Properties

Label 560.2.q.k.81.1
Level 560560
Weight 22
Character 560.81
Analytic conductor 4.4724.472
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [560,2,Mod(81,560)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
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")
 
//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

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: 4.471622513194.47162251319
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q(2,3)\Q(\sqrt{2}, \sqrt{-3})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+2x2+4 x^{4} + 2x^{2} + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 35)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 81.1
Root 0.707107+1.22474i-0.707107 + 1.22474i of defining polynomial
Character χ\chi == 560.81
Dual form 560.2.q.k.401.1

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+(0.207107+0.358719i)q3+(0.5000000.866025i)q5+(2.621320.358719i)q7+(1.41421+2.44949i)q9+(0.414214+0.717439i)q114.82843q13+0.414214q15+(2.41421+4.18154i)q17+(1.41421+2.44949i)q19+(0.6715730.866025i)q21+(0.207107+0.358719i)q23+(0.500000+0.866025i)q252.41421q271.00000q29+(3.00000+5.19615i)q31+(0.1715730.297173i)q33+(1.00000+2.44949i)q35+(1.000001.73205i)q397.82843q413.58579q43+(1.414212.44949i)q45+(1.00000+1.73205i)q47+(6.74264+1.88064i)q49+(1.000001.73205i)q51+(0.5857861.01461i)q53+0.828427q551.17157q57+(2.242643.88437i)q59+(2.742644.75039i)q61+(2.828436.92820i)q63+(2.41421+4.18154i)q65+(4.792898.30153i)q670.171573q694.48528q71+(0.4142140.717439i)q73+(0.2071070.358719i)q75+(1.343151.73205i)q77+(7.41421+12.8418i)q79+(3.74264+6.48244i)q8113.7279q83+4.82843q85+(0.2071070.358719i)q87+(4.32843+7.49706i)q89+(12.6569+1.73205i)q91+(1.242642.15232i)q93+(1.414212.44949i)q95+11.6569q972.34315q99+O(q100)q+(-0.207107 + 0.358719i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.62132 - 0.358719i) q^{7} +(1.41421 + 2.44949i) q^{9} +(-0.414214 + 0.717439i) q^{11} -4.82843 q^{13} +0.414214 q^{15} +(-2.41421 + 4.18154i) q^{17} +(1.41421 + 2.44949i) q^{19} +(0.671573 - 0.866025i) q^{21} +(0.207107 + 0.358719i) q^{23} +(-0.500000 + 0.866025i) q^{25} -2.41421 q^{27} -1.00000 q^{29} +(-3.00000 + 5.19615i) q^{31} +(-0.171573 - 0.297173i) q^{33} +(1.00000 + 2.44949i) q^{35} +(1.00000 - 1.73205i) q^{39} -7.82843 q^{41} -3.58579 q^{43} +(1.41421 - 2.44949i) q^{45} +(1.00000 + 1.73205i) q^{47} +(6.74264 + 1.88064i) q^{49} +(-1.00000 - 1.73205i) q^{51} +(0.585786 - 1.01461i) q^{53} +0.828427 q^{55} -1.17157 q^{57} +(2.24264 - 3.88437i) q^{59} +(-2.74264 - 4.75039i) q^{61} +(-2.82843 - 6.92820i) q^{63} +(2.41421 + 4.18154i) q^{65} +(4.79289 - 8.30153i) q^{67} -0.171573 q^{69} -4.48528 q^{71} +(0.414214 - 0.717439i) q^{73} +(-0.207107 - 0.358719i) q^{75} +(1.34315 - 1.73205i) q^{77} +(7.41421 + 12.8418i) q^{79} +(-3.74264 + 6.48244i) q^{81} -13.7279 q^{83} +4.82843 q^{85} +(0.207107 - 0.358719i) q^{87} +(4.32843 + 7.49706i) q^{89} +(12.6569 + 1.73205i) q^{91} +(-1.24264 - 2.15232i) q^{93} +(1.41421 - 2.44949i) q^{95} +11.6569 q^{97} -2.34315 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+2q32q52q7+4q118q134q154q17+14q212q232q254q274q2912q3112q33+4q35+4q3920q4120q43+32q99+O(q100) 4 q + 2 q^{3} - 2 q^{5} - 2 q^{7} + 4 q^{11} - 8 q^{13} - 4 q^{15} - 4 q^{17} + 14 q^{21} - 2 q^{23} - 2 q^{25} - 4 q^{27} - 4 q^{29} - 12 q^{31} - 12 q^{33} + 4 q^{35} + 4 q^{39} - 20 q^{41} - 20 q^{43}+ \cdots - 32 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(23)e\left(\frac{2}{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 −0.207107 + 0.358719i −0.119573 + 0.207107i −0.919599 0.392859i 0.871486π-0.871486\pi
0.800025 + 0.599966i 0.204819π0.204819\pi
44 0 0
55 −0.500000 0.866025i −0.223607 0.387298i
66 0 0
77 −2.62132 0.358719i −0.990766 0.135583i
88 0 0
99 1.41421 + 2.44949i 0.471405 + 0.816497i
1010 0 0
1111 −0.414214 + 0.717439i −0.124890 + 0.216316i −0.921690 0.387927i 0.873191π-0.873191\pi
0.796800 + 0.604243i 0.206524π0.206524\pi
1212 0 0
1313 −4.82843 −1.33916 −0.669582 0.742738i 0.733527π-0.733527\pi
−0.669582 + 0.742738i 0.733527π0.733527\pi
1414 0 0
1515 0.414214 0.106949
1616 0 0
1717 −2.41421 + 4.18154i −0.585533 + 1.01417i 0.409276 + 0.912411i 0.365781π0.365781\pi
−0.994809 + 0.101762i 0.967552π0.967552\pi
1818 0 0
1919 1.41421 + 2.44949i 0.324443 + 0.561951i 0.981399 0.191977i 0.0614899π-0.0614899\pi
−0.656957 + 0.753928i 0.728157π0.728157\pi
2020 0 0
2121 0.671573 0.866025i 0.146549 0.188982i
2222 0 0
2323 0.207107 + 0.358719i 0.0431847 + 0.0747982i 0.886810 0.462134i 0.152916π-0.152916\pi
−0.843625 + 0.536933i 0.819583π0.819583\pi
2424 0 0
2525 −0.500000 + 0.866025i −0.100000 + 0.173205i
2626 0 0
2727 −2.41421 −0.464616
2828 0 0
2929 −1.00000 −0.185695 −0.0928477 0.995680i 0.529597π-0.529597\pi
−0.0928477 + 0.995680i 0.529597π0.529597\pi
3030 0 0
3131 −3.00000 + 5.19615i −0.538816 + 0.933257i 0.460152 + 0.887840i 0.347795π0.347795\pi
−0.998968 + 0.0454165i 0.985539π0.985539\pi
3232 0 0
3333 −0.171573 0.297173i −0.0298670 0.0517312i
3434 0 0
3535 1.00000 + 2.44949i 0.169031 + 0.414039i
3636 0 0
3737 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
3838 0 0
3939 1.00000 1.73205i 0.160128 0.277350i
4040 0 0
4141 −7.82843 −1.22259 −0.611297 0.791401i 0.709352π-0.709352\pi
−0.611297 + 0.791401i 0.709352π0.709352\pi
4242 0 0
4343 −3.58579 −0.546827 −0.273414 0.961897i 0.588153π-0.588153\pi
−0.273414 + 0.961897i 0.588153π0.588153\pi
4444 0 0
4545 1.41421 2.44949i 0.210819 0.365148i
4646 0 0
4747 1.00000 + 1.73205i 0.145865 + 0.252646i 0.929695 0.368329i 0.120070π-0.120070\pi
