Properties

Label 560.2.q.l.401.1
Level 560560
Weight 22
Character 560.401
Analytic conductor 4.4724.472
Analytic rank 00
Dimension 66
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [560,2,Mod(81,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.81"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 560=2457 560 = 2^{4} \cdot 5 \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 560.q (of order 33, degree 22, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,0,0,0,-3,0,-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: 4.471622513194.47162251319
Analytic rank: 00
Dimension: 66
Relative dimension: 33 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: 6.0.11337408.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x6+18x4+81x2+12 x^{6} + 18x^{4} + 81x^{2} + 12 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 280)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 401.1
Root 2.78499i-2.78499i of defining polynomial
Character χ\chi == 560.401
Dual form 560.2.q.l.81.1

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+(1.644972.84918i)q3+(0.500000+0.866025i)q5+(2.644970.0641892i)q7+(3.91187+6.77556i)q9+(2.91187+5.04351i)q11+2.75615q13+3.28995q15+(1.000001.73205i)q17+(0.378076+0.654846i)q19+(4.16802+7.64158i)q21+(0.266897+0.462279i)q23+(0.5000000.866025i)q25+15.8698q270.823739q29+(1.289952.23425i)q31+(9.5798916.5929i)q33+(1.378082.25852i)q35+(2.37808+4.11895i)q37+(4.533797.85276i)q39+6.06759q410.710055q43+(3.911876.77556i)q45+(6.44566+11.1642i)q47+(6.99176+0.339557i)q49+(3.28995+5.69835i)q51+(4.20181+7.27776i)q535.82374q55+2.48770q57+(4.00000+6.92820i)q59+(4.70181+8.14378i)q61+(10.781717.6701i)q63+(1.37808+2.38690i)q65+(5.93492+10.2796i)q67+1.75615q69+(1.756153.04174i)q73+(1.64497+2.84918i)q75+(7.3780813.5268i)q77+(4.75615+8.23790i)q79+(14.369824.8893i)q81+6.71005q83+2.00000q85+(1.35503+2.34698i)q87+(0.878076+1.52087i)q89+(7.289950.176915i)q91+(4.24385+7.35056i)q93+(0.3780760.654846i)q952.00000q9745.5634q99+O(q100)q+(-1.64497 - 2.84918i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-2.64497 - 0.0641892i) q^{7} +(-3.91187 + 6.77556i) q^{9} +(2.91187 + 5.04351i) q^{11} +2.75615 q^{13} +3.28995 q^{15} +(-1.00000 - 1.73205i) q^{17} +(-0.378076 + 0.654846i) q^{19} +(4.16802 + 7.64158i) q^{21} +(-0.266897 + 0.462279i) q^{23} +(-0.500000 - 0.866025i) q^{25} +15.8698 q^{27} -0.823739 q^{29} +(-1.28995 - 2.23425i) q^{31} +(9.57989 - 16.5929i) q^{33} +(1.37808 - 2.25852i) q^{35} +(-2.37808 + 4.11895i) q^{37} +(-4.53379 - 7.85276i) q^{39} +6.06759 q^{41} -0.710055 q^{43} +(-3.91187 - 6.77556i) q^{45} +(-6.44566 + 11.1642i) q^{47} +(6.99176 + 0.339557i) q^{49} +(-3.28995 + 5.69835i) q^{51} +(4.20181 + 7.27776i) q^{53} -5.82374 q^{55} +2.48770 q^{57} +(4.00000 + 6.92820i) q^{59} +(-4.70181 + 8.14378i) q^{61} +(10.7817 - 17.6701i) q^{63} +(-1.37808 + 2.38690i) q^{65} +(5.93492 + 10.2796i) q^{67} +1.75615 q^{69} +(-1.75615 - 3.04174i) q^{73} +(-1.64497 + 2.84918i) q^{75} +(-7.37808 - 13.5268i) q^{77} +(-4.75615 + 8.23790i) q^{79} +(-14.3698 - 24.8893i) q^{81} +6.71005 q^{83} +2.00000 q^{85} +(1.35503 + 2.34698i) q^{87} +(-0.878076 + 1.52087i) q^{89} +(-7.28995 - 0.176915i) q^{91} +(-4.24385 + 7.35056i) q^{93} +(-0.378076 - 0.654846i) q^{95} -2.00000 q^{97} -45.5634 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q3q56q79q9+3q11+6q136q17+3q19+3q233q25+36q27+24q29+12q31+18q33+3q359q3718q39+18q4124q43+126q99+O(q100) 6 q - 3 q^{5} - 6 q^{7} - 9 q^{9} + 3 q^{11} + 6 q^{13} - 6 q^{17} + 3 q^{19} + 3 q^{23} - 3 q^{25} + 36 q^{27} + 24 q^{29} + 12 q^{31} + 18 q^{33} + 3 q^{35} - 9 q^{37} - 18 q^{39} + 18 q^{41} - 24 q^{43}+ \cdots - 126 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/560Z)×\left(\mathbb{Z}/560\mathbb{Z}\right)^\times.

nn 241241 337337 351351 421421
χ(n)\chi(n) e(13)e\left(\frac{1}{3}\right) 11 11 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 −1.64497 2.84918i −0.949725 1.64497i −0.746002 0.665944i 0.768029π-0.768029\pi
−0.203724 0.979028i 0.565304π-0.565304\pi
44 0 0
55 −0.500000 + 0.866025i −0.223607 + 0.387298i
66 0 0
77 −2.64497 0.0641892i −0.999706 0.0242612i
88 0 0
99 −3.91187 + 6.77556i −1.30396 + 2.25852i
1010 0 0
1111 2.91187 + 5.04351i 0.877962 + 1.52067i 0.853574 + 0.520972i 0.174430π0.174430\pi
0.0243876 + 0.999703i 0.492236π0.492236\pi
1212 0 0
1313 2.75615 0.764419 0.382209 0.924076i 0.375163π-0.375163\pi
0.382209 + 0.924076i 0.375163π0.375163\pi
1414 0 0
1515 3.28995 0.849460
1616 0 0
1717 −1.00000 1.73205i −0.242536 0.420084i 0.718900 0.695113i 0.244646π-0.244646\pi
−0.961436 + 0.275029i 0.911312π0.911312\pi
1818 0 0
1919 −0.378076 + 0.654846i −0.0867365 + 0.150232i −0.906130 0.423000i 0.860977π-0.860977\pi
0.819393 + 0.573232i 0.194310π0.194310\pi
2020 0 0
2121 4.16802 + 7.64158i 0.909537 + 1.66753i
2222 0 0
2323 −0.266897 + 0.462279i −0.0556518 + 0.0963918i −0.892509 0.451029i 0.851057π-0.851057\pi
0.836857 + 0.547421i 0.184390π0.184390\pi
2424 0 0
2525 −0.500000 0.866025i −0.100000 0.173205i
2626 0 0
2727 15.8698 3.05415
2828 0 0
2929 −0.823739 −0.152964 −0.0764822 0.997071i 0.524369π-0.524369\pi
−0.0764822 + 0.997071i 0.524369π0.524369\pi
3030 0 0
3131 −1.28995 2.23425i −0.231681 0.401283i 0.726622 0.687038i 0.241089π-0.241089\pi
−0.958303 + 0.285754i 0.907756π0.907756\pi
3232 0 0
3333 9.57989 16.5929i 1.66764 2.88845i
3434 0 0
3535 1.37808 2.25852i 0.232937 0.381759i
3636 0 0
3737 −2.37808 + 4.11895i −0.390953 + 0.677151i −0.992576 0.121630i 0.961188π-0.961188\pi
0.601622 + 0.798781i 0.294521π0.294521\pi
3838 0 0
3939 −4.53379 7.85276i −0.725988 1.25745i
