Properties

Label 650.2.bd.b.47.5
Level 650650
Weight 22
Character 650.47
Analytic conductor 5.1905.190
Analytic rank 00
Dimension 144144
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [650,2,Mod(47,650)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(650, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([17, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("650.47");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 650=25213 650 = 2 \cdot 5^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 650.bd (of order 2020, degree 88, 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: 5.190276131385.19027613138
Analytic rank: 00
Dimension: 144144
Relative dimension: 1818 over Q(ζ20)\Q(\zeta_{20})
Twist minimal: yes
Sato-Tate group: SU(2)[C20]\mathrm{SU}(2)[C_{20}]

Embedding invariants

Embedding label 47.5
Character χ\chi == 650.47
Dual form 650.2.bd.b.83.5

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+(0.9510570.309017i)q2+(1.89075+0.299466i)q3+(0.809017+0.587785i)q4+(1.55473+1.60711i)q5+(1.89075+0.299466i)q6+3.88967q7+(0.5877850.809017i)q8+(0.6321030.205383i)q9+(1.975261.04801i)q10+(1.853753.63818i)q11+(1.705670.869084i)q12+(1.996693.00220i)q13+(3.699291.20197i)q14+(2.458353.50424i)q15+(0.309017+0.951057i)q16+(0.106133+0.670099i)q170.664633q18+(0.892542+5.63529i)q19+(2.20244+0.386329i)q20+(7.35441+1.16482i)q21+(0.638758+4.03296i)q22+(2.178461.10998i)q23+(1.35363+1.35363i)q24+(0.1656044.99726i)q25+(2.82670+2.23825i)q26+(3.983382.02963i)q27+(3.14681+2.28629i)q28+(4.55237+6.26579i)q29+(3.42090+2.57306i)q30+(3.45533+0.547270i)q311.00000iq32+(4.59449+6.32378i)q33+(0.3080110.604505i)q34+(6.04740+6.25112i)q35+(0.632103+0.205383i)q36+(2.72215+8.37791i)q37+(2.590265.08367i)q38+(2.87619+6.27437i)q39+(2.21403+0.313171i)q40+(5.037859.88734i)q41+(7.35441+1.16482i)q42+(4.88202+4.88202i)q43+(0.6387584.03296i)q44+(0.652680+1.33517i)q45+(2.41484+0.382473i)q46+(3.50504+2.54656i)q47+(0.8690841.70567i)q48+8.12952q49+(1.38674+4.80385i)q501.29878iq51+(3.380011.25521i)q52+(9.826241.55632i)q53+(4.41561+0.699363i)q54+(8.72904+2.67723i)q55+(2.286293.14681i)q5610.9222iq57+(6.265794.55237i)q58+(3.25785+6.39390i)q59+(4.048581.39001i)q60+(0.840444+2.58662i)q61+(3.117101.58824i)q62+(2.458670.798871i)q63+(0.309017+0.951057i)q64+(1.72055+7.87653i)q65+(2.415477.43405i)q66+(0.740215+1.01882i)q67+(0.479738+0.479738i)q68+(3.78653+2.75108i)q69+(7.683124.07642i)q70+(2.52444+15.9387i)q71+(0.5376990.390661i)q72+(0.1436860.0466865i)q738.80905iq74+(1.80963+9.39899i)q75+(4.03442+4.03442i)q76+(7.2104614.1513i)q77+(4.674315.07849i)q78+(4.20678+5.79014i)q79+(2.008890.982016i)q80+(8.53688+6.20240i)q81+(7.84663+7.84663i)q82+(5.70478+4.14477i)q83+(6.634513.38045i)q84+(0.9119141.21239i)q85+(3.134456.15171i)q86+(6.7310113.2104i)q87+(1.85375+3.63818i)q88+(4.949002.52164i)q89+(1.033331.06814i)q90+(7.7664711.6776i)q91+(2.41484+0.382473i)q926.69707q93+(2.546563.50504i)q94+(7.6688610.1958i)q95+(0.299466+1.89075i)q96+(3.896725.36337i)q97+(7.731642.51216i)q98+(1.918981.91898i)q99+O(q100)q+(-0.951057 - 0.309017i) q^{2} +(-1.89075 + 0.299466i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.55473 + 1.60711i) q^{5} +(1.89075 + 0.299466i) q^{6} +3.88967 q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.632103 - 0.205383i) q^{9} +(1.97526 - 1.04801i) q^{10} +(-1.85375 - 3.63818i) q^{11} +(-1.70567 - 0.869084i) q^{12} +(1.99669 - 3.00220i) q^{13} +(-3.69929 - 1.20197i) q^{14} +(2.45835 - 3.50424i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.106133 + 0.670099i) q^{17} -0.664633 q^{18} +(-0.892542 + 5.63529i) q^{19} +(-2.20244 + 0.386329i) q^{20} +(-7.35441 + 1.16482i) q^{21} +(0.638758 + 4.03296i) q^{22} +(2.17846 - 1.10998i) q^{23} +(1.35363 + 1.35363i) q^{24} +(-0.165604 - 4.99726i) q^{25} +(-2.82670 + 2.23825i) q^{26} +(3.98338 - 2.02963i) q^{27} +(3.14681 + 2.28629i) q^{28} +(-4.55237 + 6.26579i) q^{29} +(-3.42090 + 2.57306i) q^{30} +(3.45533 + 0.547270i) q^{31} -1.00000i q^{32} +(4.59449 + 6.32378i) q^{33} +(0.308011 - 0.604505i) q^{34} +(-6.04740 + 6.25112i) q^{35} +(0.632103 + 0.205383i) q^{36} +(2.72215 + 8.37791i) q^{37} +(2.59026 - 5.08367i) q^{38} +(-2.87619 + 6.27437i) q^{39} +(2.21403 + 0.313171i) q^{40} +(5.03785 - 9.88734i) q^{41} +(7.35441 + 1.16482i) q^{42} +(4.88202 + 4.88202i) q^{43} +(0.638758 - 4.03296i) q^{44} +(-0.652680 + 1.33517i) q^{45} +(-2.41484 + 0.382473i) q^{46} +(3.50504 + 2.54656i) q^{47} +(-0.869084 - 1.70567i) q^{48} +8.12952 q^{49} +(-1.38674 + 4.80385i) q^{50} -1.29878i q^{51} +(3.38001 - 1.25521i) q^{52} +(9.82624 - 1.55632i) q^{53} +(-4.41561 + 0.699363i) q^{54} +(8.72904 + 2.67723i) q^{55} +(-2.28629 - 3.14681i) q^{56} -10.9222i q^{57} +(6.26579 - 4.55237i) q^{58} +(-3.25785 + 6.39390i) q^{59} +(4.04858 - 1.39001i) q^{60} +(-0.840444 + 2.58662i) q^{61} +(-3.11710 - 1.58824i) q^{62} +(2.45867 - 0.798871i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(1.72055 + 7.87653i) q^{65} +(-2.41547 - 7.43405i) q^{66} +(0.740215 + 1.01882i) q^{67} +(-0.479738 + 0.479738i) q^{68} +(-3.78653 + 2.75108i) q^{69} +(7.68312 - 4.07642i) q^{70} +(2.52444 + 15.9387i) q^{71} +(-0.537699 - 0.390661i) q^{72} +(-0.143686 - 0.0466865i) q^{73} -8.80905i q^{74} +(1.80963 + 9.39899i) q^{75} +(-4.03442 + 4.03442i) q^{76} +(-7.21046 - 14.1513i) q^{77} +(4.67431 - 5.07849i) q^{78} +(-4.20678 + 5.79014i) q^{79} +(-2.00889 - 0.982016i) q^{80} +(-8.53688 + 6.20240i) q^{81} +(-7.84663 + 7.84663i) q^{82} +(-5.70478 + 4.14477i) q^{83} +(-6.63451 - 3.38045i) q^{84} +(-0.911914 - 1.21239i) q^{85} +(-3.13445 - 6.15171i) q^{86} +(6.73101 - 13.2104i) q^{87} +(-1.85375 + 3.63818i) q^{88} +(4.94900 - 2.52164i) q^{89} +(1.03333 - 1.06814i) q^{90} +(7.76647 - 11.6776i) q^{91} +(2.41484 + 0.382473i) q^{92} -6.69707 q^{93} +(-2.54656 - 3.50504i) q^{94} +(-7.66886 - 10.1958i) q^{95} +(0.299466 + 1.89075i) q^{96} +(3.89672 - 5.36337i) q^{97} +(-7.73164 - 2.51216i) q^{98} +(-1.91898 - 1.91898i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 144q+36q42q520q9+12q1326q1536q16+6q17152q1820q198q206q2112q232q25+14q2624q27+20q2912q30+40q99+O(q100) 144 q + 36 q^{4} - 2 q^{5} - 20 q^{9} + 12 q^{13} - 26 q^{15} - 36 q^{16} + 6 q^{17} - 152 q^{18} - 20 q^{19} - 8 q^{20} - 6 q^{21} - 12 q^{23} - 2 q^{25} + 14 q^{26} - 24 q^{27} + 20 q^{29} - 12 q^{30}+ \cdots - 40 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/650Z)×\left(\mathbb{Z}/650\mathbb{Z}\right)^\times.

