Properties

Label 4000.2.c.f.1249.9
Level 40004000
Weight 22
Character 4000.1249
Analytic conductor 31.94031.940
Analytic rank 00
Dimension 1212
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4000,2,Mod(1249,4000)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4000, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4000.1249");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 4000=2553 4000 = 2^{5} \cdot 5^{3}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 4000.c (of order 22, degree 11, 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: 31.940160808531.9401608085
Analytic rank: 00
Dimension: 1212
Coefficient field: Q[x]/(x12+)\mathbb{Q}[x]/(x^{12} + \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x12+22x10+179x8+646x6+929x4+252x2+16 x^{12} + 22x^{10} + 179x^{8} + 646x^{6} + 929x^{4} + 252x^{2} + 16 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 22 2^{2}
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 1249.9
Root 1.81030i1.81030i of defining polynomial
Character χ\chi == 4000.1249
Dual form 4000.2.c.f.1249.4

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+1.81030iq34.37760iq70.277175q95.82433q115.34625iq13+5.41151iq171.59789q19+7.92476q210.340859iq23+4.92912iq27+4.96428q29+4.63796q3110.5438iq33+8.40977iq37+9.67829q392.34244q417.10407iq430.879427iq4712.1634q499.79645q51+1.30241iq532.89265iq5711.0726q5914.4423q61+1.21336iq63+3.01420iq67+0.617056q699.37319q71+13.7157iq73+25.4966iq775.85098q799.75470q81+8.54562iq83+8.98682iq87+18.0227q8923.4037q91+8.39608iq9310.0919iq97+1.61436q99+O(q100)q+1.81030i q^{3} -4.37760i q^{7} -0.277175 q^{9} -5.82433 q^{11} -5.34625i q^{13} +5.41151i q^{17} -1.59789 q^{19} +7.92476 q^{21} -0.340859i q^{23} +4.92912i q^{27} +4.96428 q^{29} +4.63796 q^{31} -10.5438i q^{33} +8.40977i q^{37} +9.67829 q^{39} -2.34244 q^{41} -7.10407i q^{43} -0.879427i q^{47} -12.1634 q^{49} -9.79645 q^{51} +1.30241i q^{53} -2.89265i q^{57} -11.0726 q^{59} -14.4423 q^{61} +1.21336i q^{63} +3.01420i q^{67} +0.617056 q^{69} -9.37319 q^{71} +13.7157i q^{73} +25.4966i q^{77} -5.85098 q^{79} -9.75470 q^{81} +8.54562i q^{83} +8.98682i q^{87} +18.0227 q^{89} -23.4037 q^{91} +8.39608i q^{93} -10.0919i q^{97} +1.61436 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q8q926q11+18q194q2924q31+52q3910q41+6q4936q51+50q5912q61+24q6968q71+32q7936q81+6q8952q91++86q99+O(q100) 12 q - 8 q^{9} - 26 q^{11} + 18 q^{19} - 4 q^{29} - 24 q^{31} + 52 q^{39} - 10 q^{41} + 6 q^{49} - 36 q^{51} + 50 q^{59} - 12 q^{61} + 24 q^{69} - 68 q^{71} + 32 q^{79} - 36 q^{81} + 6 q^{89} - 52 q^{91}+ \cdots + 86 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/4000Z)×\left(\mathbb{Z}/4000\mathbb{Z}\right)^\times.

nn 13771377 25012501 27512751
χ(n)\chi(n) 1-1 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 1.81030i 1.04518i 0.852586 + 0.522588i 0.175033π0.175033\pi
−0.852586 + 0.522588i 0.824967π0.824967\pi
44 0 0
55 0 0
66 0 0
77 − 4.37760i − 1.65458i −0.561777 0.827289i 0.689882π-0.689882\pi
0.561777 0.827289i 0.310118π-0.310118\pi
88 0 0
99 −0.277175 −0.0923916
1010 0 0
1111 −5.82433 −1.75610 −0.878051 0.478567i 0.841156π-0.841156\pi
−0.878051 + 0.478567i 0.841156π0.841156\pi
1212 0 0
1313 − 5.34625i − 1.48278i −0.671073 0.741391i 0.734166π-0.734166\pi
0.671073 0.741391i 0.265834π-0.265834\pi
1414 0 0
1515 0 0
1616 0 0
1717 5.41151i 1.31248i 0.754550 + 0.656242i 0.227855π0.227855\pi
−0.754550 + 0.656242i 0.772145π0.772145\pi
1818 0 0
1919 −1.59789 −0.366580 −0.183290 0.983059i 0.558675π-0.558675\pi
−0.183290 + 0.983059i 0.558675π0.558675\pi
2020 0 0
2121 7.92476 1.72932
2222 0 0
2323 − 0.340859i − 0.0710740i −0.999368 0.0355370i 0.988686π-0.988686\pi
0.999368 0.0355370i 0.0113142π-0.0113142\pi
2424 0 0
2525 0 0
2626 0 0
2727 4.92912i 0.948610i
2828 0 0
2929 4.96428 0.921844 0.460922 0.887441i 0.347519π-0.347519\pi
0.460922 + 0.887441i 0.347519π0.347519\pi
3030 0 0
3131 4.63796 0.833002 0.416501 0.909135i 0.363256π-0.363256\pi
0.416501 + 0.909135i 0.363256π0.363256\pi
3232 0 0
3333 − 10.5438i − 1.83543i
3434 0 0
3535 0 0
3636 0 0
3737 8.40977i 1.38256i 0.722588 + 0.691278i 0.242952π0.242952\pi
−0.722588 + 0.691278i 0.757048π0.757048\pi
3838 0 0
3939 9.67829 1.54977
4040 0 0
4141 −2.34244 −0.365828 −0.182914 0.983129i 0.558553π-0.558553\pi
−0.182914 + 0.983129i 0.558553π0.558553\pi
4242 0 0
