Properties

Label 396.2.j.d.181.2
Level 396396
Weight 22
Character 396.181
Analytic conductor 3.1623.162
Analytic rank 00
Dimension 88
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [396,2,Mod(37,396)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(396, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("396.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 396=223211 396 = 2^{2} \cdot 3^{2} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 396.j (of order 55, degree 44, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 3.162075920043.16207592004
Analytic rank: 00
Dimension: 88
Relative dimension: 22 over Q(ζ5)\Q(\zeta_{5})
Coefficient field: 8.0.484000000.6
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x8x6+16x466x2+121 x^{8} - x^{6} + 16x^{4} - 66x^{2} + 121 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C5]\mathrm{SU}(2)[C_{5}]

Embedding invariants

Embedding label 181.2
Root 1.26313+1.73855i1.26313 + 1.73855i of defining polynomial
Character χ\chi == 396.181
Dual form 396.2.j.d.361.2

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+(0.7806562.40261i)q5+(0.809017+0.587785i)q7+(2.824441.73855i)q11+(0.07294900.224514i)q13+(2.043786.29012i)q17+(3.118032.26538i)q190.964944q23+(1.118030.812299i)q25+(2.526261.83543i)q29+(2.11803+6.51864i)q31+(0.780656+2.40261i)q35+(5.427053.94298i)q37+(7.394485.37240i)q41+3.00000q43+(7.87695+5.72294i)q47+(1.85410+5.70634i)q49+(0.482472+1.48490i)q53+(1.972148.14324i)q55+(8.65761+6.29012i)q59+(0.2811530.865300i)q610.596368q65+4.32624q67+(3.30691+10.1776i)q71+(11.7082+8.50651i)q73+(1.26313+3.06668i)q77+(0.2188470.673542i)q79+(1.85950+5.72294i)q83+(13.51729.82084i)q857.21019q89+(0.190983+0.138757i)q91+(7.87695+5.72294i)q95+(3.57295+10.9964i)q97+O(q100)q+(0.780656 - 2.40261i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(2.82444 - 1.73855i) q^{11} +(-0.0729490 - 0.224514i) q^{13} +(2.04378 - 6.29012i) q^{17} +(-3.11803 - 2.26538i) q^{19} -0.964944 q^{23} +(-1.11803 - 0.812299i) q^{25} +(2.52626 - 1.83543i) q^{29} +(2.11803 + 6.51864i) q^{31} +(0.780656 + 2.40261i) q^{35} +(5.42705 - 3.94298i) q^{37} +(-7.39448 - 5.37240i) q^{41} +3.00000 q^{43} +(7.87695 + 5.72294i) q^{47} +(-1.85410 + 5.70634i) q^{49} +(0.482472 + 1.48490i) q^{53} +(-1.97214 - 8.14324i) q^{55} +(-8.65761 + 6.29012i) q^{59} +(0.281153 - 0.865300i) q^{61} -0.596368 q^{65} +4.32624 q^{67} +(-3.30691 + 10.1776i) q^{71} +(-11.7082 + 8.50651i) q^{73} +(-1.26313 + 3.06668i) q^{77} +(-0.218847 - 0.673542i) q^{79} +(-1.85950 + 5.72294i) q^{83} +(-13.5172 - 9.82084i) q^{85} -7.21019 q^{89} +(0.190983 + 0.138757i) q^{91} +(-7.87695 + 5.72294i) q^{95} +(3.57295 + 10.9964i) q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q2q714q1316q19+8q31+30q37+24q43+12q49+20q5538q6128q6740q7342q7950q85+6q91+42q97+O(q100) 8 q - 2 q^{7} - 14 q^{13} - 16 q^{19} + 8 q^{31} + 30 q^{37} + 24 q^{43} + 12 q^{49} + 20 q^{55} - 38 q^{61} - 28 q^{67} - 40 q^{73} - 42 q^{79} - 50 q^{85} + 6 q^{91} + 42 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/396Z)×\left(\mathbb{Z}/396\mathbb{Z}\right)^\times.

nn 145145 199199 353353
χ(n)\chi(n) e(25)e\left(\frac{2}{5}\right) 11 11

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 0
44 0 0
55 0.780656 2.40261i 0.349120 1.07448i −0.610221 0.792231i 0.708919π-0.708919\pi
0.959341 0.282249i 0.0910806π-0.0910806\pi
66 0 0
77 −0.809017 + 0.587785i −0.305780 + 0.222162i −0.730084 0.683358i 0.760519π-0.760519\pi
0.424304 + 0.905520i 0.360519π0.360519\pi
88 0 0
99 0 0
1010 0 0
1111 2.82444 1.73855i 0.851600 0.524191i
1212 0 0
1313 −0.0729490 0.224514i −0.0202324 0.0622690i 0.940431 0.339986i 0.110422π-0.110422\pi
−0.960663 + 0.277717i 0.910422π0.910422\pi
1414 0 0
1515 0 0
1616 0 0
1717 2.04378 6.29012i 0.495690 1.52558i −0.320188 0.947354i 0.603746π-0.603746\pi
0.815878 0.578224i 0.196254π-0.196254\pi
1818 0 0
1919 −3.11803 2.26538i −0.715326 0.519715i 0.169561 0.985520i 0.445765π-0.445765\pi
−0.884887 + 0.465805i 0.845765π0.845765\pi
2020 0 0
2121 0 0
2222 0 0
2323 −0.964944 −0.201205 −0.100602 0.994927i 0.532077π-0.532077\pi
−0.100602 + 0.994927i 0.532077π0.532077\pi
2424 0 0
2525 −1.11803 0.812299i −0.223607 0.162460i
2626 0 0
2727 0 0
2828 0 0
2929 2.52626 1.83543i 0.469114 0.340831i −0.327982 0.944684i 0.606369π-0.606369\pi
0.797096 + 0.603853i 0.206369π0.206369\pi
3030 0 0
3131 2.11803 + 6.51864i 0.380410 + 1.17078i 0.939756 + 0.341847i 0.111053π0.111053\pi
−0.559345 + 0.828935i 0.688947π0.688947\pi
3232 0 0
3333 0 0
3434 0 0
3535 0.780656 + 2.40261i 0.131955 + 0.406115i
3636 0 0
3737 5.42705 3.94298i 0.892202 0.648222i −0.0442495 0.999021i 0.514090π-0.514090\pi
0.936451 + 0.350798i 0.114090π0.114090\pi
3838 0 0
3939 0 0
4040 0 0
4141 −7.39448 5.37240i −1.15482 0.839028i −0.165709 0.986175i 0.552991π-0.552991\pi
−0.989115 + 0.147146i 0.952991π0.952991\pi
4242 0 0
4343 3.00000 0.457496 0.228748 0.973486i 0.426537π-0.426537\pi
