934\) −58317.9 15626.2i −0.0668510 0.0179127i
\(935\) 161473.i 0.184704i
\(936\) −149285. + 240665.i −0.170398 + 0.274701i
\(937\) 291324. 0.331816 0.165908 0.986141i \(-0.446945\pi\)
0.165908 + 0.986141i \(0.446945\pi\)
\(938\) −64816.2 + 241897.i −0.0736678 + 0.274932i
\(939\) −242481. 419990.i −0.275009 0.476330i
\(940\) 250611. + 144690.i 0.283625 + 0.163751i
\(941\) −1.05131e6 1.05131e6i −1.18727 1.18727i −0.977819 0.209453i \(-0.932832\pi\)
−0.209453 0.977819i \(-0.567168\pi\)
\(942\) −336348. + 90124.3i −0.379042 + 0.101564i
\(943\) 705983. + 2.63477e6i 0.793910 + 2.96291i
\(944\) −90788.2 + 90788.2i −0.101879 + 0.101879i
\(945\) −322535. + 558647.i −0.361172 + 0.625568i
\(946\) −65228.6 + 37659.7i −0.0728879 + 0.0420819i
\(947\) 1.12897e6 + 302507.i 1.25888 + 0.337315i 0.825759 0.564023i \(-0.190747\pi\)
0.433116 + 0.901338i \(0.357414\pi\)
\(948\) 716073.i 0.796784i
\(949\) −219530. 6943.11i −0.243759 0.00770942i
\(950\) −66428.6 −0.0736051
\(951\) −213528. + 796897.i −0.236099 + 0.881132i
\(952\) −243737. 422165.i −0.268935 0.465810i
\(953\) 171284. + 98891.0i 0.188596 + 0.108886i 0.591325 0.806433i \(-0.298605\pi\)
−0.402729 + 0.915319i \(0.631938\pi\)
\(954\) 153910. + 153910.i 0.169110 + 0.169110i
\(955\) 877987. 235256.i 0.962679 0.257949i
\(956\) −118969. 443997.i −0.130172 0.485808i
\(957\) 202570. 202570.i 0.221183 0.221183i
\(958\) −77733.0 + 134637.i −0.0846982 + 0.146702i
\(959\) 56192.9 32443.0i 0.0611005 0.0352764i
\(960\) 99376.4 + 26627.8i 0.107830 + 0.0288930i
\(961\) 1.50444e6i 1.62903i
\(962\) 306458. 71814.3i 0.331147 0.0775998i
\(963\) −703912. −0.759042
\(964\) −29945.4 + 111758.i −0.0322237 + 0.120261i
\(965\) 76126.0 + 131854.i 0.0817482 + 0.141592i
\(966\) −414853. 239515.i −0.444569 0.256672i
\(967\) 549664. + 549664.i 0.587820 + 0.587820i 0.937041 0.349220i \(-0.113554\pi\)
−0.349220 + 0.937041i \(0.613554\pi\)
\(968\) 501855. 134472.i 0.535584 0.143509i
\(969\) 37303.4 + 139218.i 0.0397284 + 0.148268i
\(970\) −124912. + 124912.i −0.132758 + 0.132758i
\(971\) 664057. 1.15018e6i 0.704315 1.21991i −0.262623 0.964898i \(-0.584588\pi\)
0.966938 0.255011i \(-0.0820790\pi\)
\(972\) 589433. 340310.i 0.623882 0.360198i
\(973\) −649736. 174096.i −0.686295 0.183892i
\(974\) 520190.i 0.548333i
\(975\) 428016. + 129319.i 0.450247 + 0.136036i
\(976\) 424663. 0.445805
\(977\) 157223. 586765.i 0.164713 0.614717i −0.833364 0.552725i \(-0.813588\pi\)
0.998077 0.0619919i \(-0.0197453\pi\)
\(978\) 110599. + 191563.i 0.115631 + 0.200278i
\(979\) −596577. 344434.i −0.622445 0.359369i
\(980\) 94811.3 + 94811.3i 0.0987207 + 0.0987207i
\(981\) −151108. + 40489.4i −0.157018 + 0.0420730i
\(982\) −79549.2 296882.i −0.0824922 0.307865i
\(983\) −156513. + 156513.i −0.161974 + 0.161974i −0.783441 0.621467i \(-0.786537\pi\)
0.621467 + 0.783441i \(0.286537\pi\)
\(984\) −454931. + 787963.i −0.469845 + 0.813796i
\(985\) −736224. + 425059.i −0.758818 + 0.438104i
\(986\) 228297. + 61172.1i 0.234826 + 0.0629216i
\(987\) 512180.i 0.525761i
\(988\) −121365. 226454.i −0.124331 0.231989i
\(989\) 811227. 0.829373
\(990\) −11881.4 + 44342.1i −0.0121227 + 0.0452424i
\(991\) −252070. 436598.i −0.256669 0.444564i 0.708678 0.705532i \(-0.249292\pi\)
−0.965348 + 0.260968i \(0.915958\pi\)
\(992\) −1.27171e6 734221.i −1.29230 0.746111i
\(993\) 668158. + 668158.i 0.677612 + 0.677612i
\(994\) 337674. 90479.4i 0.341763 0.0915750i
\(995\) 138770. + 517898.i 0.140169 + 0.523116i
\(996\) −269708. + 269708.i −0.271878 + 0.271878i
\(997\) 186654. 323294.i 0.187779 0.325242i −0.756731 0.653727i \(-0.773205\pi\)
0.944509 + 0.328485i \(0.106538\pi\)
\(998\) 155236. 89625.7i 0.155859 0.0899853i
\(999\) −939073. 251624.i −0.940954 0.252128i
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 13.5.f.a.11.2 yes 16
3.2 odd 2 117.5.bd.c.37.3 16
13.2 odd 12 169.5.d.d.70.4 16
13.3 even 3 169.5.d.d.99.4 16
13.6 odd 12 inner 13.5.f.a.6.2 16
13.10 even 6 169.5.d.c.99.5 16
13.11 odd 12 169.5.d.c.70.5 16
39.32 even 12 117.5.bd.c.19.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
13.5.f.a.6.2 16 13.6 odd 12 inner
13.5.f.a.11.2 yes 16 1.1 even 1 trivial
117.5.bd.c.19.3 16 39.32 even 12
117.5.bd.c.37.3 16 3.2 odd 2
169.5.d.c.70.5 16 13.11 odd 12
169.5.d.c.99.5 16 13.10 even 6
169.5.d.d.70.4 16 13.2 odd 12
169.5.d.d.99.4 16 13.3 even 3