Properties

Label 7938.2.a.bm.1.1
Level 79387938
Weight 22
Character 7938.1
Self dual yes
Analytic conductor 63.38563.385
Analytic rank 11
Dimension 22
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7938,2,Mod(1,7938)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7938, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7938.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 7938=23472 7938 = 2 \cdot 3^{4} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 7938.a (trivial)

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: yes
Analytic conductor: 63.385249124563.3852491245
Analytic rank: 11
Dimension: 22
Coefficient field: Q(6)\Q(\sqrt{6})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x26 x^{2} - 6 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 126)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 2.44949-2.44949 of defining polynomial
Character χ\chi == 7938.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q1.00000q2+1.00000q41.44949q51.00000q8+1.44949q102.00000q114.89898q13+1.00000q16+2.00000q172.55051q191.44949q20+2.00000q22+1.00000q232.89898q25+4.89898q26+6.89898q296.00000q311.00000q322.00000q34+11.7980q37+2.55051q38+1.44949q40+9.79796q41+6.89898q432.00000q441.00000q46+9.79796q47+2.89898q504.89898q52+10.8990q53+2.89898q556.89898q582.00000q596.55051q61+6.00000q62+1.00000q64+7.10102q6512.8990q67+2.00000q680.101021q71+6.89898q7311.7980q742.55051q761.89898q791.44949q809.79796q82+2.00000q832.89898q856.89898q86+2.00000q8816.8990q89+1.00000q929.79796q94+3.69694q952.89898q97+O(q100)q-1.00000 q^{2} +1.00000 q^{4} -1.44949 q^{5} -1.00000 q^{8} +1.44949 q^{10} -2.00000 q^{11} -4.89898 q^{13} +1.00000 q^{16} +2.00000 q^{17} -2.55051 q^{19} -1.44949 q^{20} +2.00000 q^{22} +1.00000 q^{23} -2.89898 q^{25} +4.89898 q^{26} +6.89898 q^{29} -6.00000 q^{31} -1.00000 q^{32} -2.00000 q^{34} +11.7980 q^{37} +2.55051 q^{38} +1.44949 q^{40} +9.79796 q^{41} +6.89898 q^{43} -2.00000 q^{44} -1.00000 q^{46} +9.79796 q^{47} +2.89898 q^{50} -4.89898 q^{52} +10.8990 q^{53} +2.89898 q^{55} -6.89898 q^{58} -2.00000 q^{59} -6.55051 q^{61} +6.00000 q^{62} +1.00000 q^{64} +7.10102 q^{65} -12.8990 q^{67} +2.00000 q^{68} -0.101021 q^{71} +6.89898 q^{73} -11.7980 q^{74} -2.55051 q^{76} -1.89898 q^{79} -1.44949 q^{80} -9.79796 q^{82} +2.00000 q^{83} -2.89898 q^{85} -6.89898 q^{86} +2.00000 q^{88} -16.8990 q^{89} +1.00000 q^{92} -9.79796 q^{94} +3.69694 q^{95} -2.89898 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q2q2+2q4+2q52q82q104q11+2q16+4q1710q19+2q20+4q22+2q23+4q25+4q2912q312q324q34+4q37+10q38++4q97+O(q100) 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} - 2 q^{8} - 2 q^{10} - 4 q^{11} + 2 q^{16} + 4 q^{17} - 10 q^{19} + 2 q^{20} + 4 q^{22} + 2 q^{23} + 4 q^{25} + 4 q^{29} - 12 q^{31} - 2 q^{32} - 4 q^{34} + 4 q^{37} + 10 q^{38}+ \cdots + 4 q^{97}+O(q^{100}) Copy content Toggle raw display

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 −1.00000 −0.707107
33 0 0
44 1.00000 0.500000
55 −1.44949 −0.648232 −0.324116 0.946017i 0.605067π-0.605067\pi
−0.324116 + 0.946017i 0.605067π0.605067\pi
66 0 0
77 0 0
88 −1.00000 −0.353553
99 0 0
1010 1.44949 0.458369
1111 −2.00000 −0.603023 −0.301511 0.953463i 0.597491π-0.597491\pi
−0.301511 + 0.953463i 0.597491π0.597491\pi
1212 0 0
1313 −4.89898 −1.35873 −0.679366 0.733799i 0.737745π-0.737745\pi
−0.679366 + 0.733799i 0.737745π0.737745\pi
1414 0 0
1515 0 0
1616 1.00000 0.250000
1717 2.00000 0.485071 0.242536 0.970143i 0.422021π-0.422021\pi
0.242536 + 0.970143i 0.422021π0.422021\pi
1818 0 0
1919 −2.55051 −0.585127 −0.292564 0.956246i 0.594508π-0.594508\pi
−0.292564 + 0.956246i 0.594508π0.594508\pi
2020 −1.44949 −0.324116
2121 0 0
2222 2.00000 0.426401
2323 1.00000 0.208514 0.104257 0.994550i 0.466753π-0.466753\pi
0.104257 + 0.994550i 0.466753π0.466753\pi
2424 0 0
2525 −2.89898 −0.579796
2626 4.89898 0.960769
2727 0 0
2828 0 0
2929 6.89898 1.28111 0.640554 0.767913i 0.278705π-0.278705\pi
0.640554 + 0.767913i 0.278705π0.278705\pi
3030 0 0
3131 −6.00000 −1.07763 −0.538816 0.842424i 0.681128π-0.681128\pi
−0.538816 + 0.842424i 0.681128π0.681128\pi
3232 −1.00000 −0.176777
3333 0 0
3434 −2.00000 −0.342997
3535 0 0
3636 0 0
3737 11.7980 1.93957 0.969786 0.243956i 0.0784453π-0.0784453\pi
0.969786 + 0.243956i 0.0784453π0.0784453\pi
3838 2.55051 0.413747
3939 0 0
4040 1.44949 0.229184
4141 9.79796 1.53018 0.765092 0.643921i 0.222693π-0.222693\pi
0.765092 + 0.643921i 0.222693π0.222693\pi
4242 0 0
4343 6.89898 1.05208 0.526042 0.850458i 0.323675π-0.323675\pi
0.526042 + 0.850458i 0.323675π0.323675\pi
4444 −2.00000 −0.301511
4545 0 0
4646 −1.00000 −0.147442
4747 9.79796 1.42918 0.714590 0.699544i 0.246613π-0.246613\pi
0.714590 + 0.699544i 0.246613π0.246613\pi
4848 0 0
4949 0 0
