Properties

Label 592.2.i.c.417.1
Level 592592
Weight 22
Character 592.417
Analytic conductor 4.7274.727
Analytic rank 00
Dimension 22
Inner twists 22

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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] = [592,2,Mod(417,592)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(592, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("592.417"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 592=2437 592 = 2^{4} \cdot 37
Weight: k k == 2 2
Character orbit: [χ][\chi] == 592.i (of order 33, degree 22, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.727143799664.72714379966
Analytic rank: 00
Dimension: 22
Coefficient field: Q(ζ6)\Q(\zeta_{6})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x2x+1 x^{2} - x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 37)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 417.1
Root 0.500000+0.866025i0.500000 + 0.866025i of defining polynomial
Character χ\chi == 592.417
Dual form 592.2.i.c.433.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(0.5000000.866025i)q5+(1.00000+1.73205i)q7+(1.500002.59808i)q9+2.00000q11+(1.00000+1.73205i)q13+(1.50000+2.59808i)q17+(3.000005.19615i)q19+4.00000q23+(2.000003.46410i)q25+9.00000q29+10.0000q31+(1.000001.73205i)q35+(5.500002.59808i)q37+(4.50000+7.79423i)q412.00000q433.00000q456.00000q47+(1.500002.59808i)q49+(1.000001.73205i)q53+(1.000001.73205i)q55+(2.00000+3.46410i)q59+(0.5000000.866025i)q61+6.00000q63+(1.000001.73205i)q65+(5.000008.66025i)q67+(3.00000+5.19615i)q7110.0000q73+(2.00000+3.46410i)q77+(5.00000+8.66025i)q79+(4.500007.79423i)q81+(6.00000+10.3923i)q83+3.00000q85+(3.50000+6.06218i)q89+(2.00000+3.46410i)q91+(3.00000+5.19615i)q95+7.00000q97+(3.000005.19615i)q99+O(q100)q+(-0.500000 - 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +2.00000 q^{11} +(1.00000 + 1.73205i) q^{13} +(-1.50000 + 2.59808i) q^{17} +(-3.00000 - 5.19615i) q^{19} +4.00000 q^{23} +(2.00000 - 3.46410i) q^{25} +9.00000 q^{29} +10.0000 q^{31} +(1.00000 - 1.73205i) q^{35} +(-5.50000 - 2.59808i) q^{37} +(4.50000 + 7.79423i) q^{41} -2.00000 q^{43} -3.00000 q^{45} -6.00000 q^{47} +(1.50000 - 2.59808i) q^{49} +(1.00000 - 1.73205i) q^{53} +(-1.00000 - 1.73205i) q^{55} +(-2.00000 + 3.46410i) q^{59} +(-0.500000 - 0.866025i) q^{61} +6.00000 q^{63} +(1.00000 - 1.73205i) q^{65} +(-5.00000 - 8.66025i) q^{67} +(3.00000 + 5.19615i) q^{71} -10.0000 q^{73} +(2.00000 + 3.46410i) q^{77} +(5.00000 + 8.66025i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-6.00000 + 10.3923i) q^{83} +3.00000 q^{85} +(-3.50000 + 6.06218i) q^{89} +(-2.00000 + 3.46410i) q^{91} +(-3.00000 + 5.19615i) q^{95} +7.00000 q^{97} +(3.00000 - 5.19615i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2qq5+2q7+3q9+4q11+2q133q176q19+8q23+4q25+18q29+20q31+2q3511q37+9q414q436q4512q47+3q49++6q99+O(q100) 2 q - q^{5} + 2 q^{7} + 3 q^{9} + 4 q^{11} + 2 q^{13} - 3 q^{17} - 6 q^{19} + 8 q^{23} + 4 q^{25} + 18 q^{29} + 20 q^{31} + 2 q^{35} - 11 q^{37} + 9 q^{41} - 4 q^{43} - 6 q^{45} - 12 q^{47} + 3 q^{49}+ \cdots + 6 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/592Z)×\left(\mathbb{Z}/592\mathbb{Z}\right)^\times.

nn 113113 149149 223223
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\right) 11 11

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 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
44 0 0
55 −0.500000 0.866025i −0.223607 0.387298i 0.732294 0.680989i 0.238450π-0.238450\pi
−0.955901 + 0.293691i 0.905116π0.905116\pi
66 0 0
77 1.00000 + 1.73205i 0.377964 + 0.654654i 0.990766 0.135583i 0.0432908π-0.0432908\pi
−0.612801 + 0.790237i 0.709957π0.709957\pi
88 0 0
99 1.50000 2.59808i 0.500000 0.866025i
1010 0 0
1111 2.00000 0.603023 0.301511 0.953463i 0.402509π-0.402509\pi
0.301511 + 0.953463i 0.402509π0.402509\pi
1212 0 0
1313 1.00000 + 1.73205i 0.277350 + 0.480384i 0.970725 0.240192i 0.0772105π-0.0772105\pi
−0.693375 + 0.720577i 0.743877π0.743877\pi
1414 0 0
1515 0 0
1616 0 0
1717 −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i 0.951855π-0.951855\pi
0.624780 + 0.780801i 0.285189π0.285189\pi
1818 0 0
1919 −3.00000 5.19615i −0.688247 1.19208i −0.972404 0.233301i 0.925047π-0.925047\pi
0.284157 0.958778i 0.408286π-0.408286\pi
2020 0 0
2121 0 0
2222 0 0
2323 4.00000 0.834058 0.417029 0.908893i 0.363071π-0.363071\pi
0.417029 + 0.908893i 0.363071π0.363071\pi
2424 0 0
2525 2.00000 3.46410i 0.400000 0.692820i
2626 0 0
2727 0 0
2828 0 0
2929 9.00000 1.67126 0.835629 0.549294i 0.185103π-0.185103\pi
0.835629 + 0.549294i 0.185103π0.185103\pi
3030 0 0
3131 10.0000 1.79605 0.898027 0.439941i 0.145001π-0.145001\pi
0.898027 + 0.439941i 0.145001π0.145001\pi
3232 0 0
3333 0 0
3434 0 0
3535 1.00000 1.73205i 0.169031 0.292770i
3636 0 0
3737 −5.50000 2.59808i −0.904194 0.427121i
3838 0 0
3939 0 0
4040 0 0
4141 4.50000 + 7.79423i 0.702782 + 1.21725i 0.967486 + 0.252924i 0.0813924π0.0813924\pi
−0.264704 + 0.964330i 0.585274π0.585274\pi
4242 0 0
