Properties

Label 3330.2.a.bl.1.2
Level 33303330
Weight 22
Character 3330.1
Self dual yes
Analytic conductor 26.59026.590
Analytic rank 00
Dimension 55
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] = [3330,2,Mod(1,3330)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3330, 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("3330.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 3330=232537 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3330.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: 26.590183873126.5901838731
Analytic rank: 00
Dimension: 55
Coefficient field: 5.5.23544108.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x5x420x3+39x2+9x36 x^{5} - x^{4} - 20x^{3} + 39x^{2} + 9x - 36 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 2 2
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 4.76376-4.76376 of defining polynomial
Character χ\chi == 3330.1

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+1.00000q2+1.00000q4+1.00000q51.19175q7+1.00000q8+1.00000q103.64179q11+4.86897q131.19175q14+1.00000q16+3.19175q17+2.27506q19+1.00000q203.64179q222.86897q23+1.00000q25+4.86897q261.19175q28+6.06072q29+5.36672q31+1.00000q32+3.19175q341.19175q35+1.00000q37+2.27506q38+1.00000q408.75471q416.75471q433.64179q442.86897q46+4.13955q475.57973q49+1.00000q50+4.86897q52+5.88574q533.64179q551.19175q56+6.06072q58+7.28357q59+14.5443q61+5.36672q62+1.00000q64+4.86897q654.90007q67+3.19175q681.19175q70+5.38798q71+11.8026q73+1.00000q74+2.27506q76+4.34010q77+7.38798q79+1.00000q808.75471q82+4.41461q83+3.19175q856.75471q863.64179q88+9.63597q895.80259q912.86897q92+4.13955q94+2.27506q95+14.8943q975.57973q98+O(q100)q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} -1.19175 q^{7} +1.00000 q^{8} +1.00000 q^{10} -3.64179 q^{11} +4.86897 q^{13} -1.19175 q^{14} +1.00000 q^{16} +3.19175 q^{17} +2.27506 q^{19} +1.00000 q^{20} -3.64179 q^{22} -2.86897 q^{23} +1.00000 q^{25} +4.86897 q^{26} -1.19175 q^{28} +6.06072 q^{29} +5.36672 q^{31} +1.00000 q^{32} +3.19175 q^{34} -1.19175 q^{35} +1.00000 q^{37} +2.27506 q^{38} +1.00000 q^{40} -8.75471 q^{41} -6.75471 q^{43} -3.64179 q^{44} -2.86897 q^{46} +4.13955 q^{47} -5.57973 q^{49} +1.00000 q^{50} +4.86897 q^{52} +5.88574 q^{53} -3.64179 q^{55} -1.19175 q^{56} +6.06072 q^{58} +7.28357 q^{59} +14.5443 q^{61} +5.36672 q^{62} +1.00000 q^{64} +4.86897 q^{65} -4.90007 q^{67} +3.19175 q^{68} -1.19175 q^{70} +5.38798 q^{71} +11.8026 q^{73} +1.00000 q^{74} +2.27506 q^{76} +4.34010 q^{77} +7.38798 q^{79} +1.00000 q^{80} -8.75471 q^{82} +4.41461 q^{83} +3.19175 q^{85} -6.75471 q^{86} -3.64179 q^{88} +9.63597 q^{89} -5.80259 q^{91} -2.86897 q^{92} +4.13955 q^{94} +2.27506 q^{95} +14.8943 q^{97} -5.57973 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 5q+5q2+5q4+5q5+3q7+5q8+5q10+5q11+5q13+3q14+5q16+7q17q19+5q20+5q22+5q23+5q25+5q26+3q28+2q29++16q98+O(q100) 5 q + 5 q^{2} + 5 q^{4} + 5 q^{5} + 3 q^{7} + 5 q^{8} + 5 q^{10} + 5 q^{11} + 5 q^{13} + 3 q^{14} + 5 q^{16} + 7 q^{17} - q^{19} + 5 q^{20} + 5 q^{22} + 5 q^{23} + 5 q^{25} + 5 q^{26} + 3 q^{28} + 2 q^{29}+ \cdots + 16 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 1.00000 0.447214
66 0 0
77 −1.19175 −0.450439 −0.225220 0.974308i 0.572310π-0.572310\pi
−0.225220 + 0.974308i 0.572310π0.572310\pi
88 1.00000 0.353553
99 0 0
1010 1.00000 0.316228
1111 −3.64179 −1.09804 −0.549020 0.835809i 0.684999π-0.684999\pi
−0.549020 + 0.835809i 0.684999π0.684999\pi
1212 0 0
1313 4.86897 1.35041 0.675204 0.737631i 0.264056π-0.264056\pi
0.675204 + 0.737631i 0.264056π0.264056\pi
1414 −1.19175 −0.318509
1515 0 0
1616 1.00000 0.250000
1717 3.19175 0.774113 0.387057 0.922056i 0.373492π-0.373492\pi
0.387057 + 0.922056i 0.373492π0.373492\pi
1818 0 0
1919 2.27506 0.521935 0.260968 0.965348i 0.415958π-0.415958\pi
0.260968 + 0.965348i 0.415958π0.415958\pi
2020 1.00000 0.223607
2121 0 0
2222 −3.64179 −0.776431
2323 −2.86897 −0.598221 −0.299110 0.954219i 0.596690π-0.596690\pi
−0.299110 + 0.954219i 0.596690π0.596690\pi
2424 0 0
2525 1.00000 0.200000
2626 4.86897 0.954883
2727 0 0
2828 −1.19175 −0.225220
2929 6.06072 1.12545 0.562723 0.826645i 0.309754π-0.309754\pi
0.562723 + 0.826645i 0.309754π0.309754\pi
3030 0 0
3131 5.36672 0.963892 0.481946 0.876201i 0.339930π-0.339930\pi
0.481946 + 0.876201i 0.339930π0.339930\pi
3232 1.00000 0.176777
3333 0 0
3434 3.19175 0.547381
3535 −1.19175 −0.201443
3636 0 0
3737 1.00000 0.164399
3838 2.27506 0.369064
3939 0 0
4040 1.00000 0.158114
4141 −8.75471 −1.36726 −0.683628 0.729831i 0.739599π-0.739599\pi
−0.683628 + 0.729831i 0.739599π0.739599\pi
4242 0 0
4343 −6.75471 −1.03008 −0.515042 0.857165i 0.672224π-0.672224\pi
−0.515042 + 0.857165i 0.672224π0.672224\pi
