Properties

Label 1470.2.n.a.79.1
Level 14701470
Weight 22
Character 1470.79
Analytic conductor 11.73811.738
Analytic rank 00
Dimension 44
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1470,2,Mod(79,1470)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1470, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1470.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1470=23572 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1470.n (of order 66, degree 22, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 11.738009097111.7380090971
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q(ζ12)\Q(\zeta_{12})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4x2+1 x^{4} - x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 30)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 79.1
Root 0.866025+0.500000i-0.866025 + 0.500000i of defining polynomial
Character χ\chi == 1470.79
Dual form 1470.2.n.a.949.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.8660250.500000i)q2+(0.8660250.500000i)q3+(0.500000+0.866025i)q4+(0.133975+2.23205i)q51.00000q61.00000iq8+(0.5000000.866025i)q9+(1.232051.86603i)q10+(1.000001.73205i)q11+(0.866025+0.500000i)q126.00000iq13+(1.00000+2.00000i)q15+(0.500000+0.866025i)q16+(1.732051.00000i)q17+(0.866025+0.500000i)q18+(2.00000+1.00000i)q20+2.00000iq22+(3.46410+2.00000i)q23+(0.5000000.866025i)q24+(4.964100.598076i)q25+(3.00000+5.19615i)q261.00000iq27+(0.1339752.23205i)q30+(4.000006.92820i)q31+(0.8660250.500000i)q32+(1.732051.00000i)q332.00000q34+1.00000q36+(1.73205+1.00000i)q37+(3.000005.19615i)q39+(2.23205+0.133975i)q402.00000q414.00000iq43+(1.000001.73205i)q44+(1.86603+1.23205i)q45+(2.000003.46410i)q46+(6.92820+4.00000i)q47+1.00000iq48+(4.00000+3.00000i)q50+(1.000001.73205i)q51+(5.196153.00000i)q52+(5.196153.00000i)q53+(0.500000+0.866025i)q54+(4.000002.00000i)q55+(5.000008.66025i)q59+(1.23205+1.86603i)q60+(1.000001.73205i)q61+8.00000iq621.00000q64+(13.3923+0.803848i)q65+(1.00000+1.73205i)q66+(6.928204.00000i)q67+(1.73205+1.00000i)q68+4.00000q69+12.0000q71+(0.8660250.500000i)q72+(3.464102.00000i)q73+(1.000001.73205i)q74+(4.59808+1.96410i)q75+6.00000iq78+(1.866031.23205i)q80+(0.5000000.866025i)q81+(1.73205+1.00000i)q82+4.00000iq83+(2.00000+4.00000i)q85+(2.00000+3.46410i)q86+(1.73205+1.00000i)q88+(5.000008.66025i)q89+(1.000002.00000i)q90+4.00000iq92+(6.928204.00000i)q93+(4.000006.92820i)q94+(0.5000000.866025i)q968.00000iq972.00000q99+O(q100)q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.133975 + 2.23205i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.23205 - 1.86603i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(0.866025 + 0.500000i) q^{12} -6.00000i q^{13} +(1.00000 + 2.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.73205 - 1.00000i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-2.00000 + 1.00000i) q^{20} +2.00000i q^{22} +(3.46410 + 2.00000i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-4.96410 - 0.598076i) q^{25} +(-3.00000 + 5.19615i) q^{26} -1.00000i q^{27} +(0.133975 - 2.23205i) q^{30} +(-4.00000 - 6.92820i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.73205 - 1.00000i) q^{33} -2.00000 q^{34} +1.00000 q^{36} +(1.73205 + 1.00000i) q^{37} +(-3.00000 - 5.19615i) q^{39} +(2.23205 + 0.133975i) q^{40} -2.00000 q^{41} -4.00000i q^{43} +(1.00000 - 1.73205i) q^{44} +(1.86603 + 1.23205i) q^{45} +(-2.00000 - 3.46410i) q^{46} +(6.92820 + 4.00000i) q^{47} +1.00000i q^{48} +(4.00000 + 3.00000i) q^{50} +(1.00000 - 1.73205i) q^{51} +(5.19615 - 3.00000i) q^{52} +(5.19615 - 3.00000i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(4.00000 - 2.00000i) q^{55} +(-5.00000 - 8.66025i) q^{59} +(-1.23205 + 1.86603i) q^{60} +(1.00000 - 1.73205i) q^{61} +8.00000i q^{62} -1.00000 q^{64} +(13.3923 + 0.803848i) q^{65} +(1.00000 + 1.73205i) q^{66} +(6.92820 - 4.00000i) q^{67} +(1.73205 + 1.00000i) q^{68} +4.00000 q^{69} +12.0000 q^{71} +(-0.866025 - 0.500000i) q^{72} +(3.46410 - 2.00000i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-4.59808 + 1.96410i) q^{75} +6.00000i q^{78} +(-1.86603 - 1.23205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.73205 + 1.00000i) q^{82} +4.00000i q^{83} +(2.00000 + 4.00000i) q^{85} +(-2.00000 + 3.46410i) q^{86} +(-1.73205 + 1.00000i) q^{88} +(5.00000 - 8.66025i) q^{89} +(-1.00000 - 2.00000i) q^{90} +4.00000i q^{92} +(-6.92820 - 4.00000i) q^{93} +(-4.00000 - 6.92820i) q^{94} +(0.500000 - 0.866025i) q^{96} -8.00000i q^{97} -2.00000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+2q44q54q6+2q92q104q11+4q152q168q202q246q2512q26+4q3016q318q34+4q3612q39+2q408q41+8q99+O(q100) 4 q + 2 q^{4} - 4 q^{5} - 4 q^{6} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 4 q^{15} - 2 q^{16} - 8 q^{20} - 2 q^{24} - 6 q^{25} - 12 q^{26} + 4 q^{30} - 16 q^{31} - 8 q^{34} + 4 q^{36} - 12 q^{39} + 2 q^{40} - 8 q^{41}+ \cdots - 8 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1470Z)×\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times.

nn 491491 10811081 11771177
χ(n)\chi(n) 11 e(13)e\left(\frac{1}{3}\right) 1-1

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 −0.866025 0.500000i −0.612372 0.353553i
33 0.866025 0.500000i 0.500000 0.288675i
44 0.500000 + 0.866025i 0.250000 + 0.433013i
55 −0.133975 + 2.23205i −0.0599153 + 0.998203i
66 −1.00000 −0.408248
77 0 0
88 1.00000i 0.353553i
99 0.500000 0.866025i 0.166667 0.288675i
1010 1.23205 1.86603i 0.389609 0.590089i
1111 −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i 0.264158π-0.264158\pi
−0.976478 + 0.215615i 0.930824π0.930824\pi
1212 0.866025 + 0.500000i 0.250000 + 0.144338i
1313 6.00000i 1.66410i −0.554700 0.832050i 0.687167π-0.687167\pi
0.554700 0.832050i 0.312833π-0.312833\pi
1414 0 0
1515 1.00000 + 2.00000i 0.258199 + 0.516398i
1616 −0.500000 + 0.866025i −0.125000 + 0.216506i
1717 1.73205 1.00000i 0.420084 0.242536i −0.275029 0.961436i 0.588688π-0.588688\pi
0.695113 + 0.718900i 0.255354π0.255354\pi
1818 −0.866025 + 0.500000i −0.204124 + 0.117851i
1919 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
2020 −2.00000 + 1.00000i −0.447214 + 0.223607i
2121 0 0
2222 2.00000i 0.426401i
2323 3.46410 + 2.00000i 0.722315 + 0.417029i 0.815604 0.578610i 0.196405π-0.196405\pi
−0.0932891 + 0.995639i 0.529738π0.529738\pi
2424 −0.500000 0.866025i −0.102062 0.176777i
2525 −4.96410 0.598076i −0.992820 0.119615i
2626 −3.00000 + 5.19615i −0.588348 + 1.01905i
2727 1.00000i 0.192450i
2828 0 0
2929 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
3030 0.133975 2.23205i 0.0244603 0.407515i
3131 −4.00000 6.92820i −0.718421 1.24434i −0.961625 0.274367i 0.911532π-0.911532\pi
0.243204 0.969975i 0.421802π-0.421802\pi
3232 0.866025 0.500000i 0.153093 0.0883883i
3333 −1.73205 1.00000i −0.301511 0.174078i
3434 −2.00000 −0.342997
3535 0 0
3636 1.00000 0.166667
3737 1.73205 + 1.00000i 0.284747 + 0.164399i 0.635571 0.772043i 0.280765π-0.280765\pi
−0.350823 + 0.936442i 0.614098π0.614098\pi
3838 0 0
3939 −3.00000 5.19615i −0.480384 0.832050i
4040 2.23205 + 0.133975i 0.352918 + 0.0211832i
