Properties

Label 637.2.f.k.393.1
Level 637637
Weight 22
Character 637.393
Analytic conductor 5.0865.086
Analytic rank 00
Dimension 1212
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] = [637,2,Mod(295,637)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 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("637.295"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 637=7213 637 = 7^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 637.f (of order 33, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [12,2,1,-4,-2] 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: 5.086470608765.08647060876
Analytic rank: 00
Dimension: 1212
Relative dimension: 66 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x12x11+7x102x9+33x811x7+55x6+17x5+47x4+x3+8x2+x+1 x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 393.1
Root 0.2179530.377506i0.217953 - 0.377506i of defining polynomial
Character χ\chi == 637.393
Dual form 637.2.f.k.295.1

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+(0.9290811.60921i)q2+(1.147031.98672i)q3+(0.726381+1.25813i)q40.197362q5+(2.13137+3.69165i)q61.01686q8+(1.13137+1.95960i)q9+(0.183365+0.317598i)q10+(2.09137+3.62236i)q11+3.33274q12+(2.72221+2.36423i)q13+(0.226381+0.392104i)q15+(2.39750+4.15260i)q16+(0.420653+0.728592i)q17+4.20455q18+(0.675876+1.17065i)q19+(0.1433600.248307i)q20+(3.886106.73092i)q22+(2.05760+3.56386i)q23+(1.16637+2.02021i)q244.96105q25+(6.33370+2.18406i)q261.69131q27+(4.11931+7.13485i)q29+(0.4206530.728592i)q301.28070q31+(3.438095.95495i)q32+(4.797748.30993i)q33+1.56328q34+(1.643622.84683i)q36+(1.522422.63692i)q37+2.51177q38+(7.81953+2.69642i)q39+0.200689q40+(2.698484.67390i)q41+(2.66389+4.61399i)q436.07652q44+(0.2232900.386750i)q45+(3.823346.62223i)q4611.6641q47+(5.500039.52634i)q48+(4.60921+7.98339i)q50+1.93001q51+(0.9971415.14222i)q52+4.64796q53+(1.57136+2.72168i)q54+(0.4127570.714916i)q55+3.10101q57+(7.6543413.2577i)q58+(3.02905+5.24648i)q590.657756q60+(5.682859.84298i)q61+(1.18987+2.06092i)q623.18704q64+(0.5372620.466609i)q6517.8300q66+(6.6985111.6022i)q67+(0.6111091.05847i)q68+(4.720268.17574i)q69+(2.985205.17051i)q71+(1.150441.99263i)q72+3.88547q73+(2.82891+4.89982i)q74+(5.69049+9.85622i)q75+(0.9818871.70068i)q76+(2.9258515.0885i)q7810.7334q79+(0.4731770.819566i)q80+(5.33411+9.23895i)q81+(5.01421+8.68486i)q82+3.07390q83+(0.08302100.143797i)q85+9.89987q86+(9.4499716.3678i)q87+(2.126623.68341i)q88+(5.99207+10.3786i)q890.829819q905.97840q92+(1.46901+2.54439i)q93+(10.8369+18.7700i)q94+(0.1333920.231042i)q9515.7744q96+(9.73637+16.8639i)q979.46448q99+O(q100)q+(-0.929081 - 1.60921i) q^{2} +(-1.14703 - 1.98672i) q^{3} +(-0.726381 + 1.25813i) q^{4} -0.197362 q^{5} +(-2.13137 + 3.69165i) q^{6} -1.01686 q^{8} +(-1.13137 + 1.95960i) q^{9} +(0.183365 + 0.317598i) q^{10} +(2.09137 + 3.62236i) q^{11} +3.33274 q^{12} +(-2.72221 + 2.36423i) q^{13} +(0.226381 + 0.392104i) q^{15} +(2.39750 + 4.15260i) q^{16} +(-0.420653 + 0.728592i) q^{17} +4.20455 q^{18} +(-0.675876 + 1.17065i) q^{19} +(0.143360 - 0.248307i) q^{20} +(3.88610 - 6.73092i) q^{22} +(2.05760 + 3.56386i) q^{23} +(1.16637 + 2.02021i) q^{24} -4.96105 q^{25} +(6.33370 + 2.18406i) q^{26} -1.69131 q^{27} +(4.11931 + 7.13485i) q^{29} +(0.420653 - 0.728592i) q^{30} -1.28070 q^{31} +(3.43809 - 5.95495i) q^{32} +(4.79774 - 8.30993i) q^{33} +1.56328 q^{34} +(-1.64362 - 2.84683i) q^{36} +(-1.52242 - 2.63692i) q^{37} +2.51177 q^{38} +(7.81953 + 2.69642i) q^{39} +0.200689 q^{40} +(-2.69848 - 4.67390i) q^{41} +(-2.66389 + 4.61399i) q^{43} -6.07652 q^{44} +(0.223290 - 0.386750i) q^{45} +(3.82334 - 6.62223i) q^{46} -11.6641 q^{47} +(5.50003 - 9.52634i) q^{48} +(4.60921 + 7.98339i) q^{50} +1.93001 q^{51} +(-0.997141 - 5.14222i) q^{52} +4.64796 q^{53} +(1.57136 + 2.72168i) q^{54} +(-0.412757 - 0.714916i) q^{55} +3.10101 q^{57} +(7.65434 - 13.2577i) q^{58} +(-3.02905 + 5.24648i) q^{59} -0.657756 q^{60} +(5.68285 - 9.84298i) q^{61} +(1.18987 + 2.06092i) q^{62} -3.18704 q^{64} +(0.537262 - 0.466609i) q^{65} -17.8300 q^{66} +(-6.69851 - 11.6022i) q^{67} +(-0.611109 - 1.05847i) q^{68} +(4.72026 - 8.17574i) q^{69} +(2.98520 - 5.17051i) q^{71} +(1.15044 - 1.99263i) q^{72} +3.88547 q^{73} +(-2.82891 + 4.89982i) q^{74} +(5.69049 + 9.85622i) q^{75} +(-0.981887 - 1.70068i) q^{76} +(-2.92585 - 15.0885i) q^{78} -10.7334 q^{79} +(-0.473177 - 0.819566i) q^{80} +(5.33411 + 9.23895i) q^{81} +(-5.01421 + 8.68486i) q^{82} +3.07390 q^{83} +(0.0830210 - 0.143797i) q^{85} +9.89987 q^{86} +(9.44997 - 16.3678i) q^{87} +(-2.12662 - 3.68341i) q^{88} +(5.99207 + 10.3786i) q^{89} -0.829819 q^{90} -5.97840 q^{92} +(1.46901 + 2.54439i) q^{93} +(10.8369 + 18.7700i) q^{94} +(0.133392 - 0.231042i) q^{95} -15.7744 q^{96} +(-9.73637 + 16.8639i) q^{97} -9.46448 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q+2q2+q34q42q59q66q8+3q9+4q10+4q1110q122q132q15+8q16+5q176q18q19q205q22q23+20q99+O(q100) 12 q + 2 q^{2} + q^{3} - 4 q^{4} - 2 q^{5} - 9 q^{6} - 6 q^{8} + 3 q^{9} + 4 q^{10} + 4 q^{11} - 10 q^{12} - 2 q^{13} - 2 q^{15} + 8 q^{16} + 5 q^{17} - 6 q^{18} - q^{19} - q^{20} - 5 q^{22} - q^{23}+ \cdots - 20 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/637Z)×\left(\mathbb{Z}/637\mathbb{Z}\right)^\times.