4444 −3.64179 −0.549020
4545 0 0
4646 −2.86897 −0.423006
4747 4.13955 0.603815 0.301907 0.953337i 0.402377π-0.402377\pi
0.301907 + 0.953337i 0.402377π0.402377\pi
4848 0 0
4949 −5.57973 −0.797105
5050 1.00000 0.141421
5151 0 0
5252 4.86897 0.675204
5353 5.88574 0.808469 0.404234 0.914655i 0.367538π-0.367538\pi
0.404234 + 0.914655i 0.367538π0.367538\pi
5454 0 0
5555 −3.64179 −0.491058
5656 −1.19175 −0.159254
5757 0 0
5858 6.06072 0.795811
5959 7.28357 0.948240 0.474120 0.880460i 0.342766π-0.342766\pi
0.474120 + 0.880460i 0.342766π0.342766\pi
6060 0 0
6161 14.5443 1.86221 0.931104 0.364755i 0.118847π-0.118847\pi
0.931104 + 0.364755i 0.118847π0.118847\pi
6262 5.36672 0.681575
6363 0 0
6464 1.00000 0.125000
6565 4.86897 0.603921
6666 0 0
6767 −4.90007 −0.598639 −0.299320 0.954153i 0.596760π-0.596760\pi
−0.299320 + 0.954153i 0.596760π0.596760\pi
6868 3.19175 0.387057
6969 0 0
7070 −1.19175 −0.142441
7171 5.38798 0.639436 0.319718 0.947513i 0.396412π-0.396412\pi
0.319718 + 0.947513i 0.396412π0.396412\pi
7272 0 0
7373 11.8026 1.38139 0.690694 0.723147i 0.257305π-0.257305\pi
0.690694 + 0.723147i 0.257305π0.257305\pi
7474 1.00000 0.116248
7575 0 0
7676 2.27506 0.260968
7777 4.34010 0.494600
7878 0 0
7979 7.38798 0.831213 0.415606 0.909545i 0.363569π-0.363569\pi
0.415606 + 0.909545i 0.363569π0.363569\pi
8080 1.00000 0.111803
8181 0 0
8282 −8.75471 −0.966796
8383 4.41461 0.484566 0.242283 0.970206i 0.422104π-0.422104\pi
0.242283 + 0.970206i 0.422104π0.422104\pi
8484 0 0
8585 3.19175 0.346194
8686 −6.75471 −0.728379
8787 0 0
8888 −3.64179 −0.388216
8989 9.63597 1.02141 0.510705 0.859756i 0.329384π-0.329384\pi
0.510705 + 0.859756i 0.329384π0.329384\pi
9090 0 0
9191 −5.80259 −0.608277
9292 −2.86897 −0.299110
9393 0 0
9494 4.13955 0.426962
9595 2.27506 0.233416
9696 0 0
9797 14.8943 1.51228 0.756141 0.654409i 0.227082π-0.227082\pi
0.756141 + 0.654409i 0.227082π0.227082\pi
9898 −5.57973 −0.563638
9999 0 0
100100 1.00000 0.100000
101101 −7.63194 −0.759406 −0.379703 0.925108i 0.623974π-0.623974\pi
−0.379703 + 0.925108i 0.623974π0.623974\pi
102102 0 0
103103 −2.13955 −0.210816 −0.105408 0.994429i 0.533615π-0.533615\pi
−0.105408 + 0.994429i 0.533615π0.533615\pi
104104 4.86897 0.477441
105105 0 0
106106 5.88574 0.571674
107107 −14.9904 −1.44918 −0.724588 0.689182i 0.757970π-0.757970\pi
−0.724588 + 0.689182i 0.757970π0.757970\pi
108108 0 0
109109 0.253804 0.0243101 0.0121550 0.999926i 0.496131π-0.496131\pi
0.0121550 + 0.999926i 0.496131π0.496131\pi
110110 −3.64179 −0.347231
111111 0 0
112112 −1.19175 −0.112610
113113 −13.3443 −1.25533 −0.627663 0.778486i 0.715988π-0.715988\pi
−0.627663 + 0.778486i 0.715988π0.715988\pi
114114 0 0
115115 −2.86897 −0.267532
116116 6.06072 0.562723
117117 0 0
118118 7.28357 0.670507
119119 −3.80377 −0.348691
120120 0 0
121121 2.26261 0.205692
122122 14.5443 1.31678
123123 0 0
124124 5.36672 0.481946
125125 1.00000 0.0894427
126126 0 0
127127 −7.21891 −0.640575 −0.320288 0.947320i 0.603780π-0.603780\pi
−0.320288 + 0.947320i 0.603780π0.603780\pi
128128 1.00000 0.0883883
129129 0 0
130130 4.86897 0.427037
131131 −20.0506 −1.75183 −0.875913 0.482468i 0.839740π-0.839740\pi
−0.875913 + 0.482468i 0.839740π0.839740\pi
132132 0 0
133133 −2.71131 −0.235100
134134 −4.90007 −0.423302
135135 0 0
136136 3.19175 0.273690
137137 9.52753 0.813992 0.406996 0.913430i 0.366576π-0.366576\pi
0.406996 + 0.913430i 0.366576π0.366576\pi
138138 0 0
139139 20.7323 1.75849 0.879244 0.476372i 0.158048π-0.158048\pi
0.879244 + 0.476372i 0.158048π0.158048\pi
140140 −1.19175 −0.100721
141141 0 0
142142 5.38798 0.452149
143143 −17.7317 −1.48280
144144 0 0
145145 6.06072 0.503315
146146 11.8026 0.976789
147147 0 0
148148 1.00000 0.0821995
149149 −9.17758 −0.751857 −0.375928 0.926649i 0.622676π-0.622676\pi
−0.375928 + 0.926649i 0.622676π0.622676\pi
150150 0 0
151151 17.6024 1.43246 0.716232 0.697862i 0.245865π-0.245865\pi
0.716232 + 0.697862i 0.245865π0.245865\pi
152152 2.27506 0.184532
153153 0 0
154154 4.34010 0.349735
155155 5.36672 0.431066
156156 0 0
157157 6.89857 0.550566 0.275283 0.961363i 0.411228π-0.411228\pi
0.275283 + 0.961363i 0.411228π0.411228\pi
158158 7.38798 0.587756
159159 0 0
160160 1.00000 0.0790569
161161 3.41909 0.269462
162162 0 0
163163 −10.8194 −0.847438 −0.423719 0.905794i 0.639276π-0.639276\pi
−0.423719 + 0.905794i 0.639276π0.639276\pi
164164 −8.75471 −0.683628
165165 0 0
166166 4.41461 0.342640
167167 2.86897 0.222007 0.111004 0.993820i 0.464593π-0.464593\pi
0.111004 + 0.993820i 0.464593π0.464593\pi
168168 0 0
169169 10.7068 0.823602
170170 3.19175 0.244796
171171 0 0
172172 −6.75471 −0.515042
173173 18.3571 1.39567 0.697833 0.716260i 0.254148π-0.254148\pi
