Properties

Label 605.2.a.e.1.2
Level 605605
Weight 22
Character 605.1
Self dual yes
Analytic conductor 4.8314.831
Analytic rank 11
Dimension 22
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [605,2,Mod(1,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, 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("605.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 605=5112 605 = 5 \cdot 11^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 605.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: 4.830949322294.83094932229
Analytic rank: 11
Dimension: 22
Coefficient field: Q(ζ12)+\Q(\zeta_{12})^+
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x23 x^{2} - 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 1.732051.73205 of defining polynomial
Character χ\chi == 605.1

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+1.73205q21.00000q3+1.00000q41.00000q51.73205q61.73205q71.73205q82.00000q91.73205q101.00000q12+3.46410q133.00000q14+1.00000q155.00000q166.92820q173.46410q183.46410q191.00000q20+1.73205q21+1.73205q24+1.00000q25+6.00000q26+5.00000q271.73205q28+1.73205q308.00000q315.19615q3212.0000q34+1.73205q352.00000q368.00000q376.00000q383.46410q39+1.73205q40+12.1244q41+3.00000q42+8.66025q43+2.00000q45+9.00000q47+5.00000q484.00000q49+1.73205q50+6.92820q51+3.46410q52+6.00000q53+8.66025q54+3.00000q56+3.46410q5712.0000q59+1.00000q60+8.66025q6113.8564q62+3.46410q63+1.00000q643.46410q655.00000q676.92820q68+3.00000q7012.0000q71+3.46410q7213.8564q741.00000q753.46410q766.00000q7810.3923q79+5.00000q80+1.00000q81+21.0000q82+3.46410q83+1.73205q84+6.92820q85+15.0000q86+3.00000q89+3.46410q906.00000q91+8.00000q93+15.5885q94+3.46410q95+5.19615q9610.0000q976.92820q98+O(q100)q+1.73205 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.73205 q^{6} -1.73205 q^{7} -1.73205 q^{8} -2.00000 q^{9} -1.73205 q^{10} -1.00000 q^{12} +3.46410 q^{13} -3.00000 q^{14} +1.00000 q^{15} -5.00000 q^{16} -6.92820 q^{17} -3.46410 q^{18} -3.46410 q^{19} -1.00000 q^{20} +1.73205 q^{21} +1.73205 q^{24} +1.00000 q^{25} +6.00000 q^{26} +5.00000 q^{27} -1.73205 q^{28} +1.73205 q^{30} -8.00000 q^{31} -5.19615 q^{32} -12.0000 q^{34} +1.73205 q^{35} -2.00000 q^{36} -8.00000 q^{37} -6.00000 q^{38} -3.46410 q^{39} +1.73205 q^{40} +12.1244 q^{41} +3.00000 q^{42} +8.66025 q^{43} +2.00000 q^{45} +9.00000 q^{47} +5.00000 q^{48} -4.00000 q^{49} +1.73205 q^{50} +6.92820 q^{51} +3.46410 q^{52} +6.00000 q^{53} +8.66025 q^{54} +3.00000 q^{56} +3.46410 q^{57} -12.0000 q^{59} +1.00000 q^{60} +8.66025 q^{61} -13.8564 q^{62} +3.46410 q^{63} +1.00000 q^{64} -3.46410 q^{65} -5.00000 q^{67} -6.92820 q^{68} +3.00000 q^{70} -12.0000 q^{71} +3.46410 q^{72} -13.8564 q^{74} -1.00000 q^{75} -3.46410 q^{76} -6.00000 q^{78} -10.3923 q^{79} +5.00000 q^{80} +1.00000 q^{81} +21.0000 q^{82} +3.46410 q^{83} +1.73205 q^{84} +6.92820 q^{85} +15.0000 q^{86} +3.00000 q^{89} +3.46410 q^{90} -6.00000 q^{91} +8.00000 q^{93} +15.5885 q^{94} +3.46410 q^{95} +5.19615 q^{96} -10.0000 q^{97} -6.92820 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q2q3+2q42q54q92q126q14+2q1510q162q20+2q25+12q26+10q2716q3124q344q3616q3712q38+6q42+20q97+O(q100) 2 q - 2 q^{3} + 2 q^{4} - 2 q^{5} - 4 q^{9} - 2 q^{12} - 6 q^{14} + 2 q^{15} - 10 q^{16} - 2 q^{20} + 2 q^{25} + 12 q^{26} + 10 q^{27} - 16 q^{31} - 24 q^{34} - 4 q^{36} - 16 q^{37} - 12 q^{38} + 6 q^{42}+ \cdots - 20 q^{97}+O(q^{100}) Copy content Toggle raw display

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.73205 1.22474 0.612372 0.790569i 0.290215π-0.290215\pi
0.612372 + 0.790569i 0.290215π0.290215\pi
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 −1.00000 −0.447214
66 −1.73205 −0.707107
77 −1.73205 −0.654654 −0.327327 0.944911i 0.606148π-0.606148\pi
−0.327327 + 0.944911i 0.606148π0.606148\pi
88 −1.73205 −0.612372
99 −2.00000 −0.666667
1010 −1.73205 −0.547723
1111 0 0
1212 −1.00000 −0.288675
1313 3.46410 0.960769 0.480384 0.877058i 0.340497π-0.340497\pi
0.480384 + 0.877058i 0.340497π0.340497\pi
1414 −3.00000 −0.801784
1515 1.00000 0.258199
1616 −5.00000 −1.25000
1717 −6.92820 −1.68034 −0.840168 0.542326i 0.817544π-0.817544\pi
−0.840168 + 0.542326i 0.817544π0.817544\pi
1818 −3.46410 −0.816497
1919 −3.46410 −0.794719 −0.397360 0.917663i 0.630073π-0.630073\pi
−0.397360 + 0.917663i 0.630073π0.630073\pi
2020 −1.00000 −0.223607
2121 1.73205 0.377964
2222 0 0
2323 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
2424 1.73205 0.353553
2525 1.00000 0.200000
2626 6.00000 1.17670
2727 5.00000 0.962250
2828 −1.73205 −0.327327
2929 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
3030 1.73205 0.316228
3131 −8.00000 −1.43684 −0.718421 0.695608i 0.755135π-0.755135\pi
−0.718421 + 0.695608i 0.755135π0.755135\pi
3232 −5.19615 −0.918559
3333 0 0
3434 −12.0000 −2.05798
3535 1.73205 0.292770
3636 −2.00000 −0.333333
3737 −8.00000 −1.31519 −0.657596 0.753371i 0.728427π-0.728427\pi
−0.657596 + 0.753371i 0.728427π0.728427\pi
3838 −6.00000 −0.973329
3939 −3.46410 −0.554700
4040 1.73205 0.273861
4141 12.1244 1.89351 0.946753 0.321960i 0.104342π-0.104342\pi
