Properties

Label 800.2.bq.d.223.1
Level 800800
Weight 22
Character 800.223
Analytic conductor 6.3886.388
Analytic rank 00
Dimension 6464
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [800,2,Mod(63,800)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(800, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([10, 0, 19]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("800.63");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 800=2552 800 = 2^{5} \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 800.bq (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: 6.388032161706.38803216170
Analytic rank: 00
Dimension: 6464
Relative dimension: 88 over Q(ζ20)\Q(\zeta_{20})
Twist minimal: yes
Sato-Tate group: SU(2)[C20]\mathrm{SU}(2)[C_{20}]

Embedding invariants

Embedding label 223.1
Character χ\chi == 800.223
Dual form 800.2.bq.d.287.1

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+(1.464552.87435i)q3+(1.81895+1.30054i)q5+(2.794692.79469i)q7+(4.35362+5.99224i)q9+(1.604282.20810i)q11+(0.6898994.35585i)q13+(6.40217+3.32360i)q15+(4.55876+2.32280i)q17+(0.743109+2.28705i)q19+(3.93994+12.1259i)q21+(0.877961+5.54323i)q23+(1.617194.73125i)q25+(14.0412+2.22390i)q27+(6.147971.99760i)q29+(3.04391+0.989025i)q31+(3.99731+7.84515i)q33+(8.71801+1.44881i)q35+(6.091920.964866i)q37+(11.5098+8.36239i)q39+(5.32289+3.86731i)q41+(2.827382.82738i)q43+(0.12588616.5617i)q45+(1.101210.561093i)q47+8.62056iq4916.5054iq51+(4.64134+2.36488i)q53+(5.78984+1.93001i)q55+(5.485475.48547i)q57+(0.2147520.156027i)q59+(0.4184950.304055i)q61+(28.91344.57944i)q63+(6.91985+7.02585i)q65+(2.64400+5.18915i)q67+(17.21905.59479i)q69+(2.214120.719412i)q71+(10.47541.65914i)q73+(15.9677+2.28079i)q75+(1.68749+10.6544i)q77+(3.73675+11.5005i)q79+(7.3053022.4834i)q81+(5.80791+2.95928i)q83+(11.3131+1.70377i)q85+(3.26225+20.5970i)q87+(7.20569+9.91778i)q89+(10.2452+14.1013i)q91+(7.30077+7.30077i)q93+(4.326093.19361i)q95+(4.944019.70316i)q97+20.2159q99+O(q100)q+(-1.46455 - 2.87435i) q^{3} +(-1.81895 + 1.30054i) q^{5} +(-2.79469 - 2.79469i) q^{7} +(-4.35362 + 5.99224i) q^{9} +(-1.60428 - 2.20810i) q^{11} +(-0.689899 - 4.35585i) q^{13} +(6.40217 + 3.32360i) q^{15} +(4.55876 + 2.32280i) q^{17} +(0.743109 + 2.28705i) q^{19} +(-3.93994 + 12.1259i) q^{21} +(-0.877961 + 5.54323i) q^{23} +(1.61719 - 4.73125i) q^{25} +(14.0412 + 2.22390i) q^{27} +(-6.14797 - 1.99760i) q^{29} +(-3.04391 + 0.989025i) q^{31} +(-3.99731 + 7.84515i) q^{33} +(8.71801 + 1.44881i) q^{35} +(6.09192 - 0.964866i) q^{37} +(-11.5098 + 8.36239i) q^{39} +(5.32289 + 3.86731i) q^{41} +(2.82738 - 2.82738i) q^{43} +(0.125886 - 16.5617i) q^{45} +(1.10121 - 0.561093i) q^{47} +8.62056i q^{49} -16.5054i q^{51} +(-4.64134 + 2.36488i) q^{53} +(5.78984 + 1.93001i) q^{55} +(5.48547 - 5.48547i) q^{57} +(-0.214752 - 0.156027i) q^{59} +(0.418495 - 0.304055i) q^{61} +(28.9134 - 4.57944i) q^{63} +(6.91985 + 7.02585i) q^{65} +(-2.64400 + 5.18915i) q^{67} +(17.2190 - 5.59479i) q^{69} +(-2.21412 - 0.719412i) q^{71} +(-10.4754 - 1.65914i) q^{73} +(-15.9677 + 2.28079i) q^{75} +(-1.68749 + 10.6544i) q^{77} +(-3.73675 + 11.5005i) q^{79} +(-7.30530 - 22.4834i) q^{81} +(5.80791 + 2.95928i) q^{83} +(-11.3131 + 1.70377i) q^{85} +(3.26225 + 20.5970i) q^{87} +(7.20569 + 9.91778i) q^{89} +(-10.2452 + 14.1013i) q^{91} +(7.30077 + 7.30077i) q^{93} +(-4.32609 - 3.19361i) q^{95} +(-4.94401 - 9.70316i) q^{97} +20.2159 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 64q+2q5+4q7+4q13+22q15+8q1718q1916q21+8q23+40q25+18q2720q31+44q33+38q3510q3736q3916q41+32q43++132q99+O(q100) 64 q + 2 q^{5} + 4 q^{7} + 4 q^{13} + 22 q^{15} + 8 q^{17} - 18 q^{19} - 16 q^{21} + 8 q^{23} + 40 q^{25} + 18 q^{27} - 20 q^{31} + 44 q^{33} + 38 q^{35} - 10 q^{37} - 36 q^{39} - 16 q^{41} + 32 q^{43}+ \cdots + 132 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/800Z)×\left(\mathbb{Z}/800\mathbb{Z}\right)^\times.

nn 101101 351351 577577
χ(n)\chi(n) 11 1-1 e(1120)e\left(\frac{11}{20}\right)

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 −1.46455 2.87435i −0.845561 1.65951i −0.747437 0.664333i 0.768716π-0.768716\pi
−0.0981245 0.995174i 0.531284π-0.531284\pi
44 0 0
55 −1.81895 + 1.30054i −0.813461 + 0.581619i
66 0 0
77 −2.79469 2.79469i −1.05629 1.05629i −0.998318 0.0579747i 0.981536π-0.981536\pi
−0.0579747 0.998318i 0.518464π-0.518464\pi
88 0 0
99 −4.35362 + 5.99224i −1.45121 + 1.99741i
1010 0 0
1111 −1.60428 2.20810i −0.483709 0.665768i 0.495504 0.868606i 0.334984π-0.334984\pi
−0.979212 + 0.202838i 0.934984π0.934984\pi
1212 0 0
1313 −0.689899 4.35585i −0.191343 1.20809i −0.877116 0.480279i 0.840535π-0.840535\pi
0.685772 0.727816i 0.259465π-0.259465\pi
1414 0 0
1515 6.40217 + 3.32360i 1.65303 + 0.858150i
1616 0 0
1717 4.55876 + 2.32280i 1.10566 + 0.563363i 0.908869 0.417082i 0.136947π-0.136947\pi
0.196793 + 0.980445i 0.436947π0.436947\pi
1818 0 0
1919 0.743109 + 2.28705i 0.170481 + 0.524686i 0.999398 0.0346847i 0.0110427π-0.0110427\pi
−0.828917 + 0.559371i 0.811043π0.811043\pi
2020 0 0
2121 −3.93994 + 12.1259i −0.859765 + 2.64609i
2222 0 0
2323 −0.877961 + 5.54323i −0.183067 + 1.15584i 0.709425 + 0.704781i 0.248955π0.248955\pi
−0.892493 + 0.451062i 0.851045π0.851045\pi
2424 0 0
2525 1.61719 4.73125i 0.323438 0.946249i
2626 0 0
2727 14.0412 + 2.22390i 2.70223 + 0.427990i
2828 0 0
2929 −6.14797 1.99760i −1.14165 0.370944i −0.323658 0.946174i 0.604913π-0.604913\pi
−0.817992 + 0.575230i 0.804913π0.804913\pi
3030 0 0
3131 −3.04391 + 0.989025i −0.546702 + 0.177634i −0.569329 0.822110i 0.692797π-0.692797\pi
0.0226272 + 0.999744i 0.492797π0.492797\pi
3232 0 0
3333 −3.99731 + 7.84515i −0.695842 + 1.36567i
3434 0 0
3535 8.71801 + 1.44881i 1.47361 + 0.244893i
3636 0 0
3737 6.09192 0.964866i 1.00151 0.158623i 0.365914 0.930649i 0.380756π-0.380756\pi
