Properties

Label 19.4.e.a.4.2
Level $19$
Weight $4$
Character 19.4
Analytic conductor $1.121$
Analytic rank $0$
Dimension $24$
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] = [19,4,Mod(4,19)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(19, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("19.4");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 19.e (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.12103629011\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 4.2
Character \(\chi\) \(=\) 19.4
Dual form 19.4.e.a.5.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.16911 - 0.789492i) q^{2} +(-0.930433 - 5.27675i) q^{3} +(-2.04660 - 1.71731i) q^{4} +(6.28846 - 5.27664i) q^{5} +(-2.14774 + 12.1804i) q^{6} +(-1.44586 + 2.50430i) q^{7} +(12.3168 + 21.3333i) q^{8} +(-1.60664 + 0.584768i) q^{9} +O(q^{10})\) \(q+(-2.16911 - 0.789492i) q^{2} +(-0.930433 - 5.27675i) q^{3} +(-2.04660 - 1.71731i) q^{4} +(6.28846 - 5.27664i) q^{5} +(-2.14774 + 12.1804i) q^{6} +(-1.44586 + 2.50430i) q^{7} +(12.3168 + 21.3333i) q^{8} +(-1.60664 + 0.584768i) q^{9} +(-17.8062 + 6.48094i) q^{10} +(14.1179 + 24.4529i) q^{11} +(-7.15756 + 12.3972i) q^{12} +(14.7989 - 83.9287i) q^{13} +(5.11336 - 4.29062i) q^{14} +(-33.6945 - 28.2730i) q^{15} +(-6.16261 - 34.9499i) q^{16} +(33.2517 + 12.1026i) q^{17} +3.94665 q^{18} +(-70.3411 + 43.7165i) q^{19} -21.9316 q^{20} +(14.5598 + 5.29935i) q^{21} +(-11.3179 - 64.1871i) q^{22} +(131.166 + 110.062i) q^{23} +(101.111 - 84.8419i) q^{24} +(-10.0043 + 56.7370i) q^{25} +(-98.3615 + 170.367i) q^{26} +(-67.7545 - 117.354i) q^{27} +(7.25975 - 2.64233i) q^{28} +(-62.1167 + 22.6086i) q^{29} +(50.7658 + 87.9290i) q^{30} +(-76.2433 + 132.057i) q^{31} +(19.9954 - 113.399i) q^{32} +(115.896 - 97.2483i) q^{33} +(-62.5718 - 52.5040i) q^{34} +(4.12208 + 23.3775i) q^{35} +(4.29238 + 1.56230i) q^{36} +129.616 q^{37} +(187.092 - 39.2921i) q^{38} -456.640 q^{39} +(190.022 + 69.1624i) q^{40} +(-27.0433 - 153.370i) q^{41} +(-27.3981 - 22.9898i) q^{42} +(242.696 - 203.646i) q^{43} +(13.0994 - 74.2902i) q^{44} +(-7.01766 + 12.1550i) q^{45} +(-197.622 - 342.291i) q^{46} +(-450.304 + 163.897i) q^{47} +(-178.688 + 65.0370i) q^{48} +(167.319 + 289.805i) q^{49} +(66.4938 - 115.171i) q^{50} +(32.9241 - 186.722i) q^{51} +(-174.419 + 146.355i) q^{52} +(518.579 + 435.139i) q^{53} +(54.3168 + 308.046i) q^{54} +(217.809 + 79.2761i) q^{55} -71.2335 q^{56} +(296.128 + 330.497i) q^{57} +152.588 q^{58} +(-202.212 - 73.5992i) q^{59} +(20.4059 + 115.727i) q^{60} +(-164.334 - 137.893i) q^{61} +(269.638 - 226.253i) q^{62} +(0.858536 - 4.86900i) q^{63} +(-274.856 + 476.065i) q^{64} +(-349.800 - 605.871i) q^{65} +(-328.168 + 119.444i) q^{66} +(-417.529 + 151.968i) q^{67} +(-47.2692 - 81.8727i) q^{68} +(458.726 - 794.536i) q^{69} +(9.51509 - 53.9628i) q^{70} +(178.870 - 150.090i) q^{71} +(-32.2637 - 27.0725i) q^{72} +(-140.645 - 797.639i) q^{73} +(-281.152 - 102.331i) q^{74} +308.695 q^{75} +(219.035 + 31.3269i) q^{76} -81.6500 q^{77} +(990.503 + 360.514i) q^{78} +(17.1116 + 97.0449i) q^{79} +(-223.171 - 187.263i) q^{80} +(-591.570 + 496.386i) q^{81} +(-62.4247 + 354.028i) q^{82} +(143.051 - 247.772i) q^{83} +(-20.6976 - 35.8494i) q^{84} +(272.964 - 99.3506i) q^{85} +(-687.211 + 250.125i) q^{86} +(177.096 + 306.738i) q^{87} +(-347.775 + 602.363i) q^{88} +(-71.1994 + 403.792i) q^{89} +(24.8183 - 20.8251i) q^{90} +(188.786 + 158.410i) q^{91} +(-79.4362 - 450.505i) q^{92} +(767.772 + 279.446i) q^{93} +1106.16 q^{94} +(-211.661 + 646.074i) q^{95} -616.984 q^{96} +(-841.874 - 306.417i) q^{97} +(-134.135 - 760.717i) q^{98} +(-36.9816 - 31.0313i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 6 q^{2} - 3 q^{3} - 24 q^{4} - 6 q^{5} + 42 q^{6} + 3 q^{7} - 75 q^{8} - 51 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 6 q^{2} - 3 q^{3} - 24 q^{4} - 6 q^{5} + 42 q^{6} + 3 q^{7} - 75 q^{8} - 51 q^{9} + 75 q^{10} + 39 q^{11} - 219 q^{12} - 156 q^{13} + 93 q^{14} - 192 q^{15} + 504 q^{16} + 12 q^{17} + 264 q^{18} + 546 q^{19} - 198 q^{20} + 453 q^{21} - 6 q^{22} + 6 q^{23} + 192 q^{24} - 498 q^{25} - 639 q^{26} - 870 q^{27} - 1368 q^{28} - 630 q^{29} - 522 q^{30} - 591 q^{31} + 147 q^{32} + 1506 q^{33} - 408 q^{34} + 2001 q^{35} + 1059 q^{36} - 72 q^{37} + 2934 q^{38} + 336 q^{39} + 2886 q^{40} - 477 q^{41} + 237 q^{42} + 588 q^{43} - 3423 q^{44} - 1569 q^{45} - 1728 q^{46} - 1242 q^{47} - 4599 q^{48} - 639 q^{49} - 1788 q^{50} + 9 q^{51} + 2733 q^{52} - 300 q^{53} + 3777 q^{54} + 315 q^{55} + 4638 q^{56} + 3342 q^{57} - 2820 q^{58} + 2097 q^{59} + 1116 q^{60} - 2316 q^{61} - 1320 q^{62} - 2979 q^{63} - 1785 q^{64} - 2433 q^{65} - 1590 q^{66} + 57 q^{67} - 438 q^{68} - 1767 q^{69} - 213 q^{70} - 792 q^{71} - 1686 q^{72} + 4068 q^{73} + 4287 q^{74} + 1332 q^{75} + 5538 q^{76} + 3786 q^{77} + 2121 q^{78} + 1824 q^{79} - 2739 q^{80} + 1536 q^{81} + 2205 q^{82} + 1071 q^{83} - 1437 q^{84} - 2394 q^{85} - 5256 q^{86} + 759 q^{87} + 1101 q^{88} - 3006 q^{89} - 3822 q^{90} - 3285 q^{91} - 1452 q^{92} - 135 q^{93} - 1086 q^{94} - 3078 q^{95} - 1590 q^{96} - 2535 q^{97} - 2403 q^{98} + 492 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/19\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.16911 0.789492i −0.766897 0.279128i −0.0711991 0.997462i \(-0.522683\pi\)
−0.695698 + 0.718334i \(0.744905\pi\)
\(3\) −0.930433 5.27675i −0.179062 1.01551i −0.933350 0.358967i \(-0.883129\pi\)
0.754288 0.656543i \(-0.227982\pi\)
\(4\) −2.04660 1.71731i −0.255826 0.214663i
\(5\) 6.28846 5.27664i 0.562457 0.471957i −0.316676 0.948534i \(-0.602567\pi\)
0.879133 + 0.476576i \(0.158122\pi\)
\(6\) −2.14774 + 12.1804i −0.146135 + 0.828773i
\(7\) −1.44586 + 2.50430i −0.0780691 + 0.135220i −0.902417 0.430864i \(-0.858209\pi\)
0.824348 + 0.566084i \(0.191542\pi\)
\(8\) 12.3168 + 21.3333i 0.544331 + 0.942809i
\(9\) −1.60664 + 0.584768i −0.0595051 + 0.0216581i
\(10\) −17.8062 + 6.48094i −0.563083 + 0.204945i
\(11\) 14.1179 + 24.4529i 0.386973 + 0.670257i 0.992041 0.125917i \(-0.0401872\pi\)
−0.605068 + 0.796174i \(0.706854\pi\)
\(12\) −7.15756 + 12.3972i −0.172184 + 0.298231i
\(13\) 14.7989 83.9287i 0.315729 1.79059i −0.252374 0.967630i \(-0.581211\pi\)
0.568103 0.822957i \(-0.307677\pi\)
\(14\) 5.11336 4.29062i 0.0976145 0.0819083i
\(15\) −33.6945 28.2730i −0.579992 0.486671i
\(16\) −6.16261 34.9499i −0.0962908 0.546092i
\(17\) 33.2517 + 12.1026i 0.474396 + 0.172666i 0.568143 0.822930i \(-0.307662\pi\)
−0.0937467 + 0.995596i \(0.529884\pi\)
\(18\) 3.94665 0.0516797
\(19\) −70.3411 + 43.7165i −0.849335 + 0.527855i
\(20\) −21.9316 −0.245203
\(21\) 14.5598 + 5.29935i 0.151296 + 0.0550673i
\(22\) −11.3179 64.1871i −0.109681 0.622033i
\(23\) 131.166 + 110.062i 1.18913 + 0.997801i 0.999874 + 0.0158739i \(0.00505302\pi\)
0.189259 + 0.981927i \(0.439391\pi\)
\(24\) 101.111 84.8419i 0.859963 0.721595i
\(25\) −10.0043 + 56.7370i −0.0800341 + 0.453896i
\(26\) −98.3615 + 170.367i −0.741934 + 1.28507i
\(27\) −67.7545 117.354i −0.482939 0.836475i
\(28\) 7.25975 2.64233i 0.0489987 0.0178341i
\(29\) −62.1167 + 22.6086i −0.397751 + 0.144770i −0.533148 0.846022i \(-0.678991\pi\)
0.135397 + 0.990791i \(0.456769\pi\)
\(30\) 50.7658 + 87.9290i 0.308951 + 0.535119i
\(31\) −76.2433 + 132.057i −0.441732 + 0.765102i −0.997818 0.0660223i \(-0.978969\pi\)
0.556086 + 0.831125i \(0.312302\pi\)
\(32\) 19.9954 113.399i 0.110460 0.626449i
\(33\) 115.896 97.2483i 0.611361 0.512993i
\(34\) −62.5718 52.5040i −0.315617 0.264834i
\(35\) 4.12208 + 23.3775i 0.0199074 + 0.112901i
\(36\) 4.29238 + 1.56230i 0.0198721 + 0.00723286i
\(37\) 129.616 0.575912 0.287956 0.957644i \(-0.407024\pi\)
0.287956 + 0.957644i \(0.407024\pi\)
\(38\) 187.092 39.2921i 0.798691 0.167738i
\(39\) −456.640 −1.87489
\(40\) 190.022 + 69.1624i 0.751128 + 0.273388i
\(41\) −27.0433 153.370i −0.103011 0.584206i −0.991996 0.126269i \(-0.959700\pi\)
0.888985 0.457937i \(-0.151411\pi\)
\(42\) −27.3981 22.9898i −0.100658 0.0844619i
