Properties

Label 2548.2.k.i.1569.3
Level 25482548
Weight 22
Character 2548.1569
Analytic conductor 20.34620.346
Analytic rank 00
Dimension 1818
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2548,2,Mod(393,2548)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2548, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2548.393");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 2548=227213 2548 = 2^{2} \cdot 7^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2548.k (of order 33, degree 22, minimal)

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: no
Analytic conductor: 20.345882435020.3458824350
Analytic rank: 00
Dimension: 1818
Relative dimension: 99 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q[x]/(x18)\mathbb{Q}[x]/(x^{18} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x18x17+19x1616x15+244x14181x13+1600x12607x11++1296 x^{18} - x^{17} + 19 x^{16} - 16 x^{15} + 244 x^{14} - 181 x^{13} + 1600 x^{12} - 607 x^{11} + \cdots + 1296 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 34 3^{4}
Twist minimal: no (minimal twist has level 364)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 1569.3
Root 0.520270+0.901135i-0.520270 + 0.901135i of defining polynomial
Character χ\chi == 2548.1569
Dual form 2548.2.k.i.393.3

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.520270+0.901135i)q3+3.18009q5+(0.958637+1.66041i)q9+(0.8524701.47652i)q11+(2.78983+2.28404i)q13+(1.65451+2.86569i)q15+(1.400012.42488i)q17+(2.74455+4.75370i)q19+(2.73500+4.73716i)q23+5.11296q255.11663q27+(3.814326.60660i)q29+2.51962q31+(0.887030+1.53638i)q33+(3.95043+6.84235i)q37+(3.50970+1.32569i)q39+(4.193647.26359i)q41+(5.61467+9.72490i)q43+(3.04855+5.28024i)q456.25007q47+2.91353q511.84212q53+(2.710934.69547i)q555.71163q57+(1.347102.33325i)q59+(3.388465.86899i)q61+(8.87191+7.26345i)q65+(1.79166+3.10325i)q67+(2.845884.92921i)q69+(2.005013.47278i)q71+11.7029q73+(2.66012+4.60746i)q75+13.2439q79+(0.213883+0.370457i)q818.55336q83+(4.452157.71134i)q85+(3.96896+6.87444i)q87+(0.1050610.181971i)q89+(1.31088+2.27052i)q93+(8.72791+15.1172i)q95+(6.3307710.9652i)q97+3.26884q99+O(q100)q+(-0.520270 + 0.901135i) q^{3} +3.18009 q^{5} +(0.958637 + 1.66041i) q^{9} +(0.852470 - 1.47652i) q^{11} +(2.78983 + 2.28404i) q^{13} +(-1.65451 + 2.86569i) q^{15} +(-1.40001 - 2.42488i) q^{17} +(2.74455 + 4.75370i) q^{19} +(-2.73500 + 4.73716i) q^{23} +5.11296 q^{25} -5.11663 q^{27} +(3.81432 - 6.60660i) q^{29} +2.51962 q^{31} +(0.887030 + 1.53638i) q^{33} +(-3.95043 + 6.84235i) q^{37} +(-3.50970 + 1.32569i) q^{39} +(4.19364 - 7.26359i) q^{41} +(5.61467 + 9.72490i) q^{43} +(3.04855 + 5.28024i) q^{45} -6.25007 q^{47} +2.91353 q^{51} -1.84212 q^{53} +(2.71093 - 4.69547i) q^{55} -5.71163 q^{57} +(-1.34710 - 2.33325i) q^{59} +(-3.38846 - 5.86899i) q^{61} +(8.87191 + 7.26345i) q^{65} +(-1.79166 + 3.10325i) q^{67} +(-2.84588 - 4.92921i) q^{69} +(-2.00501 - 3.47278i) q^{71} +11.7029 q^{73} +(-2.66012 + 4.60746i) q^{75} +13.2439 q^{79} +(-0.213883 + 0.370457i) q^{81} -8.55336 q^{83} +(-4.45215 - 7.71134i) q^{85} +(3.96896 + 6.87444i) q^{87} +(0.105061 - 0.181971i) q^{89} +(-1.31088 + 2.27052i) q^{93} +(8.72791 + 15.1172i) q^{95} +(-6.33077 - 10.9652i) q^{97} +3.26884 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 18q+q310q9+2q114q1310q15+6q17+q19+6q23+10q25+4q27+2q29+14q31+14q338q37+11q397q412q43+10q45+8q99+O(q100) 18 q + q^{3} - 10 q^{9} + 2 q^{11} - 4 q^{13} - 10 q^{15} + 6 q^{17} + q^{19} + 6 q^{23} + 10 q^{25} + 4 q^{27} + 2 q^{29} + 14 q^{31} + 14 q^{33} - 8 q^{37} + 11 q^{39} - 7 q^{41} - 2 q^{43} + 10 q^{45}+ \cdots - 8 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/2548Z)×\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times.

nn 197197 885885 12751275
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 −0.520270 + 0.901135i −0.300378 + 0.520270i −0.976222 0.216775i 0.930446π-0.930446\pi
0.675843 + 0.737045i 0.263780π0.263780\pi
44 0 0
55 3.18009 1.42218 0.711089 0.703102i 0.248202π-0.248202\pi
0.711089 + 0.703102i 0.248202π0.248202\pi
66 0 0
77 0 0
88 0 0
99 0.958637 + 1.66041i 0.319546 + 0.553470i
1010 0 0
1111 0.852470 1.47652i 0.257029 0.445188i −0.708415 0.705796i 0.750590π-0.750590\pi
0.965445 + 0.260608i 0.0839229π0.0839229\pi
1212 0 0
1313 2.78983 + 2.28404i 0.773760 + 0.633479i
1414 0 0
1515 −1.65451 + 2.86569i −0.427192 + 0.739917i
1616 0 0
1717 −1.40001 2.42488i −0.339552 0.588121i 0.644797 0.764354i 0.276942π-0.276942\pi
−0.984348 + 0.176233i 0.943609π0.943609\pi
1818 0 0
1919 2.74455 + 4.75370i 0.629643 + 1.09057i 0.987623 + 0.156844i 0.0501321π0.0501321\pi
−0.357981 + 0.933729i 0.616535π0.616535\pi
2020 0 0
2121 0 0
2222 0 0
2323 −2.73500 + 4.73716i −0.570287 + 0.987766i 0.426249 + 0.904606i 0.359835π0.359835\pi
−0.996536 + 0.0831603i 0.973499π0.973499\pi
2424 0 0
2525 5.11296 1.02259
2626 0 0
2727 −5.11663 −0.984695
2828 0 0
2929 3.81432 6.60660i 0.708302 1.22682i −0.257185 0.966362i 0.582795π-0.582795\pi
0.965487 0.260453i 0.0838718π-0.0838718\pi
3030 0 0
3131 2.51962 0.452537 0.226269 0.974065i 0.427347π-0.427347\pi
0.226269 + 0.974065i 0.427347π0.427347\pi
3232 0 0
3333 0.887030 + 1.53638i 0.154412 + 0.267450i
3434 0 0
3535 0 0
3636 0 0
3737 −3.95043 + 6.84235i −0.649447 + 1.12487i 0.333808 + 0.942641i 0.391666π0.391666\pi
