Properties

Label 722.2.a.d.1.1
Level 722722
Weight 22
Character 722.1
Self dual yes
Analytic conductor 5.7655.765
Analytic rank 11
Dimension 11
CM no
Inner twists 11

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [722,2,Mod(1,722)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(722, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("722.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 722=2192 722 = 2 \cdot 19^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 722.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: 5.765199025945.76519902594
Analytic rank: 11
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 38)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 722.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+1.00000q21.00000q3+1.00000q41.00000q64.00000q7+1.00000q82.00000q9+3.00000q111.00000q122.00000q134.00000q14+1.00000q166.00000q172.00000q18+4.00000q21+3.00000q226.00000q231.00000q245.00000q252.00000q26+5.00000q274.00000q282.00000q31+1.00000q323.00000q336.00000q342.00000q36+10.0000q37+2.00000q399.00000q41+4.00000q424.00000q43+3.00000q446.00000q461.00000q48+9.00000q495.00000q50+6.00000q512.00000q526.00000q53+5.00000q544.00000q56+9.00000q594.00000q612.00000q62+8.00000q63+1.00000q643.00000q66+7.00000q676.00000q68+6.00000q69+6.00000q712.00000q721.00000q73+10.0000q74+5.00000q7512.0000q77+2.00000q78+4.00000q79+1.00000q819.00000q82+3.00000q83+4.00000q844.00000q86+3.00000q886.00000q89+8.00000q916.00000q92+2.00000q931.00000q9617.0000q97+9.00000q986.00000q99+O(q100)q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -4.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +3.00000 q^{11} -1.00000 q^{12} -2.00000 q^{13} -4.00000 q^{14} +1.00000 q^{16} -6.00000 q^{17} -2.00000 q^{18} +4.00000 q^{21} +3.00000 q^{22} -6.00000 q^{23} -1.00000 q^{24} -5.00000 q^{25} -2.00000 q^{26} +5.00000 q^{27} -4.00000 q^{28} -2.00000 q^{31} +1.00000 q^{32} -3.00000 q^{33} -6.00000 q^{34} -2.00000 q^{36} +10.0000 q^{37} +2.00000 q^{39} -9.00000 q^{41} +4.00000 q^{42} -4.00000 q^{43} +3.00000 q^{44} -6.00000 q^{46} -1.00000 q^{48} +9.00000 q^{49} -5.00000 q^{50} +6.00000 q^{51} -2.00000 q^{52} -6.00000 q^{53} +5.00000 q^{54} -4.00000 q^{56} +9.00000 q^{59} -4.00000 q^{61} -2.00000 q^{62} +8.00000 q^{63} +1.00000 q^{64} -3.00000 q^{66} +7.00000 q^{67} -6.00000 q^{68} +6.00000 q^{69} +6.00000 q^{71} -2.00000 q^{72} -1.00000 q^{73} +10.0000 q^{74} +5.00000 q^{75} -12.0000 q^{77} +2.00000 q^{78} +4.00000 q^{79} +1.00000 q^{81} -9.00000 q^{82} +3.00000 q^{83} +4.00000 q^{84} -4.00000 q^{86} +3.00000 q^{88} -6.00000 q^{89} +8.00000 q^{91} -6.00000 q^{92} +2.00000 q^{93} -1.00000 q^{96} -17.0000 q^{97} +9.00000 q^{98} -6.00000 q^{99} +O(q^{100})

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 −1.00000 −0.577350 −0.288675 0.957427i 0.593215π-0.593215\pi
−0.288675 + 0.957427i 0.593215π0.593215\pi
44 1.00000 0.500000
55 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
66 −1.00000 −0.408248
77 −4.00000 −1.51186 −0.755929 0.654654i 0.772814π-0.772814\pi
−0.755929 + 0.654654i 0.772814π0.772814\pi
88 1.00000 0.353553
99 −2.00000 −0.666667
1010 0 0
1111 3.00000 0.904534 0.452267 0.891883i 0.350615π-0.350615\pi
0.452267 + 0.891883i 0.350615π0.350615\pi
1212 −1.00000 −0.288675
1313 −2.00000 −0.554700 −0.277350 0.960769i 0.589456π-0.589456\pi
−0.277350 + 0.960769i 0.589456π0.589456\pi
1414 −4.00000 −1.06904
1515 0 0
1616 1.00000 0.250000
1717 −6.00000 −1.45521 −0.727607 0.685994i 0.759367π-0.759367\pi
−0.727607 + 0.685994i 0.759367π0.759367\pi
1818 −2.00000 −0.471405
1919 0 0
2020 0 0
2121 4.00000 0.872872
2222 3.00000 0.639602
2323 −6.00000 −1.25109 −0.625543 0.780189i 0.715123π-0.715123\pi
−0.625543 + 0.780189i 0.715123π0.715123\pi
2424 −1.00000 −0.204124
2525 −5.00000 −1.00000
2626 −2.00000 −0.392232
2727 5.00000 0.962250
2828 −4.00000 −0.755929
2929 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
3030 0 0
3131 −2.00000 −0.359211 −0.179605 0.983739i 0.557482π-0.557482\pi
−0.179605 + 0.983739i 0.557482π0.557482\pi
3232 1.00000 0.176777
3333 −3.00000 −0.522233
3434 −6.00000 −1.02899
3535 0 0
3636 −2.00000 −0.333333
3737 10.0000 1.64399 0.821995 0.569495i 0.192861π-0.192861\pi
0.821995 + 0.569495i 0.192861π0.192861\pi
3838 0 0
3939 2.00000 0.320256
4040 0 0
4141 −9.00000 −1.40556 −0.702782 0.711405i 0.748059π-0.748059\pi
−0.702782 + 0.711405i 0.748059π0.748059\pi
4242 4.00000 0.617213
4343 −4.00000 −0.609994 −0.304997 0.952353i 0.598656π-0.598656\pi
−0.304997 + 0.952353i 0.598656π0.598656\pi
4444 3.00000 0.452267
4545 0 0
4646 −6.00000 −0.884652
4747 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
4848 −1.00000 −0.144338
4949 9.00000 1.28571
5050 −5.00000 −0.707107
5151 6.00000 0.840168
5252 −2.00000 −0.277350
5353 −6.00000 −0.824163 −0.412082 0.911147i 0.635198π-0.635198\pi
−0.412082 + 0.911147i 0.635198π0.635198\pi
5454 5.00000 0.680414
5555 0 0
5656 −4.00000 −0.534522
5757 0 0
5858 0 0
5959 9.00000 1.17170 0.585850 0.810419i 0.300761π-0.300761\pi