nn 2727 301301
χ(n)\chi(n) e(1720)e\left(\frac{17}{20}\right) 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 −0.951057 0.309017i −0.672499 0.218508i
33 −1.89075 + 0.299466i −1.09163 + 0.172897i −0.676192 0.736726i 0.736371π-0.736371\pi
−0.415436 + 0.909622i 0.636371π0.636371\pi
44 0.809017 + 0.587785i 0.404508 + 0.293893i
55 −1.55473 + 1.60711i −0.695298 + 0.718721i
66 1.89075 + 0.299466i 0.771897 + 0.122257i
77 3.88967 1.47016 0.735078 0.677982i 0.237145π-0.237145\pi
0.735078 + 0.677982i 0.237145π0.237145\pi
88 −0.587785 0.809017i −0.207813 0.286031i
99 0.632103 0.205383i 0.210701 0.0684609i
1010 1.97526 1.04801i 0.624633 0.331411i
1111 −1.85375 3.63818i −0.558926 1.09695i −0.981649 0.190695i 0.938926π-0.938926\pi
0.422724 0.906259i 0.361074π-0.361074\pi
1212 −1.70567 0.869084i −0.492386 0.250883i
1313 1.99669 3.00220i 0.553782 0.832661i
1414 −3.69929 1.20197i −0.988678 0.321241i
1515 2.45835 3.50424i 0.634742 0.904791i
1616 0.309017 + 0.951057i 0.0772542 + 0.237764i
1717 −0.106133 + 0.670099i −0.0257411 + 0.162523i −0.997210 0.0746427i 0.976218π-0.976218\pi
0.971469 + 0.237166i 0.0762184π0.0762184\pi
1818 −0.664633 −0.156655
1919 −0.892542 + 5.63529i −0.204763 + 1.29282i 0.644398 + 0.764690i 0.277108π0.277108\pi
−0.849161 + 0.528134i 0.822892π0.822892\pi
2020 −2.20244 + 0.386329i −0.492481 + 0.0863859i
2121 −7.35441 + 1.16482i −1.60486 + 0.254185i
2222 0.638758 + 4.03296i 0.136184 + 0.859829i
2323 2.17846 1.10998i 0.454240 0.231447i −0.211873 0.977297i 0.567956π-0.567956\pi
0.666114 + 0.745850i 0.267956π0.267956\pi
2424 1.35363 + 1.35363i 0.276309 + 0.276309i
2525 −0.165604 4.99726i −0.0331208 0.999451i
2626 −2.82670 + 2.23825i −0.554361 + 0.438958i
2727 3.98338 2.02963i 0.766601 0.390603i
2828 3.14681 + 2.28629i 0.594691 + 0.432068i
2929 −4.55237 + 6.26579i −0.845353 + 1.16353i 0.139514 + 0.990220i 0.455446π0.455446\pi
−0.984868 + 0.173309i 0.944554π0.944554\pi
3030 −3.42090 + 2.57306i −0.624567 + 0.469774i
3131 3.45533 + 0.547270i 0.620595 + 0.0982926i 0.458812 0.888534i 0.348275π-0.348275\pi
0.161784 + 0.986826i 0.448275π0.448275\pi
3232 1.00000i 0.176777i
3333 4.59449 + 6.32378i 0.799799 + 1.10083i
3434 0.308011 0.604505i 0.0528234 0.103672i
3535 −6.04740 + 6.25112i −1.02220 + 1.05663i
3636 0.632103 + 0.205383i 0.105351 + 0.0342305i
3737 2.72215 + 8.37791i 0.447518 + 1.37732i 0.879698 + 0.475532i 0.157744π0.157744\pi
−0.432180 + 0.901787i 0.642256π0.642256\pi
3838 2.59026 5.08367i 0.420195 0.824680i
3939 −2.87619 + 6.27437i −0.460560 + 1.00470i
4040 2.21403 + 0.313171i 0.350069 + 0.0495167i
4141 5.03785 9.88734i 0.786780 1.54414i −0.0513558 0.998680i 0.516354π-0.516354\pi
0.838136 0.545462i 0.183646π-0.183646\pi
4242 7.35441 + 1.16482i 1.13481 + 0.179736i
4343 4.88202 + 4.88202i 0.744502 + 0.744502i 0.973441 0.228939i 0.0735257π-0.0735257\pi
−0.228939 + 0.973441i 0.573526π0.573526\pi
4444 0.638758 4.03296i 0.0962963 0.607991i
4545 −0.652680 + 1.33517i −0.0972957 + 0.199036i
4646 −2.41484 + 0.382473i −0.356049 + 0.0563926i
4747 3.50504 + 2.54656i 0.511263 + 0.371455i 0.813303 0.581841i 0.197667π-0.197667\pi
−0.302039 + 0.953295i 0.597667π0.597667\pi
4848 −0.869084 1.70567i −0.125442 0.246193i
4949 8.12952 1.16136
5050 −1.38674 + 4.80385i −0.196114 + 0.679367i
5151 1.29878i 0.181865i
5252 3.38001 1.25521i 0.468723 0.174066i
5353 9.82624 1.55632i 1.34974 0.213778i 0.560648 0.828055i 0.310552π-0.310552\pi
0.789090 + 0.614277i 0.210552π0.210552\pi
5454 −4.41561 + 0.699363i −0.600888 + 0.0951713i
5555 8.72904 + 2.67723i 1.17702 + 0.360998i
5656 −2.28629 3.14681i −0.305518 0.420510i
5757 10.9222i 1.44668i
5858 6.26579 4.55237i 0.822739 0.597755i
5959 −3.25785 + 6.39390i −0.424136 + 0.832415i 0.575754 + 0.817623i 0.304709π0.304709\pi
−0.999891 + 0.0147917i 0.995291π0.995291\pi
6060 4.04858 1.39001i 0.522670 0.179450i
6161 −0.840444 + 2.58662i −0.107608 + 0.331183i −0.990334 0.138706i 0.955706π-0.955706\pi
0.882726 + 0.469888i 0.155706π0.155706\pi
6262 −3.11710 1.58824i −0.395872 0.201707i
6363 2.45867 0.798871i 0.309764 0.100648i
6464 −0.309017 + 0.951057i −0.0386271 + 0.118882i
6565 1.72055 + 7.87653i 0.213408 + 0.976963i
6666 −2.41547 7.43405i −0.297324 0.915068i
6767 0.740215 + 1.01882i 0.0904316 + 0.124468i 0.851836 0.523809i 0.175490π-0.175490\pi
−0.761404 + 0.648278i 0.775490π0.775490\pi
6868 −0.479738 + 0.479738i −0.0581768 + 0.0581768i
6969 −3.78653 + 2.75108i −0.455845 + 0.331191i
7070 7.68312 4.07642i 0.918309 0.487226i
7171 2.52444 + 15.9387i 0.299596 + 1.89158i 0.434424 + 0.900709i 0.356952π0.356952\pi
−0.134827 + 0.990869i 0.543048π0.543048\pi
7272 −0.537699 0.390661i −0.0633684 0.0460399i
7373 −0.143686 0.0466865i −0.0168172 0.00546424i 0.300596 0.953751i 0.402814π-0.402814\pi
−0.317414 + 0.948287i 0.602814π0.602814\pi
7474 8.80905i 1.02403i
7575 1.80963 + 9.39899i 0.208958 + 1.08530i
7676 −4.03442 + 4.03442i −0.462780 + 0.462780i
7777 −7.21046 14.1513i −0.821708 1.61269i
7878 4.67431 5.07849i 0.529261 0.575026i
7979 −4.20678 + 5.79014i −0.473300 + 0.651442i −0.977200 0.212320i 0.931898π-0.931898\pi
0.503900 + 0.863762i 0.331898π0.331898\pi
8080 −2.00889 0.982016i −0.224601 0.109793i
8181 −8.53688 + 6.20240i −0.948542 + 0.689156i
8282 −7.84663 + 7.84663i −0.866516 + 0.866516i
8383 −5.70478 + 4.14477i −0.626181 + 0.454947i −0.855075 0.518504i 0.826489π-0.826489\pi
0.228894 + 0.973451i 0.426489π0.426489\pi
8484 −6.63451 3.38045i −0.723884 0.368837i
8585 −0.911914 1.21239i −0.0989109 0.131503i
8686 −3.13445 6.15171i −0.337997 0.663356i
8787 6.73101 13.2104i 0.721640 1.41630i
8888 −1.85375 + 3.63818i −0.197610 + 0.387832i
8989 4.94900 2.52164i 0.524593 0.267294i −0.171577 0.985171i 0.554886π-0.554886\pi
0.696170 + 0.717877i 0.254886π0.254886\pi
9090 1.03333 1.06814i 0.108922 0.112592i
9191 7.76647 11.6776i 0.814147 1.22414i
9292 2.41484 + 0.382473i 0.251765 + 0.0398756i
9393 −6.69707 −0.694453
9494 −2.54656 3.50504i −0.262658 0.361518i
9595 −7.66886 10.1958i −0.786809 1.04607i
9696 0.299466 + 1.89075i 0.0305641 + 0.192974i
9797 3.89672 5.36337i 0.395652 0.544568i −0.563994 0.825779i 0.690736π-0.690736\pi
0.959646 + 0.281211i 0.0907360π0.0907360\pi
9898 −7.73164 2.51216i −0.781013 0.253767i
9999 −1.91898 1.91898i −0.192865 0.192865i
100100 2.80334 4.14021i 0.280334 0.414021i
101101 6.74105i 0.670760i 0.942083 + 0.335380i 0.108865π0.108865\pi
−0.942083 + 0.335380i 0.891135π0.891135\pi
102102 −0.401344 + 1.23521i −0.0397390 + 0.122304i
103103 0.169564 + 1.07058i 0.0167076 + 0.105488i 0.994633 0.103467i 0.0329938π-0.0329938\pi
−0.977925 + 0.208955i 0.932994π0.932994\pi
104104 −3.60246 + 0.149294i −0.353250 + 0.0146395i
105105 9.56215 13.6303i 0.933170 1.33018i
106106 −9.82624 1.55632i −0.954409 0.151164i
107107 0.398717 + 0.398717i 0.0385454 + 0.0385454i 0.726117 0.687571i 0.241323π-0.241323\pi
−0.687571 + 0.726117i 0.741323π0.741323\pi
108108 4.41561 + 0.699363i 0.424892 + 0.0672963i
109109 −5.14569 2.62186i −0.492868 0.251129i 0.189847 0.981814i 0.439201π-0.439201\pi
−0.682715 + 0.730685i 0.739201π0.739201\pi
110110 −7.47450 5.24362i −0.712666 0.499960i
111111 −7.65581 15.0254i −0.726657 1.42615i
112112 1.20197 + 3.69929i 0.113576 + 0.349550i
113113 14.4360 + 7.35551i 1.35802 + 0.691948i 0.972967 0.230944i 0.0741815π-0.0741815\pi
0.385058 + 0.922892i 0.374181π0.374181\pi
114114 −3.37516 + 10.3877i −0.316112 + 0.972893i
115115 −1.60307 + 5.22675i −0.149487 + 0.487397i
116116 −7.36588 + 2.39332i −0.683905 + 0.222214i
117117 0.645514 2.30779i 0.0596778 0.213355i
118118 5.07423 5.07423i 0.467120 0.467120i
119119 −0.412823 + 2.60646i −0.0378434 + 0.238934i
120120 −4.27997 + 0.0708974i −0.390706 + 0.00647202i
121121 −3.33436 + 4.58935i −0.303124 + 0.417214i
122122 1.59862 2.20031i 0.144732 0.199207i
123123 −6.56441 + 20.2032i −0.591893 + 1.82166i
124124 2.47374 + 2.47374i 0.222149 + 0.222149i
125125 8.28861 + 7.50326i 0.741356 + 0.671112i
126126 −2.58520 −0.230308
127127 −0.159680 0.313389i −0.0141693 0.0278088i 0.883813 0.467840i 0.154968π-0.154968\pi
−0.897983 + 0.440031i 0.854968π0.854968\pi
128128 0.587785 0.809017i 0.0519534 0.0715077i
129129 −10.6927 7.76871i −0.941440 0.683997i
130130 0.797644 8.02270i 0.0699580 0.703638i
131131 9.89743 7.19091i 0.864743 0.628272i −0.0644284 0.997922i 0.520522π-0.520522\pi
0.929171 + 0.369650i 0.120522π0.120522\pi
132132 7.81662i 0.680349i
133133 −3.47169 + 21.9194i −0.301034 + 1.90065i
134134 −0.389154 1.19769i −0.0336178 0.103465i
135135 −2.93125 + 9.55726i −0.252282 + 0.822558i
136136 0.604505 0.308011i 0.0518359 0.0264117i
