Properties

Label 882.4.g.d.667.1
Level 882882
Weight 44
Character 882.667
Analytic conductor 52.04052.040
Analytic rank 00
Dimension 22
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [882,4,Mod(361,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.361");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 882=23272 882 = 2 \cdot 3^{2} \cdot 7^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 882.g (of order 33, degree 22, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 52.039684625152.0396846251
Analytic rank: 00
Dimension: 22
Coefficient field: Q(ζ6)\Q(\zeta_{6})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2x+1 x^{2} - x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 667.1
Root 0.5000000.866025i0.500000 - 0.866025i of defining polynomial
Character χ\chi == 882.667
Dual form 882.4.g.d.361.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.00000+1.73205i)q2+(2.000003.46410i)q4+(3.50000+6.06218i)q5+8.00000q8+(7.0000012.1244i)q10+(17.5000+30.3109i)q1166.0000q13+(8.00000+13.8564i)q16+(29.500051.0955i)q17+(68.5000118.645i)q19+28.0000q2070.0000q22+(3.50000+6.06218i)q23+(38.0000+65.8179i)q25+(66.0000114.315i)q26106.000q29+(37.5000+64.9519i)q31+(16.000027.7128i)q32+118.000q34+(5.50000+9.52628i)q37+(137.000+237.291i)q38+(28.0000+48.4974i)q40498.000q41+260.000q43+(70.0000121.244i)q44+(7.0000012.1244i)q46+(85.5000148.090i)q47152.000q50+(132.000+228.631i)q52+(208.500361.133i)q53245.000q55+(106.000183.597i)q58+(8.50000+14.7224i)q59+(25.500044.1673i)q61150.000q62+64.0000q64+(231.000400.104i)q65+(219.500380.185i)q67+(118.000+204.382i)q68+784.000q71+(147.500+255.477i)q73+(11.000019.0526i)q74548.000q76+(247.500428.683i)q79+(56.000096.9948i)q80+(498.000862.561i)q82+932.000q83+413.000q85+(260.000+450.333i)q86+(140.000+242.487i)q88+(436.500756.040i)q89+28.0000q92+(171.000+296.181i)q94+(479.500+830.518i)q95+290.000q97+O(q100)q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-3.50000 + 6.06218i) q^{5} +8.00000 q^{8} +(-7.00000 - 12.1244i) q^{10} +(17.5000 + 30.3109i) q^{11} -66.0000 q^{13} +(-8.00000 + 13.8564i) q^{16} +(-29.5000 - 51.0955i) q^{17} +(68.5000 - 118.645i) q^{19} +28.0000 q^{20} -70.0000 q^{22} +(-3.50000 + 6.06218i) q^{23} +(38.0000 + 65.8179i) q^{25} +(66.0000 - 114.315i) q^{26} -106.000 q^{29} +(37.5000 + 64.9519i) q^{31} +(-16.0000 - 27.7128i) q^{32} +118.000 q^{34} +(-5.50000 + 9.52628i) q^{37} +(137.000 + 237.291i) q^{38} +(-28.0000 + 48.4974i) q^{40} -498.000 q^{41} +260.000 q^{43} +(70.0000 - 121.244i) q^{44} +(-7.00000 - 12.1244i) q^{46} +(85.5000 - 148.090i) q^{47} -152.000 q^{50} +(132.000 + 228.631i) q^{52} +(-208.500 - 361.133i) q^{53} -245.000 q^{55} +(106.000 - 183.597i) q^{58} +(8.50000 + 14.7224i) q^{59} +(25.5000 - 44.1673i) q^{61} -150.000 q^{62} +64.0000 q^{64} +(231.000 - 400.104i) q^{65} +(-219.500 - 380.185i) q^{67} +(-118.000 + 204.382i) q^{68} +784.000 q^{71} +(147.500 + 255.477i) q^{73} +(-11.0000 - 19.0526i) q^{74} -548.000 q^{76} +(247.500 - 428.683i) q^{79} +(-56.0000 - 96.9948i) q^{80} +(498.000 - 862.561i) q^{82} +932.000 q^{83} +413.000 q^{85} +(-260.000 + 450.333i) q^{86} +(140.000 + 242.487i) q^{88} +(436.500 - 756.040i) q^{89} +28.0000 q^{92} +(171.000 + 296.181i) q^{94} +(479.500 + 830.518i) q^{95} +290.000 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q2q24q47q5+16q814q10+35q11132q1316q1659q17+137q19+56q20140q227q23+76q25+132q26212q29+75q31++580q97+O(q100) 2 q - 2 q^{2} - 4 q^{4} - 7 q^{5} + 16 q^{8} - 14 q^{10} + 35 q^{11} - 132 q^{13} - 16 q^{16} - 59 q^{17} + 137 q^{19} + 56 q^{20} - 140 q^{22} - 7 q^{23} + 76 q^{25} + 132 q^{26} - 212 q^{29} + 75 q^{31}+ \cdots + 580 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/882Z)×\left(\mathbb{Z}/882\mathbb{Z}\right)^\times.

nn 199199 785785
χ(n)\chi(n) e(13)e\left(\frac{1}{3}\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 −1.00000 + 1.73205i −0.353553 + 0.612372i
33 0 0
44 −2.00000 3.46410i −0.250000 0.433013i
55 −3.50000 + 6.06218i −0.313050 + 0.542218i −0.979021 0.203760i 0.934684π-0.934684\pi
0.665971 + 0.745977i 0.268017π0.268017\pi
66 0 0
77 0 0
88 8.00000 0.353553
99 0 0
1010 −7.00000 12.1244i −0.221359 0.383406i
1111 17.5000 + 30.3109i 0.479677 + 0.830825i 0.999728 0.0233099i 0.00742046π-0.00742046\pi
−0.520051 + 0.854135i 0.674087π0.674087\pi
1212 0 0
1313 −66.0000 −1.40809 −0.704043 0.710158i 0.748624π-0.748624\pi
−0.704043 + 0.710158i 0.748624π0.748624\pi
1414 0 0
1515 0 0
1616 −8.00000 + 13.8564i −0.125000 + 0.216506i
1717 −29.5000 51.0955i −0.420871 0.728969i 0.575154 0.818045i 0.304942π-0.304942\pi
−0.996025 + 0.0890757i 0.971609π0.971609\pi
1818 0 0
1919 68.5000 118.645i 0.827104 1.43259i −0.0731965 0.997318i 0.523320π-0.523320\pi
0.900301 0.435269i 0.143347π-0.143347\pi
2020 28.0000 0.313050
2121 0 0
2222 −70.0000 −0.678366
2323 −3.50000 + 6.06218i −0.0317305 + 0.0549588i −0.881455 0.472269i 0.843435π-0.843435\pi
0.849724 + 0.527228i 0.176768π0.176768\pi
2424 0 0
2525 38.0000 + 65.8179i 0.304000 + 0.526543i
2626 66.0000 114.315i 0.497833 0.862273i
2727 0 0
2828 0 0
2929 −106.000 −0.678748 −0.339374 0.940651i 0.610215π-0.610215\pi
−0.339374 + 0.940651i 0.610215π0.610215\pi
3030 0 0
3131 37.5000 + 64.9519i 0.217264 + 0.376313i 0.953971 0.299900i 0.0969533π-0.0969533\pi
−0.736706 + 0.676213i 0.763620π0.763620\pi
3232 −16.0000 27.7128i −0.0883883 0.153093i
3333 0 0
3434 118.000 0.595201
3535 0 0
3636 0 0
3737 −5.50000 + 9.52628i −0.0244377 + 0.0423273i −0.877986 0.478687i 0.841113π-0.841113\pi
0.853548 + 0.521014i 0.174446π0.174446\pi
3838 137.000 + 237.291i 0.584851 + 1.01299i
3939 0 0
4040 −28.0000 + 48.4974i −0.110680 + 0.191703i
4141 −498.000 −1.89694 −0.948470 0.316867i 0.897369π-0.897369\pi
−0.948470 + 0.316867i 0.897369π0.897369\pi
4242 0 0
4343 260.000 0.922084 0.461042 0.887378i 0.347476π-0.347476\pi
0.461042 + 0.887378i 0.347476π0.347476\pi
