Properties

Label 441.2.g.f.67.4
Level 441441
Weight 22
Character 441.67
Analytic conductor 3.5213.521
Analytic rank 00
Dimension 1010
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [441,2,Mod(67,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 4])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.67"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 441=3272 441 = 3^{2} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 441.g (of order 33, degree 22, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [10,2,-2,-4,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 3.521402729143.52140272914
Analytic rank: 00
Dimension: 1010
Relative dimension: 55 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: 10.0.991381711347.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x102x9+9x88x7+40x636x5+90x43x3+36x29x+9 x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 Copy content Toggle raw display
Coefficient ring: Z[a1,,a4]\Z[a_1, \ldots, a_{4}]
Coefficient ring index: 3 3
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 67.4
Root 0.9206201.59456i0.920620 - 1.59456i of defining polynomial
Character χ\chi == 441.67
Dual form 441.2.g.f.79.4

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(0.9206201.59456i)q2+(1.58800+0.691567i)q3+(0.6950841.20392i)q41.33475q5+(2.564691.89549i)q6+1.12285q8+(2.04347+2.19641i)q9+(1.22880+2.12835i)q10+1.51302q11+(0.2711992.39252i)q12+(2.588004.48254i)q13+(2.119580.923072i)q15+(2.423884.19829i)q16+(0.774463+1.34141i)q17+(5.383581.23637i)q18+(1.25211+2.16872i)q19+(0.927765+1.60694i)q20+(1.392912.41260i)q227.36079q23+(1.78308+0.776526i)q243.21843q25+(4.765138.25344i)q26+(1.72605+4.90110i)q27+(0.03097130.0536439i)q29+(3.42323+2.53001i)q30+(1.923883.33227i)q31+(3.340115.78523i)q32+(2.40267+1.04635i)q33+(1.42597+2.46986i)q34+(1.223923.98687i)q36+(0.2816080.487760i)q37+4.61087q38+(7.209715.32849i)q391.49873q40+(4.51188+7.81481i)q41+(5.09988+8.83325i)q43+(1.051671.82155i)q44+(2.727532.93167i)q45+(6.77649+11.7372i)q46+(4.75925+8.24327i)q47+(6.752524.99060i)q48+(2.96296+5.13199i)q50+(2.15752+1.59456i)q517.19550q52+(0.7553741.30835i)q53+(9.40414+1.75975i)q542.01950q55+(0.488532+4.30983i)q570.114051q58+(4.221667.31212i)q59+(0.361984+3.19342i)q60+(1.619582.80520i)q617.08467q622.60434q64+(3.45434+5.98309i)q65+(3.880422.86790i)q66+(3.466706.00449i)q67+2.15327q68+(11.68895.09048i)q6912.3304q71+(2.29451+2.46624i)q72+(1.379362.38912i)q731.03702q74+(5.110862.22576i)q75+(1.740643.01488i)q76+(1.8592016.4018i)q78+(2.959695.12633i)q79+(3.23529+5.60368i)q80+(0.648467+8.97661i)q81+(8.30746+14.3889i)q82+(2.801114.85167i)q83+(1.033721.79045i)q85+18.7802q86+(0.01208400.106605i)q87+1.69889q88+(0.7032871.21813i)q89+(7.18575+1.65025i)q90+(5.11636+8.86180i)q92+(0.7506376.62212i)q93+(8.76293+15.1778i)q94+(1.671262.89470i)q95+(1.3032011.4968i)q96+(6.09713+10.5605i)q97+(3.09180+3.32321i)q99+O(q100)q+(0.920620 - 1.59456i) q^{2} +(1.58800 + 0.691567i) q^{3} +(-0.695084 - 1.20392i) q^{4} -1.33475 q^{5} +(2.56469 - 1.89549i) q^{6} +1.12285 q^{8} +(2.04347 + 2.19641i) q^{9} +(-1.22880 + 2.12835i) q^{10} +1.51302 q^{11} +(-0.271199 - 2.39252i) q^{12} +(2.58800 - 4.48254i) q^{13} +(-2.11958 - 0.923072i) q^{15} +(2.42388 - 4.19829i) q^{16} +(-0.774463 + 1.34141i) q^{17} +(5.38358 - 1.23637i) q^{18} +(1.25211 + 2.16872i) q^{19} +(0.927765 + 1.60694i) q^{20} +(1.39291 - 2.41260i) q^{22} -7.36079 q^{23} +(1.78308 + 0.776526i) q^{24} -3.21843 q^{25} +(-4.76513 - 8.25344i) q^{26} +(1.72605 + 4.90110i) q^{27} +(-0.0309713 - 0.0536439i) q^{29} +(-3.42323 + 2.53001i) q^{30} +(-1.92388 - 3.33227i) q^{31} +(-3.34011 - 5.78523i) q^{32} +(2.40267 + 1.04635i) q^{33} +(1.42597 + 2.46986i) q^{34} +(1.22392 - 3.98687i) q^{36} +(-0.281608 - 0.487760i) q^{37} +4.61087 q^{38} +(7.20971 - 5.32849i) q^{39} -1.49873 q^{40} +(-4.51188 + 7.81481i) q^{41} +(5.09988 + 8.83325i) q^{43} +(-1.05167 - 1.82155i) q^{44} +(-2.72753 - 2.93167i) q^{45} +(-6.77649 + 11.7372i) q^{46} +(-4.75925 + 8.24327i) q^{47} +(6.75252 - 4.99060i) q^{48} +(-2.96296 + 5.13199i) q^{50} +(-2.15752 + 1.59456i) q^{51} -7.19550 q^{52} +(0.755374 - 1.30835i) q^{53} +(9.40414 + 1.75975i) q^{54} -2.01950 q^{55} +(0.488532 + 4.30983i) q^{57} -0.114051 q^{58} +(-4.22166 - 7.31212i) q^{59} +(0.361984 + 3.19342i) q^{60} +(1.61958 - 2.80520i) q^{61} -7.08467 q^{62} -2.60434 q^{64} +(-3.45434 + 5.98309i) q^{65} +(3.88042 - 2.86790i) q^{66} +(-3.46670 - 6.00449i) q^{67} +2.15327 q^{68} +(-11.6889 - 5.09048i) q^{69} -12.3304 q^{71} +(2.29451 + 2.46624i) q^{72} +(1.37936 - 2.38912i) q^{73} -1.03702 q^{74} +(-5.11086 - 2.22576i) q^{75} +(1.74064 - 3.01488i) q^{76} +(-1.85920 - 16.4018i) q^{78} +(2.95969 - 5.12633i) q^{79} +(-3.23529 + 5.60368i) q^{80} +(-0.648467 + 8.97661i) q^{81} +(8.30746 + 14.3889i) q^{82} +(-2.80111 - 4.85167i) q^{83} +(1.03372 - 1.79045i) q^{85} +18.7802 q^{86} +(-0.0120840 - 0.106605i) q^{87} +1.69889 q^{88} +(-0.703287 - 1.21813i) q^{89} +(-7.18575 + 1.65025i) q^{90} +(5.11636 + 8.86180i) q^{92} +(-0.750637 - 6.62212i) q^{93} +(8.76293 + 15.1778i) q^{94} +(-1.67126 - 2.89470i) q^{95} +(-1.30320 - 11.4968i) q^{96} +(6.09713 + 10.5605i) q^{97} +(3.09180 + 3.32321i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 10q+2q22q34q4+8q5+2q66q84q9+7q108q1122q12+8q1319q15+2q1612q172q18q195q20q226q23++35q99+O(q100) 10 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9} + 7 q^{10} - 8 q^{11} - 22 q^{12} + 8 q^{13} - 19 q^{15} + 2 q^{16} - 12 q^{17} - 2 q^{18} - q^{19} - 5 q^{20} - q^{22} - 6 q^{23}+ \cdots + 35 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/441Z)×\left(\mathbb{Z}/441\mathbb{Z}\right)^\times.