137137 −6.68244 20.5664i −0.570919 1.75711i −0.649672 0.760214i 0.725094π-0.725094\pi
0.0787533 0.996894i 0.474906π-0.474906\pi
138138 4.45134 1.44633i 0.378923 0.123120i
139139 8.98627 + 2.91982i 0.762206 + 0.247656i 0.664225 0.747533i 0.268762π-0.268762\pi
0.0979807 + 0.995188i 0.468762π0.468762\pi
140140 −8.56677 + 1.50269i −0.724024 + 0.127001i
141141 −7.38979 3.76529i −0.622332 0.317094i
142142 2.52444 15.9387i 0.211847 1.33755i
143143 −14.6239 1.69900i −1.22291 0.142078i
144144 0.390661 + 0.537699i 0.0325551 + 0.0448083i
145145 −2.99210 17.0578i −0.248480 1.41657i
146146 0.122227 + 0.0888030i 0.0101156 + 0.00734938i
147147 −15.3709 + 2.43452i −1.26777 + 0.200796i
148148 −2.72215 + 8.37791i −0.223759 + 0.688660i
149149 3.56297 3.56297i 0.291890 0.291890i −0.545937 0.837826i 0.683826π-0.683826\pi
0.837826 + 0.545937i 0.183826π0.183826\pi
150150 1.18339 9.49818i 0.0966236 0.775523i
151151 0.937399 0.937399i 0.0762845 0.0762845i −0.667935 0.744220i 0.732822π-0.732822\pi
0.744220 + 0.667935i 0.232822π0.232822\pi
152152 5.08367 2.59026i 0.412340 0.210098i
153153 0.0705396 + 0.445370i 0.00570279 + 0.0360060i
154154 2.48456 + 15.6869i 0.200211 + 1.26408i
155155 −6.25164 + 4.70223i −0.502144 + 0.377692i
156156 −6.01487 + 3.38549i −0.481575 + 0.271056i
157157 −3.93274 3.93274i −0.313867 0.313867i 0.532539 0.846406i 0.321238π-0.321238\pi
−0.846406 + 0.532539i 0.821238π0.821238\pi
158158 5.79014 4.20678i 0.460639 0.334674i
159159 −18.1129 + 5.88525i −1.43645 + 0.466731i
160160 1.60711 + 1.55473i 0.127053 + 0.122913i
161161 8.47349 4.31746i 0.667805 0.340263i
162162 10.0357 3.26080i 0.788479 0.256192i
163163 −5.73632 + 1.86384i −0.449303 + 0.145988i −0.524924 0.851149i 0.675906π-0.675906\pi
0.0756205 + 0.997137i 0.475906π0.475906\pi
164164 9.88734 5.03785i 0.772071 0.393390i
165165 −17.3062 2.44794i −1.34729 0.190572i
166166 6.70637 2.17903i 0.520516 0.169126i
167167 −9.33556 + 6.78268i −0.722407 + 0.524860i −0.887152 0.461476i 0.847320π-0.847320\pi
0.164745 + 0.986336i 0.447320π0.447320\pi
168168 5.26518 + 5.26518i 0.406217 + 0.406217i
169169 −5.02645 11.9889i −0.386650 0.922226i
170170 0.492631 + 1.43485i 0.0377831 + 0.110048i
171171 0.593212 + 3.74540i 0.0453641 + 0.286418i
172172 1.08006 + 6.81922i 0.0823537 + 0.519961i
173173 19.1220 9.74315i 1.45382 0.740758i 0.464371 0.885641i 0.346281π-0.346281\pi
0.989449 + 0.144883i 0.0462805π0.0462805\pi
174174 −10.4838 + 10.4838i −0.794775 + 0.794775i
175175 −0.644144 19.4377i −0.0486927 1.46935i
176176 2.88728 2.88728i 0.217637 0.217637i
177177 4.24505 13.0649i 0.319077 0.982019i
178178 −5.48601 + 0.868899i −0.411194 + 0.0651267i
179179 3.11468 + 2.26295i 0.232802 + 0.169140i 0.698070 0.716029i 0.254042π-0.254042\pi
−0.465269 + 0.885170i 0.654042π0.654042\pi
180180 −1.31283 + 0.696544i −0.0978522 + 0.0519173i
181181 −12.4255 17.1023i −0.923582 1.27120i −0.962311 0.271952i 0.912331π-0.912331\pi
0.0387282 0.999250i 0.487669π-0.487669\pi
182182 −10.9949 + 8.70607i −0.814998 + 0.645337i
183183 0.814468 5.14235i 0.0602072 0.380133i
184184 −2.17846 1.10998i −0.160598 0.0818289i
185185 −17.6964 8.65063i −1.30107 0.636007i
186186 6.36929 + 2.06951i 0.467019 + 0.151744i
187187 2.63469 0.856062i 0.192667 0.0626014i
188188 1.33881 + 4.12043i 0.0976426 + 0.300513i
189189 15.4940 7.89459i 1.12702 0.574247i
190190 4.14285 + 12.0666i 0.300554 + 0.875402i
191191 6.81727 + 20.9814i 0.493280 + 1.51816i 0.819619 + 0.572908i 0.194185π0.194185\pi
−0.326339 + 0.945253i 0.605815π0.605815\pi
192192 0.299466 1.89075i 0.0216121 0.136453i
193193 15.0524i 1.08350i −0.840540 0.541749i 0.817762π-0.817762\pi
0.840540 0.541749i 0.182238π-0.182238\pi
194194 −5.36337 + 3.89672i −0.385068 + 0.279768i
195195 −5.61189 14.3773i −0.401876 1.02958i
196196 6.57692 + 4.77841i 0.469780 + 0.341315i
197197 −10.8255 + 14.9000i −0.771286 + 1.06158i 0.224905 + 0.974381i 0.427793π0.427793\pi
−0.996191 + 0.0872031i 0.972207π0.972207\pi
198198 1.23206 + 2.41806i 0.0875587 + 0.171844i
199199 13.8673 0.983025 0.491512 0.870871i 0.336444π-0.336444\pi
0.491512 + 0.870871i 0.336444π0.336444\pi
200200 −3.94553 + 3.07129i −0.278991 + 0.217173i
201201 −1.70467 1.70467i −0.120238 0.120238i
202202 2.08310 6.41112i 0.146566 0.451085i
203203 −17.7072 + 24.3719i −1.24280 + 1.71057i
204204 0.763401 1.05073i 0.0534488 0.0735660i
205205 8.05752 + 23.4686i 0.562761 + 1.63911i
206206 0.169564 1.07058i 0.0118141 0.0745910i
207207 1.14904 1.14904i 0.0798639 0.0798639i
208208 3.47228 + 0.971234i 0.240759 + 0.0673430i
209209 22.1568 7.19917i 1.53261 0.497977i
210210 −13.3061 + 10.0084i −0.918212 + 0.690642i
211211 5.30682 16.3327i 0.365337 1.12439i −0.584433 0.811442i 0.698683π-0.698683\pi
0.949770 0.312949i 0.101317π-0.101317\pi
212212 8.86438 + 4.51663i 0.608808 + 0.310203i
213213 −9.54621 29.3802i −0.654096 2.01310i
214214 −0.255992 0.502413i −0.0174993 0.0343442i
215215 −15.4362 + 0.255700i −1.05274 + 0.0174386i
216216 −3.98338 2.02963i −0.271034 0.138099i
217217 13.4401 + 2.12870i 0.912372 + 0.144506i
218218 4.08364 + 4.08364i 0.276579 + 0.276579i
219219 0.285656 + 0.0452435i 0.0193029 + 0.00305727i
220220 5.48831 + 7.29673i 0.370022 + 0.491945i
221221 1.79986 + 1.65661i 0.121072 + 0.111436i
222222 2.63801 + 16.6558i 0.177052 + 1.11786i
223223 0.157217 0.483863i 0.0105280 0.0324019i −0.945655 0.325173i 0.894577π-0.894577\pi
0.956183 + 0.292771i 0.0945774π0.0945774\pi
224224 3.88967i 0.259889i
225225 −1.13103 3.12477i −0.0754019 0.208318i
226226 −11.4565 11.4565i −0.762074 0.762074i
227227 −12.4004 4.02914i −0.823044 0.267423i −0.132931 0.991125i 0.542439π-0.542439\pi
−0.690112 + 0.723702i 0.742439π0.742439\pi
228228 6.41993 8.83627i 0.425170 0.585196i
229229 −1.89918 11.9909i −0.125501 0.792383i −0.967494 0.252894i 0.918617π-0.918617\pi
0.841993 0.539489i 0.181383π-0.181383\pi
230230 3.13976 4.47556i 0.207030 0.295110i
231231 17.8711 + 24.5974i 1.17583 + 1.61839i
232232 7.74495 0.508481
233233 −11.5577 1.83056i −0.757168 0.119924i −0.234098 0.972213i 0.575214π-0.575214\pi
−0.523071 + 0.852289i 0.675214π0.675214\pi
234234 −1.32707 + 1.99536i −0.0867530 + 0.130441i
235235 −9.54202 + 1.67376i −0.622453 + 0.109184i
236236 −6.39390 + 3.25785i −0.416207 + 0.212068i
237237 6.22004 12.2075i 0.404035 0.792964i
238238 1.19806 2.35132i 0.0776587 0.152414i
239239 11.9701 + 23.4926i 0.774280 + 1.51961i 0.852531 + 0.522676i 0.175066π0.175066\pi
−0.0782511 + 0.996934i 0.524934π0.524934\pi
240240 4.09240 + 1.25516i 0.264163 + 0.0810200i
241241 −20.2123 10.2987i −1.30199 0.663397i −0.341021 0.940056i 0.610773π-0.610773\pi
−0.960968 + 0.276659i 0.910773π0.910773\pi
242242 4.58935 3.33436i 0.295015 0.214341i
243243 4.80005 4.80005i 0.307924 0.307924i
244244 −2.20031 + 1.59862i −0.140860 + 0.102341i
245245 −12.6392 + 13.0650i −0.807492 + 0.834694i
246246 12.4863 17.1859i 0.796095 1.09573i
247247 15.1362 + 13.9315i 0.963090 + 0.886441i
248248 −1.58824 3.11710i −0.100853 0.197936i
249249 9.54513 9.54513i 0.604898 0.604898i
250250 −5.56430 9.69735i −0.351917 0.613314i
251251 19.5864i 1.23629i −0.786066 0.618143i 0.787885π-0.787885\pi
0.786066 0.618143i 0.212115π-0.212115\pi
252252 2.45867 + 0.798871i 0.154882 + 0.0503241i
253253 −8.07663 5.86802i −0.507773 0.368919i
254254 0.0550219 + 0.347395i 0.00345238 + 0.0217975i
255255 2.08728 + 2.01925i 0.130710 + 0.126450i
256256 −0.809017 + 0.587785i −0.0505636 + 0.0367366i
257257 12.5497 12.5497i 0.782827 0.782827i −0.197480 0.980307i 0.563276π-0.563276\pi
0.980307 + 0.197480i 0.0632758π0.0632758\pi
258258 7.76871 + 10.6927i 0.483659 + 0.665699i
259259 10.5882 + 32.5873i 0.657922 + 2.02487i
260260 −3.23776 + 7.38356i −0.200797 + 0.457909i
261261 −1.59068 + 4.89561i −0.0984606 + 0.303030i
262262 −11.6351 + 3.78048i −0.718821 + 0.233559i
263263 11.4540 + 5.83610i 0.706283 + 0.359869i 0.769952 0.638102i 0.220280π-0.220280\pi
−0.0636689 + 0.997971i 0.520280π0.520280\pi
264264 2.41547 7.43405i 0.148662 0.457534i
265265 −12.7760 + 18.2115i −0.784824 + 1.11872i
266266 10.0752 19.7738i 0.617753 1.21241i
267267 −8.60220 + 6.24987i −0.526446 + 0.382486i
268268 1.25933i 0.0769258i
269269 −3.81965 5.25729i −0.232888 0.320543i 0.676539 0.736407i 0.263479π-0.263479\pi
−0.909427 + 0.415864i 0.863479π0.863479\pi
270270 5.74114 8.18369i 0.349395 0.498043i
271271 24.1871 3.83086i 1.46926 0.232708i 0.630068 0.776540i 0.283027π-0.283027\pi
0.839195 + 0.543831i 0.183027π0.183027\pi
272272 −0.670099 + 0.106133i −0.0406307 + 0.00643527i
273273 −11.1874 + 24.4052i −0.677095 + 1.47707i
274274 21.6248i 1.30640i