4343 −2.00000 −0.304997 −0.152499 0.988304i 0.548732π-0.548732\pi
−0.152499 + 0.988304i 0.548732π0.548732\pi
4444 0 0
4545 −3.00000 −0.447214
4646 0 0
4747 −6.00000 −0.875190 −0.437595 0.899172i 0.644170π-0.644170\pi
−0.437595 + 0.899172i 0.644170π0.644170\pi
4848 0 0
4949 1.50000 2.59808i 0.214286 0.371154i
5050 0 0
5151 0 0
5252 0 0
5353 1.00000 1.73205i 0.137361 0.237915i −0.789136 0.614218i 0.789471π-0.789471\pi
0.926497 + 0.376303i 0.122805π0.122805\pi
5454 0 0
5555 −1.00000 1.73205i −0.134840 0.233550i
5656 0 0
5757 0 0
5858 0 0
5959 −2.00000 + 3.46410i −0.260378 + 0.450988i −0.966342 0.257260i 0.917180π-0.917180\pi
0.705965 + 0.708247i 0.250514π0.250514\pi
6060 0 0
6161 −0.500000 0.866025i −0.0640184 0.110883i 0.832240 0.554416i 0.187058π-0.187058\pi
−0.896258 + 0.443533i 0.853725π0.853725\pi
6262 0 0
6363 6.00000 0.755929
6464 0 0
6565 1.00000 1.73205i 0.124035 0.214834i
6666 0 0
6767 −5.00000 8.66025i −0.610847 1.05802i −0.991098 0.133135i 0.957496π-0.957496\pi
0.380251 0.924883i 0.375838π-0.375838\pi
6868 0 0
6969 0 0
7070 0 0
7171 3.00000 + 5.19615i 0.356034 + 0.616670i 0.987294 0.158901i 0.0507952π-0.0507952\pi
−0.631260 + 0.775571i 0.717462π0.717462\pi
7272 0 0
7373 −10.0000 −1.17041 −0.585206 0.810885i 0.698986π-0.698986\pi
−0.585206 + 0.810885i 0.698986π0.698986\pi
7474 0 0
7575 0 0
7676 0 0
7777 2.00000 + 3.46410i 0.227921 + 0.394771i
7878 0 0
7979 5.00000 + 8.66025i 0.562544 + 0.974355i 0.997274 + 0.0737937i 0.0235106π0.0235106\pi
−0.434730 + 0.900561i 0.643156π0.643156\pi
8080 0 0
8181 −4.50000 7.79423i −0.500000 0.866025i
8282 0 0
8383 −6.00000 + 10.3923i −0.658586 + 1.14070i 0.322396 + 0.946605i 0.395512π0.395512\pi
−0.980982 + 0.194099i 0.937822π0.937822\pi
8484 0 0
8585 3.00000 0.325396
8686 0 0
8787 0 0
8888 0 0
8989 −3.50000 + 6.06218i −0.370999 + 0.642590i −0.989720 0.143022i 0.954318π-0.954318\pi
0.618720 + 0.785611i 0.287651π0.287651\pi
9090 0 0
9191 −2.00000 + 3.46410i −0.209657 + 0.363137i
9292 0 0
9393 0 0
9494 0 0
9595 −3.00000 + 5.19615i −0.307794 + 0.533114i
9696 0 0
9797 7.00000 0.710742 0.355371 0.934725i 0.384354π-0.384354\pi
0.355371 + 0.934725i 0.384354π0.384354\pi
9898 0 0
9999 3.00000 5.19615i 0.301511 0.522233i
100100 0 0
101101 −3.00000 −0.298511 −0.149256 0.988799i 0.547688π-0.547688\pi
−0.149256 + 0.988799i 0.547688π0.547688\pi
102102 0 0
103103 −6.00000 −0.591198 −0.295599 0.955312i 0.595519π-0.595519\pi
−0.295599 + 0.955312i 0.595519π0.595519\pi
104104 0 0
105105 0 0
106106 0 0
107107 −9.00000 15.5885i −0.870063 1.50699i −0.861931 0.507026i 0.830745π-0.830745\pi
−0.00813215 0.999967i 0.502589π-0.502589\pi
108108 0 0
109109 −2.50000 + 4.33013i −0.239457 + 0.414751i −0.960558 0.278078i 0.910303π-0.910303\pi
0.721102 + 0.692829i 0.243636π0.243636\pi
110110 0 0
111111 0 0
112112 0 0
113113 −3.00000 + 5.19615i −0.282216 + 0.488813i −0.971930 0.235269i 0.924403π-0.924403\pi
0.689714 + 0.724082i 0.257736π0.257736\pi
114114 0 0
115115 −2.00000 3.46410i −0.186501 0.323029i
116116 0 0
117117 6.00000 0.554700
118118 0 0
119119 −6.00000 −0.550019
120120 0 0
121121 −7.00000 −0.636364
122122 0 0
123123 0 0
124124 0 0
125125 −9.00000 −0.804984
126126 0 0
127127 −4.00000 + 6.92820i −0.354943 + 0.614779i −0.987108 0.160055i 0.948833π-0.948833\pi
0.632166 + 0.774833i 0.282166π0.282166\pi
128128 0 0
129129 0 0
130130 0 0
131131 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
132132 0 0
133133 6.00000 10.3923i 0.520266 0.901127i
134134 0 0
135135 0 0
136136 0 0
137137 −9.00000 −0.768922 −0.384461 0.923141i 0.625613π-0.625613\pi
−0.384461 + 0.923141i 0.625613π0.625613\pi
138138 0 0
139139 8.00000 13.8564i 0.678551 1.17529i −0.296866 0.954919i 0.595942π-0.595942\pi
0.975417 0.220366i 0.0707252π-0.0707252\pi
140140 0 0
141141 0 0
142142 0 0
143143 2.00000 + 3.46410i 0.167248 + 0.289683i
144144 0 0
145145 −4.50000 7.79423i −0.373705 0.647275i
146146 0 0
147147 0 0
148148 0 0
149149 −11.0000 −0.901155 −0.450578 0.892737i 0.648782π-0.648782\pi
−0.450578 + 0.892737i 0.648782π0.648782\pi
150150 0 0
151151 2.00000 + 3.46410i 0.162758 + 0.281905i 0.935857 0.352381i 0.114628π-0.114628\pi
−0.773099 + 0.634285i 0.781294π0.781294\pi
152152 0 0
153153 4.50000 + 7.79423i 0.363803 + 0.630126i
154154 0 0
155155 −5.00000 8.66025i −0.401610 0.695608i
156156 0 0
157157 −8.50000 + 14.7224i −0.678374 + 1.17498i 0.297097 + 0.954847i 0.403982π0.403982\pi
−0.975470 + 0.220131i 0.929352π0.929352\pi
158158 0 0
159159 0 0
160160 0 0
161161 4.00000 + 6.92820i 0.315244 + 0.546019i
162162 0 0
163163 −3.00000 + 5.19615i −0.234978 + 0.406994i −0.959266 0.282503i 0.908835π-0.908835\pi
0.724288 + 0.689497i 0.242169π0.242169\pi
164164 0 0
165165 0 0
166166 0 0
167167 6.00000 + 10.3923i 0.464294 + 0.804181i 0.999169 0.0407502i 0.0129748π-0.0129748\pi
−0.534875 + 0.844931i 0.679641π0.679641\pi
168168 0 0
169169 4.50000 7.79423i 0.346154 0.599556i
170170 0 0
171171 −18.0000 −1.37649
172172 0 0
173173 −10.5000 + 18.1865i −0.798300 + 1.38270i 0.122422 + 0.992478i 0.460934π0.460934\pi
