Properties

Label 784.2.x.j.557.1
Level 784784
Weight 22
Character 784.557
Analytic conductor 6.2606.260
Analytic rank 00
Dimension 1616
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [784,2,Mod(165,784)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(784, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("784.165");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 784=2472 784 = 2^{4} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 784.x (of order 1212, degree 44, not 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: 6.260271518476.26027151847
Analytic rank: 00
Dimension: 1616
Relative dimension: 44 over Q(ζ12)\Q(\zeta_{12})
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: x162x15+4x14+4x1313x12+32x114x1034x9+121x8++256 x^{16} - 2 x^{15} + 4 x^{14} + 4 x^{13} - 13 x^{12} + 32 x^{11} - 4 x^{10} - 34 x^{9} + 121 x^{8} + \cdots + 256 Copy content Toggle raw display
Coefficient ring: Z[a1,,a9]\Z[a_1, \ldots, a_{9}]
Coefficient ring index: 22 2^{2}
Twist minimal: no (minimal twist has level 112)
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 557.1
Root 1.40526+0.158880i-1.40526 + 0.158880i of defining polynomial
Character χ\chi == 784.557
Dual form 784.2.x.j.373.1

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+(1.274040.613848i)q2+(2.68432+0.719263i)q3+(1.24638+1.56414i)q4+(0.8575920.229791i)q5+(3.86147+0.731395i)q6+(0.6278012.75787i)q8+(4.090182.36147i)q9+(0.951553+0.819195i)q10+(1.36269+5.08562i)q11+(4.470723.30218i)q12+(2.220662.22066i)q13+2.46733q15+(0.893069+3.89903i)q16+(1.627802.81943i)q17+(6.66066+0.497865i)q18+(0.6716532.50664i)q19+(0.7094601.62780i)q20+(1.385677.31580i)q22+(6.627743.82653i)q23+(3.66886+6.95147i)q24+(3.647472.10587i)q25+(1.46607+4.19237i)q26+(3.38567+3.38567i)q27+(1.537211.53721i)q29+(3.143491.51457i)q30+(1.22066+2.11425i)q31+(3.531224.41933i)q32+(7.3158012.6713i)q33+(3.80460+2.59286i)q34+(8.79159+3.45433i)q36+(1.72139+0.461245i)q37+(2.39441+2.78128i)q38+(7.55822+4.36374i)q39+(0.0953379+2.50939i)q40+7.77589iq41+(7.51575+7.51575i)q43+(6.25620+8.47006i)q44+(4.05035+1.08529i)q45+(10.7930+0.806742i)q46+(5.55792+9.62661i)q47+(0.40713811.1086i)q48+(3.35436+4.92196i)q50+(2.34163+8.73909i)q51+(0.7056366.24122i)q52+(1.07250+4.00262i)q53+(6.391792.23521i)q544.67452iq55+7.21173iq57+(1.01486+2.90209i)q58+(2.50344+9.34298i)q59+(3.07524+3.85926i)q60+(1.23431+4.60651i)q61+(2.853011.94435i)q62+(7.21173+3.46279i)q64+(1.39413+2.41471i)q65+(1.54238+20.6346i)q66+(1.26436+0.338785i)q67+(6.438850.967979i)q68+(15.0387+15.0387i)q6912.1113iq71+(9.080459.79767i)q72+(5.555013.20719i)q73+(1.910001.64432i)q74+(11.3057+3.02934i)q75+(4.757872.07367i)q76+(6.9508410.1992i)q78+(3.64128+6.30687i)q79+(1.661853.13856i)q80+(0.431344+0.747110i)q81+(4.773229.90684i)q82+(1.96506+1.96506i)q83+(2.04387+2.04387i)q85+(14.18894.96187i)q86+(5.23203+3.02071i)q87+(13.17006.95088i)q88+(0.576282+0.332717i)q89+(5.82653+1.10359i)q90+(14.2459+5.59741i)q92+(1.755956.55331i)q93+(1.1717715.6765i)q94+(1.15201+1.99533i)q95+(6.30029+14.4028i)q96+8.34450q97+(17.5832+17.5832i)q99+O(q100)q+(-1.27404 - 0.613848i) q^{2} +(-2.68432 + 0.719263i) q^{3} +(1.24638 + 1.56414i) q^{4} +(-0.857592 - 0.229791i) q^{5} +(3.86147 + 0.731395i) q^{6} +(-0.627801 - 2.75787i) q^{8} +(4.09018 - 2.36147i) q^{9} +(0.951553 + 0.819195i) q^{10} +(1.36269 + 5.08562i) q^{11} +(-4.47072 - 3.30218i) q^{12} +(-2.22066 - 2.22066i) q^{13} +2.46733 q^{15} +(-0.893069 + 3.89903i) q^{16} +(1.62780 - 2.81943i) q^{17} +(-6.66066 + 0.497865i) q^{18} +(0.671653 - 2.50664i) q^{19} +(-0.709460 - 1.62780i) q^{20} +(1.38567 - 7.31580i) q^{22} +(6.62774 - 3.82653i) q^{23} +(3.66886 + 6.95147i) q^{24} +(-3.64747 - 2.10587i) q^{25} +(1.46607 + 4.19237i) q^{26} +(-3.38567 + 3.38567i) q^{27} +(-1.53721 - 1.53721i) q^{29} +(-3.14349 - 1.51457i) q^{30} +(-1.22066 + 2.11425i) q^{31} +(3.53122 - 4.41933i) q^{32} +(-7.31580 - 12.6713i) q^{33} +(-3.80460 + 2.59286i) q^{34} +(8.79159 + 3.45433i) q^{36} +(1.72139 + 0.461245i) q^{37} +(-2.39441 + 2.78128i) q^{38} +(7.55822 + 4.36374i) q^{39} +(-0.0953379 + 2.50939i) q^{40} +7.77589i q^{41} +(-7.51575 + 7.51575i) q^{43} +(-6.25620 + 8.47006i) q^{44} +(-4.05035 + 1.08529i) q^{45} +(-10.7930 + 0.806742i) q^{46} +(5.55792 + 9.62661i) q^{47} +(-0.407138 - 11.1086i) q^{48} +(3.35436 + 4.92196i) q^{50} +(-2.34163 + 8.73909i) q^{51} +(0.705636 - 6.24122i) q^{52} +(1.07250 + 4.00262i) q^{53} +(6.39179 - 2.23521i) q^{54} -4.67452i q^{55} +7.21173i q^{57} +(1.01486 + 2.90209i) q^{58} +(2.50344 + 9.34298i) q^{59} +(3.07524 + 3.85926i) q^{60} +(-1.23431 + 4.60651i) q^{61} +(2.85301 - 1.94435i) q^{62} +(-7.21173 + 3.46279i) q^{64} +(1.39413 + 2.41471i) q^{65} +(1.54238 + 20.6346i) q^{66} +(-1.26436 + 0.338785i) q^{67} +(6.43885 - 0.967979i) q^{68} +(-15.0387 + 15.0387i) q^{69} -12.1113i q^{71} +(-9.08045 - 9.79767i) q^{72} +(-5.55501 - 3.20719i) q^{73} +(-1.91000 - 1.64432i) q^{74} +(11.3057 + 3.02934i) q^{75} +(4.75787 - 2.07367i) q^{76} +(-6.95084 - 10.1992i) q^{78} +(3.64128 + 6.30687i) q^{79} +(1.66185 - 3.13856i) q^{80} +(-0.431344 + 0.747110i) q^{81} +(4.77322 - 9.90684i) q^{82} +(1.96506 + 1.96506i) q^{83} +(-2.04387 + 2.04387i) q^{85} +(14.1889 - 4.96187i) q^{86} +(5.23203 + 3.02071i) q^{87} +(13.1700 - 6.95088i) q^{88} +(-0.576282 + 0.332717i) q^{89} +(5.82653 + 1.10359i) q^{90} +(14.2459 + 5.59741i) q^{92} +(1.75595 - 6.55331i) q^{93} +(-1.17177 - 15.6765i) q^{94} +(-1.15201 + 1.99533i) q^{95} +(-6.30029 + 14.4028i) q^{96} +8.34450 q^{97} +(17.5832 + 17.5832i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q2q24q44q5+32q68q8+12q1012q1216q158q16+24q176q1812q19+16q208q22+8q2624q2732q2920q30++96q99+O(q100) 16 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 32 q^{6} - 8 q^{8} + 12 q^{10} - 12 q^{12} - 16 q^{15} - 8 q^{16} + 24 q^{17} - 6 q^{18} - 12 q^{19} + 16 q^{20} - 8 q^{22} + 8 q^{26} - 24 q^{27} - 32 q^{29} - 20 q^{30}+ \cdots + 96 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/784Z)×\left(\mathbb{Z}/784\mathbb{Z}\right)^\times.

