Properties

Label 5994.2.a.ba.1.2
Level 59945994
Weight 22
Character 5994.1
Self dual yes
Analytic conductor 47.86247.862
Analytic rank 00
Dimension 1010
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] = [5994,2,Mod(1,5994)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5994, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5994.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 5994=23437 5994 = 2 \cdot 3^{4} \cdot 37
Weight: k k == 2 2
Character orbit: [χ][\chi] == 5994.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: 47.862330971647.8623309716
Analytic rank: 00
Dimension: 1010
Coefficient field: Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x102x926x8+49x7+236x6420x5860x4+1461x3+993x21638x+99 x^{10} - 2x^{9} - 26x^{8} + 49x^{7} + 236x^{6} - 420x^{5} - 860x^{4} + 1461x^{3} + 993x^{2} - 1638x + 99 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 666)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 3.14737-3.14737 of defining polynomial
Character χ\chi == 5994.1

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) == q1.00000q2+1.00000q43.49123q5+2.86107q71.00000q8+3.49123q10+5.43746q11+3.62848q132.86107q14+1.00000q164.84071q17+7.31418q193.49123q205.43746q22+6.69512q23+7.18868q253.62848q26+2.86107q28+5.81232q29+8.96928q311.00000q32+4.84071q349.98865q351.00000q377.31418q38+3.49123q40+0.660400q415.76568q43+5.43746q446.69512q46+7.40907q47+1.18572q497.18868q50+3.62848q523.88952q5318.9834q552.86107q565.81232q581.56553q59+8.49269q618.96928q62+1.00000q6412.6679q65+0.371075q674.84071q68+9.98865q70+0.584961q7111.9922q73+1.00000q74+7.31418q76+15.5570q774.13993q793.49123q800.660400q822.85366q83+16.9000q85+5.76568q865.43746q88+3.31264q89+10.3813q91+6.69512q927.40907q9425.5355q95+12.8349q971.18572q98+O(q100)q-1.00000 q^{2} +1.00000 q^{4} -3.49123 q^{5} +2.86107 q^{7} -1.00000 q^{8} +3.49123 q^{10} +5.43746 q^{11} +3.62848 q^{13} -2.86107 q^{14} +1.00000 q^{16} -4.84071 q^{17} +7.31418 q^{19} -3.49123 q^{20} -5.43746 q^{22} +6.69512 q^{23} +7.18868 q^{25} -3.62848 q^{26} +2.86107 q^{28} +5.81232 q^{29} +8.96928 q^{31} -1.00000 q^{32} +4.84071 q^{34} -9.98865 q^{35} -1.00000 q^{37} -7.31418 q^{38} +3.49123 q^{40} +0.660400 q^{41} -5.76568 q^{43} +5.43746 q^{44} -6.69512 q^{46} +7.40907 q^{47} +1.18572 q^{49} -7.18868 q^{50} +3.62848 q^{52} -3.88952 q^{53} -18.9834 q^{55} -2.86107 q^{56} -5.81232 q^{58} -1.56553 q^{59} +8.49269 q^{61} -8.96928 q^{62} +1.00000 q^{64} -12.6679 q^{65} +0.371075 q^{67} -4.84071 q^{68} +9.98865 q^{70} +0.584961 q^{71} -11.9922 q^{73} +1.00000 q^{74} +7.31418 q^{76} +15.5570 q^{77} -4.13993 q^{79} -3.49123 q^{80} -0.660400 q^{82} -2.85366 q^{83} +16.9000 q^{85} +5.76568 q^{86} -5.43746 q^{88} +3.31264 q^{89} +10.3813 q^{91} +6.69512 q^{92} -7.40907 q^{94} -25.5355 q^{95} +12.8349 q^{97} -1.18572 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 10q10q2+10q4q5+q710q8+q103q11+12q13q14+10q1612q17+24q19q20+3q223q23+21q2512q26+q284q29+35q98+O(q100) 10 q - 10 q^{2} + 10 q^{4} - q^{5} + q^{7} - 10 q^{8} + q^{10} - 3 q^{11} + 12 q^{13} - q^{14} + 10 q^{16} - 12 q^{17} + 24 q^{19} - q^{20} + 3 q^{22} - 3 q^{23} + 21 q^{25} - 12 q^{26} + q^{28} - 4 q^{29}+ \cdots - 35 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 −3.49123 −1.56133 −0.780663 0.624953i 0.785118π-0.785118\pi
−0.780663 + 0.624953i 0.785118π0.785118\pi
66 0 0
77 2.86107 1.08138 0.540691 0.841221i 0.318163π-0.318163\pi
0.540691 + 0.841221i 0.318163π0.318163\pi
88 −1.00000 −0.353553
99 0 0
1010 3.49123 1.10402
1111 5.43746 1.63946 0.819729 0.572752i 0.194124π-0.194124\pi
0.819729 + 0.572752i 0.194124π0.194124\pi
1212 0 0
1313 3.62848 1.00636 0.503180 0.864182i 0.332163π-0.332163\pi
0.503180 + 0.864182i 0.332163π0.332163\pi
1414 −2.86107 −0.764653
1515 0 0
1616 1.00000 0.250000
1717 −4.84071 −1.17404 −0.587022 0.809571i 0.699700π-0.699700\pi
−0.587022 + 0.809571i 0.699700π0.699700\pi
1818 0 0
1919 7.31418 1.67799 0.838994 0.544140i 0.183144π-0.183144\pi
0.838994 + 0.544140i 0.183144π0.183144\pi
2020 −3.49123 −0.780663
2121 0 0
2222 −5.43746 −1.15927
2323 6.69512 1.39603 0.698014 0.716084i 0.254067π-0.254067\pi
0.698014 + 0.716084i 0.254067π0.254067\pi
2424 0 0
2525 7.18868 1.43774
2626 −3.62848 −0.711604
2727 0 0
2828 2.86107 0.540691
2929 5.81232 1.07932 0.539660 0.841883i 0.318553π-0.318553\pi
0.539660 + 0.841883i 0.318553π0.318553\pi
3030 0 0
3131 8.96928 1.61093 0.805465 0.592643i 0.201916π-0.201916\pi
0.805465 + 0.592643i 0.201916π0.201916\pi
3232 −1.00000 −0.176777
3333 0 0
3434 4.84071 0.830174
3535 −9.98865 −1.68839
3636 0 0
3737 −1.00000 −0.164399
3838 −7.31418 −1.18652
3939 0 0
4040 3.49123 0.552012
4141 0.660400 0.103137 0.0515686 0.998669i 0.483578π-0.483578\pi
