Properties

Label 1458.2.a.g.1.5
Level 14581458
Weight 22
Character 1458.1
Self dual yes
Analytic conductor 11.64211.642
Analytic rank 00
Dimension 66
CM no
Inner twists 11

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1458,2,Mod(1,1458)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1458, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1458.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 1458=236 1458 = 2 \cdot 3^{6}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1458.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,6,0,6,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 11.642188614711.6421886147
Analytic rank: 00
Dimension: 66
Coefficient field: 6.6.6357609.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x69x4x3+18x28 x^{6} - 9x^{4} - x^{3} + 18x^{2} - 8 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 32 3^{2}
Twist minimal: no (minimal twist has level 54)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.5
Root 1.59848-1.59848 of defining polynomial
Character χ\chi == 1458.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+1.00000q2+1.00000q4+3.16812q5+3.68572q7+1.00000q8+3.16812q102.28507q11+3.10027q13+3.68572q14+1.00000q16+1.72576q173.39480q19+3.16812q202.28507q223.35309q23+5.03695q25+3.10027q26+3.68572q280.585444q294.63798q31+1.00000q32+1.72576q34+11.6768q357.30720q373.39480q38+3.16812q407.08052q41+1.65791q432.28507q443.35309q463.85198q47+6.58452q49+5.03695q50+3.10027q522.58267q537.23936q55+3.68572q560.585444q589.66319q59+13.0913q614.63798q62+1.00000q64+9.82203q658.60876q67+1.72576q68+11.6768q70+1.98746q71+10.6474q737.30720q743.39480q768.42212q77+14.0932q79+3.16812q807.08052q823.09842q83+5.46739q85+1.65791q862.28507q8817.3460q89+11.4267q913.35309q923.85198q9410.7551q95+9.19117q97+6.58452q98+O(q100)q+1.00000 q^{2} +1.00000 q^{4} +3.16812 q^{5} +3.68572 q^{7} +1.00000 q^{8} +3.16812 q^{10} -2.28507 q^{11} +3.10027 q^{13} +3.68572 q^{14} +1.00000 q^{16} +1.72576 q^{17} -3.39480 q^{19} +3.16812 q^{20} -2.28507 q^{22} -3.35309 q^{23} +5.03695 q^{25} +3.10027 q^{26} +3.68572 q^{28} -0.585444 q^{29} -4.63798 q^{31} +1.00000 q^{32} +1.72576 q^{34} +11.6768 q^{35} -7.30720 q^{37} -3.39480 q^{38} +3.16812 q^{40} -7.08052 q^{41} +1.65791 q^{43} -2.28507 q^{44} -3.35309 q^{46} -3.85198 q^{47} +6.58452 q^{49} +5.03695 q^{50} +3.10027 q^{52} -2.58267 q^{53} -7.23936 q^{55} +3.68572 q^{56} -0.585444 q^{58} -9.66319 q^{59} +13.0913 q^{61} -4.63798 q^{62} +1.00000 q^{64} +9.82203 q^{65} -8.60876 q^{67} +1.72576 q^{68} +11.6768 q^{70} +1.98746 q^{71} +10.6474 q^{73} -7.30720 q^{74} -3.39480 q^{76} -8.42212 q^{77} +14.0932 q^{79} +3.16812 q^{80} -7.08052 q^{82} -3.09842 q^{83} +5.46739 q^{85} +1.65791 q^{86} -2.28507 q^{88} -17.3460 q^{89} +11.4267 q^{91} -3.35309 q^{92} -3.85198 q^{94} -10.7551 q^{95} +9.19117 q^{97} +6.58452 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+6q2+6q4+3q5+6q7+6q8+3q10+3q11+9q13+6q14+6q16+6q17+9q19+3q20+3q223q23+15q25+9q26+6q28+3q29++12q98+O(q100) 6 q + 6 q^{2} + 6 q^{4} + 3 q^{5} + 6 q^{7} + 6 q^{8} + 3 q^{10} + 3 q^{11} + 9 q^{13} + 6 q^{14} + 6 q^{16} + 6 q^{17} + 9 q^{19} + 3 q^{20} + 3 q^{22} - 3 q^{23} + 15 q^{25} + 9 q^{26} + 6 q^{28} + 3 q^{29}+ \cdots + 12 q^{98}+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 1.00000 0.707107
33 0 0
44 1.00000 0.500000
55 3.16812 1.41682 0.708412 0.705799i 0.249412π-0.249412\pi
0.708412 + 0.705799i 0.249412π0.249412\pi
66 0 0
77 3.68572 1.39307 0.696535 0.717522i 0.254724π-0.254724\pi
0.696535 + 0.717522i 0.254724π0.254724\pi
88 1.00000 0.353553
99 0 0
1010 3.16812 1.00185
1111 −2.28507 −0.688974 −0.344487 0.938791i 0.611947π-0.611947\pi
−0.344487 + 0.938791i 0.611947π0.611947\pi
1212 0 0
1313 3.10027 0.859862 0.429931 0.902862i 0.358538π-0.358538\pi
0.429931 + 0.902862i 0.358538π0.358538\pi
1414 3.68572 0.985050
1515 0 0
1616 1.00000 0.250000
1717 1.72576 0.418557 0.209279 0.977856i 0.432888π-0.432888\pi
0.209279 + 0.977856i 0.432888π0.432888\pi
1818 0 0
1919 −3.39480 −0.778820 −0.389410 0.921065i 0.627321π-0.627321\pi
−0.389410 + 0.921065i 0.627321π0.627321\pi
2020 3.16812 0.708412
2121 0 0
2222 −2.28507 −0.487178
2323 −3.35309 −0.699167 −0.349584 0.936905i 0.613677π-0.613677\pi
−0.349584 + 0.936905i 0.613677π0.613677\pi
2424 0 0
2525 5.03695 1.00739
2626 3.10027 0.608014
2727 0 0
2828 3.68572 0.696535
2929 −0.585444 −0.108714 −0.0543571 0.998522i 0.517311π-0.517311\pi
−0.0543571 + 0.998522i 0.517311π0.517311\pi
3030 0 0
3131 −4.63798 −0.833005 −0.416502 0.909135i 0.636744π-0.636744\pi
−0.416502 + 0.909135i 0.636744π0.636744\pi
3232 1.00000 0.176777
3333 0 0
3434 1.72576 0.295965
3535 11.6768 1.97374
3636 0 0
3737 −7.30720 −1.20130 −0.600648 0.799514i 0.705091π-0.705091\pi
−0.600648 + 0.799514i 0.705091π0.705091\pi
3838 −3.39480 −0.550709
3939 0 0
4040 3.16812 0.500923
4141 −7.08052 −1.10579 −0.552895 0.833251i 0.686477π-0.686477\pi
