Properties

Label 720.2.z.d.163.1
Level 720720
Weight 22
Character 720.163
Analytic conductor 5.7495.749
Analytic rank 00
Dimension 22
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [720,2,Mod(163,720)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(720, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0, 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("720.163"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 720=24325 720 = 2^{4} \cdot 3^{2} \cdot 5
Weight: k k == 2 2
Character orbit: [χ][\chi] == 720.z (of order 44, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,2,0,0,4,0,-6] 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: 5.749228945535.74922894553
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]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 80)
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 163.1
Root 1.00000i-1.00000i of defining polynomial
Character χ\chi == 720.163
Dual form 720.2.z.d.667.1

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)q2+2.00000iq4+(2.00000+1.00000i)q5+(3.00000+3.00000i)q7+(2.00000+2.00000i)q8+(1.00000+3.00000i)q10+(1.00000+1.00000i)q112.00000iq136.00000q144.00000q16+(1.00000+1.00000i)q17+(3.000003.00000i)q19+(2.00000+4.00000i)q20+2.00000iq22+(1.00000+1.00000i)q23+(3.00000+4.00000i)q25+(2.000002.00000i)q26+(6.000006.00000i)q28+(7.000007.00000i)q29+2.00000iq31+(4.000004.00000i)q322.00000q34+(9.00000+3.00000i)q35+6.00000iq376.00000iq38+(6.00000+2.00000i)q40+4.00000iq41+4.00000iq43+(2.00000+2.00000i)q44+2.00000iq46+(7.00000+7.00000i)q4711.0000iq49+(1.00000+7.00000i)q50+4.00000q52+8.00000q53+(1.00000+3.00000i)q5512.0000iq56+14.0000q58+(3.00000+3.00000i)q59+(1.000001.00000i)q61+(2.00000+2.00000i)q628.00000iq64+(2.000004.00000i)q654.00000iq67+(2.000002.00000i)q68+(12.00006.00000i)q70+(3.000003.00000i)q73+(6.00000+6.00000i)q74+(6.000006.00000i)q766.00000q77+8.00000q79+(8.000004.00000i)q80+(4.00000+4.00000i)q82+2.00000q83+(3.00000+1.00000i)q85+(4.00000+4.00000i)q864.00000q88+6.00000q89+(6.00000+6.00000i)q91+(2.00000+2.00000i)q92+14.0000iq94+(3.000009.00000i)q95+(11.0000+11.0000i)q97+(11.000011.0000i)q98+O(q100)q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} +(2.00000 + 1.00000i) q^{5} +(-3.00000 + 3.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(1.00000 + 3.00000i) q^{10} +(1.00000 + 1.00000i) q^{11} -2.00000i q^{13} -6.00000 q^{14} -4.00000 q^{16} +(-1.00000 + 1.00000i) q^{17} +(-3.00000 - 3.00000i) q^{19} +(-2.00000 + 4.00000i) q^{20} +2.00000i q^{22} +(1.00000 + 1.00000i) q^{23} +(3.00000 + 4.00000i) q^{25} +(2.00000 - 2.00000i) q^{26} +(-6.00000 - 6.00000i) q^{28} +(7.00000 - 7.00000i) q^{29} +2.00000i q^{31} +(-4.00000 - 4.00000i) q^{32} -2.00000 q^{34} +(-9.00000 + 3.00000i) q^{35} +6.00000i q^{37} -6.00000i q^{38} +(-6.00000 + 2.00000i) q^{40} +4.00000i q^{41} +4.00000i q^{43} +(-2.00000 + 2.00000i) q^{44} +2.00000i q^{46} +(7.00000 + 7.00000i) q^{47} -11.0000i q^{49} +(-1.00000 + 7.00000i) q^{50} +4.00000 q^{52} +8.00000 q^{53} +(1.00000 + 3.00000i) q^{55} -12.0000i q^{56} +14.0000 q^{58} +(-3.00000 + 3.00000i) q^{59} +(-1.00000 - 1.00000i) q^{61} +(-2.00000 + 2.00000i) q^{62} -8.00000i q^{64} +(2.00000 - 4.00000i) q^{65} -4.00000i q^{67} +(-2.00000 - 2.00000i) q^{68} +(-12.0000 - 6.00000i) q^{70} +(3.00000 - 3.00000i) q^{73} +(-6.00000 + 6.00000i) q^{74} +(6.00000 - 6.00000i) q^{76} -6.00000 q^{77} +8.00000 q^{79} +(-8.00000 - 4.00000i) q^{80} +(-4.00000 + 4.00000i) q^{82} +2.00000 q^{83} +(-3.00000 + 1.00000i) q^{85} +(-4.00000 + 4.00000i) q^{86} -4.00000 q^{88} +6.00000 q^{89} +(6.00000 + 6.00000i) q^{91} +(-2.00000 + 2.00000i) q^{92} +14.0000i q^{94} +(-3.00000 - 9.00000i) q^{95} +(-11.0000 + 11.0000i) q^{97} +(11.0000 - 11.0000i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+2q2+4q56q74q8+2q10+2q1112q148q162q176q194q20+2q23+6q25+4q2612q28+14q298q324q3418q35++22q98+O(q100) 2 q + 2 q^{2} + 4 q^{5} - 6 q^{7} - 4 q^{8} + 2 q^{10} + 2 q^{11} - 12 q^{14} - 8 q^{16} - 2 q^{17} - 6 q^{19} - 4 q^{20} + 2 q^{23} + 6 q^{25} + 4 q^{26} - 12 q^{28} + 14 q^{29} - 8 q^{32} - 4 q^{34} - 18 q^{35}+ \cdots + 22 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/720Z)×\left(\mathbb{Z}/720\mathbb{Z}\right)^\times.

nn 181181 271271 577577 641641
χ(n)\chi(n) e(34)e\left(\frac{3}{4}\right) 1-1 e(34)e\left(\frac{3}{4}\right) 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 1.00000 + 1.00000i 0.707107 + 0.707107i
33 0 0
44 2.00000i 1.00000i
55 2.00000 + 1.00000i 0.894427 + 0.447214i
66 0 0
77 −3.00000 + 3.00000i −1.13389 + 1.13389i −0.144370 + 0.989524i 0.546115π0.546115\pi
−0.989524 + 0.144370i 0.953885π0.953885\pi
88 −2.00000 + 2.00000i −0.707107 + 0.707107i
99 0 0
1010 1.00000 + 3.00000i 0.316228 + 0.948683i
1111 1.00000 + 1.00000i 0.301511 + 0.301511i 0.841605 0.540094i 0.181611π-0.181611\pi
−0.540094 + 0.841605i 0.681611π0.681611\pi
1212 0 0
1313 2.00000i 0.554700i −0.960769 0.277350i 0.910544π-0.910544\pi
0.960769 0.277350i 0.0894562π-0.0894562\pi
1414 −6.00000 −1.60357
1515 0 0
1616 −4.00000 −1.00000
1717 −1.00000 + 1.00000i −0.242536 + 0.242536i −0.817898 0.575363i 0.804861π-0.804861\pi
0.575363 + 0.817898i 0.304861π0.304861\pi
1818 0 0
1919 −3.00000 3.00000i −0.688247 0.688247i 0.273597 0.961844i 0.411786π-0.411786\pi
−0.961844 + 0.273597i 0.911786π0.911786\pi
2020 −2.00000 + 4.00000i −0.447214 + 0.894427i
2121 0 0
2222 2.00000i 0.426401i
2323 1.00000 + 1.00000i 0.208514 + 0.208514i 0.803636 0.595121i 0.202896π-0.202896\pi
−0.595121 + 0.803636i 0.702896π0.702896\pi
2424 0 0
2525 3.00000 + 4.00000i 0.600000 + 0.800000i
2626 2.00000 2.00000i 0.392232 0.392232i
2727 0 0
2828 −6.00000 6.00000i −1.13389 1.13389i
2929 7.00000 7.00000i 1.29987 1.29987i 0.371391 0.928477i 0.378881π-0.378881\pi
0.928477 0.371391i 0.121119π-0.121119\pi
3030 0 0
3131 2.00000i 0.359211i 0.983739 + 0.179605i 0.0574821π0.0574821\pi
−0.983739 + 0.179605i 0.942518π0.942518\pi
3232 −4.00000 4.00000i −0.707107 0.707107i
3333 0 0
3434 −2.00000 −0.342997
3535 −9.00000 + 3.00000i −1.52128 + 0.507093i
3636 0 0
