Properties

Label 896.2.bh.a.625.15
Level 896896
Weight 22
Character 896.625
Analytic conductor 7.1557.155
Analytic rank 00
Dimension 240240
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [896,2,Mod(81,896)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(896, base_ring=CyclotomicField(24))
 
chi = DirichletCharacter(H, H._module([0, 9, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("896.81");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 896=277 896 = 2^{7} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 896.bh (of order 2424, degree 88, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 7.154596021117.15459602111
Analytic rank: 00
Dimension: 240240
Relative dimension: 3030 over Q(ζ24)\Q(\zeta_{24})
Twist minimal: no (minimal twist has level 224)
Sato-Tate group: SU(2)[C24]\mathrm{SU}(2)[C_{24}]

Embedding invariants

Embedding label 625.15
Character χ\chi == 896.625
Dual form 896.2.bh.a.529.15

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.118403+0.154306i)q3+(2.395831.83839i)q5+(1.47323+2.19764i)q7+(0.766666+2.86124i)q9+(5.43183+0.715114i)q11+(5.50652+2.28087i)q13+0.587363iq15+(3.70249+2.13763i)q17+(0.183696+1.39531i)q19+(0.1646740.487536i)q21+(0.326660+1.21911i)q23+(1.066253.97929i)q25+(1.071360.443773i)q27+(0.497218+1.20039i)q29+(0.251275+0.435222i)q31+(0.5328010.922838i)q33+(0.510497+7.97352i)q35+(5.398664.14254i)q37+(0.3000371.11975i)q39+(3.02206+3.02206i)q41+(3.498818.44689i)q43+(7.09686+5.44561i)q45+(7.99998+4.61879i)q47+(2.659206.47523i)q49+(0.1085370.824421i)q51+(7.09730+0.934377i)q53+(11.6991+11.6991i)q55+(0.1935540.193554i)q57+(0.009683330.0735522i)q59+(9.08657+1.19627i)q61+(7.417432.53040i)q63+(8.99956+15.5877i)q65+(0.469449+0.611798i)q67+(0.2267940.0939414i)q69+(7.84105+7.84105i)q71+(6.925691.85573i)q73+(0.487783+0.635691i)q75+(6.4307612.9907i)q77+(0.877666+0.506720i)q79+(7.50061+4.33048i)q81+(6.186022.56233i)q83+(4.94075+11.9280i)q85+(0.2441000.0654064i)q87+(13.9937+3.74960i)q89+(3.0998215.4616i)q91+(0.09690940.0127584i)q93+(2.12501+3.68062i)q95+0.451869q97+(6.2105114.9935i)q99+O(q100)q+(-0.118403 + 0.154306i) q^{3} +(2.39583 - 1.83839i) q^{5} +(-1.47323 + 2.19764i) q^{7} +(0.766666 + 2.86124i) q^{9} +(-5.43183 + 0.715114i) q^{11} +(-5.50652 + 2.28087i) q^{13} +0.587363i q^{15} +(-3.70249 + 2.13763i) q^{17} +(-0.183696 + 1.39531i) q^{19} +(-0.164674 - 0.487536i) q^{21} +(0.326660 + 1.21911i) q^{23} +(1.06625 - 3.97929i) q^{25} +(-1.07136 - 0.443773i) q^{27} +(0.497218 + 1.20039i) q^{29} +(0.251275 + 0.435222i) q^{31} +(0.532801 - 0.922838i) q^{33} +(0.510497 + 7.97352i) q^{35} +(5.39866 - 4.14254i) q^{37} +(0.300037 - 1.11975i) q^{39} +(-3.02206 + 3.02206i) q^{41} +(3.49881 - 8.44689i) q^{43} +(7.09686 + 5.44561i) q^{45} +(7.99998 + 4.61879i) q^{47} +(-2.65920 - 6.47523i) q^{49} +(0.108537 - 0.824421i) q^{51} +(-7.09730 + 0.934377i) q^{53} +(-11.6991 + 11.6991i) q^{55} +(-0.193554 - 0.193554i) q^{57} +(-0.00968333 - 0.0735522i) q^{59} +(9.08657 + 1.19627i) q^{61} +(-7.41743 - 2.53040i) q^{63} +(-8.99956 + 15.5877i) q^{65} +(-0.469449 + 0.611798i) q^{67} +(-0.226794 - 0.0939414i) q^{69} +(7.84105 + 7.84105i) q^{71} +(-6.92569 - 1.85573i) q^{73} +(0.487783 + 0.635691i) q^{75} +(6.43076 - 12.9907i) q^{77} +(0.877666 + 0.506720i) q^{79} +(-7.50061 + 4.33048i) q^{81} +(6.18602 - 2.56233i) q^{83} +(-4.94075 + 11.9280i) q^{85} +(-0.244100 - 0.0654064i) q^{87} +(-13.9937 + 3.74960i) q^{89} +(3.09982 - 15.4616i) q^{91} +(-0.0969094 - 0.0127584i) q^{93} +(2.12501 + 3.68062i) q^{95} +0.451869 q^{97} +(-6.21051 - 14.9935i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 240q+4q34q5+8q74q9+4q1116q13+4q198q21+12q234q25+16q2716q29+56q318q33+32q354q37+4q3916q41+8q99+O(q100) 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 4 q^{25} + 16 q^{27} - 16 q^{29} + 56 q^{31} - 8 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} - 16 q^{41}+ \cdots - 8 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/896Z)×\left(\mathbb{Z}/896\mathbb{Z}\right)^\times.

nn 127127 129129 645645
χ(n)\chi(n) 11 e(13)e\left(\frac{1}{3}\right) e(18)e\left(\frac{1}{8}\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 −0.118403 + 0.154306i −0.0683603 + 0.0890888i −0.826282 0.563257i 0.809548π-0.809548\pi
0.757922 + 0.652346i 0.226215π0.226215\pi
44 0 0
55 2.39583 1.83839i 1.07145 0.822151i 0.0867170 0.996233i 0.472362π-0.472362\pi
0.984731 + 0.174082i 0.0556958π0.0556958\pi
66 0 0
77 −1.47323 + 2.19764i −0.556828 + 0.830628i
88 0 0
99 0.766666 + 2.86124i 0.255555 + 0.953746i
1010 0 0
1111 −5.43183 + 0.715114i −1.63776 + 0.215615i −0.892464 0.451120i 0.851025π-0.851025\pi
−0.745295 + 0.666735i 0.767691π0.767691\pi
1212 0 0
1313 −5.50652 + 2.28087i −1.52723 + 0.632601i −0.979025 0.203741i 0.934690π-0.934690\pi
−0.548209 + 0.836342i 0.684690π0.684690\pi
1414 0 0
1515 0.587363i 0.151657i
1616 0 0
1717 −3.70249 + 2.13763i −0.897986 + 0.518453i −0.876546 0.481318i 0.840158π-0.840158\pi
−0.0214399 + 0.999770i 0.506825π0.506825\pi
1818 0 0
1919 −0.183696 + 1.39531i −0.0421427 + 0.320105i 0.957369 + 0.288867i 0.0932785π0.0932785\pi
−0.999512 + 0.0312385i 0.990055π0.990055\pi
2020 0 0
2121 −0.164674 0.487536i −0.0359348 0.106389i
2222 0 0
2323 0.326660 + 1.21911i 0.0681133 + 0.254202i 0.991584 0.129467i 0.0413267π-0.0413267\pi
−0.923470 + 0.383670i 0.874660π0.874660\pi
2424 0 0
2525 1.06625 3.97929i 0.213250 0.795859i
2626 0 0
2727 −1.07136 0.443773i −0.206184 0.0854042i
2828 0 0
2929 0.497218 + 1.20039i 0.0923310 + 0.222907i 0.963298 0.268435i 0.0865065π-0.0865065\pi
−0.870967 + 0.491342i 0.836507π0.836507\pi
3030 0 0
3131 0.251275 + 0.435222i 0.0451304 + 0.0781682i 0.887708 0.460406i 0.152296π-0.152296\pi
−0.842578 + 0.538575i 0.818963π0.818963\pi
3232 0 0
3333 0.532801 0.922838i 0.0927487 0.160646i
3434 0 0
3535 0.510497 + 7.97352i 0.0862897 + 1.34777i
3636 0 0
3737 5.39866 4.14254i 0.887535 0.681029i −0.0608517 0.998147i 0.519382π-0.519382\pi