0.635591 + 0.772026i 0.280756π0.280756\pi
3838 0 0
3939 −11.5098 + 8.36239i −1.84305 + 1.33905i
4040 0 0
4141 5.32289 + 3.86731i 0.831296 + 0.603972i 0.919926 0.392093i 0.128249π-0.128249\pi
−0.0886296 + 0.996065i 0.528249π0.528249\pi
4242 0 0
4343 2.82738 2.82738i 0.431172 0.431172i −0.457855 0.889027i 0.651382π-0.651382\pi
0.889027 + 0.457855i 0.151382π0.151382\pi
4444 0 0
4545 0.125886 16.5617i 0.0187659 2.46887i
4646 0 0
4747 1.10121 0.561093i 0.160628 0.0818439i −0.371829 0.928301i 0.621269π-0.621269\pi
0.532456 + 0.846458i 0.321269π0.321269\pi
4848 0 0
4949 8.62056i 1.23151i
5050 0 0
5151 16.5054i 2.31121i
5252 0 0
5353 −4.64134 + 2.36488i −0.637537 + 0.324842i −0.742711 0.669612i 0.766460π-0.766460\pi
0.105173 + 0.994454i 0.466460π0.466460\pi
5454 0 0
5555 5.78984 + 1.93001i 0.780702 + 0.260242i
5656 0 0
5757 5.48547 5.48547i 0.726569 0.726569i
5858 0 0
5959 −0.214752 0.156027i −0.0279584 0.0203129i 0.573718 0.819053i 0.305500π-0.305500\pi
−0.601677 + 0.798740i 0.705500π0.705500\pi
6060 0 0
6161 0.418495 0.304055i 0.0535828 0.0389302i −0.560671 0.828038i 0.689457π-0.689457\pi
0.614254 + 0.789108i 0.289457π0.289457\pi
6262 0 0
6363 28.9134 4.57944i 3.64275 0.576955i
6464 0 0
6565 6.91985 + 7.02585i 0.858301 + 0.871449i
6666 0 0
6767 −2.64400 + 5.18915i −0.323017 + 0.633956i −0.994225 0.107313i 0.965775π-0.965775\pi
0.671209 + 0.741268i 0.265775π0.265775\pi
6868 0 0
6969 17.2190 5.59479i 2.07292 0.673534i
7070 0 0
7171 −2.21412 0.719412i −0.262768 0.0853785i 0.174670 0.984627i 0.444114π-0.444114\pi
−0.437438 + 0.899249i 0.644114π0.644114\pi
7272 0 0
7373 −10.4754 1.65914i −1.22605 0.194188i −0.490371 0.871514i 0.663139π-0.663139\pi
−0.735683 + 0.677326i 0.763139π0.763139\pi
7474 0 0
7575 −15.9677 + 2.28079i −1.84379 + 0.263363i
7676 0 0
7777 −1.68749 + 10.6544i −0.192308 + 1.21418i
7878 0 0
7979 −3.73675 + 11.5005i −0.420418 + 1.29391i 0.486897 + 0.873459i 0.338129π0.338129\pi
−0.907314 + 0.420453i 0.861871π0.861871\pi
8080 0 0
8181 −7.30530 22.4834i −0.811700 2.49816i
8282 0 0
8383 5.80791 + 2.95928i 0.637501 + 0.324823i 0.742696 0.669629i 0.233547π-0.233547\pi
−0.105195 + 0.994452i 0.533547π0.533547\pi
8484 0 0
8585 −11.3131 + 1.70377i −1.22708 + 0.184800i
8686 0 0
8787 3.26225 + 20.5970i 0.349750 + 2.20823i
8888 0 0
8989 7.20569 + 9.91778i 0.763802 + 1.05128i 0.996888 + 0.0788270i 0.0251175π0.0251175\pi
−0.233086 + 0.972456i 0.574883π0.574883\pi
9090 0 0
9191 −10.2452 + 14.1013i −1.07399 + 1.47822i
9292 0 0
9393 7.30077 + 7.30077i 0.757055 + 0.757055i
9494 0 0
9595 −4.32609 3.19361i −0.443847 0.327657i
9696 0 0
9797 −4.94401 9.70316i −0.501988 0.985206i −0.993446 0.114305i 0.963536π-0.963536\pi
0.491458 0.870901i 0.336464π-0.336464\pi
9898 0 0
9999 20.2159 2.03177
100100 0 0
101101 −5.20311 −0.517729 −0.258864 0.965914i 0.583348π-0.583348\pi
−0.258864 + 0.965914i 0.583348π0.583348\pi
102102 0 0
103103 −3.77970 7.41808i −0.372425 0.730925i 0.626394 0.779506i 0.284530π-0.284530\pi
−0.998819 + 0.0485812i 0.984530π0.984530\pi
104104 0 0
105105 −8.60363 27.1805i −0.839628 2.65254i
106106 0 0
107107 −12.3186 12.3186i −1.19088 1.19088i −0.976819 0.214065i 0.931330π-0.931330\pi
−0.214065 0.976819i 0.568670π-0.568670\pi
108108 0 0
109109 −3.85539 + 5.30648i −0.369279 + 0.508269i −0.952705 0.303898i 0.901712π-0.901712\pi
0.583426 + 0.812166i 0.301712π0.301712\pi
110110 0 0
111111 −11.6953 16.0972i −1.11007 1.52788i
112112 0 0
113113 0.987363 + 6.23396i 0.0928833 + 0.586442i 0.989601 + 0.143839i 0.0459448π0.0459448\pi
−0.896718 + 0.442603i 0.854055π0.854055\pi
114114 0 0
115115 −5.61222 11.2247i −0.523342 1.04671i
116116 0 0
117117 29.1048 + 14.8297i 2.69074 + 1.37100i
118118 0 0
119119 −6.24880 19.2318i −0.572827 1.76298i
120120 0 0
121121 1.09718 3.37679i 0.0997441 0.306981i
122122 0 0
123123 3.32033 20.9637i 0.299384 1.89024i
124124 0 0
125125 3.21157 + 10.7091i 0.287252 + 0.957855i
126126 0 0
127127 2.85861 + 0.452759i 0.253660 + 0.0401758i 0.281970 0.959423i 0.409012π-0.409012\pi
−0.0283092 + 0.999599i 0.509012π0.509012\pi
128128 0 0
129129 −12.2677 3.98603i −1.08012 0.350951i
130130 0 0
131131 2.76968 0.899925i 0.241988 0.0786268i −0.185512 0.982642i 0.559394π-0.559394\pi
0.427500 + 0.904015i 0.359394π0.359394\pi
132132 0 0
133133 4.31485 8.46836i 0.374145 0.734300i
134134 0 0
135135 −28.4325 + 14.2159i −2.44708 + 1.22351i
136136 0 0
137137 −3.12844 + 0.495496i −0.267280 + 0.0423331i −0.288636 0.957439i 0.593202π-0.593202\pi
0.0213557 + 0.999772i 0.493202π0.493202\pi
138138 0 0
139139 −18.4701 + 13.4193i −1.56661 + 1.13821i −0.636298 + 0.771444i 0.719535π0.719535\pi
−0.930313 + 0.366766i 0.880465π0.880465\pi
140140 0 0
141141 −3.22556 2.34350i −0.271641 0.197359i
142142 0 0
143143 −8.51137 + 8.51137i −0.711756 + 0.711756i
144144 0 0
145145 13.7808 4.36214i 1.14444 0.362256i
146146 0 0
147147 24.7785 12.6253i 2.04370 1.04132i
148148 0 0
149149 7.69000i 0.629989i 0.949094 + 0.314994i 0.102003π0.102003\pi
−0.949094 + 0.314994i 0.897997π0.897997\pi
150150 0 0
151151 7.50362i 0.610636i −0.952250 0.305318i 0.901237π-0.901237\pi
0.952250 0.305318i 0.0987627π-0.0987627\pi
152152 0 0
153153 −33.7659 + 17.2046i −2.72981 + 1.39091i
154154 0 0
155155 4.25046 5.75771i 0.341405 0.462471i
156156 0 0
157157 −12.3164 + 12.3164i −0.982952 + 0.982952i −0.999857 0.0169050i 0.994619π-0.994619\pi
0.0169050 + 0.999857i 0.494619π0.494619\pi
158158 0 0
159159 13.5950 + 9.87735i 1.07815 + 0.783324i
160160 0 0
161161 17.9452 13.0380i 1.41428 1.02754i
162162 0 0
163163 −13.1012 + 2.07502i −1.02616 + 0.162529i −0.646753 0.762700i 0.723874π-0.723874\pi
−0.379412 + 0.925228i 0.623874π0.623874\pi
164164 0 0
165165 −2.93202 19.4686i −0.228257 1.51563i
166166 0 0
167167 −2.99484 + 5.87769i −0.231747 + 0.454830i −0.977370 0.211539i 0.932152π-0.932152\pi