3737 6.00000i 0.986394i 0.869918 + 0.493197i 0.164172π0.164172\pi
−0.869918 + 0.493197i 0.835828π0.835828\pi
3838 6.00000i 0.973329i
3939 0 0
4040 −6.00000 + 2.00000i −0.948683 + 0.316228i
4141 4.00000i 0.624695i 0.949968 + 0.312348i 0.101115π0.101115\pi
−0.949968 + 0.312348i 0.898885π0.898885\pi
4242 0 0
4343 4.00000i 0.609994i 0.952353 + 0.304997i 0.0986555π0.0986555\pi
−0.952353 + 0.304997i 0.901344π0.901344\pi
4444 −2.00000 + 2.00000i −0.301511 + 0.301511i
4545 0 0
4646 2.00000i 0.294884i
4747 7.00000 + 7.00000i 1.02105 + 1.02105i 0.999774 + 0.0212814i 0.00677460π0.00677460\pi
0.0212814 + 0.999774i 0.493225π0.493225\pi
4848 0 0
4949 11.0000i 1.57143i
5050 −1.00000 + 7.00000i −0.141421 + 0.989949i
5151 0 0
5252 4.00000 0.554700
5353 8.00000 1.09888 0.549442 0.835532i 0.314840π-0.314840\pi
0.549442 + 0.835532i 0.314840π0.314840\pi
5454 0 0
5555 1.00000 + 3.00000i 0.134840 + 0.404520i
5656 12.0000i 1.60357i
5757 0 0
5858 14.0000 1.83829
5959 −3.00000 + 3.00000i −0.390567 + 0.390567i −0.874889 0.484323i 0.839066π-0.839066\pi
0.484323 + 0.874889i 0.339066π0.339066\pi
6060 0 0
6161 −1.00000 1.00000i −0.128037 0.128037i 0.640184 0.768221i 0.278858π-0.278858\pi
−0.768221 + 0.640184i 0.778858π0.778858\pi
6262 −2.00000 + 2.00000i −0.254000 + 0.254000i
6363 0 0
6464 8.00000i 1.00000i
6565 2.00000 4.00000i 0.248069 0.496139i
6666 0 0
6767 4.00000i 0.488678i −0.969690 0.244339i 0.921429π-0.921429\pi
0.969690 0.244339i 0.0785709π-0.0785709\pi
6868 −2.00000 2.00000i −0.242536 0.242536i
6969 0 0
7070 −12.0000 6.00000i −1.43427 0.717137i
7171 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
7272 0 0
7373 3.00000 3.00000i 0.351123 0.351123i −0.509404 0.860527i 0.670134π-0.670134\pi
0.860527 + 0.509404i 0.170134π0.170134\pi
7474 −6.00000 + 6.00000i −0.697486 + 0.697486i
7575 0 0
7676 6.00000 6.00000i 0.688247 0.688247i
7777 −6.00000 −0.683763
7878 0 0
7979 8.00000 0.900070 0.450035 0.893011i 0.351411π-0.351411\pi
0.450035 + 0.893011i 0.351411π0.351411\pi
8080 −8.00000 4.00000i −0.894427 0.447214i
8181 0 0
8282 −4.00000 + 4.00000i −0.441726 + 0.441726i
8383 2.00000 0.219529 0.109764 0.993958i 0.464990π-0.464990\pi
0.109764 + 0.993958i 0.464990π0.464990\pi
8484 0 0
8585 −3.00000 + 1.00000i −0.325396 + 0.108465i
8686 −4.00000 + 4.00000i −0.431331 + 0.431331i
8787 0 0
8888 −4.00000 −0.426401
8989 6.00000 0.635999 0.317999 0.948091i 0.396989π-0.396989\pi
0.317999 + 0.948091i 0.396989π0.396989\pi
9090 0 0
9191 6.00000 + 6.00000i 0.628971 + 0.628971i
9292 −2.00000 + 2.00000i −0.208514 + 0.208514i
9393 0 0
9494 14.0000i 1.44399i
9595 −3.00000 9.00000i −0.307794 0.923381i
9696 0 0
9797 −11.0000 + 11.0000i −1.11688 + 1.11688i −0.124684 + 0.992196i 0.539792π0.539792\pi
−0.992196 + 0.124684i 0.960208π0.960208\pi
9898 11.0000 11.0000i 1.11117 1.11117i
9999 0 0
100100 −8.00000 + 6.00000i −0.800000 + 0.600000i
101101 5.00000 5.00000i 0.497519 0.497519i −0.413146 0.910665i 0.635570π-0.635570\pi
0.910665 + 0.413146i 0.135570π0.135570\pi
102102 0 0
103103 −5.00000 5.00000i −0.492665 0.492665i 0.416480 0.909145i 0.363264π-0.363264\pi
−0.909145 + 0.416480i 0.863264π0.863264\pi
104104 4.00000 + 4.00000i 0.392232 + 0.392232i
105105 0 0
106106 8.00000 + 8.00000i 0.777029 + 0.777029i
107107 6.00000 0.580042 0.290021 0.957020i 0.406338π-0.406338\pi
0.290021 + 0.957020i 0.406338π0.406338\pi
108108 0 0
109109 5.00000 5.00000i 0.478913 0.478913i −0.425871 0.904784i 0.640032π-0.640032\pi
0.904784 + 0.425871i 0.140032π0.140032\pi
110110 −2.00000 + 4.00000i −0.190693 + 0.381385i
111111 0 0
112112 12.0000 12.0000i 1.13389 1.13389i
113113 −13.0000 13.0000i −1.22294 1.22294i −0.966583 0.256354i 0.917479π-0.917479\pi
−0.256354 0.966583i 0.582521π-0.582521\pi
114114 0 0
115115 1.00000 + 3.00000i 0.0932505 + 0.279751i
116116 14.0000 + 14.0000i 1.29987 + 1.29987i
117117 0 0
118118 −6.00000 −0.552345
119119 6.00000i 0.550019i
120120 0 0
121121 9.00000i 0.818182i
122122 2.00000i 0.181071i
123123 0 0
124124 −4.00000 −0.359211
125125 2.00000 + 11.0000i 0.178885 + 0.983870i
126126 0 0
127127 −7.00000 7.00000i −0.621150 0.621150i 0.324676 0.945825i 0.394745π-0.394745\pi
−0.945825 + 0.324676i 0.894745π0.894745\pi
128128 8.00000 8.00000i 0.707107 0.707107i
129129 0 0
130130 6.00000 2.00000i 0.526235 0.175412i
131131 7.00000 7.00000i 0.611593 0.611593i −0.331768 0.943361i 0.607645π-0.607645\pi
0.943361 + 0.331768i 0.107645π0.107645\pi
132132 0 0
133133 18.0000 1.56080
134134 4.00000 4.00000i 0.345547 0.345547i
135135 0 0
136136 4.00000i 0.342997i
137137 9.00000 + 9.00000i 0.768922 + 0.768922i 0.977917 0.208995i 0.0670192π-0.0670192\pi
−0.208995 + 0.977917i 0.567019π0.567019\pi
138138 0 0
139139 −9.00000 + 9.00000i −0.763370 + 0.763370i −0.976930 0.213560i 0.931494π-0.931494\pi
0.213560 + 0.976930i 0.431494π0.431494\pi
140140 −6.00000 18.0000i −0.507093 1.52128i
141141 0 0
142142 0 0
143143 2.00000 2.00000i 0.167248 0.167248i
144144 0 0
145145 21.0000 7.00000i 1.74396 0.581318i
146146 6.00000 0.496564
147147 0 0
148148 −12.0000 −0.986394
149149 −1.00000 1.00000i −0.0819232 0.0819232i 0.664958 0.746881i 0.268450π-0.268450\pi
−0.746881 + 0.664958i 0.768450π0.768450\pi
150150 0 0
151151 8.00000 0.651031 0.325515 0.945537i 0.394462π-0.394462\pi
0.325515 + 0.945537i 0.394462π0.394462\pi
152152 12.0000 0.973329
153153 0 0
154154 −6.00000 6.00000i −0.483494 0.483494i
155155 −2.00000 + 4.00000i −0.160644 + 0.321288i
156156 0 0
157157 20.0000 1.59617 0.798087 0.602542i 0.205846π-0.205846\pi
0.798087 + 0.602542i 0.205846π0.205846\pi
158158 8.00000 + 8.00000i 0.636446 + 0.636446i
159159 0 0
160160 −4.00000 12.0000i −0.316228 0.948683i
161161 −6.00000 −0.472866
162162 0 0
163163 14.0000 1.09656 0.548282 0.836293i 0.315282π-0.315282\pi
0.548282 + 0.836293i 0.315282π0.315282\pi
164164 −8.00000 −0.624695
165165 0 0
166166 2.00000 + 2.00000i 0.155230 + 0.155230i
167167 3.00000 3.00000i 0.232147 0.232147i −0.581441 0.813588i 0.697511π-0.697511\pi
0.813588 + 0.581441i 0.197511π0.197511\pi
168168 0 0
169169 9.00000 0.692308
170170 −4.00000 2.00000i −0.306786 0.153393i
171171 0 0
