Properties

Label 567.2.a.e.1.2
Level 567567
Weight 22
Character 567.1
Self dual yes
Analytic conductor 4.5284.528
Analytic rank 00
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] = [567,2,Mod(1,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, 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("567.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 567=347 567 = 3^{4} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 567.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: 4.527517794614.52751779461
Analytic rank: 00
Dimension: 33
Coefficient field: 3.3.621.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x36x3 x^{3} - 6x - 3 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 0.523976-0.523976 of defining polynomial
Character χ\chi == 567.1

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) == q0.523976q21.72545q4+2.20147q5+1.00000q7+1.95205q81.15352q105.20147q11+3.15352q130.523976q14+2.42807q16+3.24943q17+7.45090q193.79853q20+2.72545q224.40294q230.153520q251.65237q261.72545q28+1.15352q29+2.00000q315.17635q321.70262q34+2.20147q35+5.00000q373.90409q38+4.29738q40+11.4509q41+9.29738q43+8.97487q44+2.30704q46+1.04795q47+1.00000q49+0.0804406q505.44124q52+0.249425q5311.4509q55+1.95205q560.604417q58+8.09591q59+8.60442q611.04795q622.14386q64+6.94239q657.60442q675.60672q681.15352q709.60442q71+0.846480q732.61988q7412.8561q765.20147q777.60442q79+5.34533q806.00000q8211.4509q83+7.15352q854.87161q8610.1535q889.24943q89+3.15352q91+7.59706q920.549103q94+16.4029q953.45090q970.523976q98+O(q100)q-0.523976 q^{2} -1.72545 q^{4} +2.20147 q^{5} +1.00000 q^{7} +1.95205 q^{8} -1.15352 q^{10} -5.20147 q^{11} +3.15352 q^{13} -0.523976 q^{14} +2.42807 q^{16} +3.24943 q^{17} +7.45090 q^{19} -3.79853 q^{20} +2.72545 q^{22} -4.40294 q^{23} -0.153520 q^{25} -1.65237 q^{26} -1.72545 q^{28} +1.15352 q^{29} +2.00000 q^{31} -5.17635 q^{32} -1.70262 q^{34} +2.20147 q^{35} +5.00000 q^{37} -3.90409 q^{38} +4.29738 q^{40} +11.4509 q^{41} +9.29738 q^{43} +8.97487 q^{44} +2.30704 q^{46} +1.04795 q^{47} +1.00000 q^{49} +0.0804406 q^{50} -5.44124 q^{52} +0.249425 q^{53} -11.4509 q^{55} +1.95205 q^{56} -0.604417 q^{58} +8.09591 q^{59} +8.60442 q^{61} -1.04795 q^{62} -2.14386 q^{64} +6.94239 q^{65} -7.60442 q^{67} -5.60672 q^{68} -1.15352 q^{70} -9.60442 q^{71} +0.846480 q^{73} -2.61988 q^{74} -12.8561 q^{76} -5.20147 q^{77} -7.60442 q^{79} +5.34533 q^{80} -6.00000 q^{82} -11.4509 q^{83} +7.15352 q^{85} -4.87161 q^{86} -10.1535 q^{88} -9.24943 q^{89} +3.15352 q^{91} +7.59706 q^{92} -0.549103 q^{94} +16.4029 q^{95} -3.45090 q^{97} -0.523976 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q+6q43q5+3q7+9q8+3q106q11+3q13+12q163q1721q203q22+6q23+6q25+27q26+6q283q29+6q31+18q32++12q97+O(q100) 3 q + 6 q^{4} - 3 q^{5} + 3 q^{7} + 9 q^{8} + 3 q^{10} - 6 q^{11} + 3 q^{13} + 12 q^{16} - 3 q^{17} - 21 q^{20} - 3 q^{22} + 6 q^{23} + 6 q^{25} + 27 q^{26} + 6 q^{28} - 3 q^{29} + 6 q^{31} + 18 q^{32}+ \cdots + 12 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 −0.523976 −0.370507 −0.185254 0.982691i 0.559311π-0.559311\pi
−0.185254 + 0.982691i 0.559311π0.559311\pi
33 0 0
44 −1.72545 −0.862724
55 2.20147 0.984528 0.492264 0.870446i 0.336169π-0.336169\pi
0.492264 + 0.870446i 0.336169π0.336169\pi
66 0 0
77 1.00000 0.377964
88 1.95205 0.690153
99 0 0
1010 −1.15352 −0.364775
1111 −5.20147 −1.56830 −0.784151 0.620569i 0.786901π-0.786901\pi
−0.784151 + 0.620569i 0.786901π0.786901\pi
1212 0 0
1313 3.15352 0.874629 0.437314 0.899309i 0.355930π-0.355930\pi
0.437314 + 0.899309i 0.355930π0.355930\pi
1414 −0.523976 −0.140039
1515 0 0
1616 2.42807 0.607018
1717 3.24943 0.788101 0.394051 0.919089i 0.371073π-0.371073\pi
0.394051 + 0.919089i 0.371073π0.371073\pi
1818 0 0
1919 7.45090 1.70935 0.854677 0.519161i 0.173755π-0.173755\pi
0.854677 + 0.519161i 0.173755π0.173755\pi
2020 −3.79853 −0.849377
2121 0 0
2222 2.72545 0.581068
2323 −4.40294 −0.918077 −0.459039 0.888416i 0.651806π-0.651806\pi
−0.459039 + 0.888416i 0.651806π0.651806\pi
2424 0 0
2525 −0.153520 −0.0307039
2626 −1.65237 −0.324056
2727 0 0
2828 −1.72545 −0.326079
2929 1.15352 0.214203 0.107102 0.994248i 0.465843π-0.465843\pi
0.107102 + 0.994248i 0.465843π0.465843\pi
3030 0 0
3131 2.00000 0.359211 0.179605 0.983739i 0.442518π-0.442518\pi
0.179605 + 0.983739i 0.442518π0.442518\pi
3232 −5.17635 −0.915057
3333 0 0
3434 −1.70262 −0.291997
3535 2.20147 0.372117
3636 0 0
3737 5.00000 0.821995 0.410997 0.911636i 0.365181π-0.365181\pi
0.410997 + 0.911636i 0.365181π0.365181\pi
3838 −3.90409 −0.633328
3939 0 0
4040 4.29738 0.679475
4141 11.4509 1.78833 0.894165 0.447738i 0.147770π-0.147770\pi
0.894165 + 0.447738i 0.147770π0.147770\pi
4242 0 0
4343 9.29738 1.41784 0.708918 0.705290i 0.249183π-0.249183\pi