nn 197197 248248
χ(n)\chi(n) e(13)e\left(\frac{1}{3}\right) 11

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 −0.929081 1.60921i −0.656959 1.13789i −0.981399 0.191980i 0.938509π-0.938509\pi
0.324440 0.945906i 0.394824π-0.394824\pi
33 −1.14703 1.98672i −0.662240 1.14703i −0.980026 0.198871i 0.936272π-0.936272\pi
0.317785 0.948163i 0.397061π-0.397061\pi
44 −0.726381 + 1.25813i −0.363191 + 0.629065i
55 −0.197362 −0.0882631 −0.0441315 0.999026i 0.514052π-0.514052\pi
−0.0441315 + 0.999026i 0.514052π0.514052\pi
66 −2.13137 + 3.69165i −0.870130 + 1.50711i
77 0 0
88 −1.01686 −0.359513
99 −1.13137 + 1.95960i −0.377125 + 0.653199i
1010 0.183365 + 0.317598i 0.0579852 + 0.100433i
1111 2.09137 + 3.62236i 0.630571 + 1.09218i 0.987435 + 0.158025i 0.0505127π0.0505127\pi
−0.356864 + 0.934156i 0.616154π0.616154\pi
1212 3.33274 0.962078
1313 −2.72221 + 2.36423i −0.755005 + 0.655719i
1414 0 0
1515 0.226381 + 0.392104i 0.0584514 + 0.101241i
1616 2.39750 + 4.15260i 0.599376 + 1.03815i
1717 −0.420653 + 0.728592i −0.102023 + 0.176709i −0.912518 0.409036i 0.865865π-0.865865\pi
0.810495 + 0.585746i 0.199198π0.199198\pi
1818 4.20455 0.991022
1919 −0.675876 + 1.17065i −0.155057 + 0.268566i −0.933080 0.359670i 0.882889π-0.882889\pi
0.778023 + 0.628236i 0.216223π0.216223\pi
2020 0.143360 0.248307i 0.0320563 0.0555232i
2121 0 0
2222 3.88610 6.73092i 0.828519 1.43504i
2323 2.05760 + 3.56386i 0.429038 + 0.743116i 0.996788 0.0800850i 0.0255192π-0.0255192\pi
−0.567750 + 0.823201i 0.692186π0.692186\pi
2424 1.16637 + 2.02021i 0.238084 + 0.412373i
2525 −4.96105 −0.992210
2626 6.33370 + 2.18406i 1.24214 + 0.428330i
2727 −1.69131 −0.325492
2828 0 0
2929 4.11931 + 7.13485i 0.764936 + 1.32491i 0.940280 + 0.340401i 0.110563π0.110563\pi
−0.175344 + 0.984507i 0.556104π0.556104\pi
3030 0.420653 0.728592i 0.0768003 0.133022i
3131 −1.28070 −0.230020 −0.115010 0.993364i 0.536690π-0.536690\pi
−0.115010 + 0.993364i 0.536690π0.536690\pi
3232 3.43809 5.95495i 0.607774 1.05270i
3333 4.79774 8.30993i 0.835180 1.44657i
3434 1.56328 0.268100
3535 0 0
3636 −1.64362 2.84683i −0.273936 0.474471i
3737 −1.52242 2.63692i −0.250285 0.433506i 0.713319 0.700839i 0.247191π-0.247191\pi
−0.963604 + 0.267333i 0.913858π0.913858\pi
3838 2.51177 0.407463
3939 7.81953 + 2.69642i 1.25213 + 0.431773i
4040 0.200689 0.0317317
4141 −2.69848 4.67390i −0.421431 0.729941i 0.574648 0.818400i 0.305139π-0.305139\pi
−0.996080 + 0.0884599i 0.971805π0.971805\pi
4242 0 0
4343 −2.66389 + 4.61399i −0.406239 + 0.703627i −0.994465 0.105070i 0.966493π-0.966493\pi
0.588226 + 0.808697i 0.299827π0.299827\pi
4444 −6.07652 −0.916070
4545 0.223290 0.386750i 0.0332862 0.0576534i
4646 3.82334 6.62223i 0.563721 0.976394i
4747 −11.6641 −1.70138 −0.850690 0.525668i 0.823815π-0.823815\pi
−0.850690 + 0.525668i 0.823815π0.823815\pi
4848 5.50003 9.52634i 0.793862 1.37501i
4949 0 0
5050 4.60921 + 7.98339i 0.651841 + 1.12902i
5151 1.93001 0.270256
5252 −0.997141 5.14222i −0.138279 0.713098i
5353 4.64796 0.638447 0.319223 0.947679i 0.396578π-0.396578\pi
0.319223 + 0.947679i 0.396578π0.396578\pi
5454 1.57136 + 2.72168i 0.213835 + 0.370373i
5555 −0.412757 0.714916i −0.0556562 0.0963993i
5656 0 0
5757 3.10101 0.410739
5858 7.65434 13.2577i 1.00506 1.74082i
5959 −3.02905 + 5.24648i −0.394349 + 0.683033i −0.993018 0.117964i 0.962363π-0.962363\pi
0.598669 + 0.800997i 0.295697π0.295697\pi
6060 −0.657756 −0.0849160
6161 5.68285 9.84298i 0.727614 1.26026i −0.230275 0.973126i 0.573962π-0.573962\pi
0.957889 0.287139i 0.0927042π-0.0927042\pi
6262 1.18987 + 2.06092i 0.151114 + 0.261737i
6363 0 0
6464 −3.18704 −0.398380
6565 0.537262 0.466609i 0.0666391 0.0578758i
6666 −17.8300 −2.19472
6767 −6.69851 11.6022i −0.818354 1.41743i −0.906895 0.421357i 0.861554π-0.861554\pi
0.0885411 0.996073i 0.471780π-0.471780\pi
6868 −0.611109 1.05847i −0.0741078 0.128358i
6969 4.72026 8.17574i 0.568253 0.984243i
7070 0 0
7171 2.98520 5.17051i 0.354278 0.613627i −0.632716 0.774384i 0.718060π-0.718060\pi
0.986994 + 0.160757i 0.0513934π0.0513934\pi
7272 1.15044 1.99263i 0.135581 0.234833i
7373 3.88547 0.454759 0.227380 0.973806i 0.426984π-0.426984\pi
0.227380 + 0.973806i 0.426984π0.426984\pi
7474 −2.82891 + 4.89982i −0.328854 + 0.569592i
7575 5.69049 + 9.85622i 0.657081 + 1.13810i
7676 −0.981887 1.70068i −0.112630 0.195081i
7777 0 0
7878 −2.92585 15.0885i −0.331287 1.70844i
7979 −10.7334 −1.20760 −0.603799 0.797136i 0.706347π-0.706347\pi
−0.603799 + 0.797136i 0.706347π0.706347\pi
8080 −0.473177 0.819566i −0.0529028 0.0916303i
8181 5.33411 + 9.23895i 0.592679 + 1.02655i
8282 −5.01421 + 8.68486i −0.553726 + 0.959082i
8383 3.07390 0.337404 0.168702 0.985667i 0.446042π-0.446042\pi
0.168702 + 0.985667i 0.446042π0.446042\pi
8484 0 0
8585 0.0830210 0.143797i 0.00900489 0.0155969i
8686 9.89987 1.06753
8787 9.44997 16.3678i 1.01314 1.75482i
8888 −2.12662 3.68341i −0.226698 0.392653i
8989 5.99207 + 10.3786i 0.635159 + 1.10013i 0.986482 + 0.163873i 0.0523986π0.0523986\pi
−0.351323 + 0.936254i 0.614268π0.614268\pi
9090 −0.829819 −0.0874706
9191 0 0
9292 −5.97840 −0.623291
9393 1.46901 + 2.54439i 0.152329 + 0.263841i
9494 10.8369 + 18.7700i 1.11774 + 1.93598i
9595 0.133392 0.231042i 0.0136858 0.0237045i
9696 −15.7744 −1.60997
9797 −9.73637 + 16.8639i −0.988578 + 1.71227i −0.363771 + 0.931488i 0.618511π0.618511\pi
−0.624807 + 0.780779i 0.714822π0.714822\pi
9898 0 0
9999 −9.46448 −0.951216
100100 3.60361 6.24164i 0.360361 0.624164i
101101 8.46697 + 14.6652i 0.842495 + 1.45924i 0.887779 + 0.460270i 0.152247π0.152247\pi
−0.0452843 + 0.998974i 0.514419π0.514419\pi
102102 −1.79314 3.10580i −0.177547 0.307520i
103103 −7.23425 −0.712811 −0.356406 0.934331i 0.615998π-0.615998\pi
−0.356406 + 0.934331i 0.615998π0.615998\pi
104104 2.76809 2.40408i 0.271434 0.235739i
105105 0 0
106106 −4.31833 7.47957i −0.419434 0.726480i
107107 4.92625 + 8.53251i 0.476238 + 0.824869i 0.999629 0.0272237i 0.00866664π-0.00866664\pi
−0.523391 + 0.852093i 0.675333π0.675333\pi
108108 1.22853 2.12788i 0.118216 0.204756i
109109 −13.8159 −1.32332 −0.661662 0.749802i 0.730149π-0.730149\pi
−0.661662 + 0.749802i 0.730149π0.730149\pi
110110 −0.766969 + 1.32843i −0.0731277 + 0.126661i
111111 −3.49255 + 6.04927i −0.331498 + 0.574171i
112112 0 0
113113 2.13432 3.69675i 0.200780 0.347761i −0.748000 0.663699i 0.768986π-0.768986\pi
0.948780 + 0.315938i 0.102319π0.102319\pi
114114 −2.88109 4.99019i −0.269839 0.467374i
115115 −0.406092 0.703371i −0.0378682 0.0655897i
116116 −11.9687 −1.11127
117117 −1.55310 8.00926i −0.143584 0.740456i
118118 11.2569 1.03629
119119 0 0
120120 −0.230197 0.398713i −0.0210140 0.0363973i
121121 −3.24765 + 5.62509i −0.295240 + 0.511372i
122122 −21.1193 −1.91205
123123 −6.19049 + 10.7222i −0.558178 + 0.966792i
124124 0.930276 1.61129i 0.0835412 0.144698i
125125 1.96593 0.175839
126126 0 0
127127 1.09512 + 1.89680i 0.0971761 + 0.168314i 0.910515 0.413477i 0.135686π-0.135686\pi
−0.813339 + 0.581791i 0.802352π0.802352\pi
128128 −3.91516 6.78126i −0.346055 0.599385i
129129 12.2223 1.07611
130130 −1.25003 0.431052i −0.109635 0.0378057i
131131 2.27612 0.198865 0.0994326 0.995044i 0.468297π-0.468297\pi
0.0994326 + 0.995044i 0.468297π0.468297\pi
132132 6.96998 + 12.0724i 0.606659 + 1.05076i
133133 0 0
134134 −12.4469 + 21.5587i −1.07525 + 1.86239i
135135 0.333800 0.0287289
136136 0.427743 0.740873i 0.0366787 0.0635293i
