Properties

Label 464.2.k.c.447.10
Level 464464
Weight 22
Character 464.447
Analytic conductor 3.7053.705
Analytic rank 00
Dimension 2020
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [464,2,Mod(191,464)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(464, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("464.191");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 464=2429 464 = 2^{4} \cdot 29
Weight: k k == 2 2
Character orbit: [χ][\chi] == 464.k (of order 44, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 3.705058653793.70505865379
Analytic rank: 00
Dimension: 2020
Relative dimension: 1010 over Q(i)\Q(i)
Coefficient field: Q[x]/(x20)\mathbb{Q}[x]/(x^{20} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x206x176x162x15+18x14+42x13+9x1230x11142x10++1024 x^{20} - 6 x^{17} - 6 x^{16} - 2 x^{15} + 18 x^{14} + 42 x^{13} + 9 x^{12} - 30 x^{11} - 142 x^{10} + \cdots + 1024 Copy content Toggle raw display
Coefficient ring: Z[a1,,a9]\Z[a_1, \ldots, a_{9}]
Coefficient ring index: 217 2^{17}
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 447.10
Root 0.7021751.22758i-0.702175 - 1.22758i of defining polynomial
Character χ\chi == 464.447
Dual form 464.2.k.c.191.10

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.929751.92975i)q32.39709iq51.01973iq74.44790iq9+(2.07012+2.07012i)q111.30477iq13+(4.625794.62579i)q15+(3.78485+3.78485i)q17+(3.70412+3.70412i)q19+(1.967821.96782i)q214.28773iq230.746041q25+(2.794092.79409i)q27+(3.15397+4.36491i)q29+(2.937832.93783i)q31+7.98963iq332.44438q35+(1.63087+1.63087i)q37+(2.517882.51788i)q39+(8.283568.28356i)q41+(8.05370+8.05370i)q4310.6620q45+(4.097924.09792i)q47+5.96016q49+14.6076q51+6.32929q53+(4.96226+4.96226i)q55+14.2961iq574.26443iq59+(8.368098.36809i)q614.53564q633.12765q65+9.62370q67+(8.274268.27426i)q69+11.5718q71+(2.47075+2.47075i)q73+(1.43968+1.43968i)q75+(2.11095+2.11095i)q77+(10.5493+10.5493i)q79+2.55989q81+0.320297iq83+(9.072629.07262i)q85+(14.5096+2.33681i)q87+(8.215758.21575i)q891.33051q9111.3386iq93+(8.87910+8.87910i)q95+(1.530891.53089i)q97+(9.20767+9.20767i)q99+O(q100)q+(1.92975 - 1.92975i) q^{3} -2.39709i q^{5} -1.01973i q^{7} -4.44790i q^{9} +(-2.07012 + 2.07012i) q^{11} -1.30477i q^{13} +(-4.62579 - 4.62579i) q^{15} +(3.78485 + 3.78485i) q^{17} +(-3.70412 + 3.70412i) q^{19} +(-1.96782 - 1.96782i) q^{21} -4.28773i q^{23} -0.746041 q^{25} +(-2.79409 - 2.79409i) q^{27} +(3.15397 + 4.36491i) q^{29} +(2.93783 - 2.93783i) q^{31} +7.98963i q^{33} -2.44438 q^{35} +(-1.63087 + 1.63087i) q^{37} +(-2.51788 - 2.51788i) q^{39} +(8.28356 - 8.28356i) q^{41} +(-8.05370 + 8.05370i) q^{43} -10.6620 q^{45} +(-4.09792 - 4.09792i) q^{47} +5.96016 q^{49} +14.6076 q^{51} +6.32929 q^{53} +(4.96226 + 4.96226i) q^{55} +14.2961i q^{57} -4.26443i q^{59} +(-8.36809 - 8.36809i) q^{61} -4.53564 q^{63} -3.12765 q^{65} +9.62370 q^{67} +(-8.27426 - 8.27426i) q^{69} +11.5718 q^{71} +(-2.47075 + 2.47075i) q^{73} +(-1.43968 + 1.43968i) q^{75} +(2.11095 + 2.11095i) q^{77} +(-10.5493 + 10.5493i) q^{79} +2.55989 q^{81} +0.320297i q^{83} +(9.07262 - 9.07262i) q^{85} +(14.5096 + 2.33681i) q^{87} +(-8.21575 - 8.21575i) q^{89} -1.33051 q^{91} -11.3386i q^{93} +(8.87910 + 8.87910i) q^{95} +(1.53089 - 1.53089i) q^{97} +(9.20767 + 9.20767i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q4q1716q2128q254q2920q374q4140q45+28q49+48q53+4q61+40q6524q6920q7316q77+108q81+16q85+36q89+36q97+O(q100) 20 q - 4 q^{17} - 16 q^{21} - 28 q^{25} - 4 q^{29} - 20 q^{37} - 4 q^{41} - 40 q^{45} + 28 q^{49} + 48 q^{53} + 4 q^{61} + 40 q^{65} - 24 q^{69} - 20 q^{73} - 16 q^{77} + 108 q^{81} + 16 q^{85} + 36 q^{89}+ \cdots - 36 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/464Z)×\left(\mathbb{Z}/464\mathbb{Z}\right)^\times.

nn 117117 175175 321321
χ(n)\chi(n) 11 1-1 e(14)e\left(\frac{1}{4}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 1.92975 1.92975i 1.11414 1.11414i 0.121560 0.992584i 0.461210π-0.461210\pi
0.992584 0.121560i 0.0387896π-0.0387896\pi
44 0 0
55 2.39709i 1.07201i −0.844214 0.536006i 0.819933π-0.819933\pi
0.844214 0.536006i 0.180067π-0.180067\pi
66 0 0
77 1.01973i 0.385420i −0.981256 0.192710i 0.938272π-0.938272\pi
0.981256 0.192710i 0.0617277π-0.0617277\pi
88 0 0
99 4.44790i 1.48263i
1010 0 0
1111 −2.07012 + 2.07012i −0.624164 + 0.624164i −0.946593 0.322430i 0.895500π-0.895500\pi
0.322430 + 0.946593i 0.395500π0.395500\pi
1212 0 0
1313 1.30477i 0.361878i −0.983494 0.180939i 0.942086π-0.942086\pi
0.983494 0.180939i 0.0579136π-0.0579136\pi
1414 0 0
1515 −4.62579 4.62579i −1.19437 1.19437i
1616 0 0
1717 3.78485 + 3.78485i 0.917960 + 0.917960i 0.996881 0.0789206i 0.0251474π-0.0251474\pi
−0.0789206 + 0.996881i 0.525147π0.525147\pi
1818 0 0
1919 −3.70412 + 3.70412i −0.849783 + 0.849783i −0.990106 0.140323i 0.955186π-0.955186\pi
0.140323 + 0.990106i 0.455186π0.455186\pi
2020 0 0
2121 −1.96782 1.96782i −0.429414 0.429414i
2222 0 0
2323 4.28773i 0.894053i −0.894521 0.447027i 0.852483π-0.852483\pi
0.894521 0.447027i 0.147517π-0.147517\pi
2424 0 0
2525 −0.746041 −0.149208
2626 0 0
2727 −2.79409 2.79409i −0.537723 0.537723i
2828 0 0
2929 3.15397 + 4.36491i 0.585678 + 0.810544i
3030 0 0
3131 2.93783 2.93783i 0.527650 0.527650i −0.392221 0.919871i 0.628293π-0.628293\pi
