Properties

Label 600.2.k.b.301.1
Level 600600
Weight 22
Character 600.301
Analytic conductor 4.7914.791
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] = [600,2,Mod(301,600)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) 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("600.301"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 600=23352 600 = 2^{3} \cdot 3 \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 600.k (of order 22, degree 11, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.791024121284.79102412128
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 24)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 301.1
Root 1.00000i-1.00000i of defining polynomial
Character χ\chi == 600.301
Dual form 600.2.k.b.301.2

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+(1.000001.00000i)q21.00000iq32.00000iq4+(1.000001.00000i)q6+2.00000q7+(2.000002.00000i)q81.00000q92.00000q124.00000iq13+(2.000002.00000i)q144.00000q16+2.00000q17+(1.00000+1.00000i)q184.00000iq192.00000iq214.00000q23+(2.00000+2.00000i)q24+(4.000004.00000i)q26+1.00000iq274.00000iq28+6.00000iq29+2.00000q31+(4.00000+4.00000i)q32+(2.000002.00000i)q34+2.00000iq36+8.00000iq37+(4.000004.00000i)q384.00000q39+2.00000q41+(2.000002.00000i)q424.00000iq43+(4.00000+4.00000i)q46+12.0000q47+4.00000iq483.00000q492.00000iq518.00000q52+6.00000iq53+(1.00000+1.00000i)q54+(4.000004.00000i)q564.00000q57+(6.00000+6.00000i)q584.00000iq59+(2.000002.00000i)q622.00000q63+8.00000iq6412.0000iq674.00000iq68+4.00000iq69+12.0000q71+(2.00000+2.00000i)q72+6.00000q73+(8.00000+8.00000i)q748.00000q76+(4.00000+4.00000i)q78+10.0000q79+1.00000q81+(2.000002.00000i)q82+16.0000iq834.00000q84+(4.000004.00000i)q86+6.00000q8710.0000q898.00000iq91+8.00000iq922.00000iq93+(12.000012.0000i)q94+(4.00000+4.00000i)q96+2.00000q97+(3.00000+3.00000i)q98+O(q100)q+(1.00000 - 1.00000i) q^{2} -1.00000i q^{3} -2.00000i q^{4} +(-1.00000 - 1.00000i) q^{6} +2.00000 q^{7} +(-2.00000 - 2.00000i) q^{8} -1.00000 q^{9} -2.00000 q^{12} -4.00000i q^{13} +(2.00000 - 2.00000i) q^{14} -4.00000 q^{16} +2.00000 q^{17} +(-1.00000 + 1.00000i) q^{18} -4.00000i q^{19} -2.00000i q^{21} -4.00000 q^{23} +(-2.00000 + 2.00000i) q^{24} +(-4.00000 - 4.00000i) q^{26} +1.00000i q^{27} -4.00000i q^{28} +6.00000i q^{29} +2.00000 q^{31} +(-4.00000 + 4.00000i) q^{32} +(2.00000 - 2.00000i) q^{34} +2.00000i q^{36} +8.00000i q^{37} +(-4.00000 - 4.00000i) q^{38} -4.00000 q^{39} +2.00000 q^{41} +(-2.00000 - 2.00000i) q^{42} -4.00000i q^{43} +(-4.00000 + 4.00000i) q^{46} +12.0000 q^{47} +4.00000i q^{48} -3.00000 q^{49} -2.00000i q^{51} -8.00000 q^{52} +6.00000i q^{53} +(1.00000 + 1.00000i) q^{54} +(-4.00000 - 4.00000i) q^{56} -4.00000 q^{57} +(6.00000 + 6.00000i) q^{58} -4.00000i q^{59} +(2.00000 - 2.00000i) q^{62} -2.00000 q^{63} +8.00000i q^{64} -12.0000i q^{67} -4.00000i q^{68} +4.00000i q^{69} +12.0000 q^{71} +(2.00000 + 2.00000i) q^{72} +6.00000 q^{73} +(8.00000 + 8.00000i) q^{74} -8.00000 q^{76} +(-4.00000 + 4.00000i) q^{78} +10.0000 q^{79} +1.00000 q^{81} +(2.00000 - 2.00000i) q^{82} +16.0000i q^{83} -4.00000 q^{84} +(-4.00000 - 4.00000i) q^{86} +6.00000 q^{87} -10.0000 q^{89} -8.00000i q^{91} +8.00000i q^{92} -2.00000i q^{93} +(12.0000 - 12.0000i) q^{94} +(4.00000 + 4.00000i) q^{96} +2.00000 q^{97} +(-3.00000 + 3.00000i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+2q22q6+4q74q82q94q12+4q148q16+4q172q188q234q248q26+4q318q32+4q348q388q39+4q41+6q98+O(q100) 2 q + 2 q^{2} - 2 q^{6} + 4 q^{7} - 4 q^{8} - 2 q^{9} - 4 q^{12} + 4 q^{14} - 8 q^{16} + 4 q^{17} - 2 q^{18} - 8 q^{23} - 4 q^{24} - 8 q^{26} + 4 q^{31} - 8 q^{32} + 4 q^{34} - 8 q^{38} - 8 q^{39} + 4 q^{41}+ \cdots - 6 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/600Z)×\left(\mathbb{Z}/600\mathbb{Z}\right)^\times.

nn 151151 301301 401401 577577
χ(n)\chi(n) 11 1-1 11 11

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.00000 1.00000i 0.707107 0.707107i
33 1.00000i 0.577350i
44 2.00000i 1.00000i
55 0 0
66 −1.00000 1.00000i −0.408248 0.408248i
77 2.00000 0.755929 0.377964 0.925820i 0.376624π-0.376624\pi
0.377964 + 0.925820i 0.376624π0.376624\pi
88 −2.00000 2.00000i −0.707107 0.707107i
99 −1.00000 −0.333333
1010 0 0
1111 0 0 1.00000 00
−1.00000 π\pi
1212 −2.00000 −0.577350
1313 4.00000i 1.10940i −0.832050 0.554700i 0.812833π-0.812833\pi
0.832050 0.554700i 0.187167π-0.187167\pi
1414 2.00000 2.00000i 0.534522 0.534522i
1515 0 0
1616 −4.00000 −1.00000
1717 2.00000 0.485071 0.242536 0.970143i 0.422021π-0.422021\pi
0.242536 + 0.970143i 0.422021π0.422021\pi
1818 −1.00000 + 1.00000i −0.235702 + 0.235702i
1919 4.00000i 0.917663i −0.888523 0.458831i 0.848268π-0.848268\pi
0.888523 0.458831i 0.151732π-0.151732\pi
2020 0 0
2121 2.00000i 0.436436i
2222 0 0
2323 −4.00000 −0.834058 −0.417029 0.908893i 0.636929π-0.636929\pi
−0.417029 + 0.908893i 0.636929π0.636929\pi
2424 −2.00000 + 2.00000i −0.408248 + 0.408248i
2525 0 0
2626 −4.00000 4.00000i −0.784465 0.784465i
2727 1.00000i 0.192450i
2828 4.00000i 0.755929i
2929 6.00000i 1.11417i 0.830455 + 0.557086i 0.188081π0.188081\pi
−0.830455 + 0.557086i 0.811919π0.811919\pi
3030 0 0
3131 2.00000 0.359211 0.179605 0.983739i 0.442518π-0.442518\pi
0.179605 + 0.983739i 0.442518π0.442518\pi
3232 −4.00000 + 4.00000i −0.707107 + 0.707107i
3333 0 0
3434 2.00000 2.00000i 0.342997 0.342997i
3535 0 0
3636 2.00000i 0.333333i
3737 8.00000i 1.31519i 0.753371 + 0.657596i 0.228427π0.228427\pi
−0.753371 + 0.657596i 0.771573π0.771573\pi
3838 −4.00000 4.00000i −0.648886 0.648886i
3939 −4.00000 −0.640513
4040 0 0
4141 2.00000 0.312348 0.156174 0.987730i 0.450084π-0.450084\pi
0.156174 + 0.987730i 0.450084π0.450084\pi
4242 −2.00000 2.00000i −0.308607 0.308607i
4343 4.00000i 0.609994i −0.952353 0.304997i 0.901344π-0.901344\pi
0.952353 0.304997i 0.0986555π-0.0986555\pi
4444 0 0
4545 0 0
4646 −4.00000 + 4.00000i −0.589768 + 0.589768i
4747 12.0000 1.75038 0.875190 0.483779i 0.160736π-0.160736\pi