0.228748 + 0.973486i 0.426537π0.426537\pi
4444 0 0
4545 0 0
4646 0 0
4747 7.87695 + 5.72294i 1.14897 + 0.834776i 0.988344 0.152239i 0.0486482π-0.0486482\pi
0.160627 + 0.987015i 0.448648π0.448648\pi
4848 0 0
4949 −1.85410 + 5.70634i −0.264872 + 0.815191i
5050 0 0
5151 0 0
5252 0 0
5353 0.482472 + 1.48490i 0.0662726 + 0.203966i 0.978709 0.205252i 0.0658015π-0.0658015\pi
−0.912437 + 0.409218i 0.865801π0.865801\pi
5454 0 0
5555 −1.97214 8.14324i −0.265923 1.09803i
5656 0 0
5757 0 0
5858 0 0
5959 −8.65761 + 6.29012i −1.12712 + 0.818904i −0.985274 0.170984i 0.945305π-0.945305\pi
−0.141851 + 0.989888i 0.545305π0.545305\pi
6060 0 0
6161 0.281153 0.865300i 0.0359979 0.110790i −0.931443 0.363888i 0.881449π-0.881449\pi
0.967441 + 0.253097i 0.0814493π0.0814493\pi
6262 0 0
6363 0 0
6464 0 0
6565 −0.596368 −0.0739703
6666 0 0
6767 4.32624 0.528534 0.264267 0.964450i 0.414870π-0.414870\pi
0.264267 + 0.964450i 0.414870π0.414870\pi
6868 0 0
6969 0 0
7070 0 0
7171 −3.30691 + 10.1776i −0.392458 + 1.20786i 0.538465 + 0.842648i 0.319004π0.319004\pi
−0.930923 + 0.365214i 0.880996π0.880996\pi
7272 0 0
7373 −11.7082 + 8.50651i −1.37034 + 0.995611i −0.372631 + 0.927979i 0.621544π0.621544\pi
−0.997710 + 0.0676320i 0.978456π0.978456\pi
7474 0 0
7575 0 0
7676 0 0
7777 −1.26313 + 3.06668i −0.143947 + 0.349480i
7878 0 0
7979 −0.218847 0.673542i −0.0246222 0.0757794i 0.937990 0.346661i 0.112685π-0.112685\pi
−0.962613 + 0.270882i 0.912685π0.912685\pi
8080 0 0
8181 0 0
8282 0 0
8383 −1.85950 + 5.72294i −0.204106 + 0.628174i 0.795643 + 0.605766i 0.207133π0.207133\pi
−0.999749 + 0.0224080i 0.992867π0.992867\pi
8484 0 0
8585 −13.5172 9.82084i −1.46615 1.06522i
8686 0 0
8787 0 0
8888 0 0
8989 −7.21019 −0.764279 −0.382139 0.924105i 0.624813π-0.624813\pi
−0.382139 + 0.924105i 0.624813π0.624813\pi
9090 0 0
9191 0.190983 + 0.138757i 0.0200205 + 0.0145457i
9292 0 0
9393 0 0
9494 0 0
9595 −7.87695 + 5.72294i −0.808158 + 0.587161i
9696 0 0
9797 3.57295 + 10.9964i 0.362778 + 1.11652i 0.951361 + 0.308079i 0.0996861π0.0996861\pi
−0.588583 + 0.808437i 0.700314π0.700314\pi
9898 0 0
9999 0 0
100100 0 0
101101 2.22807 + 6.85730i 0.221701 + 0.682327i 0.998610 + 0.0527130i 0.0167868π0.0167868\pi
−0.776908 + 0.629614i 0.783213π0.783213\pi
102102 0 0
103103 10.8541 7.88597i 1.06949 0.777027i 0.0936666 0.995604i 0.470141π-0.470141\pi
0.975820 + 0.218576i 0.0701412π0.0701412\pi
104104 0 0
105105 0 0
106106 0 0
107107 9.92073 + 7.20783i 0.959074 + 0.696808i 0.952935 0.303173i 0.0980462π-0.0980462\pi
0.00613812 + 0.999981i 0.498046π0.498046\pi
108108 0 0
109109 18.1803 1.74136 0.870680 0.491849i 0.163679π-0.163679\pi
0.870680 + 0.491849i 0.163679π0.163679\pi
110110 0 0
111111 0 0
112112 0 0
113113 −9.92073 7.20783i −0.933264 0.678056i 0.0135257 0.999909i 0.495694π-0.495694\pi
−0.946790 + 0.321852i 0.895694π0.895694\pi
114114 0 0
115115 −0.753289 + 2.31838i −0.0702446 + 0.216191i
116116 0 0
117117 0 0
118118 0 0
119119 2.04378 + 6.29012i 0.187353 + 0.576614i
120120 0 0
121121 4.95492 9.82084i 0.450447 0.892803i
122122 0 0
123123 0 0
124124 0 0
125125 7.39448 5.37240i 0.661382 0.480522i
126126 0 0
127127 −5.00000 + 15.3884i −0.443678 + 1.36550i 0.440249 + 0.897876i 0.354890π0.354890\pi
−0.883927 + 0.467625i 0.845110π0.845110\pi
128128 0 0
129129 0 0
130130 0 0
131131 −8.54371 −0.746467 −0.373234 0.927737i 0.621751π-0.621751\pi
−0.373234 + 0.927737i 0.621751π0.621751\pi
132132 0 0
133133 3.85410 0.334193
134134 0 0
135135 0 0
136136 0 0
137137 4.75433 14.6323i 0.406190 1.25012i −0.513708 0.857965i 0.671729π-0.671729\pi
0.919898 0.392158i 0.128271π-0.128271\pi
138138 0 0
139139 −10.6353 + 7.72696i −0.902071 + 0.655393i −0.938997 0.343925i 0.888243π-0.888243\pi
0.0369264 + 0.999318i 0.488243π0.488243\pi
140140 0 0
141141 0 0
142142 0 0
143143 −0.596368 0.507301i −0.0498708 0.0424226i
144144 0 0
145145 −2.43769 7.50245i −0.202439 0.623045i
146146 0 0
147147 0 0
148148 0 0
149149 −3.19302 + 9.82709i −0.261582 + 0.805067i 0.730879 + 0.682507i 0.239110π0.239110\pi
−0.992461 + 0.122560i 0.960890π0.960890\pi
150150 0 0
151151 −17.0902 12.4167i −1.39078 1.01046i −0.995779 0.0917780i 0.970745π-0.970745\pi
−0.394999 0.918682i 0.629255π-0.629255\pi
152152 0 0
153153 0 0
154154 0 0
155155 17.3152 1.39079
156156 0 0
157157 −1.85410 1.34708i −0.147973 0.107509i 0.511335 0.859381i 0.329151π-0.329151\pi
−0.659309 + 0.751872i 0.729151π0.729151\pi
158158 0 0
159159 0 0
160160 0 0
161161 0.780656 0.567180i 0.0615243 0.0447000i
162162 0 0
163163 4.44427 + 13.6781i 0.348102 + 1.07135i 0.959902 + 0.280336i 0.0904458π0.0904458\pi
−0.611800 + 0.791013i 0.709554π0.709554\pi
164164 0 0
165165 0 0
166166 0 0
167167 −6.79811 20.9224i −0.526054 1.61903i −0.762223 0.647314i 0.775892π-0.775892\pi
0.236169 0.971712i 0.424108π-0.424108\pi
168168 0 0
169169 10.4721 7.60845i 0.805549 0.585266i
170170 0 0
171171 0 0
172172 0 0
173173 7.69266 + 5.58905i 0.584862 + 0.424927i 0.840474 0.541852i 0.182277π-0.182277\pi
