Properties

Label 240.2.y.e.163.1
Level 240240
Weight 22
Character 240.163
Analytic conductor 1.9161.916
Analytic rank 00
Dimension 1616
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [240,2,Mod(163,240)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(240, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("240.163");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 240=2435 240 = 2^{4} \cdot 3 \cdot 5
Weight: k k == 2 2
Character orbit: [χ][\chi] == 240.y (of order 44, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 1.916409648511.91640964851
Analytic rank: 00
Dimension: 1616
Relative dimension: 88 over Q(i)\Q(i)
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x166x15+14x1410x1326x12+78x1166x1074x9+233x8++256 x^{16} - 6 x^{15} + 14 x^{14} - 10 x^{13} - 26 x^{12} + 78 x^{11} - 66 x^{10} - 74 x^{9} + 233 x^{8} + \cdots + 256 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 25 2^{5}
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 163.1
Root 1.40988+0.110627i-1.40988 + 0.110627i of defining polynomial
Character χ\chi == 240.163
Dual form 240.2.y.e.187.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.32675+0.489639i)q2+1.00000q3+(1.520511.29925i)q4+(2.06823+0.849960i)q5+(1.32675+0.489639i)q6+(2.08016+2.08016i)q7+(1.38116+2.46828i)q8+1.00000q9+(3.160190.114996i)q10+(3.33354+3.33354i)q11+(1.520511.29925i)q126.13735iq13+(1.741313.77837i)q14+(2.06823+0.849960i)q15+(0.6238853.95105i)q16+(2.33136+2.33136i)q17+(1.32675+0.489639i)q18+(0.834324+0.834324i)q19+(4.249071.39478i)q20+(2.08016+2.08016i)q21+(6.055002.79053i)q22+(2.95105+2.95105i)q23+(1.38116+2.46828i)q24+(3.55514+3.51582i)q25+(3.00509+8.14270i)q26+1.00000q27+(0.460244+5.86555i)q28+(0.576185+0.576185i)q29+(3.160190.114996i)q302.62300iq31+(1.10685+5.54751i)q32+(3.33354+3.33354i)q33+(1.951594.23464i)q34+(6.07029+2.53419i)q35+(1.520511.29925i)q362.07309iq37+(1.515450.698418i)q386.13735iq39+(4.95449+3.93103i)q4010.8873iq41+(1.741313.77837i)q42+5.16088iq43+(9.39979+0.737562i)q44+(2.06823+0.849960i)q45+(5.360242.47034i)q46+(8.657728.65772i)q47+(0.6238853.95105i)q481.65411iq49+(6.438242.92387i)q50+(2.33136+2.33136i)q51+(7.973979.33189i)q521.58490q53+(1.32675+0.489639i)q54+(4.06115+9.72791i)q55+(2.261378.00744i)q56+(0.834324+0.834324i)q57+(0.4823281.04657i)q58+(2.326032.32603i)q59+(4.249071.39478i)q60+(7.224997.22499i)q61+(1.28433+3.48006i)q62+(2.08016+2.08016i)q63+(4.184796.81818i)q64+(5.2165112.6934i)q65+(6.055002.79053i)q66+0.885549iq67+(0.515823+6.57387i)q68+(2.95105+2.95105i)q69+(6.812906.33448i)q70+2.56877q71+(1.38116+2.46828i)q72+(7.350337.35033i)q73+(1.01507+2.75047i)q74+(3.55514+3.51582i)q75+(2.35259+0.184598i)q7613.8686q77+(3.00509+8.14270i)q787.72612q79+(4.648577.64139i)q80+1.00000q81+(5.33084+14.4447i)q828.67714q83+(0.460244+5.86555i)q84+(6.80334+2.84022i)q85+(2.526976.84718i)q86+(0.576185+0.576185i)q87+(12.8323+3.62395i)q888.70590q89+(3.160190.114996i)q90+(12.7667+12.7667i)q91+(8.32124+0.652933i)q922.62300iq93+(15.7257+7.24743i)q94+(1.01643+2.43472i)q95+(1.10685+5.54751i)q96+(11.998511.9985i)q97+(0.809919+2.19459i)q98+(3.33354+3.33354i)q99+O(q100)q+(-1.32675 + 0.489639i) q^{2} +1.00000 q^{3} +(1.52051 - 1.29925i) q^{4} +(2.06823 + 0.849960i) q^{5} +(-1.32675 + 0.489639i) q^{6} +(-2.08016 + 2.08016i) q^{7} +(-1.38116 + 2.46828i) q^{8} +1.00000 q^{9} +(-3.16019 - 0.114996i) q^{10} +(3.33354 + 3.33354i) q^{11} +(1.52051 - 1.29925i) q^{12} -6.13735i q^{13} +(1.74131 - 3.77837i) q^{14} +(2.06823 + 0.849960i) q^{15} +(0.623885 - 3.95105i) q^{16} +(-2.33136 + 2.33136i) q^{17} +(-1.32675 + 0.489639i) q^{18} +(0.834324 + 0.834324i) q^{19} +(4.24907 - 1.39478i) q^{20} +(-2.08016 + 2.08016i) q^{21} +(-6.05500 - 2.79053i) q^{22} +(2.95105 + 2.95105i) q^{23} +(-1.38116 + 2.46828i) q^{24} +(3.55514 + 3.51582i) q^{25} +(3.00509 + 8.14270i) q^{26} +1.00000 q^{27} +(-0.460244 + 5.86555i) q^{28} +(-0.576185 + 0.576185i) q^{29} +(-3.16019 - 0.114996i) q^{30} -2.62300i q^{31} +(1.10685 + 5.54751i) q^{32} +(3.33354 + 3.33354i) q^{33} +(1.95159 - 4.23464i) q^{34} +(-6.07029 + 2.53419i) q^{35} +(1.52051 - 1.29925i) q^{36} -2.07309i q^{37} +(-1.51545 - 0.698418i) q^{38} -6.13735i q^{39} +(-4.95449 + 3.93103i) q^{40} -10.8873i q^{41} +(1.74131 - 3.77837i) q^{42} +5.16088i q^{43} +(9.39979 + 0.737562i) q^{44} +(2.06823 + 0.849960i) q^{45} +(-5.36024 - 2.47034i) q^{46} +(-8.65772 - 8.65772i) q^{47} +(0.623885 - 3.95105i) q^{48} -1.65411i q^{49} +(-6.43824 - 2.92387i) q^{50} +(-2.33136 + 2.33136i) q^{51} +(-7.97397 - 9.33189i) q^{52} -1.58490 q^{53} +(-1.32675 + 0.489639i) q^{54} +(4.06115 + 9.72791i) q^{55} +(-2.26137 - 8.00744i) q^{56} +(0.834324 + 0.834324i) q^{57} +(0.482328 - 1.04657i) q^{58} +(2.32603 - 2.32603i) q^{59} +(4.24907 - 1.39478i) q^{60} +(-7.22499 - 7.22499i) q^{61} +(1.28433 + 3.48006i) q^{62} +(-2.08016 + 2.08016i) q^{63} +(-4.18479 - 6.81818i) q^{64} +(5.21651 - 12.6934i) q^{65} +(-6.05500 - 2.79053i) q^{66} +0.885549i q^{67} +(-0.515823 + 6.57387i) q^{68} +(2.95105 + 2.95105i) q^{69} +(6.81290 - 6.33448i) q^{70} +2.56877 q^{71} +(-1.38116 + 2.46828i) q^{72} +(7.35033 - 7.35033i) q^{73} +(1.01507 + 2.75047i) q^{74} +(3.55514 + 3.51582i) q^{75} +(2.35259 + 0.184598i) q^{76} -13.8686 q^{77} +(3.00509 + 8.14270i) q^{78} -7.72612 q^{79} +(4.64857 - 7.64139i) q^{80} +1.00000 q^{81} +(5.33084 + 14.4447i) q^{82} -8.67714 q^{83} +(-0.460244 + 5.86555i) q^{84} +(-6.80334 + 2.84022i) q^{85} +(-2.52697 - 6.84718i) q^{86} +(-0.576185 + 0.576185i) q^{87} +(-12.8323 + 3.62395i) q^{88} -8.70590 q^{89} +(-3.16019 - 0.114996i) q^{90} +(12.7667 + 12.7667i) q^{91} +(8.32124 + 0.652933i) q^{92} -2.62300i q^{93} +(15.7257 + 7.24743i) q^{94} +(1.01643 + 2.43472i) q^{95} +(1.10685 + 5.54751i) q^{96} +(11.9985 - 11.9985i) q^{97} +(0.809919 + 2.19459i) q^{98} +(3.33354 + 3.33354i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q+2q2+16q38q44q5+2q64q74q8+16q914q108q124q144q158q168q17+2q18+8q1912q204q218q22++30q98+O(q100) 16 q + 2 q^{2} + 16 q^{3} - 8 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 16 q^{9} - 14 q^{10} - 8 q^{12} - 4 q^{14} - 4 q^{15} - 8 q^{16} - 8 q^{17} + 2 q^{18} + 8 q^{19} - 12 q^{20} - 4 q^{21} - 8 q^{22}+ \cdots + 30 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/240Z)×\left(\mathbb{Z}/240\mathbb{Z}\right)^\times.

