Properties

Label 7942.2.a.ca.1.5
Level 79427942
Weight 22
Character 7942.1
Self dual yes
Analytic conductor 63.41763.417
Analytic rank 00
Dimension 1515
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7942,2,Mod(1,7942)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7942, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7942.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 7942=211192 7942 = 2 \cdot 11 \cdot 19^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 7942.a (trivial)

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: yes
Analytic conductor: 63.417189285363.4171892853
Analytic rank: 00
Dimension: 1515
Coefficient field: Q[x]/(x15)\mathbb{Q}[x]/(x^{15} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x153x1433x13+101x12+408x111314x102271x9+8292x8+3592 x^{15} - 3 x^{14} - 33 x^{13} + 101 x^{12} + 408 x^{11} - 1314 x^{10} - 2271 x^{9} + 8292 x^{8} + \cdots - 3592 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 418)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.5
Root 1.52164-1.52164 of defining polynomial
Character χ\chi == 7942.1

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+1.00000q21.52164q3+1.00000q42.93560q51.52164q60.464814q7+1.00000q80.684609q92.93560q101.00000q111.52164q12+4.49956q130.464814q14+4.46693q15+1.00000q16+0.188812q170.684609q182.93560q20+0.707279q211.00000q22+2.91060q231.52164q24+3.61774q25+4.49956q26+5.60665q270.464814q28+1.72567q29+4.46693q301.87404q31+1.00000q32+1.52164q33+0.188812q34+1.36451q350.684609q366.48294q376.84672q392.93560q403.30129q41+0.707279q4210.7036q431.00000q44+2.00974q45+2.91060q464.02946q471.52164q486.78395q49+3.61774q500.287304q51+4.49956q521.35935q53+5.60665q54+2.93560q550.464814q56+1.72567q585.50657q59+4.46693q6010.9663q611.87404q62+0.318216q63+1.00000q6413.2089q65+1.52164q66+5.56717q67+0.188812q684.42889q69+1.36451q70+3.98279q710.684609q72+10.9027q736.48294q745.50491q75+0.464814q776.84672q78+5.54536q792.93560q806.47748q813.30129q8212.8465q83+0.707279q840.554277q8510.7036q862.62586q871.00000q88+16.9412q89+2.00974q902.09146q91+2.91060q92+2.85161q934.02946q941.52164q9612.1485q976.78395q98+0.684609q99+O(q100)q+1.00000 q^{2} -1.52164 q^{3} +1.00000 q^{4} -2.93560 q^{5} -1.52164 q^{6} -0.464814 q^{7} +1.00000 q^{8} -0.684609 q^{9} -2.93560 q^{10} -1.00000 q^{11} -1.52164 q^{12} +4.49956 q^{13} -0.464814 q^{14} +4.46693 q^{15} +1.00000 q^{16} +0.188812 q^{17} -0.684609 q^{18} -2.93560 q^{20} +0.707279 q^{21} -1.00000 q^{22} +2.91060 q^{23} -1.52164 q^{24} +3.61774 q^{25} +4.49956 q^{26} +5.60665 q^{27} -0.464814 q^{28} +1.72567 q^{29} +4.46693 q^{30} -1.87404 q^{31} +1.00000 q^{32} +1.52164 q^{33} +0.188812 q^{34} +1.36451 q^{35} -0.684609 q^{36} -6.48294 q^{37} -6.84672 q^{39} -2.93560 q^{40} -3.30129 q^{41} +0.707279 q^{42} -10.7036 q^{43} -1.00000 q^{44} +2.00974 q^{45} +2.91060 q^{46} -4.02946 q^{47} -1.52164 q^{48} -6.78395 q^{49} +3.61774 q^{50} -0.287304 q^{51} +4.49956 q^{52} -1.35935 q^{53} +5.60665 q^{54} +2.93560 q^{55} -0.464814 q^{56} +1.72567 q^{58} -5.50657 q^{59} +4.46693 q^{60} -10.9663 q^{61} -1.87404 q^{62} +0.318216 q^{63} +1.00000 q^{64} -13.2089 q^{65} +1.52164 q^{66} +5.56717 q^{67} +0.188812 q^{68} -4.42889 q^{69} +1.36451 q^{70} +3.98279 q^{71} -0.684609 q^{72} +10.9027 q^{73} -6.48294 q^{74} -5.50491 q^{75} +0.464814 q^{77} -6.84672 q^{78} +5.54536 q^{79} -2.93560 q^{80} -6.47748 q^{81} -3.30129 q^{82} -12.8465 q^{83} +0.707279 q^{84} -0.554277 q^{85} -10.7036 q^{86} -2.62586 q^{87} -1.00000 q^{88} +16.9412 q^{89} +2.00974 q^{90} -2.09146 q^{91} +2.91060 q^{92} +2.85161 q^{93} -4.02946 q^{94} -1.52164 q^{96} -12.1485 q^{97} -6.78395 q^{98} +0.684609 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 15q+15q2+3q3+15q4+9q5+3q6+15q8+30q9+9q1015q11+3q12+21q15+15q16+21q17+30q18+9q209q2115q22+21q23+30q99+O(q100) 15 q + 15 q^{2} + 3 q^{3} + 15 q^{4} + 9 q^{5} + 3 q^{6} + 15 q^{8} + 30 q^{9} + 9 q^{10} - 15 q^{11} + 3 q^{12} + 21 q^{15} + 15 q^{16} + 21 q^{17} + 30 q^{18} + 9 q^{20} - 9 q^{21} - 15 q^{22} + 21 q^{23}+ \cdots - 30 q^{99}+O(q^{100}) Copy content Toggle raw display

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 0.707107
33 −1.52164 −0.878520 −0.439260 0.898360i 0.644759π-0.644759\pi
−0.439260 + 0.898360i 0.644759π0.644759\pi
44 1.00000 0.500000
55 −2.93560 −1.31284 −0.656420 0.754396i 0.727930π-0.727930\pi
−0.656420 + 0.754396i 0.727930π0.727930\pi
66 −1.52164 −0.621207
77 −0.464814 −0.175683 −0.0878415 0.996134i 0.527997π-0.527997\pi
−0.0878415 + 0.996134i 0.527997π0.527997\pi
88 1.00000 0.353553
99 −0.684609 −0.228203
1010 −2.93560 −0.928318
1111 −1.00000 −0.301511
1212 −1.52164 −0.439260
1313 4.49956 1.24795 0.623977 0.781443i 0.285516π-0.285516\pi
0.623977 + 0.781443i 0.285516π0.285516\pi
1414 −0.464814 −0.124227
1515 4.46693 1.15336
1616 1.00000 0.250000
1717 0.188812 0.0457937 0.0228969 0.999738i 0.492711π-0.492711\pi
0.0228969 + 0.999738i 0.492711π0.492711\pi
1818 −0.684609 −0.161364
1919 0 0
2020 −2.93560 −0.656420
2121 0.707279 0.154341
2222 −1.00000 −0.213201
2323 2.91060 0.606903 0.303451 0.952847i 0.401861π-0.401861\pi
0.303451 + 0.952847i 0.401861π0.401861\pi
2424 −1.52164 −0.310604
2525 3.61774 0.723549
2626 4.49956 0.882437
2727 5.60665 1.07900
2828 −0.464814 −0.0878415
2929 1.72567 0.320450 0.160225 0.987081i 0.448778π-0.448778\pi
0.160225 + 0.987081i 0.448778π0.448778\pi