−0.920722 + 0.390218i 0.872399π0.872399\pi
174174 0 0
175175 8.00000 0.604743
176176 0 0
177177 0 0
178178 0 0
179179 −12.0000 −0.896922 −0.448461 0.893802i 0.648028π-0.648028\pi
−0.448461 + 0.893802i 0.648028π0.648028\pi
180180 0 0
181181 −2.50000 4.33013i −0.185824 0.321856i 0.758030 0.652219i 0.226162π-0.226162\pi
−0.943854 + 0.330364i 0.892829π0.892829\pi
182182 0 0
183183 0 0
184184 0 0
185185 0.500000 + 6.06218i 0.0367607 + 0.445700i
186186 0 0
187187 −3.00000 + 5.19615i −0.219382 + 0.379980i
188188 0 0
189189 0 0
190190 0 0
191191 4.00000 0.289430 0.144715 0.989473i 0.453773π-0.453773\pi
0.144715 + 0.989473i 0.453773π0.453773\pi
192192 0 0
193193 19.0000 1.36765 0.683825 0.729646i 0.260315π-0.260315\pi
0.683825 + 0.729646i 0.260315π0.260315\pi
194194 0 0
195195 0 0
196196 0 0
197197 7.50000 12.9904i 0.534353 0.925526i −0.464841 0.885394i 0.653889π-0.653889\pi
0.999194 0.0401324i 0.0127780π-0.0127780\pi
198198 0 0
199199 10.0000 0.708881 0.354441 0.935079i 0.384671π-0.384671\pi
0.354441 + 0.935079i 0.384671π0.384671\pi
200200 0 0
201201 0 0
202202 0 0
203203 9.00000 + 15.5885i 0.631676 + 1.09410i
204204 0 0
205205 4.50000 7.79423i 0.314294 0.544373i
206206 0 0
207207 6.00000 10.3923i 0.417029 0.722315i
208208 0 0
209209 −6.00000 10.3923i −0.415029 0.718851i
210210 0 0
211211 −2.00000 −0.137686 −0.0688428 0.997628i 0.521931π-0.521931\pi
−0.0688428 + 0.997628i 0.521931π0.521931\pi
212212 0 0
213213 0 0
214214 0 0
215215 1.00000 + 1.73205i 0.0681994 + 0.118125i
216216 0 0
217217 10.0000 + 17.3205i 0.678844 + 1.17579i
218218 0 0
219219 0 0
220220 0 0
221221 −6.00000 −0.403604
222222 0 0
223223 −28.0000 −1.87502 −0.937509 0.347960i 0.886874π-0.886874\pi
−0.937509 + 0.347960i 0.886874π0.886874\pi
224224 0 0
225225 −6.00000 10.3923i −0.400000 0.692820i
226226 0 0
227227 7.00000 + 12.1244i 0.464606 + 0.804722i 0.999184 0.0403978i 0.0128625π-0.0128625\pi
−0.534577 + 0.845120i 0.679529π0.679529\pi
228228 0 0
229229 −0.500000 0.866025i −0.0330409 0.0572286i 0.849032 0.528341i 0.177186π-0.177186\pi
−0.882073 + 0.471113i 0.843853π0.843853\pi
230230 0 0
231231 0 0
232232 0 0
233233 3.00000 0.196537 0.0982683 0.995160i 0.468670π-0.468670\pi
0.0982683 + 0.995160i 0.468670π0.468670\pi
234234 0 0
235235 3.00000 + 5.19615i 0.195698 + 0.338960i
236236 0 0
237237 0 0
238238 0 0
239239 3.00000 5.19615i 0.194054 0.336111i −0.752536 0.658551i 0.771170π-0.771170\pi
0.946590 + 0.322440i 0.104503π0.104503\pi
240240 0 0
241241 −7.00000 12.1244i −0.450910 0.780998i 0.547533 0.836784i 0.315567π-0.315567\pi
−0.998443 + 0.0557856i 0.982234π0.982234\pi
242242 0 0
243243 0 0
244244 0 0
245245 −3.00000 −0.191663
246246 0 0
247247 6.00000 10.3923i 0.381771 0.661247i
248248 0 0
249249 0 0
250250 0 0
251251 14.0000 0.883672 0.441836 0.897096i 0.354327π-0.354327\pi
0.441836 + 0.897096i 0.354327π0.354327\pi
252252 0 0
253253 8.00000 0.502956
254254 0 0
255255 0 0
256256 0 0
257257 10.5000 18.1865i 0.654972 1.13444i −0.326929 0.945049i 0.606014π-0.606014\pi
0.981901 0.189396i 0.0606529π-0.0606529\pi
258258 0 0
259259 −1.00000 12.1244i −0.0621370 0.753371i
260260 0 0
261261 13.5000 23.3827i 0.835629 1.44735i
262262 0 0
263263 2.00000 + 3.46410i 0.123325 + 0.213606i 0.921077 0.389380i 0.127311π-0.127311\pi
−0.797752 + 0.602986i 0.793977π0.793977\pi
264264 0 0
265265 −2.00000 −0.122859
266266 0 0
267267 0 0
268268 0 0
269269 18.0000 1.09748 0.548740 0.835993i 0.315108π-0.315108\pi
0.548740 + 0.835993i 0.315108π0.315108\pi
270270 0 0
271271 7.00000 12.1244i 0.425220 0.736502i −0.571221 0.820796i 0.693530π-0.693530\pi
0.996441 + 0.0842940i 0.0268635π0.0268635\pi
272272 0 0
273273 0 0
274274 0 0
275275 4.00000 6.92820i 0.241209 0.417786i
276276 0 0
277277 1.50000 + 2.59808i 0.0901263 + 0.156103i 0.907564 0.419914i 0.137940π-0.137940\pi
−0.817438 + 0.576017i 0.804606π0.804606\pi
278278 0 0
279279 15.0000 25.9808i 0.898027 1.55543i
280280 0 0
281281 −13.5000 + 23.3827i −0.805342 + 1.39489i 0.110717 + 0.993852i 0.464685π0.464685\pi
−0.916060 + 0.401042i 0.868648π0.868648\pi
282282 0 0
283283 −7.00000 12.1244i −0.416107 0.720718i 0.579437 0.815017i 0.303272π-0.303272\pi
−0.995544 + 0.0942988i 0.969939π0.969939\pi
284284 0 0
285285 0 0
286286 0 0
287287 −9.00000 + 15.5885i −0.531253 + 0.920158i
288288 0 0
289289 4.00000 + 6.92820i 0.235294 + 0.407541i
290290 0 0
291291 0 0
292292 0 0
293293 11.5000 + 19.9186i 0.671837 + 1.16366i 0.977383 + 0.211479i 0.0678279π0.0678279\pi
−0.305545 + 0.952177i 0.598839π0.598839\pi
294294 0 0
295295 4.00000 0.232889
296296 0 0
297297 0 0
298298 0 0
299299 4.00000 + 6.92820i 0.231326 + 0.400668i
300300 0 0
301301 −2.00000 3.46410i −0.115278 0.199667i
302302 0 0
303303 0 0
304304 0 0
305305 −0.500000 + 0.866025i −0.0286299 + 0.0495885i
306306 0 0
307307 14.0000 0.799022 0.399511 0.916728i 0.369180π-0.369180\pi
0.399511 + 0.916728i 0.369180π0.369180\pi
308308 0 0
309309 0 0
310310 0 0
311311 −9.00000 + 15.5885i −0.510343 + 0.883940i 0.489585 + 0.871956i 0.337148π0.337148\pi