172172 −8.00000 −0.609994
173173 6.00000i 0.456172i 0.973641 + 0.228086i 0.0732467π0.0732467\pi
−0.973641 + 0.228086i 0.926753π0.926753\pi
174174 0 0
175175 −21.0000 3.00000i −1.58745 0.226779i
176176 −4.00000 4.00000i −0.301511 0.301511i
177177 0 0
178178 6.00000 + 6.00000i 0.449719 + 0.449719i
179179 −5.00000 5.00000i −0.373718 0.373718i 0.495112 0.868829i 0.335127π-0.335127\pi
−0.868829 + 0.495112i 0.835127π0.835127\pi
180180 0 0
181181 3.00000 3.00000i 0.222988 0.222988i −0.586767 0.809756i 0.699600π-0.699600\pi
0.809756 + 0.586767i 0.199600π0.199600\pi
182182 12.0000i 0.889499i
183183 0 0
184184 −4.00000 −0.294884
185185 −6.00000 + 12.0000i −0.441129 + 0.882258i
186186 0 0
187187 −2.00000 −0.146254
188188 −14.0000 + 14.0000i −1.02105 + 1.02105i
189189 0 0
190190 6.00000 12.0000i 0.435286 0.870572i
191191 18.0000i 1.30243i −0.758891 0.651217i 0.774259π-0.774259\pi
0.758891 0.651217i 0.225741π-0.225741\pi
192192 0 0
193193 −15.0000 15.0000i −1.07972 1.07972i −0.996534 0.0831899i 0.973489π-0.973489\pi
−0.0831899 0.996534i 0.526511π-0.526511\pi
194194 −22.0000 −1.57951
195195 0 0
196196 22.0000 1.57143
197197 6.00000i 0.427482i 0.976890 + 0.213741i 0.0685649π0.0685649\pi
−0.976890 + 0.213741i 0.931435π0.931435\pi
198198 0 0
199199 10.0000i 0.708881i −0.935079 0.354441i 0.884671π-0.884671\pi
0.935079 0.354441i 0.115329π-0.115329\pi
200200 −14.0000 2.00000i −0.989949 0.141421i
201201 0 0
202202 10.0000 0.703598
203203 42.0000i 2.94782i
204204 0 0
205205 −4.00000 + 8.00000i −0.279372 + 0.558744i
206206 10.0000i 0.696733i
207207 0 0
208208 8.00000i 0.554700i
209209 6.00000i 0.415029i
210210 0 0
211211 −19.0000 + 19.0000i −1.30801 + 1.30801i −0.385167 + 0.922847i 0.625856π0.625856\pi
−0.922847 + 0.385167i 0.874144π0.874144\pi
212212 16.0000i 1.09888i
213213 0 0
214214 6.00000 + 6.00000i 0.410152 + 0.410152i
215215 −4.00000 + 8.00000i −0.272798 + 0.545595i
216216 0 0
217217 −6.00000 6.00000i −0.407307 0.407307i
218218 10.0000 0.677285
219219 0 0
220220 −6.00000 + 2.00000i −0.404520 + 0.134840i
221221 2.00000 + 2.00000i 0.134535 + 0.134535i
222222 0 0
223223 −9.00000 + 9.00000i −0.602685 + 0.602685i −0.941024 0.338340i 0.890135π-0.890135\pi
0.338340 + 0.941024i 0.390135π0.390135\pi
224224 24.0000 1.60357
225225 0 0
226226 26.0000i 1.72949i
227227 12.0000i 0.796468i 0.917284 + 0.398234i 0.130377π0.130377\pi
−0.917284 + 0.398234i 0.869623π0.869623\pi
228228 0 0
229229 1.00000 + 1.00000i 0.0660819 + 0.0660819i 0.739375 0.673293i 0.235121π-0.235121\pi
−0.673293 + 0.739375i 0.735121π0.735121\pi
230230 −2.00000 + 4.00000i −0.131876 + 0.263752i
231231 0 0
232232 28.0000i 1.83829i
233233 9.00000 9.00000i 0.589610 0.589610i −0.347916 0.937526i 0.613111π-0.613111\pi
0.937526 + 0.347916i 0.113111π0.113111\pi
234234 0 0
235235 7.00000 + 21.0000i 0.456630 + 1.36989i
236236 −6.00000 6.00000i −0.390567 0.390567i
237237 0 0
238238 6.00000 6.00000i 0.388922 0.388922i
239239 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
240240 0 0
241241 −14.0000 −0.901819 −0.450910 0.892570i 0.648900π-0.648900\pi
−0.450910 + 0.892570i 0.648900π0.648900\pi
242242 9.00000 9.00000i 0.578542 0.578542i
243243 0 0
244244 2.00000 2.00000i 0.128037 0.128037i
245245 11.0000 22.0000i 0.702764 1.40553i
246246 0 0
247247 −6.00000 + 6.00000i −0.381771 + 0.381771i
248248 −4.00000 4.00000i −0.254000 0.254000i
249249 0 0
250250 −9.00000 + 13.0000i −0.569210 + 0.822192i
251251 −11.0000 11.0000i −0.694314 0.694314i 0.268864 0.963178i 0.413352π-0.413352\pi
−0.963178 + 0.268864i 0.913352π0.913352\pi
252252 0 0
253253 2.00000i 0.125739i
254254 14.0000i 0.878438i
255255 0 0
256256 16.0000 1.00000
257257 −13.0000 + 13.0000i −0.810918 + 0.810918i −0.984771 0.173854i 0.944378π-0.944378\pi
0.173854 + 0.984771i 0.444378π0.444378\pi
258258 0 0
259259 −18.0000 18.0000i −1.11847 1.11847i
260260 8.00000 + 4.00000i 0.496139 + 0.248069i
261261 0 0
262262 14.0000 0.864923
263263 −7.00000 7.00000i −0.431638 0.431638i 0.457547 0.889185i 0.348728π-0.348728\pi
−0.889185 + 0.457547i 0.848728π0.848728\pi
264264 0 0
265265 16.0000 + 8.00000i 0.982872 + 0.491436i
266266 18.0000 + 18.0000i 1.10365 + 1.10365i
267267 0 0
268268 8.00000 0.488678
269269 −1.00000 + 1.00000i −0.0609711 + 0.0609711i −0.736935 0.675964i 0.763728π-0.763728\pi
0.675964 + 0.736935i 0.263728π0.263728\pi
270270 0 0
271271 30.0000i 1.82237i −0.411997 0.911185i 0.635169π-0.635169\pi
0.411997 0.911185i 0.364831π-0.364831\pi
272272 4.00000 4.00000i 0.242536 0.242536i
273273 0 0
274274 18.0000i 1.08742i
275275 −1.00000 + 7.00000i −0.0603023 + 0.422116i
276276 0 0
277277 18.0000i 1.08152i −0.841178 0.540758i 0.818138π-0.818138\pi
0.841178 0.540758i 0.181862π-0.181862\pi
278278 −18.0000 −1.07957
279279 0 0
280280 12.0000 24.0000i 0.717137 1.43427i
281281 16.0000i 0.954480i −0.878773 0.477240i 0.841637π-0.841637\pi
0.878773 0.477240i 0.158363π-0.158363\pi
282282 0 0
283283 12.0000i 0.713326i 0.934233 + 0.356663i 0.116086π0.116086\pi
−0.934233 + 0.356663i 0.883914π0.883914\pi
284284 0 0
285285 0 0
286286 4.00000 0.236525
287287 −12.0000 12.0000i −0.708338 0.708338i
288288 0 0
289289 15.0000i 0.882353i
290290 28.0000 + 14.0000i 1.64422 + 0.822108i
291291 0 0
292292 6.00000 + 6.00000i 0.351123 + 0.351123i
293293 12.0000 0.701047 0.350524 0.936554i 0.386004π-0.386004\pi
0.350524 + 0.936554i 0.386004π0.386004\pi
294294 0 0
295295 −9.00000 + 3.00000i −0.524000 + 0.174667i
296296 −12.0000 12.0000i −0.697486 0.697486i
297297 0 0
298298 2.00000i 0.115857i
299299 2.00000 2.00000i 0.115663 0.115663i
300300 0 0
301301 −12.0000 12.0000i −0.691669 0.691669i
302302 8.00000 + 8.00000i 0.460348 + 0.460348i
303303 0 0
304304 12.0000 + 12.0000i 0.688247 + 0.688247i
305305 −1.00000 3.00000i −0.0572598 0.171780i
306306 0 0
307307 4.00000i 0.228292i 0.993464 + 0.114146i 0.0364132π0.0364132\pi
−0.993464 + 0.114146i 0.963587π0.963587\pi
308308 12.0000i 0.683763i
309309 0 0
310310 −6.00000 + 2.00000i −0.340777 + 0.113592i
311311 −16.0000 −0.907277 −0.453638 0.891186i 0.649874π-0.649874\pi
−0.453638 + 0.891186i 0.649874π0.649874\pi