0.946753 + 0.321960i 0.104342π0.104342\pi
4242 3.00000 0.462910
4343 8.66025 1.32068 0.660338 0.750968i 0.270413π-0.270413\pi
0.660338 + 0.750968i 0.270413π0.270413\pi
4444 0 0
4545 2.00000 0.298142
4646 0 0
4747 9.00000 1.31278 0.656392 0.754420i 0.272082π-0.272082\pi
0.656392 + 0.754420i 0.272082π0.272082\pi
4848 5.00000 0.721688
4949 −4.00000 −0.571429
5050 1.73205 0.244949
5151 6.92820 0.970143
5252 3.46410 0.480384
5353 6.00000 0.824163 0.412082 0.911147i 0.364802π-0.364802\pi
0.412082 + 0.911147i 0.364802π0.364802\pi
5454 8.66025 1.17851
5555 0 0
5656 3.00000 0.400892
5757 3.46410 0.458831
5858 0 0
5959 −12.0000 −1.56227 −0.781133 0.624364i 0.785358π-0.785358\pi
−0.781133 + 0.624364i 0.785358π0.785358\pi
6060 1.00000 0.129099
6161 8.66025 1.10883 0.554416 0.832240i 0.312942π-0.312942\pi
0.554416 + 0.832240i 0.312942π0.312942\pi
6262 −13.8564 −1.75977
6363 3.46410 0.436436
6464 1.00000 0.125000
6565 −3.46410 −0.429669
6666 0 0
6767 −5.00000 −0.610847 −0.305424 0.952217i 0.598798π-0.598798\pi
−0.305424 + 0.952217i 0.598798π0.598798\pi
6868 −6.92820 −0.840168
6969 0 0
7070 3.00000 0.358569
7171 −12.0000 −1.42414 −0.712069 0.702109i 0.752242π-0.752242\pi
−0.712069 + 0.702109i 0.752242π0.752242\pi
7272 3.46410 0.408248
7373 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
7474 −13.8564 −1.61077
7575 −1.00000 −0.115470
7676 −3.46410 −0.397360
7777 0 0
7878 −6.00000 −0.679366
7979 −10.3923 −1.16923 −0.584613 0.811312i 0.698754π-0.698754\pi
−0.584613 + 0.811312i 0.698754π0.698754\pi
8080 5.00000 0.559017
8181 1.00000 0.111111
8282 21.0000 2.31906
8383 3.46410 0.380235 0.190117 0.981761i 0.439113π-0.439113\pi
0.190117 + 0.981761i 0.439113π0.439113\pi
8484 1.73205 0.188982
8585 6.92820 0.751469
8686 15.0000 1.61749
8787 0 0
8888 0 0
8989 3.00000 0.317999 0.159000 0.987279i 0.449173π-0.449173\pi
0.159000 + 0.987279i 0.449173π0.449173\pi
9090 3.46410 0.365148
9191 −6.00000 −0.628971
9292 0 0
9393 8.00000 0.829561
9494 15.5885 1.60783
9595 3.46410 0.355409
9696 5.19615 0.530330
9797 −10.0000 −1.01535 −0.507673 0.861550i 0.669494π-0.669494\pi
−0.507673 + 0.861550i 0.669494π0.669494\pi
9898 −6.92820 −0.699854
9999 0 0
100100 1.00000 0.100000
101101 −1.73205 −0.172345 −0.0861727 0.996280i 0.527464π-0.527464\pi
−0.0861727 + 0.996280i 0.527464π0.527464\pi
102102 12.0000 1.18818
103103 −4.00000 −0.394132 −0.197066 0.980390i 0.563141π-0.563141\pi
−0.197066 + 0.980390i 0.563141π0.563141\pi
104104 −6.00000 −0.588348
105105 −1.73205 −0.169031
106106 10.3923 1.00939
107107 1.73205 0.167444 0.0837218 0.996489i 0.473319π-0.473319\pi
0.0837218 + 0.996489i 0.473319π0.473319\pi
108108 5.00000 0.481125
109109 1.73205 0.165900 0.0829502 0.996554i 0.473566π-0.473566\pi
0.0829502 + 0.996554i 0.473566π0.473566\pi
110110 0 0
111111 8.00000 0.759326
112112 8.66025 0.818317
113113 −6.00000 −0.564433 −0.282216 0.959351i 0.591070π-0.591070\pi
−0.282216 + 0.959351i 0.591070π0.591070\pi
114114 6.00000 0.561951
115115 0 0
116116 0 0
117117 −6.92820 −0.640513
118118 −20.7846 −1.91338
119119 12.0000 1.10004
120120 −1.73205 −0.158114
121121 0 0
122122 15.0000 1.35804
123123 −12.1244 −1.09322
124124 −8.00000 −0.718421
125125 −1.00000 −0.0894427
126126 6.00000 0.534522
127127 1.73205 0.153695 0.0768473 0.997043i 0.475515π-0.475515\pi
0.0768473 + 0.997043i 0.475515π0.475515\pi
128128 12.1244 1.07165
129129 −8.66025 −0.762493
130130 −6.00000 −0.526235
131131 −3.46410 −0.302660 −0.151330 0.988483i 0.548356π-0.548356\pi
−0.151330 + 0.988483i 0.548356π0.548356\pi
132132 0 0
133133 6.00000 0.520266
134134 −8.66025 −0.748132
135135 −5.00000 −0.430331
136136 12.0000 1.02899
137137 18.0000 1.53784 0.768922 0.639343i 0.220793π-0.220793\pi
0.768922 + 0.639343i 0.220793π0.220793\pi
138138 0 0
139139 13.8564 1.17529 0.587643 0.809121i 0.300056π-0.300056\pi
0.587643 + 0.809121i 0.300056π0.300056\pi
140140 1.73205 0.146385
141141 −9.00000 −0.757937
142142 −20.7846 −1.74421
143143 0 0
144144 10.0000 0.833333
145145 0 0
146146 0 0
147147 4.00000 0.329914
148148 −8.00000 −0.657596
149149 −19.0526 −1.56085 −0.780423 0.625252i 0.784996π-0.784996\pi
−0.780423 + 0.625252i 0.784996π0.784996\pi
150150 −1.73205 −0.141421
151151 −20.7846 −1.69143 −0.845714 0.533637i 0.820825π-0.820825\pi
−0.845714 + 0.533637i 0.820825π0.820825\pi
152152 6.00000 0.486664
153153 13.8564 1.12022
154154 0 0
155155 8.00000 0.642575
156156 −3.46410 −0.277350
157157 4.00000 0.319235 0.159617 0.987179i 0.448974π-0.448974\pi
0.159617 + 0.987179i 0.448974π0.448974\pi
158158 −18.0000 −1.43200
159159 −6.00000 −0.475831
160160 5.19615 0.410792
161161 0 0
162162 1.73205 0.136083
163163 −19.0000 −1.48819 −0.744097 0.668071i 0.767120π-0.767120\pi
−0.744097 + 0.668071i 0.767120π0.767120\pi
164164 12.1244 0.946753
165165 0 0
166166 6.00000 0.465690
167167 −5.19615 −0.402090 −0.201045 0.979582i 0.564434π-0.564434\pi
−0.201045 + 0.979582i 0.564434π0.564434\pi
168168 −3.00000 −0.231455
169169 −1.00000 −0.0769231
170170 12.0000 0.920358
171171 6.92820 0.529813
172172 8.66025 0.660338
