Properties

Label 368.2.j.c.277.4
Level 368368
Weight 22
Character 368.277
Analytic conductor 2.9382.938
Analytic rank 00
Dimension 1212
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [368,2,Mod(93,368)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(368, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("368.93");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 368=2423 368 = 2^{4} \cdot 23
Weight: k k == 2 2
Character orbit: [χ][\chi] == 368.j (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: 2.938494794382.93849479438
Analytic rank: 00
Dimension: 1212
Relative dimension: 66 over Q(i)\Q(i)
Coefficient field: 12.0.221124989353984.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x122x112x10+2x9+12x88x714x616x5+48x4+16x3++64 x^{12} - 2 x^{11} - 2 x^{10} + 2 x^{9} + 12 x^{8} - 8 x^{7} - 14 x^{6} - 16 x^{5} + 48 x^{4} + 16 x^{3} + \cdots + 64 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 22 2^{2}
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 277.4
Root 1.41072+0.0993495i1.41072 + 0.0993495i of defining polynomial
Character χ\chi == 368.277
Dual form 368.2.j.c.93.4

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+(0.586784+1.28673i)q2+(0.955624+0.955624i)q3+(1.31137+1.51007i)q4+(2.38359+2.38359i)q5+(1.790380.668889i)q60.198699iq7+(2.712550.801301i)q8+1.17357iq9+(1.66839+4.46569i)q10+(0.1101680.110168i)q11+(0.1898822.69623i)q12+(1.693531.69353i)q13+(0.2556730.116593i)q144.55562q15+(0.5606173.96052i)q160.645369q17+(1.51007+0.688630i)q18+(0.1735670.173567i)q19+(6.72515+0.473617i)q20+(0.189882+0.189882i)q21+(0.07711200.206401i)q22+1.00000iq23+(3.357921.82643i)q24+6.36297iq25+(3.17285+1.18538i)q26+(3.988363.98836i)q27+(0.300049+0.260568i)q28+(2.988582.98858i)q29+(2.673175.86188i)q304.74204q31+(4.767173.04533i)q32+0.210558q33+(0.3786920.830418i)q34+(0.4736170.473617i)q35+(1.772171.53898i)q36+(1.537021.53702i)q37+(0.325181+0.121488i)q38+3.23674iq39+(4.555628.37556i)q40+9.42339iq41+(0.132908+0.355746i)q42+(2.469312.46931i)q43+(0.3108320.0218902i)q44+(2.79730+2.79730i)q45+(1.28673+0.586784i)q46+10.2297q47+(4.32050+3.24903i)q48+6.96052q49+(8.18746+3.73369i)q50+(0.6167300.616730i)q51+(0.336502+4.77818i)q52+(6.13987+6.13987i)q53+(2.791657.47226i)q540.525189iq55+(0.159218+0.538981i)q56+0.331730iq57+(5.59916+2.09186i)q58+(3.18941+3.18941i)q59+(5.974116.87931i)q60+(0.1340230.134023i)q61+(2.782556.10175i)q62+0.233187q63+(6.71583+4.34713i)q64+8.07333q65+(0.123552+0.270932i)q66+(8.349218.34921i)q67+(0.8463170.974552i)q68+(0.9556240.955624i)q69+(0.887329+0.331508i)q70+4.76823iq71+(0.9403803.18336i)q72+5.99750iq73+(1.075842.87963i)q74+(6.080616.08061i)q75+(0.0344876+0.489709i)q76+(0.0218902+0.0218902i)q77+(4.16483+1.89927i)q780.630585q79+(8.1039610.7765i)q80+4.10204q81+(12.1254+5.52949i)q82+(0.7112080.711208i)q83+(0.535739+0.0377293i)q84+(1.538291.53829i)q85+(1.728404.62630i)q86+5.71192iq87+(0.210558+0.387113i)q8813.8549iq89+(5.240791.95797i)q90+(0.3365020.336502i)q91+(1.510071.31137i)q92+(4.531614.53161i)q93+(6.00265+13.1630i)q94+0.827425q95+(1.64543+7.46582i)q96+7.33230q97+(4.08432+8.95634i)q98+(0.1292890.129289i)q99+O(q100)q+(0.586784 + 1.28673i) q^{2} +(-0.955624 + 0.955624i) q^{3} +(-1.31137 + 1.51007i) q^{4} +(2.38359 + 2.38359i) q^{5} +(-1.79038 - 0.668889i) q^{6} -0.198699i q^{7} +(-2.71255 - 0.801301i) q^{8} +1.17357i q^{9} +(-1.66839 + 4.46569i) q^{10} +(-0.110168 - 0.110168i) q^{11} +(-0.189882 - 2.69623i) q^{12} +(1.69353 - 1.69353i) q^{13} +(0.255673 - 0.116593i) q^{14} -4.55562 q^{15} +(-0.560617 - 3.96052i) q^{16} -0.645369 q^{17} +(-1.51007 + 0.688630i) q^{18} +(0.173567 - 0.173567i) q^{19} +(-6.72515 + 0.473617i) q^{20} +(0.189882 + 0.189882i) q^{21} +(0.0771120 - 0.206401i) q^{22} +1.00000i q^{23} +(3.35792 - 1.82643i) q^{24} +6.36297i q^{25} +(3.17285 + 1.18538i) q^{26} +(-3.98836 - 3.98836i) q^{27} +(0.300049 + 0.260568i) q^{28} +(2.98858 - 2.98858i) q^{29} +(-2.67317 - 5.86188i) q^{30} -4.74204 q^{31} +(4.76717 - 3.04533i) q^{32} +0.210558 q^{33} +(-0.378692 - 0.830418i) q^{34} +(0.473617 - 0.473617i) q^{35} +(-1.77217 - 1.53898i) q^{36} +(-1.53702 - 1.53702i) q^{37} +(0.325181 + 0.121488i) q^{38} +3.23674i q^{39} +(-4.55562 - 8.37556i) q^{40} +9.42339i q^{41} +(-0.132908 + 0.355746i) q^{42} +(-2.46931 - 2.46931i) q^{43} +(0.310832 - 0.0218902i) q^{44} +(-2.79730 + 2.79730i) q^{45} +(-1.28673 + 0.586784i) q^{46} +10.2297 q^{47} +(4.32050 + 3.24903i) q^{48} +6.96052 q^{49} +(-8.18746 + 3.73369i) q^{50} +(0.616730 - 0.616730i) q^{51} +(0.336502 + 4.77818i) q^{52} +(6.13987 + 6.13987i) q^{53} +(2.79165 - 7.47226i) q^{54} -0.525189i q^{55} +(-0.159218 + 0.538981i) q^{56} +0.331730i q^{57} +(5.59916 + 2.09186i) q^{58} +(3.18941 + 3.18941i) q^{59} +(5.97411 - 6.87931i) q^{60} +(0.134023 - 0.134023i) q^{61} +(-2.78255 - 6.10175i) q^{62} +0.233187 q^{63} +(6.71583 + 4.34713i) q^{64} +8.07333 q^{65} +(0.123552 + 0.270932i) q^{66} +(8.34921 - 8.34921i) q^{67} +(0.846317 - 0.974552i) q^{68} +(-0.955624 - 0.955624i) q^{69} +(0.887329 + 0.331508i) q^{70} +4.76823i q^{71} +(0.940380 - 3.18336i) q^{72} +5.99750i q^{73} +(1.07584 - 2.87963i) q^{74} +(-6.08061 - 6.08061i) q^{75} +(0.0344876 + 0.489709i) q^{76} +(-0.0218902 + 0.0218902i) q^{77} +(-4.16483 + 1.89927i) q^{78} -0.630585 q^{79} +(8.10396 - 10.7765i) q^{80} +4.10204 q^{81} +(-12.1254 + 5.52949i) q^{82} +(0.711208 - 0.711208i) q^{83} +(-0.535739 + 0.0377293i) q^{84} +(-1.53829 - 1.53829i) q^{85} +(1.72840 - 4.62630i) q^{86} +5.71192i q^{87} +(0.210558 + 0.387113i) q^{88} -13.8549i q^{89} +(-5.24079 - 1.95797i) q^{90} +(-0.336502 - 0.336502i) q^{91} +(-1.51007 - 1.31137i) q^{92} +(4.53161 - 4.53161i) q^{93} +(6.00265 + 13.1630i) q^{94} +0.827425 q^{95} +(-1.64543 + 7.46582i) q^{96} +7.33230 q^{97} +(4.08432 + 8.95634i) q^{98} +(0.129289 - 0.129289i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q+2q2+2q34q54q86q104q118q12+18q132q14+8q168q174q188q1932q20+8q2134q22+12q2414q26++36q99+O(q100) 12 q + 2 q^{2} + 2 q^{3} - 4 q^{5} - 4 q^{8} - 6 q^{10} - 4 q^{11} - 8 q^{12} + 18 q^{13} - 2 q^{14} + 8 q^{16} - 8 q^{17} - 4 q^{18} - 8 q^{19} - 32 q^{20} + 8 q^{21} - 34 q^{22} + 12 q^{24} - 14 q^{26}+ \cdots + 36 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/368Z)×\left(\mathbb{Z}/368\mathbb{Z}\right)^\times.