0.0515686 + 0.998669i 0.483578π0.483578\pi
4242 0 0
4343 −5.76568 −0.879258 −0.439629 0.898179i 0.644890π-0.644890\pi
−0.439629 + 0.898179i 0.644890π0.644890\pi
4444 5.43746 0.819729
4545 0 0
4646 −6.69512 −0.987141
4747 7.40907 1.08072 0.540362 0.841433i 0.318287π-0.318287\pi
0.540362 + 0.841433i 0.318287π0.318287\pi
4848 0 0
4949 1.18572 0.169388
5050 −7.18868 −1.01663
5151 0 0
5252 3.62848 0.503180
5353 −3.88952 −0.534266 −0.267133 0.963660i 0.586076π-0.586076\pi
−0.267133 + 0.963660i 0.586076π0.586076\pi
5454 0 0
5555 −18.9834 −2.55973
5656 −2.86107 −0.382326
5757 0 0
5858 −5.81232 −0.763195
5959 −1.56553 −0.203815 −0.101907 0.994794i 0.532495π-0.532495\pi
−0.101907 + 0.994794i 0.532495π0.532495\pi
6060 0 0
6161 8.49269 1.08738 0.543689 0.839287i 0.317027π-0.317027\pi
0.543689 + 0.839287i 0.317027π0.317027\pi
6262 −8.96928 −1.13910
6363 0 0
6464 1.00000 0.125000
6565 −12.6679 −1.57125
6666 0 0
6767 0.371075 0.0453340 0.0226670 0.999743i 0.492784π-0.492784\pi
0.0226670 + 0.999743i 0.492784π0.492784\pi
6868 −4.84071 −0.587022
6969 0 0
7070 9.98865 1.19387
7171 0.584961 0.0694221 0.0347110 0.999397i 0.488949π-0.488949\pi
0.0347110 + 0.999397i 0.488949π0.488949\pi
7272 0 0
7373 −11.9922 −1.40358 −0.701792 0.712382i 0.747616π-0.747616\pi
−0.701792 + 0.712382i 0.747616π0.747616\pi
7474 1.00000 0.116248
7575 0 0
7676 7.31418 0.838994
7777 15.5570 1.77288
7878 0 0
7979 −4.13993 −0.465778 −0.232889 0.972503i 0.574818π-0.574818\pi
−0.232889 + 0.972503i 0.574818π0.574818\pi
8080 −3.49123 −0.390331
8181 0 0
8282 −0.660400 −0.0729290
8383 −2.85366 −0.313230 −0.156615 0.987660i 0.550058π-0.550058\pi
−0.156615 + 0.987660i 0.550058π0.550058\pi
8484 0 0
8585 16.9000 1.83306
8686 5.76568 0.621729
8787 0 0
8888 −5.43746 −0.579636
8989 3.31264 0.351139 0.175570 0.984467i 0.443823π-0.443823\pi
0.175570 + 0.984467i 0.443823π0.443823\pi
9090 0 0
9191 10.3813 1.08826
9292 6.69512 0.698014
9393 0 0
9494 −7.40907 −0.764187
9595 −25.5355 −2.61989
9696 0 0
9797 12.8349 1.30319 0.651593 0.758569i 0.274101π-0.274101\pi
0.651593 + 0.758569i 0.274101π0.274101\pi
9898 −1.18572 −0.119776
9999 0 0
100100 7.18868 0.718868
101101 −6.80546 −0.677169 −0.338584 0.940936i 0.609948π-0.609948\pi
−0.338584 + 0.940936i 0.609948π0.609948\pi
102102 0 0
103103 −12.3966 −1.22147 −0.610737 0.791833i 0.709127π-0.709127\pi
−0.610737 + 0.791833i 0.709127π0.709127\pi
104104 −3.62848 −0.355802
105105 0 0
106106 3.88952 0.377783
107107 0.144488 0.0139682 0.00698411 0.999976i 0.497777π-0.497777\pi
0.00698411 + 0.999976i 0.497777π0.497777\pi
108108 0 0
109109 12.4288 1.19046 0.595232 0.803554i 0.297060π-0.297060\pi
0.595232 + 0.803554i 0.297060π0.297060\pi
110110 18.9834 1.81000
111111 0 0
112112 2.86107 0.270346
113113 4.15551 0.390917 0.195459 0.980712i 0.437380π-0.437380\pi
0.195459 + 0.980712i 0.437380π0.437380\pi
114114 0 0
115115 −23.3742 −2.17965
116116 5.81232 0.539660
117117 0 0
118118 1.56553 0.144119
119119 −13.8496 −1.26959
120120 0 0
121121 18.5660 1.68782
122122 −8.49269 −0.768892
123123 0 0
124124 8.96928 0.805465
125125 −7.64119 −0.683449
126126 0 0
127127 −19.5394 −1.73384 −0.866922 0.498445i 0.833905π-0.833905\pi
−0.866922 + 0.498445i 0.833905π0.833905\pi
128128 −1.00000 −0.0883883
129129 0 0
130130 12.6679 1.11104
131131 −13.7848 −1.20439 −0.602193 0.798351i 0.705706π-0.705706\pi
−0.602193 + 0.798351i 0.705706π0.705706\pi
132132 0 0
133133 20.9264 1.81455
134134 −0.371075 −0.0320560
135135 0 0
136136 4.84071 0.415087
137137 17.1391 1.46429 0.732146 0.681147i 0.238519π-0.238519\pi
0.732146 + 0.681147i 0.238519π0.238519\pi
138138 0 0
139139 −1.76011 −0.149290 −0.0746452 0.997210i 0.523782π-0.523782\pi
−0.0746452 + 0.997210i 0.523782π0.523782\pi
140140 −9.98865 −0.844195
141141 0 0
142142 −0.584961 −0.0490888
143143 19.7297 1.64988
144144 0 0
145145 −20.2921 −1.68517
146146 11.9922 0.992483
147147 0 0
148148 −1.00000 −0.0821995
149149 −16.6486 −1.36391 −0.681954 0.731395i 0.738869π-0.738869\pi
−0.681954 + 0.731395i 0.738869π0.738869\pi
150150 0 0
151151 5.70123 0.463960 0.231980 0.972721i 0.425480π-0.425480\pi
0.231980 + 0.972721i 0.425480π0.425480\pi
152152 −7.31418 −0.593259
153153 0 0
154154 −15.5570 −1.25362
155155 −31.3138 −2.51519
156156 0 0
157157 −21.7894 −1.73898 −0.869491 0.493948i 0.835553π-0.835553\pi
−0.869491 + 0.493948i 0.835553π0.835553\pi
158158 4.13993 0.329355
159159 0 0
160160 3.49123 0.276006
161161 19.1552 1.50964
162162 0 0
163163 2.37983 0.186403 0.0932013 0.995647i 0.470290π-0.470290\pi
0.0932013 + 0.995647i 0.470290π0.470290\pi
164164 0.660400 0.0515686
165165 0 0
166166 2.85366 0.221487
167167 −4.22401 −0.326864 −0.163432 0.986555i 0.552256π-0.552256\pi
−0.163432 + 0.986555i 0.552256π0.552256\pi
168168 0 0
169169 0.165868 0.0127591