0.875190 + 0.483779i 0.160736π0.160736\pi
4848 4.00000i 0.577350i
4949 −3.00000 −0.428571
5050 0 0
5151 2.00000i 0.280056i
5252 −8.00000 −1.10940
5353 6.00000i 0.824163i 0.911147 + 0.412082i 0.135198π0.135198\pi
−0.911147 + 0.412082i 0.864802π0.864802\pi
5454 1.00000 + 1.00000i 0.136083 + 0.136083i
5555 0 0
5656 −4.00000 4.00000i −0.534522 0.534522i
5757 −4.00000 −0.529813
5858 6.00000 + 6.00000i 0.787839 + 0.787839i
5959 4.00000i 0.520756i −0.965507 0.260378i 0.916153π-0.916153\pi
0.965507 0.260378i 0.0838471π-0.0838471\pi
6060 0 0
6161 0 0 1.00000 00
−1.00000 π\pi
6262 2.00000 2.00000i 0.254000 0.254000i
6363 −2.00000 −0.251976
6464 8.00000i 1.00000i
6565 0 0
6666 0 0
6767 12.0000i 1.46603i −0.680211 0.733017i 0.738112π-0.738112\pi
0.680211 0.733017i 0.261888π-0.261888\pi
6868 4.00000i 0.485071i
6969 4.00000i 0.481543i
7070 0 0
7171 12.0000 1.42414 0.712069 0.702109i 0.247758π-0.247758\pi
0.712069 + 0.702109i 0.247758π0.247758\pi
7272 2.00000 + 2.00000i 0.235702 + 0.235702i
7373 6.00000 0.702247 0.351123 0.936329i 0.385800π-0.385800\pi
0.351123 + 0.936329i 0.385800π0.385800\pi
7474 8.00000 + 8.00000i 0.929981 + 0.929981i
7575 0 0
7676 −8.00000 −0.917663
7777 0 0
7878 −4.00000 + 4.00000i −0.452911 + 0.452911i
7979 10.0000 1.12509 0.562544 0.826767i 0.309823π-0.309823\pi
0.562544 + 0.826767i 0.309823π0.309823\pi
8080 0 0
8181 1.00000 0.111111
8282 2.00000 2.00000i 0.220863 0.220863i
8383 16.0000i 1.75623i 0.478451 + 0.878114i 0.341198π0.341198\pi
−0.478451 + 0.878114i 0.658802π0.658802\pi
8484 −4.00000 −0.436436
8585 0 0
8686 −4.00000 4.00000i −0.431331 0.431331i
8787 6.00000 0.643268
8888 0 0
8989 −10.0000 −1.06000 −0.529999 0.847998i 0.677808π-0.677808\pi
−0.529999 + 0.847998i 0.677808π0.677808\pi
9090 0 0
9191 8.00000i 0.838628i
9292 8.00000i 0.834058i
9393 2.00000i 0.207390i
9494 12.0000 12.0000i 1.23771 1.23771i
9595 0 0
9696 4.00000 + 4.00000i 0.408248 + 0.408248i
9797 2.00000 0.203069 0.101535 0.994832i 0.467625π-0.467625\pi
0.101535 + 0.994832i 0.467625π0.467625\pi
9898 −3.00000 + 3.00000i −0.303046 + 0.303046i
9999 0 0
100100 0 0
101101 10.0000i 0.995037i 0.867453 + 0.497519i 0.165755π0.165755\pi
−0.867453 + 0.497519i 0.834245π0.834245\pi
102102 −2.00000 2.00000i −0.198030 0.198030i
103103 6.00000 0.591198 0.295599 0.955312i 0.404481π-0.404481\pi
0.295599 + 0.955312i 0.404481π0.404481\pi
104104 −8.00000 + 8.00000i −0.784465 + 0.784465i
105105 0 0
106106 6.00000 + 6.00000i 0.582772 + 0.582772i
107107 12.0000i 1.16008i −0.814587 0.580042i 0.803036π-0.803036\pi
0.814587 0.580042i 0.196964π-0.196964\pi
108108 2.00000 0.192450
109109 4.00000i 0.383131i −0.981480 0.191565i 0.938644π-0.938644\pi
0.981480 0.191565i 0.0613564π-0.0613564\pi
110110 0 0
111111 8.00000 0.759326
112112 −8.00000 −0.755929
113113 6.00000 0.564433 0.282216 0.959351i 0.408930π-0.408930\pi
0.282216 + 0.959351i 0.408930π0.408930\pi
114114 −4.00000 + 4.00000i −0.374634 + 0.374634i
115115 0 0
116116 12.0000 1.11417
117117 4.00000i 0.369800i
118118 −4.00000 4.00000i −0.368230 0.368230i
119119 4.00000 0.366679
120120 0 0
121121 11.0000 1.00000
122122 0 0
123123 2.00000i 0.180334i
124124 4.00000i 0.359211i
125125 0 0
126126 −2.00000 + 2.00000i −0.178174 + 0.178174i
127127 2.00000 0.177471 0.0887357 0.996055i 0.471717π-0.471717\pi
0.0887357 + 0.996055i 0.471717π0.471717\pi
128128 8.00000 + 8.00000i 0.707107 + 0.707107i
129129 −4.00000 −0.352180
130130 0 0
131131 20.0000i 1.74741i 0.486458 + 0.873704i 0.338289π0.338289\pi
−0.486458 + 0.873704i 0.661711π0.661711\pi
132132 0 0
133133 8.00000i 0.693688i
134134 −12.0000 12.0000i −1.03664 1.03664i
135135 0 0
136136 −4.00000 4.00000i −0.342997 0.342997i
137137 −18.0000 −1.53784 −0.768922 0.639343i 0.779207π-0.779207\pi
−0.768922 + 0.639343i 0.779207π0.779207\pi
138138 4.00000 + 4.00000i 0.340503 + 0.340503i
139139 4.00000i 0.339276i −0.985506 0.169638i 0.945740π-0.945740\pi
0.985506 0.169638i 0.0542598π-0.0542598\pi
140140 0 0
141141 12.0000i 1.01058i
142142 12.0000 12.0000i 1.00702 1.00702i
143143 0 0
144144 4.00000 0.333333
145145 0 0
146146 6.00000 6.00000i 0.496564 0.496564i
147147 3.00000i 0.247436i
148148 16.0000 1.31519
149149 6.00000i 0.491539i 0.969328 + 0.245770i 0.0790407π0.0790407\pi
−0.969328 + 0.245770i 0.920959π0.920959\pi
150150 0 0
151151 −18.0000 −1.46482 −0.732410 0.680864i 0.761604π-0.761604\pi
−0.732410 + 0.680864i 0.761604π0.761604\pi
152152 −8.00000 + 8.00000i −0.648886 + 0.648886i
153153 −2.00000 −0.161690
154154 0 0
155155 0 0
156156 8.00000i 0.640513i
157157 8.00000i 0.638470i 0.947676 + 0.319235i 0.103426π0.103426\pi
−0.947676 + 0.319235i 0.896574π0.896574\pi
158158 10.0000 10.0000i 0.795557 0.795557i
159159 6.00000 0.475831
160160 0 0
161161 −8.00000 −0.630488
162162 1.00000 1.00000i 0.0785674 0.0785674i
163163 4.00000i 0.313304i −0.987654 0.156652i 0.949930π-0.949930\pi
0.987654 0.156652i 0.0500701π-0.0500701\pi
164164 4.00000i 0.312348i
165165 0 0
166166 16.0000 + 16.0000i 1.24184 + 1.24184i
167167 −8.00000 −0.619059 −0.309529 0.950890i 0.600171π-0.600171\pi
−0.309529 + 0.950890i 0.600171π0.600171\pi
168168 −4.00000 + 4.00000i −0.308607 + 0.308607i
169169 −3.00000 −0.230769
170170 0 0
171171 4.00000i 0.305888i
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 6.00000 6.00000i 0.454859 0.454859i
175175 0 0
176176 0 0
177177 −4.00000 −0.300658
178178 −10.0000 + 10.0000i −0.749532 + 0.749532i
179179 4.00000i 0.298974i −0.988764 0.149487i 0.952238π-0.952238\pi
0.988764 0.149487i 0.0477622π-0.0477622\pi
180180 0 0
181181 20.0000i 1.48659i 0.668965 + 0.743294i 0.266738π0.266738\pi
−0.668965 + 0.743294i 0.733262π0.733262\pi
182182 −8.00000 8.00000i −0.592999 0.592999i
183183 0 0
184184 8.00000 + 8.00000i 0.589768 + 0.589768i
185185 0 0
186186 −2.00000 2.00000i −0.146647 0.146647i
187187 0 0
188188 24.0000i 1.75038i
189189 2.00000i 0.145479i
190190 0 0
191191 −8.00000 −0.578860 −0.289430 0.957199i 0.593466π-0.593466\pi
−0.289430 + 0.957199i 0.593466π0.593466\pi
