Properties

Label 800.3.m.b.657.6
Level 800800
Weight 33
Character 800.657
Analytic conductor 21.79821.798
Analytic rank 00
Dimension 2020
Inner twists 44

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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] = [800,3,Mod(593,800)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(800, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 3])) N = Newforms(chi, 3, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("800.593"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: N N == 800=2552 800 = 2^{5} \cdot 5^{2}
Weight: k k == 3 3
Character orbit: [χ][\chi] == 800.m (of order 44, degree 22, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 21.798421148821.7984211488
Analytic rank: 00
Dimension: 2020
Relative dimension: 1010 over Q(i)\Q(i)
Coefficient field: Q[x]/(x20)\mathbb{Q}[x]/(x^{20} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x20x183x16+11x14+x1240x10+4x8+176x6192x4256x2+1024 x^{20} - x^{18} - 3x^{16} + 11x^{14} + x^{12} - 40x^{10} + 4x^{8} + 176x^{6} - 192x^{4} - 256x^{2} + 1024 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 236 2^{36}
Twist minimal: no (minimal twist has level 40)
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 657.6
Root 0.5418281.30630i0.541828 - 1.30630i of defining polynomial
Character χ\chi == 800.657
Dual form 800.3.m.b.593.6

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+(0.130791+0.130791i)q3+(1.597131.59713i)q78.96579iq911.9427iq11+(9.59714+9.59714i)q13+(0.8572880.857288i)q1720.5611q190.417782iq21+(22.1560+22.1560i)q23+(2.349772.34977i)q27+27.3404q2940.0267q31+(1.562001.56200i)q33+(1.57131+1.57131i)q37+2.51044iq3937.5504q41+(49.260249.2602i)q43+(34.087634.0876i)q4743.8983iq490.224252iq51+(28.800228.8002i)q53+(2.689212.68921i)q57+92.7071q594.82618iq61+(14.3196+14.3196i)q63+(54.604854.6048i)q675.79564q6959.2198q71+(34.1124+34.1124i)q73+(19.0740+19.0740i)q7796.2455iq7980.0774q81+(63.6959+63.6959i)q83+(3.57588+3.57588i)q87+3.68406iq8930.6558iq91+(5.235145.23514i)q93+(46.041046.0410i)q97107.075q99+O(q100)q+(0.130791 + 0.130791i) q^{3} +(-1.59713 - 1.59713i) q^{7} -8.96579i q^{9} -11.9427i q^{11} +(9.59714 + 9.59714i) q^{13} +(-0.857288 - 0.857288i) q^{17} -20.5611 q^{19} -0.417782i q^{21} +(-22.1560 + 22.1560i) q^{23} +(2.34977 - 2.34977i) q^{27} +27.3404 q^{29} -40.0267 q^{31} +(1.56200 - 1.56200i) q^{33} +(-1.57131 + 1.57131i) q^{37} +2.51044i q^{39} -37.5504 q^{41} +(-49.2602 - 49.2602i) q^{43} +(-34.0876 - 34.0876i) q^{47} -43.8983i q^{49} -0.224252i q^{51} +(-28.8002 - 28.8002i) q^{53} +(-2.68921 - 2.68921i) q^{57} +92.7071 q^{59} -4.82618i q^{61} +(-14.3196 + 14.3196i) q^{63} +(54.6048 - 54.6048i) q^{67} -5.79564 q^{69} -59.2198 q^{71} +(-34.1124 + 34.1124i) q^{73} +(-19.0740 + 19.0740i) q^{77} -96.2455i q^{79} -80.0774 q^{81} +(63.6959 + 63.6959i) q^{83} +(3.57588 + 3.57588i) q^{87} +3.68406i q^{89} -30.6558i q^{91} +(-5.23514 - 5.23514i) q^{93} +(-46.0410 - 46.0410i) q^{97} -107.075 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q4q7+12q174q23+136q3132q338q41+188q47+40q57+228q63248q71+124q73+132q81488q87100q97+O(q100) 20 q - 4 q^{7} + 12 q^{17} - 4 q^{23} + 136 q^{31} - 32 q^{33} - 8 q^{41} + 188 q^{47} + 40 q^{57} + 228 q^{63} - 248 q^{71} + 124 q^{73} + 132 q^{81} - 488 q^{87} - 100 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/800Z)×\left(\mathbb{Z}/800\mathbb{Z}\right)^\times.

nn 101101 351351 577577
χ(n)\chi(n) 1-1 11 e(14)e\left(\frac{1}{4}\right)

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 0 0
33 0.130791 + 0.130791i 0.0435971 + 0.0435971i 0.728569 0.684972i 0.240186π-0.240186\pi
−0.684972 + 0.728569i 0.740186π0.740186\pi
44 0 0
55 0 0
66 0 0
77 −1.59713 1.59713i −0.228162 0.228162i 0.583763 0.811924i 0.301580π-0.301580\pi
−0.811924 + 0.583763i 0.801580π0.801580\pi
88 0 0
99 8.96579i 0.996199i
1010 0 0
1111 11.9427i 1.08570i −0.839831 0.542849i 0.817346π-0.817346\pi
0.839831 0.542849i 0.182654π-0.182654\pi
1212 0 0
1313 9.59714 + 9.59714i 0.738241 + 0.738241i 0.972238 0.233996i 0.0751803π-0.0751803\pi
−0.233996 + 0.972238i 0.575180π0.575180\pi
1414 0 0
1515 0 0
1616 0 0
1717 −0.857288 0.857288i −0.0504287 0.0504287i 0.681443 0.731871i 0.261353π-0.261353\pi
−0.731871 + 0.681443i 0.761353π0.761353\pi
1818 0 0
1919 −20.5611 −1.08216 −0.541082 0.840970i 0.681985π-0.681985\pi
−0.541082 + 0.840970i 0.681985π0.681985\pi
2020 0 0
2121 0.417782i 0.0198944i
2222 0 0
2323 −22.1560 + 22.1560i −0.963306 + 0.963306i −0.999350 0.0360441i 0.988524π-0.988524\pi
0.0360441 + 0.999350i 0.488524π0.488524\pi
2424 0 0
2525 0 0
2626 0 0
2727 2.34977 2.34977i 0.0870285 0.0870285i
2828 0 0
2929 27.3404 0.942771 0.471385 0.881927i 0.343754π-0.343754\pi
0.471385 + 0.881927i 0.343754π0.343754\pi
3030 0 0
3131 −40.0267 −1.29118 −0.645591 0.763683i 0.723389π-0.723389\pi
−0.645591 + 0.763683i 0.723389π0.723389\pi
3232 0 0
3333 1.56200 1.56200i 0.0473333 0.0473333i
3434 0 0
3535 0 0
3636 0 0
3737 −1.57131 + 1.57131i −0.0424677 + 0.0424677i −0.728022 0.685554i 0.759560π-0.759560\pi