4141 −2.00000 −0.312348 −0.156174 0.987730i 0.549916π-0.549916\pi
−0.156174 + 0.987730i 0.549916π0.549916\pi
4242 0 0
4343 4.00000i 0.609994i −0.952353 0.304997i 0.901344π-0.901344\pi
0.952353 0.304997i 0.0986555π-0.0986555\pi
4444 1.00000 1.73205i 0.150756 0.261116i
4545 1.86603 + 1.23205i 0.278171 + 0.183663i
4646 −2.00000 3.46410i −0.294884 0.510754i
4747 6.92820 + 4.00000i 1.01058 + 0.583460i 0.911362 0.411606i 0.135032π-0.135032\pi
0.0992202 + 0.995066i 0.468365π0.468365\pi
4848 1.00000i 0.144338i
4949 0 0
5050 4.00000 + 3.00000i 0.565685 + 0.424264i
5151 1.00000 1.73205i 0.140028 0.242536i
5252 5.19615 3.00000i 0.720577 0.416025i
5353 5.19615 3.00000i 0.713746 0.412082i −0.0987002 0.995117i 0.531468π-0.531468\pi
0.812447 + 0.583036i 0.198135π0.198135\pi
5454 −0.500000 + 0.866025i −0.0680414 + 0.117851i
5555 4.00000 2.00000i 0.539360 0.269680i
5656 0 0
5757 0 0
5858 0 0
5959 −5.00000 8.66025i −0.650945 1.12747i −0.982894 0.184172i 0.941040π-0.941040\pi
0.331949 0.943297i 0.392294π-0.392294\pi
6060 −1.23205 + 1.86603i −0.159057 + 0.240903i
6161 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i 0.792466π-0.792466\pi
0.922916 + 0.385002i 0.125799π0.125799\pi
6262 8.00000i 1.01600i
6363 0 0
6464 −1.00000 −0.125000
6565 13.3923 + 0.803848i 1.66111 + 0.0997050i
6666 1.00000 + 1.73205i 0.123091 + 0.213201i
6767 6.92820 4.00000i 0.846415 0.488678i −0.0130248 0.999915i 0.504146π-0.504146\pi
0.859440 + 0.511237i 0.170813π0.170813\pi
6868 1.73205 + 1.00000i 0.210042 + 0.121268i
6969 4.00000 0.481543
7070 0 0
7171 12.0000 1.42414 0.712069 0.702109i 0.247758π-0.247758\pi
0.712069 + 0.702109i 0.247758π0.247758\pi
7272 −0.866025 0.500000i −0.102062 0.0589256i
7373 3.46410 2.00000i 0.405442 0.234082i −0.283387 0.959006i 0.591458π-0.591458\pi
0.688830 + 0.724923i 0.258125π0.258125\pi
7474 −1.00000 1.73205i −0.116248 0.201347i
7575 −4.59808 + 1.96410i −0.530940 + 0.226795i
7676 0 0
7777 0 0
7878 6.00000i 0.679366i
7979 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
8080 −1.86603 1.23205i −0.208628 0.137747i
8181 −0.500000 0.866025i −0.0555556 0.0962250i
8282 1.73205 + 1.00000i 0.191273 + 0.110432i
8383 4.00000i 0.439057i 0.975606 + 0.219529i 0.0704519π0.0704519\pi
−0.975606 + 0.219529i 0.929548π0.929548\pi
8484 0 0
8585 2.00000 + 4.00000i 0.216930 + 0.433861i
8686 −2.00000 + 3.46410i −0.215666 + 0.373544i
8787 0 0
8888 −1.73205 + 1.00000i −0.184637 + 0.106600i
8989 5.00000 8.66025i 0.529999 0.917985i −0.469389 0.882992i 0.655526π-0.655526\pi
0.999388 0.0349934i 0.0111410π-0.0111410\pi
9090 −1.00000 2.00000i −0.105409 0.210819i
9191 0 0
9292 4.00000i 0.417029i
9393 −6.92820 4.00000i −0.718421 0.414781i
9494 −4.00000 6.92820i −0.412568 0.714590i
9595 0 0
9696 0.500000 0.866025i 0.0510310 0.0883883i
9797 8.00000i 0.812277i −0.913812 0.406138i 0.866875π-0.866875\pi
0.913812 0.406138i 0.133125π-0.133125\pi
9898 0 0
9999 −2.00000 −0.201008
100100 −1.96410 4.59808i −0.196410 0.459808i
101101 −4.00000 6.92820i −0.398015 0.689382i 0.595466 0.803380i 0.296967π-0.296967\pi
−0.993481 + 0.113998i 0.963634π0.963634\pi
102102 −1.73205 + 1.00000i −0.171499 + 0.0990148i
103103 −12.1244 7.00000i −1.19465 0.689730i −0.235291 0.971925i 0.575604π-0.575604\pi
−0.959357 + 0.282194i 0.908938π0.908938\pi
104104 −6.00000 −0.588348
105105 0 0
106106 −6.00000 −0.582772
107107 10.3923 + 6.00000i 1.00466 + 0.580042i 0.909624 0.415432i 0.136370π-0.136370\pi
0.0950377 + 0.995474i 0.469703π0.469703\pi
108108 0.866025 0.500000i 0.0833333 0.0481125i
109109 5.00000 + 8.66025i 0.478913 + 0.829502i 0.999708 0.0241802i 0.00769755π-0.00769755\pi
−0.520794 + 0.853682i 0.674364π0.674364\pi
110110 −4.46410 0.267949i −0.425635 0.0255480i
111111 2.00000 0.189832
112112 0 0
113113 6.00000i 0.564433i 0.959351 + 0.282216i 0.0910696π0.0910696\pi
−0.959351 + 0.282216i 0.908930π0.908930\pi
114114 0 0
115115 −4.92820 + 7.46410i −0.459557 + 0.696031i
116116 0 0
117117 −5.19615 3.00000i −0.480384 0.277350i
118118 10.0000i 0.920575i
119119 0 0
120120 2.00000 1.00000i 0.182574 0.0912871i
121121 3.50000 6.06218i 0.318182 0.551107i
122122 −1.73205 + 1.00000i −0.156813 + 0.0905357i
123123 −1.73205 + 1.00000i −0.156174 + 0.0901670i
124124 4.00000 6.92820i 0.359211 0.622171i
125125 2.00000 11.0000i 0.178885 0.983870i
126126 0 0
127127 2.00000i 0.177471i −0.996055 0.0887357i 0.971717π-0.971717\pi
0.996055 0.0887357i 0.0282826π-0.0282826\pi
128128 0.866025 + 0.500000i 0.0765466 + 0.0441942i
129129 −2.00000 3.46410i −0.176090 0.304997i
130130 −11.1962 7.39230i −0.981968 0.648348i
131131 −9.00000 + 15.5885i −0.786334 + 1.36197i 0.141865 + 0.989886i 0.454690π0.454690\pi
−0.928199 + 0.372084i 0.878643π0.878643\pi
132132 2.00000i 0.174078i
133133 0 0
134134 −8.00000 −0.691095
135135 2.23205 + 0.133975i 0.192104 + 0.0115307i
136136 −1.00000 1.73205i −0.0857493 0.148522i
137137 15.5885 9.00000i 1.33181 0.768922i 0.346235 0.938148i 0.387460π-0.387460\pi
0.985577 + 0.169226i 0.0541268π0.0541268\pi
138138 −3.46410 2.00000i −0.294884 0.170251i
139139 −20.0000 −1.69638 −0.848189 0.529694i 0.822307π-0.822307\pi
−0.848189 + 0.529694i 0.822307π0.822307\pi
140140 0 0
141141 8.00000 0.673722
142142 −10.3923 6.00000i −0.872103 0.503509i
143143 −10.3923 + 6.00000i −0.869048 + 0.501745i
144144 0.500000 + 0.866025i 0.0416667 + 0.0721688i
145145 0 0
146146 −4.00000 −0.331042
147147 0 0
148148 2.00000i 0.164399i
149149 −10.0000 + 17.3205i −0.819232 + 1.41895i 0.0870170 + 0.996207i 0.472267π0.472267\pi
−0.906249 + 0.422744i 0.861067π0.861067\pi
150150 4.96410 + 0.598076i 0.405317 + 0.0488327i
151151 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i 0.0611289π-0.0611289\pi
−0.656101 + 0.754673i 0.727796π0.727796\pi
152152 0 0
153153 2.00000i 0.161690i
154154 0 0
155155 16.0000 8.00000i 1.28515 0.642575i
156156 3.00000 5.19615i 0.240192 0.416025i
157157 19.0526 11.0000i 1.52056 0.877896i 0.520854 0.853646i 0.325614π-0.325614\pi
0.999706 0.0242497i 0.00771967π-0.00771967\pi
158158 0 0
159159 3.00000 5.19615i 0.237915 0.412082i
160160 1.00000 + 2.00000i 0.0790569 + 0.158114i
161161 0 0
162162 1.00000i 0.0785674i
163163 −13.8564 8.00000i −1.08532 0.626608i −0.152992 0.988227i 0.548891π-0.548891\pi
−0.932326 + 0.361619i 0.882224π0.882224\pi
164164 −1.00000 1.73205i −0.0780869 0.135250i
165165 2.46410 3.73205i 0.191830 0.290540i
166166 2.00000 3.46410i 0.155230 0.268866i
167167 12.0000i 0.928588i 0.885681 + 0.464294i 0.153692π0.153692\pi
−0.885681 + 0.464294i 0.846308π0.846308\pi
168168 0 0
169169 −23.0000 −1.76923
170170 0.267949 4.46410i 0.0205508 0.342381i
171171 0 0
172172 3.46410 2.00000i 0.264135 0.152499i
173173 −12.1244 7.00000i −0.921798 0.532200i −0.0375896 0.999293i 0.511968π-0.511968\pi
−0.884208 + 0.467093i 0.845301π0.845301\pi
174174 0 0
175175 0 0
176176 2.00000 0.150756
177177 −8.66025 5.00000i −0.650945 0.375823i
178178 −8.66025 + 5.00000i −0.649113 + 0.374766i
179179 5.00000 + 8.66025i 0.373718 + 0.647298i 0.990134 0.140122i 0.0447496π-0.0447496\pi