0.708918 + 0.705290i 0.249183π0.249183\pi
4444 8.97487 1.35301
4545 0 0
4646 2.30704 0.340154
4747 1.04795 0.152860 0.0764298 0.997075i 0.475648π-0.475648\pi
0.0764298 + 0.997075i 0.475648π0.475648\pi
4848 0 0
4949 1.00000 0.142857
5050 0.0804406 0.0113760
5151 0 0
5252 −5.44124 −0.754564
5353 0.249425 0.0342612 0.0171306 0.999853i 0.494547π-0.494547\pi
0.0171306 + 0.999853i 0.494547π0.494547\pi
5454 0 0
5555 −11.4509 −1.54404
5656 1.95205 0.260853
5757 0 0
5858 −0.604417 −0.0793638
5959 8.09591 1.05400 0.526999 0.849866i 0.323317π-0.323317\pi
0.526999 + 0.849866i 0.323317π0.323317\pi
6060 0 0
6161 8.60442 1.10168 0.550841 0.834610i 0.314307π-0.314307\pi
0.550841 + 0.834610i 0.314307π0.314307\pi
6262 −1.04795 −0.133090
6363 0 0
6464 −2.14386 −0.267982
6565 6.94239 0.861097
6666 0 0
6767 −7.60442 −0.929027 −0.464514 0.885566i 0.653771π-0.653771\pi
−0.464514 + 0.885566i 0.653771π0.653771\pi
6868 −5.60672 −0.679914
6969 0 0
7070 −1.15352 −0.137872
7171 −9.60442 −1.13983 −0.569917 0.821702i 0.693025π-0.693025\pi
−0.569917 + 0.821702i 0.693025π0.693025\pi
7272 0 0
7373 0.846480 0.0990730 0.0495365 0.998772i 0.484226π-0.484226\pi
0.0495365 + 0.998772i 0.484226π0.484226\pi
7474 −2.61988 −0.304555
7575 0 0
7676 −12.8561 −1.47470
7777 −5.20147 −0.592763
7878 0 0
7979 −7.60442 −0.855564 −0.427782 0.903882i 0.640705π-0.640705\pi
−0.427782 + 0.903882i 0.640705π0.640705\pi
8080 5.34533 0.597626
8181 0 0
8282 −6.00000 −0.662589
8383 −11.4509 −1.25690 −0.628450 0.777850i 0.716310π-0.716310\pi
−0.628450 + 0.777850i 0.716310π0.716310\pi
8484 0 0
8585 7.15352 0.775908
8686 −4.87161 −0.525319
8787 0 0
8888 −10.1535 −1.08237
8989 −9.24943 −0.980437 −0.490219 0.871600i 0.663083π-0.663083\pi
−0.490219 + 0.871600i 0.663083π0.663083\pi
9090 0 0
9191 3.15352 0.330579
9292 7.59706 0.792048
9393 0 0
9494 −0.549103 −0.0566356
9595 16.4029 1.68291
9696 0 0
9797 −3.45090 −0.350386 −0.175193 0.984534i 0.556055π-0.556055\pi
−0.175193 + 0.984534i 0.556055π0.556055\pi
9898 −0.523976 −0.0529296
9999 0 0
100100 0.264890 0.0264890
101101 16.4029 1.63215 0.816077 0.577943i 0.196144π-0.196144\pi
0.816077 + 0.577943i 0.196144π0.196144\pi
102102 0 0
103103 −1.14386 −0.112708 −0.0563539 0.998411i 0.517947π-0.517947\pi
−0.0563539 + 0.998411i 0.517947π0.517947\pi
104104 6.15582 0.603628
105105 0 0
106106 −0.130693 −0.0126940
107107 −9.10557 −0.880268 −0.440134 0.897932i 0.645069π-0.645069\pi
−0.440134 + 0.897932i 0.645069π0.645069\pi
108108 0 0
109109 −13.7483 −1.31685 −0.658423 0.752648i 0.728776π-0.728776\pi
−0.658423 + 0.752648i 0.728776π0.728776\pi
110110 6.00000 0.572078
111111 0 0
112112 2.42807 0.229431
113113 −19.9018 −1.87220 −0.936102 0.351729i 0.885594π-0.885594\pi
−0.936102 + 0.351729i 0.885594π0.885594\pi
114114 0 0
115115 −9.69296 −0.903873
116116 −1.99034 −0.184798
117117 0 0
118118 −4.24206 −0.390514
119119 3.24943 0.297874
120120 0 0
121121 16.0553 1.45957
122122 −4.50851 −0.408181
123123 0 0
124124 −3.45090 −0.309900
125125 −11.3453 −1.01476
126126 0 0
127127 9.29738 0.825009 0.412504 0.910956i 0.364654π-0.364654\pi
0.412504 + 0.910956i 0.364654π0.364654\pi
128128 11.4760 1.01435
129129 0 0
130130 −3.63765 −0.319043
131131 −7.54680 −0.659367 −0.329684 0.944091i 0.606942π-0.606942\pi
−0.329684 + 0.944091i 0.606942π0.606942\pi
132132 0 0
133133 7.45090 0.646075
134134 3.98454 0.344211
135135 0 0
136136 6.34303 0.543910
137137 1.40294 0.119862 0.0599308 0.998203i 0.480912π-0.480912\pi
0.0599308 + 0.998203i 0.480912π0.480912\pi
138138 0 0
139139 −15.4509 −1.31053 −0.655264 0.755400i 0.727443π-0.727443\pi
−0.655264 + 0.755400i 0.727443π0.727443\pi
140140 −3.79853 −0.321034
141141 0 0
142142 5.03249 0.422317
143143 −16.4029 −1.37168
144144 0 0
145145 2.53944 0.210889
146146 −0.443536 −0.0367073
147147 0 0
148148 −8.62724 −0.709155
149149 −13.4029 −1.09801 −0.549006 0.835818i 0.684994π-0.684994\pi
−0.549006 + 0.835818i 0.684994π0.684994\pi
150150 0 0
151151 11.6044 0.944354 0.472177 0.881504i 0.343468π-0.343468\pi
0.472177 + 0.881504i 0.343468π0.343468\pi
152152 14.5445 1.17972
153153 0 0
154154 2.72545 0.219623
155155 4.40294 0.353653
156156 0 0
157157 −24.3624 −1.94433 −0.972164 0.234302i 0.924719π-0.924719\pi
−0.972164 + 0.234302i 0.924719π0.924719\pi
158158 3.98454 0.316993
159159 0 0
160160 −11.3956 −0.900900
161161 −4.40294 −0.347001
162162 0 0
163163 5.60442 0.438972 0.219486 0.975616i 0.429562π-0.429562\pi
0.219486 + 0.975616i 0.429562π0.429562\pi
164164 −19.7579 −1.54284
165165 0 0
166166 6.00000 0.465690
167167 23.4509 1.81468 0.907342 0.420392i 0.138108π-0.138108\pi
0.907342 + 0.420392i 0.138108π0.138108\pi
168168 0 0
169169 −3.05531 −0.235024
170170 −3.74828 −0.287480
171171 0 0
172172 −16.0421 −1.22320
173173 22.5085 1.71129 0.855645 0.517563i 0.173161π-0.173161\pi