173173 10.3923 0.790112 0.395056 0.918657i 0.370725π-0.370725\pi
0.395056 + 0.918657i 0.370725π0.370725\pi
174174 0 0
175175 −1.73205 −0.130931
176176 0 0
177177 12.0000 0.901975
178178 5.19615 0.389468
179179 −18.0000 −1.34538 −0.672692 0.739923i 0.734862π-0.734862\pi
−0.672692 + 0.739923i 0.734862π0.734862\pi
180180 2.00000 0.149071
181181 11.0000 0.817624 0.408812 0.912619i 0.365943π-0.365943\pi
0.408812 + 0.912619i 0.365943π0.365943\pi
182182 −10.3923 −0.770329
183183 −8.66025 −0.640184
184184 0 0
185185 8.00000 0.588172
186186 13.8564 1.01600
187187 0 0
188188 9.00000 0.656392
189189 −8.66025 −0.629941
190190 6.00000 0.435286
191191 −6.00000 −0.434145 −0.217072 0.976156i 0.569651π-0.569651\pi
−0.217072 + 0.976156i 0.569651π0.569651\pi
192192 −1.00000 −0.0721688
193193 −3.46410 −0.249351 −0.124676 0.992198i 0.539789π-0.539789\pi
−0.124676 + 0.992198i 0.539789π0.539789\pi
194194 −17.3205 −1.24354
195195 3.46410 0.248069
196196 −4.00000 −0.285714
197197 −10.3923 −0.740421 −0.370211 0.928948i 0.620714π-0.620714\pi
−0.370211 + 0.928948i 0.620714π0.620714\pi
198198 0 0
199199 −14.0000 −0.992434 −0.496217 0.868199i 0.665278π-0.665278\pi
−0.496217 + 0.868199i 0.665278π0.665278\pi
200200 −1.73205 −0.122474
201201 5.00000 0.352673
202202 −3.00000 −0.211079
203203 0 0
204204 6.92820 0.485071
205205 −12.1244 −0.846802
206206 −6.92820 −0.482711
207207 0 0
208208 −17.3205 −1.20096
209209 0 0
210210 −3.00000 −0.207020
211211 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
212212 6.00000 0.412082
213213 12.0000 0.822226
214214 3.00000 0.205076
215215 −8.66025 −0.590624
216216 −8.66025 −0.589256
217217 13.8564 0.940634
218218 3.00000 0.203186
219219 0 0
220220 0 0
221221 −24.0000 −1.61441
222222 13.8564 0.929981
223223 −19.0000 −1.27233 −0.636167 0.771551i 0.719481π-0.719481\pi
−0.636167 + 0.771551i 0.719481π0.719481\pi
224224 9.00000 0.601338
225225 −2.00000 −0.133333
226226 −10.3923 −0.691286
227227 19.0526 1.26456 0.632281 0.774739i 0.282119π-0.282119\pi
0.632281 + 0.774739i 0.282119π0.282119\pi
228228 3.46410 0.229416
229229 7.00000 0.462573 0.231287 0.972886i 0.425707π-0.425707\pi
0.231287 + 0.972886i 0.425707π0.425707\pi
230230 0 0
231231 0 0
232232 0 0
233233 −3.46410 −0.226941 −0.113470 0.993541i 0.536197π-0.536197\pi
−0.113470 + 0.993541i 0.536197π0.536197\pi
234234 −12.0000 −0.784465
235235 −9.00000 −0.587095
236236 −12.0000 −0.781133
237237 10.3923 0.675053
238238 20.7846 1.34727
239239 3.46410 0.224074 0.112037 0.993704i 0.464262π-0.464262\pi
0.112037 + 0.993704i 0.464262π0.464262\pi
240240 −5.00000 −0.322749
241241 −19.0526 −1.22728 −0.613642 0.789585i 0.710296π-0.710296\pi
−0.613642 + 0.789585i 0.710296π0.710296\pi
242242 0 0
243243 −16.0000 −1.02640
244244 8.66025 0.554416
245245 4.00000 0.255551
246246 −21.0000 −1.33891
247247 −12.0000 −0.763542
248248 13.8564 0.879883
249249 −3.46410 −0.219529
250250 −1.73205 −0.109545
251251 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
252252 3.46410 0.218218
253253 0 0
254254 3.00000 0.188237
255255 −6.92820 −0.433861
256256 19.0000 1.18750
257257 12.0000 0.748539 0.374270 0.927320i 0.377893π-0.377893\pi
0.374270 + 0.927320i 0.377893π0.377893\pi
258258 −15.0000 −0.933859
259259 13.8564 0.860995
260260 −3.46410 −0.214834
261261 0 0
262262 −6.00000 −0.370681
263263 24.2487 1.49524 0.747620 0.664127i 0.231197π-0.231197\pi
0.747620 + 0.664127i 0.231197π0.231197\pi
264264 0 0
265265 −6.00000 −0.368577
266266 10.3923 0.637193
267267 −3.00000 −0.183597
268268 −5.00000 −0.305424
269269 −15.0000 −0.914566 −0.457283 0.889321i 0.651177π-0.651177\pi
−0.457283 + 0.889321i 0.651177π0.651177\pi
270270 −8.66025 −0.527046
271271 −13.8564 −0.841717 −0.420858 0.907126i 0.638271π-0.638271\pi
−0.420858 + 0.907126i 0.638271π0.638271\pi
272272 34.6410 2.10042
273273 6.00000 0.363137
274274 31.1769 1.88347
275275 0 0
276276 0 0
277277 10.3923 0.624413 0.312207 0.950014i 0.398932π-0.398932\pi
0.312207 + 0.950014i 0.398932π0.398932\pi
278278 24.0000 1.43942
279279 16.0000 0.957895
280280 −3.00000 −0.179284
281281 −6.92820 −0.413302 −0.206651 0.978415i 0.566256π-0.566256\pi
−0.206651 + 0.978415i 0.566256π0.566256\pi
282282 −15.5885 −0.928279
283283 −5.19615 −0.308879 −0.154440 0.988002i 0.549357π-0.549357\pi
−0.154440 + 0.988002i 0.549357π0.549357\pi
284284 −12.0000 −0.712069
285285 −3.46410 −0.205196
286286 0 0
287287 −21.0000 −1.23959
288288 10.3923 0.612372
289289 31.0000 1.82353
290290 0 0
291291 10.0000 0.586210
292292 0 0
293293 −6.92820 −0.404750 −0.202375 0.979308i 0.564866π-0.564866\pi
−0.202375 + 0.979308i 0.564866π0.564866\pi
294294 6.92820 0.404061
295295 12.0000 0.698667
296296 13.8564 0.805387
297297 0 0
298298 −33.0000 −1.91164
299299 0 0
300300 −1.00000 −0.0577350
301301 −15.0000 −0.864586
302302 −36.0000 −2.07157
303303 1.73205 0.0995037
304304 17.3205 0.993399
305305 −8.66025 −0.495885
306306 24.0000 1.37199
307307 −10.3923 −0.593120 −0.296560 0.955014i 0.595840π-0.595840\pi
−0.296560 + 0.955014i 0.595840π0.595840\pi
308308 0 0
309309 4.00000 0.227552
310310 13.8564 0.786991