4040 0 0
4141 6.06759 0.947598 0.473799 0.880633i 0.342882π-0.342882\pi
0.473799 + 0.880633i 0.342882π0.342882\pi
4242 0 0
4343 −0.710055 −0.108282 −0.0541412 0.998533i 0.517242π-0.517242\pi
−0.0541412 + 0.998533i 0.517242π0.517242\pi
4444 0 0
4545 −3.91187 6.77556i −0.583147 1.01004i
4646 0 0
4747 −6.44566 + 11.1642i −0.940197 + 1.62847i −0.175102 + 0.984550i 0.556026π0.556026\pi
−0.765095 + 0.643918i 0.777308π0.777308\pi
4848 0 0
4949 6.99176 + 0.339557i 0.998823 + 0.0485082i
5050 0 0
5151 −3.28995 + 5.69835i −0.460684 + 0.797929i
5252 0 0
5353 4.20181 + 7.27776i 0.577164 + 0.999677i 0.995803 + 0.0915241i 0.0291738π0.0291738\pi
−0.418639 + 0.908153i 0.637493π0.637493\pi
5454 0 0
5555 −5.82374 −0.785273
5656 0 0
5757 2.48770 0.329504
5858 0 0
5959 4.00000 + 6.92820i 0.520756 + 0.901975i 0.999709 + 0.0241347i 0.00768307π0.00768307\pi
−0.478953 + 0.877841i 0.658984π0.658984\pi
6060 0 0
6161 −4.70181 + 8.14378i −0.602006 + 1.04270i 0.390511 + 0.920598i 0.372298π0.372298\pi
−0.992517 + 0.122106i 0.961035π0.961035\pi
6262 0 0
6363 10.7817 17.6701i 1.35837 2.22622i
6464 0 0
6565 −1.37808 + 2.38690i −0.170929 + 0.296058i
6666 0 0
6767 5.93492 + 10.2796i 0.725066 + 1.25585i 0.958947 + 0.283585i 0.0915239π0.0915239\pi
−0.233881 + 0.972265i 0.575143π0.575143\pi
6868 0 0
6969 1.75615 0.211416
7070 0 0
7171 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
7272 0 0
7373 −1.75615 3.04174i −0.205542 0.356009i 0.744763 0.667329i 0.232562π-0.232562\pi
−0.950305 + 0.311320i 0.899229π0.899229\pi
7474 0 0
7575 −1.64497 + 2.84918i −0.189945 + 0.328995i
7676 0 0
7777 −7.37808 13.5268i −0.840810 1.54153i
7878 0 0
7979 −4.75615 + 8.23790i −0.535109 + 0.926836i 0.464049 + 0.885809i 0.346396π0.346396\pi
−0.999158 + 0.0410263i 0.986937π0.986937\pi
8080 0 0
8181 −14.3698 24.8893i −1.59665 2.76548i
8282 0 0
8383 6.71005 0.736524 0.368262 0.929722i 0.379953π-0.379953\pi
0.368262 + 0.929722i 0.379953π0.379953\pi
8484 0 0
8585 2.00000 0.216930
8686 0 0
8787 1.35503 + 2.34698i 0.145274 + 0.251622i
8888 0 0
8989 −0.878076 + 1.52087i −0.0930758 + 0.161212i −0.908804 0.417223i 0.863003π-0.863003\pi
0.815728 + 0.578436i 0.196337π0.196337\pi
9090 0 0
9191 −7.28995 0.176915i −0.764194 0.0185458i
9292 0 0
9393 −4.24385 + 7.35056i −0.440067 + 0.762218i
9494 0 0
9595 −0.378076 0.654846i −0.0387898 0.0671858i
9696 0 0
9797 −2.00000 −0.203069 −0.101535 0.994832i 0.532375π-0.532375\pi
−0.101535 + 0.994832i 0.532375π0.532375\pi
9898 0 0
9999 −45.5634 −4.57929
100100 0 0
101101 −1.16802 2.02307i −0.116222 0.201303i 0.802045 0.597263i 0.203745π-0.203745\pi
−0.918268 + 0.395960i 0.870412π0.870412\pi
102102 0 0
103103 −1.11118 + 1.92462i −0.109488 + 0.189638i −0.915563 0.402175i 0.868254π-0.868254\pi
0.806075 + 0.591813i 0.201588π0.201588\pi
104104 0 0
105105 −8.70181 0.211179i −0.849210 0.0206090i
106106 0 0
107107 7.93492 13.7437i 0.767097 1.32865i −0.172033 0.985091i 0.555034π-0.555034\pi
0.939131 0.343561i 0.111633π-0.111633\pi
108108 0 0
109109 1.63423 + 2.83056i 0.156531 + 0.271119i 0.933615 0.358277i 0.116636π-0.116636\pi
−0.777085 + 0.629396i 0.783302π0.783302\pi
110110 0 0
111111 15.6475 1.48519
112112 0 0
113113 −13.1598 −1.23797 −0.618984 0.785404i 0.712455π-0.712455\pi
−0.618984 + 0.785404i 0.712455π0.712455\pi
114114 0 0
115115 −0.266897 0.462279i −0.0248883 0.0431077i
116116 0 0
117117 −10.7817 + 18.6745i −0.996769 + 1.72645i
118118 0 0
119119 2.53379 + 4.64542i 0.232272 + 0.425845i
120120 0 0
121121 −11.4580 + 19.8458i −1.04163 + 1.80416i
122122 0 0
123123 −9.98101 17.2876i −0.899958 1.55877i
124124 0 0
125125 1.00000 0.0894427
126126 0 0
127127 −11.9159 −1.05737 −0.528684 0.848819i 0.677314π-0.677314\pi
−0.528684 + 0.848819i 0.677314π0.677314\pi
128128 0 0
129129 1.16802 + 2.02307i 0.102839 + 0.178122i
130130 0 0
131131 10.7817 18.6745i 0.942002 1.63160i 0.180356 0.983601i 0.442275π-0.442275\pi
0.761646 0.647994i 0.224392π-0.224392\pi
132132 0 0
133133 1.04203 1.70778i 0.0903558 0.148084i
134134 0 0
135135 −7.93492 + 13.7437i −0.682929 + 1.18287i
136136 0 0
137137 −2.00000 3.46410i −0.170872 0.295958i 0.767853 0.640626i 0.221325π-0.221325\pi
−0.938725 + 0.344668i 0.887992π0.887992\pi
138138 0 0
139139 −6.57989 −0.558099 −0.279049 0.960277i 0.590019π-0.590019\pi
−0.279049 + 0.960277i 0.590019π0.590019\pi
140140 0 0
141141 42.4118 3.57171
142142 0 0
143143 8.02555 + 13.9007i 0.671130 + 1.16243i
144144 0 0
145145 0.411869 0.713379i 0.0342039 0.0592429i
146146 0 0
147147 −10.5338 20.4793i −0.868813 1.68911i
148148 0 0
149149 −0.0543371 + 0.0941146i −0.00445147 + 0.00771017i −0.868243 0.496140i 0.834750π-0.834750\pi
0.863791 + 0.503850i 0.168084π0.168084\pi
150150 0 0
151151 −6.53379 11.3169i −0.531713 0.920953i −0.999315 0.0370142i 0.988215π-0.988215\pi
0.467602 0.883939i 0.345118π-0.345118\pi
152152 0 0
153153 15.6475 1.26502
154154 0 0
155155 2.57989 0.207222
156156 0 0
157157 −4.44566 7.70011i −0.354803 0.614536i 0.632282 0.774739i 0.282119π-0.282119\pi
−0.987084 + 0.160203i 0.948785π0.948785\pi
158158 0 0
159159 13.8237 23.9434i 1.09629 1.89884i
160160 0 0
161161 0.735608 1.20558i 0.0579740 0.0950132i
162162 0 0
163163 −5.75615 + 9.96995i −0.450857 + 0.780907i −0.998439 0.0558449i 0.982215π-0.982215\pi
0.547583 + 0.836751i 0.315548π0.315548\pi
164164 0 0
165165 9.57989 + 16.5929i 0.745793 + 1.29175i
166166 0 0
167167 −1.46621 −0.113458 −0.0567292 0.998390i 0.518067π-0.518067\pi
−0.0567292 + 0.998390i 0.518067π0.518067\pi
168168 0 0
169169 −5.40363 −0.415664
170170 0 0
171171 −2.95797 5.12335i −0.226201 0.391792i
172172 0 0