0.697833 + 0.716260i 0.254148π0.254148\pi
174174 0 0
175175 −1.19175 −0.0900878
176176 −3.64179 −0.274510
177177 0 0
178178 9.63597 0.722246
179179 −23.1259 −1.72851 −0.864256 0.503052i 0.832210π-0.832210\pi
−0.864256 + 0.503052i 0.832210π0.832210\pi
180180 0 0
181181 14.9001 1.10751 0.553757 0.832678i 0.313194π-0.313194\pi
0.553757 + 0.832678i 0.313194π0.313194\pi
182182 −5.80259 −0.430117
183183 0 0
184184 −2.86897 −0.211503
185185 1.00000 0.0735215
186186 0 0
187187 −11.6237 −0.850007
188188 4.13955 0.301907
189189 0 0
190190 2.27506 0.165050
191191 8.31766 0.601845 0.300922 0.953649i 0.402705π-0.402705\pi
0.300922 + 0.953649i 0.402705π0.402705\pi
192192 0 0
193193 −21.5445 −1.55081 −0.775405 0.631464i 0.782454π-0.782454\pi
−0.775405 + 0.631464i 0.782454π0.782454\pi
194194 14.8943 1.06934
195195 0 0
196196 −5.57973 −0.398552
197197 −3.76904 −0.268533 −0.134266 0.990945i 0.542868π-0.542868\pi
−0.134266 + 0.990945i 0.542868π0.542868\pi
198198 0 0
199199 −5.92914 −0.420306 −0.210153 0.977669i 0.567396π-0.567396\pi
−0.210153 + 0.977669i 0.567396π0.567396\pi
200200 1.00000 0.0707107
201201 0 0
202202 −7.63194 −0.536981
203203 −7.22286 −0.506945
204204 0 0
205205 −8.75471 −0.611455
206206 −2.13955 −0.149069
207207 0 0
208208 4.86897 0.337602
209209 −8.28529 −0.573105
210210 0 0
211211 −3.51059 −0.241679 −0.120840 0.992672i 0.538559π-0.538559\pi
−0.120840 + 0.992672i 0.538559π0.538559\pi
212212 5.88574 0.404234
213213 0 0
214214 −14.9904 −1.02472
215215 −6.75471 −0.460667
216216 0 0
217217 −6.39579 −0.434175
218218 0.253804 0.0171898
219219 0 0
220220 −3.64179 −0.245529
221221 15.5405 1.04537
222222 0 0
223223 19.8322 1.32806 0.664031 0.747705i 0.268844π-0.268844\pi
0.664031 + 0.747705i 0.268844π0.268844\pi
224224 −1.19175 −0.0796271
225225 0 0
226226 −13.3443 −0.887649
227227 −12.9608 −0.860238 −0.430119 0.902772i 0.641528π-0.641528\pi
−0.430119 + 0.902772i 0.641528π0.641528\pi
228228 0 0
229229 −23.2384 −1.53564 −0.767818 0.640668i 0.778657π-0.778657\pi
−0.767818 + 0.640668i 0.778657π0.778657\pi
230230 −2.86897 −0.189174
231231 0 0
232232 6.06072 0.397905
233233 −8.88196 −0.581876 −0.290938 0.956742i 0.593967π-0.593967\pi
−0.290938 + 0.956742i 0.593967π0.593967\pi
234234 0 0
235235 4.13955 0.270034
236236 7.28357 0.474120
237237 0 0
238238 −3.80377 −0.246562
239239 −25.3778 −1.64156 −0.820778 0.571247i 0.806460π-0.806460\pi
−0.820778 + 0.571247i 0.806460π0.806460\pi
240240 0 0
241241 −10.2429 −0.659801 −0.329900 0.944016i 0.607015π-0.607015\pi
−0.329900 + 0.944016i 0.607015π0.607015\pi
242242 2.26261 0.145446
243243 0 0
244244 14.5443 0.931104
245245 −5.57973 −0.356476
246246 0 0
247247 11.0772 0.704825
248248 5.36672 0.340787
249249 0 0
250250 1.00000 0.0632456
251251 −10.2258 −0.645449 −0.322725 0.946493i 0.604599π-0.604599\pi
−0.322725 + 0.946493i 0.604599π0.604599\pi
252252 0 0
253253 10.4482 0.656870
254254 −7.21891 −0.452955
255255 0 0
256256 1.00000 0.0625000
257257 18.0481 1.12581 0.562906 0.826521i 0.309683π-0.309683\pi
0.562906 + 0.826521i 0.309683π0.309683\pi
258258 0 0
259259 −1.19175 −0.0740517
260260 4.86897 0.301960
261261 0 0
262262 −20.0506 −1.23873
263263 13.5658 0.836503 0.418252 0.908331i 0.362643π-0.362643\pi
0.418252 + 0.908331i 0.362643π0.362643\pi
264264 0 0
265265 5.88574 0.361558
266266 −2.71131 −0.166241
267267 0 0
268268 −4.90007 −0.299320
269269 −18.3629 −1.11961 −0.559804 0.828625i 0.689124π-0.689124\pi
−0.559804 + 0.828625i 0.689124π0.689124\pi
270270 0 0
271271 −0.279091 −0.0169536 −0.00847678 0.999964i 0.502698π-0.502698\pi
−0.00847678 + 0.999964i 0.502698π0.502698\pi
272272 3.19175 0.193528
273273 0 0
274274 9.52753 0.575579
275275 −3.64179 −0.219608
276276 0 0
277277 24.9195 1.49727 0.748635 0.662982i 0.230710π-0.230710\pi
0.748635 + 0.662982i 0.230710π0.230710\pi
278278 20.7323 1.24344
279279 0 0
280280 −1.19175 −0.0712207
281281 2.25695 0.134638 0.0673191 0.997731i 0.478555π-0.478555\pi
0.0673191 + 0.997731i 0.478555π0.478555\pi
282282 0 0
283283 4.31884 0.256728 0.128364 0.991727i 0.459027π-0.459027\pi
0.128364 + 0.991727i 0.459027π0.459027\pi
284284 5.38798 0.319718
285285 0 0
286286 −17.7317 −1.04850
287287 10.4334 0.615865
288288 0 0
289289 −6.81273 −0.400749
290290 6.06072 0.355897
291291 0 0
292292 11.8026 0.690694
293293 7.43138 0.434146 0.217073 0.976155i 0.430349π-0.430349\pi
0.217073 + 0.976155i 0.430349π0.430349\pi
294294 0 0
295295 7.28357 0.424066
296296 1.00000 0.0581238
297297 0 0
298298 −9.17758 −0.531643
299299 −13.9689 −0.807842
300300 0 0
301301 8.04992 0.463990
302302 17.6024 1.01291
303303 0 0
304304 2.27506 0.130484
305305 14.5443 0.832804
306306 0 0