4343 − 7.10407i − 1.08336i −0.840585 0.541680i 0.817788π-0.817788\pi
0.840585 0.541680i 0.182212π-0.182212\pi
4444 0 0
4545 0 0
4646 0 0
4747 − 0.879427i − 0.128278i −0.997941 0.0641388i 0.979570π-0.979570\pi
0.997941 0.0641388i 0.0204300π-0.0204300\pi
4848 0 0
4949 −12.1634 −1.73763
5050 0 0
5151 −9.79645 −1.37178
5252 0 0
5353 1.30241i 0.178900i 0.995991 + 0.0894502i 0.0285110π0.0285110\pi
−0.995991 + 0.0894502i 0.971489π0.971489\pi
5454 0 0
5555 0 0
5656 0 0
5757 − 2.89265i − 0.383141i
5858 0 0
5959 −11.0726 −1.44153 −0.720767 0.693178i 0.756210π-0.756210\pi
−0.720767 + 0.693178i 0.756210π0.756210\pi
6060 0 0
6161 −14.4423 −1.84915 −0.924574 0.381003i 0.875579π-0.875579\pi
−0.924574 + 0.381003i 0.875579π0.875579\pi
6262 0 0
6363 1.21336i 0.152869i
6464 0 0
6565 0 0
6666 0 0
6767 3.01420i 0.368243i 0.982903 + 0.184122i 0.0589440π0.0589440\pi
−0.982903 + 0.184122i 0.941056π0.941056\pi
6868 0 0
6969 0.617056 0.0742848
7070 0 0
7171 −9.37319 −1.11239 −0.556197 0.831051i 0.687740π-0.687740\pi
−0.556197 + 0.831051i 0.687740π0.687740\pi
7272 0 0
7373 13.7157i 1.60530i 0.596451 + 0.802649i 0.296577π0.296577\pi
−0.596451 + 0.802649i 0.703423π0.703423\pi
7474 0 0
7575 0 0
7676 0 0
7777 25.4966i 2.90561i
7878 0 0
7979 −5.85098 −0.658287 −0.329143 0.944280i 0.606760π-0.606760\pi
−0.329143 + 0.944280i 0.606760π0.606760\pi
8080 0 0
8181 −9.75470 −1.08386
8282 0 0
8383 8.54562i 0.938003i 0.883197 + 0.469002i 0.155386π0.155386\pi
−0.883197 + 0.469002i 0.844614π0.844614\pi
8484 0 0
8585 0 0
8686 0 0
8787 8.98682i 0.963488i
8888 0 0
8989 18.0227 1.91040 0.955202 0.295956i 0.0956381π-0.0956381\pi
0.955202 + 0.295956i 0.0956381π0.0956381\pi
9090 0 0
9191 −23.4037 −2.45338
9292 0 0
9393 8.39608i 0.870633i
9494 0 0
9595 0 0
9696 0 0
9797 − 10.0919i − 1.02468i −0.858783 0.512340i 0.828779π-0.828779\pi
0.858783 0.512340i 0.171221π-0.171221\pi
9898 0 0
9999 1.61436 0.162249
100100 0 0
101101 −6.64409 −0.661111 −0.330556 0.943787i 0.607236π-0.607236\pi
−0.330556 + 0.943787i 0.607236π0.607236\pi
102102 0 0
103103 − 9.84923i − 0.970474i −0.874383 0.485237i 0.838733π-0.838733\pi
0.874383 0.485237i 0.161267π-0.161267\pi
104104 0 0
105105 0 0
106106 0 0
107107 0.941408i 0.0910093i 0.998964 + 0.0455047i 0.0144896π0.0144896\pi
−0.998964 + 0.0455047i 0.985510π0.985510\pi
108108 0 0
109109 −10.2276 −0.979627 −0.489813 0.871827i 0.662935π-0.662935\pi
−0.489813 + 0.871827i 0.662935π0.662935\pi
110110 0 0
111111 −15.2242 −1.44501
112112 0 0
113113 8.90474i 0.837687i 0.908058 + 0.418844i 0.137564π0.137564\pi
−0.908058 + 0.418844i 0.862436π0.862436\pi
114114 0 0
115115 0 0
116116 0 0
117117 1.48185i 0.136997i
118118 0 0
119119 23.6894 2.17161
120120 0 0
121121 22.9228 2.08389
122122 0 0
123123 − 4.24051i − 0.382354i
124124 0 0
125125 0 0
126126 0 0
127127 − 1.75678i − 0.155889i −0.996958 0.0779446i 0.975164π-0.975164\pi
0.996958 0.0779446i 0.0248357π-0.0248357\pi
128128 0 0
129129 12.8605 1.13230
130130 0 0
131131 −6.14604 −0.536982 −0.268491 0.963282i 0.586525π-0.586525\pi
−0.268491 + 0.963282i 0.586525π0.586525\pi
132132 0 0
133133 6.99491i 0.606535i
134134 0 0
135135 0 0
136136 0 0
137137 1.79739i 0.153561i 0.997048 + 0.0767806i 0.0244641π0.0244641\pi
−0.997048 + 0.0767806i 0.975536π0.975536\pi
138138 0 0
139139 −15.6284 −1.32559 −0.662793 0.748803i 0.730629π-0.730629\pi
−0.662793 + 0.748803i 0.730629π0.730629\pi
140140 0 0
141141 1.59202 0.134073
142142 0 0
143143 31.1383i 2.60392i
144144 0 0
145145 0 0
146146 0 0
147147 − 22.0193i − 1.81612i
148148 0 0
149149 −20.3836 −1.66989 −0.834944 0.550335i 0.814500π-0.814500\pi
−0.834944 + 0.550335i 0.814500π0.814500\pi
150150 0 0
151151 −14.2100 −1.15639 −0.578196 0.815898i 0.696243π-0.696243\pi
−0.578196 + 0.815898i 0.696243π0.696243\pi
152152 0 0
153153 − 1.49994i − 0.121263i
154154 0 0
155155 0 0
156156 0 0
157157 − 6.01209i − 0.479817i −0.970796 0.239908i 0.922883π-0.922883\pi
0.970796 0.239908i 0.0771174π-0.0771174\pi
158158 0 0
159159 −2.35776 −0.186982
160160 0 0
161161 −1.49215 −0.117598
162162 0 0
163163 12.5491i 0.982920i 0.870900 + 0.491460i 0.163537π0.163537\pi
−0.870900 + 0.491460i 0.836463π0.836463\pi
164164 0 0
165165 0 0
166166 0 0
167167 4.32243i 0.334480i 0.985916 + 0.167240i 0.0534854π0.0534854\pi
−0.985916 + 0.167240i 0.946515π0.946515\pi
168168 0 0
169169 −15.5824 −1.19864
170170 0 0
171171 0.442894 0.0338689
172172 0 0