137137 −6.72399 + 11.6463i −0.574469 + 0.995010i 0.421630 + 0.906768i 0.361458π0.361458\pi
−0.996099 + 0.0882417i 0.971875π0.971875\pi
138138 −17.5420 −1.49328
139139 −2.02270 + 3.50342i −0.171563 + 0.297156i −0.938966 0.344009i 0.888215π-0.888215\pi
0.767403 + 0.641165i 0.221548π0.221548\pi
140140 0 0
141141 13.3791 + 23.1733i 1.12672 + 1.95154i
142142 −11.0940 −0.930984
143143 −14.2572 4.91634i −1.19225 0.411125i
144144 −10.8499 −0.904157
145145 −0.812996 1.40815i −0.0675156 0.116940i
146146 −3.60991 6.25255i −0.298758 0.517465i
147147 0 0
148148 4.42344 0.363605
149149 −7.67596 + 13.2952i −0.628840 + 1.08918i 0.358945 + 0.933359i 0.383136π0.383136\pi
−0.987785 + 0.155823i 0.950197π0.950197\pi
150150 10.5738 18.3144i 0.863351 1.49537i
151151 6.12108 0.498127 0.249063 0.968487i 0.419877π-0.419877\pi
0.249063 + 0.968487i 0.419877π0.419877\pi
152152 0.687268 1.19038i 0.0557448 0.0965528i
153153 −0.951831 1.64862i −0.0769510 0.133283i
154154 0 0
155155 0.252762 0.0203023
156156 −9.07241 + 7.87935i −0.726374 + 0.630853i
157157 4.53668 0.362067 0.181033 0.983477i 0.442056π-0.442056\pi
0.181033 + 0.983477i 0.442056π0.442056\pi
158158 9.97217 + 17.2723i 0.793343 + 1.37411i
159159 −5.33137 9.23421i −0.422805 0.732320i
160160 −0.678549 + 1.17528i −0.0536440 + 0.0929142i
161161 0 0
162162 9.91163 17.1674i 0.778731 1.34880i
163163 −0.911271 + 1.57837i −0.0713762 + 0.123627i −0.899505 0.436911i 0.856072π-0.856072\pi
0.828128 + 0.560538i 0.189406π0.189406\pi
164164 7.84049 0.612240
165165 −0.946893 + 1.64007i −0.0737155 + 0.127679i
166166 −2.85590 4.94656i −0.221661 0.383928i
167167 5.35397 + 9.27336i 0.414303 + 0.717594i 0.995355 0.0962726i 0.0306921π-0.0306921\pi
−0.581052 + 0.813866i 0.697359π0.697359\pi
168168 0 0
169169 1.82086 12.8718i 0.140066 0.990142i
170170 −0.308533 −0.0236634
171171 −1.52934 2.64889i −0.116951 0.202566i
172172 −3.87000 6.70303i −0.295085 0.511102i
173173 6.74634 11.6850i 0.512915 0.888395i −0.486973 0.873417i 0.661899π-0.661899\pi
0.999888 0.0149778i 0.00476775π-0.00476775\pi
174174 −35.1191 −2.66237
175175 0 0
176176 −10.0281 + 17.3692i −0.755898 + 1.30925i
177177 13.8977 1.04462
178178 11.1342 19.2851i 0.834547 1.44548i
179179 −5.23458 9.06657i −0.391251 0.677667i 0.601364 0.798975i 0.294624π-0.294624\pi
−0.992615 + 0.121309i 0.961291π0.961291\pi
180180 0.324388 + 0.561857i 0.0241785 + 0.0418783i
181181 12.5209 0.930674 0.465337 0.885133i 0.345933π-0.345933\pi
0.465337 + 0.885133i 0.345933π0.345933\pi
182182 0 0
183183 −26.0737 −1.92742
184184 −2.09228 3.62393i −0.154245 0.267160i
185185 0.300469 + 0.520428i 0.0220909 + 0.0382626i
186186 2.72965 4.72789i 0.200148 0.346666i
187187 −3.51896 −0.257332
188188 8.47256 14.6749i 0.617925 1.07028i
189189 0 0
190190 −0.495729 −0.0359640
191191 −6.55685 + 11.3568i −0.474437 + 0.821749i −0.999572 0.0292704i 0.990682π-0.990682\pi
0.525135 + 0.851019i 0.324015π0.324015\pi
192192 3.65565 + 6.33176i 0.263823 + 0.456956i
193193 −0.520786 0.902028i −0.0374870 0.0649294i 0.846673 0.532113i 0.178602π-0.178602\pi
−0.884160 + 0.467184i 0.845269π0.845269\pi
194194 36.1835 2.59782
195195 −1.54328 0.532172i −0.110517 0.0381096i
196196 0 0
197197 −0.739167 1.28027i −0.0526635 0.0912158i 0.838492 0.544914i 0.183438π-0.183438\pi
−0.891155 + 0.453698i 0.850104π0.850104\pi
198198 8.79326 + 15.2304i 0.624910 + 1.08238i
199199 −7.04993 + 12.2108i −0.499756 + 0.865603i −1.00000 0.000281618i 0.999910π-0.999910\pi
0.500244 + 0.865885i 0.333244π0.333244\pi
200200 5.04467 0.356712
201201 −15.3668 + 26.6162i −1.08389 + 1.87736i
202202 15.7330 27.2503i 1.10697 1.91733i
203203 0 0
204204 −1.40192 + 2.42820i −0.0981543 + 0.170008i
205205 0.532578 + 0.922451i 0.0371968 + 0.0644268i
206206 6.72120 + 11.6415i 0.468288 + 0.811099i
207207 −9.31164 −0.647204
208208 −16.3442 5.63600i −1.13327 0.390786i
209209 −5.65402 −0.391097
210210 0 0
211211 −13.2346 22.9230i −0.911108 1.57809i −0.812501 0.582959i 0.801895π-0.801895\pi
−0.0986067 0.995126i 0.531439π-0.531439\pi
212212 −3.37619 + 5.84774i −0.231878 + 0.401624i
213213 −13.6965 −0.938468
214214 9.15376 15.8548i 0.625738 1.08381i
215215 0.525751 0.910628i 0.0358559 0.0621043i
216216 1.71981 0.117019
217217 0 0
218218 12.8361 + 22.2328i 0.869370 + 1.50579i
219219 −4.45676 7.71934i −0.301160 0.521625i
220220 1.19928 0.0808552
221221 −0.577452 2.97790i −0.0388436 0.200315i
222222 12.9794 0.871122
223223 0.364024 + 0.630508i 0.0243769 + 0.0422219i 0.877956 0.478740i 0.158907π-0.158907\pi
−0.853580 + 0.520962i 0.825573π0.825573\pi
224224 0 0
225225 5.61280 9.72165i 0.374187 0.648110i
226226 −7.93182 −0.527617
227227 1.42598 2.46986i 0.0946454 0.163931i −0.814815 0.579721i 0.803162π-0.803162\pi
0.909461 + 0.415790i 0.136495π0.136495\pi
228228 −2.25252 + 3.90147i −0.149177 + 0.258381i
229229 3.17352 0.209712 0.104856 0.994487i 0.466562π-0.466562\pi
0.104856 + 0.994487i 0.466562π0.466562\pi
230230 −0.754584 + 1.30698i −0.0497558 + 0.0861795i
231231 0 0
232232 −4.18874 7.25511i −0.275004 0.476321i
233233 13.4071 0.878327 0.439163 0.898407i 0.355275π-0.355275\pi
0.439163 + 0.898407i 0.355275π0.355275\pi
234234 −11.4457 + 9.94051i −0.748227 + 0.649832i
235235 2.30205 0.150169
236236 −4.40050 7.62188i −0.286448 0.496142i
237237 12.3115 + 21.3242i 0.799721 + 1.38516i
238238 0 0
239239 −15.5538 −1.00609 −0.503046 0.864259i 0.667788π-0.667788\pi
−0.503046 + 0.864259i 0.667788π0.667788\pi
240240 −1.08550 + 1.88014i −0.0700687 + 0.121363i
241241 3.78787 6.56078i 0.243998 0.422617i −0.717851 0.696196i 0.754874π-0.754874\pi
0.961849 + 0.273579i 0.0882076π0.0882076\pi
242242 12.0693 0.775844
243243 9.69985 16.8006i 0.622245 1.07776i
244244 8.25583 + 14.2995i 0.528525 + 0.915433i
245245 0 0
246246 23.0059 1.46680
247247 −0.927810 4.78468i −0.0590351 0.304442i
248248 1.30229 0.0826953
249249 −3.52587 6.10698i −0.223443 0.387014i
250250 −1.82651 3.16361i −0.115519 0.200084i
251251 −0.637382 + 1.10398i −0.0402312 + 0.0696825i −0.885440 0.464754i 0.846143π-0.846143\pi
0.845209 + 0.534436i 0.179476π0.179476\pi
252252 0 0
253253 −8.60638 + 14.9067i −0.541079 + 0.937176i
254254 2.03491 3.52456i 0.127682 0.221151i
255255 −0.380912 −0.0238536
256256 −10.4620 + 18.1208i −0.653878 + 1.13255i
257257 4.24010 + 7.34406i 0.264490 + 0.458110i 0.967430 0.253139i 0.0814631π-0.0814631\pi
−0.702940 + 0.711249i 0.748130π0.748130\pi
258258 −11.3555 19.6683i −0.706962 1.22449i
259259 0 0
260260 0.196798 + 1.01488i 0.0122049 + 0.0629402i
261261 −18.6419 −1.15390
262262 −2.11470 3.66276i −0.130646 0.226286i
263263 −6.39415 11.0750i −0.394280 0.682913i 0.598729 0.800952i 0.295673π-0.295673\pi
−0.993009 + 0.118038i 0.962339π0.962339\pi
264264 −4.87861 + 8.45000i −0.300258 + 0.520062i
265265 −0.917333 −0.0563513
266266 0 0
267267 13.7462 23.8092i 0.841255 1.45710i
268268 19.4627 1.18887
269269 2.35586 4.08047i 0.143639 0.248790i −0.785225 0.619210i 0.787453π-0.787453\pi
0.928864 + 0.370420i 0.120786π0.120786\pi
270270 −0.310127 0.537156i −0.0188737 0.0326903i
271271 9.00562 + 15.5982i 0.547052 + 0.947522i 0.998475 + 0.0552119i 0.0175834π0.0175834\pi
−0.451422 + 0.892310i 0.649083π0.649083\pi
272272 −4.03407 −0.244601
273273 0 0
274274 24.9885 1.50961
275275 −10.3754 17.9707i −0.625659 1.08367i
276276 6.85742 + 11.8774i 0.412768 + 0.714936i
277277 13.0604 22.6213i 0.784725 1.35918i −0.144438 0.989514i 0.546137π-0.546137\pi
0.929163 0.369670i 0.120529π-0.120529\pi
278278 7.51700 0.450840
