Properties

Label 585.2.j.i.451.3
Level 585585
Weight 22
Character 585.451
Analytic conductor 4.6714.671
Analytic rank 00
Dimension 1010
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: 1010
Relative dimension: 55 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x102x9+10x88x7+50x642x5+124x412x3+96x236x+36 x^{10} - 2x^{9} + 10x^{8} - 8x^{7} + 50x^{6} - 42x^{5} + 124x^{4} - 12x^{3} + 96x^{2} - 36x + 36 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 3 3
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 451.3
Root 0.313396+0.542817i0.313396 + 0.542817i of defining polynomial
Character χ\chi == 585.451
Dual form 585.2.j.i.406.3

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+(0.3133960.542817i)q2+(0.803566+1.39182i)q41.00000q5+(2.215633.83759i)q7+2.26092q8+(0.313396+0.542817i)q10+(3.029035.24643i)q11+(2.27075+2.80066i)q132.77748q14+(0.898570+1.55637i)q16+(2.920535.05850i)q17+(1.80357+3.12387i)q19+(0.8035661.39182i)q20+(1.898573.28842i)q22+(1.130461.95801i)q23+1.00000q25+(2.231890.354887i)q26+(3.560826.16752i)q28+(4.042537.00186i)q29+6.45826q31+(2.82414+4.89155i)q323.66112q34+(2.21563+3.83759i)q35+(0.8985701.55637i)q37+2.26092q382.26092q40+(3.99587+6.92106i)q41+(3.243755.61835i)q43+9.73610q44+(0.7085631.22727i)q46+3.22841q47+(6.31807+10.9432i)q49+(0.3133960.542817i)q50+(2.07331+5.41098i)q5210.0768q53+(3.02903+5.24643i)q55+(5.009378.67648i)q56+(2.533824.38871i)q58+(1.56460+2.70997i)q59+(1.22913+2.12892i)q61+(2.023993.50566i)q620.0539916q64+(2.270752.80066i)q65+(2.169323.75737i)q67+(4.693688.12968i)q68+2.77748q70+(4.24742+7.35675i)q710.819388q73+(0.5632160.975519i)q74+(2.89857+5.02047i)q7626.8449q778.42187q79+(0.8985701.55637i)q80+(2.50458+4.33806i)q822.35423q83+(2.92053+5.05850i)q854.06631q86+(6.8483911.8618i)q88+(0.3867060.669795i)q89+(5.7166414.9194i)q91+3.63360q92+(1.011771.75244i)q94+(1.803573.12387i)q95+(3.16052+5.47418i)q97+(3.96011+6.85911i)q98+O(q100)q+(0.313396 - 0.542817i) q^{2} +(0.803566 + 1.39182i) q^{4} -1.00000 q^{5} +(-2.21563 - 3.83759i) q^{7} +2.26092 q^{8} +(-0.313396 + 0.542817i) q^{10} +(3.02903 - 5.24643i) q^{11} +(2.27075 + 2.80066i) q^{13} -2.77748 q^{14} +(-0.898570 + 1.55637i) q^{16} +(-2.92053 - 5.05850i) q^{17} +(1.80357 + 3.12387i) q^{19} +(-0.803566 - 1.39182i) q^{20} +(-1.89857 - 3.28842i) q^{22} +(1.13046 - 1.95801i) q^{23} +1.00000 q^{25} +(2.23189 - 0.354887i) q^{26} +(3.56082 - 6.16752i) q^{28} +(4.04253 - 7.00186i) q^{29} +6.45826 q^{31} +(2.82414 + 4.89155i) q^{32} -3.66112 q^{34} +(2.21563 + 3.83759i) q^{35} +(0.898570 - 1.55637i) q^{37} +2.26092 q^{38} -2.26092 q^{40} +(-3.99587 + 6.92106i) q^{41} +(-3.24375 - 5.61835i) q^{43} +9.73610 q^{44} +(-0.708563 - 1.22727i) q^{46} +3.22841 q^{47} +(-6.31807 + 10.9432i) q^{49} +(0.313396 - 0.542817i) q^{50} +(-2.07331 + 5.41098i) q^{52} -10.0768 q^{53} +(-3.02903 + 5.24643i) q^{55} +(-5.00937 - 8.67648i) q^{56} +(-2.53382 - 4.38871i) q^{58} +(1.56460 + 2.70997i) q^{59} +(1.22913 + 2.12892i) q^{61} +(2.02399 - 3.50566i) q^{62} -0.0539916 q^{64} +(-2.27075 - 2.80066i) q^{65} +(2.16932 - 3.75737i) q^{67} +(4.69368 - 8.12968i) q^{68} +2.77748 q^{70} +(4.24742 + 7.35675i) q^{71} -0.819388 q^{73} +(-0.563216 - 0.975519i) q^{74} +(-2.89857 + 5.02047i) q^{76} -26.8449 q^{77} -8.42187 q^{79} +(0.898570 - 1.55637i) q^{80} +(2.50458 + 4.33806i) q^{82} -2.35423 q^{83} +(2.92053 + 5.05850i) q^{85} -4.06631 q^{86} +(6.84839 - 11.8618i) q^{88} +(0.386706 - 0.669795i) q^{89} +(5.71664 - 14.9194i) q^{91} +3.63360 q^{92} +(1.01177 - 1.75244i) q^{94} +(-1.80357 - 3.12387i) q^{95} +(3.16052 + 5.47418i) q^{97} +(3.96011 + 6.85911i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 10q+2q26q410q5q712q82q10+8q11+q13+8q144q16+4q19+6q2014q226q23+10q25+10q26+2q28+16q29++30q98+O(q100) 10 q + 2 q^{2} - 6 q^{4} - 10 q^{5} - q^{7} - 12 q^{8} - 2 q^{10} + 8 q^{11} + q^{13} + 8 q^{14} - 4 q^{16} + 4 q^{19} + 6 q^{20} - 14 q^{22} - 6 q^{23} + 10 q^{25} + 10 q^{26} + 2 q^{28} + 16 q^{29}+ \cdots + 30 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(23)e\left(\frac{2}{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 0.313396 0.542817i 0.221604 0.383830i −0.733691 0.679483i 0.762204π-0.762204\pi
0.955295 + 0.295653i 0.0955374π0.0955374\pi
33 0 0
44 0.803566 + 1.39182i 0.401783 + 0.695909i
55 −1.00000 −0.447214
66 0 0
77 −2.21563 3.83759i −0.837431 1.45047i −0.892036 0.451965i 0.850723π-0.850723\pi
0.0546047 0.998508i 0.482610π-0.482610\pi
88 2.26092 0.799356
99 0 0
1010 −0.313396 + 0.542817i −0.0991044 + 0.171654i
1111 3.02903 5.24643i 0.913287 1.58186i 0.103897 0.994588i 0.466869π-0.466869\pi
0.809390 0.587271i 0.199798π-0.199798\pi
1212 0 0
1313 2.27075 + 2.80066i 0.629793 + 0.776763i
1414 −2.77748 −0.742313
1515 0 0
1616 −0.898570 + 1.55637i −0.224642 + 0.389092i
1717 −2.92053 5.05850i −0.708332 1.22687i −0.965475 0.260494i 0.916115π-0.916115\pi
0.257143 0.966373i 0.417219π-0.417219\pi
1818 0 0
1919 1.80357 + 3.12387i 0.413766 + 0.716665i 0.995298 0.0968592i 0.0308797π-0.0308797\pi
−0.581532 + 0.813524i 0.697546π0.697546\pi
2020 −0.803566 1.39182i −0.179683 0.311220i
2121 0 0
2222 −1.89857 3.28842i −0.404776 0.701093i
2323 1.13046 1.95801i 0.235717 0.408274i −0.723764 0.690048i 0.757589π-0.757589\pi
0.959481 + 0.281774i 0.0909228π0.0909228\pi
2424 0 0
2525 1.00000 0.200000
2626 2.23189 0.354887i 0.437710 0.0695991i
2727 0 0
2828 3.56082 6.16752i 0.672931 1.16555i
2929 4.04253 7.00186i 0.750679 1.30021i −0.196816 0.980441i 0.563060π-0.563060\pi
0.947494 0.319773i 0.103607π-0.103607\pi
3030 0 0
3131 6.45826 1.15994 0.579969 0.814638i 0.303065π-0.303065\pi
0.579969 + 0.814638i 0.303065π0.303065\pi
3232 2.82414 + 4.89155i 0.499241 + 0.864711i
3333 0 0
3434 −3.66112 −0.627878
3535 2.21563 + 3.83759i 0.374511 + 0.648671i
3636 0 0
3737 0.898570 1.55637i 0.147724 0.255865i −0.782662 0.622447i 0.786139π-0.786139\pi
0.930386 + 0.366582i 0.119472π0.119472\pi
3838 2.26092 0.366770
3939 0 0
4040 −2.26092 −0.357483
4141 −3.99587 + 6.92106i −0.624051 + 1.08089i 0.364673 + 0.931136i 0.381181π0.381181\pi
−0.988724 + 0.149752i 0.952153π0.952153\pi
4242 0 0
