Properties

Label 1352.2.i.c.1329.1
Level 13521352
Weight 22
Character 1352.1329
Analytic conductor 10.79610.796
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] = [1352,2,Mod(529,1352)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1352, 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("1352.529"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 1352=23132 1352 = 2^{3} \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1352.i (of order 33, degree 22, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,0,-1,0,2,0,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 10.795774353310.7957743533
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,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 104)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 1329.1
Root 0.5000000.866025i0.500000 - 0.866025i of defining polynomial
Character χ\chi == 1352.1329
Dual form 1352.2.i.c.529.1

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)q3+1.00000q5+(2.500004.33013i)q7+(1.000001.73205i)q9+(1.000001.73205i)q11+(0.5000000.866025i)q15+(1.500002.59808i)q17+(1.00000+1.73205i)q195.00000q21+(2.000003.46410i)q234.00000q255.00000q27+(3.00000+5.19615i)q29+4.00000q31+(1.00000+1.73205i)q33+(2.500004.33013i)q35+(5.50000+9.52628i)q37+(4.00000+6.92820i)q41+(0.5000000.866025i)q43+(1.000001.73205i)q459.00000q47+(9.0000015.5885i)q493.00000q5112.0000q53+(1.000001.73205i)q55+2.00000q57+(3.000005.19615i)q59+(5.000008.66025i)q63+(3.00000+5.19615i)q67+(2.00000+3.46410i)q69+(3.500006.06218i)q71+2.00000q73+(2.00000+3.46410i)q7510.0000q77+12.0000q79+(0.5000000.866025i)q81+16.0000q83+(1.500002.59808i)q85+(3.000005.19615i)q87+(5.000008.66025i)q89+(2.000003.46410i)q93+(1.00000+1.73205i)q95+(5.00000+8.66025i)q974.00000q99+O(q100)q+(-0.500000 - 0.866025i) q^{3} +1.00000 q^{5} +(2.50000 - 4.33013i) q^{7} +(1.00000 - 1.73205i) q^{9} +(-1.00000 - 1.73205i) q^{11} +(-0.500000 - 0.866025i) q^{15} +(1.50000 - 2.59808i) q^{17} +(-1.00000 + 1.73205i) q^{19} -5.00000 q^{21} +(-2.00000 - 3.46410i) q^{23} -4.00000 q^{25} -5.00000 q^{27} +(3.00000 + 5.19615i) q^{29} +4.00000 q^{31} +(-1.00000 + 1.73205i) q^{33} +(2.50000 - 4.33013i) q^{35} +(5.50000 + 9.52628i) q^{37} +(4.00000 + 6.92820i) q^{41} +(0.500000 - 0.866025i) q^{43} +(1.00000 - 1.73205i) q^{45} -9.00000 q^{47} +(-9.00000 - 15.5885i) q^{49} -3.00000 q^{51} -12.0000 q^{53} +(-1.00000 - 1.73205i) q^{55} +2.00000 q^{57} +(3.00000 - 5.19615i) q^{59} +(-5.00000 - 8.66025i) q^{63} +(3.00000 + 5.19615i) q^{67} +(-2.00000 + 3.46410i) q^{69} +(3.50000 - 6.06218i) q^{71} +2.00000 q^{73} +(2.00000 + 3.46410i) q^{75} -10.0000 q^{77} +12.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +16.0000 q^{83} +(1.50000 - 2.59808i) q^{85} +(3.00000 - 5.19615i) q^{87} +(-5.00000 - 8.66025i) q^{89} +(-2.00000 - 3.46410i) q^{93} +(-1.00000 + 1.73205i) q^{95} +(-5.00000 + 8.66025i) q^{97} -4.00000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2qq3+2q5+5q7+2q92q11q15+3q172q1910q214q238q2510q27+6q29+8q312q33+5q35+11q37+8q41+q43+8q99+O(q100) 2 q - q^{3} + 2 q^{5} + 5 q^{7} + 2 q^{9} - 2 q^{11} - q^{15} + 3 q^{17} - 2 q^{19} - 10 q^{21} - 4 q^{23} - 8 q^{25} - 10 q^{27} + 6 q^{29} + 8 q^{31} - 2 q^{33} + 5 q^{35} + 11 q^{37} + 8 q^{41} + q^{43}+ \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/1352Z)×\left(\mathbb{Z}/1352\mathbb{Z}\right)^\times.

nn 677677 10151015 11851185
χ(n)\chi(n) 11 11 e(13)e\left(\frac{1}{3}\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 −0.500000 0.866025i −0.288675 0.500000i 0.684819 0.728714i 0.259881π-0.259881\pi
−0.973494 + 0.228714i 0.926548π0.926548\pi
44 0 0
55 1.00000 0.447214 0.223607 0.974679i 0.428217π-0.428217\pi
0.223607 + 0.974679i 0.428217π0.428217\pi
66 0 0
77 2.50000 4.33013i 0.944911 1.63663i 0.188982 0.981981i 0.439481π-0.439481\pi
0.755929 0.654654i 0.227186π-0.227186\pi
88 0 0
99 1.00000 1.73205i 0.333333 0.577350i
1010 0 0
1111 −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i 0.264158π-0.264158\pi
−0.976478 + 0.215615i 0.930824π0.930824\pi
1212 0 0
1313 0 0
1414 0 0
1515 −0.500000 0.866025i −0.129099 0.223607i
1616 0 0
1717 1.50000 2.59808i 0.363803 0.630126i −0.624780 0.780801i 0.714811π-0.714811\pi
0.988583 + 0.150675i 0.0481447π0.0481447\pi
1818 0 0
1919 −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i 0.907015π-0.907015\pi
0.728219 + 0.685344i 0.240348π0.240348\pi
2020 0 0
2121 −5.00000 −1.09109
2222 0 0
2323 −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i 0.303595π-0.303595\pi
−0.995639 + 0.0932891i 0.970262π0.970262\pi
2424 0 0
2525 −4.00000 −0.800000
2626 0 0
2727 −5.00000 −0.962250
2828 0 0
2929 3.00000 + 5.19615i 0.557086 + 0.964901i 0.997738 + 0.0672232i 0.0214140π0.0214140\pi
−0.440652 + 0.897678i 0.645253π0.645253\pi
3030 0 0
3131 4.00000 0.718421 0.359211 0.933257i 0.383046π-0.383046\pi
0.359211 + 0.933257i 0.383046π0.383046\pi
3232 0 0
3333 −1.00000 + 1.73205i −0.174078 + 0.301511i
3434 0 0
3535 2.50000 4.33013i 0.422577 0.731925i
3636 0 0
3737 5.50000 + 9.52628i 0.904194 + 1.56611i 0.821995 + 0.569495i 0.192861π0.192861\pi
0.0821995 + 0.996616i 0.473806π0.473806\pi
3838 0 0
3939 0 0
4040 0 0
4141 4.00000 + 6.92820i 0.624695 + 1.08200i 0.988600 + 0.150567i 0.0481100π0.0481100\pi
−0.363905 + 0.931436i 0.618557π0.618557\pi
4242 0 0
4343 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i 0.809039π-0.809039\pi