0.948386 + 0.317118i 0.102715π0.102715\pi
3838 0 0
3939 0.300037 1.11975i 0.0480444 0.179304i
4040 0 0
4141 −3.02206 + 3.02206i −0.471966 + 0.471966i −0.902550 0.430584i 0.858308π-0.858308\pi
0.430584 + 0.902550i 0.358308π0.358308\pi
4242 0 0
4343 3.49881 8.44689i 0.533564 1.28814i −0.395584 0.918430i 0.629458π-0.629458\pi
0.929148 0.369708i 0.120542π-0.120542\pi
4444 0 0
4545 7.09686 + 5.44561i 1.05794 + 0.811784i
4646 0 0
4747 7.99998 + 4.61879i 1.16692 + 0.673720i 0.952952 0.303121i 0.0980287π-0.0980287\pi
0.213965 + 0.976841i 0.431362π0.431362\pi
4848 0 0
4949 −2.65920 6.47523i −0.379886 0.925033i
5050 0 0
5151 0.108537 0.824421i 0.0151982 0.115442i
5252 0 0
5353 −7.09730 + 0.934377i −0.974889 + 0.128347i −0.601106 0.799169i 0.705273π-0.705273\pi
−0.373783 + 0.927516i 0.621940π0.621940\pi
5454 0 0
5555 −11.6991 + 11.6991i −1.57751 + 1.57751i
5656 0 0
5757 −0.193554 0.193554i −0.0256369 0.0256369i
5858 0 0
5959 −0.00968333 0.0735522i −0.00126066 0.00957568i 0.990803 0.135313i 0.0432038π-0.0432038\pi
−0.992064 + 0.125737i 0.959871π0.959871\pi
6060 0 0
6161 9.08657 + 1.19627i 1.16342 + 0.153167i 0.687406 0.726273i 0.258749π-0.258749\pi
0.476010 + 0.879440i 0.342083π0.342083\pi
6262 0 0
6363 −7.41743 2.53040i −0.934508 0.318800i
6464 0 0
6565 −8.99956 + 15.5877i −1.11626 + 1.93342i
6666 0 0
6767 −0.469449 + 0.611798i −0.0573523 + 0.0747430i −0.821149 0.570714i 0.806666π-0.806666\pi
0.763796 + 0.645457i 0.223333π0.223333\pi
6868 0 0
6969 −0.226794 0.0939414i −0.0273028 0.0113092i
7070 0 0
7171 7.84105 + 7.84105i 0.930561 + 0.930561i 0.997741 0.0671798i 0.0214001π-0.0214001\pi
−0.0671798 + 0.997741i 0.521400π0.521400\pi
7272 0 0
7373 −6.92569 1.85573i −0.810591 0.217197i −0.170362 0.985382i 0.554494π-0.554494\pi
−0.640229 + 0.768184i 0.721160π0.721160\pi
7474 0 0
7575 0.487783 + 0.635691i 0.0563243 + 0.0734033i
7676 0 0
7777 6.43076 12.9907i 0.732854 1.48043i
7878 0 0
7979 0.877666 + 0.506720i 0.0987451 + 0.0570105i 0.548559 0.836112i 0.315176π-0.315176\pi
−0.449814 + 0.893122i 0.648510π0.648510\pi
8080 0 0
8181 −7.50061 + 4.33048i −0.833402 + 0.481165i
8282 0 0
8383 6.18602 2.56233i 0.679004 0.281253i −0.0164063 0.999865i 0.505223π-0.505223\pi
0.695411 + 0.718613i 0.255223π0.255223\pi
8484 0 0
8585 −4.94075 + 11.9280i −0.535899 + 1.29378i
8686 0 0
8787 −0.244100 0.0654064i −0.0261703 0.00701231i
8888 0 0
8989 −13.9937 + 3.74960i −1.48333 + 0.397456i −0.907478 0.420100i 0.861995π-0.861995\pi
−0.575849 + 0.817556i 0.695328π0.695328\pi
9090 0 0
9191 3.09982 15.4616i 0.324950 1.62081i
9292 0 0
9393 −0.0969094 0.0127584i −0.0100490 0.00132298i
9494 0 0
9595 2.12501 + 3.68062i 0.218021 + 0.377624i
9696 0 0
9797 0.451869 0.0458804 0.0229402 0.999737i 0.492697π-0.492697\pi
0.0229402 + 0.999737i 0.492697π0.492697\pi
9898 0 0
9999 −6.21051 14.9935i −0.624180 1.50690i
100100 0 0
101101 0.453155 + 3.44206i 0.0450906 + 0.342497i 0.999089 + 0.0426844i 0.0135910π0.0135910\pi
−0.953998 + 0.299813i 0.903076π0.903076\pi
102102 0 0
103103 −8.80466 + 2.35920i −0.867549 + 0.232459i −0.665028 0.746819i 0.731580π-0.731580\pi
−0.202522 + 0.979278i 0.564914π0.564914\pi
104104 0 0
105105 −1.29081 0.865320i −0.125970 0.0844466i
106106 0 0
107107 −7.67351 10.0003i −0.741826 0.966766i −1.00000 0.000667722i 0.999787π-0.999787\pi
0.258174 0.966098i 0.416879π-0.416879\pi
108108 0 0
109109 11.0120 + 8.44984i 1.05476 + 0.809348i 0.982166 0.188014i 0.0602049π-0.0602049\pi
0.0725963 + 0.997361i 0.476872π0.476872\pi
110110 0 0
111111 1.32354i 0.125625i
112112 0 0
113113 0.0684958i 0.00644354i 0.999995 + 0.00322177i 0.00102552π0.00102552\pi
−0.999995 + 0.00322177i 0.998974π0.998974\pi
114114 0 0
115115 3.02382 + 2.32026i 0.281973 + 0.216365i
116116 0 0
117117 −10.7478 14.0068i −0.993633 1.29493i
118118 0 0
119119 0.756872 11.2859i 0.0693823 1.03458i
120120 0 0
121121 18.3682 4.92175i 1.66984 0.447432i
122122 0 0
123123 −0.108501 0.824145i −0.00978318 0.0743107i
124124 0 0
125125 1.01736 + 2.45613i 0.0909957 + 0.219683i
126126 0 0
127127 6.18288 0.548642 0.274321 0.961638i 0.411547π-0.411547\pi
0.274321 + 0.961638i 0.411547π0.411547\pi
128128 0 0
129129 0.889137 + 1.54003i 0.0782841 + 0.135592i
130130 0 0
131131 −8.65291 1.13918i −0.756009 0.0995304i −0.257337 0.966322i 0.582845π-0.582845\pi
−0.498671 + 0.866791i 0.666178π0.666178\pi
132132 0 0
133133 −2.79575 2.45930i −0.242422 0.213248i
134134 0 0
135135 −3.38263 + 0.906374i −0.291131 + 0.0780082i
136136 0 0
137137 11.1426 + 2.98566i 0.951980 + 0.255082i 0.701202 0.712962i 0.252647π-0.252647\pi
0.250778 + 0.968045i 0.419314π0.419314\pi
138138 0 0
139139 −6.81777 + 16.4595i −0.578275 + 1.39608i 0.316084 + 0.948731i 0.397632π0.397632\pi
−0.894359 + 0.447349i 0.852368π0.852368\pi
140140 0 0
141141 −1.65993 + 0.687567i −0.139792 + 0.0579036i
142142 0 0
143143 28.2794 16.3271i 2.36484 1.36534i
144144 0 0
145145 3.39803 + 1.96185i 0.282191 + 0.162923i
146146 0 0
147147 1.31403 + 0.356358i 0.108379 + 0.0293919i
148148 0 0
149149 7.52295 + 9.80409i 0.616304 + 0.803183i 0.992355 0.123416i 0.0393850π-0.0393850\pi
−0.376051 + 0.926599i 0.622718π0.622718\pi
150150 0 0
151151 6.48936 + 1.73882i 0.528097 + 0.141503i 0.513009 0.858383i 0.328531π-0.328531\pi
0.0150875 + 0.999886i 0.495197π0.495197\pi
152152 0 0
153153 −8.95485 8.95485i −0.723957 0.723957i
154154 0 0
155155 1.40212 + 0.580777i 0.112621 + 0.0466491i
156156 0 0
157157 0.632229 0.823937i 0.0504574 0.0657573i −0.767443 0.641117i 0.778471π-0.778471\pi
0.817900 + 0.575360i 0.195138π0.195138\pi
158158 0 0
159159 0.696164 1.20579i 0.0552094 0.0956255i
160160 0 0
161161 −3.16041 1.07815i −0.249075 0.0849701i
162162 0 0
163163 −2.67408 0.352050i −0.209450 0.0275747i 0.0250708 0.999686i 0.492019π-0.492019\pi
−0.234521 + 0.972111i 0.575352π0.575352\pi
164164 0 0
165165 −0.420032 3.19046i −0.0326994 0.248377i
166166 0 0
167167 −4.37579 4.37579i −0.338609 0.338609i 0.517235 0.855843i 0.326961π-0.326961\pi