192192 8.00000 0.577350
193193 6.00000 0.431889 0.215945 0.976406i 0.430717π-0.430717\pi
0.215945 + 0.976406i 0.430717π0.430717\pi
194194 2.00000 2.00000i 0.143592 0.143592i
195195 0 0
196196 6.00000i 0.428571i
197197 2.00000i 0.142494i −0.997459 0.0712470i 0.977302π-0.977302\pi
0.997459 0.0712470i 0.0226979π-0.0226979\pi
198198 0 0
199199 10.0000 0.708881 0.354441 0.935079i 0.384671π-0.384671\pi
0.354441 + 0.935079i 0.384671π0.384671\pi
200200 0 0
201201 −12.0000 −0.846415
202202 10.0000 + 10.0000i 0.703598 + 0.703598i
203203 12.0000i 0.842235i
204204 −4.00000 −0.280056
205205 0 0
206206 6.00000 6.00000i 0.418040 0.418040i
207207 4.00000 0.278019
208208 16.0000i 1.10940i
209209 0 0
210210 0 0
211211 20.0000i 1.37686i −0.725304 0.688428i 0.758301π-0.758301\pi
0.725304 0.688428i 0.241699π-0.241699\pi
212212 12.0000 0.824163
213213 12.0000i 0.822226i
214214 −12.0000 12.0000i −0.820303 0.820303i
215215 0 0
216216 2.00000 2.00000i 0.136083 0.136083i
217217 4.00000 0.271538
218218 −4.00000 4.00000i −0.270914 0.270914i
219219 6.00000i 0.405442i
220220 0 0
221221 8.00000i 0.538138i
222222 8.00000 8.00000i 0.536925 0.536925i
223223 −14.0000 −0.937509 −0.468755 0.883328i 0.655297π-0.655297\pi
−0.468755 + 0.883328i 0.655297π0.655297\pi
224224 −8.00000 + 8.00000i −0.534522 + 0.534522i
225225 0 0
226226 6.00000 6.00000i 0.399114 0.399114i
227227 8.00000i 0.530979i 0.964114 + 0.265489i 0.0855335π0.0855335\pi
−0.964114 + 0.265489i 0.914466π0.914466\pi
228228 8.00000i 0.529813i
229229 4.00000i 0.264327i −0.991228 0.132164i 0.957808π-0.957808\pi
0.991228 0.132164i 0.0421925π-0.0421925\pi
230230 0 0
231231 0 0
232232 12.0000 12.0000i 0.787839 0.787839i
233233 −14.0000 −0.917170 −0.458585 0.888650i 0.651644π-0.651644\pi
−0.458585 + 0.888650i 0.651644π0.651644\pi
234234 4.00000 + 4.00000i 0.261488 + 0.261488i
235235 0 0
236236 −8.00000 −0.520756
237237 10.0000i 0.649570i
238238 4.00000 4.00000i 0.259281 0.259281i
239239 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
240240 0 0
241241 2.00000 0.128831 0.0644157 0.997923i 0.479482π-0.479482\pi
0.0644157 + 0.997923i 0.479482π0.479482\pi
242242 11.0000 11.0000i 0.707107 0.707107i
243243 1.00000i 0.0641500i
244244 0 0
245245 0 0
246246 −2.00000 2.00000i −0.127515 0.127515i
247247 −16.0000 −1.01806
248248 −4.00000 4.00000i −0.254000 0.254000i
249249 16.0000 1.01396
250250 0 0
251251 0 0 1.00000 00
−1.00000 π\pi
252252 4.00000i 0.251976i
253253 0 0
254254 2.00000 2.00000i 0.125491 0.125491i
255255 0 0
256256 16.0000 1.00000
257257 −18.0000 −1.12281 −0.561405 0.827541i 0.689739π-0.689739\pi
−0.561405 + 0.827541i 0.689739π0.689739\pi
258258 −4.00000 + 4.00000i −0.249029 + 0.249029i
259259 16.0000i 0.994192i
260260 0 0
261261 6.00000i 0.371391i
262262 20.0000 + 20.0000i 1.23560 + 1.23560i
263263 16.0000 0.986602 0.493301 0.869859i 0.335790π-0.335790\pi
0.493301 + 0.869859i 0.335790π0.335790\pi
264264 0 0
265265 0 0
266266 −8.00000 8.00000i −0.490511 0.490511i
267267 10.0000i 0.611990i
268268 −24.0000 −1.46603
269269 6.00000i 0.365826i 0.983129 + 0.182913i 0.0585527π0.0585527\pi
−0.983129 + 0.182913i 0.941447π0.941447\pi
270270 0 0
271271 −18.0000 −1.09342 −0.546711 0.837321i 0.684120π-0.684120\pi
−0.546711 + 0.837321i 0.684120π0.684120\pi
272272 −8.00000 −0.485071
273273 −8.00000 −0.484182
274274 −18.0000 + 18.0000i −1.08742 + 1.08742i
275275 0 0
276276 8.00000 0.481543
277277 28.0000i 1.68236i 0.540758 + 0.841178i 0.318138π0.318138\pi
−0.540758 + 0.841178i 0.681862π0.681862\pi
278278 −4.00000 4.00000i −0.239904 0.239904i
279279 −2.00000 −0.119737
280280 0 0
281281 −18.0000 −1.07379 −0.536895 0.843649i 0.680403π-0.680403\pi
−0.536895 + 0.843649i 0.680403π0.680403\pi
282282 −12.0000 12.0000i −0.714590 0.714590i
283283 4.00000i 0.237775i −0.992908 0.118888i 0.962067π-0.962067\pi
0.992908 0.118888i 0.0379328π-0.0379328\pi
284284 24.0000i 1.42414i
285285 0 0
286286 0 0
287287 4.00000 0.236113
288288 4.00000 4.00000i 0.235702 0.235702i
289289 −13.0000 −0.764706
290290 0 0
291291 2.00000i 0.117242i
292292 12.0000i 0.702247i
293293 6.00000i 0.350524i 0.984522 + 0.175262i 0.0560772π0.0560772\pi
−0.984522 + 0.175262i 0.943923π0.943923\pi
294294 3.00000 + 3.00000i 0.174964 + 0.174964i
295295 0 0
296296 16.0000 16.0000i 0.929981 0.929981i
297297 0 0
298298 6.00000 + 6.00000i 0.347571 + 0.347571i
299299 16.0000i 0.925304i
300300 0 0
301301 8.00000i 0.461112i
302302 −18.0000 + 18.0000i −1.03578 + 1.03578i
303303 10.0000 0.574485
304304 16.0000i 0.917663i
305305 0 0
306306 −2.00000 + 2.00000i −0.114332 + 0.114332i
307307 12.0000i 0.684876i −0.939540 0.342438i 0.888747π-0.888747\pi
0.939540 0.342438i 0.111253π-0.111253\pi
308308 0 0
309309 6.00000i 0.341328i
310310 0 0
311311 −8.00000 −0.453638 −0.226819 0.973937i 0.572833π-0.572833\pi
−0.226819 + 0.973937i 0.572833π0.572833\pi
312312 8.00000 + 8.00000i 0.452911 + 0.452911i
313313 −14.0000 −0.791327 −0.395663 0.918396i 0.629485π-0.629485\pi
−0.395663 + 0.918396i 0.629485π0.629485\pi
314314 8.00000 + 8.00000i 0.451466 + 0.451466i
315315 0 0
316316 20.0000i 1.12509i
317317 22.0000i 1.23564i −0.786318 0.617822i 0.788015π-0.788015\pi
0.786318 0.617822i 0.211985π-0.211985\pi
318318 6.00000 6.00000i 0.336463 0.336463i
319319 0 0
320320 0 0
321321 −12.0000 −0.669775
322322 −8.00000 + 8.00000i −0.445823 + 0.445823i
323323 8.00000i 0.445132i
324324 2.00000i 0.111111i
325325 0 0
326326 −4.00000 4.00000i −0.221540 0.221540i
327327 −4.00000 −0.221201
328328 −4.00000 4.00000i −0.220863 0.220863i
329329 24.0000 1.32316
330330 0 0
331331 20.0000i 1.09930i −0.835395 0.549650i 0.814761π-0.814761\pi
0.835395 0.549650i 0.185239π-0.185239\pi
332332 32.0000 1.75623
333333 8.00000i 0.438397i
334334 −8.00000 + 8.00000i −0.437741 + 0.437741i
335335 0 0
336336 8.00000i 0.436436i
337337 2.00000 0.108947 0.0544735 0.998515i 0.482652π-0.482652\pi
0.0544735 + 0.998515i 0.482652π0.482652\pi
338338 −3.00000 + 3.00000i −0.163178 + 0.163178i
339339 6.00000i 0.325875i