nn 199199 344344
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right)

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.920620 1.59456i 0.650977 1.12753i −0.331909 0.943311i 0.607693π-0.607693\pi
0.982886 0.184214i 0.0589739π-0.0589739\pi
33 1.58800 + 0.691567i 0.916831 + 0.399277i
44 −0.695084 1.20392i −0.347542 0.601960i
55 −1.33475 −0.596920 −0.298460 0.954422i 0.596473π-0.596473\pi
−0.298460 + 0.954422i 0.596473π0.596473\pi
66 2.56469 1.89549i 1.04703 0.773830i
77 0 0
88 1.12285 0.396987
99 2.04347 + 2.19641i 0.681156 + 0.732138i
1010 −1.22880 + 2.12835i −0.388581 + 0.673042i
1111 1.51302 0.456192 0.228096 0.973639i 0.426750π-0.426750\pi
0.228096 + 0.973639i 0.426750π0.426750\pi
1212 −0.271199 2.39252i −0.0782884 0.690661i
1313 2.58800 4.48254i 0.717781 1.24323i −0.244096 0.969751i 0.578491π-0.578491\pi
0.961877 0.273482i 0.0881755π-0.0881755\pi
1414 0 0
1515 −2.11958 0.923072i −0.547274 0.238336i
1616 2.42388 4.19829i 0.605971 1.04957i
1717 −0.774463 + 1.34141i −0.187835 + 0.325340i −0.944528 0.328430i 0.893480π-0.893480\pi
0.756693 + 0.653770i 0.226814π0.226814\pi
1818 5.38358 1.23637i 1.26892 0.291416i
1919 1.25211 + 2.16872i 0.287254 + 0.497538i 0.973153 0.230158i 0.0739244π-0.0739244\pi
−0.685900 + 0.727696i 0.740591π0.740591\pi
2020 0.927765 + 1.60694i 0.207455 + 0.359322i
2121 0 0
2222 1.39291 2.41260i 0.296970 0.514367i
2323 −7.36079 −1.53483 −0.767415 0.641151i 0.778457π-0.778457\pi
−0.767415 + 0.641151i 0.778457π0.778457\pi
2424 1.78308 + 0.776526i 0.363970 + 0.158508i
2525 −3.21843 −0.643687
2626 −4.76513 8.25344i −0.934518 1.61863i
2727 1.72605 + 4.90110i 0.332179 + 0.943216i
2828 0 0
2929 −0.0309713 0.0536439i −0.00575123 0.00996143i 0.863135 0.504972i 0.168497π-0.168497\pi
−0.868887 + 0.495011i 0.835164π0.835164\pi
3030 −3.42323 + 2.53001i −0.624993 + 0.461914i
3131 −1.92388 3.33227i −0.345540 0.598493i 0.639912 0.768448i 0.278971π-0.278971\pi
−0.985452 + 0.169956i 0.945638π0.945638\pi
3232 −3.34011 5.78523i −0.590453 1.02269i
3333 2.40267 + 1.04635i 0.418250 + 0.182147i
3434 1.42597 + 2.46986i 0.244552 + 0.423577i
3535 0 0
3636 1.22392 3.98687i 0.203987 0.664478i
3737 −0.281608 0.487760i −0.0462961 0.0801872i 0.841949 0.539557i 0.181408π-0.181408\pi
−0.888245 + 0.459370i 0.848075π0.848075\pi
3838 4.61087 0.747982
3939 7.20971 5.32849i 1.15448 0.853241i
4040 −1.49873 −0.236969
4141 −4.51188 + 7.81481i −0.704638 + 1.22047i 0.262185 + 0.965018i 0.415557π0.415557\pi
−0.966822 + 0.255450i 0.917776π0.917776\pi
4242 0 0
4343 5.09988 + 8.83325i 0.777724 + 1.34706i 0.933251 + 0.359226i 0.116959π0.116959\pi
−0.155526 + 0.987832i 0.549707π0.549707\pi
4444 −1.05167 1.82155i −0.158546 0.274609i
4545 −2.72753 2.93167i −0.406596 0.437028i
4646 −6.77649 + 11.7372i −0.999139 + 1.73056i
4747 −4.75925 + 8.24327i −0.694209 + 1.20240i 0.276238 + 0.961089i 0.410912π0.410912\pi
−0.970447 + 0.241315i 0.922421π0.922421\pi
4848 6.75252 4.99060i 0.974643 0.720330i
4949 0 0
5050 −2.96296 + 5.13199i −0.419025 + 0.725773i
5151 −2.15752 + 1.59456i −0.302113 + 0.223283i
5252 −7.19550 −0.997836
5353 0.755374 1.30835i 0.103759 0.179715i −0.809472 0.587159i 0.800246π-0.800246\pi
0.913230 + 0.407444i 0.133580π0.133580\pi
5454 9.40414 + 1.75975i 1.27974 + 0.239471i
5555 −2.01950 −0.272310
5656 0 0
5757 0.488532 + 4.30983i 0.0647077 + 0.570851i
5858 −0.114051 −0.0149757
5959 −4.22166 7.31212i −0.549613 0.951957i −0.998301 0.0582689i 0.981442π-0.981442\pi
0.448688 0.893688i 0.351891π-0.351891\pi
6060 0.361984 + 3.19342i 0.0467319 + 0.412269i
6161 1.61958 2.80520i 0.207367 0.359169i −0.743518 0.668716i 0.766844π-0.766844\pi
0.950884 + 0.309547i 0.100177π0.100177\pi
6262 −7.08467 −0.899754
6363 0 0
6464 −2.60434 −0.325543
6565 −3.45434 + 5.98309i −0.428458 + 0.742111i
6666 3.88042 2.86790i 0.477646 0.353014i
6767 −3.46670 6.00449i −0.423524 0.733566i 0.572757 0.819725i 0.305874π-0.305874\pi
−0.996281 + 0.0861595i 0.972541π0.972541\pi
6868 2.15327 0.261122
6969 −11.6889 5.09048i −1.40718 0.612822i
7070 0 0
7171 −12.3304 −1.46335 −0.731673 0.681656i 0.761260π-0.761260\pi
−0.731673 + 0.681656i 0.761260π0.761260\pi
7272 2.29451 + 2.46624i 0.270410 + 0.290649i
7373 1.37936 2.38912i 0.161442 0.279625i −0.773944 0.633254i 0.781719π-0.781719\pi
0.935386 + 0.353629i 0.115052π0.115052\pi
7474 −1.03702 −0.120551
7575 −5.11086 2.22576i −0.590152 0.257009i
7676 1.74064 3.01488i 0.199665 0.345830i
7777 0 0
7878 −1.85920 16.4018i −0.210512 1.85714i
7979 2.95969 5.12633i 0.332991 0.576758i −0.650106 0.759844i 0.725275π-0.725275\pi
0.983097 + 0.183086i 0.0586087π0.0586087\pi
8080 −3.23529 + 5.60368i −0.361716 + 0.626511i
8181 −0.648467 + 8.97661i −0.0720519 + 0.997401i
8282 8.30746 + 14.3889i 0.917406 + 1.58899i
8383 −2.80111 4.85167i −0.307462 0.532540i 0.670344 0.742050i 0.266146π-0.266146\pi
−0.977806 + 0.209510i 0.932813π0.932813\pi
8484 0 0
8585 1.03372 1.79045i 0.112122 0.194202i
8686 18.7802 2.02512
8787 −0.0120840 0.106605i −0.00129554 0.0114293i
8888 1.69889 0.181102
8989 −0.703287 1.21813i −0.0745483 0.129121i 0.826341 0.563169i 0.190418π-0.190418\pi
−0.900890 + 0.434048i 0.857085π0.857085\pi
9090 −7.18575 + 1.65025i −0.757444 + 0.173952i
9191 0 0
9292 5.11636 + 8.86180i 0.533418 + 0.923906i
9393 −0.750637 6.62212i −0.0778374 0.686682i
9494 8.76293 + 15.1778i 0.903827 + 1.56548i
9595 −1.67126 2.89470i −0.171467 0.296990i
9696 −1.30320 11.4968i −0.133007 1.17339i
9797 6.09713 + 10.5605i 0.619070 + 1.07226i 0.989656 + 0.143462i 0.0458236π0.0458236\pi
−0.370586 + 0.928798i 0.620843π0.620843\pi
9898 0 0
9999 3.09180 + 3.32321i 0.310738 + 0.333995i
100100 2.23708 + 3.87474i 0.223708 + 0.387474i
101101 −1.11867 −0.111312 −0.0556560 0.998450i 0.517725π-0.517725\pi
−0.0556560 + 0.998450i 0.517725π0.517725\pi
102102 0.556368 + 4.90828i 0.0550886 + 0.485993i
103103 −1.93045 −0.190213 −0.0951063 0.995467i 0.530319π-0.530319\pi
−0.0951063 + 0.995467i 0.530319π0.530319\pi
104104 2.90593 5.03322i 0.284950 0.493548i
105105 0 0
106106 −1.39082 2.40898i −0.135089 0.233981i
107107 2.88969 + 5.00509i 0.279357 + 0.483860i 0.971225 0.238163i 0.0765454π-0.0765454\pi
−0.691868 + 0.722024i 0.743212π0.743212\pi
108108 4.70077 5.48470i 0.452332 0.527766i
109109 −4.12106 + 7.13788i −0.394726 + 0.683685i −0.993066 0.117557i 0.962494π-0.962494\pi
0.598340 + 0.801242i 0.295827π0.295827\pi
110110 −1.85920 + 3.22022i −0.177267 + 0.307036i
111111 −0.109874 0.969312i −0.0104288 0.0920030i
112112 0 0
113113 7.25105 12.5592i 0.682121 1.18147i −0.292211 0.956354i 0.594391π-0.594391\pi
0.974332 0.225115i 0.0722758π-0.0722758\pi
114114 7.32205 + 3.18873i 0.685773 + 0.298652i
115115 9.82483 0.916170
116116 −0.0430553 + 0.0745740i −0.00399759 + 0.00692403i
117117 15.1340 3.47562i 1.39914 0.321322i
118118 −15.5462 −1.43114
119119 0 0
120120 −2.37997 1.03647i −0.217261 0.0946164i
121121 −8.71078 −0.791889
122122 −2.98204 5.16505i −0.269982 0.467622i
123123 −12.5693 + 9.28962i −1.13334 + 0.837617i
124124 −2.67452 + 4.63241i −0.240179 + 0.416002i
125125 10.9696 0.981149
126126 0 0
127127 8.50004 0.754257 0.377128 0.926161i 0.376912π-0.376912\pi
0.377128 + 0.926161i 0.376912π0.376912\pi
128128 4.28260 7.41769i 0.378532 0.655637i
129129 1.98981 + 17.5541i 0.175193 + 1.54555i
130130 6.36027 + 11.0163i 0.557832 + 0.966194i
131131 2.01346 0.175917 0.0879585 0.996124i 0.471966π-0.471966\pi
0.0879585 + 0.996124i 0.471966π0.471966\pi
132132 −0.410328 3.61992i −0.0357145 0.315074i
133133 0 0
134134 −12.7660 −1.10282
135135 −2.30386 6.54175i −0.198285 0.563024i
136136 −0.869605 + 1.50620i −0.0745680 + 0.129156i
137137 2.21740 0.189445 0.0947225 0.995504i 0.469804π-0.469804\pi
0.0947225 + 0.995504i 0.469804π0.469804\pi
138138 −18.8781 + 13.9523i −1.60701 + 1.18770i
139139 −0.377669 + 0.654143i −0.0320335 + 0.0554836i −0.881598 0.472002i 0.843532π-0.843532\pi
