Properties

Label 2793.2.a.x.1.3
Level 27932793
Weight 22
Character 2793.1
Self dual yes
Analytic conductor 22.30222.302
Analytic rank 11
Dimension 33
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] = [2793,2,Mod(1,2793)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2793, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("2793.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 2793=37219 2793 = 3 \cdot 7^{2} \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2793.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: 22.302217284522.3022172845
Analytic rank: 11
Dimension: 33
Coefficient field: 3.3.148.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x3x23x+1 x^{3} - x^{2} - 3x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 399)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.3
Root 2.170092.17009 of defining polynomial
Character χ\chi == 2793.1

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+2.17009q2+1.00000q3+2.70928q43.70928q5+2.17009q6+1.53919q8+1.00000q98.04945q101.07838q11+2.70928q120.921622q133.70928q152.07838q160.290725q17+2.17009q181.00000q1910.0494q202.34017q227.60197q23+1.53919q24+8.75872q252.00000q26+1.00000q27+5.36910q298.04945q308.49693q317.58864q321.07838q330.630898q34+2.70928q3610.6803q372.17009q380.921622q395.70928q40+3.75872q418.49693q432.92162q443.70928q4516.4969q46+6.20620q472.07838q48+19.0072q500.290725q512.49693q52+4.78765q53+2.17009q54+4.00000q551.00000q57+11.6514q584.00000q5910.0494q60+2.68035q6118.4391q6212.3112q64+3.41855q652.34017q66+1.26180q670.787653q687.60197q693.86603q71+1.53919q721.41855q7323.1773q74+8.75872q752.70928q762.00000q7810.5236q79+7.70928q80+1.00000q81+8.15676q828.72979q83+1.07838q8518.4391q86+5.36910q871.65983q88+3.75872q898.04945q9020.5958q928.49693q93+13.4680q94+3.70928q957.58864q96+13.5174q971.07838q99+O(q100)q+2.17009 q^{2} +1.00000 q^{3} +2.70928 q^{4} -3.70928 q^{5} +2.17009 q^{6} +1.53919 q^{8} +1.00000 q^{9} -8.04945 q^{10} -1.07838 q^{11} +2.70928 q^{12} -0.921622 q^{13} -3.70928 q^{15} -2.07838 q^{16} -0.290725 q^{17} +2.17009 q^{18} -1.00000 q^{19} -10.0494 q^{20} -2.34017 q^{22} -7.60197 q^{23} +1.53919 q^{24} +8.75872 q^{25} -2.00000 q^{26} +1.00000 q^{27} +5.36910 q^{29} -8.04945 q^{30} -8.49693 q^{31} -7.58864 q^{32} -1.07838 q^{33} -0.630898 q^{34} +2.70928 q^{36} -10.6803 q^{37} -2.17009 q^{38} -0.921622 q^{39} -5.70928 q^{40} +3.75872 q^{41} -8.49693 q^{43} -2.92162 q^{44} -3.70928 q^{45} -16.4969 q^{46} +6.20620 q^{47} -2.07838 q^{48} +19.0072 q^{50} -0.290725 q^{51} -2.49693 q^{52} +4.78765 q^{53} +2.17009 q^{54} +4.00000 q^{55} -1.00000 q^{57} +11.6514 q^{58} -4.00000 q^{59} -10.0494 q^{60} +2.68035 q^{61} -18.4391 q^{62} -12.3112 q^{64} +3.41855 q^{65} -2.34017 q^{66} +1.26180 q^{67} -0.787653 q^{68} -7.60197 q^{69} -3.86603 q^{71} +1.53919 q^{72} -1.41855 q^{73} -23.1773 q^{74} +8.75872 q^{75} -2.70928 q^{76} -2.00000 q^{78} -10.5236 q^{79} +7.70928 q^{80} +1.00000 q^{81} +8.15676 q^{82} -8.72979 q^{83} +1.07838 q^{85} -18.4391 q^{86} +5.36910 q^{87} -1.65983 q^{88} +3.75872 q^{89} -8.04945 q^{90} -20.5958 q^{92} -8.49693 q^{93} +13.4680 q^{94} +3.70928 q^{95} -7.58864 q^{96} +13.5174 q^{97} -1.07838 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q+q2+3q3+q44q5+q6+3q8+3q96q10+q126q134q153q168q17+q183q1912q20+4q224q23+3q24+10q97+O(q100) 3 q + q^{2} + 3 q^{3} + q^{4} - 4 q^{5} + q^{6} + 3 q^{8} + 3 q^{9} - 6 q^{10} + q^{12} - 6 q^{13} - 4 q^{15} - 3 q^{16} - 8 q^{17} + q^{18} - 3 q^{19} - 12 q^{20} + 4 q^{22} - 4 q^{23} + 3 q^{24}+ \cdots - 10 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 2.17009 1.53448 0.767241 0.641358i 0.221629π-0.221629\pi
0.767241 + 0.641358i 0.221629π0.221629\pi
33 1.00000 0.577350
44 2.70928 1.35464
55 −3.70928 −1.65884 −0.829419 0.558627i 0.811328π-0.811328\pi
−0.829419 + 0.558627i 0.811328π0.811328\pi
66 2.17009 0.885934
77 0 0
88 1.53919 0.544185
99 1.00000 0.333333
1010 −8.04945 −2.54546
1111 −1.07838 −0.325143 −0.162572 0.986697i 0.551979π-0.551979\pi
−0.162572 + 0.986697i 0.551979π0.551979\pi
1212 2.70928 0.782100
1313 −0.921622 −0.255612 −0.127806 0.991799i 0.540793π-0.540793\pi
−0.127806 + 0.991799i 0.540793π0.540793\pi
1414 0 0
1515 −3.70928 −0.957731
1616 −2.07838 −0.519594
1717 −0.290725 −0.0705111 −0.0352555 0.999378i 0.511225π-0.511225\pi
−0.0352555 + 0.999378i 0.511225π0.511225\pi
1818 2.17009 0.511494
1919 −1.00000 −0.229416
2020 −10.0494 −2.24712
2121 0 0
2222 −2.34017 −0.498927
2323 −7.60197 −1.58512 −0.792560 0.609794i 0.791252π-0.791252\pi
−0.792560 + 0.609794i 0.791252π0.791252\pi
2424 1.53919 0.314186
2525 8.75872 1.75174
2626 −2.00000 −0.392232
2727 1.00000 0.192450
2828 0 0
2929 5.36910 0.997017 0.498509 0.866885i 0.333881π-0.333881\pi
0.498509 + 0.866885i 0.333881π0.333881\pi
3030 −8.04945 −1.46962
3131 −8.49693 −1.52609 −0.763047 0.646343i 0.776297π-0.776297\pi
−0.763047 + 0.646343i 0.776297π0.776297\pi
3232 −7.58864 −1.34149
3333 −1.07838 −0.187721
3434 −0.630898 −0.108198
3535 0 0
3636 2.70928 0.451546
3737 −10.6803 −1.75584 −0.877919 0.478809i 0.841069π-0.841069\pi
−0.877919 + 0.478809i 0.841069π0.841069\pi