−0.855843 + 0.517235i 0.826961π0.826961\pi
168168 0 0
169169 15.9270 15.9270i 1.22515 1.22515i
170170 0 0
171171 −4.13313 + 0.544137i −0.316069 + 0.0416112i
172172 0 0
173173 0.198608 1.50858i 0.0150999 0.114695i −0.982235 0.187655i 0.939911π-0.939911\pi
0.997335 + 0.0729600i 0.0232446π0.0232446\pi
174174 0 0
175175 7.17421 + 8.20563i 0.542319 + 0.620287i
176176 0 0
177177 0.0124961 + 0.00721463i 0.000939265 + 0.000542285i
178178 0 0
179179 17.8811 + 13.7206i 1.33650 + 1.02553i 0.996368 + 0.0851496i 0.0271368π0.0271368\pi
0.340127 + 0.940379i 0.389530π0.389530\pi
180180 0 0
181181 6.77001 16.3442i 0.503211 1.21486i −0.444515 0.895772i 0.646624π-0.646624\pi
0.947726 0.319087i 0.103376π-0.103376\pi
182182 0 0
183183 −1.26047 + 1.26047i −0.0931769 + 0.0931769i
184184 0 0
185185 5.31870 19.8496i 0.391038 1.45937i
186186 0 0
187187 18.5827 14.2590i 1.35890 1.04272i
188188 0 0
189189 2.55361 1.70069i 0.185748 0.123707i
190190 0 0
191191 −10.0442 + 17.3971i −0.726772 + 1.25881i 0.231468 + 0.972843i 0.425647π0.425647\pi
−0.958240 + 0.285964i 0.907686π0.907686\pi
192192 0 0
193193 8.76441 + 15.1804i 0.630876 + 1.09271i 0.987373 + 0.158413i 0.0506376π0.0506376\pi
−0.356497 + 0.934296i 0.616029π0.616029\pi
194194 0 0
195195 −1.33970 3.23433i −0.0959380 0.231615i
196196 0 0
197197 −8.32147 3.44687i −0.592880 0.245579i 0.0660089 0.997819i 0.478973π-0.478973\pi
−0.658889 + 0.752240i 0.728973π0.728973\pi
198198 0 0
199199 2.15738 8.05144i 0.152932 0.570751i −0.846341 0.532641i 0.821200π-0.821200\pi
0.999274 0.0381102i 0.0121338π-0.0121338\pi
200200 0 0
201201 −0.0388199 0.144878i −0.00273815 0.0102189i
202202 0 0
203203 −3.37053 0.675744i −0.236565 0.0474279i
204204 0 0
205205 −1.68463 + 12.7960i −0.117660 + 0.893715i
206206 0 0
207207 −3.23773 + 1.86930i −0.225038 + 0.129926i
208208 0 0
209209 7.71043i 0.533342i
210210 0 0
211211 0.534006 0.221193i 0.0367625 0.0152275i −0.364226 0.931310i 0.618667π-0.618667\pi
0.400989 + 0.916083i 0.368667π0.368667\pi
212212 0 0
213213 −2.13833 + 0.281517i −0.146516 + 0.0192892i
214214 0 0
215215 −7.14607 26.6695i −0.487358 1.81884i
216216 0 0
217217 −1.32664 0.0889691i −0.0900585 0.00603961i
218218 0 0
219219 1.10638 0.848953i 0.0747620 0.0573669i
220220 0 0
221221 15.5122 20.2158i 1.04346 1.35986i
222222 0 0
223223 5.07246 0.339677 0.169839 0.985472i 0.445675π-0.445675\pi
0.169839 + 0.985472i 0.445675π0.445675\pi
224224 0 0
225225 12.2032 0.813544
226226 0 0
227227 −6.69399 + 8.72378i −0.444296 + 0.579018i −0.960791 0.277272i 0.910570π-0.910570\pi
0.516496 + 0.856290i 0.327236π0.327236\pi
228228 0 0
229229 12.5005 9.59199i 0.826058 0.633856i −0.106728 0.994288i 0.534037π-0.534037\pi
0.932786 + 0.360432i 0.117371π0.117371\pi
230230 0 0
231231 1.24312 + 2.53045i 0.0817916 + 0.166492i
232232 0 0
233233 −3.50730 13.0894i −0.229771 0.857516i −0.980437 0.196834i 0.936934π-0.936934\pi
0.750666 0.660682i 0.229733π-0.229733\pi
234234 0 0
235235 27.6577 3.64121i 1.80419 0.237526i
236236 0 0
237237 −0.182109 + 0.0754319i −0.0118292 + 0.00489983i
238238 0 0
239239 5.02121i 0.324795i −0.986725 0.162397i 0.948077π-0.948077\pi
0.986725 0.162397i 0.0519227π-0.0519227\pi
240240 0 0
241241 −20.7477 + 11.9787i −1.33648 + 0.771615i −0.986283 0.165062i 0.947218π-0.947218\pi
−0.350194 + 0.936677i 0.613884π0.613884\pi
242242 0 0
243243 0.673966 5.11928i 0.0432349 0.328402i
244244 0 0
245245 −18.2750 10.6249i −1.16755 0.678802i
246246 0 0
247247 −2.17100 8.10227i −0.138137 0.515535i
248248 0 0
249249 −0.337062 + 1.25793i −0.0213604 + 0.0797182i
250250 0 0
251251 −15.8433 6.56249i −1.00002 0.414221i −0.178214 0.983992i 0.557032π-0.557032\pi
−0.821803 + 0.569771i 0.807032π0.807032\pi
252252 0 0
253253 −2.64617 6.38841i −0.166363 0.401636i
254254 0 0
255255 −1.25557 2.17471i −0.0786267 0.136185i
256256 0 0
257257 1.21717 2.10820i 0.0759249 0.131506i −0.825563 0.564310i 0.809142π-0.809142\pi
0.901488 + 0.432804i 0.142476π0.142476\pi
258258 0 0
259259 1.15033 + 17.9672i 0.0714782 + 1.11643i
260260 0 0
261261 −3.05340 + 2.34296i −0.189001 + 0.145025i
262262 0 0
263263 −7.18443 + 26.8126i −0.443011 + 1.65334i 0.278125 + 0.960545i 0.410287π0.410287\pi
−0.721136 + 0.692794i 0.756380π0.756380\pi
264264 0 0
265265 −15.2862 + 15.2862i −0.939023 + 0.939023i
266266 0 0
267267 1.07831 2.60328i 0.0659917 0.159318i
268268 0 0
269269 −7.77004 5.96216i −0.473747 0.363519i 0.344120 0.938926i 0.388177π-0.388177\pi
−0.817868 + 0.575406i 0.804844π0.804844\pi
270270 0 0
271271 −23.9839 13.8471i −1.45692 0.841152i −0.458059 0.888922i 0.651455π-0.651455\pi
−0.998858 + 0.0477701i 0.984789π0.984789\pi
272272 0 0
273273 2.01879 + 2.30903i 0.122183 + 0.139749i
274274 0 0
275275 −2.94603 + 22.3773i −0.177652 + 1.34940i
276276 0 0
277277 1.11886 0.147300i 0.0672256 0.00885042i −0.0968384 0.995300i 0.530873π-0.530873\pi
0.164064 + 0.986450i 0.447540π0.447540\pi
278278 0 0
279279 −1.05263 + 1.05263i −0.0630192 + 0.0630192i
280280 0 0
281281 6.68419 + 6.68419i 0.398746 + 0.398746i 0.877790 0.479045i 0.159017π-0.159017\pi
−0.479045 + 0.877790i 0.659017π0.659017\pi
282282 0 0
283283 2.81117 + 21.3530i 0.167107 + 1.26930i 0.845250 + 0.534372i 0.179452π0.179452\pi
−0.678143 + 0.734930i 0.737215π0.737215\pi
284284 0 0
285285 −0.819552 0.107896i −0.0485460 0.00639121i
286286 0 0
287287 −2.18920 11.0936i −0.129225 0.654832i
288288 0 0
289289 0.638965 1.10672i 0.0375862 0.0651012i
290290 0 0
291291 −0.0535029 + 0.0697263i −0.00313639 + 0.00408743i
292292 0 0
293293 −11.8675 4.91570i −0.693309 0.287178i 0.00806883 0.999967i 0.497432π-0.497432\pi
−0.701378 + 0.712789i 0.747432π0.747432\pi
294294 0 0
295295 −0.158417 0.158417i −0.00922339 0.00922339i
296296 0 0
297297 6.13682 + 1.64435i 0.356094 + 0.0954151i
298298 0 0
299299 −4.57940 5.96799i −0.264834 0.345138i
300300 0 0
301301 13.4086 + 20.1333i 0.772860 + 1.16046i
302302 0 0
303303 −0.584787 0.337627i −0.0335951 0.0193961i