0.849564 + 0.527485i 0.176865π0.176865\pi
140140 0 0
141141 −13.2585 + 9.79894i −1.11656 + 0.825220i
142142 −11.3516 + 19.6615i −0.952604 + 1.64996i
143143 3.91568 6.78216i 0.327446 0.567153i
144144 14.1743 3.25523i 1.18119 0.271269i
145145 0.0413391 + 0.0716014i 0.00343303 + 0.00594618i
146146 −2.53973 4.39894i −0.210189 0.364059i
147147 0 0
148148 −0.391482 + 0.678068i −0.0321797 + 0.0557368i
149149 6.58499 0.539463 0.269732 0.962936i 0.413065π-0.413065\pi
0.269732 + 0.962936i 0.413065π0.413065\pi
150150 −8.25428 + 6.10050i −0.673959 + 0.498104i
151151 12.6671 1.03083 0.515417 0.856939i 0.327637π-0.327637\pi
0.515417 + 0.856939i 0.327637π0.327637\pi
152152 1.40593 + 2.43514i 0.114036 + 0.197516i
153153 −4.52888 + 1.04009i −0.366138 + 0.0840861i
154154 0 0
155155 2.56791 + 4.44775i 0.206260 + 0.357252i
156156 −11.4264 4.97617i −0.914846 0.398413i
157157 −8.65372 14.9887i −0.690642 1.19623i −0.971628 0.236515i 0.923995π-0.923995\pi
0.280986 0.959712i 0.409338π-0.409338\pi
158158 −5.44950 9.43882i −0.433539 0.750912i
159159 2.10434 1.55526i 0.166885 0.123340i
160160 4.45822 + 7.72186i 0.352453 + 0.610467i
161161 0 0
162162 13.7168 + 9.29807i 1.07769 + 0.730525i
163163 6.10963 + 10.5822i 0.478543 + 0.828861i 0.999697 0.0246014i 0.00783167π-0.00783167\pi
−0.521154 + 0.853463i 0.674498π0.674498\pi
164164 12.5445 0.979564
165165 −3.20697 1.39662i −0.249662 0.108727i
166166 −10.3150 −0.800602
167167 −1.76248 + 3.05270i −0.136385 + 0.236225i −0.926126 0.377215i 0.876882π-0.876882\pi
0.789741 + 0.613440i 0.210215π0.210215\pi
168168 0 0
169169 −6.89546 11.9433i −0.530420 0.918714i
170170 −1.90332 3.29665i −0.145978 0.252842i
171171 −2.20475 + 7.18186i −0.168602 + 0.549210i
172172 7.08968 12.2797i 0.540583 0.936318i
173173 5.07046 8.78229i 0.385500 0.667705i −0.606339 0.795206i 0.707362π-0.707362\pi
0.991838 + 0.127502i 0.0406958π0.0406958\pi
174174 −0.181113 0.0788742i −0.0137302 0.00597944i
175175 0 0
176176 3.66738 6.35208i 0.276439 0.478806i
177177 −1.64715 14.5312i −0.123808 1.09223i
178178 −2.58984 −0.194117
179179 0.850579 1.47325i 0.0635752 0.110116i −0.832486 0.554046i 0.813083π-0.813083\pi
0.896061 + 0.443931i 0.146416π0.146416\pi
180180 −1.63364 + 5.32148i −0.121764 + 0.396640i
181181 16.9941 1.26316 0.631581 0.775310i 0.282406π-0.282406\pi
0.631581 + 0.775310i 0.282406π0.282406\pi
182182 0 0
183183 4.51188 3.33460i 0.333528 0.246501i
184184 −8.26505 −0.609308
185185 0.375877 + 0.651039i 0.0276351 + 0.0478653i
186186 −11.2504 4.89953i −0.824922 0.359251i
187187 −1.17178 + 2.02957i −0.0856887 + 0.148417i
188188 13.2323 0.965066
189189 0 0
190190 −6.15437 −0.446485
191191 −11.3470 + 19.6535i −0.821038 + 1.42208i 0.0838717 + 0.996477i 0.473271π0.473271\pi
−0.904910 + 0.425603i 0.860062π0.860062\pi
192192 −4.13568 1.80108i −0.298467 0.129982i
193193 −3.09349 5.35808i −0.222674 0.385683i 0.732945 0.680288i 0.238145π-0.238145\pi
−0.955619 + 0.294605i 0.904812π0.904812\pi
194194 22.4526 1.61200
195195 −9.62319 + 7.11222i −0.689131 + 0.509317i
196196 0 0
197197 9.77010 0.696091 0.348045 0.937478i 0.386846π-0.386846\pi
0.348045 + 0.937478i 0.386846π0.386846\pi
198198 8.14544 1.87065i 0.578871 0.132942i
199199 4.33973 7.51664i 0.307636 0.532840i −0.670209 0.742172i 0.733796π-0.733796\pi
0.977845 + 0.209332i 0.0671289π0.0671289\pi
200200 −3.61381 −0.255535
201201 −1.35259 11.9326i −0.0954044 0.841659i
202202 −1.02987 + 1.78379i −0.0724615 + 0.125507i
203203 0 0
204204 3.41938 + 1.48913i 0.239405 + 0.104260i
205205 6.02225 10.4308i 0.420612 0.728522i
206206 −1.77721 + 3.07822i −0.123824 + 0.214470i
207207 −15.0415 16.1673i −1.04546 1.12371i
208208 −12.5460 21.7303i −0.869909 1.50673i
209209 1.89446 + 3.28130i 0.131043 + 0.226973i
210210 0 0
211211 −2.84219 + 4.92283i −0.195665 + 0.338901i −0.947118 0.320885i 0.896020π-0.896020\pi
0.751453 + 0.659786i 0.229353π0.229353\pi
212212 −2.10019 −0.144242
213213 −19.5806 8.52728i −1.34164 0.584280i
214214 10.6412 0.727420
215215 −6.80708 11.7902i −0.464239 0.804086i
216216 1.93810 + 5.50319i 0.131871 + 0.374445i
217217 0 0
218218 7.58786 + 13.1426i 0.513915 + 0.890126i
219219 3.84265 2.83999i 0.259662 0.191909i
220220 1.40372 + 2.43132i 0.0946390 + 0.163920i
221221 4.00862 + 6.94313i 0.269649 + 0.467045i
222222 −1.64678 0.717167i −0.110525 0.0481331i
223223 −5.86133 10.1521i −0.392503 0.679836i 0.600276 0.799793i 0.295058π-0.295058\pi
−0.992779 + 0.119957i 0.961724π0.961724\pi
224224 0 0
225225 −6.57677 7.06901i −0.438451 0.471267i
226226 −13.3509 23.1245i −0.888091 1.53822i
227227 −11.1831 −0.742247 −0.371123 0.928584i 0.621027π-0.621027\pi
−0.371123 + 0.928584i 0.621027π0.621027\pi
228228 4.84913 3.58385i 0.321141 0.237346i
229229 9.65647 0.638118 0.319059 0.947735i 0.396633π-0.396633\pi
0.319059 + 0.947735i 0.396633π0.396633\pi
230230 9.04494 15.6663i 0.596406 1.03301i
231231 0 0
232232 −0.0347761 0.0602340i −0.00228317 0.00395456i
233233 −9.64492 16.7055i −0.631860 1.09441i −0.987171 0.159666i 0.948958π-0.948958\pi
0.355311 0.934748i 0.384375π-0.384375\pi
234234 8.39058 27.3318i 0.548509 1.78674i
235235 6.35243 11.0027i 0.414387 0.717739i
236236 −5.86881 + 10.1651i −0.382027 + 0.661690i
237237 8.24519 6.09378i 0.535582 0.395833i
238238 0 0
239239 −0.194641 + 0.337128i −0.0125903 + 0.0218070i −0.872252 0.489057i 0.837341π-0.837341\pi
0.859662 + 0.510864i 0.170674π0.170674\pi
240240 −9.01295 + 6.66121i −0.581784 + 0.429979i
241241 −10.6361 −0.685134 −0.342567 0.939493i 0.611296π-0.611296\pi
−0.342567 + 0.939493i 0.611296π0.611296\pi
242242 −8.01932 + 13.8899i −0.515502 + 0.892875i
243243 −7.23769 + 13.8064i −0.464298 + 0.885679i
244244 −4.50299 −0.288274
245245 0 0
246246 3.24130 + 28.5948i 0.206658 + 1.82314i
247247 12.9618 0.824741
248248 −2.16023 3.74163i −0.137175 0.237594i
249249 −1.09290 9.64159i −0.0692599 0.611011i
250250 10.0988 17.4917i 0.638705 1.10627i
251251 3.26628 0.206166 0.103083 0.994673i 0.467129π-0.467129\pi
0.103083 + 0.994673i 0.467129π0.467129\pi
252252 0 0
253253 −11.1370 −0.700176
254254 7.82531 13.5538i 0.491004 0.850443i
255255 2.87976 2.12835i 0.180337 0.133282i
256256 −10.4896 18.1686i −0.655603 1.13554i
257257 4.69573 0.292912 0.146456 0.989217i 0.453213π-0.453213\pi
0.146456 + 0.989217i 0.453213π0.453213\pi
258258 29.8229 + 12.9878i 1.85669 + 0.808584i
259259 0 0
260260 9.60421 0.595628
261261 0.0545353 0.177646i 0.00337565 0.0109960i
262262 1.85363 3.21059i 0.114518 0.198351i
263263 19.5498 1.20549 0.602747 0.797932i 0.294073π-0.294073\pi
0.602747 + 0.797932i 0.294073π0.294073\pi
264264 2.69783 + 1.17490i 0.166040 + 0.0723098i
265265 −1.00824 + 1.74632i −0.0619355 + 0.107276i
266266 0 0
267267 −0.274400 2.42076i −0.0167930 0.148148i
268268 −4.81929 + 8.34725i −0.294385 + 0.509890i
269269 −7.88365 + 13.6549i −0.480675 + 0.832553i −0.999754 0.0221730i 0.992942π-0.992942\pi
0.519079 + 0.854726i 0.326275π0.326275\pi
270270 −12.5522 2.34883i −0.763903 0.142945i
271271 −7.39882 12.8151i −0.449446 0.778464i 0.548904 0.835886i 0.315045π-0.315045\pi
−0.998350 + 0.0574218i 0.981712π0.981712\pi
272272 3.75442 + 6.50285i 0.227645 + 0.394293i
273273 0 0
274274 2.04138 3.53578i 0.123324 0.213604i
275275 −4.86954 −0.293644
276276 1.99624 + 17.6108i 0.120159 + 1.06005i
277277 −7.45122 −0.447701 −0.223850 0.974624i 0.571863π-0.571863\pi
−0.223850 + 0.974624i 0.571863π0.571863\pi
278278 0.695380 + 1.20443i 0.0417061 + 0.0722371i
279279 3.38764 11.0350i 0.202812 0.660650i
280280 0 0
281281 −12.9938 22.5060i −0.775146 1.34259i −0.934712 0.355406i 0.884343π-0.884343\pi
0.159566 0.987187i 0.448991π-0.448991\pi
282282 3.41901 + 30.1625i 0.203599 + 1.79615i
283283 9.37768 + 16.2426i 0.557445 + 0.965524i 0.997709 + 0.0676550i 0.0215517π0.0215517\pi
