Properties

Label 585.2.j.g.406.3
Level 585585
Weight 22
Character 585.406
Analytic conductor 4.6714.671
Analytic rank 00
Dimension 66
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [585,2,Mod(406,585)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(585, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("585.406");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 585=32513 585 = 3^{2} \cdot 5 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 585.j (of order 33, degree 22, 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: 4.671248518244.67124851824
Analytic rank: 00
Dimension: 66
Relative dimension: 33 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: 6.0.591408.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x6x5+4x4+x3+10x23x+1 x^{6} - x^{5} + 4x^{4} + x^{3} + 10x^{2} - 3x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 195)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 406.3
Root 0.1555540.269427i0.155554 - 0.269427i of defining polynomial
Character χ\chi == 585.406
Dual form 585.2.j.g.451.3

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+(1.10716+1.91766i)q2+(1.45161+2.51426i)q4+1.00000q5+(1.918273.32254i)q72.00000q8+(1.10716+1.91766i)q10+(2.90321+5.02851i)q11+(0.5333383.56589i)q13+8.49532q14+(0.688892+1.19320i)q16+(1.79605+3.11085i)q17+(1.07382+1.85991i)q19+(1.45161+2.51426i)q20+(6.42864+11.1347i)q22+(3.117535.39972i)q23+1.00000q25+(7.428642.92525i)q26+(5.56914+9.64603i)q28+(1.03334+1.78979i)q295.28100q31+(3.52543+6.10622i)q327.95407q34+(1.918273.32254i)q35+(2.37778+4.11844i)q374.75557q382.00000q40+(5.558779.62806i)q41+(4.747668.22318i)q4316.8573q44+(6.9032111.9567i)q462.21432q47+(3.859506.68485i)q49+(1.10716+1.91766i)q50+(8.19135+6.51721i)q52+0.815792q53+(2.90321+5.02851i)q55+(3.83654+6.64507i)q56+(2.28814+3.96318i)q58+(4.98741+8.63844i)q59+(2.64050+4.57348i)q61+(5.8469110.1271i)q6212.8573q64+(0.5333383.56589i)q65+(1.77777+3.07919i)q67+(5.214329.03147i)q68+8.49532q70+(2.869874.97077i)q712.78568q73+(5.26517+9.11955i)q74+(3.117535.39972i)q76+22.2766q77+12.3319q79+(0.688892+1.19320i)q80+(12.308921.3196i)q820.622216q83+(1.79605+3.11085i)q85+21.0257q86+(5.8064210.0570i)q88+(8.0841914.0022i)q89+(10.82478.61236i)q91+18.1017q92+(2.451614.24631i)q94+(1.07382+1.85991i)q95+(2.12544+3.68137i)q97+(8.5461714.8024i)q98+O(q100)q+(1.10716 + 1.91766i) q^{2} +(-1.45161 + 2.51426i) q^{4} +1.00000 q^{5} +(1.91827 - 3.32254i) q^{7} -2.00000 q^{8} +(1.10716 + 1.91766i) q^{10} +(2.90321 + 5.02851i) q^{11} +(0.533338 - 3.56589i) q^{13} +8.49532 q^{14} +(0.688892 + 1.19320i) q^{16} +(-1.79605 + 3.11085i) q^{17} +(-1.07382 + 1.85991i) q^{19} +(-1.45161 + 2.51426i) q^{20} +(-6.42864 + 11.1347i) q^{22} +(-3.11753 - 5.39972i) q^{23} +1.00000 q^{25} +(7.42864 - 2.92525i) q^{26} +(5.56914 + 9.64603i) q^{28} +(1.03334 + 1.78979i) q^{29} -5.28100 q^{31} +(-3.52543 + 6.10622i) q^{32} -7.95407 q^{34} +(1.91827 - 3.32254i) q^{35} +(2.37778 + 4.11844i) q^{37} -4.75557 q^{38} -2.00000 q^{40} +(-5.55877 - 9.62806i) q^{41} +(4.74766 - 8.22318i) q^{43} -16.8573 q^{44} +(6.90321 - 11.9567i) q^{46} -2.21432 q^{47} +(-3.85950 - 6.68485i) q^{49} +(1.10716 + 1.91766i) q^{50} +(8.19135 + 6.51721i) q^{52} +0.815792 q^{53} +(2.90321 + 5.02851i) q^{55} +(-3.83654 + 6.64507i) q^{56} +(-2.28814 + 3.96318i) q^{58} +(-4.98741 + 8.63844i) q^{59} +(-2.64050 + 4.57348i) q^{61} +(-5.84691 - 10.1271i) q^{62} -12.8573 q^{64} +(0.533338 - 3.56589i) q^{65} +(1.77777 + 3.07919i) q^{67} +(-5.21432 - 9.03147i) q^{68} +8.49532 q^{70} +(2.86987 - 4.97077i) q^{71} -2.78568 q^{73} +(-5.26517 + 9.11955i) q^{74} +(-3.11753 - 5.39972i) q^{76} +22.2766 q^{77} +12.3319 q^{79} +(0.688892 + 1.19320i) q^{80} +(12.3089 - 21.3196i) q^{82} -0.622216 q^{83} +(-1.79605 + 3.11085i) q^{85} +21.0257 q^{86} +(-5.80642 - 10.0570i) q^{88} +(-8.08419 - 14.0022i) q^{89} +(-10.8247 - 8.61236i) q^{91} +18.1017 q^{92} +(-2.45161 - 4.24631i) q^{94} +(-1.07382 + 1.85991i) q^{95} +(-2.12544 + 3.68137i) q^{97} +(8.54617 - 14.8024i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q2q4+6q5+5q712q8+4q11+3q13+24q14+4q164q172q2012q22+8q23+6q25+18q26+6q2918q318q328q34+2q98+O(q100) 6 q - 2 q^{4} + 6 q^{5} + 5 q^{7} - 12 q^{8} + 4 q^{11} + 3 q^{13} + 24 q^{14} + 4 q^{16} - 4 q^{17} - 2 q^{20} - 12 q^{22} + 8 q^{23} + 6 q^{25} + 18 q^{26} + 6 q^{29} - 18 q^{31} - 8 q^{32} - 8 q^{34}+ \cdots - 2 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/585Z)×\left(\mathbb{Z}/585\mathbb{Z}\right)^\times.

nn 326326 352352 496496
χ(n)\chi(n) 11 11 e(13)e\left(\frac{1}{3}\right)

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 1.10716 + 1.91766i 0.782880 + 1.35599i 0.930257 + 0.366908i 0.119584π0.119584\pi
−0.147377 + 0.989080i 0.547083π0.547083\pi
33 0 0
44 −1.45161 + 2.51426i −0.725803 + 1.25713i
55 1.00000 0.447214
66 0 0
77 1.91827 3.32254i 0.725037 1.25580i −0.233922 0.972255i 0.575156π-0.575156\pi
0.958959 0.283546i 0.0915107π-0.0915107\pi
88 −2.00000 −0.707107
99 0 0
1010 1.10716 + 1.91766i 0.350115 + 0.606416i
1111 2.90321 + 5.02851i 0.875351 + 1.51615i 0.856388 + 0.516333i 0.172703π0.172703\pi
0.0189633 + 0.999820i 0.493963π0.493963\pi
1212 0 0
1313 0.533338 3.56589i 0.147921 0.988999i
1414 8.49532 2.27047
1515 0 0
1616 0.688892 + 1.19320i 0.172223 + 0.298299i
1717 −1.79605 + 3.11085i −0.435607 + 0.754493i −0.997345 0.0728222i 0.976799π-0.976799\pi
0.561738 + 0.827315i 0.310133π0.310133\pi
1818 0 0
1919 −1.07382 + 1.85991i −0.246352 + 0.426693i −0.962511 0.271244i 0.912565π-0.912565\pi
0.716159 + 0.697937i 0.245898π0.245898\pi
2020 −1.45161 + 2.51426i −0.324589 + 0.562205i
2121 0 0
2222 −6.42864 + 11.1347i −1.37059 + 2.37393i
2323 −3.11753 5.39972i −0.650050 1.12592i −0.983110 0.183014i 0.941414π-0.941414\pi
0.333060 0.942906i 0.391919π-0.391919\pi
2424 0 0
2525 1.00000 0.200000
2626 7.42864 2.92525i 1.45688 0.573688i
2727 0 0
2828 5.56914 + 9.64603i 1.05247 + 1.82293i
2929 1.03334 + 1.78979i 0.191886 + 0.332356i 0.945875 0.324530i 0.105206π-0.105206\pi
−0.753989 + 0.656887i 0.771873π0.771873\pi
3030 0 0
3131 −5.28100 −0.948495 −0.474247 0.880392i 0.657280π-0.657280\pi
−0.474247 + 0.880392i 0.657280π0.657280\pi
3232 −3.52543 + 6.10622i −0.623213 + 1.07944i
3333 0 0