275275 −17.8739 + 9.86615i −1.07784 + 0.594951i
276276 −4.68041 −0.281728
277277 11.1948 + 21.9710i 0.672629 + 1.32011i 0.934830 + 0.355096i 0.115552π0.115552\pi
−0.262200 + 0.965013i 0.584448π0.584448\pi
278278 −7.64418 5.55382i −0.458467 0.333096i
279279 2.29652 0.363734i 0.137489 0.0217762i
280280 8.61184 + 1.21813i 0.514656 + 0.0727972i
281281 −1.25793 + 7.94226i −0.0750418 + 0.473796i 0.921337 + 0.388766i 0.127098π0.127098\pi
−0.996378 + 0.0850296i 0.972902π0.972902\pi
282282 5.86457 + 5.86457i 0.349230 + 0.349230i
283283 29.0509 + 4.60121i 1.72690 + 0.273513i 0.939404 0.342812i 0.111379π-0.111379\pi
0.787492 + 0.616325i 0.211379π0.211379\pi
284284 −7.32622 + 14.3785i −0.434731 + 0.853208i
285285 17.5532 + 16.9812i 1.03976 + 1.00588i
286286 13.3832 + 6.13489i 0.791363 + 0.362764i
287287 19.5956 38.4585i 1.15669 2.27013i
288288 −0.205383 0.632103i −0.0121023 0.0372470i
289289 15.7302 + 5.11105i 0.925305 + 0.300650i
290290 −2.42549 + 17.1475i −0.142430 + 1.00694i
291291 −5.76159 + 11.3078i −0.337750 + 0.662872i
292292 −0.0888030 0.122227i −0.00519680 0.00715278i
293293 7.86912i 0.459719i 0.973224 + 0.229859i 0.0738266π0.0738266\pi
−0.973224 + 0.229859i 0.926173π0.926173\pi
294294 15.3709 + 2.43452i 0.896451 + 0.141984i
295295 −5.21060 15.1765i −0.303373 0.883612i
296296 5.17783 7.12667i 0.300955 0.414229i
297297 −14.7683 10.7298i −0.856946 0.622608i
298298 −4.48960 + 2.28757i −0.260076 + 0.132515i
299299 1.01732 8.75647i 0.0588333 0.506400i
300300 −4.06057 + 8.66762i −0.234437 + 0.500425i
301301 18.9895 + 18.9895i 1.09453 + 1.09453i
302302 −1.18119 + 0.601847i −0.0679700 + 0.0346324i
303303 −2.01872 12.7457i −0.115972 0.732220i
304304 −5.63529 + 0.892542i −0.323206 + 0.0511908i
305305 −2.85032 5.37219i −0.163209 0.307611i
306306 0.0705396 0.445370i 0.00403248 0.0254601i
307307 −26.5283 −1.51405 −0.757026 0.653385i 0.773348π-0.773348\pi
−0.757026 + 0.653385i 0.773348π0.773348\pi
308308 2.48456 15.6869i 0.141571 0.893842i
309309 −0.641206 1.97343i −0.0364770 0.112265i
310310 7.39873 2.54023i 0.420220 0.144275i
311311 −17.0123 5.52763i −0.964679 0.313443i −0.216013 0.976391i 0.569305π-0.569305\pi
−0.748666 + 0.662948i 0.769305π0.769305\pi
312312 6.76666 1.36109i 0.383087 0.0770567i
313313 15.8187 + 8.06003i 0.894125 + 0.455580i 0.839770 0.542942i 0.182690π-0.182690\pi
0.0543551 + 0.998522i 0.482690π0.482690\pi
314314 2.52497 + 4.95554i 0.142493 + 0.279657i
315315 −2.53871 + 5.19339i −0.143040 + 0.292614i
316316 −6.80672 + 2.21164i −0.382908 + 0.124414i
317317 −14.7757 20.3369i −0.829884 1.14224i −0.987945 0.154807i 0.950524π-0.950524\pi
0.158061 0.987429i 0.449476π-0.449476\pi
318318 19.0451 1.06799
319319 31.2350 + 4.94714i 1.74883 + 0.276987i
320320 −1.04801 1.97526i −0.0585857 0.110421i
321321 −0.873279 0.634474i −0.0487417 0.0354129i
322322 −9.39294 + 1.48770i −0.523448 + 0.0829060i
323323 −3.68147 1.19618i −0.204843 0.0665574i
324324 −10.5522 −0.586231
325325 −15.3334 9.48080i −0.850546 0.525900i
326326 6.03153 0.334055
327327 10.5144 + 3.41633i 0.581447 + 0.188924i
328328 −10.9602 + 1.73592i −0.605176 + 0.0958504i
329329 13.6335 + 9.90529i 0.751637 + 0.546096i
330330 15.7027 + 7.67604i 0.864407 + 0.422552i
331331 3.20696 + 0.507932i 0.176270 + 0.0279185i 0.243946 0.969789i 0.421558π-0.421558\pi
−0.0676753 + 0.997707i 0.521558π0.521558\pi
332332 −7.05150 −0.387001
333333 3.44136 + 4.73662i 0.188585 + 0.259565i
334334 10.9746 3.56587i 0.600504 0.195116i
335335 −2.78819 0.394385i −0.152335 0.0215476i
336336 −3.38045 6.63451i −0.184419 0.361942i
337337 19.8223 + 10.0999i 1.07979 + 0.550179i 0.901049 0.433718i 0.142798π-0.142798\pi
0.178738 + 0.983897i 0.442798π0.442798\pi
338338 1.07565 + 12.9554i 0.0585077 + 0.704682i
339339 −29.4977 9.58437i −1.60209 0.520552i
340340 −0.0251266 1.51686i −0.00136268 0.0822631i
341341 −4.41423 13.5856i −0.239044 0.735702i
342342 0.593212 3.74540i 0.0320773 0.202528i
343343 4.39347 0.237225
344344 1.08006 6.81922i 0.0582329 0.367668i
345345 1.46577 10.3626i 0.0789143 0.557902i
346346 −21.1969 + 3.35726i −1.13955 + 0.180487i
347347 1.53923 + 9.71833i 0.0826303 + 0.521707i 0.993935 + 0.109973i 0.0350766π0.0350766\pi
−0.911304 + 0.411734i 0.864923π0.864923\pi
348348 13.2104 6.73101i 0.708150 0.360820i
349349 17.3121 + 17.3121i 0.926696 + 0.926696i 0.997491 0.0707944i 0.0225534π-0.0225534\pi
−0.0707944 + 0.997491i 0.522553π0.522553\pi
350350 −5.39395 + 18.6854i −0.288319 + 0.998775i
351351 1.86020 16.0115i 0.0992903 0.854628i
352352 −3.63818 + 1.85375i −0.193916 + 0.0988050i
353353 11.3776 + 8.26631i 0.605569 + 0.439971i 0.847851 0.530234i 0.177896π-0.177896\pi
−0.242282 + 0.970206i 0.577896π0.577896\pi
354354 −8.07456 + 11.1137i −0.429158 + 0.590685i
355355 −29.5401 20.7234i −1.56783 1.09988i
356356 5.48601 + 0.868899i 0.290758 + 0.0460516i
357357 5.05181i 0.267370i
358358 −2.26295 3.11468i −0.119600 0.164616i
359359 2.22821 4.37312i 0.117601 0.230804i −0.824701 0.565569i 0.808657π-0.808657\pi
0.942302 + 0.334764i 0.108657π0.108657\pi
360360 1.46381 0.256767i 0.0771498 0.0135328i
361361 −12.8898 4.18814i −0.678409 0.220428i
362362 6.53249 + 20.1049i 0.343340 + 1.05669i
363363 4.93010 9.67587i 0.258763 0.507851i
364364 13.1471 4.88234i 0.689096 0.255904i
365365 0.298424 0.158334i 0.0156202 0.00828760i
366366 −2.36368 + 4.63898i −0.123551 + 0.242483i
367367 −10.1485 1.60737i −0.529748 0.0839038i −0.114170 0.993461i 0.536421π-0.536421\pi
−0.415578 + 0.909557i 0.636421π0.636421\pi
368368 1.72884 + 1.72884i 0.0901218 + 0.0901218i
369369 1.15375 7.28450i 0.0600619 0.379216i
370370 14.1571 + 13.6957i 0.735993 + 0.712007i
371371 38.2208 6.05358i 1.98433 0.314286i
372372 −5.41804 3.93644i −0.280912 0.204095i
373373 −12.4856 24.5044i −0.646480 1.26879i −0.948889 0.315609i 0.897791π-0.897791\pi
0.302410 0.953178i 0.402209π-0.402209\pi
374374 −2.77027 −0.143247
375375 −17.9187 11.7047i −0.925318 0.604426i
376376 4.33247i 0.223430i
377377 9.72152 + 26.1780i 0.500684 + 1.34823i
378378 −17.1752 + 2.72029i −0.883399 + 0.139917i
379379 −37.2473 + 5.89939i −1.91327 + 0.303031i −0.995552 0.0942117i 0.969967π-0.969967\pi
−0.917713 + 0.397243i 0.869967π0.869967\pi
380380 −0.211306 12.7562i −0.0108398 0.654380i
381381 0.395765 + 0.544723i 0.0202756 + 0.0279070i
382382 22.0612i 1.12875i
383383 −19.4954 + 14.1642i −0.996167 + 0.723758i −0.961263 0.275633i 0.911113π-0.911113\pi
−0.0349041 + 0.999391i 0.511113π0.511113\pi
384384 −0.869084 + 1.70567i −0.0443503 + 0.0870423i
385385 33.9531 + 10.4135i 1.73041 + 0.530723i
386386 −4.65146 + 14.3157i −0.236753 + 0.728651i
387387 4.08863 + 2.08326i 0.207837 + 0.105898i
388388 6.30502 2.04863i 0.320089 0.104003i
389389 0.960723 2.95680i 0.0487106 0.149916i −0.923743 0.383014i 0.874886π-0.874886\pi
0.972453 + 0.233098i 0.0748862π0.0748862\pi
390390 0.894379 + 15.4078i 0.0452886 + 0.780206i
391391 0.512590 + 1.57759i 0.0259228 + 0.0797822i
392392 −4.77841 6.57692i −0.241346 0.332185i
393393 −16.5602 + 16.5602i −0.835351 + 0.835351i
394394 14.9000 10.8255i 0.750653 0.545381i
395395 −2.76496 15.7629i −0.139120 0.793117i
396396 −0.424539 2.68043i −0.0213339 0.134697i
397397 7.64938 + 5.55760i 0.383911 + 0.278928i 0.762956 0.646450i 0.223747π-0.223747\pi
−0.379045 + 0.925378i 0.623747π0.623747\pi
398398 −13.1886 4.28522i −0.661083 0.214799i
399399 42.4839i 2.12685i
400400 4.70150 1.70174i 0.235075 0.0850868i
401401 −9.82060 + 9.82060i −0.490417 + 0.490417i −0.908438 0.418020i 0.862724π-0.862724\pi
0.418020 + 0.908438i 0.362724π0.362724\pi
402402 1.09446 + 2.14800i 0.0545869 + 0.107133i
403403 8.54224 9.28087i 0.425519 0.462313i
404404 −3.96229 + 5.45362i −0.197131 + 0.271328i
405405 3.30463 23.3628i 0.164208 1.16091i
406406 24.3719 17.7072i 1.20956 0.878793i
407407 25.4342 25.4342i 1.26073 1.26073i
408408 −1.05073 + 0.763401i −0.0520190 + 0.0377940i
409409 −25.4043 12.9442i −1.25616 0.640047i −0.306069 0.952009i 0.599014π-0.599014\pi
−0.950095 + 0.311962i 0.899014π0.899014\pi
410410 −0.410973 24.8098i −0.0202965 1.22527i
411411 18.7938 + 36.8849i 0.927030 + 1.81940i
412412 −0.492093 + 0.965787i −0.0242437 + 0.0475809i
413413 −12.6720 + 24.8701i −0.623547 + 1.22378i
414414 −1.44788 + 0.737730i −0.0711592 + 0.0362574i
415415 2.20832 15.6122i 0.108402 0.766374i
416416 −3.00220 1.99669i −0.147195 0.0978958i
417417 −17.8652 2.82957i −0.874864 0.138565i
418418 −23.2970 −1.13949
419419 −0.526979 0.725324i −0.0257446 0.0354344i 0.795951 0.605361i 0.206971π-0.206971\pi
−0.821695 + 0.569927i 0.806971π0.806971\pi
420420 15.7477 5.40668i 0.768407 0.263819i