3838 −2.17009 −0.352035
3939 −0.921622 −0.147578
4040 −5.70928 −0.902716
4141 3.75872 0.587014 0.293507 0.955957i 0.405178π-0.405178\pi
0.293507 + 0.955957i 0.405178π0.405178\pi
4242 0 0
4343 −8.49693 −1.29577 −0.647885 0.761738i 0.724346π-0.724346\pi
−0.647885 + 0.761738i 0.724346π0.724346\pi
4444 −2.92162 −0.440451
4545 −3.70928 −0.552946
4646 −16.4969 −2.43234
4747 6.20620 0.905268 0.452634 0.891696i 0.350484π-0.350484\pi
0.452634 + 0.891696i 0.350484π0.350484\pi
4848 −2.07838 −0.299988
4949 0 0
5050 19.0072 2.68802
5151 −0.290725 −0.0407096
5252 −2.49693 −0.346262
5353 4.78765 0.657635 0.328817 0.944394i 0.393350π-0.393350\pi
0.328817 + 0.944394i 0.393350π0.393350\pi
5454 2.17009 0.295311
5555 4.00000 0.539360
5656 0 0
5757 −1.00000 −0.132453
5858 11.6514 1.52991
5959 −4.00000 −0.520756 −0.260378 0.965507i 0.583847π-0.583847\pi
−0.260378 + 0.965507i 0.583847π0.583847\pi
6060 −10.0494 −1.29738
6161 2.68035 0.343183 0.171592 0.985168i 0.445109π-0.445109\pi
0.171592 + 0.985168i 0.445109π0.445109\pi
6262 −18.4391 −2.34176
6363 0 0
6464 −12.3112 −1.53891
6565 3.41855 0.424019
6666 −2.34017 −0.288055
6767 1.26180 0.154153 0.0770764 0.997025i 0.475441π-0.475441\pi
0.0770764 + 0.997025i 0.475441π0.475441\pi
6868 −0.787653 −0.0955170
6969 −7.60197 −0.915169
7070 0 0
7171 −3.86603 −0.458813 −0.229407 0.973331i 0.573679π-0.573679\pi
−0.229407 + 0.973331i 0.573679π0.573679\pi
7272 1.53919 0.181395
7373 −1.41855 −0.166029 −0.0830144 0.996548i 0.526455π-0.526455\pi
−0.0830144 + 0.996548i 0.526455π0.526455\pi
7474 −23.1773 −2.69430
7575 8.75872 1.01137
7676 −2.70928 −0.310775
7777 0 0
7878 −2.00000 −0.226455
7979 −10.5236 −1.18400 −0.591998 0.805939i 0.701661π-0.701661\pi
−0.591998 + 0.805939i 0.701661π0.701661\pi
8080 7.70928 0.861923
8181 1.00000 0.111111
8282 8.15676 0.900763
8383 −8.72979 −0.958219 −0.479110 0.877755i 0.659040π-0.659040\pi
−0.479110 + 0.877755i 0.659040π0.659040\pi
8484 0 0
8585 1.07838 0.116966
8686 −18.4391 −1.98834
8787 5.36910 0.575628
8888 −1.65983 −0.176938
8989 3.75872 0.398424 0.199212 0.979956i 0.436162π-0.436162\pi
0.199212 + 0.979956i 0.436162π0.436162\pi
9090 −8.04945 −0.848486
9191 0 0
9292 −20.5958 −2.14726
9393 −8.49693 −0.881090
9494 13.4680 1.38912
9595 3.70928 0.380564
9696 −7.58864 −0.774512
9797 13.5174 1.37249 0.686244 0.727371i 0.259258π-0.259258\pi
0.686244 + 0.727371i 0.259258π0.259258\pi
9898 0 0
9999 −1.07838 −0.108381
100100 23.7298 2.37298
101101 2.44748 0.243533 0.121767 0.992559i 0.461144π-0.461144\pi
0.121767 + 0.992559i 0.461144π0.461144\pi
102102 −0.630898 −0.0624682
103103 −19.5174 −1.92311 −0.961556 0.274610i 0.911451π-0.911451\pi
−0.961556 + 0.274610i 0.911451π0.911451\pi
104104 −1.41855 −0.139100
105105 0 0
106106 10.3896 1.00913
107107 15.6514 1.51308 0.756540 0.653948i 0.226888π-0.226888\pi
0.756540 + 0.653948i 0.226888π0.226888\pi
108108 2.70928 0.260700
109109 14.0989 1.35043 0.675215 0.737621i 0.264051π-0.264051\pi
0.675215 + 0.737621i 0.264051π0.264051\pi
110110 8.68035 0.827639
111111 −10.6803 −1.01373
112112 0 0
113113 18.7298 1.76195 0.880975 0.473162i 0.156887π-0.156887\pi
0.880975 + 0.473162i 0.156887π0.156887\pi
114114 −2.17009 −0.203247
115115 28.1978 2.62946
116116 14.5464 1.35060
117117 −0.921622 −0.0852040
118118 −8.68035 −0.799091
119119 0 0
120120 −5.70928 −0.521183
121121 −9.83710 −0.894282
122122 5.81658 0.526609
123123 3.75872 0.338913
124124 −23.0205 −2.06730
125125 −13.9421 −1.24702
126126 0 0
127127 −15.7854 −1.40073 −0.700363 0.713787i 0.746979π-0.746979\pi
−0.700363 + 0.713787i 0.746979π0.746979\pi
128128 −11.5392 −1.01993
129129 −8.49693 −0.748113
130130 7.41855 0.650650
131131 −6.10731 −0.533598 −0.266799 0.963752i 0.585966π-0.585966\pi
−0.266799 + 0.963752i 0.585966π0.585966\pi
132132 −2.92162 −0.254295
133133 0 0
134134 2.73820 0.236545
135135 −3.70928 −0.319244
136136 −0.447480 −0.0383711
137137 18.9939 1.62275 0.811377 0.584523i 0.198718π-0.198718\pi
0.811377 + 0.584523i 0.198718π0.198718\pi
138138 −16.4969 −1.40431
139139 −0.894960 −0.0759095 −0.0379548 0.999279i 0.512084π-0.512084\pi
−0.0379548 + 0.999279i 0.512084π0.512084\pi
140140 0 0
141141 6.20620 0.522657
142142 −8.38962 −0.704041
143143 0.993857 0.0831105
144144 −2.07838 −0.173198
145145 −19.9155 −1.65389
146146 −3.07838 −0.254768
147147 0 0
148148 −28.9360 −2.37852
149149 20.9360 1.71514 0.857572 0.514364i 0.171972π-0.171972\pi
0.857572 + 0.514364i 0.171972π0.171972\pi
150150 19.0072 1.55193
151151 13.9421 1.13460 0.567298 0.823513i 0.307989π-0.307989\pi
0.567298 + 0.823513i 0.307989π0.307989\pi
152152 −1.53919 −0.124845
153153 −0.290725 −0.0235037
154154 0 0
155155 31.5174 2.53154
156156 −2.49693 −0.199914
157157 2.31351 0.184638 0.0923191 0.995729i 0.470572π-0.470572\pi
0.0923191 + 0.995729i 0.470572π0.470572\pi
158158 −22.8371 −1.81682
159159 4.78765 0.379686
160160 28.1483 2.22532
161161 0 0
162162 2.17009 0.170498
163163 −17.6598 −1.38322 −0.691612 0.722269i 0.743099π-0.743099\pi
−0.691612 + 0.722269i 0.743099π0.743099\pi
164164 10.1834 0.795191
165165 4.00000 0.311400
166166 −18.9444 −1.47037
167167 −3.05172 −0.236149 −0.118074 0.993005i 0.537672π-0.537672\pi