0.685554 + 0.728022i 0.259560π0.259560\pi
3838 0 0
3939 2.51044i 0.0643704i
4040 0 0
4141 −37.5504 −0.915864 −0.457932 0.888987i 0.651410π-0.651410\pi
−0.457932 + 0.888987i 0.651410π0.651410\pi
4242 0 0
4343 −49.2602 49.2602i −1.14558 1.14558i −0.987411 0.158174i 0.949439π-0.949439\pi
−0.158174 0.987411i 0.550561π-0.550561\pi
4444 0 0
4545 0 0
4646 0 0
4747 −34.0876 34.0876i −0.725268 0.725268i 0.244405 0.969673i 0.421407π-0.421407\pi
−0.969673 + 0.244405i 0.921407π0.921407\pi
4848 0 0
4949 43.8983i 0.895884i
5050 0 0
5151 0.224252i 0.00439709i
5252 0 0
5353 −28.8002 28.8002i −0.543401 0.543401i 0.381124 0.924524i 0.375537π-0.375537\pi
−0.924524 + 0.381124i 0.875537π0.875537\pi
5454 0 0
5555 0 0
5656 0 0
5757 −2.68921 2.68921i −0.0471792 0.0471792i
5858 0 0
5959 92.7071 1.57131 0.785653 0.618667i 0.212327π-0.212327\pi
0.785653 + 0.618667i 0.212327π0.212327\pi
6060 0 0
6161 4.82618i 0.0791176i −0.999217 0.0395588i 0.987405π-0.987405\pi
0.999217 0.0395588i 0.0125952π-0.0125952\pi
6262 0 0
6363 −14.3196 + 14.3196i −0.227294 + 0.227294i
6464 0 0
6565 0 0
6666 0 0
6767 54.6048 54.6048i 0.814997 0.814997i −0.170381 0.985378i 0.554500π-0.554500\pi
0.985378 + 0.170381i 0.0544998π0.0544998\pi
6868 0 0
6969 −5.79564 −0.0839947
7070 0 0
7171 −59.2198 −0.834082 −0.417041 0.908888i 0.636933π-0.636933\pi
−0.417041 + 0.908888i 0.636933π0.636933\pi
7272 0 0
7373 −34.1124 + 34.1124i −0.467293 + 0.467293i −0.901037 0.433743i 0.857193π-0.857193\pi
0.433743 + 0.901037i 0.357193π0.357193\pi
7474 0 0
7575 0 0
7676 0 0
7777 −19.0740 + 19.0740i −0.247715 + 0.247715i
7878 0 0
7979 96.2455i 1.21830i −0.793056 0.609149i 0.791511π-0.791511\pi
0.793056 0.609149i 0.208489π-0.208489\pi
8080 0 0
8181 −80.0774 −0.988610
8282 0 0
8383 63.6959 + 63.6959i 0.767421 + 0.767421i 0.977652 0.210231i 0.0674216π-0.0674216\pi
−0.210231 + 0.977652i 0.567422π0.567422\pi
8484 0 0
8585 0 0
8686 0 0
8787 3.57588 + 3.57588i 0.0411021 + 0.0411021i
8888 0 0
8989 3.68406i 0.0413939i 0.999786 + 0.0206970i 0.00658852π0.00658852\pi
−0.999786 + 0.0206970i 0.993411π0.993411\pi
9090 0 0
9191 30.6558i 0.336877i
9292 0 0
9393 −5.23514 5.23514i −0.0562918 0.0562918i
9494 0 0
9595 0 0
9696 0 0
9797 −46.0410 46.0410i −0.474650 0.474650i 0.428766 0.903416i 0.358949π-0.358949\pi
−0.903416 + 0.428766i 0.858949π0.858949\pi
9898 0 0
9999 −107.075 −1.08157
100100 0 0
101101 108.173i 1.07102i −0.844529 0.535510i 0.820120π-0.820120\pi
0.844529 0.535510i 0.179880π-0.179880\pi
102102 0 0
103103 −50.9112 + 50.9112i −0.494284 + 0.494284i −0.909653 0.415369i 0.863652π-0.863652\pi
0.415369 + 0.909653i 0.363652π0.363652\pi
104104 0 0
105105 0 0
106106 0 0
107107 −95.4147 + 95.4147i −0.891726 + 0.891726i −0.994686 0.102960i 0.967169π-0.967169\pi
0.102960 + 0.994686i 0.467169π0.467169\pi
108108 0 0
109109 −46.5432 −0.427002 −0.213501 0.976943i 0.568487π-0.568487\pi
−0.213501 + 0.976943i 0.568487π0.568487\pi
110110 0 0
111111 −0.411026 −0.00370294
112112 0 0
113113 −88.0400 + 88.0400i −0.779115 + 0.779115i −0.979680 0.200565i 0.935722π-0.935722\pi
0.200565 + 0.979680i 0.435722π0.435722\pi
114114 0 0
115115 0 0
116116 0 0
117117 86.0459 86.0459i 0.735435 0.735435i
118118 0 0
119119 2.73841i 0.0230118i
120120 0 0
121121 −21.6274 −0.178739
122122 0 0
123123 −4.91127 4.91127i −0.0399290 0.0399290i
124124 0 0
125125 0 0
126126 0 0
127127 44.3246 + 44.3246i 0.349012 + 0.349012i 0.859742 0.510729i 0.170625π-0.170625\pi
−0.510729 + 0.859742i 0.670625π0.670625\pi
128128 0 0
129129 12.8856i 0.0998884i
130130 0 0
131131 82.8025i 0.632080i −0.948746 0.316040i 0.897647π-0.897647\pi
0.948746 0.316040i 0.102353π-0.102353\pi
132132 0 0
133133 32.8388 + 32.8388i 0.246908 + 0.246908i
134134 0 0
135135 0 0
136136 0 0
137137 −25.0030 25.0030i −0.182503 0.182503i 0.609942 0.792446i 0.291193π-0.291193\pi
−0.792446 + 0.609942i 0.791193π0.791193\pi
138138 0 0
139139 104.684 0.753121 0.376561 0.926392i 0.377107π-0.377107\pi
0.376561 + 0.926392i 0.377107π0.377107\pi
140140 0 0
141141 8.91673i 0.0632392i
142142 0 0
143143 114.615 114.615i 0.801507 0.801507i
144144 0 0
145145 0 0
146146 0 0
147147 5.74152 5.74152i 0.0390580 0.0390580i
148148 0 0
149149 49.3481 0.331196 0.165598 0.986193i 0.447045π-0.447045\pi
0.165598 + 0.986193i 0.447045π0.447045\pi
150150 0 0
151151 22.1078 0.146409 0.0732047 0.997317i 0.476677π-0.476677\pi
0.0732047 + 0.997317i 0.476677π0.476677\pi
152152 0 0
153153 −7.68626 + 7.68626i −0.0502370 + 0.0502370i
154154 0 0
155155 0 0
156156 0 0
157157 64.7264 64.7264i 0.412270 0.412270i −0.470258 0.882529i 0.655839π-0.655839\pi
0.882529 + 0.470258i 0.155839π0.155839\pi
158158 0 0
159159 7.53364i 0.0473814i
160160 0 0
161161 70.7723 0.439579
162162 0 0
163163 25.7888 + 25.7888i 0.158213 + 0.158213i 0.781775 0.623561i 0.214315π-0.214315\pi
−0.623561 + 0.781775i 0.714315π0.714315\pi
164164 0 0
165165 0 0
166166 0 0
167167 −56.4754 56.4754i −0.338176 0.338176i 0.517504 0.855681i 0.326861π-0.326861\pi
−0.855681 + 0.517504i 0.826861π0.826861\pi
