Properties

Label 980.2.x.m.67.15
Level 980980
Weight 22
Character 980.67
Analytic conductor 7.8257.825
Analytic rank 00
Dimension 7272
Inner twists 88

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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] = [980,2,Mod(67,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 8])) 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("980.67"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 980=22572 980 = 2^{2} \cdot 5 \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 980.x (of order 1212, degree 44, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [72,2,0,0,8,16,0,-4,0,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 7.825339398097.82533939809
Analytic rank: 00
Dimension: 7272
Relative dimension: 1818 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 67.15
Character χ\chi == 980.67
Dual form 980.2.x.m.863.15

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+(1.18977+0.764487i)q2+(2.384710.638980i)q3+(0.831118+1.81913i)q4+(0.5256002.17342i)q5+(3.32575+1.06284i)q6+(0.401862+2.79973i)q8+(2.680451.54756i)q9+(2.286892.18406i)q10+(4.09588+2.36476i)q11+(3.14436+3.80703i)q12+(0.0592655+0.0592655i)q13+(0.1353705.51881i)q15+(2.61849+3.02383i)q16+(4.77484+1.27942i)q17+(4.37222+0.207927i)q18+(1.315442.27842i)q19+(4.390570.850232i)q20+(3.06534+5.94478i)q22+(0.2927741.09265i)q23+(0.830651+6.93332i)q24+(4.447492.28469i)q25+(0.115820+0.0252047i)q26+(0.1660530.166053i)q277.27332iq29+(4.058006.66962i)q30+(4.015582.31840i)q31+(5.42708+1.59587i)q32+(11.2785+3.02207i)q33+(6.659082.12809i)q34+(5.04299+3.58989i)q36+(0.596933+2.22779i)q37+(0.1767413.71644i)q38+(0.103461+0.179200i)q39+(5.87377+2.34495i)q40+5.71767q41+(1.57302+1.57302i)q43+(0.897647+9.41635i)q44+(1.954656.63914i)q45+(1.183651.07618i)q46+(2.67468+0.716679i)q47+(4.31215+8.88410i)q48+(3.544886.11832i)q50+(10.5691+6.10206i)q51+(0.1570680.0585551i)q52+(2.44441+9.12265i)q53+(0.3245100.0706197i)q54+(7.292417.65915i)q55+(4.592814.59281i)q57+(5.560368.65360i)q58+(1.67748+2.90547i)q59+(9.926944.83304i)q60+(0.978771+1.69528i)q61+(3.005245.82822i)q62+(7.677012.25021i)q64+(0.0976587+0.159959i)q65+(11.1085+12.2179i)q66+(0.131802+0.491893i)q67+(6.295897.62273i)q682.79272iq6914.4625iq71+(3.25558+8.12646i)q72+(2.48257+9.26507i)q73+(2.41333+2.19421i)q74+(12.06582.60647i)q75+(3.051454.28660i)q76+(0.260092+0.134113i)q78+(3.052045.28630i)q79+(5.19577+7.28039i)q80+(4.35280+7.53927i)q81+(6.80273+4.37109i)q82+(5.626205.62620i)q83+(0.271049+11.0502i)q85+(0.668982+3.07409i)q86+(4.6475117.3447i)q87+(8.26668+10.5171i)q88+(14.4482+8.34169i)q89+(2.749959.39337i)q90+(2.231000.375524i)q92+(11.05742.96282i)q93+(2.63437+2.89745i)q94+(5.64335+1.66148i)q95+(11.9223+7.27348i)q96+(5.815055.81505i)q97+14.6384q99+O(q100)q+(1.18977 + 0.764487i) q^{2} +(2.38471 - 0.638980i) q^{3} +(0.831118 + 1.81913i) q^{4} +(0.525600 - 2.17342i) q^{5} +(3.32575 + 1.06284i) q^{6} +(-0.401862 + 2.79973i) q^{8} +(2.68045 - 1.54756i) q^{9} +(2.28689 - 2.18406i) q^{10} +(4.09588 + 2.36476i) q^{11} +(3.14436 + 3.80703i) q^{12} +(-0.0592655 + 0.0592655i) q^{13} +(-0.135370 - 5.51881i) q^{15} +(-2.61849 + 3.02383i) q^{16} +(-4.77484 + 1.27942i) q^{17} +(4.37222 + 0.207927i) q^{18} +(-1.31544 - 2.27842i) q^{19} +(4.39057 - 0.850232i) q^{20} +(3.06534 + 5.94478i) q^{22} +(0.292774 - 1.09265i) q^{23} +(0.830651 + 6.93332i) q^{24} +(-4.44749 - 2.28469i) q^{25} +(-0.115820 + 0.0252047i) q^{26} +(0.166053 - 0.166053i) q^{27} -7.27332i q^{29} +(4.05800 - 6.66962i) q^{30} +(-4.01558 - 2.31840i) q^{31} +(-5.42708 + 1.59587i) q^{32} +(11.2785 + 3.02207i) q^{33} +(-6.65908 - 2.12809i) q^{34} +(5.04299 + 3.58989i) q^{36} +(-0.596933 + 2.22779i) q^{37} +(0.176741 - 3.71644i) q^{38} +(-0.103461 + 0.179200i) q^{39} +(5.87377 + 2.34495i) q^{40} +5.71767 q^{41} +(1.57302 + 1.57302i) q^{43} +(-0.897647 + 9.41635i) q^{44} +(-1.95465 - 6.63914i) q^{45} +(1.18365 - 1.07618i) q^{46} +(2.67468 + 0.716679i) q^{47} +(-4.31215 + 8.88410i) q^{48} +(-3.54488 - 6.11832i) q^{50} +(-10.5691 + 6.10206i) q^{51} +(-0.157068 - 0.0585551i) q^{52} +(2.44441 + 9.12265i) q^{53} +(0.324510 - 0.0706197i) q^{54} +(7.29241 - 7.65915i) q^{55} +(-4.59281 - 4.59281i) q^{57} +(5.56036 - 8.65360i) q^{58} +(-1.67748 + 2.90547i) q^{59} +(9.92694 - 4.83304i) q^{60} +(0.978771 + 1.69528i) q^{61} +(-3.00524 - 5.82822i) q^{62} +(-7.67701 - 2.25021i) q^{64} +(0.0976587 + 0.159959i) q^{65} +(11.1085 + 12.2179i) q^{66} +(0.131802 + 0.491893i) q^{67} +(-6.29589 - 7.62273i) q^{68} -2.79272i q^{69} -14.4625i q^{71} +(3.25558 + 8.12646i) q^{72} +(2.48257 + 9.26507i) q^{73} +(-2.41333 + 2.19421i) q^{74} +(-12.0658 - 2.60647i) q^{75} +(3.05145 - 4.28660i) q^{76} +(-0.260092 + 0.134113i) q^{78} +(-3.05204 - 5.28630i) q^{79} +(5.19577 + 7.28039i) q^{80} +(-4.35280 + 7.53927i) q^{81} +(6.80273 + 4.37109i) q^{82} +(-5.62620 - 5.62620i) q^{83} +(0.271049 + 11.0502i) q^{85} +(0.668982 + 3.07409i) q^{86} +(-4.64751 - 17.3447i) q^{87} +(-8.26668 + 10.5171i) q^{88} +(-14.4482 + 8.34169i) q^{89} +(2.74995 - 9.39337i) q^{90} +(2.23100 - 0.375524i) q^{92} +(-11.0574 - 2.96282i) q^{93} +(2.63437 + 2.89745i) q^{94} +(-5.64335 + 1.66148i) q^{95} +(-11.9223 + 7.27348i) q^{96} +(-5.81505 - 5.81505i) q^{97} +14.6384 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 72q+2q2+8q5+16q64q82q1010q1228q164q1720q18+56q2016q2216q25+4q2632q3038q32+64q33+16q364q37++24q97+O(q100) 72 q + 2 q^{2} + 8 q^{5} + 16 q^{6} - 4 q^{8} - 2 q^{10} - 10 q^{12} - 28 q^{16} - 4 q^{17} - 20 q^{18} + 56 q^{20} - 16 q^{22} - 16 q^{25} + 4 q^{26} - 32 q^{30} - 38 q^{32} + 64 q^{33} + 16 q^{36} - 4 q^{37}+ \cdots + 24 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/980Z)×\left(\mathbb{Z}/980\mathbb{Z}\right)^\times.

