Properties

Label 1512.2.bl.b.1025.8
Level 15121512
Weight 22
Character 1512.1025
Analytic conductor 12.07312.073
Analytic rank 00
Dimension 1616
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] = [1512,2,Mod(593,1512)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1512, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 5])) 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("1512.593"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 1512=23337 1512 = 2^{3} \cdot 3^{3} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1512.bl (of order 66, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [16,0,0,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 12.073380785612.0733807856
Analytic rank: 00
Dimension: 1616
Relative dimension: 88 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x167x14+84x12208x10+882x8+4424x6+10340x4+20412x2+17689 x^{16} - 7x^{14} + 84x^{12} - 208x^{10} + 882x^{8} + 4424x^{6} + 10340x^{4} + 20412x^{2} + 17689 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 1025.8
Root 2.236001.01798i2.23600 - 1.01798i of defining polynomial
Character χ\chi == 1512.1025
Dual form 1512.2.bl.b.593.8

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(1.99959+3.46340i)q5+(0.605908+2.57544i)q7+(4.23559+2.44542i)q11+0.678883iq13+(3.575646.19319i)q17+(4.197002.42314i)q19+(0.5569100.321532i)q23+(5.49674+9.52064i)q254.89084iq29+(4.60646+2.65954i)q31+(7.70819+7.24833i)q35+(0.09053860.156817i)q379.52435q412.28373q43+(1.62531+2.81511i)q47+(6.26575+3.12096i)q49+(5.963123.44281i)q53+19.5594iq55+(4.949328.57247i)q59+(9.15398+5.28505i)q61+(2.35124+1.35749i)q65+(5.393459.34172i)q671.03596iq71+(0.409461+0.236403i)q73+(3.73164+12.3902i)q77+(4.08467+7.07486i)q792.53549q83+28.5993q85+(8.9099515.4325i)q89+(1.74842+0.411340i)q91+(16.7846+9.69058i)q953.07058iq97+O(q100)q+(1.99959 + 3.46340i) q^{5} +(0.605908 + 2.57544i) q^{7} +(4.23559 + 2.44542i) q^{11} +0.678883i q^{13} +(3.57564 - 6.19319i) q^{17} +(4.19700 - 2.42314i) q^{19} +(0.556910 - 0.321532i) q^{23} +(-5.49674 + 9.52064i) q^{25} -4.89084i q^{29} +(4.60646 + 2.65954i) q^{31} +(-7.70819 + 7.24833i) q^{35} +(-0.0905386 - 0.156817i) q^{37} -9.52435 q^{41} -2.28373 q^{43} +(1.62531 + 2.81511i) q^{47} +(-6.26575 + 3.12096i) q^{49} +(-5.96312 - 3.44281i) q^{53} +19.5594i q^{55} +(4.94932 - 8.57247i) q^{59} +(-9.15398 + 5.28505i) q^{61} +(-2.35124 + 1.35749i) q^{65} +(5.39345 - 9.34172i) q^{67} -1.03596i q^{71} +(0.409461 + 0.236403i) q^{73} +(-3.73164 + 12.3902i) q^{77} +(4.08467 + 7.07486i) q^{79} -2.53549 q^{83} +28.5993 q^{85} +(-8.90995 - 15.4325i) q^{89} +(-1.74842 + 0.411340i) q^{91} +(16.7846 + 9.69058i) q^{95} -3.07058i q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q2q7+6q196q25+6q318q37+44q4334q496q61+20q6714q79+148q8554q91+O(q100) 16 q - 2 q^{7} + 6 q^{19} - 6 q^{25} + 6 q^{31} - 8 q^{37} + 44 q^{43} - 34 q^{49} - 6 q^{61} + 20 q^{67} - 14 q^{79} + 148 q^{85} - 54 q^{91}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1512Z)×\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times.

nn 757757 785785 10811081 11351135
χ(n)\chi(n) 11 1-1 e(16)e\left(\frac{1}{6}\right) 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 0
44 0 0
55 1.99959 + 3.46340i 0.894245 + 1.54888i 0.834736 + 0.550650i 0.185620π0.185620\pi
0.0595092 + 0.998228i 0.481046π0.481046\pi
66 0 0
77 0.605908 + 2.57544i 0.229012 + 0.973424i
88 0 0
99 0 0
1010 0 0
1111 4.23559 + 2.44542i 1.27708 + 0.737321i 0.976310 0.216376i 0.0694237π-0.0694237\pi
0.300768 + 0.953697i 0.402757π0.402757\pi
1212 0 0
1313 0.678883i 0.188288i 0.995559 + 0.0941441i 0.0300114π0.0300114\pi
−0.995559 + 0.0941441i 0.969989π0.969989\pi
1414 0 0
1515 0 0
1616 0 0
1717 3.57564 6.19319i 0.867220 1.50207i 0.00239456 0.999997i 0.499238π-0.499238\pi
0.864826 0.502072i 0.167429π-0.167429\pi
1818 0 0
1919 4.19700 2.42314i 0.962858 0.555906i 0.0658063 0.997832i 0.479038π-0.479038\pi
0.897051 + 0.441926i 0.145705π0.145705\pi
2020 0 0
2121 0 0
2222 0 0
2323 0.556910 0.321532i 0.116124 0.0670440i −0.440813 0.897599i 0.645310π-0.645310\pi
0.556937 + 0.830555i 0.311977π0.311977\pi
2424 0 0
2525 −5.49674 + 9.52064i −1.09935 + 1.90413i
2626 0 0
2727 0 0
2828 0 0
2929 4.89084i 0.908206i −0.890949 0.454103i 0.849960π-0.849960\pi
0.890949 0.454103i 0.150040π-0.150040\pi
3030 0 0
3131 4.60646 + 2.65954i 0.827345 + 0.477668i 0.852943 0.522005i 0.174816π-0.174816\pi
−0.0255979 + 0.999672i 0.508149π0.508149\pi
3232 0 0
3333 0 0
3434 0 0
3535 −7.70819 + 7.24833i −1.30292 + 1.22519i
3636 0 0
3737 −0.0905386 0.156817i −0.0148844 0.0257806i 0.858487 0.512835i 0.171405π-0.171405\pi
−0.873372 + 0.487054i 0.838071π0.838071\pi
3838 0 0
3939 0 0
4040 0 0
4141 −9.52435 −1.48745 −0.743726 0.668484i 0.766943π-0.766943\pi
−0.743726 + 0.668484i 0.766943π0.766943\pi