−0.999928 + 0.0119847i 0.996185π0.996185\pi
312312 0 0
313313 −3.50000 + 6.06218i −0.197832 + 0.342655i −0.947825 0.318791i 0.896723π-0.896723\pi
0.749993 + 0.661445i 0.230057π0.230057\pi
314314 0 0
315315 −3.00000 5.19615i −0.169031 0.292770i
316316 0 0
317317 −0.500000 + 0.866025i −0.0280828 + 0.0486408i −0.879725 0.475482i 0.842274π-0.842274\pi
0.851642 + 0.524123i 0.175607π0.175607\pi
318318 0 0
319319 18.0000 1.00781
320320 0 0
321321 0 0
322322 0 0
323323 18.0000 1.00155
324324 0 0
325325 8.00000 0.443760
326326 0 0
327327 0 0
328328 0 0
329329 −6.00000 10.3923i −0.330791 0.572946i
330330 0 0
331331 −10.0000 + 17.3205i −0.549650 + 0.952021i 0.448649 + 0.893708i 0.351905π0.351905\pi
−0.998298 + 0.0583130i 0.981428π0.981428\pi
332332 0 0
333333 −15.0000 + 10.3923i −0.821995 + 0.569495i
334334 0 0
335335 −5.00000 + 8.66025i −0.273179 + 0.473160i
336336 0 0
337337 0.500000 + 0.866025i 0.0272367 + 0.0471754i 0.879322 0.476227i 0.157996π-0.157996\pi
−0.852086 + 0.523402i 0.824663π0.824663\pi
338338 0 0
339339 0 0
340340 0 0
341341 20.0000 1.08306
342342 0 0
343343 20.0000 1.07990
344344 0 0
345345 0 0
346346 0 0
347347 16.0000 0.858925 0.429463 0.903085i 0.358703π-0.358703\pi
0.429463 + 0.903085i 0.358703π0.358703\pi
348348 0 0
349349 −4.50000 + 7.79423i −0.240879 + 0.417215i −0.960965 0.276670i 0.910769π-0.910769\pi
0.720086 + 0.693885i 0.244103π0.244103\pi
350350 0 0
351351 0 0
352352 0 0
353353 12.5000 21.6506i 0.665308 1.15235i −0.313894 0.949458i 0.601634π-0.601634\pi
0.979202 0.202889i 0.0650330π-0.0650330\pi
354354 0 0
355355 3.00000 5.19615i 0.159223 0.275783i
356356 0 0
357357 0 0
358358 0 0
359359 −24.0000 −1.26667 −0.633336 0.773877i 0.718315π-0.718315\pi
−0.633336 + 0.773877i 0.718315π0.718315\pi
360360 0 0
361361 −8.50000 + 14.7224i −0.447368 + 0.774865i
362362 0 0
363363 0 0
364364 0 0
365365 5.00000 + 8.66025i 0.261712 + 0.453298i
366366 0 0
367367 −14.0000 24.2487i −0.730794 1.26577i −0.956544 0.291587i 0.905817π-0.905817\pi
0.225750 0.974185i 0.427517π-0.427517\pi
368368 0 0
369369 27.0000 1.40556
370370 0 0
371371 4.00000 0.207670
372372 0 0
373373 −8.50000 14.7224i −0.440113 0.762299i 0.557584 0.830120i 0.311728π-0.311728\pi
−0.997697 + 0.0678218i 0.978395π0.978395\pi
374374 0 0
375375 0 0
376376 0 0
377377 9.00000 + 15.5885i 0.463524 + 0.802846i
378378 0 0
379379 3.00000 5.19615i 0.154100 0.266908i −0.778631 0.627482i 0.784086π-0.784086\pi
0.932731 + 0.360573i 0.117419π0.117419\pi
380380 0 0
381381 0 0
382382 0 0
383383 −17.0000 29.4449i −0.868659 1.50456i −0.863367 0.504576i 0.831649π-0.831649\pi
−0.00529229 0.999986i 0.501685π-0.501685\pi
384384 0 0
385385 2.00000 3.46410i 0.101929 0.176547i
386386 0 0
387387 −3.00000 + 5.19615i −0.152499 + 0.264135i
388388 0 0
389389 −12.5000 21.6506i −0.633775 1.09773i −0.986773 0.162107i 0.948171π-0.948171\pi
0.352998 0.935624i 0.385162π-0.385162\pi
390390 0 0
391391 −6.00000 + 10.3923i −0.303433 + 0.525561i
392392 0 0
393393 0 0
394394 0 0
395395 5.00000 8.66025i 0.251577 0.435745i
396396 0 0
397397 13.0000 0.652451 0.326226 0.945292i 0.394223π-0.394223\pi
0.326226 + 0.945292i 0.394223π0.394223\pi
398398 0 0
399399 0 0
400400 0 0
401401 −18.0000 −0.898877 −0.449439 0.893311i 0.648376π-0.648376\pi
−0.449439 + 0.893311i 0.648376π0.648376\pi
402402 0 0
403403 10.0000 + 17.3205i 0.498135 + 0.862796i
404404 0 0
405405 −4.50000 + 7.79423i −0.223607 + 0.387298i
406406 0 0
407407 −11.0000 5.19615i −0.545250 0.257564i
408408 0 0
409409 12.5000 21.6506i 0.618085 1.07056i −0.371750 0.928333i 0.621242π-0.621242\pi
0.989835 0.142222i 0.0454247π-0.0454247\pi
410410 0 0
411411 0 0
412412 0 0
413413 −8.00000 −0.393654
414414 0 0
415415 12.0000 0.589057
416416 0 0
417417 0 0
418418 0 0
419419 −13.0000 + 22.5167i −0.635092 + 1.10001i 0.351404 + 0.936224i 0.385704π0.385704\pi
−0.986496 + 0.163787i 0.947629π0.947629\pi
420420 0 0
421421 9.00000 0.438633 0.219317 0.975654i 0.429617π-0.429617\pi
0.219317 + 0.975654i 0.429617π0.429617\pi
422422 0 0
423423 −9.00000 + 15.5885i −0.437595 + 0.757937i
424424 0 0
425425 6.00000 + 10.3923i 0.291043 + 0.504101i
426426 0 0
427427 1.00000 1.73205i 0.0483934 0.0838198i
428428 0 0
429429 0 0
430430 0 0
431431 9.00000 + 15.5885i 0.433515 + 0.750870i 0.997173 0.0751385i 0.0239399π-0.0239399\pi
−0.563658 + 0.826008i 0.690607π0.690607\pi
432432 0 0
433433 −21.0000 −1.00920 −0.504598 0.863355i 0.668359π-0.668359\pi
−0.504598 + 0.863355i 0.668359π0.668359\pi
434434 0 0
435435 0 0
436436 0 0
437437 −12.0000 20.7846i −0.574038 0.994263i
438438 0 0
439439 −10.0000 17.3205i −0.477274 0.826663i 0.522387 0.852709i 0.325042π-0.325042\pi
−0.999661 + 0.0260459i 0.991708π0.991708\pi
440440 0 0
441441 −4.50000 7.79423i −0.214286 0.371154i
442442 0 0
443443 32.0000 1.52037 0.760183 0.649709i 0.225109π-0.225109\pi
0.760183 + 0.649709i 0.225109π0.225109\pi
444444 0 0
445445 7.00000 0.331832
446446 0 0
447447 0 0
448448 0 0