5050 2.89898 0.409978
5151 0 0
5252 −4.89898 −0.679366
5353 10.8990 1.49709 0.748545 0.663084i 0.230753π-0.230753\pi
0.748545 + 0.663084i 0.230753π0.230753\pi
5454 0 0
5555 2.89898 0.390898
5656 0 0
5757 0 0
5858 −6.89898 −0.905880
5959 −2.00000 −0.260378 −0.130189 0.991489i 0.541558π-0.541558\pi
−0.130189 + 0.991489i 0.541558π0.541558\pi
6060 0 0
6161 −6.55051 −0.838707 −0.419353 0.907823i 0.637743π-0.637743\pi
−0.419353 + 0.907823i 0.637743π0.637743\pi
6262 6.00000 0.762001
6363 0 0
6464 1.00000 0.125000
6565 7.10102 0.880773
6666 0 0
6767 −12.8990 −1.57586 −0.787931 0.615764i 0.788847π-0.788847\pi
−0.787931 + 0.615764i 0.788847π0.788847\pi
6868 2.00000 0.242536
6969 0 0
7070 0 0
7171 −0.101021 −0.0119889 −0.00599446 0.999982i 0.501908π-0.501908\pi
−0.00599446 + 0.999982i 0.501908π0.501908\pi
7272 0 0
7373 6.89898 0.807464 0.403732 0.914877i 0.367713π-0.367713\pi
0.403732 + 0.914877i 0.367713π0.367713\pi
7474 −11.7980 −1.37148
7575 0 0
7676 −2.55051 −0.292564
7777 0 0
7878 0 0
7979 −1.89898 −0.213652 −0.106826 0.994278i 0.534069π-0.534069\pi
−0.106826 + 0.994278i 0.534069π0.534069\pi
8080 −1.44949 −0.162058
8181 0 0
8282 −9.79796 −1.08200
8383 2.00000 0.219529 0.109764 0.993958i 0.464990π-0.464990\pi
0.109764 + 0.993958i 0.464990π0.464990\pi
8484 0 0
8585 −2.89898 −0.314438
8686 −6.89898 −0.743936
8787 0 0
8888 2.00000 0.213201
8989 −16.8990 −1.79129 −0.895644 0.444771i 0.853285π-0.853285\pi
−0.895644 + 0.444771i 0.853285π0.853285\pi
9090 0 0
9191 0 0
9292 1.00000 0.104257
9393 0 0
9494 −9.79796 −1.01058
9595 3.69694 0.379298
9696 0 0
9797 −2.89898 −0.294347 −0.147173 0.989111i 0.547018π-0.547018\pi
−0.147173 + 0.989111i 0.547018π0.547018\pi
9898 0 0
9999 0 0
100100 −2.89898 −0.289898
101101 −17.2474 −1.71619 −0.858093 0.513495i 0.828351π-0.828351\pi
−0.858093 + 0.513495i 0.828351π0.828351\pi
102102 0 0
103103 −14.0000 −1.37946 −0.689730 0.724066i 0.742271π-0.742271\pi
−0.689730 + 0.724066i 0.742271π0.742271\pi
104104 4.89898 0.480384
105105 0 0
106106 −10.8990 −1.05860
107107 12.0000 1.16008 0.580042 0.814587i 0.303036π-0.303036\pi
0.580042 + 0.814587i 0.303036π0.303036\pi
108108 0 0
109109 12.6969 1.21615 0.608073 0.793881i 0.291943π-0.291943\pi
0.608073 + 0.793881i 0.291943π0.291943\pi
110110 −2.89898 −0.276407
111111 0 0
112112 0 0
113113 6.10102 0.573936 0.286968 0.957940i 0.407353π-0.407353\pi
0.286968 + 0.957940i 0.407353π0.407353\pi
114114 0 0
115115 −1.44949 −0.135166
116116 6.89898 0.640554
117117 0 0
118118 2.00000 0.184115
119119 0 0
120120 0 0
121121 −7.00000 −0.636364
122122 6.55051 0.593055
123123 0 0
124124 −6.00000 −0.538816
125125 11.4495 1.02407
126126 0 0
127127 −3.00000 −0.266207 −0.133103 0.991102i 0.542494π-0.542494\pi
−0.133103 + 0.991102i 0.542494π0.542494\pi
128128 −1.00000 −0.0883883
129129 0 0
130130 −7.10102 −0.622801
131131 −8.55051 −0.747062 −0.373531 0.927618i 0.621853π-0.621853\pi
−0.373531 + 0.927618i 0.621853π0.621853\pi
132132 0 0
133133 0 0
134134 12.8990 1.11430
135135 0 0
136136 −2.00000 −0.171499
137137 −7.79796 −0.666225 −0.333112 0.942887i 0.608099π-0.608099\pi
−0.333112 + 0.942887i 0.608099π0.608099\pi
138138 0 0
139139 −4.55051 −0.385969 −0.192985 0.981202i 0.561817π-0.561817\pi
−0.192985 + 0.981202i 0.561817π0.561817\pi
140140 0 0
141141 0 0
142142 0.101021 0.00847745
143143 9.79796 0.819346
144144 0 0
145145 −10.0000 −0.830455
146146 −6.89898 −0.570964
147147 0 0
148148 11.7980 0.969786
149149 6.00000 0.491539 0.245770 0.969328i 0.420959π-0.420959\pi
0.245770 + 0.969328i 0.420959π0.420959\pi
150150 0 0
151151 −5.00000 −0.406894 −0.203447 0.979086i 0.565214π-0.565214\pi
−0.203447 + 0.979086i 0.565214π0.565214\pi
152152 2.55051 0.206874
153153 0 0
154154 0 0
155155 8.69694 0.698555
156156 0 0
157157 8.34847 0.666280 0.333140 0.942877i 0.391892π-0.391892\pi
0.333140 + 0.942877i 0.391892π0.391892\pi
158158 1.89898 0.151075
159159 0 0
160160 1.44949 0.114592
161161 0 0
162162 0 0
163163 −19.7980 −1.55070 −0.775348 0.631534i 0.782425π-0.782425\pi
−0.775348 + 0.631534i 0.782425π0.782425\pi
164164 9.79796 0.765092
165165 0 0
166166 −2.00000 −0.155230
167167 −10.6969 −0.827754 −0.413877 0.910333i 0.635826π-0.635826\pi
−0.413877 + 0.910333i 0.635826π0.635826\pi
168168 0 0
169169 11.0000 0.846154
170170 2.89898 0.222342
171171 0 0
172172 6.89898 0.526042
173173 −3.10102 −0.235766 −0.117883 0.993027i 0.537611π-0.537611\pi
−0.117883 + 0.993027i 0.537611π0.537611\pi
174174 0 0
175175 0 0
176176 −2.00000 −0.150756
177177 0 0
178178 16.8990 1.26663
179179 −20.6969 −1.54696 −0.773481 0.633820i 0.781486π-0.781486\pi
−0.773481 + 0.633820i 0.781486π0.781486\pi
180180 0 0
181181 10.3485 0.769196 0.384598 0.923084i 0.374340π-0.374340\pi
0.384598 + 0.923084i 0.374340π0.374340\pi
182182 0 0
183183 0 0