nn 197197 687687 689689
χ(n)\chi(n) e(34)e\left(\frac{3}{4}\right) 11 e(23)e\left(\frac{2}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.27404 0.613848i −0.900886 0.434056i
33 −2.68432 + 0.719263i −1.54980 + 0.415266i −0.929415 0.369035i 0.879688π-0.879688\pi
−0.620380 + 0.784301i 0.713022π0.713022\pi
44 1.24638 + 1.56414i 0.623190 + 0.782070i
55 −0.857592 0.229791i −0.383527 0.102766i 0.0619040 0.998082i 0.480283π-0.480283\pi
−0.445431 + 0.895316i 0.646949π0.646949\pi
66 3.86147 + 0.731395i 1.57644 + 0.298591i
77 0 0
88 −0.627801 2.75787i −0.221961 0.975056i
99 4.09018 2.36147i 1.36339 0.787156i
1010 0.951553 + 0.819195i 0.300908 + 0.259052i
1111 1.36269 + 5.08562i 0.410866 + 1.53337i 0.792974 + 0.609256i 0.208532π0.208532\pi
−0.382108 + 0.924118i 0.624802π0.624802\pi
1212 −4.47072 3.30218i −1.29059 0.953259i
1313 −2.22066 2.22066i −0.615901 0.615901i 0.328576 0.944477i 0.393431π-0.393431\pi
−0.944477 + 0.328576i 0.893431π0.893431\pi
1414 0 0
1515 2.46733 0.637063
1616 −0.893069 + 3.89903i −0.223267 + 0.974757i
1717 1.62780 2.81943i 0.394800 0.683813i −0.598276 0.801290i 0.704147π-0.704147\pi
0.993076 + 0.117477i 0.0374807π0.0374807\pi
1818 −6.66066 + 0.497865i −1.56993 + 0.117348i
1919 0.671653 2.50664i 0.154088 0.575063i −0.845094 0.534618i 0.820456π-0.820456\pi
0.999182 0.0404454i 0.0128777π-0.0128777\pi
2020 −0.709460 1.62780i −0.158640 0.363987i
2121 0 0
2222 1.38567 7.31580i 0.295427 1.55973i
2323 6.62774 3.82653i 1.38198 0.797887i 0.389586 0.920990i 0.372618π-0.372618\pi
0.992394 + 0.123103i 0.0392847π0.0392847\pi
2424 3.66886 + 6.95147i 0.748902 + 1.41896i
2525 −3.64747 2.10587i −0.729494 0.421173i
2626 1.46607 + 4.19237i 0.287521 + 0.822192i
2727 −3.38567 + 3.38567i −0.651573 + 0.651573i
2828 0 0
2929 −1.53721 1.53721i −0.285453 0.285453i 0.549826 0.835279i 0.314694π-0.314694\pi
−0.835279 + 0.549826i 0.814694π0.814694\pi
3030 −3.14349 1.51457i −0.573921 0.276521i
3131 −1.22066 + 2.11425i −0.219238 + 0.379731i −0.954575 0.297970i 0.903690π-0.903690\pi
0.735338 + 0.677701i 0.237024π0.237024\pi
3232 3.53122 4.41933i 0.624238 0.781234i
3333 −7.31580 12.6713i −1.27352 2.20580i
3434 −3.80460 + 2.59286i −0.652483 + 0.444672i
3535 0 0
3636 8.79159 + 3.45433i 1.46527 + 0.575722i
3737 1.72139 + 0.461245i 0.282995 + 0.0758283i 0.397524 0.917592i 0.369869π-0.369869\pi
−0.114530 + 0.993420i 0.536536π0.536536\pi
3838 −2.39441 + 2.78128i −0.388425 + 0.451183i
3939 7.55822 + 4.36374i 1.21028 + 0.698758i
4040 −0.0953379 + 2.50939i −0.0150742 + 0.396770i
4141 7.77589i 1.21439i 0.794553 + 0.607195i 0.207705π0.207705\pi
−0.794553 + 0.607195i 0.792295π0.792295\pi
4242 0 0
4343 −7.51575 + 7.51575i −1.14614 + 1.14614i −0.158836 + 0.987305i 0.550774π0.550774\pi
−0.987305 + 0.158836i 0.949226π0.949226\pi
4444 −6.25620 + 8.47006i −0.943158 + 1.27691i
4545 −4.05035 + 1.08529i −0.603790 + 0.161785i
4646 −10.7930 + 0.806742i −1.59133 + 0.118948i
4747 5.55792 + 9.62661i 0.810707 + 1.40418i 0.912370 + 0.409366i 0.134250π0.134250\pi
−0.101664 + 0.994819i 0.532417π0.532417\pi
4848 −0.407138 11.1086i −0.0587653 1.60339i
4949 0 0
5050 3.35436 + 4.92196i 0.474377 + 0.696070i
5151 −2.34163 + 8.73909i −0.327894 + 1.22372i
5252 0.705636 6.24122i 0.0978542 0.865502i
5353 1.07250 + 4.00262i 0.147319 + 0.549803i 0.999641 + 0.0267853i 0.00852703π0.00852703\pi
−0.852322 + 0.523017i 0.824806π0.824806\pi
5454 6.39179 2.23521i 0.869813 0.304174i
5555 4.67452i 0.630312i
5656 0 0
5757 7.21173i 0.955217i
5858 1.01486 + 2.90209i 0.133258 + 0.381063i
5959 2.50344 + 9.34298i 0.325921 + 1.21635i 0.913383 + 0.407101i 0.133460π0.133460\pi
−0.587463 + 0.809251i 0.699873π0.699873\pi
6060 3.07524 + 3.85926i 0.397012 + 0.498228i
6161 −1.23431 + 4.60651i −0.158037 + 0.589803i 0.840789 + 0.541363i 0.182092π0.182092\pi
−0.998826 + 0.0484399i 0.984575π0.984575\pi
6262 2.85301 1.94435i 0.362332 0.246932i
6363 0 0
6464 −7.21173 + 3.46279i −0.901467 + 0.432849i
6565 1.39413 + 2.41471i 0.172921 + 0.299508i
6666 1.54238 + 20.6346i 0.189854 + 2.53995i
6767 −1.26436 + 0.338785i −0.154467 + 0.0413892i −0.335224 0.942139i 0.608812π-0.608812\pi
0.180757 + 0.983528i 0.442145π0.442145\pi
6868 6.43885 0.967979i 0.780825 0.117385i
6969 −15.0387 + 15.0387i −1.81045 + 1.81045i
7070 0 0
7171 12.1113i 1.43735i −0.695348 0.718674i 0.744750π-0.744750\pi
0.695348 0.718674i 0.255250π-0.255250\pi
7272 −9.08045 9.79767i −1.07014 1.15467i
7373 −5.55501 3.20719i −0.650165 0.375373i 0.138354 0.990383i 0.455819π-0.455819\pi
−0.788519 + 0.615010i 0.789152π0.789152\pi
7474 −1.91000 1.64432i −0.222032 0.191148i
7575 11.3057 + 3.02934i 1.30546 + 0.349798i
7676 4.75787 2.07367i 0.545766 0.237866i
7777 0 0
7878 −6.95084 10.1992i −0.787027 1.15483i
7979 3.64128 + 6.30687i 0.409675 + 0.709579i 0.994853 0.101326i 0.0323086π-0.0323086\pi
−0.585178 + 0.810905i 0.698975π0.698975\pi
8080 1.66185 3.13856i 0.185801 0.350901i
8181 −0.431344 + 0.747110i −0.0479271 + 0.0830122i
8282 4.77322 9.90684i 0.527114 1.09403i
8383 1.96506 + 1.96506i 0.215694 + 0.215694i 0.806681 0.590987i 0.201262π-0.201262\pi
−0.590987 + 0.806681i 0.701262π0.701262\pi
8484 0 0
8585 −2.04387 + 2.04387i −0.221689 + 0.221689i
8686 14.1889 4.96187i 1.53003 0.535052i
8787 5.23203 + 3.02071i 0.560932 + 0.323854i
8888 13.1700 6.95088i 1.40393 0.740966i
8989 −0.576282 + 0.332717i −0.0610858 + 0.0352679i −0.530232 0.847853i 0.677895π-0.677895\pi
0.469146 + 0.883121i 0.344562π0.344562\pi
9090 5.82653 + 1.10359i 0.614170 + 0.116329i
9191 0 0
9292 14.2459 + 5.59741i 1.48524 + 0.583570i
9393 1.75595 6.55331i 0.182084 0.679547i
9494 −1.17177 15.6765i −0.120859 1.61690i
9595 −1.15201 + 1.99533i −0.118193 + 0.204717i
9696 −6.30029 + 14.4028i −0.643020 + 1.46998i
9797 8.34450 0.847256 0.423628 0.905836i 0.360756π-0.360756\pi
0.423628 + 0.905836i 0.360756π0.360756\pi
9898 0 0
9999 17.5832 + 17.5832i 1.76718 + 1.76718i
100100 −1.25226 8.32986i −0.125226 0.832986i
101101 1.23696 + 4.61640i 0.123082 + 0.459349i 0.999764 0.0217217i 0.00691477π-0.00691477\pi
−0.876682 + 0.481070i 0.840248π0.840248\pi
102102 8.34782 9.69659i 0.826557 0.960105i
103103 −16.6465 + 9.61088i −1.64023 + 0.946988i −0.659482 + 0.751720i 0.729224π0.729224\pi
−0.980750 + 0.195268i 0.937442π0.937442\pi
104104 −4.73017 + 7.51844i −0.463832 + 0.737244i
105105 0 0
106106 1.09059 5.75787i 0.105927 0.559254i
107107 −3.37044 0.903107i −0.325833 0.0873066i 0.0921947 0.995741i 0.470612π-0.470612\pi
−0.418028 + 0.908434i 0.637278π0.637278\pi
108108 −9.51551 1.07583i −0.915630 0.103522i
109109 −3.34112 + 0.895251i −0.320021 + 0.0857495i −0.415254 0.909706i 0.636307π-0.636307\pi
0.0952324 + 0.995455i 0.469641π0.469641\pi
110110 −2.86945 + 5.95555i −0.273591 + 0.567840i
111111 −4.95253 −0.470073
112112 0 0
113113 3.35149 0.315281 0.157641 0.987497i 0.449611π-0.449611\pi
0.157641 + 0.987497i 0.449611π0.449611\pi
114114 4.42691 9.18807i 0.414618 0.860542i
115115 −6.56320 + 1.75860i −0.612021 + 0.163991i
116116 0.488463 4.32036i 0.0453527 0.401136i
117117 −14.3269 3.83889i −1.32453 0.354906i
118118 2.54567 13.4401i 0.234348 1.23726i
119119 0 0
120120 −1.54899 6.80460i −0.141403 0.621172i
121121 −14.4804 + 8.36025i −1.31640 + 0.760022i
122122 4.40026 5.11122i 0.398381 0.462748i
123123 −5.59291 20.8730i −0.504296 1.88206i
124124 −4.82840 + 0.725873i −0.433603 + 0.0651853i
125125 5.78313 + 5.78313i 0.517259 + 0.517259i
126126 0 0
127127 −5.55623 −0.493036 −0.246518 0.969138i 0.579286π-0.579286\pi
−0.246518 + 0.969138i 0.579286π0.579286\pi
128128 11.3137 + 0.0151595i 0.999999 + 0.00133992i
129129 14.7689 25.5805i 1.30033 2.25224i
130130 −0.293923 3.93224i −0.0257788 0.344880i
131131 −3.53986 + 13.2109i −0.309279 + 1.15425i 0.619920 + 0.784665i 0.287165π0.287165\pi
−0.929199 + 0.369580i 0.879502π0.879502\pi
132132 10.7015 27.2362i 0.931444 2.37061i
133133 0 0
134134 1.81882 + 0.344500i 0.157122 + 0.0297603i
135135 3.68152 2.12553i 0.316855 0.182936i
136136 −8.79757 2.71923i −0.754386 0.233172i
