Properties

Label 480.2.v.a.257.2
Level 480480
Weight 22
Character 480.257
Analytic conductor 3.8333.833
Analytic rank 11
Dimension 44
Inner twists 44

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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] = [480,2,Mod(257,480)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(480, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 2, 1])) 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("480.257"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 480=2535 480 = 2^{5} \cdot 3 \cdot 5
Weight: k k == 2 2
Character orbit: [χ][\chi] == 480.v (of order 44, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 3.832819297023.83281929702
Analytic rank: 11
Dimension: 44
Relative dimension: 22 over Q(i)\Q(i)
Coefficient field: Q(ζ8)\Q(\zeta_{8})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x4+1 x^{4} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 257.2
Root 0.7071070.707107i0.707107 - 0.707107i of defining polynomial
Character χ\chi == 480.257
Dual form 480.2.v.a.353.2

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(0.292893+1.70711i)q3+(0.707107+2.12132i)q5+(3.000003.00000i)q7+(2.828431.00000i)q94.24264iq11+(4.00000+4.00000i)q13+(3.414211.82843i)q15+(1.414211.41421i)q17+(6.000004.24264i)q21+(4.000003.00000i)q25+(2.535534.53553i)q27+4.24264q296.00000q31+(7.24264+1.24264i)q33+(8.485284.24264i)q35+(2.000002.00000i)q37+(5.656858.00000i)q39+(6.00000+6.00000i)q43+(4.121325.29289i)q45+(8.48528+8.48528i)q47+11.0000iq49+(2.00000+2.82843i)q51+(2.828432.82843i)q53+(9.00000+3.00000i)q554.24264q596.00000q61+(5.48528+11.4853i)q63+(5.6568511.3137i)q658.48528iq71+(5.00000+5.00000i)q73+(6.292895.94975i)q75+(12.7279+12.7279i)q776.00000iq79+(7.00000+5.65685i)q81+(8.48528+8.48528i)q83+(2.00000+4.00000i)q85+(1.24264+7.24264i)q87+8.48528q89+24.0000q91+(1.7573610.2426i)q93+(5.000005.00000i)q97+(4.24264+12.0000i)q99+O(q100)q+(-0.292893 + 1.70711i) q^{3} +(-0.707107 + 2.12132i) q^{5} +(-3.00000 - 3.00000i) q^{7} +(-2.82843 - 1.00000i) q^{9} -4.24264i q^{11} +(-4.00000 + 4.00000i) q^{13} +(-3.41421 - 1.82843i) q^{15} +(1.41421 - 1.41421i) q^{17} +(6.00000 - 4.24264i) q^{21} +(-4.00000 - 3.00000i) q^{25} +(2.53553 - 4.53553i) q^{27} +4.24264 q^{29} -6.00000 q^{31} +(7.24264 + 1.24264i) q^{33} +(8.48528 - 4.24264i) q^{35} +(-2.00000 - 2.00000i) q^{37} +(-5.65685 - 8.00000i) q^{39} +(-6.00000 + 6.00000i) q^{43} +(4.12132 - 5.29289i) q^{45} +(-8.48528 + 8.48528i) q^{47} +11.0000i q^{49} +(2.00000 + 2.82843i) q^{51} +(-2.82843 - 2.82843i) q^{53} +(9.00000 + 3.00000i) q^{55} -4.24264 q^{59} -6.00000 q^{61} +(5.48528 + 11.4853i) q^{63} +(-5.65685 - 11.3137i) q^{65} -8.48528i q^{71} +(-5.00000 + 5.00000i) q^{73} +(6.29289 - 5.94975i) q^{75} +(-12.7279 + 12.7279i) q^{77} -6.00000i q^{79} +(7.00000 + 5.65685i) q^{81} +(8.48528 + 8.48528i) q^{83} +(2.00000 + 4.00000i) q^{85} +(-1.24264 + 7.24264i) q^{87} +8.48528 q^{89} +24.0000 q^{91} +(1.75736 - 10.2426i) q^{93} +(-5.00000 - 5.00000i) q^{97} +(-4.24264 + 12.0000i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q4q312q716q138q15+24q2116q254q2724q31+12q338q3724q43+8q45+8q51+36q5524q6112q6320q73+28q75+20q97+O(q100) 4 q - 4 q^{3} - 12 q^{7} - 16 q^{13} - 8 q^{15} + 24 q^{21} - 16 q^{25} - 4 q^{27} - 24 q^{31} + 12 q^{33} - 8 q^{37} - 24 q^{43} + 8 q^{45} + 8 q^{51} + 36 q^{55} - 24 q^{61} - 12 q^{63} - 20 q^{73} + 28 q^{75}+ \cdots - 20 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/480Z)×\left(\mathbb{Z}/480\mathbb{Z}\right)^\times.

nn 3131 9797 161161 421421
χ(n)\chi(n) 11 e(14)e\left(\frac{1}{4}\right) 1-1 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 −0.292893 + 1.70711i −0.169102 + 0.985599i
44 0 0
55 −0.707107 + 2.12132i −0.316228 + 0.948683i
66 0 0
77 −3.00000 3.00000i −1.13389 1.13389i −0.989524 0.144370i 0.953885π-0.953885\pi
−0.144370 0.989524i 0.546115π-0.546115\pi
88 0 0
99 −2.82843 1.00000i −0.942809 0.333333i
1010 0 0
1111 4.24264i 1.27920i −0.768706 0.639602i 0.779099π-0.779099\pi
0.768706 0.639602i 0.220901π-0.220901\pi
1212 0 0
1313 −4.00000 + 4.00000i −1.10940 + 1.10940i −0.116171 + 0.993229i 0.537062π0.537062\pi
−0.993229 + 0.116171i 0.962938π0.962938\pi
1414 0 0
1515 −3.41421 1.82843i −0.881546 0.472098i
1616 0 0
1717 1.41421 1.41421i 0.342997 0.342997i −0.514496 0.857493i 0.672021π-0.672021\pi
0.857493 + 0.514496i 0.172021π0.172021\pi
1818 0 0
1919 0 0 1.00000 00
−1.00000 π\pi
2020 0 0
2121 6.00000 4.24264i 1.30931 0.925820i
2222 0 0
2323 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
2424 0 0
2525 −4.00000 3.00000i −0.800000 0.600000i
2626 0 0
2727 2.53553 4.53553i 0.487964 0.872864i
2828 0 0
2929 4.24264 0.787839 0.393919 0.919145i 0.371119π-0.371119\pi
0.393919 + 0.919145i 0.371119π0.371119\pi
3030 0 0
3131 −6.00000 −1.07763 −0.538816 0.842424i 0.681128π-0.681128\pi
−0.538816 + 0.842424i 0.681128π0.681128\pi
3232 0 0
3333 7.24264 + 1.24264i 1.26078 + 0.216316i
3434 0 0
3535 8.48528 4.24264i 1.43427 0.717137i
3636 0 0
3737 −2.00000 2.00000i −0.328798 0.328798i 0.523331 0.852129i 0.324689π-0.324689\pi
−0.852129 + 0.523331i 0.824689π0.824689\pi
3838 0 0
3939 −5.65685 8.00000i −0.905822 1.28103i
4040 0 0
4141 0 0 1.00000 00
−1.00000 π\pi
4242 0 0