184184 −1.00000 −0.0737210
185185 −17.1010 −1.25729
186186 0 0
187187 −4.00000 −0.292509
188188 9.79796 0.714590
189189 0 0
190190 −3.69694 −0.268204
191191 −4.10102 −0.296739 −0.148370 0.988932i 0.547403π-0.547403\pi
−0.148370 + 0.988932i 0.547403π0.547403\pi
192192 0 0
193193 −17.8990 −1.28840 −0.644198 0.764858i 0.722809π-0.722809\pi
−0.644198 + 0.764858i 0.722809π0.722809\pi
194194 2.89898 0.208135
195195 0 0
196196 0 0
197197 −16.6969 −1.18961 −0.594804 0.803871i 0.702770π-0.702770\pi
−0.594804 + 0.803871i 0.702770π0.702770\pi
198198 0 0
199199 2.89898 0.205503 0.102752 0.994707i 0.467235π-0.467235\pi
0.102752 + 0.994707i 0.467235π0.467235\pi
200200 2.89898 0.204989
201201 0 0
202202 17.2474 1.21353
203203 0 0
204204 0 0
205205 −14.2020 −0.991914
206206 14.0000 0.975426
207207 0 0
208208 −4.89898 −0.339683
209209 5.10102 0.352845
210210 0 0
211211 12.8990 0.888002 0.444001 0.896026i 0.353559π-0.353559\pi
0.444001 + 0.896026i 0.353559π0.353559\pi
212212 10.8990 0.748545
213213 0 0
214214 −12.0000 −0.820303
215215 −10.0000 −0.681994
216216 0 0
217217 0 0
218218 −12.6969 −0.859945
219219 0 0
220220 2.89898 0.195449
221221 −9.79796 −0.659082
222222 0 0
223223 11.1010 0.743379 0.371690 0.928357i 0.378779π-0.378779\pi
0.371690 + 0.928357i 0.378779π0.378779\pi
224224 0 0
225225 0 0
226226 −6.10102 −0.405834
227227 −5.44949 −0.361695 −0.180848 0.983511i 0.557884π-0.557884\pi
−0.180848 + 0.983511i 0.557884π0.557884\pi
228228 0 0
229229 −1.24745 −0.0824337 −0.0412169 0.999150i 0.513123π-0.513123\pi
−0.0412169 + 0.999150i 0.513123π0.513123\pi
230230 1.44949 0.0955765
231231 0 0
232232 −6.89898 −0.452940
233233 7.00000 0.458585 0.229293 0.973358i 0.426359π-0.426359\pi
0.229293 + 0.973358i 0.426359π0.426359\pi
234234 0 0
235235 −14.2020 −0.926439
236236 −2.00000 −0.130189
237237 0 0
238238 0 0
239239 −6.79796 −0.439723 −0.219862 0.975531i 0.570561π-0.570561\pi
−0.219862 + 0.975531i 0.570561π0.570561\pi
240240 0 0
241241 −0.898979 −0.0579084 −0.0289542 0.999581i 0.509218π-0.509218\pi
−0.0289542 + 0.999581i 0.509218π0.509218\pi
242242 7.00000 0.449977
243243 0 0
244244 −6.55051 −0.419353
245245 0 0
246246 0 0
247247 12.4949 0.795031
248248 6.00000 0.381000
249249 0 0
250250 −11.4495 −0.724129
251251 17.4495 1.10140 0.550701 0.834703i 0.314360π-0.314360\pi
0.550701 + 0.834703i 0.314360π0.314360\pi
252252 0 0
253253 −2.00000 −0.125739
254254 3.00000 0.188237
255255 0 0
256256 1.00000 0.0625000
257257 8.20204 0.511629 0.255815 0.966726i 0.417656π-0.417656\pi
0.255815 + 0.966726i 0.417656π0.417656\pi
258258 0 0
259259 0 0
260260 7.10102 0.440387
261261 0 0
262262 8.55051 0.528252
263263 −25.8990 −1.59700 −0.798500 0.601995i 0.794373π-0.794373\pi
−0.798500 + 0.601995i 0.794373π0.794373\pi
264264 0 0
265265 −15.7980 −0.970461
266266 0 0
267267 0 0
268268 −12.8990 −0.787931
269269 −18.3485 −1.11873 −0.559363 0.828923i 0.688954π-0.688954\pi
−0.559363 + 0.828923i 0.688954π0.688954\pi
270270 0 0
271271 −7.10102 −0.431356 −0.215678 0.976465i 0.569196π-0.569196\pi
−0.215678 + 0.976465i 0.569196π0.569196\pi
272272 2.00000 0.121268
273273 0 0
274274 7.79796 0.471092
275275 5.79796 0.349630
276276 0 0
277277 −18.6969 −1.12339 −0.561695 0.827344i 0.689851π-0.689851\pi
−0.561695 + 0.827344i 0.689851π0.689851\pi
278278 4.55051 0.272921
279279 0 0
280280 0 0
281281 19.0000 1.13344 0.566722 0.823909i 0.308211π-0.308211\pi
0.566722 + 0.823909i 0.308211π0.308211\pi
282282 0 0
283283 25.4495 1.51282 0.756408 0.654101i 0.226953π-0.226953\pi
0.756408 + 0.654101i 0.226953π0.226953\pi
284284 −0.101021 −0.00599446
285285 0 0
286286 −9.79796 −0.579365
287287 0 0
288288 0 0
289289 −13.0000 −0.764706
290290 10.0000 0.587220
291291 0 0
292292 6.89898 0.403732
293293 2.75255 0.160806 0.0804029 0.996762i 0.474379π-0.474379\pi
0.0804029 + 0.996762i 0.474379π0.474379\pi
294294 0 0
295295 2.89898 0.168785
296296 −11.7980 −0.685742
297297 0 0
298298 −6.00000 −0.347571
299299 −4.89898 −0.283315
300300 0 0
301301 0 0
302302 5.00000 0.287718
303303 0 0
304304 −2.55051 −0.146282
305305 9.49490 0.543676
306306 0 0
307307 −25.2474 −1.44095 −0.720474 0.693482i 0.756076π-0.756076\pi
−0.720474 + 0.693482i 0.756076π0.756076\pi
308308 0 0
309309 0 0
310310 −8.69694 −0.493953
311311 30.6969 1.74066 0.870332 0.492466i 0.163904π-0.163904\pi
0.870332 + 0.492466i 0.163904π0.163904\pi
312312 0 0
313313 4.69694 0.265487 0.132743 0.991150i 0.457621π-0.457621\pi
0.132743 + 0.991150i 0.457621π0.457621\pi
314314 −8.34847 −0.471131
315315 0 0
316316 −1.89898 −0.106826
317317 −20.6969 −1.16246 −0.581228 0.813741i 0.697428π-0.697428\pi
−0.581228 + 0.813741i 0.697428π0.697428\pi
318318 0 0
319319 −13.7980 −0.772537
320320 −1.44949 −0.0810289
321321 0 0
322322 0 0
323323 −5.10102 −0.283828
324324 0 0
