Properties

Label 550.2.h.n.201.2
Level 550550
Weight 22
Character 550.201
Analytic conductor 4.3924.392
Analytic rank 00
Dimension 88
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [550,2,Mod(201,550)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(550, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("550.201");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 550=25211 550 = 2 \cdot 5^{2} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 550.h (of order 55, degree 44, 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: 4.391772111174.39177211117
Analytic rank: 00
Dimension: 88
Relative dimension: 22 over Q(ζ5)\Q(\zeta_{5})
Coefficient field: 8.0.20164000000.8
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x8+6x6+76x4+781x2+5041 x^{8} + 6x^{6} + 76x^{4} + 781x^{2} + 5041 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 110)
Sato-Tate group: SU(2)[C5]\mathrm{SU}(2)[C_{5}]

Embedding invariants

Embedding label 201.2
Root 0.8395922.58400i-0.839592 - 2.58400i of defining polynomial
Character χ\chi == 550.201
Dual form 550.2.h.n.301.2

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+(0.8090170.587785i)q2+(0.500000+1.53884i)q3+(0.3090170.951057i)q4+(1.30902+0.951057i)q6+(1.167513.59321i)q7+(0.3090170.951057i)q8+(0.3090170.224514i)q9+(2.648611.99621i)q11+1.61803q12+(2.507101.82151i)q13+(1.167513.59321i)q14+(0.8090170.587785i)q16+(2.66751+1.93806i)q17+(0.1180340.363271i)q18+(0.400863+1.23373i)q19+6.11314q21+(3.316110.0581575i)q22+0.556884q23+(1.309020.951057i)q24+(0.9576262.94727i)q26+(4.42705+3.21644i)q27+(3.056572.22073i)q28+(2.95763+9.10264i)q29+(4.32760+3.14419i)q311.00000q32+(1.747555.07390i)q33+3.29722q34+(0.1180340.363271i)q36+(2.445957.52785i)q37+(1.04947+0.762486i)q38+(4.05657+2.94727i)q39+(1.94312+5.98030i)q41+(4.945633.59321i)q42+3.61803q43+(2.71698+1.90211i)q44+(0.4505280.327328i)q46+(1.653005.08740i)q47+(0.5000001.53884i)q48+(5.884994.27570i)q49+(1.64861+5.07390i)q51+(0.9576262.94727i)q52+(8.91067+6.47398i)q53+5.47214q543.77813q56+(1.69808+1.23373i)q57+(2.95763+9.10264i)q58+(1.636935.03795i)q59+(1.988011.44437i)q61+(1.65300+5.08740i)q62+(0.4459471.37249i)q63+(0.809017+0.587785i)q64+(1.568565.13205i)q66+9.21247q67+(2.667511.93806i)q68+(0.278442+0.856956i)q69+(8.811736.40210i)q71+(0.3090170.224514i)q72+(1.04947+3.22994i)q73+(2.445957.52785i)q74+1.29722q76+(10.2651+7.18643i)q77+5.01420q78+(13.2383+9.61817i)q79+(2.38197+7.33094i)q81+(5.08714+3.69603i)q82+(0.1489230.108199i)q83+(1.889065.81394i)q84+(2.927052.12663i)q8615.4863q87+(1.08005+3.13584i)q88+6.09017q89+(3.6180311.1352i)q91+(0.1720870.529628i)q92+(7.002205.08740i)q93+(4.327603.14419i)q94+(0.5000001.53884i)q96+(9.99782+7.26384i)q977.27425q98+(1.266640.0222142i)q99+O(q100)q+(0.809017 - 0.587785i) q^{2} +(0.500000 + 1.53884i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.30902 + 0.951057i) q^{6} +(1.16751 - 3.59321i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.309017 - 0.224514i) q^{9} +(-2.64861 - 1.99621i) q^{11} +1.61803 q^{12} +(2.50710 - 1.82151i) q^{13} +(-1.16751 - 3.59321i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(2.66751 + 1.93806i) q^{17} +(0.118034 - 0.363271i) q^{18} +(0.400863 + 1.23373i) q^{19} +6.11314 q^{21} +(-3.31611 - 0.0581575i) q^{22} +0.556884 q^{23} +(1.30902 - 0.951057i) q^{24} +(0.957626 - 2.94727i) q^{26} +(4.42705 + 3.21644i) q^{27} +(-3.05657 - 2.22073i) q^{28} +(-2.95763 + 9.10264i) q^{29} +(-4.32760 + 3.14419i) q^{31} -1.00000 q^{32} +(1.74755 - 5.07390i) q^{33} +3.29722 q^{34} +(-0.118034 - 0.363271i) q^{36} +(2.44595 - 7.52785i) q^{37} +(1.04947 + 0.762486i) q^{38} +(4.05657 + 2.94727i) q^{39} +(1.94312 + 5.98030i) q^{41} +(4.94563 - 3.59321i) q^{42} +3.61803 q^{43} +(-2.71698 + 1.90211i) q^{44} +(0.450528 - 0.327328i) q^{46} +(-1.65300 - 5.08740i) q^{47} +(0.500000 - 1.53884i) q^{48} +(-5.88499 - 4.27570i) q^{49} +(-1.64861 + 5.07390i) q^{51} +(-0.957626 - 2.94727i) q^{52} +(-8.91067 + 6.47398i) q^{53} +5.47214 q^{54} -3.77813 q^{56} +(-1.69808 + 1.23373i) q^{57} +(2.95763 + 9.10264i) q^{58} +(1.63693 - 5.03795i) q^{59} +(-1.98801 - 1.44437i) q^{61} +(-1.65300 + 5.08740i) q^{62} +(-0.445947 - 1.37249i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-1.56856 - 5.13205i) q^{66} +9.21247 q^{67} +(2.66751 - 1.93806i) q^{68} +(0.278442 + 0.856956i) q^{69} +(-8.81173 - 6.40210i) q^{71} +(-0.309017 - 0.224514i) q^{72} +(-1.04947 + 3.22994i) q^{73} +(-2.44595 - 7.52785i) q^{74} +1.29722 q^{76} +(-10.2651 + 7.18643i) q^{77} +5.01420 q^{78} +(-13.2383 + 9.61817i) q^{79} +(-2.38197 + 7.33094i) q^{81} +(5.08714 + 3.69603i) q^{82} +(-0.148923 - 0.108199i) q^{83} +(1.88906 - 5.81394i) q^{84} +(2.92705 - 2.12663i) q^{86} -15.4863 q^{87} +(-1.08005 + 3.13584i) q^{88} +6.09017 q^{89} +(-3.61803 - 11.1352i) q^{91} +(0.172087 - 0.529628i) q^{92} +(-7.00220 - 5.08740i) q^{93} +(-4.32760 - 3.14419i) q^{94} +(-0.500000 - 1.53884i) q^{96} +(-9.99782 + 7.26384i) q^{97} -7.27425 q^{98} +(-1.26664 - 0.0222142i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+2q2+4q32q4+6q66q7+2q82q910q11+4q122q13+6q142q16+6q178q18+8q198q21+6q248q26+22q27++10q99+O(q100) 8 q + 2 q^{2} + 4 q^{3} - 2 q^{4} + 6 q^{6} - 6 q^{7} + 2 q^{8} - 2 q^{9} - 10 q^{11} + 4 q^{12} - 2 q^{13} + 6 q^{14} - 2 q^{16} + 6 q^{17} - 8 q^{18} + 8 q^{19} - 8 q^{21} + 6 q^{24} - 8 q^{26} + 22 q^{27}+ \cdots + 10 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/550Z)×\left(\mathbb{Z}/550\mathbb{Z}\right)^\times.