−0.783830 + 0.620975i 0.786737π0.786737\pi
4848 0 0
4949 6.74264 + 1.88064i 0.963234 + 0.268662i
5050 0 0
5151 −1.00000 1.73205i −0.140028 0.242536i
5252 0 0
5353 0.585786 1.01461i 0.0804640 0.139368i −0.822985 0.568063i 0.807693π-0.807693\pi
0.903449 + 0.428695i 0.141026π0.141026\pi
5454 0 0
5555 0.828427 0.111705
5656 0 0
5757 −1.17157 −0.155179
5858 0 0
5959 2.24264 3.88437i 0.291967 0.505702i −0.682308 0.731065i 0.739024π-0.739024\pi
0.974275 + 0.225363i 0.0723569π0.0723569\pi
6060 0 0
6161 −2.74264 4.75039i −0.351159 0.608226i 0.635294 0.772271i 0.280879π-0.280879\pi
−0.986453 + 0.164045i 0.947546π0.947546\pi
6262 0 0
6363 −2.82843 6.92820i −0.356348 0.872872i
6464 0 0
6565 2.41421 + 4.18154i 0.299446 + 0.518656i
6666 0 0
6767 4.79289 8.30153i 0.585545 1.01419i −0.409262 0.912417i 0.634214π-0.634214\pi
0.994807 0.101777i 0.0324528π-0.0324528\pi
6868 0 0
6969 −0.171573 −0.0206549
7070 0 0
7171 −4.48528 −0.532305 −0.266152 0.963931i 0.585752π-0.585752\pi
−0.266152 + 0.963931i 0.585752π0.585752\pi
7272 0 0
7373 0.414214 0.717439i 0.0484800 0.0839699i −0.840767 0.541397i 0.817896π-0.817896\pi
0.889247 + 0.457427i 0.151229π0.151229\pi
7474 0 0
7575 −0.207107 0.358719i −0.0239146 0.0414214i
7676 0 0
7777 1.34315 1.73205i 0.153066 0.197386i
7878 0 0
7979 7.41421 + 12.8418i 0.834164 + 1.44481i 0.894709 + 0.446649i 0.147383π0.147383\pi
−0.0605449 + 0.998165i 0.519284π0.519284\pi
8080 0 0
8181 −3.74264 + 6.48244i −0.415849 + 0.720272i
8282 0 0
8383 −13.7279 −1.50684 −0.753418 0.657542i 0.771596π-0.771596\pi
−0.753418 + 0.657542i 0.771596π0.771596\pi
8484 0 0
8585 4.82843 0.523716
8686 0 0
8787 0.207107 0.358719i 0.0222042 0.0384588i
8888 0 0
8989 4.32843 + 7.49706i 0.458812 + 0.794686i 0.998898 0.0469234i 0.0149417π-0.0149417\pi
−0.540086 + 0.841610i 0.681608π0.681608\pi
9090 0 0
9191 12.6569 + 1.73205i 1.32680 + 0.181568i
9292 0 0
9393 −1.24264 2.15232i −0.128856 0.223185i
9494 0 0
9595 1.41421 2.44949i 0.145095 0.251312i
9696 0 0
9797 11.6569 1.18357 0.591787 0.806094i 0.298423π-0.298423\pi
0.591787 + 0.806094i 0.298423π0.298423\pi
9898 0 0
9999 −2.34315 −0.235495
100100 0 0
101101 5.15685 8.93193i 0.513126 0.888761i −0.486758 0.873537i 0.661821π-0.661821\pi
0.999884 0.0152237i 0.00484604π-0.00484604\pi
102102 0 0
103103 −1.20711 2.09077i −0.118940 0.206010i 0.800408 0.599456i 0.204616π-0.204616\pi
−0.919348 + 0.393446i 0.871283π0.871283\pi
104104 0 0
105105 −1.08579 0.148586i −0.105962 0.0145006i
106106 0 0
107107 5.62132 + 9.73641i 0.543434 + 0.941255i 0.998704 + 0.0509012i 0.0162093π0.0162093\pi
−0.455270 + 0.890353i 0.650457π0.650457\pi
108108 0 0
109109 6.74264 11.6786i 0.645828 1.11861i −0.338282 0.941045i 0.609846π-0.609846\pi
0.984110 0.177562i 0.0568210π-0.0568210\pi
110110 0 0
111111 0 0
112112 0 0
113113 −4.48528 −0.421940 −0.210970 0.977493i 0.567662π-0.567662\pi
−0.210970 + 0.977493i 0.567662π0.567662\pi
114114 0 0
115115 0.207107 0.358719i 0.0193128 0.0334508i
116116 0 0
117117 −6.82843 11.8272i −0.631288 1.09342i
118118 0 0
119119 7.82843 10.0951i 0.717631 0.925419i
120120 0 0
121121 5.15685 + 8.93193i 0.468805 + 0.811994i
122122 0 0
123123 1.62132 2.80821i 0.146190 0.253208i
124124 0 0
125125 1.00000 0.0894427
126126 0 0
127127 9.31371 0.826458 0.413229 0.910627i 0.364401π-0.364401\pi
0.413229 + 0.910627i 0.364401π0.364401\pi
128128 0 0
129129 0.742641 1.28629i 0.0653859 0.113252i
130130 0 0
131131 −9.65685 16.7262i −0.843723 1.46137i −0.886725 0.462297i 0.847026π-0.847026\pi
0.0430021 0.999075i 0.486308π-0.486308\pi
132132 0 0
133133 −2.82843 6.92820i −0.245256 0.600751i
134134 0 0
135135 1.20711 + 2.09077i 0.103891 + 0.179945i
136136 0 0
137137 4.82843 8.36308i 0.412520 0.714506i −0.582644 0.812727i 0.697982π-0.697982\pi
0.995165 + 0.0982211i 0.0313152π0.0313152\pi
138138 0 0
139139 16.1421 1.36916 0.684579 0.728939i 0.259986π-0.259986\pi
0.684579 + 0.728939i 0.259986π0.259986\pi
140140 0 0
141141 −0.828427 −0.0697661
142142 0 0
143143 2.00000 3.46410i 0.167248 0.289683i
144144 0 0
145145 0.500000 + 0.866025i 0.0415227 + 0.0719195i
146146 0 0
147147 −2.07107 + 2.02922i −0.170819 + 0.167368i
148148 0 0
149149 1.08579 + 1.88064i 0.0889511 + 0.154068i 0.907068 0.420984i 0.138315π-0.138315\pi
−0.818117 + 0.575052i 0.804982π0.804982\pi
150150 0 0
151151 5.82843 10.0951i 0.474311 0.821530i −0.525257 0.850944i 0.676031π-0.676031\pi
0.999567 + 0.0294137i 0.00936401π0.00936401\pi
152152 0 0
153153 −13.6569 −1.10409
154154 0 0
155155 6.00000 0.481932
156156 0 0
157157 −8.65685 + 14.9941i −0.690892 + 1.19666i 0.280654 + 0.959809i 0.409449π0.409449\pi
−0.971546 + 0.236851i 0.923885π0.923885\pi
158158 0 0
159159 0.242641 + 0.420266i 0.0192427 + 0.0333293i
160160 0 0
161161 −0.414214 1.01461i −0.0326446 0.0799626i
162162 0 0
163163 6.17157 + 10.6895i 0.483395 + 0.837265i 0.999818 0.0190689i 0.00607020π-0.00607020\pi
−0.516423 + 0.856333i 0.672737π0.672737\pi
164164 0 0
165165 −0.171573 + 0.297173i −0.0133569 + 0.0231349i
166166 0 0
167167 −22.4142 −1.73446 −0.867232 0.497904i 0.834103π-0.834103\pi
−0.867232 + 0.497904i 0.834103π0.834103\pi
168168 0 0
169169 10.3137 0.793362
170170 0 0
171171 −4.00000 + 6.92820i −0.305888 + 0.529813i
172172 0 0
173173 −1.65685 2.86976i −0.125968 0.218183i 0.796143 0.605109i 0.206870π-0.206870\pi
−0.922111 + 0.386925i 0.873537π0.873537\pi
174174 0 0
175175 1.62132 2.09077i 0.122560 0.158047i
176176 0 0
177177 0.928932 + 1.60896i 0.0698228 + 0.120937i
178178 0 0
179179 −5.00000 + 8.66025i −0.373718 + 0.647298i −0.990134 0.140122i 0.955250π-0.955250\pi
0.616417 + 0.787420i 0.288584π0.288584\pi
180180 0 0