3030 4.46693 0.815546
3131 −1.87404 −0.336587 −0.168293 0.985737i 0.553826π-0.553826\pi
−0.168293 + 0.985737i 0.553826π0.553826\pi
3232 1.00000 0.176777
3333 1.52164 0.264884
3434 0.188812 0.0323810
3535 1.36451 0.230644
3636 −0.684609 −0.114102
3737 −6.48294 −1.06579 −0.532894 0.846182i 0.678896π-0.678896\pi
−0.532894 + 0.846182i 0.678896π0.678896\pi
3838 0 0
3939 −6.84672 −1.09635
4040 −2.93560 −0.464159
4141 −3.30129 −0.515575 −0.257788 0.966202i 0.582993π-0.582993\pi
−0.257788 + 0.966202i 0.582993π0.582993\pi
4242 0.707279 0.109136
4343 −10.7036 −1.63229 −0.816145 0.577847i 0.803893π-0.803893\pi
−0.816145 + 0.577847i 0.803893π0.803893\pi
4444 −1.00000 −0.150756
4545 2.00974 0.299594
4646 2.91060 0.429145
4747 −4.02946 −0.587757 −0.293878 0.955843i 0.594946π-0.594946\pi
−0.293878 + 0.955843i 0.594946π0.594946\pi
4848 −1.52164 −0.219630
4949 −6.78395 −0.969135
5050 3.61774 0.511626
5151 −0.287304 −0.0402307
5252 4.49956 0.623977
5353 −1.35935 −0.186721 −0.0933605 0.995632i 0.529761π-0.529761\pi
−0.0933605 + 0.995632i 0.529761π0.529761\pi
5454 5.60665 0.762969
5555 2.93560 0.395836
5656 −0.464814 −0.0621133
5757 0 0
5858 1.72567 0.226592
5959 −5.50657 −0.716895 −0.358447 0.933550i 0.616694π-0.616694\pi
−0.358447 + 0.933550i 0.616694π0.616694\pi
6060 4.46693 0.576678
6161 −10.9663 −1.40409 −0.702046 0.712132i 0.747730π-0.747730\pi
−0.702046 + 0.712132i 0.747730π0.747730\pi
6262 −1.87404 −0.238003
6363 0.318216 0.0400914
6464 1.00000 0.125000
6565 −13.2089 −1.63836
6666 1.52164 0.187301
6767 5.56717 0.680138 0.340069 0.940400i 0.389550π-0.389550\pi
0.340069 + 0.940400i 0.389550π0.389550\pi
6868 0.188812 0.0228969
6969 −4.42889 −0.533176
7070 1.36451 0.163090
7171 3.98279 0.472670 0.236335 0.971672i 0.424054π-0.424054\pi
0.236335 + 0.971672i 0.424054π0.424054\pi
7272 −0.684609 −0.0806820
7373 10.9027 1.27607 0.638033 0.770009i 0.279748π-0.279748\pi
0.638033 + 0.770009i 0.279748π0.279748\pi
7474 −6.48294 −0.753626
7575 −5.50491 −0.635652
7676 0 0
7777 0.464814 0.0529704
7878 −6.84672 −0.775238
7979 5.54536 0.623902 0.311951 0.950098i 0.399018π-0.399018\pi
0.311951 + 0.950098i 0.399018π0.399018\pi
8080 −2.93560 −0.328210
8181 −6.47748 −0.719720
8282 −3.30129 −0.364567
8383 −12.8465 −1.41009 −0.705043 0.709164i 0.749073π-0.749073\pi
−0.705043 + 0.709164i 0.749073π0.749073\pi
8484 0.707279 0.0771705
8585 −0.554277 −0.0601198
8686 −10.7036 −1.15420
8787 −2.62586 −0.281521
8888 −1.00000 −0.106600
8989 16.9412 1.79577 0.897884 0.440232i 0.145104π-0.145104\pi
0.897884 + 0.440232i 0.145104π0.145104\pi
9090 2.00974 0.211845
9191 −2.09146 −0.219244
9292 2.91060 0.303451
9393 2.85161 0.295698
9494 −4.02946 −0.415607
9595 0 0
9696 −1.52164 −0.155302
9797 −12.1485 −1.23350 −0.616748 0.787161i 0.711550π-0.711550\pi
−0.616748 + 0.787161i 0.711550π0.711550\pi
9898 −6.78395 −0.685282
9999 0.684609 0.0688058
100100 3.61774 0.361774
101101 8.90820 0.886399 0.443200 0.896423i 0.353843π-0.353843\pi
0.443200 + 0.896423i 0.353843π0.353843\pi
102102 −0.287304 −0.0284474
103103 1.74670 0.172108 0.0860539 0.996290i 0.472574π-0.472574\pi
0.0860539 + 0.996290i 0.472574π0.472574\pi
104104 4.49956 0.441218
105105 −2.07629 −0.202625
106106 −1.35935 −0.132032
107107 −0.0663443 −0.00641374 −0.00320687 0.999995i 0.501021π-0.501021\pi
−0.00320687 + 0.999995i 0.501021π0.501021\pi
108108 5.60665 0.539500
109109 3.81573 0.365481 0.182741 0.983161i 0.441503π-0.441503\pi
0.182741 + 0.983161i 0.441503π0.441503\pi
110110 2.93560 0.279898
111111 9.86470 0.936316
112112 −0.464814 −0.0439208
113113 −0.0177717 −0.00167182 −0.000835908 1.00000i 0.500266π-0.500266\pi
−0.000835908 1.00000i 0.500266π0.500266\pi
114114 0 0
115115 −8.54437 −0.796766
116116 1.72567 0.160225
117117 −3.08044 −0.284787
118118 −5.50657 −0.506921
119119 −0.0877625 −0.00804518
120120 4.46693 0.407773
121121 1.00000 0.0909091
122122 −10.9663 −0.992842
123123 5.02338 0.452943
124124 −1.87404 −0.168293
125125 4.05775 0.362936
126126 0.318216 0.0283489
127127 7.69028 0.682402 0.341201 0.939990i 0.389166π-0.389166\pi
0.341201 + 0.939990i 0.389166π0.389166\pi
128128 1.00000 0.0883883
129129 16.2871 1.43400
130130 −13.2089 −1.15850
131131 22.1186 1.93251 0.966257 0.257578i 0.0829246π-0.0829246\pi
0.966257 + 0.257578i 0.0829246π0.0829246\pi
132132 1.52164 0.132442
133133 0 0
134134 5.56717 0.480930
135135 −16.4589 −1.41656
136136 0.188812 0.0161905
137137 3.98966 0.340860 0.170430 0.985370i 0.445484π-0.445484\pi
0.170430 + 0.985370i 0.445484π0.445484\pi
138138 −4.42889 −0.377013
139139 1.48693 0.126120 0.0630598 0.998010i 0.479914π-0.479914\pi
0.0630598 + 0.998010i 0.479914π0.479914\pi
140140 1.36451 0.115322
141141 6.13139 0.516356
142142 3.98279 0.334228
143143 −4.49956 −0.376272
144144 −0.684609 −0.0570508
145145 −5.06589 −0.420699
146146 10.9027 0.902315
147147 10.3227 0.851405
148148 −6.48294 −0.532894
149149 8.10477 0.663969 0.331984 0.943285i 0.392282π-0.392282\pi
0.331984 + 0.943285i 0.392282π0.392282\pi
150150 −5.50491 −0.449474
151151 −16.0446 −1.30569 −0.652846 0.757490i 0.726425π-0.726425\pi
−0.652846 + 0.757490i 0.726425π0.726425\pi
152152 0 0
153153 −0.129263 −0.0104503
154154 0.464814 0.0374557
155155 5.50142 0.441885
156156 −6.84672 −0.548176
157157 18.1493 1.44847 0.724234 0.689554i 0.242194π-0.242194\pi
0.724234 + 0.689554i 0.242194π0.242194\pi
158158 5.54536 0.441165
159159 2.06844 0.164038