nn 3131 9797 161161 181181
χ(n)\chi(n) 1-1 e(34)e\left(\frac{3}{4}\right) 11 e(34)e\left(\frac{3}{4}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.32675 + 0.489639i −0.938151 + 0.346227i
33 1.00000 0.577350
44 1.52051 1.29925i 0.760254 0.649626i
55 2.06823 + 0.849960i 0.924940 + 0.380114i
66 −1.32675 + 0.489639i −0.541642 + 0.199894i
77 −2.08016 + 2.08016i −0.786226 + 0.786226i −0.980873 0.194647i 0.937644π-0.937644\pi
0.194647 + 0.980873i 0.437644π0.437644\pi
88 −1.38116 + 2.46828i −0.488314 + 0.872668i
99 1.00000 0.333333
1010 −3.16019 0.114996i −0.999339 0.0363648i
1111 3.33354 + 3.33354i 1.00510 + 1.00510i 0.999987 + 0.00511408i 0.00162787π0.00162787\pi
0.00511408 + 0.999987i 0.498372π0.498372\pi
1212 1.52051 1.29925i 0.438933 0.375062i
1313 6.13735i 1.70220i −0.525007 0.851098i 0.675937π-0.675937\pi
0.525007 0.851098i 0.324063π-0.324063\pi
1414 1.74131 3.77837i 0.465386 1.00981i
1515 2.06823 + 0.849960i 0.534014 + 0.219459i
1616 0.623885 3.95105i 0.155971 0.987762i
1717 −2.33136 + 2.33136i −0.565437 + 0.565437i −0.930847 0.365410i 0.880929π-0.880929\pi
0.365410 + 0.930847i 0.380929π0.380929\pi
1818 −1.32675 + 0.489639i −0.312717 + 0.115409i
1919 0.834324 + 0.834324i 0.191407 + 0.191407i 0.796304 0.604897i 0.206786π-0.206786\pi
−0.604897 + 0.796304i 0.706786π0.706786\pi
2020 4.24907 1.39478i 0.950121 0.311882i
2121 −2.08016 + 2.08016i −0.453928 + 0.453928i
2222 −6.05500 2.79053i −1.29093 0.594943i
2323 2.95105 + 2.95105i 0.615336 + 0.615336i 0.944331 0.328996i 0.106710π-0.106710\pi
−0.328996 + 0.944331i 0.606710π0.606710\pi
2424 −1.38116 + 2.46828i −0.281928 + 0.503835i
2525 3.55514 + 3.51582i 0.711027 + 0.703165i
2626 3.00509 + 8.14270i 0.589346 + 1.59692i
2727 1.00000 0.192450
2828 −0.460244 + 5.86555i −0.0869780 + 1.10848i
2929 −0.576185 + 0.576185i −0.106995 + 0.106995i −0.758578 0.651583i 0.774105π-0.774105\pi
0.651583 + 0.758578i 0.274105π0.274105\pi
3030 −3.16019 0.114996i −0.576968 0.0209953i
3131 2.62300i 0.471106i −0.971862 0.235553i 0.924310π-0.924310\pi
0.971862 0.235553i 0.0756900π-0.0756900\pi
3232 1.10685 + 5.54751i 0.195665 + 0.980671i
3333 3.33354 + 3.33354i 0.580295 + 0.580295i
3434 1.95159 4.23464i 0.334696 0.726235i
3535 −6.07029 + 2.53419i −1.02607 + 0.428356i
3636 1.52051 1.29925i 0.253418 0.216542i
3737 2.07309i 0.340814i −0.985374 0.170407i 0.945492π-0.945492\pi
0.985374 0.170407i 0.0545083π-0.0545083\pi
3838 −1.51545 0.698418i −0.245839 0.113298i
3939 6.13735i 0.982763i
4040 −4.95449 + 3.93103i −0.783374 + 0.621550i
4141 10.8873i 1.70031i −0.526533 0.850154i 0.676508π-0.676508\pi
0.526533 0.850154i 0.323492π-0.323492\pi
4242 1.74131 3.77837i 0.268691 0.583015i
4343 5.16088i 0.787027i 0.919319 + 0.393514i 0.128741π0.128741\pi
−0.919319 + 0.393514i 0.871259π0.871259\pi
4444 9.39979 + 0.737562i 1.41707 + 0.111192i
4545 2.06823 + 0.849960i 0.308313 + 0.126705i
4646 −5.36024 2.47034i −0.790324 0.364232i
4747 −8.65772 8.65772i −1.26286 1.26286i −0.949702 0.313156i 0.898614π-0.898614\pi
−0.313156 0.949702i 0.601386π-0.601386\pi
4848 0.623885 3.95105i 0.0900500 0.570284i
4949 1.65411i 0.236302i
5050 −6.43824 2.92387i −0.910505 0.413498i
5151 −2.33136 + 2.33136i −0.326455 + 0.326455i
5252 −7.97397 9.33189i −1.10579 1.29410i
5353 −1.58490 −0.217703 −0.108851 0.994058i 0.534717π-0.534717\pi
−0.108851 + 0.994058i 0.534717π0.534717\pi
5454 −1.32675 + 0.489639i −0.180547 + 0.0666314i
5555 4.06115 + 9.72791i 0.547605 + 1.31171i
5656 −2.26137 8.00744i −0.302189 1.07004i
5757 0.834324 + 0.834324i 0.110509 + 0.110509i
5858 0.482328 1.04657i 0.0633328 0.137422i
5959 2.32603 2.32603i 0.302824 0.302824i −0.539294 0.842118i 0.681309π-0.681309\pi
0.842118 + 0.539294i 0.181309π0.181309\pi
6060 4.24907 1.39478i 0.548552 0.180065i
6161 −7.22499 7.22499i −0.925065 0.925065i 0.0723167 0.997382i 0.476961π-0.476961\pi
−0.997382 + 0.0723167i 0.976961π0.976961\pi
6262 1.28433 + 3.48006i 0.163109 + 0.441968i
6363 −2.08016 + 2.08016i −0.262075 + 0.262075i
6464 −4.18479 6.81818i −0.523098 0.852272i
6565 5.21651 12.6934i 0.647028 1.57443i
6666 −6.05500 2.79053i −0.745318 0.343491i
6767 0.885549i 0.108187i 0.998536 + 0.0540935i 0.0172269π0.0172269\pi
−0.998536 + 0.0540935i 0.982773π0.982773\pi
6868 −0.515823 + 6.57387i −0.0625528 + 0.797198i
6969 2.95105 + 2.95105i 0.355264 + 0.355264i
7070 6.81290 6.33448i 0.814297 0.757115i
7171 2.56877 0.304857 0.152428 0.988315i 0.451291π-0.451291\pi
0.152428 + 0.988315i 0.451291π0.451291\pi
7272 −1.38116 + 2.46828i −0.162771 + 0.290889i
7373 7.35033 7.35033i 0.860291 0.860291i −0.131081 0.991372i 0.541845π-0.541845\pi
0.991372 + 0.131081i 0.0418447π0.0418447\pi
7474 1.01507 + 2.75047i 0.117999 + 0.319735i
7575 3.55514 + 3.51582i 0.410512 + 0.405972i
7676 2.35259 + 0.184598i 0.269861 + 0.0211748i
7777 −13.8686 −1.58047
7878 3.00509 + 8.14270i 0.340259 + 0.921980i
7979 −7.72612 −0.869256 −0.434628 0.900610i 0.643120π-0.643120\pi
−0.434628 + 0.900610i 0.643120π0.643120\pi
8080 4.64857 7.64139i 0.519726 0.854333i
8181 1.00000 0.111111
8282 5.33084 + 14.4447i 0.588693 + 1.59515i
8383 −8.67714 −0.952440 −0.476220 0.879326i 0.657993π-0.657993\pi
−0.476220 + 0.879326i 0.657993π0.657993\pi
8484 −0.460244 + 5.86555i −0.0502168 + 0.639984i
8585 −6.80334 + 2.84022i −0.737926 + 0.308065i
8686 −2.52697 6.84718i −0.272490 0.738350i
8787 −0.576185 + 0.576185i −0.0617735 + 0.0617735i
8888 −12.8323 + 3.62395i −1.36792 + 0.386314i
8989 −8.70590 −0.922823 −0.461412 0.887186i 0.652657π-0.652657\pi
−0.461412 + 0.887186i 0.652657π0.652657\pi
9090 −3.16019 0.114996i −0.333113 0.0121216i
9191 12.7667 + 12.7667i 1.33831 + 1.33831i
9292 8.32124 + 0.652933i 0.867550 + 0.0680729i
9393 2.62300i 0.271993i
9494 15.7257 + 7.24743i 1.62199 + 0.747516i
9595 1.01643 + 2.43472i 0.104284 + 0.249797i
9696 1.10685 + 5.54751i 0.112967 + 0.566191i
9797 11.9985 11.9985i 1.21826 1.21826i 0.250021 0.968240i 0.419562π-0.419562\pi
0.968240 0.250021i 0.0804375π-0.0804375\pi
9898 0.809919 + 2.19459i 0.0818142 + 0.221687i
9999 3.33354 + 3.33354i 0.335034 + 0.335034i
100100 9.97355 + 0.726816i 0.997355 + 0.0726816i
101101 −6.69380 + 6.69380i −0.666058 + 0.666058i −0.956801 0.290743i 0.906098π-0.906098\pi
0.290743 + 0.956801i 0.406098π0.406098\pi
102102 1.95159 4.23464i 0.193237 0.419292i
103103 −13.4242 13.4242i −1.32272 1.32272i −0.911564 0.411158i 0.865124π-0.865124\pi
−0.411158 0.911564i 0.634876π-0.634876\pi
104104 15.1487 + 8.47667i 1.48545 + 0.831206i
105105 −6.07029 + 2.53419i −0.592400 + 0.247312i
106106 2.10276 0.776029i 0.204238 0.0753746i
107107 −10.9567 −1.05922 −0.529612 0.848240i 0.677663π-0.677663\pi
−0.529612 + 0.848240i 0.677663π0.677663\pi
108108 1.52051 1.29925i 0.146311 0.125021i
109109 0.643941 0.643941i 0.0616784 0.0616784i −0.675595 0.737273i 0.736113π-0.736113\pi
0.737273 + 0.675595i 0.236113π0.236113\pi
110110 −10.1513 10.9180i −0.967886 1.04099i
111111 2.07309i 0.196769i
112112 6.92102 + 9.51658i 0.653975 + 0.899232i
113113 9.19571 + 9.19571i 0.865060 + 0.865060i 0.991921 0.126861i 0.0404901π-0.0404901\pi
−0.126861 + 0.991921i 0.540490π0.540490\pi
114114 −1.51545 0.698418i −0.141935 0.0654129i
115115 3.59517 + 8.61171i 0.335251 + 0.803046i
116116 −0.127484 + 1.62470i −0.0118366 + 0.150850i
117117 6.13735i 0.567398i
118118 −1.94714 + 4.22497i −0.179249 + 0.388940i
119119 9.69918i 0.889122i
120120 −4.95449 + 3.93103i −0.452281 + 0.358852i
121121 11.2250i 1.02046i
122122 13.1234 + 6.04809i 1.18813 + 0.547568i
123123 10.8873i 0.981674i
124124 −3.40795 3.98830i −0.306043 0.358160i
125125 4.36452 + 10.2932i 0.390375 + 0.920656i
126126 1.74131 3.77837i 0.155129 0.336604i
127127 4.80716 + 4.80716i 0.426567 + 0.426567i 0.887457 0.460890i 0.152470π-0.152470\pi
−0.460890 + 0.887457i 0.652470π0.652470\pi
128128 8.89059 + 6.99695i 0.785825 + 0.618449i
129129 5.16088i 0.454391i
130130 −0.705769 + 19.3952i −0.0619001 + 1.70107i
131131 −3.53632 + 3.53632i −0.308970 + 0.308970i −0.844510 0.535540i 0.820108π-0.820108\pi
0.535540 + 0.844510i 0.320108π0.320108\pi
132132 9.39979 + 0.737562i 0.818147 + 0.0641965i
133133 −3.47105 −0.300978
134134 −0.433599 1.17490i −0.0374573 0.101496i
135135 2.06823 + 0.849960i 0.178005 + 0.0731529i
136136 −2.53445 8.97441i −0.217328 0.769550i
137137 7.54548 + 7.54548i 0.644654 + 0.644654i 0.951696 0.307042i 0.0993392π-0.0993392\pi