3434 −7.95407 −1.36411
3535 1.91827 3.32254i 0.324246 0.561611i
3636 0 0
3737 2.37778 + 4.11844i 0.390905 + 0.677068i 0.992569 0.121681i 0.0388286π-0.0388286\pi
−0.601664 + 0.798749i 0.705495π0.705495\pi
3838 −4.75557 −0.771455
3939 0 0
4040 −2.00000 −0.316228
4141 −5.55877 9.62806i −0.868133 1.50365i −0.863902 0.503660i 0.831986π-0.831986\pi
−0.00423144 0.999991i 0.501347π-0.501347\pi
4242 0 0
4343 4.74766 8.22318i 0.724011 1.25402i −0.235369 0.971906i 0.575630π-0.575630\pi
0.959380 0.282118i 0.0910369π-0.0910369\pi
4444 −16.8573 −2.54133
4545 0 0
4646 6.90321 11.9567i 1.01782 1.76292i
4747 −2.21432 −0.322992 −0.161496 0.986873i 0.551632π-0.551632\pi
−0.161496 + 0.986873i 0.551632π0.551632\pi
4848 0 0
4949 −3.85950 6.68485i −0.551357 0.954979i
5050 1.10716 + 1.91766i 0.156576 + 0.271198i
5151 0 0
5252 8.19135 + 6.51721i 1.13594 + 0.903775i
5353 0.815792 0.112058 0.0560288 0.998429i 0.482156π-0.482156\pi
0.0560288 + 0.998429i 0.482156π0.482156\pi
5454 0 0
5555 2.90321 + 5.02851i 0.391469 + 0.678044i
5656 −3.83654 + 6.64507i −0.512679 + 0.887985i
5757 0 0
5858 −2.28814 + 3.96318i −0.300448 + 0.520391i
5959 −4.98741 + 8.63844i −0.649305 + 1.12463i 0.333984 + 0.942579i 0.391607π0.391607\pi
−0.983289 + 0.182050i 0.941727π0.941727\pi
6060 0 0
6161 −2.64050 + 4.57348i −0.338081 + 0.585574i −0.984072 0.177772i 0.943111π-0.943111\pi
0.645991 + 0.763345i 0.276445π0.276445\pi
6262 −5.84691 10.1271i −0.742558 1.28615i
6363 0 0
6464 −12.8573 −1.60716
6565 0.533338 3.56589i 0.0661525 0.442294i
6666 0 0
6767 1.77777 + 3.07919i 0.217189 + 0.376183i 0.953948 0.299973i 0.0969778π-0.0969778\pi
−0.736758 + 0.676156i 0.763645π0.763645\pi
6868 −5.21432 9.03147i −0.632329 1.09523i
6969 0 0
7070 8.49532 1.01538
7171 2.86987 4.97077i 0.340591 0.589922i −0.643951 0.765066i 0.722706π-0.722706\pi
0.984543 + 0.175145i 0.0560394π0.0560394\pi
7272 0 0
7373 −2.78568 −0.326039 −0.163020 0.986623i 0.552123π-0.552123\pi
−0.163020 + 0.986623i 0.552123π0.552123\pi
7474 −5.26517 + 9.11955i −0.612064 + 1.06013i
7575 0 0
7676 −3.11753 5.39972i −0.357605 0.619391i
7777 22.2766 2.53865
7878 0 0
7979 12.3319 1.38744 0.693721 0.720244i 0.255970π-0.255970\pi
0.693721 + 0.720244i 0.255970π0.255970\pi
8080 0.688892 + 1.19320i 0.0770205 + 0.133403i
8181 0 0
8282 12.3089 21.3196i 1.35929 2.35436i
8383 −0.622216 −0.0682970 −0.0341485 0.999417i 0.510872π-0.510872\pi
−0.0341485 + 0.999417i 0.510872π0.510872\pi
8484 0 0
8585 −1.79605 + 3.11085i −0.194809 + 0.337419i
8686 21.0257 2.26726
8787 0 0
8888 −5.80642 10.0570i −0.618967 1.07208i
8989 −8.08419 14.0022i −0.856923 1.48423i −0.874850 0.484395i 0.839040π-0.839040\pi
0.0179269 0.999839i 0.494293π-0.494293\pi
9090 0 0
9191 −10.8247 8.61236i −1.13474 0.902821i
9292 18.1017 1.88723
9393 0 0
9494 −2.45161 4.24631i −0.252864 0.437973i
9595 −1.07382 + 1.85991i −0.110172 + 0.190823i
9696 0 0
9797 −2.12544 + 3.68137i −0.215806 + 0.373787i −0.953522 0.301325i 0.902571π-0.902571\pi
0.737716 + 0.675112i 0.235905π0.235905\pi
9898 8.54617 14.8024i 0.863294 1.49527i
9999 0 0
100100 −1.45161 + 2.51426i −0.145161 + 0.251426i
101101 −1.11753 1.93562i −0.111199 0.192602i 0.805055 0.593200i 0.202136π-0.202136\pi
−0.916254 + 0.400598i 0.868802π0.868802\pi
102102 0 0
103103 −2.44446 −0.240860 −0.120430 0.992722i 0.538427π-0.538427\pi
−0.120430 + 0.992722i 0.538427π0.538427\pi
104104 −1.06668 + 7.13177i −0.104596 + 0.699328i
105105 0 0
106106 0.903212 + 1.56441i 0.0877277 + 0.151949i
107107 0.826164 + 1.43096i 0.0798682 + 0.138336i 0.903193 0.429235i 0.141217π-0.141217\pi
−0.823325 + 0.567571i 0.807883π0.807883\pi
108108 0 0
109109 −2.61285 −0.250265 −0.125133 0.992140i 0.539936π-0.539936\pi
−0.125133 + 0.992140i 0.539936π0.539936\pi
110110 −6.42864 + 11.1347i −0.612947 + 1.06165i
111111 0 0
112112 5.28592 0.499472
113113 1.21432 2.10326i 0.114234 0.197858i −0.803240 0.595656i 0.796892π-0.796892\pi
0.917473 + 0.397798i 0.130225π0.130225\pi
114114 0 0
115115 −3.11753 5.39972i −0.290711 0.503527i
116116 −6.00000 −0.557086
117117 0 0
118118 −22.0874 −2.03331
119119 6.89062 + 11.9349i 0.631662 + 1.09407i
120120 0 0
121121 −11.3573 + 19.6714i −1.03248 + 1.78831i
122122 −11.6938 −1.05871
123123 0 0
124124 7.66593 13.2778i 0.688420 1.19238i
125125 1.00000 0.0894427
126126 0 0
127127 −9.62790 16.6760i −0.854338 1.47976i −0.877258 0.480020i 0.840629π-0.840629\pi
0.0229193 0.999737i 0.492704π-0.492704\pi
128128 −7.18421 12.4434i −0.635000 1.09985i
129129 0 0
130130 7.42864 2.92525i 0.651535 0.256561i
131131 −13.4128 −1.17188 −0.585942 0.810353i 0.699275π-0.699275\pi
−0.585942 + 0.810353i 0.699275π0.699275\pi
132132 0 0
133133 4.11975 + 7.13562i 0.357228 + 0.618737i
134134 −3.93655 + 6.81830i −0.340066 + 0.589012i
135135 0 0
136136 3.59210 6.22171i 0.308020 0.533507i
137137 −2.36741 + 4.10048i −0.202262 + 0.350328i −0.949257 0.314502i 0.898162π-0.898162\pi
0.746995 + 0.664830i 0.231496π0.231496\pi
138138 0 0
139139 5.52074 9.56221i 0.468263 0.811056i −0.531079 0.847322i 0.678213π-0.678213\pi
0.999342 + 0.0362665i 0.0115465π0.0115465\pi
140140 5.56914 + 9.64603i 0.470678 + 0.815238i
141141 0 0
142142 12.7096 1.06657
143143 19.4795 7.67063i 1.62896 0.641450i
144144 0 0
145145 1.03334 + 1.78979i 0.0858141 + 0.148634i
146146 −3.08419 5.34198i −0.255250 0.442105i
147147 0 0
148148 −13.8064 −1.13488
149149 −1.00000 + 1.73205i −0.0819232 + 0.141895i −0.904076 0.427372i 0.859440π-0.859440\pi
0.822153 + 0.569267i 0.192773π0.192773\pi
150150 0 0
151151 8.81135 0.717057 0.358529 0.933519i 0.383279π-0.383279\pi
0.358529 + 0.933519i 0.383279π0.383279\pi
152152 2.14764 3.71983i 0.174197 0.301718i
153153 0 0
154154 24.6637 + 42.7188i 1.98746 + 3.44238i
155155 −5.28100 −0.424180
156156 0 0
157157 −2.73975 −0.218656 −0.109328 0.994006i 0.534870π-0.534870\pi
−0.109328 + 0.994006i 0.534870π0.534870\pi
158158 13.6533 + 23.6483i 1.08620 + 1.88135i
159159 0 0
160160 −3.52543 + 6.10622i −0.278710 + 0.482739i
161161 −23.9210 −1.88524
162162 0 0
163163 12.3469 21.3855i 0.967084 1.67504i 0.263177 0.964748i 0.415230π-0.415230\pi
0.703907 0.710292i 0.251437π-0.251437\pi
164164 32.2766 2.52038
165165 0 0
166166 −0.688892 1.19320i −0.0534684 0.0926100i
167167 3.95407 + 6.84865i 0.305975 + 0.529964i 0.977478 0.211038i 0.0676843π-0.0676843\pi
