Properties

Label 360.2.m.c.179.2
Level 360360
Weight 22
Character 360.179
Analytic conductor 2.8752.875
Analytic rank 00
Dimension 1616
Inner twists 88

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [360,2,Mod(179,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.179");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 360=23325 360 = 2^{3} \cdot 3^{2} \cdot 5
Weight: k k == 2 2
Character orbit: [χ][\chi] == 360.m (of order 22, degree 11, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 2.874614472772.87461447277
Analytic rank: 00
Dimension: 1616
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x1617x12104x10+713x8+238x6+1004x4152x2+64 x^{16} - 17x^{12} - 104x^{10} + 713x^{8} + 238x^{6} + 1004x^{4} - 152x^{2} + 64 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 28 2^{8}
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 179.2
Root 0.8778592.23141i-0.877859 - 2.23141i of defining polynomial
Character χ\chi == 360.179
Dual form 360.2.m.c.179.4

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.374910.331077i)q2+(1.78078+0.910404i)q4+(1.649011.51022i)q5+0.936426q7+(2.147001.84130i)q8+(2.76724+1.53048i)q102.20837iq11+3.33513q13+(1.287510.310029i)q14+(2.34233+3.24245i)q161.54417q173.12311q19+(4.311431.18811i)q20+(0.731140+3.03632i)q22+3.39228iq23+(0.4384474.98074i)q25+(4.585521.10418i)q26+(1.66757+0.852526i)q28+8.44804q298.30571iq31+(2.147005.23358i)q32+(2.12311+0.511240i)q34+(1.544171.41421i)q35+7.60669q37+(4.29400+1.03399i)q38+(6.32120+0.206134i)q405.83095iq417.77769iq43+(2.010513.93261i)q44+(1.123114.66410i)q46+10.7575iq476.12311q49+(2.25183+6.70293i)q50+(5.93912+3.03632i)q525.08842iq53+(3.335133.64162i)q55+(2.010511.72424i)q56+(11.61532.79695i)q58+10.6937iq59+(2.74983+11.4196i)q62+(1.21922+7.90655i)q64+(5.499665.03680i)q65+12.1453iq67+(2.749831.40582i)q68+(2.59132+1.43318i)q7011.7460q71+5.59390iq73+(10.45852.51840i)q74+(5.561552.84329i)q762.06798iq771.02248iq79+(8.75935+1.80938i)q80+(1.93049+8.01706i)q82+14.0877q83+(2.54635+2.33205i)q85+(2.57501+10.6937i)q86+(4.06627+4.74137i)q88+13.0761iq89+3.12311q91+(3.08835+6.04090i)q92+(3.5615514.7906i)q94+(5.15002+4.71659i)q95+2.18379iq97+(8.41874+2.02722i)q98+O(q100)q+(-1.37491 - 0.331077i) q^{2} +(1.78078 + 0.910404i) q^{4} +(1.64901 - 1.51022i) q^{5} +0.936426 q^{7} +(-2.14700 - 1.84130i) q^{8} +(-2.76724 + 1.53048i) q^{10} -2.20837i q^{11} +3.33513 q^{13} +(-1.28751 - 0.310029i) q^{14} +(2.34233 + 3.24245i) q^{16} -1.54417 q^{17} -3.12311 q^{19} +(4.31143 - 1.18811i) q^{20} +(-0.731140 + 3.03632i) q^{22} +3.39228i q^{23} +(0.438447 - 4.98074i) q^{25} +(-4.58552 - 1.10418i) q^{26} +(1.66757 + 0.852526i) q^{28} +8.44804 q^{29} -8.30571i q^{31} +(-2.14700 - 5.23358i) q^{32} +(2.12311 + 0.511240i) q^{34} +(1.54417 - 1.41421i) q^{35} +7.60669 q^{37} +(4.29400 + 1.03399i) q^{38} +(-6.32120 + 0.206134i) q^{40} -5.83095i q^{41} -7.77769i q^{43} +(2.01051 - 3.93261i) q^{44} +(1.12311 - 4.66410i) q^{46} +10.7575i q^{47} -6.12311 q^{49} +(-2.25183 + 6.70293i) q^{50} +(5.93912 + 3.03632i) q^{52} -5.08842i q^{53} +(-3.33513 - 3.64162i) q^{55} +(-2.01051 - 1.72424i) q^{56} +(-11.6153 - 2.79695i) q^{58} +10.6937i q^{59} +(-2.74983 + 11.4196i) q^{62} +(1.21922 + 7.90655i) q^{64} +(5.49966 - 5.03680i) q^{65} +12.1453i q^{67} +(-2.74983 - 1.40582i) q^{68} +(-2.59132 + 1.43318i) q^{70} -11.7460 q^{71} +5.59390i q^{73} +(-10.4585 - 2.51840i) q^{74} +(-5.56155 - 2.84329i) q^{76} -2.06798i q^{77} -1.02248i q^{79} +(8.75935 + 1.80938i) q^{80} +(-1.93049 + 8.01706i) q^{82} +14.0877 q^{83} +(-2.54635 + 2.33205i) q^{85} +(-2.57501 + 10.6937i) q^{86} +(-4.06627 + 4.74137i) q^{88} +13.0761i q^{89} +3.12311 q^{91} +(-3.08835 + 6.04090i) q^{92} +(3.56155 - 14.7906i) q^{94} +(-5.15002 + 4.71659i) q^{95} +2.18379i q^{97} +(8.41874 + 2.02722i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q+12q48q1012q16+16q19+40q2532q3428q4048q4632q49+36q64+32q7056q7616q91+24q94+O(q100) 16 q + 12 q^{4} - 8 q^{10} - 12 q^{16} + 16 q^{19} + 40 q^{25} - 32 q^{34} - 28 q^{40} - 48 q^{46} - 32 q^{49} + 36 q^{64} + 32 q^{70} - 56 q^{76} - 16 q^{91} + 24 q^{94}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/360Z)×\left(\mathbb{Z}/360\mathbb{Z}\right)^\times.

nn 181181 217217 271271 281281
χ(n)\chi(n) 1-1 1-1 1-1 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 −1.37491 0.331077i −0.972211 0.234107i
33 0 0
44 1.78078 + 0.910404i 0.890388 + 0.455202i
55 1.64901 1.51022i 0.737458 0.675393i
66 0 0
77 0.936426 0.353936 0.176968 0.984217i 0.443371π-0.443371\pi
0.176968 + 0.984217i 0.443371π0.443371\pi
88 −2.14700 1.84130i −0.759079 0.650998i
99 0 0
1010 −2.76724 + 1.53048i −0.875079 + 0.483980i
1111 2.20837i 0.665848i −0.942954 0.332924i 0.891965π-0.891965\pi
0.942954 0.332924i 0.108035π-0.108035\pi
1212 0 0
1313 3.33513 0.924999 0.462500 0.886619i 0.346953π-0.346953\pi
0.462500 + 0.886619i 0.346953π0.346953\pi
1414 −1.28751 0.310029i −0.344100 0.0828587i
1515 0 0
1616 2.34233 + 3.24245i 0.585582 + 0.810613i
1717 −1.54417 −0.374517 −0.187259 0.982311i 0.559960π-0.559960\pi
−0.187259 + 0.982311i 0.559960π0.559960\pi
1818 0 0
1919 −3.12311 −0.716490 −0.358245 0.933628i 0.616625π-0.616625\pi
−0.358245 + 0.933628i 0.616625π0.616625\pi
2020 4.31143 1.18811i 0.964064 0.265669i
2121 0 0
2222 −0.731140 + 3.03632i −0.155879 + 0.647345i
2323 3.39228i 0.707340i 0.935370 + 0.353670i 0.115066π0.115066\pi
−0.935370 + 0.353670i 0.884934π0.884934\pi
2424 0 0
2525 0.438447 4.98074i 0.0876894 0.996148i
2626 −4.58552 1.10418i −0.899294 0.216548i
2727 0 0
2828 1.66757 + 0.852526i 0.315140 + 0.161112i
2929 8.44804 1.56876 0.784380 0.620280i 0.212981π-0.212981\pi
0.784380 + 0.620280i 0.212981π0.212981\pi
3030 0 0
3131 8.30571i 1.49175i −0.666086 0.745875i 0.732032π-0.732032\pi
0.666086 0.745875i 0.267968π-0.267968\pi
3232 −2.14700 5.23358i −0.379540 0.925175i
3333 0 0
3434 2.12311 + 0.511240i 0.364110 + 0.0876769i
3535 1.54417 1.41421i 0.261013 0.239046i
3636 0 0
3737 7.60669 1.25053 0.625266 0.780412i 0.284990π-0.284990\pi
0.625266 + 0.780412i 0.284990π0.284990\pi
3838 4.29400 + 1.03399i 0.696579 + 0.167735i
3939 0 0
4040 −6.32120 + 0.206134i −0.999469 + 0.0325927i