−0.616417 + 0.787420i 0.711416π0.711416\pi
180180 −0.133975 + 2.23205i −0.00998588 + 0.166367i
181181 −2.00000 −0.148659 −0.0743294 0.997234i 0.523682π-0.523682\pi
−0.0743294 + 0.997234i 0.523682π0.523682\pi
182182 0 0
183183 2.00000i 0.147844i
184184 2.00000 3.46410i 0.147442 0.255377i
185185 −2.46410 + 3.73205i −0.181164 + 0.274386i
186186 4.00000 + 6.92820i 0.293294 + 0.508001i
187187 −3.46410 2.00000i −0.253320 0.146254i
188188 8.00000i 0.583460i
189189 0 0
190190 0 0
191191 −6.00000 + 10.3923i −0.434145 + 0.751961i −0.997225 0.0744412i 0.976283π-0.976283\pi
0.563081 + 0.826402i 0.309616π0.309616\pi
192192 −0.866025 + 0.500000i −0.0625000 + 0.0360844i
193193 −3.46410 + 2.00000i −0.249351 + 0.143963i −0.619467 0.785022i 0.712651π-0.712651\pi
0.370116 + 0.928986i 0.379318π0.379318\pi
194194 −4.00000 + 6.92820i −0.287183 + 0.497416i
195195 12.0000 6.00000i 0.859338 0.429669i
196196 0 0
197197 22.0000i 1.56744i −0.621117 0.783718i 0.713321π-0.713321\pi
0.621117 0.783718i 0.286679π-0.286679\pi
198198 1.73205 + 1.00000i 0.123091 + 0.0710669i
199199 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
200200 −0.598076 + 4.96410i −0.0422904 + 0.351015i
201201 4.00000 6.92820i 0.282138 0.488678i
202202 8.00000i 0.562878i
203203 0 0
204204 2.00000 0.140028
205205 0.267949 4.46410i 0.0187144 0.311786i
206206 7.00000 + 12.1244i 0.487713 + 0.844744i
207207 3.46410 2.00000i 0.240772 0.139010i
208208 5.19615 + 3.00000i 0.360288 + 0.208013i
209209 0 0
210210 0 0
211211 12.0000 0.826114 0.413057 0.910705i 0.364461π-0.364461\pi
0.413057 + 0.910705i 0.364461π0.364461\pi
212212 5.19615 + 3.00000i 0.356873 + 0.206041i
213213 10.3923 6.00000i 0.712069 0.411113i
214214 −6.00000 10.3923i −0.410152 0.710403i
215215 8.92820 + 0.535898i 0.608898 + 0.0365480i
216216 −1.00000 −0.0680414
217217 0 0
218218 10.0000i 0.677285i
219219 2.00000 3.46410i 0.135147 0.234082i
220220 3.73205 + 2.46410i 0.251615 + 0.166130i
221221 −6.00000 10.3923i −0.403604 0.699062i
222222 −1.73205 1.00000i −0.116248 0.0671156i
223223 26.0000i 1.74109i −0.492090 0.870544i 0.663767π-0.663767\pi
0.492090 0.870544i 0.336233π-0.336233\pi
224224 0 0
225225 −3.00000 + 4.00000i −0.200000 + 0.266667i
226226 3.00000 5.19615i 0.199557 0.345643i
227227 −24.2487 + 14.0000i −1.60944 + 0.929213i −0.619949 + 0.784642i 0.712847π0.712847\pi
−0.989494 + 0.144571i 0.953820π0.953820\pi
228228 0 0
229229 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i 0.726147π-0.726147\pi
0.982592 + 0.185776i 0.0594799π0.0594799\pi
230230 8.00000 4.00000i 0.527504 0.263752i
231231 0 0
232232 0 0
233233 12.1244 + 7.00000i 0.794293 + 0.458585i 0.841472 0.540301i 0.181690π-0.181690\pi
−0.0471787 + 0.998886i 0.515023π0.515023\pi
234234 3.00000 + 5.19615i 0.196116 + 0.339683i
235235 −9.85641 + 14.9282i −0.642961 + 0.973809i
236236 5.00000 8.66025i 0.325472 0.563735i
237237 0 0
238238 0 0
239239 −20.0000 −1.29369 −0.646846 0.762620i 0.723912π-0.723912\pi
−0.646846 + 0.762620i 0.723912π0.723912\pi
240240 −2.23205 0.133975i −0.144078 0.00864802i
241241 11.0000 + 19.0526i 0.708572 + 1.22728i 0.965387 + 0.260822i 0.0839937π0.0839937\pi
−0.256814 + 0.966461i 0.582673π0.582673\pi
242242 −6.06218 + 3.50000i −0.389692 + 0.224989i
243243 −0.866025 0.500000i −0.0555556 0.0320750i
244244 2.00000 0.128037
245245 0 0
246246 2.00000 0.127515
247247 0 0
248248 −6.92820 + 4.00000i −0.439941 + 0.254000i
249249 2.00000 + 3.46410i 0.126745 + 0.219529i
250250 −7.23205 + 8.52628i −0.457395 + 0.539249i
251251 18.0000 1.13615 0.568075 0.822977i 0.307688π-0.307688\pi
0.568075 + 0.822977i 0.307688π0.307688\pi
252252 0 0
253253 8.00000i 0.502956i
254254 −1.00000 + 1.73205i −0.0627456 + 0.108679i
255255 3.73205 + 2.46410i 0.233710 + 0.154308i
256256 −0.500000 0.866025i −0.0312500 0.0541266i
257257 15.5885 + 9.00000i 0.972381 + 0.561405i 0.899961 0.435970i 0.143595π-0.143595\pi
0.0724199 + 0.997374i 0.476928π0.476928\pi
258258 4.00000i 0.249029i
259259 0 0
260260 6.00000 + 12.0000i 0.372104 + 0.744208i
261261 0 0
262262 15.5885 9.00000i 0.963058 0.556022i
263263 −3.46410 + 2.00000i −0.213606 + 0.123325i −0.602986 0.797752i 0.706023π-0.706023\pi
0.389380 + 0.921077i 0.372689π0.372689\pi
264264 −1.00000 + 1.73205i −0.0615457 + 0.106600i
265265 6.00000 + 12.0000i 0.368577 + 0.737154i
266266 0 0
267267 10.0000i 0.611990i
268268 6.92820 + 4.00000i 0.423207 + 0.244339i
269269 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
270270 −1.86603 1.23205i −0.113563 0.0749802i
271271 −4.00000 + 6.92820i −0.242983 + 0.420858i −0.961563 0.274586i 0.911459π-0.911459\pi
0.718580 + 0.695444i 0.244792π0.244792\pi
272272 2.00000i 0.121268i
273273 0 0
274274 −18.0000 −1.08742
275275 3.92820 + 9.19615i 0.236880 + 0.554549i
276276 2.00000 + 3.46410i 0.120386 + 0.208514i
277277 −1.73205 + 1.00000i −0.104069 + 0.0600842i −0.551131 0.834419i 0.685804π-0.685804\pi
0.447062 + 0.894503i 0.352470π0.352470\pi
278278 17.3205 + 10.0000i 1.03882 + 0.599760i
279279 −8.00000 −0.478947
280280 0 0
281281 −18.0000 −1.07379 −0.536895 0.843649i 0.680403π-0.680403\pi
−0.536895 + 0.843649i 0.680403π0.680403\pi
282282 −6.92820 4.00000i −0.412568 0.238197i
283283 −13.8564 + 8.00000i −0.823678 + 0.475551i −0.851683 0.524057i 0.824418π-0.824418\pi
0.0280052 + 0.999608i 0.491084π0.491084\pi
284284 6.00000 + 10.3923i 0.356034 + 0.616670i
285285 0 0
286286 12.0000 0.709575
287287 0 0
288288 1.00000i 0.0589256i
289289 −6.50000 + 11.2583i −0.382353 + 0.662255i
290290 0 0
291291 −4.00000 6.92820i −0.234484 0.406138i
292292 3.46410 + 2.00000i 0.202721 + 0.117041i
293293 6.00000i 0.350524i −0.984522 0.175262i 0.943923π-0.943923\pi
0.984522 0.175262i 0.0560772π-0.0560772\pi
294294 0 0
295295 20.0000 10.0000i 1.16445 0.582223i
296296 1.00000 1.73205i 0.0581238 0.100673i
297297 −1.73205 + 1.00000i −0.100504 + 0.0580259i
298298 17.3205 10.0000i 1.00335 0.579284i
299299 12.0000 20.7846i 0.693978 1.20201i
300300 −4.00000 3.00000i −0.230940 0.173205i
301301 0 0
302302 8.00000i 0.460348i
303303 −6.92820 4.00000i −0.398015 0.229794i
304304 0 0
305305 3.73205 + 2.46410i 0.213697 + 0.141094i
306306 −1.00000 + 1.73205i −0.0571662 + 0.0990148i
307307 12.0000i 0.684876i 0.939540 + 0.342438i 0.111253π0.111253\pi
−0.939540 + 0.342438i 0.888747π0.888747\pi
308308 0 0
309309 −14.0000 −0.796432
310310 −17.8564 1.07180i −1.01418 0.0608740i
311311 6.00000 + 10.3923i 0.340229 + 0.589294i 0.984475 0.175525i 0.0561621π-0.0561621\pi
−0.644246 + 0.764818i 0.722829π0.722829\pi
312312 −5.19615 + 3.00000i −0.294174 + 0.169842i
313313 −3.46410 2.00000i −0.195803 0.113047i 0.398894 0.916997i 0.369394π-0.369394\pi
−0.594696 + 0.803951i 0.702728π0.702728\pi
314314 −22.0000 −1.24153
315315 0 0
316316 0 0
317317 1.73205 + 1.00000i 0.0972817 + 0.0561656i 0.547852 0.836576i 0.315446π-0.315446\pi
−0.450570 + 0.892741i 0.648779π0.648779\pi
318318 −5.19615 + 3.00000i −0.291386 + 0.168232i
319319 0 0
320320 0.133975 2.23205i 0.00748941 0.124775i
321321 12.0000 0.669775
322322 0 0
323323 0 0
324324 0.500000 0.866025i 0.0277778 0.0481125i