−0.440263 + 0.897869i 0.645115π0.645115\pi
284284 8.57064 + 14.8448i 0.508574 + 0.880876i
285285 −0.652070 5.75257i −0.0386253 0.340753i
286286 −7.20971 12.4876i −0.426319 0.738406i
287287 0 0
288288 5.88136 19.1582i 0.346563 1.12891i
289289 7.30041 + 12.6447i 0.429436 + 0.743805i
290290 0.152230 0.00893928
291291 2.37890 + 20.9867i 0.139454 + 1.23026i
292292 −3.83507 −0.224431
293293 1.23089 2.13196i 0.0719093 0.124551i −0.827829 0.560981i 0.810424π-0.810424\pi
0.899738 + 0.436430i 0.143757π0.143757\pi
294294 0 0
295295 5.63487 + 9.75988i 0.328075 + 0.568242i
296296 −0.316203 0.547680i −0.0183790 0.0318333i
297297 2.61155 + 7.41544i 0.151537 + 0.430287i
298298 6.06227 10.5002i 0.351178 0.608258i
299299 −19.0497 + 32.9950i −1.10167 + 1.90815i
300300 0.872835 + 7.70016i 0.0503932 + 0.444569i
301301 0 0
302302 11.6616 20.1985i 0.671050 1.16229i
303303 −1.77645 0.773637i −0.102054 0.0444443i
304304 12.1399 0.696270
305305 −2.16175 + 3.74425i −0.123781 + 0.214395i
306306 −2.51090 + 8.17911i −0.143538 + 0.467568i
307307 4.66277 0.266118 0.133059 0.991108i 0.457520π-0.457520\pi
0.133059 + 0.991108i 0.457520π0.457520\pi
308308 0 0
309309 −3.06555 1.33503i −0.174393 0.0759475i
310310 9.45629 0.537081
311311 13.7410 + 23.8002i 0.779183 + 1.34958i 0.932413 + 0.361393i 0.117699π0.117699\pi
−0.153231 + 0.988190i 0.548968π0.548968\pi
312312 8.09542 5.98309i 0.458313 0.338726i
313313 2.74666 4.75735i 0.155250 0.268901i −0.777900 0.628388i 0.783715π-0.783715\pi
0.933150 + 0.359487i 0.117048π0.117048\pi
314314 −31.8671 −1.79837
315315 0 0
316316 −8.22893 −0.462914
317317 −4.93879 + 8.55424i −0.277390 + 0.480454i −0.970735 0.240152i 0.922803π-0.922803\pi
0.693345 + 0.720606i 0.256136π0.256136\pi
318318 −0.542654 4.78730i −0.0304305 0.268459i
319319 −0.0468601 0.0811641i −0.00262366 0.00454432i
320320 3.47615 0.194323
321321 1.12746 + 9.94649i 0.0629288 + 0.555159i
322322 0 0
323323 −3.87885 −0.215825
324324 11.2579 5.45879i 0.625437 0.303266i
325325 −8.32930 + 14.4268i −0.462026 + 0.800253i
326326 22.4986 1.24608
327327 −11.4806 + 8.48494i −0.634876 + 0.469218i
328328 −5.06616 + 8.77485i −0.279732 + 0.484510i
329329 0 0
330330 −5.17940 + 3.82794i −0.285116 + 0.210721i
331331 10.3471 17.9217i 0.568729 0.985067i −0.427963 0.903796i 0.640769π-0.640769\pi
0.996692 0.0812710i 0.0258979π-0.0258979\pi
332332 −3.89401 + 6.74463i −0.213712 + 0.370160i
333333 0.495864 1.61525i 0.0271732 0.0885152i
334334 3.24514 + 5.62076i 0.177566 + 0.307554i
335335 4.62718 + 8.01452i 0.252810 + 0.437880i
336336 0 0
337337 0.748747 1.29687i 0.0407869 0.0706449i −0.844911 0.534906i 0.820347π-0.820347\pi
0.885698 + 0.464261i 0.153680π0.153680\pi
338338 −25.3924 −1.38116
339339 20.2002 14.9294i 1.09712 0.810852i
340340 −2.87408 −0.155869
341341 −2.91087 5.04177i −0.157632 0.273027i
342342 9.42217 + 10.1274i 0.509493 + 0.547626i
343343 0 0
344344 5.72639 + 9.91840i 0.308746 + 0.534764i
345345 15.6018 + 6.79453i 0.839973 + 0.365805i
346346 −9.33593 16.1703i −0.501903 0.869321i
347347 14.7694 + 25.5813i 0.792862 + 1.37328i 0.924188 + 0.381938i 0.124743π0.124743\pi
−0.131326 + 0.991339i 0.541923π0.541923\pi
348348 −0.119945 + 0.0886477i −0.00642971 + 0.00475202i
349349 −18.0006 31.1780i −0.963551 1.66892i −0.713458 0.700698i 0.752872π-0.752872\pi
−0.250094 0.968222i 0.580461π-0.580461\pi
350350 0 0
351351 26.4364 + 4.94691i 1.41107 + 0.264046i
352352 −5.05363 8.75315i −0.269360 0.466545i
353353 29.4930 1.56975 0.784877 0.619652i 0.212726π-0.212726\pi
0.784877 + 0.619652i 0.212726π0.212726\pi
354354 −24.6873 10.7512i −1.31211 0.571421i
355355 16.4580 0.873500
356356 −0.977687 + 1.69340i −0.0518173 + 0.0897502i
357357 0 0
358358 −1.56612 2.71260i −0.0827720 0.143365i
359359 2.70535 + 4.68580i 0.142783 + 0.247307i 0.928544 0.371224i 0.121062π-0.121062\pi
−0.785761 + 0.618531i 0.787728π0.787728\pi
360360 −3.06260 3.29182i −0.161413 0.173494i
361361 6.36444 11.0235i 0.334971 0.580186i
362362 15.6451 27.0981i 0.822289 1.42425i
363363 −13.8327 6.02409i −0.726028 0.316183i
364364 0 0
365365 −1.84110 + 3.18888i −0.0963676 + 0.166914i
366366 −1.16350 10.2644i −0.0608169 0.536527i
367367 23.0843 1.20499 0.602496 0.798122i 0.294173π-0.294173\pi
0.602496 + 0.798122i 0.294173π0.294173\pi
368368 −17.8417 + 30.9027i −0.930063 + 1.61092i
369369 −26.3844 + 6.05936i −1.37352 + 0.315438i
370370 1.38416 0.0719591
371371 0 0
372372 −7.45075 + 5.50664i −0.386304 + 0.285506i
373373 21.5030 1.11338 0.556692 0.830719i 0.312070π-0.312070\pi
0.556692 + 0.830719i 0.312070π0.312070\pi
374374 2.15752 + 3.73694i 0.111563 + 0.193232i
375375 17.4197 + 7.58620i 0.899548 + 0.391750i
376376 −5.34392 + 9.25595i −0.275592 + 0.477339i
377377 −0.320615 −0.0165125
378378 0 0
379379 5.72168 0.293903 0.146952 0.989144i 0.453054π-0.453054\pi
0.146952 + 0.989144i 0.453054π0.453054\pi
380380 −2.32333 + 4.02412i −0.119184 + 0.206433i
381381 13.4980 + 5.87835i 0.691526 + 0.301157i
382382 20.8925 + 36.1869i 1.06895 + 1.85148i
383383 34.9209 1.78437 0.892187 0.451666i 0.149170π-0.149170\pi
0.892187 + 0.451666i 0.149170π0.149170\pi
384384 11.9306 8.81756i 0.608831 0.449969i
385385 0 0
386386 −11.3917 −0.579823
387387 −8.98003 + 29.2519i −0.456480 + 1.48696i
388388 8.47603 14.6809i 0.430305 0.745311i
389389 −28.8822 −1.46438 −0.732192 0.681098i 0.761503π-0.761503\pi
−0.732192 + 0.681098i 0.761503π0.761503\pi
390390 2.48157 + 21.8924i 0.125659 + 1.10857i
391391 5.70066 9.87383i 0.288295 0.499341i
392392 0 0
393393 3.19737 + 1.39244i 0.161286 + 0.0702395i
394394 8.99455 15.5790i 0.453139 0.784860i
395395 −3.95046 + 6.84239i −0.198769 + 0.344278i
396396 1.85182 6.03219i 0.0930574 0.303129i
397397 −5.59226 9.68607i −0.280667 0.486130i 0.690882 0.722968i 0.257222π-0.257222\pi
−0.971549 + 0.236838i 0.923889π0.923889\pi
398398 −7.99049 13.8399i −0.400527 0.693734i
399399 0 0
400400 −7.80111 + 13.5119i −0.390056 + 0.675596i
401401 −1.08212 −0.0540386 −0.0270193 0.999635i 0.508602π-0.508602\pi
−0.0270193 + 0.999635i 0.508602π0.508602\pi
402402 −20.2724 8.82858i −1.01110 0.440330i
403403 −19.9160 −0.992088
404404 0.777570 + 1.34679i 0.0386856 + 0.0670054i
405405 0.865544 11.9816i 0.0430092 0.595368i
406406 0 0
407407 −0.426078 0.737988i −0.0211199 0.0365807i
408408 −2.42257 + 1.79045i −0.119935 + 0.0886405i
409409 −10.8674 18.8229i −0.537360 0.930735i −0.999045 0.0436908i 0.986088π-0.986088\pi
0.461685 0.887044i 0.347245π-0.347245\pi
410410 −11.0884 19.2057i −0.547618 0.948501i
411411 3.52122 + 1.53348i 0.173689 + 0.0756410i
412412 1.34182 + 2.32410i 0.0661069 + 0.114500i
413413 0 0
414414 −39.6273 + 9.10068i −1.94758 + 0.447274i
415415 3.73879 + 6.47578i 0.183530 + 0.317884i
416416 −34.5767 −1.69526
417417 −1.05212 + 0.777593i −0.0515226 + 0.0380789i
418418 6.97632 0.341223
419419 −12.5906 + 21.8075i −0.615090 + 1.06537i 0.375279 + 0.926912i 0.377547π0.377547\pi
−0.990369 + 0.138455i 0.955787π0.955787\pi
420420 0 0
421421 −14.8304 25.6869i −0.722788 1.25191i −0.959878 0.280418i 0.909527π-0.909527\pi
0.237090 0.971488i 0.423806π-0.423806\pi
422422 5.23316 + 9.06411i 0.254746 + 0.441234i
423423 −27.8310 + 6.39158i −1.35319 + 0.310769i
424424 0.848171 1.46907i 0.0411908 0.0713446i
425425 2.49256 4.31724i 0.120907 0.209417i
426426 −31.6236 + 23.3721i −1.53217 + 1.13238i
427427 0 0
428428 4.01715 6.95791i 0.194176 0.336323i
429429 10.9084 8.06209i 0.526663 0.389241i
430430 −25.0669 −1.20884
431431 2.44517 4.23516i 0.117780 0.204000i −0.801108 0.598520i 0.795756π-0.795756\pi
0.918887 + 0.394520i 0.129089π0.129089\pi
432432 24.7600 + 4.63321i 1.19127 + 0.222915i
433433 −9.71430 −0.466839 −0.233420 0.972376i 0.574992π-0.574992\pi
−0.233420 + 0.972376i 0.574992π0.574992\pi
434434 0 0
435435 0.0161292 + 0.142292i 0.000773334 + 0.00682236i
436436 11.4579 0.548735