nn 101101 177177
χ(n)\chi(n) e(45)e\left(\frac{4}{5}\right) 11

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 0.809017 0.587785i 0.572061 0.415627i
33 0.500000 + 1.53884i 0.288675 + 0.888451i 0.985273 + 0.170989i 0.0546962π0.0546962\pi
−0.696598 + 0.717462i 0.745304π0.745304\pi
44 0.309017 0.951057i 0.154508 0.475528i
55 0 0
66 1.30902 + 0.951057i 0.534404 + 0.388267i
77 1.16751 3.59321i 0.441276 1.35811i −0.445241 0.895411i 0.646882π-0.646882\pi
0.886517 0.462696i 0.153118π-0.153118\pi
88 −0.309017 0.951057i −0.109254 0.336249i
99 0.309017 0.224514i 0.103006 0.0748380i
1010 0 0
1111 −2.64861 1.99621i −0.798586 0.601881i
1212 1.61803 0.467086
1313 2.50710 1.82151i 0.695344 0.505197i −0.183069 0.983100i 0.558603π-0.558603\pi
0.878412 + 0.477903i 0.158603π0.158603\pi
1414 −1.16751 3.59321i −0.312029 0.960327i
1515 0 0
1616 −0.809017 0.587785i −0.202254 0.146946i
1717 2.66751 + 1.93806i 0.646965 + 0.470048i 0.862236 0.506507i 0.169063π-0.169063\pi
−0.215271 + 0.976554i 0.569063π0.569063\pi
1818 0.118034 0.363271i 0.0278209 0.0856239i
1919 0.400863 + 1.23373i 0.0919642 + 0.283037i 0.986451 0.164058i 0.0524586π-0.0524586\pi
−0.894486 + 0.447095i 0.852459π0.852459\pi
2020 0 0
2121 6.11314 1.33400
2222 −3.31611 0.0581575i −0.706998 0.0123992i
2323 0.556884 0.116118 0.0580591 0.998313i 0.481509π-0.481509\pi
0.0580591 + 0.998313i 0.481509π0.481509\pi
2424 1.30902 0.951057i 0.267202 0.194134i
2525 0 0
2626 0.957626 2.94727i 0.187806 0.578007i
2727 4.42705 + 3.21644i 0.851986 + 0.619004i
2828 −3.05657 2.22073i −0.577637 0.419678i
2929 −2.95763 + 9.10264i −0.549217 + 1.69032i 0.161528 + 0.986868i 0.448358π0.448358\pi
−0.710746 + 0.703449i 0.751642π0.751642\pi
3030 0 0
3131 −4.32760 + 3.14419i −0.777260 + 0.564712i −0.904155 0.427204i 0.859499π-0.859499\pi
0.126896 + 0.991916i 0.459499π0.459499\pi
3232 −1.00000 −0.176777
3333 1.74755 5.07390i 0.304210 0.883252i
3434 3.29722 0.565468
3535 0 0
3636 −0.118034 0.363271i −0.0196723 0.0605452i
3737 2.44595 7.52785i 0.402111 1.23757i −0.521172 0.853452i 0.674505π-0.674505\pi
0.923283 0.384120i 0.125495π-0.125495\pi
3838 1.04947 + 0.762486i 0.170247 + 0.123692i
3939 4.05657 + 2.94727i 0.649571 + 0.471941i
4040 0 0
4141 1.94312 + 5.98030i 0.303464 + 0.933966i 0.980246 + 0.197782i 0.0633739π0.0633739\pi
−0.676782 + 0.736183i 0.736626π0.736626\pi
4242 4.94563 3.59321i 0.763128 0.554445i
4343 3.61803 0.551745 0.275873 0.961194i 0.411033π-0.411033\pi
0.275873 + 0.961194i 0.411033π0.411033\pi
4444 −2.71698 + 1.90211i −0.409600 + 0.286754i
4545 0 0
4646 0.450528 0.327328i 0.0664268 0.0482619i
4747 −1.65300 5.08740i −0.241114 0.742073i −0.996251 0.0865064i 0.972430π-0.972430\pi
0.755137 0.655567i 0.227570π-0.227570\pi
4848 0.500000 1.53884i 0.0721688 0.222113i
4949 −5.88499 4.27570i −0.840713 0.610814i
5050 0 0
5151 −1.64861 + 5.07390i −0.230851 + 0.710488i
5252 −0.957626 2.94727i −0.132799 0.408713i
5353 −8.91067 + 6.47398i −1.22397 + 0.889270i −0.996424 0.0844964i 0.973072π-0.973072\pi
−0.227551 + 0.973766i 0.573072π0.573072\pi
5454 5.47214 0.744663
5555 0 0
5656 −3.77813 −0.504874
5757 −1.69808 + 1.23373i −0.224916 + 0.163411i
5858 2.95763 + 9.10264i 0.388355 + 1.19523i
5959 1.63693 5.03795i 0.213110 0.655886i −0.786172 0.618008i 0.787940π-0.787940\pi
0.999282 0.0378782i 0.0120599π-0.0120599\pi
6060 0 0
6161 −1.98801 1.44437i −0.254538 0.184933i 0.453197 0.891410i 0.350283π-0.350283\pi
−0.707736 + 0.706477i 0.750283π0.750283\pi
6262 −1.65300 + 5.08740i −0.209931 + 0.646100i
6363 −0.445947 1.37249i −0.0561841 0.172917i
6464 −0.809017 + 0.587785i −0.101127 + 0.0734732i
6565 0 0
6666 −1.56856 5.13205i −0.193077 0.631712i
6767 9.21247 1.12548 0.562741 0.826633i 0.309747π-0.309747\pi
0.562741 + 0.826633i 0.309747π0.309747\pi
6868 2.66751 1.93806i 0.323483 0.235024i
6969 0.278442 + 0.856956i 0.0335205 + 0.103165i
7070 0 0
7171 −8.81173 6.40210i −1.04576 0.759789i −0.0743582 0.997232i 0.523691π-0.523691\pi
−0.971402 + 0.237443i 0.923691π0.923691\pi
7272 −0.309017 0.224514i −0.0364180 0.0264592i
7373 −1.04947 + 3.22994i −0.122831 + 0.378036i −0.993500 0.113834i 0.963687π-0.963687\pi
0.870668 + 0.491871i 0.163687π0.163687\pi
7474 −2.44595 7.52785i −0.284336 0.875095i
7575 0 0
7676 1.29722 0.148801
7777 −10.2651 + 7.18643i −1.16982 + 0.818969i
7878 5.01420 0.567746
7979 −13.2383 + 9.61817i −1.48942 + 1.08213i −0.515057 + 0.857156i 0.672229π0.672229\pi
−0.974365 + 0.224972i 0.927771π0.927771\pi
8080 0 0
8181 −2.38197 + 7.33094i −0.264663 + 0.814549i
8282 5.08714 + 3.69603i 0.561781 + 0.408158i
8383 −0.148923 0.108199i −0.0163464 0.0118764i 0.579582 0.814914i 0.303216π-0.303216\pi
−0.595928 + 0.803038i 0.703216π0.703216\pi
8484 1.88906 5.81394i 0.206114 0.634353i
8585 0 0
8686 2.92705 2.12663i 0.315632 0.229320i
8787 −15.4863 −1.66031
8888 −1.08005 + 3.13584i −0.115133 + 0.334282i
8989 6.09017 0.645557 0.322778 0.946475i 0.395383π-0.395383\pi
0.322778 + 0.946475i 0.395383π0.395383\pi
9090 0 0
9191 −3.61803 11.1352i −0.379273 1.16728i
9292 0.172087 0.529628i 0.0179413 0.0552175i
9393 −7.00220 5.08740i −0.726095 0.527539i
9494 −4.32760 3.14419i −0.446358 0.324298i
9595 0 0
9696 −0.500000 1.53884i −0.0510310 0.157057i
9797 −9.99782 + 7.26384i −1.01512 + 0.737531i −0.965278 0.261226i 0.915873π-0.915873\pi
−0.0498467 + 0.998757i 0.515873π0.515873\pi
9898 −7.27425 −0.734810
9999 −1.26664 0.0222142i −0.127302 0.00223261i
100100 0 0
101101 7.29264 5.29841i 0.725645 0.527212i −0.162538 0.986702i 0.551968π-0.551968\pi
0.888183 + 0.459491i 0.151968π0.151968\pi
102102 1.64861 + 5.07390i 0.163237 + 0.502391i
103103 3.53329 10.8743i 0.348145 1.07148i −0.611733 0.791064i 0.709527π-0.709527\pi
0.959878 0.280416i 0.0904725π-0.0904725\pi
104104 −2.50710 1.82151i −0.245841 0.178614i
105105 0 0
106106 −3.40357 + 10.4751i −0.330584 + 1.01743i
107107 4.74484 + 14.6031i 0.458701 + 1.41174i 0.866734 + 0.498770i 0.166215π0.166215\pi
−0.408033 + 0.912967i 0.633785π0.633785\pi
108108 4.42705 3.21644i 0.425993 0.309502i
109109 2.42892 0.232648 0.116324 0.993211i 0.462889π-0.462889\pi
0.116324 + 0.993211i 0.462889π0.462889\pi
110110 0 0
111111 12.8071 1.21560
112112 −3.05657 + 2.22073i −0.288819 + 0.209839i
113113 2.58998 + 7.97113i 0.243644 + 0.749860i 0.995856 + 0.0909393i 0.0289869π0.0289869\pi
−0.752212 + 0.658921i 0.771013π0.771013\pi
114114 −0.648609 + 1.99621i −0.0607478 + 0.186963i
115115 0 0
116116 7.74317 + 5.62574i 0.718935 + 0.522337i
117117 0.365781 1.12576i 0.0338164 0.104076i
118118 −1.63693 5.03795i −0.150692 0.463781i
119119 10.0782 7.32222i 0.923865 0.671227i
120120 0 0
121121 3.03026 + 10.5744i 0.275478 + 0.961307i
122122 −2.45731 −0.222475
123123 −8.23117 + 5.98030i −0.742180 + 0.539225i
124124 1.65300 + 5.08740i 0.148443 + 0.456862i
125125 0 0
126126 −1.16751 0.848243i −0.104010 0.0755675i
127127 −5.62545 4.08713i −0.499178 0.362674i 0.309525 0.950891i 0.399830π-0.399830\pi
−0.808703 + 0.588217i 0.799830π0.799830\pi
128128 −0.309017 + 0.951057i −0.0273135 + 0.0840623i
129129 1.80902 + 5.56758i 0.159275 + 0.490198i
130130 0 0
131131 −5.61741 −0.490795 −0.245398 0.969423i 0.578918π-0.578918\pi
−0.245398 + 0.969423i 0.578918π0.578918\pi
132132 −4.28554 3.22994i −0.373008 0.281130i
133133 4.90106 0.424976
134134 7.45305 5.41495i 0.643845 0.467781i
135135 0 0
136136 1.01890 3.13584i 0.0873697 0.268896i
137137 −6.21969 4.51887i −0.531384 0.386073i 0.289491 0.957181i 0.406514π-0.406514\pi
−0.820875 + 0.571108i 0.806514π0.806514\pi