160160 −2.93560 −0.232080
161161 −1.35289 −0.106623
162162 −6.47748 −0.508919
163163 21.3870 1.67516 0.837579 0.546316i 0.183970π-0.183970\pi
0.837579 + 0.546316i 0.183970π0.183970\pi
164164 −3.30129 −0.257788
165165 −4.46693 −0.347750
166166 −12.8465 −0.997082
167167 11.0690 0.856548 0.428274 0.903649i 0.359122π-0.359122\pi
0.428274 + 0.903649i 0.359122π0.359122\pi
168168 0.707279 0.0545678
169169 7.24605 0.557389
170170 −0.554277 −0.0425111
171171 0 0
172172 −10.7036 −0.816145
173173 −8.71135 −0.662311 −0.331156 0.943576i 0.607439π-0.607439\pi
−0.331156 + 0.943576i 0.607439π0.607439\pi
174174 −2.62586 −0.199066
175175 −1.68158 −0.127115
176176 −1.00000 −0.0753778
177177 8.37903 0.629806
178178 16.9412 1.26980
179179 −9.62721 −0.719572 −0.359786 0.933035i 0.617150π-0.617150\pi
−0.359786 + 0.933035i 0.617150π0.617150\pi
180180 2.00974 0.149797
181181 17.8108 1.32387 0.661935 0.749561i 0.269736π-0.269736\pi
0.661935 + 0.749561i 0.269736π0.269736\pi
182182 −2.09146 −0.155029
183183 16.6868 1.23352
184184 2.91060 0.214573
185185 19.0313 1.39921
186186 2.85161 0.209090
187187 −0.188812 −0.0138073
188188 −4.02946 −0.293878
189189 −2.60605 −0.189562
190190 0 0
191191 25.2728 1.82868 0.914338 0.404952i 0.132712π-0.132712\pi
0.914338 + 0.404952i 0.132712π0.132712\pi
192192 −1.52164 −0.109815
193193 16.7371 1.20476 0.602381 0.798209i 0.294219π-0.294219\pi
0.602381 + 0.798209i 0.294219π0.294219\pi
194194 −12.1485 −0.872214
195195 20.0992 1.43933
196196 −6.78395 −0.484568
197197 8.52528 0.607401 0.303700 0.952768i 0.401778π-0.401778\pi
0.303700 + 0.952768i 0.401778π0.401778\pi
198198 0.684609 0.0486531
199199 21.7367 1.54087 0.770435 0.637518i 0.220039π-0.220039\pi
0.770435 + 0.637518i 0.220039π0.220039\pi
200200 3.61774 0.255813
201201 −8.47123 −0.597515
202202 8.90820 0.626779
203203 −0.802117 −0.0562976
204204 −0.287304 −0.0201153
205205 9.69127 0.676868
206206 1.74670 0.121699
207207 −1.99263 −0.138497
208208 4.49956 0.311988
209209 0 0
210210 −2.07629 −0.143278
211211 8.82448 0.607503 0.303751 0.952751i 0.401761π-0.401761\pi
0.303751 + 0.952751i 0.401761π0.401761\pi
212212 −1.35935 −0.0933605
213213 −6.06037 −0.415250
214214 −0.0663443 −0.00453520
215215 31.4216 2.14293
216216 5.60665 0.381484
217217 0.871078 0.0591326
218218 3.81573 0.258434
219219 −16.5900 −1.12105
220220 2.93560 0.197918
221221 0.849573 0.0571484
222222 9.86470 0.662076
223223 6.40530 0.428931 0.214465 0.976732i 0.431199π-0.431199\pi
0.214465 + 0.976732i 0.431199π0.431199\pi
224224 −0.464814 −0.0310567
225225 −2.47674 −0.165116
226226 −0.0177717 −0.00118215
227227 −13.8824 −0.921409 −0.460705 0.887554i 0.652403π-0.652403\pi
−0.460705 + 0.887554i 0.652403π0.652403\pi
228228 0 0
229229 −6.38691 −0.422059 −0.211030 0.977480i 0.567682π-0.567682\pi
−0.211030 + 0.977480i 0.567682π0.567682\pi
230230 −8.54437 −0.563399
231231 −0.707279 −0.0465356
232232 1.72567 0.113296
233233 −5.19556 −0.340372 −0.170186 0.985412i 0.554437π-0.554437\pi
−0.170186 + 0.985412i 0.554437π0.554437\pi
234234 −3.08044 −0.201375
235235 11.8289 0.771631
236236 −5.50657 −0.358447
237237 −8.43804 −0.548110
238238 −0.0877625 −0.00568880
239239 −8.20845 −0.530960 −0.265480 0.964116i 0.585530π-0.585530\pi
−0.265480 + 0.964116i 0.585530π0.585530\pi
240240 4.46693 0.288339
241241 −17.8978 −1.15290 −0.576448 0.817134i 0.695562π-0.695562\pi
−0.576448 + 0.817134i 0.695562π0.695562\pi
242242 1.00000 0.0642824
243243 −6.96355 −0.446712
244244 −10.9663 −0.702046
245245 19.9150 1.27232
246246 5.02338 0.320279
247247 0 0
248248 −1.87404 −0.119001
249249 19.5478 1.23879
250250 4.05775 0.256635
251251 11.9474 0.754111 0.377056 0.926191i 0.376937π-0.376937\pi
0.377056 + 0.926191i 0.376937π0.376937\pi
252252 0.318216 0.0200457
253253 −2.91060 −0.182988
254254 7.69028 0.482531
255255 0.843411 0.0528164
256256 1.00000 0.0625000
257257 4.07347 0.254096 0.127048 0.991897i 0.459450π-0.459450\pi
0.127048 + 0.991897i 0.459450π0.459450\pi
258258 16.2871 1.01399
259259 3.01336 0.187241
260260 −13.2089 −0.819182
261261 −1.18141 −0.0731276
262262 22.1186 1.36649
263263 7.22171 0.445310 0.222655 0.974897i 0.428528π-0.428528\pi
0.222655 + 0.974897i 0.428528π0.428528\pi
264264 1.52164 0.0936505
265265 3.99050 0.245135
266266 0 0
267267 −25.7785 −1.57762
268268 5.56717 0.340069
269269 −31.8344 −1.94098 −0.970488 0.241149i 0.922476π-0.922476\pi
−0.970488 + 0.241149i 0.922476π0.922476\pi
270270 −16.4589 −1.00166
271271 −31.2403 −1.89771 −0.948857 0.315706i 0.897759π-0.897759\pi
−0.948857 + 0.315706i 0.897759π0.897759\pi
272272 0.188812 0.0114484
273273 3.18245 0.192610
274274 3.98966 0.241024
275275 −3.61774 −0.218158
276276 −4.42889 −0.266588
277277 12.3578 0.742506 0.371253 0.928532i 0.378928π-0.378928\pi
0.371253 + 0.928532i 0.378928π0.378928\pi
278278 1.48693 0.0891800
279279 1.28298 0.0768102
280280 1.36451 0.0815449
281281 −6.73851 −0.401986 −0.200993 0.979593i 0.564417π-0.564417\pi
−0.200993 + 0.979593i 0.564417π0.564417\pi
282282 6.13139 0.365119
283283 3.67917 0.218704 0.109352 0.994003i 0.465122π-0.465122\pi
0.109352 + 0.994003i 0.465122π0.465122\pi
284284 3.98279 0.236335
285285 0 0
286286 −4.49956 −0.266065
287287 1.53449 0.0905778
288288 −0.684609 −0.0403410
289289 −16.9643 −0.997903
290290 −5.06589 −0.297479
291291 18.4857 1.08365
292292 10.9027 0.638033
293293 2.79512 0.163293 0.0816464 0.996661i 0.473982π-0.473982\pi