−0.307042 + 0.951696i 0.599339π0.599339\pi
138138 −5.36024 2.47034i −0.456294 0.210289i
139139 −2.84263 + 2.84263i −0.241109 + 0.241109i −0.817309 0.576200i 0.804535π-0.804535\pi
0.576200 + 0.817309i 0.304535π0.304535\pi
140140 −5.93737 + 11.7401i −0.501799 + 0.992219i
141141 −8.65772 8.65772i −0.729111 0.729111i
142142 −3.40810 + 1.25777i −0.286002 + 0.105550i
143143 20.4591 20.4591i 1.71088 1.71088i
144144 0.623885 3.95105i 0.0519904 0.329254i
145145 −1.68142 + 0.701948i −0.139634 + 0.0582936i
146146 −6.15301 + 13.3510i −0.509227 + 1.10494i
147147 1.65411i 0.136429i
148148 −2.69347 3.15215i −0.221402 0.259105i
149149 3.20287 + 3.20287i 0.262389 + 0.262389i 0.826024 0.563635i 0.190597π-0.190597\pi
−0.563635 + 0.826024i 0.690597π0.690597\pi
150150 −6.43824 2.92387i −0.525680 0.238733i
151151 8.82773 0.718390 0.359195 0.933262i 0.383051π-0.383051\pi
0.359195 + 0.933262i 0.383051π0.383051\pi
152152 −3.21168 + 0.907007i −0.260502 + 0.0735680i
153153 −2.33136 + 2.33136i −0.188479 + 0.188479i
154154 18.4001 6.79060i 1.48272 0.547202i
155155 2.22945 5.42497i 0.179074 0.435744i
156156 −7.97397 9.33189i −0.638429 0.747149i
157157 15.5186 1.23852 0.619258 0.785187i 0.287433π-0.287433\pi
0.619258 + 0.785187i 0.287433π0.287433\pi
158158 10.2506 3.78301i 0.815493 0.300960i
159159 −1.58490 −0.125691
160160 −2.42595 + 12.4143i −0.191788 + 0.981436i
161161 −12.2773 −0.967586
162162 −1.32675 + 0.489639i −0.104239 + 0.0384697i
163163 8.65221 0.677694 0.338847 0.940842i 0.389963π-0.389963\pi
0.338847 + 0.940842i 0.389963π0.389963\pi
164164 −14.1453 16.5542i −1.10457 1.29267i
165165 4.06115 + 9.72791i 0.316160 + 0.757316i
166166 11.5124 4.24867i 0.893532 0.329760i
167167 2.86613 2.86613i 0.221788 0.221788i −0.587463 0.809251i 0.699873π-0.699873\pi
0.809251 + 0.587463i 0.199873π0.199873\pi
168168 −2.26137 8.00744i −0.174469 0.617787i
169169 −24.6671 −1.89747
170170 7.63562 7.09942i 0.585625 0.544501i
171171 0.834324 + 0.834324i 0.0638024 + 0.0638024i
172172 6.70529 + 7.84716i 0.511274 + 0.598340i
173173 15.1143i 1.14912i 0.818464 + 0.574558i 0.194826π0.194826\pi
−0.818464 + 0.574558i 0.805174π0.805174\pi
174174 0.482328 1.04657i 0.0365652 0.0793406i
175175 −14.7087 + 0.0817750i −1.11187 + 0.00618161i
176176 15.2507 11.0912i 1.14957 0.836033i
177177 2.32603 2.32603i 0.174835 0.174835i
178178 11.5505 4.26275i 0.865747 0.319506i
179179 −12.3666 12.3666i −0.924324 0.924324i 0.0730070 0.997331i 0.476740π-0.476740\pi
−0.997331 + 0.0730070i 0.976740π0.976740\pi
180180 4.24907 1.39478i 0.316707 0.103961i
181181 −9.58991 + 9.58991i −0.712813 + 0.712813i −0.967123 0.254310i 0.918152π-0.918152\pi
0.254310 + 0.967123i 0.418152π0.418152\pi
182182 −23.1892 10.6871i −1.71890 0.792177i
183183 −7.22499 7.22499i −0.534087 0.534087i
184184 −11.3599 + 3.20813i −0.837461 + 0.236506i
185185 1.76205 4.28763i 0.129548 0.315233i
186186 1.28433 + 3.48006i 0.0941713 + 0.255170i
187187 −15.5434 −1.13664
188188 −24.4127 1.91556i −1.78048 0.139707i
189189 −2.08016 + 2.08016i −0.151309 + 0.151309i
190190 −2.54068 2.73256i −0.184320 0.198241i
191191 14.5044i 1.04950i −0.851257 0.524750i 0.824159π-0.824159\pi
0.851257 0.524750i 0.175841π-0.175841\pi
192192 −4.18479 6.81818i −0.302011 0.492060i
193193 −1.68153 1.68153i −0.121039 0.121039i 0.643992 0.765032i 0.277277π-0.277277\pi
−0.765032 + 0.643992i 0.777277π0.777277\pi
194194 −10.0440 + 21.7939i −0.721118 + 1.56471i
195195 5.21651 12.6934i 0.373562 0.908996i
196196 −2.14911 2.51509i −0.153508 0.179649i
197197 8.65121i 0.616373i −0.951326 0.308187i 0.900278π-0.900278\pi
0.951326 0.308187i 0.0997221π-0.0997221\pi
198198 −6.05500 2.79053i −0.430310 0.198314i
199199 22.3275i 1.58275i 0.611328 + 0.791377i 0.290635π0.290635\pi
−0.611328 + 0.791377i 0.709365π0.709365\pi
200200 −13.5882 + 3.91914i −0.960834 + 0.277125i
201201 0.885549i 0.0624618i
202202 5.60343 12.1585i 0.394256 0.855471i
203203 2.39711i 0.168244i
204204 −0.515823 + 6.57387i −0.0361149 + 0.460263i
205205 9.25376 22.5174i 0.646311 1.57268i
206206 24.3834 + 11.2375i 1.69887 + 0.782951i
207207 2.95105 + 2.95105i 0.205112 + 0.205112i
208208 −24.2490 3.82900i −1.68136 0.265493i
209209 5.56251i 0.384767i
210210 6.81290 6.33448i 0.470134 0.437120i
211211 5.27613 5.27613i 0.363224 0.363224i −0.501775 0.864998i 0.667319π-0.667319\pi
0.864998 + 0.501775i 0.167319π0.167319\pi
212212 −2.40985 + 2.05919i −0.165509 + 0.141426i
213213 2.56877 0.176009
214214 14.5368 5.36483i 0.993712 0.366732i
215215 −4.38655 + 10.6739i −0.299160 + 0.727953i
216216 −1.38116 + 2.46828i −0.0939761 + 0.167945i
217217 5.45626 + 5.45626i 0.370395 + 0.370395i
218218 −0.539047 + 1.16964i −0.0365089 + 0.0792183i
219219 7.35033 7.35033i 0.496689 0.496689i
220220 18.8140 + 9.51489i 1.26844 + 0.641494i
221221 14.3084 + 14.3084i 0.962484 + 0.962484i
222222 1.01507 + 2.75047i 0.0681268 + 0.184599i
223223 13.8202 13.8202i 0.925469 0.925469i −0.0719400 0.997409i 0.522919π-0.522919\pi
0.997409 + 0.0719400i 0.0229190π0.0229190\pi
224224 −13.8421 9.23728i −0.924866 0.617192i
225225 3.55514 + 3.51582i 0.237009 + 0.234388i
226226 −16.7029 7.69779i −1.11106 0.512049i
227227 1.66286i 0.110368i 0.998476 + 0.0551839i 0.0175745π0.0175745\pi
−0.998476 + 0.0551839i 0.982425π0.982425\pi
228228 2.35259 + 0.184598i 0.155804 + 0.0122253i
229229 11.3744 + 11.3744i 0.751643 + 0.751643i 0.974786 0.223142i 0.0716315π-0.0716315\pi
−0.223142 + 0.974786i 0.571632π0.571632\pi
230230 −8.98650 9.66521i −0.592552 0.637305i
231231 −13.8686 −0.912486
232232 −0.626380 2.21799i −0.0411239 0.145618i
233233 9.38976 9.38976i 0.615143 0.615143i −0.329138 0.944282i 0.606758π-0.606758\pi
0.944282 + 0.329138i 0.106758π0.106758\pi
234234 3.00509 + 8.14270i 0.196449 + 0.532305i
235235 −10.5474 25.2649i −0.688038 1.64810i
236236 0.514646 6.55886i 0.0335006 0.426945i
237237 −7.72612 −0.501865
238238 4.74910 + 12.8683i 0.307838 + 0.834131i
239239 8.88914 0.574991 0.287495 0.957782i 0.407177π-0.407177\pi
0.287495 + 0.957782i 0.407177π0.407177\pi
240240 4.64857 7.64139i 0.300064 0.493249i
241241 20.5978 1.32682 0.663411 0.748255i 0.269108π-0.269108\pi
0.663411 + 0.748255i 0.269108π0.269108\pi
242242 −5.49621 14.8927i −0.353309 0.957342i
243243 1.00000 0.0641500
244244 −20.3727 1.59856i −1.30423 0.102337i
245245 1.40593 3.42109i 0.0898217 0.218565i
246246 5.33084 + 14.4447i 0.339882 + 0.920958i
247247 5.12054 5.12054i 0.325812 0.325812i
248248 6.47430 + 3.62279i 0.411119 + 0.230048i
249249 −8.67714 −0.549891
250250 −10.8306 11.5195i −0.684986 0.728556i
251251 16.8455 + 16.8455i 1.06328 + 1.06328i 0.997858 + 0.0654195i 0.0208386π0.0208386\pi
0.0654195 + 0.997858i 0.479161π0.479161\pi
252252 −0.460244 + 5.86555i −0.0289927 + 0.369495i
253253 19.6749i 1.23695i
254254 −8.73165 4.02411i −0.547873 0.252495i
255255 −6.80334 + 2.84022i −0.426042 + 0.177861i
256256 −15.2215 4.93000i −0.951346 0.308125i
257257 −14.1500 + 14.1500i −0.882653 + 0.882653i −0.993804 0.111151i 0.964546π-0.964546\pi
0.111151 + 0.993804i 0.464546π0.464546\pi
258258 −2.52697 6.84718i −0.157322 0.426287i
259259 4.31236 + 4.31236i 0.267957 + 0.267957i
260260 −8.56026 26.0780i −0.530885 1.61729i
261261 −0.576185 + 0.576185i −0.0356650 + 0.0356650i
262262 2.96028 6.42332i 0.182887 0.396834i
263263 11.1204 + 11.1204i 0.685712 + 0.685712i 0.961281 0.275569i 0.0888664π-0.0888664\pi
−0.275569 + 0.961281i 0.588866π0.588866\pi
264264 −12.8323 + 3.62395i −0.789772 + 0.223039i
265265 −3.27794 1.34710i −0.201362 0.0827519i
266266 4.60520 1.69956i 0.282363 0.104207i
267267 −8.70590 −0.532792
268268 1.15055 + 1.34648i 0.0702811 + 0.0822496i
269269 −10.2902 + 10.2902i −0.627403 + 0.627403i −0.947414 0.320011i 0.896313π-0.896313\pi
0.320011 + 0.947414i 0.396313π0.396313\pi
270270 −3.16019 0.114996i −0.192323 0.00699842i
271271 21.3325i 1.29586i 0.761702 + 0.647928i 0.224364π0.224364\pi
−0.761702 + 0.647928i 0.775636π0.775636\pi
272272 7.75680 + 10.6658i 0.470325 + 0.646709i
273273 12.7667 + 12.7667i 0.772674 + 0.772674i
274274 −13.7055 6.31637i −0.827979 0.381586i
275275 0.131048 + 23.5713i 0.00790249 + 1.42141i
276276 8.32124 + 0.652933i 0.500880 + 0.0393019i
277277 19.0041i 1.14184i −0.821004 0.570922i 0.806586π-0.806586\pi
0.821004 0.570922i 0.193414π-0.193414\pi
278278 2.37959 5.16331i 0.142718 0.309675i