173173 5.62192 9.73746i 0.427427 0.740325i −0.569217 0.822188i 0.692753π-0.692753\pi
0.996644 + 0.0818623i 0.0260868π0.0260868\pi
174174 0 0
175175 1.26690 + 2.32271i 0.0957684 + 0.175580i
176176 0 0
177177 13.1598 22.7934i 0.989150 1.71326i
178178 0 0
179179 3.66802 + 6.35320i 0.274161 + 0.474860i 0.969923 0.243412i 0.0782666π-0.0782666\pi
−0.695762 + 0.718272i 0.744933π0.744933\pi
180180 0 0
181181 −18.4712 −1.37295 −0.686477 0.727151i 0.740844π-0.740844\pi
−0.686477 + 0.727151i 0.740844π0.740844\pi
182182 0 0
183183 30.9374 2.28696
184184 0 0
185185 −2.37808 4.11895i −0.174840 0.302831i
186186 0 0
187187 5.82374 10.0870i 0.425874 0.737635i
188188 0 0
189189 −41.9753 1.01867i −3.05325 0.0740975i
190190 0 0
191191 7.28995 12.6266i 0.527482 0.913625i −0.472005 0.881596i 0.656470π-0.656470\pi
0.999487 0.0320296i 0.0101971π-0.0101971\pi
192192 0 0
193193 9.40363 + 16.2876i 0.676888 + 1.17240i 0.975913 + 0.218159i 0.0700052π0.0700052\pi
−0.299025 + 0.954245i 0.596661π0.596661\pi
194194 0 0
195195 9.06759 0.649343
196196 0 0
197197 2.75615 0.196368 0.0981838 0.995168i 0.468697π-0.468697\pi
0.0981838 + 0.995168i 0.468697π0.468697\pi
198198 0 0
199199 7.51230 + 13.0117i 0.532533 + 0.922374i 0.999278 + 0.0379825i 0.0120931π0.0120931\pi
−0.466745 + 0.884392i 0.654574π0.654574\pi
200200 0 0
201201 19.5256 33.8192i 1.37723 2.38543i
202202 0 0
203203 2.17877 + 0.0528751i 0.152919 + 0.00371111i
204204 0 0
205205 −3.03379 + 5.25468i −0.211889 + 0.367003i
206206 0 0
207207 −2.08813 3.61675i −0.145135 0.251381i
208208 0 0
209209 −4.40363 −0.304605
210210 0 0
211211 21.9159 1.50875 0.754377 0.656441i 0.227939π-0.227939\pi
0.754377 + 0.656441i 0.227939π0.227939\pi
212212 0 0
213213 0 0
214214 0 0
215215 0.355027 0.614926i 0.0242127 0.0419376i
216216 0 0
217217 3.26845 + 5.99233i 0.221877 + 0.406786i
218218 0 0
219219 −5.77764 + 10.0072i −0.390417 + 0.676222i
220220 0 0
221221 −2.75615 4.77379i −0.185399 0.321120i
222222 0 0
223223 −18.8073 −1.25943 −0.629714 0.776827i 0.716828π-0.716828\pi
−0.629714 + 0.776827i 0.716828π0.716828\pi
224224 0 0
225225 7.82374 0.521583
226226 0 0
227227 8.33604 + 14.4384i 0.553283 + 0.958313i 0.998035 + 0.0626599i 0.0199583π0.0199583\pi
−0.444752 + 0.895654i 0.646708π0.646708\pi
228228 0 0
229229 −9.75615 + 16.8982i −0.644705 + 1.11666i 0.339665 + 0.940546i 0.389686π0.389686\pi
−0.984370 + 0.176115i 0.943647π0.943647\pi
230230 0 0
231231 −26.4036 + 43.2727i −1.73723 + 2.84714i
232232 0 0
233233 −9.00000 + 15.5885i −0.589610 + 1.02123i 0.404674 + 0.914461i 0.367385π0.367385\pi
−0.994283 + 0.106773i 0.965948π0.965948\pi
234234 0 0
235235 −6.44566 11.1642i −0.420469 0.728273i
236236 0 0
237237 31.2950 2.03283
238238 0 0
239239 16.0922 1.04092 0.520459 0.853887i 0.325761π-0.325761\pi
0.520459 + 0.853887i 0.325761π0.325761\pi
240240 0 0
241241 −0.445663 0.771911i −0.0287077 0.0497231i 0.851315 0.524655i 0.175806π-0.175806\pi
−0.880022 + 0.474932i 0.842473π0.842473\pi
242242 0 0
243243 −23.4712 + 40.6533i −1.50568 + 2.60791i
244244 0 0
245245 −3.78995 + 5.88526i −0.242131 + 0.375996i
246246 0 0
247247 −1.04203 + 1.80486i −0.0663030 + 0.114840i
248248 0 0
249249 −11.0379 19.1181i −0.699496 1.21156i
250250 0 0
251251 −17.4712 −1.10277 −0.551387 0.834250i 0.685901π-0.685901\pi
−0.551387 + 0.834250i 0.685901π0.685901\pi
252252 0 0
253253 −3.10867 −0.195441
254254 0 0
255255 −3.28995 5.69835i −0.206024 0.356845i
256256 0 0
257257 3.51230 6.08349i 0.219091 0.379478i −0.735439 0.677591i 0.763024π-0.763024\pi
0.954530 + 0.298113i 0.0963574π0.0963574\pi
258258 0 0
259259 6.55434 10.7419i 0.407267 0.667467i
260260 0 0
261261 3.22236 5.58129i 0.199459 0.345473i
262262 0 0
263263 8.88882 + 15.3959i 0.548108 + 0.949351i 0.998404 + 0.0564719i 0.0179851π0.0179851\pi
−0.450296 + 0.892879i 0.648682π0.648682\pi
264264 0 0
265265 −8.40363 −0.516231
266266 0 0
267267 5.77764 0.353586
268268 0 0
269269 4.70181 + 8.14378i 0.286675 + 0.496535i 0.973014 0.230746i 0.0741168π-0.0741168\pi
−0.686339 + 0.727282i 0.740783π0.740783\pi
270270 0 0
271271 3.51230 6.08349i 0.213357 0.369546i −0.739406 0.673260i 0.764894π-0.764894\pi
0.952763 + 0.303714i 0.0982269π0.0982269\pi
272272 0 0
273273 11.4877 + 21.0614i 0.695267 + 1.27469i
274274 0 0
275275 2.91187 5.04351i 0.175592 0.304135i
276276 0 0
277277 −13.5799 23.5211i −0.815937 1.41324i −0.908653 0.417551i 0.862889π-0.862889\pi
0.0927170 0.995693i 0.470445π-0.470445\pi
278278 0 0
279279 20.1844 1.20841
280280 0 0
281281 −0.620977 −0.0370444 −0.0185222 0.999828i 0.505896π-0.505896\pi
−0.0185222 + 0.999828i 0.505896π0.505896\pi
282282 0 0
283283 1.57989 + 2.73645i 0.0939147 + 0.162665i 0.909155 0.416458i 0.136729π-0.136729\pi
−0.815240 + 0.579123i 0.803395π0.803395\pi
284284 0 0
285285 −1.24385 + 2.15441i −0.0736792 + 0.127616i
286286 0 0
287287 −16.0486 0.389474i −0.947319 0.0229899i
288288 0 0
289289 6.50000 11.2583i 0.382353 0.662255i
290290 0 0
291291 3.28995 + 5.69835i 0.192860 + 0.334043i
292292 0 0
293293 11.2438 0.656873 0.328436 0.944526i 0.393478π-0.393478\pi
0.328436 + 0.944526i 0.393478π0.393478\pi
294294 0 0
295295 −8.00000 −0.465778
296296 0 0
297297 46.2109 + 80.0396i 2.68143 + 4.64437i
298298 0 0
299299 −0.735608 + 1.27411i −0.0425413 + 0.0736837i
300300 0 0
301301 1.87808 + 0.0455779i 0.108250 + 0.00262706i
302302 0 0
303303 −3.84272 + 6.65579i −0.220759 + 0.382365i
304304 0 0
305305 −4.70181 8.14378i −0.269225 0.466312i
306306 0 0
307307 −23.5173 −1.34220 −0.671102 0.741365i 0.734179π-0.734179\pi
−0.671102 + 0.741365i 0.734179π0.734179\pi
308308 0 0
309309 7.31144 0.415933
310310 0 0