4343 −3.24375 5.61835i −0.494668 0.856790i 0.505313 0.862936i 0.331377π-0.331377\pi
−0.999981 + 0.00614624i 0.998044π0.998044\pi
4444 9.73610 1.46777
4545 0 0
4646 −0.708563 1.22727i −0.104472 0.180951i
4747 3.22841 0.470912 0.235456 0.971885i 0.424342π-0.424342\pi
0.235456 + 0.971885i 0.424342π0.424342\pi
4848 0 0
4949 −6.31807 + 10.9432i −0.902581 + 1.56332i
5050 0.313396 0.542817i 0.0443208 0.0767660i
5151 0 0
5252 −2.07331 + 5.41098i −0.287516 + 0.750369i
5353 −10.0768 −1.38416 −0.692078 0.721823i 0.743304π-0.743304\pi
−0.692078 + 0.721823i 0.743304π0.743304\pi
5454 0 0
5555 −3.02903 + 5.24643i −0.408434 + 0.707429i
5656 −5.00937 8.67648i −0.669405 1.15944i
5757 0 0
5858 −2.53382 4.38871i −0.332707 0.576266i
5959 1.56460 + 2.70997i 0.203694 + 0.352809i 0.949716 0.313113i 0.101372π-0.101372\pi
−0.746022 + 0.665922i 0.768039π0.768039\pi
6060 0 0
6161 1.22913 + 2.12892i 0.157374 + 0.272580i 0.933921 0.357479i 0.116364π-0.116364\pi
−0.776547 + 0.630060i 0.783030π0.783030\pi
6262 2.02399 3.50566i 0.257047 0.445219i
6363 0 0
6464 −0.0539916 −0.00674895
6565 −2.27075 2.80066i −0.281652 0.347379i
6666 0 0
6767 2.16932 3.75737i 0.265025 0.459036i −0.702546 0.711639i 0.747953π-0.747953\pi
0.967570 + 0.252603i 0.0812866π0.0812866\pi
6868 4.69368 8.12968i 0.569192 0.985869i
6969 0 0
7070 2.77748 0.331972
7171 4.24742 + 7.35675i 0.504076 + 0.873086i 0.999989 + 0.00471324i 0.00150028π0.00150028\pi
−0.495913 + 0.868372i 0.665166π0.665166\pi
7272 0 0
7373 −0.819388 −0.0959021 −0.0479511 0.998850i 0.515269π-0.515269\pi
−0.0479511 + 0.998850i 0.515269π0.515269\pi
7474 −0.563216 0.975519i −0.0654725 0.113402i
7575 0 0
7676 −2.89857 + 5.02047i −0.332489 + 0.575887i
7777 −26.8449 −3.05926
7878 0 0
7979 −8.42187 −0.947535 −0.473767 0.880650i 0.657106π-0.657106\pi
−0.473767 + 0.880650i 0.657106π0.657106\pi
8080 0.898570 1.55637i 0.100463 0.174007i
8181 0 0
8282 2.50458 + 4.33806i 0.276584 + 0.479058i
8383 −2.35423 −0.258410 −0.129205 0.991618i 0.541243π-0.541243\pi
−0.129205 + 0.991618i 0.541243π0.541243\pi
8484 0 0
8585 2.92053 + 5.05850i 0.316776 + 0.548672i
8686 −4.06631 −0.438482
8787 0 0
8888 6.84839 11.8618i 0.730041 1.26447i
8989 0.386706 0.669795i 0.0409908 0.0709982i −0.844802 0.535079i 0.820282π-0.820282\pi
0.885793 + 0.464081i 0.153615π0.153615\pi
9090 0 0
9191 5.71664 14.9194i 0.599267 1.56398i
9292 3.63360 0.378829
9393 0 0
9494 1.01177 1.75244i 0.104356 0.180750i
9595 −1.80357 3.12387i −0.185042 0.320502i
9696 0 0
9797 3.16052 + 5.47418i 0.320902 + 0.555819i 0.980674 0.195647i 0.0626806π-0.0626806\pi
−0.659772 + 0.751466i 0.729347π0.729347\pi
9898 3.96011 + 6.85911i 0.400032 + 0.692875i
9999 0 0
100100 0.803566 + 1.39182i 0.0803566 + 0.139182i
101101 −4.45848 + 7.72231i −0.443635 + 0.768398i −0.997956 0.0639046i 0.979645π-0.979645\pi
0.554321 + 0.832303i 0.312978π0.312978\pi
102102 0 0
103103 0.112968 0.0111311 0.00556556 0.999985i 0.498228π-0.498228\pi
0.00556556 + 0.999985i 0.498228π0.498228\pi
104104 5.13398 + 6.33207i 0.503428 + 0.620910i
105105 0 0
106106 −3.15803 + 5.46986i −0.306735 + 0.531280i
107107 −3.87512 + 6.71191i −0.374622 + 0.648865i −0.990270 0.139156i 0.955561π-0.955561\pi
0.615648 + 0.788021i 0.288894π0.288894\pi
108108 0 0
109109 −11.4744 −1.09905 −0.549525 0.835477i 0.685191π-0.685191\pi
−0.549525 + 0.835477i 0.685191π0.685191\pi
110110 1.89857 + 3.28842i 0.181022 + 0.313539i
111111 0 0
112112 7.96361 0.752490
113113 3.12369 + 5.41040i 0.293852 + 0.508967i 0.974717 0.223442i 0.0717293π-0.0717293\pi
−0.680865 + 0.732409i 0.738396π0.738396\pi
114114 0 0
115115 −1.13046 + 1.95801i −0.105416 + 0.182586i
116116 12.9938 1.20644
117117 0 0
118118 1.96136 0.180558
119119 −12.9416 + 22.4156i −1.18636 + 2.05483i
120120 0 0
121121 −12.8500 22.2569i −1.16819 2.02336i
122122 1.54082 0.139499
123123 0 0
124124 5.18964 + 8.98873i 0.466044 + 0.807211i
125125 −1.00000 −0.0894427
126126 0 0
127127 −5.60171 + 9.70245i −0.497071 + 0.860953i −0.999994 0.00337830i 0.998925π-0.998925\pi
0.502923 + 0.864331i 0.332258π0.332258\pi
128128 −5.66519 + 9.81240i −0.500737 + 0.867302i
129129 0 0
130130 −2.23189 + 0.354887i −0.195750 + 0.0311257i
131131 0.494893 0.0432390 0.0216195 0.999766i 0.493118π-0.493118\pi
0.0216195 + 0.999766i 0.493118π0.493118\pi
132132 0 0
133133 7.99209 13.8427i 0.693002 1.20031i
134134 −1.35971 2.35509i −0.117461 0.203449i
135135 0 0
136136 −6.60308 11.4369i −0.566209 0.980704i
137137 11.5749 + 20.0483i 0.988909 + 1.71284i 0.623078 + 0.782160i 0.285882π0.285882\pi
0.365832 + 0.930681i 0.380785π0.380785\pi
138138 0 0
139139 5.97871 + 10.3554i 0.507107 + 0.878336i 0.999966 + 0.00822631i 0.00261855π0.00261855\pi
−0.492859 + 0.870109i 0.664048π0.664048\pi
140140 −3.56082 + 6.16752i −0.300944 + 0.521250i
141141 0 0
142142 5.32450 0.446822
143143 21.5716 3.43005i 1.80391 0.286835i
144144 0 0
145145 −4.04253 + 7.00186i −0.335714 + 0.581473i
146146 −0.256793 + 0.444778i −0.0212523 + 0.0368101i
147147 0 0
148148 2.88824 0.237412
149149 −10.6089 18.3752i −0.869117 1.50536i −0.862900 0.505375i 0.831354π-0.831354\pi
−0.00621731 0.999981i 0.501979π-0.501979\pi
150150 0 0
151151 19.4623 1.58382 0.791909 0.610639i 0.209087π-0.209087\pi
0.791909 + 0.610639i 0.209087π0.209087\pi
152152 4.07772 + 7.06282i 0.330747 + 0.572870i
153153 0 0
154154 −8.41307 + 14.5719i −0.677945 + 1.17423i
155155 −6.45826 −0.518740
156156 0 0
157157 20.6547 1.64842 0.824212 0.566282i 0.191618π-0.191618\pi
0.824212 + 0.566282i 0.191618π0.191618\pi
158158 −2.63938 + 4.57154i −0.209978 + 0.363692i
159159 0 0
160160 −2.82414 4.89155i −0.223268 0.386711i
161161 −10.0187 −0.789587
162162 0 0
163163 2.42990 + 4.20871i 0.190324 + 0.329652i 0.945358 0.326035i 0.105713π-0.105713\pi
−0.755033 + 0.655686i 0.772379π0.772379\pi
164164 −12.8438 −1.00293
165165 0 0
166166 −0.737805 + 1.27792i −0.0572648 + 0.0991855i
167167 1.28997 2.23430i 0.0998212 0.172895i −0.811789 0.583950i 0.801506π-0.801506\pi
0.911611 + 0.411055i 0.134840π0.134840\pi
168168 0 0
169169 −2.68740 + 12.7192i −0.206723 + 0.978400i
170170 3.66112 0.280795
171171 0 0
172172 5.21314 9.02943i 0.397498 0.688487i
173173 −5.12339 8.87397i −0.389524 0.674675i 0.602862 0.797846i 0.294027π-0.294027\pi