311311 −6.00000 −0.340229 −0.170114 0.985424i 0.554414π-0.554414\pi
−0.170114 + 0.985424i 0.554414π0.554414\pi
312312 6.00000 0.339683
313313 10.0000 0.565233 0.282617 0.959233i 0.408798π-0.408798\pi
0.282617 + 0.959233i 0.408798π0.408798\pi
314314 6.92820 0.390981
315315 −3.46410 −0.195180
316316 −10.3923 −0.584613
317317 −6.00000 −0.336994 −0.168497 0.985702i 0.553891π-0.553891\pi
−0.168497 + 0.985702i 0.553891π0.553891\pi
318318 −10.3923 −0.582772
319319 0 0
320320 −1.00000 −0.0559017
321321 −1.73205 −0.0966736
322322 0 0
323323 24.0000 1.33540
324324 1.00000 0.0555556
325325 3.46410 0.192154
326326 −32.9090 −1.82266
327327 −1.73205 −0.0957826
328328 −21.0000 −1.15953
329329 −15.5885 −0.859419
330330 0 0
331331 −34.0000 −1.86881 −0.934405 0.356214i 0.884068π-0.884068\pi
−0.934405 + 0.356214i 0.884068π0.884068\pi
332332 3.46410 0.190117
333333 16.0000 0.876795
334334 −9.00000 −0.492458
335335 5.00000 0.273179
336336 −8.66025 −0.472456
337337 10.3923 0.566105 0.283052 0.959104i 0.408653π-0.408653\pi
0.283052 + 0.959104i 0.408653π0.408653\pi
338338 −1.73205 −0.0942111
339339 6.00000 0.325875
340340 6.92820 0.375735
341341 0 0
342342 12.0000 0.648886
343343 19.0526 1.02874
344344 −15.0000 −0.808746
345345 0 0
346346 18.0000 0.967686
347347 −12.1244 −0.650870 −0.325435 0.945564i 0.605511π-0.605511\pi
−0.325435 + 0.945564i 0.605511π0.605511\pi
348348 0 0
349349 34.6410 1.85429 0.927146 0.374701i 0.122255π-0.122255\pi
0.927146 + 0.374701i 0.122255π0.122255\pi
350350 −3.00000 −0.160357
351351 17.3205 0.924500
352352 0 0
353353 24.0000 1.27739 0.638696 0.769460i 0.279474π-0.279474\pi
0.638696 + 0.769460i 0.279474π0.279474\pi
354354 20.7846 1.10469
355355 12.0000 0.636894
356356 3.00000 0.159000
357357 −12.0000 −0.635107
358358 −31.1769 −1.64775
359359 −3.46410 −0.182828 −0.0914141 0.995813i 0.529139π-0.529139\pi
−0.0914141 + 0.995813i 0.529139π0.529139\pi
360360 −3.46410 −0.182574
361361 −7.00000 −0.368421
362362 19.0526 1.00138
363363 0 0
364364 −6.00000 −0.314485
365365 0 0
366366 −15.0000 −0.784063
367367 17.0000 0.887393 0.443696 0.896177i 0.353667π-0.353667\pi
0.443696 + 0.896177i 0.353667π0.353667\pi
368368 0 0
369369 −24.2487 −1.26234
370370 13.8564 0.720360
371371 −10.3923 −0.539542
372372 8.00000 0.414781
373373 −13.8564 −0.717458 −0.358729 0.933442i 0.616790π-0.616790\pi
−0.358729 + 0.933442i 0.616790π0.616790\pi
374374 0 0
375375 1.00000 0.0516398
376376 −15.5885 −0.803913
377377 0 0
378378 −15.0000 −0.771517
379379 −34.0000 −1.74646 −0.873231 0.487306i 0.837980π-0.837980\pi
−0.873231 + 0.487306i 0.837980π0.837980\pi
380380 3.46410 0.177705
381381 −1.73205 −0.0887357
382382 −10.3923 −0.531717
383383 24.0000 1.22634 0.613171 0.789950i 0.289894π-0.289894\pi
0.613171 + 0.789950i 0.289894π0.289894\pi
384384 −12.1244 −0.618718
385385 0 0
386386 −6.00000 −0.305392
387387 −17.3205 −0.880451
388388 −10.0000 −0.507673
389389 3.00000 0.152106 0.0760530 0.997104i 0.475768π-0.475768\pi
0.0760530 + 0.997104i 0.475768π0.475768\pi
390390 6.00000 0.303822
391391 0 0
392392 6.92820 0.349927
393393 3.46410 0.174741
394394 −18.0000 −0.906827
395395 10.3923 0.522894
396396 0 0
397397 20.0000 1.00377 0.501886 0.864934i 0.332640π-0.332640\pi
0.501886 + 0.864934i 0.332640π0.332640\pi
398398 −24.2487 −1.21548
399399 −6.00000 −0.300376
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 8.66025 0.431934
403403 −27.7128 −1.38047
404404 −1.73205 −0.0861727
405405 −1.00000 −0.0496904
406406 0 0
407407 0 0
408408 −12.0000 −0.594089
409409 5.19615 0.256933 0.128467 0.991714i 0.458994π-0.458994\pi
0.128467 + 0.991714i 0.458994π0.458994\pi
410410 −21.0000 −1.03712
411411 −18.0000 −0.887875
412412 −4.00000 −0.197066
413413 20.7846 1.02274
414414 0 0
415415 −3.46410 −0.170046
416416 −18.0000 −0.882523
417417 −13.8564 −0.678551
418418 0 0
419419 18.0000 0.879358 0.439679 0.898155i 0.355092π-0.355092\pi
0.439679 + 0.898155i 0.355092π0.355092\pi
420420 −1.73205 −0.0845154
421421 −17.0000 −0.828529 −0.414265 0.910156i 0.635961π-0.635961\pi
−0.414265 + 0.910156i 0.635961π0.635961\pi
422422 0 0
423423 −18.0000 −0.875190
424424 −10.3923 −0.504695
425425 −6.92820 −0.336067
426426 20.7846 1.00702
427427 −15.0000 −0.725901
428428 1.73205 0.0837218
429429 0 0
430430 −15.0000 −0.723364
431431 38.1051 1.83546 0.917729 0.397206i 0.130020π-0.130020\pi
0.917729 + 0.397206i 0.130020π0.130020\pi
432432 −25.0000 −1.20281
433433 32.0000 1.53782 0.768911 0.639356i 0.220799π-0.220799\pi
0.768911 + 0.639356i 0.220799π0.220799\pi
434434 24.0000 1.15204
435435 0 0
436436 1.73205 0.0829502
437437 0 0
438438 0 0
439439 −27.7128 −1.32266 −0.661330 0.750095i 0.730008π-0.730008\pi
−0.661330 + 0.750095i 0.730008π0.730008\pi
440440 0 0
441441 8.00000 0.380952
442442 −41.5692 −1.97725
443443 −15.0000 −0.712672 −0.356336 0.934358i 0.615974π-0.615974\pi
−0.356336 + 0.934358i 0.615974π0.615974\pi
444444 8.00000 0.379663
445445 −3.00000 −0.142214
446446 −32.9090 −1.55828
447447 19.0526 0.901155
448448 −1.73205 −0.0818317
449449 −15.0000 −0.707894 −0.353947 0.935266i 0.615161π-0.615161\pi
−0.353947 + 0.935266i 0.615161π0.615161\pi