4242 0 0
4343 −2.28373 −0.348265 −0.174133 0.984722i 0.555712π-0.555712\pi
−0.174133 + 0.984722i 0.555712π0.555712\pi
4444 0 0
4545 0 0
4646 0 0
4747 1.62531 + 2.81511i 0.237075 + 0.410627i 0.959874 0.280432i 0.0904778π-0.0904778\pi
−0.722798 + 0.691059i 0.757144π0.757144\pi
4848 0 0
4949 −6.26575 + 3.12096i −0.895107 + 0.445851i
5050 0 0
5151 0 0
5252 0 0
5353 −5.96312 3.44281i −0.819098 0.472906i 0.0310076 0.999519i 0.490128π-0.490128\pi
−0.850105 + 0.526613i 0.823462π0.823462\pi
5454 0 0
5555 19.5594i 2.63738i
5656 0 0
5757 0 0
5858 0 0
5959 4.94932 8.57247i 0.644346 1.11604i −0.340106 0.940387i 0.610463π-0.610463\pi
0.984452 0.175653i 0.0562037π-0.0562037\pi
6060 0 0
6161 −9.15398 + 5.28505i −1.17205 + 0.676682i −0.954161 0.299293i 0.903249π-0.903249\pi
−0.217886 + 0.975974i 0.569916π0.569916\pi
6262 0 0
6363 0 0
6464 0 0
6565 −2.35124 + 1.35749i −0.291635 + 0.168376i
6666 0 0
6767 5.39345 9.34172i 0.658914 1.14127i −0.321983 0.946746i 0.604349π-0.604349\pi
0.980897 0.194527i 0.0623173π-0.0623173\pi
6868 0 0
6969 0 0
7070 0 0
7171 1.03596i 0.122945i −0.998109 0.0614727i 0.980420π-0.980420\pi
0.998109 0.0614727i 0.0195797π-0.0195797\pi
7272 0 0
7373 0.409461 + 0.236403i 0.0479238 + 0.0276688i 0.523770 0.851859i 0.324525π-0.324525\pi
−0.475847 + 0.879528i 0.657858π0.657858\pi
7474 0 0
7575 0 0
7676 0 0
7777 −3.73164 + 12.3902i −0.425260 + 1.41199i
7878 0 0
7979 4.08467 + 7.07486i 0.459562 + 0.795984i 0.998938 0.0460808i 0.0146732π-0.0146732\pi
−0.539376 + 0.842065i 0.681340π0.681340\pi
8080 0 0
8181 0 0
8282 0 0
8383 −2.53549 −0.278306 −0.139153 0.990271i 0.544438π-0.544438\pi
−0.139153 + 0.990271i 0.544438π0.544438\pi
8484 0 0
8585 28.5993 3.10203
8686 0 0
8787 0 0
8888 0 0
8989 −8.90995 15.4325i −0.944453 1.63584i −0.756843 0.653597i 0.773259π-0.773259\pi
−0.187610 0.982244i 0.560074π-0.560074\pi
9090 0 0
9191 −1.74842 + 0.411340i −0.183284 + 0.0431202i
9292 0 0
9393 0 0
9494 0 0
9595 16.7846 + 9.69058i 1.72206 + 0.994233i
9696 0 0
9797 3.07058i 0.311770i −0.987775 0.155885i 0.950177π-0.950177\pi
0.987775 0.155885i 0.0498229π-0.0498229\pi
9898 0 0
9999 0 0
100100 0 0
101101 3.26652 5.65779i 0.325031 0.562971i −0.656487 0.754337i 0.727958π-0.727958\pi
0.981519 + 0.191366i 0.0612918π0.0612918\pi
102102 0 0
103103 −15.7238 + 9.07816i −1.54932 + 0.894498i −0.551122 + 0.834425i 0.685800π0.685800\pi
−0.998194 + 0.0600728i 0.980867π0.980867\pi
104104 0 0
105105 0 0
106106 0 0
107107 −7.51173 + 4.33690i −0.726187 + 0.419264i −0.817026 0.576602i 0.804379π-0.804379\pi
0.0908388 + 0.995866i 0.471045π0.471045\pi
108108 0 0
109109 −0.211816 + 0.366876i −0.0202883 + 0.0351403i −0.875991 0.482327i 0.839792π-0.839792\pi
0.855703 + 0.517467i 0.173125π0.173125\pi
110110 0 0
111111 0 0
112112 0 0
113113 10.1027i 0.950378i −0.879884 0.475189i 0.842380π-0.842380\pi
0.879884 0.475189i 0.157620π-0.157620\pi
114114 0 0
115115 2.22719 + 1.28587i 0.207686 + 0.119908i
116116 0 0
117117 0 0
118118 0 0
119119 18.1167 + 5.45633i 1.66075 + 0.500181i
120120 0 0
121121 6.46014 + 11.1893i 0.587286 + 1.01721i
122122 0 0
123123 0 0
124124 0 0
125125 −23.9691 −2.14386
126126 0 0
127127 −12.5993 −1.11801 −0.559004 0.829165i 0.688816π-0.688816\pi
−0.559004 + 0.829165i 0.688816π0.688816\pi
128128 0 0
129129 0 0
130130 0 0
131131 −3.36188 5.82294i −0.293729 0.508753i 0.680960 0.732321i 0.261563π-0.261563\pi
−0.974688 + 0.223568i 0.928230π0.928230\pi
132132 0 0
133133 8.78364 + 9.34091i 0.761638 + 0.809959i
134134 0 0
135135 0 0
136136 0 0
137137 11.8085 + 6.81763i 1.00887 + 0.582469i 0.910860 0.412716i 0.135420π-0.135420\pi
0.0980070 + 0.995186i 0.468753π0.468753\pi
138138 0 0
139139 19.0696i 1.61746i 0.588181 + 0.808729i 0.299844π0.299844\pi
−0.588181 + 0.808729i 0.700156π0.700156\pi
140140 0 0
141141 0 0
142142 0 0
143143 −1.66015 + 2.87547i −0.138829 + 0.240459i
144144 0 0
145145 16.9389 9.77968i 1.40670 0.812158i
146146 0 0
147147 0 0
148148 0 0
149149 14.3433 8.28112i 1.17505 0.678416i 0.220186 0.975458i 0.429333π-0.429333\pi
0.954864 + 0.297042i 0.0960001π0.0960001\pi
150150 0 0
151151 4.24897 7.35944i 0.345776 0.598902i −0.639718 0.768610i 0.720949π-0.720949\pi
0.985495 + 0.169707i 0.0542822π0.0542822\pi
152152 0 0
153153 0 0
154154 0 0
155155 21.2720i 1.70861i
156156 0 0
157157 −14.8574 8.57792i −1.18575 0.684593i −0.228412 0.973565i 0.573353π-0.573353\pi
−0.957338 + 0.288972i 0.906687π0.906687\pi
158158 0 0
159159 0 0
160160 0 0
161161 1.16552 + 1.23947i 0.0918559 + 0.0976837i
162162 0 0
163163 −11.6206 20.1275i −0.910198 1.57651i −0.813784 0.581168i 0.802596π-0.802596\pi
−0.0964145 0.995341i 0.530737π-0.530737\pi
164164 0 0
165165 0 0
166166 0 0
167167 10.5685 0.817813 0.408907 0.912576i 0.365910π-0.365910\pi
0.408907 + 0.912576i 0.365910π0.365910\pi
168168 0 0
169169 12.5391 0.964548