325325 −3.58846 + 29.7846i −0.199052 + 1.65215i
326326 8.00000 + 13.8564i 0.443079 + 0.767435i
327327 8.66025 + 5.00000i 0.478913 + 0.276501i
328328 2.00000i 0.110432i
329329 0 0
330330 −4.00000 + 2.00000i −0.220193 + 0.110096i
331331 4.00000 6.92820i 0.219860 0.380808i −0.734905 0.678170i 0.762773π-0.762773\pi
0.954765 + 0.297361i 0.0961066π0.0961066\pi
332332 −3.46410 + 2.00000i −0.190117 + 0.109764i
333333 1.73205 1.00000i 0.0949158 0.0547997i
334334 6.00000 10.3923i 0.328305 0.568642i
335335 8.00000 + 16.0000i 0.437087 + 0.874173i
336336 0 0
337337 28.0000i 1.52526i 0.646837 + 0.762629i 0.276092π0.276092\pi
−0.646837 + 0.762629i 0.723908π0.723908\pi
338338 19.9186 + 11.5000i 1.08343 + 0.625518i
339339 3.00000 + 5.19615i 0.162938 + 0.282216i
340340 −2.46410 + 3.73205i −0.133635 + 0.202399i
341341 −8.00000 + 13.8564i −0.433224 + 0.750366i
342342 0 0
343343 0 0
344344 −4.00000 −0.215666
345345 −0.535898 + 8.92820i −0.0288518 + 0.480678i
346346 7.00000 + 12.1244i 0.376322 + 0.651809i
347347 −10.3923 + 6.00000i −0.557888 + 0.322097i −0.752297 0.658824i 0.771054π-0.771054\pi
0.194409 + 0.980921i 0.437721π0.437721\pi
348348 0 0
349349 10.0000 0.535288 0.267644 0.963518i 0.413755π-0.413755\pi
0.267644 + 0.963518i 0.413755π0.413755\pi
350350 0 0
351351 −6.00000 −0.320256
352352 −1.73205 1.00000i −0.0923186 0.0533002i
353353 12.1244 7.00000i 0.645314 0.372572i −0.141344 0.989960i 0.545142π-0.545142\pi
0.786659 + 0.617388i 0.211809π0.211809\pi
354354 5.00000 + 8.66025i 0.265747 + 0.460287i
355355 −1.60770 + 26.7846i −0.0853276 + 1.42158i
356356 10.0000 0.529999
357357 0 0
358358 10.0000i 0.528516i
359359 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
360360 1.23205 1.86603i 0.0649348 0.0983482i
361361 9.50000 + 16.4545i 0.500000 + 0.866025i
362362 1.73205 + 1.00000i 0.0910346 + 0.0525588i
363363 7.00000i 0.367405i
364364 0 0
365365 4.00000 + 8.00000i 0.209370 + 0.418739i
366366 −1.00000 + 1.73205i −0.0522708 + 0.0905357i
367367 1.73205 1.00000i 0.0904123 0.0521996i −0.454112 0.890945i 0.650043π-0.650043\pi
0.544524 + 0.838745i 0.316710π0.316710\pi
368368 −3.46410 + 2.00000i −0.180579 + 0.104257i
369369 −1.00000 + 1.73205i −0.0520579 + 0.0901670i
370370 4.00000 2.00000i 0.207950 0.103975i
371371 0 0
372372 8.00000i 0.414781i
373373 −5.19615 3.00000i −0.269047 0.155334i 0.359408 0.933181i 0.382979π-0.382979\pi
−0.628454 + 0.777847i 0.716312π0.716312\pi
374374 2.00000 + 3.46410i 0.103418 + 0.179124i
375375 −3.76795 10.5263i −0.194576 0.543575i
376376 4.00000 6.92820i 0.206284 0.357295i
377377 0 0
378378 0 0
379379 −20.0000 −1.02733 −0.513665 0.857991i 0.671713π-0.671713\pi
−0.513665 + 0.857991i 0.671713π0.671713\pi
380380 0 0
381381 −1.00000 1.73205i −0.0512316 0.0887357i
382382 10.3923 6.00000i 0.531717 0.306987i
383383 13.8564 + 8.00000i 0.708029 + 0.408781i 0.810331 0.585973i 0.199287π-0.199287\pi
−0.102302 + 0.994753i 0.532621π0.532621\pi
384384 1.00000 0.0510310
385385 0 0
386386 4.00000 0.203595
387387 −3.46410 2.00000i −0.176090 0.101666i
388388 6.92820 4.00000i 0.351726 0.203069i
389389 10.0000 + 17.3205i 0.507020 + 0.878185i 0.999967 + 0.00812520i 0.00258636π0.00258636\pi
−0.492947 + 0.870059i 0.664080π0.664080\pi
390390 −13.3923 0.803848i −0.678146 0.0407044i
391391 8.00000 0.404577
392392 0 0
393393 18.0000i 0.907980i
394394 −11.0000 + 19.0526i −0.554172 + 0.959854i
395395 0 0
396396 −1.00000 1.73205i −0.0502519 0.0870388i
397397 −1.73205 1.00000i −0.0869291 0.0501886i 0.455905 0.890028i 0.349316π-0.349316\pi
−0.542834 + 0.839840i 0.682649π0.682649\pi
398398 0 0
399399 0 0
400400 3.00000 4.00000i 0.150000 0.200000i
401401 −11.0000 + 19.0526i −0.549314 + 0.951439i 0.449008 + 0.893528i 0.351777π0.351777\pi
−0.998322 + 0.0579116i 0.981556π0.981556\pi
402402 −6.92820 + 4.00000i −0.345547 + 0.199502i
403403 −41.5692 + 24.0000i −2.07071 + 1.19553i
404404 4.00000 6.92820i 0.199007 0.344691i
405405 2.00000 1.00000i 0.0993808 0.0496904i
406406 0 0
407407 4.00000i 0.198273i
408408 −1.73205 1.00000i −0.0857493 0.0495074i
409409 5.00000 + 8.66025i 0.247234 + 0.428222i 0.962757 0.270367i 0.0871450π-0.0871450\pi
−0.715523 + 0.698589i 0.753812π0.753812\pi
410410 −2.46410 + 3.73205i −0.121693 + 0.184313i
411411 9.00000 15.5885i 0.443937 0.768922i
412412 14.0000i 0.689730i
413413 0 0
414414 −4.00000 −0.196589
415415 −8.92820 0.535898i −0.438268 0.0263062i
416416 −3.00000 5.19615i −0.147087 0.254762i
417417 −17.3205 + 10.0000i −0.848189 + 0.489702i
418418 0 0
419419 −10.0000 −0.488532 −0.244266 0.969708i 0.578547π-0.578547\pi
−0.244266 + 0.969708i 0.578547π0.578547\pi
420420 0 0
421421 22.0000 1.07221 0.536107 0.844150i 0.319894π-0.319894\pi
0.536107 + 0.844150i 0.319894π0.319894\pi
422422 −10.3923 6.00000i −0.505889 0.292075i
423423 6.92820 4.00000i 0.336861 0.194487i
424424 −3.00000 5.19615i −0.145693 0.252347i
425425 −9.19615 + 3.92820i −0.446079 + 0.190546i
426426 −12.0000 −0.581402
427427 0 0
428428 12.0000i 0.580042i
429429 −6.00000 + 10.3923i −0.289683 + 0.501745i
430430 −7.46410 4.92820i −0.359951 0.237659i
431431 −16.0000 27.7128i −0.770693 1.33488i −0.937184 0.348836i 0.886577π-0.886577\pi
0.166491 0.986043i 0.446756π-0.446756\pi
432432 0.866025 + 0.500000i 0.0416667 + 0.0240563i
433433 4.00000i 0.192228i 0.995370 + 0.0961139i 0.0306413π0.0306413\pi
−0.995370 + 0.0961139i 0.969359π0.969359\pi
434434 0 0
435435 0 0
436436 −5.00000 + 8.66025i −0.239457 + 0.414751i
437437 0 0
438438 −3.46410 + 2.00000i −0.165521 + 0.0955637i
439439 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
440440 −2.00000 4.00000i −0.0953463 0.190693i
441441 0 0
442442 12.0000i 0.570782i
443443 −31.1769 18.0000i −1.48126 0.855206i −0.481486 0.876454i 0.659903π-0.659903\pi
−0.999774 + 0.0212481i 0.993236π0.993236\pi
444444 1.00000 + 1.73205i 0.0474579 + 0.0821995i
445445 18.6603 + 12.3205i 0.884581 + 0.584048i
446446 −13.0000 + 22.5167i −0.615568 + 1.06619i
447447 20.0000i 0.945968i
448448 0 0
449449 −30.0000 −1.41579 −0.707894 0.706319i 0.750354π-0.750354\pi
−0.707894 + 0.706319i 0.750354π0.750354\pi
450450 4.59808 1.96410i 0.216755 0.0925886i
451451 2.00000 + 3.46410i 0.0941763 + 0.163118i
452452 −5.19615 + 3.00000i −0.244406 + 0.141108i
453453 6.92820 + 4.00000i 0.325515 + 0.187936i
454454 28.0000 1.31411
455455 0 0
456456 0 0
457457 27.7128 + 16.0000i 1.29635 + 0.748448i 0.979772 0.200118i 0.0641325π-0.0641325\pi
0.316579 + 0.948566i 0.397466π0.397466\pi
458458 −8.66025 + 5.00000i −0.404667 + 0.233635i
459459 −1.00000 1.73205i −0.0466760 0.0808452i
460460 −8.92820 0.535898i −0.416280 0.0249864i
461461 −12.0000 −0.558896 −0.279448 0.960161i 0.590151π-0.590151\pi
−0.279448 + 0.960161i 0.590151π0.590151\pi
462462 0 0
463463 6.00000i 0.278844i 0.990233 + 0.139422i 0.0445244π0.0445244\pi
−0.990233 + 0.139422i 0.955476π0.955476\pi
464464 0 0
465465 9.85641 14.9282i 0.457080 0.692279i
466466 −7.00000 12.1244i −0.324269 0.561650i
467467 −10.3923 6.00000i −0.480899 0.277647i 0.239892 0.970799i 0.422888π-0.422888\pi
−0.720791 + 0.693153i 0.756221π0.756221\pi