\(43\) 242.696 203.646i 0.860715 0.722226i −0.101407 0.994845i \(-0.532334\pi\)
0.962122 + 0.272619i \(0.0878899\pi\)
\(44\) 13.0994 74.2902i 0.0448819 0.254538i
\(45\) −7.01766 + 12.1550i −0.0232474 + 0.0402656i
\(46\) −197.622 342.291i −0.633429 1.09713i
\(47\) −450.304 + 163.897i −1.39752 + 0.508657i −0.927442 0.373966i \(-0.877998\pi\)
−0.470082 + 0.882623i \(0.655776\pi\)
\(48\) −178.688 + 65.0370i −0.537320 + 0.195568i
\(49\) 167.319 + 289.805i 0.487810 + 0.844912i
\(50\) 66.4938 115.171i 0.188073 0.325752i
\(51\) 32.9241 186.722i 0.0903979 0.512672i
\(52\) −174.419 + 146.355i −0.465145 + 0.390303i
\(53\) 518.579 + 435.139i 1.34401 + 1.12775i 0.980578 + 0.196132i \(0.0628381\pi\)
0.363428 + 0.931622i \(0.381606\pi\)
\(54\) 54.3168 + 308.046i 0.136881 + 0.776292i
\(55\) 217.809 + 79.2761i 0.533989 + 0.194356i
\(56\) −71.2335 −0.169982
\(57\) 296.128 + 330.497i 0.688125 + 0.767989i
\(58\) 152.588 0.345444
\(59\) −202.212 73.5992i −0.446200 0.162403i 0.109141 0.994026i \(-0.465190\pi\)
−0.555341 + 0.831623i \(0.687412\pi\)
\(60\) 20.4059 + 115.727i 0.0439065 + 0.249006i
\(61\) −164.334 137.893i −0.344932 0.289432i 0.453819 0.891094i \(-0.350061\pi\)
−0.798751 + 0.601662i \(0.794506\pi\)
\(62\) 269.638 226.253i 0.552324 0.463455i
\(63\) 0.858536 4.86900i 0.00171691 0.00973708i
\(64\) −274.856 + 476.065i −0.536829 + 0.929815i
\(65\) −349.800 605.871i −0.667497 1.15614i
\(66\) −328.168 + 119.444i −0.612042 + 0.222765i
\(67\) −417.529 + 151.968i −0.761332 + 0.277102i −0.693366 0.720585i \(-0.743873\pi\)
−0.0679659 + 0.997688i \(0.521651\pi\)
\(68\) −47.2692 81.8727i −0.0842976 0.146008i
\(69\) 458.726 794.536i 0.800349 1.38624i
\(70\) 9.51509 53.9628i 0.0162467 0.0921398i
\(71\) 178.870 150.090i 0.298986 0.250879i −0.480936 0.876756i \(-0.659703\pi\)
0.779922 + 0.625877i \(0.215259\pi\)
\(72\) −32.2637 27.0725i −0.0528099 0.0443128i
\(73\) −140.645 797.639i −0.225497 1.27886i −0.861732 0.507363i \(-0.830620\pi\)
0.636235 0.771495i \(-0.280491\pi\)
\(74\) −281.152 102.331i −0.441666 0.160753i
\(75\) 308.695 0.475267
\(76\) 219.035 + 31.3269i 0.330593 + 0.0472821i
\(77\) −81.6500 −0.120843
\(78\) 990.503 + 360.514i 1.43785 + 0.523335i
\(79\) 17.1116 + 97.0449i 0.0243697 + 0.138208i 0.994565 0.104116i \(-0.0332014\pi\)
−0.970195 + 0.242324i \(0.922090\pi\)
\(80\) −223.171 187.263i −0.311892 0.261708i
\(81\) −591.570 + 496.386i −0.811482 + 0.680914i
\(82\) −62.4247 + 354.028i −0.0840690 + 0.476779i
\(83\) 143.051 247.772i 0.189180 0.327669i −0.755797 0.654806i \(-0.772750\pi\)
0.944977 + 0.327137i \(0.106084\pi\)
\(84\) −20.6976 35.8494i −0.0268845 0.0465653i
\(85\) 272.964 99.3506i 0.348318 0.126778i
\(86\) −687.211 + 250.125i −0.861673 + 0.313623i
\(87\) 177.096 + 306.738i 0.218237 + 0.377998i
\(88\) −347.775 + 602.363i −0.421283 + 0.729684i
\(89\) −71.1994 + 403.792i −0.0847992 + 0.480920i 0.912601 + 0.408852i \(0.134071\pi\)
−0.997400 + 0.0720677i \(0.977040\pi\)
\(90\) 24.8183 20.8251i 0.0290676 0.0243906i
\(91\) 188.786 + 158.410i 0.217474 + 0.182482i
\(92\) −79.4362 450.505i −0.0900195 0.510526i
\(93\) 767.772 + 279.446i 0.856067 + 0.311583i
\(94\) 1106.16 1.21374
\(95\) −211.661 + 646.074i −0.228589 + 0.697745i
\(96\) −616.984 −0.655944
\(97\) −841.874 306.417i −0.881231 0.320742i −0.138524 0.990359i \(-0.544236\pi\)
−0.742706 + 0.669617i \(0.766458\pi\)
\(98\) −134.135 760.717i −0.138262 0.784122i
\(99\) −36.9816 31.0313i −0.0375434 0.0315026i
\(100\) 117.910 98.9379i 0.117910 0.0989379i
\(101\) −52.7103 + 298.935i −0.0519294 + 0.294506i −0.999701 0.0244429i \(-0.992219\pi\)
0.947772 + 0.318949i \(0.103330\pi\)
\(102\) −218.831 + 379.027i −0.212427 + 0.367934i
\(103\) 379.896 + 658.000i 0.363421 + 0.629463i 0.988521 0.151081i \(-0.0482755\pi\)
−0.625101 + 0.780544i \(0.714942\pi\)
\(104\) 1972.75 718.023i 1.86004 0.677000i
\(105\) 119.522 43.5024i 0.111087 0.0404323i
\(106\) −781.317 1353.28i −0.715926 1.24002i
\(107\) −79.2465 + 137.259i −0.0715986 + 0.124012i −0.899602 0.436711i \(-0.856143\pi\)
0.828003 + 0.560723i \(0.189477\pi\)
\(108\) −62.8663 + 356.533i −0.0560122 + 0.317661i
\(109\) −929.528 + 779.967i −0.816813 + 0.685388i −0.952224 0.305402i \(-0.901209\pi\)
0.135410 + 0.990790i \(0.456765\pi\)
\(110\) −409.865 343.917i −0.355264 0.298102i
\(111\) −120.599 683.951i −0.103124 0.584845i
\(112\) 96.4354 + 35.0996i 0.0813597 + 0.0296125i
\(113\) −1431.94 −1.19209 −0.596044 0.802951i \(-0.703262\pi\)
−0.596044 + 0.802951i \(0.703262\pi\)
\(114\) −381.411 950.676i −0.313354 0.781044i
\(115\) 1405.59 1.13976
\(116\) 165.954 + 60.4025i 0.132832 + 0.0483468i
\(117\) 25.3024 + 143.497i 0.0199932 + 0.113387i
\(118\) 380.515 + 319.290i 0.296858 + 0.249093i
\(119\) −78.3860 + 65.7737i −0.0603835 + 0.0506678i
\(120\) 188.150 1067.05i 0.143130 0.811732i
\(121\) 266.870 462.232i 0.200503 0.347282i
\(122\) 247.594 + 428.845i 0.183739 + 0.318244i
\(123\) −784.135 + 285.402i −0.574822 + 0.209218i
\(124\) 382.822 139.336i 0.277246 0.100909i
\(125\) 749.532 + 1298.23i 0.536322 + 0.928936i
\(126\) −5.70630 + 9.88360i −0.00403458 + 0.00698810i
\(127\) 249.705 1416.15i 0.174470 0.989470i −0.764283 0.644881i \(-0.776907\pi\)
0.938754 0.344589i \(-0.111982\pi\)
\(128\) 266.372 223.512i 0.183939 0.154343i
\(129\) −1300.40 1091.17i −0.887549 0.744742i
\(130\) 280.424 + 1590.37i 0.189191 + 1.07296i
\(131\) −50.0440 18.2145i −0.0333769 0.0121482i 0.325278 0.945619i \(-0.394542\pi\)
−0.358655 + 0.933470i \(0.616764\pi\)
\(132\) −404.199 −0.266522
\(133\) −7.77585 239.363i −0.00506956 0.156056i
\(134\) 1025.64 0.661210
\(135\) −1045.31 380.461i −0.666413 0.242554i
\(136\) 151.365 + 858.436i 0.0954374 + 0.541252i
\(137\) −427.730 358.908i −0.266740 0.223822i 0.499600 0.866256i \(-0.333480\pi\)
−0.766341 + 0.642434i \(0.777925\pi\)
\(138\) −1622.31 + 1361.28i −1.00072 + 0.839708i
\(139\) −5.07488 + 28.7811i −0.00309673 + 0.0175624i −0.986317 0.164860i \(-0.947283\pi\)
0.983220 + 0.182422i \(0.0583939\pi\)
\(140\) 31.7100 54.9234i 0.0191428 0.0331562i
\(141\) 1283.82 + 2223.65i 0.766790 + 1.32812i
\(142\) −506.485 + 184.345i −0.299319 + 0.108943i
\(143\) 2261.23 823.021i 1.32233 0.481290i
\(144\) 30.3387 + 52.5481i 0.0175571 + 0.0304098i
\(145\) −271.321 + 469.942i −0.155393 + 0.269148i
\(146\) −324.655 + 1841.21i −0.184032 + 1.04370i
\(147\) 1373.55 1152.54i 0.770669 0.646668i
\(148\) −265.273 222.590i −0.147333 0.123627i
\(149\) 377.120 + 2138.75i 0.207348 + 1.17593i 0.893702 + 0.448661i \(0.148099\pi\)
−0.686354 + 0.727267i \(0.740790\pi\)
\(150\) −669.594 243.712i −0.364481 0.132660i
\(151\) −849.862 −0.458018 −0.229009 0.973424i \(-0.573549\pi\)
−0.229009 + 0.973424i \(0.573549\pi\)
\(152\) −1798.99 962.163i −0.959985 0.513432i
\(153\) −60.5008 −0.0319686
\(154\) 177.108 + 64.4620i 0.0926738 + 0.0337305i
\(155\) 217.366 + 1232.75i 0.112640 + 0.638816i
\(156\) 934.561 + 784.190i 0.479646 + 0.402471i
\(157\) 1340.48 1124.80i 0.681416 0.571776i −0.235004 0.971994i \(-0.575510\pi\)
0.916420 + 0.400219i \(0.131066\pi\)
\(158\) 39.4992 224.011i 0.0198885 0.112793i
\(159\) 1813.62 3141.28i 0.904586 1.56679i
\(160\) −472.628 818.616i −0.233528 0.404483i
\(161\) −465.275 + 169.346i −0.227757 + 0.0828967i
\(162\) 1675.08 609.678i 0.812385 0.295684i
\(163\) −1661.85 2878.40i −0.798563 1.38315i −0.920552 0.390621i \(-0.872260\pi\)
0.121988 0.992532i \(-0.461073\pi\)
\(164\) −208.037 + 360.330i −0.0990546 + 0.171568i
\(165\) 215.663 1223.08i 0.101754 0.577073i
\(166\) −505.909 + 424.508i −0.236543 + 0.198483i
\(167\) 2146.56 + 1801.18i 0.994644 + 0.834605i 0.986233 0.165359i \(-0.0528783\pi\)
0.00841064 + 0.999965i \(0.497323\pi\)
\(168\) 66.2779 + 375.881i 0.0304372 + 0.172618i
\(169\) −4760.51 1732.69i −2.16682 0.788660i
\(170\) −670.525 −0.302511
\(171\) 87.4487 111.370i 0.0391074 0.0498050i
\(172\) −846.425 −0.375228
\(173\) −3146.61 1145.27i −1.38285 0.503314i −0.459806 0.888020i \(-0.652081\pi\)
−0.923039 + 0.384705i \(0.874303\pi\)
\(174\) −141.972 805.166i −0.0618558 0.350801i