279279 2.62300i 0.157035i
280280 2.12897 18.4833i 0.127230 1.10459i
281281 3.86317i 0.230457i 0.993339 + 0.115229i 0.0367600π0.0367600\pi
−0.993339 + 0.115229i 0.963240π0.963240\pi
282282 15.7257 + 7.24743i 0.936454 + 0.431578i
283283 5.89151i 0.350214i −0.984549 0.175107i 0.943973π-0.943973\pi
0.984549 0.175107i 0.0560271π-0.0560271\pi
284284 3.90583 3.33748i 0.231769 0.198043i
285285 1.01643 + 2.43472i 0.0602081 + 0.144220i
286286 −17.1265 + 37.1616i −1.01271 + 2.19741i
287287 22.6473 + 22.6473i 1.33683 + 1.33683i
288288 1.10685 + 5.54751i 0.0652218 + 0.326890i
289289 6.12955i 0.360562i
290290 1.88711 1.75459i 0.110815 0.103033i
291291 11.9985 11.9985i 0.703364 0.703364i
292292 1.62629 20.7262i 0.0951716 1.21291i
293293 −4.49132 −0.262386 −0.131193 0.991357i 0.541881π-0.541881\pi
−0.131193 + 0.991357i 0.541881π0.541881\pi
294294 0.809919 + 2.19459i 0.0472354 + 0.127991i
295295 6.78780 2.83373i 0.395201 0.164986i
296296 5.11697 + 2.86327i 0.297418 + 0.166424i
297297 3.33354 + 3.33354i 0.193432 + 0.193432i
298298 −5.81764 2.68114i −0.337007 0.155314i
299299 18.1116 18.1116i 1.04742 1.04742i
300300 9.97355 + 0.726816i 0.575823 + 0.0419627i
301301 −10.7355 10.7355i −0.618781 0.618781i
302302 −11.7121 + 4.32240i −0.673958 + 0.248726i
303303 −6.69380 + 6.69380i −0.384549 + 0.384549i
304304 3.81698 2.77593i 0.218919 0.159211i
305305 −8.80197 21.0839i −0.503999 1.20726i
306306 1.95159 4.23464i 0.111565 0.242078i
307307 3.84487i 0.219438i −0.993963 0.109719i 0.965005π-0.965005\pi
0.993963 0.109719i 0.0349951π-0.0349951\pi
308308 −21.0873 + 18.0188i −1.20156 + 1.02672i
309309 −13.4242 13.4242i −0.763674 0.763674i
310310 −0.301634 + 8.28918i −0.0171317 + 0.470794i
311311 −4.07103 −0.230847 −0.115423 0.993316i 0.536822π-0.536822\pi
−0.115423 + 0.993316i 0.536822π0.536822\pi
312312 15.1487 + 8.47667i 0.857626 + 0.479897i
313313 −1.37922 + 1.37922i −0.0779584 + 0.0779584i −0.745011 0.667052i 0.767556π-0.767556\pi
0.667052 + 0.745011i 0.267556π0.267556\pi
314314 −20.5892 + 7.59850i −1.16192 + 0.428808i
315315 −6.07029 + 2.53419i −0.342022 + 0.142785i
316316 −11.7476 + 10.0382i −0.660855 + 0.564692i
317317 9.80915 0.550937 0.275468 0.961310i 0.411167π-0.411167\pi
0.275468 + 0.961310i 0.411167π0.411167\pi
318318 2.10276 0.776029i 0.117917 0.0435176i
319319 −3.84148 −0.215081
320320 −2.85991 17.6585i −0.159874 0.987137i
321321 −10.9567 −0.611543
322322 16.2888 6.01144i 0.907741 0.335004i
323323 −3.89021 −0.216457
324324 1.52051 1.29925i 0.0844726 0.0721807i
325325 21.5778 21.8191i 1.19692 1.21031i
326326 −11.4793 + 4.23646i −0.635779 + 0.234636i
327327 0.643941 0.643941i 0.0356100 0.0356100i
328328 26.8729 + 15.0371i 1.48380 + 0.830285i
329329 36.0188 1.98578
330330 −10.1513 10.9180i −0.558809 0.601014i
331331 −7.17235 7.17235i −0.394228 0.394228i 0.481963 0.876191i 0.339924π-0.339924\pi
−0.876191 + 0.481963i 0.839924π0.839924\pi
332332 −13.1937 + 11.2738i −0.724096 + 0.618730i
333333 2.07309i 0.113605i
334334 −2.39925 + 5.20599i −0.131281 + 0.284859i
335335 −0.752681 + 1.83152i −0.0411234 + 0.100066i
336336 6.92102 + 9.51658i 0.377573 + 0.519172i
337337 −25.3587 + 25.3587i −1.38138 + 1.38138i −0.539200 + 0.842178i 0.681273π0.681273\pi
−0.842178 + 0.539200i 0.818727π0.818727\pi
338338 32.7270 12.0780i 1.78011 0.656955i
339339 9.19571 + 9.19571i 0.499442 + 0.499442i
340340 −6.65436 + 13.1578i −0.360884 + 0.713583i
341341 8.74390 8.74390i 0.473509 0.473509i
342342 −1.51545 0.698418i −0.0819463 0.0377661i
343343 −11.1203 11.1203i −0.600439 0.600439i
344344 −12.7385 7.12801i −0.686814 0.384317i
345345 3.59517 + 8.61171i 0.193557 + 0.463639i
346346 −7.40053 20.0528i −0.397855 1.07804i
347347 −8.80549 −0.472704 −0.236352 0.971668i 0.575952π-0.575952\pi
−0.236352 + 0.971668i 0.575952π0.575952\pi
348348 −0.127484 + 1.62470i −0.00683384 + 0.0870933i
349349 −14.8110 + 14.8110i −0.792815 + 0.792815i −0.981951 0.189136i 0.939431π-0.939431\pi
0.189136 + 0.981951i 0.439431π0.439431\pi
350350 19.4747 7.31045i 1.04097 0.390760i
351351 6.13735i 0.327588i
352352 −14.8031 + 22.1826i −0.789010 + 1.18234i
353353 −21.3226 21.3226i −1.13489 1.13489i −0.989353 0.145536i 0.953509π-0.953509\pi
−0.145536 0.989353i 0.546491π-0.546491\pi
354354 −1.94714 + 4.22497i −0.103489 + 0.224555i
355355 5.31280 + 2.18335i 0.281974 + 0.115880i
356356 −13.2374 + 11.3112i −0.701580 + 0.599490i
357357 9.69918i 0.513335i
358358 22.4625 + 10.3522i 1.18718 + 0.547130i
359359 9.38977i 0.495573i −0.968815 0.247787i 0.920297π-0.920297\pi
0.968815 0.247787i 0.0797032π-0.0797032\pi
360360 −4.95449 + 3.93103i −0.261125 + 0.207183i
361361 17.6078i 0.926727i
362362 8.02778 17.4190i 0.421931 0.915521i
363363 11.2250i 0.589161i
364364 35.9989 + 2.82468i 1.88686 + 0.148054i
365365 21.4496 8.95467i 1.12273 0.468709i
366366 13.1234 + 6.04809i 0.685969 + 0.316138i
367367 −0.129655 0.129655i −0.00676792 0.00676792i 0.703715 0.710483i 0.251523π-0.251523\pi
−0.710483 + 0.703715i 0.751523π0.751523\pi
368368 13.5008 9.81861i 0.703780 0.511830i
369369 10.8873i 0.566770i
370370 −0.238397 + 6.55136i −0.0123937 + 0.340589i
371371 3.29684 3.29684i 0.171164 0.171164i
372372 −3.40795 3.98830i −0.176694 0.206784i
373373 −2.85797 −0.147980 −0.0739900 0.997259i 0.523573π-0.523573\pi
−0.0739900 + 0.997259i 0.523573π0.523573\pi
374374 20.6221 7.61063i 1.06634 0.393536i
375375 4.36452 + 10.2932i 0.225383 + 0.531541i
376376 33.3274 9.41194i 1.71873 0.485384i
377377 3.53625 + 3.53625i 0.182126 + 0.182126i
378378 1.74131 3.77837i 0.0895635 0.194338i
379379 −14.8095 + 14.8095i −0.760713 + 0.760713i −0.976451 0.215739i 0.930784π-0.930784\pi
0.215739 + 0.976451i 0.430784π0.430784\pi
380380 4.70880 + 2.38140i 0.241556 + 0.122163i
381381 4.80716 + 4.80716i 0.246278 + 0.246278i
382382 7.10191 + 19.2436i 0.363365 + 0.984589i
383383 −22.2921 + 22.2921i −1.13907 + 1.13907i −0.150458 + 0.988616i 0.548075π0.548075\pi
−0.988616 + 0.150458i 0.951925π0.951925\pi
384384 8.89059 + 6.99695i 0.453696 + 0.357062i
385385 −28.6834 11.7878i −1.46184 0.600759i
386386 3.05431 + 1.40762i 0.155460 + 0.0716461i
387387 5.16088i 0.262342i
388388 2.65472 33.8328i 0.134773 1.71760i
389389 17.1132 + 17.1132i 0.867671 + 0.867671i 0.992214 0.124543i 0.0397465π-0.0397465\pi
−0.124543 + 0.992214i 0.539746π0.539746\pi
390390 −0.705769 + 19.3952i −0.0357380 + 0.982113i
391391 −13.7599 −0.695867
392392 4.08281 + 2.28460i 0.206213 + 0.115390i
393393 −3.53632 + 3.53632i −0.178384 + 0.178384i
394394 4.23597 + 11.4780i 0.213405 + 0.578251i
395395 −15.9794 6.56689i −0.804009 0.330416i
396396 9.39979 + 0.737562i 0.472357 + 0.0370639i
397397 16.2806 0.817099 0.408549 0.912736i 0.366035π-0.366035\pi
0.408549 + 0.912736i 0.366035π0.366035\pi
398398 −10.9324 29.6229i −0.547992 1.48486i
399399 −3.47105 −0.173770
400400 16.1092 11.8530i 0.805459 0.592652i
401401 5.13860 0.256609 0.128305 0.991735i 0.459046π-0.459046\pi
0.128305 + 0.991735i 0.459046π0.459046\pi
402402 −0.433599 1.17490i −0.0216260 0.0585986i
403403 −16.0983 −0.801914
404404 −1.48103 + 18.8749i −0.0736842 + 0.939062i
405405 2.06823 + 0.849960i 0.102771 + 0.0422349i
406406 1.17372 + 3.18036i 0.0582507 + 0.157839i
407407 6.91074 6.91074i 0.342553 0.342553i
408408 −2.53445 8.97441i −0.125474 0.444300i
409409 −3.88999 −0.192348 −0.0961738 0.995365i 0.530660π-0.530660\pi
−0.0961738 + 0.995365i 0.530660π0.530660\pi
410410 −1.25199 + 34.4059i −0.0618315 + 1.69918i
411411 7.54548 + 7.54548i 0.372191 + 0.372191i
412412 −37.8529 2.97016i −1.86488 0.146329i
413413 9.67703i 0.476176i
414414 −5.36024 2.47034i −0.263441 0.121411i
415415 −17.9463 7.37522i −0.880949 0.362035i
416416 34.0470 6.79313i 1.66929 0.333061i
417417 −2.84263 + 2.84263i −0.139204 + 0.139204i
418418 −2.72362 7.38004i −0.133217 0.360969i
419419 −9.68913 9.68913i −0.473345 0.473345i 0.429650 0.902995i 0.358637π-0.358637\pi
−0.902995 + 0.429650i 0.858637π0.858637\pi
420420 −5.93737 + 11.7401i −0.289714 + 0.572858i
421421 −19.2867 + 19.2867i −0.939978 + 0.939978i −0.998298 0.0583197i 0.981426π-0.981426\pi
0.0583197 + 0.998298i 0.481426π0.481426\pi
422422 −4.41668 + 9.58348i −0.215001 + 0.466516i
423423 −8.65772 8.65772i −0.420953 0.420953i
424424 2.18900 3.91198i 0.106307 0.189982i
425425 −16.4849 + 0.0916501i −0.799636 + 0.00444568i