4343 −6.00000 + 6.00000i −0.914991 + 0.914991i −0.996660 0.0816682i 0.973975π-0.973975\pi
0.0816682 + 0.996660i 0.473975π0.473975\pi
4444 0 0
4545 4.12132 5.29289i 0.614370 0.789018i
4646 0 0
4747 −8.48528 + 8.48528i −1.23771 + 1.23771i −0.276769 + 0.960936i 0.589264π0.589264\pi
−0.960936 + 0.276769i 0.910736π0.910736\pi
4848 0 0
4949 11.0000i 1.57143i
5050 0 0
5151 2.00000 + 2.82843i 0.280056 + 0.396059i
5252 0 0
5353 −2.82843 2.82843i −0.388514 0.388514i 0.485643 0.874157i 0.338586π-0.338586\pi
−0.874157 + 0.485643i 0.838586π0.838586\pi
5454 0 0
5555 9.00000 + 3.00000i 1.21356 + 0.404520i
5656 0 0
5757 0 0
5858 0 0
5959 −4.24264 −0.552345 −0.276172 0.961108i 0.589066π-0.589066\pi
−0.276172 + 0.961108i 0.589066π0.589066\pi
6060 0 0
6161 −6.00000 −0.768221 −0.384111 0.923287i 0.625492π-0.625492\pi
−0.384111 + 0.923287i 0.625492π0.625492\pi
6262 0 0
6363 5.48528 + 11.4853i 0.691080 + 1.44701i
6464 0 0
6565 −5.65685 11.3137i −0.701646 1.40329i
6666 0 0
6767 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
6868 0 0
6969 0 0
7070 0 0
7171 8.48528i 1.00702i −0.863990 0.503509i 0.832042π-0.832042\pi
0.863990 0.503509i 0.167958π-0.167958\pi
7272 0 0
7373 −5.00000 + 5.00000i −0.585206 + 0.585206i −0.936329 0.351123i 0.885800π-0.885800\pi
0.351123 + 0.936329i 0.385800π0.385800\pi
7474 0 0
7575 6.29289 5.94975i 0.726641 0.687018i
7676 0 0
7777 −12.7279 + 12.7279i −1.45048 + 1.45048i
7878 0 0
7979 6.00000i 0.675053i −0.941316 0.337526i 0.890410π-0.890410\pi
0.941316 0.337526i 0.109590π-0.109590\pi
8080 0 0
8181 7.00000 + 5.65685i 0.777778 + 0.628539i
8282 0 0
8383 8.48528 + 8.48528i 0.931381 + 0.931381i 0.997792 0.0664117i 0.0211551π-0.0211551\pi
−0.0664117 + 0.997792i 0.521155π0.521155\pi
8484 0 0
8585 2.00000 + 4.00000i 0.216930 + 0.433861i
8686 0 0
8787 −1.24264 + 7.24264i −0.133225 + 0.776493i
8888 0 0
8989 8.48528 0.899438 0.449719 0.893170i 0.351524π-0.351524\pi
0.449719 + 0.893170i 0.351524π0.351524\pi
9090 0 0
9191 24.0000 2.51588
9292 0 0
9393 1.75736 10.2426i 0.182230 1.06211i
9494 0 0
9595 0 0
9696 0 0
9797 −5.00000 5.00000i −0.507673 0.507673i 0.406138 0.913812i 0.366875π-0.366875\pi
−0.913812 + 0.406138i 0.866875π0.866875\pi
9898 0 0
9999 −4.24264 + 12.0000i −0.426401 + 1.20605i
100100 0 0
101101 9.89949i 0.985037i 0.870302 + 0.492518i 0.163924π0.163924\pi
−0.870302 + 0.492518i 0.836076π0.836076\pi
102102 0 0
103103 3.00000 3.00000i 0.295599 0.295599i −0.543688 0.839287i 0.682973π-0.682973\pi
0.839287 + 0.543688i 0.182973π0.182973\pi
104104 0 0
105105 4.75736 + 15.7279i 0.464271 + 1.53489i
106106 0 0
107107 −8.48528 + 8.48528i −0.820303 + 0.820303i −0.986151 0.165848i 0.946964π-0.946964\pi
0.165848 + 0.986151i 0.446964π0.446964\pi
108108 0 0
109109 2.00000i 0.191565i −0.995402 0.0957826i 0.969465π-0.969465\pi
0.995402 0.0957826i 0.0305354π-0.0305354\pi
110110 0 0
111111 4.00000 2.82843i 0.379663 0.268462i
112112 0 0
113113 −1.41421 1.41421i −0.133038 0.133038i 0.637452 0.770490i 0.279988π-0.279988\pi
−0.770490 + 0.637452i 0.779988π0.779988\pi
114114 0 0
115115 0 0
116116 0 0
117117 15.3137 7.31371i 1.41575 0.676153i
118118 0 0
119119 −8.48528 −0.777844
120120 0 0
121121 −7.00000 −0.636364
122122 0 0
123123 0 0
124124 0 0
125125 9.19239 6.36396i 0.822192 0.569210i
126126 0 0
127127 3.00000 + 3.00000i 0.266207 + 0.266207i 0.827570 0.561363i 0.189723π-0.189723\pi
−0.561363 + 0.827570i 0.689723π0.689723\pi
128128 0 0
129129 −8.48528 12.0000i −0.747087 1.05654i
130130 0 0
131131 12.7279i 1.11204i 0.831168 + 0.556022i 0.187673π0.187673\pi
−0.831168 + 0.556022i 0.812327π0.812327\pi
132132 0 0
133133 0 0
134134 0 0
135135 7.82843 + 8.58579i 0.673764 + 0.738947i
136136 0 0
137137 7.07107 7.07107i 0.604122 0.604122i −0.337282 0.941404i 0.609507π-0.609507\pi
0.941404 + 0.337282i 0.109507π0.109507\pi
138138 0 0
139139 12.0000i 1.01783i −0.860818 0.508913i 0.830047π-0.830047\pi
0.860818 0.508913i 0.169953π-0.169953\pi
140140 0 0
141141 −12.0000 16.9706i −1.01058 1.42918i
142142 0 0
143143 16.9706 + 16.9706i 1.41915 + 1.41915i
144144 0 0
145145 −3.00000 + 9.00000i −0.249136 + 0.747409i
146146 0 0
147147 −18.7782 3.22183i −1.54880 0.265732i
148148 0 0
149149 1.41421 0.115857 0.0579284 0.998321i 0.481550π-0.481550\pi
0.0579284 + 0.998321i 0.481550π0.481550\pi
150150 0 0
151151 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
152152 0 0
153153 −5.41421 + 2.58579i −0.437713 + 0.209048i
154154 0 0
155155 4.24264 12.7279i 0.340777 1.02233i
156156 0 0
157157 8.00000 + 8.00000i 0.638470 + 0.638470i 0.950178 0.311708i 0.100901π-0.100901\pi
−0.311708 + 0.950178i 0.600901π0.600901\pi
158158 0 0
159159 5.65685 4.00000i 0.448618 0.317221i
160160 0 0
161161 0 0
162162 0 0
163163 −12.0000 + 12.0000i −0.939913 + 0.939913i −0.998294 0.0583818i 0.981406π-0.981406\pi
0.0583818 + 0.998294i 0.481406π0.481406\pi
164164 0 0
165165 −7.75736 + 14.4853i −0.603910 + 1.12768i
166166 0 0
167167 8.48528 8.48528i 0.656611 0.656611i −0.297966 0.954577i 0.596308π-0.596308\pi
0.954577 + 0.297966i 0.0963081π0.0963081\pi
168168 0 0
169169 19.0000i 1.46154i
170170 0 0
171171 0 0
172172 0 0
173173 9.89949 + 9.89949i 0.752645 + 0.752645i 0.974972 0.222327i 0.0713654π-0.0713654\pi
−0.222327 + 0.974972i 0.571365π0.571365\pi