4141 5.83095i 0.910642i −0.890327 0.455321i 0.849525π-0.849525\pi
0.890327 0.455321i 0.150475π-0.150475\pi
4242 0 0
4343 7.77769i 1.18609i −0.805171 0.593043i 0.797926π-0.797926\pi
0.805171 0.593043i 0.202074π-0.202074\pi
4444 2.01051 3.93261i 0.303095 0.592864i
4545 0 0
4646 1.12311 4.66410i 0.165593 0.687683i
4747 10.7575i 1.56914i 0.620040 + 0.784570i 0.287116π0.287116\pi
−0.620040 + 0.784570i 0.712884π0.712884\pi
4848 0 0
4949 −6.12311 −0.874729
5050 −2.25183 + 6.70293i −0.318457 + 0.947937i
5151 0 0
5252 5.93912 + 3.03632i 0.823608 + 0.421061i
5353 5.08842i 0.698949i −0.936946 0.349474i 0.886360π-0.886360\pi
0.936946 0.349474i 0.113640π-0.113640\pi
5454 0 0
5555 −3.33513 3.64162i −0.449709 0.491035i
5656 −2.01051 1.72424i −0.268665 0.230412i
5757 0 0
5858 −11.6153 2.79695i −1.52517 0.367257i
5959 10.6937i 1.39219i 0.717947 + 0.696097i 0.245082π0.245082\pi
−0.717947 + 0.696097i 0.754918π0.754918\pi
6060 0 0
6161 0 0 1.00000 00
−1.00000 π\pi
6262 −2.74983 + 11.4196i −0.349228 + 1.45030i
6363 0 0
6464 1.21922 + 7.90655i 0.152403 + 0.988318i
6565 5.49966 5.03680i 0.682148 0.624738i
6666 0 0
6767 12.1453i 1.48378i 0.670521 + 0.741890i 0.266071π0.266071\pi
−0.670521 + 0.741890i 0.733929π0.733929\pi
6868 −2.74983 1.40582i −0.333466 0.170481i
6969 0 0
7070 −2.59132 + 1.43318i −0.309722 + 0.171298i
7171 −11.7460 −1.39400 −0.697000 0.717071i 0.745482π-0.745482\pi
−0.697000 + 0.717071i 0.745482π0.745482\pi
7272 0 0
7373 5.59390i 0.654716i 0.944900 + 0.327358i 0.106158π0.106158\pi
−0.944900 + 0.327358i 0.893842π0.893842\pi
7474 −10.4585 2.51840i −1.21578 0.292758i
7575 0 0
7676 −5.56155 2.84329i −0.637954 0.326147i
7777 2.06798i 0.235668i
7878 0 0
7979 1.02248i 0.115038i −0.998344 0.0575190i 0.981681π-0.981681\pi
0.998344 0.0575190i 0.0183190π-0.0183190\pi
8080 8.75935 + 1.80938i 0.979325 + 0.202295i
8181 0 0
8282 −1.93049 + 8.01706i −0.213187 + 0.885336i
8383 14.0877 1.54632 0.773161 0.634210i 0.218675π-0.218675\pi
0.773161 + 0.634210i 0.218675π0.218675\pi
8484 0 0
8585 −2.54635 + 2.33205i −0.276191 + 0.252946i
8686 −2.57501 + 10.6937i −0.277671 + 1.15313i
8787 0 0
8888 −4.06627 + 4.74137i −0.433466 + 0.505432i
8989 13.0761i 1.38607i 0.720906 + 0.693033i 0.243726π0.243726\pi
−0.720906 + 0.693033i 0.756274π0.756274\pi
9090 0 0
9191 3.12311 0.327390
9292 −3.08835 + 6.04090i −0.321982 + 0.629807i
9393 0 0
9494 3.56155 14.7906i 0.367346 1.52554i
9595 −5.15002 + 4.71659i −0.528381 + 0.483912i
9696 0 0
9797 2.18379i 0.221730i 0.993835 + 0.110865i 0.0353622π0.0353622\pi
−0.993835 + 0.110865i 0.964638π0.964638\pi
9898 8.41874 + 2.02722i 0.850421 + 0.204780i
9999 0 0
100100 5.31526 8.47042i 0.531526 0.847042i
101101 3.29801 0.328165 0.164082 0.986447i 0.447534π-0.447534\pi
0.164082 + 0.986447i 0.447534π0.447534\pi
102102 0 0
103103 −18.0227 −1.77583 −0.887913 0.460012i 0.847845π-0.847845\pi
−0.887913 + 0.460012i 0.847845π0.847845\pi
104104 −7.16053 6.14098i −0.702148 0.602173i
105105 0 0
106106 −1.68466 + 6.99614i −0.163628 + 0.679526i
107107 −10.9993 −1.06334 −0.531672 0.846950i 0.678436π-0.678436\pi
−0.531672 + 0.846950i 0.678436π0.678436\pi
108108 0 0
109109 11.9473i 1.14435i 0.820133 + 0.572173i 0.193900π0.193900\pi
−0.820133 + 0.572173i 0.806100π0.806100\pi
110110 3.37987 + 6.11109i 0.322257 + 0.582670i
111111 0 0
112112 2.19342 + 3.03632i 0.207259 + 0.286905i
113113 −12.5435 −1.17999 −0.589996 0.807406i 0.700871π-0.700871\pi
−0.589996 + 0.807406i 0.700871π0.700871\pi
114114 0 0
115115 5.12311 + 5.59390i 0.477732 + 0.521634i
116116 15.0441 + 7.69113i 1.39681 + 0.714103i
117117 0 0
118118 3.54042 14.7028i 0.325922 1.35351i
119119 −1.44600 −0.132555
120120 0 0
121121 6.12311 0.556646
122122 0 0
123123 0 0
124124 7.56155 14.7906i 0.679047 1.32824i
125125 −6.79903 8.87543i −0.608124 0.793842i
126126 0 0
127127 4.68213 0.415472 0.207736 0.978185i 0.433391π-0.433391\pi
0.207736 + 0.978185i 0.433391π0.433391\pi
128128 0.941346 11.2745i 0.0832041 0.996533i
129129 0 0
130130 −9.22912 + 5.10435i −0.809447 + 0.447681i
131131 0.620058i 0.0541747i −0.999633 0.0270874i 0.991377π-0.991377\pi
0.999633 0.0270874i 0.00862323π-0.00862323\pi
132132 0 0
133133 −2.92456 −0.253591
134134 4.02102 16.6987i 0.347363 1.44255i
135135 0 0
136136 3.31534 + 2.84329i 0.284288 + 0.243810i
137137 −1.54417 −0.131928 −0.0659638 0.997822i 0.521012π-0.521012\pi
−0.0659638 + 0.997822i 0.521012π0.521012\pi
138138 0 0
139139 −12.0000 −1.01783 −0.508913 0.860818i 0.669953π-0.669953\pi
−0.508913 + 0.860818i 0.669953π0.669953\pi
140140 4.03733 1.11258i 0.341217 0.0940299i
141141 0 0
142142 16.1498 + 3.88884i 1.35526 + 0.326345i
143143 7.36520i 0.615909i
144144 0 0
145145 13.9309 12.7584i 1.15690 1.05953i
146146 1.85201 7.69113i 0.153273 0.636522i
147147 0 0
148148 13.5458 + 6.92516i 1.11346 + 0.569245i
149149 1.85201 0.151722 0.0758612 0.997118i 0.475829π-0.475829\pi
0.0758612 + 0.997118i 0.475829π0.475829\pi
150150 0 0
151151 17.6339i 1.43503i 0.696545 + 0.717513i 0.254720π0.254720\pi
−0.696545 + 0.717513i 0.745280π0.745280\pi
152152 6.70531 + 5.75058i 0.543872 + 0.466433i
153153 0 0
154154 −0.684658 + 2.84329i −0.0551713 + 0.229119i
155155 −12.5435 13.6962i −1.00752 1.10010i
156156 0 0
157157 −2.80928 −0.224205 −0.112102 0.993697i 0.535758π-0.535758\pi
−0.112102 + 0.993697i 0.535758π0.535758\pi
158158 −0.338519 + 1.40582i −0.0269311 + 0.111841i
159159 0 0
160160 −11.4443 5.38776i −0.904751 0.425940i
161161 3.17662i 0.250353i
162162 0 0
163163 15.5554i 1.21839i −0.793020 0.609195i 0.791492π-0.791492\pi
0.793020 0.609195i 0.208508π-0.208508\pi
164164 5.30852 10.3836i 0.414526 0.810825i
165165 0 0
166166 −19.3693 4.66410i −1.50335 0.362004i
167167 9.43318i 0.729961i −0.931015 0.364981i 0.881076π-0.881076\pi
0.931015 0.364981i 0.118924π-0.118924\pi
168168 0 0
169169 −1.87689 −0.144376
170170 4.27310 2.36333i 0.327732 0.181259i
171171 0 0
172172 7.08084 13.8503i 0.539909 1.05608i
173173 1.69614i 0.128955i 0.997919 + 0.0644776i 0.0205381π0.0205381\pi
−0.997919 + 0.0644776i 0.979462π0.979462\pi
174174 0 0
175175 0.410574 4.66410i 0.0310364 0.352572i
176176 7.16053 5.17273i 0.539745 0.389909i