−0.671503 + 0.741002i 0.734351π0.734351\pi
168168 0 0
169169 −12.4311 3.80365i −0.956239 0.292588i
170170 −7.95407 −0.610049
171171 0 0
172172 13.7835 + 23.8736i 1.05098 + 1.82035i
173173 −1.82616 + 3.16301i −0.138841 + 0.240479i −0.927058 0.374918i 0.877671π-0.877671\pi
0.788217 + 0.615397i 0.211004π0.211004\pi
174174 0 0
175175 1.91827 3.32254i 0.145007 0.251160i
176176 −4.00000 + 6.92820i −0.301511 + 0.522233i
177177 0 0
178178 17.9010 31.0054i 1.34174 2.32395i
179179 −2.92073 5.05885i −0.218306 0.378116i 0.735985 0.676998i 0.236720π-0.236720\pi
−0.954290 + 0.298882i 0.903386π0.903386\pi
180180 0 0
181181 10.0874 0.749792 0.374896 0.927067i 0.377678π-0.377678\pi
0.374896 + 0.927067i 0.377678π0.377678\pi
182182 4.53088 30.2933i 0.335851 2.24549i
183183 0 0
184184 6.23506 + 10.7994i 0.459655 + 0.796146i
185185 2.37778 + 4.11844i 0.174818 + 0.302794i
186186 0 0
187187 −20.8573 −1.52524
188188 3.21432 5.56737i 0.234428 0.406042i
189189 0 0
190190 −4.75557 −0.345005
191191 7.98741 13.8346i 0.577948 1.00104i −0.417766 0.908555i 0.637187π-0.637187\pi
0.995714 0.0924813i 0.0294798π-0.0294798\pi
192192 0 0
193193 1.85159 + 3.20705i 0.133280 + 0.230849i 0.924939 0.380115i 0.124116π-0.124116\pi
−0.791659 + 0.610963i 0.790782π0.790782\pi
194194 −9.41282 −0.675801
195195 0 0
196196 22.4099 1.60071
197197 8.19850 + 14.2002i 0.584119 + 1.01172i 0.994985 + 0.100028i 0.0318931π0.0318931\pi
−0.410866 + 0.911696i 0.634774π0.634774\pi
198198 0 0
199199 −2.64764 + 4.58585i −0.187686 + 0.325082i −0.944478 0.328573i 0.893432π-0.893432\pi
0.756792 + 0.653656i 0.226766π0.226766\pi
200200 −2.00000 −0.141421
201201 0 0
202202 2.47457 4.28609i 0.174110 0.301568i
203203 7.92888 0.556498
204204 0 0
205205 −5.55877 9.62806i −0.388241 0.672453i
206206 −2.70641 4.68764i −0.188564 0.326603i
207207 0 0
208208 4.62222 1.82013i 0.320493 0.126204i
209209 −12.4701 −0.862577
210210 0 0
211211 −3.99532 6.92009i −0.275049 0.476399i 0.695099 0.718914i 0.255361π-0.255361\pi
−0.970147 + 0.242516i 0.922027π0.922027\pi
212212 −1.18421 + 2.05111i −0.0813318 + 0.140871i
213213 0 0
214214 −1.82939 + 3.16860i −0.125055 + 0.216601i
215215 4.74766 8.22318i 0.323788 0.560817i
216216 0 0
217217 −10.1304 + 17.5463i −0.687694 + 1.19112i
218218 −2.89284 5.01055i −0.195928 0.339357i
219219 0 0
220220 −16.8573 −1.13652
221221 10.1350 + 8.06366i 0.681757 + 0.542420i
222222 0 0
223223 4.68889 + 8.12140i 0.313991 + 0.543849i 0.979223 0.202788i 0.0650003π-0.0650003\pi
−0.665231 + 0.746637i 0.731667π0.731667\pi
224224 13.5254 + 23.4267i 0.903706 + 1.56526i
225225 0 0
226226 5.37778 0.357725
227227 7.20395 12.4776i 0.478143 0.828168i −0.521543 0.853225i 0.674643π-0.674643\pi
0.999686 + 0.0250572i 0.00797680π0.00797680\pi
228228 0 0
229229 −17.9541 −1.18644 −0.593219 0.805041i 0.702143π-0.702143\pi
−0.593219 + 0.805041i 0.702143π0.702143\pi
230230 6.90321 11.9567i 0.455184 0.788402i
231231 0 0
232232 −2.06668 3.57959i −0.135684 0.235012i
233233 −27.5210 −1.80296 −0.901480 0.432821i 0.857518π-0.857518\pi
−0.901480 + 0.432821i 0.857518π0.857518\pi
234234 0 0
235235 −2.21432 −0.144446
236236 −14.4795 25.0792i −0.942535 1.63252i
237237 0 0
238238 −15.2580 + 26.4277i −0.989031 + 1.71305i
239239 19.0321 1.23109 0.615543 0.788104i 0.288937π-0.288937\pi
0.615543 + 0.788104i 0.288937π0.288937\pi
240240 0 0
241241 −11.6407 + 20.1623i −0.749846 + 1.29877i 0.198051 + 0.980192i 0.436539π0.436539\pi
−0.947896 + 0.318579i 0.896794π0.896794\pi
242242 −50.2973 −3.23323
243243 0 0
244244 −7.66593 13.2778i −0.490761 0.850022i
245245 −3.85950 6.68485i −0.246575 0.427080i
246246 0 0
247247 6.05953 + 4.82109i 0.385559 + 0.306759i
248248 10.5620 0.670687
249249 0 0
250250 1.10716 + 1.91766i 0.0700229 + 0.121283i
251251 −13.3620 + 23.1436i −0.843400 + 1.46081i 0.0436042 + 0.999049i 0.486116π0.486116\pi
−0.887004 + 0.461762i 0.847217π0.847217\pi
252252 0 0
253253 18.1017 31.3531i 1.13804 1.97115i
254254 21.3193 36.9260i 1.33769 2.31695i
255255 0 0
256256 3.05086 5.28424i 0.190678 0.330265i
257257 −5.95952 10.3222i −0.371744 0.643880i 0.618090 0.786108i 0.287907π-0.287907\pi
−0.989834 + 0.142227i 0.954574π0.954574\pi
258258 0 0
259259 18.2449 1.13368
260260 8.19135 + 6.51721i 0.508006 + 0.404180i
261261 0 0
262262 −14.8501 25.7212i −0.917444 1.58906i
263263 7.96444 + 13.7948i 0.491108 + 0.850625i 0.999948 0.0102370i 0.00325858π-0.00325858\pi
−0.508839 + 0.860862i 0.669925π0.669925\pi
264264 0 0
265265 0.815792 0.0501137
266266 −9.12245 + 15.8006i −0.559334 + 0.968794i
267267 0 0
268268 −10.3225 −0.630546
269269 −4.79383 + 8.30316i −0.292285 + 0.506252i −0.974350 0.225039i 0.927749π-0.927749\pi
0.682065 + 0.731292i 0.261082π0.261082\pi
270270 0 0
271271 −6.86196 11.8853i −0.416835 0.721979i 0.578785 0.815481i 0.303527π-0.303527\pi
−0.995619 + 0.0935019i 0.970194π0.970194\pi
272272 −4.94914 −0.300086
273273 0 0
274274 −10.4844 −0.633387
275275 2.90321 + 5.02851i 0.175070 + 0.303231i
276276 0 0
277277 −5.90321 + 10.2247i −0.354690 + 0.614340i −0.987065 0.160322i 0.948747π-0.948747\pi
0.632375 + 0.774662i 0.282080π0.282080\pi
278278 24.4494 1.46638
279279 0 0
280280 −3.83654 + 6.64507i −0.229277 + 0.397119i
281281 10.7906 0.643713 0.321857 0.946788i 0.395693π-0.395693\pi
0.321857 + 0.946788i 0.395693π0.395693\pi
282282 0 0
283283 15.5978 + 27.0162i 0.927192 + 1.60594i 0.787997 + 0.615680i 0.211118π0.211118\pi
0.139196 + 0.990265i 0.455548π0.455548\pi
284284 8.33185 + 14.4312i 0.494404 + 0.856334i
285285 0 0
286286 36.2766 + 28.8624i 2.14508 + 1.70667i
287287 −42.6528 −2.51772
288288 0 0
289289 2.04839 + 3.54792i 0.120494 + 0.208701i
290290 −2.28814 + 3.96318i −0.134364 + 0.232726i
291291 0 0
292292 4.04371 7.00391i 0.236640 0.409873i
293293 2.95952 5.12603i 0.172897 0.299466i −0.766535 0.642203i 0.778021π-0.778021\pi
0.939431 + 0.342737i 0.111354π0.111354\pi
294294 0 0
295295 −4.98741 + 8.63844i −0.290378 + 0.502949i
296296 −4.75557 8.23689i −0.276412 0.478759i
297297 0 0
298298 −4.42864 −0.256544
299299 −20.9175 + 8.23689i −1.20969 + 0.476351i
300300 0 0
301301 −18.2146 31.5485i −1.04987 1.81843i
302302 9.75557 + 16.8971i 0.561370 + 0.972321i
303303 0 0
304304 −2.95899 −0.169710