0.855645 + 0.517563i 0.173161π0.173161\pi
174174 0 0
175175 −0.153520 −0.0116050
176176 −12.6295 −0.951988
177177 0 0
178178 4.84648 0.363259
179179 −6.49885 −0.485747 −0.242873 0.970058i 0.578090π-0.578090\pi
−0.242873 + 0.970058i 0.578090π0.578090\pi
180180 0 0
181181 2.00000 0.148659 0.0743294 0.997234i 0.476318π-0.476318\pi
0.0743294 + 0.997234i 0.476318π0.476318\pi
182182 −1.65237 −0.122482
183183 0 0
184184 −8.59476 −0.633614
185185 11.0074 0.809277
186186 0 0
187187 −16.9018 −1.23598
188188 −1.80819 −0.131876
189189 0 0
190190 −8.59476 −0.623529
191191 13.5085 0.977442 0.488721 0.872440i 0.337464π-0.337464\pi
0.488721 + 0.872440i 0.337464π0.337464\pi
192192 0 0
193193 17.7483 1.27755 0.638774 0.769394i 0.279442π-0.279442\pi
0.638774 + 0.769394i 0.279442π0.279442\pi
194194 1.80819 0.129820
195195 0 0
196196 −1.72545 −0.123246
197197 16.2088 1.15483 0.577416 0.816450i 0.304061π-0.304061\pi
0.577416 + 0.816450i 0.304061π0.304061\pi
198198 0 0
199199 −7.14386 −0.506415 −0.253207 0.967412i 0.581485π-0.581485\pi
−0.253207 + 0.967412i 0.581485π0.581485\pi
200200 −0.299677 −0.0211904
201201 0 0
202202 −8.59476 −0.604725
203203 1.15352 0.0809612
204204 0 0
205205 25.2088 1.76066
206206 0.599355 0.0417590
207207 0 0
208208 7.65697 0.530915
209209 −38.7556 −2.68078
210210 0 0
211211 3.29738 0.227001 0.113500 0.993538i 0.463794π-0.463794\pi
0.113500 + 0.993538i 0.463794π0.463794\pi
212212 −0.430370 −0.0295580
213213 0 0
214214 4.77110 0.326146
215215 20.4679 1.39590
216216 0 0
217217 2.00000 0.135769
218218 7.20377 0.487901
219219 0 0
220220 19.7579 1.33208
221221 10.2471 0.689296
222222 0 0
223223 −23.2088 −1.55418 −0.777089 0.629390i 0.783305π-0.783305\pi
−0.777089 + 0.629390i 0.783305π0.783305\pi
224224 −5.17635 −0.345859
225225 0 0
226226 10.4281 0.693665
227227 −11.6620 −0.774036 −0.387018 0.922072i 0.626495π-0.626495\pi
−0.387018 + 0.922072i 0.626495π0.626495\pi
228228 0 0
229229 1.39558 0.0922227 0.0461114 0.998936i 0.485317π-0.485317\pi
0.0461114 + 0.998936i 0.485317π0.485317\pi
230230 5.07888 0.334892
231231 0 0
232232 2.25172 0.147833
233233 8.75057 0.573269 0.286635 0.958040i 0.407463π-0.407463\pi
0.286635 + 0.958040i 0.407463π0.407463\pi
234234 0 0
235235 2.30704 0.150495
236236 −13.9691 −0.909309
237237 0 0
238238 −1.70262 −0.110365
239239 4.70262 0.304187 0.152094 0.988366i 0.451398π-0.451398\pi
0.152094 + 0.988366i 0.451398π0.451398\pi
240240 0 0
241241 −4.60442 −0.296597 −0.148298 0.988943i 0.547380π-0.547380\pi
−0.148298 + 0.988943i 0.547380π0.547380\pi
242242 −8.41261 −0.540783
243243 0 0
244244 −14.8465 −0.950449
245245 2.20147 0.140647
246246 0 0
247247 23.4966 1.49505
248248 3.90409 0.247910
249249 0 0
250250 5.94469 0.375975
251251 3.14386 0.198439 0.0992193 0.995066i 0.468365π-0.468365\pi
0.0992193 + 0.995066i 0.468365π0.468365\pi
252252 0 0
253253 22.9018 1.43982
254254 −4.87161 −0.305672
255255 0 0
256256 −1.72545 −0.107841
257257 −20.1512 −1.25700 −0.628499 0.777810i 0.716330π-0.716330\pi
−0.628499 + 0.777810i 0.716330π0.716330\pi
258258 0 0
259259 5.00000 0.310685
260260 −11.9787 −0.742889
261261 0 0
262262 3.95435 0.244300
263263 −17.2015 −1.06069 −0.530344 0.847782i 0.677937π-0.677937\pi
−0.530344 + 0.847782i 0.677937π0.677937\pi
264264 0 0
265265 0.549103 0.0337311
266266 −3.90409 −0.239375
267267 0 0
268268 13.1210 0.801495
269269 −2.75057 −0.167706 −0.0838528 0.996478i 0.526723π-0.526723\pi
−0.0838528 + 0.996478i 0.526723π0.526723\pi
270270 0 0
271271 −12.8561 −0.780955 −0.390477 0.920612i 0.627690π-0.627690\pi
−0.390477 + 0.920612i 0.627690π0.627690\pi
272272 7.88983 0.478391
273273 0 0
274274 −0.735110 −0.0444096
275275 0.798528 0.0481530
276276 0 0
277277 −16.7483 −1.00631 −0.503153 0.864197i 0.667827π-0.667827\pi
−0.503153 + 0.864197i 0.667827π0.667827\pi
278278 8.09591 0.485560
279279 0 0
280280 4.29738 0.256817
281281 −5.30704 −0.316591 −0.158296 0.987392i 0.550600π-0.550600\pi
−0.158296 + 0.987392i 0.550600π0.550600\pi
282282 0 0
283283 12.3527 0.734291 0.367146 0.930163i 0.380335π-0.380335\pi
0.367146 + 0.930163i 0.380335π0.380335\pi
284284 16.5719 0.983363
285285 0 0
286286 8.59476 0.508219
287287 11.4509 0.675925
288288 0 0
289289 −6.44124 −0.378896
290290 −1.33061 −0.0781360
291291 0 0
292292 −1.46056 −0.0854727
293293 −10.2974 −0.601579 −0.300790 0.953691i 0.597250π-0.597250\pi
−0.300790 + 0.953691i 0.597250π0.597250\pi
294294 0 0
295295 17.8229 1.03769
296296 9.76024 0.567302
297297 0 0
298298 7.02283 0.406821
299299 −13.8848 −0.802977
300300 0 0
301301 9.29738 0.535892
302302 −6.08044 −0.349890
303303 0 0
304304 18.0913 1.03761
305305 18.9424 1.08464
306306 0 0
307307 −0.307039 −0.0175236 −0.00876182 0.999962i 0.502789π-0.502789\pi
−0.00876182 + 0.999962i 0.502789π0.502789\pi
308308 8.97487 0.511391