437437 −9.21651 15.9635i −0.440885 0.763636i
438438 −0.990919 8.74189i −0.0473479 0.417704i
439439 −7.41176 + 12.8375i −0.353744 + 0.612703i −0.986902 0.161320i 0.948425π-0.948425\pi
0.633158 + 0.774022i 0.281758π0.281758\pi
440440 −2.26760 −0.108103
441441 0 0
442442 14.7617 0.702141
443443 10.9510 18.9676i 0.520297 0.901180i −0.479425 0.877583i 0.659155π-0.659155\pi
0.999722 0.0235972i 0.00751192π-0.00751192\pi
444444 −1.09060 + 0.806033i −0.0517577 + 0.0382526i
445445 0.938715 + 1.62590i 0.0444994 + 0.0770751i
446446 −21.5842 −1.02204
447447 10.4569 + 4.55396i 0.494596 + 0.215395i
448448 0 0
449449 21.4952 1.01442 0.507212 0.861822i 0.330676π-0.330676\pi
0.507212 + 0.861822i 0.330676π0.330676\pi
450450 −17.3267 + 3.97919i −0.816787 + 0.187581i
451451 −6.82655 + 11.8239i −0.321450 + 0.556767i
452452 −20.1603 −0.948263
453453 20.1153 + 8.76016i 0.945101 + 0.411588i
454454 −10.2954 + 17.8321i −0.483185 + 0.836902i
455455 0 0
456456 0.548548 + 4.83929i 0.0256881 + 0.226621i
457457 −20.3128 + 35.1827i −0.950190 + 1.64578i −0.205181 + 0.978724i 0.565778π0.565778\pi
−0.745009 + 0.667054i 0.767555π0.767555\pi
458458 8.88995 15.3978i 0.415400 0.719494i
459459 −7.91114 1.48037i −0.369261 0.0690978i
460460 −6.82908 11.8283i −0.318408 0.551498i
461461 −1.41541 2.45155i −0.0659220 0.114180i 0.831181 0.556003i 0.187666π-0.187666\pi
−0.897103 + 0.441822i 0.854332π0.854332\pi
462462 0 0
463463 −13.9324 + 24.1317i −0.647494 + 1.12149i 0.336225 + 0.941782i 0.390850π0.390850\pi
−0.983719 + 0.179711i 0.942484π0.942484\pi
464464 −0.300284 −0.0139403
465465 1.00192 + 8.83890i 0.0464627 + 0.409894i
466466 −35.5173 −1.64531
467467 13.3219 + 23.0742i 0.616464 + 1.06775i 0.990126 + 0.140182i 0.0447689π0.0447689\pi
−0.373661 + 0.927565i 0.621898π0.621898\pi
468468 −14.7038 15.8043i −0.679682 0.730554i
469469 0 0
470470 −11.6964 20.2587i −0.539513 0.934463i
471471 −3.37640 29.7866i −0.155576 1.37249i
472472 −4.74028 8.21041i −0.218189 0.377915i
473473 7.71620 + 13.3648i 0.354791 + 0.614516i
474474 −2.12622 18.7575i −0.0976604 0.861561i
475475 −4.02983 6.97987i −0.184901 0.320258i
476476 0 0
477477 4.41725 1.01445i 0.202252 0.0464485i
478478 0.358381 + 0.620734i 0.0163920 + 0.0283917i
479479 31.5791 1.44289 0.721443 0.692474i 0.243479π-0.243479\pi
0.721443 + 0.692474i 0.243479π0.243479\pi
480480 1.73945 + 15.3455i 0.0793947 + 0.700421i
481481 −2.91520 −0.132922
482482 −9.79185 + 16.9600i −0.446007 + 0.772506i
483483 0 0
484484 6.05472 + 10.4871i 0.275215 + 0.476686i
485485 −8.13817 14.0957i −0.369535 0.640054i
486486 15.3519 + 24.2514i 0.696378 + 1.10006i
487487 −0.153087 + 0.265154i −0.00693703 + 0.0120153i −0.869473 0.493980i 0.835541π-0.835541\pi
0.862536 + 0.505996i 0.168875π0.168875\pi
488488 1.81855 3.14982i 0.0823218 0.142586i
489489 2.38378 + 21.0297i 0.107798 + 0.950996i
490490 0 0
491491 −9.06981 + 15.7094i −0.409315 + 0.708954i −0.994813 0.101720i 0.967566π-0.967566\pi
0.585498 + 0.810674i 0.300899π0.300899\pi
492492 19.9207 + 8.67539i 0.898094 + 0.391117i
493493 0.0959447 0.00432113
494494 11.9329 20.6684i 0.536887 0.929916i
495495 −4.12679 4.43567i −0.185486 0.199368i
496496 −18.6531 −0.837549
497497 0 0
498498 −16.3803 7.13355i −0.734017 0.319662i
499499 −21.3091 −0.953928 −0.476964 0.878923i 0.658263π-0.658263\pi
−0.476964 + 0.878923i 0.658263π0.658263\pi
500500 −7.62478 13.2065i −0.340990 0.590613i
501501 −4.90996 + 3.62881i −0.219361 + 0.162123i
502502 3.00701 5.20829i 0.134209 0.232457i
503503 17.0738 0.761285 0.380642 0.924722i 0.375703π-0.375703\pi
0.380642 + 0.924722i 0.375703π0.375703\pi
504504 0 0
505505 1.49315 0.0664443
506506 −10.2529 + 17.7586i −0.455799 + 0.789466i
507507 −2.69038 23.7346i −0.119484 1.05409i
508508 −5.90824 10.2334i −0.262136 0.454032i
509509 −36.7735 −1.62996 −0.814979 0.579490i 0.803252π-0.803252\pi
−0.814979 + 0.579490i 0.803252π0.803252\pi
510510 −0.742614 6.55135i −0.0328835 0.290099i
511511 0 0
512512 −21.4975 −0.950065
513513 −8.46788 + 9.88003i −0.373866 + 0.436214i
514514 4.32299 7.48764i 0.190679 0.330265i
515515 2.57667 0.113542
516516 19.7506 14.5971i 0.869473 0.642603i
517517 −7.20083 + 12.4722i −0.316692 + 0.548527i
518518 0 0
519519 14.1254 10.4397i 0.620037 0.458251i
520520 −3.87870 + 6.71810i −0.170092 + 0.294608i
521521 9.57535 16.5850i 0.419504 0.726602i −0.576386 0.817178i 0.695537π-0.695537\pi
0.995890 + 0.0905758i 0.0288707π0.0288707\pi
522522 −0.233061 0.250504i −0.0102008 0.0109643i
523523 20.9715 + 36.3236i 0.917018 + 1.58832i 0.803920 + 0.594737i 0.202744π0.202744\pi
0.113097 + 0.993584i 0.463923π0.463923\pi
524524 −1.39952 2.42405i −0.0611385 0.105895i
525525 0 0
526526 17.9980 31.1734i 0.784749 1.35922i
527527 5.95991 0.259618
528528 10.2167 7.55085i 0.444624 0.328609i
529529 31.1812 1.35570
530530 1.85641 + 3.21539i 0.0806372 + 0.139668i
531531 7.43362 24.2146i 0.322592 1.05082i
532532 0 0
533533 23.3535 + 40.4494i 1.01155 + 1.75206i
534534 −4.11266 1.79105i −0.177972 0.0775063i
535535 −3.85702 6.68056i −0.166754 0.288826i
536536 −3.89258 6.74214i −0.168134 0.291216i
537537 2.36956 1.75128i 0.102254 0.0755732i
538538 14.5157 + 25.1419i 0.625816 + 1.08395i
539539 0 0
540540 −6.27438 + 7.32073i −0.270006 + 0.315034i
541541 −1.44272 2.49886i −0.0620273 0.107434i 0.833344 0.552754i 0.186423π-0.186423\pi
−0.895371 + 0.445320i 0.853090π0.853090\pi
542542 −27.2460 −1.17032
543543 26.9866 + 11.7526i 1.15811 + 0.504351i
544544 10.3472 0.443631
545545 5.50059 9.52731i 0.235620 0.408105i
546546 0 0
547547 1.38738 + 2.40301i 0.0593201 + 0.102745i 0.894160 0.447747i 0.147773π-0.147773\pi
−0.834840 + 0.550492i 0.814440π0.814440\pi
548548 −1.54128 2.66957i −0.0658401 0.114038i
549549 9.47096 2.17507i 0.404211 0.0928296i
550550 −4.48300 + 7.76478i −0.191156 + 0.331091i
551551 0.0775590 0.134336i 0.00330413 0.00572291i
552552 −13.1249 5.71584i −0.558632 0.243282i
553553 0 0
554554 −6.85975 + 11.8814i −0.291443 + 0.504794i
555555 0.146655 + 1.29379i 0.00622516 + 0.0549184i
556556 1.05005 0.0445319
557557 15.5344 26.9064i 0.658214 1.14006i −0.322864 0.946445i 0.604646π-0.604646\pi
0.981078 0.193614i 0.0620211π-0.0620211\pi
558558 −14.4773 15.5609i −0.612873 0.658744i
559559 52.7939 2.23294
560560 0 0
561561 −3.26436 + 2.41260i −0.137822 + 0.101860i
562562 −47.8495 −2.01841
563563 0.144020 + 0.249451i 0.00606973 + 0.0105131i 0.869044 0.494734i 0.164735π-0.164735\pi
−0.862975 + 0.505247i 0.831401π0.831401\pi
564564 21.0129 + 9.15104i 0.884802 + 0.385328i
565565 −9.67836 + 16.7634i −0.407172 + 0.705242i
566566 34.5331 1.45154
567567 0 0
568568 −13.8451 −0.580929
569569 8.04004 13.9258i 0.337056 0.583798i −0.646821 0.762641i 0.723902π-0.723902\pi
0.983878 + 0.178843i 0.0572354π0.0572354\pi
570570 −9.77313 4.25616i −0.409351 0.178271i
571571 7.64289 + 13.2379i 0.319845 + 0.553988i 0.980456 0.196741i 0.0630358π-0.0630358\pi
−0.660610 + 0.750729i 0.729702π0.729702\pi
572572 −10.8869 −0.455204
573573 −31.6107 + 23.3626i −1.32056 + 0.975985i
574574 0 0
575575 23.6902 0.987950
576576 −5.32189 5.72021i −0.221745 0.238342i
577577 −12.0812 + 20.9253i −0.502949 + 0.871133i 0.497045 + 0.867725i 0.334418π0.334418\pi
−0.999994 + 0.00340833i 0.998915π0.998915\pi
578578 26.8836 1.11821
579579 −1.20698 10.6480i −0.0501603 0.442515i
580580 0.0574683 0.0995380i 0.00238624 0.00413309i
581581 0 0
582582 35.6546 + 15.5275i 1.47793 + 0.643634i
583583 1.14289 1.97955i 0.0473338 0.0819845i
584584 1.54881 2.68262i 0.0640902 0.111007i
585585 −20.2002 + 4.63910i −0.835174 + 0.191803i
586586 −2.26636 3.92546i −0.0936226 0.162159i
587587 −18.0145 31.2020i −0.743537 1.28784i −0.950875 0.309574i 0.899814π-0.899814\pi
0.207339 0.978269i 0.433520π-0.433520\pi
588588 0 0
589589 4.81783 8.34472i 0.198515 0.343838i
590590 20.7503 0.854276
591591 15.5149 + 6.75668i 0.638197 + 0.277933i