449449 −3.00000 5.19615i −0.141579 0.245222i 0.786513 0.617574i 0.211885π-0.211885\pi
−0.928091 + 0.372353i 0.878551π0.878551\pi
450450 0 0
451451 9.00000 + 15.5885i 0.423793 + 0.734032i
452452 0 0
453453 0 0
454454 0 0
455455 4.00000 0.187523
456456 0 0
457457 −1.50000 2.59808i −0.0701670 0.121533i 0.828807 0.559534i 0.189020π-0.189020\pi
−0.898974 + 0.438001i 0.855687π0.855687\pi
458458 0 0
459459 0 0
460460 0 0
461461 −15.0000 + 25.9808i −0.698620 + 1.21004i 0.270326 + 0.962769i 0.412869π0.412869\pi
−0.968945 + 0.247276i 0.920465π0.920465\pi
462462 0 0
463463 −11.0000 19.0526i −0.511213 0.885448i −0.999916 0.0129968i 0.995863π-0.995863\pi
0.488702 0.872451i 0.337470π-0.337470\pi
464464 0 0
465465 0 0
466466 0 0
467467 8.00000 0.370196 0.185098 0.982720i 0.440740π-0.440740\pi
0.185098 + 0.982720i 0.440740π0.440740\pi
468468 0 0
469469 10.0000 17.3205i 0.461757 0.799787i
470470 0 0
471471 0 0
472472 0 0
473473 −4.00000 −0.183920
474474 0 0
475475 −24.0000 −1.10120
476476 0 0
477477 −3.00000 5.19615i −0.137361 0.237915i
478478 0 0
479479 −2.00000 + 3.46410i −0.0913823 + 0.158279i −0.908093 0.418769i 0.862462π-0.862462\pi
0.816711 + 0.577047i 0.195795π0.195795\pi
480480 0 0
481481 −1.00000 12.1244i −0.0455961 0.552823i
482482 0 0
483483 0 0
484484 0 0
485485 −3.50000 6.06218i −0.158927 0.275269i
486486 0 0
487487 −12.0000 −0.543772 −0.271886 0.962329i 0.587647π-0.587647\pi
−0.271886 + 0.962329i 0.587647π0.587647\pi
488488 0 0
489489 0 0
490490 0 0
491491 −2.00000 −0.0902587 −0.0451294 0.998981i 0.514370π-0.514370\pi
−0.0451294 + 0.998981i 0.514370π0.514370\pi
492492 0 0
493493 −13.5000 + 23.3827i −0.608009 + 1.05310i
494494 0 0
495495 −6.00000 −0.269680
496496 0 0
497497 −6.00000 + 10.3923i −0.269137 + 0.466159i
498498 0 0
499499 −9.00000 15.5885i −0.402895 0.697835i 0.591179 0.806541i 0.298663π-0.298663\pi
−0.994074 + 0.108705i 0.965329π0.965329\pi
500500 0 0
501501 0 0
502502 0 0
503503 −13.0000 + 22.5167i −0.579641 + 1.00397i 0.415879 + 0.909420i 0.363474π0.363474\pi
−0.995520 + 0.0945483i 0.969859π0.969859\pi
504504 0 0
505505 1.50000 + 2.59808i 0.0667491 + 0.115613i
506506 0 0
507507 0 0
508508 0 0
509509 3.50000 6.06218i 0.155135 0.268701i −0.777973 0.628297i 0.783752π-0.783752\pi
0.933108 + 0.359596i 0.117085π0.117085\pi
510510 0 0
511511 −10.0000 17.3205i −0.442374 0.766214i
512512 0 0
513513 0 0
514514 0 0
515515 3.00000 + 5.19615i 0.132196 + 0.228970i
516516 0 0
517517 −12.0000 −0.527759
518518 0 0
519519 0 0
520520 0 0
521521 21.0000 + 36.3731i 0.920027 + 1.59353i 0.799370 + 0.600839i 0.205167π0.205167\pi
0.120656 + 0.992694i 0.461500π0.461500\pi
522522 0 0
523523 4.00000 + 6.92820i 0.174908 + 0.302949i 0.940129 0.340818i 0.110704π-0.110704\pi
−0.765222 + 0.643767i 0.777371π0.777371\pi
524524 0 0
525525 0 0
526526 0 0
527527 −15.0000 + 25.9808i −0.653410 + 1.13174i
528528 0 0
529529 −7.00000 −0.304348
530530 0 0
531531 6.00000 + 10.3923i 0.260378 + 0.450988i
532532 0 0
533533 −9.00000 + 15.5885i −0.389833 + 0.675211i
534534 0 0
535535 −9.00000 + 15.5885i −0.389104 + 0.673948i
536536 0 0
537537 0 0
538538 0 0
539539 3.00000 5.19615i 0.129219 0.223814i
540540 0 0
541541 17.0000 0.730887 0.365444 0.930834i 0.380917π-0.380917\pi
0.365444 + 0.930834i 0.380917π0.380917\pi
542542 0 0
543543 0 0
544544 0 0
545545 5.00000 0.214176
546546 0 0
547547 −2.00000 −0.0855138 −0.0427569 0.999086i 0.513614π-0.513614\pi
−0.0427569 + 0.999086i 0.513614π0.513614\pi
548548 0 0
549549 −3.00000 −0.128037
550550 0 0
551551 −27.0000 46.7654i −1.15024 1.99227i
552552 0 0
553553 −10.0000 + 17.3205i −0.425243 + 0.736543i
554554 0 0
555555 0 0
556556 0 0
557557 −16.5000 + 28.5788i −0.699127 + 1.21092i 0.269642 + 0.962961i 0.413095π0.413095\pi
−0.968769 + 0.247964i 0.920239π0.920239\pi
558558 0 0
559559 −2.00000 3.46410i −0.0845910 0.146516i
560560 0 0
561561 0 0
562562 0 0
563563 24.0000 1.01148 0.505740 0.862686i 0.331220π-0.331220\pi
0.505740 + 0.862686i 0.331220π0.331220\pi
564564 0 0
565565 6.00000 0.252422
566566 0 0
567567 9.00000 15.5885i 0.377964 0.654654i
568568 0 0
569569 3.00000 0.125767 0.0628833 0.998021i 0.479970π-0.479970\pi
0.0628833 + 0.998021i 0.479970π0.479970\pi
570570 0 0
571571 −22.0000 + 38.1051i −0.920671 + 1.59465i −0.122292 + 0.992494i 0.539025π0.539025\pi
−0.798379 + 0.602155i 0.794309π0.794309\pi
572572 0 0
573573 0 0
574574 0 0
575575 8.00000 13.8564i 0.333623 0.577852i
576576 0 0
577577 9.00000 15.5885i 0.374675 0.648956i −0.615603 0.788056i 0.711088π-0.711088\pi
0.990278 + 0.139100i 0.0444210π0.0444210\pi
578578 0 0
579579 0 0
580580 0 0
581581 −24.0000 −0.995688
582582 0 0
583583 2.00000 3.46410i 0.0828315 0.143468i
584584 0 0
585585 −3.00000 5.19615i −0.124035 0.214834i
586586 0 0
587587 20.0000 + 34.6410i 0.825488 + 1.42979i 0.901546 + 0.432684i 0.142434π0.142434\pi
−0.0760572 + 0.997103i 0.524233π0.524233\pi
588588 0 0
589589 −30.0000 51.9615i −1.23613 2.14104i
590590 0 0
591591 0 0
592592 0 0
593593 −29.0000 −1.19089 −0.595444 0.803397i 0.703024π-0.703024\pi