450450 −3.46410 −0.163299
451451 0 0
452452 −6.00000 −0.282216
453453 20.7846 0.976546
454454 33.0000 1.54877
455455 6.00000 0.281284
456456 −6.00000 −0.280976
457457 20.7846 0.972263 0.486132 0.873886i 0.338408π-0.338408\pi
0.486132 + 0.873886i 0.338408π0.338408\pi
458458 12.1244 0.566534
459459 −34.6410 −1.61690
460460 0 0
461461 −12.1244 −0.564688 −0.282344 0.959313i 0.591112π-0.591112\pi
−0.282344 + 0.959313i 0.591112π0.591112\pi
462462 0 0
463463 41.0000 1.90543 0.952716 0.303863i 0.0982765π-0.0982765\pi
0.952716 + 0.303863i 0.0982765π0.0982765\pi
464464 0 0
465465 −8.00000 −0.370991
466466 −6.00000 −0.277945
467467 3.00000 0.138823 0.0694117 0.997588i 0.477888π-0.477888\pi
0.0694117 + 0.997588i 0.477888π0.477888\pi
468468 −6.92820 −0.320256
469469 8.66025 0.399893
470470 −15.5885 −0.719042
471471 −4.00000 −0.184310
472472 20.7846 0.956689
473473 0 0
474474 18.0000 0.826767
475475 −3.46410 −0.158944
476476 12.0000 0.550019
477477 −12.0000 −0.549442
478478 6.00000 0.274434
479479 10.3923 0.474837 0.237418 0.971408i 0.423699π-0.423699\pi
0.237418 + 0.971408i 0.423699π0.423699\pi
480480 −5.19615 −0.237171
481481 −27.7128 −1.26360
482482 −33.0000 −1.50311
483483 0 0
484484 0 0
485485 10.0000 0.454077
486486 −27.7128 −1.25708
487487 −20.0000 −0.906287 −0.453143 0.891438i 0.649697π-0.649697\pi
−0.453143 + 0.891438i 0.649697π0.649697\pi
488488 −15.0000 −0.679018
489489 19.0000 0.859210
490490 6.92820 0.312984
491491 24.2487 1.09433 0.547165 0.837025i 0.315707π-0.315707\pi
0.547165 + 0.837025i 0.315707π0.315707\pi
492492 −12.1244 −0.546608
493493 0 0
494494 −20.7846 −0.935144
495495 0 0
496496 40.0000 1.79605
497497 20.7846 0.932317
498498 −6.00000 −0.268866
499499 −38.0000 −1.70111 −0.850557 0.525883i 0.823735π-0.823735\pi
−0.850557 + 0.525883i 0.823735π0.823735\pi
500500 −1.00000 −0.0447214
501501 5.19615 0.232147
502502 0 0
503503 8.66025 0.386142 0.193071 0.981185i 0.438155π-0.438155\pi
0.193071 + 0.981185i 0.438155π0.438155\pi
504504 −6.00000 −0.267261
505505 1.73205 0.0770752
506506 0 0
507507 1.00000 0.0444116
508508 1.73205 0.0768473
509509 15.0000 0.664863 0.332432 0.943127i 0.392131π-0.392131\pi
0.332432 + 0.943127i 0.392131π0.392131\pi
510510 −12.0000 −0.531369
511511 0 0
512512 8.66025 0.382733
513513 −17.3205 −0.764719
514514 20.7846 0.916770
515515 4.00000 0.176261
516516 −8.66025 −0.381246
517517 0 0
518518 24.0000 1.05450
519519 −10.3923 −0.456172
520520 6.00000 0.263117
521521 15.0000 0.657162 0.328581 0.944476i 0.393430π-0.393430\pi
0.328581 + 0.944476i 0.393430π0.393430\pi
522522 0 0
523523 −17.3205 −0.757373 −0.378686 0.925525i 0.623624π-0.623624\pi
−0.378686 + 0.925525i 0.623624π0.623624\pi
524524 −3.46410 −0.151330
525525 1.73205 0.0755929
526526 42.0000 1.83129
527527 55.4256 2.41438
528528 0 0
529529 −23.0000 −1.00000
530530 −10.3923 −0.451413
531531 24.0000 1.04151
532532 6.00000 0.260133
533533 42.0000 1.81922
534534 −5.19615 −0.224860
535535 −1.73205 −0.0748831
536536 8.66025 0.374066
537537 18.0000 0.776757
538538 −25.9808 −1.12011
539539 0 0
540540 −5.00000 −0.215166
541541 −5.19615 −0.223400 −0.111700 0.993742i 0.535630π-0.535630\pi
−0.111700 + 0.993742i 0.535630π0.535630\pi
542542 −24.0000 −1.03089
543543 −11.0000 −0.472055
544544 36.0000 1.54349
545545 −1.73205 −0.0741929
546546 10.3923 0.444750
547547 −45.0333 −1.92549 −0.962743 0.270418i 0.912838π-0.912838\pi
−0.962743 + 0.270418i 0.912838π0.912838\pi
548548 18.0000 0.768922
549549 −17.3205 −0.739221
550550 0 0
551551 0 0
552552 0 0
553553 18.0000 0.765438
554554 18.0000 0.764747
555555 −8.00000 −0.339581
556556 13.8564 0.587643
557557 −6.92820 −0.293557 −0.146779 0.989169i 0.546891π-0.546891\pi
−0.146779 + 0.989169i 0.546891π0.546891\pi
558558 27.7128 1.17318
559559 30.0000 1.26886
560560 −8.66025 −0.365963
561561 0 0
562562 −12.0000 −0.506189
563563 −15.5885 −0.656975 −0.328488 0.944508i 0.606539π-0.606539\pi
−0.328488 + 0.944508i 0.606539π0.606539\pi
564564 −9.00000 −0.378968
565565 6.00000 0.252422
566566 −9.00000 −0.378298
567567 −1.73205 −0.0727393
568568 20.7846 0.872103
569569 −1.73205 −0.0726113 −0.0363057 0.999341i 0.511559π-0.511559\pi
−0.0363057 + 0.999341i 0.511559π0.511559\pi
570570 −6.00000 −0.251312
571571 −3.46410 −0.144968 −0.0724841 0.997370i 0.523093π-0.523093\pi
−0.0724841 + 0.997370i 0.523093π0.523093\pi
572572 0 0
573573 6.00000 0.250654
574574 −36.3731 −1.51818
575575 0 0
576576 −2.00000 −0.0833333
577577 −20.0000 −0.832611 −0.416305 0.909225i 0.636675π-0.636675\pi
−0.416305 + 0.909225i 0.636675π0.636675\pi
578578 53.6936 2.23336
579579 3.46410 0.143963
580580 0 0
581581 −6.00000 −0.248922
582582 17.3205 0.717958
583583 0 0
584584 0 0
585585 6.92820 0.286446
586586 −12.0000 −0.495715
587587 21.0000 0.866763 0.433381 0.901211i 0.357320π-0.357320\pi
0.433381 + 0.901211i 0.357320π0.357320\pi
588588 4.00000 0.164957
589589 27.7128 1.14189
590590 20.7846 0.855689
591591 10.3923 0.427482
592592 40.0000 1.64399
593593 24.2487 0.995775 0.497888 0.867242i 0.334109π-0.334109\pi
0.497888 + 0.867242i 0.334109π0.334109\pi