311311 −14.5799 25.2531i −0.826750 1.43197i −0.900575 0.434701i 0.856854π-0.856854\pi
0.0738250 0.997271i 0.476479π-0.476479\pi
312312 0 0
313313 12.0922 20.9443i 0.683491 1.18384i −0.290417 0.956900i 0.593794π-0.593794\pi
0.973908 0.226941i 0.0728726π-0.0728726\pi
314314 0 0
315315 9.91187 + 18.1723i 0.558471 + 1.02389i
316316 0 0
317317 −6.06759 + 10.5094i −0.340790 + 0.590265i −0.984580 0.174937i 0.944028π-0.944028\pi
0.643790 + 0.765202i 0.277361π0.277361\pi
318318 0 0
319319 −2.39862 4.15453i −0.134297 0.232609i
320320 0 0
321321 −52.2109 −2.91413
322322 0 0
323323 1.51230 0.0841468
324324 0 0
325325 −1.37808 2.38690i −0.0764419 0.132401i
326326 0 0
327327 5.37652 9.31240i 0.297322 0.514977i
328328 0 0
329329 17.7652 29.1153i 0.979428 1.60518i
330330 0 0
331331 −0.911869 + 1.57940i −0.0501209 + 0.0868119i −0.889997 0.455966i 0.849294π-0.849294\pi
0.839877 + 0.542778i 0.182627π0.182627\pi
332332 0 0
333333 −18.6054 32.2256i −1.01957 1.76595i
334334 0 0
335335 −11.8698 −0.648518
336336 0 0
337337 −17.7827 −0.968683 −0.484341 0.874879i 0.660941π-0.660941\pi
−0.484341 + 0.874879i 0.660941π0.660941\pi
338338 0 0
339339 21.6475 + 37.4945i 1.17573 + 2.03642i
340340 0 0
341341 7.51230 13.0117i 0.406814 0.704623i
342342 0 0
343343 −18.4712 1.34692i −0.997352 0.0727266i
344344 0 0
345345 −0.878076 + 1.52087i −0.0472740 + 0.0818810i
346346 0 0
347347 −0.644973 1.11713i −0.0346239 0.0599704i 0.848194 0.529685i 0.177690π-0.177690\pi
−0.882818 + 0.469715i 0.844357π0.844357\pi
348348 0 0
349349 1.31144 0.0701995 0.0350998 0.999384i 0.488825π-0.488825\pi
0.0350998 + 0.999384i 0.488825π0.488825\pi
350350 0 0
351351 43.7397 2.33465
352352 0 0
353353 5.51230 + 9.54759i 0.293390 + 0.508167i 0.974609 0.223913i 0.0718831π-0.0718831\pi
−0.681219 + 0.732080i 0.738550π0.738550\pi
354354 0 0
355355 0 0
356356 0 0
357357 9.06759 14.8608i 0.479908 0.786517i
358358 0 0
359359 5.11368 8.85716i 0.269890 0.467463i −0.698943 0.715177i 0.746346π-0.746346\pi
0.968833 + 0.247714i 0.0796794π0.0796794\pi
360360 0 0
361361 9.21412 + 15.9593i 0.484954 + 0.839964i
362362 0 0
363363 75.3922 3.95706
364364 0 0
365365 3.51230 0.183842
366366 0 0
367367 8.67053 + 15.0178i 0.452598 + 0.783922i 0.998547 0.0538962i 0.0171640π-0.0171640\pi
−0.545949 + 0.837819i 0.683831π0.683831\pi
368368 0 0
369369 −23.7356 + 41.1113i −1.23563 + 2.14017i
370370 0 0
371371 −10.6465 19.5192i −0.552740 1.01339i
372372 0 0
373373 8.89133 15.4002i 0.460375 0.797394i −0.538604 0.842559i 0.681048π-0.681048\pi
0.998980 + 0.0451654i 0.0143815π0.0143815\pi
374374 0 0
375375 −1.64497 2.84918i −0.0849460 0.147131i
376376 0 0
377377 −2.27035 −0.116929
378378 0 0
379379 33.2109 1.70593 0.852964 0.521969i 0.174802π-0.174802\pi
0.852964 + 0.521969i 0.174802π0.174802\pi
380380 0 0
381381 19.6014 + 33.9506i 1.00421 + 1.73934i
382382 0 0
383383 7.38058 12.7835i 0.377130 0.653208i −0.613513 0.789684i 0.710244π-0.710244\pi
0.990643 + 0.136476i 0.0435776π0.0435776\pi
384384 0 0
385385 15.4036 + 0.373821i 0.785042 + 0.0190517i
386386 0 0
387387 2.77764 4.81102i 0.141195 0.244558i
388388 0 0
389389 11.4036 + 19.7517i 0.578187 + 1.00145i 0.995687 + 0.0927724i 0.0295729π0.0295729\pi
−0.417500 + 0.908677i 0.637094π0.637094\pi
390390 0 0
391391 1.06759 0.0539902
392392 0 0
393393 −70.9424 −3.57857
394394 0 0
395395 −4.75615 8.23790i −0.239308 0.414494i
396396 0 0
397397 7.13517 12.3585i 0.358104 0.620255i −0.629540 0.776968i 0.716757π-0.716757\pi
0.987644 + 0.156714i 0.0500899π0.0500899\pi
398398 0 0
399399 −6.57989 0.159683i −0.329407 0.00799416i
400400 0 0
401401 5.74385 9.94864i 0.286834 0.496811i −0.686218 0.727396i 0.740730π-0.740730\pi
0.973052 + 0.230585i 0.0740638π0.0740638\pi
402402 0 0
403403 −3.55528 6.15793i −0.177101 0.306748i
404404 0 0
405405 28.7397 1.42809
406406 0 0
407407 −27.6986 −1.37297
408408 0 0
409409 −0.899566 1.55809i −0.0444807 0.0770428i 0.842928 0.538027i 0.180830π-0.180830\pi
−0.887409 + 0.460984i 0.847497π0.847497\pi
410410 0 0
411411 −6.57989 + 11.3967i −0.324562 + 0.562158i
412412 0 0
413413 −10.1352 18.5817i −0.498719 0.914344i
414414 0 0
415415 −3.35503 + 5.81108i −0.164692 + 0.285255i
416416 0 0
417417 10.8237 + 18.7473i 0.530041 + 0.918058i
418418 0 0
419419 −27.4282 −1.33996 −0.669978 0.742381i 0.733697π-0.733697\pi
−0.669978 + 0.742381i 0.733697π0.733697\pi
420420 0 0
421421 2.91593 0.142114 0.0710569 0.997472i 0.477363π-0.477363\pi
0.0710569 + 0.997472i 0.477363π0.477363\pi
422422 0 0
423423 −50.4292 87.3459i −2.45195 4.24690i
424424 0 0
425425 −1.00000 + 1.73205i −0.0485071 + 0.0840168i
426426 0 0
427427 12.9589 21.2383i 0.627126 1.02779i
428428 0 0
429429 26.4036 45.7324i 1.27478 2.20798i
430430 0 0
431431 7.28995 + 12.6266i 0.351144 + 0.608200i 0.986450 0.164061i 0.0524593π-0.0524593\pi
−0.635306 + 0.772261i 0.719126π0.719126\pi
432432 0 0
433433 21.1598 1.01687 0.508437 0.861099i 0.330223π-0.330223\pi
0.508437 + 0.861099i 0.330223π0.330223\pi
434434 0 0
435435 −2.71005 −0.129937
436436 0 0
437437 −0.201814 0.349553i −0.00965409 0.0167214i
438438 0 0
439439 −15.4712 + 26.7969i −0.738401 + 1.27895i 0.214814 + 0.976655i 0.431085π0.431085\pi
−0.953215 + 0.302293i 0.902248π0.902248\pi
440440 0 0
441441 −29.6515 + 46.0448i −1.41198 + 2.19261i
442442 0 0
443443 18.7587 32.4909i 0.891251 1.54369i 0.0528732 0.998601i 0.483162π-0.483162\pi
0.838377 0.545090i 0.183505π-0.183505\pi
444444 0 0
445445 −0.878076 1.52087i −0.0416248 0.0720962i
446446 0 0
447447 0.357532 0.0169107
448448 0 0
449449 31.0922 1.46733 0.733666 0.679511i 0.237808π-0.237808\pi
0.733666 + 0.679511i 0.237808π0.237808\pi
450450 0 0
