Properties

Label 825.2.a.m.1.3
Level 825825
Weight 22
Character 825.1
Self dual yes
Analytic conductor 6.5886.588
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] = [825,2,Mod(1,825)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(825, 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("825.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 825=35211 825 = 3 \cdot 5^{2} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 825.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: 6.587658166766.58765816676
Analytic rank: 00
Dimension: 33
Coefficient field: 3.3.568.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x3x26x2 x^{3} - x^{2} - 6x - 2 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 1.3
Root 1.76156-1.76156 of defining polynomial
Character χ\chi == 825.1

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+2.76156q2+1.00000q3+5.62620q4+2.76156q61.86464q7+10.0140q8+1.00000q9+1.00000q11+5.62620q124.62620q135.14931q14+16.4017q162.49084q17+2.76156q185.38776q191.86464q21+2.76156q227.14931q23+10.0140q2412.7755q26+1.00000q2710.4908q283.52311q29+8.62620q31+25.2663q32+1.00000q336.87859q34+5.62620q36+8.87859q3714.8786q384.62620q390.761557q415.14931q42+7.40171q43+5.62620q4419.7432q46+0.373802q47+16.4017q483.52311q492.49084q5126.0279q52+5.45856q53+2.76156q5418.6724q565.38776q579.72928q58+5.14931q59+4.42003q61+23.8217q621.86464q63+36.9711q64+2.76156q6611.9431q6714.0140q687.14931q69+11.6262q71+10.0140q726.77551q73+24.5187q7430.3126q761.86464q7712.7755q786.01395q79+1.00000q812.10308q8214.5693q8310.4908q84+20.4402q863.52311q87+10.0140q88+9.04623q89+8.62620q9140.2234q92+8.62620q93+1.03228q94+25.2663q9616.3169q979.72928q98+1.00000q99+O(q100)q+2.76156 q^{2} +1.00000 q^{3} +5.62620 q^{4} +2.76156 q^{6} -1.86464 q^{7} +10.0140 q^{8} +1.00000 q^{9} +1.00000 q^{11} +5.62620 q^{12} -4.62620 q^{13} -5.14931 q^{14} +16.4017 q^{16} -2.49084 q^{17} +2.76156 q^{18} -5.38776 q^{19} -1.86464 q^{21} +2.76156 q^{22} -7.14931 q^{23} +10.0140 q^{24} -12.7755 q^{26} +1.00000 q^{27} -10.4908 q^{28} -3.52311 q^{29} +8.62620 q^{31} +25.2663 q^{32} +1.00000 q^{33} -6.87859 q^{34} +5.62620 q^{36} +8.87859 q^{37} -14.8786 q^{38} -4.62620 q^{39} -0.761557 q^{41} -5.14931 q^{42} +7.40171 q^{43} +5.62620 q^{44} -19.7432 q^{46} +0.373802 q^{47} +16.4017 q^{48} -3.52311 q^{49} -2.49084 q^{51} -26.0279 q^{52} +5.45856 q^{53} +2.76156 q^{54} -18.6724 q^{56} -5.38776 q^{57} -9.72928 q^{58} +5.14931 q^{59} +4.42003 q^{61} +23.8217 q^{62} -1.86464 q^{63} +36.9711 q^{64} +2.76156 q^{66} -11.9431 q^{67} -14.0140 q^{68} -7.14931 q^{69} +11.6262 q^{71} +10.0140 q^{72} -6.77551 q^{73} +24.5187 q^{74} -30.3126 q^{76} -1.86464 q^{77} -12.7755 q^{78} -6.01395 q^{79} +1.00000 q^{81} -2.10308 q^{82} -14.5693 q^{83} -10.4908 q^{84} +20.4402 q^{86} -3.52311 q^{87} +10.0140 q^{88} +9.04623 q^{89} +8.62620 q^{91} -40.2234 q^{92} +8.62620 q^{93} +1.03228 q^{94} +25.2663 q^{96} -16.3169 q^{97} -9.72928 q^{98} +1.00000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q+2q2+3q3+8q4+2q63q7+6q8+3q9+3q11+8q125q13+6q14+10q16+4q17+2q18q193q21+2q22+6q248q26++3q99+O(q100) 3 q + 2 q^{2} + 3 q^{3} + 8 q^{4} + 2 q^{6} - 3 q^{7} + 6 q^{8} + 3 q^{9} + 3 q^{11} + 8 q^{12} - 5 q^{13} + 6 q^{14} + 10 q^{16} + 4 q^{17} + 2 q^{18} - q^{19} - 3 q^{21} + 2 q^{22} + 6 q^{24} - 8 q^{26}+ \cdots + 3 q^{99}+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 2.76156 1.95272 0.976358 0.216160i 0.0693534π-0.0693534\pi
0.976358 + 0.216160i 0.0693534π0.0693534\pi
33 1.00000 0.577350
44 5.62620 2.81310
55 0 0
66 2.76156 1.12740
77 −1.86464 −0.704768 −0.352384 0.935855i 0.614629π-0.614629\pi
−0.352384 + 0.935855i 0.614629π0.614629\pi
88 10.0140 3.54047
99 1.00000 0.333333
1010 0 0
1111 1.00000 0.301511
1212 5.62620 1.62414
1313 −4.62620 −1.28308 −0.641538 0.767091i 0.721703π-0.721703\pi
−0.641538 + 0.767091i 0.721703π0.721703\pi
1414 −5.14931 −1.37621
1515 0 0
1616 16.4017 4.10043
1717 −2.49084 −0.604117 −0.302059 0.953289i 0.597674π-0.597674\pi
−0.302059 + 0.953289i 0.597674π0.597674\pi
1818 2.76156 0.650905
1919 −5.38776 −1.23604 −0.618018 0.786164i 0.712064π-0.712064\pi
−0.618018 + 0.786164i 0.712064π0.712064\pi
2020 0 0
2121 −1.86464 −0.406898
2222 2.76156 0.588766
2323 −7.14931 −1.49073 −0.745367 0.666654i 0.767726π-0.767726\pi
−0.745367 + 0.666654i 0.767726π0.767726\pi
2424 10.0140 2.04409
2525 0 0
2626 −12.7755 −2.50548
2727 1.00000 0.192450
2828 −10.4908 −1.98258
2929 −3.52311 −0.654226 −0.327113 0.944985i 0.606076π-0.606076\pi
−0.327113 + 0.944985i 0.606076π0.606076\pi
3030 0 0
3131 8.62620 1.54931 0.774655 0.632384i 0.217923π-0.217923\pi
0.774655 + 0.632384i 0.217923π0.217923\pi
3232 25.2663 4.46650
3333 1.00000 0.174078
3434 −6.87859 −1.17967
3535 0 0
3636 5.62620 0.937700
3737 8.87859 1.45963 0.729816 0.683644i 0.239606π-0.239606\pi
0.729816 + 0.683644i 0.239606π0.239606\pi
3838 −14.8786 −2.41363
3939 −4.62620 −0.740785
4040 0 0
4141 −0.761557 −0.118935 −0.0594676 0.998230i 0.518940π-0.518940\pi