0.0816464 + 0.996661i 0.473982π0.473982\pi
294294 10.3227 0.602034
295295 16.1651 0.941168
296296 −6.48294 −0.376813
297297 −5.60665 −0.325331
298298 8.10477 0.469497
299299 13.0964 0.757387
300300 −5.50491 −0.317826
301301 4.97520 0.286766
302302 −16.0446 −0.923264
303303 −13.5551 −0.778719
304304 0 0
305305 32.1927 1.84335
306306 −0.129263 −0.00738945
307307 11.8371 0.675581 0.337790 0.941221i 0.390321π-0.390321\pi
0.337790 + 0.941221i 0.390321π0.390321\pi
308308 0.464814 0.0264852
309309 −2.65786 −0.151200
310310 5.50142 0.312460
311311 15.9983 0.907180 0.453590 0.891210i 0.350143π-0.350143\pi
0.453590 + 0.891210i 0.350143π0.350143\pi
312312 −6.84672 −0.387619
313313 −17.4536 −0.986539 −0.493269 0.869877i 0.664198π-0.664198\pi
−0.493269 + 0.869877i 0.664198π0.664198\pi
314314 18.1493 1.02422
315315 −0.934154 −0.0526336
316316 5.54536 0.311951
317317 −22.7519 −1.27787 −0.638936 0.769260i 0.720625π-0.720625\pi
−0.638936 + 0.769260i 0.720625π0.720625\pi
318318 2.06844 0.115992
319319 −1.72567 −0.0966192
320320 −2.93560 −0.164105
321321 0.100952 0.00563460
322322 −1.35289 −0.0753935
323323 0 0
324324 −6.47748 −0.359860
325325 16.2783 0.902955
326326 21.3870 1.18452
327327 −5.80618 −0.321082
328328 −3.30129 −0.182283
329329 1.87295 0.103259
330330 −4.46693 −0.245896
331331 −9.94526 −0.546641 −0.273320 0.961923i 0.588122π-0.588122\pi
−0.273320 + 0.961923i 0.588122π0.588122\pi
332332 −12.8465 −0.705043
333333 4.43828 0.243216
334334 11.0690 0.605671
335335 −16.3430 −0.892912
336336 0.707279 0.0385853
337337 −27.0670 −1.47443 −0.737216 0.675658i 0.763860π-0.763860\pi
−0.737216 + 0.675658i 0.763860π0.763860\pi
338338 7.24605 0.394133
339339 0.0270421 0.00146872
340340 −0.554277 −0.0300599
341341 1.87404 0.101485
342342 0 0
343343 6.40697 0.345944
344344 −10.7036 −0.577102
345345 13.0015 0.699975
346346 −8.71135 −0.468325
347347 19.4414 1.04367 0.521834 0.853047i 0.325248π-0.325248\pi
0.521834 + 0.853047i 0.325248π0.325248\pi
348348 −2.62586 −0.140761
349349 22.6056 1.21005 0.605025 0.796206i 0.293163π-0.293163\pi
0.605025 + 0.796206i 0.293163π0.293163\pi
350350 −1.68158 −0.0898840
351351 25.2275 1.34654
352352 −1.00000 −0.0533002
353353 24.0961 1.28251 0.641254 0.767328i 0.278414π-0.278414\pi
0.641254 + 0.767328i 0.278414π0.278414\pi
354354 8.37903 0.445340
355355 −11.6919 −0.620540
356356 16.9412 0.897884
357357 0.133543 0.00706785
358358 −9.62721 −0.508814
359359 25.6187 1.35210 0.676052 0.736854i 0.263689π-0.263689\pi
0.676052 + 0.736854i 0.263689π0.263689\pi
360360 2.00974 0.105923
361361 0 0
362362 17.8108 0.936117
363363 −1.52164 −0.0798654
364364 −2.09146 −0.109622
365365 −32.0060 −1.67527
366366 16.6868 0.872232
367367 −1.01974 −0.0532300 −0.0266150 0.999646i 0.508473π-0.508473\pi
−0.0266150 + 0.999646i 0.508473π0.508473\pi
368368 2.91060 0.151726
369369 2.26010 0.117656
370370 19.0313 0.989391
371371 0.631844 0.0328037
372372 2.85161 0.147849
373373 −31.7363 −1.64325 −0.821623 0.570031i 0.806931π-0.806931\pi
−0.821623 + 0.570031i 0.806931π0.806931\pi
374374 −0.188812 −0.00976325
375375 −6.17444 −0.318847
376376 −4.02946 −0.207803
377377 7.76478 0.399906
378378 −2.60605 −0.134041
379379 −19.0665 −0.979382 −0.489691 0.871896i 0.662890π-0.662890\pi
−0.489691 + 0.871896i 0.662890π0.662890\pi
380380 0 0
381381 −11.7018 −0.599504
382382 25.2728 1.29307
383383 −18.1444 −0.927137 −0.463568 0.886061i 0.653431π-0.653431\pi
−0.463568 + 0.886061i 0.653431π0.653431\pi
384384 −1.52164 −0.0776509
385385 −1.36451 −0.0695417
386386 16.7371 0.851895
387387 7.32781 0.372494
388388 −12.1485 −0.616748
389389 3.88312 0.196882 0.0984411 0.995143i 0.468614π-0.468614\pi
0.0984411 + 0.995143i 0.468614π0.468614\pi
390390 20.0992 1.01776
391391 0.549558 0.0277923
392392 −6.78395 −0.342641
393393 −33.6566 −1.69775
394394 8.52528 0.429497
395395 −16.2790 −0.819083
396396 0.684609 0.0344029
397397 17.8589 0.896311 0.448155 0.893956i 0.352081π-0.352081\pi
0.448155 + 0.893956i 0.352081π0.352081\pi
398398 21.7367 1.08956
399399 0 0
400400 3.61774 0.180887
401401 33.5041 1.67311 0.836557 0.547880i 0.184565π-0.184565\pi
0.836557 + 0.547880i 0.184565π0.184565\pi
402402 −8.47123 −0.422507
403403 −8.43234 −0.420045
404404 8.90820 0.443200
405405 19.0153 0.944877
406406 −0.802117 −0.0398084
407407 6.48294 0.321347
408408 −0.287304 −0.0142237
409409 26.3286 1.30186 0.650932 0.759136i 0.274378π-0.274378\pi
0.650932 + 0.759136i 0.274378π0.274378\pi
410410 9.69127 0.478618
411411 −6.07083 −0.299452
412412 1.74670 0.0860539
413413 2.55953 0.125946
414414 −1.99263 −0.0979323
415415 37.7122 1.85122
416416 4.49956 0.220609
417417 −2.26257 −0.110799
418418 0 0
419419 −32.1866 −1.57242 −0.786209 0.617961i 0.787959π-0.787959\pi
−0.786209 + 0.617961i 0.787959π0.787959\pi
420420 −2.07629 −0.101313
421421 20.0204 0.975733 0.487867 0.872918i 0.337775π-0.337775\pi
0.487867 + 0.872918i 0.337775π0.337775\pi
422422 8.82448 0.429569
423423 2.75860 0.134128
424424 −1.35935 −0.0660158
425425 0.683074 0.0331340
426426 −6.06037 −0.293626
427427 5.09729 0.246675
428428 −0.0663443 −0.00320687
429429 6.84672 0.330563
430430 31.4216 1.51528
431431 29.2413 1.40850 0.704252 0.709950i 0.251283π-0.251283\pi
0.704252 + 0.709950i 0.251283π0.251283\pi
432432 5.60665 0.269750
433433 21.8706 1.05103 0.525516 0.850784i 0.323872π-0.323872\pi
0.525516 + 0.850784i 0.323872π0.323872\pi