\(175\) −127.622 107.087i −0.0551275 0.0462574i
\(176\) 767.624 644.113i 0.328760 0.275863i
\(177\) −200.219 + 1135.50i −0.0850249 + 0.482200i
\(178\) 473.230 819.659i 0.199270 0.345146i
\(179\) 1167.62 + 2022.37i 0.487552 + 0.844465i 0.999898 0.0143143i \(-0.00455654\pi\)
−0.512345 + 0.858780i \(0.671223\pi\)
\(180\) 35.2361 12.8249i 0.0145908 0.00531062i
\(181\) 4318.67 1571.87i 1.77350 0.645503i 0.773574 0.633706i \(-0.218467\pi\)
0.999930 0.0117973i \(-0.00375530\pi\)
\(182\) −284.434 492.654i −0.115844 0.200648i
\(183\) −574.723 + 995.449i −0.232157 + 0.402108i
\(184\) −732.430 + 4153.82i −0.293454 + 1.66426i
\(185\) 815.086 683.938i 0.323926 0.271806i
\(186\) −1444.76 1212.30i −0.569544 0.477904i
\(187\) 173.500 + 983.966i 0.0678479 + 0.384785i
\(188\) 1203.06 + 437.877i 0.466712 + 0.169869i
\(189\) 391.854 0.150810
\(190\) 969.187 1234.30i 0.370064 0.471293i
\(191\) 375.808 0.142369 0.0711845 0.997463i \(-0.477322\pi\)
0.0711845 + 0.997463i \(0.477322\pi\)
\(192\) 2767.81 + 1007.40i 1.04036 + 0.378661i
\(193\) 502.800 + 2851.52i 0.187525 + 1.06351i 0.922668 + 0.385595i \(0.126004\pi\)
−0.735143 + 0.677912i \(0.762885\pi\)
\(194\) 1584.21 + 1329.31i 0.586285 + 0.491952i
\(195\) −2871.56 + 2409.53i −1.05455 + 0.884870i
\(196\) 155.248 880.454i 0.0565772 0.320865i
\(197\) −770.856 + 1335.16i −0.278788 + 0.482875i −0.971084 0.238739i \(-0.923266\pi\)
0.692296 + 0.721614i \(0.256599\pi\)
\(198\) 55.7184 + 96.5071i 0.0199987 + 0.0346387i
\(199\) −508.048 + 184.914i −0.180978 + 0.0658705i −0.430920 0.902390i \(-0.641811\pi\)
0.249942 + 0.968261i \(0.419589\pi\)
\(200\) −1333.61 + 485.394i −0.471502 + 0.171613i
\(201\) 1190.38 + 2061.80i 0.417726 + 0.723522i
\(202\) 350.341 606.809i 0.122029 0.211361i
\(203\) 33.1932 188.248i 0.0114764 0.0650858i
\(204\) −388.041 + 325.605i −0.133178 + 0.111749i
\(205\) −979.342 821.766i −0.333660 0.279974i
\(206\) −304.552 1727.20i −0.103006 0.584174i
\(207\) −275.097 100.127i −0.0923699 0.0336199i
\(208\) −3024.50 −1.00823
\(209\) −2062.06 1102.86i −0.682468 0.365007i
\(210\) −293.601 −0.0964780
\(211\) 2783.24 + 1013.02i 0.908085 + 0.330516i 0.753488 0.657462i \(-0.228370\pi\)
0.154597 + 0.987978i \(0.450592\pi\)
\(212\) −314.059 1781.12i −0.101744 0.577017i
\(213\) −958.414 804.205i −0.308307 0.258701i
\(214\) 280.260 235.166i 0.0895241 0.0751196i
\(215\) 451.616 2561.24i 0.143255 0.812442i
\(216\) 1669.04 2890.86i 0.525757 0.910638i
\(217\) −220.474 381.872i −0.0689712 0.119462i
\(218\) 2632.03 957.980i 0.817722 0.297627i
\(219\) −4078.08 + 1484.30i −1.25832 + 0.457989i
\(220\) −309.628 536.292i −0.0948869 0.164349i
\(221\) 1507.85 2611.67i 0.458954 0.794932i
\(222\) −278.381 + 1578.78i −0.0841610 + 0.477301i
\(223\) −2355.31 + 1976.34i −0.707280 + 0.593479i −0.923835 0.382792i \(-0.874963\pi\)
0.216554 + 0.976271i \(0.430518\pi\)
\(224\) 255.076 + 214.034i 0.0760847 + 0.0638426i
\(225\) −17.1048 97.0060i −0.00506808 0.0287425i
\(226\) 3106.05 + 1130.51i 0.914209 + 0.332745i
\(227\) 1339.90 0.391773 0.195886 0.980627i \(-0.437242\pi\)
0.195886 + 0.980627i \(0.437242\pi\)
\(228\) −38.4934 1184.94i −0.0111811 0.344186i
\(229\) 5397.19 1.55745 0.778726 0.627364i \(-0.215866\pi\)
0.778726 + 0.627364i \(0.215866\pi\)
\(230\) −3048.88 1109.70i −0.874075 0.318137i
\(231\) 75.9698 + 430.846i 0.0216383 + 0.122717i
\(232\) −1247.40 1046.69i −0.352998 0.296201i
\(233\) 279.243 234.312i 0.0785141 0.0658812i −0.602686 0.797978i \(-0.705903\pi\)
0.681200 + 0.732097i \(0.261458\pi\)
\(234\) 58.4060 331.237i 0.0163168 0.0925369i
\(235\) −1966.89 + 3406.76i −0.545983 + 0.945670i
\(236\) 287.456 + 497.888i 0.0792872 + 0.137330i
\(237\) 496.160 180.587i 0.135988 0.0494954i
\(238\) 221.956 80.7854i 0.0604507 0.0220023i
\(239\) −2227.54 3858.21i −0.602876 1.04421i −0.992383 0.123188i \(-0.960688\pi\)
0.389507 0.921023i \(-0.372645\pi\)
\(240\) −780.494 + 1351.85i −0.209919 + 0.363591i
\(241\) 980.954 5563.26i 0.262194 1.48698i −0.514714 0.857362i \(-0.672102\pi\)
0.776908 0.629614i \(-0.216787\pi\)
\(242\) −943.800 + 791.942i −0.250701 + 0.210363i
\(243\) 366.962 + 307.918i 0.0968751 + 0.0812879i
\(244\) 99.5231 + 564.424i 0.0261119 + 0.148088i
\(245\) 2581.38 + 939.544i 0.673135 + 0.245001i
\(246\) 1926.20 0.499228
\(247\) 2628.09 + 6550.59i 0.677011 + 1.68747i
\(248\) −3756.29 −0.961794
\(249\) −1440.53 524.310i −0.366626 0.133441i
\(250\) −600.879 3407.75i −0.152012 0.862101i
\(251\) −3436.36 2883.45i −0.864149 0.725107i 0.0987089 0.995116i \(-0.468529\pi\)
−0.962858 + 0.270009i \(0.912973\pi\)
\(252\) −10.1186 + 8.49055i −0.00252942 + 0.00212244i
\(253\) −839.534 + 4761.24i −0.208621 + 1.18315i
\(254\) −1659.67 + 2874.64i −0.409989 + 0.710122i
\(255\) −778.222 1347.92i −0.191114 0.331020i
\(256\) 3378.24 1229.58i 0.824764 0.300190i
\(257\) −3832.00 + 1394.73i −0.930091 + 0.338525i −0.762246 0.647288i \(-0.775903\pi\)
−0.167845 + 0.985813i \(0.553681\pi\)
\(258\) 1959.25 + 3393.52i 0.472781 + 0.818880i
\(259\) −187.407 + 324.598i −0.0449610 + 0.0778747i
\(260\) −324.563 + 1840.69i −0.0774176 + 0.439057i
\(261\) 86.5783 72.6478i 0.0205328 0.0172291i
\(262\) 94.1709 + 79.0188i 0.0222057 + 0.0186328i
\(263\) −964.755 5471.40i −0.226195 1.28282i −0.860387 0.509641i \(-0.829778\pi\)
0.634192 0.773176i \(-0.281333\pi\)
\(264\) 3502.10 + 1274.66i 0.816437 + 0.297159i
\(265\) 5557.14 1.28820
\(266\) −172.109 + 525.345i −0.0396717 + 0.121094i
\(267\) 2196.95 0.503563
\(268\) 1115.49 + 406.006i 0.254252 + 0.0925401i
\(269\) 103.353 + 586.146i 0.0234259 + 0.132855i 0.994278 0.106825i \(-0.0340686\pi\)
−0.970852 + 0.239680i \(0.922957\pi\)
\(270\) 1967.02 + 1650.52i 0.443366 + 0.372029i
\(271\) −2709.72 + 2273.72i −0.607394 + 0.509664i −0.893813 0.448441i \(-0.851980\pi\)
0.286419 + 0.958104i \(0.407535\pi\)
\(272\) 218.069 1236.73i 0.0486116 0.275690i
\(273\) 660.237 1143.56i 0.146371 0.253522i
\(274\) 644.439 + 1116.20i 0.142088 + 0.246103i
\(275\) −1528.62 + 556.374i −0.335198 + 0.122002i
\(276\) −2303.29 + 838.329i −0.502325 + 0.182831i
\(277\) 1518.38 + 2629.91i 0.329353 + 0.570456i 0.982384 0.186876i \(-0.0598361\pi\)
−0.653031 + 0.757331i \(0.726503\pi\)
\(278\) 33.7304 58.4228i 0.00727704 0.0126042i
\(279\) 45.2724 256.753i 0.00971466 0.0550946i
\(280\) −447.949 + 375.874i −0.0956074 + 0.0802241i
\(281\) 2615.44 + 2194.62i 0.555247 + 0.465907i 0.876713 0.481014i \(-0.159731\pi\)
−0.321466 + 0.946921i \(0.604176\pi\)
\(282\) −1029.20 5836.91i −0.217334 1.23256i
\(283\) −5101.09 1856.64i −1.07148 0.389986i −0.254749 0.967007i \(-0.581993\pi\)
−0.816729 + 0.577021i \(0.804215\pi\)
\(284\) −623.828 −0.130343
\(285\) 3606.11 + 515.753i 0.749499 + 0.107195i
\(286\) −5554.63 −1.14843
\(287\) 423.187 + 154.027i 0.0870381 + 0.0316793i
\(288\) 34.1870 + 193.884i 0.00699476 + 0.0396692i
\(289\) −2804.37 2353.15i −0.570806 0.478963i
\(290\) 959.541 805.150i 0.194297 0.163035i
\(291\) −833.578 + 4727.46i −0.167922 + 0.952331i
\(292\) −1081.95 + 1873.98i −0.216836 + 0.375571i
\(293\) −2004.32 3471.59i −0.399637 0.692192i 0.594044 0.804433i \(-0.297531\pi\)
−0.993681 + 0.112241i \(0.964197\pi\)
\(294\) −3889.30 + 1415.59i −0.771527 + 0.280813i
\(295\) −1659.96 + 604.176i −0.327616 + 0.119242i
\(296\) 1596.46 + 2765.14i 0.313487 + 0.542975i
\(297\) 1913.10 3313.59i 0.373769 0.647387i
\(298\) 870.513 4936.92i 0.169220 0.959692i
\(299\) 11178.4 9379.82i 2.16209 1.81421i
\(300\) −631.777 530.124i −0.121586 0.102022i
\(301\) 159.087 + 902.227i 0.0304639 + 0.172769i
\(302\) 1843.45 + 670.960i 0.351253 + 0.127846i
\(303\) 1626.45 0.308373
\(304\) 1961.37 + 2189.01i 0.370040 + 0.412987i
\(305\) −1761.02 −0.330609
\(306\) 131.233 + 47.7649i 0.0245166 + 0.00892332i
\(307\) −791.199 4487.11i −0.147088 0.834179i −0.965667 0.259784i \(-0.916348\pi\)
0.818578 0.574395i \(-0.194763\pi\)
\(308\) 167.105 + 140.218i 0.0309146 + 0.0259405i
\(309\) 3118.63 2616.84i 0.574151 0.481770i
\(310\) 501.751 2845.57i 0.0919276 0.521347i