170170 0 0
171171 0 0
172172 0 0
173173 −0.0926046 0.160396i −0.00704060 0.0121947i 0.862484 0.506085i 0.168908π-0.168908\pi
−0.869524 + 0.493890i 0.835574π0.835574\pi
174174 0 0
175175 −27.8503 8.38789i −2.10529 0.634065i
176176 0 0
177177 0 0
178178 0 0
179179 11.1115 + 6.41523i 0.830513 + 0.479497i 0.854028 0.520227i 0.174152π-0.174152\pi
−0.0235152 + 0.999723i 0.507486π0.507486\pi
180180 0 0
181181 19.0696i 1.41743i 0.705495 + 0.708715i 0.250725π0.250725\pi
−0.705495 + 0.708715i 0.749275π0.749275\pi
182182 0 0
183183 0 0
184184 0 0
185185 0.362081 0.627142i 0.0266207 0.0461084i
186186 0 0
187187 30.2899 17.4879i 2.21502 1.27884i
188188 0 0
189189 0 0
190190 0 0
191191 7.97410 4.60385i 0.576986 0.333123i −0.182949 0.983122i 0.558564π-0.558564\pi
0.759935 + 0.649999i 0.225231π0.225231\pi
192192 0 0
193193 3.19384 5.53189i 0.229897 0.398194i −0.727880 0.685704i 0.759494π-0.759494\pi
0.957778 + 0.287510i 0.0928276π0.0928276\pi
194194 0 0
195195 0 0
196196 0 0
197197 2.95121i 0.210265i −0.994458 0.105132i 0.966473π-0.966473\pi
0.994458 0.105132i 0.0335267π-0.0335267\pi
198198 0 0
199199 2.42679 + 1.40111i 0.172031 + 0.0993220i 0.583543 0.812082i 0.301666π-0.301666\pi
−0.411512 + 0.911404i 0.634999π0.634999\pi
200200 0 0
201201 0 0
202202 0 0
203203 12.5960 2.96340i 0.884069 0.207990i
204204 0 0
205205 −19.0448 32.9866i −1.33015 2.30388i
206206 0 0
207207 0 0
208208 0 0
209209 23.7023 1.63953
210210 0 0
211211 −5.60060 −0.385561 −0.192780 0.981242i 0.561751π-0.561751\pi
−0.192780 + 0.981242i 0.561751π0.561751\pi
212212 0 0
213213 0 0
214214 0 0
215215 −4.56653 7.90946i −0.311435 0.539421i
216216 0 0
217217 −4.05839 + 13.4751i −0.275501 + 0.914748i
218218 0 0
219219 0 0
220220 0 0
221221 4.20445 + 2.42744i 0.282822 + 0.163287i
222222 0 0
223223 2.76985i 0.185483i 0.995690 + 0.0927413i 0.0295630π0.0295630\pi
−0.995690 + 0.0927413i 0.970437π0.970437\pi
224224 0 0
225225 0 0
226226 0 0
227227 −4.71883 + 8.17325i −0.313200 + 0.542478i −0.979053 0.203605i 0.934734π-0.934734\pi
0.665854 + 0.746082i 0.268068π0.268068\pi
228228 0 0
229229 −23.3395 + 13.4751i −1.54232 + 0.890459i −0.543628 + 0.839326i 0.682950π0.682950\pi
−0.998692 + 0.0511324i 0.983717π0.983717\pi
230230 0 0
231231 0 0
232232 0 0
233233 −18.7010 + 10.7970i −1.22514 + 0.707338i −0.966010 0.258503i 0.916771π-0.916771\pi
−0.259135 + 0.965841i 0.583437π0.583437\pi
234234 0 0
235235 −6.49991 + 11.2582i −0.424007 + 0.734402i
236236 0 0
237237 0 0
238238 0 0
239239 15.9859i 1.03404i 0.855973 + 0.517020i 0.172959π0.172959\pi
−0.855973 + 0.517020i 0.827041π0.827041\pi
240240 0 0
241241 −17.0570 9.84788i −1.09874 0.634358i −0.162850 0.986651i 0.552069π-0.552069\pi
−0.935890 + 0.352293i 0.885402π0.885402\pi
242242 0 0
243243 0 0
244244 0 0
245245 −23.3381 15.4601i −1.49101 0.987712i
246246 0 0
247247 1.64503 + 2.84927i 0.104671 + 0.181295i
248248 0 0
249249 0 0
250250 0 0
251251 −24.3966 −1.53990 −0.769950 0.638104i 0.779719π-0.779719\pi
−0.769950 + 0.638104i 0.779719π0.779719\pi
252252 0 0
253253 3.14512 0.197732
254254 0 0
255255 0 0
256256 0 0
257257 −5.71999 9.90731i −0.356803 0.618001i 0.630622 0.776090i 0.282800π-0.282800\pi
−0.987425 + 0.158089i 0.949467π0.949467\pi
258258 0 0
259259 0.349015 0.328193i 0.0216868 0.0203929i
260260 0 0
261261 0 0
262262 0 0
263263 −9.01050 5.20222i −0.555612 0.320782i 0.195771 0.980650i 0.437279π-0.437279\pi
−0.751382 + 0.659867i 0.770613π0.770613\pi
264264 0 0
265265 27.5369i 1.69158i
266266 0 0
267267 0 0
268268 0 0
269269 4.85382 8.40706i 0.295943 0.512588i −0.679261 0.733897i 0.737700π-0.737700\pi
0.975204 + 0.221309i 0.0710329π0.0710329\pi
270270 0 0
271271 24.9184 14.3867i 1.51369 0.873928i 0.513816 0.857901i 0.328232π-0.328232\pi
0.999872 0.0160271i 0.00510181π-0.00510181\pi
272272 0 0
273273 0 0
274274 0 0
275275 −46.5639 + 26.8837i −2.80791 + 1.62115i
276276 0 0
277277 8.56550 14.8359i 0.514651 0.891401i −0.485205 0.874401i 0.661255π-0.661255\pi
0.999855 0.0170007i 0.00541176π-0.00541176\pi
278278 0 0
279279 0 0
280280 0 0
281281 2.61233i 0.155838i −0.996960 0.0779191i 0.975172π-0.975172\pi
0.996960 0.0779191i 0.0248276π-0.0248276\pi
282282 0 0
283283 2.20363 + 1.27226i 0.130992 + 0.0756283i 0.564064 0.825731i 0.309237π-0.309237\pi
−0.433072 + 0.901359i 0.642570π0.642570\pi
284284 0 0
285285 0 0
286286 0 0
287287 −5.77088 24.5294i −0.340644 1.44792i
288288 0 0
289289 −17.0704 29.5668i −1.00414 1.73922i
290290 0 0
291291 0 0
292292 0 0
293293 4.98621 0.291297 0.145649 0.989336i 0.453473π-0.453473\pi
0.145649 + 0.989336i 0.453473π0.453473\pi
294294 0 0
295295 39.5865 2.30481
296296 0 0
297297 0 0
298298 0 0
299299 0.218282 + 0.378076i 0.0126236 + 0.0218647i
300300 0 0
301301 −1.38373 5.88160i −0.0797569 0.339010i
302302 0 0
303303 0 0
304304 0 0
305305 −36.6085 21.1359i −2.09619 1.21024i