−0.0594676 + 0.998230i 0.518940π0.518940\pi
4242 −5.14931 −0.794556
4343 7.40171 1.12875 0.564375 0.825519i 0.309117π-0.309117\pi
0.564375 + 0.825519i 0.309117π0.309117\pi
4444 5.62620 0.848181
4545 0 0
4646 −19.7432 −2.91098
4747 0.373802 0.0545246 0.0272623 0.999628i 0.491321π-0.491321\pi
0.0272623 + 0.999628i 0.491321π0.491321\pi
4848 16.4017 2.36738
4949 −3.52311 −0.503302
5050 0 0
5151 −2.49084 −0.348787
5252 −26.0279 −3.60942
5353 5.45856 0.749791 0.374896 0.927067i 0.377679π-0.377679\pi
0.374896 + 0.927067i 0.377679π0.377679\pi
5454 2.76156 0.375800
5555 0 0
5656 −18.6724 −2.49521
5757 −5.38776 −0.713626
5858 −9.72928 −1.27752
5959 5.14931 0.670383 0.335192 0.942150i 0.391199π-0.391199\pi
0.335192 + 0.942150i 0.391199π0.391199\pi
6060 0 0
6161 4.42003 0.565927 0.282963 0.959131i 0.408682π-0.408682\pi
0.282963 + 0.959131i 0.408682π0.408682\pi
6262 23.8217 3.02536
6363 −1.86464 −0.234923
6464 36.9711 4.62138
6565 0 0
6666 2.76156 0.339924
6767 −11.9431 −1.45909 −0.729544 0.683934i 0.760268π-0.760268\pi
−0.729544 + 0.683934i 0.760268π0.760268\pi
6868 −14.0140 −1.69944
6969 −7.14931 −0.860676
7070 0 0
7171 11.6262 1.37978 0.689888 0.723916i 0.257660π-0.257660\pi
0.689888 + 0.723916i 0.257660π0.257660\pi
7272 10.0140 1.18016
7373 −6.77551 −0.793014 −0.396507 0.918032i 0.629778π-0.629778\pi
−0.396507 + 0.918032i 0.629778π0.629778\pi
7474 24.5187 2.85025
7575 0 0
7676 −30.3126 −3.47709
7777 −1.86464 −0.212496
7878 −12.7755 −1.44654
7979 −6.01395 −0.676623 −0.338311 0.941034i 0.609856π-0.609856\pi
−0.338311 + 0.941034i 0.609856π0.609856\pi
8080 0 0
8181 1.00000 0.111111
8282 −2.10308 −0.232247
8383 −14.5693 −1.59919 −0.799597 0.600538i 0.794953π-0.794953\pi
−0.799597 + 0.600538i 0.794953π0.794953\pi
8484 −10.4908 −1.14464
8585 0 0
8686 20.4402 2.20413
8787 −3.52311 −0.377718
8888 10.0140 1.06749
8989 9.04623 0.958898 0.479449 0.877570i 0.340836π-0.340836\pi
0.479449 + 0.877570i 0.340836π0.340836\pi
9090 0 0
9191 8.62620 0.904271
9292 −40.2234 −4.19358
9393 8.62620 0.894495
9494 1.03228 0.106471
9595 0 0
9696 25.2663 2.57874
9797 −16.3169 −1.65673 −0.828367 0.560185i 0.810730π-0.810730\pi
−0.828367 + 0.560185i 0.810730π0.810730\pi
9898 −9.72928 −0.982806
9999 1.00000 0.100504
100100 0 0
101101 −1.03228 −0.102715 −0.0513576 0.998680i 0.516355π-0.516355\pi
−0.0513576 + 0.998680i 0.516355π0.516355\pi
102102 −6.87859 −0.681082
103103 −3.04623 −0.300154 −0.150077 0.988674i 0.547952π-0.547952\pi
−0.150077 + 0.988674i 0.547952π0.547952\pi
104104 −46.3265 −4.54269
105105 0 0
106106 15.0741 1.46413
107107 8.50479 0.822189 0.411095 0.911593i 0.365147π-0.365147\pi
0.411095 + 0.911593i 0.365147π0.365147\pi
108108 5.62620 0.541381
109109 −6.14931 −0.588997 −0.294499 0.955652i 0.595153π-0.595153\pi
−0.294499 + 0.955652i 0.595153π0.595153\pi
110110 0 0
111111 8.87859 0.842719
112112 −30.5833 −2.88985
113113 6.00000 0.564433 0.282216 0.959351i 0.408930π-0.408930\pi
0.282216 + 0.959351i 0.408930π0.408930\pi
114114 −14.8786 −1.39351
115115 0 0
116116 −19.8217 −1.84040
117117 −4.62620 −0.427692
118118 14.2201 1.30907
119119 4.64452 0.425762
120120 0 0
121121 1.00000 0.0909091
122122 12.2062 1.10509
123123 −0.761557 −0.0686673
124124 48.5327 4.35837
125125 0 0
126126 −5.14931 −0.458737
127127 9.26635 0.822256 0.411128 0.911578i 0.365135π-0.365135\pi
0.411128 + 0.911578i 0.365135π0.365135\pi
128128 51.5650 4.55774
129129 7.40171 0.651684
130130 0 0
131131 4.06455 0.355121 0.177561 0.984110i 0.443179π-0.443179\pi
0.177561 + 0.984110i 0.443179π0.443179\pi
132132 5.62620 0.489698
133133 10.0462 0.871119
134134 −32.9817 −2.84918
135135 0 0
136136 −24.9431 −2.13886
137137 −5.93545 −0.507100 −0.253550 0.967322i 0.581598π-0.581598\pi
−0.253550 + 0.967322i 0.581598π0.581598\pi
138138 −19.7432 −1.68066
139139 6.71096 0.569216 0.284608 0.958644i 0.408137π-0.408137\pi
0.284608 + 0.958644i 0.408137π0.408137\pi
140140 0 0
141141 0.373802 0.0314798
142142 32.1064 2.69431
143143 −4.62620 −0.386862
144144 16.4017 1.36681
145145 0 0
146146 −18.7110 −1.54853
147147 −3.52311 −0.290582
148148 49.9527 4.10609
149149 5.74324 0.470504 0.235252 0.971934i 0.424408π-0.424408\pi
0.235252 + 0.971934i 0.424408π0.424408\pi
150150 0 0
151151 10.5616 0.859495 0.429747 0.902949i 0.358603π-0.358603\pi
0.429747 + 0.902949i 0.358603π0.358603\pi
152152 −53.9527 −4.37614
153153 −2.49084 −0.201372
154154 −5.14931 −0.414943
155155 0 0
156156 −26.0279 −2.08390
157157 −3.10308 −0.247653 −0.123827 0.992304i 0.539517π-0.539517\pi
−0.123827 + 0.992304i 0.539517π0.539517\pi
158158 −16.6079 −1.32125
159159 5.45856 0.432892
160160 0 0
161161 13.3309 1.05062
162162 2.76156 0.216968
163163 −15.6724 −1.22756 −0.613780 0.789477i 0.710352π-0.710352\pi
−0.613780 + 0.789477i 0.710352π0.710352\pi
164164 −4.28467 −0.334577
165165 0 0
166166 −40.2341 −3.12277
167167 8.98168 0.695023 0.347512 0.937676i 0.387027π-0.387027\pi
0.347512 + 0.937676i 0.387027π0.387027\pi
168168 −18.6724 −1.44061
169169 8.40171 0.646285
170170 0 0
171171 −5.38776 −0.412012
