Properties

Label 1920.2.b.g.191.6
Level 19201920
Weight 22
Character 1920.191
Analytic conductor 15.33115.331
Analytic rank 00
Dimension 88
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1920,2,Mod(191,1920)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1920, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1920.191");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1920=2735 1920 = 2^{7} \cdot 3 \cdot 5
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1920.b (of order 22, degree 11, 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: 15.331277188115.3312771881
Analytic rank: 00
Dimension: 88
Coefficient field: 8.0.619810816.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x82x5+14x48x3+2x2+2x+1 x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 25 2^{5}
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 191.6
Root 1.18254+1.18254i1.18254 + 1.18254i of defining polynomial
Character χ\chi == 1920.191
Dual form 1920.2.b.g.191.5

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+(0.759725+1.55654i)q31.00000q5+0.480550iq7+(1.84564+2.36509i)q94.73017iq11+1.59363iq13+(0.7597251.55654i)q156.32380iq172.09764q19+(0.747995+0.365086i)q215.84325q23+1.00000q25+(5.083531.07599i)q278.95633q29+8.32380iq31+(7.362703.59363i)q330.480550iq353.67143iq37+(2.48055+1.21072i)q394.53489iq418.70671q43+(1.845642.36509i)q450.578190q47+6.76907q49+(9.843254.80435i)q517.26506q53+4.73017iq55+(1.593633.26506i)q572.30873iq5913.9952iq61+(1.136540.886919i)q631.59363iq65+0.706711q67+(4.439279.09526i)q69+13.6087q71+1.80472q73+(0.759725+1.55654i)q75+2.27308q776.54996iq79+(2.187268.73017i)q81+3.92582iq83+6.32380iq85+(6.8043513.9409i)q879.26506iq890.765818q91+(12.9563+6.32380i)q93+2.09764q951.18726q97+(11.1873+8.73017i)q99+O(q100)q+(0.759725 + 1.55654i) q^{3} -1.00000 q^{5} +0.480550i q^{7} +(-1.84564 + 2.36509i) q^{9} -4.73017i q^{11} +1.59363i q^{13} +(-0.759725 - 1.55654i) q^{15} -6.32380i q^{17} -2.09764 q^{19} +(-0.747995 + 0.365086i) q^{21} -5.84325 q^{23} +1.00000 q^{25} +(-5.08353 - 1.07599i) q^{27} -8.95633 q^{29} +8.32380i q^{31} +(7.36270 - 3.59363i) q^{33} -0.480550i q^{35} -3.67143i q^{37} +(-2.48055 + 1.21072i) q^{39} -4.53489i q^{41} -8.70671 q^{43} +(1.84564 - 2.36509i) q^{45} -0.578190 q^{47} +6.76907 q^{49} +(9.84325 - 4.80435i) q^{51} -7.26506 q^{53} +4.73017i q^{55} +(-1.59363 - 3.26506i) q^{57} -2.30873i q^{59} -13.9952i q^{61} +(-1.13654 - 0.886919i) q^{63} -1.59363i q^{65} +0.706711 q^{67} +(-4.43927 - 9.09526i) q^{69} +13.6087 q^{71} +1.80472 q^{73} +(0.759725 + 1.55654i) q^{75} +2.27308 q^{77} -6.54996i q^{79} +(-2.18726 - 8.73017i) q^{81} +3.92582i q^{83} +6.32380i q^{85} +(-6.80435 - 13.9409i) q^{87} -9.26506i q^{89} -0.765818 q^{91} +(-12.9563 + 6.32380i) q^{93} +2.09764 q^{95} -1.18726 q^{97} +(11.1873 + 8.73017i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+2q38q54q92q158q194q21+12q23+8q25+14q27+8q298q3328q3936q43+4q454q47+20q51+16q6328q67++64q99+O(q100) 8 q + 2 q^{3} - 8 q^{5} - 4 q^{9} - 2 q^{15} - 8 q^{19} - 4 q^{21} + 12 q^{23} + 8 q^{25} + 14 q^{27} + 8 q^{29} - 8 q^{33} - 28 q^{39} - 36 q^{43} + 4 q^{45} - 4 q^{47} + 20 q^{51} + 16 q^{63} - 28 q^{67}+ \cdots + 64 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1920Z)×\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times.

nn 511511 641641 901901 15371537
χ(n)\chi(n) 1-1 1-1 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 0.759725 + 1.55654i 0.438628 + 0.898669i
44 0 0
55 −1.00000 −0.447214
66 0 0
77 0.480550i 0.181631i 0.995868 + 0.0908153i 0.0289473π0.0289473\pi
−0.995868 + 0.0908153i 0.971053π0.971053\pi
88 0 0
99 −1.84564 + 2.36509i −0.615212 + 0.788362i
1010 0 0
1111 4.73017i 1.42620i −0.701062 0.713100i 0.747290π-0.747290\pi
0.701062 0.713100i 0.252710π-0.252710\pi
1212 0 0
1313 1.59363i 0.441994i 0.975275 + 0.220997i 0.0709310π0.0709310\pi
−0.975275 + 0.220997i 0.929069π0.929069\pi
1414 0 0
1515 −0.759725 1.55654i −0.196160 0.401897i
1616 0 0
1717 6.32380i 1.53375i −0.641798 0.766874i 0.721811π-0.721811\pi
0.641798 0.766874i 0.278189π-0.278189\pi
1818 0 0
1919 −2.09764 −0.481232 −0.240616 0.970620i 0.577349π-0.577349\pi
−0.240616 + 0.970620i 0.577349π0.577349\pi
2020 0 0
2121 −0.747995 + 0.365086i −0.163226 + 0.0796682i
2222 0 0
2323 −5.84325 −1.21840 −0.609201 0.793016i 0.708510π-0.708510\pi
−0.609201 + 0.793016i 0.708510π0.708510\pi
2424 0 0
2525 1.00000 0.200000
2626 0 0
2727 −5.08353 1.07599i −0.978325 0.207074i
2828 0 0
2929 −8.95633 −1.66315 −0.831575 0.555413i 0.812560π-0.812560\pi
−0.831575 + 0.555413i 0.812560π0.812560\pi
3030 0 0
3131 8.32380i 1.49500i 0.664262 + 0.747499i 0.268746π0.268746\pi
−0.664262 + 0.747499i 0.731254π0.731254\pi
3232 0 0
3333 7.36270 3.59363i 1.28168 0.625571i
3434 0 0
3535 0.480550i 0.0812277i
3636 0 0
3737 3.67143i 0.603580i −0.953374 0.301790i 0.902416π-0.902416\pi
0.953374 0.301790i 0.0975841π-0.0975841\pi
3838 0 0
3939 −2.48055 + 1.21072i −0.397206 + 0.193871i
4040 0 0