−0.255611 + 0.966780i 0.582277π0.582277\pi
174174 0 0
175175 1.38197 0.104467
176176 0 0
177177 0 0
178178 0 0
179179 −12.4470 9.04327i −0.930332 0.675925i 0.0157424 0.999876i 0.494989π-0.494989\pi
−0.946074 + 0.323951i 0.894989π0.894989\pi
180180 0 0
181181 −5.01722 + 15.4414i −0.372927 + 1.14775i 0.571939 + 0.820296i 0.306191π0.306191\pi
−0.944867 + 0.327456i 0.893809π0.893809\pi
182182 0 0
183183 0 0
184184 0 0
185185 −5.23680 16.1172i −0.385017 1.18496i
186186 0 0
187187 −5.16312 21.3193i −0.377565 1.55902i
188188 0 0
189189 0 0
190190 0 0
191191 19.0608 13.8485i 1.37919 1.00204i 0.382237 0.924064i 0.375154π-0.375154\pi
0.996955 0.0779771i 0.0248461π-0.0248461\pi
192192 0 0
193193 3.44427 10.6004i 0.247924 0.763032i −0.747218 0.664579i 0.768611π-0.768611\pi
0.995142 0.0984525i 0.0313893π-0.0313893\pi
194194 0 0
195195 0 0
196196 0 0
197197 26.0867 1.85860 0.929301 0.369324i 0.120411π-0.120411\pi
0.929301 + 0.369324i 0.120411π0.120411\pi
198198 0 0
199199 4.23607 0.300287 0.150143 0.988664i 0.452026π-0.452026\pi
0.150143 + 0.988664i 0.452026π0.452026\pi
200200 0 0
201201 0 0
202202 0 0
203203 −0.964944 + 2.96979i −0.0677258 + 0.208438i
204204 0 0
205205 −18.6803 + 13.5721i −1.30469 + 0.947914i
206206 0 0
207207 0 0
208208 0 0
209209 −12.7452 0.977595i −0.881602 0.0676216i
210210 0 0
211211 3.20820 + 9.87384i 0.220862 + 0.679743i 0.998685 + 0.0512601i 0.0163238π0.0163238\pi
−0.777823 + 0.628483i 0.783676π0.783676\pi
212212 0 0
213213 0 0
214214 0 0
215215 2.34197 7.20783i 0.159721 0.491570i
216216 0 0
217217 −5.54508 4.02874i −0.376425 0.273489i
218218 0 0
219219 0 0
220220 0 0
221221 −1.56131 −0.105025
222222 0 0
223223 5.19098 + 3.77147i 0.347614 + 0.252556i 0.747867 0.663848i 0.231078π-0.231078\pi
−0.400253 + 0.916404i 0.631078π0.631078\pi
224224 0 0
225225 0 0
226226 0 0
227227 19.6572 14.2818i 1.30469 0.947915i 0.304703 0.952447i 0.401443π-0.401443\pi
0.999990 + 0.00453258i 0.00144277π0.00144277\pi
228228 0 0
229229 3.52786 + 10.8576i 0.233128 + 0.717494i 0.997364 + 0.0725574i 0.0231161π0.0231161\pi
−0.764236 + 0.644936i 0.776884π0.776884\pi
230230 0 0
231231 0 0
232232 0 0
233233 −1.74560 5.37240i −0.114358 0.351958i 0.877455 0.479660i 0.159240π-0.159240\pi
−0.991813 + 0.127702i 0.959240π0.959240\pi
234234 0 0
235235 19.8992 14.4576i 1.29808 0.943110i
236236 0 0
237237 0 0
238238 0 0
239239 −3.78938 2.75315i −0.245115 0.178086i 0.458444 0.888723i 0.348407π-0.348407\pi
−0.703559 + 0.710637i 0.748407π0.748407\pi
240240 0 0
241241 22.9443 1.47797 0.738985 0.673722i 0.235305π-0.235305\pi
0.738985 + 0.673722i 0.235305π0.235305\pi
242242 0 0
243243 0 0
244244 0 0
245245 12.2627 + 8.90937i 0.783435 + 0.569199i
246246 0 0
247247 −0.281153 + 0.865300i −0.0178893 + 0.0550577i
248248 0 0
249249 0 0
250250 0 0
251251 −5.16641 15.9006i −0.326101 1.00363i −0.970941 0.239318i 0.923076π-0.923076\pi
0.644841 0.764317i 0.276924π-0.276924\pi
252252 0 0
253253 −2.72542 + 1.67760i −0.171346 + 0.105470i
254254 0 0
255255 0 0
256256 0 0
257257 3.60510 2.61925i 0.224880 0.163385i −0.469641 0.882858i 0.655617π-0.655617\pi
0.694520 + 0.719473i 0.255617π0.255617\pi
258258 0 0
259259 −2.07295 + 6.37988i −0.128807 + 0.396427i
260260 0 0
261261 0 0
262262 0 0
263263 −10.7014 −0.659876 −0.329938 0.944003i 0.607028π-0.607028\pi
−0.329938 + 0.944003i 0.607028π0.607028\pi
264264 0 0
265265 3.94427 0.242295
266266 0 0
267267 0 0
268268 0 0
269269 −3.49120 + 10.7448i −0.212862 + 0.655122i 0.786436 + 0.617671i 0.211924π0.211924\pi
−0.999298 + 0.0374510i 0.988076π0.988076\pi
270270 0 0
271271 1.73607 1.26133i 0.105459 0.0766202i −0.533806 0.845607i 0.679239π-0.679239\pi
0.639265 + 0.768987i 0.279239π0.279239\pi
272272 0 0
273273 0 0
274274 0 0
275275 −4.57004 0.350536i −0.275584 0.0211381i
276276 0 0
277277 −2.55573 7.86572i −0.153559 0.472605i 0.844453 0.535629i 0.179926π-0.179926\pi
−0.998012 + 0.0630239i 0.979926π0.979926\pi
278278 0 0
279279 0 0
280280 0 0
281281 −5.64888 + 17.3855i −0.336984 + 1.03713i 0.628753 + 0.777605i 0.283566π0.283566\pi
−0.965737 + 0.259524i 0.916434π0.916434\pi
282282 0 0
283283 −20.5623 14.9394i −1.22230 0.888055i −0.226013 0.974124i 0.572569π-0.572569\pi
−0.996289 + 0.0860697i 0.972569π0.972569\pi
284284 0 0
285285 0 0
286286 0 0
287287 9.14008 0.539522
288288 0 0
289289 −21.6353 15.7189i −1.27266 0.924643i
290290 0 0
291291 0 0
292292 0 0
293293 −7.39448 + 5.37240i −0.431990 + 0.313859i −0.782444 0.622721i 0.786027π-0.786027\pi
0.350454 + 0.936580i 0.386027π0.386027\pi
294294 0 0
295295 8.35410 + 25.7113i 0.486395 + 1.49697i
296296 0 0
297297 0 0
298298 0 0
299299 0.0703917 + 0.216643i 0.00407086 + 0.0125288i
300300 0 0
301301 −2.42705 + 1.76336i −0.139893 + 0.101638i
302302 0 0
303303 0 0
304304 0 0
305305 −1.85950 1.35100i −0.106474 0.0773582i
306306 0 0
307307 −14.0902 −0.804168 −0.402084 0.915603i 0.631714π-0.631714\pi