173173 8.22242i 0.625139i 0.949895 + 0.312570i 0.101190π0.101190\pi
−0.949895 + 0.312570i 0.898810π0.898810\pi
174174 0 0
175175 0 0
176176 0 0
177177 − 20.0447i − 1.50666i
178178 0 0
179179 2.21704 0.165710 0.0828548 0.996562i 0.473596π-0.473596\pi
0.0828548 + 0.996562i 0.473596π0.473596\pi
180180 0 0
181181 15.6084 1.16016 0.580080 0.814559i 0.303021π-0.303021\pi
0.580080 + 0.814559i 0.303021π0.303021\pi
182182 0 0
183183 − 26.1449i − 1.93268i
184184 0 0
185185 0 0
186186 0 0
187187 − 31.5184i − 2.30486i
188188 0 0
189189 21.5777 1.56955
190190 0 0
191191 0.823027 0.0595521 0.0297761 0.999557i 0.490521π-0.490521\pi
0.0297761 + 0.999557i 0.490521π0.490521\pi
192192 0 0
193193 4.12278i 0.296764i 0.988930 + 0.148382i 0.0474066π0.0474066\pi
−0.988930 + 0.148382i 0.952593π0.952593\pi
194194 0 0
195195 0 0
196196 0 0
197197 18.3961i 1.31067i 0.755340 + 0.655333i 0.227472π0.227472\pi
−0.755340 + 0.655333i 0.772528π0.772528\pi
198198 0 0
199199 1.01893 0.0722300 0.0361150 0.999348i 0.488502π-0.488502\pi
0.0361150 + 0.999348i 0.488502π0.488502\pi
200200 0 0
201201 −5.45660 −0.384879
202202 0 0
203203 − 21.7316i − 1.52526i
204204 0 0
205205 0 0
206206 0 0
207207 0.0944776i 0.00656665i
208208 0 0
209209 9.30662 0.643752
210210 0 0
211211 8.14609 0.560800 0.280400 0.959883i 0.409533π-0.409533\pi
0.280400 + 0.959883i 0.409533π0.409533\pi
212212 0 0
213213 − 16.9683i − 1.16265i
214214 0 0
215215 0 0
216216 0 0
217217 − 20.3031i − 1.37827i
218218 0 0
219219 −24.8294 −1.67782
220220 0 0
221221 28.9313 1.94613
222222 0 0
223223 − 12.4073i − 0.830856i −0.909626 0.415428i 0.863632π-0.863632\pi
0.909626 0.415428i 0.136368π-0.136368\pi
224224 0 0
225225 0 0
226226 0 0
227227 24.5589i 1.63003i 0.579438 + 0.815016i 0.303272π0.303272\pi
−0.579438 + 0.815016i 0.696728π0.696728\pi
228228 0 0
229229 5.35261 0.353711 0.176855 0.984237i 0.443408π-0.443408\pi
0.176855 + 0.984237i 0.443408π0.443408\pi
230230 0 0
231231 −46.1564 −3.03687
232232 0 0
233233 0.350300i 0.0229489i 0.999934 + 0.0114745i 0.00365252π0.00365252\pi
−0.999934 + 0.0114745i 0.996347π0.996347\pi
234234 0 0
235235 0 0
236236 0 0
237237 − 10.5920i − 0.688025i
238238 0 0
239239 8.90513 0.576025 0.288012 0.957627i 0.407006π-0.407006\pi
0.288012 + 0.957627i 0.407006π0.407006\pi
240240 0 0
241241 −8.09465 −0.521422 −0.260711 0.965417i 0.583957π-0.583957\pi
−0.260711 + 0.965417i 0.583957π0.583957\pi
242242 0 0
243243 − 2.87154i − 0.184209i
244244 0 0
245245 0 0
246246 0 0
247247 8.54270i 0.543559i
248248 0 0
249249 −15.4701 −0.980378
250250 0 0
251251 −15.0480 −0.949821 −0.474910 0.880034i 0.657520π-0.657520\pi
−0.474910 + 0.880034i 0.657520π0.657520\pi
252252 0 0
253253 1.98528i 0.124813i
254254 0 0
255255 0 0
256256 0 0
257257 − 13.1390i − 0.819586i −0.912179 0.409793i 0.865601π-0.865601\pi
0.912179 0.409793i 0.134399π-0.134399\pi
258258 0 0
259259 36.8146 2.28755
260260 0 0
261261 −1.37597 −0.0851706
262262 0 0
263263 16.3912i 1.01072i 0.862908 + 0.505362i 0.168641π0.168641\pi
−0.862908 + 0.505362i 0.831359π0.831359\pi
264264 0 0
265265 0 0
266266 0 0
267267 32.6265i 1.99671i
268268 0 0
269269 −1.56270 −0.0952793 −0.0476397 0.998865i 0.515170π-0.515170\pi
−0.0476397 + 0.998865i 0.515170π0.515170\pi
270270 0 0
271271 −30.1625 −1.83224 −0.916121 0.400902i 0.868697π-0.868697\pi
−0.916121 + 0.400902i 0.868697π0.868697\pi
272272 0 0
273273 − 42.3677i − 2.56421i
274274 0 0
275275 0 0
276276 0 0
277277 − 17.9905i − 1.08095i −0.841361 0.540473i 0.818245π-0.818245\pi
0.841361 0.540473i 0.181755π-0.181755\pi
278278 0 0
279279 −1.28553 −0.0769624
280280 0 0
281281 −1.25760 −0.0750221 −0.0375111 0.999296i 0.511943π-0.511943\pi
−0.0375111 + 0.999296i 0.511943π0.511943\pi
282282 0 0
283283 17.4528i 1.03746i 0.854938 + 0.518729i 0.173595π0.173595\pi
−0.854938 + 0.518729i 0.826405π0.826405\pi
284284 0 0
285285 0 0
286286 0 0
287287 10.2543i 0.605290i
288288 0 0
289289 −12.2845 −0.722616
290290 0 0
291291 18.2694 1.07097
292292 0 0
293293 − 24.0216i − 1.40336i −0.712494 0.701678i 0.752435π-0.752435\pi
0.712494 0.701678i 0.247565π-0.247565\pi
294294 0 0
295295 0 0
296296 0 0
297297 − 28.7088i − 1.66586i
298298 0 0
299299 −1.82232 −0.105387
300300 0 0
301301 −31.0988 −1.79250
302302 0 0
303303 − 12.0278i − 0.690977i
304304 0 0
305305 0 0
306306 0 0
307307 11.1584i 0.636845i 0.947949 + 0.318423i 0.103153π0.103153\pi
−0.947949 + 0.318423i 0.896847π0.896847\pi