307307 3.28357 0.187403 0.0937017 0.995600i 0.470130π-0.470130\pi
0.0937017 + 0.995600i 0.470130π0.470130\pi
308308 4.34010 0.247300
309309 0 0
310310 5.36672 0.304809
311311 −11.8438 −0.671603 −0.335801 0.941933i 0.609007π-0.609007\pi
−0.335801 + 0.941933i 0.609007π0.609007\pi
312312 0 0
313313 15.4653 0.874151 0.437076 0.899425i 0.356014π-0.356014\pi
0.437076 + 0.899425i 0.356014π0.356014\pi
314314 6.89857 0.389309
315315 0 0
316316 7.38798 0.415606
317317 −16.4553 −0.924223 −0.462112 0.886822i 0.652908π-0.652908\pi
−0.462112 + 0.886822i 0.652908π0.652908\pi
318318 0 0
319319 −22.0718 −1.23579
320320 1.00000 0.0559017
321321 0 0
322322 3.41909 0.190538
323323 7.26143 0.404037
324324 0 0
325325 4.86897 0.270082
326326 −10.8194 −0.599229
327327 0 0
328328 −8.75471 −0.483398
329329 −4.93330 −0.271982
330330 0 0
331331 35.4204 1.94688 0.973442 0.228935i 0.0735243π-0.0735243\pi
0.973442 + 0.228935i 0.0735243π0.0735243\pi
332332 4.41461 0.242283
333333 0 0
334334 2.86897 0.156983
335335 −4.90007 −0.267720
336336 0 0
337337 −4.80675 −0.261840 −0.130920 0.991393i 0.541793π-0.541793\pi
−0.130920 + 0.991393i 0.541793π0.541793\pi
338338 10.7068 0.582374
339339 0 0
340340 3.19175 0.173097
341341 −19.5445 −1.05839
342342 0 0
343343 14.9919 0.809486
344344 −6.75471 −0.364189
345345 0 0
346346 18.3571 0.986885
347347 18.5049 0.993397 0.496698 0.867923i 0.334546π-0.334546\pi
0.496698 + 0.867923i 0.334546π0.334546\pi
348348 0 0
349349 −33.7975 −1.80914 −0.904568 0.426328i 0.859807π-0.859807\pi
−0.904568 + 0.426328i 0.859807π0.859807\pi
350350 −1.19175 −0.0637017
351351 0 0
352352 −3.64179 −0.194108
353353 −37.4657 −1.99410 −0.997049 0.0767613i 0.975542π-0.975542\pi
−0.997049 + 0.0767613i 0.975542π0.975542\pi
354354 0 0
355355 5.38798 0.285964
356356 9.63597 0.510705
357357 0 0
358358 −23.1259 −1.22224
359359 14.6886 0.775233 0.387617 0.921821i 0.373298π-0.373298\pi
0.387617 + 0.921821i 0.373298π0.373298\pi
360360 0 0
361361 −13.8241 −0.727584
362362 14.9001 0.783130
363363 0 0
364364 −5.80259 −0.304138
365365 11.8026 0.617776
366366 0 0
367367 16.1175 0.841326 0.420663 0.907217i 0.361797π-0.361797\pi
0.420663 + 0.907217i 0.361797π0.361797\pi
368368 −2.86897 −0.149555
369369 0 0
370370 1.00000 0.0519875
371371 −7.01433 −0.364166
372372 0 0
373373 3.25002 0.168280 0.0841399 0.996454i 0.473186π-0.473186\pi
0.0841399 + 0.996454i 0.473186π0.473186\pi
374374 −11.6237 −0.601046
375375 0 0
376376 4.13955 0.213481
377377 29.5094 1.51981
378378 0 0
379379 −33.7639 −1.73434 −0.867168 0.498016i 0.834062π-0.834062\pi
−0.867168 + 0.498016i 0.834062π0.834062\pi
380380 2.27506 0.116708
381381 0 0
382382 8.31766 0.425569
383383 −14.3859 −0.735087 −0.367544 0.930006i 0.619801π-0.619801\pi
−0.367544 + 0.930006i 0.619801π0.619801\pi
384384 0 0
385385 4.34010 0.221192
386386 −21.5445 −1.09659
387387 0 0
388388 14.8943 0.756141
389389 −25.5445 −1.29516 −0.647578 0.761999i 0.724218π-0.724218\pi
−0.647578 + 0.761999i 0.724218π0.724218\pi
390390 0 0
391391 −9.15702 −0.463090
392392 −5.57973 −0.281819
393393 0 0
394394 −3.76904 −0.189881
395395 7.38798 0.371730
396396 0 0
397397 −4.81219 −0.241517 −0.120759 0.992682i 0.538533π-0.538533\pi
−0.120759 + 0.992682i 0.538533π0.538533\pi
398398 −5.92914 −0.297201
399399 0 0
400400 1.00000 0.0500000
401401 −8.45191 −0.422068 −0.211034 0.977479i 0.567683π-0.567683\pi
−0.211034 + 0.977479i 0.567683π0.567683\pi
402402 0 0
403403 26.1304 1.30165
404404 −7.63194 −0.379703
405405 0 0
406406 −7.22286 −0.358464
407407 −3.64179 −0.180517
408408 0 0
409409 −5.51209 −0.272555 −0.136278 0.990671i 0.543514π-0.543514\pi
−0.136278 + 0.990671i 0.543514π0.543514\pi
410410 −8.75471 −0.432364
411411 0 0
412412 −2.13955 −0.105408
413413 −8.68020 −0.427125
414414 0 0
415415 4.41461 0.216705
416416 4.86897 0.238721
417417 0 0
418418 −8.28529 −0.405247
419419 −0.853529 −0.0416976 −0.0208488 0.999783i 0.506637π-0.506637\pi
−0.0208488 + 0.999783i 0.506637π0.506637\pi
420420 0 0
421421 23.5275 1.14666 0.573331 0.819324i 0.305651π-0.305651\pi
0.573331 + 0.819324i 0.305651π0.305651\pi
422422 −3.51059 −0.170893
423423 0 0
424424 5.88574 0.285837
425425 3.19175 0.154823
426426 0 0
427427 −17.3332 −0.838811
428428 −14.9904 −0.724588
429429 0 0
430430 −6.75471 −0.325741
431431 −34.1849 −1.64663 −0.823315 0.567585i 0.807878π-0.807878\pi
−0.823315 + 0.567585i 0.807878π0.807878\pi
432432 0 0
433433 −0.747535 −0.0359242 −0.0179621 0.999839i 0.505718π-0.505718\pi
−0.0179621 + 0.999839i 0.505718π0.505718\pi
434434 −6.39579 −0.307008
435435 0 0
436436 0.253804 0.0121550
437437 −6.52707 −0.312232
438438 0 0
439439 14.4504 0.689682 0.344841 0.938661i 0.387933π-0.387933\pi
0.344841 + 0.938661i 0.387933π0.387933\pi