592592 −2.73034 −0.112216
593593 −12.4668 21.5932i −0.511951 0.886726i −0.999904 0.0138558i 0.995589π-0.995589\pi
0.487953 0.872870i 0.337744π-0.337744\pi
594594 14.2286 + 2.66253i 0.583807 + 0.109245i
595595 0 0
596596 −4.57712 7.92780i −0.187486 0.324735i
597597 12.0897 8.93518i 0.494800 0.365693i
598598 35.0751 + 60.7518i 1.43433 + 2.48433i
599599 −19.7642 34.2325i −0.807542 1.39870i −0.914561 0.404447i 0.867464π-0.867464\pi
0.107019 0.994257i 0.465869π-0.465869\pi
600600 −5.73873 2.49920i −0.234283 0.102029i
601601 −1.86447 3.22936i −0.0760534 0.131728i 0.825490 0.564416i 0.190899π-0.190899\pi
−0.901544 + 0.432688i 0.857565π0.857565\pi
602602 0 0
603603 6.10427 19.8843i 0.248585 0.809751i
604604 −8.80470 15.2502i −0.358258 0.620521i
605605 11.6267 0.472694
606606 −2.86904 + 2.12043i −0.116547 + 0.0861365i
607607 −23.6528 −0.960036 −0.480018 0.877259i 0.659370π-0.659370\pi
−0.480018 + 0.877259i 0.659370π0.659370\pi
608608 8.36436 14.4875i 0.339219 0.587545i
609609 0 0
610610 3.98029 + 6.89407i 0.161157 + 0.279133i
611611 24.6339 + 42.6671i 0.996580 + 1.72613i
612612 4.40013 + 4.72947i 0.177865 + 0.191177i
613613 1.89952 3.29006i 0.0767208 0.132884i −0.825113 0.564968i 0.808888π-0.808888\pi
0.901833 + 0.432084i 0.142222π0.142222\pi
614614 4.29264 7.43507i 0.173237 0.300055i
615615 16.7769 12.3994i 0.676512 0.499990i
616616 0 0
617617 −17.5615 + 30.4174i −0.706999 + 1.22456i 0.258966 + 0.965886i 0.416618π0.416618\pi
−0.965965 + 0.258672i 0.916715π0.916715\pi
618618 −4.95100 + 3.65914i −0.199158 + 0.147192i
619619 21.1632 0.850622 0.425311 0.905047i 0.360165π-0.360165\pi
0.425311 + 0.905047i 0.360165π0.360165\pi
620620 3.56983 6.18312i 0.143368 0.248320i
621621 −12.7051 36.0759i −0.509839 1.44768i
622622 50.6011 2.02892
623623 0 0
624624 −4.89504 43.1841i −0.195959 1.72875i
625625 1.45048 0.0580192
626626 −5.05726 8.75943i −0.202129 0.350097i
627627 0.739157 + 6.52085i 0.0295191 + 0.260418i
628628 −12.0301 + 20.8368i −0.480054 + 0.831477i
629629 0.872381 0.0347841
630630 0 0
631631 4.74845 0.189033 0.0945164 0.995523i 0.469870π-0.469870\pi
0.0945164 + 0.995523i 0.469870π0.469870\pi
632632 3.32329 5.75610i 0.132193 0.228965i
633633 −7.91786 + 5.85186i −0.314707 + 0.232591i
634634 9.09350 + 15.7504i 0.361149 + 0.625529i
635635 −11.3455 −0.450231
636636 −3.33510 1.45242i −0.132245 0.0575924i
637637 0 0
638638 −0.172562 −0.00683178
639639 −25.1967 27.0826i −0.996767 1.07137i
640640 −5.71622 + 9.90078i −0.225953 + 0.391363i
641641 −9.87469 −0.390027 −0.195013 0.980801i 0.562475π-0.562475\pi
−0.195013 + 0.980801i 0.562475π0.562475\pi
642642 16.8982 + 7.35913i 0.666921 + 0.290442i
643643 −21.9748 + 38.0615i −0.866602 + 1.50100i −0.00115462 + 0.999999i 0.500368π0.500368\pi
−0.865448 + 0.501000i 0.832966π0.832966\pi
644644 0 0
645645 −2.65590 23.4304i −0.104576 0.922570i
646646 −3.57095 + 6.18507i −0.140497 + 0.243348i
647647 −22.1936 + 38.4404i −0.872521 + 1.51125i −0.0131398 + 0.999914i 0.504183π0.504183\pi
−0.859381 + 0.511336i 0.829151π0.829151\pi
648648 −0.728131 + 10.0794i −0.0286037 + 0.395955i
649649 −6.38743 11.0634i −0.250729 0.434275i
650650 15.3362 + 26.5631i 0.601537 + 1.04189i
651651 0 0
652652 8.49341 14.7110i 0.332628 0.576128i
653653 41.9912 1.64324 0.821622 0.570033i 0.193070π-0.193070\pi
0.821622 + 0.570033i 0.193070π0.193070\pi
654654 2.96053 + 26.1179i 0.115766 + 1.02129i
655655 −2.68748 −0.105008
656656 21.8726 + 37.8844i 0.853980 + 1.47914i
657657 8.06616 1.85245i 0.314691 0.0722708i
658658 0 0
659659 −19.6365 34.0114i −0.764928 1.32489i −0.940284 0.340390i 0.889441π-0.889441\pi
0.175356 0.984505i 0.443892π-0.443892\pi
660660 0.547687 + 4.83170i 0.0213187 + 0.188074i
661661 −0.0933694 0.161721i −0.00363165 0.00629020i 0.864204 0.503142i 0.167823π-0.167823\pi
−0.867836 + 0.496852i 0.834489π0.834489\pi
662662 −19.0515 32.9982i −0.740459 1.28251i
663663 1.56403 + 13.7979i 0.0607419 + 0.535866i
664664 −3.14522 5.44769i −0.122058 0.211411i
665665 0 0
666666 −2.11911 2.27772i −0.0821139 0.0882598i
667667 0.227973 + 0.394862i 0.00882717 + 0.0152891i
668668 4.90028 0.189597
669669 −2.28690 20.1750i −0.0884166 0.780012i
670670 17.0395 0.658294
671671 2.45046 4.24432i 0.0945989 0.163850i
672672 0 0
673673 −5.43382 9.41166i −0.209458 0.362793i 0.742086 0.670305i 0.233837π-0.233837\pi
−0.951544 + 0.307512i 0.900503π0.900503\pi
674674 −1.37862 2.38785i −0.0531026 0.0919764i
675675 −5.55519 15.7738i −0.213819 0.607136i
676676 −9.58584 + 16.6032i −0.368686 + 0.638583i
677677 14.1950 24.5865i 0.545560 0.944937i −0.453012 0.891505i 0.649650π-0.649650\pi
0.998571 0.0534326i 0.0170162π-0.0170162\pi
678678 −5.20910 45.9547i −0.200054 1.76488i
679679 0 0
680680 1.16071 2.01041i 0.0445111 0.0770956i
681681 −17.7587 7.73385i −0.680514 0.296362i
682682 −10.7192 −0.410460
683683 5.92034 10.2543i 0.226536 0.392371i −0.730243 0.683187i 0.760593π-0.760593\pi
0.956779 + 0.290816i 0.0939267π0.0939267\pi
684684 10.1789 2.33764i 0.389199 0.0893821i
685685 −2.95968 −0.113083
686686 0 0
687687 15.3345 + 6.67810i 0.585046 + 0.254786i
688688 49.4461 1.88511
689689 −3.90981 6.77199i −0.148952 0.257992i
690690 25.1976 18.6228i 0.959258 0.708960i
691691 5.95416 10.3129i 0.226507 0.392321i −0.730264 0.683165i 0.760603π-0.760603\pi
0.956770 + 0.290844i 0.0939361π0.0939361\pi
692692 −14.0976 −0.535909
693693 0 0
694694 54.3880 2.06454
695695 0.504096 0.873119i 0.0191214 0.0331193i
696696 −0.0135685 0.119702i −0.000514313 0.00453727i
697697 −6.98857 12.1046i −0.264711 0.458493i
698698 −66.2870 −2.50900
699699 −3.76313 33.1984i −0.142335 1.25568i
700700 0 0
701701 −31.3902 −1.18559 −0.592795 0.805353i 0.701976π-0.701976\pi
−0.592795 + 0.805353i 0.701976π0.701976\pi
702702 32.2260 37.6002i 1.21629 1.41913i
703703 0.705208 1.22146i 0.0265974 0.0460681i
704704 −3.94041 −0.148510
705705 17.6968 13.0792i 0.666499 0.492590i
706706 27.1518 47.0284i 1.02187 1.76994i
707707 0 0
708708 −16.3495 + 12.0834i −0.614451 + 0.454123i
709709 −0.312609 + 0.541455i −0.0117403 + 0.0203348i −0.871836 0.489798i 0.837070π-0.837070\pi
0.860096 + 0.510133i 0.170404π0.170404\pi
710710 15.1516 26.2433i 0.568628 0.984893i
711711 17.3076 3.97480i 0.649085 0.149067i
712712 −0.789685 1.36777i −0.0295947 0.0512595i
713713 14.1613 + 24.5281i 0.530345 + 0.918584i
714714 0 0
715715 −5.22647 + 9.05251i −0.195459 + 0.338545i
716716 −2.36489 −0.0883802
717717 −0.542236 + 0.400751i −0.0202502 + 0.0149663i
718718 9.96239 0.371793
719719 −12.1969 21.1257i −0.454869 0.787857i 0.543811 0.839208i 0.316981π-0.316981\pi
−0.998681 + 0.0513506i 0.983647π0.983647\pi
720720 −18.9192 + 4.34492i −0.705078 + 0.161926i
721721 0 0
722722 −11.7185 20.2970i −0.436116 0.755376i
723723 −16.8902 7.35561i −0.628152 0.273558i
724724 −11.8123 20.4595i −0.439002 0.760373i
725725 0.0996792 + 0.172649i 0.00370199 + 0.00641204i
726726 −22.3404 + 16.5112i −0.829132 + 0.612787i
727727 18.9253 + 32.7796i 0.701900 + 1.21573i 0.967799 + 0.251726i 0.0809980π0.0809980\pi
−0.265899 + 0.964001i 0.585669π0.585669\pi
728728 0 0
729729 −21.0415 + 16.9191i −0.779314 + 0.626634i
730730 3.38991 + 5.87150i 0.125466 + 0.217314i
731731 −15.7987 −0.584335
732732 −7.15073 3.11412i −0.264299 0.115101i
733733 −2.40155 −0.0887033 −0.0443516 0.999016i 0.514122π-0.514122\pi
−0.0443516 + 0.999016i 0.514122π0.514122\pi
734734 21.2519 36.8093i 0.784421 1.35866i
735735 0 0
736736 24.5858 + 42.5839i 0.906245 + 1.56966i
737737 −5.24517 9.08490i −0.193208 0.334646i
738738 −14.6280 + 47.6500i −0.538465 + 1.75402i
739739 −15.1940 + 26.3167i −0.558920 + 0.968077i 0.438667 + 0.898650i 0.355451π0.355451\pi
−0.997587 + 0.0694277i 0.977883π0.977883\pi
740740 0.522533 0.905053i 0.0192087 0.0332704i
741741 20.5833 + 8.96397i 0.756148 + 0.329300i
742742 0 0