4141 4.53489i 0.708231i −0.935202 0.354115i 0.884782π-0.884782\pi
0.935202 0.354115i 0.115218π-0.115218\pi
4242 0 0
4343 −8.70671 −1.32776 −0.663880 0.747839i 0.731092π-0.731092\pi
−0.663880 + 0.747839i 0.731092π0.731092\pi
4444 0 0
4545 1.84564 2.36509i 0.275131 0.352566i
4646 0 0
4747 −0.578190 −0.0843377 −0.0421688 0.999110i 0.513427π-0.513427\pi
−0.0421688 + 0.999110i 0.513427π0.513427\pi
4848 0 0
4949 6.76907 0.967010
5050 0 0
5151 9.84325 4.80435i 1.37833 0.672744i
5252 0 0
5353 −7.26506 −0.997933 −0.498966 0.866621i 0.666287π-0.666287\pi
−0.498966 + 0.866621i 0.666287π0.666287\pi
5454 0 0
5555 4.73017i 0.637816i
5656 0 0
5757 −1.59363 3.26506i −0.211081 0.432468i
5858 0 0
5959 2.30873i 0.300571i −0.988643 0.150285i 0.951981π-0.951981\pi
0.988643 0.150285i 0.0480193π-0.0480193\pi
6060 0 0
6161 13.9952i 1.79191i −0.444149 0.895953i 0.646494π-0.646494\pi
0.444149 0.895953i 0.353506π-0.353506\pi
6262 0 0
6363 −1.13654 0.886919i −0.143191 0.111741i
6464 0 0
6565 1.59363i 0.197666i
6666 0 0
6767 0.706711 0.0863385 0.0431692 0.999068i 0.486255π-0.486255\pi
0.0431692 + 0.999068i 0.486255π0.486255\pi
6868 0 0
6969 −4.43927 9.09526i −0.534425 1.09494i
7070 0 0
7171 13.6087 1.61506 0.807528 0.589829i 0.200805π-0.200805\pi
0.807528 + 0.589829i 0.200805π0.200805\pi
7272 0 0
7373 1.80472 0.211226 0.105613 0.994407i 0.466319π-0.466319\pi
0.105613 + 0.994407i 0.466319π0.466319\pi
7474 0 0
7575 0.759725 + 1.55654i 0.0877255 + 0.179734i
7676 0 0
7777 2.27308 0.259042
7878 0 0
7979 6.54996i 0.736928i −0.929642 0.368464i 0.879884π-0.879884\pi
0.929642 0.368464i 0.120116π-0.120116\pi
8080 0 0
8181 −2.18726 8.73017i −0.243029 0.970019i
8282 0 0
8383 3.92582i 0.430915i 0.976513 + 0.215457i 0.0691242π0.0691242\pi
−0.976513 + 0.215457i 0.930876π0.930876\pi
8484 0 0
8585 6.32380i 0.685913i
8686 0 0
8787 −6.80435 13.9409i −0.729503 1.49462i
8888 0 0
8989 9.26506i 0.982095i −0.871133 0.491047i 0.836614π-0.836614\pi
0.871133 0.491047i 0.163386π-0.163386\pi
9090 0 0
9191 −0.765818 −0.0802796
9292 0 0
9393 −12.9563 + 6.32380i −1.34351 + 0.655748i
9494 0 0
9595 2.09764 0.215213
9696 0 0
9797 −1.18726 −0.120548 −0.0602740 0.998182i 0.519197π-0.519197\pi
−0.0602740 + 0.998182i 0.519197π0.519197\pi
9898 0 0
9999 11.1873 + 8.73017i 1.12436 + 0.877415i
100100 0 0
101101 −6.87853 −0.684439 −0.342220 0.939620i 0.611179π-0.611179\pi
−0.342220 + 0.939620i 0.611179π0.611179\pi
102102 0 0
103103 1.94089i 0.191242i −0.995418 0.0956209i 0.969516π-0.969516\pi
0.995418 0.0956209i 0.0304837π-0.0304837\pi
104104 0 0
105105 0.747995 0.365086i 0.0729968 0.0356287i
106106 0 0
107107 7.45672i 0.720868i 0.932785 + 0.360434i 0.117371π0.117371\pi
−0.932785 + 0.360434i 0.882629π0.882629\pi
108108 0 0
109109 8.11271i 0.777057i 0.921437 + 0.388528i 0.127016π0.127016\pi
−0.921437 + 0.388528i 0.872984π0.872984\pi
110110 0 0
111111 5.71473 2.78928i 0.542418 0.264747i
112112 0 0
113113 3.94928i 0.371517i 0.982595 + 0.185759i 0.0594742π0.0594742\pi
−0.982595 + 0.185759i 0.940526π0.940526\pi
114114 0 0
115115 5.84325 0.544886
116116 0 0
117117 −3.76907 2.94126i −0.348451 0.271920i
118118 0 0
119119 3.03890 0.278576
120120 0 0
121121 −11.3745 −1.03405
122122 0 0
123123 7.05874 3.44527i 0.636465 0.310650i
124124 0 0
125125 −1.00000 −0.0894427
126126 0 0
127127 3.32417i 0.294972i 0.989064 + 0.147486i 0.0471182π0.0471182\pi
−0.989064 + 0.147486i 0.952882π0.952882\pi
128128 0 0
129129 −6.61471 13.5523i −0.582393 1.19322i
130130 0 0
131131 6.61269i 0.577754i 0.957366 + 0.288877i 0.0932818π0.0932818\pi
−0.957366 + 0.288877i 0.906718π0.906718\pi
132132 0 0
133133 1.00802i 0.0874065i
134134 0 0
135135 5.08353 + 1.07599i 0.437520 + 0.0926065i
136136 0 0
137137 8.86346i 0.757256i −0.925549 0.378628i 0.876396π-0.876396\pi
0.925549 0.378628i 0.123604π-0.123604\pi
138138 0 0
139139 −20.6278 −1.74962 −0.874812 0.484462i 0.839015π-0.839015\pi
−0.874812 + 0.484462i 0.839015π0.839015\pi
140140 0 0
141141 −0.439266 0.899976i −0.0369928 0.0757917i
142142 0 0
143143 7.53814 0.630371
144144 0 0
145145 8.95633 0.743783
146146 0 0
147147 5.14263 + 10.5363i 0.424157 + 0.869022i
148148 0 0
149149 18.8429 1.54367 0.771835 0.635823i 0.219339π-0.219339\pi
0.771835 + 0.635823i 0.219339π0.219339\pi
150150 0 0
151151 15.2143i 1.23813i 0.785341 + 0.619063i 0.212487π0.212487\pi
−0.785341 + 0.619063i 0.787513π0.787513\pi
152152 0 0
153153 14.9563 + 11.6714i 1.20915 + 0.943579i
154154 0 0
155155 8.32380i 0.668584i
156156 0 0
157157 16.9762i 1.35485i −0.735594 0.677423i 0.763097π-0.763097\pi
0.735594 0.677423i 0.236903π-0.236903\pi
158158 0 0
159159 −5.51945 11.3084i −0.437721 0.896811i
160160 0 0
161161 2.80797i 0.221299i
162162 0 0
163163 7.89397 0.618304 0.309152 0.951013i 0.399955π-0.399955\pi
0.309152 + 0.951013i 0.399955π0.399955\pi
164164 0 0
165165 −7.36270 + 3.59363i −0.573186 + 0.279764i
166166 0 0
167167 −13.0305 −1.00833 −0.504166 0.863607i 0.668200π-0.668200\pi
−0.504166 + 0.863607i 0.668200π0.668200\pi
168168 0 0
169169 10.4603 0.804642