308308 0 0
309309 17.8300 1.01432
310310 0 0
311311 −19.8088 −1.12326 −0.561628 0.827390i 0.689825π-0.689825\pi
−0.561628 + 0.827390i 0.689825π0.689825\pi
312312 0 0
313313 − 3.29732i − 0.186376i −0.995649 0.0931879i 0.970294π-0.970294\pi
0.995649 0.0931879i 0.0297057π-0.0297057\pi
314314 0 0
315315 0 0
316316 0 0
317317 17.5911i 0.988017i 0.869457 + 0.494009i 0.164469π0.164469\pi
−0.869457 + 0.494009i 0.835531π0.835531\pi
318318 0 0
319319 −28.9136 −1.61885
320320 0 0
321321 −1.70423 −0.0951207
322322 0 0
323323 − 8.64698i − 0.481131i
324324 0 0
325325 0 0
326326 0 0
327327 − 18.5150i − 1.02388i
328328 0 0
329329 −3.84978 −0.212245
330330 0 0
331331 −15.0330 −0.826288 −0.413144 0.910666i 0.635569π-0.635569\pi
−0.413144 + 0.910666i 0.635569π0.635569\pi
332332 0 0
333333 − 2.33098i − 0.127737i
334334 0 0
335335 0 0
336336 0 0
337337 − 31.7741i − 1.73084i −0.501043 0.865422i 0.667050π-0.667050\pi
0.501043 0.865422i 0.332950π-0.332950\pi
338338 0 0
339339 −16.1202 −0.875530
340340 0 0
341341 −27.0130 −1.46284
342342 0 0
343343 22.6032i 1.22046i
344344 0 0
345345 0 0
346346 0 0
347347 − 26.6632i − 1.43136i −0.698430 0.715679i 0.746118π-0.746118\pi
0.698430 0.715679i 0.253882π-0.253882\pi
348348 0 0
349349 −4.44619 −0.237999 −0.119000 0.992894i 0.537969π-0.537969\pi
−0.119000 + 0.992894i 0.537969π0.537969\pi
350350 0 0
351351 26.3523 1.40658
352352 0 0
353353 − 0.316976i − 0.0168710i −0.999964 0.00843548i 0.997315π-0.997315\pi
0.999964 0.00843548i 0.00268513π-0.00268513\pi
354354 0 0
355355 0 0
356356 0 0
357357 42.8849i 2.26971i
358358 0 0
359359 22.0361 1.16302 0.581509 0.813540i 0.302462π-0.302462\pi
0.581509 + 0.813540i 0.302462π0.302462\pi
360360 0 0
361361 −16.4468 −0.865619
362362 0 0
363363 41.4971i 2.17803i
364364 0 0
365365 0 0
366366 0 0
367367 4.44627i 0.232093i 0.993244 + 0.116047i 0.0370222π0.0370222\pi
−0.993244 + 0.116047i 0.962978π0.962978\pi
368368 0 0
369369 0.649266 0.0337994
370370 0 0
371371 5.70145 0.296005
372372 0 0
373373 − 23.3308i − 1.20802i −0.796975 0.604012i 0.793568π-0.793568\pi
0.796975 0.604012i 0.206432π-0.206432\pi
374374 0 0
375375 0 0
376376 0 0
377377 − 26.5403i − 1.36689i
378378 0 0
379379 19.0905 0.980614 0.490307 0.871550i 0.336885π-0.336885\pi
0.490307 + 0.871550i 0.336885π0.336885\pi
380380 0 0
381381 3.18030 0.162932
382382 0 0
383383 0.371944i 0.0190055i 0.999955 + 0.00950273i 0.00302486π0.00302486\pi
−0.999955 + 0.00950273i 0.996975π0.996975\pi
384384 0 0
385385 0 0
386386 0 0
387387 1.96907i 0.100093i
388388 0 0
389389 22.9338 1.16279 0.581395 0.813621i 0.302507π-0.302507\pi
0.581395 + 0.813621i 0.302507π0.302507\pi
390390 0 0
391391 1.84456 0.0932836
392392 0 0
393393 − 11.1262i − 0.561240i
394394 0 0
395395 0 0
396396 0 0
397397 14.2189i 0.713628i 0.934176 + 0.356814i 0.116137π0.116137\pi
−0.934176 + 0.356814i 0.883863π0.883863\pi
398398 0 0
399399 −12.6629 −0.633936
400400 0 0
401401 0.847710 0.0423326 0.0211663 0.999776i 0.493262π-0.493262\pi
0.0211663 + 0.999776i 0.493262π0.493262\pi
402402 0 0
403403 − 24.7957i − 1.23516i
404404 0 0
405405 0 0
406406 0 0
407407 − 48.9813i − 2.42791i
408408 0 0
409409 32.7324 1.61851 0.809256 0.587457i 0.199871π-0.199871\pi
0.809256 + 0.587457i 0.199871π0.199871\pi
410410 0 0
411411 −3.25381 −0.160498
412412 0 0
413413 48.4715i 2.38513i
414414 0 0
415415 0 0
416416 0 0
417417 − 28.2921i − 1.38547i
418418 0 0
419419 24.3482 1.18949 0.594743 0.803916i 0.297254π-0.297254\pi
0.594743 + 0.803916i 0.297254π0.297254\pi
420420 0 0
421421 −5.79282 −0.282325 −0.141162 0.989986i 0.545084π-0.545084\pi
−0.141162 + 0.989986i 0.545084π0.545084\pi
422422 0 0
423423 0.243755i 0.0118518i
424424 0 0
425425 0 0
426426 0 0
427427 63.2226i 3.05956i
428428 0 0
429429 −56.3696 −2.72155
430430 0 0
431431 27.0917 1.30496 0.652480 0.757806i 0.273728π-0.273728\pi
0.652480 + 0.757806i 0.273728π0.273728\pi
432432 0 0
433433 35.6206i 1.71182i 0.517129 + 0.855908i 0.327001π0.327001\pi
−0.517129 + 0.855908i 0.672999π0.672999\pi
434434 0 0
435435 0 0
436436 0 0
437437 0.544654i 0.0260543i
438438 0 0
439439 −35.2574 −1.68275 −0.841373 0.540455i 0.818252π-0.818252\pi
−0.841373 + 0.540455i 0.818252π0.818252\pi
440440 0 0
441441 3.37138 0.160542
442442 0 0
443443 − 33.9602i − 1.61350i −0.590896 0.806748i 0.701225π-0.701225\pi
0.590896 0.806748i 0.298775π-0.298775\pi
444444 0 0
445445 0 0