−0.402084 + 0.915603i 0.631714π0.631714\pi
308308 0 0
309309 0 0
310310 0 0
311311 −4.86822 3.53697i −0.276052 0.200563i 0.441142 0.897437i 0.354574π-0.354574\pi
−0.717193 + 0.696874i 0.754574π0.754574\pi
312312 0 0
313313 −4.07295 + 12.5352i −0.230217 + 0.708534i 0.767503 + 0.641045i 0.221499π0.221499\pi
−0.997720 + 0.0674891i 0.978501π0.978501\pi
314314 0 0
315315 0 0
316316 0 0
317317 8.47332 + 26.0782i 0.475909 + 1.46470i 0.844728 + 0.535196i 0.179762π0.179762\pi
−0.368819 + 0.929501i 0.620238π0.620238\pi
318318 0 0
319319 3.94427 9.57608i 0.220837 0.536157i
320320 0 0
321321 0 0
322322 0 0
323323 −20.6221 + 14.9828i −1.14745 + 0.833668i
324324 0 0
325325 −0.100813 + 0.310271i −0.00559210 + 0.0172107i
326326 0 0
327327 0 0
328328 0 0
329329 −9.73645 −0.536788
330330 0 0
331331 10.4164 0.572538 0.286269 0.958149i 0.407585π-0.407585\pi
0.286269 + 0.958149i 0.407585π0.407585\pi
332332 0 0
333333 0 0
334334 0 0
335335 3.37730 10.3943i 0.184522 0.567900i
336336 0 0
337337 −10.7082 + 7.77997i −0.583313 + 0.423802i −0.839917 0.542715i 0.817396π-0.817396\pi
0.256604 + 0.966517i 0.417396π0.417396\pi
338338 0 0
339339 0 0
340340 0 0
341341 17.3152 + 14.7292i 0.937671 + 0.797631i
342342 0 0
343343 −4.01722 12.3637i −0.216910 0.667579i
344344 0 0
345345 0 0
346346 0 0
347347 4.45614 13.7146i 0.239218 0.736238i −0.757316 0.653049i 0.773489π-0.773489\pi
0.996534 0.0831890i 0.0265105π-0.0265105\pi
348348 0 0
349349 −9.51722 6.91467i −0.509445 0.370134i 0.303168 0.952937i 0.401956π-0.401956\pi
−0.812613 + 0.582804i 0.801956π0.801956\pi
350350 0 0
351351 0 0
352352 0 0
353353 −18.2802 −0.972954 −0.486477 0.873693i 0.661718π-0.661718\pi
−0.486477 + 0.873693i 0.661718π0.661718\pi
354354 0 0
355355 21.8713 + 15.8904i 1.16081 + 0.843377i
356356 0 0
357357 0 0
358358 0 0
359359 −24.5254 + 17.8187i −1.29440 + 0.940438i −0.999884 0.0152088i 0.995159π-0.995159\pi
−0.294517 + 0.955646i 0.595159π0.595159\pi
360360 0 0
361361 −1.28115 3.94298i −0.0674291 0.207525i
362362 0 0
363363 0 0
364364 0 0
365365 11.2978 + 34.7709i 0.591352 + 1.81999i
366366 0 0
367367 1.26393 0.918300i 0.0659767 0.0479349i −0.554308 0.832312i 0.687017π-0.687017\pi
0.620285 + 0.784377i 0.287017π0.287017\pi
368368 0 0
369369 0 0
370370 0 0
371371 −1.26313 0.917716i −0.0655783 0.0476454i
372372 0 0
373373 13.0000 0.673114 0.336557 0.941663i 0.390737π-0.390737\pi
0.336557 + 0.941663i 0.390737π0.390737\pi
374374 0 0
375375 0 0
376376 0 0
377377 −0.596368 0.433287i −0.0307145 0.0223154i
378378 0 0
379379 6.12868 18.8621i 0.314809 0.968882i −0.661024 0.750365i 0.729878π-0.729878\pi
0.975833 0.218518i 0.0701221π-0.0701221\pi
380380 0 0
381381 0 0
382382 0 0
383383 5.71927 + 17.6021i 0.292241 + 0.899426i 0.984134 + 0.177426i 0.0567769π0.0567769\pi
−0.691893 + 0.722000i 0.743223π0.743223\pi
384384 0 0
385385 6.38197 + 5.42882i 0.325255 + 0.276679i
386386 0 0
387387 0 0
388388 0 0
389389 −20.1397 + 14.6323i −1.02112 + 0.741888i −0.966512 0.256620i 0.917391π-0.917391\pi
−0.0546085 + 0.998508i 0.517391π0.517391\pi
390390 0 0
391391 −1.97214 + 6.06961i −0.0997352 + 0.306953i
392392 0 0
393393 0 0
394394 0 0
395395 −1.78910 −0.0900196
396396 0 0
397397 21.0000 1.05396 0.526980 0.849878i 0.323324π-0.323324\pi
0.526980 + 0.849878i 0.323324π0.323324\pi
398398 0 0
399399 0 0
400400 0 0
401401 −4.57004 + 14.0651i −0.228217 + 0.702379i 0.769732 + 0.638367i 0.220390π0.220390\pi
−0.997949 + 0.0640124i 0.979610π0.979610\pi
402402 0 0
403403 1.30902 0.951057i 0.0652068 0.0473755i
404404 0 0
405405 0 0
406406 0 0
407407 8.47332 20.5719i 0.420007 1.01971i
408408 0 0
409409 5.56231 + 17.1190i 0.275038 + 0.846481i 0.989209 + 0.146510i 0.0468039π0.0468039\pi
−0.714171 + 0.699971i 0.753196π0.753196\pi
410410 0 0
411411 0 0
412412 0 0
413413 3.30691 10.1776i 0.162722 0.500808i
414414 0 0
415415 12.2984 + 8.93529i 0.603703 + 0.438616i
416416 0 0
417417 0 0
418418 0 0
419419 −32.1042 −1.56839 −0.784196 0.620514i 0.786924π-0.786924\pi
−0.784196 + 0.620514i 0.786924π0.786924\pi
420420 0 0
421421 −11.2082 8.14324i −0.546254 0.396877i 0.280148 0.959957i 0.409616π-0.409616\pi
−0.826403 + 0.563080i 0.809616π0.809616\pi
422422 0 0
423423 0 0
424424 0 0
425425 −7.39448 + 5.37240i −0.358685 + 0.260600i
426426 0 0
427427 0.281153 + 0.865300i 0.0136059 + 0.0418748i
428428 0 0
429429 0 0
430430 0 0
431431 2.64015 + 8.12555i 0.127172 + 0.391394i 0.994290 0.106707i 0.0340308π-0.0340308\pi
−0.867119 + 0.498101i 0.834031π0.834031\pi
432432 0 0
433433 8.70820 6.32688i 0.418490 0.304050i −0.358540 0.933514i 0.616725π-0.616725\pi
0.777030 + 0.629464i 0.216725π0.216725\pi
434434 0 0
435435 0 0
436436 0 0
437437 3.00873 + 2.18597i 0.143927 + 0.104569i
438438 0 0
439439 −14.7082 −0.701984 −0.350992 0.936378i 0.614156π-0.614156\pi
−0.350992 + 0.936378i 0.614156π0.614156\pi
440440 0 0
441441 0 0
442442 0 0
443443 19.8415 + 14.4157i 0.942697 + 0.684909i 0.949068 0.315071i 0.102028π-0.102028\pi