306306 0 0
307307 0.688473i 0.0392932i −0.999807 0.0196466i 0.993746π-0.993746\pi
0.999807 0.0196466i 0.00625412π-0.00625412\pi
308308 0 0
309309 0 0
310310 0 0
311311 4.61579 7.99478i 0.261737 0.453342i −0.704966 0.709241i 0.749038π-0.749038\pi
0.966704 + 0.255898i 0.0823712π0.0823712\pi
312312 0 0
313313 −6.79944 + 3.92566i −0.384327 + 0.221891i −0.679699 0.733491i 0.737890π-0.737890\pi
0.295372 + 0.955382i 0.404556π0.404556\pi
314314 0 0
315315 0 0
316316 0 0
317317 14.7913 8.53976i 0.830763 0.479641i −0.0233511 0.999727i 0.507434π-0.507434\pi
0.854114 + 0.520086i 0.174100π0.174100\pi
318318 0 0
319319 11.9601 20.7156i 0.669639 1.15985i
320320 0 0
321321 0 0
322322 0 0
323323 34.6571i 1.92837i
324324 0 0
325325 −6.46340 3.73164i −0.358525 0.206994i
326326 0 0
327327 0 0
328328 0 0
329329 −6.26536 + 5.89158i −0.345421 + 0.324813i
330330 0 0
331331 −15.9973 27.7081i −0.879291 1.52298i −0.852120 0.523346i 0.824684π-0.824684\pi
−0.0271706 0.999631i 0.508650π-0.508650\pi
332332 0 0
333333 0 0
334334 0 0
335335 43.1388 2.35692
336336 0 0
337337 25.6354 1.39645 0.698226 0.715877i 0.253973π-0.253973\pi
0.698226 + 0.715877i 0.253973π0.253973\pi
338338 0 0
339339 0 0
340340 0 0
341341 13.0074 + 22.5294i 0.704389 + 1.22004i
342342 0 0
343343 −11.8343 14.2460i −0.638992 0.769214i
344344 0 0
345345 0 0
346346 0 0
347347 5.60640 + 3.23686i 0.300967 + 0.173764i 0.642877 0.765969i 0.277740π-0.277740\pi
−0.341910 + 0.939733i 0.611074π0.611074\pi
348348 0 0
349349 27.0147i 1.44606i 0.690815 + 0.723032i 0.257252π0.257252\pi
−0.690815 + 0.723032i 0.742748π0.742748\pi
350350 0 0
351351 0 0
352352 0 0
353353 −15.7745 + 27.3222i −0.839591 + 1.45421i 0.0506462 + 0.998717i 0.483872π0.483872\pi
−0.890237 + 0.455497i 0.849461π0.849461\pi
354354 0 0
355355 3.58793 2.07149i 0.190428 0.109943i
356356 0 0
357357 0 0
358358 0 0
359359 3.82534 2.20856i 0.201894 0.116563i −0.395645 0.918404i 0.629479π-0.629479\pi
0.597538 + 0.801840i 0.296146π0.296146\pi
360360 0 0
361361 2.24320 3.88534i 0.118063 0.204491i
362362 0 0
363363 0 0
364364 0 0
365365 1.89084i 0.0989709i
366366 0 0
367367 −2.36455 1.36517i −0.123429 0.0712616i 0.437015 0.899454i 0.356036π-0.356036\pi
−0.560443 + 0.828193i 0.689369π0.689369\pi
368368 0 0
369369 0 0
370370 0 0
371371 5.25364 17.4437i 0.272755 0.905630i
372372 0 0
373373 2.99871 + 5.19391i 0.155267 + 0.268931i 0.933156 0.359471i 0.117043π-0.117043\pi
−0.777889 + 0.628402i 0.783709π0.783709\pi
374374 0 0
375375 0 0
376376 0 0
377377 3.32030 0.171004
378378 0 0
379379 16.7830 0.862083 0.431042 0.902332i 0.358146π-0.358146\pi
0.431042 + 0.902332i 0.358146π0.358146\pi
380380 0 0
381381 0 0
382382 0 0
383383 8.53825 + 14.7887i 0.436284 + 0.755667i 0.997399 0.0720712i 0.0229609π-0.0229609\pi
−0.561115 + 0.827738i 0.689628π0.689628\pi
384384 0 0
385385 −50.3739 + 11.8512i −2.56729 + 0.603992i
386386 0 0
387387 0 0
388388 0 0
389389 −30.4364 17.5725i −1.54319 0.890959i −0.998635 0.0522323i 0.983366π-0.983366\pi
−0.544552 0.838727i 0.683300π-0.683300\pi
390390 0 0
391391 4.59873i 0.232568i
392392 0 0
393393 0 0
394394 0 0
395395 −16.3354 + 28.2937i −0.821922 + 1.42361i
396396 0 0
397397 −3.74191 + 2.16039i −0.187801 + 0.108427i −0.590953 0.806706i 0.701248π-0.701248\pi
0.403152 + 0.915133i 0.367915π0.367915\pi
398398 0 0
399399 0 0
400400 0 0
401401 25.6036 14.7822i 1.27858 0.738189i 0.301994 0.953310i 0.402348π-0.402348\pi
0.976587 + 0.215121i 0.0690145π0.0690145\pi
402402 0 0
403403 −1.80552 + 3.12725i −0.0899392 + 0.155779i
404404 0 0
405405 0 0
406406 0 0
407407 0.885619i 0.0438985i
408408 0 0
409409 27.1261 + 15.6613i 1.34130 + 0.774401i 0.986998 0.160730i 0.0513849π-0.0513849\pi
0.354303 + 0.935131i 0.384718π0.384718\pi
410410 0 0
411411 0 0
412412 0 0
413413 25.0767 + 7.55253i 1.23394 + 0.371635i
414414 0 0
415415 −5.06995 8.78141i −0.248874 0.431063i
416416 0 0
417417 0 0
418418 0 0
419419 −0.552696 −0.0270010 −0.0135005 0.999909i 0.504297π-0.504297\pi
−0.0135005 + 0.999909i 0.504297π0.504297\pi
420420 0 0
421421 −23.2742 −1.13432 −0.567158 0.823609i 0.691957π-0.691957\pi
−0.567158 + 0.823609i 0.691957π0.691957\pi
422422 0 0
423423 0 0
424424 0 0
425425 39.3088 + 68.0848i 1.90676 + 3.30260i
426426 0 0
427427 −19.1578 20.3732i −0.927110 0.985930i
428428 0 0
429429 0 0
430430 0 0
431431 21.7375 + 12.5501i 1.04706 + 0.604518i 0.921824 0.387609i 0.126699π-0.126699\pi
0.125233 + 0.992127i 0.460032π0.460032\pi
432432 0 0
433433 17.3795i 0.835204i −0.908630 0.417602i 0.862871π-0.862871\pi
0.908630 0.417602i 0.137129π-0.137129\pi
434434 0 0
435435 0 0
436436 0 0
437437 1.55823 2.69894i 0.0745404 0.129108i
438438 0 0
439439 −3.78895 + 2.18755i −0.180837 + 0.104406i −0.587686 0.809089i 0.699961π-0.699961\pi
0.406849 + 0.913495i 0.366627π0.366627\pi
440440 0 0