174174 0 0
175175 3.00000 + 21.0000i 0.226779 + 1.58745i
176176 0 0
177177 1.24264 7.24264i 0.0934026 0.544390i
178178 0 0
179179 −21.2132 −1.58555 −0.792775 0.609515i 0.791364π-0.791364\pi
−0.792775 + 0.609515i 0.791364π0.791364\pi
180180 0 0
181181 2.00000 0.148659 0.0743294 0.997234i 0.476318π-0.476318\pi
0.0743294 + 0.997234i 0.476318π0.476318\pi
182182 0 0
183183 1.75736 10.2426i 0.129908 0.757158i
184184 0 0
185185 5.65685 2.82843i 0.415900 0.207950i
186186 0 0
187187 −6.00000 6.00000i −0.438763 0.438763i
188188 0 0
189189 −21.2132 + 6.00000i −1.54303 + 0.436436i
190190 0 0
191191 8.48528i 0.613973i −0.951714 0.306987i 0.900679π-0.900679\pi
0.951714 0.306987i 0.0993207π-0.0993207\pi
192192 0 0
193193 17.0000 17.0000i 1.22369 1.22369i 0.257375 0.966312i 0.417142π-0.417142\pi
0.966312 0.257375i 0.0828576π-0.0828576\pi
194194 0 0
195195 20.9706 6.34315i 1.50173 0.454242i
196196 0 0
197197 −5.65685 + 5.65685i −0.403034 + 0.403034i −0.879301 0.476267i 0.841990π-0.841990\pi
0.476267 + 0.879301i 0.341990π0.341990\pi
198198 0 0
199199 0 0 1.00000 00
−1.00000 π\pi
200200 0 0
201201 0 0
202202 0 0
203203 −12.7279 12.7279i −0.893325 0.893325i
204204 0 0
205205 0 0
206206 0 0
207207 0 0
208208 0 0
209209 0 0
210210 0 0
211211 −12.0000 −0.826114 −0.413057 0.910705i 0.635539π-0.635539\pi
−0.413057 + 0.910705i 0.635539π0.635539\pi
212212 0 0
213213 14.4853 + 2.48528i 0.992515 + 0.170289i
214214 0 0
215215 −8.48528 16.9706i −0.578691 1.15738i
216216 0 0
217217 18.0000 + 18.0000i 1.22192 + 1.22192i
218218 0 0
219219 −7.07107 10.0000i −0.477818 0.675737i
220220 0 0
221221 11.3137i 0.761042i
222222 0 0
223223 −3.00000 + 3.00000i −0.200895 + 0.200895i −0.800383 0.599489i 0.795371π-0.795371\pi
0.599489 + 0.800383i 0.295371π0.295371\pi
224224 0 0
225225 8.31371 + 12.4853i 0.554247 + 0.832352i
226226 0 0
227227 12.7279 12.7279i 0.844782 0.844782i −0.144695 0.989476i 0.546220π-0.546220\pi
0.989476 + 0.144695i 0.0462199π0.0462199\pi
228228 0 0
229229 6.00000i 0.396491i −0.980152 0.198246i 0.936476π-0.936476\pi
0.980152 0.198246i 0.0635244π-0.0635244\pi
230230 0 0
231231 −18.0000 25.4558i −1.18431 1.67487i
232232 0 0
233233 −18.3848 18.3848i −1.20443 1.20443i −0.972806 0.231621i 0.925597π-0.925597\pi
−0.231621 0.972806i 0.574403π-0.574403\pi
234234 0 0
235235 −12.0000 24.0000i −0.782794 1.56559i
236236 0 0
237237 10.2426 + 1.75736i 0.665331 + 0.114153i
238238 0 0
239239 25.4558 1.64660 0.823301 0.567605i 0.192130π-0.192130\pi
0.823301 + 0.567605i 0.192130π0.192130\pi
240240 0 0
241241 −12.0000 −0.772988 −0.386494 0.922292i 0.626314π-0.626314\pi
−0.386494 + 0.922292i 0.626314π0.626314\pi
242242 0 0
243243 −11.7071 + 10.2929i −0.751011 + 0.660289i
244244 0 0
245245 −23.3345 7.77817i −1.49079 0.496929i
246246 0 0
247247 0 0
248248 0 0
249249 −16.9706 + 12.0000i −1.07547 + 0.760469i
250250 0 0
251251 4.24264i 0.267793i 0.990995 + 0.133897i 0.0427490π0.0427490\pi
−0.990995 + 0.133897i 0.957251π0.957251\pi
252252 0 0
253253 0 0
254254 0 0
255255 −7.41421 + 2.24264i −0.464296 + 0.140440i
256256 0 0
257257 −15.5563 + 15.5563i −0.970378 + 0.970378i −0.999574 0.0291953i 0.990706π-0.990706\pi
0.0291953 + 0.999574i 0.490706π0.490706\pi
258258 0 0
259259 12.0000i 0.745644i
260260 0 0
261261 −12.0000 4.24264i −0.742781 0.262613i
262262 0 0
263263 8.48528 + 8.48528i 0.523225 + 0.523225i 0.918544 0.395319i 0.129366π-0.129366\pi
−0.395319 + 0.918544i 0.629366π0.629366\pi
264264 0 0
265265 8.00000 4.00000i 0.491436 0.245718i
266266 0 0
267267 −2.48528 + 14.4853i −0.152097 + 0.886485i
268268 0 0
269269 18.3848 1.12094 0.560470 0.828175i 0.310621π-0.310621\pi
0.560470 + 0.828175i 0.310621π0.310621\pi
270270 0 0
271271 −24.0000 −1.45790 −0.728948 0.684569i 0.759990π-0.759990\pi
−0.728948 + 0.684569i 0.759990π0.759990\pi
272272 0 0
273273 −7.02944 + 40.9706i −0.425441 + 2.47965i
274274 0 0
275275 −12.7279 + 16.9706i −0.767523 + 1.02336i
276276 0 0
277277 −22.0000 22.0000i −1.32185 1.32185i −0.912276 0.409576i 0.865677π-0.865677\pi
−0.409576 0.912276i 0.634323π-0.634323\pi
278278 0 0
279279 16.9706 + 6.00000i 1.01600 + 0.359211i
280280 0 0
281281 8.48528i 0.506189i 0.967442 + 0.253095i 0.0814484π0.0814484\pi
−0.967442 + 0.253095i 0.918552π0.918552\pi
282282 0 0
283283 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 0 0
289289 13.0000i 0.764706i
290290 0 0
291291 10.0000 7.07107i 0.586210 0.414513i
292292 0 0
293293 −22.6274 22.6274i −1.32191 1.32191i −0.912231 0.409677i 0.865641π-0.865641\pi
−0.409677 0.912231i 0.634359π-0.634359\pi
294294 0 0
295295 3.00000 9.00000i 0.174667 0.524000i
296296 0 0
297297 −19.2426 10.7574i −1.11657 0.624205i
298298 0 0
299299 0 0
300300 0 0
301301 36.0000 2.07501
302302 0 0
303303 −16.8995 2.89949i −0.970851 0.166572i
304304 0 0
305305 4.24264 12.7279i 0.242933 0.728799i
306306 0 0
307307 −18.0000 18.0000i −1.02731 1.02731i −0.999616 0.0276979i 0.991182π-0.991182\pi
−0.0276979 0.999616i 0.508818π-0.508818\pi
308308 0 0
309309 4.24264 + 6.00000i 0.241355 + 0.341328i
310310 0 0
311311 8.48528i 0.481156i −0.970630 0.240578i 0.922663π-0.922663\pi
0.970630 0.240578i 0.0773370π-0.0773370\pi
312312 0 0
313313 17.0000 17.0000i 0.960897 0.960897i −0.0383669 0.999264i 0.512216π-0.512216\pi