0.901629 + 0.432511i 0.142372π0.142372\pi
4444 0 0
4545 1.00000 1.73205i 0.149071 0.258199i
4646 0 0
4747 −9.00000 −1.31278 −0.656392 0.754420i 0.727918π-0.727918\pi
−0.656392 + 0.754420i 0.727918π0.727918\pi
4848 0 0
4949 −9.00000 15.5885i −1.28571 2.22692i
5050 0 0
5151 −3.00000 −0.420084
5252 0 0
5353 −12.0000 −1.64833 −0.824163 0.566352i 0.808354π-0.808354\pi
−0.824163 + 0.566352i 0.808354π0.808354\pi
5454 0 0
5555 −1.00000 1.73205i −0.134840 0.233550i
5656 0 0
5757 2.00000 0.264906
5858 0 0
5959 3.00000 5.19615i 0.390567 0.676481i −0.601958 0.798528i 0.705612π-0.705612\pi
0.992524 + 0.122047i 0.0389457π0.0389457\pi
6060 0 0
6161 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
6262 0 0
6363 −5.00000 8.66025i −0.629941 1.09109i
6464 0 0
6565 0 0
6666 0 0
6767 3.00000 + 5.19615i 0.366508 + 0.634811i 0.989017 0.147802i 0.0472198π-0.0472198\pi
−0.622509 + 0.782613i 0.713886π0.713886\pi
6868 0 0
6969 −2.00000 + 3.46410i −0.240772 + 0.417029i
7070 0 0
7171 3.50000 6.06218i 0.415374 0.719448i −0.580094 0.814550i 0.696984π-0.696984\pi
0.995468 + 0.0951014i 0.0303175π0.0303175\pi
7272 0 0
7373 2.00000 0.234082 0.117041 0.993127i 0.462659π-0.462659\pi
0.117041 + 0.993127i 0.462659π0.462659\pi
7474 0 0
7575 2.00000 + 3.46410i 0.230940 + 0.400000i
7676 0 0
7777 −10.0000 −1.13961
7878 0 0
7979 12.0000 1.35011 0.675053 0.737769i 0.264121π-0.264121\pi
0.675053 + 0.737769i 0.264121π0.264121\pi
8080 0 0
8181 −0.500000 0.866025i −0.0555556 0.0962250i
8282 0 0
8383 16.0000 1.75623 0.878114 0.478451i 0.158802π-0.158802\pi
0.878114 + 0.478451i 0.158802π0.158802\pi
8484 0 0
8585 1.50000 2.59808i 0.162698 0.281801i
8686 0 0
8787 3.00000 5.19615i 0.321634 0.557086i
8888 0 0
8989 −5.00000 8.66025i −0.529999 0.917985i −0.999388 0.0349934i 0.988859π-0.988859\pi
0.469389 0.882992i 0.344474π-0.344474\pi
9090 0 0
9191 0 0
9292 0 0
9393 −2.00000 3.46410i −0.207390 0.359211i
9494 0 0
9595 −1.00000 + 1.73205i −0.102598 + 0.177705i
9696 0 0
9797 −5.00000 + 8.66025i −0.507673 + 0.879316i 0.492287 + 0.870433i 0.336161π0.336161\pi
−0.999961 + 0.00888289i 0.997172π0.997172\pi
9898 0 0
9999 −4.00000 −0.402015
100100 0 0
101101 −2.00000 3.46410i −0.199007 0.344691i 0.749199 0.662344i 0.230438π-0.230438\pi
−0.948207 + 0.317653i 0.897105π0.897105\pi
102102 0 0
103103 −8.00000 −0.788263 −0.394132 0.919054i 0.628955π-0.628955\pi
−0.394132 + 0.919054i 0.628955π0.628955\pi
104104 0 0
105105 −5.00000 −0.487950
106106 0 0
107107 −10.0000 17.3205i −0.966736 1.67444i −0.704875 0.709331i 0.748997π-0.748997\pi
−0.261861 0.965106i 0.584336π-0.584336\pi
108108 0 0
109109 5.00000 0.478913 0.239457 0.970907i 0.423031π-0.423031\pi
0.239457 + 0.970907i 0.423031π0.423031\pi
110110 0 0
111111 5.50000 9.52628i 0.522037 0.904194i
112112 0 0
113113 −1.00000 + 1.73205i −0.0940721 + 0.162938i −0.909221 0.416314i 0.863322π-0.863322\pi
0.815149 + 0.579252i 0.196655π0.196655\pi
114114 0 0
115115 −2.00000 3.46410i −0.186501 0.323029i
116116 0 0
117117 0 0
118118 0 0
119119 −7.50000 12.9904i −0.687524 1.19083i
120120 0 0
121121 3.50000 6.06218i 0.318182 0.551107i
122122 0 0
123123 4.00000 6.92820i 0.360668 0.624695i
124124 0 0
125125 −9.00000 −0.804984
126126 0 0
127127 4.00000 + 6.92820i 0.354943 + 0.614779i 0.987108 0.160055i 0.0511671π-0.0511671\pi
−0.632166 + 0.774833i 0.717834π0.717834\pi
128128 0 0
129129 −1.00000 −0.0880451
130130 0 0
131131 3.00000 0.262111 0.131056 0.991375i 0.458163π-0.458163\pi
0.131056 + 0.991375i 0.458163π0.458163\pi
132132 0 0
133133 5.00000 + 8.66025i 0.433555 + 0.750939i
134134 0 0
135135 −5.00000 −0.430331
136136 0 0
137137 −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i 0.337990π0.337990\pi
−0.999893 + 0.0146279i 0.995344π0.995344\pi
138138 0 0
139139 −1.50000 + 2.59808i −0.127228 + 0.220366i −0.922602 0.385754i 0.873941π-0.873941\pi
0.795373 + 0.606120i 0.207275π0.207275\pi
140140 0 0
141141 4.50000 + 7.79423i 0.378968 + 0.656392i
142142 0 0
143143 0 0
144144 0 0
145145 3.00000 + 5.19615i 0.249136 + 0.431517i
146146 0 0
147147 −9.00000 + 15.5885i −0.742307 + 1.28571i
148148 0 0
149149 7.00000 12.1244i 0.573462 0.993266i −0.422744 0.906249i 0.638933π-0.638933\pi
0.996207 0.0870170i 0.0277334π-0.0277334\pi
150150 0 0
151151 5.00000 0.406894 0.203447 0.979086i 0.434786π-0.434786\pi
0.203447 + 0.979086i 0.434786π0.434786\pi
152152 0 0
153153 −3.00000 5.19615i −0.242536 0.420084i
154154 0 0
155155 4.00000 0.321288
156156 0 0
157157 −2.00000 −0.159617 −0.0798087 0.996810i 0.525431π-0.525431\pi
−0.0798087 + 0.996810i 0.525431π0.525431\pi
158158 0 0
159159 6.00000 + 10.3923i 0.475831 + 0.824163i
160160 0 0
161161 −20.0000 −1.57622
162162 0 0
163163 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i 0.783263π-0.783263\pi
0.933659 + 0.358162i 0.116597π0.116597\pi
164164 0 0
165165 −1.00000 + 1.73205i −0.0778499 + 0.134840i
166166 0 0
167167 4.00000 + 6.92820i 0.309529 + 0.536120i 0.978259 0.207385i 0.0664952π-0.0664952\pi
−0.668730 + 0.743505i 0.733162π0.733162\pi
168168 0 0
169169 0 0
170170 0 0
171171 2.00000 + 3.46410i 0.152944 + 0.264906i
172172 0 0
173173 6.00000 10.3923i 0.456172 0.790112i −0.542583 0.840002i 0.682554π-0.682554\pi
0.998755 + 0.0498898i 0.0158870π0.0158870\pi
174174 0 0
175175 −10.0000 + 17.3205i −0.755929 + 1.30931i
176176 0 0
177177 −6.00000 −0.450988
178178 0 0
179179 −1.50000 2.59808i −0.112115 0.194189i 0.804508 0.593942i 0.202429π-0.202429\pi