312312 0 0
313313 −13.0000 + 13.0000i −0.734803 + 0.734803i −0.971567 0.236764i 0.923913π-0.923913\pi
0.236764 + 0.971567i 0.423913π0.423913\pi
314314 20.0000 + 20.0000i 1.12867 + 1.12867i
315315 0 0
316316 16.0000i 0.900070i
317317 −8.00000 −0.449325 −0.224662 0.974437i 0.572128π-0.572128\pi
−0.224662 + 0.974437i 0.572128π0.572128\pi
318318 0 0
319319 14.0000 0.783850
320320 8.00000 16.0000i 0.447214 0.894427i
321321 0 0
322322 −6.00000 6.00000i −0.334367 0.334367i
323323 6.00000 0.333849
324324 0 0
325325 8.00000 6.00000i 0.443760 0.332820i
326326 14.0000 + 14.0000i 0.775388 + 0.775388i
327327 0 0
328328 −8.00000 8.00000i −0.441726 0.441726i
329329 −42.0000 −2.31553
330330 0 0
331331 −21.0000 21.0000i −1.15426 1.15426i −0.985689 0.168576i 0.946083π-0.946083\pi
−0.168576 0.985689i 0.553917π-0.553917\pi
332332 4.00000i 0.219529i
333333 0 0
334334 6.00000 0.328305
335335 4.00000 8.00000i 0.218543 0.437087i
336336 0 0
337337 −11.0000 + 11.0000i −0.599208 + 0.599208i −0.940102 0.340894i 0.889270π-0.889270\pi
0.340894 + 0.940102i 0.389270π0.389270\pi
338338 9.00000 + 9.00000i 0.489535 + 0.489535i
339339 0 0
340340 −2.00000 6.00000i −0.108465 0.325396i
341341 −2.00000 + 2.00000i −0.108306 + 0.108306i
342342 0 0
343343 12.0000 + 12.0000i 0.647939 + 0.647939i
344344 −8.00000 8.00000i −0.431331 0.431331i
345345 0 0
346346 −6.00000 + 6.00000i −0.322562 + 0.322562i
347347 −2.00000 −0.107366 −0.0536828 0.998558i 0.517096π-0.517096\pi
−0.0536828 + 0.998558i 0.517096π0.517096\pi
348348 0 0
349349 −3.00000 + 3.00000i −0.160586 + 0.160586i −0.782826 0.622240i 0.786223π-0.786223\pi
0.622240 + 0.782826i 0.286223π0.286223\pi
350350 −18.0000 24.0000i −0.962140 1.28285i
351351 0 0
352352 8.00000i 0.426401i
353353 −13.0000 13.0000i −0.691920 0.691920i 0.270734 0.962654i 0.412734π-0.412734\pi
−0.962654 + 0.270734i 0.912734π0.912734\pi
354354 0 0
355355 0 0
356356 12.0000i 0.635999i
357357 0 0
358358 10.0000i 0.528516i
359359 14.0000i 0.738892i −0.929252 0.369446i 0.879548π-0.879548\pi
0.929252 0.369446i 0.120452π-0.120452\pi
360360 0 0
361361 1.00000i 0.0526316i
362362 6.00000 0.315353
363363 0 0
364364 −12.0000 + 12.0000i −0.628971 + 0.628971i
365365 9.00000 3.00000i 0.471082 0.157027i
366366 0 0
367367 21.0000 + 21.0000i 1.09619 + 1.09619i 0.994852 + 0.101339i 0.0323127π0.0323127\pi
0.101339 + 0.994852i 0.467687π0.467687\pi
368368 −4.00000 4.00000i −0.208514 0.208514i
369369 0 0
370370 −18.0000 + 6.00000i −0.935775 + 0.311925i
371371 −24.0000 + 24.0000i −1.24602 + 1.24602i
372372 0 0
373373 −4.00000 −0.207112 −0.103556 0.994624i 0.533022π-0.533022\pi
−0.103556 + 0.994624i 0.533022π0.533022\pi
374374 −2.00000 2.00000i −0.103418 0.103418i
375375 0 0
376376 −28.0000 −1.44399
377377 −14.0000 14.0000i −0.721037 0.721037i
378378 0 0
379379 15.0000 15.0000i 0.770498 0.770498i −0.207695 0.978194i 0.566596π-0.566596\pi
0.978194 + 0.207695i 0.0665963π0.0665963\pi
380380 18.0000 6.00000i 0.923381 0.307794i
381381 0 0
382382 18.0000 18.0000i 0.920960 0.920960i
383383 5.00000 5.00000i 0.255488 0.255488i −0.567728 0.823216i 0.692177π-0.692177\pi
0.823216 + 0.567728i 0.192177π0.192177\pi
384384 0 0
385385 −12.0000 6.00000i −0.611577 0.305788i
386386 30.0000i 1.52696i
387387 0 0
388388 −22.0000 22.0000i −1.11688 1.11688i
389389 23.0000 + 23.0000i 1.16615 + 1.16615i 0.983105 + 0.183041i 0.0585941π0.0585941\pi
0.183041 + 0.983105i 0.441406π0.441406\pi
390390 0 0
391391 −2.00000 −0.101144
392392 22.0000 + 22.0000i 1.11117 + 1.11117i
393393 0 0
394394 −6.00000 + 6.00000i −0.302276 + 0.302276i
395395 16.0000 + 8.00000i 0.805047 + 0.402524i
396396 0 0
397397 −32.0000 −1.60603 −0.803017 0.595956i 0.796773π-0.796773\pi
−0.803017 + 0.595956i 0.796773π0.796773\pi
398398 10.0000 10.0000i 0.501255 0.501255i
399399 0 0
400400 −12.0000 16.0000i −0.600000 0.800000i
401401 2.00000 0.0998752 0.0499376 0.998752i 0.484098π-0.484098\pi
0.0499376 + 0.998752i 0.484098π0.484098\pi
402402 0 0
403403 4.00000 0.199254
404404 10.0000 + 10.0000i 0.497519 + 0.497519i
405405 0 0
406406 −42.0000 + 42.0000i −2.08443 + 2.08443i
407407 −6.00000 + 6.00000i −0.297409 + 0.297409i
408408 0 0
409409 −38.0000 −1.87898 −0.939490 0.342578i 0.888700π-0.888700\pi
−0.939490 + 0.342578i 0.888700π0.888700\pi
410410 −12.0000 + 4.00000i −0.592638 + 0.197546i
411411 0 0
412412 10.0000 10.0000i 0.492665 0.492665i
413413 18.0000i 0.885722i
414414 0 0
415415 4.00000 + 2.00000i 0.196352 + 0.0981761i
416416 −8.00000 + 8.00000i −0.392232 + 0.392232i
417417 0 0
418418 6.00000 6.00000i 0.293470 0.293470i
419419 −17.0000 17.0000i −0.830504 0.830504i 0.157081 0.987586i 0.449792π-0.449792\pi
−0.987586 + 0.157081i 0.949792π0.949792\pi
420420 0 0
421421 −5.00000 + 5.00000i −0.243685 + 0.243685i −0.818373 0.574688i 0.805124π-0.805124\pi
0.574688 + 0.818373i 0.305124π0.305124\pi
422422 −38.0000 −1.84981
423423 0 0
424424 −16.0000 + 16.0000i −0.777029 + 0.777029i
425425 −7.00000 1.00000i −0.339550 0.0485071i
426426 0 0
427427 6.00000 0.290360
428428 12.0000i 0.580042i
429429 0 0
430430 −12.0000 + 4.00000i −0.578691 + 0.192897i
431431 2.00000i 0.0963366i −0.998839 0.0481683i 0.984662π-0.984662\pi
0.998839 0.0481683i 0.0153384π-0.0153384\pi
432432 0 0
433433 5.00000 + 5.00000i 0.240285 + 0.240285i 0.816968 0.576683i 0.195653π-0.195653\pi
−0.576683 + 0.816968i 0.695653π0.695653\pi
434434 12.0000i 0.576018i
435435 0 0
436436 10.0000 + 10.0000i 0.478913 + 0.478913i
437437 6.00000i 0.287019i
438438 0 0
439439 26.0000i 1.24091i −0.784241 0.620456i 0.786947π-0.786947\pi
0.784241 0.620456i 0.213053π-0.213053\pi
440440 −8.00000 4.00000i −0.381385 0.190693i
441441 0 0
442442 4.00000i 0.190261i
443443 4.00000i 0.190046i 0.995475 + 0.0950229i 0.0302924π0.0302924\pi
−0.995475 + 0.0950229i 0.969708π0.969708\pi
444444 0 0
445445 12.0000 + 6.00000i 0.568855 + 0.284427i
446446 −18.0000 −0.852325
447447 0 0
448448 24.0000 + 24.0000i 1.13389 + 1.13389i
449449 24.0000i 1.13263i 0.824189 + 0.566315i 0.191631π0.191631\pi
−0.824189 + 0.566315i 0.808369π0.808369\pi
450450 0 0
451451 −4.00000 + 4.00000i −0.188353 + 0.188353i