309309 0 0
310310 −2.30704 −0.131031
311311 −1.04795 −0.0594240 −0.0297120 0.999559i 0.509459π-0.509459\pi
−0.0297120 + 0.999559i 0.509459π0.509459\pi
312312 0 0
313313 32.0553 1.81187 0.905937 0.423413i 0.139168π-0.139168\pi
0.905937 + 0.423413i 0.139168π0.139168\pi
314314 12.7653 0.720387
315315 0 0
316316 13.1210 0.738116
317317 6.44354 0.361905 0.180953 0.983492i 0.442082π-0.442082\pi
0.180953 + 0.983492i 0.442082π0.442082\pi
318318 0 0
319319 −6.00000 −0.335936
320320 −4.71964 −0.263836
321321 0 0
322322 2.30704 0.128566
323323 24.2111 1.34714
324324 0 0
325325 −0.484127 −0.0268545
326326 −2.93658 −0.162642
327327 0 0
328328 22.3527 1.23422
329329 1.04795 0.0577755
330330 0 0
331331 −20.6141 −1.13305 −0.566526 0.824044i 0.691713π-0.691713\pi
−0.566526 + 0.824044i 0.691713π0.691713\pi
332332 19.7579 1.08436
333333 0 0
334334 −12.2877 −0.672354
335335 −16.7409 −0.914654
336336 0 0
337337 26.4606 1.44140 0.720699 0.693248i 0.243821π-0.243821\pi
0.720699 + 0.693248i 0.243821π0.243821\pi
338338 1.60091 0.0870782
339339 0 0
340340 −12.3430 −0.669395
341341 −10.4029 −0.563351
342342 0 0
343343 1.00000 0.0539949
344344 18.1489 0.978524
345345 0 0
346346 −11.7939 −0.634046
347347 4.49149 0.241116 0.120558 0.992706i 0.461532π-0.461532\pi
0.120558 + 0.992706i 0.461532π0.461532\pi
348348 0 0
349349 3.75794 0.201158 0.100579 0.994929i 0.467931π-0.467931\pi
0.100579 + 0.994929i 0.467931π0.467931\pi
350350 0.0804406 0.00429973
351351 0 0
352352 26.9246 1.43509
353353 19.2591 1.02506 0.512529 0.858670i 0.328709π-0.328709\pi
0.512529 + 0.858670i 0.328709π0.328709\pi
354354 0 0
355355 −21.1439 −1.12220
356356 15.9594 0.845847
357357 0 0
358358 3.40524 0.179973
359359 −9.10557 −0.480573 −0.240287 0.970702i 0.577241π-0.577241\pi
−0.240287 + 0.970702i 0.577241π0.577241\pi
360360 0 0
361361 36.5159 1.92189
362362 −1.04795 −0.0550792
363363 0 0
364364 −5.44124 −0.285198
365365 1.86350 0.0975402
366366 0 0
367367 4.59476 0.239844 0.119922 0.992783i 0.461736π-0.461736\pi
0.119922 + 0.992783i 0.461736π0.461736\pi
368368 −10.6907 −0.557289
369369 0 0
370370 −5.76760 −0.299843
371371 0.249425 0.0129495
372372 0 0
373373 −21.3624 −1.10610 −0.553050 0.833148i 0.686536π-0.686536\pi
−0.553050 + 0.833148i 0.686536π0.686536\pi
374374 8.85614 0.457940
375375 0 0
376376 2.04565 0.105497
377377 3.63765 0.187348
378378 0 0
379379 −35.1203 −1.80401 −0.902004 0.431728i 0.857904π-0.857904\pi
−0.902004 + 0.431728i 0.857904π0.857904\pi
380380 −28.3024 −1.45188
381381 0 0
382382 −7.07814 −0.362149
383383 −3.19411 −0.163211 −0.0816057 0.996665i 0.526005π-0.526005\pi
−0.0816057 + 0.996665i 0.526005π0.526005\pi
384384 0 0
385385 −11.4509 −0.583592
386386 −9.29968 −0.473341
387387 0 0
388388 5.95435 0.302286
389389 −14.8059 −0.750688 −0.375344 0.926886i 0.622475π-0.622475\pi
−0.375344 + 0.926886i 0.622475π0.622475\pi
390390 0 0
391391 −14.3070 −0.723538
392392 1.95205 0.0985933
393393 0 0
394394 −8.49305 −0.427873
395395 −16.7409 −0.842327
396396 0 0
397397 26.8921 1.34968 0.674839 0.737965i 0.264213π-0.264213\pi
0.674839 + 0.737965i 0.264213π0.264213\pi
398398 3.74321 0.187630
399399 0 0
400400 −0.372756 −0.0186378
401401 −19.4029 −0.968937 −0.484468 0.874809i 0.660987π-0.660987\pi
−0.484468 + 0.874809i 0.660987π0.660987\pi
402402 0 0
403403 6.30704 0.314176
404404 −28.3024 −1.40810
405405 0 0
406406 −0.604417 −0.0299967
407407 −26.0074 −1.28914
408408 0 0
409409 −9.39558 −0.464582 −0.232291 0.972646i 0.574622π-0.574622\pi
−0.232291 + 0.972646i 0.574622π0.574622\pi
410410 −13.2088 −0.652338
411411 0 0
412412 1.97367 0.0972357
413413 8.09591 0.398373
414414 0 0
415415 −25.2088 −1.23745
416416 −16.3237 −0.800336
417417 0 0
418418 20.3070 0.993250
419419 24.6597 1.20471 0.602353 0.798230i 0.294230π-0.294230\pi
0.602353 + 0.798230i 0.294230π0.294230\pi
420420 0 0
421421 −14.2088 −0.692496 −0.346248 0.938143i 0.612544π-0.612544\pi
−0.346248 + 0.938143i 0.612544π0.612544\pi
422422 −1.72775 −0.0841055
423423 0 0
424424 0.486890 0.0236455
425425 −0.498850 −0.0241978
426426 0 0
427427 8.60442 0.416397
428428 15.7112 0.759429
429429 0 0
430430 −10.7247 −0.517191
431431 12.9977 0.626077 0.313039 0.949740i 0.398653π-0.398653\pi
0.313039 + 0.949740i 0.398653π0.398653\pi
432432 0 0
433433 −0.911456 −0.0438018 −0.0219009 0.999760i 0.506972π-0.506972\pi
−0.0219009 + 0.999760i 0.506972π0.506972\pi
434434 −1.04795 −0.0503033
435435 0 0
436436 23.7219 1.13608
437437 −32.8059 −1.56932
438438 0 0
439439 −10.5491 −0.503481 −0.251741 0.967795i 0.581003π-0.581003\pi
−0.251741 + 0.967795i 0.581003π0.581003\pi
440440 −22.3527 −1.06562
441441 0 0
442442 −5.36925 −0.255389
443443 17.4006 0.826730 0.413365 0.910566i 0.364353π-0.364353\pi
0.413365 + 0.910566i 0.364353π0.364353\pi
444444 0 0