−0.916623 + 0.399753i 0.869096π0.869096\pi
180180 0 0
181181 16.0000 1.18927 0.594635 0.803996i 0.297296π-0.297296\pi
0.594635 + 0.803996i 0.297296π0.297296\pi
182182 0 0
183183 0 0
184184 0 0
185185 5.50000 + 9.52628i 0.404368 + 0.700386i
186186 0 0
187187 −6.00000 −0.438763
188188 0 0
189189 −12.5000 + 21.6506i −0.909241 + 1.57485i
190190 0 0
191191 −5.00000 + 8.66025i −0.361787 + 0.626634i −0.988255 0.152813i 0.951167π-0.951167\pi
0.626468 + 0.779447i 0.284500π0.284500\pi
192192 0 0
193193 8.00000 + 13.8564i 0.575853 + 0.997406i 0.995948 + 0.0899262i 0.0286631π0.0286631\pi
−0.420096 + 0.907480i 0.638004π0.638004\pi
194194 0 0
195195 0 0
196196 0 0
197197 8.50000 + 14.7224i 0.605600 + 1.04893i 0.991956 + 0.126580i 0.0404001π0.0404001\pi
−0.386356 + 0.922350i 0.626267π0.626267\pi
198198 0 0
199199 9.00000 15.5885i 0.637993 1.10504i −0.347879 0.937539i 0.613098π-0.613098\pi
0.985873 0.167497i 0.0535685π-0.0535685\pi
200200 0 0
201201 3.00000 5.19615i 0.211604 0.366508i
202202 0 0
203203 30.0000 2.10559
204204 0 0
205205 4.00000 + 6.92820i 0.279372 + 0.483887i
206206 0 0
207207 −8.00000 −0.556038
208208 0 0
209209 4.00000 0.276686
210210 0 0
211211 2.50000 + 4.33013i 0.172107 + 0.298098i 0.939156 0.343490i 0.111609π-0.111609\pi
−0.767049 + 0.641588i 0.778276π0.778276\pi
212212 0 0
213213 −7.00000 −0.479632
214214 0 0
215215 0.500000 0.866025i 0.0340997 0.0590624i
216216 0 0
217217 10.0000 17.3205i 0.678844 1.17579i
218218 0 0
219219 −1.00000 1.73205i −0.0675737 0.117041i
220220 0 0
221221 0 0
222222 0 0
223223 −8.50000 14.7224i −0.569202 0.985887i −0.996645 0.0818447i 0.973919π-0.973919\pi
0.427443 0.904042i 0.359414π-0.359414\pi
224224 0 0
225225 −4.00000 + 6.92820i −0.266667 + 0.461880i
226226 0 0
227227 −8.00000 + 13.8564i −0.530979 + 0.919682i 0.468368 + 0.883534i 0.344842π0.344842\pi
−0.999346 + 0.0361484i 0.988491π0.988491\pi
228228 0 0
229229 15.0000 0.991228 0.495614 0.868543i 0.334943π-0.334943\pi
0.495614 + 0.868543i 0.334943π0.334943\pi
230230 0 0
231231 5.00000 + 8.66025i 0.328976 + 0.569803i
232232 0 0
233233 13.0000 0.851658 0.425829 0.904804i 0.359982π-0.359982\pi
0.425829 + 0.904804i 0.359982π0.359982\pi
234234 0 0
235235 −9.00000 −0.587095
236236 0 0
237237 −6.00000 10.3923i −0.389742 0.675053i
238238 0 0
239239 3.00000 0.194054 0.0970269 0.995282i 0.469067π-0.469067\pi
0.0970269 + 0.995282i 0.469067π0.469067\pi
240240 0 0
241241 1.00000 1.73205i 0.0644157 0.111571i −0.832019 0.554747i 0.812815π-0.812815\pi
0.896435 + 0.443176i 0.146148π0.146148\pi
242242 0 0
243243 −8.00000 + 13.8564i −0.513200 + 0.888889i
244244 0 0
245245 −9.00000 15.5885i −0.574989 0.995910i
246246 0 0
247247 0 0
248248 0 0
249249 −8.00000 13.8564i −0.506979 0.878114i
250250 0 0
251251 −4.00000 + 6.92820i −0.252478 + 0.437304i −0.964207 0.265149i 0.914579π-0.914579\pi
0.711730 + 0.702454i 0.247912π0.247912\pi
252252 0 0
253253 −4.00000 + 6.92820i −0.251478 + 0.435572i
254254 0 0
255255 −3.00000 −0.187867
256256 0 0
257257 15.5000 + 26.8468i 0.966863 + 1.67466i 0.704523 + 0.709681i 0.251161π0.251161\pi
0.262341 + 0.964975i 0.415506π0.415506\pi
258258 0 0
259259 55.0000 3.41753
260260 0 0
261261 12.0000 0.742781
262262 0 0
263263 −10.0000 17.3205i −0.616626 1.06803i −0.990097 0.140386i 0.955166π-0.955166\pi
0.373470 0.927642i 0.378168π-0.378168\pi
264264 0 0
265265 −12.0000 −0.737154
266266 0 0
267267 −5.00000 + 8.66025i −0.305995 + 0.529999i
268268 0 0
269269 −8.00000 + 13.8564i −0.487769 + 0.844840i −0.999901 0.0140665i 0.995522π-0.995522\pi
0.512132 + 0.858906i 0.328856π0.328856\pi
270270 0 0
271271 −3.50000 6.06218i −0.212610 0.368251i 0.739921 0.672694i 0.234863π-0.234863\pi
−0.952531 + 0.304443i 0.901530π0.901530\pi
272272 0 0
273273 0 0
274274 0 0
275275 4.00000 + 6.92820i 0.241209 + 0.417786i
276276 0 0
277277 6.00000 10.3923i 0.360505 0.624413i −0.627539 0.778585i 0.715938π-0.715938\pi
0.988044 + 0.154172i 0.0492710π0.0492710\pi
278278 0 0
279279 4.00000 6.92820i 0.239474 0.414781i
280280 0 0
281281 10.0000 0.596550 0.298275 0.954480i 0.403589π-0.403589\pi
0.298275 + 0.954480i 0.403589π0.403589\pi
282282 0 0
283283 10.0000 + 17.3205i 0.594438 + 1.02960i 0.993626 + 0.112728i 0.0359589π0.0359589\pi
−0.399188 + 0.916869i 0.630708π0.630708\pi
284284 0 0
285285 2.00000 0.118470
286286 0 0
287287 40.0000 2.36113
288288 0 0
289289 4.00000 + 6.92820i 0.235294 + 0.407541i
290290 0 0
291291 10.0000 0.586210
292292 0 0
293293 7.50000 12.9904i 0.438155 0.758906i −0.559393 0.828903i 0.688966π-0.688966\pi
0.997547 + 0.0699967i 0.0222989π0.0222989\pi
294294 0 0
295295 3.00000 5.19615i 0.174667 0.302532i
296296 0 0
297297 5.00000 + 8.66025i 0.290129 + 0.502519i
298298 0 0
299299 0 0
300300 0 0
301301 −2.50000 4.33013i −0.144098 0.249584i
302302 0 0
303303 −2.00000 + 3.46410i −0.114897 + 0.199007i
304304 0 0
305305 0 0
306306 0 0
307307 2.00000 0.114146 0.0570730 0.998370i 0.481823π-0.481823\pi
0.0570730 + 0.998370i 0.481823π0.481823\pi
308308 0 0
309309 4.00000 + 6.92820i 0.227552 + 0.394132i
310310 0 0
311311 −22.0000 −1.24751 −0.623753 0.781622i 0.714393π-0.714393\pi
−0.623753 + 0.781622i 0.714393π0.714393\pi
312312 0 0
313313 −9.00000 −0.508710 −0.254355 0.967111i 0.581863π-0.581863\pi
−0.254355 + 0.967111i 0.581863π0.581863\pi
314314 0 0
315315 −5.00000 8.66025i −0.281718 0.487950i
316316 0 0