nn 101101 197197 491491
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\right) e(14)e\left(\frac{1}{4}\right) 1-1

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 1.18977 + 0.764487i 0.841296 + 0.540574i
33 2.38471 0.638980i 1.37681 0.368915i 0.506849 0.862035i 0.330810π-0.330810\pi
0.869962 + 0.493119i 0.164143π0.164143\pi
44 0.831118 + 1.81913i 0.415559 + 0.909566i
55 0.525600 2.17342i 0.235055 0.971982i
66 3.32575 + 1.06284i 1.35773 + 0.433901i
77 0 0
88 −0.401862 + 2.79973i −0.142080 + 0.989855i
99 2.68045 1.54756i 0.893484 0.515853i
1010 2.28689 2.18406i 0.723180 0.690660i
1111 4.09588 + 2.36476i 1.23496 + 0.713002i 0.968059 0.250723i 0.0806684π-0.0806684\pi
0.266897 + 0.963725i 0.414002π0.414002\pi
1212 3.14436 + 3.80703i 0.907699 + 1.09899i
1313 −0.0592655 + 0.0592655i −0.0164373 + 0.0164373i −0.715278 0.698840i 0.753700π-0.753700\pi
0.698840 + 0.715278i 0.253700π0.253700\pi
1414 0 0
1515 −0.135370 5.51881i −0.0349524 1.42495i
1616 −2.61849 + 3.02383i −0.654621 + 0.755957i
1717 −4.77484 + 1.27942i −1.15807 + 0.310304i −0.786195 0.617979i 0.787952π-0.787952\pi
−0.371875 + 0.928283i 0.621285π0.621285\pi
1818 4.37222 + 0.207927i 1.03054 + 0.0490090i
1919 −1.31544 2.27842i −0.301784 0.522705i 0.674756 0.738041i 0.264249π-0.264249\pi
−0.976540 + 0.215336i 0.930915π0.930915\pi
2020 4.39057 0.850232i 0.981761 0.190118i
2121 0 0
2222 3.06534 + 5.94478i 0.653533 + 1.26743i
2323 0.292774 1.09265i 0.0610475 0.227832i −0.928661 0.370929i 0.879039π-0.879039\pi
0.989709 + 0.143097i 0.0457060π0.0457060\pi
2424 0.830651 + 6.93332i 0.169556 + 1.41526i
2525 −4.44749 2.28469i −0.889498 0.456939i
2626 −0.115820 + 0.0252047i −0.0227142 + 0.00494306i
2727 0.166053 0.166053i 0.0319568 0.0319568i
2828 0 0
2929 7.27332i 1.35062i −0.737533 0.675311i 0.764009π-0.764009\pi
0.737533 0.675311i 0.235991π-0.235991\pi
3030 4.05800 6.66962i 0.740886 1.21770i
3131 −4.01558 2.31840i −0.721219 0.416396i 0.0939821 0.995574i 0.470040π-0.470040\pi
−0.815201 + 0.579178i 0.803374π0.803374\pi
3232 −5.42708 + 1.59587i −0.959381 + 0.282112i
3333 11.2785 + 3.02207i 1.96334 + 0.526075i
3434 −6.65908 2.12809i −1.14202 0.364965i
3535 0 0
3636 5.04299 + 3.58989i 0.840498 + 0.598315i
3737 −0.596933 + 2.22779i −0.0981352 + 0.366246i −0.997476 0.0710024i 0.977380π-0.977380\pi
0.899341 + 0.437248i 0.144047π0.144047\pi
3838 0.176741 3.71644i 0.0286712 0.602886i
3939 −0.103461 + 0.179200i −0.0165671 + 0.0286950i
4040 5.87377 + 2.34495i 0.928725 + 0.370770i
4141 5.71767 0.892950 0.446475 0.894796i 0.352679π-0.352679\pi
0.446475 + 0.894796i 0.352679π0.352679\pi
4242 0 0
4343 1.57302 + 1.57302i 0.239883 + 0.239883i 0.816802 0.576918i 0.195745π-0.195745\pi
−0.576918 + 0.816802i 0.695745π0.695745\pi
4444 −0.897647 + 9.41635i −0.135325 + 1.41957i
4545 −1.95465 6.63914i −0.291382 0.989704i
4646 1.18365 1.07618i 0.174519 0.158674i
4747 2.67468 + 0.716679i 0.390143 + 0.104538i 0.448558 0.893754i 0.351938π-0.351938\pi
−0.0584148 + 0.998292i 0.518605π0.518605\pi
4848 −4.31215 + 8.88410i −0.622406 + 1.28231i
4949 0 0
5050 −3.54488 6.11832i −0.501322 0.865261i
5151 −10.5691 + 6.10206i −1.47997 + 0.854459i
5252 −0.157068 0.0585551i −0.0217815 0.00812014i
5353 2.44441 + 9.12265i 0.335765 + 1.25309i 0.903037 + 0.429562i 0.141332π0.141332\pi
−0.567272 + 0.823530i 0.692001π0.692001\pi
5454 0.324510 0.0706197i 0.0441602 0.00961013i
5555 7.29241 7.65915i 0.983308 1.03276i
5656 0 0
5757 −4.59281 4.59281i −0.608333 0.608333i
5858 5.56036 8.65360i 0.730112 1.13627i
5959 −1.67748 + 2.90547i −0.218389 + 0.378260i −0.954315 0.298801i 0.903413π-0.903413\pi
0.735927 + 0.677061i 0.236747π0.236747\pi
6060 9.92694 4.83304i 1.28156 0.623943i
6161 0.978771 + 1.69528i 0.125319 + 0.217058i 0.921857 0.387529i 0.126671π-0.126671\pi
−0.796539 + 0.604587i 0.793338π0.793338\pi
6262 −3.00524 5.82822i −0.381666 0.740185i
6363 0 0
6464 −7.67701 2.25021i −0.959627 0.281277i
6565 0.0976587 + 0.159959i 0.0121131 + 0.0198404i
6666 11.1085 + 12.2179i 1.36737 + 1.50391i
6767 0.131802 + 0.491893i 0.0161022 + 0.0600943i 0.973509 0.228647i 0.0734300π-0.0734300\pi
−0.957407 + 0.288741i 0.906763π0.906763\pi
6868 −6.29589 7.62273i −0.763488 0.924392i
6969 2.79272i 0.336204i
7070 0 0
7171 14.4625i 1.71638i −0.513329 0.858192i 0.671588π-0.671588\pi
0.513329 0.858192i 0.328412π-0.328412\pi
7272 3.25558 + 8.12646i 0.383674 + 0.957712i
7373 2.48257 + 9.26507i 0.290563 + 1.08439i 0.944678 + 0.327999i 0.106374π0.106374\pi
−0.654115 + 0.756395i 0.726959π0.726959\pi
7474 −2.41333 + 2.19421i −0.280544 + 0.255072i
7575 −12.0658 2.60647i −1.39324 0.300969i
7676 3.05145 4.28660i 0.350026 0.491707i
7777 0 0
7878 −0.260092 + 0.134113i −0.0294496 + 0.0151853i
7979 −3.05204 5.28630i −0.343382 0.594755i 0.641677 0.766975i 0.278239π-0.278239\pi
−0.985058 + 0.172221i 0.944906π0.944906\pi
8080 5.19577 + 7.28039i 0.580904 + 0.813972i
8181 −4.35280 + 7.53927i −0.483644 + 0.837696i
8282 6.80273 + 4.37109i 0.751235 + 0.482706i
8383 −5.62620 5.62620i −0.617555 0.617555i 0.327348 0.944904i 0.393845π-0.393845\pi
−0.944904 + 0.327348i 0.893845π0.893845\pi
8484 0 0
8585 0.271049 + 11.0502i 0.0293994 + 1.19856i
8686 0.668982 + 3.07409i 0.0721382 + 0.331488i
8787 −4.64751 17.3447i −0.498265 1.85955i
8888 −8.26668 + 10.5171i −0.881231 + 1.12112i
8989 −14.4482 + 8.34169i −1.53151 + 0.884218i −0.532217 + 0.846608i 0.678641π0.678641\pi
−0.999292 + 0.0376100i 0.988026π0.988026\pi
9090 2.74995 9.39337i 0.289870 0.990148i
9191 0 0
9292 2.23100 0.375524i 0.232598 0.0391511i
9393 −11.0574 2.96282i −1.14660 0.307230i
9494 2.63437 + 2.89745i 0.271715 + 0.298849i
9595 −5.64335 + 1.66148i −0.578996 + 0.170464i
9696 −11.9223 + 7.27348i −1.21681 + 0.742346i
9797 −5.81505 5.81505i −0.590429 0.590429i 0.347318 0.937747i 0.387092π-0.387092\pi
−0.937747 + 0.347318i 0.887092π0.887092\pi
9898 0 0
9999 14.6384 1.47122
100100 0.459773 9.98942i 0.0459773 0.998942i
101101 −4.28723 + 7.42571i −0.426596 + 0.738885i −0.996568 0.0827785i 0.973621π-0.973621\pi
0.569972 + 0.821664i 0.306954π0.306954\pi
102102 −17.2398 0.819862i −1.70699 0.0811785i
103103 0.845330 3.15482i 0.0832929 0.310853i −0.911693 0.410873i 0.865224π-0.865224\pi
0.994985 + 0.100020i 0.0318906π0.0318906\pi
104104 −0.142111 0.189744i −0.0139351 0.0186059i
105105 0 0
106106 −4.06586 + 12.7226i −0.394911 + 1.23573i
107107 −6.56081 1.75796i −0.634257 0.169949i −0.0726563 0.997357i 0.523148π-0.523148\pi
−0.561601 + 0.827408i 0.689814π0.689814\pi
108108 0.440081 + 0.164062i 0.0423468 + 0.0157869i
109109 −3.39423 1.95966i −0.325108 0.187701i 0.328559 0.944483i 0.393437π-0.393437\pi
−0.653667 + 0.756782i 0.726770π0.726770\pi
110110 14.5316 3.53770i 1.38554 0.337306i
111111 5.69404i 0.540455i
112112 0 0
113113 −0.0280186 + 0.0280186i −0.00263577 + 0.00263577i −0.708423 0.705788i 0.750593π-0.750593\pi
0.705788 + 0.708423i 0.250593π0.250593\pi
114114 −1.95326 8.97555i −0.182939 0.840637i
115115 −2.22089 1.21061i −0.207100 0.112890i
116116 13.2311 6.04499i 1.22848 0.561263i
117117 −0.0671414 + 0.250575i −0.00620723 + 0.0231657i
118118 −4.21701 + 2.17444i −0.388207 + 0.200174i
119119 0 0
120120 15.5056 + 1.83880i 1.41546 + 0.167859i
121121 5.68418 + 9.84529i 0.516744 + 0.895026i
122122 −0.131506 + 2.76526i −0.0119060 + 0.250355i
123123 13.6350 3.65348i 1.22942 0.329423i
124124 0.880048 9.23173i 0.0790306 0.829034i
125125 −7.30320 + 8.46542i −0.653218 + 0.757170i
126126 0 0
127127 6.53450 6.53450i 0.579843 0.579843i −0.355017 0.934860i 0.615525π-0.615525\pi
0.934860 + 0.355017i 0.115525π0.115525\pi
128128 −7.41364 8.54622i −0.655280 0.755386i
129129 4.75632 + 2.74606i 0.418770 + 0.241777i
130130 −0.00609459 + 0.264973i −0.000534531 + 0.0232397i
131131 3.19588 1.84514i 0.279225 0.161211i −0.353847 0.935303i 0.615127π-0.615127\pi
0.633073 + 0.774092i 0.281793π0.281793\pi
132132 3.87624 + 23.0288i 0.337383 + 2.00440i
133133 0 0
134134 −0.219231 + 0.686002i −0.0189387 + 0.0592616i
135135 −0.273625 0.448179i −0.0235499 0.0385731i
136136 −1.66319 13.8824i −0.142618 1.19041i
137137 19.1819 5.13977i 1.63882 0.439120i 0.682366 0.731010i 0.260951π-0.260951\pi
0.956452 + 0.291890i 0.0942843π0.0942843\pi