168168 0 0
169169 15.2101i 0.0900005i
170170 0 0
171171 184.346i 1.07805i
172172 0 0
173173 −135.496 135.496i −0.783216 0.783216i 0.197156 0.980372i 0.436829π-0.436829\pi
−0.980372 + 0.197156i 0.936829π0.936829\pi
174174 0 0
175175 0 0
176176 0 0
177177 12.1253 + 12.1253i 0.0685044 + 0.0685044i
178178 0 0
179179 −15.5036 −0.0866121 −0.0433061 0.999062i 0.513789π-0.513789\pi
−0.0433061 + 0.999062i 0.513789π0.513789\pi
180180 0 0
181181 263.672i 1.45675i 0.685179 + 0.728375i 0.259724π0.259724\pi
−0.685179 + 0.728375i 0.740276π0.740276\pi
182182 0 0
183183 0.631222 0.631222i 0.00344930 0.00344930i
184184 0 0
185185 0 0
186186 0 0
187187 −10.2383 + 10.2383i −0.0547503 + 0.0547503i
188188 0 0
189189 −7.50579 −0.0397132
190190 0 0
191191 120.714 0.632010 0.316005 0.948758i 0.397658π-0.397658\pi
0.316005 + 0.948758i 0.397658π0.397658\pi
192192 0 0
193193 182.404 182.404i 0.945098 0.945098i −0.0534716 0.998569i 0.517029π-0.517029\pi
0.998569 + 0.0534716i 0.0170287π0.0170287\pi
194194 0 0
195195 0 0
196196 0 0
197197 −224.288 + 224.288i −1.13852 + 1.13852i −0.149799 + 0.988716i 0.547863π0.547863\pi
−0.988716 + 0.149799i 0.952137π0.952137\pi
198198 0 0
199199 87.9089i 0.441753i 0.975302 + 0.220877i 0.0708918π0.0708918\pi
−0.975302 + 0.220877i 0.929108π0.929108\pi
200200 0 0
201201 14.2837 0.0710631
202202 0 0
203203 −43.6662 43.6662i −0.215104 0.215104i
204204 0 0
205205 0 0
206206 0 0
207207 198.646 + 198.646i 0.959644 + 0.959644i
208208 0 0
209209 245.554i 1.17490i
210210 0 0
211211 119.117i 0.564534i 0.959336 + 0.282267i 0.0910864π0.0910864\pi
−0.959336 + 0.282267i 0.908914π0.908914\pi
212212 0 0
213213 −7.74544 7.74544i −0.0363636 0.0363636i
214214 0 0
215215 0 0
216216 0 0
217217 63.9279 + 63.9279i 0.294599 + 0.294599i
218218 0 0
219219 −8.92322 −0.0407453
220220 0 0
221221 16.4550i 0.0744571i
222222 0 0
223223 111.993 111.993i 0.502212 0.502212i −0.409913 0.912125i 0.634441π-0.634441\pi
0.912125 + 0.409913i 0.134441π0.134441\pi
224224 0 0
225225 0 0
226226 0 0
227227 85.8837 85.8837i 0.378342 0.378342i −0.492162 0.870504i 0.663793π-0.663793\pi
0.870504 + 0.492162i 0.163793π0.163793\pi
228228 0 0
229229 −26.5156 −0.115789 −0.0578943 0.998323i 0.518439π-0.518439\pi
−0.0578943 + 0.998323i 0.518439π0.518439\pi
230230 0 0
231231 −4.98944 −0.0215993
232232 0 0
233233 71.6569 71.6569i 0.307541 0.307541i −0.536414 0.843955i 0.680222π-0.680222\pi
0.843955 + 0.536414i 0.180222π0.180222\pi
234234 0 0
235235 0 0
236236 0 0
237237 12.5881 12.5881i 0.0531143 0.0531143i
238238 0 0
239239 114.913i 0.480809i 0.970673 + 0.240405i 0.0772801π0.0772801\pi
−0.970673 + 0.240405i 0.922720π0.922720\pi
240240 0 0
241241 219.080 0.909045 0.454522 0.890735i 0.349810π-0.349810\pi
0.454522 + 0.890735i 0.349810π0.349810\pi
242242 0 0
243243 −31.6214 31.6214i −0.130129 0.130129i
244244 0 0
245245 0 0
246246 0 0
247247 −197.328 197.328i −0.798897 0.798897i
248248 0 0
249249 16.6618i 0.0669147i
250250 0 0
251251 95.0552i 0.378706i −0.981909 0.189353i 0.939361π-0.939361\pi
0.981909 0.189353i 0.0606390π-0.0606390\pi
252252 0 0
253253 264.602 + 264.602i 1.04586 + 1.04586i
254254 0 0
255255 0 0
256256 0 0
257257 249.128 + 249.128i 0.969369 + 0.969369i 0.999545 0.0301755i 0.00960661π-0.00960661\pi
−0.0301755 + 0.999545i 0.509607π0.509607\pi
258258 0 0
259259 5.01917 0.0193790
260260 0 0
261261 245.128i 0.939187i
262262 0 0
263263 −85.6095 + 85.6095i −0.325511 + 0.325511i −0.850877 0.525365i 0.823929π-0.823929\pi
0.525365 + 0.850877i 0.323929π0.323929\pi
264264 0 0
265265 0 0
266266 0 0
267267 −0.481843 + 0.481843i −0.00180465 + 0.00180465i
268268 0 0
269269 −192.119 −0.714196 −0.357098 0.934067i 0.616234π-0.616234\pi
−0.357098 + 0.934067i 0.616234π0.616234\pi
270270 0 0
271271 485.780 1.79255 0.896274 0.443501i 0.146264π-0.146264\pi
0.896274 + 0.443501i 0.146264π0.146264\pi
272272 0 0
273273 4.00951 4.00951i 0.0146869 0.0146869i
274274 0 0
275275 0 0
276276 0 0
277277 88.8551 88.8551i 0.320777 0.320777i −0.528288 0.849065i 0.677166π-0.677166\pi
0.849065 + 0.528288i 0.177166π0.177166\pi
278278 0 0
279279 358.871i 1.28627i
280280 0 0
281281 390.006 1.38792 0.693961 0.720012i 0.255864π-0.255864\pi
0.693961 + 0.720012i 0.255864π0.255864\pi
282282 0 0
283283 121.062 + 121.062i 0.427779 + 0.427779i 0.887871 0.460092i 0.152184π-0.152184\pi
−0.460092 + 0.887871i 0.652184π0.652184\pi
284284 0 0
285285 0 0
286286 0 0
287287 59.9730 + 59.9730i 0.208965 + 0.208965i
288288 0 0
289289 287.530i 0.994914i
290290 0 0
291291 12.0435i 0.0413867i
292292 0 0
293293 244.956 + 244.956i 0.836026 + 0.836026i 0.988333 0.152307i 0.0486702π-0.0486702\pi
−0.152307 + 0.988333i 0.548670π0.548670\pi
294294 0 0
295295 0 0
296296 0 0
297297 −28.0625 28.0625i −0.0944866 0.0944866i
298298 0 0
299299 −425.269 −1.42230
300300 0 0
301301 157.350i 0.522757i
302302 0 0
303303 14.1481 14.1481i 0.0466934 0.0466934i
304304 0 0
305305 0 0
306306 0 0
307307 −135.324 + 135.324i −0.440796 + 0.440796i −0.892280 0.451483i 0.850895π-0.850895\pi
0.451483 + 0.892280i 0.350895π0.350895\pi