434434 0.871078 0.0418131
435435 7.70846 0.369593
436436 3.81573 0.182741
437437 0 0
438438 −16.5900 −0.792702
439439 25.8255 1.23258 0.616291 0.787518i 0.288634π-0.288634\pi
0.616291 + 0.787518i 0.288634π0.288634\pi
440440 2.93560 0.139949
441441 4.64435 0.221160
442442 0.849573 0.0404100
443443 7.15530 0.339958 0.169979 0.985448i 0.445630π-0.445630\pi
0.169979 + 0.985448i 0.445630π0.445630\pi
444444 9.86470 0.468158
445445 −49.7327 −2.35756
446446 6.40530 0.303300
447447 −12.3326 −0.583310
448448 −0.464814 −0.0219604
449449 14.0318 0.662202 0.331101 0.943595i 0.392580π-0.392580\pi
0.331101 + 0.943595i 0.392580π0.392580\pi
450450 −2.47674 −0.116755
451451 3.30129 0.155452
452452 −0.0177717 −0.000835908 0
453453 24.4141 1.14708
454454 −13.8824 −0.651535
455455 6.13968 0.287833
456456 0 0
457457 −31.3113 −1.46468 −0.732340 0.680940i 0.761572π-0.761572\pi
−0.732340 + 0.680940i 0.761572π0.761572\pi
458458 −6.38691 −0.298441
459459 1.05860 0.0494114
460460 −8.54437 −0.398383
461461 12.2299 0.569603 0.284802 0.958586i 0.408072π-0.408072\pi
0.284802 + 0.958586i 0.408072π0.408072\pi
462462 −0.707279 −0.0329056
463463 −23.2772 −1.08178 −0.540892 0.841092i 0.681913π-0.681913\pi
−0.540892 + 0.841092i 0.681913π0.681913\pi
464464 1.72567 0.0801124
465465 −8.37119 −0.388205
466466 −5.19556 −0.240680
467467 17.2913 0.800146 0.400073 0.916483i 0.368985π-0.368985\pi
0.400073 + 0.916483i 0.368985π0.368985\pi
468468 −3.08044 −0.142393
469469 −2.58770 −0.119489
470470 11.8289 0.545625
471471 −27.6166 −1.27251
472472 −5.50657 −0.253461
473473 10.7036 0.492154
474474 −8.43804 −0.387572
475475 0 0
476476 −0.0877625 −0.00402259
477477 0.930623 0.0426103
478478 −8.20845 −0.375446
479479 −13.2757 −0.606584 −0.303292 0.952898i 0.598086π-0.598086\pi
−0.303292 + 0.952898i 0.598086π0.598086\pi
480480 4.46693 0.203886
481481 −29.1704 −1.33005
482482 −17.8978 −0.815221
483483 2.05861 0.0936700
484484 1.00000 0.0454545
485485 35.6632 1.61938
486486 −6.96355 −0.315873
487487 −27.2081 −1.23292 −0.616459 0.787387i 0.711434π-0.711434\pi
−0.616459 + 0.787387i 0.711434π0.711434\pi
488488 −10.9663 −0.496421
489489 −32.5433 −1.47166
490490 19.9150 0.899666
491491 35.5134 1.60270 0.801348 0.598198i 0.204116π-0.204116\pi
0.801348 + 0.598198i 0.204116π0.204116\pi
492492 5.02338 0.226471
493493 0.325829 0.0146746
494494 0 0
495495 −2.00974 −0.0903310
496496 −1.87404 −0.0841467
497497 −1.85125 −0.0830401
498498 19.5478 0.875956
499499 −9.33762 −0.418009 −0.209005 0.977915i 0.567022π-0.567022\pi
−0.209005 + 0.977915i 0.567022π0.567022\pi
500500 4.05775 0.181468
501501 −16.8431 −0.752495
502502 11.9474 0.533237
503503 14.2368 0.634787 0.317393 0.948294i 0.397192π-0.397192\pi
0.317393 + 0.948294i 0.397192π0.397192\pi
504504 0.318216 0.0141745
505505 −26.1509 −1.16370
506506 −2.91060 −0.129392
507507 −11.0259 −0.489677
508508 7.69028 0.341201
509509 20.5706 0.911778 0.455889 0.890037i 0.349321π-0.349321\pi
0.455889 + 0.890037i 0.349321π0.349321\pi
510510 0.843411 0.0373469
511511 −5.06773 −0.224183
512512 1.00000 0.0441942
513513 0 0
514514 4.07347 0.179673
515515 −5.12762 −0.225950
516516 16.2871 0.716999
517517 4.02946 0.177215
518518 3.01336 0.132399
519519 13.2555 0.581854
520520 −13.2089 −0.579249
521521 36.0695 1.58024 0.790118 0.612955i 0.210019π-0.210019\pi
0.790118 + 0.612955i 0.210019π0.210019\pi
522522 −1.18141 −0.0517090
523523 −28.4282 −1.24308 −0.621539 0.783383i 0.713492π-0.713492\pi
−0.621539 + 0.783383i 0.713492π0.713492\pi
524524 22.1186 0.966257
525525 2.55875 0.111673
526526 7.22171 0.314881
527527 −0.353841 −0.0154136
528528 1.52164 0.0662209
529529 −14.5284 −0.631669
530530 3.99050 0.173336
531531 3.76985 0.163598
532532 0 0
533533 −14.8544 −0.643414
534534 −25.7785 −1.11554
535535 0.194760 0.00842022
536536 5.56717 0.240465
537537 14.6492 0.632158
538538 −31.8344 −1.37248
539539 6.78395 0.292205
540540 −16.4589 −0.708278
541541 −13.5875 −0.584173 −0.292086 0.956392i 0.594350π-0.594350\pi
−0.292086 + 0.956392i 0.594350π0.594350\pi
542542 −31.2403 −1.34189
543543 −27.1017 −1.16305
544544 0.188812 0.00809526
545545 −11.2015 −0.479818
546546 3.18245 0.136196
547547 21.3894 0.914544 0.457272 0.889327i 0.348827π-0.348827\pi
0.457272 + 0.889327i 0.348827π0.348827\pi
548548 3.98966 0.170430
549549 7.50763 0.320418
550550 −3.61774 −0.154261
551551 0 0
552552 −4.42889 −0.188506
553553 −2.57756 −0.109609
554554 12.3578 0.525031
555555 −28.9588 −1.22923
556556 1.48693 0.0630598
557557 −21.3938 −0.906484 −0.453242 0.891387i 0.649733π-0.649733\pi
−0.453242 + 0.891387i 0.649733π0.649733\pi
558558 1.28298 0.0543130
559559 −48.1617 −2.03702
560560 1.36451 0.0576609
561561 0.287304 0.0121300
562562 −6.73851 −0.284247
563563 20.1053 0.847337 0.423669 0.905817i 0.360742π-0.360742\pi
0.423669 + 0.905817i 0.360742π0.360742\pi
564564 6.13139 0.258178
565565 0.0521705 0.00219483
566566 3.67917 0.154647
567567 3.01082 0.126443
568568 3.98279 0.167114
569569 −12.2391 −0.513089 −0.256544 0.966532i 0.582584π-0.582584\pi
−0.256544 + 0.966532i 0.582584π0.582584\pi
570570 0 0
571571 −8.38225 −0.350786 −0.175393 0.984498i 0.556120π-0.556120\pi
−0.175393 + 0.984498i 0.556120π0.556120\pi
572572 −4.49956 −0.188136
573573 −38.4561 −1.60653
574574 1.53449 0.0640482
575575 10.5298 0.439124
576576 −0.684609 −0.0285254
577577 20.3140 0.845683 0.422841 0.906204i 0.361033π-0.361033\pi