137137 4.26568 + 2.46279i 0.364441 + 0.210410i 0.671027 0.741433i 0.265853π-0.265853\pi
−0.306586 + 0.951843i 0.599187π0.599187\pi
138138 28.3915 9.92852i 2.41685 0.845172i
139139 −7.58393 + 7.58393i −0.643261 + 0.643261i −0.951356 0.308095i 0.900309π-0.900309\pi
0.308095 + 0.951356i 0.400309π0.400309\pi
140140 0 0
141141 −21.8433 21.8433i −1.83954 1.83954i
142142 −7.43450 + 15.4303i −0.623889 + 1.29489i
143143 8.26738 14.3195i 0.691353 1.19746i
144144 5.55461 + 18.0567i 0.462885 + 1.50472i
145145 0.965062 + 1.67154i 0.0801440 + 0.138814i
146146 5.10861 + 7.49604i 0.422792 + 0.620376i
147147 0 0
148148 1.42406 + 3.26738i 0.117057 + 0.268577i
149149 3.68278 + 0.986799i 0.301705 + 0.0808417i 0.406496 0.913653i 0.366751π-0.366751\pi
−0.104790 + 0.994494i 0.533417π0.533417\pi
150150 −12.5444 10.7995i −1.02424 0.881773i
151151 1.87431 + 1.08213i 0.152529 + 0.0880625i 0.574322 0.818630i 0.305266π-0.305266\pi
−0.421793 + 0.906692i 0.638599π0.638599\pi
152152 −7.33466 0.278662i −0.594920 0.0226024i
153153 15.3760i 1.24308i
154154 0 0
155155 1.53267 1.53267i 0.123107 0.123107i
156156 2.59492 + 17.2610i 0.207760 + 1.38199i
157157 5.38577 1.44311i 0.429831 0.115173i −0.0374157 0.999300i 0.511913π-0.511913\pi
0.467247 + 0.884127i 0.345246π0.345246\pi
158158 −0.767685 10.2704i −0.0610738 0.817072i
159159 −5.75787 9.97293i −0.456629 0.790905i
160160 −4.04387 + 2.97854i −0.319696 + 0.235474i
161161 0 0
162162 1.00816 0.687072i 0.0792088 0.0539815i
163163 −3.01390 + 11.2480i −0.236067 + 0.881015i 0.741598 + 0.670845i 0.234068π0.234068\pi
−0.977665 + 0.210170i 0.932598π0.932598\pi
164164 −12.1626 + 9.69172i −0.949738 + 0.756797i
165165 3.36221 + 12.5479i 0.261748 + 0.976855i
166166 −1.29733 3.70983i −0.100692 0.287938i
167167 12.4649i 0.964562i 0.876016 + 0.482281i 0.160192π0.160192\pi
−0.876016 + 0.482281i 0.839808π0.839808\pi
168168 0 0
169169 3.13731i 0.241332i
170170 3.85861 1.34936i 0.295942 0.103491i
171171 −3.17217 11.8387i −0.242582 0.905328i
172172 −21.1232 2.38820i −1.61063 0.182098i
173173 5.09752 19.0242i 0.387557 1.44638i −0.446539 0.894764i 0.647344π-0.647344\pi
0.834096 0.551619i 0.185990π-0.185990\pi
174174 −4.81158 7.06020i −0.364765 0.535232i
175175 0 0
176176 −21.0460 + 0.771348i −1.58640 + 0.0581426i
177177 −13.4401 23.2789i −1.01022 1.74975i
178178 0.938447 0.0701462i 0.0703396 0.00525768i
179179 −1.33542 + 0.357825i −0.0998139 + 0.0267451i −0.308380 0.951263i 0.599787π-0.599787\pi
0.208566 + 0.978008i 0.433120π0.433120\pi
180180 −6.74582 4.98263i −0.502804 0.371384i
181181 16.0038 16.0038i 1.18955 1.18955i 0.212362 0.977191i 0.431885π-0.431885\pi
0.977191 0.212362i 0.0681154π-0.0681154\pi
182182 0 0
183183 13.2532i 0.979702i
184184 −14.7140 15.8762i −1.08473 1.17041i
185185 −1.37026 0.791120i −0.100744 0.0581643i
186186 −6.25990 + 7.27132i −0.458998 + 0.533159i
187187 16.5568 + 4.43637i 1.21075 + 0.324420i
188188 −8.13007 + 20.6918i −0.592947 + 1.50910i
189189 0 0
190190 2.69254 1.83499i 0.195337 0.133124i
191191 −1.25560 2.17477i −0.0908521 0.157360i 0.817018 0.576612i 0.195626π-0.195626\pi
−0.907870 + 0.419252i 0.862292π0.862292\pi
192192 16.8680 14.4824i 1.21734 1.04518i
193193 −5.04719 + 8.74199i −0.363305 + 0.629262i −0.988503 0.151204i 0.951685π-0.951685\pi
0.625198 + 0.780466i 0.285018π0.285018\pi
194194 −10.6313 5.12226i −0.763281 0.367757i
195195 −5.47912 5.47912i −0.392368 0.392368i
196196 0 0
197197 −13.5617 + 13.5617i −0.966232 + 0.966232i −0.999448 0.0332158i 0.989425π-0.989425\pi
0.0332158 + 0.999448i 0.489425π0.489425\pi
198198 −11.6084 33.1952i −0.824970 2.35908i
199199 −4.86063 2.80629i −0.344561 0.198932i 0.317726 0.948183i 0.397081π-0.397081\pi
−0.662287 + 0.749250i 0.730414π0.730414\pi
200200 −3.51783 + 11.3813i −0.248748 + 0.804781i
201201 3.15029 1.81882i 0.222204 0.128290i
202202 1.25782 6.64080i 0.0885002 0.467245i
203203 0 0
204204 −16.5877 + 7.22959i −1.16137 + 0.506173i
205205 1.78683 6.66854i 0.124798 0.465751i
206206 27.1081 2.02625i 1.88871 0.141176i
207207 18.0725 31.3024i 1.25612 2.17567i
208208 10.6416 6.67522i 0.737865 0.462843i
209209 13.6631 0.945096
210210 0 0
211211 3.86025 + 3.86025i 0.265750 + 0.265750i 0.827385 0.561635i 0.189827π-0.189827\pi
−0.561635 + 0.827385i 0.689827π0.689827\pi
212212 −4.92392 + 6.66633i −0.338176 + 0.457846i
213213 8.71121 + 32.5107i 0.596882 + 2.22759i
214214 3.73972 + 3.21954i 0.255642 + 0.220083i
215215 8.17249 4.71839i 0.557359 0.321792i
216216 11.4628 + 7.21173i 0.779944 + 0.490696i
217217 0 0
218218 4.80629 + 0.910351i 0.325523 + 0.0616568i
219219 17.2183 + 4.61362i 1.16350 + 0.311760i
220220 7.31161 5.82624i 0.492949 0.392805i
221221 −9.87581 + 2.64621i −0.664319 + 0.178004i
222222 6.30974 + 3.04010i 0.423482 + 0.204038i
223223 12.5348 0.839390 0.419695 0.907665i 0.362137π-0.362137\pi
0.419695 + 0.907665i 0.362137π0.362137\pi
224224 0 0
225225 −19.8917 −1.32612
226226 −4.26994 2.05730i −0.284032 0.136850i
227227 −21.4525 + 5.74818i −1.42385 + 0.381520i −0.886849 0.462059i 0.847111π-0.847111\pi
−0.537004 + 0.843580i 0.680444π0.680444\pi
228228 −11.2802 + 8.98857i −0.747047 + 0.595282i
229229 9.96527 + 2.67019i 0.658524 + 0.176451i 0.572580 0.819849i 0.305943π-0.305943\pi
0.0859440 + 0.996300i 0.472609π0.472609\pi
230230 9.44133 + 1.78827i 0.622543 + 0.117915i
231231 0 0
232232 −3.27437 + 5.20449i −0.214973 + 0.341692i
233233 −0.158206 + 0.0913400i −0.0103644 + 0.00598388i −0.505173 0.863018i 0.668571π-0.668571\pi
0.494809 + 0.869002i 0.335238π0.335238\pi
234234 15.8967 + 13.6855i 1.03920 + 0.894648i
235235 −2.55432 9.53286i −0.166626 0.621855i
236236 −11.4935 + 15.5606i −0.748162 + 1.01291i
237237 −14.3107 14.3107i −0.929577 0.929577i
238238 0 0
239239 0.261087 0.0168883 0.00844417 0.999964i 0.497312π-0.497312\pi
0.00844417 + 0.999964i 0.497312π0.497312\pi
240240 −2.20350 + 9.62021i −0.142235 + 0.620982i
241241 3.76511 6.52137i 0.242532 0.420078i −0.718903 0.695111i 0.755355π-0.755355\pi
0.961435 + 0.275033i 0.0886887π0.0886887\pi
242242 23.5806 1.76258i 1.51582 0.113303i
243243 4.33823 16.1905i 0.278297 1.03862i
244244 −8.74365 + 3.81083i −0.559755 + 0.243963i
245245 0 0
246246 −5.68725 + 30.0264i −0.362606 + 1.91441i
247247 −7.05792 + 4.07489i −0.449085 + 0.259279i
248248 6.59717 + 2.03911i 0.418921 + 0.129483i
249249 −6.68826 3.86147i −0.423851 0.244711i
250250 −3.81800 10.9179i −0.241472 0.690511i
251251 2.22521 2.22521i 0.140454 0.140454i −0.633384 0.773838i 0.718335π-0.718335\pi
0.773838 + 0.633384i 0.218335π0.218335\pi
252252 0 0
253253 28.4918 + 28.4918i 1.79127 + 1.79127i
254254 7.07889 + 3.41068i 0.444169 + 0.214005i
255255 4.01633 6.95648i 0.251512 0.435632i
256256 −14.4049 6.96421i −0.900303 0.435263i
257257 −1.40714 2.43723i −0.0877748 0.152030i 0.818795 0.574085i 0.194642π-0.194642\pi
−0.906570 + 0.422055i 0.861309π0.861309\pi
258258 −34.5188 + 23.5248i −2.14905 + 1.46459i
259259 0 0
260260 −2.03932 + 5.19027i −0.126474 + 0.321887i
261261 −9.91754 2.65740i −0.613881 0.164489i
262262 12.6195 14.6584i 0.779632 0.905598i
263263 7.38346 + 4.26284i 0.455283 + 0.262858i 0.710059 0.704142i 0.248668π-0.248668\pi
−0.254776 + 0.967000i 0.582002π0.582002\pi
264264 −30.3531 + 28.1311i −1.86810 + 1.73135i
265265 3.67907i 0.226003i
266266 0 0
267267 1.30762 1.30762i 0.0800249 0.0800249i
268268 −2.10579 1.55539i −0.128631 0.0950104i
269269 −15.7335 + 4.21577i −0.959286 + 0.257040i −0.704298 0.709904i 0.748738π-0.748738\pi
−0.254988 + 0.966944i 0.582071π0.582071\pi
270270 −5.99518 + 0.448122i −0.364855 + 0.0272719i
271271 13.3688 + 23.1554i 0.812094 + 1.40659i 0.911396 + 0.411531i 0.135006π0.135006\pi
−0.0993018 + 0.995057i 0.531661π0.531661\pi
272272 9.53931 + 8.86479i 0.578406 + 0.537507i
273273 0 0
274274 −3.92288 5.75618i −0.236990 0.347744i
275275 5.73928 21.4193i 0.346092 1.29163i
276276 −42.2667 4.77870i −2.54415 0.287644i
277277 3.31891 + 12.3863i 0.199414 + 0.744223i 0.991080 + 0.133269i 0.0425475π0.0425475\pi
−0.791666 + 0.610954i 0.790786π0.790786\pi