170170 0 0
171171 3.87148 4.96110i 0.296059 0.379385i
172172 0 0
173173 −10.1556 −0.772116 −0.386058 0.922474i 0.626164π-0.626164\pi
−0.386058 + 0.922474i 0.626164π0.626164\pi
174174 0 0
175175 0.480550i 0.0363261i
176176 0 0
177177 3.59363 1.75400i 0.270114 0.131839i
178178 0 0
179179 3.76907i 0.281714i 0.990030 + 0.140857i 0.0449857π0.0449857\pi
−0.990030 + 0.140857i 0.955014π0.955014\pi
180180 0 0
181181 8.45232i 0.628256i −0.949381 0.314128i 0.898288π-0.898288\pi
0.949381 0.314128i 0.101712π-0.101712\pi
182182 0 0
183183 21.7841 10.6325i 1.61033 0.785979i
184184 0 0
185185 3.67143i 0.269929i
186186 0 0
187187 −29.9127 −2.18743
188188 0 0
189189 0.517067 2.44289i 0.0376111 0.177694i
190190 0 0
191191 −21.5690 −1.56068 −0.780340 0.625356i 0.784954π-0.784954\pi
−0.780340 + 0.625356i 0.784954π0.784954\pi
192192 0 0
193193 15.7174 1.13136 0.565681 0.824624i 0.308613π-0.308613\pi
0.565681 + 0.824624i 0.308613π0.308613\pi
194194 0 0
195195 2.48055 1.21072i 0.177636 0.0867015i
196196 0 0
197197 −22.0301 −1.56958 −0.784791 0.619760i 0.787230π-0.787230\pi
−0.784791 + 0.619760i 0.787230π0.787230\pi
198198 0 0
199199 5.08962i 0.360794i 0.983594 + 0.180397i 0.0577382π0.0577382\pi
−0.983594 + 0.180397i 0.942262π0.942262\pi
200200 0 0
201201 0.536906 + 1.10002i 0.0378704 + 0.0775897i
202202 0 0
203203 4.30396i 0.302079i
204204 0 0
205205 4.53489i 0.316730i
206206 0 0
207207 10.7845 13.8198i 0.749575 0.960542i
208208 0 0
209209 9.92220i 0.686333i
210210 0 0
211211 18.2365 1.25545 0.627725 0.778435i 0.283986π-0.283986\pi
0.627725 + 0.778435i 0.283986π0.283986\pi
212212 0 0
213213 10.3389 + 21.1825i 0.708408 + 1.45140i
214214 0 0
215215 8.70671 0.593793
216216 0 0
217217 −4.00000 −0.271538
218218 0 0
219219 1.37109 + 2.80912i 0.0926497 + 0.189823i
220220 0 0
221221 10.0778 0.677906
222222 0 0
223223 24.1671i 1.61835i 0.587571 + 0.809173i 0.300084π0.300084\pi
−0.587571 + 0.809173i 0.699916π0.699916\pi
224224 0 0
225225 −1.84564 + 2.36509i −0.123042 + 0.157672i
226226 0 0
227227 14.3473i 0.952261i 0.879375 + 0.476131i 0.157961π0.157961\pi
−0.879375 + 0.476131i 0.842039π0.842039\pi
228228 0 0
229229 10.5698i 0.698472i −0.937035 0.349236i 0.886441π-0.886441\pi
0.937035 0.349236i 0.113559π-0.113559\pi
230230 0 0
231231 1.72692 + 3.53814i 0.113623 + 0.232793i
232232 0 0
233233 8.44128i 0.553007i −0.961013 0.276503i 0.910824π-0.910824\pi
0.961013 0.276503i 0.0891757π-0.0891757\pi
234234 0 0
235235 0.578190 0.0377170
236236 0 0
237237 10.1953 4.97617i 0.662255 0.323237i
238238 0 0
239239 11.8047 0.763584 0.381792 0.924248i 0.375307π-0.375307\pi
0.381792 + 0.924248i 0.375307π0.375307\pi
240240 0 0
241241 −27.6817 −1.78314 −0.891569 0.452885i 0.850395π-0.850395\pi
−0.891569 + 0.452885i 0.850395π0.850395\pi
242242 0 0
243243 11.9271 10.0371i 0.765127 0.643880i
244244 0 0
245245 −6.76907 −0.432460
246246 0 0
247247 3.34286i 0.212701i
248248 0 0
249249 −6.11070 + 2.98254i −0.387250 + 0.189011i
250250 0 0
251251 4.73017i 0.298566i −0.988795 0.149283i 0.952303π-0.952303\pi
0.988795 0.149283i 0.0476965π-0.0476965\pi
252252 0 0
253253 27.6396i 1.73769i
254254 0 0
255255 −9.84325 + 4.80435i −0.616408 + 0.300860i
256256 0 0
257257 22.9714i 1.43292i 0.697630 + 0.716458i 0.254238π0.254238\pi
−0.697630 + 0.716458i 0.745762π0.745762\pi
258258 0 0
259259 1.76431 0.109629
260260 0 0
261261 16.5301 21.1825i 1.02319 1.31116i
262262 0 0
263263 −19.6171 −1.20964 −0.604821 0.796362i 0.706755π-0.706755\pi
−0.604821 + 0.796362i 0.706755π0.706755\pi
264264 0 0
265265 7.26506 0.446289
266266 0 0
267267 14.4214 7.03890i 0.882578 0.430774i
268268 0 0
269269 −8.46836 −0.516325 −0.258163 0.966101i 0.583117π-0.583117\pi
−0.258163 + 0.966101i 0.583117π0.583117\pi
270270 0 0
271271 15.4714i 0.939820i −0.882714 0.469910i 0.844286π-0.844286\pi
0.882714 0.469910i 0.155714π-0.155714\pi
272272 0 0
273273 −0.581812 1.19203i −0.0352128 0.0721448i
274274 0 0
275275 4.73017i 0.285240i
276276 0 0
277277 24.7096i 1.48466i 0.670037 + 0.742328i 0.266278π0.266278\pi
−0.670037 + 0.742328i 0.733722π0.733722\pi
278278 0 0
279279 −19.6865 15.3627i −1.17860 0.919741i
280280 0 0
281281 27.0033i 1.61088i −0.592678 0.805440i 0.701929π-0.701929\pi
0.592678 0.805440i 0.298071π-0.298071\pi
282282 0 0
283283 −20.9020 −1.24249 −0.621247 0.783615i 0.713374π-0.713374\pi
−0.621247 + 0.783615i 0.713374π0.713374\pi
284284 0 0
285285 1.59363 + 3.26506i 0.0943985 + 0.193406i
286286 0 0
287287 2.17924 0.128636
288288 0 0
289289 −22.9905 −1.35238
290290 0 0
291291 −0.901992 1.84802i −0.0528757 0.108333i
292292 0 0
293293 0.374521 0.0218797 0.0109399 0.999940i 0.496518π-0.496518\pi
0.0109399 + 0.999940i 0.496518π0.496518\pi
294294 0 0
295295 2.30873i 0.134419i
296296 0 0
297297 −5.08962 + 24.0460i −0.295330 + 1.39529i
298298 0 0
299299 9.31198i 0.538526i
300300 0 0
301301 4.18401i 0.241162i
302302 0 0
303303 −5.22579 10.7067i −0.300214 0.615084i
304304 0 0
305305 13.9952i 0.801365i
306306 0 0