441441 0 0
442442 0 0
443443 20.1887 11.6559i 0.959193 0.553790i 0.0632686 0.997997i 0.479848π-0.479848\pi
0.895925 + 0.444206i 0.146514π0.146514\pi
444444 0 0
445445 35.6326 61.7174i 1.68915 2.92569i
446446 0 0
447447 0 0
448448 0 0
449449 24.0524i 1.13510i 0.823338 + 0.567551i 0.192109π0.192109\pi
−0.823338 + 0.567551i 0.807891π0.807891\pi
450450 0 0
451451 −40.3412 23.2910i −1.89959 1.09673i
452452 0 0
453453 0 0
454454 0 0
455455 −4.92076 5.23296i −0.230689 0.245325i
456456 0 0
457457 0.467757 + 0.810180i 0.0218808 + 0.0378986i 0.876758 0.480931i 0.159701π-0.159701\pi
−0.854878 + 0.518830i 0.826368π0.826368\pi
458458 0 0
459459 0 0
460460 0 0
461461 7.93609 0.369621 0.184810 0.982774i 0.440833π-0.440833\pi
0.184810 + 0.982774i 0.440833π0.440833\pi
462462 0 0
463463 −0.0963291 −0.00447679 −0.00223840 0.999997i 0.500713π-0.500713\pi
−0.00223840 + 0.999997i 0.500713π0.500713\pi
464464 0 0
465465 0 0
466466 0 0
467467 −14.6205 25.3234i −0.676555 1.17183i −0.976012 0.217718i 0.930139π-0.930139\pi
0.299456 0.954110i 0.403195π-0.403195\pi
468468 0 0
469469 27.3269 + 8.23026i 1.26184 + 0.380038i
470470 0 0
471471 0 0
472472 0 0
473473 −9.67294 5.58467i −0.444762 0.256784i
474474 0 0
475475 53.2775i 2.44454i
476476 0 0
477477 0 0
478478 0 0
479479 −4.93986 + 8.55609i −0.225708 + 0.390938i −0.956532 0.291629i 0.905803π-0.905803\pi
0.730824 + 0.682566i 0.239136π0.239136\pi
480480 0 0
481481 0.106461 0.0614650i 0.00485418 0.00280256i
482482 0 0
483483 0 0
484484 0 0
485485 10.6346 6.13990i 0.482893 0.278799i
486486 0 0
487487 4.10907 7.11712i 0.186200 0.322507i −0.757780 0.652510i 0.773716π-0.773716\pi
0.943980 + 0.330002i 0.107050π0.107050\pi
488488 0 0
489489 0 0
490490 0 0
491491 14.0806i 0.635450i 0.948183 + 0.317725i 0.102919π0.102919\pi
−0.948183 + 0.317725i 0.897081π0.897081\pi
492492 0 0
493493 −30.2899 17.4879i −1.36419 0.787614i
494494 0 0
495495 0 0
496496 0 0
497497 2.66804 0.627694i 0.119678 0.0281559i
498498 0 0
499499 8.08403 + 14.0019i 0.361891 + 0.626813i 0.988272 0.152704i 0.0487980π-0.0487980\pi
−0.626381 + 0.779517i 0.715465π0.715465\pi
500500 0 0
501501 0 0
502502 0 0
503503 36.8914 1.64491 0.822453 0.568834i 0.192605π-0.192605\pi
0.822453 + 0.568834i 0.192605π0.192605\pi
504504 0 0
505505 26.1269 1.16263
506506 0 0
507507 0 0
508508 0 0
509509 7.90414 + 13.6904i 0.350345 + 0.606815i 0.986310 0.164903i 0.0527311π-0.0527311\pi
−0.635965 + 0.771718i 0.719398π0.719398\pi
510510 0 0
511511 −0.360744 + 1.19778i −0.0159584 + 0.0529867i
512512 0 0
513513 0 0
514514 0 0
515515 −62.8825 36.3053i −2.77094 1.59980i
516516 0 0
517517 15.8982i 0.699203i
518518 0 0
519519 0 0
520520 0 0
521521 7.71479 13.3624i 0.337991 0.585417i −0.646064 0.763283i 0.723586π-0.723586\pi
0.984055 + 0.177866i 0.0569193π0.0569193\pi
522522 0 0
523523 −27.0967 + 15.6443i −1.18486 + 0.684077i −0.957133 0.289649i 0.906461π-0.906461\pi
−0.227723 + 0.973726i 0.573128π0.573128\pi
524524 0 0
525525 0 0
526526 0 0
527527 32.9421 19.0191i 1.43498 0.828486i
528528 0 0
529529 −11.2932 + 19.5605i −0.491010 + 0.850455i
530530 0 0
531531 0 0
532532 0 0
533533 6.46591i 0.280070i
534534 0 0
535535 −30.0408 17.3441i −1.29878 0.749850i
536536 0 0
537537 0 0
538538 0 0
539539 −34.1712 2.10330i −1.47186 0.0905955i
540540 0 0
541541 −2.65929 4.60603i −0.114332 0.198029i 0.803181 0.595736i 0.203139π-0.203139\pi
−0.917512 + 0.397707i 0.869806π0.869806\pi
542542 0 0
543543 0 0
544544 0 0
545545 −1.69418 −0.0725708
546546 0 0
547547 14.0296 0.599864 0.299932 0.953961i 0.403036π-0.403036\pi
0.299932 + 0.953961i 0.403036π0.403036\pi
548548 0 0
549549 0 0
550550 0 0
551551 −11.8512 20.5268i −0.504877 0.874473i
552552 0 0
553553 −15.7459 + 14.8065i −0.669585 + 0.629638i
554554 0 0
555555 0 0
556556 0 0
557557 −6.06802 3.50337i −0.257110 0.148443i 0.365905 0.930652i 0.380759π-0.380759\pi
−0.623016 + 0.782209i 0.714093π0.714093\pi
558558 0 0
559559 1.55038i 0.0655743i
560560 0 0
561561 0 0
562562 0 0
563563 −10.5937 + 18.3488i −0.446471 + 0.773311i −0.998153 0.0607435i 0.980653π-0.980653\pi
0.551682 + 0.834054i 0.313986π0.313986\pi
564564 0 0
565565 34.9895 20.2012i 1.47202 0.849871i
566566 0 0
567567 0 0
568568 0 0
569569 27.1180 15.6566i 1.13685 0.656358i 0.191198 0.981551i 0.438763π-0.438763\pi
0.945648 + 0.325193i 0.105429π0.105429\pi
570570 0 0
571571 −11.5820 + 20.0606i −0.484690 + 0.839508i −0.999845 0.0175887i 0.994401π-0.994401\pi
0.515155 + 0.857097i 0.327734π0.327734\pi
572572 0 0
573573 0 0
574574 0 0
575575 7.06952i 0.294819i
576576 0 0
577577 17.2908 + 9.98287i 0.719827 + 0.415592i 0.814689 0.579898i 0.196908π-0.196908\pi
−0.0948620 + 0.995490i 0.530241π0.530241\pi
578578 0 0
579579 0 0
580580 0 0
581581 −1.53627 6.53000i −0.0637354 0.270910i
582582 0 0
583583 −16.8382 29.1646i −0.697368 1.20788i
