Properties

Label 400.2.bi.c.127.1
Level 400400
Weight 22
Character 400.127
Analytic conductor 3.1943.194
Analytic rank 00
Dimension 1616
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [400,2,Mod(47,400)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(400, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([10, 0, 17]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("400.47");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 400=2452 400 = 2^{4} \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 400.bi (of order 2020, degree 88, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 3.194016080853.19401608085
Analytic rank: 00
Dimension: 1616
Relative dimension: 22 over Q(ζ20)\Q(\zeta_{20})
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: x168x15+32x1464x13+66x1228x11+160x10392x9+419x8++1 x^{16} - 8 x^{15} + 32 x^{14} - 64 x^{13} + 66 x^{12} - 28 x^{11} + 160 x^{10} - 392 x^{9} + 419 x^{8} + \cdots + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a9]\Z[a_1, \ldots, a_{9}]
Coefficient ring index: 24 2^{4}
Twist minimal: yes
Sato-Tate group: SU(2)[C20]\mathrm{SU}(2)[C_{20}]

Embedding invariants

Embedding label 127.1
Root 1.313771.31377i1.31377 - 1.31377i of defining polynomial
Character χ\chi == 400.127
Dual form 400.2.bi.c.63.1

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+(2.58417+1.31670i)q32.23607q5+(1.62753+1.62753i)q7+(3.180884.37811i)q9+(1.12460+1.54787i)q11+(0.951057+0.150633i)q13+(5.778382.94423i)q15+(2.489904.88670i)q17+(1.877515.77838i)q19+(2.062856.34879i)q21+(2.553740.404473i)q23+5.00000q25+(1.09417+6.90832i)q27+(2.65063+0.861243i)q29+(9.866543.20583i)q31+(4.944242.51921i)q33+(3.639273.63927i)q35+(1.58628+10.0154i)q37+(2.259351.64152i)q39+(8.524886.19369i)q41+(6.174216.17421i)q43+(7.11267+9.78975i)q45+(0.4942910.970102i)q47+1.70228iq49+15.9065iq51+(4.264458.36946i)q53+(2.514673.46115i)q55+(12.4602+12.4602i)q57+(7.859625.71035i)q59+(0.975062+0.708424i)q61+(1.94852+12.3025i)q63+(2.126630.336825i)q65+(5.77838+2.94423i)q67+(7.131882.31729i)q69+(8.832702.86992i)q71+(0.212028+1.33869i)q73+(12.9209+6.58350i)q75+(4.349530.688898i)q77+(2.28496+7.03239i)q79+(1.251803.85265i)q81+(6.9715413.6824i)q83+(5.56758+10.9270i)q85+(7.98369+1.26449i)q87+(1.957882.69479i)q89+(1.302721.79303i)q91+(21.2757+21.2757i)q93+(4.19824+12.9209i)q95+(2.239551.14111i)q97+10.3540q99+O(q100)q+(-2.58417 + 1.31670i) q^{3} -2.23607 q^{5} +(-1.62753 + 1.62753i) q^{7} +(3.18088 - 4.37811i) q^{9} +(1.12460 + 1.54787i) q^{11} +(-0.951057 + 0.150633i) q^{13} +(5.77838 - 2.94423i) q^{15} +(2.48990 - 4.88670i) q^{17} +(-1.87751 - 5.77838i) q^{19} +(2.06285 - 6.34879i) q^{21} +(-2.55374 - 0.404473i) q^{23} +5.00000 q^{25} +(-1.09417 + 6.90832i) q^{27} +(2.65063 + 0.861243i) q^{29} +(9.86654 - 3.20583i) q^{31} +(-4.94424 - 2.51921i) q^{33} +(3.63927 - 3.63927i) q^{35} +(1.58628 + 10.0154i) q^{37} +(2.25935 - 1.64152i) q^{39} +(-8.52488 - 6.19369i) q^{41} +(-6.17421 - 6.17421i) q^{43} +(-7.11267 + 9.78975i) q^{45} +(-0.494291 - 0.970102i) q^{47} +1.70228i q^{49} +15.9065i q^{51} +(-4.26445 - 8.36946i) q^{53} +(-2.51467 - 3.46115i) q^{55} +(12.4602 + 12.4602i) q^{57} +(-7.85962 - 5.71035i) q^{59} +(-0.975062 + 0.708424i) q^{61} +(1.94852 + 12.3025i) q^{63} +(2.12663 - 0.336825i) q^{65} +(5.77838 + 2.94423i) q^{67} +(7.13188 - 2.31729i) q^{69} +(-8.83270 - 2.86992i) q^{71} +(-0.212028 + 1.33869i) q^{73} +(-12.9209 + 6.58350i) q^{75} +(-4.34953 - 0.688898i) q^{77} +(-2.28496 + 7.03239i) q^{79} +(-1.25180 - 3.85265i) q^{81} +(6.97154 - 13.6824i) q^{83} +(-5.56758 + 10.9270i) q^{85} +(-7.98369 + 1.26449i) q^{87} +(-1.95788 - 2.69479i) q^{89} +(1.30272 - 1.79303i) q^{91} +(-21.2757 + 21.2757i) q^{93} +(4.19824 + 12.9209i) q^{95} +(2.23955 - 1.14111i) q^{97} +10.3540 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q+20q9+20q21+80q25+20q2920q3340q3712q41+20q4540q53+20q5712q6160q6940q73100q7724q8160q89100q93+80q97+O(q100) 16 q + 20 q^{9} + 20 q^{21} + 80 q^{25} + 20 q^{29} - 20 q^{33} - 40 q^{37} - 12 q^{41} + 20 q^{45} - 40 q^{53} + 20 q^{57} - 12 q^{61} - 60 q^{69} - 40 q^{73} - 100 q^{77} - 24 q^{81} - 60 q^{89} - 100 q^{93}+ \cdots - 80 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/400Z)×\left(\mathbb{Z}/400\mathbb{Z}\right)^\times.

nn 101101 177177 351351
χ(n)\chi(n) 11 e(120)e\left(\frac{1}{20}\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 0
33 −2.58417 + 1.31670i −1.49197 + 0.760198i −0.994244 0.107136i 0.965832π-0.965832\pi
−0.497727 + 0.867334i 0.665832π0.665832\pi
44 0 0
55 −2.23607 −1.00000
66 0 0
77 −1.62753 + 1.62753i −0.615149 + 0.615149i −0.944283 0.329134i 0.893243π-0.893243\pi
0.329134 + 0.944283i 0.393243π0.393243\pi
88 0 0
99 3.18088 4.37811i 1.06029 1.45937i
1010 0 0
1111 1.12460 + 1.54787i 0.339079 + 0.466702i 0.944172 0.329453i 0.106864π-0.106864\pi
−0.605093 + 0.796154i 0.706864π0.706864\pi
1212 0 0
1313 −0.951057 + 0.150633i −0.263776 + 0.0417780i −0.286921 0.957954i 0.592632π-0.592632\pi
0.0231457 + 0.999732i 0.492632π0.492632\pi
1414 0 0
1515 5.77838 2.94423i 1.49197 0.760198i
1616 0 0
1717 2.48990 4.88670i 0.603889 1.18520i −0.363426 0.931623i 0.618393π-0.618393\pi
0.967315 0.253576i 0.0816068π-0.0816068\pi
1818 0 0
1919 −1.87751 5.77838i −0.430730 1.32565i −0.897399 0.441219i 0.854546π-0.854546\pi
0.466669 0.884432i 0.345454π-0.345454\pi
2020 0 0
2121 2.06285 6.34879i 0.450150 1.38542i
2222 0 0
2323 −2.55374 0.404473i −0.532493 0.0843385i −0.115603 0.993296i 0.536880π-0.536880\pi
−0.416890 + 0.908957i 0.636880π0.636880\pi
2424 0 0
2525 5.00000 1.00000
2626 0 0
2727 −1.09417 + 6.90832i −0.210573 + 1.32951i
2828 0 0
2929 2.65063 + 0.861243i 0.492210 + 0.159929i 0.544597 0.838698i 0.316683π-0.316683\pi
−0.0523865 + 0.998627i 0.516683π0.516683\pi
3030 0 0