317317 2.00000 0.112331 0.0561656 0.998421i 0.482113π-0.482113\pi
0.0561656 + 0.998421i 0.482113π0.482113\pi
318318 0 0
319319 6.00000 10.3923i 0.335936 0.581857i
320320 0 0
321321 −10.0000 + 17.3205i −0.558146 + 0.966736i
322322 0 0
323323 3.00000 + 5.19615i 0.166924 + 0.289122i
324324 0 0
325325 0 0
326326 0 0
327327 −2.50000 4.33013i −0.138250 0.239457i
328328 0 0
329329 −22.5000 + 38.9711i −1.24047 + 2.14855i
330330 0 0
331331 6.00000 10.3923i 0.329790 0.571213i −0.652680 0.757634i 0.726355π-0.726355\pi
0.982470 + 0.186421i 0.0596888π0.0596888\pi
332332 0 0
333333 22.0000 1.20559
334334 0 0
335335 3.00000 + 5.19615i 0.163908 + 0.283896i
336336 0 0
337337 15.0000 0.817102 0.408551 0.912735i 0.366034π-0.366034\pi
0.408551 + 0.912735i 0.366034π0.366034\pi
338338 0 0
339339 2.00000 0.108625
340340 0 0
341341 −4.00000 6.92820i −0.216612 0.375183i
342342 0 0
343343 −55.0000 −2.96972
344344 0 0
345345 −2.00000 + 3.46410i −0.107676 + 0.186501i
346346 0 0
347347 −1.50000 + 2.59808i −0.0805242 + 0.139472i −0.903475 0.428640i 0.858993π-0.858993\pi
0.822951 + 0.568112i 0.192326π0.192326\pi
348348 0 0
349349 −4.50000 7.79423i −0.240879 0.417215i 0.720086 0.693885i 0.244103π-0.244103\pi
−0.960965 + 0.276670i 0.910769π0.910769\pi
350350 0 0
351351 0 0
352352 0 0
353353 −14.0000 24.2487i −0.745145 1.29063i −0.950127 0.311863i 0.899047π-0.899047\pi
0.204982 0.978766i 0.434286π-0.434286\pi
354354 0 0
355355 3.50000 6.06218i 0.185761 0.321747i
356356 0 0
357357 −7.50000 + 12.9904i −0.396942 + 0.687524i
358358 0 0
359359 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
360360 0 0
361361 7.50000 + 12.9904i 0.394737 + 0.683704i
362362 0 0
363363 −7.00000 −0.367405
364364 0 0
365365 2.00000 0.104685
366366 0 0
367367 9.00000 + 15.5885i 0.469796 + 0.813711i 0.999404 0.0345320i 0.0109941π-0.0109941\pi
−0.529607 + 0.848243i 0.677661π0.677661\pi
368368 0 0
369369 16.0000 0.832927
370370 0 0
371371 −30.0000 + 51.9615i −1.55752 + 2.69771i
372372 0 0
373373 2.00000 3.46410i 0.103556 0.179364i −0.809591 0.586994i 0.800311π-0.800311\pi
0.913147 + 0.407630i 0.133645π0.133645\pi
374374 0 0
375375 4.50000 + 7.79423i 0.232379 + 0.402492i
376376 0 0
377377 0 0
378378 0 0
379379 12.0000 + 20.7846i 0.616399 + 1.06763i 0.990137 + 0.140100i 0.0447423π0.0447423\pi
−0.373739 + 0.927534i 0.621924π0.621924\pi
380380 0 0
381381 4.00000 6.92820i 0.204926 0.354943i
382382 0 0
383383 7.50000 12.9904i 0.383232 0.663777i −0.608290 0.793715i 0.708144π-0.708144\pi
0.991522 + 0.129937i 0.0414776π0.0414776\pi
384384 0 0
385385 −10.0000 −0.509647
386386 0 0
387387 −1.00000 1.73205i −0.0508329 0.0880451i
388388 0 0
389389 −6.00000 −0.304212 −0.152106 0.988364i 0.548606π-0.548606\pi
−0.152106 + 0.988364i 0.548606π0.548606\pi
390390 0 0
391391 −12.0000 −0.606866
392392 0 0
393393 −1.50000 2.59808i −0.0756650 0.131056i
394394 0 0
395395 12.0000 0.603786
396396 0 0
397397 5.00000 8.66025i 0.250943 0.434646i −0.712843 0.701324i 0.752593π-0.752593\pi
0.963786 + 0.266678i 0.0859261π0.0859261\pi
398398 0 0
399399 5.00000 8.66025i 0.250313 0.433555i
400400 0 0
401401 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
402402 0 0
403403 0 0
404404 0 0
405405 −0.500000 0.866025i −0.0248452 0.0430331i
406406 0 0
407407 11.0000 19.0526i 0.545250 0.944400i
408408 0 0
409409 −2.00000 + 3.46410i −0.0988936 + 0.171289i −0.911227 0.411905i 0.864864π-0.864864\pi
0.812333 + 0.583193i 0.198197π0.198197\pi
410410 0 0
411411 12.0000 0.591916
412412 0 0
413413 −15.0000 25.9808i −0.738102 1.27843i
414414 0 0
415415 16.0000 0.785409
416416 0 0
417417 3.00000 0.146911
418418 0 0
419419 19.5000 + 33.7750i 0.952637 + 1.65002i 0.739685 + 0.672954i 0.234975π0.234975\pi
0.212953 + 0.977062i 0.431692π0.431692\pi
420420 0 0
421421 −11.0000 −0.536107 −0.268054 0.963404i 0.586380π-0.586380\pi
−0.268054 + 0.963404i 0.586380π0.586380\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 0 0
428428 0 0
429429 0 0
430430 0 0
431431 −5.50000 9.52628i −0.264926 0.458865i 0.702618 0.711567i 0.252014π-0.252014\pi
−0.967544 + 0.252702i 0.918681π0.918681\pi
432432 0 0
433433 8.50000 14.7224i 0.408484 0.707515i −0.586236 0.810140i 0.699391π-0.699391\pi
0.994720 + 0.102625i 0.0327243π0.0327243\pi
434434 0 0
435435 3.00000 5.19615i 0.143839 0.249136i
436436 0 0
437437 8.00000 0.382692
438438 0 0
439439 −5.00000 8.66025i −0.238637 0.413331i 0.721686 0.692220i 0.243367π-0.243367\pi
−0.960323 + 0.278889i 0.910034π0.910034\pi
440440 0 0
441441 −36.0000 −1.71429
442442 0 0
443443 −27.0000 −1.28281 −0.641404 0.767203i 0.721648π-0.721648\pi
−0.641404 + 0.767203i 0.721648π0.721648\pi
444444 0 0
445445 −5.00000 8.66025i −0.237023 0.410535i
446446 0 0
447447 −14.0000 −0.662177
448448 0 0
449449 −9.00000 + 15.5885i −0.424736 + 0.735665i −0.996396 0.0848262i 0.972967π-0.972967\pi
0.571660 + 0.820491i 0.306300π0.306300\pi
450450 0 0
451451 8.00000 13.8564i 0.376705 0.652473i
452452 0 0
453453 −2.50000 4.33013i −0.117460 0.203447i
454454 0 0
455455 0 0
456456 0 0
457457 5.00000 + 8.66025i 0.233890 + 0.405110i 0.958950 0.283577i 0.0915211π-0.0915211\pi
−0.725059 + 0.688686i 0.758188π0.758188\pi
458458 0 0
459459 −7.50000 + 12.9904i −0.350070 + 0.606339i
460460 0 0
461461 1.50000 2.59808i 0.0698620 0.121004i −0.828978 0.559281i 0.811077π-0.811077\pi
0.898840 + 0.438276i 0.144411π0.144411\pi
462462 0 0
463463 −24.0000 −1.11537 −0.557687 0.830051i 0.688311π-0.688311\pi