279279 1.44895 2.50965i 0.0867463 0.150249i
280280 0 0
281281 −3.66197 −0.218455 −0.109227 0.994017i 0.534838π-0.534838\pi
−0.109227 + 0.994017i 0.534838π0.534838\pi
282282 24.8605 43.0596i 1.48042 2.56416i
283283 −3.82263 6.62099i −0.227232 0.393577i 0.729755 0.683709i 0.239634π-0.239634\pi
−0.956987 + 0.290132i 0.906301π0.906301\pi
284284 4.33678 + 7.51153i 0.257341 + 0.445727i
285285 −0.612022 −0.0362531
286286 5.33465 + 27.5106i 0.315445 + 1.62674i
287287 0 0
288288 7.77953 + 13.4745i 0.458413 + 0.793995i
289289 8.14610 + 14.1095i 0.479183 + 0.829968i
290290 −1.51068 + 2.61657i −0.0887100 + 0.153650i
291291 44.6718 2.61871
292292 −2.82233 + 4.88842i −0.165164 + 0.286073i
293293 8.57670 14.8553i 0.501056 0.867855i −0.498943 0.866635i 0.666278π-0.666278\pi
0.999999 0.00122001i 0.000388343π-0.000388343\pi
294294 0 0
295295 0.597821 1.03546i 0.0348065 0.0602866i
296296 1.54809 + 2.68136i 0.0899807 + 0.155851i
297297 −3.53715 6.12652i −0.205246 0.355497i
298298 28.5264 1.65249
299299 −14.0270 4.83695i −0.811201 0.279728i
300300 −16.5339 −0.954583
301301 0 0
302302 −5.68698 9.85014i −0.327249 0.566812i
303303 19.4238 33.6430i 1.11587 1.93274i
304304 −6.48166 −0.371749
305305 −1.12158 + 1.94263i −0.0642215 + 0.111235i
306306 −1.76866 + 3.06340i −0.101107 + 0.175123i
307307 −28.0696 −1.60201 −0.801007 0.598655i 0.795702π-0.795702\pi
−0.801007 + 0.598655i 0.795702π0.795702\pi
308308 0 0
309309 8.29793 + 14.3724i 0.472052 + 0.817619i
310310 −0.234836 0.406748i −0.0133378 0.0231017i
311311 −23.5341 −1.33450 −0.667248 0.744836i 0.732528π-0.732528\pi
−0.667248 + 0.744836i 0.732528π0.732528\pi
312312 −7.95133 2.74187i −0.450155 0.155228i
313313 −3.34860 −0.189274 −0.0946370 0.995512i 0.530169π-0.530169\pi
−0.0946370 + 0.995512i 0.530169π0.530169\pi
314314 −4.21494 7.30050i −0.237863 0.411991i
315315 0 0
316316 7.79652 13.5040i 0.438588 0.759658i
317317 −7.27834 −0.408793 −0.204396 0.978888i 0.565523π-0.565523\pi
−0.204396 + 0.978888i 0.565523π0.565523\pi
318318 −9.90655 + 17.1586i −0.555532 + 0.962209i
319319 −17.2300 + 29.8432i −0.964694 + 1.67090i
320320 0.629002 0.0351623
321321 11.3011 19.5742i 0.630768 1.09252i
322322 0 0
323323 −0.568618 0.984875i −0.0316388 0.0547999i
324324 −15.4984 −0.861021
325325 13.5050 11.7290i 0.749123 0.650610i
326326 3.38658 0.187565
327327 15.8473 + 27.4484i 0.876359 + 1.51790i
328328 2.74396 + 4.75268i 0.151510 + 0.262423i
329329 0 0
330330 3.51896 0.193712
331331 7.16168 12.4044i 0.393642 0.681807i −0.599285 0.800536i 0.704548π-0.704548\pi
0.992927 + 0.118728i 0.0378818π0.0378818\pi
332332 −2.23282 + 3.86736i −0.122542 + 0.212249i
333333 6.88973 0.377555
334334 9.94855 17.2314i 0.544360 0.942860i
335335 1.32203 + 2.28983i 0.0722304 + 0.125107i
336336 0 0
337337 17.1802 0.935868 0.467934 0.883764i 0.344999π-0.344999\pi
0.467934 + 0.883764i 0.344999π0.344999\pi
338338 −22.4053 + 9.02883i −1.21869 + 0.491104i
339339 −9.79255 −0.531858
340340 0.120610 + 0.208902i 0.00654098 + 0.0113293i
341341 −2.67841 4.63915i −0.145044 0.251224i
342342 −2.84175 + 4.92206i −0.153664 + 0.266155i
343343 0 0
344344 2.70879 4.69176i 0.146048 0.252963i
345345 −0.931602 + 1.61358i −0.0501558 + 0.0868723i
346346 −25.0716 −1.34786
347347 3.85139 6.67080i 0.206753 0.358107i −0.743937 0.668250i 0.767044π-0.767044\pi
0.950690 + 0.310143i 0.100377π0.100377\pi
348348 13.7286 + 23.7786i 0.735928 + 1.27466i
349349 −11.1850 19.3730i −0.598721 1.03702i −0.993010 0.118029i 0.962343π-0.962343\pi
0.394289 0.918986i 0.370991π-0.370991\pi
350350 0 0
351351 4.60409 3.99863i 0.245748 0.213431i
352352 28.7613 1.53298
353353 11.1311 + 19.2797i 0.592451 + 1.02616i 0.993901 + 0.110275i 0.0351731π0.0351731\pi
−0.401450 + 0.915881i 0.631494π0.631494\pi
354354 −12.9121 22.3644i −0.686270 1.18865i
355355 −0.589165 + 1.02046i −0.0312697 + 0.0541606i
356356 −17.4101 −0.922735
357357 0 0
358358 −9.72670 + 16.8471i −0.514072 + 0.890399i
359359 −2.75842 −0.145584 −0.0727920 0.997347i 0.523191π-0.523191\pi
−0.0727920 + 0.997347i 0.523191π0.523191\pi
360360 −0.227054 + 0.393269i −0.0119668 + 0.0207271i
361361 8.58638 + 14.8721i 0.451915 + 0.782740i
362362 −11.6330 20.1489i −0.611415 1.05900i
363363 14.9006 0.782081
364364 0 0
365365 −0.766844 −0.0401385
366366 24.2246 + 41.9582i 1.26624 + 2.19319i
367367 7.07485 + 12.2540i 0.369304 + 0.639654i 0.989457 0.144827i 0.0462626π-0.0462626\pi
−0.620153 + 0.784481i 0.712929π0.712929\pi
368368 −9.86618 + 17.0887i −0.514310 + 0.890812i
369369 12.2119 0.635729
370370 0.558320 0.967039i 0.0290257 0.0502740i
371371 0 0
372372 −4.26823 −0.221298
373373 2.52142 4.36723i 0.130554 0.226127i −0.793336 0.608784i 0.791658π-0.791658\pi
0.923890 + 0.382657i 0.124991π0.124991\pi
374374 3.26940 + 5.66276i 0.169056 + 0.292814i
375375 −2.25499 3.90576i −0.116447 0.201693i
376376 11.8607 0.611668
377377 −28.0820 9.68358i −1.44630 0.498730i
378378 0 0
379379 3.02982 + 5.24780i 0.155631 + 0.269561i 0.933289 0.359127i 0.116925π-0.116925\pi
−0.777657 + 0.628688i 0.783592π0.783592\pi
380380 0.193787 + 0.335650i 0.00994109 + 0.0172185i
381381 2.51228 4.35139i 0.128708 0.222929i
382382 24.3674 1.24674
383383 2.27052 3.93266i 0.116018 0.200950i −0.802168 0.597098i 0.796320π-0.796320\pi
0.918186 + 0.396149i 0.129654π0.129654\pi
384384 −8.98165 + 15.5567i −0.458343 + 0.793873i
385385 0 0
386386 −0.967705 + 1.67611i −0.0492549 + 0.0853120i
387387 −6.02771 10.4403i −0.306406 0.530710i
388388 −14.1446 24.4992i −0.718085 1.24376i
389389 4.50765 0.228547 0.114273 0.993449i 0.463546π-0.463546\pi
0.114273 + 0.993449i 0.463546π0.463546\pi
390390 0.577452 + 2.97790i 0.0292404 + 0.150792i
391391 −3.46213 −0.175088
392392 0 0
393393 −2.61078 4.52201i −0.131697 0.228105i
394394 −1.37349 + 2.37896i −0.0691955 + 0.119850i
395395 2.11836 0.106586
396396 6.87482 11.9075i 0.345473 0.598376i
397397 −2.00174 + 3.46712i −0.100465 + 0.174010i −0.911876 0.410465i 0.865366π-0.865366\pi
0.811412 + 0.584475i 0.198700π0.198700\pi
398398 26.1998 1.31328
399399 0 0
400400 −11.8941 20.6012i −0.594706 1.03006i
401401 −6.30674 10.9236i −0.314944 0.545498i 0.664482 0.747304i 0.268652π-0.268652\pi
−0.979426 + 0.201806i 0.935319π0.935319\pi
402402 57.1081 2.84829
403403 3.48633 3.02786i 0.173667 0.150829i
404404 −24.6010 −1.22394
405405 −1.05275 1.82342i −0.0523116 0.0906064i
406406 0 0
407407 6.36790 11.0295i 0.315645 0.546713i
408408 −1.96254 −0.0971604
409409 −10.3476 + 17.9226i −0.511657 + 0.886216i 0.488252 + 0.872703i 0.337635π0.337635\pi
−0.999909 + 0.0135128i 0.995699π0.995699\pi
410410 0.989615 1.71406i 0.0488736 0.0846516i
411411 30.8506 1.52175
412412 5.25482 9.10162i 0.258886 0.448404i
413413 0 0
414414 8.65126 + 14.9844i 0.425186 + 0.736444i
415415 −0.606672 −0.0297803
416416 4.71965 + 24.3391i 0.231400 + 1.19332i
417417 9.28042 0.454464
418418 5.25304 + 9.09854i 0.256935 + 0.445024i
419419 10.9088 + 18.8945i 0.532928 + 0.923058i 0.999261 + 0.0384484i 0.0122415π0.0122415\pi
−0.466333 + 0.884609i 0.654425π0.654425\pi
420420 0 0
421421 9.42727 0.459457 0.229728 0.973255i 0.426216π-0.426216\pi
0.229728 + 0.973255i 0.426216π0.426216\pi
422422 −24.5920 + 42.5947i −1.19712 + 2.07348i
423423 13.1964 22.8569i 0.641632 1.11134i
424424 −4.72631 −0.229530
425425 2.08688 3.61458i 0.101228 0.175333i
426426 12.7251 + 22.0406i 0.616535 + 1.06787i
427427 0 0
428428 −14.3133 −0.691861
429429 6.58611 + 33.9643i 0.317980 + 1.63981i
430430 −1.95386 −0.0942235