307307 −14.3623 −0.819702 −0.409851 0.912153i 0.634419π-0.634419\pi
−0.409851 + 0.912153i 0.634419π0.634419\pi
308308 0 0
309309 3.02108 1.47454i 0.171863 0.0838839i
310310 0 0
311311 22.2166 1.25979 0.629895 0.776681i 0.283098π-0.283098\pi
0.629895 + 0.776681i 0.283098π0.283098\pi
312312 0 0
313313 33.6697 1.90313 0.951563 0.307455i 0.0994772π-0.0994772\pi
0.951563 + 0.307455i 0.0994772π0.0994772\pi
314314 0 0
315315 1.13654 + 0.886919i 0.0640368 + 0.0499722i
316316 0 0
317317 29.7952 1.67346 0.836732 0.547612i 0.184463π-0.184463\pi
0.836732 + 0.547612i 0.184463π0.184463\pi
318318 0 0
319319 42.3650i 2.37198i
320320 0 0
321321 −11.6067 + 5.66506i −0.647822 + 0.316193i
322322 0 0
323323 13.2651i 0.738088i
324324 0 0
325325 1.59363i 0.0883987i
326326 0 0
327327 −12.6278 + 6.16343i −0.698317 + 0.340839i
328328 0 0
329329 0.277849i 0.0153183i
330330 0 0
331331 −23.7063 −1.30302 −0.651509 0.758641i 0.725864π-0.725864\pi
−0.651509 + 0.758641i 0.725864π0.725864\pi
332332 0 0
333333 8.68325 + 6.77612i 0.475839 + 0.371329i
334334 0 0
335335 −0.706711 −0.0386117
336336 0 0
337337 −27.9127 −1.52050 −0.760250 0.649631i 0.774924π-0.774924\pi
−0.760250 + 0.649631i 0.774924π0.774924\pi
338338 0 0
339339 −6.14721 + 3.00037i −0.333871 + 0.162958i
340340 0 0
341341 39.3730 2.13217
342342 0 0
343343 6.61672i 0.357269i
344344 0 0
345345 4.43927 + 9.09526i 0.239002 + 0.489672i
346346 0 0
347347 14.4956i 0.778166i −0.921203 0.389083i 0.872792π-0.872792\pi
0.921203 0.389083i 0.127208π-0.127208\pi
348348 0 0
349349 2.73494i 0.146398i 0.997317 + 0.0731989i 0.0233208π0.0233208\pi
−0.997317 + 0.0731989i 0.976679π0.976679\pi
350350 0 0
351351 1.71473 8.10126i 0.0915256 0.432413i
352352 0 0
353353 35.3936i 1.88381i 0.335879 + 0.941905i 0.390967π0.390967\pi
−0.335879 + 0.941905i 0.609033π0.609033\pi
354354 0 0
355355 −13.6087 −0.722275
356356 0 0
357357 2.30873 + 4.73017i 0.122191 + 0.250347i
358358 0 0
359359 −11.1777 −0.589938 −0.294969 0.955507i 0.595309π-0.595309\pi
−0.294969 + 0.955507i 0.595309π0.595309\pi
360360 0 0
361361 −14.5999 −0.768416
362362 0 0
363363 −8.64151 17.7049i −0.453562 0.929266i
364364 0 0
365365 −1.80472 −0.0944633
366366 0 0
367367 8.18383i 0.427192i 0.976922 + 0.213596i 0.0685177π0.0685177\pi
−0.976922 + 0.213596i 0.931482π0.931482\pi
368368 0 0
369369 10.7254 + 8.36975i 0.558342 + 0.435712i
370370 0 0
371371 3.49122i 0.181255i
372372 0 0
373373 14.2016i 0.735329i 0.929959 + 0.367664i 0.119842π0.119842\pi
−0.929959 + 0.367664i 0.880158π0.880158\pi
374374 0 0
375375 −0.759725 1.55654i −0.0392320 0.0803794i
376376 0 0
377377 14.2731i 0.735101i
378378 0 0
379379 10.0976 0.518681 0.259340 0.965786i 0.416495π-0.416495\pi
0.259340 + 0.965786i 0.416495π0.416495\pi
380380 0 0
381381 −5.17420 + 2.52546i −0.265082 + 0.129383i
382382 0 0
383383 −9.35125 −0.477827 −0.238913 0.971041i 0.576791π-0.576791\pi
−0.238913 + 0.971041i 0.576791π0.576791\pi
384384 0 0
385385 −2.27308 −0.115847
386386 0 0
387387 16.0694 20.5921i 0.816854 1.04676i
388388 0 0
389389 12.5301 0.635302 0.317651 0.948208i 0.397106π-0.397106\pi
0.317651 + 0.948208i 0.397106π0.397106\pi
390390 0 0
391391 36.9516i 1.86872i
392392 0 0
393393 −10.2929 + 5.02383i −0.519209 + 0.253419i
394394 0 0
395395 6.54996i 0.329564i
396396 0 0
397397 28.3492i 1.42280i −0.702785 0.711402i 0.748060π-0.748060\pi
0.702785 0.711402i 0.251940π-0.251940\pi
398398 0 0
399399 1.56902 0.765818i 0.0785495 0.0383389i
400400 0 0
401401 17.7571i 0.886745i 0.896337 + 0.443373i 0.146218π0.146218\pi
−0.896337 + 0.443373i 0.853782π0.853782\pi
402402 0 0
403403 −13.2651 −0.660780
404404 0 0
405405 2.18726 + 8.73017i 0.108686 + 0.433806i
406406 0 0
407407 −17.3665 −0.860825
408408 0 0
409409 −23.2294 −1.14862 −0.574310 0.818638i 0.694730π-0.694730\pi
−0.574310 + 0.818638i 0.694730π0.694730\pi
410410 0 0
411411 13.7963 6.73379i 0.680523 0.332154i
412412 0 0
413413 1.10946 0.0545929
414414 0 0
415415 3.92582i 0.192711i
416416 0 0
417417 −15.6714 32.1079i −0.767433 1.57233i
418418 0 0
419419 36.4167i 1.77907i −0.456866 0.889536i 0.651028π-0.651028\pi
0.456866 0.889536i 0.348972π-0.348972\pi
420420 0 0
421421 21.8301i 1.06393i −0.846765 0.531967i 0.821453π-0.821453\pi
0.846765 0.531967i 0.178547π-0.178547\pi
422422 0 0
423423 1.06713 1.36747i 0.0518855 0.0664886i
424424 0 0
425425 6.32380i 0.306749i
426426 0 0
427427 6.72540 0.325465
428428 0 0
429429 5.72692 + 11.7334i 0.276498 + 0.566495i
430430 0 0
431431 −32.4355 −1.56237 −0.781183 0.624303i 0.785383π-0.785383\pi
−0.781183 + 0.624303i 0.785383π0.785383\pi
432432 0 0
433433 19.5618 0.940079 0.470040 0.882645i 0.344240π-0.344240\pi
0.470040 + 0.882645i 0.344240π0.344240\pi
434434 0 0
435435 6.80435 + 13.9409i 0.326244 + 0.668415i
436436 0 0
437437 12.2570 0.586334
438438 0 0
439439 9.89283i 0.472159i −0.971734 0.236079i 0.924137π-0.924137\pi
0.971734 0.236079i 0.0758625π-0.0758625\pi
440440 0 0
441441 −12.4932 + 16.0094i −0.594916 + 0.762354i
442442 0 0
443443 39.2519i 1.86491i 0.361281 + 0.932457i 0.382340π0.382340\pi
