Properties

Label 735.2.p.f.374.3
Level 735735
Weight 22
Character 735.374
Analytic conductor 5.8695.869
Analytic rank 00
Dimension 2424
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] = [735,2,Mod(374,735)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) 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("735.374"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 735=3572 735 = 3 \cdot 5 \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 735.p (of order 66, degree 22, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 5.869004548565.86900454856
Analytic rank: 00
Dimension: 2424
Relative dimension: 1212 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 374.3
Character χ\chi == 735.374
Dual form 735.2.p.f.509.3

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+(0.7573441.31176i)q2+(0.419611+1.68045i)q3+(0.147140+0.254854i)q4+(2.20411+0.376714i)q5+(2.522140.722254i)q62.58363q8+(2.647851.41027i)q9+(2.16343+2.60595i)q10+(1.86048+1.07415i)q11+(0.3665290.354202i)q12+3.48097q13+(0.2918173.86197i)q15+(2.25098+3.89881i)q16+(3.097931.78859i)q17+(0.155396+4.54141i)q18+(1.058580.611171i)q19+(0.2283050.617156i)q203.25401iq22+(0.757344+1.31176i)q23+(1.084124.34168i)q24+(4.716171.66064i)q25+(2.636294.56619i)q26+(3.480973.85783i)q275.95645iq29+(5.28698+2.54205i)q30+(2.750981.58828i)q31+(0.8258991.43050i)q32+(2.58574+2.67573i)q33+5.41832iq34+(0.7490200.467309i)q36+(6.758033.90175i)q37+(1.603420.925734i)q38+(1.46065+5.84961i)q39+(5.694600.973292i)q40+11.8685q41+2.99294iq43+(0.547504+0.316101i)q44+(6.36742+2.11091i)q45+(1.147141.98691i)q46+(5.284203.05084i)q47+(7.49631+2.14668i)q48+(5.750124.92881i)q50+(4.305574.45542i)q51+(0.512191+0.887140i)q52+(5.613019.72202i)q53+(7.696831.64449i)q54+(4.505351.66667i)q55+(0.582853+2.03535i)q57+(7.81342+4.51108i)q58+(1.084671.87871i)q59+(0.941303+0.642622i)q60+(2.943381.69936i)q61+4.81149iq62+6.50196q64+(7.67243+1.31133i)q65+(5.46821+1.36542i)q66+(8.935345.15882i)q67+(0.9116600.526347i)q68+(2.52214+0.722254i)q69+10.3968iq71+(6.84108+3.64363i)q72+(3.427795.93710i)q73+(10.23635.90993i)q74+(0.811666+8.62213i)q75+0.359711iq76+(8.779502.51414i)q78+(0.941421+1.63059i)q79+(6.430147.74542i)q80+(5.02225+7.46840i)q81+(8.9885315.5686i)q829.10486iq83+(7.50196+2.77521i)q85+(3.926012.26668i)q86+(10.0095+2.49939i)q87+(4.806812.77521i)q88+(0.8899621.54146i)q89+(2.053329.95121i)q900.445743q92+(3.823373.95644i)q93+(8.003924.62107i)q94+(2.10299+1.74587i)q95+(2.05733+1.98814i)q961.32584q97+(3.411445.46799i)q99+O(q100)q+(-0.757344 - 1.31176i) q^{2} +(-0.419611 + 1.68045i) q^{3} +(-0.147140 + 0.254854i) q^{4} +(-2.20411 + 0.376714i) q^{5} +(2.52214 - 0.722254i) q^{6} -2.58363 q^{8} +(-2.64785 - 1.41027i) q^{9} +(2.16343 + 2.60595i) q^{10} +(1.86048 + 1.07415i) q^{11} +(-0.366529 - 0.354202i) q^{12} +3.48097 q^{13} +(0.291817 - 3.86197i) q^{15} +(2.25098 + 3.89881i) q^{16} +(-3.09793 - 1.78859i) q^{17} +(0.155396 + 4.54141i) q^{18} +(1.05858 - 0.611171i) q^{19} +(0.228305 - 0.617156i) q^{20} -3.25401i q^{22} +(0.757344 + 1.31176i) q^{23} +(1.08412 - 4.34168i) q^{24} +(4.71617 - 1.66064i) q^{25} +(-2.63629 - 4.56619i) q^{26} +(3.48097 - 3.85783i) q^{27} -5.95645i q^{29} +(-5.28698 + 2.54205i) q^{30} +(-2.75098 - 1.58828i) q^{31} +(0.825899 - 1.43050i) q^{32} +(-2.58574 + 2.67573i) q^{33} +5.41832i q^{34} +(0.749020 - 0.467309i) q^{36} +(6.75803 - 3.90175i) q^{37} +(-1.60342 - 0.925734i) q^{38} +(-1.46065 + 5.84961i) q^{39} +(5.69460 - 0.973292i) q^{40} +11.8685 q^{41} +2.99294i q^{43} +(-0.547504 + 0.316101i) q^{44} +(6.36742 + 2.11091i) q^{45} +(1.14714 - 1.98691i) q^{46} +(5.28420 - 3.05084i) q^{47} +(-7.49631 + 2.14668i) q^{48} +(-5.75012 - 4.92881i) q^{50} +(4.30557 - 4.45542i) q^{51} +(-0.512191 + 0.887140i) q^{52} +(5.61301 - 9.72202i) q^{53} +(-7.69683 - 1.64449i) q^{54} +(-4.50535 - 1.66667i) q^{55} +(0.582853 + 2.03535i) q^{57} +(-7.81342 + 4.51108i) q^{58} +(1.08467 - 1.87871i) q^{59} +(0.941303 + 0.642622i) q^{60} +(2.94338 - 1.69936i) q^{61} +4.81149i q^{62} +6.50196 q^{64} +(-7.67243 + 1.31133i) q^{65} +(5.46821 + 1.36542i) q^{66} +(-8.93534 - 5.15882i) q^{67} +(0.911660 - 0.526347i) q^{68} +(-2.52214 + 0.722254i) q^{69} +10.3968i q^{71} +(6.84108 + 3.64363i) q^{72} +(3.42779 - 5.93710i) q^{73} +(-10.2363 - 5.90993i) q^{74} +(0.811666 + 8.62213i) q^{75} +0.359711i q^{76} +(8.77950 - 2.51414i) q^{78} +(0.941421 + 1.63059i) q^{79} +(-6.43014 - 7.74542i) q^{80} +(5.02225 + 7.46840i) q^{81} +(-8.98853 - 15.5686i) q^{82} -9.10486i q^{83} +(7.50196 + 2.77521i) q^{85} +(3.92601 - 2.26668i) q^{86} +(10.0095 + 2.49939i) q^{87} +(-4.80681 - 2.77521i) q^{88} +(-0.889962 - 1.54146i) q^{89} +(-2.05332 - 9.95121i) q^{90} -0.445743 q^{92} +(3.82337 - 3.95644i) q^{93} +(-8.00392 - 4.62107i) q^{94} +(-2.10299 + 1.74587i) q^{95} +(2.05733 + 1.98814i) q^{96} -1.32584 q^{97} +(-3.41144 - 5.46799i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q12q46q924q1512q1618q2412q25+18q30+84q3612q39+72q40+18q45+36q4612q51+36q54+12q6036q61+24q64+48q99+O(q100) 24 q - 12 q^{4} - 6 q^{9} - 24 q^{15} - 12 q^{16} - 18 q^{24} - 12 q^{25} + 18 q^{30} + 84 q^{36} - 12 q^{39} + 72 q^{40} + 18 q^{45} + 36 q^{46} - 12 q^{51} + 36 q^{54} + 12 q^{60} - 36 q^{61} + 24 q^{64}+ \cdots - 48 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/735Z)×\left(\mathbb{Z}/735\mathbb{Z}\right)^\times.

nn 346346 442442 491491
χ(n)\chi(n) e(16)e\left(\frac{1}{6}\right) 1-1 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 −0.757344 1.31176i −0.535523 0.927553i −0.999138 0.0415164i 0.986781π-0.986781\pi
0.463615 0.886037i 0.346552π-0.346552\pi
33 −0.419611 + 1.68045i −0.242263 + 0.970211i
44 −0.147140 + 0.254854i −0.0735701 + 0.127427i
55 −2.20411 + 0.376714i −0.985706 + 0.168472i
66 2.52214 0.722254i 1.02966 0.294859i
77 0 0
88 −2.58363 −0.913452
99 −2.64785 1.41027i −0.882618 0.470092i
1010 2.16343 + 2.60595i 0.684135 + 0.824075i
1111 1.86048 + 1.07415i 0.560957 + 0.323869i 0.753529 0.657414i 0.228350π-0.228350\pi
−0.192573 + 0.981283i 0.561683π0.561683\pi
1212 −0.366529 0.354202i −0.105808 0.102249i
1313 3.48097 0.965448 0.482724 0.875773i 0.339647π-0.339647\pi
0.482724 + 0.875773i 0.339647π0.339647\pi
1414 0 0
1515 0.291817 3.86197i 0.0753468 0.997157i
1616 2.25098 + 3.89881i 0.562745 + 0.974703i
1717 −3.09793 1.78859i −0.751359 0.433797i 0.0748259 0.997197i 0.476160π-0.476160\pi
−0.826185 + 0.563399i 0.809493π0.809493\pi
1818 0.155396 + 4.54141i 0.0366272 + 1.07042i
1919 1.05858 0.611171i 0.242855 0.140212i −0.373633 0.927576i 0.621888π-0.621888\pi
0.616488 + 0.787364i 0.288555π0.288555\pi
2020 0.228305 0.617156i 0.0510506 0.138000i
2121 0 0
2222 3.25401i 0.693757i
2323 0.757344 + 1.31176i 0.157917 + 0.273521i 0.934117 0.356966i 0.116189π-0.116189\pi
−0.776200 + 0.630486i 0.782855π0.782855\pi
2424 1.08412 4.34168i 0.221295 0.886241i
2525 4.71617 1.66064i 0.943235 0.332127i
2626 −2.63629 4.56619i −0.517020 0.895504i
2727 3.48097 3.85783i 0.669913 0.742439i
2828 0 0
2929 5.95645i 1.10608i −0.833153 0.553042i 0.813467π-0.813467\pi
0.833153 0.553042i 0.186533π-0.186533\pi
3030 −5.28698 + 2.54205i −0.965267 + 0.464113i
3131 −2.75098 1.58828i −0.494091 0.285263i 0.232179 0.972673i 0.425414π-0.425414\pi
−0.726270 + 0.687410i 0.758748π0.758748\pi
3232 0.825899 1.43050i 0.146000 0.252879i
3333 −2.58574 + 2.67573i −0.450120 + 0.465785i
3434 5.41832i 0.929234i
3535 0 0
3636 0.749020 0.467309i 0.124837 0.0778848i
3737 6.75803 3.90175i 1.11101 0.641444i 0.171921 0.985111i 0.445002π-0.445002\pi