325325 14.2020 0.787787
326326 19.7980 1.09651
327327 0 0
328328 −9.79796 −0.541002
329329 0 0
330330 0 0
331331 4.69694 0.258167 0.129084 0.991634i 0.458796π-0.458796\pi
0.129084 + 0.991634i 0.458796π0.458796\pi
332332 2.00000 0.109764
333333 0 0
334334 10.6969 0.585310
335335 18.6969 1.02152
336336 0 0
337337 −23.3939 −1.27435 −0.637173 0.770721i 0.719896π-0.719896\pi
−0.637173 + 0.770721i 0.719896π0.719896\pi
338338 −11.0000 −0.598321
339339 0 0
340340 −2.89898 −0.157219
341341 12.0000 0.649836
342342 0 0
343343 0 0
344344 −6.89898 −0.371968
345345 0 0
346346 3.10102 0.166712
347347 −19.5959 −1.05196 −0.525982 0.850496i 0.676302π-0.676302\pi
−0.525982 + 0.850496i 0.676302π0.676302\pi
348348 0 0
349349 −11.1010 −0.594224 −0.297112 0.954843i 0.596023π-0.596023\pi
−0.297112 + 0.954843i 0.596023π0.596023\pi
350350 0 0
351351 0 0
352352 2.00000 0.106600
353353 −6.00000 −0.319348 −0.159674 0.987170i 0.551044π-0.551044\pi
−0.159674 + 0.987170i 0.551044π0.551044\pi
354354 0 0
355355 0.146428 0.00777160
356356 −16.8990 −0.895644
357357 0 0
358358 20.6969 1.09387
359359 8.79796 0.464339 0.232169 0.972675i 0.425418π-0.425418\pi
0.232169 + 0.972675i 0.425418π0.425418\pi
360360 0 0
361361 −12.4949 −0.657626
362362 −10.3485 −0.543903
363363 0 0
364364 0 0
365365 −10.0000 −0.523424
366366 0 0
367367 13.7980 0.720248 0.360124 0.932905i 0.382734π-0.382734\pi
0.360124 + 0.932905i 0.382734π0.382734\pi
368368 1.00000 0.0521286
369369 0 0
370370 17.1010 0.889040
371371 0 0
372372 0 0
373373 −6.89898 −0.357216 −0.178608 0.983920i 0.557159π-0.557159\pi
−0.178608 + 0.983920i 0.557159π0.557159\pi
374374 4.00000 0.206835
375375 0 0
376376 −9.79796 −0.505291
377377 −33.7980 −1.74068
378378 0 0
379379 22.4949 1.15549 0.577743 0.816219i 0.303934π-0.303934\pi
0.577743 + 0.816219i 0.303934π0.303934\pi
380380 3.69694 0.189649
381381 0 0
382382 4.10102 0.209826
383383 −2.89898 −0.148131 −0.0740655 0.997253i 0.523597π-0.523597\pi
−0.0740655 + 0.997253i 0.523597π0.523597\pi
384384 0 0
385385 0 0
386386 17.8990 0.911034
387387 0 0
388388 −2.89898 −0.147173
389389 24.8990 1.26243 0.631214 0.775609i 0.282557π-0.282557\pi
0.631214 + 0.775609i 0.282557π0.282557\pi
390390 0 0
391391 2.00000 0.101144
392392 0 0
393393 0 0
394394 16.6969 0.841180
395395 2.75255 0.138496
396396 0 0
397397 −38.6969 −1.94214 −0.971072 0.238788i 0.923250π-0.923250\pi
−0.971072 + 0.238788i 0.923250π0.923250\pi
398398 −2.89898 −0.145313
399399 0 0
400400 −2.89898 −0.144949
401401 19.8990 0.993708 0.496854 0.867834i 0.334489π-0.334489\pi
0.496854 + 0.867834i 0.334489π0.334489\pi
402402 0 0
403403 29.3939 1.46421
404404 −17.2474 −0.858093
405405 0 0
406406 0 0
407407 −23.5959 −1.16961
408408 0 0
409409 13.7980 0.682265 0.341133 0.940015i 0.389189π-0.389189\pi
0.341133 + 0.940015i 0.389189π0.389189\pi
410410 14.2020 0.701389
411411 0 0
412412 −14.0000 −0.689730
413413 0 0
414414 0 0
415415 −2.89898 −0.142305
416416 4.89898 0.240192
417417 0 0
418418 −5.10102 −0.249499
419419 29.4495 1.43870 0.719351 0.694647i 0.244439π-0.244439\pi
0.719351 + 0.694647i 0.244439π0.244439\pi
420420 0 0
421421 22.8990 1.11603 0.558014 0.829832i 0.311564π-0.311564\pi
0.558014 + 0.829832i 0.311564π0.311564\pi
422422 −12.8990 −0.627912
423423 0 0
424424 −10.8990 −0.529301
425425 −5.79796 −0.281242
426426 0 0
427427 0 0
428428 12.0000 0.580042
429429 0 0
430430 10.0000 0.482243
431431 −31.5959 −1.52192 −0.760961 0.648798i 0.775272π-0.775272\pi
−0.760961 + 0.648798i 0.775272π0.775272\pi
432432 0 0
433433 7.79796 0.374746 0.187373 0.982289i 0.440003π-0.440003\pi
0.187373 + 0.982289i 0.440003π0.440003\pi
434434 0 0
435435 0 0
436436 12.6969 0.608073
437437 −2.55051 −0.122007
438438 0 0
439439 −2.20204 −0.105098 −0.0525488 0.998618i 0.516735π-0.516735\pi
−0.0525488 + 0.998618i 0.516735π0.516735\pi
440440 −2.89898 −0.138203
441441 0 0
442442 9.79796 0.466041
443443 14.8990 0.707872 0.353936 0.935270i 0.384843π-0.384843\pi
0.353936 + 0.935270i 0.384843π0.384843\pi
444444 0 0
445445 24.4949 1.16117
446446 −11.1010 −0.525649
447447 0 0
448448 0 0
449449 −20.5959 −0.971981 −0.485991 0.873964i 0.661541π-0.661541\pi
−0.485991 + 0.873964i 0.661541π0.661541\pi
450450 0 0
451451 −19.5959 −0.922736
452452 6.10102 0.286968
453453 0 0
454454 5.44949 0.255757
455455 0 0
456456 0 0
457457 −17.4949 −0.818377 −0.409188 0.912450i 0.634188π-0.634188\pi
−0.409188 + 0.912450i 0.634188π0.634188\pi
458458 1.24745 0.0582895
459459 0 0
460460 −1.44949 −0.0675828
461461 5.65153 0.263218 0.131609 0.991302i 0.457986π-0.457986\pi
0.131609 + 0.991302i 0.457986π0.457986\pi
462462 0 0
463463 3.69694 0.171811 0.0859057 0.996303i 0.472622π-0.472622\pi
0.0859057 + 0.996303i 0.472622π0.472622\pi
464464 6.89898 0.320277
465465 0 0
466466 −7.00000 −0.324269