−0.118074 + 0.993005i 0.537672π0.537672\pi
168168 0 0
169169 −12.1506 −0.934662
170170 2.34017 0.179483
171171 −1.00000 −0.0764719
172172 −23.0205 −1.75530
173173 −9.60197 −0.730024 −0.365012 0.931003i 0.618935π-0.618935\pi
−0.365012 + 0.931003i 0.618935π0.618935\pi
174174 11.6514 0.883292
175175 0 0
176176 2.24128 0.168943
177177 −4.00000 −0.300658
178178 8.15676 0.611375
179179 −0.814315 −0.0608648 −0.0304324 0.999537i 0.509688π-0.509688\pi
−0.0304324 + 0.999537i 0.509688π0.509688\pi
180180 −10.0494 −0.749042
181181 −20.1568 −1.49824 −0.749120 0.662434i 0.769523π-0.769523\pi
−0.749120 + 0.662434i 0.769523π0.769523\pi
182182 0 0
183183 2.68035 0.198137
184184 −11.7009 −0.862599
185185 39.6163 2.91265
186186 −18.4391 −1.35202
187187 0.313511 0.0229262
188188 16.8143 1.22631
189189 0 0
190190 8.04945 0.583968
191191 5.44521 0.394002 0.197001 0.980403i 0.436880π-0.436880\pi
0.197001 + 0.980403i 0.436880π0.436880\pi
192192 −12.3112 −0.888487
193193 1.68649 0.121396 0.0606981 0.998156i 0.480667π-0.480667\pi
0.0606981 + 0.998156i 0.480667π0.480667\pi
194194 29.3340 2.10606
195195 3.41855 0.244808
196196 0 0
197197 −10.3668 −0.738606 −0.369303 0.929309i 0.620404π-0.620404\pi
−0.369303 + 0.929309i 0.620404π0.620404\pi
198198 −2.34017 −0.166309
199199 2.42469 0.171882 0.0859410 0.996300i 0.472610π-0.472610\pi
0.0859410 + 0.996300i 0.472610π0.472610\pi
200200 13.4813 0.953274
201201 1.26180 0.0890002
202202 5.31124 0.373698
203203 0 0
204204 −0.787653 −0.0551467
205205 −13.9421 −0.973761
206206 −42.3545 −2.95098
207207 −7.60197 −0.528373
208208 1.91548 0.132815
209209 1.07838 0.0745929
210210 0 0
211211 19.5174 1.34364 0.671818 0.740716i 0.265514π-0.265514\pi
0.671818 + 0.740716i 0.265514π0.265514\pi
212212 12.9711 0.890857
213213 −3.86603 −0.264896
214214 33.9649 2.32179
215215 31.5174 2.14947
216216 1.53919 0.104729
217217 0 0
218218 30.5958 2.07221
219219 −1.41855 −0.0958568
220220 10.8371 0.730637
221221 0.267938 0.0180235
222222 −23.1773 −1.55556
223223 −19.0205 −1.27371 −0.636854 0.770984i 0.719765π-0.719765\pi
−0.636854 + 0.770984i 0.719765π0.719765\pi
224224 0 0
225225 8.75872 0.583915
226226 40.6453 2.70368
227227 −11.7321 −0.778684 −0.389342 0.921093i 0.627298π-0.627298\pi
−0.389342 + 0.921093i 0.627298π0.627298\pi
228228 −2.70928 −0.179426
229229 27.4596 1.81458 0.907290 0.420505i 0.138147π-0.138147\pi
0.907290 + 0.420505i 0.138147π0.138147\pi
230230 61.1917 4.03486
231231 0 0
232232 8.26406 0.542562
233233 −5.10504 −0.334442 −0.167221 0.985919i 0.553479π-0.553479\pi
−0.167221 + 0.985919i 0.553479π0.553479\pi
234234 −2.00000 −0.130744
235235 −23.0205 −1.50169
236236 −10.8371 −0.705435
237237 −10.5236 −0.683581
238238 0 0
239239 −10.6537 −0.689130 −0.344565 0.938763i 0.611973π-0.611973\pi
−0.344565 + 0.938763i 0.611973π0.611973\pi
240240 7.70928 0.497632
241241 13.5174 0.870735 0.435368 0.900253i 0.356618π-0.356618\pi
0.435368 + 0.900253i 0.356618π0.356618\pi
242242 −21.3474 −1.37226
243243 1.00000 0.0641500
244244 7.26180 0.464889
245245 0 0
246246 8.15676 0.520056
247247 0.921622 0.0586414
248248 −13.0784 −0.830478
249249 −8.72979 −0.553228
250250 −30.2557 −1.91354
251251 18.2062 1.14917 0.574583 0.818447i 0.305164π-0.305164\pi
0.574583 + 0.818447i 0.305164π0.305164\pi
252252 0 0
253253 8.19779 0.515391
254254 −34.2557 −2.14939
255255 1.07838 0.0675306
256256 −0.418551 −0.0261594
257257 −12.3402 −0.769759 −0.384879 0.922967i 0.625757π-0.625757\pi
−0.384879 + 0.922967i 0.625757π0.625757\pi
258258 −18.4391 −1.14797
259259 0 0
260260 9.26180 0.574392
261261 5.36910 0.332339
262262 −13.2534 −0.818797
263263 7.50307 0.462659 0.231330 0.972875i 0.425692π-0.425692\pi
0.231330 + 0.972875i 0.425692π0.425692\pi
264264 −1.65983 −0.102155
265265 −17.7587 −1.09091
266266 0 0
267267 3.75872 0.230030
268268 3.41855 0.208821
269269 4.34017 0.264625 0.132313 0.991208i 0.457760π-0.457760\pi
0.132313 + 0.991208i 0.457760π0.457760\pi
270270 −8.04945 −0.489874
271271 −26.0410 −1.58188 −0.790940 0.611893i 0.790408π-0.790408\pi
−0.790940 + 0.611893i 0.790408π0.790408\pi
272272 0.604236 0.0366372
273273 0 0
274274 41.2183 2.49009
275275 −9.44521 −0.569568
276276 −20.5958 −1.23972
277277 6.59583 0.396305 0.198152 0.980171i 0.436506π-0.436506\pi
0.198152 + 0.980171i 0.436506π0.436506\pi
278278 −1.94214 −0.116482
279279 −8.49693 −0.508698
280280 0 0
281281 −11.6248 −0.693475 −0.346737 0.937962i 0.612710π-0.612710\pi
−0.346737 + 0.937962i 0.612710π0.612710\pi
282282 13.4680 0.802008
283283 17.9421 1.06655 0.533275 0.845942i 0.320961π-0.320961\pi
0.533275 + 0.845942i 0.320961π0.320961\pi
284284 −10.4741 −0.621526
285285 3.70928 0.219719
286286 2.15676 0.127532
287287 0 0
288288 −7.58864 −0.447165
289289 −16.9155 −0.995028
290290 −43.2183 −2.53787
291291 13.5174 0.792407
292292 −3.84324 −0.224909
293293 23.7587 1.38800 0.694000 0.719975i 0.255847π-0.255847\pi
0.694000 + 0.719975i 0.255847π0.255847\pi
294294 0 0
295295 14.8371 0.863849
296296 −16.4391 −0.955502
297297 −1.07838 −0.0625738
298298 45.4329 2.63186
299299 7.00614 0.405176
300300 23.7298 1.37004
301301 0 0
302302 30.2557 1.74102