743743 −2.54785 + 4.41300i −0.0934715 + 0.161897i −0.908970 0.416862i 0.863130π-0.863130\pi
0.815498 + 0.578760i 0.196463π0.196463\pi
744744 −0.842852 7.43565i −0.0309004 0.272604i
745745 −8.78934 −0.322016
746746 19.7961 34.2879i 0.724787 1.25537i
747747 4.93228 16.0666i 0.180463 0.587847i
748748 3.25793 0.119122
749749 0 0
750750 28.1336 20.7927i 1.02729 0.759242i
751751 −0.975011 −0.0355787 −0.0177893 0.999842i 0.505663π-0.505663\pi
−0.0177893 + 0.999842i 0.505663π0.505663\pi
752752 23.0718 + 39.9615i 0.841341 + 1.45724i
753753 5.18685 + 2.25885i 0.189019 + 0.0823172i
754754 −0.295165 + 0.511240i −0.0107493 + 0.0186183i
755755 −16.9075 −0.615326
756756 0 0
757757 11.6346 0.422865 0.211433 0.977393i 0.432187π-0.432187\pi
0.211433 + 0.977393i 0.432187π0.432187\pi
758758 5.26750 9.12357i 0.191324 0.331383i
759759 −17.6855 7.70198i −0.641943 0.279564i
760760 −1.87657 3.25031i −0.0680703 0.117901i
761761 54.1749 1.96384 0.981920 0.189298i 0.0606213π-0.0606213\pi
0.981920 + 0.189298i 0.0606213π0.0606213\pi
762762 21.8000 16.1117i 0.789729 0.583666i
763763 0 0
764764 31.5484 1.14138
765765 6.04494 1.38826i 0.218555 0.0501927i
766766 32.1489 55.6835i 1.16159 2.01193i
767767 −43.7025 −1.57801
768768 −4.09272 36.1060i −0.147683 1.30286i
769769 10.4326 18.0698i 0.376208 0.651612i −0.614299 0.789074i 0.710561π-0.710561\pi
0.990507 + 0.137462i 0.0438943π0.0438943\pi
770770 0 0
771771 7.45681 + 3.24742i 0.268551 + 0.116953i
772772 −4.30047 + 7.44863i −0.154777 + 0.268082i
773773 27.4972 47.6266i 0.989007 1.71301i 0.366447 0.930439i 0.380574π-0.380574\pi
0.622561 0.782572i 0.286092π-0.286092\pi
774774 38.3768 + 41.2491i 1.37942 + 1.48267i
775775 6.19189 + 10.7247i 0.222419 + 0.385242i
776776 6.84616 + 11.8579i 0.245763 + 0.425674i
777777 0 0
778778 −26.5895 + 46.0544i −0.953281 + 1.65113i
779779 −22.5975 −0.809639
780780 15.2515 + 6.64196i 0.546090 + 0.237820i
781781 −18.6560 −0.667566
782782 −10.4963 18.1801i −0.375346 0.650119i
783783 0.209456 0.244386i 0.00748534 0.00873364i
784784 0 0
785785 11.5506 + 20.0062i 0.412258 + 0.714051i
786786 5.16390 3.81649i 0.184190 0.136130i
787787 4.59475 + 7.95833i 0.163785 + 0.283684i 0.936223 0.351406i 0.114296π-0.114296\pi
−0.772438 + 0.635090i 0.780963π0.780963\pi
788788 −6.79103 11.7624i −0.241921 0.419019i
789789 31.0451 + 13.5200i 1.10523 + 0.481325i
790790 7.27374 + 12.5985i 0.258788 + 0.448234i
791791 0 0
792792 3.47163 + 3.73146i 0.123359 + 0.132592i
793793 −8.38296 14.5197i −0.297688 0.515610i
794794 −20.5934 −0.730832
795795 −2.80878 + 2.07588i −0.0996170 + 0.0736241i
796796 −12.0659 −0.427665
797797 −3.53774 + 6.12754i −0.125313 + 0.217049i −0.921855 0.387534i 0.873327π-0.873327\pi
0.796542 + 0.604583i 0.206660π0.206660\pi
798798 0 0
799799 −7.37174 12.7682i −0.260793 0.451707i
800800 10.7499 + 18.6194i 0.380067 + 0.658295i
801801 1.23837 4.03392i 0.0437556 0.142532i
802802 −0.996224 + 1.72551i −0.0351779 + 0.0609299i
803803 2.08699 3.61477i 0.0736483 0.127563i
804804 −13.4257 + 9.92255i −0.473488 + 0.349941i
805805 0 0
806806 −18.3351 + 31.7573i −0.645827 + 1.11860i
807807 −21.9625 + 16.2318i −0.773116 + 0.571388i
808808 −1.25610 −0.0441894
809809 −2.97060 + 5.14522i −0.104441 + 0.180896i −0.913510 0.406817i 0.866639π-0.866639\pi
0.809069 + 0.587714i 0.199972π0.199972\pi
810810 −18.3085 12.4106i −0.643295 0.436065i
811811 −44.4139 −1.55958 −0.779791 0.626039i 0.784675π-0.784675\pi
−0.779791 + 0.626039i 0.784675π0.784675\pi
812812 0 0
813813 −2.88678 25.4672i −0.101244 0.893173i
814814 −1.56902 −0.0549942
815815 −8.15485 14.1246i −0.285652 0.494764i
816816 1.46485 + 12.9229i 0.0512801 + 0.452393i
817817 −12.7712 + 22.1204i −0.446808 + 0.773894i
818818 −40.0191 −1.39924
819819 0 0
820820 −16.7439 −0.584721
821821 −3.17761 + 5.50378i −0.110899 + 0.192083i −0.916133 0.400874i 0.868706π-0.868706\pi
0.805234 + 0.592958i 0.202040π0.202040\pi
822822 5.68693 4.20305i 0.198355 0.146598i
823823 4.73216 + 8.19635i 0.164953 + 0.285707i 0.936639 0.350297i 0.113919π-0.113919\pi
−0.771686 + 0.636004i 0.780586π0.780586\pi
824824 −2.16760 −0.0755120
825825 −7.73282 3.36762i −0.269222 0.117245i
826826 0 0
827827 −4.86261 −0.169090 −0.0845448 0.996420i 0.526944π-0.526944\pi
−0.0845448 + 0.996420i 0.526944π0.526944\pi
828828 −9.00905 + 29.3465i −0.313086 + 1.01986i
829829 −20.3926 + 35.3211i −0.708266 + 1.22675i 0.257234 + 0.966349i 0.417189π0.417189\pi
−0.965500 + 0.260403i 0.916145π0.916145\pi
830830 13.7680 0.477896
831831 −11.8325 5.15302i −0.410466 0.178756i
832832 −6.74003 + 11.6741i −0.233668 + 0.404725i
833833 0 0
834834 0.271315 + 2.39354i 0.00939486 + 0.0828815i
835835 2.35247 4.07460i 0.0814107 0.141007i
836836 2.63362 4.56156i 0.0910856 0.157765i
837837 13.0110 15.1808i 0.449727 0.524726i
838838 23.1823 + 40.1529i 0.800818 + 1.38706i
839839 −9.60171 16.6307i −0.331488 0.574154i 0.651316 0.758807i 0.274217π-0.274217\pi
−0.982804 + 0.184653i 0.940884π0.940884\pi
840840 0 0
841841 14.4981 25.1114i 0.499934 0.865911i
842842 −54.6126 −1.88207
843843 −5.06976 44.7255i −0.174612 1.54043i
844844 7.90225 0.272007
845845 9.20374 + 15.9413i 0.316618 + 0.548399i
846846 −15.4300 + 50.2625i −0.530496 + 1.72806i
847847 0 0
848848 −3.66188 6.34256i −0.125749 0.217804i
849849 3.65886 + 32.2785i 0.125572 + 1.10780i
850850 −4.58940 7.94907i −0.157415 0.272651i
851851 2.07286 + 3.59029i 0.0710566 + 0.123074i
852852 3.34398 + 29.5006i 0.114563 + 1.01068i
853853 6.95055 + 12.0387i 0.237982 + 0.412198i 0.960135 0.279536i 0.0901806π-0.0901806\pi
−0.722153 + 0.691734i 0.756847π0.756847\pi
854854 0 0
855855 2.94280 9.58601i 0.100642 0.327835i
856856 3.24469 + 5.61996i 0.110901 + 0.192086i
857857 −56.9838 −1.94653 −0.973265 0.229686i 0.926230π-0.926230\pi
−0.973265 + 0.229686i 0.926230π0.926230\pi
858858 −2.81299 24.8163i −0.0960340 0.847213i
859859 20.1002 0.685810 0.342905 0.939370i 0.388589π-0.388589\pi
0.342905 + 0.939370i 0.388589π0.388589\pi
860860 −9.46298 + 16.3904i −0.322685 + 0.558907i
861861 0 0
862862 −4.50214 7.79794i −0.153344 0.265599i
863863 −3.08893 5.35018i −0.105148 0.182122i 0.808650 0.588289i 0.200198π-0.200198\pi
−0.913799 + 0.406167i 0.866865π0.866865\pi
864864 22.5888 26.3558i 0.768486 0.896643i
865865 −6.76781 + 11.7222i −0.230112 + 0.398566i
866866 −8.94318 + 15.4900i −0.303902 + 0.526373i
867867 2.84838 + 25.1285i 0.0967361 + 0.853407i
868868 0 0
869869 4.47806 7.75623i 0.151908 0.263112i
870870 0.241742 + 0.105278i 0.00819581 + 0.00356925i
871871 −35.8872 −1.21599
872872 −4.62732 + 8.01476i −0.156701 + 0.271414i
873873 −10.7360 + 34.9720i −0.363359 + 1.18362i
874874 −33.9396 −1.14802
875875 0 0
876876 −6.09009 2.65221i −0.205765 0.0896099i
877877 −37.2574 −1.25809 −0.629046 0.777368i 0.716554π-0.716554\pi
−0.629046 + 0.777368i 0.716554π0.716554\pi
878878 13.6468 + 23.6370i 0.460558 + 0.797710i
879879 3.42905 2.53431i 0.115659 0.0854801i
880880 −4.89504 + 8.47846i −0.165012 + 0.285809i
881881 11.7848 0.397041 0.198520 0.980097i 0.436386π-0.436386\pi
0.198520 + 0.980097i 0.436386π0.436386\pi
882882 0 0
883883 −29.2308 −0.983693 −0.491847 0.870682i 0.663678π-0.663678\pi
−0.491847 + 0.870682i 0.663678π0.663678\pi
884884 5.57265 9.65211i 0.187428 0.324636i
885885 2.19854 + 19.3956i 0.0739032 + 0.651974i
886886 −20.1634 34.9240i −0.677402 1.17329i
887887 −28.5161 −0.957479 −0.478739 0.877957i 0.658906π-0.658906\pi
−0.478739 + 0.877957i 0.658906π0.658906\pi
888888 −0.123372 1.08839i −0.00414010 0.0365240i
889889 0 0
890890 3.45680 0.115872
891891 −0.981141 + 13.5818i −0.0328695 + 0.455006i
892892 −8.14822 + 14.1131i −0.272823 + 0.472543i
893893 −23.8364 −0.797656
894894 16.8884 12.4818i 0.564834 0.417453i
895895 −1.13531 + 1.96642i −0.0379493 + 0.0657301i
896896 0 0
897897 −53.0691 + 39.2219i −1.77193 + 1.30958i