421421 2.22292 + 14.0350i 0.108339 + 0.684024i 0.980752 + 0.195256i 0.0625536π0.0625536\pi
−0.872414 + 0.488768i 0.837446π0.837446\pi
422422 −10.0942 + 13.8934i −0.491377 + 0.676322i
423423 2.73857 + 0.889815i 0.133154 + 0.0432643i
424424 −7.03481 7.03481i −0.341641 0.341641i
425425 3.36623 + 0.419404i 0.163286 + 0.0203441i
426426 30.8922i 1.49673i
427427 −3.26905 + 10.0611i −0.158200 + 0.486891i
428428 0.0882089 + 0.556929i 0.00426374 + 0.0269202i
429429 28.1590 1.16697i 1.35953 0.0563421i
430430 14.7597 + 4.52686i 0.711776 + 0.218305i
431431 8.76048 + 1.38752i 0.421978 + 0.0668347i 0.363812 0.931472i 0.381475π-0.381475\pi
0.0581653 + 0.998307i 0.481475π0.481475\pi
432432 3.16123 + 3.16123i 0.152095 + 0.152095i
433433 −21.0492 3.33387i −1.01156 0.160215i −0.371413 0.928468i 0.621127π-0.621127\pi
−0.640147 + 0.768252i 0.721127π0.721127\pi
434434 −12.1245 6.17773i −0.581993 0.296540i
435435 10.7656 + 31.3561i 0.516169 + 1.50341i
436436 −2.62186 5.14569i −0.125564 0.246434i
437437 4.31070 + 13.2670i 0.206209 + 0.634645i
438438 −0.257694 0.131302i −0.0123131 0.00627384i
439439 −5.69517 + 17.5279i −0.271816 + 0.836563i 0.718229 + 0.695807i 0.244953π0.244953\pi
−0.990044 + 0.140755i 0.955047π0.955047\pi
440440 −2.96488 8.63558i −0.141345 0.411685i
441441 5.13870 1.66966i 0.244700 0.0795078i
442442 −1.19985 2.13172i −0.0570708 0.101396i
443443 13.2539 13.2539i 0.629713 0.629713i −0.318283 0.947996i 0.603106π-0.603106\pi
0.947996 + 0.318283i 0.103106π0.103106\pi
444444 2.63801 16.6558i 0.125195 0.790447i
445445 −3.64183 + 11.8741i −0.172639 + 0.562885i
446446 −0.299044 + 0.411598i −0.0141601 + 0.0194898i
447447 −5.66971 + 7.80369i −0.268168 + 0.369102i
448448 −1.20197 + 3.69929i −0.0567879 + 0.174775i
449449 −12.6619 12.6619i −0.597552 0.597552i 0.342109 0.939660i 0.388859π-0.388859\pi
−0.939660 + 0.342109i 0.888859π0.888859\pi
450450 0.110066 + 3.32134i 0.00518855 + 0.156569i
451451 −45.3108 −2.13360
452452 7.35551 + 14.4360i 0.345974 + 0.679012i
453453 −1.49167 + 2.05311i −0.0700849 + 0.0964636i
454454 10.5484 + 7.66387i 0.495062 + 0.359683i
455455 6.69236 + 30.6371i 0.313743 + 1.43629i
456456 −8.83627 + 6.41993i −0.413796 + 0.300641i
457457 13.8927i 0.649872i 0.945736 + 0.324936i 0.105343π0.105343\pi
−0.945736 + 0.324936i 0.894657π0.894657\pi
458458 −1.89918 + 11.9909i −0.0887427 + 0.560300i
459459 0.937285 + 2.88467i 0.0437487 + 0.134645i
460460 −4.36911 + 3.28627i −0.203711 + 0.153223i
461461 −36.1814 + 18.4353i −1.68514 + 0.858620i −0.694918 + 0.719089i 0.744559π0.744559\pi
−0.990218 + 0.139531i 0.955441π0.955441\pi
462462 −9.39537 28.9160i −0.437112 1.34529i
463463 16.1061 5.23317i 0.748512 0.243206i 0.0901710 0.995926i 0.471259π-0.471259\pi
0.658341 + 0.752720i 0.271259π0.271259\pi
464464 −7.36588 2.39332i −0.341953 0.111107i
465465 10.4122 10.7629i 0.482852 0.499118i
466466 10.4263 + 5.31248i 0.482990 + 0.246096i
467467 1.06486 6.72323i 0.0492756 0.311114i −0.950724 0.310039i 0.899658π-0.899658\pi
0.999999 0.00107500i 0.000342184π-0.000342184\pi
468468 1.87872 1.48762i 0.0868437 0.0687651i
469469 2.87919 + 3.96287i 0.132949 + 0.182988i
470470 9.59222 + 1.35680i 0.442456 + 0.0625847i
471471 8.61357 + 6.25812i 0.396892 + 0.288359i
472472 7.08769 1.12258i 0.326237 0.0516709i
473473 8.71166 26.8117i 0.400563 1.23280i
474474 −9.68794 + 9.68794i −0.444982 + 0.444982i
475475 28.3088 + 3.52704i 1.29890 + 0.161831i
476476 −1.86602 + 1.86602i −0.0855290 + 0.0855290i
477477 5.89156 3.00190i 0.269756 0.137447i
478478 −4.12461 26.0418i −0.188655 1.19112i
479479 −4.98097 31.4486i −0.227586 1.43692i −0.791540 0.611118i 0.790720π-0.790720\pi
0.563953 0.825807i 0.309280π-0.309280\pi
480480 −3.50424 2.45835i −0.159946 0.112208i
481481 30.5875 + 8.55565i 1.39467 + 0.390104i
482482 16.0406 + 16.0406i 0.730628 + 0.730628i
483483 −14.7284 + 10.7008i −0.670164 + 0.486902i
484484 −5.39511 + 1.75298i −0.245232 + 0.0796808i
485485 2.56117 + 14.6011i 0.116297 + 0.663001i
486486 −6.04842 + 3.08182i −0.274362 + 0.139794i
487487 13.8681 4.50602i 0.628424 0.204187i 0.0225471 0.999746i 0.492822π-0.492822\pi
0.605877 + 0.795558i 0.292822π0.292822\pi
488488 2.58662 0.840444i 0.117091 0.0380451i
489489 10.2878 5.24191i 0.465231 0.237047i
490490 16.0580 8.51985i 0.725424 0.384887i
491491 −1.36023 + 0.441967i −0.0613865 + 0.0199457i −0.339549 0.940588i 0.610275π-0.610275\pi
0.278163 + 0.960534i 0.410275π0.410275\pi
492492 −17.1859 + 12.4863i −0.774798 + 0.562924i
493493 −3.71555 3.71555i −0.167340 0.167340i
494494 −10.0903 17.9270i −0.453982 0.806573i
495495 6.06751 0.100508i 0.272714 0.00451750i
496496 0.547270 + 3.45533i 0.0245732 + 0.155149i
497497 9.81925 + 61.9963i 0.440454 + 2.78092i
498498 −12.0276 + 6.12835i −0.538968 + 0.274618i
499499 11.2486 11.2486i 0.503557 0.503557i −0.408984 0.912541i 0.634117π-0.634117\pi
0.912541 + 0.408984i 0.134117π0.134117\pi
500500 2.29532 + 10.9422i 0.102650 + 0.489350i
501501 15.6201 15.6201i 0.697853 0.697853i
502502 −6.05254 + 18.6278i −0.270138 + 0.831400i
503503 37.8822 5.99996i 1.68909 0.267525i 0.763430 0.645891i 0.223514π-0.223514\pi
0.925656 + 0.378366i 0.123514π0.123514\pi
504504 −2.09147 1.51954i −0.0931615 0.0676858i
505505 −10.8336 10.4805i −0.482089 0.466378i
506506 5.86802 + 8.07663i 0.260865 + 0.359050i
507507 13.0941 + 21.1629i 0.581528 + 0.939877i
508508 0.0550219 0.347395i 0.00244120 0.0154131i
509509 −30.8560 15.7219i −1.36767 0.696863i −0.392797 0.919625i 0.628493π-0.628493\pi
−0.974873 + 0.222763i 0.928493π0.928493\pi
510510 −1.36113 2.56543i −0.0602720 0.113599i
511511 −0.558892 0.181595i −0.0247239 0.00803329i
512512 0.951057 0.309017i 0.0420312 0.0136568i
513513 7.88223 + 24.2590i 0.348009 + 1.07106i
514514 −15.8135 + 8.05738i −0.697504 + 0.355396i
515515 −1.98417 1.39196i −0.0874330 0.0613373i
516516 −4.08425 12.5700i −0.179799 0.553365i
517517 2.76740 17.4727i 0.121710 0.768448i
518518 34.2643i 1.50549i
519519 −33.2373 + 24.1483i −1.45895 + 1.05999i
520520 5.36093 6.02166i 0.235093 0.264067i
521521 27.6680 + 20.1020i 1.21216 + 0.880683i 0.995425 0.0955488i 0.0304606π-0.0304606\pi
0.216731 + 0.976231i 0.430461π0.430461\pi
522522 3.02565 4.16445i 0.132429 0.182273i
523523 −11.8866 23.3287i −0.519764 1.02009i −0.990460 0.137799i 0.955997π-0.955997\pi
0.470696 0.882296i 0.344003π-0.344003\pi
524524 12.2339 0.534440
525525 7.03884 + 36.5590i 0.307200 + 1.59556i
526526 −9.08994 9.08994i −0.396340 0.396340i
527527 −0.733451 + 2.25733i −0.0319496 + 0.0983308i
528528 −4.59449 + 6.32378i −0.199950 + 0.275207i
529529 −10.0054 + 13.7713i −0.435019 + 0.598752i
530530 17.7784 13.3722i 0.772243 0.580850i
531531 −0.746103 + 4.71071i −0.0323781 + 0.204427i
532532 −15.6926 + 15.6926i −0.680359 + 0.680359i
533533 −19.6248 34.8666i −0.850043 1.51024i
534534 10.1125 3.28575i 0.437611 0.142188i
535535 −1.26068 + 0.0208831i −0.0545040 + 0.000902855i
536536 0.389154 1.19769i 0.0168089 0.0517325i
537537 −6.56677 3.34593i −0.283377 0.144388i
538538 2.00811 + 6.18032i 0.0865756 + 0.266452i
539539 −15.0701 29.5767i −0.649114 1.27396i
540540 −7.98905 + 6.00904i −0.343794 + 0.258588i
541541 5.71604 + 2.91247i 0.245752 + 0.125217i 0.572529 0.819885i 0.305963π-0.305963\pi
−0.326777 + 0.945102i 0.605963π0.605963\pi
542542 −24.1871 3.83086i −1.03893 0.164550i
543543 28.6152 + 28.6152i 1.22799 + 1.22799i
544544 0.670099 + 0.106133i 0.0287303 + 0.00455043i
545545 12.2138 4.19339i 0.523182 0.179625i
546546 18.1815 19.7536i 0.778097 0.845378i
547547 −2.84708 17.9758i −0.121733 0.768589i −0.970727 0.240187i 0.922791π-0.922791\pi
0.848994 0.528402i 0.177209π-0.177209\pi
548548 6.68244 20.5664i 0.285460 0.878554i
549549 1.80762i 0.0771475i
550550 20.0479 3.85991i 0.854847 0.164587i
551551 −31.2464 31.2464i −1.33114 1.33114i
552552 4.45134 + 1.44633i 0.189461 + 0.0615598i
553553 −16.3630 + 22.5217i −0.695825 + 0.957721i
554554 −3.85746 24.3550i −0.163888 1.03475i
555555 36.0502 + 11.0567i 1.53024 + 0.469332i
556556 5.55382 + 7.64418i 0.235535 + 0.324185i
557557 −6.95857 −0.294844 −0.147422 0.989074i 0.547098π-0.547098\pi
−0.147422 + 0.989074i 0.547098π0.547098\pi
558558 −2.29652 0.363734i −0.0972196 0.0153981i
559559 24.4047 4.90894i 1.03221 0.207626i
560560 −7.81392 3.81972i −0.330198 0.161412i
561561 −4.72519 + 2.40760i −0.199497 + 0.101649i
562562 3.65066 7.16482i 0.153994 0.302230i
563563 −6.82574 + 13.3963i −0.287671 + 0.564585i −0.988941 0.148310i 0.952617π-0.952617\pi
0.701270 + 0.712895i 0.252617π0.252617\pi
564564 −3.76529 7.38979i −0.158547 0.311166i
565565 −34.2653 + 11.7644i −1.44155 + 0.494931i