340340 0 0
341341 0 0
342342 4.00000 + 4.00000i 0.216295 + 0.216295i
343343 −20.0000 −1.07990
344344 −8.00000 + 8.00000i −0.431331 + 0.431331i
345345 0 0
346346 6.00000 + 6.00000i 0.322562 + 0.322562i
347347 8.00000i 0.429463i 0.976673 + 0.214731i 0.0688876π0.0688876\pi
−0.976673 + 0.214731i 0.931112π0.931112\pi
348348 12.0000i 0.643268i
349349 16.0000i 0.856460i 0.903670 + 0.428230i 0.140863π0.140863\pi
−0.903670 + 0.428230i 0.859137π0.859137\pi
350350 0 0
351351 4.00000 0.213504
352352 0 0
353353 6.00000 0.319348 0.159674 0.987170i 0.448956π-0.448956\pi
0.159674 + 0.987170i 0.448956π0.448956\pi
354354 −4.00000 + 4.00000i −0.212598 + 0.212598i
355355 0 0
356356 20.0000i 1.06000i
357357 4.00000i 0.211702i
358358 −4.00000 4.00000i −0.211407 0.211407i
359359 −20.0000 −1.05556 −0.527780 0.849381i 0.676975π-0.676975\pi
−0.527780 + 0.849381i 0.676975π0.676975\pi
360360 0 0
361361 3.00000 0.157895
362362 20.0000 + 20.0000i 1.05118 + 1.05118i
363363 11.0000i 0.577350i
364364 −16.0000 −0.838628
365365 0 0
366366 0 0
367367 −18.0000 −0.939592 −0.469796 0.882775i 0.655673π-0.655673\pi
−0.469796 + 0.882775i 0.655673π0.655673\pi
368368 16.0000 0.834058
369369 −2.00000 −0.104116
370370 0 0
371371 12.0000i 0.623009i
372372 −4.00000 −0.207390
373373 16.0000i 0.828449i 0.910175 + 0.414224i 0.135947π0.135947\pi
−0.910175 + 0.414224i 0.864053π0.864053\pi
374374 0 0
375375 0 0
376376 −24.0000 24.0000i −1.23771 1.23771i
377377 24.0000 1.23606
378378 2.00000 + 2.00000i 0.102869 + 0.102869i
379379 4.00000i 0.205466i −0.994709 0.102733i 0.967241π-0.967241\pi
0.994709 0.102733i 0.0327588π-0.0327588\pi
380380 0 0
381381 2.00000i 0.102463i
382382 −8.00000 + 8.00000i −0.409316 + 0.409316i
383383 −24.0000 −1.22634 −0.613171 0.789950i 0.710106π-0.710106\pi
−0.613171 + 0.789950i 0.710106π0.710106\pi
384384 8.00000 8.00000i 0.408248 0.408248i
385385 0 0
386386 6.00000 6.00000i 0.305392 0.305392i
387387 4.00000i 0.203331i
388388 4.00000i 0.203069i
389389 34.0000i 1.72387i −0.507020 0.861934i 0.669253π-0.669253\pi
0.507020 0.861934i 0.330747π-0.330747\pi
390390 0 0
391391 −8.00000 −0.404577
392392 6.00000 + 6.00000i 0.303046 + 0.303046i
393393 20.0000 1.00887
394394 −2.00000 2.00000i −0.100759 0.100759i
395395 0 0
396396 0 0
397397 32.0000i 1.60603i −0.595956 0.803017i 0.703227π-0.703227\pi
0.595956 0.803017i 0.296773π-0.296773\pi
398398 10.0000 10.0000i 0.501255 0.501255i
399399 −8.00000 −0.400501
400400 0 0
401401 −18.0000 −0.898877 −0.449439 0.893311i 0.648376π-0.648376\pi
−0.449439 + 0.893311i 0.648376π0.648376\pi
402402 −12.0000 + 12.0000i −0.598506 + 0.598506i
403403 8.00000i 0.398508i
404404 20.0000 0.995037
405405 0 0
406406 12.0000 + 12.0000i 0.595550 + 0.595550i
407407 0 0
408408 −4.00000 + 4.00000i −0.198030 + 0.198030i
409409 10.0000 0.494468 0.247234 0.968956i 0.420478π-0.420478\pi
0.247234 + 0.968956i 0.420478π0.420478\pi
410410 0 0
411411 18.0000i 0.887875i
412412 12.0000i 0.591198i
413413 8.00000i 0.393654i
414414 4.00000 4.00000i 0.196589 0.196589i
415415 0 0
416416 16.0000 + 16.0000i 0.784465 + 0.784465i
417417 −4.00000 −0.195881
418418 0 0
419419 24.0000i 1.17248i −0.810139 0.586238i 0.800608π-0.800608\pi
0.810139 0.586238i 0.199392π-0.199392\pi
420420 0 0
421421 20.0000i 0.974740i 0.873195 + 0.487370i 0.162044π0.162044\pi
−0.873195 + 0.487370i 0.837956π0.837956\pi
422422 −20.0000 20.0000i −0.973585 0.973585i
423423 −12.0000 −0.583460
424424 12.0000 12.0000i 0.582772 0.582772i
425425 0 0
426426 −12.0000 12.0000i −0.581402 0.581402i
427427 0 0
428428 −24.0000 −1.16008
429429 0 0
430430 0 0
431431 12.0000 0.578020 0.289010 0.957326i 0.406674π-0.406674\pi
0.289010 + 0.957326i 0.406674π0.406674\pi
432432 4.00000i 0.192450i
433433 −14.0000 −0.672797 −0.336399 0.941720i 0.609209π-0.609209\pi
−0.336399 + 0.941720i 0.609209π0.609209\pi
434434 4.00000 4.00000i 0.192006 0.192006i
435435 0 0
436436 −8.00000 −0.383131
437437 16.0000i 0.765384i
438438 −6.00000 6.00000i −0.286691 0.286691i
439439 −30.0000 −1.43182 −0.715911 0.698192i 0.753988π-0.753988\pi
−0.715911 + 0.698192i 0.753988π0.753988\pi
440440 0 0
441441 3.00000 0.142857
442442 −8.00000 8.00000i −0.380521 0.380521i
443443 24.0000i 1.14027i −0.821549 0.570137i 0.806890π-0.806890\pi
0.821549 0.570137i 0.193110π-0.193110\pi
444444 16.0000i 0.759326i
445445 0 0
446446 −14.0000 + 14.0000i −0.662919 + 0.662919i
447447 6.00000 0.283790
448448 16.0000i 0.755929i
449449 30.0000 1.41579 0.707894 0.706319i 0.249646π-0.249646\pi
0.707894 + 0.706319i 0.249646π0.249646\pi
450450 0 0
451451 0 0
452452 12.0000i 0.564433i
453453 18.0000i 0.845714i
454454 8.00000 + 8.00000i 0.375459 + 0.375459i
455455 0 0
456456 8.00000 + 8.00000i 0.374634 + 0.374634i
457457 22.0000 1.02912 0.514558 0.857455i 0.327956π-0.327956\pi
0.514558 + 0.857455i 0.327956π0.327956\pi
458458 −4.00000 4.00000i −0.186908 0.186908i
459459 2.00000i 0.0933520i
460460 0 0
461461 30.0000i 1.39724i −0.715493 0.698620i 0.753798π-0.753798\pi
0.715493 0.698620i 0.246202π-0.246202\pi
462462 0 0
463463 26.0000 1.20832 0.604161 0.796862i 0.293508π-0.293508\pi
0.604161 + 0.796862i 0.293508π0.293508\pi
464464 24.0000i 1.11417i
465465 0 0
466466 −14.0000 + 14.0000i −0.648537 + 0.648537i
467467 8.00000i 0.370196i 0.982720 + 0.185098i 0.0592602π0.0592602\pi
−0.982720 + 0.185098i 0.940740π0.940740\pi
468468 8.00000 0.369800
469469 24.0000i 1.10822i
470470 0 0
471471 8.00000 0.368621
472472 −8.00000 + 8.00000i −0.368230 + 0.368230i
473473 0 0
474474 −10.0000 10.0000i −0.459315 0.459315i
475475 0 0
476476 8.00000i 0.366679i
477477 6.00000i 0.274721i
478478 0 0
479479 20.0000 0.913823 0.456912 0.889512i 0.348956π-0.348956\pi
0.456912 + 0.889512i 0.348956π0.348956\pi
480480 0 0
481481 32.0000 1.45907
482482 2.00000 2.00000i 0.0910975 0.0910975i
483483 8.00000i 0.364013i
484484 22.0000i 1.00000i
485485 0 0
486486 −1.00000 1.00000i −0.0453609 0.0453609i
487487 −38.0000 −1.72194 −0.860972 0.508652i 0.830144π-0.830144\pi