\(311\) −1659.45 + 2874.24i −0.302568 + 0.524063i −0.976717 0.214533i \(-0.931177\pi\)
0.674149 + 0.738595i \(0.264510\pi\)
\(312\) −5624.34 9741.64i −1.02056 1.76767i
\(313\) −825.518 + 300.464i −0.149077 + 0.0542595i −0.415481 0.909602i \(-0.636387\pi\)
0.266404 + 0.963861i \(0.414164\pi\)
\(314\) −3795.68 + 1381.52i −0.682174 + 0.248291i
\(315\) −20.2931 35.1487i −0.00362980 0.00628700i
\(316\) 131.635 227.998i 0.0234337 0.0405883i
\(317\) −173.100 + 981.701i −0.0306697 + 0.173936i −0.996295 0.0860016i \(-0.972591\pi\)
0.965625 + 0.259938i \(0.0837021\pi\)
\(318\) −6413.95 + 5381.94i −1.13106 + 0.949071i
\(319\) −1429.81 1199.75i −0.250952 0.210574i
\(320\) 783.603 + 4444.04i 0.136890 + 0.776341i
\(321\) 798.014 + 290.453i 0.138756 + 0.0505032i
\(322\) 1142.93 0.197805
\(323\) −2868.05 + 602.335i −0.494064 + 0.103761i
\(324\) 2063.16 0.353765
\(325\) 4613.81 + 1679.29i 0.787472 + 0.286616i
\(326\) 1332.25 + 7555.59i 0.226340 + 1.28364i
\(327\) 4980.55 + 4179.18i 0.842278 + 0.706755i
\(328\) 2938.81 2465.96i 0.494722 0.415121i
\(329\) 240.628 1364.67i 0.0403230 0.228683i
\(330\) −1433.41 + 2482.74i −0.239111 + 0.414153i
\(331\) −2105.07 3646.09i −0.349562 0.605459i 0.636610 0.771186i \(-0.280336\pi\)
−0.986172 + 0.165727i \(0.947003\pi\)
\(332\) −718.270 + 261.429i −0.118736 + 0.0432162i
\(333\) −208.246 + 75.7954i −0.0342697 + 0.0124732i
\(334\) −3234.11 5601.64i −0.529828 0.917689i
\(335\) −1823.73 + 3158.80i −0.297436 + 0.515174i
\(336\) 95.4851 541.523i 0.0155034 0.0879241i
\(337\) −6894.59 + 5785.24i −1.11446 + 0.935140i −0.998311 0.0580918i \(-0.981498\pi\)
−0.116146 + 0.993232i \(0.537054\pi\)
\(338\) 8958.15 + 7516.78i 1.44159 + 1.20964i
\(339\) 1332.33 + 7556.01i 0.213458 + 1.21058i
\(340\) −729.264 265.430i −0.116323 0.0423382i
\(341\) −4305.58 −0.683754
\(342\) −277.612 + 172.533i −0.0438933 + 0.0272794i
\(343\) −1959.54 −0.308470
\(344\) 7333.68 + 2669.24i 1.14944 + 0.418360i
\(345\) −1307.81 7416.94i −0.204087 1.15743i
\(346\) 5921.16 + 4968.45i 0.920011 + 0.771981i
\(347\) 8596.78 7213.55i 1.32997 1.11598i 0.345884 0.938277i \(-0.387579\pi\)
0.984085 0.177699i \(-0.0568653\pi\)
\(348\) 164.319 931.899i 0.0253116 0.143549i
\(349\) −1836.77 + 3181.37i −0.281719 + 0.487951i −0.971808 0.235773i \(-0.924238\pi\)
0.690089 + 0.723724i \(0.257571\pi\)
\(350\) 192.281 + 333.041i 0.0293654 + 0.0508623i
\(351\) −10852.1 + 3949.83i −1.65026 + 0.600645i
\(352\) 3055.24 1112.02i 0.462627 0.168382i
\(353\) 5820.93 + 10082.1i 0.877668 + 1.52016i 0.853894 + 0.520447i \(0.174235\pi\)
0.0237739 + 0.999717i \(0.492432\pi\)
\(354\) 1330.77 2304.96i 0.199801 0.346065i
\(355\) 332.847 1887.67i 0.0497625 0.282217i
\(356\) 839.151 704.132i 0.124930 0.104828i
\(357\) 420.004 + 352.425i 0.0622660 + 0.0522474i
\(358\) −936.046 5308.58i −0.138189 0.783707i
\(359\) 847.286 + 308.387i 0.124563 + 0.0453372i 0.403550 0.914958i \(-0.367776\pi\)
−0.278987 + 0.960295i \(0.589999\pi\)
\(360\) −345.741 −0.0506170
\(361\) 3036.74 6150.13i 0.442738 0.896651i
\(362\) −10608.7 −1.54027
\(363\) −2687.39 978.129i −0.388571 0.141428i
\(364\) −114.331 648.405i −0.0164632 0.0933672i
\(365\) −5093.30 4273.79i −0.730399 0.612878i
\(366\) 2032.54 1705.50i 0.290280 0.243574i
\(367\) −38.0243 + 215.646i −0.00540831 + 0.0306721i −0.987392 0.158291i \(-0.949402\pi\)
0.981984 + 0.188963i \(0.0605127\pi\)
\(368\) 3038.31 5262.51i 0.430389 0.745455i
\(369\) 133.135 + 230.597i 0.0187825 + 0.0325322i
\(370\) −2307.98 + 840.035i −0.324287 + 0.118031i
\(371\) −1839.51 + 669.528i −0.257420 + 0.0936931i
\(372\) −1091.43 1890.41i −0.152118 0.263477i
\(373\) 1916.57 3319.60i 0.266049 0.460811i −0.701789 0.712385i \(-0.747615\pi\)
0.967838 + 0.251574i \(0.0809483\pi\)
\(374\) 400.493 2271.31i 0.0553717 0.314028i
\(375\) 6153.03 5163.01i 0.847310 0.710977i
\(376\) −9042.78 7587.80i −1.24028 1.04072i
\(377\) 978.255 + 5547.96i 0.133641 + 0.757916i
\(378\) −849.975 309.366i −0.115656 0.0420954i
\(379\) −3205.78 −0.434486 −0.217243 0.976118i \(-0.569706\pi\)
−0.217243 + 0.976118i \(0.569706\pi\)
\(380\) 1542.69 958.772i 0.208259 0.129431i
\(381\) −7704.98 −1.03606
\(382\) −815.169 296.697i −0.109182 0.0397391i
\(383\) 711.867 + 4037.20i 0.0949731 + 0.538619i 0.994756 + 0.102280i \(0.0326139\pi\)
−0.899783 + 0.436339i \(0.856275\pi\)
\(384\) −1427.26 1197.61i −0.189673 0.159155i
\(385\) −513.453 + 430.838i −0.0679688 + 0.0570326i
\(386\) 1160.62 6582.22i 0.153042 0.867944i
\(387\) −270.839 + 469.106i −0.0355749 + 0.0616176i
\(388\) 1196.77 + 2072.87i 0.156590 + 0.271222i
\(389\) 1309.99 476.798i 0.170743 0.0621455i −0.255234 0.966879i \(-0.582153\pi\)
0.425977 + 0.904734i \(0.359930\pi\)
\(390\) 8131.04 2959.46i 1.05572 0.384251i
\(391\) 3029.47 + 5247.20i 0.391834 + 0.678676i
\(392\) −4121.67 + 7138.94i −0.531061 + 0.919824i
\(393\) −49.5509 + 281.017i −0.00636008 + 0.0360698i
\(394\) 2726.17 2287.53i 0.348585 0.292498i
\(395\) 619.677 + 519.971i 0.0789351 + 0.0662344i
\(396\) 22.3966 + 127.018i 0.00284210 + 0.0161184i
\(397\) 2430.12 + 884.491i 0.307215 + 0.111817i 0.491027 0.871144i \(-0.336622\pi\)
−0.183812 + 0.982961i \(0.558844\pi\)
\(398\) 1248.00 0.157178
\(399\) −1255.82 + 263.743i −0.157569 + 0.0330918i
\(400\) 2044.61 0.255576
\(401\) −3379.27 1229.95i −0.420830 0.153170i 0.122920 0.992417i \(-0.460774\pi\)
−0.543751 + 0.839247i \(0.682996\pi\)
\(402\) −954.293 5412.06i −0.118398 0.671466i
\(403\) 9955.07 + 8353.30i 1.23052 + 1.03252i
\(404\) 621.240 521.282i 0.0765045 0.0641949i
\(405\) −1100.81 + 6243.01i −0.135061 + 0.765970i
\(406\) −220.620 + 382.125i −0.0269685 + 0.0467108i
\(407\) 1829.91 + 3169.49i 0.222863 + 0.386010i
\(408\) 4388.91 1597.43i 0.532558 0.193835i
\(409\) −5497.35 + 2000.87i −0.664612 + 0.241899i −0.652226 0.758024i \(-0.726165\pi\)
−0.0123857 + 0.999923i \(0.503943\pi\)
\(410\) 1475.53 + 2555.69i 0.177734 + 0.307845i
\(411\) −1495.89 + 2590.96i −0.179530 + 0.310956i
\(412\) 352.489 1999.06i 0.0421502 0.239046i
\(413\) 476.685 399.986i 0.0567945 0.0476562i
\(414\) 517.667 + 434.374i 0.0614540 + 0.0515660i
\(415\) −407.833 2312.94i −0.0482403 0.273585i
\(416\) −9221.55 3356.37i −1.08684 0.395576i
\(417\) 156.592 0.0183893
\(418\) 3602.15 + 4020.21i 0.421499 + 0.470419i
\(419\) 7193.31 0.838702 0.419351 0.907824i \(-0.362258\pi\)
0.419351 + 0.907824i \(0.362258\pi\)
\(420\) −319.321 116.223i −0.0370982 0.0135026i
\(421\) −129.270 733.127i −0.0149649 0.0848704i 0.976411 0.215922i \(-0.0692757\pi\)
−0.991376 + 0.131052i \(0.958165\pi\)
\(422\) −5237.39 4394.69i −0.604152 0.506944i
\(423\) 627.634 526.647i 0.0721433 0.0605354i
\(424\) −2895.74 + 16422.5i −0.331673 + 1.88101i
\(425\) −1019.33 + 1765.53i −0.116340 + 0.201507i
\(426\) 1443.99 + 2501.07i 0.164229 + 0.284454i
\(427\) 582.929 212.169i 0.0660654 0.0240458i
\(428\) 397.902 144.824i 0.0449377 0.0163560i
\(429\) −6446.79 11166.2i −0.725534 1.25666i
\(430\) −3001.68 + 5199.07i −0.336637 + 0.583073i
\(431\) 207.779 1178.37i 0.0232213 0.131694i −0.970993 0.239107i \(-0.923145\pi\)
0.994215 + 0.107412i \(0.0342565\pi\)
\(432\) −3683.97 + 3091.22i −0.410290 + 0.344274i
\(433\) −2731.59 2292.07i −0.303168 0.254388i 0.478494 0.878091i \(-0.341183\pi\)
−0.781661 + 0.623703i \(0.785627\pi\)
\(434\) 176.748 + 1002.39i 0.0195488 + 0.110867i
\(435\) 2732.21 + 994.442i 0.301148 + 0.109609i
\(436\) 3241.82 0.356089
\(437\) −14037.9 2007.73i −1.53667 0.219777i
\(438\) 10017.7 1.09284
\(439\) −1894.29 689.465i −0.205944 0.0749576i 0.236988 0.971513i \(-0.423840\pi\)
−0.442933 + 0.896555i \(0.646062\pi\)
\(440\) 991.491 + 5623.02i 0.107426 + 0.609243i
\(441\) −438.290 367.769i −0.0473264 0.0397116i
\(442\) −5332.59 + 4474.57i −0.573858 + 0.481524i
\(443\) 1948.81 11052.3i 0.209009 1.18535i −0.681997 0.731355i \(-0.738888\pi\)
0.891006 0.453992i \(-0.150000\pi\)
\(444\) −927.735 + 1606.88i −0.0991629 + 0.171755i
\(445\) 1682.93 + 2914.92i 0.179278 + 0.310518i
\(446\) 6669.25 2427.41i 0.708068 0.257716i
\(447\) 10934.8 3979.93i 1.15704 0.421128i