278278 14.3177 5.00689i 0.858716 0.300293i
279279 11.5302i 0.690296i
280280 0 0
281281 28.4095i 1.69477i 0.530980 + 0.847384i 0.321824π0.321824\pi
−0.530980 + 0.847384i 0.678176π0.678176\pi
282282 14.4209 + 41.2379i 0.858752 + 2.45568i
283283 −1.95496 7.29602i −0.116210 0.433703i 0.883164 0.469064i 0.155409π-0.155409\pi
−0.999375 + 0.0353608i 0.988742π0.988742\pi
284284 18.9438 15.0953i 1.12411 0.895741i
285285 1.65719 6.18472i 0.0981635 0.366351i
286286 −19.3230 + 13.1688i −1.14260 + 0.778688i
287287 0 0
288288 4.00724 26.4147i 0.236129 1.55650i
289289 3.20053 + 5.54348i 0.188266 + 0.326087i
290290 −0.203463 2.72201i −0.0119477 0.159842i
291291 −22.3993 + 6.00189i −1.31307 + 0.351837i
292292 −1.90717 12.6862i −0.111609 0.742404i
293293 8.64751 8.64751i 0.505193 0.505193i −0.407854 0.913047i 0.633723π-0.633723\pi
0.913047 + 0.407854i 0.133723π0.133723\pi
294294 0 0
295295 8.58773i 0.499997i
296296 0.191366 5.03695i 0.0111229 0.292767i
297297 −21.8319 12.6046i −1.26681 0.731396i
298298 −4.08629 3.51790i −0.236712 0.203786i
299299 −23.2154 6.22055i −1.34258 0.359744i
300300 9.35284 + 21.4593i 0.539986 + 1.23896i
301301 0 0
302302 −1.72369 2.52922i −0.0991869 0.145540i
303303 −6.64080 11.5022i −0.381504 0.660785i
304304 9.17364 + 4.85740i 0.526144 + 0.278591i
305305 2.11707 3.66687i 0.121223 0.209964i
306306 −9.43853 + 19.5897i −0.539565 + 1.11987i
307307 −22.9681 22.9681i −1.31086 1.31086i −0.920782 0.390077i 0.872448π-0.872448\pi
−0.390077 0.920782i 0.627552π-0.627552\pi
308308 0 0
309309 37.7720 37.7720i 2.14877 2.14877i
310310 −2.89351 + 1.01186i −0.164340 + 0.0574699i
311311 22.9893 + 13.2729i 1.30360 + 0.752635i 0.981020 0.193906i 0.0621156π-0.0621156\pi
0.322583 + 0.946541i 0.395449π0.395449\pi
312312 7.28959 23.5842i 0.412692 1.33519i
313313 17.4811 10.0927i 0.988088 0.570473i 0.0833856 0.996517i 0.473427π-0.473427\pi
0.904702 + 0.426045i 0.140093π0.140093\pi
314314 −7.74756 1.46745i −0.437220 0.0828132i
315315 0 0
316316 −5.32642 + 13.5562i −0.299634 + 0.762598i
317317 −0.340449 + 1.27057i −0.0191215 + 0.0713624i −0.974827 0.222961i 0.928428π-0.928428\pi
0.955706 + 0.294324i 0.0950944π0.0950944\pi
318318 1.21393 + 16.2404i 0.0680735 + 0.910718i
319319 5.72294 9.91241i 0.320423 0.554989i
320320 6.98044 1.31247i 0.390218 0.0733692i
321321 9.69693 0.541230
322322 0 0
323323 −5.97399 5.97399i −0.332402 0.332402i
324324 −1.70620 + 0.256501i −0.0947891 + 0.0142500i
325325 3.42338 + 12.7762i 0.189895 + 0.708697i
326326 10.7444 12.4804i 0.595079 0.691227i
327327 8.32473 4.80629i 0.460359 0.265788i
328328 21.4449 4.88171i 1.18410 0.269547i
329329 0 0
330330 3.41892 18.0505i 0.188205 0.993648i
331331 −14.2631 3.82179i −0.783972 0.210065i −0.155437 0.987846i 0.549678π-0.549678\pi
−0.628535 + 0.777781i 0.716345π0.716345\pi
332332 −0.624417 + 5.52285i −0.0342693 + 0.303106i
333333 8.13002 2.17843i 0.445522 0.119377i
334334 7.65155 15.8808i 0.418674 0.868961i
335335 1.16216 0.0634955
336336 0 0
337337 −27.6212 −1.50462 −0.752312 0.658807i 0.771061π-0.771061\pi
−0.752312 + 0.658807i 0.771061π0.771061\pi
338338 −1.92583 + 3.99708i −0.104752 + 0.217412i
339339 −8.99647 + 2.41060i −0.488621 + 0.130926i
340340 −5.74434 0.649458i −0.311530 0.0352218i
341341 −12.4157 3.32677i −0.672346 0.180155i
342342 −3.22568 + 17.0303i −0.174425 + 0.920892i
343343 0 0
344344 25.4459 + 16.0091i 1.37195 + 0.863152i
345345 16.3529 9.44133i 0.880408 0.508304i
346346 −18.1724 + 21.1086i −0.976956 + 1.13480i
347347 3.05763 + 11.4112i 0.164142 + 0.612586i 0.998148 + 0.0608309i 0.0193750π0.0193750\pi
−0.834006 + 0.551755i 0.813958π0.813958\pi
348348 1.79628 + 11.9486i 0.0962908 + 0.640512i
349349 7.97685 + 7.97685i 0.426991 + 0.426991i 0.887602 0.460611i 0.152370π-0.152370\pi
−0.460611 + 0.887602i 0.652370π0.652370\pi
350350 0 0
351351 15.0369 0.802609
352352 27.2870 + 11.9363i 1.45440 + 0.636207i
353353 −5.38113 + 9.32039i −0.286409 + 0.496074i −0.972950 0.231017i 0.925795π-0.925795\pi
0.686541 + 0.727091i 0.259128π0.259128\pi
354354 2.83356 + 37.9086i 0.150602 + 2.01482i
355355 −2.78307 + 10.3866i −0.147710 + 0.551261i
356356 −1.23868 0.486694i −0.0656500 0.0257947i
357357 0 0
358358 1.92103 + 0.363860i 0.101530 + 0.0192306i
359359 15.5646 8.98625i 0.821470 0.474276i −0.0294531 0.999566i 0.509377π-0.509377\pi
0.850923 + 0.525290i 0.176043π0.176043\pi
360360 5.53590 + 10.4890i 0.291767 + 0.552819i
361361 10.6223 + 6.13282i 0.559071 + 0.322780i
362362 −30.2135 + 10.5657i −1.58798 + 0.555318i
363363 32.8568 32.8568i 1.72453 1.72453i
364364 0 0
365365 4.02695 + 4.02695i 0.210780 + 0.210780i
366366 −8.13543 + 16.8851i −0.425246 + 0.882599i
367367 −8.35453 + 14.4705i −0.436103 + 0.755352i −0.997385 0.0722722i 0.976975π-0.976975\pi
0.561282 + 0.827625i 0.310308π0.310308\pi
368368 9.00071 + 29.2591i 0.469195 + 1.52524i
369369 18.3625 + 31.8048i 0.955915 + 1.65569i
370370 1.26015 + 1.84905i 0.0655119 + 0.0961278i
371371 0 0
372372 12.4389 5.42136i 0.644926 0.281085i
373373 21.2808 + 5.70218i 1.10188 + 0.295248i 0.763529 0.645773i 0.223465π-0.223465\pi
0.338349 + 0.941021i 0.390131π0.390131\pi
374374 −18.3708 15.8155i −0.949932 0.817799i
375375 −19.6834 11.3642i −1.01645 0.586845i
376376 23.0597 21.3716i 1.18921 1.10216i
377377 6.82725i 0.351621i
378378 0 0
379379 23.6361 23.6361i 1.21411 1.21411i 0.244443 0.969664i 0.421395π-0.421395\pi
0.969664 0.244443i 0.0786052π-0.0786052\pi
380380 −4.55682 + 0.685047i −0.233760 + 0.0351421i
381381 14.9147 3.99639i 0.764105 0.204741i
382382 0.264717 + 3.54150i 0.0135441 + 0.181199i
383383 4.91665 + 8.51589i 0.251229 + 0.435141i 0.963864 0.266393i 0.0858319π-0.0858319\pi
−0.712635 + 0.701535i 0.752499π0.752499\pi
384384 −30.3805 + 8.09683i −1.55035 + 0.413189i
385385 0 0
386386 11.7966 8.03948i 0.600431 0.409199i
387387 −12.9926 + 48.4890i −0.660450 + 2.46483i
388388 10.4004 + 13.0520i 0.528002 + 0.662613i
389389 3.78801 + 14.1371i 0.192060 + 0.716777i 0.993008 + 0.118044i 0.0376624π0.0376624\pi
−0.800948 + 0.598733i 0.795671π0.795671\pi
390390 3.61730 + 10.3440i 0.183169 + 0.523788i
391391 24.9153i 1.26002i
392392 0 0
393393 38.0085i 1.91728i
394394 25.6031 8.95340i 1.28986 0.451066i
395395 −1.67346 6.24545i −0.0842011 0.314243i
396396 −5.58722 + 49.4179i −0.280768 + 2.48334i
397397 −6.60834 + 24.6626i −0.331663 + 1.23778i 0.575779 + 0.817605i 0.304699π0.304699\pi
−0.907442 + 0.420177i 0.861968π0.861968\pi
398398 4.47003 + 6.55902i 0.224062 + 0.328774i
399399 0 0
400400 11.4683 12.3409i 0.573414 0.617045i
401401 −9.40322 16.2869i −0.469575 0.813327i 0.529820 0.848110i 0.322259π-0.322259\pi
−0.999395 + 0.0347829i 0.988926π0.988926\pi
402402 −5.13009 + 0.383459i −0.255866 + 0.0191252i
403403 7.40572 1.98436i 0.368905 0.0988478i
404404 −5.67897 + 7.68857i −0.282539 + 0.382521i
405405 0.541596 0.541596i 0.0269121 0.0269121i
406406 0 0
407407 9.38288i 0.465092i
408408 25.5714 + 0.971519i 1.26597 + 0.0480974i
409409 25.6410 + 14.8038i 1.26787 + 0.732003i 0.974584 0.224023i 0.0719190π-0.0719190\pi
0.293283 + 0.956026i 0.405252π0.405252\pi
410410 −6.36997 + 7.39918i −0.314591 + 0.365419i
411411 −13.2219 3.54278i −0.652186 0.174753i
412412 −35.7807 14.0587i −1.76279 0.692622i
413413 0 0
414414 −42.2400 + 28.7869i −2.07598 + 1.41480i
415415 −1.23367 2.13677i −0.0605583 0.104890i
416416 −17.6555 + 1.97219i −0.865632 + 0.0966944i
417417 14.9029 25.8126i 0.729798 1.26405i
418418 −17.4074 8.38706i −0.851423 0.410225i
419419 −1.15229 1.15229i −0.0562929 0.0562929i 0.678400 0.734693i 0.262674π-0.262674\pi
−0.734693 + 0.678400i 0.762674π0.762674\pi
420420 0 0
421421 19.7275 19.7275i 0.961459 0.961459i −0.0378258 0.999284i 0.512043π-0.512043\pi
0.999284 + 0.0378258i 0.0120432π0.0120432\pi
422422 −2.54852 7.28773i −0.124060 0.354761i
423423 45.4658 + 26.2497i 2.21062 + 1.27630i
424424 10.3654 5.47067i 0.503389 0.265679i
425425 −11.8747 + 6.85586i −0.576008 + 0.332558i
426426 8.85814 46.7674i 0.429178 2.26589i
427427 0 0