177177 0 0
178178 4.32920 17.9785i 0.324487 1.34755i
179179 8.21342i 0.613900i 0.951726 + 0.306950i 0.0993084π0.0993084\pi
−0.951726 + 0.306950i 0.900692π0.900692\pi
180180 0 0
181181 4.66410i 0.346680i 0.984862 + 0.173340i 0.0554559π0.0554559\pi
−0.984862 + 0.173340i 0.944544π0.944544\pi
182182 −4.29400 1.03399i −0.318293 0.0766443i
183183 0 0
184184 6.24621 7.28323i 0.460477 0.536927i
185185 12.5435 11.4878i 0.922215 0.844600i
186186 0 0
187187 3.41011i 0.249372i
188188 −9.79366 + 19.1567i −0.714276 + 1.39714i
189189 0 0
190190 8.64239 4.77985i 0.626985 0.346767i
191191 13.1921 0.954544 0.477272 0.878756i 0.341626π-0.341626\pi
0.477272 + 0.878756i 0.341626π0.341626\pi
192192 0 0
193193 23.3331i 1.67955i 0.542934 + 0.839775i 0.317313π0.317313\pi
−0.542934 + 0.839775i 0.682687π0.682687\pi
194194 0.723002 3.00252i 0.0519085 0.215569i
195195 0 0
196196 −10.9039 5.57450i −0.778849 0.398179i
197197 4.92539i 0.350920i −0.984487 0.175460i 0.943859π-0.943859\pi
0.984487 0.175460i 0.0561412π-0.0561412\pi
198198 0 0
199199 17.6339i 1.25003i 0.780611 + 0.625017i 0.214908π0.214908\pi
−0.780611 + 0.625017i 0.785092π0.785092\pi
200200 −10.1124 + 9.88634i −0.715054 + 0.699070i
201201 0 0
202202 −4.53448 1.09190i −0.319045 0.0768255i
203203 7.91096 0.555241
204204 0 0
205205 −8.80604 9.61528i −0.615041 0.671560i
206206 24.7796 + 5.96688i 1.72648 + 0.415732i
207207 0 0
208208 7.81198 + 10.8140i 0.541663 + 0.749816i
209209 6.89697i 0.477073i
210210 0 0
211211 4.00000 0.275371 0.137686 0.990476i 0.456034π-0.456034\pi
0.137686 + 0.990476i 0.456034π0.456034\pi
212212 4.63252 9.06134i 0.318163 0.622336i
213213 0 0
214214 15.1231 + 3.64162i 1.03379 + 0.248936i
215215 −11.7460 12.8255i −0.801074 0.874689i
216216 0 0
217217 7.77769i 0.527984i
218218 3.95548 16.4265i 0.267899 1.11255i
219219 0 0
220220 −2.62378 9.52122i −0.176895 0.641921i
221221 −5.15002 −0.346428
222222 0 0
223223 21.9989 1.47316 0.736578 0.676352i 0.236440π-0.236440\pi
0.736578 + 0.676352i 0.236440π0.236440\pi
224224 −2.01051 4.90086i −0.134333 0.327453i
225225 0 0
226226 17.2462 + 4.15286i 1.14720 + 0.276244i
227227 −3.08835 −0.204981 −0.102490 0.994734i 0.532681π-0.532681\pi
−0.102490 + 0.994734i 0.532681π0.532681\pi
228228 0 0
229229 2.61914i 0.173077i 0.996248 + 0.0865387i 0.0275806π0.0275806\pi
−0.996248 + 0.0865387i 0.972419π0.972419\pi
230230 −5.19182 9.38727i −0.342338 0.618978i
231231 0 0
232232 −18.1379 15.5554i −1.19081 1.02126i
233233 −20.4544 −1.34002 −0.670008 0.742354i 0.733709π-0.733709\pi
−0.670008 + 0.742354i 0.733709π0.733709\pi
234234 0 0
235235 16.2462 + 17.7392i 1.05979 + 1.15718i
236236 −9.73554 + 19.0430i −0.633730 + 1.23959i
237237 0 0
238238 1.98813 + 0.478739i 0.128871 + 0.0310320i
239239 23.4921 1.51958 0.759789 0.650170i 0.225302π-0.225302\pi
0.759789 + 0.650170i 0.225302π0.225302\pi
240240 0 0
241241 −4.00000 −0.257663 −0.128831 0.991667i 0.541123π-0.541123\pi
−0.128831 + 0.991667i 0.541123π0.541123\pi
242242 −8.41874 2.02722i −0.541177 0.130314i
243243 0 0
244244 0 0
245245 −10.0970 + 9.24726i −0.645076 + 0.590786i
246246 0 0
247247 −10.4160 −0.662752
248248 −15.2933 + 17.8324i −0.971126 + 1.13236i
249249 0 0
250250 6.40963 + 14.4539i 0.405381 + 0.914148i
251251 3.44849i 0.217666i −0.994060 0.108833i 0.965289π-0.965289\pi
0.994060 0.108833i 0.0347114π-0.0347114\pi
252252 0 0
253253 7.49141 0.470981
254254 −6.43753 1.55014i −0.403926 0.0972647i
255255 0 0
256256 −5.02699 + 15.1898i −0.314187 + 0.949361i
257257 15.6318 0.975087 0.487543 0.873099i 0.337893π-0.337893\pi
0.487543 + 0.873099i 0.337893π0.337893\pi
258258 0 0
259259 7.12311 0.442608
260260 14.3792 3.96250i 0.891759 0.245744i
261261 0 0
262262 −0.205287 + 0.852526i −0.0126827 + 0.0526693i
263263 14.7304i 0.908316i −0.890921 0.454158i 0.849940π-0.849940\pi
0.890921 0.454158i 0.150060π-0.150060\pi
264264 0 0
265265 −7.68466 8.39084i −0.472065 0.515445i
266266 4.02102 + 0.968253i 0.246544 + 0.0593674i
267267 0 0
268268 −11.0571 + 21.6280i −0.675420 + 1.32114i
269269 −15.0441 −0.917253 −0.458626 0.888629i 0.651658π-0.651658\pi
−0.458626 + 0.888629i 0.651658π0.651658\pi
270270 0 0
271271 10.3507i 0.628758i −0.949297 0.314379i 0.898204π-0.898204\pi
0.949297 0.314379i 0.101796π-0.101796\pi
272272 −3.61696 5.00691i −0.219311 0.303588i
273273 0 0
274274 2.12311 + 0.511240i 0.128262 + 0.0308851i
275275 −10.9993 0.968253i −0.663283 0.0583879i
276276 0 0
277277 −23.3459 −1.40272 −0.701360 0.712807i 0.747424π-0.747424\pi
−0.701360 + 0.712807i 0.747424π0.747424\pi
278278 16.4990 + 3.97292i 0.989542 + 0.238280i
279279 0 0
280280 −5.91933 + 0.193030i −0.353748 + 0.0115357i
281281 3.00252i 0.179116i −0.995982 0.0895578i 0.971455π-0.971455\pi
0.995982 0.0895578i 0.0285454π-0.0285454\pi
282282 0 0
283283 23.3331i 1.38701i −0.720453 0.693503i 0.756066π-0.756066\pi
0.720453 0.693503i 0.243934π-0.243934\pi
284284 −20.9171 10.6937i −1.24120 0.634551i
285285 0 0
286286 −2.43845 + 10.1265i −0.144188 + 0.598794i
287287 5.46026i 0.322309i
288288 0 0
289289 −14.6155 −0.859737
290290 −23.3778 + 12.9296i −1.37279 + 0.759249i
291291 0 0
292292 −5.09271 + 9.96148i −0.298028 + 0.582951i
293293 29.8326i 1.74284i 0.490536 + 0.871421i 0.336801π0.336801\pi
−0.490536 + 0.871421i 0.663199π0.663199\pi
294294 0 0
295295 16.1498 + 17.6339i 0.940278 + 1.02669i
296296 −16.3316 14.0062i −0.949253 0.814094i
297297 0 0
298298 −2.54635 0.613157i −0.147506 0.0355192i
299299 11.3137i 0.654289i
300300 0 0
301301 7.28323i 0.419799i
302302 5.83817 24.2451i 0.335949 1.39515i
303303 0 0
304304 −7.31534 10.1265i −0.419564 0.580796i
305305 0 0
306306 0 0
307307 4.36758i 0.249271i −0.992203 0.124636i 0.960224π-0.960224\pi
0.992203 0.124636i 0.0397762π-0.0397762\pi
308308 1.88269 3.68260i 0.107276 0.209836i
309309 0 0
310310 12.7117 + 22.9839i 0.721978 + 1.30540i
311311 10.3000 0.584062 0.292031 0.956409i 0.405669π-0.405669\pi
0.292031 + 0.956409i 0.405669π0.405669\pi
312312 0 0
313313 32.0682i 1.81260i 0.422631 + 0.906302i 0.361107π0.361107\pi
−0.422631 + 0.906302i 0.638893π0.638893\pi
314314 3.86252 + 0.930087i 0.217974 + 0.0524878i
315315 0 0
316316 0.930870 1.82081i 0.0523655 0.102428i