431431 −10.2138 17.6908i −0.491980 0.852134i 0.507977 0.861370i 0.330393π-0.330393\pi
−0.999957 + 0.00923613i 0.997060π0.997060\pi
432432 −4.05491 7.02332i −0.195092 0.337909i
433433 −13.1743 + 22.8186i −0.633117 + 1.09659i 0.353794 + 0.935323i 0.384891π0.384891\pi
−0.986911 + 0.161267i 0.948442π0.948442\pi
434434 0 0
435435 −1.86507 + 3.23039i −0.0894231 + 0.154885i
436436 10.0356 17.3822i 0.480619 0.832457i
437437 −5.56272 −0.266101
438438 −8.28138 + 14.3438i −0.395700 + 0.685372i
439439 −12.5655 21.7641i −0.599720 1.03875i −0.992862 0.119267i 0.961945π-0.961945\pi
0.393142 0.919478i 0.371388π-0.371388\pi
440440 0.419714 + 0.726967i 0.0200091 + 0.0346568i
441441 0 0
442442 −4.25558 + 3.69595i −0.202417 + 0.175799i
443443 18.5199 0.879907 0.439953 0.898021i 0.354995π-0.354995\pi
0.439953 + 0.898021i 0.354995π0.354995\pi
444444 −5.07384 8.78815i −0.240794 0.417067i
445445 −1.18261 2.04834i −0.0560611 0.0971006i
446446 0.676415 1.17159i 0.0320292 0.0554762i
447447 35.2184 1.66577
448448 0 0
449449 −5.82155 + 10.0832i −0.274736 + 0.475856i −0.970068 0.242832i 0.921924π-0.921924\pi
0.695333 + 0.718688i 0.255257π0.255257\pi
450450 −20.8590 −0.983301
451451 11.2870 19.5497i 0.531485 0.920559i
452452 3.10066 + 5.37050i 0.145843 + 0.252607i
453453 −7.02109 12.1609i −0.329880 0.571368i
454454 −5.29939 −0.248713
455455 0 0
456456 −3.15328 −0.147666
457457 −10.2592 17.7695i −0.479906 0.831222i 0.519828 0.854271i 0.325996π-0.325996\pi
−0.999734 + 0.0230490i 0.992663π0.992663\pi
458458 −2.94845 5.10687i −0.137772 0.238629i
459459 0.711453 1.23227i 0.0332078 0.0575176i
460460 1.17991 0.0550136
461461 −1.02038 + 1.76734i −0.0475236 + 0.0823134i −0.888809 0.458278i 0.848466π-0.848466\pi
0.841285 + 0.540592i 0.181800π0.181800\pi
462462 0 0
463463 3.03155 0.140888 0.0704441 0.997516i 0.477558π-0.477558\pi
0.0704441 + 0.997516i 0.477558π0.477558\pi
464464 −19.7521 + 34.2116i −0.916968 + 1.58824i
465465 −0.289926 0.502167i −0.0134450 0.0232874i
466466 −12.4563 21.5749i −0.577025 0.999436i
467467 −12.9274 −0.598210 −0.299105 0.954220i 0.596688π-0.596688\pi
−0.299105 + 0.954220i 0.596688π0.596688\pi
468468 11.2048 + 3.86378i 0.517943 + 0.178603i
469469 0 0
470470 −2.13879 3.70449i −0.0986549 0.170875i
471471 −5.20373 9.01312i −0.239775 0.415303i
472472 3.08011 5.33491i 0.141774 0.245559i
473473 −22.2847 −1.02465
474474 22.8768 39.6238i 1.05077 1.81998i
475475 3.35305 5.80766i 0.153849 0.266474i
476476 0 0
477477 −5.25858 + 9.10814i −0.240774 + 0.417033i
478478 14.4507 + 25.0294i 0.660962 + 1.14482i
479479 −18.2911 31.6810i −0.835740 1.44754i −0.893427 0.449209i 0.851706π-0.851706\pi
0.0576873 0.998335i 0.481627π-0.481627\pi
480480 3.11328 0.142101
481481 10.3786 + 3.57888i 0.473225 + 0.163183i
482482 −14.0769 −0.641187
483483 0 0
484484 −4.71806 8.17191i −0.214457 0.371451i
485485 1.92159 3.32829i 0.0872550 0.151130i
486486 −36.0478 −1.63516
487487 −18.3748 + 31.8261i −0.832642 + 1.44218i 0.0632939 + 0.997995i 0.479839π0.479839\pi
−0.895936 + 0.444183i 0.853494π0.853494\pi
488488 −5.77864 + 10.0089i −0.261587 + 0.453081i
489489 4.18103 0.189073
490490 0 0
491491 4.09899 + 7.09965i 0.184985 + 0.320403i 0.943571 0.331169i 0.107443π-0.107443\pi
−0.758587 + 0.651572i 0.774110π0.774110\pi
492492 −8.99331 15.5769i −0.405450 0.702260i
493493 −6.93119 −0.312165
494494 −6.83757 + 5.93840i −0.307637 + 0.267181i
495495 1.86793 0.0839572
496496 −3.07048 5.31823i −0.137869 0.238795i
497497 0 0
498498 −6.55163 + 11.3478i −0.293585 + 0.508505i
499499 −43.2532 −1.93628 −0.968141 0.250407i 0.919436π-0.919436\pi
−0.968141 + 0.250407i 0.919436π0.919436\pi
500500 −1.42802 + 2.47340i −0.0638629 + 0.110614i
501501 12.2824 21.2737i 0.548736 0.950439i
502502 2.36872 0.105721
503503 −0.00909609 + 0.0157549i −0.000405575 + 0.000702476i −0.866228 0.499649i 0.833462π-0.833462\pi
0.865823 + 0.500351i 0.166796π0.166796\pi
504504 0 0
505505 −1.67106 2.89436i −0.0743612 0.128797i
506506 31.9841 1.42187
507507 −27.6614 + 11.1469i −1.22848 + 0.495052i
508508 −3.18190 −0.141174
509509 −21.5503 37.3262i −0.955200 1.65446i −0.733909 0.679248i 0.762306π-0.762306\pi
−0.221292 0.975208i 0.571027π-0.571027\pi
510510 0.353897 + 0.612968i 0.0156708 + 0.0271427i
511511 0 0
512512 23.2197 1.02617
513513 1.14311 1.97993i 0.0504697 0.0874161i
514514 7.87878 13.6464i 0.347518 0.601919i
515515 1.42777 0.0629149
516516 −8.87804 + 15.3772i −0.390834 + 0.676944i
517517 −24.3939 42.2514i −1.07284 1.85822i
518518 0 0
519519 −30.9531 −1.35869
520520 −0.546317 + 0.474474i −0.0239576 + 0.0208071i
521521 20.9540 0.918012 0.459006 0.888433i 0.348206π-0.348206\pi
0.459006 + 0.888433i 0.348206π0.348206\pi
522522 17.3198 + 29.9988i 0.758068 + 1.31301i
523523 17.3701 + 30.0860i 0.759543 + 1.31557i 0.943084 + 0.332555i 0.107911π0.107911\pi
−0.183541 + 0.983012i 0.558756π0.558756\pi
524524 −1.65333 + 2.86365i −0.0722260 + 0.125099i
525525 0 0
526526 −11.8814 + 20.5791i −0.518052 + 0.897292i
527527 0.538730 0.933107i 0.0234674 0.0406468i
528528 46.0104 2.00235
529529 3.03260 5.25262i 0.131852 0.228375i
530530 0.852276 + 1.47619i 0.0370205 + 0.0641214i
531531 −6.85398 11.8714i −0.297438 0.515177i
532532 0 0
533533 18.3960 + 6.34352i 0.796819 + 0.274769i
534534 −51.0854 −2.21068
535535 −0.972255 1.68400i −0.0420343 0.0728055i
536536 6.81142 + 11.7977i 0.294209 + 0.509584i
537537 −12.0085 + 20.7993i −0.518205 + 0.897557i
538538 −8.75513 −0.377460
539539 0 0
540540 −0.242466 + 0.419964i −0.0104341 + 0.0180724i
541541 −3.29846 −0.141812 −0.0709059 0.997483i 0.522589π-0.522589\pi
−0.0709059 + 0.997483i 0.522589π0.522589\pi
542542 16.7339 28.9839i 0.718782 1.24497i
543543 −14.3619 24.8756i −0.616330 1.06752i
544544 2.89249 + 5.00993i 0.124014 + 0.214799i
545545 2.72674 0.116801
546546 0 0
547547 21.9417 0.938161 0.469080 0.883155i 0.344585π-0.344585\pi
0.469080 + 0.883155i 0.344585π0.344585\pi
548548 −9.76836 16.9193i −0.417284 0.722756i
549549 12.8589 + 22.2722i 0.548803 + 0.950554i
550550 −19.2791 + 33.3924i −0.822065 + 1.42386i
551551 −11.1366 −0.474434
552552 −4.79983 + 8.31354i −0.204294 + 0.353848i
553553 0 0
554554 −48.5368 −2.06213
555555 0.689297 1.19390i 0.0292590 0.0506781i
556556 −2.93850 5.08963i −0.124620 0.215848i
557557 7.14329 + 12.3725i 0.302671 + 0.524241i 0.976740 0.214427i 0.0687884π-0.0687884\pi
−0.674069 + 0.738668i 0.735455π0.735455\pi
558558 −5.38476 −0.227955
559559 −3.65686 18.8583i −0.154669 0.797621i
560560 0 0
561561 4.03637 + 6.99119i 0.170416 + 0.295168i
562562 3.40226 + 5.89289i 0.143516 + 0.248577i
563563 −3.39392 + 5.87844i −0.143037 + 0.247747i −0.928639 0.370985i 0.879020π-0.879020\pi
0.785602 + 0.618732i 0.212353π0.212353\pi
564564 −38.8733 −1.63686
565565 −0.421234 + 0.729599i −0.0177215 + 0.0306945i
566566 −7.10307 + 12.3029i −0.298564 + 0.517128i
567567 0 0
568568 −3.03552 + 5.25767i −0.127367 + 0.220607i
569569 8.66061 + 15.0006i 0.363072 + 0.628859i 0.988465 0.151451i 0.0483947π-0.0483947\pi
−0.625393 + 0.780310i 0.715061π0.715061\pi
570570 0.568618 + 0.984875i 0.0238168 + 0.0412519i
571571 −13.0116 −0.544520 −0.272260 0.962224i 0.587771π-0.587771\pi
−0.272260 + 0.962224i 0.587771π0.587771\pi
572572 16.5416 14.3663i 0.691638 0.600685i
573573 30.0837 1.25676
574574 0 0
575575 −10.2078 17.6805i −0.425696 0.737327i
576576 3.60574 6.24532i 0.150239 0.260222i
577577 −0.731535 −0.0304542 −0.0152271 0.999884i 0.504847π-0.504847\pi