428428 −2.78827 6.39746i −0.134776 0.309233i
429429 −11.8928 + 44.3847i −0.574192 + 2.14291i
430430 −13.3085 + 0.994772i −0.641793 + 0.0479722i
431431 −10.1980 + 17.6634i −0.491219 + 0.850817i −0.999949 0.0101095i 0.996782π-0.996782\pi
0.508730 + 0.860926i 0.330115π0.330115\pi
432432 −10.1772 16.2245i −0.489651 0.780601i
433433 −28.3107 −1.36052 −0.680262 0.732969i 0.738134π-0.738134\pi
−0.680262 + 0.732969i 0.738134π0.738134\pi
434434 0 0
435435 −3.79281 3.79281i −0.181851 0.181851i
436436 −5.56461 4.11016i −0.266496 0.196841i
437437 −5.14020 19.1835i −0.245889 0.917670i
438438 −19.1048 16.4474i −0.912862 0.785885i
439439 3.95973 2.28615i 0.188988 0.109112i −0.402521 0.915411i 0.631866π-0.631866\pi
0.591509 + 0.806299i 0.298533π0.298533\pi
440440 −12.8917 + 2.93467i −0.614590 + 0.139905i
441441 0 0
442442 14.2066 + 2.69085i 0.675739 + 0.127991i
443443 −9.74483 2.61112i −0.462991 0.124058i 0.0197808 0.999804i 0.493703π-0.493703\pi
−0.482772 + 0.875746i 0.660370π0.660370\pi
444444 −6.17274 7.74645i −0.292945 0.367630i
445445 0.570670 0.152911i 0.0270523 0.00724865i
446446 −15.9699 7.69444i −0.756195 0.364343i
447447 −10.5956 −0.501153
448448 0 0
449449 13.0695 0.616790 0.308395 0.951258i 0.400208π-0.400208\pi
0.308395 + 0.951258i 0.400208π0.400208\pi
450450 25.3430 + 12.2105i 1.19468 + 0.575609i
451451 −39.5453 + 10.5961i −1.86211 + 0.498952i
452452 4.17723 + 5.24219i 0.196480 + 0.246572i
453453 −5.80958 1.55667i −0.272958 0.0731388i
454454 30.8600 + 5.84514i 1.44833 + 0.274326i
455455 0 0
456456 19.8890 4.52753i 0.931390 0.212021i
457457 −27.6363 + 15.9559i −1.29277 + 0.746383i −0.979145 0.203162i 0.934878π-0.934878\pi
−0.313629 + 0.949546i 0.601545π0.601545\pi
458458 −11.0571 9.51910i −0.516665 0.444798i
459459 4.03448 + 15.0569i 0.188313 + 0.702795i
460460 −10.9309 8.07387i −0.509658 0.376446i
461461 11.2878 + 11.2878i 0.525727 + 0.525727i 0.919295 0.393568i 0.128759π-0.128759\pi
−0.393568 + 0.919295i 0.628759π0.628759\pi
462462 0 0
463463 −21.0406 −0.977839 −0.488919 0.872329i 0.662609π-0.662609\pi
−0.488919 + 0.872329i 0.662609π0.662609\pi
464464 7.36646 4.62079i 0.341980 0.214515i
465465 −3.01178 + 5.21656i −0.139668 + 0.241912i
466466 0.257630 0.0192571i 0.0119345 0.000892068i
467467 2.47257 9.22775i 0.114417 0.427009i −0.884826 0.465922i 0.845723π-0.845723\pi
0.999243 + 0.0389127i 0.0123894π0.0123894\pi
468468 −11.8523 27.1941i −0.547871 1.25705i
469469 0 0
470470 −2.59741 + 13.7133i −0.119809 + 0.632545i
471471 −13.4192 + 7.74756i −0.618323 + 0.356989i
472472 24.1951 12.7697i 1.11367 0.587773i
473473 −48.4639 27.9806i −2.22837 1.28655i
474474 9.44785 + 27.0170i 0.433954 + 1.24093i
475475 −7.72848 + 7.72848i −0.354607 + 0.354607i
476476 0 0
477477 13.8388 + 13.8388i 0.633634 + 0.633634i
478478 −0.332637 0.160268i −0.0152145 0.00733049i
479479 −5.26638 + 9.12164i −0.240627 + 0.416778i −0.960893 0.276920i 0.910686π-0.910686\pi
0.720266 + 0.693698i 0.244020π0.244020\pi
480480 8.71270 10.9040i 0.397679 0.497695i
481481 −2.79836 4.84690i −0.127594 0.221000i
482482 −8.80005 + 5.99731i −0.400831 + 0.273170i
483483 0 0
484484 −31.1247 12.2293i −1.41476 0.555876i
485485 −7.15617 1.91749i −0.324945 0.0870688i
486486 −15.4656 + 17.9644i −0.701534 + 0.814881i
487487 −2.99593 1.72970i −0.135759 0.0783803i 0.430582 0.902551i 0.358308π-0.358308\pi
−0.566341 + 0.824171i 0.691642π0.691642\pi
488488 13.4791 + 0.512103i 0.610169 + 0.0231818i
489489 32.3612i 1.46342i
490490 0 0
491491 0.356972 0.356972i 0.0161099 0.0161099i −0.699006 0.715116i 0.746374π-0.746374\pi
0.715116 + 0.699006i 0.246374π0.246374\pi
492492 25.6774 34.7638i 1.15763 1.56727i
493493 −6.83633 + 1.83179i −0.307893 + 0.0824997i
494494 11.4935 0.859104i 0.517116 0.0386529i
495495 −11.0387 19.1196i −0.496154 0.859364i
496496 −7.15339 6.64757i −0.321197 0.298485i
497497 0 0
498498 6.15079 + 9.02526i 0.275623 + 0.404431i
499499 5.96768 22.2717i 0.267150 0.997018i −0.693771 0.720196i 0.744052π-0.744052\pi
0.960921 0.276822i 0.0892814π-0.0892814\pi
500500 −1.83764 + 16.2536i −0.0821819 + 0.726884i
501501 −8.96553 33.4598i −0.400550 1.49487i
502502 −4.20095 + 1.46907i −0.187498 + 0.0655680i
503503 27.6867i 1.23449i 0.786772 + 0.617243i 0.211751π0.211751\pi
−0.786772 + 0.617243i 0.788249π0.788249\pi
504504 0 0
505505 4.24323i 0.188821i
506506 −18.8102 53.7896i −0.836216 2.39124i
507507 2.25655 + 8.42156i 0.100217 + 0.374015i
508508 −6.92518 8.69073i −0.307255 0.385589i
509509 8.79130 32.8096i 0.389667 1.45426i −0.441009 0.897503i 0.645379π-0.645379\pi
0.830676 0.556756i 0.187954π-0.187954\pi
510510 −9.38721 + 6.39746i −0.415673 + 0.283284i
511511 0 0
512512 14.0775 + 17.7151i 0.622142 + 0.782904i
513513 6.21267 + 10.7607i 0.274296 + 0.475095i
514514 0.296665 + 3.96891i 0.0130853 + 0.175061i
515515 16.4844 4.41699i 0.726390 0.194636i
516516 58.4192 8.78240i 2.57176 0.386624i
517517 −41.3836 + 41.3836i −1.82005 + 1.82005i
518518 0 0
519519 54.7336i 2.40254i
520520 5.78423 5.36080i 0.253655 0.235087i
521521 −16.9294 9.77420i −0.741691 0.428216i 0.0809928 0.996715i 0.474191π-0.474191\pi
−0.822684 + 0.568499i 0.807524π0.807524\pi
522522 11.0042 + 9.47351i 0.481639 + 0.414644i
523523 −9.83797 2.63608i −0.430184 0.115268i 0.0372283 0.999307i 0.488147π-0.488147\pi
−0.467413 + 0.884039i 0.654814π0.654814\pi
524524 −25.0758 + 10.9290i −1.09544 + 0.477437i
525525 0 0
526526 −6.79012 9.96337i −0.296063 0.434424i
527527 3.97399 + 6.88316i 0.173110 + 0.299835i
528528 55.9394 17.2081i 2.43445 0.748888i
529529 17.7847 30.8039i 0.773246 1.33930i
530530 −2.25839 + 4.68730i −0.0980981 + 0.203603i
531531 32.3027 + 32.3027i 1.40182 + 1.40182i
532532 0 0
533533 17.2676 17.2676i 0.747944 0.747944i
534534 −2.46864 + 0.863285i −0.106829 + 0.0373580i
535535 2.68294 + 1.54899i 0.115993 + 0.0669688i
536536 1.72810 + 3.27427i 0.0746424 + 0.141427i
537537 3.32733 1.92103i 0.143585 0.0828988i
538538 22.6330 + 4.28688i 0.975777 + 0.184820i
539539 0 0
540540 7.91320 + 3.10920i 0.340530 + 0.133799i
541541 −0.575849 + 2.14910i −0.0247577 + 0.0923970i −0.977199 0.212324i 0.931897π-0.931897\pi
0.952442 + 0.304721i 0.0985633π0.0985633\pi
542542 −2.81852 37.7074i −0.121066 1.61967i
543543 −31.4484 + 54.4703i −1.34958 + 2.33754i
544544 −6.71188 17.1498i −0.287769 0.735293i
545545 3.07104 0.131549
546546 0 0
547547 −6.76891 6.76891i −0.289418 0.289418i 0.547432 0.836850i 0.315605π-0.315605\pi
−0.836850 + 0.547432i 0.815605π0.815605\pi
548548 1.46451 + 9.74169i 0.0625607 + 0.416144i
549549 5.82957 + 21.7562i 0.248800 + 0.928534i
550550 −20.4603 + 23.7661i −0.872430 + 1.01339i
551551 −4.88571 + 2.82076i −0.208138 + 0.120169i
552552 50.9162 + 32.0336i 2.16714 + 1.36344i
553553 0 0
554554 3.37489 17.8181i 0.143385 0.757017i
555555 4.24725 + 1.13805i 0.180286 + 0.0483074i
556556 −21.3148 2.40987i −0.903949 0.102201i
557557 −4.53648 + 1.21555i −0.192217 + 0.0515043i −0.353643 0.935380i 0.615057π-0.615057\pi
0.161426 + 0.986885i 0.448391π0.448391\pi
558558 7.07781 14.6900i 0.299627 0.621878i
559559 33.3799 1.41182
560560 0 0
561561 −47.6346 −2.01114
562562 17.4391 36.1950i 0.735625 1.52679i
563563 25.6398 6.87017i 1.08059 0.289543i 0.325752 0.945455i 0.394382π-0.394382\pi
0.754837 + 0.655912i 0.227716π0.227716\pi
564564 6.94092 61.3911i 0.292266 2.58503i
565565 −2.87421 0.770141i −0.120919 0.0324001i
566566 −1.98794 + 10.4955i −0.0835592 + 0.441159i
567567 0 0
568568 −33.4014 + 7.60348i −1.40149 + 0.319035i
569569 −20.3493 + 11.7487i −0.853086 + 0.492530i −0.861691 0.507433i 0.830594π-0.830594\pi
0.00860467 + 0.999963i 0.497261π0.497261\pi
570570 −5.90782 + 6.86235i −0.247451 + 0.287432i
571571 9.13856 + 34.1056i 0.382437 + 1.42727i 0.842168 + 0.539215i 0.181279π0.181279\pi
−0.459731 + 0.888058i 0.652054π0.652054\pi
572572 32.7021 4.91624i 1.36734 0.205558i
573573 4.93467 + 4.93467i 0.206149 + 0.206149i
574574 0 0
575575 −32.2326 −1.34419
576576 −21.3200 + 31.1937i −0.888335 + 1.29974i
577577 −7.20904 + 12.4864i −0.300116 + 0.519817i −0.976162 0.217043i 0.930359π-0.930359\pi