\(448\) −794.807 1376.65i −0.0838194 0.145180i
\(449\) 2795.84 4842.55i 0.293862 0.508984i −0.680857 0.732416i \(-0.738393\pi\)
0.974720 + 0.223432i \(0.0717260\pi\)
\(450\) −39.4833 + 223.921i −0.00413614 + 0.0234572i
\(451\) 3368.56 2826.56i 0.351706 0.295116i
\(452\) 2930.62 + 2459.09i 0.304967 + 0.255898i
\(453\) 790.739 + 4484.51i 0.0820136 + 0.465122i
\(454\) −2906.40 1057.84i −0.300449 0.109355i
\(455\) 2023.04 0.208444
\(456\) −3403.25 + 10388.1i −0.349499 + 1.06681i
\(457\) 11052.0 1.13127 0.565635 0.824655i \(-0.308631\pi\)
0.565635 + 0.824655i \(0.308631\pi\)
\(458\) −11707.1 4261.04i −1.19441 0.434728i
\(459\) −832.658 4722.24i −0.0846735 0.480207i
\(460\) −2876.69 2413.83i −0.291579 0.244664i
\(461\) −12252.0 + 10280.7i −1.23782 + 1.03865i −0.240127 + 0.970742i \(0.577189\pi\)
−0.997691 + 0.0679113i \(0.978367\pi\)
\(462\) 175.363 994.532i 0.0176593 0.100151i
\(463\) 7314.72 12669.5i 0.734220 1.27171i −0.220845 0.975309i \(-0.570881\pi\)
0.955065 0.296397i \(-0.0957852\pi\)
\(464\) 1172.97 + 2031.65i 0.117357 + 0.203269i
\(465\) 6302.64 2293.97i 0.628555 0.228775i
\(466\) −790.697 + 287.790i −0.0786015 + 0.0286086i
\(467\) −1918.37 3322.72i −0.190089 0.329244i 0.755190 0.655505i \(-0.227544\pi\)
−0.945280 + 0.326261i \(0.894211\pi\)
\(468\) 194.644 337.133i 0.0192253 0.0332991i
\(469\) 223.114 1265.34i 0.0219668 0.124580i
\(470\) 6956.02 5836.79i 0.682675 0.572832i
\(471\) −7182.51 6026.84i −0.702660 0.589601i
\(472\) −920.491 5220.36i −0.0897649 0.509082i
\(473\) 8406.09 + 3059.57i 0.817151 + 0.297419i
\(474\) −1218.80 −0.118104
\(475\) −1776.63 4428.30i −0.171616 0.427756i
\(476\) 273.379 0.0263241
\(477\) −1087.62 395.863i −0.104400 0.0379986i
\(478\) 1785.75 + 10127.5i 0.170875 + 0.969082i
\(479\) 1570.98 + 1318.20i 0.149853 + 0.125742i 0.714632 0.699500i \(-0.246594\pi\)
−0.564779 + 0.825242i \(0.691039\pi\)
\(480\) −3879.88 + 3255.60i −0.368940 + 0.309578i
\(481\) 1918.18 10878.5i 0.181832 1.03122i
\(482\) −6519.95 + 11292.9i −0.616132 + 1.06717i
\(483\) 1326.51 + 2297.57i 0.124965 + 0.216446i
\(484\) −1339.97 + 487.710i −0.125843 + 0.0458029i
\(485\) −6910.95 + 2515.38i −0.647031 + 0.235500i
\(486\) −552.884 957.623i −0.0516035 0.0893799i
\(487\) −1689.16 + 2925.72i −0.157173 + 0.272232i −0.933848 0.357670i \(-0.883571\pi\)
0.776675 + 0.629901i \(0.216905\pi\)
\(488\) 917.639 5204.19i 0.0851221 0.482751i
\(489\) −13642.4 + 11447.3i −1.26161 + 1.05862i
\(490\) −4857.53 4075.95i −0.447839 0.375781i
\(491\) −3674.60 20839.7i −0.337744 1.91544i −0.398259 0.917273i \(-0.630385\pi\)
0.0605149 0.998167i \(-0.480726\pi\)
\(492\) 2094.94 + 762.494i 0.191965 + 0.0698697i
\(493\) −2339.11 −0.213688
\(494\) −528.989 16283.8i −0.0481788 1.48309i
\(495\) −396.299 −0.0359844
\(496\) 5085.24 + 1850.88i 0.460351 + 0.167554i
\(497\) 117.249 + 664.955i 0.0105822 + 0.0600147i
\(498\) 2710.73 + 2274.58i 0.243917 + 0.204671i
\(499\) −12405.1 + 10409.2i −1.11289 + 0.933823i −0.998223 0.0595812i \(-0.981023\pi\)
−0.114664 + 0.993404i \(0.536579\pi\)
\(500\) 695.458 3944.14i 0.0622036 0.352774i
\(501\) 7507.12 13002.7i 0.669448 1.15952i
\(502\) 5177.40 + 8967.51i 0.460316 + 0.797290i
\(503\) 16004.5 5825.17i 1.41870 0.516365i 0.485030 0.874497i \(-0.338809\pi\)
0.933671 + 0.358132i \(0.116586\pi\)
\(504\) 114.446 41.6551i 0.0101148 0.00368148i
\(505\) 1245.91 + 2157.97i 0.109786 + 0.190156i
\(506\) 5580.00 9664.85i 0.490240 0.849121i
\(507\) −4713.60 + 26732.2i −0.412896 + 2.34165i
\(508\) −2943.00 + 2469.47i −0.257037 + 0.215679i
\(509\) 4582.39 + 3845.08i 0.399039 + 0.334833i 0.820122 0.572189i \(-0.193906\pi\)
−0.421083 + 0.907022i \(0.638350\pi\)
\(510\) 623.879 + 3538.19i 0.0541683 + 0.307203i
\(511\) 2200.88 + 801.056i 0.190531 + 0.0693476i
\(512\) −11080.3 −0.956416
\(513\) 9896.23 + 5292.84i 0.851714 + 0.455525i
\(514\) 9413.16 0.807776
\(515\) 5861.00 + 2133.23i 0.501488 + 0.182527i
\(516\) 787.541 + 4466.37i 0.0671891 + 0.381048i
\(517\) −10365.1 8697.37i −0.881736 0.739864i
\(518\) 662.774 556.133i 0.0562174 0.0471720i
\(519\) −3115.60 + 17669.4i −0.263506 + 1.49442i
\(520\) 8616.83 14924.8i 0.726679 1.25864i
\(521\) 11626.8 + 20138.2i 0.977695 + 1.69342i 0.670740 + 0.741693i \(0.265977\pi\)
0.306955 + 0.951724i \(0.400690\pi\)
\(522\) −245.153 + 89.2284i −0.0205557 + 0.00748165i
\(523\) 6686.10 2433.54i 0.559011 0.203463i −0.0470348 0.998893i \(-0.514977\pi\)
0.606045 + 0.795430i \(0.292755\pi\)
\(524\) 71.1404 + 123.219i 0.00593089 + 0.0102726i
\(525\) −446.330 + 773.066i −0.0371037 + 0.0642655i
\(526\) −2226.96 + 12629.7i −0.184601 + 1.04693i
\(527\) −4133.46 + 3468.39i −0.341663 + 0.286689i
\(528\) −4113.04 3451.25i −0.339010 0.284463i
\(529\) 2978.26 + 16890.6i 0.244782 + 1.38823i
\(530\) −12054.1 4387.32i −0.987915 0.359572i
\(531\) 367.920 0.0300685
\(532\) −395.146 + 503.235i −0.0322025 + 0.0410113i
\(533\) −13272.4 −1.07860
\(534\) −4765.44 1734.48i −0.386181 0.140558i
\(535\) 225.928 + 1281.30i 0.0182575 + 0.103543i
\(536\) −8384.60 7035.52i −0.675671 0.566955i
\(537\) 9585.16 8042.90i 0.770261 0.646326i
\(538\) 238.573 1353.01i 0.0191182 0.108425i
\(539\) −4724.38 + 8182.87i −0.377539 + 0.653917i
\(540\) 1485.96 + 2573.76i 0.118418 + 0.205106i
\(541\) −3361.41 + 1223.45i −0.267132 + 0.0972279i −0.472113 0.881538i \(-0.656509\pi\)
0.204982 + 0.978766i \(0.434286\pi\)
\(542\) 7672.77 2792.66i 0.608070 0.221319i
\(543\) −12312.6 21326.0i −0.973082 1.68543i
\(544\) 2037.31 3528.73i 0.160568 0.278112i
\(545\) −1729.69 + 9809.58i −0.135948 + 0.771002i
\(546\) −2334.96 + 1959.27i −0.183017 + 0.153569i
\(547\) 6284.63 + 5273.43i 0.491246 + 0.412204i 0.854473 0.519497i \(-0.173881\pi\)
−0.363227 + 0.931701i \(0.618325\pi\)
\(548\) 259.040 + 1469.09i 0.0201927 + 0.114519i
\(549\) 344.661 + 125.446i 0.0267937 + 0.00975212i
\(550\) 3755.01 0.291117
\(551\) 3380.99 4305.84i 0.261407 0.332913i
\(552\) 22600.1 1.74262
\(553\) −267.771 97.4606i −0.0205909 0.00749448i
\(554\) −1217.24 6903.33i −0.0933497 0.529412i
\(555\) −4367.35 3664.64i −0.334025 0.280280i
\(556\) 59.8122 50.1884i 0.00456223 0.00382817i
\(557\) 2975.28 16873.6i 0.226331 1.28359i −0.633792 0.773503i \(-0.718503\pi\)
0.860124 0.510086i \(-0.170386\pi\)
\(558\) −300.905 + 521.183i −0.0228286 + 0.0395402i
\(559\) −13500.1 23382.9i −1.02146 1.76921i
\(560\) 791.638 288.133i 0.0597372 0.0217426i
\(561\) 5030.71 1831.03i 0.378604 0.137800i
\(562\) −3940.56 6825.25i −0.295769 0.512288i
\(563\) −2994.16 + 5186.04i −0.224137 + 0.388216i −0.956060 0.293171i \(-0.905290\pi\)
0.731923 + 0.681387i \(0.238623\pi\)
\(564\) 1191.20 6755.64i 0.0889337 0.504368i
\(565\) −9004.73 + 7555.86i −0.670499 + 0.562615i
\(566\) 9599.03 + 8054.54i 0.712857 + 0.598158i
\(567\) −387.774 2199.18i −0.0287213 0.162887i
\(568\) 5405.03 + 1967.27i 0.399278 + 0.145325i
\(569\) −2828.73 −0.208413 −0.104206 0.994556i \(-0.533230\pi\)
−0.104206 + 0.994556i \(0.533230\pi\)
\(570\) −7414.87 3965.72i −0.544868 0.291414i
\(571\) −14475.6 −1.06092 −0.530459 0.847711i \(-0.677980\pi\)
−0.530459 + 0.847711i \(0.677980\pi\)
\(572\) −6041.22 2198.83i −0.441602 0.160730i
\(573\) −349.664 1983.04i −0.0254929 0.144577i
\(574\) −796.336 668.206i −0.0579067 0.0485895i
\(575\) −7556.79 + 6340.90i −0.548069 + 0.459885i
\(576\) 163.207 925.591i 0.0118060 0.0669554i
\(577\) 8589.46 14877.4i 0.619729 1.07340i −0.369805 0.929109i \(-0.620576\pi\)
0.989535 0.144294i \(-0.0460910\pi\)
\(578\) 4225.21 + 7318.27i 0.304058 + 0.526644i
\(579\) 14578.9 5306.29i 1.04642 0.380867i
\(580\) 1362.32 495.844i 0.0975297 0.0354979i
\(581\) 413.664 + 716.488i 0.0295382 + 0.0511616i
\(582\) 5540.42 9596.28i 0.394601 0.683468i
\(583\) −3319.18 + 18824.0i −0.235792 + 1.33724i
\(584\) 15284.0 12824.8i 1.08297 0.908723i
\(585\) 916.295 + 768.863i 0.0647592 + 0.0543395i
\(586\) 1606.81 + 9112.66i 0.113271 + 0.642390i
\(587\) −18207.6 6627.03i −1.28025 0.465974i −0.389737 0.920926i \(-0.627434\pi\)
−0.890516 + 0.454952i \(0.849656\pi\)
\(588\) −4790.38 −0.335973