0.939092 + 0.343667i 0.111669π0.111669\pi
3838 −1.60342 0.925734i −0.260109 0.150174i
3939 −1.46065 + 5.84961i −0.233892 + 0.936688i
4040 5.69460 0.973292i 0.900396 0.153891i
4141 11.8685 1.85355 0.926773 0.375622i 0.122571π-0.122571\pi
0.926773 + 0.375622i 0.122571π0.122571\pi
4242 0 0
4343 2.99294i 0.456419i 0.973612 + 0.228209i 0.0732871π0.0732871\pi
−0.973612 + 0.228209i 0.926713π0.926713\pi
4444 −0.547504 + 0.316101i −0.0825393 + 0.0476541i
4545 6.36742 + 2.11091i 0.949199 + 0.314676i
4646 1.14714 1.98691i 0.169137 0.292953i
4747 5.28420 3.05084i 0.770780 0.445010i −0.0623727 0.998053i 0.519867π-0.519867\pi
0.833153 + 0.553043i 0.186533π0.186533\pi
4848 −7.49631 + 2.14668i −1.08200 + 0.309847i
4949 0 0
5050 −5.75012 4.92881i −0.813190 0.697038i
5151 4.30557 4.45542i 0.602901 0.623883i
5252 −0.512191 + 0.887140i −0.0710281 + 0.123024i
5353 5.61301 9.72202i 0.771006 1.33542i −0.166006 0.986125i 0.553087π-0.553087\pi
0.937012 0.349297i 0.113580π-0.113580\pi
5454 −7.69683 1.64449i −1.04741 0.223787i
5555 −4.50535 1.66667i −0.607502 0.224734i
5656 0 0
5757 0.582853 + 2.03535i 0.0772008 + 0.269589i
5858 −7.81342 + 4.51108i −1.02595 + 0.592334i
5959 1.08467 1.87871i 0.141213 0.244587i −0.786741 0.617283i 0.788233π-0.788233\pi
0.927954 + 0.372696i 0.121567π0.121567\pi
6060 0.941303 + 0.642622i 0.121522 + 0.0829622i
6161 2.94338 1.69936i 0.376861 0.217581i −0.299591 0.954068i 0.596850π-0.596850\pi
0.676452 + 0.736487i 0.263517π0.263517\pi
6262 4.81149i 0.611060i
6363 0 0
6464 6.50196 0.812745
6565 −7.67243 + 1.31133i −0.951648 + 0.162651i
6666 5.46821 + 1.36542i 0.673090 + 0.168071i
6767 −8.93534 5.15882i −1.09163 0.630250i −0.157617 0.987500i 0.550381π-0.550381\pi
−0.934009 + 0.357250i 0.883714π0.883714\pi
6868 0.911660 0.526347i 0.110555 0.0638290i
6969 −2.52214 + 0.722254i −0.303630 + 0.0869491i
7070 0 0
7171 10.3968i 1.23387i 0.787013 + 0.616936i 0.211626π0.211626\pi
−0.787013 + 0.616936i 0.788374π0.788374\pi
7272 6.84108 + 3.64363i 0.806229 + 0.429406i
7373 3.42779 5.93710i 0.401192 0.694885i −0.592678 0.805439i 0.701929π-0.701929\pi
0.993870 + 0.110555i 0.0352627π0.0352627\pi
7474 −10.2363 5.90993i −1.18995 0.687016i
7575 0.811666 + 8.62213i 0.0937231 + 0.995598i
7676 0.359711i 0.0412617i
7777 0 0
7878 8.77950 2.51414i 0.994082 0.284671i
7979 0.941421 + 1.63059i 0.105918 + 0.183456i 0.914113 0.405460i 0.132889π-0.132889\pi
−0.808195 + 0.588915i 0.799555π0.799555\pi
8080 −6.43014 7.74542i −0.718911 0.865964i
8181 5.02225 + 7.46840i 0.558028 + 0.829822i
8282 −8.98853 15.5686i −0.992617 1.71926i
8383 9.10486i 0.999388i −0.866202 0.499694i 0.833446π-0.833446\pi
0.866202 0.499694i 0.166554π-0.166554\pi
8484 0 0
8585 7.50196 + 2.77521i 0.813702 + 0.301014i
8686 3.92601 2.26668i 0.423353 0.244423i
8787 10.0095 + 2.49939i 1.07313 + 0.267963i
8888 −4.80681 2.77521i −0.512407 0.295839i
8989 −0.889962 1.54146i −0.0943358 0.163394i 0.814995 0.579467i 0.196739π-0.196739\pi
−0.909331 + 0.416073i 0.863406π0.863406\pi
9090 −2.05332 9.95121i −0.216439 1.04895i
9191 0 0
9292 −0.445743 −0.0464719
9393 3.82337 3.95644i 0.396465 0.410263i
9494 −8.00392 4.62107i −0.825541 0.476626i
9595 −2.10299 + 1.74587i −0.215762 + 0.179122i
9696 2.05733 + 1.98814i 0.209976 + 0.202914i
9797 −1.32584 −0.134618 −0.0673092 0.997732i 0.521441π-0.521441\pi
−0.0673092 + 0.997732i 0.521441π0.521441\pi
9898 0 0
9999 −3.41144 5.46799i −0.342863 0.549553i
100100 −0.270718 + 1.44628i −0.0270718 + 0.144628i
101101 −6.71005 + 11.6221i −0.667675 + 1.15645i 0.310878 + 0.950450i 0.399377π0.399377\pi
−0.978553 + 0.205997i 0.933956π0.933956\pi
102102 −9.10523 2.27359i −0.901553 0.225119i
103103 2.89342 + 5.01154i 0.285097 + 0.493802i 0.972633 0.232348i 0.0746409π-0.0746409\pi
−0.687536 + 0.726150i 0.741308π0.741308\pi
104104 −8.99355 −0.881890
105105 0 0
106106 −17.0039 −1.65157
107107 1.94323 + 3.36576i 0.187859 + 0.325381i 0.944536 0.328408i 0.106512π-0.106512\pi
−0.756677 + 0.653788i 0.773179π0.773179\pi
108108 0.470993 + 1.45478i 0.0453214 + 0.139986i
109109 −2.60384 + 4.50998i −0.249403 + 0.431978i −0.963360 0.268211i 0.913568π-0.913568\pi
0.713958 + 0.700189i 0.246901π0.246901\pi
110110 1.22583 + 7.17218i 0.116878 + 0.683840i
111111 3.72097 + 12.9938i 0.353179 + 1.23331i
112112 0 0
113113 −9.36235 −0.880736 −0.440368 0.897817i 0.645152π-0.645152\pi
−0.440368 + 0.897817i 0.645152π0.645152\pi
114114 2.22847 2.30602i 0.208715 0.215979i
115115 −2.16343 2.60595i −0.201740 0.243006i
116116 1.51803 + 0.876432i 0.140945 + 0.0813747i
117117 −9.21710 4.90913i −0.852121 0.453849i
118118 −3.28589 −0.302490
119119 0 0
120120 −0.753947 + 9.97793i −0.0688257 + 0.910856i
121121 −3.19240 5.52940i −0.290218 0.502673i
122122 −4.45830 2.57400i −0.403636 0.233039i
123123 −4.98015 + 19.9444i −0.449045 + 1.79833i
124124 0.809559 0.467399i 0.0727006 0.0419737i
125125 −9.76936 + 5.43687i −0.873798 + 0.486289i
126126 0 0
127127 9.57778i 0.849891i −0.905219 0.424945i 0.860293π-0.860293\pi
0.905219 0.424945i 0.139707π-0.139707\pi
128128 −6.57602 11.3900i −0.581243 1.00674i
129129 −5.02950 1.25587i −0.442823 0.110573i
130130 7.53082 + 9.07125i 0.660497 + 0.795601i
131131 4.72508 + 8.18408i 0.412832 + 0.715047i 0.995198 0.0978802i 0.0312062π-0.0312062\pi
−0.582366 + 0.812927i 0.697873π0.697873\pi
132132 −0.301455 1.05269i −0.0262383 0.0916253i
133133 0 0
134134 15.6280i 1.35005i
135135 −6.21913 + 9.81440i −0.535258 + 0.844689i
136136 8.00392 + 4.62107i 0.686330 + 0.396253i
137137 5.35276 9.27125i 0.457317 0.792096i −0.541501 0.840700i 0.682144π-0.682144\pi
0.998818 + 0.0486038i 0.0154772π0.0154772\pi
138138 2.85755 + 2.76144i 0.243251 + 0.235070i
139139 4.11136i 0.348721i −0.984682 0.174360i 0.944214π-0.944214\pi
0.984682 0.174360i 0.0557858π-0.0557858\pi
140140 0 0
141141 2.90948 + 10.1600i 0.245022 + 0.855629i
142142 13.6381 7.87395i 1.14448 0.660767i
143143 6.47629 + 3.73909i 0.541575 + 0.312678i
144144 −0.461868 13.4980i −0.0384890 1.12483i
145145 2.24388 + 13.1286i 0.186344 + 1.09027i
146146 −10.3841 −0.859390
147147 0 0
148148 2.29642i 0.188764i
149149 −2.20294 + 1.27187i −0.180472 + 0.104196i −0.587514 0.809214i 0.699893π-0.699893\pi
0.407042 + 0.913409i 0.366560π0.366560\pi
150150 10.6954 7.59463i 0.873280 0.620099i
151151 2.80956 4.86630i 0.228639 0.396014i −0.728766 0.684763i 0.759906π-0.759906\pi
0.957405 + 0.288749i 0.0932392π0.0932392\pi
152152 −2.73498 + 1.57904i −0.221836 + 0.128077i
153153 5.68046 + 9.10486i 0.459238 + 0.736084i
154154 0 0
155155 6.66178 + 2.46440i 0.535087 + 0.197946i
156156 −1.27588 1.23297i −0.102152 0.0987164i
157157 −6.96194 + 12.0584i −0.555623 + 0.962368i 0.442231 + 0.896901i 0.354187π0.354187\pi
−0.997855 + 0.0654670i 0.979146π0.979146\pi
158158 1.42596 2.46983i 0.113443 0.196489i
159159 13.9821 + 13.5119i 1.10885 + 1.07156i
160160 −1.28148 + 3.46410i −0.101310 + 0.273861i
161161 0 0
162162 5.99317 12.2441i 0.470868 0.961990i
163163 −3.52533 + 2.03535i −0.276125 + 0.159421i −0.631668 0.775239i 0.717629π-0.717629\pi
0.355543 + 0.934660i 0.384296π0.384296\pi
164164 −1.74633 + 3.02473i −0.136366 + 0.236192i
165165 4.69126 6.87168i 0.365214 0.534960i
166166 −11.9434 + 6.89551i −0.926986 + 0.535196i
167167 13.9722i 1.08120i 0.841279 + 0.540602i 0.181803π0.181803\pi
−0.841279 + 0.540602i 0.818197π0.818197\pi
168168 0 0
169169 −0.882841 −0.0679109
170170 −2.04116 11.9425i −0.156550 0.915952i
171171 −3.66488 + 0.125403i −0.280261 + 0.00958983i
172172 −0.762763 0.440382i −0.0581602 0.0335788i
173173 8.66256 5.00133i 0.658602 0.380244i −0.133142 0.991097i 0.542507π-0.542507\pi
