Properties

Label 320.2.o.b.287.1
Level 320320
Weight 22
Character 320.287
Analytic conductor 2.5552.555
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] = [320,2,Mod(223,320)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(320, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 3])) 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("320.223"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 320=265 320 = 2^{6} \cdot 5
Weight: k k == 2 2
Character orbit: [χ][\chi] == 320.o (of order 44, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,0,-2,0,2,0,2] 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: 2.555212864682.55521286468
Analytic rank: 00
Dimension: 22
Coefficient field: Q(i)\Q(i)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x2+1 x^{2} + 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: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 287.1
Root 1.00000i1.00000i of defining polynomial
Character χ\chi == 320.287
Dual form 320.2.o.b.223.1

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+(1.00000+1.00000i)q3+(1.00000+2.00000i)q5+(1.000001.00000i)q7+1.00000iq94.00000q11+(3.00000+3.00000i)q13+(3.000001.00000i)q15+(3.000003.00000i)q17+6.00000iq19+2.00000iq21+(3.00000+3.00000i)q23+(3.00000+4.00000i)q25+(4.000004.00000i)q272.00000q29+6.00000iq31+(4.000004.00000i)q33+(3.00000+1.00000i)q35+(3.000003.00000i)q376.00000q39+6.00000q41+(3.000003.00000i)q43+(2.00000+1.00000i)q45+(9.000009.00000i)q47+5.00000iq49+6.00000q51+(5.000005.00000i)q53+(4.000008.00000i)q55+(6.000006.00000i)q5710.0000iq5912.0000iq61+(1.00000+1.00000i)q63+(3.00000+9.00000i)q65+(9.00000+9.00000i)q676.00000q69+6.00000iq71+(5.000005.00000i)q73+(1.000007.00000i)q75+(4.00000+4.00000i)q77+5.00000q81+(3.000003.00000i)q83+(3.000009.00000i)q85+(2.000002.00000i)q87+6.00000q91+(6.000006.00000i)q93+(12.0000+6.00000i)q95+(7.000007.00000i)q974.00000iq99+O(q100)q+(-1.00000 + 1.00000i) q^{3} +(1.00000 + 2.00000i) q^{5} +(1.00000 - 1.00000i) q^{7} +1.00000i q^{9} -4.00000 q^{11} +(3.00000 + 3.00000i) q^{13} +(-3.00000 - 1.00000i) q^{15} +(-3.00000 - 3.00000i) q^{17} +6.00000i q^{19} +2.00000i q^{21} +(3.00000 + 3.00000i) q^{23} +(-3.00000 + 4.00000i) q^{25} +(-4.00000 - 4.00000i) q^{27} -2.00000 q^{29} +6.00000i q^{31} +(4.00000 - 4.00000i) q^{33} +(3.00000 + 1.00000i) q^{35} +(3.00000 - 3.00000i) q^{37} -6.00000 q^{39} +6.00000 q^{41} +(3.00000 - 3.00000i) q^{43} +(-2.00000 + 1.00000i) q^{45} +(9.00000 - 9.00000i) q^{47} +5.00000i q^{49} +6.00000 q^{51} +(-5.00000 - 5.00000i) q^{53} +(-4.00000 - 8.00000i) q^{55} +(-6.00000 - 6.00000i) q^{57} -10.0000i q^{59} -12.0000i q^{61} +(1.00000 + 1.00000i) q^{63} +(-3.00000 + 9.00000i) q^{65} +(9.00000 + 9.00000i) q^{67} -6.00000 q^{69} +6.00000i q^{71} +(5.00000 - 5.00000i) q^{73} +(-1.00000 - 7.00000i) q^{75} +(-4.00000 + 4.00000i) q^{77} +5.00000 q^{81} +(3.00000 - 3.00000i) q^{83} +(3.00000 - 9.00000i) q^{85} +(2.00000 - 2.00000i) q^{87} +6.00000 q^{91} +(-6.00000 - 6.00000i) q^{93} +(-12.0000 + 6.00000i) q^{95} +(-7.00000 - 7.00000i) q^{97} -4.00000i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q2q3+2q5+2q78q11+6q136q156q17+6q236q258q274q29+8q33+6q35+6q3712q39+12q41+6q434q45+18q47+14q97+O(q100) 2 q - 2 q^{3} + 2 q^{5} + 2 q^{7} - 8 q^{11} + 6 q^{13} - 6 q^{15} - 6 q^{17} + 6 q^{23} - 6 q^{25} - 8 q^{27} - 4 q^{29} + 8 q^{33} + 6 q^{35} + 6 q^{37} - 12 q^{39} + 12 q^{41} + 6 q^{43} - 4 q^{45} + 18 q^{47}+ \cdots - 14 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/320Z)×\left(\mathbb{Z}/320\mathbb{Z}\right)^\times.

nn 191191 257257 261261
χ(n)\chi(n) 1-1 e(14)e\left(\frac{1}{4}\right) 1-1

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 −1.00000 + 1.00000i −0.577350 + 0.577350i −0.934172 0.356822i 0.883860π-0.883860\pi
0.356822 + 0.934172i 0.383860π0.383860\pi
44 0 0
55 1.00000 + 2.00000i 0.447214 + 0.894427i
66 0 0
77 1.00000 1.00000i 0.377964 0.377964i −0.492403 0.870367i 0.663881π-0.663881\pi
0.870367 + 0.492403i 0.163881π0.163881\pi
88 0 0
99 1.00000i 0.333333i
1010 0 0
1111 −4.00000 −1.20605 −0.603023 0.797724i 0.706037π-0.706037\pi
−0.603023 + 0.797724i 0.706037π0.706037\pi
1212 0 0
1313 3.00000 + 3.00000i 0.832050 + 0.832050i 0.987797 0.155747i 0.0497784π-0.0497784\pi
−0.155747 + 0.987797i 0.549778π0.549778\pi
1414 0 0
1515 −3.00000 1.00000i −0.774597 0.258199i
1616 0 0
1717 −3.00000 3.00000i −0.727607 0.727607i 0.242536 0.970143i 0.422021π-0.422021\pi
−0.970143 + 0.242536i 0.922021π0.922021\pi
1818 0 0
1919 6.00000i 1.37649i 0.725476 + 0.688247i 0.241620π0.241620\pi
−0.725476 + 0.688247i 0.758380π0.758380\pi
2020 0 0
2121 2.00000i 0.436436i
2222 0 0
2323 3.00000 + 3.00000i 0.625543 + 0.625543i 0.946943 0.321400i 0.104153π-0.104153\pi
−0.321400 + 0.946943i 0.604153π0.604153\pi
2424 0 0
2525 −3.00000 + 4.00000i −0.600000 + 0.800000i
2626 0 0
2727 −4.00000 4.00000i −0.769800 0.769800i
2828 0 0
2929 −2.00000 −0.371391 −0.185695 0.982607i 0.559454π-0.559454\pi
−0.185695 + 0.982607i 0.559454π0.559454\pi
3030 0 0
3131 6.00000i 1.07763i 0.842424 + 0.538816i 0.181128π0.181128\pi
−0.842424 + 0.538816i 0.818872π0.818872\pi
3232 0 0
3333 4.00000 4.00000i 0.696311 0.696311i
3434 0 0
3535 3.00000 + 1.00000i 0.507093 + 0.169031i
3636 0 0
3737 3.00000 3.00000i 0.493197 0.493197i −0.416115 0.909312i 0.636609π-0.636609\pi
0.909312 + 0.416115i 0.136609π0.136609\pi
3838 0 0
3939 −6.00000 −0.960769
4040 0 0