308308 0 0
309309 −13.3175 −0.0430987
310310 0 0
311311 −225.951 −0.726531 −0.363266 0.931686i 0.618338π-0.618338\pi
−0.363266 + 0.931686i 0.618338π0.618338\pi
312312 0 0
313313 230.622 230.622i 0.736812 0.736812i −0.235148 0.971960i 0.575557π-0.575557\pi
0.971960 + 0.235148i 0.0755575π0.0755575\pi
314314 0 0
315315 0 0
316316 0 0
317317 −221.563 + 221.563i −0.698938 + 0.698938i −0.964182 0.265243i 0.914548π-0.914548\pi
0.265243 + 0.964182i 0.414548π0.414548\pi
318318 0 0
319319 326.517i 1.02356i
320320 0 0
321321 −24.9588 −0.0777534
322322 0 0
323323 17.6268 + 17.6268i 0.0545721 + 0.0545721i
324324 0 0
325325 0 0
326326 0 0
327327 −6.08745 6.08745i −0.0186161 0.0186161i
328328 0 0
329329 108.885i 0.330957i
330330 0 0
331331 141.212i 0.426624i −0.976984 0.213312i 0.931575π-0.931575\pi
0.976984 0.213312i 0.0684250π-0.0684250\pi
332332 0 0
333333 14.0880 + 14.0880i 0.0423063 + 0.0423063i
334334 0 0
335335 0 0
336336 0 0
337337 −225.465 225.465i −0.669035 0.669035i 0.288458 0.957493i 0.406858π-0.406858\pi
−0.957493 + 0.288458i 0.906858π0.906858\pi
338338 0 0
339339 −23.0297 −0.0679343
340340 0 0
341341 478.025i 1.40183i
342342 0 0
343343 −148.371 + 148.371i −0.432568 + 0.432568i
344344 0 0
345345 0 0
346346 0 0
347347 346.013 346.013i 0.997155 0.997155i −0.00284067 0.999996i 0.500904π-0.500904\pi
0.999996 + 0.00284067i 0.000904214π0.000904214\pi
348348 0 0
349349 428.411 1.22754 0.613769 0.789486i 0.289653π-0.289653\pi
0.613769 + 0.789486i 0.289653π0.289653\pi
350350 0 0
351351 45.1021 0.128496
352352 0 0
353353 −25.9724 + 25.9724i −0.0735762 + 0.0735762i −0.742937 0.669361i 0.766568π-0.766568\pi
0.669361 + 0.742937i 0.266568π0.266568\pi
354354 0 0
355355 0 0
356356 0 0
357357 −0.358160 + 0.358160i −0.00100325 + 0.00100325i
358358 0 0
359359 288.043i 0.802348i 0.916002 + 0.401174i 0.131398π0.131398\pi
−0.916002 + 0.401174i 0.868602π0.868602\pi
360360 0 0
361361 61.7587 0.171077
362362 0 0
363363 −2.82868 2.82868i −0.00779249 0.00779249i
364364 0 0
365365 0 0
366366 0 0
367367 160.854 + 160.854i 0.438295 + 0.438295i 0.891438 0.453143i 0.149697π-0.149697\pi
−0.453143 + 0.891438i 0.649697π0.649697\pi
368368 0 0
369369 336.669i 0.912382i
370370 0 0
371371 91.9956i 0.247966i
372372 0 0
373373 −360.121 360.121i −0.965471 0.965471i 0.0339529 0.999423i 0.489190π-0.489190\pi
−0.999423 + 0.0339529i 0.989190π0.989190\pi
374374 0 0
375375 0 0
376376 0 0
377377 262.389 + 262.389i 0.695992 + 0.695992i
378378 0 0
379379 −64.1572 −0.169280 −0.0846402 0.996412i 0.526974π-0.526974\pi
−0.0846402 + 0.996412i 0.526974π0.526974\pi
380380 0 0
381381 11.5945i 0.0304319i
382382 0 0
383383 376.877 376.877i 0.984014 0.984014i −0.0158604 0.999874i 0.505049π-0.505049\pi
0.999874 + 0.0158604i 0.00504875π0.00504875\pi
384384 0 0
385385 0 0
386386 0 0
387387 −441.656 + 441.656i −1.14123 + 1.14123i
388388 0 0
389389 −10.3794 −0.0266823 −0.0133411 0.999911i 0.504247π-0.504247\pi
−0.0133411 + 0.999911i 0.504247π0.504247\pi
390390 0 0
391391 37.9882 0.0971566
392392 0 0
393393 10.8298 10.8298i 0.0275569 0.0275569i
394394 0 0
395395 0 0
396396 0 0
397397 184.458 184.458i 0.464630 0.464630i −0.435540 0.900169i 0.643442π-0.643442\pi
0.900169 + 0.435540i 0.143442π0.143442\pi
398398 0 0
399399 8.59006i 0.0215290i
400400 0 0
401401 −262.943 −0.655719 −0.327859 0.944727i 0.606327π-0.606327\pi
−0.327859 + 0.944727i 0.606327π0.606327\pi
402402 0 0
403403 −384.141 384.141i −0.953204 0.953204i
404404 0 0
405405 0 0
406406 0 0
407407 18.7656 + 18.7656i 0.0461071 + 0.0461071i
408408 0 0
409409 245.618i 0.600532i −0.953855 0.300266i 0.902925π-0.902925\pi
0.953855 0.300266i 0.0970755π-0.0970755\pi
410410 0 0
411411 6.54034i 0.0159132i
412412 0 0
413413 −148.065 148.065i −0.358512 0.358512i
414414 0 0
415415 0 0
416416 0 0
417417 13.6917 + 13.6917i 0.0328339 + 0.0328339i
418418 0 0
419419 673.011 1.60623 0.803116 0.595823i 0.203174π-0.203174\pi
0.803116 + 0.595823i 0.203174π0.203174\pi
420420 0 0
421421 701.227i 1.66562i −0.553557 0.832811i 0.686730π-0.686730\pi
0.553557 0.832811i 0.313270π-0.313270\pi
422422 0 0
423423 −305.622 + 305.622i −0.722511 + 0.722511i
424424 0 0
425425 0 0
426426 0 0
427427 −7.70804 + 7.70804i −0.0180516 + 0.0180516i
428428 0 0
429429 29.9814 0.0698868
430430 0 0
431431 −405.559 −0.940973 −0.470486 0.882407i 0.655922π-0.655922\pi
−0.470486 + 0.882407i 0.655922π0.655922\pi
432432 0 0
433433 −145.764 + 145.764i −0.336638 + 0.336638i −0.855100 0.518462i 0.826505π-0.826505\pi
0.518462 + 0.855100i 0.326505π0.326505\pi
434434 0 0
435435 0 0
436436 0 0
437437 455.553 455.553i 1.04245 1.04245i
438438 0 0
439439 62.3888i 0.142116i −0.997472 0.0710579i 0.977362π-0.977362\pi
0.997472 0.0710579i 0.0226375π-0.0226375\pi
440440 0 0
441441 −393.583 −0.892479
442442 0 0
443443 169.632 + 169.632i 0.382918 + 0.382918i 0.872152 0.489235i 0.162724π-0.162724\pi
−0.489235 + 0.872152i 0.662724π0.662724\pi
444444 0 0
445445 0 0
446446 0 0
447447 6.45431 + 6.45431i 0.0144392 + 0.0144392i
448448 0 0