0.585850 + 0.810419i 0.300761π0.300761\pi
6060 0 0
6161 −4.00000 −0.512148 −0.256074 0.966657i 0.582429π-0.582429\pi
−0.256074 + 0.966657i 0.582429π0.582429\pi
6262 −2.00000 −0.254000
6363 8.00000 1.00791
6464 1.00000 0.125000
6565 0 0
6666 −3.00000 −0.369274
6767 7.00000 0.855186 0.427593 0.903971i 0.359362π-0.359362\pi
0.427593 + 0.903971i 0.359362π0.359362\pi
6868 −6.00000 −0.727607
6969 6.00000 0.722315
7070 0 0
7171 6.00000 0.712069 0.356034 0.934473i 0.384129π-0.384129\pi
0.356034 + 0.934473i 0.384129π0.384129\pi
7272 −2.00000 −0.235702
7373 −1.00000 −0.117041 −0.0585206 0.998286i 0.518638π-0.518638\pi
−0.0585206 + 0.998286i 0.518638π0.518638\pi
7474 10.0000 1.16248
7575 5.00000 0.577350
7676 0 0
7777 −12.0000 −1.36753
7878 2.00000 0.226455
7979 4.00000 0.450035 0.225018 0.974355i 0.427756π-0.427756\pi
0.225018 + 0.974355i 0.427756π0.427756\pi
8080 0 0
8181 1.00000 0.111111
8282 −9.00000 −0.993884
8383 3.00000 0.329293 0.164646 0.986353i 0.447352π-0.447352\pi
0.164646 + 0.986353i 0.447352π0.447352\pi
8484 4.00000 0.436436
8585 0 0
8686 −4.00000 −0.431331
8787 0 0
8888 3.00000 0.319801
8989 −6.00000 −0.635999 −0.317999 0.948091i 0.603011π-0.603011\pi
−0.317999 + 0.948091i 0.603011π0.603011\pi
9090 0 0
9191 8.00000 0.838628
9292 −6.00000 −0.625543
9393 2.00000 0.207390
9494 0 0
9595 0 0
9696 −1.00000 −0.102062
9797 −17.0000 −1.72609 −0.863044 0.505128i 0.831445π-0.831445\pi
−0.863044 + 0.505128i 0.831445π0.831445\pi
9898 9.00000 0.909137
9999 −6.00000 −0.603023
100100 −5.00000 −0.500000
101101 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
102102 6.00000 0.594089
103103 −2.00000 −0.197066 −0.0985329 0.995134i 0.531415π-0.531415\pi
−0.0985329 + 0.995134i 0.531415π0.531415\pi
104104 −2.00000 −0.196116
105105 0 0
106106 −6.00000 −0.582772
107107 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
108108 5.00000 0.481125
109109 16.0000 1.53252 0.766261 0.642529i 0.222115π-0.222115\pi
0.766261 + 0.642529i 0.222115π0.222115\pi
110110 0 0
111111 −10.0000 −0.949158
112112 −4.00000 −0.377964
113113 −15.0000 −1.41108 −0.705541 0.708669i 0.749296π-0.749296\pi
−0.705541 + 0.708669i 0.749296π0.749296\pi
114114 0 0
115115 0 0
116116 0 0
117117 4.00000 0.369800
118118 9.00000 0.828517
119119 24.0000 2.20008
120120 0 0
121121 −2.00000 −0.181818
122122 −4.00000 −0.362143
123123 9.00000 0.811503
124124 −2.00000 −0.179605
125125 0 0
126126 8.00000 0.712697
127127 −2.00000 −0.177471 −0.0887357 0.996055i 0.528283π-0.528283\pi
−0.0887357 + 0.996055i 0.528283π0.528283\pi
128128 1.00000 0.0883883
129129 4.00000 0.352180
130130 0 0
131131 9.00000 0.786334 0.393167 0.919467i 0.371379π-0.371379\pi
0.393167 + 0.919467i 0.371379π0.371379\pi
132132 −3.00000 −0.261116
133133 0 0
134134 7.00000 0.604708
135135 0 0
136136 −6.00000 −0.514496
137137 9.00000 0.768922 0.384461 0.923141i 0.374387π-0.374387\pi
0.384461 + 0.923141i 0.374387π0.374387\pi
138138 6.00000 0.510754
139139 11.0000 0.933008 0.466504 0.884519i 0.345513π-0.345513\pi
0.466504 + 0.884519i 0.345513π0.345513\pi
140140 0 0
141141 0 0
142142 6.00000 0.503509
143143 −6.00000 −0.501745
144144 −2.00000 −0.166667
145145 0 0
146146 −1.00000 −0.0827606
147147 −9.00000 −0.742307
148148 10.0000 0.821995
149149 18.0000 1.47462 0.737309 0.675556i 0.236096π-0.236096\pi
0.737309 + 0.675556i 0.236096π0.236096\pi
150150 5.00000 0.408248
151151 10.0000 0.813788 0.406894 0.913475i 0.366612π-0.366612\pi
0.406894 + 0.913475i 0.366612π0.366612\pi
152152 0 0
153153 12.0000 0.970143
154154 −12.0000 −0.966988
155155 0 0
156156 2.00000 0.160128
157157 −16.0000 −1.27694 −0.638470 0.769647i 0.720432π-0.720432\pi
−0.638470 + 0.769647i 0.720432π0.720432\pi
158158 4.00000 0.318223
159159 6.00000 0.475831
160160 0 0
161161 24.0000 1.89146
162162 1.00000 0.0785674
163163 −19.0000 −1.48819 −0.744097 0.668071i 0.767120π-0.767120\pi
−0.744097 + 0.668071i 0.767120π0.767120\pi
164164 −9.00000 −0.702782
165165 0 0
166166 3.00000 0.232845
167167 24.0000 1.85718 0.928588 0.371113i 0.121024π-0.121024\pi
0.928588 + 0.371113i 0.121024π0.121024\pi
168168 4.00000 0.308607
169169 −9.00000 −0.692308
170170 0 0
171171 0 0
172172 −4.00000 −0.304997
173173 −6.00000 −0.456172 −0.228086 0.973641i 0.573247π-0.573247\pi
−0.228086 + 0.973641i 0.573247π0.573247\pi
174174 0 0
175175 20.0000 1.51186
176176 3.00000 0.226134
177177 −9.00000 −0.676481
178178 −6.00000 −0.449719
179179 −9.00000 −0.672692 −0.336346 0.941739i 0.609191π-0.609191\pi
−0.336346 + 0.941739i 0.609191π0.609191\pi
180180 0 0
181181 −2.00000 −0.148659 −0.0743294 0.997234i 0.523682π-0.523682\pi
−0.0743294 + 0.997234i 0.523682π0.523682\pi
182182 8.00000 0.592999
183183 4.00000 0.295689
184184 −6.00000 −0.442326
185185 0 0
186186 2.00000 0.146647
187187 −18.0000 −1.31629
188188 0 0
189189 −20.0000 −1.45479
190190 0 0
191191 12.0000 0.868290 0.434145 0.900843i 0.357051π-0.357051\pi
0.434145 + 0.900843i 0.357051π0.357051\pi
192192 −1.00000 −0.0721688
193193 −2.00000 −0.143963 −0.0719816 0.997406i 0.522932π-0.522932\pi
−0.0719816 + 0.997406i 0.522932π0.522932\pi