4141 6.00000 0.937043 0.468521 0.883452i 0.344787π-0.344787\pi
0.468521 + 0.883452i 0.344787π0.344787\pi
4242 0 0
4343 3.00000 3.00000i 0.457496 0.457496i −0.440337 0.897833i 0.645141π-0.645141\pi
0.897833 + 0.440337i 0.145141π0.145141\pi
4444 0 0
4545 −2.00000 + 1.00000i −0.298142 + 0.149071i
4646 0 0
4747 9.00000 9.00000i 1.31278 1.31278i 0.393431 0.919354i 0.371288π-0.371288\pi
0.919354 0.393431i 0.128712π-0.128712\pi
4848 0 0
4949 5.00000i 0.714286i
5050 0 0
5151 6.00000 0.840168
5252 0 0
5353 −5.00000 5.00000i −0.686803 0.686803i 0.274721 0.961524i 0.411414π-0.411414\pi
−0.961524 + 0.274721i 0.911414π0.911414\pi
5454 0 0
5555 −4.00000 8.00000i −0.539360 1.07872i
5656 0 0
5757 −6.00000 6.00000i −0.794719 0.794719i
5858 0 0
5959 10.0000i 1.30189i −0.759125 0.650945i 0.774373π-0.774373\pi
0.759125 0.650945i 0.225627π-0.225627\pi
6060 0 0
6161 12.0000i 1.53644i −0.640184 0.768221i 0.721142π-0.721142\pi
0.640184 0.768221i 0.278858π-0.278858\pi
6262 0 0
6363 1.00000 + 1.00000i 0.125988 + 0.125988i
6464 0 0
6565 −3.00000 + 9.00000i −0.372104 + 1.11631i
6666 0 0
6767 9.00000 + 9.00000i 1.09952 + 1.09952i 0.994466 + 0.105059i 0.0335031π0.0335031\pi
0.105059 + 0.994466i 0.466497π0.466497\pi
6868 0 0
6969 −6.00000 −0.722315
7070 0 0
7171 6.00000i 0.712069i 0.934473 + 0.356034i 0.115871π0.115871\pi
−0.934473 + 0.356034i 0.884129π0.884129\pi
7272 0 0
7373 5.00000 5.00000i 0.585206 0.585206i −0.351123 0.936329i 0.614200π-0.614200\pi
0.936329 + 0.351123i 0.114200π0.114200\pi
7474 0 0
7575 −1.00000 7.00000i −0.115470 0.808290i
7676 0 0
7777 −4.00000 + 4.00000i −0.455842 + 0.455842i
7878 0 0
7979 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
8080 0 0
8181 5.00000 0.555556
8282 0 0
8383 3.00000 3.00000i 0.329293 0.329293i −0.523025 0.852318i 0.675196π-0.675196\pi
0.852318 + 0.523025i 0.175196π0.175196\pi
8484 0 0
8585 3.00000 9.00000i 0.325396 0.976187i
8686 0 0
8787 2.00000 2.00000i 0.214423 0.214423i
8888 0 0
8989 0 0 1.00000 00
−1.00000 π\pi
9090 0 0
9191 6.00000 0.628971
9292 0 0
9393 −6.00000 6.00000i −0.622171 0.622171i
9494 0 0
9595 −12.0000 + 6.00000i −1.23117 + 0.615587i
9696 0 0
9797 −7.00000 7.00000i −0.710742 0.710742i 0.255948 0.966691i 0.417612π-0.417612\pi
−0.966691 + 0.255948i 0.917612π0.917612\pi
9898 0 0
9999 4.00000i 0.402015i
100100 0 0
101101 8.00000i 0.796030i 0.917379 + 0.398015i 0.130301π0.130301\pi
−0.917379 + 0.398015i 0.869699π0.869699\pi
102102 0 0
103103 11.0000 + 11.0000i 1.08386 + 1.08386i 0.996145 + 0.0877167i 0.0279570π0.0279570\pi
0.0877167 + 0.996145i 0.472043π0.472043\pi
104104 0 0
105105 −4.00000 + 2.00000i −0.390360 + 0.195180i
106106 0 0
107107 −3.00000 3.00000i −0.290021 0.290021i 0.547068 0.837088i 0.315744π-0.315744\pi
−0.837088 + 0.547068i 0.815744π0.815744\pi
108108 0 0
109109 18.0000 1.72409 0.862044 0.506834i 0.169184π-0.169184\pi
0.862044 + 0.506834i 0.169184π0.169184\pi
110110 0 0
111111 6.00000i 0.569495i
112112 0 0
113113 −3.00000 + 3.00000i −0.282216 + 0.282216i −0.833992 0.551776i 0.813950π-0.813950\pi
0.551776 + 0.833992i 0.313950π0.313950\pi
114114 0 0
115115 −3.00000 + 9.00000i −0.279751 + 0.839254i
116116 0 0
117117 −3.00000 + 3.00000i −0.277350 + 0.277350i
118118 0 0
119119 −6.00000 −0.550019
120120 0 0
121121 5.00000 0.454545
122122 0 0
123123 −6.00000 + 6.00000i −0.541002 + 0.541002i
124124 0 0
125125 −11.0000 2.00000i −0.983870 0.178885i
126126 0 0
127127 5.00000 5.00000i 0.443678 0.443678i −0.449568 0.893246i 0.648422π-0.648422\pi
0.893246 + 0.449568i 0.148422π0.148422\pi
128128 0 0
129129 6.00000i 0.528271i
130130 0 0
131131 −4.00000 −0.349482 −0.174741 0.984614i 0.555909π-0.555909\pi
−0.174741 + 0.984614i 0.555909π0.555909\pi
132132 0 0
133133 6.00000 + 6.00000i 0.520266 + 0.520266i
134134 0 0
135135 4.00000 12.0000i 0.344265 1.03280i
136136 0 0
137137 −3.00000 3.00000i −0.256307 0.256307i 0.567243 0.823550i 0.308010π-0.308010\pi
−0.823550 + 0.567243i 0.808010π0.808010\pi
138138 0 0
139139 6.00000i 0.508913i 0.967084 + 0.254457i 0.0818966π0.0818966\pi
−0.967084 + 0.254457i 0.918103π0.918103\pi
140140 0 0
141141 18.0000i 1.51587i
142142 0 0
143143 −12.0000 12.0000i −1.00349 1.00349i
144144 0 0
145145 −2.00000 4.00000i −0.166091 0.332182i
146146 0 0
147147 −5.00000 5.00000i −0.412393 0.412393i
148148 0 0
149149 2.00000 0.163846 0.0819232 0.996639i 0.473894π-0.473894\pi
0.0819232 + 0.996639i 0.473894π0.473894\pi
150150 0 0
151151 10.0000i 0.813788i −0.913475 0.406894i 0.866612π-0.866612\pi
0.913475 0.406894i 0.133388π-0.133388\pi
152152 0 0
153153 3.00000 3.00000i 0.242536 0.242536i
154154 0 0
155155 −12.0000 + 6.00000i −0.963863 + 0.481932i
156156 0 0
157157 3.00000 3.00000i 0.239426 0.239426i −0.577186 0.816612i 0.695849π-0.695849\pi
0.816612 + 0.577186i 0.195849π0.195849\pi
158158 0 0
159159 10.0000 0.793052
160160 0 0
161161 6.00000 0.472866
162162 0 0
163163 −9.00000 + 9.00000i −0.704934 + 0.704934i −0.965465 0.260531i 0.916102π-0.916102\pi
0.260531 + 0.965465i 0.416102π0.416102\pi
164164 0 0
165165 12.0000 + 4.00000i 0.934199 + 0.311400i
166166 0 0
167167 −3.00000 + 3.00000i −0.232147 + 0.232147i −0.813588 0.581441i 0.802489π-0.802489\pi
0.581441 + 0.813588i 0.302489π0.302489\pi
168168 0 0
169169 5.00000i 0.384615i
170170 0 0
171171 −6.00000 −0.458831
172172 0 0
173173 15.0000 + 15.0000i 1.14043 + 1.14043i 0.988372 + 0.152057i 0.0485898π0.0485898\pi
0.152057 + 0.988372i 0.451410π0.451410\pi