−0.992386 + 0.123170i 0.960694π0.960694\pi
174174 0 0
175175 −2.21563 3.83759i −0.167486 0.290095i
176176 5.44359 + 9.42857i 0.410326 + 0.710706i
177177 0 0
178178 −0.242384 0.419822i −0.0181675 0.0314670i
179179 −5.30141 + 9.18232i −0.396246 + 0.686319i −0.993259 0.115913i 0.963021π-0.963021\pi
0.597013 + 0.802231i 0.296354π0.296354\pi
180180 0 0
181181 16.8618 1.25333 0.626664 0.779289i 0.284420π-0.284420\pi
0.626664 + 0.779289i 0.284420π0.284420\pi
182182 −6.30696 7.77878i −0.467503 0.576602i
183183 0 0
184184 2.55588 4.42691i 0.188422 0.326356i
185185 −0.898570 + 1.55637i −0.0660642 + 0.114427i
186186 0 0
187187 −35.3855 −2.58764
188188 2.59424 + 4.49336i 0.189204 + 0.327712i
189189 0 0
190190 −2.26092 −0.164024
191191 −5.49549 9.51847i −0.397640 0.688732i 0.595795 0.803137i 0.296837π-0.296837\pi
−0.993434 + 0.114405i 0.963504π0.963504\pi
192192 0 0
193193 3.32586 5.76057i 0.239401 0.414655i −0.721142 0.692788i 0.756382π-0.756382\pi
0.960543 + 0.278133i 0.0897156π0.0897156\pi
194194 3.96197 0.284453
195195 0 0
196196 −20.3079 −1.45057
197197 11.9930 20.7725i 0.854466 1.47998i −0.0226743 0.999743i 0.507218π-0.507218\pi
0.877140 0.480235i 0.159449π-0.159449\pi
198198 0 0
199199 10.4552 + 18.1089i 0.741147 + 1.28370i 0.951973 + 0.306181i 0.0990512π0.0990512\pi
−0.210826 + 0.977524i 0.567615π0.567615\pi
200200 2.26092 0.159871
201201 0 0
202202 2.79454 + 4.84028i 0.196623 + 0.340561i
203203 −35.8270 −2.51457
204204 0 0
205205 3.99587 6.92106i 0.279084 0.483387i
206206 0.0354038 0.0613212i 0.00246670 0.00427245i
207207 0 0
208208 −6.39929 + 1.01753i −0.443711 + 0.0705533i
209209 21.8522 1.51155
210210 0 0
211211 −6.56540 + 11.3716i −0.451981 + 0.782853i −0.998509 0.0545873i 0.982616π-0.982616\pi
0.546528 + 0.837441i 0.315949π0.315949\pi
212212 −8.09738 14.0251i −0.556130 0.963246i
213213 0 0
214214 2.42889 + 4.20697i 0.166036 + 0.287582i
215215 3.24375 + 5.61835i 0.221222 + 0.383168i
216216 0 0
217217 −14.3091 24.7842i −0.971368 1.68246i
218218 −3.59603 + 6.22851i −0.243554 + 0.421848i
219219 0 0
220220 −9.73610 −0.656408
221221 7.53536 19.6660i 0.506883 1.32288i
222222 0 0
223223 10.6003 18.3603i 0.709851 1.22950i −0.255061 0.966925i 0.582095π-0.582095\pi
0.964912 0.262574i 0.0845712π-0.0845712\pi
224224 12.5145 21.6758i 0.836160 1.44827i
225225 0 0
226226 3.91581 0.260476
227227 4.61972 + 8.00159i 0.306622 + 0.531084i 0.977621 0.210374i 0.0674681π-0.0674681\pi
−0.670999 + 0.741458i 0.734135π0.734135\pi
228228 0 0
229229 3.16502 0.209150 0.104575 0.994517i 0.466652π-0.466652\pi
0.104575 + 0.994517i 0.466652π0.466652\pi
230230 0.708563 + 1.22727i 0.0467212 + 0.0809235i
231231 0 0
232232 9.13983 15.8307i 0.600059 1.03933i
233233 −2.83723 −0.185873 −0.0929364 0.995672i 0.529625π-0.529625\pi
−0.0929364 + 0.995672i 0.529625π0.529625\pi
234234 0 0
235235 −3.22841 −0.210598
236236 −2.51453 + 4.35529i −0.163682 + 0.283505i
237237 0 0
238238 8.11171 + 14.0499i 0.525804 + 0.910720i
239239 −0.634366 −0.0410337 −0.0205169 0.999790i 0.506531π-0.506531\pi
−0.0205169 + 0.999790i 0.506531π0.506531\pi
240240 0 0
241241 0.449233 + 0.778094i 0.0289376 + 0.0501215i 0.880132 0.474730i 0.157454π-0.157454\pi
−0.851194 + 0.524851i 0.824121π0.824121\pi
242242 −16.1086 −1.03550
243243 0 0
244244 −1.97538 + 3.42146i −0.126461 + 0.219036i
245245 6.31807 10.9432i 0.403647 0.699136i
246246 0 0
247247 −4.65345 + 12.1447i −0.296092 + 0.772749i
248248 14.6016 0.927204
249249 0 0
250250 −0.313396 + 0.542817i −0.0198209 + 0.0343308i
251251 7.22838 + 12.5199i 0.456252 + 0.790251i 0.998759 0.0498000i 0.0158584π-0.0158584\pi
−0.542508 + 0.840051i 0.682525π0.682525\pi
252252 0 0
253253 −6.84839 11.8618i −0.430555 0.745743i
254254 3.51110 + 6.08141i 0.220306 + 0.381582i
255255 0 0
256256 3.49690 + 6.05681i 0.218556 + 0.378551i
257257 −0.209252 + 0.362435i −0.0130528 + 0.0226081i −0.872478 0.488653i 0.837488π-0.837488\pi
0.859425 + 0.511261i 0.170822π0.170822\pi
258258 0 0
259259 −7.96361 −0.494835
260260 2.07331 5.41098i 0.128581 0.335575i
261261 0 0
262262 0.155097 0.268636i 0.00958194 0.0165964i
263263 1.24526 2.15686i 0.0767861 0.132997i −0.825075 0.565022i 0.808867π-0.808867\pi
0.901862 + 0.432025i 0.142201π0.142201\pi
264264 0 0
265265 10.0768 0.619013
266266 −5.00937 8.67648i −0.307144 0.531989i
267267 0 0
268268 6.97277 0.425930
269269 0.884288 + 1.53163i 0.0539160 + 0.0933853i 0.891724 0.452580i 0.149496π-0.149496\pi
−0.837808 + 0.545965i 0.816163π0.816163\pi
270270 0 0
271271 10.2018 17.6700i 0.619714 1.07338i −0.369824 0.929102i 0.620582π-0.620582\pi
0.989538 0.144274i 0.0460845π-0.0460845\pi
272272 10.4972 0.636486
273273 0 0
274274 14.5101 0.876586
275275 3.02903 5.24643i 0.182657 0.316372i
276276 0 0
277277 2.42247 + 4.19584i 0.145552 + 0.252103i 0.929579 0.368624i 0.120171π-0.120171\pi
−0.784027 + 0.620727i 0.786838π0.786838\pi
278278 7.49480 0.449508
279279 0 0
280280 5.00937 + 8.67648i 0.299367 + 0.518519i
281281 −5.20237 −0.310347 −0.155174 0.987887i 0.549594π-0.549594\pi
−0.155174 + 0.987887i 0.549594π0.549594\pi
282282 0 0
283283 −5.01017 + 8.67787i −0.297824 + 0.515846i −0.975638 0.219388i 0.929594π-0.929594\pi
0.677814 + 0.735233i 0.262927π0.262927\pi
284284 −6.82617 + 11.8233i −0.405059 + 0.701582i
285285 0 0
286286 4.89857 12.7844i 0.289659 0.755959i
287287 35.4136 2.09040
288288 0 0
289289 −8.55897 + 14.8246i −0.503469 + 0.872034i
290290 2.53382 + 4.38871i 0.148791 + 0.257714i
291291 0 0
292292 −0.658433 1.14044i −0.0385319 0.0667391i
293293 3.75349 + 6.50123i 0.219281 + 0.379806i 0.954588 0.297928i 0.0962955π-0.0962955\pi
−0.735307 + 0.677734i 0.762962π0.762962\pi
294294 0 0
295295 −1.56460 2.70997i −0.0910948 0.157781i
296296 2.03159 3.51882i 0.118084 0.204528i
297297 0 0
298298 −13.2992 −0.770400
299299 8.05072 1.28012i 0.465585 0.0740315i
300300 0 0
301301 −14.3739 + 24.8964i −0.828500 + 1.43500i
302302 6.09940 10.5645i 0.350981 0.607917i
303303 0 0
304304 −6.48252 −0.371798
305305 −1.22913 2.12892i −0.0703799 0.121902i
306306 0 0
307307 −11.4404 −0.652940 −0.326470 0.945208i 0.605859π-0.605859\pi
−0.326470 + 0.945208i 0.605859π0.605859\pi