−0.983255 + 0.182234i 0.941667π0.941667\pi
3838 0 0
3939 −3.50970 + 1.32569i −0.562001 + 0.212281i
4040 0 0
4141 4.19364 7.26359i 0.654936 1.13438i −0.326974 0.945033i 0.606029π-0.606029\pi
0.981910 0.189349i 0.0606379π-0.0606379\pi
4242 0 0
4343 5.61467 + 9.72490i 0.856230 + 1.48303i 0.875499 + 0.483219i 0.160533π0.160533\pi
−0.0192697 + 0.999814i 0.506134π0.506134\pi
4444 0 0
4545 3.04855 + 5.28024i 0.454451 + 0.787132i
4646 0 0
4747 −6.25007 −0.911666 −0.455833 0.890065i 0.650659π-0.650659\pi
−0.455833 + 0.890065i 0.650659π0.650659\pi
4848 0 0
4949 0 0
5050 0 0
5151 2.91353 0.407976
5252 0 0
5353 −1.84212 −0.253035 −0.126517 0.991964i 0.540380π-0.540380\pi
−0.126517 + 0.991964i 0.540380π0.540380\pi
5454 0 0
5555 2.71093 4.69547i 0.365542 0.633137i
5656 0 0
5757 −5.71163 −0.756524
5858 0 0
5959 −1.34710 2.33325i −0.175378 0.303764i 0.764914 0.644132i 0.222781π-0.222781\pi
−0.940292 + 0.340369i 0.889448π0.889448\pi
6060 0 0
6161 −3.38846 5.86899i −0.433848 0.751447i 0.563353 0.826217i 0.309511π-0.309511\pi
−0.997201 + 0.0747693i 0.976178π0.976178\pi
6262 0 0
6363 0 0
6464 0 0
6565 8.87191 + 7.26345i 1.10042 + 0.900920i
6666 0 0
6767 −1.79166 + 3.10325i −0.218887 + 0.379123i −0.954468 0.298314i 0.903576π-0.903576\pi
0.735581 + 0.677437i 0.236909π0.236909\pi
6868 0 0
6969 −2.84588 4.92921i −0.342604 0.593407i
7070 0 0
7171 −2.00501 3.47278i −0.237951 0.412143i 0.722175 0.691710i 0.243142π-0.243142\pi
−0.960126 + 0.279567i 0.909809π0.909809\pi
7272 0 0
7373 11.7029 1.36972 0.684862 0.728673i 0.259862π-0.259862\pi
0.684862 + 0.728673i 0.259862π0.259862\pi
7474 0 0
7575 −2.66012 + 4.60746i −0.307164 + 0.532024i
7676 0 0
7777 0 0
7878 0 0
7979 13.2439 1.49005 0.745027 0.667034i 0.232436π-0.232436\pi
0.745027 + 0.667034i 0.232436π0.232436\pi
8080 0 0
8181 −0.213883 + 0.370457i −0.0237648 + 0.0411618i
8282 0 0
8383 −8.55336 −0.938853 −0.469426 0.882972i 0.655539π-0.655539\pi
−0.469426 + 0.882972i 0.655539π0.655539\pi
8484 0 0
8585 −4.45215 7.71134i −0.482903 0.836413i
8686 0 0
8787 3.96896 + 6.87444i 0.425517 + 0.737017i
8888 0 0
8989 0.105061 0.181971i 0.0111364 0.0192889i −0.860403 0.509613i 0.829788π-0.829788\pi
0.871540 + 0.490325i 0.163122π0.163122\pi
9090 0 0
9191 0 0
9292 0 0
9393 −1.31088 + 2.27052i −0.135932 + 0.235442i
9494 0 0
9595 8.72791 + 15.1172i 0.895464 + 1.55099i
9696 0 0
9797 −6.33077 10.9652i −0.642792 1.11335i −0.984807 0.173654i 0.944443π-0.944443\pi
0.342015 0.939695i 0.388891π-0.388891\pi
9898 0 0
9999 3.26884 0.328531
100100 0 0
101101 5.77693 10.0059i 0.574826 0.995628i −0.421234 0.906952i 0.638403π-0.638403\pi
0.996061 0.0886761i 0.0282636π-0.0282636\pi
102102 0 0
103103 12.2027 1.20237 0.601183 0.799111i 0.294696π-0.294696\pi
0.601183 + 0.799111i 0.294696π0.294696\pi
104104 0 0
105105 0 0
106106 0 0
107107 1.13656 1.96858i 0.109875 0.190310i −0.805844 0.592128i 0.798288π-0.798288\pi
0.915720 + 0.401818i 0.131621π0.131621\pi
108108 0 0
109109 −4.85215 −0.464751 −0.232376 0.972626i 0.574650π-0.574650\pi
−0.232376 + 0.972626i 0.574650π0.574650\pi
110110 0 0
111111 −4.11058 7.11974i −0.390159 0.675776i
112112 0 0
113113 −0.333301 0.577294i −0.0313543 0.0543072i 0.849922 0.526908i 0.176649π-0.176649\pi
−0.881277 + 0.472601i 0.843315π0.843315\pi
114114 0 0
115115 −8.69754 + 15.0646i −0.811050 + 1.40478i
116116 0 0
117117 −1.11801 + 6.82183i −0.103360 + 0.630678i
118118 0 0
119119 0 0
120120 0 0
121121 4.04659 + 7.00890i 0.367872 + 0.637172i
122122 0 0
123123 4.36365 + 7.55807i 0.393457 + 0.681488i
124124 0 0
125125 0.359215 0.0321292
126126 0 0
127127 −9.03831 + 15.6548i −0.802020 + 1.38914i 0.116264 + 0.993218i 0.462908π0.462908\pi
−0.918284 + 0.395922i 0.870425π0.870425\pi
128128 0 0
129129 −11.6846 −1.02877
130130 0 0
131131 −18.7051 −1.63427 −0.817135 0.576446i 0.804439π-0.804439\pi
−0.817135 + 0.576446i 0.804439π0.804439\pi
132132 0 0
133133 0 0
134134 0 0
135135 −16.2713 −1.40041
136136 0 0
137137 11.2574 + 19.4984i 0.961786 + 1.66586i 0.718012 + 0.696031i 0.245052π0.245052\pi
0.243775 + 0.969832i 0.421614π0.421614\pi
138138 0 0
139139 −3.61314 6.25815i −0.306463 0.530809i 0.671123 0.741346i 0.265812π-0.265812\pi
−0.977586 + 0.210537i 0.932479π0.932479\pi
140140 0 0
141141 3.25173 5.63215i 0.273845 0.474313i
142142 0 0
143143 5.75068 2.17217i 0.480896 0.181646i
144144 0 0
145145 12.1299 21.0096i 1.00733 1.74475i
146146 0 0
147147 0 0
148148 0 0
149149 3.74931 + 6.49399i 0.307155 + 0.532009i 0.977739 0.209825i 0.0672895π-0.0672895\pi
−0.670584 + 0.741834i 0.733956π0.733956\pi
150150 0 0
151151 −1.98514 −0.161549 −0.0807743 0.996732i 0.525739π-0.525739\pi
−0.0807743 + 0.996732i 0.525739π0.525739\pi
152152 0 0
153153 2.68420 4.64917i 0.217005 0.375863i
154154 0 0
155155 8.01261 0.643589
156156 0 0
157157 −4.02469 −0.321205 −0.160603 0.987019i 0.551344π-0.551344\pi
−0.160603 + 0.987019i 0.551344π0.551344\pi
158158 0 0
159159 0.958401 1.66000i 0.0760061 0.131646i
160160 0 0
161161 0 0
162162 0 0
163163 1.99358 + 3.45298i 0.156149 + 0.270458i 0.933477 0.358638i 0.116759π-0.116759\pi
−0.777328 + 0.629096i 0.783425π0.783425\pi
164164 0 0
165165 2.82083 + 4.88583i 0.219602 + 0.380361i
166166 0 0
167167 1.98915 3.44532i 0.153925 0.266607i −0.778742 0.627345i 0.784142π-0.784142\pi
0.932667 + 0.360738i 0.117475π0.117475\pi