−0.860972 + 0.508652i 0.830144π0.830144\pi
488488 0 0
489489 −4.00000 −0.180886
490490 0 0
491491 20.0000i 0.902587i 0.892375 + 0.451294i 0.149037π0.149037\pi
−0.892375 + 0.451294i 0.850963π0.850963\pi
492492 −4.00000 −0.180334
493493 12.0000i 0.540453i
494494 −16.0000 + 16.0000i −0.719874 + 0.719874i
495495 0 0
496496 −8.00000 −0.359211
497497 24.0000 1.07655
498498 16.0000 16.0000i 0.716977 0.716977i
499499 36.0000i 1.61158i 0.592200 + 0.805791i 0.298259π0.298259\pi
−0.592200 + 0.805791i 0.701741π0.701741\pi
500500 0 0
501501 8.00000i 0.357414i
502502 0 0
503503 36.0000 1.60516 0.802580 0.596544i 0.203460π-0.203460\pi
0.802580 + 0.596544i 0.203460π0.203460\pi
504504 4.00000 + 4.00000i 0.178174 + 0.178174i
505505 0 0
506506 0 0
507507 3.00000i 0.133235i
508508 4.00000i 0.177471i
509509 6.00000i 0.265945i 0.991120 + 0.132973i 0.0424523π0.0424523\pi
−0.991120 + 0.132973i 0.957548π0.957548\pi
510510 0 0
511511 12.0000 0.530849
512512 16.0000 16.0000i 0.707107 0.707107i
513513 4.00000 0.176604
514514 −18.0000 + 18.0000i −0.793946 + 0.793946i
515515 0 0
516516 8.00000i 0.352180i
517517 0 0
518518 16.0000 + 16.0000i 0.703000 + 0.703000i
519519 6.00000 0.263371
520520 0 0
521521 42.0000 1.84005 0.920027 0.391856i 0.128167π-0.128167\pi
0.920027 + 0.391856i 0.128167π0.128167\pi
522522 −6.00000 6.00000i −0.262613 0.262613i
523523 36.0000i 1.57417i 0.616844 + 0.787085i 0.288411π0.288411\pi
−0.616844 + 0.787085i 0.711589π0.711589\pi
524524 40.0000 1.74741
525525 0 0
526526 16.0000 16.0000i 0.697633 0.697633i
527527 4.00000 0.174243
528528 0 0
529529 −7.00000 −0.304348
530530 0 0
531531 4.00000i 0.173585i
532532 −16.0000 −0.693688
533533 8.00000i 0.346518i
534534 10.0000 + 10.0000i 0.432742 + 0.432742i
535535 0 0
536536 −24.0000 + 24.0000i −1.03664 + 1.03664i
537537 −4.00000 −0.172613
538538 6.00000 + 6.00000i 0.258678 + 0.258678i
539539 0 0
540540 0 0
541541 20.0000i 0.859867i −0.902861 0.429934i 0.858537π-0.858537\pi
0.902861 0.429934i 0.141463π-0.141463\pi
542542 −18.0000 + 18.0000i −0.773166 + 0.773166i
543543 20.0000 0.858282
544544 −8.00000 + 8.00000i −0.342997 + 0.342997i
545545 0 0
546546 −8.00000 + 8.00000i −0.342368 + 0.342368i
547547 28.0000i 1.19719i 0.801050 + 0.598597i 0.204275π0.204275\pi
−0.801050 + 0.598597i 0.795725π0.795725\pi
548548 36.0000i 1.53784i
549549 0 0
550550 0 0
551551 24.0000 1.02243
552552 8.00000 8.00000i 0.340503 0.340503i
553553 20.0000 0.850487
554554 28.0000 + 28.0000i 1.18961 + 1.18961i
555555 0 0
556556 −8.00000 −0.339276
557557 42.0000i 1.77960i −0.456354 0.889799i 0.650845π-0.650845\pi
0.456354 0.889799i 0.349155π-0.349155\pi
558558 −2.00000 + 2.00000i −0.0846668 + 0.0846668i
559559 −16.0000 −0.676728
560560 0 0
561561 0 0
562562 −18.0000 + 18.0000i −0.759284 + 0.759284i
563563 24.0000i 1.01148i −0.862686 0.505740i 0.831220π-0.831220\pi
0.862686 0.505740i 0.168780π-0.168780\pi
564564 −24.0000 −1.01058
565565 0 0
566566 −4.00000 4.00000i −0.168133 0.168133i
567567 2.00000 0.0839921
568568 −24.0000 24.0000i −1.00702 1.00702i
569569 −30.0000 −1.25767 −0.628833 0.777541i 0.716467π-0.716467\pi
−0.628833 + 0.777541i 0.716467π0.716467\pi
570570 0 0
571571 20.0000i 0.836974i 0.908223 + 0.418487i 0.137439π0.137439\pi
−0.908223 + 0.418487i 0.862561π0.862561\pi
572572 0 0
573573 8.00000i 0.334205i
574574 4.00000 4.00000i 0.166957 0.166957i
575575 0 0
576576 8.00000i 0.333333i
577577 42.0000 1.74848 0.874241 0.485491i 0.161359π-0.161359\pi
0.874241 + 0.485491i 0.161359π0.161359\pi
578578 −13.0000 + 13.0000i −0.540729 + 0.540729i
579579 6.00000i 0.249351i
580580 0 0
581581 32.0000i 1.32758i
582582 −2.00000 2.00000i −0.0829027 0.0829027i
583583 0 0
584584 −12.0000 12.0000i −0.496564 0.496564i
585585 0 0
586586 6.00000 + 6.00000i 0.247858 + 0.247858i
587587 28.0000i 1.15568i 0.816149 + 0.577842i 0.196105π0.196105\pi
−0.816149 + 0.577842i 0.803895π0.803895\pi
588588 6.00000 0.247436
589589 8.00000i 0.329634i
590590 0 0
591591 −2.00000 −0.0822690
592592 32.0000i 1.31519i
593593 6.00000 0.246390 0.123195 0.992382i 0.460686π-0.460686\pi
0.123195 + 0.992382i 0.460686π0.460686\pi
594594 0 0
595595 0 0
596596 12.0000 0.491539
597597 10.0000i 0.409273i
598598 16.0000 + 16.0000i 0.654289 + 0.654289i
599599 −20.0000 −0.817178 −0.408589 0.912719i 0.633979π-0.633979\pi
−0.408589 + 0.912719i 0.633979π0.633979\pi
600600 0 0
601601 2.00000 0.0815817 0.0407909 0.999168i 0.487012π-0.487012\pi
0.0407909 + 0.999168i 0.487012π0.487012\pi
602602 −8.00000 8.00000i −0.326056 0.326056i
603603 12.0000i 0.488678i
604604 36.0000i 1.46482i
605605 0 0
606606 10.0000 10.0000i 0.406222 0.406222i
607607 2.00000 0.0811775 0.0405887 0.999176i 0.487077π-0.487077\pi
0.0405887 + 0.999176i 0.487077π0.487077\pi
608608 16.0000 + 16.0000i 0.648886 + 0.648886i
609609 12.0000 0.486265
610610 0 0
611611 48.0000i 1.94187i
612612 4.00000i 0.161690i
613613 16.0000i 0.646234i 0.946359 + 0.323117i 0.104731π0.104731\pi
−0.946359 + 0.323117i 0.895269π0.895269\pi
614614 −12.0000 12.0000i −0.484281 0.484281i
615615 0 0
616616 0 0
617617 2.00000 0.0805170 0.0402585 0.999189i 0.487182π-0.487182\pi
0.0402585 + 0.999189i 0.487182π0.487182\pi
618618 −6.00000 6.00000i −0.241355 0.241355i
619619 36.0000i 1.44696i 0.690344 + 0.723481i 0.257459π0.257459\pi
−0.690344 + 0.723481i 0.742541π0.742541\pi
620620 0 0
621621 4.00000i 0.160514i
622622 −8.00000 + 8.00000i −0.320771 + 0.320771i
623623 −20.0000 −0.801283
624624 16.0000 0.640513
625625 0 0
626626 −14.0000 + 14.0000i −0.559553 + 0.559553i
627627 0 0
628628 16.0000 0.638470
629629 16.0000i 0.637962i
630630 0 0
631631 22.0000 0.875806 0.437903 0.899022i 0.355721π-0.355721\pi
0.437903 + 0.899022i 0.355721π0.355721\pi
632632 −20.0000 20.0000i −0.795557 0.795557i
633633 −20.0000 −0.794929
634634 −22.0000 22.0000i −0.873732 0.873732i
635635 0 0
636636 12.0000i 0.475831i
637637 12.0000i 0.475457i
638638 0 0
639639 −12.0000 −0.474713
640640 0 0
641641 22.0000 0.868948 0.434474 0.900684i 0.356934π-0.356934\pi