440440 −3.64179 −0.173615
441441 0 0
442442 15.5405 0.739187
443443 −34.8974 −1.65803 −0.829013 0.559230i 0.811097π-0.811097\pi
−0.829013 + 0.559230i 0.811097π0.811097\pi
444444 0 0
445445 9.63597 0.456789
446446 19.8322 0.939082
447447 0 0
448448 −1.19175 −0.0563049
449449 −7.54564 −0.356101 −0.178050 0.984021i 0.556979π-0.556979\pi
−0.178050 + 0.984021i 0.556979π0.556979\pi
450450 0 0
451451 31.8828 1.50130
452452 −13.3443 −0.627663
453453 0 0
454454 −12.9608 −0.608280
455455 −5.80259 −0.272030
456456 0 0
457457 −5.70645 −0.266936 −0.133468 0.991053i 0.542611π-0.542611\pi
−0.133468 + 0.991053i 0.542611π0.542611\pi
458458 −23.2384 −1.08586
459459 0 0
460460 −2.86897 −0.133766
461461 18.0324 0.839851 0.419926 0.907559i 0.362056π-0.362056\pi
0.419926 + 0.907559i 0.362056π0.362056\pi
462462 0 0
463463 −25.3869 −1.17983 −0.589914 0.807466i 0.700839π-0.700839\pi
−0.589914 + 0.807466i 0.700839π0.700839\pi
464464 6.06072 0.281362
465465 0 0
466466 −8.88196 −0.411449
467467 23.6153 1.09279 0.546393 0.837529i 0.316000π-0.316000\pi
0.546393 + 0.837529i 0.316000π0.316000\pi
468468 0 0
469469 5.83966 0.269651
470470 4.13955 0.190943
471471 0 0
472472 7.28357 0.335254
473473 24.5992 1.13107
474474 0 0
475475 2.27506 0.104387
476476 −3.80377 −0.174345
477477 0 0
478478 −25.3778 −1.16076
479479 −34.7981 −1.58997 −0.794983 0.606632i 0.792520π-0.792520\pi
−0.794983 + 0.606632i 0.792520π0.792520\pi
480480 0 0
481481 4.86897 0.222006
482482 −10.2429 −0.466550
483483 0 0
484484 2.26261 0.102846
485485 14.8943 0.676313
486486 0 0
487487 −8.65612 −0.392246 −0.196123 0.980579i 0.562835π-0.562835\pi
−0.196123 + 0.980579i 0.562835π0.562835\pi
488488 14.5443 0.658390
489489 0 0
490490 −5.57973 −0.252067
491491 12.0632 0.544407 0.272203 0.962240i 0.412248π-0.412248\pi
0.272203 + 0.962240i 0.412248π0.412248\pi
492492 0 0
493493 19.3443 0.871223
494494 11.0772 0.498387
495495 0 0
496496 5.36672 0.240973
497497 −6.42113 −0.288027
498498 0 0
499499 1.14647 0.0513231 0.0256616 0.999671i 0.491831π-0.491831\pi
0.0256616 + 0.999671i 0.491831π0.491831\pi
500500 1.00000 0.0447214
501501 0 0
502502 −10.2258 −0.456402
503503 6.98795 0.311577 0.155789 0.987790i 0.450208π-0.450208\pi
0.155789 + 0.987790i 0.450208π0.450208\pi
504504 0 0
505505 −7.63194 −0.339617
506506 10.4482 0.464477
507507 0 0
508508 −7.21891 −0.320288
509509 −27.9592 −1.23927 −0.619634 0.784891i 0.712719π-0.712719\pi
−0.619634 + 0.784891i 0.712719π0.712719\pi
510510 0 0
511511 −14.0657 −0.622232
512512 1.00000 0.0441942
513513 0 0
514514 18.0481 0.796069
515515 −2.13955 −0.0942796
516516 0 0
517517 −15.0753 −0.663013
518518 −1.19175 −0.0523625
519519 0 0
520520 4.86897 0.213518
521521 29.5052 1.29265 0.646323 0.763064i 0.276306π-0.276306\pi
0.646323 + 0.763064i 0.276306π0.276306\pi
522522 0 0
523523 13.0588 0.571022 0.285511 0.958375i 0.407837π-0.407837\pi
0.285511 + 0.958375i 0.407837π0.407837\pi
524524 −20.0506 −0.875913
525525 0 0
526526 13.5658 0.591497
527527 17.1292 0.746162
528528 0 0
529529 −14.7690 −0.642132
530530 5.88574 0.255660
531531 0 0
532532 −2.71131 −0.117550
533533 −42.6264 −1.84635
534534 0 0
535535 −14.9904 −0.648091
536536 −4.90007 −0.211651
537537 0 0
538538 −18.3629 −0.791683
539539 20.3202 0.875253
540540 0 0
541541 −23.5134 −1.01092 −0.505461 0.862850i 0.668678π-0.668678\pi
−0.505461 + 0.862850i 0.668678π0.668678\pi
542542 −0.279091 −0.0119880
543543 0 0
544544 3.19175 0.136845
545545 0.253804 0.0108718
546546 0 0
547547 −33.5166 −1.43307 −0.716533 0.697553i 0.754272π-0.754272\pi
−0.716533 + 0.697553i 0.754272π0.754272\pi
548548 9.52753 0.406996
549549 0 0
550550 −3.64179 −0.155286
551551 13.7885 0.587410
552552 0 0
553553 −8.80463 −0.374411
554554 24.9195 1.05873
555555 0 0
556556 20.7323 0.879244
557557 −11.6308 −0.492815 −0.246407 0.969166i 0.579250π-0.579250\pi
−0.246407 + 0.969166i 0.579250π0.579250\pi
558558 0 0
559559 −32.8884 −1.39103
560560 −1.19175 −0.0503606
561561 0 0
562562 2.25695 0.0952036
563563 2.37336 0.100025 0.0500125 0.998749i 0.484074π-0.484074\pi
0.0500125 + 0.998749i 0.484074π0.484074\pi
564564 0 0
565565 −13.3443 −0.561398
566566 4.31884 0.181534
567567 0 0
568568 5.38798 0.226075
569569 3.83093 0.160601 0.0803005 0.996771i 0.474412π-0.474412\pi
0.0803005 + 0.996771i 0.474412π0.474412\pi
570570 0 0
571571 3.85678 0.161401 0.0807007 0.996738i 0.474284π-0.474284\pi
0.0807007 + 0.996738i 0.474284π0.474284\pi
572572 −17.7317 −0.741401
573573 0 0
574574 10.4334 0.435483
575575 −2.86897 −0.119644
576576 0 0
577577 −15.2565 −0.635136 −0.317568 0.948235i 0.602866π-0.602866\pi
−0.317568 + 0.948235i 0.602866π0.602866\pi
578578 −6.81273 −0.283372
579579 0 0
580580 6.06072 0.251658