−0.552895 + 0.833251i 0.686477π0.686477\pi
4242 0 0
4343 1.65791 0.252830 0.126415 0.991977i 0.459653π-0.459653\pi
0.126415 + 0.991977i 0.459653π0.459653\pi
4444 −2.28507 −0.344487
4545 0 0
4646 −3.35309 −0.494386
4747 −3.85198 −0.561869 −0.280935 0.959727i 0.590644π-0.590644\pi
−0.280935 + 0.959727i 0.590644π0.590644\pi
4848 0 0
4949 6.58452 0.940646
5050 5.03695 0.712333
5151 0 0
5252 3.10027 0.429931
5353 −2.58267 −0.354757 −0.177379 0.984143i 0.556762π-0.556762\pi
−0.177379 + 0.984143i 0.556762π0.556762\pi
5454 0 0
5555 −7.23936 −0.976155
5656 3.68572 0.492525
5757 0 0
5858 −0.585444 −0.0768726
5959 −9.66319 −1.25804 −0.629020 0.777389i 0.716544π-0.716544\pi
−0.629020 + 0.777389i 0.716544π0.716544\pi
6060 0 0
6161 13.0913 1.67617 0.838087 0.545537i 0.183674π-0.183674\pi
0.838087 + 0.545537i 0.183674π0.183674\pi
6262 −4.63798 −0.589023
6363 0 0
6464 1.00000 0.125000
6565 9.82203 1.21827
6666 0 0
6767 −8.60876 −1.05173 −0.525864 0.850569i 0.676258π-0.676258\pi
−0.525864 + 0.850569i 0.676258π0.676258\pi
6868 1.72576 0.209279
6969 0 0
7070 11.6768 1.39564
7171 1.98746 0.235869 0.117934 0.993021i 0.462373π-0.462373\pi
0.117934 + 0.993021i 0.462373π0.462373\pi
7272 0 0
7373 10.6474 1.24619 0.623094 0.782147i 0.285876π-0.285876\pi
0.623094 + 0.782147i 0.285876π0.285876\pi
7474 −7.30720 −0.849444
7575 0 0
7676 −3.39480 −0.389410
7777 −8.42212 −0.959789
7878 0 0
7979 14.0932 1.58561 0.792804 0.609477i 0.208620π-0.208620\pi
0.792804 + 0.609477i 0.208620π0.208620\pi
8080 3.16812 0.354206
8181 0 0
8282 −7.08052 −0.781912
8383 −3.09842 −0.340096 −0.170048 0.985436i 0.554392π-0.554392\pi
−0.170048 + 0.985436i 0.554392π0.554392\pi
8484 0 0
8585 5.46739 0.593022
8686 1.65791 0.178778
8787 0 0
8888 −2.28507 −0.243589
8989 −17.3460 −1.83867 −0.919336 0.393472i 0.871274π-0.871274\pi
−0.919336 + 0.393472i 0.871274π0.871274\pi
9090 0 0
9191 11.4267 1.19785
9292 −3.35309 −0.349584
9393 0 0
9494 −3.85198 −0.397302
9595 −10.7551 −1.10345
9696 0 0
9797 9.19117 0.933221 0.466611 0.884463i 0.345475π-0.345475\pi
0.466611 + 0.884463i 0.345475π0.345475\pi
9898 6.58452 0.665137
9999 0 0
100100 5.03695 0.503695
101101 11.9602 1.19008 0.595041 0.803695i 0.297136π-0.297136\pi
0.595041 + 0.803695i 0.297136π0.297136\pi
102102 0 0
103103 −12.7465 −1.25595 −0.627974 0.778234i 0.716115π-0.716115\pi
−0.627974 + 0.778234i 0.716115π0.716115\pi
104104 3.10027 0.304007
105105 0 0
106106 −2.58267 −0.250851
107107 6.09894 0.589607 0.294803 0.955558i 0.404746π-0.404746\pi
0.294803 + 0.955558i 0.404746π0.404746\pi
108108 0 0
109109 11.2390 1.07650 0.538250 0.842785i 0.319086π-0.319086\pi
0.538250 + 0.842785i 0.319086π0.319086\pi
110110 −7.23936 −0.690246
111111 0 0
112112 3.68572 0.348268
113113 −7.03695 −0.661981 −0.330990 0.943634i 0.607383π-0.607383\pi
−0.330990 + 0.943634i 0.607383π0.607383\pi
114114 0 0
115115 −10.6230 −0.990597
116116 −0.585444 −0.0543571
117117 0 0
118118 −9.66319 −0.889568
119119 6.36065 0.583080
120120 0 0
121121 −5.77847 −0.525315
122122 13.0913 1.18523
123123 0 0
124124 −4.63798 −0.416502
125125 0.117076 0.0104716
126126 0 0
127127 5.98500 0.531082 0.265541 0.964100i 0.414449π-0.414449\pi
0.265541 + 0.964100i 0.414449π0.414449\pi
128128 1.00000 0.0883883
129129 0 0
130130 9.82203 0.861449
131131 16.4150 1.43419 0.717094 0.696976i 0.245472π-0.245472\pi
0.717094 + 0.696976i 0.245472π0.245472\pi
132132 0 0
133133 −12.5123 −1.08495
134134 −8.60876 −0.743684
135135 0 0
136136 1.72576 0.147982
137137 −0.211159 −0.0180405 −0.00902025 0.999959i 0.502871π-0.502871\pi
−0.00902025 + 0.999959i 0.502871π0.502871\pi
138138 0 0
139139 3.67151 0.311413 0.155707 0.987803i 0.450235π-0.450235\pi
0.155707 + 0.987803i 0.450235π0.450235\pi
140140 11.6768 0.986868
141141 0 0
142142 1.98746 0.166784
143143 −7.08434 −0.592422
144144 0 0
145145 −1.85475 −0.154029
146146 10.6474 0.881188
147147 0 0
148148 −7.30720 −0.600648
149149 15.4744 1.26771 0.633856 0.773451i 0.281471π-0.281471\pi
0.633856 + 0.773451i 0.281471π0.281471\pi
150150 0 0
151151 20.1457 1.63944 0.819718 0.572768i 0.194130π-0.194130\pi
0.819718 + 0.572768i 0.194130π0.194130\pi
152152 −3.39480 −0.275354
153153 0 0
154154 −8.42212 −0.678673
155155 −14.6936 −1.18022
156156 0 0
157157 17.9974 1.43635 0.718176 0.695862i 0.244977π-0.244977\pi
0.718176 + 0.695862i 0.244977π0.244977\pi
158158 14.0932 1.12119
159159 0 0
160160 3.16812 0.250462
161161 −12.3585 −0.973989
162162 0 0
163163 3.05289 0.239121 0.119560 0.992827i 0.461851π-0.461851\pi
0.119560 + 0.992827i 0.461851π0.461851\pi
164164 −7.08052 −0.552895
165165 0 0
166166 −3.09842 −0.240484
167167 −4.10119 −0.317360 −0.158680 0.987330i 0.550724π-0.550724\pi
−0.158680 + 0.987330i 0.550724π0.550724\pi
168168 0 0
169169 −3.38830 −0.260638
170170 5.46739 0.419330
171171 0 0
172172 1.65791 0.126415
173173 −17.0271 −1.29455 −0.647273 0.762258i 0.724091π-0.724091\pi