451451 17.6680 + 30.6019i 0.831955 + 1.44099i
452452 0 0
453453 −21.4958 + 37.2319i −1.00996 + 1.74931i
454454 0 0
455455 3.79819 6.22482i 0.178062 0.291824i
456456 0 0
457457 2.17626 3.76940i 0.101801 0.176325i −0.810626 0.585565i 0.800873π-0.800873\pi
0.912427 + 0.409240i 0.134206π0.134206\pi
458458 0 0
459459 −15.8698 27.4874i −0.740740 1.28300i
460460 0 0
461461 37.2950 1.73700 0.868500 0.495690i 0.165085π-0.165085\pi
0.868500 + 0.495690i 0.165085π0.165085\pi
462462 0 0
463463 9.81873 0.456315 0.228158 0.973624i 0.426730π-0.426730\pi
0.228158 + 0.973624i 0.426730π0.426730\pi
464464 0 0
465465 −4.24385 7.35056i −0.196804 0.340874i
466466 0 0
467467 −11.4011 + 19.7473i −0.527581 + 0.913797i 0.471902 + 0.881651i 0.343568π0.343568\pi
−0.999483 + 0.0321463i 0.989766π0.989766\pi
468468 0 0
469469 −15.0379 27.5702i −0.694384 1.27307i
470470 0 0
471471 −14.6260 + 25.3330i −0.673930 + 1.16728i
472472 0 0
473473 −2.06759 3.58117i −0.0950678 0.164662i
474474 0 0
475475 0.756152 0.0346946
476476 0 0
477477 −65.7478 −3.01038
478478 0 0
479479 −10.2224 17.7056i −0.467071 0.808991i 0.532221 0.846606i 0.321358π-0.321358\pi
−0.999292 + 0.0376140i 0.988024π0.988024\pi
480480 0 0
481481 −6.55434 + 11.3524i −0.298852 + 0.517627i
482482 0 0
483483 −4.64497 0.112726i −0.211354 0.00512921i
484484 0 0
485485 1.00000 1.73205i 0.0454077 0.0786484i
486486 0 0
487487 −21.4036 37.0722i −0.969891 1.67990i −0.695857 0.718181i 0.744975π-0.744975\pi
−0.274034 0.961720i 0.588358π-0.588358\pi
488488 0 0
489489 37.8748 1.71276
490490 0 0
491491 18.8502 0.850699 0.425350 0.905029i 0.360151π-0.360151\pi
0.425350 + 0.905029i 0.360151π0.360151\pi
492492 0 0
493493 0.823739 + 1.42676i 0.0370993 + 0.0642579i
494494 0 0
495495 22.7817 39.4591i 1.02396 1.77355i
496496 0 0
497497 0 0
498498 0 0
499499 13.8698 24.0233i 0.620899 1.07543i −0.368420 0.929660i 0.620101π-0.620101\pi
0.989319 0.145769i 0.0465657π-0.0465657\pi
500500 0 0
501501 2.41187 + 4.17748i 0.107754 + 0.186636i
502502 0 0
503503 −14.7101 −0.655889 −0.327944 0.944697i 0.606356π-0.606356\pi
−0.327944 + 0.944697i 0.606356π0.606356\pi
504504 0 0
505505 2.33604 0.103952
506506 0 0
507507 8.88882 + 15.3959i 0.394766 + 0.683755i
508508 0 0
509509 6.99176 12.1101i 0.309904 0.536770i −0.668437 0.743769i 0.733036π-0.733036\pi
0.978341 + 0.206999i 0.0663697π0.0663697\pi
510510 0 0
511511 4.44973 + 8.15805i 0.196844 + 0.360891i
512512 0 0
513513 −6.00000 + 10.3923i −0.264906 + 0.458831i
514514 0 0
515515 −1.11118 1.92462i −0.0489644 0.0848088i
516516 0 0
517517 −75.0757 −3.30183
518518 0 0
519519 −36.9916 −1.62375
520520 0 0
521521 −10.3616 17.9468i −0.453950 0.786264i 0.544677 0.838646i 0.316652π-0.316652\pi
−0.998627 + 0.0523817i 0.983319π0.983319\pi
522522 0 0
523523 −11.1763 + 19.3579i −0.488704 + 0.846460i −0.999916 0.0129950i 0.995863π-0.995863\pi
0.511212 + 0.859455i 0.329197π0.329197\pi
524524 0 0
525525 4.53379 7.43040i 0.197871 0.324289i
526526 0 0
527527 −2.57989 + 4.46850i −0.112382 + 0.194651i
528528 0 0
529529 11.3575 + 19.6718i 0.493806 + 0.855297i
530530 0 0
531531 −62.5899 −2.71617
532532 0 0
533533 16.7232 0.724362
534534 0 0
535535 7.93492 + 13.7437i 0.343056 + 0.594191i
536536 0 0
537537 12.0676 20.9017i 0.520755 0.901974i
538538 0 0
539539 18.6465 + 36.2517i 0.803163 + 1.56147i
540540 0 0
541541 −16.3278 + 28.2806i −0.701987 + 1.21588i 0.265781 + 0.964033i 0.414370π0.414370\pi
−0.967768 + 0.251844i 0.918963π0.918963\pi
542542 0 0
543543 30.3846 + 52.6277i 1.30393 + 2.25847i
544544 0 0
545545 −3.26845 −0.140005
546546 0 0
547547 −31.1648 −1.33251 −0.666255 0.745724i 0.732104π-0.732104\pi
−0.666255 + 0.745724i 0.732104π0.732104\pi
548548 0 0
549549 −36.7858 63.7148i −1.56998 2.71928i
550550 0 0
551551 0.311436 0.539422i 0.0132676 0.0229802i
552552 0 0
553553 13.1087 21.4837i 0.557438 0.913581i
554554 0 0
555555 −7.82374 + 13.5511i −0.332099 + 0.575213i
556556 0 0
557557 22.3616 + 38.7314i 0.947491 + 1.64110i 0.750685 + 0.660660i 0.229724π0.229724\pi
0.196806 + 0.980442i 0.436943π0.436943\pi
558558 0 0
559559 −1.95702 −0.0827731
560560 0 0
561561 −38.3196 −1.61785
562562 0 0
563563 −16.2464 28.1395i −0.684702 1.18594i −0.973530 0.228558i 0.926599π-0.926599\pi
0.288828 0.957381i 0.406734π-0.406734\pi
564564 0 0
565565 6.57989 11.3967i 0.276818 0.479463i
566566 0 0
567567 36.4102 + 66.7539i 1.52908 + 2.80340i
568568 0 0
569569 −17.3370 + 30.0285i −0.726804 + 1.25886i 0.231423 + 0.972853i 0.425662π0.425662\pi
−0.958227 + 0.286009i 0.907671π0.907671\pi
570570 0 0
571571 1.55528 + 2.69383i 0.0650866 + 0.112733i 0.896732 0.442573i 0.145934π-0.145934\pi
−0.831646 + 0.555306i 0.812601π0.812601\pi
572572 0 0
573573 −47.9670 −2.00385
574574 0 0
575575 0.533794 0.0222607
576576 0 0
577577 −0.336042 0.582041i −0.0139896 0.0242307i 0.858946 0.512066i 0.171120π-0.171120\pi
−0.872935 + 0.487836i 0.837787π0.837787\pi
578578 0 0
579579 30.9374 53.5852i 1.28572 2.22692i
580580 0 0
581581 −17.7479 0.430713i −0.736307 0.0178690i
582582 0 0
583583 −24.4703 + 42.3837i −1.01345 + 1.75536i
584584 0 0
585585 −10.7817 18.6745i −0.445769 0.772094i
586586 0 0
587587 4.67208 0.192838 0.0964188 0.995341i 0.469261π-0.469261\pi
0.0964188 + 0.995341i 0.469261π0.469261\pi
588588 0 0
589589 1.95079 0.0803808
590590 0 0
591591 −4.53379 7.85276i −0.186495 0.323019i
592592 0 0
593593 −10.0922 + 17.4802i −0.414437 + 0.717825i −0.995369 0.0961264i 0.969355π-0.969355\pi
0.580932 + 0.813952i 0.302688π0.302688\pi
594594 0 0
595595 −5.28995 0.128378i −0.216867 0.00526300i
596596 0 0
597597 24.7151 42.8077i 1.01152 1.75200i
598598 0 0