446446 0 0
447447 − 36.9003i − 1.74533i
448448 0 0
449449 −13.2446 −0.625050 −0.312525 0.949910i 0.601175π-0.601175\pi
−0.312525 + 0.949910i 0.601175π0.601175\pi
450450 0 0
451451 13.6432 0.642431
452452 0 0
453453 − 25.7243i − 1.20863i
454454 0 0
455455 0 0
456456 0 0
457457 − 2.86349i − 0.133949i −0.997755 0.0669743i 0.978665π-0.978665\pi
0.997755 0.0669743i 0.0213345π-0.0213345\pi
458458 0 0
459459 −26.6740 −1.24504
460460 0 0
461461 22.8968 1.06641 0.533206 0.845986i 0.320987π-0.320987\pi
0.533206 + 0.845986i 0.320987π0.320987\pi
462462 0 0
463463 − 15.0334i − 0.698659i −0.937000 0.349330i 0.886409π-0.886409\pi
0.937000 0.349330i 0.113591π-0.113591\pi
464464 0 0
465465 0 0
466466 0 0
467467 − 16.2490i − 0.751913i −0.926637 0.375957i 0.877314π-0.877314\pi
0.926637 0.375957i 0.122686π-0.122686\pi
468468 0 0
469469 13.1950 0.609287
470470 0 0
471471 10.8837 0.501493
472472 0 0
473473 41.3764i 1.90249i
474474 0 0
475475 0 0
476476 0 0
477477 − 0.360997i − 0.0165289i
478478 0 0
479479 16.8024 0.767722 0.383861 0.923391i 0.374594π-0.374594\pi
0.383861 + 0.923391i 0.374594π0.374594\pi
480480 0 0
481481 44.9607 2.05003
482482 0 0
483483 − 2.70123i − 0.122910i
484484 0 0
485485 0 0
486486 0 0
487487 17.0426i 0.772276i 0.922441 + 0.386138i 0.126191π0.126191\pi
−0.922441 + 0.386138i 0.873809π0.873809\pi
488488 0 0
489489 −22.7176 −1.02732
490490 0 0
491491 −25.5972 −1.15518 −0.577592 0.816326i 0.696007π-0.696007\pi
−0.577592 + 0.816326i 0.696007π0.696007\pi
492492 0 0
493493 26.8643i 1.20991i
494494 0 0
495495 0 0
496496 0 0
497497 41.0321i 1.84054i
498498 0 0
499499 2.10330 0.0941565 0.0470783 0.998891i 0.485009π-0.485009\pi
0.0470783 + 0.998891i 0.485009π0.485009\pi
500500 0 0
501501 −7.82489 −0.349590
502502 0 0
503503 − 1.80566i − 0.0805105i −0.999189 0.0402552i 0.987183π-0.987183\pi
0.999189 0.0402552i 0.0128171π-0.0128171\pi
504504 0 0
505505 0 0
506506 0 0
507507 − 28.2087i − 1.25279i
508508 0 0
509509 16.5594 0.733980 0.366990 0.930225i 0.380388π-0.380388\pi
0.366990 + 0.930225i 0.380388π0.380388\pi
510510 0 0
511511 60.0417 2.65609
512512 0 0
513513 − 7.87618i − 0.347742i
514514 0 0
515515 0 0
516516 0 0
517517 5.12207i 0.225269i
518518 0 0
519519 −14.8850 −0.653380
520520 0 0
521521 −22.9830 −1.00690 −0.503452 0.864023i 0.667937π-0.667937\pi
−0.503452 + 0.864023i 0.667937π0.667937\pi
522522 0 0
523523 9.47128i 0.414150i 0.978325 + 0.207075i 0.0663944π0.0663944\pi
−0.978325 + 0.207075i 0.933606π0.933606\pi
524524 0 0
525525 0 0
526526 0 0
527527 25.0984i 1.09330i
528528 0 0
529529 22.8838 0.994948
530530 0 0
531531 3.06905 0.133186
532532 0 0
533533 12.5233i 0.542443i
534534 0 0
535535 0 0
536536 0 0
537537 4.01351i 0.173196i
538538 0 0
539539 70.8436 3.05145
540540 0 0
541541 13.2203 0.568386 0.284193 0.958767i 0.408274π-0.408274\pi
0.284193 + 0.958767i 0.408274π0.408274\pi
542542 0 0
543543 28.2558i 1.21257i
544544 0 0
545545 0 0
546546 0 0
547547 − 33.1211i − 1.41616i −0.706133 0.708079i 0.749562π-0.749562\pi
0.706133 0.708079i 0.250438π-0.250438\pi
548548 0 0
549549 4.00304 0.170846
550550 0 0
551551 −7.93236 −0.337930
552552 0 0
553553 25.6133i 1.08919i
554554 0 0
555555 0 0
556556 0 0
557557 8.75852i 0.371110i 0.982634 + 0.185555i 0.0594083π0.0594083\pi
−0.982634 + 0.185555i 0.940592π0.940592\pi
558558 0 0
559559 −37.9801 −1.60639
560560 0 0
561561 57.0577 2.40898
562562 0 0
563563 1.05986i 0.0446678i 0.999751 + 0.0223339i 0.00710970π0.00710970\pi
−0.999751 + 0.0223339i 0.992890π0.992890\pi
564564 0 0
565565 0 0
566566 0 0
567567 42.7022i 1.79332i
568568 0 0
569569 −38.9002 −1.63078 −0.815390 0.578912i 0.803477π-0.803477\pi
−0.815390 + 0.578912i 0.803477π0.803477\pi
570570 0 0
571571 −33.4842 −1.40127 −0.700635 0.713520i 0.747100π-0.747100\pi
−0.700635 + 0.713520i 0.747100π0.747100\pi
572572 0 0
573573 1.48992i 0.0622424i
574574 0 0
575575 0 0
576576 0 0
577577 17.5217i 0.729436i 0.931118 + 0.364718i 0.118835π0.118835\pi
−0.931118 + 0.364718i 0.881165π0.881165\pi
578578 0 0
579579 −7.46346 −0.310171
580580 0 0
581581 37.4093 1.55200
582582 0 0
583583 − 7.58569i − 0.314167i
584584 0 0
585585 0 0
586586 0 0
587587 − 21.6889i − 0.895195i −0.894235 0.447598i 0.852280π-0.852280\pi
0.894235 0.447598i 0.147720π-0.147720\pi
588588 0 0
589589 −7.41093 −0.305362
590590 0 0
591591 −33.3024 −1.36988
592592 0 0
593593 − 34.8683i − 1.43187i −0.698167 0.715935i 0.746001π-0.746001\pi