305305 −2.64050 + 4.57348i −0.151194 + 0.261877i
306306 0 0
307307 14.5877 0.832562 0.416281 0.909236i 0.363333π-0.363333\pi
0.416281 + 0.909236i 0.363333π0.363333\pi
308308 −32.3368 + 56.0089i −1.84256 + 3.19141i
309309 0 0
310310 −5.84691 10.1271i −0.332082 0.575183i
311311 −17.9748 −1.01926 −0.509629 0.860394i 0.670217π-0.670217\pi
−0.509629 + 0.860394i 0.670217π0.670217\pi
312312 0 0
313313 −5.79060 −0.327304 −0.163652 0.986518i 0.552327π-0.552327\pi
−0.163652 + 0.986518i 0.552327π0.552327\pi
314314 −3.03334 5.25390i −0.171181 0.296495i
315315 0 0
316316 −17.9010 + 31.0054i −1.00701 + 1.74419i
317317 −4.78415 −0.268705 −0.134352 0.990934i 0.542895π-0.542895\pi
−0.134352 + 0.990934i 0.542895π0.542895\pi
318318 0 0
319319 −6.00000 + 10.3923i −0.335936 + 0.581857i
320320 −12.8573 −0.718744
321321 0 0
322322 −26.4844 45.8724i −1.47592 2.55637i
323323 −3.85728 6.68100i −0.214625 0.371741i
324324 0 0
325325 0.533338 3.56589i 0.0295843 0.197800i
326326 54.6800 3.02845
327327 0 0
328328 11.1175 + 19.2561i 0.613863 + 1.06324i
329329 −4.24766 + 7.35716i −0.234181 + 0.405613i
330330 0 0
331331 −1.33654 + 2.31495i −0.0734626 + 0.127241i −0.900417 0.435028i 0.856738π-0.856738\pi
0.826954 + 0.562269i 0.190072π0.190072\pi
332332 0.903212 1.56441i 0.0495702 0.0858581i
333333 0 0
334334 −8.75557 + 15.1651i −0.479083 + 0.829797i
335335 1.77777 + 3.07919i 0.0971299 + 0.168234i
336336 0 0
337337 −29.0350 −1.58164 −0.790820 0.612049i 0.790345π-0.790345\pi
−0.790820 + 0.612049i 0.790345π0.790345\pi
338338 −6.46912 28.0498i −0.351874 1.52571i
339339 0 0
340340 −5.21432 9.03147i −0.282786 0.489800i
341341 −15.3319 26.5555i −0.830266 1.43806i
342342 0 0
343343 −2.75848 −0.148944
344344 −9.49532 + 16.4464i −0.511953 + 0.886729i
345345 0 0
346346 −8.08742 −0.434782
347347 14.1541 24.5156i 0.759832 1.31607i −0.183104 0.983093i 0.558615π-0.558615\pi
0.942936 0.332974i 0.108052π-0.108052\pi
348348 0 0
349349 16.0232 + 27.7530i 0.857702 + 1.48558i 0.874115 + 0.485719i 0.161442π0.161442\pi
−0.0164125 + 0.999865i 0.505225π0.505225\pi
350350 8.49532 0.454094
351351 0 0
352352 −40.9403 −2.18212
353353 −7.24443 12.5477i −0.385582 0.667848i 0.606268 0.795261i 0.292666π-0.292666\pi
−0.991850 + 0.127413i 0.959333π0.959333\pi
354354 0 0
355355 2.86987 4.97077i 0.152317 0.263821i
356356 46.9403 2.48783
357357 0 0
358358 6.46743 11.2019i 0.341814 0.592039i
359359 24.2701 1.28093 0.640463 0.767989i 0.278742π-0.278742\pi
0.640463 + 0.767989i 0.278742π0.278742\pi
360360 0 0
361361 7.19381 + 12.4601i 0.378622 + 0.655792i
362362 11.1684 + 19.3442i 0.586997 + 1.01671i
363363 0 0
364364 37.3669 14.7143i 1.95856 0.771240i
365365 −2.78568 −0.145809
366366 0 0
367367 1.11899 + 1.93815i 0.0584107 + 0.101170i 0.893752 0.448561i 0.148063π-0.148063\pi
−0.835341 + 0.549732i 0.814730π0.814730\pi
368368 4.29529 7.43965i 0.223907 0.387819i
369369 0 0
370370 −5.26517 + 9.11955i −0.273723 + 0.474103i
371371 1.56491 2.71050i 0.0812459 0.140722i
372372 0 0
373373 −14.0565 + 24.3466i −0.727820 + 1.26062i 0.229982 + 0.973195i 0.426133π0.426133\pi
−0.957803 + 0.287427i 0.907200π0.907200\pi
374374 −23.0923 39.9971i −1.19408 2.06820i
375375 0 0
376376 4.42864 0.228390
377377 6.93332 2.73020i 0.357084 0.140613i
378378 0 0
379379 9.80888 + 16.9895i 0.503849 + 0.872691i 0.999990 + 0.00444967i 0.00141638π0.00141638\pi
−0.496142 + 0.868242i 0.665250π0.665250\pi
380380 −3.11753 5.39972i −0.159926 0.277000i
381381 0 0
382382 35.3733 1.80986
383383 −9.72001 + 16.8355i −0.496669 + 0.860256i −0.999993 0.00384183i 0.998777π-0.998777\pi
0.503323 + 0.864098i 0.332110π0.332110\pi
384384 0 0
385385 22.2766 1.13532
386386 −4.10001 + 7.10143i −0.208685 + 0.361453i
387387 0 0
388388 −6.17061 10.6878i −0.313265 0.542591i
389389 2.81579 0.142766 0.0713832 0.997449i 0.477259π-0.477259\pi
0.0713832 + 0.997449i 0.477259π0.477259\pi
390390 0 0
391391 22.3970 1.13266
392392 7.71900 + 13.3697i 0.389869 + 0.675272i
393393 0 0
394394 −18.1541 + 31.4438i −0.914590 + 1.58412i
395395 12.3319 0.620483
396396 0 0
397397 6.33976 10.9808i 0.318184 0.551110i −0.661926 0.749570i 0.730261π-0.730261\pi
0.980109 + 0.198460i 0.0635938π0.0635938\pi
398398 −11.7255 −0.587744
399399 0 0
400400 0.688892 + 1.19320i 0.0344446 + 0.0596598i
401401 0.453829 + 0.786055i 0.0226631 + 0.0392537i 0.877135 0.480245i 0.159452π-0.159452\pi
−0.854471 + 0.519498i 0.826119π0.826119\pi
402402 0 0
403403 −2.81656 + 18.8314i −0.140303 + 0.938061i
404404 6.48886 0.322833
405405 0 0
406406 8.77854 + 15.2049i 0.435671 + 0.754605i
407407 −13.8064 + 23.9134i −0.684359 + 1.18534i
408408 0 0
409409 16.7881 29.0779i 0.830120 1.43781i −0.0678223 0.997697i 0.521605π-0.521605\pi
0.897942 0.440113i 0.145062π-0.145062\pi
410410 12.3089 21.3196i 0.607892 1.05290i
411411 0 0
412412 3.54839 6.14600i 0.174817 0.302792i
413413 19.1344 + 33.1417i 0.941540 + 1.63080i
414414 0 0
415415 −0.622216 −0.0305434
416416 19.8938 + 15.8280i 0.975376 + 0.776029i
417417 0 0
418418 −13.8064 23.9134i −0.675294 1.16964i
419419 11.4763 + 19.8775i 0.560652 + 0.971078i 0.997440 + 0.0715136i 0.0227829π0.0227829\pi
−0.436787 + 0.899565i 0.643884π0.643884\pi
420420 0 0
421421 −31.0874 −1.51511 −0.757554 0.652772i 0.773606π-0.773606\pi
−0.757554 + 0.652772i 0.773606π0.773606\pi
422422 8.84691 15.3233i 0.430661 0.745926i
423423 0 0
424424 −1.63158 −0.0792367
425425 −1.79605 + 3.11085i −0.0871213 + 0.150899i
426426 0 0
427427 10.1304 + 17.5463i 0.490243 + 0.849125i
428428 −4.79706 −0.231874
429429 0 0
430430 21.0257 1.01395
431431 8.52543 + 14.7665i 0.410655 + 0.711276i 0.994962 0.100257i 0.0319666π-0.0319666\pi
−0.584306 + 0.811533i 0.698633π0.698633\pi
432432 0 0
433433 1.29605 2.24483i 0.0622843 0.107880i −0.833202 0.552969i 0.813495π-0.813495\pi
0.895486 + 0.445089i 0.146828π0.146828\pi
434434 −44.8637 −2.15353
435435 0 0
436436 3.79283 6.56937i 0.181643 0.314616i
437437 13.3907 0.640564
438438 0 0
439439 6.88493 + 11.9250i 0.328600 + 0.569151i 0.982234 0.187659i 0.0600900π-0.0600900\pi
−0.653635 + 0.756810i 0.726757π0.726757\pi
440440 −5.80642 10.0570i −0.276810 0.479450i
441441 0 0
442442 −4.24221 + 28.3633i −0.201781 + 1.34910i
443443 −4.71609 −0.224068 −0.112034 0.993704i 0.535737π-0.535737\pi
−0.112034 + 0.993704i 0.535737π0.535737\pi