0.422841 + 0.906204i 0.361033π0.361033\pi
578578 −16.9643 −0.705624
579579 −25.4678 −1.05841
580580 −5.06589 −0.210350
581581 5.97123 0.247728
582582 18.4857 0.766257
583583 1.35935 0.0562985
584584 10.9027 0.451158
585585 9.04294 0.373880
586586 2.79512 0.115465
587587 −6.13299 −0.253136 −0.126568 0.991958i 0.540396π-0.540396\pi
−0.126568 + 0.991958i 0.540396π0.540396\pi
588588 10.3227 0.425702
589589 0 0
590590 16.1651 0.665507
591591 −12.9724 −0.533614
592592 −6.48294 −0.266447
593593 43.8711 1.80157 0.900785 0.434266i 0.142992π-0.142992\pi
0.900785 + 0.434266i 0.142992π0.142992\pi
594594 −5.60665 −0.230044
595595 0.257636 0.0105620
596596 8.10477 0.331984
597597 −33.0754 −1.35369
598598 13.0964 0.535553
599599 36.7077 1.49984 0.749919 0.661530i 0.230093π-0.230093\pi
0.749919 + 0.661530i 0.230093π0.230093\pi
600600 −5.50491 −0.224737
601601 25.0723 1.02272 0.511361 0.859366i 0.329142π-0.329142\pi
0.511361 + 0.859366i 0.329142π0.329142\pi
602602 4.97520 0.202774
603603 −3.81134 −0.155210
604604 −16.0446 −0.652846
605605 −2.93560 −0.119349
606606 −13.5551 −0.550638
607607 11.3520 0.460765 0.230382 0.973100i 0.426002π-0.426002\pi
0.230382 + 0.973100i 0.426002π0.426002\pi
608608 0 0
609609 1.22053 0.0494585
610610 32.1927 1.30344
611611 −18.1308 −0.733493
612612 −0.129263 −0.00522513
613613 −19.4685 −0.786325 −0.393162 0.919469i 0.628619π-0.628619\pi
−0.393162 + 0.919469i 0.628619π0.628619\pi
614614 11.8371 0.477708
615615 −14.7466 −0.594642
616616 0.464814 0.0187279
617617 −25.2893 −1.01811 −0.509055 0.860734i 0.670005π-0.670005\pi
−0.509055 + 0.860734i 0.670005π0.670005\pi
618618 −2.65786 −0.106915
619619 11.1209 0.446986 0.223493 0.974705i 0.428254π-0.428254\pi
0.223493 + 0.974705i 0.428254π0.428254\pi
620620 5.50142 0.220942
621621 16.3187 0.654849
622622 15.9983 0.641473
623623 −7.87452 −0.315486
624624 −6.84672 −0.274088
625625 −30.0007 −1.20003
626626 −17.4536 −0.697588
627627 0 0
628628 18.1493 0.724234
629629 −1.22406 −0.0488064
630630 −0.934154 −0.0372176
631631 32.3028 1.28596 0.642978 0.765885i 0.277699π-0.277699\pi
0.642978 + 0.765885i 0.277699π0.277699\pi
632632 5.54536 0.220583
633633 −13.4277 −0.533703
634634 −22.7519 −0.903591
635635 −22.5756 −0.895885
636636 2.06844 0.0820190
637637 −30.5248 −1.20944
638638 −1.72567 −0.0683201
639639 −2.72665 −0.107865
640640 −2.93560 −0.116040
641641 −38.5887 −1.52416 −0.762080 0.647483i 0.775822π-0.775822\pi
−0.762080 + 0.647483i 0.775822π0.775822\pi
642642 0.100952 0.00398426
643643 −41.6452 −1.64233 −0.821163 0.570693i 0.806675π-0.806675\pi
−0.821163 + 0.570693i 0.806675π0.806675\pi
644644 −1.35289 −0.0533113
645645 −47.8124 −1.88261
646646 0 0
647647 11.2852 0.443667 0.221834 0.975085i 0.428796π-0.428796\pi
0.221834 + 0.975085i 0.428796π0.428796\pi
648648 −6.47748 −0.254460
649649 5.50657 0.216152
650650 16.2783 0.638486
651651 −1.32547 −0.0519492
652652 21.3870 0.837579
653653 6.98352 0.273286 0.136643 0.990620i 0.456369π-0.456369\pi
0.136643 + 0.990620i 0.456369π0.456369\pi
654654 −5.80618 −0.227039
655655 −64.9315 −2.53708
656656 −3.30129 −0.128894
657657 −7.46410 −0.291202
658658 1.87295 0.0730151
659659 −34.6339 −1.34915 −0.674573 0.738208i 0.735672π-0.735672\pi
−0.674573 + 0.738208i 0.735672π0.735672\pi
660660 −4.46693 −0.173875
661661 −4.29030 −0.166873 −0.0834367 0.996513i 0.526590π-0.526590\pi
−0.0834367 + 0.996513i 0.526590π0.526590\pi
662662 −9.94526 −0.386533
663663 −1.29274 −0.0502060
664664 −12.8465 −0.498541
665665 0 0
666666 4.43828 0.171980
667667 5.02276 0.194482
668668 11.0690 0.428274
669669 −9.74657 −0.376824
670670 −16.3430 −0.631384
671671 10.9663 0.423349
672672 0.707279 0.0272839
673673 45.7513 1.76358 0.881792 0.471638i 0.156337π-0.156337\pi
0.881792 + 0.471638i 0.156337π0.156337\pi
674674 −27.0670 −1.04258
675675 20.2834 0.780709
676676 7.24605 0.278694
677677 6.11715 0.235101 0.117551 0.993067i 0.462496π-0.462496\pi
0.117551 + 0.993067i 0.462496π0.462496\pi
678678 0.0270421 0.00103854
679679 5.64680 0.216704
680680 −0.554277 −0.0212556
681681 21.1241 0.809476
682682 1.87404 0.0717606
683683 8.43385 0.322712 0.161356 0.986896i 0.448413π-0.448413\pi
0.161356 + 0.986896i 0.448413π0.448413\pi
684684 0 0
685685 −11.7120 −0.447494
686686 6.40697 0.244619
687687 9.71859 0.370787
688688 −10.7036 −0.408072
689689 −6.11647 −0.233019
690690 13.0015 0.494957
691691 0.287350 0.0109313 0.00546566 0.999985i 0.498260π-0.498260\pi
0.00546566 + 0.999985i 0.498260π0.498260\pi
692692 −8.71135 −0.331156
693693 −0.318216 −0.0120880
694694 19.4414 0.737985
695695 −4.36503 −0.165575
696696 −2.62586 −0.0995328
697697 −0.623324 −0.0236101
698698 22.6056 0.855635
699699 7.90578 0.299024
700700 −1.68158 −0.0635576
701701 −2.87902 −0.108739 −0.0543696 0.998521i 0.517315π-0.517315\pi
−0.0543696 + 0.998521i 0.517315π0.517315\pi
702702 25.2275 0.952150
703703 0 0
704704 −1.00000 −0.0376889
705705 −17.9993 −0.677893
706706 24.0961 0.906870
707707 −4.14065 −0.155725
708708 8.37903 0.314903
709709 −37.7391 −1.41732 −0.708662 0.705548i 0.750701π-0.750701\pi
−0.708662 + 0.705548i 0.750701π0.750701\pi
710710 −11.6919 −0.438788
711711 −3.79640 −0.142376
712712 16.9412 0.634900
713713 −5.45458 −0.204276
714714 0.133543 0.00499772
715715 13.2089 0.493985
716716 −9.62721 −0.359786
717717 12.4903 0.466459
718718 25.6187 0.956082
719719 44.2686 1.65094 0.825469 0.564447i 0.190911π-0.190911\pi