0.745622 + 0.666369i 0.232152π0.232152\pi
168168 0 0
169169 −6.13372 + 1.99297i −0.471824 + 0.153305i
170170 0 0
171171 −16.9398 5.50407i −1.29542 0.420907i
172172 0 0
173173 9.68291 + 1.53362i 0.736178 + 0.116599i 0.513254 0.858237i 0.328440π-0.328440\pi
0.222924 + 0.974836i 0.428440π0.428440\pi
174174 0 0
175175 −17.7419 + 8.70281i −1.34116 + 0.657870i
176176 0 0
177177 −0.133959 + 0.845783i −0.0100690 + 0.0635729i
178178 0 0
179179 −4.31387 + 13.2767i −0.322433 + 0.992348i 0.650152 + 0.759804i 0.274705π0.274705\pi
−0.972586 + 0.232544i 0.925295π0.925295\pi
180180 0 0
181181 3.79297 + 11.6736i 0.281929 + 0.867688i 0.987302 + 0.158852i 0.0507794π0.0507794\pi
−0.705373 + 0.708836i 0.749221π0.749221\pi
182182 0 0
183183 −1.48687 0.757598i −0.109913 0.0560032i
184184 0 0
185185 −9.82608 + 9.67783i −0.722428 + 0.711528i
186186 0 0
187187 −2.18454 13.7926i −0.159749 1.00862i
188188 0 0
189189 −33.0256 45.4558i −2.40226 3.30642i
190190 0 0
191191 5.62078 7.73634i 0.406705 0.559782i −0.555706 0.831379i 0.687552π-0.687552\pi
0.962411 + 0.271597i 0.0875518π0.0875518\pi
192192 0 0
193193 −5.15678 5.15678i −0.371193 0.371193i 0.496719 0.867912i 0.334538π-0.334538\pi
−0.867912 + 0.496719i 0.834538π0.834538\pi
194194 0 0
195195 10.0603 30.1798i 0.720430 2.16122i
196196 0 0
197197 −1.57698 3.09500i −0.112355 0.220510i 0.827981 0.560756i 0.189490π-0.189490\pi
−0.940336 + 0.340246i 0.889490π0.889490\pi
198198 0 0
199199 −7.93232 −0.562307 −0.281154 0.959663i 0.590717π-0.590717\pi
−0.281154 + 0.959663i 0.590717π0.590717\pi
200200 0 0
201201 18.7877 1.32518
202202 0 0
203203 11.5990 + 22.7643i 0.814090 + 1.59774i
204204 0 0
205205 −14.7117 0.111824i −1.02751 0.00781012i
206206 0 0
207207 −29.3940 29.3940i −2.04303 2.04303i
208208 0 0
209209 3.85790 5.30994i 0.266856 0.367296i
210210 0 0
211211 12.3726 + 17.0295i 0.851768 + 1.17236i 0.983471 + 0.181068i 0.0579555π0.0579555\pi
−0.131703 + 0.991289i 0.542045π0.542045\pi
212212 0 0
213213 1.17486 + 7.41778i 0.0805002 + 0.508258i
214214 0 0
215215 −1.46576 + 8.82001i −0.0999638 + 0.601519i
216216 0 0
217217 11.2708 + 5.74275i 0.765111 + 0.389843i
218218 0 0
219219 10.5729 + 32.5399i 0.714448 + 2.19884i
220220 0 0
221221 6.97270 21.4598i 0.469035 1.44354i
222222 0 0
223223 −1.07738 + 6.80229i −0.0721465 + 0.455515i 0.924996 + 0.379976i 0.124068π0.124068\pi
−0.997143 + 0.0755389i 0.975932π0.975932\pi
224224 0 0
225225 21.3101 + 30.2886i 1.42067 + 2.01924i
226226 0 0
227227 −16.2657 2.57623i −1.07959 0.170991i −0.408791 0.912628i 0.634050π-0.634050\pi
−0.670801 + 0.741637i 0.734050π0.734050\pi
228228 0 0
229229 −11.5696 3.75919i −0.764541 0.248414i −0.0993145 0.995056i 0.531665π-0.531665\pi
−0.665226 + 0.746642i 0.731665π0.731665\pi
230230 0 0
231231 33.0960 10.7535i 2.17756 0.707531i
232232 0 0
233233 12.0215 23.5935i 0.787552 1.54566i −0.0496507 0.998767i 0.515811π-0.515811\pi
0.837203 0.546892i 0.184189π-0.184189\pi
234234 0 0
235235 −1.27332 + 2.45277i −0.0830624 + 0.160001i
236236 0 0
237237 38.5293 6.10244i 2.50275 0.396396i
238238 0 0
239239 17.2941 12.5649i 1.11866 0.812758i 0.134659 0.990892i 0.457006π-0.457006\pi
0.984006 + 0.178134i 0.0570062π0.0570062\pi
240240 0 0
241241 11.6753 + 8.48263i 0.752075 + 0.546414i 0.896469 0.443106i 0.146123π-0.146123\pi
−0.144394 + 0.989520i 0.546123π0.546123\pi
242242 0 0
243243 −23.7690 + 23.7690i −1.52479 + 1.52479i
244244 0 0
245245 −11.2114 15.6804i −0.716269 1.00178i
246246 0 0
247247 9.44939 4.81471i 0.601250 0.306352i
248248 0 0
249249 21.0280i 1.33260i
250250 0 0
251251 8.72581i 0.550768i 0.961334 + 0.275384i 0.0888050π0.0888050\pi
−0.961334 + 0.275384i 0.911195π0.911195\pi
252252 0 0
253253 13.6485 6.95426i 0.858074 0.437211i
254254 0 0
255255 21.4659 + 30.0225i 1.34424 + 1.88008i
256256 0 0
257257 −11.5328 + 11.5328i −0.719397 + 0.719397i −0.968482 0.249084i 0.919870π-0.919870\pi
0.249084 + 0.968482i 0.419870π0.419870\pi
258258 0 0
259259 −19.7215 14.3285i −1.22544 0.890331i
260260 0 0
261261 38.7360 28.1433i 2.39770 1.74203i
262262 0 0
263263 18.1552 2.87549i 1.11949 0.177311i 0.430860 0.902419i 0.358210π-0.358210\pi
0.688635 + 0.725108i 0.258210π0.258210\pi
264264 0 0
265265 5.36677 10.3379i 0.329678 0.635050i
266266 0 0
267267 17.9541 35.2368i 1.09877 2.15646i
268268 0 0
269269 −11.0677 + 3.59613i −0.674812 + 0.219260i −0.626323 0.779564i 0.715441π-0.715441\pi
−0.0484895 + 0.998824i 0.515441π0.515441\pi
270270 0 0
271271 −7.19982 2.33936i −0.437358 0.142106i 0.0820585 0.996628i 0.473851π-0.473851\pi
−0.519416 + 0.854521i 0.673851π0.673851\pi
272272 0 0
273273 55.5367 + 8.79615i 3.36123 + 0.532367i
274274 0 0
275275 −13.0415 + 4.01932i −0.786433 + 0.242374i
276276 0 0
277277 3.99596 25.2295i 0.240094 1.51589i −0.513234 0.858249i 0.671553π-0.671553\pi
0.753328 0.657645i 0.228447π-0.228447\pi
278278 0 0
279279 7.32552 22.5456i 0.438568 1.34977i
280280 0 0
281281 −4.41297 13.5817i −0.263256 0.810217i −0.992090 0.125527i 0.959938π-0.959938\pi
0.728835 0.684690i 0.240062π-0.240062\pi
282282 0 0
283283 1.41981 + 0.723431i 0.0843991 + 0.0430035i 0.495681 0.868505i 0.334919π-0.334919\pi
−0.411281 + 0.911508i 0.634919π0.634919\pi
284284 0 0
285285 −2.84375 + 17.1119i −0.168449 + 1.01362i
286286 0 0
287287 −4.06791 25.6837i −0.240121 1.51606i
288288 0 0
289289 5.39453 + 7.42494i 0.317325 + 0.436761i
290290 0 0
291291 −20.6495 + 28.4216i −1.21050 + 1.66610i
292292 0 0
293293 12.2420 + 12.2420i 0.715187 + 0.715187i 0.967615 0.252429i 0.0812294π-0.0812294\pi
−0.252429 + 0.967615i 0.581229π0.581229\pi
294294 0 0
295295 0.593543 + 0.00451154i 0.0345574 + 0.000262672i
296296 0 0
297297 −17.6154 34.5721i −1.02215 2.00608i
298298 0 0
299299 24.7512 1.43140
300300 0 0
301301 −15.8033 −0.910888
302302 0 0