170170 −16.9000 −1.29617
171171 0 0
172172 −5.76568 −0.439629
173173 3.83472 0.291548 0.145774 0.989318i 0.453433π-0.453433\pi
0.145774 + 0.989318i 0.453433π0.453433\pi
174174 0 0
175175 20.5673 1.55474
176176 5.43746 0.409864
177177 0 0
178178 −3.31264 −0.248293
179179 4.36893 0.326549 0.163275 0.986581i 0.447794π-0.447794\pi
0.163275 + 0.986581i 0.447794π0.447794\pi
180180 0 0
181181 −3.71793 −0.276352 −0.138176 0.990408i 0.544124π-0.544124\pi
−0.138176 + 0.990408i 0.544124π0.544124\pi
182182 −10.3813 −0.769516
183183 0 0
184184 −6.69512 −0.493571
185185 3.49123 0.256680
186186 0 0
187187 −26.3212 −1.92479
188188 7.40907 0.540362
189189 0 0
190190 25.5355 1.85254
191191 5.53343 0.400385 0.200193 0.979757i 0.435843π-0.435843\pi
0.200193 + 0.979757i 0.435843π0.435843\pi
192192 0 0
193193 −23.0916 −1.66217 −0.831084 0.556147i 0.812279π-0.812279\pi
−0.831084 + 0.556147i 0.812279π0.812279\pi
194194 −12.8349 −0.921492
195195 0 0
196196 1.18572 0.0846941
197197 −14.5861 −1.03922 −0.519609 0.854404i 0.673922π-0.673922\pi
−0.519609 + 0.854404i 0.673922π0.673922\pi
198198 0 0
199199 19.8939 1.41024 0.705121 0.709087i 0.250893π-0.250893\pi
0.705121 + 0.709087i 0.250893π0.250893\pi
200200 −7.18868 −0.508317
201201 0 0
202202 6.80546 0.478831
203203 16.6295 1.16716
204204 0 0
205205 −2.30561 −0.161031
206206 12.3966 0.863713
207207 0 0
208208 3.62848 0.251590
209209 39.7706 2.75099
210210 0 0
211211 −19.4285 −1.33752 −0.668758 0.743481i 0.733174π-0.733174\pi
−0.668758 + 0.743481i 0.733174π0.733174\pi
212212 −3.88952 −0.267133
213213 0 0
214214 −0.144488 −0.00987702
215215 20.1293 1.37281
216216 0 0
217217 25.6617 1.74203
218218 −12.4288 −0.841786
219219 0 0
220220 −18.9834 −1.27986
221221 −17.5644 −1.18151
222222 0 0
223223 13.2705 0.888657 0.444328 0.895864i 0.353442π-0.353442\pi
0.444328 + 0.895864i 0.353442π0.353442\pi
224224 −2.86107 −0.191163
225225 0 0
226226 −4.15551 −0.276420
227227 8.11658 0.538717 0.269358 0.963040i 0.413188π-0.413188\pi
0.269358 + 0.963040i 0.413188π0.413188\pi
228228 0 0
229229 17.7272 1.17145 0.585723 0.810511i 0.300811π-0.300811\pi
0.585723 + 0.810511i 0.300811π0.300811\pi
230230 23.3742 1.54125
231231 0 0
232232 −5.81232 −0.381598
233233 −9.99766 −0.654968 −0.327484 0.944857i 0.606201π-0.606201\pi
−0.327484 + 0.944857i 0.606201π0.606201\pi
234234 0 0
235235 −25.8668 −1.68736
236236 −1.56553 −0.101907
237237 0 0
238238 13.8496 0.897736
239239 16.5064 1.06771 0.533856 0.845575i 0.320742π-0.320742\pi
0.533856 + 0.845575i 0.320742π0.320742\pi
240240 0 0
241241 16.9919 1.09454 0.547272 0.836955i 0.315666π-0.315666\pi
0.547272 + 0.836955i 0.315666π0.315666\pi
242242 −18.5660 −1.19347
243243 0 0
244244 8.49269 0.543689
245245 −4.13961 −0.264470
246246 0 0
247247 26.5394 1.68866
248248 −8.96928 −0.569550
249249 0 0
250250 7.64119 0.483271
251251 22.2583 1.40493 0.702467 0.711716i 0.252082π-0.252082\pi
0.702467 + 0.711716i 0.252082π0.252082\pi
252252 0 0
253253 36.4045 2.28873
254254 19.5394 1.22601
255255 0 0
256256 1.00000 0.0625000
257257 −7.59811 −0.473957 −0.236979 0.971515i 0.576157π-0.576157\pi
−0.236979 + 0.971515i 0.576157π0.576157\pi
258258 0 0
259259 −2.86107 −0.177778
260260 −12.6679 −0.785627
261261 0 0
262262 13.7848 0.851629
263263 −27.5780 −1.70053 −0.850265 0.526355i 0.823558π-0.823558\pi
−0.850265 + 0.526355i 0.823558π0.823558\pi
264264 0 0
265265 13.5792 0.834163
266266 −20.9264 −1.28308
267267 0 0
268268 0.371075 0.0226670
269269 5.98578 0.364959 0.182480 0.983210i 0.441588π-0.441588\pi
0.182480 + 0.983210i 0.441588π0.441588\pi
270270 0 0
271271 −17.3044 −1.05117 −0.525583 0.850742i 0.676153π-0.676153\pi
−0.525583 + 0.850742i 0.676153π0.676153\pi
272272 −4.84071 −0.293511
273273 0 0
274274 −17.1391 −1.03541
275275 39.0882 2.35711
276276 0 0
277277 −4.11281 −0.247115 −0.123558 0.992337i 0.539430π-0.539430\pi
−0.123558 + 0.992337i 0.539430π0.539430\pi
278278 1.76011 0.105564
279279 0 0
280280 9.98865 0.596936
281281 −5.24793 −0.313065 −0.156533 0.987673i 0.550032π-0.550032\pi
−0.156533 + 0.987673i 0.550032π0.550032\pi
282282 0 0
283283 1.87337 0.111360 0.0556801 0.998449i 0.482267π-0.482267\pi
0.0556801 + 0.998449i 0.482267π0.482267\pi
284284 0.584961 0.0347110
285285 0 0
286286 −19.7297 −1.16664
287287 1.88945 0.111531
288288 0 0
289289 6.43244 0.378379
290290 20.2921 1.19160
291291 0 0
292292 −11.9922 −0.701792
293293 8.40851 0.491231 0.245615 0.969367i 0.421010π-0.421010\pi
0.245615 + 0.969367i 0.421010π0.421010\pi
294294 0 0
295295 5.46563 0.318221
296296 1.00000 0.0581238
297297 0 0
298298 16.6486 0.964428
299299 24.2931 1.40491
300300 0 0
301301 −16.4960 −0.950814
302302 −5.70123 −0.328069
303303 0 0
304304 7.31418 0.419497
305305 −29.6499 −1.69775
306306 0 0