−0.0152271 + 0.999884i 0.504847π0.504847\pi
578578 15.1368 26.2177i 0.629607 1.09051i
579579 −1.19472 + 2.06931i −0.0496508 + 0.0859978i
580580 2.36218 0.0980842
581581 0 0
582582 −41.5037 71.8865i −1.72038 2.97979i
583583 9.72061 + 16.8366i 0.402586 + 0.697300i
584584 −3.95096 −0.163492
585585 0.306522 + 1.58073i 0.0126731 + 0.0653550i
586586 −31.8738 −1.31669
587587 4.26142 + 7.38099i 0.175888 + 0.304646i 0.940468 0.339882i 0.110387π-0.110387\pi
−0.764581 + 0.644528i 0.777054π0.777054\pi
588588 0 0
589589 0.865594 1.49925i 0.0356662 0.0617756i
590590 −2.22170 −0.0914657
591591 −1.69570 + 2.93704i −0.0697517 + 0.120814i
592592 7.30004 12.6440i 0.300030 0.519667i
593593 −31.3093 −1.28572 −0.642860 0.765984i 0.722252π-0.722252\pi
−0.642860 + 0.765984i 0.722252π0.722252\pi
594594 −6.57259 + 11.3841i −0.269677 + 0.467093i
595595 0 0
596596 −11.1514 19.3147i −0.456777 0.791161i
597597 32.3460 1.32383
598598 5.24850 + 27.0663i 0.214627 + 1.10683i
599599 −0.750232 −0.0306537 −0.0153268 0.999883i 0.504879π-0.504879\pi
−0.0153268 + 0.999883i 0.504879π0.504879\pi
600600 −5.78641 10.0224i −0.236229 0.409161i
601601 4.77652 + 8.27318i 0.194838 + 0.337470i 0.946848 0.321683i 0.104248π-0.104248\pi
−0.752009 + 0.659153i 0.770915π0.770915\pi
602602 0 0
603603 30.3141 1.23449
604604 −4.44624 + 7.70111i −0.180915 + 0.313354i
605605 0.640963 1.11018i 0.0260588 0.0451352i
606606 −72.1851 −2.93232
607607 −11.1197 + 19.2599i −0.451336 + 0.781737i −0.998469 0.0553087i 0.982386π-0.982386\pi
0.547133 + 0.837045i 0.315719π0.315719\pi
608608 4.64745 + 8.04961i 0.188479 + 0.326455i
609609 0 0
610610 4.16815 0.168764
611611 31.7521 27.5765i 1.28455 1.11563i
612612 2.76557 0.111791
613613 4.13993 + 7.17057i 0.167210 + 0.289617i 0.937438 0.348152i 0.113191π-0.113191\pi
−0.770228 + 0.637769i 0.779857π0.779857\pi
614614 26.0789 + 45.1699i 1.05246 + 1.82291i
615615 1.22177 2.11617i 0.0492665 0.0853321i
616616 0 0
617617 −10.1656 + 17.6073i −0.409252 + 0.708845i −0.994806 0.101789i 0.967543π-0.967543\pi
0.585554 + 0.810633i 0.300877π0.300877\pi
618618 15.4189 26.7063i 0.620238 1.07428i
619619 5.34097 0.214672 0.107336 0.994223i 0.465768π-0.465768\pi
0.107336 + 0.994223i 0.465768π0.465768\pi
620620 −0.183601 + 0.318007i −0.00737361 + 0.0127715i
621621 −3.48003 6.02758i −0.139649 0.241879i
622622 21.8651 + 37.8714i 0.876709 + 1.51850i
623623 0 0
624624 7.55018 + 38.9360i 0.302249 + 1.55869i
625625 24.4172 0.976690
626626 3.11112 + 5.38862i 0.124345 + 0.215372i
627627 6.48536 + 11.2330i 0.259000 + 0.448601i
628628 −3.29536 + 5.70773i −0.131499 + 0.227763i
629629 2.56165 0.102140
630630 0 0
631631 −3.23331 + 5.60026i −0.128716 + 0.222943i −0.923179 0.384369i 0.874419π-0.874419\pi
0.794463 + 0.607312i 0.207752π0.207752\pi
632632 10.9143 0.434147
633633 −30.3611 + 52.5870i −1.20675 + 2.09014i
634634 6.76217 + 11.7124i 0.268560 + 0.465160i
635635 −0.216135 0.374357i −0.00857707 0.0148559i
636636 15.4904 0.614236
637637 0 0
638638 64.0322 2.53506
639639 6.75475 + 11.6996i 0.267214 + 0.462828i
640640 0.772706 + 1.33837i 0.0305439 + 0.0529035i
641641 −11.6644 + 20.2034i −0.460717 + 0.797985i −0.998997 0.0447808i 0.985741π-0.985741\pi
0.538280 + 0.842766i 0.319074π0.319074\pi
642642 −41.9987 −1.65756
643643 1.79439 3.10797i 0.0707637 0.122566i −0.828472 0.560030i 0.810790π-0.810790\pi
0.899236 + 0.437463i 0.144123π0.144123\pi
644644 0 0
645645 −2.41222 −0.0949810
646646 −1.05658 + 1.83006i −0.0415707 + 0.0720026i
647647 19.8262 + 34.3400i 0.779448 + 1.35004i 0.932260 + 0.361788i 0.117834π0.117834\pi
−0.152812 + 0.988255i 0.548833π0.548833\pi
648648 −5.42402 9.39467i −0.213076 0.369058i
649649 −25.3395 −0.994661
650650 −31.4218 10.8352i −1.23246 0.424993i
651651 0 0
652652 −1.32386 2.29299i −0.0518464 0.0898005i
653653 −9.06777 15.7058i −0.354849 0.614617i 0.632243 0.774770i 0.282135π-0.282135\pi
−0.987092 + 0.160153i 0.948801π0.948801\pi
654654 29.4469 51.0035i 1.15146 1.99439i
655655 −0.449219 −0.0175525
656656 12.9392 22.4114i 0.505192 0.875017i
657657 −4.39592 + 7.61395i −0.171501 + 0.297048i
658658 0 0
659659 −6.74052 + 11.6749i −0.262573 + 0.454791i −0.966925 0.255061i 0.917905π-0.917905\pi
0.704352 + 0.709851i 0.251238π0.251238\pi
660660 −1.37561 2.38263i −0.0535456 0.0927437i
661661 −5.15611 8.93064i −0.200549 0.347362i 0.748156 0.663523i 0.230939π-0.230939\pi
−0.948706 + 0.316161i 0.897606π0.897606\pi
662662 −26.6151 −1.03443
663663 −5.25390 + 4.56299i −0.204044 + 0.177212i
664664 −3.12571 −0.121301
665665 0 0
666666 −6.40111 11.0870i −0.248038 0.429614i
667667 −16.9517 + 29.3613i −0.656374 + 1.13687i
668668 −15.5561 −0.601884
669669 0.835096 1.44643i 0.0322867 0.0559222i
670670 2.45655 4.25487i 0.0949049 0.164380i
671671 47.5397 1.83525
672672 0 0
673673 4.61528 + 7.99390i 0.177906 + 0.308142i 0.941163 0.337953i 0.109734π-0.109734\pi
−0.763257 + 0.646095i 0.776401π0.776401\pi
674674 −15.9618 27.6467i −0.614827 1.06491i
675675 8.39066 0.322956
676676 14.8718 + 11.6407i 0.571993 + 0.447721i
677677 −21.0934 −0.810687 −0.405343 0.914165i 0.632848π-0.632848\pi
−0.405343 + 0.914165i 0.632848π0.632848\pi
678678 9.09807 + 15.7583i 0.349409 + 0.605194i
679679 0 0
680680 −0.0844203 + 0.146220i −0.00323737 + 0.00560729i
681681 −6.54258 −0.250712
682682 −4.97693 + 8.62029i −0.190576 + 0.330088i
683683 19.1106 33.1005i 0.731246 1.26656i −0.225104 0.974335i 0.572272π-0.572272\pi
0.956351 0.292221i 0.0943944π-0.0943944\pi
684684 4.44353 0.169902
685685 1.32706 2.29854i 0.0507044 0.0878226i
686686 0 0
687687 −3.64013 6.30490i −0.138880 0.240547i
688688 −25.5467 −0.973960
689689 −12.6527 + 10.9888i −0.482031 + 0.418642i
690690 3.46213 0.131801
691691 13.1161 + 22.7178i 0.498960 + 0.864224i 0.999999 0.00120019i 0.000382034π-0.000382034\pi
−0.501039 + 0.865425i 0.667049π0.667049\pi
692692 9.80084 + 16.9755i 0.372572 + 0.645313i
693693 0 0
694694 −14.3130 −0.543314
695695 0.399204 0.691442i 0.0151427 0.0262279i
696696 −9.60925 + 16.6437i −0.364238 + 0.630878i
697697 4.54049 0.171983
698698 −20.7836 + 35.9982i −0.786670 + 1.36255i
699699 −15.3784 26.6361i −0.581664 1.00747i
700700 0 0
701701 −46.7346 −1.76514 −0.882570 0.470180i 0.844189π-0.844189\pi
−0.882570 + 0.470180i 0.844189π0.844189\pi
702702 −10.7122 3.69392i −0.404307 0.139418i
703703 4.11588 0.155233
704704 −6.66528 11.5446i −0.251207 0.435104i
705705 −2.64053 4.57353i −0.0994480 0.172249i
706706 20.6835 35.8248i 0.778433 1.34828i
707707 0 0
708708 −10.0950 + 17.4851i −0.379395 + 0.657131i
709709 23.7232 41.0898i 0.890944 1.54316i 0.0521988 0.998637i 0.483377π-0.483377\pi
0.838745 0.544524i 0.183290π-0.183290\pi
710710 2.18953 0.0821715
711711 12.1435 21.0331i 0.455415 0.788802i
712712 −6.09307 10.5535i −0.228348 0.395510i
713713 −2.63516 4.56423i −0.0986876 0.170932i
714714 0 0
715715 2.81384 + 0.970301i 0.105232 + 0.0362872i
716716 15.2092 0.568395
717717 17.8408 + 30.9011i 0.666275 + 1.15402i
718718 2.56280 + 4.43890i 0.0956428 + 0.165658i
719719 24.6190 42.6413i 0.918133 1.59025i 0.115884 0.993263i 0.463030π-0.463030\pi
0.802249 0.596990i 0.203637π-0.203637\pi
720720 2.14136 0.0798037
721721 0 0
722722 15.9549 27.6347i 0.593779 1.02846i
723723 −17.3793 −0.646342
724724 −9.09498 + 15.7530i −0.338012 + 0.585454i
725725 −20.4361 35.3963i −0.758977 1.31459i
726726 −13.8439 23.9783i −0.513795 0.889919i
727727 −32.0495 −1.18865 −0.594325 0.804225i 0.702581π-0.702581\pi