468468 6.00000i 0.277350i
469469 0 0
470470 16.0000 8.00000i 0.738025 0.369012i
471471 11.0000 19.0526i 0.506853 0.877896i
472472 −8.66025 + 5.00000i −0.398621 + 0.230144i
473473 −6.92820 + 4.00000i −0.318559 + 0.183920i
474474 0 0
475475 0 0
476476 0 0
477477 6.00000i 0.274721i
478478 17.3205 + 10.0000i 0.792222 + 0.457389i
479479 −10.0000 17.3205i −0.456912 0.791394i 0.541884 0.840453i 0.317711π-0.317711\pi
−0.998796 + 0.0490589i 0.984378π0.984378\pi
480480 1.86603 + 1.23205i 0.0851720 + 0.0562352i
481481 6.00000 10.3923i 0.273576 0.473848i
482482 22.0000i 1.00207i
483483 0 0
484484 7.00000 0.318182
485485 17.8564 + 1.07180i 0.810818 + 0.0486678i
486486 0.500000 + 0.866025i 0.0226805 + 0.0392837i
487487 15.5885 9.00000i 0.706380 0.407829i −0.103339 0.994646i 0.532953π-0.532953\pi
0.809719 + 0.586817i 0.199619π0.199619\pi
488488 −1.73205 1.00000i −0.0784063 0.0452679i
489489 −16.0000 −0.723545
490490 0 0
491491 −18.0000 −0.812329 −0.406164 0.913800i 0.633134π-0.633134\pi
−0.406164 + 0.913800i 0.633134π0.633134\pi
492492 −1.73205 1.00000i −0.0780869 0.0450835i
493493 0 0
494494 0 0
495495 0.267949 4.46410i 0.0120434 0.200646i
496496 8.00000 0.359211
497497 0 0
498498 4.00000i 0.179244i
499499 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
500500 10.5263 3.76795i 0.470750 0.168508i
501501 6.00000 + 10.3923i 0.268060 + 0.464294i
502502 −15.5885 9.00000i −0.695747 0.401690i
503503 24.0000i 1.07011i 0.844818 + 0.535054i 0.179709π0.179709\pi
−0.844818 + 0.535054i 0.820291π0.820291\pi
504504 0 0
505505 16.0000 8.00000i 0.711991 0.355995i
506506 −4.00000 + 6.92820i −0.177822 + 0.307996i
507507 −19.9186 + 11.5000i −0.884615 + 0.510733i
508508 1.73205 1.00000i 0.0768473 0.0443678i
509509 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
510510 −2.00000 4.00000i −0.0885615 0.177123i
511511 0 0
512512 1.00000i 0.0441942i
513513 0 0
514514 −9.00000 15.5885i −0.396973 0.687577i
515515 17.2487 26.1244i 0.760069 1.15118i
516516 2.00000 3.46410i 0.0880451 0.152499i
517517 16.0000i 0.703679i
518518 0 0
519519 −14.0000 −0.614532
520520 0.803848 13.3923i 0.0352510 0.587291i
521521 11.0000 + 19.0526i 0.481919 + 0.834708i 0.999785 0.0207541i 0.00660670π-0.00660670\pi
−0.517866 + 0.855462i 0.673273π0.673273\pi
522522 0 0
523523 13.8564 + 8.00000i 0.605898 + 0.349816i 0.771358 0.636401i 0.219578π-0.219578\pi
−0.165460 + 0.986216i 0.552911π0.552911\pi
524524 −18.0000 −0.786334
525525 0 0
526526 4.00000 0.174408
527527 −13.8564 8.00000i −0.603595 0.348485i
528528 1.73205 1.00000i 0.0753778 0.0435194i
529529 −3.50000 6.06218i −0.152174 0.263573i
530530 0.803848 13.3923i 0.0349169 0.581725i
531531 −10.0000 −0.433963
532532 0 0
533533 12.0000i 0.519778i
534534 −5.00000 + 8.66025i −0.216371 + 0.374766i
535535 −14.7846 + 22.3923i −0.639194 + 0.968104i
536536 −4.00000 6.92820i −0.172774 0.299253i
537537 8.66025 + 5.00000i 0.373718 + 0.215766i
538538 0 0
539539 0 0
540540 1.00000 + 2.00000i 0.0430331 + 0.0860663i
541541 19.0000 32.9090i 0.816874 1.41487i −0.0911008 0.995842i 0.529039π-0.529039\pi
0.907975 0.419025i 0.137628π-0.137628\pi
542542 6.92820 4.00000i 0.297592 0.171815i
543543 −1.73205 + 1.00000i −0.0743294 + 0.0429141i
544544 1.00000 1.73205i 0.0428746 0.0742611i
545545 −20.0000 + 10.0000i −0.856706 + 0.428353i
546546 0 0
547547 28.0000i 1.19719i 0.801050 + 0.598597i 0.204275π0.204275\pi
−0.801050 + 0.598597i 0.795725π0.795725\pi
548548 15.5885 + 9.00000i 0.665906 + 0.384461i
549549 −1.00000 1.73205i −0.0426790 0.0739221i
550550 1.19615 9.92820i 0.0510041 0.423340i
551551 0 0
552552 4.00000i 0.170251i
553553 0 0
554554 2.00000 0.0849719
555555 −0.267949 + 4.46410i −0.0113738 + 0.189491i
556556 −10.0000 17.3205i −0.424094 0.734553i
557557 15.5885 9.00000i 0.660504 0.381342i −0.131965 0.991254i 0.542129π-0.542129\pi
0.792469 + 0.609912i 0.208795π0.208795\pi
558558 6.92820 + 4.00000i 0.293294 + 0.169334i
559559 −24.0000 −1.01509
560560 0 0
561561 −4.00000 −0.168880
562562 15.5885 + 9.00000i 0.657559 + 0.379642i
563563 38.1051 22.0000i 1.60594 0.927189i 0.615673 0.788002i 0.288884π-0.288884\pi
0.990266 0.139188i 0.0444492π-0.0444492\pi
564564 4.00000 + 6.92820i 0.168430 + 0.291730i
565565 −13.3923 0.803848i −0.563418 0.0338181i
566566 16.0000 0.672530
567567 0 0
568568 12.0000i 0.503509i
569569 −5.00000 + 8.66025i −0.209611 + 0.363057i −0.951592 0.307364i 0.900553π-0.900553\pi
0.741981 + 0.670421i 0.233886π0.233886\pi
570570 0 0
571571 4.00000 + 6.92820i 0.167395 + 0.289936i 0.937503 0.347977i 0.113131π-0.113131\pi
−0.770108 + 0.637913i 0.779798π0.779798\pi
572572 −10.3923 6.00000i −0.434524 0.250873i
573573 12.0000i 0.501307i
574574 0 0
575575 −16.0000 12.0000i −0.667246 0.500435i
576576 −0.500000 + 0.866025i −0.0208333 + 0.0360844i
577577 27.7128 16.0000i 1.15370 0.666089i 0.203913 0.978989i 0.434634π-0.434634\pi
0.949786 + 0.312900i 0.101301π0.101301\pi
578578 11.2583 6.50000i 0.468285 0.270364i
579579 −2.00000 + 3.46410i −0.0831172 + 0.143963i
580580 0 0
581581 0 0
582582 8.00000i 0.331611i
583583 −10.3923 6.00000i −0.430405 0.248495i
584584 −2.00000 3.46410i −0.0827606 0.143346i
585585 7.39230 11.1962i 0.305634 0.462904i
586586 −3.00000 + 5.19615i −0.123929 + 0.214651i
587587 12.0000i 0.495293i 0.968850 + 0.247647i 0.0796572π0.0796572\pi
−0.968850 + 0.247647i 0.920343π0.920343\pi
588588 0 0
589589 0 0
590590 −22.3205 1.33975i −0.918921 0.0551565i
591591 −11.0000 19.0526i −0.452480 0.783718i
592592 −1.73205 + 1.00000i −0.0711868 + 0.0410997i
593593 5.19615 + 3.00000i 0.213380 + 0.123195i 0.602881 0.797831i 0.294019π-0.294019\pi
−0.389501 + 0.921026i 0.627353π0.627353\pi
594594 2.00000 0.0820610
595595 0 0
596596 −20.0000 −0.819232
597597 0 0
598598 −20.7846 + 12.0000i −0.849946 + 0.490716i
599599 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
600600 1.96410 + 4.59808i 0.0801841 + 0.187716i
601601 −2.00000 −0.0815817 −0.0407909 0.999168i 0.512988π-0.512988\pi
−0.0407909 + 0.999168i 0.512988π0.512988\pi
602602 0 0
603603 8.00000i 0.325785i
604604 −4.00000 + 6.92820i −0.162758 + 0.281905i
605605 13.0622 + 8.62436i 0.531053 + 0.350630i
606606 4.00000 + 6.92820i 0.162489 + 0.281439i
607607 −19.0526 11.0000i −0.773320 0.446476i 0.0607380 0.998154i 0.480655π-0.480655\pi
−0.834058 + 0.551678i 0.813988π0.813988\pi
608608 0 0
609609 0 0
610610 −2.00000 4.00000i −0.0809776 0.161955i
611611 24.0000 41.5692i 0.970936 1.68171i
612612 1.73205 1.00000i 0.0700140 0.0404226i
613613 22.5167 13.0000i 0.909439 0.525065i 0.0291886 0.999574i 0.490708π-0.490708\pi
0.880251 + 0.474509i 0.157374π0.157374\pi
614614 6.00000 10.3923i 0.242140 0.419399i
615615 −2.00000 4.00000i −0.0806478 0.161296i
616616 0 0
617617 2.00000i 0.0805170i −0.999189 0.0402585i 0.987182π-0.987182\pi
0.999189 0.0402585i 0.0128181π-0.0128181\pi
618618 12.1244 + 7.00000i 0.487713 + 0.281581i
619619 −10.0000 17.3205i −0.401934 0.696170i 0.592025 0.805919i 0.298329π-0.298329\pi
−0.993959 + 0.109749i 0.964995π0.964995\pi
620620 14.9282 + 9.85641i 0.599531 + 0.395843i