194194 −17.0000 −1.22053
195195 0 0
196196 9.00000 0.642857
197197 18.0000 1.28245 0.641223 0.767354i 0.278427π-0.278427\pi
0.641223 + 0.767354i 0.278427π0.278427\pi
198198 −6.00000 −0.426401
199199 −10.0000 −0.708881 −0.354441 0.935079i 0.615329π-0.615329\pi
−0.354441 + 0.935079i 0.615329π0.615329\pi
200200 −5.00000 −0.353553
201201 −7.00000 −0.493742
202202 0 0
203203 0 0
204204 6.00000 0.420084
205205 0 0
206206 −2.00000 −0.139347
207207 12.0000 0.834058
208208 −2.00000 −0.138675
209209 0 0
210210 0 0
211211 −20.0000 −1.37686 −0.688428 0.725304i 0.741699π-0.741699\pi
−0.688428 + 0.725304i 0.741699π0.741699\pi
212212 −6.00000 −0.412082
213213 −6.00000 −0.411113
214214 0 0
215215 0 0
216216 5.00000 0.340207
217217 8.00000 0.543075
218218 16.0000 1.08366
219219 1.00000 0.0675737
220220 0 0
221221 12.0000 0.807207
222222 −10.0000 −0.671156
223223 −14.0000 −0.937509 −0.468755 0.883328i 0.655297π-0.655297\pi
−0.468755 + 0.883328i 0.655297π0.655297\pi
224224 −4.00000 −0.267261
225225 10.0000 0.666667
226226 −15.0000 −0.997785
227227 −3.00000 −0.199117 −0.0995585 0.995032i 0.531743π-0.531743\pi
−0.0995585 + 0.995032i 0.531743π0.531743\pi
228228 0 0
229229 −16.0000 −1.05731 −0.528655 0.848837i 0.677303π-0.677303\pi
−0.528655 + 0.848837i 0.677303π0.677303\pi
230230 0 0
231231 12.0000 0.789542
232232 0 0
233233 3.00000 0.196537 0.0982683 0.995160i 0.468670π-0.468670\pi
0.0982683 + 0.995160i 0.468670π0.468670\pi
234234 4.00000 0.261488
235235 0 0
236236 9.00000 0.585850
237237 −4.00000 −0.259828
238238 24.0000 1.55569
239239 −12.0000 −0.776215 −0.388108 0.921614i 0.626871π-0.626871\pi
−0.388108 + 0.921614i 0.626871π0.626871\pi
240240 0 0
241241 −5.00000 −0.322078 −0.161039 0.986948i 0.551485π-0.551485\pi
−0.161039 + 0.986948i 0.551485π0.551485\pi
242242 −2.00000 −0.128565
243243 −16.0000 −1.02640
244244 −4.00000 −0.256074
245245 0 0
246246 9.00000 0.573819
247247 0 0
248248 −2.00000 −0.127000
249249 −3.00000 −0.190117
250250 0 0
251251 −3.00000 −0.189358 −0.0946792 0.995508i 0.530183π-0.530183\pi
−0.0946792 + 0.995508i 0.530183π0.530183\pi
252252 8.00000 0.503953
253253 −18.0000 −1.13165
254254 −2.00000 −0.125491
255255 0 0
256256 1.00000 0.0625000
257257 −3.00000 −0.187135 −0.0935674 0.995613i 0.529827π-0.529827\pi
−0.0935674 + 0.995613i 0.529827π0.529827\pi
258258 4.00000 0.249029
259259 −40.0000 −2.48548
260260 0 0
261261 0 0
262262 9.00000 0.556022
263263 −12.0000 −0.739952 −0.369976 0.929041i 0.620634π-0.620634\pi
−0.369976 + 0.929041i 0.620634π0.620634\pi
264264 −3.00000 −0.184637
265265 0 0
266266 0 0
267267 6.00000 0.367194
268268 7.00000 0.427593
269269 −12.0000 −0.731653 −0.365826 0.930683i 0.619214π-0.619214\pi
−0.365826 + 0.930683i 0.619214π0.619214\pi
270270 0 0
271271 −16.0000 −0.971931 −0.485965 0.873978i 0.661532π-0.661532\pi
−0.485965 + 0.873978i 0.661532π0.661532\pi
272272 −6.00000 −0.363803
273273 −8.00000 −0.484182
274274 9.00000 0.543710
275275 −15.0000 −0.904534
276276 6.00000 0.361158
277277 8.00000 0.480673 0.240337 0.970690i 0.422742π-0.422742\pi
0.240337 + 0.970690i 0.422742π0.422742\pi
278278 11.0000 0.659736
279279 4.00000 0.239474
280280 0 0
281281 −27.0000 −1.61068 −0.805342 0.592810i 0.798019π-0.798019\pi
−0.805342 + 0.592810i 0.798019π0.798019\pi
282282 0 0
283283 5.00000 0.297219 0.148610 0.988896i 0.452520π-0.452520\pi
0.148610 + 0.988896i 0.452520π0.452520\pi
284284 6.00000 0.356034
285285 0 0
286286 −6.00000 −0.354787
287287 36.0000 2.12501
288288 −2.00000 −0.117851
289289 19.0000 1.11765
290290 0 0
291291 17.0000 0.996558
292292 −1.00000 −0.0585206
293293 −24.0000 −1.40209 −0.701047 0.713115i 0.747284π-0.747284\pi
−0.701047 + 0.713115i 0.747284π0.747284\pi
294294 −9.00000 −0.524891
295295 0 0
296296 10.0000 0.581238
297297 15.0000 0.870388
298298 18.0000 1.04271
299299 12.0000 0.693978
300300 5.00000 0.288675
301301 16.0000 0.922225
302302 10.0000 0.575435
303303 0 0
304304 0 0
305305 0 0
306306 12.0000 0.685994
307307 7.00000 0.399511 0.199756 0.979846i 0.435985π-0.435985\pi
0.199756 + 0.979846i 0.435985π0.435985\pi
308308 −12.0000 −0.683763
309309 2.00000 0.113776
310310 0 0
311311 −30.0000 −1.70114 −0.850572 0.525859i 0.823744π-0.823744\pi
−0.850572 + 0.525859i 0.823744π0.823744\pi
312312 2.00000 0.113228
313313 −19.0000 −1.07394 −0.536972 0.843600i 0.680432π-0.680432\pi
−0.536972 + 0.843600i 0.680432π0.680432\pi
314314 −16.0000 −0.902932
315315 0 0
316316 4.00000 0.225018
317317 18.0000 1.01098 0.505490 0.862832i 0.331312π-0.331312\pi
0.505490 + 0.862832i 0.331312π0.331312\pi
318318 6.00000 0.336463
319319 0 0
320320 0 0
321321 0 0
322322 24.0000 1.33747
323323 0 0
324324 1.00000 0.0555556
325325 10.0000 0.554700
326326 −19.0000 −1.05231
327327 −16.0000 −0.884802
328328 −9.00000 −0.496942
329329 0 0
330330 0 0
331331 −5.00000 −0.274825 −0.137412 0.990514i 0.543879π-0.543879\pi
−0.137412 + 0.990514i 0.543879π0.543879\pi
332332 3.00000 0.164646
333333 −20.0000 −1.09599
334334 24.0000 1.31322
335335 0 0
336336 4.00000 0.218218