444444 0 0
445445 −8.08419 14.0022i −0.383228 0.663770i
446446 −10.3827 + 17.9834i −0.491635 + 0.851537i
447447 0 0
448448 −24.6637 + 42.7188i −1.16525 + 2.01827i
449449 −5.16839 + 8.95191i −0.243911 + 0.422467i −0.961825 0.273665i 0.911764π-0.911764\pi
0.717914 + 0.696132i 0.245097π0.245097\pi
450450 0 0
451451 32.2766 55.9046i 1.51984 2.63245i
452452 3.52543 + 6.10622i 0.165822 + 0.287212i
453453 0 0
454454 31.9037 1.49731
455455 −10.8247 8.61236i −0.507470 0.403754i
456456 0 0
457457 9.81433 + 16.9989i 0.459095 + 0.795176i 0.998913 0.0466054i 0.0148403π-0.0148403\pi
−0.539818 + 0.841782i 0.681507π0.681507\pi
458458 −19.8780 34.4297i −0.928839 1.60880i
459459 0 0
460460 18.1017 0.843997
461461 12.6003 21.8243i 0.586852 1.01646i −0.407789 0.913076i 0.633700π-0.633700\pi
0.994642 0.103382i 0.0329664π-0.0329664\pi
462462 0 0
463463 28.8129 1.33905 0.669524 0.742790i 0.266498π-0.266498\pi
0.669524 + 0.742790i 0.266498π0.266498\pi
464464 −1.42372 + 2.46595i −0.0660944 + 0.114479i
465465 0 0
466466 −30.4701 52.7758i −1.41150 2.44479i
467467 32.3575 1.49733 0.748664 0.662950i 0.230696π-0.230696\pi
0.748664 + 0.662950i 0.230696π0.230696\pi
468468 0 0
469469 13.6410 0.629881
470470 −2.45161 4.24631i −0.113084 0.195867i
471471 0 0
472472 9.97481 17.2769i 0.459128 0.795233i
473473 55.1338 2.53506
474474 0 0
475475 −1.07382 + 1.85991i −0.0492703 + 0.0853387i
476476 −40.0098 −1.83385
477477 0 0
478478 21.0716 + 36.4971i 0.963792 + 1.66934i
479479 2.96666 + 5.13841i 0.135550 + 0.234780i 0.925808 0.377995i 0.123386π-0.123386\pi
−0.790257 + 0.612775i 0.790053π0.790053\pi
480480 0 0
481481 15.9541 6.28239i 0.727443 0.286452i
482482 −51.5526 −2.34816
483483 0 0
484484 −32.9726 57.1102i −1.49875 2.59592i
485485 −2.12544 + 3.68137i −0.0965114 + 0.167163i
486486 0 0
487487 2.42149 4.19415i 0.109728 0.190055i −0.805932 0.592008i 0.798335π-0.798335\pi
0.915660 + 0.401953i 0.131669π0.131669\pi
488488 5.28100 9.14695i 0.239059 0.414063i
489489 0 0
490490 8.54617 14.8024i 0.386077 0.668704i
491491 0.0382604 + 0.0662690i 0.00172667 + 0.00299068i 0.866887 0.498504i 0.166117π-0.166117\pi
−0.865161 + 0.501495i 0.832784π0.832784\pi
492492 0 0
493493 −7.42372 −0.334347
494494 −2.53633 + 16.9578i −0.114115 + 0.762968i
495495 0 0
496496 −3.63804 6.30127i −0.163353 0.282935i
497497 −11.0104 19.0705i −0.493883 0.855430i
498498 0 0
499499 38.0687 1.70419 0.852094 0.523388i 0.175332π-0.175332\pi
0.852094 + 0.523388i 0.175332π0.175332\pi
500500 −1.45161 + 2.51426i −0.0649178 + 0.112441i
501501 0 0
502502 −59.1753 −2.64112
503503 6.62714 11.4785i 0.295489 0.511803i −0.679609 0.733574i 0.737851π-0.737851\pi
0.975099 + 0.221772i 0.0711839π0.0711839\pi
504504 0 0
505505 −1.11753 1.93562i −0.0497295 0.0861340i
506506 80.1659 3.56381
507507 0 0
508508 55.9037 2.48033
509509 −14.2351 24.6559i −0.630958 1.09285i −0.987356 0.158517i 0.949329π-0.949329\pi
0.356398 0.934334i 0.384005π-0.384005\pi
510510 0 0
511511 −5.34368 + 9.25553i −0.236391 + 0.409440i
512512 −15.2257 −0.672887
513513 0 0
514514 13.1963 22.8566i 0.582063 1.00816i
515515 −2.44446 −0.107716
516516 0 0
517517 −6.42864 11.1347i −0.282731 0.489705i
518518 20.2000 + 34.9875i 0.887538 + 1.53726i
519519 0 0
520520 −1.06668 + 7.13177i −0.0467769 + 0.312749i
521521 −17.1175 −0.749933 −0.374966 0.927038i 0.622346π-0.622346\pi
−0.374966 + 0.927038i 0.622346π0.622346\pi
522522 0 0
523523 −0.0666765 0.115487i −0.00291556 0.00504990i 0.864564 0.502523i 0.167595π-0.167595\pi
−0.867480 + 0.497473i 0.834261π0.834261\pi
524524 19.4701 33.7232i 0.850556 1.47321i
525525 0 0
526526 −17.6358 + 30.5461i −0.768958 + 1.33187i
527527 9.48494 16.4284i 0.413171 0.715633i
528528 0 0
529529 −7.93801 + 13.7490i −0.345131 + 0.597784i
530530 0.903212 + 1.56441i 0.0392330 + 0.0679536i
531531 0 0
532532 −23.9210 −1.03711
533533 −37.2973 + 14.6869i −1.61553 + 0.636161i
534534 0 0
535535 0.826164 + 1.43096i 0.0357182 + 0.0618657i
536536 −3.55554 6.15837i −0.153576 0.266001i
537537 0 0
538538 −21.2301 −0.915296
539539 22.4099 38.8151i 0.965263 1.67188i
540540 0 0
541541 −26.3876 −1.13449 −0.567246 0.823548i 0.691991π-0.691991\pi
−0.567246 + 0.823548i 0.691991π0.691991\pi
542542 15.1946 26.3178i 0.652663 1.13045i
543543 0 0
544544 −12.6637 21.9342i −0.542952 0.940420i
545545 −2.61285 −0.111922
546546 0 0
547547 −0.0573086 −0.00245034 −0.00122517 0.999999i 0.500390π-0.500390\pi
−0.00122517 + 0.999999i 0.500390π0.500390\pi
548548 −6.87310 11.9046i −0.293604 0.508538i
549549 0 0
550550 −6.42864 + 11.1347i −0.274118 + 0.474786i
551551 −4.43848 −0.189086
552552 0 0
553553 23.6558 40.9730i 1.00595 1.74235i
554554 −26.1432 −1.11072
555555 0 0
556556 16.0279 + 27.7611i 0.679734 + 1.17733i
557557 20.5210 + 35.5434i 0.869502 + 1.50602i 0.862507 + 0.506046i 0.168893π0.168893\pi
0.00699538 + 0.999976i 0.497773π0.497773\pi
558558 0 0
559559 −26.7908 21.3154i −1.13313 0.901543i
560560 5.28592 0.223371
561561 0 0
562562 11.9469 + 20.6927i 0.503950 + 0.872868i
563563 10.6128 18.3820i 0.447278 0.774709i −0.550930 0.834552i 0.685727π-0.685727\pi
0.998208 + 0.0598432i 0.0190601π0.0190601\pi
564564 0 0
565565 1.21432 2.10326i 0.0510868 0.0884850i
566566 −34.5385 + 59.8224i −1.45176 + 2.51452i
567567 0 0
568568 −5.73975 + 9.94153i −0.240834 + 0.417137i
569569 8.18098 + 14.1699i 0.342965 + 0.594032i 0.984982 0.172658i 0.0552356π-0.0552356\pi
−0.642017 + 0.766690i 0.721902π0.721902\pi
570570 0 0
571571 −37.7101 −1.57812 −0.789060 0.614317i 0.789432π-0.789432\pi
−0.789060 + 0.614317i 0.789432π0.789432\pi
572572 −8.99063 + 60.1112i −0.375917 + 2.51337i
573573 0 0
574574 −47.2235 81.7935i −1.97107 3.41399i
575575 −3.11753 5.39972i −0.130010 0.225184i
576576 0 0
577577 42.7150 1.77825 0.889125 0.457664i 0.151314π-0.151314\pi
0.889125 + 0.457664i 0.151314π0.151314\pi
578578 −4.53580 + 7.85623i −0.188664 + 0.326776i
579579 0 0
580580 −6.00000 −0.249136
581581 −1.19358 + 2.06733i −0.0495179 + 0.0857675i
582582 0 0
583583 2.36842 + 4.10222i 0.0980898 + 0.169896i
584584 5.57136 0.230545
585585 0 0
586586 13.1066 0.541430
587587 4.81187 + 8.33441i 0.198607 + 0.343998i 0.948077 0.318041i 0.103025π-0.103025\pi
−0.749470 + 0.662039i 0.769692π0.769692\pi
588588 0 0