4444 70.0000 121.244i 0.239839 0.415413i
4545 0 0
4646 −7.00000 12.1244i −0.0224368 0.0388617i
4747 85.5000 148.090i 0.265350 0.459600i −0.702305 0.711876i 0.747846π-0.747846\pi
0.967655 + 0.252276i 0.0811791π0.0811791\pi
4848 0 0
4949 0 0
5050 −152.000 −0.429921
5151 0 0
5252 132.000 + 228.631i 0.352021 + 0.609719i
5353 −208.500 361.133i −0.540371 0.935951i −0.998883 0.0472619i 0.984950π-0.984950\pi
0.458511 0.888689i 0.348383π-0.348383\pi
5454 0 0
5555 −245.000 −0.600651
5656 0 0
5757 0 0
5858 106.000 183.597i 0.239974 0.415647i
5959 8.50000 + 14.7224i 0.0187560 + 0.0324864i 0.875251 0.483669i 0.160696π-0.160696\pi
−0.856495 + 0.516155i 0.827363π0.827363\pi
6060 0 0
6161 25.5000 44.1673i 0.0535236 0.0927056i −0.838022 0.545636i 0.816288π-0.816288\pi
0.891546 + 0.452930i 0.149621π0.149621\pi
6262 −150.000 −0.307258
6363 0 0
6464 64.0000 0.125000
6565 231.000 400.104i 0.440800 0.763489i
6666 0 0
6767 −219.500 380.185i −0.400242 0.693239i 0.593513 0.804824i 0.297740π-0.297740\pi
−0.993755 + 0.111585i 0.964407π0.964407\pi
6868 −118.000 + 204.382i −0.210435 + 0.364485i
6969 0 0
7070 0 0
7171 784.000 1.31047 0.655237 0.755423i 0.272569π-0.272569\pi
0.655237 + 0.755423i 0.272569π0.272569\pi
7272 0 0
7373 147.500 + 255.477i 0.236487 + 0.409608i 0.959704 0.281013i 0.0906705π-0.0906705\pi
−0.723217 + 0.690621i 0.757337π0.757337\pi
7474 −11.0000 19.0526i −0.0172801 0.0299299i
7575 0 0
7676 −548.000 −0.827104
7777 0 0
7878 0 0
7979 247.500 428.683i 0.352480 0.610513i −0.634203 0.773166i 0.718672π-0.718672\pi
0.986683 + 0.162653i 0.0520051π0.0520051\pi
8080 −56.0000 96.9948i −0.0782624 0.135554i
8181 0 0
8282 498.000 862.561i 0.670670 1.16163i
8383 932.000 1.23253 0.616267 0.787537i 0.288644π-0.288644\pi
0.616267 + 0.787537i 0.288644π0.288644\pi
8484 0 0
8585 413.000 0.527013
8686 −260.000 + 450.333i −0.326006 + 0.564659i
8787 0 0
8888 140.000 + 242.487i 0.169591 + 0.293741i
8989 436.500 756.040i 0.519875 0.900451i −0.479858 0.877346i 0.659312π-0.659312\pi
0.999733 0.0231042i 0.00735495π-0.00735495\pi
9090 0 0
9191 0 0
9292 28.0000 0.0317305
9393 0 0
9494 171.000 + 296.181i 0.187631 + 0.324986i
9595 479.500 + 830.518i 0.517849 + 0.896941i
9696 0 0
9797 290.000 0.303557 0.151779 0.988415i 0.451500π-0.451500\pi
0.151779 + 0.988415i 0.451500π0.451500\pi
9898 0 0
9999 0 0
100100 152.000 263.272i 0.152000 0.263272i
101101 542.500 + 939.638i 0.534463 + 0.925717i 0.999189 + 0.0402627i 0.0128195π0.0128195\pi
−0.464726 + 0.885454i 0.653847π0.653847\pi
102102 0 0
103103 776.500 1344.94i 0.742823 1.28661i −0.208381 0.978048i 0.566819π-0.566819\pi
0.951205 0.308560i 0.0998472π-0.0998472\pi
104104 −528.000 −0.497833
105105 0 0
106106 834.000 0.764200
107107 64.5000 111.717i 0.0582752 0.100936i −0.835416 0.549618i 0.814773π-0.814773\pi
0.893691 + 0.448682i 0.148107π0.148107\pi
108108 0 0
109109 482.500 + 835.715i 0.423992 + 0.734376i 0.996326 0.0856452i 0.0272952π-0.0272952\pi
−0.572334 + 0.820021i 0.693962π0.693962\pi
110110 245.000 424.352i 0.212362 0.367822i
111111 0 0
112112 0 0
113113 50.0000 0.0416248 0.0208124 0.999783i 0.493375π-0.493375\pi
0.0208124 + 0.999783i 0.493375π0.493375\pi
114114 0 0
115115 −24.5000 42.4352i −0.0198664 0.0344096i
116116 212.000 + 367.195i 0.169687 + 0.293907i
117117 0 0
118118 −34.0000 −0.0265250
119119 0 0
120120 0 0
121121 53.0000 91.7987i 0.0398197 0.0689697i
122122 51.0000 + 88.3346i 0.0378469 + 0.0655528i
123123 0 0
124124 150.000 259.808i 0.108632 0.188157i
125125 −1407.00 −1.00677
126126 0 0
127127 936.000 0.653989 0.326994 0.945026i 0.393964π-0.393964\pi
0.326994 + 0.945026i 0.393964π0.393964\pi
128128 −64.0000 + 110.851i −0.0441942 + 0.0765466i
129129 0 0
130130 462.000 + 800.207i 0.311693 + 0.539868i
131131 377.500 653.849i 0.251773 0.436084i −0.712241 0.701935i 0.752320π-0.752320\pi
0.964014 + 0.265851i 0.0856529π0.0856529\pi
132132 0 0
133133 0 0
134134 878.000 0.566027
135135 0 0
136136 −236.000 408.764i −0.148800 0.257730i
137137 −1178.50 2041.22i −0.734935 1.27294i −0.954752 0.297403i 0.903879π-0.903879\pi
0.219817 0.975541i 0.429454π-0.429454\pi
138138 0 0
139139 −28.0000 −0.0170858 −0.00854291 0.999964i 0.502719π-0.502719\pi
−0.00854291 + 0.999964i 0.502719π0.502719\pi
140140 0 0
141141 0 0
142142 −784.000 + 1357.93i −0.463323 + 0.802498i
143143 −1155.00 2000.52i −0.675426 1.16987i
144144 0 0
145145 371.000 642.591i 0.212482 0.368029i
146146 −590.000 −0.334443
147147 0 0
148148 44.0000 0.0244377
149149 1147.50 1987.53i 0.630919 1.09278i −0.356446 0.934316i 0.616012π-0.616012\pi
0.987364 0.158467i 0.0506551π-0.0506551\pi
150150 0 0
151151 554.500 + 960.422i 0.298838 + 0.517603i 0.975870 0.218350i 0.0700676π-0.0700676\pi
−0.677032 + 0.735953i 0.736734π0.736734\pi
152152 548.000 949.164i 0.292425 0.506496i
153153 0 0
154154 0 0
155155 −525.000 −0.272058
156156 0 0
157157 779.500 + 1350.13i 0.396248 + 0.686321i 0.993260 0.115911i 0.0369789π-0.0369789\pi
−0.597012 + 0.802232i 0.703646π0.703646\pi
158158 495.000 + 857.365i 0.249241 + 0.431698i
159159 0 0
160160 224.000 0.110680
161161 0 0
162162 0 0
163163 1125.50 1949.42i 0.540834 0.936752i −0.458022 0.888941i 0.651442π-0.651442\pi
0.998856 0.0478115i 0.0152247π-0.0152247\pi
164164 996.000 + 1725.12i 0.474235 + 0.821399i
165165 0 0
166166 −932.000 + 1614.27i −0.435766 + 0.754770i
167167 2788.00 1.29187 0.645934 0.763393i 0.276468π-0.276468\pi
0.645934 + 0.763393i 0.276468π0.276468\pi
168168 0 0
169169 2159.00 0.982704
170170 −413.000 + 715.337i −0.186327 + 0.322728i
171171 0 0
172172 −520.000 900.666i −0.230521 0.399274i
173173 −789.500 + 1367.45i −0.346963 + 0.600957i −0.985708 0.168461i 0.946120π-0.946120\pi
0.638746 + 0.769418i 0.279454π0.279454\pi
174174 0 0
175175 0 0
176176 −560.000 −0.239839
177177 0 0
178178 873.000 + 1512.08i 0.367607 + 0.636715i
179179 1225.50 + 2122.63i 0.511722 + 0.886328i 0.999908 + 0.0135883i 0.00432541π0.00432541\pi