0.791744 + 0.610853i 0.209173π0.209173\pi
174174 −4.30206 15.0230i −0.326139 1.13889i
175175 0 0
176176 9.67157i 0.729022i
177177 2.70195 + 2.61107i 0.203091 + 0.196260i
178178 −1.34801 + 2.33483i −0.101038 + 0.175003i
179179 14.0378 + 8.10475i 1.04924 + 0.605777i 0.922436 0.386151i 0.126196π-0.126196\pi
0.126801 + 0.991928i 0.459529π0.459529\pi
180180 −1.47488 + 1.31216i −0.109931 + 0.0978030i
181181 19.4123i 1.44290i −0.692465 0.721451i 0.743475π-0.743475\pi
0.692465 0.721451i 0.256525π-0.256525\pi
182182 0 0
183183 1.62062 + 5.65929i 0.119800 + 0.418347i
184184 −1.95670 3.38910i −0.144250 0.249848i
185185 −13.4256 + 11.1457i −0.987068 + 0.819450i
186186 −8.08550 2.01896i −0.592857 0.148037i
187187 −3.84243 6.65529i −0.280987 0.486683i
188188 1.79560i 0.130958i
189189 0 0
190190 3.88284 + 1.43639i 0.281691 + 0.104206i
191191 11.0018 6.35188i 0.796061 0.459606i −0.0460309 0.998940i 0.514657π-0.514657\pi
0.842092 + 0.539334i 0.181324π0.181324\pi
192192 −2.72830 + 10.9262i −0.196898 + 0.788534i
193193 18.0302 + 10.4098i 1.29785 + 0.749311i 0.980032 0.198842i 0.0637181π-0.0637181\pi
0.317813 + 0.948153i 0.397051π0.397051\pi
194194 1.00411 + 1.73918i 0.0720912 + 0.124866i
195195 1.01581 13.4434i 0.0727433 0.962703i
196196 0 0
197197 2.23465 0.159212 0.0796062 0.996826i 0.474634π-0.474634\pi
0.0796062 + 0.996826i 0.474634π0.474634\pi
198198 −4.58904 + 8.61613i −0.326129 + 0.612322i
199199 21.5831 + 12.4610i 1.52998 + 0.883337i 0.999362 + 0.0357284i 0.0113751π0.0113751\pi
0.530622 + 0.847608i 0.321958π0.321958\pi
200200 −12.1849 + 4.29048i −0.861600 + 0.303383i
201201 12.4185 12.8507i 0.875936 0.906421i
202202 20.3273 1.43022
203203 0 0
204204 0.501960 + 1.75286i 0.0351442 + 0.122725i
205205 −26.1594 + 4.47103i −1.82705 + 0.312270i
206206 4.38262 7.59093i 0.305352 0.528885i
207207 −0.155396 4.54141i −0.0108008 0.315650i
208208 7.83560 + 13.5716i 0.543301 + 0.941025i
209209 2.62596 0.181641
210210 0 0
211211 −6.61520 −0.455409 −0.227705 0.973730i 0.573122π-0.573122\pi
−0.227705 + 0.973730i 0.573122π0.573122\pi
212212 1.65180 + 2.86100i 0.113446 + 0.196494i
213213 −17.4713 4.36261i −1.19712 0.298921i
214214 2.94338 5.09808i 0.201205 0.348498i
215215 −1.12748 6.59676i −0.0768937 0.449895i
216216 −8.99355 + 9.96721i −0.611934 + 0.678183i
217217 0 0
218218 7.88801 0.534243
219219 8.53868 + 8.25151i 0.576991 + 0.557585i
220220 1.08768 0.902974i 0.0733312 0.0608785i
221221 −10.7838 6.22604i −0.725398 0.418808i
222222 14.2266 14.7218i 0.954830 0.988060i
223223 4.31027 0.288637 0.144318 0.989531i 0.453901π-0.453901\pi
0.144318 + 0.989531i 0.453901π0.453901\pi
224224 0 0
225225 −14.8297 2.25398i −0.988646 0.150265i
226226 7.09052 + 12.2811i 0.471654 + 0.816929i
227227 −9.62260 5.55561i −0.638675 0.368739i 0.145429 0.989369i 0.453544π-0.453544\pi
−0.784104 + 0.620630i 0.786877π0.786877\pi
228228 −0.604478 0.150939i −0.0400326 0.00999617i
229229 −8.63774 + 4.98700i −0.570798 + 0.329550i −0.757468 0.652872i 0.773564π-0.773564\pi
0.186670 + 0.982423i 0.440230π0.440230\pi
230230 −1.77992 + 4.81149i −0.117365 + 0.317261i
231231 0 0
232232 15.3893i 1.01036i
233233 10.3144 + 17.8650i 0.675716 + 1.17037i 0.976259 + 0.216606i 0.0694988π0.0694988\pi
−0.300543 + 0.953768i 0.597168π0.597168\pi
234234 0.540929 + 15.8085i 0.0353616 + 1.03343i
235235 −10.4977 + 8.71500i −0.684791 + 0.568504i
236236 0.319198 + 0.552868i 0.0207780 + 0.0359886i
237237 −3.13516 + 0.897801i −0.203650 + 0.0583184i
238238 0 0
239239 2.87353i 0.185873i −0.995672 0.0929365i 0.970375π-0.970375\pi
0.995672 0.0929365i 0.0296254π-0.0296254\pi
240240 15.7140 7.55549i 1.01433 0.487705i
241241 −22.5792 13.0361i −1.45445 0.839728i −0.455722 0.890122i 0.650619π-0.650619\pi
−0.998729 + 0.0503940i 0.983952π0.983952\pi
242242 −4.83549 + 8.37532i −0.310837 + 0.538386i
243243 −14.6577 + 5.30584i −0.940292 + 0.340370i
244244 1.00018i 0.0640298i
245245 0 0
246246 29.9340 8.57206i 1.90852 0.546534i
247247 3.68488 2.12747i 0.234464 0.135368i
248248 7.10752 + 4.10353i 0.451328 + 0.260574i
249249 15.3003 + 3.82050i 0.969617 + 0.242114i
250250 14.5306 + 8.69746i 0.918998 + 0.550076i
251251 −0.161120 −0.0101698 −0.00508489 0.999987i 0.501619π-0.501619\pi
−0.00508489 + 0.999987i 0.501619π0.501619\pi
252252 0 0
253253 3.25401i 0.204578i
254254 −12.5637 + 7.25368i −0.788319 + 0.455136i
255255 −7.81152 + 11.4422i −0.489177 + 0.716538i
256256 −3.45866 + 5.99057i −0.216166 + 0.374411i
257257 11.3712 6.56514i 0.709314 0.409522i −0.101493 0.994836i 0.532362π-0.532362\pi
0.810807 + 0.585314i 0.199029π0.199029\pi
258258 2.16166 + 7.54861i 0.134579 + 0.469956i
259259 0 0
260260 0.794725 2.14830i 0.0492867 0.133232i
261261 −8.40022 + 15.7718i −0.519961 + 0.976249i
262262 7.15703 12.3963i 0.442163 0.765848i
263263 8.86526 15.3551i 0.546655 0.946835i −0.451846 0.892096i 0.649234π-0.649234\pi
0.998501 0.0547384i 0.0174325π-0.0174325\pi
264264 6.68061 6.91311i 0.411163 0.425473i
265265 −8.70925 + 23.5429i −0.535005 + 1.44623i
266266 0 0
267267 2.96379 0.848727i 0.181381 0.0519412i
268268 2.62950 1.51814i 0.160622 0.0927352i
269269 −2.20294 + 3.81561i −0.134316 + 0.232642i −0.925336 0.379148i 0.876217π-0.876217\pi
0.791020 + 0.611790i 0.209550π0.209550\pi
270270 17.5841 + 0.725124i 1.07014 + 0.0441296i
271271 −20.4287 + 11.7945i −1.24095 + 0.716465i −0.969288 0.245927i 0.920908π-0.920908\pi
−0.271665 + 0.962392i 0.587574π0.587574\pi
272272 16.1043i 0.976469i
273273 0 0
274274 −16.2155 −0.979615
275275 10.5581 + 1.97629i 0.636680 + 0.119175i
276276 0.187039 0.749051i 0.0112584 0.0450876i
277277 −11.1127 6.41589i −0.667695 0.385494i 0.127508 0.991838i 0.459302π-0.459302\pi
−0.795203 + 0.606344i 0.792636π0.792636\pi
278278 −5.39311 + 3.11371i −0.323457 + 0.186748i
279279 5.04428 + 8.08517i 0.301993 + 0.484046i
280280 0 0
281281 21.2397i 1.26706i −0.773719 0.633528i 0.781606π-0.781606\pi
0.773719 0.633528i 0.218394π-0.218394\pi
282282 11.1240 11.5112i 0.662426 0.685480i
283283 −3.27706 + 5.67603i −0.194801 + 0.337405i −0.946835 0.321719i 0.895739π-0.895739\pi
0.752034 + 0.659124i 0.229073π0.229073\pi
284284 −2.64967 1.52979i −0.157229 0.0907761i
285285 −2.05142 4.26656i −0.121515 0.252729i
286286 11.3271i 0.669786i
287287 0 0
288288 −4.20426 + 2.62301i −0.247738 + 0.154562i
289289 −2.10188 3.64056i −0.123640 0.214151i
290290 15.5222 12.8863i 0.911496 0.756711i
291291 0.556336 2.22801i 0.0326130 0.130608i
292292 1.00873 + 1.74717i 0.0590315 + 0.102245i
293293 3.71937i 0.217288i −0.994081 0.108644i 0.965349π-0.965349\pi
0.994081 0.108644i 0.0346509π-0.0346509\pi
294294 0 0
295295 −1.68300 + 4.54949i −0.0979881 + 0.264882i
296296 −17.4603 + 10.0807i −1.01486 + 0.585928i
297297 10.6202 3.43834i 0.616245 0.199513i
298298 3.33677 + 1.92648i 0.193294 + 0.111598i
299299 2.63629 + 4.56619i 0.152461 + 0.264070i
300300 −2.31682 1.06181i −0.133761 0.0613034i
301301 0 0
302302 −8.51121 −0.489765
303303 −16.7149 16.1527i −0.960245 0.927949i
304304 4.76568 + 2.75147i 0.273331 + 0.157808i
305305 −5.84735 + 4.85439i −0.334818 + 0.277961i
306306 7.64132 14.3469i 0.436825 0.820158i
307307 −11.2102 −0.639800 −0.319900 0.947451i 0.603649π-0.603649\pi
−0.319900 + 0.947451i 0.603649π0.603649\pi
308308 0 0
309309 −9.63578 + 2.75935i −0.548160 + 0.156974i
310310 −1.81256 10.6050i −0.102946 0.602326i
311311 9.46050 16.3861i 0.536456 0.929168i −0.462636 0.886548i 0.653096π-0.653096\pi
0.999091 0.0426199i 0.0135704π-0.0135704\pi
312312 3.77380 15.1133i 0.213649 0.855620i