452452 26.0000 26.0000i 1.22294 1.22294i
453453 0 0
454454 −12.0000 + 12.0000i −0.563188 + 0.563188i
455455 6.00000 + 18.0000i 0.281284 + 0.843853i
456456 0 0
457457 7.00000 + 7.00000i 0.327446 + 0.327446i 0.851615 0.524168i 0.175624π-0.175624\pi
−0.524168 + 0.851615i 0.675624π0.675624\pi
458458 2.00000i 0.0934539i
459459 0 0
460460 −6.00000 + 2.00000i −0.279751 + 0.0932505i
461461 21.0000 + 21.0000i 0.978068 + 0.978068i 0.999765 0.0216971i 0.00690694π-0.00690694\pi
−0.0216971 + 0.999765i 0.506907π0.506907\pi
462462 0 0
463463 19.0000 19.0000i 0.883005 0.883005i −0.110834 0.993839i 0.535352π-0.535352\pi
0.993839 + 0.110834i 0.0353522π0.0353522\pi
464464 −28.0000 + 28.0000i −1.29987 + 1.29987i
465465 0 0
466466 18.0000 0.833834
467467 28.0000i 1.29569i −0.761774 0.647843i 0.775671π-0.775671\pi
0.761774 0.647843i 0.224329π-0.224329\pi
468468 0 0
469469 12.0000 + 12.0000i 0.554109 + 0.554109i
470470 −14.0000 + 28.0000i −0.645772 + 1.29154i
471471 0 0
472472 12.0000i 0.552345i
473473 −4.00000 + 4.00000i −0.183920 + 0.183920i
474474 0 0
475475 3.00000 21.0000i 0.137649 0.963546i
476476 12.0000 0.550019
477477 0 0
478478 0 0
479479 32.0000 1.46212 0.731059 0.682315i 0.239027π-0.239027\pi
0.731059 + 0.682315i 0.239027π0.239027\pi
480480 0 0
481481 12.0000 0.547153
482482 −14.0000 14.0000i −0.637683 0.637683i
483483 0 0
484484 18.0000 0.818182
485485 −33.0000 + 11.0000i −1.49845 + 0.499484i
486486 0 0
487487 −15.0000 + 15.0000i −0.679715 + 0.679715i −0.959936 0.280221i 0.909592π-0.909592\pi
0.280221 + 0.959936i 0.409592π0.409592\pi
488488 4.00000 0.181071
489489 0 0
490490 33.0000 11.0000i 1.49079 0.496929i
491491 9.00000 + 9.00000i 0.406164 + 0.406164i 0.880399 0.474234i 0.157275π-0.157275\pi
−0.474234 + 0.880399i 0.657275π0.657275\pi
492492 0 0
493493 14.0000i 0.630528i
494494 −12.0000 −0.539906
495495 0 0
496496 8.00000i 0.359211i
497497 0 0
498498 0 0
499499 29.0000 + 29.0000i 1.29822 + 1.29822i 0.929568 + 0.368650i 0.120180π0.120180\pi
0.368650 + 0.929568i 0.379820π0.379820\pi
500500 −22.0000 + 4.00000i −0.983870 + 0.178885i
501501 0 0
502502 22.0000i 0.981908i
503503 29.0000 + 29.0000i 1.29305 + 1.29305i 0.932893 + 0.360153i 0.117275π0.117275\pi
0.360153 + 0.932893i 0.382725π0.382725\pi
504504 0 0
505505 15.0000 5.00000i 0.667491 0.222497i
506506 −2.00000 + 2.00000i −0.0889108 + 0.0889108i
507507 0 0
508508 14.0000 14.0000i 0.621150 0.621150i
509509 −17.0000 + 17.0000i −0.753512 + 0.753512i −0.975133 0.221621i 0.928865π-0.928865\pi
0.221621 + 0.975133i 0.428865π0.428865\pi
510510 0 0
511511 18.0000i 0.796273i
512512 16.0000 + 16.0000i 0.707107 + 0.707107i
513513 0 0
514514 −26.0000 −1.14681
515515 −5.00000 15.0000i −0.220326 0.660979i
516516 0 0
517517 14.0000i 0.615719i
518518 36.0000i 1.58175i
519519 0 0
520520 4.00000 + 12.0000i 0.175412 + 0.526235i
521521 16.0000i 0.700973i 0.936568 + 0.350486i 0.113984π0.113984\pi
−0.936568 + 0.350486i 0.886016π0.886016\pi
522522 0 0
523523 20.0000i 0.874539i 0.899331 + 0.437269i 0.144054π0.144054\pi
−0.899331 + 0.437269i 0.855946π0.855946\pi
524524 14.0000 + 14.0000i 0.611593 + 0.611593i
525525 0 0
526526 14.0000i 0.610429i
527527 −2.00000 2.00000i −0.0871214 0.0871214i
528528 0 0
529529 21.0000i 0.913043i
530530 8.00000 + 24.0000i 0.347498 + 1.04249i
531531 0 0
532532 36.0000i 1.56080i
533533 8.00000 0.346518
534534 0 0
535535 12.0000 + 6.00000i 0.518805 + 0.259403i
536536 8.00000 + 8.00000i 0.345547 + 0.345547i
537537 0 0
538538 −2.00000 −0.0862261
539539 11.0000 11.0000i 0.473804 0.473804i
540540 0 0
541541 15.0000 + 15.0000i 0.644900 + 0.644900i 0.951756 0.306856i 0.0992769π-0.0992769\pi
−0.306856 + 0.951756i 0.599277π0.599277\pi
542542 30.0000 30.0000i 1.28861 1.28861i
543543 0 0
544544 8.00000 0.342997
545545 15.0000 5.00000i 0.642529 0.214176i
546546 0 0
547547 28.0000i 1.19719i −0.801050 0.598597i 0.795725π-0.795725\pi
0.801050 0.598597i 0.204275π-0.204275\pi
548548 −18.0000 + 18.0000i −0.768922 + 0.768922i
549549 0 0
550550 −8.00000 + 6.00000i −0.341121 + 0.255841i
551551 −42.0000 −1.78926
552552 0 0
553553 −24.0000 + 24.0000i −1.02058 + 1.02058i
554554 18.0000 18.0000i 0.764747 0.764747i
555555 0 0
556556 −18.0000 18.0000i −0.763370 0.763370i
557557 −28.0000 −1.18640 −0.593199 0.805056i 0.702135π-0.702135\pi
−0.593199 + 0.805056i 0.702135π0.702135\pi
558558 0 0
559559 8.00000 0.338364
560560 36.0000 12.0000i 1.52128 0.507093i
561561 0 0
562562 16.0000 16.0000i 0.674919 0.674919i
563563 18.0000 0.758610 0.379305 0.925272i 0.376163π-0.376163\pi
0.379305 + 0.925272i 0.376163π0.376163\pi
564564 0 0
565565 −13.0000 39.0000i −0.546914 1.64074i
566566 −12.0000 + 12.0000i −0.504398 + 0.504398i
567567 0 0
568568 0 0
569569 6.00000 0.251533 0.125767 0.992060i 0.459861π-0.459861\pi
0.125767 + 0.992060i 0.459861π0.459861\pi
570570 0 0
571571 −25.0000 25.0000i −1.04622 1.04622i −0.998879 0.0473385i 0.984926π-0.984926\pi
−0.0473385 0.998879i 0.515074π-0.515074\pi
572572 4.00000 + 4.00000i 0.167248 + 0.167248i
573573 0 0
574574 24.0000i 1.00174i
575575 −1.00000 + 7.00000i −0.0417029 + 0.291920i
576576 0 0
577577 9.00000 9.00000i 0.374675 0.374675i −0.494502 0.869177i 0.664649π-0.664649\pi
0.869177 + 0.494502i 0.164649π0.164649\pi
578578 −15.0000 + 15.0000i −0.623918 + 0.623918i
579579 0 0
580580 14.0000 + 42.0000i 0.581318 + 1.74396i
581581 −6.00000 + 6.00000i −0.248922 + 0.248922i
582582 0 0
583583 8.00000 + 8.00000i 0.331326 + 0.331326i
584584 12.0000i 0.496564i
585585 0 0
586586 12.0000 + 12.0000i 0.495715 + 0.495715i
587587 −2.00000 −0.0825488 −0.0412744 0.999148i 0.513142π-0.513142\pi
−0.0412744 + 0.999148i 0.513142π0.513142\pi
588588 0 0
589589 6.00000 6.00000i 0.247226 0.247226i
590590 −12.0000 6.00000i −0.494032 0.247016i
591591 0 0
592592 24.0000i 0.986394i
593593 −17.0000 17.0000i −0.698106 0.698106i 0.265896 0.964002i 0.414332π-0.414332\pi
−0.964002 + 0.265896i 0.914332π0.914332\pi
594594 0 0
595595 6.00000 12.0000i 0.245976 0.491952i
596596 2.00000 2.00000i 0.0819232 0.0819232i
597597 0 0
598598 4.00000 0.163572