0.676046 + 0.736860i 0.263692π0.263692\pi
578578 −0.674764 9.02728i −0.0280665 0.375485i
579579 7.26051 27.0966i 0.301737 1.12610i
580580 −1.41168 + 3.59286i −0.0586169 + 0.149185i
581581 0 0
582582 32.2220 + 6.10312i 1.33565 + 0.252983i
583583 −18.8944 + 10.9087i −0.782524 + 0.451791i
584584 −5.35758 + 17.3335i −0.221698 + 0.717265i
585585 11.4045 + 6.58440i 0.471519 + 0.272232i
586586 −16.3256 + 5.70906i −0.674403 + 0.235839i
587587 13.2110 13.2110i 0.545276 0.545276i −0.379795 0.925071i 0.624005π-0.624005\pi
0.925071 + 0.379795i 0.124005π0.124005\pi
588588 0 0
589589 4.47981 + 4.47981i 0.184587 + 0.184587i
590590 −5.27156 + 10.9411i −0.217027 + 0.450440i
591591 26.6496 46.1585i 1.09622 1.89871i
592592 −3.33573 + 6.29983i −0.137098 + 0.258921i
593593 8.19296 + 14.1906i 0.336445 + 0.582739i 0.983761 0.179482i 0.0574422π-0.0574422\pi
−0.647317 + 0.762221i 0.724109π0.724109\pi
594594 20.0775 + 29.4603i 0.823788 + 1.20877i
595595 0 0
596596 3.04666 + 6.99032i 0.124796 + 0.286335i
597597 15.0660 + 4.03691i 0.616609 + 0.165220i
598598 25.7590 + 22.1760i 1.05336 + 0.906844i
599599 29.4485 + 17.0021i 1.20323 + 0.694687i 0.961273 0.275599i 0.0888762π-0.0888762\pi
0.241961 + 0.970286i 0.422210π0.422210\pi
600600 1.25684 33.0814i 0.0513104 1.35054i
601601 3.33457i 0.136020i 0.997685 + 0.0680099i 0.0216649π0.0216649\pi
−0.997685 + 0.0680099i 0.978335π0.978335\pi
602602 0 0
603603 −4.37145 + 4.37145i −0.178019 + 0.178019i
604604 0.643494 + 4.28042i 0.0261834 + 0.174168i
605605 14.3394 3.84222i 0.582978 0.156208i
606606 1.40007 + 18.7308i 0.0568741 + 0.760886i
607607 −5.23683 9.07046i −0.212556 0.368159i 0.739957 0.672654i 0.234846π-0.234846\pi
−0.952514 + 0.304495i 0.901512π0.901512\pi
608608 −8.70592 11.8198i −0.353072 0.479355i
609609 0 0
610610 −4.94814 + 3.37220i −0.200344 + 0.136536i
611611 9.03517 33.7197i 0.365524 1.36415i
612612 24.0502 19.1643i 0.972172 0.774673i
613613 −3.29334 12.2909i −0.133017 0.496425i 0.866982 0.498340i 0.166057π-0.166057\pi
−0.999998 + 0.00191560i 0.999390π0.999390\pi
614614 15.1635 + 43.3613i 0.611948 + 1.74992i
615615 19.1857i 0.773643i
616616 0 0
617617 2.93899i 0.118319i 0.998249 + 0.0591597i 0.0188421π0.0188421\pi
−0.998249 + 0.0591597i 0.981158π0.981158\pi
618618 −71.3094 + 24.9369i −2.86848 + 1.00311i
619619 −2.65281 9.90042i −0.106625 0.397932i 0.891899 0.452235i 0.149373π-0.149373\pi
−0.998525 + 0.0543029i 0.982706π0.982706\pi
620620 4.30759 + 0.487019i 0.172997 + 0.0195592i
621621 −9.48400 + 35.3948i −0.380580 + 1.42034i
622622 −21.1419 31.0222i −0.847711 1.24388i
623623 0 0
624624 −23.7644 + 25.5726i −0.951336 + 1.02372i
625625 6.89868 + 11.9489i 0.275947 + 0.477954i
626626 −28.4670 + 2.12783i −1.13777 + 0.0850452i
627627 −36.6762 + 9.82735i −1.46470 + 0.392466i
628628 8.96995 + 6.62543i 0.357940 + 0.264383i
629629 4.10253 4.10253i 0.163579 0.163579i
630630 0 0
631631 9.59471i 0.381959i 0.981594 + 0.190980i 0.0611665π0.0611665\pi
−0.981594 + 0.190980i 0.938834π0.938834\pi
632632 15.1076 14.0016i 0.600947 0.556955i
633633 −13.1387 7.58562i −0.522216 0.301501i
634634 1.21369 1.40978i 0.0482016 0.0559896i
635635 4.76498 + 1.27677i 0.189092 + 0.0506672i
636636 8.42256 21.4362i 0.333976 0.850000i
637637 0 0
638638 −13.3760 + 9.11585i −0.529561 + 0.360900i
639639 −28.6005 49.5374i −1.13142 1.95967i
640640 −9.69905 2.61279i −0.383389 0.103279i
641641 7.91443 13.7082i 0.312601 0.541441i −0.666324 0.745663i 0.732133π-0.732133\pi
0.978925 + 0.204222i 0.0654664π0.0654664\pi
642642 −12.3543 5.95244i −0.487586 0.234924i
643643 −10.3033 10.3033i −0.406321 0.406321i 0.474132 0.880454i 0.342762π-0.342762\pi
−0.880454 + 0.474132i 0.842762π0.842762\pi
644644 0 0
645645 −18.5439 + 18.5439i −0.730164 + 0.730164i
646646 3.94401 + 11.2783i 0.155175 + 0.443737i
647647 9.11681 + 5.26359i 0.358419 + 0.206933i 0.668387 0.743814i 0.266985π-0.266985\pi
−0.309968 + 0.950747i 0.600318π0.600318\pi
648648 2.33123 + 0.720557i 0.0915795 + 0.0283061i
649649 −44.1035 + 25.4631i −1.73121 + 0.999516i
650650 3.48112 18.3789i 0.136541 0.720880i
651651 0 0
652652 −21.3500 + 9.30518i −0.836130 + 0.364419i
653653 8.64357 32.2582i 0.338249 1.26236i −0.562054 0.827100i 0.689989π-0.689989\pi
0.900304 0.435263i 0.143344π-0.143344\pi
654654 −13.5564 + 1.01330i −0.530098 + 0.0396233i
655655 6.07151 10.5162i 0.237233 0.410900i
656656 −30.3184 6.94441i −1.18374 0.271134i
657657 −30.2947 −1.18191
658658 0 0
659659 −14.9087 14.9087i −0.580759 0.580759i 0.354353 0.935112i 0.384701π-0.384701\pi
−0.935112 + 0.354353i 0.884701π0.884701\pi
660660 −15.4361 + 20.8985i −0.600851 + 0.813472i
661661 −8.12957 30.3400i −0.316204 1.18009i −0.922864 0.385126i 0.874158π-0.874158\pi
0.606660 0.794961i 0.292509π-0.292509\pi
662662 15.8259 + 13.6245i 0.615089 + 0.529532i
663663 24.6065 14.2066i 0.955639 0.551739i
664664 4.18572 6.65306i 0.162438 0.258189i
665665 0 0
666666 −11.6952 2.21518i −0.453181 0.0858364i
667667 −16.0704 4.30606i −0.622249 0.166731i
668668 −19.4968 + 15.5360i −0.754355 + 0.601106i
669669 −33.6474 + 9.01579i −1.30088 + 0.348571i
670670 −1.48064 0.713389i −0.0572022 0.0275606i
671671 −25.1090 −0.969321
672672 0 0
673673 45.9274 1.77037 0.885186 0.465237i 0.154031π-0.154031\pi
0.885186 + 0.465237i 0.154031π0.154031\pi
674674 35.1907 + 16.9552i 1.35549 + 0.653091i
675675 19.4789 5.21936i 0.749744 0.200893i
676676 4.90720 3.91029i 0.188738 0.150396i
677677 42.3069 + 11.3361i 1.62599 + 0.435682i 0.952752 0.303748i 0.0982381π-0.0982381\pi
0.673234 + 0.739430i 0.264905π0.264905\pi
678678 12.9417 + 2.45126i 0.497021 + 0.0941400i
679679 0 0
680680 6.91987 + 4.35359i 0.265365 + 0.166953i
681681 53.4510 30.8600i 2.04825 1.18256i
682682 13.7760 + 11.8598i 0.527510 + 0.454135i
683683 −4.61649 17.2290i −0.176645 0.659248i −0.996266 0.0863413i 0.972482π-0.972482\pi
0.819621 0.572907i 0.194184π-0.194184\pi
684684 14.5637 19.7173i 0.556855 0.753908i
685685 −3.09228 3.09228i −0.118150 0.118150i
686686 0 0
687687 −28.6706 −1.09385
688688 −22.5920 36.0162i −0.861313 1.37310i
689689 6.50682 11.2701i 0.247890 0.429358i
690690 −26.6298 + 1.99050i −1.01378 + 0.0757771i
691691 −8.45153 + 31.5415i −0.321511 + 1.19990i 0.596262 + 0.802790i 0.296652π0.296652\pi
−0.917773 + 0.397106i 0.870015π0.870015\pi
692692 36.1100 15.7382i 1.37269 0.598275i
693693 0 0
694694 3.10920 16.4153i 0.118024 0.623117i
695695 8.24664 4.76120i 0.312813 0.180603i
696696 5.04607 16.3257i 0.191271 0.618823i
697697 21.9236 + 12.6576i 0.830416 + 0.479441i
698698 −5.26629 15.0594i −0.199332 0.570008i
699699 0.358977 0.358977i 0.0135778 0.0135778i
700700 0 0
701701 23.1180 + 23.1180i 0.873153 + 0.873153i 0.992815 0.119662i 0.0381810π-0.0381810\pi
−0.119662 + 0.992815i 0.538181π0.538181\pi
702702 −19.1577 9.23036i −0.723059 0.348378i
703703 2.31235 4.00511i 0.0872121 0.151056i
704704 −27.4378 31.9575i −1.03410 1.20444i
705705 13.7133 + 23.7521i 0.516471 + 0.894554i
706706 12.5771 8.57140i 0.473346 0.322589i
707707 0 0
708708 19.6600 50.0366i 0.738870 1.88049i
709709 40.4313 + 10.8335i 1.51843 + 0.406862i 0.919224 0.393734i 0.128817π-0.128817\pi
0.599205 + 0.800596i 0.295484π0.295484\pi
710710 9.92152 11.5246i 0.372348 0.432509i
711711 29.7870 + 17.1975i 1.11710 + 0.644957i
712712 1.27938 + 1.38043i 0.0479468 + 0.0517339i
713713 18.6836i 0.699707i
714714 0 0
715715 −10.3805 + 10.3805i −0.388210 + 0.388210i
716716 −2.22413 1.64280i −0.0831196 0.0613942i
717717 −0.700843 + 0.187790i −0.0261735 + 0.00701316i
718718 −25.3462 + 1.89456i −0.945913 + 0.0707043i
719719 −23.9987 41.5669i −0.894999 1.55018i −0.833806 0.552058i 0.813843π-0.813843\pi
−0.0611931 0.998126i 0.519491π-0.519491\pi
720720 −0.614326 16.7617i −0.0228946 0.624670i
721721 0 0
722722 −9.76873 14.3340i −0.363555 0.533456i
723723 −5.41621 + 20.2136i −0.201431 + 0.751751i
724724 44.9790 + 5.08536i 1.67163 + 0.188996i
725725 2.36977 + 8.84409i 0.0880109 + 0.328461i
726726 −62.0301 + 21.6920i −2.30215 + 0.805064i