nn 4747 9797 277277
χ(n)\chi(n) 11 11 e(14)e\left(\frac{1}{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 0.586784 + 1.28673i 0.414919 + 0.909859i
33 −0.955624 + 0.955624i −0.551730 + 0.551730i −0.926940 0.375210i 0.877571π-0.877571\pi
0.375210 + 0.926940i 0.377571π0.377571\pi
44 −1.31137 + 1.51007i −0.655685 + 0.755035i
55 2.38359 + 2.38359i 1.06597 + 1.06597i 0.997664 + 0.0683082i 0.0217601π0.0217601\pi
0.0683082 + 0.997664i 0.478240π0.478240\pi
66 −1.79038 0.668889i −0.730919 0.273073i
77 0.198699i 0.0751012i −0.999295 0.0375506i 0.988044π-0.988044\pi
0.999295 0.0375506i 0.0119555π-0.0119555\pi
88 −2.71255 0.801301i −0.959031 0.283303i
99 1.17357i 0.391189i
1010 −1.66839 + 4.46569i −0.527592 + 1.41218i
1111 −0.110168 0.110168i −0.0332168 0.0332168i 0.690303 0.723520i 0.257477π-0.257477\pi
−0.723520 + 0.690303i 0.757477π0.757477\pi
1212 −0.189882 2.69623i −0.0548141 0.778336i
1313 1.69353 1.69353i 0.469699 0.469699i −0.432118 0.901817i 0.642234π-0.642234\pi
0.901817 + 0.432118i 0.142234π0.142234\pi
1414 0.255673 0.116593i 0.0683315 0.0311609i
1515 −4.55562 −1.17626
1616 −0.560617 3.96052i −0.140154 0.990130i
1717 −0.645369 −0.156525 −0.0782625 0.996933i 0.524937π-0.524937\pi
−0.0782625 + 0.996933i 0.524937π0.524937\pi
1818 −1.51007 + 0.688630i −0.355927 + 0.162312i
1919 0.173567 0.173567i 0.0398190 0.0398190i −0.686917 0.726736i 0.741036π-0.741036\pi
0.726736 + 0.686917i 0.241036π0.241036\pi
2020 −6.72515 + 0.473617i −1.50379 + 0.105904i
2121 0.189882 + 0.189882i 0.0414355 + 0.0414355i
2222 0.0771120 0.206401i 0.0164403 0.0440049i
2323 1.00000i 0.208514i
2424 3.35792 1.82643i 0.685432 0.372819i
2525 6.36297i 1.27259i
2626 3.17285 + 1.18538i 0.622247 + 0.232473i
2727 −3.98836 3.98836i −0.767560 0.767560i
2828 0.300049 + 0.260568i 0.0567040 + 0.0492427i
2929 2.98858 2.98858i 0.554966 0.554966i −0.372904 0.927870i 0.621638π-0.621638\pi
0.927870 + 0.372904i 0.121638π0.121638\pi
3030 −2.67317 5.86188i −0.488051 1.07023i
3131 −4.74204 −0.851696 −0.425848 0.904795i 0.640024π-0.640024\pi
−0.425848 + 0.904795i 0.640024π0.640024\pi
3232 4.76717 3.04533i 0.842725 0.538344i
3333 0.210558 0.0366534
3434 −0.378692 0.830418i −0.0649451 0.142416i
3535 0.473617 0.473617i 0.0800558 0.0800558i
3636 −1.77217 1.53898i −0.295361 0.256497i
3737 −1.53702 1.53702i −0.252684 0.252684i 0.569386 0.822070i 0.307181π-0.307181\pi
−0.822070 + 0.569386i 0.807181π0.807181\pi
3838 0.325181 + 0.121488i 0.0527514 + 0.0197080i
3939 3.23674i 0.518294i
4040 −4.55562 8.37556i −0.720307 1.32429i
4141 9.42339i 1.47169i 0.677152 + 0.735843i 0.263214π0.263214\pi
−0.677152 + 0.735843i 0.736786π0.736786\pi
4242 −0.132908 + 0.355746i −0.0205081 + 0.0548929i
4343 −2.46931 2.46931i −0.376566 0.376566i 0.493295 0.869862i 0.335792π-0.335792\pi
−0.869862 + 0.493295i 0.835792π0.835792\pi
4444 0.310832 0.0218902i 0.0468597 0.00330008i
4545 −2.79730 + 2.79730i −0.416997 + 0.416997i
4646 −1.28673 + 0.586784i −0.189719 + 0.0865165i
4747 10.2297 1.49216 0.746081 0.665855i 0.231933π-0.231933\pi
0.746081 + 0.665855i 0.231933π0.231933\pi
4848 4.32050 + 3.24903i 0.623611 + 0.468956i
4949 6.96052 0.994360
5050 −8.18746 + 3.73369i −1.15788 + 0.528023i
5151 0.616730 0.616730i 0.0863594 0.0863594i
5252 0.336502 + 4.77818i 0.0466644 + 0.662614i
5353 6.13987 + 6.13987i 0.843377 + 0.843377i 0.989296 0.145920i 0.0466141π-0.0466141\pi
−0.145920 + 0.989296i 0.546614π0.546614\pi
5454 2.79165 7.47226i 0.379896 1.01685i
5555 0.525189i 0.0708165i
5656 −0.159218 + 0.538981i −0.0212764 + 0.0720243i
5757 0.331730i 0.0439387i
5858 5.59916 + 2.09186i 0.735206 + 0.274675i
5959 3.18941 + 3.18941i 0.415225 + 0.415225i 0.883554 0.468329i 0.155144π-0.155144\pi
−0.468329 + 0.883554i 0.655144π0.655144\pi
6060 5.97411 6.87931i 0.771254 0.888115i
6161 0.134023 0.134023i 0.0171599 0.0171599i −0.698475 0.715635i 0.746138π-0.746138\pi
0.715635 + 0.698475i 0.246138π0.246138\pi
6262 −2.78255 6.10175i −0.353385 0.774923i
6363 0.233187 0.0293788
6464 6.71583 + 4.34713i 0.839479 + 0.543392i
6565 8.07333 1.00137
6666 0.123552 + 0.270932i 0.0152082 + 0.0333494i
6767 8.34921 8.34921i 1.02002 1.02002i 0.0202224 0.999796i 0.493563π-0.493563\pi
0.999796 0.0202224i 0.00643742π-0.00643742\pi
6868 0.846317 0.974552i 0.102631 0.118182i
6969 −0.955624 0.955624i −0.115044 0.115044i
7070 0.887329 + 0.331508i 0.106056 + 0.0396228i
7171 4.76823i 0.565885i 0.959137 + 0.282942i 0.0913105π0.0913105\pi
−0.959137 + 0.282942i 0.908689π0.908689\pi
7272 0.940380 3.18336i 0.110825 0.375162i
7373 5.99750i 0.701954i 0.936384 + 0.350977i 0.114150π0.114150\pi
−0.936384 + 0.350977i 0.885850π0.885850\pi
7474 1.07584 2.87963i 0.125063 0.334750i
7575 −6.08061 6.08061i −0.702128 0.702128i
7676 0.0344876 + 0.489709i 0.00395600 + 0.0561735i
7777 −0.0218902 + 0.0218902i −0.00249463 + 0.00249463i
7878 −4.16483 + 1.89927i −0.471574 + 0.215050i
7979 −0.630585 −0.0709463 −0.0354732 0.999371i 0.511294π-0.511294\pi
−0.0354732 + 0.999371i 0.511294π0.511294\pi
8080 8.10396 10.7765i 0.906050 1.20485i
8181 4.10204 0.455782
8282 −12.1254 + 5.52949i −1.33903 + 0.610630i
8383 0.711208 0.711208i 0.0780653 0.0780653i −0.666996 0.745061i 0.732420π-0.732420\pi
0.745061 + 0.666996i 0.232420π0.232420\pi
8484 −0.535739 + 0.0377293i −0.0584539 + 0.00411660i
8585 −1.53829 1.53829i −0.166851 0.166851i
8686 1.72840 4.62630i 0.186378 0.498867i
8787 5.71192i 0.612382i
8888 0.210558 + 0.387113i 0.0224456 + 0.0412664i
8989 13.8549i 1.46862i −0.678815 0.734310i 0.737506π-0.737506\pi
0.678815 0.734310i 0.262494π-0.262494\pi
9090 −5.24079 1.95797i −0.552428 0.206388i
9191 −0.336502 0.336502i −0.0352750 0.0352750i
9292 −1.51007 1.31137i −0.157436 0.136720i
9393 4.53161 4.53161i 0.469906 0.469906i
9494 6.00265 + 13.1630i 0.619126 + 1.35766i
9595 0.827425 0.0848920
9696 −1.64543 + 7.46582i −0.167936 + 0.761977i
9797 7.33230 0.744482 0.372241 0.928136i 0.378589π-0.378589\pi
0.372241 + 0.928136i 0.378589π0.378589\pi
9898 4.08432 + 8.95634i 0.412578 + 0.904727i
9999 0.129289 0.129289i 0.0129941 0.0129941i
100100 −9.60853 8.34421i −0.960853 0.834421i
101101 −9.48832 9.48832i −0.944123 0.944123i 0.0543965 0.998519i 0.482677π-0.482677\pi
−0.998519 + 0.0543965i 0.982677π0.982677\pi
102102 1.15545 + 0.431680i 0.114407 + 0.0427427i
103103 17.8894i 1.76270i 0.472467 + 0.881348i 0.343363π0.343363\pi
−0.472467 + 0.881348i 0.656637π0.656637\pi
104104 −5.95079 + 3.23674i −0.583523 + 0.317389i
105105 0.905198i 0.0883383i
106106 −4.29761 + 11.5032i −0.417421 + 1.11729i
107107 −0.476373 0.476373i −0.0460527 0.0460527i 0.683705 0.729758i 0.260367π-0.260367\pi
−0.729758 + 0.683705i 0.760367π0.760367\pi
108108 11.2529 0.792483i 1.08281 0.0762567i
109109 −13.5122 + 13.5122i −1.29423 + 1.29423i −0.362092 + 0.932142i 0.617937π0.617937\pi
−0.932142 + 0.362092i 0.882063π0.882063\pi
110110 0.675779 0.308172i 0.0644330 0.0293831i
111111 2.93762 0.278826
112112 −0.786951 + 0.111394i −0.0743599 + 0.0105258i
113113 0.977296 0.0919363 0.0459681 0.998943i 0.485363π-0.485363\pi
0.0459681 + 0.998943i 0.485363π0.485363\pi
114114 −0.426848 + 0.194654i −0.0399780 + 0.0182310i
115115 −2.38359 + 2.38359i −0.222271 + 0.222271i
116116 0.593828 + 8.43210i 0.0551356 + 0.782901i
117117 1.98747 + 1.98747i 0.183741 + 0.183741i
118118 −2.23243 + 5.97541i −0.205512 + 0.550081i
119119 0.128234i 0.0117552i
120120 12.3573 + 3.65043i 1.12807 + 0.333237i
121121 10.9757i 0.997793i
122122 0.251094 + 0.0938095i 0.0227330 + 0.00849311i
123123 −9.00521 9.00521i −0.811973 0.811973i
124124 6.21857 7.16081i 0.558444 0.643060i
125125 −3.24877 + 3.24877i −0.290578 + 0.290578i
126126 0.136830 + 0.300049i 0.0121898 + 0.0267305i
127127 −15.5758 −1.38212 −0.691062 0.722795i 0.742857π-0.742857\pi
−0.691062 + 0.722795i 0.742857π0.742857\pi
128128 −1.65287 + 11.1923i −0.146094 + 0.989271i
129129 4.71946 0.415526
130130 4.73730 + 10.3882i 0.415488 + 0.911108i
131131 5.80329 5.80329i 0.507036 0.507036i −0.406579 0.913615i 0.633279π-0.633279\pi
0.913615 + 0.406579i 0.133279π0.133279\pi
132132 −0.276119 + 0.317957i −0.0240331 + 0.0276746i
133133 −0.0344876 0.0344876i −0.00299046 0.00299046i