138138 0.728970 + 0.529628i 0.0620541 + 0.0450849i
139139 0.297218 0.914744i 0.0252097 0.0775876i −0.937660 0.347554i 0.887012π-0.887012\pi
0.962870 + 0.269966i 0.0870125π0.0870125\pi
140140 0 0
141141 7.00220 5.08740i 0.589692 0.428436i
142142 −10.8919 −0.914028
143143 −10.2765 0.180227i −0.859360 0.0150713i
144144 −0.381966 −0.0318305
145145 0 0
146146 1.04947 + 3.22994i 0.0868549 + 0.267312i
147147 3.63712 11.1939i 0.299985 0.923259i
148148 −6.40357 4.65247i −0.526371 0.382431i
149149 7.11314 + 5.16800i 0.582731 + 0.423379i 0.839708 0.543039i 0.182726π-0.182726\pi
−0.256977 + 0.966418i 0.582726π0.582726\pi
150150 0 0
151151 −2.76194 8.50038i −0.224764 0.691751i −0.998316 0.0580184i 0.981522π-0.981522\pi
0.773552 0.633733i 0.218478π-0.218478\pi
152152 1.04947 0.762486i 0.0851234 0.0618458i
153153 1.25943 0.101819
154154 −4.08056 + 11.8476i −0.328820 + 0.954707i
155155 0 0
156156 4.05657 2.94727i 0.324785 0.235970i
157157 5.45137 + 16.7776i 0.435067 + 1.33900i 0.893018 + 0.450020i 0.148583π0.148583\pi
−0.457952 + 0.888977i 0.651417π0.651417\pi
158158 −5.05657 + 15.5625i −0.402279 + 1.23809i
159159 −14.4178 10.4751i −1.14340 0.830731i
160160 0 0
161161 0.650165 2.00100i 0.0512402 0.157701i
162162 2.38197 + 7.33094i 0.187145 + 0.575973i
163163 0.141003 0.102445i 0.0110442 0.00802409i −0.582249 0.813010i 0.697827π-0.697827\pi
0.593294 + 0.804986i 0.297827π0.297827\pi
164164 6.28806 0.491015
165165 0 0
166166 −0.184079 −0.0142873
167167 4.43854 3.22478i 0.343464 0.249541i −0.402658 0.915351i 0.631914π-0.631914\pi
0.746122 + 0.665809i 0.231914π0.231914\pi
168168 −1.88906 5.81394i −0.145744 0.448555i
169169 −1.04959 + 3.23031i −0.0807378 + 0.248485i
170170 0 0
171171 0.400863 + 0.291244i 0.0306547 + 0.0222720i
172172 1.11803 3.44095i 0.0852493 0.262370i
173173 7.41518 + 22.8216i 0.563766 + 1.73509i 0.671591 + 0.740922i 0.265611π0.265611\pi
−0.107825 + 0.994170i 0.534389π0.534389\pi
174174 −12.5287 + 9.10264i −0.949799 + 0.690069i
175175 0 0
176176 0.969425 + 3.17178i 0.0730731 + 0.239082i
177177 8.57108 0.644242
178178 4.92705 3.57971i 0.369298 0.268311i
179179 −0.0658512 0.202669i −0.00492195 0.0151482i 0.948565 0.316581i 0.102535π-0.102535\pi
−0.953487 + 0.301433i 0.902535π0.902535\pi
180180 0 0
181181 −0.839906 0.610228i −0.0624297 0.0453579i 0.556133 0.831094i 0.312285π-0.312285\pi
−0.618562 + 0.785736i 0.712285π0.712285\pi
182182 −9.47214 6.88191i −0.702121 0.510121i
183183 1.22866 3.78141i 0.0908249 0.279530i
184184 −0.172087 0.529628i −0.0126864 0.0390447i
185185 0 0
186186 −8.65520 −0.634630
187187 −3.19641 10.4581i −0.233744 0.764769i
188188 −5.34921 −0.390131
189189 16.7260 12.1521i 1.21663 0.883937i
190190 0 0
191191 −5.54206 + 17.0567i −0.401009 + 1.23418i 0.523172 + 0.852227i 0.324748π0.324748\pi
−0.924182 + 0.381953i 0.875252π0.875252\pi
192192 −1.30902 0.951057i −0.0944702 0.0686366i
193193 −7.29722 5.30174i −0.525265 0.381628i 0.293318 0.956015i 0.405240π-0.405240\pi
−0.818584 + 0.574387i 0.805240π0.805240\pi
194194 −3.81883 + 11.7531i −0.274176 + 0.843826i
195195 0 0
196196 −5.88499 + 4.27570i −0.420357 + 0.305407i
197197 3.68422 0.262490 0.131245 0.991350i 0.458103π-0.458103\pi
0.131245 + 0.991350i 0.458103π0.458103\pi
198198 −1.03779 + 0.726543i −0.0737527 + 0.0516331i
199199 −4.23544 −0.300242 −0.150121 0.988668i 0.547966π-0.547966\pi
−0.150121 + 0.988668i 0.547966π0.547966\pi
200200 0 0
201201 4.60624 + 14.1765i 0.324899 + 0.999936i
202202 2.78554 8.57301i 0.195990 0.603195i
203203 29.2547 + 21.2548i 2.05328 + 1.49179i
204204 4.31611 + 3.13584i 0.302188 + 0.219553i
205205 0 0
206206 −3.53329 10.8743i −0.246176 0.757651i
207207 0.172087 0.125028i 0.0119608 0.00869006i
208208 −3.09894 −0.214873
209209 1.40106 4.06787i 0.0969131 0.281380i
210210 0 0
211211 11.0596 8.03527i 0.761374 0.553171i −0.137958 0.990438i 0.544054π-0.544054\pi
0.899331 + 0.437268i 0.144054π0.144054\pi
212212 3.40357 + 10.4751i 0.233758 + 0.719434i
213213 5.44595 16.7609i 0.373150 1.14844i
214214 12.4222 + 9.02522i 0.849161 + 0.616952i
215215 0 0
216216 1.69098 5.20431i 0.115057 0.354108i
217217 6.24523 + 19.2208i 0.423954 + 1.30480i
218218 1.96504 1.42768i 0.133089 0.0966949i
219219 −5.49511 −0.371325
220220 0 0
221221 10.2179 0.687330
222222 10.3612 7.52785i 0.695398 0.505236i
223223 −7.40777 22.7988i −0.496061 1.52672i −0.815297 0.579043i 0.803426π-0.803426\pi
0.319236 0.947675i 0.396574π-0.396574\pi
224224 −1.16751 + 3.59321i −0.0780073 + 0.240082i
225225 0 0
226226 6.78064 + 4.92643i 0.451042 + 0.327701i
227227 −6.39803 + 19.6911i −0.424652 + 1.30695i 0.478675 + 0.877992i 0.341117π0.341117\pi
−0.903327 + 0.428953i 0.858883π0.858883\pi
228228 0.648609 + 1.99621i 0.0429552 + 0.132202i
229229 13.2199 9.60481i 0.873594 0.634704i −0.0579546 0.998319i 0.518458π-0.518458\pi
0.931549 + 0.363616i 0.118458π0.118458\pi
230230 0 0
231231 −16.1913 12.2031i −1.06531 0.802907i
232232 9.57108 0.628372
233233 0.388556 0.282302i 0.0254551 0.0184942i −0.574985 0.818164i 0.694992π-0.694992\pi
0.600440 + 0.799670i 0.294992π0.294992\pi
234234 −0.365781 1.12576i −0.0239118 0.0735930i
235235 0 0
236236 −4.28554 3.11363i −0.278965 0.202680i
237237 −21.4200 15.5625i −1.39138 1.01089i
238238 3.84952 11.8476i 0.249527 0.767966i
239239 0.348754 + 1.07335i 0.0225590 + 0.0694295i 0.961702 0.274096i 0.0883787π-0.0883787\pi
−0.939143 + 0.343526i 0.888379π0.888379\pi
240240 0 0
241241 −12.7220 −0.819497 −0.409748 0.912199i 0.634384π-0.634384\pi
−0.409748 + 0.912199i 0.634384π0.634384\pi
242242 8.66700 + 6.77371i 0.557136 + 0.435431i
243243 3.94427 0.253025
244244 −1.98801 + 1.44437i −0.127269 + 0.0924664i
245245 0 0
246246 −3.14403 + 9.67632i −0.200456 + 0.616940i
247247 3.25225 + 2.36290i 0.206936 + 0.150348i
248248 4.32760 + 3.14419i 0.274803 + 0.199656i
249249 0.0920396 0.283269i 0.00583277 0.0179514i
250250 0 0
251251 2.29722 1.66903i 0.144999 0.105348i −0.512921 0.858436i 0.671437π-0.671437\pi
0.657920 + 0.753088i 0.271437π0.271437\pi
252252 −1.44312 −0.0909078
253253 −1.47497 1.11166i −0.0927304 0.0698894i
254254 −6.95343 −0.436297
255255 0 0
256256 0.309017 + 0.951057i 0.0193136 + 0.0594410i
257257 9.53038 29.3315i 0.594489 1.82965i 0.0372347 0.999307i 0.488145π-0.488145\pi
0.557254 0.830342i 0.311855π-0.311855\pi
258258 4.73607 + 3.44095i 0.294855 + 0.214224i
259259 −24.1935 17.5776i −1.50331 1.09222i
260260 0 0
261261 1.12971 + 3.47690i 0.0699275 + 0.215215i
262262 −4.54458 + 3.30183i −0.280765 + 0.203988i
263263 −27.7069 −1.70848 −0.854242 0.519876i 0.825978π-0.825978\pi
−0.854242 + 0.519876i 0.825978π0.825978\pi
264264 −5.36559 0.0941007i −0.330229 0.00579150i
265265 0 0
266266 3.96504 2.88077i 0.243112 0.176631i
267267 3.04508 + 9.37181i 0.186356 + 0.573545i
268268 2.84681 8.76158i 0.173897 0.535199i
269269 −10.3224 7.49966i −0.629367 0.457262i 0.226814 0.973938i 0.427169π-0.427169\pi
−0.856181 + 0.516676i 0.827169π0.827169\pi
270270 0 0
271271 1.76218 5.42344i 0.107045 0.329450i −0.883160 0.469072i 0.844589π-0.844589\pi
0.990205 + 0.139621i 0.0445885π0.0445885\pi
272272 −1.01890 3.13584i −0.0617797 0.190138i
273273 15.3262 11.1352i 0.927586 0.673931i
274274 −7.68796 −0.464447
275275 0 0
276276 0.901057 0.0542372
277277 25.6680 18.6489i 1.54224 1.12050i 0.593333 0.804957i 0.297812π-0.297812\pi
0.948910 0.315548i 0.102188π-0.102188\pi
278278 −0.297218 0.914744i −0.0178260 0.0548627i
279279 −0.631388 + 1.94321i −0.0378002 + 0.116337i
280280 0 0
281281 1.56805 + 1.13926i 0.0935423 + 0.0679624i 0.633573 0.773683i 0.281588π-0.281588\pi