\(589\) −410.037 12622.1i −0.0286847 0.882998i
\(590\) 4077.63 0.284531
\(591\) 7762.53 + 2825.33i 0.540284 + 0.196647i
\(592\) −798.774 4530.07i −0.0554551 0.314501i
\(593\) 7818.84 + 6560.79i 0.541453 + 0.454333i 0.872034 0.489445i \(-0.162800\pi\)
−0.330582 + 0.943777i \(0.607245\pi\)
\(594\) −6765.78 + 5677.17i −0.467346 + 0.392150i
\(595\) −145.863 + 827.231i −0.0100501 + 0.0569969i
\(596\) 2901.07 5024.81i 0.199384 0.345343i
\(597\) 1448.45 + 2508.79i 0.0992984 + 0.171990i
\(598\) −31652.6 + 11520.6i −2.16450 + 0.787813i
\(599\) −1493.84 + 543.713i −0.101898 + 0.0370877i −0.392466 0.919767i \(-0.628378\pi\)
0.290568 + 0.956854i \(0.406156\pi\)
\(600\) 3802.14 + 6585.49i 0.258703 + 0.448086i
\(601\) −457.078 + 791.682i −0.0310226 + 0.0537327i −0.881120 0.472893i \(-0.843210\pi\)
0.850097 + 0.526626i \(0.176543\pi\)
\(602\) 367.224 2082.63i 0.0248620 0.140999i
\(603\) 581.951 488.315i 0.0393016 0.0329780i
\(604\) 1739.33 + 1459.47i 0.117173 + 0.0983197i
\(605\) −760.835 4314.91i −0.0511278 0.289960i
\(606\) −3527.95 1284.07i −0.236490 0.0860754i
\(607\) 8012.94 0.535807 0.267904 0.963446i \(-0.413669\pi\)
0.267904 + 0.963446i \(0.413669\pi\)
\(608\) 3550.92 + 8850.76i 0.236857 + 0.590371i
\(609\) −1024.22 −0.0681503
\(610\) 3819.85 + 1390.31i 0.253543 + 0.0922821i
\(611\) 7091.69 + 40219.0i 0.469556 + 2.66299i
\(612\) 123.821 + 103.898i 0.00817839 + 0.00686248i
\(613\) 2659.88 2231.90i 0.175255 0.147056i −0.550941 0.834544i \(-0.685731\pi\)
0.726196 + 0.687488i \(0.241287\pi\)
\(614\) −1826.34 + 10357.7i −0.120041 + 0.680786i
\(615\) −3425.04 + 5932.34i −0.224570 + 0.388967i
\(616\) −1005.67 1741.87i −0.0657784 0.113931i
\(617\) −4629.25 + 1684.91i −0.302053 + 0.109938i −0.488600 0.872508i \(-0.662492\pi\)
0.186547 + 0.982446i \(0.440270\pi\)
\(618\) −8830.64 + 3214.09i −0.574790 + 0.209207i
\(619\) 4647.29 + 8049.34i 0.301762 + 0.522666i 0.976535 0.215359i \(-0.0690920\pi\)
−0.674774 + 0.738025i \(0.735759\pi\)
\(620\) 1672.14 2896.23i 0.108314 0.187605i
\(621\) 4029.08 22850.1i 0.260357 1.47656i
\(622\) 5868.72 4924.44i 0.378319 0.317447i
\(623\) −908.273 762.132i −0.0584096 0.0490115i
\(624\) 2814.09 + 15959.5i 0.180535 + 1.02386i
\(625\) 4796.46 + 1745.77i 0.306974 + 0.111729i
\(626\) 2027.86 0.129472
\(627\) −3900.91 + 11907.1i −0.248464 + 0.758412i
\(628\) −4675.07 −0.297063
\(629\) 4309.96 + 1568.70i 0.273211 + 0.0994405i
\(630\) 16.2684 + 92.2628i 0.00102881 + 0.00583466i
\(631\) 16192.7 + 13587.3i 1.02159 + 0.857212i 0.989826 0.142284i \(-0.0454445\pi\)
0.0317593 + 0.999496i \(0.489889\pi\)
\(632\) −1859.53 + 1560.33i −0.117038 + 0.0982067i
\(633\) 2755.81 15629.0i 0.173039 0.981353i
\(634\) 1150.52 1992.76i 0.0720709 0.124830i
\(635\) −5902.24 10223.0i −0.368856 0.638877i
\(636\) −9106.29 + 3314.42i −0.567748 + 0.206643i
\(637\) 26799.1 9754.07i 1.66691 0.606704i
\(638\) 2154.22 + 3731.21i 0.133677 + 0.231536i
\(639\) −199.612 + 345.738i −0.0123576 + 0.0214041i
\(640\) 495.673 2811.10i 0.0306143 0.173623i
\(641\) 5782.43 4852.03i 0.356306 0.298976i −0.447010 0.894529i \(-0.647511\pi\)
0.803316 + 0.595552i \(0.203067\pi\)
\(642\) −1501.67 1260.05i −0.0923151 0.0774615i
\(643\) −3213.94 18227.2i −0.197116 1.11790i −0.909373 0.415981i \(-0.863438\pi\)
0.712257 0.701918i \(-0.247673\pi\)
\(644\) 1243.05 + 452.435i 0.0760609 + 0.0276839i
\(645\) −13935.2 −0.850695
\(646\) 6696.66 + 957.771i 0.407858 + 0.0583328i
\(647\) 6739.57 0.409521 0.204760 0.978812i \(-0.434359\pi\)
0.204760 + 0.978812i \(0.434359\pi\)
\(648\) −17875.8 6506.27i −1.08369 0.394430i
\(649\) −1055.09 5983.74i −0.0638153 0.361914i
\(650\) −8682.09 7285.14i −0.523907 0.439610i
\(651\) −1809.91 + 1518.69i −0.108964 + 0.0914320i
\(652\) −1541.95 + 8744.85i −0.0926189 + 0.525268i
\(653\) −10072.9 + 17446.7i −0.603647 + 1.04555i 0.388617 + 0.921399i \(0.372953\pi\)
−0.992264 + 0.124147i \(0.960380\pi\)
\(654\) −7503.94 12997.2i −0.448666 0.777112i
\(655\) −410.812 + 149.523i −0.0245065 + 0.00891963i
\(656\) −5193.62 + 1890.32i −0.309111 + 0.112507i
\(657\) 692.400 + 1199.27i 0.0411159 + 0.0712147i
\(658\) −1599.35 + 2770.15i −0.0947554 + 0.164121i
\(659\) 874.078 4957.14i 0.0516681 0.293024i −0.948014 0.318228i \(-0.896912\pi\)
0.999682 + 0.0252036i \(0.00802341\pi\)
\(660\) −2541.79 + 2132.81i −0.149907 + 0.125787i
\(661\) −13584.8 11399.0i −0.799377 0.670757i 0.148670 0.988887i \(-0.452501\pi\)
−0.948047 + 0.318130i \(0.896945\pi\)
\(662\) 1687.57 + 9570.71i 0.0990777 + 0.561897i
\(663\) −15184.1 5526.55i −0.889442 0.323731i
\(664\) 7047.74 0.411906
\(665\) −1311.93 1464.20i −0.0765031 0.0853821i
\(666\) 511.549 0.0297630
\(667\) −10636.0 3871.18i −0.617431 0.224726i
\(668\) −1299.99 7372.59i −0.0752964 0.427027i
\(669\) 12620.1 + 10589.5i 0.729331 + 0.611981i
\(670\) 6449.72 5411.96i 0.371902 0.312063i
\(671\) 1051.83 5965.20i 0.0605146 0.343195i
\(672\) 892.072 1545.11i 0.0512090 0.0886965i
\(673\) 57.3669 + 99.3624i 0.00328578 + 0.00569114i 0.867664 0.497152i \(-0.165621\pi\)
−0.864378 + 0.502843i \(0.832287\pi\)
\(674\) 19522.5 7105.62i 1.11570 0.406081i
\(675\) 7336.16 2670.14i 0.418324 0.152258i
\(676\) 6767.34 + 11721.4i 0.385033 + 0.666897i
\(677\) −15180.1 + 26292.8i −0.861773 + 1.49263i 0.00844344 + 0.999964i \(0.497312\pi\)
−0.870216 + 0.492670i \(0.836021\pi\)
\(678\) 3075.44 17441.7i 0.174206 0.987971i
\(679\) 1984.59 1665.27i 0.112167 0.0941197i
\(680\) 5481.52 + 4599.54i 0.309127 + 0.259389i
\(681\) −1246.69 7070.32i −0.0701515 0.397849i
\(682\) 9339.28 + 3399.22i 0.524369 + 0.190855i
\(683\) −11815.2 −0.661925 −0.330962 0.943644i \(-0.607373\pi\)
−0.330962 + 0.943644i \(0.607373\pi\)
\(684\) −370.229 + 77.7538i −0.0206960 + 0.00434648i
\(685\) −4583.59 −0.255664
\(686\) 4250.46 + 1547.04i 0.236565 + 0.0861025i
\(687\) −5021.72 28479.6i −0.278880 1.58161i
\(688\) −8613.04 7227.20i −0.477281 0.400486i
\(689\) 44195.1 37084.1i 2.44368 2.05049i
\(690\) −3018.84 + 17120.7i −0.166558 + 0.944599i
\(691\) −7277.33 + 12604.7i −0.400641 + 0.693930i −0.993803 0.111153i \(-0.964546\pi\)
0.593163 + 0.805083i \(0.297879\pi\)
\(692\) 4473.08 + 7747.61i 0.245724 + 0.425607i
\(693\) 131.182 47.7463i 0.00719075 0.00261722i
\(694\) −24342.4 + 8859.92i −1.33145 + 0.484608i
\(695\) 119.954 + 207.767i 0.00654695 + 0.0113396i
\(696\) −4362.50 + 7556.07i −0.237586 + 0.411512i
\(697\) 956.950 5427.13i 0.0520044 0.294931i
\(698\) 6495.82 5450.64i 0.352250 0.295573i
\(699\) −1496.22 1255.48i −0.0809619 0.0679351i
\(700\) 77.2897 + 438.331i 0.00417325 + 0.0236677i
\(701\) 28341.4 + 10315.4i 1.52702 + 0.555789i 0.962889 0.269897i \(-0.0869898\pi\)
0.564129 + 0.825687i \(0.309212\pi\)
\(702\) 26657.7 1.43324
\(703\) −9117.34 + 5666.36i −0.489142 + 0.303998i
\(704\) −15521.6 −0.830954
\(705\) 19806.7 + 7209.03i 1.05810 + 0.385118i
\(706\) −4666.47 26464.9i −0.248761 1.41079i
\(707\) −672.412 564.220i −0.0357689 0.0300137i
\(708\) 2359.77 1980.08i 0.125262 0.105107i
\(709\) −1539.66 + 8731.85i −0.0815560 + 0.462527i 0.916491 + 0.400056i \(0.131009\pi\)
−0.998047 + 0.0624711i \(0.980102\pi\)
\(710\) −2212.29 + 3831.79i −0.116937 + 0.202542i
\(711\) −84.2410 145.910i −0.00444344 0.00769626i
\(712\) −9491.18 + 3454.51i −0.499574 + 0.181830i
\(713\) −24535.0 + 8930.00i −1.28870 + 0.469048i
\(714\) −632.799 1096.04i −0.0331679 0.0574485i
\(715\) 9876.87 17107.2i 0.516607 0.894790i
\(716\) 1083.38 6144.15i 0.0565472 0.320695i
\(717\) −18286.2 + 15343.9i −0.952456 + 0.799205i
\(718\) −1594.39 1337.85i −0.0828720 0.0695379i
\(719\) 1324.91 + 7513.95i 0.0687217 + 0.389740i 0.999696 + 0.0246554i \(0.00784886\pi\)
−0.930974 + 0.365085i \(0.881040\pi\)
\(720\) 468.061 + 170.360i 0.0242272 + 0.00881800i
\(721\) −2197.11 −0.113488
\(722\) −11442.5 + 10942.8i −0.589815 + 0.564058i
\(723\) −30268.6 −1.55699
\(724\) −11538.0 4199.49i −0.592274 0.215570i
\(725\) −661.315 3750.50i −0.0338767 0.192124i
\(726\) 5057.02 + 4243.34i 0.258517 + 0.216922i
\(727\) −5040.04 + 4229.10i −0.257118 + 0.215748i −0.762230 0.647306i \(-0.775896\pi\)