3131 9.86654 3.20583i 1.77208 0.575784i 0.773749 0.633492i 0.218379π-0.218379\pi
0.998334 + 0.0577079i 0.0183792π0.0183792\pi
3232 0 0
3333 −4.94424 2.51921i −0.860681 0.438539i
3434 0 0
3535 3.63927 3.63927i 0.615149 0.615149i
3636 0 0
3737 1.58628 + 10.0154i 0.260782 + 1.64651i 0.676080 + 0.736829i 0.263678π0.263678\pi
−0.415297 + 0.909686i 0.636322π0.636322\pi
3838 0 0
3939 2.25935 1.64152i 0.361786 0.262853i
4040 0 0
4141 −8.52488 6.19369i −1.33136 0.967292i −0.999715 0.0238886i 0.992395π-0.992395\pi
−0.331648 0.943403i 0.607605π-0.607605\pi
4242 0 0
4343 −6.17421 6.17421i −0.941558 0.941558i 0.0568258 0.998384i 0.481902π-0.481902\pi
−0.998384 + 0.0568258i 0.981902π0.981902\pi
4444 0 0
4545 −7.11267 + 9.78975i −1.06029 + 1.45937i
4646 0 0
4747 −0.494291 0.970102i −0.0720998 0.141504i 0.852143 0.523309i 0.175303π-0.175303\pi
−0.924243 + 0.381805i 0.875303π0.875303\pi
4848 0 0
4949 1.70228i 0.243183i
5050 0 0
5151 15.9065i 2.22736i
5252 0 0
5353 −4.26445 8.36946i −0.585768 1.14963i −0.973676 0.227936i 0.926802π-0.926802\pi
0.387909 0.921698i 0.373198π-0.373198\pi
5454 0 0
5555 −2.51467 3.46115i −0.339079 0.466702i
5656 0 0
5757 12.4602 + 12.4602i 1.65039 + 1.65039i
5858 0 0
5959 −7.85962 5.71035i −1.02323 0.743424i −0.0562914 0.998414i 0.517928π-0.517928\pi
−0.966944 + 0.254991i 0.917928π0.917928\pi
6060 0 0
6161 −0.975062 + 0.708424i −0.124844 + 0.0907044i −0.648455 0.761253i 0.724585π-0.724585\pi
0.523611 + 0.851957i 0.324585π0.324585\pi
6262 0 0
6363 1.94852 + 12.3025i 0.245491 + 1.54997i
6464 0 0
6565 2.12663 0.336825i 0.263776 0.0417780i
6666 0 0
6767 5.77838 + 2.94423i 0.705942 + 0.359695i 0.769819 0.638263i 0.220347π-0.220347\pi
−0.0638771 + 0.997958i 0.520347π0.520347\pi
6868 0 0
6969 7.13188 2.31729i 0.858578 0.278969i
7070 0 0
7171 −8.83270 2.86992i −1.04825 0.340597i −0.266268 0.963899i 0.585790π-0.585790\pi
−0.781981 + 0.623303i 0.785790π0.785790\pi
7272 0 0
7373 −0.212028 + 1.33869i −0.0248160 + 0.156682i −0.996985 0.0776007i 0.975274π-0.975274\pi
0.972169 + 0.234282i 0.0752741π0.0752741\pi
7474 0 0
7575 −12.9209 + 6.58350i −1.49197 + 0.760198i
7676 0 0
7777 −4.34953 0.688898i −0.495675 0.0785072i
7878 0 0
7979 −2.28496 + 7.03239i −0.257078 + 0.791206i 0.736335 + 0.676617i 0.236555π0.236555\pi
−0.993413 + 0.114588i 0.963445π0.963445\pi
8080 0 0
8181 −1.25180 3.85265i −0.139089 0.428072i
8282 0 0
8383 6.97154 13.6824i 0.765225 1.50184i −0.0969830 0.995286i 0.530919π-0.530919\pi
0.862209 0.506554i 0.169081π-0.169081\pi
8484 0 0
8585 −5.56758 + 10.9270i −0.603889 + 1.18520i
8686 0 0
8787 −7.98369 + 1.26449i −0.855941 + 0.135568i
8888 0 0
8989 −1.95788 2.69479i −0.207534 0.285647i 0.692543 0.721377i 0.256490π-0.256490\pi
−0.900077 + 0.435730i 0.856490π0.856490\pi
9090 0 0
9191 1.30272 1.79303i 0.136562 0.187961i
9292 0 0
9393 −21.2757 + 21.2757i −2.20619 + 2.20619i
9494 0 0
9595 4.19824 + 12.9209i 0.430730 + 1.32565i
9696 0 0
9797 2.23955 1.14111i 0.227392 0.115862i −0.336583 0.941654i 0.609271π-0.609271\pi
0.563975 + 0.825792i 0.309271π0.309271\pi
9898 0 0
9999 10.3540 1.04061
100100 0 0
101101 2.89806 0.288367 0.144184 0.989551i 0.453944π-0.453944\pi
0.144184 + 0.989551i 0.453944π0.453944\pi
102102 0 0
103103 −7.80741 + 3.97807i −0.769287 + 0.391971i −0.794152 0.607720i 0.792084π-0.792084\pi
0.0248649 + 0.999691i 0.492084π0.492084\pi
104104 0 0
105105 −4.61267 + 14.1963i −0.450150 + 1.38542i
106106 0 0
107107 11.2441 11.2441i 1.08701 1.08701i 0.0911721 0.995835i 0.470939π-0.470939\pi
0.995835 0.0911721i 0.0290613π-0.0290613\pi
108108 0 0
109109 5.03556 6.93085i 0.482319 0.663855i −0.496629 0.867963i 0.665429π-0.665429\pi
0.978949 + 0.204107i 0.0654292π0.0654292\pi
110110 0 0
111111 −17.2864 23.7927i −1.64076 2.25831i
112112 0 0
113113 −5.16807 + 0.818542i −0.486171 + 0.0770020i −0.394708 0.918806i 0.629154π-0.629154\pi
−0.0914631 + 0.995808i 0.529154π0.529154\pi
114114 0 0
115115 5.71035 + 0.904430i 0.532493 + 0.0843385i
116116 0 0
117117 −2.36571 + 4.64297i −0.218710 + 0.429243i
118118 0 0
119119 3.90087 + 12.0056i 0.357592 + 1.10056i
120120 0 0
121121 2.26799 6.98015i 0.206181 0.634559i
122122 0 0
123123 30.1850 + 4.78083i 2.72169 + 0.431073i
124124 0 0
125125 −11.1803 −1.00000
126126 0 0
127127 2.77391 17.5138i 0.246145 1.55410i −0.486619 0.873614i 0.661770π-0.661770\pi
0.732764 0.680483i 0.238230π-0.238230\pi
128128 0 0
129129 24.0848 + 7.82563i 2.12055 + 0.689008i
130130 0 0
131131 14.5010 4.71166i 1.26696 0.411660i 0.402989 0.915205i 0.367971π-0.367971\pi
0.863969 + 0.503545i 0.167971π0.167971\pi
132132 0 0
133133 12.4602 + 6.34879i 1.08044 + 0.550510i
134134 0 0
135135 2.44664 15.4475i 0.210573 1.32951i
136136 0 0
137137 0.153395 + 0.968498i 0.0131054 + 0.0827443i 0.993374 0.114925i 0.0366628π-0.0366628\pi
−0.980269 + 0.197669i 0.936663π0.936663\pi
138138 0 0
139139 −3.91731 + 2.84609i −0.332262 + 0.241403i −0.741390 0.671075i 0.765833π-0.765833\pi
0.409128 + 0.912477i 0.365833π0.365833\pi
140140 0 0
141141 2.55467 + 1.85607i 0.215142 + 0.156310i
142142 0 0
143143 −1.30272 1.30272i −0.108939 0.108939i
144144 0 0
145145 −5.92699 1.92580i −0.492210 0.159929i
146146 0 0
147147 −2.24140 4.39899i −0.184867 0.362822i
148148 0 0
149149 9.16129i 0.750522i −0.926919 0.375261i 0.877553π-0.877553\pi
0.926919 0.375261i 0.122447π-0.122447\pi
150150 0 0
151151 15.6035i 1.26979i 0.772597 + 0.634897i 0.218957π0.218957\pi
−0.772597 + 0.634897i 0.781043π0.781043\pi
152152 0 0
153153 −13.4744 26.4451i −1.08934 2.13796i
154154 0 0
155155 −22.0622 + 7.16846i −1.77208 + 0.575784i
156156 0 0
157157 −5.05644 5.05644i −0.403548 0.403548i 0.475933 0.879481i 0.342110π-0.342110\pi
−0.879481 + 0.475933i 0.842110π0.842110\pi
158158 0 0
159159 22.0401 + 16.0131i 1.74790 + 1.26992i
160160 0 0
161161 4.81459 3.49801i 0.379443 0.275682i
162162 0 0