449449 17.0056i 0.0378743i 0.999821 + 0.0189371i 0.00602824π0.00602824\pi
−0.999821 + 0.0189371i 0.993972π0.993972\pi
450450 0 0
451451 448.452i 0.994351i
452452 0 0
453453 2.89151 + 2.89151i 0.00638303 + 0.00638303i
454454 0 0
455455 0 0
456456 0 0
457457 −559.163 559.163i −1.22355 1.22355i −0.966360 0.257191i 0.917203π-0.917203\pi
−0.257191 0.966360i 0.582797π-0.582797\pi
458458 0 0
459459 −4.02886 −0.00877747
460460 0 0
461461 327.625i 0.710683i 0.934737 + 0.355341i 0.115635π0.115635\pi
−0.934737 + 0.355341i 0.884365π0.884365\pi
462462 0 0
463463 605.934 605.934i 1.30871 1.30871i 0.386367 0.922345i 0.373730π-0.373730\pi
0.922345 0.386367i 0.126270π-0.126270\pi
464464 0 0
465465 0 0
466466 0 0
467467 83.9231 83.9231i 0.179707 0.179707i −0.611521 0.791228i 0.709442π-0.709442\pi
0.791228 + 0.611521i 0.209442π0.209442\pi
468468 0 0
469469 −174.422 −0.371903
470470 0 0
471471 16.9313 0.0359476
472472 0 0
473473 −588.298 + 588.298i −1.24376 + 1.24376i
474474 0 0
475475 0 0
476476 0 0
477477 −258.217 + 258.217i −0.541335 + 0.541335i
478478 0 0
479479 831.992i 1.73694i −0.495746 0.868468i 0.665105π-0.665105\pi
0.495746 0.868468i 0.334895π-0.334895\pi
480480 0 0
481481 −30.1601 −0.0627028
482482 0 0
483483 9.25640 + 9.25640i 0.0191644 + 0.0191644i
484484 0 0
485485 0 0
486486 0 0
487487 −373.676 373.676i −0.767301 0.767301i 0.210329 0.977631i 0.432546π-0.432546\pi
−0.977631 + 0.210329i 0.932546π0.932546\pi
488488 0 0
489489 6.74590i 0.0137953i
490490 0 0
491491 42.8051i 0.0871795i 0.999050 + 0.0435898i 0.0138794π0.0138794\pi
−0.999050 + 0.0435898i 0.986121π0.986121\pi
492492 0 0
493493 −23.4386 23.4386i −0.0475427 0.0475427i
494494 0 0
495495 0 0
496496 0 0
497497 94.5819 + 94.5819i 0.190306 + 0.190306i
498498 0 0
499499 485.100 0.972143 0.486072 0.873919i 0.338429π-0.338429\pi
0.486072 + 0.873919i 0.338429π0.338429\pi
500500 0 0
501501 14.7730i 0.0294870i
502502 0 0
503503 −666.926 + 666.926i −1.32590 + 1.32590i −0.416980 + 0.908916i 0.636912π0.636912\pi
−0.908916 + 0.416980i 0.863088π0.863088\pi
504504 0 0
505505 0 0
506506 0 0
507507 −1.98935 + 1.98935i −0.00392376 + 0.00392376i
508508 0 0
509509 −779.971 −1.53236 −0.766180 0.642626i 0.777845π-0.777845\pi
−0.766180 + 0.642626i 0.777845π0.777845\pi
510510 0 0
511511 108.964 0.213237
512512 0 0
513513 −48.3138 + 48.3138i −0.0941790 + 0.0941790i
514514 0 0
515515 0 0
516516 0 0
517517 −407.097 + 407.097i −0.787422 + 0.787422i
518518 0 0
519519 35.4435i 0.0682919i
520520 0 0
521521 −736.972 −1.41453 −0.707267 0.706947i 0.750072π-0.750072\pi
−0.707267 + 0.706947i 0.750072π0.750072\pi
522522 0 0
523523 671.690 + 671.690i 1.28430 + 1.28430i 0.938195 + 0.346108i 0.112497π0.112497\pi
0.346108 + 0.938195i 0.387503π0.387503\pi
524524 0 0
525525 0 0
526526 0 0
527527 34.3144 + 34.3144i 0.0651127 + 0.0651127i
528528 0 0
529529 452.780i 0.855917i
530530 0 0
531531 831.192i 1.56533i
532532 0 0
533533 −360.377 360.377i −0.676129 0.676129i
534534 0 0
535535 0 0
536536 0 0
537537 −2.02773 2.02773i −0.00377604 0.00377604i
538538 0 0
539539 −524.263 −0.972659
540540 0 0
541541 1039.61i 1.92164i −0.277168 0.960822i 0.589396π-0.589396\pi
0.277168 0.960822i 0.410604π-0.410604\pi
542542 0 0
543543 −34.4860 + 34.4860i −0.0635101 + 0.0635101i
544544 0 0
545545 0 0
546546 0 0
547547 238.506 238.506i 0.436026 0.436026i −0.454646 0.890672i 0.650234π-0.650234\pi
0.890672 + 0.454646i 0.150234π0.150234\pi
548548 0 0
549549 −43.2705 −0.0788169
550550 0 0
551551 −562.148 −1.02023
552552 0 0
553553 −153.717 + 153.717i −0.277969 + 0.277969i
554554 0 0
555555 0 0
556556 0 0
557557 263.387 263.387i 0.472867 0.472867i −0.429974 0.902841i 0.641477π-0.641477\pi
0.902841 + 0.429974i 0.141477π0.141477\pi
558558 0 0
559559 945.513i 1.69144i
560560 0 0
561561 −2.67816 −0.00477391
562562 0 0
563563 160.698 + 160.698i 0.285431 + 0.285431i 0.835270 0.549839i 0.185311π-0.185311\pi
−0.549839 + 0.835270i 0.685311π0.685311\pi
564564 0 0
565565 0 0
566566 0 0
567567 127.894 + 127.894i 0.225563 + 0.225563i
568568 0 0
569569 407.195i 0.715633i 0.933792 + 0.357817i 0.116479π0.116479\pi
−0.933792 + 0.357817i 0.883521π0.883521\pi
570570 0 0
571571 131.146i 0.229678i 0.993384 + 0.114839i 0.0366351π0.0366351\pi
−0.993384 + 0.114839i 0.963365π0.963365\pi
572572 0 0
573573 15.7883 + 15.7883i 0.0275538 + 0.0275538i
574574 0 0
575575 0 0
576576 0 0
577577 −417.933 417.933i −0.724321 0.724321i 0.245162 0.969482i 0.421159π-0.421159\pi
−0.969482 + 0.245162i 0.921159π0.921159\pi
578578 0 0
579579 47.7137 0.0824071
580580 0 0
581581 203.462i 0.350192i
582582 0 0
583583 −343.952 + 343.952i −0.589969 + 0.589969i
584584 0 0
585585 0 0
586586 0 0
587587 212.882 212.882i 0.362660 0.362660i −0.502131 0.864791i 0.667451π-0.667451\pi
0.864791 + 0.502131i 0.167451π0.167451\pi
588588 0 0
589589 822.992 1.39727
590590 0 0
591591 −58.6697 −0.0992720
592592 0 0
593593 −97.2530 + 97.2530i −0.164002 + 0.164002i −0.784337 0.620335i 0.786997π-0.786997\pi
0.620335 + 0.784337i 0.286997π0.286997\pi
594594 0 0
595595 0 0
596596 0 0