−0.361281 + 0.932457i 0.617660π0.617660\pi
444444 0 0
445445 9.26506i 0.439206i
446446 0 0
447447 14.3154 + 29.3297i 0.677096 + 1.38725i
448448 0 0
449449 12.7302i 0.600774i 0.953817 + 0.300387i 0.0971158π0.0971158\pi
−0.953817 + 0.300387i 0.902884π0.902884\pi
450450 0 0
451451 −21.4508 −1.01008
452452 0 0
453453 −23.6817 + 11.5587i −1.11267 + 0.543076i
454454 0 0
455455 0.765818 0.0359021
456456 0 0
457457 −5.14758 −0.240794 −0.120397 0.992726i 0.538417π-0.538417\pi
−0.120397 + 0.992726i 0.538417π0.538417\pi
458458 0 0
459459 −6.80435 + 32.1472i −0.317600 + 1.50050i
460460 0 0
461461 9.11194 0.424385 0.212193 0.977228i 0.431940π-0.431940\pi
0.212193 + 0.977228i 0.431940π0.431940\pi
462462 0 0
463463 36.4542i 1.69417i −0.531456 0.847086i 0.678355π-0.678355\pi
0.531456 0.847086i 0.321645π-0.321645\pi
464464 0 0
465465 12.9563 6.32380i 0.600836 0.293259i
466466 0 0
467467 10.5425i 0.487851i −0.969794 0.243925i 0.921565π-0.921565\pi
0.969794 0.243925i 0.0784352π-0.0784352\pi
468468 0 0
469469 0.339610i 0.0156817i
470470 0 0
471471 26.4241 12.8972i 1.21756 0.594273i
472472 0 0
473473 41.1842i 1.89365i
474474 0 0
475475 −2.09764 −0.0962463
476476 0 0
477477 13.4087 17.1825i 0.613940 0.786732i
478478 0 0
479479 31.0221 1.41744 0.708719 0.705491i 0.249274π-0.249274\pi
0.708719 + 0.705491i 0.249274π0.249274\pi
480480 0 0
481481 5.85090 0.266778
482482 0 0
483483 4.37072 2.13329i 0.198875 0.0970679i
484484 0 0
485485 1.18726 0.0539107
486486 0 0
487487 18.7536i 0.849808i −0.905238 0.424904i 0.860308π-0.860308\pi
0.905238 0.424904i 0.139692π-0.139692\pi
488488 0 0
489489 5.99725 + 12.2873i 0.271205 + 0.555650i
490490 0 0
491491 16.9255i 0.763835i 0.924196 + 0.381917i 0.124736π0.124736\pi
−0.924196 + 0.381917i 0.875264π0.875264\pi
492492 0 0
493493 56.6381i 2.55085i
494494 0 0
495495 −11.1873 8.73017i −0.502830 0.392392i
496496 0 0
497497 6.53966i 0.293344i
498498 0 0
499499 −5.90236 −0.264226 −0.132113 0.991235i 0.542176π-0.542176\pi
−0.132113 + 0.991235i 0.542176π0.542176\pi
500500 0 0
501501 −9.89961 20.2825i −0.442282 0.906156i
502502 0 0
503503 −20.2647 −0.903558 −0.451779 0.892130i 0.649210π-0.649210\pi
−0.451779 + 0.892130i 0.649210π0.649210\pi
504504 0 0
505505 6.87853 0.306091
506506 0 0
507507 7.94699 + 16.2819i 0.352938 + 0.723107i
508508 0 0
509509 12.5040 0.554231 0.277115 0.960837i 0.410622π-0.410622\pi
0.277115 + 0.960837i 0.410622π0.410622\pi
510510 0 0
511511 0.867257i 0.0383652i
512512 0 0
513513 10.6634 + 2.25704i 0.470801 + 0.0996508i
514514 0 0
515515 1.94089i 0.0855259i
516516 0 0
517517 2.73494i 0.120282i
518518 0 0
519519 −7.71547 15.8076i −0.338671 0.693877i
520520 0 0
521521 23.6697i 1.03699i 0.855081 + 0.518495i 0.173507π0.173507\pi
−0.855081 + 0.518495i 0.826493π0.826493\pi
522522 0 0
523523 43.1655 1.88750 0.943749 0.330664i 0.107273π-0.107273\pi
0.943749 + 0.330664i 0.107273π0.107273\pi
524524 0 0
525525 −0.747995 + 0.365086i −0.0326452 + 0.0159336i
526526 0 0
527527 52.6381 2.29295
528528 0 0
529529 11.1436 0.484504
530530 0 0
531531 5.46034 + 4.26107i 0.236959 + 0.184915i
532532 0 0
533533 7.22694 0.313033
534534 0 0
535535 7.45672i 0.322382i
536536 0 0
537537 −5.86671 + 2.86346i −0.253167 + 0.123567i
538538 0 0
539539 32.0189i 1.37915i
540540 0 0
541541 6.99198i 0.300609i −0.988640 0.150304i 0.951975π-0.951975\pi
0.988640 0.150304i 0.0480254π-0.0480254\pi
542542 0 0
543543 13.1564 6.42144i 0.564594 0.275570i
544544 0 0
545545 8.11271i 0.347510i
546546 0 0
547547 15.8227 0.676529 0.338264 0.941051i 0.390160π-0.390160\pi
0.338264 + 0.941051i 0.390160π0.390160\pi
548548 0 0
549549 33.0999 + 25.8301i 1.41267 + 1.10240i
550550 0 0
551551 18.7872 0.800360
552552 0 0
553553 3.14758 0.133849
554554 0 0
555555 −5.71473 + 2.78928i −0.242577 + 0.118398i
556556 0 0
557557 16.3032 0.690790 0.345395 0.938457i 0.387745π-0.387745\pi
0.345395 + 0.938457i 0.387745π0.387745\pi
558558 0 0
559559 13.8753i 0.586862i
560560 0 0
561561 −22.7254 46.5603i −0.959467 1.96578i
562562 0 0
563563 15.4567i 0.651423i 0.945469 + 0.325712i 0.105604π0.105604\pi
−0.945469 + 0.325712i 0.894396π0.894396\pi
564564 0 0
565565 3.94928i 0.166147i
566566 0 0
567567 4.19528 1.05109i 0.176185 0.0441415i
568568 0 0
569569 2.64284i 0.110793i 0.998464 + 0.0553967i 0.0176424π0.0176424\pi
−0.998464 + 0.0553967i 0.982358π0.982358\pi
570570 0 0
571571 5.43326 0.227375 0.113687 0.993517i 0.463734π-0.463734\pi
0.113687 + 0.993517i 0.463734π0.463734\pi
572572 0 0
573573 −16.3865 33.5731i −0.684557 1.40253i
574574 0 0
575575 −5.84325 −0.243680
576576 0 0
577577 16.7651 0.697940 0.348970 0.937134i 0.386532π-0.386532\pi
0.348970 + 0.937134i 0.386532π0.386532\pi
578578 0 0
579579 11.9409 + 24.4647i 0.496247 + 1.01672i
580580 0 0
581581 −1.88655 −0.0782673
582582 0 0
583583 34.3650i 1.42325i
584584 0 0
585585 3.76907 + 2.94126i 0.155832 + 0.121606i
586586 0 0
587587 4.87014i 0.201012i −0.994936 0.100506i 0.967954π-0.967954\pi
0.994936 0.100506i 0.0320462π-0.0320462\pi