0.434474 + 0.900684i 0.356934π0.356934\pi
642642 −12.0000 + 12.0000i −0.473602 + 0.473602i
643643 4.00000i 0.157745i −0.996885 0.0788723i 0.974868π-0.974868\pi
0.996885 0.0788723i 0.0251319π-0.0251319\pi
644644 16.0000i 0.630488i
645645 0 0
646646 −8.00000 8.00000i −0.314756 0.314756i
647647 12.0000 0.471769 0.235884 0.971781i 0.424201π-0.424201\pi
0.235884 + 0.971781i 0.424201π0.424201\pi
648648 −2.00000 2.00000i −0.0785674 0.0785674i
649649 0 0
650650 0 0
651651 4.00000i 0.156772i
652652 −8.00000 −0.313304
653653 6.00000i 0.234798i 0.993085 + 0.117399i 0.0374557π0.0374557\pi
−0.993085 + 0.117399i 0.962544π0.962544\pi
654654 −4.00000 + 4.00000i −0.156412 + 0.156412i
655655 0 0
656656 −8.00000 −0.312348
657657 −6.00000 −0.234082
658658 24.0000 24.0000i 0.935617 0.935617i
659659 36.0000i 1.40236i 0.712984 + 0.701180i 0.247343π0.247343\pi
−0.712984 + 0.701180i 0.752657π0.752657\pi
660660 0 0
661661 40.0000i 1.55582i 0.628376 + 0.777910i 0.283720π0.283720\pi
−0.628376 + 0.777910i 0.716280π0.716280\pi
662662 −20.0000 20.0000i −0.777322 0.777322i
663663 −8.00000 −0.310694
664664 32.0000 32.0000i 1.24184 1.24184i
665665 0 0
666666 −8.00000 8.00000i −0.309994 0.309994i
667667 24.0000i 0.929284i
668668 16.0000i 0.619059i
669669 14.0000i 0.541271i
670670 0 0
671671 0 0
672672 8.00000 + 8.00000i 0.308607 + 0.308607i
673673 −14.0000 −0.539660 −0.269830 0.962908i 0.586968π-0.586968\pi
−0.269830 + 0.962908i 0.586968π0.586968\pi
674674 2.00000 2.00000i 0.0770371 0.0770371i
675675 0 0
676676 6.00000i 0.230769i
677677 18.0000i 0.691796i 0.938272 + 0.345898i 0.112426π0.112426\pi
−0.938272 + 0.345898i 0.887574π0.887574\pi
678678 −6.00000 6.00000i −0.230429 0.230429i
679679 4.00000 0.153506
680680 0 0
681681 8.00000 0.306561
682682 0 0
683683 16.0000i 0.612223i 0.951996 + 0.306111i 0.0990280π0.0990280\pi
−0.951996 + 0.306111i 0.900972π0.900972\pi
684684 8.00000 0.305888
685685 0 0
686686 −20.0000 + 20.0000i −0.763604 + 0.763604i
687687 −4.00000 −0.152610
688688 16.0000i 0.609994i
689689 24.0000 0.914327
690690 0 0
691691 20.0000i 0.760836i 0.924815 + 0.380418i 0.124220π0.124220\pi
−0.924815 + 0.380418i 0.875780π0.875780\pi
692692 12.0000 0.456172
693693 0 0
694694 8.00000 + 8.00000i 0.303676 + 0.303676i
695695 0 0
696696 −12.0000 12.0000i −0.454859 0.454859i
697697 4.00000 0.151511
698698 16.0000 + 16.0000i 0.605609 + 0.605609i
699699 14.0000i 0.529529i
700700 0 0
701701 50.0000i 1.88847i −0.329267 0.944237i 0.606802π-0.606802\pi
0.329267 0.944237i 0.393198π-0.393198\pi
702702 4.00000 4.00000i 0.150970 0.150970i
703703 32.0000 1.20690
704704 0 0
705705 0 0
706706 6.00000 6.00000i 0.225813 0.225813i
707707 20.0000i 0.752177i
708708 8.00000i 0.300658i
709709 4.00000i 0.150223i −0.997175 0.0751116i 0.976069π-0.976069\pi
0.997175 0.0751116i 0.0239313π-0.0239313\pi
710710 0 0
711711 −10.0000 −0.375029
712712 20.0000 + 20.0000i 0.749532 + 0.749532i
713713 −8.00000 −0.299602
714714 −4.00000 4.00000i −0.149696 0.149696i
715715 0 0
716716 −8.00000 −0.298974
717717 0 0
718718 −20.0000 + 20.0000i −0.746393 + 0.746393i
719719 −20.0000 −0.745874 −0.372937 0.927857i 0.621649π-0.621649\pi
−0.372937 + 0.927857i 0.621649π0.621649\pi
720720 0 0
721721 12.0000 0.446903
722722 3.00000 3.00000i 0.111648 0.111648i
723723 2.00000i 0.0743808i
724724 40.0000 1.48659
725725 0 0
726726 −11.0000 11.0000i −0.408248 0.408248i
727727 42.0000 1.55769 0.778847 0.627214i 0.215805π-0.215805\pi
0.778847 + 0.627214i 0.215805π0.215805\pi
728728 −16.0000 + 16.0000i −0.592999 + 0.592999i
729729 −1.00000 −0.0370370
730730 0 0
731731 8.00000i 0.295891i
732732 0 0
733733 4.00000i 0.147743i −0.997268 0.0738717i 0.976464π-0.976464\pi
0.997268 0.0738717i 0.0235355π-0.0235355\pi
734734 −18.0000 + 18.0000i −0.664392 + 0.664392i
735735 0 0
736736 16.0000 16.0000i 0.589768 0.589768i
737737 0 0
738738 −2.00000 + 2.00000i −0.0736210 + 0.0736210i
739739 44.0000i 1.61857i −0.587419 0.809283i 0.699856π-0.699856\pi
0.587419 0.809283i 0.300144π-0.300144\pi
740740 0 0
741741 16.0000i 0.587775i
742742 12.0000 + 12.0000i 0.440534 + 0.440534i
743743 16.0000 0.586983 0.293492 0.955962i 0.405183π-0.405183\pi
0.293492 + 0.955962i 0.405183π0.405183\pi
744744 −4.00000 + 4.00000i −0.146647 + 0.146647i
745745 0 0
746746 16.0000 + 16.0000i 0.585802 + 0.585802i
747747 16.0000i 0.585409i
748748 0 0
749749 24.0000i 0.876941i
750750 0 0
751751 2.00000 0.0729810 0.0364905 0.999334i 0.488382π-0.488382\pi
0.0364905 + 0.999334i 0.488382π0.488382\pi
752752 −48.0000 −1.75038
753753 0 0
754754 24.0000 24.0000i 0.874028 0.874028i
755755 0 0
756756 4.00000 0.145479
757757 12.0000i 0.436147i −0.975932 0.218074i 0.930023π-0.930023\pi
0.975932 0.218074i 0.0699773π-0.0699773\pi
758758 −4.00000 4.00000i −0.145287 0.145287i
759759 0 0
760760 0 0
761761 −38.0000 −1.37750 −0.688749 0.724999i 0.741840π-0.741840\pi
−0.688749 + 0.724999i 0.741840π0.741840\pi
762762 −2.00000 2.00000i −0.0724524 0.0724524i
763763 8.00000i 0.289619i
764764 16.0000i 0.578860i
765765 0 0
766766 −24.0000 + 24.0000i −0.867155 + 0.867155i
767767 −16.0000 −0.577727
768768 16.0000i 0.577350i
769769 10.0000 0.360609 0.180305 0.983611i 0.442292π-0.442292\pi
0.180305 + 0.983611i 0.442292π0.442292\pi
770770 0 0
771771 18.0000i 0.648254i
772772 12.0000i 0.431889i
773773 34.0000i 1.22290i −0.791285 0.611448i 0.790588π-0.790588\pi
0.791285 0.611448i 0.209412π-0.209412\pi
774774 4.00000 + 4.00000i 0.143777 + 0.143777i
775775 0 0
776776 −4.00000 4.00000i −0.143592 0.143592i
777777 16.0000 0.573997
778778 −34.0000 34.0000i −1.21896 1.21896i
779779 8.00000i 0.286630i
780780 0 0
781781 0 0
782782 −8.00000 + 8.00000i −0.286079 + 0.286079i
783783 −6.00000 −0.214423
784784 12.0000 0.428571
785785 0 0
786786 20.0000 20.0000i 0.713376 0.713376i
787787 12.0000i 0.427754i −0.976861 0.213877i 0.931391π-0.931391\pi
0.976861 0.213877i 0.0686091π-0.0686091\pi
788788 −4.00000 −0.142494
789789 16.0000i 0.569615i
790790 0 0
791791 12.0000 0.426671