−0.557687 + 0.830051i 0.688311π0.688311\pi
464464 0 0
465465 −2.00000 3.46410i −0.0927478 0.160644i
466466 0 0
467467 −20.0000 −0.925490 −0.462745 0.886492i 0.653135π-0.653135\pi
−0.462745 + 0.886492i 0.653135π0.653135\pi
468468 0 0
469469 30.0000 1.38527
470470 0 0
471471 1.00000 + 1.73205i 0.0460776 + 0.0798087i
472472 0 0
473473 −2.00000 −0.0919601
474474 0 0
475475 4.00000 6.92820i 0.183533 0.317888i
476476 0 0
477477 −12.0000 + 20.7846i −0.549442 + 0.951662i
478478 0 0
479479 4.50000 + 7.79423i 0.205610 + 0.356127i 0.950327 0.311253i 0.100749π-0.100749\pi
−0.744717 + 0.667381i 0.767415π0.767415\pi
480480 0 0
481481 0 0
482482 0 0
483483 10.0000 + 17.3205i 0.455016 + 0.788110i
484484 0 0
485485 −5.00000 + 8.66025i −0.227038 + 0.393242i
486486 0 0
487487 4.00000 6.92820i 0.181257 0.313947i −0.761052 0.648691i 0.775317π-0.775317\pi
0.942309 + 0.334744i 0.108650π0.108650\pi
488488 0 0
489489 −4.00000 −0.180886
490490 0 0
491491 −7.50000 12.9904i −0.338470 0.586248i 0.645675 0.763612i 0.276576π-0.276576\pi
−0.984145 + 0.177365i 0.943243π0.943243\pi
492492 0 0
493493 18.0000 0.810679
494494 0 0
495495 −4.00000 −0.179787
496496 0 0
497497 −17.5000 30.3109i −0.784982 1.35963i
498498 0 0
499499 24.0000 1.07439 0.537194 0.843459i 0.319484π-0.319484\pi
0.537194 + 0.843459i 0.319484π0.319484\pi
500500 0 0
501501 4.00000 6.92820i 0.178707 0.309529i
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 −2.00000 3.46410i −0.0889988 0.154150i
506506 0 0
507507 0 0
508508 0 0
509509 1.00000 + 1.73205i 0.0443242 + 0.0767718i 0.887336 0.461123i 0.152553π-0.152553\pi
−0.843012 + 0.537895i 0.819220π0.819220\pi
510510 0 0
511511 5.00000 8.66025i 0.221187 0.383107i
512512 0 0
513513 5.00000 8.66025i 0.220755 0.382360i
514514 0 0
515515 −8.00000 −0.352522
516516 0 0
517517 9.00000 + 15.5885i 0.395820 + 0.685580i
518518 0 0
519519 −12.0000 −0.526742
520520 0 0
521521 15.0000 0.657162 0.328581 0.944476i 0.393430π-0.393430\pi
0.328581 + 0.944476i 0.393430π0.393430\pi
522522 0 0
523523 −10.0000 17.3205i −0.437269 0.757373i 0.560208 0.828352i 0.310721π-0.310721\pi
−0.997478 + 0.0709788i 0.977388π0.977388\pi
524524 0 0
525525 20.0000 0.872872
526526 0 0
527527 6.00000 10.3923i 0.261364 0.452696i
528528 0 0
529529 3.50000 6.06218i 0.152174 0.263573i
530530 0 0
531531 −6.00000 10.3923i −0.260378 0.450988i
532532 0 0
533533 0 0
534534 0 0
535535 −10.0000 17.3205i −0.432338 0.748831i
536536 0 0
537537 −1.50000 + 2.59808i −0.0647298 + 0.112115i
538538 0 0
539539 −18.0000 + 31.1769i −0.775315 + 1.34288i
540540 0 0
541541 −9.00000 −0.386940 −0.193470 0.981106i 0.561974π-0.561974\pi
−0.193470 + 0.981106i 0.561974π0.561974\pi
542542 0 0
543543 −8.00000 13.8564i −0.343313 0.594635i
544544 0 0
545545 5.00000 0.214176
546546 0 0
547547 −39.0000 −1.66752 −0.833760 0.552127i 0.813816π-0.813816\pi
−0.833760 + 0.552127i 0.813816π0.813816\pi
548548 0 0
549549 0 0
550550 0 0
551551 −12.0000 −0.511217
552552 0 0
553553 30.0000 51.9615i 1.27573 2.20963i
554554 0 0
555555 5.50000 9.52628i 0.233462 0.404368i
556556 0 0
557557 −11.5000 19.9186i −0.487271 0.843978i 0.512622 0.858614i 0.328674π-0.328674\pi
−0.999893 + 0.0146368i 0.995341π0.995341\pi
558558 0 0
559559 0 0
560560 0 0
561561 3.00000 + 5.19615i 0.126660 + 0.219382i
562562 0 0
563563 −19.5000 + 33.7750i −0.821827 + 1.42345i 0.0824933 + 0.996592i 0.473712π0.473712\pi
−0.904320 + 0.426855i 0.859622π0.859622\pi
564564 0 0
565565 −1.00000 + 1.73205i −0.0420703 + 0.0728679i
566566 0 0
567567 −5.00000 −0.209980
568568 0 0
569569 8.50000 + 14.7224i 0.356339 + 0.617196i 0.987346 0.158580i 0.0506917π-0.0506917\pi
−0.631008 + 0.775777i 0.717358π0.717358\pi
570570 0 0
571571 37.0000 1.54840 0.774201 0.632940i 0.218152π-0.218152\pi
0.774201 + 0.632940i 0.218152π0.218152\pi
572572 0 0
573573 10.0000 0.417756
574574 0 0
575575 8.00000 + 13.8564i 0.333623 + 0.577852i
576576 0 0
577577 38.0000 1.58196 0.790980 0.611842i 0.209571π-0.209571\pi
0.790980 + 0.611842i 0.209571π0.209571\pi
578578 0 0
579579 8.00000 13.8564i 0.332469 0.575853i
580580 0 0
581581 40.0000 69.2820i 1.65948 2.87430i
582582 0 0
583583 12.0000 + 20.7846i 0.496989 + 0.860811i
584584 0 0
585585 0 0
586586 0 0
587587 6.00000 + 10.3923i 0.247647 + 0.428936i 0.962872 0.269957i 0.0870095π-0.0870095\pi
−0.715226 + 0.698893i 0.753676π0.753676\pi
588588 0 0
589589 −4.00000 + 6.92820i −0.164817 + 0.285472i
590590 0 0
591591 8.50000 14.7224i 0.349643 0.605600i
592592 0 0
593593 −2.00000 −0.0821302 −0.0410651 0.999156i 0.513075π-0.513075\pi
−0.0410651 + 0.999156i 0.513075π0.513075\pi
594594 0 0
595595 −7.50000 12.9904i −0.307470 0.532554i
596596 0 0
597597 −18.0000 −0.736691
598598 0 0
599599 −2.00000 −0.0817178 −0.0408589 0.999165i 0.513009π-0.513009\pi
−0.0408589 + 0.999165i 0.513009π0.513009\pi
600600 0 0
601601 1.50000 + 2.59808i 0.0611863 + 0.105978i 0.894996 0.446074i 0.147178π-0.147178\pi
−0.833810 + 0.552052i 0.813845π0.813845\pi
602602 0 0
603603 12.0000 0.488678
604604 0 0
605605 3.50000 6.06218i 0.142295 0.246463i
606606 0 0
607607 5.00000 8.66025i 0.202944 0.351509i −0.746532 0.665350i 0.768282π-0.768282\pi
0.949476 + 0.313841i 0.101616π0.101616\pi
608608 0 0
609609 −15.0000 25.9808i −0.607831 1.05279i
610610 0 0
611611 0 0
612612 0 0
613613 −3.00000 5.19615i −0.121169 0.209871i 0.799060 0.601251i 0.205331π-0.205331\pi