594594 0 0
595595 −12.0000 −0.491952
596596 −19.0526 −0.780423
597597 14.0000 0.572982
598598 0 0
599599 30.0000 1.22577 0.612883 0.790173i 0.290010π-0.290010\pi
0.612883 + 0.790173i 0.290010π0.290010\pi
600600 1.73205 0.0707107
601601 20.7846 0.847822 0.423911 0.905704i 0.360657π-0.360657\pi
0.423911 + 0.905704i 0.360657π0.360657\pi
602602 −25.9808 −1.05890
603603 10.0000 0.407231
604604 −20.7846 −0.845714
605605 0 0
606606 3.00000 0.121867
607607 −3.46410 −0.140604 −0.0703018 0.997526i 0.522396π-0.522396\pi
−0.0703018 + 0.997526i 0.522396π0.522396\pi
608608 18.0000 0.729996
609609 0 0
610610 −15.0000 −0.607332
611611 31.1769 1.26128
612612 13.8564 0.560112
613613 −10.3923 −0.419741 −0.209871 0.977729i 0.567304π-0.567304\pi
−0.209871 + 0.977729i 0.567304π0.567304\pi
614614 −18.0000 −0.726421
615615 12.1244 0.488901
616616 0 0
617617 −36.0000 −1.44931 −0.724653 0.689114i 0.758000π-0.758000\pi
−0.724653 + 0.689114i 0.758000π0.758000\pi
618618 6.92820 0.278693
619619 20.0000 0.803868 0.401934 0.915669i 0.368338π-0.368338\pi
0.401934 + 0.915669i 0.368338π0.368338\pi
620620 8.00000 0.321288
621621 0 0
622622 −10.3923 −0.416693
623623 −5.19615 −0.208179
624624 17.3205 0.693375
625625 1.00000 0.0400000
626626 17.3205 0.692267
627627 0 0
628628 4.00000 0.159617
629629 55.4256 2.20996
630630 −6.00000 −0.239046
631631 28.0000 1.11466 0.557331 0.830290i 0.311825π-0.311825\pi
0.557331 + 0.830290i 0.311825π0.311825\pi
632632 18.0000 0.716002
633633 0 0
634634 −10.3923 −0.412731
635635 −1.73205 −0.0687343
636636 −6.00000 −0.237915
637637 −13.8564 −0.549011
638638 0 0
639639 24.0000 0.949425
640640 −12.1244 −0.479257
641641 30.0000 1.18493 0.592464 0.805597i 0.298155π-0.298155\pi
0.592464 + 0.805597i 0.298155π0.298155\pi
642642 −3.00000 −0.118401
643643 −31.0000 −1.22252 −0.611260 0.791430i 0.709337π-0.709337\pi
−0.611260 + 0.791430i 0.709337π0.709337\pi
644644 0 0
645645 8.66025 0.340997
646646 41.5692 1.63552
647647 33.0000 1.29736 0.648682 0.761060i 0.275321π-0.275321\pi
0.648682 + 0.761060i 0.275321π0.275321\pi
648648 −1.73205 −0.0680414
649649 0 0
650650 6.00000 0.235339
651651 −13.8564 −0.543075
652652 −19.0000 −0.744097
653653 −30.0000 −1.17399 −0.586995 0.809590i 0.699689π-0.699689\pi
−0.586995 + 0.809590i 0.699689π0.699689\pi
654654 −3.00000 −0.117309
655655 3.46410 0.135354
656656 −60.6218 −2.36688
657657 0 0
658658 −27.0000 −1.05257
659659 3.46410 0.134942 0.0674711 0.997721i 0.478507π-0.478507\pi
0.0674711 + 0.997721i 0.478507π0.478507\pi
660660 0 0
661661 37.0000 1.43913 0.719567 0.694423i 0.244340π-0.244340\pi
0.719567 + 0.694423i 0.244340π0.244340\pi
662662 −58.8897 −2.28881
663663 24.0000 0.932083
664664 −6.00000 −0.232845
665665 −6.00000 −0.232670
666666 27.7128 1.07385
667667 0 0
668668 −5.19615 −0.201045
669669 19.0000 0.734582
670670 8.66025 0.334575
671671 0 0
672672 −9.00000 −0.347183
673673 −20.7846 −0.801188 −0.400594 0.916256i 0.631196π-0.631196\pi
−0.400594 + 0.916256i 0.631196π0.631196\pi
674674 18.0000 0.693334
675675 5.00000 0.192450
676676 −1.00000 −0.0384615
677677 27.7128 1.06509 0.532545 0.846402i 0.321236π-0.321236\pi
0.532545 + 0.846402i 0.321236π0.321236\pi
678678 10.3923 0.399114
679679 17.3205 0.664700
680680 −12.0000 −0.460179
681681 −19.0526 −0.730096
682682 0 0
683683 −21.0000 −0.803543 −0.401771 0.915740i 0.631605π-0.631605\pi
−0.401771 + 0.915740i 0.631605π0.631605\pi
684684 6.92820 0.264906
685685 −18.0000 −0.687745
686686 33.0000 1.25995
687687 −7.00000 −0.267067
688688 −43.3013 −1.65085
689689 20.7846 0.791831
690690 0 0
691691 −10.0000 −0.380418 −0.190209 0.981744i 0.560917π-0.560917\pi
−0.190209 + 0.981744i 0.560917π0.560917\pi
692692 10.3923 0.395056
693693 0 0
694694 −21.0000 −0.797149
695695 −13.8564 −0.525603
696696 0 0
697697 −84.0000 −3.18173
698698 60.0000 2.27103
699699 3.46410 0.131024
700700 −1.73205 −0.0654654
701701 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
702702 30.0000 1.13228
703703 27.7128 1.04521
704704 0 0
705705 9.00000 0.338960
706706 41.5692 1.56448
707707 3.00000 0.112827
708708 12.0000 0.450988
709709 25.0000 0.938895 0.469447 0.882960i 0.344453π-0.344453\pi
0.469447 + 0.882960i 0.344453π0.344453\pi
710710 20.7846 0.780033
711711 20.7846 0.779484
712712 −5.19615 −0.194734
713713 0 0
714714 −20.7846 −0.777844
715715 0 0
716716 −18.0000 −0.672692
717717 −3.46410 −0.129369
718718 −6.00000 −0.223918
719719 6.00000 0.223762 0.111881 0.993722i 0.464312π-0.464312\pi
0.111881 + 0.993722i 0.464312π0.464312\pi
720720 −10.0000 −0.372678
721721 6.92820 0.258020
722722 −12.1244 −0.451222
723723 19.0526 0.708572
724724 11.0000 0.408812
725725 0 0
726726 0 0
727727 1.00000 0.0370879 0.0185440 0.999828i 0.494097π-0.494097\pi
0.0185440 + 0.999828i 0.494097π0.494097\pi
728728 10.3923 0.385164
729729 13.0000 0.481481
730730 0 0
731731 −60.0000 −2.21918
732732 −8.66025 −0.320092
733733 −20.7846 −0.767697 −0.383849 0.923396i 0.625402π-0.625402\pi
−0.383849 + 0.923396i 0.625402π0.625402\pi
734734 29.4449 1.08683
735735 −4.00000 −0.147542
736736 0 0
737737 0 0
738738 −42.0000 −1.54604