467467 10.0000 0.462745 0.231372 0.972865i 0.425678π-0.425678\pi
0.231372 + 0.972865i 0.425678π0.425678\pi
468468 0 0
469469 0 0
470470 14.2020 0.655091
471471 0 0
472472 2.00000 0.0920575
473473 −13.7980 −0.634431
474474 0 0
475475 7.39388 0.339254
476476 0 0
477477 0 0
478478 6.79796 0.310931
479479 9.59592 0.438449 0.219224 0.975674i 0.429647π-0.429647\pi
0.219224 + 0.975674i 0.429647π0.429647\pi
480480 0 0
481481 −57.7980 −2.63536
482482 0.898979 0.0409474
483483 0 0
484484 −7.00000 −0.318182
485485 4.20204 0.190805
486486 0 0
487487 −36.3939 −1.64916 −0.824582 0.565742i 0.808590π-0.808590\pi
−0.824582 + 0.565742i 0.808590π0.808590\pi
488488 6.55051 0.296528
489489 0 0
490490 0 0
491491 −15.7980 −0.712952 −0.356476 0.934304i 0.616022π-0.616022\pi
−0.356476 + 0.934304i 0.616022π0.616022\pi
492492 0 0
493493 13.7980 0.621429
494494 −12.4949 −0.562172
495495 0 0
496496 −6.00000 −0.269408
497497 0 0
498498 0 0
499499 −25.3939 −1.13679 −0.568393 0.822757i 0.692435π-0.692435\pi
−0.568393 + 0.822757i 0.692435π0.692435\pi
500500 11.4495 0.512037
501501 0 0
502502 −17.4495 −0.778809
503503 −24.4949 −1.09217 −0.546087 0.837729i 0.683883π-0.683883\pi
−0.546087 + 0.837729i 0.683883π0.683883\pi
504504 0 0
505505 25.0000 1.11249
506506 2.00000 0.0889108
507507 0 0
508508 −3.00000 −0.133103
509509 −7.10102 −0.314747 −0.157374 0.987539i 0.550303π-0.550303\pi
−0.157374 + 0.987539i 0.550303π0.550303\pi
510510 0 0
511511 0 0
512512 −1.00000 −0.0441942
513513 0 0
514514 −8.20204 −0.361777
515515 20.2929 0.894210
516516 0 0
517517 −19.5959 −0.861827
518518 0 0
519519 0 0
520520 −7.10102 −0.311400
521521 −9.30306 −0.407575 −0.203787 0.979015i 0.565325π-0.565325\pi
−0.203787 + 0.979015i 0.565325π0.565325\pi
522522 0 0
523523 14.3485 0.627415 0.313707 0.949520i 0.398429π-0.398429\pi
0.313707 + 0.949520i 0.398429π0.398429\pi
524524 −8.55051 −0.373531
525525 0 0
526526 25.8990 1.12925
527527 −12.0000 −0.522728
528528 0 0
529529 −22.0000 −0.956522
530530 15.7980 0.686219
531531 0 0
532532 0 0
533533 −48.0000 −2.07911
534534 0 0
535535 −17.3939 −0.752003
536536 12.8990 0.557151
537537 0 0
538538 18.3485 0.791059
539539 0 0
540540 0 0
541541 −18.4949 −0.795158 −0.397579 0.917568i 0.630149π-0.630149\pi
−0.397579 + 0.917568i 0.630149π0.630149\pi
542542 7.10102 0.305015
543543 0 0
544544 −2.00000 −0.0857493
545545 −18.4041 −0.788344
546546 0 0
547547 −7.59592 −0.324778 −0.162389 0.986727i 0.551920π-0.551920\pi
−0.162389 + 0.986727i 0.551920π0.551920\pi
548548 −7.79796 −0.333112
549549 0 0
550550 −5.79796 −0.247226
551551 −17.5959 −0.749611
552552 0 0
553553 0 0
554554 18.6969 0.794357
555555 0 0
556556 −4.55051 −0.192985
557557 12.8990 0.546547 0.273274 0.961936i 0.411894π-0.411894\pi
0.273274 + 0.961936i 0.411894π0.411894\pi
558558 0 0
559559 −33.7980 −1.42950
560560 0 0
561561 0 0
562562 −19.0000 −0.801467
563563 −39.9444 −1.68346 −0.841728 0.539902i 0.818461π-0.818461\pi
−0.841728 + 0.539902i 0.818461π0.818461\pi
564564 0 0
565565 −8.84337 −0.372043
566566 −25.4495 −1.06972
567567 0 0
568568 0.101021 0.00423873
569569 30.0000 1.25767 0.628833 0.777541i 0.283533π-0.283533\pi
0.628833 + 0.777541i 0.283533π0.283533\pi
570570 0 0
571571 33.7980 1.41440 0.707200 0.707013i 0.249958π-0.249958\pi
0.707200 + 0.707013i 0.249958π0.249958\pi
572572 9.79796 0.409673
573573 0 0
574574 0 0
575575 −2.89898 −0.120896
576576 0 0
577577 15.5959 0.649267 0.324633 0.945840i 0.394759π-0.394759\pi
0.324633 + 0.945840i 0.394759π0.394759\pi
578578 13.0000 0.540729
579579 0 0
580580 −10.0000 −0.415227
581581 0 0
582582 0 0
583583 −21.7980 −0.902779
584584 −6.89898 −0.285482
585585 0 0
586586 −2.75255 −0.113707
587587 16.1464 0.666434 0.333217 0.942850i 0.391866π-0.391866\pi
0.333217 + 0.942850i 0.391866π0.391866\pi
588588 0 0
589589 15.3031 0.630552
590590 −2.89898 −0.119349
591591 0 0
592592 11.7980 0.484893
593593 14.6969 0.603531 0.301765 0.953382i 0.402424π-0.402424\pi
0.301765 + 0.953382i 0.402424π0.402424\pi
594594 0 0
595595 0 0
596596 6.00000 0.245770
597597 0 0
598598 4.89898 0.200334
599599 33.7980 1.38095 0.690474 0.723358i 0.257402π-0.257402\pi
0.690474 + 0.723358i 0.257402π0.257402\pi
600600 0 0
601601 −16.6969 −0.681082 −0.340541 0.940230i 0.610610π-0.610610\pi
−0.340541 + 0.940230i 0.610610π0.610610\pi
602602 0 0
603603 0 0
604604 −5.00000 −0.203447
605605 10.1464 0.412511
606606 0 0
607607 −20.6969 −0.840063 −0.420031 0.907510i 0.637981π-0.637981\pi
−0.420031 + 0.907510i 0.637981π0.637981\pi
608608 2.55051 0.103437
609609 0 0
610610 −9.49490 −0.384437
611611 −48.0000 −1.94187
612612 0 0
613613 −14.6969 −0.593604 −0.296802 0.954939i 0.595920π-0.595920\pi
−0.296802 + 0.954939i 0.595920π0.595920\pi
614614 25.2474 1.01890
615615 0 0
616616 0 0