174174 0 0
175175 1.00000 + 7.00000i 0.0755929 + 0.529150i
176176 0 0
177177 10.0000 + 10.0000i 0.751646 + 0.751646i
178178 0 0
179179 2.00000i 0.149487i −0.997203 0.0747435i 0.976186π-0.976186\pi
0.997203 0.0747435i 0.0238138π-0.0238138\pi
180180 0 0
181181 0 0 1.00000 00
−1.00000 π\pi
182182 0 0
183183 12.0000 + 12.0000i 0.887066 + 0.887066i
184184 0 0
185185 9.00000 + 3.00000i 0.661693 + 0.220564i
186186 0 0
187187 12.0000 + 12.0000i 0.877527 + 0.877527i
188188 0 0
189189 −8.00000 −0.581914
190190 0 0
191191 6.00000i 0.434145i 0.976156 + 0.217072i 0.0696508π0.0696508\pi
−0.976156 + 0.217072i 0.930349π0.930349\pi
192192 0 0
193193 5.00000 5.00000i 0.359908 0.359908i −0.503871 0.863779i 0.668091π-0.668091\pi
0.863779 + 0.503871i 0.168091π0.168091\pi
194194 0 0
195195 −6.00000 12.0000i −0.429669 0.859338i
196196 0 0
197197 −5.00000 + 5.00000i −0.356235 + 0.356235i −0.862423 0.506188i 0.831054π-0.831054\pi
0.506188 + 0.862423i 0.331054π0.331054\pi
198198 0 0
199199 −16.0000 −1.13421 −0.567105 0.823646i 0.691937π-0.691937\pi
−0.567105 + 0.823646i 0.691937π0.691937\pi
200200 0 0
201201 −18.0000 −1.26962
202202 0 0
203203 −2.00000 + 2.00000i −0.140372 + 0.140372i
204204 0 0
205205 6.00000 + 12.0000i 0.419058 + 0.838116i
206206 0 0
207207 −3.00000 + 3.00000i −0.208514 + 0.208514i
208208 0 0
209209 24.0000i 1.66011i
210210 0 0
211211 −12.0000 −0.826114 −0.413057 0.910705i 0.635539π-0.635539\pi
−0.413057 + 0.910705i 0.635539π0.635539\pi
212212 0 0
213213 −6.00000 6.00000i −0.411113 0.411113i
214214 0 0
215215 9.00000 + 3.00000i 0.613795 + 0.204598i
216216 0 0
217217 6.00000 + 6.00000i 0.407307 + 0.407307i
218218 0 0
219219 10.0000i 0.675737i
220220 0 0
221221 18.0000i 1.21081i
222222 0 0
223223 −13.0000 13.0000i −0.870544 0.870544i 0.121987 0.992532i 0.461073π-0.461073\pi
−0.992532 + 0.121987i 0.961073π0.961073\pi
224224 0 0
225225 −4.00000 3.00000i −0.266667 0.200000i
226226 0 0
227227 −11.0000 11.0000i −0.730096 0.730096i 0.240543 0.970639i 0.422675π-0.422675\pi
−0.970639 + 0.240543i 0.922675π0.922675\pi
228228 0 0
229229 6.00000 0.396491 0.198246 0.980152i 0.436476π-0.436476\pi
0.198246 + 0.980152i 0.436476π0.436476\pi
230230 0 0
231231 8.00000i 0.526361i
232232 0 0
233233 −15.0000 + 15.0000i −0.982683 + 0.982683i −0.999853 0.0171699i 0.994534π-0.994534\pi
0.0171699 + 0.999853i 0.494534π0.494534\pi
234234 0 0
235235 27.0000 + 9.00000i 1.76129 + 0.587095i
236236 0 0
237237 0 0
238238 0 0
239239 24.0000 1.55243 0.776215 0.630468i 0.217137π-0.217137\pi
0.776215 + 0.630468i 0.217137π0.217137\pi
240240 0 0
241241 −18.0000 −1.15948 −0.579741 0.814801i 0.696846π-0.696846\pi
−0.579741 + 0.814801i 0.696846π0.696846\pi
242242 0 0
243243 7.00000 7.00000i 0.449050 0.449050i
244244 0 0
245245 −10.0000 + 5.00000i −0.638877 + 0.319438i
246246 0 0
247247 −18.0000 + 18.0000i −1.14531 + 1.14531i
248248 0 0
249249 6.00000i 0.380235i
250250 0 0
251251 4.00000 0.252478 0.126239 0.992000i 0.459709π-0.459709\pi
0.126239 + 0.992000i 0.459709π0.459709\pi
252252 0 0
253253 −12.0000 12.0000i −0.754434 0.754434i
254254 0 0
255255 6.00000 + 12.0000i 0.375735 + 0.751469i
256256 0 0
257257 −3.00000 3.00000i −0.187135 0.187135i 0.607321 0.794456i 0.292244π-0.292244\pi
−0.794456 + 0.607321i 0.792244π0.792244\pi
258258 0 0
259259 6.00000i 0.372822i
260260 0 0
261261 2.00000i 0.123797i
262262 0 0
263263 −9.00000 9.00000i −0.554964 0.554964i 0.372906 0.927869i 0.378362π-0.378362\pi
−0.927869 + 0.372906i 0.878362π0.878362\pi
264264 0 0
265265 5.00000 15.0000i 0.307148 0.921443i
266266 0 0
267267 0 0
268268 0 0
269269 −14.0000 −0.853595 −0.426798 0.904347i 0.640358π-0.640358\pi
−0.426798 + 0.904347i 0.640358π0.640358\pi
270270 0 0
271271 2.00000i 0.121491i −0.998153 0.0607457i 0.980652π-0.980652\pi
0.998153 0.0607457i 0.0193479π-0.0193479\pi
272272 0 0
273273 −6.00000 + 6.00000i −0.363137 + 0.363137i
274274 0 0
275275 12.0000 16.0000i 0.723627 0.964836i
276276 0 0
277277 15.0000 15.0000i 0.901263 0.901263i −0.0942828 0.995545i 0.530056π-0.530056\pi
0.995545 + 0.0942828i 0.0300558π0.0300558\pi
278278 0 0
279279 −6.00000 −0.359211
280280 0 0
281281 6.00000 0.357930 0.178965 0.983855i 0.442725π-0.442725\pi
0.178965 + 0.983855i 0.442725π0.442725\pi
282282 0 0
283283 15.0000 15.0000i 0.891657 0.891657i −0.103022 0.994679i 0.532851π-0.532851\pi
0.994679 + 0.103022i 0.0328511π0.0328511\pi
284284 0 0
285285 6.00000 18.0000i 0.355409 1.06623i
286286 0 0
287287 6.00000 6.00000i 0.354169 0.354169i
288288 0 0
289289 1.00000i 0.0588235i
290290 0 0
291291 14.0000 0.820695
292292 0 0
293293 −1.00000 1.00000i −0.0584206 0.0584206i 0.677293 0.735714i 0.263153π-0.263153\pi
−0.735714 + 0.677293i 0.763153π0.763153\pi
294294 0 0
295295 20.0000 10.0000i 1.16445 0.582223i
296296 0 0
297297 16.0000 + 16.0000i 0.928414 + 0.928414i
298298 0 0
299299 18.0000i 1.04097i
300300 0 0
301301 6.00000i 0.345834i
302302 0 0
303303 −8.00000 8.00000i −0.459588 0.459588i
304304 0 0
305305 24.0000 12.0000i 1.37424 0.687118i
306306 0 0
307307 −15.0000 15.0000i −0.856095 0.856095i 0.134780 0.990876i 0.456967π-0.456967\pi
−0.990876 + 0.134780i 0.956967π0.956967\pi
308308 0 0
309309 −22.0000 −1.25154
310310 0 0
311311 18.0000i 1.02069i −0.859971 0.510343i 0.829518π-0.829518\pi
0.859971 0.510343i 0.170482π-0.170482\pi
312312 0 0
313313 1.00000 1.00000i 0.0565233 0.0565233i −0.678280 0.734803i 0.737274π-0.737274\pi