566566 −26.2072 13.3532i −1.10157 0.561278i
567567 −33.2056 + 24.1253i −1.39451 + 1.01317i
568568 11.4109 11.4109i 0.478789 0.478789i
569569 −20.4965 + 14.8916i −0.859259 + 0.624288i −0.927683 0.373368i 0.878203π-0.878203\pi
0.0684244 + 0.997656i 0.478203π0.478203\pi
570570 −11.4466 21.5743i −0.479447 0.903648i
571571 −6.55592 + 9.02345i −0.274357 + 0.377620i −0.923855 0.382744i 0.874979π-0.874979\pi
0.649498 + 0.760364i 0.274979π0.274979\pi
572572 −10.8324 9.97025i −0.452924 0.416877i
573573 −19.1730 37.6291i −0.800964 1.57198i
574574 −30.5208 + 30.5208i −1.27391 + 1.27391i
575575 −5.90762 10.7025i −0.246365 0.446326i
576576 0.664633i 0.0276930i
577577 −15.5914 5.06596i −0.649079 0.210899i −0.0340710 0.999419i 0.510847π-0.510847\pi
−0.615008 + 0.788521i 0.710847π0.710847\pi
578578 −13.3809 9.72179i −0.556572 0.404373i
579579 4.50770 + 28.4605i 0.187333 + 1.18278i
580580 7.60566 15.5588i 0.315808 0.646042i
581581 −22.1897 + 16.1218i −0.920585 + 0.668844i
582582 8.97389 8.97389i 0.371980 0.371980i
583583 −23.8776 32.8646i −0.988907 1.36111i
584584 0.0466865 + 0.143686i 0.00193190 + 0.00594578i
585585 2.70527 + 4.62541i 0.111849 + 0.191237i
586586 2.43169 7.48397i 0.100452 0.309160i
587587 13.8544 4.50158i 0.571834 0.185800i −0.00880497 0.999961i 0.502803π-0.502803\pi
0.580639 + 0.814161i 0.302803π0.302803\pi
588588 −13.8663 7.06524i −0.571837 0.291366i
589589 −6.16805 + 18.9833i −0.254150 + 0.782194i
590590 0.265766 + 16.0439i 0.0109414 + 0.660517i
591591 16.0063 31.4142i 0.658412 1.29221i
592592 −7.12667 + 5.17783i −0.292904 + 0.212808i
593593 28.7290i 1.17976i −0.807492 0.589879i 0.799176π-0.799176\pi
0.807492 0.589879i 0.200824π-0.200824\pi
594594 10.7298 + 14.7683i 0.440250 + 0.605952i
595595 −3.54704 4.71581i −0.145415 0.193329i
596596 4.97677 0.788242i 0.203856 0.0322877i
597597 −26.2196 + 4.15278i −1.07310 + 0.169962i
598598 −3.67343 + 8.01353i −0.150218 + 0.327698i
599599 7.24455i 0.296004i −0.988987 0.148002i 0.952716π-0.952716\pi
0.988987 0.148002i 0.0472843π-0.0472843\pi
600600 6.54027 6.98861i 0.267006 0.285309i
601601 −11.7289 −0.478432 −0.239216 0.970966i 0.576890π-0.576890\pi
−0.239216 + 0.970966i 0.576890π0.576890\pi
602602 −12.1920 23.9281i −0.496908 0.975237i
603603 0.677140 + 0.491971i 0.0275753 + 0.0200346i
604604 1.30936 0.207382i 0.0532772 0.00843827i
605605 −2.19155 12.4939i −0.0890992 0.507950i
606606 −2.01872 + 12.7457i −0.0820047 + 0.517757i
607607 2.49552 + 2.49552i 0.101290 + 0.101290i 0.755936 0.654646i 0.227182π-0.227182\pi
−0.654646 + 0.755936i 0.727182π0.727182\pi
608608 5.63529 + 0.892542i 0.228541 + 0.0361974i
609609 26.1814 51.3839i 1.06092 2.08218i
610610 1.05071 + 5.99005i 0.0425421 + 0.242530i
611611 14.6438 5.43816i 0.592424 0.220004i
612612 −0.204714 + 0.401774i −0.00827507 + 0.0162407i
613613 −6.95283 21.3986i −0.280822 0.864282i −0.987620 0.156866i 0.949861π-0.949861\pi
0.706798 0.707416i 0.250139π-0.250139\pi
614614 25.2299 + 8.19771i 1.01820 + 0.330833i
615615 −22.2628 41.9603i −0.897724 1.69200i
616616 −7.21046 + 14.1513i −0.290518 + 0.570173i
617617 1.13165 + 1.55758i 0.0455583 + 0.0627057i 0.831188 0.555991i 0.187661π-0.187661\pi
−0.785630 + 0.618697i 0.787661π0.787661\pi
618618 2.07499i 0.0834682i
619619 −36.9288 5.84895i −1.48429 0.235089i −0.638924 0.769270i 0.720620π-0.720620\pi
−0.845370 + 0.534181i 0.820620π0.820620\pi
620620 −7.82159 + 0.129564i −0.314122 + 0.00520342i
621621 6.42478 8.84295i 0.257817 0.354855i
622622 14.4715 + 10.5142i 0.580255 + 0.421580i
623623 19.2500 9.80836i 0.771234 0.392963i
624624 −6.85607 0.796536i −0.274463 0.0318870i
625625 −24.9452 + 1.65513i −0.997806 + 0.0662052i
626626 −12.5538 12.5538i −0.501750 0.501750i
627627 −39.7371 + 20.2471i −1.58695 + 0.808589i
628628 −0.870047 5.49326i −0.0347186 0.219205i
629629 −5.90294 + 0.934933i −0.235366 + 0.0372782i
630630 4.01930 4.15470i 0.160133 0.165527i
631631 −0.587195 + 3.70740i −0.0233759 + 0.147589i −0.996616 0.0822025i 0.973805π-0.973805\pi
0.973240 + 0.229792i 0.0738046π0.0738046\pi
632632 7.15701 0.284690
633633 −5.14280 + 32.4704i −0.204408 + 1.29058i
634634 7.76802 + 23.9075i 0.308508 + 0.949489i
635635 0.751910 + 0.230614i 0.0298386 + 0.00915163i
636636 −18.1129 5.88525i −0.718225 0.233365i
637637 16.2321 24.4065i 0.643141 0.967020i
638638 −28.1775 14.3572i −1.11556 0.568406i
639639 4.86925 + 9.55644i 0.192624 + 0.378047i
640640 0.386329 + 2.20244i 0.0152710 + 0.0870592i
641641 −17.6506 + 5.73504i −0.697158 + 0.226520i −0.636092 0.771613i 0.719450π-0.719450\pi
−0.0610664 + 0.998134i 0.519450π0.519450\pi
642642 0.634474 + 0.873279i 0.0250407 + 0.0344656i
643643 −15.6297 −0.616376 −0.308188 0.951325i 0.599723π-0.599723\pi
−0.308188 + 0.951325i 0.599723π0.599723\pi
644644 9.39294 + 1.48770i 0.370134 + 0.0586234i
645645 29.1095 5.10608i 1.14618 0.201052i
646646 3.13165 + 2.27528i 0.123213 + 0.0895195i
647647 −3.98190 + 0.630671i −0.156545 + 0.0247942i −0.234215 0.972185i 0.575252π-0.575252\pi
0.0776702 + 0.996979i 0.475252π0.475252\pi
648648 10.0357 + 3.26080i 0.394240 + 0.128096i
649649 29.3014 1.15018
650650 11.6532 + 13.7551i 0.457078 + 0.539518i
651651 −26.0494 −1.02096
652652 −5.73632 1.86384i −0.224652 0.0729938i
653653 32.7342 5.18459i 1.28099 0.202889i 0.521411 0.853306i 0.325406π-0.325406\pi
0.759577 + 0.650417i 0.225406π0.225406\pi
654654 −8.94408 6.49825i −0.349741 0.254102i
655655 −3.83130 + 27.0862i −0.149701 + 1.05835i
656656 10.9602 + 1.73592i 0.427924 + 0.0677765i
657657 −0.100413 −0.00391749
658658 −9.90529 13.6335i −0.386148 0.531488i
659659 32.3279 10.5040i 1.25932 0.409177i 0.398067 0.917357i 0.369681π-0.369681\pi
0.861251 + 0.508179i 0.169681π0.169681\pi
660660 −12.5622 12.1528i −0.488982 0.473046i
661661 −16.6325 32.6431i −0.646929 1.26967i −0.948666 0.316279i 0.897566π-0.897566\pi
0.301737 0.953391i 0.402434π-0.402434\pi
662662 −2.89304 1.47408i −0.112441 0.0572916i
663663 −3.89919 2.59325i −0.151432 0.100714i
664664 6.70637 + 2.17903i 0.260258 + 0.0845629i
665665 −29.8293 39.6582i −1.15673 1.53788i
666666 −1.80923 5.56823i −0.0701061 0.215765i
667667 −2.96224 + 18.7028i −0.114698 + 0.724176i
668668 −11.5394 −0.446472
669669 −0.152357 + 0.961947i −0.00589048 + 0.0371910i
670670 2.52986 + 1.23668i 0.0977368 + 0.0477771i
671671 10.9686 1.73725i 0.423437 0.0670658i
672672 1.16482 + 7.35441i 0.0449341 + 0.283702i
673673 −30.3373 + 15.4576i −1.16942 + 0.595848i −0.927271 0.374392i 0.877851π-0.877851\pi
−0.242146 + 0.970240i 0.577851π0.577851\pi
674674 −15.7310 15.7310i −0.605937 0.605937i
675675 −10.8023 19.5698i −0.415779 0.753243i
676676 2.98044 12.6537i 0.114632 0.486682i
677677 0.724748 0.369278i 0.0278543 0.0141925i −0.440008 0.897994i 0.645024π-0.645024\pi
0.467862 + 0.883801i 0.345024π0.345024\pi
678678 25.0922 + 18.2306i 0.963661 + 0.700140i
679679 15.1569 20.8617i 0.581670 0.800600i
680680 −0.444838 + 1.45038i −0.0170587 + 0.0556196i
681681 24.6527 + 3.90461i 0.944694 + 0.149625i
682682 14.2848i 0.546992i
683683 −0.564313 0.776711i −0.0215929 0.0297200i 0.798084 0.602546i 0.205847π-0.205847\pi
−0.819677 + 0.572826i 0.805847π0.805847\pi
684684 −1.72157 + 3.37877i −0.0658259 + 0.129191i
685685 43.4419 + 21.2359i 1.65983 + 0.811383i
686686 −4.17844 1.35766i −0.159533 0.0518356i
687687 7.18176 + 22.1032i 0.274001 + 0.843289i
688688 −3.13445 + 6.15171i −0.119500 + 0.234532i
689689 14.9476 32.6079i 0.569457 1.24226i
690690 −4.59624 + 9.40244i −0.174976 + 0.357945i
691691 −15.5342 + 30.4875i −0.590948 + 1.15980i 0.380993 + 0.924578i 0.375582π0.375582\pi
−0.971941 + 0.235223i 0.924418π0.924418\pi
692692 21.1969 + 3.35726i 0.805786 + 0.127624i
693693 −7.46419 7.46419i −0.283541 0.283541i
694694 1.53923 9.71833i 0.0584284 0.368903i
695695 −18.6637 + 9.90239i −0.707956 + 0.375619i
696696 −14.6438 + 2.31935i −0.555072 + 0.0879147i
697697 6.09081 + 4.42523i 0.230706 + 0.167618i
698698 −11.1151 21.8145i −0.420711 0.825693i
699699 22.4009 0.847280
700700 10.9041 16.1040i 0.412135 0.608675i
701701 18.9933i 0.717365i 0.933460 + 0.358683i 0.116774π0.116774\pi
−0.933460 + 0.358683i 0.883226π0.883226\pi
702702 −6.71697 + 14.6530i −0.253516 + 0.553040i
703703 −49.6415 + 7.86245i −1.87227 + 0.296538i
704704 4.03296 0.638758i 0.151998 0.0240741i
705705 17.5404 6.02218i 0.660609 0.226809i
706706 −8.26631 11.3776i −0.311107 0.428202i
707707 26.2205i 0.986122i
708708 11.1137 8.07456i 0.417677 0.303460i
709709 −0.217945 + 0.427742i −0.00818511 + 0.0160642i −0.895063 0.445940i 0.852869π-0.852869\pi
0.886878 + 0.462004i 0.152869π0.152869\pi
710710 21.6904 + 28.8375i 0.814027 + 1.08225i