599599 30.0000i 1.22577i −0.790173 0.612883i 0.790010π-0.790010\pi
0.790173 0.612883i 0.209990π-0.209990\pi
600600 0 0
601601 16.0000i 0.652654i 0.945257 + 0.326327i 0.105811π0.105811\pi
−0.945257 + 0.326327i 0.894189π0.894189\pi
602602 24.0000i 0.978167i
603603 0 0
604604 16.0000i 0.651031i
605605 9.00000 18.0000i 0.365902 0.731804i
606606 0 0
607607 −23.0000 23.0000i −0.933541 0.933541i 0.0643840 0.997925i 0.479492π-0.479492\pi
−0.997925 + 0.0643840i 0.979492π0.979492\pi
608608 24.0000i 0.973329i
609609 0 0
610610 2.00000 4.00000i 0.0809776 0.161955i
611611 14.0000 14.0000i 0.566379 0.566379i
612612 0 0
613613 8.00000 0.323117 0.161558 0.986863i 0.448348π-0.448348\pi
0.161558 + 0.986863i 0.448348π0.448348\pi
614614 −4.00000 + 4.00000i −0.161427 + 0.161427i
615615 0 0
616616 12.0000 12.0000i 0.483494 0.483494i
617617 25.0000 + 25.0000i 1.00646 + 1.00646i 0.999979 + 0.00648312i 0.00206366π0.00206366\pi
0.00648312 + 0.999979i 0.497936π0.497936\pi
618618 0 0
619619 7.00000 7.00000i 0.281354 0.281354i −0.552295 0.833649i 0.686248π-0.686248\pi
0.833649 + 0.552295i 0.186248π0.186248\pi
620620 −8.00000 4.00000i −0.321288 0.160644i
621621 0 0
622622 −16.0000 16.0000i −0.641542 0.641542i
623623 −18.0000 + 18.0000i −0.721155 + 0.721155i
624624 0 0
625625 −7.00000 + 24.0000i −0.280000 + 0.960000i
626626 −26.0000 −1.03917
627627 0 0
628628 40.0000i 1.59617i
629629 −6.00000 6.00000i −0.239236 0.239236i
630630 0 0
631631 24.0000 0.955425 0.477712 0.878516i 0.341466π-0.341466\pi
0.477712 + 0.878516i 0.341466π0.341466\pi
632632 −16.0000 + 16.0000i −0.636446 + 0.636446i
633633 0 0
634634 −8.00000 8.00000i −0.317721 0.317721i
635635 −7.00000 21.0000i −0.277787 0.833360i
636636 0 0
637637 −22.0000 −0.871672
638638 14.0000 + 14.0000i 0.554265 + 0.554265i
639639 0 0
640640 24.0000 8.00000i 0.948683 0.316228i
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 −26.0000 −1.02534 −0.512670 0.858586i 0.671344π-0.671344\pi
−0.512670 + 0.858586i 0.671344π0.671344\pi
644644 12.0000i 0.472866i
645645 0 0
646646 6.00000 + 6.00000i 0.236067 + 0.236067i
647647 15.0000 15.0000i 0.589711 0.589711i −0.347842 0.937553i 0.613086π-0.613086\pi
0.937553 + 0.347842i 0.113086π0.113086\pi
648648 0 0
649649 −6.00000 −0.235521
650650 14.0000 + 2.00000i 0.549125 + 0.0784465i
651651 0 0
652652 28.0000i 1.09656i
653653 2.00000i 0.0782660i 0.999234 + 0.0391330i 0.0124596π0.0124596\pi
−0.999234 + 0.0391330i 0.987540π0.987540\pi
654654 0 0
655655 21.0000 7.00000i 0.820538 0.273513i
656656 16.0000i 0.624695i
657657 0 0
658658 −42.0000 42.0000i −1.63733 1.63733i
659659 11.0000 + 11.0000i 0.428499 + 0.428499i 0.888117 0.459618i 0.152014π-0.152014\pi
−0.459618 + 0.888117i 0.652014π0.652014\pi
660660 0 0
661661 −25.0000 + 25.0000i −0.972387 + 0.972387i −0.999629 0.0272416i 0.991328π-0.991328\pi
0.0272416 + 0.999629i 0.491328π0.491328\pi
662662 42.0000i 1.63238i
663663 0 0
664664 −4.00000 + 4.00000i −0.155230 + 0.155230i
665665 36.0000 + 18.0000i 1.39602 + 0.698010i
666666 0 0
667667 14.0000 0.542082
668668 6.00000 + 6.00000i 0.232147 + 0.232147i
669669 0 0
670670 12.0000 4.00000i 0.463600 0.154533i
671671 2.00000i 0.0772091i
672672 0 0
673673 1.00000 + 1.00000i 0.0385472 + 0.0385472i 0.726118 0.687570i 0.241323π-0.241323\pi
−0.687570 + 0.726118i 0.741323π0.741323\pi
674674 −22.0000 −0.847408
675675 0 0
676676 18.0000i 0.692308i
677677 42.0000i 1.61419i −0.590421 0.807096i 0.701038π-0.701038\pi
0.590421 0.807096i 0.298962π-0.298962\pi
678678 0 0
679679 66.0000i 2.53285i
680680 4.00000 8.00000i 0.153393 0.306786i
681681 0 0
682682 −4.00000 −0.153168
683683 4.00000i 0.153056i 0.997067 + 0.0765279i 0.0243834π0.0243834\pi
−0.997067 + 0.0765279i 0.975617π0.975617\pi
684684 0 0
685685 9.00000 + 27.0000i 0.343872 + 1.03162i
686686 24.0000i 0.916324i
687687 0 0
688688 16.0000i 0.609994i
689689 16.0000i 0.609551i
690690 0 0
691691 21.0000 21.0000i 0.798878 0.798878i −0.184041 0.982919i 0.558918π-0.558918\pi
0.982919 + 0.184041i 0.0589179π0.0589179\pi
692692 −12.0000 −0.456172
693693 0 0
694694 −2.00000 2.00000i −0.0759190 0.0759190i
695695 −27.0000 + 9.00000i −1.02417 + 0.341389i
696696 0 0
697697 −4.00000 4.00000i −0.151511 0.151511i
698698 −6.00000 −0.227103
699699 0 0
700700 6.00000 42.0000i 0.226779 1.58745i
701701 13.0000 + 13.0000i 0.491003 + 0.491003i 0.908622 0.417619i 0.137135π-0.137135\pi
−0.417619 + 0.908622i 0.637135π0.637135\pi
702702 0 0
703703 18.0000 18.0000i 0.678883 0.678883i
704704 8.00000 8.00000i 0.301511 0.301511i
705705 0 0
706706 26.0000i 0.978523i
707707 30.0000i 1.12827i
708708 0 0
709709 1.00000 + 1.00000i 0.0375558 + 0.0375558i 0.725635 0.688080i 0.241546π-0.241546\pi
−0.688080 + 0.725635i 0.741546π0.741546\pi
710710 0 0
711711 0 0
712712 −12.0000 + 12.0000i −0.449719 + 0.449719i
713713 −2.00000 + 2.00000i −0.0749006 + 0.0749006i
714714 0 0
715715 6.00000 2.00000i 0.224387 0.0747958i
716716 10.0000 10.0000i 0.373718 0.373718i
717717 0 0
718718 14.0000 14.0000i 0.522475 0.522475i
719719 32.0000 1.19340 0.596699 0.802465i 0.296479π-0.296479\pi
0.596699 + 0.802465i 0.296479π0.296479\pi
720720 0 0
721721 30.0000 1.11726
722722 1.00000 1.00000i 0.0372161 0.0372161i
723723 0 0
724724 6.00000 + 6.00000i 0.222988 + 0.222988i
725725 49.0000 + 7.00000i 1.81981 + 0.259973i
726726 0 0
727727 −7.00000 + 7.00000i −0.259616 + 0.259616i −0.824898 0.565282i 0.808767π-0.808767\pi
0.565282 + 0.824898i 0.308767π0.308767\pi
728728 −24.0000 −0.889499
729729 0 0
730730 12.0000 + 6.00000i 0.444140 + 0.222070i
731731 −4.00000 4.00000i −0.147945 0.147945i
732732 0 0
733733 30.0000i 1.10808i −0.832492 0.554038i 0.813086π-0.813086\pi
0.832492 0.554038i 0.186914π-0.186914\pi
734734 42.0000i 1.55025i
735735 0 0
736736 8.00000i 0.294884i
737737 4.00000 4.00000i 0.147342 0.147342i
738738 0 0
739739 21.0000 + 21.0000i 0.772497 + 0.772497i 0.978543 0.206045i 0.0660593π-0.0660593\pi
−0.206045 + 0.978543i 0.566059π0.566059\pi
740740 −24.0000 12.0000i −0.882258 0.441129i
741741 0 0
742742 −48.0000 −1.76214
743743 −31.0000 31.0000i −1.13728 1.13728i −0.988936 0.148344i 0.952606π-0.952606\pi