303303 2.44748 0.140604
304304 2.07838 0.119203
305305 −9.94214 −0.569285
306306 −0.630898 −0.0360660
307307 24.0144 1.37057 0.685286 0.728274i 0.259677π-0.259677\pi
0.685286 + 0.728274i 0.259677π0.259677\pi
308308 0 0
309309 −19.5174 −1.11031
310310 68.3956 3.88461
311311 −22.9854 −1.30339 −0.651693 0.758483i 0.725941π-0.725941\pi
−0.651693 + 0.758483i 0.725941π0.725941\pi
312312 −1.41855 −0.0803096
313313 −0.523590 −0.0295951 −0.0147975 0.999891i 0.504710π-0.504710\pi
−0.0147975 + 0.999891i 0.504710π0.504710\pi
314314 5.02052 0.283324
315315 0 0
316316 −28.5113 −1.60389
317317 −17.1012 −0.960497 −0.480249 0.877132i 0.659454π-0.659454\pi
−0.480249 + 0.877132i 0.659454π0.659454\pi
318318 10.3896 0.582621
319319 −5.78992 −0.324173
320320 45.6658 2.55280
321321 15.6514 0.873577
322322 0 0
323323 0.290725 0.0161764
324324 2.70928 0.150515
325325 −8.07223 −0.447767
326326 −38.3234 −2.12253
327327 14.0989 0.779671
328328 5.78539 0.319444
329329 0 0
330330 8.68035 0.477837
331331 25.1461 1.38215 0.691077 0.722781i 0.257137π-0.257137\pi
0.691077 + 0.722781i 0.257137π0.257137\pi
332332 −23.6514 −1.29804
333333 −10.6803 −0.585279
334334 −6.62249 −0.362366
335335 −4.68035 −0.255715
336336 0 0
337337 −11.5753 −0.630547 −0.315274 0.949001i 0.602096π-0.602096\pi
−0.315274 + 0.949001i 0.602096π0.602096\pi
338338 −26.3679 −1.43422
339339 18.7298 1.01726
340340 2.92162 0.158447
341341 9.16290 0.496199
342342 −2.17009 −0.117345
343343 0 0
344344 −13.0784 −0.705139
345345 28.1978 1.51812
346346 −20.8371 −1.12021
347347 −32.0144 −1.71862 −0.859311 0.511454i 0.829107π-0.829107\pi
−0.859311 + 0.511454i 0.829107π0.829107\pi
348348 14.5464 0.779768
349349 2.36683 0.126694 0.0633469 0.997992i 0.479823π-0.479823\pi
0.0633469 + 0.997992i 0.479823π0.479823\pi
350350 0 0
351351 −0.921622 −0.0491926
352352 8.18342 0.436178
353353 −15.4413 −0.821859 −0.410930 0.911667i 0.634796π-0.634796\pi
−0.410930 + 0.911667i 0.634796π0.634796\pi
354354 −8.68035 −0.461355
355355 14.3402 0.761097
356356 10.1834 0.539720
357357 0 0
358358 −1.76713 −0.0933959
359359 23.4329 1.23674 0.618371 0.785886i 0.287793π-0.287793\pi
0.618371 + 0.785886i 0.287793π0.287793\pi
360360 −5.70928 −0.300905
361361 1.00000 0.0526316
362362 −43.7419 −2.29902
363363 −9.83710 −0.516314
364364 0 0
365365 5.26180 0.275415
366366 5.81658 0.304038
367367 31.3028 1.63399 0.816997 0.576642i 0.195637π-0.195637\pi
0.816997 + 0.576642i 0.195637π0.195637\pi
368368 15.7998 0.823620
369369 3.75872 0.195671
370370 85.9709 4.46941
371371 0 0
372372 −23.0205 −1.19356
373373 −23.6742 −1.22580 −0.612902 0.790159i 0.709998π-0.709998\pi
−0.612902 + 0.790159i 0.709998π0.709998\pi
374374 0.680346 0.0351799
375375 −13.9421 −0.719969
376376 9.55252 0.492634
377377 −4.94828 −0.254850
378378 0 0
379379 −7.41855 −0.381065 −0.190533 0.981681i 0.561022π-0.561022\pi
−0.190533 + 0.981681i 0.561022π0.561022\pi
380380 10.0494 0.515526
381381 −15.7854 −0.808710
382382 11.8166 0.604589
383383 7.10504 0.363051 0.181525 0.983386i 0.441897π-0.441897\pi
0.181525 + 0.983386i 0.441897π0.441897\pi
384384 −11.5392 −0.588857
385385 0 0
386386 3.65983 0.186280
387387 −8.49693 −0.431923
388388 36.6225 1.85923
389389 16.2557 0.824194 0.412097 0.911140i 0.364796π-0.364796\pi
0.412097 + 0.911140i 0.364796π0.364796\pi
390390 7.41855 0.375653
391391 2.21008 0.111769
392392 0 0
393393 −6.10731 −0.308073
394394 −22.4969 −1.13338
395395 39.0349 1.96406
396396 −2.92162 −0.146817
397397 −26.5113 −1.33056 −0.665282 0.746592i 0.731689π-0.731689\pi
−0.665282 + 0.746592i 0.731689π0.731689\pi
398398 5.26180 0.263750
399399 0 0
400400 −18.2039 −0.910197
401401 −6.04945 −0.302095 −0.151048 0.988527i 0.548265π-0.548265\pi
−0.151048 + 0.988527i 0.548265π0.548265\pi
402402 2.73820 0.136569
403403 7.83096 0.390088
404404 6.63090 0.329899
405405 −3.70928 −0.184315
406406 0 0
407407 11.5174 0.570899
408408 −0.447480 −0.0221536
409409 −37.1194 −1.83544 −0.917718 0.397231i 0.869971π-0.869971\pi
−0.917718 + 0.397231i 0.869971π0.869971\pi
410410 −30.2557 −1.49422
411411 18.9939 0.936898
412412 −52.8781 −2.60512
413413 0 0
414414 −16.4969 −0.810780
415415 32.3812 1.58953
416416 6.99386 0.342902
417417 −0.894960 −0.0438264
418418 2.34017 0.114462
419419 23.3523 1.14083 0.570417 0.821355i 0.306782π-0.306782\pi
0.570417 + 0.821355i 0.306782π0.306782\pi
420420 0 0
421421 7.57531 0.369198 0.184599 0.982814i 0.440901π-0.440901\pi
0.184599 + 0.982814i 0.440901π0.440901\pi
422422 42.3545 2.06179
423423 6.20620 0.301756
424424 7.36910 0.357875
425425 −2.54638 −0.123517
426426 −8.38962 −0.406478
427427 0 0
428428 42.4040 2.04967
429429 0.993857 0.0479839
430430 68.3956 3.29833
431431 −5.90707 −0.284533 −0.142267 0.989828i 0.545439π-0.545439\pi
−0.142267 + 0.989828i 0.545439π0.545439\pi
432432 −2.07838 −0.0999960
433433 7.47641 0.359293 0.179647 0.983731i 0.442505π-0.442505\pi
0.179647 + 0.983731i 0.442505π0.442505\pi
434434 0 0
435435 −19.9155 −0.954874
436436 38.1978 1.82934
437437 7.60197 0.363651
438438 −3.07838 −0.147091
439439 9.49079 0.452970 0.226485 0.974015i 0.427276π-0.427276\pi
0.226485 + 0.974015i 0.427276π0.427276\pi
440440 6.15676 0.293512