138138 2.13500 3.32270i 0.181743 0.282847i
139139 1.15593 0.0980447 0.0490223 0.998798i 0.484389π-0.484389\pi
0.0490223 + 0.998798i 0.484389π0.484389\pi
140140 0 0
141141 6.83628 0.575719
142142 11.0564 17.2071i 0.927833 1.44399i
143143 −0.382893 + 0.102596i −0.0320191 + 0.00857950i
144144 −2.33917 + 12.1575i −0.194931 + 1.01312i
145145 −15.8080 3.82286i −1.31278 0.317471i
146146 −4.12934 + 12.9212i −0.341746 + 1.06937i
147147 0 0
148148 −4.54876 + 0.765652i −0.373906 + 0.0629362i
149149 −5.37045 + 3.10063i −0.439965 + 0.254014i −0.703583 0.710613i 0.748418π-0.748418\pi
0.263618 + 0.964627i 0.415084π0.415084\pi
150150 −12.3630 12.3253i −1.00943 1.00636i
151151 −8.72300 5.03623i −0.709868 0.409842i 0.101144 0.994872i 0.467750π-0.467750\pi
−0.811012 + 0.585029i 0.801083π0.801083\pi
152152 6.90759 2.76729i 0.560279 0.224457i
153153 −10.8188 + 10.8188i −0.874646 + 0.874646i
154154 0 0
155155 −7.14943 + 7.50898i −0.574256 + 0.603136i
156156 −0.411977 0.0392732i −0.0329846 0.00314438i
157157 14.0732 3.77089i 1.12316 0.300950i 0.350999 0.936376i 0.385842π-0.385842\pi
0.772162 + 0.635426i 0.219175π0.219175\pi
158158 0.410067 8.62274i 0.0326232 0.685988i
159159 11.6584 + 20.1929i 0.924570 + 1.60140i
160160 0.616019 + 12.6341i 0.0487006 + 0.998813i
161161 0 0
162162 −10.9425 + 5.64235i −0.859725 + 0.443305i
163163 0.763938 2.85106i 0.0598363 0.223312i −0.929533 0.368740i 0.879789π-0.879789\pi
0.989369 + 0.145428i 0.0464559π0.0464559\pi
164164 4.75206 + 10.4012i 0.371073 + 0.812197i
165165 12.4962 22.9245i 0.972828 1.78467i
166166 −2.39274 10.9950i −0.185713 0.853381i
167167 −6.13096 + 6.13096i −0.474428 + 0.474428i −0.903344 0.428916i 0.858895π-0.858895\pi
0.428916 + 0.903344i 0.358895π0.358895\pi
168168 0 0
169169 12.9930i 0.999460i
170170 −8.12525 + 13.3544i −0.623178 + 1.02424i
171171 −7.05197 4.07146i −0.539278 0.311352i
172172 −1.55417 + 4.16890i −0.118504 + 0.317875i
173173 −1.73431 0.464708i −0.131857 0.0353311i 0.192287 0.981339i 0.438410π-0.438410\pi
−0.324144 + 0.946008i 0.605076π0.605076\pi
174174 7.73035 24.1893i 0.586037 1.83378i
175175 0 0
176176 −17.8756 + 6.19316i −1.34743 + 0.466827i
177177 −2.14375 + 8.00057i −0.161134 + 0.601360i
178178 −23.5672 1.12078i −1.76644 0.0840057i
179179 −10.7713 + 18.6564i −0.805084 + 1.39445i 0.111150 + 0.993804i 0.464547π0.464547\pi
−0.916234 + 0.400643i 0.868787π0.868787\pi
180180 10.4529 9.07368i 0.779115 0.676312i
181181 16.2122 1.20504 0.602520 0.798104i 0.294163π-0.294163\pi
0.602520 + 0.798104i 0.294163π0.294163\pi
182182 0 0
183183 3.41733 + 3.41733i 0.252616 + 0.252616i
184184 2.94146 + 1.25878i 0.216848 + 0.0927986i
185185 4.52816 + 2.46831i 0.332917 + 0.181474i
186186 −10.8907 11.9783i −0.798548 0.878292i
187187 −22.5827 6.05102i −1.65141 0.442495i
188188 0.919244 + 5.46125i 0.0670427 + 0.398303i
189189 0 0
190190 −7.98448 2.33749i −0.579255 0.169579i
191191 14.2331 8.21746i 1.02987 0.594595i 0.112921 0.993604i 0.463979π-0.463979\pi
0.916947 + 0.399009i 0.130646π0.130646\pi
192192 −19.7453 0.460637i −1.42499 0.0332436i
193193 1.28369 + 4.79080i 0.0924021 + 0.344849i 0.996613 0.0822374i 0.0262066π-0.0262066\pi
−0.904211 + 0.427087i 0.859540π0.859540\pi
194194 −2.47306 11.3641i −0.177555 0.815897i
195195 0.335098 + 0.319052i 0.0239968 + 0.0228478i
196196 0 0
197197 −3.89922 3.89922i −0.277808 0.277808i 0.554425 0.832233i 0.312938π-0.312938\pi
−0.832233 + 0.554425i 0.812938π0.812938\pi
198198 17.4164 + 11.1909i 1.23773 + 0.795302i
199199 9.44788 16.3642i 0.669743 1.16003i −0.308233 0.951311i 0.599738π-0.599738\pi
0.977976 0.208717i 0.0669289π-0.0669289\pi
200200 8.18381 11.5337i 0.578683 0.815553i
201201 0.628620 + 1.08880i 0.0443394 + 0.0767981i
202202 −10.7777 + 5.55737i −0.758316 + 0.391015i
203203 0 0
204204 −19.8846 14.1550i −1.39220 0.991050i
205205 3.00520 12.4269i 0.209893 0.867931i
206206 3.41757 3.10727i 0.238113 0.216494i
207207 −0.906169 3.38187i −0.0629831 0.235056i
208208 −0.0240228 0.334394i −0.00166568 0.0231861i
209209 12.4428i 0.860690i
210210 0 0
211211 10.9795i 0.755859i −0.925834 0.377929i 0.876636π-0.876636\pi
0.925834 0.377929i 0.123364π-0.123364\pi
212212 −14.5637 + 12.0287i −1.00024 + 0.826135i
213213 −9.24126 34.4888i −0.633201 2.36314i
214214 −6.46193 7.10723i −0.441728 0.485840i
215215 4.24561 2.59205i 0.289548 0.176776i
216216 0.398173 + 0.531633i 0.0270922 + 0.0361731i
217217 0 0
218218 −2.54022 4.92639i −0.172046 0.333657i
219219 11.8404 + 20.5082i 0.800099 + 1.38581i
220220 19.9939 + 6.90019i 1.34799 + 0.465211i
221221 0.207158 0.358809i 0.0139350 0.0241361i
222222 −4.35302 + 6.77462i −0.292156 + 0.454683i
223223 13.6990 + 13.6990i 0.917356 + 0.917356i 0.996836 0.0794806i 0.0253262π-0.0253262\pi
−0.0794806 + 0.996836i 0.525326π0.525326\pi
224224 0 0
225225 −15.4570 + 0.758741i −1.03047 + 0.0505828i
226226 −0.0547556 + 0.0119159i −0.00364229 + 0.000792634i
227227 5.94107 + 22.1724i 0.394322 + 1.47163i 0.822931 + 0.568141i 0.192337π0.192337\pi
−0.428609 + 0.903490i 0.640996π0.640996\pi
228228 4.53776 12.1721i 0.300521 0.806117i
229229 10.3396 5.96955i 0.683258 0.394479i −0.117824 0.993035i 0.537592π-0.537592\pi
0.801081 + 0.598556i 0.204258π0.204258\pi
230230 −1.71686 3.13820i −0.113206 0.206927i
231231 0 0
232232 20.3634 + 2.92287i 1.33692 + 0.191896i
233233 22.9805 + 6.15761i 1.50550 + 0.403399i 0.914939 0.403592i 0.132238π-0.132238\pi
0.590565 + 0.806990i 0.298905π0.298905\pi
234234 −0.271445 + 0.246799i −0.0177449 + 0.0161337i
235235 2.96346 5.43652i 0.193315 0.354639i
236236 −6.67962 0.636759i −0.434806 0.0414495i
237237 −10.6561 10.6561i −0.692186 0.692186i
238238 0 0
239239 −1.50749 −0.0975113 −0.0487556 0.998811i 0.515526π-0.515526\pi
−0.0487556 + 0.998811i 0.515526π0.515526\pi
240240 17.0424 + 14.0416i 1.10008 + 0.906381i
241241 −9.26556 + 16.0484i −0.596847 + 1.03377i 0.396436 + 0.918062i 0.370247π0.370247\pi
−0.993283 + 0.115708i 0.963086π0.963086\pi
242242 −0.763716 + 16.0591i −0.0490935 + 1.03232i
243243 −5.74504 + 21.4408i −0.368544 + 1.37543i
244244 −2.27047 + 3.18949i −0.145352 + 0.204186i
245245 0 0
246246 19.0155 + 6.07695i 1.21239 + 0.387452i
247247 0.212992 + 0.0570710i 0.0135524 + 0.00363134i
248248 8.10460 10.3109i 0.514642 0.654741i
249249 −17.0119 9.82180i −1.07808 0.622431i
250250 −15.1608 + 4.48872i −0.958856 + 0.283892i
251251 18.0219i 1.13753i −0.822500 0.568765i 0.807421π-0.807421\pi
0.822500 0.568765i 0.192579π-0.192579\pi
252252 0 0
253253 3.78301 3.78301i 0.237836 0.237836i
254254 12.7701 2.77903i 0.801268 0.174372i
255255 7.70722 + 26.1783i 0.482645 + 1.63935i
256256 −2.28707 15.8357i −0.142942 0.989731i
257257 3.85933 14.4032i 0.240738 0.898448i −0.734739 0.678350i 0.762696π-0.762696\pi
0.975478 0.220098i 0.0706378π-0.0706378\pi
258258 3.55961 + 6.90333i 0.221611 + 0.429783i
259259 0 0
260260 −0.209820 + 0.310599i −0.0130125 + 0.0192625i
261261 −11.2559 19.4958i −0.696723 1.20676i
262262 5.21295 + 0.247910i 0.322057 + 0.0153159i
263263 6.84826 1.83499i 0.422282 0.113150i −0.0414191 0.999142i 0.513188π-0.513188\pi
0.463701 + 0.885992i 0.346521π0.346521\pi
264264 −12.9934 + 30.3624i −0.799688 + 1.86868i
265265 21.1121 0.517856i 1.29691 0.0318117i
266266 0 0
267267 −29.1246 + 29.1246i −1.78240 + 1.78240i
268268 −0.785275 + 0.648587i −0.0479683 + 0.0396188i
269269 −5.23463 3.02221i −0.319161 0.184268i 0.331858 0.943329i 0.392325π-0.392325\pi
−0.651019 + 0.759062i 0.725658π0.725658\pi
270270 0.0170761 0.742414i 0.00103922 0.0451819i
271271 20.3476 11.7477i 1.23603 0.713622i 0.267750 0.963488i 0.413720π-0.413720\pi
0.968280 + 0.249866i 0.0803866π0.0803866\pi
272272 8.63413 17.7884i 0.523521 1.07858i
273273 0 0
274274 26.7514 + 8.54914i 1.61611 + 0.516473i
275275 −12.8137 19.8751i −0.772692 1.19851i
276276 5.08032 2.32108i 0.305799 0.139712i
277277 −22.5298 + 6.03684i −1.35369 + 0.362719i −0.861494 0.507768i 0.830471π-0.830471\pi
−0.492191 + 0.870487i 0.663804π0.663804\pi
278278 1.37529 + 0.883694i 0.0824846 + 0.0530004i
279279 −14.3514 −0.859197
280280 0 0
281281 −19.3011 −1.15141 −0.575703 0.817659i 0.695272π-0.695272\pi
−0.575703 + 0.817659i 0.695272π0.695272\pi
282282 8.13362 + 5.22625i 0.484350 + 0.311219i