−0.488186 + 0.872740i 0.662341π0.662341\pi
180180 0 0
181181 1170.00 0.480472 0.240236 0.970715i 0.422775π-0.422775\pi
0.240236 + 0.970715i 0.422775π0.422775\pi
182182 0 0
183183 0 0
184184 −28.0000 + 48.4974i −0.0112184 + 0.0194309i
185185 −38.5000 66.6840i −0.0153004 0.0265011i
186186 0 0
187187 1032.50 1788.34i 0.403764 0.699340i
188188 −684.000 −0.265350
189189 0 0
190190 −1918.00 −0.732349
191191 −637.500 + 1104.18i −0.241507 + 0.418303i −0.961144 0.276048i 0.910975π-0.910975\pi
0.719637 + 0.694351i 0.244308π0.244308\pi
192192 0 0
193193 −17.5000 30.3109i −0.00652683 0.0113048i 0.862744 0.505642i 0.168744π-0.168744\pi
−0.869270 + 0.494337i 0.835411π0.835411\pi
194194 −290.000 + 502.295i −0.107324 + 0.185890i
195195 0 0
196196 0 0
197197 2734.00 0.988779 0.494389 0.869241i 0.335392π-0.335392\pi
0.494389 + 0.869241i 0.335392π0.335392\pi
198198 0 0
199199 1121.50 + 1942.49i 0.399503 + 0.691959i 0.993665 0.112387i 0.0358495π-0.0358495\pi
−0.594162 + 0.804345i 0.702516π0.702516\pi
200200 304.000 + 526.543i 0.107480 + 0.186161i
201201 0 0
202202 −2170.00 −0.755845
203203 0 0
204204 0 0
205205 1743.00 3018.96i 0.593836 1.02855i
206206 1553.00 + 2689.87i 0.525256 + 0.909769i
207207 0 0
208208 528.000 914.523i 0.176011 0.304859i
209209 4795.00 1.58697
210210 0 0
211211 1172.00 0.382388 0.191194 0.981552i 0.438764π-0.438764\pi
0.191194 + 0.981552i 0.438764π0.438764\pi
212212 −834.000 + 1444.53i −0.270186 + 0.467975i
213213 0 0
214214 129.000 + 223.435i 0.0412068 + 0.0713723i
215215 −910.000 + 1576.17i −0.288658 + 0.499970i
216216 0 0
217217 0 0
218218 −1930.00 −0.599615
219219 0 0
220220 490.000 + 848.705i 0.150163 + 0.260089i
221221 1947.00 + 3372.30i 0.592622 + 1.02645i
222222 0 0
223223 −2024.00 −0.607790 −0.303895 0.952706i 0.598287π-0.598287\pi
−0.303895 + 0.952706i 0.598287π0.598287\pi
224224 0 0
225225 0 0
226226 −50.0000 + 86.6025i −0.0147166 + 0.0254899i
227227 −1285.50 2226.55i −0.375866 0.651019i 0.614590 0.788847i 0.289321π-0.289321\pi
−0.990456 + 0.137827i 0.955988π0.955988\pi
228228 0 0
229229 447.500 775.093i 0.129134 0.223666i −0.794207 0.607647i 0.792114π-0.792114\pi
0.923341 + 0.383980i 0.125447π0.125447\pi
230230 98.0000 0.0280953
231231 0 0
232232 −848.000 −0.239974
233233 893.500 1547.59i 0.251224 0.435132i −0.712639 0.701531i 0.752500π-0.752500\pi
0.963863 + 0.266398i 0.0858337π0.0858337\pi
234234 0 0
235235 598.500 + 1036.63i 0.166135 + 0.287755i
236236 34.0000 58.8897i 0.00937801 0.0162432i
237237 0 0
238238 0 0
239239 5100.00 1.38030 0.690150 0.723667i 0.257545π-0.257545\pi
0.690150 + 0.723667i 0.257545π0.257545\pi
240240 0 0
241241 −2088.50 3617.39i −0.558225 0.966873i −0.997645 0.0685917i 0.978149π-0.978149\pi
0.439420 0.898282i 0.355184π-0.355184\pi
242242 106.000 + 183.597i 0.0281568 + 0.0487690i
243243 0 0
244244 −204.000 −0.0535236
245245 0 0
246246 0 0
247247 −4521.00 + 7830.60i −1.16463 + 2.01720i
248248 300.000 + 519.615i 0.0768146 + 0.133047i
249249 0 0
250250 1407.00 2437.00i 0.355946 0.616517i
251251 −4680.00 −1.17689 −0.588444 0.808538i 0.700259π-0.700259\pi
−0.588444 + 0.808538i 0.700259π0.700259\pi
252252 0 0
253253 −245.000 −0.0608815
254254 −936.000 + 1621.20i −0.231220 + 0.400485i
255255 0 0
256256 −128.000 221.703i −0.0312500 0.0541266i
257257 874.500 1514.68i 0.212256 0.367638i −0.740164 0.672426i 0.765252π-0.765252\pi
0.952420 + 0.304788i 0.0985856π0.0985856\pi
258258 0 0
259259 0 0
260260 −1848.00 −0.440800
261261 0 0
262262 755.000 + 1307.70i 0.178031 + 0.308358i
263263 −2236.50 3873.73i −0.524367 0.908230i −0.999598 0.0283689i 0.990969π-0.990969\pi
0.475231 0.879861i 0.342365π-0.342365\pi
264264 0 0
265265 2919.00 0.676652
266266 0 0
267267 0 0
268268 −878.000 + 1520.74i −0.200121 + 0.346619i
269269 −987.500 1710.40i −0.223825 0.387676i 0.732141 0.681153i 0.238521π-0.238521\pi
−0.955966 + 0.293476i 0.905188π0.905188\pi
270270 0 0
271271 −4219.50 + 7308.39i −0.945817 + 1.63820i −0.191710 + 0.981452i 0.561403π0.561403\pi
−0.754107 + 0.656751i 0.771930π0.771930\pi
272272 944.000 0.210435
273273 0 0
274274 4714.00 1.03935
275275 −1330.00 + 2303.63i −0.291644 + 0.505142i
276276 0 0
277277 −263.500 456.395i −0.0571559 0.0989969i 0.836032 0.548681i 0.184870π-0.184870\pi
−0.893188 + 0.449684i 0.851537π0.851537\pi
278278 28.0000 48.4974i 0.00604075 0.0104629i
279279 0 0
280280 0 0
281281 202.000 0.0428837 0.0214418 0.999770i 0.493174π-0.493174\pi
0.0214418 + 0.999770i 0.493174π0.493174\pi
282282 0 0
283283 −3974.50 6884.04i −0.834839 1.44598i −0.894161 0.447745i 0.852227π-0.852227\pi
0.0593220 0.998239i 0.481106π-0.481106\pi
284284 −1568.00 2715.86i −0.327619 0.567452i
285285 0 0
286286 4620.00 0.955197
287287 0 0
288288 0 0
289289 716.000 1240.15i 0.145736 0.252422i
290290 742.000 + 1285.18i 0.150247 + 0.260236i
291291 0 0
292292 590.000 1021.91i 0.118244 0.204804i
293293 318.000 0.0634053 0.0317027 0.999497i 0.489907π-0.489907\pi
0.0317027 + 0.999497i 0.489907π0.489907\pi
294294 0 0
295295 −119.000 −0.0234863
296296 −44.0000 + 76.2102i −0.00864003 + 0.0149650i
297297 0 0
298298 2295.00 + 3975.06i 0.446127 + 0.772714i
299299 231.000 400.104i 0.0446792 0.0773866i
300300 0 0
301301 0 0
302302 −2218.00 −0.422621
303303 0 0
304304 1096.00 + 1898.33i 0.206776 + 0.358147i
305305 178.500 + 309.171i 0.0335111 + 0.0580429i
306306 0 0
307307 8132.00 1.51178 0.755892 0.654696i 0.227203π-0.227203\pi
0.755892 + 0.654696i 0.227203π0.227203\pi
308308 0 0
309309 0 0
310310 525.000 909.327i 0.0961871 0.166601i
311311 464.500 + 804.538i 0.0846925 + 0.146692i 0.905260 0.424858i 0.139676π-0.139676\pi
−0.820568 + 0.571549i 0.806343π0.806343\pi
312312 0 0
313313 −104.500 + 180.999i −0.0188712 + 0.0326859i −0.875307 0.483568i 0.839341π-0.839341\pi
0.856436 + 0.516254i 0.172674π0.172674\pi
314314 −3118.00 −0.560379
315315 0 0
316316 −1980.00 −0.352480