0.825469 + 0.564447i 0.190911π0.190911\pi
720720 2.00974 0.0748985
721721 −0.811892 −0.0302364
722722 0 0
723723 27.2340 1.01284
724724 17.8108 0.661935
725725 6.24305 0.231861
726726 −1.52164 −0.0564734
727727 −10.9177 −0.404917 −0.202458 0.979291i 0.564893π-0.564893\pi
−0.202458 + 0.979291i 0.564893π0.564893\pi
728728 −2.09146 −0.0775146
729729 30.0285 1.11217
730730 −32.0060 −1.18460
731731 −2.02098 −0.0747486
732732 16.6868 0.616761
733733 35.3266 1.30482 0.652409 0.757867i 0.273758π-0.273758\pi
0.652409 + 0.757867i 0.273758π0.273758\pi
734734 −1.01974 −0.0376393
735735 −30.3034 −1.11776
736736 2.91060 0.107286
737737 −5.56717 −0.205069
738738 2.26010 0.0831952
739739 1.14794 0.0422276 0.0211138 0.999777i 0.493279π-0.493279\pi
0.0211138 + 0.999777i 0.493279π0.493279\pi
740740 19.0313 0.699605
741741 0 0
742742 0.631844 0.0231957
743743 10.9608 0.402114 0.201057 0.979580i 0.435562π-0.435562\pi
0.201057 + 0.979580i 0.435562π0.435562\pi
744744 2.85161 0.104545
745745 −23.7924 −0.871685
746746 −31.7363 −1.16195
747747 8.79484 0.321786
748748 −0.188812 −0.00690366
749749 0.0308377 0.00112679
750750 −6.17444 −0.225459
751751 20.6039 0.751847 0.375923 0.926651i 0.377326π-0.377326\pi
0.375923 + 0.926651i 0.377326π0.377326\pi
752752 −4.02946 −0.146939
753753 −18.1796 −0.662502
754754 7.76478 0.282777
755755 47.1006 1.71417
756756 −2.60605 −0.0947810
757757 34.2368 1.24436 0.622178 0.782875i 0.286248π-0.286248\pi
0.622178 + 0.782875i 0.286248π0.286248\pi
758758 −19.0665 −0.692527
759759 4.42889 0.160759
760760 0 0
761761 −43.6051 −1.58069 −0.790343 0.612665i 0.790097π-0.790097\pi
−0.790343 + 0.612665i 0.790097π0.790097\pi
762762 −11.7018 −0.423913
763763 −1.77360 −0.0642088
764764 25.2728 0.914338
765765 0.379463 0.0137195
766766 −18.1444 −0.655585
767767 −24.7772 −0.894652
768768 −1.52164 −0.0549075
769769 36.4963 1.31609 0.658045 0.752979i 0.271384π-0.271384\pi
0.658045 + 0.752979i 0.271384π0.271384\pi
770770 −1.36451 −0.0491734
771771 −6.19836 −0.223228
772772 16.7371 0.602381
773773 46.1555 1.66010 0.830049 0.557690i 0.188312π-0.188312\pi
0.830049 + 0.557690i 0.188312π0.188312\pi
774774 7.32781 0.263393
775775 −6.77978 −0.243537
776776 −12.1485 −0.436107
777777 −4.58525 −0.164495
778778 3.88312 0.139217
779779 0 0
780780 20.0992 0.719667
781781 −3.98279 −0.142515
782782 0.549558 0.0196522
783783 9.67526 0.345765
784784 −6.78395 −0.242284
785785 −53.2789 −1.90161
786786 −33.6566 −1.20049
787787 29.8430 1.06379 0.531893 0.846811i 0.321481π-0.321481\pi
0.531893 + 0.846811i 0.321481π0.321481\pi
788788 8.52528 0.303700
789789 −10.9888 −0.391213
790790 −16.2790 −0.579179
791791 0.00826051 0.000293710 0
792792 0.684609 0.0243265
793793 −49.3436 −1.75224
794794 17.8589 0.633787
795795 −6.07211 −0.215356
796796 21.7367 0.770435
797797 −26.9999 −0.956386 −0.478193 0.878255i 0.658708π-0.658708\pi
−0.478193 + 0.878255i 0.658708π0.658708\pi
798798 0 0
799799 −0.760811 −0.0269156
800800 3.61774 0.127907
801801 −11.5981 −0.409800
802802 33.5041 1.18307
803803 −10.9027 −0.384749
804804 −8.47123 −0.298757
805805 3.97154 0.139978
806806 −8.43234 −0.297017
807807 48.4405 1.70519
808808 8.90820 0.313390
809809 41.6163 1.46315 0.731575 0.681761i 0.238786π-0.238786\pi
0.731575 + 0.681761i 0.238786π0.238786\pi
810810 19.0153 0.668129
811811 17.0281 0.597937 0.298968 0.954263i 0.403357π-0.403357\pi
0.298968 + 0.954263i 0.403357π0.403357\pi
812812 −0.802117 −0.0281488
813813 47.5365 1.66718
814814 6.48294 0.227227
815815 −62.7836 −2.19921
816816 −0.287304 −0.0100577
817817 0 0
818818 26.3286 0.920556
819819 1.43183 0.0500322
820820 9.69127 0.338434
821821 24.8643 0.867771 0.433885 0.900968i 0.357142π-0.357142\pi
0.433885 + 0.900968i 0.357142π0.357142\pi
822822 −6.07083 −0.211745
823823 38.2993 1.33503 0.667514 0.744597i 0.267358π-0.267358\pi
0.667514 + 0.744597i 0.267358π0.267358\pi
824824 1.74670 0.0608493
825825 5.50491 0.191656
826826 2.55953 0.0890575
827827 −4.14004 −0.143963 −0.0719816 0.997406i 0.522932π-0.522932\pi
−0.0719816 + 0.997406i 0.522932π0.522932\pi
828828 −1.99263 −0.0692486
829829 −22.6282 −0.785909 −0.392955 0.919558i 0.628547π-0.628547\pi
−0.392955 + 0.919558i 0.628547π0.628547\pi
830830 37.7122 1.30901
831831 −18.8041 −0.652306
832832 4.49956 0.155994
833833 −1.28089 −0.0443803
834834 −2.26257 −0.0783464
835835 −32.4943 −1.12451
836836 0 0
837837 −10.5071 −0.363178
838838 −32.1866 −1.11187
839839 −15.4313 −0.532746 −0.266373 0.963870i 0.585825π-0.585825\pi
−0.266373 + 0.963870i 0.585825π0.585825\pi
840840 −2.07629 −0.0716388
841841 −26.0220 −0.897312
842842 20.0204 0.689948
843843 10.2536 0.353152
844844 8.82448 0.303751
845845 −21.2715 −0.731762
846846 2.75860 0.0948428
847847 −0.464814 −0.0159712
848848 −1.35935 −0.0466802
849849 −5.59838 −0.192136
850850 0.683074 0.0234293
851851 −18.8693 −0.646830
852852 −6.06037 −0.207625
853853 −34.6022 −1.18476 −0.592379 0.805659i 0.701811π-0.701811\pi
−0.592379 + 0.805659i 0.701811π0.701811\pi
854854 5.09729 0.174426
855855 0 0
856856 −0.0663443 −0.00226760
857857 47.4450 1.62069 0.810345 0.585953i 0.199280π-0.199280\pi
0.810345 + 0.585953i 0.199280π0.199280\pi
858858 6.84672 0.233743
859859 41.6905 1.42246 0.711230 0.702959i 0.248138π-0.248138\pi
0.711230 + 0.702959i 0.248138π0.248138\pi
860860 31.4216 1.07147
861861 −2.33494 −0.0795744
862862 29.2413 0.995963