0.734803 + 0.678280i 0.237274π0.237274\pi
314314 0 0
315315 −1.00000 + 3.00000i −0.0563436 + 0.169031i
316316 0 0
317317 3.00000 3.00000i 0.168497 0.168497i −0.617822 0.786318i 0.711985π-0.711985\pi
0.786318 + 0.617822i 0.211985π0.211985\pi
318318 0 0
319319 8.00000 0.447914
320320 0 0
321321 6.00000 0.334887
322322 0 0
323323 18.0000 18.0000i 1.00155 1.00155i
324324 0 0
325325 −21.0000 + 3.00000i −1.16487 + 0.166410i
326326 0 0
327327 −18.0000 + 18.0000i −0.995402 + 0.995402i
328328 0 0
329329 18.0000i 0.992372i
330330 0 0
331331 12.0000 0.659580 0.329790 0.944054i 0.393022π-0.393022\pi
0.329790 + 0.944054i 0.393022π0.393022\pi
332332 0 0
333333 3.00000 + 3.00000i 0.164399 + 0.164399i
334334 0 0
335335 −9.00000 + 27.0000i −0.491723 + 1.47517i
336336 0 0
337337 25.0000 + 25.0000i 1.36184 + 1.36184i 0.871576 + 0.490261i 0.163099π0.163099\pi
0.490261 + 0.871576i 0.336901π0.336901\pi
338338 0 0
339339 6.00000i 0.325875i
340340 0 0
341341 24.0000i 1.29967i
342342 0 0
343343 12.0000 + 12.0000i 0.647939 + 0.647939i
344344 0 0
345345 −6.00000 12.0000i −0.323029 0.646058i
346346 0 0
347347 17.0000 + 17.0000i 0.912608 + 0.912608i 0.996477 0.0838690i 0.0267277π-0.0267277\pi
−0.0838690 + 0.996477i 0.526728π0.526728\pi
348348 0 0
349349 −18.0000 −0.963518 −0.481759 0.876304i 0.660002π-0.660002\pi
−0.481759 + 0.876304i 0.660002π0.660002\pi
350350 0 0
351351 24.0000i 1.28103i
352352 0 0
353353 −15.0000 + 15.0000i −0.798369 + 0.798369i −0.982838 0.184469i 0.940943π-0.940943\pi
0.184469 + 0.982838i 0.440943π0.440943\pi
354354 0 0
355355 −12.0000 + 6.00000i −0.636894 + 0.318447i
356356 0 0
357357 6.00000 6.00000i 0.317554 0.317554i
358358 0 0
359359 24.0000 1.26667 0.633336 0.773877i 0.281685π-0.281685\pi
0.633336 + 0.773877i 0.281685π0.281685\pi
360360 0 0
361361 −17.0000 −0.894737
362362 0 0
363363 −5.00000 + 5.00000i −0.262432 + 0.262432i
364364 0 0
365365 15.0000 + 5.00000i 0.785136 + 0.261712i
366366 0 0
367367 −11.0000 + 11.0000i −0.574195 + 0.574195i −0.933298 0.359103i 0.883083π-0.883083\pi
0.359103 + 0.933298i 0.383083π0.383083\pi
368368 0 0
369369 6.00000i 0.312348i
370370 0 0
371371 −10.0000 −0.519174
372372 0 0
373373 3.00000 + 3.00000i 0.155334 + 0.155334i 0.780496 0.625161i 0.214967π-0.214967\pi
−0.625161 + 0.780496i 0.714967π0.714967\pi
374374 0 0
375375 13.0000 9.00000i 0.671317 0.464758i
376376 0 0
377377 −6.00000 6.00000i −0.309016 0.309016i
378378 0 0
379379 18.0000i 0.924598i −0.886724 0.462299i 0.847025π-0.847025\pi
0.886724 0.462299i 0.152975π-0.152975\pi
380380 0 0
381381 10.0000i 0.512316i
382382 0 0
383383 −21.0000 21.0000i −1.07305 1.07305i −0.997113 0.0759373i 0.975805π-0.975805\pi
−0.0759373 0.997113i 0.524195π-0.524195\pi
384384 0 0
385385 −12.0000 4.00000i −0.611577 0.203859i
386386 0 0
387387 3.00000 + 3.00000i 0.152499 + 0.152499i
388388 0 0
389389 26.0000 1.31825 0.659126 0.752032i 0.270926π-0.270926\pi
0.659126 + 0.752032i 0.270926π0.270926\pi
390390 0 0
391391 18.0000i 0.910299i
392392 0 0
393393 4.00000 4.00000i 0.201773 0.201773i
394394 0 0
395395 0 0
396396 0 0
397397 −9.00000 + 9.00000i −0.451697 + 0.451697i −0.895918 0.444220i 0.853481π-0.853481\pi
0.444220 + 0.895918i 0.353481π0.353481\pi
398398 0 0
399399 −12.0000 −0.600751
400400 0 0
401401 −30.0000 −1.49813 −0.749064 0.662497i 0.769497π-0.769497\pi
−0.749064 + 0.662497i 0.769497π0.769497\pi
402402 0 0
403403 −18.0000 + 18.0000i −0.896644 + 0.896644i
404404 0 0
405405 5.00000 + 10.0000i 0.248452 + 0.496904i
406406 0 0
407407 −12.0000 + 12.0000i −0.594818 + 0.594818i
408408 0 0
409409 12.0000i 0.593362i −0.954977 0.296681i 0.904120π-0.904120\pi
0.954977 0.296681i 0.0958798π-0.0958798\pi
410410 0 0
411411 6.00000 0.295958
412412 0 0
413413 −10.0000 10.0000i −0.492068 0.492068i
414414 0 0
415415 9.00000 + 3.00000i 0.441793 + 0.147264i
416416 0 0
417417 −6.00000 6.00000i −0.293821 0.293821i
418418 0 0
419419 10.0000i 0.488532i −0.969708 0.244266i 0.921453π-0.921453\pi
0.969708 0.244266i 0.0785470π-0.0785470\pi
420420 0 0
421421 12.0000i 0.584844i 0.956289 + 0.292422i 0.0944612π0.0944612\pi
−0.956289 + 0.292422i 0.905539π0.905539\pi
422422 0 0
423423 9.00000 + 9.00000i 0.437595 + 0.437595i
424424 0 0
425425 21.0000 3.00000i 1.01865 0.145521i
426426 0 0
427427 −12.0000 12.0000i −0.580721 0.580721i
428428 0 0
429429 24.0000 1.15873
430430 0 0
431431 30.0000i 1.44505i 0.691345 + 0.722525i 0.257018π0.257018\pi
−0.691345 + 0.722525i 0.742982π0.742982\pi
432432 0 0
433433 −7.00000 + 7.00000i −0.336399 + 0.336399i −0.855010 0.518611i 0.826449π-0.826449\pi
0.518611 + 0.855010i 0.326449π0.326449\pi
434434 0 0
435435 6.00000 + 2.00000i 0.287678 + 0.0958927i
436436 0 0
437437 −18.0000 + 18.0000i −0.861057 + 0.861057i
438438 0 0
439439 −8.00000 −0.381819 −0.190910 0.981608i 0.561144π-0.561144\pi
−0.190910 + 0.981608i 0.561144π0.561144\pi
440440 0 0
441441 −5.00000 −0.238095
442442 0 0
443443 −25.0000 + 25.0000i −1.18779 + 1.18779i −0.210108 + 0.977678i 0.567381π0.567381\pi
−0.977678 + 0.210108i 0.932619π0.932619\pi
444444 0 0
445445 0 0
446446 0 0
447447 −2.00000 + 2.00000i −0.0945968 + 0.0945968i
448448 0 0
449449 12.0000i 0.566315i 0.959073 + 0.283158i 0.0913819π0.0913819\pi
−0.959073 + 0.283158i 0.908618π0.908618\pi
450450 0 0
451451 −24.0000 −1.13012
452452 0 0
453453 10.0000 + 10.0000i 0.469841 + 0.469841i
454454 0 0
455455 6.00000 + 12.0000i 0.281284 + 0.562569i
456456 0 0