441441 0 0
442442 0.581449 0.0276567
443443 −25.1773 −1.19621 −0.598104 0.801418i 0.704079π-0.704079\pi
−0.598104 + 0.801418i 0.704079π0.704079\pi
444444 −28.9360 −1.37324
445445 −13.9421 −0.660921
446446 −41.2762 −1.95448
447447 20.9360 0.990239
448448 0 0
449449 −32.4040 −1.52924 −0.764620 0.644482i 0.777073π-0.777073\pi
−0.764620 + 0.644482i 0.777073π0.777073\pi
450450 19.0072 0.896007
451451 −4.05332 −0.190864
452452 50.7442 2.38680
453453 13.9421 0.655059
454454 −25.4596 −1.19488
455455 0 0
456456 −1.53919 −0.0720791
457457 8.86830 0.414841 0.207421 0.978252i 0.433493π-0.433493\pi
0.207421 + 0.978252i 0.433493π0.433493\pi
458458 59.5897 2.78444
459459 −0.290725 −0.0135699
460460 76.3956 3.56196
461461 −8.70313 −0.405345 −0.202673 0.979247i 0.564963π-0.564963\pi
−0.202673 + 0.979247i 0.564963π0.564963\pi
462462 0 0
463463 −6.21008 −0.288607 −0.144303 0.989533i 0.546094π-0.546094\pi
−0.144303 + 0.989533i 0.546094π0.546094\pi
464464 −11.1590 −0.518045
465465 31.5174 1.46159
466466 −11.0784 −0.513196
467467 −16.4619 −0.761764 −0.380882 0.924624i 0.624380π-0.624380\pi
−0.380882 + 0.924624i 0.624380π0.624380\pi
468468 −2.49693 −0.115421
469469 0 0
470470 −49.9565 −2.30432
471471 2.31351 0.106601
472472 −6.15676 −0.283388
473473 9.16290 0.421311
474474 −22.8371 −1.04894
475475 −8.75872 −0.401878
476476 0 0
477477 4.78765 0.219212
478478 −23.1194 −1.05746
479479 −16.5320 −0.755366 −0.377683 0.925935i 0.623279π-0.623279\pi
−0.377683 + 0.925935i 0.623279π0.623279\pi
480480 28.1483 1.28479
481481 9.84324 0.448813
482482 29.3340 1.33613
483483 0 0
484484 −26.6514 −1.21143
485485 −50.1399 −2.27674
486486 2.17009 0.0984371
487487 −25.6742 −1.16341 −0.581705 0.813400i 0.697614π-0.697614\pi
−0.581705 + 0.813400i 0.697614π0.697614\pi
488488 4.12556 0.186755
489489 −17.6598 −0.798605
490490 0 0
491491 27.3340 1.23357 0.616784 0.787133i 0.288435π-0.288435\pi
0.616784 + 0.787133i 0.288435π0.288435\pi
492492 10.1834 0.459104
493493 −1.56093 −0.0703008
494494 2.00000 0.0899843
495495 4.00000 0.179787
496496 17.6598 0.792950
497497 0 0
498498 −18.9444 −0.848919
499499 −10.0410 −0.449499 −0.224749 0.974417i 0.572156π-0.572156\pi
−0.224749 + 0.974417i 0.572156π0.572156\pi
500500 −37.7731 −1.68926
501501 −3.05172 −0.136341
502502 39.5090 1.76337
503503 −36.8287 −1.64211 −0.821055 0.570849i 0.806614π-0.806614\pi
−0.821055 + 0.570849i 0.806614π0.806614\pi
504504 0 0
505505 −9.07838 −0.403983
506506 17.7899 0.790858
507507 −12.1506 −0.539628
508508 −42.7670 −1.89748
509509 14.1301 0.626305 0.313153 0.949703i 0.398615π-0.398615\pi
0.313153 + 0.949703i 0.398615π0.398615\pi
510510 2.34017 0.103625
511511 0 0
512512 22.1701 0.979789
513513 −1.00000 −0.0441511
514514 −26.7792 −1.18118
515515 72.3956 3.19013
516516 −23.0205 −1.01342
517517 −6.69263 −0.294342
518518 0 0
519519 −9.60197 −0.421480
520520 5.26180 0.230745
521521 −28.1711 −1.23420 −0.617100 0.786885i 0.711693π-0.711693\pi
−0.617100 + 0.786885i 0.711693π0.711693\pi
522522 11.6514 0.509969
523523 32.1834 1.40728 0.703641 0.710555i 0.251556π-0.251556\pi
0.703641 + 0.710555i 0.251556π0.251556\pi
524524 −16.5464 −0.722832
525525 0 0
526526 16.2823 0.709943
527527 2.47027 0.107606
528528 2.24128 0.0975390
529529 34.7899 1.51261
530530 −38.5380 −1.67398
531531 −4.00000 −0.173585
532532 0 0
533533 −3.46412 −0.150048
534534 8.15676 0.352977
535535 −58.0554 −2.50995
536536 1.94214 0.0838877
537537 −0.814315 −0.0351403
538538 9.41855 0.406063
539539 0 0
540540 −10.0494 −0.432459
541541 −41.0349 −1.76423 −0.882114 0.471036i 0.843880π-0.843880\pi
−0.882114 + 0.471036i 0.843880π0.843880\pi
542542 −56.5113 −2.42737
543543 −20.1568 −0.865009
544544 2.20620 0.0945902
545545 −52.2967 −2.24014
546546 0 0
547547 9.67420 0.413639 0.206820 0.978379i 0.433689π-0.433689\pi
0.206820 + 0.978379i 0.433689π0.433689\pi
548548 51.4596 2.19824
549549 2.68035 0.114394
550550 −20.4969 −0.873992
551551 −5.36910 −0.228731
552552 −11.7009 −0.498022
553553 0 0
554554 14.3135 0.608123
555555 39.6163 1.68162
556556 −2.42469 −0.102830
557557 −40.1399 −1.70078 −0.850392 0.526150i 0.823635π-0.823635\pi
−0.850392 + 0.526150i 0.823635π0.823635\pi
558558 −18.4391 −0.780588
559559 7.83096 0.331214
560560 0 0
561561 0.313511 0.0132364
562562 −25.2267 −1.06413
563563 −44.0989 −1.85855 −0.929273 0.369393i 0.879566π-0.879566\pi
−0.929273 + 0.369393i 0.879566π0.879566\pi
564564 16.8143 0.708010
565565 −69.4740 −2.92279
566566 38.9360 1.63660
567567 0 0
568568 −5.95055 −0.249680
569569 −13.4147 −0.562372 −0.281186 0.959653i 0.590728π-0.590728\pi
−0.281186 + 0.959653i 0.590728π0.590728\pi
570570 8.04945 0.337154
571571 −27.8310 −1.16469 −0.582345 0.812942i 0.697865π-0.697865\pi
−0.582345 + 0.812942i 0.697865π0.697865\pi
572572 2.69263 0.112585
573573 5.44521 0.227477
574574 0 0
575575 −66.5835 −2.77673
576576 −12.3112 −0.512968
577577 34.1978 1.42367 0.711836 0.702345i 0.247864π-0.247864\pi
0.711836 + 0.702345i 0.247864π0.247864\pi
578578 −36.7081 −1.52685
579579 1.68649 0.0700881
580580 −53.9565 −2.24042
581581 0 0
582582 29.3340 1.21593
583583 −5.16290 −0.213825
584584 −2.18342 −0.0903505