308308 −21.5716 37.3632i −1.22916 2.12897i
309309 0 0
310310 −2.02399 + 3.50566i −0.114955 + 0.199108i
311311 −24.2351 −1.37424 −0.687122 0.726542i 0.741126π-0.741126\pi
−0.687122 + 0.726542i 0.741126π0.741126\pi
312312 0 0
313313 −18.8796 −1.06714 −0.533570 0.845756i 0.679150π-0.679150\pi
−0.533570 + 0.845756i 0.679150π0.679150\pi
314314 6.47309 11.2117i 0.365298 0.632714i
315315 0 0
316316 −6.76753 11.7217i −0.380703 0.659398i
317317 −22.3459 −1.25507 −0.627534 0.778589i 0.715936π-0.715936\pi
−0.627534 + 0.778589i 0.715936π0.715936\pi
318318 0 0
319319 −24.4899 42.4177i −1.37117 2.37494i
320320 0.0539916 0.00301822
321321 0 0
322322 −3.13983 + 5.43835i −0.174976 + 0.303067i
323323 10.5347 18.2467i 0.586168 1.01527i
324324 0 0
325325 2.27075 + 2.80066i 0.125959 + 0.155353i
326326 3.04608 0.168707
327327 0 0
328328 −9.03435 + 15.6479i −0.498838 + 0.864013i
329329 −7.15297 12.3893i −0.394356 0.683045i
330330 0 0
331331 11.3443 + 19.6490i 0.623541 + 1.08001i 0.988821 + 0.149107i 0.0476400π0.0476400\pi
−0.365280 + 0.930898i 0.619027π0.619027\pi
332332 −1.89178 3.27666i −0.103825 0.179830i
333333 0 0
334334 −0.808545 1.40044i −0.0442416 0.0766287i
335335 −2.16932 + 3.75737i −0.118523 + 0.205287i
336336 0 0
337337 −0.166960 −0.00909489 −0.00454745 0.999990i 0.501448π-0.501448\pi
−0.00454745 + 0.999990i 0.501448π0.501448\pi
338338 6.06198 + 5.44491i 0.329728 + 0.296164i
339339 0 0
340340 −4.69368 + 8.12968i −0.254550 + 0.440894i
341341 19.5623 33.8829i 1.05936 1.83486i
342342 0 0
343343 24.9752 1.34854
344344 −7.33387 12.7026i −0.395416 0.684880i
345345 0 0
346346 −6.42259 −0.345281
347347 7.31716 + 12.6737i 0.392806 + 0.680359i 0.992818 0.119631i 0.0381712π-0.0381712\pi
−0.600013 + 0.799990i 0.704838π0.704838\pi
348348 0 0
349349 −1.11356 + 1.92874i −0.0596074 + 0.103243i −0.894289 0.447489i 0.852318π-0.852318\pi
0.834682 + 0.550733i 0.185652π0.185652\pi
350350 −2.77748 −0.148463
351351 0 0
352352 34.2176 1.82380
353353 2.96970 5.14366i 0.158061 0.273770i −0.776108 0.630599i 0.782809π-0.782809\pi
0.934169 + 0.356830i 0.116142π0.116142\pi
354354 0 0
355355 −4.24742 7.35675i −0.225430 0.390456i
356356 1.24298 0.0658777
357357 0 0
358358 3.32288 + 5.75540i 0.175620 + 0.304182i
359359 −10.9234 −0.576516 −0.288258 0.957553i 0.593076π-0.593076\pi
−0.288258 + 0.957553i 0.593076π0.593076\pi
360360 0 0
361361 2.99430 5.18628i 0.157595 0.272962i
362362 5.28442 9.15288i 0.277743 0.481065i
363363 0 0
364364 25.3588 4.03224i 1.32916 0.211347i
365365 0.819388 0.0428887
366366 0 0
367367 −4.32224 + 7.48634i −0.225619 + 0.390784i −0.956505 0.291716i 0.905774π-0.905774\pi
0.730886 + 0.682500i 0.239107π0.239107\pi
368368 2.03159 + 3.51882i 0.105904 + 0.183431i
369369 0 0
370370 0.563216 + 0.975519i 0.0292802 + 0.0507148i
371371 22.3265 + 38.6706i 1.15913 + 2.00768i
372372 0 0
373373 −9.15260 15.8528i −0.473904 0.820826i 0.525650 0.850701i 0.323822π-0.323822\pi
−0.999554 + 0.0298755i 0.990489π0.990489\pi
374374 −11.0897 + 19.2078i −0.573432 + 0.993214i
375375 0 0
376376 7.29917 0.376426
377377 28.7894 4.57773i 1.48273 0.235765i
378378 0 0
379379 15.0031 25.9861i 0.770657 1.33482i −0.166546 0.986034i 0.553262π-0.553262\pi
0.937203 0.348783i 0.113405π-0.113405\pi
380380 2.89857 5.02047i 0.148694 0.257545i
381381 0 0
382382 −6.88905 −0.352474
383383 7.26799 + 12.5885i 0.371377 + 0.643244i 0.989778 0.142619i 0.0455524π-0.0455524\pi
−0.618401 + 0.785863i 0.712219π0.712219\pi
384384 0 0
385385 26.8449 1.36814
386386 −2.08462 3.61067i −0.106105 0.183778i
387387 0 0
388388 −5.07937 + 8.79773i −0.257866 + 0.446637i
389389 −24.5259 −1.24351 −0.621756 0.783211i 0.713581π-0.713581\pi
−0.621756 + 0.783211i 0.713581π0.713581\pi
390390 0 0
391391 −13.2062 −0.667864
392392 −14.2846 + 24.7417i −0.721484 + 1.24965i
393393 0 0
394394 −7.51711 13.0200i −0.378706 0.655939i
395395 8.42187 0.423750
396396 0 0
397397 4.72045 + 8.17606i 0.236913 + 0.410345i 0.959827 0.280593i 0.0905312π-0.0905312\pi
−0.722914 + 0.690938i 0.757198π0.757198\pi
398398 13.1064 0.656965
399399 0 0
400400 −0.898570 + 1.55637i −0.0449285 + 0.0778184i
401401 0.244187 0.422945i 0.0121941 0.0211209i −0.859864 0.510523i 0.829452π-0.829452\pi
0.872058 + 0.489402i 0.162785π0.162785\pi
402402 0 0
403403 14.6651 + 18.0874i 0.730521 + 0.900998i
404404 −14.3307 −0.712980
405405 0 0
406406 −11.2280 + 19.4475i −0.557238 + 0.965165i
407407 −5.44359 9.42857i −0.269829 0.467357i
408408 0 0
409409 −10.3602 17.9443i −0.512277 0.887290i −0.999899 0.0142348i 0.995469π-0.995469\pi
0.487622 0.873055i 0.337865π-0.337865\pi
410410 −2.50458 4.33806i −0.123692 0.214241i
411411 0 0
412412 0.0907776 + 0.157231i 0.00447229 + 0.00774624i
413413 6.93318 12.0086i 0.341160 0.590906i
414414 0 0
415415 2.35423 0.115565
416416 −7.28666 + 19.0169i −0.357258 + 0.932381i
417417 0 0
418418 6.84839 11.8618i 0.334966 0.580178i
419419 2.27374 3.93823i 0.111079 0.192395i −0.805126 0.593103i 0.797903π-0.797903\pi
0.916206 + 0.400708i 0.131236π0.131236\pi
420420 0 0
421421 31.0991 1.51568 0.757840 0.652441i 0.226255π-0.226255\pi
0.757840 + 0.652441i 0.226255π0.226255\pi
422422 4.11513 + 7.12762i 0.200322 + 0.346967i
423423 0 0
424424 −22.7828 −1.10643
425425 −2.92053 5.05850i −0.141666 0.245373i
426426 0 0
427427 5.44661 9.43381i 0.263580 0.456534i
428428 −12.4557 −0.602068
429429 0 0
430430 4.06631 0.196095
431431 17.1081 29.6321i 0.824067 1.42733i −0.0785630 0.996909i 0.525033π-0.525033\pi
0.902630 0.430417i 0.141633π-0.141633\pi
432432 0 0
433433 2.78163 + 4.81792i 0.133676 + 0.231534i 0.925091 0.379745i 0.123988π-0.123988\pi
−0.791415 + 0.611280i 0.790655π0.790655\pi
434434 −17.9377 −0.861037
435435 0 0
436436 −9.22045 15.9703i −0.441580 0.764838i
437437 8.15544 0.390127
438438 0 0
439439 1.40974 2.44175i 0.0672834 0.116538i −0.830421 0.557136i 0.811900π-0.811900\pi
0.897705 + 0.440598i 0.145234π0.145234\pi
440440 −6.84839 + 11.8618i −0.326484 + 0.565487i
441441 0 0
442442 −8.31349 10.2536i −0.395433 0.487712i
443443 15.0635 0.715686 0.357843 0.933782i 0.383512π-0.383512\pi
0.357843 + 0.933782i 0.383512π0.383512\pi
444444 0 0
445445 −0.386706 + 0.669795i −0.0183316 + 0.0317513i