621621 2.00000 3.46410i 0.0802572 0.139010i
622622 12.0000i 0.481156i
623623 0 0
624624 6.00000 0.240192
625625 24.2846 + 5.93782i 0.971384 + 0.237513i
626626 2.00000 + 3.46410i 0.0799361 + 0.138453i
627627 0 0
628628 19.0526 + 11.0000i 0.760280 + 0.438948i
629629 4.00000 0.159490
630630 0 0
631631 32.0000 1.27390 0.636950 0.770905i 0.280196π-0.280196\pi
0.636950 + 0.770905i 0.280196π0.280196\pi
632632 0 0
633633 10.3923 6.00000i 0.413057 0.238479i
634634 −1.00000 1.73205i −0.0397151 0.0687885i
635635 4.46410 + 0.267949i 0.177152 + 0.0106332i
636636 6.00000 0.237915
637637 0 0
638638 0 0
639639 6.00000 10.3923i 0.237356 0.411113i
640640 −1.23205 + 1.86603i −0.0487011 + 0.0737611i
641641 −1.00000 1.73205i −0.0394976 0.0684119i 0.845601 0.533816i 0.179242π-0.179242\pi
−0.885098 + 0.465404i 0.845909π0.845909\pi
642642 −10.3923 6.00000i −0.410152 0.236801i
643643 24.0000i 0.946468i 0.880937 + 0.473234i 0.156913π0.156913\pi
−0.880937 + 0.473234i 0.843087π0.843087\pi
644644 0 0
645645 8.00000 4.00000i 0.315000 0.157500i
646646 0 0
647647 −41.5692 + 24.0000i −1.63425 + 0.943537i −0.651494 + 0.758654i 0.725858π0.725858\pi
−0.982760 + 0.184884i 0.940809π0.940809\pi
648648 −0.866025 + 0.500000i −0.0340207 + 0.0196419i
649649 −10.0000 + 17.3205i −0.392534 + 0.679889i
650650 18.0000 24.0000i 0.706018 0.941357i
651651 0 0
652652 16.0000i 0.626608i
653653 −22.5167 13.0000i −0.881145 0.508729i −0.0101092 0.999949i 0.503218π-0.503218\pi
−0.871036 + 0.491220i 0.836551π0.836551\pi
654654 −5.00000 8.66025i −0.195515 0.338643i
655655 −33.5885 22.1769i −1.31241 0.866524i
656656 1.00000 1.73205i 0.0390434 0.0676252i
657657 4.00000i 0.156055i
658658 0 0
659659 50.0000 1.94772 0.973862 0.227142i 0.0729380π-0.0729380\pi
0.973862 + 0.227142i 0.0729380π0.0729380\pi
660660 4.46410 + 0.267949i 0.173765 + 0.0104299i
661661 1.00000 + 1.73205i 0.0388955 + 0.0673690i 0.884818 0.465937i 0.154283π-0.154283\pi
−0.845922 + 0.533306i 0.820949π0.820949\pi
662662 −6.92820 + 4.00000i −0.269272 + 0.155464i
663663 −10.3923 6.00000i −0.403604 0.233021i
664664 4.00000 0.155230
665665 0 0
666666 −2.00000 −0.0774984
667667 0 0
668668 −10.3923 + 6.00000i −0.402090 + 0.232147i
669669 −13.0000 22.5167i −0.502609 0.870544i
670670 1.07180 17.8564i 0.0414071 0.689853i
671671 −4.00000 −0.154418
672672 0 0
673673 36.0000i 1.38770i 0.720121 + 0.693849i 0.244086π0.244086\pi
−0.720121 + 0.693849i 0.755914π0.755914\pi
674674 14.0000 24.2487i 0.539260 0.934025i
675675 −0.598076 + 4.96410i −0.0230200 + 0.191068i
676676 −11.5000 19.9186i −0.442308 0.766099i
677677 −1.73205 1.00000i −0.0665681 0.0384331i 0.466347 0.884602i 0.345570π-0.345570\pi
−0.532915 + 0.846169i 0.678903π0.678903\pi
678678 6.00000i 0.230429i
679679 0 0
680680 4.00000 2.00000i 0.153393 0.0766965i
681681 −14.0000 + 24.2487i −0.536481 + 0.929213i
682682 13.8564 8.00000i 0.530589 0.306336i
683683 −3.46410 + 2.00000i −0.132550 + 0.0765279i −0.564809 0.825222i 0.691050π-0.691050\pi
0.432259 + 0.901750i 0.357717π0.357717\pi
684684 0 0
685685 18.0000 + 36.0000i 0.687745 + 1.37549i
686686 0 0
687687 10.0000i 0.381524i
688688 3.46410 + 2.00000i 0.132068 + 0.0762493i
689689 −18.0000 31.1769i −0.685745 1.18775i
690690 4.92820 7.46410i 0.187613 0.284153i
691691 −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i 0.881959π-0.881959\pi
0.779857 + 0.625958i 0.215292π0.215292\pi
692692 14.0000i 0.532200i
693693 0 0
694694 12.0000 0.455514
695695 2.67949 44.6410i 0.101639 1.69333i
696696 0 0
697697 −3.46410 + 2.00000i −0.131212 + 0.0757554i
698698 −8.66025 5.00000i −0.327795 0.189253i
699699 14.0000 0.529529
700700 0 0
701701 32.0000 1.20862 0.604312 0.796748i 0.293448π-0.293448\pi
0.604312 + 0.796748i 0.293448π0.293448\pi
702702 5.19615 + 3.00000i 0.196116 + 0.113228i
703703 0 0
704704 1.00000 + 1.73205i 0.0376889 + 0.0652791i
705705 −1.07180 + 17.8564i −0.0403662 + 0.672511i
706706 −14.0000 −0.526897
707707 0 0
708708 10.0000i 0.375823i
709709 15.0000 25.9808i 0.563337 0.975728i −0.433865 0.900978i 0.642851π-0.642851\pi
0.997202 0.0747503i 0.0238160π-0.0238160\pi
710710 14.7846 22.3923i 0.554857 0.840368i
711711 0 0
712712 −8.66025 5.00000i −0.324557 0.187383i
713713 32.0000i 1.19841i
714714 0 0
715715 −12.0000 24.0000i −0.448775 0.897549i
716716 −5.00000 + 8.66025i −0.186859 + 0.323649i
717717 −17.3205 + 10.0000i −0.646846 + 0.373457i
718718 0 0
719719 20.0000 34.6410i 0.745874 1.29189i −0.203911 0.978989i 0.565365π-0.565365\pi
0.949785 0.312903i 0.101301π-0.101301\pi
720720 −2.00000 + 1.00000i −0.0745356 + 0.0372678i
721721 0 0
722722 19.0000i 0.707107i
723723 19.0526 + 11.0000i 0.708572 + 0.409094i
724724 −1.00000 1.73205i −0.0371647 0.0643712i
725725 0 0
726726 −3.50000 + 6.06218i −0.129897 + 0.224989i
727727 18.0000i 0.667583i −0.942647 0.333792i 0.891672π-0.891672\pi
0.942647 0.333792i 0.108328π-0.108328\pi
728728 0 0
729729 −1.00000 −0.0370370
730730 0.535898 8.92820i 0.0198345 0.330448i
731731 −4.00000 6.92820i −0.147945 0.256249i
732732 1.73205 1.00000i 0.0640184 0.0369611i
733733 −12.1244 7.00000i −0.447823 0.258551i 0.259087 0.965854i 0.416578π-0.416578\pi
−0.706910 + 0.707303i 0.749912π0.749912\pi
734734 −2.00000 −0.0738213
735735 0 0
736736 4.00000 0.147442
737737 −13.8564 8.00000i −0.510407 0.294684i
738738 1.73205 1.00000i 0.0637577 0.0368105i
739739 20.0000 + 34.6410i 0.735712 + 1.27429i 0.954410 + 0.298498i 0.0964856π0.0964856\pi
−0.218698 + 0.975793i 0.570181π0.570181\pi
740740 −4.46410 0.267949i −0.164104 0.00985001i
741741 0 0
742742 0 0
743743 24.0000i 0.880475i −0.897881 0.440237i 0.854894π-0.854894\pi
0.897881 0.440237i 0.145106π-0.145106\pi
744744 −4.00000 + 6.92820i −0.146647 + 0.254000i
745745 −37.3205 24.6410i −1.36732 0.902777i
746746 3.00000 + 5.19615i 0.109838 + 0.190245i
747747 3.46410 + 2.00000i 0.126745 + 0.0731762i
748748 4.00000i 0.146254i
749749 0 0
750750 −2.00000 + 11.0000i −0.0730297 + 0.401663i
751751 −16.0000 + 27.7128i −0.583848 + 1.01125i 0.411170 + 0.911559i 0.365120π0.365120\pi
−0.995018 + 0.0996961i 0.968213π0.968213\pi
752752 −6.92820 + 4.00000i −0.252646 + 0.145865i
753753 15.5885 9.00000i 0.568075 0.327978i
754754 0 0
755755 −16.0000 + 8.00000i −0.582300 + 0.291150i
756756 0 0
757757 2.00000i 0.0726912i −0.999339 0.0363456i 0.988428π-0.988428\pi
0.999339 0.0363456i 0.0115717π-0.0115717\pi
758758 17.3205 + 10.0000i 0.629109 + 0.363216i
759759 −4.00000 6.92820i −0.145191 0.251478i
760760 0 0
761761 −9.00000 + 15.5885i −0.326250 + 0.565081i −0.981764 0.190101i 0.939118π-0.939118\pi
0.655515 + 0.755182i 0.272452π0.272452\pi
762762 2.00000i 0.0724524i
763763 0 0
764764 −12.0000 −0.434145
765765 4.46410 + 0.267949i 0.161400 + 0.00968772i
766766 −8.00000 13.8564i −0.289052 0.500652i
767767 −51.9615 + 30.0000i −1.87622 + 1.08324i
768768 −0.866025 0.500000i −0.0312500 0.0180422i
769769 −30.0000 −1.08183 −0.540914 0.841078i 0.681921π-0.681921\pi
−0.540914 + 0.841078i 0.681921π0.681921\pi
770770 0 0
771771 18.0000 0.648254
772772 −3.46410 2.00000i −0.124676 0.0719816i