313313 −8.19024 14.1859i −0.462940 0.801835i 0.536166 0.844112i 0.319872π-0.319872\pi
−0.999106 + 0.0422775i 0.986539π0.986539\pi
314314 21.0903 1.19020
315315 0 0
316316 −0.554083 −0.0311696
317317 −5.05836 8.76134i −0.284106 0.492086i 0.688286 0.725439i 0.258363π-0.258363\pi
−0.972392 + 0.233353i 0.925030π0.925030\pi
318318 7.13503 28.5743i 0.400113 1.60237i
319319 6.39812 11.0819i 0.358226 0.620466i
320320 −14.3310 + 2.44938i −0.801128 + 0.136925i
321321 −6.47141 + 1.85319i −0.361199 + 0.103435i
322322 0 0
323323 −4.37254 −0.243295
324324 −2.64233 + 0.181040i −0.146796 + 0.0100578i
325325 16.4169 5.78063i 0.910644 0.320652i
326326 5.33977 + 3.08292i 0.295743 + 0.170747i
327327 −6.48622 6.26807i −0.358689 0.346625i
328328 −30.6638 −1.69313
329329 0 0
330330 −12.5669 0.949574i −0.691785 0.0522723i
331331 −9.63774 16.6931i −0.529738 0.917533i −0.999398 0.0346861i 0.988957π-0.988957\pi
0.469660 0.882847i 0.344376π-0.344376\pi
332332 2.32041 + 1.33969i 0.127349 + 0.0735251i
333333 −23.3968 + 0.800582i −1.28214 + 0.0438716i
334334 18.3282 10.5818i 1.00287 0.579009i
335335 21.6378 + 8.00452i 1.18220 + 0.437334i
336336 0 0
337337 23.6381i 1.28765i −0.765174 0.643824i 0.777347π-0.777347\pi
0.765174 0.643824i 0.222653π-0.222653\pi
338338 0.668614 + 1.15807i 0.0363678 + 0.0629909i
339339 3.92855 15.7330i 0.213369 0.854499i
340340 −1.81111 + 1.50356i −0.0982215 + 0.0815421i
341341 −3.41210 5.90993i −0.184776 0.320041i
342342 2.94008 + 4.71247i 0.158981 + 0.254821i
343343 0 0
344344 7.73266i 0.416917i
345345 5.28698 2.54205i 0.284642 0.136859i
346346 −13.1211 7.57546i −0.705394 0.407259i
347347 −7.95360 + 13.7760i −0.426971 + 0.739536i −0.996602 0.0823644i 0.973753π-0.973753\pi
0.569631 + 0.821901i 0.307086π0.307086\pi
348348 −2.10979 + 2.18321i −0.113096 + 0.117032i
349349 0.0192397i 0.00102988i −1.00000 0.000514938i 0.999836π-0.999836\pi
1.00000 0.000514938i 0.000163910π-0.000163910\pi
350350 0 0
351351 12.1172 13.4290i 0.646766 0.716786i
352352 3.07314 1.77428i 0.163799 0.0945695i
353353 22.0143 + 12.7100i 1.17170 + 0.676484i 0.954081 0.299549i 0.0968362π-0.0968362\pi
0.217624 + 0.976033i 0.430170π0.430170\pi
354354 1.37880 5.52178i 0.0732821 0.293479i
355355 −3.91662 22.9156i −0.207873 1.21624i
356356 0.523797 0.0277612
357357 0 0
358358 24.5523i 1.29763i
359359 20.9396 12.0895i 1.10515 0.638057i 0.167579 0.985859i 0.446405π-0.446405\pi
0.937568 + 0.347801i 0.113072π0.113072\pi
360360 −16.4511 5.45382i −0.867048 0.287442i
361361 −8.75294 + 15.1605i −0.460681 + 0.797923i
362362 −25.4642 + 14.7018i −1.33837 + 0.772708i
363363 10.6315 3.04448i 0.558007 0.159794i
364364 0 0
365365 −5.31861 + 14.3773i −0.278389 + 0.752542i
366366 6.19625 6.41189i 0.323883 0.335155i
367367 4.53636 7.85721i 0.236796 0.410143i −0.722997 0.690851i 0.757236π-0.757236\pi
0.959793 + 0.280708i 0.0905693π0.0905693\pi
368368 −3.40953 + 5.90548i −0.177734 + 0.307845i
369369 −31.4260 16.7378i −1.63597 0.871336i
370370 24.7883 + 9.16996i 1.28868 + 0.476724i
371371 0 0
372372 0.445743 + 1.55655i 0.0231107 + 0.0807035i
373373 13.4785 7.78183i 0.697891 0.402928i −0.108670 0.994078i 0.534659π-0.534659\pi
0.806562 + 0.591150i 0.201326π0.201326\pi
374374 −5.82009 + 10.0807i −0.300950 + 0.521260i
375375 −5.03708 18.6983i −0.260114 0.965578i
376376 −13.6524 + 7.88224i −0.704071 + 0.406496i
377377 20.7342i 1.06787i
378378 0 0
379379 34.0984 1.75152 0.875758 0.482751i 0.160362π-0.160362\pi
0.875758 + 0.482751i 0.160362π0.160362\pi
380380 −0.135508 0.792842i −0.00695143 0.0406719i
381381 16.0950 + 4.01894i 0.824573 + 0.205897i
382382 −16.6643 9.62112i −0.852618 0.492259i
383383 9.15965 5.28833i 0.468036 0.270221i −0.247381 0.968918i 0.579570π-0.579570\pi
0.715417 + 0.698697i 0.246237π0.246237\pi
384384 21.8997 6.27133i 1.11757 0.320032i
385385 0 0
386386 31.5351i 1.60509i
387387 4.22087 7.92486i 0.214559 0.402843i
388388 0.195084 0.337895i 0.00990388 0.0171540i
389389 14.6659 + 8.46736i 0.743590 + 0.429312i 0.823373 0.567500i 0.192089π-0.192089\pi
−0.0797828 + 0.996812i 0.525423π0.525423\pi
390390 −18.4038 + 8.84880i −0.931914 + 0.448077i
391391 5.41832i 0.274016i
392392 0 0
393393 −15.7357 + 4.50615i −0.793760 + 0.227305i
394394 −1.69240 2.93132i −0.0852619 0.147678i
395395 −2.68926 3.23934i −0.135311 0.162989i
396396 1.89550 0.0648594i 0.0952524 0.00325931i
397397 −0.203913 0.353188i −0.0102341 0.0177260i 0.860863 0.508837i 0.169924π-0.169924\pi
−0.871097 + 0.491111i 0.836591π0.836591\pi
398398 37.7491i 1.89219i
399399 0 0
400400 17.0905 + 14.6494i 0.854526 + 0.732470i
401401 −24.2302 + 13.9893i −1.21000 + 0.698593i −0.962759 0.270361i 0.912857π-0.912857\pi
−0.247240 + 0.968954i 0.579524π0.579524\pi
402402 −26.2622 6.55769i −1.30984 0.327068i
403403 −9.57608 5.52875i −0.477019 0.275407i
404404 −1.97464 3.42017i −0.0982418 0.170160i
405405 −13.8830 14.5692i −0.689853 0.723949i
406406 0 0
407407 16.7643 0.830974
408408 −11.1240 + 11.5112i −0.550721 + 0.569888i
409409 −2.26960 1.31036i −0.112225 0.0647929i 0.442837 0.896602i 0.353972π-0.353972\pi
−0.555062 + 0.831809i 0.687305π0.687305\pi
410410 25.6766 + 30.9287i 1.26808 + 1.52746i
411411 13.3338 + 12.8854i 0.657709 + 0.635589i
412412 −1.70295 −0.0838984
413413 0 0
414414 −5.83954 + 3.64325i −0.286998 + 0.179056i
415415 3.42993 + 20.0681i 0.168369 + 0.985104i
416416 2.87493 4.97953i 0.140955 0.244141i
417417 6.90895 + 1.72517i 0.338333 + 0.0844820i
418418 −1.98876 3.44462i −0.0972732 0.168482i
419419 8.39649 0.410195 0.205098 0.978742i 0.434249π-0.434249\pi
0.205098 + 0.978742i 0.434249π0.434249\pi
420420 0 0
421421 −7.84952 −0.382562 −0.191281 0.981535i 0.561264π-0.561264\pi
−0.191281 + 0.981535i 0.561264π0.561264\pi
422422 5.00998 + 8.67754i 0.243882 + 0.422416i
423423 −18.2943 + 0.625987i −0.889500 + 0.0304365i
424424 −14.5020 + 25.1181i −0.704277 + 1.21984i
425425 −17.5806 3.29077i −0.852783 0.159626i
426426 7.50912 + 26.2222i 0.363818 + 1.27047i
427427 0 0
428428 −1.14371 −0.0552831
429429 −9.00089 + 9.31415i −0.434567 + 0.449691i
430430 −7.79946 + 6.47500i −0.376123 + 0.312252i
431431 −10.6154 6.12880i −0.511326 0.295214i 0.222053 0.975035i 0.428724π-0.428724\pi
−0.733378 + 0.679821i 0.762058π0.762058\pi
432432 22.8765 + 4.88776i 1.10065 + 0.235162i
433433 5.13957 0.246992 0.123496 0.992345i 0.460589π-0.460589\pi
0.123496 + 0.992345i 0.460589π0.460589\pi
434434 0 0
435435 −23.0036 1.73819i −1.10294 0.0833398i
436436 −0.766259 1.32720i −0.0366971 0.0635613i
437437 1.60342 + 0.925734i 0.0767019 + 0.0442838i
438438 4.35726 17.4499i 0.208198 0.833790i
439439 14.4620 8.34964i 0.690234 0.398507i −0.113466 0.993542i 0.536195π-0.536195\pi
0.803700 + 0.595035i 0.202862π0.202862\pi
440440 11.6402 + 4.30607i 0.554924 + 0.205284i
441441 0 0
442442 18.8610i 0.897127i
443443 −0.126110 0.218429i −0.00599167 0.0103779i 0.863014 0.505180i 0.168574π-0.168574\pi
−0.869006 + 0.494802i 0.835241π0.835241\pi
444444 −3.85902 0.963602i −0.183141 0.0457305i
445445 2.54226 + 3.06228i 0.120515 + 0.145166i
446446 −3.26436 5.65403i −0.154572 0.267726i
447447 −1.21294 4.23563i −0.0573700 0.200339i
448448 0 0
449449 28.8710i 1.36250i −0.732049 0.681252i 0.761436π-0.761436\pi
0.732049 0.681252i 0.238564π-0.238564\pi
450450 8.27450 + 21.1600i 0.390064 + 0.997492i
451451 22.0811 + 12.7485i 1.03976 + 0.600305i
452452 1.37758 2.38603i 0.0647958 0.112230i
453453 6.99867 + 6.76329i 0.328826 + 0.317767i
454454 16.8300i 0.789873i
455455 0 0
456456 −1.50588 5.25859i −0.0705193 0.246256i
457457 −20.8483 + 12.0368i −0.975242 + 0.563056i −0.900830 0.434171i 0.857041π-0.857041\pi