0.698167 0.715935i 0.253999π-0.253999\pi
594594 0 0
595595 0 0
596596 0 0
597597 1.84456i 0.0754930i
598598 0 0
599599 14.6435 0.598317 0.299158 0.954203i 0.403294π-0.403294\pi
0.299158 + 0.954203i 0.403294π0.403294\pi
600600 0 0
601601 −9.69821 −0.395598 −0.197799 0.980243i 0.563379π-0.563379\pi
−0.197799 + 0.980243i 0.563379π0.563379\pi
602602 0 0
603603 − 0.835460i − 0.0340226i
604604 0 0
605605 0 0
606606 0 0
607607 2.94086i 0.119366i 0.998217 + 0.0596829i 0.0190090π0.0190090\pi
−0.998217 + 0.0596829i 0.980991π0.980991\pi
608608 0 0
609609 39.3407 1.59417
610610 0 0
611611 −4.70163 −0.190208
612612 0 0
613613 17.0019i 0.686702i 0.939207 + 0.343351i 0.111562π0.111562\pi
−0.939207 + 0.343351i 0.888438π0.888438\pi
614614 0 0
615615 0 0
616616 0 0
617617 17.7996i 0.716583i 0.933610 + 0.358292i 0.116641π0.116641\pi
−0.933610 + 0.358292i 0.883359π0.883359\pi
618618 0 0
619619 27.5237 1.10627 0.553135 0.833092i 0.313431π-0.313431\pi
0.553135 + 0.833092i 0.313431π0.313431\pi
620620 0 0
621621 1.68014 0.0674215
622622 0 0
623623 − 78.8962i − 3.16091i
624624 0 0
625625 0 0
626626 0 0
627627 16.8477i 0.672834i
628628 0 0
629629 −45.5096 −1.81458
630630 0 0
631631 47.3515 1.88503 0.942517 0.334158i 0.108452π-0.108452\pi
0.942517 + 0.334158i 0.108452π0.108452\pi
632632 0 0
633633 14.7468i 0.586134i
634634 0 0
635635 0 0
636636 0 0
637637 65.0285i 2.57652i
638638 0 0
639639 2.59801 0.102776
640640 0 0
641641 −15.3183 −0.605037 −0.302518 0.953144i 0.597827π-0.597827\pi
−0.302518 + 0.953144i 0.597827π0.597827\pi
642642 0 0
643643 38.4573i 1.51661i 0.651901 + 0.758304i 0.273972π0.273972\pi
−0.651901 + 0.758304i 0.726028π0.726028\pi
644644 0 0
645645 0 0
646646 0 0
647647 3.46190i 0.136101i 0.997682 + 0.0680507i 0.0216780π0.0216780\pi
−0.997682 + 0.0680507i 0.978322π0.978322\pi
648648 0 0
649649 64.4906 2.53148
650650 0 0
651651 36.7547 1.44053
652652 0 0
653653 37.9039i 1.48329i 0.670790 + 0.741647i 0.265955π0.265955\pi
−0.670790 + 0.741647i 0.734045π0.734045\pi
654654 0 0
655655 0 0
656656 0 0
657657 − 3.80164i − 0.148316i
658658 0 0
659659 −22.2876 −0.868203 −0.434102 0.900864i 0.642934π-0.642934\pi
−0.434102 + 0.900864i 0.642934π0.642934\pi
660660 0 0
661661 −10.1877 −0.396257 −0.198129 0.980176i 0.563486π-0.563486\pi
−0.198129 + 0.980176i 0.563486π0.563486\pi
662662 0 0
663663 52.3742i 2.03405i
664664 0 0
665665 0 0
666666 0 0
667667 − 1.69212i − 0.0655192i
668668 0 0
669669 22.4609 0.868390
670670 0 0
671671 84.1168 3.24729
672672 0 0
673673 − 22.6737i − 0.874008i −0.899460 0.437004i 0.856040π-0.856040\pi
0.899460 0.437004i 0.143960π-0.143960\pi
674674 0 0
675675 0 0
676676 0 0
677677 − 8.30011i − 0.318999i −0.987198 0.159500i 0.949012π-0.949012\pi
0.987198 0.159500i 0.0509881π-0.0509881\pi
678678 0 0
679679 −44.1784 −1.69541
680680 0 0
681681 −44.4589 −1.70367
682682 0 0
683683 8.62826i 0.330151i 0.986281 + 0.165076i 0.0527868π0.0527868\pi
−0.986281 + 0.165076i 0.947213π0.947213\pi
684684 0 0
685685 0 0
686686 0 0
687687 9.68982i 0.369690i
688688 0 0
689689 6.96303 0.265270
690690 0 0
691691 42.6346 1.62190 0.810949 0.585117i 0.198951π-0.198951\pi
0.810949 + 0.585117i 0.198951π0.198951\pi
692692 0 0
693693 − 7.06701i − 0.268454i
694694 0 0
695695 0 0
696696 0 0
697697 − 12.6762i − 0.480143i
698698 0 0
699699 −0.634147 −0.0239857
700700 0 0
701701 −38.4312 −1.45153 −0.725763 0.687945i 0.758513π-0.758513\pi
−0.725763 + 0.687945i 0.758513π0.758513\pi
702702 0 0
703703 − 13.4379i − 0.506818i
704704 0 0
705705 0 0
706706 0 0
707707 29.0852i 1.09386i
708708 0 0
709709 −19.9047 −0.747537 −0.373769 0.927522i 0.621935π-0.621935\pi
−0.373769 + 0.927522i 0.621935π0.621935\pi
710710 0 0
711711 1.62175 0.0608202
712712 0 0
713713 − 1.58089i − 0.0592048i
714714 0 0
715715 0 0
716716 0 0
717717 16.1209i 0.602047i
718718 0 0
719719 14.9260 0.556644 0.278322 0.960488i 0.410222π-0.410222\pi
0.278322 + 0.960488i 0.410222π0.410222\pi
720720 0 0
721721 −43.1160 −1.60572
722722 0 0
723723 − 14.6537i − 0.544978i
724724 0 0
725725 0 0
726726 0 0
727727 25.6583i 0.951615i 0.879549 + 0.475808i 0.157844π0.157844\pi
−0.879549 + 0.475808i 0.842156π0.842156\pi
728728 0 0
729729 −24.0658 −0.891325
730730 0 0
731731 38.4437 1.42189
732732 0 0
733733 − 45.1247i − 1.66672i −0.552731 0.833360i 0.686414π-0.686414\pi
0.552731 0.833360i 0.313586π-0.313586\pi