739739 3.46410 0.127429 0.0637145 0.997968i 0.479705π-0.479705\pi
0.0637145 + 0.997968i 0.479705π0.479705\pi
740740 8.00000 0.294086
741741 12.0000 0.440831
742742 −18.0000 −0.660801
743743 5.19615 0.190628 0.0953142 0.995447i 0.469614π-0.469614\pi
0.0953142 + 0.995447i 0.469614π0.469614\pi
744744 −13.8564 −0.508001
745745 19.0526 0.698032
746746 −24.0000 −0.878702
747747 −6.92820 −0.253490
748748 0 0
749749 −3.00000 −0.109618
750750 1.73205 0.0632456
751751 −14.0000 −0.510867 −0.255434 0.966827i 0.582218π-0.582218\pi
−0.255434 + 0.966827i 0.582218π0.582218\pi
752752 −45.0000 −1.64098
753753 0 0
754754 0 0
755755 20.7846 0.756429
756756 −8.66025 −0.314970
757757 −2.00000 −0.0726912 −0.0363456 0.999339i 0.511572π-0.511572\pi
−0.0363456 + 0.999339i 0.511572π0.511572\pi
758758 −58.8897 −2.13897
759759 0 0
760760 −6.00000 −0.217643
761761 34.6410 1.25574 0.627868 0.778320i 0.283928π-0.283928\pi
0.627868 + 0.778320i 0.283928π0.283928\pi
762762 −3.00000 −0.108679
763763 −3.00000 −0.108607
764764 −6.00000 −0.217072
765765 −13.8564 −0.500979
766766 41.5692 1.50196
767767 −41.5692 −1.50098
768768 −19.0000 −0.685603
769769 27.7128 0.999350 0.499675 0.866213i 0.333453π-0.333453\pi
0.499675 + 0.866213i 0.333453π0.333453\pi
770770 0 0
771771 −12.0000 −0.432169
772772 −3.46410 −0.124676
773773 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
774774 −30.0000 −1.07833
775775 −8.00000 −0.287368
776776 17.3205 0.621770
777777 −13.8564 −0.497096
778778 5.19615 0.186291
779779 −42.0000 −1.50481
780780 3.46410 0.124035
781781 0 0
782782 0 0
783783 0 0
784784 20.0000 0.714286
785785 −4.00000 −0.142766
786786 6.00000 0.214013
787787 −25.9808 −0.926114 −0.463057 0.886328i 0.653248π-0.653248\pi
−0.463057 + 0.886328i 0.653248π0.653248\pi
788788 −10.3923 −0.370211
789789 −24.2487 −0.863277
790790 18.0000 0.640411
791791 10.3923 0.369508
792792 0 0
793793 30.0000 1.06533
794794 34.6410 1.22936
795795 6.00000 0.212798
796796 −14.0000 −0.496217
797797 −12.0000 −0.425062 −0.212531 0.977154i 0.568171π-0.568171\pi
−0.212531 + 0.977154i 0.568171π0.568171\pi
798798 −10.3923 −0.367884
799799 −62.3538 −2.20592
800800 −5.19615 −0.183712
801801 −6.00000 −0.212000
802802 46.7654 1.65134
803803 0 0
804804 5.00000 0.176336
805805 0 0
806806 −48.0000 −1.69073
807807 15.0000 0.528025
808808 3.00000 0.105540
809809 −48.4974 −1.70508 −0.852539 0.522663i 0.824939π-0.824939\pi
−0.852539 + 0.522663i 0.824939π0.824939\pi
810810 −1.73205 −0.0608581
811811 6.92820 0.243282 0.121641 0.992574i 0.461184π-0.461184\pi
0.121641 + 0.992574i 0.461184π0.461184\pi
812812 0 0
813813 13.8564 0.485965
814814 0 0
815815 19.0000 0.665541
816816 −34.6410 −1.21268
817817 −30.0000 −1.04957
818818 9.00000 0.314678
819819 12.0000 0.419314
820820 −12.1244 −0.423401
821821 29.4449 1.02763 0.513816 0.857900i 0.328231π-0.328231\pi
0.513816 + 0.857900i 0.328231π0.328231\pi
822822 −31.1769 −1.08742
823823 17.0000 0.592583 0.296291 0.955098i 0.404250π-0.404250\pi
0.296291 + 0.955098i 0.404250π0.404250\pi
824824 6.92820 0.241355
825825 0 0
826826 36.0000 1.25260
827827 29.4449 1.02390 0.511949 0.859016i 0.328924π-0.328924\pi
0.511949 + 0.859016i 0.328924π0.328924\pi
828828 0 0
829829 29.0000 1.00721 0.503606 0.863934i 0.332006π-0.332006\pi
0.503606 + 0.863934i 0.332006π0.332006\pi
830830 −6.00000 −0.208263
831831 −10.3923 −0.360505
832832 3.46410 0.120096
833833 27.7128 0.960192
834834 −24.0000 −0.831052
835835 5.19615 0.179820
836836 0 0
837837 −40.0000 −1.38260
838838 31.1769 1.07699
839839 −42.0000 −1.45000 −0.725001 0.688748i 0.758161π-0.758161\pi
−0.725001 + 0.688748i 0.758161π0.758161\pi
840840 3.00000 0.103510
841841 −29.0000 −1.00000
842842 −29.4449 −1.01474
843843 6.92820 0.238620
844844 0 0
845845 1.00000 0.0344010
846846 −31.1769 −1.07188
847847 0 0
848848 −30.0000 −1.03020
849849 5.19615 0.178331
850850 −12.0000 −0.411597
851851 0 0
852852 12.0000 0.411113
853853 −34.6410 −1.18609 −0.593043 0.805171i 0.702074π-0.702074\pi
−0.593043 + 0.805171i 0.702074π0.702074\pi
854854 −25.9808 −0.889043
855855 −6.92820 −0.236940
856856 −3.00000 −0.102538
857857 −10.3923 −0.354994 −0.177497 0.984121i 0.556800π-0.556800\pi
−0.177497 + 0.984121i 0.556800π0.556800\pi
858858 0 0
859859 14.0000 0.477674 0.238837 0.971060i 0.423234π-0.423234\pi
0.238837 + 0.971060i 0.423234π0.423234\pi
860860 −8.66025 −0.295312
861861 21.0000 0.715678
862862 66.0000 2.24797
863863 21.0000 0.714848 0.357424 0.933942i 0.383655π-0.383655\pi
0.357424 + 0.933942i 0.383655π0.383655\pi
864864 −25.9808 −0.883883
865865 −10.3923 −0.353349
866866 55.4256 1.88344
867867 −31.0000 −1.05282
868868 13.8564 0.470317
869869 0 0
870870 0 0
871871 −17.3205 −0.586883
872872 −3.00000 −0.101593
873873 20.0000 0.676897
874874 0 0
875875 1.73205 0.0585540
876876 0 0
877877 −27.7128 −0.935795 −0.467898 0.883783i 0.654988π-0.654988\pi
−0.467898 + 0.883783i 0.654988π0.654988\pi
878878 −48.0000 −1.61992
879879 6.92820 0.233682
880880 0 0
881881 −21.0000 −0.707508 −0.353754 0.935339i 0.615095π-0.615095\pi
−0.353754 + 0.935339i 0.615095π0.615095\pi