457457 17.0000 + 17.0000i 0.795226 + 0.795226i 0.982339 0.187112i 0.0599128π-0.0599128\pi
−0.187112 + 0.982339i 0.559913π0.559913\pi
458458 0 0
459459 24.0000i 1.12022i
460460 0 0
461461 40.0000i 1.86299i 0.363760 + 0.931493i 0.381493π0.381493\pi
−0.363760 + 0.931493i 0.618507π0.618507\pi
462462 0 0
463463 −1.00000 1.00000i −0.0464739 0.0464739i 0.683488 0.729962i 0.260462π-0.260462\pi
−0.729962 + 0.683488i 0.760462π0.760462\pi
464464 0 0
465465 6.00000 18.0000i 0.278243 0.834730i
466466 0 0
467467 21.0000 + 21.0000i 0.971764 + 0.971764i 0.999612 0.0278481i 0.00886546π-0.00886546\pi
−0.0278481 + 0.999612i 0.508865π0.508865\pi
468468 0 0
469469 18.0000 0.831163
470470 0 0
471471 6.00000i 0.276465i
472472 0 0
473473 −12.0000 + 12.0000i −0.551761 + 0.551761i
474474 0 0
475475 −24.0000 18.0000i −1.10120 0.825897i
476476 0 0
477477 5.00000 5.00000i 0.228934 0.228934i
478478 0 0
479479 24.0000 1.09659 0.548294 0.836286i 0.315277π-0.315277\pi
0.548294 + 0.836286i 0.315277π0.315277\pi
480480 0 0
481481 18.0000 0.820729
482482 0 0
483483 −6.00000 + 6.00000i −0.273009 + 0.273009i
484484 0 0
485485 7.00000 21.0000i 0.317854 0.953561i
486486 0 0
487487 1.00000 1.00000i 0.0453143 0.0453143i −0.684087 0.729401i 0.739799π-0.739799\pi
0.729401 + 0.684087i 0.239799π0.239799\pi
488488 0 0
489489 18.0000i 0.813988i
490490 0 0
491491 −20.0000 −0.902587 −0.451294 0.892375i 0.649037π-0.649037\pi
−0.451294 + 0.892375i 0.649037π0.649037\pi
492492 0 0
493493 6.00000 + 6.00000i 0.270226 + 0.270226i
494494 0 0
495495 8.00000 4.00000i 0.359573 0.179787i
496496 0 0
497497 6.00000 + 6.00000i 0.269137 + 0.269137i
498498 0 0
499499 6.00000i 0.268597i 0.990941 + 0.134298i 0.0428781π0.0428781\pi
−0.990941 + 0.134298i 0.957122π0.957122\pi
500500 0 0
501501 6.00000i 0.268060i
502502 0 0
503503 −21.0000 21.0000i −0.936344 0.936344i 0.0617480 0.998092i 0.480332π-0.480332\pi
−0.998092 + 0.0617480i 0.980332π0.980332\pi
504504 0 0
505505 −16.0000 + 8.00000i −0.711991 + 0.355995i
506506 0 0
507507 −5.00000 5.00000i −0.222058 0.222058i
508508 0 0
509509 14.0000 0.620539 0.310270 0.950649i 0.399581π-0.399581\pi
0.310270 + 0.950649i 0.399581π0.399581\pi
510510 0 0
511511 10.0000i 0.442374i
512512 0 0
513513 24.0000 24.0000i 1.05963 1.05963i
514514 0 0
515515 −11.0000 + 33.0000i −0.484718 + 1.45415i
516516 0 0
517517 −36.0000 + 36.0000i −1.58328 + 1.58328i
518518 0 0
519519 −30.0000 −1.31685
520520 0 0
521521 18.0000 0.788594 0.394297 0.918983i 0.370988π-0.370988\pi
0.394297 + 0.918983i 0.370988π0.370988\pi
522522 0 0
523523 15.0000 15.0000i 0.655904 0.655904i −0.298504 0.954408i 0.596488π-0.596488\pi
0.954408 + 0.298504i 0.0964877π0.0964877\pi
524524 0 0
525525 −8.00000 6.00000i −0.349149 0.261861i
526526 0 0
527527 18.0000 18.0000i 0.784092 0.784092i
528528 0 0
529529 5.00000i 0.217391i
530530 0 0
531531 10.0000 0.433963
532532 0 0
533533 18.0000 + 18.0000i 0.779667 + 0.779667i
534534 0 0
535535 3.00000 9.00000i 0.129701 0.389104i
536536 0 0
537537 2.00000 + 2.00000i 0.0863064 + 0.0863064i
538538 0 0
539539 20.0000i 0.861461i
540540 0 0
541541 24.0000i 1.03184i 0.856637 + 0.515920i 0.172550π0.172550\pi
−0.856637 + 0.515920i 0.827450π0.827450\pi
542542 0 0
543543 0 0
544544 0 0
545545 18.0000 + 36.0000i 0.771035 + 1.54207i
546546 0 0
547547 −3.00000 3.00000i −0.128271 0.128271i 0.640057 0.768328i 0.278911π-0.278911\pi
−0.768328 + 0.640057i 0.778911π0.778911\pi
548548 0 0
549549 12.0000 0.512148
550550 0 0
551551 12.0000i 0.511217i
552552 0 0
553553 0 0
554554 0 0
555555 −12.0000 + 6.00000i −0.509372 + 0.254686i
556556 0 0
557557 31.0000 31.0000i 1.31351 1.31351i 0.394704 0.918808i 0.370847π-0.370847\pi
0.918808 0.394704i 0.129153π-0.129153\pi
558558 0 0
559559 18.0000 0.761319
560560 0 0
561561 −24.0000 −1.01328
562562 0 0
563563 −1.00000 + 1.00000i −0.0421450 + 0.0421450i −0.727865 0.685720i 0.759487π-0.759487\pi
0.685720 + 0.727865i 0.259487π0.259487\pi
564564 0 0
565565 −9.00000 3.00000i −0.378633 0.126211i
566566 0 0
567567 5.00000 5.00000i 0.209980 0.209980i
568568 0 0
569569 12.0000i 0.503066i 0.967849 + 0.251533i 0.0809347π0.0809347\pi
−0.967849 + 0.251533i 0.919065π0.919065\pi
570570 0 0
571571 12.0000 0.502184 0.251092 0.967963i 0.419210π-0.419210\pi
0.251092 + 0.967963i 0.419210π0.419210\pi
572572 0 0
573573 −6.00000 6.00000i −0.250654 0.250654i
574574 0 0
575575 −21.0000 + 3.00000i −0.875761 + 0.125109i
576576 0 0
577577 −19.0000 19.0000i −0.790980 0.790980i 0.190673 0.981654i 0.438933π-0.438933\pi
−0.981654 + 0.190673i 0.938933π0.938933\pi
578578 0 0
579579 10.0000i 0.415586i
580580 0 0
581581 6.00000i 0.248922i
582582 0 0
583583 20.0000 + 20.0000i 0.828315 + 0.828315i
584584 0 0
585585 −9.00000 3.00000i −0.372104 0.124035i
586586 0 0
587587 −15.0000 15.0000i −0.619116 0.619116i 0.326188 0.945305i 0.394236π-0.394236\pi
−0.945305 + 0.326188i 0.894236π0.894236\pi
588588 0 0
589589 −36.0000 −1.48335
590590 0 0
591591 10.0000i 0.411345i
592592 0 0
593593 −15.0000 + 15.0000i −0.615976 + 0.615976i −0.944497 0.328521i 0.893450π-0.893450\pi
0.328521 + 0.944497i 0.393450π0.393450\pi
594594 0 0
595595 −6.00000 12.0000i −0.245976 0.491952i
596596 0 0
597597 16.0000 16.0000i 0.654836 0.654836i
598598 0 0
599599 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
600600 0 0
601601 −10.0000 −0.407909 −0.203954 0.978980i 0.565379π-0.565379\pi
−0.203954 + 0.978980i 0.565379π0.565379\pi
602602 0 0
603603 −9.00000 + 9.00000i −0.366508 + 0.366508i