181181 2.65685 0.197482 0.0987412 0.995113i 0.468518π-0.468518\pi
0.0987412 + 0.995113i 0.468518π0.468518\pi
182182 0 0
183183 2.27208 0.167957
184184 0 0
185185 0 0
186186 0 0
187187 −2.00000 3.46410i −0.146254 0.253320i
188188 0 0
189189 6.32843 + 0.866025i 0.460325 + 0.0629941i
190190 0 0
191191 −6.41421 11.1097i −0.464116 0.803873i 0.535045 0.844824i 0.320295π-0.320295\pi
−0.999161 + 0.0409507i 0.986961π0.986961\pi
192192 0 0
193193 1.00000 1.73205i 0.0719816 0.124676i −0.827788 0.561041i 0.810401π-0.810401\pi
0.899770 + 0.436365i 0.143734π0.143734\pi
194194 0 0
195195 −2.00000 −0.143223
196196 0 0
197197 −12.3431 −0.879413 −0.439706 0.898142i 0.644917π-0.644917\pi
−0.439706 + 0.898142i 0.644917π0.644917\pi
198198 0 0
199199 −4.82843 + 8.36308i −0.342278 + 0.592843i −0.984855 0.173378i 0.944532π-0.944532\pi
0.642577 + 0.766221i 0.277865π0.277865\pi
200200 0 0
201201 1.98528 + 3.43861i 0.140031 + 0.242541i
202202 0 0
203203 2.62132 + 0.358719i 0.183981 + 0.0251772i
204204 0 0
205205 3.91421 + 6.77962i 0.273381 + 0.473509i
206206 0 0
207207 −0.585786 + 1.01461i −0.0407150 + 0.0705204i
208208 0 0
209209 −2.34315 −0.162079
210210 0 0
211211 −20.4853 −1.41026 −0.705132 0.709076i 0.749112π-0.749112\pi
−0.705132 + 0.709076i 0.749112π0.749112\pi
212212 0 0
213213 0.928932 1.60896i 0.0636494 0.110244i
214214 0 0
215215 1.79289 + 3.10538i 0.122274 + 0.211785i
216216 0 0
217217 9.72792 12.5446i 0.660374 0.851584i
218218 0 0
219219 0.171573 + 0.297173i 0.0115938 + 0.0200811i
220220 0 0
221221 11.6569 20.1903i 0.784125 1.35814i
222222 0 0
223223 −0.343146 −0.0229787 −0.0114894 0.999934i 0.503657π-0.503657\pi
−0.0114894 + 0.999934i 0.503657π0.503657\pi
224224 0 0
225225 −2.82843 −0.188562
226226 0 0
227227 −3.48528 + 6.03668i −0.231326 + 0.400669i −0.958199 0.286104i 0.907640π-0.907640\pi
0.726872 + 0.686773i 0.240973π0.240973\pi
228228 0 0
229229 5.82843 + 10.0951i 0.385153 + 0.667105i 0.991790 0.127874i 0.0408152π-0.0408152\pi
−0.606637 + 0.794979i 0.707482π0.707482\pi
230230 0 0
231231 0.343146 + 0.840532i 0.0225773 + 0.0553029i
232232 0 0
233233 8.41421 + 14.5738i 0.551233 + 0.954764i 0.998186 + 0.0602067i 0.0191760π0.0191760\pi
−0.446952 + 0.894558i 0.647491π0.647491\pi
234234 0 0
235235 1.00000 1.73205i 0.0652328 0.112987i
236236 0 0
237237 −6.14214 −0.398975
238238 0 0
239239 21.3137 1.37867 0.689335 0.724443i 0.257903π-0.257903\pi
0.689335 + 0.724443i 0.257903π0.257903\pi
240240 0 0
241241 −13.8284 + 23.9515i −0.890767 + 1.54285i −0.0518100 + 0.998657i 0.516499π0.516499\pi
−0.838957 + 0.544197i 0.816834π0.816834\pi
242242 0 0
243243 −5.17157 8.95743i −0.331757 0.574619i
244244 0 0
245245 −1.74264 6.77962i −0.111333 0.433134i
246246 0 0
247247 −6.82843 11.8272i −0.434482 0.752546i
248248 0 0
249249 2.84315 4.92447i 0.180177 0.312076i
250250 0 0
251251 9.31371 0.587876 0.293938 0.955824i 0.405034π-0.405034\pi
0.293938 + 0.955824i 0.405034π0.405034\pi
252252 0 0
253253 −0.343146 −0.0215734
254254 0 0
255255 −1.00000 + 1.73205i −0.0626224 + 0.108465i
256256 0 0
257257 −3.17157 5.49333i −0.197837 0.342664i 0.749990 0.661450i 0.230058π-0.230058\pi
−0.947827 + 0.318785i 0.896725π0.896725\pi
258258 0 0
259259 0 0
260260 0 0
261261 −1.41421 2.44949i −0.0875376 0.151620i
262262 0 0
263263 −14.5208 + 25.1508i −0.895392 + 1.55086i −0.0620729 + 0.998072i 0.519771π0.519771\pi
−0.833319 + 0.552793i 0.813562π0.813562\pi
264264 0 0
265265 −1.17157 −0.0719691
266266 0 0
267267 −3.58579 −0.219447
268268 0 0
269269 −10.2279 + 17.7153i −0.623607 + 1.08012i 0.365201 + 0.930929i 0.381000π0.381000\pi
−0.988808 + 0.149191i 0.952333π0.952333\pi
270270 0 0
271271 8.24264 + 14.2767i 0.500705 + 0.867246i 1.00000 0.000813982i 0.000259099π0.000259099\pi
−0.499295 + 0.866432i 0.666408π0.666408\pi
272272 0 0
273273 −3.24264 + 4.18154i −0.196254 + 0.253078i
274274 0 0
275275 −0.414214 0.717439i −0.0249780 0.0432632i
276276 0 0
277277 −8.07107 + 13.9795i −0.484943 + 0.839947i −0.999850 0.0172994i 0.994493π-0.994493\pi
0.514907 + 0.857246i 0.327826π0.327826\pi
278278 0 0
279279 −16.9706 −1.01600
280280 0 0
281281 −30.2843 −1.80661 −0.903304 0.429001i 0.858866π-0.858866\pi
−0.903304 + 0.429001i 0.858866π0.858866\pi
282282 0 0
283283 7.00000 12.1244i 0.416107 0.720718i −0.579437 0.815017i 0.696728π-0.696728\pi
0.995544 + 0.0942988i 0.0300609π0.0300609\pi
284284 0 0
285285 0.585786 + 1.01461i 0.0346990 + 0.0601004i
286286 0 0
287287 20.5208 + 2.80821i 1.21131 + 0.165763i
288288 0 0
289289 −3.15685 5.46783i −0.185697 0.321637i
290290 0 0
291291 −2.41421 + 4.18154i −0.141524 + 0.245126i
292292 0 0
293293 −16.0000 −0.934730 −0.467365 0.884064i 0.654797π-0.654797\pi
−0.467365 + 0.884064i 0.654797π0.654797\pi
294294 0 0
295295 −4.48528 −0.261143
296296 0 0
297297 1.00000 1.73205i 0.0580259 0.100504i
298298 0 0
299299 −1.00000 1.73205i −0.0578315 0.100167i
300300 0 0
301301 9.39949 + 1.28629i 0.541778 + 0.0741406i
302302 0 0
303303 2.13604 + 3.69973i 0.122712 + 0.212544i
304304 0 0
305305 −2.74264 + 4.75039i −0.157043 + 0.272007i
306306 0 0
307307 4.75736 0.271517 0.135758 0.990742i 0.456653π-0.456653\pi
0.135758 + 0.990742i 0.456653π0.456653\pi
308308 0 0
309309 1.00000 0.0568880
310310 0 0
311311 −6.58579 + 11.4069i −0.373446 + 0.646827i −0.990093 0.140413i 0.955157π-0.955157\pi
0.616647 + 0.787239i 0.288490π0.288490\pi
312312 0 0
313313 3.17157 + 5.49333i 0.179268 + 0.310501i 0.941630 0.336650i 0.109294π-0.109294\pi
−0.762362 + 0.647151i 0.775960π0.775960\pi
314314 0 0
315315 −4.58579 + 5.91359i −0.258380 + 0.333193i
316316 0 0
317317 6.89949 + 11.9503i 0.387514 + 0.671194i 0.992115 0.125335i 0.0400005π-0.0400005\pi