585585 3.41855 0.141340
586586 51.5585 2.12986
587587 −33.1422 −1.36793 −0.683963 0.729517i 0.739745π-0.739745\pi
−0.683963 + 0.729517i 0.739745π0.739745\pi
588588 0 0
589589 8.49693 0.350110
590590 32.1978 1.32556
591591 −10.3668 −0.426435
592592 22.1978 0.912324
593593 −29.7503 −1.22170 −0.610849 0.791747i 0.709172π-0.709172\pi
−0.610849 + 0.791747i 0.709172π0.709172\pi
594594 −2.34017 −0.0960185
595595 0 0
596596 56.7214 2.32340
597597 2.42469 0.0992361
598598 15.2039 0.621735
599599 2.19183 0.0895557 0.0447778 0.998997i 0.485742π-0.485742\pi
0.0447778 + 0.998997i 0.485742π0.485742\pi
600600 13.4813 0.550373
601601 −31.9877 −1.30481 −0.652403 0.757872i 0.726239π-0.726239\pi
−0.652403 + 0.757872i 0.726239π0.726239\pi
602602 0 0
603603 1.26180 0.0513843
604604 37.7731 1.53697
605605 36.4885 1.48347
606606 5.31124 0.215755
607607 27.5174 1.11690 0.558449 0.829539i 0.311397π-0.311397\pi
0.558449 + 0.829539i 0.311397π0.311397\pi
608608 7.58864 0.307760
609609 0 0
610610 −21.5753 −0.873559
611611 −5.71978 −0.231397
612612 −0.787653 −0.0318390
613613 6.59583 0.266403 0.133201 0.991089i 0.457474π-0.457474\pi
0.133201 + 0.991089i 0.457474π0.457474\pi
614614 52.1133 2.10312
615615 −13.9421 −0.562201
616616 0 0
617617 −3.47641 −0.139955 −0.0699775 0.997549i 0.522293π-0.522293\pi
−0.0699775 + 0.997549i 0.522293π0.522293\pi
618618 −42.3545 −1.70375
619619 −26.9893 −1.08479 −0.542396 0.840123i 0.682483π-0.682483\pi
−0.542396 + 0.840123i 0.682483π0.682483\pi
620620 85.3894 3.42932
621621 −7.60197 −0.305056
622622 −49.8804 −2.00002
623623 0 0
624624 1.91548 0.0766805
625625 7.92162 0.316865
626626 −1.13624 −0.0454131
627627 1.07838 0.0430663
628628 6.26794 0.250118
629629 3.10504 0.123806
630630 0 0
631631 −10.3402 −0.411636 −0.205818 0.978590i 0.565985π-0.565985\pi
−0.205818 + 0.978590i 0.565985π0.565985\pi
632632 −16.1978 −0.644314
633633 19.5174 0.775749
634634 −37.1110 −1.47387
635635 58.5523 2.32358
636636 12.9711 0.514336
637637 0 0
638638 −12.5646 −0.497438
639639 −3.86603 −0.152938
640640 42.8020 1.69190
641641 35.1955 1.39014 0.695070 0.718942i 0.255373π-0.255373\pi
0.695070 + 0.718942i 0.255373π0.255373\pi
642642 33.9649 1.34049
643643 −12.4657 −0.491600 −0.245800 0.969321i 0.579051π-0.579051\pi
−0.245800 + 0.969321i 0.579051π0.579051\pi
644644 0 0
645645 31.5174 1.24100
646646 0.630898 0.0248223
647647 11.8804 0.467067 0.233533 0.972349i 0.424971π-0.424971\pi
0.233533 + 0.972349i 0.424971π0.424971\pi
648648 1.53919 0.0604650
649649 4.31351 0.169320
650650 −17.5174 −0.687091
651651 0 0
652652 −47.8453 −1.87377
653653 6.00000 0.234798 0.117399 0.993085i 0.462544π-0.462544\pi
0.117399 + 0.993085i 0.462544π0.462544\pi
654654 30.5958 1.19639
655655 22.6537 0.885153
656656 −7.81205 −0.305009
657657 −1.41855 −0.0553429
658658 0 0
659659 12.5464 0.488737 0.244369 0.969682i 0.421419π-0.421419\pi
0.244369 + 0.969682i 0.421419π0.421419\pi
660660 10.8371 0.421834
661661 −11.6430 −0.452860 −0.226430 0.974027i 0.572706π-0.572706\pi
−0.226430 + 0.974027i 0.572706π0.572706\pi
662662 54.5692 2.12089
663663 0.267938 0.0104059
664664 −13.4368 −0.521449
665665 0 0
666666 −23.1773 −0.898101
667667 −40.8157 −1.58039
668668 −8.26794 −0.319896
669669 −19.0205 −0.735376
670670 −10.1568 −0.392390
671671 −2.89043 −0.111584
672672 0 0
673673 41.3484 1.59386 0.796932 0.604069i 0.206455π-0.206455\pi
0.796932 + 0.604069i 0.206455π0.206455\pi
674674 −25.1194 −0.967564
675675 8.75872 0.337123
676676 −32.9194 −1.26613
677677 19.1773 0.737043 0.368521 0.929619i 0.379864π-0.379864\pi
0.368521 + 0.929619i 0.379864π0.379864\pi
678678 40.6453 1.56097
679679 0 0
680680 1.65983 0.0636515
681681 −11.7321 −0.449574
682682 19.8843 0.761409
683683 −22.2907 −0.852931 −0.426465 0.904504i 0.640241π-0.640241\pi
−0.426465 + 0.904504i 0.640241π0.640241\pi
684684 −2.70928 −0.103592
685685 −70.4534 −2.69189
686686 0 0
687687 27.4596 1.04765
688688 17.6598 0.673275
689689 −4.41241 −0.168099
690690 61.1917 2.32953
691691 30.0410 1.14281 0.571407 0.820666i 0.306398π-0.306398\pi
0.571407 + 0.820666i 0.306398π0.306398\pi
692692 −26.0144 −0.988918
693693 0 0
694694 −69.4740 −2.63720
695695 3.31965 0.125922
696696 8.26406 0.313248
697697 −1.09275 −0.0413910
698698 5.13624 0.194409
699699 −5.10504 −0.193090
700700 0 0
701701 −1.20394 −0.0454721 −0.0227360 0.999742i 0.507238π-0.507238\pi
−0.0227360 + 0.999742i 0.507238π0.507238\pi
702702 −2.00000 −0.0754851
703703 10.6803 0.402817
704704 13.2762 0.500365
705705 −23.0205 −0.867003
706706 −33.5090 −1.26113
707707 0 0
708708 −10.8371 −0.407283
709709 −33.2351 −1.24817 −0.624086 0.781356i 0.714528π-0.714528\pi
−0.624086 + 0.781356i 0.714528π0.714528\pi
710710 31.1194 1.16789
711711 −10.5236 −0.394665
712712 5.78539 0.216816
713713 64.5934 2.41904
714714 0 0
715715 −3.68649 −0.137867
716716 −2.20620 −0.0824497
717717 −10.6537 −0.397869
718718 50.8515 1.89776
719719 −10.2062 −0.380627 −0.190314 0.981723i 0.560950π-0.560950\pi
−0.190314 + 0.981723i 0.560950π0.560950\pi
720720 7.70928 0.287308
721721 0 0
722722 2.17009 0.0807623
723723 13.5174 0.502719
724724 −54.6102 −2.02957
725725 47.0265 1.74652