−0.00637170 + 0.999980i 0.502028π0.502028\pi
444444 0 0
445445 −5.62868 + 17.3233i −0.266825 + 0.821203i
446446 0 0
447447 0 0
448448 0 0
449449 2.89483 + 8.90937i 0.136616 + 0.420459i 0.995838 0.0911431i 0.0290521π-0.0290521\pi
−0.859222 + 0.511602i 0.829052π0.829052\pi
450450 0 0
451451 −30.2254 2.31838i −1.42326 0.109168i
452452 0 0
453453 0 0
454454 0 0
455455 0.482472 0.350536i 0.0226186 0.0164334i
456456 0 0
457457 7.50000 23.0826i 0.350835 1.07976i −0.607550 0.794281i 0.707848π-0.707848\pi
0.958385 0.285478i 0.0921524π-0.0921524\pi
458458 0 0
459459 0 0
460460 0 0
461461 −27.0517 −1.25992 −0.629961 0.776627i 0.716929π-0.716929\pi
−0.629961 + 0.776627i 0.716929π0.716929\pi
462462 0 0
463463 −32.5623 −1.51330 −0.756649 0.653821i 0.773165π-0.773165\pi
−0.756649 + 0.653821i 0.773165π0.773165\pi
464464 0 0
465465 0 0
466466 0 0
467467 4.01718 12.3636i 0.185893 0.572119i −0.814070 0.580767i 0.802753π-0.802753\pi
0.999963 + 0.00864799i 0.00275277π0.00275277\pi
468468 0 0
469469 −3.50000 + 2.54290i −0.161615 + 0.117420i
470470 0 0
471471 0 0
472472 0 0
473473 8.47332 5.21564i 0.389604 0.239815i
474474 0 0
475475 1.64590 + 5.06555i 0.0755190 + 0.232424i
476476 0 0
477477 0 0
478478 0 0
479479 −0.482472 + 1.48490i −0.0220447 + 0.0678466i −0.961474 0.274897i 0.911356π-0.911356\pi
0.939429 + 0.342744i 0.111356π0.111356\pi
480480 0 0
481481 −1.28115 0.930812i −0.0584155 0.0424414i
482482 0 0
483483 0 0
484484 0 0
485485 29.2093 1.32633
486486 0 0
487487 −1.42705 1.03681i −0.0646659 0.0469825i 0.554983 0.831862i 0.312725π-0.312725\pi
−0.619649 + 0.784879i 0.712725π0.712725\pi
488488 0 0
489489 0 0
490490 0 0
491491 23.6308 17.1688i 1.06645 0.774818i 0.0911754 0.995835i 0.470938π-0.470938\pi
0.975270 + 0.221017i 0.0709376π0.0709376\pi
492492 0 0
493493 −6.38197 19.6417i −0.287429 0.884616i
494494 0 0
495495 0 0
496496 0 0
497497 −3.30691 10.1776i −0.148335 0.456529i
498498 0 0
499499 −7.73607 + 5.62058i −0.346314 + 0.251612i −0.747321 0.664463i 0.768660π-0.768660\pi
0.401007 + 0.916075i 0.368660π0.368660\pi
500500 0 0
501501 0 0
502502 0 0
503503 −36.1917 26.2948i −1.61371 1.17243i −0.849799 0.527106i 0.823277π-0.823277\pi
−0.763910 0.645322i 0.776723π-0.776723\pi
504504 0 0
505505 18.2148 0.810547
506506 0 0
507507 0 0
508508 0 0
509509 16.0521 + 11.6625i 0.711496 + 0.516932i 0.883656 0.468137i 0.155075π-0.155075\pi
−0.172160 + 0.985069i 0.555075π0.555075\pi
510510 0 0
511511 4.47214 13.7638i 0.197836 0.608876i
512512 0 0
513513 0 0
514514 0 0
515515 −10.4736 32.2344i −0.461522 1.42042i
516516 0 0
517517 32.1976 + 2.46965i 1.41605 + 0.108615i
518518 0 0
519519 0 0
520520 0 0
521521 −9.14008 + 6.64066i −0.400434 + 0.290932i −0.769718 0.638384i 0.779603π-0.779603\pi
0.369284 + 0.929317i 0.379603π0.379603\pi
522522 0 0
523523 −8.97214 + 27.6134i −0.392324 + 1.20745i 0.538702 + 0.842496i 0.318915π0.318915\pi
−0.931026 + 0.364953i 0.881085π0.881085\pi
524524 0 0
525525 0 0
526526 0 0
527527 45.3318 1.97468
528528 0 0
529529 −22.0689 −0.959517
530530 0 0
531531 0 0
532532 0 0
533533 −0.666760 + 2.05208i −0.0288806 + 0.0888852i
534534 0 0
535535 25.0623 18.2088i 1.08354 0.787236i
536536 0 0
537537 0 0
538538 0 0
539539 4.68393 + 19.3407i 0.201751 + 0.833061i
540540 0 0
541541 −3.66312 11.2739i −0.157490 0.484704i 0.840915 0.541167i 0.182017π-0.182017\pi
−0.998405 + 0.0564637i 0.982017π0.982017\pi
542542 0 0
543543 0 0
544544 0 0
545545 14.1926 43.6803i 0.607944 1.87106i
546546 0 0
547547 20.4894 + 14.8864i 0.876062 + 0.636496i 0.932207 0.361927i 0.117881π-0.117881\pi
−0.0561450 + 0.998423i 0.517881π0.517881\pi
548548 0 0
549549 0 0
550550 0 0
551551 −12.0349 −0.512704
552552 0 0
553553 0.572949 + 0.416272i 0.0243643 + 0.0177017i
554554 0 0
555555 0 0
556556 0 0
557557 23.4466 17.0349i 0.993463 0.721793i 0.0327861 0.999462i 0.489562π-0.489562\pi
0.960677 + 0.277669i 0.0895620π0.0895620\pi
558558 0 0
559559 −0.218847 0.673542i −0.00925624 0.0284878i
560560 0 0
561561 0 0
562562 0 0
563563 0.0703917 + 0.216643i 0.00296666 + 0.00913043i 0.952529 0.304448i 0.0984721π-0.0984721\pi
−0.949562 + 0.313579i 0.898472π0.898472\pi
564564 0 0
565565 −25.0623 + 18.2088i −1.05438 + 0.766051i
566566 0 0
567567 0 0
568568 0 0
569569 −16.7188 12.1470i −0.700890 0.509227i 0.179332 0.983789i 0.442606π-0.442606\pi
−0.880222 + 0.474562i 0.842606π0.842606\pi
570570 0 0
571571 −25.9230 −1.08484 −0.542422 0.840106i 0.682492π-0.682492\pi
−0.542422 + 0.840106i 0.682492π0.682492\pi
572572 0 0
573573 0 0
574574 0 0
575575 1.07884 + 0.783823i 0.0449907 + 0.0326877i
576576 0 0
577577 −6.85410 + 21.0948i −0.285340 + 0.878186i 0.700957 + 0.713204i 0.252757π0.252757\pi
−0.986297 + 0.164982i 0.947243π0.947243\pi
578578 0 0
579579 0 0
580580 0 0
581581 −1.85950 5.72294i −0.0771449 0.237428i
582582 0 0
583583 3.94427 + 3.35520i 0.163355 + 0.138958i
584584 0 0
585585 0 0
586586 0 0
587587 14.6047 10.6109i 0.602799 0.437959i −0.244072 0.969757i 0.578483π-0.578483\pi