172172 41.6435 3.17529
173173 11.5092 0.875025 0.437513 0.899212i 0.355860π-0.355860\pi
0.437513 + 0.899212i 0.355860π0.355860\pi
174174 −9.72928 −0.737575
175175 0 0
176176 16.4017 1.23633
177177 5.14931 0.387046
178178 24.9817 1.87246
179179 10.3738 0.775374 0.387687 0.921791i 0.373274π-0.373274\pi
0.387687 + 0.921791i 0.373274π0.373274\pi
180180 0 0
181181 −2.66473 −0.198068 −0.0990339 0.995084i 0.531575π-0.531575\pi
−0.0990339 + 0.995084i 0.531575π0.531575\pi
182182 23.8217 1.76578
183183 4.42003 0.326738
184184 −71.5929 −5.27790
185185 0 0
186186 23.8217 1.74669
187187 −2.49084 −0.182148
188188 2.10308 0.153383
189189 −1.86464 −0.135633
190190 0 0
191191 14.6724 1.06166 0.530830 0.847478i 0.321880π-0.321880\pi
0.530830 + 0.847478i 0.321880π0.321880\pi
192192 36.9711 2.66816
193193 −5.10308 −0.367328 −0.183664 0.982989i 0.558796π-0.558796\pi
−0.183664 + 0.982989i 0.558796π0.558796\pi
194194 −45.0602 −3.23513
195195 0 0
196196 −19.8217 −1.41584
197197 −3.74324 −0.266694 −0.133347 0.991069i 0.542573π-0.542573\pi
−0.133347 + 0.991069i 0.542573π0.542573\pi
198198 2.76156 0.196255
199199 −8.08476 −0.573114 −0.286557 0.958063i 0.592511π-0.592511\pi
−0.286557 + 0.958063i 0.592511π0.592511\pi
200200 0 0
201201 −11.9431 −0.842404
202202 −2.85069 −0.200574
203203 6.56934 0.461077
204204 −14.0140 −0.981173
205205 0 0
206206 −8.41233 −0.586115
207207 −7.14931 −0.496912
208208 −75.8776 −5.26116
209209 −5.38776 −0.372679
210210 0 0
211211 −15.9431 −1.09757 −0.548786 0.835963i 0.684910π-0.684910\pi
−0.548786 + 0.835963i 0.684910π0.684910\pi
212212 30.7110 2.10924
213213 11.6262 0.796614
214214 23.4865 1.60550
215215 0 0
216216 10.0140 0.681363
217217 −16.0848 −1.09190
218218 −16.9817 −1.15014
219219 −6.77551 −0.457847
220220 0 0
221221 11.5231 0.775129
222222 24.5187 1.64559
223223 22.1772 1.48510 0.742548 0.669793i 0.233617π-0.233617\pi
0.742548 + 0.669793i 0.233617π0.233617\pi
224224 −47.1127 −3.14785
225225 0 0
226226 16.5693 1.10218
227227 −5.93545 −0.393950 −0.196975 0.980409i 0.563112π-0.563112\pi
−0.196975 + 0.980409i 0.563112π0.563112\pi
228228 −30.3126 −2.00750
229229 −8.31695 −0.549599 −0.274800 0.961502i 0.588612π-0.588612\pi
−0.274800 + 0.961502i 0.588612π0.588612\pi
230230 0 0
231231 −1.86464 −0.122684
232232 −35.2803 −2.31627
233233 −28.5187 −1.86833 −0.934163 0.356848i 0.883852π-0.883852\pi
−0.934163 + 0.356848i 0.883852π0.883852\pi
234234 −12.7755 −0.835161
235235 0 0
236236 28.9711 1.88585
237237 −6.01395 −0.390648
238238 12.8261 0.831393
239239 24.0925 1.55841 0.779206 0.626768i 0.215623π-0.215623\pi
0.779206 + 0.626768i 0.215623π0.215623\pi
240240 0 0
241241 −5.16763 −0.332877 −0.166438 0.986052i 0.553227π-0.553227\pi
−0.166438 + 0.986052i 0.553227π0.553227\pi
242242 2.76156 0.177520
243243 1.00000 0.0641500
244244 24.8680 1.59201
245245 0 0
246246 −2.10308 −0.134088
247247 24.9248 1.58593
248248 86.3823 5.48528
249249 −14.5693 −0.923295
250250 0 0
251251 −9.25240 −0.584006 −0.292003 0.956417i 0.594322π-0.594322\pi
−0.292003 + 0.956417i 0.594322π0.594322\pi
252252 −10.4908 −0.660861
253253 −7.14931 −0.449473
254254 25.5896 1.60563
255255 0 0
256256 68.4575 4.27860
257257 25.2158 1.57292 0.786458 0.617644i 0.211913π-0.211913\pi
0.786458 + 0.617644i 0.211913π0.211913\pi
258258 20.4402 1.27255
259259 −16.5554 −1.02870
260260 0 0
261261 −3.52311 −0.218075
262262 11.2245 0.693451
263263 −5.45856 −0.336589 −0.168295 0.985737i 0.553826π-0.553826\pi
−0.168295 + 0.985737i 0.553826π0.553826\pi
264264 10.0140 0.616316
265265 0 0
266266 27.7432 1.70105
267267 9.04623 0.553620
268268 −67.1945 −4.10456
269269 17.0741 1.04103 0.520514 0.853853i 0.325740π-0.325740\pi
0.520514 + 0.853853i 0.325740π0.325740\pi
270270 0 0
271271 9.77988 0.594085 0.297043 0.954864i 0.404000π-0.404000\pi
0.297043 + 0.954864i 0.404000π0.404000\pi
272272 −40.8540 −2.47714
273273 8.62620 0.522081
274274 −16.3911 −0.990221
275275 0 0
276276 −40.2234 −2.42117
277277 −5.91524 −0.355412 −0.177706 0.984084i 0.556868π-0.556868\pi
−0.177706 + 0.984084i 0.556868π0.556868\pi
278278 18.5327 1.11152
279279 8.62620 0.516437
280280 0 0
281281 −6.76156 −0.403361 −0.201680 0.979451i 0.564640π-0.564640\pi
−0.201680 + 0.979451i 0.564640π0.564640\pi
282282 1.03228 0.0614711
283283 −8.81841 −0.524200 −0.262100 0.965041i 0.584415π-0.584415\pi
−0.262100 + 0.965041i 0.584415π0.584415\pi
284284 65.4113 3.88145
285285 0 0
286286 −12.7755 −0.755432
287287 1.42003 0.0838218
288288 25.2663 1.48883
289289 −10.7957 −0.635042
290290 0 0
291291 −16.3169 −0.956516
292292 −38.1204 −2.23083
293293 30.4908 1.78129 0.890647 0.454696i 0.150252π-0.150252\pi
0.890647 + 0.454696i 0.150252π0.150252\pi
294294 −9.72928 −0.567423
295295 0 0
296296 88.9098 5.16778
297297 1.00000 0.0580259
298298 15.8603 0.918761
299299 33.0741 1.91273
300300 0 0
301301 −13.8015 −0.795507
302302 29.1666 1.67835
303303 −1.03228 −0.0593027
304304 −88.3684 −5.06827
305305 0 0
306306 −6.87859 −0.393223
307307 −0.767815 −0.0438215 −0.0219107 0.999760i 0.506975π-0.506975\pi