−0.647273 + 0.762258i 0.724091π0.724091\pi
174174 0 0
175175 18.5648 1.40337
176176 −2.28507 −0.172243
177177 0 0
178178 −17.3460 −1.30014
179179 −14.5560 −1.08797 −0.543985 0.839095i 0.683085π-0.683085\pi
−0.543985 + 0.839095i 0.683085π0.683085\pi
180180 0 0
181181 −13.0238 −0.968052 −0.484026 0.875054i 0.660826π-0.660826\pi
−0.484026 + 0.875054i 0.660826π0.660826\pi
182182 11.4267 0.847006
183183 0 0
184184 −3.35309 −0.247193
185185 −23.1500 −1.70203
186186 0 0
187187 −3.94347 −0.288375
188188 −3.85198 −0.280935
189189 0 0
190190 −10.7551 −0.780258
191191 3.60287 0.260695 0.130347 0.991468i 0.458391π-0.458391\pi
0.130347 + 0.991468i 0.458391π0.458391\pi
192192 0 0
193193 1.47487 0.106163 0.0530817 0.998590i 0.483096π-0.483096\pi
0.0530817 + 0.998590i 0.483096π0.483096\pi
194194 9.19117 0.659887
195195 0 0
196196 6.58452 0.470323
197197 2.53862 0.180869 0.0904346 0.995902i 0.471174π-0.471174\pi
0.0904346 + 0.995902i 0.471174π0.471174\pi
198198 0 0
199199 −1.85178 −0.131269 −0.0656347 0.997844i 0.520907π-0.520907\pi
−0.0656347 + 0.997844i 0.520907π0.520907\pi
200200 5.03695 0.356166
201201 0 0
202202 11.9602 0.841515
203203 −2.15778 −0.151447
204204 0 0
205205 −22.4319 −1.56671
206206 −12.7465 −0.888089
207207 0 0
208208 3.10027 0.214965
209209 7.75734 0.536586
210210 0 0
211211 −18.9883 −1.30721 −0.653604 0.756837i 0.726744π-0.726744\pi
−0.653604 + 0.756837i 0.726744π0.726744\pi
212212 −2.58267 −0.177379
213213 0 0
214214 6.09894 0.416915
215215 5.25247 0.358215
216216 0 0
217217 −17.0943 −1.16043
218218 11.2390 0.761201
219219 0 0
220220 −7.23936 −0.488077
221221 5.35032 0.359901
222222 0 0
223223 −7.25436 −0.485788 −0.242894 0.970053i 0.578097π-0.578097\pi
−0.242894 + 0.970053i 0.578097π0.578097\pi
224224 3.68572 0.246262
225225 0 0
226226 −7.03695 −0.468091
227227 −28.5272 −1.89342 −0.946708 0.322095i 0.895613π-0.895613\pi
−0.946708 + 0.322095i 0.895613π0.895613\pi
228228 0 0
229229 1.85538 0.122607 0.0613036 0.998119i 0.480474π-0.480474\pi
0.0613036 + 0.998119i 0.480474π0.480474\pi
230230 −10.6230 −0.700458
231231 0 0
232232 −0.585444 −0.0384363
233233 8.53469 0.559126 0.279563 0.960127i 0.409810π-0.409810\pi
0.279563 + 0.960127i 0.409810π0.409810\pi
234234 0 0
235235 −12.2035 −0.796070
236236 −9.66319 −0.629020
237237 0 0
238238 6.36065 0.412300
239239 −7.28796 −0.471419 −0.235710 0.971824i 0.575741π-0.575741\pi
−0.235710 + 0.971824i 0.575741π0.575741\pi
240240 0 0
241241 −1.33492 −0.0859897 −0.0429948 0.999075i 0.513690π-0.513690\pi
−0.0429948 + 0.999075i 0.513690π0.513690\pi
242242 −5.77847 −0.371454
243243 0 0
244244 13.0913 0.838087
245245 20.8605 1.33273
246246 0 0
247247 −10.5248 −0.669677
248248 −4.63798 −0.294512
249249 0 0
250250 0.117076 0.00740453
251251 −2.87856 −0.181693 −0.0908466 0.995865i 0.528957π-0.528957\pi
−0.0908466 + 0.995865i 0.528957π0.528957\pi
252252 0 0
253253 7.66203 0.481708
254254 5.98500 0.375532
255255 0 0
256256 1.00000 0.0625000
257257 −25.7779 −1.60798 −0.803991 0.594641i 0.797294π-0.797294\pi
−0.803991 + 0.594641i 0.797294π0.797294\pi
258258 0 0
259259 −26.9323 −1.67349
260260 9.82203 0.609136
261261 0 0
262262 16.4150 1.01412
263263 −15.0697 −0.929237 −0.464619 0.885511i 0.653809π-0.653809\pi
−0.464619 + 0.885511i 0.653809π0.653809\pi
264264 0 0
265265 −8.18220 −0.502629
266266 −12.5123 −0.767176
267267 0 0
268268 −8.60876 −0.525864
269269 16.0615 0.979286 0.489643 0.871923i 0.337127π-0.337127\pi
0.489643 + 0.871923i 0.337127π0.337127\pi
270270 0 0
271271 9.41446 0.571888 0.285944 0.958246i 0.407693π-0.407693\pi
0.285944 + 0.958246i 0.407693π0.407693\pi
272272 1.72576 0.104639
273273 0 0
274274 −0.211159 −0.0127566
275275 −11.5098 −0.694066
276276 0 0
277277 5.57476 0.334955 0.167477 0.985876i 0.446438π-0.446438\pi
0.167477 + 0.985876i 0.446438π0.446438\pi
278278 3.67151 0.220203
279279 0 0
280280 11.6768 0.697821
281281 28.0048 1.67063 0.835313 0.549775i 0.185286π-0.185286\pi
0.835313 + 0.549775i 0.185286π0.185286\pi
282282 0 0
283283 6.15522 0.365890 0.182945 0.983123i 0.441437π-0.441437\pi
0.182945 + 0.983123i 0.441437π0.441437\pi
284284 1.98746 0.117934
285285 0 0
286286 −7.08434 −0.418906
287287 −26.0968 −1.54044
288288 0 0
289289 −14.0218 −0.824810
290290 −1.85475 −0.108915
291291 0 0
292292 10.6474 0.623094
293293 2.33510 0.136418 0.0682090 0.997671i 0.478272π-0.478272\pi
0.0682090 + 0.997671i 0.478272π0.478272\pi
294294 0 0
295295 −30.6141 −1.78242
296296 −7.30720 −0.424722
297297 0 0
298298 15.4744 0.896408
299299 −10.3955 −0.601187
300300 0 0
301301 6.11061 0.352210
302302 20.1457 1.15926
303303 0 0
304304 −3.39480 −0.194705
305305 41.4749 2.37484
306306 0 0
307307 6.82529 0.389540 0.194770 0.980849i 0.437604π-0.437604\pi
0.194770 + 0.980849i 0.437604π0.437604\pi
308308 −8.42212 −0.479895
309309 0 0
310310 −14.6936 −0.834543