0.919871 + 0.392221i 0.128293π0.128293\pi
3232 0 0
3333 7.98963i 1.39082i
3434 0 0
3535 −2.44438 −0.413175
3636 0 0
3737 −1.63087 + 1.63087i −0.268114 + 0.268114i −0.828340 0.560226i 0.810714π-0.810714\pi
0.560226 + 0.828340i 0.310714π0.310714\pi
3838 0 0
3939 −2.51788 2.51788i −0.403184 0.403184i
4040 0 0
4141 8.28356 8.28356i 1.29367 1.29367i 0.361177 0.932497i 0.382375π-0.382375\pi
0.932497 0.361177i 0.117625π-0.117625\pi
4242 0 0
4343 −8.05370 + 8.05370i −1.22818 + 1.22818i −0.263526 + 0.964652i 0.584885π0.584885\pi
−0.964652 + 0.263526i 0.915115π0.915115\pi
4444 0 0
4545 −10.6620 −1.58940
4646 0 0
4747 −4.09792 4.09792i −0.597743 0.597743i 0.341968 0.939711i 0.388906π-0.388906\pi
−0.939711 + 0.341968i 0.888906π0.888906\pi
4848 0 0
4949 5.96016 0.851451
5050 0 0
5151 14.6076 2.04548
5252 0 0
5353 6.32929 0.869394 0.434697 0.900577i 0.356855π-0.356855\pi
0.434697 + 0.900577i 0.356855π0.356855\pi
5454 0 0
5555 4.96226 + 4.96226i 0.669111 + 0.669111i
5656 0 0
5757 14.2961i 1.89356i
5858 0 0
5959 4.26443i 0.555182i −0.960699 0.277591i 0.910464π-0.910464\pi
0.960699 0.277591i 0.0895359π-0.0895359\pi
6060 0 0
6161 −8.36809 8.36809i −1.07142 1.07142i −0.997245 0.0741794i 0.976366π-0.976366\pi
−0.0741794 0.997245i 0.523634π-0.523634\pi
6262 0 0
6363 −4.53564 −0.571437
6464 0 0
6565 −3.12765 −0.387937
6666 0 0
6767 9.62370 1.17572 0.587861 0.808962i 0.299970π-0.299970\pi
0.587861 + 0.808962i 0.299970π0.299970\pi
6868 0 0
6969 −8.27426 8.27426i −0.996104 0.996104i
7070 0 0
7171 11.5718 1.37332 0.686658 0.726981i 0.259077π-0.259077\pi
0.686658 + 0.726981i 0.259077π0.259077\pi
7272 0 0
7373 −2.47075 + 2.47075i −0.289179 + 0.289179i −0.836756 0.547577i 0.815550π-0.815550\pi
0.547577 + 0.836756i 0.315550π0.315550\pi
7474 0 0
7575 −1.43968 + 1.43968i −0.166240 + 0.166240i
7676 0 0
7777 2.11095 + 2.11095i 0.240565 + 0.240565i
7878 0 0
7979 −10.5493 + 10.5493i −1.18689 + 1.18689i −0.208966 + 0.977923i 0.567010π0.567010\pi
−0.977923 + 0.208966i 0.932990π0.932990\pi
8080 0 0
8181 2.55989 0.284432
8282 0 0
8383 0.320297i 0.0351572i 0.999845 + 0.0175786i 0.00559573π0.00559573\pi
−0.999845 + 0.0175786i 0.994404π0.994404\pi
8484 0 0
8585 9.07262 9.07262i 0.984064 0.984064i
8686 0 0
8787 14.5096 + 2.33681i 1.55559 + 0.250532i
8888 0 0
8989 −8.21575 8.21575i −0.870868 0.870868i 0.121699 0.992567i 0.461166π-0.461166\pi
−0.992567 + 0.121699i 0.961166π0.961166\pi
9090 0 0
9191 −1.33051 −0.139475
9292 0 0
9393 11.3386i 1.17576i
9494 0 0
9595 8.87910 + 8.87910i 0.910977 + 0.910977i
9696 0 0
9797 1.53089 1.53089i 0.155438 0.155438i −0.625104 0.780542i 0.714943π-0.714943\pi
0.780542 + 0.625104i 0.214943π0.214943\pi
9898 0 0
9999 9.20767 + 9.20767i 0.925406 + 0.925406i
100100 0 0
101101 1.65372 + 1.65372i 0.164551 + 0.164551i 0.784579 0.620028i 0.212879π-0.212879\pi
−0.620028 + 0.784579i 0.712879π0.712879\pi
102102 0 0
103103 7.31685i 0.720951i 0.932769 + 0.360475i 0.117386π0.117386\pi
−0.932769 + 0.360475i 0.882614π0.882614\pi
104104 0 0
105105 −4.71704 + 4.71704i −0.460336 + 0.460336i
106106 0 0
107107 2.77845i 0.268603i 0.990941 + 0.134302i 0.0428791π0.0428791\pi
−0.990941 + 0.134302i 0.957121π0.957121\pi
108108 0 0
109109 7.65884i 0.733583i 0.930303 + 0.366792i 0.119544π0.119544\pi
−0.930303 + 0.366792i 0.880456π0.880456\pi
110110 0 0
111111 6.29437i 0.597435i
112112 0 0
113113 −13.6620 + 13.6620i −1.28521 + 1.28521i −0.347555 + 0.937660i 0.612988π0.612988\pi
−0.937660 + 0.347555i 0.887012π0.887012\pi
114114 0 0
115115 −10.2781 −0.958435
116116 0 0
117117 −5.80348 −0.536532
118118 0 0
119119 3.85951 3.85951i 0.353800 0.353800i
120120 0 0
121121 2.42923i 0.220839i
122122 0 0
123123 31.9704i 2.88268i
124124 0 0
125125 10.1971i 0.912058i
126126 0 0
127127 −11.7272 + 11.7272i −1.04062 + 1.04062i −0.0414774 + 0.999139i 0.513206π0.513206\pi
−0.999139 + 0.0414774i 0.986794π0.986794\pi
128128 0 0
129129 31.0833i 2.73673i
130130 0 0
131131 3.45621 + 3.45621i 0.301970 + 0.301970i 0.841784 0.539814i 0.181505π-0.181505\pi
−0.539814 + 0.841784i 0.681505π0.681505\pi
132132 0 0
133133 3.77719 + 3.77719i 0.327524 + 0.327524i
134134 0 0
135135 −6.69769 + 6.69769i −0.576445 + 0.576445i
136136 0 0
137137 10.6008 + 10.6008i 0.905691 + 0.905691i 0.995921 0.0902302i 0.0287603π-0.0287603\pi
−0.0902302 + 0.995921i 0.528760π0.528760\pi
138138 0 0
139139 7.28724i 0.618096i 0.951046 + 0.309048i 0.100010π0.100010\pi
−0.951046 + 0.309048i 0.899990π0.899990\pi
140140 0 0
141141 −15.8160 −1.33194
142142 0 0
143143 2.70102 + 2.70102i 0.225871 + 0.225871i
144144 0 0
145145 10.4631 7.56036i 0.868912 0.627854i
146146 0 0
147147 11.5016 11.5016i 0.948639 0.948639i
148148 0 0
149149 19.0251i 1.55860i 0.626652 + 0.779299i 0.284425π0.284425\pi
−0.626652 + 0.779299i 0.715575π0.715575\pi
150150 0 0
151151 2.57130 0.209249 0.104625 0.994512i 0.466636π-0.466636\pi
0.104625 + 0.994512i 0.466636π0.466636\pi
152152 0 0
153153 16.8346 16.8346i 1.36100 1.36100i
154154 0 0
155155 −7.04225 7.04225i −0.565647 0.565647i
156156 0 0
157157 −12.2269 + 12.2269i −0.975812 + 0.975812i −0.999714 0.0239018i 0.992391π-0.992391\pi
0.0239018 + 0.999714i 0.492391π0.492391\pi
158158 0 0
159159 12.2140 12.2140i 0.968630 0.968630i
160160 0 0
161161 −4.37231 −0.344586