317317 3565.50 6175.63i 0.631730 1.09419i −0.355468 0.934689i 0.615678π-0.615678\pi
0.987198 0.159500i 0.0509882π-0.0509882\pi
318318 0 0
319319 −1855.00 3212.95i −0.325580 0.563921i
320320 −224.000 + 387.979i −0.0391312 + 0.0677772i
321321 0 0
322322 0 0
323323 −8083.00 −1.39242
324324 0 0
325325 −2508.00 4343.98i −0.428058 0.741418i
326326 2251.00 + 3898.85i 0.382427 + 0.662384i
327327 0 0
328328 −3984.00 −0.670670
329329 0 0
330330 0 0
331331 3285.50 5690.65i 0.545581 0.944975i −0.452989 0.891516i 0.649642π-0.649642\pi
0.998570 0.0534583i 0.0170244π-0.0170244\pi
332332 −1864.00 3228.54i −0.308133 0.533703i
333333 0 0
334334 −2788.00 + 4828.96i −0.456744 + 0.791104i
335335 3073.00 0.501182
336336 0 0
337337 −11466.0 −1.85339 −0.926696 0.375813i 0.877364π-0.877364\pi
−0.926696 + 0.375813i 0.877364π0.877364\pi
338338 −2159.00 + 3739.50i −0.347438 + 0.601781i
339339 0 0
340340 −826.000 1430.67i −0.131753 0.228203i
341341 −1312.50 + 2273.32i −0.208434 + 0.361018i
342342 0 0
343343 0 0
344344 2080.00 0.326006
345345 0 0
346346 −1579.00 2734.91i −0.245340 0.424941i
347347 −4888.50 8467.13i −0.756278 1.30991i −0.944737 0.327831i 0.893682π-0.893682\pi
0.188459 0.982081i 0.439651π-0.439651\pi
348348 0 0
349349 −11914.0 −1.82734 −0.913670 0.406456i 0.866764π-0.866764\pi
−0.913670 + 0.406456i 0.866764π0.866764\pi
350350 0 0
351351 0 0
352352 560.000 969.948i 0.0847957 0.146871i
353353 −4561.50 7900.75i −0.687774 1.19126i −0.972556 0.232667i 0.925255π-0.925255\pi
0.284783 0.958592i 0.408079π-0.408079\pi
354354 0 0
355355 −2744.00 + 4752.75i −0.410243 + 0.710562i
356356 −3492.00 −0.519875
357357 0 0
358358 −4902.00 −0.723684
359359 4074.50 7057.24i 0.599008 1.03751i −0.393960 0.919128i 0.628895π-0.628895\pi
0.992968 0.118385i 0.0377716π-0.0377716\pi
360360 0 0
361361 −5955.00 10314.4i −0.868202 1.50377i
362362 −1170.00 + 2026.50i −0.169872 + 0.294228i
363363 0 0
364364 0 0
365365 −2065.00 −0.296129
366366 0 0
367367 4835.50 + 8375.33i 0.687769 + 1.19125i 0.972558 + 0.232660i 0.0747429π0.0747429\pi
−0.284790 + 0.958590i 0.591924π0.591924\pi
368368 −56.0000 96.9948i −0.00793261 0.0137397i
369369 0 0
370370 154.000 0.0216381
371371 0 0
372372 0 0
373373 2054.50 3558.50i 0.285196 0.493973i −0.687461 0.726221i 0.741275π-0.741275\pi
0.972657 + 0.232248i 0.0746081π0.0746081\pi
374374 2065.00 + 3576.68i 0.285504 + 0.494508i
375375 0 0
376376 684.000 1184.72i 0.0938154 0.162493i
377377 6996.00 0.955736
378378 0 0
379379 −3488.00 −0.472735 −0.236367 0.971664i 0.575957π-0.575957\pi
−0.236367 + 0.971664i 0.575957π0.575957\pi
380380 1918.00 3322.07i 0.258925 0.448470i
381381 0 0
382382 −1275.00 2208.36i −0.170771 0.295785i
383383 −4358.50 + 7549.14i −0.581485 + 1.00716i 0.413818 + 0.910360i 0.364195π0.364195\pi
−0.995304 + 0.0968028i 0.969138π0.969138\pi
384384 0 0
385385 0 0
386386 70.0000 0.00923033
387387 0 0
388388 −580.000 1004.59i −0.0758893 0.131444i
389389 81.5000 + 141.162i 0.0106227 + 0.0183990i 0.871288 0.490772i 0.163285π-0.163285\pi
−0.860665 + 0.509171i 0.829952π0.829952\pi
390390 0 0
391391 413.000 0.0534177
392392 0 0
393393 0 0
394394 −2734.00 + 4735.43i −0.349586 + 0.605501i
395395 1732.50 + 3000.78i 0.220687 + 0.382242i
396396 0 0
397397 499.500 865.159i 0.0631466 0.109373i −0.832724 0.553689i 0.813220π-0.813220\pi
0.895870 + 0.444316i 0.146553π0.146553\pi
398398 −4486.00 −0.564982
399399 0 0
400400 −1216.00 −0.152000
401401 −7378.50 + 12779.9i −0.918865 + 1.59152i −0.117722 + 0.993047i 0.537559π0.537559\pi
−0.801143 + 0.598474i 0.795774π0.795774\pi
402402 0 0
403403 −2475.00 4286.83i −0.305927 0.529881i
404404 2170.00 3758.55i 0.267232 0.462859i
405405 0 0
406406 0 0
407407 −385.000 −0.0468888
408408 0 0
409409 −66.5000 115.181i −0.00803964 0.0139251i 0.861978 0.506946i 0.169226π-0.169226\pi
−0.870017 + 0.493021i 0.835892π0.835892\pi
410410 3486.00 + 6037.93i 0.419906 + 0.727298i
411411 0 0
412412 −6212.00 −0.742823
413413 0 0
414414 0 0
415415 −3262.00 + 5649.95i −0.385844 + 0.668302i
416416 1056.00 + 1829.05i 0.124458 + 0.215568i
417417 0 0
418418 −4795.00 + 8305.18i −0.561079 + 0.971818i
419419 −6420.00 −0.748538 −0.374269 0.927320i 0.622106π-0.622106\pi
−0.374269 + 0.927320i 0.622106π0.622106\pi
420420 0 0
421421 10266.0 1.18844 0.594221 0.804302i 0.297460π-0.297460\pi
0.594221 + 0.804302i 0.297460π0.297460\pi
422422 −1172.00 + 2029.96i −0.135194 + 0.234164i
423423 0 0
424424 −1668.00 2889.06i −0.191050 0.330908i
425425 2242.00 3883.26i 0.255889 0.443213i
426426 0 0
427427 0 0
428428 −516.000 −0.0582752
429429 0 0
430430 −1820.00 3152.33i −0.204112 0.353532i
431431 −7606.50 13174.8i −0.850098 1.47241i −0.881119 0.472894i 0.843209π-0.843209\pi
0.0310213 0.999519i 0.490124π-0.490124\pi
432432 0 0
433433 1378.00 0.152939 0.0764693 0.997072i 0.475635π-0.475635\pi
0.0764693 + 0.997072i 0.475635π0.475635\pi
434434 0 0
435435 0 0
436436 1930.00 3342.86i 0.211996 0.367188i
437437 479.500 + 830.518i 0.0524888 + 0.0909132i
438438 0 0
439439 −1381.50 + 2392.83i −0.150195 + 0.260145i −0.931299 0.364256i 0.881323π-0.881323\pi
0.781104 + 0.624401i 0.214657π0.214657\pi
440440 −1960.00 −0.212362
441441 0 0
442442 −7788.00 −0.838094
443443 2924.50 5065.38i 0.313651 0.543259i −0.665499 0.746399i 0.731781π-0.731781\pi
0.979150 + 0.203140i 0.0651146π0.0651146\pi
444444 0 0
445445 3055.50 + 5292.28i 0.325493 + 0.563771i
446446 2024.00 3505.67i 0.214886 0.372194i
447447 0 0
448448 0 0
449449 −4582.00 −0.481599 −0.240799 0.970575i 0.577410π-0.577410\pi
−0.240799 + 0.970575i 0.577410π0.577410\pi
450450 0 0
451451 −8715.00 15094.8i −0.909919 1.57603i
452452 −100.000 173.205i −0.0104062 0.0180241i
453453 0 0
454454 5142.00 0.531555
455455 0 0
456456 0 0
457457 −5775.50 + 10003.5i −0.591174 + 1.02394i 0.402901 + 0.915244i 0.368002π0.368002\pi
−0.994075 + 0.108700i 0.965331π0.965331\pi
458458 895.000 + 1550.19i 0.0913114 + 0.158156i