426426 −3.40810 + 1.25777i −0.165123 + 0.0609391i
427427 30.0582 1.45462
428428 −16.6597 + 14.2355i −0.805279 + 0.688100i
429429 20.4591 20.4591i 0.987776 0.987776i
430430 0.593480 16.3094i 0.0286201 0.786507i
431431 4.13031i 0.198950i 0.995040 + 0.0994751i 0.0317164π0.0317164\pi
−0.995040 + 0.0994751i 0.968284π0.968284\pi
432432 0.623885 3.95105i 0.0300167 0.190095i
433433 13.3312 + 13.3312i 0.640655 + 0.640655i 0.950716 0.310062i 0.100350π-0.100350\pi
−0.310062 + 0.950716i 0.600350π0.600350\pi
434434 −9.91067 4.56747i −0.475728 0.219246i
435435 −1.68142 + 0.701948i −0.0806178 + 0.0336558i
436436 0.142475 1.81576i 0.00682331 0.0869591i
437437 4.92426i 0.235559i
438438 −6.15301 + 13.3510i −0.294002 + 0.637937i
439439 22.0770i 1.05368i −0.849965 0.526839i 0.823377π-0.823377\pi
0.849965 0.526839i 0.176623π-0.176623\pi
440440 −29.6203 3.41177i −1.41209 0.162650i
441441 1.65411i 0.0787673i
442442 −25.9895 11.9776i −1.23619 0.569717i
443443 8.44869i 0.401409i 0.979652 + 0.200705i 0.0643231π0.0643231\pi
−0.979652 + 0.200705i 0.935677π0.935677\pi
444444 −2.69347 3.15215i −0.127826 0.149594i
445445 −18.0058 7.39967i −0.853556 0.350778i
446446 −11.5690 + 25.1028i −0.547807 + 1.18865i
447447 3.20287 + 3.20287i 0.151491 + 0.151491i
448448 22.8879 + 5.47787i 1.08135 + 0.258805i
449449 12.3249i 0.581648i −0.956777 0.290824i 0.906071π-0.906071\pi
0.956777 0.290824i 0.0939293π-0.0939293\pi
450450 −6.43824 2.92387i −0.303502 0.137833i
451451 36.2932 36.2932i 1.70898 1.70898i
452452 25.9297 + 2.03459i 1.21963 + 0.0956992i
453453 8.82773 0.414763
454454 −0.814200 2.20619i −0.0382123 0.103542i
455455 15.5532 + 37.2555i 0.729146 + 1.74657i
456456 −3.21168 + 0.907007i −0.150401 + 0.0424745i
457457 10.5838 + 10.5838i 0.495089 + 0.495089i 0.909905 0.414816i 0.136154π-0.136154\pi
−0.414816 + 0.909905i 0.636154π0.636154\pi
458458 −20.6603 9.52161i −0.965394 0.444916i
459459 −2.33136 + 2.33136i −0.108818 + 0.108818i
460460 16.6553 + 8.42314i 0.776556 + 0.392731i
461461 −6.77081 6.77081i −0.315348 0.315348i 0.531629 0.846977i 0.321580π-0.321580\pi
−0.846977 + 0.531629i 0.821580π0.821580\pi
462462 18.4001 6.79060i 0.856050 0.315927i
463463 −11.3573 + 11.3573i −0.527819 + 0.527819i −0.919921 0.392103i 0.871748π-0.871748\pi
0.392103 + 0.919921i 0.371748π0.371748\pi
464464 1.91706 + 2.63601i 0.0889973 + 0.122374i
465465 2.22945 5.42497i 0.103388 0.251577i
466466 −7.86023 + 17.0554i −0.364118 + 0.790077i
467467 3.11578i 0.144181i −0.997398 0.0720906i 0.977033π-0.977033\pi
0.997398 0.0720906i 0.0229671π-0.0229671\pi
468468 −7.97397 9.33189i −0.368597 0.431367i
469469 −1.84208 1.84208i −0.0850594 0.0850594i
470470 26.3644 + 28.3556i 1.21610 + 1.30795i
471471 15.5186 0.715058
472472 2.52867 + 8.95392i 0.116391 + 0.412138i
473473 −17.2040 + 17.2040i −0.791042 + 0.791042i
474474 10.2506 3.78301i 0.470825 0.173759i
475475 0.0327989 + 5.89947i 0.00150492 + 0.270686i
476476 −12.6017 14.7477i −0.577597 0.675958i
477477 −1.58490 −0.0725676
478478 −11.7936 + 4.35247i −0.539428 + 0.199077i
479479 −15.3508 −0.701396 −0.350698 0.936489i 0.614056π-0.614056\pi
−0.350698 + 0.936489i 0.614056π0.614056\pi
480480 −2.42595 + 12.4143i −0.110729 + 0.566633i
481481 −12.7233 −0.580132
482482 −27.3281 + 10.0855i −1.24476 + 0.459382i
483483 −12.2773 −0.558636
484484 14.5841 + 17.0677i 0.662915 + 0.775805i
485485 35.0138 14.6174i 1.58990 0.663740i
486486 −1.32675 + 0.489639i −0.0601824 + 0.0222105i
487487 8.51351 8.51351i 0.385784 0.385784i −0.487397 0.873181i 0.662053π-0.662053\pi
0.873181 + 0.487397i 0.162053π0.162053\pi
488488 27.8122 7.85440i 1.25900 0.355552i
489489 8.65221 0.391267
490490 −0.190216 + 5.22731i −0.00859309 + 0.236146i
491491 −6.16348 6.16348i −0.278154 0.278154i 0.554218 0.832372i 0.313017π-0.313017\pi
−0.832372 + 0.554218i 0.813017π0.813017\pi
492492 −14.1453 16.5542i −0.637721 0.746321i
493493 2.68659i 0.120998i
494494 −4.28644 + 9.30087i −0.192856 + 0.418466i
495495 4.06115 + 9.72791i 0.182535 + 0.437237i
496496 −10.3636 1.63645i −0.465340 0.0734789i
497497 −5.34345 + 5.34345i −0.239686 + 0.239686i
498498 11.5124 4.24867i 0.515881 0.190387i
499499 −16.1961 16.1961i −0.725037 0.725037i 0.244589 0.969627i 0.421347π-0.421347\pi
−0.969627 + 0.244589i 0.921347π0.921347\pi
500500 20.0098 + 9.98034i 0.894866 + 0.446335i
501501 2.86613 2.86613i 0.128049 0.128049i
502502 −30.5979 14.1015i −1.36565 0.629379i
503503 8.39462 + 8.39462i 0.374298 + 0.374298i 0.869040 0.494742i 0.164737π-0.164737\pi
−0.494742 + 0.869040i 0.664737π0.664737\pi
504504 −2.26137 8.00744i −0.100730 0.356680i
505505 −19.5338 + 8.15485i −0.869242 + 0.362886i
506506 −9.63359 26.1036i −0.428265 1.16044i
507507 −24.6671 −1.09550
508508 13.5550 + 1.06361i 0.601408 + 0.0471899i
509509 5.50555 5.50555i 0.244029 0.244029i −0.574486 0.818515i 0.694798π-0.694798\pi
0.818515 + 0.574486i 0.194798π0.194798\pi
510510 7.63562 7.09942i 0.338111 0.314368i
511511 30.5797i 1.35277i
512512 22.6090 0.912208i 0.999187 0.0403143i
513513 0.834324 + 0.834324i 0.0368363 + 0.0368363i
514514 11.8451 25.7018i 0.522463 1.13366i
515515 −16.3542 39.1742i −0.720653 1.72622i
516516 6.70529 + 7.84716i 0.295184 + 0.345452i
517517 57.7217i 2.53860i
518518 −7.83290 3.60990i −0.344158 0.158610i
519519 15.1143i 0.663442i
520520 24.1261 + 30.4075i 1.05800 + 1.33346i
521521 39.2289i 1.71865i −0.511430 0.859325i 0.670884π-0.670884\pi
0.511430 0.859325i 0.329116π-0.329116\pi
522522 0.482328 1.04657i 0.0211109 0.0458073i
523523 16.7434i 0.732137i 0.930588 + 0.366068i 0.119296π0.119296\pi
−0.930588 + 0.366068i 0.880704π0.880704\pi
524524 −0.782428 + 9.97158i −0.0341805 + 0.435611i
525525 −14.7087 + 0.0817750i −0.641941 + 0.00356895i
526526 −20.1989 9.30894i −0.880713 0.405889i
527527 6.11516 + 6.11516i 0.266381 + 0.266381i
528528 15.2507 11.0912i 0.663703 0.482684i
529529 5.58265i 0.242724i
530530 5.00858 + 0.182257i 0.217559 + 0.00791673i
531531 2.32603 2.32603i 0.100941 0.100941i
532532 −5.27776 + 4.50977i −0.228820 + 0.195524i
533533 −66.8191 −2.89426
534534 11.5505 4.26275i 0.499839 0.184467i
535535 −22.6610 9.31276i −0.979719 0.402626i
536536 −2.18578 1.22309i −0.0944113 0.0528293i
537537 −12.3666 12.3666i −0.533659 0.533659i
538538 8.61398 18.6909i 0.371375 0.805823i
539539 5.51406 5.51406i 0.237507 0.237507i
540540 4.24907 1.39478i 0.182851 0.0600218i
541541 3.45427 + 3.45427i 0.148511 + 0.148511i 0.777452 0.628942i 0.216512π-0.216512\pi
−0.628942 + 0.777452i 0.716512π0.716512\pi
542542 −10.4452 28.3028i −0.448660 1.21571i
543543 −9.58991 + 9.58991i −0.411543 + 0.411543i
544544 −15.5137 10.3528i −0.665144 0.443871i
545545 1.87914 0.784493i 0.0804936 0.0336040i
546546 −23.1892 10.6871i −0.992405 0.457364i
547547 18.1175i 0.774647i 0.921944 + 0.387324i 0.126600π0.126600\pi
−0.921944 + 0.387324i 0.873400π0.873400\pi
548548 21.2764 + 1.66947i 0.908885 + 0.0713163i
549549 −7.22499 7.22499i −0.308355 0.308355i
550550 −11.7153 31.2090i −0.499543 1.33076i
551551 −0.961451 −0.0409592
552552 −11.3599 + 3.20813i −0.483508 + 0.136547i
553553 16.0715 16.0715i 0.683431 0.683431i
554554 9.30514 + 25.2136i 0.395337 + 1.07122i
555555 1.76205 4.28763i 0.0747947 0.182000i
556556 −0.628946 + 8.01554i −0.0266732 + 0.339935i
557557 21.1776 0.897324 0.448662 0.893701i 0.351901π-0.351901\pi
0.448662 + 0.893701i 0.351901π0.351901\pi
558558 1.28433 + 3.48006i 0.0543698 + 0.147323i
559559 31.6742 1.33967
560560 6.22554 + 25.5651i 0.263077 + 1.08032i
561561 −15.5434 −0.656241
562562 −1.89156 5.12544i −0.0797905 0.216204i
563563 44.5712 1.87845 0.939226 0.343298i 0.111544π-0.111544\pi
0.939226 + 0.343298i 0.111544π0.111544\pi
564564 −24.4127 1.91556i −1.02796 0.0806596i
565565 11.2028 + 26.8348i 0.471307 + 1.12895i
566566 2.88471 + 7.81653i 0.121253 + 0.328553i
567567 −2.08016 + 2.08016i −0.0873584 + 0.0873584i
568568 −3.54788 + 6.34044i −0.148866 + 0.266039i
569569 −5.14194 −0.215562 −0.107781 0.994175i 0.534374π-0.534374\pi
−0.107781 + 0.994175i 0.534374π0.534374\pi
570570 −2.54068 2.73256i −0.106417 0.114454i
571571 −17.4873 17.4873i −0.731820 0.731820i 0.239160 0.970980i 0.423128π-0.423128\pi
−0.970980 + 0.239160i 0.923128π0.923128\pi
572572 4.52668 57.6898i 0.189270 2.41213i
573573 14.5044i 0.605929i
574574 −41.1362 18.9582i −1.71699 0.791299i
575575 0.116011 + 20.8667i 0.00483801 + 0.870203i