727727 35.3027i 1.30931i −0.755930 0.654653i 0.772815π-0.772815\pi
0.755930 0.654653i 0.227185π-0.227185\pi
728728 0 0
729729 43.9928i 1.62936i
730730 −2.65858 7.60245i −0.0983984 0.281379i
731731 8.95601 + 33.4243i 0.331250 + 1.23624i
732732 20.7298 16.5185i 0.766195 0.610541i
733733 2.32031 8.65952i 0.0857026 0.319847i −0.909744 0.415170i 0.863722π-0.863722\pi
0.995446 + 0.0953238i 0.0303887π0.0303887\pi
734734 19.5267 13.3076i 0.720744 0.491193i
735735 0 0
736736 6.49334 42.8025i 0.239348 1.57772i
737737 −3.44587 5.96842i −0.126930 0.219850i
738738 −3.87135 51.7926i −0.142506 1.90651i
739739 −1.14785 + 0.307565i −0.0422243 + 0.0113140i −0.279869 0.960038i 0.590291π-0.590291\pi
0.237645 + 0.971352i 0.423624π0.423624\pi
740740 −0.470443 3.12932i −0.0172938 0.115036i
741741 16.0148 16.0148i 0.588319 0.588319i
742742 0 0
743743 46.9253i 1.72152i −0.509008 0.860762i 0.669988π-0.669988\pi
0.509008 0.860762i 0.330012π-0.330012\pi
744744 −19.1756 0.728527i −0.703011 0.0267091i
745745 −2.93157 1.69254i −0.107404 0.0620099i
746746 −23.6124 20.3280i −0.864513 0.744262i
747747 12.6779 + 3.39703i 0.463860 + 0.124291i
748748 13.6969 + 31.4265i 0.500809 + 1.14907i
749749 0 0
750750 18.1016 + 26.5611i 0.660978 + 0.969875i
751751 5.75909 + 9.97504i 0.210152 + 0.363995i 0.951762 0.306837i 0.0992707π-0.0992707\pi
−0.741610 + 0.670832i 0.765937π0.765937\pi
752752 −42.4980 + 13.0733i −1.54974 + 0.476733i
753753 −4.37267 + 7.57369i −0.159349 + 0.276000i
754754 4.19090 8.69823i 0.152623 0.316771i
755755 −1.35872 1.35872i −0.0494491 0.0494491i
756756 0 0
757757 −14.6371 + 14.6371i −0.531994 + 0.531994i −0.921165 0.389172i 0.872761π-0.872761\pi
0.389172 + 0.921165i 0.372761π0.372761\pi
758758 −44.6225 + 15.6045i −1.62076 + 0.566781i
759759 −96.9745 55.9882i −3.51995 2.03224i
760760 6.22611 + 1.92442i 0.225845 + 0.0698060i
761761 5.84549 3.37489i 0.211899 0.122340i −0.390295 0.920690i 0.627627π-0.627627\pi
0.602194 + 0.798350i 0.294294π0.294294\pi
762762 −21.4552 4.06380i −0.777240 0.147216i
763763 0 0
764764 1.83668 4.67452i 0.0664488 0.169118i
765765 −3.53326 + 13.1863i −0.127745 + 0.476753i
766766 −1.03657 13.8677i −0.0374528 0.501060i
767767 15.1883 26.3069i 0.548418 0.949887i
768768 43.6764 + 8.33332i 1.57604 + 0.300703i
769769 2.23508 0.0805990 0.0402995 0.999188i 0.487169π-0.487169\pi
0.0402995 + 0.999188i 0.487169π0.487169\pi
770770 0 0
771771 5.53022 + 5.53022i 0.199166 + 0.199166i
772772 −19.9644 + 3.00134i −0.718535 + 0.108020i
773773 −6.08368 22.7046i −0.218815 0.816627i −0.984789 0.173756i 0.944410π-0.944410\pi
0.765974 0.642871i 0.222257π-0.222257\pi
774774 46.3180 53.8016i 1.66487 1.93386i
775775 8.90466 5.14111i 0.319865 0.184674i
776776 −5.23868 23.0131i −0.188058 0.826121i
777777 0 0
778778 3.85191 20.3365i 0.138098 0.729099i
779779 19.4914 + 5.22270i 0.698351 + 0.187123i
780780 1.74104 15.3992i 0.0623393 0.551379i
781781 61.5935 16.5039i 2.20399 0.590557i
782782 −15.2942 + 31.7432i −0.546920 + 1.13514i
783783 10.4090 0.371987
784784 0 0
785785 −4.95040 −0.176688
786786 −23.3315 + 48.4246i −0.832206 + 1.72725i
787787 5.48157 1.46878i 0.195397 0.0523564i −0.159793 0.987150i 0.551083π-0.551083\pi
0.355190 + 0.934794i 0.384416π0.384416\pi
788788 −38.1155 4.30936i −1.35781 0.153515i
789789 −22.8857 6.13220i −0.814752 0.218312i
790790 −1.70169 + 8.98424i −0.0605435 + 0.319645i
791791 0 0
792792 37.4535 59.5309i 1.33085 2.11534i
793793 12.9705 7.48852i 0.460596 0.265925i
794794 23.5584 27.3648i 0.836058 0.971141i
795795 2.64621 + 9.87581i 0.0938516 + 0.350259i
796796 −1.66877 11.1004i −0.0591480 0.393444i
797797 −26.5404 26.5404i −0.940110 0.940110i 0.0581955 0.998305i 0.481465π-0.481465\pi
−0.998305 + 0.0581955i 0.981465π0.981465\pi
798798 0 0
799799 36.1888 1.28027
800800 −22.1865 + 8.68308i −0.784412 + 0.306993i
801801 −1.57140 + 2.72174i −0.0555226 + 0.0961681i
802802 1.98247 + 26.5223i 0.0700034 + 0.936536i
803803 8.74080 32.6211i 0.308456 1.15117i
804804 6.77135 + 2.66055i 0.238807 + 0.0938304i
805805 0 0
806806 −10.6533 2.01783i −0.375247 0.0710749i
807807 39.2015 22.6330i 1.37996 0.796718i
808808 11.9549 6.30956i 0.420571 0.221969i
809809 −5.44560 3.14402i −0.191457 0.110538i 0.401207 0.915987i 0.368591π-0.368591\pi
−0.592665 + 0.805449i 0.701924π0.701924\pi
810810 −1.02248 + 0.357560i −0.0359261 + 0.0125634i
811811 −28.2328 + 28.2328i −0.991388 + 0.991388i −0.999963 0.00857565i 0.997270π-0.997270\pi
0.00857565 + 0.999963i 0.497270π0.497270\pi
812812 0 0
813813 −52.5409 52.5409i −1.84269 1.84269i
814814 5.75967 11.9542i 0.201876 0.418995i
815815 5.16940 8.95366i 0.181076 0.313633i
816816 −31.9827 16.9347i −1.11962 0.592833i
817817 13.7913 + 23.8873i 0.482497 + 0.835709i
818818 −23.5805 34.6005i −0.824472 1.20978i
819819 0 0
820820 12.6576 5.51669i 0.442023 0.192651i
821821 16.3630 + 4.38445i 0.571072 + 0.153018i 0.532788 0.846249i 0.321144π-0.321144\pi
0.0382839 + 0.999267i 0.487811π0.487811\pi
822822 14.6705 + 12.6299i 0.511692 + 0.440517i
823823 −32.3363 18.6694i −1.12717 0.650774i −0.183951 0.982935i 0.558889π-0.558889\pi
−0.943223 + 0.332162i 0.892222π0.892222\pi
824824 36.9563 + 39.8753i 1.28743 + 1.38912i
825825 61.6244i 2.14549i
826826 0 0
827827 −5.32642 + 5.32642i −0.185218 + 0.185218i −0.793625 0.608407i 0.791809π-0.791809\pi
0.608407 + 0.793625i 0.291809π0.291809\pi
828828 71.4865 10.7469i 2.48433 0.373480i
829829 −7.89725 + 2.11606i −0.274283 + 0.0734939i −0.393339 0.919394i 0.628680π-0.628680\pi
0.119056 + 0.992888i 0.462013π0.462013\pi
830830 0.260092 + 3.47963i 0.00902794 + 0.120780i
831831 −17.8181 30.8618i −0.618102 1.07058i
832832 23.7045 + 8.32514i 0.821806 + 0.288622i
833833 0 0
834834 −34.8320 + 23.7383i −1.20613 + 0.821989i
835835 2.86432 10.6898i 0.0991239 0.369935i
836836 17.0294 + 21.3710i 0.588975 + 0.739131i
837837 −3.02540 11.2909i −0.104573 0.390272i
838838 0.760736 + 2.17539i 0.0262792 + 0.0751477i
839839 7.20540i 0.248758i 0.992235 + 0.124379i 0.0396939π0.0396939\pi
−0.992235 + 0.124379i 0.960306π0.960306\pi
840840 0 0
841841 24.2740i 0.837033i
842842 −37.2434 + 13.0240i −1.28349 + 0.448837i
843843 −20.4339 76.2603i −0.703780 2.62654i
844844 −1.22663 + 10.8493i −0.0422223 + 0.373448i
845845 −0.720926 + 2.69053i −0.0248006 + 0.0925571i
846846 −41.8122 61.3524i −1.43753 2.10934i
847847 0 0
848848 −16.5642 + 0.607087i −0.568816 + 0.0208475i
849849 10.4955 + 18.1787i 0.360205 + 0.623893i
850850 19.3374 1.44541i 0.663266 0.0495772i
851851 13.1739 3.52994i 0.451596 0.121005i
852852 −39.9938 + 54.1462i −1.37016 + 1.85502i
853853 13.0316 13.0316i 0.446192 0.446192i −0.447894 0.894086i 0.647826π-0.647826\pi
0.894086 + 0.447894i 0.147826π0.147826\pi
854854 0 0
855855 10.8817i 0.372147i
856856 −0.374690 + 9.86222i −0.0128066 + 0.337084i
857857 −11.8030 6.81447i −0.403183 0.232778i 0.284674 0.958625i 0.408115π-0.408115\pi
−0.687856 + 0.725847i 0.741448π0.741448\pi
858858 42.3975 49.2477i 1.44743 1.68129i
859859 −43.5800 11.6772i −1.48693 0.398422i −0.578231 0.815873i 0.696257π-0.696257\pi
−0.908699 + 0.417451i 0.862923π0.862923\pi
860860 17.5663 + 6.90201i 0.599005 + 0.235357i
861861 0 0
862862 23.8353 16.2440i 0.811835 0.553272i
863863 25.5923 + 44.3271i 0.871171 + 1.50891i 0.860786 + 0.508966i 0.169972π0.169972\pi
0.0103847 + 0.999946i 0.496694π0.496694\pi
864864 3.00684 + 26.9180i 0.102295 + 0.915768i
865865 −8.74318 + 15.1436i −0.297277 + 0.514899i
866866 36.0691 + 17.3784i 1.22568 + 0.590544i
867867 −12.5785 12.5785i −0.427188 0.427188i
868868 0 0
869869 −27.1125 + 27.1125i −0.919727 + 0.919727i
870870 2.50400 + 7.16042i 0.0848936 + 0.242761i
871871 3.56006 + 2.05540i 0.120628 + 0.0696445i
872872 4.56655 + 8.65235i 0.154643 + 0.293006i
873873 34.1305 19.7053i 1.15514 0.666922i
874874 −5.22690 + 27.5959i −0.176802 + 0.933445i
875875 0 0
876876 14.2442 + 32.6821i 0.481266 + 1.10423i
877877 7.83642 29.2459i 0.264617 0.987564i −0.697867 0.716227i 0.745867π-0.745867\pi
0.962484 0.271337i 0.0874659π-0.0874659\pi