−0.604600 + 0.796529i 0.706667π0.706667\pi
318318 0 0
319319 0.414214 0.717439i 0.0231915 0.0401689i
320320 0 0
321321 −4.65685 −0.259920
322322 0 0
323323 −13.6569 −0.759888
324324 0 0
325325 2.41421 4.18154i 0.133916 0.231950i
326326 0 0
327327 2.79289 + 4.83743i 0.154447 + 0.267511i
328328 0 0
329329 −2.00000 4.89898i −0.110264 0.270089i
330330 0 0
331331 11.4853 + 19.8931i 0.631288 + 1.09342i 0.987289 + 0.158937i 0.0508068π0.0508068\pi
−0.356001 + 0.934486i 0.615860π0.615860\pi
332332 0 0
333333 0 0
334334 0 0
335335 −9.58579 −0.523727
336336 0 0
337337 9.17157 0.499607 0.249804 0.968296i 0.419634π-0.419634\pi
0.249804 + 0.968296i 0.419634π0.419634\pi
338338 0 0
339339 0.928932 1.60896i 0.0504527 0.0873866i
340340 0 0
341341 −2.48528 4.30463i −0.134586 0.233109i
342342 0 0
343343 −17.0000 7.34847i −0.917914 0.396780i
344344 0 0
345345 0.0857864 + 0.148586i 0.00461859 + 0.00799963i
346346 0 0
347347 3.96447 6.86666i 0.212824 0.368621i −0.739773 0.672856i 0.765067π-0.765067\pi
0.952597 + 0.304235i 0.0984007π0.0984007\pi
348348 0 0
349349 −15.3431 −0.821300 −0.410650 0.911793i 0.634698π-0.634698\pi
−0.410650 + 0.911793i 0.634698π0.634698\pi
350350 0 0
351351 11.6569 0.622197
352352 0 0
353353 13.4142 23.2341i 0.713967 1.23663i −0.249390 0.968403i 0.580230π-0.580230\pi
0.963357 0.268223i 0.0864365π-0.0864365\pi
354354 0 0
355355 2.24264 + 3.88437i 0.119027 + 0.206161i
356356 0 0
357357 2.00000 + 4.89898i 0.105851 + 0.259281i
358358 0 0
359359 −5.00000 8.66025i −0.263890 0.457071i 0.703382 0.710812i 0.251672π-0.251672\pi
−0.967272 + 0.253741i 0.918339π0.918339\pi
360360 0 0
361361 5.50000 9.52628i 0.289474 0.501383i
362362 0 0
363363 −4.27208 −0.224226
364364 0 0
365365 −0.828427 −0.0433619
366366 0 0
367367 −1.37868 + 2.38794i −0.0719665 + 0.124650i −0.899763 0.436379i 0.856261π-0.856261\pi
0.827797 + 0.561028i 0.189594π0.189594\pi
368368 0 0
369369 −11.0711 19.1757i −0.576337 0.998245i
370370 0 0
371371 −1.89949 + 2.44949i −0.0986169 + 0.127171i
372372 0 0
373373 10.4853 + 18.1610i 0.542907 + 0.940343i 0.998735 + 0.0502752i 0.0160098π0.0160098\pi
−0.455828 + 0.890068i 0.650657π0.650657\pi
374374 0 0
375375 −0.207107 + 0.358719i −0.0106949 + 0.0185242i
376376 0 0
377377 4.82843 0.248677
378378 0 0
379379 −26.8284 −1.37808 −0.689042 0.724722i 0.741968π-0.741968\pi
−0.689042 + 0.724722i 0.741968π0.741968\pi
380380 0 0
381381 −1.92893 + 3.34101i −0.0988222 + 0.171165i
382382 0 0
383383 −1.44975 2.51104i −0.0740786 0.128308i 0.826607 0.562780i 0.190268π-0.190268\pi
−0.900685 + 0.434472i 0.856935π0.856935\pi
384384 0 0
385385 −2.17157 0.297173i −0.110674 0.0151453i
386386 0 0
387387 −5.07107 8.78335i −0.257777 0.446483i
388388 0 0
389389 −11.8284 + 20.4874i −0.599725 + 1.03875i 0.393136 + 0.919480i 0.371390π0.371390\pi
−0.992861 + 0.119274i 0.961943π0.961943\pi
390390 0 0
391391 −2.00000 −0.101144
392392 0 0
393393 8.00000 0.403547
394394 0 0
395395 7.41421 12.8418i 0.373050 0.646141i
396396 0 0
397397 8.31371 + 14.3998i 0.417253 + 0.722704i 0.995662 0.0930434i 0.0296595π-0.0296595\pi
−0.578409 + 0.815747i 0.696326π0.696326\pi
398398 0 0
399399 3.07107 + 0.420266i 0.153746 + 0.0210396i
400400 0 0
401401 −15.1569 26.2524i −0.756897 1.31098i −0.944426 0.328725i 0.893381π-0.893381\pi
0.187528 0.982259i 0.439952π-0.439952\pi
402402 0 0
403403 14.4853 25.0892i 0.721563 1.24978i
404404 0 0
405405 7.48528 0.371947
406406 0 0
407407 0 0
408408 0 0
409409 7.39949 12.8163i 0.365881 0.633725i −0.623036 0.782193i 0.714101π-0.714101\pi
0.988917 + 0.148468i 0.0474342π0.0474342\pi
410410 0 0
411411 2.00000 + 3.46410i 0.0986527 + 0.170872i
412412 0 0
413413 −7.27208 + 9.37769i −0.357836 + 0.461446i
414414 0 0
415415 6.86396 + 11.8887i 0.336939 + 0.583595i
416416 0 0
417417 −3.34315 + 5.79050i −0.163715 + 0.283562i
418418 0 0
419419 0.686292 0.0335275 0.0167638 0.999859i 0.494664π-0.494664\pi
0.0167638 + 0.999859i 0.494664π0.494664\pi
420420 0 0
421421 13.4853 0.657232 0.328616 0.944464i 0.393418π-0.393418\pi
0.328616 + 0.944464i 0.393418π0.393418\pi
422422 0 0
423423 −2.82843 + 4.89898i −0.137523 + 0.238197i
424424 0 0
425425 −2.41421 4.18154i −0.117107 0.202835i
426426 0 0
427427 5.48528 + 13.4361i 0.265451 + 0.650220i
428428 0 0
429429 0.828427 + 1.43488i 0.0399968 + 0.0692766i
430430 0 0
431431 8.89949 15.4144i 0.428674 0.742484i −0.568082 0.822972i 0.692314π-0.692314\pi
0.996756 + 0.0804875i 0.0256477π0.0256477\pi
432432 0 0
433433 7.79899 0.374796 0.187398 0.982284i 0.439995π-0.439995\pi
0.187398 + 0.982284i 0.439995π0.439995\pi
434434 0 0
435435 −0.414214 −0.0198600
436436 0 0
437437 −0.585786 + 1.01461i −0.0280220 + 0.0485355i
438438 0 0
439439 −16.9706 29.3939i −0.809961 1.40289i −0.912890 0.408205i 0.866155π-0.866155\pi
0.102930 0.994689i 0.467178π-0.467178\pi
440440 0 0
441441 4.92893 + 19.1757i 0.234711 + 0.913126i
442442 0 0
443443 15.1066 + 26.1654i 0.717736 + 1.24316i 0.961895 + 0.273420i 0.0881550π0.0881550\pi
−0.244158 + 0.969735i 0.578512π0.578512\pi
444444 0 0
445445 4.32843 7.49706i 0.205187 0.355395i
446446 0 0
447447 −0.899495 −0.0425447
448448 0 0
449449 3.82843 0.180675 0.0903373 0.995911i 0.471205π-0.471205\pi
0.0903373 + 0.995911i 0.471205π0.471205\pi
450450 0 0
451451 3.24264 5.61642i 0.152690 0.264467i
452452 0 0
453453 2.41421 + 4.18154i 0.113430 + 0.196466i
454454 0 0
455455 −4.82843 11.8272i −0.226360 0.554467i
456456 0 0
457457 −12.1421 21.0308i −0.567985 0.983779i −0.996765 0.0803702i 0.974390π-0.974390\pi
0.428780 0.903409i 0.358944π-0.358944\pi
458458 0 0
459459 5.82843 10.0951i 0.272048 0.471200i