163163 0.542005 + 3.42208i 0.0424531 + 0.268038i 0.999780 0.0209686i 0.00667499π-0.00667499\pi
−0.957327 + 0.289007i 0.906675π0.906675\pi
164164 0 0
165165 11.0557 + 5.63314i 0.860681 + 0.438539i
166166 0 0
167167 −12.2007 6.21658i −0.944121 0.481054i −0.0870224 0.996206i 0.527735π-0.527735\pi
−0.857098 + 0.515153i 0.827735π0.827735\pi
168168 0 0
169169 −11.4819 + 3.73070i −0.883224 + 0.286977i
170170 0 0
171171 −31.2705 10.1604i −2.39132 0.776986i
172172 0 0
173173 −0.0270578 + 0.170836i −0.00205716 + 0.0129884i −0.988696 0.149937i 0.952093π-0.952093\pi
0.986638 + 0.162925i 0.0520930π0.0520930\pi
174174 0 0
175175 −8.13766 + 8.13766i −0.615149 + 0.615149i
176176 0 0
177177 27.8294 + 4.40775i 2.09179 + 0.331306i
178178 0 0
179179 −3.01577 + 9.28158i −0.225409 + 0.693738i 0.772841 + 0.634600i 0.218835π0.218835\pi
−0.998250 + 0.0591379i 0.981165π0.981165\pi
180180 0 0
181181 −5.57180 17.1482i −0.414148 1.27462i −0.913010 0.407936i 0.866249π-0.866249\pi
0.498862 0.866681i 0.333751π-0.333751\pi
182182 0 0
183183 1.58694 3.11455i 0.117310 0.230234i
184184 0 0
185185 −3.54702 22.3950i −0.260782 1.64651i
186186 0 0
187187 10.3641 1.64152i 0.757900 0.120040i
188188 0 0
189189 −9.46271 13.0243i −0.688311 0.947379i
190190 0 0
191191 3.50986 4.83091i 0.253965 0.349552i −0.662930 0.748681i 0.730687π-0.730687\pi
0.916895 + 0.399129i 0.130687π0.130687\pi
192192 0 0
193193 5.93294 5.93294i 0.427062 0.427062i −0.460564 0.887626i 0.652353π-0.652353\pi
0.887626 + 0.460564i 0.152353π0.152353\pi
194194 0 0
195195 −5.05207 + 3.67054i −0.361786 + 0.262853i
196196 0 0
197197 9.22957 4.70270i 0.657580 0.335054i −0.0931606 0.995651i 0.529697π-0.529697\pi
0.750740 + 0.660598i 0.229697π0.229697\pi
198198 0 0
199199 −12.1515 −0.861397 −0.430698 0.902496i 0.641733π-0.641733\pi
−0.430698 + 0.902496i 0.641733π0.641733\pi
200200 0 0
201201 −18.8090 −1.32668
202202 0 0
203203 −5.71569 + 2.91229i −0.401163 + 0.204403i
204204 0 0
205205 19.0622 + 13.8495i 1.33136 + 0.967292i
206206 0 0
207207 −9.89399 + 9.89399i −0.687680 + 0.687680i
208208 0 0
209209 6.83277 9.40450i 0.472632 0.650523i
210210 0 0
211211 0.265481 + 0.365404i 0.0182765 + 0.0251554i 0.818057 0.575137i 0.195051π-0.195051\pi
−0.799781 + 0.600292i 0.795051π0.795051\pi
212212 0 0
213213 26.6040 4.21366i 1.82288 0.288715i
214214 0 0
215215 13.8060 + 13.8060i 0.941558 + 0.941558i
216216 0 0
217217 −10.8405 + 21.2757i −0.735902 + 1.44429i
218218 0 0
219219 −1.21474 3.73858i −0.0820844 0.252630i
220220 0 0
221221 −1.63194 + 5.02259i −0.109776 + 0.337856i
222222 0 0
223223 8.45289 + 1.33881i 0.566048 + 0.0896531i 0.432898 0.901443i 0.357491π-0.357491\pi
0.133149 + 0.991096i 0.457491π0.457491\pi
224224 0 0
225225 15.9044 21.8905i 1.06029 1.45937i
226226 0 0
227227 −0.623179 + 3.93460i −0.0413619 + 0.261149i −0.999700 0.0244872i 0.992205π-0.992205\pi
0.958338 + 0.285636i 0.0922047π0.0922047\pi
228228 0 0
229229 −6.21003 2.01776i −0.410371 0.133337i 0.0965543 0.995328i 0.469218π-0.469218\pi
−0.506925 + 0.861990i 0.669218π0.669218\pi
230230 0 0
231231 12.1470 3.94680i 0.799214 0.259680i
232232 0 0
233233 −12.7395 6.49110i −0.834592 0.425246i −0.0161739 0.999869i 0.505149π-0.505149\pi
−0.818418 + 0.574623i 0.805149π0.805149\pi
234234 0 0
235235 1.10527 + 2.16921i 0.0720998 + 0.141504i
236236 0 0
237237 −3.35482 21.1815i −0.217919 1.37589i
238238 0 0
239239 −6.67715 + 4.85123i −0.431909 + 0.313800i −0.782412 0.622762i 0.786011π-0.786011\pi
0.350503 + 0.936562i 0.386011π0.386011\pi
240240 0 0
241241 6.93466 + 5.03832i 0.446700 + 0.324547i 0.788292 0.615302i 0.210966π-0.210966\pi
−0.341591 + 0.939849i 0.610966π0.610966\pi
242242 0 0
243243 −6.52978 6.52978i −0.418885 0.418885i
244244 0 0
245245 3.80642i 0.243183i
246246 0 0
247247 2.65603 + 5.21275i 0.168999 + 0.331680i
248248 0 0
249249 44.5371i 2.82242i
250250 0 0
251251 17.5281i 1.10636i 0.833061 + 0.553182i 0.186586π0.186586\pi
−0.833061 + 0.553182i 0.813414π0.813414\pi
252252 0 0
253253 −2.24586 4.40775i −0.141196 0.277113i
254254 0 0
255255 35.5681i 2.22736i
256256 0 0
257257 −12.1447 12.1447i −0.757568 0.757568i 0.218311 0.975879i 0.429945π-0.429945\pi
−0.975879 + 0.218311i 0.929945π0.929945\pi
258258 0 0
259259 −18.8820 13.7186i −1.17327 0.852432i
260260 0 0
261261 12.2020 8.86524i 0.755282 0.548745i
262262 0 0
263263 −0.382691 2.41621i −0.0235977 0.148990i 0.973076 0.230484i 0.0740309π-0.0740309\pi
−0.996674 + 0.0814938i 0.974031π0.974031\pi
264264 0 0
265265 9.53560 + 18.7147i 0.585768 + 1.14963i
266266 0 0
267267 8.60771 + 4.38585i 0.526783 + 0.268410i
268268 0 0
269269 −7.51890 + 2.44304i −0.458436 + 0.148955i −0.529126 0.848544i 0.677480π-0.677480\pi
0.0706899 + 0.997498i 0.477480π0.477480\pi
270270 0 0
271271 10.8617 + 3.52919i 0.659803 + 0.214383i 0.619731 0.784814i 0.287242π-0.287242\pi
0.0400712 + 0.999197i 0.487242π0.487242\pi
272272 0 0
273273 −1.00555 + 6.34879i −0.0608586 + 0.384246i
274274 0 0
275275 5.62298 + 7.73937i 0.339079 + 0.466702i
276276 0 0
277277 −5.09695 0.807278i −0.306246 0.0485047i 0.00141993 0.999999i 0.499548π-0.499548\pi
−0.307666 + 0.951494i 0.599548π0.599548\pi
278278 0 0
279279 17.3488 53.3941i 1.03865 3.19662i
280280 0 0
281281 0.292927 + 0.901537i 0.0174746 + 0.0537812i 0.959414 0.282003i 0.0909988π-0.0909988\pi
−0.941939 + 0.335784i 0.890999π0.890999\pi
282282 0 0
283283 2.13911 4.19824i 0.127157 0.249559i −0.818648 0.574296i 0.805276π-0.805276\pi
0.945804 + 0.324737i 0.105276π0.105276\pi
284284 0 0
285285 −27.8619 27.8619i −1.65039 1.65039i
286286 0 0
287287 23.9549 3.79409i 1.41402 0.223958i
288288 0 0
289289 −7.68790 10.5815i −0.452229 0.622440i
290290 0 0
291291 −4.28488 + 5.89763i −0.251184 + 0.345725i
292292 0 0
293293 −17.4021 + 17.4021i −1.01664 + 1.01664i −0.0167798 + 0.999859i 0.505341π0.505341\pi
−0.999859 + 0.0167798i 0.994659π0.994659\pi
294294 0 0