−0.920229 + 0.391381i 0.871998π0.871998\pi
614614 0 0
615615 4.00000 6.92820i 0.161296 0.279372i
616616 0 0
617617 16.0000 27.7128i 0.644136 1.11568i −0.340365 0.940294i 0.610551π-0.610551\pi
0.984500 0.175382i 0.0561162π-0.0561162\pi
618618 0 0
619619 −28.0000 −1.12542 −0.562708 0.826656i 0.690240π-0.690240\pi
−0.562708 + 0.826656i 0.690240π0.690240\pi
620620 0 0
621621 10.0000 + 17.3205i 0.401286 + 0.695048i
622622 0 0
623623 −50.0000 −2.00321
624624 0 0
625625 11.0000 0.440000
626626 0 0
627627 −2.00000 3.46410i −0.0798723 0.138343i
628628 0 0
629629 33.0000 1.31580
630630 0 0
631631 7.50000 12.9904i 0.298570 0.517139i −0.677239 0.735763i 0.736824π-0.736824\pi
0.975809 + 0.218624i 0.0701569π0.0701569\pi
632632 0 0
633633 2.50000 4.33013i 0.0993661 0.172107i
634634 0 0
635635 4.00000 + 6.92820i 0.158735 + 0.274937i
636636 0 0
637637 0 0
638638 0 0
639639 −7.00000 12.1244i −0.276916 0.479632i
640640 0 0
641641 17.0000 29.4449i 0.671460 1.16300i −0.306031 0.952022i 0.599001π-0.599001\pi
0.977490 0.210981i 0.0676657π-0.0676657\pi
642642 0 0
643643 −13.0000 + 22.5167i −0.512670 + 0.887970i 0.487222 + 0.873278i 0.338010π0.338010\pi
−0.999892 + 0.0146923i 0.995323π0.995323\pi
644644 0 0
645645 −1.00000 −0.0393750
646646 0 0
647647 −21.0000 36.3731i −0.825595 1.42997i −0.901464 0.432855i 0.857506π-0.857506\pi
0.0758684 0.997118i 0.475827π-0.475827\pi
648648 0 0
649649 −12.0000 −0.471041
650650 0 0
651651 −20.0000 −0.783862
652652 0 0
653653 −12.0000 20.7846i −0.469596 0.813365i 0.529799 0.848123i 0.322267π-0.322267\pi
−0.999396 + 0.0347583i 0.988934π0.988934\pi
654654 0 0
655655 3.00000 0.117220
656656 0 0
657657 2.00000 3.46410i 0.0780274 0.135147i
658658 0 0
659659 −14.0000 + 24.2487i −0.545363 + 0.944596i 0.453221 + 0.891398i 0.350275π0.350275\pi
−0.998584 + 0.0531977i 0.983059π0.983059\pi
660660 0 0
661661 19.0000 + 32.9090i 0.739014 + 1.28001i 0.952940 + 0.303160i 0.0980418π0.0980418\pi
−0.213925 + 0.976850i 0.568625π0.568625\pi
662662 0 0
663663 0 0
664664 0 0
665665 5.00000 + 8.66025i 0.193892 + 0.335830i
666666 0 0
667667 12.0000 20.7846i 0.464642 0.804783i
668668 0 0
669669 −8.50000 + 14.7224i −0.328629 + 0.569202i
670670 0 0
671671 0 0
672672 0 0
673673 −10.5000 18.1865i −0.404745 0.701039i 0.589547 0.807734i 0.299306π-0.299306\pi
−0.994292 + 0.106695i 0.965973π0.965973\pi
674674 0 0
675675 20.0000 0.769800
676676 0 0
677677 −36.0000 −1.38359 −0.691796 0.722093i 0.743180π-0.743180\pi
−0.691796 + 0.722093i 0.743180π0.743180\pi
678678 0 0
679679 25.0000 + 43.3013i 0.959412 + 1.66175i
680680 0 0
681681 16.0000 0.613121
682682 0 0
683683 −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i 0.907070π-0.907070\pi
0.728101 + 0.685470i 0.240403π0.240403\pi
684684 0 0
685685 −6.00000 + 10.3923i −0.229248 + 0.397070i
686686 0 0
687687 −7.50000 12.9904i −0.286143 0.495614i
688688 0 0
689689 0 0
690690 0 0
691691 20.0000 + 34.6410i 0.760836 + 1.31781i 0.942420 + 0.334431i 0.108544π0.108544\pi
−0.181584 + 0.983375i 0.558123π0.558123\pi
692692 0 0
693693 −10.0000 + 17.3205i −0.379869 + 0.657952i
694694 0 0
695695 −1.50000 + 2.59808i −0.0568982 + 0.0985506i
696696 0 0
697697 24.0000 0.909065
698698 0 0
699699 −6.50000 11.2583i −0.245853 0.425829i
700700 0 0
701701 −4.00000 −0.151078 −0.0755390 0.997143i 0.524068π-0.524068\pi
−0.0755390 + 0.997143i 0.524068π0.524068\pi
702702 0 0
703703 −22.0000 −0.829746
704704 0 0
705705 4.50000 + 7.79423i 0.169480 + 0.293548i
706706 0 0
707707 −20.0000 −0.752177
708708 0 0
709709 11.0000 19.0526i 0.413114 0.715534i −0.582115 0.813107i 0.697775π-0.697775\pi
0.995228 + 0.0975728i 0.0311079π0.0311079\pi
710710 0 0
711711 12.0000 20.7846i 0.450035 0.779484i
712712 0 0
713713 −8.00000 13.8564i −0.299602 0.518927i
714714 0 0
715715 0 0
716716 0 0
717717 −1.50000 2.59808i −0.0560185 0.0970269i
718718 0 0
719719 15.0000 25.9808i 0.559406 0.968919i −0.438141 0.898906i 0.644363π-0.644363\pi
0.997546 0.0700124i 0.0223039π-0.0223039\pi
720720 0 0
721721 −20.0000 + 34.6410i −0.744839 + 1.29010i
722722 0 0
723723 −2.00000 −0.0743808
724724 0 0
725725 −12.0000 20.7846i −0.445669 0.771921i
726726 0 0
727727 −14.0000 −0.519231 −0.259616 0.965712i 0.583596π-0.583596\pi
−0.259616 + 0.965712i 0.583596π0.583596\pi
728728 0 0
729729 13.0000 0.481481
730730 0 0
731731 −1.50000 2.59808i −0.0554795 0.0960933i
732732 0 0
733733 −37.0000 −1.36663 −0.683313 0.730125i 0.739462π-0.739462\pi
−0.683313 + 0.730125i 0.739462π0.739462\pi
734734 0 0
735735 −9.00000 + 15.5885i −0.331970 + 0.574989i
736736 0 0
737737 6.00000 10.3923i 0.221013 0.382805i
738738 0 0
739739 26.0000 + 45.0333i 0.956425 + 1.65658i 0.731072 + 0.682300i 0.239020π0.239020\pi
0.225354 + 0.974277i 0.427646π0.427646\pi
740740 0 0
741741 0 0
742742 0 0
743743 14.5000 + 25.1147i 0.531953 + 0.921370i 0.999304 + 0.0372984i 0.0118752π0.0118752\pi
−0.467351 + 0.884072i 0.654791π0.654791\pi
744744 0 0
745745 7.00000 12.1244i 0.256460 0.444202i
746746 0 0
747747 16.0000 27.7128i 0.585409 1.01396i
748748 0 0
749749 −100.000 −3.65392
750750 0 0
751751 −16.0000 27.7128i −0.583848 1.01125i −0.995018 0.0996961i 0.968213π-0.968213\pi
0.411170 0.911559i 0.365120π-0.365120\pi
752752 0 0
753753 8.00000 0.291536
754754 0 0
755755 5.00000 0.181969
756756 0 0
757757 26.0000 + 45.0333i 0.944986 + 1.63676i 0.755779 + 0.654827i 0.227258π0.227258\pi
0.189207 + 0.981937i 0.439408π0.439408\pi