337337 −11.0000 −0.599208 −0.299604 0.954064i 0.596855π-0.596855\pi
−0.299604 + 0.954064i 0.596855π0.596855\pi
338338 −9.00000 −0.489535
339339 15.0000 0.814688
340340 0 0
341341 −6.00000 −0.324918
342342 0 0
343343 −8.00000 −0.431959
344344 −4.00000 −0.215666
345345 0 0
346346 −6.00000 −0.322562
347347 −9.00000 −0.483145 −0.241573 0.970383i 0.577663π-0.577663\pi
−0.241573 + 0.970383i 0.577663π0.577663\pi
348348 0 0
349349 −4.00000 −0.214115 −0.107058 0.994253i 0.534143π-0.534143\pi
−0.107058 + 0.994253i 0.534143π0.534143\pi
350350 20.0000 1.06904
351351 −10.0000 −0.533761
352352 3.00000 0.159901
353353 3.00000 0.159674 0.0798369 0.996808i 0.474560π-0.474560\pi
0.0798369 + 0.996808i 0.474560π0.474560\pi
354354 −9.00000 −0.478345
355355 0 0
356356 −6.00000 −0.317999
357357 −24.0000 −1.27021
358358 −9.00000 −0.475665
359359 −6.00000 −0.316668 −0.158334 0.987386i 0.550612π-0.550612\pi
−0.158334 + 0.987386i 0.550612π0.550612\pi
360360 0 0
361361 0 0
362362 −2.00000 −0.105118
363363 2.00000 0.104973
364364 8.00000 0.419314
365365 0 0
366366 4.00000 0.209083
367367 −22.0000 −1.14839 −0.574195 0.818718i 0.694685π-0.694685\pi
−0.574195 + 0.818718i 0.694685π0.694685\pi
368368 −6.00000 −0.312772
369369 18.0000 0.937043
370370 0 0
371371 24.0000 1.24602
372372 2.00000 0.103695
373373 4.00000 0.207112 0.103556 0.994624i 0.466978π-0.466978\pi
0.103556 + 0.994624i 0.466978π0.466978\pi
374374 −18.0000 −0.930758
375375 0 0
376376 0 0
377377 0 0
378378 −20.0000 −1.02869
379379 28.0000 1.43826 0.719132 0.694874i 0.244540π-0.244540\pi
0.719132 + 0.694874i 0.244540π0.244540\pi
380380 0 0
381381 2.00000 0.102463
382382 12.0000 0.613973
383383 36.0000 1.83951 0.919757 0.392488i 0.128386π-0.128386\pi
0.919757 + 0.392488i 0.128386π0.128386\pi
384384 −1.00000 −0.0510310
385385 0 0
386386 −2.00000 −0.101797
387387 8.00000 0.406663
388388 −17.0000 −0.863044
389389 −36.0000 −1.82527 −0.912636 0.408773i 0.865957π-0.865957\pi
−0.912636 + 0.408773i 0.865957π0.865957\pi
390390 0 0
391391 36.0000 1.82060
392392 9.00000 0.454569
393393 −9.00000 −0.453990
394394 18.0000 0.906827
395395 0 0
396396 −6.00000 −0.301511
397397 −10.0000 −0.501886 −0.250943 0.968002i 0.580741π-0.580741\pi
−0.250943 + 0.968002i 0.580741π0.580741\pi
398398 −10.0000 −0.501255
399399 0 0
400400 −5.00000 −0.250000
401401 27.0000 1.34832 0.674158 0.738587i 0.264507π-0.264507\pi
0.674158 + 0.738587i 0.264507π0.264507\pi
402402 −7.00000 −0.349128
403403 4.00000 0.199254
404404 0 0
405405 0 0
406406 0 0
407407 30.0000 1.48704
408408 6.00000 0.297044
409409 −5.00000 −0.247234 −0.123617 0.992330i 0.539449π-0.539449\pi
−0.123617 + 0.992330i 0.539449π0.539449\pi
410410 0 0
411411 −9.00000 −0.443937
412412 −2.00000 −0.0985329
413413 −36.0000 −1.77144
414414 12.0000 0.589768
415415 0 0
416416 −2.00000 −0.0980581
417417 −11.0000 −0.538672
418418 0 0
419419 −12.0000 −0.586238 −0.293119 0.956076i 0.594693π-0.594693\pi
−0.293119 + 0.956076i 0.594693π0.594693\pi
420420 0 0
421421 10.0000 0.487370 0.243685 0.969854i 0.421644π-0.421644\pi
0.243685 + 0.969854i 0.421644π0.421644\pi
422422 −20.0000 −0.973585
423423 0 0
424424 −6.00000 −0.291386
425425 30.0000 1.45521
426426 −6.00000 −0.290701
427427 16.0000 0.774294
428428 0 0
429429 6.00000 0.289683
430430 0 0
431431 30.0000 1.44505 0.722525 0.691345i 0.242982π-0.242982\pi
0.722525 + 0.691345i 0.242982π0.242982\pi
432432 5.00000 0.240563
433433 −26.0000 −1.24948 −0.624740 0.780833i 0.714795π-0.714795\pi
−0.624740 + 0.780833i 0.714795π0.714795\pi
434434 8.00000 0.384012
435435 0 0
436436 16.0000 0.766261
437437 0 0
438438 1.00000 0.0477818
439439 −14.0000 −0.668184 −0.334092 0.942541i 0.608430π-0.608430\pi
−0.334092 + 0.942541i 0.608430π0.608430\pi
440440 0 0
441441 −18.0000 −0.857143
442442 12.0000 0.570782
443443 9.00000 0.427603 0.213801 0.976877i 0.431415π-0.431415\pi
0.213801 + 0.976877i 0.431415π0.431415\pi
444444 −10.0000 −0.474579
445445 0 0
446446 −14.0000 −0.662919
447447 −18.0000 −0.851371
448448 −4.00000 −0.188982
449449 −9.00000 −0.424736 −0.212368 0.977190i 0.568118π-0.568118\pi
−0.212368 + 0.977190i 0.568118π0.568118\pi
450450 10.0000 0.471405
451451 −27.0000 −1.27138
452452 −15.0000 −0.705541
453453 −10.0000 −0.469841
454454 −3.00000 −0.140797
455455 0 0
456456 0 0
457457 5.00000 0.233890 0.116945 0.993138i 0.462690π-0.462690\pi
0.116945 + 0.993138i 0.462690π0.462690\pi
458458 −16.0000 −0.747631
459459 −30.0000 −1.40028
460460 0 0
461461 6.00000 0.279448 0.139724 0.990190i 0.455378π-0.455378\pi
0.139724 + 0.990190i 0.455378π0.455378\pi
462462 12.0000 0.558291
463463 −34.0000 −1.58011 −0.790057 0.613033i 0.789949π-0.789949\pi
−0.790057 + 0.613033i 0.789949π0.789949\pi
464464 0 0
465465 0 0
466466 3.00000 0.138972
467467 −27.0000 −1.24941 −0.624705 0.780860i 0.714781π-0.714781\pi
−0.624705 + 0.780860i 0.714781π0.714781\pi
468468 4.00000 0.184900
469469 −28.0000 −1.29292
470470 0 0
471471 16.0000 0.737241
472472 9.00000 0.414259
473473 −12.0000 −0.551761
474474 −4.00000 −0.183726
475475 0 0
476476 24.0000 1.10004