−0.0219107 + 0.999760i 0.506975π0.506975\pi
308308 −10.4908 −0.597771
309309 −3.04623 −0.173294
310310 0 0
311311 −33.8496 −1.91944 −0.959719 0.280963i 0.909346π-0.909346\pi
−0.959719 + 0.280963i 0.909346π0.909346\pi
312312 −46.3265 −2.62272
313313 8.11078 0.458448 0.229224 0.973374i 0.426381π-0.426381\pi
0.229224 + 0.973374i 0.426381π0.426381\pi
314314 −8.56934 −0.483596
315315 0 0
316316 −33.8357 −1.90341
317317 −8.06455 −0.452950 −0.226475 0.974017i 0.572720π-0.572720\pi
−0.226475 + 0.974017i 0.572720π0.572720\pi
318318 15.0741 0.845316
319319 −3.52311 −0.197257
320320 0 0
321321 8.50479 0.474691
322322 36.8140 2.05157
323323 13.4200 0.746710
324324 5.62620 0.312567
325325 0 0
326326 −43.2803 −2.39707
327327 −6.14931 −0.340058
328328 −7.62620 −0.421086
329329 −0.697006 −0.0384272
330330 0 0
331331 22.4769 1.23544 0.617721 0.786398i 0.288056π-0.288056\pi
0.617721 + 0.786398i 0.288056π0.288056\pi
332332 −81.9700 −4.49869
333333 8.87859 0.486544
334334 24.8034 1.35718
335335 0 0
336336 −30.5833 −1.66846
337337 −6.32757 −0.344685 −0.172342 0.985037i 0.555134π-0.555134\pi
−0.172342 + 0.985037i 0.555134π0.555134\pi
338338 23.2018 1.26201
339339 6.00000 0.325875
340340 0 0
341341 8.62620 0.467135
342342 −14.8786 −0.804542
343343 19.6218 1.05948
344344 74.1204 3.99630
345345 0 0
346346 31.7832 1.70868
347347 0.178261 0.00956954 0.00478477 0.999989i 0.498477π-0.498477\pi
0.00478477 + 0.999989i 0.498477π0.498477\pi
348348 −19.8217 −1.06256
349349 −19.7293 −1.05608 −0.528042 0.849218i 0.677074π-0.677074\pi
−0.528042 + 0.849218i 0.677074π0.677074\pi
350350 0 0
351351 −4.62620 −0.246928
352352 25.2663 1.34670
353353 19.5231 1.03911 0.519555 0.854437i 0.326098π-0.326098\pi
0.519555 + 0.854437i 0.326098π0.326098\pi
354354 14.2201 0.755791
355355 0 0
356356 50.8959 2.69748
357357 4.64452 0.245814
358358 28.6478 1.51409
359359 35.6926 1.88379 0.941893 0.335914i 0.109045π-0.109045\pi
0.941893 + 0.335914i 0.109045π0.109045\pi
360360 0 0
361361 10.0279 0.527785
362362 −7.35881 −0.386770
363363 1.00000 0.0524864
364364 48.5327 2.54380
365365 0 0
366366 12.2062 0.638027
367367 −20.1127 −1.04987 −0.524936 0.851141i 0.675911π-0.675911\pi
−0.524936 + 0.851141i 0.675911π0.675911\pi
368368 −117.261 −6.11265
369369 −0.761557 −0.0396451
370370 0 0
371371 −10.1783 −0.528429
372372 48.5327 2.51630
373373 2.56165 0.132637 0.0663185 0.997799i 0.478875π-0.478875\pi
0.0663185 + 0.997799i 0.478875π0.478875\pi
374374 −6.87859 −0.355684
375375 0 0
376376 3.74324 0.193043
377377 16.2986 0.839422
378378 −5.14931 −0.264852
379379 23.2601 1.19479 0.597395 0.801947i 0.296202π-0.296202\pi
0.597395 + 0.801947i 0.296202π0.296202\pi
380380 0 0
381381 9.26635 0.474729
382382 40.5187 2.07312
383383 −25.7938 −1.31800 −0.659002 0.752142i 0.729021π-0.729021\pi
−0.659002 + 0.752142i 0.729021π0.729021\pi
384384 51.5650 2.63141
385385 0 0
386386 −14.0925 −0.717287
387387 7.40171 0.376250
388388 −91.8024 −4.66056
389389 2.33527 0.118403 0.0592014 0.998246i 0.481145π-0.481145\pi
0.0592014 + 0.998246i 0.481145π0.481145\pi
390390 0 0
391391 17.8078 0.900578
392392 −35.2803 −1.78192
393393 4.06455 0.205029
394394 −10.3372 −0.520778
395395 0 0
396396 5.62620 0.282727
397397 −17.1955 −0.863019 −0.431510 0.902108i 0.642019π-0.642019\pi
−0.431510 + 0.902108i 0.642019π0.642019\pi
398398 −22.3265 −1.11913
399399 10.0462 0.502941
400400 0 0
401401 −26.5693 −1.32681 −0.663405 0.748261i 0.730889π-0.730889\pi
−0.663405 + 0.748261i 0.730889π0.730889\pi
402402 −32.9817 −1.64498
403403 −39.9065 −1.98788
404404 −5.80779 −0.288948
405405 0 0
406406 18.1416 0.900353
407407 8.87859 0.440096
408408 −24.9431 −1.23487
409409 −20.4200 −1.00971 −0.504853 0.863205i 0.668453π-0.668453\pi
−0.504853 + 0.863205i 0.668453π0.668453\pi
410410 0 0
411411 −5.93545 −0.292774
412412 −17.1387 −0.844362
413413 −9.60162 −0.472465
414414 −19.7432 −0.970327
415415 0 0
416416 −116.887 −5.73086
417417 6.71096 0.328637
418418 −14.8786 −0.727736
419419 −13.5896 −0.663893 −0.331947 0.943298i 0.607705π-0.607705\pi
−0.331947 + 0.943298i 0.607705π0.607705\pi
420420 0 0
421421 −39.6175 −1.93084 −0.965418 0.260705i 0.916045π-0.916045\pi
−0.965418 + 0.260705i 0.916045π0.916045\pi
422422 −44.0279 −2.14324
423423 0.373802 0.0181749
424424 54.6618 2.65461
425425 0 0
426426 32.1064 1.55556
427427 −8.24177 −0.398847
428428 47.8496 2.31290
429429 −4.62620 −0.223355
430430 0 0
431431 −6.56934 −0.316434 −0.158217 0.987404i 0.550575π-0.550575\pi
−0.158217 + 0.987404i 0.550575π0.550575\pi
432432 16.4017 0.789128
433433 36.4113 1.74982 0.874908 0.484290i 0.160922π-0.160922\pi
0.874908 + 0.484290i 0.160922π0.160922\pi
434434 −44.4190 −2.13218
435435 0 0
436436 −34.5972 −1.65691
437437 38.5187 1.84260
438438 −18.7110 −0.894044
439439 25.3878 1.21169 0.605846 0.795582i 0.292835π-0.292835\pi
0.605846 + 0.795582i 0.292835π0.292835\pi
440440 0 0
441441 −3.52311 −0.167767
442442 31.8217 1.51361
443443 20.9065 0.993298 0.496649 0.867952i 0.334564π-0.334564\pi
0.496649 + 0.867952i 0.334564π0.334564\pi