459459 0 0
460460 −98.0000 + 169.741i −0.00993320 + 0.0172048i
461461 −9494.00 −0.959175 −0.479587 0.877494i 0.659214π-0.659214\pi
−0.479587 + 0.877494i 0.659214π0.659214\pi
462462 0 0
463463 −10160.0 −1.01982 −0.509908 0.860229i 0.670321π-0.670321\pi
−0.509908 + 0.860229i 0.670321π0.670321\pi
464464 848.000 1468.78i 0.0848436 0.146953i
465465 0 0
466466 1787.00 + 3095.17i 0.177642 + 0.307685i
467467 653.500 1131.90i 0.0647545 0.112158i −0.831831 0.555030i 0.812707π-0.812707\pi
0.896585 + 0.442872i 0.146040π0.146040\pi
468468 0 0
469469 0 0
470470 −2394.00 −0.234951
471471 0 0
472472 68.0000 + 117.779i 0.00663126 + 0.0114857i
473473 4550.00 + 7880.83i 0.442303 + 0.766091i
474474 0 0
475475 10412.0 1.00576
476476 0 0
477477 0 0
478478 −5100.00 + 8833.46i −0.488010 + 0.845257i
479479 −9143.50 15837.0i −0.872186 1.51067i −0.859730 0.510748i 0.829368π-0.829368\pi
−0.0124559 0.999922i 0.503965π-0.503965\pi
480480 0 0
481481 363.000 628.734i 0.0344103 0.0596005i
482482 8354.00 0.789449
483483 0 0
484484 −424.000 −0.0398197
485485 −1015.00 + 1758.03i −0.0950284 + 0.164594i
486486 0 0
487487 7476.50 + 12949.7i 0.695673 + 1.20494i 0.969953 + 0.243291i 0.0782269π0.0782269\pi
−0.274281 + 0.961650i 0.588440π0.588440\pi
488488 204.000 353.338i 0.0189235 0.0327764i
489489 0 0
490490 0 0
491491 −14352.0 −1.31914 −0.659569 0.751644i 0.729261π-0.729261\pi
−0.659569 + 0.751644i 0.729261π0.729261\pi
492492 0 0
493493 3127.00 + 5416.12i 0.285665 + 0.494787i
494494 −9042.00 15661.2i −0.823520 1.42638i
495495 0 0
496496 −1200.00 −0.108632
497497 0 0
498498 0 0
499499 2765.50 4789.99i 0.248098 0.429718i −0.714900 0.699226i 0.753528π-0.753528\pi
0.962998 + 0.269509i 0.0868612π0.0868612\pi
500500 2814.00 + 4873.99i 0.251692 + 0.435943i
501501 0 0
502502 4680.00 8106.00i 0.416093 0.720694i
503503 8400.00 0.744607 0.372304 0.928111i 0.378568π-0.378568\pi
0.372304 + 0.928111i 0.378568π0.378568\pi
504504 0 0
505505 −7595.00 −0.669254
506506 245.000 424.352i 0.0215249 0.0372821i
507507 0 0
508508 −1872.00 3242.40i −0.163497 0.283185i
509509 1192.50 2065.47i 0.103844 0.179863i −0.809421 0.587228i 0.800219π-0.800219\pi
0.913265 + 0.407365i 0.133552π0.133552\pi
510510 0 0
511511 0 0
512512 512.000 0.0441942
513513 0 0
514514 1749.00 + 3029.36i 0.150088 + 0.259960i
515515 5435.50 + 9414.56i 0.465081 + 0.805544i
516516 0 0
517517 5985.00 0.509130
518518 0 0
519519 0 0
520520 1848.00 3200.83i 0.155846 0.269934i
521521 4576.50 + 7926.73i 0.384837 + 0.666557i 0.991747 0.128214i 0.0409243π-0.0409243\pi
−0.606910 + 0.794771i 0.707591π0.707591\pi
522522 0 0
523523 −6903.50 + 11957.2i −0.577187 + 0.999718i 0.418613 + 0.908165i 0.362516π0.362516\pi
−0.995800 + 0.0915530i 0.970817π0.970817\pi
524524 −3020.00 −0.251773
525525 0 0
526526 8946.00 0.741567
527527 2212.50 3832.16i 0.182880 0.316758i
528528 0 0
529529 6059.00 + 10494.5i 0.497986 + 0.862538i
530530 −2919.00 + 5055.86i −0.239233 + 0.414363i
531531 0 0
532532 0 0
533533 32868.0 2.67105
534534 0 0
535535 451.500 + 782.021i 0.0364861 + 0.0631957i
536536 −1756.00 3041.48i −0.141507 0.245097i
537537 0 0
538538 3950.00 0.316536
539539 0 0
540540 0 0
541541 −4087.50 + 7079.76i −0.324834 + 0.562629i −0.981479 0.191571i 0.938642π-0.938642\pi
0.656645 + 0.754200i 0.271975π0.271975\pi
542542 −8439.00 14616.8i −0.668794 1.15838i
543543 0 0
544544 −944.000 + 1635.06i −0.0744001 + 0.128865i
545545 −6755.00 −0.530922
546546 0 0
547547 4656.00 0.363942 0.181971 0.983304i 0.441752π-0.441752\pi
0.181971 + 0.983304i 0.441752π0.441752\pi
548548 −4714.00 + 8164.89i −0.367467 + 0.636472i
549549 0 0
550550 −2660.00 4607.26i −0.206223 0.357189i
551551 −7261.00 + 12576.4i −0.561396 + 0.972366i
552552 0 0
553553 0 0
554554 1054.00 0.0808306
555555 0 0
556556 56.0000 + 96.9948i 0.00427146 + 0.00739838i
557557 3501.50 + 6064.78i 0.266361 + 0.461352i 0.967919 0.251261i 0.0808452π-0.0808452\pi
−0.701558 + 0.712612i 0.747512π0.747512\pi
558558 0 0
559559 −17160.0 −1.29837
560560 0 0
561561 0 0
562562 −202.000 + 349.874i −0.0151617 + 0.0262608i
563563 9876.50 + 17106.6i 0.739334 + 1.28056i 0.952796 + 0.303612i 0.0981927π0.0981927\pi
−0.213462 + 0.976951i 0.568474π0.568474\pi
564564 0 0
565565 −175.000 + 303.109i −0.0130306 + 0.0225697i
566566 15898.0 1.18064
567567 0 0
568568 6272.00 0.463323
569569 −3448.50 + 5972.98i −0.254075 + 0.440071i −0.964644 0.263557i 0.915104π-0.915104\pi
0.710569 + 0.703628i 0.248438π0.248438\pi
570570 0 0
571571 −12457.5 21577.0i −0.913013 1.58138i −0.809785 0.586726i 0.800416π-0.800416\pi
−0.103227 0.994658i 0.532917π-0.532917\pi
572572 −4620.00 + 8002.07i −0.337713 + 0.584936i
573573 0 0
574574 0 0
575575 −532.000 −0.0385842
576576 0 0
577577 63.5000 + 109.985i 0.00458152 + 0.00793543i 0.868307 0.496027i 0.165208π-0.165208\pi
−0.863726 + 0.503962i 0.831875π0.831875\pi
578578 1432.00 + 2480.30i 0.103051 + 0.178489i
579579 0 0
580580 −2968.00 −0.212482
581581 0 0
582582 0 0
583583 7297.50 12639.6i 0.518407 0.897908i
584584 1180.00 + 2043.82i 0.0836109 + 0.144818i
585585 0 0
586586 −318.000 + 550.792i −0.0224172 + 0.0388277i
587587 9044.00 0.635921 0.317961 0.948104i 0.397002π-0.397002\pi
0.317961 + 0.948104i 0.397002π0.397002\pi
588588 0 0
589589 10275.0 0.718801
590590 119.000 206.114i 0.00830365 0.0143823i
591591 0 0
592592 −88.0000 152.420i −0.00610942 0.0105818i
593593 5350.50 9267.34i 0.370521 0.641760i −0.619125 0.785292i 0.712513π-0.712513\pi
0.989646 + 0.143532i 0.0458460π0.0458460\pi
594594 0 0
595595 0 0
596596 −9180.00 −0.630919
597597 0 0
598598 462.000 + 800.207i 0.0315930 + 0.0547206i
599599 10399.5 + 18012.5i 0.709369 + 1.22866i 0.965091 + 0.261913i 0.0843533π0.0843533\pi
−0.255722 + 0.966750i 0.582313π0.582313\pi
600600 0 0
601601 1402.00 0.0951560 0.0475780 0.998868i 0.484850π-0.484850\pi
0.0475780 + 0.998868i 0.484850π0.484850\pi
602602 0 0