311311 8.59522 0.487390 0.243695 0.969852i 0.421640π-0.421640\pi
0.243695 + 0.969852i 0.421640π0.421640\pi
312312 0 0
313313 −21.6689 −1.22480 −0.612399 0.790549i 0.709795π-0.709795\pi
−0.612399 + 0.790549i 0.709795π0.709795\pi
314314 17.9974 1.01565
315315 0 0
316316 14.0932 0.792804
317317 35.3200 1.98377 0.991883 0.127153i 0.0405838π-0.0405838\pi
0.991883 + 0.127153i 0.0405838π0.0405838\pi
318318 0 0
319319 1.33778 0.0749013
320320 3.16812 0.177103
321321 0 0
322322 −12.3585 −0.688715
323323 −5.85859 −0.325981
324324 0 0
325325 15.6159 0.866217
326326 3.05289 0.169084
327327 0 0
328328 −7.08052 −0.390956
329329 −14.1973 −0.782724
330330 0 0
331331 −25.8137 −1.41885 −0.709423 0.704783i 0.751045π-0.751045\pi
−0.709423 + 0.704783i 0.751045π0.751045\pi
332332 −3.09842 −0.170048
333333 0 0
334334 −4.10119 −0.224407
335335 −27.2735 −1.49011
336336 0 0
337337 −3.38459 −0.184370 −0.0921851 0.995742i 0.529385π-0.529385\pi
−0.0921851 + 0.995742i 0.529385π0.529385\pi
338338 −3.38830 −0.184299
339339 0 0
340340 5.46739 0.296511
341341 10.5981 0.573919
342342 0 0
343343 −1.53133 −0.0826839
344344 1.65791 0.0893888
345345 0 0
346346 −17.0271 −0.915382
347347 −16.2000 −0.869663 −0.434831 0.900512i 0.643192π-0.643192\pi
−0.434831 + 0.900512i 0.643192π0.643192\pi
348348 0 0
349349 4.49253 0.240480 0.120240 0.992745i 0.461634π-0.461634\pi
0.120240 + 0.992745i 0.461634π0.461634\pi
350350 18.5648 0.992330
351351 0 0
352352 −2.28507 −0.121795
353353 −23.2267 −1.23623 −0.618116 0.786087i 0.712104π-0.712104\pi
−0.618116 + 0.786087i 0.712104π0.712104\pi
354354 0 0
355355 6.29651 0.334184
356356 −17.3460 −0.919336
357357 0 0
358358 −14.5560 −0.769311
359359 −11.5539 −0.609794 −0.304897 0.952385i 0.598622π-0.598622\pi
−0.304897 + 0.952385i 0.598622π0.598622\pi
360360 0 0
361361 −7.47535 −0.393440
362362 −13.0238 −0.684516
363363 0 0
364364 11.4267 0.598924
365365 33.7323 1.76563
366366 0 0
367367 15.5697 0.812733 0.406366 0.913710i 0.366796π-0.366796\pi
0.406366 + 0.913710i 0.366796π0.366796\pi
368368 −3.35309 −0.174792
369369 0 0
370370 −23.1500 −1.20351
371371 −9.51900 −0.494202
372372 0 0
373373 −9.75726 −0.505212 −0.252606 0.967569i 0.581288π-0.581288\pi
−0.252606 + 0.967569i 0.581288π0.581288\pi
374374 −3.94347 −0.203912
375375 0 0
376376 −3.85198 −0.198651
377377 −1.81504 −0.0934792
378378 0 0
379379 −18.7904 −0.965197 −0.482599 0.875842i 0.660307π-0.660307\pi
−0.482599 + 0.875842i 0.660307π0.660307\pi
380380 −10.7551 −0.551725
381381 0 0
382382 3.60287 0.184339
383383 30.7680 1.57217 0.786086 0.618117i 0.212104π-0.212104\pi
0.786086 + 0.618117i 0.212104π0.212104\pi
384384 0 0
385385 −26.6822 −1.35985
386386 1.47487 0.0750689
387387 0 0
388388 9.19117 0.466611
389389 29.6007 1.50081 0.750407 0.660976i 0.229858π-0.229858\pi
0.750407 + 0.660976i 0.229858π0.229858\pi
390390 0 0
391391 −5.78661 −0.292641
392392 6.58452 0.332569
393393 0 0
394394 2.53862 0.127894
395395 44.6489 2.24653
396396 0 0
397397 16.1427 0.810178 0.405089 0.914277i 0.367241π-0.367241\pi
0.405089 + 0.914277i 0.367241π0.367241\pi
398398 −1.85178 −0.0928215
399399 0 0
400400 5.03695 0.251848
401401 25.3624 1.26654 0.633268 0.773932i 0.281713π-0.281713\pi
0.633268 + 0.773932i 0.281713π0.281713\pi
402402 0 0
403403 −14.3790 −0.716269
404404 11.9602 0.595041
405405 0 0
406406 −2.15778 −0.107089
407407 16.6974 0.827661
408408 0 0
409409 −22.7713 −1.12597 −0.562984 0.826468i 0.690347π-0.690347\pi
−0.562984 + 0.826468i 0.690347π0.690347\pi
410410 −22.4319 −1.10783
411411 0 0
412412 −12.7465 −0.627974
413413 −35.6158 −1.75254
414414 0 0
415415 −9.81616 −0.481856
416416 3.10027 0.152003
417417 0 0
418418 7.75734 0.379424
419419 −4.92276 −0.240492 −0.120246 0.992744i 0.538368π-0.538368\pi
−0.120246 + 0.992744i 0.538368π0.538368\pi
420420 0 0
421421 19.7176 0.960977 0.480489 0.877001i 0.340459π-0.340459\pi
0.480489 + 0.877001i 0.340459π0.340459\pi
422422 −18.9883 −0.924336
423423 0 0
424424 −2.58267 −0.125426
425425 8.69255 0.421651
426426 0 0
427427 48.2510 2.33503
428428 6.09894 0.294803
429429 0 0
430430 5.25247 0.253296
431431 −6.16323 −0.296873 −0.148436 0.988922i 0.547424π-0.547424\pi
−0.148436 + 0.988922i 0.547424π0.547424\pi
432432 0 0
433433 −14.7838 −0.710466 −0.355233 0.934778i 0.615599π-0.615599\pi
−0.355233 + 0.934778i 0.615599π0.615599\pi
434434 −17.0943 −0.820551
435435 0 0
436436 11.2390 0.538250
437437 11.3831 0.544525
438438 0 0
439439 29.7670 1.42070 0.710352 0.703847i 0.248536π-0.248536\pi
0.710352 + 0.703847i 0.248536π0.248536\pi
440440 −7.23936 −0.345123
441441 0 0
442442 5.35032 0.254489
443443 30.4744 1.44788 0.723940 0.689862i 0.242329π-0.242329\pi
0.723940 + 0.689862i 0.242329π0.242329\pi
444444 0 0
445445 −54.9541 −2.60508
446446 −7.25436 −0.343504
447447 0 0
448448 3.68572 0.174134
449449 11.8411 0.558816 0.279408 0.960172i 0.409862π-0.409862\pi
0.279408 + 0.960172i 0.409862π0.409862\pi
450450 0 0