−0.595444 + 0.803397i 0.703024π0.703024\pi
594594 0 0
595595 3.00000 + 5.19615i 0.122988 + 0.213021i
596596 0 0
597597 0 0
598598 0 0
599599 −19.0000 32.9090i −0.776319 1.34462i −0.934050 0.357142i 0.883751π-0.883751\pi
0.157731 0.987482i 0.449582π-0.449582\pi
600600 0 0
601601 −11.5000 + 19.9186i −0.469095 + 0.812496i −0.999376 0.0353259i 0.988753π-0.988753\pi
0.530281 + 0.847822i 0.322086π0.322086\pi
602602 0 0
603603 −30.0000 −1.22169
604604 0 0
605605 3.50000 + 6.06218i 0.142295 + 0.246463i
606606 0 0
607607 −7.00000 + 12.1244i −0.284121 + 0.492112i −0.972396 0.233338i 0.925035π-0.925035\pi
0.688274 + 0.725450i 0.258368π0.258368\pi
608608 0 0
609609 0 0
610610 0 0
611611 −6.00000 10.3923i −0.242734 0.420428i
612612 0 0
613613 −16.5000 + 28.5788i −0.666429 + 1.15429i 0.312467 + 0.949929i 0.398845π0.398845\pi
−0.978896 + 0.204360i 0.934489π0.934489\pi
614614 0 0
615615 0 0
616616 0 0
617617 11.0000 19.0526i 0.442843 0.767027i −0.555056 0.831813i 0.687303π-0.687303\pi
0.997899 + 0.0647859i 0.0206365π0.0206365\pi
618618 0 0
619619 10.0000 0.401934 0.200967 0.979598i 0.435592π-0.435592\pi
0.200967 + 0.979598i 0.435592π0.435592\pi
620620 0 0
621621 0 0
622622 0 0
623623 −14.0000 −0.560898
624624 0 0
625625 −5.50000 9.52628i −0.220000 0.381051i
626626 0 0
627627 0 0
628628 0 0
629629 15.0000 10.3923i 0.598089 0.414368i
630630 0 0
631631 10.0000 17.3205i 0.398094 0.689519i −0.595397 0.803432i 0.703005π-0.703005\pi
0.993491 + 0.113913i 0.0363385π0.0363385\pi
632632 0 0
633633 0 0
634634 0 0
635635 8.00000 0.317470
636636 0 0
637637 6.00000 0.237729
638638 0 0
639639 18.0000 0.712069
640640 0 0
641641 18.5000 32.0429i 0.730706 1.26562i −0.225876 0.974156i 0.572524π-0.572524\pi
0.956582 0.291464i 0.0941423π-0.0941423\pi
642642 0 0
643643 −14.0000 −0.552106 −0.276053 0.961142i 0.589027π-0.589027\pi
−0.276053 + 0.961142i 0.589027π0.589027\pi
644644 0 0
645645 0 0
646646 0 0
647647 −7.00000 12.1244i −0.275198 0.476658i 0.694987 0.719023i 0.255410π-0.255410\pi
−0.970185 + 0.242365i 0.922077π0.922077\pi
648648 0 0
649649 −4.00000 + 6.92820i −0.157014 + 0.271956i
650650 0 0
651651 0 0
652652 0 0
653653 19.5000 + 33.7750i 0.763094 + 1.32172i 0.941248 + 0.337715i 0.109654π0.109654\pi
−0.178154 + 0.984003i 0.557013π0.557013\pi
654654 0 0
655655 0 0
656656 0 0
657657 −15.0000 + 25.9808i −0.585206 + 1.01361i
658658 0 0
659659 −18.0000 31.1769i −0.701180 1.21448i −0.968052 0.250748i 0.919323π-0.919323\pi
0.266872 0.963732i 0.414010π-0.414010\pi
660660 0 0
661661 3.50000 + 6.06218i 0.136134 + 0.235791i 0.926030 0.377450i 0.123199π-0.123199\pi
−0.789896 + 0.613241i 0.789865π0.789865\pi
662662 0 0
663663 0 0
664664 0 0
665665 −12.0000 −0.465340
666666 0 0
667667 36.0000 1.39393
668668 0 0
669669 0 0
670670 0 0
671671 −1.00000 1.73205i −0.0386046 0.0668651i
672672 0 0
673673 −3.00000 5.19615i −0.115642 0.200297i 0.802395 0.596794i 0.203559π-0.203559\pi
−0.918036 + 0.396497i 0.870226π0.870226\pi
674674 0 0
675675 0 0
676676 0 0
677677 13.0000 0.499631 0.249815 0.968294i 0.419630π-0.419630\pi
0.249815 + 0.968294i 0.419630π0.419630\pi
678678 0 0
679679 7.00000 + 12.1244i 0.268635 + 0.465290i
680680 0 0
681681 0 0
682682 0 0
683683 −15.0000 + 25.9808i −0.573959 + 0.994126i 0.422195 + 0.906505i 0.361260π0.361260\pi
−0.996154 + 0.0876211i 0.972074π0.972074\pi
684684 0 0
685685 4.50000 + 7.79423i 0.171936 + 0.297802i
686686 0 0
687687 0 0
688688 0 0
689689 4.00000 0.152388
690690 0 0
691691 −7.00000 + 12.1244i −0.266293 + 0.461232i −0.967901 0.251330i 0.919132π-0.919132\pi
0.701609 + 0.712562i 0.252465π0.252465\pi
692692 0 0
693693 12.0000 0.455842
694694 0 0
695695 −16.0000 −0.606915
696696 0 0
697697 −27.0000 −1.02270
698698 0 0
699699 0 0
700700 0 0
701701 −3.00000 + 5.19615i −0.113308 + 0.196256i −0.917102 0.398652i 0.869478π-0.869478\pi
0.803794 + 0.594908i 0.202811π0.202811\pi
702702 0 0
703703 3.00000 + 36.3731i 0.113147 + 1.37184i
704704 0 0
705705 0 0
706706 0 0
707707 −3.00000 5.19615i −0.112827 0.195421i
708708 0 0
709709 10.0000 0.375558 0.187779 0.982211i 0.439871π-0.439871\pi
0.187779 + 0.982211i 0.439871π0.439871\pi
710710 0 0
711711 30.0000 1.12509
712712 0 0
713713 40.0000 1.49801
714714 0 0
715715 2.00000 3.46410i 0.0747958 0.129550i
716716 0 0
717717 0 0
718718 0 0
719719 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
720720 0 0
721721 −6.00000 10.3923i −0.223452 0.387030i
722722 0 0
723723 0 0
724724 0 0
725725 18.0000 31.1769i 0.668503 1.15788i
726726 0 0
727727 20.0000 + 34.6410i 0.741759 + 1.28476i 0.951694 + 0.307049i 0.0993415π0.0993415\pi
−0.209935 + 0.977715i 0.567325π0.567325\pi
728728 0 0
729729 −27.0000 −1.00000
730730 0 0
731731 3.00000 5.19615i 0.110959 0.192187i
732732 0 0
733733 −11.0000 19.0526i −0.406294 0.703722i 0.588177 0.808732i 0.299846π-0.299846\pi
−0.994471 + 0.105010i 0.966513π0.966513\pi
734734 0 0
735735 0 0
736736 0 0
737737 −10.0000 17.3205i −0.368355 0.638009i
738738 0 0
739739 −12.0000 −0.441427 −0.220714 0.975339i 0.570839π-0.570839\pi