445445 −20.3624 −0.965268
446446 12.1609 0.575834
447447 0 0
448448 −2.14386 −0.101288
449449 −0.748275 −0.0353133 −0.0176566 0.999844i 0.505621π-0.505621\pi
−0.0176566 + 0.999844i 0.505621π0.505621\pi
450450 0 0
451451 −59.5615 −2.80464
452452 34.3395 1.61520
453453 0 0
454454 6.11063 0.286786
455455 6.94239 0.325464
456456 0 0
457457 −1.00000 −0.0467780 −0.0233890 0.999726i 0.507446π-0.507446\pi
−0.0233890 + 0.999726i 0.507446π0.507446\pi
458458 −0.731253 −0.0341692
459459 0 0
460460 16.7247 0.779793
461461 38.0457 1.77196 0.885981 0.463721i 0.153486π-0.153486\pi
0.885981 + 0.463721i 0.153486π0.153486\pi
462462 0 0
463463 −25.8921 −1.20331 −0.601655 0.798756i 0.705492π-0.705492\pi
−0.601655 + 0.798756i 0.705492π0.705492\pi
464464 2.80083 0.130025
465465 0 0
466466 −4.58509 −0.212400
467467 −17.0627 −0.789566 −0.394783 0.918774i 0.629180π-0.629180\pi
−0.394783 + 0.918774i 0.629180π0.629180\pi
468468 0 0
469469 −7.60442 −0.351139
470470 −1.20883 −0.0557594
471471 0 0
472472 15.8036 0.727419
473473 −48.3601 −2.22360
474474 0 0
475475 −1.14386 −0.0524838
476476 −5.60672 −0.256983
477477 0 0
478478 −2.46406 −0.112704
479479 −2.80589 −0.128204 −0.0641022 0.997943i 0.520418π-0.520418\pi
−0.0641022 + 0.997943i 0.520418π0.520418\pi
480480 0 0
481481 15.7676 0.718941
482482 2.41261 0.109891
483483 0 0
484484 −27.7026 −1.25921
485485 −7.59706 −0.344965
486486 0 0
487487 −6.50621 −0.294825 −0.147412 0.989075i 0.547094π-0.547094\pi
−0.147412 + 0.989075i 0.547094π0.547094\pi
488488 16.7962 0.760330
489489 0 0
490490 −1.15352 −0.0521107
491491 −4.61408 −0.208230 −0.104115 0.994565i 0.533201π-0.533201\pi
−0.104115 + 0.994565i 0.533201π0.533201\pi
492492 0 0
493493 3.74828 0.168814
494494 −12.3116 −0.553927
495495 0 0
496496 4.85614 0.218047
497497 −9.60442 −0.430817
498498 0 0
499499 −35.4966 −1.58904 −0.794522 0.607235i 0.792278π-0.792278\pi
−0.794522 + 0.607235i 0.792278π0.792278\pi
500500 19.5758 0.875456
501501 0 0
502502 −1.64731 −0.0735229
503503 18.9211 0.843651 0.421825 0.906677i 0.361389π-0.361389\pi
0.421825 + 0.906677i 0.361389π0.361389\pi
504504 0 0
505505 36.1106 1.60690
506506 −12.0000 −0.533465
507507 0 0
508508 −16.0421 −0.711755
509509 14.8059 0.656260 0.328130 0.944633i 0.393582π-0.393582\pi
0.328130 + 0.944633i 0.393582π0.393582\pi
510510 0 0
511511 0.846480 0.0374461
512512 −22.0480 −0.974391
513513 0 0
514514 10.5588 0.465727
515515 −2.51817 −0.110964
516516 0 0
517517 −5.45090 −0.239730
518518 −2.61988 −0.115111
519519 0 0
520520 13.5519 0.594289
521521 12.7100 0.556834 0.278417 0.960460i 0.410190π-0.410190\pi
0.278417 + 0.960460i 0.410190π0.410190\pi
522522 0 0
523523 0.352692 0.0154222 0.00771108 0.999970i 0.497545π-0.497545\pi
0.00771108 + 0.999970i 0.497545π0.497545\pi
524524 13.0216 0.568852
525525 0 0
526526 9.01317 0.392993
527527 6.49885 0.283094
528528 0 0
529529 −3.61408 −0.157134
530530 −0.287717 −0.0124976
531531 0 0
532532 −12.8561 −0.557384
533533 36.1106 1.56412
534534 0 0
535535 −20.0457 −0.866649
536536 −14.8442 −0.641171
537537 0 0
538538 1.44124 0.0621361
539539 −5.20147 −0.224043
540540 0 0
541541 −22.6930 −0.975647 −0.487823 0.872942i 0.662209π-0.662209\pi
−0.487823 + 0.872942i 0.662209π0.662209\pi
542542 6.73631 0.289349
543543 0 0
544544 −16.8201 −0.721158
545545 −30.2664 −1.29647
546546 0 0
547547 −1.49379 −0.0638698 −0.0319349 0.999490i 0.510167π-0.510167\pi
−0.0319349 + 0.999490i 0.510167π0.510167\pi
548548 −2.42071 −0.103408
549549 0 0
550550 −0.418410 −0.0178410
551551 8.59476 0.366149
552552 0 0
553553 −7.60442 −0.323373
554554 8.77570 0.372844
555555 0 0
556556 26.6597 1.13062
557557 8.50115 0.360205 0.180103 0.983648i 0.442357π-0.442357\pi
0.180103 + 0.983648i 0.442357π0.442357\pi
558558 0 0
559559 29.3195 1.24008
560560 5.34533 0.225881
561561 0 0
562562 2.78076 0.117299
563563 −23.4006 −0.986220 −0.493110 0.869967i 0.664140π-0.664140\pi
−0.493110 + 0.869967i 0.664140π0.664140\pi
564564 0 0
565565 −43.8133 −1.84324
566566 −6.47252 −0.272060
567567 0 0
568568 −18.7483 −0.786660
569569 8.11293 0.340112 0.170056 0.985434i 0.445605π-0.445605\pi
0.170056 + 0.985434i 0.445605π0.445605\pi
570570 0 0
571571 16.5948 0.694469 0.347234 0.937778i 0.387121π-0.387121\pi
0.347234 + 0.937778i 0.387121π0.387121\pi
572572 28.3024 1.18338
573573 0 0
574574 −6.00000 −0.250435
575575 0.675938 0.0281886
576576 0 0
577577 −10.8921 −0.453445 −0.226723 0.973959i 0.572801π-0.572801\pi
−0.226723 + 0.973959i 0.572801π0.572801\pi
578578 3.37506 0.140384
579579 0 0
580580 −4.38168 −0.181939
581581 −11.4509 −0.475063
582582 0 0
583583 −1.29738 −0.0537319
584584 1.65237 0.0683755
585585 0 0
586586 5.39558 0.222889
587587 43.3195 1.78799 0.893993 0.448081i 0.147893π-0.147893\pi
0.893993 + 0.448081i 0.147893π0.147893\pi
588588 0 0