581581 −5.26111 −0.218268
582582 0 0
583583 −21.4346 −0.887731
584584 11.8026 0.488395
585585 0 0
586586 7.43138 0.306988
587587 20.0442 0.827312 0.413656 0.910433i 0.364252π-0.364252\pi
0.413656 + 0.910433i 0.364252π0.364252\pi
588588 0 0
589589 12.2096 0.503089
590590 7.28357 0.299860
591591 0 0
592592 1.00000 0.0410997
593593 38.0414 1.56217 0.781087 0.624422i 0.214666π-0.214666\pi
0.781087 + 0.624422i 0.214666π0.214666\pi
594594 0 0
595595 −3.80377 −0.155939
596596 −9.17758 −0.375928
597597 0 0
598598 −13.9689 −0.571230
599599 0.900073 0.0367760 0.0183880 0.999831i 0.494147π-0.494147\pi
0.0183880 + 0.999831i 0.494147π0.494147\pi
600600 0 0
601601 17.8298 0.727291 0.363645 0.931537i 0.381532π-0.381532\pi
0.363645 + 0.931537i 0.381532π0.381532\pi
602602 8.04992 0.328090
603603 0 0
604604 17.6024 0.716232
605605 2.26261 0.0919881
606606 0 0
607607 −38.6109 −1.56717 −0.783585 0.621285i 0.786611π-0.786611\pi
−0.783585 + 0.621285i 0.786611π0.786611\pi
608608 2.27506 0.0922659
609609 0 0
610610 14.5443 0.588882
611611 20.1553 0.815396
612612 0 0
613613 13.7108 0.553773 0.276886 0.960903i 0.410697π-0.410697\pi
0.276886 + 0.960903i 0.410697π0.410697\pi
614614 3.28357 0.132514
615615 0 0
616616 4.34010 0.174868
617617 −23.0875 −0.929468 −0.464734 0.885450i 0.653850π-0.653850\pi
−0.464734 + 0.885450i 0.653850π0.653850\pi
618618 0 0
619619 28.4872 1.14500 0.572499 0.819905i 0.305974π-0.305974\pi
0.572499 + 0.819905i 0.305974π0.305974\pi
620620 5.36672 0.215533
621621 0 0
622622 −11.8438 −0.474895
623623 −11.4837 −0.460083
624624 0 0
625625 1.00000 0.0400000
626626 15.4653 0.618118
627627 0 0
628628 6.89857 0.275283
629629 3.19175 0.127263
630630 0 0
631631 5.84975 0.232875 0.116437 0.993198i 0.462853π-0.462853\pi
0.116437 + 0.993198i 0.462853π0.462853\pi
632632 7.38798 0.293878
633633 0 0
634634 −16.4553 −0.653525
635635 −7.21891 −0.286474
636636 0 0
637637 −27.1675 −1.07642
638638 −22.0718 −0.873832
639639 0 0
640640 1.00000 0.0395285
641641 −16.5884 −0.655203 −0.327601 0.944816i 0.606240π-0.606240\pi
−0.327601 + 0.944816i 0.606240π0.606240\pi
642642 0 0
643643 −23.3695 −0.921603 −0.460801 0.887503i 0.652438π-0.652438\pi
−0.460801 + 0.887503i 0.652438π0.652438\pi
644644 3.41909 0.134731
645645 0 0
646646 7.26143 0.285697
647647 25.8618 1.01673 0.508366 0.861141i 0.330250π-0.330250\pi
0.508366 + 0.861141i 0.330250π0.330250\pi
648648 0 0
649649 −26.5252 −1.04121
650650 4.86897 0.190977
651651 0 0
652652 −10.8194 −0.423719
653653 34.9853 1.36908 0.684540 0.728976i 0.260003π-0.260003\pi
0.684540 + 0.728976i 0.260003π0.260003\pi
654654 0 0
655655 −20.0506 −0.783441
656656 −8.75471 −0.341814
657657 0 0
658658 −4.93330 −0.192320
659659 −21.3274 −0.830796 −0.415398 0.909640i 0.636358π-0.636358\pi
−0.415398 + 0.909640i 0.636358π0.636358\pi
660660 0 0
661661 −13.8420 −0.538390 −0.269195 0.963086i 0.586758π-0.586758\pi
−0.269195 + 0.963086i 0.586758π0.586758\pi
662662 35.4204 1.37665
663663 0 0
664664 4.41461 0.171320
665665 −2.71131 −0.105140
666666 0 0
667667 −17.3880 −0.673265
668668 2.86897 0.111004
669669 0 0
670670 −4.90007 −0.189306
671671 −52.9672 −2.04478
672672 0 0
673673 −34.5866 −1.33322 −0.666608 0.745409i 0.732254π-0.732254\pi
−0.666608 + 0.745409i 0.732254π0.732254\pi
674674 −4.80675 −0.185149
675675 0 0
676676 10.7068 0.411801
677677 32.0401 1.23140 0.615700 0.787981i 0.288873π-0.288873\pi
0.615700 + 0.787981i 0.288873π0.288873\pi
678678 0 0
679679 −17.7502 −0.681191
680680 3.19175 0.122398
681681 0 0
682682 −19.5445 −0.748396
683683 −25.2036 −0.964391 −0.482195 0.876064i 0.660160π-0.660160\pi
−0.482195 + 0.876064i 0.660160π0.660160\pi
684684 0 0
685685 9.52753 0.364028
686686 14.9919 0.572393
687687 0 0
688688 −6.75471 −0.257521
689689 28.6575 1.09176
690690 0 0
691691 −21.5818 −0.821009 −0.410505 0.911859i 0.634647π-0.634647\pi
−0.410505 + 0.911859i 0.634647π0.634647\pi
692692 18.3571 0.697833
693693 0 0
694694 18.5049 0.702438
695695 20.7323 0.786420
696696 0 0
697697 −27.9428 −1.05841
698698 −33.7975 −1.27925
699699 0 0
700700 −1.19175 −0.0450439
701701 14.0622 0.531123 0.265561 0.964094i 0.414443π-0.414443\pi
0.265561 + 0.964094i 0.414443π0.414443\pi
702702 0 0
703703 2.27506 0.0858056
704704 −3.64179 −0.137255
705705 0 0
706706 −37.4657 −1.41004
707707 9.09536 0.342066
708708 0 0
709709 −3.83300 −0.143951 −0.0719756 0.997406i 0.522930π-0.522930\pi
−0.0719756 + 0.997406i 0.522930π0.522930\pi
710710 5.38798 0.202207
711711 0 0
712712 9.63597 0.361123
713713 −15.3969 −0.576620
714714 0 0
715715 −17.7317 −0.663129
716716 −23.1259 −0.864256
717717 0 0
718718 14.6886 0.548173
719719 −40.5298 −1.51151 −0.755754 0.654856i 0.772729π-0.772729\pi