303303 7.62024 + 14.9556i 0.437771 + 0.859175i
304304 0 0
305305 −0.365789 + 1.09733i −0.0209450 + 0.0628330i
306306 0 0
307307 10.0589 + 10.0589i 0.574089 + 0.574089i 0.933269 0.359179i 0.116943π-0.116943\pi
−0.359179 + 0.933269i 0.616943π0.616943\pi
308308 0 0
309309 −15.7866 + 21.7284i −0.898068 + 1.23608i
310310 0 0
311311 6.07301 + 8.35878i 0.344369 + 0.473983i 0.945711 0.325009i 0.105367π-0.105367\pi
−0.601342 + 0.798991i 0.705367π0.705367\pi
312312 0 0
313313 2.55644 + 16.1407i 0.144498 + 0.912326i 0.948288 + 0.317412i 0.102814π0.102814\pi
−0.803789 + 0.594914i 0.797186π0.797186\pi
314314 0 0
315315 −46.6365 + 45.9329i −2.62767 + 2.58802i
316316 0 0
317317 −29.7982 15.1829i −1.67363 0.852758i −0.992727 0.120387i 0.961586π-0.961586\pi
−0.680906 0.732371i 0.738414π-0.738414\pi
318318 0 0
319319 5.45217 + 16.7801i 0.305263 + 0.939503i
320320 0 0
321321 −17.3667 + 53.4493i −0.969316 + 2.98325i
322322 0 0
323323 −1.92472 + 12.1522i −0.107095 + 0.676168i
324324 0 0
325325 −21.7243 3.78016i −1.20505 0.209686i
326326 0 0
327327 20.8991 + 3.31009i 1.15572 + 0.183049i
328328 0 0
329329 −4.64561 1.50945i −0.256121 0.0832187i
330330 0 0
331331 −3.88228 + 1.26143i −0.213390 + 0.0693345i −0.413761 0.910386i 0.635785π-0.635785\pi
0.200371 + 0.979720i 0.435785π0.435785\pi
332332 0 0
333333 −20.7402 + 40.7049i −1.13655 + 2.23061i
334334 0 0
335335 −1.93937 12.8775i −0.105959 0.703571i
336336 0 0
337337 −28.5845 + 4.52734i −1.55710 + 0.246620i −0.874811 0.484465i 0.839014π-0.839014\pi
−0.682286 + 0.731085i 0.739014π0.739014\pi
338338 0 0
339339 16.4726 11.9680i 0.894666 0.650013i
340340 0 0
341341 7.06715 + 5.13458i 0.382708 + 0.278053i
342342 0 0
343343 4.52896 4.52896i 0.244541 0.244541i
344344 0 0
345345 −24.0443 + 32.5707i −1.29450 + 1.75355i
346346 0 0
347347 23.8682 12.1615i 1.28131 0.652862i 0.325141 0.945666i 0.394588π-0.394588\pi
0.956173 + 0.292804i 0.0945883π0.0945883\pi
348348 0 0
349349 9.07661i 0.485860i −0.970044 0.242930i 0.921892π-0.921892\pi
0.970044 0.242930i 0.0781085π-0.0781085\pi
350350 0 0
351351 62.6955i 3.34644i
352352 0 0
353353 −2.80378 + 1.42860i −0.149230 + 0.0760364i −0.527011 0.849859i 0.676687π-0.676687\pi
0.377781 + 0.925895i 0.376687π0.376687\pi
354354 0 0
355355 4.96301 1.57098i 0.263409 0.0833788i
356356 0 0
357357 −46.1273 + 46.1273i −2.44132 + 2.44132i
358358 0 0
359359 −16.3120 11.8514i −0.860914 0.625490i 0.0672196 0.997738i 0.478587π-0.478587\pi
−0.928133 + 0.372248i 0.878587π0.878587\pi
360360 0 0
361361 10.6929 7.76886i 0.562785 0.408887i
362362 0 0
363363 −11.3130 + 1.79180i −0.593776 + 0.0940449i
364364 0 0
365365 21.2121 10.6058i 1.11029 0.555132i
366366 0 0
367367 −15.3915 + 30.2076i −0.803431 + 1.57682i 0.0133758 + 0.999911i 0.495742π0.495742\pi
−0.816807 + 0.576911i 0.804258π0.804258\pi
368368 0 0
369369 −46.3477 + 15.0593i −2.41276 + 0.783954i
370370 0 0
371371 19.5802 + 6.36200i 1.01655 + 0.330298i
372372 0 0
373373 −0.0157471 0.00249409i −0.000815354 0.000129139i 0.156027 0.987753i 0.450131π-0.450131\pi
−0.156842 + 0.987624i 0.550131π0.550131\pi
374374 0 0
375375 26.0783 24.9153i 1.34668 1.28662i
376376 0 0
377377 −4.45975 + 28.1578i −0.229689 + 1.45020i
378378 0 0
379379 9.53680 29.3513i 0.489873 1.50767i −0.334925 0.942245i 0.608711π-0.608711\pi
0.824798 0.565428i 0.191289π-0.191289\pi
380380 0 0
381381 −2.88520 8.87973i −0.147813 0.454922i
382382 0 0
383383 18.6404 + 9.49776i 0.952480 + 0.485313i 0.859939 0.510396i 0.170501π-0.170501\pi
0.0925405 + 0.995709i 0.470501π0.470501\pi
384384 0 0
385385 −10.7870 21.5746i −0.549758 1.09954i
386386 0 0
387387 4.63301 + 29.2517i 0.235509 + 1.48695i
388388 0 0
389389 20.0307 + 27.5699i 1.01560 + 1.39785i 0.915245 + 0.402898i 0.131997π0.131997\pi
0.100353 + 0.994952i 0.468003π0.468003\pi
390390 0 0
391391 −16.8782 + 23.2309i −0.853570 + 1.17484i
392392 0 0
393393 −6.64305 6.64305i −0.335098 0.335098i
394394 0 0
395395 −8.15993 25.7788i −0.410571 1.29707i
396396 0 0
397397 0.451213 + 0.885556i 0.0226457 + 0.0444448i 0.902052 0.431627i 0.142060π-0.142060\pi
−0.879406 + 0.476072i 0.842060π0.842060\pi
398398 0 0
399399 −30.6604 −1.53494
400400 0 0
401401 18.8940 0.943521 0.471761 0.881727i 0.343619π-0.343619\pi
0.471761 + 0.881727i 0.343619π0.343619\pi
402402 0 0
403403 6.40803 + 12.5765i 0.319207 + 0.626478i
404404 0 0
405405 42.5286 + 31.3955i 2.11326 + 1.56005i
406406 0 0
407407 −11.9037 11.9037i −0.590043 0.590043i
408408 0 0
409409 22.9396 31.5737i 1.13429 1.56122i 0.354638 0.935004i 0.384604π-0.384604\pi
0.779652 0.626213i 0.215396π-0.215396\pi
410410 0 0
411411 6.00600 + 8.26654i 0.296254 + 0.407759i
412412 0 0
413413 0.164120 + 1.03621i 0.00807580 + 0.0509886i
414414 0 0
415415 −14.4130 + 2.17063i −0.707506 + 0.106552i
416416 0 0
417417 65.6222 + 33.4362i 3.21353 + 1.63738i
418418 0 0
419419 4.82220 + 14.8412i 0.235580 + 0.725041i 0.997044 + 0.0768334i 0.0244810π0.0244810\pi
−0.761464 + 0.648207i 0.775519π0.775519\pi
420420 0 0
421421 −4.85470 + 14.9412i −0.236604 + 0.728192i 0.760301 + 0.649571i 0.225052π0.225052\pi
−0.996905 + 0.0786205i 0.974948π0.974948\pi
422422 0 0
423423 −1.43203 + 9.04148i −0.0696277 + 0.439612i
424424 0 0
425425 18.3622 17.8122i 0.890695 0.864019i
426426 0 0
427427 −2.01930 0.319826i −0.0977209 0.0154775i
428428 0 0
429429 36.9300 + 11.9993i 1.78300 + 0.579331i
430430 0 0
431431 −34.4523 + 11.1942i −1.65951 + 0.539207i −0.980769 0.195173i 0.937473π-0.937473\pi
−0.678738 + 0.734380i 0.737473π0.737473\pi
432432 0 0
433433 −4.66192 + 9.14954i −0.224038 + 0.439699i −0.975476 0.220104i 0.929360π-0.929360\pi
0.751439 + 0.659803i 0.229360π0.229360\pi
434434 0 0
435435 −32.7211 33.2223i −1.56886 1.59289i
436436 0 0
437437 −13.3301 + 2.11128i −0.637664 + 0.100996i
438438 0 0
439439 5.27551 3.83288i 0.251786 0.182933i −0.454732 0.890628i 0.650265π-0.650265\pi