604604 0 0
605605 5.00000 + 10.0000i 0.203279 + 0.406558i
606606 0 0
607607 −7.00000 + 7.00000i −0.284121 + 0.284121i −0.834750 0.550629i 0.814388π-0.814388\pi
0.550629 + 0.834750i 0.314388π0.314388\pi
608608 0 0
609609 4.00000i 0.162088i
610610 0 0
611611 54.0000 2.18461
612612 0 0
613613 −9.00000 9.00000i −0.363507 0.363507i 0.501596 0.865102i 0.332747π-0.332747\pi
−0.865102 + 0.501596i 0.832747π0.832747\pi
614614 0 0
615615 −18.0000 6.00000i −0.725830 0.241943i
616616 0 0
617617 −15.0000 15.0000i −0.603877 0.603877i 0.337462 0.941339i 0.390432π-0.390432\pi
−0.941339 + 0.337462i 0.890432π0.890432\pi
618618 0 0
619619 42.0000i 1.68812i −0.536247 0.844061i 0.680158π-0.680158\pi
0.536247 0.844061i 0.319842π-0.319842\pi
620620 0 0
621621 24.0000i 0.963087i
622622 0 0
623623 0 0
624624 0 0
625625 −7.00000 24.0000i −0.280000 0.960000i
626626 0 0
627627 24.0000 + 24.0000i 0.958468 + 0.958468i
628628 0 0
629629 −18.0000 −0.717707
630630 0 0
631631 30.0000i 1.19428i 0.802137 + 0.597141i 0.203697π0.203697\pi
−0.802137 + 0.597141i 0.796303π0.796303\pi
632632 0 0
633633 12.0000 12.0000i 0.476957 0.476957i
634634 0 0
635635 15.0000 + 5.00000i 0.595257 + 0.198419i
636636 0 0
637637 −15.0000 + 15.0000i −0.594322 + 0.594322i
638638 0 0
639639 −6.00000 −0.237356
640640 0 0
641641 30.0000 1.18493 0.592464 0.805597i 0.298155π-0.298155\pi
0.592464 + 0.805597i 0.298155π0.298155\pi
642642 0 0
643643 3.00000 3.00000i 0.118308 0.118308i −0.645474 0.763782i 0.723340π-0.723340\pi
0.763782 + 0.645474i 0.223340π0.223340\pi
644644 0 0
645645 −12.0000 + 6.00000i −0.472500 + 0.236250i
646646 0 0
647647 9.00000 9.00000i 0.353827 0.353827i −0.507705 0.861531i 0.669506π-0.669506\pi
0.861531 + 0.507705i 0.169506π0.169506\pi
648648 0 0
649649 40.0000i 1.57014i
650650 0 0
651651 −12.0000 −0.470317
652652 0 0
653653 −33.0000 33.0000i −1.29139 1.29139i −0.933928 0.357462i 0.883642π-0.883642\pi
−0.357462 0.933928i 0.616358π-0.616358\pi
654654 0 0
655655 −4.00000 8.00000i −0.156293 0.312586i
656656 0 0
657657 5.00000 + 5.00000i 0.195069 + 0.195069i
658658 0 0
659659 22.0000i 0.856998i 0.903542 + 0.428499i 0.140958π0.140958\pi
−0.903542 + 0.428499i 0.859042π0.859042\pi
660660 0 0
661661 12.0000i 0.466746i −0.972387 0.233373i 0.925024π-0.925024\pi
0.972387 0.233373i 0.0749763π-0.0749763\pi
662662 0 0
663663 18.0000 + 18.0000i 0.699062 + 0.699062i
664664 0 0
665665 −6.00000 + 18.0000i −0.232670 + 0.698010i
666666 0 0
667667 −6.00000 6.00000i −0.232321 0.232321i
668668 0 0
669669 26.0000 1.00522
670670 0 0
671671 48.0000i 1.85302i
672672 0 0
673673 25.0000 25.0000i 0.963679 0.963679i −0.0356839 0.999363i 0.511361π-0.511361\pi
0.999363 + 0.0356839i 0.0113610π0.0113610\pi
674674 0 0
675675 28.0000 4.00000i 1.07772 0.153960i
676676 0 0
677677 27.0000 27.0000i 1.03769 1.03769i 0.0384331 0.999261i 0.487763π-0.487763\pi
0.999261 0.0384331i 0.0122367π-0.0122367\pi
678678 0 0
679679 −14.0000 −0.537271
680680 0 0
681681 22.0000 0.843042
682682 0 0
683683 27.0000 27.0000i 1.03313 1.03313i 0.0336941 0.999432i 0.489273π-0.489273\pi
0.999432 0.0336941i 0.0107272π-0.0107272\pi
684684 0 0
685685 3.00000 9.00000i 0.114624 0.343872i
686686 0 0
687687 −6.00000 + 6.00000i −0.228914 + 0.228914i
688688 0 0
689689 30.0000i 1.14291i
690690 0 0
691691 −12.0000 −0.456502 −0.228251 0.973602i 0.573301π-0.573301\pi
−0.228251 + 0.973602i 0.573301π0.573301\pi
692692 0 0
693693 −4.00000 4.00000i −0.151947 0.151947i
694694 0 0
695695 −12.0000 + 6.00000i −0.455186 + 0.227593i
696696 0 0
697697 −18.0000 18.0000i −0.681799 0.681799i
698698 0 0
699699 30.0000i 1.13470i
700700 0 0
701701 20.0000i 0.755390i −0.925930 0.377695i 0.876717π-0.876717\pi
0.925930 0.377695i 0.123283π-0.123283\pi
702702 0 0
703703 18.0000 + 18.0000i 0.678883 + 0.678883i
704704 0 0
705705 −36.0000 + 18.0000i −1.35584 + 0.677919i
706706 0 0
707707 8.00000 + 8.00000i 0.300871 + 0.300871i
708708 0 0
709709 −42.0000 −1.57734 −0.788672 0.614815i 0.789231π-0.789231\pi
−0.788672 + 0.614815i 0.789231π0.789231\pi
710710 0 0
711711 0 0
712712 0 0
713713 −18.0000 + 18.0000i −0.674105 + 0.674105i
714714 0 0
715715 12.0000 36.0000i 0.448775 1.34632i
716716 0 0
717717 −24.0000 + 24.0000i −0.896296 + 0.896296i
718718 0 0
719719 −24.0000 −0.895049 −0.447524 0.894272i 0.647694π-0.647694\pi
−0.447524 + 0.894272i 0.647694π0.647694\pi
720720 0 0
721721 22.0000 0.819323
722722 0 0
723723 18.0000 18.0000i 0.669427 0.669427i
724724 0 0
725725 6.00000 8.00000i 0.222834 0.297113i
726726 0 0
727727 25.0000 25.0000i 0.927199 0.927199i −0.0703254 0.997524i 0.522404π-0.522404\pi
0.997524 + 0.0703254i 0.0224038π0.0224038\pi
728728 0 0
729729 29.0000i 1.07407i
730730 0 0
731731 −18.0000 −0.665754
732732 0 0
733733 15.0000 + 15.0000i 0.554038 + 0.554038i 0.927604 0.373566i 0.121865π-0.121865\pi
−0.373566 + 0.927604i 0.621865π0.621865\pi
734734 0 0
735735 5.00000 15.0000i 0.184428 0.553283i
736736 0 0
737737 −36.0000 36.0000i −1.32608 1.32608i
738738 0 0
739739 30.0000i 1.10357i 0.833987 + 0.551784i 0.186053π0.186053\pi
−0.833987 + 0.551784i 0.813947π0.813947\pi
740740 0 0
741741 36.0000i 1.32249i
742742 0 0
743743 −9.00000 9.00000i −0.330178 0.330178i 0.522476 0.852654i 0.325008π-0.325008\pi
−0.852654 + 0.522476i 0.825008π0.825008\pi
744744 0 0
745745 2.00000 + 4.00000i 0.0732743 + 0.146549i
746746 0 0
747747 3.00000 + 3.00000i 0.109764 + 0.109764i
748748 0 0