−0.540031 + 0.841645i 0.681588π0.681588\pi
282282 2.67460 8.23158i 0.159270 0.490184i
283283 1.51909 + 4.67528i 0.0903006 + 0.277917i 0.986000 0.166742i 0.0533249π-0.0533249\pi
−0.895700 + 0.444659i 0.853325π0.853325\pi
284284 −8.81173 + 6.40210i −0.522880 + 0.379894i
285285 0 0
286286 −8.41976 + 5.89454i −0.497871 + 0.348551i
287287 23.7571 1.40234
288288 −0.309017 + 0.224514i −0.0182090 + 0.0132296i
289289 −1.89376 5.82841i −0.111398 0.342848i
290290 0 0
291291 −16.1768 11.7531i −0.948301 0.688981i
292292 2.74755 + 1.99621i 0.160788 + 0.116820i
293293 −0.0583193 + 0.179488i −0.00340705 + 0.0104858i −0.952746 0.303769i 0.901755π-0.901755\pi
0.949339 + 0.314255i 0.101755π0.101755\pi
294294 −3.63712 11.1939i −0.212121 0.652843i
295295 0 0
296296 −7.91525 −0.460065
297297 −5.30482 17.3564i −0.307817 1.00712i
298298 8.79232 0.509326
299299 1.39616 1.01437i 0.0807421 0.0586626i
300300 0 0
301301 4.22408 13.0004i 0.243472 0.749329i
302302 −7.23086 5.25353i −0.416089 0.302306i
303303 11.7997 + 8.57301i 0.677877 + 0.492507i
304304 0.400863 1.23373i 0.0229910 0.0707592i
305305 0 0
306306 1.01890 0.740272i 0.0582464 0.0423185i
307307 −12.3820 −0.706676 −0.353338 0.935496i 0.614953π-0.614953\pi
−0.353338 + 0.935496i 0.614953π0.614953\pi
308308 3.66261 + 11.9834i 0.208697 + 0.682818i
309309 18.5005 1.05246
310310 0 0
311311 −6.52587 20.0846i −0.370048 1.13889i −0.946759 0.321943i 0.895664π-0.895664\pi
0.576711 0.816949i 0.304336π-0.304336\pi
312312 1.54947 4.76878i 0.0877216 0.269979i
313313 −13.4129 9.74502i −0.758140 0.550821i 0.140199 0.990123i 0.455226π-0.455226\pi
−0.898339 + 0.439302i 0.855226π0.855226\pi
314314 14.2719 + 10.3691i 0.805408 + 0.585163i
315315 0 0
316316 5.05657 + 15.5625i 0.284454 + 0.875460i
317317 15.8867 11.5424i 0.892285 0.648283i −0.0441877 0.999023i 0.514070π-0.514070\pi
0.936473 + 0.350740i 0.114070π0.114070\pi
318318 −17.8213 −0.999371
319319 26.0044 18.2053i 1.45597 1.01930i
320320 0 0
321321 −20.0995 + 14.6031i −1.12184 + 0.815067i
322322 −0.650165 2.00100i −0.0362323 0.111511i
323323 −1.32173 + 4.06787i −0.0735431 + 0.226342i
324324 6.23607 + 4.53077i 0.346448 + 0.251709i
325325 0 0
326326 0.0538584 0.165759i 0.00298294 0.00918055i
327327 1.21446 + 3.73772i 0.0671598 + 0.206697i
328328 5.08714 3.69603i 0.280891 0.204079i
329329 −20.2100 −1.11421
330330 0 0
331331 −23.4826 −1.29072 −0.645360 0.763879i 0.723293π-0.723293\pi
−0.645360 + 0.763879i 0.723293π0.723293\pi
332332 −0.148923 + 0.108199i −0.00817322 + 0.00593820i
333333 −0.934269 2.87538i −0.0511976 0.157570i
334334 1.69537 5.21781i 0.0927665 0.285506i
335335 0 0
336336 −4.94563 3.59321i −0.269806 0.196026i
337337 3.96317 12.1974i 0.215888 0.664434i −0.783202 0.621768i 0.786415π-0.786415\pi
0.999089 0.0426660i 0.0135851π-0.0135851\pi
338338 1.04959 + 3.23031i 0.0570903 + 0.175706i
339339 −10.9713 + 7.97113i −0.595880 + 0.432932i
340340 0 0
341341 17.7386 + 0.311096i 0.960598 + 0.0168468i
342342 0.495493 0.0267932
343343 −0.838262 + 0.609033i −0.0452619 + 0.0328847i
344344 −1.11803 3.44095i −0.0602804 0.185524i
345345 0 0
346346 19.4132 + 14.1045i 1.04366 + 0.758263i
347347 −16.7415 12.1634i −0.898730 0.652966i 0.0394093 0.999223i 0.487452π-0.487452\pi
−0.938140 + 0.346257i 0.887452π0.887452\pi
348348 −4.78554 + 14.7284i −0.256532 + 0.789524i
349349 6.71104 + 20.6544i 0.359233 + 1.10561i 0.953514 + 0.301349i 0.0974369π0.0974369\pi
−0.594280 + 0.804258i 0.702563π0.702563\pi
350350 0 0
351351 16.9578 0.905143
352352 2.64861 + 1.99621i 0.141171 + 0.106399i
353353 −0.260293 −0.0138540 −0.00692701 0.999976i 0.502205π-0.502205\pi
−0.00692701 + 0.999976i 0.502205π0.502205\pi
354354 6.93415 5.03795i 0.368546 0.267764i
355355 0 0
356356 1.88197 5.79210i 0.0997440 0.306980i
357357 16.3068 + 11.8476i 0.863049 + 0.627042i
358358 −0.172401 0.125256i −0.00911165 0.00662000i
359359 2.54070 7.81947i 0.134093 0.412696i −0.861355 0.508004i 0.830384π-0.830384\pi
0.995448 + 0.0953081i 0.0303836π0.0303836\pi
360360 0 0
361361 14.0099 10.1788i 0.737365 0.535727i
362362 −1.03818 −0.0545656
363363 −14.7572 + 9.95028i −0.774550 + 0.522254i
364364 −11.7082 −0.613677
365365 0 0
366366 −1.22866 3.78141i −0.0642229 0.197658i
367367 2.22904 6.86029i 0.116355 0.358104i −0.875872 0.482543i 0.839713π-0.839713\pi
0.992227 + 0.124439i 0.0397131π0.0397131\pi
368368 −0.450528 0.327328i −0.0234854 0.0170632i
369369 1.94312 + 1.41176i 0.101155 + 0.0734931i
370370 0 0
371371 12.8591 + 39.5764i 0.667613 + 2.05470i
372372 −7.00220 + 5.08740i −0.363047 + 0.263769i
373373 29.9629 1.55142 0.775709 0.631090i 0.217392π-0.217392\pi
0.775709 + 0.631090i 0.217392π0.217392\pi
374374 −8.73304 6.58195i −0.451575 0.340345i
375375 0 0
376376 −4.32760 + 3.14419i −0.223179 + 0.162149i
377377 9.16552 + 28.2086i 0.472048 + 1.45281i
378378 6.38875 19.6626i 0.328602 1.01133i
379379 29.6962 + 21.5756i 1.52539 + 1.10826i 0.958732 + 0.284312i 0.0917651π0.0917651\pi
0.566661 + 0.823951i 0.308235π0.308235\pi
380380 0 0
381381 3.47672 10.7002i 0.178118 0.548190i
382382 5.54206 + 17.0567i 0.283556 + 0.872697i
383383 5.21666 3.79013i 0.266559 0.193666i −0.446475 0.894796i 0.647321π-0.647321\pi
0.713034 + 0.701130i 0.247321π0.247321\pi
384384 −1.61803 −0.0825700
385385 0 0
386386 −9.01986 −0.459099
387387 1.11803 0.812299i 0.0568329 0.0412915i
388388 3.81883 + 11.7531i 0.193872 + 0.596675i
389389 −8.83792 + 27.2003i −0.448100 + 1.37911i 0.430948 + 0.902377i 0.358179π0.358179\pi
−0.879048 + 0.476734i 0.841821π0.841821\pi
390390 0 0
391391 1.48549 + 1.07927i 0.0751245 + 0.0545811i
392392 −2.24787 + 6.91822i −0.113534 + 0.349423i
393393 −2.80870 8.64430i −0.141680 0.436047i
394394 2.98060 2.16553i 0.150160 0.109098i
395395 0 0
396396 −0.412541 + 1.19778i −0.0207310 + 0.0601909i
397397 −24.5049 −1.22987 −0.614934 0.788579i 0.710817π-0.710817\pi
−0.614934 + 0.788579i 0.710817π0.710817\pi
398398 −3.42654 + 2.48953i −0.171757 + 0.124789i
399399 2.45053 + 7.54195i 0.122680 + 0.377570i
400400 0 0
401401 24.8467 + 18.0522i 1.24079 + 0.901483i 0.997650 0.0685091i 0.0218242π-0.0218242\pi
0.243135 + 0.969992i 0.421824π0.421824\pi
402402 12.0593 + 8.76158i 0.601462 + 0.436988i
403403 −5.12254 + 15.7656i −0.255172 + 0.785338i
404404 −2.78554 8.57301i −0.138586 0.426523i
405405 0 0
406406 36.1608 1.79463
407407 −21.5056 + 15.0557i −1.06599 + 0.746284i
408408 5.33501 0.264122
409409 −17.6836 + 12.8479i −0.874397 + 0.635287i −0.931763 0.363066i 0.881730π-0.881730\pi
0.0573660 + 0.998353i 0.481730π0.481730\pi
410410 0 0
411411 3.84398 11.8306i 0.189609 0.583558i
412412 −9.25026 6.72071i −0.455728 0.331106i
413413 −16.1913 11.7637i −0.796723 0.578853i
414414 0.0657312 0.202300i 0.00323051 0.00994249i
415415 0 0
416416 −2.50710 + 1.82151i −0.122921 + 0.0893070i
417417 1.55626 0.0762102
418418 −1.25756 4.11450i −0.0615091 0.201247i
419419 4.17764 0.204091 0.102046 0.994780i 0.467461π-0.467461\pi
0.102046 + 0.994780i 0.467461π0.467461\pi
420420 0 0
421421 3.92266 + 12.0727i 0.191179 + 0.588388i 1.00000 0.000333393i 0.000106122π0.000106122\pi
−0.808821 + 0.588055i 0.799894π0.799894\pi
422422 4.22439 13.0013i 0.205640 0.632895i
423423 −1.65300 1.20097i −0.0803714 0.0583932i
424424 8.91067 + 6.47398i 0.432740 + 0.314404i
425425 0 0
426426 −5.44595 16.7609i −0.263857 0.812068i
427427 −7.51095 + 5.45702i −0.363480 + 0.264084i
428428 15.3546 0.742194
429429 −4.86089 15.9039i −0.234686 0.767850i
430430 0 0
431431 0.591217 0.429545i 0.0284779 0.0206904i −0.573455 0.819237i 0.694397π-0.694397\pi