597597 −11.4977 + 11.4977i −0.0192592 + 0.0192592i
598598 0 0
599599 712.479i 1.18945i 0.803930 + 0.594723i 0.202738π0.202738\pi
−0.803930 + 0.594723i 0.797262π0.797262\pi
600600 0 0
601601 217.550 0.361980 0.180990 0.983485i 0.442070π-0.442070\pi
0.180990 + 0.983485i 0.442070π0.442070\pi
602602 0 0
603603 −489.575 489.575i −0.811899 0.811899i
604604 0 0
605605 0 0
606606 0 0
607607 12.6560 + 12.6560i 0.0208501 + 0.0208501i 0.717455 0.696605i 0.245307π-0.245307\pi
−0.696605 + 0.717455i 0.745307π0.745307\pi
608608 0 0
609609 11.4223i 0.0187558i
610610 0 0
611611 654.287i 1.07085i
612612 0 0
613613 523.841 + 523.841i 0.854552 + 0.854552i 0.990690 0.136138i 0.0434689π-0.0434689\pi
−0.136138 + 0.990690i 0.543469π0.543469\pi
614614 0 0
615615 0 0
616616 0 0
617617 331.035 + 331.035i 0.536523 + 0.536523i 0.922506 0.385983i 0.126138π-0.126138\pi
−0.385983 + 0.922506i 0.626138π0.626138\pi
618618 0 0
619619 277.907 0.448961 0.224481 0.974479i 0.427931π-0.427931\pi
0.224481 + 0.974479i 0.427931π0.427931\pi
620620 0 0
621621 104.123i 0.167670i
622622 0 0
623623 5.88393 5.88393i 0.00944451 0.00944451i
624624 0 0
625625 0 0
626626 0 0
627627 −32.1164 + 32.1164i −0.0512223 + 0.0512223i
628628 0 0
629629 2.69412 0.00428318
630630 0 0
631631 −425.237 −0.673910 −0.336955 0.941521i 0.609397π-0.609397\pi
−0.336955 + 0.941521i 0.609397π0.609397\pi
632632 0 0
633633 −15.5794 + 15.5794i −0.0246121 + 0.0246121i
634634 0 0
635635 0 0
636636 0 0
637637 421.298 421.298i 0.661379 0.661379i
638638 0 0
639639 530.952i 0.830911i
640640 0 0
641641 −474.056 −0.739558 −0.369779 0.929120i 0.620567π-0.620567\pi
−0.369779 + 0.929120i 0.620567π0.620567\pi
642642 0 0
643643 −490.408 490.408i −0.762687 0.762687i 0.214121 0.976807i 0.431311π-0.431311\pi
−0.976807 + 0.214121i 0.931311π0.931311\pi
644644 0 0
645645 0 0
646646 0 0
647647 −319.187 319.187i −0.493334 0.493334i 0.416021 0.909355i 0.363424π-0.363424\pi
−0.909355 + 0.416021i 0.863424π0.863424\pi
648648 0 0
649649 1107.17i 1.70596i
650650 0 0
651651 16.7224i 0.0256873i
652652 0 0
653653 −95.6351 95.6351i −0.146455 0.146455i 0.630077 0.776532i 0.283023π-0.283023\pi
−0.776532 + 0.630077i 0.783023π0.783023\pi
654654 0 0
655655 0 0
656656 0 0
657657 305.845 + 305.845i 0.465517 + 0.465517i
658658 0 0
659659 −295.703 −0.448715 −0.224358 0.974507i 0.572028π-0.572028\pi
−0.224358 + 0.974507i 0.572028π0.572028\pi
660660 0 0
661661 1223.87i 1.85154i 0.378088 + 0.925770i 0.376582π0.376582\pi
−0.378088 + 0.925770i 0.623418π0.623418\pi
662662 0 0
663663 2.15217 2.15217i 0.00324611 0.00324611i
664664 0 0
665665 0 0
666666 0 0
667667 −605.754 + 605.754i −0.908177 + 0.908177i
668668 0 0
669669 29.2955 0.0437900
670670 0 0
671671 −57.6374 −0.0858978
672672 0 0
673673 95.3663 95.3663i 0.141703 0.141703i −0.632697 0.774400i 0.718052π-0.718052\pi
0.774400 + 0.632697i 0.218052π0.218052\pi
674674 0 0
675675 0 0
676676 0 0
677677 −208.006 + 208.006i −0.307247 + 0.307247i −0.843841 0.536594i 0.819711π-0.819711\pi
0.536594 + 0.843841i 0.319711π0.319711\pi
678678 0 0
679679 147.067i 0.216594i
680680 0 0
681681 22.4657 0.0329892
682682 0 0
683683 −704.881 704.881i −1.03204 1.03204i −0.999470 0.0325668i 0.989632π-0.989632\pi
−0.0325668 0.999470i 0.510368π-0.510368\pi
684684 0 0
685685 0 0
686686 0 0
687687 −3.46801 3.46801i −0.00504805 0.00504805i
688688 0 0
689689 552.800i 0.802321i
690690 0 0
691691 814.437i 1.17864i 0.807901 + 0.589318i 0.200603π0.200603\pi
−0.807901 + 0.589318i 0.799397π0.799397\pi
692692 0 0
693693 171.014 + 171.014i 0.246773 + 0.246773i
694694 0 0
695695 0 0
696696 0 0
697697 32.1915 + 32.1915i 0.0461858 + 0.0461858i
698698 0 0
699699 18.7442 0.0268158
700700 0 0
701701 39.4607i 0.0562920i 0.999604 + 0.0281460i 0.00896033π0.00896033\pi
−0.999604 + 0.0281460i 0.991040π0.991040\pi
702702 0 0
703703 32.3078 32.3078i 0.0459570 0.0459570i
704704 0 0
705705 0 0
706706 0 0
707707 −172.767 + 172.767i −0.244366 + 0.244366i
708708 0 0
709709 1177.86 1.66130 0.830648 0.556798i 0.187970π-0.187970\pi
0.830648 + 0.556798i 0.187970π0.187970\pi
710710 0 0
711711 −862.917 −1.21367
712712 0 0
713713 886.832 886.832i 1.24380 1.24380i
714714 0 0
715715 0 0
716716 0 0
717717 −15.0297 + 15.0297i −0.0209619 + 0.0209619i
718718 0 0
719719 242.835i 0.337740i −0.985638 0.168870i 0.945988π-0.945988\pi
0.985638 0.168870i 0.0540119π-0.0540119\pi
720720 0 0
721721 162.624 0.225553
722722 0 0
723723 28.6537 + 28.6537i 0.0396317 + 0.0396317i
724724 0 0
725725 0 0
726726 0 0
727727 −619.622 619.622i −0.852300 0.852300i 0.138116 0.990416i 0.455895π-0.455895\pi
−0.990416 + 0.138116i 0.955895π0.955895\pi
728728 0 0
729729 712.425i 0.977264i
730730 0 0
731731 84.4603i 0.115541i
732732 0 0
733733 −281.127 281.127i −0.383529 0.383529i 0.488843 0.872372i 0.337419π-0.337419\pi
−0.872372 + 0.488843i 0.837419π0.837419\pi
734734 0 0
735735 0 0
736736 0 0
737737 −652.127 652.127i −0.884841 0.884841i
738738 0 0
739739 −1109.74 −1.50168 −0.750839 0.660485i 0.770351π-0.770351\pi
−0.750839 + 0.660485i 0.770351π0.770351\pi