−0.755754 + 0.654856i 0.772729π0.772729\pi
720720 0 0
721721 2.54980 0.0949596
722722 −13.8241 −0.514479
723723 0 0
724724 14.9001 0.553757
725725 6.06072 0.225089
726726 0 0
727727 29.5871 1.09732 0.548662 0.836044i 0.315137π-0.315137\pi
0.548662 + 0.836044i 0.315137π0.315137\pi
728728 −5.80259 −0.215058
729729 0 0
730730 11.8026 0.436833
731731 −21.5593 −0.797401
732732 0 0
733733 −30.5400 −1.12802 −0.564010 0.825768i 0.690742π-0.690742\pi
−0.564010 + 0.825768i 0.690742π0.690742\pi
734734 16.1175 0.594907
735735 0 0
736736 −2.86897 −0.105751
737737 17.8450 0.657330
738738 0 0
739739 −1.49357 −0.0549419 −0.0274709 0.999623i 0.508745π-0.508745\pi
−0.0274709 + 0.999623i 0.508745π0.508745\pi
740740 1.00000 0.0367607
741741 0 0
742742 −7.01433 −0.257504
743743 −25.2442 −0.926120 −0.463060 0.886327i 0.653249π-0.653249\pi
−0.463060 + 0.886327i 0.653249π0.653249\pi
744744 0 0
745745 −9.17758 −0.336240
746746 3.25002 0.118992
747747 0 0
748748 −11.6237 −0.425004
749749 17.8648 0.652766
750750 0 0
751751 8.44304 0.308091 0.154045 0.988064i 0.450770π-0.450770\pi
0.154045 + 0.988064i 0.450770π0.450770\pi
752752 4.13955 0.150954
753753 0 0
754754 29.5094 1.07467
755755 17.6024 0.640617
756756 0 0
757757 35.8169 1.30179 0.650894 0.759168i 0.274394π-0.274394\pi
0.650894 + 0.759168i 0.274394π0.274394\pi
758758 −33.7639 −1.22636
759759 0 0
760760 2.27506 0.0825252
761761 27.0428 0.980299 0.490150 0.871638i 0.336942π-0.336942\pi
0.490150 + 0.871638i 0.336942π0.336942\pi
762762 0 0
763763 −0.302471 −0.0109502
764764 8.31766 0.300922
765765 0 0
766766 −14.3859 −0.519785
767767 35.4635 1.28051
768768 0 0
769769 −42.3051 −1.52556 −0.762780 0.646658i 0.776166π-0.776166\pi
−0.762780 + 0.646658i 0.776166π0.776166\pi
770770 4.34010 0.156406
771771 0 0
772772 −21.5445 −0.775405
773773 11.5566 0.415661 0.207830 0.978165i 0.433360π-0.433360\pi
0.207830 + 0.978165i 0.433360π0.433360\pi
774774 0 0
775775 5.36672 0.192778
776776 14.8943 0.534672
777777 0 0
778778 −25.5445 −0.915813
779779 −19.9175 −0.713618
780780 0 0
781781 −19.6219 −0.702126
782782 −9.15702 −0.327454
783783 0 0
784784 −5.57973 −0.199276
785785 6.89857 0.246221
786786 0 0
787787 33.9099 1.20876 0.604379 0.796697i 0.293421π-0.293421\pi
0.604379 + 0.796697i 0.293421π0.293421\pi
788788 −3.76904 −0.134266
789789 0 0
790790 7.38798 0.262853
791791 15.9031 0.565448
792792 0 0
793793 70.8157 2.51474
794794 −4.81219 −0.170778
795795 0 0
796796 −5.92914 −0.210153
797797 −20.6886 −0.732827 −0.366413 0.930452i 0.619414π-0.619414\pi
−0.366413 + 0.930452i 0.619414π0.619414\pi
798798 0 0
799799 13.2124 0.467421
800800 1.00000 0.0353553
801801 0 0
802802 −8.45191 −0.298447
803803 −42.9825 −1.51682
804804 0 0
805805 3.41909 0.120507
806806 26.1304 0.920404
807807 0 0
808808 −7.63194 −0.268491
809809 −44.3868 −1.56056 −0.780278 0.625433i 0.784922π-0.784922\pi
−0.780278 + 0.625433i 0.784922π0.784922\pi
810810 0 0
811811 −41.4929 −1.45701 −0.728506 0.685039i 0.759785π-0.759785\pi
−0.728506 + 0.685039i 0.759785π0.759785\pi
812812 −7.22286 −0.253473
813813 0 0
814814 −3.64179 −0.127645
815815 −10.8194 −0.378986
816816 0 0
817817 −15.3674 −0.537636
818818 −5.51209 −0.192726
819819 0 0
820820 −8.75471 −0.305728
821821 21.9624 0.766494 0.383247 0.923646i 0.374806π-0.374806\pi
0.383247 + 0.923646i 0.374806π0.374806\pi
822822 0 0
823823 31.5911 1.10120 0.550598 0.834770i 0.314400π-0.314400\pi
0.550598 + 0.834770i 0.314400π0.314400\pi
824824 −2.13955 −0.0745346
825825 0 0
826826 −8.68020 −0.302023
827827 5.42271 0.188566 0.0942831 0.995545i 0.469944π-0.469944\pi
0.0942831 + 0.995545i 0.469944π0.469944\pi
828828 0 0
829829 −54.0226 −1.87628 −0.938141 0.346252i 0.887454π-0.887454\pi
−0.938141 + 0.346252i 0.887454π0.887454\pi
830830 4.41461 0.153233
831831 0 0
832832 4.86897 0.168801
833833 −17.8091 −0.617049
834834 0 0
835835 2.86897 0.0992846
836836 −8.28529 −0.286553
837837 0 0
838838 −0.853529 −0.0294847
839839 −22.4803 −0.776108 −0.388054 0.921637i 0.626853π-0.626853\pi
−0.388054 + 0.921637i 0.626853π0.626853\pi
840840 0 0
841841 7.73227 0.266630
842842 23.5275 0.810812
843843 0 0
844844 −3.51059 −0.120840
845845 10.7068 0.368326
846846 0 0
847847 −2.69646 −0.0926516
848848 5.88574 0.202117
849849 0 0
850850 3.19175 0.109476
851851 −2.86897 −0.0983469
852852 0 0
853853 24.4482 0.837089 0.418545 0.908196i 0.362540π-0.362540\pi
0.418545 + 0.908196i 0.362540π0.362540\pi
854854 −17.3332 −0.593129
855855 0 0
856856 −14.9904 −0.512361
857857 19.1295 0.653452 0.326726 0.945119i 0.394054π-0.394054\pi
0.326726 + 0.945119i 0.394054π0.394054\pi
858858 0 0
859859 −11.5662 −0.394634 −0.197317 0.980340i 0.563223π-0.563223\pi
−0.197317 + 0.980340i 0.563223π0.563223\pi