0.601933 + 0.798546i 0.294397π0.294397\pi
432432 −1.69098 5.20431i −0.0813575 0.250393i
433433 −1.74465 + 5.36947i −0.0838424 + 0.258040i −0.984186 0.177140i 0.943315π-0.943315\pi
0.900343 + 0.435180i 0.143315π0.143315\pi
434434 16.3502 + 11.8791i 0.784836 + 0.570217i
435435 0 0
436436 0.750578 2.31004i 0.0359462 0.110631i
437437 0.223234 + 0.687043i 0.0106787 + 0.0328657i
438438 −4.44563 + 3.22994i −0.212421 + 0.154333i
439439 13.7074 0.654220 0.327110 0.944986i 0.393925π-0.393925\pi
0.327110 + 0.944986i 0.393925π0.393925\pi
440440 0 0
441441 −2.77852 −0.132310
442442 8.26645 6.00593i 0.393195 0.285673i
443443 −4.33967 13.3561i −0.206184 0.634568i −0.999663 0.0259707i 0.991732π-0.991732\pi
0.793479 0.608598i 0.208268π-0.208268\pi
444444 3.95763 12.1803i 0.187821 0.578052i
445445 0 0
446446 −19.3938 14.0904i −0.918322 0.667200i
447447 −4.39616 + 13.5300i −0.207931 + 0.639947i
448448 1.16751 + 3.59321i 0.0551595 + 0.169763i
449449 −7.81141 + 5.67532i −0.368643 + 0.267835i −0.756648 0.653822i 0.773164π-0.773164\pi
0.388005 + 0.921657i 0.373164π0.373164\pi
450450 0 0
451451 6.79140 19.7183i 0.319794 0.928501i
452452 8.38134 0.394225
453453 11.6998 8.50038i 0.549703 0.399383i
454454 6.39803 + 19.6911i 0.300274 + 0.924150i
455455 0 0
456456 1.69808 + 1.23373i 0.0795199 + 0.0577746i
457457 −0.832300 0.604702i −0.0389334 0.0282867i 0.568148 0.822926i 0.307660π-0.307660\pi
−0.607082 + 0.794639i 0.707660π0.707660\pi
458458 5.04955 15.5409i 0.235950 0.726179i
459459 5.57554 + 17.1597i 0.260244 + 0.800948i
460460 0 0
461461 −8.05882 −0.375336 −0.187668 0.982232i 0.560093π-0.560093\pi
−0.187668 + 0.982232i 0.560093π0.560093\pi
462462 −20.2719 0.355525i −0.943133 0.0165405i
463463 7.46633 0.346990 0.173495 0.984835i 0.444494π-0.444494\pi
0.173495 + 0.984835i 0.444494π0.444494\pi
464464 7.74317 5.62574i 0.359467 0.261168i
465465 0 0
466466 0.148415 0.456775i 0.00687520 0.0211597i
467467 9.05238 + 6.57694i 0.418894 + 0.304344i 0.777193 0.629263i 0.216643π-0.216643\pi
−0.358299 + 0.933607i 0.616643π0.616643\pi
468468 −0.957626 0.695756i −0.0442663 0.0321613i
469469 10.7556 33.1024i 0.496648 1.52853i
470470 0 0
471471 −23.0924 + 16.7776i −1.06404 + 0.773071i
472472 −5.29722 −0.243824
473473 −9.58276 7.22237i −0.440616 0.332085i
474474 −26.4765 −1.21611
475475 0 0
476476 −3.84952 11.8476i −0.176443 0.543034i
477477 −1.30005 + 4.00114i −0.0595252 + 0.183200i
478478 0.913049 + 0.663369i 0.0417619 + 0.0303418i
479479 −21.6571 15.7348i −0.989536 0.718940i −0.0297167 0.999558i 0.509461π-0.509461\pi
−0.959819 + 0.280618i 0.909461π0.909461\pi
480480 0 0
481481 −7.57985 23.3284i −0.345612 1.06368i
482482 −10.2923 + 7.47781i −0.468802 + 0.340605i
483483 3.40431 0.154901
484484 10.9932 + 0.385714i 0.499693 + 0.0175324i
485485 0 0
486486 3.19098 2.31838i 0.144746 0.105164i
487487 −5.67918 17.4787i −0.257348 0.792037i −0.993358 0.115066i 0.963292π-0.963292\pi
0.736009 0.676971i 0.236708π-0.236708\pi
488488 −0.759351 + 2.33704i −0.0343742 + 0.105793i
489489 0.228148 + 0.165759i 0.0103172 + 0.00749589i
490490 0 0
491491 −8.02923 + 24.7114i −0.362354 + 1.11521i 0.589268 + 0.807938i 0.299416π0.299416\pi
−0.951622 + 0.307273i 0.900584π0.900584\pi
492492 3.14403 + 9.67632i 0.141744 + 0.436242i
493493 −25.5309 + 18.5493i −1.14985 + 0.835418i
494494 4.02001 0.180869
495495 0 0
496496 5.34921 0.240186
497497 −33.2918 + 24.1879i −1.49334 + 1.08498i
498498 −0.0920396 0.283269i −0.00412439 0.0126936i
499499 5.24736 16.1497i 0.234904 0.722960i −0.762230 0.647306i 0.775896π-0.775896\pi
0.997134 0.0756541i 0.0241045π-0.0241045\pi
500500 0 0
501501 7.18170 + 5.21781i 0.320855 + 0.233115i
502502 0.877459 2.70054i 0.0391629 0.120531i
503503 4.13825 + 12.7362i 0.184515 + 0.567880i 0.999940 0.0109840i 0.00349637π-0.00349637\pi
−0.815424 + 0.578864i 0.803496π0.803496\pi
504504 −1.16751 + 0.848243i −0.0520048 + 0.0377837i
505505 0 0
506506 −1.84669 0.0323869i −0.0820954 0.00143977i
507507 −5.49573 −0.244074
508508 −5.62545 + 4.08713i −0.249589 + 0.181337i
509509 −6.18963 19.0497i −0.274351 0.844365i −0.989390 0.145281i 0.953591π-0.953591\pi
0.715040 0.699084i 0.246409π-0.246409\pi
510510 0 0
511511 10.3806 + 7.54195i 0.459211 + 0.333636i
512512 0.809017 + 0.587785i 0.0357538 + 0.0259767i
513513 −2.19357 + 6.75113i −0.0968487 + 0.298070i
514514 −9.53038 29.3315i −0.420367 1.29376i
515515 0 0
516516 5.85410 0.257712
517517 −5.77739 + 16.7743i −0.254090 + 0.737731i
518518 −29.9048 −1.31394
519519 −31.4112 + 22.8216i −1.37880 + 1.00176i
520520 0 0
521521 0.718847 2.21238i 0.0314933 0.0969263i −0.934074 0.357079i 0.883773π-0.883773\pi
0.965568 + 0.260152i 0.0837728π0.0837728\pi
522522 2.95763 + 2.14884i 0.129452 + 0.0940522i
523523 −15.4672 11.2376i −0.676335 0.491386i 0.195805 0.980643i 0.437268π-0.437268\pi
−0.872140 + 0.489257i 0.837268π0.837268\pi
524524 −1.73587 + 5.34247i −0.0758320 + 0.233387i
525525 0 0
526526 −22.4154 + 16.2857i −0.977358 + 0.710092i
527527 −17.6375 −0.768302
528528 −4.39616 + 3.07768i −0.191318 + 0.133939i
529529 −22.6899 −0.986517
530530 0 0
531531 −0.625252 1.92433i −0.0271336 0.0835087i
532532 1.51451 4.66118i 0.0656623 0.202088i
533533 15.7648 + 11.4538i 0.682848 + 0.496118i
534534 7.97214 + 5.79210i 0.344988 + 0.250648i
535535 0 0
536536 −2.84681 8.76158i −0.122963 0.378443i
537537 0.278950 0.202669i 0.0120376 0.00874581i
538538 −12.7592 −0.550087
539539 7.05184 + 23.0723i 0.303744 + 0.993796i
540540 0 0
541541 −24.1108 + 17.5175i −1.03660 + 0.753136i −0.969619 0.244618i 0.921337π-0.921337\pi
−0.0669831 + 0.997754i 0.521337π0.521337\pi
542542 −1.76218 5.42344i −0.0756922 0.232957i
543543 0.519091 1.59760i 0.0222763 0.0685594i
544544 −2.66751 1.93806i −0.114368 0.0830935i
545545 0 0
546546 5.85410 18.0171i 0.250532 0.771060i
547547 −5.85573 18.0221i −0.250373 0.770569i −0.994706 0.102760i 0.967233π-0.967233\pi
0.744333 0.667808i 0.232767π-0.232767\pi
548548 −6.21969 + 4.51887i −0.265692 + 0.193036i
549549 −0.938610 −0.0400589
550550 0 0
551551 −12.4158 −0.528930
552552 0.728970 0.529628i 0.0310270 0.0225425i
553553 19.1044 + 58.7972i 0.812400 + 2.50031i
554554 9.80432 30.1746i 0.416545 1.28200i
555555 0 0
556556 −0.778128 0.565343i −0.0330000 0.0239759i
557557 −2.06534 + 6.35647i −0.0875114 + 0.269332i −0.985230 0.171237i 0.945224π-0.945224\pi
0.897718 + 0.440570i 0.145224π0.145224\pi
558558 0.631388 + 1.94321i 0.0267288 + 0.0822628i
559559 9.07077 6.59030i 0.383652 0.278740i
560560 0 0
561561 14.4951 10.1478i 0.611984 0.428440i
562562 1.93822 0.0817589
563563 7.70518 5.59814i 0.324735 0.235933i −0.413459 0.910523i 0.635679π-0.635679\pi
0.738193 + 0.674589i 0.235679π0.235679\pi
564564 −2.67460 8.23158i −0.112621 0.346612i
565565 0 0
566566 3.97703 + 2.88948i 0.167167 + 0.121454i
567567 23.5607 + 17.1178i 0.989455 + 0.718881i
568568 −3.36578 + 10.3588i −0.141225 + 0.434646i
569569 8.67150 + 26.6881i 0.363528 + 1.11883i 0.950897 + 0.309506i 0.100164π0.100164\pi
−0.587369 + 0.809319i 0.699836π0.699836\pi
570570 0 0
571571 −1.61429 −0.0675561 −0.0337781 0.999429i 0.510754π-0.510754\pi
−0.0337781 + 0.999429i 0.510754π0.510754\pi
572572 −3.34700 + 9.71779i −0.139945 + 0.406321i
573573 −29.0186 −1.21227
574574 19.2199 13.9641i 0.802222 0.582849i
575575 0 0
576576 −0.118034 + 0.363271i −0.00491808 + 0.0151363i
577577 −2.64516 1.92182i −0.110120 0.0800066i 0.531363 0.847145i 0.321680π-0.321680\pi
−0.641482 + 0.767138i 0.721680π0.721680\pi
578578 −4.95794 3.60215i −0.206223 0.149830i