304304 0 0
305305 23.9691 13.8386i 1.37247 0.792394i
306306 0 0
307307 −18.8697 + 7.81608i −1.07695 + 0.446087i −0.849438 0.527688i 0.823059π-0.823059\pi
−0.227512 + 0.973775i 0.573059π0.573059\pi
308308 0 0
309309 0.678463 1.63795i 0.0385964 0.0931799i
310310 0 0
311311 −2.85627 0.765335i −0.161964 0.0433981i 0.176926 0.984224i 0.443385π-0.443385\pi
−0.338890 + 0.940826i 0.610051π0.610051\pi
312312 0 0
313313 26.9261 7.21483i 1.52195 0.407806i 0.601569 0.798821i 0.294542π-0.294542\pi
0.920384 + 0.391015i 0.127876π0.127876\pi
314314 0 0
315315 −22.4228 + 7.57368i −1.26338 + 0.426729i
316316 0 0
317317 −32.5474 4.28495i −1.82805 0.240667i −0.863457 0.504422i 0.831705π-0.831705\pi
−0.964590 + 0.263756i 0.915039π0.915039\pi
318318 0 0
319319 −3.55922 6.16475i −0.199278 0.345160i
320320 0 0
321321 2.45168 0.136839
322322 0 0
323323 −2.30252 5.55878i −0.128116 0.309299i
324324 0 0
325325 3.20495 + 24.3440i 0.177779 + 1.35036i
326326 0 0
327327 −2.60773 + 0.698739i −0.144208 + 0.0386403i
328328 0 0
329329 −21.9362 + 10.7765i −1.20938 + 0.594128i
330330 0 0
331331 −3.65442 4.76253i −0.200865 0.261772i 0.682050 0.731306i 0.261089π-0.261089\pi
−0.882915 + 0.469534i 0.844422π0.844422\pi
332332 0 0
333333 15.9918 + 12.2709i 0.876343 + 0.672441i
334334 0 0
335335 2.32879i 0.127236i
336336 0 0
337337 8.26077i 0.449993i 0.974360 + 0.224996i 0.0722370π0.0722370\pi
−0.974360 + 0.224996i 0.927763π0.927763\pi
338338 0 0
339339 −0.0105693 0.00811014i −0.000574048 0.000440482i
340340 0 0
341341 −1.67612 2.18436i −0.0907670 0.118290i
342342 0 0
343343 18.1478 + 3.69554i 0.979890 + 0.199540i
344344 0 0
345345 −0.716062 + 0.191868i −0.0385515 + 0.0103298i
346346 0 0
347347 −3.23389 24.5639i −0.173605 1.31866i −0.827240 0.561848i 0.810090π-0.810090\pi
0.653636 0.756809i 0.273243π-0.273243\pi
348348 0 0
349349 7.17014 + 17.3102i 0.383809 + 0.926596i 0.991222 + 0.132210i 0.0422073π0.0422073\pi
−0.607413 + 0.794386i 0.707793π0.707793\pi
350350 0 0
351351 6.91168 0.368918
352352 0 0
353353 −1.24335 2.15355i −0.0661769 0.114622i 0.831039 0.556215i 0.187747π-0.187747\pi
−0.897215 + 0.441593i 0.854413π0.854413\pi
354354 0 0
355355 33.2007 + 4.37095i 1.76211 + 0.231986i
356356 0 0
357357 1.65188 + 1.45309i 0.0874266 + 0.0769054i
358358 0 0
359359 16.1733 4.33362i 0.853594 0.228720i 0.194614 0.980880i 0.437655π-0.437655\pi
0.658980 + 0.752160i 0.270988π0.270988\pi
360360 0 0
361361 16.4395 + 4.40494i 0.865234 + 0.231839i
362362 0 0
363363 −1.41540 + 3.41709i −0.0742894 + 0.179350i
364364 0 0
365365 −20.0043 + 8.28607i −1.04707 + 0.433712i
366366 0 0
367367 6.07154 3.50540i 0.316932 0.182981i −0.333092 0.942894i 0.608092π-0.608092\pi
0.650024 + 0.759914i 0.274759π0.274759\pi
368368 0 0
369369 −10.9637 6.32991i −0.570749 0.329522i
370370 0 0
371371 8.40252 16.9738i 0.436237 0.881237i
372372 0 0
373373 10.9932 + 14.3266i 0.569207 + 0.741805i 0.985917 0.167234i 0.0534836π-0.0534836\pi
−0.416710 + 0.909039i 0.636817π0.636817\pi
374374 0 0
375375 −0.499456 0.133829i −0.0257918 0.00691089i
376376 0 0
377377 −5.47588 5.47588i −0.282022 0.282022i
378378 0 0
379379 3.29244 + 1.36377i 0.169121 + 0.0700523i 0.465638 0.884975i 0.345825π-0.345825\pi
−0.296516 + 0.955028i 0.595825π0.595825\pi
380380 0 0
381381 −0.732074 + 0.954058i −0.0375053 + 0.0488779i
382382 0 0
383383 10.0023 17.3246i 0.511096 0.885244i −0.488821 0.872384i 0.662573π-0.662573\pi
0.999917 0.0128604i 0.00409371π-0.00409371\pi
384384 0 0
385385 −8.47491 42.9458i −0.431922 2.18872i
386386 0 0
387387 26.8510 + 3.53500i 1.36491 + 0.179694i
388388 0 0
389389 −0.604023 4.58801i −0.0306252 0.232621i 0.969286 0.245936i 0.0790952π-0.0790952\pi
−0.999911 + 0.0133142i 0.995762π0.995762\pi
390390 0 0
391391 −3.81547 3.81547i −0.192957 0.192957i
392392 0 0
393393 1.20032 1.20032i 0.0605480 0.0605480i
394394 0 0
395395 3.03429 0.399471i 0.152671 0.0200996i
396396 0 0
397397 3.56041 27.0440i 0.178692 1.35730i −0.633425 0.773804i 0.718352π-0.718352\pi
0.812117 0.583495i 0.198315π-0.198315\pi
398398 0 0
399399 0.710512 0.140212i 0.0355701 0.00701940i
400400 0 0
401401 1.09372 + 0.631459i 0.0546177 + 0.0315336i 0.527060 0.849828i 0.323294π-0.323294\pi
−0.472442 + 0.881362i 0.656628π0.656628\pi
402402 0 0
403403 −2.37634 1.82343i −0.118374 0.0908315i
404404 0 0
405405 −10.0091 + 24.1641i −0.497357 + 1.20072i
406406 0 0
407407 −26.3622 + 26.3622i −1.30673 + 1.30673i
408408 0 0
409409 −2.26792 + 8.46400i −0.112142 + 0.418518i −0.999057 0.0434134i 0.986177π-0.986177\pi
0.886916 + 0.461931i 0.152843π0.152843\pi
410410 0 0
411411 −1.78003 + 1.36587i −0.0878026 + 0.0673733i
412412 0 0
413413 0.175907 + 0.0870787i 0.00865580 + 0.00428486i
414414 0 0
415415 10.1101 17.5112i 0.496286 0.859592i
416416 0 0
417417 −1.73257 3.00089i −0.0848441 0.146954i
418418 0 0
419419 −0.789499 1.90602i −0.0385696 0.0931152i 0.903421 0.428755i 0.141048π-0.141048\pi
−0.941990 + 0.335640i 0.891048π0.891048\pi
420420 0 0
421421 8.35055 + 3.45891i 0.406981 + 0.168577i 0.576776 0.816902i 0.304311π-0.304311\pi
−0.169795 + 0.985479i 0.554311π0.554311\pi
422422 0 0
423423 −7.08214 + 26.4309i −0.344346 + 1.28512i
424424 0 0
425425 4.55850 + 17.0126i 0.221120 + 0.825230i
426426 0 0
427427 −16.0156 + 18.2066i −0.775047 + 0.881079i
428428 0 0
429429 −0.829000 + 6.29688i −0.0400245 + 0.304016i
430430 0 0
431431 −2.36261 + 1.36406i −0.113803 + 0.0657043i −0.555821 0.831302i 0.687596π-0.687596\pi
0.442018 + 0.897006i 0.354263π0.354263\pi
432432 0 0
433433 23.1713i 1.11354i 0.830666 + 0.556771i 0.187960π0.187960\pi
−0.830666 + 0.556771i 0.812040π0.812040\pi
434434 0 0
435435 −0.705065 + 0.292047i −0.0338053 + 0.0140026i
436436 0 0
437437 −1.76104 + 0.231845i −0.0842420 + 0.0110907i
438438 0 0
439439 4.54888 + 16.9766i 0.217106 + 0.810251i 0.985415 + 0.170171i 0.0544320π0.0544320\pi
−0.768308 + 0.640080i 0.778901π0.778901\pi
440440 0 0
441441 16.4885 12.5729i 0.785165 0.598712i