446446 −6.64420 11.5081i −0.314612 0.544924i
447447 0 0
448448 0.119626 + 0.207198i 0.00565178 + 0.00978918i
449449 1.92228 + 3.32949i 0.0907181 + 0.157128i 0.907813 0.419374i 0.137750π-0.137750\pi
−0.817095 + 0.576502i 0.804417π0.804417\pi
450450 0 0
451451 24.2072 + 41.9282i 1.13987 + 1.97432i
452452 −5.02019 + 8.69522i −0.236130 + 0.408989i
453453 0 0
454454 5.79120 0.271795
455455 −5.71664 + 14.9194i −0.268000 + 0.699434i
456456 0 0
457457 −15.2140 + 26.3515i −0.711682 + 1.23267i 0.252544 + 0.967586i 0.418733π0.418733\pi
−0.964225 + 0.265084i 0.914600π0.914600\pi
458458 0.991904 1.71803i 0.0463486 0.0802782i
459459 0 0
460460 −3.63360 −0.169417
461461 15.3961 + 26.6667i 0.717066 + 1.24199i 0.962157 + 0.272494i 0.0878486π0.0878486\pi
−0.245092 + 0.969500i 0.578818π0.578818\pi
462462 0 0
463463 −12.9034 −0.599674 −0.299837 0.953991i 0.596932π-0.596932\pi
−0.299837 + 0.953991i 0.596932π0.596932\pi
464464 7.26499 + 12.5833i 0.337269 + 0.584166i
465465 0 0
466466 −0.889174 + 1.54010i −0.0411902 + 0.0713435i
467467 −10.2346 −0.473601 −0.236800 0.971558i 0.576099π-0.576099\pi
−0.236800 + 0.971558i 0.576099π0.576099\pi
468468 0 0
469469 −19.2257 −0.887759
470470 −1.01177 + 1.75244i −0.0466694 + 0.0808338i
471471 0 0
472472 3.53745 + 6.12704i 0.162824 + 0.282020i
473473 −39.3017 −1.80709
474474 0 0
475475 1.80357 + 3.12387i 0.0827533 + 0.143333i
476476 −41.5979 −1.90664
477477 0 0
478478 −0.198808 + 0.344345i −0.00909325 + 0.0157500i
479479 17.5021 30.3146i 0.799693 1.38511i −0.120122 0.992759i 0.538329π-0.538329\pi
0.919816 0.392351i 0.128338π-0.128338\pi
480480 0 0
481481 6.39929 1.01753i 0.291782 0.0463956i
482482 0.563151 0.0256508
483483 0 0
484484 20.6517 35.7698i 0.938715 1.62590i
485485 −3.16052 5.47418i −0.143512 0.248570i
486486 0 0
487487 0.765925 + 1.32662i 0.0347074 + 0.0601149i 0.882857 0.469641i 0.155617π-0.155617\pi
−0.848150 + 0.529756i 0.822283π0.822283\pi
488488 2.77897 + 4.81332i 0.125798 + 0.217889i
489489 0 0
490490 −3.96011 6.85911i −0.178900 0.309863i
491491 −12.5124 + 21.6721i −0.564676 + 0.978048i 0.432404 + 0.901680i 0.357666π0.357666\pi
−0.997080 + 0.0763675i 0.975668π0.975668\pi
492492 0 0
493493 −47.2253 −2.12692
494494 5.13398 + 6.33207i 0.230989 + 0.284893i
495495 0 0
496496 −5.80320 + 10.0514i −0.260571 + 0.451323i
497497 18.8215 32.5997i 0.844258 1.46230i
498498 0 0
499499 27.7838 1.24377 0.621887 0.783107i 0.286366π-0.286366\pi
0.621887 + 0.783107i 0.286366π0.286366\pi
500500 −0.803566 1.39182i −0.0359366 0.0622440i
501501 0 0
502502 9.06138 0.404429
503503 21.5069 + 37.2511i 0.958947 + 1.66094i 0.725067 + 0.688679i 0.241809π0.241809\pi
0.233880 + 0.972266i 0.424858π0.424858\pi
504504 0 0
505505 4.45848 7.72231i 0.198400 0.343638i
506506 −8.58503 −0.381651
507507 0 0
508508 −18.0054 −0.798860
509509 0.568519 0.984703i 0.0251992 0.0436462i −0.853151 0.521664i 0.825311π-0.825311\pi
0.878350 + 0.478018i 0.158645π0.158645\pi
510510 0 0
511511 1.81546 + 3.14448i 0.0803114 + 0.139103i
512512 −18.2771 −0.807742
513513 0 0
514514 0.131157 + 0.227171i 0.00578510 + 0.0100201i
515515 −0.112968 −0.00497798
516516 0 0
517517 9.77894 16.9376i 0.430077 0.744916i
518518 −2.49576 + 4.32278i −0.109657 + 0.189932i
519519 0 0
520520 −5.13398 6.33207i −0.225140 0.277680i
521521 −30.7311 −1.34635 −0.673177 0.739481i 0.735071π-0.735071\pi
−0.673177 + 0.739481i 0.735071π0.735071\pi
522522 0 0
523523 8.63268 14.9522i 0.377481 0.653816i −0.613214 0.789917i 0.710124π-0.710124\pi
0.990695 + 0.136101i 0.0434571π0.0434571\pi
524524 0.397679 + 0.688801i 0.0173727 + 0.0300904i
525525 0 0
526526 −0.780519 1.35190i −0.0340322 0.0589456i
527527 −18.8615 32.6691i −0.821622 1.42309i
528528 0 0
529529 8.94412 + 15.4917i 0.388875 + 0.673551i
530530 3.15803 5.46986i 0.137176 0.237596i
531531 0 0
532532 25.6887 1.11375
533533 −28.4571 + 4.52490i −1.23262 + 0.195995i
534534 0 0
535535 3.87512 6.71191i 0.167536 0.290181i
536536 4.90466 8.49511i 0.211849 0.366933i
537537 0 0
538538 1.10853 0.0477921
539539 38.2752 + 66.2947i 1.64863 + 2.85551i
540540 0 0
541541 −17.8625 −0.767970 −0.383985 0.923339i 0.625449π-0.625449\pi
−0.383985 + 0.923339i 0.625449π0.625449\pi
542542 −6.39438 11.0754i −0.274662 0.475729i
543543 0 0
544544 16.4959 28.5718i 0.707257 1.22501i
545545 11.4744 0.491510
546546 0 0
547547 −4.97952 −0.212909 −0.106455 0.994318i 0.533950π-0.533950\pi
−0.106455 + 0.994318i 0.533950π0.533950\pi
548548 −18.6024 + 32.2203i −0.794654 + 1.37638i
549549 0 0
550550 −1.89857 3.28842i −0.0809553 0.140219i
551551 29.1639 1.24242
552552 0 0
553553 18.6598 + 32.3197i 0.793495 + 1.37437i
554554 3.03676 0.129020
555555 0 0
556556 −9.60857 + 16.6425i −0.407494 + 0.705801i
557557 −18.4656 + 31.9833i −0.782412 + 1.35518i 0.148121 + 0.988969i 0.452678π0.452678\pi
−0.930533 + 0.366208i 0.880656π0.880656\pi
558558 0 0
559559 8.36933 21.8425i 0.353985 0.923840i
560560 −7.96361 −0.336524
561561 0 0
562562 −1.63040 + 2.82394i −0.0687743 + 0.119121i
563563 −4.68284 8.11092i −0.197358 0.341835i 0.750313 0.661083i 0.229903π-0.229903\pi
−0.947671 + 0.319248i 0.896570π0.896570\pi
564564 0 0
565565 −3.12369 5.41040i −0.131415 0.227617i
566566 3.14033 + 5.43921i 0.131998 + 0.228627i
567567 0 0
568568 9.60308 + 16.6330i 0.402936 + 0.697906i
569569 −0.218417 + 0.378309i −0.00915650 + 0.0158595i −0.870567 0.492049i 0.836248π-0.836248\pi
0.861411 + 0.507909i 0.169581π0.169581\pi
570570 0 0
571571 −4.69561 −0.196505 −0.0982525 0.995162i 0.531325π-0.531325\pi
−0.0982525 + 0.995162i 0.531325π0.531325\pi
572572 22.1083 + 27.2675i 0.924392 + 1.14011i
573573 0 0
574574 11.0985 19.2231i 0.463241 0.802357i
575575 1.13046 1.95801i 0.0471434 0.0816548i
576576 0 0
577577 −30.2121 −1.25775 −0.628873 0.777508i 0.716483π-0.716483\pi
−0.628873 + 0.777508i 0.716483π0.716483\pi
578578 5.36469 + 9.29191i 0.223142 + 0.386493i
579579 0 0
580580 −12.9938 −0.539536
581581 5.21611 + 9.03457i 0.216401 + 0.374817i
582582 0 0
583583 −30.5229 + 52.8673i −1.26413 + 2.18954i
584584 −1.85257 −0.0766599
585585 0 0
586586 4.70531 0.194375
587587 −21.8769 + 37.8919i −0.902956 + 1.56397i −0.0793186 + 0.996849i 0.525274π0.525274\pi