758758 0 0
759759 8.00000 0.290382
760760 0 0
761761 15.0000 25.9808i 0.543750 0.941802i −0.454935 0.890525i 0.650337π-0.650337\pi
0.998684 0.0512772i 0.0163292π-0.0163292\pi
762762 0 0
763763 12.5000 21.6506i 0.452530 0.783806i
764764 0 0
765765 −3.00000 5.19615i −0.108465 0.187867i
766766 0 0
767767 0 0
768768 0 0
769769 8.00000 + 13.8564i 0.288487 + 0.499675i 0.973449 0.228904i 0.0735143π-0.0735143\pi
−0.684962 + 0.728579i 0.740181π0.740181\pi
770770 0 0
771771 15.5000 26.8468i 0.558219 0.966863i
772772 0 0
773773 13.5000 23.3827i 0.485561 0.841017i −0.514301 0.857610i 0.671949π-0.671949\pi
0.999862 + 0.0165929i 0.00528194π0.00528194\pi
774774 0 0
775775 −16.0000 −0.574737
776776 0 0
777777 −27.5000 47.6314i −0.986557 1.70877i
778778 0 0
779779 −16.0000 −0.573259
780780 0 0
781781 −14.0000 −0.500959
782782 0 0
783783 −15.0000 25.9808i −0.536056 0.928477i
784784 0 0
785785 −2.00000 −0.0713831
786786 0 0
787787 −12.0000 + 20.7846i −0.427754 + 0.740891i −0.996673 0.0815020i 0.974028π-0.974028\pi
0.568919 + 0.822393i 0.307362π0.307362\pi
788788 0 0
789789 −10.0000 + 17.3205i −0.356009 + 0.616626i
790790 0 0
791791 5.00000 + 8.66025i 0.177780 + 0.307923i
792792 0 0
793793 0 0
794794 0 0
795795 6.00000 + 10.3923i 0.212798 + 0.368577i
796796 0 0
797797 −19.0000 + 32.9090i −0.673015 + 1.16570i 0.304030 + 0.952662i 0.401668π0.401668\pi
−0.977045 + 0.213033i 0.931666π0.931666\pi
798798 0 0
799799 −13.5000 + 23.3827i −0.477596 + 0.827220i
800800 0 0
801801 −20.0000 −0.706665
802802 0 0
803803 −2.00000 3.46410i −0.0705785 0.122245i
804804 0 0
805805 −20.0000 −0.704907
806806 0 0
807807 16.0000 0.563227
808808 0 0
809809 −7.50000 12.9904i −0.263686 0.456717i 0.703533 0.710663i 0.251605π-0.251605\pi
−0.967219 + 0.253946i 0.918272π0.918272\pi
810810 0 0
811811 28.0000 0.983213 0.491606 0.870817i 0.336410π-0.336410\pi
0.491606 + 0.870817i 0.336410π0.336410\pi
812812 0 0
813813 −3.50000 + 6.06218i −0.122750 + 0.212610i
814814 0 0
815815 2.00000 3.46410i 0.0700569 0.121342i
816816 0 0
817817 1.00000 + 1.73205i 0.0349856 + 0.0605968i
818818 0 0
819819 0 0
820820 0 0
821821 −20.5000 35.5070i −0.715455 1.23920i −0.962784 0.270273i 0.912886π-0.912886\pi
0.247329 0.968932i 0.420447π-0.420447\pi
822822 0 0
823823 13.0000 22.5167i 0.453152 0.784881i −0.545428 0.838157i 0.683633π-0.683633\pi
0.998580 + 0.0532760i 0.0169663π0.0169663\pi
824824 0 0
825825 4.00000 6.92820i 0.139262 0.241209i
826826 0 0
827827 10.0000 0.347734 0.173867 0.984769i 0.444374π-0.444374\pi
0.173867 + 0.984769i 0.444374π0.444374\pi
828828 0 0
829829 3.00000 + 5.19615i 0.104194 + 0.180470i 0.913409 0.407044i 0.133440π-0.133440\pi
−0.809214 + 0.587513i 0.800107π0.800107\pi
830830 0 0
831831 −12.0000 −0.416275
832832 0 0
833833 −54.0000 −1.87099
834834 0 0
835835 4.00000 + 6.92820i 0.138426 + 0.239760i
836836 0 0
837837 −20.0000 −0.691301
838838 0 0
839839 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
840840 0 0
841841 −3.50000 + 6.06218i −0.120690 + 0.209041i
842842 0 0
843843 −5.00000 8.66025i −0.172209 0.298275i
844844 0 0
845845 0 0
846846 0 0
847847 −17.5000 30.3109i −0.601307 1.04149i
848848 0 0
849849 10.0000 17.3205i 0.343199 0.594438i
850850 0 0
851851 22.0000 38.1051i 0.754150 1.30623i
852852 0 0
853853 47.0000 1.60925 0.804625 0.593784i 0.202367π-0.202367\pi
0.804625 + 0.593784i 0.202367π0.202367\pi
854854 0 0
855855 2.00000 + 3.46410i 0.0683986 + 0.118470i
856856 0 0
857857 30.0000 1.02478 0.512390 0.858753i 0.328760π-0.328760\pi
0.512390 + 0.858753i 0.328760π0.328760\pi
858858 0 0
859859 44.0000 1.50126 0.750630 0.660722i 0.229750π-0.229750\pi
0.750630 + 0.660722i 0.229750π0.229750\pi
860860 0 0
861861 −20.0000 34.6410i −0.681598 1.18056i
862862 0 0
863863 7.00000 0.238283 0.119141 0.992877i 0.461986π-0.461986\pi
0.119141 + 0.992877i 0.461986π0.461986\pi
864864 0 0
865865 6.00000 10.3923i 0.204006 0.353349i
866866 0 0
867867 4.00000 6.92820i 0.135847 0.235294i
868868 0 0
869869 −12.0000 20.7846i −0.407072 0.705070i
870870 0 0
871871 0 0
872872 0 0
873873 10.0000 + 17.3205i 0.338449 + 0.586210i
874874 0 0
875875 −22.5000 + 38.9711i −0.760639 + 1.31747i
876876 0 0
877877 −3.50000 + 6.06218i −0.118187 + 0.204705i −0.919049 0.394143i 0.871041π-0.871041\pi
0.800862 + 0.598848i 0.204375π0.204375\pi
878878 0 0
879879 −15.0000 −0.505937
880880 0 0
881881 13.5000 + 23.3827i 0.454827 + 0.787783i 0.998678 0.0513987i 0.0163679π-0.0163679\pi
−0.543852 + 0.839181i 0.683035π0.683035\pi
882882 0 0
883883 −51.0000 −1.71629 −0.858143 0.513410i 0.828382π-0.828382\pi
−0.858143 + 0.513410i 0.828382π0.828382\pi
884884 0 0
885885 −6.00000 −0.201688
886886 0 0
887887 24.0000 + 41.5692i 0.805841 + 1.39576i 0.915722 + 0.401813i 0.131620π0.131620\pi
−0.109881 + 0.993945i 0.535047π0.535047\pi
888888 0 0
889889 40.0000 1.34156
890890 0 0
891891 −1.00000 + 1.73205i −0.0335013 + 0.0580259i
892892 0 0
893893 9.00000 15.5885i 0.301174 0.521648i
894894 0 0
895895 −1.50000 2.59808i −0.0501395 0.0868441i
896896 0 0
897897 0 0
898898 0 0
899899 12.0000 + 20.7846i 0.400222 + 0.693206i
900900 0 0
901901 −18.0000 + 31.1769i −0.599667 + 1.03865i
902902 0 0
903903 −2.50000 + 4.33013i −0.0831948 + 0.144098i
904904 0 0
905905 16.0000 0.531858
906906 0 0
907907 2.50000 + 4.33013i 0.0830111 + 0.143780i 0.904542 0.426385i 0.140213π-0.140213\pi
−0.821531 + 0.570164i 0.806880π0.806880\pi
908908 0 0