−0.594325 + 0.804225i 0.702581π0.702581\pi
728728 0 0
729729 −12.4996 −0.462947
730730 0.712460 + 1.23402i 0.0263693 + 0.0456730i
731731 −2.24114 3.88178i −0.0828917 0.143573i
732732 18.9394 32.8041i 0.700022 1.21247i
733733 28.2010 1.04163 0.520813 0.853670i 0.325629π-0.325629\pi
0.520813 + 0.853670i 0.325629π0.325629\pi
734734 13.1462 22.7699i 0.485236 0.840453i
735735 0 0
736736 28.2968 1.04303
737737 28.0181 48.5288i 1.03206 1.78758i
738738 −11.3459 19.6516i −0.417648 0.723387i
739739 21.2685 + 36.8381i 0.782375 + 1.35511i 0.930555 + 0.366153i 0.119325π0.119325\pi
−0.148180 + 0.988960i 0.547342π0.547342\pi
740740 −0.873021 −0.0320929
741741 −8.44160 + 7.33149i −0.310110 + 0.269329i
742742 0 0
743743 −7.95711 13.7821i −0.291918 0.505617i 0.682345 0.731030i 0.260960π-0.260960\pi
−0.974263 + 0.225413i 0.927627π0.927627\pi
744744 −1.49377 2.58728i −0.0547641 0.0948543i
745745 1.51495 2.62396i 0.0555033 0.0961346i
746746 −9.37042 −0.343075
747747 −3.47773 + 6.02360i −0.127243 + 0.220392i
748748 2.55611 4.42731i 0.0934605 0.161878i
749749 0 0
750750 −4.19014 + 7.25754i −0.153002 + 0.265008i
751751 −9.09981 15.7613i −0.332057 0.575139i 0.650858 0.759199i 0.274409π-0.274409\pi
−0.982915 + 0.184060i 0.941076π0.941076\pi
752752 −27.9646 48.4362i −1.01977 1.76629i
753753 2.92440 0.106571
754754 10.5075 + 54.1868i 0.382661 + 1.97337i
755755 −1.20807 −0.0439662
756756 0 0
757757 22.4502 + 38.8849i 0.815967 + 1.41330i 0.908632 + 0.417598i 0.137128π0.137128\pi
−0.0926649 + 0.995697i 0.529539π0.529539\pi
758758 5.62989 9.75126i 0.204487 0.354182i
759759 39.4872 1.43330
760760 −0.135641 + 0.234937i −0.00492021 + 0.00852205i
761761 13.2444 22.9399i 0.480108 0.831572i −0.519631 0.854391i 0.673931π-0.673931\pi
0.999740 + 0.0228184i 0.00726396π0.00726396\pi
762762 −9.33644 −0.338223
763763 0 0
764764 −9.52554 16.4987i −0.344622 0.596903i
765765 0.187856 + 0.325375i 0.00679193 + 0.0117640i
766766 −8.43800 −0.304877
767767 −4.15814 21.4434i −0.150142 0.774276i
768768 48.0013 1.73210
769769 −6.98127 12.0919i −0.251751 0.436045i 0.712257 0.701919i 0.247673π-0.247673\pi
−0.964008 + 0.265873i 0.914340π0.914340\pi
770770 0 0
771771 9.72707 16.8478i 0.350312 0.606758i
772772 1.51316 0.0544597
773773 −6.40564 + 11.0949i −0.230395 + 0.399056i −0.957924 0.287021i 0.907335π-0.907335\pi
0.727529 + 0.686077i 0.240668π0.240668\pi
774774 −11.2005 + 19.3998i −0.402592 + 0.697310i
775775 6.35361 0.228228
776776 9.90048 17.1481i 0.355406 0.615582i
777777 0 0
778778 −4.18797 7.25378i −0.150146 0.260061i
779779 7.29534 0.261383
780780 1.79055 1.55509i 0.0641120 0.0556810i
781781 24.9726 0.893590
782782 3.21660 + 5.57132i 0.115025 + 0.199230i
783783 −6.96701 12.0672i −0.248981 0.431247i
784784 0 0
785785 −0.895370 −0.0319571
786786 −4.85125 + 8.40262i −0.173039 + 0.299712i
787787 13.6599 23.6597i 0.486924 0.843377i −0.512963 0.858411i 0.671452π-0.671452\pi
0.999887 + 0.0150334i 0.00478545π0.00478545\pi
788788 2.14767 0.0765075
789789 −14.6686 + 25.4068i −0.522217 + 0.904506i
790790 −1.96813 3.40890i −0.0700229 0.121283i
791791 0 0
792792 9.62401 0.341974
793793 7.80114 + 40.2302i 0.277027 + 1.42862i
794794 7.43912 0.264005
795795 1.05221 + 1.82248i 0.0373181 + 0.0646369i
796796 −10.2419 17.7394i −0.363013 0.628758i
797797 14.7002 25.4614i 0.520707 0.901891i −0.479003 0.877813i 0.659002π-0.659002\pi
0.999710 0.0240775i 0.00766483π-0.00766483\pi
798798 0 0
799799 4.90652 8.49835i 0.173580 0.300650i
800800 −17.0565 + 29.5428i −0.603040 + 1.04450i
801801 −27.1171 −0.958136
802802 −11.7189 + 20.2978i −0.413810 + 0.716740i
803803 8.12594 + 14.0745i 0.286758 + 0.496680i
804804 −22.3244 38.6669i −0.787320 1.36368i
805805 0 0
806806 −8.11157 2.79713i −0.285718 0.0985246i
807807 −10.8090 −0.380495
808808 −8.60968 14.9124i −0.302888 0.524617i
809809 3.00617 + 5.20683i 0.105691 + 0.183063i 0.914020 0.405668i 0.132961π-0.132961\pi
−0.808329 + 0.588731i 0.799628π0.799628\pi
810810 −1.95618 + 3.38821i −0.0687332 + 0.119049i
811811 8.44807 0.296652 0.148326 0.988939i 0.452612π-0.452612\pi
0.148326 + 0.988939i 0.452612π0.452612\pi
812812 0 0
813813 20.6595 35.7833i 0.724560 1.25497i
814814 −23.6652 −0.829464
815815 0.179850 0.311510i 0.00629989 0.0109117i
816816 4.62721 + 8.01456i 0.161985 + 0.280566i
817817 −3.60092 6.23697i −0.125980 0.218204i
818818 38.4551 1.34455
819819 0 0
820820 −1.54742 −0.0540382
821821 17.1318 + 29.6731i 0.597903 + 1.03560i 0.993130 + 0.117014i 0.0373324π0.0373324\pi
−0.395228 + 0.918583i 0.629334π0.629334\pi
822822 −28.6627 49.6452i −0.999725 1.73157i
823823 3.11866 5.40168i 0.108710 0.188291i −0.806538 0.591182i 0.798661π-0.798661\pi
0.915248 + 0.402891i 0.131995π0.131995\pi
824824 7.35618 0.256265
825825 −23.8018 + 41.2260i −0.828673 + 1.43530i
826826 0 0
827827 19.5232 0.678889 0.339445 0.940626i 0.389761π-0.389761\pi
0.339445 + 0.940626i 0.389761π0.389761\pi
828828 6.76380 11.7152i 0.235058 0.407133i
829829 −16.3383 28.2988i −0.567453 0.982857i −0.996817 0.0797254i 0.974596π-0.974596\pi
0.429364 0.903131i 0.358738π-0.358738\pi
830830 0.563647 + 0.976265i 0.0195645 + 0.0338866i
831831 −59.9230 −2.07871
832832 8.67580 7.53489i 0.300779 0.261225i
833833 0 0
834834 −8.62225 14.9342i −0.298564 0.517128i
835835 −1.05667 1.83021i −0.0365677 0.0633370i
836836 4.10698 7.11349i 0.142043 0.246025i
837837 2.16606 0.0748698
838838 20.2702 35.1091i 0.700223 1.21282i
839839 −12.3713 + 21.4278i −0.427106 + 0.739769i −0.996615 0.0822161i 0.973800π-0.973800\pi
0.569508 + 0.821985i 0.307134π0.307134\pi
840840 0 0
841841 −19.4374 + 33.6665i −0.670255 + 1.16092i
842842 −8.75869 15.1705i −0.301844 0.522810i
843843 4.20040 + 7.27531i 0.144669 + 0.250575i
844844 38.4535 1.32362
845845 −0.359368 + 2.54042i −0.0123626 + 0.0873930i
846846 −49.0422 −1.68610
847847 0 0
848848 11.1435 + 19.3011i 0.382670 + 0.662803i
849849 −8.76938 + 15.1890i −0.300964 + 0.521285i
850850 −7.75551 −0.266012
851851 6.26507 10.8514i 0.214764 0.371982i
852852 9.94888 17.2320i 0.340843 0.590357i
853853 18.2245 0.623994 0.311997 0.950083i 0.399002π-0.399002\pi
0.311997 + 0.950083i 0.399002π0.399002\pi
854854 0 0
855855 0.301833 + 0.522791i 0.0103225 + 0.0178791i
856856 −5.00928 8.67633i −0.171214 0.296551i
857857 2.54679 0.0869967 0.0434984 0.999053i 0.486150π-0.486150\pi
0.0434984 + 0.999053i 0.486150π0.486150\pi
858858 48.5369 42.1541i 1.65702 1.43912i
859859 54.0090 1.84276 0.921382 0.388657i 0.127061π-0.127061\pi
0.921382 + 0.388657i 0.127061π0.127061\pi
860860 0.763792 + 1.32293i 0.0260451 + 0.0451114i
861861 0 0
862862 −18.9788 + 32.8723i −0.646421 + 1.11963i
863863 1.24309 0.0423153 0.0211576 0.999776i 0.493265π-0.493265\pi
0.0211576 + 0.999776i 0.493265π0.493265\pi
864864 −5.81487 + 10.0716i −0.197826 + 0.342644i
865865 −1.33147 + 2.30618i −0.0452715 + 0.0784125i
866866 48.9600 1.66373
867867 18.6877 32.3681i 0.634668 1.09928i
868868 0 0
869869 −22.4474 38.8801i −0.761477 1.31892i
870870 6.93119 0.234989
871871 45.6649 + 15.7467i 1.54730 + 0.533557i
872872 14.0488 0.475752
873873 −22.0309 38.1587i −0.745634 1.29148i
874874 5.16821 + 8.95161i 0.174817 + 0.302793i
875875 0 0
876876 12.9492 0.437514
877877 −0.401330 + 0.695125i −0.0135520 + 0.0234727i −0.872722 0.488218i 0.837647π-0.837647\pi
0.859170 + 0.511690i 0.170981π0.170981\pi
878878 −23.3488 + 40.4412i −0.787983 + 1.36483i
879879 −39.3511 −1.32728
880880 1.97917 3.42803i 0.0667179 0.115559i