617617 15.3939 0.619734 0.309867 0.950780i 0.399715π-0.399715\pi
0.309867 + 0.950780i 0.399715π0.399715\pi
618618 0 0
619619 −30.1464 −1.21169 −0.605844 0.795584i 0.707164π-0.707164\pi
−0.605844 + 0.795584i 0.707164π0.707164\pi
620620 8.69694 0.349277
621621 0 0
622622 −30.6969 −1.23084
623623 0 0
624624 0 0
625625 −2.10102 −0.0840408
626626 −4.69694 −0.187727
627627 0 0
628628 8.34847 0.333140
629629 23.5959 0.940831
630630 0 0
631631 27.8990 1.11064 0.555320 0.831636i 0.312596π-0.312596\pi
0.555320 + 0.831636i 0.312596π0.312596\pi
632632 1.89898 0.0755373
633633 0 0
634634 20.6969 0.821980
635635 4.34847 0.172564
636636 0 0
637637 0 0
638638 13.7980 0.546266
639639 0 0
640640 1.44949 0.0572961
641641 7.49490 0.296031 0.148015 0.988985i 0.452712π-0.452712\pi
0.148015 + 0.988985i 0.452712π0.452712\pi
642642 0 0
643643 39.3939 1.55354 0.776771 0.629783i 0.216856π-0.216856\pi
0.776771 + 0.629783i 0.216856π0.216856\pi
644644 0 0
645645 0 0
646646 5.10102 0.200697
647647 −50.6969 −1.99310 −0.996551 0.0829807i 0.973556π-0.973556\pi
−0.996551 + 0.0829807i 0.973556π0.973556\pi
648648 0 0
649649 4.00000 0.157014
650650 −14.2020 −0.557050
651651 0 0
652652 −19.7980 −0.775348
653653 −9.79796 −0.383424 −0.191712 0.981451i 0.561404π-0.561404\pi
−0.191712 + 0.981451i 0.561404π0.561404\pi
654654 0 0
655655 12.3939 0.484269
656656 9.79796 0.382546
657657 0 0
658658 0 0
659659 24.6969 0.962056 0.481028 0.876705i 0.340264π-0.340264\pi
0.481028 + 0.876705i 0.340264π0.340264\pi
660660 0 0
661661 −4.55051 −0.176994 −0.0884972 0.996076i 0.528206π-0.528206\pi
−0.0884972 + 0.996076i 0.528206π0.528206\pi
662662 −4.69694 −0.182552
663663 0 0
664664 −2.00000 −0.0776151
665665 0 0
666666 0 0
667667 6.89898 0.267130
668668 −10.6969 −0.413877
669669 0 0
670670 −18.6969 −0.722326
671671 13.1010 0.505759
672672 0 0
673673 −8.59592 −0.331348 −0.165674 0.986181i 0.552980π-0.552980\pi
−0.165674 + 0.986181i 0.552980π0.552980\pi
674674 23.3939 0.901098
675675 0 0
676676 11.0000 0.423077
677677 14.6969 0.564849 0.282425 0.959289i 0.408861π-0.408861\pi
0.282425 + 0.959289i 0.408861π0.408861\pi
678678 0 0
679679 0 0
680680 2.89898 0.111171
681681 0 0
682682 −12.0000 −0.459504
683683 −51.7980 −1.98199 −0.990997 0.133885i 0.957255π-0.957255\pi
−0.990997 + 0.133885i 0.957255π0.957255\pi
684684 0 0
685685 11.3031 0.431868
686686 0 0
687687 0 0
688688 6.89898 0.263021
689689 −53.3939 −2.03414
690690 0 0
691691 −51.0454 −1.94186 −0.970929 0.239366i 0.923060π-0.923060\pi
−0.970929 + 0.239366i 0.923060π0.923060\pi
692692 −3.10102 −0.117883
693693 0 0
694694 19.5959 0.743851
695695 6.59592 0.250197
696696 0 0
697697 19.5959 0.742248
698698 11.1010 0.420180
699699 0 0
700700 0 0
701701 7.39388 0.279263 0.139631 0.990204i 0.455408π-0.455408\pi
0.139631 + 0.990204i 0.455408π0.455408\pi
702702 0 0
703703 −30.0908 −1.13490
704704 −2.00000 −0.0753778
705705 0 0
706706 6.00000 0.225813
707707 0 0
708708 0 0
709709 27.5959 1.03639 0.518193 0.855264i 0.326605π-0.326605\pi
0.518193 + 0.855264i 0.326605π0.326605\pi
710710 −0.146428 −0.00549535
711711 0 0
712712 16.8990 0.633316
713713 −6.00000 −0.224702
714714 0 0
715715 −14.2020 −0.531126
716716 −20.6969 −0.773481
717717 0 0
718718 −8.79796 −0.328337
719719 9.79796 0.365402 0.182701 0.983169i 0.441516π-0.441516\pi
0.182701 + 0.983169i 0.441516π0.441516\pi
720720 0 0
721721 0 0
722722 12.4949 0.465012
723723 0 0
724724 10.3485 0.384598
725725 −20.0000 −0.742781
726726 0 0
727727 8.49490 0.315058 0.157529 0.987514i 0.449647π-0.449647\pi
0.157529 + 0.987514i 0.449647π0.449647\pi
728728 0 0
729729 0 0
730730 10.0000 0.370117
731731 13.7980 0.510336
732732 0 0
733733 17.4495 0.644512 0.322256 0.946653i 0.395559π-0.395559\pi
0.322256 + 0.946653i 0.395559π0.395559\pi
734734 −13.7980 −0.509292
735735 0 0
736736 −1.00000 −0.0368605
737737 25.7980 0.950280
738738 0 0
739739 13.5959 0.500134 0.250067 0.968229i 0.419547π-0.419547\pi
0.250067 + 0.968229i 0.419547π0.419547\pi
740740 −17.1010 −0.628646
741741 0 0
742742 0 0
743743 −36.0000 −1.32071 −0.660356 0.750953i 0.729595π-0.729595\pi
−0.660356 + 0.750953i 0.729595π0.729595\pi
744744 0 0
745745 −8.69694 −0.318631
746746 6.89898 0.252590
747747 0 0
748748 −4.00000 −0.146254
749749 0 0
750750 0 0
751751 1.40408 0.0512357 0.0256178 0.999672i 0.491845π-0.491845\pi
0.0256178 + 0.999672i 0.491845π0.491845\pi
752752 9.79796 0.357295
753753 0 0
754754 33.7980 1.23085
755755 7.24745 0.263762
756756 0 0
757757 −35.3939 −1.28641 −0.643206 0.765693i 0.722396π-0.722396\pi
−0.643206 + 0.765693i 0.722396π0.722396\pi
758758 −22.4949 −0.817051
759759 0 0
760760 −3.69694 −0.134102
761761 2.00000 0.0724999 0.0362500 0.999343i 0.488459π-0.488459\pi
0.0362500 + 0.999343i 0.488459π0.488459\pi
762762 0 0
763763 0 0
764764 −4.10102 −0.148370