863863 −39.0792 −1.33027 −0.665136 0.746722i 0.731626π-0.731626\pi
−0.665136 + 0.746722i 0.731626π0.731626\pi
864864 5.60665 0.190742
865865 25.5730 0.869509
866866 21.8706 0.743192
867867 25.8136 0.876677
868868 0.871078 0.0295663
869869 −5.54536 −0.188113
870870 7.70846 0.261341
871871 25.0498 0.848781
872872 3.81573 0.129217
873873 8.31700 0.281488
874874 0 0
875875 −1.88610 −0.0637618
876876 −16.5900 −0.560525
877877 5.61044 0.189451 0.0947255 0.995503i 0.469803π-0.469803\pi
0.0947255 + 0.995503i 0.469803π0.469803\pi
878878 25.8255 0.871567
879879 −4.25317 −0.143456
880880 2.93560 0.0989590
881881 14.5597 0.490530 0.245265 0.969456i 0.421125π-0.421125\pi
0.245265 + 0.969456i 0.421125π0.421125\pi
882882 4.64435 0.156384
883883 0.760531 0.0255939 0.0127969 0.999918i 0.495926π-0.495926\pi
0.0127969 + 0.999918i 0.495926π0.495926\pi
884884 0.849573 0.0285742
885885 −24.5975 −0.826835
886886 7.15530 0.240387
887887 37.0738 1.24482 0.622409 0.782692i 0.286154π-0.286154\pi
0.622409 + 0.782692i 0.286154π0.286154\pi
888888 9.86470 0.331038
889889 −3.57455 −0.119886
890890 −49.7327 −1.66704
891891 6.47748 0.217004
892892 6.40530 0.214465
893893 0 0
894894 −12.3326 −0.412462
895895 28.2616 0.944682
896896 −0.464814 −0.0155283
897897 −19.9281 −0.665379
898898 14.0318 0.468248
899899 −3.23398 −0.107859
900900 −2.47674 −0.0825580
901901 −0.256662 −0.00855064
902902 3.30129 0.109921
903903 −7.57046 −0.251929
904904 −0.0177717 −0.000591077 0
905905 −52.2855 −1.73803
906906 24.4141 0.811106
907907 −16.2729 −0.540333 −0.270166 0.962814i 0.587079π-0.587079\pi
−0.270166 + 0.962814i 0.587079π0.587079\pi
908908 −13.8824 −0.460705
909909 −6.09864 −0.202279
910910 6.13968 0.203528
911911 −17.9183 −0.593659 −0.296830 0.954930i 0.595929π-0.595929\pi
−0.296830 + 0.954930i 0.595929π0.595929\pi
912912 0 0
913913 12.8465 0.425157
914914 −31.3113 −1.03568
915915 −48.9857 −1.61942
916916 −6.38691 −0.211030
917917 −10.2810 −0.339510
918918 1.05860 0.0349392
919919 −34.5775 −1.14061 −0.570303 0.821435i 0.693174π-0.693174\pi
−0.570303 + 0.821435i 0.693174π0.693174\pi
920920 −8.54437 −0.281699
921921 −18.0119 −0.593511
922922 12.2299 0.402770
923923 17.9208 0.589870
924924 −0.707279 −0.0232678
925925 −23.4536 −0.771150
926926 −23.2772 −0.764937
927927 −1.19581 −0.0392756
928928 1.72567 0.0566480
929929 −19.0657 −0.625524 −0.312762 0.949831i 0.601254π-0.601254\pi
−0.312762 + 0.949831i 0.601254π0.601254\pi
930930 −8.37119 −0.274502
931931 0 0
932932 −5.19556 −0.170186
933933 −24.3437 −0.796976
934934 17.2913 0.565789
935935 0.554277 0.0181268
936936 −3.08044 −0.100687
937937 −49.0690 −1.60301 −0.801507 0.597985i 0.795968π-0.795968\pi
−0.801507 + 0.597985i 0.795968π0.795968\pi
938938 −2.58770 −0.0844913
939939 26.5582 0.866694
940940 11.8289 0.385815
941941 26.1208 0.851512 0.425756 0.904838i 0.360008π-0.360008\pi
0.425756 + 0.904838i 0.360008π0.360008\pi
942942 −27.6166 −0.899799
943943 −9.60875 −0.312904
944944 −5.50657 −0.179224
945945 7.65031 0.248865
946946 10.7036 0.348005
947947 16.5343 0.537294 0.268647 0.963239i 0.413424π-0.413424\pi
0.268647 + 0.963239i 0.413424π0.413424\pi
948948 −8.43804 −0.274055
949949 49.0574 1.59247
950950 0 0
951951 34.6201 1.12264
952952 −0.0877625 −0.00284440
953953 −14.5445 −0.471142 −0.235571 0.971857i 0.575696π-0.575696\pi
−0.235571 + 0.971857i 0.575696π0.575696\pi
954954 0.930623 0.0301300
955955 −74.1908 −2.40076
956956 −8.20845 −0.265480
957957 2.62586 0.0848819
958958 −13.2757 −0.428919
959959 −1.85445 −0.0598833
960960 4.46693 0.144169
961961 −27.4880 −0.886709
962962 −29.1704 −0.940491
963963 0.0454199 0.00146364
964964 −17.8978 −0.576448
965965 −49.1334 −1.58166
966966 2.05861 0.0662347
967967 −17.1147 −0.550371 −0.275186 0.961391i 0.588739π-0.588739\pi
−0.275186 + 0.961391i 0.588739π0.588739\pi
968968 1.00000 0.0321412
969969 0 0
970970 35.6632 1.14508
971971 −17.0715 −0.547850 −0.273925 0.961751i 0.588322π-0.588322\pi
−0.273925 + 0.961751i 0.588322π0.588322\pi
972972 −6.96355 −0.223356
973973 −0.691145 −0.0221571
974974 −27.2081 −0.871805
975975 −24.7697 −0.793264
976976 −10.9663 −0.351023
977977 21.8610 0.699396 0.349698 0.936862i 0.386284π-0.386284\pi
0.349698 + 0.936862i 0.386284π0.386284\pi
978978 −32.5433 −1.04062
979979 −16.9412 −0.541444
980980 19.9150 0.636160
981981 −2.61229 −0.0834039
982982 35.5134 1.13328
983983 29.5680 0.943072 0.471536 0.881847i 0.343700π-0.343700\pi
0.471536 + 0.881847i 0.343700π0.343700\pi
984984 5.02338 0.160140
985985 −25.0268 −0.797420
986986 0.325829 0.0103765
987987 −2.84995 −0.0907150
988988 0 0
989989 −31.1541 −0.990641
990990 −2.00974 −0.0638737
991991 −33.6392 −1.06858 −0.534292 0.845300i 0.679422π-0.679422\pi
−0.534292 + 0.845300i 0.679422π0.679422\pi
992992 −1.87404 −0.0595007
993993 15.1331 0.480235
994994 −1.85125 −0.0587182
995995 −63.8101 −2.02292
996996 19.5478 0.619395
997997 50.8390 1.61009 0.805043 0.593216i 0.202142π-0.202142\pi
0.805043 + 0.593216i 0.202142π0.202142\pi
998998 −9.33762 −0.295577
999999 −36.3476 −1.14999
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 7942.2.a.ca.1.5 15
19.6 even 9 418.2.j.d.397.2 yes 30
19.16 even 9 418.2.j.d.199.2 30
19.18 odd 2 7942.2.a.by.1.11 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.j.d.199.2 30 19.16 even 9
418.2.j.d.397.2 yes 30 19.6 even 9
7942.2.a.by.1.11 15 19.18 odd 2
7942.2.a.ca.1.5 15 1.1 even 1 trivial