0.999264 + 0.0383669i 0.0122156π0.0122156\pi
314314 0 0
315315 −28.2426 + 3.51472i −1.59129 + 0.198032i
316316 0 0
317317 9.89949 9.89949i 0.556011 0.556011i −0.372158 0.928169i 0.621382π-0.621382\pi
0.928169 + 0.372158i 0.121382π0.121382\pi
318318 0 0
319319 18.0000i 1.00781i
320320 0 0
321321 −12.0000 16.9706i −0.669775 0.947204i
322322 0 0
323323 0 0
324324 0 0
325325 28.0000 4.00000i 1.55316 0.221880i
326326 0 0
327327 3.41421 + 0.585786i 0.188806 + 0.0323941i
328328 0 0
329329 50.9117 2.80685
330330 0 0
331331 12.0000 0.659580 0.329790 0.944054i 0.393022π-0.393022\pi
0.329790 + 0.944054i 0.393022π0.393022\pi
332332 0 0
333333 3.65685 + 7.65685i 0.200394 + 0.419593i
334334 0 0
335335 0 0
336336 0 0
337337 7.00000 + 7.00000i 0.381314 + 0.381314i 0.871576 0.490261i 0.163099π-0.163099\pi
−0.490261 + 0.871576i 0.663099π0.663099\pi
338338 0 0
339339 2.82843 2.00000i 0.153619 0.108625i
340340 0 0
341341 25.4558i 1.37851i
342342 0 0
343343 12.0000 12.0000i 0.647939 0.647939i
344344 0 0
345345 0 0
346346 0 0
347347 12.7279 12.7279i 0.683271 0.683271i −0.277465 0.960736i 0.589494π-0.589494\pi
0.960736 + 0.277465i 0.0894943π0.0894943\pi
348348 0 0
349349 18.0000i 0.963518i −0.876304 0.481759i 0.839998π-0.839998\pi
0.876304 0.481759i 0.160002π-0.160002\pi
350350 0 0
351351 8.00000 + 28.2843i 0.427008 + 1.50970i
352352 0 0
353353 1.41421 + 1.41421i 0.0752710 + 0.0752710i 0.743740 0.668469i 0.233050π-0.233050\pi
−0.668469 + 0.743740i 0.733050π0.733050\pi
354354 0 0
355355 18.0000 + 6.00000i 0.955341 + 0.318447i
356356 0 0
357357 2.48528 14.4853i 0.131535 0.766642i
358358 0 0
359359 −16.9706 −0.895672 −0.447836 0.894116i 0.647805π-0.647805\pi
−0.447836 + 0.894116i 0.647805π0.647805\pi
360360 0 0
361361 19.0000 1.00000
362362 0 0
363363 2.05025 11.9497i 0.107610 0.627199i
364364 0 0
365365 −7.07107 14.1421i −0.370117 0.740233i
366366 0 0
367367 15.0000 + 15.0000i 0.782994 + 0.782994i 0.980335 0.197341i 0.0632307π-0.0632307\pi
−0.197341 + 0.980335i 0.563231π0.563231\pi
368368 0 0
369369 0 0
370370 0 0
371371 16.9706i 0.881068i
372372 0 0
373373 −20.0000 + 20.0000i −1.03556 + 1.03556i −0.0362168 + 0.999344i 0.511531π0.511531\pi
−0.999344 + 0.0362168i 0.988469π0.988469\pi
374374 0 0
375375 8.17157 + 17.5563i 0.421978 + 0.906606i
376376 0 0
377377 −16.9706 + 16.9706i −0.874028 + 0.874028i
378378 0 0
379379 36.0000i 1.84920i 0.380945 + 0.924598i 0.375599π0.375599\pi
−0.380945 + 0.924598i 0.624401π0.624401\pi
380380 0 0
381381 −6.00000 + 4.24264i −0.307389 + 0.217357i
382382 0 0
383383 −25.4558 25.4558i −1.30073 1.30073i −0.927898 0.372835i 0.878386π-0.878386\pi
−0.372835 0.927898i 0.621614π-0.621614\pi
384384 0 0
385385 −18.0000 36.0000i −0.917365 1.83473i
386386 0 0
387387 22.9706 10.9706i 1.16766 0.557665i
388388 0 0
389389 15.5563 0.788738 0.394369 0.918952i 0.370963π-0.370963\pi
0.394369 + 0.918952i 0.370963π0.370963\pi
390390 0 0
391391 0 0
392392 0 0
393393 −21.7279 3.72792i −1.09603 0.188049i
394394 0 0
395395 12.7279 + 4.24264i 0.640411 + 0.213470i
396396 0 0
397397 −14.0000 14.0000i −0.702640 0.702640i 0.262337 0.964976i 0.415507π-0.415507\pi
−0.964976 + 0.262337i 0.915507π0.915507\pi
398398 0 0
399399 0 0
400400 0 0
401401 14.1421i 0.706225i −0.935581 0.353112i 0.885123π-0.885123\pi
0.935581 0.353112i 0.114877π-0.114877\pi
402402 0 0
403403 24.0000 24.0000i 1.19553 1.19553i
404404 0 0
405405 −16.9497 + 10.8492i −0.842240 + 0.539103i
406406 0 0
407407 −8.48528 + 8.48528i −0.420600 + 0.420600i
408408 0 0
409409 32.0000i 1.58230i 0.611623 + 0.791149i 0.290517π0.290517\pi
−0.611623 + 0.791149i 0.709483π0.709483\pi
410410 0 0
411411 10.0000 + 14.1421i 0.493264 + 0.697580i
412412 0 0
413413 12.7279 + 12.7279i 0.626300 + 0.626300i
414414 0 0
415415 −24.0000 + 12.0000i −1.17811 + 0.589057i
416416 0 0
417417 20.4853 + 3.51472i 1.00317 + 0.172117i
418418 0 0
419419 29.6985 1.45087 0.725433 0.688293i 0.241640π-0.241640\pi
0.725433 + 0.688293i 0.241640π0.241640\pi
420420 0 0
421421 6.00000 0.292422 0.146211 0.989253i 0.453292π-0.453292\pi
0.146211 + 0.989253i 0.453292π0.453292\pi
422422 0 0
423423 32.4853 15.5147i 1.57949 0.754351i
424424 0 0
425425 −9.89949 + 1.41421i −0.480196 + 0.0685994i
426426 0 0
427427 18.0000 + 18.0000i 0.871081 + 0.871081i
428428 0 0
429429 −33.9411 + 24.0000i −1.63869 + 1.15873i
430430 0 0
431431 16.9706i 0.817443i 0.912659 + 0.408722i 0.134025π0.134025\pi
−0.912659 + 0.408722i 0.865975π0.865975\pi
432432 0 0
433433 7.00000 7.00000i 0.336399 0.336399i −0.518611 0.855010i 0.673551π-0.673551\pi
0.855010 + 0.518611i 0.173551π0.173551\pi
434434 0 0
435435 −14.4853 7.75736i −0.694516 0.371937i
436436 0 0
437437 0 0
438438 0 0
439439 24.0000i 1.14546i 0.819745 + 0.572729i 0.194115π0.194115\pi
−0.819745 + 0.572729i 0.805885π0.805885\pi
440440 0 0
441441 11.0000 31.1127i 0.523810 1.48156i
442442 0 0
443443 −12.7279 12.7279i −0.604722 0.604722i 0.336840 0.941562i 0.390642π-0.390642\pi
−0.941562 + 0.336840i 0.890642π0.890642\pi
444444 0 0
445445 −6.00000 + 18.0000i −0.284427 + 0.853282i
446446 0 0
447447 −0.414214 + 2.41421i −0.0195916 + 0.114188i
448448 0 0
449449 −31.1127 −1.46830 −0.734150 0.678988i 0.762419π-0.762419\pi
−0.734150 + 0.678988i 0.762419π0.762419\pi
450450 0 0
451451 0 0
452452 0 0