881881 18.5318 + 32.0980i 0.624352 + 1.08141i 0.988666 + 0.150133i 0.0479703π0.0479703\pi
−0.364314 + 0.931276i 0.618696π0.618696\pi
882882 0 0
883883 −22.8671 −0.769539 −0.384770 0.923013i 0.625719π-0.625719\pi
−0.384770 + 0.923013i 0.625719π0.625719\pi
884884 4.16603 + 1.43658i 0.140119 + 0.0483174i
885885 −2.74288 −0.0922010
886886 −17.2065 29.8025i −0.578063 1.00123i
887887 24.6287 + 42.6581i 0.826950 + 1.43232i 0.900420 + 0.435022i 0.143259π0.143259\pi
−0.0734699 + 0.997297i 0.523407π0.523407\pi
888888 3.55141 6.15123i 0.119178 0.206422i
889889 0 0
890890 −2.19748 + 3.80614i −0.0736597 + 0.127582i
891891 −22.3112 + 38.6441i −0.747452 + 1.29463i
892892 −1.05768 −0.0354138
893893 7.88347 13.6546i 0.263810 0.456932i
894894 −32.7207 56.6739i −1.09434 1.89546i
895895 1.03311 + 1.78940i 0.0345330 + 0.0598130i
896896 0 0
897897 6.47975 + 33.4159i 0.216353 + 1.11572i
898898 21.6347 0.721961
899899 −5.27559 9.13760i −0.175951 0.304756i
900900 8.15406 + 14.1233i 0.271802 + 0.470775i
901901 −1.95518 + 3.38647i −0.0651365 + 0.112820i
902902 −41.9462 −1.39666
903903 0 0
904904 −2.17029 + 3.75906i −0.0721829 + 0.125024i
905905 −2.47116 −0.0821442
906906 −13.0463 + 22.5969i −0.433435 + 0.750731i
907907 2.50228 + 4.33407i 0.0830867 + 0.143910i 0.904574 0.426316i 0.140189π-0.140189\pi
−0.821488 + 0.570226i 0.806855π0.806855\pi
908908 2.07161 + 3.58813i 0.0687487 + 0.119076i
909909 −38.3172 −1.27090
910910 0 0
911911 49.0582 1.62537 0.812685 0.582703i 0.198005π-0.198005\pi
0.812685 + 0.582703i 0.198005π0.198005\pi
912912 7.43468 + 12.8772i 0.246187 + 0.426408i
913913 6.42866 + 11.1348i 0.212757 + 0.368507i
914914 −19.0633 + 33.0186i −0.630557 + 1.09216i
915915 5.14596 0.170120
916916 −2.30518 + 3.99270i −0.0761654 + 0.131922i
917917 0 0
918918 −2.64399 −0.0872646
919919 −14.8028 + 25.6392i −0.488299 + 0.845758i −0.999909 0.0134590i 0.995716π-0.995716\pi
0.511611 + 0.859217i 0.329049π0.329049\pi
920920 0.412937 + 0.715227i 0.0136141 + 0.0235803i
921921 32.1967 + 55.7664i 1.06092 + 1.83756i
922922 3.79205 0.124884
923923 4.09794 + 21.1329i 0.134885 + 0.695598i
924924 0 0
925925 7.55282 + 13.0819i 0.248335 + 0.430129i
926926 −2.81656 4.87842i −0.0925578 0.160315i
927927 8.18464 14.1762i 0.268819 0.465608i
928928 56.6502 1.85963
929929 −8.41525 + 14.5756i −0.276095 + 0.478211i −0.970411 0.241460i 0.922374π-0.922374\pi
0.694316 + 0.719671i 0.255707π0.255707\pi
930930 −0.538730 + 0.933107i −0.0176656 + 0.0305978i
931931 0 0
932932 −9.73865 + 16.8678i −0.319000 + 0.552524i
933933 26.9944 + 46.7557i 0.883757 + 1.53071i
934934 12.0106 + 20.8030i 0.392999 + 0.680695i
935935 0.694510 0.0227129
936936 1.57927 + 8.14426i 0.0516202 + 0.266203i
937937 44.0131 1.43784 0.718922 0.695091i 0.244636π-0.244636\pi
0.718922 + 0.695091i 0.244636π0.244636\pi
938938 0 0
939939 3.84096 + 6.65273i 0.125345 + 0.217104i
940940 −1.67216 + 2.89627i −0.0545400 + 0.0944660i
941941 53.0675 1.72995 0.864976 0.501814i 0.167334π-0.167334\pi
0.864976 + 0.501814i 0.167334π0.167334\pi
942942 −9.66937 + 16.7478i −0.315045 + 0.545674i
943943 11.1048 19.2340i 0.361620 0.626345i
944944 −29.0487 −0.945453
945945 0 0
946946 20.7043 + 35.8609i 0.673154 + 1.16594i
947947 13.9409 + 24.1463i 0.453017 + 0.784649i 0.998572 0.0534265i 0.0170143π-0.0170143\pi
−0.545555 + 0.838075i 0.683681π0.683681\pi
948948 −35.7715 −1.16180
949949 −10.5771 + 9.18613i −0.343346 + 0.298194i
950950 −12.4610 −0.404289
951951 8.34851 + 14.4600i 0.270719 + 0.468899i
952952 0 0
953953 18.1784 31.4859i 0.588856 1.01993i −0.405527 0.914083i 0.632912π-0.632912\pi
0.994383 0.105845i 0.0337548π-0.0337548\pi
954954 19.5426 0.632715
955955 1.29407 2.24140i 0.0418753 0.0725301i
956956 11.2980 19.5687i 0.365403 0.632897i
957957 79.0535 2.55544
958958 −33.9877 + 58.8685i −1.09809 + 1.90195i
959959 0 0
960960 −0.721486 1.24965i −0.0232859 0.0403323i
961961 −29.3598 −0.947091
962962 −3.88339 20.0265i −0.125206 0.645681i
963963 −22.2937 −0.718405
964964 5.50287 + 9.53126i 0.177236 + 0.306981i
965965 0.102784 + 0.178026i 0.00330872 + 0.00573087i
966966 0 0
967967 −15.2681 −0.490988 −0.245494 0.969398i 0.578950π-0.578950\pi
−0.245494 + 0.969398i 0.578950π0.578950\pi
968968 3.30239 5.71990i 0.106143 0.183845i
969969 −1.30445 + 2.25937i −0.0419049 + 0.0725815i
970970 −7.14125 −0.229292
971971 18.4460 31.9494i 0.591961 1.02531i −0.402008 0.915636i 0.631687π-0.631687\pi
0.993968 0.109669i 0.0349792π-0.0349792\pi
972972 14.0916 + 24.4073i 0.451987 + 0.782865i
973973 0 0
974974 68.2867 2.18805
975975 −38.7931 13.3771i −1.24237 0.428410i
976976 54.4986 1.74446
977977 0.221957 + 0.384441i 0.00710104 + 0.0122994i 0.869554 0.493838i 0.164406π-0.164406\pi
−0.862453 + 0.506137i 0.831073π0.831073\pi
978978 −3.88452 6.72818i −0.124213 0.215144i
979979 −25.0633 + 43.4109i −0.801026 + 1.38742i
980980 0 0
981981 15.6310 27.0736i 0.499058 0.864394i
982982 7.61658 13.1923i 0.243055 0.420983i
983983 45.5603 1.45315 0.726575 0.687088i 0.241111π-0.241111\pi
0.726575 + 0.687088i 0.241111π0.241111\pi
984984 6.29483 10.9030i 0.200672 0.347574i
985985 0.145884 + 0.252678i 0.00464824 + 0.00805099i
986986 6.43964 + 11.1538i 0.205080 + 0.355209i
987987 0 0
988988 6.69369 + 2.30820i 0.212955 + 0.0734336i
989989 −21.9248 −0.697169
990990 −1.73546 3.00590i −0.0551565 0.0955338i
991991 −26.8148 46.4445i −0.851799 1.47536i −0.879583 0.475745i 0.842178π-0.842178\pi
0.0277842 0.999614i 0.491155π-0.491155\pi
992992 −4.40316 + 7.62650i −0.139801 + 0.242142i
993993 −32.8588 −1.04274
994994 0 0
995995 1.39139 2.40996i 0.0441100 0.0764008i
996996 10.2445 0.324609
997997 −14.5426 + 25.1886i −0.460569 + 0.797730i −0.998989 0.0449470i 0.985688π-0.985688\pi
0.538420 + 0.842677i 0.319021π0.319021\pi
998998 40.1857 + 69.6038i 1.27206 + 2.20327i
999999 2.57489 + 4.45984i 0.0814658 + 0.141103i
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 637.2.f.k.393.1 12
7.2 even 3 91.2.g.b.81.1 yes 12
7.3 odd 6 637.2.h.l.471.6 12
7.4 even 3 91.2.h.b.16.6 yes 12
7.5 odd 6 637.2.g.l.263.1 12
7.6 odd 2 637.2.f.j.393.1 12
13.3 even 3 8281.2.a.bz.1.6 6
13.9 even 3 inner 637.2.f.k.295.1 12
13.10 even 6 8281.2.a.ce.1.1 6
21.2 odd 6 819.2.n.d.172.6 12
21.11 odd 6 819.2.s.d.289.1 12
91.9 even 3 91.2.h.b.74.6 yes 12
91.16 even 3 1183.2.e.h.508.1 12
91.23 even 6 1183.2.e.g.508.6 12
91.48 odd 6 637.2.f.j.295.1 12
91.55 odd 6 8281.2.a.ca.1.6 6
91.61 odd 6 637.2.h.l.165.6 12
91.62 odd 6 8281.2.a.cf.1.1 6
91.74 even 3 91.2.g.b.9.1 12
91.81 even 3 1183.2.e.h.170.1 12
91.87 odd 6 637.2.g.l.373.1 12
91.88 even 6 1183.2.e.g.170.6 12
273.74 odd 6 819.2.n.d.100.6 12
273.191 odd 6 819.2.s.d.802.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.g.b.9.1 12 91.74 even 3
91.2.g.b.81.1 yes 12 7.2 even 3
91.2.h.b.16.6 yes 12 7.4 even 3
91.2.h.b.74.6 yes 12 91.9 even 3
637.2.f.j.295.1 12 91.48 odd 6
637.2.f.j.393.1 12 7.6 odd 2
637.2.f.k.295.1 12 13.9 even 3 inner
637.2.f.k.393.1 12 1.1 even 1 trivial
637.2.g.l.263.1 12 7.5 odd 6
637.2.g.l.373.1 12 91.87 odd 6
637.2.h.l.165.6 12 91.61 odd 6
637.2.h.l.471.6 12 7.3 odd 6
819.2.n.d.100.6 12 273.74 odd 6
819.2.n.d.172.6 12 21.2 odd 6
819.2.s.d.289.1 12 21.11 odd 6
819.2.s.d.802.1 12 273.191 odd 6
1183.2.e.g.170.6 12 91.88 even 6
1183.2.e.g.508.6 12 91.23 even 6
1183.2.e.h.170.1 12 91.81 even 3
1183.2.e.h.508.1 12 91.16 even 3
8281.2.a.bz.1.6 6 13.3 even 3
8281.2.a.ca.1.6 6 91.55 odd 6
8281.2.a.ce.1.1 6 13.10 even 6
8281.2.a.cf.1.1 6 91.62 odd 6