878878 −6.44823 + 0.481987i −0.217617 + 0.0162663i
879879 −16.9929 + 29.4326i −0.573156 + 0.992735i
880880 18.2261 + 4.17467i 0.614402 + 0.140728i
881881 −29.7369 −1.00186 −0.500930 0.865488i 0.667009π-0.667009\pi
−0.500930 + 0.865488i 0.667009π0.667009\pi
882882 0 0
883883 14.3040 + 14.3040i 0.481368 + 0.481368i 0.905568 0.424200i 0.139445π-0.139445\pi
−0.424200 + 0.905568i 0.639445π0.639445\pi
884884 −16.4481 12.1490i −0.553208 0.408614i
885885 6.17683 + 23.0522i 0.207632 + 0.774893i
886886 10.8125 + 9.30853i 0.363254 + 0.312726i
887887 −49.1086 + 28.3528i −1.64890 + 0.951995i −0.671395 + 0.741099i 0.734305π0.734305\pi
−0.977509 + 0.210896i 0.932362π0.932362\pi
888888 3.10920 + 13.6584i 0.104338 + 0.458347i
889889 0 0
890890 −0.820923 0.155490i −0.0275174 0.00521203i
891891 −4.38731 1.17558i −0.146980 0.0393833i
892892 15.6231 + 19.6061i 0.523100 + 0.656462i
893893 27.8634 7.46599i 0.932415 0.249840i
894894 13.4992 + 6.50406i 0.451481 + 0.217528i
895895 1.22747 0.0410298
896896 0 0
897897 66.7919 2.23012
898898 −16.6512 8.02271i −0.555657 0.267721i
899899 5.12646 1.37363i 0.170977 0.0458132i
900900 −24.7927 31.1135i −0.826423 1.03712i
901901 13.0309 + 3.49163i 0.434124 + 0.116323i
902902 56.8869 + 10.7749i 1.89413 + 0.358763i
903903 0 0
904904 −2.10406 9.24297i −0.0699802 0.307417i
905905 −17.4022 + 10.0472i −0.578470 + 0.333980i
906906 6.44610 + 5.54947i 0.214157 + 0.184369i
907907 −5.58142 20.8301i −0.185328 0.691653i −0.994560 0.104164i 0.966783π-0.966783\pi
0.809232 0.587489i 0.199883π-0.199883\pi
908908 −35.7290 26.3903i −1.18571 0.875793i
909909 15.9609 + 15.9609i 0.529389 + 0.529389i
910910 0 0
911911 −7.88055 −0.261094 −0.130547 0.991442i 0.541673π-0.541673\pi
−0.130547 + 0.991442i 0.541673π0.541673\pi
912912 −28.1188 6.44058i −0.931105 0.213269i
913913 −7.31580 + 12.6713i −0.242118 + 0.419360i
914914 45.0044 3.36395i 1.48861 0.111270i
915915 −3.04546 + 11.3658i −0.100680 + 0.375742i
916916 8.24398 + 18.9151i 0.272389 + 0.624974i
917917 0 0
918918 4.10253 21.6597i 0.135404 0.714877i
919919 −1.83468 + 1.05925i −0.0605206 + 0.0349416i −0.529955 0.848026i 0.677791π-0.677791\pi
0.469434 + 0.882967i 0.344458π0.344458\pi
920920 8.97039 + 16.9964i 0.295745 + 0.560355i
921921 78.1739 + 45.1337i 2.57592 + 1.48721i
922922 −7.45220 21.3102i −0.245425 0.701816i
923923 −26.8951 + 26.8951i −0.885264 + 0.885264i
924924 0 0
925925 −5.30740 5.30740i −0.174506 0.174506i
926926 26.8066 + 12.9157i 0.880921 + 0.424437i
927927 −45.3916 + 78.6205i −1.49085 + 2.58224i
928928 −12.2217 + 1.36521i −0.401196 + 0.0448151i
929929 −16.1033 27.8918i −0.528333 0.915099i −0.999454 0.0330307i 0.989484π-0.989484\pi
0.471122 0.882068i 0.343849π-0.343849\pi
930930 7.03932 4.79736i 0.230829 0.157312i
931931 0 0
932932 −0.340053 0.133611i −0.0111388 0.00437658i
933933 −71.2574 19.0934i −2.33286 0.625088i
934934 −8.81460 + 10.2388i −0.288422 + 0.335023i
935935 −13.1795 7.60919i −0.431016 0.248847i
936936 −1.59272 + 41.9219i −0.0520596 + 1.37026i
937937 17.8409i 0.582836i −0.956596 0.291418i 0.905873π-0.905873\pi
0.956596 0.291418i 0.0941271π-0.0941271\pi
938938 0 0
939939 −39.6655 + 39.6655i −1.29444 + 1.29444i
940940 11.7271 15.8769i 0.382495 0.517847i
941941 −27.3429 + 7.32652i −0.891354 + 0.238838i −0.675300 0.737544i 0.735986π-0.735986\pi
−0.216055 + 0.976381i 0.569319π0.569319\pi
942942 21.8525 1.63341i 0.711992 0.0532193i
943943 29.7547 + 51.5366i 0.968946 + 1.67826i
944944 −38.6643 + 1.41707i −1.25842 + 0.0461217i
945945 0 0
946946 44.5693 + 65.3981i 1.44907 + 2.12627i
947947 6.15356 22.9654i 0.199964 0.746275i −0.790962 0.611865i 0.790419π-0.790419\pi
0.990926 0.134410i 0.0429138π-0.0429138\pi
948948 4.54735 40.2204i 0.147691 1.30630i
949949 5.21373 + 19.4579i 0.169245 + 0.631630i
950950 14.5905 5.10232i 0.473380 0.165541i
951951 3.65550i 0.118538i
952952 0 0
953953 30.3038i 0.981636i 0.871262 + 0.490818i 0.163302π0.163302\pi
−0.871262 + 0.490818i 0.836698π0.836698\pi
954954 −9.13632 26.1261i −0.295799 0.845865i
955955 0.577052 + 2.15359i 0.0186730 + 0.0696884i
956956 0.325414 + 0.408377i 0.0105247 + 0.0132079i
957957 −8.23259 + 30.7244i −0.266122 + 0.993180i
958958 12.3089 8.38862i 0.397683 0.271024i
959959 0 0
960960 −17.7938 + 8.54386i −0.574291 + 0.275752i
961961 12.5200 + 21.6852i 0.403870 + 0.699523i
962962 0.589974 + 7.89294i 0.0190215 + 0.254478i
963963 −15.9184 + 4.26532i −0.512962 + 0.137448i
964964 14.8931 2.23894i 0.479674 0.0721115i
965965 6.33726 6.33726i 0.204004 0.204004i
966966 0 0
967967 13.3675i 0.429869i −0.976629 0.214934i 0.931046π-0.931046\pi
0.976629 0.214934i 0.0689537π-0.0689537\pi
968968 32.1473 + 34.6865i 1.03325 + 1.11487i
969969 20.3330 + 11.7393i 0.653190 + 0.377119i
970970 7.94024 + 6.83577i 0.254946 + 0.219483i
971971 12.7754 + 3.42316i 0.409982 + 0.109854i 0.457914 0.888996i 0.348597π-0.348597\pi
−0.0479326 + 0.998851i 0.515263π0.515263\pi
972972 30.7313 13.3939i 0.985706 0.429610i
973973 0 0
974974 2.75518 + 4.04277i 0.0882816 + 0.129539i
975975 −18.3789 31.8332i −0.588596 1.01948i
976976 −16.8586 8.92655i −0.539630 0.285732i
977977 −26.6156 + 46.0996i −0.851509 + 1.47486i 0.0283371 + 0.999598i 0.490979π0.490979\pi
−0.879846 + 0.475259i 0.842355π0.842355\pi
978978 −19.8648 + 41.2296i −0.635208 + 1.31838i
979979 −2.47736 2.47736i −0.0791769 0.0791769i
980980 0 0
981981 −11.5517 + 11.5517i −0.368817 + 0.368817i
982982 −0.673925 + 0.235672i −0.0215058 + 0.00752059i
983983 −0.255896 0.147742i −0.00816182 0.00471223i 0.495914 0.868372i 0.334833π-0.334833\pi
−0.504075 + 0.863660i 0.668167π0.668167\pi
984984 −54.0539 + 28.5286i −1.72318 + 0.909459i
985985 14.7468 8.51406i 0.469871 0.271280i
986986 9.83424 + 1.86269i 0.313186 + 0.0593201i
987987 0 0
988988 −15.1706 5.96071i −0.482640 0.189635i
989989 −21.0532 + 78.5717i −0.669453 + 2.49843i
990990 2.32728 + 31.1354i 0.0739659 + 0.989548i
991991 21.0182 36.4046i 0.667665 1.15643i −0.310890 0.950446i 0.600627π-0.600627\pi
0.978555 0.205985i 0.0660397π-0.0660397\pi
992992 5.03314 + 12.8604i 0.159802 + 0.408318i
993993 41.0357 1.30223
994994 0 0
995995 3.52358 + 3.52358i 0.111705 + 0.111705i
996996 −2.29624 15.2742i −0.0727592 0.483983i
997997 11.9231 + 44.4977i 0.377609 + 1.40926i 0.849495 + 0.527597i 0.176907π0.176907\pi
−0.471885 + 0.881660i 0.656426π0.656426\pi
998998 −21.2745 + 24.7119i −0.673434 + 0.782241i
999999 −7.38970 + 4.26644i −0.233800 + 0.134984i
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 784.2.x.j.557.1 16
7.2 even 3 inner 784.2.x.j.765.3 16
7.3 odd 6 112.2.m.c.29.3 8
7.4 even 3 784.2.m.g.589.3 8
7.5 odd 6 784.2.x.k.765.3 16
7.6 odd 2 784.2.x.k.557.1 16
16.5 even 4 inner 784.2.x.j.165.3 16
28.3 even 6 448.2.m.c.337.4 8
56.3 even 6 896.2.m.f.673.1 8
56.45 odd 6 896.2.m.e.673.4 8
112.3 even 12 896.2.m.f.225.1 8
112.5 odd 12 784.2.x.k.373.1 16
112.37 even 12 inner 784.2.x.j.373.1 16
112.45 odd 12 896.2.m.e.225.4 8
112.53 even 12 784.2.m.g.197.3 8
112.59 even 12 448.2.m.c.113.4 8
112.69 odd 4 784.2.x.k.165.3 16
112.101 odd 12 112.2.m.c.85.3 yes 8
224.59 even 24 7168.2.a.bd.1.1 8
224.101 odd 24 7168.2.a.bc.1.8 8
224.171 even 24 7168.2.a.bd.1.8 8
224.213 odd 24 7168.2.a.bc.1.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
112.2.m.c.29.3 8 7.3 odd 6
112.2.m.c.85.3 yes 8 112.101 odd 12
448.2.m.c.113.4 8 112.59 even 12
448.2.m.c.337.4 8 28.3 even 6
784.2.m.g.197.3 8 112.53 even 12
784.2.m.g.589.3 8 7.4 even 3
784.2.x.j.165.3 16 16.5 even 4 inner
784.2.x.j.373.1 16 112.37 even 12 inner
784.2.x.j.557.1 16 1.1 even 1 trivial
784.2.x.j.765.3 16 7.2 even 3 inner
784.2.x.k.165.3 16 112.69 odd 4
784.2.x.k.373.1 16 112.5 odd 12
784.2.x.k.557.1 16 7.6 odd 2
784.2.x.k.765.3 16 7.5 odd 6
896.2.m.e.225.4 8 112.45 odd 12
896.2.m.e.673.4 8 56.45 odd 6
896.2.m.f.225.1 8 112.3 even 12
896.2.m.f.673.1 8 56.3 even 6
7168.2.a.bc.1.1 8 224.213 odd 24
7168.2.a.bc.1.8 8 224.101 odd 24
7168.2.a.bd.1.1 8 224.59 even 24
7168.2.a.bd.1.8 8 224.171 even 24