162162 0 0
163163 −10.5052 10.5052i −0.822832 0.822832i 0.163682 0.986513i 0.447663π-0.447663\pi
−0.986513 + 0.163682i 0.947663π0.947663\pi
164164 0 0
165165 19.1519 1.49097
166166 0 0
167167 0.0200904 0.00155464 0.000777320 1.00000i 0.499753π-0.499753\pi
0.000777320 1.00000i 0.499753π0.499753\pi
168168 0 0
169169 11.2976 0.869045
170170 0 0
171171 16.4755 + 16.4755i 1.25992 + 1.25992i
172172 0 0
173173 5.67975i 0.431823i 0.976413 + 0.215912i 0.0692723π0.0692723\pi
−0.976413 + 0.215912i 0.930728π0.930728\pi
174174 0 0
175175 0.760758i 0.0575079i
176176 0 0
177177 −8.22930 8.22930i −0.618552 0.618552i
178178 0 0
179179 3.66020 0.273576 0.136788 0.990600i 0.456322π-0.456322\pi
0.136788 + 0.990600i 0.456322π0.456322\pi
180180 0 0
181181 −24.3983 −1.81351 −0.906755 0.421657i 0.861449π-0.861449\pi
−0.906755 + 0.421657i 0.861449π0.861449\pi
182182 0 0
183183 −32.2967 −2.38744
184184 0 0
185185 3.90935 + 3.90935i 0.287421 + 0.287421i
186186 0 0
187187 −15.6702 −1.14591
188188 0 0
189189 −2.84921 + 2.84921i −0.207249 + 0.207249i
190190 0 0
191191 −5.04414 + 5.04414i −0.364981 + 0.364981i −0.865643 0.500662i 0.833090π-0.833090\pi
0.500662 + 0.865643i 0.333090π0.333090\pi
192192 0 0
193193 −13.3530 13.3530i −0.961172 0.961172i 0.0381016 0.999274i 0.487869π-0.487869\pi
−0.999274 + 0.0381016i 0.987869π0.987869\pi
194194 0 0
195195 −6.03559 + 6.03559i −0.432217 + 0.432217i
196196 0 0
197197 8.14197 0.580091 0.290046 0.957013i 0.406329π-0.406329\pi
0.290046 + 0.957013i 0.406329π0.406329\pi
198198 0 0
199199 17.8100i 1.26252i −0.775572 0.631259i 0.782538π-0.782538\pi
0.775572 0.631259i 0.217462π-0.217462\pi
200200 0 0
201201 18.5714 18.5714i 1.30992 1.30992i
202202 0 0
203203 4.45101 3.21619i 0.312400 0.225732i
204204 0 0
205205 −19.8564 19.8564i −1.38683 1.38683i
206206 0 0
207207 −19.0714 −1.32555
208208 0 0
209209 15.3359i 1.06081i
210210 0 0
211211 −11.9689 11.9689i −0.823976 0.823976i 0.162699 0.986676i 0.447980π-0.447980\pi
−0.986676 + 0.162699i 0.947980π0.947980\pi
212212 0 0
213213 22.3307 22.3307i 1.53007 1.53007i
214214 0 0
215215 19.3055 + 19.3055i 1.31662 + 1.31662i
216216 0 0
217217 −2.99578 2.99578i −0.203367 0.203367i
218218 0 0
219219 9.53586i 0.644374i
220220 0 0
221221 4.93835 4.93835i 0.332189 0.332189i
222222 0 0
223223 1.58592i 0.106201i −0.998589 0.0531007i 0.983090π-0.983090\pi
0.998589 0.0531007i 0.0169104π-0.0169104\pi
224224 0 0
225225 3.31832i 0.221221i
226226 0 0
227227 0.875438i 0.0581049i 0.999578 + 0.0290524i 0.00924898π0.00924898\pi
−0.999578 + 0.0290524i 0.990751π0.990751\pi
228228 0 0
229229 7.50804 7.50804i 0.496145 0.496145i −0.414090 0.910236i 0.635900π-0.635900\pi
0.910236 + 0.414090i 0.135900π0.135900\pi
230230 0 0
231231 8.14724 0.536049
232232 0 0
233233 8.17093 0.535296 0.267648 0.963517i 0.413754π-0.413754\pi
0.267648 + 0.963517i 0.413754π0.413754\pi
234234 0 0
235235 −9.82308 + 9.82308i −0.640787 + 0.640787i
236236 0 0
237237 40.7151i 2.64473i
238238 0 0
239239 27.7911i 1.79766i −0.438299 0.898829i 0.644419π-0.644419\pi
0.438299 0.898829i 0.355581π-0.355581\pi
240240 0 0
241241 17.5034i 1.12749i −0.825948 0.563747i 0.809359π-0.809359\pi
0.825948 0.563747i 0.190641π-0.190641\pi
242242 0 0
243243 13.3222 13.3222i 0.854621 0.854621i
244244 0 0
245245 14.2870i 0.912765i
246246 0 0
247247 4.83301 + 4.83301i 0.307517 + 0.307517i
248248 0 0
249249 0.618095 + 0.618095i 0.0391702 + 0.0391702i
250250 0 0
251251 15.4849 15.4849i 0.977396 0.977396i −0.0223544 0.999750i 0.507116π-0.507116\pi
0.999750 + 0.0223544i 0.00711621π0.00711621\pi
252252 0 0
253253 8.87610 + 8.87610i 0.558035 + 0.558035i
254254 0 0
255255 35.0158i 2.19278i
256256 0 0
257257 −4.86005 −0.303162 −0.151581 0.988445i 0.548436π-0.548436\pi
−0.151581 + 0.988445i 0.548436π0.548436\pi
258258 0 0
259259 1.66304 + 1.66304i 0.103336 + 0.103336i
260260 0 0
261261 19.4147 14.0286i 1.20174 0.868346i
262262 0 0
263263 11.3440 11.3440i 0.699503 0.699503i −0.264800 0.964303i 0.585306π-0.585306\pi
0.964303 + 0.264800i 0.0853060π0.0853060\pi
264264 0 0
265265 15.1719i 0.932001i
266266 0 0
267267 −31.7088 −1.94054
268268 0 0
269269 −6.29276 + 6.29276i −0.383677 + 0.383677i −0.872425 0.488748i 0.837454π-0.837454\pi
0.488748 + 0.872425i 0.337454π0.337454\pi
270270 0 0
271271 18.2544 + 18.2544i 1.10888 + 1.10888i 0.993298 + 0.115579i 0.0368724π0.0368724\pi
0.115579 + 0.993298i 0.463128π0.463128\pi
272272 0 0
273273 −2.56755 + 2.56755i −0.155395 + 0.155395i
274274 0 0
275275 1.54439 1.54439i 0.0931304 0.0931304i
276276 0 0
277277 −21.9576 −1.31930 −0.659651 0.751572i 0.729296π-0.729296\pi
−0.659651 + 0.751572i 0.729296π0.729296\pi
278278 0 0
279279 −13.0672 13.0672i −0.782312 0.782312i
280280 0 0
281281 −14.5131 −0.865780 −0.432890 0.901447i 0.642506π-0.642506\pi
−0.432890 + 0.901447i 0.642506π0.642506\pi
282282 0 0
283283 8.00022 0.475564 0.237782 0.971319i 0.423580π-0.423580\pi
0.237782 + 0.971319i 0.423580π0.423580\pi
284284 0 0
285285 34.2690 2.02992
286286 0 0
287287 −8.44696 8.44696i −0.498608 0.498608i
288288 0 0
289289 11.6501i 0.685302i
290290 0 0
291291 5.90848i 0.346361i
292292 0 0
293293 −11.2820 11.2820i −0.659102 0.659102i 0.296066 0.955168i 0.404325π-0.404325\pi
−0.955168 + 0.296066i 0.904325π0.904325\pi