576576 −4.18479 6.81818i −0.174366 0.284091i
577577 −2.82131 + 2.82131i −0.117453 + 0.117453i −0.763390 0.645938i 0.776467π-0.776467\pi
0.645938 + 0.763390i 0.276467π0.276467\pi
578578 −3.00127 8.13236i −0.124836 0.338261i
579579 −1.68153 1.68153i −0.0698822 0.0698822i
580580 −1.64460 + 3.25190i −0.0682883 + 0.135028i
581581 18.0498 18.0498i 0.748833 0.748833i
582582 −10.0440 + 21.7939i −0.416338 + 0.903385i
583583 −5.28334 5.28334i −0.218813 0.218813i
584584 7.99066 + 28.2946i 0.330656 + 1.17084i
585585 5.21651 12.6934i 0.215676 0.524809i
586586 5.95884 2.19913i 0.246158 0.0908451i
587587 −45.9941 −1.89838 −0.949191 0.314702i 0.898095π-0.898095\pi
−0.949191 + 0.314702i 0.898095π0.898095\pi
588588 −2.14911 2.51509i −0.0886279 0.103721i
589589 2.18844 2.18844i 0.0901729 0.0901729i
590590 −7.61818 + 7.08321i −0.313636 + 0.291611i
591591 8.65121i 0.355863i
592592 −8.19088 1.29337i −0.336643 0.0531572i
593593 −7.77054 7.77054i −0.319098 0.319098i 0.529323 0.848421i 0.322446π-0.322446\pi
−0.848421 + 0.529323i 0.822446π0.822446\pi
594594 −6.05500 2.79053i −0.248439 0.114497i
595595 8.24392 20.0601i 0.337968 0.822385i
596596 9.03132 + 0.708650i 0.369937 + 0.0290274i
597597 22.3275i 0.913804i
598598 −15.1613 + 32.8977i −0.619994 + 1.34529i
599599 16.1877i 0.661413i 0.943734 + 0.330707i 0.107287π0.107287\pi
−0.943734 + 0.330707i 0.892713π0.892713\pi
600600 −13.5882 + 3.91914i −0.554738 + 0.159998i
601601 14.1986i 0.579174i −0.957152 0.289587i 0.906482π-0.906482\pi
0.957152 0.289587i 0.0935180π-0.0935180\pi
602602 19.4997 + 8.98672i 0.794749 + 0.366271i
603603 0.885549i 0.0360623i
604604 13.4226 11.4694i 0.546159 0.466685i
605605 −9.54082 + 23.2159i −0.387889 + 0.943860i
606606 5.60343 12.1585i 0.227624 0.493906i
607607 22.9646 + 22.9646i 0.932105 + 0.932105i 0.997837 0.0657320i 0.0209383π-0.0209383\pi
−0.0657320 + 0.997837i 0.520938π0.520938\pi
608608 −3.70495 + 5.55190i −0.150256 + 0.225159i
609609 2.39711i 0.0971359i
610610 22.0015 + 23.6632i 0.890813 + 0.958093i
611611 −53.1355 + 53.1355i −2.14963 + 2.14963i
612612 −0.515823 + 6.57387i −0.0208509 + 0.265733i
613613 37.1155 1.49908 0.749541 0.661958i 0.230274π-0.230274\pi
0.749541 + 0.661958i 0.230274π0.230274\pi
614614 1.88260 + 5.10116i 0.0759754 + 0.205866i
615615 9.25376 22.5174i 0.373148 0.907989i
616616 19.1548 34.2315i 0.771767 1.37923i
617617 −1.45005 1.45005i −0.0583767 0.0583767i 0.677316 0.735692i 0.263143π-0.263143\pi
−0.735692 + 0.677316i 0.763143π0.763143\pi
618618 24.3834 + 11.2375i 0.980846 + 0.452037i
619619 13.2111 13.2111i 0.530998 0.530998i −0.389872 0.920869i 0.627481π-0.627481\pi
0.920869 + 0.389872i 0.127481π0.127481\pi
620620 −3.65852 11.1453i −0.146930 0.447607i
621621 2.95105 + 2.95105i 0.118421 + 0.118421i
622622 5.40122 1.99333i 0.216569 0.0799254i
623623 18.1096 18.1096i 0.725548 0.725548i
624624 −24.2490 3.82900i −0.970735 0.153283i
625625 0.277973 + 24.9985i 0.0111189 + 0.999938i
626626 1.15456 2.50520i 0.0461454 0.100128i
627627 5.56251i 0.222145i
628628 23.5961 20.1625i 0.941587 0.804573i
629629 4.83312 + 4.83312i 0.192709 + 0.192709i
630630 6.81290 6.33448i 0.271432 0.252372i
631631 11.6636 0.464322 0.232161 0.972677i 0.425420π-0.425420\pi
0.232161 + 0.972677i 0.425420π0.425420\pi
632632 10.6710 19.0702i 0.424470 0.758572i
633633 5.27613 5.27613i 0.209707 0.209707i
634634 −13.0143 + 4.80294i −0.516862 + 0.190749i
635635 5.85641 + 14.0282i 0.232405 + 0.556692i
636636 −2.40985 + 2.05919i −0.0955569 + 0.0816521i
637637 −10.1519 −0.402232
638638 5.09666 1.88094i 0.201779 0.0744670i
639639 2.56877 0.101619
640640 12.4406 + 22.0279i 0.491760 + 0.870731i
641641 −20.8880 −0.825025 −0.412512 0.910952i 0.635349π-0.635349\pi
−0.412512 + 0.910952i 0.635349π0.635349\pi
642642 14.5368 5.36483i 0.573720 0.211733i
643643 −36.6130 −1.44388 −0.721939 0.691957i 0.756749π-0.756749\pi
−0.721939 + 0.691957i 0.756749π0.756749\pi
644644 −18.6677 + 15.9513i −0.735611 + 0.628569i
645645 −4.38655 + 10.6739i −0.172720 + 0.420284i
646646 5.16132 1.90480i 0.203070 0.0749434i
647647 23.8735 23.8735i 0.938562 0.938562i −0.0596566 0.998219i 0.519001π-0.519001\pi
0.998219 + 0.0596566i 0.0190006π0.0190006\pi
648648 −1.38116 + 2.46828i −0.0542571 + 0.0969631i
649649 15.5079 0.608737
650650 −17.9448 + 39.5138i −0.703854 + 1.54986i
651651 5.45626 + 5.45626i 0.213848 + 0.213848i
652652 13.1558 11.2414i 0.515219 0.440248i
653653 22.3501i 0.874627i −0.899309 0.437313i 0.855930π-0.855930\pi
0.899309 0.437313i 0.144070π-0.144070\pi
654654 −0.539047 + 1.16964i −0.0210784 + 0.0457367i
655655 −10.3197 + 4.30819i −0.403222 + 0.168335i
656656 −43.0162 6.79241i −1.67950 0.265199i
657657 7.35033 7.35033i 0.286764 0.286764i
658658 −47.7878 + 17.6362i −1.86296 + 0.687532i
659659 15.9700 + 15.9700i 0.622102 + 0.622102i 0.946068 0.323967i 0.105017π-0.105017\pi
−0.323967 + 0.946068i 0.605017π0.605017\pi
660660 18.8140 + 9.51489i 0.732334 + 0.370367i
661661 −15.1592 + 15.1592i −0.589624 + 0.589624i −0.937530 0.347906i 0.886893π-0.886893\pi
0.347906 + 0.937530i 0.386893π0.386893\pi
662662 13.0277 + 6.00402i 0.506338 + 0.233353i
663663 14.3084 + 14.3084i 0.555691 + 0.555691i
664664 11.9845 21.4176i 0.465090 0.831164i
665665 −7.17893 2.95026i −0.278387 0.114406i
666666 1.01507 + 2.75047i 0.0393330 + 0.106578i
667667 −3.40070 −0.131676
668668 0.634144 8.08179i 0.0245358 0.312694i
669669 13.8202 13.8202i 0.534320 0.534320i
670670 0.101834 2.79850i 0.00393420 0.108115i
671671 48.1696i 1.85957i
672672 −13.8421 9.23728i −0.533971 0.356336i
673673 15.2524 + 15.2524i 0.587938 + 0.587938i 0.937073 0.349134i 0.113524π-0.113524\pi
−0.349134 + 0.937073i 0.613524π0.613524\pi
674674 21.2280 46.0612i 0.817670 1.77421i
675675 3.55514 + 3.51582i 0.136837 + 0.135324i
676676 −37.5065 + 32.0488i −1.44256 + 1.23265i
677677 3.95511i 0.152007i 0.997108 + 0.0760036i 0.0242161π0.0242161\pi
−0.997108 + 0.0760036i 0.975784π0.975784\pi
678678 −16.7029 7.69779i −0.641473 0.295632i
679679 49.9175i 1.91566i
680680 2.38606 20.7153i 0.0915014 0.794396i
681681 1.66286i 0.0637209i
682682 −7.31957 + 15.8823i −0.280281 + 0.608164i
683683 50.9345i 1.94895i 0.224490 + 0.974476i 0.427928π0.427928\pi
−0.224490 + 0.974476i 0.572072π0.572072\pi
684684 2.35259 + 0.184598i 0.0899537 + 0.00705828i
685685 9.19242 + 22.0191i 0.351224 + 0.841308i
686686 20.1987 + 9.30886i 0.771191 + 0.355414i
687687 11.3744 + 11.3744i 0.433962 + 0.433962i
688688 20.3909 + 3.21980i 0.777395 + 0.122754i
689689 9.72710i 0.370573i
690690 −8.98650 9.66521i −0.342110 0.367948i
691691 −13.5869 + 13.5869i −0.516870 + 0.516870i −0.916623 0.399753i 0.869096π-0.869096\pi
0.399753 + 0.916623i 0.369096π0.369096\pi
692692 19.6372 + 22.9813i 0.746496 + 0.873619i
693693 −13.8686 −0.526824
694694 11.6826 4.31151i 0.443467 0.163663i
695695 −8.29534 + 3.46309i −0.314660 + 0.131362i
696696 −0.626380 2.21799i −0.0237429 0.0840727i
697697 25.3822 + 25.3822i 0.961418 + 0.961418i
698698 12.3984 26.9025i 0.469286 1.01827i
699699 9.38976 9.38976i 0.355153 0.355153i
700700 −22.2585 + 19.2347i −0.841291 + 0.727002i
701701 −0.627254 0.627254i −0.0236911 0.0236911i 0.695162 0.718853i 0.255333π-0.255333\pi
−0.718853 + 0.695162i 0.755333π0.755333\pi
702702 3.00509 + 8.14270i 0.113420 + 0.307327i
703703 1.72963 1.72963i 0.0652343 0.0652343i
704704 8.77853 36.6789i 0.330853 1.38239i
705705 −10.5474 25.2649i −0.397239 0.951529i
706706 38.7301 + 17.8493i 1.45763 + 0.671768i
707707 27.8483i 1.04734i
708708 0.514646 6.55886i 0.0193416 0.246497i
709709 26.7170 + 26.7170i 1.00338 + 1.00338i 0.999994 + 0.00338478i 0.00107741π0.00107741\pi
0.00338478 + 0.999994i 0.498923π0.498923\pi
710710 −8.11779 0.295398i −0.304655 0.0110861i
711711 −7.72612 −0.289752
712712 12.0243 21.4886i 0.450628 0.805318i
713713 7.74061 7.74061i 0.289888 0.289888i
714714 4.74910 + 12.8683i 0.177730 + 0.481586i
715715 59.7036 24.9247i 2.23279 0.932131i
716716 −34.8709 2.73617i −1.30319 0.102256i
717717 8.88914 0.331971
718718 4.59760 + 12.4578i 0.171581 + 0.464922i
719719 −27.5794 −1.02854 −0.514269 0.857629i 0.671937π-0.671937\pi
−0.514269 + 0.857629i 0.671937π0.671937\pi
720720 4.64857 7.64139i 0.173242 0.284778i
721721 55.8488 2.07992
722722 8.62147 + 23.3611i 0.320858 + 0.869409i
723723 20.5978 0.766041
724724 −2.12181 + 27.0413i −0.0788565 + 1.00498i