134134 15.6424 + 5.84403i 1.35130 + 0.504847i
135135 19.0132i 1.63640i
136136 1.75059 + 0.517135i 0.150112 + 0.0443439i
137137 21.8496i 1.86674i −0.358915 0.933370i 0.616853π-0.616853\pi
0.358915 0.933370i 0.383147π-0.383147\pi
138138 0.668889 1.79038i 0.0569396 0.152407i
139139 −11.8543 11.8543i −1.00547 1.00547i −0.999985 0.00548673i 0.998254π-0.998254\pi
−0.00548673 0.999985i 0.501746π-0.501746\pi
140140 0.0941072 + 1.33628i 0.00795351 + 0.112936i
141141 −9.77579 + 9.77579i −0.823270 + 0.823270i
142142 −6.13544 + 2.79792i −0.514875 + 0.234796i
143143 −0.373144 −0.0312039
144144 4.64793 0.657922i 0.387328 0.0548268i
145145 14.2471 1.18316
146146 −7.71718 + 3.51923i −0.638679 + 0.291254i
147147 −6.65164 + 6.65164i −0.548618 + 0.548618i
148148 4.33660 0.305404i 0.356466 0.0251040i
149149 −8.38711 8.38711i −0.687099 0.687099i 0.274491 0.961590i 0.411491π-0.411491\pi
−0.961590 + 0.274491i 0.911491π0.911491\pi
150150 4.25613 11.3921i 0.347511 0.930163i
151151 15.0923i 1.22819i 0.789230 + 0.614097i 0.210480π0.210480\pi
−0.789230 + 0.614097i 0.789520π0.789520\pi
152152 −0.609889 + 0.331730i −0.0494685 + 0.0269068i
153153 0.757384i 0.0612308i
154154 −0.0410118 0.0153221i −0.00330482 0.00123469i
155155 −11.3031 11.3031i −0.907884 0.907884i
156156 −4.88771 4.24457i −0.391330 0.339838i
157157 11.9073 11.9073i 0.950307 0.950307i −0.0485157 0.998822i 0.515449π-0.515449\pi
0.998822 + 0.0485157i 0.0154491π0.0154491\pi
158158 −0.370017 0.811395i −0.0294370 0.0645511i
159159 −11.7348 −0.930632
160160 18.6218 + 4.10416i 1.47218 + 0.324462i
161161 0.198699 0.0156597
162162 2.40701 + 5.27823i 0.189112 + 0.414697i
163163 4.28797 4.28797i 0.335860 0.335860i −0.518947 0.854807i 0.673676π-0.673676\pi
0.854807 + 0.518947i 0.173676π0.173676\pi
164164 −14.2300 12.3575i −1.11117 0.964962i
165165 0.501883 + 0.501883i 0.0390716 + 0.0390716i
166166 1.33246 + 0.497811i 0.103419 + 0.0386376i
167167 6.68260i 0.517115i −0.965996 0.258557i 0.916753π-0.916753\pi
0.965996 0.258557i 0.0832471π-0.0832471\pi
168168 −0.362911 0.667215i −0.0279992 0.0514768i
169169 7.26395i 0.558765i
170170 1.07673 2.88202i 0.0825813 0.221041i
171171 0.203693 + 0.203693i 0.0155768 + 0.0155768i
172172 6.96701 0.490650i 0.531230 0.0374117i
173173 −3.18817 + 3.18817i −0.242392 + 0.242392i −0.817839 0.575447i 0.804828π-0.804828\pi
0.575447 + 0.817839i 0.304828π0.304828\pi
174174 −7.34972 + 3.35166i −0.557181 + 0.254089i
175175 1.26432 0.0955734
176176 −0.374560 + 0.498084i −0.0282335 + 0.0375445i
177177 −6.09574 −0.458184
178178 17.8276 8.12984i 1.33624 0.609358i
179179 −4.02322 + 4.02322i −0.300709 + 0.300709i −0.841291 0.540582i 0.818204π-0.818204\pi
0.540582 + 0.841291i 0.318204π0.318204\pi
180180 −0.555821 7.89241i −0.0414284 0.588266i
181181 −7.39749 7.39749i −0.549851 0.549851i 0.376546 0.926398i 0.377112π-0.377112\pi
−0.926398 + 0.376546i 0.877112π0.877112\pi
182182 0.235535 0.630442i 0.0174590 0.0467315i
183183 0.256151i 0.0189352i
184184 0.801301 2.71255i 0.0590727 0.199972i
185185 7.32722i 0.538708i
186186 8.49005 + 3.17190i 0.622520 + 0.232575i
187187 0.0710989 + 0.0710989i 0.00519926 + 0.00519926i
188188 −13.4150 + 15.4476i −0.978388 + 1.12663i
189189 −0.792483 + 0.792483i −0.0576447 + 0.0576447i
190190 0.485519 + 1.06468i 0.0352233 + 0.0772397i
191191 22.3903 1.62011 0.810054 0.586356i 0.199438π-0.199438\pi
0.810054 + 0.586356i 0.199438π0.199438\pi
192192 −10.5720 + 2.26358i −0.762971 + 0.163360i
193193 18.2552 1.31404 0.657018 0.753875i 0.271818π-0.271818\pi
0.657018 + 0.753875i 0.271818π0.271818\pi
194194 4.30247 + 9.43472i 0.308900 + 0.677374i
195195 −7.71506 + 7.71506i −0.552487 + 0.552487i
196196 −9.12782 + 10.5109i −0.651987 + 0.750776i
197197 −8.05327 8.05327i −0.573772 0.573772i 0.359409 0.933180i 0.382978π-0.382978\pi
−0.933180 + 0.359409i 0.882978π0.882978\pi
198198 0.242226 + 0.0904962i 0.0172142 + 0.00643128i
199199 17.8585i 1.26595i 0.774170 + 0.632977i 0.218167π0.218167\pi
−0.774170 + 0.632977i 0.781833π0.781833\pi
200200 5.09866 17.2599i 0.360529 1.22046i
201201 15.9574i 1.12555i
202202 6.64135 17.7765i 0.467284 1.25075i
203203 −0.593828 0.593828i −0.0416786 0.0416786i
204204 0.122544 + 1.74007i 0.00857977 + 0.121829i
205205 −22.4615 + 22.4615i −1.56878 + 1.56878i
206206 −23.0189 + 10.4972i −1.60380 + 0.731376i
207207 −1.17357 −0.0815686
208208 −7.65666 5.75782i −0.530894 0.399233i
209209 −0.0382430 −0.00264533
210210 −1.16475 + 0.531156i −0.0803754 + 0.0366532i
211211 2.27372 2.27372i 0.156530 0.156530i −0.624497 0.781027i 0.714696π-0.714696\pi
0.781027 + 0.624497i 0.214696π0.214696\pi
212212 −17.3233 + 1.21999i −1.18977 + 0.0837891i
213213 −4.55663 4.55663i −0.312215 0.312215i
214214 0.333438 0.892494i 0.0227933 0.0610096i
215215 11.7716i 0.802819i
216216 7.62274 + 14.0145i 0.518662 + 0.953565i
217217 0.942239i 0.0639634i
218218 −25.3154 9.45788i −1.71457 0.640568i
219219 −5.73135 5.73135i −0.387289 0.387289i
220220 0.793072 + 0.688717i 0.0534689 + 0.0464333i
221221 −1.09295 + 1.09295i −0.0735197 + 0.0735197i
222222 1.72375 + 3.77993i 0.115690 + 0.253692i
223223 −3.29492 −0.220644 −0.110322 0.993896i 0.535188π-0.535188\pi
−0.110322 + 0.993896i 0.535188π0.535188\pi
224224 −0.605105 0.947233i −0.0404303 0.0632897i
225225 −7.46738 −0.497825
226226 0.573461 + 1.25752i 0.0381461 + 0.0836490i
227227 18.7245 18.7245i 1.24279 1.24279i 0.283953 0.958838i 0.408354π-0.408354\pi
0.958838 0.283953i 0.0916459π-0.0916459\pi
228228 −0.500935 0.435021i −0.0331752 0.0288099i
229229 −9.90184 9.90184i −0.654332 0.654332i 0.299701 0.954033i 0.403113π-0.403113\pi
−0.954033 + 0.299701i 0.903113π0.903113\pi
230230 −4.46569 1.66839i −0.294459 0.110011i
231231 0.0418377i 0.00275272i
232232 −10.5014 + 5.71192i −0.689452 + 0.375006i
233233 16.7592i 1.09793i −0.835846 0.548964i 0.815022π-0.815022\pi
0.835846 0.548964i 0.184978π-0.184978\pi
234234 −1.39113 + 3.72355i −0.0909409 + 0.243416i
235235 24.3835 + 24.3835i 1.59060 + 1.59060i
236236 −8.99872 + 0.633732i −0.585766 + 0.0412524i
237237 0.602602 0.602602i 0.0391432 0.0391432i
238238 −0.165003 + 0.0752457i −0.0106956 + 0.00487746i
239239 −16.9820 −1.09847 −0.549237 0.835667i 0.685082π-0.685082\pi
−0.549237 + 0.835667i 0.685082π0.685082\pi
240240 2.55396 + 18.0426i 0.164858 + 1.16465i
241241 −23.6419 −1.52291 −0.761455 0.648218i 0.775514π-0.775514\pi
−0.761455 + 0.648218i 0.775514π0.775514\pi
242242 14.1228 6.44038i 0.907851 0.414003i
243243 8.04507 8.04507i 0.516092 0.516092i
244244 0.0266302 + 0.378138i 0.00170483 + 0.0242078i
245245 16.5910 + 16.5910i 1.05996 + 1.05996i
246246 6.30320 16.8714i 0.401878 1.07568i
247247 0.587881i 0.0374060i
248248 12.8630 + 3.79980i 0.816802 + 0.241288i
249249 1.35929i 0.0861418i
250250 −6.08662 2.27398i −0.384952 0.143819i
251251 10.3035 + 10.3035i 0.650352 + 0.650352i 0.953078 0.302726i 0.0978966π-0.0978966\pi
−0.302726 + 0.953078i 0.597897π0.597897\pi
252252 −0.305794 + 0.352128i −0.0192632 + 0.0221820i
253253 0.110168 0.110168i 0.00692619 0.00692619i
254254 −9.13960 20.0419i −0.573469 1.25754i
255255 2.94006 0.184114
256256 −15.3714 + 4.44067i −0.960714 + 0.277542i
257257 0.589308 0.0367600 0.0183800 0.999831i 0.494149π-0.494149\pi
0.0183800 + 0.999831i 0.494149π0.494149\pi
258258 2.76930 + 6.07270i 0.172409 + 0.378070i
259259 −0.305404 + 0.305404i −0.0189769 + 0.0189769i
260260 −10.5871 + 12.1913i −0.656585 + 0.756071i
261261 3.50730 + 3.50730i 0.217096 + 0.217096i
262262 10.8726 + 4.06202i 0.671710 + 0.250952i
263263 5.79720i 0.357471i 0.983897 + 0.178735i 0.0572006π0.0572006\pi
−0.983897 + 0.178735i 0.942799π0.942799\pi
264264 −0.571149 0.168720i −0.0351518 0.0103840i
265265 29.2699i 1.79803i
266266 0.0241396 0.0646132i 0.00148010 0.00396169i
267267 13.2401 + 13.2401i 0.810281 + 0.810281i
268268 1.65898 + 23.5568i 0.101338 + 1.43896i
269269 5.32110 5.32110i 0.324433 0.324433i −0.526032 0.850465i 0.676321π-0.676321\pi
0.850465 + 0.526032i 0.176321π0.176321\pi
270270 24.4649 11.1566i 1.48889 0.678971i
271271 −17.3009 −1.05096 −0.525479 0.850807i 0.676114π-0.676114\pi
−0.525479 + 0.850807i 0.676114π0.676114\pi
272272 0.361805 + 2.55600i 0.0219376 + 0.154980i