711711 −1.46993 + 4.52397i −0.0551265 + 0.169662i
712712 −4.94900 2.52164i −0.185472 0.0945026i
713713 8.13476 2.64314i 0.304649 0.0989865i
714714 −1.56109 + 4.80456i −0.0584225 + 0.179806i
715715 25.4668 20.8608i 0.952404 0.780148i
716716 1.18970 + 3.66152i 0.0444612 + 0.136838i
717717 −29.6677 40.8341i −1.10796 1.52498i
718718 −3.47053 + 3.47053i −0.129519 + 0.129519i
719719 −31.2418 + 22.6985i −1.16512 + 0.846511i −0.990417 0.138110i 0.955897π-0.955897\pi
−0.174705 + 0.984621i 0.555897π0.555897\pi
720720 −1.47152 0.208144i −0.0548402 0.00775705i
721721 0.659546 + 4.16421i 0.0245628 + 0.155083i
722722 10.9647 + 7.96631i 0.408063 + 0.296475i
723723 41.3006 + 13.4194i 1.53599 + 0.499072i
724724 21.1396i 0.785646i
725725 32.0657 + 21.7117i 1.19089 + 0.806352i
726726 −7.67881 + 7.67881i −0.284987 + 0.284987i
727727 −19.3657 38.0072i −0.718232 1.40961i −0.904224 0.427059i 0.859550π-0.859550\pi
0.185991 0.982551i 0.440450π-0.440450\pi
728728 −14.0124 + 0.580705i −0.519333 + 0.0215223i
729729 10.9689 15.0975i 0.406257 0.559165i
730730 −0.332746 + 0.0583669i −0.0123155 + 0.00216026i
731731 −3.78958 + 2.75329i −0.140163 + 0.101834i
732732 3.68152 3.68152i 0.136073 0.136073i
733733 31.8055 23.1080i 1.17476 0.853515i 0.183191 0.983077i 0.441357π-0.441357\pi
0.991571 + 0.129563i 0.0413574π0.0413574\pi
734734 9.15510 + 4.66476i 0.337921 + 0.172179i
735735 19.9852 28.4878i 0.737164 1.05079i
736736 −1.10998 2.17846i −0.0409145 0.0802991i
737737 2.33448 4.58167i 0.0859916 0.168768i
738738 −3.34832 + 6.57145i −0.123253 + 0.241898i
739739 18.7224 9.53955i 0.688716 0.350918i −0.0743563 0.997232i 0.523690π-0.523690\pi
0.763072 + 0.646314i 0.223690π0.223690\pi
740740 −9.23200 17.4002i −0.339375 0.639644i
741741 −32.7908 21.8083i −1.20460 0.801149i
742742 −38.2208 6.05358i −1.40313 0.222234i
743743 14.7474 0.541031 0.270516 0.962716i 0.412806π-0.412806\pi
0.270516 + 0.962716i 0.412806π0.412806\pi
744744 3.93644 + 5.41804i 0.144317 + 0.198635i
745745 0.186613 + 11.2656i 0.00683698 + 0.412738i
746746 4.30224 + 27.1633i 0.157516 + 0.994519i
747747 −2.75475 + 3.79159i −0.100791 + 0.138727i
748748 2.63469 + 0.856062i 0.0963337 + 0.0313007i
749749 1.55088 + 1.55088i 0.0566678 + 0.0566678i
750750 13.4248 + 16.6690i 0.490203 + 0.608665i
751751 25.8314i 0.942602i 0.881972 + 0.471301i 0.156215π0.156215\pi
−0.881972 + 0.471301i 0.843785π0.843785\pi
752752 −1.33881 + 4.12043i −0.0488213 + 0.150257i
753753 5.86547 + 37.0332i 0.213750 + 1.34956i
754754 −1.15628 27.9009i −0.0421091 1.01609i
755755 0.0490970 + 2.96391i 0.00178682 + 0.107868i
756756 17.1752 + 2.72029i 0.624658 + 0.0989361i
757757 17.4682 + 17.4682i 0.634894 + 0.634894i 0.949291 0.314397i 0.101802π-0.101802\pi
−0.314397 + 0.949291i 0.601802π0.601802\pi
758758 37.2473 + 5.89939i 1.35288 + 0.214276i
759759 17.0282 + 8.67630i 0.618084 + 0.314930i
760760 −3.74092 + 12.1972i −0.135697 + 0.442438i
761761 21.4915 + 42.1794i 0.779065 + 1.52900i 0.847169 + 0.531324i 0.178305π0.178305\pi
−0.0681036 + 0.997678i 0.521695π0.521695\pi
762762 −0.208066 0.640361i −0.00753743 0.0231978i
763763 −20.0150 10.1982i −0.724593 0.369198i
764764 −6.81727 + 20.9814i −0.246640 + 0.759081i
765765 −0.825428 0.579067i −0.0298434 0.0209362i
766766 22.9182 7.44657i 0.828068 0.269056i
767767 12.6909 + 22.5474i 0.458240 + 0.814139i
768768 1.35363 1.35363i 0.0488449 0.0488449i
769769 −2.34328 + 14.7949i −0.0845009 + 0.533518i 0.908732 + 0.417380i 0.137051π0.137051\pi
−0.993233 + 0.116138i 0.962949π0.962949\pi
770770 −29.0733 20.3960i −1.04773 0.735019i
771771 −19.9701 + 27.4865i −0.719207 + 0.989904i
772772 8.84760 12.1777i 0.318432 0.438284i
773773 4.92374 15.1537i 0.177095 0.545041i −0.822628 0.568579i 0.807493π-0.807493\pi
0.999723 + 0.0235383i 0.00749317π0.00749317\pi
774774 −3.24475 3.24475i −0.116630 0.116630i
775775 2.16263 17.3578i 0.0776841 0.623510i
776776 −6.62949 −0.237985
777777 −29.7786 58.4437i −1.06830 2.09666i
778778 −1.82740 + 2.51521i −0.0655156 + 0.0901745i
779779 51.2215 + 37.2146i 1.83520 + 1.33335i
780780 3.91068 14.9301i 0.140025 0.534583i
781781 53.3083 38.7307i 1.90752 1.38589i
782782 1.65878i 0.0593177i
783783 −5.41653 + 34.1986i −0.193571 + 1.22216i
784784 2.51216 + 7.73164i 0.0897200 + 0.276130i
785785 12.4347 0.205980i 0.443814 0.00735174i
786786 20.8670 10.6323i 0.744303 0.379241i
787787 12.3713 + 38.0749i 0.440989 + 1.35722i 0.886823 + 0.462109i 0.152907π0.152907\pi
−0.445834 + 0.895116i 0.647093π0.647093\pi
788788 −17.5160 + 5.69131i −0.623983 + 0.202744i
789789 −23.4044 7.60455i −0.833218 0.270729i
790790 −2.24137 + 15.8458i −0.0797442 + 0.563769i
791791 56.1513 + 28.6105i 1.99651 + 1.01727i
792792 −0.424539 + 2.68043i −0.0150853 + 0.0952451i
793793 6.08745 + 7.68786i 0.216172 + 0.273004i
794794 −5.55760 7.64938i −0.197232 0.271466i
795795 18.7026 38.2595i 0.663312 1.35692i
796796 11.2189 + 8.15098i 0.397642 + 0.288904i
797797 −3.42447 + 0.542383i −0.121301 + 0.0192122i −0.216790 0.976218i 0.569559π-0.569559\pi
0.0954887 + 0.995431i 0.469559π0.469559\pi
798798 −13.1282 + 40.4046i −0.464735 + 1.43031i
799799 −2.07845 + 2.07845i −0.0735303 + 0.0735303i
800800 −4.99726 + 0.165604i −0.176680 + 0.00585498i
801801 2.61038 2.61038i 0.0922332 0.0922332i
802802 12.3747 6.30521i 0.436965 0.222645i
803803 0.0965039 + 0.609302i 0.00340555 + 0.0215018i
804804 −0.377126 2.38108i −0.0133002 0.0839743i
805805 −6.23539 + 20.3303i −0.219769 + 0.716550i
806806 −10.9921 + 6.18693i −0.387180 + 0.217925i
807807 8.79639 + 8.79639i 0.309648 + 0.309648i
808808 5.45362 3.96229i 0.191858 0.139393i
809809 −30.5484 + 9.92578i −1.07403 + 0.348972i −0.792054 0.610451i 0.790988π-0.790988\pi
−0.281971 + 0.959423i 0.590988π0.590988\pi
810810 −10.3624 + 21.1981i −0.364097 + 0.744827i
811811 13.9262 7.09577i 0.489016 0.249166i −0.192054 0.981384i 0.561515π-0.561515\pi
0.681070 + 0.732218i 0.261515π0.261515\pi
812812 −28.6508 + 9.30922i −1.00545 + 0.326690i
813813 −44.5847 + 14.4864i −1.56365 + 0.508062i
814814 −32.0489 + 16.3298i −1.12331 + 0.572357i
815815 5.92305 12.1167i 0.207476 0.424429i
816816 1.23521 0.401344i 0.0432410 0.0140498i
817817 −31.8690 + 23.1542i −1.11496 + 0.810063i
818818 20.1610 + 20.1610i 0.704913 + 0.704913i
819819 2.51083 8.97653i 0.0877357 0.313665i
820820 −7.27580 + 23.7225i −0.254082 + 0.828427i
821821 −0.439121 2.77250i −0.0153254 0.0967610i 0.978840 0.204627i 0.0655982π-0.0655982\pi
−0.994165 + 0.107866i 0.965598π0.965598\pi
822822 −6.47590 40.8872i −0.225873 1.42611i
823823 −6.41600 + 3.26912i −0.223648 + 0.113954i −0.562225 0.826984i 0.690054π-0.690054\pi
0.338577 + 0.940939i 0.390054π0.390054\pi
824824 0.766453 0.766453i 0.0267006 0.0267006i
825825 30.8407 24.0071i 1.07373 0.835820i
826826 19.7371 19.7371i 0.686740 0.686740i
827827 −1.58965 + 4.89245i −0.0552776 + 0.170127i −0.974884 0.222715i 0.928508π-0.928508\pi
0.919606 + 0.392842i 0.128508π0.128508\pi
828828 1.60498 0.254204i 0.0557770 0.00883421i
829829 −14.1320 10.2675i −0.490825 0.356605i 0.314676 0.949199i 0.398104π-0.398104\pi
−0.805502 + 0.592594i 0.798104π0.798104\pi
830830 −6.92468 + 14.1657i −0.240359 + 0.491699i
831831 −27.7462 38.1893i −0.962504 1.32477i
832832 2.23825 + 2.82670i 0.0775975 + 0.0979981i
833833 −0.862813 + 5.44759i −0.0298947 + 0.188748i
834834 16.1164 + 8.21174i 0.558067 + 0.284349i
835835 3.61380 25.5485i 0.125061 0.884144i
836836 22.1568 + 7.19917i 0.766307 + 0.248988i
837837 14.8746 4.83306i 0.514142 0.167055i
838838 0.277049 + 0.852669i 0.00957050 + 0.0294550i
839839 −31.7125 + 16.1583i −1.09484 + 0.557847i −0.905621 0.424088i 0.860595π-0.860595\pi
−0.189216 + 0.981936i 0.560595π0.560595\pi
840840 −16.6477 + 0.275767i −0.574399 + 0.00951488i
841841 −9.57465 29.4678i −0.330160 1.01613i
842842 2.22292 14.0350i 0.0766071 0.483678i
843843 15.3936i 0.530183i
844844 13.8934 10.0942i 0.478232 0.347456i
845845 27.0823 + 10.5616i 0.931661 + 0.363329i
846846 −2.32957 1.69253i −0.0800922 0.0581904i
847847 −12.9696 + 17.8511i −0.445639 + 0.613370i
848848 4.51663 + 8.86438i 0.155102 + 0.304404i
849849 −56.3060 −1.93242
850850 −3.07188 1.43910i −0.105364 0.0493607i
851851 15.2294 + 15.2294i 0.522057 + 0.522057i
852852 9.54621 29.3802i 0.327048 1.00655i
853853 −13.9074 + 19.1419i −0.476181 + 0.655407i −0.977765 0.209701i 0.932751π-0.932751\pi
0.501584 + 0.865109i 0.332751π0.332751\pi
854854 6.21810 8.55848i 0.212779 0.292865i
855855 −6.94155 4.86974i −0.237396 0.166542i
856856 0.0882089 0.556929i 0.00301492 0.0190354i
857857 13.4342 13.4342i 0.458905 0.458905i −0.439391 0.898296i 0.644806π-0.644806\pi