603603 0 0
604604 2218.00 3841.69i 0.149419 0.258801i
605605 371.000 + 642.591i 0.0249311 + 0.0431819i
606606 0 0
607607 3262.50 5650.82i 0.218156 0.377858i −0.736088 0.676886i 0.763329π-0.763329\pi
0.954244 + 0.299028i 0.0966625π0.0966625\pi
608608 −4384.00 −0.292425
609609 0 0
610610 −714.000 −0.0473918
611611 −5643.00 + 9773.96i −0.373636 + 0.647156i
612612 0 0
613613 −7525.50 13034.5i −0.495844 0.858826i 0.504145 0.863619i 0.331808π-0.331808\pi
−0.999989 + 0.00479285i 0.998474π0.998474\pi
614614 −8132.00 + 14085.0i −0.534496 + 0.925775i
615615 0 0
616616 0 0
617617 −11150.0 −0.727524 −0.363762 0.931492i 0.618508π-0.618508\pi
−0.363762 + 0.931492i 0.618508π0.618508\pi
618618 0 0
619619 1707.50 + 2957.48i 0.110873 + 0.192037i 0.916122 0.400899i 0.131302π-0.131302\pi
−0.805250 + 0.592936i 0.797969π0.797969\pi
620620 1050.00 + 1818.65i 0.0680145 + 0.117805i
621621 0 0
622622 −1858.00 −0.119773
623623 0 0
624624 0 0
625625 174.500 302.243i 0.0111680 0.0193435i
626626 −209.000 361.999i −0.0133440 0.0231124i
627627 0 0
628628 3118.00 5400.53i 0.198124 0.343160i
629629 649.000 0.0411404
630630 0 0
631631 −21184.0 −1.33648 −0.668242 0.743944i 0.732953π-0.732953\pi
−0.668242 + 0.743944i 0.732953π0.732953\pi
632632 1980.00 3429.46i 0.124621 0.215849i
633633 0 0
634634 7131.00 + 12351.3i 0.446701 + 0.773708i
635635 −3276.00 + 5674.20i −0.204731 + 0.354604i
636636 0 0
637637 0 0
638638 7420.00 0.460440
639639 0 0
640640 −448.000 775.959i −0.0276699 0.0479257i
641641 −5352.50 9270.80i −0.329814 0.571255i 0.652660 0.757651i 0.273653π-0.273653\pi
−0.982475 + 0.186395i 0.940320π0.940320\pi
642642 0 0
643643 −6860.00 −0.420734 −0.210367 0.977622i 0.567466π-0.567466\pi
−0.210367 + 0.977622i 0.567466π0.567466\pi
644644 0 0
645645 0 0
646646 8083.00 14000.2i 0.492293 0.852677i
647647 −7231.50 12525.3i −0.439412 0.761084i 0.558232 0.829685i 0.311480π-0.311480\pi
−0.997644 + 0.0686008i 0.978147π0.978147\pi
648648 0 0
649649 −297.500 + 515.285i −0.0179937 + 0.0311660i
650650 10032.0 0.605365
651651 0 0
652652 −9004.00 −0.540834
653653 2989.50 5177.97i 0.179155 0.310305i −0.762436 0.647063i 0.775997π-0.775997\pi
0.941591 + 0.336758i 0.109330π0.109330\pi
654654 0 0
655655 2642.50 + 4576.94i 0.157635 + 0.273032i
656656 3984.00 6900.49i 0.237117 0.410700i
657657 0 0
658658 0 0
659659 6940.00 0.410234 0.205117 0.978737i 0.434243π-0.434243\pi
0.205117 + 0.978737i 0.434243π0.434243\pi
660660 0 0
661661 6699.50 + 11603.9i 0.394221 + 0.682812i 0.993001 0.118102i 0.0376810π-0.0376810\pi
−0.598780 + 0.800914i 0.704348π0.704348\pi
662662 6571.00 + 11381.3i 0.385784 + 0.668198i
663663 0 0
664664 7456.00 0.435766
665665 0 0
666666 0 0
667667 371.000 642.591i 0.0215370 0.0373032i
668668 −5576.00 9657.92i −0.322967 0.559395i
669669 0 0
670670 −3073.00 + 5322.59i −0.177195 + 0.306910i
671671 1785.00 0.102696
672672 0 0
673673 29510.0 1.69023 0.845117 0.534582i 0.179531π-0.179531\pi
0.845117 + 0.534582i 0.179531π0.179531\pi
674674 11466.0 19859.7i 0.655273 1.13497i
675675 0 0
676676 −4318.00 7479.00i −0.245676 0.425523i
677677 13000.5 22517.5i 0.738035 1.27831i −0.215344 0.976538i 0.569087π-0.569087\pi
0.953379 0.301776i 0.0975795π-0.0975795\pi
678678 0 0
679679 0 0
680680 3304.00 0.186327
681681 0 0
682682 −2625.00 4546.63i −0.147385 0.255278i
683683 −4402.50 7625.35i −0.246643 0.427198i 0.715949 0.698152i 0.245994π-0.245994\pi
−0.962592 + 0.270954i 0.912661π0.912661\pi
684684 0 0
685685 16499.0 0.920284
686686 0 0
687687 0 0
688688 −2080.00 + 3602.67i −0.115261 + 0.199637i
689689 13761.0 + 23834.8i 0.760889 + 1.31790i
690690 0 0
691691 14342.5 24841.9i 0.789601 1.36763i −0.136610 0.990625i 0.543621π-0.543621\pi
0.926211 0.377004i 0.123046π-0.123046\pi
692692 6316.00 0.346963
693693 0 0
694694 19554.0 1.06954
695695 98.0000 169.741i 0.00534871 0.00926423i
696696 0 0
697697 14691.0 + 25445.6i 0.798366 + 1.38281i
698698 11914.0 20635.7i 0.646062 1.11901i
699699 0 0
700700 0 0
701701 3146.00 0.169505 0.0847523 0.996402i 0.472990π-0.472990\pi
0.0847523 + 0.996402i 0.472990π0.472990\pi
702702 0 0
703703 753.500 + 1305.10i 0.0404250 + 0.0700182i
704704 1120.00 + 1939.90i 0.0599596 + 0.103853i
705705 0 0
706706 18246.0 0.972659
707707 0 0
708708 0 0
709709 −629.500 + 1090.33i −0.0333447 + 0.0577547i −0.882216 0.470845i 0.843949π-0.843949\pi
0.848871 + 0.528599i 0.177283π0.177283\pi
710710 −5488.00 9505.49i −0.290086 0.502443i
711711 0 0
712712 3492.00 6048.32i 0.183804 0.318357i
713713 −525.000 −0.0275756
714714 0 0
715715 16170.0 0.845767
716716 4902.00 8490.51i 0.255861 0.443164i
717717 0 0
718718 8149.00 + 14114.5i 0.423563 + 0.733632i
719719 −8212.50 + 14224.5i −0.425973 + 0.737807i −0.996511 0.0834645i 0.973401π-0.973401\pi
0.570538 + 0.821271i 0.306735π0.306735\pi
720720 0 0
721721 0 0
722722 23820.0 1.22782
723723 0 0
724724 −2340.00 4053.00i −0.120118 0.208050i
725725 −4028.00 6976.70i −0.206340 0.357391i
726726 0 0
727727 6032.00 0.307723 0.153861 0.988092i 0.450829π-0.450829\pi
0.153861 + 0.988092i 0.450829π0.450829\pi
728728 0 0
729729 0 0
730730 2065.00 3576.68i 0.104697 0.181341i
731731 −7670.00 13284.8i −0.388078 0.672171i
732732 0 0
733733 7621.50 13200.8i 0.384047 0.665189i −0.607589 0.794251i 0.707863π-0.707863\pi
0.991636 + 0.129062i 0.0411967π0.0411967\pi
734734 −19342.0 −0.972652
735735 0 0
736736 224.000 0.0112184
737737 7682.50 13306.5i 0.383974 0.665062i
738738 0 0
739739 5026.50 + 8706.15i 0.250207 + 0.433371i 0.963583 0.267411i 0.0861681π-0.0861681\pi
−0.713376 + 0.700782i 0.752835π0.752835\pi
740740 −154.000 + 266.736i −0.00765021 + 0.0132505i
741741 0 0
742742 0 0
743743 −24384.0 −1.20399 −0.601993 0.798501i 0.705627π-0.705627\pi
−0.601993 + 0.798501i 0.705627π0.705627\pi
744744 0 0
745745 8032.50 + 13912.7i 0.395017 + 0.684190i
746746 4109.00 + 7117.00i 0.201664 + 0.349292i
747747 0 0
748748 −8260.00 −0.403764