765765 0 0
766766 2.89898 0.104744
767767 9.79796 0.353784
768768 0 0
769769 34.0908 1.22935 0.614673 0.788782i 0.289288π-0.289288\pi
0.614673 + 0.788782i 0.289288π0.289288\pi
770770 0 0
771771 0 0
772772 −17.8990 −0.644198
773773 33.9444 1.22089 0.610447 0.792057i 0.290990π-0.290990\pi
0.610447 + 0.792057i 0.290990π0.290990\pi
774774 0 0
775775 17.3939 0.624807
776776 2.89898 0.104067
777777 0 0
778778 −24.8990 −0.892672
779779 −24.9898 −0.895352
780780 0 0
781781 0.202041 0.00722960
782782 −2.00000 −0.0715199
783783 0 0
784784 0 0
785785 −12.1010 −0.431904
786786 0 0
787787 11.3939 0.406148 0.203074 0.979163i 0.434907π-0.434907\pi
0.203074 + 0.979163i 0.434907π0.434907\pi
788788 −16.6969 −0.594804
789789 0 0
790790 −2.75255 −0.0979314
791791 0 0
792792 0 0
793793 32.0908 1.13958
794794 38.6969 1.37330
795795 0 0
796796 2.89898 0.102752
797797 −17.9444 −0.635623 −0.317811 0.948154i 0.602948π-0.602948\pi
−0.317811 + 0.948154i 0.602948π0.602948\pi
798798 0 0
799799 19.5959 0.693254
800800 2.89898 0.102494
801801 0 0
802802 −19.8990 −0.702657
803803 −13.7980 −0.486919
804804 0 0
805805 0 0
806806 −29.3939 −1.03536
807807 0 0
808808 17.2474 0.606763
809809 16.2020 0.569633 0.284817 0.958582i 0.408067π-0.408067\pi
0.284817 + 0.958582i 0.408067π0.408067\pi
810810 0 0
811811 2.00000 0.0702295 0.0351147 0.999383i 0.488820π-0.488820\pi
0.0351147 + 0.999383i 0.488820π0.488820\pi
812812 0 0
813813 0 0
814814 23.5959 0.827036
815815 28.6969 1.00521
816816 0 0
817817 −17.5959 −0.615603
818818 −13.7980 −0.482434
819819 0 0
820820 −14.2020 −0.495957
821821 −0.404082 −0.0141026 −0.00705128 0.999975i 0.502245π-0.502245\pi
−0.00705128 + 0.999975i 0.502245π0.502245\pi
822822 0 0
823823 −13.3939 −0.466881 −0.233441 0.972371i 0.574998π-0.574998\pi
−0.233441 + 0.972371i 0.574998π0.574998\pi
824824 14.0000 0.487713
825825 0 0
826826 0 0
827827 36.4949 1.26905 0.634526 0.772902i 0.281195π-0.281195\pi
0.634526 + 0.772902i 0.281195π0.281195\pi
828828 0 0
829829 −1.30306 −0.0452572 −0.0226286 0.999744i 0.507204π-0.507204\pi
−0.0226286 + 0.999744i 0.507204π0.507204\pi
830830 2.89898 0.100625
831831 0 0
832832 −4.89898 −0.169842
833833 0 0
834834 0 0
835835 15.5051 0.536576
836836 5.10102 0.176422
837837 0 0
838838 −29.4495 −1.01732
839839 −35.1010 −1.21182 −0.605911 0.795533i 0.707191π-0.707191\pi
−0.605911 + 0.795533i 0.707191π0.707191\pi
840840 0 0
841841 18.5959 0.641239
842842 −22.8990 −0.789151
843843 0 0
844844 12.8990 0.444001
845845 −15.9444 −0.548504
846846 0 0
847847 0 0
848848 10.8990 0.374272
849849 0 0
850850 5.79796 0.198868
851851 11.7980 0.404429
852852 0 0
853853 −24.8434 −0.850621 −0.425310 0.905048i 0.639835π-0.639835\pi
−0.425310 + 0.905048i 0.639835π0.639835\pi
854854 0 0
855855 0 0
856856 −12.0000 −0.410152
857857 −34.8990 −1.19213 −0.596063 0.802938i 0.703269π-0.703269\pi
−0.596063 + 0.802938i 0.703269π0.703269\pi
858858 0 0
859859 10.0000 0.341196 0.170598 0.985341i 0.445430π-0.445430\pi
0.170598 + 0.985341i 0.445430π0.445430\pi
860860 −10.0000 −0.340997
861861 0 0
862862 31.5959 1.07616
863863 −11.8990 −0.405046 −0.202523 0.979278i 0.564914π-0.564914\pi
−0.202523 + 0.979278i 0.564914π0.564914\pi
864864 0 0
865865 4.49490 0.152831
866866 −7.79796 −0.264985
867867 0 0
868868 0 0
869869 3.79796 0.128837
870870 0 0
871871 63.1918 2.14117
872872 −12.6969 −0.429973
873873 0 0
874874 2.55051 0.0862723
875875 0 0
876876 0 0
877877 22.4949 0.759599 0.379799 0.925069i 0.375993π-0.375993\pi
0.379799 + 0.925069i 0.375993π0.375993\pi
878878 2.20204 0.0743153
879879 0 0
880880 2.89898 0.0977246
881881 19.5959 0.660203 0.330102 0.943945i 0.392917π-0.392917\pi
0.330102 + 0.943945i 0.392917π0.392917\pi
882882 0 0
883883 −19.7980 −0.666254 −0.333127 0.942882i 0.608104π-0.608104\pi
−0.333127 + 0.942882i 0.608104π0.608104\pi
884884 −9.79796 −0.329541
885885 0 0
886886 −14.8990 −0.500541
887887 −14.2020 −0.476858 −0.238429 0.971160i 0.576632π-0.576632\pi
−0.238429 + 0.971160i 0.576632π0.576632\pi
888888 0 0
889889 0 0
890890 −24.4949 −0.821071
891891 0 0
892892 11.1010 0.371690
893893 −24.9898 −0.836252
894894 0 0
895895 30.0000 1.00279
896896 0 0
897897 0 0
898898 20.5959 0.687295
899899 −41.3939 −1.38056
900900 0 0
901901 21.7980 0.726195
902902 19.5959 0.652473
903903 0 0
904904 −6.10102 −0.202917
905905 −15.0000 −0.498617
906906 0 0
907907 2.69694 0.0895504 0.0447752 0.998997i 0.485743π-0.485743\pi
0.0447752 + 0.998997i 0.485743π0.485743\pi
908908 −5.44949 −0.180848
909909 0 0
910910 0 0
911911 −51.9898 −1.72250 −0.861249 0.508183i 0.830318π-0.830318\pi
−0.861249 + 0.508183i 0.830318π0.830318\pi
912912 0 0
913913 −4.00000 −0.132381
914914 17.4949 0.578680
915915 0 0
916916 −1.24745 −0.0412169
917917 0 0
918918 0 0