740740 0 0
741741 51.6175i 0.0696592i
742742 0 0
743743 −339.850 + 339.850i −0.457403 + 0.457403i −0.897802 0.440399i 0.854837π-0.854837\pi
0.440399 + 0.897802i 0.354837π0.354837\pi
744744 0 0
745745 0 0
746746 0 0
747747 571.084 571.084i 0.764504 0.764504i
748748 0 0
749749 304.780 0.406916
750750 0 0
751751 980.557 1.30567 0.652834 0.757501i 0.273580π-0.273580\pi
0.652834 + 0.757501i 0.273580π0.273580\pi
752752 0 0
753753 12.4324 12.4324i 0.0165105 0.0165105i
754754 0 0
755755 0 0
756756 0 0
757757 101.564 101.564i 0.134166 0.134166i −0.636834 0.771001i 0.719757π-0.719757\pi
0.771001 + 0.636834i 0.219757π0.219757\pi
758758 0 0
759759 69.2154i 0.0911929i
760760 0 0
761761 767.675 1.00877 0.504386 0.863478i 0.331719π-0.331719\pi
0.504386 + 0.863478i 0.331719π0.331719\pi
762762 0 0
763763 74.3357 + 74.3357i 0.0974256 + 0.0974256i
764764 0 0
765765 0 0
766766 0 0
767767 889.722 + 889.722i 1.16000 + 1.16000i
768768 0 0
769769 331.840i 0.431522i 0.976446 + 0.215761i 0.0692232π0.0692232\pi
−0.976446 + 0.215761i 0.930777π0.930777\pi
770770 0 0
771771 65.1675i 0.0845234i
772772 0 0
773773 180.328 + 180.328i 0.233283 + 0.233283i 0.814061 0.580779i 0.197252π-0.197252\pi
−0.580779 + 0.814061i 0.697252π0.697252\pi
774774 0 0
775775 0 0
776776 0 0
777777 0.656463 + 0.656463i 0.000844869 + 0.000844869i
778778 0 0
779779 772.078 0.991114
780780 0 0
781781 707.243i 0.905561i
782782 0 0
783783 64.2435 64.2435i 0.0820479 0.0820479i
784784 0 0
785785 0 0
786786 0 0
787787 945.029 945.029i 1.20080 1.20080i 0.226876 0.973924i 0.427149π-0.427149\pi
0.973924 0.226876i 0.0728513π-0.0728513\pi
788788 0 0
789789 −22.3940 −0.0283827
790790 0 0
791791 281.223 0.355529
792792 0 0
793793 46.3175 46.3175i 0.0584079 0.0584079i
794794 0 0
795795 0 0
796796 0 0
797797 −680.774 + 680.774i −0.854171 + 0.854171i −0.990644 0.136473i 0.956423π-0.956423\pi
0.136473 + 0.990644i 0.456423π0.456423\pi
798798 0 0
799799 58.4458i 0.0731487i
800800 0 0
801801 33.0305 0.0412366
802802 0 0
803803 407.393 + 407.393i 0.507339 + 0.507339i
804804 0 0
805805 0 0
806806 0 0
807807 −25.1275 25.1275i −0.0311369 0.0311369i
808808 0 0
809809 427.952i 0.528989i 0.964387 + 0.264495i 0.0852051π0.0852051\pi
−0.964387 + 0.264495i 0.914795π0.914795\pi
810810 0 0
811811 1222.46i 1.50735i −0.657245 0.753677i 0.728278π-0.728278\pi
0.657245 0.753677i 0.271722π-0.271722\pi
812812 0 0
813813 63.5359 + 63.5359i 0.0781499 + 0.0781499i
814814 0 0
815815 0 0
816816 0 0
817817 1012.84 + 1012.84i 1.23971 + 1.23971i
818818 0 0
819819 −274.853 −0.335596
820820 0 0
821821 1019.26i 1.24148i −0.784015 0.620742i 0.786831π-0.786831\pi
0.784015 0.620742i 0.213169π-0.213169\pi
822822 0 0
823823 −158.477 + 158.477i −0.192560 + 0.192560i −0.796801 0.604241i 0.793476π-0.793476\pi
0.604241 + 0.796801i 0.293476π0.293476\pi
824824 0 0
825825 0 0
826826 0 0
827827 −573.534 + 573.534i −0.693511 + 0.693511i −0.963003 0.269492i 0.913144π-0.913144\pi
0.269492 + 0.963003i 0.413144π0.413144\pi
828828 0 0
829829 −1133.71 −1.36756 −0.683782 0.729686i 0.739666π-0.739666\pi
−0.683782 + 0.729686i 0.739666π0.739666\pi
830830 0 0
831831 23.2430 0.0279699
832832 0 0
833833 −37.6335 + 37.6335i −0.0451783 + 0.0451783i
834834 0 0
835835 0 0
836836 0 0
837837 −94.0534 + 94.0534i −0.112370 + 0.112370i
838838 0 0
839839 1109.49i 1.32240i 0.750212 + 0.661198i 0.229952π0.229952\pi
−0.750212 + 0.661198i 0.770048π0.770048\pi
840840 0 0
841841 −93.5052 −0.111183
842842 0 0
843843 51.0094 + 51.0094i 0.0605094 + 0.0605094i
844844 0 0
845845 0 0
846846 0 0
847847 34.5418 + 34.5418i 0.0407814 + 0.0407814i
848848 0 0
849849 31.6676i 0.0372999i
850850 0 0
851851 69.6278i 0.0818188i
852852 0 0
853853 1.51055 + 1.51055i 0.00177087 + 0.00177087i 0.707992 0.706221i 0.249601π-0.249601\pi
−0.706221 + 0.707992i 0.749601π0.749601\pi
854854 0 0
855855 0 0
856856 0 0
857857 396.892 + 396.892i 0.463118 + 0.463118i 0.899676 0.436558i 0.143803π-0.143803\pi
−0.436558 + 0.899676i 0.643803π0.643803\pi
858858 0 0
859859 941.956 1.09657 0.548286 0.836291i 0.315280π-0.315280\pi
0.548286 + 0.836291i 0.315280π0.315280\pi
860860 0 0
861861 15.6879i 0.0182206i
862862 0 0
863863 833.800 833.800i 0.966164 0.966164i −0.0332818 0.999446i 0.510596π-0.510596\pi
0.999446 + 0.0332818i 0.0105959π0.0105959\pi
864864 0 0
865865 0 0
866866 0 0
867867 37.6064 37.6064i 0.0433754 0.0433754i
868868 0 0
869869 −1149.43 −1.32270
870870 0 0
871871 1048.10 1.20333
872872 0 0
873873 −412.794 + 412.794i −0.472846 + 0.472846i
874874 0 0
875875 0 0
876876 0 0
877877 33.6015 33.6015i 0.0383142 0.0383142i −0.687690 0.726004i 0.741375π-0.741375\pi
0.726004 + 0.687690i 0.241375π0.241375\pi
878878 0 0
879879 64.0762i 0.0728967i
880880 0 0
881881 1084.55 1.23104 0.615521 0.788121i 0.288946π-0.288946\pi
0.615521 + 0.788121i 0.288946π0.288946\pi
882882 0 0
883883 1165.53 + 1165.53i 1.31997 + 1.31997i 0.913796 + 0.406174i 0.133137π0.133137\pi
0.406174 + 0.913796i 0.366863π0.366863\pi
884884 0 0
885885 0 0
886886 0 0
887887 −381.705 381.705i −0.430333 0.430333i 0.458409 0.888742i 0.348420π-0.348420\pi