749749 −6.00000 −0.219235
750750 0 0
751751 42.0000i 1.53260i −0.642482 0.766301i 0.722095π-0.722095\pi
0.642482 0.766301i 0.277905π-0.277905\pi
752752 0 0
753753 −4.00000 + 4.00000i −0.145768 + 0.145768i
754754 0 0
755755 20.0000 10.0000i 0.727875 0.363937i
756756 0 0
757757 −9.00000 + 9.00000i −0.327111 + 0.327111i −0.851487 0.524376i 0.824299π-0.824299\pi
0.524376 + 0.851487i 0.324299π0.324299\pi
758758 0 0
759759 24.0000 0.871145
760760 0 0
761761 18.0000 0.652499 0.326250 0.945284i 0.394215π-0.394215\pi
0.326250 + 0.945284i 0.394215π0.394215\pi
762762 0 0
763763 18.0000 18.0000i 0.651644 0.651644i
764764 0 0
765765 9.00000 + 3.00000i 0.325396 + 0.108465i
766766 0 0
767767 30.0000 30.0000i 1.08324 1.08324i
768768 0 0
769769 40.0000i 1.44244i 0.692708 + 0.721218i 0.256418π0.256418\pi
−0.692708 + 0.721218i 0.743582π0.743582\pi
770770 0 0
771771 6.00000 0.216085
772772 0 0
773773 −9.00000 9.00000i −0.323708 0.323708i 0.526480 0.850188i 0.323511π-0.323511\pi
−0.850188 + 0.526480i 0.823511π0.823511\pi
774774 0 0
775775 −24.0000 18.0000i −0.862105 0.646579i
776776 0 0
777777 6.00000 + 6.00000i 0.215249 + 0.215249i
778778 0 0
779779 36.0000i 1.28983i
780780 0 0
781781 24.0000i 0.858788i
782782 0 0
783783 8.00000 + 8.00000i 0.285897 + 0.285897i
784784 0 0
785785 9.00000 + 3.00000i 0.321224 + 0.107075i
786786 0 0
787787 −15.0000 15.0000i −0.534692 0.534692i 0.387273 0.921965i 0.373417π-0.373417\pi
−0.921965 + 0.387273i 0.873417π0.873417\pi
788788 0 0
789789 18.0000 0.640817
790790 0 0
791791 6.00000i 0.213335i
792792 0 0
793793 36.0000 36.0000i 1.27840 1.27840i
794794 0 0
795795 10.0000 + 20.0000i 0.354663 + 0.709327i
796796 0 0
797797 3.00000 3.00000i 0.106265 0.106265i −0.651975 0.758240i 0.726059π-0.726059\pi
0.758240 + 0.651975i 0.226059π0.226059\pi
798798 0 0
799799 −54.0000 −1.91038
800800 0 0
801801 0 0
802802 0 0
803803 −20.0000 + 20.0000i −0.705785 + 0.705785i
804804 0 0
805805 6.00000 + 12.0000i 0.211472 + 0.422944i
806806 0 0
807807 14.0000 14.0000i 0.492823 0.492823i
808808 0 0
809809 48.0000i 1.68759i −0.536666 0.843795i 0.680316π-0.680316\pi
0.536666 0.843795i 0.319684π-0.319684\pi
810810 0 0
811811 −12.0000 −0.421377 −0.210688 0.977553i 0.567571π-0.567571\pi
−0.210688 + 0.977553i 0.567571π0.567571\pi
812812 0 0
813813 2.00000 + 2.00000i 0.0701431 + 0.0701431i
814814 0 0
815815 −27.0000 9.00000i −0.945769 0.315256i
816816 0 0
817817 18.0000 + 18.0000i 0.629740 + 0.629740i
818818 0 0
819819 6.00000i 0.209657i
820820 0 0
821821 52.0000i 1.81481i 0.420255 + 0.907406i 0.361941π0.361941\pi
−0.420255 + 0.907406i 0.638059π0.638059\pi
822822 0 0
823823 −5.00000 5.00000i −0.174289 0.174289i 0.614572 0.788861i 0.289329π-0.289329\pi
−0.788861 + 0.614572i 0.789329π0.789329\pi
824824 0 0
825825 4.00000 + 28.0000i 0.139262 + 0.974835i
826826 0 0
827827 −23.0000 23.0000i −0.799788 0.799788i 0.183274 0.983062i 0.441331π-0.441331\pi
−0.983062 + 0.183274i 0.941331π0.941331\pi
828828 0 0
829829 −30.0000 −1.04194 −0.520972 0.853574i 0.674430π-0.674430\pi
−0.520972 + 0.853574i 0.674430π0.674430\pi
830830 0 0
831831 30.0000i 1.04069i
832832 0 0
833833 15.0000 15.0000i 0.519719 0.519719i
834834 0 0
835835 −9.00000 3.00000i −0.311458 0.103819i
836836 0 0
837837 24.0000 24.0000i 0.829561 0.829561i
838838 0 0
839839 48.0000 1.65714 0.828572 0.559883i 0.189154π-0.189154\pi
0.828572 + 0.559883i 0.189154π0.189154\pi
840840 0 0
841841 −25.0000 −0.862069
842842 0 0
843843 −6.00000 + 6.00000i −0.206651 + 0.206651i
844844 0 0
845845 −10.0000 + 5.00000i −0.344010 + 0.172005i
846846 0 0
847847 5.00000 5.00000i 0.171802 0.171802i
848848 0 0
849849 30.0000i 1.02960i
850850 0 0
851851 18.0000 0.617032
852852 0 0
853853 −9.00000 9.00000i −0.308154 0.308154i 0.536039 0.844193i 0.319920π-0.319920\pi
−0.844193 + 0.536039i 0.819920π0.819920\pi
854854 0 0
855855 −6.00000 12.0000i −0.205196 0.410391i
856856 0 0
857857 −27.0000 27.0000i −0.922302 0.922302i 0.0748894 0.997192i 0.476140π-0.476140\pi
−0.997192 + 0.0748894i 0.976140π0.976140\pi
858858 0 0
859859 6.00000i 0.204717i 0.994748 + 0.102359i 0.0326389π0.0326389\pi
−0.994748 + 0.102359i 0.967361π0.967361\pi
860860 0 0
861861 12.0000i 0.408959i
862862 0 0
863863 15.0000 + 15.0000i 0.510606 + 0.510606i 0.914712 0.404106i 0.132417π-0.132417\pi
−0.404106 + 0.914712i 0.632417π0.632417\pi
864864 0 0
865865 −15.0000 + 45.0000i −0.510015 + 1.53005i
866866 0 0
867867 −1.00000 1.00000i −0.0339618 0.0339618i
868868 0 0
869869 0 0
870870 0 0
871871 54.0000i 1.82972i
872872 0 0
873873 7.00000 7.00000i 0.236914 0.236914i
874874 0 0
875875 −13.0000 + 9.00000i −0.439480 + 0.304256i
876876 0 0
877877 27.0000 27.0000i 0.911725 0.911725i −0.0846827 0.996408i 0.526988π-0.526988\pi
0.996408 + 0.0846827i 0.0269877π0.0269877\pi
878878 0 0
879879 2.00000 0.0674583
880880 0 0
881881 30.0000 1.01073 0.505363 0.862907i 0.331359π-0.331359\pi
0.505363 + 0.862907i 0.331359π0.331359\pi
882882 0 0
883883 −9.00000 + 9.00000i −0.302874 + 0.302874i −0.842137 0.539263i 0.818703π-0.818703\pi
0.539263 + 0.842137i 0.318703π0.318703\pi
884884 0 0
885885 −10.0000 + 30.0000i −0.336146 + 1.00844i
886886 0 0
887887 9.00000 9.00000i 0.302190 0.302190i −0.539680 0.841870i 0.681455π-0.681455\pi
0.841870 + 0.539680i 0.181455π0.181455\pi
888888 0 0
889889 10.0000i 0.335389i
890890 0 0
891891 −20.0000 −0.670025
892892 0 0
893893 54.0000 + 54.0000i 1.80704 + 1.80704i
894894 0 0