725725 −4.07418 + 0.0226510i −0.151311 + 0.000841235i
726726 −5.49621 14.8927i −0.203983 0.552721i
727727 8.11985 8.11985i 0.301148 0.301148i −0.540315 0.841463i 0.681695π-0.681695\pi
0.841463 + 0.540315i 0.181695π0.181695\pi
728728 −49.1445 + 13.8788i −1.82142 + 0.514384i
729729 1.00000 0.0370370
730730 −24.0737 + 22.3831i −0.891006 + 0.828437i
731731 −12.0319 12.0319i −0.445014 0.445014i
732732 −20.3727 1.59856i −0.752998 0.0590845i
733733 12.3271i 0.455313i 0.973742 + 0.227656i 0.0731063π0.0731063\pi
−0.973742 + 0.227656i 0.926894π0.926894\pi
734734 0.235503 + 0.108535i 0.00869256 + 0.00400609i
735735 1.40593 3.42109i 0.0518586 0.126189i
736736 −13.1046 + 19.6373i −0.483042 + 0.723842i
737737 −2.95201 + 2.95201i −0.108739 + 0.108739i
738738 5.33084 + 14.4447i 0.196231 + 0.531715i
739739 24.8212 + 24.8212i 0.913062 + 0.913062i 0.996512 0.0834496i 0.0265938π-0.0265938\pi
−0.0834496 + 0.996512i 0.526594π0.526594\pi
740740 −2.89151 8.80871i −0.106294 0.323815i
741741 5.12054 5.12054i 0.188108 0.188108i
742742 −2.75981 + 5.98834i −0.101316 + 0.219839i
743743 −26.8731 26.8731i −0.985877 0.985877i 0.0140246 0.999902i 0.495536π-0.495536\pi
−0.999902 + 0.0140246i 0.995536π0.995536\pi
744744 6.47430 + 3.62279i 0.237359 + 0.132818i
745745 3.90195 + 9.34658i 0.142957 + 0.342432i
746746 3.79180 1.39937i 0.138828 0.0512347i
747747 −8.67714 −0.317480
748748 −23.6338 + 20.1947i −0.864137 + 0.738393i
749749 22.7917 22.7917i 0.832789 0.832789i
750750 −10.8306 11.5195i −0.395477 0.420632i
751751 24.7594i 0.903484i −0.892149 0.451742i 0.850803π-0.850803\pi
0.892149 0.451742i 0.149197π-0.149197\pi
752752 −39.6085 + 28.8056i −1.44437 + 1.05043i
753753 16.8455 + 16.8455i 0.613883 + 0.613883i
754754 −6.42319 2.96022i −0.233919 0.107805i
755755 18.2578 + 7.50322i 0.664468 + 0.273070i
756756 −0.460244 + 5.86555i −0.0167389 + 0.213328i
757757 35.5014i 1.29032i 0.764047 + 0.645160i 0.223209π0.223209\pi
−0.764047 + 0.645160i 0.776791π0.776791\pi
758758 12.3971 26.8997i 0.450284 0.977042i
759759 19.6749i 0.714153i
760760 −7.41341 0.853903i −0.268913 0.0309743i
761761 19.8569i 0.719812i −0.932989 0.359906i 0.882809π-0.882809\pi
0.932989 0.359906i 0.117191π-0.117191\pi
762762 −8.73165 4.02411i −0.316314 0.145778i
763763 2.67900i 0.0969862i
764764 −18.8448 22.0540i −0.681782 0.797886i
765765 −6.80334 + 2.84022i −0.245975 + 0.102688i
766766 18.6609 40.4911i 0.674245 1.46300i
767767 −14.2757 14.2757i −0.515465 0.515465i
768768 −15.2215 4.93000i −0.549260 0.177896i
769769 37.1951i 1.34129i −0.741779 0.670644i 0.766018π-0.766018\pi
0.741779 0.670644i 0.233982π-0.233982\pi
770770 43.8273 + 1.59483i 1.57943 + 0.0574736i
771771 −14.1500 + 14.1500i −0.509600 + 0.509600i
772772 −4.74152 0.372047i −0.170651 0.0133903i
773773 13.2454 0.476402 0.238201 0.971216i 0.423442π-0.423442\pi
0.238201 + 0.971216i 0.423442π0.423442\pi
774774 −2.52697 6.84718i −0.0908301 0.246117i
775775 9.22202 9.32514i 0.331265 0.334969i
776776 13.0437 + 46.1874i 0.468243 + 1.65803i
777777 4.31236 + 4.31236i 0.154705 + 0.154705i
778778 −31.0841 14.3255i −1.11442 0.513595i
779779 9.08353 9.08353i 0.325451 0.325451i
780780 −8.56026 26.0780i −0.306506 0.933743i
781781 8.56310 + 8.56310i 0.306412 + 0.306412i
782782 18.2559 6.73738i 0.652828 0.240928i
783783 −0.576185 + 0.576185i −0.0205912 + 0.0205912i
784784 −6.53548 1.03198i −0.233410 0.0368563i
785785 32.0959 + 13.1902i 1.14555 + 0.470777i
786786 2.96028 6.42332i 0.105590 0.229112i
787787 12.0292i 0.428794i 0.976747 + 0.214397i 0.0687786π0.0687786\pi
−0.976747 + 0.214397i 0.931221π0.931221\pi
788788 −11.2401 13.1542i −0.400412 0.468600i
789789 11.1204 + 11.1204i 0.395896 + 0.395896i
790790 24.4160 + 0.888470i 0.868681 + 0.0316104i
791791 −38.2571 −1.36026
792792 −12.8323 + 3.62395i −0.455975 + 0.128771i
793793 −44.3423 + 44.3423i −1.57464 + 1.57464i
794794 −21.6002 + 7.97161i −0.766562 + 0.282902i
795795 −3.27794 1.34710i −0.116256 0.0477768i
796796 29.0091 + 33.9491i 1.02820 + 1.20329i
797797 −45.2714 −1.60359 −0.801797 0.597597i 0.796122π-0.796122\pi
−0.801797 + 0.597597i 0.796122π0.796122\pi
798798 4.60520 1.69956i 0.163022 0.0601639i
799799 40.3685 1.42813
800800 −15.5691 + 23.6136i −0.550450 + 0.834868i
801801 −8.70590 −0.307608
802802 −6.81762 + 2.51606i −0.240738 + 0.0888451i
803803 49.0053 1.72936
804804 1.15055 + 1.34648i 0.0405768 + 0.0474868i
805805 −25.3922 10.4352i −0.894958 0.367793i
806806 21.3584 7.88236i 0.752316 0.277644i
807807 −10.2902 + 10.2902i −0.362231 + 0.362231i
808808 −7.27694 25.7674i −0.256002 0.906494i
809809 5.16391 0.181553 0.0907767 0.995871i 0.471065π-0.471065\pi
0.0907767 + 0.995871i 0.471065π0.471065\pi
810810 −3.16019 0.114996i −0.111038 0.00404054i
811811 15.7171 + 15.7171i 0.551903 + 0.551903i 0.926990 0.375087i 0.122387π-0.122387\pi
−0.375087 + 0.926990i 0.622387π0.622387\pi
812812 −3.11446 3.64483i −0.109296 0.127908i
813813 21.3325i 0.748163i
814814 −5.78503 + 12.5526i −0.202765 + 0.439967i
815815 17.8947 + 7.35404i 0.626826 + 0.257601i
816816 7.75680 + 10.6658i 0.271542 + 0.373378i
817817 −4.30585 + 4.30585i −0.150643 + 0.150643i
818818 5.16103 1.90469i 0.180451 0.0665959i
819819 12.7667 + 12.7667i 0.446103 + 0.446103i
820820 −15.1854 46.2608i −0.530296 1.61550i
821821 −15.6816 + 15.6816i −0.547293 + 0.547293i −0.925657 0.378364i 0.876487π-0.876487\pi
0.378364 + 0.925657i 0.376487π0.376487\pi
822822 −13.7055 6.31637i −0.478034 0.220309i
823823 −3.65203 3.65203i −0.127302 0.127302i 0.640585 0.767887i 0.278692π-0.278692\pi
−0.767887 + 0.640585i 0.778692π0.778692\pi
824824 51.6755 14.5936i 1.80020 0.508393i
825825 0.131048 + 23.5713i 0.00456251 + 0.820649i
826826 −4.73825 12.8390i −0.164865 0.446725i
827827 14.0926 0.490046 0.245023 0.969517i 0.421204π-0.421204\pi
0.245023 + 0.969517i 0.421204π0.421204\pi
828828 8.32124 + 0.652933i 0.289183 + 0.0226910i
829829 −12.1216 + 12.1216i −0.421000 + 0.421000i −0.885548 0.464548i 0.846217π-0.846217\pi
0.464548 + 0.885548i 0.346217π0.346217\pi
830830 27.4214 + 0.997834i 0.951810 + 0.0346353i
831831 19.0041i 0.659244i
832832 −41.8456 + 25.6835i −1.45073 + 0.890415i
833833 3.85633 + 3.85633i 0.133614 + 0.133614i
834834 2.37959 5.16331i 0.0823983 0.178791i
835835 8.36390 3.49171i 0.289445 0.120836i
836836 7.22711 + 8.45784i 0.249955 + 0.292520i
837837 2.62300i 0.0906643i
838838 17.5992 + 8.11083i 0.607954 + 0.280184i
839839 14.6206i 0.504759i −0.967628 0.252380i 0.918787π-0.918787\pi
0.967628 0.252380i 0.0812132π-0.0812132\pi
840840 2.12897 18.4833i 0.0734565 0.637734i
841841 28.3360i 0.977104i
842842 16.1451 35.0321i 0.556395 1.20729i
843843 3.86317i 0.133054i
844844 1.16737 14.8774i 0.0401825 0.512102i
845845 −51.0172 20.9661i −1.75504 0.721254i
846846 15.7257 + 7.24743i 0.540662 + 0.249172i
847847 −23.3498 23.3498i −0.802309 0.802309i
848848 −0.988796 + 6.26202i −0.0339554 + 0.215039i
849849 5.89151i 0.202196i
850850 21.8264 8.19326i 0.748640 0.281026i
851851 6.11779 6.11779i 0.209715 0.209715i
852852 3.90583 3.33748i 0.133812 0.114340i
853853 13.7252 0.469940 0.234970 0.972003i 0.424501π-0.424501\pi
0.234970 + 0.972003i 0.424501π0.424501\pi
854854 −39.8796 + 14.7177i −1.36465 + 0.503629i
855855 1.01643 + 2.43472i 0.0347612 + 0.0832655i
856856 15.1330 27.0442i 0.517234 0.924351i
857857 18.7921 + 18.7921i 0.641927 + 0.641927i 0.951029 0.309102i 0.100028π-0.100028\pi
−0.309102 + 0.951029i 0.600028π0.600028\pi
858858 −17.1265 + 37.1616i −0.584688 + 1.26868i
859859 23.1774 23.1774i 0.790803 0.790803i −0.190822 0.981625i 0.561115π-0.561115\pi
0.981625 + 0.190822i 0.0611152π0.0611152\pi
860860 7.19830 + 21.9290i 0.245460 + 0.747771i
861861 22.6473 + 22.6473i 0.771817 + 0.771817i
862862 −2.02236 5.47988i −0.0688820 0.186645i
863863 −8.96863 + 8.96863i −0.305296 + 0.305296i −0.843082 0.537786i 0.819261π-0.819261\pi
0.537786 + 0.843082i 0.319261π0.319261\pi
864864 1.10685 + 5.54751i 0.0376558 + 0.188730i
865865 −12.8465 + 31.2597i −0.436795 + 1.06286i
866866 −24.2145 11.1596i −0.822843 0.379219i
867867 6.12955i 0.208171i
868868 15.3854 + 1.20722i 0.522213 + 0.0409758i
869869 −25.7553 25.7553i −0.873690 0.873690i
870870 1.88711 1.75459i 0.0639791 0.0594863i
871871 5.43492 0.184155
872872 0.700039 + 2.47881i 0.0237063 + 0.0839431i
873873 11.9985 11.9985i 0.406087 0.406087i