0.898296 + 0.439391i 0.144806π0.144806\pi
858858 −27.1415 7.59176i −0.926594 0.259179i
859859 3.83810 1.24708i 0.130954 0.0425497i −0.242807 0.970075i 0.578068π-0.578068\pi
0.373761 + 0.927525i 0.378068π0.378068\pi
860860 −12.6384 8.86630i −0.430967 0.302338i
861861 −25.5334 + 78.5837i −0.870176 + 2.67813i
862862 −7.90295 4.02675i −0.269175 0.137152i
863863 −9.32901 28.7117i −0.317563 0.977359i −0.974686 0.223576i 0.928227π-0.928227\pi
0.657123 0.753783i 0.271773π-0.271773\pi
864864 −2.02963 3.98338i −0.0690495 0.135517i
865865 −14.0713 + 45.8792i −0.478440 + 1.55994i
866866 18.9888 + 9.67525i 0.645264 + 0.328779i
867867 −31.2725 4.95308i −1.06207 0.168215i
868868 9.62204 + 9.62204i 0.326593 + 0.326593i
869869 28.8639 + 4.57159i 0.979141 + 0.155081i
870870 −0.549097 33.1481i −0.0186161 1.12383i
871871 4.53668 0.188010i 0.153720 0.00637049i
872872 0.903431 + 5.70404i 0.0305940 + 0.193163i
873873 1.36158 4.19052i 0.0460826 0.141828i
874874 13.9497i 0.471856i
875875 32.2399 + 29.1852i 1.08991 + 0.986640i
876876 0.204507 + 0.204507i 0.00690966 + 0.00690966i
877877 27.9593 + 9.08454i 0.944120 + 0.306763i 0.740324 0.672250i 0.234672π-0.234672\pi
0.203796 + 0.979013i 0.434672π0.434672\pi
878878 10.8329 14.9101i 0.365591 0.503193i
879879 −2.35653 14.8786i −0.0794839 0.501842i
880880 0.151223 + 9.12912i 0.00509774 + 0.307743i
881881 −14.9501 20.5770i −0.503682 0.693258i 0.479156 0.877730i 0.340943π-0.340943\pi
−0.982838 + 0.184471i 0.940943π0.940943\pi
882882 −5.40315 −0.181933
883883 8.97825 + 1.42202i 0.302142 + 0.0478546i 0.305665 0.952139i 0.401121π-0.401121\pi
−0.00352267 + 0.999994i 0.501121π0.501121\pi
884884 0.482383 + 2.39816i 0.0162243 + 0.0806588i
885885 14.3968 + 27.1347i 0.483944 + 0.912123i
886886 −16.7009 + 8.50954i −0.561078 + 0.285883i
887887 9.12815 17.9150i 0.306493 0.601527i −0.685463 0.728107i 0.740400π-0.740400\pi
0.991956 + 0.126581i 0.0404002π0.0404002\pi
888888 −7.65581 + 15.0254i −0.256912 + 0.504218i
889889 −0.621101 1.21898i −0.0208311 0.0408833i
890890 7.13287 10.1675i 0.239094 0.340816i
891891 38.3907 + 19.5610i 1.28614 + 0.655319i
892892 0.411598 0.299044i 0.0137813 0.0100127i
893893 −17.4790 + 17.4790i −0.584913 + 0.584913i
894894 7.80369 5.66971i 0.260994 0.189624i
895895 −8.47930 + 1.48735i −0.283432 + 0.0497166i
896896 2.28629 3.14681i 0.0763796 0.105127i
897897 0.698758 + 16.8610i 0.0233308 + 0.562972i
898898 8.12943 + 15.9549i 0.271283 + 0.532422i
899899 −19.1590 + 19.1590i −0.638989 + 0.638989i
900900 0.921672 3.19279i 0.0307224 0.106426i
901901 6.74973i 0.224866i
902902 43.0932 + 14.0018i 1.43485 + 0.466210i
903903 −41.5911 30.2177i −1.38406 1.00558i
904904 −2.53454 16.0024i −0.0842974 0.532233i
905905 46.8036 + 6.62030i 1.55581 + 0.220066i
906906 2.05311 1.49167i 0.0682101 0.0495575i
907907 0.620702 0.620702i 0.0206101 0.0206101i −0.696727 0.717337i 0.745361π-0.745361\pi
0.717337 + 0.696727i 0.245361π0.245361\pi
908908 −7.66387 10.5484i −0.254334 0.350061i
909909 1.38450 + 4.26104i 0.0459208 + 0.141330i
910910 3.10257 31.2057i 0.102849 1.03446i
911911 −14.8952 + 45.8426i −0.493499 + 1.51883i 0.325784 + 0.945444i 0.394372π0.394372\pi
−0.819283 + 0.573389i 0.805628π0.805628\pi
912912 10.3877 3.37516i 0.343970 0.111763i
913913 25.6546 + 13.0717i 0.849045 + 0.432610i
914914 4.29307 13.2127i 0.142002 0.437038i
915915 6.99804 + 9.30392i 0.231348 + 0.307578i
916916 5.51163 10.8172i 0.182109 0.357410i
917917 38.4977 27.9702i 1.27131 0.923659i
918918 3.03312i 0.100108i
919919 10.3648 + 14.2659i 0.341902 + 0.470588i 0.944996 0.327082i 0.106065π-0.106065\pi
−0.603093 + 0.797671i 0.706065π0.706065\pi
920920 5.17079 1.77530i 0.170476 0.0585299i
921921 50.1586 7.94434i 1.65278 0.261775i
922922 40.1074 6.35239i 1.32087 0.209205i
923923 52.8918 + 24.2458i 1.74096 + 0.798060i
924924 30.4041i 1.00022i
925925 41.4157 14.9907i 1.36174 0.492890i
926926 −16.9349 −0.556515
927927 0.327061 + 0.641893i 0.0107421 + 0.0210825i
928928 6.26579 + 4.55237i 0.205685 + 0.149439i
929929 40.2288 6.37161i 1.31986 0.209046i 0.543541 0.839382i 0.317083π-0.317083\pi
0.776322 + 0.630336i 0.217083π0.217083\pi
930930 −13.2285 + 7.01861i −0.433779 + 0.230149i
931931 −7.25594 + 45.8122i −0.237804 + 1.50143i
932932 −8.27438 8.27438i −0.271036 0.271036i
933933 33.8214 + 5.35678i 1.10726 + 0.175373i
934934 −3.09033 + 6.06512i −0.101119 + 0.198457i
935935 −2.72045 + 5.56518i −0.0889683 + 0.182001i
936936 −2.24646 + 0.834252i −0.0734280 + 0.0272684i
937937 −14.0153 + 27.5065i −0.457859 + 0.898598i 0.540501 + 0.841343i 0.318235π0.318235\pi
−0.998360 + 0.0572549i 0.981765π0.981765\pi
938938 −1.51368 4.65863i −0.0494234 0.152110i
939939 −32.3230 10.5024i −1.05482 0.342732i
940940 −8.70347 4.25456i −0.283876 0.138768i
941941 2.62791 5.15756i 0.0856674 0.168132i −0.844198 0.536031i 0.819923π-0.819923\pi
0.929866 + 0.367899i 0.119923π0.119923\pi
942942 −6.25812 8.61357i −0.203901 0.280645i
943943 27.1311i 0.883510i
944944 −7.08769 1.12258i −0.230685 0.0365369i
945945 −11.4016 + 37.1746i −0.370894 + 1.20929i
946946 −16.5706 + 22.8074i −0.538755 + 0.741533i
947947 31.8898 + 23.1693i 1.03628 + 0.752901i 0.969556 0.244870i 0.0787454π-0.0787454\pi
0.0667236 + 0.997771i 0.478745π0.478745\pi
948948 12.2075 6.22004i 0.396482 0.202018i
949949 −0.427059 + 0.338157i −0.0138629 + 0.0109770i
950950 −25.8333 12.1023i −0.838144 0.392651i
951951 34.0274 + 34.0274i 1.10341 + 1.10341i
952952 2.35132 1.19806i 0.0762069 0.0388293i
953953 3.23344 + 20.4151i 0.104741 + 0.661310i 0.983067 + 0.183247i 0.0586609π0.0586609\pi
−0.878326 + 0.478063i 0.841339π0.841339\pi
954954 −6.53084 + 1.03438i −0.211444 + 0.0334894i
955955 −44.3185 21.6644i −1.43411 0.701044i
956956 −4.12461 + 26.0418i −0.133399 + 0.842250i
957957 −60.5393 −1.95696
958958 −4.98097 + 31.4486i −0.160928 + 1.01606i
959959 −25.9925 79.9966i −0.839341 2.58322i
960960 2.57306 + 3.42090i 0.0830452 + 0.110409i
961961 −17.8430 5.79753i −0.575580 0.187017i
962962 −26.4466 17.5890i −0.852671 0.567091i
963963 0.333920 + 0.170141i 0.0107604 + 0.00548271i
964964 −10.2987 20.2123i −0.331698 0.650995i
965965 24.1909 + 23.4025i 0.778733 + 0.753354i
966966 17.3142 5.62573i 0.557076 0.181005i
967967 −21.6677 29.8230i −0.696786 0.959044i −0.999981 0.00611541i 0.998053π-0.998053\pi
0.303195 0.952928i 0.401947π-0.401947\pi
968968 5.67275 0.182329
969969 7.31898 + 1.15921i 0.235119 + 0.0372393i
970970 2.07616 14.6779i 0.0666616 0.471279i
971971 −22.0955 16.0533i −0.709079 0.515176i 0.173797 0.984781i 0.444396π-0.444396\pi
−0.882877 + 0.469605i 0.844396π0.844396\pi
972972 6.70473 1.06192i 0.215054 0.0340612i
973973 34.9536 + 11.3571i 1.12056 + 0.364093i
974974 −14.5818 −0.467231
975975 31.8310 + 13.3340i 1.01941 + 0.427030i
976976 −2.71973 −0.0870566
977977 24.3498 + 7.91172i 0.779018 + 0.253118i 0.671421 0.741076i 0.265684π-0.265684\pi
0.107597 + 0.994195i 0.465684π0.465684\pi
978978 −11.4041 + 1.80624i −0.364664 + 0.0577571i
979979 −18.3484 13.3309i −0.586417 0.426057i
980980 −17.9048 + 3.14067i −0.571948 + 0.100325i
981981 −3.79109 0.600450i −0.121040 0.0191709i
982982 1.43023 0.0456406
983983 −13.9121 19.1484i −0.443728 0.610739i 0.527308 0.849674i 0.323202π-0.323202\pi
−0.971035 + 0.238936i 0.923202π0.923202\pi
984984 20.2032 6.56441i 0.644054 0.209266i
985985 −7.11521 40.5634i −0.226709 1.29246i
986986 2.38553 + 4.68186i 0.0759707 + 0.149101i
987987 −28.7438 14.6457i −0.914926 0.466178i
988988 4.05666 + 20.1676i 0.129060 + 0.641618i
989989 16.0543 + 5.21634i 0.510496 + 0.165870i
990990 −5.80161 1.77938i −0.184387 0.0565523i
991991 −16.2423 49.9886i −0.515953 1.58794i −0.781541 0.623853i 0.785566π-0.785566\pi
0.265588 0.964087i 0.414434π-0.414434\pi
992992 0.547270 3.45533i 0.0173758 0.109707i
993993 −6.21568 −0.197249
994994 9.81925 61.9963i 0.311448 1.96640i
995995 −21.5599 + 22.2862i −0.683495 + 0.706521i
996996 13.3327 2.11169i 0.422461 0.0669113i
997997 −7.90923 49.9369i −0.250488 1.58152i −0.717045 0.697026i 0.754506π-0.754506\pi
0.466558 0.884491i 0.345494π-0.345494\pi
998998 −14.1741 + 7.22206i −0.448673 + 0.228610i
999999 27.8474 + 27.8474i 0.881053 + 0.881053i
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 650.2.bd.b.47.5 yes 144
13.5 odd 4 650.2.ba.b.447.5 yes 144
25.8 odd 20 650.2.ba.b.333.5 144
325.83 even 20 inner 650.2.bd.b.83.5 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
650.2.ba.b.333.5 144 25.8 odd 20
650.2.ba.b.447.5 yes 144 13.5 odd 4
650.2.bd.b.47.5 yes 144 1.1 even 1 trivial
650.2.bd.b.83.5 yes 144 325.83 even 20 inner