295295 17.5746 + 12.7687i 1.02323 + 0.743424i
296296 0 0
297297 −11.9237 + 6.07543i −0.691884 + 0.352532i
298298 0 0
299299 2.48968 0.143982
300300 0 0
301301 20.0974 1.15840
302302 0 0
303303 −7.48907 + 3.81587i −0.430236 + 0.219216i
304304 0 0
305305 2.18031 1.58408i 0.124844 0.0907044i
306306 0 0
307307 −9.15421 + 9.15421i −0.522458 + 0.522458i −0.918313 0.395855i 0.870448π-0.870448\pi
0.395855 + 0.918313i 0.370448π0.370448\pi
308308 0 0
309309 14.9377 20.5600i 0.849778 1.16962i
310310 0 0
311311 14.5504 + 20.0269i 0.825079 + 1.13562i 0.988819 + 0.149120i 0.0476441π0.0476441\pi
−0.163740 + 0.986504i 0.552356π0.552356\pi
312312 0 0
313313 24.1995 3.83282i 1.36784 0.216644i 0.571055 0.820912i 0.306534π-0.306534\pi
0.796781 + 0.604268i 0.206534π0.206534\pi
314314 0 0
315315 −4.35703 27.5092i −0.245491 1.54997i
316316 0 0
317317 5.10607 10.0212i 0.286785 0.562848i −0.702003 0.712174i 0.747711π-0.747711\pi
0.988788 + 0.149326i 0.0477105π0.0477105\pi
318318 0 0
319319 1.64780 + 5.07140i 0.0922589 + 0.283944i
320320 0 0
321321 −14.2515 + 43.8618i −0.795444 + 2.44812i
322322 0 0
323323 −32.9120 5.21275i −1.83127 0.290045i
324324 0 0
325325 −4.75528 + 0.753163i −0.263776 + 0.0417780i
326326 0 0
327327 −3.88689 + 24.5408i −0.214945 + 1.35711i
328328 0 0
329329 2.38335 + 0.774396i 0.131398 + 0.0426938i
330330 0 0
331331 20.0332 6.50919i 1.10113 0.357777i 0.298590 0.954382i 0.403484π-0.403484\pi
0.802536 + 0.596604i 0.203484π0.203484\pi
332332 0 0
333333 48.8941 + 24.9128i 2.67938 + 1.36521i
334334 0 0
335335 −12.9209 6.58350i −0.705942 0.359695i
336336 0 0
337337 −0.744661 4.70160i −0.0405643 0.256113i 0.959070 0.283170i 0.0913862π-0.0913862\pi
−0.999634 + 0.0270577i 0.991386π0.991386\pi
338338 0 0
339339 12.2774 8.92006i 0.666817 0.484471i
340340 0 0
341341 16.0581 + 11.6669i 0.869595 + 0.631798i
342342 0 0
343343 −14.1632 14.1632i −0.764743 0.764743i
344344 0 0
345345 −15.9474 + 5.18162i −0.858578 + 0.278969i
346346 0 0
347347 2.39689 + 4.70415i 0.128672 + 0.252532i 0.946350 0.323143i 0.104739π-0.104739\pi
−0.817679 + 0.575675i 0.804739π0.804739\pi
348348 0 0
349349 1.87772i 0.100512i 0.998736 + 0.0502560i 0.0160037π0.0160037\pi
−0.998736 + 0.0502560i 0.983996π0.983996\pi
350350 0 0
351351 6.73502i 0.359489i
352352 0 0
353353 −2.87675 5.64593i −0.153114 0.300503i 0.801690 0.597740i 0.203935π-0.203935\pi
−0.954804 + 0.297238i 0.903935π0.903935\pi
354354 0 0
355355 19.7505 + 6.41733i 1.04825 + 0.340597i
356356 0 0
357357 −25.8884 25.8884i −1.37016 1.37016i
358358 0 0
359359 −9.96018 7.23649i −0.525678 0.381928i 0.293060 0.956094i 0.405326π-0.405326\pi
−0.818739 + 0.574166i 0.805326π0.805326\pi
360360 0 0
361361 −14.4933 + 10.5300i −0.762806 + 0.554211i
362362 0 0
363363 3.32990 + 21.0242i 0.174774 + 1.10348i
364364 0 0
365365 0.474108 2.99340i 0.0248160 0.156682i
366366 0 0
367367 −8.31332 4.23585i −0.433952 0.221109i 0.223348 0.974739i 0.428301π-0.428301\pi
−0.657300 + 0.753629i 0.728301π0.728301\pi
368368 0 0
369369 −54.2333 + 17.6215i −2.82327 + 0.917336i
370370 0 0
371371 20.5621 + 6.68103i 1.06753 + 0.346862i
372372 0 0
373373 −0.744661 + 4.70160i −0.0385571 + 0.243440i −0.999438 0.0335221i 0.989328π-0.989328\pi
0.960881 + 0.276962i 0.0893276π0.0893276\pi
374374 0 0
375375 28.8919 14.7212i 1.49197 0.760198i
376376 0 0
377377 −2.65063 0.419819i −0.136515 0.0216218i
378378 0 0
379379 −8.61253 + 26.5066i −0.442396 + 1.36155i 0.442918 + 0.896562i 0.353943π0.353943\pi
−0.885314 + 0.464993i 0.846057π0.846057\pi
380380 0 0
381381 15.8922 + 48.9110i 0.814180 + 2.50579i
382382 0 0
383383 −5.76109 + 11.3068i −0.294378 + 0.577750i −0.990067 0.140593i 0.955099π-0.955099\pi
0.695689 + 0.718343i 0.255099π0.255099\pi
384384 0 0
385385 9.72585 + 1.54042i 0.495675 + 0.0785072i
386386 0 0
387387 −46.6708 + 7.39193i −2.37241 + 0.375753i
388388 0 0
389389 3.10772 + 4.27741i 0.157568 + 0.216873i 0.880501 0.474045i 0.157207π-0.157207\pi
−0.722933 + 0.690918i 0.757207π0.757207\pi
390390 0 0
391391 −8.33510 + 11.4723i −0.421524 + 0.580178i
392392 0 0
393393 −31.2692 + 31.2692i −1.57732 + 1.57732i
394394 0 0
395395 5.10933 15.7249i 0.257078 0.791206i
396396 0 0
397397 −24.5503 + 12.5090i −1.23214 + 0.627808i −0.944053 0.329795i 0.893020π-0.893020\pi
−0.288091 + 0.957603i 0.593020π0.593020\pi
398398 0 0
399399 −40.5588 −2.03048
400400 0 0
401401 −32.1362 −1.60481 −0.802403 0.596783i 0.796445π-0.796445\pi
−0.802403 + 0.596783i 0.796445π0.796445\pi
402402 0 0
403403 −8.90073 + 4.53515i −0.443377 + 0.225912i
404404 0 0
405405 2.79911 + 8.61479i 0.139089 + 0.428072i
406406 0 0
407407 −13.7186 + 13.7186i −0.680005 + 0.680005i
408408 0 0
409409 −17.8888 + 24.6219i −0.884546 + 1.21747i 0.0905950 + 0.995888i 0.471123π0.471123\pi
−0.975141 + 0.221585i 0.928877π0.928877\pi
410410 0 0
411411 −1.67162 2.30079i −0.0824549 0.113489i
412412 0 0
413413 22.0855 3.49801i 1.08676 0.172126i
414414 0 0
415415 −15.5888 + 30.5948i −0.765225 + 1.50184i
416416 0 0
417417 6.37555 12.5127i 0.312212 0.612751i
418418 0 0
419419 −5.60088 17.2377i −0.273621 0.842118i −0.989581 0.143977i 0.954011π-0.954011\pi
0.715960 0.698141i 0.245989π-0.245989\pi
420420 0 0
421421 8.04143 24.7490i 0.391915 1.20619i −0.539423 0.842035i 0.681358π-0.681358\pi
0.931338 0.364156i 0.118642π-0.118642\pi
422422 0 0
423423 −5.81949 0.921717i −0.282953 0.0448154i
424424 0 0
425425 12.4495 24.4335i 0.603889 1.18520i
426426 0 0
427427 0.433962 2.73993i 0.0210009 0.132594i
428428 0 0
429429 5.08172 + 1.65115i 0.245348 + 0.0797184i
430430 0 0
431431 −25.3453 + 8.23518i −1.22084 + 0.396675i −0.847388 0.530975i 0.821826π-0.821826\pi
−0.373452 + 0.927650i 0.621826π0.621826\pi
432432 0 0
433433 27.7248 + 14.1265i 1.33237 + 0.678876i 0.967663 0.252246i 0.0811693π-0.0811693\pi
0.364706 + 0.931123i 0.381169π0.381169\pi
434434 0 0