453453 0 0
454454 0 0
455455 −16.9706 + 50.9117i −0.795592 + 2.38678i
456456 0 0
457457 −7.00000 7.00000i −0.327446 0.327446i 0.524168 0.851615i 0.324376π-0.324376\pi
−0.851615 + 0.524168i 0.824376π0.824376\pi
458458 0 0
459459 −2.82843 10.0000i −0.132020 0.466760i
460460 0 0
461461 15.5563i 0.724531i −0.932075 0.362266i 0.882003π-0.882003\pi
0.932075 0.362266i 0.117997π-0.117997\pi
462462 0 0
463463 15.0000 15.0000i 0.697109 0.697109i −0.266677 0.963786i 0.585926π-0.585926\pi
0.963786 + 0.266677i 0.0859256π0.0859256\pi
464464 0 0
465465 20.4853 + 10.9706i 0.949982 + 0.508748i
466466 0 0
467467 −8.48528 + 8.48528i −0.392652 + 0.392652i −0.875632 0.482980i 0.839555π-0.839555\pi
0.482980 + 0.875632i 0.339555π0.339555\pi
468468 0 0
469469 0 0
470470 0 0
471471 −16.0000 + 11.3137i −0.737241 + 0.521308i
472472 0 0
473473 25.4558 + 25.4558i 1.17046 + 1.17046i
474474 0 0
475475 0 0
476476 0 0
477477 5.17157 + 10.8284i 0.236790 + 0.495800i
478478 0 0
479479 8.48528 0.387702 0.193851 0.981031i 0.437902π-0.437902\pi
0.193851 + 0.981031i 0.437902π0.437902\pi
480480 0 0
481481 16.0000 0.729537
482482 0 0
483483 0 0
484484 0 0
485485 14.1421 7.07107i 0.642161 0.321081i
486486 0 0
487487 3.00000 + 3.00000i 0.135943 + 0.135943i 0.771804 0.635861i 0.219355π-0.219355\pi
−0.635861 + 0.771804i 0.719355π0.719355\pi
488488 0 0
489489 −16.9706 24.0000i −0.767435 1.08532i
490490 0 0
491491 12.7279i 0.574403i 0.957870 + 0.287202i 0.0927249π0.0927249\pi
−0.957870 + 0.287202i 0.907275π0.907275\pi
492492 0 0
493493 6.00000 6.00000i 0.270226 0.270226i
494494 0 0
495495 −22.4558 17.4853i −1.00932 0.785905i
496496 0 0
497497 −25.4558 + 25.4558i −1.14185 + 1.14185i
498498 0 0
499499 24.0000i 1.07439i 0.843459 + 0.537194i 0.180516π0.180516\pi
−0.843459 + 0.537194i 0.819484π0.819484\pi
500500 0 0
501501 12.0000 + 16.9706i 0.536120 + 0.758189i
502502 0 0
503503 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
504504 0 0
505505 −21.0000 7.00000i −0.934488 0.311496i
506506 0 0
507507 32.4350 + 5.56497i 1.44049 + 0.247149i
508508 0 0
509509 −12.7279 −0.564155 −0.282078 0.959392i 0.591024π-0.591024\pi
−0.282078 + 0.959392i 0.591024π0.591024\pi
510510 0 0
511511 30.0000 1.32712
512512 0 0
513513 0 0
514514 0 0
515515 4.24264 + 8.48528i 0.186953 + 0.373906i
516516 0 0
517517 36.0000 + 36.0000i 1.58328 + 1.58328i
518518 0 0
519519 −19.7990 + 14.0000i −0.869079 + 0.614532i
520520 0 0
521521 31.1127i 1.36307i 0.731785 + 0.681536i 0.238688π0.238688\pi
−0.731785 + 0.681536i 0.761312π0.761312\pi
522522 0 0
523523 −12.0000 + 12.0000i −0.524723 + 0.524723i −0.918994 0.394271i 0.870997π-0.870997\pi
0.394271 + 0.918994i 0.370997π0.370997\pi
524524 0 0
525525 −36.7279 1.02944i −1.60294 0.0449283i
526526 0 0
527527 −8.48528 + 8.48528i −0.369625 + 0.369625i
528528 0 0
529529 23.0000i 1.00000i
530530 0 0
531531 12.0000 + 4.24264i 0.520756 + 0.184115i
532532 0 0
533533 0 0
534534 0 0
535535 −12.0000 24.0000i −0.518805 1.03761i
536536 0 0
537537 6.21320 36.2132i 0.268120 1.56272i
538538 0 0
539539 46.6690 2.01018
540540 0 0
541541 −2.00000 −0.0859867 −0.0429934 0.999075i 0.513689π-0.513689\pi
−0.0429934 + 0.999075i 0.513689π0.513689\pi
542542 0 0
543543 −0.585786 + 3.41421i −0.0251385 + 0.146518i
544544 0 0
545545 4.24264 + 1.41421i 0.181735 + 0.0605783i
546546 0 0
547547 18.0000 + 18.0000i 0.769624 + 0.769624i 0.978040 0.208416i 0.0668307π-0.0668307\pi
−0.208416 + 0.978040i 0.566831π0.566831\pi
548548 0 0
549549 16.9706 + 6.00000i 0.724286 + 0.256074i
550550 0 0
551551 0 0
552552 0 0
553553 −18.0000 + 18.0000i −0.765438 + 0.765438i
554554 0 0
555555 3.17157 + 10.4853i 0.134626 + 0.445075i
556556 0 0
557557 11.3137 11.3137i 0.479377 0.479377i −0.425555 0.904932i 0.639921π-0.639921\pi
0.904932 + 0.425555i 0.139921π0.139921\pi
558558 0 0
559559 48.0000i 2.03018i
560560 0 0
561561 12.0000 8.48528i 0.506640 0.358249i
562562 0 0
563563 −21.2132 21.2132i −0.894030 0.894030i 0.100870 0.994900i 0.467837π-0.467837\pi
−0.994900 + 0.100870i 0.967837π0.967837\pi
564564 0 0
565565 4.00000 2.00000i 0.168281 0.0841406i
566566 0 0
567567 −4.02944 37.9706i −0.169220 1.59461i
568568 0 0
569569 2.82843 0.118574 0.0592869 0.998241i 0.481117π-0.481117\pi
0.0592869 + 0.998241i 0.481117π0.481117\pi
570570 0 0
571571 −12.0000 −0.502184 −0.251092 0.967963i 0.580790π-0.580790\pi
−0.251092 + 0.967963i 0.580790π0.580790\pi
572572 0 0
573573 14.4853 + 2.48528i 0.605131 + 0.103824i
574574 0 0
575575 0 0
576576 0 0
577577 5.00000 + 5.00000i 0.208153 + 0.208153i 0.803482 0.595329i 0.202978π-0.202978\pi
−0.595329 + 0.803482i 0.702978π0.702978\pi
578578 0 0
579579 24.0416 + 34.0000i 0.999136 + 1.41299i
580580 0 0
581581 50.9117i 2.11217i
582582 0 0
583583 −12.0000 + 12.0000i −0.496989 + 0.496989i
584584 0 0
585585 4.68629 + 37.6569i 0.193754 + 1.55692i
586586 0 0
587587 −8.48528 + 8.48528i −0.350225 + 0.350225i −0.860193 0.509968i 0.829657π-0.829657\pi
0.509968 + 0.860193i 0.329657π0.329657\pi
588588 0 0
589589 0 0
590590 0 0
591591 −8.00000 11.3137i −0.329076 0.465384i
592592 0 0
593593 −24.0416 24.0416i −0.987271 0.987271i 0.0126486 0.999920i 0.495974π-0.495974\pi
−0.999920 + 0.0126486i 0.995974π0.995974\pi
594594 0 0
595595 6.00000 18.0000i 0.245976 0.737928i