898898 19.7890 34.2755i 0.660366 1.14379i
899899 −0.119171 + 0.206410i −0.00397456 + 0.00688414i
900900 −3.93912 + 12.8315i −0.131304 + 0.427715i
901901 1.17002 + 2.02653i 0.0389790 + 0.0675135i
902902 12.5693 + 21.7707i 0.418513 + 0.724885i
903903 0 0
904904 8.14183 14.1021i 0.270793 0.469028i
905905 −22.6829 −0.754006
906906 32.4872 24.0104i 1.07931 0.797690i
907907 −7.89155 −0.262035 −0.131017 0.991380i 0.541824π-0.541824\pi
−0.131017 + 0.991380i 0.541824π0.541824\pi
908908 7.77317 + 13.4635i 0.257962 + 0.446803i
909909 −2.28597 2.45707i −0.0758209 0.0814957i
910910 0 0
911911 −14.2206 24.6308i −0.471150 0.816055i 0.528306 0.849054i 0.322827π-0.322827\pi
−0.999455 + 0.0329991i 0.989494π0.989494\pi
912912 19.2781 + 8.39554i 0.638361 + 0.278004i
913913 −4.23813 7.34065i −0.140262 0.242940i
914914 37.4007 + 64.7798i 1.23710 + 2.14273i
915915 −6.02225 + 4.45087i −0.199089 + 0.147141i
916916 −6.71206 11.6256i −0.221773 0.384121i
917917 0 0
918918 −9.64370 + 11.2519i −0.318290 + 0.371369i
919919 3.99271 + 6.91558i 0.131707 + 0.228124i 0.924335 0.381582i 0.124621π-0.124621\pi
−0.792627 + 0.609706i 0.791287π0.791287\pi
920920 11.0318 0.363708
921921 7.40446 + 3.22462i 0.243985 + 0.106255i
922922 −5.21221 −0.171655
923923 −31.9110 + 55.2714i −1.05036 + 1.81928i
924924 0 0
925925 0.906337 + 1.56982i 0.0298002 + 0.0516154i
926926 25.6529 + 44.4322i 0.843008 + 1.46013i
927927 −3.94481 4.24006i −0.129565 0.139262i
928928 −0.206895 + 0.358353i −0.00679167 + 0.0117635i
929929 9.40031 16.2818i 0.308414 0.534189i −0.669601 0.742721i 0.733535π-0.733535\pi
0.978016 + 0.208531i 0.0668684π0.0668684\pi
930930 15.0166 + 6.53966i 0.492412 + 0.214444i
931931 0 0
932932 −13.4081 + 23.2234i −0.439196 + 0.760709i
933933 5.36130 + 47.2974i 0.175521 + 1.54845i
934934 49.0577 1.60522
935935 1.56403 2.70898i 0.0511493 0.0885932i
936936 16.9932 3.90260i 0.555440 0.127561i
937937 −48.5788 −1.58700 −0.793500 0.608570i 0.791744π-0.791744\pi
−0.793500 + 0.608570i 0.791744π0.791744\pi
938938 0 0
939939 7.65172 5.65516i 0.249704 0.184549i
940940 −17.6619 −0.576067
941941 10.2425 + 17.7406i 0.333898 + 0.578328i 0.983272 0.182141i 0.0583027π-0.0583027\pi
−0.649375 + 0.760468i 0.724969π0.724969\pi
942942 −50.6049 22.0383i −1.64880 0.718046i
943943 33.2110 57.5231i 1.08150 1.87321i
944944 −40.9312 −1.33220
945945 0 0
946946 28.4148 0.923843
947947 7.42524 12.8609i 0.241288 0.417923i −0.719793 0.694188i 0.755764π-0.755764\pi
0.961081 + 0.276265i 0.0890969π0.0890969\pi
948948 −13.0675 5.69086i −0.424413 0.184831i
949949 −7.13954 12.3661i −0.231759 0.401419i
950950 −14.8398 −0.481466
951951 −13.7586 + 10.1686i −0.446154 + 0.329739i
952952 0 0
953953 46.4678 1.50524 0.752620 0.658456i 0.228790π-0.228790\pi
0.752620 + 0.658456i 0.228790π0.228790\pi
954954 2.44901 7.97750i 0.0792896 0.258281i
955955 15.1454 26.2326i 0.490094 0.848868i
956956 0.541167 0.0175026
957957 −0.0182833 0.161295i −0.000591015 0.00521394i
958958 29.0724 50.3548i 0.939285 1.62689i
959959 0 0
960960 5.52012 + 2.40399i 0.178161 + 0.0775886i
961961 8.09733 14.0250i 0.261204 0.452419i
962962 −2.68380 + 4.64847i −0.0865291 + 0.149873i
963963 −5.08826 + 16.5747i −0.163967 + 0.534112i
964964 7.39301 + 12.8051i 0.238113 + 0.412423i
965965 4.12905 + 7.15172i 0.132919 + 0.230222i
966966 0 0
967967 0.863670 1.49592i 0.0277738 0.0481056i −0.851804 0.523860i 0.824492π-0.824492\pi
0.879578 + 0.475754i 0.157825π0.157825\pi
968968 −9.78089 −0.314370
969969 −6.15960 2.68249i −0.197875 0.0861739i
970970 −29.9687 −0.962235
971971 3.78085 + 6.54863i 0.121333 + 0.210156i 0.920294 0.391228i 0.127950π-0.127950\pi
−0.798960 + 0.601384i 0.794616π0.794616\pi
972972 21.6526 0.882976i 0.694506 0.0283215i
973973 0 0
974974 0.281870 + 0.488213i 0.00903169 + 0.0156434i
975975 −23.2040 + 17.1494i −0.743122 + 0.549220i
976976 −7.85137 13.5990i −0.251316 0.435293i
977977 28.3101 + 49.0345i 0.905721 + 1.56875i 0.819947 + 0.572440i 0.194003π0.194003\pi
0.0857737 + 0.996315i 0.472664π0.472664\pi
978978 35.7277 + 15.5593i 1.14245 + 0.497531i
979979 −1.06408 1.84305i −0.0340083 0.0589041i
980980 0 0
981981 −24.0990 + 5.53449i −0.769422 + 0.176703i
982982 16.6997 + 28.9247i 0.532909 + 0.923025i
983983 −32.2972 −1.03012 −0.515061 0.857154i 0.672231π-0.672231\pi
−0.515061 + 0.857154i 0.672231π0.672231\pi
984984 −14.1134 + 10.4308i −0.449920 + 0.332523i
985985 −13.0407 −0.415510
986986 0.0883286 0.152990i 0.00281296 0.00487218i
987987 0 0
988988 −9.00955 15.6050i −0.286632 0.496461i
989989 −37.5391 65.0197i −1.19367 2.06750i
990990 −10.8721 + 2.49686i −0.345540 + 0.0793554i
991991 −7.15502 + 12.3929i −0.227287 + 0.393672i −0.957003 0.290078i 0.906319π-0.906319\pi
0.729716 + 0.683750i 0.239652π0.239652\pi
992992 −12.8520 + 22.2602i −0.408050 + 0.706764i
993993 28.8253 21.3039i 0.914742 0.676059i
994994 0 0
995995 −5.79247 + 10.0329i −0.183634 + 0.318063i
996996 −10.8480 + 8.01748i −0.343734 + 0.254044i
997997 −56.2524 −1.78153 −0.890765 0.454463i 0.849831π-0.849831\pi
−0.890765 + 0.454463i 0.849831π0.849831\pi
998998 −19.6176 + 33.9787i −0.620985 + 1.07558i
999999 1.90449 2.22209i 0.0602553 0.0703038i
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 441.2.g.f.67.4 10
3.2 odd 2 1323.2.g.f.361.2 10
7.2 even 3 441.2.h.f.373.2 10
7.3 odd 6 441.2.f.e.148.4 10
7.4 even 3 441.2.f.f.148.4 10
7.5 odd 6 63.2.h.b.58.2 yes 10
7.6 odd 2 63.2.g.b.4.4 10
9.2 odd 6 1323.2.h.f.802.4 10
9.7 even 3 441.2.h.f.214.2 10
21.2 odd 6 1323.2.h.f.226.4 10
21.5 even 6 189.2.h.b.37.4 10
21.11 odd 6 1323.2.f.f.442.2 10
21.17 even 6 1323.2.f.e.442.2 10
21.20 even 2 189.2.g.b.172.2 10
28.19 even 6 1008.2.q.i.625.2 10
28.27 even 2 1008.2.t.i.193.5 10
63.2 odd 6 1323.2.g.f.667.2 10
63.4 even 3 3969.2.a.ba.1.2 5
63.5 even 6 567.2.e.e.163.2 10
63.11 odd 6 1323.2.f.f.883.2 10
63.13 odd 6 567.2.e.f.487.4 10
63.16 even 3 inner 441.2.g.f.79.4 10
63.20 even 6 189.2.h.b.46.4 10
63.25 even 3 441.2.f.f.295.4 10
63.31 odd 6 3969.2.a.z.1.2 5
63.32 odd 6 3969.2.a.bb.1.4 5
63.34 odd 6 63.2.h.b.25.2 yes 10
63.38 even 6 1323.2.f.e.883.2 10
63.40 odd 6 567.2.e.f.163.4 10
63.41 even 6 567.2.e.e.487.2 10
63.47 even 6 189.2.g.b.100.2 10
63.52 odd 6 441.2.f.e.295.4 10
63.59 even 6 3969.2.a.bc.1.4 5
63.61 odd 6 63.2.g.b.16.4 yes 10
84.47 odd 6 3024.2.q.i.2305.4 10
84.83 odd 2 3024.2.t.i.1873.2 10
252.47 odd 6 3024.2.t.i.289.2 10
252.83 odd 6 3024.2.q.i.2881.4 10
252.187 even 6 1008.2.t.i.961.5 10
252.223 even 6 1008.2.q.i.529.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.g.b.4.4 10 7.6 odd 2
63.2.g.b.16.4 yes 10 63.61 odd 6
63.2.h.b.25.2 yes 10 63.34 odd 6
63.2.h.b.58.2 yes 10 7.5 odd 6
189.2.g.b.100.2 10 63.47 even 6
189.2.g.b.172.2 10 21.20 even 2
189.2.h.b.37.4 10 21.5 even 6
189.2.h.b.46.4 10 63.20 even 6
441.2.f.e.148.4 10 7.3 odd 6
441.2.f.e.295.4 10 63.52 odd 6
441.2.f.f.148.4 10 7.4 even 3
441.2.f.f.295.4 10 63.25 even 3
441.2.g.f.67.4 10 1.1 even 1 trivial
441.2.g.f.79.4 10 63.16 even 3 inner
441.2.h.f.214.2 10 9.7 even 3
441.2.h.f.373.2 10 7.2 even 3
567.2.e.e.163.2 10 63.5 even 6
567.2.e.e.487.2 10 63.41 even 6
567.2.e.f.163.4 10 63.40 odd 6
567.2.e.f.487.4 10 63.13 odd 6
1008.2.q.i.529.2 10 252.223 even 6
1008.2.q.i.625.2 10 28.19 even 6
1008.2.t.i.193.5 10 28.27 even 2
1008.2.t.i.961.5 10 252.187 even 6
1323.2.f.e.442.2 10 21.17 even 6
1323.2.f.e.883.2 10 63.38 even 6
1323.2.f.f.442.2 10 21.11 odd 6
1323.2.f.f.883.2 10 63.11 odd 6
1323.2.g.f.361.2 10 3.2 odd 2
1323.2.g.f.667.2 10 63.2 odd 6
1323.2.h.f.226.4 10 21.2 odd 6
1323.2.h.f.802.4 10 9.2 odd 6
3024.2.q.i.2305.4 10 84.47 odd 6
3024.2.q.i.2881.4 10 252.83 odd 6
3024.2.t.i.289.2 10 252.47 odd 6
3024.2.t.i.1873.2 10 84.83 odd 2
3969.2.a.z.1.2 5 63.31 odd 6
3969.2.a.ba.1.2 5 63.4 even 3
3969.2.a.bb.1.4 5 63.32 odd 6
3969.2.a.bc.1.4 5 63.59 even 6