584584 0 0
585585 0 0
586586 0 0
587587 −22.7290 −0.938127 −0.469063 0.883164i 0.655408π-0.655408\pi
−0.469063 + 0.883164i 0.655408π0.655408\pi
588588 0 0
589589 25.7777 1.06215
590590 0 0
591591 0 0
592592 0 0
593593 9.90166 + 17.1502i 0.406612 + 0.704273i 0.994508 0.104664i 0.0333767π-0.0333767\pi
−0.587895 + 0.808937i 0.700043π0.700043\pi
594594 0 0
595595 17.3285 + 73.6557i 0.710401 + 3.01959i
596596 0 0
597597 0 0
598598 0 0
599599 −13.6917 7.90491i −0.559428 0.322986i 0.193488 0.981103i 0.438020π-0.438020\pi
−0.752916 + 0.658117i 0.771353π0.771353\pi
600600 0 0
601601 32.2987i 1.31749i 0.752366 + 0.658746i 0.228913π0.228913\pi
−0.752366 + 0.658746i 0.771087π0.771087\pi
602602 0 0
603603 0 0
604604 0 0
605605 −25.8353 + 44.7481i −1.05035 + 1.81927i
606606 0 0
607607 1.26070 0.727866i 0.0511703 0.0295432i −0.474197 0.880419i 0.657261π-0.657261\pi
0.525367 + 0.850876i 0.323928π0.323928\pi
608608 0 0
609609 0 0
610610 0 0
611611 −1.91113 + 1.10339i −0.0773161 + 0.0446385i
612612 0 0
613613 −1.57946 + 2.73570i −0.0637936 + 0.110494i −0.896158 0.443735i 0.853653π-0.853653\pi
0.832365 + 0.554228i 0.186987π0.186987\pi
614614 0 0
615615 0 0
616616 0 0
617617 28.7984i 1.15938i −0.814837 0.579691i 0.803173π-0.803173\pi
0.814837 0.579691i 0.196827π-0.196827\pi
618618 0 0
619619 20.3013 + 11.7210i 0.815979 + 0.471106i 0.849028 0.528348i 0.177188π-0.177188\pi
−0.0330487 + 0.999454i 0.510522π0.510522\pi
620620 0 0
621621 0 0
622622 0 0
623623 34.3468 32.2977i 1.37608 1.29398i
624624 0 0
625625 −20.4447 35.4112i −0.817787 1.41645i
626626 0 0
627627 0 0
628628 0 0
629629 −1.29493 −0.0516324
630630 0 0
631631 41.0358 1.63361 0.816804 0.576915i 0.195744π-0.195744\pi
0.816804 + 0.576915i 0.195744π0.195744\pi
632632 0 0
633633 0 0
634634 0 0
635635 −25.1935 43.6364i −0.999773 1.73166i
636636 0 0
637637 −2.11876 4.25371i −0.0839484 0.168538i
638638 0 0
639639 0 0
640640 0 0
641641 −13.2162 7.63040i −0.522010 0.301383i 0.215747 0.976449i 0.430781π-0.430781\pi
−0.737757 + 0.675067i 0.764115π0.764115\pi
642642 0 0
643643 30.2829i 1.19424i 0.802151 + 0.597121i 0.203689π0.203689\pi
−0.802151 + 0.597121i 0.796311π0.796311\pi
644644 0 0
645645 0 0
646646 0 0
647647 −3.17732 + 5.50328i −0.124913 + 0.216356i −0.921699 0.387906i 0.873199π-0.873199\pi
0.796786 + 0.604262i 0.206532π0.206532\pi
648648 0 0
649649 41.9265 24.2063i 1.64576 0.950180i
650650 0 0
651651 0 0
652652 0 0
653653 −2.14653 + 1.23930i −0.0840002 + 0.0484975i −0.541412 0.840758i 0.682110π-0.682110\pi
0.457412 + 0.889255i 0.348777π0.348777\pi
654654 0 0
655655 13.4448 23.2870i 0.525331 0.909899i
656656 0 0
657657 0 0
658658 0 0
659659 36.8651i 1.43606i 0.696011 + 0.718031i 0.254956π0.254956\pi
−0.696011 + 0.718031i 0.745044π0.745044\pi
660660 0 0
661661 16.8816 + 9.74661i 0.656619 + 0.379099i 0.790988 0.611832i 0.209567π-0.209567\pi
−0.134369 + 0.990931i 0.542901π0.542901\pi
662662 0 0
663663 0 0
664664 0 0
665665 −14.7876 + 49.0992i −0.573437 + 1.90399i
666666 0 0
667667 −1.57256 2.72375i −0.0608898 0.105464i
668668 0 0
669669 0 0
670670 0 0
671671 −51.6967 −1.99573
672672 0 0
673673 −19.7560 −0.761538 −0.380769 0.924670i 0.624341π-0.624341\pi
−0.380769 + 0.924670i 0.624341π0.624341\pi
674674 0 0
675675 0 0
676676 0 0
677677 −4.42478 7.66394i −0.170058 0.294549i 0.768382 0.639992i 0.221062π-0.221062\pi
−0.938440 + 0.345442i 0.887729π0.887729\pi
678678 0 0
679679 7.90807 1.86049i 0.303484 0.0713989i
680680 0 0
681681 0 0
682682 0 0
683683 2.07247 + 1.19654i 0.0793008 + 0.0457843i 0.539126 0.842225i 0.318755π-0.318755\pi
−0.459825 + 0.888009i 0.652088π0.652088\pi
684684 0 0
685685 54.5299i 2.08348i
686686 0 0
687687 0 0
688688 0 0
689689 2.33726 4.04826i 0.0890426 0.154226i
690690 0 0
691691 −1.87166 + 1.08060i −0.0712013 + 0.0411081i −0.535178 0.844739i 0.679755π-0.679755\pi
0.463977 + 0.885847i 0.346422π0.346422\pi
692692 0 0
693693 0 0
694694 0 0
695695 −66.0454 + 38.1314i −2.50525 + 1.44640i
696696 0 0
697697 −34.0556 + 58.9861i −1.28995 + 2.23426i
698698 0 0
699699 0 0
700700 0 0
701701 32.7240i 1.23597i 0.786191 + 0.617984i 0.212050π0.212050\pi
−0.786191 + 0.617984i 0.787950π0.787950\pi
702702 0 0
703703 −0.759980 0.438775i −0.0286632 0.0165487i
704704 0 0
705705 0 0
706706 0 0
707707 16.5505 + 4.98463i 0.622445 + 0.187466i
708708 0 0
709709 16.7348 + 28.9856i 0.628490 + 1.08858i 0.987855 + 0.155380i 0.0496601π0.0496601\pi
−0.359365 + 0.933197i 0.617007π0.617007\pi
710710 0 0
711711 0 0
712712 0 0
713713 3.42051 0.128099
714714 0 0
715715 −13.2785 −0.496588
716716 0 0
717717 0 0
718718 0 0
719719 −15.2023 26.3312i −0.566952 0.981989i −0.996865 0.0791190i 0.974789π-0.974789\pi
0.429914 0.902870i 0.358544π-0.358544\pi
720720 0 0
721721 −32.9074 34.9952i −1.22554 1.30329i
722722 0 0
723723 0 0
724724 0 0