895895 4.00000 2.00000i 0.133705 0.0668526i
896896 0 0
897897 −18.0000 18.0000i −0.601003 0.601003i
898898 0 0
899899 12.0000i 0.400222i
900900 0 0
901901 30.0000i 0.999445i
902902 0 0
903903 6.00000 + 6.00000i 0.199667 + 0.199667i
904904 0 0
905905 0 0
906906 0 0
907907 −3.00000 3.00000i −0.0996134 0.0996134i 0.655544 0.755157i 0.272439π-0.272439\pi
−0.755157 + 0.655544i 0.772439π0.772439\pi
908908 0 0
909909 −8.00000 −0.265343
910910 0 0
911911 6.00000i 0.198789i 0.995048 + 0.0993944i 0.0316906π0.0316906\pi
−0.995048 + 0.0993944i 0.968309π0.968309\pi
912912 0 0
913913 −12.0000 + 12.0000i −0.397142 + 0.397142i
914914 0 0
915915 −12.0000 + 36.0000i −0.396708 + 1.19012i
916916 0 0
917917 −4.00000 + 4.00000i −0.132092 + 0.132092i
918918 0 0
919919 −48.0000 −1.58337 −0.791687 0.610927i 0.790797π-0.790797\pi
−0.791687 + 0.610927i 0.790797π0.790797\pi
920920 0 0
921921 30.0000 0.988534
922922 0 0
923923 −18.0000 + 18.0000i −0.592477 + 0.592477i
924924 0 0
925925 3.00000 + 21.0000i 0.0986394 + 0.690476i
926926 0 0
927927 −11.0000 + 11.0000i −0.361287 + 0.361287i
928928 0 0
929929 12.0000i 0.393707i −0.980433 0.196854i 0.936928π-0.936928\pi
0.980433 0.196854i 0.0630724π-0.0630724\pi
930930 0 0
931931 −30.0000 −0.983210
932932 0 0
933933 18.0000 + 18.0000i 0.589294 + 0.589294i
934934 0 0
935935 −12.0000 + 36.0000i −0.392442 + 1.17733i
936936 0 0
937937 −23.0000 23.0000i −0.751377 0.751377i 0.223359 0.974736i 0.428298π-0.428298\pi
−0.974736 + 0.223359i 0.928298π0.928298\pi
938938 0 0
939939 2.00000i 0.0652675i
940940 0 0
941941 32.0000i 1.04317i −0.853199 0.521585i 0.825341π-0.825341\pi
0.853199 0.521585i 0.174659π-0.174659\pi
942942 0 0
943943 18.0000 + 18.0000i 0.586161 + 0.586161i
944944 0 0
945945 −8.00000 16.0000i −0.260240 0.520480i
946946 0 0
947947 −7.00000 7.00000i −0.227469 0.227469i 0.584165 0.811635i 0.301422π-0.301422\pi
−0.811635 + 0.584165i 0.801422π0.801422\pi
948948 0 0
949949 30.0000 0.973841
950950 0 0
951951 6.00000i 0.194563i
952952 0 0
953953 9.00000 9.00000i 0.291539 0.291539i −0.546149 0.837688i 0.683907π-0.683907\pi
0.837688 + 0.546149i 0.183907π0.183907\pi
954954 0 0
955955 −12.0000 + 6.00000i −0.388311 + 0.194155i
956956 0 0
957957 −8.00000 + 8.00000i −0.258603 + 0.258603i
958958 0 0
959959 −6.00000 −0.193750
960960 0 0
961961 −5.00000 −0.161290
962962 0 0
963963 3.00000 3.00000i 0.0966736 0.0966736i
964964 0 0
965965 15.0000 + 5.00000i 0.482867 + 0.160956i
966966 0 0
967967 5.00000 5.00000i 0.160789 0.160789i −0.622127 0.782916i 0.713731π-0.713731\pi
0.782916 + 0.622127i 0.213731π0.213731\pi
968968 0 0
969969 36.0000i 1.15649i
970970 0 0
971971 20.0000 0.641831 0.320915 0.947108i 0.396010π-0.396010\pi
0.320915 + 0.947108i 0.396010π0.396010\pi
972972 0 0
973973 6.00000 + 6.00000i 0.192351 + 0.192351i
974974 0 0
975975 18.0000 24.0000i 0.576461 0.768615i
976976 0 0
977977 9.00000 + 9.00000i 0.287936 + 0.287936i 0.836263 0.548328i 0.184735π-0.184735\pi
−0.548328 + 0.836263i 0.684735π0.684735\pi
978978 0 0
979979 0 0
980980 0 0
981981 18.0000i 0.574696i
982982 0 0
983983 −33.0000 33.0000i −1.05254 1.05254i −0.998541 0.0539954i 0.982804π-0.982804\pi
−0.0539954 0.998541i 0.517196π-0.517196\pi
984984 0 0
985985 −15.0000 5.00000i −0.477940 0.159313i
986986 0 0
987987 18.0000 + 18.0000i 0.572946 + 0.572946i
988988 0 0
989989 18.0000 0.572367
990990 0 0
991991 2.00000i 0.0635321i −0.999495 0.0317660i 0.989887π-0.989887\pi
0.999495 0.0317660i 0.0101131π-0.0101131\pi
992992 0 0
993993 −12.0000 + 12.0000i −0.380808 + 0.380808i
994994 0 0
995995 −16.0000 32.0000i −0.507234 1.01447i
996996 0 0
997997 −9.00000 + 9.00000i −0.285033 + 0.285033i −0.835112 0.550079i 0.814597π-0.814597\pi
0.550079 + 0.835112i 0.314597π0.314597\pi
998998 0 0
999999 −24.0000 −0.759326
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 320.2.o.b.287.1 yes 2
4.3 odd 2 320.2.o.d.287.1 yes 2
5.2 odd 4 1600.2.o.d.543.1 2
5.3 odd 4 320.2.o.a.223.1 2
5.4 even 2 1600.2.o.c.607.1 2
8.3 odd 2 320.2.o.a.287.1 yes 2
8.5 even 2 320.2.o.c.287.1 yes 2
16.3 odd 4 1280.2.n.j.767.1 2
16.5 even 4 1280.2.n.i.767.1 2
16.11 odd 4 1280.2.n.c.767.1 2
16.13 even 4 1280.2.n.d.767.1 2
20.3 even 4 320.2.o.c.223.1 yes 2
20.7 even 4 1600.2.o.a.543.1 2
20.19 odd 2 1600.2.o.b.607.1 2
40.3 even 4 inner 320.2.o.b.223.1 yes 2
40.13 odd 4 320.2.o.d.223.1 yes 2
40.19 odd 2 1600.2.o.d.607.1 2
40.27 even 4 1600.2.o.c.543.1 2
40.29 even 2 1600.2.o.a.607.1 2
40.37 odd 4 1600.2.o.b.543.1 2
80.3 even 4 1280.2.n.d.1023.1 2
80.13 odd 4 1280.2.n.j.1023.1 2
80.43 even 4 1280.2.n.i.1023.1 2
80.53 odd 4 1280.2.n.c.1023.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
320.2.o.a.223.1 2 5.3 odd 4
320.2.o.a.287.1 yes 2 8.3 odd 2
320.2.o.b.223.1 yes 2 40.3 even 4 inner
320.2.o.b.287.1 yes 2 1.1 even 1 trivial
320.2.o.c.223.1 yes 2 20.3 even 4
320.2.o.c.287.1 yes 2 8.5 even 2
320.2.o.d.223.1 yes 2 40.13 odd 4
320.2.o.d.287.1 yes 2 4.3 odd 2
1280.2.n.c.767.1 2 16.11 odd 4
1280.2.n.c.1023.1 2 80.53 odd 4
1280.2.n.d.767.1 2 16.13 even 4
1280.2.n.d.1023.1 2 80.3 even 4
1280.2.n.i.767.1 2 16.5 even 4
1280.2.n.i.1023.1 2 80.43 even 4
1280.2.n.j.767.1 2 16.3 odd 4
1280.2.n.j.1023.1 2 80.13 odd 4
1600.2.o.a.543.1 2 20.7 even 4
1600.2.o.a.607.1 2 40.29 even 2
1600.2.o.b.543.1 2 40.37 odd 4
1600.2.o.b.607.1 2 20.19 odd 2
1600.2.o.c.543.1 2 40.27 even 4
1600.2.o.c.607.1 2 5.4 even 2
1600.2.o.d.543.1 2 5.2 odd 4
1600.2.o.d.607.1 2 40.19 odd 2