435435 17.8521 2.82749i 0.855941 0.135568i
436436 0 0
437437 2.45748 + 15.5159i 0.117557 + 0.742227i
438438 0 0
439439 7.74387 5.62625i 0.369595 0.268526i −0.387448 0.921891i 0.626643π-0.626643\pi
0.757043 + 0.653365i 0.226643π0.226643\pi
440440 0 0
441441 7.45277 + 5.41476i 0.354894 + 0.257846i
442442 0 0
443443 9.95720 + 9.95720i 0.473081 + 0.473081i 0.902910 0.429829i 0.141426π-0.141426\pi
−0.429829 + 0.902910i 0.641426π0.641426\pi
444444 0 0
445445 4.37794 + 6.02572i 0.207534 + 0.285647i
446446 0 0
447447 12.0627 + 23.6743i 0.570545 + 1.11976i
448448 0 0
449449 24.2916i 1.14639i 0.819419 + 0.573195i 0.194296π0.194296\pi
−0.819419 + 0.573195i 0.805704π0.805704\pi
450450 0 0
451451 20.1608i 0.949337i
452452 0 0
453453 −20.5451 40.3221i −0.965294 1.89450i
454454 0 0
455455 −2.91296 + 4.00935i −0.136562 + 0.187961i
456456 0 0
457457 19.1711 + 19.1711i 0.896786 + 0.896786i 0.995150 0.0983649i 0.0313612π-0.0313612\pi
−0.0983649 + 0.995150i 0.531361π0.531361\pi
458458 0 0
459459 31.0345 + 22.5479i 1.44857 + 1.05245i
460460 0 0
461461 −11.1879 + 8.12849i −0.521073 + 0.378582i −0.817008 0.576626i 0.804369π-0.804369\pi
0.295935 + 0.955208i 0.404369π0.404369\pi
462462 0 0
463463 −4.57144 28.8629i −0.212453 1.34137i −0.831283 0.555850i 0.812393π-0.812393\pi
0.618830 0.785525i 0.287607π-0.287607\pi
464464 0 0
465465 47.5739 47.5739i 2.20619 2.20619i
466466 0 0
467467 −1.17085 0.596577i −0.0541804 0.0276063i 0.426690 0.904398i 0.359679π-0.359679\pi
−0.480871 + 0.876791i 0.659679π0.659679\pi
468468 0 0
469469 −14.1963 + 4.61267i −0.655526 + 0.212993i
470470 0 0
471471 19.7245 + 6.40889i 0.908858 + 0.295306i
472472 0 0
473473 2.61341 16.5004i 0.120165 0.758689i
474474 0 0
475475 −9.38755 28.8919i −0.430730 1.32565i
476476 0 0
477477 −50.2071 7.95202i −2.29883 0.364098i
478478 0 0
479479 1.74144 5.35960i 0.0795684 0.244886i −0.903357 0.428888i 0.858905π-0.858905\pi
0.982926 + 0.184002i 0.0589053π0.0589053\pi
480480 0 0
481481 −3.01728 9.28622i −0.137576 0.423415i
482482 0 0
483483 −7.83590 + 15.3788i −0.356546 + 0.699761i
484484 0 0
485485 −5.00778 + 2.55159i −0.227392 + 0.115862i
486486 0 0
487487 21.6062 3.42208i 0.979070 0.155069i 0.353667 0.935371i 0.384935π-0.384935\pi
0.625403 + 0.780302i 0.284935π0.284935\pi
488488 0 0
489489 −5.90649 8.12959i −0.267101 0.367633i
490490 0 0
491491 24.4969 33.7171i 1.10553 1.52163i 0.277691 0.960671i 0.410431π-0.410431\pi
0.827841 0.560963i 0.189569π-0.189569\pi
492492 0 0
493493 10.8084 10.8084i 0.486788 0.486788i
494494 0 0
495495 −23.1522 −1.04061
496496 0 0
497497 19.0464 9.70461i 0.854347 0.435311i
498498 0 0
499499 31.4385 1.40738 0.703690 0.710508i 0.251535π-0.251535\pi
0.703690 + 0.710508i 0.251535π0.251535\pi
500500 0 0
501501 39.7141 1.77430
502502 0 0
503503 25.4190 12.9516i 1.13338 0.577483i 0.216351 0.976316i 0.430584π-0.430584\pi
0.917024 + 0.398832i 0.130584π0.130584\pi
504504 0 0
505505 −6.48025 −0.288367
506506 0 0
507507 24.7590 24.7590i 1.09959 1.09959i
508508 0 0
509509 −11.3987 + 15.6889i −0.505237 + 0.695400i −0.983107 0.183031i 0.941409π-0.941409\pi
0.477870 + 0.878431i 0.341409π0.341409\pi
510510 0 0
511511 −1.83368 2.52384i −0.0811171 0.111648i
512512 0 0
513513 41.9732 6.64791i 1.85316 0.293512i
514514 0 0
515515 17.4579 8.89524i 0.769287 0.391971i
516516 0 0
517517 0.945717 1.85607i 0.0415926 0.0816300i
518518 0 0
519519 −0.155018 0.477096i −0.00680453 0.0209422i
520520 0 0
521521 −3.07842 + 9.47439i −0.134868 + 0.415081i −0.995569 0.0940291i 0.970025π-0.970025\pi
0.860702 + 0.509110i 0.170025π0.170025\pi
522522 0 0
523523 −6.66792 1.05610i −0.291568 0.0461798i 0.00893708 0.999960i 0.497155π-0.497155\pi
−0.300505 + 0.953780i 0.597155π0.597155\pi
524524 0 0
525525 10.3142 31.7440i 0.450150 1.38542i
526526 0 0
527527 8.90073 56.1970i 0.387722 2.44798i
528528 0 0
529529 −15.5163 5.04155i −0.674621 0.219198i
530530 0 0
531531 −50.0010 + 16.2463i −2.16986 + 0.705030i
532532 0 0
533533 9.04062 + 4.60642i 0.391593 + 0.199526i
534534 0 0
535535 −25.1426 + 25.1426i −1.08701 + 1.08701i
536536 0 0
537537 −4.42780 27.9561i −0.191074 1.20639i
538538 0 0
539539 −2.63492 + 1.91438i −0.113494 + 0.0824582i
540540 0 0
541541 −35.9536 26.1218i −1.54577 1.12306i −0.946587 0.322449i 0.895494π-0.895494\pi
−0.599179 0.800615i 0.704506π-0.704506\pi
542542 0 0
543543 36.9776 + 36.9776i 1.58686 + 1.58686i
544544 0 0
545545 −11.2599 + 15.4979i −0.482319 + 0.663855i
546546 0 0
547547 −13.3756 26.2510i −0.571897 1.12241i −0.978004 0.208586i 0.933114π-0.933114\pi
0.406107 0.913826i 0.366886π-0.366886\pi
548548 0 0
549549 6.52234i 0.278367i
550550 0 0
551551 16.9334i 0.721385i
552552 0 0
553553 −7.72659 15.1643i −0.328568 0.644851i
554554 0 0
555555 38.6536 + 53.2022i 1.64076 + 2.25831i
556556 0 0
557557 8.25814 + 8.25814i 0.349908 + 0.349908i 0.860075 0.510167i 0.170416π-0.170416\pi
−0.510167 + 0.860075i 0.670416π0.670416\pi
558558 0 0
559559 6.80206 + 4.94199i 0.287697 + 0.209024i
560560 0 0
561561 −24.6213 + 17.8884i −1.03951 + 0.755250i
562562 0 0
563563 −2.84609 17.9695i −0.119949 0.757325i −0.972193 0.234181i 0.924759π-0.924759\pi
0.852244 0.523144i 0.175241π-0.175241\pi
564564 0 0
565565 11.5562 1.83032i 0.486171 0.0770020i
566566 0 0
567567 8.30766 + 4.23296i 0.348889 + 0.177768i
568568 0 0
569569 22.1612 7.20061i 0.929046 0.301865i 0.194873 0.980828i 0.437570π-0.437570\pi
0.734172 + 0.678963i 0.237570π0.237570\pi
570570 0 0
571571 −4.48095 1.45595i −0.187522 0.0609296i 0.213751 0.976888i 0.431432π-0.431432\pi
−0.401273 + 0.915959i 0.631432π0.631432\pi
572572 0 0
573573 −2.70922 + 17.1053i −0.113179 + 0.714585i
574574 0 0
575575 −12.7687 2.02237i −0.532493 0.0843385i
576576 0 0
577577 −25.3479 4.01471i −1.05525 0.167135i −0.395380 0.918517i 0.629387π-0.629387\pi
−0.659867 + 0.751383i 0.729387π0.729387\pi
578578 0 0