317317 24.5354i 1.37805i 0.724739 + 0.689023i 0.241960π0.241960\pi
−0.724739 + 0.689023i 0.758040π0.758040\pi
318318 0 0
319319 18.6564i 1.04456i
320320 13.9512 + 11.1967i 0.779894 + 0.625912i
321321 0 0
322322 1.05171 4.36758i 0.0586093 0.243396i
323323 4.82262 0.268338
324324 0 0
325325 1.46228 16.6114i 0.0811127 0.921436i
326326 −5.15002 + 21.3873i −0.285233 + 1.18453i
327327 0 0
328328 −10.7365 + 12.5191i −0.592826 + 0.691249i
329329 10.0736i 0.555375i
330330 0 0
331331 −1.36932 −0.0752645 −0.0376322 0.999292i 0.511982π-0.511982\pi
−0.0376322 + 0.999292i 0.511982π0.511982\pi
332332 25.0870 + 12.8255i 1.37683 + 0.703889i
333333 0 0
334334 −3.12311 + 12.9698i −0.170889 + 0.709676i
335335 18.3421 + 20.0276i 1.00213 + 1.09423i
336336 0 0
337337 29.8844i 1.62791i −0.580929 0.813954i 0.697310π-0.697310\pi
0.580929 0.813954i 0.302690π-0.302690\pi
338338 2.58057 + 0.621396i 0.140364 + 0.0337995i
339339 0 0
340340 −6.65759 + 1.83465i −0.361059 + 0.0994977i
341341 −18.3421 −0.993279
342342 0 0
343343 −12.2888 −0.663534
344344 −14.3211 + 16.6987i −0.772140 + 0.900334i
345345 0 0
346346 0.561553 2.33205i 0.0301893 0.125372i
347347 14.0877 0.756265 0.378133 0.925751i 0.376566π-0.376566\pi
0.378133 + 0.925751i 0.376566π0.376566\pi
348348 0 0
349349 33.2228i 1.77838i −0.457540 0.889189i 0.651269π-0.651269\pi
0.457540 0.889189i 0.348731π-0.348731\pi
350350 −2.10868 + 6.27680i −0.112714 + 0.335509i
351351 0 0
352352 −11.5577 + 4.74137i −0.616027 + 0.252716i
353353 7.72087 0.410940 0.205470 0.978663i 0.434128π-0.434128\pi
0.205470 + 0.978663i 0.434128π0.434128\pi
354354 0 0
355355 −19.3693 + 17.7392i −1.02802 + 0.941497i
356356 −11.9045 + 23.2856i −0.630940 + 1.23414i
357357 0 0
358358 2.71927 11.2927i 0.143718 0.596840i
359359 −1.44600 −0.0763172 −0.0381586 0.999272i 0.512149π-0.512149\pi
−0.0381586 + 0.999272i 0.512149π0.512149\pi
360360 0 0
361361 −9.24621 −0.486643
362362 1.54417 6.41273i 0.0811600 0.337046i
363363 0 0
364364 5.56155 + 2.84329i 0.291505 + 0.149029i
365365 8.44804 + 9.22437i 0.442190 + 0.482826i
366366 0 0
367367 32.4149 1.69204 0.846022 0.533148i 0.178991π-0.178991\pi
0.846022 + 0.533148i 0.178991π0.178991\pi
368368 −10.9993 + 7.94584i −0.573379 + 0.414206i
369369 0 0
370370 −21.0496 + 11.6419i −1.09431 + 0.605233i
371371 4.76493i 0.247383i
372372 0 0
373373 9.47954 0.490832 0.245416 0.969418i 0.421075π-0.421075\pi
0.245416 + 0.969418i 0.421075π0.421075\pi
374374 1.12901 4.68860i 0.0583795 0.242442i
375375 0 0
376376 19.8078 23.0963i 1.02151 1.19110i
377377 28.1753 1.45110
378378 0 0
379379 −16.4924 −0.847159 −0.423579 0.905859i 0.639227π-0.639227\pi
−0.423579 + 0.905859i 0.639227π0.639227\pi
380380 −13.4650 + 3.71059i −0.690742 + 0.190349i
381381 0 0
382382 −18.1379 4.36758i −0.928018 0.223465i
383383 10.0138i 0.511682i 0.966719 + 0.255841i 0.0823524π0.0823524\pi
−0.966719 + 0.255841i 0.917648π0.917648\pi
384384 0 0
385385 −3.12311 3.41011i −0.159168 0.173795i
386386 7.72503 32.0810i 0.393194 1.63288i
387387 0 0
388388 −1.98813 + 3.88884i −0.100932 + 0.197426i
389389 9.89404 0.501648 0.250824 0.968033i 0.419298π-0.419298\pi
0.250824 + 0.968033i 0.419298π0.419298\pi
390390 0 0
391391 5.23827i 0.264911i
392392 13.1463 + 11.2745i 0.663989 + 0.569447i
393393 0 0
394394 −1.63068 + 6.77199i −0.0821526 + 0.341168i
395395 −1.54417 1.68608i −0.0776958 0.0848357i
396396 0 0
397397 −10.3007 −0.516977 −0.258488 0.966014i 0.583224π-0.583224\pi
−0.258488 + 0.966014i 0.583224π0.583224\pi
398398 5.83817 24.2451i 0.292641 1.21530i
399399 0 0
400400 17.1768 10.2449i 0.858840 0.512244i
401401 0.522293i 0.0260821i −0.999915 0.0130410i 0.995849π-0.995849\pi
0.999915 0.0130410i 0.00415121π-0.00415121\pi
402402 0 0
403403 27.7006i 1.37987i
404404 5.87302 + 3.00252i 0.292194 + 0.149381i
405405 0 0
406406 −10.8769 2.61914i −0.539811 0.129986i
407407 16.7984i 0.832665i
408408 0 0
409409 3.12311 0.154428 0.0772138 0.997015i 0.475398π-0.475398\pi
0.0772138 + 0.997015i 0.475398π0.475398\pi
410410 8.92416 + 16.1357i 0.440733 + 0.796883i
411411 0 0
412412 −32.0943 16.4079i −1.58117 0.808359i
413413 10.0138i 0.492748i
414414 0 0
415415 23.2306 21.2755i 1.14035 1.04437i
416416 −7.16053 17.4547i −0.351074 0.855787i
417417 0 0
418418 2.28343 9.48274i 0.111686 0.463816i
419419 32.4291i 1.58427i −0.610348 0.792134i 0.708970π-0.708970\pi
0.610348 0.792134i 0.291030π-0.291030\pi
420420 0 0
421421 30.6037i 1.49153i −0.666207 0.745767i 0.732083π-0.732083\pi
0.666207 0.745767i 0.267917π-0.267917\pi
422422 −5.49966 1.32431i −0.267719 0.0644663i
423423 0 0
424424 −9.36932 + 10.9248i −0.455014 + 0.530558i
425425 −0.677039 + 7.69113i −0.0328412 + 0.373074i
426426 0 0
427427 0 0
428428 −19.5873 10.0138i −0.946789 0.484036i
429429 0 0
430430 11.9036 + 21.5227i 0.574042 + 1.03792i
431431 1.44600 0.0696516 0.0348258 0.999393i 0.488912π-0.488912\pi
0.0348258 + 0.999393i 0.488912π0.488912\pi
432432 0 0
433433 15.5554i 0.747544i 0.927521 + 0.373772i 0.121936π0.121936\pi
−0.927521 + 0.373772i 0.878064π0.878064\pi
434434 −2.57501 + 10.6937i −0.123604 + 0.513312i
435435 0 0
436436 −10.8769 + 21.2755i −0.520909 + 1.01891i
437437 10.5945i 0.506802i
438438 0 0
439439 26.9621i 1.28683i 0.765517 + 0.643415i 0.222483π0.222483\pi
−0.765517 + 0.643415i 0.777517π0.777517\pi
440440 0.455221 + 13.9595i 0.0217018 + 0.665495i
441441 0 0
442442 7.08084 + 1.70505i 0.336801 + 0.0811011i
443443 25.0870 1.19192 0.595959 0.803015i 0.296772π-0.296772\pi
0.595959 + 0.803015i 0.296772π0.296772\pi
444444 0 0
445445 19.7479 + 21.5626i 0.936139 + 1.02217i
446446 −30.2466 7.28333i −1.43222 0.344876i
447447 0 0
448448 1.14171 + 7.40390i 0.0539409 + 0.349801i
449449 9.89949i 0.467186i −0.972334 0.233593i 0.924952π-0.924952\pi
0.972334 0.233593i 0.0750483π-0.0750483\pi
450450 0 0
451451 −12.8769 −0.606349
452452 −22.3371 11.4196i −1.05065 0.537135i
453453 0 0
454454 4.24621 + 1.02248i 0.199285 + 0.0479874i
455455 5.15002 4.71659i 0.241437 0.221117i
456456 0 0
457457 13.3716i 0.625496i −0.949836 0.312748i 0.898750π-0.898750\pi
0.949836 0.312748i 0.101250π-0.101250\pi
458458 0.867135 3.60109i 0.0405186 0.168268i