579579 4.50993 13.8801i 0.187426 0.576839i
580580 0 0
581581 −0.562651 + 0.408790i −0.0233427 + 0.0169595i
582582 −19.9956 −0.828846
583583 36.5243 + 0.640558i 1.51268 + 0.0265292i
584584 3.39616 0.140534
585585 0 0
586586 0.0583193 + 0.179488i 0.00240915 + 0.00741459i
587587 1.08288 3.33276i 0.0446952 0.137558i −0.926219 0.376987i 0.876960π-0.876960\pi
0.970914 + 0.239429i 0.0769603π0.0769603\pi
588588 −9.52212 6.91822i −0.392685 0.285303i
589589 −5.61384 4.07869i −0.231314 0.168060i
590590 0 0
591591 1.84211 + 5.66943i 0.0757742 + 0.233209i
592592 −6.40357 + 4.65247i −0.263185 + 0.191215i
593593 −27.6283 −1.13456 −0.567278 0.823526i 0.692004π-0.692004\pi
−0.567278 + 0.823526i 0.692004π0.692004\pi
594594 −14.4935 10.9236i −0.594678 0.448199i
595595 0 0
596596 7.11314 5.16800i 0.291366 0.211689i
597597 −2.11772 6.51767i −0.0866725 0.266751i
598598 0.533286 1.64129i 0.0218077 0.0671172i
599599 6.43434 + 4.67482i 0.262900 + 0.191008i 0.711425 0.702762i 0.248050π-0.248050\pi
−0.448524 + 0.893771i 0.648050π0.648050\pi
600600 0 0
601601 2.01909 6.21412i 0.0823604 0.253479i −0.901394 0.433000i 0.857455π-0.857455\pi
0.983754 + 0.179521i 0.0574548π0.0574548\pi
602602 −4.22408 13.0004i −0.172160 0.529855i
603603 2.84681 2.06833i 0.115931 0.0842288i
604604 −8.93783 −0.363675
605605 0 0
606606 14.5853 0.592486
607607 6.77813 4.92460i 0.275116 0.199883i −0.441668 0.897178i 0.645613π-0.645613\pi
0.716784 + 0.697295i 0.245613π0.245613\pi
608608 −0.400863 1.23373i −0.0162571 0.0500343i
609609 −18.0804 + 55.6457i −0.732654 + 2.25488i
610610 0 0
611611 −13.4110 9.74365i −0.542550 0.394186i
612612 0.389184 1.19778i 0.0157318 0.0484176i
613613 −5.53528 17.0358i −0.223568 0.688071i −0.998434 0.0559453i 0.982183π-0.982183\pi
0.774866 0.632125i 0.217817π-0.217817\pi
614614 −10.0172 + 7.27794i −0.404262 + 0.293714i
615615 0 0
616616 10.0068 + 7.54195i 0.403185 + 0.303874i
617617 21.3999 0.861529 0.430765 0.902464i 0.358244π-0.358244\pi
0.430765 + 0.902464i 0.358244π0.358244\pi
618618 14.9672 10.8743i 0.602071 0.437430i
619619 −1.82954 5.63076i −0.0735356 0.226319i 0.907533 0.419981i 0.137963π-0.137963\pi
−0.981068 + 0.193662i 0.937963π0.937963\pi
620620 0 0
621621 2.46535 + 1.79118i 0.0989312 + 0.0718777i
622622 −17.0850 12.4130i −0.685045 0.497714i
623623 7.11031 21.8833i 0.284868 0.876735i
624624 −1.54947 4.76878i −0.0620285 0.190904i
625625 0 0
626626 −16.5792 −0.662639
627627 6.96034 + 0.122069i 0.277969 + 0.00487497i
628628 17.6410 0.703953
629629 21.1140 15.3402i 0.841870 0.611654i
630630 0 0
631631 5.62521 17.3126i 0.223936 0.689204i −0.774462 0.632620i 0.781979π-0.781979\pi
0.998398 0.0565834i 0.0180207π-0.0180207\pi
632632 13.2383 + 9.61817i 0.526590 + 0.382590i
633633 17.8948 + 13.0013i 0.711254 + 0.516757i
634634 6.06817 18.6759i 0.240998 0.741716i
635635 0 0
636636 −14.4178 + 10.4751i −0.571702 + 0.415366i
637637 −22.5425 −0.893166
638638 10.3372 30.0134i 0.409254 1.18824i
639639 −4.16033 −0.164580
640640 0 0
641641 5.44931 + 16.7712i 0.215235 + 0.662424i 0.999137 + 0.0415398i 0.0132263π0.0132263\pi
−0.783902 + 0.620884i 0.786774π0.786774\pi
642642 −7.67731 + 23.6283i −0.302999 + 0.932536i
643643 −35.5559 25.8329i −1.40219 1.01875i −0.994401 0.105673i 0.966300π-0.966300\pi
−0.407788 0.913077i 0.633700π-0.633700\pi
644644 −1.70215 1.23669i −0.0670742 0.0487323i
645645 0 0
646646 1.32173 + 4.06787i 0.0520028 + 0.160048i
647647 0.401371 0.291613i 0.0157795 0.0114645i −0.579868 0.814711i 0.696896π-0.696896\pi
0.595647 + 0.803246i 0.296896π0.296896\pi
648648 7.70820 0.302807
649649 −14.3924 + 10.0759i −0.564952 + 0.395514i
650650 0 0
651651 −26.4552 + 19.2208i −1.03686 + 0.753324i
652652 −0.0538584 0.165759i −0.00210926 0.00649163i
653653 −5.61086 + 17.2685i −0.219570 + 0.675767i 0.779228 + 0.626741i 0.215612π0.215612\pi
−0.998798 + 0.0490258i 0.984388π0.984388\pi
654654 3.17950 + 2.31004i 0.124328 + 0.0903297i
655655 0 0
656656 1.94312 5.98030i 0.0758659 0.233491i
657657 0.400863 + 1.23373i 0.0156391 + 0.0481323i
658658 −16.3502 + 11.8791i −0.637398 + 0.463097i
659659 −14.4974 −0.564739 −0.282370 0.959306i 0.591120π-0.591120\pi
−0.282370 + 0.959306i 0.591120π0.591120\pi
660660 0 0
661661 −11.6178 −0.451880 −0.225940 0.974141i 0.572545π-0.572545\pi
−0.225940 + 0.974141i 0.572545π0.572545\pi
662662 −18.9978 + 13.8027i −0.738371 + 0.536458i
663663 5.10895 + 15.7237i 0.198415 + 0.610659i
664664 −0.0568836 + 0.175070i −0.00220751 + 0.00679402i
665665 0 0
666666 −2.44595 1.77708i −0.0947785 0.0688606i
667667 −1.64705 + 5.06911i −0.0637742 + 0.196277i
668668 −1.69537 5.21781i −0.0655958 0.201883i
669669 31.3798 22.7988i 1.21321 0.881451i
670670 0 0
671671 2.38218 + 7.79406i 0.0919630 + 0.300886i
672672 −6.11314 −0.235819
673673 28.8239 20.9418i 1.11108 0.807246i 0.128245 0.991743i 0.459066π-0.459066\pi
0.982833 + 0.184497i 0.0590656π0.0590656\pi
674674 −3.96317 12.1974i −0.152656 0.469825i
675675 0 0
676676 2.74787 + 1.99644i 0.105687 + 0.0767862i
677677 19.8288 + 14.4064i 0.762081 + 0.553684i 0.899548 0.436822i 0.143896π-0.143896\pi
−0.137467 + 0.990506i 0.543896π0.543896\pi
678678 −4.19067 + 12.8976i −0.160942 + 0.495328i
679679 14.4280 + 44.4049i 0.553696 + 1.70410i
680680 0 0
681681 −33.5005 −1.28374
682682 14.5337 10.1748i 0.556523 0.389613i
683683 25.5212 0.976540 0.488270 0.872693i 0.337628π-0.337628\pi
0.488270 + 0.872693i 0.337628π0.337628\pi
684684 0.400863 0.291244i 0.0153274 0.0111360i
685685 0 0
686686 −0.320187 + 0.985436i −0.0122248 + 0.0376241i
687687 21.3902 + 15.5409i 0.816088 + 0.592922i
688688 −2.92705 2.12663i −0.111593 0.0810769i
689689 −10.5475 + 32.4618i −0.401827 + 1.23670i
690690 0 0
691691 36.7992 26.7362i 1.39991 1.01709i 0.405215 0.914222i 0.367197π-0.367197\pi
0.994695 0.102872i 0.0328032π-0.0328032\pi
692692 23.9960 0.912192
693693 −1.55863 + 4.52538i −0.0592076 + 0.171905i
694694 −20.6936 −0.785519
695695 0 0
696696 4.78554 + 14.7284i 0.181395 + 0.558278i
697697 −6.40688 + 19.7183i −0.242678 + 0.746886i
698698 17.5697 + 12.7651i 0.665024 + 0.483168i
699699 0.628696 + 0.456775i 0.0237795 + 0.0172768i
700700 0 0
701701 −9.00678 27.7200i −0.340182 1.04697i −0.964113 0.265492i 0.914466π-0.914466\pi
0.623932 0.781479i 0.285534π-0.285534\pi
702702 13.7192 9.96757i 0.517797 0.376202i
703703 10.2678 0.387258
704704 3.31611 + 0.0581575i 0.124981 + 0.00219189i
705705 0 0
706706 −0.210582 + 0.152997i −0.00792535 + 0.00575810i
707707 −10.5241 32.3899i −0.395800 1.21815i
708708 2.64861 8.15158i 0.0995408 0.306355i
709709 −25.0122 18.1724i −0.939353 0.682480i 0.00891175 0.999960i 0.497163π-0.497163\pi
−0.948265 + 0.317480i 0.897163π0.897163\pi
710710 0 0
711711 −1.93144 + 5.94435i −0.0724346 + 0.222931i
712712 −1.88197 5.79210i −0.0705297 0.217068i
713713 −2.40997 + 1.75095i −0.0902541 + 0.0655734i
714714 20.1564 0.754333
715715 0 0
716716 −0.213099 −0.00796388
717717 −1.47734 + 1.07335i −0.0551725 + 0.0400851i
718718 −2.54070 7.81947i −0.0948180 0.291820i
719719 −5.42235 + 16.6883i −0.202220 + 0.622368i 0.797597 + 0.603191i 0.206104π0.206104\pi
−0.999816 + 0.0191765i 0.993896π0.993896\pi
720720 0 0
721721 −34.9487 25.3917i −1.30156 0.945636i
722722 5.35132 16.4697i 0.199155 0.612937i
723723 −6.36101 19.5772i −0.236568 0.728083i
724724 −0.839906 + 0.610228i −0.0312149 + 0.0226789i
725725 0 0
726726 −6.09017 + 16.7240i −0.226027 + 0.620686i
727727 16.7731 0.622080 0.311040 0.950397i 0.399323π-0.399323\pi
0.311040 + 0.950397i 0.399323π0.399323\pi