307307 0.609988 0.0348138 0.0174069 0.999848i 0.494459π-0.494459\pi
0.0174069 + 0.999848i 0.494459π0.494459\pi
308308 15.5570 0.886440
309309 0 0
310310 31.3138 1.77850
311311 2.93104 0.166204 0.0831021 0.996541i 0.473517π-0.473517\pi
0.0831021 + 0.996541i 0.473517π0.473517\pi
312312 0 0
313313 13.6998 0.774359 0.387179 0.922004i 0.373449π-0.373449\pi
0.387179 + 0.922004i 0.373449π0.373449\pi
314314 21.7894 1.22965
315315 0 0
316316 −4.13993 −0.232889
317317 4.46543 0.250803 0.125402 0.992106i 0.459978π-0.459978\pi
0.125402 + 0.992106i 0.459978π0.459978\pi
318318 0 0
319319 31.6043 1.76950
320320 −3.49123 −0.195166
321321 0 0
322322 −19.1552 −1.06748
323323 −35.4058 −1.97003
324324 0 0
325325 26.0840 1.44688
326326 −2.37983 −0.131806
327327 0 0
328328 −0.660400 −0.0364645
329329 21.1979 1.16868
330330 0 0
331331 −30.0470 −1.65153 −0.825765 0.564014i 0.809256π-0.809256\pi
−0.825765 + 0.564014i 0.809256π0.809256\pi
332332 −2.85366 −0.156615
333333 0 0
334334 4.22401 0.231128
335335 −1.29551 −0.0707812
336336 0 0
337337 3.62683 0.197566 0.0987829 0.995109i 0.468505π-0.468505\pi
0.0987829 + 0.995109i 0.468505π0.468505\pi
338338 −0.165868 −0.00902204
339339 0 0
340340 16.9000 0.916532
341341 48.7701 2.64105
342342 0 0
343343 −16.6351 −0.898209
344344 5.76568 0.310865
345345 0 0
346346 −3.83472 −0.206156
347347 25.2388 1.35489 0.677446 0.735572i 0.263087π-0.263087\pi
0.677446 + 0.735572i 0.263087π0.263087\pi
348348 0 0
349349 28.8966 1.54680 0.773401 0.633917i 0.218554π-0.218554\pi
0.773401 + 0.633917i 0.218554π0.218554\pi
350350 −20.5673 −1.09937
351351 0 0
352352 −5.43746 −0.289818
353353 −4.43635 −0.236123 −0.118062 0.993006i 0.537668π-0.537668\pi
−0.118062 + 0.993006i 0.537668π0.537668\pi
354354 0 0
355355 −2.04223 −0.108390
356356 3.31264 0.175570
357357 0 0
358358 −4.36893 −0.230905
359359 22.3860 1.18149 0.590743 0.806860i 0.298835π-0.298835\pi
0.590743 + 0.806860i 0.298835π0.298835\pi
360360 0 0
361361 34.4973 1.81565
362362 3.71793 0.195410
363363 0 0
364364 10.3813 0.544130
365365 41.8676 2.19145
366366 0 0
367367 −10.4628 −0.546152 −0.273076 0.961992i 0.588041π-0.588041\pi
−0.273076 + 0.961992i 0.588041π0.588041\pi
368368 6.69512 0.349007
369369 0 0
370370 −3.49123 −0.181500
371371 −11.1282 −0.577746
372372 0 0
373373 −13.1068 −0.678646 −0.339323 0.940670i 0.610198π-0.610198\pi
−0.339323 + 0.940670i 0.610198π0.610198\pi
374374 26.3212 1.36104
375375 0 0
376376 −7.40907 −0.382094
377377 21.0899 1.08618
378378 0 0
379379 −10.8284 −0.556219 −0.278110 0.960549i 0.589708π-0.589708\pi
−0.278110 + 0.960549i 0.589708π0.589708\pi
380380 −25.5355 −1.30994
381381 0 0
382382 −5.53343 −0.283115
383383 23.3409 1.19266 0.596331 0.802739i 0.296625π-0.296625\pi
0.596331 + 0.802739i 0.296625π0.296625\pi
384384 0 0
385385 −54.3129 −2.76804
386386 23.0916 1.17533
387387 0 0
388388 12.8349 0.651593
389389 10.9206 0.553696 0.276848 0.960914i 0.410710π-0.410710\pi
0.276848 + 0.960914i 0.410710π0.410710\pi
390390 0 0
391391 −32.4091 −1.63900
392392 −1.18572 −0.0598878
393393 0 0
394394 14.5861 0.734838
395395 14.4534 0.727231
396396 0 0
397397 −1.28277 −0.0643805 −0.0321902 0.999482i 0.510248π-0.510248\pi
−0.0321902 + 0.999482i 0.510248π0.510248\pi
398398 −19.8939 −0.997192
399399 0 0
400400 7.18868 0.359434
401401 −5.44679 −0.272000 −0.136000 0.990709i 0.543425π-0.543425\pi
−0.136000 + 0.990709i 0.543425π0.543425\pi
402402 0 0
403403 32.5448 1.62117
404404 −6.80546 −0.338584
405405 0 0
406406 −16.6295 −0.825306
407407 −5.43746 −0.269525
408408 0 0
409409 4.04403 0.199965 0.0999823 0.994989i 0.468121π-0.468121\pi
0.0999823 + 0.994989i 0.468121π0.468121\pi
410410 2.30561 0.113866
411411 0 0
412412 −12.3966 −0.610737
413413 −4.47909 −0.220402
414414 0 0
415415 9.96277 0.489053
416416 −3.62848 −0.177901
417417 0 0
418418 −39.7706 −1.94524
419419 11.3722 0.555570 0.277785 0.960643i 0.410400π-0.410400\pi
0.277785 + 0.960643i 0.410400π0.410400\pi
420420 0 0
421421 36.4875 1.77829 0.889145 0.457626i 0.151300π-0.151300\pi
0.889145 + 0.457626i 0.151300π0.151300\pi
422422 19.4285 0.945766
423423 0 0
424424 3.88952 0.188892
425425 −34.7983 −1.68797
426426 0 0
427427 24.2982 1.17587
428428 0.144488 0.00698411
429429 0 0
430430 −20.1293 −0.970722
431431 −21.7781 −1.04901 −0.524506 0.851407i 0.675750π-0.675750\pi
−0.524506 + 0.851407i 0.675750π0.675750\pi
432432 0 0
433433 15.7500 0.756897 0.378448 0.925622i 0.376458π-0.376458\pi
0.378448 + 0.925622i 0.376458π0.376458\pi
434434 −25.6617 −1.23180
435435 0 0
436436 12.4288 0.595232
437437 48.9693 2.34252
438438 0 0
439439 −29.8767 −1.42594 −0.712968 0.701196i 0.752650π-0.752650\pi
−0.712968 + 0.701196i 0.752650π0.752650\pi
440440 18.9834 0.905000
441441 0 0
442442 17.5644 0.835454