579579 −7.51982 + 23.1436i −0.312513 + 0.961816i
580580 0 0
581581 10.9222 + 33.6149i 0.453128 + 1.39458i
582582 0 0
583583 8.15908 16.0131i 0.337915 0.663195i
584584 0 0
585585 5.28989 10.3820i 0.218710 0.429243i
586586 0 0
587587 −3.46115 + 0.548193i −0.142857 + 0.0226263i −0.227453 0.973789i 0.573040π-0.573040\pi
0.0845963 + 0.996415i 0.473040π0.473040\pi
588588 0 0
589589 −37.0490 50.9936i −1.52658 2.10116i
590590 0 0
591591 −17.6587 + 24.3052i −0.726383 + 0.999781i
592592 0 0
593593 −9.16670 + 9.16670i −0.376431 + 0.376431i −0.869813 0.493382i 0.835761π-0.835761\pi
0.493382 + 0.869813i 0.335761π0.335761\pi
594594 0 0
595595 −8.72261 26.8454i −0.357592 1.10056i
596596 0 0
597597 31.4015 15.9999i 1.28518 0.654832i
598598 0 0
599599 1.02128 0.0417284 0.0208642 0.999782i 0.493358π-0.493358\pi
0.0208642 + 0.999782i 0.493358π0.493358\pi
600600 0 0
601601 24.7175 1.00825 0.504124 0.863631i 0.331816π-0.331816\pi
0.504124 + 0.863631i 0.331816π0.331816\pi
602602 0 0
603603 31.2705 15.9331i 1.27343 0.648847i
604604 0 0
605605 −5.07138 + 15.6081i −0.206181 + 0.634559i
606606 0 0
607607 15.6989 15.6989i 0.637199 0.637199i −0.312664 0.949864i 0.601222π-0.601222\pi
0.949864 + 0.312664i 0.101222π0.101222\pi
608608 0 0
609609 10.9357 15.0517i 0.443137 0.609926i
610610 0 0
611611 0.616228 + 0.848165i 0.0249299 + 0.0343131i
612612 0 0
613613 24.4360 3.87028i 0.986961 0.156319i 0.357971 0.933733i 0.383469π-0.383469\pi
0.628990 + 0.777413i 0.283469π0.283469\pi
614614 0 0
615615 −67.4957 10.6903i −2.72169 0.431073i
616616 0 0
617617 20.2483 39.7395i 0.815166 1.59985i 0.0151422 0.999885i 0.495180π-0.495180\pi
0.800024 0.599968i 0.204820π-0.204820\pi
618618 0 0
619619 5.01747 + 15.4422i 0.201669 + 0.620674i 0.999834 + 0.0182344i 0.00580452π0.00580452\pi
−0.798165 + 0.602439i 0.794195π0.794195\pi
620620 0 0
621621 5.58846 17.1995i 0.224257 0.690193i
622622 0 0
623623 7.57235 + 1.19934i 0.303380 + 0.0480507i
624624 0 0
625625 25.0000 1.00000
626626 0 0
627627 −5.27413 + 33.2995i −0.210628 + 1.32986i
628628 0 0
629629 52.8917 + 17.1856i 2.10893 + 0.685233i
630630 0 0
631631 −33.0642 + 10.7432i −1.31626 + 0.427680i −0.881210 0.472725i 0.843270π-0.843270\pi
−0.435053 + 0.900405i 0.643270π0.643270\pi
632632 0 0
633633 −1.16718 0.594706i −0.0463911 0.0236374i
634634 0 0
635635 −6.20265 + 39.1620i −0.246145 + 1.55410i
636636 0 0
637637 −0.256419 1.61897i −0.0101597 0.0641458i
638638 0 0
639639 −40.6606 + 29.5416i −1.60851 + 1.16865i
640640 0 0
641641 24.7800 + 18.0037i 0.978751 + 0.711104i 0.957429 0.288668i 0.0932125π-0.0932125\pi
0.0213220 + 0.999773i 0.493212π0.493212\pi
642642 0 0
643643 14.8959 + 14.8959i 0.587438 + 0.587438i 0.936937 0.349499i 0.113648π-0.113648\pi
−0.349499 + 0.936937i 0.613648π0.613648\pi
644644 0 0
645645 −53.8553 17.4986i −2.12055 0.689008i
646646 0 0
647647 6.63750 + 13.0268i 0.260947 + 0.512137i 0.983891 0.178769i 0.0572116π-0.0572116\pi
−0.722944 + 0.690907i 0.757212π0.757212\pi
648648 0 0
649649 18.5875i 0.729625i
650650 0 0
651651 69.2537i 2.71427i
652652 0 0
653653 11.8246 + 23.2070i 0.462731 + 0.908161i 0.997984 + 0.0634688i 0.0202163π0.0202163\pi
−0.535253 + 0.844692i 0.679784π0.679784\pi
654654 0 0
655655 −32.4252 + 10.5356i −1.26696 + 0.411660i
656656 0 0
657657 5.18649 + 5.18649i 0.202344 + 0.202344i
658658 0 0
659659 −24.4969 17.7981i −0.954265 0.693314i −0.00245356 0.999997i 0.500781π-0.500781\pi
−0.951812 + 0.306683i 0.900781π0.900781\pi
660660 0 0
661661 22.1513 16.0939i 0.861587 0.625980i −0.0667289 0.997771i 0.521256π-0.521256\pi
0.928316 + 0.371791i 0.121256π0.121256\pi
662662 0 0
663663 −2.39604 15.1280i −0.0930545 0.587523i
664664 0 0
665665 −27.8619 14.1963i −1.08044 0.550510i
666666 0 0
667667 −6.42069 3.27150i −0.248610 0.126673i
668668 0 0
669669 −23.6065 + 7.67022i −0.912681 + 0.296548i
670670 0 0
671671 −2.19310 0.712582i −0.0846638 0.0275089i
672672 0 0
673673 2.72840 17.2265i 0.105172 0.664031i −0.877626 0.479347i 0.840874π-0.840874\pi
0.982798 0.184684i 0.0591263π-0.0591263\pi
674674 0 0
675675 −5.47085 + 34.5416i −0.210573 + 1.32951i
676676 0 0
677677 −30.9741 4.90581i −1.19043 0.188546i −0.470377 0.882465i 0.655882π-0.655882\pi
−0.720052 + 0.693920i 0.755882π0.755882\pi
678678 0 0
679679 −1.78775 + 5.50212i −0.0686075 + 0.211152i
680680 0 0
681681 −3.57029 10.9882i −0.136814 0.421069i
682682 0 0
683683 −12.0790 + 23.7064i −0.462191 + 0.907101i 0.535836 + 0.844322i 0.319996π0.319996\pi
−0.998027 + 0.0627792i 0.980004π0.980004\pi
684684 0 0
685685 −0.343002 2.16563i −0.0131054 0.0827443i
686686 0 0
687687 18.7046 2.96251i 0.713624 0.113027i
688688 0 0
689689 5.31645 + 7.31746i 0.202541 + 0.278773i
690690 0 0
691691 −12.0424 + 16.5750i −0.458115 + 0.630541i −0.974116 0.226047i 0.927420π-0.927420\pi
0.516002 + 0.856588i 0.327420π0.327420\pi
692692 0 0
693693 −16.8514 + 16.8514i −0.640132 + 0.640132i
694694 0 0
695695 8.75938 6.36406i 0.332262 0.241403i
696696 0 0
697697 −51.4928 + 26.2369i −1.95043 + 0.993793i
698698 0 0
699699 41.4679 1.56846
700700 0 0
701701 0.0556153 0.00210056 0.00105028 0.999999i 0.499666π-0.499666\pi
0.00105028 + 0.999999i 0.499666π0.499666\pi
702702 0 0
703703 54.8943 27.9700i 2.07038 1.05491i
704704 0 0
705705 −5.71241 4.15031i −0.215142 0.156310i
706706 0 0
707707 −4.71668 + 4.71668i −0.177389 + 0.177389i
708708 0 0
709709 26.2864 36.1801i 0.987206 1.35877i 0.0543509 0.998522i 0.482691π-0.482691\pi
0.932855 0.360251i 0.117309π-0.117309\pi
710710 0 0
711711 23.5204 + 32.3730i 0.882082 + 1.21408i
712712 0 0
713713 −26.4933 + 4.19612i −0.992181 + 0.157146i
714714 0 0
715715 2.91296 + 2.91296i 0.108939 + 0.108939i
716716 0 0
717717 10.8673 21.3282i 0.405845 0.796517i
718718 0 0
719719 6.24759 + 19.2281i 0.232996 + 0.717087i 0.997381 + 0.0723273i 0.0230426π0.0230426\pi
−0.764385 + 0.644760i 0.776957π0.776957\pi