294294 0 0
295295 −10.2222 −0.595161
296296 0 0
297297 11.5682 0.671254
298298 0 0
299299 −5.59449 −0.323538
300300 0 0
301301 8.21257 + 8.21257i 0.473365 + 0.473365i
302302 0 0
303303 6.38254 0.366667
304304 0 0
305305 −20.0591 + 20.0591i −1.14858 + 1.14858i
306306 0 0
307307 −11.8614 + 11.8614i −0.676966 + 0.676966i −0.959312 0.282347i 0.908887π-0.908887\pi
0.282347 + 0.959312i 0.408887π0.408887\pi
308308 0 0
309309 14.1197 + 14.1197i 0.803243 + 0.803243i
310310 0 0
311311 −12.8979 + 12.8979i −0.731374 + 0.731374i −0.970892 0.239518i 0.923011π-0.923011\pi
0.239518 + 0.970892i 0.423011π0.423011\pi
312312 0 0
313313 −2.84860 −0.161012 −0.0805061 0.996754i 0.525654π-0.525654\pi
−0.0805061 + 0.996754i 0.525654π0.525654\pi
314314 0 0
315315 10.8723i 0.612587i
316316 0 0
317317 8.05244 8.05244i 0.452270 0.452270i −0.443837 0.896107i 0.646383π-0.646383\pi
0.896107 + 0.443837i 0.146383π0.146383\pi
318318 0 0
319319 −15.5650 2.50678i −0.871471 0.140353i
320320 0 0
321321 5.36173 + 5.36173i 0.299263 + 0.299263i
322322 0 0
323323 −28.0390 −1.56013
324324 0 0
325325 0.973411i 0.0539951i
326326 0 0
327327 14.7797 + 14.7797i 0.817317 + 0.817317i
328328 0 0
329329 −4.17876 + 4.17876i −0.230382 + 0.230382i
330330 0 0
331331 17.1099 + 17.1099i 0.940446 + 0.940446i 0.998324 0.0578780i 0.0184334π-0.0184334\pi
−0.0578780 + 0.998324i 0.518433π0.518433\pi
332332 0 0
333333 7.25396 + 7.25396i 0.397514 + 0.397514i
334334 0 0
335335 23.0689i 1.26039i
336336 0 0
337337 −19.0347 + 19.0347i −1.03689 + 1.03689i −0.0375939 + 0.999293i 0.511969π0.511969\pi
−0.999293 + 0.0375939i 0.988031π0.988031\pi
338338 0 0
339339 52.7287i 2.86383i
340340 0 0
341341 12.1633i 0.658680i
342342 0 0
343343 13.2158i 0.713587i
344344 0 0
345345 −19.8341 + 19.8341i −1.06783 + 1.06783i
346346 0 0
347347 −5.24183 −0.281396 −0.140698 0.990053i 0.544935π-0.544935\pi
−0.140698 + 0.990053i 0.544935π0.544935\pi
348348 0 0
349349 3.74531 0.200482 0.100241 0.994963i 0.468039π-0.468039\pi
0.100241 + 0.994963i 0.468039π0.468039\pi
350350 0 0
351351 −3.64564 + 3.64564i −0.194590 + 0.194590i
352352 0 0
353353 3.55110i 0.189006i 0.995525 + 0.0945030i 0.0301262π0.0301262\pi
−0.995525 + 0.0945030i 0.969874π0.969874\pi
354354 0 0
355355 27.7386i 1.47221i
356356 0 0
357357 14.8958i 0.788369i
358358 0 0
359359 4.54790 4.54790i 0.240029 0.240029i −0.576833 0.816862i 0.695712π-0.695712\pi
0.816862 + 0.576833i 0.195712π0.195712\pi
360360 0 0
361361 8.44098i 0.444262i
362362 0 0
363363 4.68782 + 4.68782i 0.246047 + 0.246047i
364364 0 0
365365 5.92260 + 5.92260i 0.310003 + 0.310003i
366366 0 0
367367 −16.0417 + 16.0417i −0.837372 + 0.837372i −0.988512 0.151141i 0.951705π-0.951705\pi
0.151141 + 0.988512i 0.451705π0.451705\pi
368368 0 0
369369 −36.8444 36.8444i −1.91804 1.91804i
370370 0 0
371371 6.45414i 0.335082i
372372 0 0
373373 13.3301 0.690209 0.345104 0.938564i 0.387843π-0.387843\pi
0.345104 + 0.938564i 0.387843π0.387843\pi
374374 0 0
375375 −19.6779 19.6779i −1.01616 1.01616i
376376 0 0
377377 5.69520 4.11521i 0.293317 0.211944i
378378 0 0
379379 −1.77935 + 1.77935i −0.0913989 + 0.0913989i −0.751328 0.659929i 0.770586π-0.770586\pi
0.659929 + 0.751328i 0.270586π0.270586\pi
380380 0 0
381381 45.2610i 2.31879i
382382 0 0
383383 3.05809 0.156261 0.0781304 0.996943i 0.475105π-0.475105\pi
0.0781304 + 0.996943i 0.475105π0.475105\pi
384384 0 0
385385 5.06014 5.06014i 0.257889 0.257889i
386386 0 0
387387 35.8221 + 35.8221i 1.82094 + 1.82094i
388388 0 0
389389 7.57632 7.57632i 0.384135 0.384135i −0.488455 0.872589i 0.662439π-0.662439\pi
0.872589 + 0.488455i 0.162439π0.162439\pi
390390 0 0
391391 16.2284 16.2284i 0.820705 0.820705i
392392 0 0
393393 13.3393 0.672876
394394 0 0
395395 25.2876 + 25.2876i 1.27236 + 1.27236i
396396 0 0
397397 −29.7428 −1.49275 −0.746374 0.665526i 0.768207π-0.768207\pi
−0.746374 + 0.665526i 0.768207π0.768207\pi
398398 0 0
399399 14.5781 0.729817
400400 0 0
401401 −30.4125 −1.51873 −0.759365 0.650665i 0.774490π-0.774490\pi
−0.759365 + 0.650665i 0.774490π0.774490\pi
402402 0 0
403403 −3.83319 3.83319i −0.190945 0.190945i
404404 0 0
405405 6.13628i 0.304914i
406406 0 0
407407 6.75219i 0.334694i
408408 0 0
409409 1.35062 + 1.35062i 0.0667840 + 0.0667840i 0.739710 0.672926i 0.234963π-0.234963\pi
−0.672926 + 0.739710i 0.734963π0.734963\pi
410410 0 0
411411 40.9140 2.01814
412412 0 0
413413 −4.34855 −0.213978
414414 0 0
415415 0.767781 0.0376889
416416 0 0
417417 14.0626 + 14.0626i 0.688648 + 0.688648i
418418 0 0
419419 −10.2511 −0.500798 −0.250399 0.968143i 0.580562π-0.580562\pi
−0.250399 + 0.968143i 0.580562π0.580562\pi
420420 0 0
421421 −15.2038 + 15.2038i −0.740987 + 0.740987i −0.972768 0.231781i 0.925545π-0.925545\pi
0.231781 + 0.972768i 0.425545π0.425545\pi
422422 0 0
423423 −18.2271 + 18.2271i −0.886234 + 0.886234i
424424 0 0
425425 −2.82365 2.82365i −0.136967 0.136967i
426426 0 0
427427 −8.53316 + 8.53316i −0.412949 + 0.412949i
428428 0 0
429429 10.4246 0.503305
430430 0 0
431431 30.8075i 1.48395i 0.670430 + 0.741973i 0.266110π0.266110\pi
−0.670430 + 0.741973i 0.733890π0.733890\pi
432432 0 0
433433 19.4713 19.4713i 0.935729 0.935729i −0.0623269 0.998056i 0.519852π-0.519852\pi
0.998056 + 0.0623269i 0.0198521π0.0198521\pi