443443 −33.1876 −1.57679 −0.788395 0.615169i 0.789088π-0.789088\pi
−0.788395 + 0.615169i 0.789088π0.789088\pi
444444 0 0
445445 −11.5652 −0.548243
446446 −13.2705 −0.628375
447447 0 0
448448 2.86107 0.135173
449449 −33.4784 −1.57994 −0.789972 0.613144i 0.789905π-0.789905\pi
−0.789972 + 0.613144i 0.789905π0.789905\pi
450450 0 0
451451 3.59090 0.169089
452452 4.15551 0.195459
453453 0 0
454454 −8.11658 −0.380930
455455 −36.2436 −1.69913
456456 0 0
457457 15.5789 0.728750 0.364375 0.931252i 0.381283π-0.381283\pi
0.364375 + 0.931252i 0.381283π0.381283\pi
458458 −17.7272 −0.828338
459459 0 0
460460 −23.3742 −1.08983
461461 −19.6290 −0.914212 −0.457106 0.889412i 0.651114π-0.651114\pi
−0.457106 + 0.889412i 0.651114π0.651114\pi
462462 0 0
463463 26.0267 1.20956 0.604782 0.796391i 0.293260π-0.293260\pi
0.604782 + 0.796391i 0.293260π0.293260\pi
464464 5.81232 0.269830
465465 0 0
466466 9.99766 0.463132
467467 27.4418 1.26986 0.634929 0.772571i 0.281029π-0.281029\pi
0.634929 + 0.772571i 0.281029π0.281029\pi
468468 0 0
469469 1.06167 0.0490234
470470 25.8668 1.19314
471471 0 0
472472 1.56553 0.0720594
473473 −31.3507 −1.44151
474474 0 0
475475 52.5793 2.41251
476476 −13.8496 −0.634795
477477 0 0
478478 −16.5064 −0.754987
479479 −20.6312 −0.942662 −0.471331 0.881956i 0.656226π-0.656226\pi
−0.471331 + 0.881956i 0.656226π0.656226\pi
480480 0 0
481481 −3.62848 −0.165444
482482 −16.9919 −0.773959
483483 0 0
484484 18.5660 0.843910
485485 −44.8096 −2.03470
486486 0 0
487487 −1.04823 −0.0474997 −0.0237499 0.999718i 0.507561π-0.507561\pi
−0.0237499 + 0.999718i 0.507561π0.507561\pi
488488 −8.49269 −0.384446
489489 0 0
490490 4.13961 0.187009
491491 −33.0819 −1.49296 −0.746482 0.665406i 0.768259π-0.768259\pi
−0.746482 + 0.665406i 0.768259π0.768259\pi
492492 0 0
493493 −28.1357 −1.26717
494494 −26.5394 −1.19406
495495 0 0
496496 8.96928 0.402733
497497 1.67361 0.0750718
498498 0 0
499499 −6.65247 −0.297805 −0.148903 0.988852i 0.547574π-0.547574\pi
−0.148903 + 0.988852i 0.547574π0.547574\pi
500500 −7.64119 −0.341724
501501 0 0
502502 −22.2583 −0.993438
503503 −17.2357 −0.768500 −0.384250 0.923229i 0.625540π-0.625540\pi
−0.384250 + 0.923229i 0.625540π0.625540\pi
504504 0 0
505505 23.7594 1.05728
506506 −36.4045 −1.61838
507507 0 0
508508 −19.5394 −0.866922
509509 21.2969 0.943970 0.471985 0.881606i 0.343538π-0.343538\pi
0.471985 + 0.881606i 0.343538π0.343538\pi
510510 0 0
511511 −34.3106 −1.51781
512512 −1.00000 −0.0441942
513513 0 0
514514 7.59811 0.335138
515515 43.2794 1.90712
516516 0 0
517517 40.2866 1.77180
518518 2.86107 0.125708
519519 0 0
520520 12.6679 0.555522
521521 −20.1473 −0.882668 −0.441334 0.897343i 0.645495π-0.645495\pi
−0.441334 + 0.897343i 0.645495π0.645495\pi
522522 0 0
523523 −4.80666 −0.210181 −0.105090 0.994463i 0.533513π-0.533513\pi
−0.105090 + 0.994463i 0.533513π0.533513\pi
524524 −13.7848 −0.602193
525525 0 0
526526 27.5780 1.20246
527527 −43.4176 −1.89130
528528 0 0
529529 21.8246 0.948896
530530 −13.5792 −0.589842
531531 0 0
532532 20.9264 0.907274
533533 2.39625 0.103793
534534 0 0
535535 −0.504442 −0.0218089
536536 −0.371075 −0.0160280
537537 0 0
538538 −5.98578 −0.258065
539539 6.44729 0.277705
540540 0 0
541541 −19.3496 −0.831904 −0.415952 0.909386i 0.636552π-0.636552\pi
−0.415952 + 0.909386i 0.636552π0.636552\pi
542542 17.3044 0.743287
543543 0 0
544544 4.84071 0.207544
545545 −43.3918 −1.85870
546546 0 0
547547 23.5743 1.00796 0.503982 0.863714i 0.331868π-0.331868\pi
0.503982 + 0.863714i 0.331868π0.331868\pi
548548 17.1391 0.732146
549549 0 0
550550 −39.0882 −1.66673
551551 42.5124 1.81109
552552 0 0
553553 −11.8446 −0.503685
554554 4.11281 0.174737
555555 0 0
556556 −1.76011 −0.0746452
557557 13.9116 0.589453 0.294727 0.955582i 0.404771π-0.404771\pi
0.294727 + 0.955582i 0.404771π0.404771\pi
558558 0 0
559559 −20.9207 −0.884850
560560 −9.98865 −0.422097
561561 0 0
562562 5.24793 0.221370
563563 −39.4046 −1.66071 −0.830354 0.557236i 0.811862π-0.811862\pi
−0.830354 + 0.557236i 0.811862π0.811862\pi
564564 0 0
565565 −14.5078 −0.610349
566566 −1.87337 −0.0787436
567567 0 0
568568 −0.584961 −0.0245444
569569 −9.12190 −0.382410 −0.191205 0.981550i 0.561240π-0.561240\pi
−0.191205 + 0.981550i 0.561240π0.561240\pi
570570 0 0
571571 −20.3135 −0.850095 −0.425047 0.905171i 0.639743π-0.639743\pi
−0.425047 + 0.905171i 0.639743π0.639743\pi
572572 19.7297 0.824941
573573 0 0
574574 −1.88945 −0.0788641
575575 48.1291 2.00712
576576 0 0
577577 −11.2761 −0.469428 −0.234714 0.972064i 0.575415π-0.575415\pi
−0.234714 + 0.972064i 0.575415π0.575415\pi
578578 −6.43244 −0.267554
579579 0 0
580580 −20.2921 −0.842585
581581 −8.16451 −0.338721
582582 0 0
583583 −21.1491 −0.875906
584584 11.9922 0.496242
585585 0 0