451451 16.1795 0.761861
452452 −7.03695 −0.330990
453453 0 0
454454 −28.5272 −1.33885
455455 36.2012 1.69714
456456 0 0
457457 −0.186393 −0.00871910 −0.00435955 0.999990i 0.501388π-0.501388\pi
−0.00435955 + 0.999990i 0.501388π0.501388\pi
458458 1.85538 0.0866963
459459 0 0
460460 −10.6230 −0.495299
461461 10.4054 0.484626 0.242313 0.970198i 0.422094π-0.422094\pi
0.242313 + 0.970198i 0.422094π0.422094\pi
462462 0 0
463463 25.7884 1.19849 0.599245 0.800566i 0.295468π-0.295468\pi
0.599245 + 0.800566i 0.295468π0.295468\pi
464464 −0.585444 −0.0271786
465465 0 0
466466 8.53469 0.395362
467467 21.7011 1.00421 0.502104 0.864807i 0.332559π-0.332559\pi
0.502104 + 0.864807i 0.332559π0.332559\pi
468468 0 0
469469 −31.7295 −1.46513
470470 −12.2035 −0.562906
471471 0 0
472472 −9.66319 −0.444784
473473 −3.78845 −0.174193
474474 0 0
475475 −17.0994 −0.784576
476476 6.36065 0.291540
477477 0 0
478478 −7.28796 −0.333344
479479 −39.1212 −1.78749 −0.893747 0.448571i 0.851933π-0.851933\pi
−0.893747 + 0.448571i 0.851933π0.851933\pi
480480 0 0
481481 −22.6543 −1.03295
482482 −1.33492 −0.0608039
483483 0 0
484484 −5.77847 −0.262658
485485 29.1187 1.32221
486486 0 0
487487 −10.4833 −0.475043 −0.237522 0.971382i 0.576335π-0.576335\pi
−0.237522 + 0.971382i 0.576335π0.576335\pi
488488 13.0913 0.592617
489489 0 0
490490 20.8605 0.942383
491491 6.85702 0.309453 0.154727 0.987957i 0.450550π-0.450550\pi
0.154727 + 0.987957i 0.450550π0.450550\pi
492492 0 0
493493 −1.01033 −0.0455031
494494 −10.5248 −0.473533
495495 0 0
496496 −4.63798 −0.208251
497497 7.32523 0.328582
498498 0 0
499499 18.7737 0.840427 0.420213 0.907425i 0.361955π-0.361955\pi
0.420213 + 0.907425i 0.361955π0.361955\pi
500500 0.117076 0.00523579
501501 0 0
502502 −2.87856 −0.128476
503503 −12.4270 −0.554092 −0.277046 0.960857i 0.589356π-0.589356\pi
−0.277046 + 0.960857i 0.589356π0.589356\pi
504504 0 0
505505 37.8912 1.68614
506506 7.66203 0.340619
507507 0 0
508508 5.98500 0.265541
509509 32.9777 1.46171 0.730856 0.682532i 0.239121π-0.239121\pi
0.730856 + 0.682532i 0.239121π0.239121\pi
510510 0 0
511511 39.2434 1.73603
512512 1.00000 0.0441942
513513 0 0
514514 −25.7779 −1.13702
515515 −40.3823 −1.77946
516516 0 0
517517 8.80204 0.387113
518518 −26.9323 −1.18334
519519 0 0
520520 9.82203 0.430724
521521 14.3320 0.627895 0.313947 0.949440i 0.398348π-0.398348\pi
0.313947 + 0.949440i 0.398348π0.398348\pi
522522 0 0
523523 −5.70884 −0.249630 −0.124815 0.992180i 0.539834π-0.539834\pi
−0.124815 + 0.992180i 0.539834π0.539834\pi
524524 16.4150 0.717094
525525 0 0
526526 −15.0697 −0.657070
527527 −8.00401 −0.348660
528528 0 0
529529 −11.7568 −0.511165
530530 −8.18220 −0.355412
531531 0 0
532532 −12.5123 −0.542476
533533 −21.9515 −0.950827
534534 0 0
535535 19.3221 0.835369
536536 −8.60876 −0.371842
537537 0 0
538538 16.0615 0.692459
539539 −15.0461 −0.648081
540540 0 0
541541 18.0099 0.774305 0.387153 0.922016i 0.373459π-0.373459\pi
0.387153 + 0.922016i 0.373459π0.373459\pi
542542 9.41446 0.404386
543543 0 0
544544 1.72576 0.0739911
545545 35.6064 1.52521
546546 0 0
547547 −20.6277 −0.881977 −0.440989 0.897513i 0.645372π-0.645372\pi
−0.440989 + 0.897513i 0.645372π0.645372\pi
548548 −0.211159 −0.00902025
549549 0 0
550550 −11.5098 −0.490779
551551 1.98746 0.0846688
552552 0 0
553553 51.9435 2.20886
554554 5.57476 0.236849
555555 0 0
556556 3.67151 0.155707
557557 −3.80418 −0.161188 −0.0805942 0.996747i 0.525682π-0.525682\pi
−0.0805942 + 0.996747i 0.525682π0.525682\pi
558558 0 0
559559 5.13999 0.217398
560560 11.6768 0.493434
561561 0 0
562562 28.0048 1.18131
563563 −11.0714 −0.466602 −0.233301 0.972405i 0.574953π-0.574953\pi
−0.233301 + 0.972405i 0.574953π0.574953\pi
564564 0 0
565565 −22.2939 −0.937911
566566 6.15522 0.258723
567567 0 0
568568 1.98746 0.0833921
569569 46.7153 1.95841 0.979203 0.202881i 0.0650306π-0.0650306\pi
0.979203 + 0.202881i 0.0650306π0.0650306\pi
570570 0 0
571571 −31.6862 −1.32603 −0.663013 0.748608i 0.730723π-0.730723\pi
−0.663013 + 0.748608i 0.730723π0.730723\pi
572572 −7.08434 −0.296211
573573 0 0
574574 −26.0968 −1.08926
575575 −16.8894 −0.704335
576576 0 0
577577 44.3284 1.84541 0.922707 0.385502i 0.125972π-0.125972\pi
0.922707 + 0.385502i 0.125972π0.125972\pi
578578 −14.0218 −0.583229
579579 0 0
580580 −1.85475 −0.0770145
581581 −11.4199 −0.473778
582582 0 0
583583 5.90158 0.244418
584584 10.6474 0.440594
585585 0 0
586586 2.33510 0.0964621
587587 41.0447 1.69409 0.847047 0.531518i 0.178378π-0.178378\pi
0.847047 + 0.531518i 0.178378π0.178378\pi
588588 0 0
589589 15.7450 0.648761
590590 −30.6141 −1.26036
591591 0 0
592592 −7.30720 −0.300324
593593 −9.69265 −0.398029 −0.199015 0.979996i 0.563774π-0.563774\pi
−0.199015 + 0.979996i 0.563774π0.563774\pi
594594 0 0
595595 20.1513 0.826121
596596 15.4744 0.633856
597597 0 0
598598 −10.3955 −0.425103
599599 −29.8379 −1.21914 −0.609572 0.792731i 0.708659π-0.708659\pi