459459 0 0
460460 4.03040 + 14.6256i 0.187918 + 0.681921i
461461 1.85201 0.0862567 0.0431283 0.999070i 0.486268π-0.486268\pi
0.0431283 + 0.999070i 0.486268π0.486268\pi
462462 0 0
463463 13.2252 0.614629 0.307315 0.951608i 0.400570π-0.400570\pi
0.307315 + 0.951608i 0.400570π0.400570\pi
464464 19.7881 + 27.3924i 0.918639 + 1.27166i
465465 0 0
466466 28.1231 + 6.77199i 1.30278 + 0.313706i
467467 −18.9103 −0.875063 −0.437532 0.899203i 0.644147π-0.644147\pi
−0.437532 + 0.899203i 0.644147π0.644147\pi
468468 0 0
469469 11.3732i 0.525163i
470470 −16.4641 29.7686i −0.759433 1.37312i
471471 0 0
472472 19.6902 22.9593i 0.906316 1.05679i
473473 −17.1760 −0.789754
474474 0 0
475475 −1.36932 + 15.5554i −0.0628286 + 0.713730i
476476 −2.57501 1.31645i −0.118025 0.0603393i
477477 0 0
478478 −32.2996 7.77769i −1.47735 0.355743i
479479 14.6381 0.668830 0.334415 0.942426i 0.391461π-0.391461\pi
0.334415 + 0.942426i 0.391461π0.391461\pi
480480 0 0
481481 25.3693 1.15674
482482 5.49966 + 1.32431i 0.250502 + 0.0603205i
483483 0 0
484484 10.9039 + 5.57450i 0.495631 + 0.253386i
485485 3.29801 + 3.60109i 0.149755 + 0.163517i
486486 0 0
487487 −29.4903 −1.33633 −0.668167 0.744011i 0.732921π-0.732921\pi
−0.668167 + 0.744011i 0.732921π0.732921\pi
488488 0 0
489489 0 0
490490 16.9441 9.37129i 0.765457 0.423352i
491491 16.3505i 0.737888i −0.929452 0.368944i 0.879719π-0.879719\pi
0.929452 0.368944i 0.120281π-0.120281\pi
492492 0 0
493493 −13.0452 −0.587528
494494 14.3211 + 3.44849i 0.644335 + 0.155155i
495495 0 0
496496 26.9309 19.4547i 1.20923 0.873542i
497497 −10.9993 −0.493387
498498 0 0
499499 16.8769 0.755514 0.377757 0.925905i 0.376696π-0.376696\pi
0.377757 + 0.925905i 0.376696π0.376696\pi
500500 −4.02733 21.9950i −0.180108 0.983647i
501501 0 0
502502 −1.14171 + 4.74137i −0.0509572 + 0.211618i
503503 16.0547i 0.715844i −0.933751 0.357922i 0.883485π-0.883485\pi
0.933751 0.357922i 0.116515π-0.116515\pi
504504 0 0
505505 5.43845 4.98074i 0.242008 0.221640i
506506 −10.3000 2.48023i −0.457893 0.110260i
507507 0 0
508508 8.33783 + 4.26263i 0.369931 + 0.189124i
509509 3.29801 0.146182 0.0730909 0.997325i 0.476714π-0.476714\pi
0.0730909 + 0.997325i 0.476714π0.476714\pi
510510 0 0
511511 5.23827i 0.231728i
512512 11.9407 19.2203i 0.527707 0.849426i
513513 0 0
514514 −21.4924 5.17534i −0.947990 0.228274i
515515 −29.7195 + 27.2183i −1.30960 + 1.19938i
516516 0 0
517517 23.7565 1.04481
518518 −9.79366 2.35829i −0.430309 0.103618i
519519 0 0
520520 −21.0820 + 0.687485i −0.924508 + 0.0301482i
521521 2.65433i 0.116288i −0.998308 0.0581441i 0.981482π-0.981482\pi
0.998308 0.0581441i 0.0185183π-0.0185183\pi
522522 0 0
523523 4.36758i 0.190981i 0.995430 + 0.0954905i 0.0304420π0.0304420\pi
−0.995430 + 0.0954905i 0.969558π0.969558\pi
524524 0.564503 1.10418i 0.0246604 0.0482365i
525525 0 0
526526 −4.87689 + 20.2530i −0.212643 + 0.883074i
527527 12.8255i 0.558686i
528528 0 0
529529 11.4924 0.499671
530530 7.78773 + 14.0809i 0.338277 + 0.611635i
531531 0 0
532532 −5.20798 2.66253i −0.225795 0.115435i
533533 19.4470i 0.842343i
534534 0 0
535535 −18.1379 + 16.6114i −0.784172 + 0.718174i
536536 22.3631 26.0759i 0.965939 1.12631i
537537 0 0
538538 20.6843 + 4.98074i 0.891763 + 0.214735i
539539 13.5221i 0.582437i
540540 0 0
541541 9.90237i 0.425736i 0.977081 + 0.212868i 0.0682804π0.0682804\pi
−0.977081 + 0.212868i 0.931720π0.931720\pi
542542 −3.42687 + 14.2313i −0.147197 + 0.611286i
543543 0 0
544544 3.31534 + 8.08156i 0.142144 + 0.346494i
545545 18.0431 + 19.7012i 0.772883 + 0.843908i
546546 0 0
547547 16.5129i 0.706039i −0.935616 0.353019i 0.885155π-0.885155\pi
0.935616 0.353019i 0.114845π-0.114845\pi
548548 −2.74983 1.40582i −0.117467 0.0600537i
549549 0 0
550550 14.8025 + 4.97288i 0.631182 + 0.212044i
551551 −26.3841 −1.12400
552552 0 0
553553 0.957477i 0.0407161i
554554 32.0986 + 7.72929i 1.36374 + 0.328386i
555555 0 0
556556 −21.3693 10.9248i −0.906261 0.463317i
557557 32.6443i 1.38318i −0.722289 0.691591i 0.756910π-0.756910\pi
0.722289 0.691591i 0.243090π-0.243090\pi
558558 0 0
559559 25.9396i 1.09713i
560560 8.20248 + 1.69435i 0.346618 + 0.0715995i
561561 0 0
562562 −0.994066 + 4.12821i −0.0419321 + 0.174138i
563563 −14.0877 −0.593724 −0.296862 0.954920i 0.595940π-0.595940\pi
−0.296862 + 0.954920i 0.595940π0.595940\pi
564564 0 0
565565 −20.6843 + 18.9435i −0.870195 + 0.796958i
566566 −7.72503 + 32.0810i −0.324707 + 1.34846i
567567 0 0
568568 25.2188 + 21.6280i 1.05816 + 0.907491i
569569 30.0467i 1.25962i −0.776748 0.629811i 0.783132π-0.783132\pi
0.776748 0.629811i 0.216868π-0.216868\pi
570570 0 0
571571 33.8617 1.41707 0.708535 0.705676i 0.249356π-0.249356\pi
0.708535 + 0.705676i 0.249356π0.249356\pi
572572 6.70531 13.1158i 0.280363 0.548398i
573573 0 0
574574 −1.80776 + 7.50738i −0.0754546 + 0.313352i
575575 16.8961 + 1.48734i 0.704615 + 0.0620262i
576576 0 0
577577 7.77769i 0.323789i 0.986808 + 0.161895i 0.0517605π0.0517605\pi
−0.986808 + 0.161895i 0.948240π0.948240\pi
578578 20.0951 + 4.83886i 0.835846 + 0.201270i
579579 0 0
580580 36.4231 10.0372i 1.51239 0.416771i
581581 13.1921 0.547299
582582 0 0
583583 −11.2371 −0.465394
584584 10.3000 12.0101i 0.426219 0.496981i
585585 0 0
586586 9.87689 41.0173i 0.408011 1.69441i
587587 10.9993 0.453990 0.226995 0.973896i 0.427110π-0.427110\pi
0.226995 + 0.973896i 0.427110π0.427110\pi
588588 0 0
589589 25.9396i 1.06882i
590590 −16.3664 29.5919i −0.673795 1.21828i
591591 0 0
592592 17.8174 + 24.6643i 0.732290 + 1.01370i
593593 −43.8071 −1.79894 −0.899472 0.436978i 0.856049π-0.856049\pi
−0.899472 + 0.436978i 0.856049π0.856049\pi
594594 0 0
595595 −2.38447 + 2.18379i −0.0977538 + 0.0895267i
596596 3.29801 + 1.68608i 0.135092 + 0.0690644i
597597 0 0
598598 3.74571 15.5554i 0.153173 0.636107i
599599 −45.5382 −1.86064 −0.930320 0.366749i 0.880471π-0.880471\pi
−0.930320 + 0.366749i 0.880471π0.880471\pi
600600 0 0
601601 −23.3693 −0.953254 −0.476627 0.879106i 0.658141π-0.658141\pi
−0.476627 + 0.879106i 0.658141π0.658141\pi
602602 −2.41131 + 10.0138i −0.0982776 + 0.408133i
603603 0 0
604604 −16.0540 + 31.4020i −0.653227 + 1.27773i
605605 10.0970 9.24726i 0.410503 0.375955i