589589 5.67085 9.82220i 0.233663 0.404717i
590590 −22.0874 −0.909325
591591 0 0
592592 −3.27607 + 5.67433i −0.134646 + 0.233213i
593593 24.5018 1.00617 0.503084 0.864238i 0.332199π-0.332199\pi
0.503084 + 0.864238i 0.332199π0.332199\pi
594594 0 0
595595 6.89062 + 11.9349i 0.282488 + 0.489283i
596596 −2.90321 5.02851i −0.118920 0.205976i
597597 0 0
598598 −38.9545 30.9930i −1.59297 1.26740i
599599 16.9654 0.693189 0.346595 0.938015i 0.387338π-0.387338\pi
0.346595 + 0.938015i 0.387338π0.387338\pi
600600 0 0
601601 10.7835 + 18.6775i 0.439866 + 0.761871i 0.997679 0.0680961i 0.0216925π-0.0216925\pi
−0.557812 + 0.829967i 0.688359π0.688359\pi
602602 40.3329 69.8586i 1.64384 2.84722i
603603 0 0
604604 −12.7906 + 22.1540i −0.520442 + 0.901432i
605605 −11.3573 + 19.6714i −0.461739 + 0.799755i
606606 0 0
607607 9.99285 17.3081i 0.405597 0.702515i −0.588793 0.808284i 0.700397π-0.700397\pi
0.994391 + 0.105768i 0.0337301π0.0337301\pi
608608 −7.57136 13.1140i −0.307059 0.531842i
609609 0 0
610610 −11.6938 −0.473469
611611 −1.18098 + 7.89601i −0.0477774 + 0.319439i
612612 0 0
613613 −5.60001 9.69951i −0.226182 0.391760i 0.730491 0.682922i 0.239291π-0.239291\pi
−0.956674 + 0.291163i 0.905958π0.905958\pi
614614 16.1509 + 27.9741i 0.651796 + 1.12894i
615615 0 0
616616 −44.5531 −1.79510
617617 0.295286 0.511451i 0.0118878 0.0205902i −0.860020 0.510260i 0.829549π-0.829549\pi
0.871908 + 0.489670i 0.162883π0.162883\pi
618618 0 0
619619 −12.2573 −0.492664 −0.246332 0.969186i 0.579225π-0.579225\pi
−0.246332 + 0.969186i 0.579225π0.579225\pi
620620 7.66593 13.2778i 0.307871 0.533248i
621621 0 0
622622 −19.9010 34.4695i −0.797957 1.38210i
623623 −62.0306 −2.48520
624624 0 0
625625 1.00000 0.0400000
626626 −6.41112 11.1044i −0.256240 0.443821i
627627 0 0
628628 3.97703 6.88842i 0.158701 0.274878i
629629 −17.0825 −0.681124
630630 0 0
631631 −18.3200 + 31.7312i −0.729309 + 1.26320i 0.227867 + 0.973692i 0.426825π0.426825\pi
−0.957176 + 0.289507i 0.906509π0.906509\pi
632632 −24.6637 −0.981069
633633 0 0
634634 −5.29682 9.17436i −0.210364 0.364360i
635635 −9.62790 16.6760i −0.382072 0.661768i
636636 0 0
637637 −25.8959 + 10.1973i −1.02603 + 0.404030i
638638 −26.5718 −1.05199
639639 0 0
640640 −7.18421 12.4434i −0.283981 0.491869i
641641 −10.5827 + 18.3298i −0.417993 + 0.723985i −0.995737 0.0922326i 0.970600π-0.970600\pi
0.577745 + 0.816218i 0.303933π0.303933\pi
642642 0 0
643643 −6.09602 + 10.5586i −0.240404 + 0.416391i −0.960829 0.277141i 0.910613π-0.910613\pi
0.720426 + 0.693532i 0.243946π0.243946\pi
644644 34.7239 60.1436i 1.36831 2.36999i
645645 0 0
646646 8.54125 14.7939i 0.336051 0.582057i
647647 4.73038 + 8.19326i 0.185970 + 0.322110i 0.943903 0.330223i 0.107124π-0.107124\pi
−0.757933 + 0.652333i 0.773790π0.773790\pi
648648 0 0
649649 −57.9180 −2.27348
650650 7.42864 2.92525i 0.291375 0.114738i
651651 0 0
652652 35.8457 + 62.0866i 1.40383 + 2.43150i
653653 10.1995 + 17.6661i 0.399137 + 0.691326i 0.993620 0.112782i 0.0359763π-0.0359763\pi
−0.594482 + 0.804109i 0.702643π0.702643\pi
654654 0 0
655655 −13.4128 −0.524082
656656 7.65878 13.2654i 0.299025 0.517927i
657657 0 0
658658 −18.8113 −0.733343
659659 17.4859 30.2866i 0.681156 1.17980i −0.293473 0.955967i 0.594811π-0.594811\pi
0.974628 0.223829i 0.0718557π-0.0718557\pi
660660 0 0
661661 9.73014 + 16.8531i 0.378459 + 0.655510i 0.990838 0.135054i 0.0431209π-0.0431209\pi
−0.612380 + 0.790564i 0.709788π0.709788\pi
662662 −5.91903 −0.230050
663663 0 0
664664 1.24443 0.0482933
665665 4.11975 + 7.13562i 0.159757 + 0.276708i
666666 0 0
667667 6.44293 11.1595i 0.249471 0.432097i
668668 −22.9590 −0.888310
669669 0 0
670670 −3.93655 + 6.81830i −0.152082 + 0.263414i
671671 −30.6637 −1.18376
672672 0 0
673673 −7.13259 12.3540i −0.274941 0.476212i 0.695179 0.718836i 0.255325π-0.255325\pi
−0.970120 + 0.242625i 0.921992π0.921992\pi
674674 −32.1464 55.6792i −1.23823 2.14468i
675675 0 0
676676 27.6084 25.7336i 1.06186 0.989752i
677677 34.0415 1.30832 0.654160 0.756356i 0.273022π-0.273022\pi
0.654160 + 0.756356i 0.273022π0.273022\pi
678678 0 0
679679 8.15433 + 14.1237i 0.312935 + 0.542019i
680680 3.59210 6.22171i 0.137751 0.238592i
681681 0 0
682682 33.9496 58.8025i 1.30000 2.25166i
683683 14.6692 25.4077i 0.561300 0.972199i −0.436084 0.899906i 0.643635π-0.643635\pi
0.997383 0.0722933i 0.0230318π-0.0230318\pi
684684 0 0
685685 −2.36741 + 4.10048i −0.0904542 + 0.156671i
686686 −3.05408 5.28982i −0.116605 0.201966i
687687 0 0
688688 13.0825 0.498766
689689 0.435093 2.90902i 0.0165757 0.110825i
690690 0 0
691691 −1.59457 2.76187i −0.0606601 0.105066i 0.834101 0.551612i 0.185987π-0.185987\pi
−0.894761 + 0.446546i 0.852654π0.852654\pi
692692 −5.30174 9.18288i −0.201542 0.349081i
693693 0 0
694694 62.6834 2.37943
695695 5.52074 9.56221i 0.209414 0.362715i
696696 0 0
697697 39.9353 1.51266
698698 −35.4805 + 61.4540i −1.34296 + 2.32607i
699699 0 0
700700 5.56914 + 9.64603i 0.210494 + 0.364586i
701701 −2.44738 −0.0924361 −0.0462180 0.998931i 0.514717π-0.514717\pi
−0.0462180 + 0.998931i 0.514717π0.514717\pi
702702 0 0
703703 −10.2133 −0.385201
704704 −37.3274 64.6530i −1.40683 2.43670i
705705 0 0
706706 16.0415 27.7847i 0.603729 1.04569i
707707 −8.57490 −0.322492
708708 0 0
709709 0.301502 0.522216i 0.0113231 0.0196122i −0.860308 0.509774i 0.829729π-0.829729\pi
0.871631 + 0.490162i 0.163062π0.163062\pi
710710 12.7096 0.476984
711711 0 0
712712 16.1684 + 28.0045i 0.605936 + 1.04951i
713713 16.4637 + 28.5159i 0.616569 + 1.06793i
714714 0 0
715715 19.4795 7.67063i 0.728492 0.286865i
716716 16.9590 0.633787
717717 0 0
718718 26.8709 + 46.5417i 1.00281 + 1.73692i
719719 21.7988 37.7565i 0.812956 1.40808i −0.0978299 0.995203i 0.531190π-0.531190\pi
0.910786 0.412878i 0.135477π-0.135477\pi
720720 0 0
721721 −4.68913 + 8.12181i −0.174632 + 0.302472i
722722 −15.9294 + 27.5905i −0.592831 + 1.02681i
723723 0 0
724724 −14.6430 + 25.3623i −0.544201 + 0.942584i
725725 1.03334 + 1.78979i 0.0383772 + 0.0664713i
726726 0 0
727727 32.8642 1.21887 0.609433 0.792838i 0.291397π-0.291397\pi
0.609433 + 0.792838i 0.291397π0.291397\pi
728728 21.6494 + 17.2247i 0.802381 + 0.638391i
729729 0 0
730730 −3.08419 5.34198i −0.114151 0.197716i
731731 17.0541 + 29.5385i 0.630768 + 1.09252i
732732 0 0