168168 0 0
169169 2.56631 + 12.7442i 0.197409 + 0.980321i
170170 0 0
171171 −5.26206 + 9.11415i −0.402399 + 0.696976i
172172 0 0
173173 11.3603 + 19.6766i 0.863706 + 1.49598i 0.868326 + 0.495993i 0.165196π0.165196\pi
−0.00462066 + 0.999989i 0.501471π0.501471\pi
174174 0 0
175175 0 0
176176 0 0
177177 2.80343 0.210719
178178 0 0
179179 2.06510 3.57686i 0.154353 0.267347i −0.778470 0.627681i 0.784004π-0.784004\pi
0.932823 + 0.360334i 0.117337π0.117337\pi
180180 0 0
181181 −2.63446 −0.195818 −0.0979091 0.995195i 0.531215π-0.531215\pi
−0.0979091 + 0.995195i 0.531215π0.531215\pi
182182 0 0
183183 7.05167 0.521274
184184 0 0
185185 −12.5627 + 21.7593i −0.923629 + 1.59977i
186186 0 0
187187 −4.77386 −0.349099
188188 0 0
189189 0 0
190190 0 0
191191 2.34005 + 4.05309i 0.169320 + 0.293271i 0.938181 0.346145i 0.112509π-0.112509\pi
−0.768861 + 0.639416i 0.779176π0.779176\pi
192192 0 0
193193 8.96829 15.5335i 0.645551 1.11813i −0.338622 0.940922i 0.609961π-0.609961\pi
0.984174 0.177206i 0.0567057π-0.0567057\pi
194194 0 0
195195 −11.1611 + 4.21583i −0.799266 + 0.301902i
196196 0 0
197197 11.3526 19.6632i 0.808838 1.40095i −0.104832 0.994490i 0.533430π-0.533430\pi
0.913669 0.406458i 0.133236π-0.133236\pi
198198 0 0
199199 −3.97980 6.89322i −0.282121 0.488648i 0.689786 0.724013i 0.257705π-0.257705\pi
−0.971907 + 0.235366i 0.924371π0.924371\pi
200200 0 0
201201 −1.86430 3.22906i −0.131498 0.227761i
202202 0 0
203203 0 0
204204 0 0
205205 13.3361 23.0989i 0.931436 1.61329i
206206 0 0
207207 −10.4875 −0.728931
208208 0 0
209209 9.35859 0.647347
210210 0 0
211211 −5.08147 + 8.80136i −0.349823 + 0.605911i −0.986218 0.165453i 0.947092π-0.947092\pi
0.636395 + 0.771363i 0.280425π0.280425\pi
212212 0 0
213213 4.17259 0.285901
214214 0 0
215215 17.8552 + 30.9260i 1.21771 + 2.10914i
216216 0 0
217217 0 0
218218 0 0
219219 −6.08869 + 10.5459i −0.411435 + 0.712627i
220220 0 0
221221 1.63275 9.96269i 0.109831 0.670163i
222222 0 0
223223 −1.33387 + 2.31033i −0.0893224 + 0.154711i −0.907225 0.420646i 0.861803π-0.861803\pi
0.817902 + 0.575357i 0.195137π0.195137\pi
224224 0 0
225225 4.90147 + 8.48960i 0.326765 + 0.565973i
226226 0 0
227227 −12.5757 21.7817i −0.834677 1.44570i −0.894293 0.447482i 0.852321π-0.852321\pi
0.0596159 0.998221i 0.481012π-0.481012\pi
228228 0 0
229229 12.3075 0.813301 0.406651 0.913584i 0.366697π-0.366697\pi
0.406651 + 0.913584i 0.366697π0.366697\pi
230230 0 0
231231 0 0
232232 0 0
233233 −21.1440 −1.38519 −0.692594 0.721327i 0.743532π-0.743532\pi
−0.692594 + 0.721327i 0.743532π0.743532\pi
234234 0 0
235235 −19.8758 −1.29655
236236 0 0
237237 −6.89041 + 11.9345i −0.447580 + 0.775231i
238238 0 0
239239 −27.3984 −1.77225 −0.886127 0.463443i 0.846614π-0.846614\pi
−0.886127 + 0.463443i 0.846614π0.846614\pi
240240 0 0
241241 8.57805 + 14.8576i 0.552561 + 0.957064i 0.998089 + 0.0617955i 0.0196827π0.0196827\pi
−0.445528 + 0.895268i 0.646984π0.646984\pi
242242 0 0
243243 −7.89749 13.6789i −0.506624 0.877499i
244244 0 0
245245 0 0
246246 0 0
247247 −3.20082 + 19.5307i −0.203663 + 1.24271i
248248 0 0
249249 4.45006 7.70773i 0.282011 0.488457i
250250 0 0
251251 13.4469 + 23.2907i 0.848759 + 1.47009i 0.882317 + 0.470656i 0.155983π0.155983\pi
−0.0335582 + 0.999437i 0.510684π0.510684\pi
252252 0 0
253253 4.66301 + 8.07658i 0.293161 + 0.507770i
254254 0 0
255255 9.26528 0.580214
256256 0 0
257257 −5.65006 + 9.78619i −0.352441 + 0.610446i −0.986677 0.162694i 0.947982π-0.947982\pi
0.634235 + 0.773140i 0.281315π0.281315\pi
258258 0 0
259259 0 0
260260 0 0
261261 14.6262 0.905340
262262 0 0
263263 0.498739 0.863842i 0.0307536 0.0532668i −0.850239 0.526397i 0.823543π-0.823543\pi
0.880993 + 0.473130i 0.156876π0.156876\pi
264264 0 0
265265 −5.85810 −0.359860
266266 0 0
267267 0.109320 + 0.189348i 0.00669029 + 0.0115879i
268268 0 0
269269 6.56406 + 11.3693i 0.400218 + 0.693198i 0.993752 0.111611i 0.0356010π-0.0356010\pi
−0.593534 + 0.804809i 0.702268π0.702268\pi
270270 0 0
271271 3.22120 5.57928i 0.195674 0.338917i −0.751447 0.659793i 0.770644π-0.770644\pi
0.947121 + 0.320876i 0.103977π0.103977\pi
272272 0 0
273273 0 0
274274 0 0
275275 4.35864 7.54939i 0.262836 0.455246i
276276 0 0
277277 11.9907 + 20.7685i 0.720451 + 1.24786i 0.960819 + 0.277175i 0.0893983π0.0893983\pi
−0.240369 + 0.970682i 0.577268π0.577268\pi
278278 0 0
279279 2.41540 + 4.18360i 0.144606 + 0.250466i
280280 0 0
281281 −10.3602 −0.618035 −0.309018 0.951056i 0.600000π-0.600000\pi
−0.309018 + 0.951056i 0.600000π0.600000\pi
282282 0 0
283283 14.9565 25.9054i 0.889071 1.53992i 0.0480964 0.998843i 0.484685π-0.484685\pi
0.840975 0.541074i 0.181982π-0.181982\pi
284284 0 0
285285 −18.1635 −1.07591
286286 0 0
287287 0 0
288288 0 0
289289 4.57996 7.93272i 0.269409 0.466631i
290290 0 0
291291 13.1748 0.772323
292292 0 0
293293 −0.184399 0.319389i −0.0107727 0.0186589i 0.860589 0.509300i 0.170096π-0.170096\pi
−0.871362 + 0.490642i 0.836762π0.836762\pi
294294 0 0
295295 −4.28391 7.41995i −0.249419 0.432006i
296296 0 0
297297 −4.36177 + 7.55481i −0.253096 + 0.438374i
298298 0 0
299299 −18.4501 + 6.96902i −1.06699 + 0.403029i
300300 0 0
301301 0 0
302302 0 0
303303 6.01113 + 10.4116i 0.345331 + 0.598130i
304304 0 0
305305 −10.7756 18.6639i −0.617010 1.06869i
306306 0 0