444444 49.9527 2.37065
445445 0 0
446446 61.2437 2.89997
447447 5.74324 0.271646
448448 −68.9377 −3.25700
449449 −34.9450 −1.64916 −0.824579 0.565747i 0.808588π-0.808588\pi
−0.824579 + 0.565747i 0.808588π0.808588\pi
450450 0 0
451451 −0.761557 −0.0358603
452452 33.7572 1.58780
453453 10.5616 0.496229
454454 −16.3911 −0.769272
455455 0 0
456456 −53.9527 −2.52657
457457 −7.31695 −0.342272 −0.171136 0.985247i 0.554744π-0.554744\pi
−0.171136 + 0.985247i 0.554744π0.554744\pi
458458 −22.9677 −1.07321
459459 −2.49084 −0.116262
460460 0 0
461461 −14.0279 −0.653345 −0.326672 0.945138i 0.605927π-0.605927\pi
−0.326672 + 0.945138i 0.605927π0.605927\pi
462462 −5.14931 −0.239568
463463 4.33527 0.201477 0.100739 0.994913i 0.467879π-0.467879\pi
0.100739 + 0.994913i 0.467879π0.467879\pi
464464 −57.7851 −2.68261
465465 0 0
466466 −78.7561 −3.64831
467467 3.70138 0.171279 0.0856396 0.996326i 0.472707π-0.472707\pi
0.0856396 + 0.996326i 0.472707π0.472707\pi
468468 −26.0279 −1.20314
469469 22.2697 1.02832
470470 0 0
471471 −3.10308 −0.142983
472472 51.5650 2.37347
473473 7.40171 0.340331
474474 −16.6079 −0.762825
475475 0 0
476476 26.1310 1.19771
477477 5.45856 0.249930
478478 66.5327 3.04313
479479 −22.8680 −1.04486 −0.522432 0.852681i 0.674975π-0.674975\pi
−0.522432 + 0.852681i 0.674975π0.674975\pi
480480 0 0
481481 −41.0741 −1.87282
482482 −14.2707 −0.650013
483483 13.3309 0.606577
484484 5.62620 0.255736
485485 0 0
486486 2.76156 0.125267
487487 −5.42962 −0.246039 −0.123020 0.992404i 0.539258π-0.539258\pi
−0.123020 + 0.992404i 0.539258π0.539258\pi
488488 44.2620 2.00365
489489 −15.6724 −0.708732
490490 0 0
491491 21.2803 0.960367 0.480183 0.877168i 0.340570π-0.340570\pi
0.480183 + 0.877168i 0.340570π0.340570\pi
492492 −4.28467 −0.193168
493493 8.77551 0.395229
494494 68.8313 3.09687
495495 0 0
496496 141.484 6.35284
497497 −21.6787 −0.972422
498498 −40.2341 −1.80293
499499 −16.0077 −0.716603 −0.358301 0.933606i 0.616644π-0.616644\pi
−0.358301 + 0.933606i 0.616644π0.616644\pi
500500 0 0
501501 8.98168 0.401272
502502 −25.5510 −1.14040
503503 12.0925 0.539176 0.269588 0.962976i 0.413112π-0.413112\pi
0.269588 + 0.962976i 0.413112π0.413112\pi
504504 −18.6724 −0.831736
505505 0 0
506506 −19.7432 −0.877694
507507 8.40171 0.373133
508508 52.1343 2.31309
509509 14.7110 0.652052 0.326026 0.945361i 0.394290π-0.394290\pi
0.326026 + 0.945361i 0.394290π0.394290\pi
510510 0 0
511511 12.6339 0.558891
512512 85.9194 3.79714
513513 −5.38776 −0.237875
514514 69.6347 3.07146
515515 0 0
516516 41.6435 1.83325
517517 0.373802 0.0164398
518518 −45.7187 −2.00876
519519 11.5092 0.505196
520520 0 0
521521 −17.2803 −0.757064 −0.378532 0.925588i 0.623571π-0.623571\pi
−0.378532 + 0.925588i 0.623571π0.623571\pi
522522 −9.72928 −0.425839
523523 −42.7326 −1.86857 −0.934283 0.356532i 0.883959π-0.883959\pi
−0.934283 + 0.356532i 0.883959π0.883959\pi
524524 22.8680 0.998992
525525 0 0
526526 −15.0741 −0.657264
527527 −21.4865 −0.935965
528528 16.4017 0.713793
529529 28.1127 1.22229
530530 0 0
531531 5.14931 0.223461
532532 56.5221 2.45054
533533 3.52311 0.152603
534534 24.9817 1.08106
535535 0 0
536536 −119.598 −5.16585
537537 10.3738 0.447663
538538 47.1512 2.03283
539539 −3.52311 −0.151751
540540 0 0
541541 8.69075 0.373644 0.186822 0.982394i 0.440181π-0.440181\pi
0.186822 + 0.982394i 0.440181π0.440181\pi
542542 27.0077 1.16008
543543 −2.66473 −0.114355
544544 −62.9344 −2.69829
545545 0 0
546546 23.8217 1.01948
547547 44.1064 1.88585 0.942927 0.333000i 0.108061π-0.108061\pi
0.942927 + 0.333000i 0.108061π0.108061\pi
548548 −33.3940 −1.42652
549549 4.42003 0.188642
550550 0 0
551551 18.9817 0.808647
552552 −71.5929 −3.04720
553553 11.2139 0.476862
554554 −16.3353 −0.694019
555555 0 0
556556 37.7572 1.60126
557557 7.69264 0.325948 0.162974 0.986630i 0.447891π-0.447891\pi
0.162974 + 0.986630i 0.447891π0.447891\pi
558558 23.8217 1.00845
559559 −34.2418 −1.44827
560560 0 0
561561 −2.49084 −0.105163
562562 −18.6724 −0.787649
563563 −9.25240 −0.389942 −0.194971 0.980809i 0.562461π-0.562461\pi
−0.194971 + 0.980809i 0.562461π0.562461\pi
564564 2.10308 0.0885558
565565 0 0
566566 −24.3525 −1.02361
567567 −1.86464 −0.0783076
568568 116.424 4.88505
569569 4.96772 0.208258 0.104129 0.994564i 0.466795π-0.466795\pi
0.104129 + 0.994564i 0.466795π0.466795\pi
570570 0 0
571571 6.02021 0.251938 0.125969 0.992034i 0.459796π-0.459796\pi
0.125969 + 0.992034i 0.459796π0.459796\pi
572572 −26.0279 −1.08828
573573 14.6724 0.612949
574574 3.92150 0.163680
575575 0 0
576576 36.9711 1.54046
577577 −8.25240 −0.343552 −0.171776 0.985136i 0.554950π-0.554950\pi
−0.171776 + 0.985136i 0.554950π0.554950\pi
578578 −29.8130 −1.24006
579579 −5.10308 −0.212077
580580 0 0
581581 27.1666 1.12706
582582 −45.0602 −1.86780
583583 5.45856 0.226071
584584 −67.8496 −2.80764
585585 0 0
586586 84.2022 3.47836
587587 11.4846 0.474019 0.237010 0.971507i 0.423833π-0.423833\pi
0.237010 + 0.971507i 0.423833π0.423833\pi
588588 −19.8217 −0.817435