434434 0 0
435435 5.60154 34.7808i 0.268573 1.66761i
436436 0 0
437437 15.8822 + 15.8822i 0.759751 + 0.759751i
438438 0 0
439439 18.0950 0.863629 0.431815 0.901962i 0.357873π-0.357873\pi
0.431815 + 0.901962i 0.357873π0.357873\pi
440440 0 0
441441 26.5102i 1.26239i
442442 0 0
443443 −25.8647 25.8647i −1.22887 1.22887i −0.964391 0.264479i 0.914800π-0.914800\pi
−0.264479 0.964391i 0.585200π-0.585200\pi
444444 0 0
445445 −19.6939 + 19.6939i −0.933580 + 0.933580i
446446 0 0
447447 36.7138 + 36.7138i 1.73650 + 1.73650i
448448 0 0
449449 9.87295 + 9.87295i 0.465933 + 0.465933i 0.900594 0.434661i 0.143132π-0.143132\pi
−0.434661 + 0.900594i 0.643132π0.643132\pi
450450 0 0
451451 34.2959i 1.61493i
452452 0 0
453453 4.96197 4.96197i 0.233134 0.233134i
454454 0 0
455455 3.18934i 0.149519i
456456 0 0
457457 15.9119i 0.744327i −0.928167 0.372163i 0.878616π-0.878616\pi
0.928167 0.372163i 0.121384π-0.121384\pi
458458 0 0
459459 21.1504i 0.987217i
460460 0 0
461461 3.12029 3.12029i 0.145326 0.145326i −0.630700 0.776026i 0.717232π-0.717232\pi
0.776026 + 0.630700i 0.217232π0.217232\pi
462462 0 0
463463 30.3565 1.41078 0.705392 0.708817i 0.250771π-0.250771\pi
0.705392 + 0.708817i 0.250771π0.250771\pi
464464 0 0
465465 −27.1796 −1.26042
466466 0 0
467467 15.6312 15.6312i 0.723325 0.723325i −0.245956 0.969281i 0.579102π-0.579102\pi
0.969281 + 0.245956i 0.0791018π0.0791018\pi
468468 0 0
469469 9.81354i 0.453147i
470470 0 0
471471 47.1898i 2.17439i
472472 0 0
473473 33.3442i 1.53317i
474474 0 0
475475 2.76343 2.76343i 0.126795 0.126795i
476476 0 0
477477 28.1520i 1.28899i
478478 0 0
479479 10.3990 + 10.3990i 0.475141 + 0.475141i 0.903574 0.428433i 0.140934π-0.140934\pi
−0.428433 + 0.903574i 0.640934π0.640934\pi
480480 0 0
481481 2.12791 + 2.12791i 0.0970244 + 0.0970244i
482482 0 0
483483 −8.43748 + 8.43748i −0.383919 + 0.383919i
484484 0 0
485485 −3.66968 3.66968i −0.166632 0.166632i
486486 0 0
487487 21.1081i 0.956500i −0.878224 0.478250i 0.841271π-0.841271\pi
0.878224 0.478250i 0.158729π-0.158729\pi
488488 0 0
489489 −40.5449 −1.83351
490490 0 0
491491 4.39350 + 4.39350i 0.198276 + 0.198276i 0.799261 0.600985i 0.205225π-0.205225\pi
−0.600985 + 0.799261i 0.705225π0.705225\pi
492492 0 0
493493 −4.58321 + 28.4578i −0.206417 + 1.28168i
494494 0 0
495495 22.0716 22.0716i 0.992046 0.992046i
496496 0 0
497497 11.8000i 0.529304i
498498 0 0
499499 −4.86379 −0.217733 −0.108866 0.994056i 0.534722π-0.534722\pi
−0.108866 + 0.994056i 0.534722π0.534722\pi
500500 0 0
501501 0.0387695 0.0387695i 0.00173209 0.00173209i
502502 0 0
503503 −22.7249 22.7249i −1.01325 1.01325i −0.999911 0.0133431i 0.995753π-0.995753\pi
−0.0133431 0.999911i 0.504247π-0.504247\pi
504504 0 0
505505 3.96411 3.96411i 0.176401 0.176401i
506506 0 0
507507 21.8015 21.8015i 0.968241 0.968241i
508508 0 0
509509 11.3980 0.505205 0.252603 0.967570i 0.418713π-0.418713\pi
0.252603 + 0.967570i 0.418713π0.418713\pi
510510 0 0
511511 2.51948 + 2.51948i 0.111455 + 0.111455i
512512 0 0
513513 20.6993 0.913895
514514 0 0
515515 17.5392 0.772868
516516 0 0
517517 16.9663 0.746179
518518 0 0
519519 10.9605 + 10.9605i 0.481113 + 0.481113i
520520 0 0
521521 20.6772i 0.905885i 0.891540 + 0.452942i 0.149626π0.149626\pi
−0.891540 + 0.452942i 0.850374π0.850374\pi
522522 0 0
523523 10.4479i 0.456856i −0.973561 0.228428i 0.926641π-0.926641\pi
0.973561 0.228428i 0.0733586π-0.0733586\pi
524524 0 0
525525 1.46808 + 1.46808i 0.0640721 + 0.0640721i
526526 0 0
527527 22.2385 0.968724
528528 0 0
529529 4.61539 0.200669
530530 0 0
531531 −18.9678 −0.823131
532532 0 0
533533 −10.8081 10.8081i −0.468152 0.468152i
534534 0 0
535535 6.66020 0.287946
536536 0 0
537537 7.06329 7.06329i 0.304803 0.304803i
538538 0 0
539539 −12.3382 + 12.3382i −0.531445 + 0.531445i
540540 0 0
541541 −8.11668 8.11668i −0.348963 0.348963i 0.510760 0.859723i 0.329364π-0.329364\pi
−0.859723 + 0.510760i 0.829364π0.829364\pi
542542 0 0
543543 −47.0827 + 47.0827i −2.02051 + 2.02051i
544544 0 0
545545 18.3589 0.786410
546546 0 0
547547 25.6172i 1.09531i 0.836703 + 0.547656i 0.184480π0.184480\pi
−0.836703 + 0.547656i 0.815520π0.815520\pi
548548 0 0
549549 −37.2204 + 37.2204i −1.58853 + 1.58853i
550550 0 0
551551 −27.8508 4.48545i −1.18649 0.191087i
552552 0 0
553553 10.7574 + 10.7574i 0.457451 + 0.457451i
554554 0 0
555555 15.0882 0.640457
556556 0 0
557557 5.26149i 0.222937i −0.993768 0.111468i 0.964445π-0.964445\pi
0.993768 0.111468i 0.0355554π-0.0355554\pi
558558 0 0
559559 10.5082 + 10.5082i 0.444450 + 0.444450i
560560 0 0
561561 −30.2395 + 30.2395i −1.27671 + 1.27671i
562562 0 0
563563 −18.2037 18.2037i −0.767192 0.767192i 0.210419 0.977611i 0.432517π-0.432517\pi
−0.977611 + 0.210419i 0.932517π0.932517\pi
564564 0 0
565565 32.7491 + 32.7491i 1.37776 + 1.37776i
566566 0 0
567567 2.61038i 0.109626i
568568 0 0
569569 32.9411 32.9411i 1.38096 1.38096i 0.538049 0.842914i 0.319162π-0.319162\pi
0.842914 0.538049i 0.180838π-0.180838\pi
570570 0 0
571571 41.7994i 1.74925i −0.484799 0.874626i 0.661107π-0.661107\pi
0.484799 0.874626i 0.338893π-0.338893\pi
572572 0 0
573573 19.4679i 0.813283i
574574 0 0
575575 3.19882i 0.133400i
576576 0 0
577577 1.98390 1.98390i 0.0825910 0.0825910i −0.664604 0.747195i 0.731400π-0.731400\pi