−0.148344 0.988936i 0.547394π-0.547394\pi
744744 0 0
745745 −1.00000 3.00000i −0.0366372 0.109911i
746746 −4.00000 4.00000i −0.146450 0.146450i
747747 0 0
748748 4.00000i 0.146254i
749749 −18.0000 + 18.0000i −0.657706 + 0.657706i
750750 0 0
751751 50.0000i 1.82453i 0.409605 + 0.912263i 0.365667π0.365667\pi
−0.409605 + 0.912263i 0.634333π0.634333\pi
752752 −28.0000 28.0000i −1.02105 1.02105i
753753 0 0
754754 28.0000i 1.01970i
755755 16.0000 + 8.00000i 0.582300 + 0.291150i
756756 0 0
757757 2.00000i 0.0726912i −0.999339 0.0363456i 0.988428π-0.988428\pi
0.999339 0.0363456i 0.0115717π-0.0115717\pi
758758 30.0000 1.08965
759759 0 0
760760 24.0000 + 12.0000i 0.870572 + 0.435286i
761761 40.0000i 1.45000i −0.688749 0.724999i 0.741840π-0.741840\pi
0.688749 0.724999i 0.258160π-0.258160\pi
762762 0 0
763763 30.0000i 1.08607i
764764 36.0000 1.30243
765765 0 0
766766 10.0000 0.361315
767767 6.00000 + 6.00000i 0.216647 + 0.216647i
768768 0 0
769769 4.00000i 0.144244i −0.997396 0.0721218i 0.977023π-0.977023\pi
0.997396 0.0721218i 0.0229770π-0.0229770\pi
770770 −6.00000 18.0000i −0.216225 0.648675i
771771 0 0
772772 30.0000 30.0000i 1.07972 1.07972i
773773 −48.0000 −1.72644 −0.863220 0.504828i 0.831556π-0.831556\pi
−0.863220 + 0.504828i 0.831556π0.831556\pi
774774 0 0
775775 −8.00000 + 6.00000i −0.287368 + 0.215526i
776776 44.0000i 1.57951i
777777 0 0
778778 46.0000i 1.64918i
779779 12.0000 12.0000i 0.429945 0.429945i
780780 0 0
781781 0 0
782782 −2.00000 2.00000i −0.0715199 0.0715199i
783783 0 0
784784 44.0000i 1.57143i
785785 40.0000 + 20.0000i 1.42766 + 0.713831i
786786 0 0
787787 4.00000i 0.142585i 0.997455 + 0.0712923i 0.0227123π0.0227123\pi
−0.997455 + 0.0712923i 0.977288π0.977288\pi
788788 −12.0000 −0.427482
789789 0 0
790790 8.00000 + 24.0000i 0.284627 + 0.853882i
791791 78.0000 2.77336
792792 0 0
793793 −2.00000 + 2.00000i −0.0710221 + 0.0710221i
794794 −32.0000 32.0000i −1.13564 1.13564i
795795 0 0
796796 20.0000 0.708881
797797 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
798798 0 0
799799 −14.0000 −0.495284
800800 4.00000 28.0000i 0.141421 0.989949i
801801 0 0
802802 2.00000 + 2.00000i 0.0706225 + 0.0706225i
803803 6.00000 0.211735
804804 0 0
805805 −12.0000 6.00000i −0.422944 0.211472i
806806 4.00000 + 4.00000i 0.140894 + 0.140894i
807807 0 0
808808 20.0000i 0.703598i
809809 26.0000 0.914111 0.457056 0.889438i 0.348904π-0.348904\pi
0.457056 + 0.889438i 0.348904π0.348904\pi
810810 0 0
811811 −9.00000 9.00000i −0.316033 0.316033i 0.531208 0.847241i 0.321738π-0.321738\pi
−0.847241 + 0.531208i 0.821738π0.821738\pi
812812 −84.0000 −2.94782
813813 0 0
814814 −12.0000 −0.420600
815815 28.0000 + 14.0000i 0.980797 + 0.490399i
816816 0 0
817817 12.0000 12.0000i 0.419827 0.419827i
818818 −38.0000 38.0000i −1.32864 1.32864i
819819 0 0
820820 −16.0000 8.00000i −0.558744 0.279372i
821821 −15.0000 + 15.0000i −0.523504 + 0.523504i −0.918628 0.395124i 0.870702π-0.870702\pi
0.395124 + 0.918628i 0.370702π0.370702\pi
822822 0 0
823823 −21.0000 21.0000i −0.732014 0.732014i 0.239004 0.971018i 0.423179π-0.423179\pi
−0.971018 + 0.239004i 0.923179π0.923179\pi
824824 20.0000 0.696733
825825 0 0
826826 18.0000 18.0000i 0.626300 0.626300i
827827 54.0000 1.87776 0.938882 0.344239i 0.111863π-0.111863\pi
0.938882 + 0.344239i 0.111863π0.111863\pi
828828 0 0
829829 −27.0000 + 27.0000i −0.937749 + 0.937749i −0.998173 0.0604240i 0.980755π-0.980755\pi
0.0604240 + 0.998173i 0.480755π0.480755\pi
830830 2.00000 + 6.00000i 0.0694210 + 0.208263i
831831 0 0
832832 −16.0000 −0.554700
833833 11.0000 + 11.0000i 0.381127 + 0.381127i
834834 0 0
835835 9.00000 3.00000i 0.311458 0.103819i
836836 12.0000 0.415029
837837 0 0
838838 34.0000i 1.17451i
839839 18.0000i 0.621429i 0.950503 + 0.310715i 0.100568π0.100568\pi
−0.950503 + 0.310715i 0.899432π0.899432\pi
840840 0 0
841841 69.0000i 2.37931i
842842 −10.0000 −0.344623
843843 0 0
844844 −38.0000 38.0000i −1.30801 1.30801i
845845 18.0000 + 9.00000i 0.619219 + 0.309609i
846846 0 0
847847 27.0000 + 27.0000i 0.927731 + 0.927731i
848848 −32.0000 −1.09888
849849 0 0
850850 −6.00000 8.00000i −0.205798 0.274398i
851851 −6.00000 + 6.00000i −0.205677 + 0.205677i
852852 0 0
853853 16.0000 0.547830 0.273915 0.961754i 0.411681π-0.411681\pi
0.273915 + 0.961754i 0.411681π0.411681\pi
854854 6.00000 + 6.00000i 0.205316 + 0.205316i
855855 0 0
856856 −12.0000 + 12.0000i −0.410152 + 0.410152i
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 19.0000 19.0000i 0.648272 0.648272i −0.304303 0.952575i 0.598424π-0.598424\pi
0.952575 + 0.304303i 0.0984237π0.0984237\pi
860860 −16.0000 8.00000i −0.545595 0.272798i
861861 0 0
862862 2.00000 2.00000i 0.0681203 0.0681203i
863863 5.00000 5.00000i 0.170202 0.170202i −0.616866 0.787068i 0.711598π-0.711598\pi
0.787068 + 0.616866i 0.211598π0.211598\pi
864864 0 0
865865 −6.00000 + 12.0000i −0.204006 + 0.408012i
866866 10.0000i 0.339814i
867867 0 0
868868 12.0000 12.0000i 0.407307 0.407307i
869869 8.00000 + 8.00000i 0.271381 + 0.271381i
870870 0 0
871871 −8.00000 −0.271070
872872 20.0000i 0.677285i
873873 0 0
874874 6.00000 6.00000i 0.202953 0.202953i
875875 −39.0000 27.0000i −1.31844 0.912767i
876876 0 0
877877 4.00000 0.135070 0.0675352 0.997717i 0.478487π-0.478487\pi
0.0675352 + 0.997717i 0.478487π0.478487\pi
878878 26.0000 26.0000i 0.877457 0.877457i
879879 0 0
880880 −4.00000 12.0000i −0.134840 0.404520i
881881 −46.0000 −1.54978 −0.774890 0.632096i 0.782195π-0.782195\pi
−0.774890 + 0.632096i 0.782195π0.782195\pi
882882 0 0
883883 6.00000 0.201916 0.100958 0.994891i 0.467809π-0.467809\pi
0.100958 + 0.994891i 0.467809π0.467809\pi
884884 −4.00000 + 4.00000i −0.134535 + 0.134535i
885885 0 0
886886 −4.00000 + 4.00000i −0.134383 + 0.134383i
887887 23.0000 23.0000i 0.772264 0.772264i −0.206238 0.978502i 0.566122π-0.566122\pi
0.978502 + 0.206238i 0.0661220π0.0661220\pi
888888 0 0
889889 42.0000 1.40863
890890 6.00000 + 18.0000i 0.201120 + 0.603361i
891891 0 0
892892 −18.0000 18.0000i −0.602685 0.602685i
893893 42.0000i 1.40548i
894894 0 0
895895 −5.00000 15.0000i −0.167132 0.501395i