0.706518 + 0.707695i 0.250265π0.250265\pi
440440 0 0
441441 −51.6565 37.5306i −2.45983 1.78717i
442442 0 0
443443 21.4275 21.4275i 1.01805 1.01805i 0.0182176 0.999834i 0.494201π-0.494201\pi
0.999834 0.0182176i 0.00579917π-0.00579917\pi
444444 0 0
445445 −26.0053 8.66871i −1.23277 0.410936i
446446 0 0
447447 22.1037 11.2624i 1.04547 0.532694i
448448 0 0
449449 26.5999i 1.25533i −0.778485 0.627663i 0.784012π-0.784012\pi
0.778485 0.627663i 0.215988π-0.215988\pi
450450 0 0
451451 17.9577i 0.845597i
452452 0 0
453453 −21.5680 + 10.9895i −1.01335 + 0.516330i
454454 0 0
455455 0.296241 38.9739i 0.0138880 1.82712i
456456 0 0
457457 −28.1522 + 28.1522i −1.31690 + 1.31690i −0.400687 + 0.916215i 0.631229π0.631229\pi
−0.916215 + 0.400687i 0.868771π0.868771\pi
458458 0 0
459459 58.8447 + 42.7532i 2.74663 + 1.99555i
460460 0 0
461461 −1.83986 + 1.33674i −0.0856908 + 0.0622580i −0.629806 0.776753i 0.716866π-0.716866\pi
0.544115 + 0.839011i 0.316866π0.316866\pi
462462 0 0
463463 32.0023 5.06867i 1.48728 0.235561i 0.640684 0.767805i 0.278651π-0.278651\pi
0.846591 + 0.532244i 0.178651π0.178651\pi
464464 0 0
465465 −22.7747 3.78483i −1.05615 0.175517i
466466 0 0
467467 −11.7289 + 23.0192i −0.542747 + 1.06520i 0.442929 + 0.896556i 0.353939π0.353939\pi
−0.985677 + 0.168645i 0.946061π0.946061\pi
468468 0 0
469469 21.8912 7.11289i 1.01084 0.328443i
470470 0 0
471471 53.4395 + 17.3635i 2.46236 + 0.800070i
472472 0 0
473473 −10.7791 1.70724i −0.495622 0.0784988i
474474 0 0
475475 12.0224 + 0.182775i 0.551624 + 0.00838630i
476476 0 0
477477 6.03568 38.1078i 0.276355 1.74484i
478478 0 0
479479 −2.02478 + 6.23165i −0.0925148 + 0.284731i −0.986598 0.163170i 0.947828π-0.947828\pi
0.894083 + 0.447901i 0.147828π0.147828\pi
480480 0 0
481481 −8.40562 25.8698i −0.383263 1.17956i
482482 0 0
483483 −63.7574 32.4860i −2.90106 1.47817i
484484 0 0
485485 21.6123 + 11.2197i 0.981362 + 0.509462i
486486 0 0
487487 −3.57636 22.5803i −0.162061 1.02321i −0.925890 0.377792i 0.876683π-0.876683\pi
0.763830 0.645418i 0.223317π-0.223317\pi
488488 0 0
489489 25.1518 + 34.6184i 1.13740 + 1.56550i
490490 0 0
491491 −10.8187 + 14.8906i −0.488239 + 0.672004i −0.980062 0.198692i 0.936331π-0.936331\pi
0.491823 + 0.870695i 0.336331π0.336331\pi
492492 0 0
493493 −23.3871 23.3871i −1.05330 1.05330i
494494 0 0
495495 −36.7718 + 26.2916i −1.65277 + 1.18172i
496496 0 0
497497 4.17725 + 8.19831i 0.187375 + 0.367745i
498498 0 0
499499 −26.3658 −1.18030 −0.590148 0.807295i 0.700931π-0.700931\pi
−0.590148 + 0.807295i 0.700931π0.700931\pi
500500 0 0
501501 21.2807 0.950750
502502 0 0
503503 3.47288 + 6.81591i 0.154848 + 0.303907i 0.955378 0.295387i 0.0954484π-0.0954484\pi
−0.800530 + 0.599293i 0.795448π0.795448\pi
504504 0 0
505505 9.46422 6.76685i 0.421152 0.301121i
506506 0 0
507507 14.7116 + 14.7116i 0.653367 + 0.653367i
508508 0 0
509509 −15.3150 + 21.0793i −0.678824 + 0.934321i −0.999919 0.0127257i 0.995949π-0.995949\pi
0.321095 + 0.947047i 0.395949π0.395949\pi
510510 0 0
511511 24.6387 + 33.9123i 1.08995 + 1.50019i
512512 0 0
513513 5.34794 + 33.7655i 0.236117 + 1.49079i
514514 0 0
515515 16.5226 + 8.57750i 0.728073 + 0.377970i
516516 0 0
517517 −3.00560 1.53143i −0.132186 0.0673521i
518518 0 0
519519 −9.77299 30.0782i −0.428987 1.32028i
520520 0 0
521521 −6.19545 + 19.0676i −0.271428 + 0.835368i 0.718715 + 0.695305i 0.244731π0.244731\pi
−0.990143 + 0.140063i 0.955269π0.955269\pi
522522 0 0
523523 1.37408 8.67559i 0.0600843 0.379357i −0.939262 0.343201i 0.888489π-0.888489\pi
0.999346 0.0361559i 0.0115113π-0.0115113\pi
524524 0 0
525525 50.9989 + 38.2507i 2.22578 + 1.66940i
526526 0 0
527527 −16.1738 2.56167i −0.704540 0.111588i
528528 0 0
529529 −8.08224 2.62608i −0.351402 0.114177i
530530 0 0
531531 1.86990 0.607566i 0.0811466 0.0263661i
532532 0 0
533533 13.1731 25.8538i 0.570592 1.11985i
534534 0 0
535535 38.4278 + 6.38615i 1.66138 + 0.276097i
536536 0 0
537537 44.4798 7.04491i 1.91945 0.304010i
538538 0 0
539539 19.0351 13.8298i 0.819899 0.595692i
540540 0 0
541541 −17.8972 13.0031i −0.769461 0.559046i 0.132336 0.991205i 0.457752π-0.457752\pi
−0.901798 + 0.432159i 0.857752π0.857752\pi
542542 0 0
543543 27.9989 27.9989i 1.20155 1.20155i
544544 0 0
545545 0.111479 14.6663i 0.00477524 0.628237i
546546 0 0
547547 2.19922 1.12056i 0.0940320 0.0479117i −0.406342 0.913721i 0.633196π-0.633196\pi
0.500374 + 0.865809i 0.333196π0.333196\pi
548548 0 0
549549 3.83146i 0.163523i
550550 0 0
551551 15.5452i 0.662247i
552552 0 0
553553 42.5835 21.6974i 1.81083 0.922666i
554554 0 0
555555 42.2083 + 14.0699i 1.79164 + 0.597234i
556556 0 0
557557 7.90748 7.90748i 0.335051 0.335051i −0.519450 0.854501i 0.673863π-0.673863\pi
0.854501 + 0.519450i 0.173863π0.173863\pi
558558 0 0
559559 −14.2663 10.3650i −0.603398 0.438395i
560560 0 0
561561 −36.4455 + 26.4792i −1.53873 + 1.11795i
562562 0 0
563563 −15.7185 + 2.48957i −0.662457 + 0.104923i −0.478604 0.878031i 0.658857π-0.658857\pi
−0.183853 + 0.982954i 0.558857π0.558857\pi
564564 0 0
565565 −9.90349 10.0552i −0.416643 0.423025i
566566 0 0
567567 −42.4181 + 83.2501i −1.78139 + 3.49618i
568568 0 0
569569 −40.4687 + 13.1491i −1.69654 + 0.551238i −0.988002 0.154439i 0.950643π-0.950643\pi
−0.708533 + 0.705677i 0.750643π0.750643\pi
570570 0 0
571571 −16.6012 5.39406i −0.694739 0.225734i −0.0597020 0.998216i 0.519015π-0.519015\pi
−0.635037 + 0.772482i 0.719015π0.719015\pi
572572 0 0
573573 −30.4689 4.82580i −1.27286 0.201601i
574574 0 0
575575 24.8065 + 13.1183i 1.03450 + 0.547071i
576576 0 0
577577 5.79961 36.6173i 0.241441 1.52440i −0.507437 0.861689i 0.669407π-0.669407\pi
0.748877 0.662709i 0.230593π-0.230593\pi
578578 0 0
579579 −7.27001 + 22.3748i −0.302131 + 0.929864i
580580 0 0
581581 −7.96104 24.5016i −0.330280 1.01650i