874874 −2.41111 6.53324i −0.0815570 0.220990i
875875 −30.4905 12.3327i −1.03077 0.416921i
876876 1.62629 20.7262i 0.0549474 0.700272i
877877 −47.1944 −1.59364 −0.796822 0.604215i 0.793487π-0.793487\pi
−0.796822 + 0.604215i 0.793487π0.793487\pi
878878 10.8098 + 29.2906i 0.364812 + 0.988510i
879879 −4.49132 −0.151489
880880 40.9691 9.97669i 1.38107 0.336314i
881881 51.5667 1.73733 0.868663 0.495403i 0.164980π-0.164980\pi
0.868663 + 0.495403i 0.164980π0.164980\pi
882882 0.809919 + 2.19459i 0.0272714 + 0.0738956i
883883 −33.7083 −1.13438 −0.567188 0.823589i 0.691969π-0.691969\pi
−0.567188 + 0.823589i 0.691969π0.691969\pi
884884 40.3461 + 3.16579i 1.35699 + 0.106477i
885885 6.78780 2.83373i 0.228170 0.0952548i
886886 −4.13681 11.2093i −0.138979 0.376582i
887887 4.91204 4.91204i 0.164930 0.164930i −0.619817 0.784747i 0.712793π-0.712793\pi
0.784747 + 0.619817i 0.212793π0.212793\pi
888888 5.11697 + 2.86327i 0.171714 + 0.0960852i
889889 −19.9993 −0.670755
890890 27.5123 + 1.00114i 0.922213 + 0.0335583i
891891 3.33354 + 3.33354i 0.111678 + 0.111678i
892892 3.05778 38.9696i 0.102382 1.30480i
893893 14.4467i 0.483440i
894894 −5.81764 2.68114i −0.194571 0.0896708i
895895 −15.0659 36.0881i −0.503596 1.20629i
896896 −33.0486 + 3.93907i −1.10408 + 0.131595i
897897 18.1116 18.1116i 0.604729 0.604729i
898898 6.03475 + 16.3520i 0.201382 + 0.545673i
899899 1.51134 + 1.51134i 0.0504059 + 0.0504059i
900900 9.97355 + 0.726816i 0.332452 + 0.0242272i
901901 3.69497 3.69497i 0.123097 0.123097i
902902 −30.3813 + 65.9225i −1.01159 + 2.19498i
903903 −10.7355 10.7355i −0.357254 0.357254i
904904 −35.3983 + 9.99680i −1.17733 + 0.332489i
905905 −27.9852 + 11.6831i −0.930259 + 0.388359i
906906 −11.7121 + 4.32240i −0.389110 + 0.143602i
907907 −39.4081 −1.30852 −0.654262 0.756268i 0.727021π-0.727021\pi
−0.654262 + 0.756268i 0.727021π0.727021\pi
908908 2.16047 + 2.52839i 0.0716978 + 0.0839075i
909909 −6.69380 + 6.69380i −0.222019 + 0.222019i
910910 −38.8769 41.8131i −1.28876 1.38609i
911911 7.29607i 0.241729i −0.992669 0.120865i 0.961433π-0.961433\pi
0.992669 0.120865i 0.0385667π-0.0385667\pi
912912 3.81698 2.77593i 0.126393 0.0919203i
913913 −28.9256 28.9256i −0.957298 0.957298i
914914 −19.2243 8.85977i −0.635882 0.293055i
915915 −8.80197 21.0839i −0.290984 0.697012i
916916 32.0732 + 2.51664i 1.05973 + 0.0831523i
917917 14.7122i 0.485840i
918918 1.95159 4.23464i 0.0644122 0.139764i
919919 52.5346i 1.73296i −0.499215 0.866478i 0.666378π-0.666378\pi
0.499215 0.866478i 0.333622π-0.333622\pi
920920 −26.2216 3.02030i −0.864500 0.0995762i
921921 3.84487i 0.126693i
922922 12.2984 + 5.66789i 0.405026 + 0.186662i
923923 15.7654i 0.518926i
924924 −21.0873 + 18.0188i −0.693721 + 0.592775i
925925 7.28862 7.37012i 0.239648 0.242328i
926926 9.50727 20.6292i 0.312428 0.677918i
927927 −13.4242 13.4242i −0.440907 0.440907i
928928 −3.83415 2.55864i −0.125862 0.0839916i
929929 48.7878i 1.60068i 0.599549 + 0.800338i 0.295346π0.295346\pi
−0.599549 + 0.800338i 0.704654π0.704654\pi
930930 −0.301634 + 8.28918i −0.00989098 + 0.271813i
931931 1.38007 1.38007i 0.0452299 0.0452299i
932932 2.07753 26.4769i 0.0680517 0.867278i
933933 −4.07103 −0.133279
934934 1.52561 + 4.13385i 0.0499194 + 0.135264i
935935 −32.1472 13.2112i −1.05133 0.432054i
936936 15.1487 + 8.47667i 0.495150 + 0.277069i
937937 −29.3163 29.3163i −0.957722 0.957722i 0.0414198 0.999142i 0.486812π-0.486812\pi
−0.999142 + 0.0414198i 0.986812π0.986812\pi
938938 3.34593 + 1.54202i 0.109248 + 0.0503487i
939939 −1.37922 + 1.37922i −0.0450093 + 0.0450093i
940940 −48.8629 24.7116i −1.59373 0.806004i
941941 −7.65378 7.65378i −0.249506 0.249506i 0.571262 0.820768i 0.306454π-0.306454\pi
−0.820768 + 0.571262i 0.806454π0.806454\pi
942942 −20.5892 + 7.59850i −0.670832 + 0.247572i
943943 32.1289 32.1289i 1.04626 1.04626i
944944 −7.73909 10.6414i −0.251886 0.346349i
945945 −6.07029 + 2.53419i −0.197467 + 0.0824372i
946946 14.4016 31.2491i 0.468237 1.01600i
947947 39.6694i 1.28908i −0.764569 0.644541i 0.777048π-0.777048\pi
0.764569 0.644541i 0.222952π-0.222952\pi
948948 −11.7476 + 10.0382i −0.381545 + 0.326025i
949949 −45.1116 45.1116i −1.46438 1.46438i
950950 −2.93213 7.81104i −0.0951308 0.253424i
951951 9.80915 0.318084
952952 23.9403 + 13.3961i 0.775908 + 0.434171i
953953 8.83095 8.83095i 0.286063 0.286063i −0.549458 0.835521i 0.685166π-0.685166\pi
0.835521 + 0.549458i 0.185166π0.185166\pi
954954 2.10276 0.776029i 0.0680794 0.0251249i
955955 12.3281 29.9983i 0.398929 0.970724i
956956 13.5160 11.5492i 0.437139 0.373529i
957957 −3.84148 −0.124177
958958 20.3666 7.51635i 0.658015 0.242842i
959959 −31.3916 −1.01369
960960 −2.85991 17.6585i −0.0923033 0.569924i
961961 24.1198 0.778060
962962 16.8806 6.22982i 0.544252 0.200858i
963963 −10.9567 −0.353075
964964 31.3191 26.7618i 1.00872 0.861938i
965965 −2.04856 4.90703i −0.0659455 0.157963i
966966 16.2888 6.01144i 0.524085 0.193415i
967967 −2.42314 + 2.42314i −0.0779231 + 0.0779231i −0.744994 0.667071i 0.767548π-0.767548\pi
0.667071 + 0.744994i 0.267548π0.267548\pi
968968 −27.7065 15.5036i −0.890519 0.498303i
969969 −3.89021 −0.124972
970970 −39.2972 + 36.5377i −1.26176 + 1.17315i
971971 21.9788 + 21.9788i 0.705334 + 0.705334i 0.965550 0.260216i 0.0837939π-0.0837939\pi
−0.260216 + 0.965550i 0.583794π0.583794\pi
972972 1.52051 1.29925i 0.0487703 0.0416735i
973973 11.8263i 0.379132i
974974 −7.12671 + 15.4638i −0.228355 + 0.495492i
975975 21.5778 21.8191i 0.691044 0.698771i
976976 −33.0538 + 24.0387i −1.05803 + 0.769460i
977977 32.7193 32.7193i 1.04678 1.04678i 0.0479337 0.998851i 0.484736π-0.484736\pi
0.998851 0.0479337i 0.0152636π-0.0152636\pi
978978 −11.4793 + 4.23646i −0.367067 + 0.135467i
979979 −29.0215 29.0215i −0.927531 0.927531i
980980 −2.30713 7.02845i −0.0736984 0.224515i
981981 0.643941 0.643941i 0.0205595 0.0205595i
982982 11.1952 + 5.15949i 0.357255 + 0.164646i
983983 27.7480 + 27.7480i 0.885023 + 0.885023i 0.994040 0.109017i 0.0347703π-0.0347703\pi
−0.109017 + 0.994040i 0.534770π0.534770\pi
984984 26.8729 + 15.0371i 0.856675 + 0.479365i
985985 7.35318 17.8927i 0.234292 0.570108i
986986 1.31546 + 3.56442i 0.0418927 + 0.113514i
987987 36.0188 1.14649
988988 1.13294 14.4387i 0.0360437 0.459356i
989989 −15.2300 + 15.2300i −0.484286 + 0.484286i
990990 −10.1513 10.9180i −0.322629 0.346996i
991991 24.6172i 0.781991i −0.920393 0.390996i 0.872131π-0.872131\pi
0.920393 0.390996i 0.127869π-0.127869\pi
992992 14.5511 2.90327i 0.461999 0.0921790i
993993 −7.17235 7.17235i −0.227608 0.227608i
994994 4.47303 9.70575i 0.141876 0.307848i
995995 −18.9775 + 46.1784i −0.601627 + 1.46395i
996996 −13.1937 + 11.2738i −0.418057 + 0.357224i
997997 36.9465i 1.17011i 0.810995 + 0.585053i 0.198926π0.198926\pi
−0.810995 + 0.585053i 0.801074π0.801074\pi
998998 29.4184 + 13.5579i 0.931222 + 0.429167i
999999 2.07309i 0.0655897i
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 240.2.y.e.163.1 16
3.2 odd 2 720.2.z.f.163.8 16
4.3 odd 2 960.2.y.e.943.7 16
5.2 odd 4 240.2.bc.e.67.4 yes 16
8.3 odd 2 1920.2.y.j.223.2 16
8.5 even 2 1920.2.y.i.223.2 16
15.2 even 4 720.2.bd.f.307.5 16
16.3 odd 4 1920.2.bc.i.1183.6 16
16.5 even 4 960.2.bc.e.463.3 16
16.11 odd 4 240.2.bc.e.43.4 yes 16
16.13 even 4 1920.2.bc.j.1183.6 16
20.7 even 4 960.2.bc.e.367.3 16
40.27 even 4 1920.2.bc.j.607.6 16
40.37 odd 4 1920.2.bc.i.607.6 16
48.11 even 4 720.2.bd.f.523.5 16
80.27 even 4 inner 240.2.y.e.187.1 yes 16
80.37 odd 4 960.2.y.e.847.7 16
80.67 even 4 1920.2.y.i.1567.2 16
80.77 odd 4 1920.2.y.j.1567.2 16
240.107 odd 4 720.2.z.f.667.8 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
240.2.y.e.163.1 16 1.1 even 1 trivial
240.2.y.e.187.1 yes 16 80.27 even 4 inner
240.2.bc.e.43.4 yes 16 16.11 odd 4
240.2.bc.e.67.4 yes 16 5.2 odd 4
720.2.z.f.163.8 16 3.2 odd 2
720.2.z.f.667.8 16 240.107 odd 4
720.2.bd.f.307.5 16 15.2 even 4
720.2.bd.f.523.5 16 48.11 even 4
960.2.y.e.847.7 16 80.37 odd 4
960.2.y.e.943.7 16 4.3 odd 2
960.2.bc.e.367.3 16 20.7 even 4
960.2.bc.e.463.3 16 16.5 even 4
1920.2.y.i.223.2 16 8.5 even 2
1920.2.y.i.1567.2 16 80.67 even 4
1920.2.y.j.223.2 16 8.3 odd 2
1920.2.y.j.1567.2 16 80.77 odd 4
1920.2.bc.i.607.6 16 40.37 odd 4
1920.2.bc.i.1183.6 16 16.3 odd 4
1920.2.bc.j.607.6 16 40.27 even 4
1920.2.bc.j.1183.6 16 16.13 even 4