283283 6.88593 1.84508i 0.409326 0.109679i −0.0482794 0.998834i 0.515374π-0.515374\pi
0.457606 + 0.889155i 0.348707π0.348707\pi
284284 26.3092 12.0201i 1.56117 0.713259i
285285 −12.3961 + 7.56812i −0.734281 + 0.448297i
286286 −0.533989 0.170651i −0.0315754 0.0100908i
287287 0 0
288288 −12.0773 + 12.6764i −0.711663 + 0.746963i
289289 6.43980 3.71802i 0.378812 0.218707i
290290 −15.8854 16.6333i −0.932821 0.976742i
291291 −17.5829 10.1515i −1.03073 0.595091i
292292 −14.7911 + 12.2165i −0.865583 + 0.714916i
293293 −1.29442 + 1.29442i −0.0756208 + 0.0756208i −0.743906 0.668285i 0.767029π-0.767029\pi
0.668285 + 0.743906i 0.267029π0.267029\pi
294294 0 0
295295 5.43312 + 5.17297i 0.316329 + 0.301182i
296296 −5.99732 2.56652i −0.348587 0.149176i
297297 1.07281 0.287458i 0.0622506 0.0166800i
298298 −8.76001 0.416596i −0.507454 0.0241327i
299299 0.0474048 + 0.0821076i 0.00274149 + 0.00474840i
300300 −5.28662 24.1156i −0.305223 1.39232i
301301 0 0
302302 −6.52826 12.6606i −0.375659 0.728535i
303303 −5.47891 + 20.4476i −0.314755 + 1.17468i
304304 10.3340 + 1.98832i 0.592696 + 0.114038i
305305 4.19899 1.23624i 0.240434 0.0707868i
306306 −21.1427 + 4.60106i −1.20865 + 0.263025i
307307 3.86175 3.86175i 0.220402 0.220402i −0.588266 0.808667i 0.700189π-0.700189\pi
0.808667 + 0.588266i 0.200189π0.200189\pi
308308 0 0
309309 8.06346i 0.458714i
310310 −14.2467 + 3.46833i −0.809159 + 0.196988i
311311 −17.7808 10.2657i −1.00826 0.582116i −0.0975749 0.995228i 0.531109π-0.531109\pi
−0.910680 + 0.413112i 0.864442π0.864442\pi
312312 −0.460136 0.361678i −0.0260501 0.0204760i
313313 26.9598 + 7.22385i 1.52386 + 0.408316i 0.921009 0.389540i 0.127366π-0.127366\pi
0.602847 + 0.797856i 0.294033π0.294033\pi
314314 19.6267 + 6.27225i 1.10760 + 0.353964i
315315 0 0
316316 7.07986 9.94561i 0.398273 0.559484i
317317 −3.35388 + 12.5169i −0.188373 + 0.703016i 0.805511 + 0.592581i 0.201891π0.201891\pi
−0.993883 + 0.110435i 0.964776π0.964776\pi
318318 −1.56640 + 32.9377i −0.0878394 + 1.84705i
319319 17.1997 29.7907i 0.962996 1.66796i
320320 −8.92569 + 15.5026i −0.498961 + 0.866624i
321321 −16.7689 −0.935949
322322 0 0
323323 9.19609 + 9.19609i 0.511684 + 0.511684i
324324 −17.3326 1.65229i −0.962923 0.0917941i
325325 0.398986 0.128179i 0.0221318 0.00711010i
326326 3.08851 2.80809i 0.171057 0.155526i
327327 −9.34642 2.50436i −0.516858 0.138492i
328328 −2.29771 + 16.0079i −0.126870 + 0.883891i
329329 0 0
330330 32.3932 17.7218i 1.78318 0.975552i
331331 6.41324 3.70269i 0.352504 0.203518i −0.313284 0.949660i 0.601429π-0.601429\pi
0.665787 + 0.746142i 0.268096π0.268096\pi
332332 5.55876 14.9108i 0.305077 0.818338i
333333 1.84758 + 6.89526i 0.101247 + 0.377858i
334334 −11.9815 + 2.60741i −0.655598 + 0.142671i
335335 1.13836 0.0279228i 0.0621955 0.00152559i
336336 0 0
337337 −5.81990 5.81990i −0.317030 0.317030i 0.530595 0.847625i 0.321968π-0.321968\pi
−0.847625 + 0.530595i 0.821968π0.821968\pi
338338 −9.93297 + 15.4587i −0.540282 + 0.840842i
339339 −0.0489128 + 0.0847195i −0.00265658 + 0.00460133i
340340 −19.8765 + 9.67709i −1.07795 + 0.524814i
341341 −10.9649 18.9918i −0.593782 1.02846i
342342 −5.27767 10.2353i −0.285384 0.553459i
343343 0 0
344344 −5.03617 + 3.77190i −0.271532 + 0.203367i
345345 −6.06974 1.46785i −0.326784 0.0790264i
346346 −1.70817 1.87876i −0.0918320 0.101003i
347347 2.85823 + 10.6671i 0.153438 + 0.572638i 0.999234 + 0.0391317i 0.0124592π0.0124592\pi
−0.845796 + 0.533506i 0.820874π0.820874\pi
348348 27.6897 22.8700i 1.48433 1.22596i
349349 10.3995i 0.556672i 0.960484 + 0.278336i 0.0897829π0.0897829\pi
−0.960484 + 0.278336i 0.910217π0.910217\pi
350350 0 0
351351 0.0196824i 0.00105057i
352352 −26.0025 6.29725i −1.38594 0.335644i
353353 1.95306 + 7.28892i 0.103951 + 0.387950i 0.998224 0.0595714i 0.0189734π-0.0189734\pi
−0.894273 + 0.447522i 0.852307π0.852307\pi
354354 −8.66691 + 7.87999i −0.460641 + 0.418817i
355355 −31.4331 7.60149i −1.66829 0.403445i
356356 −27.1828 19.3503i −1.44069 1.02556i
357357 0 0
358358 −27.0780 + 13.9624i −1.43112 + 0.737935i
359359 5.74179 + 9.94507i 0.303040 + 0.524881i 0.976823 0.214049i 0.0686651π-0.0686651\pi
−0.673783 + 0.738929i 0.735332π0.735332\pi
360360 19.3733 2.80448i 1.02106 0.147809i
361361 6.03921 10.4602i 0.317853 0.550538i
362362 19.2888 + 12.3940i 1.01380 + 0.651413i
363363 19.8460 + 19.8460i 1.04165 + 1.04165i
364364 0 0
365365 21.4417 0.525941i 1.12231 0.0275290i
366366 1.45334 + 6.67835i 0.0759673 + 0.349083i
367367 3.27735 + 12.2312i 0.171076 + 0.638465i 0.997187 + 0.0749570i 0.0238820π0.0238820\pi
−0.826111 + 0.563508i 0.809451π0.809451\pi
368368 2.53735 + 3.74637i 0.132269 + 0.195293i
369369 15.3259 8.84843i 0.797836 0.460631i
370370 3.50049 + 6.39845i 0.181982 + 0.332639i
371371 0 0
372372 −3.80024 22.5773i −0.197033 1.17058i
373373 24.0550 + 6.44552i 1.24552 + 0.333737i 0.820605 0.571496i 0.193637π-0.193637\pi
0.424917 + 0.905232i 0.360303π0.360303\pi
374374 −22.2424 24.4635i −1.15013 1.26498i
375375 −12.0067 + 24.8541i −0.620025 + 1.28346i
376376 −3.08137 + 7.20040i −0.158909 + 0.371332i
377377 0.431057 + 0.431057i 0.0222006 + 0.0222006i
378378 0 0
379379 −4.18354 −0.214894 −0.107447 0.994211i 0.534268π-0.534268\pi
−0.107447 + 0.994211i 0.534268π0.534268\pi
380380 −7.71274 8.88512i −0.395655 0.455797i
381381 11.4074 19.7583i 0.584421 1.01225i
382382 23.2163 + 1.10408i 1.18785 + 0.0564898i
383383 3.47535 12.9702i 0.177582 0.662745i −0.818515 0.574484i 0.805203π-0.805203\pi
0.996097 0.0882604i 0.0281308π-0.0281308\pi
384384 −23.1402 15.6431i −1.18087 0.798282i
385385 0 0
386386 −2.13521 + 6.68133i −0.108679 + 0.340071i
387387 6.65075 + 1.78206i 0.338076 + 0.0905873i
388388 5.74535 15.4113i 0.291676 0.782393i
389389 −15.5106 8.95506i −0.786419 0.454039i 0.0522811 0.998632i 0.483351π-0.483351\pi
−0.838700 + 0.544593i 0.816684π0.816684\pi
390390 0.154779 + 0.635778i 0.00783753 + 0.0321938i
391391 5.59179i 0.282789i
392392 0 0
393393 6.44222 6.44222i 0.324967 0.324967i
394394 −1.65828 7.62009i −0.0835430 0.383895i
395395 −13.0935 + 3.85489i −0.658805 + 0.193961i
396396 12.1663 + 26.6292i 0.611378 + 1.33817i
397397 1.58258 5.90626i 0.0794273 0.296427i −0.914773 0.403967i 0.867631π-0.867631\pi
0.994201 + 0.107541i 0.0342976π0.0342976\pi
398398 23.7511 12.2469i 1.19053 0.613882i
399399 0 0
400400 18.5542 7.46601i 0.927711 0.373300i
401401 −9.81777 17.0049i −0.490276 0.849183i 0.509662 0.860375i 0.329771π-0.329771\pi
−0.999937 + 0.0111923i 0.996437π0.996437\pi
402402 −0.0844603 + 1.77600i −0.00421250 + 0.0885788i
403403 0.375386 0.100584i 0.0186993 0.00501046i
404404 −17.0715 1.62741i −0.849341 0.0809665i
405405 14.0981 + 13.4231i 0.700542 + 0.666998i
406406 0 0
407407 −7.71315 + 7.71315i −0.382327 + 0.382327i
408408 −12.8368 32.0428i −0.635518 1.58635i
409409 −8.70611 5.02647i −0.430489 0.248543i 0.269066 0.963122i 0.413285π-0.413285\pi
−0.699555 + 0.714579i 0.746618π0.746618\pi
410410 13.0757 12.4877i 0.645763 0.616725i
411411 42.4589 24.5137i 2.09434 1.20917i
412412 6.44160 1.08426i 0.317355 0.0534175i
413413 0 0
414414 1.50726 4.71641i 0.0740779 0.231799i
415415 −15.1852 + 9.27095i −0.745412 + 0.455093i
416416 0.227059 0.416218i 0.0111325 0.0204068i
417417 2.75655 0.738616i 0.134989 0.0361702i
418418 9.51240 14.8042i 0.465267 0.724095i
419419 −17.7853 −0.868870 −0.434435 0.900703i 0.643052π-0.643052\pi
−0.434435 + 0.900703i 0.643052π0.643052\pi
420420 0 0
421421 39.6482 1.93234 0.966168 0.257913i 0.0830348π-0.0830348\pi
0.966168 + 0.257913i 0.0830348π0.0830348\pi
422422 8.39368 13.0631i 0.408598 0.635901i
423423 8.27847 2.21821i 0.402513 0.107853i
424424 −26.5233 + 3.17764i −1.28809 + 0.154320i
425425 24.1591 + 5.21887i 1.17189 + 0.253153i
426426 15.3713 48.0987i 0.744741 2.33039i
427427 0 0
428428 −2.25484 13.3960i −0.108992 0.647522i
429429 −0.847531 + 0.489322i −0.0409192 + 0.0236247i
430430 7.03290 + 0.161762i 0.339156 + 0.00780087i
431431 −21.7939 12.5827i −1.04977 0.606087i −0.127187 0.991879i 0.540595π-0.540595\pi
−0.922586 + 0.385792i 0.873928π0.873928\pi
432432 0.0673082 + 0.936921i 0.00323837 + 0.0450776i
433433 −9.19231 + 9.19231i −0.441754 + 0.441754i −0.892601 0.450847i 0.851122π-0.851122\pi
0.450847 + 0.892601i 0.351122π0.351122\pi