606606 0 0
607607 −9.71010 −0.394121 −0.197060 0.980391i 0.563140π-0.563140\pi
−0.197060 + 0.980391i 0.563140π0.563140\pi
608608 6.70531 + 16.3450i 0.271936 + 0.662879i
609609 0 0
610610 0 0
611611 35.8776i 1.45145i
612612 0 0
613613 23.8718 0.964172 0.482086 0.876124i 0.339879π-0.339879\pi
0.482086 + 0.876124i 0.339879π0.339879\pi
614614 −1.44600 + 6.00505i −0.0583560 + 0.242344i
615615 0 0
616616 −3.80776 + 4.43994i −0.153419 + 0.178890i
617617 −15.6318 −0.629314 −0.314657 0.949205i 0.601889π-0.601889\pi
−0.314657 + 0.949205i 0.601889π0.601889\pi
618618 0 0
619619 18.7386 0.753169 0.376585 0.926382i 0.377098π-0.377098\pi
0.376585 + 0.926382i 0.377098π0.377098\pi
620620 −9.86809 35.8095i −0.396312 1.43814i
621621 0 0
622622 −14.1617 3.41011i −0.567831 0.136733i
623623 12.2448i 0.490578i
624624 0 0
625625 −24.6155 4.36758i −0.984621 0.174703i
626626 10.6170 44.0911i 0.424342 1.76223i
627627 0 0
628628 −5.00270 2.55758i −0.199629 0.102059i
629629 −11.7460 −0.468346
630630 0 0
631631 17.6339i 0.701995i 0.936376 + 0.350997i 0.114157π0.114157\pi
−0.936376 + 0.350997i 0.885843π0.885843\pi
632632 −1.88269 + 2.19526i −0.0748895 + 0.0873229i
633633 0 0
634634 8.12311 33.7341i 0.322610 1.33975i
635635 7.72087 7.07107i 0.306393 0.280607i
636636 0 0
637637 −20.4214 −0.809124
638638 −6.17669 + 25.6509i −0.244538 + 1.01553i
639639 0 0
640640 −15.4747 20.0133i −0.611691 0.791097i
641641 7.07107i 0.279290i −0.990202 0.139645i 0.955404π-0.955404\pi
0.990202 0.139645i 0.0445962π-0.0445962\pi
642642 0 0
643643 8.73516i 0.344481i 0.985055 + 0.172241i 0.0551007π0.0551007\pi
−0.985055 + 0.172241i 0.944899π0.944899\pi
644644 −2.89201 + 5.65685i −0.113961 + 0.222911i
645645 0 0
646646 −6.63068 1.59666i −0.260881 0.0628196i
647647 1.32431i 0.0520639i −0.999661 0.0260319i 0.991713π-0.991713\pi
0.999661 0.0260319i 0.00828716π-0.00828716\pi
648648 0 0
649649 23.6155 0.926991
650650 −7.51016 + 22.3551i −0.294573 + 0.876841i
651651 0 0
652652 14.1617 27.7006i 0.554614 1.08484i
653653 15.8459i 0.620098i −0.950721 0.310049i 0.899654π-0.899654\pi
0.950721 0.310049i 0.100346π-0.100346\pi
654654 0 0
655655 −0.936426 1.02248i −0.0365892 0.0399516i
656656 18.9066 13.6580i 0.738178 0.533256i
657657 0 0
658658 3.33513 13.8503i 0.130017 0.539942i
659659 33.3211i 1.29800i −0.760786 0.649002i 0.775187π-0.775187\pi
0.760786 0.649002i 0.224813π-0.224813\pi
660660 0 0
661661 44.5960i 1.73458i 0.497800 + 0.867292i 0.334141π0.334141\pi
−0.497800 + 0.867292i 0.665859π0.665859\pi
662662 1.88269 + 0.453349i 0.0731729 + 0.0176199i
663663 0 0
664664 −30.2462 25.9396i −1.17378 1.00665i
665665 −4.82262 + 4.41674i −0.187013 + 0.171274i
666666 0 0
667667 28.6581i 1.10965i
668668 8.58800 16.7984i 0.332280 0.649949i
669669 0 0
670670 −18.5881 33.6089i −0.718121 1.29843i
671671 0 0
672672 0 0
673673 0 0 1.00000 00
−1.00000 π\pi
674674 −9.89404 + 41.0885i −0.381104 + 1.58267i
675675 0 0
676676 −3.34233 1.70873i −0.128551 0.0657205i
677677 5.25145i 0.201830i −0.994895 0.100915i 0.967823π-0.967823\pi
0.994895 0.100915i 0.0321770π-0.0321770\pi
678678 0 0
679679 2.04496i 0.0784783i
680680 9.76102 0.318307i 0.374318 0.0122065i
681681 0 0
682682 25.2188 + 6.07263i 0.965677 + 0.232533i
683683 20.2644 0.775394 0.387697 0.921787i 0.373271π-0.373271\pi
0.387697 + 0.921787i 0.373271π0.373271\pi
684684 0 0
685685 −2.54635 + 2.33205i −0.0972911 + 0.0891030i
686686 16.8961 + 4.06854i 0.645095 + 0.155338i
687687 0 0
688688 25.2188 18.2179i 0.961457 0.694551i
689689 16.9706i 0.646527i
690690 0 0
691691 −23.1231 −0.879644 −0.439822 0.898085i 0.644959π-0.644959\pi
−0.439822 + 0.898085i 0.644959π0.644959\pi
692692 −1.54417 + 3.02045i −0.0587007 + 0.114820i
693693 0 0
694694 −19.3693 4.66410i −0.735249 0.177047i
695695 −19.7881 + 18.1227i −0.750605 + 0.687433i
696696 0 0
697697 9.00400i 0.341051i
698698 −10.9993 + 45.6786i −0.416330 + 1.72896i
699699 0 0
700700 4.97735 7.93192i 0.188126 0.299799i
701701 20.1941 0.762720 0.381360 0.924427i 0.375456π-0.375456\pi
0.381360 + 0.924427i 0.375456π0.375456\pi
702702 0 0
703703 −23.7565 −0.895993
704704 17.4606 2.69250i 0.658070 0.101477i
705705 0 0
706706 −10.6155 2.55620i −0.399521 0.0962038i
707707 3.08835 0.116149
708708 0 0
709709 30.6037i 1.14935i −0.818383 0.574673i 0.805129π-0.805129\pi
0.818383 0.574673i 0.194871π-0.194871\pi
710710 32.5042 17.9771i 1.21986 0.674668i
711711 0 0
712712 24.0771 28.0744i 0.902326 1.05213i
713713 28.1753 1.05517
714714 0 0
715715 −11.1231 12.1453i −0.415981 0.454207i
716716 −7.47753 + 14.6263i −0.279448 + 0.546609i
717717 0 0
718718 1.98813 + 0.478739i 0.0741964 + 0.0178664i
719719 −32.3461 −1.20631 −0.603154 0.797625i 0.706089π-0.706089\pi
−0.603154 + 0.797625i 0.706089π0.706089\pi
720720 0 0
721721 −16.8769 −0.628528
722722 12.7127 + 3.06121i 0.473119 + 0.113926i
723723 0 0
724724 −4.24621 + 8.30571i −0.157809 + 0.308679i
725725 3.70402 42.0775i 0.137564 1.56272i
726726 0 0
727727 −9.47954 −0.351577 −0.175788 0.984428i 0.556247π-0.556247\pi
−0.175788 + 0.984428i 0.556247π0.556247\pi
728728 −6.70531 5.75058i −0.248515 0.213131i
729729 0 0
730730 −8.56135 15.4797i −0.316870 0.572928i
731731 12.0101i 0.444210i
732732 0 0
733733 19.6002 0.723951 0.361975 0.932188i 0.382102π-0.382102\pi
0.361975 + 0.932188i 0.382102π0.382102\pi
734734 −44.5677 10.7318i −1.64502 0.396119i
735735 0 0
736736 17.7538 7.28323i 0.654413 0.268463i
737737 26.8212 0.987973
738738 0 0
739739 35.6155 1.31014 0.655069 0.755569i 0.272639π-0.272639\pi
0.655069 + 0.755569i 0.272639π0.272639\pi
740740 32.7957 9.03758i 1.20559 0.332228i
741741 0 0
742742 −1.57756 + 6.55137i −0.0579140 + 0.240508i
743743 10.0138i 0.367371i 0.982985 + 0.183686i 0.0588028π0.0588028\pi
−0.982985 + 0.183686i 0.941197π0.941197\pi
744744 0 0
745745 3.05398 2.79695i 0.111889 0.102472i
746746 −13.0336 3.13846i −0.477192 0.114907i
747747 0 0
748748 −3.10457 + 6.07263i −0.113514 + 0.222038i
749749 −10.3000 −0.376355
750750 0 0
751751 41.5286i 1.51540i −0.652604 0.757699i 0.726323π-0.726323\pi
0.652604 0.757699i 0.273677π-0.273677\pi
752752 −34.8806 + 25.1976i −1.27197 + 0.918861i
753753 0 0
754754 −38.7386 9.32819i −1.41078 0.339713i