273273 0.643138 0.0389245
274274 28.1147 12.8210i 1.69847 0.774545i
275275 0.700995 0.700995i 0.0422716 0.0422716i
276276 2.69623 0.189882i 0.162294 0.0114295i
277277 −7.24556 7.24556i −0.435343 0.435343i 0.455098 0.890441i 0.349604π-0.349604\pi
−0.890441 + 0.455098i 0.849604π0.849604\pi
278278 8.29745 22.2093i 0.497648 1.33203i
279279 5.56510i 0.333174i
280280 −1.66422 + 0.905198i −0.0994560 + 0.0540959i
281281 4.03701i 0.240828i 0.992724 + 0.120414i 0.0384221π0.0384221\pi
−0.992724 + 0.120414i 0.961578π0.961578\pi
282282 −18.3151 6.84257i −1.09065 0.407469i
283283 10.6603 + 10.6603i 0.633689 + 0.633689i 0.948991 0.315303i 0.102106π-0.102106\pi
−0.315303 + 0.948991i 0.602106π0.602106\pi
284284 −7.20036 6.25291i −0.427262 0.371042i
285285 −0.790707 + 0.790707i −0.0468374 + 0.0468374i
286286 −0.218955 0.480137i −0.0129471 0.0283911i
287287 1.87242 0.110525
288288 3.57390 + 5.59460i 0.210594 + 0.329665i
289289 −16.5835 −0.975500
290290 8.35996 + 18.3322i 0.490913 + 1.07650i
291291 −7.00692 + 7.00692i −0.410753 + 0.410753i
292292 −9.05663 7.86494i −0.529999 0.460261i
293293 9.87783 + 9.87783i 0.577069 + 0.577069i 0.934095 0.357026i 0.116209π-0.116209\pi
−0.357026 + 0.934095i 0.616209π0.616209\pi
294294 −12.4620 4.65582i −0.726796 0.271533i
295295 15.2045i 0.885238i
296296 2.93762 + 5.40084i 0.170746 + 0.313918i
297297 0.878778i 0.0509919i
298298 5.87057 15.7134i 0.340073 0.910253i
299299 1.69353 + 1.69353i 0.0979391 + 0.0979391i
300300 17.1561 1.20821i 0.990506 0.0697561i
301301 −0.490650 + 0.490650i −0.0282806 + 0.0282806i
302302 −19.4198 + 8.85592i −1.11748 + 0.509601i
303303 18.1345 1.04180
304304 −0.784721 0.590111i −0.0450068 0.0338452i
305305 0.638911 0.0365839
306306 0.974552 0.444420i 0.0557114 0.0254058i
307307 13.7274 13.7274i 0.783464 0.783464i −0.196950 0.980414i 0.563104π-0.563104\pi
0.980414 + 0.196950i 0.0631036π0.0631036\pi
308308 −0.00434957 0.0617620i −0.000247840 0.00351922i
309309 −17.0955 17.0955i −0.972532 0.972532i
310310 7.91159 21.1765i 0.449348 1.20274i
311311 27.0977i 1.53657i −0.640110 0.768284i 0.721111π-0.721111\pi
0.640110 0.768284i 0.278889π-0.278889\pi
312312 2.59361 8.77983i 0.146834 0.497060i
313313 8.78013i 0.496282i −0.968724 0.248141i 0.920180π-0.920180\pi
0.968724 0.248141i 0.0798196π-0.0798196\pi
314314 22.3086 + 8.33453i 1.25894 + 0.470345i
315315 0.555821 + 0.555821i 0.0313170 + 0.0313170i
316316 0.826930 0.952227i 0.0465185 0.0535669i
317317 −5.92370 + 5.92370i −0.332708 + 0.332708i −0.853614 0.520906i 0.825594π-0.825594\pi
0.520906 + 0.853614i 0.325594π0.325594\pi
318318 −6.88580 15.0996i −0.386136 0.846743i
319319 −0.658491 −0.0368684
320320 5.64600 + 26.3695i 0.315621 + 1.47410i
321321 0.910467 0.0508173
322322 0.116593 + 0.255673i 0.00649749 + 0.0142481i
323323 −0.112015 + 0.112015i −0.00623267 + 0.00623267i
324324 −5.37929 + 6.19436i −0.298849 + 0.344131i
325325 10.7759 + 10.7759i 0.597737 + 0.597737i
326326 8.03360 + 3.00137i 0.444940 + 0.166231i
327327 25.8252i 1.42813i
328328 7.55097 25.5614i 0.416933 1.41139i
329329 2.03264i 0.112063i
330330 −0.351293 + 0.940287i −0.0193381 + 0.0517611i
331331 21.1008 + 21.1008i 1.15981 + 1.15981i 0.984517 + 0.175289i 0.0560860π0.0560860\pi
0.175289 + 0.984517i 0.443914π0.443914\pi
332332 0.141316 + 2.00663i 0.00775575 + 0.110128i
333333 1.80379 1.80379i 0.0988472 0.0988472i
334334 8.59873 3.92124i 0.470501 0.214561i
335335 39.8021 2.17462
336336 0.645578 0.858480i 0.0352192 0.0468339i
337337 −13.0955 −0.713357 −0.356678 0.934227i 0.616091π-0.616091\pi
−0.356678 + 0.934227i 0.616091π0.616091\pi
338338 −9.34677 + 4.26236i −0.508397 + 0.231842i
339339 −0.933927 + 0.933927i −0.0507239 + 0.0507239i
340340 4.34020 0.305657i 0.235380 0.0165766i
341341 0.522420 + 0.522420i 0.0282907 + 0.0282907i
342342 −0.142575 + 0.381622i −0.00770957 + 0.0206358i
343343 2.77394i 0.149779i
344344 4.71946 + 8.67679i 0.254456 + 0.467821i
345345 4.55562i 0.245267i
346346 −5.97309 2.23156i −0.321116 0.119970i
347347 −18.5247 18.5247i −0.994460 0.994460i 0.00552468 0.999985i 0.498241π-0.498241\pi
−0.999985 + 0.00552468i 0.998241π0.998241\pi
348348 −8.62539 7.49044i −0.462369 0.401530i
349349 14.6830 14.6830i 0.785961 0.785961i −0.194868 0.980829i 0.562428π-0.562428\pi
0.980829 + 0.194868i 0.0624279π0.0624279\pi
350350 0.741881 + 1.62684i 0.0396552 + 0.0869583i
351351 −13.5088 −0.721045
352352 −0.860687 0.189691i −0.0458748 0.0101106i
353353 1.40458 0.0747581 0.0373790 0.999301i 0.488099π-0.488099\pi
0.0373790 + 0.999301i 0.488099π0.488099\pi
354354 −3.57688 7.84360i −0.190109 0.416883i
355355 −11.3655 + 11.3655i −0.603217 + 0.603217i
356356 20.9219 + 18.1689i 1.10886 + 0.962952i
357357 −0.122544 0.122544i −0.00648570 0.00648570i
358358 −7.53757 2.81605i −0.398373 0.148833i
359359 27.5559i 1.45435i 0.686454 + 0.727174i 0.259166π0.259166\pi
−0.686454 + 0.727174i 0.740834π0.740834\pi
360360 9.82929 5.34633i 0.518049 0.281776i
361361 18.9397i 0.996829i
362362 5.17788 13.8593i 0.272143 0.728430i
363363 10.4887 + 10.4887i 0.550512 + 0.550512i
364364 0.949420 0.0668626i 0.0497631 0.00350455i
365365 −14.2956 + 14.2956i −0.748264 + 0.748264i
366366 −0.329598 + 0.150305i −0.0172284 + 0.00785658i
367367 2.58686 0.135033 0.0675165 0.997718i 0.478492π-0.478492\pi
0.0675165 + 0.997718i 0.478492π0.478492\pi
368368 3.96052 0.560617i 0.206456 0.0292242i
369369 −11.0590 −0.575707
370370 9.42819 4.29949i 0.490148 0.223520i
371371 1.21999 1.21999i 0.0633386 0.0633386i
372372 0.900426 + 12.7857i 0.0466849 + 0.662905i
373373 −6.22966 6.22966i −0.322560 0.322560i 0.527189 0.849748i 0.323246π-0.323246\pi
−0.849748 + 0.527189i 0.823246π0.823246\pi
374374 −0.0497657 + 0.133205i −0.00257332 + 0.00688787i
375375 6.20919i 0.320641i
376376 −27.7487 8.19710i −1.43103 0.422733i
377377 10.1225i 0.521334i
378378 −1.48473 0.554699i −0.0763664 0.0285306i
379379 1.65615 + 1.65615i 0.0850706 + 0.0850706i 0.748362 0.663291i 0.230841π-0.230841\pi
−0.663291 + 0.748362i 0.730841π0.730841\pi
380380 −1.08506 + 1.24947i −0.0556624 + 0.0640964i
381381 14.8846 14.8846i 0.762559 0.762559i
382382 13.1383 + 28.8104i 0.672213 + 1.47407i
383383 17.3779 0.887968 0.443984 0.896035i 0.353565π-0.353565\pi
0.443984 + 0.896035i 0.353565π0.353565\pi
384384 −9.11613 12.2752i −0.465205 0.626414i
385385 −0.104355 −0.00531840
386386 10.7118 + 23.4895i 0.545218 + 1.19559i
387387 2.89790 2.89790i 0.147309 0.147309i
388388 −9.61536 + 11.0723i −0.488146 + 0.562110i
389389 10.5112 + 10.5112i 0.532941 + 0.532941i 0.921446 0.388505i 0.127008π-0.127008\pi
−0.388505 + 0.921446i 0.627008π0.627008\pi
390390 −14.4543 5.40016i −0.731922 0.273448i
391391 0.645369i 0.0326377i
392392 −18.8807 5.57747i −0.953621 0.281705i
393393 11.0915i 0.559494i
394394 5.63689 15.0879i 0.283982 0.760120i
395395 −1.50305 1.50305i −0.0756269 0.0756269i
396396 0.0256897 + 0.364782i 0.00129095 + 0.0183310i
397397 23.9835 23.9835i 1.20370 1.20370i 0.230666 0.973033i 0.425909π-0.425909\pi
0.973033 0.230666i 0.0740906π-0.0740906\pi
398398 −22.9791 + 10.4791i −1.15184 + 0.525268i
399399 0.0659144 0.00329985
400400 25.2007 3.56719i 1.26003 0.178360i
401401 −6.10812 −0.305025 −0.152513 0.988302i 0.548736π-0.548736\pi
−0.152513 + 0.988302i 0.548736π0.548736\pi
402402 −20.5329 + 9.36354i −1.02409 + 0.467011i
403403 −8.03077 + 8.03077i −0.400041 + 0.400041i
404404 26.7707 1.88532i 1.33189 0.0937982i
405405 9.77757 + 9.77757i 0.485851 + 0.485851i
406406 0.415650 1.11255i 0.0206284 0.0552148i
407407 0.338659i 0.0167867i
408408 −2.16709 + 1.17872i −0.107287 + 0.0583555i
409409 32.3334i 1.59878i −0.600810 0.799392i 0.705155π-0.705155\pi
0.600810 0.799392i 0.294845π-0.294845\pi
410410 −42.0820 15.7219i −2.07828 0.776450i
411411 20.8800 + 20.8800i 1.02994 + 1.02994i
412412 −27.0143 23.4596i −1.33090 1.15577i
413413 0.633732 0.633732i 0.0311839 0.0311839i
414414 −0.688630 1.51007i −0.0338443 0.0742158i
415415 3.39045 0.166431
416416 2.91598 13.2307i 0.142968 0.648687i
417417 22.6566 1.10950
418418 −0.0224404 0.0492086i −0.00109760 0.00240687i
419419 9.28588 9.28588i 0.453645 0.453645i −0.442917 0.896562i 0.646057π-0.646057\pi