589589 14.9018 0.614018
590590 −9.33879 −0.384472
591591 0 0
592592 12.1404 0.498965
593593 −28.4583 −1.16864 −0.584320 0.811523i 0.698639π-0.698639\pi
−0.584320 + 0.811523i 0.698639π0.698639\pi
594594 0 0
595595 7.15352 0.293266
596596 23.1261 0.947282
597597 0 0
598598 7.27529 0.297509
599599 29.7003 1.21352 0.606761 0.794884i 0.292468π-0.292468\pi
0.606761 + 0.794884i 0.292468π0.292468\pi
600600 0 0
601601 37.5062 1.52991 0.764955 0.644084i 0.222761π-0.222761\pi
0.764955 + 0.644084i 0.222761π0.222761\pi
602602 −4.87161 −0.198552
603603 0 0
604604 −20.0228 −0.814717
605605 35.3453 1.43699
606606 0 0
607607 2.65973 0.107955 0.0539776 0.998542i 0.482810π-0.482810\pi
0.0539776 + 0.998542i 0.482810π0.482810\pi
608608 −38.5684 −1.56416
609609 0 0
610610 −9.92536 −0.401866
611611 3.30474 0.133695
612612 0 0
613613 −41.6694 −1.68301 −0.841505 0.540249i 0.818330π-0.818330\pi
−0.841505 + 0.540249i 0.818330π0.818330\pi
614614 0.160881 0.00649264
615615 0 0
616616 −10.1535 −0.409097
617617 43.5519 1.75333 0.876666 0.481099i 0.159762π-0.159762\pi
0.876666 + 0.481099i 0.159762π0.159762\pi
618618 0 0
619619 −14.0650 −0.565319 −0.282660 0.959220i 0.591217π-0.591217\pi
−0.282660 + 0.959220i 0.591217π0.591217\pi
620620 −7.59706 −0.305105
621621 0 0
622622 0.549103 0.0220170
623623 −9.24943 −0.370570
624624 0 0
625625 −24.2088 −0.968353
626626 −16.7962 −0.671312
627627 0 0
628628 42.0360 1.67742
629629 16.2471 0.647815
630630 0 0
631631 −0.594756 −0.0236769 −0.0118384 0.999930i 0.503768π-0.503768\pi
−0.0118384 + 0.999930i 0.503768π0.503768\pi
632632 −14.8442 −0.590470
633633 0 0
634634 −3.37626 −0.134088
635635 20.4679 0.812245
636636 0 0
637637 3.15352 0.124947
638638 3.14386 0.124467
639639 0 0
640640 25.2641 0.998653
641641 7.69066 0.303763 0.151881 0.988399i 0.451467π-0.451467\pi
0.151881 + 0.988399i 0.451467π0.451467\pi
642642 0 0
643643 49.8229 1.96482 0.982412 0.186727i 0.0597878π-0.0597878\pi
0.982412 + 0.186727i 0.0597878π0.0597878\pi
644644 7.59706 0.299366
645645 0 0
646646 −12.6861 −0.499126
647647 −28.2761 −1.11165 −0.555824 0.831300i 0.687597π-0.687597\pi
−0.555824 + 0.831300i 0.687597π0.687597\pi
648648 0 0
649649 −42.1106 −1.65299
650650 0.253671 0.00994980
651651 0 0
652652 −9.67013 −0.378712
653653 9.55416 0.373883 0.186942 0.982371i 0.440142π-0.440142\pi
0.186942 + 0.982371i 0.440142π0.440142\pi
654654 0 0
655655 −16.6141 −0.649166
656656 27.8036 1.08555
657657 0 0
658658 −0.549103 −0.0214062
659659 −48.1992 −1.87757 −0.938787 0.344499i 0.888049π-0.888049\pi
−0.938787 + 0.344499i 0.888049π0.888049\pi
660660 0 0
661661 2.05531 0.0799425 0.0399712 0.999201i 0.487273π-0.487273\pi
0.0399712 + 0.999201i 0.487273π0.487273\pi
662662 10.8013 0.419804
663663 0 0
664664 −22.3527 −0.867453
665665 16.4029 0.636079
666666 0 0
667667 −5.07888 −0.196655
668668 −40.4633 −1.56557
669669 0 0
670670 8.77184 0.338886
671671 −44.7556 −1.72777
672672 0 0
673673 3.79117 0.146139 0.0730694 0.997327i 0.476721π-0.476721\pi
0.0730694 + 0.997327i 0.476721π0.476721\pi
674674 −13.8647 −0.534049
675675 0 0
676676 5.27179 0.202761
677677 −22.5136 −0.865267 −0.432633 0.901570i 0.642416π-0.642416\pi
−0.432633 + 0.901570i 0.642416π0.642416\pi
678678 0 0
679679 −3.45090 −0.132433
680680 13.9640 0.535495
681681 0 0
682682 5.45090 0.208726
683683 15.3933 0.589008 0.294504 0.955650i 0.404846π-0.404846\pi
0.294504 + 0.955650i 0.404846π0.404846\pi
684684 0 0
685685 3.08854 0.118007
686686 −0.523976 −0.0200055
687687 0 0
688688 22.5747 0.860652
689689 0.786567 0.0299658
690690 0 0
691691 −23.2088 −0.882906 −0.441453 0.897284i 0.645537π-0.645537\pi
−0.441453 + 0.897284i 0.645537π0.645537\pi
692692 −38.8373 −1.47637
693693 0 0
694694 −2.35343 −0.0893351
695695 −34.0147 −1.29025
696696 0 0
697697 37.2088 1.40939
698698 −1.96907 −0.0745304
699699 0 0
700700 0.264890 0.0100119
701701 −15.0000 −0.566542 −0.283271 0.959040i 0.591420π-0.591420\pi
−0.283271 + 0.959040i 0.591420π0.591420\pi
702702 0 0
703703 37.2545 1.40508
704704 11.1512 0.420277
705705 0 0
706706 −10.0913 −0.379791
707707 16.4029 0.616896
708708 0 0
709709 −31.0000 −1.16423 −0.582115 0.813107i 0.697775π-0.697775\pi
−0.582115 + 0.813107i 0.697775π0.697775\pi
710710 11.0789 0.415783
711711 0 0
712712 −18.0553 −0.676652
713713 −8.80589 −0.329783
714714 0 0
715715 −36.1106 −1.35046
716716 11.2134 0.419066
717717 0 0
718718 4.77110 0.178056
719719 18.2111 0.679161 0.339580 0.940577i 0.389715π-0.389715\pi
0.339580 + 0.940577i 0.389715π0.389715\pi
720720 0 0
721721 −1.14386 −0.0425995
722722 −19.1335 −0.712073
723723 0 0
724724 −3.45090 −0.128252
725725 −0.177088 −0.00657688
726726 0 0
727727 8.83682 0.327739 0.163870 0.986482i 0.447602π-0.447602\pi
0.163870 + 0.986482i 0.447602π0.447602\pi
728728 6.15582 0.228150
729729 0 0