307307 13.8684 0.791511 0.395756 0.918356i 0.370483π-0.370483\pi
0.395756 + 0.918356i 0.370483π0.370483\pi
308308 0 0
309309 −6.34869 + 10.9963i −0.361165 + 0.625555i
310310 0 0
311311 1.18119 0.0669791 0.0334895 0.999439i 0.489338π-0.489338\pi
0.0334895 + 0.999439i 0.489338π0.489338\pi
312312 0 0
313313 10.5862 0.598368 0.299184 0.954195i 0.403286π-0.403286\pi
0.299184 + 0.954195i 0.403286π0.403286\pi
314314 0 0
315315 0 0
316316 0 0
317317 8.48888 0.476783 0.238392 0.971169i 0.423380π-0.423380\pi
0.238392 + 0.971169i 0.423380π0.423380\pi
318318 0 0
319319 −6.50319 11.2639i −0.364109 0.630655i
320320 0 0
321321 1.18264 + 2.04839i 0.0660084 + 0.114330i
322322 0 0
323323 7.68478 13.3104i 0.427592 0.740612i
324324 0 0
325325 14.2643 + 11.6782i 0.791240 + 0.647790i
326326 0 0
327327 2.52443 4.37244i 0.139601 0.241796i
328328 0 0
329329 0 0
330330 0 0
331331 −2.17210 3.76219i −0.119389 0.206788i 0.800136 0.599818i 0.204760π-0.204760\pi
−0.919526 + 0.393030i 0.871427π0.871427\pi
332332 0 0
333333 −15.1481 −0.830112
334334 0 0
335335 −5.69765 + 9.86862i −0.311296 + 0.539180i
336336 0 0
337337 8.59397 0.468143 0.234072 0.972219i 0.424795π-0.424795\pi
0.234072 + 0.972219i 0.424795π0.424795\pi
338338 0 0
339339 0.693626 0.0376726
340340 0 0
341341 2.14790 3.72027i 0.116315 0.201464i
342342 0 0
343343 0 0
344344 0 0
345345 −9.05015 15.6753i −0.487244 0.843931i
346346 0 0
347347 −10.4098 18.0304i −0.558829 0.967920i −0.997595 0.0693188i 0.977917π-0.977917\pi
0.438765 0.898602i 0.355416π-0.355416\pi
348348 0 0
349349 0.115786 0.200546i 0.00619786 0.0107350i −0.862910 0.505358i 0.831360π-0.831360\pi
0.869108 + 0.494623i 0.164694π0.164694\pi
350350 0 0
351351 −14.2745 11.6866i −0.761917 0.623784i
352352 0 0
353353 −9.09972 + 15.7612i −0.484329 + 0.838883i −0.999838 0.0180014i 0.994270π-0.994270\pi
0.515509 + 0.856884i 0.327603π0.327603\pi
354354 0 0
355355 −6.37611 11.0437i −0.338409 0.586141i
356356 0 0
357357 0 0
358358 0 0
359359 4.54298 0.239769 0.119885 0.992788i 0.461748π-0.461748\pi
0.119885 + 0.992788i 0.461748π0.461748\pi
360360 0 0
361361 −5.56510 + 9.63904i −0.292900 + 0.507318i
362362 0 0
363363 −8.42128 −0.442003
364364 0 0
365365 37.2163 1.94799
366366 0 0
367367 5.01139 8.67998i 0.261592 0.453091i −0.705073 0.709135i 0.749086π-0.749086\pi
0.966665 + 0.256044i 0.0824190π0.0824190\pi
368368 0 0
369369 16.0807 0.837128
370370 0 0
371371 0 0
372372 0 0
373373 −4.21567 7.30176i −0.218279 0.378071i 0.736003 0.676979i 0.236711π-0.236711\pi
−0.954282 + 0.298908i 0.903378π0.903378\pi
374374 0 0
375375 −0.186889 + 0.323702i −0.00965092 + 0.0167159i
376376 0 0
377377 25.7311 9.71923i 1.32522 0.500566i
378378 0 0
379379 −5.15804 + 8.93398i −0.264951 + 0.458908i −0.967551 0.252677i 0.918689π-0.918689\pi
0.702600 + 0.711585i 0.252022π0.252022\pi
380380 0 0
381381 −9.40473 16.2895i −0.481819 0.834535i
382382 0 0
383383 −1.09813 1.90201i −0.0561116 0.0971881i 0.836605 0.547806i 0.184537π-0.184537\pi
−0.892717 + 0.450618i 0.851204π0.851204\pi
384384 0 0
385385 0 0
386386 0 0
387387 −10.7649 + 18.6453i −0.547209 + 0.947794i
388388 0 0
389389 −32.7955 −1.66280 −0.831398 0.555677i 0.812459π-0.812459\pi
−0.831398 + 0.555677i 0.812459π0.812459\pi
390390 0 0
391391 15.3161 0.774568
392392 0 0
393393 9.73170 16.8558i 0.490899 0.850262i
394394 0 0
395395 42.1167 2.11912
396396 0 0
397397 −2.75848 4.77782i −0.138444 0.239792i 0.788464 0.615081i 0.210877π-0.210877\pi
−0.926908 + 0.375289i 0.877543π0.877543\pi
398398 0 0
399399 0 0
400400 0 0
401401 9.66790 16.7453i 0.482792 0.836220i −0.517013 0.855977i 0.672956π-0.672956\pi
0.999805 + 0.0197577i 0.00628949π0.00628949\pi
402402 0 0
403403 7.02931 + 5.75492i 0.350155 + 0.286673i
404404 0 0
405405 −0.680167 + 1.17808i −0.0337978 + 0.0585395i
406406 0 0
407407 6.73525 + 11.6658i 0.333854 + 0.578252i
408408 0 0
409409 −18.0322 31.2326i −0.891633 1.54435i −0.837918 0.545797i 0.816227π-0.816227\pi
−0.0537150 0.998556i 0.517106π-0.517106\pi
410410 0 0
411411 −23.4276 −1.15560
412412 0 0
413413 0 0
414414 0 0
415415 −27.2004 −1.33522
416416 0 0
417417 7.51925 0.368219
418418 0 0
419419 4.22915 7.32510i 0.206607 0.357854i −0.744036 0.668139i 0.767091π-0.767091\pi
0.950644 + 0.310285i 0.100424π0.100424\pi
420420 0 0
421421 −40.2697 −1.96262 −0.981312 0.192424i 0.938365π-0.938365\pi
−0.981312 + 0.192424i 0.938365π0.938365\pi
422422 0 0
423423 −5.99155 10.3777i −0.291319 0.504579i
424424 0 0
425425 −7.15818 12.3983i −0.347223 0.601407i
426426 0 0
427427 0 0
428428 0 0
429429 −1.03449 + 6.31226i −0.0499458 + 0.304759i
430430 0 0
431431 6.53799 11.3241i 0.314924 0.545464i −0.664498 0.747290i 0.731354π-0.731354\pi
0.979421 + 0.201827i 0.0646877π0.0646877\pi
432432 0 0
433433 −9.78438 16.9470i −0.470207 0.814423i 0.529212 0.848490i 0.322488π-0.322488\pi
−0.999420 + 0.0340664i 0.989154π0.989154\pi
434434 0 0
435435 12.6216 + 21.8613i 0.605161 + 1.04817i
436436 0 0
437437 −30.0254 −1.43631
438438 0 0
439439 7.19768 12.4667i 0.343527 0.595006i −0.641558 0.767074i 0.721712π-0.721712\pi
0.985085 + 0.172069i 0.0550451π0.0550451\pi
440440 0 0
441441 0 0
442442 0 0
443443 8.63764 0.410386 0.205193 0.978721i 0.434218π-0.434218\pi
0.205193 + 0.978721i 0.434218π0.434218\pi
444444 0 0
445445 0.334103 0.578684i 0.0158380 0.0274322i
446446 0 0
447447 −7.80262 −0.369051