−0.823638 + 0.567117i 0.808059π0.808059\pi
588588 0 0
589589 11.6479 + 20.1748i 0.479944 + 0.831287i
590590 −1.96136 −0.0807480
591591 0 0
592592 1.61486 + 2.79701i 0.0663702 + 0.114957i
593593 5.94151 0.243989 0.121994 0.992531i 0.461071π-0.461071\pi
0.121994 + 0.992531i 0.461071π0.461071\pi
594594 0 0
595595 12.9416 22.4156i 0.530556 0.918949i
596596 17.0500 29.5314i 0.698393 1.20965i
597597 0 0
598598 1.82819 4.77126i 0.0747602 0.195111i
599599 37.0505 1.51384 0.756922 0.653506i 0.226702π-0.226702\pi
0.756922 + 0.653506i 0.226702π0.226702\pi
600600 0 0
601601 18.6411 32.2874i 0.760387 1.31703i −0.182264 0.983250i 0.558343π-0.558343\pi
0.942651 0.333779i 0.108324π-0.108324\pi
602602 9.00946 + 15.6048i 0.367198 + 0.636006i
603603 0 0
604604 15.6392 + 27.0879i 0.636351 + 1.10219i
605605 12.8500 + 22.2569i 0.522429 + 0.904873i
606606 0 0
607607 −12.2464 21.2115i −0.497068 0.860946i 0.502927 0.864329i 0.332257π-0.332257\pi
−0.999994 + 0.00338281i 0.998923π0.998923\pi
608608 −10.1870 + 17.6445i −0.413139 + 0.715577i
609609 0 0
610610 −1.54082 −0.0623859
611611 7.33091 + 9.04167i 0.296577 + 0.365787i
612612 0 0
613613 −4.73601 + 8.20301i −0.191286 + 0.331316i −0.945677 0.325109i 0.894599π-0.894599\pi
0.754391 + 0.656425i 0.227932π0.227932\pi
614614 −3.58538 + 6.21006i −0.144694 + 0.250618i
615615 0 0
616616 −60.6941 −2.44544
617617 0.599037 + 1.03756i 0.0241163 + 0.0417707i 0.877832 0.478969i 0.158989π-0.158989\pi
−0.853715 + 0.520740i 0.825656π0.825656\pi
618618 0 0
619619 −19.2559 −0.773959 −0.386979 0.922088i 0.626482π-0.626482\pi
−0.386979 + 0.922088i 0.626482π0.626482\pi
620620 −5.18964 8.98873i −0.208421 0.360996i
621621 0 0
622622 −7.59517 + 13.1552i −0.304538 + 0.527476i
623623 −3.42720 −0.137308
624624 0 0
625625 1.00000 0.0400000
626626 −5.91680 + 10.2482i −0.236483 + 0.409600i
627627 0 0
628628 16.5974 + 28.7476i 0.662309 + 1.14715i
629629 −10.4972 −0.418551
630630 0 0
631631 −3.12995 5.42123i −0.124601 0.215816i 0.796976 0.604011i 0.206432π-0.206432\pi
−0.921577 + 0.388196i 0.873099π0.873099\pi
632632 −19.0412 −0.757417
633633 0 0
634634 −7.00310 + 12.1297i −0.278128 + 0.481733i
635635 5.60171 9.70245i 0.222297 0.385030i
636636 0 0
637637 −44.9950 + 7.15454i −1.78277 + 0.283473i
638638 −30.7001 −1.21543
639639 0 0
640640 5.66519 9.81240i 0.223936 0.387869i
641641 4.42209 + 7.65928i 0.174662 + 0.302523i 0.940044 0.341053i 0.110783π-0.110783\pi
−0.765382 + 0.643576i 0.777450π0.777450\pi
642642 0 0
643643 16.0506 + 27.8004i 0.632973 + 1.09634i 0.986941 + 0.161084i 0.0514990π0.0514990\pi
−0.353968 + 0.935258i 0.615168π0.615168\pi
644644 −8.05072 13.9443i −0.317243 0.549481i
645645 0 0
646646 −6.60308 11.4369i −0.259795 0.449978i
647647 −7.37834 + 12.7797i −0.290072 + 0.502420i −0.973827 0.227292i 0.927013π-0.927013\pi
0.683754 + 0.729712i 0.260346π0.260346\pi
648648 0 0
649649 18.9569 0.744125
650650 2.23189 0.354887i 0.0875419 0.0139198i
651651 0 0
652652 −3.90517 + 6.76395i −0.152938 + 0.264897i
653653 13.3246 23.0788i 0.521430 0.903144i −0.478259 0.878219i 0.658732π-0.658732\pi
0.999689 0.0249251i 0.00793473π-0.00793473\pi
654654 0 0
655655 −0.494893 −0.0193371
656656 −7.18114 12.4381i −0.280377 0.485626i
657657 0 0
658658 −8.96684 −0.349564
659659 1.22477 + 2.12136i 0.0477101 + 0.0826363i 0.888894 0.458112i 0.151474π-0.151474\pi
−0.841184 + 0.540749i 0.818141π0.818141\pi
660660 0 0
661661 −8.23556 + 14.2644i −0.320326 + 0.554821i −0.980555 0.196243i 0.937126π-0.937126\pi
0.660229 + 0.751064i 0.270459π0.270459\pi
662662 14.2211 0.552718
663663 0 0
664664 −5.32272 −0.206562
665665 −7.99209 + 13.8427i −0.309920 + 0.536797i
666666 0 0
667667 −9.13983 15.8307i −0.353896 0.612965i
668668 4.14632 0.160426
669669 0 0
670670 1.35971 + 2.35509i 0.0525302 + 0.0909850i
671671 14.8923 0.574911
672672 0 0
673673 0.693745 1.20160i 0.0267419 0.0463184i −0.852345 0.522980i 0.824820π-0.824820\pi
0.879087 + 0.476662i 0.158153π0.158153\pi
674674 −0.0523246 + 0.0906288i −0.00201547 + 0.00349089i
675675 0 0
676676 −19.8623 + 6.48035i −0.763935 + 0.249244i
677677 −23.0636 −0.886407 −0.443203 0.896421i 0.646158π-0.646158\pi
−0.443203 + 0.896421i 0.646158π0.646158\pi
678678 0 0
679679 14.0051 24.2576i 0.537467 0.930920i
680680 6.60308 + 11.4369i 0.253217 + 0.438584i
681681 0 0
682682 −12.2615 21.2375i −0.469516 0.813225i
683683 10.5080 + 18.2004i 0.402078 + 0.696419i 0.993976 0.109593i 0.0349549π-0.0349549\pi
−0.591899 + 0.806012i 0.701622π0.701622\pi
684684 0 0
685685 −11.5749 20.0483i −0.442254 0.766006i
686686 7.82713 13.5570i 0.298841 0.517608i
687687 0 0
688688 11.6590 0.444494
689689 −22.8819 28.2217i −0.871731 1.07516i
690690 0 0
691691 12.0289 20.8346i 0.457600 0.792587i −0.541234 0.840872i 0.682043π-0.682043\pi
0.998834 + 0.0482858i 0.0153758π0.0153758\pi
692692 8.23396 14.2616i 0.313008 0.542146i
693693 0 0
694694 9.17266 0.348190
695695 −5.97871 10.3554i −0.226785 0.392804i
696696 0 0
697697 46.6802 1.76814
698698 0.697969 + 1.20892i 0.0264185 + 0.0457582i
699699 0 0
700700 3.56082 6.16752i 0.134586 0.233110i
701701 −20.0188 −0.756099 −0.378050 0.925785i 0.623405π-0.623405\pi
−0.378050 + 0.925785i 0.623405π0.623405\pi
702702 0 0
703703 6.48252 0.244493
704704 −0.163542 + 0.283264i −0.00616373 + 0.0106759i
705705 0 0
706706 −1.86138 3.22400i −0.0700539 0.121337i
707707 39.5134 1.48605
708708 0 0
709709 −8.52960 14.7737i −0.320336 0.554838i 0.660221 0.751071i 0.270462π-0.270462\pi
−0.980557 + 0.196233i 0.937129π0.937129\pi
710710 −5.32450 −0.199825
711711 0 0
712712 0.874312 1.51435i 0.0327662 0.0567528i
713713 7.30081 12.6454i 0.273417 0.473573i
714714 0 0
715715 −21.5716 + 3.43005i −0.806734 + 0.128277i
716716 −17.0401 −0.636820
717717 0 0
718718 −3.42335 + 5.92942i −0.127758 + 0.221284i
719719 −21.0559 36.4700i −0.785254 1.36010i −0.928847 0.370463i 0.879199π-0.879199\pi
0.143593 0.989637i 0.454134π-0.454134\pi
720720 0 0
721721 −0.250297 0.433527i −0.00932154 0.0161454i
722722 −1.87680 3.25071i −0.0698473 0.120979i
723723 0 0
724724 13.5496 + 23.4686i 0.503566 + 0.872202i
725725 4.04253 7.00186i 0.150136 0.260043i
726726 0 0
727727 3.62167 0.134320 0.0671601 0.997742i 0.478606π-0.478606\pi