442442 0 0
443443 −5.38327 + 4.13073i −0.255767 + 0.196257i −0.728684 0.684850i 0.759868π-0.759868\pi
0.472917 + 0.881107i 0.343201π0.343201\pi
444444 0 0
445445 −26.6333 + 34.7092i −1.26254 + 1.64537i
446446 0 0
447447 −2.40358 −0.113685
448448 0 0
449449 18.3637 0.866635 0.433318 0.901241i 0.357343π-0.357343\pi
0.433318 + 0.901241i 0.357343π0.357343\pi
450450 0 0
451451 14.2542 18.5764i 0.671204 0.874730i
452452 0 0
453453 −1.03667 + 0.795468i −0.0487072 + 0.0373743i
454454 0 0
455455 −20.9977 42.7420i −0.984386 2.00377i
456456 0 0
457457 −6.02250 22.4763i −0.281720 1.05140i −0.951203 0.308567i 0.900151π-0.900151\pi
0.669482 0.742828i 0.266516π-0.266516\pi
458458 0 0
459459 4.91534 0.647117i 0.229428 0.0302048i
460460 0 0
461461 −25.1245 + 10.4069i −1.17016 + 0.484698i −0.881247 0.472657i 0.843295π-0.843295\pi
−0.288917 + 0.957354i 0.593295π0.593295\pi
462462 0 0
463463 11.5497i 0.536761i 0.963313 + 0.268381i 0.0864885π0.0864885\pi
−0.963313 + 0.268381i 0.913512π0.913512\pi
464464 0 0
465465 −0.255633 + 0.147590i −0.0118547 + 0.00684432i
466466 0 0
467467 −1.34169 + 10.1912i −0.0620861 + 0.471590i 0.931954 + 0.362576i 0.118103π0.118103\pi
−0.994040 + 0.109014i 0.965231π0.965231\pi
468468 0 0
469469 −0.652903 1.93299i −0.0301483 0.0892574i
470470 0 0
471471 0.0522806 + 0.195114i 0.00240896 + 0.00899037i
472472 0 0
473473 −12.9645 + 48.3841i −0.596108 + 2.22470i
474474 0 0
475475 5.35647 + 2.21872i 0.245772 + 0.101802i
476476 0 0
477477 −8.11473 19.5907i −0.371548 0.896997i
478478 0 0
479479 8.77291 + 15.1951i 0.400844 + 0.694283i 0.993828 0.110932i 0.0353834π-0.0353834\pi
−0.592984 + 0.805215i 0.702050π0.702050\pi
480480 0 0
481481 −20.2792 + 35.1246i −0.924653 + 1.60155i
482482 0 0
483483 0.540569 0.360015i 0.0245967 0.0163812i
484484 0 0
485485 1.08260 0.830710i 0.0491584 0.0377206i
486486 0 0
487487 3.33054 12.4297i 0.150921 0.563245i −0.848499 0.529197i 0.822493π-0.822493\pi
0.999420 0.0340483i 0.0108400π-0.0108400\pi
488488 0 0
489489 0.370944 0.370944i 0.0167747 0.0167747i
490490 0 0
491491 −15.2024 + 36.7019i −0.686076 + 1.65633i 0.0664663 + 0.997789i 0.478828π0.478828\pi
−0.752542 + 0.658544i 0.771172π0.771172\pi
492492 0 0
493493 −4.40694 3.38156i −0.198479 0.152298i
494494 0 0
495495 −42.4432 24.5046i −1.90768 1.10140i
496496 0 0
497497 −28.7834 + 5.68011i −1.29111 + 0.254788i
498498 0 0
499499 −3.23014 + 24.5353i −0.144601 + 1.09835i 0.753150 + 0.657849i 0.228533π0.228533\pi
−0.897751 + 0.440504i 0.854800π0.854800\pi
500500 0 0
501501 1.19332 0.157104i 0.0533136 0.00701887i
502502 0 0
503503 13.6066 13.6066i 0.606689 0.606689i −0.335390 0.942079i 0.608868π-0.608868\pi
0.942079 + 0.335390i 0.108868π0.108868\pi
504504 0 0
505505 7.41351 + 7.41351i 0.329897 + 0.329897i
506506 0 0
507507 0.571825 + 4.34344i 0.0253956 + 0.192899i
508508 0 0
509509 −24.1716 3.18225i −1.07139 0.141051i −0.425861 0.904789i 0.640029π-0.640029\pi
−0.645527 + 0.763738i 0.723362π0.723362\pi
510510 0 0
511511 14.2813 12.4862i 0.631769 0.552358i
512512 0 0
513513 0.816005 1.41336i 0.0360275 0.0624014i
514514 0 0
515515 −16.7574 + 21.8386i −0.738418 + 0.962324i
516516 0 0
517517 −46.7575 19.3676i −2.05639 0.851786i
518518 0 0
519519 0.209268 + 0.209268i 0.00918583 + 0.00918583i
520520 0 0
521521 19.7383 + 5.28886i 0.864750 + 0.231709i 0.663816 0.747896i 0.268936π-0.268936\pi
0.200934 + 0.979605i 0.435602π0.435602\pi
522522 0 0
523523 21.5776 + 28.1205i 0.943525 + 1.22963i 0.973175 + 0.230065i 0.0738939π0.0738939\pi
−0.0296506 + 0.999560i 0.509439π0.509439\pi
524524 0 0
525525 −2.11563 + 0.135451i −0.0923338 + 0.00591158i
526526 0 0
527527 −1.86069 1.07427i −0.0810530 0.0467960i
528528 0 0
529529 18.5391 10.7035i 0.806046 0.465371i
530530 0 0
531531 0.203026 0.0840963i 0.00881059 0.00364947i
532532 0 0
533533 9.74808 23.5340i 0.422236 1.01937i
534534 0 0
535535 −36.7688 9.85218i −1.58966 0.425947i
536536 0 0
537537 −4.23437 + 1.13459i −0.182726 + 0.0489614i
538538 0 0
539539 19.0749 + 33.2707i 0.821613 + 1.43307i
540540 0 0
541541 9.81306 + 1.29191i 0.421896 + 0.0555437i 0.338486 0.940972i 0.390085π-0.390085\pi
0.0834107 + 0.996515i 0.473419π0.473419\pi
542542 0 0
543543 1.72043 + 2.97987i 0.0738307 + 0.127878i
544544 0 0
545545 41.9171 1.79553
546546 0 0
547547 2.30920 + 5.57491i 0.0987344 + 0.238366i 0.965527 0.260303i 0.0838224π-0.0838224\pi
−0.866793 + 0.498669i 0.833822π0.833822\pi
548548 0 0
549549 3.54356 + 26.9160i 0.151235 + 1.14875i
550550 0 0
551551 −1.76625 + 0.473265i −0.0752447 + 0.0201618i
552552 0 0
553553 −2.40659 + 1.18227i −0.102339 + 0.0502754i
554554 0 0
555555 2.43317 + 3.17098i 0.103283 + 0.134600i
556556 0 0
557557 −26.1993 20.1034i −1.11010 0.851810i −0.120085 0.992764i 0.538317π-0.538317\pi
−0.990016 + 0.140953i 0.954983π0.954983\pi
558558 0 0
559559 54.4933i 2.30482i
560560 0 0
561561 4.55574i 0.192343i
562562 0 0
563563 −33.6425 25.8148i −1.41786 1.08797i −0.982196 0.187858i 0.939846π-0.939846\pi
−0.435668 0.900108i 0.643488π-0.643488\pi
564564 0 0
565565 0.125922 + 0.164104i 0.00529757 + 0.00690392i
566566 0 0
567567 1.53329 22.8634i 0.0643922 0.960172i
568568 0 0
569569 −0.667826 + 0.178943i −0.0279967 + 0.00750170i −0.272790 0.962074i 0.587946π-0.587946\pi
0.244794 + 0.969575i 0.421280π0.421280\pi
570570 0 0
571571 0.400155 + 3.03948i 0.0167460 + 0.127198i 0.997776 0.0666583i 0.0212337π-0.0212337\pi
−0.981030 + 0.193856i 0.937900π0.937900\pi
572572 0 0
573573 −1.49521 3.60975i −0.0624633 0.150800i
574574 0 0
575575 5.19951 0.216834
576576 0 0
577577 −23.0936 39.9993i −0.961399 1.66519i −0.718993 0.695017i 0.755397π-0.755397\pi
−0.242406 0.970175i 0.577936π-0.577936\pi
578578 0 0
579579 −3.38017 0.445008i −0.140475 0.0184939i
580580 0 0
581581 −3.48234 + 17.3695i −0.144472 + 0.720609i
582582 0 0
583583 37.8832 10.1508i 1.56896 0.420402i
584584 0 0
585585 −51.4997 13.7993i −2.12925 0.570531i
586586 0 0