792792 0 0
793793 0 0
794794 −32.0000 32.0000i −1.13564 1.13564i
795795 0 0
796796 20.0000i 0.708881i
797797 2.00000i 0.0708436i −0.999372 0.0354218i 0.988723π-0.988723\pi
0.999372 0.0354218i 0.0112775π-0.0112775\pi
798798 −8.00000 + 8.00000i −0.283197 + 0.283197i
799799 24.0000 0.849059
800800 0 0
801801 10.0000 0.353333
802802 −18.0000 + 18.0000i −0.635602 + 0.635602i
803803 0 0
804804 24.0000i 0.846415i
805805 0 0
806806 −8.00000 8.00000i −0.281788 0.281788i
807807 6.00000 0.211210
808808 20.0000 20.0000i 0.703598 0.703598i
809809 −30.0000 −1.05474 −0.527372 0.849635i 0.676823π-0.676823\pi
−0.527372 + 0.849635i 0.676823π0.676823\pi
810810 0 0
811811 20.0000i 0.702295i −0.936320 0.351147i 0.885792π-0.885792\pi
0.936320 0.351147i 0.114208π-0.114208\pi
812812 24.0000 0.842235
813813 18.0000i 0.631288i
814814 0 0
815815 0 0
816816 8.00000i 0.280056i
817817 −16.0000 −0.559769
818818 10.0000 10.0000i 0.349642 0.349642i
819819 8.00000i 0.279543i
820820 0 0
821821 10.0000i 0.349002i 0.984657 + 0.174501i 0.0558313π0.0558313\pi
−0.984657 + 0.174501i 0.944169π0.944169\pi
822822 18.0000 + 18.0000i 0.627822 + 0.627822i
823823 −14.0000 −0.488009 −0.244005 0.969774i 0.578461π-0.578461\pi
−0.244005 + 0.969774i 0.578461π0.578461\pi
824824 −12.0000 12.0000i −0.418040 0.418040i
825825 0 0
826826 −8.00000 8.00000i −0.278356 0.278356i
827827 12.0000i 0.417281i −0.977992 0.208640i 0.933096π-0.933096\pi
0.977992 0.208640i 0.0669038π-0.0669038\pi
828828 8.00000i 0.278019i
829829 4.00000i 0.138926i −0.997585 0.0694629i 0.977871π-0.977871\pi
0.997585 0.0694629i 0.0221285π-0.0221285\pi
830830 0 0
831831 28.0000 0.971309
832832 32.0000 1.10940
833833 −6.00000 −0.207888
834834 −4.00000 + 4.00000i −0.138509 + 0.138509i
835835 0 0
836836 0 0
837837 2.00000i 0.0691301i
838838 −24.0000 24.0000i −0.829066 0.829066i
839839 20.0000 0.690477 0.345238 0.938515i 0.387798π-0.387798\pi
0.345238 + 0.938515i 0.387798π0.387798\pi
840840 0 0
841841 −7.00000 −0.241379
842842 20.0000 + 20.0000i 0.689246 + 0.689246i
843843 18.0000i 0.619953i
844844 −40.0000 −1.37686
845845 0 0
846846 −12.0000 + 12.0000i −0.412568 + 0.412568i
847847 22.0000 0.755929
848848 24.0000i 0.824163i
849849 −4.00000 −0.137280
850850 0 0
851851 32.0000i 1.09695i
852852 −24.0000 −0.822226
853853 24.0000i 0.821744i −0.911693 0.410872i 0.865224π-0.865224\pi
0.911693 0.410872i 0.134776π-0.134776\pi
854854 0 0
855855 0 0
856856 −24.0000 + 24.0000i −0.820303 + 0.820303i
857857 −18.0000 −0.614868 −0.307434 0.951569i 0.599470π-0.599470\pi
−0.307434 + 0.951569i 0.599470π0.599470\pi
858858 0 0
859859 44.0000i 1.50126i −0.660722 0.750630i 0.729750π-0.729750\pi
0.660722 0.750630i 0.270250π-0.270250\pi
860860 0 0
861861 4.00000i 0.136320i
862862 12.0000 12.0000i 0.408722 0.408722i
863863 −24.0000 −0.816970 −0.408485 0.912765i 0.633943π-0.633943\pi
−0.408485 + 0.912765i 0.633943π0.633943\pi
864864 −4.00000 4.00000i −0.136083 0.136083i
865865 0 0
866866 −14.0000 + 14.0000i −0.475739 + 0.475739i
867867 13.0000i 0.441503i
868868 8.00000i 0.271538i
869869 0 0
870870 0 0
871871 −48.0000 −1.62642
872872 −8.00000 + 8.00000i −0.270914 + 0.270914i
873873 −2.00000 −0.0676897
874874 16.0000 + 16.0000i 0.541208 + 0.541208i
875875 0 0
876876 −12.0000 −0.405442
877877 32.0000i 1.08056i −0.841484 0.540282i 0.818318π-0.818318\pi
0.841484 0.540282i 0.181682π-0.181682\pi
878878 −30.0000 + 30.0000i −1.01245 + 1.01245i
879879 6.00000 0.202375
880880 0 0
881881 2.00000 0.0673817 0.0336909 0.999432i 0.489274π-0.489274\pi
0.0336909 + 0.999432i 0.489274π0.489274\pi
882882 3.00000 3.00000i 0.101015 0.101015i
883883 4.00000i 0.134611i −0.997732 0.0673054i 0.978560π-0.978560\pi
0.997732 0.0673054i 0.0214402π-0.0214402\pi
884884 −16.0000 −0.538138
885885 0 0
886886 −24.0000 24.0000i −0.806296 0.806296i
887887 −48.0000 −1.61168 −0.805841 0.592132i 0.798286π-0.798286\pi
−0.805841 + 0.592132i 0.798286π0.798286\pi
888888 −16.0000 16.0000i −0.536925 0.536925i
889889 4.00000 0.134156
890890 0 0
891891 0 0
892892 28.0000i 0.937509i
893893 48.0000i 1.60626i
894894 6.00000 6.00000i 0.200670 0.200670i
895895 0 0
896896 16.0000 + 16.0000i 0.534522 + 0.534522i
897897 16.0000 0.534224
898898 30.0000 30.0000i 1.00111 1.00111i
899899 12.0000i 0.400222i
900900 0 0
901901 12.0000i 0.399778i
902902 0 0
903903 −8.00000 −0.266223
904904 −12.0000 12.0000i −0.399114 0.399114i
905905 0 0
906906 18.0000 + 18.0000i 0.598010 + 0.598010i
907907 28.0000i 0.929725i 0.885383 + 0.464862i 0.153896π0.153896\pi
−0.885383 + 0.464862i 0.846104π0.846104\pi
908908 16.0000 0.530979
909909 10.0000i 0.331679i
910910 0 0
911911 −48.0000 −1.59031 −0.795155 0.606406i 0.792611π-0.792611\pi
−0.795155 + 0.606406i 0.792611π0.792611\pi
912912 16.0000 0.529813
913913 0 0
914914 22.0000 22.0000i 0.727695 0.727695i
915915 0 0
916916 −8.00000 −0.264327
917917 40.0000i 1.32092i
918918 2.00000 + 2.00000i 0.0660098 + 0.0660098i
919919 30.0000 0.989609 0.494804 0.869004i 0.335240π-0.335240\pi
0.494804 + 0.869004i 0.335240π0.335240\pi
920920 0 0
921921 −12.0000 −0.395413
922922 −30.0000 30.0000i −0.987997 0.987997i
923923 48.0000i 1.57994i
924924 0 0
925925 0 0
926926 26.0000 26.0000i 0.854413 0.854413i
927927 −6.00000 −0.197066
928928 −24.0000 24.0000i −0.787839 0.787839i
929929 −50.0000 −1.64045 −0.820223 0.572043i 0.806151π-0.806151\pi
−0.820223 + 0.572043i 0.806151π0.806151\pi
930930 0 0
931931 12.0000i 0.393284i
932932 28.0000i 0.917170i
933933 8.00000i 0.261908i
934934 8.00000 + 8.00000i 0.261768 + 0.261768i
935935 0 0
936936 8.00000 8.00000i 0.261488 0.261488i
937937 −38.0000 −1.24141 −0.620703 0.784046i 0.713153π-0.713153\pi
−0.620703 + 0.784046i 0.713153π0.713153\pi
938938 −24.0000 24.0000i −0.783628 0.783628i
939939 14.0000i 0.456873i
940940 0 0
941941 30.0000i 0.977972i −0.872292 0.488986i 0.837367π-0.837367\pi
0.872292 0.488986i 0.162633π-0.162633\pi
942942 8.00000 8.00000i 0.260654 0.260654i
943943 −8.00000 −0.260516
944944 16.0000i 0.520756i
945945 0 0