−0.220714 + 0.975339i 0.570839π0.570839\pi
740740 0 0
741741 0 0
742742 0 0
743743 3.00000 + 5.19615i 0.110059 + 0.190628i 0.915794 0.401648i 0.131563π-0.131563\pi
−0.805735 + 0.592277i 0.798229π0.798229\pi
744744 0 0
745745 5.50000 + 9.52628i 0.201504 + 0.349016i
746746 0 0
747747 18.0000 + 31.1769i 0.658586 + 1.14070i
748748 0 0
749749 18.0000 31.1769i 0.657706 1.13918i
750750 0 0
751751 −10.0000 −0.364905 −0.182453 0.983215i 0.558404π-0.558404\pi
−0.182453 + 0.983215i 0.558404π0.558404\pi
752752 0 0
753753 0 0
754754 0 0
755755 2.00000 3.46410i 0.0727875 0.126072i
756756 0 0
757757 −6.50000 + 11.2583i −0.236247 + 0.409191i −0.959634 0.281251i 0.909251π-0.909251\pi
0.723388 + 0.690442i 0.242584π0.242584\pi
758758 0 0
759759 0 0
760760 0 0
761761 −3.50000 + 6.06218i −0.126875 + 0.219754i −0.922464 0.386082i 0.873828π-0.873828\pi
0.795589 + 0.605836i 0.207161π0.207161\pi
762762 0 0
763763 −10.0000 −0.362024
764764 0 0
765765 4.50000 7.79423i 0.162698 0.281801i
766766 0 0
767767 −8.00000 −0.288863
768768 0 0
769769 14.0000 0.504853 0.252426 0.967616i 0.418771π-0.418771\pi
0.252426 + 0.967616i 0.418771π0.418771\pi
770770 0 0
771771 0 0
772772 0 0
773773 −10.5000 18.1865i −0.377659 0.654124i 0.613062 0.790034i 0.289937π-0.289937\pi
−0.990721 + 0.135910i 0.956604π0.956604\pi
774774 0 0
775775 20.0000 34.6410i 0.718421 1.24434i
776776 0 0
777777 0 0
778778 0 0
779779 27.0000 46.7654i 0.967375 1.67554i
780780 0 0
781781 6.00000 + 10.3923i 0.214697 + 0.371866i
782782 0 0
783783 0 0
784784 0 0
785785 17.0000 0.606756
786786 0 0
787787 −4.00000 −0.142585 −0.0712923 0.997455i 0.522712π-0.522712\pi
−0.0712923 + 0.997455i 0.522712π0.522712\pi
788788 0 0
789789 0 0
790790 0 0
791791 −12.0000 −0.426671
792792 0 0
793793 1.00000 1.73205i 0.0355110 0.0615069i
794794 0 0
795795 0 0
796796 0 0
797797 13.0000 22.5167i 0.460484 0.797581i −0.538501 0.842625i 0.681009π-0.681009\pi
0.998985 + 0.0450436i 0.0143427π0.0143427\pi
798798 0 0
799799 9.00000 15.5885i 0.318397 0.551480i
800800 0 0
801801 10.5000 + 18.1865i 0.370999 + 0.642590i
802802 0 0
803803 −20.0000 −0.705785
804804 0 0
805805 4.00000 6.92820i 0.140981 0.244187i
806806 0 0
807807 0 0
808808 0 0
809809 5.00000 + 8.66025i 0.175791 + 0.304478i 0.940435 0.339975i 0.110418π-0.110418\pi
−0.764644 + 0.644453i 0.777085π0.777085\pi
810810 0 0
811811 −8.00000 13.8564i −0.280918 0.486564i 0.690693 0.723148i 0.257306π-0.257306\pi
−0.971611 + 0.236584i 0.923972π0.923972\pi
812812 0 0
813813 0 0
814814 0 0
815815 6.00000 0.210171
816816 0 0
817817 6.00000 + 10.3923i 0.209913 + 0.363581i
818818 0 0
819819 6.00000 + 10.3923i 0.209657 + 0.363137i
820820 0 0
821821 −5.00000 8.66025i −0.174501 0.302245i 0.765487 0.643451i 0.222498π-0.222498\pi
−0.939989 + 0.341206i 0.889165π0.889165\pi
822822 0 0
823823 −8.00000 + 13.8564i −0.278862 + 0.483004i −0.971102 0.238664i 0.923291π-0.923291\pi
0.692240 + 0.721668i 0.256624π0.256624\pi
824824 0 0
825825 0 0
826826 0 0
827827 −4.00000 6.92820i −0.139094 0.240917i 0.788060 0.615598i 0.211086π-0.211086\pi
−0.927154 + 0.374681i 0.877752π0.877752\pi
828828 0 0
829829 −19.0000 + 32.9090i −0.659897 + 1.14298i 0.320745 + 0.947166i 0.396067π0.396067\pi
−0.980642 + 0.195810i 0.937266π0.937266\pi
830830 0 0
831831 0 0
832832 0 0
833833 4.50000 + 7.79423i 0.155916 + 0.270054i
834834 0 0
835835 6.00000 10.3923i 0.207639 0.359641i
836836 0 0
837837 0 0
838838 0 0
839839 −20.0000 + 34.6410i −0.690477 + 1.19594i 0.281205 + 0.959648i 0.409266π0.409266\pi
−0.971682 + 0.236293i 0.924067π0.924067\pi
840840 0 0
841841 52.0000 1.79310
842842 0 0
843843 0 0
844844 0 0
845845 −9.00000 −0.309609
846846 0 0
847847 −7.00000 12.1244i −0.240523 0.416598i
848848 0 0
849849 0 0
850850 0 0
851851 −22.0000 10.3923i −0.754150 0.356244i
852852 0 0
853853 9.50000 16.4545i 0.325274 0.563391i −0.656294 0.754505i 0.727877π-0.727877\pi
0.981568 + 0.191115i 0.0612102π0.0612102\pi
854854 0 0
855855 9.00000 + 15.5885i 0.307794 + 0.533114i
856856 0 0
857857 −45.0000 −1.53717 −0.768585 0.639747i 0.779039π-0.779039\pi
−0.768585 + 0.639747i 0.779039π0.779039\pi
858858 0 0
859859 50.0000 1.70598 0.852989 0.521929i 0.174787π-0.174787\pi
0.852989 + 0.521929i 0.174787π0.174787\pi
860860 0 0
861861 0 0
862862 0 0
863863 18.0000 31.1769i 0.612727 1.06127i −0.378052 0.925785i 0.623406π-0.623406\pi
0.990779 0.135490i 0.0432609π-0.0432609\pi
864864 0 0
865865 21.0000 0.714021
866866 0 0
867867 0 0
868868 0 0
869869 10.0000 + 17.3205i 0.339227 + 0.587558i
870870 0 0
871871 10.0000 17.3205i 0.338837 0.586883i
872872 0 0
873873 10.5000 18.1865i 0.355371 0.615521i
874874 0 0
875875 −9.00000 15.5885i −0.304256 0.526986i
876876 0 0
877877 17.0000 0.574049 0.287025 0.957923i 0.407334π-0.407334\pi
0.287025 + 0.957923i 0.407334π0.407334\pi
878878 0 0
879879 0 0
880880 0 0
881881 −9.50000 16.4545i −0.320063 0.554366i 0.660438 0.750881i 0.270371π-0.270371\pi
−0.980501 + 0.196515i 0.937037π0.937037\pi
882882 0 0