0.0671601 + 0.997742i 0.478606π0.478606\pi
728728 12.9249 33.7317i 0.479027 1.25018i
729729 0 0
730730 0.256793 0.444778i 0.00950432 0.0164620i
731731 −18.9469 + 32.8171i −0.700778 + 1.21378i
732732 0 0
733733 −10.2438 −0.378362 −0.189181 0.981942i 0.560583π-0.560583\pi
−0.189181 + 0.981942i 0.560583π0.560583\pi
734734 2.70914 + 4.69237i 0.0999963 + 0.173199i
735735 0 0
736736 12.7703 0.470719
737737 −13.1419 22.7624i −0.484087 0.838463i
738738 0 0
739739 −4.63472 + 8.02758i −0.170491 + 0.295299i −0.938592 0.345030i 0.887869π-0.887869\pi
0.768101 + 0.640329i 0.221202π0.221202\pi
740740 −2.88824 −0.106174
741741 0 0
742742 27.9881 1.02748
743743 22.3835 38.7694i 0.821172 1.42231i −0.0836373 0.996496i 0.526654π-0.526654\pi
0.904810 0.425816i 0.140013π-0.140013\pi
744744 0 0
745745 10.6089 + 18.3752i 0.388681 + 0.673215i
746746 −11.4735 −0.420076
747747 0 0
748748 −28.4346 49.2501i −1.03967 1.80076i
749749 34.3434 1.25488
750750 0 0
751751 −7.67016 + 13.2851i −0.279888 + 0.484780i −0.971357 0.237626i 0.923631π-0.923631\pi
0.691469 + 0.722406i 0.256964π0.256964\pi
752752 −2.90095 + 5.02459i −0.105787 + 0.183228i
753753 0 0
754754 6.53761 17.0620i 0.238086 0.621362i
755755 −19.4623 −0.708305
756756 0 0
757757 −3.00148 + 5.19872i −0.109091 + 0.188951i −0.915402 0.402541i 0.868127π-0.868127\pi
0.806311 + 0.591491i 0.201461π0.201461\pi
758758 −9.40381 16.2879i −0.341562 0.591602i
759759 0 0
760760 −4.07772 7.06282i −0.147914 0.256195i
761761 −10.4825 18.1563i −0.379992 0.658165i 0.611069 0.791578i 0.290740π-0.290740\pi
−0.991061 + 0.133412i 0.957407π0.957407\pi
762762 0 0
763763 25.4231 + 44.0341i 0.920378 + 1.59414i
764764 8.83198 15.2974i 0.319530 0.553442i
765765 0 0
766766 9.11103 0.329195
767767 −4.03689 + 10.5356i −0.145764 + 0.380418i
768768 0 0
769769 21.9076 37.9451i 0.790008 1.36833i −0.135953 0.990715i 0.543410π-0.543410\pi
0.925961 0.377619i 0.123257π-0.123257\pi
770770 8.41307 14.5719i 0.303186 0.525134i
771771 0 0
772772 10.6902 0.384749
773773 −1.68610 2.92041i −0.0606449 0.105040i 0.834109 0.551600i 0.185982π-0.185982\pi
−0.894754 + 0.446560i 0.852649π0.852649\pi
774774 0 0
775775 6.45826 0.231988
776776 7.14568 + 12.3767i 0.256515 + 0.444297i
777777 0 0
778778 −7.68631 + 13.3131i −0.275568 + 0.477297i
779779 −28.8273 −1.03284
780780 0 0
781781 51.4623 1.84146
782782 −4.13875 + 7.16853i −0.148002 + 0.256346i
783783 0 0
784784 −11.3545 19.6665i −0.405516 0.702375i
785785 −20.6547 −0.737198
786786 0 0
787787 17.8922 + 30.9902i 0.637789 + 1.10468i 0.985917 + 0.167235i 0.0534840π0.0534840\pi
−0.348128 + 0.937447i 0.613183π0.613183\pi
788788 38.5487 1.37324
789789 0 0
790790 2.63938 4.57154i 0.0939049 0.162648i
791791 13.8419 23.9749i 0.492162 0.852450i
792792 0 0
793793 −3.17133 + 8.27662i −0.112617 + 0.293911i
794794 5.91748 0.210003
795795 0 0
796796 −16.8028 + 29.1034i −0.595561 + 1.03154i
797797 −14.1625 24.5303i −0.501663 0.868906i −0.999998 0.00192156i 0.999388π-0.999388\pi
0.498335 0.866985i 0.333945π-0.333945\pi
798798 0 0
799799 −9.42866 16.3309i −0.333562 0.577746i
800800 2.82414 + 4.89155i 0.0998483 + 0.172942i
801801 0 0
802802 −0.153055 0.265098i −0.00540455 0.00936095i
803803 −2.48195 + 4.29887i −0.0875861 + 0.151704i
804804 0 0
805805 10.0187 0.353114
806806 14.4141 2.29195i 0.507716 0.0807306i
807807 0 0
808808 −10.0803 + 17.4595i −0.354622 + 0.614224i
809809 −14.5698 + 25.2357i −0.512248 + 0.887239i 0.487651 + 0.873038i 0.337854π0.337854\pi
−0.999899 + 0.0142007i 0.995480π0.995480\pi
810810 0 0
811811 −16.3733 −0.574946 −0.287473 0.957789i 0.592815π-0.592815\pi
−0.287473 + 0.957789i 0.592815π0.592815\pi
812812 −28.7894 49.8647i −1.01031 1.74991i
813813 0 0
814814 −6.82399 −0.239181
815815 −2.42990 4.20871i −0.0851157 0.147425i
816816 0 0
817817 11.7006 20.2661i 0.409354 0.709022i
818818 −12.9873 −0.454091
819819 0 0
820820 12.8438 0.448525
821821 17.5806 30.4505i 0.613566 1.06273i −0.377068 0.926186i 0.623068π-0.623068\pi
0.990634 0.136543i 0.0435990π-0.0435990\pi
822822 0 0
823823 −9.84233 17.0474i −0.343082 0.594236i 0.641921 0.766771i 0.278138π-0.278138\pi
−0.985003 + 0.172535i 0.944804π0.944804\pi
824824 0.255413 0.00889772
825825 0 0
826826 −4.34566 7.52690i −0.151205 0.261894i
827827 −11.6881 −0.406436 −0.203218 0.979134i 0.565140π-0.565140\pi
−0.203218 + 0.979134i 0.565140π0.565140\pi
828828 0 0
829829 22.7601 39.4217i 0.790493 1.36917i −0.135170 0.990822i 0.543158π-0.543158\pi
0.925662 0.378351i 0.123509π-0.123509\pi
830830 0.737805 1.27792i 0.0256096 0.0443571i
831831 0 0
832832 −0.122601 0.151212i −0.00425044 0.00524234i
833833 73.8084 2.55731
834834 0 0
835835 −1.28997 + 2.23430i −0.0446414 + 0.0773212i
836836 17.5597 + 30.4143i 0.607315 + 1.05190i
837837 0 0
838838 −1.42516 2.46845i −0.0492313 0.0852711i
839839 14.5239 + 25.1561i 0.501420 + 0.868485i 0.999999 + 0.00164022i 0.000522098π0.000522098\pi
−0.498579 + 0.866844i 0.666145π0.666145\pi
840840 0 0
841841 −18.1841 31.4957i −0.627037 1.08606i
842842 9.74634 16.8812i 0.335881 0.581763i
843843 0 0
844844 −21.1029 −0.726393
845845 2.68740 12.7192i 0.0924492 0.437554i
846846 0 0
847847 −56.9420 + 98.6264i −1.95655 + 3.38884i
848848 9.05471 15.6832i 0.310940 0.538564i
849849 0 0
850850 −3.66112 −0.125576
851851 −2.03159 3.51882i −0.0696422 0.120624i
852852 0 0
853853 −48.3320 −1.65486 −0.827429 0.561571i 0.810197π-0.810197\pi
−0.827429 + 0.561571i 0.810197π0.810197\pi
854854 −3.41389 5.91303i −0.116821 0.202340i
855855 0 0
856856 −8.76134 + 15.1751i −0.299457 + 0.518674i
857857 41.2151 1.40788 0.703940 0.710260i 0.251422π-0.251422\pi
0.703940 + 0.710260i 0.251422π0.251422\pi
858858 0 0
859859 −52.5448 −1.79280 −0.896402 0.443242i 0.853828π-0.853828\pi
−0.896402 + 0.443242i 0.853828π0.853828\pi
860860 −5.21314 + 9.02943i −0.177767 + 0.307901i
861861 0 0
862862 −10.7232 18.5731i −0.365234 0.632603i
863863 22.9888 0.782549 0.391275 0.920274i 0.372034π-0.372034\pi
0.391275 + 0.920274i 0.372034π0.372034\pi
864864 0 0
865865 5.12339 + 8.87397i 0.174200 + 0.301724i
866866 3.48700 0.118493
867867 0 0
868868 22.9967 39.8315i 0.780559 1.35197i