946946 0 0
947947 12.0000i 0.389948i −0.980808 0.194974i 0.937538π-0.937538\pi
0.980808 0.194974i 0.0624622π-0.0624622\pi
948948 −20.0000 −0.649570
949949 24.0000i 0.779073i
950950 0 0
951951 −22.0000 −0.713399
952952 −8.00000 8.00000i −0.259281 0.259281i
953953 6.00000 0.194359 0.0971795 0.995267i 0.469018π-0.469018\pi
0.0971795 + 0.995267i 0.469018π0.469018\pi
954954 −6.00000 6.00000i −0.194257 0.194257i
955955 0 0
956956 0 0
957957 0 0
958958 20.0000 20.0000i 0.646171 0.646171i
959959 −36.0000 −1.16250
960960 0 0
961961 −27.0000 −0.870968
962962 32.0000 32.0000i 1.03172 1.03172i
963963 12.0000i 0.386695i
964964 4.00000i 0.128831i
965965 0 0
966966 8.00000 + 8.00000i 0.257396 + 0.257396i
967967 22.0000 0.707472 0.353736 0.935345i 0.384911π-0.384911\pi
0.353736 + 0.935345i 0.384911π0.384911\pi
968968 −22.0000 22.0000i −0.707107 0.707107i
969969 −8.00000 −0.256997
970970 0 0
971971 0 0 1.00000 00
−1.00000 π\pi
972972 −2.00000 −0.0641500
973973 8.00000i 0.256468i
974974 −38.0000 + 38.0000i −1.21760 + 1.21760i
975975 0 0
976976 0 0
977977 2.00000 0.0639857 0.0319928 0.999488i 0.489815π-0.489815\pi
0.0319928 + 0.999488i 0.489815π0.489815\pi
978978 −4.00000 + 4.00000i −0.127906 + 0.127906i
979979 0 0
980980 0 0
981981 4.00000i 0.127710i
982982 20.0000 + 20.0000i 0.638226 + 0.638226i
983983 16.0000 0.510321 0.255160 0.966899i 0.417872π-0.417872\pi
0.255160 + 0.966899i 0.417872π0.417872\pi
984984 −4.00000 + 4.00000i −0.127515 + 0.127515i
985985 0 0
986986 12.0000 + 12.0000i 0.382158 + 0.382158i
987987 24.0000i 0.763928i
988988 32.0000i 1.01806i
989989 16.0000i 0.508770i
990990 0 0
991991 2.00000 0.0635321 0.0317660 0.999495i 0.489887π-0.489887\pi
0.0317660 + 0.999495i 0.489887π0.489887\pi
992992 −8.00000 + 8.00000i −0.254000 + 0.254000i
993993 −20.0000 −0.634681
994994 24.0000 24.0000i 0.761234 0.761234i
995995 0 0
996996 32.0000i 1.01396i
997997 48.0000i 1.52018i 0.649821 + 0.760088i 0.274844π0.274844\pi
−0.649821 + 0.760088i 0.725156π0.725156\pi
998998 36.0000 + 36.0000i 1.13956 + 1.13956i
999999 −8.00000 −0.253109
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 600.2.k.b.301.1 2
3.2 odd 2 1800.2.k.a.901.2 2
4.3 odd 2 2400.2.k.a.1201.2 2
5.2 odd 4 600.2.d.c.349.2 2
5.3 odd 4 600.2.d.b.349.1 2
5.4 even 2 24.2.d.a.13.2 yes 2
8.3 odd 2 2400.2.k.a.1201.1 2
8.5 even 2 inner 600.2.k.b.301.2 2
12.11 even 2 7200.2.k.d.3601.1 2
15.2 even 4 1800.2.d.b.1549.1 2
15.8 even 4 1800.2.d.i.1549.2 2
15.14 odd 2 72.2.d.b.37.1 2
20.3 even 4 2400.2.d.b.49.2 2
20.7 even 4 2400.2.d.c.49.1 2
20.19 odd 2 96.2.d.a.49.1 2
24.5 odd 2 1800.2.k.a.901.1 2
24.11 even 2 7200.2.k.d.3601.2 2
35.34 odd 2 1176.2.c.a.589.2 2
40.3 even 4 2400.2.d.c.49.2 2
40.13 odd 4 600.2.d.c.349.1 2
40.19 odd 2 96.2.d.a.49.2 2
40.27 even 4 2400.2.d.b.49.1 2
40.29 even 2 24.2.d.a.13.1 2
40.37 odd 4 600.2.d.b.349.2 2
45.4 even 6 648.2.n.k.541.1 4
45.14 odd 6 648.2.n.c.541.2 4
45.29 odd 6 648.2.n.c.109.1 4
45.34 even 6 648.2.n.k.109.2 4
60.23 odd 4 7200.2.d.g.2449.2 2
60.47 odd 4 7200.2.d.d.2449.1 2
60.59 even 2 288.2.d.b.145.2 2
80.19 odd 4 768.2.a.e.1.1 1
80.29 even 4 768.2.a.a.1.1 1
80.59 odd 4 768.2.a.d.1.1 1
80.69 even 4 768.2.a.h.1.1 1
120.29 odd 2 72.2.d.b.37.2 2
120.53 even 4 1800.2.d.b.1549.2 2
120.59 even 2 288.2.d.b.145.1 2
120.77 even 4 1800.2.d.i.1549.1 2
120.83 odd 4 7200.2.d.d.2449.2 2
120.107 odd 4 7200.2.d.g.2449.1 2
140.139 even 2 4704.2.c.a.2353.2 2
180.59 even 6 2592.2.r.g.2161.2 4
180.79 odd 6 2592.2.r.f.433.2 4
180.119 even 6 2592.2.r.g.433.1 4
180.139 odd 6 2592.2.r.f.2161.1 4
240.29 odd 4 2304.2.a.o.1.1 1
240.59 even 4 2304.2.a.b.1.1 1
240.149 odd 4 2304.2.a.e.1.1 1
240.179 even 4 2304.2.a.l.1.1 1
280.69 odd 2 1176.2.c.a.589.1 2
280.139 even 2 4704.2.c.a.2353.1 2
360.29 odd 6 648.2.n.c.109.2 4
360.59 even 6 2592.2.r.g.2161.1 4
360.139 odd 6 2592.2.r.f.2161.2 4
360.149 odd 6 648.2.n.c.541.1 4
360.229 even 6 648.2.n.k.541.2 4
360.259 odd 6 2592.2.r.f.433.1 4
360.299 even 6 2592.2.r.g.433.2 4
360.349 even 6 648.2.n.k.109.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
24.2.d.a.13.1 2 40.29 even 2
24.2.d.a.13.2 yes 2 5.4 even 2
72.2.d.b.37.1 2 15.14 odd 2
72.2.d.b.37.2 2 120.29 odd 2
96.2.d.a.49.1 2 20.19 odd 2
96.2.d.a.49.2 2 40.19 odd 2
288.2.d.b.145.1 2 120.59 even 2
288.2.d.b.145.2 2 60.59 even 2
600.2.d.b.349.1 2 5.3 odd 4
600.2.d.b.349.2 2 40.37 odd 4
600.2.d.c.349.1 2 40.13 odd 4
600.2.d.c.349.2 2 5.2 odd 4
600.2.k.b.301.1 2 1.1 even 1 trivial
600.2.k.b.301.2 2 8.5 even 2 inner
648.2.n.c.109.1 4 45.29 odd 6
648.2.n.c.109.2 4 360.29 odd 6
648.2.n.c.541.1 4 360.149 odd 6
648.2.n.c.541.2 4 45.14 odd 6
648.2.n.k.109.1 4 360.349 even 6
648.2.n.k.109.2 4 45.34 even 6
648.2.n.k.541.1 4 45.4 even 6
648.2.n.k.541.2 4 360.229 even 6
768.2.a.a.1.1 1 80.29 even 4
768.2.a.d.1.1 1 80.59 odd 4
768.2.a.e.1.1 1 80.19 odd 4
768.2.a.h.1.1 1 80.69 even 4
1176.2.c.a.589.1 2 280.69 odd 2
1176.2.c.a.589.2 2 35.34 odd 2
1800.2.d.b.1549.1 2 15.2 even 4
1800.2.d.b.1549.2 2 120.53 even 4
1800.2.d.i.1549.1 2 120.77 even 4
1800.2.d.i.1549.2 2 15.8 even 4
1800.2.k.a.901.1 2 24.5 odd 2
1800.2.k.a.901.2 2 3.2 odd 2
2304.2.a.b.1.1 1 240.59 even 4
2304.2.a.e.1.1 1 240.149 odd 4
2304.2.a.l.1.1 1 240.179 even 4
2304.2.a.o.1.1 1 240.29 odd 4
2400.2.d.b.49.1 2 40.27 even 4
2400.2.d.b.49.2 2 20.3 even 4
2400.2.d.c.49.1 2 20.7 even 4
2400.2.d.c.49.2 2 40.3 even 4
2400.2.k.a.1201.1 2 8.3 odd 2
2400.2.k.a.1201.2 2 4.3 odd 2
2592.2.r.f.433.1 4 360.259 odd 6
2592.2.r.f.433.2 4 180.79 odd 6
2592.2.r.f.2161.1 4 180.139 odd 6
2592.2.r.f.2161.2 4 360.139 odd 6
2592.2.r.g.433.1 4 180.119 even 6
2592.2.r.g.433.2 4 360.299 even 6
2592.2.r.g.2161.1 4 360.59 even 6
2592.2.r.g.2161.2 4 180.59 even 6
4704.2.c.a.2353.1 2 280.139 even 2
4704.2.c.a.2353.2 2 140.139 even 2
7200.2.d.d.2449.1 2 60.47 odd 4
7200.2.d.d.2449.2 2 120.83 odd 4
7200.2.d.g.2449.1 2 120.107 odd 4
7200.2.d.g.2449.2 2 60.23 odd 4
7200.2.k.d.3601.1 2 12.11 even 2
7200.2.k.d.3601.2 2 24.11 even 2