749749 0 0
750750 0 0
751751 −5794.50 + 10036.4i −0.281550 + 0.487660i −0.971767 0.235943i 0.924182π-0.924182\pi
0.690216 + 0.723603i 0.257515π0.257515\pi
752752 1368.00 + 2369.45i 0.0663375 + 0.114900i
753753 0 0
754754 −6996.00 + 12117.4i −0.337904 + 0.585266i
755755 −7763.00 −0.374205
756756 0 0
757757 14562.0 0.699161 0.349581 0.936906i 0.386324π-0.386324\pi
0.349581 + 0.936906i 0.386324π0.386324\pi
758758 3488.00 6041.39i 0.167137 0.289490i
759759 0 0
760760 3836.00 + 6644.15i 0.183087 + 0.317116i
761761 11382.5 19715.1i 0.542201 0.939120i −0.456576 0.889684i 0.650924π-0.650924\pi
0.998777 0.0494360i 0.0157424π-0.0157424\pi
762762 0 0
763763 0 0
764764 5100.00 0.241507
765765 0 0
766766 −8717.00 15098.3i −0.411172 0.712171i
767767 −561.000 971.681i −0.0264101 0.0457436i
768768 0 0
769769 −3766.00 −0.176600 −0.0883000 0.996094i 0.528143π-0.528143\pi
−0.0883000 + 0.996094i 0.528143π0.528143\pi
770770 0 0
771771 0 0
772772 −70.0000 + 121.244i −0.00326341 + 0.00565240i
773773 13430.5 + 23262.3i 0.624918 + 1.08239i 0.988557 + 0.150849i 0.0482009π0.0482009\pi
−0.363639 + 0.931540i 0.618466π0.618466\pi
774774 0 0
775775 −2850.00 + 4936.34i −0.132097 + 0.228798i
776776 2320.00 0.107324
777777 0 0
778778 −326.000 −0.0150227
779779 −34113.0 + 59085.4i −1.56897 + 2.71753i
780780 0 0
781781 13720.0 + 23763.7i 0.628605 + 1.08878i
782782 −413.000 + 715.337i −0.0188860 + 0.0327115i
783783 0 0
784784 0 0
785785 −10913.0 −0.496180
786786 0 0
787787 −1048.50 1816.06i −0.0474905 0.0822559i 0.841303 0.540564i 0.181789π-0.181789\pi
−0.888793 + 0.458308i 0.848456π0.848456\pi
788788 −5468.00 9470.85i −0.247195 0.428154i
789789 0 0
790790 −6930.00 −0.312099
791791 0 0
792792 0 0
793793 −1683.00 + 2915.04i −0.0753658 + 0.130537i
794794 999.000 + 1730.32i 0.0446514 + 0.0773384i
795795 0 0
796796 4486.00 7769.98i 0.199751 0.345979i
797797 −35334.0 −1.57038 −0.785191 0.619254i 0.787435π-0.787435\pi
−0.785191 + 0.619254i 0.787435π0.787435\pi
798798 0 0
799799 −10089.0 −0.446712
800800 1216.00 2106.17i 0.0537401 0.0930806i
801801 0 0
802802 −14757.0 25559.9i −0.649735 1.12537i
803803 −5162.50 + 8941.71i −0.226875 + 0.392959i
804804 0 0
805805 0 0
806806 9900.00 0.432646
807807 0 0
808808 4340.00 + 7517.10i 0.188961 + 0.327290i
809809 21267.5 + 36836.4i 0.924259 + 1.60086i 0.792749 + 0.609549i 0.208649π0.208649\pi
0.131510 + 0.991315i 0.458017π0.458017\pi
810810 0 0
811811 −30676.0 −1.32821 −0.664106 0.747638i 0.731188π-0.731188\pi
−0.664106 + 0.747638i 0.731188π0.731188\pi
812812 0 0
813813 0 0
814814 385.000 666.840i 0.0165777 0.0287134i
815815 7878.50 + 13646.0i 0.338616 + 0.586500i
816816 0 0
817817 17810.0 30847.8i 0.762660 1.32097i
818818 266.000 0.0113698
819819 0 0
820820 −13944.0 −0.593836
821821 18671.5 32340.0i 0.793715 1.37475i −0.129937 0.991522i 0.541478π-0.541478\pi
0.923652 0.383232i 0.125189π-0.125189\pi
822822 0 0
823823 −1407.50 2437.86i −0.0596141 0.103255i 0.834678 0.550738i 0.185654π-0.185654\pi
−0.894292 + 0.447483i 0.852320π0.852320\pi
824824 6212.00 10759.5i 0.262628 0.454885i
825825 0 0
826826 0 0
827827 9276.00 0.390034 0.195017 0.980800i 0.437524π-0.437524\pi
0.195017 + 0.980800i 0.437524π0.437524\pi
828828 0 0
829829 9285.50 + 16083.0i 0.389021 + 0.673805i 0.992318 0.123712i 0.0394799π-0.0394799\pi
−0.603297 + 0.797517i 0.706147π0.706147\pi
830830 −6524.00 11299.9i −0.272833 0.472561i
831831 0 0
832832 −4224.00 −0.176011
833833 0 0
834834 0 0
835835 −9758.00 + 16901.4i −0.404419 + 0.700474i
836836 −9590.00 16610.4i −0.396743 0.687179i
837837 0 0
838838 6420.00 11119.8i 0.264648 0.458384i
839839 29048.0 1.19529 0.597645 0.801761i 0.296103π-0.296103\pi
0.597645 + 0.801761i 0.296103π0.296103\pi
840840 0 0
841841 −13153.0 −0.539301
842842 −10266.0 + 17781.2i −0.420178 + 0.727769i
843843 0 0
844844 −2344.00 4059.93i −0.0955969 0.165579i
845845 −7556.50 + 13088.2i −0.307635 + 0.532839i
846846 0 0
847847 0 0
848848 6672.00 0.270186
849849 0 0
850850 4484.00 + 7766.52i 0.180941 + 0.313399i
851851 −38.5000 66.6840i −0.00155084 0.00268613i
852852 0 0
853853 −32090.0 −1.28809 −0.644045 0.764988i 0.722745π-0.722745\pi
−0.644045 + 0.764988i 0.722745π0.722745\pi
854854 0 0
855855 0 0
856856 516.000 893.738i 0.0206034 0.0356861i
857857 12268.5 + 21249.7i 0.489013 + 0.846995i 0.999920 0.0126408i 0.00402379π-0.00402379\pi
−0.510907 + 0.859636i 0.670690π0.670690\pi
858858 0 0
859859 10412.5 18035.0i 0.413585 0.716351i −0.581693 0.813408i 0.697610π-0.697610\pi
0.995279 + 0.0970571i 0.0309430π0.0309430\pi
860860 7280.00 0.288658
861861 0 0
862862 30426.0 1.20222
863863 −11423.5 + 19786.1i −0.450591 + 0.780447i −0.998423 0.0561414i 0.982120π-0.982120\pi
0.547831 + 0.836589i 0.315454π0.315454\pi
864864 0 0
865865 −5526.50 9572.18i −0.217233 0.376259i
866866 −1378.00 + 2386.77i −0.0540720 + 0.0936554i
867867 0 0
868868 0 0
869869 17325.0 0.676307
870870 0 0
871871 14487.0 + 25092.2i 0.563574 + 0.976139i
872872 3860.00 + 6685.72i 0.149904 + 0.259641i
873873 0 0
874874 −1918.00 −0.0742303
875875 0 0
876876 0 0
877877 21368.5 37011.3i 0.822763 1.42507i −0.0808543 0.996726i 0.525765π-0.525765\pi
0.903617 0.428341i 0.140902π-0.140902\pi
878878 −2763.00 4785.66i −0.106204 0.183950i
879879 0 0
880880 1960.00 3394.82i 0.0750813 0.130045i
881881 6162.00 0.235645 0.117822 0.993035i 0.462409π-0.462409\pi
0.117822 + 0.993035i 0.462409π0.462409\pi
882882 0 0
883883 7748.00 0.295290 0.147645 0.989040i 0.452831π-0.452831\pi
0.147645 + 0.989040i 0.452831π0.452831\pi
884884 7788.00 13489.2i 0.296311 0.513225i
885885 0 0
886886 5849.00 + 10130.8i 0.221784 + 0.384142i
887887 12961.5 22450.0i 0.490648 0.849827i −0.509294 0.860592i 0.670094π-0.670094\pi
0.999942 + 0.0107656i 0.00342685π0.00342685\pi
888888 0 0
889889 0 0
890890 −12222.0 −0.460317
891891 0 0
892892 4048.00 + 7011.34i 0.151947 + 0.263181i
893893 −11713.5 20288.4i −0.438944 0.760274i