599599 10.7562 + 18.6302i 0.439484 + 0.761209i 0.997650 0.0685204i 0.0218278π-0.0218278\pi
−0.558165 + 0.829730i 0.688494π0.688494\pi
600600 0 0
601601 5.29495 0.215986 0.107993 0.994152i 0.465558π-0.465558\pi
0.107993 + 0.994152i 0.465558π0.465558\pi
602602 0 0
603603 −92.8665 −3.78182
604604 0 0
605605 −11.4580 19.8458i −0.465833 0.806846i
606606 0 0
607607 18.3591 31.7989i 0.745172 1.29068i −0.204942 0.978774i 0.565700π-0.565700\pi
0.950114 0.311902i 0.100966π-0.100966\pi
608608 0 0
609609 −3.43336 6.29467i −0.139127 0.255073i
610610 0 0
611611 −17.7652 + 30.7703i −0.718704 + 1.24483i
612612 0 0
613613 −20.3616 35.2673i −0.822397 1.42443i −0.903892 0.427760i 0.859303π-0.859303\pi
0.0814954 0.996674i 0.474030π-0.474030\pi
614614 0 0
615615 19.9620 0.804947
616616 0 0
617617 16.8073 0.676635 0.338317 0.941032i 0.390142π-0.390142\pi
0.338317 + 0.941032i 0.390142π0.390142\pi
618618 0 0
619619 −17.8954 30.9957i −0.719276 1.24582i −0.961287 0.275550i 0.911140π-0.911140\pi
0.242010 0.970274i 0.422193π-0.422193\pi
620620 0 0
621621 −4.23561 + 7.33629i −0.169969 + 0.294395i
622622 0 0
623623 2.42011 3.96630i 0.0969597 0.158907i
624624 0 0
625625 −0.500000 + 0.866025i −0.0200000 + 0.0346410i
626626 0 0
627627 7.24385 + 12.5467i 0.289291 + 0.501067i
628628 0 0
629629 9.51230 0.379280
630630 0 0
631631 32.4447 1.29160 0.645802 0.763505i 0.276523π-0.276523\pi
0.645802 + 0.763505i 0.276523π0.276523\pi
632632 0 0
633633 −36.0511 62.4423i −1.43290 2.48186i
634634 0 0
635635 5.95797 10.3195i 0.236435 0.409517i
636636 0 0
637637 19.2703 + 0.935872i 0.763519 + 0.0370806i
638638 0 0
639639 0 0
640640 0 0
641641 −8.45390 14.6426i −0.333909 0.578348i 0.649366 0.760476i 0.275035π-0.275035\pi
−0.983275 + 0.182129i 0.941701π0.941701\pi
642642 0 0
643643 −0.135174 −0.00533075 −0.00266538 0.999996i 0.500848π-0.500848\pi
−0.00266538 + 0.999996i 0.500848π0.500848\pi
644644 0 0
645645 −2.33604 −0.0919816
646646 0 0
647647 −2.04454 3.54125i −0.0803791 0.139221i 0.823034 0.567993i 0.192280π-0.192280\pi
−0.903413 + 0.428772i 0.858946π0.858946\pi
648648 0 0
649649 −23.2950 + 40.3480i −0.914407 + 1.58380i
650650 0 0
651651 11.6967 19.1696i 0.458429 0.751317i
652652 0 0
653653 −15.9580 + 27.6400i −0.624483 + 1.08164i 0.364157 + 0.931338i 0.381357π0.381357\pi
−0.988641 + 0.150300i 0.951976π0.951976\pi
654654 0 0
655655 10.7817 + 18.6745i 0.421276 + 0.729672i
656656 0 0
657657 27.4793 1.07207
658658 0 0
659659 −4.70505 −0.183283 −0.0916413 0.995792i 0.529211π-0.529211\pi
−0.0916413 + 0.995792i 0.529211π0.529211\pi
660660 0 0
661661 −2.25710 3.90941i −0.0877910 0.152058i 0.818786 0.574099i 0.194647π-0.194647\pi
−0.906577 + 0.422040i 0.861314π0.861314\pi
662662 0 0
663663 −9.06759 + 15.7055i −0.352156 + 0.609952i
664664 0 0
665665 0.957966 + 1.75632i 0.0371483 + 0.0681071i
666666 0 0
667667 0.219853 0.380797i 0.00851275 0.0147445i
668668 0 0
669669 30.9374 + 53.5852i 1.19611 + 2.07172i
670670 0 0
671671 −54.7643 −2.11415
672672 0 0
673673 46.9424 1.80950 0.904749 0.425945i 0.140058π-0.140058\pi
0.904749 + 0.425945i 0.140058π0.140058\pi
674674 0 0
675675 −7.93492 13.7437i −0.305415 0.528995i
676676 0 0
677677 5.20181 9.00981i 0.199922 0.346275i −0.748581 0.663043i 0.769264π-0.769264\pi
0.948503 + 0.316768i 0.102598π0.102598\pi
678678 0 0
679679 5.28995 + 0.128378i 0.203009 + 0.00492671i
680680 0 0
681681 27.4251 47.5017i 1.05093 1.82027i
682682 0 0
683683 2.53129 + 4.38432i 0.0968571 + 0.167761i 0.910382 0.413768i 0.135788π-0.135788\pi
−0.813525 + 0.581530i 0.802454π0.802454\pi
684684 0 0
685685 4.00000 0.152832
686686 0 0
687687 64.1944 2.44917
688688 0 0
689689 11.5808 + 20.0586i 0.441195 + 0.764172i
690690 0 0
691691 −2.22236 + 3.84924i −0.0845425 + 0.146432i −0.905196 0.424994i 0.860276π-0.860276\pi
0.820654 + 0.571426i 0.193610π0.193610\pi
692692 0 0
693693 120.514 + 2.92468i 4.57795 + 0.111099i
694694 0 0
695695 3.28995 5.69835i 0.124795 0.216151i
696696 0 0
697697 −6.06759 10.5094i −0.229826 0.398071i
698698 0 0
699699 59.2190 2.23987
700700 0 0
701701 21.7562 0.821719 0.410859 0.911699i 0.365229π-0.365229\pi
0.410859 + 0.911699i 0.365229π0.365229\pi
702702 0 0
703703 −1.79819 3.11455i −0.0678199 0.117467i
704704 0 0
705705 −21.2059 + 36.7297i −0.798660 + 1.38332i
706706 0 0
707707 2.95952 + 5.42594i 0.111304 + 0.204064i
708708 0 0
709709 20.5041 35.5141i 0.770046 1.33376i −0.167491 0.985874i 0.553566π-0.553566\pi
0.937537 0.347886i 0.113100π-0.113100\pi
710710 0 0
711711 −37.2109 64.4511i −1.39552 2.41711i
712712 0 0
713713 1.37713 0.0515739
714714 0 0
715715 −16.0511 −0.600277
716716 0 0
717717 −26.4712 45.8495i −0.988586 1.71228i
718718 0 0
719719 11.8698 20.5592i 0.442670 0.766727i −0.555216 0.831706i 0.687365π-0.687365\pi
0.997887 + 0.0649787i 0.0206979π0.0206979\pi
720720 0 0
721721 3.06258 5.01924i 0.114056 0.186926i
722722 0 0
723723 −1.46621 + 2.53954i −0.0545288 + 0.0944467i
724724 0 0
725725 0.411869 + 0.713379i 0.0152964 + 0.0264942i
726726 0 0
727727 28.8534 1.07011 0.535056 0.844817i 0.320291π-0.320291\pi
0.535056 + 0.844817i 0.320291π0.320291\pi
728728 0 0
729729 68.2190 2.52663
730730 0 0
731731 0.710055 + 1.22985i 0.0262623 + 0.0454877i
732732 0 0
733733 −23.4292 + 40.5805i −0.865377 + 1.49888i 0.00129620 + 0.999999i 0.499587π0.499587\pi
−0.866673 + 0.498877i 0.833746π0.833746\pi
734734 0 0
735735 23.0025 + 1.11713i 0.848460 + 0.0412058i
736736 0 0
737737 −34.5634 + 59.8656i −1.27316 + 2.20518i
738738 0 0
739739 8.07165 + 13.9805i 0.296920 + 0.514281i 0.975430 0.220310i 0.0707071π-0.0707071\pi
−0.678509 + 0.734592i 0.737374π0.737374\pi
740740 0 0
741741 6.85647 0.251879