477477 12.0000 0.549442
478478 −12.0000 −0.548867
479479 36.0000 1.64488 0.822441 0.568850i 0.192612π-0.192612\pi
0.822441 + 0.568850i 0.192612π0.192612\pi
480480 0 0
481481 −20.0000 −0.911922
482482 −5.00000 −0.227744
483483 −24.0000 −1.09204
484484 −2.00000 −0.0909091
485485 0 0
486486 −16.0000 −0.725775
487487 −2.00000 −0.0906287 −0.0453143 0.998973i 0.514429π-0.514429\pi
−0.0453143 + 0.998973i 0.514429π0.514429\pi
488488 −4.00000 −0.181071
489489 19.0000 0.859210
490490 0 0
491491 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
492492 9.00000 0.405751
493493 0 0
494494 0 0
495495 0 0
496496 −2.00000 −0.0898027
497497 −24.0000 −1.07655
498498 −3.00000 −0.134433
499499 −25.0000 −1.11915 −0.559577 0.828778i 0.689036π-0.689036\pi
−0.559577 + 0.828778i 0.689036π0.689036\pi
500500 0 0
501501 −24.0000 −1.07224
502502 −3.00000 −0.133897
503503 6.00000 0.267527 0.133763 0.991013i 0.457294π-0.457294\pi
0.133763 + 0.991013i 0.457294π0.457294\pi
504504 8.00000 0.356348
505505 0 0
506506 −18.0000 −0.800198
507507 9.00000 0.399704
508508 −2.00000 −0.0887357
509509 24.0000 1.06378 0.531891 0.846813i 0.321482π-0.321482\pi
0.531891 + 0.846813i 0.321482π0.321482\pi
510510 0 0
511511 4.00000 0.176950
512512 1.00000 0.0441942
513513 0 0
514514 −3.00000 −0.132324
515515 0 0
516516 4.00000 0.176090
517517 0 0
518518 −40.0000 −1.75750
519519 6.00000 0.263371
520520 0 0
521521 −9.00000 −0.394297 −0.197149 0.980374i 0.563168π-0.563168\pi
−0.197149 + 0.980374i 0.563168π0.563168\pi
522522 0 0
523523 28.0000 1.22435 0.612177 0.790721i 0.290294π-0.290294\pi
0.612177 + 0.790721i 0.290294π0.290294\pi
524524 9.00000 0.393167
525525 −20.0000 −0.872872
526526 −12.0000 −0.523225
527527 12.0000 0.522728
528528 −3.00000 −0.130558
529529 13.0000 0.565217
530530 0 0
531531 −18.0000 −0.781133
532532 0 0
533533 18.0000 0.779667
534534 6.00000 0.259645
535535 0 0
536536 7.00000 0.302354
537537 9.00000 0.388379
538538 −12.0000 −0.517357
539539 27.0000 1.16297
540540 0 0
541541 44.0000 1.89171 0.945854 0.324593i 0.105227π-0.105227\pi
0.945854 + 0.324593i 0.105227π0.105227\pi
542542 −16.0000 −0.687259
543543 2.00000 0.0858282
544544 −6.00000 −0.257248
545545 0 0
546546 −8.00000 −0.342368
547547 4.00000 0.171028 0.0855138 0.996337i 0.472747π-0.472747\pi
0.0855138 + 0.996337i 0.472747π0.472747\pi
548548 9.00000 0.384461
549549 8.00000 0.341432
550550 −15.0000 −0.639602
551551 0 0
552552 6.00000 0.255377
553553 −16.0000 −0.680389
554554 8.00000 0.339887
555555 0 0
556556 11.0000 0.466504
557557 24.0000 1.01691 0.508456 0.861088i 0.330216π-0.330216\pi
0.508456 + 0.861088i 0.330216π0.330216\pi
558558 4.00000 0.169334
559559 8.00000 0.338364
560560 0 0
561561 18.0000 0.759961
562562 −27.0000 −1.13893
563563 21.0000 0.885044 0.442522 0.896758i 0.354084π-0.354084\pi
0.442522 + 0.896758i 0.354084π0.354084\pi
564564 0 0
565565 0 0
566566 5.00000 0.210166
567567 −4.00000 −0.167984
568568 6.00000 0.251754
569569 6.00000 0.251533 0.125767 0.992060i 0.459861π-0.459861\pi
0.125767 + 0.992060i 0.459861π0.459861\pi
570570 0 0
571571 −7.00000 −0.292941 −0.146470 0.989215i 0.546791π-0.546791\pi
−0.146470 + 0.989215i 0.546791π0.546791\pi
572572 −6.00000 −0.250873
573573 −12.0000 −0.501307
574574 36.0000 1.50261
575575 30.0000 1.25109
576576 −2.00000 −0.0833333
577577 11.0000 0.457936 0.228968 0.973434i 0.426465π-0.426465\pi
0.228968 + 0.973434i 0.426465π0.426465\pi
578578 19.0000 0.790296
579579 2.00000 0.0831172
580580 0 0
581581 −12.0000 −0.497844
582582 17.0000 0.704673
583583 −18.0000 −0.745484
584584 −1.00000 −0.0413803
585585 0 0
586586 −24.0000 −0.991431
587587 −12.0000 −0.495293 −0.247647 0.968850i 0.579657π-0.579657\pi
−0.247647 + 0.968850i 0.579657π0.579657\pi
588588 −9.00000 −0.371154
589589 0 0
590590 0 0
591591 −18.0000 −0.740421
592592 10.0000 0.410997
593593 −21.0000 −0.862367 −0.431183 0.902264i 0.641904π-0.641904\pi
−0.431183 + 0.902264i 0.641904π0.641904\pi
594594 15.0000 0.615457
595595 0 0
596596 18.0000 0.737309
597597 10.0000 0.409273
598598 12.0000 0.490716
599599 6.00000 0.245153 0.122577 0.992459i 0.460884π-0.460884\pi
0.122577 + 0.992459i 0.460884π0.460884\pi
600600 5.00000 0.204124
601601 13.0000 0.530281 0.265141 0.964210i 0.414582π-0.414582\pi
0.265141 + 0.964210i 0.414582π0.414582\pi
602602 16.0000 0.652111
603603 −14.0000 −0.570124
604604 10.0000 0.406894
605605 0 0
606606 0 0
607607 −20.0000 −0.811775 −0.405887 0.913923i 0.633038π-0.633038\pi
−0.405887 + 0.913923i 0.633038π0.633038\pi
608608 0 0
609609 0 0
610610 0 0
611611 0 0
612612 12.0000 0.485071
613613 2.00000 0.0807792 0.0403896 0.999184i 0.487140π-0.487140\pi
0.0403896 + 0.999184i 0.487140π0.487140\pi
614614 7.00000 0.282497
615615 0 0
616616 −12.0000 −0.483494
617617 3.00000 0.120775 0.0603877 0.998175i 0.480766π-0.480766\pi
0.0603877 + 0.998175i 0.480766π0.480766\pi
618618 2.00000 0.0804518
619619 −4.00000 −0.160774 −0.0803868 0.996764i 0.525616π-0.525616\pi
−0.0803868 + 0.996764i 0.525616π0.525616\pi
620620 0 0
621621 −30.0000 −1.20386
622622 −30.0000 −1.20289