0.747195 + 0.664604i 0.231400π0.231400\pi
578578 0 0
579579 −51.5361 −2.14177
580580 0 0
581581 0.326615 0.0135503
582582 0 0
583583 −13.1024 + 13.1024i −0.542644 + 0.542644i
584584 0 0
585585 13.9115i 0.575168i
586586 0 0
587587 1.01770i 0.0420051i 0.999779 + 0.0210025i 0.00668581π0.00668581\pi
−0.999779 + 0.0210025i 0.993314π0.993314\pi
588588 0 0
589589 21.7641i 0.896776i
590590 0 0
591591 15.7120 15.7120i 0.646305 0.646305i
592592 0 0
593593 17.2975i 0.710323i 0.934805 + 0.355162i 0.115574π0.115574\pi
−0.934805 + 0.355162i 0.884426π0.884426\pi
594594 0 0
595595 −9.25159 9.25159i −0.379278 0.379278i
596596 0 0
597597 −34.3690 34.3690i −1.40663 1.40663i
598598 0 0
599599 −18.4376 + 18.4376i −0.753339 + 0.753339i −0.975101 0.221762i 0.928819π-0.928819\pi
0.221762 + 0.975101i 0.428819π0.428819\pi
600600 0 0
601601 −4.48215 4.48215i −0.182831 0.182831i 0.609757 0.792588i 0.291267π-0.291267\pi
−0.792588 + 0.609757i 0.791267π0.791267\pi
602602 0 0
603603 42.8052i 1.74316i
604604 0 0
605605 5.82309 0.236742
606606 0 0
607607 3.31696 + 3.31696i 0.134631 + 0.134631i 0.771211 0.636580i 0.219651π-0.219651\pi
−0.636580 + 0.771211i 0.719651π0.719651\pi
608608 0 0
609609 2.38290 14.7958i 0.0965602 0.599557i
610610 0 0
611611 −5.34684 + 5.34684i −0.216310 + 0.216310i
612612 0 0
613613 25.9090i 1.04646i −0.852193 0.523228i 0.824728π-0.824728\pi
0.852193 0.523228i 0.175272π-0.175272\pi
614614 0 0
615615 −76.6361 −3.09026
616616 0 0
617617 −15.0531 + 15.0531i −0.606014 + 0.606014i −0.941902 0.335888i 0.890964π-0.890964\pi
0.335888 + 0.941902i 0.390964π0.390964\pi
618618 0 0
619619 29.7437 + 29.7437i 1.19550 + 1.19550i 0.975500 + 0.220000i 0.0706058π0.0706058\pi
0.220000 + 0.975500i 0.429394π0.429394\pi
620620 0 0
621621 −11.9803 + 11.9803i −0.480753 + 0.480753i
622622 0 0
623623 −8.37782 + 8.37782i −0.335650 + 0.335650i
624624 0 0
625625 −28.1736 −1.12695
626626 0 0
627627 −29.5945 29.5945i −1.18189 1.18189i
628628 0 0
629629 −12.3452 −0.492236
630630 0 0
631631 −46.8743 −1.86604 −0.933018 0.359831i 0.882834π-0.882834\pi
−0.933018 + 0.359831i 0.882834π0.882834\pi
632632 0 0
633633 −46.1942 −1.83606
634634 0 0
635635 28.1111 + 28.1111i 1.11555 + 1.11555i
636636 0 0
637637 7.77662i 0.308121i
638638 0 0
639639 51.4701i 2.03612i
640640 0 0
641641 22.5210 + 22.5210i 0.889527 + 0.889527i 0.994477 0.104950i 0.0334683π-0.0334683\pi
−0.104950 + 0.994477i 0.533468π0.533468\pi
642642 0 0
643643 −3.60602 −0.142208 −0.0711038 0.997469i 0.522652π-0.522652\pi
−0.0711038 + 0.997469i 0.522652π0.522652\pi
644644 0 0
645645 74.5095 2.93381
646646 0 0
647647 8.60945 0.338473 0.169236 0.985576i 0.445870π-0.445870\pi
0.169236 + 0.985576i 0.445870π0.445870\pi
648648 0 0
649649 8.82787 + 8.82787i 0.346524 + 0.346524i
650650 0 0
651651 −11.5622 −0.453160
652652 0 0
653653 9.68383 9.68383i 0.378957 0.378957i −0.491769 0.870726i 0.663649π-0.663649\pi
0.870726 + 0.491769i 0.163649π0.163649\pi
654654 0 0
655655 8.28484 8.28484i 0.323715 0.323715i
656656 0 0
657657 10.9896 + 10.9896i 0.428746 + 0.428746i
658658 0 0
659659 −1.84113 + 1.84113i −0.0717203 + 0.0717203i −0.742057 0.670337i 0.766150π-0.766150\pi
0.670337 + 0.742057i 0.266150π0.266150\pi
660660 0 0
661661 23.7086 0.922157 0.461078 0.887359i 0.347463π-0.347463\pi
0.461078 + 0.887359i 0.347463π0.347463\pi
662662 0 0
663663 19.0596i 0.740213i
664664 0 0
665665 9.05425 9.05425i 0.351109 0.351109i
666666 0 0
667667 18.7155 13.5234i 0.724669 0.523628i
668668 0 0
669669 −3.06044 3.06044i −0.118324 0.118324i
670670 0 0
671671 34.6459 1.33749
672672 0 0
673673 15.8919i 0.612587i −0.951937 0.306294i 0.900911π-0.900911\pi
0.951937 0.306294i 0.0990889π-0.0990889\pi
674674 0 0
675675 2.08451 + 2.08451i 0.0802327 + 0.0802327i
676676 0 0
677677 3.48507 3.48507i 0.133942 0.133942i −0.636957 0.770899i 0.719807π-0.719807\pi
0.770899 + 0.636957i 0.219807π0.219807\pi
678678 0 0
679679 −1.56109 1.56109i −0.0599090 0.0599090i
680680 0 0
681681 1.68938 + 1.68938i 0.0647372 + 0.0647372i
682682 0 0
683683 16.1199i 0.616809i 0.951255 + 0.308405i 0.0997951π0.0997951\pi
−0.951255 + 0.308405i 0.900205π0.900205\pi
684684 0 0
685685 25.4112 25.4112i 0.970911 0.970911i
686686 0 0
687687 28.9773i 1.10555i
688688 0 0
689689 8.25825i 0.314614i
690690 0 0
691691 35.7904i 1.36153i −0.732502 0.680765i 0.761647π-0.761647\pi
0.732502 0.680765i 0.238353π-0.238353\pi
692692 0 0
693693 9.38930 9.38930i 0.356670 0.356670i
694694 0 0
695695 17.4682 0.662606
696696 0 0
697697 62.7040 2.37508
698698 0 0
699699 15.7679 15.7679i 0.596396 0.596396i
700700 0 0
701701 2.21227i 0.0835563i −0.999127 0.0417782i 0.986698π-0.986698\pi
0.999127 0.0417782i 0.0133023π-0.0133023\pi
702702 0 0
703703 12.0819i 0.455677i
704704 0 0
705705 37.9123i 1.42786i
706706 0 0
707707 1.68634 1.68634i 0.0634214 0.0634214i
708708 0 0
709709 31.0570i 1.16637i 0.812340 + 0.583184i 0.198193π0.198193\pi
−0.812340 + 0.583184i 0.801807π0.801807\pi
710710 0 0
711711 46.9222 + 46.9222i 1.75972 + 1.75972i
712712 0 0
713713 −12.5966 12.5966i −0.471747 0.471747i
714714 0 0
715715 6.47459 6.47459i 0.242136 0.242136i
716716 0 0
717717 −53.6300 53.6300i −2.00285 2.00285i
718718 0 0
719719 36.2112i 1.35045i 0.737611 + 0.675226i 0.235954π0.235954\pi