894894 0 0
895895 −17157.0 −0.640777
896896 0 0
897897 0 0
898898 4582.00 7936.26i 0.170271 0.294918i
899899 −3975.00 6884.90i −0.147468 0.255422i
900900 0 0
901901 −12301.5 + 21306.8i −0.454853 + 0.787828i
902902 34860.0 1.28682
903903 0 0
904904 400.000 0.0147166
905905 −4095.00 + 7092.75i −0.150411 + 0.260520i
906906 0 0
907907 −15967.5 27656.5i −0.584556 1.01248i −0.994931 0.100563i 0.967935π-0.967935\pi
0.410375 0.911917i 0.365398π-0.365398\pi
908908 −5142.00 + 8906.21i −0.187933 + 0.325510i
909909 0 0
910910 0 0
911911 −3408.00 −0.123943 −0.0619715 0.998078i 0.519739π-0.519739\pi
−0.0619715 + 0.998078i 0.519739π0.519739\pi
912912 0 0
913913 16310.0 + 28249.7i 0.591218 + 1.02402i
914914 −11551.0 20006.9i −0.418023 0.724037i
915915 0 0
916916 −3580.00 −0.129134
917917 0 0
918918 0 0
919919 −6954.50 + 12045.5i −0.249628 + 0.432368i −0.963423 0.267987i 0.913642π-0.913642\pi
0.713795 + 0.700355i 0.246975π0.246975\pi
920920 −196.000 339.482i −0.00702384 0.0121656i
921921 0 0
922922 9494.00 16444.1i 0.339120 0.587372i
923923 −51744.0 −1.84526
924924 0 0
925925 −836.000 −0.0297162
926926 10160.0 17597.6i 0.360560 0.624508i
927927 0 0
928928 1696.00 + 2937.56i 0.0599935 + 0.103912i
929929 12268.5 21249.7i 0.433279 0.750462i −0.563874 0.825861i 0.690690π-0.690690\pi
0.997153 + 0.0753990i 0.0240231π0.0240231\pi
930930 0 0
931931 0 0
932932 −7148.00 −0.251224
933933 0 0
934934 1307.00 + 2263.79i 0.0457884 + 0.0793078i
935935 7227.50 + 12518.4i 0.252796 + 0.437856i
936936 0 0
937937 32758.0 1.14211 0.571055 0.820912i 0.306534π-0.306534\pi
0.571055 + 0.820912i 0.306534π0.306534\pi
938938 0 0
939939 0 0
940940 2394.00 4146.53i 0.0830677 0.143878i
941941 19280.5 + 33394.8i 0.667934 + 1.15690i 0.978481 + 0.206338i 0.0661547π0.0661547\pi
−0.310546 + 0.950558i 0.600512π0.600512\pi
942942 0 0
943943 1743.00 3018.96i 0.0601908 0.104253i
944944 −272.000 −0.00937801
945945 0 0
946946 −18200.0 −0.625511
947947 19830.5 34347.4i 0.680470 1.17861i −0.294368 0.955692i 0.595109π-0.595109\pi
0.974838 0.222916i 0.0715575π-0.0715575\pi
948948 0 0
949949 −9735.00 16861.5i −0.332994 0.576763i
950950 −10412.0 + 18034.1i −0.355589 + 0.615899i
951951 0 0
952952 0 0
953953 46618.0 1.58458 0.792290 0.610144i 0.208889π-0.208889\pi
0.792290 + 0.610144i 0.208889π0.208889\pi
954954 0 0
955955 −4462.50 7729.28i −0.151207 0.261899i
956956 −10200.0 17666.9i −0.345075 0.597687i
957957 0 0
958958 36574.0 1.23346
959959 0 0
960960 0 0
961961 12083.0 20928.4i 0.405592 0.702506i
962962 726.000 + 1257.47i 0.0243318 + 0.0421439i
963963 0 0
964964 −8354.00 + 14469.6i −0.279112 + 0.483437i
965965 245.000 0.00817288
966966 0 0
967967 14816.0 0.492710 0.246355 0.969180i 0.420767π-0.420767\pi
0.246355 + 0.969180i 0.420767π0.420767\pi
968968 424.000 734.390i 0.0140784 0.0243845i
969969 0 0
970970 −2030.00 3516.06i −0.0671952 0.116386i
971971 8437.50 14614.2i 0.278859 0.482998i −0.692242 0.721665i 0.743377π-0.743377\pi
0.971102 + 0.238667i 0.0767104π0.0767104\pi
972972 0 0
973973 0 0
974974 −29906.0 −0.983830
975975 0 0
976976 408.000 + 706.677i 0.0133809 + 0.0231764i
977977 −7918.50 13715.2i −0.259299 0.449119i 0.706755 0.707458i 0.250158π-0.250158\pi
−0.966054 + 0.258339i 0.916825π0.916825\pi
978978 0 0
979979 30555.0 0.997489
980980 0 0
981981 0 0
982982 14352.0 24858.4i 0.466386 0.807804i
983983 −4957.50 8586.64i −0.160854 0.278608i 0.774321 0.632793i 0.218092π-0.218092\pi
−0.935175 + 0.354185i 0.884758π0.884758\pi
984984 0 0
985985 −9569.00 + 16574.0i −0.309537 + 0.536133i
986986 −12508.0 −0.403992
987987 0 0
988988 36168.0 1.16463
989989 −910.000 + 1576.17i −0.0292582 + 0.0506766i
990990 0 0
991991 21840.5 + 37828.9i 0.700087 + 1.21259i 0.968435 + 0.249265i 0.0801889π0.0801889\pi
−0.268348 + 0.963322i 0.586478π0.586478\pi
992992 1200.00 2078.46i 0.0384073 0.0665234i
993993 0 0
994994 0 0
995995 −15701.0 −0.500256
996996 0 0
997997 −23556.5 40801.1i −0.748287 1.29607i −0.948643 0.316348i 0.897543π-0.897543\pi
0.200357 0.979723i 0.435790π-0.435790\pi
998998 5531.00 + 9579.97i 0.175432 + 0.303856i
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 882.4.g.d.667.1 2
3.2 odd 2 98.4.c.e.79.1 2
7.2 even 3 882.4.a.p.1.1 1
7.3 odd 6 126.4.g.c.109.1 2
7.4 even 3 inner 882.4.g.d.361.1 2
7.5 odd 6 882.4.a.k.1.1 1
7.6 odd 2 126.4.g.c.37.1 2
21.2 odd 6 98.4.a.c.1.1 1
21.5 even 6 98.4.a.b.1.1 1
21.11 odd 6 98.4.c.e.67.1 2
21.17 even 6 14.4.c.b.11.1 yes 2
21.20 even 2 14.4.c.b.9.1 2
84.23 even 6 784.4.a.j.1.1 1
84.47 odd 6 784.4.a.l.1.1 1
84.59 odd 6 112.4.i.b.81.1 2
84.83 odd 2 112.4.i.b.65.1 2
105.17 odd 12 350.4.j.d.249.1 4
105.38 odd 12 350.4.j.d.249.2 4
105.44 odd 6 2450.4.a.bf.1.1 1
105.59 even 6 350.4.e.b.151.1 2
105.62 odd 4 350.4.j.d.149.2 4
105.83 odd 4 350.4.j.d.149.1 4
105.89 even 6 2450.4.a.bh.1.1 1
105.104 even 2 350.4.e.b.51.1 2
168.59 odd 6 448.4.i.d.193.1 2
168.83 odd 2 448.4.i.d.65.1 2
168.101 even 6 448.4.i.c.193.1 2
168.125 even 2 448.4.i.c.65.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.4.c.b.9.1 2 21.20 even 2
14.4.c.b.11.1 yes 2 21.17 even 6
98.4.a.b.1.1 1 21.5 even 6
98.4.a.c.1.1 1 21.2 odd 6
98.4.c.e.67.1 2 21.11 odd 6
98.4.c.e.79.1 2 3.2 odd 2
112.4.i.b.65.1 2 84.83 odd 2
112.4.i.b.81.1 2 84.59 odd 6
126.4.g.c.37.1 2 7.6 odd 2
126.4.g.c.109.1 2 7.3 odd 6
350.4.e.b.51.1 2 105.104 even 2
350.4.e.b.151.1 2 105.59 even 6
350.4.j.d.149.1 4 105.83 odd 4
350.4.j.d.149.2 4 105.62 odd 4
350.4.j.d.249.1 4 105.17 odd 12
350.4.j.d.249.2 4 105.38 odd 12
448.4.i.c.65.1 2 168.125 even 2
448.4.i.c.193.1 2 168.101 even 6
448.4.i.d.65.1 2 168.83 odd 2
448.4.i.d.193.1 2 168.59 odd 6
784.4.a.j.1.1 1 84.23 even 6
784.4.a.l.1.1 1 84.47 odd 6
882.4.a.k.1.1 1 7.5 odd 6
882.4.a.p.1.1 1 7.2 even 3
882.4.g.d.361.1 2 7.4 even 3 inner
882.4.g.d.667.1 2 1.1 even 1 trivial
2450.4.a.bf.1.1 1 105.44 odd 6
2450.4.a.bh.1.1 1 105.89 even 6