919919 −25.6969 −0.847664 −0.423832 0.905741i 0.639315π-0.639315\pi
−0.423832 + 0.905741i 0.639315π0.639315\pi
920920 1.44949 0.0477883
921921 0 0
922922 −5.65153 −0.186123
923923 0.494897 0.0162897
924924 0 0
925925 −34.2020 −1.12456
926926 −3.69694 −0.121489
927927 0 0
928928 −6.89898 −0.226470
929929 34.2929 1.12511 0.562556 0.826759i 0.309818π-0.309818\pi
0.562556 + 0.826759i 0.309818π0.309818\pi
930930 0 0
931931 0 0
932932 7.00000 0.229293
933933 0 0
934934 −10.0000 −0.327210
935935 5.79796 0.189614
936936 0 0
937937 −45.5959 −1.48955 −0.744777 0.667314i 0.767444π-0.767444\pi
−0.744777 + 0.667314i 0.767444π0.767444\pi
938938 0 0
939939 0 0
940940 −14.2020 −0.463220
941941 −1.44949 −0.0472520 −0.0236260 0.999721i 0.507521π-0.507521\pi
−0.0236260 + 0.999721i 0.507521π0.507521\pi
942942 0 0
943943 9.79796 0.319065
944944 −2.00000 −0.0650945
945945 0 0
946946 13.7980 0.448610
947947 −52.4949 −1.70585 −0.852927 0.522029i 0.825175π-0.825175\pi
−0.852927 + 0.522029i 0.825175π0.825175\pi
948948 0 0
949949 −33.7980 −1.09713
950950 −7.39388 −0.239889
951951 0 0
952952 0 0
953953 3.39388 0.109938 0.0549692 0.998488i 0.482494π-0.482494\pi
0.0549692 + 0.998488i 0.482494π0.482494\pi
954954 0 0
955955 5.94439 0.192356
956956 −6.79796 −0.219862
957957 0 0
958958 −9.59592 −0.310030
959959 0 0
960960 0 0
961961 5.00000 0.161290
962962 57.7980 1.86348
963963 0 0
964964 −0.898979 −0.0289542
965965 25.9444 0.835179
966966 0 0
967967 24.5959 0.790951 0.395476 0.918476i 0.370580π-0.370580\pi
0.395476 + 0.918476i 0.370580π0.370580\pi
968968 7.00000 0.224989
969969 0 0
970970 −4.20204 −0.134919
971971 −0.0556128 −0.00178470 −0.000892350 1.00000i 0.500284π-0.500284\pi
−0.000892350 1.00000i 0.500284π0.500284\pi
972972 0 0
973973 0 0
974974 36.3939 1.16614
975975 0 0
976976 −6.55051 −0.209677
977977 37.5959 1.20280 0.601400 0.798948i 0.294610π-0.294610\pi
0.601400 + 0.798948i 0.294610π0.294610\pi
978978 0 0
979979 33.7980 1.08019
980980 0 0
981981 0 0
982982 15.7980 0.504133
983983 −33.1918 −1.05866 −0.529328 0.848418i 0.677556π-0.677556\pi
−0.529328 + 0.848418i 0.677556π0.677556\pi
984984 0 0
985985 24.2020 0.771141
986986 −13.7980 −0.439417
987987 0 0
988988 12.4949 0.397516
989989 6.89898 0.219375
990990 0 0
991991 −1.79796 −0.0571140 −0.0285570 0.999592i 0.509091π-0.509091\pi
−0.0285570 + 0.999592i 0.509091π0.509091\pi
992992 6.00000 0.190500
993993 0 0
994994 0 0
995995 −4.20204 −0.133214
996996 0 0
997997 −52.1464 −1.65149 −0.825747 0.564041i 0.809246π-0.809246\pi
−0.825747 + 0.564041i 0.809246π0.809246\pi
998998 25.3939 0.803829
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 7938.2.a.bm.1.1 2
3.2 odd 2 7938.2.a.bn.1.2 2
7.6 odd 2 1134.2.a.i.1.2 2
9.2 odd 6 882.2.f.j.589.2 4
9.4 even 3 2646.2.f.k.883.2 4
9.5 odd 6 882.2.f.j.295.1 4
9.7 even 3 2646.2.f.k.1765.2 4
21.20 even 2 1134.2.a.p.1.1 2
28.27 even 2 9072.2.a.bd.1.2 2
63.2 odd 6 882.2.h.l.67.1 4
63.4 even 3 2646.2.h.n.667.1 4
63.5 even 6 882.2.e.m.655.1 4
63.11 odd 6 882.2.e.n.373.2 4
63.13 odd 6 378.2.f.d.127.1 4
63.16 even 3 2646.2.h.n.361.1 4
63.20 even 6 126.2.f.c.85.1 yes 4
63.23 odd 6 882.2.e.n.655.2 4
63.25 even 3 2646.2.e.k.1549.2 4
63.31 odd 6 2646.2.h.m.667.2 4
63.32 odd 6 882.2.h.l.79.1 4
63.34 odd 6 378.2.f.d.253.1 4
63.38 even 6 882.2.e.m.373.1 4
63.40 odd 6 2646.2.e.l.2125.1 4
63.41 even 6 126.2.f.c.43.2 4
63.47 even 6 882.2.h.k.67.2 4
63.52 odd 6 2646.2.e.l.1549.1 4
63.58 even 3 2646.2.e.k.2125.2 4
63.59 even 6 882.2.h.k.79.2 4
63.61 odd 6 2646.2.h.m.361.2 4
84.83 odd 2 9072.2.a.bk.1.1 2
252.83 odd 6 1008.2.r.e.337.2 4
252.139 even 6 3024.2.r.e.2017.1 4
252.167 odd 6 1008.2.r.e.673.1 4
252.223 even 6 3024.2.r.e.1009.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.f.c.43.2 4 63.41 even 6
126.2.f.c.85.1 yes 4 63.20 even 6
378.2.f.d.127.1 4 63.13 odd 6
378.2.f.d.253.1 4 63.34 odd 6
882.2.e.m.373.1 4 63.38 even 6
882.2.e.m.655.1 4 63.5 even 6
882.2.e.n.373.2 4 63.11 odd 6
882.2.e.n.655.2 4 63.23 odd 6
882.2.f.j.295.1 4 9.5 odd 6
882.2.f.j.589.2 4 9.2 odd 6
882.2.h.k.67.2 4 63.47 even 6
882.2.h.k.79.2 4 63.59 even 6
882.2.h.l.67.1 4 63.2 odd 6
882.2.h.l.79.1 4 63.32 odd 6
1008.2.r.e.337.2 4 252.83 odd 6
1008.2.r.e.673.1 4 252.167 odd 6
1134.2.a.i.1.2 2 7.6 odd 2
1134.2.a.p.1.1 2 21.20 even 2
2646.2.e.k.1549.2 4 63.25 even 3
2646.2.e.k.2125.2 4 63.58 even 3
2646.2.e.l.1549.1 4 63.52 odd 6
2646.2.e.l.2125.1 4 63.40 odd 6
2646.2.f.k.883.2 4 9.4 even 3
2646.2.f.k.1765.2 4 9.7 even 3
2646.2.h.m.361.2 4 63.61 odd 6
2646.2.h.m.667.2 4 63.31 odd 6
2646.2.h.n.361.1 4 63.16 even 3
2646.2.h.n.667.1 4 63.4 even 3
3024.2.r.e.1009.1 4 252.223 even 6
3024.2.r.e.2017.1 4 252.139 even 6
7938.2.a.bm.1.1 2 1.1 even 1 trivial
7938.2.a.bn.1.2 2 3.2 odd 2
9072.2.a.bd.1.2 2 28.27 even 2
9072.2.a.bk.1.1 2 84.83 odd 2