−0.609572 + 0.792731i 0.708659π0.708659\pi
600600 0 0
601601 12.5507 0.511954 0.255977 0.966683i 0.417603π-0.417603\pi
0.255977 + 0.966683i 0.417603π0.417603\pi
602602 6.11061 0.249050
603603 0 0
604604 20.1457 0.819718
605605 −18.3068 −0.744279
606606 0 0
607607 −2.78013 −0.112842 −0.0564211 0.998407i 0.517969π-0.517969\pi
−0.0564211 + 0.998407i 0.517969π0.517969\pi
608608 −3.39480 −0.137677
609609 0 0
610610 41.4749 1.67927
611611 −11.9422 −0.483130
612612 0 0
613613 −8.59291 −0.347064 −0.173532 0.984828i 0.555518π-0.555518\pi
−0.173532 + 0.984828i 0.555518π0.555518\pi
614614 6.82529 0.275446
615615 0 0
616616 −8.42212 −0.339337
617617 −20.0790 −0.808351 −0.404176 0.914681i 0.632442π-0.632442\pi
−0.404176 + 0.914681i 0.632442π0.632442\pi
618618 0 0
619619 8.39185 0.337297 0.168648 0.985676i 0.446060π-0.446060\pi
0.168648 + 0.985676i 0.446060π0.446060\pi
620620 −14.6936 −0.590111
621621 0 0
622622 8.59522 0.344637
623623 −63.9325 −2.56140
624624 0 0
625625 −24.8139 −0.992554
626626 −21.6689 −0.866063
627627 0 0
628628 17.9974 0.718176
629629 −12.6104 −0.502811
630630 0 0
631631 17.5631 0.699178 0.349589 0.936903i 0.386321π-0.386321\pi
0.349589 + 0.936903i 0.386321π0.386321\pi
632632 14.0932 0.560597
633633 0 0
634634 35.3200 1.40273
635635 18.9612 0.752450
636636 0 0
637637 20.4138 0.808826
638638 1.33778 0.0529632
639639 0 0
640640 3.16812 0.125231
641641 −13.4146 −0.529846 −0.264923 0.964270i 0.585347π-0.585347\pi
−0.264923 + 0.964270i 0.585347π0.585347\pi
642642 0 0
643643 −10.4351 −0.411520 −0.205760 0.978602i 0.565967π-0.565967\pi
−0.205760 + 0.978602i 0.565967π0.565967\pi
644644 −12.3585 −0.486995
645645 0 0
646646 −5.85859 −0.230503
647647 −37.9585 −1.49230 −0.746152 0.665775i 0.768101π-0.768101\pi
−0.746152 + 0.665775i 0.768101π0.768101\pi
648648 0 0
649649 22.0810 0.866756
650650 15.6159 0.612508
651651 0 0
652652 3.05289 0.119560
653653 −27.3063 −1.06858 −0.534289 0.845302i 0.679421π-0.679421\pi
−0.534289 + 0.845302i 0.679421π0.679421\pi
654654 0 0
655655 52.0047 2.03199
656656 −7.08052 −0.276448
657657 0 0
658658 −14.1973 −0.553469
659659 −34.3549 −1.33828 −0.669139 0.743138i 0.733337π-0.733337\pi
−0.669139 + 0.743138i 0.733337π0.733337\pi
660660 0 0
661661 −24.5777 −0.955962 −0.477981 0.878370i 0.658631π-0.658631\pi
−0.477981 + 0.878370i 0.658631π0.658631\pi
662662 −25.8137 −1.00328
663663 0 0
664664 −3.09842 −0.120242
665665 −39.6403 −1.53719
666666 0 0
667667 1.96305 0.0760094
668668 −4.10119 −0.158680
669669 0 0
670670 −27.2735 −1.05367
671671 −29.9146 −1.15484
672672 0 0
673673 42.8754 1.65273 0.826363 0.563137i 0.190406π-0.190406\pi
0.826363 + 0.563137i 0.190406π0.190406\pi
674674 −3.38459 −0.130369
675675 0 0
676676 −3.38830 −0.130319
677677 7.48743 0.287765 0.143883 0.989595i 0.454041π-0.454041\pi
0.143883 + 0.989595i 0.454041π0.454041\pi
678678 0 0
679679 33.8761 1.30004
680680 5.46739 0.209665
681681 0 0
682682 10.5981 0.405822
683683 16.7545 0.641093 0.320546 0.947233i 0.396134π-0.396134\pi
0.320546 + 0.947233i 0.396134π0.396134\pi
684684 0 0
685685 −0.668975 −0.0255602
686686 −1.53133 −0.0584664
687687 0 0
688688 1.65791 0.0632074
689689 −8.00699 −0.305042
690690 0 0
691691 −14.9534 −0.568856 −0.284428 0.958697i 0.591804π-0.591804\pi
−0.284428 + 0.958697i 0.591804π0.591804\pi
692692 −17.0271 −0.647273
693693 0 0
694694 −16.2000 −0.614945
695695 11.6318 0.441218
696696 0 0
697697 −12.2192 −0.462837
698698 4.49253 0.170045
699699 0 0
700700 18.5648 0.701683
701701 −42.1025 −1.59019 −0.795094 0.606486i 0.792579π-0.792579\pi
−0.795094 + 0.606486i 0.792579π0.792579\pi
702702 0 0
703703 24.8065 0.935593
704704 −2.28507 −0.0861217
705705 0 0
706706 −23.2267 −0.874147
707707 44.0819 1.65787
708708 0 0
709709 28.4856 1.06980 0.534899 0.844916i 0.320350π-0.320350\pi
0.534899 + 0.844916i 0.320350π0.320350\pi
710710 6.29651 0.236304
711711 0 0
712712 −17.3460 −0.650069
713713 15.5515 0.582410
714714 0 0
715715 −22.4440 −0.839358
716716 −14.5560 −0.543985
717717 0 0
718718 −11.5539 −0.431189
719719 2.53487 0.0945348 0.0472674 0.998882i 0.484949π-0.484949\pi
0.0472674 + 0.998882i 0.484949π0.484949\pi
720720 0 0
721721 −46.9799 −1.74962
722722 −7.47535 −0.278204
723723 0 0
724724 −13.0238 −0.484026
725725 −2.94885 −0.109518
726726 0 0
727727 19.8834 0.737434 0.368717 0.929542i 0.379797π-0.379797\pi
0.368717 + 0.929542i 0.379797π0.379797\pi
728728 11.4267 0.423503
729729 0 0
730730 33.7323 1.24849
731731 2.86116 0.105824
732732 0 0
733733 −10.0111 −0.369767 −0.184884 0.982760i 0.559191π-0.559191\pi
−0.184884 + 0.982760i 0.559191π0.559191\pi
734734 15.5697 0.574689
735735 0 0
736736 −3.35309 −0.123596
737737 19.6716 0.724613
738738 0 0
739739 −40.3914 −1.48582 −0.742911 0.669390i 0.766556π-0.766556\pi
−0.742911 + 0.669390i 0.766556π0.766556\pi
740740 −23.1500 −0.851013
741741 0 0
742742 −9.51900 −0.349453