860860 −6.75471 −0.230334
861861 0 0
862862 −34.1849 −1.16434
863863 14.2397 0.484726 0.242363 0.970186i 0.422078π-0.422078\pi
0.242363 + 0.970186i 0.422078π0.422078\pi
864864 0 0
865865 18.3571 0.624161
866866 −0.747535 −0.0254023
867867 0 0
868868 −6.39579 −0.217087
869869 −26.9055 −0.912705
870870 0 0
871871 −23.8583 −0.808407
872872 0.253804 0.00859490
873873 0 0
874874 −6.52707 −0.220782
875875 −1.19175 −0.0402885
876876 0 0
877877 −36.8021 −1.24272 −0.621358 0.783526i 0.713419π-0.713419\pi
−0.621358 + 0.783526i 0.713419π0.713419\pi
878878 14.4504 0.487679
879879 0 0
880880 −3.64179 −0.122765
881881 5.78645 0.194951 0.0974753 0.995238i 0.468923π-0.468923\pi
0.0974753 + 0.995238i 0.468923π0.468923\pi
882882 0 0
883883 8.30279 0.279411 0.139706 0.990193i 0.455384π-0.455384\pi
0.139706 + 0.990193i 0.455384π0.455384\pi
884884 15.5405 0.522684
885885 0 0
886886 −34.8974 −1.17240
887887 40.2125 1.35020 0.675101 0.737725i 0.264100π-0.264100\pi
0.675101 + 0.737725i 0.264100π0.264100\pi
888888 0 0
889889 8.60314 0.288540
890890 9.63597 0.322998
891891 0 0
892892 19.8322 0.664031
893893 9.41772 0.315152
894894 0 0
895895 −23.1259 −0.773014
896896 −1.19175 −0.0398136
897897 0 0
898898 −7.54564 −0.251801
899899 32.5262 1.08481
900900 0 0
901901 18.7858 0.625846
902902 31.8828 1.06158
903903 0 0
904904 −13.3443 −0.443824
905905 14.9001 0.495295
906906 0 0
907907 17.9432 0.595795 0.297898 0.954598i 0.403715π-0.403715\pi
0.297898 + 0.954598i 0.403715π0.403715\pi
908908 −12.9608 −0.430119
909909 0 0
910910 −5.80259 −0.192354
911911 10.0090 0.331612 0.165806 0.986158i 0.446977π-0.446977\pi
0.165806 + 0.986158i 0.446977π0.446977\pi
912912 0 0
913913 −16.0771 −0.532073
914914 −5.70645 −0.188752
915915 0 0
916916 −23.2384 −0.767818
917917 23.8953 0.789091
918918 0 0
919919 53.4439 1.76295 0.881476 0.472228i 0.156550π-0.156550\pi
0.881476 + 0.472228i 0.156550π0.156550\pi
920920 −2.86897 −0.0945870
921921 0 0
922922 18.0324 0.593865
923923 26.2339 0.863499
924924 0 0
925925 1.00000 0.0328798
926926 −25.3869 −0.834265
927927 0 0
928928 6.06072 0.198953
929929 17.5723 0.576528 0.288264 0.957551i 0.406922π-0.406922\pi
0.288264 + 0.957551i 0.406922π0.406922\pi
930930 0 0
931931 −12.6942 −0.416037
932932 −8.88196 −0.290938
933933 0 0
934934 23.6153 0.772717
935935 −11.6237 −0.380135
936936 0 0
937937 −32.5641 −1.06382 −0.531912 0.846800i 0.678526π-0.678526\pi
−0.531912 + 0.846800i 0.678526π0.678526\pi
938938 5.83966 0.190672
939939 0 0
940940 4.13955 0.135017
941941 17.0656 0.556323 0.278161 0.960534i 0.410275π-0.410275\pi
0.278161 + 0.960534i 0.410275π0.410275\pi
942942 0 0
943943 25.1169 0.817920
944944 7.28357 0.237060
945945 0 0
946946 24.5992 0.799789
947947 −25.2036 −0.819009 −0.409504 0.912308i 0.634298π-0.634298\pi
−0.409504 + 0.912308i 0.634298π0.634298\pi
948948 0 0
949949 57.4664 1.86544
950950 2.27506 0.0738128
951951 0 0
952952 −3.80377 −0.123281
953953 21.7560 0.704747 0.352374 0.935859i 0.385375π-0.385375\pi
0.352374 + 0.935859i 0.385375π0.385375\pi
954954 0 0
955955 8.31766 0.269153
956956 −25.3778 −0.820778
957957 0 0
958958 −34.7981 −1.12428
959959 −11.3544 −0.366654
960960 0 0
961961 −2.19827 −0.0709119
962962 4.86897 0.156982
963963 0 0
964964 −10.2429 −0.329900
965965 −21.5445 −0.693544
966966 0 0
967967 −12.3654 −0.397644 −0.198822 0.980036i 0.563712π-0.563712\pi
−0.198822 + 0.980036i 0.563712π0.563712\pi
968968 2.26261 0.0727230
969969 0 0
970970 14.8943 0.478226
971971 50.2114 1.61136 0.805680 0.592351i 0.201800π-0.201800\pi
0.805680 + 0.592351i 0.201800π0.201800\pi
972972 0 0
973973 −24.7077 −0.792092
974974 −8.65612 −0.277360
975975 0 0
976976 14.5443 0.465552
977977 8.06724 0.258094 0.129047 0.991638i 0.458808π-0.458808\pi
0.129047 + 0.991638i 0.458808π0.458808\pi
978978 0 0
979979 −35.0921 −1.12155
980980 −5.57973 −0.178238
981981 0 0
982982 12.0632 0.384954
983983 −42.2151 −1.34645 −0.673227 0.739436i 0.735092π-0.735092\pi
−0.673227 + 0.739436i 0.735092π0.735092\pi
984984 0 0
985985 −3.76904 −0.120092
986986 19.3443 0.616048
987987 0 0
988988 11.0772 0.352413
989989 19.3790 0.616217
990990 0 0
991991 −16.9294 −0.537780 −0.268890 0.963171i 0.586657π-0.586657\pi
−0.268890 + 0.963171i 0.586657π0.586657\pi
992992 5.36672 0.170394
993993 0 0
994994 −6.42113 −0.203666
995995 −5.92914 −0.187966
996996 0 0
997997 −8.75699 −0.277337 −0.138668 0.990339i 0.544282π-0.544282\pi
−0.138668 + 0.990339i 0.544282π0.544282\pi
998998 1.14647 0.0362909
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 3330.2.a.bl.1.2 yes 5
3.2 odd 2 3330.2.a.bk.1.2 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3330.2.a.bk.1.2 5 3.2 odd 2
3330.2.a.bl.1.2 yes 5 1.1 even 1 trivial