460460 0 0
461461 41.3137 1.92417 0.962086 0.272748i 0.0879324π-0.0879324\pi
0.962086 + 0.272748i 0.0879324π0.0879324\pi
462462 0 0
463463 37.0416 1.72147 0.860735 0.509053i 0.170004π-0.170004\pi
0.860735 + 0.509053i 0.170004π0.170004\pi
464464 0 0
465465 −1.24264 + 2.15232i −0.0576261 + 0.0998113i
466466 0 0
467467 −1.55025 2.68512i −0.0717371 0.124252i 0.827926 0.560838i 0.189521π-0.189521\pi
−0.899663 + 0.436586i 0.856188π0.856188\pi
468468 0 0
469469 −15.5416 + 20.0417i −0.717646 + 0.925439i
470470 0 0
471471 −3.58579 6.21076i −0.165224 0.286177i
472472 0 0
473473 1.48528 2.57258i 0.0682933 0.118287i
474474 0 0
475475 −2.82843 −0.129777
476476 0 0
477477 3.31371 0.151724
478478 0 0
479479 −17.8284 + 30.8797i −0.814602 + 1.41093i 0.0950120 + 0.995476i 0.469711π0.469711\pi
−0.909614 + 0.415455i 0.863622π0.863622\pi
480480 0 0
481481 0 0
482482 0 0
483483 0.449747 + 0.0615465i 0.0204642 + 0.00280046i
484484 0 0
485485 −5.82843 10.0951i −0.264655 0.458396i
486486 0 0
487487 2.17157 3.76127i 0.0984034 0.170440i −0.812621 0.582793i 0.801960π-0.801960\pi
0.911024 + 0.412353i 0.135293π0.135293\pi
488488 0 0
489489 −5.11270 −0.231204
490490 0 0
491491 −9.31371 −0.420322 −0.210161 0.977667i 0.567399π-0.567399\pi
−0.210161 + 0.977667i 0.567399π0.567399\pi
492492 0 0
493493 2.41421 4.18154i 0.108731 0.188327i
494494 0 0
495495 1.17157 + 2.02922i 0.0526583 + 0.0912068i
496496 0 0
497497 11.7574 + 1.60896i 0.527390 + 0.0721716i
498498 0 0
499499 −0.414214 0.717439i −0.0185427 0.0321170i 0.856605 0.515973i 0.172569π-0.172569\pi
−0.875148 + 0.483856i 0.839236π0.839236\pi
500500 0 0
501501 4.64214 8.04041i 0.207395 0.359219i
502502 0 0
503503 15.8701 0.707611 0.353805 0.935319i 0.384887π-0.384887\pi
0.353805 + 0.935319i 0.384887π0.384887\pi
504504 0 0
505505 −10.3137 −0.458954
506506 0 0
507507 −2.13604 + 3.69973i −0.0948648 + 0.164311i
508508 0 0
509509 −6.67157 11.5555i −0.295712 0.512189i 0.679438 0.733733i 0.262224π-0.262224\pi
−0.975150 + 0.221544i 0.928890π0.928890\pi
510510 0 0
511511 −1.34315 + 1.73205i −0.0594173 + 0.0766214i
512512 0 0
513513 −3.41421 5.91359i −0.150741 0.261091i
514514 0 0
515515 −1.20711 + 2.09077i −0.0531915 + 0.0921303i
516516 0 0
517517 −1.65685 −0.0728684
518518 0 0
519519 1.37258 0.0602497
520520 0 0
521521 −7.48528 + 12.9649i −0.327936 + 0.568002i −0.982102 0.188349i 0.939686π-0.939686\pi
0.654166 + 0.756351i 0.273020π0.273020\pi
522522 0 0
523523 17.8284 + 30.8797i 0.779583 + 1.35028i 0.932182 + 0.361989i 0.117902π0.117902\pi
−0.152600 + 0.988288i 0.548765π0.548765\pi
524524 0 0
525525 0.414214 + 1.01461i 0.0180778 + 0.0442813i
526526 0 0
527527 −14.4853 25.0892i −0.630989 1.09290i
528528 0 0
529529 11.4142 19.7700i 0.496270 0.859565i
530530 0 0
531531 12.6863 0.550538
532532 0 0
533533 37.7990 1.63726
534534 0 0
535535 5.62132 9.73641i 0.243031 0.420942i
536536 0 0
537537 −2.07107 3.58719i −0.0893732 0.154799i
538538 0 0
539539 −4.14214 + 4.05845i −0.178414 + 0.174810i
540540 0 0
541541 −3.67157 6.35935i −0.157853 0.273410i 0.776241 0.630436i 0.217124π-0.217124\pi
−0.934094 + 0.357026i 0.883791π0.883791\pi
542542 0 0
543543 −0.550253 + 0.953065i −0.0236136 + 0.0408999i
544544 0 0
545545 −13.4853 −0.577646
546546 0 0
547547 −24.8995 −1.06463 −0.532313 0.846548i 0.678677π-0.678677\pi
−0.532313 + 0.846548i 0.678677π0.678677\pi
548548 0 0
549549 7.75736 13.4361i 0.331076 0.573441i
550550 0 0
551551 −1.41421 2.44949i −0.0602475 0.104352i
552552 0 0
553553 −14.8284 36.3221i −0.630569 1.54457i
554554 0 0
555555 0 0
556556 0 0
557557 −11.1421 + 19.2987i −0.472107 + 0.817714i −0.999491 0.0319135i 0.989840π-0.989840\pi
0.527383 + 0.849628i 0.323173π0.323173\pi
558558 0 0
559559 17.3137 0.732292
560560 0 0
561561 1.65685 0.0699524
562562 0 0
563563 20.8640 36.1374i 0.879311 1.52301i 0.0272129 0.999630i 0.491337π-0.491337\pi
0.852098 0.523382i 0.175330π-0.175330\pi
564564 0 0
565565 2.24264 + 3.88437i 0.0943486 + 0.163417i
566566 0 0
567567 12.1360 15.6500i 0.509666 0.657238i
568568 0 0
569569 −3.82843 6.63103i −0.160496 0.277987i 0.774551 0.632512i 0.217976π-0.217976\pi
−0.935047 + 0.354525i 0.884643π0.884643\pi
570570 0 0
571571 4.58579 7.94282i 0.191909 0.332396i −0.753974 0.656905i 0.771865π-0.771865\pi
0.945883 + 0.324508i 0.105199π0.105199\pi
572572 0 0
573573 5.31371 0.221983
574574 0 0
575575 −0.414214 −0.0172739
576576 0 0
577577 21.9706 38.0541i 0.914646 1.58421i 0.107228 0.994234i 0.465802π-0.465802\pi
0.807418 0.589980i 0.200864π-0.200864\pi
578578 0 0
579579 0.414214 + 0.717439i 0.0172141 + 0.0298157i
580580 0 0
581581 35.9853 + 4.92447i 1.49292 + 0.204302i
582582 0 0
583583 0.485281 + 0.840532i 0.0200983 + 0.0348113i
584584 0 0
585585 −6.82843 + 11.8272i −0.282321 + 0.488994i
586586 0 0
587587 34.2843 1.41506 0.707532 0.706682i 0.249809π-0.249809\pi
0.707532 + 0.706682i 0.249809π0.249809\pi
588588 0 0
589589 −16.9706 −0.699260
590590 0 0
591591 2.55635 4.42773i 0.105154 0.182132i
592592 0 0
593593 −2.10051 3.63818i −0.0862574 0.149402i 0.819669 0.572838i 0.194157π-0.194157\pi
−0.905926 + 0.423435i 0.860824π0.860824\pi
594594 0 0
595595 −12.6569 1.73205i −0.518880 0.0710072i
596596 0 0
597597 −2.00000 3.46410i −0.0818546 0.141776i
598598 0 0
599599 3.17157 5.49333i 0.129587 0.224451i −0.793930 0.608010i 0.791968π-0.791968\pi
0.923517 + 0.383558i 0.125302π0.125302\pi
600600 0 0
601601 19.6569 0.801820 0.400910 0.916117i 0.368694π-0.368694\pi
0.400910 + 0.916117i 0.368694π0.368694\pi
602602 0 0
603603 27.1127 1.10411
604604 0 0
605605 5.15685 8.93193i 0.209656 0.363135i
606606 0 0