0.846871 + 0.531798i 0.178483π0.178483\pi
588588 0 0
589589 8.16312 25.1235i 0.336355 1.03520i
590590 0 0
591591 0 0
592592 0 0
593593 1.78910 0.0734697 0.0367348 0.999325i 0.488304π-0.488304\pi
0.0367348 + 0.999325i 0.488304π0.488304\pi
594594 0 0
595595 16.7082 0.684970
596596 0 0
597597 0 0
598598 0 0
599599 0 0 −0.951057 0.309017i 0.900000π-0.900000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
600600 0 0
601601 10.0451 7.29818i 0.409748 0.297699i −0.363752 0.931496i 0.618504π-0.618504\pi
0.773500 + 0.633797i 0.218504π0.218504\pi
602602 0 0
603603 0 0
604604 0 0
605605 −19.7276 19.5714i −0.802040 0.795692i
606606 0 0
607607 −1.77051 5.44907i −0.0718628 0.221171i 0.908674 0.417506i 0.137096π-0.137096\pi
−0.980537 + 0.196335i 0.937096π0.937096\pi
608608 0 0
609609 0 0
610610 0 0
611611 0.710264 2.18597i 0.0287342 0.0884348i
612612 0 0
613613 29.7984 + 21.6498i 1.20354 + 0.874427i 0.994629 0.103507i 0.0330064π-0.0330064\pi
0.208916 + 0.977934i 0.433006π0.433006\pi
614614 0 0
615615 0 0
616616 0 0
617617 33.6655 1.35532 0.677661 0.735375i 0.262994π-0.262994\pi
0.677661 + 0.735375i 0.262994π0.262994\pi
618618 0 0
619619 28.9336 + 21.0215i 1.16294 + 0.844926i 0.990147 0.140032i 0.0447206π-0.0447206\pi
0.172794 + 0.984958i 0.444721π0.444721\pi
620620 0 0
621621 0 0
622622 0 0
623623 5.83317 4.23804i 0.233701 0.169794i
624624 0 0
625625 −9.27051 28.5317i −0.370820 1.14127i
626626 0 0
627627 0 0
628628 0 0
629629 −13.7101 42.1954i −0.546658 1.68244i
630630 0 0
631631 10.8713 7.89848i 0.432781 0.314433i −0.349979 0.936757i 0.613811π-0.613811\pi
0.782760 + 0.622324i 0.213811π0.213811\pi
632632 0 0
633633 0 0
634634 0 0
635635 33.0691 + 24.0261i 1.31231 + 0.953447i
636636 0 0
637637 1.41641 0.0561201
638638 0 0
639639 0 0
640640 0 0
641641 −15.2714 11.0953i −0.603185 0.438240i 0.243823 0.969820i 0.421598π-0.421598\pi
−0.847008 + 0.531580i 0.821598π0.821598\pi
642642 0 0
643643 14.2082 43.7284i 0.560317 1.72448i −0.121155 0.992634i 0.538660π-0.538660\pi
0.681472 0.731844i 0.261340π-0.261340\pi
644644 0 0
645645 0 0
646646 0 0
647647 0.113896 + 0.350536i 0.00447772 + 0.0137810i 0.953270 0.302118i 0.0976938π-0.0976938\pi
−0.948793 + 0.315899i 0.897694π0.897694\pi
648648 0 0
649649 −13.5172 + 32.8177i −0.530597 + 1.28821i
650650 0 0
651651 0 0
652652 0 0
653653 22.0695 16.0345i 0.863648 0.627477i −0.0652271 0.997870i 0.520777π-0.520777\pi
0.928875 + 0.370394i 0.120777π0.120777\pi
654654 0 0
655655 −6.66970 + 20.5272i −0.260607 + 0.802065i
656656 0 0
657657 0 0
658658 0 0
659659 −12.0349 −0.468813 −0.234407 0.972139i 0.575315π-0.575315\pi
−0.234407 + 0.972139i 0.575315π0.575315\pi
660660 0 0
661661 −3.90983 −0.152075 −0.0760374 0.997105i 0.524227π-0.524227\pi
−0.0760374 + 0.997105i 0.524227π0.524227\pi
662662 0 0
663663 0 0
664664 0 0
665665 3.00873 9.25991i 0.116673 0.359084i
666666 0 0
667667 −2.43769 + 1.77109i −0.0943879 + 0.0685768i
668668 0 0
669669 0 0
670670 0 0
671671 −0.710264 2.93278i −0.0274194 0.113219i
672672 0 0
673673 3.12868 + 9.62908i 0.120602 + 0.371174i 0.993074 0.117490i 0.0374847π-0.0374847\pi
−0.872472 + 0.488663i 0.837485π0.837485\pi
674674 0 0
675675 0 0
676676 0 0
677677 −3.12262 + 9.61045i −0.120012 + 0.369359i −0.992959 0.118455i 0.962206π-0.962206\pi
0.872947 + 0.487815i 0.162206π0.162206\pi
678678 0 0
679679 −9.35410 6.79615i −0.358977 0.260812i
680680 0 0
681681 0 0
682682 0 0
683683 −16.5781 −0.634342 −0.317171 0.948368i 0.602733π-0.602733\pi
−0.317171 + 0.948368i 0.602733π0.602733\pi
684684 0 0
685685 −31.4443 22.8456i −1.20142 0.872886i
686686 0 0
687687 0 0
688688 0 0
689689 0.298184 0.216643i 0.0113599 0.00825345i
690690 0 0
691691 −10.2918 31.6749i −0.391518 1.20497i −0.931640 0.363383i 0.881622π-0.881622\pi
0.540122 0.841587i 0.318378π-0.318378\pi
692692 0 0
693693 0 0
694694 0 0
695695 10.2624 + 31.5845i 0.389276 + 1.19807i
696696 0 0
697697 −48.9058 + 35.5321i −1.85244 + 1.34587i
698698 0 0
699699 0 0
700700 0 0
701701 18.3941 + 13.3641i 0.694734 + 0.504754i 0.878213 0.478270i 0.158736π-0.158736\pi
−0.183479 + 0.983024i 0.558736π0.558736\pi
702702 0 0
703703 −25.8541 −0.975106
704704 0 0
705705 0 0
706706 0 0
707707 −5.83317 4.23804i −0.219379 0.159388i
708708 0 0
709709 7.00658 21.5640i 0.263138 0.809854i −0.728979 0.684536i 0.760005π-0.760005\pi
0.992117 0.125318i 0.0399951π-0.0399951\pi
710710 0 0
711711 0 0
712712 0 0
713713 −2.04378 6.29012i −0.0765403 0.235567i
714714 0 0
715715 −1.68441 + 1.03681i −0.0629932 + 0.0387746i
716716 0 0
717717 0 0
718718 0 0
719719 9.92073 7.20783i 0.369981 0.268807i −0.387222 0.921986i 0.626565π-0.626565\pi
0.757203 + 0.653180i 0.226565π0.226565\pi
720720 0 0
721721 −4.14590 + 12.7598i −0.154401 + 0.475198i
722722 0 0
723723 0 0
724724 0 0
725725 −4.31536 −0.160268
726726 0 0
727727 −13.4377 −0.498376 −0.249188 0.968455i 0.580164π-0.580164\pi
−0.249188 + 0.968455i 0.580164π0.580164\pi