589589 −46.4758 −1.91500
590590 0 0
591591 −3.74324 −0.153976
592592 145.624 5.98511
593593 39.0375 1.60308 0.801539 0.597943i 0.204015π-0.204015\pi
0.801539 + 0.597943i 0.204015π0.204015\pi
594594 2.76156 0.113308
595595 0 0
596596 32.3126 1.32357
597597 −8.08476 −0.330887
598598 91.3361 3.73501
599599 −30.1589 −1.23226 −0.616130 0.787645i 0.711300π-0.711300\pi
−0.616130 + 0.787645i 0.711300π0.711300\pi
600600 0 0
601601 19.1310 0.780369 0.390185 0.920737i 0.372411π-0.372411\pi
0.390185 + 0.920737i 0.372411π0.372411\pi
602602 −38.1137 −1.55340
603603 −11.9431 −0.486362
604604 59.4219 2.41784
605605 0 0
606606 −2.85069 −0.115801
607607 −4.20617 −0.170723 −0.0853615 0.996350i 0.527205π-0.527205\pi
−0.0853615 + 0.996350i 0.527205π0.527205\pi
608608 −136.129 −5.52076
609609 6.56934 0.266203
610610 0 0
611611 −1.72928 −0.0699593
612612 −14.0140 −0.566480
613613 −5.45856 −0.220469 −0.110235 0.993906i 0.535160π-0.535160\pi
−0.110235 + 0.993906i 0.535160π0.535160\pi
614614 −2.12036 −0.0855709
615615 0 0
616616 −18.6724 −0.752334
617617 −30.1974 −1.21570 −0.607851 0.794051i 0.707968π-0.707968\pi
−0.607851 + 0.794051i 0.707968π0.707968\pi
618618 −8.41233 −0.338394
619619 23.1955 0.932308 0.466154 0.884704i 0.345639π-0.345639\pi
0.466154 + 0.884704i 0.345639π0.345639\pi
620620 0 0
621621 −7.14931 −0.286892
622622 −93.4777 −3.74812
623623 −16.8680 −0.675801
624624 −75.8776 −3.03753
625625 0 0
626626 22.3984 0.895219
627627 −5.38776 −0.215166
628628 −17.4586 −0.696673
629629 −22.1151 −0.881789
630630 0 0
631631 −3.19554 −0.127212 −0.0636062 0.997975i 0.520260π-0.520260\pi
−0.0636062 + 0.997975i 0.520260π0.520260\pi
632632 −60.2234 −2.39556
633633 −15.9431 −0.633683
634634 −22.2707 −0.884483
635635 0 0
636636 30.7110 1.21777
637637 16.2986 0.645775
638638 −9.72928 −0.385186
639639 11.6262 0.459925
640640 0 0
641641 28.1974 1.11373 0.556866 0.830603i 0.312004π-0.312004\pi
0.556866 + 0.830603i 0.312004π0.312004\pi
642642 23.4865 0.926937
643643 −17.9634 −0.708406 −0.354203 0.935169i 0.615248π-0.615248\pi
−0.354203 + 0.935169i 0.615248π0.615248\pi
644644 75.0023 2.95550
645645 0 0
646646 37.0602 1.45811
647647 40.9990 1.61184 0.805918 0.592028i 0.201672π-0.201672\pi
0.805918 + 0.592028i 0.201672π0.201672\pi
648648 10.0140 0.393385
649649 5.14931 0.202128
650650 0 0
651651 −16.0848 −0.630412
652652 −88.1762 −3.45325
653653 −11.6926 −0.457568 −0.228784 0.973477i 0.573475π-0.573475\pi
−0.228784 + 0.973477i 0.573475π0.573475\pi
654654 −16.9817 −0.664036
655655 0 0
656656 −12.4908 −0.487685
657657 −6.77551 −0.264338
658658 −1.92482 −0.0750374
659659 −1.72928 −0.0673633 −0.0336816 0.999433i 0.510723π-0.510723\pi
−0.0336816 + 0.999433i 0.510723π0.510723\pi
660660 0 0
661661 0.232185 0.00903096 0.00451548 0.999990i 0.498563π-0.498563\pi
0.00451548 + 0.999990i 0.498563π0.498563\pi
662662 62.0712 2.41247
663663 11.5231 0.447521
664664 −145.897 −5.66189
665665 0 0
666666 24.5187 0.950082
667667 25.1878 0.975277
668668 50.5327 1.95517
669669 22.1772 0.857421
670670 0 0
671671 4.42003 0.170633
672672 −47.1127 −1.81741
673673 −33.5144 −1.29188 −0.645942 0.763386i 0.723535π-0.723535\pi
−0.645942 + 0.763386i 0.723535π0.723535\pi
674674 −17.4740 −0.673072
675675 0 0
676676 47.2697 1.81806
677677 13.0183 0.500335 0.250167 0.968203i 0.419514π-0.419514\pi
0.250167 + 0.968203i 0.419514π0.419514\pi
678678 16.5693 0.636342
679679 30.4252 1.16761
680680 0 0
681681 −5.93545 −0.227447
682682 23.8217 0.912182
683683 4.54333 0.173846 0.0869228 0.996215i 0.472297π-0.472297\pi
0.0869228 + 0.996215i 0.472297π0.472297\pi
684684 −30.3126 −1.15903
685685 0 0
686686 54.1868 2.06886
687687 −8.31695 −0.317311
688688 121.401 4.62836
689689 −25.2524 −0.962040
690690 0 0
691691 −19.8988 −0.756986 −0.378493 0.925604i 0.623558π-0.623558\pi
−0.378493 + 0.925604i 0.623558π0.623558\pi
692692 64.7528 2.46153
693693 −1.86464 −0.0708319
694694 0.492277 0.0186866
695695 0 0
696696 −35.2803 −1.33730
697697 1.89692 0.0718508
698698 −54.4835 −2.06223
699699 −28.5187 −1.07868
700700 0 0
701701 −15.8444 −0.598436 −0.299218 0.954185i 0.596726π-0.596726\pi
−0.299218 + 0.954185i 0.596726π0.596726\pi
702702 −12.7755 −0.482181
703703 −47.8357 −1.80416
704704 36.9711 1.39340
705705 0 0
706706 53.9142 2.02909
707707 1.92482 0.0723904
708708 28.9711 1.08880
709709 8.82174 0.331307 0.165654 0.986184i 0.447027π-0.447027\pi
0.165654 + 0.986184i 0.447027π0.447027\pi
710710 0 0
711711 −6.01395 −0.225541
712712 90.5885 3.39495
713713 −61.6714 −2.30961
714714 12.8261 0.480005
715715 0 0
716716 58.3651 2.18120
717717 24.0925 0.899749
718718 98.5673 3.67850
719719 36.7668 1.37117 0.685585 0.727993i 0.259547π-0.259547\pi
0.685585 + 0.727993i 0.259547π0.259547\pi
720720 0 0
721721 5.68012 0.211539
722722 27.6926 1.03061
723723 −5.16763 −0.192186
724724 −14.9923 −0.557185
725725 0 0
726726 2.76156 0.102491
727727 5.27261 0.195550 0.0977751 0.995209i 0.468827π-0.468827\pi
0.0977751 + 0.995209i 0.468827π0.468827\pi
728728 86.3823 3.20154
729729 1.00000 0.0370370