733733 17.4035 0.642811 0.321406 0.946942i 0.395845π-0.395845\pi
0.321406 + 0.946942i 0.395845π0.395845\pi
734734 −2.47780 + 4.29167i −0.0914572 + 0.158409i
735735 0 0
736736 43.9625 1.62048
737737 −10.3225 + 17.8791i −0.380234 + 0.658584i
738738 0 0
739739 −21.2924 36.8795i −0.783253 1.35663i −0.930037 0.367465i 0.880226π-0.880226\pi
0.146785 0.989168i 0.453107π-0.453107\pi
740740 −13.8064 −0.507534
741741 0 0
742742 6.93041 0.254423
743743 −16.4232 28.4458i −0.602508 1.04358i −0.992440 0.122731i 0.960835π-0.960835\pi
0.389932 0.920844i 0.372499π-0.372499\pi
744744 0 0
745745 −1.00000 + 1.73205i −0.0366372 + 0.0634574i
746746 −62.2514 −2.27918
747747 0 0
748748 30.2766 52.4405i 1.10702 1.91742i
749749 6.33921 0.231630
750750 0 0
751751 −6.23729 10.8033i −0.227602 0.394218i 0.729495 0.683986i 0.239755π-0.239755\pi
−0.957097 + 0.289768i 0.906422π0.906422\pi
752752 −1.52543 2.64212i −0.0556266 0.0963481i
753753 0 0
754754 12.9119 + 10.2730i 0.470223 + 0.374119i
755755 8.81135 0.320678
756756 0 0
757757 2.43732 + 4.22155i 0.0885858 + 0.153435i 0.906914 0.421317i 0.138432π-0.138432\pi
−0.818328 + 0.574752i 0.805099π0.805099\pi
758758 −21.7200 + 37.6202i −0.788906 + 1.36643i
759759 0 0
760760 2.14764 3.71983i 0.0779032 0.134932i
761761 −2.05086 + 3.55219i −0.0743434 + 0.128767i −0.900801 0.434233i 0.857019π-0.857019\pi
0.826457 + 0.563000i 0.190353π0.190353\pi
762762 0 0
763763 −5.01214 + 8.68128i −0.181452 + 0.314284i
764764 23.1891 + 40.1648i 0.838953 + 1.45311i
765765 0 0
766766 −43.0464 −1.55533
767767 28.1437 + 22.3917i 1.01621 + 0.808519i
768768 0 0
769769 24.0486 + 41.6535i 0.867216 + 1.50206i 0.864830 + 0.502065i 0.167426π0.167426\pi
0.00238584 + 0.999997i 0.499241π0.499241\pi
770770 24.6637 + 42.7188i 0.888818 + 1.53948i
771771 0 0
772772 −10.7511 −0.386941
773773 9.09679 15.7561i 0.327189 0.566707i −0.654764 0.755833i 0.727232π-0.727232\pi
0.981953 + 0.189126i 0.0605654π0.0605654\pi
774774 0 0
775775 −5.28100 −0.189699
776776 4.25088 7.36275i 0.152598 0.264307i
777777 0 0
778778 3.11753 + 5.39972i 0.111769 + 0.193589i
779779 23.8765 0.855464
780780 0 0
781781 33.3274 1.19255
782782 24.7971 + 42.9498i 0.886741 + 1.53588i
783783 0 0
784784 5.31756 9.21029i 0.189913 0.328939i
785785 −2.73975 −0.0977858
786786 0 0
787787 14.6486 25.3722i 0.522168 0.904421i −0.477500 0.878632i 0.658457π-0.658457\pi
0.999667 0.0257893i 0.00820989π-0.00820989\pi
788788 −47.6040 −1.69582
789789 0 0
790790 13.6533 + 23.6483i 0.485764 + 0.841367i
791791 −4.65878 8.06924i −0.165647 0.286909i
792792 0 0
793793 14.9002 + 11.8549i 0.529122 + 0.420981i
794794 28.0765 0.996398
795795 0 0
796796 −7.68667 13.3137i −0.272447 0.471892i
797797 13.4390 23.2771i 0.476034 0.824515i −0.523589 0.851971i 0.675407π-0.675407\pi
0.999623 + 0.0274557i 0.00874051π0.00874051\pi
798798 0 0
799799 3.97703 6.88842i 0.140697 0.243695i
800800 −3.52543 + 6.10622i −0.124643 + 0.215887i
801801 0 0
802802 −1.00492 + 1.74058i −0.0354850 + 0.0614619i
803803 −8.08742 14.0078i −0.285399 0.494325i
804804 0 0
805805 −23.9210 −0.843106
806806 −39.2306 + 15.4482i −1.38184 + 0.544140i
807807 0 0
808808 2.23506 + 3.87124i 0.0786293 + 0.136190i
809809 −14.2286 24.6447i −0.500251 0.866461i −1.00000 0.000290180i 0.999908π-0.999908\pi
0.499749 0.866170i 0.333426π-0.333426\pi
810810 0 0
811811 −16.6316 −0.584014 −0.292007 0.956416i 0.594323π-0.594323\pi
−0.292007 + 0.956416i 0.594323π0.594323\pi
812812 −11.5096 + 19.9352i −0.403908 + 0.699589i
813813 0 0
814814 −61.1437 −2.14308
815815 12.3469 21.3855i 0.432493 0.749100i
816816 0 0
817817 10.1963 + 17.6605i 0.356723 + 0.617862i
818818 74.3486 2.59954
819819 0 0
820820 32.2766 1.12715
821821 −17.4844 30.2839i −0.610210 1.05692i −0.991205 0.132338i 0.957752π-0.957752\pi
0.380994 0.924577i 0.375582π-0.375582\pi
822822 0 0
823823 −9.33185 + 16.1632i −0.325288 + 0.563415i −0.981571 0.191100i 0.938795π-0.938795\pi
0.656283 + 0.754515i 0.272128π0.272128\pi
824824 4.88892 0.170314
825825 0 0
826826 −42.3696 + 73.3863i −1.47423 + 2.55344i
827827 −21.2968 −0.740563 −0.370281 0.928920i 0.620739π-0.620739\pi
−0.370281 + 0.928920i 0.620739π0.620739\pi
828828 0 0
829829 3.59610 + 6.22862i 0.124898 + 0.216329i 0.921693 0.387920i 0.126806π-0.126806\pi
−0.796795 + 0.604249i 0.793473π0.793473\pi
830830 −0.688892 1.19320i −0.0239118 0.0414164i
831831 0 0
832832 −6.85728 + 45.8476i −0.237733 + 1.58948i
833833 27.7275 0.960700
834834 0 0
835835 3.95407 + 6.84865i 0.136836 + 0.237007i
836836 18.1017 31.3531i 0.626061 1.08437i
837837 0 0
838838 −25.4121 + 44.0151i −0.877847 + 1.52048i
839839 −0.790602 + 1.36936i −0.0272946 + 0.0472757i −0.879350 0.476176i 0.842023π-0.842023\pi
0.852055 + 0.523452i 0.175356π0.175356\pi
840840 0 0
841841 12.3644 21.4158i 0.426359 0.738476i
842842 −34.4187 59.6150i −1.18615 2.05447i
843843 0 0
844844 23.1985 0.798525
845845 −12.4311 3.80365i −0.427643 0.130849i
846846 0 0
847847 43.5726 + 75.4700i 1.49717 + 2.59318i
848848 0.561993 + 0.973400i 0.0192989 + 0.0334267i
849849 0 0
850850 −7.95407 −0.272822
851851 14.8256 25.6788i 0.508216 0.880256i
852852 0 0
853853 −23.0207 −0.788215 −0.394108 0.919064i 0.628946π-0.628946\pi
−0.394108 + 0.919064i 0.628946π0.628946\pi
854854 −22.4319 + 38.8531i −0.767603 + 1.32953i
855855 0 0
856856 −1.65233 2.86191i −0.0564754 0.0978182i
857857 −47.4499 −1.62086 −0.810428 0.585838i 0.800765π-0.800765\pi
−0.810428 + 0.585838i 0.800765π0.800765\pi
858858 0 0
859859 −49.0241 −1.67268 −0.836341 0.548210i 0.815310π-0.815310\pi
−0.836341 + 0.548210i 0.815310π0.815310\pi
860860 13.7835 + 23.8736i 0.470012 + 0.814085i
861861 0 0
862862 −18.8780 + 32.6977i −0.642988 + 1.11369i
863863 37.3590 1.27172 0.635858 0.771806i 0.280646π-0.280646\pi
0.635858 + 0.771806i 0.280646π0.280646\pi
864864 0 0
865865 −1.82616 + 3.16301i −0.0620914 + 0.107546i
866866 5.73975 0.195045
867867 0 0
868868 −29.4106 50.9406i −0.998261 1.72904i
869869 35.8020 + 62.0108i 1.21450 + 2.10357i
870870 0 0
871871 11.9282 4.69708i 0.404171 0.159154i
872872 5.22570 0.176964
873873 0 0
874874 14.8256 + 25.6788i 0.501485 + 0.868597i
875875 1.91827 3.32254i 0.0648493 0.112322i
876876 0 0
877877 −10.3985 + 18.0108i −0.351133 + 0.608181i −0.986448 0.164072i 0.947537π-0.947537\pi