448448 0 0
449449 −11.4447 19.8228i −0.540110 0.935498i −0.998897 0.0469519i 0.985049π-0.985049\pi
0.458787 0.888546i 0.348284π-0.348284\pi
450450 0 0
451451 −7.14990 12.3840i −0.336676 0.583140i
452452 0 0
453453 1.03281 1.78888i 0.0485257 0.0840490i
454454 0 0
455455 0 0
456456 0 0
457457 12.9024 22.3476i 0.603548 1.04538i −0.388732 0.921351i 0.627087π-0.627087\pi
0.992279 0.124024i 0.0395800π-0.0395800\pi
458458 0 0
459459 7.16331 + 12.4072i 0.334355 + 0.579119i
460460 0 0
461461 3.84106 + 6.65291i 0.178896 + 0.309857i 0.941503 0.337005i 0.109414π-0.109414\pi
−0.762607 + 0.646862i 0.776081π0.776081\pi
462462 0 0
463463 7.95930 0.369900 0.184950 0.982748i 0.440788π-0.440788\pi
0.184950 + 0.982748i 0.440788π0.440788\pi
464464 0 0
465465 −4.16873 + 7.22044i −0.193320 + 0.334840i
466466 0 0
467467 −21.5156 −0.995621 −0.497810 0.867286i 0.665862π-0.665862\pi
−0.497810 + 0.867286i 0.665862π0.665862\pi
468468 0 0
469469 0 0
470470 0 0
471471 2.09393 3.62679i 0.0964831 0.167114i
472472 0 0
473473 19.1454 0.880305
474474 0 0
475475 14.0328 + 24.3055i 0.643867 + 1.11521i
476476 0 0
477477 −1.76593 3.05867i −0.0808562 0.140047i
478478 0 0
479479 16.7505 29.0126i 0.765348 1.32562i −0.174715 0.984619i 0.555900π-0.555900\pi
0.940063 0.341002i 0.110766π-0.110766\pi
480480 0 0
481481 −26.6492 + 10.0660i −1.21510 + 0.458972i
482482 0 0
483483 0 0
484484 0 0
485485 −20.1324 34.8703i −0.914165 1.58338i
486486 0 0
487487 −7.62298 13.2034i −0.345430 0.598303i 0.640001 0.768374i 0.278934π-0.278934\pi
−0.985432 + 0.170071i 0.945600π0.945600\pi
488488 0 0
489489 −4.14880 −0.187615
490490 0 0
491491 10.9575 18.9790i 0.494507 0.856510i −0.505473 0.862842i 0.668682π-0.668682\pi
0.999980 + 0.00633175i 0.00201547π0.00201547\pi
492492 0 0
493493 −21.3603 −0.962020
494494 0 0
495495 10.3952 0.467229
496496 0 0
497497 0 0
498498 0 0
499499 −36.3127 −1.62558 −0.812791 0.582555i 0.802053π-0.802053\pi
−0.812791 + 0.582555i 0.802053π0.802053\pi
500500 0 0
501501 2.06980 + 3.58499i 0.0924717 + 0.160166i
502502 0 0
503503 −13.2906 23.0199i −0.592597 1.02641i −0.993881 0.110454i 0.964769π-0.964769\pi
0.401285 0.915953i 0.368564π-0.368564\pi
504504 0 0
505505 18.3711 31.8198i 0.817505 1.41596i
506506 0 0
507507 −12.8194 4.31782i −0.569329 0.191761i
508508 0 0
509509 17.5859 30.4597i 0.779483 1.35010i −0.152757 0.988264i 0.548815π-0.548815\pi
0.932240 0.361841i 0.117852π-0.117852\pi
510510 0 0
511511 0 0
512512 0 0
513513 −14.0428 24.3229i −0.620006 1.07388i
514514 0 0
515515 38.8056 1.70998
516516 0 0
517517 −5.32800 + 9.22836i −0.234325 + 0.405863i
518518 0 0
519519 −23.6417 −1.03775
520520 0 0
521521 −7.61490 −0.333615 −0.166807 0.985989i 0.553346π-0.553346\pi
−0.166807 + 0.985989i 0.553346π0.553346\pi
522522 0 0
523523 19.0037 32.9154i 0.830975 1.43929i −0.0662915 0.997800i 0.521117π-0.521117\pi
0.897266 0.441490i 0.145550π-0.145550\pi
524524 0 0
525525 0 0
526526 0 0
527527 −3.52749 6.10979i −0.153660 0.266146i
528528 0 0
529529 −3.46046 5.99369i −0.150455 0.260595i
530530 0 0
531531 2.58277 4.47349i 0.112083 0.194133i
532532 0 0
533533 28.2899 10.6858i 1.22537 0.462852i
534534 0 0
535535 3.61436 6.26026i 0.156262 0.270654i
536536 0 0
537537 2.14882 + 3.72187i 0.0927286 + 0.160611i
538538 0 0
539539 0 0
540540 0 0
541541 −8.91225 −0.383168 −0.191584 0.981476i 0.561362π-0.561362\pi
−0.191584 + 0.981476i 0.561362π0.561362\pi
542542 0 0
543543 1.37063 2.37401i 0.0588195 0.101878i
544544 0 0
545545 −15.4303 −0.660960
546546 0 0
547547 −16.7066 −0.714321 −0.357161 0.934043i 0.616255π-0.616255\pi
−0.357161 + 0.934043i 0.616255π0.616255\pi
548548 0 0
549549 6.49662 11.2525i 0.277269 0.480244i
550550 0 0
551551 41.8744 1.78391
552552 0 0
553553 0 0
554554 0 0
555555 −13.0720 22.6414i −0.554876 0.961074i
556556 0 0
557557 18.3262 31.7419i 0.776507 1.34495i −0.157437 0.987529i 0.550323π-0.550323\pi
0.933944 0.357420i 0.116343π-0.116343\pi
558558 0 0
559559 −6.54808 + 39.9550i −0.276954 + 1.68992i
560560 0 0
561561 2.48370 4.30189i 0.104862 0.181626i
562562 0 0
563563 −1.96094 3.39646i −0.0826440 0.143144i 0.821741 0.569861i 0.193003π-0.193003\pi
−0.904385 + 0.426718i 0.859670π0.859670\pi
564564 0 0
565565 −1.05993 1.83585i −0.0445914 0.0772346i
566566 0 0
567567 0 0
568568 0 0
569569 1.00915 1.74790i 0.0423058 0.0732757i −0.844097 0.536190i 0.819863π-0.819863\pi
0.886403 + 0.462914i 0.153196π0.153196\pi
570570 0 0
571571 5.56366 0.232832 0.116416 0.993201i 0.462859π-0.462859\pi
0.116416 + 0.993201i 0.462859π0.462859\pi
572572 0 0
573573 −4.86984 −0.203441
574574 0 0
575575 −13.9839 + 24.2209i −0.583171 + 1.01008i
576576 0 0
577577 1.08138 0.0450186 0.0225093 0.999747i 0.492834π-0.492834\pi
0.0225093 + 0.999747i 0.492834π0.492834\pi
578578 0 0
579579 9.33187 + 16.1633i 0.387819 + 0.671723i
580580 0 0
581581 0 0
582582 0 0
583583 −1.57035 + 2.71993i −0.0650374 + 0.112648i
584584 0 0
585585 −3.55536 + 21.6940i −0.146996 + 0.896937i
586586 0 0
587587 11.3515 19.6613i 0.468526 0.811510i −0.530827 0.847480i 0.678119π-0.678119\pi
0.999353 + 0.0359699i 0.0114520π0.0114520\pi
588588 0 0
589589 6.91522 + 11.9775i 0.284937 + 0.493525i
590590 0 0
591591 11.8128 + 20.4604i 0.485915 + 0.841629i
592592 0 0
593593 −22.0550 −0.905692 −0.452846 0.891589i 0.649591π-0.649591\pi