582582 0 0
583583 12.6679 + 6.45463i 0.524652 + 0.267323i
584584 0 0
585585 −72.2269 + 10.8775i −2.98622 + 0.449730i
586586 0 0
587587 3.95971 + 25.0006i 0.163435 + 1.03189i 0.923935 + 0.382549i 0.124954π0.124954\pi
−0.760501 + 0.649337i 0.775046π0.775046\pi
588588 0 0
589589 −4.52391 6.22663i −0.186404 0.256564i
590590 0 0
591591 −6.58655 + 9.06560i −0.270934 + 0.372909i
592592 0 0
593593 −16.2733 16.2733i −0.668266 0.668266i 0.289049 0.957314i 0.406661π-0.406661\pi
−0.957314 + 0.289049i 0.906661π0.906661\pi
594594 0 0
595595 36.3780 + 26.8550i 1.49135 + 1.10095i
596596 0 0
597597 11.6173 + 22.8003i 0.475465 + 0.933153i
598598 0 0
599599 −12.7517 −0.521019 −0.260509 0.965471i 0.583890π-0.583890\pi
−0.260509 + 0.965471i 0.583890π0.583890\pi
600600 0 0
601601 5.60928 0.228807 0.114404 0.993434i 0.463504π-0.463504\pi
0.114404 + 0.993434i 0.463504π0.463504\pi
602602 0 0
603603 −19.5836 38.4351i −0.797508 1.56520i
604604 0 0
605605 2.39592 + 7.56916i 0.0974079 + 0.307730i
606606 0 0
607607 −8.41059 8.41059i −0.341375 0.341375i 0.515509 0.856884i 0.327603π-0.327603\pi
−0.856884 + 0.515509i 0.827603π0.827603\pi
608608 0 0
609609 48.4453 66.6792i 1.96310 2.70198i
610610 0 0
611611 −3.20376 4.40959i −0.129610 0.178393i
612612 0 0
613613 2.17512 + 13.7332i 0.0878523 + 0.554677i 0.991877 + 0.127198i 0.0405984π0.0405984\pi
−0.904025 + 0.427479i 0.859402π0.859402\pi
614614 0 0
615615 21.2247 + 42.4503i 0.855861 + 1.71176i
616616 0 0
617617 −30.4274 15.5035i −1.22496 0.624149i −0.282758 0.959191i 0.591249π-0.591249\pi
−0.942203 + 0.335042i 0.891249π0.891249\pi
618618 0 0
619619 3.44153 + 10.5920i 0.138327 + 0.425727i 0.996093 0.0883143i 0.0281480π-0.0281480\pi
−0.857766 + 0.514041i 0.828148π0.828148\pi
620620 0 0
621621 −24.6552 + 75.8809i −0.989379 + 3.04500i
622622 0 0
623623 7.57945 47.8548i 0.303664 1.91726i
624624 0 0
625625 −19.7694 15.3027i −0.790775 0.612107i
626626 0 0
627627 −20.9127 3.31225i −0.835174 0.132279i
628628 0 0
629629 30.0128 + 9.75175i 1.19669 + 0.388828i
630630 0 0
631631 30.9083 10.0427i 1.23044 0.399794i 0.379565 0.925165i 0.376074π-0.376074\pi
0.850873 + 0.525371i 0.176074π0.176074\pi
632632 0 0
633633 30.8283 60.5039i 1.22531 2.40481i
634634 0 0
635635 −5.78851 + 2.89418i −0.229710 + 0.114852i
636636 0 0
637637 37.5499 5.94731i 1.48778 0.235641i
638638 0 0
639639 13.9503 10.1355i 0.551866 0.400954i
640640 0 0
641641 27.5141 + 19.9901i 1.08674 + 0.789563i 0.978846 0.204599i 0.0655890π-0.0655890\pi
0.107895 + 0.994162i 0.465589π0.465589\pi
642642 0 0
643643 −20.5380 + 20.5380i −0.809941 + 0.809941i −0.984625 0.174684i 0.944110π-0.944110\pi
0.174684 + 0.984625i 0.444110π0.444110\pi
644644 0 0
645645 27.4985 8.70428i 1.08275 0.342731i
646646 0 0
647647 −2.67176 + 1.36133i −0.105038 + 0.0535193i −0.505720 0.862698i 0.668773π-0.668773\pi
0.400682 + 0.916217i 0.368773π0.368773\pi
648648 0 0
649649 0.724506i 0.0284393i
650650 0 0
651651 40.8068i 1.59934i
652652 0 0
653653 −14.3147 + 7.29369i −0.560177 + 0.285424i −0.711065 0.703127i 0.751787π-0.751787\pi
0.150888 + 0.988551i 0.451787π0.451787\pi
654654 0 0
655655 −3.86754 + 5.23901i −0.151117 + 0.204705i
656656 0 0
657657 55.5479 55.5479i 2.16713 2.16713i
658658 0 0
659659 1.06188 + 0.771504i 0.0413651 + 0.0300535i 0.608276 0.793726i 0.291862π-0.291862\pi
−0.566911 + 0.823779i 0.691862π0.691862\pi
660660 0 0
661661 34.8370 25.3105i 1.35500 0.984466i 0.356256 0.934388i 0.384053π-0.384053\pi
0.998745 0.0500779i 0.0159469π-0.0159469\pi
662662 0 0
663663 −71.8948 + 11.3870i −2.79216 + 0.442235i
664664 0 0
665665 3.16493 + 21.0152i 0.122731 + 0.814934i
666666 0 0
667667 16.4708 32.3258i 0.637752 1.25166i
668668 0 0
669669 21.1300 6.86556i 0.816934 0.265438i
670670 0 0
671671 −1.34277 0.436292i −0.0518370 0.0168429i
672672 0 0
673673 −46.9047 7.42897i −1.80804 0.286366i −0.841010 0.541019i 0.818039π-0.818039\pi
−0.967032 + 0.254653i 0.918039π0.918039\pi
674674 0 0
675675 33.2291 62.8358i 1.27899 2.41855i
676676 0 0
677677 5.40918 34.1522i 0.207892 1.31258i −0.634170 0.773194i 0.718658π-0.718658\pi
0.842061 0.539382i 0.181342π-0.181342\pi
678678 0 0
679679 −13.3003 + 40.9342i −0.510420 + 1.57091i
680680 0 0
681681 16.4170 + 50.5264i 0.629101 + 1.93617i
682682 0 0
683683 24.9863 + 12.7312i 0.956074 + 0.487144i 0.861156 0.508341i 0.169741π-0.169741\pi
0.0949182 + 0.995485i 0.469741π0.469741\pi
684684 0 0
685685 5.04607 4.96994i 0.192801 0.189892i
686686 0 0
687687 6.13908 + 38.7606i 0.234221 + 1.47881i
688688 0 0
689689 13.5031 + 18.5855i 0.514428 + 0.708049i
690690 0 0
691691 −8.46130 + 11.6460i −0.321883 + 0.443034i −0.939041 0.343805i 0.888284π-0.888284\pi
0.617158 + 0.786839i 0.288284π0.288284\pi
692692 0 0
693693 −56.4971 56.4971i −2.14615 2.14615i
694694 0 0
695695 16.1439 48.4301i 0.612373 1.83706i
696696 0 0
697697 15.2828 + 29.9942i 0.578877 + 1.13611i
698698 0 0
699699 −85.4220 −3.23096
700700 0 0
701701 23.6691 0.893968 0.446984 0.894542i 0.352498π-0.352498\pi
0.446984 + 0.894542i 0.352498π0.352498\pi
702702 0 0
703703 6.73366 + 13.2156i 0.253965 + 0.498434i
704704 0 0
705705 8.91496 + 0.0677629i 0.335757 + 0.00255210i
706706 0 0
707707 14.5411 + 14.5411i 0.546873 + 0.546873i
708708 0 0
709709 −10.7394 + 14.7815i −0.403326 + 0.555131i −0.961575 0.274543i 0.911474π-0.911474\pi
0.558249 + 0.829674i 0.311474π0.311474\pi
710710 0 0
711711 −52.6456 72.4605i −1.97436 2.71748i
712712 0 0
713713 −2.80996 17.7414i −0.105234 0.664420i
714714 0 0
715715 4.41242 26.5512i 0.165015 0.992958i
716716 0 0
717717 −61.4442 31.3074i −2.29468 1.16920i
718718 0 0
719719 8.20814 + 25.2621i 0.306112 + 0.942116i 0.979260 + 0.202608i 0.0649417π0.0649417\pi
−0.673148 + 0.739508i 0.735058π0.735058\pi
720720 0 0
721721 −10.1681 + 31.2943i −0.378681 + 1.16546i