755755 26.6311 + 29.0784i 0.969207 + 1.05827i
756756 0 0
757757 3.33513 0.121217 0.0606087 0.998162i 0.480696π-0.480696\pi
0.0606087 + 0.998162i 0.480696π0.480696\pi
758758 22.6757 + 5.46026i 0.823617 + 0.198325i
759759 0 0
760760 19.7418 0.643779i 0.716109 0.0233523i
761761 49.3019i 1.78719i 0.448870 + 0.893597i 0.351827π0.351827\pi
−0.448870 + 0.893597i 0.648173π0.648173\pi
762762 0 0
763763 11.1878i 0.405025i
764764 23.4921 + 12.0101i 0.849914 + 0.434510i
765765 0 0
766766 3.31534 13.7681i 0.119788 0.497463i
767767 35.6647i 1.28778i
768768 0 0
769769 25.6155 0.923720 0.461860 0.886953i 0.347182π-0.347182\pi
0.461860 + 0.886953i 0.347182π0.347182\pi
770770 3.16499 + 5.72259i 0.114058 + 0.206228i
771771 0 0
772772 −21.2425 + 41.5510i −0.764535 + 1.49545i
773773 2.27678i 0.0818901i 0.999161 + 0.0409450i 0.0130369π0.0130369\pi
−0.999161 + 0.0409450i 0.986963π0.986963\pi
774774 0 0
775775 −41.3686 3.64162i −1.48600 0.130811i
776776 4.02102 4.68860i 0.144346 0.168311i
777777 0 0
778778 −13.6035 3.27569i −0.487707 0.117439i
779779 18.2107i 0.652465i
780780 0 0
781781 25.9396i 0.928192i
782782 −1.73427 + 7.20217i −0.0620174 + 0.257549i
783783 0 0
784784 −14.3423 19.8539i −0.512226 0.709067i
785785 −4.63252 + 4.24264i −0.165342 + 0.151426i
786786 0 0
787787 19.9230i 0.710177i 0.934833 + 0.355088i 0.115549π0.115549\pi
−0.934833 + 0.355088i 0.884451π0.884451\pi
788788 4.48410 8.77102i 0.159739 0.312455i
789789 0 0
790790 1.56489 + 2.82945i 0.0556761 + 0.100667i
791791 −11.7460 −0.417641
792792 0 0
793793 0 0
794794 14.1626 + 3.41032i 0.502611 + 0.121028i
795795 0 0
796796 −16.0540 + 31.4020i −0.569018 + 1.11302i
797797 15.6829i 0.555516i 0.960651 + 0.277758i 0.0895913π0.0895913\pi
−0.960651 + 0.277758i 0.910409π0.910409\pi
798798 0 0
799799 16.6114i 0.587670i
800800 −27.0085 + 8.39900i −0.954893 + 0.296950i
801801 0 0
802802 −0.172919 + 0.718108i −0.00610598 + 0.0253573i
803803 12.3534 0.435942
804804 0 0
805805 4.79741 + 5.23827i 0.169087 + 0.184625i
806806 −9.17104 + 38.0860i −0.323036 + 1.34152i
807807 0 0
808808 −7.08084 6.07263i −0.249103 0.213635i
809809 20.6695i 0.726700i −0.931653 0.363350i 0.881633π-0.881633\pi
0.931653 0.363350i 0.118367π-0.118367\pi
810810 0 0
811811 −49.4773 −1.73738 −0.868691 0.495354i 0.835038π-0.835038\pi
−0.868691 + 0.495354i 0.835038π0.835038\pi
812812 14.0877 + 7.20217i 0.494380 + 0.252747i
813813 0 0
814814 −5.56155 + 23.0963i −0.194932 + 0.809526i
815815 −23.4921 25.6509i −0.822892 0.898513i
816816 0 0
817817 24.2905i 0.849818i
818818 −4.29400 1.03399i −0.150136 0.0361525i
819819 0 0
820820 −6.92781 25.1397i −0.241929 0.877917i
821821 12.1521 0.424110 0.212055 0.977258i 0.431984π-0.431984\pi
0.212055 + 0.977258i 0.431984π0.431984\pi
822822 0 0
823823 −28.6692 −0.999345 −0.499673 0.866214i 0.666546π-0.666546\pi
−0.499673 + 0.866214i 0.666546π0.666546\pi
824824 38.6947 + 33.1851i 1.34799 + 1.15606i
825825 0 0
826826 3.31534 13.7681i 0.115355 0.479055i
827827 −39.1746 −1.36224 −0.681118 0.732174i 0.738506π-0.738506\pi
−0.681118 + 0.732174i 0.738506π0.738506\pi
828828 0 0
829829 4.66410i 0.161991i 0.996714 + 0.0809954i 0.0258099π0.0258099\pi
−0.996714 + 0.0809954i 0.974190π0.974190\pi
830830 −38.9840 + 21.5609i −1.35315 + 0.748389i
831831 0 0
832832 4.06627 + 26.3694i 0.140973 + 0.914194i
833833 9.45514 0.327601
834834 0 0
835835 −14.2462 15.5554i −0.493010 0.538316i
836836 −6.27903 + 12.2820i −0.217165 + 0.424781i
837837 0 0
838838 −10.7365 + 44.5873i −0.370887 + 1.54024i
839839 −24.9381 −0.860959 −0.430479 0.902600i 0.641656π-0.641656\pi
−0.430479 + 0.902600i 0.641656π0.641656\pi
840840 0 0
841841 42.3693 1.46101
842842 −10.1322 + 42.0775i −0.349178 + 1.45009i
843843 0 0
844844 7.12311 + 3.64162i 0.245187 + 0.125350i
845845 −3.09501 + 2.83453i −0.106472 + 0.0975108i
846846 0 0
847847 5.73384 0.197017
848848 16.4990 11.9188i 0.566577 0.409292i
849849 0 0
850850 3.47722 10.3505i 0.119268 0.355019i
851851 25.8040i 0.884551i
852852 0 0
853853 −45.5249 −1.55874 −0.779371 0.626563i 0.784461π-0.784461\pi
−0.779371 + 0.626563i 0.784461π0.784461\pi
854854 0 0
855855 0 0
856856 23.6155 + 20.2530i 0.807162 + 0.692235i
857857 −40.7188 −1.39093 −0.695464 0.718561i 0.744801π-0.744801\pi
−0.695464 + 0.718561i 0.744801π0.744801\pi
858858 0 0
859859 −33.7538 −1.15166 −0.575832 0.817568i 0.695322π-0.695322\pi
−0.575832 + 0.817568i 0.695322π0.695322\pi
860860 −9.24074 33.5329i −0.315107 1.14346i
861861 0 0
862862 −1.98813 0.478739i −0.0677160 0.0163059i
863863 45.6786i 1.55492i 0.628935 + 0.777458i 0.283491π0.283491\pi
−0.628935 + 0.777458i 0.716509π0.716509\pi
864864 0 0
865865 2.56155 + 2.79695i 0.0870954 + 0.0950991i
866866 5.15002 21.3873i 0.175005 0.726770i
867867 0 0
868868 7.08084 13.8503i 0.240339 0.470111i
869869 −2.25801 −0.0765978
870870 0 0
871871 40.5061i 1.37250i
872872 21.9986 25.6509i 0.744967 0.868650i
873873 0 0
874874 −3.50758 + 14.5665i −0.118646 + 0.492718i
875875 −6.36679 8.31118i −0.215237 0.280969i
876876 0 0
877877 46.5766 1.57278 0.786389 0.617731i 0.211948π-0.211948\pi
0.786389 + 0.617731i 0.211948π0.211948\pi
878878 8.92652 37.0706i 0.301256 1.25107i
879879 0 0
880880 3.99579 19.3439i 0.134698 0.652082i
881881 5.83095i 0.196450i 0.995164 + 0.0982249i 0.0313164π0.0313164\pi
−0.995164 + 0.0982249i 0.968684π0.968684\pi
882882 0 0
883883 0 0 1.00000 00
−1.00000 π\pi
884884 −9.17104 4.68860i −0.308455 0.157695i
885885 0 0
886886 −34.4924 8.30571i −1.15880 0.279036i
887887 16.2177i 0.544538i 0.962221 + 0.272269i 0.0877741π0.0877741\pi
−0.962221 + 0.272269i 0.912226π0.912226\pi
888888 0 0
889889 4.38447 0.147050
890890 −20.0127 36.1848i −0.670828 1.21292i
891891 0 0
892892 39.1752 + 20.0279i 1.31168 + 0.670584i
893893 33.5968i 1.12427i
894894 0 0
895895 12.4041 + 13.5440i 0.414623 + 0.452725i
896896 0.881502 10.5577i 0.0294489 0.352709i
897897 0 0
898898 −3.27749 + 13.6110i −0.109371 + 0.454203i
899899 70.1670i 2.34020i
900900 0 0
901901 7.85741i 0.261768i
902902 17.7046 + 4.26324i 0.589499 + 0.141950i
903903 0 0
904904 26.9309 + 23.0963i 0.895707 + 0.768172i
905905 7.04383 + 7.69113i 0.234145 + 0.255662i