0.635315 + 0.772253i 0.280870π0.280870\pi
878878 −15.2454 + 26.4059i −0.514509 + 0.891155i
879879 0 0
880880 −4.00000 + 6.92820i −0.134840 + 0.233550i
881881 14.8780 + 25.7695i 0.501253 + 0.868196i 0.999999 + 0.00144781i 0.000460852π0.000460852\pi
−0.498746 + 0.866748i 0.666206π0.666206\pi
882882 0 0
883883 −40.5975 −1.36621 −0.683107 0.730318i 0.739372π-0.739372\pi
−0.683107 + 0.730318i 0.739372π0.739372\pi
884884 −34.9862 + 13.7768i −1.17671 + 0.463366i
885885 0 0
886886 −5.22146 9.04384i −0.175419 0.303834i
887887 24.2153 + 41.9422i 0.813071 + 1.40828i 0.910705 + 0.413058i 0.135539π0.135539\pi
−0.0976338 + 0.995222i 0.531127π0.531127\pi
888888 0 0
889889 −73.8756 −2.47771
890890 17.9010 31.0054i 0.600043 1.03930i
891891 0 0
892892 −27.2257 −0.911584
893893 2.37778 4.11844i 0.0795695 0.137818i
894894 0 0
895895 −2.92073 5.05885i −0.0976292 0.169099i
896896 −55.1249 −1.84159
897897 0 0
898898 −22.8889 −0.763813
899899 −5.45706 9.45190i −0.182003 0.315238i
900900 0 0
901901 −1.46520 + 2.53781i −0.0488130 + 0.0845467i
902902 142.941 4.75942
903903 0 0
904904 −2.42864 + 4.20653i −0.0807753 + 0.139907i
905905 10.0874 0.335317
906906 0 0
907907 5.14987 + 8.91983i 0.170998 + 0.296178i 0.938769 0.344547i 0.111967π-0.111967\pi
−0.767771 + 0.640725i 0.778634π0.778634\pi
908908 20.9146 + 36.2251i 0.694075 + 1.20217i
909909 0 0
910910 4.53088 30.2933i 0.150197 1.00421i
911911 −7.35905 −0.243816 −0.121908 0.992541i 0.538901π-0.538901\pi
−0.121908 + 0.992541i 0.538901π0.538901\pi
912912 0 0
913913 −1.80642 3.12882i −0.0597839 0.103549i
914914 −21.7321 + 37.6411i −0.718833 + 1.24506i
915915 0 0
916916 26.0622 45.1411i 0.861120 1.49150i
917917 −25.7294 + 44.5646i −0.849659 + 1.47165i
918918 0 0
919919 −0.391383 + 0.677895i −0.0129105 + 0.0223617i −0.872408 0.488777i 0.837443π-0.837443\pi
0.859498 + 0.511139i 0.170776π0.170776\pi
920920 6.23506 + 10.7994i 0.205564 + 0.356047i
921921 0 0
922922 55.8020 1.83774
923923 −16.1946 12.8847i −0.533051 0.424107i
924924 0 0
925925 2.37778 + 4.11844i 0.0781811 + 0.135414i
926926 31.9005 + 55.2532i 1.04831 + 1.81573i
927927 0 0
928928 −14.5718 −0.478344
929929 −14.2208 + 24.6311i −0.466568 + 0.808120i −0.999271 0.0381824i 0.987843π-0.987843\pi
0.532702 + 0.846303i 0.321177π0.321177\pi
930930 0 0
931931 16.5777 0.543311
932932 39.9496 69.1948i 1.30859 2.26655i
933933 0 0
934934 35.8249 + 62.0506i 1.17223 + 2.03036i
935935 −20.8573 −0.682106
936936 0 0
937937 −21.3747 −0.698282 −0.349141 0.937070i 0.613527π-0.613527\pi
−0.349141 + 0.937070i 0.613527π0.613527\pi
938938 15.1027 + 26.1587i 0.493121 + 0.854111i
939939 0 0
940940 3.21432 5.56737i 0.104840 0.181587i
941941 38.2830 1.24799 0.623995 0.781428i 0.285508π-0.285508\pi
0.623995 + 0.781428i 0.285508π0.285508\pi
942942 0 0
943943 −34.6593 + 60.0316i −1.12866 + 1.95490i
944944 −13.7431 −0.447301
945945 0 0
946946 61.0420 + 105.728i 1.98465 + 3.43751i
947947 3.80251 + 6.58613i 0.123565 + 0.214021i 0.921171 0.389158i 0.127234π-0.127234\pi
−0.797606 + 0.603179i 0.793901π0.793901\pi
948948 0 0
949949 −1.48571 + 9.93342i −0.0482282 + 0.322452i
950950 −4.75557 −0.154291
951951 0 0
952952 −13.7812 23.8698i −0.446652 0.773625i
953953 −16.6780 + 28.8871i −0.540253 + 0.935746i 0.458636 + 0.888624i 0.348338π0.348338\pi
−0.998889 + 0.0471217i 0.984995π0.984995\pi
954954 0 0
955955 7.98741 13.8346i 0.258466 0.447677i
956956 −27.6271 + 47.8516i −0.893525 + 1.54763i
957957 0 0
958958 −6.56914 + 11.3781i −0.212239 + 0.367609i
959959 9.08266 + 15.7316i 0.293294 + 0.508001i
960960 0 0
961961 −3.11108 −0.100357
962962 29.7112 + 23.6388i 0.957926 + 0.762146i
963963 0 0
964964 −33.7955 58.5356i −1.08848 1.88530i
965965 1.85159 + 3.20705i 0.0596048 + 0.103239i
966966 0 0
967967 −40.8988 −1.31522 −0.657608 0.753360i 0.728432π-0.728432\pi
−0.657608 + 0.753360i 0.728432π0.728432\pi
968968 22.7146 39.3428i 0.730074 1.26452i
969969 0 0
970970 −9.41282 −0.302227
971971 −2.11753 + 3.66767i −0.0679548 + 0.117701i −0.898001 0.439994i 0.854981π-0.854981\pi
0.830046 + 0.557695i 0.188314π0.188314\pi
972972 0 0
973973 −21.1805 36.6858i −0.679017 1.17609i
974974 10.7239 0.343617
975975 0 0
976976 −7.27607 −0.232901
977977 −19.3941 33.5915i −0.620472 1.07469i −0.989398 0.145230i 0.953608π-0.953608\pi
0.368926 0.929459i 0.379725π-0.379725\pi
978978 0 0
979979 46.9403 81.3029i 1.50022 2.59845i
980980 22.4099 0.715858
981981 0 0
982982 −0.0847209 + 0.146741i −0.00270355 + 0.00468269i
983983 −21.4479 −0.684080 −0.342040 0.939685i 0.611118π-0.611118\pi
−0.342040 + 0.939685i 0.611118π0.611118\pi
984984 0 0
985985 8.19850 + 14.2002i 0.261226 + 0.452456i
986986 −8.21924 14.2361i −0.261754 0.453371i
987987 0 0
988988 −20.9175 + 8.23689i −0.665474 + 0.262050i
989989 −59.2039 −1.88257
990990 0 0
991991 5.65010 + 9.78627i 0.179481 + 0.310871i 0.941703 0.336445i 0.109225π-0.109225\pi
−0.762222 + 0.647316i 0.775891π0.775891\pi
992992 18.6178 32.2469i 0.591115 1.02384i
993993 0 0
994994 24.3805 42.2282i 0.773302 1.33940i
995995 −2.64764 + 4.58585i −0.0839359 + 0.145381i
996996 0 0
997997 27.1123 46.9599i 0.858656 1.48724i −0.0145557 0.999894i 0.504633π-0.504633\pi
0.873212 0.487341i 0.162033π-0.162033\pi
998998 42.1481 + 73.0027i 1.33418 + 2.31086i
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 585.2.j.g.406.3 6
3.2 odd 2 195.2.i.e.16.1 6
13.3 even 3 7605.2.a.bu.1.1 3
13.9 even 3 inner 585.2.j.g.451.3 6
13.10 even 6 7605.2.a.bt.1.3 3
15.2 even 4 975.2.bb.j.874.6 12
15.8 even 4 975.2.bb.j.874.1 12
15.14 odd 2 975.2.i.m.601.3 6
39.23 odd 6 2535.2.a.z.1.1 3
39.29 odd 6 2535.2.a.y.1.3 3
39.35 odd 6 195.2.i.e.61.1 yes 6
195.74 odd 6 975.2.i.m.451.3 6
195.113 even 12 975.2.bb.j.724.6 12
195.152 even 12 975.2.bb.j.724.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.i.e.16.1 6 3.2 odd 2
195.2.i.e.61.1 yes 6 39.35 odd 6
585.2.j.g.406.3 6 1.1 even 1 trivial
585.2.j.g.451.3 6 13.9 even 3 inner
975.2.i.m.451.3 6 195.74 odd 6
975.2.i.m.601.3 6 15.14 odd 2
975.2.bb.j.724.1 12 195.152 even 12
975.2.bb.j.724.6 12 195.113 even 12
975.2.bb.j.874.1 12 15.8 even 4
975.2.bb.j.874.6 12 15.2 even 4
2535.2.a.y.1.3 3 39.29 odd 6
2535.2.a.z.1.1 3 39.23 odd 6
7605.2.a.bt.1.3 3 13.10 even 6
7605.2.a.bu.1.1 3 13.3 even 3