726726 −21.3474 −0.792275
727727 26.8371 0.995333 0.497666 0.867368i 0.334190π-0.334190\pi
0.497666 + 0.867368i 0.334190π0.334190\pi
728728 0 0
729729 1.00000 0.0370370
730730 11.4186 0.422620
731731 2.47027 0.0913661
732732 7.26180 0.268404
733733 −2.46573 −0.0910739 −0.0455369 0.998963i 0.514500π-0.514500\pi
−0.0455369 + 0.998963i 0.514500π0.514500\pi
734734 67.9299 2.50734
735735 0 0
736736 57.6886 2.12643
737737 −1.36069 −0.0501217
738738 8.15676 0.300254
739739 0.863763 0.0317741 0.0158870 0.999874i 0.494943π-0.494943\pi
0.0158870 + 0.999874i 0.494943π0.494943\pi
740740 107.332 3.94559
741741 0.921622 0.0338566
742742 0 0
743743 −36.1171 −1.32501 −0.662505 0.749058i 0.730507π-0.730507\pi
−0.662505 + 0.749058i 0.730507π0.730507\pi
744744 −13.0784 −0.479477
745745 −77.6574 −2.84515
746746 −51.3751 −1.88097
747747 −8.72979 −0.319406
748748 0.849388 0.0310567
749749 0 0
750750 −30.2557 −1.10478
751751 −33.8264 −1.23434 −0.617172 0.786828i 0.711722π-0.711722\pi
−0.617172 + 0.786828i 0.711722π0.711722\pi
752752 −12.8988 −0.470372
753753 18.2062 0.663471
754754 −10.7382 −0.391062
755755 −51.7152 −1.88211
756756 0 0
757757 −13.6865 −0.497444 −0.248722 0.968575i 0.580011π-0.580011\pi
−0.248722 + 0.968575i 0.580011π0.580011\pi
758758 −16.0989 −0.584738
759759 8.19779 0.297561
760760 5.70928 0.207097
761761 7.86150 0.284979 0.142490 0.989796i 0.454489π-0.454489\pi
0.142490 + 0.989796i 0.454489π0.454489\pi
762762 −34.2557 −1.24095
763763 0 0
764764 14.7526 0.533730
765765 1.07838 0.0389888
766766 15.4186 0.557095
767767 3.68649 0.133111
768768 −0.418551 −0.0151031
769769 −2.31351 −0.0834273 −0.0417137 0.999130i 0.513282π-0.513282\pi
−0.0417137 + 0.999130i 0.513282π0.513282\pi
770770 0 0
771771 −12.3402 −0.444420
772772 4.56916 0.164448
773773 32.9216 1.18411 0.592054 0.805898i 0.298317π-0.298317\pi
0.592054 + 0.805898i 0.298317π0.298317\pi
774774 −18.4391 −0.662779
775775 −74.4222 −2.67333
776776 20.8059 0.746888
777777 0 0
778778 35.2762 1.26471
779779 −3.75872 −0.134670
780780 9.26180 0.331625
781781 4.16904 0.149180
782782 4.79606 0.171507
783783 5.36910 0.191876
784784 0 0
785785 −8.58145 −0.306285
786786 −13.2534 −0.472733
787787 −24.8104 −0.884397 −0.442198 0.896917i 0.645801π-0.645801\pi
−0.442198 + 0.896917i 0.645801π0.645801\pi
788788 −28.0866 −1.00054
789789 7.50307 0.267116
790790 84.7091 3.01381
791791 0 0
792792 −1.65983 −0.0589794
793793 −2.47027 −0.0877217
794794 −57.5318 −2.04173
795795 −17.7587 −0.629837
796796 6.56916 0.232838
797797 −2.59583 −0.0919488 −0.0459744 0.998943i 0.514639π-0.514639\pi
−0.0459744 + 0.998943i 0.514639π0.514639\pi
798798 0 0
799799 −1.80430 −0.0638314
800800 −66.4668 −2.34996
801801 3.75872 0.132808
802802 −13.1278 −0.463560
803803 1.52973 0.0539831
804804 3.41855 0.120563
805805 0 0
806806 16.9939 0.598583
807807 4.34017 0.152781
808808 3.76713 0.132527
809809 38.6803 1.35993 0.679964 0.733245i 0.261995π-0.261995\pi
0.679964 + 0.733245i 0.261995π0.261995\pi
810810 −8.04945 −0.282829
811811 44.9939 1.57995 0.789974 0.613140i 0.210094π-0.210094\pi
0.789974 + 0.613140i 0.210094π0.210094\pi
812812 0 0
813813 −26.0410 −0.913299
814814 24.9939 0.876034
815815 65.5052 2.29455
816816 0.604236 0.0211525
817817 8.49693 0.297270
818818 −80.5523 −2.81645
819819 0 0
820820 −37.7731 −1.31909
821821 3.77310 0.131682 0.0658410 0.997830i 0.479027π-0.479027\pi
0.0658410 + 0.997830i 0.479027π0.479027\pi
822822 41.2183 1.43765
823823 −14.6537 −0.510795 −0.255398 0.966836i 0.582206π-0.582206\pi
−0.255398 + 0.966836i 0.582206π0.582206\pi
824824 −30.0410 −1.04653
825825 −9.44521 −0.328840
826826 0 0
827827 −15.4368 −0.536790 −0.268395 0.963309i 0.586493π-0.586493\pi
−0.268395 + 0.963309i 0.586493π0.586493\pi
828828 −20.5958 −0.715754
829829 −8.57691 −0.297889 −0.148944 0.988846i 0.547588π-0.547588\pi
−0.148944 + 0.988846i 0.547588π0.547588\pi
830830 70.2700 2.43911
831831 6.59583 0.228807
832832 11.3463 0.393363
833833 0 0
834834 −1.94214 −0.0672508
835835 11.3197 0.391733
836836 2.92162 0.101046
837837 −8.49693 −0.293697
838838 50.6765 1.75059
839839 −31.0349 −1.07144 −0.535722 0.844395i 0.679960π-0.679960\pi
−0.535722 + 0.844395i 0.679960π0.679960\pi
840840 0 0
841841 −0.172740 −0.00595654
842842 16.4391 0.566528
843843 −11.6248 −0.400378
844844 52.8781 1.82014
845845 45.0700 1.55045
846846 13.4680 0.463039
847847 0 0
848848 −9.95055 −0.341703
849849 17.9421 0.615773
850850 −5.52586 −0.189535
851851 81.1917 2.78321
852852 −10.4741 −0.358838
853853 −11.4140 −0.390808 −0.195404 0.980723i 0.562602π-0.562602\pi
−0.195404 + 0.980723i 0.562602π0.562602\pi
854854 0 0
855855 3.70928 0.126855
856856 24.0905 0.823396
857857 −22.7936 −0.778615 −0.389308 0.921108i 0.627286π-0.627286\pi
−0.389308 + 0.921108i 0.627286π0.627286\pi
858858 2.15676 0.0736304
859859 30.7838 1.05033 0.525164 0.851001i 0.324004π-0.324004\pi
0.525164 + 0.851001i 0.324004π0.324004\pi
860860 85.3894 2.91176
861861 0 0
862862 −12.8188 −0.436612
863863 10.0228 0.341180 0.170590 0.985342i 0.445433π-0.445433\pi
0.170590 + 0.985342i 0.445433π0.445433\pi
864864 −7.58864 −0.258171
865865 35.6163 1.21099
866866 16.2245 0.551329