742742 0 0
743743 16.2243 0.595210 0.297605 0.954689i 0.403812π-0.403812\pi
0.297605 + 0.954689i 0.403812π0.403812\pi
744744 0 0
745745 −0.0543371 0.0941146i −0.00199076 0.00344809i
746746 0 0
747747 −26.2489 + 45.4644i −0.960395 + 1.66345i
748748 0 0
749749 −21.8698 + 35.8423i −0.799106 + 1.30965i
750750 0 0
751751 10.7562 18.6302i 0.392498 0.679826i −0.600281 0.799789i 0.704944π-0.704944\pi
0.992778 + 0.119964i 0.0382778π0.0382778\pi
752752 0 0
753753 28.7397 + 49.7786i 1.04733 + 1.81403i
754754 0 0
755755 13.0676 0.475578
756756 0 0
757757 0.840220 0.0305383 0.0152692 0.999883i 0.495139π-0.495139\pi
0.0152692 + 0.999883i 0.495139π0.495139\pi
758758 0 0
759759 5.11368 + 8.85716i 0.185615 + 0.321495i
760760 0 0
761761 14.4457 25.0206i 0.523655 0.906997i −0.475966 0.879464i 0.657901π-0.657901\pi
0.999621 0.0275332i 0.00876519π-0.00876519\pi
762762 0 0
763763 −4.14079 7.59167i −0.149907 0.274837i
764764 0 0
765765 −7.82374 + 13.5511i −0.282868 + 0.489942i
766766 0 0
767767 11.0246 + 19.0952i 0.398075 + 0.689487i
768768 0 0
769769 −27.3790 −0.987313 −0.493656 0.869657i 0.664340π-0.664340\pi
−0.493656 + 0.869657i 0.664340π0.664340\pi
770770 0 0
771771 −23.1106 −0.832307
772772 0 0
773773 19.1177 + 33.1129i 0.687618 + 1.19099i 0.972607 + 0.232458i 0.0746767π0.0746767\pi
−0.284989 + 0.958531i 0.591990π0.591990\pi
774774 0 0
775775 −1.28995 + 2.23425i −0.0463362 + 0.0802566i
776776 0 0
777777 −41.3871 1.00440i −1.48476 0.0360326i
778778 0 0
779779 −2.29401 + 3.97334i −0.0821914 + 0.142360i
780780 0 0
781781 0 0
782782 0 0
783783 −13.0726 −0.467176
784784 0 0
785785 8.89133 0.317345
786786 0 0
787787 3.66646 + 6.35050i 0.130695 + 0.226371i 0.923945 0.382526i 0.124946π-0.124946\pi
−0.793249 + 0.608897i 0.791612π0.791612\pi
788788 0 0
789789 29.2437 50.6516i 1.04110 1.80325i
790790 0 0
791791 34.8073 + 0.844716i 1.23760 + 0.0300346i
792792 0 0
793793 −12.9589 + 22.4455i −0.460184 + 0.797063i
794794 0 0
795795 13.8237 + 23.9434i 0.490277 + 0.849186i
796796 0 0
797797 14.4877 0.513181 0.256590 0.966520i 0.417401π-0.417401\pi
0.256590 + 0.966520i 0.417401π0.417401\pi
798798 0 0
799799 25.7827 0.912125
800800 0 0
801801 −6.86984 11.8989i −0.242734 0.420427i
802802 0 0
803803 10.2274 17.7143i 0.360916 0.625125i
804804 0 0
805805 0.676261 + 1.23985i 0.0238351 + 0.0436989i
806806 0 0
807807 15.4687 26.7926i 0.544524 0.943144i
808808 0 0
809809 5.67626 + 9.83157i 0.199567 + 0.345660i 0.948388 0.317112i 0.102713π-0.102713\pi
−0.748821 + 0.662772i 0.769380π0.769380\pi
810810 0 0
811811 28.7662 1.01012 0.505058 0.863085i 0.331471π-0.331471\pi
0.505058 + 0.863085i 0.331471π0.331471\pi
812812 0 0
813813 −23.1106 −0.810523
814814 0 0
815815 −5.75615 9.96995i −0.201629 0.349232i
816816 0 0
817817 0.268455 0.464977i 0.00939204 0.0162675i
818818 0 0
819819 29.7160 48.7014i 1.03836 1.70176i
820820 0 0
821821 8.02461 13.8990i 0.280061 0.485079i −0.691339 0.722531i 0.742979π-0.742979\pi
0.971399 + 0.237451i 0.0763121π0.0763121\pi
822822 0 0
823823 7.00250 + 12.1287i 0.244092 + 0.422780i 0.961876 0.273486i 0.0881768π-0.0881768\pi
−0.717784 + 0.696266i 0.754843π0.754843\pi
824824 0 0
825825 −19.1598 −0.667058
826826 0 0
827827 −15.2899 −0.531683 −0.265842 0.964017i 0.585650π-0.585650\pi
−0.265842 + 0.964017i 0.585650π0.585650\pi
828828 0 0
829829 10.6475 + 18.4420i 0.369802 + 0.640516i 0.989534 0.144297i 0.0460921π-0.0460921\pi
−0.619732 + 0.784813i 0.712759π0.712759\pi
830830 0 0
831831 −44.6771 + 77.3830i −1.54983 + 2.68439i
832832 0 0
833833 −6.40363 12.4496i −0.221873 0.431354i
834834 0 0
835835 0.733103 1.26977i 0.0253701 0.0439423i
836836 0 0
837837 −20.4712 35.4572i −0.707589 1.22558i
838838 0 0
839839 −42.2274 −1.45785 −0.728925 0.684593i 0.759980π-0.759980\pi
−0.728925 + 0.684593i 0.759980π0.759980\pi
840840 0 0
841841 −28.3215 −0.976602
842842 0 0
843843 1.02149 + 1.76927i 0.0351820 + 0.0609370i
844844 0 0
845845 2.70181 4.67968i 0.0929452 0.160986i
846846 0 0
847847 31.5799 51.7561i 1.08510 1.77836i
848848 0 0
849849 5.19775 9.00277i 0.178386 0.308974i
850850 0 0
851851 −1.26940 2.19867i −0.0435145 0.0753694i
852852 0 0
853853 −13.2931 −0.455146 −0.227573 0.973761i 0.573079π-0.573079\pi
−0.227573 + 0.973761i 0.573079π0.573079\pi
854854 0 0
855855 5.91593 0.202321
856856 0 0
857857 −19.2274 33.3028i −0.656794 1.13760i −0.981441 0.191766i 0.938579π-0.938579\pi
0.324646 0.945835i 0.394755π-0.394755\pi
858858 0 0
859859 4.00000 6.92820i 0.136478 0.236387i −0.789683 0.613515i 0.789755π-0.789755\pi
0.926161 + 0.377128i 0.123088π0.123088\pi
860860 0 0
861861 25.2898 + 46.3660i 0.861875 + 1.58015i
862862 0 0
863863 −23.5404 + 40.7731i −0.801323 + 1.38793i 0.117422 + 0.993082i 0.462537π0.462537\pi
−0.918745 + 0.394850i 0.870796π0.870796\pi
864864 0 0
865865 5.62192 + 9.73746i 0.191151 + 0.331084i
866866 0 0
867867 −42.7693 −1.45252
868868 0 0
869869 −55.3972 −1.87922
870870 0 0
871871 16.3575 + 28.3321i 0.554254 + 0.959996i
872872 0 0
873873 7.82374 13.5511i 0.264793 0.458636i
874874 0 0
875875 −2.64497 0.0641892i −0.0894164 0.00216999i
876876 0 0
877877 2.28588 3.95926i 0.0771888 0.133695i −0.824847 0.565356i 0.808739π-0.808739\pi
0.902036 + 0.431661i 0.142072π0.142072\pi
878878 0 0
879879 −18.4958 32.0357i −0.623849 1.08054i
880880 0 0
881881 −14.2849 −0.481272 −0.240636 0.970615i 0.577356π-0.577356\pi
−0.240636 + 0.970615i 0.577356π0.577356\pi
882882 0 0
883883 15.9670 0.537334 0.268667 0.963233i 0.413417π-0.413417\pi
0.268667 + 0.963233i 0.413417π0.413417\pi
884884 0 0
885885 13.1598 + 22.7934i 0.442361 + 0.766192i
886886 0 0