730730 −0.976432 −0.0361394
731731 30.2111 1.11740
732732 0 0
733733 −44.6404 −1.64883 −0.824416 0.565985i 0.808496π-0.808496\pi
−0.824416 + 0.565985i 0.808496π0.808496\pi
734734 −2.40754 −0.0888641
735735 0 0
736736 22.7912 0.840094
737737 39.5542 1.45700
738738 0 0
739739 11.6044 0.426875 0.213438 0.976957i 0.431534π-0.431534\pi
0.213438 + 0.976957i 0.431534π0.431534\pi
740740 −18.9926 −0.698183
741741 0 0
742742 −0.130693 −0.00479789
743743 −26.7939 −0.982974 −0.491487 0.870885i 0.663546π-0.663546\pi
−0.491487 + 0.870885i 0.663546π0.663546\pi
744744 0 0
745745 −29.5062 −1.08102
746746 11.1934 0.409818
747747 0 0
748748 29.1632 1.06631
749749 −9.10557 −0.332710
750750 0 0
751751 −18.2185 −0.664802 −0.332401 0.943138i 0.607859π-0.607859\pi
−0.332401 + 0.943138i 0.607859π0.607859\pi
752752 2.54450 0.0927885
753753 0 0
754754 −1.90604 −0.0694139
755755 25.5468 0.929743
756756 0 0
757757 12.9018 0.468924 0.234462 0.972125i 0.424667π-0.424667\pi
0.234462 + 0.972125i 0.424667π0.424667\pi
758758 18.4022 0.668398
759759 0 0
760760 32.0193 1.16146
761761 −18.2162 −0.660337 −0.330168 0.943922i 0.607106π-0.607106\pi
−0.330168 + 0.943922i 0.607106π0.607106\pi
762762 0 0
763763 −13.7483 −0.497721
764764 −23.3082 −0.843263
765765 0 0
766766 1.67364 0.0604710
767767 25.5306 0.921856
768768 0 0
769769 38.6044 1.39211 0.696055 0.717988i 0.254937π-0.254937\pi
0.696055 + 0.717988i 0.254937π0.254937\pi
770770 6.00000 0.216225
771771 0 0
772772 −30.6237 −1.10217
773773 −33.9594 −1.22144 −0.610718 0.791849i 0.709119π-0.709119\pi
−0.610718 + 0.791849i 0.709119π0.709119\pi
774774 0 0
775775 −0.307039 −0.0110292
776776 −6.73631 −0.241820
777777 0 0
778778 7.75794 0.278136
779779 85.3195 3.05689
780780 0 0
781781 49.9571 1.78761
782782 7.49655 0.268076
783783 0 0
784784 2.42807 0.0867168
785785 −53.6330 −1.91425
786786 0 0
787787 −6.85614 −0.244395 −0.122198 0.992506i 0.538994π-0.538994\pi
−0.122198 + 0.992506i 0.538994π0.538994\pi
788788 −27.9675 −0.996301
789789 0 0
790790 8.77184 0.312088
791791 −19.9018 −0.707626
792792 0 0
793793 27.1342 0.963564
794794 −14.0908 −0.500065
795795 0 0
796796 12.3264 0.436896
797797 −26.6501 −0.943994 −0.471997 0.881600i 0.656467π-0.656467\pi
−0.471997 + 0.881600i 0.656467π0.656467\pi
798798 0 0
799799 3.40524 0.120469
800800 0.794670 0.0280958
801801 0 0
802802 10.1667 0.358998
803803 −4.40294 −0.155377
804804 0 0
805805 −9.69296 −0.341632
806806 −3.30474 −0.116404
807807 0 0
808808 32.0193 1.12644
809809 45.7100 1.60708 0.803539 0.595252i 0.202948π-0.202948\pi
0.803539 + 0.595252i 0.202948π0.202948\pi
810810 0 0
811811 33.2088 1.16612 0.583060 0.812429i 0.301855π-0.301855\pi
0.583060 + 0.812429i 0.301855π0.301855\pi
812812 −1.99034 −0.0698472
813813 0 0
814814 13.6272 0.477635
815815 12.3380 0.432180
816816 0 0
817817 69.2738 2.42358
818818 4.92306 0.172131
819819 0 0
820820 −43.4966 −1.51897
821821 −0.304740 −0.0106355 −0.00531774 0.999986i 0.501693π-0.501693\pi
−0.00531774 + 0.999986i 0.501693π0.501693\pi
822822 0 0
823823 46.4177 1.61802 0.809009 0.587796i 0.200004π-0.200004\pi
0.809009 + 0.587796i 0.200004π0.200004\pi
824824 −2.23287 −0.0777856
825825 0 0
826826 −4.24206 −0.147600
827827 40.8133 1.41922 0.709608 0.704597i 0.248872π-0.248872\pi
0.709608 + 0.704597i 0.248872π0.248872\pi
828828 0 0
829829 −7.40524 −0.257195 −0.128597 0.991697i 0.541047π-0.541047\pi
−0.128597 + 0.991697i 0.541047π0.541047\pi
830830 13.2088 0.458485
831831 0 0
832832 −6.76070 −0.234385
833833 3.24943 0.112586
834834 0 0
835835 51.6265 1.78661
836836 66.8709 2.31278
837837 0 0
838838 −12.9211 −0.446353
839839 −18.3720 −0.634272 −0.317136 0.948380i 0.602721π-0.602721\pi
−0.317136 + 0.948380i 0.602721π0.602721\pi
840840 0 0
841841 −27.6694 −0.954117
842842 7.44509 0.256575
843843 0 0
844844 −5.68946 −0.195839
845845 −6.72619 −0.231388
846846 0 0
847847 16.0553 0.551667
848848 0.605622 0.0207971
849849 0 0
850850 0.261386 0.00896546
851851 −22.0147 −0.754655
852852 0 0
853853 37.5615 1.28608 0.643041 0.765832i 0.277672π-0.277672\pi
0.643041 + 0.765832i 0.277672π0.277672\pi
854854 −4.50851 −0.154278
855855 0 0
856856 −17.7745 −0.607520
857857 2.15122 0.0734843 0.0367421 0.999325i 0.488302π-0.488302\pi
0.0367421 + 0.999325i 0.488302π0.488302\pi
858858 0 0
859859 14.2877 0.487491 0.243745 0.969839i 0.421624π-0.421624\pi
0.243745 + 0.969839i 0.421624π0.421624\pi
860860 −35.3163 −1.20428
861861 0 0
862862 −6.81049 −0.231966
863863 −27.6810 −0.942272 −0.471136 0.882061i 0.656156π-0.656156\pi
−0.471136 + 0.882061i 0.656156π0.656156\pi
864864 0 0
865865 49.5519 1.68481
866866 0.477581 0.0162289
867867 0 0
868868 −3.45090 −0.117131
869869 39.5542 1.34178
870870 0 0
871871 −23.9807 −0.812554
872872 −26.8373 −0.908825
873873 0 0
874874 17.1895 0.581444