−0.737611 + 0.675226i 0.764046π0.764046\pi
720720 0 0
721721 7.46119 0.277869
722722 0 0
723723 −33.7773 33.7773i −1.25619 1.25619i
724724 0 0
725725 −2.35300 3.25640i −0.0873881 0.120940i
726726 0 0
727727 20.7794 20.7794i 0.770667 0.770667i −0.207556 0.978223i 0.566551π-0.566551\pi
0.978223 + 0.207556i 0.0665510π0.0665510\pi
728728 0 0
729729 43.7376i 1.61991i
730730 0 0
731731 −60.9641 −2.25484
732732 0 0
733733 −8.22927 + 8.22927i −0.303955 + 0.303955i −0.842559 0.538604i 0.818952π-0.818952\pi
0.538604 + 0.842559i 0.318952π0.318952\pi
734734 0 0
735735 −27.5705 27.5705i −1.01695 1.01695i
736736 0 0
737737 −19.9222 + 19.9222i −0.733843 + 0.733843i
738738 0 0
739739 14.6530 14.6530i 0.539017 0.539017i −0.384223 0.923240i 0.625531π-0.625531\pi
0.923240 + 0.384223i 0.125531π0.125531\pi
740740 0 0
741741 18.6531 0.685237
742742 0 0
743743 −24.0803 24.0803i −0.883419 0.883419i 0.110462 0.993880i 0.464767π-0.464767\pi
−0.993880 + 0.110462i 0.964767π0.964767\pi
744744 0 0
745745 45.6049 1.67084
746746 0 0
747747 1.42465 0.0521252
748748 0 0
749749 2.83326 0.103525
750750 0 0
751751 3.36482 + 3.36482i 0.122784 + 0.122784i 0.765829 0.643045i 0.222329π-0.222329\pi
−0.643045 + 0.765829i 0.722329π0.722329\pi
752752 0 0
753753 59.7639i 2.17792i
754754 0 0
755755 6.16363i 0.224317i
756756 0 0
757757 22.8533 + 22.8533i 0.830619 + 0.830619i 0.987601 0.156983i 0.0501767π-0.0501767\pi
−0.156983 + 0.987601i 0.550177π0.550177\pi
758758 0 0
759759 34.2574 1.24346
760760 0 0
761761 −24.7027 −0.895473 −0.447736 0.894166i 0.647770π-0.647770\pi
−0.447736 + 0.894166i 0.647770π0.647770\pi
762762 0 0
763763 7.80991 0.282738
764764 0 0
765765 −40.3541 40.3541i −1.45901 1.45901i
766766 0 0
767767 −5.56409 −0.200908
768768 0 0
769769 25.9480 25.9480i 0.935710 0.935710i −0.0623451 0.998055i 0.519858π-0.519858\pi
0.998055 + 0.0623451i 0.0198580π0.0198580\pi
770770 0 0
771771 −9.37870 + 9.37870i −0.337766 + 0.337766i
772772 0 0
773773 −34.1840 34.1840i −1.22951 1.22951i −0.964147 0.265367i 0.914507π-0.914507\pi
−0.265367 0.964147i 0.585493π-0.585493\pi
774774 0 0
775775 −2.19174 + 2.19174i −0.0787298 + 0.0787298i
776776 0 0
777777 6.41853 0.230263
778778 0 0
779779 61.3665i 2.19868i
780780 0 0
781781 −23.9549 + 23.9549i −0.857174 + 0.857174i
782782 0 0
783783 3.38346 21.0084i 0.120915 0.750780i
784784 0 0
785785 29.3090 + 29.3090i 1.04608 + 1.04608i
786786 0 0
787787 28.0749 1.00076 0.500381 0.865805i 0.333193π-0.333193\pi
0.500381 + 0.865805i 0.333193π0.333193\pi
788788 0 0
789789 43.7824i 1.55869i
790790 0 0
791791 13.9315 + 13.9315i 0.495348 + 0.495348i
792792 0 0
793793 −10.9184 + 10.9184i −0.387724 + 0.387724i
794794 0 0
795795 −29.2780 29.2780i −1.03838 1.03838i
796796 0 0
797797 −10.3597 10.3597i −0.366958 0.366958i 0.499409 0.866367i 0.333551π-0.333551\pi
−0.866367 + 0.499409i 0.833551π0.833551\pi
798798 0 0
799799 31.0200i 1.09741i
800800 0 0
801801 −36.5428 + 36.5428i −1.29118 + 1.29118i
802802 0 0
803803 10.2295i 0.360990i
804804 0 0
805805 10.4808i 0.369400i
806806 0 0
807807 24.2870i 0.854942i
808808 0 0
809809 −16.1015 + 16.1015i −0.566100 + 0.566100i −0.931033 0.364934i 0.881092π-0.881092\pi
0.364934 + 0.931033i 0.381092π0.381092\pi
810810 0 0
811811 4.16152 0.146131 0.0730654 0.997327i 0.476722π-0.476722\pi
0.0730654 + 0.997327i 0.476722π0.476722\pi
812812 0 0
813813 70.4531 2.47090
814814 0 0
815815 −25.1819 + 25.1819i −0.882085 + 0.882085i
816816 0 0
817817 59.6637i 2.08737i
818818 0 0
819819 5.91796i 0.206790i
820820 0 0
821821 7.38797i 0.257842i 0.991655 + 0.128921i 0.0411514π0.0411514\pi
−0.991655 + 0.128921i 0.958849π0.958849\pi
822822 0 0
823823 −30.7910 + 30.7910i −1.07331 + 1.07331i −0.0762167 + 0.997091i 0.524284π0.524284\pi
−0.997091 + 0.0762167i 0.975716π0.975716\pi
824824 0 0
825825 5.96060i 0.207521i
826826 0 0
827827 30.1364 + 30.1364i 1.04794 + 1.04794i 0.998791 + 0.0491533i 0.0156523π0.0156523\pi
0.0491533 + 0.998791i 0.484348π0.484348\pi
828828 0 0
829829 −28.4455 28.4455i −0.987954 0.987954i 0.0119743 0.999928i 0.496188π-0.496188\pi
−0.999928 + 0.0119743i 0.996188π0.996188\pi
830830 0 0
831831 −42.3727 + 42.3727i −1.46989 + 1.46989i
832832 0 0
833833 22.5583 + 22.5583i 0.781598 + 0.781598i
834834 0 0
835835 0.0481585i 0.00166659i
836836 0 0
837837 −16.4171 −0.567459
838838 0 0
839839 −35.9098 35.9098i −1.23975 1.23975i −0.960105 0.279640i 0.909785π-0.909785\pi
−0.279640 0.960105i 0.590215π-0.590215\pi
840840 0 0
841841 −9.10489 + 27.5336i −0.313962 + 0.949436i
842842 0 0
843843 −28.0068 + 28.0068i −0.964604 + 0.964604i
844844 0 0
845845 27.0813i 0.931626i
846846 0 0
847847 2.47715 0.0851160
848848 0 0
849849 15.4385 15.4385i 0.529847 0.529847i
850850 0 0
851851 6.99274 + 6.99274i 0.239708 + 0.239708i
852852 0 0
853853 −29.1924 + 29.1924i −0.999528 + 0.999528i −1.00000 0.000471811i 0.999850π-0.999850\pi
0.000471811 1.00000i 0.499850π0.499850\pi
854854 0 0
855855 39.4934 39.4934i 1.35064 1.35064i
856856 0 0
857857 14.8618 0.507669 0.253834 0.967248i 0.418308π-0.418308\pi
0.253834 + 0.967248i 0.418308π0.418308\pi
858858 0 0
859859 19.8098 + 19.8098i 0.675901 + 0.675901i 0.959070 0.283169i 0.0913858π-0.0913858\pi
−0.283169 + 0.959070i 0.591386π0.591386\pi
860860 0 0
861861 −32.6011 −1.11104