869869 −25.5101 + 44.1848i −0.865371 + 1.49887i
870870 0 0
871871 15.4491 2.45652i 0.523473 0.0832360i
872872 −25.9427 −0.878532
873873 0 0
874874 2.55588 4.42691i 0.0864539 0.149743i
875875 2.21563 + 3.83759i 0.0749021 + 0.129734i
876876 0 0
877877 26.1492 + 45.2917i 0.882995 + 1.52939i 0.847994 + 0.530006i 0.177810π0.177810\pi
0.0350015 + 0.999387i 0.488856π0.488856\pi
878878 −0.883615 1.53047i −0.0298206 0.0516508i
879879 0 0
880880 −5.44359 9.42857i −0.183503 0.317837i
881881 −16.8483 + 29.1821i −0.567634 + 0.983171i 0.429165 + 0.903226i 0.358808π0.358808\pi
−0.996799 + 0.0799447i 0.974526π0.974526\pi
882882 0 0
883883 −20.4392 −0.687835 −0.343917 0.939000i 0.611754π-0.611754\pi
−0.343917 + 0.939000i 0.611754π0.611754\pi
884884 33.4266 5.31508i 1.12426 0.178766i
885885 0 0
886886 4.72082 8.17671i 0.158599 0.274702i
887887 −10.1003 + 17.4942i −0.339134 + 0.587397i −0.984270 0.176670i 0.943467π-0.943467\pi
0.645136 + 0.764068i 0.276801π0.276801\pi
888888 0 0
889889 49.6454 1.66505
890890 0.242384 + 0.419822i 0.00812474 + 0.0140725i
891891 0 0
892892 34.0723 1.14083
893893 5.82265 + 10.0851i 0.194847 + 0.337486i
894894 0 0
895895 5.30141 9.18232i 0.177207 0.306931i
896896 50.2080 1.67733
897897 0 0
898898 2.40974 0.0804140
899899 26.1077 45.2199i 0.870741 1.50817i
900900 0 0
901901 29.4296 + 50.9735i 0.980442 + 1.69817i
902902 30.3458 1.01040
903903 0 0
904904 7.06242 + 12.2325i 0.234893 + 0.406846i
905905 −16.8618 −0.560505
906906 0 0
907907 20.9015 36.2024i 0.694022 1.20208i −0.276488 0.961017i 0.589170π-0.589170\pi
0.970509 0.241063i 0.0774962π-0.0774962\pi
908908 −7.42450 + 12.8596i −0.246391 + 0.426761i
909909 0 0
910910 6.30696 + 7.77878i 0.209074 + 0.257864i
911911 3.42332 0.113420 0.0567098 0.998391i 0.481939π-0.481939\pi
0.0567098 + 0.998391i 0.481939π0.481939\pi
912912 0 0
913913 −7.13103 + 12.3513i −0.236003 + 0.408769i
914914 9.53602 + 16.5169i 0.315423 + 0.546329i
915915 0 0
916916 2.54330 + 4.40513i 0.0840331 + 0.145550i
917917 −1.09650 1.89920i −0.0362097 0.0627170i
918918 0 0
919919 −3.52603 6.10727i −0.116313 0.201460i 0.801991 0.597336i 0.203774π-0.203774\pi
−0.918304 + 0.395876i 0.870441π0.870441\pi
920920 −2.55588 + 4.42691i −0.0842648 + 0.145951i
921921 0 0
922922 19.3002 0.635619
923923 −10.9589 + 28.6009i −0.360718 + 0.941411i
924924 0 0
925925 0.898570 1.55637i 0.0295448 0.0511731i
926926 −4.04388 + 7.00421i −0.132890 + 0.230173i
927927 0 0
928928 45.6666 1.49908
929929 −5.02099 8.69661i −0.164733 0.285326i 0.771827 0.635832i 0.219343π-0.219343\pi
−0.936561 + 0.350506i 0.886010π0.886010\pi
930930 0 0
931931 −45.5802 −1.49383
932932 −2.27990 3.94890i −0.0746806 0.129351i
933933 0 0
934934 −3.20748 + 5.55552i −0.104952 + 0.181782i
935935 35.3855 1.15723
936936 0 0
937937 5.84613 0.190985 0.0954924 0.995430i 0.469557π-0.469557\pi
0.0954924 + 0.995430i 0.469557π0.469557\pi
938938 −6.02524 + 10.4360i −0.196731 + 0.340748i
939939 0 0
940940 −2.59424 4.49336i −0.0846148 0.146557i
941941 46.1640 1.50490 0.752452 0.658647i 0.228871π-0.228871\pi
0.752452 + 0.658647i 0.228871π0.228871\pi
942942 0 0
943943 9.03435 + 15.6479i 0.294199 + 0.509567i
944944 −5.62363 −0.183033
945945 0 0
946946 −12.3170 + 21.3336i −0.400460 + 0.693617i
947947 −7.24152 + 12.5427i −0.235318 + 0.407582i −0.959365 0.282168i 0.908946π-0.908946\pi
0.724047 + 0.689750i 0.242280π0.242280\pi
948948 0 0
949949 −1.86062 2.29483i −0.0603984 0.0744933i
950950 2.26092 0.0733539
951951 0 0
952952 −29.2600 + 50.6798i −0.948323 + 1.64254i
953953 −19.2212 33.2920i −0.622635 1.07843i −0.988993 0.147961i 0.952729π-0.952729\pi
0.366359 0.930474i 0.380604π-0.380604\pi
954954 0 0
955955 5.49549 + 9.51847i 0.177830 + 0.308010i
956956 −0.509755 0.882922i −0.0164867 0.0285557i
957957 0 0
958958 −10.9702 19.0009i −0.354431 0.613892i
959959 51.2914 88.8394i 1.65629 2.86877i
960960 0 0
961961 10.7092 0.345457
962962 1.45317 3.79253i 0.0468522 0.122276i
963963 0 0
964964 −0.721977 + 1.25050i −0.0232533 + 0.0402759i
965965 −3.32586 + 5.76057i −0.107063 + 0.185439i
966966 0 0
967967 44.2627 1.42339 0.711696 0.702487i 0.247927π-0.247927\pi
0.711696 + 0.702487i 0.247927π0.247927\pi
968968 −29.0529 50.3211i −0.933796 1.61738i
969969 0 0
970970 −3.96197 −0.127211
971971 −22.2030 38.4567i −0.712527 1.23413i −0.963906 0.266244i 0.914217π-0.914217\pi
0.251378 0.967889i 0.419116π-0.419116\pi
972972 0 0
973973 26.4933 45.8877i 0.849335 1.47109i
974974 0.960150 0.0307652
975975 0 0
976976 −4.41784 −0.141412
977977 −1.69219 + 2.93096i −0.0541379 + 0.0937696i −0.891824 0.452382i 0.850574π-0.850574\pi
0.837686 + 0.546152i 0.183908π0.183908\pi
978978 0 0
979979 −2.34269 4.05766i −0.0748727 0.129683i
980980 20.3079 0.648714
981981 0 0
982982 7.84266 + 13.5839i 0.250269 + 0.433479i
983983 −39.6424 −1.26440 −0.632198 0.774807i 0.717847π-0.717847\pi
−0.632198 + 0.774807i 0.717847π0.717847\pi
984984 0 0
985985 −11.9930 + 20.7725i −0.382129 + 0.661866i
986986 −14.8002 + 25.6347i −0.471334 + 0.816375i
987987 0 0
988988 −20.6426 + 3.28232i −0.656727 + 0.104424i
989989 −14.6677 −0.466407
990990 0 0
991991 22.6722 39.2693i 0.720205 1.24743i −0.240712 0.970596i 0.577381π-0.577381\pi
0.960917 0.276835i 0.0892856π-0.0892856\pi
992992 18.2390 + 31.5909i 0.579089 + 1.00301i
993993 0 0
994994 −11.7971 20.4332i −0.374182 0.648103i
995995 −10.4552 18.1089i −0.331451 0.574090i
996996 0 0
997997 −26.9984 46.7626i −0.855048 1.48099i −0.876601 0.481218i 0.840194π-0.840194\pi
0.0215531 0.999768i 0.493139π-0.493139\pi
998998 8.70733 15.0815i 0.275626 0.477398i
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.i.451.3 yes 10
3.2 odd 2 585.2.j.h.451.3 yes 10
13.3 even 3 inner 585.2.j.i.406.3 yes 10
13.4 even 6 7605.2.a.cn.1.3 5
13.9 even 3 7605.2.a.cm.1.3 5
39.17 odd 6 7605.2.a.cl.1.3 5
39.29 odd 6 585.2.j.h.406.3 10
39.35 odd 6 7605.2.a.co.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
585.2.j.h.406.3 10 39.29 odd 6
585.2.j.h.451.3 yes 10 3.2 odd 2
585.2.j.i.406.3 yes 10 13.3 even 3 inner
585.2.j.i.451.3 yes 10 1.1 even 1 trivial
7605.2.a.cl.1.3 5 39.17 odd 6
7605.2.a.cm.1.3 5 13.9 even 3
7605.2.a.cn.1.3 5 13.4 even 6
7605.2.a.co.1.3 5 39.35 odd 6