586586 −8.40851 −0.347352
587587 48.2944 1.99333 0.996663 0.0816316i 0.0260131π-0.0260131\pi
0.996663 + 0.0816316i 0.0260131π0.0260131\pi
588588 0 0
589589 65.6030 2.70312
590590 −5.46563 −0.225016
591591 0 0
592592 −1.00000 −0.0410997
593593 9.83676 0.403947 0.201974 0.979391i 0.435264π-0.435264\pi
0.201974 + 0.979391i 0.435264π0.435264\pi
594594 0 0
595595 48.3521 1.98224
596596 −16.6486 −0.681954
597597 0 0
598598 −24.2931 −0.993419
599599 4.67625 0.191066 0.0955332 0.995426i 0.469544π-0.469544\pi
0.0955332 + 0.995426i 0.469544π0.469544\pi
600600 0 0
601601 −8.37334 −0.341556 −0.170778 0.985310i 0.554628π-0.554628\pi
−0.170778 + 0.985310i 0.554628π0.554628\pi
602602 16.4960 0.672327
603603 0 0
604604 5.70123 0.231980
605605 −64.8182 −2.63524
606606 0 0
607607 −38.4154 −1.55923 −0.779616 0.626258i 0.784586π-0.784586\pi
−0.779616 + 0.626258i 0.784586π0.784586\pi
608608 −7.31418 −0.296629
609609 0 0
610610 29.6499 1.20049
611611 26.8837 1.08760
612612 0 0
613613 18.6423 0.752955 0.376477 0.926426i 0.377135π-0.377135\pi
0.376477 + 0.926426i 0.377135π0.377135\pi
614614 −0.609988 −0.0246171
615615 0 0
616616 −15.5570 −0.626808
617617 15.6409 0.629678 0.314839 0.949145i 0.398050π-0.398050\pi
0.314839 + 0.949145i 0.398050π0.398050\pi
618618 0 0
619619 16.3358 0.656591 0.328296 0.944575i 0.393526π-0.393526\pi
0.328296 + 0.944575i 0.393526π0.393526\pi
620620 −31.3138 −1.25759
621621 0 0
622622 −2.93104 −0.117524
623623 9.47770 0.379716
624624 0 0
625625 −9.26626 −0.370650
626626 −13.6998 −0.547554
627627 0 0
628628 −21.7894 −0.869491
629629 4.84071 0.193012
630630 0 0
631631 26.0065 1.03530 0.517650 0.855592i 0.326807π-0.326807\pi
0.517650 + 0.855592i 0.326807π0.326807\pi
632632 4.13993 0.164677
633633 0 0
634634 −4.46543 −0.177345
635635 68.2166 2.70709
636636 0 0
637637 4.30235 0.170465
638638 −31.6043 −1.25123
639639 0 0
640640 3.49123 0.138003
641641 35.3060 1.39450 0.697251 0.716827i 0.254406π-0.254406\pi
0.697251 + 0.716827i 0.254406π0.254406\pi
642642 0 0
643643 45.2085 1.78285 0.891425 0.453167i 0.149706π-0.149706\pi
0.891425 + 0.453167i 0.149706π0.149706\pi
644644 19.1552 0.754820
645645 0 0
646646 35.4058 1.39302
647647 −7.32633 −0.288028 −0.144014 0.989576i 0.546001π-0.546001\pi
−0.144014 + 0.989576i 0.546001π0.546001\pi
648648 0 0
649649 −8.51252 −0.334146
650650 −26.0840 −1.02310
651651 0 0
652652 2.37983 0.0932013
653653 −23.2699 −0.910620 −0.455310 0.890333i 0.650472π-0.650472\pi
−0.455310 + 0.890333i 0.650472π0.650472\pi
654654 0 0
655655 48.1260 1.88044
656656 0.660400 0.0257843
657657 0 0
658658 −21.1979 −0.826379
659659 −24.7534 −0.964257 −0.482128 0.876101i 0.660136π-0.660136\pi
−0.482128 + 0.876101i 0.660136π0.660136\pi
660660 0 0
661661 −15.8312 −0.615763 −0.307881 0.951425i 0.599620π-0.599620\pi
−0.307881 + 0.951425i 0.599620π0.599620\pi
662662 30.0470 1.16781
663663 0 0
664664 2.85366 0.110743
665665 −73.0588 −2.83310
666666 0 0
667667 38.9142 1.50676
668668 −4.22401 −0.163432
669669 0 0
670670 1.29551 0.0500499
671671 46.1787 1.78271
672672 0 0
673673 10.2447 0.394903 0.197452 0.980313i 0.436733π-0.436733\pi
0.197452 + 0.980313i 0.436733π0.436733\pi
674674 −3.62683 −0.139700
675675 0 0
676676 0.165868 0.00637955
677677 25.9343 0.996735 0.498367 0.866966i 0.333933π-0.333933\pi
0.498367 + 0.866966i 0.333933π0.333933\pi
678678 0 0
679679 36.7215 1.40924
680680 −16.9000 −0.648086
681681 0 0
682682 −48.7701 −1.86750
683683 24.9994 0.956574 0.478287 0.878204i 0.341258π-0.341258\pi
0.478287 + 0.878204i 0.341258π0.341258\pi
684684 0 0
685685 −59.8366 −2.28624
686686 16.6351 0.635130
687687 0 0
688688 −5.76568 −0.219815
689689 −14.1130 −0.537664
690690 0 0
691691 −0.0335560 −0.00127653 −0.000638266 1.00000i 0.500203π-0.500203\pi
−0.000638266 1.00000i 0.500203π0.500203\pi
692692 3.83472 0.145774
693693 0 0
694694 −25.2388 −0.958053
695695 6.14494 0.233091
696696 0 0
697697 −3.19680 −0.121088
698698 −28.8966 −1.09375
699699 0 0
700700 20.5673 0.777372
701701 −9.20230 −0.347566 −0.173783 0.984784i 0.555599π-0.555599\pi
−0.173783 + 0.984784i 0.555599π0.555599\pi
702702 0 0
703703 −7.31418 −0.275860
704704 5.43746 0.204932
705705 0 0
706706 4.43635 0.166964
707707 −19.4709 −0.732279
708708 0 0
709709 −36.9470 −1.38758 −0.693788 0.720180i 0.744059π-0.744059\pi
−0.693788 + 0.720180i 0.744059π0.744059\pi
710710 2.04223 0.0766436
711711 0 0
712712 −3.31264 −0.124147
713713 60.0504 2.24890
714714 0 0
715715 −68.8810 −2.57600
716716 4.36893 0.163275
717717 0 0
718718 −22.3860 −0.835437
719719 18.1986 0.678695 0.339347 0.940661i 0.389794π-0.389794\pi
0.339347 + 0.940661i 0.389794π0.389794\pi
720720 0 0
721721 −35.4676 −1.32088
722722 −34.4973 −1.28386
723723 0 0
724724 −3.71793 −0.138176
725725 41.7829 1.55178