743743 35.6502 1.30788 0.653939 0.756547i 0.273115π-0.273115\pi
0.653939 + 0.756547i 0.273115π0.273115\pi
744744 0 0
745745 49.0247 1.79612
746746 −9.75726 −0.357239
747747 0 0
748748 −3.94347 −0.144187
749749 22.4790 0.821364
750750 0 0
751751 −9.46873 −0.345519 −0.172759 0.984964i 0.555268π-0.555268\pi
−0.172759 + 0.984964i 0.555268π0.555268\pi
752752 −3.85198 −0.140467
753753 0 0
754754 −1.81504 −0.0660998
755755 63.8240 2.32279
756756 0 0
757757 −37.9651 −1.37987 −0.689933 0.723873i 0.742360π-0.742360\pi
−0.689933 + 0.723873i 0.742360π0.742360\pi
758758 −18.7904 −0.682498
759759 0 0
760760 −10.7551 −0.390129
761761 44.8858 1.62711 0.813554 0.581490i 0.197530π-0.197530\pi
0.813554 + 0.581490i 0.197530π0.197530\pi
762762 0 0
763763 41.4238 1.49964
764764 3.60287 0.130347
765765 0 0
766766 30.7680 1.11169
767767 −29.9585 −1.08174
768768 0 0
769769 45.7368 1.64931 0.824656 0.565634i 0.191369π-0.191369\pi
0.824656 + 0.565634i 0.191369π0.191369\pi
770770 −26.6822 −0.961561
771771 0 0
772772 1.47487 0.0530817
773773 −20.5707 −0.739876 −0.369938 0.929056i 0.620621π-0.620621\pi
−0.369938 + 0.929056i 0.620621π0.620621\pi
774774 0 0
775775 −23.3613 −0.839162
776776 9.19117 0.329944
777777 0 0
778778 29.6007 1.06124
779779 24.0369 0.861212
780780 0 0
781781 −4.54149 −0.162507
782782 −5.78661 −0.206929
783783 0 0
784784 6.58452 0.235162
785785 57.0180 2.03506
786786 0 0
787787 44.5635 1.58852 0.794259 0.607579i 0.207859π-0.207859\pi
0.794259 + 0.607579i 0.207859π0.207859\pi
788788 2.53862 0.0904346
789789 0 0
790790 44.6489 1.58853
791791 −25.9362 −0.922186
792792 0 0
793793 40.5867 1.44128
794794 16.1427 0.572882
795795 0 0
796796 −1.85178 −0.0656347
797797 43.8601 1.55361 0.776803 0.629744i 0.216840π-0.216840\pi
0.776803 + 0.629744i 0.216840π0.216840\pi
798798 0 0
799799 −6.64758 −0.235174
800800 5.03695 0.178083
801801 0 0
802802 25.3624 0.895577
803803 −24.3301 −0.858590
804804 0 0
805805 −39.1533 −1.37997
806806 −14.3790 −0.506479
807807 0 0
808808 11.9602 0.420758
809809 −15.5821 −0.547836 −0.273918 0.961753i 0.588320π-0.588320\pi
−0.273918 + 0.961753i 0.588320π0.588320\pi
810810 0 0
811811 −30.4691 −1.06992 −0.534958 0.844879i 0.679673π-0.679673\pi
−0.534958 + 0.844879i 0.679673π0.679673\pi
812812 −2.15778 −0.0757233
813813 0 0
814814 16.6974 0.585245
815815 9.67191 0.338792
816816 0 0
817817 −5.62828 −0.196909
818818 −22.7713 −0.796180
819819 0 0
820820 −22.4319 −0.783356
821821 −1.90102 −0.0663460 −0.0331730 0.999450i 0.510561π-0.510561\pi
−0.0331730 + 0.999450i 0.510561π0.510561\pi
822822 0 0
823823 −22.0410 −0.768302 −0.384151 0.923270i 0.625506π-0.625506\pi
−0.384151 + 0.923270i 0.625506π0.625506\pi
824824 −12.7465 −0.444045
825825 0 0
826826 −35.6158 −1.23923
827827 48.4976 1.68643 0.843213 0.537579i 0.180661π-0.180661\pi
0.843213 + 0.537579i 0.180661π0.180661\pi
828828 0 0
829829 −20.3186 −0.705693 −0.352846 0.935681i 0.614786π-0.614786\pi
−0.352846 + 0.935681i 0.614786π0.614786\pi
830830 −9.81616 −0.340724
831831 0 0
832832 3.10027 0.107483
833833 11.3633 0.393714
834834 0 0
835835 −12.9931 −0.449643
836836 7.75734 0.268293
837837 0 0
838838 −4.92276 −0.170054
839839 −5.06635 −0.174910 −0.0874549 0.996168i 0.527873π-0.527873\pi
−0.0874549 + 0.996168i 0.527873π0.527873\pi
840840 0 0
841841 −28.6573 −0.988181
842842 19.7176 0.679514
843843 0 0
844844 −18.9883 −0.653604
845845 −10.7345 −0.369278
846846 0 0
847847 −21.2978 −0.731801
848848 −2.58267 −0.0886893
849849 0 0
850850 8.69255 0.298152
851851 24.5017 0.839907
852852 0 0
853853 26.4679 0.906242 0.453121 0.891449i 0.350311π-0.350311\pi
0.453121 + 0.891449i 0.350311π0.350311\pi
854854 48.2510 1.65112
855855 0 0
856856 6.09894 0.208457
857857 −18.3116 −0.625514 −0.312757 0.949833i 0.601252π-0.601252\pi
−0.312757 + 0.949833i 0.601252π0.601252\pi
858858 0 0
859859 −9.43937 −0.322067 −0.161034 0.986949i 0.551483π-0.551483\pi
−0.161034 + 0.986949i 0.551483π0.551483\pi
860860 5.25247 0.179108
861861 0 0
862862 −6.16323 −0.209921
863863 −14.2154 −0.483898 −0.241949 0.970289i 0.577787π-0.577787\pi
−0.241949 + 0.970289i 0.577787π0.577787\pi
864864 0 0
865865 −53.9438 −1.83414
866866 −14.7838 −0.502375
867867 0 0
868868 −17.0943 −0.580217
869869 −32.2039 −1.09244
870870 0 0
871871 −26.6895 −0.904340
872872 11.2390 0.380600
873873 0 0
874874 11.3831 0.385038
875875 0.431509 0.0145877
876876 0 0
877877 39.1054 1.32050 0.660248 0.751047i 0.270451π-0.270451\pi
0.660248 + 0.751047i 0.270451π0.270451\pi
878878 29.7670 1.00459
879879 0 0
880880 −7.23936 −0.244039
881881 −22.8938 −0.771313 −0.385657 0.922642i 0.626025π-0.626025\pi
−0.385657 + 0.922642i 0.626025π0.626025\pi
882882 0 0
883883 −17.1509 −0.577174 −0.288587 0.957454i 0.593185π-0.593185\pi
−0.288587 + 0.957454i 0.593185π0.593185\pi
884884 5.35032 0.179951
885885 0 0
886886 30.4744 1.02381
887887 18.2570 0.613011 0.306506 0.951869i 0.400840π-0.400840\pi