867867 −16.9155 −0.574480
868868 0 0
869869 11.3484 0.384968
870870 −43.2183 −1.46524
871871 −1.16290 −0.0394033
872872 21.7009 0.734884
873873 13.5174 0.457496
874874 16.4969 0.558017
875875 0 0
876876 −3.84324 −0.129851
877877 −32.8371 −1.10883 −0.554415 0.832240i 0.687058π-0.687058\pi
−0.554415 + 0.832240i 0.687058π0.687058\pi
878878 20.5958 0.695075
879879 23.7587 0.801362
880880 −8.31351 −0.280248
881881 45.0700 1.51845 0.759223 0.650831i 0.225579π-0.225579\pi
0.759223 + 0.650831i 0.225579π0.225579\pi
882882 0 0
883883 54.5523 1.83583 0.917916 0.396774i 0.129870π-0.129870\pi
0.917916 + 0.396774i 0.129870π0.129870\pi
884884 0.725919 0.0244153
885885 14.8371 0.498744
886886 −54.6369 −1.83556
887887 −16.4657 −0.552865 −0.276433 0.961033i 0.589152π-0.589152\pi
−0.276433 + 0.961033i 0.589152π0.589152\pi
888888 −16.4391 −0.551659
889889 0 0
890890 −30.2557 −1.01417
891891 −1.07838 −0.0361270
892892 −51.5318 −1.72541
893893 −6.20620 −0.207683
894894 45.4329 1.51950
895895 3.02052 0.100965
896896 0 0
897897 7.00614 0.233928
898898 −70.3195 −2.34659
899899 −45.6209 −1.52154
900900 23.7298 0.790993
901901 −1.39189 −0.0463705
902902 −8.79606 −0.292877
903903 0 0
904904 28.8287 0.958828
905905 74.7670 2.48534
906906 30.2557 1.00518
907907 −23.5708 −0.782655 −0.391327 0.920252i 0.627984π-0.627984\pi
−0.391327 + 0.920252i 0.627984π0.627984\pi
908908 −31.7854 −1.05484
909909 2.44748 0.0811778
910910 0 0
911911 −0.616522 −0.0204263 −0.0102131 0.999948i 0.503251π-0.503251\pi
−0.0102131 + 0.999948i 0.503251π0.503251\pi
912912 2.07838 0.0688220
913913 9.41402 0.311558
914914 19.2450 0.636567
915915 −9.94214 −0.328677
916916 74.3956 2.45810
917917 0 0
918918 −0.630898 −0.0208227
919919 53.6742 1.77055 0.885274 0.465069i 0.153971π-0.153971\pi
0.885274 + 0.465069i 0.153971π0.153971\pi
920920 43.4017 1.43091
921921 24.0144 0.791301
922922 −18.8865 −0.621995
923923 3.56302 0.117278
924924 0 0
925925 −93.5462 −3.07578
926926 −13.4764 −0.442862
927927 −19.5174 −0.641037
928928 −40.7442 −1.33749
929929 50.2616 1.64903 0.824515 0.565840i 0.191448π-0.191448\pi
0.824515 + 0.565840i 0.191448π0.191448\pi
930930 68.3956 2.24278
931931 0 0
932932 −13.8310 −0.453048
933933 −22.9854 −0.752510
934934 −35.7237 −1.16891
935935 −1.16290 −0.0380308
936936 −1.41855 −0.0463668
937937 −8.63931 −0.282234 −0.141117 0.989993i 0.545069π-0.545069\pi
−0.141117 + 0.989993i 0.545069π0.545069\pi
938938 0 0
939939 −0.523590 −0.0170867
940940 −62.3689 −2.03425
941941 −30.2122 −0.984889 −0.492444 0.870344i 0.663896π-0.663896\pi
−0.492444 + 0.870344i 0.663896π0.663896\pi
942942 5.02052 0.163577
943943 −28.5737 −0.930488
944944 8.31351 0.270582
945945 0 0
946946 19.8843 0.646494
947947 27.1727 0.882995 0.441498 0.897262i 0.354447π-0.354447\pi
0.441498 + 0.897262i 0.354447π0.354447\pi
948948 −28.5113 −0.926004
949949 1.30737 0.0424390
950950 −19.0072 −0.616675
951951 −17.1012 −0.554543
952952 0 0
953953 44.5029 1.44159 0.720795 0.693148i 0.243777π-0.243777\pi
0.720795 + 0.693148i 0.243777π0.243777\pi
954954 10.3896 0.336376
955955 −20.1978 −0.653585
956956 −28.8638 −0.933521
957957 −5.78992 −0.187162
958958 −35.8759 −1.15910
959959 0 0
960960 45.6658 1.47386
961961 41.1978 1.32896
962962 21.3607 0.688696
963963 15.6514 0.504360
964964 36.6225 1.17953
965965 −6.25565 −0.201377
966966 0 0
967967 −18.6004 −0.598147 −0.299074 0.954230i 0.596678π-0.596678\pi
−0.299074 + 0.954230i 0.596678π0.596678\pi
968968 −15.1412 −0.486655
969969 0.290725 0.00933942
970970 −108.808 −3.49361
971971 −16.0533 −0.515176 −0.257588 0.966255i 0.582928π-0.582928\pi
−0.257588 + 0.966255i 0.582928π0.582928\pi
972972 2.70928 0.0869000
973973 0 0
974974 −55.7152 −1.78523
975975 −8.07223 −0.258518
976976 −5.57077 −0.178316
977977 −15.8394 −0.506746 −0.253373 0.967369i 0.581540π-0.581540\pi
−0.253373 + 0.967369i 0.581540π0.581540\pi
978978 −38.3234 −1.22545
979979 −4.05332 −0.129545
980980 0 0
981981 14.0989 0.450143
982982 59.3172 1.89289
983983 23.0349 0.734699 0.367350 0.930083i 0.380265π-0.380265\pi
0.367350 + 0.930083i 0.380265π0.380265\pi
984984 5.78539 0.184431
985985 38.4534 1.22523
986986 −3.38735 −0.107875
987987 0 0
988988 2.49693 0.0794379
989989 64.5934 2.05395
990990 8.68035 0.275880
991991 −42.8371 −1.36077 −0.680383 0.732857i 0.738186π-0.738186\pi
−0.680383 + 0.732857i 0.738186π0.738186\pi
992992 64.4801 2.04725
993993 25.1461 0.797987
994994 0 0
995995 −8.99386 −0.285124
996996 −23.6514 −0.749424
997997 23.7899 0.753434 0.376717 0.926328i 0.377053π-0.377053\pi
0.376717 + 0.926328i 0.377053π0.377053\pi
998998 −21.7899 −0.689748
999999 −10.6803 −0.337911
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 2793.2.a.x.1.3 3
3.2 odd 2 8379.2.a.bp.1.1 3
7.6 odd 2 399.2.a.d.1.3 3
21.20 even 2 1197.2.a.l.1.1 3
28.27 even 2 6384.2.a.bx.1.3 3
35.34 odd 2 9975.2.a.z.1.1 3
133.132 even 2 7581.2.a.n.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
399.2.a.d.1.3 3 7.6 odd 2
1197.2.a.l.1.1 3 21.20 even 2
2793.2.a.x.1.3 3 1.1 even 1 trivial
6384.2.a.bx.1.3 3 28.27 even 2
7581.2.a.n.1.1 3 133.132 even 2
8379.2.a.bp.1.1 3 3.2 odd 2
9975.2.a.z.1.1 3 35.34 odd 2