726726 0 0
727727 −40.9131 −1.51738 −0.758692 0.651450i 0.774161π-0.774161\pi
−0.758692 + 0.651450i 0.774161π0.774161\pi
728728 −10.3813 −0.384758
729729 0 0
730730 −41.8676 −1.54959
731731 27.9100 1.03229
732732 0 0
733733 31.2487 1.15420 0.577099 0.816674i 0.304185π-0.304185\pi
0.577099 + 0.816674i 0.304185π0.304185\pi
734734 10.4628 0.386188
735735 0 0
736736 −6.69512 −0.246785
737737 2.01771 0.0743232
738738 0 0
739739 53.2276 1.95801 0.979004 0.203841i 0.0653427π-0.0653427\pi
0.979004 + 0.203841i 0.0653427π0.0653427\pi
740740 3.49123 0.128340
741741 0 0
742742 11.1282 0.408528
743743 −14.3198 −0.525343 −0.262672 0.964885i 0.584604π-0.584604\pi
−0.262672 + 0.964885i 0.584604π0.584604\pi
744744 0 0
745745 58.1241 2.12950
746746 13.1068 0.479875
747747 0 0
748748 −26.3212 −0.962397
749749 0.413391 0.0151050
750750 0 0
751751 13.6154 0.496835 0.248417 0.968653i 0.420090π-0.420090\pi
0.248417 + 0.968653i 0.420090π0.420090\pi
752752 7.40907 0.270181
753753 0 0
754754 −21.0899 −0.768049
755755 −19.9043 −0.724392
756756 0 0
757757 −1.08985 −0.0396112 −0.0198056 0.999804i 0.506305π-0.506305\pi
−0.0198056 + 0.999804i 0.506305π0.506305\pi
758758 10.8284 0.393307
759759 0 0
760760 25.5355 0.926270
761761 −0.380018 −0.0137757 −0.00688783 0.999976i 0.502192π-0.502192\pi
−0.00688783 + 0.999976i 0.502192π0.502192\pi
762762 0 0
763763 35.5597 1.28735
764764 5.53343 0.200193
765765 0 0
766766 −23.3409 −0.843339
767767 −5.68050 −0.205111
768768 0 0
769769 −36.7259 −1.32437 −0.662185 0.749340i 0.730371π-0.730371\pi
−0.662185 + 0.749340i 0.730371π0.730371\pi
770770 54.3129 1.95730
771771 0 0
772772 −23.0916 −0.831084
773773 32.3346 1.16299 0.581497 0.813548i 0.302467π-0.302467\pi
0.581497 + 0.813548i 0.302467π0.302467\pi
774774 0 0
775775 64.4773 2.31609
776776 −12.8349 −0.460746
777777 0 0
778778 −10.9206 −0.391522
779779 4.83029 0.173063
780780 0 0
781781 3.18070 0.113815
782782 32.4091 1.15895
783783 0 0
784784 1.18572 0.0423470
785785 76.0717 2.71512
786786 0 0
787787 24.8290 0.885059 0.442529 0.896754i 0.354081π-0.354081\pi
0.442529 + 0.896754i 0.354081π0.354081\pi
788788 −14.5861 −0.519609
789789 0 0
790790 −14.4534 −0.514230
791791 11.8892 0.422731
792792 0 0
793793 30.8156 1.09429
794794 1.28277 0.0455239
795795 0 0
796796 19.8939 0.705121
797797 44.2527 1.56751 0.783756 0.621069i 0.213301π-0.213301\pi
0.783756 + 0.621069i 0.213301π0.213301\pi
798798 0 0
799799 −35.8651 −1.26882
800800 −7.18868 −0.254158
801801 0 0
802802 5.44679 0.192333
803803 −65.2073 −2.30111
804804 0 0
805805 −66.8752 −2.35704
806806 −32.5448 −1.14634
807807 0 0
808808 6.80546 0.239415
809809 46.5615 1.63701 0.818507 0.574497i 0.194802π-0.194802\pi
0.818507 + 0.574497i 0.194802π0.194802\pi
810810 0 0
811811 −43.6323 −1.53214 −0.766068 0.642759i 0.777789π-0.777789\pi
−0.766068 + 0.642759i 0.777789π0.777789\pi
812812 16.6295 0.583579
813813 0 0
814814 5.43746 0.190583
815815 −8.30852 −0.291035
816816 0 0
817817 −42.1713 −1.47539
818818 −4.04403 −0.141396
819819 0 0
820820 −2.30561 −0.0805153
821821 −25.5524 −0.891783 −0.445892 0.895087i 0.647113π-0.647113\pi
−0.445892 + 0.895087i 0.647113π0.647113\pi
822822 0 0
823823 −28.7281 −1.00140 −0.500699 0.865622i 0.666924π-0.666924\pi
−0.500699 + 0.865622i 0.666924π0.666924\pi
824824 12.3966 0.431857
825825 0 0
826826 4.47909 0.155848
827827 −10.3886 −0.361248 −0.180624 0.983552i 0.557812π-0.557812\pi
−0.180624 + 0.983552i 0.557812π0.557812\pi
828828 0 0
829829 −43.4017 −1.50740 −0.753702 0.657216i 0.771734π-0.771734\pi
−0.753702 + 0.657216i 0.771734π0.771734\pi
830830 −9.96277 −0.345813
831831 0 0
832832 3.62848 0.125795
833833 −5.73971 −0.198869
834834 0 0
835835 14.7470 0.510341
836836 39.7706 1.37550
837837 0 0
838838 −11.3722 −0.392847
839839 −43.9907 −1.51873 −0.759363 0.650667i 0.774489π-0.774489\pi
−0.759363 + 0.650667i 0.774489π0.774489\pi
840840 0 0
841841 4.78307 0.164934
842842 −36.4875 −1.25744
843843 0 0
844844 −19.4285 −0.668758
845845 −0.579084 −0.0199211
846846 0 0
847847 53.1187 1.82518
848848 −3.88952 −0.133567
849849 0 0
850850 34.7983 1.19357
851851 −6.69512 −0.229506
852852 0 0
853853 11.3844 0.389794 0.194897 0.980824i 0.437563π-0.437563\pi
0.194897 + 0.980824i 0.437563π0.437563\pi
854854 −24.2982 −0.831467
855855 0 0
856856 −0.144488 −0.00493851
857857 −20.7779 −0.709760 −0.354880 0.934912i 0.615478π-0.615478\pi
−0.354880 + 0.934912i 0.615478π0.615478\pi
858858 0 0
859859 −0.522296 −0.0178205 −0.00891025 0.999960i 0.502836π-0.502836\pi
−0.00891025 + 0.999960i 0.502836π0.502836\pi
860860 20.1293 0.686404
861861 0 0
862862 21.7781 0.741764
863863 −21.6000 −0.735273 −0.367637 0.929969i 0.619833π-0.619833\pi
−0.367637 + 0.929969i 0.619833π0.619833\pi
864864 0 0
865865 −13.3879 −0.455202