728728 0 0
729729 0 0
730730 0 0
731731 6.13135 18.8704i 0.226776 0.697945i
732732 0 0
733733 9.47214 6.88191i 0.349861 0.254189i −0.398950 0.916973i 0.630625π-0.630625\pi
0.748811 + 0.662784i 0.230625π0.230625\pi
734734 0 0
735735 0 0
736736 0 0
737737 12.2192 7.52136i 0.450100 0.277053i
738738 0 0
739739 4.89261 + 15.0579i 0.179978 + 0.553914i 0.999826 0.0186670i 0.00594224π-0.00594224\pi
−0.819848 + 0.572581i 0.805942π0.805942\pi
740740 0 0
741741 0 0
742742 0 0
743743 −15.8243 + 48.7022i −0.580537 + 1.78671i 0.0359618 + 0.999353i 0.488551π0.488551\pi
−0.616499 + 0.787356i 0.711449π0.711449\pi
744744 0 0
745745 21.1180 + 15.3431i 0.773705 + 0.562130i
746746 0 0
747747 0 0
748748 0 0
749749 −12.2627 −0.448069
750750 0 0
751751 28.9164 + 21.0090i 1.05517 + 0.766629i 0.973190 0.230004i 0.0738740π-0.0738740\pi
0.0819851 + 0.996634i 0.473874π0.473874\pi
752752 0 0
753753 0 0
754754 0 0
755755 −43.1741 + 31.3678i −1.57127 + 1.14159i
756756 0 0
757757 −10.3435 31.8339i −0.375939 1.15702i −0.942843 0.333238i 0.891859π-0.891859\pi
0.566903 0.823784i 0.308141π-0.308141\pi
758758 0 0
759759 0 0
760760 0 0
761761 −6.54343 20.1386i −0.237199 0.730024i −0.996822 0.0796602i 0.974616π-0.974616\pi
0.759623 0.650364i 0.225384π-0.225384\pi
762762 0 0
763763 −14.7082 + 10.6861i −0.532473 + 0.386864i
764764 0 0
765765 0 0
766766 0 0
767767 2.04378 + 1.48490i 0.0737967 + 0.0536165i
768768 0 0
769769 7.85410 0.283226 0.141613 0.989922i 0.454771π-0.454771\pi
0.141613 + 0.989922i 0.454771π0.454771\pi
770770 0 0
771771 0 0
772772 0 0
773773 −31.3235 22.7579i −1.12663 0.818543i −0.141428 0.989949i 0.545169π-0.545169\pi
−0.985201 + 0.171405i 0.945169π0.945169\pi
774774 0 0
775775 2.92705 9.00854i 0.105143 0.323596i
776776 0 0
777777 0 0
778778 0 0
779779 10.8857 + 33.5027i 0.390020 + 1.20036i
780780 0 0
781781 8.35410 + 34.4953i 0.298933 + 1.23434i
782782 0 0
783783 0 0
784784 0 0
785785 −4.68393 + 3.40308i −0.167177 + 0.121461i
786786 0 0
787787 12.5836 38.7283i 0.448557 1.38052i −0.429979 0.902839i 0.641479π-0.641479\pi
0.878536 0.477677i 0.158521π-0.158521\pi
788788 0 0
789789 0 0
790790 0 0
791791 12.2627 0.436011
792792 0 0
793793 −0.214782 −0.00762712
794794 0 0
795795 0 0
796796 0 0
797797 −0.824160 + 2.53650i −0.0291933 + 0.0898476i −0.964592 0.263748i 0.915041π-0.915041\pi
0.935398 + 0.353596i 0.115041π0.115041\pi
798798 0 0
799799 52.0967 37.8505i 1.84305 1.33905i
800800 0 0
801801 0 0
802802 0 0
803803 −18.2802 + 44.3814i −0.645093 + 1.56618i
804804 0 0
805805 −0.753289 2.31838i −0.0265499 0.0817123i
806806 0 0
807807 0 0
808808 0 0
809809 −12.6748 + 39.0090i −0.445622 + 1.37148i 0.436179 + 0.899860i 0.356331π0.356331\pi
−0.881801 + 0.471622i 0.843669π0.843669\pi
810810 0 0
811811 43.5238 + 31.6219i 1.52833 + 1.11039i 0.957159 + 0.289561i 0.0935095π0.0935095\pi
0.571168 + 0.820833i 0.306491π0.306491\pi
812812 0 0
813813 0 0
814814 0 0
815815 36.3325 1.27267
816816 0 0
817817 −9.35410 6.79615i −0.327259 0.237767i
818818 0 0
819819 0 0
820820 0 0
821821 −29.7622 + 21.6235i −1.03871 + 0.754666i −0.970033 0.242974i 0.921877π-0.921877\pi
−0.0686751 + 0.997639i 0.521877π0.521877\pi
822822 0 0
823823 7.30902 + 22.4948i 0.254776 + 0.784121i 0.993874 + 0.110522i 0.0352523π0.0352523\pi
−0.739097 + 0.673599i 0.764748π0.764748\pi
824824 0 0
825825 0 0
826826 0 0
827827 8.54371 + 26.2948i 0.297094 + 0.914361i 0.982510 + 0.186209i 0.0596203π0.0596203\pi
−0.685416 + 0.728152i 0.740380π0.740380\pi
828828 0 0
829829 5.01722 3.64522i 0.174255 0.126604i −0.497239 0.867614i 0.665653π-0.665653\pi
0.671494 + 0.741010i 0.265653π0.265653\pi
830830 0 0
831831 0 0
832832 0 0
833833 32.1042 + 23.3250i 1.11234 + 0.808165i
834834 0 0
835835 −55.5755 −1.92327
836836 0 0
837837 0 0
838838 0 0
839839 −36.9724 26.8620i −1.27643 0.927380i −0.276990 0.960873i 0.589337π-0.589337\pi
−0.999439 + 0.0334932i 0.989337π0.989337\pi
840840 0 0
841841 −5.94834 + 18.3071i −0.205115 + 0.631279i
842842 0 0
843843 0 0
844844 0 0
845845 −10.1050 31.1001i −0.347623 1.06987i
846846 0 0
847847 1.76393 + 10.8576i 0.0606094 + 0.373073i
848848 0 0
849849 0 0
850850 0 0
851851 −5.23680 + 3.80476i −0.179515 + 0.130425i
852852 0 0
853853 10.2533 31.5564i 0.351066 1.08047i −0.607190 0.794557i 0.707703π-0.707703\pi
0.958256 0.285913i 0.0922968π-0.0922968\pi
854854 0 0
855855 0 0
856856 0 0
857857 −24.2976 −0.829991 −0.414995 0.909824i 0.636217π-0.636217\pi
−0.414995 + 0.909824i 0.636217π0.636217\pi
858858 0 0
859859 −19.6525 −0.670534 −0.335267 0.942123i 0.608826π-0.608826\pi
−0.335267 + 0.942123i 0.608826π0.608826\pi
860860 0 0
861861 0 0
862862 0 0
863863 −12.4905 + 38.4418i −0.425181 + 1.30857i 0.477639 + 0.878556i 0.341493π0.341493\pi
−0.902821 + 0.430018i 0.858507π0.858507\pi
864864 0 0
865865 19.4336 14.1194i 0.660763 0.480073i
866866 0 0
867867 0 0
868868 0 0
869869 −1.78910 1.52190i −0.0606912 0.0516270i
870870 0 0
871871 −0.315595 0.971301i −0.0106935 0.0329113i