734734 0 0
735735 0 0
736736 0 0
737737 − 17.5557i − 0.646672i
738738 0 0
739739 −4.88625 −0.179743 −0.0898717 0.995953i 0.528646π-0.528646\pi
−0.0898717 + 0.995953i 0.528646π0.528646\pi
740740 0 0
741741 −15.4648 −0.568114
742742 0 0
743743 31.3357i 1.14960i 0.818295 + 0.574798i 0.194919π0.194919\pi
−0.818295 + 0.574798i 0.805081π0.805081\pi
744744 0 0
745745 0 0
746746 0 0
747747 − 2.36863i − 0.0866637i
748748 0 0
749749 4.12111 0.150582
750750 0 0
751751 −2.75676 −0.100596 −0.0502978 0.998734i 0.516017π-0.516017\pi
−0.0502978 + 0.998734i 0.516017π0.516017\pi
752752 0 0
753753 − 27.2413i − 0.992729i
754754 0 0
755755 0 0
756756 0 0
757757 27.7888i 1.01000i 0.863119 + 0.505000i 0.168508π0.168508\pi
−0.863119 + 0.505000i 0.831492π0.831492\pi
758758 0 0
759759 −3.59394 −0.130452
760760 0 0
761761 38.2357 1.38604 0.693022 0.720916i 0.256279π-0.256279\pi
0.693022 + 0.720916i 0.256279π0.256279\pi
762762 0 0
763763 44.7724i 1.62087i
764764 0 0
765765 0 0
766766 0 0
767767 59.1970i 2.13748i
768768 0 0
769769 −41.3417 −1.49082 −0.745409 0.666607i 0.767746π-0.767746\pi
−0.745409 + 0.666607i 0.767746π0.767746\pi
770770 0 0
771771 23.7854 0.856611
772772 0 0
773773 − 4.31886i − 0.155339i −0.996979 0.0776693i 0.975252π-0.975252\pi
0.996979 0.0776693i 0.0247478π-0.0247478\pi
774774 0 0
775775 0 0
776776 0 0
777777 66.6453i 2.39089i
778778 0 0
779779 3.74296 0.134105
780780 0 0
781781 54.5926 1.95348
782782 0 0
783783 24.4695i 0.874470i
784784 0 0
785785 0 0
786786 0 0
787787 − 8.48163i − 0.302337i −0.988508 0.151169i 0.951696π-0.951696\pi
0.988508 0.151169i 0.0483037π-0.0483037\pi
788788 0 0
789789 −29.6729 −1.05638
790790 0 0
791791 38.9814 1.38602
792792 0 0
793793 77.2121i 2.74188i
794794 0 0
795795 0 0
796796 0 0
797797 − 13.6851i − 0.484750i −0.970183 0.242375i 0.922074π-0.922074\pi
0.970183 0.242375i 0.0779265π-0.0779265\pi
798798 0 0
799799 4.75903 0.168362
800800 0 0
801801 −4.99544 −0.176505
802802 0 0
803803 − 79.8846i − 2.81907i
804804 0 0
805805 0 0
806806 0 0
807807 − 2.82895i − 0.0995836i
808808 0 0
809809 5.08132 0.178650 0.0893249 0.996003i 0.471529π-0.471529\pi
0.0893249 + 0.996003i 0.471529π0.471529\pi
810810 0 0
811811 −24.9990 −0.877834 −0.438917 0.898528i 0.644638π-0.644638\pi
−0.438917 + 0.898528i 0.644638π0.644638\pi
812812 0 0
813813 − 54.6031i − 1.91501i
814814 0 0
815815 0 0
816816 0 0
817817 11.3515i 0.397138i
818818 0 0
819819 6.48693 0.226672
820820 0 0
821821 −25.8738 −0.903002 −0.451501 0.892271i 0.649111π-0.649111\pi
−0.451501 + 0.892271i 0.649111π0.649111\pi
822822 0 0
823823 11.0152i 0.383965i 0.981398 + 0.191982i 0.0614916π0.0614916\pi
−0.981398 + 0.191982i 0.938508π0.938508\pi
824824 0 0
825825 0 0
826826 0 0
827827 − 13.5502i − 0.471185i −0.971852 0.235592i 0.924297π-0.924297\pi
0.971852 0.235592i 0.0757031π-0.0757031\pi
828828 0 0
829829 38.5707 1.33962 0.669808 0.742534i 0.266376π-0.266376\pi
0.669808 + 0.742534i 0.266376π0.266376\pi
830830 0 0
831831 32.5682 1.12978
832832 0 0
833833 − 65.8223i − 2.28061i
834834 0 0
835835 0 0
836836 0 0
837837 22.8611i 0.790194i
838838 0 0
839839 −4.38927 −0.151535 −0.0757673 0.997126i 0.524141π-0.524141\pi
−0.0757673 + 0.997126i 0.524141π0.524141\pi
840840 0 0
841841 −4.35591 −0.150204
842842 0 0
843843 − 2.27663i − 0.0784113i
844844 0 0
845845 0 0
846846 0 0
847847 − 100.347i − 3.44796i
848848 0 0
849849 −31.5947 −1.08433
850850 0 0
851851 2.86655 0.0982639
852852 0 0
853853 − 35.3589i − 1.21067i −0.795972 0.605333i 0.793040π-0.793040\pi
0.795972 0.605333i 0.206960π-0.206960\pi
854854 0 0
855855 0 0
856856 0 0
857857 − 56.4133i − 1.92704i −0.267636 0.963520i 0.586242π-0.586242\pi
0.267636 0.963520i 0.413758π-0.413758\pi
858858 0 0
859859 28.2629 0.964319 0.482160 0.876083i 0.339853π-0.339853\pi
0.482160 + 0.876083i 0.339853π0.339853\pi
860860 0 0
861861 −18.5633 −0.632635
862862 0 0
863863 11.3915i 0.387772i 0.981024 + 0.193886i 0.0621092π0.0621092\pi
−0.981024 + 0.193886i 0.937891π0.937891\pi
864864 0 0
865865 0 0
866866 0 0
867867 − 22.2385i − 0.755261i
868868 0 0
869869 34.0781 1.15602
870870 0 0
871871 16.1147 0.546024
872872 0 0
873873 2.79723i 0.0946718i
874874 0 0
875875 0 0
876876 0 0
877877 17.1016i 0.577479i 0.957408 + 0.288740i 0.0932362π0.0932362\pi
−0.957408 + 0.288740i 0.906764π0.906764\pi
878878 0 0
879879 43.4862 1.46675
880880 0 0
881881 −53.3569 −1.79764 −0.898821 0.438317i 0.855575π-0.855575\pi