588588 0 0
589589 17.4603i 0.719441i
590590 0 0
591591 −16.7369 34.2908i −0.688462 1.41054i
592592 0 0
593593 23.5492i 0.967049i 0.875331 + 0.483525i 0.160644π0.160644\pi
−0.875331 + 0.483525i 0.839356π0.839356\pi
594594 0 0
595595 −3.03890 −0.124583
596596 0 0
597597 −7.92220 + 3.86671i −0.324234 + 0.158254i
598598 0 0
599599 39.1160 1.59824 0.799118 0.601175i 0.205300π-0.205300\pi
0.799118 + 0.601175i 0.205300π0.205300\pi
600600 0 0
601601 −33.9945 −1.38666 −0.693332 0.720618i 0.743858π-0.743858\pi
−0.693332 + 0.720618i 0.743858π0.743858\pi
602602 0 0
603603 −1.30433 + 1.67143i −0.0531164 + 0.0680660i
604604 0 0
605605 11.3745 0.462440
606606 0 0
607607 38.7441i 1.57257i 0.617861 + 0.786287i 0.287999π0.287999\pi
−0.617861 + 0.786287i 0.712001π0.712001\pi
608608 0 0
609609 6.69929 3.26983i 0.271469 0.132500i
610610 0 0
611611 0.921421i 0.0372767i
612612 0 0
613613 21.4190i 0.865104i 0.901609 + 0.432552i 0.142387π0.142387\pi
−0.901609 + 0.432552i 0.857613π0.857613\pi
614614 0 0
615615 −7.05874 + 3.44527i −0.284636 + 0.138927i
616616 0 0
617617 10.4794i 0.421885i −0.977498 0.210942i 0.932347π-0.932347\pi
0.977498 0.210942i 0.0676533π-0.0676533\pi
618618 0 0
619619 23.4943 0.944315 0.472158 0.881514i 0.343475π-0.343475\pi
0.472158 + 0.881514i 0.343475π0.343475\pi
620620 0 0
621621 29.7043 + 6.28728i 1.19199 + 0.252300i
622622 0 0
623623 4.45232 0.178379
624624 0 0
625625 1.00000 0.0400000
626626 0 0
627627 −15.4443 + 7.53814i −0.616786 + 0.301044i
628628 0 0
629629 −23.2174 −0.925739
630630 0 0
631631 43.5809i 1.73493i −0.497500 0.867464i 0.665749π-0.665749\pi
0.497500 0.867464i 0.334251π-0.334251\pi
632632 0 0
633633 13.8547 + 28.3858i 0.550675 + 1.12823i
634634 0 0
635635 3.32417i 0.131916i
636636 0 0
637637 10.7874i 0.427412i
638638 0 0
639639 −25.1167 + 32.1857i −0.993601 + 1.27325i
640640 0 0
641641 6.29195i 0.248517i −0.992250 0.124259i 0.960345π-0.960345\pi
0.992250 0.124259i 0.0396552π-0.0396552\pi
642642 0 0
643643 −25.6583 −1.01186 −0.505932 0.862573i 0.668851π-0.668851\pi
−0.505932 + 0.862573i 0.668851π0.668851\pi
644644 0 0
645645 6.61471 + 13.5523i 0.260454 + 0.533623i
646646 0 0
647647 −6.22575 −0.244760 −0.122380 0.992483i 0.539053π-0.539053\pi
−0.122380 + 0.992483i 0.539053π0.539053\pi
648648 0 0
649649 −10.9207 −0.428674
650650 0 0
651651 −3.03890 6.22616i −0.119104 0.244022i
652652 0 0
653653 −35.0382 −1.37115 −0.685575 0.728002i 0.740449π-0.740449\pi
−0.685575 + 0.728002i 0.740449π0.740449\pi
654654 0 0
655655 6.61269i 0.258379i
656656 0 0
657657 −3.33085 + 4.26832i −0.129949 + 0.166523i
658658 0 0
659659 17.5166i 0.682350i 0.940000 + 0.341175i 0.110825π0.110825\pi
−0.940000 + 0.341175i 0.889175π0.889175\pi
660660 0 0
661661 14.5509i 0.565966i 0.959125 + 0.282983i 0.0913239π0.0913239\pi
−0.959125 + 0.282983i 0.908676π0.908676\pi
662662 0 0
663663 7.65636 + 15.6865i 0.297348 + 0.609213i
664664 0 0
665665 1.00802i 0.0390894i
666666 0 0
667667 52.3341 2.02638
668668 0 0
669669 −37.6170 + 18.3603i −1.45436 + 0.709851i
670670 0 0
671671 −66.1999 −2.55562
672672 0 0
673673 17.3429 0.668518 0.334259 0.942481i 0.391514π-0.391514\pi
0.334259 + 0.942481i 0.391514π0.391514\pi
674674 0 0
675675 −5.08353 1.07599i −0.195665 0.0414149i
676676 0 0
677677 15.0382 0.577964 0.288982 0.957335i 0.406683π-0.406683\pi
0.288982 + 0.957335i 0.406683π0.406683\pi
678678 0 0
679679 0.570538i 0.0218952i
680680 0 0
681681 −22.3321 + 10.9000i −0.855768 + 0.417688i
682682 0 0
683683 12.5566i 0.480467i −0.970715 0.240233i 0.922776π-0.922776\pi
0.970715 0.240233i 0.0772240π-0.0772240\pi
684684 0 0
685685 8.86346i 0.338655i
686686 0 0
687687 16.4523 8.03014i 0.627695 0.306369i
688688 0 0
689689 11.5778i 0.441080i
690690 0 0
691691 −34.2365 −1.30242 −0.651208 0.758899i 0.725738π-0.725738\pi
−0.651208 + 0.758899i 0.725738π0.725738\pi
692692 0 0
693693 −4.19528 + 5.37603i −0.159366 + 0.204219i
694694 0 0
695695 20.6278 0.782456
696696 0 0
697697 −28.6777 −1.08625
698698 0 0
699699 13.1392 6.41305i 0.496970 0.242564i
700700 0 0
701701 −7.29521 −0.275536 −0.137768 0.990465i 0.543993π-0.543993\pi
−0.137768 + 0.990465i 0.543993π0.543993\pi
702702 0 0
703703 7.70134i 0.290462i
704704 0 0
705705 0.439266 + 0.899976i 0.0165437 + 0.0338951i
706706 0 0
707707 3.30548i 0.124315i
708708 0 0
709709 19.6396i 0.737580i −0.929513 0.368790i 0.879772π-0.879772\pi
0.929513 0.368790i 0.120228π-0.120228\pi
710710 0 0
711711 15.4912 + 12.0888i 0.580966 + 0.453367i
712712 0 0
713713 48.6381i 1.82151i
714714 0 0
715715 −7.53814 −0.281911
716716 0 0
717717 8.96834 + 18.3745i 0.334929 + 0.686209i
718718 0 0
719719 45.1541 1.68396 0.841982 0.539506i 0.181389π-0.181389\pi
0.841982 + 0.539506i 0.181389π0.181389\pi
720720 0 0
721721 0.932695 0.0347354
722722 0 0
723723 −21.0305 43.0877i −0.782133 1.60245i
724724 0 0
725725 −8.95633 −0.332630
726726 0 0
727727 5.93365i 0.220067i 0.993928 + 0.110033i 0.0350958π0.0350958\pi
−0.993928 + 0.110033i 0.964904π0.964904\pi