722722 0 0
723723 7.28288 45.9823i 0.270853 1.71010i
724724 0 0
725725 −19.3936 + 25.8571i −0.720259 + 0.960307i
726726 0 0
727727 −14.2659 2.25950i −0.529094 0.0838002i −0.113828 0.993500i 0.536311π-0.536311\pi
−0.415266 + 0.909700i 0.636311π0.636311\pi
728728 0 0
729729 35.6815 + 11.5936i 1.32154 + 0.429393i
730730 0 0
731731 19.4568 6.32191i 0.719637 0.233824i
732732 0 0
733733 20.1391 39.5251i 0.743853 1.45989i −0.139024 0.990289i 0.544396π-0.544396\pi
0.882877 0.469605i 0.155604π-0.155604\pi
734734 0 0
735735 −28.6513 + 55.1903i −1.05682 + 2.03572i
736736 0 0
737737 15.6999 2.48662i 0.578313 0.0915959i
738738 0 0
739739 −18.5363 + 13.4674i −0.681870 + 0.495408i −0.873978 0.485966i 0.838468π-0.838468\pi
0.192108 + 0.981374i 0.438468π0.438468\pi
740740 0 0
741741 −27.6783 20.1095i −1.01679 0.738740i
742742 0 0
743743 −16.8830 + 16.8830i −0.619377 + 0.619377i −0.945372 0.325994i 0.894301π-0.894301\pi
0.325994 + 0.945372i 0.394301π0.394301\pi
744744 0 0
745745 −10.0011 13.9878i −0.366414 0.512472i
746746 0 0
747747 −43.0181 + 21.9188i −1.57395 + 0.801968i
748748 0 0
749749 68.8533i 2.51585i
750750 0 0
751751 14.8477i 0.541801i 0.962607 + 0.270900i 0.0873214π0.0873214\pi
−0.962607 + 0.270900i 0.912679π0.912679\pi
752752 0 0
753753 25.0810 12.7794i 0.914003 0.465708i
754754 0 0
755755 9.75876 + 13.6487i 0.355158 + 0.496729i
756756 0 0
757757 −6.81120 + 6.81120i −0.247557 + 0.247557i −0.819967 0.572410i 0.806009π-0.806009\pi
0.572410 + 0.819967i 0.306009π0.306009\pi
758758 0 0
759759 −39.9780 29.0457i −1.45111 1.05429i
760760 0 0
761761 0.259631 0.188633i 0.00941163 0.00683795i −0.583069 0.812422i 0.698148π-0.698148\pi
0.592481 + 0.805584i 0.298148π0.298148\pi
762762 0 0
763763 25.6046 4.05536i 0.926947 0.146814i
764764 0 0
765765 39.0434 75.2082i 1.41162 2.71916i
766766 0 0
767767 −0.531471 + 1.04307i −0.0191903 + 0.0376631i
768768 0 0
769769 6.96700 2.26371i 0.251236 0.0816316i −0.180691 0.983540i 0.557834π-0.557834\pi
0.431928 + 0.901908i 0.357834π0.357834\pi
770770 0 0
771771 50.0398 + 16.2589i 1.80214 + 0.585551i
772772 0 0
773773 −22.7703 3.60646i −0.818991 0.129715i −0.267140 0.963658i 0.586078π-0.586078\pi
−0.551851 + 0.833942i 0.686078π0.686078\pi
774774 0 0
775775 −0.243261 + 16.0009i −0.00873818 + 0.574770i
776776 0 0
777777 −12.3020 + 77.6715i −0.441330 + 2.78645i
778778 0 0
779779 −4.88925 + 15.0476i −0.175176 + 0.539135i
780780 0 0
781781 1.96354 + 6.04315i 0.0702609 + 0.216241i
782782 0 0
783783 −81.8823 41.7211i −2.92623 1.49099i
784784 0 0
785785 6.38498 38.4208i 0.227890 1.37130i
786786 0 0
787787 −5.09483 32.1675i −0.181611 1.14665i −0.895062 0.445942i 0.852869π-0.852869\pi
0.713451 0.700705i 0.247131π-0.247131\pi
788788 0 0
789789 −34.8544 47.9730i −1.24085 1.70788i
790790 0 0
791791 14.6626 20.1814i 0.521342 0.717566i
792792 0 0
793793 −1.61314 1.61314i −0.0572841 0.0572841i
794794 0 0
795795 −37.5746 0.285605i −1.33263 0.0101294i
796796 0 0
797797 −24.3883 47.8648i −0.863879 1.69546i −0.706255 0.707958i 0.749617π-0.749617\pi
−0.157624 0.987499i 0.550383π-0.550383\pi
798798 0 0
799799 6.32345 0.223708
800800 0 0
801801 −90.8005 −3.20828
802802 0 0
803803 13.1419 + 25.7925i 0.463769 + 0.910198i
804804 0 0
805805 −15.6851 + 47.0539i −0.552829 + 1.65843i
806806 0 0
807807 26.5458 + 26.5458i 0.934458 + 0.934458i
808808 0 0
809809 −22.6777 + 31.2132i −0.797307 + 1.09740i 0.195852 + 0.980633i 0.437253π0.437253\pi
−0.993159 + 0.116766i 0.962747π0.962747\pi
810810 0 0
811811 −20.6446 28.4149i −0.724931 0.997782i −0.999346 0.0361702i 0.988484π-0.988484\pi
0.274415 0.961611i 0.411516π-0.411516\pi
812812 0 0
813813 3.82038 + 24.1209i 0.133987 + 0.845958i
814814 0 0
815815 21.1318 20.8130i 0.740215 0.729048i
816816 0 0
817817 8.56743 + 4.36533i 0.299737 + 0.152723i
818818 0 0
819819 −39.8947 122.783i −1.39403 4.29039i
820820 0 0
821821 1.41608 4.35825i 0.0494216 0.152104i −0.923300 0.384079i 0.874519π-0.874519\pi
0.972722 + 0.231975i 0.0745189π0.0745189\pi
822822 0 0
823823 5.97979 37.7549i 0.208442 1.31605i −0.632345 0.774687i 0.717907π-0.717907\pi
0.840787 0.541366i 0.182093π-0.182093\pi
824824 0 0
825825 30.6529 + 31.5994i 1.06720 + 1.10015i
826826 0 0
827827 6.05062 + 0.958323i 0.210401 + 0.0333242i 0.260745 0.965408i 0.416032π-0.416032\pi
−0.0503443 + 0.998732i 0.516032π0.516032\pi
828828 0 0
829829 6.18322 + 2.00905i 0.214752 + 0.0697772i 0.414417 0.910087i 0.363985π-0.363985\pi
−0.199665 + 0.979864i 0.563985π0.563985\pi
830830 0 0
831831 −78.3707 + 25.4642i −2.71865 + 0.883343i
832832 0 0
833833 −20.0239 + 39.2991i −0.693786 + 1.36163i
834834 0 0
835835 −2.19671 14.5862i −0.0760202 0.504775i
836836 0 0
837837 −44.9395 + 7.11772i −1.55334 + 0.246024i
838838 0 0
839839 −9.69717 + 7.04541i −0.334783 + 0.243234i −0.742458 0.669893i 0.766340π-0.766340\pi
0.407674 + 0.913127i 0.366340π0.366340\pi
840840 0 0
841841 10.3456 + 7.51655i 0.356747 + 0.259192i
842842 0 0
843843 −32.5756 + 32.5756i −1.12196 + 1.12196i
844844 0 0
845845 8.56502 11.6023i 0.294646 0.399130i
846846 0 0
847847 −12.5034 + 6.37078i −0.429620 + 0.218903i
848848 0 0
849849 5.14055i 0.176423i
850850 0 0
851851 34.6160i 1.18662i
852852 0 0
853853 39.4367 20.0940i 1.35029 0.688006i 0.378884 0.925444i 0.376308π-0.376308\pi
0.971403 + 0.237438i 0.0763078π0.0763078\pi
854854 0 0
855855 37.9710 12.0192i 1.29858 0.411048i
856856 0 0
857857 12.1177 12.1177i 0.413934 0.413934i −0.469173 0.883106i 0.655448π-0.655448\pi
0.883106 + 0.469173i 0.155448π0.155448\pi
858858 0 0
859859 −16.2646 11.8169i −0.554941 0.403188i 0.274663 0.961541i 0.411434π-0.411434\pi
−0.829604 + 0.558352i 0.811434π0.811434\pi
860860 0 0
861861 −67.8664 + 49.3078i −2.31288 + 1.68041i
862862 0 0
863863 −8.81063 + 1.39547i −0.299917 + 0.0475023i −0.304580 0.952487i 0.598516π-0.598516\pi