−0.898821 + 0.438317i 0.855575π0.855575\pi
882882 0 0
883883 − 35.9395i − 1.20946i −0.796430 0.604730i 0.793281π-0.793281\pi
0.796430 0.604730i 0.206719π-0.206719\pi
884884 0 0
885885 0 0
886886 0 0
887887 − 48.4603i − 1.62714i −0.581468 0.813569i 0.697521π-0.697521\pi
0.581468 0.813569i 0.302479π-0.302479\pi
888888 0 0
889889 −7.69049 −0.257931
890890 0 0
891891 56.8146 1.90336
892892 0 0
893893 1.40522i 0.0470241i
894894 0 0
895895 0 0
896896 0 0
897897 − 3.29894i − 0.110148i
898898 0 0
899899 23.0241 0.767898
900900 0 0
901901 −7.04803 −0.234804
902902 0 0
903903 − 56.2980i − 1.87348i
904904 0 0
905905 0 0
906906 0 0
907907 − 21.2305i − 0.704948i −0.935822 0.352474i 0.885341π-0.885341\pi
0.935822 0.352474i 0.114659π-0.114659\pi
908908 0 0
909909 1.84157 0.0610811
910910 0 0
911911 −23.2599 −0.770634 −0.385317 0.922784i 0.625908π-0.625908\pi
−0.385317 + 0.922784i 0.625908π0.625908\pi
912912 0 0
913913 − 49.7725i − 1.64723i
914914 0 0
915915 0 0
916916 0 0
917917 26.9049i 0.888478i
918918 0 0
919919 −43.5439 −1.43638 −0.718191 0.695846i 0.755029π-0.755029\pi
−0.718191 + 0.695846i 0.755029π0.755029\pi
920920 0 0
921921 −20.2001 −0.665615
922922 0 0
923923 50.1114i 1.64944i
924924 0 0
925925 0 0
926926 0 0
927927 2.72996i 0.0896637i
928928 0 0
929929 −1.93781 −0.0635776 −0.0317888 0.999495i 0.510120π-0.510120\pi
−0.0317888 + 0.999495i 0.510120π0.510120\pi
930930 0 0
931931 19.4357 0.636980
932932 0 0
933933 − 35.8599i − 1.17400i
934934 0 0
935935 0 0
936936 0 0
937937 12.2146i 0.399032i 0.979895 + 0.199516i 0.0639370π0.0639370\pi
−0.979895 + 0.199516i 0.936063π0.936063\pi
938938 0 0
939939 5.96913 0.194795
940940 0 0
941941 19.4761 0.634902 0.317451 0.948275i 0.397173π-0.397173\pi
0.317451 + 0.948275i 0.397173π0.397173\pi
942942 0 0
943943 0.798442i 0.0260009i
944944 0 0
945945 0 0
946946 0 0
947947 1.77050i 0.0575335i 0.999586 + 0.0287667i 0.00915800π0.00915800\pi
−0.999586 + 0.0287667i 0.990842π0.990842\pi
948948 0 0
949949 73.3274 2.38031
950950 0 0
951951 −31.8452 −1.03265
952952 0 0
953953 − 26.4519i − 0.856860i −0.903575 0.428430i 0.859067π-0.859067\pi
0.903575 0.428430i 0.140933π-0.140933\pi
954954 0 0
955955 0 0
956956 0 0
957957 − 52.3422i − 1.69198i
958958 0 0
959959 7.86824 0.254079
960960 0 0
961961 −9.48935 −0.306108
962962 0 0
963963 − 0.260935i − 0.00840850i
964964 0 0
965965 0 0
966966 0 0
967967 29.5985i 0.951822i 0.879493 + 0.475911i 0.157882π0.157882\pi
−0.879493 + 0.475911i 0.842118π0.842118\pi
968968 0 0
969969 15.6536 0.502866
970970 0 0
971971 −3.26775 −0.104867 −0.0524335 0.998624i 0.516698π-0.516698\pi
−0.0524335 + 0.998624i 0.516698π0.516698\pi
972972 0 0
973973 68.4150i 2.19328i
974974 0 0
975975 0 0
976976 0 0
977977 − 11.6591i − 0.373009i −0.982454 0.186504i 0.940284π-0.940284\pi
0.982454 0.186504i 0.0597158π-0.0597158\pi
978978 0 0
979979 −104.970 −3.35486
980980 0 0
981981 2.83483 0.0905093
982982 0 0
983983 − 37.8109i − 1.20598i −0.797749 0.602990i 0.793976π-0.793976\pi
0.797749 0.602990i 0.206024π-0.206024\pi
984984 0 0
985985 0 0
986986 0 0
987987 − 6.96925i − 0.221834i
988988 0 0
989989 −2.42149 −0.0769988
990990 0 0
991991 10.0303 0.318623 0.159311 0.987228i 0.449073π-0.449073\pi
0.159311 + 0.987228i 0.449073π0.449073\pi
992992 0 0
993993 − 27.2142i − 0.863616i
994994 0 0
995995 0 0
996996 0 0
997997 − 45.2025i − 1.43158i −0.698317 0.715788i 0.746067π-0.746067\pi
0.698317 0.715788i 0.253933π-0.253933\pi
998998 0 0
999999 −41.4528 −1.31151
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 4000.2.c.f.1249.9 12
4.3 odd 2 4000.2.c.g.1249.4 12
5.2 odd 4 4000.2.a.m.1.5 yes 6
5.3 odd 4 4000.2.a.k.1.2 6
5.4 even 2 inner 4000.2.c.f.1249.4 12
20.3 even 4 4000.2.a.n.1.5 yes 6
20.7 even 4 4000.2.a.l.1.2 yes 6
20.19 odd 2 4000.2.c.g.1249.9 12
40.3 even 4 8000.2.a.bw.1.2 6
40.13 odd 4 8000.2.a.bv.1.5 6
40.27 even 4 8000.2.a.bu.1.5 6
40.37 odd 4 8000.2.a.bx.1.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4000.2.a.k.1.2 6 5.3 odd 4
4000.2.a.l.1.2 yes 6 20.7 even 4
4000.2.a.m.1.5 yes 6 5.2 odd 4
4000.2.a.n.1.5 yes 6 20.3 even 4
4000.2.c.f.1249.4 12 5.4 even 2 inner
4000.2.c.f.1249.9 12 1.1 even 1 trivial
4000.2.c.g.1249.4 12 4.3 odd 2
4000.2.c.g.1249.9 12 20.19 odd 2
8000.2.a.bu.1.5 6 40.27 even 4
8000.2.a.bv.1.5 6 40.13 odd 4
8000.2.a.bw.1.2 6 40.3 even 4
8000.2.a.bx.1.2 6 40.37 odd 4