587587 0.997077 2.40716i 0.0411538 0.0993540i −0.901966 0.431807i 0.857876π-0.857876\pi
0.943120 + 0.332453i 0.107876π0.107876\pi
588588 0 0
589589 −0.653426 + 0.270658i −0.0269239 + 0.0111523i
590590 0 0
591591 1.51716 0.875935i 0.0624078 0.0360312i
592592 0 0
593593 19.2249 + 11.0995i 0.789473 + 0.455802i 0.839777 0.542932i 0.182686π-0.182686\pi
−0.0503042 + 0.998734i 0.516019π0.516019\pi
594594 0 0
595595 −18.9346 28.4306i −0.776243 1.16554i
596596 0 0
597597 0.986948 + 1.28622i 0.0403931 + 0.0526413i
598598 0 0
599599 19.3702 + 5.19023i 0.791446 + 0.212067i 0.631825 0.775111i 0.282306π-0.282306\pi
0.159621 + 0.987178i 0.448973π0.448973\pi
600600 0 0
601601 17.5555 + 17.5555i 0.716102 + 0.716102i 0.967805 0.251703i 0.0809905π-0.0809905\pi
−0.251703 + 0.967805i 0.580991π0.580991\pi
602602 0 0
603603 −2.11041 0.874160i −0.0859425 0.0355985i
604604 0 0
605605 34.9591 45.5596i 1.42129 1.85226i
606606 0 0
607607 −15.1703 + 26.2757i −0.615742 + 1.06650i 0.374512 + 0.927222i 0.377810π0.377810\pi
−0.990254 + 0.139274i 0.955523π0.955523\pi
608608 0 0
609609 0.503355 0.440084i 0.0203970 0.0178331i
610610 0 0
611611 −54.5869 7.18651i −2.20835 0.290735i
612612 0 0
613613 −0.908361 6.89968i −0.0366883 0.278676i −0.999949 0.0101071i 0.996783π-0.996783\pi
0.963261 0.268569i 0.0865506π-0.0865506\pi
614614 0 0
615615 −1.77505 1.77505i −0.0715768 0.0715768i
616616 0 0
617617 3.00134 3.00134i 0.120829 0.120829i −0.644106 0.764936i 0.722771π-0.722771\pi
0.764936 + 0.644106i 0.222771π0.222771\pi
618618 0 0
619619 −0.367838 + 0.0484268i −0.0147847 + 0.00194644i −0.137915 0.990444i 0.544040π-0.544040\pi
0.123130 + 0.992391i 0.460707π0.460707\pi
620620 0 0
621621 0.191038 1.45108i 0.00766608 0.0582297i
622622 0 0
623623 12.3756 36.2770i 0.495819 1.45341i
624624 0 0
625625 24.7914 + 14.3133i 0.991657 + 0.572534i
626626 0 0
627627 1.18977 + 0.912942i 0.0475148 + 0.0364594i
628628 0 0
629629 −11.1333 + 26.8781i −0.443912 + 1.07170i
630630 0 0
631631 34.5848 34.5848i 1.37680 1.37680i 0.526830 0.849971i 0.323381π-0.323381\pi
0.849971 0.526830i 0.176619π-0.176619\pi
632632 0 0
633633 −0.0290967 + 0.108591i −0.00115649 + 0.00431609i
634634 0 0
635635 14.8131 11.3665i 0.587841 0.451067i
636636 0 0
637637 29.4121 + 29.5907i 1.16535 + 1.17243i
638638 0 0
639639 −16.4236 + 28.4466i −0.649709 + 1.12533i
640640 0 0
641641 3.23073 + 5.59579i 0.127606 + 0.221021i 0.922749 0.385402i 0.125937π-0.125937\pi
−0.795142 + 0.606423i 0.792604π0.792604\pi
642642 0 0
643643 −2.82466 6.81934i −0.111394 0.268929i 0.858345 0.513073i 0.171493π-0.171493\pi
−0.969739 + 0.244144i 0.921493π0.921493\pi
644644 0 0
645645 4.96139 + 2.05508i 0.195355 + 0.0809185i
646646 0 0
647647 0.271500 1.01325i 0.0106738 0.0398351i −0.960384 0.278682i 0.910103π-0.910103\pi
0.971057 + 0.238846i 0.0767693π0.0767693\pi
648648 0 0
649649 0.105196 + 0.392598i 0.00412932 + 0.0154108i
650650 0 0
651651 0.170808 0.194176i 0.00669449 0.00761034i
652652 0 0
653653 1.71660 13.0389i 0.0671757 0.510250i −0.924470 0.381256i 0.875492π-0.875492\pi
0.991645 0.128994i 0.0411749π-0.0411749\pi
654654 0 0
655655 −22.8252 + 13.1781i −0.891853 + 0.514912i
656656 0 0
657657 21.2388i 0.828603i
658658 0 0
659659 9.08982 3.76512i 0.354089 0.146668i −0.198547 0.980091i 0.563622π-0.563622\pi
0.552636 + 0.833423i 0.313622π0.313622\pi
660660 0 0
661661 26.6893 3.51371i 1.03809 0.136668i 0.407837 0.913055i 0.366283π-0.366283\pi
0.630256 + 0.776387i 0.282950π0.282950\pi
662662 0 0
663663 1.28274 + 4.78725i 0.0498175 + 0.185921i
664664 0 0
665665 −11.2193 0.752401i −0.435065 0.0291769i
666666 0 0
667667 −1.30099 + 0.998284i −0.0503745 + 0.0386537i
668668 0 0
669669 −0.600597 + 0.782713i −0.0232204 + 0.0302614i
670670 0 0
671671 −50.2122 −1.93842
672672 0 0
673673 −28.1530 −1.08522 −0.542609 0.839985i 0.682563π-0.682563\pi
−0.542609 + 0.839985i 0.682563π0.682563\pi
674674 0 0
675675 −2.90824 + 3.79010i −0.111938 + 0.145881i
676676 0 0
677677 20.6879 15.8744i 0.795102 0.610103i −0.129264 0.991610i 0.541261π-0.541261\pi
0.924366 + 0.381507i 0.124595π0.124595\pi
678678 0 0
679679 −0.665706 + 0.993044i −0.0255475 + 0.0381095i
680680 0 0
681681 −0.553543 2.06585i −0.0212118 0.0791636i
682682 0 0
683683 −3.51722 + 0.463050i −0.134583 + 0.0177181i −0.197516 0.980300i 0.563288π-0.563288\pi
0.0629339 + 0.998018i 0.479954π0.479954\pi
684684 0 0
685685 32.1847 13.3313i 1.22971 0.509364i
686686 0 0
687687 3.06463i 0.116923i
688688 0 0
689689 36.9502 21.3332i 1.40769 0.812731i
690690 0 0
691691 0.159432 1.21101i 0.00606507 0.0460688i −0.988145 0.153525i 0.950937π-0.950937\pi
0.994210 + 0.107457i 0.0342707π0.0342707\pi
692692 0 0
693693 42.0997 + 8.44040i 1.59924 + 0.320624i
694694 0 0
695695 13.9248 + 51.9680i 0.528197 + 1.97126i
696696 0 0
697697 4.72909 17.6492i 0.179127 0.668511i
698698 0 0
699699 2.43506 + 1.00863i 0.0921023 + 0.0381500i
700700 0 0
701701 9.67092 + 23.3477i 0.365266 + 0.881830i 0.994512 + 0.104623i 0.0333637π0.0333637\pi
−0.629246 + 0.777206i 0.716636π0.716636\pi
702702 0 0
703703 4.78840 + 8.29375i 0.180598 + 0.312805i
704704 0 0
705705 −2.71291 + 4.69890i −0.102174 + 0.176971i
706706 0 0
707707 −8.23199 4.07506i −0.309596 0.153259i
708708 0 0
709709 −1.27025 + 0.974694i −0.0477051 + 0.0366054i −0.632339 0.774692i 0.717905π-0.717905\pi
0.584634 + 0.811297i 0.301238π0.301238\pi
710710 0 0
711711 −0.776971 + 2.89969i −0.0291387 + 0.108747i
712712 0 0
713713 −0.448503 + 0.448503i −0.0167966 + 0.0167966i
714714 0 0
715715 37.7371 91.1054i 1.41129 3.40715i
716716 0 0
717717 0.774804 + 0.594528i 0.0289356 + 0.0222031i
718718 0 0
719719 6.32208 + 3.65005i 0.235774 + 0.136124i 0.613233 0.789902i 0.289869π-0.289869\pi
−0.377459 + 0.926026i 0.623202π0.623202\pi
720720 0 0
721721 7.78661 22.8251i 0.289988 0.850050i
722722 0 0
723723 0.608211 4.61982i 0.0226196 0.171813i
724724 0 0
725725 5.30686 0.698662i 0.197092 0.0259476i
726726 0 0
727727 15.9338 15.9338i 0.590952 0.590952i −0.346937 0.937888i 0.612778π-0.612778\pi