623623 24.0000 0.961540
624624 2.00000 0.0800641
625625 25.0000 1.00000
626626 −19.0000 −0.759393
627627 0 0
628628 −16.0000 −0.638470
629629 −60.0000 −2.39236
630630 0 0
631631 −28.0000 −1.11466 −0.557331 0.830290i 0.688175π-0.688175\pi
−0.557331 + 0.830290i 0.688175π0.688175\pi
632632 4.00000 0.159111
633633 20.0000 0.794929
634634 18.0000 0.714871
635635 0 0
636636 6.00000 0.237915
637637 −18.0000 −0.713186
638638 0 0
639639 −12.0000 −0.474713
640640 0 0
641641 39.0000 1.54041 0.770204 0.637798i 0.220155π-0.220155\pi
0.770204 + 0.637798i 0.220155π0.220155\pi
642642 0 0
643643 −43.0000 −1.69575 −0.847877 0.530193i 0.822120π-0.822120\pi
−0.847877 + 0.530193i 0.822120π0.822120\pi
644644 24.0000 0.945732
645645 0 0
646646 0 0
647647 18.0000 0.707653 0.353827 0.935311i 0.384880π-0.384880\pi
0.353827 + 0.935311i 0.384880π0.384880\pi
648648 1.00000 0.0392837
649649 27.0000 1.05984
650650 10.0000 0.392232
651651 −8.00000 −0.313545
652652 −19.0000 −0.744097
653653 −12.0000 −0.469596 −0.234798 0.972044i 0.575443π-0.575443\pi
−0.234798 + 0.972044i 0.575443π0.575443\pi
654654 −16.0000 −0.625650
655655 0 0
656656 −9.00000 −0.351391
657657 2.00000 0.0780274
658658 0 0
659659 −36.0000 −1.40236 −0.701180 0.712984i 0.747343π-0.747343\pi
−0.701180 + 0.712984i 0.747343π0.747343\pi
660660 0 0
661661 40.0000 1.55582 0.777910 0.628376i 0.216280π-0.216280\pi
0.777910 + 0.628376i 0.216280π0.216280\pi
662662 −5.00000 −0.194331
663663 −12.0000 −0.466041
664664 3.00000 0.116423
665665 0 0
666666 −20.0000 −0.774984
667667 0 0
668668 24.0000 0.928588
669669 14.0000 0.541271
670670 0 0
671671 −12.0000 −0.463255
672672 4.00000 0.154303
673673 −14.0000 −0.539660 −0.269830 0.962908i 0.586968π-0.586968\pi
−0.269830 + 0.962908i 0.586968π0.586968\pi
674674 −11.0000 −0.423704
675675 −25.0000 −0.962250
676676 −9.00000 −0.346154
677677 42.0000 1.61419 0.807096 0.590421i 0.201038π-0.201038\pi
0.807096 + 0.590421i 0.201038π0.201038\pi
678678 15.0000 0.576072
679679 68.0000 2.60960
680680 0 0
681681 3.00000 0.114960
682682 −6.00000 −0.229752
683683 36.0000 1.37750 0.688751 0.724998i 0.258159π-0.258159\pi
0.688751 + 0.724998i 0.258159π0.258159\pi
684684 0 0
685685 0 0
686686 −8.00000 −0.305441
687687 16.0000 0.610438
688688 −4.00000 −0.152499
689689 12.0000 0.457164
690690 0 0
691691 44.0000 1.67384 0.836919 0.547326i 0.184354π-0.184354\pi
0.836919 + 0.547326i 0.184354π0.184354\pi
692692 −6.00000 −0.228086
693693 24.0000 0.911685
694694 −9.00000 −0.341635
695695 0 0
696696 0 0
697697 54.0000 2.04540
698698 −4.00000 −0.151402
699699 −3.00000 −0.113470
700700 20.0000 0.755929
701701 −24.0000 −0.906467 −0.453234 0.891392i 0.649730π-0.649730\pi
−0.453234 + 0.891392i 0.649730π0.649730\pi
702702 −10.0000 −0.377426
703703 0 0
704704 3.00000 0.113067
705705 0 0
706706 3.00000 0.112906
707707 0 0
708708 −9.00000 −0.338241
709709 14.0000 0.525781 0.262891 0.964826i 0.415324π-0.415324\pi
0.262891 + 0.964826i 0.415324π0.415324\pi
710710 0 0
711711 −8.00000 −0.300023
712712 −6.00000 −0.224860
713713 12.0000 0.449404
714714 −24.0000 −0.898177
715715 0 0
716716 −9.00000 −0.336346
717717 12.0000 0.448148
718718 −6.00000 −0.223918
719719 30.0000 1.11881 0.559406 0.828894i 0.311029π-0.311029\pi
0.559406 + 0.828894i 0.311029π0.311029\pi
720720 0 0
721721 8.00000 0.297936
722722 0 0
723723 5.00000 0.185952
724724 −2.00000 −0.0743294
725725 0 0
726726 2.00000 0.0742270
727727 32.0000 1.18681 0.593407 0.804902i 0.297782π-0.297782\pi
0.593407 + 0.804902i 0.297782π0.297782\pi
728728 8.00000 0.296500
729729 13.0000 0.481481
730730 0 0
731731 24.0000 0.887672
732732 4.00000 0.147844
733733 −22.0000 −0.812589 −0.406294 0.913742i 0.633179π-0.633179\pi
−0.406294 + 0.913742i 0.633179π0.633179\pi
734734 −22.0000 −0.812035
735735 0 0
736736 −6.00000 −0.221163
737737 21.0000 0.773545
738738 18.0000 0.662589
739739 35.0000 1.28750 0.643748 0.765238i 0.277379π-0.277379\pi
0.643748 + 0.765238i 0.277379π0.277379\pi
740740 0 0
741741 0 0
742742 24.0000 0.881068
743743 18.0000 0.660356 0.330178 0.943919i 0.392891π-0.392891\pi
0.330178 + 0.943919i 0.392891π0.392891\pi
744744 2.00000 0.0733236
745745 0 0
746746 4.00000 0.146450
747747 −6.00000 −0.219529
748748 −18.0000 −0.658145
749749 0 0
750750 0 0
751751 −38.0000 −1.38664 −0.693320 0.720630i 0.743853π-0.743853\pi
−0.693320 + 0.720630i 0.743853π0.743853\pi
752752 0 0
753753 3.00000 0.109326
754754 0 0
755755 0 0
756756 −20.0000 −0.727393
757757 −10.0000 −0.363456 −0.181728 0.983349i 0.558169π-0.558169\pi
−0.181728 + 0.983349i 0.558169π0.558169\pi
758758 28.0000 1.01701
759759 18.0000 0.653359
760760 0 0
761761 −39.0000 −1.41375 −0.706874 0.707339i 0.749895π-0.749895\pi
−0.706874 + 0.707339i 0.749895π0.749895\pi
762762 2.00000 0.0724524
763763 −64.0000 −2.31696
764764 12.0000 0.434145
765765 0 0
766766 36.0000 1.30073
767767 −18.0000 −0.649942
768768 −1.00000 −0.0360844
769769 2.00000 0.0721218 0.0360609 0.999350i 0.488519π-0.488519\pi
0.0360609 + 0.999350i 0.488519π0.488519\pi
770770 0 0
771771 3.00000 0.108042