725725 46.5639 + 26.8837i 1.72934 + 0.998435i
726726 0 0
727727 12.4585i 0.462061i −0.972946 0.231031i 0.925790π-0.925790\pi
0.972946 0.231031i 0.0742098π-0.0742098\pi
728728 0 0
729729 0 0
730730 0 0
731731 −8.16580 + 14.1436i −0.302023 + 0.523119i
732732 0 0
733733 2.77872 1.60430i 0.102634 0.0592560i −0.447804 0.894132i 0.647794π-0.647794\pi
0.550439 + 0.834876i 0.314460π0.314460\pi
734734 0 0
735735 0 0
736736 0 0
737737 45.6888 26.3785i 1.68297 0.971663i
738738 0 0
739739 −3.11747 + 5.39962i −0.114678 + 0.198628i −0.917651 0.397387i 0.869917π-0.869917\pi
0.802973 + 0.596015i 0.203250π0.203250\pi
740740 0 0
741741 0 0
742742 0 0
743743 44.5451i 1.63420i −0.576495 0.817101i 0.695580π-0.695580\pi
0.576495 0.817101i 0.304420π-0.304420\pi
744744 0 0
745745 57.3616 + 33.1177i 2.10157 + 1.21334i
746746 0 0
747747 0 0
748748 0 0
749749 −15.7208 16.7182i −0.574427 0.610871i
750750 0 0
751751 8.74572 + 15.1480i 0.319136 + 0.552759i 0.980308 0.197475i 0.0632741π-0.0632741\pi
−0.661172 + 0.750234i 0.729941π0.729941\pi
752752 0 0
753753 0 0
754754 0 0
755755 33.9849 1.23684
756756 0 0
757757 −25.5174 −0.927445 −0.463722 0.885981i 0.653486π-0.653486\pi
−0.463722 + 0.885981i 0.653486π0.653486\pi
758758 0 0
759759 0 0
760760 0 0
761761 8.89391 + 15.4047i 0.322404 + 0.558420i 0.980984 0.194091i 0.0621757π-0.0621757\pi
−0.658580 + 0.752511i 0.728842π0.728842\pi
762762 0 0
763763 −1.07321 0.323225i −0.0388527 0.0117015i
764764 0 0
765765 0 0
766766 0 0
767767 5.81970 + 3.36000i 0.210137 + 0.121323i
768768 0 0
769769 38.3951i 1.38456i 0.721627 + 0.692282i 0.243394π0.243394\pi
−0.721627 + 0.692282i 0.756606π0.756606\pi
770770 0 0
771771 0 0
772772 0 0
773773 13.7588 23.8310i 0.494871 0.857142i −0.505111 0.863054i 0.668549π-0.668549\pi
0.999983 + 0.00591211i 0.00188189π0.00188189\pi
774774 0 0
775775 −50.6411 + 29.2376i −1.81908 + 1.05025i
776776 0 0
777777 0 0
778778 0 0
779779 −39.9737 + 23.0788i −1.43221 + 0.826884i
780780 0 0
781781 2.53335 4.38789i 0.0906503 0.157011i
782782 0 0
783783 0 0
784784 0 0
785785 68.6094i 2.44877i
786786 0 0
787787 −11.6948 6.75200i −0.416875 0.240683i 0.276864 0.960909i 0.410705π-0.410705\pi
−0.693739 + 0.720226i 0.744038π0.744038\pi
788788 0 0
789789 0 0
790790 0 0
791791 26.0187 6.12128i 0.925120 0.217648i
792792 0 0
793793 −3.58793 6.21448i −0.127411 0.220683i
794794 0 0
795795 0 0
796796 0 0
797797 −32.1072 −1.13729 −0.568647 0.822582i 0.692533π-0.692533\pi
−0.568647 + 0.822582i 0.692533π0.692533\pi
798798 0 0
799799 23.2461 0.822386
800800 0 0
801801 0 0
802802 0 0
803803 1.15621 + 2.00261i 0.0408017 + 0.0706705i
804804 0 0
805805 −1.96220 + 6.51509i −0.0691584 + 0.229627i
806806 0 0
807807 0 0
808808 0 0
809809 1.84513 + 1.06529i 0.0648713 + 0.0374534i 0.532085 0.846691i 0.321409π-0.321409\pi
−0.467214 + 0.884145i 0.654742π0.654742\pi
810810 0 0
811811 18.7062i 0.656864i −0.944528 0.328432i 0.893480π-0.893480\pi
0.944528 0.328432i 0.106520π-0.106520\pi
812812 0 0
813813 0 0
814814 0 0
815815 46.4731 80.4937i 1.62788 2.81957i
816816 0 0
817817 −9.58481 + 5.53379i −0.335330 + 0.193603i
818818 0 0
819819 0 0
820820 0 0
821821 20.6223 11.9063i 0.719724 0.415533i −0.0949272 0.995484i 0.530262π-0.530262\pi
0.814651 + 0.579951i 0.196929π0.196929\pi
822822 0 0
823823 −3.91318 + 6.77782i −0.136405 + 0.236260i −0.926133 0.377197i 0.876888π-0.876888\pi
0.789728 + 0.613457i 0.210221π0.210221\pi
824824 0 0
825825 0 0
826826 0 0
827827 5.94710i 0.206801i 0.994640 + 0.103400i 0.0329723π0.0329723\pi
−0.994640 + 0.103400i 0.967028π0.967028\pi
828828 0 0
829829 −10.5009 6.06269i −0.364711 0.210566i 0.306435 0.951892i 0.400864π-0.400864\pi
−0.671145 + 0.741326i 0.734197π0.734197\pi
830830 0 0
831831 0 0
832832 0 0
833833 −3.07540 + 49.9644i −0.106556 + 1.73116i
834834 0 0
835835 21.1327 + 36.6028i 0.731326 + 1.26669i
836836 0 0
837837 0 0
838838 0 0
839839 29.5941 1.02170 0.510851 0.859669i 0.329330π-0.329330\pi
0.510851 + 0.859669i 0.329330π0.329330\pi
840840 0 0
841841 5.07972 0.175163
842842 0 0
843843 0 0
844844 0 0
845845 25.0731 + 43.4279i 0.862542 + 1.49397i
846846 0 0
847847 −24.9031 + 23.4174i −0.855680 + 0.804630i
848848 0 0
849849 0 0
850850 0 0
851851 −0.100844 0.0582221i −0.00345687 0.00199583i
852852 0 0
853853 5.00490i 0.171364i 0.996323 + 0.0856822i 0.0273070π0.0273070\pi
−0.996323 + 0.0856822i 0.972693π0.972693\pi
854854 0 0
855855 0 0
856856 0 0
857857 −22.3412 + 38.6961i −0.763160 + 1.32183i 0.178053 + 0.984021i 0.443020π0.443020\pi
−0.941214 + 0.337812i 0.890313π0.890313\pi
858858 0 0
859859 17.4974 10.1021i 0.597003 0.344680i −0.170858 0.985296i 0.554654π-0.554654\pi
0.767862 + 0.640616i 0.221321π0.221321\pi
860860 0 0
861861 0 0
862862 0 0
863863 −25.2738 + 14.5919i −0.860331 + 0.496713i −0.864123 0.503280i 0.832126π-0.832126\pi