872872 0 0
873873 0 0
874874 0 0
875875 −2.82444 + 8.69273i −0.0954835 + 0.293868i
876876 0 0
877877 28.1353 + 20.4415i 0.950060 + 0.690259i 0.950821 0.309741i 0.100242π-0.100242\pi
−0.000761020 1.00000i 0.500242π0.500242\pi
878878 0 0
879879 0 0
880880 0 0
881881 −15.9817 −0.538437 −0.269218 0.963079i 0.586765π-0.586765\pi
−0.269218 + 0.963079i 0.586765π0.586765\pi
882882 0 0
883883 −12.0000 8.71851i −0.403832 0.293401i 0.367268 0.930115i 0.380293π-0.380293\pi
−0.771100 + 0.636714i 0.780293π0.780293\pi
884884 0 0
885885 0 0
886886 0 0
887887 11.4820 8.34219i 0.385529 0.280103i −0.378092 0.925768i 0.623420π-0.623420\pi
0.763621 + 0.645665i 0.223420π0.223420\pi
888888 0 0
889889 −5.00000 15.3884i −0.167695 0.516111i
890890 0 0
891891 0 0
892892 0 0
893893 −11.5959 35.6886i −0.388043 1.19427i
894894 0 0
895895 −31.4443 + 22.8456i −1.05107 + 0.763644i
896896 0 0
897897 0 0
898898 0 0
899899 17.3152 + 12.5802i 0.577495 + 0.419574i
900900 0 0
901901 10.3262 0.344017
902902 0 0
903903 0 0
904904 0 0
905905 33.1830 + 24.1089i 1.10304 + 0.801406i
906906 0 0
907907 0.225425 0.693786i 0.00748511 0.0230368i −0.947244 0.320513i 0.896145π-0.896145\pi
0.954729 + 0.297476i 0.0961448π0.0961448\pi
908908 0 0
909909 0 0
910910 0 0
911911 12.5609 + 38.6584i 0.416161 + 1.28081i 0.911209 + 0.411945i 0.135150π0.135150\pi
−0.495048 + 0.868866i 0.664850π0.664850\pi
912912 0 0
913913 4.69756 + 19.3969i 0.155467 + 0.641944i
914914 0 0
915915 0 0
916916 0 0
917917 6.91201 5.02187i 0.228255 0.165837i
918918 0 0
919919 −16.6353 + 51.1981i −0.548746 + 1.68887i 0.163165 + 0.986599i 0.447830π0.447830\pi
−0.711912 + 0.702269i 0.752170π0.752170\pi
920920 0 0
921921 0 0
922922 0 0
923923 2.52626 0.0831527
924924 0 0
925925 −9.27051 −0.304812
926926 0 0
927927 0 0
928928 0 0
929929 −12.3331 + 37.9574i −0.404636 + 1.24534i 0.516563 + 0.856249i 0.327211π0.327211\pi
−0.921199 + 0.389092i 0.872789π0.872789\pi
930930 0 0
931931 18.7082 13.5923i 0.613137 0.445470i
932932 0 0
933933 0 0
934934 0 0
935935 −55.2525 4.23804i −1.80695 0.138599i
936936 0 0
937937 −13.6353 41.9650i −0.445444 1.37094i −0.881996 0.471257i 0.843800π-0.843800\pi
0.436551 0.899679i 0.356200π-0.356200\pi
938938 0 0
939939 0 0
940940 0 0
941941 −3.83289 + 11.7964i −0.124949 + 0.384552i −0.993892 0.110360i 0.964800π-0.964800\pi
0.868943 + 0.494912i 0.164800π0.164800\pi
942942 0 0
943943 7.13525 + 5.18407i 0.232356 + 0.168816i
944944 0 0
945945 0 0
946946 0 0
947947 −10.7014 −0.347748 −0.173874 0.984768i 0.555629π-0.555629\pi
−0.173874 + 0.984768i 0.555629π0.555629\pi
948948 0 0
949949 2.76393 + 2.00811i 0.0897210 + 0.0651861i
950950 0 0
951951 0 0
952952 0 0
953953 23.9290 17.3855i 0.775137 0.563170i −0.128378 0.991725i 0.540977π-0.540977\pi
0.903516 + 0.428555i 0.140977π0.140977\pi
954954 0 0
955955 −18.3926 56.6066i −0.595171 1.83175i
956956 0 0
957957 0 0
958958 0 0
959959 4.75433 + 14.6323i 0.153525 + 0.472502i
960960 0 0
961961 −12.9271 + 9.39205i −0.417002 + 0.302969i
962962 0 0
963963 0 0
964964 0 0
965965 −22.7798 16.5505i −0.733308 0.532779i
966966 0 0
967967 −57.5623 −1.85108 −0.925539 0.378651i 0.876388π-0.876388\pi
−0.925539 + 0.378651i 0.876388π0.876388\pi
968968 0 0
969969 0 0
970970 0 0
971971 20.4378 + 14.8490i 0.655881 + 0.476526i 0.865270 0.501307i 0.167147π-0.167147\pi
−0.209388 + 0.977833i 0.567147π0.567147\pi
972972 0 0
973973 4.06231 12.5025i 0.130232 0.400811i
974974 0 0
975975 0 0
976976 0 0
977977 −7.50837 23.1084i −0.240214 0.739303i −0.996387 0.0849311i 0.972933π-0.972933\pi
0.756173 0.654372i 0.227067π-0.227067\pi
978978 0 0
979979 −20.3647 + 12.5352i −0.650860 + 0.400628i
980980 0 0
981981 0 0
982982 0 0
983983 −7.57877 + 5.50630i −0.241725 + 0.175624i −0.702051 0.712126i 0.747732π-0.747732\pi
0.460326 + 0.887750i 0.347732π0.347732\pi
984984 0 0
985985 20.3647 62.6762i 0.648875 1.99703i
986986 0 0
987987 0 0
988988 0 0
989989 −2.89483 −0.0920503
990990 0 0
991991 −20.3951 −0.647872 −0.323936 0.946079i 0.605006π-0.605006\pi
−0.323936 + 0.946079i 0.605006π0.605006\pi
992992 0 0
993993 0 0
994994 0 0
995995 3.30691 10.1776i 0.104836 0.322652i
996996 0 0
997997 −9.73607 + 7.07367i −0.308344 + 0.224025i −0.731186 0.682178i 0.761033π-0.761033\pi
0.422841 + 0.906204i 0.361033π0.361033\pi
998998 0 0
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 396.2.j.d.181.2 yes 8
3.2 odd 2 inner 396.2.j.d.181.1 8
11.3 even 5 4356.2.a.z.1.3 4
11.8 odd 10 4356.2.a.x.1.3 4
11.9 even 5 inner 396.2.j.d.361.2 yes 8
33.8 even 10 4356.2.a.x.1.2 4
33.14 odd 10 4356.2.a.z.1.2 4
33.20 odd 10 inner 396.2.j.d.361.1 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
396.2.j.d.181.1 8 3.2 odd 2 inner
396.2.j.d.181.2 yes 8 1.1 even 1 trivial
396.2.j.d.361.1 yes 8 33.20 odd 10 inner
396.2.j.d.361.2 yes 8 11.9 even 5 inner
4356.2.a.x.1.2 4 33.8 even 10
4356.2.a.x.1.3 4 11.8 odd 10
4356.2.a.z.1.2 4 33.14 odd 10
4356.2.a.z.1.3 4 11.3 even 5