772772 −2.00000 −0.0719816
773773 48.0000 1.72644 0.863220 0.504828i 0.168444π-0.168444\pi
0.863220 + 0.504828i 0.168444π0.168444\pi
774774 8.00000 0.287554
775775 10.0000 0.359211
776776 −17.0000 −0.610264
777777 40.0000 1.43499
778778 −36.0000 −1.29066
779779 0 0
780780 0 0
781781 18.0000 0.644091
782782 36.0000 1.28736
783783 0 0
784784 9.00000 0.321429
785785 0 0
786786 −9.00000 −0.321019
787787 7.00000 0.249523 0.124762 0.992187i 0.460183π-0.460183\pi
0.124762 + 0.992187i 0.460183π0.460183\pi
788788 18.0000 0.641223
789789 12.0000 0.427211
790790 0 0
791791 60.0000 2.13335
792792 −6.00000 −0.213201
793793 8.00000 0.284088
794794 −10.0000 −0.354887
795795 0 0
796796 −10.0000 −0.354441
797797 −6.00000 −0.212531 −0.106265 0.994338i 0.533889π-0.533889\pi
−0.106265 + 0.994338i 0.533889π0.533889\pi
798798 0 0
799799 0 0
800800 −5.00000 −0.176777
801801 12.0000 0.423999
802802 27.0000 0.953403
803803 −3.00000 −0.105868
804804 −7.00000 −0.246871
805805 0 0
806806 4.00000 0.140894
807807 12.0000 0.422420
808808 0 0
809809 45.0000 1.58212 0.791058 0.611741i 0.209531π-0.209531\pi
0.791058 + 0.611741i 0.209531π0.209531\pi
810810 0 0
811811 16.0000 0.561836 0.280918 0.959732i 0.409361π-0.409361\pi
0.280918 + 0.959732i 0.409361π0.409361\pi
812812 0 0
813813 16.0000 0.561144
814814 30.0000 1.05150
815815 0 0
816816 6.00000 0.210042
817817 0 0
818818 −5.00000 −0.174821
819819 −16.0000 −0.559085
820820 0 0
821821 18.0000 0.628204 0.314102 0.949389i 0.398297π-0.398297\pi
0.314102 + 0.949389i 0.398297π0.398297\pi
822822 −9.00000 −0.313911
823823 14.0000 0.488009 0.244005 0.969774i 0.421539π-0.421539\pi
0.244005 + 0.969774i 0.421539π0.421539\pi
824824 −2.00000 −0.0696733
825825 15.0000 0.522233
826826 −36.0000 −1.25260
827827 39.0000 1.35616 0.678081 0.734987i 0.262812π-0.262812\pi
0.678081 + 0.734987i 0.262812π0.262812\pi
828828 12.0000 0.417029
829829 −44.0000 −1.52818 −0.764092 0.645108i 0.776812π-0.776812\pi
−0.764092 + 0.645108i 0.776812π0.776812\pi
830830 0 0
831831 −8.00000 −0.277517
832832 −2.00000 −0.0693375
833833 −54.0000 −1.87099
834834 −11.0000 −0.380899
835835 0 0
836836 0 0
837837 −10.0000 −0.345651
838838 −12.0000 −0.414533
839839 12.0000 0.414286 0.207143 0.978311i 0.433583π-0.433583\pi
0.207143 + 0.978311i 0.433583π0.433583\pi
840840 0 0
841841 −29.0000 −1.00000
842842 10.0000 0.344623
843843 27.0000 0.929929
844844 −20.0000 −0.688428
845845 0 0
846846 0 0
847847 8.00000 0.274883
848848 −6.00000 −0.206041
849849 −5.00000 −0.171600
850850 30.0000 1.02899
851851 −60.0000 −2.05677
852852 −6.00000 −0.205557
853853 −22.0000 −0.753266 −0.376633 0.926363i 0.622918π-0.622918\pi
−0.376633 + 0.926363i 0.622918π0.622918\pi
854854 16.0000 0.547509
855855 0 0
856856 0 0
857857 3.00000 0.102478 0.0512390 0.998686i 0.483683π-0.483683\pi
0.0512390 + 0.998686i 0.483683π0.483683\pi
858858 6.00000 0.204837
859859 −43.0000 −1.46714 −0.733571 0.679613i 0.762148π-0.762148\pi
−0.733571 + 0.679613i 0.762148π0.762148\pi
860860 0 0
861861 −36.0000 −1.22688
862862 30.0000 1.02180
863863 −18.0000 −0.612727 −0.306364 0.951915i 0.599112π-0.599112\pi
−0.306364 + 0.951915i 0.599112π0.599112\pi
864864 5.00000 0.170103
865865 0 0
866866 −26.0000 −0.883516
867867 −19.0000 −0.645274
868868 8.00000 0.271538
869869 12.0000 0.407072
870870 0 0
871871 −14.0000 −0.474372
872872 16.0000 0.541828
873873 34.0000 1.15073
874874 0 0
875875 0 0
876876 1.00000 0.0337869
877877 −20.0000 −0.675352 −0.337676 0.941262i 0.609641π-0.609641\pi
−0.337676 + 0.941262i 0.609641π0.609641\pi
878878 −14.0000 −0.472477
879879 24.0000 0.809500
880880 0 0
881881 −9.00000 −0.303218 −0.151609 0.988441i 0.548445π-0.548445\pi
−0.151609 + 0.988441i 0.548445π0.548445\pi
882882 −18.0000 −0.606092
883883 −19.0000 −0.639401 −0.319700 0.947519i 0.603582π-0.603582\pi
−0.319700 + 0.947519i 0.603582π0.603582\pi
884884 12.0000 0.403604
885885 0 0
886886 9.00000 0.302361
887887 −48.0000 −1.61168 −0.805841 0.592132i 0.798286π-0.798286\pi
−0.805841 + 0.592132i 0.798286π0.798286\pi
888888 −10.0000 −0.335578
889889 8.00000 0.268311
890890 0 0
891891 3.00000 0.100504
892892 −14.0000 −0.468755
893893 0 0
894894 −18.0000 −0.602010
895895 0 0
896896 −4.00000 −0.133631
897897 −12.0000 −0.400668
898898 −9.00000 −0.300334
899899 0 0
900900 10.0000 0.333333
901901 36.0000 1.19933
902902 −27.0000 −0.899002
903903 −16.0000 −0.532447
904904 −15.0000 −0.498893
905905 0 0
906906 −10.0000 −0.332228
907907 −17.0000 −0.564476 −0.282238 0.959344i 0.591077π-0.591077\pi
−0.282238 + 0.959344i 0.591077π0.591077\pi
908908 −3.00000 −0.0995585
909909 0 0
910910 0 0
911911 −30.0000 −0.993944 −0.496972 0.867766i 0.665555π-0.665555\pi
−0.496972 + 0.867766i 0.665555π0.665555\pi
912912 0 0
913913 9.00000 0.297857
914914 5.00000 0.165385
915915 0 0
916916 −16.0000 −0.528655
917917 −36.0000 −1.18882
918918 −30.0000 −0.990148
919919 −10.0000 −0.329870 −0.164935 0.986304i 0.552741π-0.552741\pi
−0.164935 + 0.986304i 0.552741π0.552741\pi
920920 0 0
921921 −7.00000 −0.230658
922922 6.00000 0.197599