728728 0 0
729729 24.6845 + 10.9397i 0.914240 + 0.405172i
730730 0 0
731731 55.0595i 2.03645i
732732 0 0
733733 26.0460i 0.962029i 0.876713 + 0.481015i 0.159732π0.159732\pi
−0.876713 + 0.481015i 0.840268π0.840268\pi
734734 0 0
735735 −5.14263 10.5363i −0.189689 0.388639i
736736 0 0
737737 3.34286i 0.123136i
738738 0 0
739739 −1.11976 −0.0411912 −0.0205956 0.999788i 0.506556π-0.506556\pi
−0.0205956 + 0.999788i 0.506556π0.506556\pi
740740 0 0
741741 5.20330 2.53966i 0.191148 0.0932966i
742742 0 0
743743 13.7250 0.503523 0.251761 0.967789i 0.418990π-0.418990\pi
0.251761 + 0.967789i 0.418990π0.418990\pi
744744 0 0
745745 −18.8429 −0.690350
746746 0 0
747747 −9.28490 7.24563i −0.339717 0.265104i
748748 0 0
749749 −3.58332 −0.130932
750750 0 0
751751 41.2826i 1.50642i −0.657778 0.753212i 0.728503π-0.728503\pi
0.657778 0.753212i 0.271497π-0.271497\pi
752752 0 0
753753 7.36270 3.59363i 0.268312 0.130959i
754754 0 0
755755 15.2143i 0.553707i
756756 0 0
757757 46.4270i 1.68742i −0.536801 0.843709i 0.680368π-0.680368\pi
0.536801 0.843709i 0.319632π-0.319632\pi
758758 0 0
759759 −43.0221 + 20.9985i −1.56160 + 0.762197i
760760 0 0
761761 49.4413i 1.79224i −0.443807 0.896122i 0.646372π-0.646372\pi
0.443807 0.896122i 0.353628π-0.353628\pi
762762 0 0
763763 −3.89856 −0.141137
764764 0 0
765765 −14.9563 11.6714i −0.540747 0.421982i
766766 0 0
767767 3.67926 0.132850
768768 0 0
769769 −11.3047 −0.407659 −0.203830 0.979006i 0.565339π-0.565339\pi
−0.203830 + 0.979006i 0.565339π0.565339\pi
770770 0 0
771771 −35.7559 + 17.4520i −1.28772 + 0.628517i
772772 0 0
773773 −4.34438 −0.156256 −0.0781282 0.996943i 0.524894π-0.524894\pi
−0.0781282 + 0.996943i 0.524894π0.524894\pi
774774 0 0
775775 8.32380i 0.299000i
776776 0 0
777777 1.34039 + 2.74621i 0.0480861 + 0.0985198i
778778 0 0
779779 9.51257i 0.340823i
780780 0 0
781781 64.3715i 2.30339i
782782 0 0
783783 45.5298 + 9.63693i 1.62710 + 0.344396i
784784 0 0
785785 16.9762i 0.605906i
786786 0 0
787787 −5.58121 −0.198949 −0.0994743 0.995040i 0.531716π-0.531716\pi
−0.0994743 + 0.995040i 0.531716π0.531716\pi
788788 0 0
789789 −14.9036 30.5348i −0.530582 1.08707i
790790 0 0
791791 −1.89783 −0.0674789
792792 0 0
793793 22.3032 0.792011
794794 0 0
795795 5.51945 + 11.3084i 0.195755 + 0.401066i
796796 0 0
797797 −20.7159 −0.733794 −0.366897 0.930262i 0.619580π-0.619580\pi
−0.366897 + 0.930262i 0.619580π0.619580\pi
798798 0 0
799799 3.65636i 0.129353i
800800 0 0
801801 21.9127 + 17.0999i 0.774246 + 0.604196i
802802 0 0
803803 8.53663i 0.301251i
804804 0 0
805805 2.80797i 0.0989680i
806806 0 0
807807 −6.43363 13.1813i −0.226474 0.464005i
808808 0 0
809809 12.2570i 0.430935i −0.976511 0.215467i 0.930873π-0.930873\pi
0.976511 0.215467i 0.0691275π-0.0691275\pi
810810 0 0
811811 22.6285 0.794594 0.397297 0.917690i 0.369948π-0.369948\pi
0.397297 + 0.917690i 0.369948π0.369948\pi
812812 0 0
813813 24.0818 11.7540i 0.844587 0.412231i
814814 0 0
815815 −7.89397 −0.276514
816816 0 0
817817 18.2635 0.638961
818818 0 0
819819 1.41342 1.81123i 0.0493889 0.0632894i
820820 0 0
821821 −25.0618 −0.874663 −0.437331 0.899300i 0.644076π-0.644076\pi
−0.437331 + 0.899300i 0.644076π0.644076\pi
822822 0 0
823823 33.3139i 1.16125i −0.814171 0.580625i 0.802808π-0.802808\pi
0.814171 0.580625i 0.197192π-0.197192\pi
824824 0 0
825825 7.36270 3.59363i 0.256336 0.125114i
826826 0 0
827827 17.9098i 0.622784i 0.950282 + 0.311392i 0.100795π0.100795\pi
−0.950282 + 0.311392i 0.899205π0.899205\pi
828828 0 0
829829 16.1127i 0.559618i −0.960056 0.279809i 0.909729π-0.909729\pi
0.960056 0.279809i 0.0902711π-0.0902711\pi
830830 0 0
831831 −38.4615 + 18.7725i −1.33421 + 0.651211i
832832 0 0
833833 42.8063i 1.48315i
834834 0 0
835835 13.0305 0.450939
836836 0 0
837837 8.95633 42.3143i 0.309576 1.46260i
838838 0 0
839839 −12.8032 −0.442016 −0.221008 0.975272i 0.570935π-0.570935\pi
−0.221008 + 0.975272i 0.570935π0.570935\pi
840840 0 0
841841 51.2159 1.76607
842842 0 0
843843 42.0317 20.5151i 1.44765 0.706576i
844844 0 0
845845 −10.4603 −0.359847
846846 0 0
847847 5.46602i 0.187815i
848848 0 0
849849 −15.8798 32.5348i −0.544992 1.11659i
850850 0 0
851851 21.4531i 0.735403i
852852 0 0
853853 32.9365i 1.12772i −0.825869 0.563862i 0.809315π-0.809315\pi
0.825869 0.563862i 0.190685π-0.190685\pi
854854 0 0
855855 −3.87148 + 4.96110i −0.132402 + 0.169666i
856856 0 0
857857 10.4889i 0.358295i −0.983822 0.179148i 0.942666π-0.942666\pi
0.983822 0.179148i 0.0573340π-0.0573340\pi
858858 0 0
859859 11.9405 0.407404 0.203702 0.979033i 0.434703π-0.434703\pi
0.203702 + 0.979033i 0.434703π0.434703\pi
860860 0 0
861861 1.65562 + 3.39207i 0.0564235 + 0.115602i
862862 0 0
863863 −38.1869 −1.29990 −0.649948 0.759978i 0.725210π-0.725210\pi
−0.649948 + 0.759978i 0.725210π0.725210\pi
864864 0 0
865865 10.1556 0.345301
866866 0 0
867867 −17.4664 35.7856i −0.593191 1.21534i
868868 0 0
869869 −30.9824 −1.05101
870870 0 0
871871 1.12624i 0.0381610i
872872 0 0
873873 2.19125 2.80797i 0.0741626 0.0950355i