−0.0744117 + 0.997228i 0.523708π0.523708\pi
458458 13.0835 + 7.55375i 0.611351 + 0.352964i
459459 −17.6839 + 5.72525i −0.825413 + 0.267232i
460460 0.982465 0.167918i 0.0458077 0.00782921i
461461 −39.8709 −1.85697 −0.928486 0.371367i 0.878889π-0.878889\pi
−0.928486 + 0.371367i 0.878889π0.878889\pi
462462 0 0
463463 29.8417i 1.38686i 0.720524 + 0.693430i 0.243901π0.243901\pi
−0.720524 + 0.693430i 0.756099π0.756099\pi
464464 23.2231 13.4078i 1.07810 0.622443i
465465 −6.93667 + 10.1607i −0.321681 + 0.471192i
466466 15.6230 27.0599i 0.723723 1.25353i
467467 3.62140 2.09082i 0.167579 0.0967515i −0.413865 0.910338i 0.635821π-0.635821\pi
0.581444 + 0.813587i 0.302488π0.302488\pi
468468 2.60732 1.62669i 0.120523 0.0751937i
469469 0 0
470470 19.3823 + 7.17013i 0.894039 + 0.330733i
471471 −17.3423 16.7591i −0.799093 0.772218i
472472 −2.80240 + 4.85390i −0.128991 + 0.223419i
473473 −3.21487 + 5.56831i −0.147820 + 0.256031i
474474 3.55209 + 3.43263i 0.163153 + 0.157666i
475475 3.97751 4.64030i 0.182501 0.212912i
476476 0 0
477477 −28.5731 + 17.8266i −1.30827 + 0.816223i
478478 −3.76937 + 2.17625i −0.172407 + 0.0995393i
479479 13.9676 24.1926i 0.638196 1.10539i −0.347632 0.937631i 0.613014π-0.613014\pi
0.985828 0.167757i 0.0536525π-0.0536525\pi
480480 −5.28354 3.60705i −0.241160 0.164638i
481481 23.5245 13.5819i 1.07262 0.619280i
482482 39.4912i 1.79878i
483483 0 0
484484 1.87892 0.0854055
485485 2.92229 0.499462i 0.132694 0.0226794i
486486 18.0609 + 15.2090i 0.819259 + 0.689895i
487487 32.2536 + 18.6216i 1.46155 + 0.843826i 0.999083 0.0428116i 0.0136315π-0.0136315\pi
0.462466 + 0.886637i 0.346965π0.346965\pi
488488 −7.60462 + 4.39053i −0.344245 + 0.198750i
489489 −1.94104 6.77821i −0.0877770 0.306521i
490490 0 0
491491 5.90572i 0.266522i −0.991081 0.133261i 0.957455π-0.957455\pi
0.991081 0.133261i 0.0425448π-0.0425448\pi
492492 −4.35015 4.20384i −0.196120 0.189524i
493493 −10.6536 + 18.4527i −0.479816 + 0.831066i
494494 −5.58145 3.22245i −0.251121 0.144985i
495495 9.57904 + 10.7669i 0.430546 + 0.483936i
496496 14.3007i 0.642122i
497497 0 0
498498 −6.57602 22.9637i −0.294678 1.02903i
499499 9.37010 + 16.2295i 0.419463 + 0.726532i 0.995886 0.0906204i 0.0288850π-0.0288850\pi
−0.576422 + 0.817152i 0.695552π0.695552\pi
500500 0.0518560 3.28975i 0.00231907 0.147122i
501501 −23.4797 5.86290i −1.04899 0.261935i
502502 0.122023 + 0.211350i 0.00544615 + 0.00943301i
503503 32.0398i 1.42858i 0.699849 + 0.714291i 0.253251π0.253251\pi
−0.699849 + 0.714291i 0.746749π0.746749\pi
504504 0 0
505505 10.4114 28.1442i 0.463303 1.25240i
506506 4.26847 2.46440i 0.189757 0.109556i
507507 0.370450 1.48357i 0.0164523 0.0658878i
508508 2.44094 + 1.40928i 0.108299 + 0.0625265i
509509 −9.57465 16.5838i −0.424389 0.735063i 0.571974 0.820272i 0.306178π-0.306178\pi
−0.996363 + 0.0852085i 0.972844π0.972844\pi
510510 20.9254 + 1.58116i 0.926592 + 0.0700147i
511511 0 0
512512 −15.8265 −0.699439
513513 1.32709 6.21129i 0.0585925 0.274235i
514514 −17.2238 9.94415i −0.759708 0.438617i
515515 −8.26532 9.95599i −0.364213 0.438713i
516516 1.06011 1.09700i 0.0466685 0.0482927i
517517 13.1082 0.576499
518518 0 0
519519 4.76960 + 16.6557i 0.209362 + 0.731102i
520520 19.8228 3.38800i 0.869285 0.148574i
521521 −1.94104 + 3.36199i −0.0850387 + 0.147291i −0.905408 0.424543i 0.860435π-0.860435\pi
0.820369 + 0.571834i 0.193768π0.193768\pi
522522 27.0506 0.925607i 1.18397 0.0405127i
523523 1.06192 + 1.83929i 0.0464343 + 0.0804266i 0.888308 0.459247i 0.151881π-0.151881\pi
−0.841874 + 0.539674i 0.818548π0.818548\pi
524524 −2.78100 −0.121488
525525 0 0
526526 −26.8562 −1.17099
527527 5.68157 + 9.84076i 0.247493 + 0.428670i
528528 −16.2526 4.05830i −0.707305 0.176615i
529529 10.3529 17.9317i 0.450124 0.779638i
530530 37.4785 6.40562i 1.62796 0.278242i
531531 −5.52156 + 3.44486i −0.239615 + 0.149494i
532532 0 0
533533 41.3138 1.78950
534534 −3.35793 3.24500i −0.145312 0.140425i
535535 −5.55101 6.68646i −0.239991 0.289081i
536536 23.0856 + 13.3285i 0.997148 + 0.575704i
537537 −19.5101 + 20.1891i −0.841922 + 0.871224i
538538 6.67354 0.287717
539539 0 0
540540 −1.58616 3.02906i −0.0682573 0.130350i
541541 7.59052 + 13.1472i 0.326342 + 0.565241i 0.981783 0.190005i 0.0608506π-0.0608506\pi
−0.655441 + 0.755246i 0.727517π0.727517\pi
542542 30.9431 + 17.8650i 1.32912 + 0.767367i
543543 32.6214 + 8.14561i 1.39992 + 0.349561i
544544 −5.11716 + 2.95439i −0.219396 + 0.126669i
545545 4.04017 10.9214i 0.173062 0.467821i
546546 0 0
547547 11.7540i 0.502566i −0.967914 0.251283i 0.919148π-0.919148\pi
0.967914 0.251283i 0.0808525π-0.0808525\pi
548548 1.57521 + 2.72835i 0.0672897 + 0.116549i
549549 −10.1902 + 0.348684i −0.434907 + 0.0148815i
550550 −5.40372 15.3465i −0.230416 0.654375i
551551 −3.64041 6.30537i −0.155087 0.268618i
552552 6.51629 1.86604i 0.277352 0.0794239i
553553 0 0
554554 19.4362i 0.825763i
555555 −13.0963 27.2379i −0.555909 1.15619i
556556 1.04780 + 0.604946i 0.0444365 + 0.0256554i
557557 −4.70135 + 8.14298i −0.199203 + 0.345029i −0.948270 0.317465i 0.897169π-0.897169\pi
0.749068 + 0.662494i 0.230502π0.230502\pi
558558 6.78553 12.7401i 0.287254 0.539333i
559559 10.4183i 0.440649i
560560 0 0
561561 12.7962 3.66440i 0.540258 0.154711i
562562 −27.8614 + 16.0858i −1.17526 + 0.678538i
563563 −16.9106 9.76331i −0.712695 0.411475i 0.0993632 0.995051i 0.468319π-0.468319\pi
−0.812058 + 0.583577i 0.801653π0.801653\pi
564564 −3.01743 0.753455i −0.127057 0.0317262i
565565 20.6356 3.52693i 0.868147 0.148379i
566566 9.92744 0.417281
567567 0 0
568568 26.8615i 1.12708i
569569 −11.1702 + 6.44911i −0.468279 + 0.270361i −0.715519 0.698593i 0.753810π-0.753810\pi
0.247240 + 0.968954i 0.420476π0.420476\pi
570570 −4.04306 + 5.92221i −0.169345 + 0.248054i
571571 20.8321 36.0823i 0.871796 1.51000i 0.0116595 0.999932i 0.496289π-0.496289\pi
0.860137 0.510063i 0.170378π-0.170378\pi
572572 −1.90584 + 1.10034i −0.0796874 + 0.0460075i
573573 6.05758 + 21.1533i 0.253059 + 0.883692i
574574 0 0
575575 5.75012 + 4.92881i 0.239797 + 0.205545i
576576 −17.2162 9.16955i −0.717343 0.382065i
577577 −3.74489 + 6.48634i −0.155902 + 0.270030i −0.933387 0.358871i 0.883162π-0.883162\pi
0.777485 + 0.628901i 0.216495π0.216495\pi
578578 −3.18369 + 5.51432i −0.132424 + 0.229365i
579579 −25.0588 + 25.9309i −1.04141 + 1.07765i
580580 −3.67605 1.35989i −0.152640 0.0564663i
581581 0 0
582582 −3.34395 + 0.957590i −0.138611 + 0.0396934i
583583 20.8858 12.0584i 0.865003 0.499409i
584584 −8.85614 + 15.3393i −0.366470 + 0.634744i
585585 22.1648 + 7.34802i 0.916402 + 0.303803i
586586 −4.87892 + 2.81685i −0.201546 + 0.116363i
587587 22.1920i 0.915961i −0.888962 0.457981i 0.848573π-0.848573\pi
0.888962 0.457981i 0.151427π-0.151427\pi
588588 0 0
589589 −3.88284 −0.159990
590590 7.24245 1.23784i 0.298167 0.0509611i
591591 −0.937685 + 3.75523i −0.0385712 + 0.154470i
592592 30.4244 + 17.5655i 1.25043 + 0.721938i
593593 −5.46787 + 3.15687i −0.224538 + 0.129637i −0.608050 0.793899i 0.708048π-0.708048\pi
0.383512 + 0.923536i 0.374715π0.374715\pi
594594 −12.5534 11.3271i −0.515072 0.464757i
595595 0 0
596596 0.748572i 0.0306627i
597597 −29.9966 + 31.0406i −1.22768 + 1.27041i
598598 3.99316 6.91636i 0.163293 0.282831i
599599 −17.8962 10.3324i −0.731219 0.422170i 0.0876487 0.996151i 0.472065π-0.472065\pi
−0.818868 + 0.573982i 0.805398π0.805398\pi
600600 −2.09705 22.2764i −0.0856116 0.909432i
601601 12.5956i 0.513785i −0.966440 0.256892i 0.917301π-0.917301\pi
0.966440 0.256892i 0.0826986π-0.0826986\pi
602602 0 0