0.937888 + 0.346937i 0.112778π0.112778\pi
728728 0 0
729729 −17.6625 17.6625i −0.654168 0.654168i
730730 0 0
731731 5.10202 + 38.7537i 0.188705 + 1.43336i
732732 0 0
733733 8.04946 + 1.05973i 0.297314 + 0.0391421i 0.277707 0.960666i 0.410425π-0.410425\pi
0.0196063 + 0.999808i 0.493759π0.493759\pi
734734 0 0
735735 3.80331 1.56192i 0.140287 0.0576122i
736736 0 0
737737 2.11246 3.65889i 0.0778135 0.134777i
738738 0 0
739739 24.1438 31.4648i 0.888143 1.15745i −0.0985941 0.995128i 0.531435π-0.531435\pi
0.986738 0.162323i 0.0518988π-0.0518988\pi
740740 0 0
741741 1.50728 + 0.624338i 0.0553715 + 0.0229356i
742742 0 0
743743 33.9729 + 33.9729i 1.24634 + 1.24634i 0.957323 + 0.289020i 0.0933295π0.0933295\pi
0.289020 + 0.957323i 0.406671π0.406671\pi
744744 0 0
745745 36.0474 + 9.65887i 1.32067 + 0.353874i
746746 0 0
747747 12.0741 + 15.7352i 0.441767 + 0.575722i
748748 0 0
749749 33.2818 2.13084i 1.21609 0.0778591i
750750 0 0
751751 −9.05161 5.22595i −0.330298 0.190698i 0.325675 0.945482i 0.394408π-0.394408\pi
−0.655973 + 0.754784i 0.727742π0.727742\pi
752752 0 0
753753 2.88853 1.66769i 0.105264 0.0607741i
754754 0 0
755755 18.7440 7.76403i 0.682165 0.282562i
756756 0 0
757757 2.64470 6.38487i 0.0961232 0.232062i −0.868503 0.495684i 0.834917π-0.834917\pi
0.964626 + 0.263622i 0.0849173π0.0849173\pi
758758 0 0
759759 1.29909 + 0.348090i 0.0471539 + 0.0126349i
760760 0 0
761761 −43.3060 + 11.6038i −1.56984 + 0.420637i −0.935762 0.352632i 0.885287π-0.885287\pi
−0.634078 + 0.773269i 0.718620π0.718620\pi
762762 0 0
763763 −34.7929 + 11.7519i −1.25959 + 0.425448i
764764 0 0
765765 −37.9168 4.99184i −1.37088 0.180480i
766766 0 0
767767 0.221085 + 0.382930i 0.00798291 + 0.0138268i
768768 0 0
769769 −24.3333 −0.877480 −0.438740 0.898614i 0.644575π-0.644575\pi
−0.438740 + 0.898614i 0.644575π0.644575\pi
770770 0 0
771771 0.181191 + 0.437435i 0.00652545 + 0.0157538i
772772 0 0
773773 1.78908 + 13.5894i 0.0643486 + 0.488776i 0.993027 + 0.117890i 0.0376129π0.0376129\pi
−0.928678 + 0.370887i 0.879054π0.879054\pi
774774 0 0
775775 1.99980 0.535844i 0.0718349 0.0192481i
776776 0 0
777777 −2.90866 1.94987i −0.104347 0.0699513i
778778 0 0
779779 −3.66156 4.77184i −0.131189 0.170969i
780780 0 0
781781 −48.1985 36.9840i −1.72468 1.32339i
782782 0 0
783783 1.50671i 0.0538453i
784784 0 0
785785 3.13629i 0.111939i
786786 0 0
787787 −43.4167 33.3148i −1.54764 1.18754i −0.908076 0.418804i 0.862449π-0.862449\pi
−0.639561 0.768740i 0.720884π-0.720884\pi
788788 0 0
789789 −3.28670 4.28331i −0.117010 0.152490i
790790 0 0
791791 −0.150529 0.100910i −0.00535219 0.00358794i
792792 0 0
793793 −52.7639 + 14.1381i −1.87370 + 0.502057i
794794 0 0
795795 −0.548819 4.16869i −0.0194646 0.147848i
796796 0 0
797797 13.4980 + 32.5870i 0.478122 + 1.15429i 0.960489 + 0.278320i 0.0897774π0.0897774\pi
−0.482366 + 0.875970i 0.660223π0.660223\pi
798798 0 0
799799 −39.4932 −1.39717
800800 0 0
801801 −21.4570 37.1645i −0.758144 1.31314i
802802 0 0
803803 38.9462 + 5.12737i 1.37438 + 0.180941i
804804 0 0
805805 −9.55386 + 3.22699i −0.336729 + 0.113736i
806806 0 0
807807 1.84000 0.493026i 0.0647710 0.0173553i
808808 0 0
809809 23.5700 + 6.31557i 0.828678 + 0.222043i 0.648137 0.761524i 0.275549π-0.275549\pi
0.180541 + 0.983567i 0.442215π0.442215\pi
810810 0 0
811811 16.1023 38.8745i 0.565429 1.36507i −0.339942 0.940446i 0.610407π-0.610407\pi
0.905371 0.424621i 0.139593π-0.139593\pi
812812 0 0
813813 4.97647 2.06132i 0.174532 0.0722937i
814814 0 0
815815 −7.05385 + 4.07254i −0.247086 + 0.142655i
816816 0 0
817817 11.1433 + 6.43357i 0.389854 + 0.225082i
818818 0 0
819819 46.6157 2.98453i 1.62889 0.104288i
820820 0 0
821821 0.799478 + 1.04190i 0.0279020 + 0.0363625i 0.807096 0.590420i 0.201038π-0.201038\pi
−0.779194 + 0.626783i 0.784371π0.784371\pi
822822 0 0
823823 −8.10536 2.17183i −0.282535 0.0757051i 0.114768 0.993392i 0.463387π-0.463387\pi
−0.397304 + 0.917687i 0.630054π0.630054\pi
824824 0 0
825825 −3.10415 3.10415i −0.108072 0.108072i
826826 0 0
827827 9.70756 + 4.02100i 0.337565 + 0.139824i 0.545026 0.838419i 0.316520π-0.316520\pi
−0.207461 + 0.978243i 0.566520π0.566520\pi
828828 0 0
829829 −9.33231 + 12.1621i −0.324125 + 0.422407i −0.926786 0.375589i 0.877440π-0.877440\pi
0.602661 + 0.797997i 0.294107π0.294107\pi
830830 0 0
831831 −0.109747 + 0.190088i −0.00380709 + 0.00659407i
832832 0 0
833833 23.6874 + 18.2901i 0.820718 + 0.633714i
834834 0 0
835835 −18.5280 2.43926i −0.641189 0.0844141i
836836 0 0
837837 −0.0760675 0.577790i −0.00262928 0.0199714i
838838 0 0
839839 −13.7601 13.7601i −0.475050 0.475050i 0.428494 0.903545i 0.359044π-0.359044\pi
−0.903545 + 0.428494i 0.859044π0.859044\pi
840840 0 0
841841 19.3124 19.3124i 0.665944 0.665944i
842842 0 0
843843 −1.82285 + 0.239982i −0.0627821 + 0.00826542i
844844 0 0
845845 8.87841 67.4382i 0.305427 2.31995i
846846 0 0
847847 −16.2444 + 47.6175i −0.558163 + 1.63616i
848848 0 0
849849 −3.62775 2.09448i −0.124504 0.0718825i
850850 0 0
851851 6.81375 + 5.22837i 0.233572 + 0.179226i
852852 0 0
853853 18.5187 44.7080i 0.634067 1.53077i −0.200400 0.979714i 0.564224π-0.564224\pi
0.834467 0.551058i 0.185776π-0.185776\pi
854854 0 0
855855 −8.90196 + 8.90196i −0.304441 + 0.304441i
856856 0 0
857857 −6.34114 + 23.6655i −0.216609 + 0.808397i 0.768985 + 0.639267i 0.220762π0.220762\pi
−0.985594 + 0.169129i 0.945904π0.945904\pi
858858 0 0
859859 −4.83863 + 3.71281i −0.165092 + 0.126680i −0.688003 0.725708i 0.741513π-0.741513\pi
0.522911 + 0.852387i 0.324846π0.324846\pi
860860 0 0
861861 1.97102 + 0.975708i 0.0671721 + 0.0332520i
862862 0 0
863863 24.9061 43.1386i 0.847814 1.46846i −0.0353411 0.999375i 0.511252π-0.511252\pi
0.883155 0.469081i 0.155415π-0.155415\pi
864864 0 0
865865 −2.29752 3.97942i −0.0781181 0.135304i
866866 0 0
867867 0.0951183 + 0.229636i 0.00323039 + 0.00779884i
868868 0 0
869869 −5.12969 2.12479i −0.174013 0.0720785i