0.896562 + 0.442917i 0.146057π0.146057\pi
420420 −1.36691 1.18705i −0.0666985 0.0579221i
421421 −4.53002 4.53002i −0.220779 0.220779i 0.588047 0.808827i 0.299897π-0.299897\pi
−0.808827 + 0.588047i 0.799897π0.799897\pi
422422 4.25986 + 1.59149i 0.207367 + 0.0774727i
423423 12.0053i 0.583717i
424424 −11.7348 21.5746i −0.569893 1.04775i
425425 4.10646i 0.199193i
426426 3.18942 8.53693i 0.154528 0.413616i
427427 −0.0266302 0.0266302i −0.00128873 0.00128873i
428428 1.34406 0.0946550i 0.0649675 0.00457532i
429429 0.356585 0.356585i 0.0172161 0.0172161i
430430 15.1470 6.90740i 0.730452 0.333105i
431431 24.7717 1.19321 0.596605 0.802535i 0.296516π-0.296516\pi
0.596605 + 0.802535i 0.296516π0.296516\pi
432432 −13.5600 + 18.0319i −0.652407 + 0.867561i
433433 18.8955 0.908059 0.454030 0.890987i 0.349986π-0.349986\pi
0.454030 + 0.890987i 0.349986π0.349986\pi
434434 −1.21241 + 0.552891i −0.0581976 + 0.0265396i
435435 −13.6148 + 13.6148i −0.652782 + 0.652782i
436436 −2.68486 38.1239i −0.128582 1.82580i
437437 0.173567 + 0.173567i 0.00830285 + 0.00830285i
438438 4.01166 10.7378i 0.191685 0.513071i
439439 11.0160i 0.525766i 0.964828 + 0.262883i 0.0846733π0.0846733\pi
−0.964828 + 0.262883i 0.915327π0.915327\pi
440440 −0.420835 + 1.42460i −0.0200625 + 0.0679152i
441441 8.16864i 0.388983i
442442 −2.04766 0.765010i −0.0973972 0.0363878i
443443 3.85949 + 3.85949i 0.183370 + 0.183370i 0.792822 0.609453i 0.208611π-0.208611\pi
−0.609453 + 0.792822i 0.708611π0.708611\pi
444444 −3.85230 + 4.43601i −0.182822 + 0.210523i
445445 33.0244 33.0244i 1.56551 1.56551i
446446 −1.93340 4.23968i −0.0915493 0.200755i
447447 16.0298 0.758186
448448 0.863772 1.33443i 0.0408094 0.0630459i
449449 −38.5451 −1.81905 −0.909527 0.415644i 0.863556π-0.863556\pi
−0.909527 + 0.415644i 0.863556π0.863556\pi
450450 −4.38173 9.60853i −0.206557 0.452950i
451451 1.03815 1.03815i 0.0488848 0.0488848i
452452 −1.28160 + 1.47578i −0.0602812 + 0.0694150i
453453 −14.4226 14.4226i −0.677631 0.677631i
454454 35.0808 + 13.1063i 1.64642 + 0.615107i
455455 1.60416i 0.0752043i
456456 0.265815 0.899833i 0.0124479 0.0421385i
457457 18.3632i 0.858996i 0.903068 + 0.429498i 0.141309π0.141309\pi
−0.903068 + 0.429498i 0.858691π0.858691\pi
458458 6.93080 18.5513i 0.323855 0.866844i
459459 2.57396 + 2.57396i 0.120142 + 0.120142i
460460 −0.473617 6.72515i −0.0220825 0.313562i
461461 8.09188 8.09188i 0.376876 0.376876i −0.493098 0.869974i 0.664135π-0.664135\pi
0.869974 + 0.493098i 0.164135π0.164135\pi
462462 0.0538340 0.0245497i 0.00250458 0.00114215i
463463 −26.6880 −1.24030 −0.620148 0.784485i 0.712927π-0.712927\pi
−0.620148 + 0.784485i 0.712927π0.712927\pi
464464 −13.5118 10.1609i −0.627269 0.471707i
465465 21.6030 1.00181
466466 21.5646 9.83399i 0.998960 0.455551i
467467 10.7335 10.7335i 0.496689 0.496689i −0.413717 0.910406i 0.635770π-0.635770\pi
0.910406 + 0.413717i 0.135770π0.135770\pi
468468 −5.60751 + 0.394908i −0.259207 + 0.0182546i
469469 −1.65898 1.65898i −0.0766046 0.0766046i
470470 −17.0672 + 45.6829i −0.787253 + 2.10720i
471471 22.7578i 1.04862i
472472 −6.09574 11.2071i −0.280579 0.515848i
473473 0.544077i 0.0250167i
474474 1.12899 + 0.421792i 0.0518560 + 0.0193735i
475475 1.10440 + 1.10440i 0.0506735 + 0.0506735i
476476 −0.193643 0.168162i −0.00887559 0.00770771i
477477 −7.20556 + 7.20556i −0.329920 + 0.329920i
478478 −9.96476 21.8513i −0.455777 0.999456i
479479 −15.0208 −0.686317 −0.343159 0.939277i 0.611497π-0.611497\pi
−0.343159 + 0.939277i 0.611497π0.611497\pi
480480 −21.7175 + 13.8734i −0.991261 + 0.633231i
481481 −5.20595 −0.237371
482482 −13.8727 30.4209i −0.631883 1.38563i
483483 −0.189882 + 0.189882i −0.00863991 + 0.00863991i
484484 16.5741 + 14.3932i 0.753368 + 0.654238i
485485 17.4772 + 17.4772i 0.793598 + 0.793598i
486486 15.0726 + 5.63115i 0.683706 + 0.255434i
487487 35.4382i 1.60586i 0.596073 + 0.802930i 0.296727π0.296727\pi
−0.596073 + 0.802930i 0.703273π0.703273\pi
488488 −0.470936 + 0.256151i −0.0213183 + 0.0115954i
489489 8.19538i 0.370608i
490490 −11.6129 + 31.0835i −0.524617 + 1.40421i
491491 −19.3127 19.3127i −0.871572 0.871572i 0.121072 0.992644i 0.461367π-0.461367\pi
−0.992644 + 0.121072i 0.961367π0.961367\pi
492492 25.4077 1.78933i 1.14547 0.0806691i
493493 −1.92874 + 1.92874i −0.0868659 + 0.0868659i
494494 0.756446 0.344959i 0.0340341 0.0155204i
495495 0.616345 0.0277026
496496 2.65847 + 18.7809i 0.119369 + 0.843289i
497497 0.947443 0.0424986
498498 −1.74905 + 0.797612i −0.0783769 + 0.0357418i
499499 −17.7085 + 17.7085i −0.792743 + 0.792743i −0.981939 0.189197i 0.939412π-0.939412\pi
0.189197 + 0.981939i 0.439412π0.439412\pi
500500 −0.645527 9.16619i −0.0288688 0.409925i
501501 6.38605 + 6.38605i 0.285308 + 0.285308i
502502 −7.21195 + 19.3038i −0.321885 + 0.861571i
503503 36.4638i 1.62584i −0.582375 0.812921i 0.697876π-0.697876\pi
0.582375 0.812921i 0.302124π-0.302124\pi
504504 −0.632530 0.186853i −0.0281751 0.00832308i
505505 45.2325i 2.01282i
506506 0.206401 + 0.0771120i 0.00917566 + 0.00342805i
507507 −6.94160 6.94160i −0.308287 0.308287i
508508 20.4256 23.5205i 0.906238 1.04355i
509509 −15.9196 + 15.9196i −0.705624 + 0.705624i −0.965612 0.259988i 0.916281π-0.916281\pi
0.259988 + 0.965612i 0.416281π0.416281\pi
510510 1.72518 + 3.78307i 0.0763921 + 0.167517i
511511 1.19170 0.0527176
512512 −14.7337 17.1732i −0.651142 0.758956i
513513 −1.38450 −0.0611270
514514 0.345796 + 0.758282i 0.0152524 + 0.0334464i
515515 −42.6410 + 42.6410i −1.87899 + 1.87899i
516516 −6.18896 + 7.12672i −0.272454 + 0.313736i
517517 −1.12699 1.12699i −0.0495649 0.0495649i
518518 −0.572179 0.213767i −0.0251401 0.00939240i
519519 6.09338i 0.267470i
520520 −21.8993 6.46917i −0.960347 0.283692i
521521 33.2196i 1.45538i 0.685909 + 0.727688i 0.259405π0.259405\pi
−0.685909 + 0.727688i 0.740595π0.740595\pi
522522 −2.45494 + 6.57099i −0.107450 + 0.287604i
523523 −27.4509 27.4509i −1.20034 1.20034i −0.974062 0.226282i 0.927343π-0.927343\pi
−0.226282 0.974062i 0.572657π-0.572657\pi
524524 1.15311 + 16.3736i 0.0503738 + 0.715286i
525525 −1.20821 + 1.20821i −0.0527307 + 0.0527307i
526526 −7.45946 + 3.40170i −0.325248 + 0.148321i
527527 3.06037 0.133312
528528 −0.118042 0.833919i −0.00513714 0.0362917i
529529 −1.00000 −0.0434783
530530 −37.6625 + 17.1751i −1.63596 + 0.746037i
531531 −3.74298 + 3.74298i −0.162432 + 0.162432i
532532 0.0973048 0.00685266i 0.00421870 0.000297101i
533533 15.9587 + 15.9587i 0.691250 + 0.691250i
534534 −9.26741 + 24.8056i −0.401040 + 1.07344i
535535 2.27095i 0.0981819i
536536 −29.3378 + 15.9574i −1.26720 + 0.689255i
537537 7.68936i 0.331821i
538538 9.96917 + 3.72451i 0.429802 + 0.160575i
539539 −0.766825 0.766825i −0.0330295 0.0330295i
540540 28.7112 + 24.9333i 1.23554 + 1.07296i
541541 −19.2548 + 19.2548i −0.827830 + 0.827830i −0.987216 0.159386i 0.949048π-0.949048\pi
0.159386 + 0.987216i 0.449048π0.449048\pi
542542 −10.1519 22.2617i −0.436062 0.956222i
543543 14.1384 0.606738
544544 −3.07659 + 1.96536i −0.131908 + 0.0842642i
545545 −64.4150 −2.75924
546546 0.377383 + 0.827548i 0.0161505 + 0.0354158i
547547 13.3090 13.3090i 0.569051 0.569051i −0.362812 0.931862i 0.618183π-0.618183\pi
0.931862 + 0.362812i 0.118183π0.118183\pi
548548 32.9945 + 28.6530i 1.40945 + 1.22399i
549549 0.157285 + 0.157285i 0.00671276 + 0.00671276i
550550 1.31333 + 0.490662i 0.0560004 + 0.0209219i
551551 1.03744i 0.0441964i
552552 1.82643 + 3.35792i 0.0777381 + 0.142922i
553553 0.125297i 0.00532816i
554554 5.07153 13.5747i 0.215469 0.576733i
555555 7.00207 + 7.00207i 0.297221 + 0.297221i
556556 33.4463 2.35545i 1.41844 0.0998932i
557557 −15.1073 + 15.1073i −0.640118 + 0.640118i −0.950584 0.310467i 0.899515π-0.899515\pi
0.310467 + 0.950584i 0.399515π0.399515\pi
558558 7.16081 3.26551i 0.303141 0.138240i
559559 −8.36368 −0.353746
560560 −2.14128 1.61025i −0.0904858 0.0680455i
561561 −0.135888 −0.00573718
562562 −5.19455 + 2.36885i −0.219119 + 0.0999239i
563563 −18.6896 + 18.6896i −0.787673 + 0.787673i −0.981112 0.193439i 0.938036π-0.938036\pi
0.193439 + 0.981112i 0.438036π0.438036\pi
564564 −1.94244 27.5818i −0.0817915 1.16140i