603603 16.3841 + 26.2611i 0.667213 + 1.06943i
604604 0.826798 + 1.43206i 0.0336419 + 0.0582695i
605605 9.11940 + 10.9848i 0.370756 + 0.446594i
606606 −8.52955 + 34.1590i −0.346489 + 1.38762i
607607 21.3383 + 36.9590i 0.866095 + 1.50012i 0.865956 + 0.500121i 0.166711π0.166711\pi
0.000139312 1.00000i 0.499956π0.499956\pi
608608 2.01906i 0.0818838i
609609 0 0
610610 10.7962 + 3.99387i 0.437127 + 0.161707i
611611 18.3942 10.6199i 0.744148 0.429634i
612612 −3.15624 + 0.107999i −0.127583 + 0.00436559i
613613 4.60972 + 2.66142i 0.186185 + 0.107494i 0.590195 0.807261i 0.299051π-0.299051\pi
−0.404011 + 0.914754i 0.632384π0.632384\pi
614614 8.48998 + 14.7051i 0.342628 + 0.593448i
615615 3.46342 45.8358i 0.139659 1.84828i
616616 0 0
617617 30.1002 1.21179 0.605895 0.795545i 0.292815π-0.292815\pi
0.605895 + 0.795545i 0.292815π0.292815\pi
618618 10.9172 + 10.5500i 0.439154 + 0.424385i
619619 −11.0265 6.36613i −0.443191 0.255876i 0.261759 0.965133i 0.415697π-0.415697\pi
−0.704950 + 0.709257i 0.749031π0.749031\pi
620620 −1.60828 + 1.33517i −0.0645900 + 0.0536217i
621621 7.69683 + 1.64449i 0.308863 + 0.0659911i
622622 −28.6594 −1.14914
623623 0 0
624624 −26.0944 + 7.47254i −1.04461 + 0.299141i
625625 19.4846 15.6637i 0.779383 0.626548i
626626 −12.4057 + 21.4872i −0.495830 + 0.858802i
627627 −1.10188 + 4.41281i −0.0440049 + 0.176230i
628628 −2.04876 3.54856i −0.0817545 0.141603i
629629 −27.9145 −1.11303
630630 0 0
631631 −17.4114 −0.693138 −0.346569 0.938024i 0.612653π-0.612653\pi
−0.346569 + 0.938024i 0.612653π0.612653\pi
632632 −2.43229 4.21284i −0.0967511 0.167578i
633633 2.77581 11.1165i 0.110329 0.441843i
634634 −7.66184 + 13.2707i −0.304291 + 0.527047i
635635 3.60809 + 21.1104i 0.143183 + 0.837743i
636636 −5.50089 + 1.57526i −0.218125 + 0.0624633i
637637 0 0
638638 −19.3823 −0.767353
639639 14.6623 27.5292i 0.580033 1.08904i
640640 18.7850 + 22.6275i 0.742543 + 0.894430i
641641 −1.13893 0.657564i −0.0449852 0.0259722i 0.477339 0.878719i 0.341601π-0.341601\pi
−0.522324 + 0.852747i 0.674935π0.674935\pi
642642 7.33202 + 7.08543i 0.289372 + 0.279640i
643643 39.2223 1.54678 0.773389 0.633932i 0.218560π-0.218560\pi
0.773389 + 0.633932i 0.218560π0.218560\pi
644644 0 0
645645 11.5587 + 0.873390i 0.455121 + 0.0343897i
646646 3.31152 + 5.73572i 0.130290 + 0.225669i
647647 −5.39634 3.11558i −0.212152 0.122486i 0.390159 0.920747i 0.372420π-0.372420\pi
−0.602311 + 0.798261i 0.705753π0.705753\pi
648648 −12.9757 19.2956i −0.509732 0.758003i
649649 4.03604 2.33021i 0.158428 0.0914687i
650650 −20.0160 17.1570i −0.785092 0.672954i
651651 0 0
652652 1.19793i 0.0469144i
653653 9.43091 + 16.3348i 0.369060 + 0.639230i 0.989419 0.145088i 0.0463464π-0.0463464\pi
−0.620359 + 0.784318i 0.713013π0.713013\pi
654654 −3.30990 + 13.2554i −0.129427 + 0.518329i
655655 −13.4976 16.2586i −0.527397 0.635275i
656656 26.7157 + 46.2730i 1.04307 + 1.80666i
657657 −17.4492 + 10.8864i −0.680759 + 0.424721i
658658 0 0
659659 41.6170i 1.62117i 0.585622 + 0.810584i 0.300850π0.300850\pi
−0.585622 + 0.810584i 0.699150π0.699150\pi
660660 1.06100 + 2.20669i 0.0412996 + 0.0858953i
661661 −3.27232 1.88927i −0.127278 0.0734842i 0.435009 0.900426i 0.356745π-0.356745\pi
−0.562287 + 0.826942i 0.690079π0.690079\pi
662662 −14.5982 + 25.2848i −0.567374 + 0.982721i
663663 14.9876 15.5092i 0.582069 0.602327i
664664 23.5236i 0.912894i
665665 0 0
666666 18.7696 + 30.0846i 0.727307 + 1.16576i
667667 7.81342 4.51108i 0.302537 0.174670i
668668 −3.56088 2.05588i −0.137775 0.0795442i
669669 −1.80864 + 7.24321i −0.0699259 + 0.280039i
670670 −5.88730 34.4458i −0.227446 1.33076i
671671 7.30148 0.281871
672672 0 0
673673 31.2573i 1.20488i 0.798163 + 0.602441i 0.205805π0.205805\pi
−0.798163 + 0.602441i 0.794195π0.794195\pi
674674 −31.0075 + 17.9022i −1.19436 + 0.689565i
675675 10.0104 23.9748i 0.385301 0.922791i
676676 0.129901 0.224996i 0.00499621 0.00865369i
677677 −7.56724 + 4.36895i −0.290832 + 0.167912i −0.638317 0.769773i 0.720369π-0.720369\pi
0.347485 + 0.937686i 0.387036π0.387036\pi
678678 −23.6132 + 6.76199i −0.906858 + 0.259693i
679679 0 0
680680 −19.3823 7.17013i −0.743278 0.274962i
681681 13.3737 13.8391i 0.512481 0.530317i
682682 −5.16827 + 8.95171i −0.197903 + 0.342779i
683683 −10.9346 + 18.9393i −0.418401 + 0.724691i −0.995779 0.0917858i 0.970743π-0.970743\pi
0.577378 + 0.816477i 0.304076π0.304076\pi
684684 0.507292 0.952463i 0.0193968 0.0364183i
685685 −8.30544 + 22.4513i −0.317334 + 0.857819i
686686 0 0
687687 −4.75594 16.6079i −0.181450 0.633632i
688688 −11.6689 + 6.73705i −0.444873 + 0.256847i
689689 19.5387 33.8421i 0.744366 1.28928i
690690 −7.33862 5.01004i −0.279377 0.190729i
691691 −19.5167 + 11.2680i −0.742449 + 0.428653i −0.822959 0.568101i 0.807678π-0.807678\pi
0.0805102 + 0.996754i 0.474345π0.474345\pi
692692 2.94359i 0.111898i
693693 0 0
694694 24.0944 0.914612
695695 1.54881 + 9.06187i 0.0587496 + 0.343736i
696696 −25.8610 6.45751i −0.980257 0.244771i
697697 −36.7678 21.2279i −1.39268 0.804063i
698698 −0.0252378 + 0.0145711i −0.000955266 + 0.000551523i
699699 −34.3493 + 9.83646i −1.29921 + 0.372049i
700700 0 0
701701 35.5019i 1.34089i 0.741960 + 0.670444i 0.233896π0.233896\pi
−0.741960 + 0.670444i 0.766104π0.766104\pi
702702 −26.7924 5.72442i −1.01122 0.216054i
703703 4.76927 8.26062i 0.179877 0.311555i
704704 12.0968 + 6.98408i 0.455915 + 0.263223i
705705 −10.2402 21.2977i −0.385669 0.802119i
706706 38.5033i 1.44909i
707707 0 0
708708 −1.06301 + 0.304409i −0.0399503 + 0.0114404i
709709 −2.03390 3.52282i −0.0763847 0.132302i 0.825303 0.564690i 0.191004π-0.191004\pi
−0.901688 + 0.432388i 0.857671π0.857671\pi
710710 −27.0936 + 22.4927i −1.01680 + 0.844135i
711711 −0.193166 5.64522i −0.00724428 0.211712i
712712 2.29934 + 3.98257i 0.0861712 + 0.149253i
713713 4.81149i 0.180192i
714714 0 0
715715 −15.6830 5.80164i −0.586511 0.216969i
716716 −4.13106 + 2.38507i −0.154385 + 0.0891342i
717717 4.82883 + 1.20576i 0.180336 + 0.0450301i
718718 −31.7169 18.3118i −1.18366 0.683389i
719719 15.2703 + 26.4489i 0.569484 + 0.986376i 0.996617 + 0.0821868i 0.0261904π0.0261904\pi
−0.427133 + 0.904189i 0.640476π0.640476\pi
720720 6.10289 + 29.5770i 0.227441 + 1.10227i
721721 0 0
722722 26.5159 0.986821
723723 31.3810 32.4732i 1.16707 1.20769i
724724 4.94730 + 2.85632i 0.183865 + 0.106154i
725725 −9.89149 28.0916i −0.367361 1.04330i
726726 −12.0453 11.6402i −0.447043 0.432008i
727727 −23.4181 −0.868528 −0.434264 0.900786i 0.642992π-0.642992\pi
−0.434264 + 0.900786i 0.642992π0.642992\pi
728728 0 0
729729 −2.76568 26.8580i −0.102433 0.994740i
730730 22.8876 3.91182i 0.847107 0.144783i
731731 5.35315 9.27192i 0.197993 0.342934i
732732 −1.68075 0.419686i −0.0621224 0.0155120i
733733 −8.44533 14.6277i −0.311935 0.540288i 0.666846 0.745196i 0.267644π-0.267644\pi
−0.978781 + 0.204908i 0.934311π0.934311\pi
734734 −13.7423 −0.507239
735735 0 0
736736 2.50196 0.0922235
737737 −11.0827 19.1958i −0.408237 0.707087i
738738 1.84431 + 53.8996i 0.0678901 + 1.98407i
739739 −13.8321 + 23.9579i −0.508822 + 0.881306i 0.491126 + 0.871089i 0.336586π0.336586\pi
−0.999948 + 0.0102170i 0.996748π0.996748\pi
740740 −0.865093 5.06155i −0.0318014 0.186066i
741741 2.02890 + 7.08499i 0.0745333 + 0.260274i
742742 0 0
743743 −40.1701 −1.47370 −0.736850 0.676056i 0.763688π-0.763688\pi
−0.736850 + 0.676056i 0.763688π0.763688\pi
744744 −9.87819 + 10.2220i −0.362152 + 0.374756i
745745 4.37639 3.63321i 0.160338 0.133111i
746746 −20.4158 11.7870i −0.747474 0.431554i
747747 −12.8404 + 24.1083i −0.469804 + 0.882078i