906906 0 0
907907 16.5129i 0.548300i 0.961687 + 0.274150i 0.0883965π0.0883965\pi
−0.961687 + 0.274150i 0.911603π0.911603\pi
908908 −5.49966 2.81164i −0.182512 0.0933077i
909909 0 0
910910 −8.64239 + 4.77985i −0.286492 + 0.158451i
911911 36.6842 1.21540 0.607700 0.794167i 0.292092π-0.292092\pi
0.607700 + 0.794167i 0.292092π0.292092\pi
912912 0 0
913913 31.1107i 1.02962i
914914 −4.42702 + 18.3848i −0.146433 + 0.608114i
915915 0 0
916916 −2.38447 + 4.66410i −0.0787852 + 0.154106i
917917 0.580639i 0.0191744i
918918 0 0
919919 30.1554i 0.994735i −0.867540 0.497368i 0.834300π-0.834300\pi
0.867540 0.497368i 0.165700π-0.165700\pi
920920 −0.699266 21.4433i −0.0230541 0.706964i
921921 0 0
922922 −2.54635 0.613157i −0.0838597 0.0201933i
923923 −39.1746 −1.28945
924924 0 0
925925 3.33513 37.8869i 0.109658 1.24571i
926926 −18.1836 4.37857i −0.597549 0.143889i
927927 0 0
928928 −18.1379 44.2135i −0.595407 1.45138i
929929 3.00252i 0.0985096i 0.998786 + 0.0492548i 0.0156846π0.0156846\pi
−0.998786 + 0.0492548i 0.984315π0.984315\pi
930930 0 0
931931 19.1231 0.626734
932932 −36.4248 18.6218i −1.19313 0.609978i
933933 0 0
934934 26.0000 + 6.26075i 0.850746 + 0.204858i
935935 5.15002 + 5.62329i 0.168424 + 0.183901i
936936 0 0
937937 0 0 1.00000 00
−1.00000 π\pi
938938 3.76539 15.6371i 0.122944 0.510570i
939939 0 0
940940 12.7811 + 46.3801i 0.416872 + 1.51275i
941941 −3.29801 −0.107512 −0.0537561 0.998554i 0.517119π-0.517119\pi
−0.0537561 + 0.998554i 0.517119π0.517119\pi
942942 0 0
943943 19.7802 0.644133
944944 −34.6736 + 25.0481i −1.12853 + 0.815245i
945945 0 0
946946 23.6155 + 5.68658i 0.767807 + 0.184887i
947947 32.9979 1.07229 0.536144 0.844126i 0.319880π-0.319880\pi
0.536144 + 0.844126i 0.319880π0.319880\pi
948948 0 0
949949 18.6564i 0.605612i
950950 7.03272 20.9340i 0.228171 0.679187i
951951 0 0
952952 3.10457 + 2.66253i 0.100620 + 0.0862931i
953953 12.5435 0.406323 0.203162 0.979145i 0.434878π-0.434878\pi
0.203162 + 0.979145i 0.434878π0.434878\pi
954954 0 0
955955 21.7538 19.9230i 0.703936 0.644692i
956956 41.8342 + 21.3873i 1.35301 + 0.691715i
957957 0 0
958958 −20.1261 4.84632i −0.650244 0.156578i
959959 −1.44600 −0.0466939
960960 0 0
961961 −37.9848 −1.22532
962962 −34.8806 8.39919i −1.12460 0.270801i
963963 0 0
964964 −7.12311 3.64162i −0.229420 0.117289i
965965 35.2381 + 38.4764i 1.13436 + 1.23860i
966966 0 0
967967 15.0981 0.485522 0.242761 0.970086i 0.421947π-0.421947\pi
0.242761 + 0.970086i 0.421947π0.421947\pi
968968 −13.1463 11.2745i −0.422538 0.362375i
969969 0 0
970970 −3.34225 6.04308i −0.107313 0.194032i
971971 19.8753i 0.637829i −0.947783 0.318915i 0.896682π-0.896682\pi
0.947783 0.318915i 0.103318π-0.103318\pi
972972 0 0
973973 −11.2371 −0.360245
974974 40.5467 + 9.76356i 1.29920 + 0.312845i
975975 0 0
976976 0 0
977977 −37.6305 −1.20390 −0.601952 0.798532i 0.705610π-0.705610\pi
−0.601952 + 0.798532i 0.705610π0.705610\pi
978978 0 0
979979 28.8769 0.922910
980980 −26.3993 + 7.27492i −0.843295 + 0.232389i
981981 0 0
982982 −5.41327 + 22.4805i −0.172744 + 0.717383i
983983 53.0438i 1.69183i −0.533315 0.845917i 0.679054π-0.679054\pi
0.533315 0.845917i 0.320946π-0.320946\pi
984984 0 0
985985 −7.43845 8.12201i −0.237009 0.258789i
986986 17.9361 + 4.31897i 0.571201 + 0.137544i
987987 0 0
988988 −18.5485 9.48274i −0.590107 0.301686i
989989 26.3841 0.838966
990990 0 0
991991 17.6339i 0.560159i −0.959977 0.280080i 0.909639π-0.909639\pi
0.959977 0.280080i 0.0903609π-0.0903609\pi
992992 −43.4686 + 17.8324i −1.38013 + 0.566178i
993993 0 0
994994 15.1231 + 3.64162i 0.479676 + 0.115505i
995995 26.6311 + 29.0784i 0.844264 + 0.921848i
996996 0 0
997997 25.5141 0.808039 0.404019 0.914750i 0.367613π-0.367613\pi
0.404019 + 0.914750i 0.367613π0.367613\pi
998998 −23.2043 5.58755i −0.734519 0.176871i
999999 0 0
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 360.2.m.c.179.2 yes 16
3.2 odd 2 inner 360.2.m.c.179.15 yes 16
4.3 odd 2 1440.2.m.c.719.9 16
5.2 odd 4 1800.2.b.g.251.10 16
5.3 odd 4 1800.2.b.g.251.7 16
5.4 even 2 inner 360.2.m.c.179.16 yes 16
8.3 odd 2 inner 360.2.m.c.179.3 yes 16
8.5 even 2 1440.2.m.c.719.8 16
12.11 even 2 1440.2.m.c.719.7 16
15.2 even 4 1800.2.b.g.251.8 16
15.8 even 4 1800.2.b.g.251.9 16
15.14 odd 2 inner 360.2.m.c.179.1 16
20.3 even 4 7200.2.b.i.4751.12 16
20.7 even 4 7200.2.b.i.4751.7 16
20.19 odd 2 1440.2.m.c.719.12 16
24.5 odd 2 1440.2.m.c.719.10 16
24.11 even 2 inner 360.2.m.c.179.14 yes 16
40.3 even 4 1800.2.b.g.251.12 16
40.13 odd 4 7200.2.b.i.4751.8 16
40.19 odd 2 inner 360.2.m.c.179.13 yes 16
40.27 even 4 1800.2.b.g.251.5 16
40.29 even 2 1440.2.m.c.719.5 16
40.37 odd 4 7200.2.b.i.4751.11 16
60.23 odd 4 7200.2.b.i.4751.9 16
60.47 odd 4 7200.2.b.i.4751.6 16
60.59 even 2 1440.2.m.c.719.6 16
120.29 odd 2 1440.2.m.c.719.11 16
120.53 even 4 7200.2.b.i.4751.5 16
120.59 even 2 inner 360.2.m.c.179.4 yes 16
120.77 even 4 7200.2.b.i.4751.10 16
120.83 odd 4 1800.2.b.g.251.6 16
120.107 odd 4 1800.2.b.g.251.11 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.m.c.179.1 16 15.14 odd 2 inner
360.2.m.c.179.2 yes 16 1.1 even 1 trivial
360.2.m.c.179.3 yes 16 8.3 odd 2 inner
360.2.m.c.179.4 yes 16 120.59 even 2 inner
360.2.m.c.179.13 yes 16 40.19 odd 2 inner
360.2.m.c.179.14 yes 16 24.11 even 2 inner
360.2.m.c.179.15 yes 16 3.2 odd 2 inner
360.2.m.c.179.16 yes 16 5.4 even 2 inner
1440.2.m.c.719.5 16 40.29 even 2
1440.2.m.c.719.6 16 60.59 even 2
1440.2.m.c.719.7 16 12.11 even 2
1440.2.m.c.719.8 16 8.5 even 2
1440.2.m.c.719.9 16 4.3 odd 2
1440.2.m.c.719.10 16 24.5 odd 2
1440.2.m.c.719.11 16 120.29 odd 2
1440.2.m.c.719.12 16 20.19 odd 2
1800.2.b.g.251.5 16 40.27 even 4
1800.2.b.g.251.6 16 120.83 odd 4
1800.2.b.g.251.7 16 5.3 odd 4
1800.2.b.g.251.8 16 15.2 even 4
1800.2.b.g.251.9 16 15.8 even 4
1800.2.b.g.251.10 16 5.2 odd 4
1800.2.b.g.251.11 16 120.107 odd 4
1800.2.b.g.251.12 16 40.3 even 4
7200.2.b.i.4751.5 16 120.53 even 4
7200.2.b.i.4751.6 16 60.47 odd 4
7200.2.b.i.4751.7 16 20.7 even 4
7200.2.b.i.4751.8 16 40.13 odd 4
7200.2.b.i.4751.9 16 60.23 odd 4
7200.2.b.i.4751.10 16 120.77 even 4
7200.2.b.i.4751.11 16 40.37 odd 4
7200.2.b.i.4751.12 16 20.3 even 4