866866 −15.7500 −0.535207
867867 0 0
868868 25.6617 0.871016
869869 −22.5107 −0.763624
870870 0 0
871871 1.34644 0.0456223
872872 −12.4288 −0.420893
873873 0 0
874874 −48.9693 −1.65641
875875 −21.8620 −0.739070
876876 0 0
877877 −30.1710 −1.01880 −0.509401 0.860529i 0.670133π-0.670133\pi
−0.509401 + 0.860529i 0.670133π0.670133\pi
878878 29.8767 1.00829
879879 0 0
880880 −18.9834 −0.639931
881881 7.64922 0.257709 0.128854 0.991664i 0.458870π-0.458870\pi
0.128854 + 0.991664i 0.458870π0.458870\pi
882882 0 0
883883 −1.50660 −0.0507012 −0.0253506 0.999679i 0.508070π-0.508070\pi
−0.0253506 + 0.999679i 0.508070π0.508070\pi
884884 −17.5644 −0.590755
885885 0 0
886886 33.1876 1.11496
887887 −39.8124 −1.33677 −0.668385 0.743816i 0.733014π-0.733014\pi
−0.668385 + 0.743816i 0.733014π0.733014\pi
888888 0 0
889889 −55.9036 −1.87495
890890 11.5652 0.387666
891891 0 0
892892 13.2705 0.444328
893893 54.1913 1.81344
894894 0 0
895895 −15.2529 −0.509850
896896 −2.86107 −0.0955816
897897 0 0
898898 33.4784 1.11719
899899 52.1323 1.73871
900900 0 0
901901 18.8280 0.627252
902902 −3.59090 −0.119564
903903 0 0
904904 −4.15551 −0.138210
905905 12.9802 0.431475
906906 0 0
907907 −9.53619 −0.316644 −0.158322 0.987388i 0.550608π-0.550608\pi
−0.158322 + 0.987388i 0.550608π0.550608\pi
908908 8.11658 0.269358
909909 0 0
910910 36.2436 1.20146
911911 5.26468 0.174427 0.0872133 0.996190i 0.472204π-0.472204\pi
0.0872133 + 0.996190i 0.472204π0.472204\pi
912912 0 0
913913 −15.5167 −0.513526
914914 −15.5789 −0.515304
915915 0 0
916916 17.7272 0.585723
917917 −39.4393 −1.30240
918918 0 0
919919 −37.6756 −1.24280 −0.621401 0.783492i 0.713436π-0.713436\pi
−0.621401 + 0.783492i 0.713436π0.713436\pi
920920 23.3742 0.770624
921921 0 0
922922 19.6290 0.646445
923923 2.12252 0.0698636
924924 0 0
925925 −7.18868 −0.236362
926926 −26.0267 −0.855291
927927 0 0
928928 −5.81232 −0.190799
929929 2.88639 0.0946995 0.0473497 0.998878i 0.484922π-0.484922\pi
0.0473497 + 0.998878i 0.484922π0.484922\pi
930930 0 0
931931 8.67255 0.284231
932932 −9.99766 −0.327484
933933 0 0
934934 −27.4418 −0.897925
935935 91.8932 3.00523
936936 0 0
937937 23.2591 0.759842 0.379921 0.925019i 0.375951π-0.375951\pi
0.379921 + 0.925019i 0.375951π0.375951\pi
938938 −1.06167 −0.0346648
939939 0 0
940940 −25.8668 −0.843681
941941 26.7089 0.870686 0.435343 0.900265i 0.356627π-0.356627\pi
0.435343 + 0.900265i 0.356627π0.356627\pi
942942 0 0
943943 4.42146 0.143982
944944 −1.56553 −0.0509537
945945 0 0
946946 31.3507 1.01930
947947 54.1066 1.75823 0.879115 0.476610i 0.158135π-0.158135\pi
0.879115 + 0.476610i 0.158135π0.158135\pi
948948 0 0
949949 −43.5135 −1.41251
950950 −52.5793 −1.70590
951951 0 0
952952 13.8496 0.448868
953953 35.2174 1.14080 0.570402 0.821366i 0.306787π-0.306787\pi
0.570402 + 0.821366i 0.306787π0.306787\pi
954954 0 0
955955 −19.3185 −0.625131
956956 16.5064 0.533856
957957 0 0
958958 20.6312 0.666563
959959 49.0362 1.58346
960960 0 0
961961 49.4480 1.59510
962962 3.62848 0.116987
963963 0 0
964964 16.9919 0.547272
965965 80.6180 2.59518
966966 0 0
967967 −14.2979 −0.459790 −0.229895 0.973215i 0.573838π-0.573838\pi
−0.229895 + 0.973215i 0.573838π0.573838\pi
968968 −18.5660 −0.596734
969969 0 0
970970 44.8096 1.43875
971971 10.0236 0.321672 0.160836 0.986981i 0.448581π-0.448581\pi
0.160836 + 0.986981i 0.448581π0.448581\pi
972972 0 0
973973 −5.03579 −0.161440
974974 1.04823 0.0335874
975975 0 0
976976 8.49269 0.271845
977977 −0.00109169 −3.49262e−5 0 −1.74631e−5 1.00000i 0.500006π-0.500006\pi
−1.74631e−5 1.00000i 0.500006π0.500006\pi
978978 0 0
979979 18.0124 0.575678
980980 −4.13961 −0.132235
981981 0 0
982982 33.0819 1.05568
983983 28.0299 0.894016 0.447008 0.894530i 0.352490π-0.352490\pi
0.447008 + 0.894530i 0.352490π0.352490\pi
984984 0 0
985985 50.9235 1.62256
986986 28.1357 0.896025
987987 0 0
988988 26.5394 0.844330
989989 −38.6019 −1.22747
990990 0 0
991991 −25.5039 −0.810157 −0.405078 0.914282i 0.632756π-0.632756\pi
−0.405078 + 0.914282i 0.632756π0.632756\pi
992992 −8.96928 −0.284775
993993 0 0
994994 −1.67361 −0.0530838
995995 −69.4542 −2.20185
996996 0 0
997997 −43.2073 −1.36839 −0.684195 0.729300i 0.739846π-0.739846\pi
−0.684195 + 0.729300i 0.739846π0.739846\pi
998998 6.65247 0.210580
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 5994.2.a.ba.1.2 10
3.2 odd 2 5994.2.a.bb.1.9 10
9.2 odd 6 666.2.e.e.445.8 yes 20
9.4 even 3 1998.2.e.e.667.9 20
9.5 odd 6 666.2.e.e.223.8 20
9.7 even 3 1998.2.e.e.1333.9 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
666.2.e.e.223.8 20 9.5 odd 6
666.2.e.e.445.8 yes 20 9.2 odd 6
1998.2.e.e.667.9 20 9.4 even 3
1998.2.e.e.1333.9 20 9.7 even 3
5994.2.a.ba.1.2 10 1.1 even 1 trivial
5994.2.a.bb.1.9 10 3.2 odd 2