870870 0 0
871871 1.18960 4.43963i 0.0403079 0.150431i
872872 0 0
873873 0.346433 + 1.29290i 0.0117250 + 0.0437582i
874874 0 0
875875 −6.89649 1.38265i −0.233144 0.0467420i
876876 0 0
877877 −4.30096 + 32.6691i −0.145233 + 1.10316i 0.751231 + 0.660039i 0.229460π0.229460\pi
−0.896464 + 0.443116i 0.853873π0.853873\pi
878878 0 0
879879 2.16368 1.24920i 0.0729792 0.0421345i
880880 0 0
881881 6.14703i 0.207099i −0.994624 0.103549i 0.966980π-0.966980\pi
0.994624 0.103549i 0.0330200π-0.0330200\pi
882882 0 0
883883 −36.8658 + 15.2703i −1.24063 + 0.513887i −0.903913 0.427717i 0.859318π-0.859318\pi
−0.336721 + 0.941604i 0.609318π0.609318\pi
884884 0 0
885885 0.0432018 0.00568763i 0.00145221 0.000191188i
886886 0 0
887887 7.05302 + 26.3222i 0.236817 + 0.883814i 0.977321 + 0.211762i 0.0679202π0.0679202\pi
−0.740504 + 0.672052i 0.765413π0.765413\pi
888888 0 0
889889 −9.10879 + 13.5877i −0.305499 + 0.455717i
890890 0 0
891891 37.6453 28.8862i 1.26116 0.967725i
892892 0 0
893893 −7.91419 + 10.3140i −0.264838 + 0.345144i
894894 0 0
895895 68.0639 2.27513
896896 0 0
897897 1.46312 0.0488520
898898 0 0
899899 −0.397497 + 0.518029i −0.0132573 + 0.0172772i
900900 0 0
901901 24.2803 18.6310i 0.808895 0.620687i
902902 0 0
903903 −4.69432 0.314816i −0.156217 0.0104764i
904904 0 0
905905 −13.8272 51.6039i −0.459633 1.71537i
906906 0 0
907907 −19.5273 + 2.57082i −0.648394 + 0.0853627i −0.447548 0.894260i 0.647703π-0.647703\pi
−0.200847 + 0.979623i 0.564369π0.564369\pi
908908 0 0
909909 −9.50112 + 3.93549i −0.315132 + 0.130532i
910910 0 0
911911 15.2338i 0.504719i −0.967634 0.252360i 0.918793π-0.918793\pi
0.967634 0.252360i 0.0812066π-0.0812066\pi
912912 0 0
913913 −31.7691 + 18.3419i −1.05140 + 0.607028i
914914 0 0
915915 −0.702645 + 5.33712i −0.0232287 + 0.176440i
916916 0 0
917917 15.2512 17.3377i 0.503639 0.572541i
918918 0 0
919919 13.9437 + 52.0387i 0.459961 + 1.71660i 0.673079 + 0.739571i 0.264971π0.264971\pi
−0.213118 + 0.977026i 0.568362π0.568362\pi
920920 0 0
921921 1.02816 3.83716i 0.0338792 0.126439i
922922 0 0
923923 −61.0613 25.2924i −2.00986 0.832510i
924924 0 0
925925 −10.7281 25.8998i −0.352737 0.851581i
926926 0 0
927927 −13.5005 23.3835i −0.443414 0.768015i
928928 0 0
929929 −11.2640 + 19.5098i −0.369559 + 0.640095i −0.989497 0.144556i 0.953824π-0.953824\pi
0.619938 + 0.784651i 0.287158π0.287158\pi
930930 0 0
931931 9.52342 2.52093i 0.312117 0.0826201i
932932 0 0
933933 0.456288 0.350122i 0.0149382 0.0114625i
934934 0 0
935935 18.3074 68.3242i 0.598716 2.23444i
936936 0 0
937937 −10.5179 + 10.5179i −0.343606 + 0.343606i −0.857721 0.514115i 0.828120π-0.828120\pi
0.514115 + 0.857721i 0.328120π0.328120\pi
938938 0 0
939939 −2.07485 + 5.00913i −0.0677102 + 0.163467i
940940 0 0
941941 23.6476 + 18.1455i 0.770890 + 0.591525i 0.917531 0.397665i 0.130179π-0.130179\pi
−0.146640 + 0.989190i 0.546846π0.546846\pi
942942 0 0
943943 −4.67141 2.69704i −0.152122 0.0878278i
944944 0 0
945945 2.99151 8.76909i 0.0973138 0.285258i
946946 0 0
947947 6.68210 50.7556i 0.217139 1.64934i −0.441781 0.897123i 0.645653π-0.645653\pi
0.658920 0.752213i 0.271013π-0.271013\pi
948948 0 0
949949 42.3691 5.57800i 1.37536 0.181070i
950950 0 0
951951 4.51493 4.51493i 0.146406 0.146406i
952952 0 0
953953 −6.86940 6.86940i −0.222522 0.222522i 0.587038 0.809560i 0.300294π-0.300294\pi
−0.809560 + 0.587038i 0.800294π0.800294\pi
954954 0 0
955955 7.91831 + 60.1455i 0.256230 + 1.94626i
956956 0 0
957957 1.37268 + 0.180717i 0.0443726 + 0.00584176i
958958 0 0
959959 −22.9770 + 20.0889i −0.741967 + 0.648704i
960960 0 0
961961 15.3737 26.6281i 0.495926 0.858970i
962962 0 0
963963 22.7302 29.6226i 0.732471 0.954575i
964964 0 0
965965 48.9055 + 20.2573i 1.57432 + 0.652106i
966966 0 0
967967 −10.0451 10.0451i −0.323029 0.323029i 0.526899 0.849928i 0.323355π-0.323355\pi
−0.849928 + 0.526899i 0.823355π0.823355\pi
968968 0 0
969969 1.13038 + 0.302885i 0.0363131 + 0.00973007i
970970 0 0
971971 −3.80805 4.96274i −0.122206 0.159262i 0.728244 0.685318i 0.240337π-0.240337\pi
−0.850450 + 0.526056i 0.823670π0.823670\pi
972972 0 0
973973 −26.1280 39.2316i −0.837624 1.25771i
974974 0 0
975975 −4.13592 2.38787i −0.132455 0.0764731i
976976 0 0
977977 −42.1874 + 24.3569i −1.34969 + 0.779246i −0.988206 0.153131i 0.951064π-0.951064\pi
−0.361488 + 0.932377i 0.617731π0.617731\pi
978978 0 0
979979 73.3299 30.3743i 2.34363 0.970765i
980980 0 0
981981 −15.7344 + 37.9863i −0.502362 + 1.21281i
982982 0 0
983983 49.5761 + 13.2839i 1.58123 + 0.423690i 0.939307 0.343078i 0.111470π-0.111470\pi
0.641925 + 0.766768i 0.278136π0.278136\pi
984984 0 0
985985 −26.2735 + 7.03997i −0.837144 + 0.224312i
986986 0 0
987987 0.934439 4.66087i 0.0297435 0.148357i
988988 0 0
989989 11.4406 + 1.50619i 0.363791 + 0.0478940i
990990 0 0
991991 26.5712 + 46.0226i 0.844062 + 1.46196i 0.886434 + 0.462856i 0.153175π0.153175\pi
−0.0423722 + 0.999102i 0.513492π0.513492\pi
992992 0 0
993993 1.16758 0.0370522
994994 0 0
995995 −9.63294 23.2560i −0.305385 0.737264i
996996 0 0
997997 4.40157 + 33.4332i 0.139399 + 1.05884i 0.907958 + 0.419062i 0.137641π0.137641\pi
−0.768559 + 0.639779i 0.779026π0.779026\pi
998998 0 0
999999 −7.62228 + 2.04238i −0.241158 + 0.0646182i
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 896.2.bh.a.625.15 240
4.3 odd 2 224.2.bd.a.37.15 240
7.4 even 3 inner 896.2.bh.a.753.16 240
28.11 odd 6 224.2.bd.a.165.5 yes 240
32.13 even 8 inner 896.2.bh.a.401.16 240
32.19 odd 8 224.2.bd.a.205.5 yes 240
224.109 even 24 inner 896.2.bh.a.529.15 240
224.179 odd 24 224.2.bd.a.109.15 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
224.2.bd.a.37.15 240 4.3 odd 2
224.2.bd.a.109.15 yes 240 224.179 odd 24
224.2.bd.a.165.5 yes 240 28.11 odd 6
224.2.bd.a.205.5 yes 240 32.19 odd 8
896.2.bh.a.401.16 240 32.13 even 8 inner
896.2.bh.a.529.15 240 224.109 even 24 inner
896.2.bh.a.625.15 240 1.1 even 1 trivial
896.2.bh.a.753.16 240 7.4 even 3 inner