−0.452846 + 0.891589i 0.649591π0.649591\pi
594594 0 0
595595 0 0
596596 0 0
597597 8.28230 0.338972
598598 0 0
599599 6.16283 0.251807 0.125903 0.992043i 0.459817π-0.459817\pi
0.125903 + 0.992043i 0.459817π0.459817\pi
600600 0 0
601601 9.13735 15.8264i 0.372720 0.645571i −0.617263 0.786757i 0.711758π-0.711758\pi
0.989983 + 0.141187i 0.0450917π0.0450917\pi
602602 0 0
603603 −6.87023 −0.279777
604604 0 0
605605 12.8685 + 22.2889i 0.523179 + 0.906173i
606606 0 0
607607 7.45389 + 12.9105i 0.302544 + 0.524022i 0.976712 0.214557i 0.0688307π-0.0688307\pi
−0.674167 + 0.738579i 0.735497π0.735497\pi
608608 0 0
609609 0 0
610610 0 0
611611 −17.4366 14.2754i −0.705411 0.577521i
612612 0 0
613613 −2.32174 + 4.02137i −0.0937742 + 0.162422i −0.909096 0.416586i 0.863227π-0.863227\pi
0.815322 + 0.579008i 0.196560π0.196560\pi
614614 0 0
615615 13.8768 + 24.0353i 0.559566 + 0.969197i
616616 0 0
617617 −5.34393 9.25597i −0.215139 0.372631i 0.738177 0.674607i 0.235687π-0.235687\pi
−0.953315 + 0.301976i 0.902354π0.902354\pi
618618 0 0
619619 20.5826 0.827283 0.413642 0.910440i 0.364257π-0.364257\pi
0.413642 + 0.910440i 0.364257π0.364257\pi
620620 0 0
621621 13.9940 24.2383i 0.561559 0.972648i
622622 0 0
623623 0 0
624624 0 0
625625 −24.4225 −0.976898
626626 0 0
627627 −4.86900 + 8.43335i −0.194449 + 0.336796i
628628 0 0
629629 22.1225 0.882083
630630 0 0
631631 −21.9750 38.0619i −0.874812 1.51522i −0.856963 0.515379i 0.827651π-0.827651\pi
−0.0178498 0.999841i 0.505682π-0.505682\pi
632632 0 0
633633 −5.28748 9.15818i −0.210158 0.364005i
634634 0 0
635635 −28.7426 + 49.7837i −1.14062 + 1.97560i
636636 0 0
637637 0 0
638638 0 0
639639 3.84415 6.65827i 0.152072 0.263397i
640640 0 0
641641 −24.3981 42.2587i −0.963666 1.66912i −0.713157 0.701005i 0.752735π-0.752735\pi
−0.250509 0.968114i 0.580598π-0.580598\pi
642642 0 0
643643 2.08350 + 3.60873i 0.0821653 + 0.142315i 0.904180 0.427152i 0.140483π-0.140483\pi
−0.822014 + 0.569467i 0.807150π0.807150\pi
644644 0 0
645645 −37.1580 −1.46310
646646 0 0
647647 8.13081 14.0830i 0.319655 0.553659i −0.660761 0.750596i 0.729766π-0.729766\pi
0.980416 + 0.196938i 0.0630996π0.0630996\pi
648648 0 0
649649 −4.59346 −0.180309
650650 0 0
651651 0 0
652652 0 0
653653 −3.91378 + 6.77886i −0.153158 + 0.265277i −0.932387 0.361462i 0.882278π-0.882278\pi
0.779229 + 0.626740i 0.215611π0.215611\pi
654654 0 0
655655 −59.4838 −2.32422
656656 0 0
657657 11.2189 + 19.4316i 0.437690 + 0.758100i
658658 0 0
659659 20.3114 + 35.1805i 0.791221 + 1.37044i 0.925211 + 0.379453i 0.123888π0.123888\pi
−0.133990 + 0.990983i 0.542779π0.542779\pi
660660 0 0
661661 −15.4342 + 26.7328i −0.600320 + 1.03979i 0.392452 + 0.919773i 0.371627π0.371627\pi
−0.992772 + 0.120013i 0.961706π0.961706\pi
662662 0 0
663663 8.12825 + 6.65462i 0.315675 + 0.258444i
664664 0 0
665665 0 0
666666 0 0
667667 20.8644 + 36.1381i 0.807871 + 1.39927i
668668 0 0
669669 −1.38794 2.40399i −0.0536610 0.0929436i
670670 0 0
671671 −11.5543 −0.446047
672672 0 0
673673 −13.5310 + 23.4364i −0.521581 + 0.903405i 0.478104 + 0.878303i 0.341324π0.341324\pi
−0.999685 + 0.0251020i 0.992009π0.992009\pi
674674 0 0
675675 −26.1611 −1.00694
676676 0 0
677677 −16.8472 −0.647490 −0.323745 0.946144i 0.604942π-0.604942\pi
−0.323745 + 0.946144i 0.604942π0.604942\pi
678678 0 0
679679 0 0
680680 0 0
681681 26.1710 1.00288
682682 0 0
683683 −9.89038 17.1306i −0.378445 0.655486i 0.612391 0.790555i 0.290208π-0.290208\pi
−0.990836 + 0.135069i 0.956874π0.956874\pi
684684 0 0
685685 35.7996 + 62.0067i 1.36783 + 2.36915i
686686 0 0
687687 −6.40322 + 11.0907i −0.244298 + 0.423137i
688688 0 0
689689 −5.13920 4.20748i −0.195788 0.160292i
690690 0 0
691691 −4.64021 + 8.03707i −0.176522 + 0.305745i −0.940687 0.339276i 0.889818π-0.889818\pi
0.764165 + 0.645021i 0.223151π0.223151\pi
692692 0 0
693693 0 0
694694 0 0
695695 −11.4901 19.9015i −0.435845 0.754905i
696696 0 0
697697 −23.4845 −0.889539
698698 0 0
699699 11.0006 19.0536i 0.416081 0.720673i
700700 0 0
701701 34.6015 1.30688 0.653441 0.756977i 0.273325π-0.273325\pi
0.653441 + 0.756977i 0.273325π0.273325\pi
702702 0 0
703703 −43.3686 −1.63568
704704 0 0
705705 10.3408 17.9107i 0.389456 0.674558i
706706 0 0
707707 0 0
708708 0 0
709709 7.55823 + 13.0912i 0.283855 + 0.491652i 0.972331 0.233608i 0.0750531π-0.0750531\pi
−0.688476 + 0.725260i 0.741720π0.741720\pi
710710 0 0
711711 12.6961 + 21.9903i 0.476141 + 0.824700i
712712 0 0
713713 −6.89116 + 11.9358i −0.258076 + 0.447001i
714714 0 0
715715 18.2877 6.90769i 0.683920 0.258333i
716716 0 0
717717 14.2546 24.6896i 0.532346 0.922051i
718718 0 0
719719 −10.6380 18.4255i −0.396730 0.687157i 0.596590 0.802546i 0.296522π-0.296522\pi
−0.993320 + 0.115389i 0.963188π0.963188\pi
720720 0 0
721721 0 0
722722 0 0
723723 −17.8516 −0.663909
724724 0 0
725725 19.5025 33.7793i 0.724304 1.25453i
726726 0 0
727727 −10.5609 −0.391684 −0.195842 0.980635i 0.562744π-0.562744\pi
−0.195842 + 0.980635i 0.562744π0.562744\pi
728728 0 0
729729 15.1520 0.561186
730730 0 0
731731 15.7212 27.2299i 0.581468 1.00713i
732732 0 0
733733 −8.81656 −0.325647 −0.162824 0.986655i 0.552060π-0.552060\pi
−0.162824 + 0.986655i 0.552060π0.552060\pi
734734 0 0
735735 0 0
736736 0 0
737737 3.05468 + 5.29086i 0.112521 + 0.194891i
738738 0 0