596596 0 0
597597 0 0
598598 0 0
599599 16.9706 0.693398 0.346699 0.937976i 0.387302π-0.387302\pi
0.346699 + 0.937976i 0.387302π0.387302\pi
600600 0 0
601601 −42.0000 −1.71322 −0.856608 0.515968i 0.827432π-0.827432\pi
−0.856608 + 0.515968i 0.827432π0.827432\pi
602602 0 0
603603 0 0
604604 0 0
605605 4.94975 14.8492i 0.201236 0.603708i
606606 0 0
607607 9.00000 + 9.00000i 0.365299 + 0.365299i 0.865759 0.500461i 0.166836π-0.166836\pi
−0.500461 + 0.865759i 0.666836π0.666836\pi
608608 0 0
609609 25.4558 18.0000i 1.03152 0.729397i
610610 0 0
611611 67.8823i 2.74622i
612612 0 0
613613 −10.0000 + 10.0000i −0.403896 + 0.403896i −0.879604 0.475707i 0.842192π-0.842192\pi
0.475707 + 0.879604i 0.342192π0.342192\pi
614614 0 0
615615 0 0
616616 0 0
617617 26.8701 26.8701i 1.08175 1.08175i 0.0854011 0.996347i 0.472783π-0.472783\pi
0.996347 0.0854011i 0.0272172π-0.0272172\pi
618618 0 0
619619 36.0000i 1.44696i −0.690344 0.723481i 0.742541π-0.742541\pi
0.690344 0.723481i 0.257459π-0.257459\pi
620620 0 0
621621 0 0
622622 0 0
623623 −25.4558 25.4558i −1.01987 1.01987i
624624 0 0
625625 7.00000 + 24.0000i 0.280000 + 0.960000i
626626 0 0
627627 0 0
628628 0 0
629629 −5.65685 −0.225554
630630 0 0
631631 −18.0000 −0.716569 −0.358284 0.933613i 0.616638π-0.616638\pi
−0.358284 + 0.933613i 0.616638π0.616638\pi
632632 0 0
633633 3.51472 20.4853i 0.139698 0.814217i
634634 0 0
635635 −8.48528 + 4.24264i −0.336728 + 0.168364i
636636 0 0
637637 −44.0000 44.0000i −1.74334 1.74334i
638638 0 0
639639 −8.48528 + 24.0000i −0.335673 + 0.949425i
640640 0 0
641641 16.9706i 0.670297i 0.942165 + 0.335148i 0.108786π0.108786\pi
−0.942165 + 0.335148i 0.891214π0.891214\pi
642642 0 0
643643 24.0000 24.0000i 0.946468 0.946468i −0.0521706 0.998638i 0.516614π-0.516614\pi
0.998638 + 0.0521706i 0.0166140π0.0166140\pi
644644 0 0
645645 31.4558 9.51472i 1.23857 0.374642i
646646 0 0
647647 16.9706 16.9706i 0.667182 0.667182i −0.289881 0.957063i 0.593616π-0.593616\pi
0.957063 + 0.289881i 0.0936157π0.0936157\pi
648648 0 0
649649 18.0000i 0.706562i
650650 0 0
651651 −36.0000 + 25.4558i −1.41095 + 0.997693i
652652 0 0
653653 −7.07107 7.07107i −0.276712 0.276712i 0.555083 0.831795i 0.312687π-0.312687\pi
−0.831795 + 0.555083i 0.812687π0.812687\pi
654654 0 0
655655 −27.0000 9.00000i −1.05498 0.351659i
656656 0 0
657657 19.1421 9.14214i 0.746806 0.356669i
658658 0 0
659659 −38.1838 −1.48743 −0.743714 0.668498i 0.766938π-0.766938\pi
−0.743714 + 0.668498i 0.766938π0.766938\pi
660660 0 0
661661 −30.0000 −1.16686 −0.583432 0.812162i 0.698291π-0.698291\pi
−0.583432 + 0.812162i 0.698291π0.698291\pi
662662 0 0
663663 −19.3137 3.31371i −0.750082 0.128694i
664664 0 0
665665 0 0
666666 0 0
667667 0 0
668668 0 0
669669 −4.24264 6.00000i −0.164030 0.231973i
670670 0 0
671671 25.4558i 0.982712i
672672 0 0
673673 −11.0000 + 11.0000i −0.424019 + 0.424019i −0.886585 0.462566i 0.846929π-0.846929\pi
0.462566 + 0.886585i 0.346929π0.346929\pi
674674 0 0
675675 −23.7487 + 10.5355i −0.914089 + 0.405513i
676676 0 0
677677 −26.8701 + 26.8701i −1.03270 + 1.03270i −0.0332533 + 0.999447i 0.510587π0.510587\pi
−0.999447 + 0.0332533i 0.989413π0.989413\pi
678678 0 0
679679 30.0000i 1.15129i
680680 0 0
681681 18.0000 + 25.4558i 0.689761 + 0.975470i
682682 0 0
683683 8.48528 + 8.48528i 0.324680 + 0.324680i 0.850559 0.525879i 0.176264π-0.176264\pi
−0.525879 + 0.850559i 0.676264π0.676264\pi
684684 0 0
685685 10.0000 + 20.0000i 0.382080 + 0.764161i
686686 0 0
687687 10.2426 + 1.75736i 0.390781 + 0.0670474i
688688 0 0
689689 22.6274 0.862036
690690 0 0
691691 −48.0000 −1.82601 −0.913003 0.407953i 0.866243π-0.866243\pi
−0.913003 + 0.407953i 0.866243π0.866243\pi
692692 0 0
693693 48.7279 23.2721i 1.85102 0.884033i
694694 0 0
695695 25.4558 + 8.48528i 0.965595 + 0.321865i
696696 0 0
697697 0 0
698698 0 0
699699 36.7696 26.0000i 1.39075 0.983410i
700700 0 0
701701 29.6985i 1.12170i 0.827919 + 0.560848i 0.189525π0.189525\pi
−0.827919 + 0.560848i 0.810475π0.810475\pi
702702 0 0
703703 0 0
704704 0 0
705705 44.4853 13.4558i 1.67541 0.506776i
706706 0 0
707707 29.6985 29.6985i 1.11693 1.11693i
708708 0 0
709709 30.0000i 1.12667i −0.826227 0.563337i 0.809517π-0.809517\pi
0.826227 0.563337i 0.190483π-0.190483\pi
710710 0 0
711711 −6.00000 + 16.9706i −0.225018 + 0.636446i
712712 0 0
713713 0 0
714714 0 0
715715 −48.0000 + 24.0000i −1.79510 + 0.897549i
716716 0 0
717717 −7.45584 + 43.4558i −0.278444 + 1.62289i
718718 0 0
719719 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
720720 0 0
721721 −18.0000 −0.670355
722722 0 0
723723 3.51472 20.4853i 0.130714 0.761856i
724724 0 0
725725 −16.9706 12.7279i −0.630271 0.472703i
726726 0 0
727727 −33.0000 33.0000i −1.22390 1.22390i −0.966233 0.257669i 0.917046π-0.917046\pi
−0.257669 0.966233i 0.582954π-0.582954\pi
728728 0 0
729729 −14.1421 23.0000i −0.523783 0.851852i
730730 0 0
731731 16.9706i 0.627679i
732732 0 0
733733 −2.00000 + 2.00000i −0.0738717 + 0.0738717i −0.743077 0.669206i 0.766635π-0.766635\pi
0.669206 + 0.743077i 0.266635π0.266635\pi
734734 0 0
735735 20.1127 37.5563i 0.741868 1.38529i
736736 0 0
737737 0 0
738738 0 0
739739 12.0000i 0.441427i 0.975339 + 0.220714i 0.0708386π0.0708386\pi
−0.975339 + 0.220714i 0.929161π0.929161\pi
740740 0 0