875875 −11.3453 −0.383542
876876 0 0
877877 −19.0000 −0.641584 −0.320792 0.947150i 0.603949π-0.603949\pi
−0.320792 + 0.947150i 0.603949π0.603949\pi
878878 5.52748 0.186543
879879 0 0
880880 −27.8036 −0.937259
881881 4.06498 0.136953 0.0684763 0.997653i 0.478186π-0.478186\pi
0.0684763 + 0.997653i 0.478186π0.478186\pi
882882 0 0
883883 −20.5255 −0.690739 −0.345370 0.938467i 0.612246π-0.612246\pi
−0.345370 + 0.938467i 0.612246π0.612246\pi
884884 −17.6809 −0.594673
885885 0 0
886886 −9.11753 −0.306309
887887 −10.1152 −0.339636 −0.169818 0.985475i 0.554318π-0.554318\pi
−0.169818 + 0.985475i 0.554318π0.554318\pi
888888 0 0
889889 9.29738 0.311824
890890 10.6694 0.357639
891891 0 0
892892 40.0457 1.34083
893893 7.80819 0.261291
894894 0 0
895895 −14.3070 −0.478232
896896 11.4760 0.383387
897897 0 0
898898 0.392079 0.0130838
899899 2.30704 0.0769441
900900 0 0
901901 0.810488 0.0270013
902902 31.2088 1.03914
903903 0 0
904904 −38.8492 −1.29211
905905 4.40294 0.146359
906906 0 0
907907 22.3956 0.743633 0.371817 0.928306i 0.378735π-0.378735\pi
0.371817 + 0.928306i 0.378735π0.378735\pi
908908 20.1222 0.667780
909909 0 0
910910 −3.63765 −0.120587
911911 −33.8036 −1.11996 −0.559981 0.828505i 0.689192π-0.689192\pi
−0.559981 + 0.828505i 0.689192π0.689192\pi
912912 0 0
913913 59.5615 1.97120
914914 0.523976 0.0173316
915915 0 0
916916 −2.40801 −0.0795628
917917 −7.54680 −0.249217
918918 0 0
919919 35.6044 1.17448 0.587241 0.809412i 0.300214π-0.300214\pi
0.587241 + 0.809412i 0.300214π0.300214\pi
920920 −18.9211 −0.623811
921921 0 0
922922 −19.9350 −0.656525
923923 −30.2877 −0.996932
924924 0 0
925925 −0.767598 −0.0252385
926926 13.5669 0.445835
927927 0 0
928928 −5.97102 −0.196008
929929 −32.4126 −1.06342 −0.531712 0.846926i 0.678451π-0.678451\pi
−0.531712 + 0.846926i 0.678451π0.678451\pi
930930 0 0
931931 7.45090 0.244193
932932 −15.0987 −0.494573
933933 0 0
934934 8.94044 0.292540
935935 −37.2088 −1.21686
936936 0 0
937937 −4.34303 −0.141881 −0.0709403 0.997481i 0.522600π-0.522600\pi
−0.0709403 + 0.997481i 0.522600π0.522600\pi
938938 3.98454 0.130100
939939 0 0
940940 −3.98068 −0.129835
941941 −31.9401 −1.04122 −0.520609 0.853796i 0.674295π-0.674295\pi
−0.520609 + 0.853796i 0.674295π0.674295\pi
942942 0 0
943943 −50.4177 −1.64183
944944 19.6574 0.639795
945945 0 0
946946 25.3395 0.823859
947947 −40.5136 −1.31651 −0.658257 0.752793i 0.728706π-0.728706\pi
−0.658257 + 0.752793i 0.728706π0.728706\pi
948948 0 0
949949 2.66939 0.0866522
950950 0.599355 0.0194456
951951 0 0
952952 6.34303 0.205579
953953 9.74828 0.315778 0.157889 0.987457i 0.449531π-0.449531\pi
0.157889 + 0.987457i 0.449531π0.449531\pi
954954 0 0
955955 29.7386 0.962319
956956 −8.11413 −0.262430
957957 0 0
958958 1.47022 0.0475006
959959 1.40294 0.0453034
960960 0 0
961961 −27.0000 −0.870968
962962 −8.26185 −0.266373
963963 0 0
964964 7.94469 0.255881
965965 39.0723 1.25778
966966 0 0
967967 29.6930 0.954861 0.477431 0.878669i 0.341568π-0.341568\pi
0.477431 + 0.878669i 0.341568π0.341568\pi
968968 31.3407 1.00733
969969 0 0
970970 3.98068 0.127812
971971 31.9954 1.02678 0.513391 0.858155i 0.328389π-0.328389\pi
0.513391 + 0.858155i 0.328389π0.328389\pi
972972 0 0
973973 −15.4509 −0.495333
974974 3.40910 0.109235
975975 0 0
976976 20.8921 0.668741
977977 1.80819 0.0578491 0.0289245 0.999582i 0.490792π-0.490792\pi
0.0289245 + 0.999582i 0.490792π0.490792\pi
978978 0 0
979979 48.1106 1.53762
980980 −3.79853 −0.121340
981981 0 0
982982 2.41767 0.0771509
983983 43.5468 1.38893 0.694464 0.719528i 0.255642π-0.255642\pi
0.694464 + 0.719528i 0.255642π0.255642\pi
984984 0 0
985985 35.6833 1.13696
986986 −1.96401 −0.0625468
987987 0 0
988988 −40.5421 −1.28982
989989 −40.9358 −1.30168
990990 0 0
991991 −33.1010 −1.05149 −0.525743 0.850643i 0.676213π-0.676213\pi
−0.525743 + 0.850643i 0.676213π0.676213\pi
992992 −10.3527 −0.328698
993993 0 0
994994 5.03249 0.159621
995995 −15.7270 −0.498580
996996 0 0
997997 −0.539441 −0.0170843 −0.00854214 0.999964i 0.502719π-0.502719\pi
−0.00854214 + 0.999964i 0.502719π0.502719\pi
998998 18.5994 0.588752
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 567.2.a.e.1.2 3
3.2 odd 2 567.2.a.f.1.2 yes 3
4.3 odd 2 9072.2.a.bu.1.3 3
7.6 odd 2 3969.2.a.o.1.2 3
9.2 odd 6 567.2.f.l.190.2 6
9.4 even 3 567.2.f.m.379.2 6
9.5 odd 6 567.2.f.l.379.2 6
9.7 even 3 567.2.f.m.190.2 6
12.11 even 2 9072.2.a.cb.1.1 3
21.20 even 2 3969.2.a.n.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
567.2.a.e.1.2 3 1.1 even 1 trivial
567.2.a.f.1.2 yes 3 3.2 odd 2
567.2.f.l.190.2 6 9.2 odd 6
567.2.f.l.379.2 6 9.5 odd 6
567.2.f.m.190.2 6 9.7 even 3
567.2.f.m.379.2 6 9.4 even 3
3969.2.a.n.1.2 3 21.20 even 2
3969.2.a.o.1.2 3 7.6 odd 2
9072.2.a.bu.1.3 3 4.3 odd 2
9072.2.a.cb.1.1 3 12.11 even 2