607607 19.1066 + 33.0936i 0.775513 + 1.34323i 0.934506 + 0.355948i 0.115842π0.115842\pi
−0.158993 + 0.987280i 0.550825π0.550825\pi
608608 0 0
609609 −0.671573 + 0.866025i −0.0272135 + 0.0350931i
610610 0 0
611611 −4.82843 8.36308i −0.195337 0.338334i
612612 0 0
613613 −17.7279 + 30.7057i −0.716024 + 1.24019i 0.246539 + 0.969133i 0.420707π0.420707\pi
−0.962563 + 0.271057i 0.912627π0.912627\pi
614614 0 0
615615 −3.24264 −0.130756
616616 0 0
617617 11.3137 0.455473 0.227736 0.973723i 0.426868π-0.426868\pi
0.227736 + 0.973723i 0.426868π0.426868\pi
618618 0 0
619619 12.7574 22.0964i 0.512762 0.888129i −0.487129 0.873330i 0.661956π-0.661956\pi
0.999890 0.0147990i 0.00471084π-0.00471084\pi
620620 0 0
621621 −0.500000 0.866025i −0.0200643 0.0347524i
622622 0 0
623623 −8.65685 21.2049i −0.346830 0.849555i
624624 0 0
625625 −0.500000 0.866025i −0.0200000 0.0346410i
626626 0 0
627627 0.485281 0.840532i 0.0193803 0.0335676i
628628 0 0
629629 0 0
630630 0 0
631631 20.1421 0.801846 0.400923 0.916112i 0.368690π-0.368690\pi
0.400923 + 0.916112i 0.368690π0.368690\pi
632632 0 0
633633 4.24264 7.34847i 0.168630 0.292075i
634634 0 0
635635 −4.65685 8.06591i −0.184802 0.320086i
636636 0 0
637637 −32.5563 9.08052i −1.28993 0.359783i
638638 0 0
639639 −6.34315 10.9867i −0.250931 0.434625i
640640 0 0
641641 −15.7426 + 27.2671i −0.621797 + 1.07698i 0.367354 + 0.930081i 0.380264π0.380264\pi
−0.989151 + 0.146903i 0.953070π0.953070\pi
642642 0 0
643643 −26.2843 −1.03655 −0.518275 0.855214i 0.673426π-0.673426\pi
−0.518275 + 0.855214i 0.673426π0.673426\pi
644644 0 0
645645 −1.48528 −0.0584829
646646 0 0
647647 −15.5208 + 26.8828i −0.610186 + 1.05687i 0.381022 + 0.924566i 0.375572π0.375572\pi
−0.991209 + 0.132308i 0.957761π0.957761\pi
648648 0 0
649649 1.85786 + 3.21792i 0.0729276 + 0.126314i
650650 0 0
651651 2.48528 + 6.08767i 0.0974059 + 0.238595i
652652 0 0
653653 9.58579 + 16.6031i 0.375121 + 0.649728i 0.990345 0.138624i 0.0442679π-0.0442679\pi
−0.615224 + 0.788352i 0.710935π0.710935\pi
654654 0 0
655655 −9.65685 + 16.7262i −0.377325 + 0.653545i
656656 0 0
657657 2.34315 0.0914148
658658 0 0
659659 −21.1716 −0.824727 −0.412364 0.911019i 0.635297π-0.635297\pi
−0.412364 + 0.911019i 0.635297π0.635297\pi
660660 0 0
661661 −15.9142 + 27.5642i −0.618991 + 1.07212i 0.370679 + 0.928761i 0.379125π0.379125\pi
−0.989670 + 0.143363i 0.954208π0.954208\pi
662662 0 0
663663 4.82843 + 8.36308i 0.187521 + 0.324795i
664664 0 0
665665 −4.58579 + 5.91359i −0.177829 + 0.229319i
666666 0 0
667667 −0.207107 0.358719i −0.00801921 0.0138897i
668668 0 0
669669 0.0710678 0.123093i 0.00274764 0.00475905i
670670 0 0
671671 4.54416 0.175425
672672 0 0
673673 29.6569 1.14319 0.571594 0.820537i 0.306325π-0.306325\pi
0.571594 + 0.820537i 0.306325π0.306325\pi
674674 0 0
675675 1.20711 2.09077i 0.0464616 0.0804738i
676676 0 0
677677 14.0711 + 24.3718i 0.540795 + 0.936685i 0.998859 + 0.0477651i 0.0152099π0.0152099\pi
−0.458064 + 0.888919i 0.651457π0.651457\pi
678678 0 0
679679 −30.5563 4.18154i −1.17265 0.160473i
680680 0 0
681681 −1.44365 2.50048i −0.0553208 0.0958185i
682682 0 0
683683 −17.3787 + 30.1008i −0.664977 + 1.15177i 0.314315 + 0.949319i 0.398225π0.398225\pi
−0.979292 + 0.202455i 0.935108π0.935108\pi
684684 0 0
685685 −9.65685 −0.368969
686686 0 0
687687 −4.82843 −0.184216
688688 0 0
689689 −2.82843 + 4.89898i −0.107754 + 0.186636i
690690 0 0
691691 0.414214 + 0.717439i 0.0157574 + 0.0272927i 0.873797 0.486292i 0.161651π-0.161651\pi
−0.858039 + 0.513584i 0.828317π0.828317\pi
692692 0 0
693693 6.14214 + 0.840532i 0.233320 + 0.0319292i
694694 0 0
695695 −8.07107 13.9795i −0.306153 0.530273i
696696 0 0
697697 18.8995 32.7349i 0.715869 1.23992i
698698 0 0
699699 −6.97056 −0.263651
700700 0 0
701701 −3.20101 −0.120900 −0.0604502 0.998171i 0.519254π-0.519254\pi
−0.0604502 + 0.998171i 0.519254π0.519254\pi
702702 0 0
703703 0 0
704704 0 0
705705 0.414214 + 0.717439i 0.0156002 + 0.0270203i
706706 0 0
707707 −16.7218 + 21.5636i −0.628889 + 0.810982i
708708 0 0
709709 −7.84315 13.5847i −0.294556 0.510185i 0.680326 0.732910i 0.261838π-0.261838\pi
−0.974881 + 0.222725i 0.928505π0.928505\pi
710710 0 0
711711 −20.9706 + 36.3221i −0.786458 + 1.36218i
712712 0 0
713713 −2.48528 −0.0930745
714714 0 0
715715 −4.00000 −0.149592
716716 0 0
717717 −4.41421 + 7.64564i −0.164852 + 0.285532i
718718 0 0
719719 10.5563 + 18.2841i 0.393685 + 0.681883i 0.992932 0.118681i 0.0378666π-0.0378666\pi
−0.599247 + 0.800564i 0.704533π0.704533\pi
720720 0 0
721721 2.41421 + 5.91359i 0.0899100 + 0.220234i
722722 0 0
723723 −5.72792 9.92105i −0.213024 0.368968i
724724 0 0
725725 0.500000 0.866025i 0.0185695 0.0321634i
726726 0 0
727727 37.5858 1.39398 0.696990 0.717081i 0.254522π-0.254522\pi
0.696990 + 0.717081i 0.254522π0.254522\pi
728728 0 0
729729 −18.1716 −0.673021
730730 0 0
731731 8.65685 14.9941i 0.320185 0.554577i
732732 0 0
733733 11.0000 + 19.0526i 0.406294 + 0.703722i 0.994471 0.105010i 0.0334875π-0.0334875\pi
−0.588177 + 0.808732i 0.700154π0.700154\pi
734734 0 0
735735 2.79289 + 0.778985i 0.103017 + 0.0287333i
736736 0 0
737737 3.97056 + 6.87722i 0.146258 + 0.253326i
738738 0 0
739739 −10.5563 + 18.2841i −0.388322 + 0.672593i −0.992224 0.124466i 0.960278π-0.960278\pi
0.603902 + 0.797058i 0.293612π0.293612\pi
740740 0 0
741741 5.65685 0.207810
742742 0 0
743743 16.0711 0.589590 0.294795 0.955560i 0.404749π-0.404749\pi
0.294795 + 0.955560i 0.404749π0.404749\pi
744744 0 0
745745 1.08579 1.88064i 0.0397801 0.0689012i
746746 0 0
747747 −19.4142 33.6264i −0.710329 1.23033i
748748 0 0
749749 −11.2426 27.5387i −0.410797 1.00624i