730730 0 0
731731 −18.4365 −0.681897
732732 24.8680 0.919147
733733 −37.9508 −1.40175 −0.700873 0.713286i 0.747206π-0.747206\pi
−0.700873 + 0.713286i 0.747206π0.747206\pi
734734 −55.5423 −2.05010
735735 0 0
736736 −180.637 −6.65837
737737 −11.9431 −0.439931
738738 −2.10308 −0.0774156
739739 37.2943 1.37189 0.685946 0.727653i 0.259389π-0.259389\pi
0.685946 + 0.727653i 0.259389π0.259389\pi
740740 0 0
741741 24.9248 0.915636
742742 −28.1078 −1.03187
743743 −22.5693 −0.827989 −0.413994 0.910279i 0.635867π-0.635867\pi
−0.413994 + 0.910279i 0.635867π0.635867\pi
744744 86.3823 3.16693
745745 0 0
746746 7.07414 0.259002
747747 −14.5693 −0.533064
748748 −14.0140 −0.512401
749749 −15.8584 −0.579453
750750 0 0
751751 −9.55102 −0.348522 −0.174261 0.984700i 0.555754π-0.555754\pi
−0.174261 + 0.984700i 0.555754π0.555754\pi
752752 6.13099 0.223574
753753 −9.25240 −0.337176
754754 45.0096 1.63915
755755 0 0
756756 −10.4908 −0.381548
757757 −30.3188 −1.10196 −0.550978 0.834519i 0.685745π-0.685745\pi
−0.550978 + 0.834519i 0.685745π0.685745\pi
758758 64.2341 2.33309
759759 −7.14931 −0.259504
760760 0 0
761761 −1.43066 −0.0518613 −0.0259306 0.999664i 0.508255π-0.508255\pi
−0.0259306 + 0.999664i 0.508255π0.508255\pi
762762 25.5896 0.927012
763763 11.4663 0.415106
764764 82.5500 2.98655
765765 0 0
766766 −71.2311 −2.57369
767767 −23.8217 −0.860153
768768 68.4575 2.47025
769769 −35.4017 −1.27662 −0.638309 0.769780i 0.720366π-0.720366\pi
−0.638309 + 0.769780i 0.720366π0.720366\pi
770770 0 0
771771 25.2158 0.908123
772772 −28.7110 −1.03333
773773 13.4094 0.482303 0.241151 0.970488i 0.422475π-0.422475\pi
0.241151 + 0.970488i 0.422475π0.422475\pi
774774 20.4402 0.734709
775775 0 0
776776 −163.397 −5.86562
777777 −16.5554 −0.593921
778778 6.44898 0.231207
779779 4.10308 0.147008
780780 0 0
781781 11.6262 0.416018
782782 49.1772 1.75857
783783 −3.52311 −0.125906
784784 −57.7851 −2.06375
785785 0 0
786786 11.2245 0.400364
787787 37.3232 1.33043 0.665214 0.746653i 0.268340π-0.268340\pi
0.665214 + 0.746653i 0.268340π0.268340\pi
788788 −21.0602 −0.750238
789789 −5.45856 −0.194330
790790 0 0
791791 −11.1878 −0.397794
792792 10.0140 0.355830
793793 −20.4479 −0.726128
794794 −47.4865 −1.68523
795795 0 0
796796 −45.4865 −1.61223
797797 8.05581 0.285352 0.142676 0.989769i 0.454429π-0.454429\pi
0.142676 + 0.989769i 0.454429π0.454429\pi
798798 27.7432 0.982100
799799 −0.931080 −0.0329393
800800 0 0
801801 9.04623 0.319633
802802 −73.3728 −2.59088
803803 −6.77551 −0.239103
804804 −67.1945 −2.36977
805805 0 0
806806 −110.204 −3.88177
807807 17.0741 0.601038
808808 −10.3372 −0.363660
809809 −42.3771 −1.48990 −0.744950 0.667120i 0.767527π-0.767527\pi
−0.744950 + 0.667120i 0.767527π0.767527\pi
810810 0 0
811811 −21.3878 −0.751026 −0.375513 0.926817i 0.622533π-0.622533\pi
−0.375513 + 0.926817i 0.622533π0.622533\pi
812812 36.9604 1.29706
813813 9.77988 0.342995
814814 24.5187 0.859382
815815 0 0
816816 −40.8540 −1.43018
817817 −39.8786 −1.39518
818818 −56.3911 −1.97167
819819 8.62620 0.301424
820820 0 0
821821 −47.8776 −1.67094 −0.835469 0.549537i 0.814804π-0.814804\pi
−0.835469 + 0.549537i 0.814804π0.814804\pi
822822 −16.3911 −0.571705
823823 −16.3555 −0.570116 −0.285058 0.958510i 0.592013π-0.592013\pi
−0.285058 + 0.958510i 0.592013π0.592013\pi
824824 −30.5048 −1.06268
825825 0 0
826826 −26.5154 −0.922589
827827 44.7110 1.55475 0.777376 0.629036i 0.216550π-0.216550\pi
0.777376 + 0.629036i 0.216550π0.216550\pi
828828 −40.2234 −1.39786
829829 −38.5972 −1.34054 −0.670269 0.742118i 0.733821π-0.733821\pi
−0.670269 + 0.742118i 0.733821π0.733821\pi
830830 0 0
831831 −5.91524 −0.205197
832832 −171.035 −5.92959
833833 8.77551 0.304053
834834 18.5327 0.641735
835835 0 0
836836 −30.3126 −1.04838
837837 8.62620 0.298165
838838 −37.5283 −1.29639
839839 −0.710960 −0.0245451 −0.0122725 0.999925i 0.503907π-0.503907\pi
−0.0122725 + 0.999925i 0.503907π0.503907\pi
840840 0 0
841841 −16.5877 −0.571988
842842 −109.406 −3.77038
843843 −6.76156 −0.232880
844844 −89.6993 −3.08758
845845 0 0
846846 1.03228 0.0354904
847847 −1.86464 −0.0640698
848848 89.5298 3.07446
849849 −8.81841 −0.302647
850850 0 0
851851 −63.4758 −2.17592
852852 65.4113 2.24095
853853 −52.7187 −1.80505 −0.902526 0.430635i 0.858290π-0.858290\pi
−0.902526 + 0.430635i 0.858290π0.858290\pi
854854 −22.7601 −0.778835
855855 0 0
856856 85.1666 2.91093
857857 −16.7124 −0.570885 −0.285442 0.958396i 0.592141π-0.592141\pi
−0.285442 + 0.958396i 0.592141π0.592141\pi
858858 −12.7755 −0.436149
859859 −41.9142 −1.43009 −0.715047 0.699076i 0.753595π-0.753595\pi
−0.715047 + 0.699076i 0.753595π0.753595\pi
860860 0 0
861861 1.42003 0.0483945
862862 −18.1416 −0.617906
863863 41.4219 1.41002 0.705009 0.709198i 0.250943π-0.250943\pi
0.705009 + 0.709198i 0.250943π0.250943\pi
864864 25.2663 0.859579
865865 0 0
866866 100.552 3.41689
867867 −10.7957 −0.366642
868868 −90.4961 −3.07164
869869 −6.01395 −0.204009
870870 0 0
871871 55.2514 1.87212
872872 −61.5789 −2.08533
873873 −16.3169 −0.552245