882882 13.8564 0.466569
883883 −56.0000 −1.88455 −0.942275 0.334840i 0.891318π-0.891318\pi
−0.942275 + 0.334840i 0.891318π0.891318\pi
884884 −24.0000 −0.807207
885885 −12.0000 −0.403376
886886 −25.9808 −0.872841
887887 −32.9090 −1.10497 −0.552487 0.833521i 0.686321π-0.686321\pi
−0.552487 + 0.833521i 0.686321π0.686321\pi
888888 −13.8564 −0.464991
889889 −3.00000 −0.100617
890890 −5.19615 −0.174175
891891 0 0
892892 −19.0000 −0.636167
893893 −31.1769 −1.04330
894894 33.0000 1.10369
895895 18.0000 0.601674
896896 −21.0000 −0.701561
897897 0 0
898898 −25.9808 −0.866989
899899 0 0
900900 −2.00000 −0.0666667
901901 −41.5692 −1.38487
902902 0 0
903903 15.0000 0.499169
904904 10.3923 0.345643
905905 −11.0000 −0.365652
906906 36.0000 1.19602
907907 17.0000 0.564476 0.282238 0.959344i 0.408923π-0.408923\pi
0.282238 + 0.959344i 0.408923π0.408923\pi
908908 19.0526 0.632281
909909 3.46410 0.114897
910910 10.3923 0.344502
911911 6.00000 0.198789 0.0993944 0.995048i 0.468309π-0.468309\pi
0.0993944 + 0.995048i 0.468309π0.468309\pi
912912 −17.3205 −0.573539
913913 0 0
914914 36.0000 1.19077
915915 8.66025 0.286299
916916 7.00000 0.231287
917917 6.00000 0.198137
918918 −60.0000 −1.98030
919919 38.1051 1.25697 0.628486 0.777821i 0.283675π-0.283675\pi
0.628486 + 0.777821i 0.283675π0.283675\pi
920920 0 0
921921 10.3923 0.342438
922922 −21.0000 −0.691598
923923 −41.5692 −1.36827
924924 0 0
925925 −8.00000 −0.263038
926926 71.0141 2.33367
927927 8.00000 0.262754
928928 0 0
929929 18.0000 0.590561 0.295280 0.955411i 0.404587π-0.404587\pi
0.295280 + 0.955411i 0.404587π0.404587\pi
930930 −13.8564 −0.454369
931931 13.8564 0.454125
932932 −3.46410 −0.113470
933933 6.00000 0.196431
934934 5.19615 0.170023
935935 0 0
936936 12.0000 0.392232
937937 −24.2487 −0.792171 −0.396085 0.918214i 0.629632π-0.629632\pi
−0.396085 + 0.918214i 0.629632π0.629632\pi
938938 15.0000 0.489767
939939 −10.0000 −0.326338
940940 −9.00000 −0.293548
941941 −50.2295 −1.63743 −0.818717 0.574197i 0.805314π-0.805314\pi
−0.818717 + 0.574197i 0.805314π0.805314\pi
942942 −6.92820 −0.225733
943943 0 0
944944 60.0000 1.95283
945945 8.66025 0.281718
946946 0 0
947947 −12.0000 −0.389948 −0.194974 0.980808i 0.562462π-0.562462\pi
−0.194974 + 0.980808i 0.562462π0.562462\pi
948948 10.3923 0.337526
949949 0 0
950950 −6.00000 −0.194666
951951 6.00000 0.194563
952952 −20.7846 −0.673633
953953 55.4256 1.79541 0.897706 0.440595i 0.145232π-0.145232\pi
0.897706 + 0.440595i 0.145232π0.145232\pi
954954 −20.7846 −0.672927
955955 6.00000 0.194155
956956 3.46410 0.112037
957957 0 0
958958 18.0000 0.581554
959959 −31.1769 −1.00676
960960 1.00000 0.0322749
961961 33.0000 1.06452
962962 −48.0000 −1.54758
963963 −3.46410 −0.111629
964964 −19.0526 −0.613642
965965 3.46410 0.111513
966966 0 0
967967 38.1051 1.22538 0.612689 0.790324i 0.290088π-0.290088\pi
0.612689 + 0.790324i 0.290088π0.290088\pi
968968 0 0
969969 −24.0000 −0.770991
970970 17.3205 0.556128
971971 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
972972 −16.0000 −0.513200
973973 −24.0000 −0.769405
974974 −34.6410 −1.10997
975975 −3.46410 −0.110940
976976 −43.3013 −1.38604
977977 −24.0000 −0.767828 −0.383914 0.923369i 0.625424π-0.625424\pi
−0.383914 + 0.923369i 0.625424π0.625424\pi
978978 32.9090 1.05231
979979 0 0
980980 4.00000 0.127775
981981 −3.46410 −0.110600
982982 42.0000 1.34027
983983 −3.00000 −0.0956851 −0.0478426 0.998855i 0.515235π-0.515235\pi
−0.0478426 + 0.998855i 0.515235π0.515235\pi
984984 21.0000 0.669456
985985 10.3923 0.331126
986986 0 0
987987 15.5885 0.496186
988988 −12.0000 −0.381771
989989 0 0
990990 0 0
991991 −2.00000 −0.0635321 −0.0317660 0.999495i 0.510113π-0.510113\pi
−0.0317660 + 0.999495i 0.510113π0.510113\pi
992992 41.5692 1.31982
993993 34.0000 1.07896
994994 36.0000 1.14185
995995 14.0000 0.443830
996996 −3.46410 −0.109764
997997 −45.0333 −1.42622 −0.713110 0.701052i 0.752714π-0.752714\pi
−0.713110 + 0.701052i 0.752714π0.752714\pi
998998 −65.8179 −2.08343
999999 −40.0000 −1.26554
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 605.2.a.e.1.2 yes 2
3.2 odd 2 5445.2.a.u.1.1 2
4.3 odd 2 9680.2.a.bu.1.2 2
5.4 even 2 3025.2.a.l.1.1 2
11.2 odd 10 605.2.g.i.81.2 8
11.3 even 5 605.2.g.i.251.2 8
11.4 even 5 605.2.g.i.511.2 8
11.5 even 5 605.2.g.i.366.1 8
11.6 odd 10 605.2.g.i.366.2 8
11.7 odd 10 605.2.g.i.511.1 8
11.8 odd 10 605.2.g.i.251.1 8
11.9 even 5 605.2.g.i.81.1 8
11.10 odd 2 inner 605.2.a.e.1.1 2
33.32 even 2 5445.2.a.u.1.2 2
44.43 even 2 9680.2.a.bu.1.1 2
55.54 odd 2 3025.2.a.l.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
605.2.a.e.1.1 2 11.10 odd 2 inner
605.2.a.e.1.2 yes 2 1.1 even 1 trivial
605.2.g.i.81.1 8 11.9 even 5
605.2.g.i.81.2 8 11.2 odd 10
605.2.g.i.251.1 8 11.8 odd 10
605.2.g.i.251.2 8 11.3 even 5
605.2.g.i.366.1 8 11.5 even 5
605.2.g.i.366.2 8 11.6 odd 10
605.2.g.i.511.1 8 11.7 odd 10
605.2.g.i.511.2 8 11.4 even 5
3025.2.a.l.1.1 2 5.4 even 2
3025.2.a.l.1.2 2 55.54 odd 2
5445.2.a.u.1.1 2 3.2 odd 2
5445.2.a.u.1.2 2 33.32 even 2
9680.2.a.bu.1.1 2 44.43 even 2
9680.2.a.bu.1.2 2 4.3 odd 2