739739 −14.5384 + 25.1812i −0.534803 + 0.926307i 0.464369 + 0.885642i 0.346281π0.346281\pi
−0.999173 + 0.0406651i 0.987052π0.987052\pi
740740 0 0
741741 −15.9345 13.0456i −0.585368 0.479242i
742742 0 0
743743 −19.3225 + 33.4675i −0.708872 + 1.22780i 0.256404 + 0.966570i 0.417462π0.417462\pi
−0.965276 + 0.261233i 0.915871π0.915871\pi
744744 0 0
745745 11.9231 + 20.6515i 0.436830 + 0.756611i
746746 0 0
747747 −8.19957 14.2021i −0.300006 0.519626i
748748 0 0
749749 0 0
750750 0 0
751751 20.1942 34.9775i 0.736898 1.27635i −0.216987 0.976174i 0.569623π-0.569623\pi
0.953885 0.300171i 0.0970437π-0.0970437\pi
752752 0 0
753753 −27.9840 −1.01979
754754 0 0
755755 −6.31293 −0.229751
756756 0 0
757757 11.2192 19.4322i 0.407768 0.706275i −0.586871 0.809680i 0.699641π-0.699641\pi
0.994639 + 0.103405i 0.0329739π0.0329739\pi
758758 0 0
759759 −9.70411 −0.352237
760760 0 0
761761 −8.58250 14.8653i −0.311115 0.538868i 0.667489 0.744620i 0.267369π-0.267369\pi
−0.978604 + 0.205752i 0.934036π0.934036\pi
762762 0 0
763763 0 0
764764 0 0
765765 8.53599 14.7848i 0.308619 0.534544i
766766 0 0
767767 1.57105 9.58622i 0.0567274 0.346138i
768768 0 0
769769 −21.4658 + 37.1798i −0.774076 + 1.34074i 0.161236 + 0.986916i 0.448452π0.448452\pi
−0.935312 + 0.353823i 0.884881π0.884881\pi
770770 0 0
771771 −5.87912 10.1829i −0.211731 0.366729i
772772 0 0
773773 3.36534 + 5.82893i 0.121043 + 0.209652i 0.920179 0.391498i 0.128043π-0.128043\pi
−0.799136 + 0.601150i 0.794710π0.794710\pi
774774 0 0
775775 12.8827 0.462761
776776 0 0
777777 0 0
778778 0 0
779779 46.0386 1.64950
780780 0 0
781781 −6.83685 −0.244642
782782 0 0
783783 −19.5165 + 33.8035i −0.697461 + 1.20804i
784784 0 0
785785 −12.7989 −0.456811
786786 0 0
787787 19.1240 + 33.1238i 0.681699 + 1.18074i 0.974462 + 0.224552i 0.0720918π0.0720918\pi
−0.292764 + 0.956185i 0.594575π0.594575\pi
788788 0 0
789789 0.518959 + 0.898863i 0.0184754 + 0.0320004i
790790 0 0
791791 0 0
792792 0 0
793793 3.95178 24.1129i 0.140332 0.856274i
794794 0 0
795795 3.04780 5.27894i 0.108094 0.187225i
796796 0 0
797797 21.3120 + 36.9134i 0.754909 + 1.30754i 0.945420 + 0.325855i 0.105652π0.105652\pi
−0.190511 + 0.981685i 0.561015π0.561015\pi
798798 0 0
799799 8.75014 + 15.1557i 0.309558 + 0.536170i
800800 0 0
801801 0.402862 0.0142344
802802 0 0
803803 9.97640 17.2796i 0.352059 0.609785i
804804 0 0
805805 0 0
806806 0 0
807807 −13.6604 −0.480867
808808 0 0
809809 18.7448 32.4670i 0.659033 1.14148i −0.321833 0.946797i 0.604299π-0.604299\pi
0.980866 0.194683i 0.0623678π-0.0623678\pi
810810 0 0
811811 25.4069 0.892156 0.446078 0.894994i 0.352820π-0.352820\pi
0.446078 + 0.894994i 0.352820π0.352820\pi
812812 0 0
813813 3.35179 + 5.80547i 0.117552 + 0.203607i
814814 0 0
815815 6.33975 + 10.9808i 0.222072 + 0.384640i
816816 0 0
817817 −30.8195 + 53.3809i −1.07824 + 1.86756i
818818 0 0
819819 0 0
820820 0 0
821821 0.0406154 0.0703480i 0.00141749 0.00245516i −0.865316 0.501227i 0.832882π-0.832882\pi
0.866733 + 0.498772i 0.166215π0.166215\pi
822822 0 0
823823 0.624767 + 1.08213i 0.0217780 + 0.0377206i 0.876709 0.481021i 0.159734π-0.159734\pi
−0.854931 + 0.518742i 0.826401π0.826401\pi
824824 0 0
825825 4.53535 + 7.85545i 0.157901 + 0.273492i
826826 0 0
827827 32.9535 1.14591 0.572954 0.819588i 0.305798π-0.305798\pi
0.572954 + 0.819588i 0.305798π0.305798\pi
828828 0 0
829829 −8.61206 + 14.9165i −0.299109 + 0.518072i −0.975932 0.218073i 0.930023π-0.930023\pi
0.676823 + 0.736146i 0.263356π0.263356\pi
830830 0 0
831831 −24.9536 −0.865631
832832 0 0
833833 0 0
834834 0 0
835835 6.32569 10.9564i 0.218909 0.379162i
836836 0 0
837837 −12.8920 −0.445611
838838 0 0
839839 −14.7357 25.5229i −0.508731 0.881149i −0.999949 0.0101117i 0.996781π-0.996781\pi
0.491217 0.871037i 0.336552π-0.336552\pi
840840 0 0
841841 −14.5981 25.2847i −0.503383 0.871886i
842842 0 0
843843 5.39008 9.33590i 0.185644 0.321545i
844844 0 0
845845 8.16110 + 40.5276i 0.280750 + 1.39419i
846846 0 0
847847 0 0
848848 0 0
849849 15.5628 + 26.9556i 0.534115 + 0.925115i
850850 0 0
851851 −21.6089 37.4276i −0.740742 1.28300i
852852 0 0
853853 −17.8668 −0.611747 −0.305873 0.952072i 0.598948π-0.598948\pi
−0.305873 + 0.952072i 0.598948π0.598948\pi
854854 0 0
855855 −16.7338 + 28.9838i −0.572284 + 0.991225i
856856 0 0
857857 −20.1614 −0.688701 −0.344351 0.938841i 0.611901π-0.611901\pi
−0.344351 + 0.938841i 0.611901π0.611901\pi
858858 0 0
859859 −11.9734 −0.408526 −0.204263 0.978916i 0.565480π-0.565480\pi
−0.204263 + 0.978916i 0.565480π0.565480\pi
860860 0 0
861861 0 0
862862 0 0
863863 39.7010 1.35144 0.675719 0.737160i 0.263833π-0.263833\pi
0.675719 + 0.737160i 0.263833π0.263833\pi
864864 0 0
865865 36.1267 + 62.5732i 1.22834 + 2.12755i
866866 0 0
867867 4.76564 + 8.25432i 0.161849 + 0.280331i
868868 0 0
869869 11.2900 19.5549i 0.382988 0.663355i
870870 0 0
871871 −12.0864 + 4.56532i −0.409532 + 0.154690i
872872 0 0
873873 12.1378 21.0233i 0.410803 0.711532i
874874 0 0
875875 0 0
876876 0 0
877877 22.8328 + 39.5476i 0.771010 + 1.33543i 0.937010 + 0.349302i 0.113581π0.113581\pi
−0.166000 + 0.986126i 0.553085π0.553085\pi
878878 0 0
879879 0.383750 0.0129436
880880 0 0
881881 16.6420 28.8249i 0.560685 0.971134i −0.436752 0.899582i 0.643871π-0.643871\pi
0.997437 0.0715523i 0.0227953π-0.0227953\pi
882882 0 0