874874 106.372 3.59808
875875 0 0
876876 −38.1204 −1.28797
877877 12.0848 0.408073 0.204037 0.978963i 0.434594π-0.434594\pi
0.204037 + 0.978963i 0.434594π0.434594\pi
878878 70.1097 2.36609
879879 30.4908 1.02843
880880 0 0
881881 −31.8130 −1.07181 −0.535904 0.844279i 0.680029π-0.680029\pi
−0.535904 + 0.844279i 0.680029π0.680029\pi
882882 −9.72928 −0.327602
883883 20.9894 0.706349 0.353174 0.935558i 0.385102π-0.385102\pi
0.353174 + 0.935558i 0.385102π0.385102\pi
884884 64.8313 2.18051
885885 0 0
886886 57.7345 1.93963
887887 −49.2032 −1.65208 −0.826042 0.563609i 0.809412π-0.809412\pi
−0.826042 + 0.563609i 0.809412π0.809412\pi
888888 88.9098 2.98362
889889 −17.2784 −0.579499
890890 0 0
891891 1.00000 0.0335013
892892 124.773 4.17772
893893 −2.01395 −0.0673944
894894 15.8603 0.530447
895895 0 0
896896 −96.1502 −3.21215
897897 33.0741 1.10431
898898 −96.5027 −3.22034
899899 −30.3911 −1.01360
900900 0 0
901901 −13.5964 −0.452962
902902 −2.10308 −0.0700250
903903 −13.8015 −0.459286
904904 60.0837 1.99835
905905 0 0
906906 29.1666 0.968995
907907 24.8526 0.825216 0.412608 0.910909i 0.364618π-0.364618\pi
0.412608 + 0.910909i 0.364618π0.364618\pi
908908 −33.3940 −1.10822
909909 −1.03228 −0.0342384
910910 0 0
911911 45.4758 1.50668 0.753341 0.657630i 0.228441π-0.228441\pi
0.753341 + 0.657630i 0.228441π0.228441\pi
912912 −88.3684 −2.92617
913913 −14.5693 −0.482175
914914 −20.2062 −0.668361
915915 0 0
916916 −46.7928 −1.54608
917917 −7.57893 −0.250278
918918 −6.87859 −0.227027
919919 −15.7355 −0.519068 −0.259534 0.965734i 0.583569π-0.583569\pi
−0.259534 + 0.965734i 0.583569π0.583569\pi
920920 0 0
921921 −0.767815 −0.0253004
922922 −38.7389 −1.27580
923923 −53.7851 −1.77036
924924 −10.4908 −0.345123
925925 0 0
926926 11.9721 0.393427
927927 −3.04623 −0.100051
928928 −89.0162 −2.92210
929929 −2.06455 −0.0677357 −0.0338679 0.999426i 0.510783π-0.510783\pi
−0.0338679 + 0.999426i 0.510783π0.510783\pi
930930 0 0
931931 18.9817 0.622099
932932 −160.452 −5.25578
933933 −33.8496 −1.10819
934934 10.2216 0.334460
935935 0 0
936936 −46.3265 −1.51423
937937 −40.1493 −1.31162 −0.655810 0.754926i 0.727673π-0.727673\pi
−0.655810 + 0.754926i 0.727673π0.727673\pi
938938 61.4990 2.00801
939939 8.11078 0.264685
940940 0 0
941941 26.4050 0.860780 0.430390 0.902643i 0.358376π-0.358376\pi
0.430390 + 0.902643i 0.358376π0.358376\pi
942942 −8.56934 −0.279204
943943 5.44461 0.177301
944944 84.4575 2.74886
945945 0 0
946946 20.4402 0.664570
947947 −8.67243 −0.281816 −0.140908 0.990023i 0.545002π-0.545002\pi
−0.140908 + 0.990023i 0.545002π0.545002\pi
948948 −33.8357 −1.09893
949949 31.3449 1.01750
950950 0 0
951951 −8.06455 −0.261511
952952 46.5100 1.50740
953953 26.8540 0.869887 0.434943 0.900458i 0.356768π-0.356768\pi
0.434943 + 0.900458i 0.356768π0.356768\pi
954954 15.0741 0.488043
955955 0 0
956956 135.549 4.38397
957957 −3.52311 −0.113886
958958 −63.1512 −2.04032
959959 11.0675 0.357388
960960 0 0
961961 43.4113 1.40036
962962 −113.429 −3.65708
963963 8.50479 0.274063
964964 −29.0741 −0.936415
965965 0 0
966966 36.8140 1.18447
967967 55.8496 1.79600 0.898002 0.439992i 0.145019π-0.145019\pi
0.898002 + 0.439992i 0.145019π0.145019\pi
968968 10.0140 0.321861
969969 13.4200 0.431113
970970 0 0
971971 30.0664 0.964878 0.482439 0.875930i 0.339751π-0.339751\pi
0.482439 + 0.875930i 0.339751π0.339751\pi
972972 5.62620 0.180460
973973 −12.5135 −0.401165
974974 −14.9942 −0.480445
975975 0 0
976976 72.4961 2.32054
977977 −15.7014 −0.502331 −0.251166 0.967944i 0.580814π-0.580814\pi
−0.251166 + 0.967944i 0.580814π0.580814\pi
978978 −43.2803 −1.38395
979979 9.04623 0.289119
980980 0 0
981981 −6.14931 −0.196332
982982 58.7668 1.87532
983983 51.9894 1.65820 0.829102 0.559098i 0.188852π-0.188852\pi
0.829102 + 0.559098i 0.188852π0.188852\pi
984984 −7.62620 −0.243114
985985 0 0
986986 24.2341 0.771770
987987 −0.697006 −0.0221860
988988 140.232 4.46137
989989 −52.9171 −1.68267
990990 0 0
991991 27.6445 0.878157 0.439079 0.898449i 0.355305π-0.355305\pi
0.439079 + 0.898449i 0.355305π0.355305\pi
992992 217.953 6.92000
993993 22.4769 0.713282
994994 −59.8669 −1.89886
995995 0 0
996996 −81.9700 −2.59732
997997 −40.5048 −1.28280 −0.641400 0.767207i 0.721646π-0.721646\pi
−0.641400 + 0.767207i 0.721646π0.721646\pi
998998 −44.2062 −1.39932
999999 8.87859 0.280906
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 825.2.a.m.1.3 yes 3
3.2 odd 2 2475.2.a.z.1.1 3
5.2 odd 4 825.2.c.f.199.6 6
5.3 odd 4 825.2.c.f.199.1 6
5.4 even 2 825.2.a.i.1.1 3
11.10 odd 2 9075.2.a.cd.1.1 3
15.2 even 4 2475.2.c.q.199.1 6
15.8 even 4 2475.2.c.q.199.6 6
15.14 odd 2 2475.2.a.bd.1.3 3
55.54 odd 2 9075.2.a.cj.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
825.2.a.i.1.1 3 5.4 even 2
825.2.a.m.1.3 yes 3 1.1 even 1 trivial
825.2.c.f.199.1 6 5.3 odd 4
825.2.c.f.199.6 6 5.2 odd 4
2475.2.a.z.1.1 3 3.2 odd 2
2475.2.a.bd.1.3 3 15.14 odd 2
2475.2.c.q.199.1 6 15.2 even 4
2475.2.c.q.199.6 6 15.8 even 4
9075.2.a.cd.1.1 3 11.10 odd 2
9075.2.a.cj.1.3 3 55.54 odd 2