862862 0 0
863863 52.8614 1.79942 0.899712 0.436484i 0.143776π-0.143776\pi
0.899712 + 0.436484i 0.143776π0.143776\pi
864864 0 0
865865 13.6149 0.462919
866866 0 0
867867 22.4819 + 22.4819i 0.763525 + 0.763525i
868868 0 0
869869 43.6766i 1.48163i
870870 0 0
871871 12.5567i 0.425467i
872872 0 0
873873 −6.80924 6.80924i −0.230458 0.230458i
874874 0 0
875875 −10.3983 −0.351526
876876 0 0
877877 −2.66279 −0.0899161 −0.0449580 0.998989i 0.514315π-0.514315\pi
−0.0449580 + 0.998989i 0.514315π0.514315\pi
878878 0 0
879879 −43.5430 −1.46867
880880 0 0
881881 13.4842 + 13.4842i 0.454293 + 0.454293i 0.896777 0.442484i 0.145903π-0.145903\pi
−0.442484 + 0.896777i 0.645903π0.645903\pi
882882 0 0
883883 36.1788 1.21751 0.608756 0.793357i 0.291669π-0.291669\pi
0.608756 + 0.793357i 0.291669π0.291669\pi
884884 0 0
885885 −19.7264 + 19.7264i −0.663095 + 0.663095i
886886 0 0
887887 0.606597 0.606597i 0.0203675 0.0203675i −0.696850 0.717217i 0.745416π-0.745416\pi
0.717217 + 0.696850i 0.245416π0.245416\pi
888888 0 0
889889 11.9585 + 11.9585i 0.401075 + 0.401075i
890890 0 0
891891 −5.29927 + 5.29927i −0.177532 + 0.177532i
892892 0 0
893893 30.3584 1.01590
894894 0 0
895895 8.77383i 0.293277i
896896 0 0
897897 −10.7960 + 10.7960i −0.360468 + 0.360468i
898898 0 0
899899 22.0892 + 3.55753i 0.736717 + 0.118650i
900900 0 0
901901 23.9554 + 23.9554i 0.798069 + 0.798069i
902902 0 0
903903 31.6965 1.05479
904904 0 0
905905 58.4849i 1.94410i
906906 0 0
907907 −40.2170 40.2170i −1.33538 1.33538i −0.900475 0.434907i 0.856781π-0.856781\pi
−0.434907 0.900475i 0.643219π-0.643219\pi
908908 0 0
909909 7.35558 7.35558i 0.243969 0.243969i
910910 0 0
911911 −23.3002 23.3002i −0.771968 0.771968i 0.206482 0.978450i 0.433799π-0.433799\pi
−0.978450 + 0.206482i 0.933799π0.933799\pi
912912 0 0
913913 −0.663052 0.663052i −0.0219438 0.0219438i
914914 0 0
915915 77.4181i 2.55936i
916916 0 0
917917 3.52438 3.52438i 0.116385 0.116385i
918918 0 0
919919 27.0113i 0.891021i −0.895277 0.445511i 0.853022π-0.853022\pi
0.895277 0.445511i 0.146978π-0.146978\pi
920920 0 0
921921 45.7792i 1.50847i
922922 0 0
923923 15.0985i 0.496972i
924924 0 0
925925 1.21670 1.21670i 0.0400048 0.0400048i
926926 0 0
927927 32.5446 1.06891
928928 0 0
929929 −35.3035 −1.15827 −0.579136 0.815231i 0.696610π-0.696610\pi
−0.579136 + 0.815231i 0.696610π0.696610\pi
930930 0 0
931931 −22.0771 + 22.0771i −0.723549 + 0.723549i
932932 0 0
933933 49.7796i 1.62971i
934934 0 0
935935 37.5628i 1.22843i
936936 0 0
937937 32.2106i 1.05228i 0.850399 + 0.526138i 0.176360π0.176360\pi
−0.850399 + 0.526138i 0.823640π0.823640\pi
938938 0 0
939939 −5.49709 + 5.49709i −0.179391 + 0.179391i
940940 0 0
941941 16.7561i 0.546235i −0.961981 0.273117i 0.911945π-0.911945\pi
0.961981 0.273117i 0.0880547π-0.0880547\pi
942942 0 0
943943 −35.5176 35.5176i −1.15661 1.15661i
944944 0 0
945945 6.82981 + 6.82981i 0.222174 + 0.222174i
946946 0 0
947947 19.1359 19.1359i 0.621834 0.621834i −0.324166 0.946000i 0.605084π-0.605084\pi
0.946000 + 0.324166i 0.105084π0.105084\pi
948948 0 0
949949 3.22375 + 3.22375i 0.104647 + 0.104647i
950950 0 0
951951 31.0785i 1.00779i
952952 0 0
953953 −10.6671 −0.345543 −0.172771 0.984962i 0.555272π-0.555272\pi
−0.172771 + 0.984962i 0.555272π0.555272\pi
954954 0 0
955955 12.0913 + 12.0913i 0.391264 + 0.391264i
956956 0 0
957957 −34.8740 + 25.1991i −1.12732 + 0.814571i
958958 0 0
959959 10.8100 10.8100i 0.349072 0.349072i
960960 0 0
961961 13.7383i 0.443171i
962962 0 0
963963 12.3583 0.398240
964964 0 0
965965 −32.0084 + 32.0084i −1.03039 + 1.03039i
966966 0 0
967967 18.6237 + 18.6237i 0.598898 + 0.598898i 0.940019 0.341121i 0.110807π-0.110807\pi
−0.341121 + 0.940019i 0.610807π0.610807\pi
968968 0 0
969969 −54.1084 + 54.1084i −1.73821 + 1.73821i
970970 0 0
971971 14.0949 14.0949i 0.452326 0.452326i −0.443800 0.896126i 0.646370π-0.646370\pi
0.896126 + 0.443800i 0.146370π0.146370\pi
972972 0 0
973973 7.43099 0.238227
974974 0 0
975975 1.87844 + 1.87844i 0.0601583 + 0.0601583i
976976 0 0
977977 −12.0214 −0.384598 −0.192299 0.981336i 0.561594π-0.561594\pi
−0.192299 + 0.981336i 0.561594π0.561594\pi
978978 0 0
979979 34.0151 1.08713
980980 0 0
981981 34.0657 1.08764
982982 0 0
983983 18.0750 + 18.0750i 0.576502 + 0.576502i 0.933938 0.357436i 0.116349π-0.116349\pi
−0.357436 + 0.933938i 0.616349π0.616349\pi
984984 0 0
985985 19.5170i 0.621865i
986986 0 0
987987 16.1279i 0.513358i
988988 0 0
989989 34.5321 + 34.5321i 1.09806 + 1.09806i
990990 0 0
991991 48.5529 1.54233 0.771167 0.636633i 0.219674π-0.219674\pi
0.771167 + 0.636633i 0.219674π0.219674\pi
992992 0 0
993993 66.0358 2.09558
994994 0 0
995995 −42.6922 −1.35343
996996 0 0
997997 4.56165 + 4.56165i 0.144469 + 0.144469i 0.775642 0.631173i 0.217426π-0.217426\pi
−0.631173 + 0.775642i 0.717426π0.717426\pi
998998 0 0
999999 9.11361 0.288342
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 464.2.k.c.447.10 yes 20
4.3 odd 2 inner 464.2.k.c.447.1 yes 20
29.17 odd 4 inner 464.2.k.c.191.1 20
116.75 even 4 inner 464.2.k.c.191.10 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
464.2.k.c.191.1 20 29.17 odd 4 inner
464.2.k.c.191.10 yes 20 116.75 even 4 inner
464.2.k.c.447.1 yes 20 4.3 odd 2 inner
464.2.k.c.447.10 yes 20 1.1 even 1 trivial