883883 32.3115 1.08737 0.543685 0.839289i 0.317029π-0.317029\pi
0.543685 + 0.839289i 0.317029π0.317029\pi
884884 0 0
885885 8.91516 0.299680
886886 0 0
887887 −16.7530 + 29.0170i −0.562509 + 0.974295i 0.434767 + 0.900543i 0.356831π0.356831\pi
−0.997277 + 0.0737520i 0.976503π0.976503\pi
888888 0 0
889889 0 0
890890 0 0
891891 0.364658 + 0.631606i 0.0122165 + 0.0211596i
892892 0 0
893893 −17.1536 29.7109i −0.574024 0.994239i
894894 0 0
895895 6.56721 11.3747i 0.219517 0.380215i
896896 0 0
897897 3.31899 20.2518i 0.110818 0.676187i
898898 0 0
899899 9.61064 16.6461i 0.320533 0.555179i
900900 0 0
901901 2.57898 + 4.46693i 0.0859183 + 0.148815i
902902 0 0
903903 0 0
904904 0 0
905905 −8.37783 −0.278488
906906 0 0
907907 19.4451 33.6798i 0.645663 1.11832i −0.338485 0.940972i 0.609915π-0.609915\pi
0.984148 0.177349i 0.0567521π-0.0567521\pi
908908 0 0
909909 22.1519 0.734733
910910 0 0
911911 −41.0133 −1.35883 −0.679415 0.733754i 0.737766π-0.737766\pi
−0.679415 + 0.733754i 0.737766π0.737766\pi
912912 0 0
913913 −7.29148 + 12.6292i −0.241313 + 0.417966i
914914 0 0
915915 22.4249 0.741345
916916 0 0
917917 0 0
918918 0 0
919919 −11.9574 20.7108i −0.394438 0.683186i 0.598592 0.801054i 0.295727π-0.295727\pi
−0.993029 + 0.117868i 0.962394π0.962394\pi
920920 0 0
921921 −7.21532 + 12.4973i −0.237753 + 0.411800i
922922 0 0
923923 2.33833 14.2680i 0.0769671 0.469637i
924924 0 0
925925 −20.1984 + 34.9846i −0.664119 + 1.15029i
926926 0 0
927927 11.6979 + 20.2614i 0.384211 + 0.665473i
928928 0 0
929929 −7.74124 13.4082i −0.253982 0.439909i 0.710637 0.703559i 0.248407π-0.248407\pi
−0.964618 + 0.263650i 0.915074π0.915074\pi
930930 0 0
931931 0 0
932932 0 0
933933 −0.614538 + 1.06441i −0.0201191 + 0.0348472i
934934 0 0
935935 −15.1813 −0.496481
936936 0 0
937937 −38.8172 −1.26810 −0.634052 0.773290i 0.718609π-0.718609\pi
−0.634052 + 0.773290i 0.718609π0.718609\pi
938938 0 0
939939 −5.50770 + 9.53961i −0.179737 + 0.311313i
940940 0 0
941941 5.28344 0.172235 0.0861177 0.996285i 0.472554π-0.472554\pi
0.0861177 + 0.996285i 0.472554π0.472554\pi
942942 0 0
943943 22.9392 + 39.7319i 0.747003 + 1.29385i
944944 0 0
945945 0 0
946946 0 0
947947 −3.98486 + 6.90198i −0.129491 + 0.224284i −0.923479 0.383648i 0.874668π-0.874668\pi
0.793989 + 0.607932i 0.208001π0.208001\pi
948948 0 0
949949 32.6492 + 26.7300i 1.05984 + 0.867691i
950950 0 0
951951 −4.41651 + 7.64963i −0.143215 + 0.248056i
952952 0 0
953953 −8.48138 14.6902i −0.274739 0.475862i 0.695330 0.718690i 0.255258π-0.255258\pi
−0.970069 + 0.242829i 0.921925π0.921925\pi
954954 0 0
955955 7.44157 + 12.8892i 0.240804 + 0.417084i
956956 0 0
957957 13.5337 0.437482
958958 0 0
959959 0 0
960960 0 0
961961 −24.6515 −0.795210
962962 0 0
963963 4.35820 0.140441
964964 0 0
965965 28.5199 49.3980i 0.918089 1.59018i
966966 0 0
967967 21.4177 0.688746 0.344373 0.938833i 0.388092π-0.388092\pi
0.344373 + 0.938833i 0.388092π0.388092\pi
968968 0 0
969969 7.99633 + 13.8500i 0.256879 + 0.444927i
970970 0 0
971971 −8.46512 14.6620i −0.271659 0.470527i 0.697628 0.716460i 0.254239π-0.254239\pi
−0.969287 + 0.245933i 0.920906π0.920906\pi
972972 0 0
973973 0 0
974974 0 0
975975 −17.9449 + 6.77822i −0.574698 + 0.217077i
976976 0 0
977977 −20.4387 + 35.4008i −0.653891 + 1.13257i 0.328279 + 0.944581i 0.393531π0.393531\pi
−0.982171 + 0.187992i 0.939802π0.939802\pi
978978 0 0
979979 −0.179123 0.310250i −0.00572479 0.00991562i
980980 0 0
981981 −4.65145 8.05655i −0.148509 0.257226i
982982 0 0
983983 8.53733 0.272299 0.136149 0.990688i 0.456527π-0.456527\pi
0.136149 + 0.990688i 0.456527π0.456527\pi
984984 0 0
985985 36.1022 62.5308i 1.15031 1.99240i
986986 0 0
987987 0 0
988988 0 0
989989 −61.4245 −1.95319
990990 0 0
991991 −17.5874 + 30.4623i −0.558682 + 0.967666i 0.438924 + 0.898524i 0.355360π0.355360\pi
−0.997607 + 0.0691423i 0.977974π0.977974\pi
992992 0 0
993993 4.52032 0.143448
994994 0 0
995995 −12.6561 21.9211i −0.401226 0.694944i
996996 0 0
997997 −20.3109 35.1795i −0.643252 1.11414i −0.984702 0.174245i 0.944251π-0.944251\pi
0.341450 0.939900i 0.389082π-0.389082\pi
998998 0 0
999999 20.2129 35.0097i 0.639507 1.10766i
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 2548.2.k.i.1569.3 18
7.2 even 3 2548.2.i.n.165.3 18
7.3 odd 6 364.2.l.a.9.3 yes 18
7.4 even 3 2548.2.l.n.373.7 18
7.5 odd 6 364.2.i.a.165.7 18
7.6 odd 2 2548.2.k.h.1569.7 18
13.3 even 3 inner 2548.2.k.i.393.3 18
21.5 even 6 3276.2.u.k.1621.1 18
21.17 even 6 3276.2.x.k.2557.1 18
91.3 odd 6 364.2.i.a.289.7 yes 18
91.16 even 3 2548.2.l.n.1537.7 18
91.55 odd 6 2548.2.k.h.393.7 18
91.68 odd 6 364.2.l.a.81.3 yes 18
91.81 even 3 2548.2.i.n.1745.3 18
273.68 even 6 3276.2.x.k.2629.1 18
273.185 even 6 3276.2.u.k.289.1 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
364.2.i.a.165.7 18 7.5 odd 6
364.2.i.a.289.7 yes 18 91.3 odd 6
364.2.l.a.9.3 yes 18 7.3 odd 6
364.2.l.a.81.3 yes 18 91.68 odd 6
2548.2.i.n.165.3 18 7.2 even 3
2548.2.i.n.1745.3 18 91.81 even 3
2548.2.k.h.393.7 18 91.55 odd 6
2548.2.k.h.1569.7 18 7.6 odd 2
2548.2.k.i.393.3 18 13.3 even 3 inner
2548.2.k.i.1569.3 18 1.1 even 1 trivial
2548.2.l.n.373.7 18 7.4 even 3
2548.2.l.n.1537.7 18 91.16 even 3
3276.2.u.k.289.1 18 273.185 even 6
3276.2.u.k.1621.1 18 21.5 even 6
3276.2.x.k.2557.1 18 21.17 even 6
3276.2.x.k.2629.1 18 273.68 even 6