923923 −12.0000 −0.394985
924924 12.0000 0.394771
925925 −50.0000 −1.64399
926926 −34.0000 −1.11731
927927 4.00000 0.131377
928928 0 0
929929 −3.00000 −0.0984268 −0.0492134 0.998788i 0.515671π-0.515671\pi
−0.0492134 + 0.998788i 0.515671π0.515671\pi
930930 0 0
931931 0 0
932932 3.00000 0.0982683
933933 30.0000 0.982156
934934 −27.0000 −0.883467
935935 0 0
936936 4.00000 0.130744
937937 35.0000 1.14340 0.571700 0.820463i 0.306284π-0.306284\pi
0.571700 + 0.820463i 0.306284π0.306284\pi
938938 −28.0000 −0.914232
939939 19.0000 0.620042
940940 0 0
941941 42.0000 1.36916 0.684580 0.728937i 0.259985π-0.259985\pi
0.684580 + 0.728937i 0.259985π0.259985\pi
942942 16.0000 0.521308
943943 54.0000 1.75848
944944 9.00000 0.292925
945945 0 0
946946 −12.0000 −0.390154
947947 60.0000 1.94974 0.974869 0.222779i 0.0715128π-0.0715128\pi
0.974869 + 0.222779i 0.0715128π0.0715128\pi
948948 −4.00000 −0.129914
949949 2.00000 0.0649227
950950 0 0
951951 −18.0000 −0.583690
952952 24.0000 0.777844
953953 15.0000 0.485898 0.242949 0.970039i 0.421885π-0.421885\pi
0.242949 + 0.970039i 0.421885π0.421885\pi
954954 12.0000 0.388514
955955 0 0
956956 −12.0000 −0.388108
957957 0 0
958958 36.0000 1.16311
959959 −36.0000 −1.16250
960960 0 0
961961 −27.0000 −0.870968
962962 −20.0000 −0.644826
963963 0 0
964964 −5.00000 −0.161039
965965 0 0
966966 −24.0000 −0.772187
967967 −34.0000 −1.09337 −0.546683 0.837340i 0.684110π-0.684110\pi
−0.546683 + 0.837340i 0.684110π0.684110\pi
968968 −2.00000 −0.0642824
969969 0 0
970970 0 0
971971 −21.0000 −0.673922 −0.336961 0.941519i 0.609399π-0.609399\pi
−0.336961 + 0.941519i 0.609399π0.609399\pi
972972 −16.0000 −0.513200
973973 −44.0000 −1.41058
974974 −2.00000 −0.0640841
975975 −10.0000 −0.320256
976976 −4.00000 −0.128037
977977 −33.0000 −1.05576 −0.527882 0.849318i 0.677014π-0.677014\pi
−0.527882 + 0.849318i 0.677014π0.677014\pi
978978 19.0000 0.607553
979979 −18.0000 −0.575282
980980 0 0
981981 −32.0000 −1.02168
982982 0 0
983983 −24.0000 −0.765481 −0.382741 0.923856i 0.625020π-0.625020\pi
−0.382741 + 0.923856i 0.625020π0.625020\pi
984984 9.00000 0.286910
985985 0 0
986986 0 0
987987 0 0
988988 0 0
989989 24.0000 0.763156
990990 0 0
991991 −8.00000 −0.254128 −0.127064 0.991894i 0.540555π-0.540555\pi
−0.127064 + 0.991894i 0.540555π0.540555\pi
992992 −2.00000 −0.0635001
993993 5.00000 0.158670
994994 −24.0000 −0.761234
995995 0 0
996996 −3.00000 −0.0950586
997997 −4.00000 −0.126681 −0.0633406 0.997992i 0.520175π-0.520175\pi
−0.0633406 + 0.997992i 0.520175π0.520175\pi
998998 −25.0000 −0.791361
999999 50.0000 1.58193
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 722.2.a.d.1.1 1
3.2 odd 2 6498.2.a.e.1.1 1
4.3 odd 2 5776.2.a.n.1.1 1
19.2 odd 18 722.2.e.j.99.1 6
19.3 odd 18 722.2.e.j.389.1 6
19.4 even 9 722.2.e.i.415.1 6
19.5 even 9 722.2.e.i.595.1 6
19.6 even 9 722.2.e.i.245.1 6
19.7 even 3 722.2.c.b.429.1 2
19.8 odd 6 38.2.c.a.7.1 2
19.9 even 9 722.2.e.i.423.1 6
19.10 odd 18 722.2.e.j.423.1 6
19.11 even 3 722.2.c.b.653.1 2
19.12 odd 6 38.2.c.a.11.1 yes 2
19.13 odd 18 722.2.e.j.245.1 6
19.14 odd 18 722.2.e.j.595.1 6
19.15 odd 18 722.2.e.j.415.1 6
19.16 even 9 722.2.e.i.389.1 6
19.17 even 9 722.2.e.i.99.1 6
19.18 odd 2 722.2.a.c.1.1 1
57.8 even 6 342.2.g.b.235.1 2
57.50 even 6 342.2.g.b.163.1 2
57.56 even 2 6498.2.a.s.1.1 1
76.27 even 6 304.2.i.c.273.1 2
76.31 even 6 304.2.i.c.49.1 2
76.75 even 2 5776.2.a.g.1.1 1
95.8 even 12 950.2.j.e.349.2 4
95.12 even 12 950.2.j.e.49.2 4
95.27 even 12 950.2.j.e.349.1 4
95.69 odd 6 950.2.e.d.201.1 2
95.84 odd 6 950.2.e.d.501.1 2
95.88 even 12 950.2.j.e.49.1 4
152.27 even 6 1216.2.i.d.577.1 2
152.69 odd 6 1216.2.i.h.961.1 2
152.107 even 6 1216.2.i.d.961.1 2
152.141 odd 6 1216.2.i.h.577.1 2
228.107 odd 6 2736.2.s.m.1873.1 2
228.179 odd 6 2736.2.s.m.577.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.2.c.a.7.1 2 19.8 odd 6
38.2.c.a.11.1 yes 2 19.12 odd 6
304.2.i.c.49.1 2 76.31 even 6
304.2.i.c.273.1 2 76.27 even 6
342.2.g.b.163.1 2 57.50 even 6
342.2.g.b.235.1 2 57.8 even 6
722.2.a.c.1.1 1 19.18 odd 2
722.2.a.d.1.1 1 1.1 even 1 trivial
722.2.c.b.429.1 2 19.7 even 3
722.2.c.b.653.1 2 19.11 even 3
722.2.e.i.99.1 6 19.17 even 9
722.2.e.i.245.1 6 19.6 even 9
722.2.e.i.389.1 6 19.16 even 9
722.2.e.i.415.1 6 19.4 even 9
722.2.e.i.423.1 6 19.9 even 9
722.2.e.i.595.1 6 19.5 even 9
722.2.e.j.99.1 6 19.2 odd 18
722.2.e.j.245.1 6 19.13 odd 18
722.2.e.j.389.1 6 19.3 odd 18
722.2.e.j.415.1 6 19.15 odd 18
722.2.e.j.423.1 6 19.10 odd 18
722.2.e.j.595.1 6 19.14 odd 18
950.2.e.d.201.1 2 95.69 odd 6
950.2.e.d.501.1 2 95.84 odd 6
950.2.j.e.49.1 4 95.88 even 12
950.2.j.e.49.2 4 95.12 even 12
950.2.j.e.349.1 4 95.27 even 12
950.2.j.e.349.2 4 95.8 even 12
1216.2.i.d.577.1 2 152.27 even 6
1216.2.i.d.961.1 2 152.107 even 6
1216.2.i.h.577.1 2 152.141 odd 6
1216.2.i.h.961.1 2 152.69 odd 6
2736.2.s.m.577.1 2 228.179 odd 6
2736.2.s.m.1873.1 2 228.107 odd 6
5776.2.a.g.1.1 1 76.75 even 2
5776.2.a.n.1.1 1 4.3 odd 2
6498.2.a.e.1.1 1 3.2 odd 2
6498.2.a.s.1.1 1 57.56 even 2