748748 2.26151 0.0826888
749749 0 0
750750 −20.7129 + 20.7685i −0.756328 + 0.758359i
751751 24.8188 + 42.9874i 0.905650 + 1.56863i 0.820042 + 0.572303i 0.193950π0.193950\pi
0.0856082 + 0.996329i 0.472717π0.472717\pi
752752 23.7893 + 13.7347i 0.867505 + 0.500854i
753753 0.0676076 0.270754i 0.00246376 0.00986683i
754754 −27.1983 + 15.7029i −0.990503 + 0.571867i
755755 −4.35936 + 11.7842i −0.158654 + 0.428873i
756756 0 0
757757 47.7116i 1.73411i 0.498214 + 0.867054i 0.333989π0.333989\pi
−0.498214 + 0.867054i 0.666011π0.666011\pi
758758 −25.8242 44.7288i −0.937977 1.62462i
759759 −5.46821 1.36542i −0.198483 0.0495615i
760760 5.43334 4.51068i 0.197088 0.163620i
761761 −9.91711 17.1769i −0.359495 0.622663i 0.628382 0.777905i 0.283718π-0.283718\pi
−0.987876 + 0.155242i 0.950384π0.950384\pi
762762 −6.91759 24.1565i −0.250598 0.875098i
763763 0 0
764764 3.73847i 0.135253i
765765 −15.9503 17.9282i −0.576683 0.648195i
766766 −13.8740 8.01017i −0.501289 0.289419i
767767 3.77572 6.53974i 0.136333 0.236136i
768768 −8.61559 8.32583i −0.310888 0.300433i
769769 10.6337i 0.383461i −0.981448 0.191731i 0.938590π-0.938590\pi
0.981448 0.191731i 0.0614100π-0.0614100\pi
770770 0 0
771771 6.26096 + 21.8635i 0.225483 + 0.787396i
772772 −5.30595 + 3.06339i −0.190965 + 0.110254i
773773 12.4039 + 7.16138i 0.446136 + 0.257577i 0.706197 0.708015i 0.250409π-0.250409\pi
−0.260061 + 0.965592i 0.583743π0.583743\pi
774774 −13.5922 + 0.465090i −0.488560 + 0.0167173i
775775 −15.6117 2.92222i −0.560787 0.104969i
776776 3.42548 0.122967
777777 0 0
778778 25.6508i 0.919626i
779779 12.5637 7.25368i 0.450142 0.259890i
780780 3.27665 + 2.23695i 0.117323 + 0.0800956i
781781 −11.1677 + 19.3431i −0.399613 + 0.692149i
782782 −7.10752 + 4.10353i −0.254165 + 0.146742i
783783 −22.9789 20.7342i −0.821200 0.740980i
784784 0 0
785785 10.8023 29.2007i 0.385550 1.04222i
786786 17.8283 + 17.2287i 0.635914 + 0.614527i
787787 18.4671 31.9859i 0.658280 1.14017i −0.322781 0.946474i 0.604618π-0.604618\pi
0.981061 0.193700i 0.0620490π-0.0620490\pi
788788 −0.328807 + 0.569511i −0.0117133 + 0.0202880i
789789 22.0835 + 21.3408i 0.786195 + 0.759753i
790790 −2.21254 + 5.98095i −0.0787188 + 0.212793i
791791 0 0
792792 8.81391 + 14.1273i 0.313189 + 0.501991i
793793 10.2458 5.91543i 0.363840 0.210063i
794794 −0.308865 + 0.534970i −0.0109612 + 0.0189854i
795795 −35.9082 24.5143i −1.27353 0.869434i
796796 −6.35148 + 3.66703i −0.225122 + 0.129974i
797797 37.4862i 1.32783i 0.747809 + 0.663914i 0.231106π0.231106\pi
−0.747809 + 0.663914i 0.768894π0.768894\pi
798798 0 0
799799 −21.8268 −0.772177
800800 1.51954 8.11800i 0.0537240 0.287015i
801801 0.182607 + 5.33665i 0.00645210 + 0.188561i
802802 36.7012 + 21.1895i 1.29597 + 0.748226i
803803 12.7547 7.36392i 0.450103 0.259867i
804804 1.44780 + 5.05578i 0.0510599 + 0.178303i
805805 0 0
806806 16.7487i 0.589947i
807807 −5.48757 5.30301i −0.193172 0.186675i
808808 17.3363 30.0274i 0.609889 1.05636i
809809 −22.1518 12.7893i −0.778814 0.449649i 0.0571956 0.998363i 0.481784π-0.481784\pi
−0.836010 + 0.548714i 0.815117π0.815117\pi
810810 −8.59704 + 29.2451i −0.302069 + 1.02757i
811811 7.28791i 0.255913i 0.991780 + 0.127957i 0.0408418π0.0408418\pi
−0.991780 + 0.127957i 0.959158π0.959158\pi
812812 0 0
813813 −11.2480 39.2786i −0.394485 1.37756i
814814 −12.6963 21.9907i −0.445006 0.770773i
815815 7.00345 5.81417i 0.245320 0.203661i
816816 27.0626 + 6.75756i 0.947380 + 0.236562i
817817 1.82920 + 3.16826i 0.0639955 + 0.110844i
818818 3.96956i 0.138792i
819819 0 0
820820 2.70964 7.32470i 0.0946247 0.255790i
821821 −0.00729231 + 0.00421022i −0.000254504 + 0.000146938i −0.500127 0.865952i 0.666713π-0.666713\pi
0.499873 + 0.866099i 0.333380π0.333380\pi
822822 6.80421 27.2494i 0.237324 0.950433i
823823 −27.0406 15.6119i −0.942578 0.544198i −0.0518103 0.998657i 0.516499π-0.516499\pi
−0.890767 + 0.454459i 0.849832π0.849832\pi
824824 −7.47553 12.9480i −0.260422 0.451065i
825825 −7.75138 + 16.9132i −0.269868 + 0.588842i
826826 0 0
827827 −38.3189 −1.33248 −0.666239 0.745738i 0.732097π-0.732097\pi
−0.666239 + 0.745738i 0.732097π0.732097\pi
828828 1.18026 + 0.628620i 0.0410169 + 0.0218461i
829829 1.94142 + 1.12088i 0.0674283 + 0.0389298i 0.533335 0.845904i 0.320938π-0.320938\pi
−0.465907 + 0.884834i 0.654272π0.654272\pi
830830 23.7268 19.6977i 0.823571 0.683717i
831831 15.4446 15.9821i 0.535768 0.554414i
832832 22.6331 0.784663
833833 0 0
834834 −2.96944 10.3694i −0.102823 0.359064i
835835 −5.26354 30.7963i −0.182152 1.06575i
836836 −0.386384 + 0.669237i −0.0133634 + 0.0231460i
837837 −15.7034 + 5.08406i −0.542789 + 0.175731i
838838 −6.35903 11.0142i −0.219669 0.380478i
839839 −20.6544 −0.713069 −0.356535 0.934282i 0.616042π-0.616042\pi
−0.356535 + 0.934282i 0.616042π0.616042\pi
840840 0 0
841841 −6.47924 −0.223422
842842 5.94479 + 10.2967i 0.204871 + 0.354847i
843843 35.6924 + 8.91243i 1.22931 + 0.306961i
844844 0.973362 1.68591i 0.0335045 0.0580315i
845845 1.94588 0.332579i 0.0669402 0.0114411i
846846 14.6762 + 23.5236i 0.504579 + 0.808759i
847847 0 0
848848 50.5391 1.73552
849849 −8.16322 7.88867i −0.280161 0.270738i
850850 8.99786 + 25.5537i 0.308624 + 0.876485i
851851 10.2363 + 5.90993i 0.350896 + 0.202590i
852852 3.68257 3.81073i 0.126163 0.130553i
853853 −7.06831 −0.242014 −0.121007 0.992652i 0.538612π-0.538612\pi
−0.121007 + 0.992652i 0.538612π0.538612\pi
854854 0 0
855855 8.03055 1.65702i 0.274639 0.0566687i
856856 −5.02058 8.69590i −0.171600 0.297220i
857857 −14.5780 8.41661i −0.497975 0.287506i 0.229902 0.973214i 0.426159π-0.426159\pi
−0.727877 + 0.685708i 0.759493π0.759493\pi
858858 19.0347 + 4.75298i 0.649833 + 0.162264i
859859 30.4698 17.5918i 1.03962 0.600223i 0.119893 0.992787i 0.461745π-0.461745\pi
0.919725 + 0.392563i 0.128412π0.128412\pi
860860 1.84711 + 0.683304i 0.0629859 + 0.0233005i
861861 0 0
862862 18.5665i 0.632376i
863863 18.9879 + 32.8880i 0.646356 + 1.11952i 0.983986 + 0.178243i 0.0570414π0.0570414\pi
−0.337630 + 0.941279i 0.609625π0.609625\pi
864864 −2.64369 8.16571i −0.0899402 0.277803i
865865 −17.2091 + 14.2868i −0.585128 + 0.485765i
866866 −3.89242 6.74187i −0.132270 0.229098i
867867 6.99977 2.00449i 0.237725 0.0680761i
868868 0 0
869869 4.04491i 0.137214i
870870 15.1416 + 31.4916i 0.513348 + 1.06767i
871871 −31.1037 17.9577i −1.05391 0.608474i
872872 6.72737 11.6521i 0.227817 0.394591i
873873 3.51062 + 1.86979i 0.118817 + 0.0632829i
874874 2.80440i 0.0948601i
875875 0 0
876876 −3.35932 + 0.961992i −0.113501 + 0.0325027i
877877 −9.91566 + 5.72481i −0.334828 + 0.193313i −0.657983 0.753033i 0.728590π-0.728590\pi
0.323155 + 0.946346i 0.395257π0.395257\pi
878878 −21.9054 12.6471i −0.739272 0.426819i
879879 6.25024 + 1.56069i 0.210815 + 0.0526408i
880880 −3.64342 21.3172i −0.122820 0.718601i
881881 23.6698 0.797455 0.398728 0.917069i 0.369452π-0.369452\pi
0.398728 + 0.917069i 0.369452π0.369452\pi
882882 0 0
883883 16.8355i 0.566560i −0.959037 0.283280i 0.908577π-0.908577\pi
0.959037 0.283280i 0.0914226π-0.0914226\pi
884884 3.17346 1.83220i 0.106735 0.0616236i
885885 −6.93901 4.73722i −0.233252 0.159240i
886886 −0.191017 + 0.330852i −0.00641735 + 0.0111152i
887887 45.5385 26.2917i 1.52903 0.882789i 0.529632 0.848227i 0.322330π-0.322330\pi
0.999403 0.0345613i 0.0110034π-0.0110034\pi
888888 −9.61362 33.5712i −0.322612 1.12657i
889889 0 0
890890 2.09160 5.65403i 0.0701107 0.189524i
891891 1.32163 + 19.2895i 0.0442761 + 0.646222i
892892 −0.634214 + 1.09849i −0.0212350 + 0.0367802i
893893 3.72917 6.45910i 0.124792 0.216146i