720720 0 0
721721 6.23236 19.1812i 0.232105 0.714347i
722722 0 0
723723 −24.5543 3.88902i −0.913184 0.144634i
724724 0 0
725725 13.2532 + 4.30621i 0.492210 + 0.159929i
726726 0 0
727727 1.18294 7.46881i 0.0438729 0.277003i −0.955993 0.293390i 0.905217π-0.905217\pi
0.999866 + 0.0163874i 0.00521652π0.00521652\pi
728728 0 0
729729 37.0298 + 12.0317i 1.37147 + 0.445619i
730730 0 0
731731 −45.5447 + 14.7984i −1.68453 + 0.547337i
732732 0 0
733733 −4.47992 2.28263i −0.165470 0.0843110i 0.369294 0.929313i 0.379599π-0.379599\pi
−0.534764 + 0.845002i 0.679599π0.679599\pi
734734 0 0
735735 5.01191 + 9.83643i 0.184867 + 0.362822i
736736 0 0
737737 1.94105 + 12.2553i 0.0714994 + 0.451429i
738738 0 0
739739 25.4921 18.5211i 0.937743 0.681310i −0.0101332 0.999949i 0.503226π-0.503226\pi
0.947876 + 0.318638i 0.103226π0.103226\pi
740740 0 0
741741 −13.7273 9.97345i −0.504284 0.366384i
742742 0 0
743743 −4.53704 4.53704i −0.166448 0.166448i 0.618968 0.785416i 0.287551π-0.287551\pi
−0.785416 + 0.618968i 0.787551π0.787551\pi
744744 0 0
745745 20.4853i 0.750522i
746746 0 0
747747 −37.7274 74.0443i −1.38037 2.70914i
748748 0 0
749749 36.6002i 1.33734i
750750 0 0
751751 45.1400i 1.64718i −0.567184 0.823591i 0.691967π-0.691967\pi
0.567184 0.823591i 0.308033π-0.308033\pi
752752 0 0
753753 −23.0793 45.2956i −0.841055 1.65066i
754754 0 0
755755 34.8905i 1.26979i
756756 0 0
757757 −11.2118 11.2118i −0.407500 0.407500i 0.473366 0.880866i 0.343039π-0.343039\pi
−0.880866 + 0.473366i 0.843039π0.843039\pi
758758 0 0
759759 11.6074 + 8.43324i 0.421321 + 0.306107i
760760 0 0
761761 16.6208 12.0757i 0.602503 0.437744i −0.244263 0.969709i 0.578546π-0.578546\pi
0.846767 + 0.531965i 0.178546π0.178546\pi
762762 0 0
763763 3.08465 + 19.4757i 0.111672 + 0.705068i
764764 0 0
765765 30.1297 + 59.1329i 1.08934 + 2.13796i
766766 0 0
767767 8.33510 + 4.24695i 0.300963 + 0.153348i
768768 0 0
769769 −22.0022 + 7.14894i −0.793419 + 0.257797i −0.677559 0.735468i 0.736962π-0.736962\pi
−0.115859 + 0.993266i 0.536962π0.536962\pi
770770 0 0
771771 47.3751 + 15.3931i 1.70617 + 0.554369i
772772 0 0
773773 −6.27729 + 39.6333i −0.225779 + 1.42551i 0.570857 + 0.821050i 0.306611π0.306611\pi
−0.796635 + 0.604460i 0.793389π0.793389\pi
774774 0 0
775775 49.3327 16.0292i 1.77208 0.575784i
776776 0 0
777777 66.8577 + 10.5892i 2.39850 + 0.379886i
778778 0 0
779779 −19.7839 + 60.8887i −0.708833 + 2.18157i
780780 0 0
781781 −5.49095 16.8994i −0.196482 0.604708i
782782 0 0
783783 −8.84998 + 17.3691i −0.316273 + 0.620720i
784784 0 0
785785 11.3065 + 11.3065i 0.403548 + 0.403548i
786786 0 0
787787 −14.5622 + 2.30642i −0.519085 + 0.0822150i −0.410479 0.911870i 0.634639π-0.634639\pi
−0.108606 + 0.994085i 0.534639π0.534639\pi
788788 0 0
789789 4.17037 + 5.74002i 0.148469 + 0.204350i
790790 0 0
791791 7.07900 9.74341i 0.251700 0.346436i
792792 0 0
793793 0.820627 0.820627i 0.0291413 0.0291413i
794794 0 0
795795 −49.2833 35.8064i −1.74790 1.26992i
796796 0 0
797797 17.3154 8.82266i 0.613344 0.312515i −0.119580 0.992825i 0.538155π-0.538155\pi
0.732924 + 0.680310i 0.238155π0.238155\pi
798798 0 0
799799 −5.97133 −0.211251
800800 0 0
801801 −18.0258 −0.636911
802802 0 0
803803 −2.31057 + 1.17729i −0.0815382 + 0.0415458i
804804 0 0
805805 −10.7658 + 7.82178i −0.379443 + 0.275682i
806806 0 0
807807 16.2134 16.2134i 0.570738 0.570738i
808808 0 0
809809 12.0110 16.5317i 0.422284 0.581224i −0.543877 0.839165i 0.683044π-0.683044\pi
0.966161 + 0.257941i 0.0830441π0.0830441\pi
810810 0 0
811811 7.49205 + 10.3119i 0.263081 + 0.362101i 0.920039 0.391827i 0.128157π-0.128157\pi
−0.656957 + 0.753928i 0.728157π0.728157\pi
812812 0 0
813813 −32.7154 + 5.18162i −1.14738 + 0.181727i
814814 0 0
815815 −1.21196 7.65201i −0.0424531 0.268038i
816816 0 0
817817 −24.0848 + 47.2691i −0.842621 + 1.65374i
818818 0 0
819819 −3.70631 11.4069i −0.129509 0.398588i
820820 0 0
821821 −13.2734 + 40.8514i −0.463246 + 1.42572i 0.397929 + 0.917416i 0.369729π0.369729\pi
−0.861175 + 0.508309i 0.830271π0.830271\pi
822822 0 0
823823 −14.1588 2.24253i −0.493545 0.0781698i −0.0952992 0.995449i 0.530381π-0.530381\pi
−0.398246 + 0.917279i 0.630381π0.630381\pi
824824 0 0
825825 −24.7212 12.5961i −0.860681 0.438539i
826826 0 0
827827 −3.59722 + 22.7120i −0.125088 + 0.789773i 0.842770 + 0.538274i 0.180923π0.180923\pi
−0.967858 + 0.251499i 0.919077π0.919077\pi
828828 0 0
829829 −53.7472 17.4635i −1.86672 0.606533i −0.992695 0.120648i 0.961503π-0.961503\pi
−0.874022 0.485886i 0.838497π-0.838497\pi
830830 0 0
831831 14.2343 4.62502i 0.493784 0.160440i
832832 0 0
833833 8.31854 + 4.23851i 0.288220 + 0.146856i
834834 0 0
835835 27.2817 + 13.9007i 0.944121 + 0.481054i
836836 0 0
837837 11.3512 + 71.6689i 0.392356 + 2.47724i
838838 0 0
839839 45.5611 33.1021i 1.57294 1.14281i 0.648678 0.761063i 0.275322π-0.275322\pi
0.924266 0.381748i 0.124678π-0.124678\pi
840840 0 0
841841 −17.1774 12.4801i −0.592323 0.430348i
842842 0 0
843843 −1.94403 1.94403i −0.0669559 0.0669559i
844844 0 0
845845 25.6743 8.34210i 0.883224 0.286977i
846846 0 0
847847 7.66920 + 15.0516i 0.263517 + 0.517181i
848848 0 0
849849 13.6655i 0.469000i
850850 0 0
851851 26.2183i 0.898751i
852852 0 0
853853 2.05888 + 4.04078i 0.0704948 + 0.138354i 0.923564 0.383443i 0.125262π-0.125262\pi
−0.853070 + 0.521797i 0.825262π0.825262\pi
854854 0 0
855855 69.9230 + 22.7194i 2.39132 + 0.776986i
856856 0 0
857857 31.5213 + 31.5213i 1.07675 + 1.07675i 0.996799 + 0.0799464i 0.0254749π0.0254749\pi
0.0799464 + 0.996799i 0.474525π0.474525\pi
858858 0 0
859859 −44.9222 32.6379i −1.53272 1.11359i −0.954700 0.297570i 0.903824π-0.903824\pi
−0.578025 0.816019i 0.696176π-0.696176\pi
860860 0 0
861861 −56.9080 + 41.3461i −1.93942 + 1.40907i
862862 0 0
863863 −5.82545 36.7804i −0.198301 1.25202i −0.863113 0.505010i 0.831489π-0.831489\pi