565565 2.32947 + 2.32947i 0.0980015 + 0.0980015i
566566 −7.46168 + 19.9722i −0.313638 + 0.839496i
567567 0.815071i 0.0342298i
568568 3.82079 12.9341i 0.160317 0.542701i
569569 11.4387i 0.479536i 0.970830 + 0.239768i 0.0770714π0.0770714\pi
−0.970830 + 0.239768i 0.922929π0.922929\pi
570570 −1.48140 0.553456i −0.0620492 0.0231817i
571571 −11.6909 11.6909i −0.489249 0.489249i 0.418820 0.908069i 0.362444π-0.362444\pi
−0.908069 + 0.418820i 0.862444π0.862444\pi
572572 0.489330 0.563473i 0.0204599 0.0235600i
573573 −21.3967 + 21.3967i −0.893861 + 0.893861i
574574 1.09870 + 2.40931i 0.0458590 + 0.100562i
575575 −6.36297 −0.265354
576576 −5.10165 + 7.88148i −0.212569 + 0.328395i
577577 −35.4727 −1.47675 −0.738374 0.674391i 0.764406π-0.764406\pi
−0.738374 + 0.674391i 0.764406π0.764406\pi
578578 −9.73093 21.3386i −0.404753 0.887567i
579579 −17.4451 + 17.4451i −0.724992 + 0.724992i
580580 −18.6832 + 21.5141i −0.775778 + 0.893324i
581581 −0.141316 0.141316i −0.00586279 0.00586279i
582582 −13.1276 4.90450i −0.544156 0.203298i
583583 1.35283i 0.0560286i
584584 4.80580 16.2685i 0.198865 0.673195i
585585 9.47459i 0.391726i
586586 −6.91399 + 18.5063i −0.285614 + 0.764488i
587587 9.32268 + 9.32268i 0.384788 + 0.384788i 0.872824 0.488036i 0.162286π-0.162286\pi
−0.488036 + 0.872824i 0.662286π0.662286\pi
588588 −1.32167 18.7672i −0.0545049 0.773946i
589589 −0.823063 + 0.823063i −0.0339137 + 0.0339137i
590590 −19.5641 + 8.92172i −0.805441 + 0.367302i
591591 15.3918 0.633134
592592 −5.22570 + 6.94906i −0.214775 + 0.285605i
593593 8.32328 0.341796 0.170898 0.985289i 0.445333π-0.445333\pi
0.170898 + 0.985289i 0.445333π0.445333\pi
594594 −1.13075 + 0.515652i −0.0463954 + 0.0211575i
595595 −0.305657 + 0.305657i −0.0125307 + 0.0125307i
596596 23.6637 1.66651i 0.969304 0.0682630i
597597 −17.0660 17.0660i −0.698464 0.698464i
598598 −1.18538 + 3.17285i −0.0484740 + 0.129747i
599599 40.0370i 1.63587i 0.575313 + 0.817933i 0.304880π0.304880\pi
−0.575313 + 0.817933i 0.695120π0.695120\pi
600600 11.6215 + 21.3663i 0.474448 + 0.872277i
601601 9.90326i 0.403963i −0.979389 0.201981i 0.935262π-0.935262\pi
0.979389 0.201981i 0.0647380π-0.0647380\pi
602602 −0.919241 0.343431i −0.0374655 0.0139972i
603603 9.79835 + 9.79835i 0.399020 + 0.399020i
604604 −22.7904 19.7916i −0.927330 0.805309i
605605 26.1616 26.1616i 1.06362 1.06362i
606606 10.6410 + 23.3343i 0.432263 + 0.947891i
607607 −33.7530 −1.36999 −0.684995 0.728548i 0.740196π-0.740196\pi
−0.684995 + 0.728548i 0.740196π0.740196\pi
608608 0.298855 1.35599i 0.0121202 0.0549929i
609609 1.13495 0.0459906
610610 0.374902 + 0.822108i 0.0151794 + 0.0332862i
611611 17.3243 17.3243i 0.700867 0.700867i
612612 1.14370 + 0.993210i 0.0462314 + 0.0401481i
613613 12.9941 + 12.9941i 0.524827 + 0.524827i 0.919026 0.394198i 0.128978π-0.128978\pi
−0.394198 + 0.919026i 0.628978π0.628978\pi
614614 25.7185 + 9.60850i 1.03791 + 0.387767i
615615 42.9294i 1.73108i
616616 0.0769190 0.0418377i 0.00309916 0.00168569i
617617 42.9224i 1.72799i −0.503501 0.863995i 0.667955π-0.667955\pi
0.503501 0.863995i 0.332045π-0.332045\pi
618618 11.9660 32.0288i 0.481345 1.28839i
619619 4.50065 + 4.50065i 0.180896 + 0.180896i 0.791746 0.610850i 0.209172π-0.209172\pi
−0.610850 + 0.791746i 0.709172π0.709172\pi
620620 31.8909 2.24591i 1.28077 0.0901979i
621621 3.98836 3.98836i 0.160047 0.160047i
622622 34.8675 15.9005i 1.39806 0.637550i
623623 −2.75296 −0.110295
624624 12.8192 1.81458i 0.513178 0.0726412i
625625 16.3274 0.653097
626626 11.2977 5.15203i 0.451546 0.205917i
627627 0.0365460 0.0365460i 0.00145950 0.00145950i
628628 2.36597 + 33.5957i 0.0944125 + 1.34062i
629629 0.991942 + 0.991942i 0.0395513 + 0.0395513i
630630 −0.389047 + 1.04134i −0.0155000 + 0.0414880i
631631 21.5372i 0.857383i −0.903451 0.428691i 0.858975π-0.858975\pi
0.903451 0.428691i 0.141025π-0.141025\pi
632632 1.71049 + 0.505288i 0.0680397 + 0.0200993i
633633 4.34565i 0.172724i
634634 −11.0982 4.14630i −0.440764 0.164670i
635635 −37.1262 37.1262i −1.47331 1.47331i
636636 15.3887 17.7204i 0.610201 0.702659i
637637 11.7878 11.7878i 0.467050 0.467050i
638638 −0.386392 0.847303i −0.0152974 0.0335450i
639639 −5.59584 −0.221368
640640 −30.6176 + 22.7381i −1.21027 + 0.898803i
641641 19.9600 0.788373 0.394187 0.919030i 0.371026π-0.371026\pi
0.394187 + 0.919030i 0.371026π0.371026\pi
642642 0.534247 + 1.17153i 0.0210851 + 0.0462366i
643643 11.5859 11.5859i 0.456905 0.456905i −0.440733 0.897638i 0.645282π-0.645282\pi
0.897638 + 0.440733i 0.145282π0.145282\pi
644644 −0.260568 + 0.300049i −0.0102678 + 0.0118236i
645645 11.2493 + 11.2493i 0.442939 + 0.442939i
646646 −0.209862 0.0784049i −0.00825690 0.00308480i
647647 21.3677i 0.840053i −0.907512 0.420026i 0.862021π-0.862021\pi
0.907512 0.420026i 0.137979π-0.137979\pi
648648 −11.1270 3.28697i −0.437109 0.129124i
649649 0.702740i 0.0275850i
650650 −7.54257 + 20.1888i −0.295844 + 0.791868i
651651 −0.900426 0.900426i −0.0352905 0.0352905i
652652 0.852017 + 12.0983i 0.0333675 + 0.473804i
653653 −35.5745 + 35.5745i −1.39214 + 1.39214i −0.571615 + 0.820522i 0.693683π0.693683\pi
−0.820522 + 0.571615i 0.806317π0.806317\pi
654654 33.2301 15.1538i 1.29940 0.592560i
655655 27.6653 1.08097
656656 37.3215 5.28292i 1.45716 0.206263i
657657 −7.03847 −0.274597
658658 2.61547 1.19272i 0.101962 0.0464971i
659659 23.0602 23.0602i 0.898296 0.898296i −0.0969891 0.995285i 0.530921π-0.530921\pi
0.995285 + 0.0969891i 0.0309212π0.0309212\pi
660660 −1.41603 + 0.0997237i −0.0551190 + 0.00388174i
661661 −26.3968 26.3968i −1.02671 1.02671i −0.999633 0.0270814i 0.991379π-0.991379\pi
−0.0270814 0.999633i 0.508621π-0.508621\pi
662662 −14.7695 + 39.5328i −0.574034 + 1.53648i
663663 2.08889i 0.0811259i
664664 −2.49908 + 1.35929i −0.0969831 + 0.0527509i
665665 0.164409i 0.00637549i
666666 3.37944 + 1.26257i 0.130950 + 0.0489234i
667667 2.98858 + 2.98858i 0.115718 + 0.115718i
668668 10.0912 + 8.76336i 0.390440 + 0.339064i
669669 3.14870 3.14870i 0.121736 0.121736i
670670 23.3552 + 51.2147i 0.902291 + 1.97860i
671671 −0.0295300 −0.00113999
672672 1.48345 + 0.326946i 0.0572254 + 0.0126122i
673673 −26.3257 −1.01478 −0.507391 0.861716i 0.669390π-0.669390\pi
−0.507391 + 0.861716i 0.669390π0.669390\pi
674674 −7.68422 16.8504i −0.295985 0.649054i
675675 25.3778 25.3778i 0.976793 0.976793i
676676 −10.9691 9.52572i −0.421887 0.366374i
677677 34.7259 + 34.7259i 1.33462 + 1.33462i 0.901180 + 0.433445i 0.142702π0.142702\pi
0.433445 + 0.901180i 0.357298π0.357298\pi
678678 −1.74973 0.653703i −0.0671979 0.0251053i
679679 1.45692i 0.0559115i
680680 2.94006 + 5.40533i 0.112746 + 0.207285i
681681 35.7872i 1.37137i
682682 −0.365669 + 0.978764i −0.0140022 + 0.0374788i
683683 −21.2863 21.2863i −0.814498 0.814498i 0.170807 0.985305i 0.445363π-0.445363\pi
−0.985305 + 0.170807i 0.945363π0.945363\pi
684684 −0.574707 + 0.0404736i −0.0219745 + 0.00154755i
685685 52.0805 52.0805i 1.98989 1.98989i
686686 3.56933 1.62770i 0.136278 0.0621460i
687687 18.9249 0.722029
688688 −8.39541 + 11.1641i −0.320072 + 0.425627i
689689 20.7961 0.792267
690690 5.86188 2.67317i 0.223158 0.101766i
691691 −16.7977 + 16.7977i −0.639016 + 0.639016i −0.950313 0.311296i 0.899237π-0.899237\pi
0.311296 + 0.950313i 0.399237π0.399237\pi
692692 −0.633487 8.99523i −0.0240815 0.341947i
693693 −0.0256897 0.0256897i −0.000975870 0.000975870i
694694 12.9664 34.7064i 0.492198 1.31744i
695695 56.5117i 2.14361i
696696 4.57696 15.4938i 0.173489 0.587293i
697697 6.08156i 0.230356i
698698 27.5088 + 10.2774i 1.04122 + 0.389004i
699699 16.0154 + 16.0154i 0.605760 + 0.605760i
700700 −1.65799 + 1.90921i −0.0626660 + 0.0721612i
701701 9.14173 9.14173i 0.345279 0.345279i −0.513069 0.858347i 0.671491π-0.671491\pi
0.858347 + 0.513069i 0.171491π0.171491\pi
702702 −7.92673 17.3822i −0.299175 0.656049i
703703 −0.533551 −0.0201233
704704 −0.260954 1.21878i −0.00983509 0.0459346i
705705 −46.6029 −1.75517
706706 0.824182 + 1.80732i 0.0310185 + 0.0680193i
707707 −1.88532 + 1.88532i −0.0709048 + 0.0709048i
708708 7.99378 9.20499i 0.300424 0.345945i
709709 6.26542 + 6.26542i 0.235303 + 0.235303i 0.814902 0.579599i 0.196791π-0.196791\pi