434434 0 0
435435 −40.1401 + 0.984591i −1.92457 + 0.0472075i
436436 0.743873 7.80325i 0.0356251 0.373708i
437437 −2.87463 + 0.770255i −0.137512 + 0.0368463i
438438 −1.59085 + 33.4519i −0.0760139 + 1.59839i
439439 14.8997 + 25.8071i 0.711125 + 1.23170i 0.964435 + 0.264320i 0.0851474π0.0851474\pi
−0.253310 + 0.967385i 0.581519π0.581519\pi
440440 18.5130 + 23.4947i 0.882575 + 1.12007i
441441 0 0
442442 0.520776 0.268531i 0.0247708 0.0127727i
443443 10.5682 39.4412i 0.502112 1.87391i 0.0162556 0.999868i 0.494825π-0.494825\pi
0.485856 0.874039i 0.338508π-0.338508\pi
444444 −10.3582 + 4.73242i −0.491579 + 0.224591i
445445 10.5360 + 35.7864i 0.499454 + 1.69644i
446446 5.82600 + 26.7715i 0.275869 + 1.26767i
447447 −10.8257 + 10.8257i −0.512039 + 0.512039i
448448 0 0
449449 20.7052i 0.977139i −0.872525 0.488570i 0.837519π-0.837519\pi
0.872525 0.488570i 0.162481π-0.162481\pi
450450 −18.9703 10.9139i −0.894271 0.514488i
451451 23.4189 + 13.5209i 1.10275 + 0.636675i
452452 −0.0742563 0.0276828i −0.00349272 0.00130209i
453453 −24.0199 6.43610i −1.12855 0.302394i
454454 −9.88197 + 30.9219i −0.463784 + 1.45124i
455455 0 0
456456 14.7043 11.0130i 0.688593 0.515730i
457457 0.969683 3.61891i 0.0453599 0.169285i −0.939530 0.342466i 0.888738π-0.888738\pi
0.984890 + 0.173181i 0.0554045π0.0554045\pi
458458 16.8654 + 0.802058i 0.788067 + 0.0374777i
459459 −0.580425 + 1.00533i −0.0270919 + 0.0469246i
460460 0.356441 5.04626i 0.0166191 0.235283i
461461 6.66823 0.310570 0.155285 0.987870i 0.450370π-0.450370\pi
0.155285 + 0.987870i 0.450370π0.450370\pi
462462 0 0
463463 14.7884 + 14.7884i 0.687277 + 0.687277i 0.961629 0.274353i 0.0884635π-0.0884635\pi
−0.274353 + 0.961629i 0.588464π0.588464\pi
464464 21.9933 + 19.0451i 1.02101 + 0.884146i
465465 −12.2512 + 22.4751i −0.568136 + 1.04226i
466466 22.6342 + 24.8945i 1.04851 + 1.15321i
467467 27.1281 + 7.26895i 1.25534 + 0.336367i 0.824396 0.566013i 0.191515π-0.191515\pi
0.430941 + 0.902380i 0.358182π0.358182\pi
468468 −0.511632 + 0.0861184i −0.0236502 + 0.00398083i
469469 0 0
470470 7.68199 4.20270i 0.354344 0.193856i
471471 31.1509 17.9850i 1.43536 0.828703i
472472 −7.46043 5.86408i −0.343394 0.269916i
473473 2.72309 + 10.1627i 0.125208 + 0.467282i
474474 −4.53187 20.8247i −0.208156 0.956511i
475475 0.644940 + 13.1386i 0.0295919 + 0.602842i
476476 0 0
477477 20.6700 + 20.6700i 0.946413 + 0.946413i
478478 −1.79357 1.15246i −0.0820359 0.0527121i
479479 −5.27141 + 9.13034i −0.240857 + 0.417176i −0.960959 0.276692i 0.910762π-0.910762\pi
0.720102 + 0.693868i 0.244095π0.244095\pi
480480 9.54196 + 29.7350i 0.435529 + 1.35721i
481481 −0.0966532 0.167408i −0.00440701 0.00763316i
482482 −23.2927 + 12.0106i −1.06096 + 0.547067i
483483 0 0
484484 −13.1857 + 18.5229i −0.599348 + 0.841949i
485485 −15.6949 + 9.58215i −0.712670 + 0.435103i
486486 −23.2265 + 21.1176i −1.05358 + 0.957916i
487487 9.85078 + 36.7636i 0.446381 + 1.66592i 0.712263 + 0.701913i 0.247670π0.247670\pi
−0.265882 + 0.964006i 0.585663π0.585663\pi
488488 −5.13966 + 2.05903i −0.232662 + 0.0932078i
489489 7.28707i 0.329533i
490490 0 0
491491 3.59770i 0.162362i 0.996699 + 0.0811809i 0.0258691π0.0258691\pi
−0.996699 + 0.0811809i 0.974131π0.974131\pi
492492 17.9784 + 21.7673i 0.810530 + 0.981347i
493493 9.30560 + 34.7290i 0.419103 + 1.56411i
494494 0.209782 + 0.230731i 0.00943854 + 0.0103811i
495495 7.69395 31.8154i 0.345817 1.43000i
496496 17.5252 6.07173i 0.786903 0.272629i
497497 0 0
498498 −12.7316 24.6910i −0.570516 1.10643i
499499 5.11616 + 8.86145i 0.229031 + 0.396693i 0.957521 0.288363i 0.0931110π-0.0931110\pi
−0.728490 + 0.685056i 0.759778π0.759778\pi
500500 −21.4695 6.24972i −0.960147 0.279496i
501501 −10.7030 + 18.5381i −0.478174 + 0.828221i
502502 13.7775 21.4419i 0.614920 0.957000i
503503 −30.0943 30.0943i −1.34184 1.34184i −0.894231 0.447605i 0.852277π-0.852277\pi
−0.447605 0.894231i 0.647723π-0.647723\pi
504504 0 0
505505 13.8858 + 13.2209i 0.617910 + 0.588322i
506506 7.39299 1.60886i 0.328659 0.0715225i
507507 8.30225 + 30.9844i 0.368716 + 1.37607i
508508 17.3181 + 6.45618i 0.768365 + 0.286447i
509509 −0.0145211 + 0.00838376i −0.000643637 + 0.000371604i −0.500322 0.865840i 0.666785π-0.666785\pi
0.499678 + 0.866211i 0.333452π0.333452\pi
510510 −10.8431 + 37.0383i −0.480141 + 1.64008i
511511 0 0
512512 9.38510 20.5893i 0.414767 0.909928i
513513 −0.596770 0.159904i −0.0263481 0.00705994i
514514 15.6028 14.1861i 0.688210 0.625724i
515515 −6.41243 3.49543i −0.282565 0.154027i
516516 −1.04239 + 10.9347i −0.0458885 + 0.481372i
517517 9.26042 + 9.26042i 0.407273 + 0.407273i
518518 0 0
519519 −4.43276 −0.194577
520520 −0.487087 + 0.209137i −0.0213602 + 0.00917127i
521521 −0.00830997 + 0.0143933i −0.000364066 + 0.000630582i −0.866207 0.499685i 0.833449π-0.833449\pi
0.865843 + 0.500315i 0.166783π0.166783\pi
522522 1.51232 31.8006i 0.0661926 1.39187i
523523 −8.00409 + 29.8717i −0.349994 + 1.30620i 0.536674 + 0.843790i 0.319681π0.319681\pi
−0.886668 + 0.462407i 0.846986π0.846986\pi
524524 6.01271 + 4.28019i 0.262666 + 0.186981i
525525 0 0
526526 9.55070 + 3.05219i 0.416430 + 0.133082i
527527 22.1400 + 5.93238i 0.964432 + 0.258419i
528528 −38.6708 + 26.1910i −1.68293 + 1.13982i
529529 18.8104 + 10.8602i 0.817845 + 0.472183i
530530 25.5145 + 15.5238i 1.10828 + 0.674311i
531531 10.3840i 0.450626i
532532 0 0
533533 −0.338860 + 0.338860i −0.0146777 + 0.0146777i
534534 −56.9171 + 12.3863i −2.46304 + 0.536007i
535535 −7.26914 + 13.3354i −0.314272 + 0.576539i
536536 −1.43014 + 0.171338i −0.0617725 + 0.00740069i
537537 −13.7653 + 51.3727i −0.594016 + 2.21690i
538538 −3.91757 7.59756i −0.168899 0.327554i
539539 0 0
540540 0.587882 0.870249i 0.0252984 0.0374496i
541541 −14.5885 25.2681i −0.627211 1.08636i −0.988109 0.153756i 0.950863π-0.950863\pi
0.360898 0.932605i 0.382470π-0.382470\pi
542542 33.1900 + 1.57840i 1.42563 + 0.0677981i
543543 38.6612 10.3592i 1.65911 0.444558i
544544 23.8717 14.5635i 1.02349 0.624406i
545545 −6.04316 + 6.34708i −0.258860 + 0.271879i
546546 0 0
547547 −0.913792 + 0.913792i −0.0390709 + 0.0390709i −0.726372 0.687301i 0.758795π-0.758795\pi
0.687301 + 0.726372i 0.258795π0.258795\pi
548548 25.2923 + 30.6226i 1.08043 + 1.30813i
549549 5.24710 + 3.02941i 0.223941 + 0.129292i
550550 −0.0510742 33.4427i −0.00217781 1.42600i
551551 −16.5717 + 9.56766i −0.705977 + 0.407596i
552552 7.81886 + 1.12229i 0.332793 + 0.0477677i
553553 0 0
554554 −31.4204 10.0413i −1.33493 0.426613i
555555 12.3755 + 2.99279i 0.525312 + 0.127037i
556556 0.960714 + 2.10279i 0.0407434 + 0.0891781i
557557 −2.78027 + 0.744970i −0.117804 + 0.0315654i −0.317239 0.948346i 0.602756π-0.602756\pi
0.199436 + 0.979911i 0.436089π0.436089\pi
558558 −17.0749 10.9715i −0.722839 0.464460i
559559 −0.186452 −0.00788606
560560 0 0
561561 −57.7196 −2.43693
562562 −22.9639 14.7554i −0.968674 0.622421i
563563 26.9945 7.23315i 1.13768 0.304841i 0.359663 0.933082i 0.382892π-0.382892\pi
0.778018 + 0.628241i 0.216225π0.216225\pi
564564 5.68176 + 12.4361i 0.239245 + 0.523654i
565565 0.0461696 + 0.0756227i 0.00194237 + 0.00318147i
566566 9.60324 + 3.06898i 0.403654 + 0.128999i
567567 0 0
568568 40.4912 + 5.81193i 1.69897 + 0.243863i
569569 −31.8950 + 18.4146i −1.33711 + 0.771981i −0.986378 0.164495i 0.947400π-0.947400\pi
−0.350732 + 0.936476i 0.614067π0.614067\pi
570570 −20.5343 0.472304i −0.860085 0.0197826i
571571 35.5147 + 20.5044i 1.48624 + 0.858084i 0.999877 0.0156706i 0.00498830π-0.00498830\pi
0.486367 + 0.873754i 0.338322π0.338322\pi
572572 −0.504865 0.611264i −0.0211095 0.0255582i
573573 28.6909 28.6909i 1.19858 1.19858i
574574 0 0
575575 −3.79847 + 4.19063i −0.158407 + 0.174762i
576576 −24.0602 + 5.84905i −1.00251 + 0.243710i
577577 20.6267 5.52692i 0.858703 0.230089i 0.197506 0.980302i 0.436716π-0.436716\pi
0.661196 + 0.750213i 0.270049π0.270049\pi
578578 10.5043 + 0.499547i 0.436921 + 0.0207784i
579579 6.12245 + 10.6044i 0.254440 + 0.440704i
580580 −6.18401 31.9340i −0.256777 1.32599i
581581 0 0
582582 −13.1590 25.5199i −0.545457 1.05783i
583583 −11.5609 + 43.1458i −0.478802 + 1.78691i
584584 −26.9374 + 3.22725i −1.11468 + 0.133545i
585585 0.509315 + 0.277629i 0.0210576 + 0.0114785i