773773 46.7654 27.0000i 1.68203 0.971123i 0.721726 0.692179i 0.243349π-0.243349\pi
0.960307 0.278944i 0.0899843π-0.0899843\pi
774774 2.00000 + 3.46410i 0.0718885 + 0.124515i
775775 15.7128 + 36.7846i 0.564421 + 1.32134i
776776 −8.00000 −0.287183
777777 0 0
778778 20.0000i 0.717035i
779779 0 0
780780 11.1962 + 7.39230i 0.400887 + 0.264687i
781781 −12.0000 20.7846i −0.429394 0.743732i
782782 −6.92820 4.00000i −0.247752 0.143040i
783783 0 0
784784 0 0
785785 22.0000 + 44.0000i 0.785214 + 1.57043i
786786 9.00000 15.5885i 0.321019 0.556022i
787787 27.7128 16.0000i 0.987855 0.570338i 0.0832226 0.996531i 0.473479π-0.473479\pi
0.904632 + 0.426193i 0.140145π0.140145\pi
788788 19.0526 11.0000i 0.678719 0.391859i
789789 −2.00000 + 3.46410i −0.0712019 + 0.123325i
790790 0 0
791791 0 0
792792 2.00000i 0.0710669i
793793 −10.3923 6.00000i −0.369042 0.213066i
794794 1.00000 + 1.73205i 0.0354887 + 0.0614682i
795795 11.1962 + 7.39230i 0.397087 + 0.262178i
796796 0 0
797797 2.00000i 0.0708436i 0.999372 + 0.0354218i 0.0112775π0.0112775\pi
−0.999372 + 0.0354218i 0.988723π0.988723\pi
798798 0 0
799799 16.0000 0.566039
800800 −4.59808 + 1.96410i −0.162567 + 0.0694415i
801801 −5.00000 8.66025i −0.176666 0.305995i
802802 19.0526 11.0000i 0.672769 0.388424i
803803 −6.92820 4.00000i −0.244491 0.141157i
804804 8.00000 0.282138
805805 0 0
806806 48.0000 1.69073
807807 0 0
808808 −6.92820 + 4.00000i −0.243733 + 0.140720i
809809 −15.0000 25.9808i −0.527372 0.913435i −0.999491 0.0319002i 0.989844π-0.989844\pi
0.472119 0.881535i 0.343489π-0.343489\pi
810810 −2.23205 0.133975i −0.0784263 0.00470739i
811811 −52.0000 −1.82597 −0.912983 0.407997i 0.866228π-0.866228\pi
−0.912983 + 0.407997i 0.866228π0.866228\pi
812812 0 0
813813 8.00000i 0.280572i
814814 −2.00000 + 3.46410i −0.0701000 + 0.121417i
815815 19.7128 29.8564i 0.690510 1.04582i
816816 1.00000 + 1.73205i 0.0350070 + 0.0606339i
817817 0 0
818818 10.0000i 0.349642i
819819 0 0
820820 4.00000 2.00000i 0.139686 0.0698430i
821821 4.00000 6.92820i 0.139601 0.241796i −0.787745 0.616002i 0.788751π-0.788751\pi
0.927346 + 0.374206i 0.122085π0.122085\pi
822822 −15.5885 + 9.00000i −0.543710 + 0.313911i
823823 5.19615 3.00000i 0.181126 0.104573i −0.406695 0.913564i 0.633319π-0.633319\pi
0.587822 + 0.808990i 0.299986π0.299986\pi
824824 −7.00000 + 12.1244i −0.243857 + 0.422372i
825825 8.00000 + 6.00000i 0.278524 + 0.208893i
826826 0 0
827827 28.0000i 0.973655i 0.873498 + 0.486828i 0.161846π0.161846\pi
−0.873498 + 0.486828i 0.838154π0.838154\pi
828828 3.46410 + 2.00000i 0.120386 + 0.0695048i
829829 15.0000 + 25.9808i 0.520972 + 0.902349i 0.999703 + 0.0243876i 0.00776357π0.00776357\pi
−0.478731 + 0.877962i 0.658903π0.658903\pi
830830 7.46410 + 4.92820i 0.259083 + 0.171060i
831831 −1.00000 + 1.73205i −0.0346896 + 0.0600842i
832832 6.00000i 0.208013i
833833 0 0
834834 20.0000 0.692543
835835 −26.7846 1.60770i −0.926920 0.0556366i
836836 0 0
837837 −6.92820 + 4.00000i −0.239474 + 0.138260i
838838 8.66025 + 5.00000i 0.299164 + 0.172722i
839839 40.0000 1.38095 0.690477 0.723355i 0.257401π-0.257401\pi
0.690477 + 0.723355i 0.257401π0.257401\pi
840840 0 0
841841 −29.0000 −1.00000
842842 −19.0526 11.0000i −0.656595 0.379085i
843843 −15.5885 + 9.00000i −0.536895 + 0.309976i
844844 6.00000 + 10.3923i 0.206529 + 0.357718i
845845 3.08142 51.3372i 0.106004 1.76605i
846846 −8.00000 −0.275046
847847 0 0
848848 6.00000i 0.206041i
849849 −8.00000 + 13.8564i −0.274559 + 0.475551i
850850 9.92820 + 1.19615i 0.340535 + 0.0410277i
851851 4.00000 + 6.92820i 0.137118 + 0.237496i
852852 10.3923 + 6.00000i 0.356034 + 0.205557i
853853 14.0000i 0.479351i 0.970853 + 0.239675i 0.0770410π0.0770410\pi
−0.970853 + 0.239675i 0.922959π0.922959\pi
854854 0 0
855855 0 0
856856 6.00000 10.3923i 0.205076 0.355202i
857857 36.3731 21.0000i 1.24248 0.717346i 0.272882 0.962048i 0.412023π-0.412023\pi
0.969599 + 0.244701i 0.0786899π0.0786899\pi
858858 10.3923 6.00000i 0.354787 0.204837i
859859 −10.0000 + 17.3205i −0.341196 + 0.590968i −0.984655 0.174512i 0.944165π-0.944165\pi
0.643459 + 0.765480i 0.277499π0.277499\pi
860860 4.00000 + 8.00000i 0.136399 + 0.272798i
861861 0 0
862862 32.0000i 1.08992i
863863 −31.1769 18.0000i −1.06127 0.612727i −0.135490 0.990779i 0.543261π-0.543261\pi
−0.925785 + 0.378052i 0.876594π0.876594\pi
864864 −0.500000 0.866025i −0.0170103 0.0294628i
865865 17.2487 26.1244i 0.586474 0.888255i
866866 2.00000 3.46410i 0.0679628 0.117715i
867867 13.0000i 0.441503i
868868 0 0
869869 0 0
870870 0 0
871871 −24.0000 41.5692i −0.813209 1.40852i
872872 8.66025 5.00000i 0.293273 0.169321i
873873 −6.92820 4.00000i −0.234484 0.135379i
874874 0 0
875875 0 0
876876 4.00000 0.135147
877877 19.0526 + 11.0000i 0.643359 + 0.371444i 0.785907 0.618344i 0.212196π-0.212196\pi
−0.142548 + 0.989788i 0.545530π0.545530\pi
878878 0 0
879879 −3.00000 5.19615i −0.101187 0.175262i
880880 −0.267949 + 4.46410i −0.00903257 + 0.150485i
881881 18.0000 0.606435 0.303218 0.952921i 0.401939π-0.401939\pi
0.303218 + 0.952921i 0.401939π0.401939\pi
882882 0 0
883883 24.0000i 0.807664i −0.914833 0.403832i 0.867678π-0.867678\pi
0.914833 0.403832i 0.132322π-0.132322\pi
884884 6.00000 10.3923i 0.201802 0.349531i
885885 12.3205 18.6603i 0.414149 0.627258i
886886 18.0000 + 31.1769i 0.604722 + 1.04741i
887887 −10.3923 6.00000i −0.348939 0.201460i 0.315279 0.948999i 0.397902π-0.397902\pi
−0.664218 + 0.747539i 0.731235π0.731235\pi
888888 2.00000i 0.0671156i
889889 0 0
890890 −10.0000 20.0000i −0.335201 0.670402i
891891 −1.00000 + 1.73205i −0.0335013 + 0.0580259i
892892 22.5167 13.0000i 0.753914 0.435272i
893893 0 0
894894 10.0000 17.3205i 0.334450 0.579284i
895895 −20.0000 + 10.0000i −0.668526 + 0.334263i
896896 0 0
897897 24.0000i 0.801337i
898898 25.9808 + 15.0000i 0.866989 + 0.500556i
899899 0 0
900900 −4.96410 0.598076i −0.165470 0.0199359i
901901 6.00000 10.3923i 0.199889 0.346218i
902902 4.00000i 0.133185i
903903 0 0
904904 6.00000 0.199557
905905 0.267949 4.46410i 0.00890693 0.148392i
906906 −4.00000 6.92820i −0.132891 0.230174i
907907 −10.3923 + 6.00000i −0.345071 + 0.199227i −0.662512 0.749051i 0.730510π-0.730510\pi
0.317441 + 0.948278i 0.397176π0.397176\pi
908908 −24.2487 14.0000i −0.804722 0.464606i
909909 −8.00000 −0.265343
910910 0 0
911911 −48.0000 −1.59031 −0.795155 0.606406i 0.792611π-0.792611\pi
−0.795155 + 0.606406i 0.792611π0.792611\pi
912912 0 0
913913 6.92820 4.00000i 0.229290 0.132381i
914914 −16.0000 27.7128i −0.529233 0.916658i
915915 4.46410 + 0.267949i 0.147579 + 0.00885813i
916916 10.0000 0.330409
917917 0 0
918918 2.00000i 0.0660098i
919919 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
920920 7.46410 + 4.92820i 0.246084 + 0.162478i
921921 6.00000 + 10.3923i 0.197707 + 0.342438i
922922 10.3923 + 6.00000i 0.342252 + 0.197599i
923923 72.0000i 2.36991i
924924 0 0
925925 −8.00000 6.00000i −0.263038 0.197279i
926926 3.00000 5.19615i 0.0985861 0.170756i
927927 −12.1244 + 7.00000i −0.398216 + 0.229910i
928928 0 0