−0.888742 + 0.458409i 0.848420π0.848420\pi
888888 0 0
889889 141.584i 0.159263i
890890 0 0
891891 956.338i 1.07333i
892892 0 0
893893 700.879 + 700.879i 0.784859 + 0.784859i
894894 0 0
895895 0 0
896896 0 0
897897 −55.6215 55.6215i −0.0620084 0.0620084i
898898 0 0
899899 −1094.34 −1.21729
900900 0 0
901901 49.3802i 0.0548060i
902902 0 0
903903 −20.5800 + 20.5800i −0.0227907 + 0.0227907i
904904 0 0
905905 0 0
906906 0 0
907907 −457.511 + 457.511i −0.504422 + 0.504422i −0.912809 0.408387i 0.866092π-0.866092\pi
0.408387 + 0.912809i 0.366092π0.366092\pi
908908 0 0
909909 −969.856 −1.06695
910910 0 0
911911 620.530 0.681152 0.340576 0.940217i 0.389378π-0.389378\pi
0.340576 + 0.940217i 0.389378π0.389378\pi
912912 0 0
913913 760.699 760.699i 0.833187 0.833187i
914914 0 0
915915 0 0
916916 0 0
917917 −132.247 + 132.247i −0.144216 + 0.144216i
918918 0 0
919919 981.064i 1.06753i −0.845631 0.533767i 0.820776π-0.820776\pi
0.845631 0.533767i 0.179224π-0.179224\pi
920920 0 0
921921 −35.3985 −0.0384349
922922 0 0
923923 −568.341 568.341i −0.615754 0.615754i
924924 0 0
925925 0 0
926926 0 0
927927 456.459 + 456.459i 0.492405 + 0.492405i
928928 0 0
929929 776.484i 0.835827i 0.908487 + 0.417914i 0.137239π0.137239\pi
−0.908487 + 0.417914i 0.862761π0.862761\pi
930930 0 0
931931 902.598i 0.969493i
932932 0 0
933933 −29.5525 29.5525i −0.0316747 0.0316747i
934934 0 0
935935 0 0
936936 0 0
937937 −759.800 759.800i −0.810885 0.810885i 0.173881 0.984767i 0.444369π-0.444369\pi
−0.984767 + 0.173881i 0.944369π0.944369\pi
938938 0 0
939939 60.3267 0.0642457
940940 0 0
941941 759.500i 0.807120i −0.914953 0.403560i 0.867773π-0.867773\pi
0.914953 0.403560i 0.132227π-0.132227\pi
942942 0 0
943943 831.969 831.969i 0.882257 0.882257i
944944 0 0
945945 0 0
946946 0 0
947947 −822.618 + 822.618i −0.868657 + 0.868657i −0.992324 0.123667i 0.960535π-0.960535\pi
0.123667 + 0.992324i 0.460535π0.460535\pi
948948 0 0
949949 −654.763 −0.689951
950950 0 0
951951 −57.9572 −0.0609434
952952 0 0
953953 −659.139 + 659.139i −0.691647 + 0.691647i −0.962594 0.270947i 0.912663π-0.912663\pi
0.270947 + 0.962594i 0.412663π0.412663\pi
954954 0 0
955955 0 0
956956 0 0
957957 42.7056 42.7056i 0.0446244 0.0446244i
958958 0 0
959959 79.8661i 0.0832806i
960960 0 0
961961 641.133 0.667152
962962 0 0
963963 855.468 + 855.468i 0.888336 + 0.888336i
964964 0 0
965965 0 0
966966 0 0
967967 332.005 + 332.005i 0.343335 + 0.343335i 0.857620 0.514284i 0.171942π-0.171942\pi
−0.514284 + 0.857620i 0.671942π0.671942\pi
968968 0 0
969969 4.61086i 0.00475837i
970970 0 0
971971 960.961i 0.989661i 0.868989 + 0.494831i 0.164770π0.164770\pi
−0.868989 + 0.494831i 0.835230π0.835230\pi
972972 0 0
973973 −167.194 167.194i −0.171834 0.171834i
974974 0 0
975975 0 0
976976 0 0
977977 −69.4628 69.4628i −0.0710980 0.0710980i 0.670664 0.741762i 0.266009π-0.266009\pi
−0.741762 + 0.670664i 0.766009π0.766009\pi
978978 0 0
979979 43.9975 0.0449413
980980 0 0
981981 417.297i 0.425379i
982982 0 0
983983 234.943 234.943i 0.239006 0.239006i −0.577433 0.816438i 0.695945π-0.695945\pi
0.816438 + 0.577433i 0.195945π0.195945\pi
984984 0 0
985985 0 0
986986 0 0
987987 −14.2412 + 14.2412i −0.0144288 + 0.0144288i
988988 0 0
989989 2182.82 2.20710
990990 0 0
991991 919.592 0.927944 0.463972 0.885850i 0.346424π-0.346424\pi
0.463972 + 0.885850i 0.346424π0.346424\pi
992992 0 0
993993 18.4694 18.4694i 0.0185996 0.0185996i
994994 0 0
995995 0 0
996996 0 0
997997 835.935 835.935i 0.838450 0.838450i −0.150205 0.988655i 0.547993π-0.547993\pi
0.988655 + 0.150205i 0.0479932π0.0479932\pi
998998 0 0
999999 7.38441i 0.00739180i
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 800.3.m.b.657.6 20
4.3 odd 2 200.3.i.b.157.2 20
5.2 odd 4 160.3.m.a.113.6 20
5.3 odd 4 inner 800.3.m.b.593.5 20
5.4 even 2 160.3.m.a.17.5 20
8.3 odd 2 200.3.i.b.157.4 20
8.5 even 2 inner 800.3.m.b.657.5 20
20.3 even 4 200.3.i.b.93.4 20
20.7 even 4 40.3.i.a.13.7 20
20.19 odd 2 40.3.i.a.37.9 yes 20
40.3 even 4 200.3.i.b.93.2 20
40.13 odd 4 inner 800.3.m.b.593.6 20
40.19 odd 2 40.3.i.a.37.7 yes 20
40.27 even 4 40.3.i.a.13.9 yes 20
40.29 even 2 160.3.m.a.17.6 20
40.37 odd 4 160.3.m.a.113.5 20
60.47 odd 4 360.3.u.b.253.4 20
60.59 even 2 360.3.u.b.37.2 20
120.59 even 2 360.3.u.b.37.4 20
120.107 odd 4 360.3.u.b.253.2 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.3.i.a.13.7 20 20.7 even 4
40.3.i.a.13.9 yes 20 40.27 even 4
40.3.i.a.37.7 yes 20 40.19 odd 2
40.3.i.a.37.9 yes 20 20.19 odd 2
160.3.m.a.17.5 20 5.4 even 2
160.3.m.a.17.6 20 40.29 even 2
160.3.m.a.113.5 20 40.37 odd 4
160.3.m.a.113.6 20 5.2 odd 4
200.3.i.b.93.2 20 40.3 even 4
200.3.i.b.93.4 20 20.3 even 4
200.3.i.b.157.2 20 4.3 odd 2
200.3.i.b.157.4 20 8.3 odd 2
360.3.u.b.37.2 20 60.59 even 2
360.3.u.b.37.4 20 120.59 even 2
360.3.u.b.253.2 20 120.107 odd 4
360.3.u.b.253.4 20 60.47 odd 4
800.3.m.b.593.5 20 5.3 odd 4 inner
800.3.m.b.593.6 20 40.13 odd 4 inner
800.3.m.b.657.5 20 8.5 even 2 inner
800.3.m.b.657.6 20 1.1 even 1 trivial