586586 −2.52963 + 0.550498i −0.104498 + 0.0227408i
587587 −0.870374 + 0.870374i −0.0359242 + 0.0359242i −0.724841 0.688917i 0.758087π-0.758087\pi
0.688917 + 0.724841i 0.258087π0.258087\pi
588588 0 0
589589 12.1989i 0.502646i
590590 2.50951 + 10.3082i 0.103315 + 0.424382i
591591 −11.7900 6.80697i −0.484977 0.280001i
592592 −5.17338 7.63845i −0.212625 0.313938i
593593 2.04214 + 0.547190i 0.0838607 + 0.0224704i 0.300505 0.953780i 0.402845π-0.402845\pi
−0.216645 + 0.976251i 0.569511π0.569511\pi
594594 1.49615 + 0.478138i 0.0613880 + 0.0196182i
595595 0 0
596596 −10.1039 7.19257i −0.413874 0.294619i
597597 12.0740 45.0608i 0.494157 1.84422i
598598 −0.00636923 + 0.133930i −0.000260457 + 0.00547679i
599599 12.9248 22.3864i 0.528092 0.914683i −0.471371 0.881935i 0.656241π-0.656241\pi
0.999464 0.0327479i 0.0104258π-0.0104258\pi
600600 12.1462 32.7337i 0.495867 1.33635i
601601 −20.5570 −0.838537 −0.419269 0.907862i 0.637713π-0.637713\pi
−0.419269 + 0.907862i 0.637713π0.637713\pi
602602 0 0
603603 1.11452 + 1.11452i 0.0453869 + 0.0453869i
604604 1.91172 20.0540i 0.0777868 0.815986i
605605 24.3855 7.17942i 0.991412 0.291885i
606606 −22.1506 + 20.1394i −0.899806 + 0.818108i
607607 21.6414 + 5.79881i 0.878399 + 0.235366i 0.669716 0.742617i 0.266416π-0.266416\pi
0.208683 + 0.977983i 0.433082π0.433082\pi
608608 10.7751 + 10.2659i 0.436987 + 0.416336i
609609 0 0
610610 5.94094 + 1.73923i 0.240542 + 0.0704196i
611611 −0.200991 + 0.116042i −0.00813122 + 0.00469456i
612612 −28.6725 10.6891i −1.15902 0.432081i
613613 −8.56832 31.9774i −0.346071 1.29156i −0.891356 0.453304i 0.850245π-0.850245\pi
0.545285 0.838251i 0.316422π-0.316422\pi
614614 7.54686 1.64234i 0.304566 0.0662796i
615615 −0.774002 31.5547i −0.0312108 1.27241i
616616 0 0
617617 27.2948 + 27.2948i 1.09885 + 1.09885i 0.994546 + 0.104300i 0.0332603π0.0332603\pi
0.104300 + 0.994546i 0.466740π0.466740\pi
618618 6.16441 9.59368i 0.247969 0.385914i
619619 18.1903 31.5065i 0.731130 1.26635i −0.225270 0.974296i 0.572326π-0.572326\pi
0.956400 0.292059i 0.0943402π-0.0943402\pi
620620 −19.6019 6.76490i −0.787229 0.271685i
621621 −0.132821 0.230053i −0.00532992 0.00923169i
622622 −13.3071 25.8071i −0.533564 1.03477i
623623 0 0
624624 −0.270959 0.782082i −0.0108470 0.0313083i
625625 14.5603 + 20.3223i 0.582414 + 0.812893i
626626 26.5535 + 29.2052i 1.06129 + 1.16727i
627627 −7.95073 29.6725i −0.317522 1.18501i
628628 18.5562 + 22.4669i 0.740474 + 0.896527i
629629 11.4011i 0.454590i
630630 0 0
631631 10.6984i 0.425897i −0.977063 0.212949i 0.931693π-0.931693\pi
0.977063 0.212949i 0.0683067π-0.0683067\pi
632632 16.0267 6.42055i 0.637509 0.255396i
633633 −7.01567 26.1828i −0.278848 1.04067i
634634 −13.5593 + 12.3282i −0.538510 + 0.489616i
635635 −10.7677 17.6367i −0.427302 0.699892i
636636 −27.0441 + 37.9908i −1.07237 + 1.50643i
637637 0 0
638638 43.2383 22.2952i 1.71182 0.882676i
639639 −22.3816 38.7661i −0.885402 1.53356i
640640 −22.4711 + 11.6211i −0.888249 + 0.459362i
641641 −2.64450 + 4.58042i −0.104452 + 0.180916i −0.913514 0.406807i 0.866642π-0.866642\pi
0.809062 + 0.587723i 0.199975π0.199975\pi
642642 −19.9512 12.8196i −0.787410 0.505950i
643643 −6.36844 6.36844i −0.251147 0.251147i 0.570294 0.821441i 0.306829π-0.306829\pi
−0.821441 + 0.570294i 0.806829π0.806829\pi
644644 0 0
645645 8.46826 8.89414i 0.333437 0.350206i
646646 3.91096 + 17.9715i 0.153875 + 0.707081i
647647 1.58576 + 5.91812i 0.0623425 + 0.232665i 0.990066 0.140602i 0.0449039π-0.0449039\pi
−0.927724 + 0.373268i 0.878237π0.878237\pi
648648 −19.3587 15.2164i −0.760482 0.597757i
649649 −13.7415 + 7.93365i −0.539401 + 0.311423i
650650 0.572694 + 0.152516i 0.0224629 + 0.00598217i
651651 0 0
652652 5.82137 0.979860i 0.227983 0.0383743i
653653 −37.7871 10.1250i −1.47872 0.396223i −0.572812 0.819687i 0.694147π-0.694147\pi
−0.905913 + 0.423464i 0.860814π0.860814\pi
654654 −9.20555 10.1248i −0.359966 0.395913i
655655 −2.33051 7.91578i −0.0910606 0.309295i
656656 −14.9716 + 17.2892i −0.584544 + 0.675032i
657657 20.9927 + 20.9927i 0.819001 + 0.819001i
658658 0 0
659659 7.96382 0.310226 0.155113 0.987897i 0.450426π-0.450426\pi
0.155113 + 0.987897i 0.450426π0.450426\pi
660660 52.0886 + 3.67925i 2.02754 + 0.143215i
661661 17.8362 30.8932i 0.693748 1.20161i −0.276854 0.960912i 0.589292π-0.589292\pi
0.970601 0.240694i 0.0773750π-0.0773750\pi
662662 10.4610 + 0.497486i 0.406577 + 0.0193354i
663663 0.264740 0.988023i 0.0102817 0.0383716i
664664 18.0128 13.4909i 0.699032 0.523548i
665665 0 0
666666 −3.07314 + 9.61625i −0.119082 + 0.372622i
667667 −7.94717 2.12944i −0.307716 0.0824521i
668668 −16.2486 6.05747i −0.628676 0.234371i
669669 41.4216 + 23.9148i 1.60145 + 0.924599i
670670 1.37574 + 0.837044i 0.0531495 + 0.0323378i
671671 9.25823i 0.357410i
672672 0 0
673673 −29.4853 + 29.4853i −1.13657 + 1.13657i −0.147515 + 0.989060i 0.547127π0.547127\pi
−0.989060 + 0.147515i 0.952873π0.952873\pi
674674 −2.47512 11.3736i −0.0953380 0.438094i
675675 −1.11790 + 0.359138i −0.0430279 + 0.0138232i
676676 −23.6359 + 10.7987i −0.909075 + 0.415335i
677677 −11.9320 + 44.5308i −0.458584 + 1.71146i 0.218750 + 0.975781i 0.429802π0.429802\pi
−0.677333 + 0.735676i 0.736864π0.736864\pi
678678 −0.122962 + 0.0634037i −0.00472233 + 0.00243500i
679679 0 0
680680 −31.0465 3.68179i −1.19058 0.141190i
681681 28.3354 + 49.0783i 1.08581 + 1.88069i
682682 1.47322 30.9784i 0.0564127 1.18622i
683683 −40.1276 + 10.7522i −1.53544 + 0.411420i −0.924790 0.380479i 0.875759π-0.875759\pi
−0.610652 + 0.791899i 0.709093π0.709093\pi
684684 1.54550 16.2123i 0.0590936 0.619894i
685685 −1.08888 44.3917i −0.0416039 1.69612i
686686 0 0
687687 20.8424 20.8424i 0.795187 0.795187i
688688 −8.87547 + 0.637612i −0.338374 + 0.0243087i
689689 −0.685527 0.395789i −0.0261165 0.0150784i
690690 −6.09946 6.38665i −0.232202 0.243136i
691691 15.8798 9.16821i 0.604096 0.348775i −0.166555 0.986032i 0.553264π-0.553264\pi
0.770651 + 0.637257i 0.219931π0.219931\pi
692692 −0.596054 3.54117i −0.0226586 0.134615i
693693 0 0
694694 −4.75419 + 14.8765i −0.180466 + 0.564703i
695695 0.607556 2.51232i 0.0230459 0.0952977i
696696 50.4283 6.04159i 1.91148 0.229006i
697697 −27.3010 + 7.31528i −1.03410 + 0.277086i
698698 −7.95028 + 12.3730i −0.300922 + 0.468326i
699699 58.7364 2.22161
700700 0 0
701701 3.42628 0.129409 0.0647045 0.997904i 0.479390π-0.479390\pi
0.0647045 + 0.997904i 0.479390π0.479390\pi
702702 −0.0150469 + 0.0234176i −0.000567910 + 0.000883839i
703703 5.86106 1.57047i 0.221054 0.0592312i
704704 −26.1229 27.3709i −0.984546 1.03158i
705705 3.59315 14.8581i 0.135326 0.559588i
706706 −3.24859 + 10.1653i −0.122262 + 0.382574i
707707 0 0
708708 −16.3358 + 2.74966i −0.613937 + 0.103339i
709709 26.8261 15.4881i 1.00748 0.581667i 0.0970248 0.995282i 0.469067π-0.469067\pi
0.910452 + 0.413615i 0.135734π0.135734\pi
710710 −31.5870 33.0742i −1.18544 1.24125i
711711 −16.3617 9.44644i −0.613612 0.354269i
712712 −17.5483 43.8034i −0.657651 1.64160i
713713 −3.70884 + 3.70884i −0.138897 + 0.138897i
714714 0 0
715715 0.0217353 + 0.886111i 0.000812854 + 0.0331387i
716716 −42.8907 4.08871i −1.60290 0.152802i
717717 −3.59492 + 0.963255i −0.134255 + 0.0359734i
718718 −0.771456 + 16.2219i −0.0287905 + 0.605396i
719719 −21.3674 37.0094i −0.796869 1.38022i −0.921646 0.388033i 0.873155π-0.873155\pi
0.124777 0.992185i 0.460179π-0.460179\pi
720720 25.1938 + 11.4740i 0.938919 + 0.427609i
721721 0 0
722722 15.1820 7.82838i 0.565015 0.291342i
723723 −11.8410 + 44.1913i −0.440372 + 1.64349i
724724 13.4742 + 29.4920i 0.500765 + 1.09606i
725725 −16.6173 + 32.3480i −0.617152 + 1.20138i
726726 8.44023 + 38.7843i 0.313246 + 1.43942i
727727 21.7303 21.7303i 0.805931 0.805931i −0.178084 0.984015i 0.556990π-0.556990\pi
0.984015 + 0.178084i 0.0569900π0.0569900\pi
728728 0 0
729729 28.6841i 1.06238i
730730 25.9128 + 15.7662i 0.959077 + 0.583532i
731731 −9.52347 5.49838i −0.352238 0.203365i
732732 −3.37637 + 9.05678i −0.124794 + 0.334748i
733733 3.68215 + 0.986629i 0.136003 + 0.0364420i 0.326179 0.945308i 0.394239π-0.394239\pi
−0.190175 + 0.981750i 0.560906π0.560906\pi
734734 −5.45132 + 17.0579i −0.201212 + 0.629618i
735735 0 0