0.505112 + 0.863054i \(0.331451\pi\)
\(728\) −1054.18 + 5978.53i −0.0536681 + 0.304367i
\(729\) −9141.87 + 15834.2i −0.464455 + 0.804460i
\(730\) 7673.82 + 13291.5i 0.389070 + 0.673889i
\(731\) 10534.7 3834.32i 0.533024 0.194005i
\(732\) 2885.72 1050.32i 0.145709 0.0530339i
\(733\) 3341.60 + 5787.83i 0.168383 + 0.291648i 0.937852 0.347037i \(-0.112812\pi\)
−0.769468 + 0.638685i \(0.779479\pi\)
\(734\) 252.730 437.741i 0.0127090 0.0220127i
\(735\) 2555.94 14495.5i 0.128268 0.727446i
\(736\) 15103.6 12673.4i 0.756423 0.634714i
\(737\) −9610.69 8064.33i −0.480345 0.403057i
\(738\) −106.731 605.299i −0.00532359 0.0301916i
\(739\) 11769.3 + 4283.68i 0.585848 + 0.213231i 0.617902 0.786255i \(-0.287983\pi\)
−0.0320543 + 0.999486i \(0.510205\pi\)
\(740\) −2842.69 −0.141215
\(741\) 32120.5 19962.7i 1.59241 0.989672i
\(742\) 4518.70 0.223567
\(743\) 14254.7 + 5188.28i 0.703841 + 0.256177i 0.669050 0.743217i \(-0.266701\pi\)
0.0347911 + 0.999395i \(0.488923\pi\)
\(744\) 3494.98 + 19821.0i 0.172221 + 0.976711i
\(745\) 13656.9 + 11459.5i 0.671612 + 0.563550i
\(746\) −6778.06 + 5687.47i −0.332657 + 0.279133i
\(747\) −84.9424 + 481.732i −0.00416048 + 0.0235953i
\(748\) 1334.68 2311.74i 0.0652419 0.113002i
\(749\) −229.159 396.915i −0.0111793 0.0193631i
\(750\) −17422.8 + 6341.37i −0.848253 + 0.308739i
\(751\) −16800.1 + 6114.75i −0.816306 + 0.297111i −0.716226 0.697868i \(-0.754132\pi\)
−0.100080 + 0.994979i \(0.531910\pi\)
\(752\) 8503.24 + 14728.1i 0.412342 + 0.714198i
\(753\) −12017.9 + 20815.7i −0.581617 + 1.00739i
\(754\) 2258.13 12806.5i 0.109067 0.618547i
\(755\) −5344.32 + 4484.42i −0.257616 + 0.216165i
\(756\) −801.970 672.932i −0.0385812 0.0323734i
\(757\) −431.651 2448.01i −0.0207247 0.117536i 0.972690 0.232107i \(-0.0745618\pi\)
−0.993415 + 0.114571i \(0.963451\pi\)
\(758\) 6953.71 + 2530.94i 0.333206 + 0.121277i
\(759\) 25905.0 1.23885
\(760\) −16389.9 + 3442.13i −0.782269 + 0.164289i
\(761\) −8995.52 −0.428498 −0.214249 0.976779i \(-0.568730\pi\)
−0.214249 + 0.976779i \(0.568730\pi\)
\(762\) 16713.0 + 6083.02i 0.794550 + 0.289192i
\(763\) −609.305 3455.54i −0.0289100 0.163957i
\(764\) −769.130 645.376i −0.0364216 0.0305614i
\(765\) −380.457 + 319.241i −0.0179810 + 0.0150878i
\(766\) 1643.22 9319.15i 0.0775089 0.439575i
\(767\) −9169.60 + 15882.2i −0.431675 + 0.747684i
\(768\) −9631.39 16682.0i −0.452530 0.783804i
\(769\) 7137.38 2597.80i 0.334695 0.121819i −0.169205 0.985581i \(-0.554120\pi\)
0.503900 + 0.863762i \(0.331898\pi\)
\(770\) 1453.88 529.169i 0.0680444 0.0247661i
\(771\) 10925.1 + 18922.8i 0.510320 + 0.883900i
\(772\) 3867.90 6699.39i 0.180322 0.312327i
\(773\) 746.091 4231.29i 0.0347154 0.196881i −0.962518 0.271219i \(-0.912573\pi\)
0.997233 + 0.0743379i \(0.0236843\pi\)
\(774\) 957.835 803.719i 0.0444815 0.0373244i
\(775\) −6729.78 5646.95i −0.311923 0.261735i
\(776\) −3832.30 21734.1i −0.177283 1.00542i
\(777\) 1887.19 + 686.881i 0.0871333 + 0.0317139i
\(778\) −3217.95 −0.148289
\(779\) 8607.07 + 9606.01i 0.395867 + 0.441811i
\(780\) 10014.8 0.459729
\(781\) 6195.41 + 2254.95i 0.283853 + 0.103314i
\(782\) −2428.64 13773.5i −0.111059 0.629846i
\(783\) 6861.91 + 5757.82i 0.313186 + 0.262794i
\(784\) 9097.53 7633.73i 0.414428 0.347747i
\(785\) 2494.41 14146.5i 0.113413 0.643199i
\(786\) 329.342 570.438i 0.0149456 0.0258866i
\(787\) −12826.2 22215.6i −0.580945 1.00623i −0.995368 0.0961423i \(-0.969350\pi\)
0.414422 0.910085i \(-0.363984\pi\)
\(788\) 3870.52 1408.75i 0.174976 0.0636862i
\(789\) −27973.5 + 10181.5i −1.26221 + 0.459407i
\(790\) −933.637 1617.11i −0.0420472 0.0728279i
\(791\) 2070.39 3586.02i 0.0930653 0.161194i
\(792\) 206.505 1171.15i 0.00926494 0.0525441i
\(793\) −14005.1 + 11751.7i −0.627158 + 0.526248i
\(794\) −4572.90 3837.12i −0.204391 0.171504i
\(795\) −5170.54 29323.6i −0.230667 1.30818i
\(796\) 1357.33 + 494.027i 0.0604387 + 0.0219979i
\(797\) −19912.2 −0.884978 −0.442489 0.896774i \(-0.645904\pi\)
−0.442489 + 0.896774i \(0.645904\pi\)
\(798\) 2932.25 + 419.376i 0.130076 + 0.0186037i
\(799\) −16957.0 −0.750808
\(800\) 6233.90 + 2268.95i 0.275502 + 0.100275i
\(801\) −121.733 690.383i −0.00536982 0.0304538i
\(802\) 6358.98 + 5335.82i 0.279979 + 0.234931i
\(803\) 17519.0 14700.2i 0.769903 0.646025i
\(804\) 1104.50 6263.93i 0.0484486 0.274766i
\(805\) −2032.29 + 3520.02i −0.0889797 + 0.154117i
\(806\) −14998.8 25978.7i −0.655472 1.13531i
\(807\) 2996.78 1090.74i 0.130721 0.0475784i
\(808\) −7026.50 + 2557.44i −0.305930 + 0.111349i
\(809\) −12817.7 22200.9i −0.557040 0.964822i −0.997742 0.0671685i \(-0.978603\pi\)
0.440701 0.897654i \(-0.354730\pi\)
\(810\) 7316.59 12672.7i 0.317381 0.549721i
\(811\) −184.217 + 1044.74i −0.00797623 + 0.0452354i −0.988536 0.150985i \(-0.951756\pi\)
0.980560 + 0.196220i \(0.0628667\pi\)
\(812\) −391.213 + 328.266i −0.0169075 + 0.0141871i
\(813\) 14519.1 + 12182.9i 0.626330 + 0.525553i
\(814\) −1466.98 8319.68i −0.0631668 0.358237i
\(815\) −25638.8 9331.74i −1.10195 0.401076i
\(816\) −6728.80 −0.288671
\(817\) −8168.81 + 24934.5i −0.349805 + 1.06774i
\(818\) 13504.0 0.577210
\(819\) −395.943 144.112i −0.0168930 0.00614856i
\(820\) 593.104 + 3363.66i 0.0252586 + 0.143249i
\(821\) −29115.3 24430.6i −1.23768 1.03853i −0.997702 0.0677532i \(-0.978417\pi\)
−0.239973 0.970780i \(-0.577139\pi\)
\(822\) 5290.31 4439.09i 0.224478 0.188359i
\(823\) −6311.23 + 35792.8i −0.267309 + 1.51599i 0.495068 + 0.868854i \(0.335143\pi\)
−0.762377 + 0.647133i \(0.775968\pi\)
\(824\) −9358.22 + 16208.9i −0.395642 + 0.685272i
\(825\) 4358.13 + 7548.50i 0.183916 + 0.318551i
\(826\) −1349.77 + 491.276i −0.0568577 + 0.0206945i
\(827\) 36176.5 13167.2i 1.52114 0.553648i 0.559704 0.828693i \(-0.310915\pi\)
0.961432 + 0.275044i \(0.0886926\pi\)
\(828\) 391.066 + 677.347i 0.0164136 + 0.0284293i
\(829\) 10889.6 18861.4i 0.456227 0.790208i −0.542531 0.840036i \(-0.682534\pi\)
0.998758 + 0.0498281i \(0.0158673\pi\)
\(830\) −941.410 + 5339.00i −0.0393697 + 0.223276i
\(831\) 12464.6 10459.1i 0.520329 0.436608i
\(832\) 35888.0 + 30113.6i 1.49542 + 1.25481i
\(833\) 2056.24 + 11661.5i 0.0855277 + 0.485051i
\(834\) −339.666 123.628i −0.0141027 0.00513298i
\(835\) 23002.7 0.953343
\(836\) 2326.28 + 5798.31i 0.0962393 + 0.239879i
\(837\) 20663.3 0.853319
\(838\) −15603.1 5679.06i −0.643198 0.234105i
\(839\) 3543.68 + 20097.2i 0.145818 + 0.826976i 0.966707 + 0.255887i \(0.0823676\pi\)
−0.820888 + 0.571089i \(0.806521\pi\)
\(840\) 2400.18 + 2013.99i 0.0985880 + 0.0827252i
\(841\) −15335.7 + 12868.2i −0.628797 + 0.527623i
\(842\) −298.397 + 1692.29i −0.0122131 + 0.0692640i
\(843\) 9146.95 15843.0i 0.373710 0.647285i
\(844\) −3956.53 6852.91i −0.161362 0.279487i
\(845\) −39079.1 + 14223.6i −1.59096 + 0.579062i
\(846\) −1777.19 + 646.845i −0.0722236 + 0.0262872i
\(847\) 771.713 + 1336.65i 0.0313062 + 0.0542240i
\(848\) 12012.3 20805.9i 0.486442 0.842543i
\(849\) −5050.82 + 28644.6i −0.204174 + 1.15793i
\(850\) 3604.91 3024.88i 0.145467 0.122062i
\(851\) 17001.3 + 14265.8i 0.684837 + 0.574646i
\(852\) 580.429 + 3291.78i 0.0233394 + 0.132364i
\(853\) 33402.0 + 12157.3i 1.34075 + 0.487995i 0.910050 0.414498i \(-0.136043\pi\)
0.430705 + 0.902493i \(0.358265\pi\)
\(854\) −1431.94 −0.0573772
\(855\) −37.7411 1161.78i −0.00150961 0.0464702i
\(856\) −3904.25 −0.155893
\(857\) −13505.0 4915.41i −0.538298 0.195925i 0.0585415 0.998285i \(-0.481355\pi\)
−0.596840 + 0.802360i \(0.703577\pi\)
\(858\) 5168.21 + 29310.4i 0.205641 + 1.16625i
\(859\) 13143.2 + 11028.5i 0.522049 + 0.438051i 0.865345 0.501176i \(-0.167099\pi\)
−0.343296 + 0.939227i \(0.611543\pi\)
\(860\) −5322.71 + 4466.28i −0.211050 + 0.177092i
\(861\) 419.017 2376.36i 0.0165854 0.0940606i
\(862\) −1381.01 + 2391.98i −0.0545678 + 0.0945143i
\(863\) −16963.8 29382.1i −0.669123 1.15895i −0.978150 0.207901i \(-0.933337\pi\)
0.309027 0.951053i \(-0.399997\pi\)
\(864\) −14662.7 + 5336.77i −0.577354 + 0.210140i
\(865\) −25830.5 + 9401.54i −1.01533 + 0.369551i