883883 24.0000 + 41.5692i 0.807664 + 1.39892i 0.914478 + 0.404637i 0.132602π0.132602\pi
−0.106813 + 0.994279i 0.534065π0.534065\pi
884884 0 0
885885 0 0
886886 0 0
887887 8.00000 0.268614 0.134307 0.990940i 0.457119π-0.457119\pi
0.134307 + 0.990940i 0.457119π0.457119\pi
888888 0 0
889889 −16.0000 −0.536623
890890 0 0
891891 −9.00000 15.5885i −0.301511 0.522233i
892892 0 0
893893 18.0000 + 31.1769i 0.602347 + 1.04330i
894894 0 0
895895 6.00000 + 10.3923i 0.200558 + 0.347376i
896896 0 0
897897 0 0
898898 0 0
899899 90.0000 3.00167
900900 0 0
901901 3.00000 + 5.19615i 0.0999445 + 0.173109i
902902 0 0
903903 0 0
904904 0 0
905905 −2.50000 + 4.33013i −0.0831028 + 0.143938i
906906 0 0
907907 −19.0000 32.9090i −0.630885 1.09272i −0.987371 0.158424i 0.949359π-0.949359\pi
0.356487 0.934300i 0.383975π-0.383975\pi
908908 0 0
909909 −4.50000 + 7.79423i −0.149256 + 0.258518i
910910 0 0
911911 40.0000 1.32526 0.662630 0.748947i 0.269440π-0.269440\pi
0.662630 + 0.748947i 0.269440π0.269440\pi
912912 0 0
913913 −12.0000 + 20.7846i −0.397142 + 0.687870i
914914 0 0
915915 0 0
916916 0 0
917917 0 0
918918 0 0
919919 4.00000 0.131948 0.0659739 0.997821i 0.478985π-0.478985\pi
0.0659739 + 0.997821i 0.478985π0.478985\pi
920920 0 0
921921 0 0
922922 0 0
923923 −6.00000 + 10.3923i −0.197492 + 0.342067i
924924 0 0
925925 −20.0000 + 13.8564i −0.657596 + 0.455596i
926926 0 0
927927 −9.00000 + 15.5885i −0.295599 + 0.511992i
928928 0 0
929929 −7.50000 12.9904i −0.246067 0.426201i 0.716364 0.697727i 0.245805π-0.245805\pi
−0.962431 + 0.271526i 0.912472π0.912472\pi
930930 0 0
931931 −18.0000 −0.589926
932932 0 0
933933 0 0
934934 0 0
935935 6.00000 0.196221
936936 0 0
937937 2.50000 4.33013i 0.0816714 0.141459i −0.822297 0.569059i 0.807308π-0.807308\pi
0.903968 + 0.427600i 0.140641π0.140641\pi
938938 0 0
939939 0 0
940940 0 0
941941 −8.50000 + 14.7224i −0.277092 + 0.479938i −0.970661 0.240453i 0.922704π-0.922704\pi
0.693569 + 0.720390i 0.256037π0.256037\pi
942942 0 0
943943 18.0000 + 31.1769i 0.586161 + 1.01526i
944944 0 0
945945 0 0
946946 0 0
947947 18.0000 31.1769i 0.584921 1.01311i −0.409964 0.912102i 0.634459π-0.634459\pi
0.994885 0.101012i 0.0322080π-0.0322080\pi
948948 0 0
949949 −10.0000 17.3205i −0.324614 0.562247i
950950 0 0
951951 0 0
952952 0 0
953953 25.0000 43.3013i 0.809829 1.40267i −0.103152 0.994666i 0.532893π-0.532893\pi
0.912982 0.408000i 0.133774π-0.133774\pi
954954 0 0
955955 −2.00000 3.46410i −0.0647185 0.112096i
956956 0 0
957957 0 0
958958 0 0
959959 −9.00000 15.5885i −0.290625 0.503378i
960960 0 0
961961 69.0000 2.22581
962962 0 0
963963 −54.0000 −1.74013
964964 0 0
965965 −9.50000 16.4545i −0.305816 0.529689i
966966 0 0
967967 −4.00000 6.92820i −0.128631 0.222796i 0.794515 0.607244i 0.207725π-0.207725\pi
−0.923147 + 0.384448i 0.874392π0.874392\pi
968968 0 0
969969 0 0
970970 0 0
971971 14.0000 24.2487i 0.449281 0.778178i −0.549058 0.835784i 0.685013π-0.685013\pi
0.998339 + 0.0576061i 0.0183467π0.0183467\pi
972972 0 0
973973 32.0000 1.02587
974974 0 0
975975 0 0
976976 0 0
977977 1.00000 1.73205i 0.0319928 0.0554132i −0.849586 0.527451i 0.823148π-0.823148\pi
0.881579 + 0.472037i 0.156481π0.156481\pi
978978 0 0
979979 −7.00000 + 12.1244i −0.223721 + 0.387496i
980980 0 0
981981 7.50000 + 12.9904i 0.239457 + 0.414751i
982982 0 0
983983 −9.00000 + 15.5885i −0.287055 + 0.497195i −0.973106 0.230360i 0.926010π-0.926010\pi
0.686050 + 0.727554i 0.259343π0.259343\pi
984984 0 0
985985 −15.0000 −0.477940
986986 0 0
987987 0 0
988988 0 0
989989 −8.00000 −0.254385
990990 0 0
991991 30.0000 0.952981 0.476491 0.879180i 0.341909π-0.341909\pi
0.476491 + 0.879180i 0.341909π0.341909\pi
992992 0 0
993993 0 0
994994 0 0
995995 −5.00000 8.66025i −0.158511 0.274549i
996996 0 0
997997 9.00000 15.5885i 0.285033 0.493691i −0.687584 0.726105i 0.741329π-0.741329\pi
0.972617 + 0.232413i 0.0746622π0.0746622\pi
998998 0 0
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 592.2.i.c.417.1 2
4.3 odd 2 37.2.c.a.10.1 2
12.11 even 2 333.2.f.a.10.1 2
20.3 even 4 925.2.o.a.824.2 4
20.7 even 4 925.2.o.a.824.1 4
20.19 odd 2 925.2.e.a.676.1 2
37.26 even 3 inner 592.2.i.c.433.1 2
148.23 even 12 1369.2.b.b.1368.1 2
148.27 odd 6 1369.2.a.b.1.1 1
148.47 odd 6 1369.2.a.d.1.1 1
148.51 even 12 1369.2.b.b.1368.2 2
148.63 odd 6 37.2.c.a.26.1 yes 2
444.359 even 6 333.2.f.a.100.1 2
740.63 even 12 925.2.o.a.174.1 4
740.359 odd 6 925.2.e.a.26.1 2
740.507 even 12 925.2.o.a.174.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
37.2.c.a.10.1 2 4.3 odd 2
37.2.c.a.26.1 yes 2 148.63 odd 6
333.2.f.a.10.1 2 12.11 even 2
333.2.f.a.100.1 2 444.359 even 6
592.2.i.c.417.1 2 1.1 even 1 trivial
592.2.i.c.433.1 2 37.26 even 3 inner
925.2.e.a.26.1 2 740.359 odd 6
925.2.e.a.676.1 2 20.19 odd 2
925.2.o.a.174.1 4 740.63 even 12
925.2.o.a.174.2 4 740.507 even 12
925.2.o.a.824.1 4 20.7 even 4
925.2.o.a.824.2 4 20.3 even 4
1369.2.a.b.1.1 1 148.27 odd 6
1369.2.a.d.1.1 1 148.47 odd 6
1369.2.b.b.1368.1 2 148.23 even 12
1369.2.b.b.1368.2 2 148.51 even 12