728728 −9.47214 + 6.88191i −0.351061 + 0.255061i
729729 9.11803 + 28.0624i 0.337705 + 1.03935i
730730 0 0
731731 9.65113 + 7.01195i 0.356960 + 0.259346i
732732 −3.21666 2.33704i −0.118891 0.0863796i
733733 2.85868 8.79812i 0.105588 0.324966i −0.884280 0.466957i 0.845350π-0.845350\pi
0.989868 + 0.141991i 0.0453503π0.0453503\pi
734734 −2.22904 6.86029i −0.0822755 0.253218i
735735 0 0
736736 −0.556884 −0.0205270
737737 −24.4002 18.3901i −0.898794 0.677407i
738738 2.40182 0.0884124
739739 −6.06468 + 4.40625i −0.223093 + 0.162087i −0.693718 0.720247i 0.744029π-0.744029\pi
0.470625 + 0.882333i 0.344029π0.344029\pi
740740 0 0
741741 −2.01000 + 6.18615i −0.0738393 + 0.227254i
742742 33.6657 + 24.4595i 1.23591 + 0.897938i
743743 −5.26124 3.82251i −0.193016 0.140234i 0.487080 0.873357i 0.338062π-0.338062\pi
−0.680096 + 0.733123i 0.738062π0.738062\pi
744744 −2.67460 + 8.23158i −0.0980557 + 0.301784i
745745 0 0
746746 24.2405 17.6117i 0.887507 0.644811i
747747 −0.0703120 −0.00257258
748748 −10.9340 0.191758i −0.399785 0.00701136i
749749 58.0118 2.11970
750750 0 0
751751 6.27064 + 19.2991i 0.228819 + 0.704232i 0.997881 + 0.0650587i 0.0207235π0.0207235\pi
−0.769062 + 0.639174i 0.779277π0.779277\pi
752752 −1.65300 + 5.08740i −0.0602786 + 0.185518i
753753 3.71698 + 2.70054i 0.135454 + 0.0984132i
754754 23.9956 + 17.4338i 0.873869 + 0.634903i
755755 0 0
756756 −6.38875 19.6626i −0.232357 0.715120i
757757 14.9271 10.8452i 0.542534 0.394174i −0.282492 0.959270i 0.591161π-0.591161\pi
0.825025 + 0.565096i 0.191161π0.191161\pi
758758 36.7066 1.33324
759759 0.973183 2.82557i 0.0353243 0.102562i
760760 0 0
761761 11.0383 8.01981i 0.400139 0.290718i −0.369459 0.929247i 0.620457π-0.620457\pi
0.769598 + 0.638529i 0.220457π0.220457\pi
762762 −3.47672 10.7002i −0.125948 0.387629i
763763 2.83578 8.72763i 0.102662 0.315961i
764764 14.5093 + 10.5416i 0.524928 + 0.381383i
765765 0 0
766766 1.99259 6.13256i 0.0719951 0.221578i
767767 −5.07275 15.6123i −0.183167 0.563729i
768768 −1.30902 + 0.951057i −0.0472351 + 0.0343183i
769769 −6.77400 −0.244277 −0.122138 0.992513i 0.538975π-0.538975\pi
−0.122138 + 0.992513i 0.538975π0.538975\pi
770770 0 0
771771 49.9017 1.79717
772772 −7.29722 + 5.30174i −0.262633 + 0.190814i
773773 −5.80173 17.8559i −0.208674 0.642231i −0.999542 0.0302456i 0.990371π-0.990371\pi
0.790869 0.611986i 0.209629π-0.209629\pi
774774 0.427051 1.31433i 0.0153500 0.0472425i
775775 0 0
776776 9.99782 + 7.26384i 0.358901 + 0.260757i
777777 14.9524 46.0188i 0.536415 1.65092i
778778 8.83792 + 27.2003i 0.316855 + 0.975178i
779779 −6.59914 + 4.79455i −0.236439 + 0.171783i
780780 0 0
781781 10.5589 + 34.5467i 0.377826 + 1.23618i
782782 1.83617 0.0656612
783783 −42.3717 + 30.7848i −1.51424 + 1.10016i
784784 2.24787 + 6.91822i 0.0802810 + 0.247079i
785785 0 0
786786 −7.35328 5.34247i −0.262283 0.190560i
787787 22.1990 + 16.1285i 0.791310 + 0.574921i 0.908352 0.418206i 0.137341π-0.137341\pi
−0.117042 + 0.993127i 0.537341π0.537341\pi
788788 1.13849 3.50390i 0.0405569 0.124821i
789789 −13.8535 42.6366i −0.493197 1.51790i
790790 0 0
791791 31.6658 1.12590
792792 0.370287 + 1.21151i 0.0131576 + 0.0430493i
793793 −7.61507 −0.270419
794794 −19.8249 + 14.4036i −0.703560 + 0.511166i
795795 0 0
796796 −1.30882 + 4.02814i −0.0463900 + 0.142774i
797797 −43.5855 31.6667i −1.54388 1.12169i −0.947845 0.318732i 0.896743π-0.896743\pi
−0.596032 0.802960i 0.703257π-0.703257\pi
798798 6.41557 + 4.66118i 0.227109 + 0.165004i
799799 5.45029 16.7743i 0.192817 0.593431i
800800 0 0
801801 1.88197 1.36733i 0.0664960 0.0483122i
802802 30.7122 1.08449
803803 9.22729 6.45988i 0.325624 0.227964i
804804 14.9061 0.525697
805805 0 0
806806 5.12254 + 15.7656i 0.180434 + 0.555318i
807807 6.37959 19.6344i 0.224572 0.691162i
808808 −7.29264 5.29841i −0.256554 0.186397i
809809 −26.1612 19.0073i −0.919781 0.668260i 0.0236888 0.999719i 0.492459π-0.492459\pi
−0.943469 + 0.331460i 0.892459π0.892459\pi
810810 0 0
811811 14.1920 + 43.6785i 0.498349 + 1.53376i 0.811671 + 0.584114i 0.198558π0.198558\pi
−0.313322 + 0.949647i 0.601442π0.601442\pi
812812 29.2547 21.2548i 1.02664 0.745896i
813813 9.22691 0.323602
814814 −8.54884 + 24.8210i −0.299637 + 0.869975i
815815 0 0
816816 4.31611 3.13584i 0.151094 0.109776i
817817 1.45033 + 4.46367i 0.0507408 + 0.156164i
818818 −6.75453 + 20.7883i −0.236167 + 0.726846i
819819 −3.61803 2.62866i −0.126424 0.0918527i
820820 0 0
821821 8.78690 27.0433i 0.306665 0.943818i −0.672386 0.740201i 0.734730π-0.734730\pi
0.979051 0.203617i 0.0652697π-0.0652697\pi
822822 −3.84398 11.8306i −0.134074 0.412638i
823823 −8.38417 + 6.09146i −0.292254 + 0.212335i −0.724245 0.689543i 0.757811π-0.757811\pi
0.431991 + 0.901878i 0.357811π0.357811\pi
824824 −11.4340 −0.398321
825825 0 0
826826 −20.0136 −0.696361
827827 15.8634 11.5254i 0.551625 0.400779i −0.276760 0.960939i 0.589261π-0.589261\pi
0.828384 + 0.560161i 0.189261π0.189261\pi
828828 −0.0657312 0.202300i −0.00228432 0.00703040i
829829 15.4118 47.4327i 0.535275 1.64741i −0.207780 0.978176i 0.566624π-0.566624\pi
0.743054 0.669231i 0.233376π-0.233376\pi
830830 0 0
831831 41.5317 + 30.1746i 1.44072 + 1.04674i
832832 −0.957626 + 2.94727i −0.0331997 + 0.102178i
833833 −7.41171 22.8109i −0.256800 0.790350i
834834 1.25904 0.914744i 0.0435969 0.0316750i
835835 0 0
836836 −3.43582 2.58953i −0.118830 0.0895606i
837837 −29.2716 −1.01177
838838 3.37978 2.45556i 0.116753 0.0848258i
839839 −3.25249 10.0101i −0.112289 0.345589i 0.879083 0.476668i 0.158156π-0.158156\pi
−0.991372 + 0.131080i 0.958156π0.958156\pi
840840 0 0
841841 −50.6490 36.7986i −1.74652 1.26892i
842842 10.2697 + 7.46135i 0.353916 + 0.257135i
843843 −0.969111 + 2.98262i −0.0333779 + 0.102727i
844844 −4.22439 13.0013i −0.145409 0.447524i
845845 0 0
846846 −2.04322 −0.0702472
847847 41.5338 + 1.45728i 1.42712 + 0.0500726i
848848 11.0142 0.378229
849849 −6.43497 + 4.67528i −0.220848 + 0.160455i
850850 0 0
851851 1.36211 4.19214i 0.0466925 0.143705i
852852 −14.2577 10.3588i −0.488460 0.354887i
853853 −12.7180 9.24016i −0.435456 0.316377i 0.348371 0.937357i 0.386735π-0.386735\pi
−0.783827 + 0.620980i 0.786735π0.786735\pi
854854 −2.86893 + 8.82965i −0.0981726 + 0.302144i
855855 0 0
856856 12.4222 9.02522i 0.424581 0.308476i
857857 37.8967 1.29453 0.647263 0.762267i 0.275914π-0.275914\pi
0.647263 + 0.762267i 0.275914π0.275914\pi
858858 −13.2806 10.0094i −0.453394 0.341716i
859859 20.5913 0.702567 0.351283 0.936269i 0.385745π-0.385745\pi
0.351283 + 0.936269i 0.385745π0.385745\pi
860860 0 0
861861 11.8785 + 36.5584i 0.404820 + 1.24591i
862862 0.225825 0.695018i 0.00769163 0.0236724i
863863 −6.95203 5.05094i −0.236650 0.171936i 0.463140 0.886285i 0.346723π-0.346723\pi
−0.699789 + 0.714349i 0.746723π0.746723\pi
864864 −4.42705 3.21644i −0.150611 0.109426i
865865 0 0
866866 1.74465 + 5.36947i 0.0592855 + 0.182462i
867867 8.02212 5.82841i 0.272445 0.197943i
868868 20.2100 0.685972
869869 54.2629 + 0.951654i 1.84074 + 0.0322826i
870870 0 0
871871 23.0966 16.7806i 0.782597 0.568590i
872872 −0.750578 2.31004i −0.0254178 0.0782279i
873873 −1.45866 + 4.48930i −0.0493682 + 0.151940i
874874 0.584434 + 0.424616i 0.0197688 + 0.0143628i
875875 0 0
876876 −1.69808 + 5.22616i −0.0573728 + 0.176575i
877877 13.9519 + 42.9395i 0.471122 + 1.44996i 0.851117 + 0.524976i 0.175926π0.175926\pi
−0.379995 + 0.924989i 0.624074π0.624074\pi
878878 11.0895 8.05702i 0.374254 0.271911i
879879 −0.305364 −0.0102997
880880 0 0