0.00466216 + 0.999989i 0.498516π0.498516\pi
864864 0 0
865865 −19.6073 + 9.80342i −0.666669 + 0.333326i
866866 0 0
867867 13.4413 26.3800i 0.456490 0.895912i
868868 0 0
869869 31.3892 10.1990i 1.06481 0.345976i
870870 0 0
871871 24.4272 + 7.93689i 0.827686 + 0.268931i
872872 0 0
873873 79.6679 + 12.6182i 2.69635 + 0.427060i
874874 0 0
875875 20.9534 38.9041i 0.708353 1.31520i
876876 0 0
877877 0.402784 2.54308i 0.0136011 0.0858737i −0.979954 0.199223i 0.936158π-0.936158\pi
0.993555 + 0.113350i 0.0361580π0.0361580\pi
878878 0 0
879879 17.2588 53.1170i 0.582123 1.79159i
880880 0 0
881881 10.1043 + 31.0979i 0.340423 + 1.04771i 0.963989 + 0.265944i 0.0856835π0.0856835\pi
−0.623565 + 0.781771i 0.714316π0.714316\pi
882882 0 0
883883 −32.7812 16.7029i −1.10317 0.562096i −0.195049 0.980793i 0.562487π-0.562487\pi
−0.908126 + 0.418698i 0.862487π0.862487\pi
884884 0 0
885885 −0.856309 1.71266i −0.0287845 0.0575704i
886886 0 0
887887 3.43852 + 21.7100i 0.115454 + 0.728949i 0.975707 + 0.219081i 0.0703058π0.0703058\pi
−0.860253 + 0.509868i 0.829694π0.829694\pi
888888 0 0
889889 −6.72359 9.25423i −0.225502 0.310377i
890890 0 0
891891 −37.9259 + 52.2005i −1.27057 + 1.74878i
892892 0 0
893893 2.10157 + 2.10157i 0.0703263 + 0.0703263i
894894 0 0
895895 −9.42017 29.7601i −0.314882 0.994770i
896896 0 0
897897 −36.2494 71.1435i −1.21033 2.37541i
898898 0 0
899899 20.6895 0.690034
900900 0 0
901901 −26.6519 −0.887905
902902 0 0
903903 23.1448 + 45.4242i 0.770211 + 1.51162i
904904 0 0
905905 −22.0812 16.3008i −0.734002 0.541856i
906906 0 0
907907 −37.9456 37.9456i −1.25996 1.25996i −0.951109 0.308854i 0.900054π-0.900054\pi
−0.308854 0.951109i 0.599946π-0.599946\pi
908908 0 0
909909 22.6523 31.1783i 0.751331 1.03412i
910910 0 0
911911 −33.3609 45.9174i −1.10530 1.52131i −0.828170 0.560478i 0.810618π-0.810618\pi
−0.277127 0.960833i 0.589382π-0.589382\pi
912912 0 0
913913 −2.78313 17.5720i −0.0921081 0.581548i
914914 0 0
915915 3.68983 0.555697i 0.121982 0.0183708i
916916 0 0
917917 −10.2554 5.22539i −0.338664 0.172558i
918918 0 0
919919 1.38497 + 4.26249i 0.0456859 + 0.140607i 0.971297 0.237868i 0.0764486π-0.0764486\pi
−0.925612 + 0.378475i 0.876449π0.876449\pi
920920 0 0
921921 14.1809 43.6444i 0.467278 1.43813i
922922 0 0
923923 −1.60613 + 10.1407i −0.0528664 + 0.333785i
924924 0 0
925925 5.28679 30.3828i 0.173829 0.998979i
926926 0 0
927927 60.9063 + 9.64661i 2.00042 + 0.316836i
928928 0 0
929929 19.4161 + 6.30868i 0.637022 + 0.206981i 0.609683 0.792645i 0.291297π-0.291297\pi
0.0273390 + 0.999626i 0.491297π0.491297\pi
930930 0 0
931931 −19.7157 + 6.40602i −0.646156 + 0.209949i
932932 0 0
933933 15.1318 29.6978i 0.495393 0.972263i
934934 0 0
935935 21.9115 + 22.2471i 0.716582 + 0.727558i
936936 0 0
937937 −48.4276 + 7.67018i −1.58206 + 0.250574i −0.884705 0.466151i 0.845640π-0.845640\pi
−0.697356 + 0.716725i 0.745640π0.745640\pi
938938 0 0
939939 42.6500 30.9870i 1.39183 1.01122i
940940 0 0
941941 −21.1187 15.3436i −0.688450 0.500189i 0.187700 0.982226i 0.439897π-0.439897\pi
−0.876150 + 0.482038i 0.839897π0.839897\pi
942942 0 0
943943 −26.1107 + 26.1107i −0.850280 + 0.850280i
944944 0 0
945945 119.189 + 39.7310i 3.87722 + 1.29245i
946946 0 0
947947 −35.0327 + 17.8501i −1.13841 + 0.580049i −0.918480 0.395467i 0.870583π-0.870583\pi
−0.219930 + 0.975516i 0.570583π0.570583\pi
948948 0 0
949949 46.7740i 1.51835i
950950 0 0
951951 107.887i 3.49846i
952952 0 0
953953 −28.6513 + 14.5986i −0.928106 + 0.472894i −0.851610 0.524176i 0.824373π-0.824373\pi
−0.0764965 + 0.997070i 0.524373π0.524373\pi
954954 0 0
955955 −0.162526 + 21.3821i −0.00525921 + 0.691909i
956956 0 0
957957 40.2468 40.2468i 1.30099 1.30099i
958958 0 0
959959 10.1278 + 7.35825i 0.327042 + 0.237610i
960960 0 0
961961 −16.7923 + 12.2003i −0.541688 + 0.393559i
962962 0 0
963963 127.446 20.1855i 4.10691 0.650470i
964964 0 0
965965 16.0865 + 2.67335i 0.517844 + 0.0860582i
966966 0 0
967967 −11.7698 + 23.0996i −0.378492 + 0.742832i −0.999149 0.0412505i 0.986866π-0.986866\pi
0.620657 + 0.784082i 0.286866π0.286866\pi
968968 0 0
969969 37.7486 12.2653i 1.21266 0.394018i
970970 0 0
971971 −41.7528 13.5663i −1.33991 0.435364i −0.450625 0.892714i 0.648799π-0.648799\pi
−0.889287 + 0.457350i 0.848799π0.848799\pi
972972 0 0
973973 89.1208 + 14.1154i 2.85708 + 0.452517i
974974 0 0
975975 20.9509 + 67.9795i 0.670966 + 2.17709i
976976 0 0
977977 1.09435 6.90944i 0.0350113 0.221052i −0.963979 0.265978i 0.914305π-0.914305\pi
0.998990 + 0.0449257i 0.0143051π0.0143051\pi
978978 0 0
979979 10.3395 31.8218i 0.330453 1.01703i
980980 0 0
981981 −15.0128 46.2048i −0.479323 1.47520i
982982 0 0
983983 2.60540 + 1.32752i 0.0830993 + 0.0423412i 0.495046 0.868867i 0.335151π-0.335151\pi
−0.411947 + 0.911208i 0.635151π0.635151\pi
984984 0 0
985985 6.89363 + 3.57874i 0.219649 + 0.114028i
986986 0 0
987987 2.46506 + 15.5638i 0.0784638 + 0.495401i
988988 0 0
989989 13.1905 + 18.1552i 0.419433 + 0.577300i
990990 0 0
991991 11.1499 15.3466i 0.354189 0.487499i −0.594329 0.804222i 0.702582π-0.702582\pi
0.948518 + 0.316722i 0.102582π0.102582\pi
992992 0 0
993993 9.31161 + 9.31161i 0.295495 + 0.295495i
994994 0 0
995995 14.4285 10.3163i 0.457415 0.327049i
996996 0 0
997997 27.4234 + 53.8214i 0.868508 + 1.70454i 0.694112 + 0.719867i 0.255797π0.255797\pi
0.174395 + 0.984676i 0.444203π0.444203\pi
998998 0 0
999999 87.6835 2.77418
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 800.2.bq.d.223.1 yes 64
4.3 odd 2 800.2.bq.c.223.8 64
25.12 odd 20 800.2.bq.c.287.8 yes 64
100.87 even 20 inner 800.2.bq.d.287.1 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
800.2.bq.c.223.8 64 4.3 odd 2
800.2.bq.c.287.8 yes 64 25.12 odd 20
800.2.bq.d.223.1 yes 64 1.1 even 1 trivial
800.2.bq.d.287.1 yes 64 100.87 even 20 inner