750750 0 0
751751 −15.1716 26.2779i −0.553619 0.958895i −0.998010 0.0630625i 0.979913π-0.979913\pi
0.444391 0.895833i 0.353420π-0.353420\pi
752752 0 0
753753 −1.92893 + 3.34101i −0.0702942 + 0.121753i
754754 0 0
755755 −11.6569 −0.424236
756756 0 0
757757 −31.4558 −1.14328 −0.571641 0.820504i 0.693693π-0.693693\pi
−0.571641 + 0.820504i 0.693693π0.693693\pi
758758 0 0
759759 0.0710678 0.123093i 0.00257960 0.00446800i
760760 0 0
761761 −4.65685 8.06591i −0.168811 0.292389i 0.769191 0.639019i 0.220659π-0.220659\pi
−0.938002 + 0.346630i 0.887326π0.887326\pi
762762 0 0
763763 −21.8640 + 28.1946i −0.791529 + 1.02071i
764764 0 0
765765 6.82843 + 11.8272i 0.246882 + 0.427613i
766766 0 0
767767 −10.8284 + 18.7554i −0.390992 + 0.677218i
768768 0 0
769769 −0.627417 −0.0226252 −0.0113126 0.999936i 0.503601π-0.503601\pi
−0.0113126 + 0.999936i 0.503601π0.503601\pi
770770 0 0
771771 2.62742 0.0946241
772772 0 0
773773 18.5563 32.1405i 0.667425 1.15601i −0.311196 0.950346i 0.600730π-0.600730\pi
0.978622 0.205669i 0.0659371π-0.0659371\pi
774774 0 0
775775 −3.00000 5.19615i −0.107763 0.186651i
776776 0 0
777777 0 0
778778 0 0
779779 −11.0711 19.1757i −0.396662 0.687039i
780780 0 0
781781 1.85786 3.21792i 0.0664796 0.115146i
782782 0 0
783783 2.41421 0.0862770
784784 0 0
785785 17.3137 0.617953
786786 0 0
787787 1.27817 2.21386i 0.0455620 0.0789157i −0.842345 0.538939i 0.818825π-0.818825\pi
0.887907 + 0.460023i 0.152159π0.152159\pi
788788 0 0
789789 −6.01472 10.4178i −0.214130 0.370883i
790790 0 0
791791 11.7574 + 1.60896i 0.418044 + 0.0572080i
792792 0 0
793793 13.2426 + 22.9369i 0.470260 + 0.814514i
794794 0 0
795795 0.242641 0.420266i 0.00860558 0.0149053i
796796 0 0
797797 −8.00000 −0.283375 −0.141687 0.989911i 0.545253π-0.545253\pi
−0.141687 + 0.989911i 0.545253π0.545253\pi
798798 0 0
799799 −9.65685 −0.341635
800800 0 0
801801 −12.2426 + 21.2049i −0.432572 + 0.749237i
802802 0 0
803803 0.343146 + 0.594346i 0.0121094 + 0.0209740i
804804 0 0
805805 −0.671573 + 0.866025i −0.0236698 + 0.0305234i
806806 0 0
807807 −4.23654 7.33791i −0.149133 0.258307i
808808 0 0
809809 −17.8137 + 30.8542i −0.626297 + 1.08478i 0.361992 + 0.932181i 0.382097π0.382097\pi
−0.988289 + 0.152596i 0.951237π0.951237\pi
810810 0 0
811811 20.6274 0.724327 0.362163 0.932115i 0.382038π-0.382038\pi
0.362163 + 0.932115i 0.382038π0.382038\pi
812812 0 0
813813 −6.82843 −0.239483
814814 0 0
815815 6.17157 10.6895i 0.216181 0.374436i
816816 0 0
817817 −5.07107 8.78335i −0.177414 0.307290i
818818 0 0
819819 13.6569 + 33.4523i 0.477209 + 1.16892i
820820 0 0
821821 −23.9706 41.5182i −0.836578 1.44900i −0.892739 0.450575i 0.851219π-0.851219\pi
0.0561604 0.998422i 0.482114π-0.482114\pi
822822 0 0
823823 1.03553 1.79360i 0.0360964 0.0625209i −0.847413 0.530935i 0.821841π-0.821841\pi
0.883509 + 0.468414i 0.155174π0.155174\pi
824824 0 0
825825 0.343146 0.0119468
826826 0 0
827827 26.2132 0.911522 0.455761 0.890102i 0.349367π-0.349367\pi
0.455761 + 0.890102i 0.349367π0.349367\pi
828828 0 0
829829 −14.6569 + 25.3864i −0.509054 + 0.881707i 0.490891 + 0.871221i 0.336671π0.336671\pi
−0.999945 + 0.0104859i 0.996662π0.996662\pi
830830 0 0
831831 −3.34315 5.79050i −0.115972 0.200870i
832832 0 0
833833 −24.1421 + 23.6544i −0.836475 + 0.819575i
834834 0 0
835835 11.2071 + 19.4113i 0.387838 + 0.671755i
836836 0 0
837837 7.24264 12.5446i 0.250342 0.433606i
838838 0 0
839839 −15.1716 −0.523781 −0.261890 0.965098i 0.584346π-0.584346\pi
−0.261890 + 0.965098i 0.584346π0.584346\pi
840840 0 0
841841 −28.0000 −0.965517
842842 0 0
843843 6.27208 10.8636i 0.216022 0.374161i
844844 0 0
845845 −5.15685 8.93193i −0.177401 0.307268i
846846 0 0
847847 −10.3137 25.2633i −0.354383 0.868058i
848848 0 0
849849 2.89949 + 5.02207i 0.0995104 + 0.172357i
850850 0 0
851851 0 0
852852 0 0
853853 2.54416 0.0871102 0.0435551 0.999051i 0.486132π-0.486132\pi
0.0435551 + 0.999051i 0.486132π0.486132\pi
854854 0 0
855855 8.00000 0.273594
856856 0 0
857857 −17.1421 + 29.6910i −0.585564 + 1.01423i 0.409241 + 0.912426i 0.365794π0.365794\pi
−0.994805 + 0.101800i 0.967540π0.967540\pi
858858 0 0
859859 0.686292 + 1.18869i 0.0234160 + 0.0405576i 0.877496 0.479584i 0.159212π-0.159212\pi
−0.854080 + 0.520142i 0.825879π0.825879\pi
860860 0 0
861861 −5.25736 + 6.77962i −0.179170 + 0.231049i
862862 0 0
863863 7.27817 + 12.6062i 0.247752 + 0.429119i 0.962902 0.269852i 0.0869749π-0.0869749\pi
−0.715150 + 0.698971i 0.753642π0.753642\pi
864864 0 0
865865 −1.65685 + 2.86976i −0.0563347 + 0.0975746i
866866 0 0
867867 2.61522 0.0888177
868868 0 0
869869 −12.2843 −0.416715
870870 0 0
871871 −23.1421 + 40.0834i −0.784141 + 1.35817i
872872 0 0
873873 16.4853 + 28.5533i 0.557942 + 0.966384i
874874 0 0
875875 −2.62132 0.358719i −0.0886168 0.0121269i
876876 0 0
877877 −12.5858 21.7992i −0.424992 0.736107i 0.571428 0.820652i 0.306390π-0.306390\pi
−0.996420 + 0.0845449i 0.973056π0.973056\pi
878878 0 0
879879 3.31371 5.73951i 0.111769 0.193589i
880880 0 0
881881 1.82843 0.0616013 0.0308006 0.999526i 0.490194π-0.490194\pi
0.0308006 + 0.999526i 0.490194π0.490194\pi
882882 0 0
883883 −18.2843 −0.615315 −0.307657 0.951497i 0.599545π-0.599545\pi
−0.307657 + 0.951497i 0.599545π0.599545\pi
884884 0 0
885885 0.928932 1.60896i 0.0312257 0.0540845i
886886 0 0
887887 14.9645 + 25.9192i 0.502458 + 0.870282i 0.999996 + 0.00284012i 0.000904038π0.000904038\pi
−0.497538 + 0.867442i 0.665763π0.665763\pi
888888 0 0
889889 −24.4142 3.34101i −0.818826 0.112054i
890890 0 0
891891 −3.10051 5.37023i −0.103871 0.179910i
892892 0 0
893893 −2.82843 + 4.89898i −0.0946497 + 0.163938i