0.306506 + 0.951869i 0.400840π0.400840\pi
888888 0 0
889889 22.0590 0.739835
890890 −54.9541 −1.84207
891891 0 0
892892 −7.25436 −0.242894
893893 13.0767 0.437595
894894 0 0
895895 −46.1152 −1.54146
896896 3.68572 0.123131
897897 0 0
898898 11.8411 0.395143
899899 2.71527 0.0905595
900900 0 0
901901 −4.45706 −0.148486
902902 16.1795 0.538717
903903 0 0
904904 −7.03695 −0.234046
905905 −41.2609 −1.37156
906906 0 0
907907 29.1916 0.969293 0.484646 0.874710i 0.338948π-0.338948\pi
0.484646 + 0.874710i 0.338948π0.338948\pi
908908 −28.5272 −0.946708
909909 0 0
910910 36.2012 1.20006
911911 54.6359 1.81017 0.905084 0.425233i 0.139808π-0.139808\pi
0.905084 + 0.425233i 0.139808π0.139808\pi
912912 0 0
913913 7.08010 0.234317
914914 −0.186393 −0.00616533
915915 0 0
916916 1.85538 0.0613036
917917 60.5012 1.99793
918918 0 0
919919 41.0995 1.35575 0.677873 0.735179i 0.262902π-0.262902\pi
0.677873 + 0.735179i 0.262902π0.262902\pi
920920 −10.6230 −0.350229
921921 0 0
922922 10.4054 0.342682
923923 6.16168 0.202814
924924 0 0
925925 −36.8060 −1.21017
926926 25.7884 0.847460
927927 0 0
928928 −0.585444 −0.0192181
929929 14.5961 0.478882 0.239441 0.970911i 0.423036π-0.423036\pi
0.239441 + 0.970911i 0.423036π0.423036\pi
930930 0 0
931931 −22.3531 −0.732594
932932 8.53469 0.279563
933933 0 0
934934 21.7011 0.710083
935935 −12.4934 −0.408576
936936 0 0
937937 24.9282 0.814370 0.407185 0.913346i 0.366511π-0.366511\pi
0.407185 + 0.913346i 0.366511π0.366511\pi
938938 −31.7295 −1.03600
939939 0 0
940940 −12.2035 −0.398035
941941 20.8443 0.679506 0.339753 0.940515i 0.389657π-0.389657\pi
0.339753 + 0.940515i 0.389657π0.389657\pi
942942 0 0
943943 23.7416 0.773133
944944 −9.66319 −0.314510
945945 0 0
946946 −3.78845 −0.123173
947947 35.9130 1.16702 0.583508 0.812107i 0.301680π-0.301680\pi
0.583508 + 0.812107i 0.301680π0.301680\pi
948948 0 0
949949 33.0100 1.07155
950950 −17.0994 −0.554779
951951 0 0
952952 6.36065 0.206150
953953 5.80207 0.187947 0.0939737 0.995575i 0.470043π-0.470043\pi
0.0939737 + 0.995575i 0.470043π0.470043\pi
954954 0 0
955955 11.4143 0.369359
956956 −7.28796 −0.235710
957957 0 0
958958 −39.1212 −1.26395
959959 −0.778271 −0.0251317
960960 0 0
961961 −9.48919 −0.306103
962962 −22.6543 −0.730405
963963 0 0
964964 −1.33492 −0.0429948
965965 4.67256 0.150415
966966 0 0
967967 29.6589 0.953766 0.476883 0.878967i 0.341767π-0.341767\pi
0.476883 + 0.878967i 0.341767π0.341767\pi
968968 −5.77847 −0.185727
969969 0 0
970970 29.1187 0.934944
971971 47.1522 1.51318 0.756592 0.653887i 0.226863π-0.226863\pi
0.756592 + 0.653887i 0.226863π0.226863\pi
972972 0 0
973973 13.5322 0.433821
974974 −10.4833 −0.335906
975975 0 0
976976 13.0913 0.419044
977977 −23.8029 −0.761524 −0.380762 0.924673i 0.624338π-0.624338\pi
−0.380762 + 0.924673i 0.624338π0.624338\pi
978978 0 0
979979 39.6368 1.26680
980980 20.8605 0.666365
981981 0 0
982982 6.85702 0.218816
983983 11.0823 0.353469 0.176734 0.984259i 0.443447π-0.443447\pi
0.176734 + 0.984259i 0.443447π0.443447\pi
984984 0 0
985985 8.04264 0.256260
986986 −1.01033 −0.0321756
987987 0 0
988988 −10.5248 −0.334839
989989 −5.55913 −0.176770
990990 0 0
991991 11.4369 0.363306 0.181653 0.983363i 0.441855π-0.441855\pi
0.181653 + 0.983363i 0.441855π0.441855\pi
992992 −4.63798 −0.147256
993993 0 0
994994 7.32523 0.232342
995995 −5.86666 −0.185986
996996 0 0
997997 −27.8945 −0.883428 −0.441714 0.897156i 0.645629π-0.645629\pi
−0.441714 + 0.897156i 0.645629π0.645629\pi
998998 18.7737 0.594271
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 1458.2.a.g.1.5 6
3.2 odd 2 1458.2.a.f.1.2 6
9.2 odd 6 1458.2.c.g.973.5 12
9.4 even 3 1458.2.c.f.487.2 12
9.5 odd 6 1458.2.c.g.487.5 12
9.7 even 3 1458.2.c.f.973.2 12
27.2 odd 18 486.2.e.g.433.1 12
27.4 even 9 486.2.e.h.379.1 12
27.5 odd 18 162.2.e.b.73.1 12
27.7 even 9 486.2.e.h.109.1 12
27.11 odd 18 162.2.e.b.91.1 12
27.13 even 9 486.2.e.f.55.2 12
27.14 odd 18 486.2.e.g.55.1 12
27.16 even 9 54.2.e.b.13.1 12
27.20 odd 18 486.2.e.e.109.2 12
27.22 even 9 54.2.e.b.25.1 yes 12
27.23 odd 18 486.2.e.e.379.2 12
27.25 even 9 486.2.e.f.433.2 12
108.43 odd 18 432.2.u.b.337.2 12
108.103 odd 18 432.2.u.b.241.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
54.2.e.b.13.1 12 27.16 even 9
54.2.e.b.25.1 yes 12 27.22 even 9
162.2.e.b.73.1 12 27.5 odd 18
162.2.e.b.91.1 12 27.11 odd 18
432.2.u.b.241.2 12 108.103 odd 18
432.2.u.b.337.2 12 108.43 odd 18
486.2.e.e.109.2 12 27.20 odd 18
486.2.e.e.379.2 12 27.23 odd 18
486.2.e.f.55.2 12 27.13 even 9
486.2.e.f.433.2 12 27.25 even 9
486.2.e.g.55.1 12 27.14 odd 18
486.2.e.g.433.1 12 27.2 odd 18
486.2.e.h.109.1 12 27.7 even 9
486.2.e.h.379.1 12 27.4 even 9
1458.2.a.f.1.2 6 3.2 odd 2
1458.2.a.g.1.5 6 1.1 even 1 trivial
1458.2.c.f.487.2 12 9.4 even 3
1458.2.c.f.973.2 12 9.7 even 3
1458.2.c.g.487.5 12 9.5 odd 6
1458.2.c.g.973.5 12 9.2 odd 6