887887 −3.58239 + 6.20489i −0.120285 + 0.208340i −0.919880 0.392200i 0.871714π-0.871714\pi
0.799595 + 0.600540i 0.205048π0.205048\pi
888888 0 0
889889 31.5173 + 0.764874i 1.05706 + 0.0256531i
890890 0 0
891891 83.6862 144.949i 2.80359 4.85596i
892892 0 0
893893 −4.87390 8.44184i −0.163099 0.282495i
894894 0 0
895895 −7.33604 −0.245217
896896 0 0
897897 4.84022 0.161610
898898 0 0
899899 1.06258 + 1.84044i 0.0354389 + 0.0613821i
900900 0 0
901901 8.40363 14.5555i 0.279965 0.484914i
902902 0 0
903903 −2.95952 5.42594i −0.0984868 0.180564i
904904 0 0
905905 9.23561 15.9965i 0.307002 0.531743i
906906 0 0
907907 4.13267 + 7.15799i 0.137223 + 0.237677i 0.926444 0.376431i 0.122849π-0.122849\pi
−0.789221 + 0.614109i 0.789516π0.789516\pi
908908 0 0
909909 18.2766 0.606196
910910 0 0
911911 −26.2274 −0.868951 −0.434476 0.900684i 0.643066π-0.643066\pi
−0.434476 + 0.900684i 0.643066π0.643066\pi
912912 0 0
913913 19.5388 + 33.8422i 0.646640 + 1.12001i
914914 0 0
915915 −15.4687 + 26.7926i −0.511380 + 0.885736i
916916 0 0
917917 −29.7160 + 48.7014i −0.981309 + 1.60826i
918918 0 0
919919 −9.37902 + 16.2449i −0.309385 + 0.535871i −0.978228 0.207533i 0.933457π-0.933457\pi
0.668843 + 0.743404i 0.266790π0.266790\pi
920920 0 0
921921 38.6853 + 67.0050i 1.27473 + 2.20789i
922922 0 0
923923 0 0
924924 0 0
925925 4.75615 0.156381
926926 0 0
927927 −8.69357 15.0577i −0.285534 0.494560i
928928 0 0
929929 6.45390 11.1785i 0.211746 0.366754i −0.740515 0.672040i 0.765418π-0.765418\pi
0.952261 + 0.305285i 0.0987518π0.0987518\pi
930930 0 0
931931 −2.86577 + 4.45015i −0.0939219 + 0.145848i
932932 0 0
933933 −47.9670 + 83.0813i −1.57037 + 2.71996i
934934 0 0
935935 5.82374 + 10.0870i 0.190457 + 0.329881i
936936 0 0
937937 1.78265 0.0582367 0.0291183 0.999576i 0.490730π-0.490730\pi
0.0291183 + 0.999576i 0.490730π0.490730\pi
938938 0 0
939939 −79.5653 −2.59652
940940 0 0
941941 22.5634 + 39.0810i 0.735546 + 1.27400i 0.954483 + 0.298264i 0.0964077π0.0964077\pi
−0.218937 + 0.975739i 0.570259π0.570259\pi
942942 0 0
943943 −1.61942 + 2.80492i −0.0527356 + 0.0913407i
944944 0 0
945945 21.8698 35.8423i 0.711426 1.16595i
946946 0 0
947947 11.0436 19.1281i 0.358869 0.621579i −0.628904 0.777483i 0.716496π-0.716496\pi
0.987772 + 0.155905i 0.0498293π0.0498293\pi
948948 0 0
949949 −4.84022 8.38351i −0.157120 0.272140i
950950 0 0
951951 39.9241 1.29463
952952 0 0
953953 −45.3442 −1.46884 −0.734421 0.678694i 0.762546π-0.762546\pi
−0.734421 + 0.678694i 0.762546π0.762546\pi
954954 0 0
955955 7.28995 + 12.6266i 0.235897 + 0.408586i
956956 0 0
957957 −7.89133 + 13.6682i −0.255090 + 0.441829i
958958 0 0
959959 5.06759 + 9.29083i 0.163641 + 0.300017i
960960 0 0
961961 12.1721 21.0827i 0.392648 0.680086i
962962 0 0
963963 62.0807 + 107.527i 2.00052 + 3.46501i
964964 0 0
965965 −18.8073 −0.605427
966966 0 0
967967 17.0296 0.547636 0.273818 0.961782i 0.411713π-0.411713\pi
0.273818 + 0.961782i 0.411713π0.411713\pi
968968 0 0
969969 −2.48770 4.30882i −0.0799163 0.138419i
970970 0 0
971971 −14.6054 + 25.2974i −0.468711 + 0.811831i −0.999360 0.0357602i 0.988615π-0.988615\pi
0.530649 + 0.847591i 0.321948π0.321948\pi
972972 0 0
973973 17.4036 + 0.422358i 0.557935 + 0.0135402i
974974 0 0
975975 −4.53379 + 7.85276i −0.145198 + 0.251490i
976976 0 0
977977 −0.420110 0.727652i −0.0134405 0.0232796i 0.859227 0.511595i 0.170945π-0.170945\pi
−0.872667 + 0.488315i 0.837612π0.837612\pi
978978 0 0
979979 −10.2274 −0.326868
980980 0 0
981981 −25.5715 −0.816436
982982 0 0
983983 4.15822 + 7.20225i 0.132627 + 0.229716i 0.924688 0.380725i 0.124326π-0.124326\pi
−0.792062 + 0.610441i 0.790992π0.790992\pi
984984 0 0
985985 −1.37808 + 2.38690i −0.0439091 + 0.0760529i
986986 0 0
987987 −112.178 2.72238i −3.57066 0.0866542i
988988 0 0
989989 0.189511 0.328243i 0.00602611 0.0104375i
990990 0 0
991991 −10.1302 17.5460i −0.321795 0.557366i 0.659063 0.752088i 0.270953π-0.270953\pi
−0.980859 + 0.194722i 0.937620π0.937620\pi
992992 0 0
993993 6.00000 0.190404
994994 0 0
995995 −15.0246 −0.476312
996996 0 0
997997 26.5388 + 45.9666i 0.840492 + 1.45578i 0.889479 + 0.456976i 0.151067π0.151067\pi
−0.0489867 + 0.998799i 0.515599π0.515599\pi
998998 0 0
999999 −37.7397 + 65.3670i −1.19403 + 2.06812i
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 560.2.q.l.401.1 6
4.3 odd 2 280.2.q.e.121.3 yes 6
7.2 even 3 3920.2.a.cc.1.3 3
7.4 even 3 inner 560.2.q.l.81.1 6
7.5 odd 6 3920.2.a.cb.1.1 3
12.11 even 2 2520.2.bi.q.1801.3 6
20.3 even 4 1400.2.bh.i.849.1 12
20.7 even 4 1400.2.bh.i.849.6 12
20.19 odd 2 1400.2.q.j.401.1 6
28.3 even 6 1960.2.q.w.361.1 6
28.11 odd 6 280.2.q.e.81.3 6
28.19 even 6 1960.2.a.v.1.3 3
28.23 odd 6 1960.2.a.w.1.1 3
28.27 even 2 1960.2.q.w.961.1 6
84.11 even 6 2520.2.bi.q.361.3 6
140.19 even 6 9800.2.a.cf.1.1 3
140.39 odd 6 1400.2.q.j.1201.1 6
140.67 even 12 1400.2.bh.i.249.1 12
140.79 odd 6 9800.2.a.ce.1.3 3
140.123 even 12 1400.2.bh.i.249.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.q.e.81.3 6 28.11 odd 6
280.2.q.e.121.3 yes 6 4.3 odd 2
560.2.q.l.81.1 6 7.4 even 3 inner
560.2.q.l.401.1 6 1.1 even 1 trivial
1400.2.q.j.401.1 6 20.19 odd 2
1400.2.q.j.1201.1 6 140.39 odd 6
1400.2.bh.i.249.1 12 140.67 even 12
1400.2.bh.i.249.6 12 140.123 even 12
1400.2.bh.i.849.1 12 20.3 even 4
1400.2.bh.i.849.6 12 20.7 even 4
1960.2.a.v.1.3 3 28.19 even 6
1960.2.a.w.1.1 3 28.23 odd 6
1960.2.q.w.361.1 6 28.3 even 6
1960.2.q.w.961.1 6 28.27 even 2
2520.2.bi.q.361.3 6 84.11 even 6
2520.2.bi.q.1801.3 6 12.11 even 2
3920.2.a.cb.1.1 3 7.5 odd 6
3920.2.a.cc.1.3 3 7.2 even 3
9800.2.a.ce.1.3 3 140.79 odd 6
9800.2.a.cf.1.1 3 140.19 even 6