736736 0.154814 + 6.39711i 0.00570652 + 0.235800i
737737 −0.623362 + 2.32642i −0.0229618 + 0.0856947i
738738 24.9989 + 1.18886i 0.920222 + 0.0437625i
739739 −6.00177 + 10.3954i −0.220779 + 0.382400i −0.955045 0.296462i 0.904193π-0.904193\pi
0.734266 + 0.678862i 0.237526π0.237526\pi
740740 −0.726743 + 10.2888i −0.0267156 + 0.378223i
741741 0.544391 0.0199987
742742 0 0
743743 7.86007 + 7.86007i 0.288358 + 0.288358i 0.836431 0.548073i 0.184638π-0.184638\pi
−0.548073 + 0.836431i 0.684638π0.684638\pi
744744 12.7386 29.7671i 0.467021 1.09131i
745745 3.91626 + 13.3019i 0.143481 + 0.487345i
746746 23.6925 + 26.0585i 0.867443 + 0.954068i
747747 −23.7876 6.37387i −0.870344 0.233208i
748748 −7.76130 46.1101i −0.283781 1.68595i
749749 0 0
750750 −33.2860 + 20.3918i −1.21543 + 0.744602i
751751 −1.00430 + 0.579834i −0.0366475 + 0.0211584i −0.518212 0.855252i 0.673402π-0.673402\pi
0.481564 + 0.876411i 0.340069π0.340069\pi
752752 −9.17074 + 6.21117i −0.334422 + 0.226498i
753753 −11.5156 42.9769i −0.419653 1.56616i
754754 0.183322 + 0.842397i 0.00667620 + 0.0306783i
755755 −15.5306 + 16.3117i −0.565218 + 0.593643i
756756 0 0
757757 −15.7431 15.7431i −0.572192 0.572192i 0.360549 0.932740i 0.382590π-0.382590\pi
−0.932740 + 0.360549i 0.882590π0.882590\pi
758758 −4.97747 3.19827i −0.180790 0.116166i
759759 6.60410 11.4386i 0.239714 0.415196i
760760 −2.38384 16.4676i −0.0864711 0.597341i
761761 −9.62047 16.6631i −0.348742 0.604039i 0.637284 0.770629i 0.280058π-0.280058\pi
−0.986026 + 0.166590i 0.946724π0.946724\pi
762762 28.6772 14.7870i 1.03887 0.535677i
763763 0 0
764764 26.7780 + 19.0621i 0.968794 + 0.689644i
765765 17.8274 + 29.2000i 0.644550 + 1.05573i
766766 14.0504 12.7747i 0.507662 0.461569i
767767 −0.0727778 0.271611i −0.00262786 0.00980729i
768768 −15.5727 36.3021i −0.561931 1.30994i
769769 30.8833i 1.11368i 0.830620 + 0.556840i 0.187986π0.187986\pi
−0.830620 + 0.556840i 0.812014π0.812014\pi
770770 0 0
771771 36.8135i 1.32580i
772772 −7.64820 + 6.31693i −0.275265 + 0.227351i
773773 4.19873 + 15.6699i 0.151018 + 0.563607i 0.999414 + 0.0342438i 0.0109023π0.0109023\pi
−0.848396 + 0.529363i 0.822431π0.822431\pi
774774 6.55051 + 7.20466i 0.235453 + 0.258966i
775775 12.5624 + 19.4854i 0.451255 + 0.699937i
776776 18.6174 13.9437i 0.668327 0.500551i
777777 0 0
778778 −11.6081 22.5122i −0.416170 0.807100i
779779 −7.52128 13.0272i −0.269478 0.466749i
780780 −0.301892 + 0.874757i −0.0108095 + 0.0313213i
781781 34.2004 59.2368i 1.22379 2.11966i
782782 −4.27486 + 6.65296i −0.152869 + 0.237910i
783783 −1.20775 1.20775i −0.0431616 0.0431616i
784784 0 0
785785 −0.798877 32.5689i −0.0285132 1.16243i
786786 12.5898 2.73978i 0.449062 0.0977248i
787787 −10.8721 40.5750i −0.387547 1.44634i −0.834113 0.551594i 0.814020π-0.814020\pi
0.446566 0.894751i 0.352647π-0.352647\pi
788788 3.85249 10.3339i 0.137239 0.368130i
789789 15.1586 8.75180i 0.539659 0.311572i
790790 −18.5253 5.42336i −0.659100 0.192954i
791791 0 0
792792 −5.88263 + 40.9837i −0.209030 + 1.45629i
793793 −0.158479 0.0424643i −0.00562775 0.00150795i
794794 6.39817 5.81724i 0.227062 0.206446i
795795 50.0153 14.7252i 1.77386 0.522247i
796796 37.6210 + 3.58635i 1.33344 + 0.127115i
797797 −5.01705 5.01705i −0.177713 0.177713i 0.612645 0.790358i 0.290106π-0.290106\pi
−0.790358 + 0.612645i 0.790106π0.790106\pi
798798 0 0
799799 −13.6881 −0.484251
800800 27.7830 + 5.30161i 0.982276 + 0.187440i
801801 −25.8185 + 44.7190i −0.912253 + 1.58007i
802802 1.31910 27.7375i 0.0465790 0.979445i
803803 −11.7414 + 43.8193i −0.414343 + 1.54635i
804804 −1.45822 + 2.04847i −0.0514273 + 0.0722438i
805805 0 0
806806 0.523519 + 0.167305i 0.0184402 + 0.00589308i
807807 −14.4142 3.86227i −0.507403 0.135958i
808808 −19.0671 14.9872i −0.670779 0.527249i
809809 −16.3576 9.44409i −0.575104 0.332036i 0.184081 0.982911i 0.441069π-0.441069\pi
−0.759185 + 0.650875i 0.774402π0.774402\pi
810810 6.51181 + 26.7483i 0.228802 + 0.939838i
811811 21.4189i 0.752118i 0.926596 + 0.376059i 0.122721π0.122721\pi
−0.926596 + 0.376059i 0.877279π0.877279\pi
812812 0 0
813813 41.0166 41.0166i 1.43851 1.43851i
814814 −15.0735 + 3.28029i −0.528326 + 0.114974i
815815 −5.79501 3.15887i −0.202990 0.110650i
816816 9.22340 47.9372i 0.322883 1.67814i
817817 1.51477 5.65322i 0.0529953 0.197781i
818818 −6.51561 12.6361i −0.227813 0.441810i
819819 0 0
820820 25.1038 4.86134i 0.876664 0.169765i
821821 20.8528 + 36.1180i 0.727766 + 1.26053i 0.957825 + 0.287351i 0.0927747π0.0927747\pi
−0.230059 + 0.973177i 0.573892π0.573892\pi
822822 69.2569 + 3.29361i 2.41561 + 0.114878i
823823 −39.0933 + 10.4750i −1.36271 + 0.365136i −0.864809 0.502100i 0.832561π-0.832561\pi
−0.497897 + 0.867236i 0.665894π0.665894\pi
824824 8.49294 + 3.63450i 0.295865 + 0.126614i
825825 −43.2566 39.2086i −1.50600 1.36507i
826826 0 0
827827 30.7849 30.7849i 1.07050 1.07050i 0.0731766 0.997319i 0.476686π-0.476686\pi
0.997319 0.0731766i 0.0233137π-0.0233137\pi
828828 5.39894 4.45918i 0.187626 0.154967i
829829 −36.1486 20.8704i −1.25549 0.724859i −0.283298 0.959032i 0.591429π-0.591429\pi
−0.972195 + 0.234172i 0.924762π0.924762\pi
830830 −25.1545 0.578573i −0.873124 0.0200825i
831831 −49.8696 + 28.7922i −1.72996 + 0.998790i
832832 0.588342 0.321622i 0.0203971 0.0111502i
833833 0 0
834834 3.84433 + 1.22856i 0.133118 + 0.0425417i
835835 10.1027 + 16.5476i 0.349619 + 0.572652i
836836 22.6352 10.3415i 0.782854 0.357667i
837837 −1.05177 + 0.281822i −0.0363546 + 0.00974118i
838838 −21.1605 13.5967i −0.730977 0.469689i
839839 −20.9842 −0.724456 −0.362228 0.932090i 0.617984π-0.617984\pi
−0.362228 + 0.932090i 0.617984π0.617984\pi
840840 0 0
841841 −23.9012 −0.824180
842842 47.1724 + 30.3106i 1.62567 + 1.04457i
843843 −46.0274 + 12.3330i −1.58527 + 0.424772i
844844 19.9731 9.12525i 0.687504 0.314104i
845845 28.2392 + 6.82910i 0.971457 + 0.234928i
846846 11.5453 + 3.68962i 0.396935 + 0.126852i
847847 0 0
848848 −33.9860 16.4961i −1.16708 0.566477i
849849 15.2420 8.79995i 0.523103 0.302014i
850850 24.7541 + 24.6786i 0.849060 + 0.846470i
851851 2.25941 + 1.30447i 0.0774517 + 0.0447168i
852852 55.0592 45.4754i 1.88630 1.55796i
853853 −19.9509 + 19.9509i −0.683106 + 0.683106i −0.960699 0.277593i 0.910463π-0.910463\pi
0.277593 + 0.960699i 0.410463π0.410463\pi
854854 0 0
855855 −12.5555 + 13.1869i −0.429389 + 0.450983i
856856 7.55837 17.6620i 0.258340 0.603676i
857857 −37.0531 + 9.92835i −1.26571 + 0.339146i −0.828386 0.560158i 0.810740π-0.810740\pi
−0.437324 + 0.899304i 0.644074π0.644074\pi
858858 −1.38245 0.0657445i −0.0471961 0.00224448i
859859 3.51740 + 6.09232i 0.120012 + 0.207867i 0.919772 0.392453i 0.128373π-0.128373\pi
−0.799760 + 0.600320i 0.795040π0.795040\pi
860860 8.24388 + 5.56902i 0.281114 + 0.189902i
861861 0 0
862862 −16.3104 31.6317i −0.555536 1.07738i
863863 11.5958 43.2762i 0.394726 1.47314i −0.427520 0.904006i 0.640613π-0.640613\pi
0.822246 0.569132i 0.192721π-0.192721\pi
864864 −0.636183 + 1.16618i −0.0216434 + 0.0396742i
865865 −1.92156 + 3.52514i −0.0653349 + 0.119858i
866866 −17.9642 + 3.90936i −0.610447 + 0.132845i
867867 12.9813 12.9813i 0.440868 0.440868i
868868 0 0
869869 28.8694i 0.979328i
870870 −48.5103 29.5152i −1.64465 1.00066i
871871 −0.0369636 0.0213410i −0.00125246 0.000723111i
872872 6.85053 8.71542i 0.231988 0.295141i
873873 −24.5861 6.58783i −0.832114 0.222964i
874874 −4.00901 1.28119i −0.135607 0.0433369i
875875 0 0
876876 −27.4663 + 38.5839i −0.928000 + 1.30363i
877877 1.48622 5.54663i 0.0501860 0.187297i −0.936282 0.351248i 0.885757π-0.885757\pi
0.986468 + 0.163951i 0.0524241π0.0524241\pi
878878 −2.00190 + 42.0952i −0.0675609 + 1.42064i
879879 −2.25970 + 3.91392i −0.0762179 + 0.132013i
880880 4.06490 + 42.1064i 0.137028 + 1.41940i
881881 −3.68416 −0.124122 −0.0620612 0.998072i 0.519767π-0.519767\pi
−0.0620612 + 0.998072i 0.519767π0.519767\pi
882882 0 0
883883 10.4605 + 10.4605i 0.352023 + 0.352023i 0.860862 0.508839i 0.169925π-0.169925\pi
−0.508839 + 0.860862i 0.669925π0.669925\pi
884884 0.824893 + 0.0786359i 0.0277442 + 0.00264481i
885885 16.2618 + 8.86435i 0.546635 + 0.297972i
886886 42.7261 38.8468i 1.43541 1.30508i
887887 −30.8995 8.27950i −1.03750 0.277998i −0.300426 0.953805i 0.597129π-0.597129\pi