881881 −38.4847 −1.29658 −0.648291 0.761393i 0.724516π-0.724516\pi
−0.648291 + 0.761393i 0.724516π0.724516\pi
882882 −2.24787 + 1.63317i −0.0756896 + 0.0549917i
883883 12.1504 + 37.3951i 0.408894 + 1.25845i 0.917600 + 0.397505i 0.130124π0.130124\pi
−0.508706 + 0.860940i 0.669876π0.669876\pi
884884 3.15750 9.71779i 0.106198 0.326845i
885885 0 0
886886 −11.3614 8.25454i −0.381693 0.277317i
887887 2.42395 7.46016i 0.0813883 0.250488i −0.902080 0.431570i 0.857960π-0.857960\pi
0.983468 + 0.181082i 0.0579600π0.0579600\pi
888888 −3.95763 12.1803i −0.132809 0.408745i
889889 −21.2537 + 15.4417i −0.712825 + 0.517897i
890890 0 0
891891 20.9430 14.6619i 0.701617 0.491191i
892892 −23.9720 −0.802643
893893 5.61384 4.07869i 0.187860 0.136488i
894894 4.39616 + 13.5300i 0.147030 + 0.452511i
895895 0 0
896896 3.05657 + 2.22073i 0.102113 + 0.0741893i
897897 2.25904 + 1.64129i 0.0754271 + 0.0548010i
898898 −2.98369 + 9.18287i −0.0995672 + 0.306436i
899899 −15.8210 48.6919i −0.527658 1.62397i
900900 0 0
901901 −36.3162 −1.20987
902902 −6.09580 19.9444i −0.202968 0.664075i
903903 22.1175 0.736026
904904 6.78064 4.92643i 0.225521 0.163851i
905905 0 0
906906 4.46892 13.7539i 0.148470 0.456943i
907907 −35.8908 26.0762i −1.19173 0.865845i −0.198287 0.980144i 0.563538π-0.563538\pi
−0.993446 + 0.114299i 0.963538π0.963538\pi
908908 16.7503 + 12.1698i 0.555877 + 0.403868i
909909 1.06398 3.27460i 0.0352900 0.108612i
910910 0 0
911911 −11.2063 + 8.14186i −0.371282 + 0.269752i −0.757742 0.652554i 0.773698π-0.773698\pi
0.386460 + 0.922306i 0.373698π0.373698\pi
912912 2.09894 0.0695030
913913 0.178451 + 0.583860i 0.00590587 + 0.0193229i
914914 −1.02878 −0.0340290
915915 0 0
916916 −5.04955 15.5409i −0.166842 0.513486i
917917 −6.55835 + 20.1845i −0.216576 + 0.666552i
918918 14.5970 + 10.6053i 0.481771 + 0.350027i
919919 12.3286 + 8.95726i 0.406684 + 0.295473i 0.772258 0.635309i 0.219127π-0.219127\pi
−0.365574 + 0.930782i 0.619127π0.619127\pi
920920 0 0
921921 −6.19098 19.0539i −0.204000 0.627847i
922922 −6.51972 + 4.73685i −0.214716 + 0.156000i
923923 −33.7534 −1.11101
924924 −16.6093 + 11.6279i −0.546405 + 0.382529i
925925 0 0
926926 6.04038 4.38860i 0.198499 0.144218i
927927 −1.34960 4.15363i −0.0443265 0.136423i
928928 2.95763 9.10264i 0.0970888 0.298809i
929929 −30.6793 22.2898i −1.00656 0.731306i −0.0430721 0.999072i 0.513715π-0.513715\pi
−0.963484 + 0.267766i 0.913715π0.913715\pi
930930 0 0
931931 2.91597 8.97444i 0.0955672 0.294126i
932932 −0.148415 0.456775i −0.00486150 0.0149621i
933933 27.6440 20.0846i 0.905025 0.657540i
934934 11.1894 0.366127
935935 0 0
936936 −1.18369 −0.0386902
937937 −4.43144 + 3.21963i −0.144769 + 0.105181i −0.657812 0.753182i 0.728518π-0.728518\pi
0.513043 + 0.858363i 0.328518π0.328518\pi
938938 −10.7556 33.1024i −0.351183 1.08083i
939939 8.28961 25.5128i 0.270521 0.832579i
940940 0 0
941941 −37.5713 27.2971i −1.22479 0.889861i −0.228301 0.973591i 0.573317π-0.573317\pi
−0.996489 + 0.0837293i 0.973317π0.973317\pi
942942 −8.82050 + 27.1467i −0.287387 + 0.884488i
943943 1.08209 + 3.33033i 0.0352377 + 0.108450i
944944 −4.28554 + 3.11363i −0.139482 + 0.101340i
945945 0 0
946946 −11.9978 0.210416i −0.390083 0.00684120i
947947 22.7220 0.738366 0.369183 0.929357i 0.379638π-0.379638\pi
0.369183 + 0.929357i 0.379638π0.379638\pi
948948 −21.4200 + 15.5625i −0.695688 + 0.505447i
949949 3.25225 + 10.0094i 0.105573 + 0.324919i
950950 0 0
951951 25.7052 + 18.6759i 0.833548 + 0.605608i
952952 −10.0782 7.32222i −0.326636 0.237315i
953953 11.1302 34.2554i 0.360544 1.10964i −0.592181 0.805805i 0.701733π-0.701733\pi
0.952725 0.303835i 0.0982671π-0.0982671\pi
954954 1.30005 + 4.00114i 0.0420907 + 0.129542i
955955 0 0
956956 1.12859 0.0365012
957957 41.0172 + 30.9140i 1.32590 + 0.999309i
958958 −26.7696 −0.864886
959959 −23.4988 + 17.0729i −0.758815 + 0.551311i
960960 0 0
961961 −0.737310 + 2.26921i −0.0237842 + 0.0732002i
962962 −19.8443 14.4177i −0.639806 0.464846i
963963 4.74484 + 3.44733i 0.152900 + 0.111089i
964964 −3.93132 + 12.0994i −0.126619 + 0.389694i
965965 0 0
966966 2.75414 2.00100i 0.0886131 0.0643812i
967967 23.8349 0.766479 0.383240 0.923649i 0.374808π-0.374808\pi
0.383240 + 0.923649i 0.374808π0.374808\pi
968968 9.12043 6.14961i 0.293142 0.197656i
969969 −6.92067 −0.222324
970970 0 0
971971 −10.9297 33.6381i −0.350750 1.07950i −0.958433 0.285319i 0.907901π-0.907901\pi
0.607682 0.794180i 0.292099π-0.292099\pi
972972 1.21885 3.75123i 0.0390945 0.120321i
973973 −2.93987 2.13594i −0.0942478 0.0684750i
974974 −14.8683 10.8025i −0.476411 0.346133i
975975 0 0
976976 0.759351 + 2.33704i 0.0243062 + 0.0748069i
977977 −9.12632 + 6.63066i −0.291977 + 0.212134i −0.724124 0.689669i 0.757756π-0.757756\pi
0.432148 + 0.901803i 0.357756π0.357756\pi
978978 0.282006 0.00901757
979979 −16.1305 12.1573i −0.515532 0.388548i
980980 0 0
981981 0.750578 0.545327i 0.0239641 0.0174109i
982982 8.02923 + 24.7114i 0.256223 + 0.788573i
983983 2.64643 8.14486i 0.0844079 0.259781i −0.899941 0.436012i 0.856391π-0.856391\pi
0.984349 + 0.176231i 0.0563906π0.0563906\pi
984984 8.23117 + 5.98030i 0.262400 + 0.190645i
985985 0 0
986986 −9.75194 + 30.0134i −0.310565 + 0.955821i
987987 −10.1050 31.1000i −0.321645 0.989923i
988988 3.25225 2.36290i 0.103468 0.0751739i
989989 2.01482 0.0640677
990990 0 0
991991 −15.9978 −0.508185 −0.254093 0.967180i 0.581777π-0.581777\pi
−0.254093 + 0.967180i 0.581777π0.581777\pi
992992 4.32760 3.14419i 0.137401 0.0998280i
993993 −11.7413 36.1360i −0.372599 1.14674i
994994 −12.7163 + 39.1369i −0.403338 + 1.24135i
995995 0 0
996996 −0.240963 0.175070i −0.00763520 0.00554730i
997997 8.77729 27.0137i 0.277979 0.855533i −0.710436 0.703762i 0.751502π-0.751502\pi
0.988416 0.151771i 0.0484977π-0.0484977\pi
998998 −5.24736 16.1497i −0.166102 0.511210i
999999 35.0412 25.4589i 1.10866 0.805485i
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 550.2.h.n.201.2 8
5.2 odd 4 110.2.j.b.69.3 yes 16
5.3 odd 4 110.2.j.b.69.1 yes 16
5.4 even 2 550.2.h.j.201.1 8
11.2 odd 10 6050.2.a.dl.1.3 4
11.4 even 5 inner 550.2.h.n.301.2 8
11.9 even 5 6050.2.a.dd.1.4 4
15.2 even 4 990.2.ba.h.289.2 16
15.8 even 4 990.2.ba.h.289.4 16
20.3 even 4 880.2.cd.b.289.3 16
20.7 even 4 880.2.cd.b.289.1 16
55.2 even 20 1210.2.b.l.969.6 8
55.4 even 10 550.2.h.j.301.1 8
55.9 even 10 6050.2.a.di.1.1 4
55.13 even 20 1210.2.b.l.969.4 8
55.24 odd 10 6050.2.a.da.1.2 4
55.37 odd 20 110.2.j.b.59.1 16
55.42 odd 20 1210.2.b.k.969.2 8
55.48 odd 20 110.2.j.b.59.3 yes 16
55.53 odd 20 1210.2.b.k.969.8 8
165.92 even 20 990.2.ba.h.829.4 16
165.158 even 20 990.2.ba.h.829.2 16
220.103 even 20 880.2.cd.b.609.1 16
220.147 even 20 880.2.cd.b.609.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
110.2.j.b.59.1 16 55.37 odd 20
110.2.j.b.59.3 yes 16 55.48 odd 20
110.2.j.b.69.1 yes 16 5.3 odd 4
110.2.j.b.69.3 yes 16 5.2 odd 4
550.2.h.j.201.1 8 5.4 even 2
550.2.h.j.301.1 8 55.4 even 10
550.2.h.n.201.2 8 1.1 even 1 trivial
550.2.h.n.301.2 8 11.4 even 5 inner
880.2.cd.b.289.1 16 20.7 even 4
880.2.cd.b.289.3 16 20.3 even 4
880.2.cd.b.609.1 16 220.103 even 20
880.2.cd.b.609.3 16 220.147 even 20
990.2.ba.h.289.2 16 15.2 even 4
990.2.ba.h.289.4 16 15.8 even 4
990.2.ba.h.829.2 16 165.158 even 20
990.2.ba.h.829.4 16 165.92 even 20
1210.2.b.k.969.2 8 55.42 odd 20
1210.2.b.k.969.8 8 55.53 odd 20
1210.2.b.l.969.4 8 55.13 even 20
1210.2.b.l.969.6 8 55.2 even 20
6050.2.a.da.1.2 4 55.24 odd 10
6050.2.a.dd.1.4 4 11.9 even 5
6050.2.a.di.1.1 4 55.9 even 10
6050.2.a.dl.1.3 4 11.2 odd 10