0.664813 0.747010i 0.268511π-0.268511\pi
864864 0 0
865865 0.0605030 0.382001i 0.00205716 0.0129884i
866866 0 0
867867 33.7995 + 17.2217i 1.14789 + 0.584880i
868868 0 0
869869 −13.4549 + 4.37177i −0.456427 + 0.148302i
870870 0 0
871871 −5.93906 1.92972i −0.201238 0.0653860i
872872 0 0
873873 2.12785 13.4347i 0.0720168 0.454696i
874874 0 0
875875 18.1964 18.1964i 0.615149 0.615149i
876876 0 0
877877 33.6877 + 5.33560i 1.13755 + 0.180170i 0.696668 0.717394i 0.254665π-0.254665\pi
0.440884 + 0.897564i 0.354665π0.354665\pi
878878 0 0
879879 22.0566 67.8832i 0.743950 2.28964i
880880 0 0
881881 −10.0398 30.8993i −0.338250 1.04103i −0.965099 0.261885i 0.915656π-0.915656\pi
0.626849 0.779140i 0.284344π-0.284344\pi
882882 0 0
883883 −19.0062 + 37.3018i −0.639611 + 1.25531i 0.312606 + 0.949883i 0.398798π0.398798\pi
−0.952216 + 0.305424i 0.901202π0.901202\pi
884884 0 0
885885 −62.2284 9.85602i −2.09179 0.331306i
886886 0 0
887887 −15.7111 + 2.48840i −0.527528 + 0.0835522i −0.414517 0.910042i 0.636049π-0.636049\pi
−0.113011 + 0.993594i 0.536049π0.536049\pi
888888 0 0
889889 23.9896 + 33.0189i 0.804586 + 1.10742i
890890 0 0
891891 4.55565 6.27031i 0.152620 0.210063i
892892 0 0
893893 −4.67758 + 4.67758i −0.156529 + 0.156529i
894894 0 0
895895 6.74346 20.7542i 0.225409 0.693738i
896896 0 0
897897 −6.43376 + 3.27817i −0.214817 + 0.109455i
898898 0 0
899899 28.9136 0.964321
900900 0 0
901901 −51.5171 −1.71628
902902 0 0
903903 −51.9352 + 26.4623i −1.72830 + 0.880611i
904904 0 0
905905 12.4589 + 38.3446i 0.414148 + 1.27462i
906906 0 0
907907 −26.6340 + 26.6340i −0.884368 + 0.884368i −0.993975 0.109607i 0.965041π-0.965041\pi
0.109607 + 0.993975i 0.465041π0.465041\pi
908908 0 0
909909 9.21837 12.6880i 0.305754 0.420834i
910910 0 0
911911 10.7990 + 14.8635i 0.357786 + 0.492450i 0.949530 0.313676i 0.101560π-0.101560\pi
−0.591744 + 0.806126i 0.701560π0.701560\pi
912912 0 0
913913 29.0188 4.59613i 0.960383 0.152110i
914914 0 0
915915 −3.54852 + 6.96435i −0.117310 + 0.230234i
916916 0 0
917917 −15.9325 + 31.2692i −0.526136 + 1.03260i
918918 0 0
919919 −3.79079 11.6668i −0.125047 0.384854i 0.868863 0.495053i 0.164851π-0.164851\pi
−0.993910 + 0.110199i 0.964851π0.964851\pi
920920 0 0
921921 11.6027 35.7094i 0.382322 1.17666i
922922 0 0
923923 8.83270 + 1.39896i 0.290732 + 0.0460474i
924924 0 0
925925 7.93138 + 50.0768i 0.260782 + 1.64651i
926926 0 0
927927 −7.41801 + 46.8354i −0.243639 + 1.53828i
928928 0 0
929929 −22.8891 7.43712i −0.750967 0.244004i −0.0915697 0.995799i 0.529188π-0.529188\pi
−0.659397 + 0.751795i 0.729188π0.729188\pi
930930 0 0
931931 9.83643 3.19605i 0.322376 0.104746i
932932 0 0
933933 −63.9703 32.5945i −2.09429 1.06710i
934934 0 0
935935 −23.1749 + 3.67054i −0.757900 + 0.120040i
936936 0 0
937937 −4.35021 27.4661i −0.142115 0.897280i −0.950973 0.309275i 0.899914π-0.899914\pi
0.808858 0.588005i 0.200086π-0.200086\pi
938938 0 0
939939 −57.4889 + 41.7682i −1.87608 + 1.36305i
940940 0 0
941941 26.2811 + 19.0943i 0.856739 + 0.622458i 0.926996 0.375071i 0.122382π-0.122382\pi
−0.0702566 + 0.997529i 0.522382π0.522382\pi
942942 0 0
943943 19.2652 + 19.2652i 0.627361 + 0.627361i
944944 0 0
945945 21.1593 + 29.1232i 0.688311 + 0.947379i
946946 0 0
947947 19.6510 + 38.5672i 0.638570 + 1.25327i 0.952708 + 0.303888i 0.0982847π0.0982847\pi
−0.314137 + 0.949378i 0.601715π0.601715\pi
948948 0 0
949949 1.30511i 0.0423656i
950950 0 0
951951 32.6197i 1.05777i
952952 0 0
953953 −17.2271 33.8100i −0.558039 1.09521i −0.981885 0.189479i 0.939320π-0.939320\pi
0.423845 0.905735i 0.360680π-0.360680\pi
954954 0 0
955955 −7.84829 + 10.8022i −0.253965 + 0.349552i
956956 0 0
957957 −10.9357 10.9357i −0.353501 0.353501i
958958 0 0
959959 −1.82592 1.32661i −0.0589619 0.0428383i
960960 0 0
961961 61.9917 45.0396i 1.99973 1.45289i
962962 0 0
963963 −13.4617 84.9940i −0.433798 2.73889i
964964 0 0
965965 −13.2665 + 13.2665i −0.427062 + 0.427062i
966966 0 0
967967 −34.9580 17.8120i −1.12417 0.572795i −0.209832 0.977738i 0.567292π-0.567292\pi
−0.914342 + 0.404942i 0.867292π0.867292\pi
968968 0 0
969969 91.9139 29.8646i 2.95270 0.959391i
970970 0 0
971971 17.7840 + 5.77838i 0.570717 + 0.185437i 0.580138 0.814519i 0.302999π-0.302999\pi
−0.00942088 + 0.999956i 0.502999π0.502999\pi
972972 0 0
973973 1.74344 11.0077i 0.0558922 0.352889i
974974 0 0
975975 11.2968 8.20758i 0.361786 0.262853i
976976 0 0
977977 39.6220 + 6.27550i 1.26762 + 0.200771i 0.753786 0.657119i 0.228225π-0.228225\pi
0.513832 + 0.857891i 0.328225π0.328225\pi
978978 0 0
979979 1.96937 6.06109i 0.0629413 0.193713i
980980 0 0
981981 −14.3265 44.0924i −0.457410 1.40776i
982982 0 0
983983 −14.9499 + 29.3408i −0.476827 + 0.935826i 0.519841 + 0.854263i 0.325991π0.325991\pi
−0.996668 + 0.0815629i 0.974009π0.974009\pi
984984 0 0
985985 −20.6379 + 10.5156i −0.657580 + 0.335054i
986986 0 0
987987 −7.17862 + 1.13698i −0.228498 + 0.0361905i
988988 0 0
989989 13.2701 + 18.2647i 0.421963 + 0.580782i
990990 0 0
991991 −5.75905 + 7.92666i −0.182942 + 0.251799i −0.890632 0.454725i 0.849738π-0.849738\pi
0.707690 + 0.706524i 0.249738π0.249738\pi
992992 0 0
993993 −43.1986 + 43.1986i −1.37087 + 1.37087i
994994 0 0
995995 27.1716 0.861397
996996 0 0
997997 19.0371 9.69989i 0.602911 0.307198i −0.125762 0.992060i 0.540138π-0.540138\pi
0.728673 + 0.684862i 0.240138π0.240138\pi
998998 0 0
999999 −70.9249 −2.24397
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 400.2.bi.c.127.1 yes 16
4.3 odd 2 inner 400.2.bi.c.127.2 yes 16
25.13 odd 20 inner 400.2.bi.c.63.2 yes 16
100.63 even 20 inner 400.2.bi.c.63.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
400.2.bi.c.63.1 16 100.63 even 20 inner
400.2.bi.c.63.2 yes 16 25.13 odd 20 inner
400.2.bi.c.127.1 yes 16 1.1 even 1 trivial
400.2.bi.c.127.2 yes 16 4.3 odd 2 inner