929929 −15.0000 + 25.9808i −0.492134 + 0.852401i −0.999959 0.00905914i 0.997116π-0.997116\pi
0.507825 + 0.861460i 0.330450π0.330450\pi
930930 −16.0000 + 8.00000i −0.524661 + 0.262330i
931931 0 0
932932 14.0000i 0.458585i
933933 10.3923 + 6.00000i 0.340229 + 0.196431i
934934 6.00000 + 10.3923i 0.196326 + 0.340047i
935935 4.92820 7.46410i 0.161169 0.244102i
936936 −3.00000 + 5.19615i −0.0980581 + 0.169842i
937937 8.00000i 0.261349i −0.991425 0.130674i 0.958286π-0.958286\pi
0.991425 0.130674i 0.0417142π-0.0417142\pi
938938 0 0
939939 −4.00000 −0.130535
940940 −17.8564 1.07180i −0.582412 0.0349582i
941941 −14.0000 24.2487i −0.456387 0.790485i 0.542380 0.840133i 0.317523π-0.317523\pi
−0.998767 + 0.0496480i 0.984190π0.984190\pi
942942 −19.0526 + 11.0000i −0.620766 + 0.358399i
943943 −6.92820 4.00000i −0.225613 0.130258i
944944 10.0000 0.325472
945945 0 0
946946 8.00000 0.260102
947947 10.3923 + 6.00000i 0.337705 + 0.194974i 0.659256 0.751918i 0.270871π-0.270871\pi
−0.321552 + 0.946892i 0.604204π0.604204\pi
948948 0 0
949949 −12.0000 20.7846i −0.389536 0.674697i
950950 0 0
951951 2.00000 0.0648544
952952 0 0
953953 46.0000i 1.49009i 0.667016 + 0.745043i 0.267571π0.267571\pi
−0.667016 + 0.745043i 0.732429π0.732429\pi
954954 −3.00000 + 5.19615i −0.0971286 + 0.168232i
955955 −22.3923 14.7846i −0.724598 0.478419i
956956 −10.0000 17.3205i −0.323423 0.560185i
957957 0 0
958958 20.0000i 0.646171i
959959 0 0
960960 −1.00000 2.00000i −0.0322749 0.0645497i
961961 −16.5000 + 28.5788i −0.532258 + 0.921898i
962962 −10.3923 + 6.00000i −0.335061 + 0.193448i
963963 10.3923 6.00000i 0.334887 0.193347i
964964 −11.0000 + 19.0526i −0.354286 + 0.613642i
965965 −4.00000 8.00000i −0.128765 0.257529i
966966 0 0
967967 38.0000i 1.22200i 0.791632 + 0.610999i 0.209232π0.209232\pi
−0.791632 + 0.610999i 0.790768π0.790768\pi
968968 −6.06218 3.50000i −0.194846 0.112494i
969969 0 0
970970 −14.9282 9.85641i −0.479316 0.316470i
971971 −9.00000 + 15.5885i −0.288824 + 0.500257i −0.973529 0.228562i 0.926597π-0.926597\pi
0.684706 + 0.728820i 0.259931π0.259931\pi
972972 1.00000i 0.0320750i
973973 0 0
974974 −18.0000 −0.576757
975975 11.7846 + 27.5885i 0.377410 + 0.883538i
976976 1.00000 + 1.73205i 0.0320092 + 0.0554416i
977977 −36.3731 + 21.0000i −1.16368 + 0.671850i −0.952183 0.305530i 0.901167π-0.901167\pi
−0.211495 + 0.977379i 0.567833π0.567833\pi
978978 13.8564 + 8.00000i 0.443079 + 0.255812i
979979 −20.0000 −0.639203
980980 0 0
981981 10.0000 0.319275
982982 15.5885 + 9.00000i 0.497448 + 0.287202i
983983 −13.8564 + 8.00000i −0.441951 + 0.255160i −0.704425 0.709779i 0.748795π-0.748795\pi
0.262474 + 0.964939i 0.415462π0.415462\pi
984984 1.00000 + 1.73205i 0.0318788 + 0.0552158i
985985 49.1051 + 2.94744i 1.56462 + 0.0939133i
986986 0 0
987987 0 0
988988 0 0
989989 8.00000 13.8564i 0.254385 0.440608i
990990 −2.46410 + 3.73205i −0.0783143 + 0.118612i
991991 4.00000 + 6.92820i 0.127064 + 0.220082i 0.922538 0.385906i 0.126111π-0.126111\pi
−0.795474 + 0.605988i 0.792778π0.792778\pi
992992 −6.92820 4.00000i −0.219971 0.127000i
993993 8.00000i 0.253872i
994994 0 0
995995 0 0
996996 −2.00000 + 3.46410i −0.0633724 + 0.109764i
997997 −15.5885 + 9.00000i −0.493691 + 0.285033i −0.726105 0.687584i 0.758671π-0.758671\pi
0.232413 + 0.972617i 0.425338π0.425338\pi
998998 0 0
999999 1.00000 1.73205i 0.0316386 0.0547997i
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 1470.2.n.a.79.1 4
5.4 even 2 inner 1470.2.n.a.79.2 4
7.2 even 3 1470.2.g.g.589.2 2
7.3 odd 6 1470.2.n.h.949.2 4
7.4 even 3 inner 1470.2.n.a.949.2 4
7.5 odd 6 30.2.c.a.19.2 yes 2
7.6 odd 2 1470.2.n.h.79.1 4
21.5 even 6 90.2.c.a.19.1 2
28.19 even 6 240.2.f.a.49.2 2
35.2 odd 12 7350.2.a.bg.1.1 1
35.4 even 6 inner 1470.2.n.a.949.1 4
35.9 even 6 1470.2.g.g.589.1 2
35.12 even 12 150.2.a.a.1.1 1
35.19 odd 6 30.2.c.a.19.1 2
35.23 odd 12 7350.2.a.cc.1.1 1
35.24 odd 6 1470.2.n.h.949.1 4
35.33 even 12 150.2.a.c.1.1 1
35.34 odd 2 1470.2.n.h.79.2 4
56.5 odd 6 960.2.f.h.769.2 2
56.19 even 6 960.2.f.i.769.1 2
63.5 even 6 810.2.i.b.379.2 4
63.40 odd 6 810.2.i.e.379.1 4
63.47 even 6 810.2.i.b.109.1 4
63.61 odd 6 810.2.i.e.109.2 4
84.47 odd 6 720.2.f.f.289.1 2
105.47 odd 12 450.2.a.f.1.1 1
105.68 odd 12 450.2.a.b.1.1 1
105.89 even 6 90.2.c.a.19.2 2
112.5 odd 12 3840.2.d.g.2689.1 2
112.19 even 12 3840.2.d.j.2689.2 2
112.61 odd 12 3840.2.d.y.2689.2 2
112.75 even 12 3840.2.d.x.2689.1 2
140.19 even 6 240.2.f.a.49.1 2
140.47 odd 12 1200.2.a.m.1.1 1
140.103 odd 12 1200.2.a.g.1.1 1
168.5 even 6 2880.2.f.e.1729.2 2
168.131 odd 6 2880.2.f.c.1729.2 2
280.19 even 6 960.2.f.i.769.2 2
280.117 even 12 4800.2.a.cg.1.1 1
280.173 even 12 4800.2.a.l.1.1 1
280.187 odd 12 4800.2.a.m.1.1 1
280.229 odd 6 960.2.f.h.769.1 2
280.243 odd 12 4800.2.a.cj.1.1 1
315.124 odd 6 810.2.i.e.109.1 4
315.194 even 6 810.2.i.b.379.1 4
315.229 odd 6 810.2.i.e.379.2 4
315.299 even 6 810.2.i.b.109.2 4
420.47 even 12 3600.2.a.o.1.1 1
420.299 odd 6 720.2.f.f.289.2 2
420.383 even 12 3600.2.a.bg.1.1 1
560.19 even 12 3840.2.d.x.2689.2 2
560.229 odd 12 3840.2.d.y.2689.1 2
560.299 even 12 3840.2.d.j.2689.1 2
560.509 odd 12 3840.2.d.g.2689.2 2
840.299 odd 6 2880.2.f.c.1729.1 2
840.509 even 6 2880.2.f.e.1729.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
30.2.c.a.19.1 2 35.19 odd 6
30.2.c.a.19.2 yes 2 7.5 odd 6
90.2.c.a.19.1 2 21.5 even 6
90.2.c.a.19.2 2 105.89 even 6
150.2.a.a.1.1 1 35.12 even 12
150.2.a.c.1.1 1 35.33 even 12
240.2.f.a.49.1 2 140.19 even 6
240.2.f.a.49.2 2 28.19 even 6
450.2.a.b.1.1 1 105.68 odd 12
450.2.a.f.1.1 1 105.47 odd 12
720.2.f.f.289.1 2 84.47 odd 6
720.2.f.f.289.2 2 420.299 odd 6
810.2.i.b.109.1 4 63.47 even 6
810.2.i.b.109.2 4 315.299 even 6
810.2.i.b.379.1 4 315.194 even 6
810.2.i.b.379.2 4 63.5 even 6
810.2.i.e.109.1 4 315.124 odd 6
810.2.i.e.109.2 4 63.61 odd 6
810.2.i.e.379.1 4 63.40 odd 6
810.2.i.e.379.2 4 315.229 odd 6
960.2.f.h.769.1 2 280.229 odd 6
960.2.f.h.769.2 2 56.5 odd 6
960.2.f.i.769.1 2 56.19 even 6
960.2.f.i.769.2 2 280.19 even 6
1200.2.a.g.1.1 1 140.103 odd 12
1200.2.a.m.1.1 1 140.47 odd 12
1470.2.g.g.589.1 2 35.9 even 6
1470.2.g.g.589.2 2 7.2 even 3
1470.2.n.a.79.1 4 1.1 even 1 trivial
1470.2.n.a.79.2 4 5.4 even 2 inner
1470.2.n.a.949.1 4 35.4 even 6 inner
1470.2.n.a.949.2 4 7.4 even 3 inner
1470.2.n.h.79.1 4 7.6 odd 2
1470.2.n.h.79.2 4 35.34 odd 2
1470.2.n.h.949.1 4 35.24 odd 6
1470.2.n.h.949.2 4 7.3 odd 6
2880.2.f.c.1729.1 2 840.299 odd 6
2880.2.f.c.1729.2 2 168.131 odd 6
2880.2.f.e.1729.1 2 840.509 even 6
2880.2.f.e.1729.2 2 168.5 even 6
3600.2.a.o.1.1 1 420.47 even 12
3600.2.a.bg.1.1 1 420.383 even 12
3840.2.d.g.2689.1 2 112.5 odd 12
3840.2.d.g.2689.2 2 560.509 odd 12
3840.2.d.j.2689.1 2 560.299 even 12
3840.2.d.j.2689.2 2 112.19 even 12
3840.2.d.x.2689.1 2 112.75 even 12
3840.2.d.x.2689.2 2 560.19 even 12
3840.2.d.y.2689.1 2 560.229 odd 12
3840.2.d.y.2689.2 2 112.61 odd 12
4800.2.a.l.1.1 1 280.173 even 12
4800.2.a.m.1.1 1 280.187 odd 12
4800.2.a.cg.1.1 1 280.117 even 12
4800.2.a.cj.1.1 1 280.243 odd 12
7350.2.a.bg.1.1 1 35.2 odd 12
7350.2.a.cc.1.1 1 35.23 odd 12