−0.737079 + 0.675807i 0.763795π0.763795\pi
888888 −15.9418 2.28822i −0.534972 0.0767876i
889889 0 0
890890 −14.8228 + 50.6324i −0.496863 + 1.69720i
891891 −35.6571 + 20.5866i −1.19456 + 0.689678i
892892 −13.5348 + 36.3059i −0.453180 + 1.21561i
893893 −1.88550 7.03680i −0.0630960 0.235477i
894894 −21.1563 + 4.60402i −0.707571 + 0.153981i
895895 34.8868 + 33.2163i 1.16614 + 1.11030i
896896 0 0
897897 0.165512 + 0.165512i 0.00552627 + 0.00552627i
898898 15.8289 24.6345i 0.528216 0.822064i
899899 −16.8624 + 29.2066i −0.562394 + 0.974095i
900900 −14.2268 27.4877i −0.474228 0.916257i
901901 −23.3433 40.4318i −0.777679 1.34698i
902902 17.5266 + 33.9903i 0.583572 + 1.13175i
903903 0 0
904904 −0.0671850 0.0897042i −0.00223454 0.00298352i
905905 8.52110 35.2358i 0.283251 1.17128i
906906 −23.6578 26.0204i −0.785979 0.864469i
907907 −3.58771 13.3895i −0.119128 0.444592i 0.880435 0.474168i 0.157251π-0.157251\pi
−0.999563 + 0.0295760i 0.990584π0.990584\pi
908908 −35.3967 + 29.2354i −1.17468 + 0.970212i
909909 26.5390i 0.880243i
910910 0 0
911911 47.8573i 1.58558i 0.609494 + 0.792791i 0.291373π0.291373\pi
−0.609494 + 0.792791i 0.708627π0.708627\pi
912912 25.9141 1.86166i 0.858101 0.0616458i
913913 −9.73964 36.3488i −0.322335 1.20297i
914914 3.92031 3.56437i 0.129672 0.117899i
915915 9.22344 5.63114i 0.304917 0.186160i
916916 19.4528 + 13.8476i 0.642739 + 0.457539i
917917 0 0
918918 −1.45913 + 0.752382i −0.0481586 + 0.0248323i
919919 3.56719 + 6.17855i 0.117671 + 0.203812i 0.918844 0.394620i 0.129124π-0.129124\pi
−0.801173 + 0.598432i 0.795791π0.795791\pi
920920 4.28189 5.73141i 0.141170 0.188959i
921921 6.74155 11.6767i 0.222142 0.384761i
922922 7.93367 + 5.09778i 0.261282 + 0.167886i
923923 0.857128 + 0.857128i 0.0282127 + 0.0282127i
924924 0 0
925925 7.74467 8.54424i 0.254643 0.280933i
926926 6.28930 + 28.9004i 0.206679 + 0.949727i
927927 −2.61640 9.76453i −0.0859338 0.320709i
928928 11.6073 + 39.4729i 0.381027 + 1.29576i
929929 22.9712 13.2625i 0.753662 0.435127i −0.0733534 0.997306i 0.523370π-0.523370\pi
0.827016 + 0.562179i 0.190037π0.190037\pi
930930 −31.7580 + 17.3743i −1.04139 + 0.569727i
931931 0 0
932932 7.89802 + 46.9223i 0.258708 + 1.53699i
933933 −48.9615 13.1192i −1.60293 0.429503i
934934 26.7192 + 29.3875i 0.874280 + 0.961587i
935935 −25.0209 + 45.9013i −0.818270 + 1.50113i
936936 −0.674562 0.288675i −0.0220487 0.00943563i
937937 −4.34151 4.34151i −0.141831 0.141831i 0.632626 0.774457i 0.281977π-0.281977\pi
−0.774457 + 0.632626i 0.781977π0.781977\pi
938938 0 0
939939 68.9071 2.24870
940940 12.3527 + 0.872530i 0.402902 + 0.0284588i
941941 12.9331 22.4008i 0.421607 0.730245i −0.574490 0.818512i 0.694800π-0.694800\pi
0.996097 + 0.0882670i 0.0281329π0.0281329\pi
942942 50.8117 + 2.41643i 1.65553 + 0.0787314i
943943 1.67398 6.24739i 0.0545124 0.203443i
944944 −4.39320 12.6803i −0.142987 0.412710i
945945 0 0
946946 −4.52941 + 14.1731i −0.147264 + 0.460807i
947947 −28.6706 7.68227i −0.931670 0.249640i −0.239103 0.970994i 0.576853π-0.576853\pi
−0.692567 + 0.721354i 0.743520π0.743520\pi
948948 10.5283 28.2413i 0.341945 0.917233i
949949 −0.696229 0.401968i −0.0226006 0.0130484i
950950 −9.27698 + 16.1250i −0.300985 + 0.523165i
951951 31.9921i 1.03741i
952952 0 0
953953 −33.9836 + 33.9836i −1.10084 + 1.10084i −0.106528 + 0.994310i 0.533973π0.533973\pi
−0.994310 + 0.106528i 0.966027π0.966027\pi
954954 8.79063 + 40.3945i 0.284607 + 1.30782i
955955 −10.3791 35.2535i −0.335859 1.14078i
956956 −1.25290 2.74232i −0.0405217 0.0886930i
957957 21.9805 82.0323i 0.710528 2.65173i
958958 −13.2518 + 6.83311i −0.428146 + 0.220768i
959959 0 0
960960 −11.3793 + 42.6726i −0.367264 + 1.37725i
961961 −4.75009 8.22739i −0.153229 0.265400i
962962 0.0129862 0.273068i 0.000418691 0.00880407i
963963 −20.3065 + 5.44110i −0.654367 + 0.175337i
964964 −36.8950 3.51715i −1.18831 0.113280i
965965 11.0871 0.271955i 0.356907 0.00875453i
966966 0 0
967967 −26.2766 + 26.2766i −0.844999 + 0.844999i −0.989504 0.144505i 0.953841π-0.953841\pi
0.144505 + 0.989504i 0.453841π0.453841\pi
968968 −29.8484 + 11.9577i −0.959365 + 0.384336i
969969 27.8061 + 16.0539i 0.893260 + 0.515724i
970970 −25.9988 0.597994i −0.834772 0.0192004i
971971 40.7412 23.5219i 1.30745 0.754855i 0.325778 0.945446i 0.394374π-0.394374\pi
0.981670 + 0.190591i 0.0610404π0.0610404\pi
972972 −43.7784 + 7.36883i −1.40419 + 0.236355i
973973 0 0
974974 −16.3851 + 51.2711i −0.525013 + 1.64283i
975975 0.869561 0.560614i 0.0278482 0.0179540i
976976 −7.68913 1.47943i −0.246123 0.0473555i
977977 21.3849 5.73007i 0.684163 0.183321i 0.100037 0.994984i 0.468104π-0.468104\pi
0.584126 + 0.811663i 0.301437π0.301437\pi
978978 5.57087 8.66996i 0.178137 0.277235i
979979 −78.9044 −2.52180
980980 0 0
981981 −12.1307 −0.387305
982982 −2.75039 + 4.28044i −0.0877686 + 0.136594i
983983 −17.0668 + 4.57305i −0.544348 + 0.145858i −0.520506 0.853858i 0.674257π-0.674257\pi
−0.0238421 + 0.999716i 0.507590π0.507590\pi
984984 4.74939 + 39.6424i 0.151405 + 1.26376i
985985 −10.5241 + 6.42521i −0.335325 + 0.204724i
986986 −15.4783 + 48.4336i −0.492930 + 1.54244i
987987 0 0
988988 0.0732017 + 0.434893i 0.00232886 + 0.0138358i
989989 2.17929 1.25821i 0.0692975 0.0400089i
990990 33.4765 31.9712i 1.06395 1.01611i
991991 3.59673 + 2.07657i 0.114254 + 0.0659645i 0.556038 0.831157i 0.312321π-0.312321\pi
−0.441784 + 0.897121i 0.645654π0.645654\pi
992992 25.4927 + 6.17378i 0.809395 + 0.196018i
993993 12.9278 12.9278i 0.410250 0.410250i
994994 0 0
995995 −30.6005 29.1352i −0.970100 0.923649i
996996 3.72829 39.1099i 0.118135 1.23924i
997997 −23.3879 + 6.26677i −0.740702 + 0.198471i −0.609390 0.792870i 0.708586π-0.708586\pi
−0.131312 + 0.991341i 0.541919π0.541919\pi
998998 −0.687398 + 14.4544i −0.0217592 + 0.457545i
999999 0.270807 + 0.469052i 0.00856796 + 0.0148401i
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 980.2.x.m.67.15 72
4.3 odd 2 inner 980.2.x.m.67.1 72
5.3 odd 4 inner 980.2.x.m.263.12 72
7.2 even 3 inner 980.2.x.m.667.9 72
7.3 odd 6 980.2.k.k.687.4 36
7.4 even 3 980.2.k.j.687.4 36
7.5 odd 6 140.2.w.b.107.9 yes 72
7.6 odd 2 140.2.w.b.67.15 yes 72
20.3 even 4 inner 980.2.x.m.263.9 72
28.3 even 6 980.2.k.k.687.14 36
28.11 odd 6 980.2.k.j.687.14 36
28.19 even 6 140.2.w.b.107.12 yes 72
28.23 odd 6 inner 980.2.x.m.667.12 72
28.27 even 2 140.2.w.b.67.1 yes 72
35.3 even 12 980.2.k.k.883.14 36
35.12 even 12 700.2.be.e.443.18 72
35.13 even 4 140.2.w.b.123.12 yes 72
35.18 odd 12 980.2.k.j.883.14 36
35.19 odd 6 700.2.be.e.107.10 72
35.23 odd 12 inner 980.2.x.m.863.1 72
35.27 even 4 700.2.be.e.543.7 72
35.33 even 12 140.2.w.b.23.1 72
35.34 odd 2 700.2.be.e.207.4 72
140.3 odd 12 980.2.k.k.883.4 36
140.19 even 6 700.2.be.e.107.7 72
140.23 even 12 inner 980.2.x.m.863.15 72
140.27 odd 4 700.2.be.e.543.10 72
140.47 odd 12 700.2.be.e.443.4 72
140.83 odd 4 140.2.w.b.123.9 yes 72
140.103 odd 12 140.2.w.b.23.15 yes 72
140.123 even 12 980.2.k.j.883.4 36
140.139 even 2 700.2.be.e.207.18 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.w.b.23.1 72 35.33 even 12
140.2.w.b.23.15 yes 72 140.103 odd 12
140.2.w.b.67.1 yes 72 28.27 even 2
140.2.w.b.67.15 yes 72 7.6 odd 2
140.2.w.b.107.9 yes 72 7.5 odd 6
140.2.w.b.107.12 yes 72 28.19 even 6
140.2.w.b.123.9 yes 72 140.83 odd 4
140.2.w.b.123.12 yes 72 35.13 even 4
700.2.be.e.107.7 72 140.19 even 6
700.2.be.e.107.10 72 35.19 odd 6
700.2.be.e.207.4 72 35.34 odd 2
700.2.be.e.207.18 72 140.139 even 2
700.2.be.e.443.4 72 140.47 odd 12
700.2.be.e.443.18 72 35.12 even 12
700.2.be.e.543.7 72 35.27 even 4
700.2.be.e.543.10 72 140.27 odd 4
980.2.k.j.687.4 36 7.4 even 3
980.2.k.j.687.14 36 28.11 odd 6
980.2.k.j.883.4 36 140.123 even 12
980.2.k.j.883.14 36 35.18 odd 12
980.2.k.k.687.4 36 7.3 odd 6
980.2.k.k.687.14 36 28.3 even 6
980.2.k.k.883.4 36 140.3 odd 12
980.2.k.k.883.14 36 35.3 even 12
980.2.x.m.67.1 72 4.3 odd 2 inner
980.2.x.m.67.15 72 1.1 even 1 trivial
980.2.x.m.263.9 72 20.3 even 4 inner
980.2.x.m.263.12 72 5.3 odd 4 inner
980.2.x.m.667.9 72 7.2 even 3 inner
980.2.x.m.667.12 72 28.23 odd 6 inner
980.2.x.m.863.1 72 35.23 odd 12 inner
980.2.x.m.863.15 72 140.23 even 12 inner