874874 0 0
875875 0.480550i 0.0162455i
876876 0 0
877877 3.83657i 0.129552i −0.997900 0.0647758i 0.979367π-0.979367\pi
0.997900 0.0647758i 0.0206332π-0.0206332\pi
878878 0 0
879879 0.284533 + 0.582957i 0.00959706 + 0.0196626i
880880 0 0
881881 15.0650i 0.507553i −0.967263 0.253777i 0.918327π-0.918327\pi
0.967263 0.253777i 0.0816728π-0.0816728\pi
882882 0 0
883883 39.9878 1.34570 0.672849 0.739780i 0.265071π-0.265071\pi
0.672849 + 0.739780i 0.265071π0.265071\pi
884884 0 0
885885 −3.59363 + 1.75400i −0.120799 + 0.0589601i
886886 0 0
887887 −43.1289 −1.44813 −0.724064 0.689733i 0.757728π-0.757728\pi
−0.724064 + 0.689733i 0.757728π0.757728\pi
888888 0 0
889889 −1.59743 −0.0535760
890890 0 0
891891 −41.2952 + 10.3461i −1.38344 + 0.346608i
892892 0 0
893893 1.21283 0.0405860
894894 0 0
895895 3.76907i 0.125986i
896896 0 0
897897 14.4945 7.07455i 0.483956 0.236212i
898898 0 0
899899 74.5507i 2.48641i
900900 0 0
901901 45.9428i 1.53058i
902902 0 0
903903 6.51258 3.17870i 0.216725 0.105780i
904904 0 0
905905 8.45232i 0.280965i
906906 0 0
907907 0.316149 0.0104976 0.00524878 0.999986i 0.498329π-0.498329\pi
0.00524878 + 0.999986i 0.498329π0.498329\pi
908908 0 0
909909 12.6953 16.2683i 0.421075 0.539586i
910910 0 0
911911 −9.06254 −0.300255 −0.150128 0.988667i 0.547968π-0.547968\pi
−0.150128 + 0.988667i 0.547968π0.547968\pi
912912 0 0
913913 18.5698 0.614571
914914 0 0
915915 −21.7841 + 10.6325i −0.720162 + 0.351501i
916916 0 0
917917 −3.17773 −0.104938
918918 0 0
919919 19.3326i 0.637722i −0.947801 0.318861i 0.896700π-0.896700\pi
0.947801 0.318861i 0.103300π-0.103300\pi
920920 0 0
921921 −10.9114 22.3556i −0.359544 0.736640i
922922 0 0
923923 21.6872i 0.713844i
924924 0 0
925925 3.67143i 0.120716i
926926 0 0
927927 4.59038 + 3.58218i 0.150768 + 0.117654i
928928 0 0
929929 15.8160i 0.518906i 0.965756 + 0.259453i 0.0835422π0.0835422\pi
−0.965756 + 0.259453i 0.916458π0.916458\pi
930930 0 0
931931 −14.1991 −0.465356
932932 0 0
933933 16.8785 + 34.5811i 0.552578 + 1.13213i
934934 0 0
935935 29.9127 0.978249
936936 0 0
937937 16.8810 0.551478 0.275739 0.961232i 0.411077π-0.411077\pi
0.275739 + 0.961232i 0.411077π0.411077\pi
938938 0 0
939939 25.5797 + 52.4083i 0.834763 + 1.71028i
940940 0 0
941941 −20.6596 −0.673484 −0.336742 0.941597i 0.609325π-0.609325\pi
−0.336742 + 0.941597i 0.609325π0.609325\pi
942942 0 0
943943 26.4985i 0.862910i
944944 0 0
945945 −0.517067 + 2.44289i −0.0168202 + 0.0794671i
946946 0 0
947947 41.1028i 1.33566i −0.744313 0.667831i 0.767223π-0.767223\pi
0.744313 0.667831i 0.232777π-0.232777\pi
948948 0 0
949949 2.87605i 0.0933607i
950950 0 0
951951 22.6362 + 46.3774i 0.734028 + 1.50389i
952952 0 0
953953 10.4252i 0.337707i −0.985641 0.168853i 0.945994π-0.945994\pi
0.985641 0.168853i 0.0540064π-0.0540064\pi
954954 0 0
955955 21.5690 0.697957
956956 0 0
957957 −65.9428 + 32.1857i −2.13163 + 1.04042i
958958 0 0
959959 4.25933 0.137541
960960 0 0
961961 −38.2857 −1.23502
962962 0 0
963963 −17.6358 13.7624i −0.568305 0.443487i
964964 0 0
965965 −15.7174 −0.505960
966966 0 0
967967 30.7273i 0.988124i 0.869427 + 0.494062i 0.164488π0.164488\pi
−0.869427 + 0.494062i 0.835512π0.835512\pi
968968 0 0
969969 −20.6476 + 10.0778i −0.663297 + 0.323746i
970970 0 0
971971 11.1047i 0.356367i −0.983997 0.178183i 0.942978π-0.942978\pi
0.983997 0.178183i 0.0570220π-0.0570220\pi
972972 0 0
973973 9.91266i 0.317785i
974974 0 0
975975 −2.48055 + 1.21072i −0.0794412 + 0.0387741i
976976 0 0
977977 34.3143i 1.09781i −0.835885 0.548905i 0.815045π-0.815045\pi
0.835885 0.548905i 0.184955π-0.184955\pi
978978 0 0
979979 −43.8253 −1.40066
980980 0 0
981981 −19.1873 14.9731i −0.612602 0.478055i
982982 0 0
983983 −6.72729 −0.214567 −0.107284 0.994228i 0.534215π-0.534215\pi
−0.107284 + 0.994228i 0.534215π0.534215\pi
984984 0 0
985985 22.0301 0.701939
986986 0 0
987987 0.432483 0.211089i 0.0137661 0.00671903i
988988 0 0
989989 50.8755 1.61775
990990 0 0
991991 43.0191i 1.36655i −0.730163 0.683273i 0.760556π-0.760556\pi
0.730163 0.683273i 0.239444π-0.239444\pi
992992 0 0
993993 −18.0103 36.8999i −0.571540 1.17098i
994994 0 0
995995 5.08962i 0.161352i
996996 0 0
997997 24.9365i 0.789747i 0.918736 + 0.394873i 0.129212π0.129212\pi
−0.918736 + 0.394873i 0.870788π0.870788\pi
998998 0 0
999999 −3.95043 + 18.6638i −0.124986 + 0.590497i
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 1920.2.b.g.191.6 yes 8
3.2 odd 2 1920.2.b.h.191.5 yes 8
4.3 odd 2 1920.2.b.a.191.3 8
8.3 odd 2 1920.2.b.h.191.6 yes 8
8.5 even 2 1920.2.b.b.191.3 yes 8
12.11 even 2 1920.2.b.b.191.4 yes 8
24.5 odd 2 1920.2.b.a.191.4 yes 8
24.11 even 2 inner 1920.2.b.g.191.5 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1920.2.b.a.191.3 8 4.3 odd 2
1920.2.b.a.191.4 yes 8 24.5 odd 2
1920.2.b.b.191.3 yes 8 8.5 even 2
1920.2.b.b.191.4 yes 8 12.11 even 2
1920.2.b.g.191.5 yes 8 24.11 even 2 inner
1920.2.b.g.191.6 yes 8 1.1 even 1 trivial
1920.2.b.h.191.5 yes 8 3.2 odd 2
1920.2.b.h.191.6 yes 8 8.3 odd 2