−0.579599 + 0.814902i 0.696791π0.696791\pi
710710 −21.2934 7.95528i −0.799129 0.298556i
711711 0.740034i 0.0277534i
712712 −11.1020 + 37.5822i −0.416064 + 1.40845i
713713 4.74204i 0.177591i
714714 0.0857745 0.229588i 0.00321003 0.00859210i
715715 −0.889421 0.889421i −0.0332625 0.0332625i
716716 −0.799410 11.3513i −0.0298753 0.424217i
717717 16.2284 16.2284i 0.606061 0.606061i
718718 −35.4572 + 16.1694i −1.32325 + 0.603436i
719719 −14.6826 −0.547569 −0.273784 0.961791i 0.588275π-0.588275\pi
−0.273784 + 0.961791i 0.588275π0.588275\pi
720720 12.6470 + 9.51054i 0.471325 + 0.354437i
721721 3.55461 0.132381
722722 −24.3704 + 11.1135i −0.906973 + 0.413603i
723723 22.5928 22.5928i 0.840234 0.840234i
724724 20.8716 1.46988i 0.775686 0.0546275i
725725 19.0163 + 19.0163i 0.706246 + 0.706246i
726726 −7.34155 + 19.6507i −0.272470 + 0.729306i
727727 38.0962i 1.41291i −0.707757 0.706456i 0.750293π-0.750293\pi
0.707757 0.706456i 0.249707π-0.249707\pi
728728 0.643138 + 1.18242i 0.0238363 + 0.0438233i
729729 27.6822i 1.02527i
730730 −26.7830 10.0062i −0.991282 0.370345i
731731 1.59362 + 1.59362i 0.0589420 + 0.0589420i
732732 −0.386806 0.335909i −0.0142968 0.0124155i
733733 −9.11245 + 9.11245i −0.336576 + 0.336576i −0.855077 0.518501i 0.826490π-0.826490\pi
0.518501 + 0.855077i 0.326490π0.326490\pi
734734 1.51793 + 3.32860i 0.0560277 + 0.122861i
735735 −31.7095 −1.16962
736736 3.04533 + 4.76717i 0.112252 + 0.175720i
737737 −1.83963 −0.0677636
738738 −6.48923 14.2300i −0.238872 0.523812i
739739 −24.5125 + 24.5125i −0.901708 + 0.901708i −0.995584 0.0938755i 0.970074π-0.970074\pi
0.0938755 + 0.995584i 0.470074π0.470074\pi
740740 11.0646 + 9.60870i 0.406743 + 0.353223i
741741 0.561793 + 0.561793i 0.0206380 + 0.0206380i
742742 2.28567 + 0.853931i 0.0839095 + 0.0313488i
743743 35.3509i 1.29690i −0.761258 0.648449i 0.775418π-0.775418\pi
0.761258 0.648449i 0.224582π-0.224582\pi
744744 −15.9234 + 8.66102i −0.583780 + 0.317528i
745745 39.9828i 1.46486i
746746 4.36045 11.6714i 0.159648 0.427320i
747747 0.834651 + 0.834651i 0.0305383 + 0.0305383i
748748 −0.200601 + 0.0141273i −0.00733470 + 0.000516545i
749749 −0.0946550 + 0.0946550i −0.00345862 + 0.00345862i
750750 7.98958 3.64345i 0.291738 0.133040i
751751 −47.2423 −1.72390 −0.861948 0.506997i 0.830755π-0.830755\pi
−0.861948 + 0.506997i 0.830755π0.830755\pi
752752 −5.73497 40.5151i −0.209133 1.47743i
753753 −19.6926 −0.717637
754754 13.0249 5.93970i 0.474340 0.216311i
755755 −35.9738 + 35.9738i −1.30922 + 1.30922i
756756 −0.157466 2.23594i −0.00572697 0.0813205i
757757 −3.51361 3.51361i −0.127704 0.127704i 0.640366 0.768070i 0.278783π-0.278783\pi
−0.768070 + 0.640366i 0.778783π0.778783\pi
758758 −1.15922 + 3.10282i −0.0421048 + 0.112700i
759759 0.210558i 0.00764277i
760760 −2.24443 0.663016i −0.0814140 0.0240501i
761761 15.6852i 0.568587i 0.958737 + 0.284294i 0.0917591π0.0917591\pi
−0.958737 + 0.284294i 0.908241π0.908241\pi
762762 27.8865 + 10.4185i 1.01022 + 0.377421i
763763 2.68486 + 2.68486i 0.0971986 + 0.0971986i
764764 −29.3620 + 33.8109i −1.06228 + 1.22324i
765765 1.80529 1.80529i 0.0652704 0.0652704i
766766 10.1971 + 22.3607i 0.368435 + 0.807925i
767767 10.8027 0.390062
768768 10.4457 18.9329i 0.376926 0.683182i
769769 36.5815 1.31916 0.659582 0.751632i 0.270733π-0.270733\pi
0.659582 + 0.751632i 0.270733π0.270733\pi
770770 −0.0612336 0.134277i −0.00220670 0.00483899i
771771 −0.563156 + 0.563156i −0.0202816 + 0.0202816i
772772 −23.9393 + 27.5666i −0.861593 + 0.992142i
773773 8.64036 + 8.64036i 0.310772 + 0.310772i 0.845209 0.534436i 0.179476π-0.179476\pi
−0.534436 + 0.845209i 0.679476π0.679476\pi
774774 5.42927 + 2.02839i 0.195151 + 0.0729089i
775775 30.1735i 1.08386i
776776 −19.8892 5.87538i −0.713981 0.210914i
777777 0.583702i 0.0209402i
778778 −7.35735 + 19.6930i −0.263774 + 0.706028i
779779 1.63559 + 1.63559i 0.0586011 + 0.0586011i
780780 −1.53298 21.7676i −0.0548893 0.779404i
781781 0.525305 0.525305i 0.0187969 0.0187969i
782782 0.830418 0.378692i 0.0296957 0.0135420i
783783 −23.8391 −0.851939
784784 −3.90219 27.5673i −0.139364 0.984545i
785785 56.7642 2.02600
786786 −14.2718 + 6.50833i −0.509060 + 0.232144i
787787 −16.4340 + 16.4340i −0.585810 + 0.585810i −0.936494 0.350684i 0.885949π-0.885949\pi
0.350684 + 0.936494i 0.385949π0.385949\pi
788788 22.7218 1.60018i 0.809431 0.0570040i
789789 −5.53994 5.53994i −0.197227 0.197227i
790790 1.05206 2.81600i 0.0374307 0.100189i
791791 0.194188i 0.00690452i
792792 −0.454303 + 0.247104i −0.0161430 + 0.00878045i
793793 0.453943i 0.0161200i
794794 44.9336 + 16.7873i 1.59463 + 0.595759i
795795 −27.9710 27.9710i −0.992028 0.992028i
796796 −26.9675 23.4191i −0.955839 0.830067i
797797 25.2190 25.2190i 0.893301 0.893301i −0.101531 0.994832i 0.532374π-0.532374\pi
0.994832 + 0.101531i 0.0323742π0.0323742\pi
798798 0.0386775 + 0.0848143i 0.00136917 + 0.00300239i
799799 −6.60196 −0.233561
800800 19.3774 + 30.3334i 0.685094 + 1.07245i
801801 16.2597 0.574508
802802 −3.58415 7.85953i −0.126561 0.277530i
803803 0.660731 0.660731i 0.0233167 0.0233167i
804804 −24.0968 20.9261i −0.849828 0.738005i
805805 0.473617 + 0.473617i 0.0166928 + 0.0166928i
806806 −15.0458 5.62114i −0.529965 0.197996i
807807 10.1699i 0.357999i
808808 18.1345 + 33.3405i 0.637970 + 1.17292i
809809 4.15515i 0.146087i 0.997329 + 0.0730437i 0.0232713π0.0232713\pi
−0.997329 + 0.0730437i 0.976729π0.976729\pi
810810 −6.84381 + 18.3184i −0.240467 + 0.643644i
811811 17.1267 + 17.1267i 0.601401 + 0.601401i 0.940684 0.339283i 0.110184π-0.110184\pi
−0.339283 + 0.940684i 0.610184π0.610184\pi
812812 1.67545 0.117993i 0.0587968 0.00414075i
813813 16.5332 16.5332i 0.579844 0.579844i
814814 −0.435765 + 0.198720i −0.0152735 + 0.00696512i
815815 20.4415 0.716035
816816 −2.78832 2.09682i −0.0976107 0.0734034i
817817 −0.857183 −0.0299890
818818 41.6045 18.9727i 1.45467 0.663365i
819819 0.394908 0.394908i 0.0137992 0.0137992i
820820 −4.46307 63.3737i −0.155857 2.21310i
821821 3.56382 + 3.56382i 0.124378 + 0.124378i 0.766556 0.642178i 0.221969π-0.221969\pi
−0.642178 + 0.766556i 0.721969π0.721969\pi
822822 −14.6150 + 39.1191i −0.509756 + 1.36444i
823823 3.74854i 0.130666i 0.997864 + 0.0653330i 0.0208110π0.0208110\pi
−0.997864 + 0.0653330i 0.979189π0.979189\pi
824824 14.3348 48.5259i 0.499377 1.69048i
825825 1.33977i 0.0466450i
826826 1.18731 + 0.443581i 0.0413117 + 0.0154342i
827827 30.9923 + 30.9923i 1.07771 + 1.07771i 0.996715 + 0.0809919i 0.0258088π0.0258088\pi
0.0809919 + 0.996715i 0.474191π0.474191\pi
828828 1.53898 1.77217i 0.0534833 0.0615871i
829829 35.4267 35.4267i 1.23042 1.23042i 0.266617 0.963802i 0.414094π-0.414094\pi
0.963802 0.266617i 0.0859060π-0.0859060\pi
830830 1.98946 + 4.36261i 0.0690553 + 0.151429i
831831 13.8481 0.480384
832832 18.7354 4.01145i 0.649534 0.139072i
833833 −4.49210 −0.155642
834834 13.2945 + 29.1530i 0.460351 + 1.00949i
835835 15.9286 15.9286i 0.551230 0.551230i
836836 0.0501508 0.0577496i 0.00173450 0.00199731i
837837 18.9130 + 18.9130i 0.653728 + 0.653728i
838838 17.3973 + 6.49966i 0.600978 + 0.224527i
839839 21.5359i 0.743503i −0.928332 0.371751i 0.878757π-0.878757\pi
0.928332 0.371751i 0.121243π-0.121243\pi
840840 0.725336 2.45539i 0.0250265 0.0847191i
841841 11.1368i 0.384027i
842842 3.17079 8.48707i 0.109273 0.292484i
843843 −3.85786 3.85786i −0.132872 0.132872i
844844 0.451787 + 6.41517i 0.0155511 + 0.220819i
845845 −17.3142 + 17.3142i −0.595628 + 0.595628i
846846 −15.4476 + 7.04451i −0.531100 + 0.242195i
847847 −2.18087 −0.0749355
848848 20.8750 27.7592i 0.716849 0.953255i
849849 −20.3745 −0.699249
850850 5.28393 2.40961i 0.181237 0.0826488i
851851 1.53702 1.53702i 0.0526882 0.0526882i
852852 12.8563 0.905399i 0.440448 0.0310184i
853853 −5.87912 5.87912i −0.201297 0.201297i 0.599258 0.800556i 0.295462π-0.295462\pi
−0.800556 + 0.599258i 0.795462π0.795462\pi
854854 0.0186399 0.0498922i 0.000637843 0.00170728i
855855 0.971039i 0.0332088i
856856 0.910467 + 1.67390i 0.0311191 + 0.0572129i
857857 22.1495i 0.756611i 0.925681 + 0.378306i 0.123493π0.123493\pi
−0.925681 + 0.378306i 0.876507π0.876507\pi