909909 −8.00000 −0.265343
910910 0 0
911911 26.0000 0.861418 0.430709 0.902491i 0.358263π-0.358263\pi
0.430709 + 0.902491i 0.358263π0.358263\pi
912912 0 0
913913 −16.0000 27.7128i −0.529523 0.917160i
914914 0 0
915915 0 0
916916 0 0
917917 7.50000 12.9904i 0.247672 0.428980i
918918 0 0
919919 12.0000 20.7846i 0.395843 0.685621i −0.597365 0.801970i 0.703786π-0.703786\pi
0.993208 + 0.116348i 0.0371189π0.0371189\pi
920920 0 0
921921 −1.00000 1.73205i −0.0329511 0.0570730i
922922 0 0
923923 0 0
924924 0 0
925925 −22.0000 38.1051i −0.723356 1.25289i
926926 0 0
927927 −8.00000 + 13.8564i −0.262754 + 0.455104i
928928 0 0
929929 −10.0000 + 17.3205i −0.328089 + 0.568267i −0.982133 0.188190i 0.939738π-0.939738\pi
0.654043 + 0.756457i 0.273071π0.273071\pi
930930 0 0
931931 36.0000 1.17985
932932 0 0
933933 11.0000 + 19.0526i 0.360124 + 0.623753i
934934 0 0
935935 −6.00000 −0.196221
936936 0 0
937937 22.0000 0.718709 0.359354 0.933201i 0.382997π-0.382997\pi
0.359354 + 0.933201i 0.382997π0.382997\pi
938938 0 0
939939 4.50000 + 7.79423i 0.146852 + 0.254355i
940940 0 0
941941 7.00000 0.228193 0.114097 0.993470i 0.463603π-0.463603\pi
0.114097 + 0.993470i 0.463603π0.463603\pi
942942 0 0
943943 16.0000 27.7128i 0.521032 0.902453i
944944 0 0
945945 −12.5000 + 21.6506i −0.406625 + 0.704295i
946946 0 0
947947 −9.00000 15.5885i −0.292461 0.506557i 0.681930 0.731417i 0.261141π-0.261141\pi
−0.974391 + 0.224860i 0.927807π0.927807\pi
948948 0 0
949949 0 0
950950 0 0
951951 −1.00000 1.73205i −0.0324272 0.0561656i
952952 0 0
953953 4.50000 7.79423i 0.145769 0.252480i −0.783890 0.620899i 0.786768π-0.786768\pi
0.929660 + 0.368419i 0.120101π0.120101\pi
954954 0 0
955955 −5.00000 + 8.66025i −0.161796 + 0.280239i
956956 0 0
957957 −12.0000 −0.387905
958958 0 0
959959 30.0000 + 51.9615i 0.968751 + 1.67793i
960960 0 0
961961 −15.0000 −0.483871
962962 0 0
963963 −40.0000 −1.28898
964964 0 0
965965 8.00000 + 13.8564i 0.257529 + 0.446054i
966966 0 0
967967 13.0000 0.418052 0.209026 0.977910i 0.432971π-0.432971\pi
0.209026 + 0.977910i 0.432971π0.432971\pi
968968 0 0
969969 3.00000 5.19615i 0.0963739 0.166924i
970970 0 0
971971 −22.5000 + 38.9711i −0.722059 + 1.25064i 0.238114 + 0.971237i 0.423471π0.423471\pi
−0.960173 + 0.279406i 0.909862π0.909862\pi
972972 0 0
973973 7.50000 + 12.9904i 0.240439 + 0.416452i
974974 0 0
975975 0 0
976976 0 0
977977 −15.0000 25.9808i −0.479893 0.831198i 0.519841 0.854263i 0.325991π-0.325991\pi
−0.999734 + 0.0230645i 0.992658π0.992658\pi
978978 0 0
979979 −10.0000 + 17.3205i −0.319601 + 0.553566i
980980 0 0
981981 5.00000 8.66025i 0.159638 0.276501i
982982 0 0
983983 −5.00000 −0.159475 −0.0797376 0.996816i 0.525408π-0.525408\pi
−0.0797376 + 0.996816i 0.525408π0.525408\pi
984984 0 0
985985 8.50000 + 14.7224i 0.270833 + 0.469096i
986986 0 0
987987 45.0000 1.43237
988988 0 0
989989 −4.00000 −0.127193
990990 0 0
991991 −29.0000 50.2295i −0.921215 1.59559i −0.797537 0.603269i 0.793864π-0.793864\pi
−0.123678 0.992322i 0.539469π-0.539469\pi
992992 0 0
993993 −12.0000 −0.380808
994994 0 0
995995 9.00000 15.5885i 0.285319 0.494187i
996996 0 0
997997 −7.00000 + 12.1244i −0.221692 + 0.383982i −0.955322 0.295567i 0.904491π-0.904491\pi
0.733630 + 0.679549i 0.237825π0.237825\pi
998998 0 0
999999 −27.5000 47.6314i −0.870061 1.50699i
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 1352.2.i.c.1329.1 2
13.2 odd 12 1352.2.f.b.337.1 2
13.3 even 3 1352.2.a.b.1.1 1
13.4 even 6 1352.2.i.b.529.1 2
13.5 odd 4 1352.2.o.a.361.1 4
13.6 odd 12 1352.2.o.a.1161.1 4
13.7 odd 12 1352.2.o.a.1161.2 4
13.8 odd 4 1352.2.o.a.361.2 4
13.9 even 3 inner 1352.2.i.c.529.1 2
13.10 even 6 104.2.a.a.1.1 1
13.11 odd 12 1352.2.f.b.337.2 2
13.12 even 2 1352.2.i.b.1329.1 2
39.23 odd 6 936.2.a.f.1.1 1
52.3 odd 6 2704.2.a.d.1.1 1
52.11 even 12 2704.2.f.e.337.2 2
52.15 even 12 2704.2.f.e.337.1 2
52.23 odd 6 208.2.a.b.1.1 1
65.23 odd 12 2600.2.d.f.1249.2 2
65.49 even 6 2600.2.a.e.1.1 1
65.62 odd 12 2600.2.d.f.1249.1 2
91.62 odd 6 5096.2.a.c.1.1 1
104.75 odd 6 832.2.a.h.1.1 1
104.101 even 6 832.2.a.c.1.1 1
156.23 even 6 1872.2.a.l.1.1 1
208.75 odd 12 3328.2.b.t.1665.2 2
208.101 even 12 3328.2.b.a.1665.1 2
208.179 odd 12 3328.2.b.t.1665.1 2
208.205 even 12 3328.2.b.a.1665.2 2
260.179 odd 6 5200.2.a.bb.1.1 1
312.101 odd 6 7488.2.a.x.1.1 1
312.179 even 6 7488.2.a.u.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
104.2.a.a.1.1 1 13.10 even 6
208.2.a.b.1.1 1 52.23 odd 6
832.2.a.c.1.1 1 104.101 even 6
832.2.a.h.1.1 1 104.75 odd 6
936.2.a.f.1.1 1 39.23 odd 6
1352.2.a.b.1.1 1 13.3 even 3
1352.2.f.b.337.1 2 13.2 odd 12
1352.2.f.b.337.2 2 13.11 odd 12
1352.2.i.b.529.1 2 13.4 even 6
1352.2.i.b.1329.1 2 13.12 even 2
1352.2.i.c.529.1 2 13.9 even 3 inner
1352.2.i.c.1329.1 2 1.1 even 1 trivial
1352.2.o.a.361.1 4 13.5 odd 4
1352.2.o.a.361.2 4 13.8 odd 4
1352.2.o.a.1161.1 4 13.6 odd 12
1352.2.o.a.1161.2 4 13.7 odd 12
1872.2.a.l.1.1 1 156.23 even 6
2600.2.a.e.1.1 1 65.49 even 6
2600.2.d.f.1249.1 2 65.62 odd 12
2600.2.d.f.1249.2 2 65.23 odd 12
2704.2.a.d.1.1 1 52.3 odd 6
2704.2.f.e.337.1 2 52.15 even 12
2704.2.f.e.337.2 2 52.11 even 12
3328.2.b.a.1665.1 2 208.101 even 12
3328.2.b.a.1665.2 2 208.205 even 12
3328.2.b.t.1665.1 2 208.179 odd 12
3328.2.b.t.1665.2 2 208.75 odd 12
5096.2.a.c.1.1 1 91.62 odd 6
5200.2.a.bb.1.1 1 260.179 odd 6
7488.2.a.u.1.1 1 312.179 even 6
7488.2.a.x.1.1 1 312.101 odd 6