741741 0 0
742742 0 0
743743 −16.9706 16.9706i −0.622590 0.622590i 0.323603 0.946193i 0.395106π-0.395106\pi
−0.946193 + 0.323603i 0.895106π0.895106\pi
744744 0 0
745745 −1.00000 + 3.00000i −0.0366372 + 0.109911i
746746 0 0
747747 −15.5147 32.4853i −0.567654 1.18857i
748748 0 0
749749 50.9117 1.86027
750750 0 0
751751 6.00000 0.218943 0.109472 0.993990i 0.465084π-0.465084\pi
0.109472 + 0.993990i 0.465084π0.465084\pi
752752 0 0
753753 −7.24264 1.24264i −0.263936 0.0452843i
754754 0 0
755755 0 0
756756 0 0
757757 26.0000 + 26.0000i 0.944986 + 0.944986i 0.998564 0.0535776i 0.0170625π-0.0170625\pi
−0.0535776 + 0.998564i 0.517062π0.517062\pi
758758 0 0
759759 0 0
760760 0 0
761761 36.7696i 1.33290i 0.745552 + 0.666448i 0.232186π0.232186\pi
−0.745552 + 0.666448i 0.767814π0.767814\pi
762762 0 0
763763 −6.00000 + 6.00000i −0.217215 + 0.217215i
764764 0 0
765765 −1.65685 13.3137i −0.0599037 0.481358i
766766 0 0
767767 16.9706 16.9706i 0.612772 0.612772i
768768 0 0
769769 42.0000i 1.51456i 0.653091 + 0.757279i 0.273472π0.273472\pi
−0.653091 + 0.757279i 0.726528π0.726528\pi
770770 0 0
771771 −22.0000 31.1127i −0.792311 1.12050i
772772 0 0
773773 −26.8701 26.8701i −0.966449 0.966449i 0.0330063 0.999455i 0.489492π-0.489492\pi
−0.999455 + 0.0330063i 0.989492π0.989492\pi
774774 0 0
775775 24.0000 + 18.0000i 0.862105 + 0.646579i
776776 0 0
777777 −20.4853 3.51472i −0.734905 0.126090i
778778 0 0
779779 0 0
780780 0 0
781781 −36.0000 −1.28818
782782 0 0
783783 10.7574 19.2426i 0.384437 0.687676i
784784 0 0
785785 −22.6274 + 11.3137i −0.807607 + 0.403804i
786786 0 0
787787 −24.0000 24.0000i −0.855508 0.855508i 0.135297 0.990805i 0.456801π-0.456801\pi
−0.990805 + 0.135297i 0.956801π0.956801\pi
788788 0 0
789789 −16.9706 + 12.0000i −0.604168 + 0.427211i
790790 0 0
791791 8.48528i 0.301702i
792792 0 0
793793 24.0000 24.0000i 0.852265 0.852265i
794794 0 0
795795 4.48528 + 14.8284i 0.159077 + 0.525910i
796796 0 0
797797 1.41421 1.41421i 0.0500940 0.0500940i −0.681616 0.731710i 0.738723π-0.738723\pi
0.731710 + 0.681616i 0.238723π0.238723\pi
798798 0 0
799799 24.0000i 0.849059i
800800 0 0
801801 −24.0000 8.48528i −0.847998 0.299813i
802802 0 0
803803 21.2132 + 21.2132i 0.748598 + 0.748598i
804804 0 0
805805 0 0
806806 0 0
807807 −5.38478 + 31.3848i −0.189553 + 1.10480i
808808 0 0
809809 −33.9411 −1.19331 −0.596653 0.802499i 0.703503π-0.703503\pi
−0.596653 + 0.802499i 0.703503π0.703503\pi
810810 0 0
811811 24.0000 0.842754 0.421377 0.906886i 0.361547π-0.361547\pi
0.421377 + 0.906886i 0.361547π0.361547\pi
812812 0 0
813813 7.02944 40.9706i 0.246533 1.43690i
814814 0 0
815815 −16.9706 33.9411i −0.594453 1.18891i
816816 0 0
817817 0 0
818818 0 0
819819 −67.8823 24.0000i −2.37200 0.838628i
820820 0 0
821821 21.2132i 0.740346i −0.928963 0.370173i 0.879298π-0.879298\pi
0.928963 0.370173i 0.120702π-0.120702\pi
822822 0 0
823823 −27.0000 + 27.0000i −0.941161 + 0.941161i −0.998363 0.0572018i 0.981782π-0.981782\pi
0.0572018 + 0.998363i 0.481782π0.481782\pi
824824 0 0
825825 −25.2426 26.6985i −0.878836 0.929522i
826826 0 0
827827 −21.2132 + 21.2132i −0.737655 + 0.737655i −0.972124 0.234468i 0.924665π-0.924665\pi
0.234468 + 0.972124i 0.424665π0.424665\pi
828828 0 0
829829 38.0000i 1.31979i 0.751356 + 0.659897i 0.229400π0.229400\pi
−0.751356 + 0.659897i 0.770600π0.770600\pi
830830 0 0
831831 44.0000 31.1127i 1.52634 1.07929i
832832 0 0
833833 15.5563 + 15.5563i 0.538996 + 0.538996i
834834 0 0
835835 12.0000 + 24.0000i 0.415277 + 0.830554i
836836 0 0
837837 −15.2132 + 27.2132i −0.525845 + 0.940626i
838838 0 0
839839 33.9411 1.17178 0.585889 0.810391i 0.300745π-0.300745\pi
0.585889 + 0.810391i 0.300745π0.300745\pi
840840 0 0
841841 −11.0000 −0.379310
842842 0 0
843843 −14.4853 2.48528i −0.498900 0.0855976i
844844 0 0
845845 40.3051 + 13.4350i 1.38654 + 0.462179i
846846 0 0
847847 21.0000 + 21.0000i 0.721569 + 0.721569i
848848 0 0
849849 0 0
850850 0 0
851851 0 0
852852 0 0
853853 −22.0000 + 22.0000i −0.753266 + 0.753266i −0.975087 0.221822i 0.928800π-0.928800\pi
0.221822 + 0.975087i 0.428800π0.428800\pi
854854 0 0
855855 0 0
856856 0 0
857857 −9.89949 + 9.89949i −0.338160 + 0.338160i −0.855675 0.517514i 0.826857π-0.826857\pi
0.517514 + 0.855675i 0.326857π0.326857\pi
858858 0 0
859859 36.0000i 1.22830i −0.789188 0.614152i 0.789498π-0.789498\pi
0.789188 0.614152i 0.210502π-0.210502\pi
860860 0 0
861861 0 0
862862 0 0
863863 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
864864 0 0
865865 −28.0000 + 14.0000i −0.952029 + 0.476014i
866866 0 0
867867 −22.1924 3.80761i −0.753693 0.129313i
868868 0 0
869869 −25.4558 −0.863530
870870 0 0
871871 0 0
872872 0 0
873873 9.14214 + 19.1421i 0.309414 + 0.647863i
874874 0 0
875875 −46.6690 8.48528i −1.57770 0.286855i
876876 0 0
877877 −4.00000 4.00000i −0.135070 0.135070i 0.636339 0.771409i 0.280448π-0.280448\pi
−0.771409 + 0.636339i 0.780448π0.780448\pi
878878 0 0
879879 45.2548 32.0000i 1.52641 1.07933i
880880 0 0
881881 25.4558i 0.857629i 0.903393 + 0.428815i 0.141069π0.141069\pi
−0.903393 + 0.428815i 0.858931π0.858931\pi
882882 0 0
883883 12.0000 12.0000i 0.403832 0.403832i −0.475749 0.879581i 0.657823π-0.657823\pi
0.879581 + 0.475749i 0.157823π0.157823\pi
884884 0 0