896896 48.0000i 1.60357i
897897 0 0
898898 −24.0000 + 24.0000i −0.800890 + 0.800890i
899899 14.0000 + 14.0000i 0.466926 + 0.466926i
900900 0 0
901901 −8.00000 + 8.00000i −0.266519 + 0.266519i
902902 −8.00000 −0.266371
903903 0 0
904904 52.0000 1.72949
905905 9.00000 3.00000i 0.299170 0.0997234i
906906 0 0
907907 50.0000 1.66022 0.830111 0.557598i 0.188277π-0.188277\pi
0.830111 + 0.557598i 0.188277π0.188277\pi
908908 −24.0000 −0.796468
909909 0 0
910910 −12.0000 + 24.0000i −0.397796 + 0.795592i
911911 38.0000i 1.25900i 0.777002 + 0.629498i 0.216739π0.216739\pi
−0.777002 + 0.629498i 0.783261π0.783261\pi
912912 0 0
913913 2.00000 + 2.00000i 0.0661903 + 0.0661903i
914914 14.0000i 0.463079i
915915 0 0
916916 −2.00000 + 2.00000i −0.0660819 + 0.0660819i
917917 42.0000i 1.38696i
918918 0 0
919919 46.0000i 1.51740i 0.651440 + 0.758700i 0.274165π0.274165\pi
−0.651440 + 0.758700i 0.725835π0.725835\pi
920920 −8.00000 4.00000i −0.263752 0.131876i
921921 0 0
922922 42.0000i 1.38320i
923923 0 0
924924 0 0
925925 −24.0000 + 18.0000i −0.789115 + 0.591836i
926926 38.0000 1.24876
927927 0 0
928928 −56.0000 −1.83829
929929 16.0000i 0.524943i −0.964940 0.262471i 0.915462π-0.915462\pi
0.964940 0.262471i 0.0845376π-0.0845376\pi
930930 0 0
931931 −33.0000 + 33.0000i −1.08153 + 1.08153i
932932 18.0000 + 18.0000i 0.589610 + 0.589610i
933933 0 0
934934 28.0000 28.0000i 0.916188 0.916188i
935935 −4.00000 2.00000i −0.130814 0.0654070i
936936 0 0
937937 3.00000 + 3.00000i 0.0980057 + 0.0980057i 0.754410 0.656404i 0.227923π-0.227923\pi
−0.656404 + 0.754410i 0.727923π0.727923\pi
938938 24.0000i 0.783628i
939939 0 0
940940 −42.0000 + 14.0000i −1.36989 + 0.456630i
941941 1.00000 + 1.00000i 0.0325991 + 0.0325991i 0.723218 0.690619i 0.242662π-0.242662\pi
−0.690619 + 0.723218i 0.742662π0.742662\pi
942942 0 0
943943 −4.00000 + 4.00000i −0.130258 + 0.130258i
944944 12.0000 12.0000i 0.390567 0.390567i
945945 0 0
946946 −8.00000 −0.260102
947947 28.0000i 0.909878i 0.890523 + 0.454939i 0.150339π0.150339\pi
−0.890523 + 0.454939i 0.849661π0.849661\pi
948948 0 0
949949 −6.00000 6.00000i −0.194768 0.194768i
950950 24.0000 18.0000i 0.778663 0.583997i
951951 0 0
952952 12.0000 + 12.0000i 0.388922 + 0.388922i
953953 −31.0000 + 31.0000i −1.00419 + 1.00419i −0.00419731 + 0.999991i 0.501336π0.501336\pi
−0.999991 + 0.00419731i 0.998664π0.998664\pi
954954 0 0
955955 18.0000 36.0000i 0.582466 1.16493i
956956 0 0
957957 0 0
958958 32.0000 + 32.0000i 1.03387 + 1.03387i
959959 −54.0000 −1.74375
960960 0 0
961961 27.0000 0.870968
962962 12.0000 + 12.0000i 0.386896 + 0.386896i
963963 0 0
964964 28.0000i 0.901819i
965965 −15.0000 45.0000i −0.482867 1.44860i
966966 0 0
967967 33.0000 33.0000i 1.06121 1.06121i 0.0632081 0.998000i 0.479867π-0.479867\pi
0.998000 0.0632081i 0.0201332π-0.0201332\pi
968968 18.0000 + 18.0000i 0.578542 + 0.578542i
969969 0 0
970970 −44.0000 22.0000i −1.41275 0.706377i
971971 −31.0000 31.0000i −0.994837 0.994837i 0.00514940 0.999987i 0.498361π-0.498361\pi
−0.999987 + 0.00514940i 0.998361π0.998361\pi
972972 0 0
973973 54.0000i 1.73116i
974974 −30.0000 −0.961262
975975 0 0
976976 4.00000 + 4.00000i 0.128037 + 0.128037i
977977 −17.0000 + 17.0000i −0.543878 + 0.543878i −0.924663 0.380785i 0.875654π-0.875654\pi
0.380785 + 0.924663i 0.375654π0.375654\pi
978978 0 0
979979 6.00000 + 6.00000i 0.191761 + 0.191761i
980980 44.0000 + 22.0000i 1.40553 + 0.702764i
981981 0 0
982982 18.0000i 0.574403i
983983 5.00000 + 5.00000i 0.159475 + 0.159475i 0.782334 0.622859i 0.214029π-0.214029\pi
−0.622859 + 0.782334i 0.714029π0.714029\pi
984984 0 0
985985 −6.00000 + 12.0000i −0.191176 + 0.382352i
986986 −14.0000 + 14.0000i −0.445851 + 0.445851i
987987 0 0
988988 −12.0000 12.0000i −0.381771 0.381771i
989989 −4.00000 + 4.00000i −0.127193 + 0.127193i
990990 0 0
991991 10.0000i 0.317660i 0.987306 + 0.158830i 0.0507723π0.0507723\pi
−0.987306 + 0.158830i 0.949228π0.949228\pi
992992 8.00000 8.00000i 0.254000 0.254000i
993993 0 0
994994 0 0
995995 10.0000 20.0000i 0.317021 0.634043i
996996 0 0
997997 22.0000i 0.696747i −0.937356 0.348373i 0.886734π-0.886734\pi
0.937356 0.348373i 0.113266π-0.113266\pi
998998 58.0000i 1.83596i
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 720.2.z.d.163.1 2
3.2 odd 2 80.2.s.a.3.1 yes 2
5.2 odd 4 720.2.bd.a.307.1 2
12.11 even 2 320.2.s.a.303.1 2
15.2 even 4 80.2.j.a.67.1 yes 2
15.8 even 4 400.2.j.a.307.1 2
15.14 odd 2 400.2.s.a.243.1 2
16.11 odd 4 720.2.bd.a.523.1 2
24.5 odd 2 640.2.s.b.223.1 2
24.11 even 2 640.2.s.a.223.1 2
48.5 odd 4 320.2.j.a.143.1 2
48.11 even 4 80.2.j.a.43.1 2
48.29 odd 4 640.2.j.b.543.1 2
48.35 even 4 640.2.j.a.543.1 2
60.23 odd 4 1600.2.j.a.1007.1 2
60.47 odd 4 320.2.j.a.47.1 2
60.59 even 2 1600.2.s.a.943.1 2
80.27 even 4 inner 720.2.z.d.667.1 2
120.77 even 4 640.2.j.a.607.1 2
120.107 odd 4 640.2.j.b.607.1 2
240.53 even 4 1600.2.s.a.207.1 2
240.59 even 4 400.2.j.a.43.1 2
240.77 even 4 640.2.s.a.287.1 2
240.107 odd 4 80.2.s.a.27.1 yes 2
240.149 odd 4 1600.2.j.a.143.1 2
240.197 even 4 320.2.s.a.207.1 2
240.203 odd 4 400.2.s.a.107.1 2
240.227 odd 4 640.2.s.b.287.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
80.2.j.a.43.1 2 48.11 even 4
80.2.j.a.67.1 yes 2 15.2 even 4
80.2.s.a.3.1 yes 2 3.2 odd 2
80.2.s.a.27.1 yes 2 240.107 odd 4
320.2.j.a.47.1 2 60.47 odd 4
320.2.j.a.143.1 2 48.5 odd 4
320.2.s.a.207.1 2 240.197 even 4
320.2.s.a.303.1 2 12.11 even 2
400.2.j.a.43.1 2 240.59 even 4
400.2.j.a.307.1 2 15.8 even 4
400.2.s.a.107.1 2 240.203 odd 4
400.2.s.a.243.1 2 15.14 odd 2
640.2.j.a.543.1 2 48.35 even 4
640.2.j.a.607.1 2 120.77 even 4
640.2.j.b.543.1 2 48.29 odd 4
640.2.j.b.607.1 2 120.107 odd 4
640.2.s.a.223.1 2 24.11 even 2
640.2.s.a.287.1 2 240.77 even 4
640.2.s.b.223.1 2 24.5 odd 2
640.2.s.b.287.1 2 240.227 odd 4
720.2.z.d.163.1 2 1.1 even 1 trivial
720.2.z.d.667.1 2 80.27 even 4 inner
720.2.bd.a.307.1 2 5.2 odd 4
720.2.bd.a.523.1 2 16.11 odd 4
1600.2.j.a.143.1 2 240.149 odd 4
1600.2.j.a.1007.1 2 60.23 odd 4
1600.2.s.a.207.1 2 240.53 even 4
1600.2.s.a.943.1 2 60.59 even 2