0.00379192 + 0.999993i 0.498793π0.498793\pi
864864 0 0
865865 0.370343 0.641453i 0.0125920 0.0218100i
866866 0 0
867867 0 0
868868 0 0
869869 39.9549i 1.35538i
870870 0 0
871871 6.34193 + 3.66152i 0.214888 + 0.124066i
872872 0 0
873873 0 0
874874 0 0
875875 −14.5231 61.7308i −0.490969 2.08688i
876876 0 0
877877 4.27851 + 7.41060i 0.144475 + 0.250238i 0.929177 0.369635i 0.120517π-0.120517\pi
−0.784702 + 0.619873i 0.787184π0.787184\pi
878878 0 0
879879 0 0
880880 0 0
881881 26.2255 0.883561 0.441781 0.897123i 0.354347π-0.354347\pi
0.441781 + 0.897123i 0.354347π0.354347\pi
882882 0 0
883883 49.3518 1.66082 0.830410 0.557153i 0.188106π-0.188106\pi
0.830410 + 0.557153i 0.188106π0.188106\pi
884884 0 0
885885 0 0
886886 0 0
887887 4.96343 + 8.59691i 0.166656 + 0.288656i 0.937242 0.348680i 0.113370π-0.113370\pi
−0.770586 + 0.637336i 0.780037π0.780037\pi
888888 0 0
889889 −7.63402 32.4487i −0.256037 1.08829i
890890 0 0
891891 0 0
892892 0 0
893893 13.6428 + 7.87669i 0.456540 + 0.263583i
894894 0 0
895895 51.3114i 1.71515i
896896 0 0
897897 0 0
898898 0 0
899899 13.0074 22.5294i 0.433820 0.751399i
900900 0 0
901901 −42.6440 + 24.6205i −1.42068 + 0.820228i
902902 0 0
903903 0 0
904904 0 0
905905 −66.0454 + 38.1314i −2.19543 + 1.26753i
906906 0 0
907907 7.92790 13.7315i 0.263242 0.455948i −0.703860 0.710339i 0.748542π-0.748542\pi
0.967101 + 0.254391i 0.0818750π0.0818750\pi
908908 0 0
909909 0 0
910910 0 0
911911 7.46438i 0.247306i 0.992326 + 0.123653i 0.0394610π0.0394610\pi
−0.992326 + 0.123653i 0.960539π0.960539\pi
912912 0 0
913913 −10.7393 6.20034i −0.355419 0.205201i
914914 0 0
915915 0 0
916916 0 0
917917 12.9596 12.1865i 0.427965 0.402433i
918918 0 0
919919 1.70138 + 2.94688i 0.0561233 + 0.0972085i 0.892722 0.450608i 0.148793π-0.148793\pi
−0.836599 + 0.547816i 0.815459π0.815459\pi
920920 0 0
921921 0 0
922922 0 0
923923 0.703293 0.0231492
924924 0 0
925925 1.99067 0.0654528
926926 0 0
927927 0 0
928928 0 0
929929 −23.3809 40.4968i −0.767101 1.32866i −0.939128 0.343566i 0.888365π-0.888365\pi
0.172027 0.985092i 0.444968π-0.444968\pi
930930 0 0
931931 −18.7348 + 28.2814i −0.614010 + 0.926886i
932932 0 0
933933 0 0
934934 0 0
935935 121.135 + 69.9373i 3.96153 + 2.28719i
936936 0 0
937937 14.2702i 0.466187i 0.972454 + 0.233093i 0.0748848π0.0748848\pi
−0.972454 + 0.233093i 0.925115π0.925115\pi
938938 0 0
939939 0 0
940940 0 0
941941 2.70002 4.67658i 0.0880183 0.152452i −0.818655 0.574285i 0.805280π-0.805280\pi
0.906673 + 0.421833i 0.138613π0.138613\pi
942942 0 0
943943 −5.30420 + 3.06238i −0.172729 + 0.0997249i
944944 0 0
945945 0 0
946946 0 0
947947 −40.0390 + 23.1165i −1.30109 + 0.751186i −0.980591 0.196062i 0.937184π-0.937184\pi
−0.320501 + 0.947248i 0.603851π0.603851\pi
948948 0 0
949949 −0.160490 + 0.277976i −0.00520971 + 0.00902349i
950950 0 0
951951 0 0
952952 0 0
953953 8.50095i 0.275373i −0.990476 0.137686i 0.956033π-0.956033\pi
0.990476 0.137686i 0.0439666π-0.0439666\pi
954954 0 0
955955 31.8899 + 18.4117i 1.03193 + 0.595787i
956956 0 0
957957 0 0
958958 0 0
959959 −10.4035 + 34.5429i −0.335947 + 1.11545i
960960 0 0
961961 −1.35368 2.34464i −0.0436671 0.0756337i
962962 0 0
963963 0 0
964964 0 0
965965 25.5455 0.822339
966966 0 0
967967 19.4198 0.624497 0.312249 0.950000i 0.398918π-0.398918\pi
0.312249 + 0.950000i 0.398918π0.398918\pi
968968 0 0
969969 0 0
970970 0 0
971971 −4.34427 7.52449i −0.139414 0.241472i 0.787861 0.615853i 0.211189π-0.211189\pi
−0.927275 + 0.374381i 0.877855π0.877855\pi
972972 0 0
973973 −49.1124 + 11.5544i −1.57447 + 0.370417i
974974 0 0
975975 0 0
976976 0 0
977977 22.2821 + 12.8646i 0.712869 + 0.411575i 0.812122 0.583487i 0.198312π-0.198312\pi
−0.0992537 + 0.995062i 0.531646π0.531646\pi
978978 0 0
979979 87.1542i 2.78546i
980980 0 0
981981 0 0
982982 0 0
983983 5.51952 9.56009i 0.176045 0.304920i −0.764477 0.644651i 0.777003π-0.777003\pi
0.940523 + 0.339731i 0.110336π0.110336\pi
984984 0 0
985985 10.2212 5.90122i 0.325675 0.188028i
986986 0 0
987987 0 0
988988 0 0
989989 −1.27183 + 0.734292i −0.0404419 + 0.0233491i
990990 0 0
991991 −7.68283 + 13.3070i −0.244053 + 0.422712i −0.961865 0.273525i 0.911810π-0.911810\pi
0.717812 + 0.696237i 0.245144π0.245144\pi
992992 0 0
993993 0 0
994994 0 0
995995 11.2066i 0.355273i
996996 0 0
997997 −54.1503 31.2637i −1.71496 0.990132i −0.927549 0.373702i 0.878088π-0.878088\pi
−0.787410 0.616430i 0.788578π-0.788578\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 1512.2.bl.b.1025.8 yes 16
3.2 odd 2 inner 1512.2.bl.b.1025.1 yes 16
7.5 odd 6 inner 1512.2.bl.b.593.1 16
21.5 even 6 inner 1512.2.bl.b.593.8 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1512.2.bl.b.593.1 16 7.5 odd 6 inner
1512.2.bl.b.593.8 yes 16 21.5 even 6 inner
1512.2.bl.b.1025.1 yes 16 3.2 odd 2 inner
1512.2.bl.b.1025.8 yes 16 1.1 even 1 trivial