885885 14.4853 + 7.75736i 0.486917 + 0.260761i
886886 0 0
887887 16.9706 16.9706i 0.569816 0.569816i −0.362261 0.932077i 0.617995π-0.617995\pi
0.932077 + 0.362261i 0.117995π0.117995\pi
888888 0 0
889889 18.0000i 0.603701i
890890 0 0
891891 24.0000 29.6985i 0.804030 0.994937i
892892 0 0
893893 0 0
894894 0 0
895895 15.0000 45.0000i 0.501395 1.50418i
896896 0 0
897897 0 0
898898 0 0
899899 −25.4558 −0.849000
900900 0 0
901901 −8.00000 −0.266519
902902 0 0
903903 −10.5442 + 61.4558i −0.350888 + 2.04512i
904904 0 0
905905 −1.41421 + 4.24264i −0.0470100 + 0.141030i
906906 0 0
907907 6.00000 + 6.00000i 0.199227 + 0.199227i 0.799668 0.600442i 0.205009π-0.205009\pi
−0.600442 + 0.799668i 0.705009π0.705009\pi
908908 0 0
909909 9.89949 28.0000i 0.328346 0.928701i
910910 0 0
911911 33.9411i 1.12452i −0.826961 0.562260i 0.809932π-0.809932\pi
0.826961 0.562260i 0.190068π-0.190068\pi
912912 0 0
913913 36.0000 36.0000i 1.19143 1.19143i
914914 0 0
915915 20.4853 + 10.9706i 0.677223 + 0.362676i
916916 0 0
917917 38.1838 38.1838i 1.26094 1.26094i
918918 0 0
919919 42.0000i 1.38545i 0.721201 + 0.692726i 0.243591π0.243591\pi
−0.721201 + 0.692726i 0.756409π0.756409\pi
920920 0 0
921921 36.0000 25.4558i 1.18624 0.838799i
922922 0 0
923923 33.9411 + 33.9411i 1.11719 + 1.11719i
924924 0 0
925925 2.00000 + 14.0000i 0.0657596 + 0.460317i
926926 0 0
927927 −11.4853 + 5.48528i −0.377226 + 0.180160i
928928 0 0
929929 −2.82843 −0.0927977 −0.0463988 0.998923i 0.514775π-0.514775\pi
−0.0463988 + 0.998923i 0.514775π0.514775\pi
930930 0 0
931931 0 0
932932 0 0
933933 14.4853 + 2.48528i 0.474227 + 0.0813645i
934934 0 0
935935 16.9706 8.48528i 0.554997 0.277498i
936936 0 0
937937 11.0000 + 11.0000i 0.359354 + 0.359354i 0.863575 0.504221i 0.168220π-0.168220\pi
−0.504221 + 0.863575i 0.668220π0.668220\pi
938938 0 0
939939 24.0416 + 34.0000i 0.784569 + 1.10955i
940940 0 0
941941 1.41421i 0.0461020i −0.999734 0.0230510i 0.992662π-0.992662\pi
0.999734 0.0230510i 0.00733802π-0.00733802\pi
942942 0 0
943943 0 0
944944 0 0
945945 2.27208 49.2426i 0.0739107 1.60186i
946946 0 0
947947 −21.2132 + 21.2132i −0.689336 + 0.689336i −0.962085 0.272749i 0.912067π-0.912067\pi
0.272749 + 0.962085i 0.412067π0.412067\pi
948948 0 0
949949 40.0000i 1.29845i
950950 0 0
951951 14.0000 + 19.7990i 0.453981 + 0.642026i
952952 0 0
953953 24.0416 + 24.0416i 0.778785 + 0.778785i 0.979624 0.200839i 0.0643669π-0.0643669\pi
−0.200839 + 0.979624i 0.564367π0.564367\pi
954954 0 0
955955 18.0000 + 6.00000i 0.582466 + 0.194155i
956956 0 0
957957 30.7279 + 5.27208i 0.993293 + 0.170422i
958958 0 0
959959 −42.4264 −1.37002
960960 0 0
961961 5.00000 0.161290
962962 0 0
963963 32.4853 15.5147i 1.04682 0.499955i
964964 0 0
965965 24.0416 + 48.0833i 0.773927 + 1.54785i
966966 0 0
967967 −15.0000 15.0000i −0.482367 0.482367i 0.423520 0.905887i 0.360795π-0.360795\pi
−0.905887 + 0.423520i 0.860795π0.860795\pi
968968 0 0
969969 0 0
970970 0 0
971971 46.6690i 1.49768i 0.662750 + 0.748841i 0.269389π0.269389\pi
−0.662750 + 0.748841i 0.730611π0.730611\pi
972972 0 0
973973 −36.0000 + 36.0000i −1.15411 + 1.15411i
974974 0 0
975975 −1.37258 + 48.9706i −0.0439578 + 1.56831i
976976 0 0
977977 32.5269 32.5269i 1.04063 1.04063i 0.0414892 0.999139i 0.486790π-0.486790\pi
0.999139 0.0414892i 0.0132102π-0.0132102\pi
978978 0 0
979979 36.0000i 1.15056i
980980 0 0
981981 −2.00000 + 5.65685i −0.0638551 + 0.180609i
982982 0 0
983983 33.9411 + 33.9411i 1.08255 + 1.08255i 0.996271 + 0.0862831i 0.0274990π0.0274990\pi
0.0862831 + 0.996271i 0.472501π0.472501\pi
984984 0 0
985985 −8.00000 16.0000i −0.254901 0.509802i
986986 0 0
987987 −14.9117 + 86.9117i −0.474644 + 2.76643i
988988 0 0
989989 0 0
990990 0 0
991991 48.0000 1.52477 0.762385 0.647124i 0.224028π-0.224028\pi
0.762385 + 0.647124i 0.224028π0.224028\pi
992992 0 0
993993 −3.51472 + 20.4853i −0.111536 + 0.650081i
994994 0 0
995995 0 0
996996 0 0
997997 −28.0000 28.0000i −0.886769 0.886769i 0.107442 0.994211i 0.465734π-0.465734\pi
−0.994211 + 0.107442i 0.965734π0.965734\pi
998998 0 0
999999 −14.1421 + 4.00000i −0.447437 + 0.126554i
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 480.2.v.a.257.2 yes 4
3.2 odd 2 inner 480.2.v.a.257.1 4
4.3 odd 2 480.2.v.b.257.1 yes 4
5.3 odd 4 inner 480.2.v.a.353.1 yes 4
8.3 odd 2 960.2.v.d.257.2 4
8.5 even 2 960.2.v.j.257.1 4
12.11 even 2 480.2.v.b.257.2 yes 4
15.8 even 4 inner 480.2.v.a.353.2 yes 4
20.3 even 4 480.2.v.b.353.2 yes 4
24.5 odd 2 960.2.v.j.257.2 4
24.11 even 2 960.2.v.d.257.1 4
40.3 even 4 960.2.v.d.833.1 4
40.13 odd 4 960.2.v.j.833.2 4
60.23 odd 4 480.2.v.b.353.1 yes 4
120.53 even 4 960.2.v.j.833.1 4
120.83 odd 4 960.2.v.d.833.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
480.2.v.a.257.1 4 3.2 odd 2 inner
480.2.v.a.257.2 yes 4 1.1 even 1 trivial
480.2.v.a.353.1 yes 4 5.3 odd 4 inner
480.2.v.a.353.2 yes 4 15.8 even 4 inner
480.2.v.b.257.1 yes 4 4.3 odd 2
480.2.v.b.257.2 yes 4 12.11 even 2
480.2.v.b.353.1 yes 4 60.23 odd 4
480.2.v.b.353.2 yes 4 20.3 even 4
960.2.v.d.257.1 4 24.11 even 2
960.2.v.d.257.2 4 8.3 odd 2
960.2.v.d.833.1 4 40.3 even 4
960.2.v.d.833.2 4 120.83 odd 4
960.2.v.j.257.1 4 8.5 even 2
960.2.v.j.257.2 4 24.5 odd 2
960.2.v.j.833.1 4 120.53 even 4
960.2.v.j.833.2 4 40.13 odd 4