894894 0 0
895895 10.0000 0.334263
896896 0 0
897897 0.828427 0.0276604
898898 0 0
899899 3.00000 5.19615i 0.100056 0.173301i
900900 0 0
901901 2.82843 + 4.89898i 0.0942286 + 0.163209i
902902 0 0
903903 −2.40812 + 3.10538i −0.0801371 + 0.103341i
904904 0 0
905905 −1.32843 2.30090i −0.0441584 0.0764846i
906906 0 0
907907 −7.10660 + 12.3090i −0.235971 + 0.408713i −0.959554 0.281523i 0.909160π-0.909160\pi
0.723584 + 0.690237i 0.242494π0.242494\pi
908908 0 0
909909 29.1716 0.967560
910910 0 0
911911 10.2010 0.337975 0.168987 0.985618i 0.445950π-0.445950\pi
0.168987 + 0.985618i 0.445950π0.445950\pi
912912 0 0
913913 5.68629 9.84895i 0.188189 0.325953i
914914 0 0
915915 −1.13604 1.96768i −0.0375563 0.0650494i
916916 0 0
917917 19.3137 + 47.3087i 0.637795 + 1.56227i
918918 0 0
919919 −21.5563 37.3367i −0.711078 1.23162i −0.964453 0.264256i 0.914874π-0.914874\pi
0.253374 0.967368i 0.418460π-0.418460\pi
920920 0 0
921921 −0.985281 + 1.70656i −0.0324661 + 0.0562330i
922922 0 0
923923 21.6569 0.712844
924924 0 0
925925 0 0
926926 0 0
927927 3.41421 5.91359i 0.112137 0.194228i
928928 0 0
929929 −2.74264 4.75039i −0.0899831 0.155855i 0.817521 0.575899i 0.195348π-0.195348\pi
−0.907504 + 0.420044i 0.862015π0.862015\pi
930930 0 0
931931 4.92893 + 19.1757i 0.161539 + 0.628457i
932932 0 0
933933 −2.72792 4.72490i −0.0893082 0.154686i
934934 0 0
935935 −2.00000 + 3.46410i −0.0654070 + 0.113288i
936936 0 0
937937 34.6274 1.13123 0.565614 0.824670i 0.308639π-0.308639\pi
0.565614 + 0.824670i 0.308639π0.308639\pi
938938 0 0
939939 −2.62742 −0.0857425
940940 0 0
941941 23.1421 40.0834i 0.754412 1.30668i −0.191254 0.981541i 0.561255π-0.561255\pi
0.945666 0.325139i 0.105411π-0.105411\pi
942942 0 0
943943 −1.62132 2.80821i −0.0527975 0.0914479i
944944 0 0
945945 −2.41421 5.91359i −0.0785344 0.192369i
946946 0 0
947947 16.5919 + 28.7380i 0.539164 + 0.933859i 0.998949 + 0.0458290i 0.0145929π0.0145929\pi
−0.459786 + 0.888030i 0.652074π0.652074\pi
948948 0 0
949949 −2.00000 + 3.46410i −0.0649227 + 0.112449i
950950 0 0
951951 −5.71573 −0.185345
952952 0 0
953953 −13.6569 −0.442389 −0.221194 0.975230i 0.570996π-0.570996\pi
−0.221194 + 0.975230i 0.570996π0.570996\pi
954954 0 0
955955 −6.41421 + 11.1097i −0.207559 + 0.359503i
956956 0 0
957957 0.171573 + 0.297173i 0.00554616 + 0.00960624i
958958 0 0
959959 −15.6569 + 20.1903i −0.505586 + 0.651978i
960960 0 0
961961 −2.50000 4.33013i −0.0806452 0.139682i
962962 0 0
963963 −15.8995 + 27.5387i −0.512354 + 0.887423i
964964 0 0
965965 −2.00000 −0.0643823
966966 0 0
967967 −37.5269 −1.20678 −0.603392 0.797445i 0.706185π-0.706185\pi
−0.603392 + 0.797445i 0.706185π0.706185\pi
968968 0 0
969969 2.82843 4.89898i 0.0908622 0.157378i
970970 0 0
971971 −12.0000 20.7846i −0.385098 0.667010i 0.606685 0.794943i 0.292499π-0.292499\pi
−0.991783 + 0.127933i 0.959166π0.959166\pi
972972 0 0
973973 −42.3137 5.79050i −1.35652 0.185635i
974974 0 0
975975 1.00000 + 1.73205i 0.0320256 + 0.0554700i
976976 0 0
977977 0.656854 1.13770i 0.0210146 0.0363984i −0.855327 0.518089i 0.826644π-0.826644\pi
0.876341 + 0.481690i 0.159977π0.159977\pi
978978 0 0
979979 −7.17157 −0.229204
980980 0 0
981981 38.1421 1.21778
982982 0 0
983983 14.1066 24.4334i 0.449931 0.779303i −0.548450 0.836183i 0.684782π-0.684782\pi
0.998381 + 0.0568803i 0.0181153π0.0181153\pi
984984 0 0
985985 6.17157 + 10.6895i 0.196643 + 0.340595i
986986 0 0
987987 2.17157 + 0.297173i 0.0691219 + 0.00945912i
988988 0 0
989989 −0.742641 1.28629i −0.0236146 0.0409017i
990990 0 0
991991 −2.17157 + 3.76127i −0.0689823 + 0.119481i −0.898454 0.439069i 0.855309π-0.855309\pi
0.829471 + 0.558549i 0.188642π0.188642\pi
992992 0 0
993993 −9.51472 −0.301940
994994 0 0
995995 9.65685 0.306143
996996 0 0
997997 −16.7279 + 28.9736i −0.529779 + 0.917603i 0.469618 + 0.882870i 0.344392π0.344392\pi
−0.999397 + 0.0347337i 0.988942π0.988942\pi
998998 0 0
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 560.2.q.k.81.1 4
4.3 odd 2 35.2.e.a.11.1 4
7.2 even 3 inner 560.2.q.k.401.1 4
7.3 odd 6 3920.2.a.bv.1.1 2
7.4 even 3 3920.2.a.bq.1.2 2
12.11 even 2 315.2.j.e.46.2 4
20.3 even 4 175.2.k.a.74.1 8
20.7 even 4 175.2.k.a.74.4 8
20.19 odd 2 175.2.e.c.151.2 4
28.3 even 6 245.2.a.g.1.2 2
28.11 odd 6 245.2.a.h.1.2 2
28.19 even 6 245.2.e.e.226.1 4
28.23 odd 6 35.2.e.a.16.1 yes 4
28.27 even 2 245.2.e.e.116.1 4
84.11 even 6 2205.2.a.n.1.1 2
84.23 even 6 315.2.j.e.226.2 4
84.59 odd 6 2205.2.a.q.1.1 2
140.3 odd 12 1225.2.b.h.99.1 4
140.23 even 12 175.2.k.a.149.4 8
140.39 odd 6 1225.2.a.k.1.1 2
140.59 even 6 1225.2.a.m.1.1 2
140.67 even 12 1225.2.b.g.99.4 4
140.79 odd 6 175.2.e.c.51.2 4
140.87 odd 12 1225.2.b.h.99.4 4
140.107 even 12 175.2.k.a.149.1 8
140.123 even 12 1225.2.b.g.99.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.2.e.a.11.1 4 4.3 odd 2
35.2.e.a.16.1 yes 4 28.23 odd 6
175.2.e.c.51.2 4 140.79 odd 6
175.2.e.c.151.2 4 20.19 odd 2
175.2.k.a.74.1 8 20.3 even 4
175.2.k.a.74.4 8 20.7 even 4
175.2.k.a.149.1 8 140.107 even 12
175.2.k.a.149.4 8 140.23 even 12
245.2.a.g.1.2 2 28.3 even 6
245.2.a.h.1.2 2 28.11 odd 6
245.2.e.e.116.1 4 28.27 even 2
245.2.e.e.226.1 4 28.19 even 6
315.2.j.e.46.2 4 12.11 even 2
315.2.j.e.226.2 4 84.23 even 6
560.2.q.k.81.1 4 1.1 even 1 trivial
560.2.q.k.401.1 4 7.2 even 3 inner
1225.2.a.k.1.1 2 140.39 odd 6
1225.2.a.m.1.1 2 140.59 even 6
1225.2.b.g.99.1 4 140.123 even 12
1225.2.b.g.99.4 4 140.67 even 12
1225.2.b.h.99.1 4 140.3 odd 12
1225.2.b.h.99.4 4 140.87 odd 12
2205.2.a.n.1.1 2 84.11 even 6
2205.2.a.q.1.1 2 84.59 odd 6
3920.2.a.bq.1.2 2 7.4 even 3
3920.2.a.bv.1.1 2 7.3 odd 6