858858 0.668069 + 0.249592i 0.0228075 + 0.00852093i
859859 −21.2141 21.2141i −0.723817 0.723817i 0.245564 0.969380i 0.421027π-0.421027\pi
−0.969380 + 0.245564i 0.921027π0.921027\pi
860860 17.7760 + 15.4370i 0.606156 + 0.526396i
861861 −1.78933 + 1.78933i −0.0609801 + 0.0609801i
862862 14.5356 + 31.8745i 0.495085 + 1.08565i
863863 −18.1225 −0.616897 −0.308448 0.951241i 0.599810π-0.599810\pi
−0.308448 + 0.951241i 0.599810π0.599810\pi
864864 −31.1591 6.86732i −1.06005 0.233631i
865865 −15.1986 −0.516767
866866 11.0876 + 24.3135i 0.376771 + 0.826205i
867867 15.8476 15.8476i 0.538212 0.538212i
868868 −1.42285 1.23562i −0.0482946 0.0419398i
869869 0.0694702 + 0.0694702i 0.00235661 + 0.00235661i
870870 −25.5077 9.52972i −0.864791 0.323088i
871871 28.2792i 0.958203i
872872 47.4798 25.8252i 1.60787 0.874550i
873873 8.60495i 0.291233i
874874 −0.121488 + 0.325181i −0.00410941 + 0.0109994i
875875 0.645527 + 0.645527i 0.0218228 + 0.0218228i
876876 16.1707 1.13881i 0.546356 0.0384770i
877877 −16.3977 + 16.3977i −0.553712 + 0.553712i −0.927510 0.373798i 0.878055π-0.878055\pi
0.373798 + 0.927510i 0.378055π0.378055\pi
878878 −14.1747 + 6.46402i −0.478373 + 0.218150i
879879 −18.8790 −0.636772
880880 −2.08002 + 0.294430i −0.0701175 + 0.00992524i
881881 17.3802 0.585554 0.292777 0.956181i 0.405421π-0.405421\pi
0.292777 + 0.956181i 0.405421π0.405421\pi
882882 −10.5109 + 4.79322i −0.353919 + 0.161396i
883883 −32.1303 + 32.1303i −1.08127 + 1.08127i −0.0848783 + 0.996391i 0.527050π0.527050\pi
−0.996391 + 0.0848783i 0.972950π0.972950\pi
884884 −0.217168 3.08369i −0.00730414 0.103716i
885885 −14.5297 14.5297i −0.488412 0.488412i
886886 −2.70145 + 7.23081i −0.0907570 + 0.242924i
887887 19.2567i 0.646577i 0.946301 + 0.323288i 0.104788π0.104788\pi
−0.946301 + 0.323288i 0.895212π0.895212\pi
888888 −7.96843 2.35392i −0.267403 0.0789922i
889889 3.09489i 0.103799i
890890 61.8718 + 23.1155i 2.07395 + 0.774832i
891891 −0.451913 0.451913i −0.0151396 0.0151396i
892892 4.32085 4.97555i 0.144673 0.166594i
893893 1.77555 1.77555i 0.0594165 0.0594165i
894894 9.40605 + 20.6262i 0.314585 + 0.689842i
895895 −19.1794 −0.641096
896896 2.22390 + 0.328423i 0.0742954 + 0.0109718i
897897 −3.23674 −0.108072
898898 −22.6176 49.5973i −0.754760 1.65508i
899899 −14.1720 + 14.1720i −0.472662 + 0.472662i
900900 9.79249 11.2763i 0.326416 0.375875i
901901 −3.96248 3.96248i −0.132009 0.132009i
902902 1.94500 + 0.726657i 0.0647614 + 0.0241950i
903903 0.937753i 0.0312065i
904904 −2.65096 0.783108i −0.0881697 0.0260458i
905905 35.2651i 1.17225i
906906 10.0951 27.0209i 0.335387 0.897711i
907907 10.0733 + 10.0733i 0.334478 + 0.334478i 0.854284 0.519806i 0.173996π-0.173996\pi
−0.519806 + 0.854284i 0.673996π0.673996\pi
908908 3.72055 + 52.8301i 0.123471 + 1.75323i
909909 11.1352 11.1352i 0.369331 0.369331i
910910 2.06413 0.941297i 0.0684253 0.0312037i
911911 −15.0348 −0.498123 −0.249062 0.968488i 0.580122π-0.580122\pi
−0.249062 + 0.968488i 0.580122π0.580122\pi
912912 1.31382 0.185974i 0.0435050 0.00615820i
913913 −0.156705 −0.00518616
914914 −23.6286 + 10.7752i −0.781565 + 0.356413i
915915 −0.610558 + 0.610558i −0.0201844 + 0.0201844i
916916 27.9374 1.96749i 0.923079 0.0650076i
917917 −1.15311 1.15311i −0.0380790 0.0380790i
918918 −1.80165 + 4.82236i −0.0594632 + 0.159162i
919919 7.04804i 0.232493i 0.993220 + 0.116247i 0.0370863π0.0370863\pi
−0.993220 + 0.116247i 0.962914π0.962914\pi
920920 8.37556 4.55562i 0.276134 0.150194i
921921 26.2364i 0.864520i
922922 15.1603 + 5.66391i 0.499277 + 0.186531i
923923 8.07512 + 8.07512i 0.265796 + 0.265796i
924924 0.0631778 + 0.0548647i 0.00207840 + 0.00180492i
925925 9.77999 9.77999i 0.321564 0.321564i
926926 −15.6601 34.3403i −0.514622 1.12849i
927927 −20.9944 −0.689548
928928 5.14586 23.3483i 0.168921 0.766446i
929929 18.2295 0.598092 0.299046 0.954239i 0.403332π-0.403332\pi
0.299046 + 0.954239i 0.403332π0.403332\pi
930930 12.6763 + 27.7973i 0.415671 + 0.911508i
931931 1.20812 1.20812i 0.0395945 0.0395945i
932932 25.3075 + 21.9774i 0.828974 + 0.719895i
933933 25.8952 + 25.8952i 0.847770 + 0.847770i
934934 20.1095 + 7.51295i 0.658003 + 0.245831i
935935 0.338941i 0.0110845i
936936 −3.79854 6.98365i −0.124159 0.228268i
937937 3.46482i 0.113191i −0.998397 0.0565954i 0.981976π-0.981976\pi
0.998397 0.0565954i 0.0180245π-0.0180245\pi
938938 1.16120 3.10813i 0.0379147 0.101484i
939939 8.39050 + 8.39050i 0.273813 + 0.273813i
940940 −68.7965 + 4.84498i −2.24390 + 0.158026i
941941 −37.0149 + 37.0149i −1.20665 + 1.20665i −0.234548 + 0.972105i 0.575361π0.575361\pi
−0.972105 + 0.234548i 0.924639π0.924639\pi
942942 −29.2833 + 13.3539i −0.954100 + 0.435094i
943943 −9.42339 −0.306868
944944 10.8437 14.4197i 0.352931 0.469323i
945945 −3.77791 −0.122895
946946 −0.700083 + 0.319256i −0.0227617 + 0.0103799i
947947 11.3604 11.3604i 0.369162 0.369162i −0.498009 0.867172i 0.665935π-0.665935\pi
0.867172 + 0.498009i 0.165935π0.165935\pi
948948 0.119736 + 1.70020i 0.00388886 + 0.0552201i
949949 10.1569 + 10.1569i 0.329707 + 0.329707i
950950 −0.773028 + 2.06912i −0.0250803 + 0.0671311i
951951 11.3217i 0.367130i
952952 0.102754 0.347841i 0.00333028 0.0112736i
953953 20.7206i 0.671205i 0.942004 + 0.335602i 0.108940π0.108940\pi
−0.942004 + 0.335602i 0.891060π0.891060\pi
954954 −13.4997 5.04353i −0.437070 0.163290i
955955 53.3693 + 53.3693i 1.72699 + 1.72699i
956956 22.2697 25.6440i 0.720253 0.829386i
957957 0.629269 0.629269i 0.0203414 0.0203414i
958958 −8.81395 19.3278i −0.284766 0.624452i
959959 −4.34150 −0.140194
960960 −30.5948 19.8039i −0.987443 0.639168i
961961 −8.51304 −0.274614
962962 −3.05477 6.69867i −0.0984896 0.215974i
963963 0.559056 0.559056i 0.0180153 0.0180153i
964964 31.0033 35.7009i 0.998549 1.14985i
965965 43.5128 + 43.5128i 1.40073 + 1.40073i
966966 −0.355746 0.132908i −0.0114460 0.00427624i
967967 2.41108i 0.0775351i 0.999248 + 0.0387676i 0.0123432π0.0123432\pi
−0.999248 + 0.0387676i 0.987657π0.987657\pi
968968 −8.79486 + 29.7722i −0.282677 + 0.956914i
969969 0.214088i 0.00687750i
970970 −12.2332 + 32.7438i −0.392783 + 1.05134i
971971 21.2034 + 21.2034i 0.680450 + 0.680450i 0.960101 0.279652i 0.0902191π-0.0902191\pi
−0.279652 + 0.960101i 0.590219π0.590219\pi
972972 1.59855 + 22.6987i 0.0512735 + 0.728061i
973973 −2.35545 + 2.35545i −0.0755121 + 0.0755121i
974974 −45.5996 + 20.7946i −1.46111 + 0.666301i
975975 −20.5953 −0.659578
976976 −0.605936 0.455665i −0.0193955 0.0145855i
977977 54.6270 1.74767 0.873836 0.486221i 0.161625π-0.161625\pi
0.873836 + 0.486221i 0.161625π0.161625\pi
978978 −10.5453 + 4.80891i −0.337201 + 0.153772i
979979 −1.52637 + 1.52637i −0.0487829 + 0.0487829i
980980 −46.8105 + 3.29662i −1.49531 + 0.105307i
981981 −15.8575 15.8575i −0.506290 0.506290i
982982 13.5180 36.1828i 0.431376 1.15464i
983983 50.7618i 1.61905i 0.587086 + 0.809525i 0.300275π0.300275\pi
−0.587086 + 0.809525i 0.699725π0.699725\pi
984984 17.2112 + 31.6430i 0.548673 + 1.00874i
985985 38.3913i 1.22325i
986986 −3.61352 1.35002i −0.115078 0.0429934i
987987 1.94244 + 1.94244i 0.0618285 + 0.0618285i
988988 0.887741 + 0.770929i 0.0282428 + 0.0245265i
989989 2.46931 2.46931i 0.0785195 0.0785195i
990990 0.361661 + 0.793072i 0.0114943 + 0.0252055i
991991 −1.15359 −0.0366450 −0.0183225 0.999832i 0.505833π-0.505833\pi
−0.0183225 + 0.999832i 0.505833π0.505833\pi
992992 −22.6061 + 14.4411i −0.717746 + 0.458505i
993993 −40.3289 −1.27980
994994 0.555944 + 1.21911i 0.0176335 + 0.0386677i
995995 −42.5672 + 42.5672i −1.34947 + 1.34947i
996996 −2.05263 1.78254i −0.0650400 0.0564819i
997997 27.0122 + 27.0122i 0.855484 + 0.855484i 0.990802 0.135318i 0.0432057π-0.0432057\pi
−0.135318 + 0.990802i 0.543206π0.543206\pi
998998 −33.1772 12.3951i −1.05021 0.392360i
999999 12.2603i 0.387900i
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 368.2.j.c.277.4 yes 12
4.3 odd 2 1472.2.j.c.369.5 12
16.3 odd 4 1472.2.j.c.1105.5 12
16.13 even 4 inner 368.2.j.c.93.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
368.2.j.c.93.4 12 16.13 even 4 inner
368.2.j.c.277.4 yes 12 1.1 even 1 trivial
1472.2.j.c.369.5 12 4.3 odd 2
1472.2.j.c.1105.5 12 16.3 odd 4