\(866\) 4115.54 + 7128.33i 0.161492 + 0.279712i
\(867\) −9807.68 + 16987.4i −0.384183 + 0.665424i
\(868\) −204.568 + 1160.16i −0.00799942 + 0.0453669i
\(869\) −2131.45 + 1788.50i −0.0832043 + 0.0698167i
\(870\) −5141.36 4314.12i −0.200355 0.168117i
\(871\) 6575.51 + 37291.6i 0.255801 + 1.45072i
\(872\) −28088.1 10223.2i −1.09081 0.397021i
\(873\) 1531.77 0.0593844
\(874\) 28864.7 + 15437.8i 1.11712 + 0.597473i
\(875\) −4334.87 −0.167481
\(876\) 10895.2 + 3965.53i 0.420223 + 0.152949i
\(877\) −6443.83 36544.8i −0.248110 1.40710i −0.813157 0.582044i \(-0.802253\pi\)
0.565047 0.825059i \(-0.308858\pi\)
\(878\) 3564.60 + 2991.06i 0.137015 + 0.114970i
\(879\) −16453.8 + 13806.4i −0.631368 + 0.529781i
\(880\) 1428.42 8100.96i 0.0547181 0.310322i
\(881\) 12253.3 21223.4i 0.468587 0.811616i −0.530769 0.847517i \(-0.678097\pi\)
0.999355 + 0.0359006i \(0.0114300\pi\)
\(882\) 660.349 + 1143.76i 0.0252099 + 0.0436648i
\(883\) 35378.6 12876.8i 1.34834 0.490756i 0.435912 0.899989i \(-0.356426\pi\)
0.912430 + 0.409233i \(0.134204\pi\)
\(884\) −7571.00 + 2755.62i −0.288055 + 0.104843i
\(885\) 4732.56 + 8197.04i 0.179755 + 0.311345i
\(886\) −12952.9 + 22435.0i −0.491151 + 0.850699i
\(887\) −2593.78 + 14710.1i −0.0981856 + 0.556838i 0.895539 + 0.444983i \(0.146790\pi\)
−0.993725 + 0.111855i \(0.964321\pi\)
\(888\) 13105.6 10996.9i 0.495263 0.415575i
\(889\) 3185.42 + 2672.89i 0.120175 + 0.100839i
\(890\) −1349.16 7651.46i −0.0508134 0.288177i
\(891\) −20489.8 7457.68i −0.770409 0.280406i
\(892\) 8214.38 0.308338
\(893\) 24509.9 31214.4i 0.918468 1.16971i
\(894\) −26860.8 −1.00488
\(895\) 18013.9 + 6556.51i 0.672779 + 0.244871i
\(896\) 174.607 + 990.243i 0.00651026 + 0.0369215i
\(897\) −59895.7 50258.5i −2.22950 1.87077i
\(898\) −9887.66 + 8296.73i −0.367434 + 0.308313i
\(899\) 1750.35 9926.72i 0.0649359 0.368270i
\(900\) −131.582 + 227.907i −0.00487342 + 0.00844100i
\(901\) 11977.3 + 20745.3i 0.442866 + 0.767066i
\(902\) −9538.33 + 3471.67i −0.352097 + 0.128153i
\(903\) 4612.80 1678.92i 0.169994 0.0618727i
\(904\) −17637.0 30548.1i −0.648891 1.12391i
\(905\) 18863.6 32672.7i 0.692870 1.20009i
\(906\) 1825.28 10351.7i 0.0669325 0.379593i
\(907\) 3979.99 3339.61i 0.145704 0.122260i −0.567022 0.823702i \(-0.691905\pi\)
0.712726 + 0.701442i \(0.247460\pi\)
\(908\) −2742.25 2301.02i −0.100225 0.0840992i
\(909\) −90.1213 511.103i −0.00328838 0.0186493i
\(910\) −4388.21 1597.18i −0.159855 0.0581824i
\(911\) 46091.3 1.67626 0.838130 0.545470i \(-0.183649\pi\)
0.838130 + 0.545470i \(0.183649\pi\)
\(912\) 9725.91 12386.4i 0.353133 0.449730i
\(913\) 8078.34 0.292830
\(914\) −23973.0 8725.47i −0.867568 0.315769i
\(915\) 1638.51 + 9292.45i 0.0591994 + 0.335737i
\(916\) −11045.9 9268.63i −0.398436 0.334328i
\(917\) 117.971 98.9897i 0.00424837 0.00356481i
\(918\) −1922.04 + 10900.4i −0.0691033 + 0.391904i
\(919\) 14318.6 24800.5i 0.513957 0.890200i −0.485912 0.874008i \(-0.661512\pi\)
0.999869 0.0161922i \(-0.00515436\pi\)
\(920\) 17312.4 + 29985.9i 0.620404 + 1.07457i
\(921\) −22941.2 + 8349.91i −0.820780 + 0.298739i
\(922\) 34692.6 12627.1i 1.23920 0.451030i
\(923\) −9949.78 17233.5i −0.354822 0.614570i
\(924\) 584.414 1012.24i 0.0208072 0.0360391i
\(925\) −1296.71 + 7354.03i −0.0460927 + 0.261404i
\(926\) −25868.9 + 21706.6i −0.918039 + 0.770327i
\(927\) −995.134 835.016i −0.0352583 0.0295853i
\(928\) 1321.76 + 7496.07i 0.0467552 + 0.265162i
\(929\) 18005.8 + 6553.57i 0.635899 + 0.231448i 0.639797 0.768544i \(-0.279018\pi\)
−0.00389775 + 0.999992i \(0.501241\pi\)
\(930\) −15482.2 −0.545894
\(931\) −24438.6 13070.6i −0.860305 0.460120i
\(932\) −973.885 −0.0342282
\(933\) 16710.7 + 6082.18i 0.586369 + 0.213421i
\(934\) 1537.90 + 8721.89i 0.0538777 + 0.305556i
\(935\) 6283.09 + 5272.14i 0.219764 + 0.184403i
\(936\) −2749.62 + 2307.21i −0.0960195 + 0.0805699i
\(937\) 6334.38 35924.1i 0.220849 1.25250i −0.649615 0.760263i \(-0.725070\pi\)
0.870464 0.492232i \(-0.163819\pi\)
\(938\) −1482.94 + 2568.52i −0.0516201 + 0.0894086i
\(939\) 2353.56 + 4076.49i 0.0817951 + 0.141673i
\(940\) 9875.89 3594.53i 0.342677 0.124724i
\(941\) −11897.6 + 4330.37i −0.412168 + 0.150017i −0.539778 0.841807i \(-0.681492\pi\)
0.127610 + 0.991824i \(0.459270\pi\)
\(942\) 10821.5 + 18743.4i 0.374294 + 0.648295i
\(943\) 13333.0 23093.5i 0.460427 0.797483i
\(944\) −1326.13 + 7520.85i −0.0457223 + 0.259304i
\(945\) 2464.16 2067.67i 0.0848244 0.0711761i
\(946\) −15818.3 13273.1i −0.543653 0.456179i
\(947\) −486.150 2757.10i −0.0166819 0.0946078i 0.975330 0.220752i \(-0.0708510\pi\)
−0.992012 + 0.126144i \(0.959740\pi\)
\(948\) −1325.57 482.467i −0.0454140 0.0165293i
\(949\) −69026.2 −2.36110
\(950\) 357.604 + 11008.1i 0.0122129 + 0.375948i
\(951\) 5341.24 0.182126
\(952\) −2368.64 862.113i −0.0806386 0.0293501i
\(953\) 1703.59 + 9661.53i 0.0579062 + 0.328402i 0.999975 0.00701619i \(-0.00223334\pi\)
−0.942069 + 0.335419i \(0.891122\pi\)
\(954\) 2046.65 + 1717.34i 0.0694577 + 0.0582820i
\(955\) 2363.25 1983.00i 0.0800765 0.0671921i
\(956\) −2066.83 + 11721.6i −0.0699227 + 0.396551i
\(957\) −5000.43 + 8661.00i −0.168904 + 0.292550i
\(958\) −2366.91 4099.61i −0.0798240 0.138259i
\(959\) 1517.25 552.235i 0.0510893 0.0185950i
\(960\) 22721.0 8269.75i 0.763870 0.278026i
\(961\) 3269.43 + 5662.81i 0.109745 + 0.190085i
\(962\) −12749.2 + 22082.3i −0.427289 + 0.740086i
\(963\) 47.0557 266.866i 0.00157461 0.00893006i
\(964\) −11561.4 + 9701.21i −0.386275 + 0.324123i
\(965\) 18208.3 + 15278.6i 0.607405 + 0.509673i
\(966\) −1063.42 6030.96i −0.0354193 0.200873i
\(967\) 3374.58 + 1228.25i 0.112223 + 0.0408457i 0.397521 0.917593i \(-0.369871\pi\)
−0.285299 + 0.958439i \(0.592093\pi\)
\(968\) 13147.9 0.436561
\(969\) 5846.89 + 14573.5i 0.193838 + 0.483147i
\(970\) 16976.5 0.561941
\(971\) −22358.1 8137.68i −0.738935 0.268950i −0.0549927 0.998487i \(-0.517514\pi\)
−0.683942 + 0.729537i \(0.739736\pi\)
\(972\) −222.238 1260.37i −0.00733362 0.0415910i
\(973\) −64.7390 54.3224i −0.00213303 0.00178982i
\(974\) 5973.82 5012.63i 0.196523 0.164902i
\(975\) 4568.35 25908.4i 0.150056 0.851007i
\(976\) −3806.61 + 6593.24i −0.124843 + 0.216234i
\(977\) 3207.81 + 5556.09i 0.105043 + 0.181940i 0.913756 0.406264i \(-0.133169\pi\)
−0.808713 + 0.588204i \(0.799835\pi\)
\(978\) 38629.4 14059.9i 1.26302 0.459701i
\(979\) −10879.1 + 3959.66i −0.355155 + 0.129266i
\(980\) −3669.57 6355.89i −0.119612 0.207175i
\(981\) 1037.31 1796.68i 0.0337604 0.0584747i
\(982\) −8482.15 + 48104.7i −0.275638 + 1.56322i
\(983\) 849.162 712.531i 0.0275525 0.0231193i −0.628907 0.777480i \(-0.716498\pi\)
0.656460 + 0.754361i \(0.272053\pi\)
\(984\) −15746.6 13213.0i −0.510146 0.428063i
\(985\) 2197.68 + 12463.6i 0.0710901 + 0.403172i
\(986\) 5073.80 + 1846.71i 0.163877 + 0.0596464i
\(987\) −7424.91 −0.239450
\(988\) 5870.70 17919.7i 0.189040 0.577026i
\(989\) 54247.1 1.74414
\(990\) 859.616 + 312.875i 0.0275964 + 0.0100443i
\(991\) 31.9956 + 181.456i 0.00102560 + 0.00581648i 0.985316 0.170739i \(-0.0546156\pi\)
−0.984291 + 0.176556i \(0.943504\pi\)
\(992\) 13450.7 + 11286.5i 0.430504 + 0.361236i
\(993\) −17280.8 + 14500.4i −0.552257 + 0.463399i
\(994\) 270.649 1534.93i 0.00863630 0.0489789i
\(995\) −2219.11 + 3843.62i −0.0707041 + 0.122463i
\(996\) 2047.80 + 3546.89i 0.0651475 + 0.112839i
\(997\) 12241.5 4455.53i 0.388858 0.141533i −0.140190 0.990125i \(-0.544771\pi\)
0.529048 + 0.848592i \(0.322549\pi\)
\(998\) 35126.1 12784.9i 1.11413 0.405509i
\(999\) −8782.07 15211.0i −0.278131 0.481736i
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 19.4.e.a.4.2 24
3.2 odd 2 171.4.u.b.118.3 24
19.5 even 9 inner 19.4.e.a.5.2 yes 24
19.9 even 9 361.4.a.n.1.8 12
19.10 odd 18 361.4.a.m.1.5 12
57.5 odd 18 171.4.u.b.100.3 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
19.4.e.a.4.2 24 1.1 even 1 trivial
19.4.e.a.5.2 yes 24 19.5 even 9 inner
171.4.u.b.100.3 24 57.5 odd 18
171.4.u.b.118.3 24 3.2 odd 2
361.4.a.m.1.5 12 19.10 odd 18
361.4.a.n.1.8 12 19.9 even 9