894894 −4.63752 + 4.79891i −0.155102 + 0.160500i
895895 −33.9941 12.5755i −1.13630 0.420352i
896896 0 0
897897 −8.77950 + 2.51414i −0.293139 + 0.0839448i
898898 −37.8717 + 21.8652i −1.26380 + 0.729653i
899899 −9.46050 + 16.3861i −0.315525 + 0.546506i
900900 2.75648 3.44776i 0.0918826 0.114925i
901901 −34.7774 + 20.0788i −1.15860 + 0.668921i
902902 38.6201i 1.28591i
903903 0 0
904904 24.1889 0.804510
905905 7.31288 + 42.7867i 0.243088 + 1.42228i
906906 3.57140 14.3027i 0.118652 0.475176i
907907 43.9694 + 25.3858i 1.45998 + 0.842920i 0.999010 0.0444946i 0.0141678π-0.0141678\pi
0.460971 + 0.887415i 0.347501π0.347501\pi
908908 2.83174 1.63491i 0.0939747 0.0542563i
909909 34.1577 21.3107i 1.13294 0.706832i
910910 0 0
911911 16.1165i 0.533963i 0.963702 + 0.266981i 0.0860262π0.0860262\pi
−0.963702 + 0.266981i 0.913974π0.913974\pi
912912 −6.62345 + 6.85396i −0.219324 + 0.226957i
913913 9.77999 16.9394i 0.323671 0.560614i
914914 31.5787 + 18.2319i 1.04453 + 0.603059i
915915 −5.70396 11.8632i −0.188567 0.392184i
916916 2.93515i 0.0969802i
917917 0 0
918918 20.9029 + 18.8610i 0.689900 + 0.622506i
919919 −19.8721 34.4194i −0.655519 1.13539i −0.981763 0.190106i 0.939117π-0.939117\pi
0.326245 0.945285i 0.394217π-0.394217\pi
920920 5.58950 + 6.73283i 0.184280 + 0.221975i
921921 4.70392 18.8382i 0.155000 0.620740i
922922 30.1960 + 52.3010i 0.994452 + 1.72244i
923923 36.1909i 1.19124i
924924 0 0
925925 25.3926 29.6240i 0.834905 0.974030i
926926 39.1451 22.6004i 1.28639 0.742696i
927927 −0.593686 17.3503i −0.0194992 0.569860i
928928 −8.52069 4.91942i −0.279705 0.161488i
929929 −18.2593 31.6261i −0.599069 1.03762i −0.992959 0.118461i 0.962204π-0.962204\pi
0.393889 0.919158i 0.371129π-0.371129\pi
930930 18.5819 + 1.40407i 0.609323 + 0.0460414i
931931 0 0
932932 −6.07063 −0.198850
933933 23.5663 + 22.7737i 0.771526 + 0.745578i
934934 −5.48530 3.16694i −0.179484 0.103625i
935935 10.9763 + 13.2215i 0.358963 + 0.432388i
936936 23.8136 + 12.6834i 0.778372 + 0.414569i
937937 −7.60980 −0.248601 −0.124301 0.992245i 0.539669π-0.539669\pi
−0.124301 + 0.992245i 0.539669π0.539669\pi
938938 0 0
939939 27.2755 7.81075i 0.890102 0.254894i
940940 −0.676429 3.95770i −0.0220627 0.129086i
941941 −11.0121 + 19.0735i −0.358985 + 0.621780i −0.987791 0.155782i 0.950210π-0.950210\pi
0.628807 + 0.777562i 0.283544π0.283544\pi
942942 −8.84974 + 35.4414i −0.288340 + 1.15474i
943943 8.98853 + 15.5686i 0.292707 + 0.506983i
944944 9.76632 0.317867
945945 0 0
946946 9.73904 0.316644
947947 −24.6291 42.6589i −0.800339 1.38623i −0.919393 0.393341i 0.871319π-0.871319\pi
0.119053 0.992888i 0.462014π-0.462014\pi
948948 0.232499 0.931111i 0.00755123 0.0302411i
949949 11.9320 20.6669i 0.387330 0.670875i
950950 −9.09930 1.70323i −0.295220 0.0552599i
951951 16.8456 4.82399i 0.546255 0.156429i
952952 0 0
953953 10.2538 0.332154 0.166077 0.986113i 0.446890π-0.446890\pi
0.166077 + 0.986113i 0.446890π0.446890\pi
954954 45.0239 + 23.9802i 1.45770 + 0.776388i
955955 −21.8563 + 18.1448i −0.707252 + 0.587150i
956956 0.732331 + 0.422811i 0.0236853 + 0.0136747i
957957 15.9379 + 15.4018i 0.515198 + 0.497870i
958958 −42.3131 −1.36708
959959 0 0
960960 1.89738 25.1104i 0.0612377 0.810435i
961961 −10.4547 18.1081i −0.337250 0.584134i
962962 −35.6323 20.5723i −1.14883 0.663278i
963963 −0.398721 11.6525i −0.0128486 0.375498i
964964 6.64460 3.83626i 0.214008 0.123558i
965965 −43.6621 16.1520i −1.40553 0.519951i
966966 0 0
967967 4.62632i 0.148772i 0.997230 + 0.0743862i 0.0236998π0.0236998\pi
−0.997230 + 0.0743862i 0.976300π0.976300\pi
968968 8.24799 + 14.2859i 0.265101 + 0.459168i
969969 1.83477 7.34786i 0.0589412 0.236047i
970970 −2.86835 3.45507i −0.0920971 0.110936i
971971 −12.6443 21.9006i −0.405775 0.702822i 0.588637 0.808398i 0.299665π-0.299665\pi
−0.994411 + 0.105575i 0.966332π0.966332\pi
972972 0.804521 4.51628i 0.0258050 0.144860i
973973 0 0
974974 56.4119i 1.80755i
975975 2.82538 + 30.0134i 0.0904847 + 0.961198i
976976 13.2510 + 7.65046i 0.424154 + 0.244885i
977977 12.0549 20.8797i 0.385670 0.668000i −0.606192 0.795318i 0.707304π-0.707304\pi
0.991862 + 0.127318i 0.0406370π0.0406370\pi
978978 −7.42133 + 7.67961i −0.237308 + 0.245567i
979979 3.82381i 0.122210i
980980 0 0
981981 13.2549 8.26964i 0.423196 0.264029i
982982 −7.74688 + 4.47267i −0.247213 + 0.142728i
983983 −41.6456 24.0441i −1.32829 0.766888i −0.343254 0.939243i 0.611529π-0.611529\pi
−0.985035 + 0.172354i 0.944863π0.944863\pi
984984 12.8669 51.5291i 0.410181 1.64269i
985985 −4.92541 + 0.841825i −0.156937 + 0.0268228i
986986 32.2739 1.02781
987987 0 0
988988 1.25214i 0.0398360i
989989 −3.92601 + 2.26668i −0.124840 + 0.0720764i
990990 6.86892 20.7196i 0.218309 0.658513i
991991 −14.8587 + 25.7361i −0.472003 + 0.817534i −0.999487 0.0320314i 0.989802π-0.989802\pi
0.527483 + 0.849565i 0.323136π0.323136\pi
992992 −4.54406 + 2.62352i −0.144274 + 0.0832967i
993993 32.0960 9.19119i 1.01854 0.291674i
994994 0 0
995995 −52.2656 19.3347i −1.65693 0.612952i
996996 −3.22496 + 3.33720i −0.102187 + 0.105743i
997997 −13.3742 + 23.1647i −0.423564 + 0.733634i −0.996285 0.0861161i 0.972554π-0.972554\pi
0.572721 + 0.819750i 0.305888π0.305888\pi
998998 14.1928 24.5826i 0.449265 0.778149i
999999 8.47222 39.6532i 0.268049 1.25457i
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 735.2.p.f.374.3 24
3.2 odd 2 inner 735.2.p.f.374.9 24
5.4 even 2 inner 735.2.p.f.374.10 24
7.2 even 3 105.2.p.a.89.3 yes 24
7.3 odd 6 735.2.g.b.734.18 24
7.4 even 3 735.2.g.b.734.19 24
7.5 odd 6 inner 735.2.p.f.509.4 24
7.6 odd 2 105.2.p.a.59.4 yes 24
15.14 odd 2 inner 735.2.p.f.374.4 24
21.2 odd 6 105.2.p.a.89.9 yes 24
21.5 even 6 inner 735.2.p.f.509.10 24
21.11 odd 6 735.2.g.b.734.8 24
21.17 even 6 735.2.g.b.734.5 24
21.20 even 2 105.2.p.a.59.10 yes 24
35.2 odd 12 525.2.t.j.26.3 24
35.4 even 6 735.2.g.b.734.6 24
35.9 even 6 105.2.p.a.89.10 yes 24
35.13 even 4 525.2.t.j.101.4 24
35.19 odd 6 inner 735.2.p.f.509.9 24
35.23 odd 12 525.2.t.j.26.10 24
35.24 odd 6 735.2.g.b.734.7 24
35.27 even 4 525.2.t.j.101.9 24
35.34 odd 2 105.2.p.a.59.9 yes 24
105.2 even 12 525.2.t.j.26.9 24
105.23 even 12 525.2.t.j.26.4 24
105.44 odd 6 105.2.p.a.89.4 yes 24
105.59 even 6 735.2.g.b.734.20 24
105.62 odd 4 525.2.t.j.101.3 24
105.74 odd 6 735.2.g.b.734.17 24
105.83 odd 4 525.2.t.j.101.10 24
105.89 even 6 inner 735.2.p.f.509.3 24
105.104 even 2 105.2.p.a.59.3 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.p.a.59.3 24 105.104 even 2
105.2.p.a.59.4 yes 24 7.6 odd 2
105.2.p.a.59.9 yes 24 35.34 odd 2
105.2.p.a.59.10 yes 24 21.20 even 2
105.2.p.a.89.3 yes 24 7.2 even 3
105.2.p.a.89.4 yes 24 105.44 odd 6
105.2.p.a.89.9 yes 24 21.2 odd 6
105.2.p.a.89.10 yes 24 35.9 even 6
525.2.t.j.26.3 24 35.2 odd 12
525.2.t.j.26.4 24 105.23 even 12
525.2.t.j.26.9 24 105.2 even 12
525.2.t.j.26.10 24 35.23 odd 12
525.2.t.j.101.3 24 105.62 odd 4
525.2.t.j.101.4 24 35.13 even 4
525.2.t.j.101.9 24 35.27 even 4
525.2.t.j.101.10 24 105.83 odd 4
735.2.g.b.734.5 24 21.17 even 6
735.2.g.b.734.6 24 35.4 even 6
735.2.g.b.734.7 24 35.24 odd 6
735.2.g.b.734.8 24 21.11 odd 6
735.2.g.b.734.17 24 105.74 odd 6
735.2.g.b.734.18 24 7.3 odd 6
735.2.g.b.734.19 24 7.4 even 3
735.2.g.b.734.20 24 105.59 even 6
735.2.p.f.374.3 24 1.1 even 1 trivial
735.2.p.f.374.4 24 15.14 odd 2 inner
735.2.p.f.374.9 24 3.2 odd 2 inner
735.2.p.f.374.10 24 5.4 even 2 inner
735.2.p.f.509.3 24 105.89 even 6 inner
735.2.p.f.509.4 24 7.5 odd 6 inner
735.2.p.f.509.9 24 35.19 odd 6 inner
735.2.p.f.509.10 24 21.5 even 6 inner